Properties

Label 76.8.d.a.75.5
Level $76$
Weight $8$
Character 76.75
Analytic conductor $23.741$
Analytic rank $0$
Dimension $68$
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] = [76,8,Mod(75,76)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(76, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("76.75");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 76 = 2^{2} \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 76.d (of order \(2\), degree \(1\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(23.7412619368\)
Analytic rank: \(0\)
Dimension: \(68\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 75.5
Character \(\chi\) \(=\) 76.75
Dual form 76.8.d.a.75.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-10.9753 - 2.74630i) q^{2} -8.30507 q^{3} +(112.916 + 60.2831i) q^{4} -360.155 q^{5} +(91.1509 + 22.8082i) q^{6} +965.147i q^{7} +(-1073.73 - 971.727i) q^{8} -2118.03 q^{9} +O(q^{10})\) \(q+(-10.9753 - 2.74630i) q^{2} -8.30507 q^{3} +(112.916 + 60.2831i) q^{4} -360.155 q^{5} +(91.1509 + 22.8082i) q^{6} +965.147i q^{7} +(-1073.73 - 971.727i) q^{8} -2118.03 q^{9} +(3952.82 + 989.094i) q^{10} -3964.61i q^{11} +(-937.773 - 500.655i) q^{12} +11892.9i q^{13} +(2650.58 - 10592.8i) q^{14} +2991.12 q^{15} +(9115.91 + 13613.8i) q^{16} -33048.5 q^{17} +(23246.0 + 5816.73i) q^{18} +(22720.7 + 19433.0i) q^{19} +(-40667.2 - 21711.3i) q^{20} -8015.61i q^{21} +(-10888.0 + 43512.9i) q^{22} +20031.3i q^{23} +(8917.42 + 8070.26i) q^{24} +51586.9 q^{25} +(32661.5 - 130529. i) q^{26} +35753.5 q^{27} +(-58182.0 + 108980. i) q^{28} -6526.34i q^{29} +(-32828.5 - 8214.50i) q^{30} +56888.3 q^{31} +(-62662.5 - 174451. i) q^{32} +32926.4i q^{33} +(362719. + 90761.2i) q^{34} -347603. i q^{35} +(-239158. - 127681. i) q^{36} -468695. i q^{37} +(-195998. - 275681. i) q^{38} -98771.6i q^{39} +(386710. + 349973. i) q^{40} -668641. i q^{41} +(-22013.3 + 87974.0i) q^{42} -932141. i q^{43} +(238999. - 447667. i) q^{44} +762818. q^{45} +(55011.8 - 219850. i) q^{46} +378820. i q^{47} +(-75708.2 - 113064. i) q^{48} -107965. q^{49} +(-566184. - 141673. i) q^{50} +274471. q^{51} +(-716942. + 1.34290e6i) q^{52} +1.24150e6i q^{53} +(-392407. - 98189.9i) q^{54} +1.42788e6i q^{55} +(937859. - 1.03631e6i) q^{56} +(-188697. - 161392. i) q^{57} +(-17923.3 + 71628.7i) q^{58} +1.58920e6 q^{59} +(337744. + 180314. i) q^{60} +423764. q^{61} +(-624368. - 156232. i) q^{62} -2.04421e6i q^{63} +(208647. + 2.08675e6i) q^{64} -4.28330e6i q^{65} +(90425.7 - 361378. i) q^{66} -3.95935e6 q^{67} +(-3.73170e6 - 1.99227e6i) q^{68} -166361. i q^{69} +(-954621. + 3.81506e6i) q^{70} +2.83400e6 q^{71} +(2.27419e6 + 2.05814e6i) q^{72} +582613. q^{73} +(-1.28718e6 + 5.14408e6i) q^{74} -428433. q^{75} +(1.39404e6 + 3.56396e6i) q^{76} +3.82643e6 q^{77} +(-271256. + 1.08405e6i) q^{78} -4.06561e6 q^{79} +(-3.28314e6 - 4.90309e6i) q^{80} +4.33519e6 q^{81} +(-1.83629e6 + 7.33856e6i) q^{82} +4.76177e6i q^{83} +(483206. - 905088. i) q^{84} +1.19026e7 q^{85} +(-2.55994e6 + 1.02306e7i) q^{86} +54201.7i q^{87} +(-3.85252e6 + 4.25693e6i) q^{88} -3.77882e6i q^{89} +(-8.37218e6 - 2.09493e6i) q^{90} -1.14784e7 q^{91} +(-1.20755e6 + 2.26184e6i) q^{92} -472462. q^{93} +(1.04035e6 - 4.15768e6i) q^{94} +(-8.18298e6 - 6.99890e6i) q^{95} +(520416. + 1.44883e6i) q^{96} -6.84934e6i q^{97} +(1.18495e6 + 296505. i) q^{98} +8.39716e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 68 q - 54 q^{4} - 4 q^{5} - 150 q^{6} + 48888 q^{9} + 13050 q^{16} + 23968 q^{17} - 79660 q^{20} - 232154 q^{24} + 937496 q^{25} - 391242 q^{26} - 37666 q^{28} - 468496 q^{30} - 1128652 q^{36} - 530466 q^{38} + 651806 q^{42} + 1433776 q^{44} - 321252 q^{45} - 4014380 q^{49} + 1697586 q^{54} + 137420 q^{57} + 2227894 q^{58} - 3042164 q^{61} + 2261524 q^{62} + 9825150 q^{64} - 749476 q^{66} - 11176962 q^{68} + 598424 q^{73} - 6195964 q^{74} - 1714536 q^{76} - 2556764 q^{77} + 16623216 q^{80} + 43726748 q^{81} - 20460388 q^{82} + 27222844 q^{85} - 61733582 q^{92} + 17778200 q^{93} - 36370886 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).

\(n\) \(21\) \(39\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −10.9753 2.74630i −0.970091 0.242741i
\(3\) −8.30507 −0.177590 −0.0887951 0.996050i \(-0.528302\pi\)
−0.0887951 + 0.996050i \(0.528302\pi\)
\(4\) 112.916 + 60.2831i 0.882154 + 0.470961i
\(5\) −360.155 −1.28853 −0.644266 0.764802i \(-0.722837\pi\)
−0.644266 + 0.764802i \(0.722837\pi\)
\(6\) 91.1509 + 22.8082i 0.172279 + 0.0431084i
\(7\) 965.147i 1.06353i 0.846892 + 0.531766i \(0.178471\pi\)
−0.846892 + 0.531766i \(0.821529\pi\)
\(8\) −1073.73 971.727i −0.741448 0.671010i
\(9\) −2118.03 −0.968462
\(10\) 3952.82 + 989.094i 1.24999 + 0.312779i
\(11\) 3964.61i 0.898104i −0.893506 0.449052i \(-0.851762\pi\)
0.893506 0.449052i \(-0.148238\pi\)
\(12\) −937.773 500.655i −0.156662 0.0836381i
\(13\) 11892.9i 1.50137i 0.660662 + 0.750684i \(0.270276\pi\)
−0.660662 + 0.750684i \(0.729724\pi\)
\(14\) 2650.58 10592.8i 0.258162 1.03172i
\(15\) 2991.12 0.228831
\(16\) 9115.91 + 13613.8i 0.556391 + 0.830921i
\(17\) −33048.5 −1.63148 −0.815739 0.578420i \(-0.803669\pi\)
−0.815739 + 0.578420i \(0.803669\pi\)
\(18\) 23246.0 + 5816.73i 0.939496 + 0.235085i
\(19\) 22720.7 + 19433.0i 0.759948 + 0.649983i
\(20\) −40667.2 21711.3i −1.13668 0.606848i
\(21\) 8015.61i 0.188873i
\(22\) −10888.0 + 43512.9i −0.218006 + 0.871243i
\(23\) 20031.3i 0.343290i 0.985159 + 0.171645i \(0.0549082\pi\)
−0.985159 + 0.171645i \(0.945092\pi\)
\(24\) 8917.42 + 8070.26i 0.131674 + 0.119165i
\(25\) 51586.9 0.660313
\(26\) 32661.5 130529.i 0.364443 1.45646i
\(27\) 35753.5 0.349580
\(28\) −58182.0 + 108980.i −0.500882 + 0.938198i
\(29\) 6526.34i 0.0496909i −0.999691 0.0248454i \(-0.992091\pi\)
0.999691 0.0248454i \(-0.00790936\pi\)
\(30\) −32828.5 8214.50i −0.221986 0.0555465i
\(31\) 56888.3 0.342971 0.171485 0.985187i \(-0.445143\pi\)
0.171485 + 0.985187i \(0.445143\pi\)
\(32\) −62662.5 174451.i −0.338051 0.941128i
\(33\) 32926.4i 0.159494i
\(34\) 362719. + 90761.2i 1.58268 + 0.396026i
\(35\) 347603.i 1.37039i
\(36\) −239158. 127681.i −0.854332 0.456108i
\(37\) 468695.i 1.52119i −0.649224 0.760597i \(-0.724906\pi\)
0.649224 0.760597i \(-0.275094\pi\)
\(38\) −195998. 275681.i −0.579442 0.815014i
\(39\) 98771.6i 0.266628i
\(40\) 386710. + 349973.i 0.955379 + 0.864618i
\(41\) 668641.i 1.51513i −0.652760 0.757564i \(-0.726389\pi\)
0.652760 0.757564i \(-0.273611\pi\)
\(42\) −22013.3 + 87974.0i −0.0458471 + 0.183224i
\(43\) 932141.i 1.78790i −0.448171 0.893948i \(-0.647925\pi\)
0.448171 0.893948i \(-0.352075\pi\)
\(44\) 238999. 447667.i 0.422972 0.792266i
\(45\) 762818. 1.24789
\(46\) 55011.8 219850.i 0.0833304 0.333022i
\(47\) 378820.i 0.532219i 0.963943 + 0.266110i \(0.0857383\pi\)
−0.963943 + 0.266110i \(0.914262\pi\)
\(48\) −75708.2 113064.i −0.0988095 0.147563i
\(49\) −107965. −0.131098
\(50\) −566184. 141673.i −0.640564 0.160285i
\(51\) 274471. 0.289734
\(52\) −716942. + 1.34290e6i −0.707086 + 1.32444i
\(53\) 1.24150e6i 1.14547i 0.819742 + 0.572733i \(0.194117\pi\)
−0.819742 + 0.572733i \(0.805883\pi\)
\(54\) −392407. 98189.9i −0.339124 0.0848572i
\(55\) 1.42788e6i 1.15723i
\(56\) 937859. 1.03631e6i 0.713640 0.788553i
\(57\) −188697. 161392.i −0.134959 0.115431i
\(58\) −17923.3 + 71628.7i −0.0120620 + 0.0482047i
\(59\) 1.58920e6 1.00739 0.503694 0.863882i \(-0.331974\pi\)
0.503694 + 0.863882i \(0.331974\pi\)
\(60\) 337744. + 180314.i 0.201864 + 0.107770i
\(61\) 423764. 0.239040 0.119520 0.992832i \(-0.461864\pi\)
0.119520 + 0.992832i \(0.461864\pi\)
\(62\) −624368. 156232.i −0.332713 0.0832530i
\(63\) 2.04421e6i 1.02999i
\(64\) 208647. + 2.08675e6i 0.0994905 + 0.995039i
\(65\) 4.28330e6i 1.93456i
\(66\) 90425.7 361378.i 0.0387158 0.154724i
\(67\) −3.95935e6 −1.60828 −0.804140 0.594440i \(-0.797374\pi\)
−0.804140 + 0.594440i \(0.797374\pi\)
\(68\) −3.73170e6 1.99227e6i −1.43921 0.768363i
\(69\) 166361.i 0.0609649i
\(70\) −954621. + 3.81506e6i −0.332650 + 1.32941i
\(71\) 2.83400e6 0.939713 0.469856 0.882743i \(-0.344306\pi\)
0.469856 + 0.882743i \(0.344306\pi\)
\(72\) 2.27419e6 + 2.05814e6i 0.718064 + 0.649848i
\(73\) 582613. 0.175287 0.0876436 0.996152i \(-0.472066\pi\)
0.0876436 + 0.996152i \(0.472066\pi\)
\(74\) −1.28718e6 + 5.14408e6i −0.369256 + 1.47570i
\(75\) −428433. −0.117265
\(76\) 1.39404e6 + 3.56396e6i 0.364274 + 0.931292i
\(77\) 3.82643e6 0.955161
\(78\) −271256. + 1.08405e6i −0.0647215 + 0.258654i
\(79\) −4.06561e6 −0.927749 −0.463875 0.885901i \(-0.653541\pi\)
−0.463875 + 0.885901i \(0.653541\pi\)
\(80\) −3.28314e6 4.90309e6i −0.716927 1.07067i
\(81\) 4.33519e6 0.906380
\(82\) −1.83629e6 + 7.33856e6i −0.367784 + 1.46981i
\(83\) 4.76177e6i 0.914102i 0.889440 + 0.457051i \(0.151094\pi\)
−0.889440 + 0.457051i \(0.848906\pi\)
\(84\) 483206. 905088.i 0.0889518 0.166615i
\(85\) 1.19026e7 2.10221
\(86\) −2.55994e6 + 1.02306e7i −0.433995 + 1.73442i
\(87\) 54201.7i 0.00882461i
\(88\) −3.85252e6 + 4.25693e6i −0.602637 + 0.665897i
\(89\) 3.77882e6i 0.568187i −0.958797 0.284093i \(-0.908307\pi\)
0.958797 0.284093i \(-0.0916926\pi\)
\(90\) −8.37218e6 2.09493e6i −1.21057 0.302915i
\(91\) −1.14784e7 −1.59675
\(92\) −1.20755e6 + 2.26184e6i −0.161676 + 0.302834i
\(93\) −472462. −0.0609083
\(94\) 1.04035e6 4.15768e6i 0.129191 0.516301i
\(95\) −8.18298e6 6.99890e6i −0.979217 0.837524i
\(96\) 520416. + 1.44883e6i 0.0600346 + 0.167135i
\(97\) 6.84934e6i 0.761987i −0.924578 0.380993i \(-0.875582\pi\)
0.924578 0.380993i \(-0.124418\pi\)
\(98\) 1.18495e6 + 296505.i 0.127177 + 0.0318229i
\(99\) 8.39716e6i 0.869779i
\(100\) 5.82497e6 + 3.10982e6i 0.582497 + 0.310982i
\(101\) −3.81550e6 −0.368491 −0.184246 0.982880i \(-0.558984\pi\)
−0.184246 + 0.982880i \(0.558984\pi\)
\(102\) −3.01240e6 753778.i −0.281069 0.0703304i
\(103\) 1.28044e7 1.15460 0.577298 0.816533i \(-0.304107\pi\)
0.577298 + 0.816533i \(0.304107\pi\)
\(104\) 1.15567e7 1.27698e7i 1.00743 1.11319i
\(105\) 2.88687e6i 0.243368i
\(106\) 3.40954e6 1.36259e7i 0.278051 1.11121i
\(107\) 9.00442e6 0.710579 0.355290 0.934756i \(-0.384382\pi\)
0.355290 + 0.934756i \(0.384382\pi\)
\(108\) 4.03714e6 + 2.15533e6i 0.308383 + 0.164638i
\(109\) 6.98563e6i 0.516670i 0.966055 + 0.258335i \(0.0831738\pi\)
−0.966055 + 0.258335i \(0.916826\pi\)
\(110\) 3.92138e6 1.56714e7i 0.280908 1.12262i
\(111\) 3.89255e6i 0.270149i
\(112\) −1.31393e7 + 8.79819e6i −0.883710 + 0.591739i
\(113\) 2.32744e6i 0.151742i 0.997118 + 0.0758708i \(0.0241737\pi\)
−0.997118 + 0.0758708i \(0.975826\pi\)
\(114\) 1.62778e6 + 2.28955e6i 0.102903 + 0.144738i
\(115\) 7.21437e6i 0.442340i
\(116\) 393428. 736926.i 0.0234025 0.0438350i
\(117\) 2.51895e7i 1.45402i
\(118\) −1.74420e7 4.36442e6i −0.977259 0.244534i
\(119\) 3.18967e7i 1.73513i
\(120\) −3.21166e6 2.90655e6i −0.169666 0.153548i
\(121\) 3.76900e6 0.193409
\(122\) −4.65095e6 1.16378e6i −0.231890 0.0580247i
\(123\) 5.55311e6i 0.269072i
\(124\) 6.42359e6 + 3.42940e6i 0.302553 + 0.161526i
\(125\) 9.55783e6 0.437698
\(126\) −5.61400e6 + 2.24358e7i −0.250020 + 0.999183i
\(127\) −709860. −0.0307511 −0.0153755 0.999882i \(-0.504894\pi\)
−0.0153755 + 0.999882i \(0.504894\pi\)
\(128\) 3.44086e6 2.34757e7i 0.145022 0.989428i
\(129\) 7.74150e6i 0.317513i
\(130\) −1.17632e7 + 4.70107e7i −0.469596 + 1.87670i
\(131\) 3.97921e7i 1.54649i 0.634108 + 0.773245i \(0.281368\pi\)
−0.634108 + 0.773245i \(0.718632\pi\)
\(132\) −1.98490e6 + 3.71791e6i −0.0751157 + 0.140699i
\(133\) −1.87557e7 + 2.19288e7i −0.691278 + 0.808229i
\(134\) 4.34551e7 + 1.08735e7i 1.56018 + 0.390395i
\(135\) −1.28768e7 −0.450444
\(136\) 3.54853e7 + 3.21142e7i 1.20966 + 1.09474i
\(137\) −3.43128e7 −1.14008 −0.570039 0.821618i \(-0.693072\pi\)
−0.570039 + 0.821618i \(0.693072\pi\)
\(138\) −456877. + 1.82587e6i −0.0147987 + 0.0591415i
\(139\) 3.76453e7i 1.18894i −0.804118 0.594469i \(-0.797362\pi\)
0.804118 0.594469i \(-0.202638\pi\)
\(140\) 2.09546e7 3.92498e7i 0.645402 1.20890i
\(141\) 3.14613e6i 0.0945169i
\(142\) −3.11040e7 7.78300e6i −0.911607 0.228107i
\(143\) 4.71509e7 1.34838
\(144\) −1.93077e7 2.88344e7i −0.538843 0.804715i
\(145\) 2.35050e6i 0.0640282i
\(146\) −6.39437e6 1.60003e6i −0.170044 0.0425493i
\(147\) 896658. 0.0232818
\(148\) 2.82544e7 5.29230e7i 0.716424 1.34193i
\(149\) −5.87834e7 −1.45580 −0.727902 0.685682i \(-0.759504\pi\)
−0.727902 + 0.685682i \(0.759504\pi\)
\(150\) 4.70219e6 + 1.17661e6i 0.113758 + 0.0284650i
\(151\) 7.70255e7 1.82060 0.910302 0.413945i \(-0.135849\pi\)
0.910302 + 0.413945i \(0.135849\pi\)
\(152\) −5.51236e6 4.29441e7i −0.127317 0.991862i
\(153\) 6.99977e7 1.58002
\(154\) −4.19964e7 1.05085e7i −0.926594 0.231857i
\(155\) −2.04886e7 −0.441929
\(156\) 5.95426e6 1.11529e7i 0.125572 0.235207i
\(157\) −1.81922e7 −0.375176 −0.187588 0.982248i \(-0.560067\pi\)
−0.187588 + 0.982248i \(0.560067\pi\)
\(158\) 4.46214e7 + 1.11654e7i 0.900002 + 0.225203i
\(159\) 1.03108e7i 0.203423i
\(160\) 2.25682e7 + 6.28295e7i 0.435590 + 1.21267i
\(161\) −1.93331e7 −0.365099
\(162\) −4.75801e7 1.19057e7i −0.879271 0.220015i
\(163\) 3.88437e7i 0.702528i 0.936276 + 0.351264i \(0.114248\pi\)
−0.936276 + 0.351264i \(0.885752\pi\)
\(164\) 4.03077e7 7.55001e7i 0.713567 1.33658i
\(165\) 1.18586e7i 0.205514i
\(166\) 1.30772e7 5.22619e7i 0.221890 0.886762i
\(167\) 2.26519e7 0.376354 0.188177 0.982135i \(-0.439742\pi\)
0.188177 + 0.982135i \(0.439742\pi\)
\(168\) −7.78898e6 + 8.60662e6i −0.126736 + 0.140039i
\(169\) −7.86933e7 −1.25411
\(170\) −1.30635e8 3.26881e7i −2.03934 0.510292i
\(171\) −4.81230e7 4.11596e7i −0.735981 0.629484i
\(172\) 5.61923e7 1.05253e8i 0.842030 1.57720i
\(173\) 1.21339e8i 1.78172i 0.454273 + 0.890862i \(0.349899\pi\)
−0.454273 + 0.890862i \(0.650101\pi\)
\(174\) 148854. 594881.i 0.00214209 0.00856068i
\(175\) 4.97890e7i 0.702263i
\(176\) 5.39735e7 3.61411e7i 0.746253 0.499697i
\(177\) −1.31984e7 −0.178902
\(178\) −1.03778e7 + 4.14738e7i −0.137922 + 0.551193i
\(179\) −1.47765e8 −1.92569 −0.962844 0.270057i \(-0.912957\pi\)
−0.962844 + 0.270057i \(0.912957\pi\)
\(180\) 8.61342e7 + 4.59850e7i 1.10083 + 0.587710i
\(181\) 8.83586e7i 1.10758i −0.832657 0.553788i \(-0.813182\pi\)
0.832657 0.553788i \(-0.186818\pi\)
\(182\) 1.25979e8 + 3.15232e7i 1.54899 + 0.387597i
\(183\) −3.51939e6 −0.0424511
\(184\) 1.94649e7 2.15082e7i 0.230351 0.254532i
\(185\) 1.68803e8i 1.96011i
\(186\) 5.18542e6 + 1.29752e6i 0.0590866 + 0.0147849i
\(187\) 1.31025e8i 1.46524i
\(188\) −2.28364e7 + 4.27747e7i −0.250655 + 0.469499i
\(189\) 3.45074e7i 0.371789i
\(190\) 7.05899e7 + 9.92882e7i 0.746629 + 1.05017i
\(191\) 1.40988e8i 1.46408i −0.681261 0.732041i \(-0.738568\pi\)
0.681261 0.732041i \(-0.261432\pi\)
\(192\) −1.73283e6 1.73306e7i −0.0176685 0.176709i
\(193\) 5.03272e7i 0.503909i −0.967739 0.251955i \(-0.918927\pi\)
0.967739 0.251955i \(-0.0810733\pi\)
\(194\) −1.88103e7 + 7.51737e7i −0.184965 + 0.739197i
\(195\) 3.55731e7i 0.343559i
\(196\) −1.21910e7 6.50847e6i −0.115649 0.0617423i
\(197\) −4.41428e7 −0.411366 −0.205683 0.978619i \(-0.565942\pi\)
−0.205683 + 0.978619i \(0.565942\pi\)
\(198\) 2.30611e7 9.21615e7i 0.211131 0.843765i
\(199\) 1.14883e7i 0.103341i 0.998664 + 0.0516703i \(0.0164545\pi\)
−0.998664 + 0.0516703i \(0.983546\pi\)
\(200\) −5.53905e7 5.01284e7i −0.489588 0.443077i
\(201\) 3.28826e7 0.285615
\(202\) 4.18764e7 + 1.04785e7i 0.357470 + 0.0894478i
\(203\) 6.29887e6 0.0528478
\(204\) 3.09920e7 + 1.65459e7i 0.255590 + 0.136454i
\(205\) 2.40815e8i 1.95229i
\(206\) −1.40533e8 3.51648e7i −1.12006 0.280268i
\(207\) 4.24267e7i 0.332463i
\(208\) −1.61908e8 + 1.08415e8i −1.24752 + 0.835347i
\(209\) 7.70444e7 9.00788e7i 0.583753 0.682513i
\(210\) 7.92820e6 3.16843e7i 0.0590754 0.236090i
\(211\) 7.95830e7 0.583219 0.291610 0.956537i \(-0.405809\pi\)
0.291610 + 0.956537i \(0.405809\pi\)
\(212\) −7.48415e7 + 1.40185e8i −0.539470 + 1.01048i
\(213\) −2.35365e7 −0.166884
\(214\) −9.88264e7 2.47288e7i −0.689326 0.172487i
\(215\) 3.35716e8i 2.30376i
\(216\) −3.83897e7 3.47427e7i −0.259195 0.234571i
\(217\) 5.49056e7i 0.364760i
\(218\) 1.91846e7 7.66696e7i 0.125417 0.501217i
\(219\) −4.83864e6 −0.0311293
\(220\) −8.60768e7 + 1.61230e8i −0.545013 + 1.02086i
\(221\) 3.93044e8i 2.44945i
\(222\) 1.06901e7 4.27220e7i 0.0655762 0.262069i
\(223\) −1.80079e8 −1.08742 −0.543708 0.839275i \(-0.682980\pi\)
−0.543708 + 0.839275i \(0.682980\pi\)
\(224\) 1.68371e8 6.04785e7i 1.00092 0.359528i
\(225\) −1.09262e8 −0.639488
\(226\) 6.39186e6 2.55445e7i 0.0368339 0.147203i
\(227\) 3.27877e8 1.86046 0.930230 0.366976i \(-0.119607\pi\)
0.930230 + 0.366976i \(0.119607\pi\)
\(228\) −1.15776e7 2.95990e7i −0.0646915 0.165388i
\(229\) 1.98216e7 0.109072 0.0545362 0.998512i \(-0.482632\pi\)
0.0545362 + 0.998512i \(0.482632\pi\)
\(230\) −1.98128e7 + 7.91801e7i −0.107374 + 0.429110i
\(231\) −3.17788e7 −0.169627
\(232\) −6.34182e6 + 7.00753e6i −0.0333431 + 0.0368432i
\(233\) 1.59540e8 0.826272 0.413136 0.910669i \(-0.364433\pi\)
0.413136 + 0.910669i \(0.364433\pi\)
\(234\) −6.91780e7 + 2.76463e8i −0.352949 + 1.41053i
\(235\) 1.36434e8i 0.685781i
\(236\) 1.79446e8 + 9.58020e7i 0.888672 + 0.474441i
\(237\) 3.37652e7 0.164759
\(238\) −8.75979e7 + 3.50077e8i −0.421186 + 1.68323i
\(239\) 2.64735e8i 1.25435i −0.778878 0.627176i \(-0.784211\pi\)
0.778878 0.627176i \(-0.215789\pi\)
\(240\) 2.72667e7 + 4.07205e7i 0.127319 + 0.190140i
\(241\) 8.30066e7i 0.381991i 0.981591 + 0.190995i \(0.0611716\pi\)
−0.981591 + 0.190995i \(0.938828\pi\)
\(242\) −4.13660e7 1.03508e7i −0.187625 0.0469484i
\(243\) −1.14197e8 −0.510544
\(244\) 4.78497e7 + 2.55458e7i 0.210870 + 0.112578i
\(245\) 3.88842e7 0.168924
\(246\) 1.52505e7 6.09472e7i 0.0653148 0.261024i
\(247\) −2.31115e8 + 2.70216e8i −0.975864 + 1.14096i
\(248\) −6.10828e7 5.52799e7i −0.254295 0.230137i
\(249\) 3.95468e7i 0.162336i
\(250\) −1.04900e8 2.62487e7i −0.424607 0.106247i
\(251\) 3.61723e8i 1.44384i −0.691978 0.721919i \(-0.743260\pi\)
0.691978 0.721919i \(-0.256740\pi\)
\(252\) 1.23231e8 2.30823e8i 0.485085 0.908609i
\(253\) 7.94162e7 0.308310
\(254\) 7.79095e6 + 1.94949e6i 0.0298313 + 0.00746453i
\(255\) −9.88521e7 −0.373332
\(256\) −1.02236e8 + 2.48204e8i −0.380859 + 0.924633i
\(257\) 2.17294e8i 0.798511i 0.916840 + 0.399256i \(0.130731\pi\)
−0.916840 + 0.399256i \(0.869269\pi\)
\(258\) 2.12605e7 8.49655e7i 0.0770733 0.308016i
\(259\) 4.52360e8 1.61784
\(260\) 2.58211e8 4.83652e8i 0.911103 1.70658i
\(261\) 1.38230e7i 0.0481237i
\(262\) 1.09281e8 4.36731e8i 0.375396 1.50024i
\(263\) 1.68696e8i 0.571820i −0.958256 0.285910i \(-0.907704\pi\)
0.958256 0.285910i \(-0.0922959\pi\)
\(264\) 3.19955e7 3.53541e7i 0.107022 0.118257i
\(265\) 4.47134e8i 1.47597i
\(266\) 2.66073e8 1.89167e8i 0.866792 0.616254i
\(267\) 3.13834e7i 0.100904i
\(268\) −4.47072e8 2.38681e8i −1.41875 0.757438i
\(269\) 1.58558e8i 0.496657i −0.968676 0.248328i \(-0.920119\pi\)
0.968676 0.248328i \(-0.0798812\pi\)
\(270\) 1.41327e8 + 3.53636e7i 0.436972 + 0.109341i
\(271\) 9.95154e7i 0.303737i −0.988401 0.151869i \(-0.951471\pi\)
0.988401 0.151869i \(-0.0485290\pi\)
\(272\) −3.01267e8 4.49917e8i −0.907739 1.35563i
\(273\) 9.53291e7 0.283567
\(274\) 3.76594e8 + 9.42332e7i 1.10598 + 0.276743i
\(275\) 2.04522e8i 0.593029i
\(276\) 1.00288e7 1.87848e7i 0.0287121 0.0537804i
\(277\) −2.17548e8 −0.615002 −0.307501 0.951548i \(-0.599493\pi\)
−0.307501 + 0.951548i \(0.599493\pi\)
\(278\) −1.03385e8 + 4.13170e8i −0.288604 + 1.15338i
\(279\) −1.20491e8 −0.332154
\(280\) −3.37775e8 + 3.73232e8i −0.919548 + 1.01608i
\(281\) 5.39415e8i 1.45028i −0.688603 0.725138i \(-0.741776\pi\)
0.688603 0.725138i \(-0.258224\pi\)
\(282\) −8.64021e6 + 3.45298e7i −0.0229431 + 0.0916900i
\(283\) 6.70172e6i 0.0175765i 0.999961 + 0.00878827i \(0.00279743\pi\)
−0.999961 + 0.00878827i \(0.997203\pi\)
\(284\) 3.20003e8 + 1.70842e8i 0.828971 + 0.442568i
\(285\) 6.79603e7 + 5.81264e7i 0.173899 + 0.148736i
\(286\) −5.17496e8 1.29490e8i −1.30806 0.327308i
\(287\) 6.45337e8 1.61139
\(288\) 1.32721e8 + 3.69492e8i 0.327390 + 0.911446i
\(289\) 6.81868e8 1.66172
\(290\) 6.45516e6 2.57975e7i 0.0155423 0.0621132i
\(291\) 5.68842e7i 0.135321i
\(292\) 6.57861e7 + 3.51217e7i 0.154630 + 0.0825535i
\(293\) 4.38051e8i 1.01739i −0.860947 0.508695i \(-0.830128\pi\)
0.860947 0.508695i \(-0.169872\pi\)
\(294\) −9.84112e6 2.46249e6i −0.0225855 0.00565144i
\(295\) −5.72360e8 −1.29805
\(296\) −4.55444e8 + 5.03253e8i −1.02074 + 1.12789i
\(297\) 1.41749e8i 0.313959i
\(298\) 6.45167e8 + 1.61437e8i 1.41226 + 0.353383i
\(299\) −2.38230e8 −0.515404
\(300\) −4.83768e7 2.58273e7i −0.103446 0.0552273i
\(301\) 8.99653e8 1.90148
\(302\) −8.45381e8 2.11535e8i −1.76615 0.441935i
\(303\) 3.16880e7 0.0654404
\(304\) −5.74374e7 + 4.86465e8i −0.117257 + 0.993102i
\(305\) −1.52621e8 −0.308010
\(306\) −7.68248e8 1.92235e8i −1.53277 0.383536i
\(307\) 3.46252e8 0.682980 0.341490 0.939885i \(-0.389069\pi\)
0.341490 + 0.939885i \(0.389069\pi\)
\(308\) 4.32065e8 + 2.30669e8i 0.842599 + 0.449844i
\(309\) −1.06342e8 −0.205045
\(310\) 2.24870e8 + 5.62679e7i 0.428711 + 0.107274i
\(311\) 1.84289e7i 0.0347407i −0.999849 0.0173703i \(-0.994471\pi\)
0.999849 0.0173703i \(-0.00552943\pi\)
\(312\) −9.59790e7 + 1.06054e8i −0.178910 + 0.197691i
\(313\) −2.62310e8 −0.483515 −0.241758 0.970337i \(-0.577724\pi\)
−0.241758 + 0.970337i \(0.577724\pi\)
\(314\) 1.99665e8 + 4.99611e7i 0.363955 + 0.0910706i
\(315\) 7.36232e8i 1.32717i
\(316\) −4.59071e8 2.45087e8i −0.818418 0.436934i
\(317\) 1.06461e8i 0.187708i 0.995586 + 0.0938541i \(0.0299187\pi\)
−0.995586 + 0.0938541i \(0.970081\pi\)
\(318\) −2.83164e7 + 1.13164e8i −0.0493792 + 0.197339i
\(319\) −2.58744e7 −0.0446276
\(320\) −7.51453e7 7.51553e8i −0.128197 1.28214i
\(321\) −7.47823e7 −0.126192
\(322\) 2.12187e8 + 5.30945e7i 0.354180 + 0.0886245i
\(323\) −7.50886e8 6.42233e8i −1.23984 1.06043i
\(324\) 4.89511e8 + 2.61338e8i 0.799566 + 0.426870i
\(325\) 6.13520e8i 0.991372i
\(326\) 1.06676e8 4.26322e8i 0.170532 0.681516i
\(327\) 5.80162e7i 0.0917555i
\(328\) −6.49736e8 + 7.17941e8i −1.01667 + 1.12339i
\(329\) −3.65617e8 −0.566032
\(330\) −3.25673e7 + 1.30152e8i −0.0498865 + 0.199367i
\(331\) −6.30158e8 −0.955106 −0.477553 0.878603i \(-0.658476\pi\)
−0.477553 + 0.878603i \(0.658476\pi\)
\(332\) −2.87054e8 + 5.37678e8i −0.430507 + 0.806379i
\(333\) 9.92709e8i 1.47322i
\(334\) −2.48612e8 6.22089e7i −0.365098 0.0913565i
\(335\) 1.42598e9 2.07232
\(336\) 1.09123e8 7.30696e7i 0.156938 0.105087i
\(337\) 2.99624e8i 0.426454i −0.977003 0.213227i \(-0.931603\pi\)
0.977003 0.213227i \(-0.0683973\pi\)
\(338\) 8.63684e8 + 2.16115e8i 1.21660 + 0.304423i
\(339\) 1.93296e7i 0.0269478i
\(340\) 1.34399e9 + 7.17526e8i 1.85447 + 0.990060i
\(341\) 2.25540e8i 0.308024i
\(342\) 4.15129e8 + 5.83900e8i 0.561167 + 0.789310i
\(343\) 6.90638e8i 0.924104i
\(344\) −9.05786e8 + 1.00087e9i −1.19970 + 1.32563i
\(345\) 5.99158e7i 0.0785552i
\(346\) 3.33234e8 1.33174e9i 0.432497 1.72844i
\(347\) 8.25153e8i 1.06018i 0.847940 + 0.530092i \(0.177843\pi\)
−0.847940 + 0.530092i \(0.822157\pi\)
\(348\) −3.26744e6 + 6.12022e6i −0.00415605 + 0.00778466i
\(349\) −5.77527e8 −0.727250 −0.363625 0.931545i \(-0.618461\pi\)
−0.363625 + 0.931545i \(0.618461\pi\)
\(350\) 1.36735e8 5.46450e8i 0.170468 0.681259i
\(351\) 4.25214e8i 0.524847i
\(352\) −6.91631e8 + 2.48433e8i −0.845230 + 0.303605i
\(353\) −1.55713e8 −0.188414 −0.0942069 0.995553i \(-0.530032\pi\)
−0.0942069 + 0.995553i \(0.530032\pi\)
\(354\) 1.44857e8 + 3.62469e7i 0.173552 + 0.0434269i
\(355\) −1.02068e9 −1.21085
\(356\) 2.27799e8 4.26688e8i 0.267594 0.501228i
\(357\) 2.64904e8i 0.308142i
\(358\) 1.62177e9 + 4.05807e8i 1.86809 + 0.467443i
\(359\) 2.95213e7i 0.0336748i −0.999858 0.0168374i \(-0.994640\pi\)
0.999858 0.0168374i \(-0.00535977\pi\)
\(360\) −8.19062e8 7.41251e8i −0.925248 0.837349i
\(361\) 1.38589e8 + 8.83063e8i 0.155043 + 0.987908i
\(362\) −2.42659e8 + 9.69765e8i −0.268854 + 1.07445i
\(363\) −3.13018e7 −0.0343476
\(364\) −1.29609e9 6.91954e8i −1.40858 0.752008i
\(365\) −2.09831e8 −0.225863
\(366\) 3.86265e7 + 9.66531e6i 0.0411814 + 0.0103046i
\(367\) 1.48210e9i 1.56512i −0.622577 0.782559i \(-0.713914\pi\)
0.622577 0.782559i \(-0.286086\pi\)
\(368\) −2.72702e8 + 1.82603e8i −0.285247 + 0.191003i
\(369\) 1.41620e9i 1.46734i
\(370\) 4.63584e8 1.85267e9i 0.475798 1.90148i
\(371\) −1.19823e9 −1.21824
\(372\) −5.33483e7 2.84814e7i −0.0537305 0.0286854i
\(373\) 1.26382e9i 1.26097i −0.776202 0.630484i \(-0.782856\pi\)
0.776202 0.630484i \(-0.217144\pi\)
\(374\) 3.59833e8 1.43804e9i 0.355673 1.42141i
\(375\) −7.93785e7 −0.0777308
\(376\) 3.68110e8 4.06751e8i 0.357125 0.394613i
\(377\) 7.76173e7 0.0746043
\(378\) 9.47677e7 3.78730e8i 0.0902483 0.360669i
\(379\) 2.55223e7 0.0240814 0.0120407 0.999928i \(-0.496167\pi\)
0.0120407 + 0.999928i \(0.496167\pi\)
\(380\) −5.02072e8 1.28358e9i −0.469379 1.20000i
\(381\) 5.89544e6 0.00546109
\(382\) −3.87195e8 + 1.54739e9i −0.355392 + 1.42029i
\(383\) 1.64139e9 1.49285 0.746424 0.665471i \(-0.231769\pi\)
0.746424 + 0.665471i \(0.231769\pi\)
\(384\) −2.85766e7 + 1.94968e8i −0.0257544 + 0.175713i
\(385\) −1.37811e9 −1.23076
\(386\) −1.38214e8 + 5.52358e8i −0.122319 + 0.488838i
\(387\) 1.97430e9i 1.73151i
\(388\) 4.12899e8 7.73398e8i 0.358866 0.672190i
\(389\) 2.02068e8 0.174050 0.0870250 0.996206i \(-0.472264\pi\)
0.0870250 + 0.996206i \(0.472264\pi\)
\(390\) 9.76945e7 3.90427e8i 0.0833957 0.333283i
\(391\) 6.62004e8i 0.560070i
\(392\) 1.15926e8 + 1.04913e8i 0.0972026 + 0.0879683i
\(393\) 3.30476e8i 0.274641i
\(394\) 4.84482e8 + 1.21229e8i 0.399062 + 0.0998553i
\(395\) 1.46425e9 1.19543
\(396\) −5.06206e8 + 9.48171e8i −0.409632 + 0.767279i
\(397\) 1.46254e9 1.17311 0.586557 0.809908i \(-0.300483\pi\)
0.586557 + 0.809908i \(0.300483\pi\)
\(398\) 3.15504e7 1.26088e8i 0.0250850 0.100250i
\(399\) 1.55767e8 1.82120e8i 0.122764 0.143533i
\(400\) 4.70262e8 + 7.02294e8i 0.367392 + 0.548668i
\(401\) 3.44403e7i 0.0266724i 0.999911 + 0.0133362i \(0.00424517\pi\)
−0.999911 + 0.0133362i \(0.995755\pi\)
\(402\) −3.60898e8 9.03056e7i −0.277072 0.0693303i
\(403\) 6.76569e8i 0.514926i
\(404\) −4.30830e8 2.30010e8i −0.325066 0.173545i
\(405\) −1.56134e9 −1.16790
\(406\) −6.91322e7 1.72986e7i −0.0512672 0.0128283i
\(407\) −1.85820e9 −1.36619
\(408\) −2.94708e8 2.66710e8i −0.214823 0.194415i
\(409\) 4.84225e8i 0.349958i −0.984572 0.174979i \(-0.944014\pi\)
0.984572 0.174979i \(-0.0559857\pi\)
\(410\) 6.61349e8 2.64302e9i 0.473901 1.89390i
\(411\) 2.84970e8 0.202467
\(412\) 1.44582e9 + 7.71891e8i 1.01853 + 0.543770i
\(413\) 1.53381e9i 1.07139i
\(414\) −1.16516e8 + 4.65647e8i −0.0807023 + 0.322519i
\(415\) 1.71498e9i 1.17785i
\(416\) 2.07473e9 7.45240e8i 1.41298 0.507539i
\(417\) 3.12647e8i 0.211144i
\(418\) −1.09297e9 + 7.77058e8i −0.731967 + 0.520399i
\(419\) 1.25832e8i 0.0835682i −0.999127 0.0417841i \(-0.986696\pi\)
0.999127 0.0417841i \(-0.0133042\pi\)
\(420\) −1.74029e8 + 3.25972e8i −0.114617 + 0.214688i
\(421\) 2.64151e7i 0.0172530i −0.999963 0.00862650i \(-0.997254\pi\)
0.999963 0.00862650i \(-0.00274594\pi\)
\(422\) −8.73450e8 2.18559e8i −0.565776 0.141571i
\(423\) 8.02351e8i 0.515434i
\(424\) 1.20640e9 1.33304e9i 0.768619 0.849303i
\(425\) −1.70487e9 −1.07729
\(426\) 2.58321e8 + 6.46384e7i 0.161892 + 0.0405095i
\(427\) 4.08995e8i 0.254226i
\(428\) 1.01674e9 + 5.42814e8i 0.626840 + 0.334655i
\(429\) −3.91591e8 −0.239460
\(430\) 9.21976e8 3.68459e9i 0.559216 2.23486i
\(431\) 1.99243e9 1.19870 0.599352 0.800486i \(-0.295425\pi\)
0.599352 + 0.800486i \(0.295425\pi\)
\(432\) 3.25926e8 + 4.86742e8i 0.194503 + 0.290473i
\(433\) 1.61300e9i 0.954834i −0.878677 0.477417i \(-0.841573\pi\)
0.878677 0.477417i \(-0.158427\pi\)
\(434\) 1.50787e8 6.02607e8i 0.0885422 0.353851i
\(435\) 1.95210e7i 0.0113708i
\(436\) −4.21115e8 + 7.88787e8i −0.243331 + 0.455782i
\(437\) −3.89268e8 + 4.55124e8i −0.223133 + 0.260883i
\(438\) 5.31057e7 + 1.32884e7i 0.0301982 + 0.00755634i
\(439\) 4.42728e7 0.0249753 0.0124877 0.999922i \(-0.496025\pi\)
0.0124877 + 0.999922i \(0.496025\pi\)
\(440\) 1.38751e9 1.53316e9i 0.776516 0.858030i
\(441\) 2.28673e8 0.126964
\(442\) −1.07942e9 + 4.31379e9i −0.594581 + 2.37619i
\(443\) 2.34668e8i 0.128245i −0.997942 0.0641226i \(-0.979575\pi\)
0.997942 0.0641226i \(-0.0204249\pi\)
\(444\) −2.34655e8 + 4.39530e8i −0.127230 + 0.238313i
\(445\) 1.36096e9i 0.732126i
\(446\) 1.97642e9 + 4.94550e8i 1.05489 + 0.263960i
\(447\) 4.88200e8 0.258536
\(448\) −2.01402e9 + 2.01375e8i −1.05825 + 0.105811i
\(449\) 2.40151e9i 1.25205i 0.779802 + 0.626026i \(0.215320\pi\)
−0.779802 + 0.626026i \(0.784680\pi\)
\(450\) 1.19919e9 + 3.00067e8i 0.620361 + 0.155230i
\(451\) −2.65090e9 −1.36074
\(452\) −1.40305e8 + 2.62805e8i −0.0714645 + 0.133859i
\(453\) −6.39703e8 −0.323321
\(454\) −3.59856e9 9.00448e8i −1.80482 0.451610i
\(455\) 4.13402e9 2.05746
\(456\) 4.57806e7 + 3.56654e8i 0.0226102 + 0.176145i
\(457\) 1.41435e9 0.693188 0.346594 0.938015i \(-0.387338\pi\)
0.346594 + 0.938015i \(0.387338\pi\)
\(458\) −2.17549e8 5.44361e7i −0.105810 0.0264763i
\(459\) −1.18160e9 −0.570331
\(460\) 4.34904e8 8.14615e8i 0.208325 0.390212i
\(461\) −2.77312e9 −1.31830 −0.659152 0.752010i \(-0.729085\pi\)
−0.659152 + 0.752010i \(0.729085\pi\)
\(462\) 3.48783e8 + 8.72741e7i 0.164554 + 0.0411755i
\(463\) 1.11850e8i 0.0523725i −0.999657 0.0261863i \(-0.991664\pi\)
0.999657 0.0261863i \(-0.00833630\pi\)
\(464\) 8.88483e7 5.94935e7i 0.0412892 0.0276475i
\(465\) 1.70160e8 0.0784822
\(466\) −1.75100e9 4.38144e8i −0.801560 0.200570i
\(467\) 1.47119e9i 0.668434i 0.942496 + 0.334217i \(0.108472\pi\)
−0.942496 + 0.334217i \(0.891528\pi\)
\(468\) 1.51850e9 2.84429e9i 0.684786 1.28267i
\(469\) 3.82135e9i 1.71046i
\(470\) −3.74689e8 + 1.49741e9i −0.166467 + 0.665270i
\(471\) 1.51087e8 0.0666276
\(472\) −1.70638e9 1.54427e9i −0.746927 0.675968i
\(473\) −3.69558e9 −1.60572
\(474\) −3.70584e8 9.27292e7i −0.159831 0.0399938i
\(475\) 1.17209e9 + 1.00249e9i 0.501804 + 0.429192i
\(476\) 1.92283e9 3.60164e9i 0.817178 1.53065i
\(477\) 2.62953e9i 1.10934i
\(478\) −7.27042e8 + 2.90556e9i −0.304482 + 1.21684i
\(479\) 3.39386e7i 0.0141097i 0.999975 + 0.00705487i \(0.00224565\pi\)
−0.999975 + 0.00705487i \(0.997754\pi\)
\(480\) −1.87431e8 5.21803e8i −0.0773565 0.215359i
\(481\) 5.57416e9 2.28387
\(482\) 2.27961e8 9.11025e8i 0.0927248 0.370566i
\(483\) 1.60563e8 0.0648381
\(484\) 4.25579e8 + 2.27207e8i 0.170617 + 0.0910884i
\(485\) 2.46683e9i 0.981844i
\(486\) 1.25335e9 + 3.13619e8i 0.495274 + 0.123930i
\(487\) 8.44255e8 0.331224 0.165612 0.986191i \(-0.447040\pi\)
0.165612 + 0.986191i \(0.447040\pi\)
\(488\) −4.55009e8 4.11783e8i −0.177236 0.160398i
\(489\) 3.22600e8i 0.124762i
\(490\) −4.26767e8 1.06788e8i −0.163872 0.0410048i
\(491\) 5.23656e8i 0.199646i −0.995005 0.0998231i \(-0.968172\pi\)
0.995005 0.0998231i \(-0.0318277\pi\)
\(492\) −3.34759e8 + 6.27033e8i −0.126723 + 0.237363i
\(493\) 2.15686e8i 0.0810695i
\(494\) 3.27866e9 2.33099e9i 1.22364 0.869955i
\(495\) 3.02428e9i 1.12074i
\(496\) 5.18589e8 + 7.74467e8i 0.190826 + 0.284982i
\(497\) 2.73522e9i 0.999414i
\(498\) −1.08607e8 + 4.34039e8i −0.0394055 + 0.157480i
\(499\) 3.55186e9i 1.27969i 0.768505 + 0.639844i \(0.221001\pi\)
−0.768505 + 0.639844i \(0.778999\pi\)
\(500\) 1.07923e9 + 5.76175e8i 0.386117 + 0.206139i
\(501\) −1.88126e8 −0.0668368
\(502\) −9.93400e8 + 3.97003e9i −0.350478 + 1.40065i
\(503\) 3.25375e9i 1.13998i −0.821653 0.569988i \(-0.806948\pi\)
0.821653 0.569988i \(-0.193052\pi\)
\(504\) −1.98641e9 + 2.19493e9i −0.691133 + 0.763683i
\(505\) 1.37417e9 0.474812
\(506\) −8.71619e8 2.18101e8i −0.299089 0.0748394i
\(507\) 6.53553e8 0.222717
\(508\) −8.01544e7 4.27926e7i −0.0271272 0.0144826i
\(509\) 5.07091e9i 1.70441i −0.523209 0.852204i \(-0.675265\pi\)
0.523209 0.852204i \(-0.324735\pi\)
\(510\) 1.08493e9 + 2.71477e8i 0.362166 + 0.0906229i
\(511\) 5.62307e8i 0.186423i
\(512\) 1.80372e9 2.44335e9i 0.593914 0.804529i
\(513\) 8.12346e8 + 6.94799e8i 0.265662 + 0.227221i
\(514\) 5.96753e8 2.38487e9i 0.193831 0.774629i
\(515\) −4.61159e9 −1.48773
\(516\) −4.66681e8 + 8.74137e8i −0.149536 + 0.280095i
\(517\) 1.50188e9 0.477988
\(518\) −4.96480e9 1.24231e9i −1.56945 0.392715i
\(519\) 1.00773e9i 0.316417i
\(520\) −4.16220e9 + 4.59912e9i −1.29811 + 1.43438i
\(521\) 1.53300e9i 0.474910i −0.971399 0.237455i \(-0.923687\pi\)
0.971399 0.237455i \(-0.0763132\pi\)
\(522\) 3.79620e7 1.51711e8i 0.0116816 0.0466844i
\(523\) −2.40775e9 −0.735961 −0.367980 0.929834i \(-0.619951\pi\)
−0.367980 + 0.929834i \(0.619951\pi\)
\(524\) −2.39879e9 + 4.49315e9i −0.728337 + 1.36424i
\(525\) 4.13501e8i 0.124715i
\(526\) −4.63289e8 + 1.85149e9i −0.138804 + 0.554718i
\(527\) −1.88008e9 −0.559549
\(528\) −4.48254e8 + 3.00154e8i −0.132527 + 0.0887412i
\(529\) 3.00357e9 0.882152
\(530\) −1.22796e9 + 4.90744e9i −0.358278 + 1.43182i
\(531\) −3.36597e9 −0.975618
\(532\) −3.43975e9 + 1.34546e9i −0.990458 + 0.387417i
\(533\) 7.95210e9 2.27477
\(534\) 8.61881e7 3.44443e8i 0.0244936 0.0978865i
\(535\) −3.24299e9 −0.915603
\(536\) 4.25127e9 + 3.84740e9i 1.19246 + 1.07917i
\(537\) 1.22720e9 0.341983
\(538\) −4.35449e8 + 1.74023e9i −0.120559 + 0.481802i
\(539\) 4.28040e8i 0.117740i
\(540\) −1.45400e9 7.76255e8i −0.397361 0.212142i
\(541\) 6.65433e9 1.80682 0.903408 0.428782i \(-0.141057\pi\)
0.903408 + 0.428782i \(0.141057\pi\)
\(542\) −2.73299e8 + 1.09221e9i −0.0737294 + 0.294653i
\(543\) 7.33824e8i 0.196695i
\(544\) 2.07090e9 + 5.76535e9i 0.551523 + 1.53543i
\(545\) 2.51591e9i 0.665745i
\(546\) −1.04627e9 2.61802e8i −0.275086 0.0688334i
\(547\) −5.23461e9 −1.36750 −0.683752 0.729714i \(-0.739653\pi\)
−0.683752 + 0.729714i \(0.739653\pi\)
\(548\) −3.87445e9 2.06848e9i −1.00572 0.536932i
\(549\) −8.97544e8 −0.231501
\(550\) −5.61679e8 + 2.24470e9i −0.143952 + 0.575293i
\(551\) 1.26826e8 1.48283e8i 0.0322982 0.0377625i
\(552\) −1.61657e8 + 1.78627e8i −0.0409081 + 0.0452023i
\(553\) 3.92391e9i 0.986690i
\(554\) 2.38766e9 + 5.97452e8i 0.596608 + 0.149286i
\(555\) 1.40192e9i 0.348096i
\(556\) 2.26938e9 4.25075e9i 0.559944 1.04883i
\(557\) −3.43562e9 −0.842387 −0.421193 0.906971i \(-0.638389\pi\)
−0.421193 + 0.906971i \(0.638389\pi\)
\(558\) 1.32243e9 + 3.30904e8i 0.322220 + 0.0806274i
\(559\) 1.10859e10 2.68429
\(560\) 4.73220e9 3.16871e9i 1.13869 0.762474i
\(561\) 1.08817e9i 0.260212i
\(562\) −1.48139e9 + 5.92026e9i −0.352041 + 1.40690i
\(563\) −1.27168e9 −0.300329 −0.150164 0.988661i \(-0.547980\pi\)
−0.150164 + 0.988661i \(0.547980\pi\)
\(564\) 1.89658e8 3.55247e8i 0.0445138 0.0833785i
\(565\) 8.38242e8i 0.195524i
\(566\) 1.84049e7 7.35536e7i 0.00426655 0.0170509i
\(567\) 4.18409e9i 0.963963i
\(568\) −3.04295e9 2.75387e9i −0.696748 0.630557i
\(569\) 1.21543e9i 0.276590i −0.990391 0.138295i \(-0.955838\pi\)
0.990391 0.138295i \(-0.0441621\pi\)
\(570\) −5.86254e8 8.24595e8i −0.132594 0.186500i
\(571\) 4.02806e9i 0.905460i −0.891648 0.452730i \(-0.850450\pi\)
0.891648 0.452730i \(-0.149550\pi\)
\(572\) 5.32407e9 + 2.84240e9i 1.18948 + 0.635037i
\(573\) 1.17092e9i 0.260007i
\(574\) −7.08278e9 1.77229e9i −1.56319 0.391149i
\(575\) 1.03335e9i 0.226679i
\(576\) −4.41919e8 4.41978e9i −0.0963528 0.963657i
\(577\) −7.38889e9 −1.60127 −0.800634 0.599154i \(-0.795504\pi\)
−0.800634 + 0.599154i \(0.795504\pi\)
\(578\) −7.48372e9 1.87261e9i −1.61202 0.403367i
\(579\) 4.17971e8i 0.0894893i
\(580\) −1.41695e8 + 2.65408e8i −0.0301548 + 0.0564827i
\(581\) −4.59580e9 −0.972176
\(582\) 1.56221e8 6.24323e8i 0.0328480 0.131274i
\(583\) 4.92208e9 1.02875
\(584\) −6.25570e8 5.66140e8i −0.129966 0.117619i
\(585\) 9.07215e9i 1.87355i
\(586\) −1.20302e9 + 4.80775e9i −0.246962 + 0.986962i
\(587\) 2.35339e8i 0.0480242i 0.999712 + 0.0240121i \(0.00764402\pi\)
−0.999712 + 0.0240121i \(0.992356\pi\)
\(588\) 1.01247e8 + 5.40533e7i 0.0205381 + 0.0109648i
\(589\) 1.29254e9 + 1.10551e9i 0.260640 + 0.222925i
\(590\) 6.28184e9 + 1.57187e9i 1.25923 + 0.315090i
\(591\) 3.66609e8 0.0730545
\(592\) 6.38073e9 4.27258e9i 1.26399 0.846378i
\(593\) 3.76769e9 0.741965 0.370983 0.928640i \(-0.379021\pi\)
0.370983 + 0.928640i \(0.379021\pi\)
\(594\) −3.89285e8 + 1.55574e9i −0.0762106 + 0.304569i
\(595\) 1.14878e10i 2.23577i
\(596\) −6.63757e9 3.54364e9i −1.28424 0.685627i
\(597\) 9.54113e7i 0.0183523i
\(598\) 2.61466e9 + 6.54252e8i 0.499989 + 0.125110i
\(599\) −1.38664e9 −0.263616 −0.131808 0.991275i \(-0.542078\pi\)
−0.131808 + 0.991275i \(0.542078\pi\)
\(600\) 4.60022e8 + 4.16320e8i 0.0869460 + 0.0786861i
\(601\) 3.07925e9i 0.578608i −0.957237 0.289304i \(-0.906576\pi\)
0.957237 0.289304i \(-0.0934239\pi\)
\(602\) −9.87399e9 2.47072e9i −1.84461 0.461567i
\(603\) 8.38600e9 1.55756
\(604\) 8.69739e9 + 4.64334e9i 1.60605 + 0.857434i
\(605\) −1.35743e9 −0.249214
\(606\) −3.47786e8 8.70248e7i −0.0634832 0.0158851i
\(607\) −4.43504e9 −0.804892 −0.402446 0.915444i \(-0.631840\pi\)
−0.402446 + 0.915444i \(0.631840\pi\)
\(608\) 1.96637e9 5.18137e9i 0.354816 0.934936i
\(609\) −5.23126e7 −0.00938525
\(610\) 1.67507e9 + 4.19143e8i 0.298798 + 0.0747666i
\(611\) −4.50528e9 −0.799057
\(612\) 7.90384e9 + 4.21967e9i 1.39382 + 0.744130i
\(613\) 2.20653e9 0.386899 0.193450 0.981110i \(-0.438032\pi\)
0.193450 + 0.981110i \(0.438032\pi\)
\(614\) −3.80023e9 9.50911e8i −0.662552 0.165787i
\(615\) 1.99998e9i 0.346708i
\(616\) −4.10856e9 3.71825e9i −0.708203 0.640923i
\(617\) −2.90373e8 −0.0497689 −0.0248844 0.999690i \(-0.507922\pi\)
−0.0248844 + 0.999690i \(0.507922\pi\)
\(618\) 1.16714e9 + 2.92046e8i 0.198912 + 0.0497728i
\(619\) 4.84893e9i 0.821729i −0.911696 0.410865i \(-0.865227\pi\)
0.911696 0.410865i \(-0.134773\pi\)
\(620\) −2.31349e9 1.23512e9i −0.389849 0.208131i
\(621\) 7.16189e8i 0.120007i
\(622\) −5.06113e7 + 2.02263e8i −0.00843298 + 0.0337016i
\(623\) 3.64712e9 0.604284
\(624\) 1.34466e9 9.00393e8i 0.221547 0.148349i
\(625\) −7.47253e9 −1.22430
\(626\) 2.87894e9 + 7.20383e8i 0.469054 + 0.117369i
\(627\) −6.39859e8 + 7.48111e8i −0.103669 + 0.121208i
\(628\) −2.05418e9 1.09668e9i −0.330963 0.176694i
\(629\) 1.54897e10i 2.48179i
\(630\) 2.02191e9 8.08039e9i 0.322159 1.28748i
\(631\) 8.68083e9i 1.37549i −0.725951 0.687747i \(-0.758600\pi\)
0.725951 0.687747i \(-0.241400\pi\)
\(632\) 4.36537e9 + 3.95066e9i 0.687878 + 0.622529i
\(633\) −6.60943e8 −0.103574
\(634\) 2.92374e8 1.16845e9i 0.0455645 0.182094i
\(635\) 2.55660e8 0.0396237
\(636\) 6.21564e8 1.16425e9i 0.0958046 0.179451i
\(637\) 1.28402e9i 0.196827i
\(638\) 2.83980e8 + 7.10589e7i 0.0432928 + 0.0108329i
\(639\) −6.00248e9 −0.910076
\(640\) −1.23925e9 + 8.45492e9i −0.186865 + 1.27491i
\(641\) 4.15561e9i 0.623205i −0.950212 0.311603i \(-0.899134\pi\)
0.950212 0.311603i \(-0.100866\pi\)
\(642\) 8.20761e8 + 2.05375e8i 0.122418 + 0.0306319i
\(643\) 3.22611e9i 0.478565i 0.970950 + 0.239282i \(0.0769121\pi\)
−0.970950 + 0.239282i \(0.923088\pi\)
\(644\) −2.18301e9 1.16546e9i −0.322074 0.171948i
\(645\) 2.78814e9i 0.409125i
\(646\) 6.47746e9 + 9.11087e9i 0.945346 + 1.32968i
\(647\) 1.44465e9i 0.209700i −0.994488 0.104850i \(-0.966564\pi\)
0.994488 0.104850i \(-0.0334362\pi\)
\(648\) −4.65483e9 4.21262e9i −0.672034 0.608190i
\(649\) 6.30057e9i 0.904740i
\(650\) 1.68491e9 6.73358e9i 0.240646 0.961722i
\(651\) 4.55995e8i 0.0647778i
\(652\) −2.34162e9 + 4.38606e9i −0.330864 + 0.619738i
\(653\) −3.36633e9 −0.473108 −0.236554 0.971618i \(-0.576018\pi\)
−0.236554 + 0.971618i \(0.576018\pi\)
\(654\) −1.59330e8 + 6.36747e8i −0.0222728 + 0.0890112i
\(655\) 1.43313e10i 1.99270i
\(656\) 9.10275e9 6.09527e9i 1.25895 0.843004i
\(657\) −1.23399e9 −0.169759
\(658\) 4.01277e9 + 1.00409e9i 0.549102 + 0.137399i
\(659\) 8.36290e9 1.13830 0.569152 0.822232i \(-0.307272\pi\)
0.569152 + 0.822232i \(0.307272\pi\)
\(660\) 7.14874e8 1.33902e9i 0.0967890 0.181295i
\(661\) 4.13787e9i 0.557277i −0.960396 0.278639i \(-0.910117\pi\)
0.960396 0.278639i \(-0.0898832\pi\)
\(662\) 6.91620e9 + 1.73060e9i 0.926540 + 0.231843i
\(663\) 3.26426e9i 0.434998i
\(664\) 4.62713e9 5.11286e9i 0.613372 0.677759i
\(665\) 6.75497e9 7.89778e9i 0.890733 1.04143i
\(666\) 2.72627e9 1.08953e10i 0.357610 1.42916i
\(667\) 1.30731e8 0.0170584
\(668\) 2.55775e9 + 1.36553e9i 0.332002 + 0.177248i
\(669\) 1.49557e9 0.193114
\(670\) −1.56506e10 3.91617e9i −2.01034 0.503036i
\(671\) 1.68006e9i 0.214682i
\(672\) −1.39833e9 + 5.02278e8i −0.177753 + 0.0638487i
\(673\) 1.32538e10i 1.67605i −0.545629 0.838027i \(-0.683709\pi\)
0.545629 0.838027i \(-0.316291\pi\)
\(674\) −8.22857e8 + 3.28847e9i −0.103518 + 0.413699i
\(675\) 1.84442e9 0.230832
\(676\) −8.88570e9 4.74387e9i −1.10631 0.590635i
\(677\) 8.35900e9i 1.03537i 0.855573 + 0.517683i \(0.173205\pi\)
−0.855573 + 0.517683i \(0.826795\pi\)
\(678\) −5.30848e7 + 2.12149e8i −0.00654134 + 0.0261419i
\(679\) 6.61062e9 0.810397
\(680\) −1.27802e10 1.15661e10i −1.55868 1.41060i
\(681\) −2.72304e9 −0.330400
\(682\) −6.19401e8 + 2.47538e9i −0.0747699 + 0.298811i
\(683\) −1.24346e9 −0.149334 −0.0746671 0.997209i \(-0.523789\pi\)
−0.0746671 + 0.997209i \(0.523789\pi\)
\(684\) −2.95262e9 7.54857e9i −0.352786 0.901920i
\(685\) 1.23579e10 1.46903
\(686\) 1.89670e9 7.57997e9i 0.224318 0.896465i
\(687\) −1.64620e8 −0.0193702
\(688\) 1.26900e10 8.49731e9i 1.48560 0.994768i
\(689\) −1.47651e10 −1.71976
\(690\) 1.64547e8 6.57596e8i 0.0190685 0.0762057i
\(691\) 4.21392e9i 0.485863i 0.970043 + 0.242931i \(0.0781090\pi\)
−0.970043 + 0.242931i \(0.921891\pi\)
\(692\) −7.31471e9 + 1.37011e10i −0.839124 + 1.57176i
\(693\) −8.10449e9 −0.925037
\(694\) 2.26612e9 9.05632e9i 0.257350 1.02847i
\(695\) 1.35582e10i 1.53198i
\(696\) 5.26692e7 5.81981e7i 0.00592140 0.00654299i
\(697\) 2.20976e10i 2.47190i
\(698\) 6.33855e9 + 1.58606e9i 0.705499 + 0.176533i
\(699\) −1.32499e9 −0.146738
\(700\) −3.00143e9 + 5.62195e9i −0.330739 + 0.619504i
\(701\) 6.46782e9 0.709161 0.354580 0.935026i \(-0.384624\pi\)
0.354580 + 0.935026i \(0.384624\pi\)
\(702\) 1.16777e9 4.66687e9i 0.127402 0.509150i
\(703\) 9.10816e9 1.06491e10i 0.988751 1.15603i
\(704\) 8.27315e9 8.27204e8i 0.893648 0.0893528i
\(705\) 1.13310e9i 0.121788i
\(706\) 1.70900e9 + 4.27634e8i 0.182778 + 0.0457357i
\(707\) 3.68252e9i 0.391902i
\(708\) −1.49031e9 7.95642e8i −0.157819 0.0842561i
\(709\) −1.57425e10 −1.65887 −0.829433 0.558606i \(-0.811336\pi\)
−0.829433 + 0.558606i \(0.811336\pi\)
\(710\) 1.12023e10 + 2.80309e9i 1.17463 + 0.293923i
\(711\) 8.61106e9 0.898490
\(712\) −3.67198e9 + 4.05744e9i −0.381259 + 0.421281i
\(713\) 1.13955e9i 0.117738i
\(714\) 7.27506e8 2.90741e9i 0.0747985 0.298925i
\(715\) −1.69816e10 −1.73744
\(716\) −1.66850e10 8.90773e9i −1.69875 0.906925i
\(717\) 2.19865e9i 0.222760i
\(718\) −8.10744e7 + 3.24006e8i −0.00817426 + 0.0326677i
\(719\) 6.96744e9i 0.699072i −0.936923 0.349536i \(-0.886339\pi\)
0.936923 0.349536i \(-0.113661\pi\)
\(720\) 6.95378e9 + 1.03849e10i 0.694316 + 1.03690i
\(721\) 1.23582e10i 1.22795i
\(722\) 9.04100e8 1.00725e10i 0.0893997 0.995996i
\(723\) 6.89376e8i 0.0678378i
\(724\) 5.32653e9 9.97707e9i 0.521626 0.977053i
\(725\) 3.36674e8i 0.0328115i
\(726\) 3.43548e8 + 8.59642e7i 0.0333203 + 0.00833757i
\(727\) 3.61410e9i 0.348843i 0.984671 + 0.174422i \(0.0558056\pi\)
−0.984671 + 0.174422i \(0.944194\pi\)
\(728\) 1.23247e10 + 1.11539e10i 1.18391 + 1.07144i
\(729\) −8.53264e9 −0.815712
\(730\) 2.30297e9 + 5.76259e8i 0.219108 + 0.0548261i
\(731\) 3.08059e10i 2.91691i
\(732\) −3.97395e8 2.12160e8i −0.0374484 0.0199928i
\(733\) −1.90486e10 −1.78649 −0.893243 0.449575i \(-0.851575\pi\)
−0.893243 + 0.449575i \(0.851575\pi\)
\(734\) −4.07030e9 + 1.62666e10i −0.379918 + 1.51831i
\(735\) −3.22936e8 −0.0299993
\(736\) 3.49447e9 1.25521e9i 0.323080 0.116050i
\(737\) 1.56973e10i 1.44440i
\(738\) 3.88931e9 1.55432e10i 0.356184 1.42346i
\(739\) 1.51227e10i 1.37839i 0.724575 + 0.689196i \(0.242036\pi\)
−0.724575 + 0.689196i \(0.757964\pi\)
\(740\) −1.01760e10 + 1.90605e10i −0.923134 + 1.72911i
\(741\) 1.91943e9 2.24416e9i 0.173304 0.202624i
\(742\) 1.31510e10 + 3.29070e9i 1.18180 + 0.295716i
\(743\) −9.37736e8 −0.0838725 −0.0419363 0.999120i \(-0.513353\pi\)
−0.0419363 + 0.999120i \(0.513353\pi\)
\(744\) 5.07297e8 + 4.59104e8i 0.0451603 + 0.0408701i
\(745\) 2.11712e10 1.87585
\(746\) −3.47083e9 + 1.38708e10i −0.306088 + 1.22325i
\(747\) 1.00855e10i 0.885273i
\(748\) −7.89857e9 + 1.47948e10i −0.690070 + 1.29256i
\(749\) 8.69058e9i 0.755723i
\(750\) 8.71205e8 + 2.17997e8i 0.0754060 + 0.0188684i
\(751\) 7.92462e9 0.682714 0.341357 0.939934i \(-0.389113\pi\)
0.341357 + 0.939934i \(0.389113\pi\)
\(752\) −5.15718e9 + 3.45329e9i −0.442232 + 0.296122i
\(753\) 3.00414e9i 0.256411i
\(754\) −8.51875e8 2.13160e8i −0.0723729 0.0181095i
\(755\) −2.77412e10 −2.34590
\(756\) −2.08021e9 + 3.89643e9i −0.175098 + 0.327975i
\(757\) 1.25260e10 1.04949 0.524744 0.851260i \(-0.324161\pi\)
0.524744 + 0.851260i \(0.324161\pi\)
\(758\) −2.80115e8 7.00918e7i −0.0233612 0.00584555i
\(759\) −6.59558e8 −0.0547528
\(760\) 1.98531e9 + 1.54666e10i 0.164052 + 1.27805i
\(761\) 4.74611e8 0.0390383 0.0195192 0.999809i \(-0.493786\pi\)
0.0195192 + 0.999809i \(0.493786\pi\)
\(762\) −6.47044e7 1.61906e7i −0.00529775 0.00132563i
\(763\) −6.74216e9 −0.549494
\(764\) 8.49919e9 1.59198e10i 0.689526 1.29154i
\(765\) −2.52100e10 −2.03591
\(766\) −1.80148e10 4.50774e9i −1.44820 0.362375i
\(767\) 1.89003e10i 1.51246i
\(768\) 8.49077e8 2.06135e9i 0.0676368 0.164206i
\(769\) 1.98171e9 0.157144 0.0785719 0.996908i \(-0.474964\pi\)
0.0785719 + 0.996908i \(0.474964\pi\)
\(770\) 1.51252e10 + 3.78470e9i 1.19394 + 0.298755i
\(771\) 1.80464e9i 0.141808i
\(772\) 3.03388e9 5.68273e9i 0.237322 0.444525i
\(773\) 5.26122e9i 0.409693i −0.978794 0.204846i \(-0.934330\pi\)
0.978794 0.204846i \(-0.0656695\pi\)
\(774\) 5.42201e9 2.16686e10i 0.420308 1.67972i
\(775\) 2.93469e9 0.226468
\(776\) −6.65568e9 + 7.35435e9i −0.511301 + 0.564974i
\(777\) −3.75688e9 −0.287312
\(778\) −2.21776e9 5.54939e8i −0.168844 0.0422490i
\(779\) 1.29937e10 1.51920e10i 0.984809 1.15142i
\(780\) −2.14446e9 + 4.01677e9i −0.161803 + 0.303072i
\(781\) 1.12357e10i 0.843960i
\(782\) −1.81806e9 + 7.26571e9i −0.135952 + 0.543319i
\(783\) 2.33340e8i 0.0173709i
\(784\) −9.84200e8 1.46982e9i −0.0729419 0.108932i
\(785\) 6.55200e9 0.483426
\(786\) −9.07586e8 + 3.62708e9i −0.0666667 + 0.266427i
\(787\) 9.21236e9 0.673689 0.336844 0.941560i \(-0.390640\pi\)
0.336844 + 0.941560i \(0.390640\pi\)
\(788\) −4.98442e9 2.66106e9i −0.362888 0.193737i
\(789\) 1.40103e9i 0.101550i
\(790\) −1.60706e10 4.02127e9i −1.15968 0.290181i
\(791\) −2.24633e9 −0.161382
\(792\) 8.15974e9 9.01629e9i 0.583631 0.644896i
\(793\) 5.03980e9i 0.358887i
\(794\) −1.60518e10 4.01656e9i −1.13803 0.284762i
\(795\) 3.71348e9i 0.262117i
\(796\) −6.92551e8 + 1.29721e9i −0.0486694 + 0.0911622i
\(797\) 1.08189e10i 0.756974i −0.925607 0.378487i \(-0.876445\pi\)
0.925607 0.378487i \(-0.123555\pi\)
\(798\) −2.20976e9 + 1.57105e9i −0.153934 + 0.109441i
\(799\) 1.25195e10i 0.868304i
\(800\) −3.23256e9 8.99939e9i −0.223220 0.621439i
\(801\) 8.00364e9i 0.550267i
\(802\) 9.45835e7 3.77994e8i 0.00647448 0.0258747i
\(803\) 2.30984e9i 0.157426i
\(804\) 3.71297e9 + 1.98227e9i 0.251956 + 0.134514i
\(805\) 6.96292e9 0.470442
\(806\) 1.85806e9 7.42557e9i 0.124993 0.499525i
\(807\) 1.31684e9i 0.0882014i
\(808\) 4.09683e9 + 3.70763e9i 0.273217 + 0.247261i
\(809\) 1.44475e9 0.0959338 0.0479669 0.998849i \(-0.484726\pi\)
0.0479669 + 0.998849i \(0.484726\pi\)
\(810\) 1.71362e10 + 4.28791e9i 1.13297 + 0.283497i
\(811\) −2.67454e10 −1.76066 −0.880332 0.474357i \(-0.842680\pi\)
−0.880332 + 0.474357i \(0.842680\pi\)
\(812\) 7.11242e8 + 3.79715e8i 0.0466199 + 0.0248893i
\(813\) 8.26483e8i 0.0539407i
\(814\) 2.03943e10 + 5.10316e9i 1.32533 + 0.331630i
\(815\) 1.39898e10i 0.905230i
\(816\) 2.50205e9 + 3.73659e9i 0.161206 + 0.240746i
\(817\) 1.81143e10 2.11789e10i 1.16210 1.35871i
\(818\) −1.32983e9 + 5.31453e9i −0.0849490 + 0.339491i
\(819\) 2.43116e10 1.54639
\(820\) −1.45170e10 + 2.71918e10i −0.919454 + 1.72222i
\(821\) 7.52716e9 0.474712 0.237356 0.971423i \(-0.423719\pi\)
0.237356 + 0.971423i \(0.423719\pi\)
\(822\) −3.12764e9 7.82614e8i −0.196411 0.0491469i
\(823\) 8.01305e8i 0.0501070i −0.999686 0.0250535i \(-0.992024\pi\)
0.999686 0.0250535i \(-0.00797561\pi\)
\(824\) −1.37485e10 1.24424e10i −0.856073 0.774746i
\(825\) 1.69857e9i 0.105316i
\(826\) 4.21231e9 1.68341e10i 0.260070 1.03935i
\(827\) −2.45940e10 −1.51203 −0.756014 0.654556i \(-0.772856\pi\)
−0.756014 + 0.654556i \(0.772856\pi\)
\(828\) 2.55761e9 4.79064e9i 0.156577 0.293284i
\(829\) 2.17049e10i 1.32317i −0.749869 0.661586i \(-0.769884\pi\)
0.749869 0.661586i \(-0.230116\pi\)
\(830\) −4.70984e9 + 1.88224e10i −0.285912 + 1.14262i
\(831\) 1.80675e9 0.109218
\(832\) −2.48175e10 + 2.48142e9i −1.49392 + 0.149372i
\(833\) 3.56809e9 0.213884
\(834\) 8.58623e8 3.43141e9i 0.0512532 0.204829i
\(835\) −8.15820e9 −0.484944
\(836\) 1.41297e10 5.52684e9i 0.836397 0.327156i
\(837\) 2.03396e9 0.119896
\(838\) −3.45571e8 + 1.38104e9i −0.0202854 + 0.0810688i
\(839\) −1.03002e10 −0.602114 −0.301057 0.953606i \(-0.597339\pi\)
−0.301057 + 0.953606i \(0.597339\pi\)
\(840\) 2.80524e9 3.09972e9i 0.163303 0.180445i
\(841\) 1.72073e10 0.997531
\(842\) −7.25437e7 + 2.89914e8i −0.00418801 + 0.0167370i
\(843\) 4.47988e9i 0.257555i
\(844\) 8.98617e9 + 4.79751e9i 0.514489 + 0.274674i
\(845\) 2.83418e10 1.61595
\(846\) −2.20349e9 + 8.80606e9i −0.125117 + 0.500018i
\(847\) 3.63764e9i 0.205697i
\(848\) −1.69016e10 + 1.13174e10i −0.951791 + 0.637326i
\(849\) 5.56582e7i 0.00312142i
\(850\) 1.87115e10 + 4.68209e9i 1.04507 + 0.261501i
\(851\) 9.38856e9 0.522210
\(852\) −2.65765e9 1.41886e9i −0.147217 0.0785958i
\(853\) 7.96085e9 0.439175 0.219588 0.975593i \(-0.429529\pi\)
0.219588 + 0.975593i \(0.429529\pi\)
\(854\) 1.12322e9 4.48885e9i 0.0617111 0.246623i
\(855\) 1.73318e10 + 1.48239e10i 0.948334 + 0.811110i
\(856\) −9.66833e9 8.74983e9i −0.526857 0.476806i
\(857\) 2.11539e10i 1.14804i −0.818840 0.574021i \(-0.805383\pi\)
0.818840 0.574021i \(-0.194617\pi\)
\(858\) 4.29784e9 + 1.07543e9i 0.232298 + 0.0581267i
\(859\) 1.99252e10i 1.07257i 0.844036 + 0.536286i \(0.180173\pi\)
−0.844036 + 0.536286i \(0.819827\pi\)
\(860\) −2.02380e10 + 3.79076e10i −1.08498 + 2.03227i
\(861\) −5.35957e9 −0.286166
\(862\) −2.18675e10 5.47180e9i −1.16285 0.290974i
\(863\) 8.56324e8 0.0453524 0.0226762 0.999743i \(-0.492781\pi\)
0.0226762 + 0.999743i \(0.492781\pi\)
\(864\) −2.24041e9 6.23724e9i −0.118176 0.328999i
\(865\) 4.37011e10i 2.29581i
\(866\) −4.42979e9 + 1.77033e10i −0.231777 + 0.926276i
\(867\) −5.66296e9 −0.295105
\(868\) −3.30988e9 + 6.19970e9i −0.171788 + 0.321775i
\(869\) 1.61186e10i 0.833215i
\(870\) −5.36106e7 + 2.14250e8i −0.00276015 + 0.0110307i
\(871\) 4.70882e10i 2.41462i
\(872\) 6.78812e9 7.50069e9i 0.346691 0.383084i
\(873\) 1.45071e10i 0.737955i
\(874\) 5.52225e9 3.92609e9i 0.279786 0.198916i
\(875\) 9.22471e9i 0.465505i
\(876\) −5.46358e8 2.91688e8i −0.0274608 0.0146607i
\(877\) 9.40744e9i 0.470948i 0.971881 + 0.235474i \(0.0756642\pi\)
−0.971881 + 0.235474i \(0.924336\pi\)
\(878\) −4.85908e8 1.21586e8i −0.0242283 0.00606253i
\(879\) 3.63804e9i 0.180679i
\(880\) −1.94388e10 + 1.30164e10i −0.961571 + 0.643875i
\(881\) −3.05311e10 −1.50427 −0.752137 0.659007i \(-0.770977\pi\)
−0.752137 + 0.659007i \(0.770977\pi\)
\(882\) −2.50976e9 6.28004e8i −0.123166 0.0308193i
\(883\) 3.85968e10i 1.88664i −0.331884 0.943320i \(-0.607684\pi\)
0.331884 0.943320i \(-0.392316\pi\)
\(884\) 2.36939e10 4.43808e10i 1.15360 2.16079i
\(885\) 4.75349e9 0.230521
\(886\) −6.44469e8 + 2.57556e9i −0.0311304 + 0.124410i
\(887\) 1.44349e9 0.0694514 0.0347257 0.999397i \(-0.488944\pi\)
0.0347257 + 0.999397i \(0.488944\pi\)
\(888\) 3.78249e9 4.17955e9i 0.181273 0.200302i
\(889\) 6.85119e8i 0.0327047i
\(890\) 3.73761e9 1.49370e10i 0.177717 0.710229i
\(891\) 1.71873e10i 0.814023i
\(892\) −2.03337e10 1.08557e10i −0.959268 0.512131i
\(893\) −7.36161e9 + 8.60706e9i −0.345934 + 0.404459i
\(894\) −5.35816e9 1.34074e9i −0.250804 0.0627573i
\(895\) 5.32184e10 2.48131
\(896\) 2.26575e10 + 3.32094e9i 1.05229 + 0.154235i
\(897\) 1.97852e9 0.0915307
\(898\) 6.59527e9 2.63574e10i 0.303924 1.21460i
\(899\) 3.71272e8i 0.0170425i
\(900\) −1.23374e10 6.58667e9i −0.564126 0.301174i
\(901\) 4.10298e10i 1.86880i
\(902\) 2.90945e10 + 7.28017e9i 1.32004 + 0.330308i
\(903\) −7.47168e9 −0.337685
\(904\) 2.26164e9 2.49905e9i 0.101820 0.112509i
\(905\) 3.18228e10i 1.42715i
\(906\) 7.02095e9 + 1.75681e9i 0.313651 + 0.0784833i
\(907\) −7.77220e9 −0.345875 −0.172937 0.984933i \(-0.555326\pi\)
−0.172937 + 0.984933i \(0.555326\pi\)
\(908\) 3.70225e10 + 1.97654e10i 1.64121 + 0.876205i
\(909\) 8.08133e9 0.356869
\(910\) −4.53722e10 1.13532e10i −1.99593 0.499430i
\(911\) 2.17755e10 0.954232 0.477116 0.878840i \(-0.341682\pi\)
0.477116 + 0.878840i \(0.341682\pi\)
\(912\) 4.77022e8 4.04012e9i 0.0208236 0.176365i
\(913\) 1.88786e10 0.820959
\(914\) −1.55230e10 3.88424e9i −0.672456 0.168265i
\(915\) 1.26753e9 0.0546996
\(916\) 2.23817e9 + 1.19491e9i 0.0962187 + 0.0513689i
\(917\) −3.84052e10 −1.64474
\(918\) 1.29685e10 + 3.24503e9i 0.553273 + 0.138443i
\(919\) 1.80795e10i 0.768390i −0.923252 0.384195i \(-0.874479\pi\)
0.923252 0.384195i \(-0.125521\pi\)
\(920\) −7.01039e9 + 7.74629e9i −0.296814 + 0.327972i
\(921\) −2.87565e9 −0.121290
\(922\) 3.04359e10 + 7.61582e9i 1.27888 + 0.320006i
\(923\) 3.37045e10i 1.41085i
\(924\) −3.58833e9 1.91572e9i −0.149637 0.0798879i
\(925\) 2.41786e10i 1.00446i
\(926\) −3.07174e8 + 1.22759e9i −0.0127130 + 0.0508061i
\(927\) −2.71201e10 −1.11818
\(928\) −1.13853e9 + 4.08956e8i −0.0467654 + 0.0167981i
\(929\) −2.99533e10 −1.22572 −0.612858 0.790193i \(-0.709980\pi\)
−0.612858 + 0.790193i \(0.709980\pi\)
\(930\) −1.86756e9 4.67309e8i −0.0761349 0.0190508i
\(931\) −2.45304e9 2.09809e9i −0.0996280 0.0852118i
\(932\) 1.80145e10 + 9.61755e9i 0.728899 + 0.389142i
\(933\) 1.53053e8i 0.00616960i
\(934\) 4.04032e9 1.61468e10i 0.162256 0.648442i
\(935\) 4.71893e10i 1.88800i
\(936\) −2.44773e10 + 2.70468e10i −0.975660 + 1.07808i
\(937\) 2.33735e10 0.928188 0.464094 0.885786i \(-0.346380\pi\)
0.464094 + 0.885786i \(0.346380\pi\)
\(938\) −1.04946e10 + 4.19406e10i −0.415197 + 1.65930i
\(939\) 2.17851e9 0.0858676
\(940\) 8.22467e9 1.54056e10i 0.322976 0.604964i
\(941\) 4.03649e10i 1.57921i 0.613615 + 0.789606i \(0.289715\pi\)
−0.613615 + 0.789606i \(0.710285\pi\)
\(942\) −1.65823e9 4.14930e8i −0.0646349 0.0161732i
\(943\) 1.33937e10 0.520128
\(944\) 1.44870e10 + 2.16351e10i 0.560502 + 0.837060i
\(945\) 1.24280e10i 0.479061i
\(946\) 4.05602e10 + 1.01492e10i 1.55769 + 0.389773i
\(947\) 4.50109e10i 1.72224i 0.508405 + 0.861118i \(0.330235\pi\)
−0.508405 + 0.861118i \(0.669765\pi\)
\(948\) 3.81262e9 + 2.03547e9i 0.145343 + 0.0775952i
\(949\) 6.92897e9i 0.263170i
\(950\) −1.01110e10 1.42216e10i −0.382613 0.538164i
\(951\) 8.84167e8i 0.0333351i
\(952\) −3.09949e10 + 3.42485e10i −1.16429 + 1.28651i
\(953\) 4.53955e10i 1.69898i −0.527607 0.849488i \(-0.676911\pi\)
0.527607 0.849488i \(-0.323089\pi\)
\(954\) −7.22148e9 + 2.88600e10i −0.269282 + 1.07616i
\(955\) 5.07776e10i 1.88651i
\(956\) 1.59591e10 2.98928e10i 0.590751 1.10653i
\(957\) 2.14889e8 0.00792542
\(958\) 9.32054e7 3.72487e8i 0.00342501 0.0136877i
\(959\) 3.31169e10i 1.21251i
\(960\) 6.24087e8 + 6.24170e9i 0.0227665 + 0.227695i
\(961\) −2.42763e10 −0.882371
\(962\) −6.11782e10 1.53083e10i −2.21556 0.554389i
\(963\) −1.90716e10 −0.688169
\(964\) −5.00389e9 + 9.37275e9i −0.179903 + 0.336975i
\(965\) 1.81256e10i 0.649303i
\(966\) −1.76223e9 4.40953e8i −0.0628988 0.0157388i
\(967\) 4.26740e10i 1.51765i 0.651296 + 0.758824i \(0.274226\pi\)
−0.651296 + 0.758824i \(0.725774\pi\)
\(968\) −4.04690e9 3.66244e9i −0.143403 0.129780i
\(969\) 6.23616e9 + 5.33379e9i 0.220183 + 0.188323i
\(970\) 6.77464e9 2.70742e10i 0.238334 0.952478i
\(971\) 2.37027e10 0.830864 0.415432 0.909624i \(-0.363630\pi\)
0.415432 + 0.909624i \(0.363630\pi\)
\(972\) −1.28946e10 6.88415e9i −0.450378 0.240446i
\(973\) 3.63333e10 1.26447
\(974\) −9.26598e9 2.31858e9i −0.321318 0.0804017i
\(975\) 5.09533e9i 0.176058i
\(976\) 3.86300e9 + 5.76905e9i 0.132999 + 0.198623i
\(977\) 2.06467e10i 0.708305i 0.935188 + 0.354152i \(0.115231\pi\)
−0.935188 + 0.354152i \(0.884769\pi\)
\(978\) −8.85955e8 + 3.54064e9i −0.0302849 + 0.121031i
\(979\) −1.49816e10 −0.510291
\(980\) 4.39064e9 + 2.34406e9i 0.149017 + 0.0795568i
\(981\) 1.47957e10i 0.500375i
\(982\) −1.43812e9 + 5.74730e9i −0.0484623 + 0.193675i
\(983\) −7.69478e9 −0.258380 −0.129190 0.991620i \(-0.541238\pi\)
−0.129190 + 0.991620i \(0.541238\pi\)
\(984\) 5.39611e9 5.96255e9i 0.180550 0.199503i
\(985\) 1.58983e10 0.530058
\(986\) 5.92338e8 2.36722e9i 0.0196789 0.0786448i
\(987\) 3.03648e9 0.100522
\(988\) −4.23860e10 + 1.65792e10i −1.39821 + 0.546910i
\(989\) 1.86720e10 0.613766
\(990\) −8.30558e9 + 3.31925e10i −0.272049 + 1.08722i
\(991\) −4.90220e9 −0.160005 −0.0800024 0.996795i \(-0.525493\pi\)
−0.0800024 + 0.996795i \(0.525493\pi\)
\(992\) −3.56476e9 9.92423e9i −0.115942 0.322779i
\(993\) 5.23351e9 0.169618
\(994\) 7.51174e9 3.00200e10i 0.242598 0.969522i
\(995\) 4.13758e9i 0.133157i
\(996\) 2.38400e9 4.46545e9i 0.0764538 0.143205i
\(997\) 3.98588e10 1.27377 0.636885 0.770959i \(-0.280223\pi\)
0.636885 + 0.770959i \(0.280223\pi\)
\(998\) 9.75448e9 3.89829e10i 0.310633 1.24141i
\(999\) 1.67575e10i 0.531778i
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 76.8.d.a.75.5 68
4.3 odd 2 inner 76.8.d.a.75.63 yes 68
19.18 odd 2 inner 76.8.d.a.75.64 yes 68
76.75 even 2 inner 76.8.d.a.75.6 yes 68
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
76.8.d.a.75.5 68 1.1 even 1 trivial
76.8.d.a.75.6 yes 68 76.75 even 2 inner
76.8.d.a.75.63 yes 68 4.3 odd 2 inner
76.8.d.a.75.64 yes 68 19.18 odd 2 inner