Properties

Label 75.9.d.c.74.15
Level $75$
Weight $9$
Character 75.74
Analytic conductor $30.553$
Analytic rank $0$
Dimension $20$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [75,9,Mod(74,75)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(75, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 9, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("75.74");
 
S:= CuspForms(chi, 9);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 75 = 3 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 9 \)
Character orbit: \([\chi]\) \(=\) 75.d (of order \(2\), degree \(1\), not 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: \(30.5533957546\)
Analytic rank: \(0\)
Dimension: \(20\)
Coefficient field: \(\mathbb{Q}[x]/(x^{20} + \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{20} + 943 x^{18} + 318815 x^{16} + 48938090 x^{14} + 3842259173 x^{12} + 159675554657 x^{10} + 3390679484573 x^{8} + 32981662033730 x^{6} + \cdots + 336685801 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{28}\cdot 3^{22}\cdot 5^{32} \)
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 74.15
Root \(7.34058i\) of defining polynomial
Character \(\chi\) \(=\) 75.74
Dual form 75.9.d.c.74.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+10.2357 q^{2} +(56.7364 - 57.8099i) q^{3} -151.230 q^{4} +(580.739 - 591.726i) q^{6} -3448.05i q^{7} -4168.30 q^{8} +(-122.959 - 6559.85i) q^{9} +O(q^{10})\) \(q+10.2357 q^{2} +(56.7364 - 57.8099i) q^{3} -151.230 q^{4} +(580.739 - 591.726i) q^{6} -3448.05i q^{7} -4168.30 q^{8} +(-122.959 - 6559.85i) q^{9} +7123.65i q^{11} +(-8580.23 + 8742.57i) q^{12} +41361.3i q^{13} -35293.4i q^{14} -3950.77 q^{16} -119540. q^{17} +(-1258.58 - 67144.9i) q^{18} +86288.8 q^{19} +(-199331. - 195630. i) q^{21} +72915.8i q^{22} -317353. q^{23} +(-236494. + 240969. i) q^{24} +423364. i q^{26} +(-386200. - 365074. i) q^{27} +521448. i q^{28} +59853.0i q^{29} -1.02106e6 q^{31} +1.02664e6 q^{32} +(411817. + 404170. i) q^{33} -1.22358e6 q^{34} +(18595.0 + 992044. i) q^{36} -877366. i q^{37} +883230. q^{38} +(2.39109e6 + 2.34669e6i) q^{39} +1.55753e6i q^{41} +(-2.04030e6 - 2.00242e6i) q^{42} -2.56966e6i q^{43} -1.07731e6i q^{44} -3.24834e6 q^{46} -8.98739e6 q^{47} +(-224153. + 228394. i) q^{48} -6.12427e6 q^{49} +(-6.78229e6 + 6.91061e6i) q^{51} -6.25506e6i q^{52} +6.22182e6 q^{53} +(-3.95304e6 - 3.73680e6i) q^{54} +1.43725e7i q^{56} +(4.89572e6 - 4.98835e6i) q^{57} +612639. i q^{58} +3.96940e6i q^{59} -563629. q^{61} -1.04513e7 q^{62} +(-2.26187e7 + 423969. i) q^{63} +1.15199e7 q^{64} +(4.21525e6 + 4.13698e6i) q^{66} -1.34009e7i q^{67} +1.80781e7 q^{68} +(-1.80055e7 + 1.83461e7i) q^{69} -3.56270e7i q^{71} +(512529. + 2.73434e7i) q^{72} +970897. i q^{73} -8.98049e6i q^{74} -1.30494e7 q^{76} +2.45627e7 q^{77} +(2.44746e7 + 2.40201e7i) q^{78} +2.78755e7 q^{79} +(-4.30165e7 + 1.61318e6i) q^{81} +1.59425e7i q^{82} -2.25794e7 q^{83} +(3.01448e7 + 2.95851e7i) q^{84} -2.63024e7i q^{86} +(3.46009e6 + 3.39584e6i) q^{87} -2.96935e7i q^{88} -5.73209e7i q^{89} +1.42616e8 q^{91} +4.79932e7 q^{92} +(-5.79313e7 + 5.90274e7i) q^{93} -9.19926e7 q^{94} +(5.82481e7 - 5.93502e7i) q^{96} +3.31851e7i q^{97} -6.26864e7 q^{98} +(4.67301e7 - 875917. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 20 q + 1572 q^{4} - 10564 q^{6} - 7844 q^{9} + 560772 q^{16} + 463032 q^{19} + 579144 q^{21} - 2272668 q^{24} + 1763240 q^{31} + 2222552 q^{34} - 1337324 q^{36} - 3653584 q^{39} - 50849208 q^{46} - 18708428 q^{49} - 55465384 q^{51} + 15959596 q^{54} + 44834040 q^{61} + 45870004 q^{64} - 54839600 q^{66} - 67125264 q^{69} + 397844872 q^{76} - 324621848 q^{79} - 187150780 q^{81} + 394693536 q^{84} + 888576928 q^{91} + 184100072 q^{94} - 721614812 q^{96} + 67930400 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).

\(n\) \(26\) \(52\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 10.2357 0.639734 0.319867 0.947463i \(-0.396362\pi\)
0.319867 + 0.947463i \(0.396362\pi\)
\(3\) 56.7364 57.8099i 0.700450 0.713702i
\(4\) −151.230 −0.590741
\(5\) 0 0
\(6\) 580.739 591.726i 0.448101 0.456579i
\(7\) 3448.05i 1.43609i −0.695996 0.718045i \(-0.745037\pi\)
0.695996 0.718045i \(-0.254963\pi\)
\(8\) −4168.30 −1.01765
\(9\) −122.959 6559.85i −0.0187409 0.999824i
\(10\) 0 0
\(11\) 7123.65i 0.486555i 0.969957 + 0.243277i \(0.0782225\pi\)
−0.969957 + 0.243277i \(0.921777\pi\)
\(12\) −8580.23 + 8742.57i −0.413784 + 0.421613i
\(13\) 41361.3i 1.44818i 0.689708 + 0.724088i \(0.257739\pi\)
−0.689708 + 0.724088i \(0.742261\pi\)
\(14\) 35293.4i 0.918715i
\(15\) 0 0
\(16\) −3950.77 −0.0602840
\(17\) −119540. −1.43126 −0.715631 0.698479i \(-0.753861\pi\)
−0.715631 + 0.698479i \(0.753861\pi\)
\(18\) −1258.58 67144.9i −0.0119892 0.639621i
\(19\) 86288.8 0.662125 0.331063 0.943609i \(-0.392593\pi\)
0.331063 + 0.943609i \(0.392593\pi\)
\(20\) 0 0
\(21\) −199331. 195630.i −1.02494 1.00591i
\(22\) 72915.8i 0.311265i
\(23\) −317353. −1.13405 −0.567024 0.823701i \(-0.691905\pi\)
−0.567024 + 0.823701i \(0.691905\pi\)
\(24\) −236494. + 240969.i −0.712813 + 0.726299i
\(25\) 0 0
\(26\) 423364.i 0.926447i
\(27\) −386200. 365074.i −0.726704 0.686951i
\(28\) 521448.i 0.848358i
\(29\) 59853.0i 0.0846240i 0.999104 + 0.0423120i \(0.0134724\pi\)
−0.999104 + 0.0423120i \(0.986528\pi\)
\(30\) 0 0
\(31\) −1.02106e6 −1.10562 −0.552809 0.833308i \(-0.686444\pi\)
−0.552809 + 0.833308i \(0.686444\pi\)
\(32\) 1.02664e6 0.979085
\(33\) 411817. + 404170.i 0.347255 + 0.340807i
\(34\) −1.22358e6 −0.915626
\(35\) 0 0
\(36\) 18595.0 + 992044.i 0.0110710 + 0.590637i
\(37\) 877366.i 0.468138i −0.972220 0.234069i \(-0.924796\pi\)
0.972220 0.234069i \(-0.0752042\pi\)
\(38\) 883230. 0.423584
\(39\) 2.39109e6 + 2.34669e6i 1.03357 + 1.01437i
\(40\) 0 0
\(41\) 1.55753e6i 0.551189i 0.961274 + 0.275595i \(0.0888747\pi\)
−0.961274 + 0.275595i \(0.911125\pi\)
\(42\) −2.04030e6 2.00242e6i −0.655689 0.643514i
\(43\) 2.56966e6i 0.751626i −0.926696 0.375813i \(-0.877364\pi\)
0.926696 0.375813i \(-0.122636\pi\)
\(44\) 1.07731e6i 0.287428i
\(45\) 0 0
\(46\) −3.24834e6 −0.725489
\(47\) −8.98739e6 −1.84180 −0.920899 0.389800i \(-0.872544\pi\)
−0.920899 + 0.389800i \(0.872544\pi\)
\(48\) −224153. + 228394.i −0.0422259 + 0.0430248i
\(49\) −6.12427e6 −1.06236
\(50\) 0 0
\(51\) −6.78229e6 + 6.91061e6i −1.00253 + 1.02149i
\(52\) 6.25506e6i 0.855497i
\(53\) 6.22182e6 0.788522 0.394261 0.918999i \(-0.371001\pi\)
0.394261 + 0.918999i \(0.371001\pi\)
\(54\) −3.95304e6 3.73680e6i −0.464897 0.439466i
\(55\) 0 0
\(56\) 1.43725e7i 1.46144i
\(57\) 4.89572e6 4.98835e6i 0.463785 0.472560i
\(58\) 612639.i 0.0541368i
\(59\) 3.96940e6i 0.327580i 0.986495 + 0.163790i \(0.0523719\pi\)
−0.986495 + 0.163790i \(0.947628\pi\)
\(60\) 0 0
\(61\) −563629. −0.0407074 −0.0203537 0.999793i \(-0.506479\pi\)
−0.0203537 + 0.999793i \(0.506479\pi\)
\(62\) −1.04513e7 −0.707300
\(63\) −2.26187e7 + 423969.i −1.43584 + 0.0269136i
\(64\) 1.15199e7 0.686637
\(65\) 0 0
\(66\) 4.21525e6 + 4.13698e6i 0.222151 + 0.218026i
\(67\) 1.34009e7i 0.665021i −0.943100 0.332510i \(-0.892104\pi\)
0.943100 0.332510i \(-0.107896\pi\)
\(68\) 1.80781e7 0.845505
\(69\) −1.80055e7 + 1.83461e7i −0.794343 + 0.809372i
\(70\) 0 0
\(71\) 3.56270e7i 1.40199i −0.713165 0.700997i \(-0.752739\pi\)
0.713165 0.700997i \(-0.247261\pi\)
\(72\) 512529. + 2.73434e7i 0.0190717 + 1.01747i
\(73\) 970897.i 0.0341886i 0.999854 + 0.0170943i \(0.00544155\pi\)
−0.999854 + 0.0170943i \(0.994558\pi\)
\(74\) 8.98049e6i 0.299484i
\(75\) 0 0
\(76\) −1.30494e7 −0.391145
\(77\) 2.45627e7 0.698737
\(78\) 2.44746e7 + 2.40201e7i 0.661207 + 0.648929i
\(79\) 2.78755e7 0.715672 0.357836 0.933784i \(-0.383515\pi\)
0.357836 + 0.933784i \(0.383515\pi\)
\(80\) 0 0
\(81\) −4.30165e7 + 1.61318e6i −0.999298 + 0.0374752i
\(82\) 1.59425e7i 0.352614i
\(83\) −2.25794e7 −0.475773 −0.237886 0.971293i \(-0.576455\pi\)
−0.237886 + 0.971293i \(0.576455\pi\)
\(84\) 3.01448e7 + 2.95851e7i 0.605474 + 0.594232i
\(85\) 0 0
\(86\) 2.63024e7i 0.480840i
\(87\) 3.46009e6 + 3.39584e6i 0.0603963 + 0.0592749i
\(88\) 2.96935e7i 0.495143i
\(89\) 5.73209e7i 0.913593i −0.889571 0.456796i \(-0.848997\pi\)
0.889571 0.456796i \(-0.151003\pi\)
\(90\) 0 0
\(91\) 1.42616e8 2.07971
\(92\) 4.79932e7 0.669929
\(93\) −5.79313e7 + 5.90274e7i −0.774429 + 0.789081i
\(94\) −9.19926e7 −1.17826
\(95\) 0 0
\(96\) 5.82481e7 5.93502e7i 0.685799 0.698775i
\(97\) 3.31851e7i 0.374848i 0.982279 + 0.187424i \(0.0600139\pi\)
−0.982279 + 0.187424i \(0.939986\pi\)
\(98\) −6.26864e7 −0.679625
\(99\) 4.67301e7 875917.i 0.486469 0.00911847i
\(100\) 0 0
\(101\) 65955.2i 0.000633816i −1.00000 0.000316908i \(-0.999899\pi\)
1.00000 0.000316908i \(-0.000100875\pi\)
\(102\) −6.94218e7 + 7.07352e7i −0.641350 + 0.653484i
\(103\) 2.03592e8i 1.80889i −0.426593 0.904444i \(-0.640286\pi\)
0.426593 0.904444i \(-0.359714\pi\)
\(104\) 1.72406e8i 1.47374i
\(105\) 0 0
\(106\) 6.36849e7 0.504444
\(107\) 3.26956e7 0.249433 0.124716 0.992192i \(-0.460198\pi\)
0.124716 + 0.992192i \(0.460198\pi\)
\(108\) 5.84049e7 + 5.52100e7i 0.429294 + 0.405810i
\(109\) 6.88723e7 0.487909 0.243954 0.969787i \(-0.421555\pi\)
0.243954 + 0.969787i \(0.421555\pi\)
\(110\) 0 0
\(111\) −5.07204e7 4.97786e7i −0.334111 0.327907i
\(112\) 1.36225e7i 0.0865733i
\(113\) 2.24841e8 1.37899 0.689497 0.724289i \(-0.257832\pi\)
0.689497 + 0.724289i \(0.257832\pi\)
\(114\) 5.01113e7 5.10594e7i 0.296699 0.302313i
\(115\) 0 0
\(116\) 9.05155e6i 0.0499909i
\(117\) 2.71324e8 5.08575e6i 1.44792 0.0271401i
\(118\) 4.06297e7i 0.209564i
\(119\) 4.12182e8i 2.05542i
\(120\) 0 0
\(121\) 1.63612e8 0.763264
\(122\) −5.76915e6 −0.0260419
\(123\) 9.00405e7 + 8.83686e7i 0.393385 + 0.386080i
\(124\) 1.54415e8 0.653133
\(125\) 0 0
\(126\) −2.31519e8 + 4.33964e6i −0.918554 + 0.0172175i
\(127\) 1.02495e7i 0.0393993i 0.999806 + 0.0196996i \(0.00627099\pi\)
−0.999806 + 0.0196996i \(0.993729\pi\)
\(128\) −1.44907e8 −0.539820
\(129\) −1.48552e8 1.45793e8i −0.536437 0.526476i
\(130\) 0 0
\(131\) 8.55607e7i 0.290529i −0.989393 0.145264i \(-0.953597\pi\)
0.989393 0.145264i \(-0.0464033\pi\)
\(132\) −6.22790e7 6.11226e7i −0.205138 0.201329i
\(133\) 2.97529e8i 0.950872i
\(134\) 1.37168e8i 0.425436i
\(135\) 0 0
\(136\) 4.98280e8 1.45652
\(137\) −2.41199e7 −0.0684688 −0.0342344 0.999414i \(-0.510899\pi\)
−0.0342344 + 0.999414i \(0.510899\pi\)
\(138\) −1.84299e8 + 1.87786e8i −0.508168 + 0.517783i
\(139\) −4.84604e8 −1.29816 −0.649079 0.760721i \(-0.724846\pi\)
−0.649079 + 0.760721i \(0.724846\pi\)
\(140\) 0 0
\(141\) −5.09912e8 + 5.19560e8i −1.29009 + 1.31450i
\(142\) 3.64669e8i 0.896902i
\(143\) −2.94644e8 −0.704617
\(144\) 485783. + 2.59165e7i 0.00112978 + 0.0602734i
\(145\) 0 0
\(146\) 9.93784e6i 0.0218716i
\(147\) −3.47469e8 + 3.54043e8i −0.744127 + 0.758206i
\(148\) 1.32684e8i 0.276548i
\(149\) 6.26323e8i 1.27073i 0.772212 + 0.635365i \(0.219150\pi\)
−0.772212 + 0.635365i \(0.780850\pi\)
\(150\) 0 0
\(151\) −9.61203e8 −1.84887 −0.924437 0.381334i \(-0.875465\pi\)
−0.924437 + 0.381334i \(0.875465\pi\)
\(152\) −3.59677e8 −0.673812
\(153\) 1.46986e7 + 7.84167e8i 0.0268231 + 1.43101i
\(154\) 2.51418e8 0.447005
\(155\) 0 0
\(156\) −3.61604e8 3.54890e8i −0.610570 0.599232i
\(157\) 9.24294e8i 1.52129i −0.649169 0.760644i \(-0.724883\pi\)
0.649169 0.760644i \(-0.275117\pi\)
\(158\) 2.85326e8 0.457839
\(159\) 3.53004e8 3.59682e8i 0.552320 0.562770i
\(160\) 0 0
\(161\) 1.09425e9i 1.62860i
\(162\) −4.40305e8 + 1.65121e7i −0.639284 + 0.0239741i
\(163\) 1.30110e9i 1.84315i −0.388200 0.921575i \(-0.626903\pi\)
0.388200 0.921575i \(-0.373097\pi\)
\(164\) 2.35545e8i 0.325610i
\(165\) 0 0
\(166\) −2.31117e8 −0.304368
\(167\) −1.12208e9 −1.44263 −0.721317 0.692605i \(-0.756463\pi\)
−0.721317 + 0.692605i \(0.756463\pi\)
\(168\) 8.30873e8 + 8.15444e8i 1.04303 + 1.02366i
\(169\) −8.95030e8 −1.09721
\(170\) 0 0
\(171\) −1.06100e7 5.66042e8i −0.0124088 0.662009i
\(172\) 3.88609e8i 0.444016i
\(173\) −1.21708e9 −1.35874 −0.679369 0.733797i \(-0.737746\pi\)
−0.679369 + 0.733797i \(0.737746\pi\)
\(174\) 3.54166e7 + 3.47590e7i 0.0386376 + 0.0379201i
\(175\) 0 0
\(176\) 2.81439e7i 0.0293315i
\(177\) 2.29471e8 + 2.25210e8i 0.233794 + 0.229453i
\(178\) 5.86721e8i 0.584456i
\(179\) 3.40141e8i 0.331320i −0.986183 0.165660i \(-0.947025\pi\)
0.986183 0.165660i \(-0.0529754\pi\)
\(180\) 0 0
\(181\) 1.89427e9 1.76493 0.882466 0.470377i \(-0.155882\pi\)
0.882466 + 0.470377i \(0.155882\pi\)
\(182\) 1.45978e9 1.33046
\(183\) −3.19783e7 + 3.25833e7i −0.0285135 + 0.0290530i
\(184\) 1.32282e9 1.15406
\(185\) 0 0
\(186\) −5.92970e8 + 6.04189e8i −0.495428 + 0.504802i
\(187\) 8.51564e8i 0.696387i
\(188\) 1.35916e9 1.08803
\(189\) −1.25879e9 + 1.33164e9i −0.986524 + 1.04361i
\(190\) 0 0
\(191\) 1.22208e9i 0.918262i 0.888369 + 0.459131i \(0.151839\pi\)
−0.888369 + 0.459131i \(0.848161\pi\)
\(192\) 6.53596e8 6.65962e8i 0.480955 0.490054i
\(193\) 3.63918e8i 0.262286i 0.991363 + 0.131143i \(0.0418646\pi\)
−0.991363 + 0.131143i \(0.958135\pi\)
\(194\) 3.39674e8i 0.239803i
\(195\) 0 0
\(196\) 9.26172e8 0.627577
\(197\) 1.98338e9 1.31687 0.658434 0.752639i \(-0.271219\pi\)
0.658434 + 0.752639i \(0.271219\pi\)
\(198\) 4.78317e8 8.96565e6i 0.311211 0.00583339i
\(199\) −6.06495e8 −0.386736 −0.193368 0.981126i \(-0.561941\pi\)
−0.193368 + 0.981126i \(0.561941\pi\)
\(200\) 0 0
\(201\) −7.74705e8 7.60320e8i −0.474627 0.465814i
\(202\) 675100.i 0.000405474i
\(203\) 2.06376e8 0.121528
\(204\) 1.02568e9 1.04509e9i 0.592233 0.603438i
\(205\) 0 0
\(206\) 2.08391e9i 1.15721i
\(207\) 3.90214e7 + 2.08179e9i 0.0212531 + 1.13385i
\(208\) 1.63409e8i 0.0873019i
\(209\) 6.14691e8i 0.322160i
\(210\) 0 0
\(211\) −4.10164e8 −0.206932 −0.103466 0.994633i \(-0.532993\pi\)
−0.103466 + 0.994633i \(0.532993\pi\)
\(212\) −9.40924e8 −0.465812
\(213\) −2.05959e9 2.02135e9i −1.00061 0.982026i
\(214\) 3.34663e8 0.159571
\(215\) 0 0
\(216\) 1.60980e9 + 1.52174e9i 0.739530 + 0.699076i
\(217\) 3.52067e9i 1.58777i
\(218\) 7.04958e8 0.312131
\(219\) 5.61274e7 + 5.50852e7i 0.0244005 + 0.0239474i
\(220\) 0 0
\(221\) 4.94435e9i 2.07272i
\(222\) −5.19161e8 5.09521e8i −0.213742 0.209773i
\(223\) 4.68112e8i 0.189291i −0.995511 0.0946455i \(-0.969828\pi\)
0.995511 0.0946455i \(-0.0301718\pi\)
\(224\) 3.53993e9i 1.40605i
\(225\) 0 0
\(226\) 2.30142e9 0.882188
\(227\) −2.13615e9 −0.804503 −0.402251 0.915529i \(-0.631772\pi\)
−0.402251 + 0.915529i \(0.631772\pi\)
\(228\) −7.40378e8 + 7.54386e8i −0.273977 + 0.279161i
\(229\) 7.50976e8 0.273076 0.136538 0.990635i \(-0.456402\pi\)
0.136538 + 0.990635i \(0.456402\pi\)
\(230\) 0 0
\(231\) 1.39360e9 1.41997e9i 0.489430 0.498690i
\(232\) 2.49485e8i 0.0861177i
\(233\) −2.03107e9 −0.689129 −0.344565 0.938763i \(-0.611973\pi\)
−0.344565 + 0.938763i \(0.611973\pi\)
\(234\) 2.77720e9 5.20564e7i 0.926284 0.0173624i
\(235\) 0 0
\(236\) 6.00291e8i 0.193515i
\(237\) 1.58156e9 1.61148e9i 0.501292 0.510777i
\(238\) 4.21898e9i 1.31492i
\(239\) 1.54091e9i 0.472265i −0.971721 0.236133i \(-0.924120\pi\)
0.971721 0.236133i \(-0.0758800\pi\)
\(240\) 0 0
\(241\) −9.80028e8 −0.290516 −0.145258 0.989394i \(-0.546401\pi\)
−0.145258 + 0.989394i \(0.546401\pi\)
\(242\) 1.67469e9 0.488286
\(243\) −2.34734e9 + 2.57830e9i −0.673211 + 0.739450i
\(244\) 8.52374e7 0.0240475
\(245\) 0 0
\(246\) 9.21631e8 + 9.04518e8i 0.251661 + 0.246988i
\(247\) 3.56902e9i 0.958874i
\(248\) 4.25608e9 1.12513
\(249\) −1.28107e9 + 1.30531e9i −0.333255 + 0.339560i
\(250\) 0 0
\(251\) 3.36978e9i 0.848997i 0.905429 + 0.424499i \(0.139550\pi\)
−0.905429 + 0.424499i \(0.860450\pi\)
\(252\) 3.42062e9 6.41167e7i 0.848209 0.0158990i
\(253\) 2.26071e9i 0.551777i
\(254\) 1.04911e8i 0.0252050i
\(255\) 0 0
\(256\) −4.43231e9 −1.03198
\(257\) −6.58864e8 −0.151030 −0.0755150 0.997145i \(-0.524060\pi\)
−0.0755150 + 0.997145i \(0.524060\pi\)
\(258\) −1.52054e9 1.49230e9i −0.343177 0.336804i
\(259\) −3.02521e9 −0.672289
\(260\) 0 0
\(261\) 3.92626e8 7.35946e6i 0.0846092 0.00158593i
\(262\) 8.75777e8i 0.185861i
\(263\) −1.12759e9 −0.235682 −0.117841 0.993032i \(-0.537597\pi\)
−0.117841 + 0.993032i \(0.537597\pi\)
\(264\) −1.71658e9 1.68470e9i −0.353384 0.346822i
\(265\) 0 0
\(266\) 3.04542e9i 0.608305i
\(267\) −3.31371e9 3.25218e9i −0.652033 0.639926i
\(268\) 2.02662e9i 0.392855i
\(269\) 5.06830e9i 0.967950i 0.875082 + 0.483975i \(0.160807\pi\)
−0.875082 + 0.483975i \(0.839193\pi\)
\(270\) 0 0
\(271\) −2.89969e9 −0.537618 −0.268809 0.963194i \(-0.586630\pi\)
−0.268809 + 0.963194i \(0.586630\pi\)
\(272\) 4.72277e8 0.0862822
\(273\) 8.09153e9 8.24462e9i 1.45673 1.48429i
\(274\) −2.46885e8 −0.0438018
\(275\) 0 0
\(276\) 2.72296e9 2.77448e9i 0.469251 0.478129i
\(277\) 6.70508e9i 1.13890i −0.822027 0.569449i \(-0.807157\pi\)
0.822027 0.569449i \(-0.192843\pi\)
\(278\) −4.96028e9 −0.830476
\(279\) 1.25549e8 + 6.69800e9i 0.0207202 + 1.10542i
\(280\) 0 0
\(281\) 1.08727e10i 1.74387i 0.489625 + 0.871933i \(0.337134\pi\)
−0.489625 + 0.871933i \(0.662866\pi\)
\(282\) −5.21933e9 + 5.31808e9i −0.825312 + 0.840927i
\(283\) 3.48119e9i 0.542728i 0.962477 + 0.271364i \(0.0874747\pi\)
−0.962477 + 0.271364i \(0.912525\pi\)
\(284\) 5.38786e9i 0.828215i
\(285\) 0 0
\(286\) −3.01590e9 −0.450767
\(287\) 5.37044e9 0.791558
\(288\) −1.26235e8 6.73463e9i −0.0183489 0.978913i
\(289\) 7.31415e9 1.04851
\(290\) 0 0
\(291\) 1.91842e9 + 1.88280e9i 0.267530 + 0.262562i
\(292\) 1.46828e8i 0.0201966i
\(293\) 9.46915e9 1.28481 0.642407 0.766364i \(-0.277936\pi\)
0.642407 + 0.766364i \(0.277936\pi\)
\(294\) −3.55660e9 + 3.62389e9i −0.476043 + 0.485050i
\(295\) 0 0
\(296\) 3.65712e9i 0.476401i
\(297\) 2.60066e9 2.75115e9i 0.334239 0.353581i
\(298\) 6.41088e9i 0.812929i
\(299\) 1.31262e10i 1.64230i
\(300\) 0 0
\(301\) −8.86032e9 −1.07940
\(302\) −9.83862e9 −1.18279
\(303\) −3.81286e6 3.74206e6i −0.000452356 0.000443956i
\(304\) −3.40908e8 −0.0399156
\(305\) 0 0
\(306\) 1.50451e8 + 8.02652e9i 0.0171596 + 0.915465i
\(307\) 8.28984e9i 0.933239i −0.884458 0.466619i \(-0.845472\pi\)
0.884458 0.466619i \(-0.154528\pi\)
\(308\) −3.71461e9 −0.412773
\(309\) −1.17696e10 1.15511e10i −1.29101 1.26703i
\(310\) 0 0
\(311\) 8.23247e9i 0.880012i 0.897995 + 0.440006i \(0.145024\pi\)
−0.897995 + 0.440006i \(0.854976\pi\)
\(312\) −9.96679e9 9.78172e9i −1.05181 1.03228i
\(313\) 1.27222e10i 1.32551i 0.748835 + 0.662757i \(0.230614\pi\)
−0.748835 + 0.662757i \(0.769386\pi\)
\(314\) 9.46083e9i 0.973219i
\(315\) 0 0
\(316\) −4.21560e9 −0.422777
\(317\) −6.36014e9 −0.629839 −0.314920 0.949118i \(-0.601978\pi\)
−0.314920 + 0.949118i \(0.601978\pi\)
\(318\) 3.61325e9 3.68161e9i 0.353338 0.360023i
\(319\) −4.26372e8 −0.0411742
\(320\) 0 0
\(321\) 1.85503e9 1.89013e9i 0.174715 0.178021i
\(322\) 1.12005e10i 1.04187i
\(323\) −1.03150e10 −0.947674
\(324\) 6.50537e9 2.43961e8i 0.590326 0.0221381i
\(325\) 0 0
\(326\) 1.33177e10i 1.17913i
\(327\) 3.90757e9 3.98150e9i 0.341755 0.348221i
\(328\) 6.49224e9i 0.560918i
\(329\) 3.09890e10i 2.64499i
\(330\) 0 0
\(331\) 1.25518e9 0.104567 0.0522836 0.998632i \(-0.483350\pi\)
0.0522836 + 0.998632i \(0.483350\pi\)
\(332\) 3.41467e9 0.281059
\(333\) −5.75539e9 + 1.07880e8i −0.468056 + 0.00877332i
\(334\) −1.14853e10 −0.922902
\(335\) 0 0
\(336\) 7.87514e8 + 7.72891e8i 0.0617875 + 0.0606402i
\(337\) 8.02773e9i 0.622405i 0.950344 + 0.311203i \(0.100732\pi\)
−0.950344 + 0.311203i \(0.899268\pi\)
\(338\) −9.16129e9 −0.701924
\(339\) 1.27567e10 1.29980e10i 0.965915 0.984190i
\(340\) 0 0
\(341\) 7.27368e9i 0.537943i
\(342\) −1.08601e8 5.79385e9i −0.00793834 0.423509i
\(343\) 1.23948e9i 0.0895491i
\(344\) 1.07111e10i 0.764892i
\(345\) 0 0
\(346\) −1.24577e10 −0.869230
\(347\) −6.89272e9 −0.475415 −0.237707 0.971337i \(-0.576396\pi\)
−0.237707 + 0.971337i \(0.576396\pi\)
\(348\) −5.23269e8 5.13552e8i −0.0356786 0.0350161i
\(349\) 1.26058e10 0.849703 0.424852 0.905263i \(-0.360326\pi\)
0.424852 + 0.905263i \(0.360326\pi\)
\(350\) 0 0
\(351\) 1.51000e10 1.59738e10i 0.994826 1.05239i
\(352\) 7.31346e9i 0.476378i
\(353\) 1.83440e10 1.18139 0.590697 0.806894i \(-0.298853\pi\)
0.590697 + 0.806894i \(0.298853\pi\)
\(354\) 2.34880e9 + 2.30519e9i 0.149566 + 0.146789i
\(355\) 0 0
\(356\) 8.66862e9i 0.539697i
\(357\) 2.38282e10 + 2.33857e10i 1.46696 + 1.43972i
\(358\) 3.48160e9i 0.211956i
\(359\) 1.55471e7i 0.000935992i −1.00000 0.000467996i \(-0.999851\pi\)
1.00000 0.000467996i \(-0.000148968\pi\)
\(360\) 0 0
\(361\) −9.53780e9 −0.561590
\(362\) 1.93893e10 1.12909
\(363\) 9.28279e9 9.45842e9i 0.534628 0.544743i
\(364\) −2.15678e10 −1.22857
\(365\) 0 0
\(366\) −3.27321e8 + 3.33514e8i −0.0182410 + 0.0185862i
\(367\) 4.76932e9i 0.262901i 0.991323 + 0.131450i \(0.0419634\pi\)
−0.991323 + 0.131450i \(0.958037\pi\)
\(368\) 1.25379e9 0.0683650
\(369\) 1.02172e10 1.91512e8i 0.551092 0.0103298i
\(370\) 0 0
\(371\) 2.14532e10i 1.13239i
\(372\) 8.76094e9 8.92669e9i 0.457487 0.466143i
\(373\) 2.29205e10i 1.18410i 0.805901 + 0.592051i \(0.201681\pi\)
−0.805901 + 0.592051i \(0.798319\pi\)
\(374\) 8.71638e9i 0.445502i
\(375\) 0 0
\(376\) 3.74621e10 1.87431
\(377\) −2.47560e9 −0.122550
\(378\) −1.28847e10 + 1.36303e10i −0.631112 + 0.667634i
\(379\) 6.81528e9 0.330314 0.165157 0.986267i \(-0.447187\pi\)
0.165157 + 0.986267i \(0.447187\pi\)
\(380\) 0 0
\(381\) 5.92522e8 + 5.81520e8i 0.0281193 + 0.0275972i
\(382\) 1.25089e10i 0.587443i
\(383\) −1.07682e10 −0.500437 −0.250219 0.968189i \(-0.580503\pi\)
−0.250219 + 0.968189i \(0.580503\pi\)
\(384\) −8.22149e9 + 8.37704e9i −0.378116 + 0.385270i
\(385\) 0 0
\(386\) 3.72497e9i 0.167793i
\(387\) −1.68566e10 + 3.15963e8i −0.751494 + 0.0140861i
\(388\) 5.01857e9i 0.221438i
\(389\) 3.21668e10i 1.40479i −0.711790 0.702393i \(-0.752115\pi\)
0.711790 0.702393i \(-0.247885\pi\)
\(390\) 0 0
\(391\) 3.79365e10 1.62312
\(392\) 2.55278e10 1.08111
\(393\) −4.94625e9 4.85441e9i −0.207351 0.203501i
\(394\) 2.03014e10 0.842444
\(395\) 0 0
\(396\) −7.06697e9 + 1.32465e8i −0.287377 + 0.00538665i
\(397\) 3.26005e10i 1.31239i −0.754592 0.656194i \(-0.772165\pi\)
0.754592 0.656194i \(-0.227835\pi\)
\(398\) −6.20792e9 −0.247408
\(399\) −1.72001e10 1.68807e10i −0.678639 0.666038i
\(400\) 0 0
\(401\) 2.38085e10i 0.920778i −0.887717 0.460389i \(-0.847710\pi\)
0.887717 0.460389i \(-0.152290\pi\)
\(402\) −7.92968e9 7.78244e9i −0.303635 0.297997i
\(403\) 4.22324e10i 1.60113i
\(404\) 9.97438e6i 0.000374421i
\(405\) 0 0
\(406\) 2.11241e9 0.0777454
\(407\) 6.25005e9 0.227775
\(408\) 2.82706e10 2.88055e10i 1.02022 1.03952i
\(409\) 3.89304e10 1.39122 0.695609 0.718420i \(-0.255134\pi\)
0.695609 + 0.718420i \(0.255134\pi\)
\(410\) 0 0
\(411\) −1.36847e9 + 1.39437e9i −0.0479589 + 0.0488663i
\(412\) 3.07891e10i 1.06858i
\(413\) 1.36867e10 0.470434
\(414\) 3.99413e8 + 2.13086e10i 0.0135963 + 0.725361i
\(415\) 0 0
\(416\) 4.24634e10i 1.41789i
\(417\) −2.74947e10 + 2.80149e10i −0.909295 + 0.926498i
\(418\) 6.29182e9i 0.206097i
\(419\) 3.25983e10i 1.05764i −0.848733 0.528821i \(-0.822634\pi\)
0.848733 0.528821i \(-0.177366\pi\)
\(420\) 0 0
\(421\) −4.59023e9 −0.146119 −0.0730594 0.997328i \(-0.523276\pi\)
−0.0730594 + 0.997328i \(0.523276\pi\)
\(422\) −4.19833e9 −0.132381
\(423\) 1.10508e9 + 5.89559e10i 0.0345169 + 1.84148i
\(424\) −2.59344e10 −0.802440
\(425\) 0 0
\(426\) −2.10814e10 2.06900e10i −0.640121 0.628235i
\(427\) 1.94342e9i 0.0584596i
\(428\) −4.94454e9 −0.147350
\(429\) −1.67170e10 + 1.70333e10i −0.493549 + 0.502886i
\(430\) 0 0
\(431\) 1.76624e10i 0.511848i −0.966697 0.255924i \(-0.917620\pi\)
0.966697 0.255924i \(-0.0823797\pi\)
\(432\) 1.52579e9 + 1.44232e9i 0.0438086 + 0.0414122i
\(433\) 2.38480e10i 0.678424i −0.940710 0.339212i \(-0.889840\pi\)
0.940710 0.339212i \(-0.110160\pi\)
\(434\) 3.60367e10i 1.01575i
\(435\) 0 0
\(436\) −1.04155e10 −0.288228
\(437\) −2.73840e10 −0.750882
\(438\) 5.74505e8 + 5.63838e8i 0.0156098 + 0.0153200i
\(439\) −1.28782e10 −0.346734 −0.173367 0.984857i \(-0.555465\pi\)
−0.173367 + 0.984857i \(0.555465\pi\)
\(440\) 0 0
\(441\) 7.53034e8 + 4.01743e10i 0.0199095 + 1.06217i
\(442\) 5.06091e10i 1.32599i
\(443\) 1.07169e10 0.278261 0.139131 0.990274i \(-0.455569\pi\)
0.139131 + 0.990274i \(0.455569\pi\)
\(444\) 7.67043e9 + 7.52800e9i 0.197373 + 0.193708i
\(445\) 0 0
\(446\) 4.79147e9i 0.121096i
\(447\) 3.62076e10 + 3.55353e10i 0.906923 + 0.890082i
\(448\) 3.97211e10i 0.986073i
\(449\) 1.78639e10i 0.439532i −0.975553 0.219766i \(-0.929471\pi\)
0.975553 0.219766i \(-0.0705294\pi\)
\(450\) 0 0
\(451\) −1.10953e10 −0.268184
\(452\) −3.40027e10 −0.814628
\(453\) −5.45352e10 + 5.55670e10i −1.29504 + 1.31955i
\(454\) −2.18650e10 −0.514667
\(455\) 0 0
\(456\) −2.04068e10 + 2.07929e10i −0.471971 + 0.480901i
\(457\) 6.60639e10i 1.51460i −0.653064 0.757302i \(-0.726517\pi\)
0.653064 0.757302i \(-0.273483\pi\)
\(458\) 7.68679e9 0.174696
\(459\) 4.61665e10 + 4.36411e10i 1.04010 + 0.983207i
\(460\) 0 0
\(461\) 6.51600e10i 1.44270i 0.692569 + 0.721352i \(0.256479\pi\)
−0.692569 + 0.721352i \(0.743521\pi\)
\(462\) 1.42645e10 1.45344e10i 0.313105 0.319029i
\(463\) 1.65087e10i 0.359244i 0.983736 + 0.179622i \(0.0574874\pi\)
−0.983736 + 0.179622i \(0.942513\pi\)
\(464\) 2.36466e8i 0.00510148i
\(465\) 0 0
\(466\) −2.07895e10 −0.440859
\(467\) 3.64524e10 0.766404 0.383202 0.923664i \(-0.374821\pi\)
0.383202 + 0.923664i \(0.374821\pi\)
\(468\) −4.10323e10 + 7.69116e8i −0.855347 + 0.0160328i
\(469\) −4.62071e10 −0.955030
\(470\) 0 0
\(471\) −5.34333e10 5.24411e10i −1.08575 1.06559i
\(472\) 1.65456e10i 0.333362i
\(473\) 1.83054e10 0.365707
\(474\) 1.61884e10 1.64947e10i 0.320693 0.326761i
\(475\) 0 0
\(476\) 6.23341e10i 1.21422i
\(477\) −7.65028e8 4.08142e10i −0.0147776 0.788384i
\(478\) 1.57724e10i 0.302124i
\(479\) 5.54555e10i 1.05342i 0.850044 + 0.526711i \(0.176575\pi\)
−0.850044 + 0.526711i \(0.823425\pi\)
\(480\) 0 0
\(481\) 3.62890e10 0.677946
\(482\) −1.00313e10 −0.185853
\(483\) 6.32585e10 + 6.20839e10i 1.16233 + 1.14075i
\(484\) −2.47431e10 −0.450892
\(485\) 0 0
\(486\) −2.40268e10 + 2.63908e10i −0.430676 + 0.473051i
\(487\) 4.92651e10i 0.875837i 0.899015 + 0.437919i \(0.144284\pi\)
−0.899015 + 0.437919i \(0.855716\pi\)
\(488\) 2.34937e9 0.0414259
\(489\) −7.52165e10 7.38198e10i −1.31546 1.29103i
\(490\) 0 0
\(491\) 6.73149e10i 1.15820i 0.815255 + 0.579102i \(0.196597\pi\)
−0.815255 + 0.579102i \(0.803403\pi\)
\(492\) −1.36168e10 1.33640e10i −0.232389 0.228073i
\(493\) 7.15485e9i 0.121119i
\(494\) 3.65316e10i 0.613424i
\(495\) 0 0
\(496\) 4.03398e9 0.0666511
\(497\) −1.22844e11 −2.01339
\(498\) −1.31127e10 + 1.33608e10i −0.213194 + 0.217228i
\(499\) 8.14015e10 1.31290 0.656448 0.754371i \(-0.272058\pi\)
0.656448 + 0.754371i \(0.272058\pi\)
\(500\) 0 0
\(501\) −6.36626e10 + 6.48670e10i −1.01049 + 1.02961i
\(502\) 3.44922e10i 0.543132i
\(503\) 4.27491e10 0.667814 0.333907 0.942606i \(-0.391633\pi\)
0.333907 + 0.942606i \(0.391633\pi\)
\(504\) 9.42815e10 1.76723e9i 1.46118 0.0273886i
\(505\) 0 0
\(506\) 2.31401e10i 0.352990i
\(507\) −5.07808e10 + 5.17416e10i −0.768542 + 0.783083i
\(508\) 1.55003e9i 0.0232748i
\(509\) 6.30456e10i 0.939255i −0.882865 0.469628i \(-0.844388\pi\)
0.882865 0.469628i \(-0.155612\pi\)
\(510\) 0 0
\(511\) 3.34770e9 0.0490980
\(512\) −8.27185e9 −0.120371
\(513\) −3.33248e10 3.15018e10i −0.481169 0.454848i
\(514\) −6.74396e9 −0.0966189
\(515\) 0 0
\(516\) 2.24654e10 + 2.20483e10i 0.316895 + 0.311011i
\(517\) 6.40230e10i 0.896136i
\(518\) −3.09652e10 −0.430086
\(519\) −6.90529e10 + 7.03594e10i −0.951727 + 0.969734i
\(520\) 0 0
\(521\) 7.92618e10i 1.07575i −0.843023 0.537877i \(-0.819226\pi\)
0.843023 0.537877i \(-0.180774\pi\)
\(522\) 4.01882e9 7.53295e7i 0.0541273 0.00101457i
\(523\) 8.10207e10i 1.08290i −0.840732 0.541451i \(-0.817875\pi\)
0.840732 0.541451i \(-0.182125\pi\)
\(524\) 1.29393e10i 0.171627i
\(525\) 0 0
\(526\) −1.15417e10 −0.150774
\(527\) 1.22058e11 1.58243
\(528\) −1.62700e9 1.59679e9i −0.0209339 0.0205452i
\(529\) 2.24020e10 0.286065
\(530\) 0 0
\(531\) 2.60387e10 4.88073e8i 0.327522 0.00613913i
\(532\) 4.49951e10i 0.561719i
\(533\) −6.44215e10 −0.798219
\(534\) −3.39183e10 3.32885e10i −0.417127 0.409382i
\(535\) 0 0
\(536\) 5.58590e10i 0.676759i
\(537\) −1.96635e10 1.92984e10i −0.236463 0.232073i
\(538\) 5.18778e10i 0.619230i
\(539\) 4.36272e10i 0.516895i
\(540\) 0 0
\(541\) 7.57616e10 0.884423 0.442212 0.896911i \(-0.354194\pi\)
0.442212 + 0.896911i \(0.354194\pi\)
\(542\) −2.96804e10 −0.343932
\(543\) 1.07474e11 1.09508e11i 1.23625 1.25963i
\(544\) −1.22726e11 −1.40133
\(545\) 0 0
\(546\) 8.28227e10 8.43897e10i 0.931921 0.949553i
\(547\) 1.08131e11i 1.20782i −0.797053 0.603909i \(-0.793609\pi\)
0.797053 0.603909i \(-0.206391\pi\)
\(548\) 3.64764e9 0.0404473
\(549\) 6.93032e7 + 3.69732e9i 0.000762893 + 0.0407003i
\(550\) 0 0
\(551\) 5.16464e9i 0.0560317i
\(552\) 7.50522e10 7.64721e10i 0.808364 0.823658i
\(553\) 9.61162e10i 1.02777i
\(554\) 6.86314e10i 0.728591i
\(555\) 0 0
\(556\) 7.32865e10 0.766876
\(557\) 1.02611e11 1.06604 0.533019 0.846103i \(-0.321057\pi\)
0.533019 + 0.846103i \(0.321057\pi\)
\(558\) 1.28508e9 + 6.85590e10i 0.0132554 + 0.707176i
\(559\) 1.06285e11 1.08849
\(560\) 0 0
\(561\) −4.92288e10 4.83147e10i −0.497013 0.487784i
\(562\) 1.11290e11i 1.11561i
\(563\) −8.67308e10 −0.863256 −0.431628 0.902052i \(-0.642061\pi\)
−0.431628 + 0.902052i \(0.642061\pi\)
\(564\) 7.71139e10 7.85729e10i 0.762107 0.776526i
\(565\) 0 0
\(566\) 3.56326e10i 0.347201i
\(567\) 5.56235e9 + 1.48323e11i 0.0538178 + 1.43508i
\(568\) 1.48504e11i 1.42674i
\(569\) 1.42835e11i 1.36265i 0.731981 + 0.681325i \(0.238596\pi\)
−0.731981 + 0.681325i \(0.761404\pi\)
\(570\) 0 0
\(571\) 4.15522e10 0.390886 0.195443 0.980715i \(-0.437386\pi\)
0.195443 + 0.980715i \(0.437386\pi\)
\(572\) 4.45589e10 0.416246
\(573\) 7.06483e10 + 6.93365e10i 0.655365 + 0.643196i
\(574\) 5.49704e10 0.506386
\(575\) 0 0
\(576\) −1.41647e9 7.55685e10i −0.0128682 0.686517i
\(577\) 1.37843e11i 1.24360i 0.783176 + 0.621800i \(0.213598\pi\)
−0.783176 + 0.621800i \(0.786402\pi\)
\(578\) 7.48657e10 0.670767
\(579\) 2.10381e10 + 2.06474e10i 0.187194 + 0.183718i
\(580\) 0 0
\(581\) 7.78549e10i 0.683253i
\(582\) 1.96365e10 + 1.92719e10i 0.171148 + 0.167970i
\(583\) 4.43221e10i 0.383659i
\(584\) 4.04699e9i 0.0347921i
\(585\) 0 0
\(586\) 9.69237e10 0.821939
\(587\) 2.08977e11 1.76014 0.880068 0.474848i \(-0.157497\pi\)
0.880068 + 0.474848i \(0.157497\pi\)
\(588\) 5.25477e10 5.35419e10i 0.439586 0.447903i
\(589\) −8.81061e10 −0.732057
\(590\) 0 0
\(591\) 1.12530e11 1.14659e11i 0.922399 0.939851i
\(592\) 3.46627e9i 0.0282212i
\(593\) −4.25547e10 −0.344135 −0.172067 0.985085i \(-0.555045\pi\)
−0.172067 + 0.985085i \(0.555045\pi\)
\(594\) 2.66197e10 2.81601e10i 0.213824 0.226198i
\(595\) 0 0
\(596\) 9.47187e10i 0.750672i
\(597\) −3.44104e10 + 3.50614e10i −0.270889 + 0.276014i
\(598\) 1.34356e11i 1.05063i
\(599\) 6.86408e10i 0.533182i 0.963810 + 0.266591i \(0.0858972\pi\)
−0.963810 + 0.266591i \(0.914103\pi\)
\(600\) 0 0
\(601\) −2.16080e11 −1.65622 −0.828109 0.560567i \(-0.810583\pi\)
−0.828109 + 0.560567i \(0.810583\pi\)
\(602\) −9.06919e10 −0.690530
\(603\) −8.79080e10 + 1.64776e9i −0.664904 + 0.0124631i
\(604\) 1.45363e11 1.09221
\(605\) 0 0
\(606\) −3.90274e7 3.83027e7i −0.000289387 0.000284014i
\(607\) 2.36866e10i 0.174481i −0.996187 0.0872405i \(-0.972195\pi\)
0.996187 0.0872405i \(-0.0278049\pi\)
\(608\) 8.85880e10 0.648277
\(609\) 1.17090e10 1.19306e10i 0.0851241 0.0867346i
\(610\) 0 0
\(611\) 3.71731e11i 2.66725i
\(612\) −2.22286e9 1.18589e11i −0.0158455 0.845356i
\(613\) 1.04944e9i 0.00743219i 0.999993 + 0.00371609i \(0.00118287\pi\)
−0.999993 + 0.00371609i \(0.998817\pi\)
\(614\) 8.48526e10i 0.597024i
\(615\) 0 0
\(616\) −1.02385e11 −0.711070
\(617\) −1.92658e11 −1.32937 −0.664684 0.747124i \(-0.731434\pi\)
−0.664684 + 0.747124i \(0.731434\pi\)
\(618\) −1.20471e11 1.18234e11i −0.825900 0.810565i
\(619\) −3.90898e10 −0.266257 −0.133129 0.991099i \(-0.542502\pi\)
−0.133129 + 0.991099i \(0.542502\pi\)
\(620\) 0 0
\(621\) 1.22562e11 + 1.15857e11i 0.824117 + 0.779036i
\(622\) 8.42654e10i 0.562973i
\(623\) −1.97645e11 −1.31200
\(624\) −9.44667e9 9.27126e9i −0.0623075 0.0611506i
\(625\) 0 0
\(626\) 1.30221e11i 0.847976i
\(627\) 3.55352e10 + 3.48754e10i 0.229926 + 0.225657i
\(628\) 1.39781e11i 0.898687i
\(629\) 1.04881e11i 0.670028i
\(630\) 0 0
\(631\) −1.46902e10 −0.0926636 −0.0463318 0.998926i \(-0.514753\pi\)
−0.0463318 + 0.998926i \(0.514753\pi\)
\(632\) −1.16193e11 −0.728304
\(633\) −2.32712e10 + 2.37115e10i −0.144945 + 0.147688i
\(634\) −6.51007e10 −0.402929
\(635\) 0 0
\(636\) −5.33846e10 + 5.43947e10i −0.326278 + 0.332451i
\(637\) 2.53308e11i 1.53848i
\(638\) −4.36423e9 −0.0263405
\(639\) −2.33708e11 + 4.38066e9i −1.40175 + 0.0262746i
\(640\) 0 0
\(641\) 1.98992e11i 1.17870i 0.807879 + 0.589349i \(0.200616\pi\)
−0.807879 + 0.589349i \(0.799384\pi\)
\(642\) 1.89876e10 1.93468e10i 0.111771 0.113886i
\(643\) 1.32563e11i 0.775495i 0.921766 + 0.387748i \(0.126747\pi\)
−0.921766 + 0.387748i \(0.873253\pi\)
\(644\) 1.65483e11i 0.962078i
\(645\) 0 0
\(646\) −1.05582e11 −0.606259
\(647\) 1.66551e10 0.0950453 0.0475227 0.998870i \(-0.484867\pi\)
0.0475227 + 0.998870i \(0.484867\pi\)
\(648\) 1.79305e11 6.72423e9i 1.01694 0.0381366i
\(649\) −2.82766e10 −0.159385
\(650\) 0 0
\(651\) 2.03530e11 + 1.99750e11i 1.13319 + 1.11215i
\(652\) 1.96765e11i 1.08882i
\(653\) −6.15244e10 −0.338372 −0.169186 0.985584i \(-0.554114\pi\)
−0.169186 + 0.985584i \(0.554114\pi\)
\(654\) 3.99968e10 4.07535e10i 0.218632 0.222769i
\(655\) 0 0
\(656\) 6.15344e9i 0.0332279i
\(657\) 6.36894e9 1.19380e8i 0.0341826 0.000640725i
\(658\) 3.17195e11i 1.69209i
\(659\) 6.62231e10i 0.351130i −0.984468 0.175565i \(-0.943825\pi\)
0.984468 0.175565i \(-0.0561752\pi\)
\(660\) 0 0
\(661\) −3.16830e11 −1.65966 −0.829832 0.558014i \(-0.811564\pi\)
−0.829832 + 0.558014i \(0.811564\pi\)
\(662\) 1.28477e10 0.0668951
\(663\) −2.85832e11 2.80525e11i −1.47930 1.45183i
\(664\) 9.41176e10 0.484171
\(665\) 0 0
\(666\) −5.89106e10 + 1.10423e9i −0.299431 + 0.00561259i
\(667\) 1.89945e10i 0.0959677i
\(668\) 1.69691e11 0.852223
\(669\) −2.70615e10 2.65590e10i −0.135097 0.132589i
\(670\) 0 0
\(671\) 4.01509e9i 0.0198064i
\(672\) −2.04643e11 2.00843e11i −1.00350 0.984870i
\(673\) 2.15656e10i 0.105124i −0.998618 0.0525618i \(-0.983261\pi\)
0.998618 0.0525618i \(-0.0167387\pi\)
\(674\) 8.21697e10i 0.398173i
\(675\) 0 0
\(676\) 1.35355e11 0.648169
\(677\) −2.05571e11 −0.978605 −0.489303 0.872114i \(-0.662749\pi\)
−0.489303 + 0.872114i \(0.662749\pi\)
\(678\) 1.30574e11 1.33045e11i 0.617928 0.629620i
\(679\) 1.14424e11 0.538316
\(680\) 0 0
\(681\) −1.21197e11 + 1.23490e11i −0.563514 + 0.574175i
\(682\) 7.44515e10i 0.344140i
\(683\) 3.27181e11 1.50351 0.751753 0.659445i \(-0.229209\pi\)
0.751753 + 0.659445i \(0.229209\pi\)
\(684\) 1.60455e9 + 8.56023e10i 0.00733040 + 0.391076i
\(685\) 0 0
\(686\) 1.26869e10i 0.0572876i
\(687\) 4.26077e10 4.34138e10i 0.191276 0.194895i
\(688\) 1.01521e10i 0.0453110i
\(689\) 2.57343e11i 1.14192i
\(690\) 0 0
\(691\) 5.11252e10 0.224245 0.112122 0.993694i \(-0.464235\pi\)
0.112122 + 0.993694i \(0.464235\pi\)
\(692\) 1.84059e11 0.802662
\(693\) −3.02021e9 1.61128e11i −0.0130949 0.698614i
\(694\) −7.05521e10 −0.304139
\(695\) 0 0
\(696\) −1.44227e10 1.41549e10i −0.0614624 0.0603211i
\(697\) 1.86188e11i 0.788896i
\(698\) 1.29029e11 0.543584
\(699\) −1.15235e11 + 1.17416e11i −0.482700 + 0.491833i
\(700\) 0 0
\(701\) 1.49396e11i 0.618681i 0.950951 + 0.309341i \(0.100108\pi\)
−0.950951 + 0.309341i \(0.899892\pi\)
\(702\) 1.54559e11 1.63503e11i 0.636424 0.673252i
\(703\) 7.57069e10i 0.309966i
\(704\) 8.20635e10i 0.334087i
\(705\) 0 0
\(706\) 1.87764e11 0.755777
\(707\) −2.27417e8 −0.000910218
\(708\) −3.47028e10 3.40584e10i −0.138112 0.135547i
\(709\) −1.80177e10 −0.0713041 −0.0356520 0.999364i \(-0.511351\pi\)
−0.0356520 + 0.999364i \(0.511351\pi\)
\(710\) 0 0
\(711\) −3.42754e9 1.82859e11i −0.0134123 0.715546i
\(712\) 2.38930e11i 0.929718i
\(713\) 3.24037e11 1.25382
\(714\) 2.43899e11 + 2.39370e11i 0.938462 + 0.921036i
\(715\) 0 0
\(716\) 5.14395e10i 0.195724i
\(717\) −8.90799e10 8.74258e10i −0.337057 0.330798i
\(718\) 1.59136e8i 0.000598785i
\(719\) 4.58130e11i 1.71425i −0.515112 0.857123i \(-0.672250\pi\)
0.515112 0.857123i \(-0.327750\pi\)
\(720\) 0 0
\(721\) −7.01996e11 −2.59773
\(722\) −9.76264e10 −0.359268
\(723\) −5.56032e10 + 5.66552e10i −0.203492 + 0.207342i
\(724\) −2.86470e11 −1.04262
\(725\) 0 0
\(726\) 9.50162e10 9.68138e10i 0.342020 0.348491i
\(727\) 1.27196e11i 0.455342i 0.973738 + 0.227671i \(0.0731110\pi\)
−0.973738 + 0.227671i \(0.926889\pi\)
\(728\) −5.94466e11 −2.11642
\(729\) 1.58715e10 + 2.81983e11i 0.0561963 + 0.998420i
\(730\) 0 0
\(731\) 3.07178e11i 1.07577i
\(732\) 4.83606e9 4.92756e9i 0.0168441 0.0171628i
\(733\) 2.10630e11i 0.729631i 0.931080 + 0.364816i \(0.118868\pi\)
−0.931080 + 0.364816i \(0.881132\pi\)
\(734\) 4.88175e10i 0.168186i
\(735\) 0 0
\(736\) −3.25809e11 −1.11033
\(737\) 9.54634e10 0.323569
\(738\) 1.04580e11 1.96027e9i 0.352552 0.00660830i
\(739\) −2.18560e11 −0.732811 −0.366405 0.930455i \(-0.619412\pi\)
−0.366405 + 0.930455i \(0.619412\pi\)
\(740\) 0 0
\(741\) 2.06325e11 + 2.02494e11i 0.684350 + 0.671643i
\(742\) 2.19589e11i 0.724427i
\(743\) −1.82763e11 −0.599700 −0.299850 0.953986i \(-0.596937\pi\)
−0.299850 + 0.953986i \(0.596937\pi\)
\(744\) 2.41475e11 2.46044e11i 0.788098 0.803009i
\(745\) 0 0
\(746\) 2.34608e11i 0.757509i
\(747\) 2.77634e9 + 1.48117e11i 0.00891641 + 0.475689i
\(748\) 1.28782e11i 0.411384i
\(749\) 1.12736e11i 0.358208i
\(750\) 0 0
\(751\) 5.51243e11 1.73294 0.866469 0.499230i \(-0.166384\pi\)
0.866469 + 0.499230i \(0.166384\pi\)
\(752\) 3.55071e10 0.111031
\(753\) 1.94806e11 + 1.91189e11i 0.605931 + 0.594680i
\(754\) −2.53396e10 −0.0783996
\(755\) 0 0
\(756\) 1.90367e11 2.01383e11i 0.582780 0.616505i
\(757\) 4.36075e10i 0.132794i 0.997793 + 0.0663969i \(0.0211504\pi\)
−0.997793 + 0.0663969i \(0.978850\pi\)
\(758\) 6.97594e10 0.211313
\(759\) −1.30691e11 1.28265e11i −0.393804 0.386492i
\(760\) 0 0
\(761\) 4.60493e11i 1.37304i −0.727110 0.686521i \(-0.759137\pi\)
0.727110 0.686521i \(-0.240863\pi\)
\(762\) 6.06490e9 + 5.95229e9i 0.0179889 + 0.0176548i
\(763\) 2.37475e11i 0.700681i
\(764\) 1.84815e11i 0.542455i
\(765\) 0 0
\(766\) −1.10221e11 −0.320147
\(767\) −1.64180e11 −0.474393
\(768\) −2.51473e11 + 2.56231e11i −0.722849 + 0.736525i
\(769\) 1.46976e11 0.420281 0.210140 0.977671i \(-0.432608\pi\)
0.210140 + 0.977671i \(0.432608\pi\)
\(770\) 0 0
\(771\) −3.73816e10 + 3.80888e10i −0.105789 + 0.107790i
\(772\) 5.50352e10i 0.154943i
\(773\) −1.06663e11 −0.298741 −0.149371 0.988781i \(-0.547725\pi\)
−0.149371 + 0.988781i \(0.547725\pi\)
\(774\) −1.72539e11 + 3.23411e9i −0.480756 + 0.00901137i
\(775\) 0 0
\(776\) 1.38325e11i 0.381465i
\(777\) −1.71639e11 + 1.74887e11i −0.470904 + 0.479814i
\(778\) 3.29251e11i 0.898688i
\(779\) 1.34397e11i 0.364956i
\(780\) 0 0
\(781\) 2.53794e11 0.682147
\(782\) 3.88308e11 1.03836
\(783\) 2.18508e10 2.31152e10i 0.0581326 0.0614966i
\(784\) 2.41956e10 0.0640431
\(785\) 0 0
\(786\) −5.06285e10 4.96885e10i −0.132649 0.130186i
\(787\) 6.64587e11i 1.73242i 0.499682 + 0.866209i \(0.333450\pi\)
−0.499682 + 0.866209i \(0.666550\pi\)
\(788\) −2.99947e11 −0.777928
\(789\) −6.39752e10 + 6.51856e10i −0.165083 + 0.168207i
\(790\) 0 0
\(791\) 7.75265e11i 1.98036i
\(792\) −1.94785e11 + 3.65108e9i −0.495056 + 0.00927941i
\(793\) 2.33124e10i 0.0589515i
\(794\) 3.33690e11i 0.839578i
\(795\) 0 0
\(796\) 9.17201e10 0.228461
\(797\) −2.85566e11 −0.707738 −0.353869 0.935295i \(-0.615134\pi\)
−0.353869 + 0.935295i \(0.615134\pi\)
\(798\) −1.76055e11 1.72786e11i −0.434148 0.426087i
\(799\) 1.07436e12 2.63610
\(800\) 0 0
\(801\) −3.76016e11 + 7.04811e9i −0.913432 + 0.0171215i
\(802\) 2.43698e11i 0.589052i
\(803\) −6.91633e9 −0.0166346
\(804\) 1.17158e11 + 1.14983e11i 0.280381 + 0.275175i
\(805\) 0 0
\(806\) 4.32280e11i 1.02430i
\(807\) 2.92998e11 + 2.87557e11i 0.690828 + 0.678000i
\(808\) 2.74921e8i 0.000645003i
\(809\) 6.31328e10i 0.147388i −0.997281 0.0736938i \(-0.976521\pi\)
0.997281 0.0736938i \(-0.0234788\pi\)
\(810\) 0 0
\(811\) 6.09177e11 1.40819 0.704093 0.710107i \(-0.251354\pi\)
0.704093 + 0.710107i \(0.251354\pi\)
\(812\) −3.12102e10 −0.0717914
\(813\) −1.64518e11 + 1.67630e11i −0.376574 + 0.383699i
\(814\) 6.39738e10 0.145715
\(815\) 0 0
\(816\) 2.67953e10 2.73023e10i 0.0604363 0.0615798i
\(817\) 2.21733e11i 0.497671i
\(818\) 3.98481e11 0.890009
\(819\) −1.75359e10 9.35540e11i −0.0389756 2.07935i
\(820\) 0 0
\(821\) 4.63422e11i 1.02001i 0.860172 + 0.510004i \(0.170356\pi\)
−0.860172 + 0.510004i \(0.829644\pi\)
\(822\) −1.40073e10 + 1.42724e10i −0.0306809 + 0.0312614i
\(823\) 6.84569e11i 1.49217i 0.665851 + 0.746085i \(0.268069\pi\)
−0.665851 + 0.746085i \(0.731931\pi\)
\(824\) 8.48631e11i 1.84082i
\(825\) 0 0
\(826\) 1.40094e11 0.300952
\(827\) 5.73805e11 1.22671 0.613355 0.789807i \(-0.289819\pi\)
0.613355 + 0.789807i \(0.289819\pi\)
\(828\) −5.90120e9 3.14828e11i −0.0125551 0.669811i
\(829\) −5.68680e11 −1.20407 −0.602033 0.798471i \(-0.705642\pi\)
−0.602033 + 0.798471i \(0.705642\pi\)
\(830\) 0 0
\(831\) −3.87620e11 3.80422e11i −0.812834 0.797741i
\(832\) 4.76477e11i 0.994371i
\(833\) 7.32098e11 1.52051
\(834\) −2.81428e11 + 2.86753e11i −0.581706 + 0.592712i
\(835\) 0 0
\(836\) 9.29596e10i 0.190313i
\(837\) 3.94334e11 + 3.72763e11i 0.803456 + 0.759505i
\(838\) 3.33668e11i 0.676609i
\(839\) 2.49035e10i 0.0502588i −0.999684 0.0251294i \(-0.992000\pi\)
0.999684 0.0251294i \(-0.00799977\pi\)
\(840\) 0 0
\(841\) 4.96664e11 0.992839
\(842\) −4.69844e10 −0.0934772
\(843\) 6.28551e11 + 6.16880e11i 1.24460 + 1.22149i
\(844\) 6.20289e10 0.122243
\(845\) 0 0
\(846\) 1.13113e10 + 6.03457e11i 0.0220816 + 1.17805i
\(847\) 5.64145e11i 1.09612i
\(848\) −2.45810e10 −0.0475353
\(849\) 2.01247e11 + 1.97510e11i 0.387346 + 0.380154i
\(850\) 0 0
\(851\) 2.78435e11i 0.530891i
\(852\) 3.11471e11 + 3.05688e11i 0.591099 + 0.580123i
\(853\) 7.97637e11i 1.50664i −0.657655 0.753319i \(-0.728451\pi\)
0.657655 0.753319i \(-0.271549\pi\)
\(854\) 1.98924e10i 0.0373985i
\(855\) 0 0
\(856\) −1.36285e11 −0.253836
\(857\) 7.68355e11 1.42442 0.712211 0.701965i \(-0.247694\pi\)
0.712211 + 0.701965i \(0.247694\pi\)
\(858\) −1.71111e11 + 1.74348e11i −0.315740 + 0.321713i
\(859\) 5.30152e10 0.0973706 0.0486853 0.998814i \(-0.484497\pi\)
0.0486853 + 0.998814i \(0.484497\pi\)
\(860\) 0 0
\(861\) 3.04700e11 3.10465e11i 0.554446 0.564936i
\(862\) 1.80788e11i 0.327447i
\(863\) −8.01812e11 −1.44554 −0.722769 0.691090i \(-0.757131\pi\)
−0.722769 + 0.691090i \(0.757131\pi\)
\(864\) −3.96490e11 3.74801e11i −0.711504 0.672583i
\(865\) 0 0
\(866\) 2.44102e11i 0.434010i
\(867\) 4.14978e11 4.22830e11i 0.734428 0.748323i
\(868\) 5.32430e11i 0.937959i
\(869\) 1.98575e11i 0.348214i
\(870\) 0 0
\(871\) 5.54280e11 0.963067
\(872\) −2.87080e11 −0.496520
\(873\) 2.17689e11 4.08040e9i 0.374783 0.00702499i
\(874\) −2.80296e11 −0.480364
\(875\) 0 0
\(876\) −8.48813e9 8.33052e9i −0.0144144 0.0141467i
\(877\) 5.88957e11i 0.995601i −0.867292 0.497800i \(-0.834141\pi\)
0.867292 0.497800i \(-0.165859\pi\)
\(878\) −1.31818e11 −0.221817
\(879\) 5.37245e11 5.47410e11i 0.899948 0.916974i
\(880\) 0 0
\(881\) 7.89776e11i 1.31099i 0.755198 + 0.655497i \(0.227541\pi\)
−0.755198 + 0.655497i \(0.772459\pi\)
\(882\) 7.70786e9 + 4.11213e11i 0.0127368 + 0.679506i
\(883\) 4.30157e11i 0.707594i −0.935322 0.353797i \(-0.884890\pi\)
0.935322 0.353797i \(-0.115110\pi\)
\(884\) 7.47733e11i 1.22444i
\(885\) 0 0
\(886\) 1.09695e11 0.178013
\(887\) −1.14158e12 −1.84421 −0.922107 0.386934i \(-0.873534\pi\)
−0.922107 + 0.386934i \(0.873534\pi\)
\(888\) 2.11418e11 + 2.07492e11i 0.340008 + 0.333695i
\(889\) 3.53408e10 0.0565809
\(890\) 0 0
\(891\) −1.14918e10 3.06434e11i −0.0182337 0.486213i
\(892\) 7.07924e10i 0.111822i
\(893\) −7.75511e11 −1.21950
\(894\) 3.70612e11 + 3.63730e11i 0.580189 + 0.569416i
\(895\) 0 0
\(896\) 4.99646e11i 0.775230i
\(897\) −7.58821e11 7.44731e11i −1.17211 1.15035i
\(898\) 1.82850e11i 0.281183i
\(899\) 6.11135e10i 0.0935618i
\(900\) 0 0
\(901\) −7.43759e11 −1.12858
\(902\) −1.13568e11 −0.171566
\(903\) −5.02703e11 + 5.12214e11i −0.756067 + 0.770372i
\(904\) −9.37205e11 −1.40333
\(905\) 0 0
\(906\) −5.58208e11 + 5.68769e11i −0.828483 + 0.844158i
\(907\) 3.91779e11i 0.578911i 0.957191 + 0.289455i \(0.0934742\pi\)
−0.957191 + 0.289455i \(0.906526\pi\)
\(908\) 3.23049e11 0.475253
\(909\) −4.32656e8 + 8.10978e6i −0.000633705 + 1.18783e-5i
\(910\) 0 0
\(911\) 2.39414e11i 0.347597i −0.984781 0.173799i \(-0.944396\pi\)
0.984781 0.173799i \(-0.0556042\pi\)
\(912\) −1.93419e10 + 1.97078e10i −0.0279588 + 0.0284878i
\(913\) 1.60848e11i 0.231490i
\(914\) 6.76212e11i 0.968943i
\(915\) 0 0
\(916\) −1.13570e11 −0.161317
\(917\) −2.95018e11 −0.417226
\(918\) 4.72548e11 + 4.46699e11i 0.665389 + 0.628990i
\(919\) −2.64317e11 −0.370563 −0.185282 0.982685i \(-0.559320\pi\)
−0.185282 + 0.982685i \(0.559320\pi\)
\(920\) 0 0
\(921\) −4.79235e11 4.70336e11i −0.666054 0.653687i
\(922\) 6.66960e11i 0.922946i
\(923\) 1.47358e12 2.03033
\(924\) −2.10754e11 + 2.14741e11i −0.289126 + 0.294597i
\(925\) 0 0
\(926\) 1.68979e11i 0.229820i
\(927\) −1.33553e12 + 2.50335e10i −1.80857 + 0.0339002i
\(928\) 6.14477e10i 0.0828541i
\(929\) 8.24093e11i 1.10640i −0.833047 0.553202i \(-0.813406\pi\)
0.833047 0.553202i \(-0.186594\pi\)
\(930\) 0 0
\(931\) −5.28456e11 −0.703413
\(932\) 3.07158e11 0.407097
\(933\) 4.75918e11 + 4.67081e11i 0.628066 + 0.616404i
\(934\) 3.73117e11 0.490295
\(935\) 0 0
\(936\) −1.13096e12 + 2.11989e10i −1.47348 + 0.0276191i
\(937\) 3.88885e11i 0.504502i −0.967662 0.252251i \(-0.918829\pi\)
0.967662 0.252251i \(-0.0811709\pi\)
\(938\) −4.72964e11 −0.610965
\(939\) 7.35467e11 + 7.21811e11i 0.946022 + 0.928455i
\(940\) 0 0
\(941\) 5.71451e11i 0.728821i 0.931239 + 0.364410i \(0.118729\pi\)
−0.931239 + 0.364410i \(0.881271\pi\)
\(942\) −5.46929e11 5.36774e11i −0.694588 0.681691i
\(943\) 4.94287e11i 0.625075i
\(944\) 1.56822e10i 0.0197478i
\(945\) 0 0
\(946\) 1.87369e11 0.233955
\(947\) −7.99848e10 −0.0994507 −0.0497253 0.998763i \(-0.515835\pi\)
−0.0497253 + 0.998763i \(0.515835\pi\)
\(948\) −2.39178e11 + 2.43703e11i −0.296134 + 0.301737i
\(949\) −4.01576e10 −0.0495111
\(950\) 0 0
\(951\) −3.60852e11 + 3.67679e11i −0.441171 + 0.449517i
\(952\) 1.71810e12i 2.09170i
\(953\) −1.05398e12 −1.27779 −0.638894 0.769294i \(-0.720608\pi\)
−0.638894 + 0.769294i \(0.720608\pi\)
\(954\) −7.83063e9 4.17763e11i −0.00945373 0.504355i
\(955\) 0 0
\(956\) 2.33032e11i 0.278987i
\(957\) −2.41908e10 + 2.46485e10i −0.0288405 + 0.0293861i
\(958\) 5.67628e11i 0.673910i
\(959\) 8.31666e10i 0.0983274i
\(960\) 0 0
\(961\) 1.89674e11 0.222389
\(962\) 3.71445e11 0.433705
\(963\) −4.02021e9 2.14478e11i −0.00467459 0.249389i
\(964\) 1.48209e11 0.171620
\(965\) 0 0
\(966\) 6.47497e11 + 6.35474e11i 0.743583 + 0.729775i
\(967\) 4.82707e11i 0.552049i 0.961151 + 0.276025i \(0.0890172\pi\)
−0.961151 + 0.276025i \(0.910983\pi\)
\(968\) −6.81985e11 −0.776736
\(969\) −5.85236e11 + 5.96309e11i −0.663798 + 0.676357i
\(970\) 0 0
\(971\) 9.01068e11i 1.01363i −0.862054 0.506817i \(-0.830822\pi\)
0.862054 0.506817i \(-0.169178\pi\)
\(972\) 3.54988e11 3.89916e11i 0.397694 0.436823i
\(973\) 1.67094e12i 1.86427i
\(974\) 5.04264e11i 0.560302i
\(975\) 0 0
\(976\) 2.22677e9 0.00245401
\(977\) 2.30964e11 0.253493 0.126747 0.991935i \(-0.459546\pi\)
0.126747 + 0.991935i \(0.459546\pi\)
\(978\) −7.69896e11 7.55600e11i −0.841544 0.825918i
\(979\) 4.08334e11 0.444513
\(980\) 0 0
\(981\) −8.46846e9 4.51792e11i −0.00914384 0.487823i
\(982\) 6.89017e11i 0.740942i
\(983\) 1.09320e10 0.0117080 0.00585402 0.999983i \(-0.498137\pi\)
0.00585402 + 0.999983i \(0.498137\pi\)
\(984\) −3.75316e11 3.68346e11i −0.400328 0.392895i
\(985\) 0 0
\(986\) 7.32351e10i 0.0774840i
\(987\) 1.79147e12 + 1.75820e12i 1.88773 + 1.85268i
\(988\) 5.39742e11i 0.566446i
\(989\) 8.15489e11i 0.852380i
\(990\) 0 0
\(991\) 5.43139e10 0.0563140 0.0281570 0.999604i \(-0.491036\pi\)
0.0281570 + 0.999604i \(0.491036\pi\)
\(992\) −1.04827e12 −1.08249
\(993\) 7.12146e10 7.25620e10i 0.0732440 0.0746298i
\(994\) −1.25740e12 −1.28803
\(995\) 0 0
\(996\) 1.93736e11 1.97402e11i 0.196867 0.200592i
\(997\) 1.85628e12i 1.87872i −0.342929 0.939361i \(-0.611419\pi\)
0.342929 0.939361i \(-0.388581\pi\)
\(998\) 8.33205e11 0.839904
\(999\) −3.20304e11 + 3.38839e11i −0.321588 + 0.340198i
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 75.9.d.c.74.15 20
3.2 odd 2 inner 75.9.d.c.74.5 20
5.2 odd 4 15.9.c.a.11.8 yes 10
5.3 odd 4 75.9.c.g.26.3 10
5.4 even 2 inner 75.9.d.c.74.6 20
15.2 even 4 15.9.c.a.11.3 10
15.8 even 4 75.9.c.g.26.8 10
15.14 odd 2 inner 75.9.d.c.74.16 20
20.7 even 4 240.9.l.b.161.8 10
60.47 odd 4 240.9.l.b.161.7 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.9.c.a.11.3 10 15.2 even 4
15.9.c.a.11.8 yes 10 5.2 odd 4
75.9.c.g.26.3 10 5.3 odd 4
75.9.c.g.26.8 10 15.8 even 4
75.9.d.c.74.5 20 3.2 odd 2 inner
75.9.d.c.74.6 20 5.4 even 2 inner
75.9.d.c.74.15 20 1.1 even 1 trivial
75.9.d.c.74.16 20 15.14 odd 2 inner
240.9.l.b.161.7 10 60.47 odd 4
240.9.l.b.161.8 10 20.7 even 4