Properties

Label 33.8.d.b.32.2
Level $33$
Weight $8$
Character 33.32
Analytic conductor $10.309$
Analytic rank $0$
Dimension $24$
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] = [33,8,Mod(32,33)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(33, 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("33.32");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 33 = 3 \cdot 11 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 33.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: \(10.3087058410\)
Analytic rank: \(0\)
Dimension: \(24\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 32.2
Character \(\chi\) \(=\) 33.32
Dual form 33.8.d.b.32.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-21.2791 q^{2} +(13.2650 + 44.8446i) q^{3} +324.799 q^{4} -116.081i q^{5} +(-282.268 - 954.252i) q^{6} +73.6975i q^{7} -4187.71 q^{8} +(-1835.08 + 1189.73i) q^{9} +O(q^{10})\) \(q-21.2791 q^{2} +(13.2650 + 44.8446i) q^{3} +324.799 q^{4} -116.081i q^{5} +(-282.268 - 954.252i) q^{6} +73.6975i q^{7} -4187.71 q^{8} +(-1835.08 + 1189.73i) q^{9} +2470.10i q^{10} +(1337.24 - 4207.01i) q^{11} +(4308.48 + 14565.5i) q^{12} -11437.6i q^{13} -1568.22i q^{14} +(5205.60 - 1539.82i) q^{15} +47536.4 q^{16} +19264.4 q^{17} +(39048.8 - 25316.4i) q^{18} +42528.5i q^{19} -37703.0i q^{20} +(-3304.93 + 977.600i) q^{21} +(-28455.2 + 89521.4i) q^{22} -38757.4i q^{23} +(-55550.2 - 187796. i) q^{24} +64650.2 q^{25} +243381. i q^{26} +(-77695.4 - 66511.5i) q^{27} +23936.9i q^{28} +115979. q^{29} +(-110771. + 32765.9i) q^{30} +157493. q^{31} -475503. q^{32} +(206400. + 4161.63i) q^{33} -409928. q^{34} +8554.87 q^{35} +(-596032. + 386424. i) q^{36} -205289. q^{37} -904967. i q^{38} +(512913. - 151720. i) q^{39} +486114. i q^{40} +457481. q^{41} +(70326.0 - 20802.4i) q^{42} -215319. i q^{43} +(434334. - 1.36644e6i) q^{44} +(138105. + 213018. i) q^{45} +824722. i q^{46} +682721. i q^{47} +(630572. + 2.13175e6i) q^{48} +818112. q^{49} -1.37570e6 q^{50} +(255543. + 863903. i) q^{51} -3.71491e6i q^{52} -1.29875e6i q^{53} +(1.65329e6 + 1.41530e6i) q^{54} +(-488354. - 155228. i) q^{55} -308624. i q^{56} +(-1.90717e6 + 564142. i) q^{57} -2.46794e6 q^{58} +2.61276e6i q^{59} +(1.69078e6 - 500132. i) q^{60} -1.67910e6i q^{61} -3.35131e6 q^{62} +(-87680.2 - 135241. i) q^{63} +4.03362e6 q^{64} -1.32768e6 q^{65} +(-4.39201e6 - 88555.7i) q^{66} +2.45218e6 q^{67} +6.25706e6 q^{68} +(1.73806e6 - 514118. i) q^{69} -182040. q^{70} -658125. i q^{71} +(7.68478e6 - 4.98225e6i) q^{72} -1.22508e6i q^{73} +4.36836e6 q^{74} +(857588. + 2.89921e6i) q^{75} +1.38132e7i q^{76} +(310046. + 98551.0i) q^{77} +(-1.09143e7 + 3.22845e6i) q^{78} -6.39822e6i q^{79} -5.51807e6i q^{80} +(1.95205e6 - 4.36650e6i) q^{81} -9.73478e6 q^{82} -8.51697e6 q^{83} +(-1.07344e6 + 317524. i) q^{84} -2.23623e6i q^{85} +4.58180e6i q^{86} +(1.53847e6 + 5.20105e6i) q^{87} +(-5.59996e6 + 1.76178e7i) q^{88} -2.50924e6i q^{89} +(-2.93875e6 - 4.53282e6i) q^{90} +842919. q^{91} -1.25884e7i q^{92} +(2.08915e6 + 7.06272e6i) q^{93} -1.45277e7i q^{94} +4.93675e6 q^{95} +(-6.30757e6 - 2.13238e7i) q^{96} +5.77174e6 q^{97} -1.74087e7 q^{98} +(2.55128e6 + 9.31115e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 24 q + 120 q^{3} + 1788 q^{4} - 5940 q^{9} - 6936 q^{12} + 23160 q^{15} + 5844 q^{16} - 17556 q^{22} - 34704 q^{25} + 7560 q^{27} + 131328 q^{31} + 28644 q^{33} - 436080 q^{34} - 302832 q^{36} + 1072488 q^{37} - 100296 q^{42} - 1854252 q^{45} + 3172548 q^{48} - 1169304 q^{49} - 4401936 q^{55} - 2920440 q^{58} + 1981452 q^{60} + 14578596 q^{64} + 2895156 q^{66} + 7729200 q^{67} - 4614108 q^{69} - 6924504 q^{70} - 4375800 q^{75} - 26237448 q^{78} + 22367340 q^{81} - 23600232 q^{82} - 25179660 q^{88} + 9380640 q^{91} + 25396908 q^{93} + 72948360 q^{97} + 53650080 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/33\mathbb{Z}\right)^\times\).

\(n\) \(13\) \(23\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −21.2791 −1.88082 −0.940412 0.340038i \(-0.889560\pi\)
−0.940412 + 0.340038i \(0.889560\pi\)
\(3\) 13.2650 + 44.8446i 0.283651 + 0.958928i
\(4\) 324.799 2.53750
\(5\) 116.081i 0.415304i −0.978203 0.207652i \(-0.933418\pi\)
0.978203 0.207652i \(-0.0665821\pi\)
\(6\) −282.268 954.252i −0.533497 1.80357i
\(7\) 73.6975i 0.0812100i 0.999175 + 0.0406050i \(0.0129285\pi\)
−0.999175 + 0.0406050i \(0.987071\pi\)
\(8\) −4187.71 −2.89176
\(9\) −1835.08 + 1189.73i −0.839084 + 0.544001i
\(10\) 2470.10i 0.781113i
\(11\) 1337.24 4207.01i 0.302924 0.953015i
\(12\) 4308.48 + 14565.5i 0.719763 + 2.43327i
\(13\) 11437.6i 1.44388i −0.691955 0.721940i \(-0.743250\pi\)
0.691955 0.721940i \(-0.256750\pi\)
\(14\) 1568.22i 0.152742i
\(15\) 5205.60 1539.82i 0.398246 0.117801i
\(16\) 47536.4 2.90139
\(17\) 19264.4 0.951007 0.475503 0.879714i \(-0.342266\pi\)
0.475503 + 0.879714i \(0.342266\pi\)
\(18\) 39048.8 25316.4i 1.57817 1.02317i
\(19\) 42528.5i 1.42247i 0.702956 + 0.711234i \(0.251863\pi\)
−0.702956 + 0.711234i \(0.748137\pi\)
\(20\) 37703.0i 1.05383i
\(21\) −3304.93 + 977.600i −0.0778745 + 0.0230353i
\(22\) −28455.2 + 89521.4i −0.569747 + 1.79245i
\(23\) 38757.4i 0.664212i −0.943242 0.332106i \(-0.892241\pi\)
0.943242 0.332106i \(-0.107759\pi\)
\(24\) −55550.2 187796.i −0.820250 2.77299i
\(25\) 64650.2 0.827523
\(26\) 243381.i 2.71568i
\(27\) −77695.4 66511.5i −0.759665 0.650315i
\(28\) 23936.9i 0.206070i
\(29\) 115979. 0.883056 0.441528 0.897247i \(-0.354437\pi\)
0.441528 + 0.897247i \(0.354437\pi\)
\(30\) −110771. + 32765.9i −0.749031 + 0.221563i
\(31\) 157493. 0.949502 0.474751 0.880120i \(-0.342538\pi\)
0.474751 + 0.880120i \(0.342538\pi\)
\(32\) −475503. −2.56524
\(33\) 206400. + 4161.63i 0.999797 + 0.0201588i
\(34\) −409928. −1.78868
\(35\) 8554.87 0.0337268
\(36\) −596032. + 386424.i −2.12917 + 1.38040i
\(37\) −205289. −0.666284 −0.333142 0.942877i \(-0.608109\pi\)
−0.333142 + 0.942877i \(0.608109\pi\)
\(38\) 904967.i 2.67541i
\(39\) 512913. 151720.i 1.38458 0.409558i
\(40\) 486114.i 1.20096i
\(41\) 457481. 1.03664 0.518322 0.855185i \(-0.326557\pi\)
0.518322 + 0.855185i \(0.326557\pi\)
\(42\) 70326.0 20802.4i 0.146468 0.0433253i
\(43\) 215319.i 0.412994i −0.978447 0.206497i \(-0.933794\pi\)
0.978447 0.206497i \(-0.0662063\pi\)
\(44\) 434334. 1.36644e6i 0.768669 2.41827i
\(45\) 138105. + 213018.i 0.225926 + 0.348475i
\(46\) 824722.i 1.24927i
\(47\) 682721.i 0.959181i 0.877492 + 0.479591i \(0.159215\pi\)
−0.877492 + 0.479591i \(0.840785\pi\)
\(48\) 630572. + 2.13175e6i 0.822982 + 2.78222i
\(49\) 818112. 0.993405
\(50\) −1.37570e6 −1.55642
\(51\) 255543. + 863903.i 0.269754 + 0.911947i
\(52\) 3.71491e6i 3.66384i
\(53\) 1.29875e6i 1.19829i −0.800642 0.599143i \(-0.795508\pi\)
0.800642 0.599143i \(-0.204492\pi\)
\(54\) 1.65329e6 + 1.41530e6i 1.42880 + 1.22313i
\(55\) −488354. 155228.i −0.395791 0.125806i
\(56\) 308624.i 0.234840i
\(57\) −1.90717e6 + 564142.i −1.36404 + 0.403484i
\(58\) −2.46794e6 −1.66087
\(59\) 2.61276e6i 1.65622i 0.560567 + 0.828109i \(0.310583\pi\)
−0.560567 + 0.828109i \(0.689417\pi\)
\(60\) 1.69078e6 500132.i 1.01055 0.298920i
\(61\) 1.67910e6i 0.947156i −0.880752 0.473578i \(-0.842962\pi\)
0.880752 0.473578i \(-0.157038\pi\)
\(62\) −3.35131e6 −1.78585
\(63\) −87680.2 135241.i −0.0441783 0.0681420i
\(64\) 4.03362e6 1.92338
\(65\) −1.32768e6 −0.599649
\(66\) −4.39201e6 88555.7i −1.88044 0.0379152i
\(67\) 2.45218e6 0.996070 0.498035 0.867157i \(-0.334055\pi\)
0.498035 + 0.867157i \(0.334055\pi\)
\(68\) 6.25706e6 2.41318
\(69\) 1.73806e6 514118.i 0.636932 0.188404i
\(70\) −182040. −0.0634342
\(71\) 658125.i 0.218225i −0.994029 0.109112i \(-0.965199\pi\)
0.994029 0.109112i \(-0.0348009\pi\)
\(72\) 7.68478e6 4.98225e6i 2.42643 1.57312i
\(73\) 1.22508e6i 0.368583i −0.982872 0.184291i \(-0.941001\pi\)
0.982872 0.184291i \(-0.0589990\pi\)
\(74\) 4.36836e6 1.25316
\(75\) 857588. + 2.89921e6i 0.234728 + 0.793534i
\(76\) 1.38132e7i 3.60950i
\(77\) 310046. + 98551.0i 0.0773943 + 0.0246005i
\(78\) −1.09143e7 + 3.22845e6i −2.60415 + 0.770306i
\(79\) 6.39822e6i 1.46004i −0.683426 0.730020i \(-0.739511\pi\)
0.683426 0.730020i \(-0.260489\pi\)
\(80\) 5.51807e6i 1.20496i
\(81\) 1.95205e6 4.36650e6i 0.408125 0.912926i
\(82\) −9.73478e6 −1.94975
\(83\) −8.51697e6 −1.63498 −0.817488 0.575945i \(-0.804634\pi\)
−0.817488 + 0.575945i \(0.804634\pi\)
\(84\) −1.07344e6 + 317524.i −0.197606 + 0.0584520i
\(85\) 2.23623e6i 0.394957i
\(86\) 4.58180e6i 0.776768i
\(87\) 1.53847e6 + 5.20105e6i 0.250480 + 0.846787i
\(88\) −5.59996e6 + 1.76178e7i −0.875983 + 2.75589i
\(89\) 2.50924e6i 0.377292i −0.982045 0.188646i \(-0.939590\pi\)
0.982045 0.188646i \(-0.0604099\pi\)
\(90\) −2.93875e6 4.53282e6i −0.424927 0.655420i
\(91\) 842919. 0.117258
\(92\) 1.25884e7i 1.68544i
\(93\) 2.08915e6 + 7.06272e6i 0.269327 + 0.910504i
\(94\) 1.45277e7i 1.80405i
\(95\) 4.93675e6 0.590756
\(96\) −6.30757e6 2.13238e7i −0.727634 2.45988i
\(97\) 5.77174e6 0.642104 0.321052 0.947062i \(-0.395964\pi\)
0.321052 + 0.947062i \(0.395964\pi\)
\(98\) −1.74087e7 −1.86842
\(99\) 2.55128e6 + 9.31115e6i 0.264262 + 0.964451i
\(100\) 2.09984e7 2.09984
\(101\) −4.05710e6 −0.391823 −0.195912 0.980622i \(-0.562767\pi\)
−0.195912 + 0.980622i \(0.562767\pi\)
\(102\) −5.43771e6 1.83831e7i −0.507359 1.71521i
\(103\) −1.06050e7 −0.956267 −0.478133 0.878287i \(-0.658686\pi\)
−0.478133 + 0.878287i \(0.658686\pi\)
\(104\) 4.78972e7i 4.17535i
\(105\) 113481. + 383640.i 0.00956664 + 0.0323416i
\(106\) 2.76362e7i 2.25376i
\(107\) 1.68359e7 1.32860 0.664298 0.747468i \(-0.268731\pi\)
0.664298 + 0.747468i \(0.268731\pi\)
\(108\) −2.52354e7 2.16029e7i −1.92765 1.65017i
\(109\) 4.01015e6i 0.296597i 0.988943 + 0.148299i \(0.0473797\pi\)
−0.988943 + 0.148299i \(0.952620\pi\)
\(110\) 1.03917e7 + 3.30310e6i 0.744412 + 0.236618i
\(111\) −2.72317e6 9.20610e6i −0.188992 0.638918i
\(112\) 3.50331e6i 0.235622i
\(113\) 3.24480e6i 0.211550i −0.994390 0.105775i \(-0.966268\pi\)
0.994390 0.105775i \(-0.0337324\pi\)
\(114\) 4.05829e7 1.20044e7i 2.56552 0.758882i
\(115\) −4.49899e6 −0.275850
\(116\) 3.76701e7 2.24075
\(117\) 1.36076e7 + 2.09888e7i 0.785473 + 1.21154i
\(118\) 5.55972e7i 3.11505i
\(119\) 1.41974e6i 0.0772313i
\(120\) −2.17996e7 + 6.44832e6i −1.15163 + 0.340653i
\(121\) −1.59108e7 1.12515e7i −0.816474 0.577382i
\(122\) 3.57297e7i 1.78143i
\(123\) 6.06851e6 + 2.05156e7i 0.294045 + 0.994067i
\(124\) 5.11537e7 2.40936
\(125\) 1.65735e7i 0.758977i
\(126\) 1.86575e6 + 2.87780e6i 0.0830917 + 0.128163i
\(127\) 2.48533e7i 1.07664i −0.842739 0.538322i \(-0.819059\pi\)
0.842739 0.538322i \(-0.180941\pi\)
\(128\) −2.49673e7 −1.05229
\(129\) 9.65591e6 2.85622e6i 0.396031 0.117146i
\(130\) 2.82519e7 1.12783
\(131\) 2.73219e7 1.06185 0.530924 0.847420i \(-0.321845\pi\)
0.530924 + 0.847420i \(0.321845\pi\)
\(132\) 6.70387e7 + 1.35170e6i 2.53698 + 0.0511529i
\(133\) −3.13424e6 −0.115519
\(134\) −5.21801e7 −1.87343
\(135\) −7.72072e6 + 9.01895e6i −0.270078 + 0.315492i
\(136\) −8.06737e7 −2.75008
\(137\) 1.91331e7i 0.635716i −0.948138 0.317858i \(-0.897036\pi\)
0.948138 0.317858i \(-0.102964\pi\)
\(138\) −3.69843e7 + 1.09400e7i −1.19796 + 0.354355i
\(139\) 8.95211e6i 0.282731i −0.989957 0.141366i \(-0.954851\pi\)
0.989957 0.141366i \(-0.0451493\pi\)
\(140\) 2.77862e6 0.0855817
\(141\) −3.06164e7 + 9.05632e6i −0.919786 + 0.272073i
\(142\) 1.40043e7i 0.410442i
\(143\) −4.81180e7 1.52947e7i −1.37604 0.437386i
\(144\) −8.72329e7 + 5.65555e7i −2.43451 + 1.57836i
\(145\) 1.34630e7i 0.366737i
\(146\) 2.60686e7i 0.693239i
\(147\) 1.08523e7 + 3.66879e7i 0.281780 + 0.952603i
\(148\) −6.66778e7 −1.69069
\(149\) 96814.2 0.00239766 0.00119883 0.999999i \(-0.499618\pi\)
0.00119883 + 0.999999i \(0.499618\pi\)
\(150\) −1.82487e7 6.16926e7i −0.441481 1.49250i
\(151\) 6.10092e7i 1.44204i 0.692917 + 0.721018i \(0.256325\pi\)
−0.692917 + 0.721018i \(0.743675\pi\)
\(152\) 1.78097e8i 4.11343i
\(153\) −3.53516e7 + 2.29194e7i −0.797975 + 0.517349i
\(154\) −6.59750e6 2.09707e6i −0.145565 0.0462691i
\(155\) 1.82820e7i 0.394332i
\(156\) 1.66594e8 4.92784e7i 3.51336 1.03925i
\(157\) −1.55235e7 −0.320141 −0.160071 0.987106i \(-0.551172\pi\)
−0.160071 + 0.987106i \(0.551172\pi\)
\(158\) 1.36148e8i 2.74608i
\(159\) 5.82420e7 1.72280e7i 1.14907 0.339895i
\(160\) 5.51969e7i 1.06536i
\(161\) 2.85632e6 0.0539407
\(162\) −4.15378e7 + 9.29151e7i −0.767611 + 1.71705i
\(163\) 1.97076e7 0.356432 0.178216 0.983991i \(-0.442967\pi\)
0.178216 + 0.983991i \(0.442967\pi\)
\(164\) 1.48590e8 2.63048
\(165\) 483086. 2.39592e7i 0.00837203 0.415219i
\(166\) 1.81233e8 3.07510
\(167\) −4.16534e7 −0.692058 −0.346029 0.938224i \(-0.612470\pi\)
−0.346029 + 0.938224i \(0.612470\pi\)
\(168\) 1.38401e7 4.09391e6i 0.225194 0.0666125i
\(169\) −6.80691e7 −1.08479
\(170\) 4.75849e7i 0.742844i
\(171\) −5.05974e7 7.80431e7i −0.773824 1.19357i
\(172\) 6.99356e7i 1.04797i
\(173\) −5.29067e7 −0.776871 −0.388436 0.921476i \(-0.626984\pi\)
−0.388436 + 0.921476i \(0.626984\pi\)
\(174\) −3.27373e7 1.10674e8i −0.471108 1.59266i
\(175\) 4.76456e6i 0.0672031i
\(176\) 6.35674e7 1.99986e8i 0.878901 2.76507i
\(177\) −1.17168e8 + 3.46584e7i −1.58819 + 0.469788i
\(178\) 5.33944e7i 0.709620i
\(179\) 1.87430e7i 0.244260i 0.992514 + 0.122130i \(0.0389725\pi\)
−0.992514 + 0.122130i \(0.961027\pi\)
\(180\) 4.48565e7 + 6.91880e7i 0.573286 + 0.884254i
\(181\) 1.34869e7 0.169059 0.0845293 0.996421i \(-0.473061\pi\)
0.0845293 + 0.996421i \(0.473061\pi\)
\(182\) −1.79365e7 −0.220541
\(183\) 7.52985e7 2.22733e7i 0.908254 0.268662i
\(184\) 1.62305e8i 1.92074i
\(185\) 2.38301e7i 0.276710i
\(186\) −4.44553e7 1.50288e8i −0.506557 1.71250i
\(187\) 2.57610e7 8.10455e7i 0.288083 0.906323i
\(188\) 2.21747e8i 2.43392i
\(189\) 4.90173e6 5.72595e6i 0.0528121 0.0616924i
\(190\) −1.05049e8 −1.11111
\(191\) 8.65128e7i 0.898387i −0.893434 0.449194i \(-0.851711\pi\)
0.893434 0.449194i \(-0.148289\pi\)
\(192\) 5.35061e7 + 1.80886e8i 0.545568 + 1.84438i
\(193\) 1.50178e8i 1.50368i 0.659347 + 0.751838i \(0.270833\pi\)
−0.659347 + 0.751838i \(0.729167\pi\)
\(194\) −1.22817e8 −1.20768
\(195\) −1.76118e7 5.95394e7i −0.170091 0.575020i
\(196\) 2.65722e8 2.52076
\(197\) −8.80966e7 −0.820971 −0.410485 0.911867i \(-0.634641\pi\)
−0.410485 + 0.911867i \(0.634641\pi\)
\(198\) −5.42890e7 1.98133e8i −0.497031 1.81396i
\(199\) −6.12483e6 −0.0550945 −0.0275472 0.999621i \(-0.508770\pi\)
−0.0275472 + 0.999621i \(0.508770\pi\)
\(200\) −2.70737e8 −2.39300
\(201\) 3.25282e7 + 1.09967e8i 0.282536 + 0.955159i
\(202\) 8.63313e7 0.736951
\(203\) 8.54740e6i 0.0717130i
\(204\) 8.30001e7 + 2.80595e8i 0.684499 + 2.31406i
\(205\) 5.31049e7i 0.430522i
\(206\) 2.25664e8 1.79857
\(207\) 4.61109e7 + 7.11228e7i 0.361332 + 0.557330i
\(208\) 5.43700e8i 4.18926i
\(209\) 1.78918e8 + 5.68706e7i 1.35563 + 0.430900i
\(210\) −2.41477e6 8.16351e6i −0.0179932 0.0608288i
\(211\) 1.45369e8i 1.06533i 0.846327 + 0.532664i \(0.178809\pi\)
−0.846327 + 0.532664i \(0.821191\pi\)
\(212\) 4.21834e8i 3.04065i
\(213\) 2.95134e7 8.73006e6i 0.209262 0.0618997i
\(214\) −3.58253e8 −2.49885
\(215\) −2.49945e7 −0.171518
\(216\) 3.25366e8 + 2.78531e8i 2.19677 + 1.88055i
\(217\) 1.16069e7i 0.0771091i
\(218\) 8.53322e7i 0.557847i
\(219\) 5.49383e7 1.62508e7i 0.353444 0.104549i
\(220\) −1.58617e8 5.04179e7i −1.00432 0.319231i
\(221\) 2.20337e8i 1.37314i
\(222\) 5.79465e7 + 1.95897e8i 0.355461 + 1.20169i
\(223\) 2.55101e8 1.54044 0.770220 0.637778i \(-0.220146\pi\)
0.770220 + 0.637778i \(0.220146\pi\)
\(224\) 3.50434e7i 0.208323i
\(225\) −1.18638e8 + 7.69164e7i −0.694361 + 0.450173i
\(226\) 6.90464e7i 0.397889i
\(227\) 3.50553e7 0.198913 0.0994564 0.995042i \(-0.468290\pi\)
0.0994564 + 0.995042i \(0.468290\pi\)
\(228\) −6.19449e8 + 1.83233e8i −3.46125 + 1.02384i
\(229\) −9.43843e7 −0.519369 −0.259684 0.965694i \(-0.583618\pi\)
−0.259684 + 0.965694i \(0.583618\pi\)
\(230\) 9.57345e7 0.518825
\(231\) −306702. + 1.52112e7i −0.00163710 + 0.0811935i
\(232\) −4.85689e8 −2.55358
\(233\) 1.32885e7 0.0688227 0.0344114 0.999408i \(-0.489044\pi\)
0.0344114 + 0.999408i \(0.489044\pi\)
\(234\) −2.89558e8 4.46622e8i −1.47734 2.27869i
\(235\) 7.92509e7 0.398352
\(236\) 8.48623e8i 4.20265i
\(237\) 2.86926e8 8.48727e7i 1.40007 0.414141i
\(238\) 3.02107e7i 0.145258i
\(239\) 1.59568e8 0.756053 0.378026 0.925795i \(-0.376603\pi\)
0.378026 + 0.925795i \(0.376603\pi\)
\(240\) 2.47456e8 7.31974e7i 1.15547 0.341788i
\(241\) 2.64943e8i 1.21925i 0.792689 + 0.609626i \(0.208680\pi\)
−0.792689 + 0.609626i \(0.791320\pi\)
\(242\) 3.38567e8 + 2.39423e8i 1.53564 + 1.08595i
\(243\) 2.21708e8 + 2.96172e7i 0.991195 + 0.132410i
\(244\) 5.45370e8i 2.40340i
\(245\) 9.49672e7i 0.412565i
\(246\) −1.29132e8 4.36553e8i −0.553047 1.86966i
\(247\) 4.86422e8 2.05387
\(248\) −6.59536e8 −2.74573
\(249\) −1.12978e8 3.81940e8i −0.463763 1.56782i
\(250\) 3.52669e8i 1.42750i
\(251\) 7.51774e7i 0.300075i 0.988680 + 0.150037i \(0.0479394\pi\)
−0.988680 + 0.150037i \(0.952061\pi\)
\(252\) −2.84785e7 4.39261e7i −0.112102 0.172910i
\(253\) −1.63053e8 5.18278e7i −0.633004 0.201206i
\(254\) 5.28856e8i 2.02498i
\(255\) 1.00283e8 2.96636e7i 0.378735 0.112030i
\(256\) 1.49782e7 0.0557980
\(257\) 1.43540e8i 0.527482i −0.964593 0.263741i \(-0.915044\pi\)
0.964593 0.263741i \(-0.0849565\pi\)
\(258\) −2.05469e8 + 6.07777e7i −0.744864 + 0.220331i
\(259\) 1.51293e7i 0.0541090i
\(260\) −4.31230e8 −1.52161
\(261\) −2.12831e8 + 1.37984e8i −0.740958 + 0.480384i
\(262\) −5.81386e8 −1.99715
\(263\) −1.37060e8 −0.464585 −0.232293 0.972646i \(-0.574623\pi\)
−0.232293 + 0.972646i \(0.574623\pi\)
\(264\) −8.64346e8 1.74277e7i −2.89117 0.0582944i
\(265\) −1.50760e8 −0.497653
\(266\) 6.66938e7 0.217270
\(267\) 1.12526e8 3.32852e7i 0.361796 0.107019i
\(268\) 7.96466e8 2.52752
\(269\) 5.97463e7i 0.187145i −0.995612 0.0935725i \(-0.970171\pi\)
0.995612 0.0935725i \(-0.0298287\pi\)
\(270\) 1.64290e8 1.91915e8i 0.507969 0.593384i
\(271\) 5.05492e8i 1.54284i −0.636325 0.771421i \(-0.719546\pi\)
0.636325 0.771421i \(-0.280454\pi\)
\(272\) 9.15758e8 2.75924
\(273\) 1.11814e7 + 3.78004e7i 0.0332602 + 0.112442i
\(274\) 4.07135e8i 1.19567i
\(275\) 8.64526e7 2.71984e8i 0.250677 0.788641i
\(276\) 5.64521e8 1.66985e8i 1.61621 0.478076i
\(277\) 4.20567e8i 1.18893i 0.804121 + 0.594465i \(0.202636\pi\)
−0.804121 + 0.594465i \(0.797364\pi\)
\(278\) 1.90493e8i 0.531767i
\(279\) −2.89012e8 + 1.87375e8i −0.796712 + 0.516530i
\(280\) −3.58254e7 −0.0975298
\(281\) 2.17377e8 0.584442 0.292221 0.956351i \(-0.405606\pi\)
0.292221 + 0.956351i \(0.405606\pi\)
\(282\) 6.51488e8 1.92710e8i 1.72995 0.511721i
\(283\) 1.24453e8i 0.326403i −0.986593 0.163202i \(-0.947818\pi\)
0.986593 0.163202i \(-0.0521821\pi\)
\(284\) 2.13759e8i 0.553745i
\(285\) 6.54861e7 + 2.21386e8i 0.167568 + 0.566492i
\(286\) 1.02391e9 + 3.25457e8i 2.58809 + 0.822646i
\(287\) 3.37152e7i 0.0841859i
\(288\) 8.72585e8 5.65721e8i 2.15246 1.39550i
\(289\) −3.92227e7 −0.0955862
\(290\) 2.86481e8i 0.689767i
\(291\) 7.65623e7 + 2.58831e8i 0.182133 + 0.615731i
\(292\) 3.97906e8i 0.935277i
\(293\) −7.39068e8 −1.71651 −0.858257 0.513220i \(-0.828453\pi\)
−0.858257 + 0.513220i \(0.828453\pi\)
\(294\) −2.30927e8 7.80685e8i −0.529979 1.79168i
\(295\) 3.03292e8 0.687834
\(296\) 8.59691e8 1.92673
\(297\) −3.83712e8 + 2.37924e8i −0.849880 + 0.526976i
\(298\) −2.06012e6 −0.00450957
\(299\) −4.43290e8 −0.959044
\(300\) 2.78544e8 + 9.41663e8i 0.595620 + 2.01359i
\(301\) 1.58685e7 0.0335392
\(302\) 1.29822e9i 2.71221i
\(303\) −5.38175e7 1.81939e8i −0.111141 0.375730i
\(304\) 2.02165e9i 4.12713i
\(305\) −1.94911e8 −0.393358
\(306\) 7.52250e8 4.87704e8i 1.50085 0.973042i
\(307\) 6.55755e8i 1.29347i 0.762713 + 0.646737i \(0.223867\pi\)
−0.762713 + 0.646737i \(0.776133\pi\)
\(308\) 1.00703e8 + 3.20093e7i 0.196388 + 0.0624236i
\(309\) −1.40675e8 4.75576e8i −0.271246 0.916991i
\(310\) 3.89023e8i 0.741669i
\(311\) 6.55393e8i 1.23549i 0.786377 + 0.617746i \(0.211954\pi\)
−0.786377 + 0.617746i \(0.788046\pi\)
\(312\) −2.14793e9 + 6.35358e8i −4.00386 + 1.18434i
\(313\) −8.32166e8 −1.53393 −0.766963 0.641691i \(-0.778233\pi\)
−0.766963 + 0.641691i \(0.778233\pi\)
\(314\) 3.30326e8 0.602129
\(315\) −1.56989e7 + 1.01780e7i −0.0282997 + 0.0183474i
\(316\) 2.07814e9i 3.70484i
\(317\) 7.71297e7i 0.135992i −0.997686 0.0679961i \(-0.978339\pi\)
0.997686 0.0679961i \(-0.0216605\pi\)
\(318\) −1.23934e9 + 3.66596e8i −2.16120 + 0.639282i
\(319\) 1.55092e8 4.87927e8i 0.267499 0.841565i
\(320\) 4.68226e8i 0.798787i
\(321\) 2.23329e8 + 7.54999e8i 0.376858 + 1.27403i
\(322\) −6.07799e7 −0.101453
\(323\) 8.19284e8i 1.35278i
\(324\) 6.34025e8 1.41824e9i 1.03562 2.31655i
\(325\) 7.39440e8i 1.19484i
\(326\) −4.19359e8 −0.670386
\(327\) −1.79833e8 + 5.31947e7i −0.284416 + 0.0841301i
\(328\) −1.91580e9 −2.99773
\(329\) −5.03148e7 −0.0778951
\(330\) −1.02796e7 + 5.09829e8i −0.0157463 + 0.780954i
\(331\) −6.98515e8 −1.05871 −0.529356 0.848400i \(-0.677566\pi\)
−0.529356 + 0.848400i \(0.677566\pi\)
\(332\) −2.76631e9 −4.14875
\(333\) 3.76721e8 2.44239e8i 0.559069 0.362460i
\(334\) 8.86346e8 1.30164
\(335\) 2.84651e8i 0.413672i
\(336\) −1.57105e8 + 4.64716e7i −0.225944 + 0.0668344i
\(337\) 5.36311e8i 0.763330i −0.924301 0.381665i \(-0.875351\pi\)
0.924301 0.381665i \(-0.124649\pi\)
\(338\) 1.44845e9 2.04030
\(339\) 1.45512e8 4.30424e7i 0.202861 0.0600064i
\(340\) 7.26325e8i 1.00220i
\(341\) 2.10606e8 6.62576e8i 0.287627 0.904889i
\(342\) 1.07667e9 + 1.66068e9i 1.45543 + 2.24489i
\(343\) 1.20986e8i 0.161884i
\(344\) 9.01695e8i 1.19428i
\(345\) −5.96793e7 2.01756e8i −0.0782451 0.264520i
\(346\) 1.12581e9 1.46116
\(347\) 5.95942e8 0.765687 0.382843 0.923813i \(-0.374945\pi\)
0.382843 + 0.923813i \(0.374945\pi\)
\(348\) 4.99695e8 + 1.68930e9i 0.635591 + 2.14872i
\(349\) 7.19204e8i 0.905655i −0.891598 0.452828i \(-0.850415\pi\)
0.891598 0.452828i \(-0.149585\pi\)
\(350\) 1.01385e8i 0.126397i
\(351\) −7.60729e8 + 8.88645e8i −0.938977 + 1.09687i
\(352\) −6.35860e8 + 2.00045e9i −0.777074 + 2.44471i
\(353\) 1.09245e8i 0.132188i 0.997813 + 0.0660938i \(0.0210536\pi\)
−0.997813 + 0.0660938i \(0.978946\pi\)
\(354\) 2.49323e9 7.37498e8i 2.98711 0.883588i
\(355\) −7.63958e7 −0.0906296
\(356\) 8.15001e8i 0.957378i
\(357\) −6.36675e7 + 1.88328e7i −0.0740592 + 0.0219067i
\(358\) 3.98833e8i 0.459410i
\(359\) 1.53339e9 1.74913 0.874567 0.484904i \(-0.161146\pi\)
0.874567 + 0.484904i \(0.161146\pi\)
\(360\) −5.78345e8 8.92056e8i −0.653323 1.00771i
\(361\) −9.14800e8 −1.02341
\(362\) −2.86989e8 −0.317970
\(363\) 2.93514e8 8.62764e8i 0.322074 0.946714i
\(364\) 2.73780e8 0.297541
\(365\) −1.42209e8 −0.153074
\(366\) −1.60228e9 + 4.73955e8i −1.70827 + 0.505305i
\(367\) −4.93917e8 −0.521582 −0.260791 0.965395i \(-0.583983\pi\)
−0.260791 + 0.965395i \(0.583983\pi\)
\(368\) 1.84239e9i 1.92714i
\(369\) −8.39514e8 + 5.44280e8i −0.869832 + 0.563936i
\(370\) 5.07084e8i 0.520443i
\(371\) 9.57147e7 0.0973128
\(372\) 6.78556e8 + 2.29397e9i 0.683416 + 2.31040i
\(373\) 1.69102e9i 1.68721i 0.536965 + 0.843605i \(0.319571\pi\)
−0.536965 + 0.843605i \(0.680429\pi\)
\(374\) −5.48171e8 + 1.72457e9i −0.541833 + 1.70463i
\(375\) 7.43231e8 2.19848e8i 0.727804 0.215285i
\(376\) 2.85904e9i 2.77372i
\(377\) 1.32652e9i 1.27503i
\(378\) −1.04304e8 + 1.21843e8i −0.0993301 + 0.116032i
\(379\) 9.30338e8 0.877817 0.438908 0.898532i \(-0.355365\pi\)
0.438908 + 0.898532i \(0.355365\pi\)
\(380\) 1.60345e9 1.49904
\(381\) 1.11454e9 3.29681e8i 1.03242 0.305391i
\(382\) 1.84091e9i 1.68971i
\(383\) 2.08513e8i 0.189643i 0.995494 + 0.0948214i \(0.0302280\pi\)
−0.995494 + 0.0948214i \(0.969772\pi\)
\(384\) −3.31192e8 1.11965e9i −0.298484 1.00907i
\(385\) 1.14399e7 3.59905e7i 0.0102167 0.0321422i
\(386\) 3.19564e9i 2.82815i
\(387\) 2.56172e8 + 3.95127e8i 0.224669 + 0.346536i
\(388\) 1.87466e9 1.62934
\(389\) 6.01312e8i 0.517936i −0.965886 0.258968i \(-0.916618\pi\)
0.965886 0.258968i \(-0.0833825\pi\)
\(390\) 3.74762e8 + 1.26694e9i 0.319911 + 1.08151i
\(391\) 7.46637e8i 0.631671i
\(392\) −3.42602e9 −2.87269
\(393\) 3.62427e8 + 1.22524e9i 0.301194 + 1.01823i
\(394\) 1.87462e9 1.54410
\(395\) −7.42712e8 −0.606360
\(396\) 8.28655e8 + 3.02426e9i 0.670565 + 2.44729i
\(397\) −2.59934e8 −0.208495 −0.104248 0.994551i \(-0.533243\pi\)
−0.104248 + 0.994551i \(0.533243\pi\)
\(398\) 1.30331e8 0.103623
\(399\) −4.15758e7 1.40554e8i −0.0327669 0.110774i
\(400\) 3.07324e9 2.40097
\(401\) 1.85389e9i 1.43575i 0.696174 + 0.717873i \(0.254884\pi\)
−0.696174 + 0.717873i \(0.745116\pi\)
\(402\) −6.92171e8 2.34000e9i −0.531401 1.79649i
\(403\) 1.80134e9i 1.37097i
\(404\) −1.31774e9 −0.994250
\(405\) −5.06867e8 2.26596e8i −0.379142 0.169496i
\(406\) 1.81881e8i 0.134879i
\(407\) −2.74520e8 + 8.63654e8i −0.201834 + 0.634979i
\(408\) −1.07014e9 3.61778e9i −0.780063 2.63713i
\(409\) 4.43794e8i 0.320738i 0.987057 + 0.160369i \(0.0512684\pi\)
−0.987057 + 0.160369i \(0.948732\pi\)
\(410\) 1.13002e9i 0.809737i
\(411\) 8.58016e8 2.53801e8i 0.609606 0.180321i
\(412\) −3.44449e9 −2.42652
\(413\) −1.92554e8 −0.134501
\(414\) −9.81197e8 1.51343e9i −0.679602 1.04824i
\(415\) 9.88658e8i 0.679012i
\(416\) 5.43859e9i 3.70391i
\(417\) 4.01454e8 1.18750e8i 0.271119 0.0801969i
\(418\) −3.80721e9 1.21016e9i −2.54970 0.810446i
\(419\) 9.87687e8i 0.655950i 0.944686 + 0.327975i \(0.106366\pi\)
−0.944686 + 0.327975i \(0.893634\pi\)
\(420\) 3.68585e7 + 1.24606e8i 0.0242753 + 0.0820666i
\(421\) 2.40008e8 0.156761 0.0783805 0.996924i \(-0.475025\pi\)
0.0783805 + 0.996924i \(0.475025\pi\)
\(422\) 3.09332e9i 2.00369i
\(423\) −8.12254e8 1.25285e9i −0.521796 0.804834i
\(424\) 5.43880e9i 3.46515i
\(425\) 1.24545e9 0.786980
\(426\) −6.28017e8 + 1.85768e8i −0.393585 + 0.116422i
\(427\) 1.23745e8 0.0769185
\(428\) 5.46829e9 3.37131
\(429\) 4.75989e7 2.36072e9i 0.0291069 1.44359i
\(430\) 5.31859e8 0.322595
\(431\) −5.62589e8 −0.338470 −0.169235 0.985576i \(-0.554130\pi\)
−0.169235 + 0.985576i \(0.554130\pi\)
\(432\) −3.69336e9 3.16172e9i −2.20408 1.88682i
\(433\) 6.74068e8 0.399021 0.199511 0.979896i \(-0.436065\pi\)
0.199511 + 0.979896i \(0.436065\pi\)
\(434\) 2.46983e8i 0.145029i
\(435\) 6.03743e8 1.78587e8i 0.351674 0.104025i
\(436\) 1.30249e9i 0.752615i
\(437\) 1.64829e9 0.944820
\(438\) −1.16904e9 + 3.45801e8i −0.664766 + 0.196638i
\(439\) 1.29876e9i 0.732661i 0.930485 + 0.366331i \(0.119386\pi\)
−0.930485 + 0.366331i \(0.880614\pi\)
\(440\) 2.04509e9 + 6.50049e8i 1.14453 + 0.363799i
\(441\) −1.50130e9 + 9.73333e8i −0.833551 + 0.540414i
\(442\) 4.68858e9i 2.58263i
\(443\) 9.82222e8i 0.536780i −0.963310 0.268390i \(-0.913508\pi\)
0.963310 0.268390i \(-0.0864917\pi\)
\(444\) −8.84483e8 2.99014e9i −0.479567 1.62125i
\(445\) −2.91275e8 −0.156691
\(446\) −5.42831e9 −2.89730
\(447\) 1.28424e6 + 4.34159e6i 0.000680098 + 0.00229918i
\(448\) 2.97268e8i 0.156198i
\(449\) 3.16711e9i 1.65120i 0.564253 + 0.825602i \(0.309164\pi\)
−0.564253 + 0.825602i \(0.690836\pi\)
\(450\) 2.52451e9 1.63671e9i 1.30597 0.846697i
\(451\) 6.11761e8 1.92463e9i 0.314025 0.987937i
\(452\) 1.05391e9i 0.536808i
\(453\) −2.73593e9 + 8.09289e8i −1.38281 + 0.409035i
\(454\) −7.45944e8 −0.374120
\(455\) 9.78468e7i 0.0486975i
\(456\) 7.98669e9 2.36246e9i 3.94448 1.16678i
\(457\) 3.03618e9i 1.48806i −0.668146 0.744031i \(-0.732912\pi\)
0.668146 0.744031i \(-0.267088\pi\)
\(458\) 2.00841e9 0.976840
\(459\) −1.49675e9 1.28130e9i −0.722446 0.618454i
\(460\) −1.46127e9 −0.699968
\(461\) −1.09519e9 −0.520637 −0.260319 0.965523i \(-0.583828\pi\)
−0.260319 + 0.965523i \(0.583828\pi\)
\(462\) 6.52634e6 3.23680e8i 0.00307909 0.152711i
\(463\) 3.57109e9 1.67212 0.836060 0.548639i \(-0.184854\pi\)
0.836060 + 0.548639i \(0.184854\pi\)
\(464\) 5.51324e9 2.56209
\(465\) 8.19847e8 2.42511e8i 0.378136 0.111853i
\(466\) −2.82768e8 −0.129443
\(467\) 9.84786e8i 0.447438i 0.974654 + 0.223719i \(0.0718198\pi\)
−0.974654 + 0.223719i \(0.928180\pi\)
\(468\) 4.41974e9 + 6.81715e9i 1.99313 + 3.07427i
\(469\) 1.80719e8i 0.0808909i
\(470\) −1.68639e9 −0.749229
\(471\) −2.05920e8 6.96146e8i −0.0908083 0.306992i
\(472\) 1.09415e10i 4.78938i
\(473\) −9.05851e8 2.87933e8i −0.393589 0.125106i
\(474\) −6.10552e9 + 1.80601e9i −2.63329 + 0.778927i
\(475\) 2.74948e9i 1.17712i
\(476\) 4.61129e8i 0.195974i
\(477\) 1.54516e9 + 2.38331e9i 0.651869 + 1.00546i
\(478\) −3.39545e9 −1.42200
\(479\) −1.72008e9 −0.715113 −0.357556 0.933892i \(-0.616390\pi\)
−0.357556 + 0.933892i \(0.616390\pi\)
\(480\) −2.47528e9 + 7.32189e8i −1.02160 + 0.302189i
\(481\) 2.34800e9i 0.962035i
\(482\) 5.63775e9i 2.29320i
\(483\) 3.78892e7 + 1.28091e8i 0.0153003 + 0.0517252i
\(484\) −5.16781e9 3.65450e9i −2.07180 1.46511i
\(485\) 6.69989e8i 0.266668i
\(486\) −4.71774e9 6.30226e8i −1.86426 0.249040i
\(487\) −1.16488e9 −0.457015 −0.228508 0.973542i \(-0.573385\pi\)
−0.228508 + 0.973542i \(0.573385\pi\)
\(488\) 7.03158e9i 2.73895i
\(489\) 2.61422e8 + 8.83779e8i 0.101102 + 0.341793i
\(490\) 2.02081e9i 0.775962i
\(491\) −2.41653e9 −0.921313 −0.460657 0.887578i \(-0.652386\pi\)
−0.460657 + 0.887578i \(0.652386\pi\)
\(492\) 1.97105e9 + 6.66345e9i 0.746138 + 2.52244i
\(493\) 2.23427e9 0.839792
\(494\) −1.03506e10 −3.86297
\(495\) 1.08085e9 2.96155e8i 0.400540 0.109749i
\(496\) 7.48666e9 2.75488
\(497\) 4.85022e7 0.0177220
\(498\) 2.40407e9 + 8.12733e9i 0.872255 + 2.94880i
\(499\) −3.43329e9 −1.23697 −0.618484 0.785797i \(-0.712253\pi\)
−0.618484 + 0.785797i \(0.712253\pi\)
\(500\) 5.38306e9i 1.92590i
\(501\) −5.52534e8 1.86793e9i −0.196303 0.663634i
\(502\) 1.59971e9i 0.564387i
\(503\) 1.05168e9 0.368464 0.184232 0.982883i \(-0.441020\pi\)
0.184232 + 0.982883i \(0.441020\pi\)
\(504\) 3.67179e8 + 5.66349e8i 0.127753 + 0.197050i
\(505\) 4.70952e8i 0.162726i
\(506\) 3.46962e9 + 1.10285e9i 1.19057 + 0.378433i
\(507\) −9.02939e8 3.05253e9i −0.307702 1.04024i
\(508\) 8.07235e9i 2.73198i
\(509\) 7.06309e7i 0.0237401i 0.999930 + 0.0118700i \(0.00377844\pi\)
−0.999930 + 0.0118700i \(0.996222\pi\)
\(510\) −2.13392e9 + 6.31215e8i −0.712333 + 0.210708i
\(511\) 9.02855e7 0.0299326
\(512\) 2.87709e9 0.947347
\(513\) 2.82863e9 3.30427e9i 0.925051 1.08060i
\(514\) 3.05441e9i 0.992101i
\(515\) 1.23103e9i 0.397141i
\(516\) 3.13623e9 9.27698e8i 1.00493 0.297257i
\(517\) 2.87222e9 + 9.12959e8i 0.914114 + 0.290559i
\(518\) 3.21937e8i 0.101769i
\(519\) −7.01809e8 2.37258e9i −0.220360 0.744963i
\(520\) 5.55995e9 1.73404
\(521\) 3.88780e9i 1.20440i 0.798344 + 0.602202i \(0.205710\pi\)
−0.798344 + 0.602202i \(0.794290\pi\)
\(522\) 4.52886e9 2.93618e9i 1.39361 0.903517i
\(523\) 1.58766e9i 0.485292i 0.970115 + 0.242646i \(0.0780153\pi\)
−0.970115 + 0.242646i \(0.921985\pi\)
\(524\) 8.87415e9 2.69443
\(525\) −2.13665e8 + 6.32020e7i −0.0644429 + 0.0190622i
\(526\) 2.91651e9 0.873802
\(527\) 3.03401e9 0.902983
\(528\) 9.81153e9 + 1.97829e8i 2.90080 + 0.0584886i
\(529\) 1.90269e9 0.558822
\(530\) 3.20804e9 0.935997
\(531\) −3.10848e9 4.79462e9i −0.900985 1.38971i
\(532\) −1.01800e9 −0.293128
\(533\) 5.23247e9i 1.49679i
\(534\) −2.39445e9 + 7.08279e8i −0.680474 + 0.201284i
\(535\) 1.95433e9i 0.551771i
\(536\) −1.02690e10 −2.88039
\(537\) −8.40521e8 + 2.48626e8i −0.234228 + 0.0692847i
\(538\) 1.27135e9i 0.351987i
\(539\) 1.09401e9 3.44181e9i 0.300926 0.946729i
\(540\) −2.50769e9 + 2.92935e9i −0.685322 + 0.800559i
\(541\) 5.30861e8i 0.144142i −0.997400 0.0720709i \(-0.977039\pi\)
0.997400 0.0720709i \(-0.0229608\pi\)
\(542\) 1.07564e10i 2.90181i
\(543\) 1.78904e8 + 6.04815e8i 0.0479536 + 0.162115i
\(544\) −9.16027e9 −2.43956
\(545\) 4.65502e8 0.123178
\(546\) −2.37929e8 8.04357e8i −0.0625566 0.211483i
\(547\) 3.43126e9i 0.896391i 0.893936 + 0.448195i \(0.147933\pi\)
−0.893936 + 0.448195i \(0.852067\pi\)
\(548\) 6.21442e9i 1.61313i
\(549\) 1.99767e9 + 3.08127e9i 0.515254 + 0.794744i
\(550\) −1.83963e9 + 5.78758e9i −0.471478 + 1.48329i
\(551\) 4.93243e9i 1.25612i
\(552\) −7.27849e9 + 2.15298e9i −1.84185 + 0.544820i
\(553\) 4.71533e8 0.118570
\(554\) 8.94929e9i 2.23617i
\(555\) −1.06865e9 + 3.16108e8i −0.265345 + 0.0784892i
\(556\) 2.90764e9i 0.717429i
\(557\) 1.86574e9 0.457464 0.228732 0.973489i \(-0.426542\pi\)
0.228732 + 0.973489i \(0.426542\pi\)
\(558\) 6.14992e9 3.98716e9i 1.49848 0.971502i
\(559\) −2.46273e9 −0.596313
\(560\) 4.06668e8 0.0978547
\(561\) 3.97617e9 + 8.01712e7i 0.950813 + 0.0191712i
\(562\) −4.62558e9 −1.09923
\(563\) 5.10827e9 1.20641 0.603204 0.797587i \(-0.293890\pi\)
0.603204 + 0.797587i \(0.293890\pi\)
\(564\) −9.94418e9 + 2.94149e9i −2.33395 + 0.690383i
\(565\) −3.76660e8 −0.0878576
\(566\) 2.64825e9i 0.613906i
\(567\) 3.21800e8 + 1.43861e8i 0.0741387 + 0.0331438i
\(568\) 2.75604e9i 0.631054i
\(569\) 1.72525e8 0.0392607 0.0196303 0.999807i \(-0.493751\pi\)
0.0196303 + 0.999807i \(0.493751\pi\)
\(570\) −1.39349e9 4.71090e9i −0.315167 1.06547i
\(571\) 2.09567e9i 0.471083i 0.971864 + 0.235541i \(0.0756863\pi\)
−0.971864 + 0.235541i \(0.924314\pi\)
\(572\) −1.56287e10 4.96771e9i −3.49170 1.10987i
\(573\) 3.87963e9 1.14760e9i 0.861488 0.254828i
\(574\) 7.17429e8i 0.158339i
\(575\) 2.50567e9i 0.549651i
\(576\) −7.40200e9 + 4.79892e9i −1.61388 + 1.04632i
\(577\) 9.05678e8 0.196272 0.0981360 0.995173i \(-0.468712\pi\)
0.0981360 + 0.995173i \(0.468712\pi\)
\(578\) 8.34624e8 0.179781
\(579\) −6.73465e9 + 1.99211e9i −1.44192 + 0.426519i
\(580\) 4.37278e9i 0.930592i
\(581\) 6.27679e8i 0.132776i
\(582\) −1.62918e9 5.50769e9i −0.342561 1.15808i
\(583\) −5.46386e9 1.73674e9i −1.14198 0.362990i
\(584\) 5.13029e9i 1.06585i
\(585\) 2.43640e9 1.57958e9i 0.503156 0.326210i
\(586\) 1.57267e10 3.22846
\(587\) 2.37789e9i 0.485241i 0.970121 + 0.242621i \(0.0780070\pi\)
−0.970121 + 0.242621i \(0.921993\pi\)
\(588\) 3.52482e9 + 1.19162e10i 0.715016 + 2.41723i
\(589\) 6.69795e9i 1.35064i
\(590\) −6.45377e9 −1.29369
\(591\) −1.16861e9 3.95066e9i −0.232869 0.787251i
\(592\) −9.75869e9 −1.93315
\(593\) −6.48663e9 −1.27740 −0.638701 0.769455i \(-0.720528\pi\)
−0.638701 + 0.769455i \(0.720528\pi\)
\(594\) 8.16504e9 5.06281e9i 1.59847 0.991148i
\(595\) 1.64804e8 0.0320744
\(596\) 3.14452e7 0.00608405
\(597\) −8.12461e7 2.74666e8i −0.0156276 0.0528316i
\(598\) 9.43280e9 1.80379
\(599\) 1.63992e9i 0.311767i 0.987775 + 0.155883i \(0.0498224\pi\)
−0.987775 + 0.155883i \(0.950178\pi\)
\(600\) −3.59133e9 1.21411e10i −0.678775 2.29471i
\(601\) 2.98244e9i 0.560416i 0.959939 + 0.280208i \(0.0904035\pi\)
−0.959939 + 0.280208i \(0.909597\pi\)
\(602\) −3.37667e8 −0.0630813
\(603\) −4.49994e9 + 2.91743e9i −0.835787 + 0.541864i
\(604\) 1.98157e10i 3.65916i
\(605\) −1.30609e9 + 1.84694e9i −0.239789 + 0.339085i
\(606\) 1.14519e9 + 3.87149e9i 0.209037 + 0.706682i
\(607\) 8.17709e9i 1.48402i 0.670391 + 0.742008i \(0.266126\pi\)
−0.670391 + 0.742008i \(0.733874\pi\)
\(608\) 2.02224e10i 3.64897i
\(609\) −3.83305e8 + 1.13382e8i −0.0687676 + 0.0203414i
\(610\) 4.14753e9 0.739836
\(611\) 7.80866e9 1.38494
\(612\) −1.14822e10 + 7.44421e9i −2.02486 + 1.31277i
\(613\) 1.01160e10i 1.77378i −0.461985 0.886888i \(-0.652863\pi\)
0.461985 0.886888i \(-0.347137\pi\)
\(614\) 1.39539e10i 2.43279i
\(615\) 2.38147e9 7.04438e8i 0.412840 0.122118i
\(616\) −1.29839e9 4.12703e8i −0.223806 0.0711386i
\(617\) 1.05718e10i 1.81198i −0.423303 0.905988i \(-0.639130\pi\)
0.423303 0.905988i \(-0.360870\pi\)
\(618\) 2.99344e9 + 1.01198e10i 0.510166 + 1.72470i
\(619\) −6.19329e9 −1.04955 −0.524776 0.851240i \(-0.675851\pi\)
−0.524776 + 0.851240i \(0.675851\pi\)
\(620\) 5.93797e9i 1.00062i
\(621\) −2.57781e9 + 3.01127e9i −0.431947 + 0.504579i
\(622\) 1.39462e10i 2.32374i
\(623\) 1.84925e8 0.0306399
\(624\) 2.43820e10 7.21220e9i 4.01720 1.18829i
\(625\) 3.12693e9 0.512317
\(626\) 1.77077e10 2.88504
\(627\) −1.76988e8 + 8.77790e9i −0.0286753 + 1.42218i
\(628\) −5.04203e9 −0.812357
\(629\) −3.95476e9 −0.633641
\(630\) 3.34057e8 2.16579e8i 0.0532266 0.0345083i
\(631\) −3.29651e9 −0.522338 −0.261169 0.965293i \(-0.584108\pi\)
−0.261169 + 0.965293i \(0.584108\pi\)
\(632\) 2.67939e10i 4.22208i
\(633\) −6.51902e9 + 1.92833e9i −1.02157 + 0.302181i
\(634\) 1.64125e9i 0.255777i
\(635\) −2.88500e9 −0.447134
\(636\) 1.89170e10 5.59564e9i 2.91576 0.862482i
\(637\) 9.35720e9i 1.43436i
\(638\) −3.30022e9 + 1.03826e10i −0.503118 + 1.58284i
\(639\) 7.82992e8 + 1.20771e9i 0.118715 + 0.183109i
\(640\) 2.89823e9i 0.437021i
\(641\) 1.09738e10i 1.64571i −0.568253 0.822854i \(-0.692380\pi\)
0.568253 0.822854i \(-0.307620\pi\)
\(642\) −4.75223e9 1.60657e10i −0.708802 2.39622i
\(643\) −8.87778e9 −1.31694 −0.658470 0.752607i \(-0.728796\pi\)
−0.658470 + 0.752607i \(0.728796\pi\)
\(644\) 9.27732e8 0.136874
\(645\) −3.31553e8 1.12087e9i −0.0486512 0.164473i
\(646\) 1.74336e10i 2.54433i
\(647\) 1.21358e10i 1.76159i 0.473498 + 0.880795i \(0.342991\pi\)
−0.473498 + 0.880795i \(0.657009\pi\)
\(648\) −8.17462e9 + 1.82856e10i −1.18020 + 2.63996i
\(649\) 1.09919e10 + 3.49388e9i 1.57840 + 0.501708i
\(650\) 1.57346e10i 2.24729i
\(651\) −5.20505e8 + 1.53965e8i −0.0739420 + 0.0218721i
\(652\) 6.40101e9 0.904445
\(653\) 1.91875e9i 0.269663i 0.990869 + 0.134832i \(0.0430493\pi\)
−0.990869 + 0.134832i \(0.956951\pi\)
\(654\) 3.82669e9 1.13194e9i 0.534935 0.158234i
\(655\) 3.17156e9i 0.440989i
\(656\) 2.17470e10 3.00771
\(657\) 1.45752e9 + 2.24812e9i 0.200510 + 0.309272i
\(658\) 1.07065e9 0.146507
\(659\) −1.08084e10 −1.47117 −0.735587 0.677431i \(-0.763093\pi\)
−0.735587 + 0.677431i \(0.763093\pi\)
\(660\) 1.56906e8 7.78192e9i 0.0212440 1.05362i
\(661\) −6.26254e9 −0.843423 −0.421711 0.906730i \(-0.638570\pi\)
−0.421711 + 0.906730i \(0.638570\pi\)
\(662\) 1.48638e10 1.99125
\(663\) 9.88094e9 2.92278e9i 1.31674 0.389493i
\(664\) 3.56666e10 4.72796
\(665\) 3.63826e8i 0.0479753i
\(666\) −8.01628e9 + 5.19717e9i −1.05151 + 0.681722i
\(667\) 4.49506e9i 0.586537i
\(668\) −1.35290e10 −1.75610
\(669\) 3.38392e9 + 1.14399e10i 0.436947 + 1.47717i
\(670\) 6.05711e9i 0.778044i
\(671\) −7.06399e9 2.24535e9i −0.902654 0.286916i
\(672\) 1.57151e9 4.64852e8i 0.199767 0.0590911i
\(673\) 1.29760e10i 1.64093i −0.571699 0.820463i \(-0.693716\pi\)
0.571699 0.820463i \(-0.306284\pi\)
\(674\) 1.14122e10i 1.43569i
\(675\) −5.02302e9 4.29998e9i −0.628640 0.538150i
\(676\) −2.21088e10 −2.75266
\(677\) 1.37621e10 1.70461 0.852305 0.523045i \(-0.175204\pi\)
0.852305 + 0.523045i \(0.175204\pi\)
\(678\) −3.09636e9 + 9.15903e8i −0.381546 + 0.112861i
\(679\) 4.25362e8i 0.0521453i
\(680\) 9.36467e9i 1.14212i
\(681\) 4.65010e8 + 1.57204e9i 0.0564218 + 0.190743i
\(682\) −4.48150e9 + 1.40990e10i −0.540976 + 1.70194i
\(683\) 4.38092e9i 0.526130i −0.964778 0.263065i \(-0.915267\pi\)
0.964778 0.263065i \(-0.0847334\pi\)
\(684\) −1.64340e10 2.53483e10i −1.96358 3.02868i
\(685\) −2.22099e9 −0.264015
\(686\) 2.57447e9i 0.304476i
\(687\) −1.25201e9 4.23263e9i −0.147319 0.498037i
\(688\) 1.02355e10i 1.19826i
\(689\) −1.48545e10 −1.73018
\(690\) 1.26992e9 + 4.29318e9i 0.147165 + 0.497516i
\(691\) −1.01743e10 −1.17309 −0.586544 0.809917i \(-0.699512\pi\)
−0.586544 + 0.809917i \(0.699512\pi\)
\(692\) −1.71841e10 −1.97131
\(693\) −6.86208e8 + 1.88023e8i −0.0783231 + 0.0214607i
\(694\) −1.26811e10 −1.44012
\(695\) −1.03917e9 −0.117419
\(696\) −6.44268e9 2.17805e10i −0.724326 2.44870i
\(697\) 8.81309e9 0.985856
\(698\) 1.53040e10i 1.70338i
\(699\) 1.76273e8 + 5.95920e8i 0.0195216 + 0.0659960i
\(700\) 1.54753e9i 0.170528i
\(701\) −7.87337e9 −0.863272 −0.431636 0.902048i \(-0.642063\pi\)
−0.431636 + 0.902048i \(0.642063\pi\)
\(702\) 1.61876e10 1.89096e10i 1.76605 2.06301i
\(703\) 8.73063e9i 0.947768i
\(704\) 5.39390e9 1.69695e10i 0.582638 1.83301i
\(705\) 1.05127e9 + 3.55398e9i 0.112993 + 0.381991i
\(706\) 2.32464e9i 0.248621i
\(707\) 2.98998e8i 0.0318200i
\(708\) −3.80562e10 + 1.12570e10i −4.03003 + 1.19208i
\(709\) 1.55379e10 1.63731 0.818654 0.574287i \(-0.194721\pi\)
0.818654 + 0.574287i \(0.194721\pi\)
\(710\) 1.62563e9 0.170458
\(711\) 7.61216e9 + 1.17412e10i 0.794263 + 1.22510i
\(712\) 1.05080e10i 1.09104i
\(713\) 6.10403e9i 0.630671i
\(714\) 1.35479e9 4.00746e8i 0.139292 0.0412027i
\(715\) −1.77542e9 + 5.58558e9i −0.181648 + 0.571475i
\(716\) 6.08771e9i 0.619810i
\(717\) 2.11667e9 + 7.15575e9i 0.214455 + 0.725000i
\(718\) −3.26292e10 −3.28981
\(719\) 7.61998e8i 0.0764545i −0.999269 0.0382272i \(-0.987829\pi\)
0.999269 0.0382272i \(-0.0121711\pi\)
\(720\) 6.56502e9 + 1.01261e10i 0.655499 + 1.01106i
\(721\) 7.81559e8i 0.0776584i
\(722\) 1.94661e10 1.92486
\(723\) −1.18813e10 + 3.51448e9i −1.16917 + 0.345842i
\(724\) 4.38054e9 0.428986
\(725\) 7.49810e9 0.730749
\(726\) −6.24571e9 + 1.83588e10i −0.605765 + 1.78060i
\(727\) 1.10918e10 1.07061 0.535307 0.844658i \(-0.320196\pi\)
0.535307 + 0.844658i \(0.320196\pi\)
\(728\) −3.52990e9 −0.339081
\(729\) 1.61279e9 + 1.03353e10i 0.154182 + 0.988043i
\(730\) 3.02607e9 0.287905
\(731\) 4.14799e9i 0.392760i
\(732\) 2.44569e10 7.23435e9i 2.30469 0.681728i
\(733\) 1.36766e10i 1.28267i 0.767262 + 0.641333i \(0.221618\pi\)
−0.767262 + 0.641333i \(0.778382\pi\)
\(734\) 1.05101e10 0.981003
\(735\) 4.25877e9 1.25974e9i 0.395620 0.117024i
\(736\) 1.84293e10i 1.70387i
\(737\) 3.27914e9 1.03163e10i 0.301734 0.949270i
\(738\) 1.78641e10 1.15818e10i 1.63600 1.06066i
\(739\) 1.59670e10i 1.45536i −0.685919 0.727678i \(-0.740600\pi\)
0.685919 0.727678i \(-0.259400\pi\)
\(740\) 7.74002e9i 0.702152i
\(741\) 6.45240e9 + 2.18134e10i 0.582583 + 1.96952i
\(742\) −2.03672e9 −0.183028
\(743\) −1.12516e10 −1.00636 −0.503180 0.864182i \(-0.667837\pi\)
−0.503180 + 0.864182i \(0.667837\pi\)
\(744\) −8.74878e9 2.95767e10i −0.778829 2.63296i
\(745\) 1.12383e7i 0.000995756i
\(746\) 3.59834e10i 3.17334i
\(747\) 1.56293e10 1.01329e10i 1.37188 0.889430i
\(748\) 8.36717e9 2.63235e10i 0.731009 2.29979i
\(749\) 1.24076e9i 0.107895i
\(750\) −1.58153e10 + 4.67816e9i −1.36887 + 0.404912i
\(751\) 1.39812e10 1.20449 0.602246 0.798310i \(-0.294273\pi\)
0.602246 + 0.798310i \(0.294273\pi\)
\(752\) 3.24541e10i 2.78296i
\(753\) −3.37130e9 + 9.97231e8i −0.287750 + 0.0851164i
\(754\) 2.82272e10i 2.39810i
\(755\) 7.08200e9 0.598883
\(756\) 1.59208e9 1.85979e9i 0.134010 0.156544i
\(757\) −2.10157e10 −1.76079 −0.880397 0.474237i \(-0.842724\pi\)
−0.880397 + 0.474237i \(0.842724\pi\)
\(758\) −1.97968e10 −1.65102
\(759\) 1.61294e8 7.99954e9i 0.0133897 0.664077i
\(760\) −2.06737e10 −1.70832
\(761\) 2.06241e10 1.69640 0.848200 0.529676i \(-0.177686\pi\)
0.848200 + 0.529676i \(0.177686\pi\)
\(762\) −2.37164e10 + 7.01530e9i −1.94181 + 0.574386i
\(763\) −2.95538e8 −0.0240867
\(764\) 2.80993e10i 2.27965i
\(765\) 2.66051e9 + 4.10365e9i 0.214857 + 0.331402i
\(766\) 4.43696e9i 0.356685i
\(767\) 2.98836e10 2.39138
\(768\) 1.98686e8 + 6.71690e8i 0.0158272 + 0.0535063i
\(769\) 8.45536e9i 0.670487i −0.942132 0.335243i \(-0.891181\pi\)
0.942132 0.335243i \(-0.108819\pi\)
\(770\) −2.43430e8 + 7.65845e8i −0.0192157 + 0.0604537i
\(771\) 6.43701e9 1.90407e9i 0.505817 0.149621i
\(772\) 4.87776e10i 3.81557i
\(773\) 3.75493e9i 0.292397i −0.989255 0.146199i \(-0.953296\pi\)
0.989255 0.146199i \(-0.0467038\pi\)
\(774\) −5.45110e9 8.40795e9i −0.422563 0.651774i
\(775\) 1.01820e10 0.785735
\(776\) −2.41704e10 −1.85681
\(777\) 6.78467e8 2.00690e8i 0.0518866 0.0153481i
\(778\) 1.27954e10i 0.974147i
\(779\) 1.94560e10i 1.47459i
\(780\) −5.72029e9 1.93384e10i −0.431605 1.45911i
\(781\) −2.76874e9 8.80069e8i −0.207972 0.0661056i
\(782\) 1.58877e10i 1.18806i
\(783\) −9.01107e9 7.71397e9i −0.670827 0.574264i
\(784\) 3.88901e10 2.88226
\(785\) 1.80199e9i 0.132956i
\(786\) −7.71211e9 2.60720e10i −0.566492 1.91512i
\(787\) 9.67085e9i 0.707218i 0.935393 + 0.353609i \(0.115046\pi\)
−0.935393 + 0.353609i \(0.884954\pi\)
\(788\) −2.86137e10 −2.08321
\(789\) −1.81810e9 6.14640e9i −0.131780 0.445504i
\(790\) 1.58042e10 1.14046
\(791\) 2.39134e8 0.0171800
\(792\) −1.06840e10 3.89924e10i −0.764183 2.78896i
\(793\) −1.92048e10 −1.36758
\(794\) 5.53116e9 0.392143
\(795\) −1.99984e9 6.76079e9i −0.141160 0.477213i
\(796\) −1.98934e9 −0.139802
\(797\) 2.79433e9i 0.195512i −0.995210 0.0977559i \(-0.968834\pi\)
0.995210 0.0977559i \(-0.0311665\pi\)
\(798\) 8.84696e8 + 2.99086e9i 0.0616288 + 0.208346i
\(799\) 1.31522e10i 0.912188i
\(800\) −3.07414e10 −2.12280
\(801\) 2.98533e9 + 4.60466e9i 0.205248 + 0.316580i
\(802\) 3.94490e10i 2.70038i
\(803\) −5.15394e9 1.63822e9i −0.351265 0.111653i
\(804\) 1.05652e10 + 3.57172e10i 0.716935 + 2.42371i
\(805\) 3.31565e8i 0.0224018i
\(806\) 3.83308e10i 2.57855i
\(807\) 2.67930e9 7.92537e8i 0.179459 0.0530838i
\(808\) 1.69900e10 1.13306
\(809\) −1.68092e10 −1.11616 −0.558081 0.829787i \(-0.688462\pi\)
−0.558081 + 0.829787i \(0.688462\pi\)
\(810\) 1.07857e10 + 4.82175e9i 0.713098 + 0.318792i
\(811\) 4.67476e9i 0.307742i −0.988091 0.153871i \(-0.950826\pi\)
0.988091 0.153871i \(-0.0491740\pi\)
\(812\) 2.77619e9i 0.181971i
\(813\) 2.26686e10 6.70537e9i 1.47947 0.437629i
\(814\) 5.84153e9 1.83778e10i 0.379613 1.19428i
\(815\) 2.28768e9i 0.148028i
\(816\) 1.21476e10 + 4.10668e10i 0.782661 + 2.64591i
\(817\) 9.15720e9 0.587470
\(818\) 9.44354e9i 0.603251i
\(819\) −1.54682e9 + 1.00285e9i −0.0983890 + 0.0637883i
\(820\) 1.72484e10i 1.09245i
\(821\) −1.33329e10 −0.840862 −0.420431 0.907325i \(-0.638121\pi\)
−0.420431 + 0.907325i \(0.638121\pi\)
\(822\) −1.82578e10 + 5.40066e9i −1.14656 + 0.339153i
\(823\) 2.50853e10 1.56863 0.784314 0.620364i \(-0.213015\pi\)
0.784314 + 0.620364i \(0.213015\pi\)
\(824\) 4.44106e10 2.76529
\(825\) 1.33438e10 + 2.69050e8i 0.827355 + 0.0166819i
\(826\) 4.09737e9 0.252974
\(827\) −1.67010e9 −0.102677 −0.0513385 0.998681i \(-0.516349\pi\)
−0.0513385 + 0.998681i \(0.516349\pi\)
\(828\) 1.49768e10 + 2.31006e10i 0.916880 + 1.41422i
\(829\) −1.58908e10 −0.968734 −0.484367 0.874865i \(-0.660950\pi\)
−0.484367 + 0.874865i \(0.660950\pi\)
\(830\) 2.10377e10i 1.27710i
\(831\) −1.88602e10 + 5.57884e9i −1.14010 + 0.337241i
\(832\) 4.61347e10i 2.77713i
\(833\) 1.57604e10 0.944735
\(834\) −8.54257e9 + 2.52689e9i −0.509926 + 0.150836i
\(835\) 4.83517e9i 0.287415i
\(836\) 5.81125e10 + 1.84716e10i 3.43991 + 1.09341i
\(837\) −1.22365e10 1.04751e10i −0.721303 0.617475i
\(838\) 2.10171e10i 1.23373i
\(839\) 2.09530e10i 1.22484i −0.790533 0.612419i \(-0.790197\pi\)
0.790533 0.612419i \(-0.209803\pi\)
\(840\) −4.75225e8 1.60657e9i −0.0276644 0.0935240i
\(841\) −3.79863e9 −0.220212
\(842\) −5.10714e9 −0.294840
\(843\) 2.88351e9 + 9.74818e9i 0.165777 + 0.560438i
\(844\) 4.72158e10i 2.70327i
\(845\) 7.90153e9i 0.450518i
\(846\) 1.72840e10 + 2.66594e10i 0.981406 + 1.51375i
\(847\) 8.29211e8 1.17258e9i 0.0468892 0.0663059i
\(848\) 6.17379e10i 3.47669i
\(849\) 5.58106e9 1.65088e9i 0.312997 0.0925845i
\(850\) −2.65019e10 −1.48017
\(851\) 7.95646e9i 0.442554i
\(852\) 9.58593e9 2.83552e9i 0.531001 0.157070i
\(853\) 1.13843e10i 0.628038i 0.949417 + 0.314019i \(0.101676\pi\)
−0.949417 + 0.314019i \(0.898324\pi\)
\(854\) −2.63319e9 −0.144670
\(855\) −9.05931e9 + 5.87340e9i −0.495694 + 0.321372i
\(856\) −7.05039e10 −3.84198
\(857\) −9.61380e9 −0.521749 −0.260875 0.965373i \(-0.584011\pi\)
−0.260875 + 0.965373i \(0.584011\pi\)
\(858\) −1.01286e9 + 5.02339e10i −0.0547450 + 2.71513i
\(859\) 9.04935e9 0.487126 0.243563 0.969885i \(-0.421684\pi\)
0.243563 + 0.969885i \(0.421684\pi\)
\(860\) −8.11819e9 −0.435226
\(861\) −1.51195e9 + 4.47234e8i −0.0807282 + 0.0238794i
\(862\) 1.19714e10 0.636603
\(863\) 2.62910e10i 1.39242i 0.717840 + 0.696208i \(0.245131\pi\)
−0.717840 + 0.696208i \(0.754869\pi\)
\(864\) 3.69444e10 + 3.16264e10i 1.94873 + 1.66822i
\(865\) 6.14146e9i 0.322638i
\(866\) −1.43435e10 −0.750488
\(867\) −5.20291e8 1.75893e9i −0.0271131 0.0916603i
\(868\) 3.76990e9i 0.195664i
\(869\) −2.69174e10 8.55594e9i −1.39144 0.442281i
\(870\) −1.28471e10 + 3.80018e9i −0.661436 + 0.195653i
\(871\) 2.80469e10i 1.43821i
\(872\) 1.67933e10i 0.857688i
\(873\) −1.05916e10 + 6.86681e9i −0.538780 + 0.349305i
\(874\) −3.50742e10 −1.77704
\(875\) 1.22142e9 0.0616365
\(876\) 1.78439e10 5.27824e9i 0.896863 0.265292i
\(877\) 2.46243e10i 1.23272i 0.787464 + 0.616361i \(0.211394\pi\)
−0.787464 + 0.616361i \(0.788606\pi\)
\(878\) 2.76364e10i 1.37801i
\(879\) −9.80376e9 3.31432e10i −0.486891 1.64601i
\(880\) −2.32146e10 7.37896e9i −1.14834 0.365011i
\(881\) 2.84916e10i 1.40379i −0.712282 0.701893i \(-0.752338\pi\)
0.712282 0.701893i \(-0.247662\pi\)
\(882\) 3.19463e10 2.07116e10i 1.56776 1.01642i
\(883\) 1.42961e10 0.698802 0.349401 0.936973i \(-0.386385\pi\)
0.349401 + 0.936973i \(0.386385\pi\)
\(884\) 7.15654e10i 3.48434i
\(885\) 4.02318e9 + 1.36010e10i 0.195105 + 0.659583i
\(886\) 2.09008e10i 1.00959i
\(887\) 2.01976e9 0.0971780 0.0485890 0.998819i \(-0.484528\pi\)
0.0485890 + 0.998819i \(0.484528\pi\)
\(888\) 1.14038e10 + 3.85525e10i 0.546520 + 1.84760i
\(889\) 1.83163e9 0.0874342
\(890\) 6.19808e9 0.294708
\(891\) −1.57596e10 1.40513e10i −0.746401 0.665497i
\(892\) 8.28566e10 3.90886
\(893\) −2.90351e10 −1.36440
\(894\) −2.73275e7 9.23852e7i −0.00127914 0.00432435i
\(895\) 2.17570e9 0.101442
\(896\) 1.84003e9i 0.0854567i
\(897\) −5.88025e9 1.98791e10i −0.272034 0.919654i
\(898\) 6.73932e10i 3.10562i
\(899\) 1.82660e10 0.838463
\(900\) −3.85336e10 + 2.49824e10i −1.76194 + 1.14231i
\(901\) 2.50196e10i 1.13958i
\(902\) −1.30177e10 + 4.09544e10i −0.590625 + 1.85814i
\(903\) 2.10496e8 + 7.11616e8i 0.00951342 + 0.0321617i
\(904\) 1.35883e10i 0.611752i
\(905\) 1.56557e9i 0.0702107i
\(906\) 5.82181e10 1.72209e10i 2.60082 0.769322i
\(907\) −1.89029e10 −0.841208 −0.420604 0.907244i \(-0.638182\pi\)
−0.420604 + 0.907244i \(0.638182\pi\)
\(908\) 1.13859e10 0.504741
\(909\) 7.44509e9 4.82685e9i 0.328773 0.213152i
\(910\) 2.08209e9i 0.0915914i
\(911\) 1.87105e10i 0.819918i 0.912104 + 0.409959i \(0.134457\pi\)
−0.912104 + 0.409959i \(0.865543\pi\)
\(912\) −9.06601e10 + 2.68173e10i −3.95762 + 1.17066i
\(913\) −1.13892e10 + 3.58310e10i −0.495274 + 1.55816i
\(914\) 6.46071e10i 2.79878i
\(915\) −2.58551e9 8.74072e9i −0.111576 0.377201i
\(916\) −3.06560e10 −1.31790
\(917\) 2.01356e9i 0.0862326i
\(918\) 3.18495e10 + 2.72649e10i 1.35879 + 1.16320i
\(919\) 6.43421e9i 0.273458i −0.990608 0.136729i \(-0.956341\pi\)
0.990608 0.136729i \(-0.0436590\pi\)
\(920\) 1.88405e10 0.797691
\(921\) −2.94071e10 + 8.69862e9i −1.24035 + 0.366895i
\(922\) 2.33046e10 0.979226
\(923\) −7.52734e9 −0.315091
\(924\) −9.96166e7 + 4.94059e9i −0.00415413 + 0.206028i
\(925\) −1.32720e10 −0.551365
\(926\) −7.59895e10 −3.14496
\(927\) 1.94609e10 1.26171e10i 0.802388 0.520210i
\(928\) −5.51486e10 −2.26525
\(929\) 4.41197e9i 0.180542i 0.995917 + 0.0902708i \(0.0287733\pi\)
−0.995917 + 0.0902708i \(0.971227\pi\)
\(930\) −1.74456e10 + 5.16041e9i −0.711206 + 0.210375i
\(931\) 3.47930e10i 1.41309i
\(932\) 4.31611e9 0.174637
\(933\) −2.93908e10 + 8.69381e9i −1.18475 + 0.350449i
\(934\) 2.09553e10i 0.841551i
\(935\) −9.40784e9 2.99036e9i −0.376400 0.119642i
\(936\) −5.69848e10 8.78951e10i −2.27140 3.50347i
\(937\) 2.10425e8i 0.00835619i −0.999991 0.00417809i \(-0.998670\pi\)
0.999991 0.00417809i \(-0.00132993\pi\)
\(938\) 3.84554e9i 0.152141i
\(939\) −1.10387e10 3.73181e10i −0.435100 1.47092i
\(940\) 2.57407e10 1.01082
\(941\) 3.06020e10 1.19725 0.598627 0.801028i \(-0.295713\pi\)
0.598627 + 0.801028i \(0.295713\pi\)
\(942\) 4.38179e9 + 1.48134e10i 0.170794 + 0.577398i
\(943\) 1.77308e10i 0.688552i
\(944\) 1.24201e11i 4.80534i
\(945\) −6.64674e8 5.68998e8i −0.0256211 0.0219331i
\(946\) 1.92757e10 + 6.12694e9i 0.740271 + 0.235302i
\(947\) 1.68029e10i 0.642925i 0.946922 + 0.321463i \(0.104174\pi\)
−0.946922 + 0.321463i \(0.895826\pi\)
\(948\) 9.31934e10 2.75666e10i 3.55268 1.05088i
\(949\) −1.40119e10 −0.532190
\(950\) 5.85063e10i 2.21396i
\(951\) 3.45885e9 1.02313e9i 0.130407 0.0385743i
\(952\) 5.94545e9i 0.223334i
\(953\) 4.57844e8 0.0171353 0.00856767 0.999963i \(-0.497273\pi\)
0.00856767 + 0.999963i \(0.497273\pi\)
\(954\) −3.28797e10 5.07146e10i −1.22605 1.89110i
\(955\) −1.00425e10 −0.373104
\(956\) 5.18275e10 1.91848
\(957\) 2.39382e10 + 4.82664e8i 0.882876 + 0.0178014i
\(958\) 3.66017e10 1.34500
\(959\) 1.41006e9 0.0516265
\(960\) 2.09974e10 6.21104e9i 0.765979 0.226577i
\(961\) −2.70850e9 −0.0984457
\(962\) 4.99634e10i 1.80942i
\(963\) −3.08952e10 + 2.00302e10i −1.11480 + 0.722758i
\(964\) 8.60535e10i 3.09385i
\(965\) 1.74328e10 0.624483
\(966\) −8.06248e8 2.72565e9i −0.0287772 0.0972860i
\(967\) 1.99002e10i 0.707726i 0.935297 + 0.353863i \(0.115132\pi\)
−0.935297 + 0.353863i \(0.884868\pi\)
\(968\) 6.66297e10 + 4.71182e10i 2.36105 + 1.66965i
\(969\) −3.67405e10 + 1.08678e10i −1.29721 + 0.383716i
\(970\) 1.42567e10i 0.501556i
\(971\) 2.59685e10i 0.910291i 0.890417 + 0.455145i \(0.150413\pi\)
−0.890417 + 0.455145i \(0.849587\pi\)
\(972\) 7.20106e10 + 9.61964e9i 2.51515 + 0.335990i
\(973\) 6.59748e8 0.0229606
\(974\) 2.47876e10 0.859564
\(975\) 3.31599e10 9.80870e9i 1.14577 0.338919i
\(976\) 7.98182e10i 2.74807i
\(977\) 2.89249e10i 0.992296i −0.868238 0.496148i \(-0.834747\pi\)
0.868238 0.496148i \(-0.165253\pi\)
\(978\) −5.56282e9 1.88060e10i −0.190156 0.642851i
\(979\) −1.05564e10 3.35545e9i −0.359565 0.114291i
\(980\) 3.08453e10i 1.04688i
\(981\) −4.77099e9 7.35893e9i −0.161349 0.248870i
\(982\) 5.14216e10 1.73283
\(983\) 5.49184e10i 1.84408i 0.387089 + 0.922042i \(0.373481\pi\)
−0.387089 + 0.922042i \(0.626519\pi\)
\(984\) −2.54132e10 8.59133e10i −0.850307 2.87460i
\(985\) 1.02263e10i 0.340952i
\(986\) −4.75433e10 −1.57950
\(987\) −6.67428e8 2.25635e9i −0.0220950 0.0746958i
\(988\) 1.57990e11 5.21170
\(989\) −8.34521e9 −0.274315
\(990\) −2.29994e10 + 6.30191e9i −0.753345 + 0.206419i
\(991\) 5.40673e10 1.76472 0.882362 0.470571i \(-0.155952\pi\)
0.882362 + 0.470571i \(0.155952\pi\)
\(992\) −7.48885e10 −2.43570
\(993\) −9.26583e9 3.13246e10i −0.300304 1.01523i
\(994\) −1.03208e9 −0.0333320
\(995\) 7.10976e8i 0.0228810i
\(996\) −3.66952e10 1.24054e11i −1.17680 3.97835i
\(997\) 3.57762e10i 1.14330i 0.820497 + 0.571651i \(0.193697\pi\)
−0.820497 + 0.571651i \(0.806303\pi\)
\(998\) 7.30573e10 2.32652
\(999\) 1.59500e10 + 1.36541e10i 0.506153 + 0.433294i
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 33.8.d.b.32.2 yes 24
3.2 odd 2 inner 33.8.d.b.32.23 yes 24
11.10 odd 2 inner 33.8.d.b.32.24 yes 24
33.32 even 2 inner 33.8.d.b.32.1 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
33.8.d.b.32.1 24 33.32 even 2 inner
33.8.d.b.32.2 yes 24 1.1 even 1 trivial
33.8.d.b.32.23 yes 24 3.2 odd 2 inner
33.8.d.b.32.24 yes 24 11.10 odd 2 inner