Properties

Label 38.8.c.b.11.6
Level $38$
Weight $8$
Character 38.11
Analytic conductor $11.871$
Analytic rank $0$
Dimension $14$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [38,8,Mod(7,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.7");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 38.c (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(11.8706309684\)
Analytic rank: \(0\)
Dimension: \(14\)
Relative dimension: \(7\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{14} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{14} - x^{13} + 9740 x^{12} + 37173 x^{11} + 71393485 x^{10} + 196352446 x^{9} + 218671355941 x^{8} - 33116965187 x^{7} + 501909199155445 x^{6} + \cdots + 66\!\cdots\!81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{19}]\)
Coefficient ring index: \( 2^{8}\cdot 3^{6} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 11.6
Root \(-32.4887 - 56.2721i\) of defining polynomial
Character \(\chi\) \(=\) 38.11
Dual form 38.8.c.b.7.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.00000 - 6.92820i) q^{2} +(36.4887 - 63.2003i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(-170.433 + 295.199i) q^{5} +(-291.910 - 505.603i) q^{6} -1668.31 q^{7} -512.000 q^{8} +(-1569.35 - 2718.20i) q^{9} +O(q^{10})\) \(q+(4.00000 - 6.92820i) q^{2} +(36.4887 - 63.2003i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(-170.433 + 295.199i) q^{5} +(-291.910 - 505.603i) q^{6} -1668.31 q^{7} -512.000 q^{8} +(-1569.35 - 2718.20i) q^{9} +(1363.47 + 2361.59i) q^{10} +1788.65 q^{11} -4670.56 q^{12} +(-993.344 - 1720.52i) q^{13} +(-6673.24 + 11558.4i) q^{14} +(12437.8 + 21542.9i) q^{15} +(-2048.00 + 3547.24i) q^{16} +(13112.3 - 22711.2i) q^{17} -25109.7 q^{18} +(-21533.5 - 20740.8i) q^{19} +21815.5 q^{20} +(-60874.5 + 105438. i) q^{21} +(7154.60 - 12392.1i) q^{22} +(-42121.6 - 72956.7i) q^{23} +(-18682.2 + 32358.6i) q^{24} +(-19032.5 - 32965.3i) q^{25} -15893.5 q^{26} -69453.2 q^{27} +(53385.9 + 92467.1i) q^{28} +(93652.5 + 162211. i) q^{29} +199005. q^{30} -153392. q^{31} +(16384.0 + 28377.9i) q^{32} +(65265.6 - 113043. i) q^{33} +(-104899. - 181690. i) q^{34} +(284336. - 492484. i) q^{35} +(-100439. + 173965. i) q^{36} -48243.2 q^{37} +(-229830. + 66225.2i) q^{38} -144983. q^{39} +(87261.9 - 151142. i) q^{40} +(306861. - 531499. i) q^{41} +(486996. + 843501. i) q^{42} +(-154825. + 268165. i) q^{43} +(-57236.8 - 99137.0i) q^{44} +1.06988e6 q^{45} -673945. q^{46} +(-505445. - 875456. i) q^{47} +(149458. + 258869. i) q^{48} +1.95971e6 q^{49} -304521. q^{50} +(-956904. - 1.65741e6i) q^{51} +(-63574.0 + 110113. i) q^{52} +(344813. + 597234. i) q^{53} +(-277813. + 481186. i) q^{54} +(-304846. + 528008. i) q^{55} +854174. q^{56} +(-2.09655e6 + 604118. i) q^{57} +1.49844e6 q^{58} +(-323373. + 560099. i) q^{59} +(796019. - 1.37874e6i) q^{60} +(-398341. - 689947. i) q^{61} +(-613569. + 1.06273e6i) q^{62} +(2.61817e6 + 4.53480e6i) q^{63} +262144. q^{64} +677196. q^{65} +(-522124. - 904346. i) q^{66} +(-1.22054e6 - 2.11403e6i) q^{67} -1.67838e6 q^{68} -6.14785e6 q^{69} +(-2.27468e6 - 3.93987e6i) q^{70} +(-1.44847e6 + 2.50883e6i) q^{71} +(803509. + 1.39172e6i) q^{72} +(-903424. + 1.56478e6i) q^{73} +(-192973. + 334239. i) q^{74} -2.77789e6 q^{75} +(-460500. + 1.85721e6i) q^{76} -2.98402e6 q^{77} +(-579934. + 1.00447e6i) q^{78} +(3.82045e6 - 6.61721e6i) q^{79} +(-698095. - 1.20914e6i) q^{80} +(897919. - 1.55524e6i) q^{81} +(-2.45489e6 - 4.25199e6i) q^{82} -2.25232e6 q^{83} +7.79193e6 q^{84} +(4.46956e6 + 7.74150e6i) q^{85} +(1.23860e6 + 2.14532e6i) q^{86} +1.36690e7 q^{87} -915789. q^{88} +(5.42728e6 + 9.40033e6i) q^{89} +(4.27952e6 - 7.41235e6i) q^{90} +(1.65720e6 + 2.87036e6i) q^{91} +(-2.69578e6 + 4.66923e6i) q^{92} +(-5.59709e6 + 9.69444e6i) q^{93} -8.08712e6 q^{94} +(9.79269e6 - 2.82175e6i) q^{95} +2.39132e6 q^{96} +(4.56753e6 - 7.91120e6i) q^{97} +(7.83885e6 - 1.35773e7i) q^{98} +(-2.80702e6 - 4.86191e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 14 q + 56 q^{2} + 55 q^{3} - 448 q^{4} - 126 q^{5} - 440 q^{6} + 1928 q^{7} - 7168 q^{8} - 4602 q^{9} + 1008 q^{10} + 646 q^{11} - 7040 q^{12} - 1308 q^{13} + 7712 q^{14} + 8740 q^{15} - 28672 q^{16} + 10528 q^{17} - 73632 q^{18} - 87463 q^{19} + 16128 q^{20} - 30584 q^{21} + 2584 q^{22} - 113822 q^{23} - 28160 q^{24} - 50143 q^{25} - 20928 q^{26} - 319898 q^{27} - 61696 q^{28} + 167706 q^{29} + 139840 q^{30} + 201780 q^{31} + 229376 q^{32} + 377473 q^{33} - 84224 q^{34} - 33168 q^{35} - 294528 q^{36} + 380924 q^{37} - 384064 q^{38} + 1379564 q^{39} + 64512 q^{40} + 66301 q^{41} + 244672 q^{42} + 726564 q^{43} - 20672 q^{44} + 428936 q^{45} - 1821152 q^{46} - 2373788 q^{47} + 225280 q^{48} + 5898846 q^{49} - 802288 q^{50} + 3264054 q^{51} - 83712 q^{52} + 161792 q^{53} - 1279592 q^{54} - 53424 q^{55} - 987136 q^{56} - 4487994 q^{57} + 2683296 q^{58} - 1845767 q^{59} + 559360 q^{60} - 1600418 q^{61} + 807120 q^{62} - 3064040 q^{63} + 3670016 q^{64} + 6534852 q^{65} - 3019784 q^{66} - 8911929 q^{67} - 1347584 q^{68} - 8860208 q^{69} + 265344 q^{70} + 517154 q^{71} + 2356224 q^{72} - 9558049 q^{73} + 1523696 q^{74} - 24621450 q^{75} + 2525120 q^{76} - 9188192 q^{77} + 5518256 q^{78} + 7963520 q^{79} - 516096 q^{80} - 4125855 q^{81} - 530408 q^{82} + 30616886 q^{83} + 3914752 q^{84} + 6973266 q^{85} - 5812512 q^{86} + 25084136 q^{87} - 330752 q^{88} + 11829436 q^{89} + 1715744 q^{90} + 4017336 q^{91} - 7284608 q^{92} + 396810 q^{93} - 37980608 q^{94} + 7058892 q^{95} + 3604480 q^{96} - 8033723 q^{97} + 23595384 q^{98} + 24812606 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/38\mathbb{Z}\right)^\times\).

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.00000 6.92820i 0.353553 0.612372i
\(3\) 36.4887 63.2003i 0.780251 1.35143i −0.151545 0.988450i \(-0.548425\pi\)
0.931795 0.362984i \(-0.118242\pi\)
\(4\) −32.0000 55.4256i −0.250000 0.433013i
\(5\) −170.433 + 295.199i −0.609761 + 1.05614i 0.381519 + 0.924361i \(0.375401\pi\)
−0.991280 + 0.131776i \(0.957932\pi\)
\(6\) −291.910 505.603i −0.551721 0.955608i
\(7\) −1668.31 −1.83837 −0.919186 0.393824i \(-0.871152\pi\)
−0.919186 + 0.393824i \(0.871152\pi\)
\(8\) −512.000 −0.353553
\(9\) −1569.35 2718.20i −0.717583 1.24289i
\(10\) 1363.47 + 2361.59i 0.431166 + 0.746801i
\(11\) 1788.65 0.405183 0.202591 0.979263i \(-0.435064\pi\)
0.202591 + 0.979263i \(0.435064\pi\)
\(12\) −4670.56 −0.780251
\(13\) −993.344 1720.52i −0.125400 0.217199i 0.796489 0.604653i \(-0.206688\pi\)
−0.921889 + 0.387453i \(0.873355\pi\)
\(14\) −6673.24 + 11558.4i −0.649963 + 1.12577i
\(15\) 12437.8 + 21542.9i 0.951533 + 1.64810i
\(16\) −2048.00 + 3547.24i −0.125000 + 0.216506i
\(17\) 13112.3 22711.2i 0.647305 1.12116i −0.336459 0.941698i \(-0.609230\pi\)
0.983764 0.179467i \(-0.0574372\pi\)
\(18\) −25109.7 −1.01482
\(19\) −21533.5 20740.8i −0.720239 0.693726i
\(20\) 21815.5 0.609761
\(21\) −60874.5 + 105438.i −1.43439 + 2.48444i
\(22\) 7154.60 12392.1i 0.143254 0.248123i
\(23\) −42121.6 72956.7i −0.721867 1.25031i −0.960251 0.279139i \(-0.909951\pi\)
0.238384 0.971171i \(-0.423382\pi\)
\(24\) −18682.2 + 32358.6i −0.275860 + 0.477804i
\(25\) −19032.5 32965.3i −0.243617 0.421956i
\(26\) −15893.5 −0.177343
\(27\) −69453.2 −0.679077
\(28\) 53385.9 + 92467.1i 0.459593 + 0.796038i
\(29\) 93652.5 + 162211.i 0.713061 + 1.23506i 0.963703 + 0.266978i \(0.0860250\pi\)
−0.250642 + 0.968080i \(0.580642\pi\)
\(30\) 199005. 1.34567
\(31\) −153392. −0.924778 −0.462389 0.886677i \(-0.653008\pi\)
−0.462389 + 0.886677i \(0.653008\pi\)
\(32\) 16384.0 + 28377.9i 0.0883883 + 0.153093i
\(33\) 65265.6 113043.i 0.316144 0.547578i
\(34\) −104899. 181690.i −0.457713 0.792783i
\(35\) 284336. 492484.i 1.12097 1.94157i
\(36\) −100439. + 173965.i −0.358791 + 0.621445i
\(37\) −48243.2 −0.156578 −0.0782889 0.996931i \(-0.524946\pi\)
−0.0782889 + 0.996931i \(0.524946\pi\)
\(38\) −229830. + 66225.2i −0.679462 + 0.195786i
\(39\) −144983. −0.391374
\(40\) 87261.9 151142.i 0.215583 0.373401i
\(41\) 306861. 531499.i 0.695341 1.20437i −0.274724 0.961523i \(-0.588587\pi\)
0.970065 0.242843i \(-0.0780801\pi\)
\(42\) 486996. + 843501.i 1.01427 + 1.75676i
\(43\) −154825. + 268165.i −0.296963 + 0.514355i −0.975440 0.220267i \(-0.929307\pi\)
0.678477 + 0.734622i \(0.262640\pi\)
\(44\) −57236.8 99137.0i −0.101296 0.175449i
\(45\) 1.06988e6 1.75022
\(46\) −673945. −1.02087
\(47\) −505445. 875456.i −0.710119 1.22996i −0.964812 0.262941i \(-0.915308\pi\)
0.254693 0.967022i \(-0.418026\pi\)
\(48\) 149458. + 258869.i 0.195063 + 0.337859i
\(49\) 1.95971e6 2.37961
\(50\) −304521. −0.344526
\(51\) −956904. 1.65741e6i −1.01012 1.74958i
\(52\) −63574.0 + 110113.i −0.0627001 + 0.108600i
\(53\) 344813. + 597234.i 0.318140 + 0.551035i 0.980100 0.198505i \(-0.0636085\pi\)
−0.661960 + 0.749539i \(0.730275\pi\)
\(54\) −277813. + 481186.i −0.240090 + 0.415848i
\(55\) −304846. + 528008.i −0.247065 + 0.427928i
\(56\) 854174. 0.649963
\(57\) −2.09655e6 + 604118.i −1.49949 + 0.432076i
\(58\) 1.49844e6 1.00842
\(59\) −323373. + 560099.i −0.204985 + 0.355044i −0.950128 0.311860i \(-0.899048\pi\)
0.745143 + 0.666905i \(0.232381\pi\)
\(60\) 796019. 1.37874e6i 0.475766 0.824052i
\(61\) −398341. 689947.i −0.224699 0.389190i 0.731530 0.681809i \(-0.238807\pi\)
−0.956229 + 0.292619i \(0.905473\pi\)
\(62\) −613569. + 1.06273e6i −0.326958 + 0.566309i
\(63\) 2.61817e6 + 4.53480e6i 1.31918 + 2.28489i
\(64\) 262144. 0.125000
\(65\) 677196. 0.305856
\(66\) −522124. 904346.i −0.223548 0.387196i
\(67\) −1.22054e6 2.11403e6i −0.495781 0.858718i 0.504207 0.863583i \(-0.331785\pi\)
−0.999988 + 0.00486504i \(0.998451\pi\)
\(68\) −1.67838e6 −0.647305
\(69\) −6.14785e6 −2.25295
\(70\) −2.27468e6 3.93987e6i −0.792644 1.37290i
\(71\) −1.44847e6 + 2.50883e6i −0.480293 + 0.831892i −0.999744 0.0226081i \(-0.992803\pi\)
0.519451 + 0.854500i \(0.326136\pi\)
\(72\) 803509. + 1.39172e6i 0.253704 + 0.439428i
\(73\) −903424. + 1.56478e6i −0.271808 + 0.470785i −0.969325 0.245783i \(-0.920955\pi\)
0.697517 + 0.716568i \(0.254288\pi\)
\(74\) −192973. + 334239.i −0.0553586 + 0.0958839i
\(75\) −2.77789e6 −0.760328
\(76\) −460500. + 1.85721e6i −0.120332 + 0.485304i
\(77\) −2.98402e6 −0.744877
\(78\) −579934. + 1.00447e6i −0.138372 + 0.239667i
\(79\) 3.82045e6 6.61721e6i 0.871805 1.51001i 0.0116780 0.999932i \(-0.496283\pi\)
0.860127 0.510079i \(-0.170384\pi\)
\(80\) −698095. 1.20914e6i −0.152440 0.264034i
\(81\) 897919. 1.55524e6i 0.187733 0.325162i
\(82\) −2.45489e6 4.25199e6i −0.491681 0.851616i
\(83\) −2.25232e6 −0.432371 −0.216185 0.976352i \(-0.569362\pi\)
−0.216185 + 0.976352i \(0.569362\pi\)
\(84\) 7.79193e6 1.43439
\(85\) 4.46956e6 + 7.74150e6i 0.789402 + 1.36728i
\(86\) 1.23860e6 + 2.14532e6i 0.209985 + 0.363704i
\(87\) 1.36690e7 2.22546
\(88\) −915789. −0.143254
\(89\) 5.42728e6 + 9.40033e6i 0.816052 + 1.41344i 0.908570 + 0.417732i \(0.137175\pi\)
−0.0925188 + 0.995711i \(0.529492\pi\)
\(90\) 4.27952e6 7.41235e6i 0.618795 1.07178i
\(91\) 1.65720e6 + 2.87036e6i 0.230532 + 0.399293i
\(92\) −2.69578e6 + 4.66923e6i −0.360933 + 0.625155i
\(93\) −5.59709e6 + 9.69444e6i −0.721559 + 1.24978i
\(94\) −8.08712e6 −1.00426
\(95\) 9.79269e6 2.82175e6i 1.17184 0.337664i
\(96\) 2.39132e6 0.275860
\(97\) 4.56753e6 7.91120e6i 0.508137 0.880119i −0.491819 0.870698i \(-0.663668\pi\)
0.999956 0.00942116i \(-0.00299889\pi\)
\(98\) 7.83885e6 1.35773e7i 0.841320 1.45721i
\(99\) −2.80702e6 4.86191e6i −0.290752 0.503598i
\(100\) −1.21808e6 + 2.10978e6i −0.121808 + 0.210978i
\(101\) 1.64721e6 + 2.85305e6i 0.159083 + 0.275540i 0.934538 0.355863i \(-0.115813\pi\)
−0.775455 + 0.631403i \(0.782480\pi\)
\(102\) −1.53105e7 −1.42853
\(103\) 7.23955e6 0.652802 0.326401 0.945231i \(-0.394164\pi\)
0.326401 + 0.945231i \(0.394164\pi\)
\(104\) 508592. + 880907.i 0.0443356 + 0.0767916i
\(105\) −2.07501e7 3.59402e7i −1.74927 3.02983i
\(106\) 5.51701e6 0.449918
\(107\) −1.37901e7 −1.08824 −0.544120 0.839008i \(-0.683136\pi\)
−0.544120 + 0.839008i \(0.683136\pi\)
\(108\) 2.22250e6 + 3.84949e6i 0.169769 + 0.294049i
\(109\) 744061. 1.28875e6i 0.0550320 0.0953183i −0.837197 0.546901i \(-0.815807\pi\)
0.892229 + 0.451583i \(0.149141\pi\)
\(110\) 2.43876e6 + 4.22406e6i 0.174701 + 0.302591i
\(111\) −1.76033e6 + 3.04898e6i −0.122170 + 0.211604i
\(112\) 3.41670e6 5.91789e6i 0.229797 0.398019i
\(113\) 4.40429e6 0.287145 0.143572 0.989640i \(-0.454141\pi\)
0.143572 + 0.989640i \(0.454141\pi\)
\(114\) −4.20076e6 + 1.69418e7i −0.265559 + 1.07101i
\(115\) 2.87157e7 1.76066
\(116\) 5.99376e6 1.03815e7i 0.356530 0.617529i
\(117\) −3.11782e6 + 5.40022e6i −0.179970 + 0.311717i
\(118\) 2.58698e6 + 4.48079e6i 0.144946 + 0.251054i
\(119\) −2.18754e7 + 3.78893e7i −1.18999 + 2.06112i
\(120\) −6.36815e6 1.10300e7i −0.336418 0.582693i
\(121\) −1.62879e7 −0.835827
\(122\) −6.37346e6 −0.317772
\(123\) −2.23939e7 3.87874e7i −1.08508 1.87942i
\(124\) 4.90855e6 + 8.50186e6i 0.231194 + 0.400441i
\(125\) −1.36551e7 −0.625330
\(126\) 4.18907e7 1.86561
\(127\) 1.50772e7 + 2.61145e7i 0.653144 + 1.13128i 0.982356 + 0.187022i \(0.0598837\pi\)
−0.329212 + 0.944256i \(0.606783\pi\)
\(128\) 1.04858e6 1.81619e6i 0.0441942 0.0765466i
\(129\) 1.12988e7 + 1.95700e7i 0.463411 + 0.802652i
\(130\) 2.70878e6 4.69175e6i 0.108137 0.187298i
\(131\) 8.48539e6 1.46971e7i 0.329779 0.571193i −0.652689 0.757626i \(-0.726359\pi\)
0.982468 + 0.186433i \(0.0596926\pi\)
\(132\) −8.35399e6 −0.316144
\(133\) 3.59245e7 + 3.46021e7i 1.32407 + 1.27533i
\(134\) −1.95286e7 −0.701140
\(135\) 1.18371e7 2.05025e7i 0.414074 0.717198i
\(136\) −6.71351e6 + 1.16281e7i −0.228857 + 0.396392i
\(137\) −1.87704e7 3.25113e7i −0.623665 1.08022i −0.988797 0.149264i \(-0.952310\pi\)
0.365132 0.930956i \(-0.381024\pi\)
\(138\) −2.45914e7 + 4.25935e7i −0.796538 + 1.37964i
\(139\) 2.90112e7 + 5.02488e7i 0.916249 + 1.58699i 0.805063 + 0.593189i \(0.202132\pi\)
0.111186 + 0.993800i \(0.464535\pi\)
\(140\) −3.63949e7 −1.12097
\(141\) −7.37722e7 −2.21629
\(142\) 1.15878e7 + 2.00706e7i 0.339618 + 0.588236i
\(143\) −1.77674e6 3.07741e6i −0.0508100 0.0880054i
\(144\) 1.28561e7 0.358791
\(145\) −6.38461e7 −1.73919
\(146\) 7.22739e6 + 1.25182e7i 0.192197 + 0.332895i
\(147\) 7.15074e7 1.23854e8i 1.85669 3.21589i
\(148\) 1.54378e6 + 2.67391e6i 0.0391444 + 0.0678001i
\(149\) 7.97384e6 1.38111e7i 0.197477 0.342039i −0.750233 0.661174i \(-0.770059\pi\)
0.947710 + 0.319134i \(0.103392\pi\)
\(150\) −1.11116e7 + 1.92458e7i −0.268817 + 0.465604i
\(151\) −1.69234e7 −0.400008 −0.200004 0.979795i \(-0.564096\pi\)
−0.200004 + 0.979795i \(0.564096\pi\)
\(152\) 1.10251e7 + 1.06193e7i 0.254643 + 0.245269i
\(153\) −8.23115e7 −1.85798
\(154\) −1.19361e7 + 2.06739e7i −0.263354 + 0.456142i
\(155\) 2.61432e7 4.52813e7i 0.563893 0.976692i
\(156\) 4.63947e6 + 8.03580e6i 0.0978435 + 0.169470i
\(157\) 2.39243e7 4.14381e7i 0.493390 0.854576i −0.506581 0.862192i \(-0.669091\pi\)
0.999971 + 0.00761638i \(0.00242439\pi\)
\(158\) −3.05636e7 5.29377e7i −0.616459 1.06774i
\(159\) 5.03272e7 0.992916
\(160\) −1.11695e7 −0.215583
\(161\) 7.02718e7 + 1.21714e8i 1.32706 + 2.29853i
\(162\) −7.18335e6 1.24419e7i −0.132747 0.229925i
\(163\) 3.48181e6 0.0629722 0.0314861 0.999504i \(-0.489976\pi\)
0.0314861 + 0.999504i \(0.489976\pi\)
\(164\) −3.92782e7 −0.695341
\(165\) 2.22469e7 + 3.85327e7i 0.385545 + 0.667783i
\(166\) −9.00927e6 + 1.56045e7i −0.152866 + 0.264772i
\(167\) −4.56446e7 7.90588e7i −0.758372 1.31354i −0.943681 0.330858i \(-0.892662\pi\)
0.185309 0.982680i \(-0.440671\pi\)
\(168\) 3.11677e7 5.39841e7i 0.507134 0.878382i
\(169\) 2.94008e7 5.09237e7i 0.468550 0.811552i
\(170\) 7.15129e7 1.11638
\(171\) −2.25840e7 + 9.10820e7i −0.345393 + 1.39298i
\(172\) 1.98176e7 0.296963
\(173\) −3.48554e7 + 6.03713e7i −0.511810 + 0.886481i 0.488096 + 0.872790i \(0.337691\pi\)
−0.999906 + 0.0136911i \(0.995642\pi\)
\(174\) 5.46762e7 9.47019e7i 0.786821 1.36281i
\(175\) 3.17522e7 + 5.49964e7i 0.447858 + 0.775713i
\(176\) −3.66316e6 + 6.34477e6i −0.0506478 + 0.0877246i
\(177\) 2.35989e7 + 4.08746e7i 0.319879 + 0.554047i
\(178\) 8.68366e7 1.15407
\(179\) 8.39321e6 0.109381 0.0546905 0.998503i \(-0.482583\pi\)
0.0546905 + 0.998503i \(0.482583\pi\)
\(180\) −3.42362e7 5.92988e7i −0.437554 0.757866i
\(181\) −4.32127e7 7.48465e7i −0.541671 0.938203i −0.998808 0.0488061i \(-0.984458\pi\)
0.457137 0.889396i \(-0.348875\pi\)
\(182\) 2.65153e7 0.326022
\(183\) −5.81399e7 −0.701286
\(184\) 2.15662e7 + 3.73538e7i 0.255218 + 0.442051i
\(185\) 8.22225e6 1.42414e7i 0.0954750 0.165367i
\(186\) 4.47767e7 + 7.75555e7i 0.510219 + 0.883725i
\(187\) 2.34534e7 4.06224e7i 0.262277 0.454277i
\(188\) −3.23485e7 + 5.60292e7i −0.355060 + 0.614981i
\(189\) 1.15869e8 1.24840
\(190\) 1.96211e7 7.91327e7i 0.207533 0.836987i
\(191\) 2.66878e7 0.277137 0.138569 0.990353i \(-0.455750\pi\)
0.138569 + 0.990353i \(0.455750\pi\)
\(192\) 9.56530e6 1.65676e7i 0.0975314 0.168929i
\(193\) −6.56992e6 + 1.13794e7i −0.0657824 + 0.113938i −0.897041 0.441948i \(-0.854288\pi\)
0.831258 + 0.555886i \(0.187621\pi\)
\(194\) −3.65403e7 6.32896e7i −0.359307 0.622338i
\(195\) 2.47100e7 4.27990e7i 0.238645 0.413345i
\(196\) −6.27108e7 1.08618e8i −0.594903 1.03040i
\(197\) 2.30171e6 0.0214496 0.0107248 0.999942i \(-0.496586\pi\)
0.0107248 + 0.999942i \(0.496586\pi\)
\(198\) −4.49124e7 −0.411186
\(199\) 6.94129e7 + 1.20227e8i 0.624388 + 1.08147i 0.988659 + 0.150179i \(0.0479849\pi\)
−0.364271 + 0.931293i \(0.618682\pi\)
\(200\) 9.74466e6 + 1.68783e7i 0.0861315 + 0.149184i
\(201\) −1.78144e8 −1.54733
\(202\) 2.63554e7 0.224977
\(203\) −1.56241e8 2.70618e8i −1.31087 2.27050i
\(204\) −6.12419e7 + 1.06074e8i −0.505060 + 0.874790i
\(205\) 1.04599e8 + 1.81170e8i 0.847984 + 1.46875i
\(206\) 2.89582e7 5.01571e7i 0.230800 0.399758i
\(207\) −1.32207e8 + 2.28990e8i −1.03600 + 1.79440i
\(208\) 8.13747e6 0.0627001
\(209\) −3.85159e7 3.70980e7i −0.291829 0.281086i
\(210\) −3.32001e8 −2.47384
\(211\) −3.26383e7 + 5.65311e7i −0.239187 + 0.414285i −0.960481 0.278344i \(-0.910214\pi\)
0.721294 + 0.692629i \(0.243548\pi\)
\(212\) 2.20680e7 3.82230e7i 0.159070 0.275517i
\(213\) 1.05706e8 + 1.83088e8i 0.749498 + 1.29817i
\(214\) −5.51604e7 + 9.55407e7i −0.384751 + 0.666408i
\(215\) −5.27748e7 9.14086e7i −0.362153 0.627267i
\(216\) 3.55600e7 0.240090
\(217\) 2.55906e8 1.70009
\(218\) −5.95249e6 1.03100e7i −0.0389135 0.0674002i
\(219\) 6.59296e7 + 1.14193e8i 0.424156 + 0.734660i
\(220\) 3.90202e7 0.247065
\(221\) −5.21002e7 −0.324688
\(222\) 1.40827e7 + 2.43919e7i 0.0863872 + 0.149627i
\(223\) 1.15422e8 1.99917e8i 0.696984 1.20721i −0.272523 0.962149i \(-0.587858\pi\)
0.969507 0.245063i \(-0.0788086\pi\)
\(224\) −2.73336e7 4.73431e7i −0.162491 0.281442i
\(225\) −5.97376e7 + 1.03469e8i −0.349630 + 0.605577i
\(226\) 1.76171e7 3.05138e7i 0.101521 0.175840i
\(227\) −9.31373e7 −0.528486 −0.264243 0.964456i \(-0.585122\pi\)
−0.264243 + 0.964456i \(0.585122\pi\)
\(228\) 1.00573e8 + 9.68711e7i 0.561967 + 0.541280i
\(229\) −1.77863e8 −0.978728 −0.489364 0.872080i \(-0.662771\pi\)
−0.489364 + 0.872080i \(0.662771\pi\)
\(230\) 1.14863e8 1.98948e8i 0.622489 1.07818i
\(231\) −1.08883e8 + 1.88591e8i −0.581191 + 1.00665i
\(232\) −4.79501e7 8.30520e7i −0.252105 0.436659i
\(233\) 9.33717e7 1.61725e8i 0.483581 0.837588i −0.516241 0.856443i \(-0.672669\pi\)
0.999822 + 0.0188559i \(0.00600237\pi\)
\(234\) 2.49425e7 + 4.32017e7i 0.127258 + 0.220417i
\(235\) 3.44579e8 1.73201
\(236\) 4.13918e7 0.204985
\(237\) −2.78807e8 4.82907e8i −1.36045 2.35637i
\(238\) 1.75003e8 + 3.03115e8i 0.841448 + 1.45743i
\(239\) −2.33729e8 −1.10744 −0.553720 0.832703i \(-0.686792\pi\)
−0.553720 + 0.832703i \(0.686792\pi\)
\(240\) −1.01890e8 −0.475766
\(241\) 3.99849e7 + 6.92558e7i 0.184008 + 0.318711i 0.943242 0.332107i \(-0.107760\pi\)
−0.759234 + 0.650818i \(0.774426\pi\)
\(242\) −6.51516e7 + 1.12846e8i −0.295509 + 0.511837i
\(243\) −1.41475e8 2.45042e8i −0.632495 1.09551i
\(244\) −2.54938e7 + 4.41566e7i −0.112349 + 0.194595i
\(245\) −3.34000e8 + 5.78506e8i −1.45099 + 2.51320i
\(246\) −3.58303e8 −1.53454
\(247\) −1.42948e7 + 5.76516e7i −0.0603587 + 0.243429i
\(248\) 7.85368e7 0.326958
\(249\) −8.21842e7 + 1.42347e8i −0.337358 + 0.584321i
\(250\) −5.46203e7 + 9.46052e7i −0.221088 + 0.382935i
\(251\) −7.90336e7 1.36890e8i −0.315467 0.546404i 0.664070 0.747671i \(-0.268828\pi\)
−0.979537 + 0.201266i \(0.935494\pi\)
\(252\) 1.67563e8 2.90227e8i 0.659592 1.14245i
\(253\) −7.53407e7 1.30494e8i −0.292488 0.506604i
\(254\) 2.41236e8 0.923685
\(255\) 6.52354e8 2.46373
\(256\) −8.38861e6 1.45295e7i −0.0312500 0.0541266i
\(257\) −2.01771e7 3.49478e7i −0.0741470 0.128426i 0.826568 0.562837i \(-0.190290\pi\)
−0.900715 + 0.434411i \(0.856957\pi\)
\(258\) 1.80780e8 0.655362
\(259\) 8.04846e7 0.287848
\(260\) −2.16703e7 3.75340e7i −0.0764641 0.132440i
\(261\) 2.93948e8 5.09133e8i 1.02336 1.77251i
\(262\) −6.78831e7 1.17577e8i −0.233189 0.403895i
\(263\) 6.99503e7 1.21157e8i 0.237107 0.410681i −0.722776 0.691082i \(-0.757134\pi\)
0.959883 + 0.280401i \(0.0904675\pi\)
\(264\) −3.34160e7 + 5.78781e7i −0.111774 + 0.193598i
\(265\) −2.35071e8 −0.775957
\(266\) 3.83428e8 1.10484e8i 1.24910 0.359927i
\(267\) 7.92139e8 2.54690
\(268\) −7.81145e7 + 1.35298e8i −0.247890 + 0.429359i
\(269\) −2.97557e7 + 5.15384e7i −0.0932046 + 0.161435i −0.908858 0.417106i \(-0.863044\pi\)
0.815653 + 0.578541i \(0.196378\pi\)
\(270\) −9.46971e7 1.64020e8i −0.292795 0.507136i
\(271\) −1.02780e8 + 1.78021e8i −0.313702 + 0.543348i −0.979161 0.203087i \(-0.934903\pi\)
0.665459 + 0.746435i \(0.268236\pi\)
\(272\) 5.37081e7 + 9.30252e7i 0.161826 + 0.280291i
\(273\) 2.41877e8 0.719491
\(274\) −3.00326e8 −0.881996
\(275\) −3.40426e7 5.89635e7i −0.0987093 0.170969i
\(276\) 1.96731e8 + 3.40748e8i 0.563237 + 0.975555i
\(277\) −3.76577e7 −0.106457 −0.0532286 0.998582i \(-0.516951\pi\)
−0.0532286 + 0.998582i \(0.516951\pi\)
\(278\) 4.64179e8 1.29577
\(279\) 2.40727e8 + 4.16951e8i 0.663605 + 1.14940i
\(280\) −1.45580e8 + 2.52152e8i −0.396322 + 0.686450i
\(281\) −1.54846e8 2.68202e8i −0.416321 0.721090i 0.579245 0.815154i \(-0.303348\pi\)
−0.995566 + 0.0940638i \(0.970014\pi\)
\(282\) −2.95089e8 + 5.11109e8i −0.783575 + 1.35719i
\(283\) 2.10551e8 3.64686e8i 0.552212 0.956459i −0.445903 0.895081i \(-0.647117\pi\)
0.998115 0.0613776i \(-0.0195494\pi\)
\(284\) 1.85405e8 0.480293
\(285\) 1.78988e8 7.21863e8i 0.458000 1.84713i
\(286\) −2.84279e7 −0.0718561
\(287\) −5.11939e8 + 8.86704e8i −1.27830 + 2.21407i
\(288\) 5.14246e7 8.90700e7i 0.126852 0.219714i
\(289\) −1.38697e8 2.40231e8i −0.338007 0.585444i
\(290\) −2.55384e8 + 4.42338e8i −0.614895 + 1.06503i
\(291\) −3.33327e8 5.77339e8i −0.792948 1.37343i
\(292\) 1.15638e8 0.271808
\(293\) 1.58161e8 0.367336 0.183668 0.982988i \(-0.441203\pi\)
0.183668 + 0.982988i \(0.441203\pi\)
\(294\) −5.72059e8 9.90836e8i −1.31288 2.27398i
\(295\) −1.10227e8 1.90919e8i −0.249984 0.432984i
\(296\) 2.47005e7 0.0553586
\(297\) −1.24227e8 −0.275150
\(298\) −6.37907e7 1.10489e8i −0.139637 0.241858i
\(299\) −8.36824e7 + 1.44942e8i −0.181044 + 0.313578i
\(300\) 8.88926e7 + 1.53966e8i 0.190082 + 0.329232i
\(301\) 2.58296e8 4.47383e8i 0.545928 0.945576i
\(302\) −6.76937e7 + 1.17249e8i −0.141424 + 0.244954i
\(303\) 2.40418e8 0.496499
\(304\) 1.17673e8 3.39073e7i 0.240226 0.0692207i
\(305\) 2.71563e8 0.548050
\(306\) −3.29246e8 + 5.70271e8i −0.656895 + 1.13777i
\(307\) −4.90351e8 + 8.49312e8i −0.967214 + 1.67526i −0.263668 + 0.964613i \(0.584932\pi\)
−0.703546 + 0.710650i \(0.748401\pi\)
\(308\) 9.54887e7 + 1.65391e8i 0.186219 + 0.322541i
\(309\) 2.64162e8 4.57542e8i 0.509349 0.882219i
\(310\) −2.09145e8 3.62250e8i −0.398733 0.690626i
\(311\) 1.82338e8 0.343729 0.171865 0.985121i \(-0.445021\pi\)
0.171865 + 0.985121i \(0.445021\pi\)
\(312\) 7.42315e7 0.138372
\(313\) −2.65171e8 4.59290e8i −0.488788 0.846606i 0.511129 0.859504i \(-0.329228\pi\)
−0.999917 + 0.0128982i \(0.995894\pi\)
\(314\) −1.91394e8 3.31504e8i −0.348879 0.604276i
\(315\) −1.78489e9 −3.21755
\(316\) −4.89017e8 −0.871805
\(317\) 4.26094e8 + 7.38016e8i 0.751273 + 1.30124i 0.947206 + 0.320626i \(0.103893\pi\)
−0.195933 + 0.980617i \(0.562774\pi\)
\(318\) 2.01309e8 3.48677e8i 0.351049 0.608034i
\(319\) 1.67512e8 + 2.90139e8i 0.288920 + 0.500424i
\(320\) −4.46781e7 + 7.73847e7i −0.0762201 + 0.132017i
\(321\) −5.03183e8 + 8.71539e8i −0.849100 + 1.47068i
\(322\) 1.12435e9 1.87675
\(323\) −7.53403e8 + 2.17092e8i −1.24399 + 0.358455i
\(324\) −1.14934e8 −0.187733
\(325\) −3.78117e7 + 6.54918e7i −0.0610991 + 0.105827i
\(326\) 1.39273e7 2.41227e7i 0.0222640 0.0385624i
\(327\) −5.42996e7 9.40497e7i −0.0858776 0.148744i
\(328\) −1.57113e8 + 2.72127e8i −0.245840 + 0.425808i
\(329\) 8.43239e8 + 1.46053e9i 1.30546 + 2.26113i
\(330\) 3.55950e8 0.545243
\(331\) 5.48911e8 0.831962 0.415981 0.909373i \(-0.363438\pi\)
0.415981 + 0.909373i \(0.363438\pi\)
\(332\) 7.20742e7 + 1.24836e8i 0.108093 + 0.187222i
\(333\) 7.57106e7 + 1.31135e8i 0.112357 + 0.194609i
\(334\) −7.30314e8 −1.07250
\(335\) 8.32082e8 1.20923
\(336\) −2.49342e8 4.31873e8i −0.358598 0.621110i
\(337\) −3.82231e7 + 6.62043e7i −0.0544028 + 0.0942284i −0.891944 0.452145i \(-0.850659\pi\)
0.837541 + 0.546374i \(0.183992\pi\)
\(338\) −2.35206e8 4.07389e8i −0.331315 0.573854i
\(339\) 1.60707e8 2.78352e8i 0.224045 0.388057i
\(340\) 2.86052e8 4.95456e8i 0.394701 0.683642i
\(341\) −2.74365e8 −0.374704
\(342\) 5.40699e8 + 5.20794e8i 0.730910 + 0.704004i
\(343\) −1.89548e9 −2.53624
\(344\) 7.92706e7 1.37301e8i 0.104992 0.181852i
\(345\) 1.04780e9 1.81484e9i 1.37376 2.37942i
\(346\) 2.78843e8 + 4.82971e8i 0.361904 + 0.626837i
\(347\) −3.27090e8 + 5.66537e8i −0.420256 + 0.727905i −0.995964 0.0897500i \(-0.971393\pi\)
0.575708 + 0.817655i \(0.304727\pi\)
\(348\) −4.37409e8 7.57615e8i −0.556366 0.963655i
\(349\) 1.11203e9 1.40032 0.700158 0.713988i \(-0.253113\pi\)
0.700158 + 0.713988i \(0.253113\pi\)
\(350\) 5.08035e8 0.633367
\(351\) 6.89909e7 + 1.19496e8i 0.0851563 + 0.147495i
\(352\) 2.93052e7 + 5.07582e7i 0.0358134 + 0.0620307i
\(353\) −2.60979e8 −0.315787 −0.157894 0.987456i \(-0.550470\pi\)
−0.157894 + 0.987456i \(0.550470\pi\)
\(354\) 3.77583e8 0.452378
\(355\) −4.93736e8 8.55176e8i −0.585728 1.01451i
\(356\) 3.47346e8 6.01621e8i 0.408026 0.706721i
\(357\) 1.59641e9 + 2.76507e9i 1.85698 + 3.21638i
\(358\) 3.35728e7 5.81498e7i 0.0386721 0.0669820i
\(359\) 2.78100e8 4.81683e8i 0.317227 0.549453i −0.662682 0.748901i \(-0.730582\pi\)
0.979908 + 0.199448i \(0.0639151\pi\)
\(360\) −5.47779e8 −0.618795
\(361\) 3.35105e7 + 8.93243e8i 0.0374892 + 0.999297i
\(362\) −6.91403e8 −0.766039
\(363\) −5.94325e8 + 1.02940e9i −0.652155 + 1.12957i
\(364\) 1.06061e8 1.83703e8i 0.115266 0.199647i
\(365\) −3.07947e8 5.33380e8i −0.331475 0.574132i
\(366\) −2.32559e8 + 4.02805e8i −0.247942 + 0.429448i
\(367\) −6.41343e8 1.11084e9i −0.677266 1.17306i −0.975801 0.218660i \(-0.929831\pi\)
0.298535 0.954399i \(-0.403502\pi\)
\(368\) 3.45060e8 0.360933
\(369\) −1.92629e9 −1.99586
\(370\) −6.57780e7 1.13931e8i −0.0675110 0.116932i
\(371\) −5.75255e8 9.96371e8i −0.584860 1.01301i
\(372\) 7.16427e8 0.721559
\(373\) −1.83560e8 −0.183146 −0.0915729 0.995798i \(-0.529189\pi\)
−0.0915729 + 0.995798i \(0.529189\pi\)
\(374\) −1.87627e8 3.24979e8i −0.185458 0.321222i
\(375\) −4.98257e8 + 8.63006e8i −0.487914 + 0.845093i
\(376\) 2.58788e8 + 4.48234e8i 0.251065 + 0.434858i
\(377\) 1.86058e8 3.22263e8i 0.178836 0.309753i
\(378\) 4.63477e8 8.02766e8i 0.441375 0.764483i
\(379\) 9.57969e8 0.903887 0.451944 0.892047i \(-0.350731\pi\)
0.451944 + 0.892047i \(0.350731\pi\)
\(380\) −4.69763e8 4.52470e8i −0.439174 0.423007i
\(381\) 2.20060e9 2.03846
\(382\) 1.06751e8 1.84898e8i 0.0979829 0.169711i
\(383\) 5.79600e8 1.00390e9i 0.527148 0.913048i −0.472351 0.881410i \(-0.656595\pi\)
0.999499 0.0316371i \(-0.0100721\pi\)
\(384\) −7.65224e7 1.32541e8i −0.0689651 0.119451i
\(385\) 5.08577e8 8.80881e8i 0.454197 0.786692i
\(386\) 5.25594e7 + 9.10355e7i 0.0465152 + 0.0805666i
\(387\) 9.71903e8 0.852382
\(388\) −5.84644e8 −0.508137
\(389\) −6.83441e8 1.18376e9i −0.588678 1.01962i −0.994406 0.105626i \(-0.966315\pi\)
0.405728 0.913994i \(-0.367018\pi\)
\(390\) −1.97680e8 3.42392e8i −0.168747 0.292279i
\(391\) −2.20925e9 −1.86907
\(392\) −1.00337e9 −0.841320
\(393\) −6.19242e8 1.07256e9i −0.514620 0.891348i
\(394\) 9.20683e6 1.59467e7i 0.00758356 0.0131351i
\(395\) 1.30226e9 + 2.25559e9i 1.06319 + 1.84149i
\(396\) −1.79650e8 + 3.11162e8i −0.145376 + 0.251799i
\(397\) 7.10196e8 1.23009e9i 0.569654 0.986670i −0.426946 0.904277i \(-0.640411\pi\)
0.996600 0.0823927i \(-0.0262562\pi\)
\(398\) 1.11061e9 0.883018
\(399\) 3.49770e9 1.00786e9i 2.75662 0.794316i
\(400\) 1.55915e8 0.121808
\(401\) −6.18701e8 + 1.07162e9i −0.479154 + 0.829920i −0.999714 0.0239054i \(-0.992390\pi\)
0.520560 + 0.853825i \(0.325723\pi\)
\(402\) −7.12574e8 + 1.23421e9i −0.547065 + 0.947545i
\(403\) 1.52371e8 + 2.63915e8i 0.115967 + 0.200861i
\(404\) 1.05421e8 1.82595e8i 0.0795415 0.137770i
\(405\) 3.06071e8 + 5.30130e8i 0.228944 + 0.396543i
\(406\) −2.49986e9 −1.85385
\(407\) −8.62902e7 −0.0634426
\(408\) 4.89935e8 + 8.48592e8i 0.357131 + 0.618570i
\(409\) −5.02157e8 8.69762e8i −0.362918 0.628592i 0.625522 0.780207i \(-0.284886\pi\)
−0.988440 + 0.151615i \(0.951553\pi\)
\(410\) 1.67358e9 1.19923
\(411\) −2.73963e9 −1.94646
\(412\) −2.31666e8 4.01257e8i −0.163200 0.282672i
\(413\) 5.39486e8 9.34418e8i 0.376839 0.652703i
\(414\) 1.05766e9 + 1.83192e9i 0.732561 + 1.26883i
\(415\) 3.83870e8 6.64882e8i 0.263643 0.456643i
\(416\) 3.25499e7 5.63781e7i 0.0221678 0.0383958i
\(417\) 4.23432e9 2.85962
\(418\) −4.11086e8 + 1.18454e8i −0.275306 + 0.0793289i
\(419\) 2.28526e9 1.51770 0.758850 0.651266i \(-0.225762\pi\)
0.758850 + 0.651266i \(0.225762\pi\)
\(420\) −1.32801e9 + 2.30017e9i −0.874636 + 1.51491i
\(421\) 7.89145e7 1.36684e8i 0.0515430 0.0892750i −0.839103 0.543973i \(-0.816919\pi\)
0.890646 + 0.454698i \(0.150253\pi\)
\(422\) 2.61106e8 + 4.52249e8i 0.169131 + 0.292944i
\(423\) −1.58644e9 + 2.74780e9i −1.01914 + 1.76520i
\(424\) −1.76544e8 3.05784e8i −0.112479 0.194820i
\(425\) −9.98244e8 −0.630777
\(426\) 1.69129e9 1.05995
\(427\) 6.64556e8 + 1.15105e9i 0.413080 + 0.715476i
\(428\) 4.41283e8 + 7.64325e8i 0.272060 + 0.471221i
\(429\) −2.59325e8 −0.158578
\(430\) −8.44397e8 −0.512161
\(431\) −1.12746e9 1.95281e9i −0.678312 1.17487i −0.975489 0.220048i \(-0.929379\pi\)
0.297177 0.954822i \(-0.403955\pi\)
\(432\) 1.42240e8 2.46367e8i 0.0848846 0.147024i
\(433\) 5.25465e8 + 9.10132e8i 0.311054 + 0.538762i 0.978591 0.205815i \(-0.0659846\pi\)
−0.667537 + 0.744577i \(0.732651\pi\)
\(434\) 1.02362e9 1.77297e9i 0.601071 1.04109i
\(435\) −2.32966e9 + 4.03509e9i −1.35700 + 2.35040i
\(436\) −9.52398e7 −0.0550320
\(437\) −6.06156e8 + 2.44465e9i −0.347455 + 1.40130i
\(438\) 1.05487e9 0.599848
\(439\) 8.75455e8 1.51633e9i 0.493865 0.855399i −0.506110 0.862469i \(-0.668917\pi\)
0.999975 + 0.00706990i \(0.00225044\pi\)
\(440\) 1.56081e8 2.70340e8i 0.0873505 0.151296i
\(441\) −3.07548e9 5.32689e9i −1.70757 2.95760i
\(442\) −2.08401e8 + 3.60961e8i −0.114795 + 0.198830i
\(443\) −8.07380e8 1.39842e9i −0.441230 0.764233i 0.556551 0.830814i \(-0.312124\pi\)
−0.997781 + 0.0665805i \(0.978791\pi\)
\(444\) 2.25323e8 0.122170
\(445\) −3.69996e9 −1.99039
\(446\) −9.23379e8 1.59934e9i −0.492842 0.853628i
\(447\) −5.81910e8 1.00790e9i −0.308162 0.533753i
\(448\) −4.37337e8 −0.229797
\(449\) −2.27952e9 −1.18845 −0.594224 0.804299i \(-0.702541\pi\)
−0.594224 + 0.804299i \(0.702541\pi\)
\(450\) 4.77901e8 + 8.27748e8i 0.247226 + 0.428208i
\(451\) 5.48867e8 9.50665e8i 0.281740 0.487989i
\(452\) −1.40937e8 2.44110e8i −0.0717862 0.124337i
\(453\) −6.17514e8 + 1.06957e9i −0.312107 + 0.540585i
\(454\) −3.72549e8 + 6.45274e8i −0.186848 + 0.323630i
\(455\) −1.12977e9 −0.562278
\(456\) 1.07344e9 3.09309e8i 0.530150 0.152762i
\(457\) −1.62189e9 −0.794906 −0.397453 0.917622i \(-0.630106\pi\)
−0.397453 + 0.917622i \(0.630106\pi\)
\(458\) −7.11453e8 + 1.23227e9i −0.346033 + 0.599346i
\(459\) −9.10693e8 + 1.57737e9i −0.439570 + 0.761357i
\(460\) −9.18902e8 1.59158e9i −0.440166 0.762390i
\(461\) −1.50991e9 + 2.61524e9i −0.717792 + 1.24325i 0.244081 + 0.969755i \(0.421514\pi\)
−0.961873 + 0.273497i \(0.911820\pi\)
\(462\) 8.71065e8 + 1.50873e9i 0.410964 + 0.711810i
\(463\) −1.45390e8 −0.0680772 −0.0340386 0.999421i \(-0.510837\pi\)
−0.0340386 + 0.999421i \(0.510837\pi\)
\(464\) −7.67202e8 −0.356530
\(465\) −1.90786e9 3.30451e9i −0.879957 1.52413i
\(466\) −7.46974e8 1.29380e9i −0.341944 0.592264i
\(467\) 4.27348e9 1.94166 0.970830 0.239770i \(-0.0770721\pi\)
0.970830 + 0.239770i \(0.0770721\pi\)
\(468\) 3.99080e8 0.179970
\(469\) 2.03624e9 + 3.52686e9i 0.911430 + 1.57864i
\(470\) 1.37831e9 2.38731e9i 0.612359 1.06064i
\(471\) −1.74593e9 3.02404e9i −0.769935 1.33357i
\(472\) 1.65567e8 2.86771e8i 0.0724731 0.125527i
\(473\) −2.76928e8 + 4.79654e8i −0.120324 + 0.208408i
\(474\) −4.46090e9 −1.92397
\(475\) −2.73890e8 + 1.10461e9i −0.117260 + 0.472913i
\(476\) 2.80005e9 1.18999
\(477\) 1.08227e9 1.87454e9i 0.456584 0.790826i
\(478\) −9.34917e8 + 1.61932e9i −0.391539 + 0.678166i
\(479\) −4.75468e8 8.23535e8i −0.197673 0.342379i 0.750101 0.661324i \(-0.230005\pi\)
−0.947773 + 0.318944i \(0.896672\pi\)
\(480\) −4.07561e8 + 7.05917e8i −0.168209 + 0.291346i
\(481\) 4.79221e7 + 8.30035e7i 0.0196349 + 0.0340086i
\(482\) 6.39758e8 0.260226
\(483\) 1.02565e10 4.14176
\(484\) 5.21213e8 + 9.02767e8i 0.208957 + 0.361924i
\(485\) 1.55692e9 + 2.69666e9i 0.619684 + 1.07332i
\(486\) −2.26360e9 −0.894484
\(487\) 3.20901e9 1.25898 0.629491 0.777008i \(-0.283263\pi\)
0.629491 + 0.777008i \(0.283263\pi\)
\(488\) 2.03951e8 + 3.53253e8i 0.0794430 + 0.137599i
\(489\) 1.27047e8 2.20052e8i 0.0491341 0.0851028i
\(490\) 2.67200e9 + 4.62805e9i 1.02601 + 1.77710i
\(491\) −1.35999e9 + 2.35558e9i −0.518503 + 0.898074i 0.481266 + 0.876575i \(0.340177\pi\)
−0.999769 + 0.0214990i \(0.993156\pi\)
\(492\) −1.43321e9 + 2.48239e9i −0.542541 + 0.939708i
\(493\) 4.91201e9 1.84627
\(494\) 3.42243e8 + 3.29644e8i 0.127729 + 0.123027i
\(495\) 1.91364e9 0.709157
\(496\) 3.14147e8 5.44119e8i 0.115597 0.200220i
\(497\) 2.41650e9 4.18550e9i 0.882957 1.52933i
\(498\) 6.57474e8 + 1.13878e9i 0.238548 + 0.413177i
\(499\) 1.56901e8 2.71761e8i 0.0565293 0.0979117i −0.836376 0.548156i \(-0.815330\pi\)
0.892905 + 0.450245i \(0.148663\pi\)
\(500\) 4.36963e8 + 7.56842e8i 0.156333 + 0.270776i
\(501\) −6.66206e9 −2.36688
\(502\) −1.26454e9 −0.446137
\(503\) −1.89684e9 3.28543e9i −0.664574 1.15108i −0.979401 0.201927i \(-0.935280\pi\)
0.314827 0.949149i \(-0.398054\pi\)
\(504\) −1.34050e9 2.32182e9i −0.466402 0.807832i
\(505\) −1.12296e9 −0.388011
\(506\) −1.20545e9 −0.413640
\(507\) −2.14559e9 3.71628e9i −0.731173 1.26643i
\(508\) 9.64943e8 1.67133e9i 0.326572 0.565639i
\(509\) 2.15764e8 + 3.73714e8i 0.0725214 + 0.125611i 0.900006 0.435878i \(-0.143562\pi\)
−0.827484 + 0.561489i \(0.810229\pi\)
\(510\) 2.60941e9 4.51964e9i 0.871059 1.50872i
\(511\) 1.50719e9 2.61053e9i 0.499684 0.865477i
\(512\) −1.34218e8 −0.0441942
\(513\) 1.49557e9 + 1.44051e9i 0.489098 + 0.471093i
\(514\) −3.22834e8 −0.104860
\(515\) −1.23386e9 + 2.13711e9i −0.398053 + 0.689448i
\(516\) 7.23120e8 1.25248e9i 0.231706 0.401326i
\(517\) −9.04064e8 1.56589e9i −0.287728 0.498360i
\(518\) 3.21938e8 5.57613e8i 0.101770 0.176270i
\(519\) 2.54366e9 + 4.40575e9i 0.798680 + 1.38336i
\(520\) −3.46724e8 −0.108137
\(521\) −1.87361e9 −0.580427 −0.290214 0.956962i \(-0.593726\pi\)
−0.290214 + 0.956962i \(0.593726\pi\)
\(522\) −2.35158e9 4.07306e9i −0.723625 1.25336i
\(523\) 1.23005e9 + 2.13052e9i 0.375983 + 0.651222i 0.990474 0.137702i \(-0.0439718\pi\)
−0.614491 + 0.788924i \(0.710638\pi\)
\(524\) −1.08613e9 −0.329779
\(525\) 4.63439e9 1.39777
\(526\) −5.59602e8 9.69259e8i −0.167660 0.290395i
\(527\) −2.01133e9 + 3.48373e9i −0.598613 + 1.03683i
\(528\) 2.67328e8 + 4.63025e8i 0.0790361 + 0.136894i
\(529\) −1.84604e9 + 3.19743e9i −0.542183 + 0.939089i
\(530\) −9.40282e8 + 1.62862e9i −0.274342 + 0.475175i
\(531\) 2.02995e9 0.588375
\(532\) 7.68256e8 3.09840e9i 0.221215 0.892170i
\(533\) −1.21927e9 −0.348784
\(534\) 3.16855e9 5.48810e9i 0.900465 1.55965i
\(535\) 2.35029e9 4.07083e9i 0.663566 1.14933i
\(536\) 6.24916e8 + 1.08239e9i 0.175285 + 0.303603i
\(537\) 3.06257e8 5.30453e8i 0.0853447 0.147821i
\(538\) 2.38046e8 + 4.12307e8i 0.0659056 + 0.114152i
\(539\) 3.50524e9 0.964178
\(540\) −1.51515e9 −0.414074
\(541\) 2.50067e9 + 4.33129e9i 0.678995 + 1.17605i 0.975284 + 0.220955i \(0.0709174\pi\)
−0.296289 + 0.955098i \(0.595749\pi\)
\(542\) 8.22243e8 + 1.42417e9i 0.221821 + 0.384205i
\(543\) −6.30710e9 −1.69056
\(544\) 8.59330e8 0.228857
\(545\) 2.53626e8 + 4.39292e8i 0.0671128 + 0.116243i
\(546\) 9.67509e8 1.67577e9i 0.254379 0.440597i
\(547\) −1.25370e9 2.17148e9i −0.327521 0.567283i 0.654498 0.756063i \(-0.272880\pi\)
−0.982019 + 0.188781i \(0.939547\pi\)
\(548\) −1.20131e9 + 2.08072e9i −0.311833 + 0.540110i
\(549\) −1.25028e9 + 2.16554e9i −0.322480 + 0.558552i
\(550\) −5.44681e8 −0.139596
\(551\) 1.34772e9 5.43540e9i 0.343217 1.38421i
\(552\) 3.14770e9 0.796538
\(553\) −6.37369e9 + 1.10396e10i −1.60270 + 2.77596i
\(554\) −1.50631e8 + 2.60900e8i −0.0376383 + 0.0651914i
\(555\) −6.00039e8 1.03930e9i −0.148989 0.258056i
\(556\) 1.85671e9 3.21592e9i 0.458124 0.793495i
\(557\) −1.48401e9 2.57039e9i −0.363869 0.630239i 0.624725 0.780845i \(-0.285211\pi\)
−0.988594 + 0.150606i \(0.951878\pi\)
\(558\) 3.85163e9 0.938479
\(559\) 6.15179e8 0.148957
\(560\) 1.16464e9 + 2.01721e9i 0.280242 + 0.485393i
\(561\) −1.71157e9 2.96452e9i −0.409283 0.708899i
\(562\) −2.47754e9 −0.588767
\(563\) −8.36370e8 −0.197524 −0.0987619 0.995111i \(-0.531488\pi\)
−0.0987619 + 0.995111i \(0.531488\pi\)
\(564\) 2.36071e9 + 4.08887e9i 0.554071 + 0.959680i
\(565\) −7.50637e8 + 1.30014e9i −0.175090 + 0.303264i
\(566\) −1.68441e9 2.91749e9i −0.390473 0.676319i
\(567\) −1.49801e9 + 2.59462e9i −0.345122 + 0.597770i
\(568\) 7.41618e8 1.28452e9i 0.169809 0.294118i
\(569\) −1.94042e9 −0.441572 −0.220786 0.975322i \(-0.570862\pi\)
−0.220786 + 0.975322i \(0.570862\pi\)
\(570\) −4.28526e9 4.12751e9i −0.969205 0.933526i
\(571\) −6.81678e9 −1.53233 −0.766166 0.642643i \(-0.777838\pi\)
−0.766166 + 0.642643i \(0.777838\pi\)
\(572\) −1.13712e8 + 1.96954e8i −0.0254050 + 0.0440027i
\(573\) 9.73802e8 1.68667e9i 0.216237 0.374533i
\(574\) 4.09551e9 + 7.09363e9i 0.903892 + 1.56559i
\(575\) −1.60336e9 + 2.77710e9i −0.351717 + 0.609192i
\(576\) −4.11397e8 7.12560e8i −0.0896979 0.155361i
\(577\) 3.90313e9 0.845859 0.422930 0.906163i \(-0.361002\pi\)
0.422930 + 0.906163i \(0.361002\pi\)
\(578\) −2.21915e9 −0.478013
\(579\) 4.79456e8 + 8.30442e8i 0.102654 + 0.177801i
\(580\) 2.04307e9 + 3.53871e9i 0.434797 + 0.753090i
\(581\) 3.75756e9 0.794858
\(582\) −5.33323e9 −1.12140
\(583\) 6.16750e8 + 1.06824e9i 0.128905 + 0.223270i
\(584\) 4.62553e8 8.01166e8i 0.0960985 0.166448i
\(585\) −1.06276e9 1.84075e9i −0.219477 0.380146i
\(586\) 6.32645e8 1.09577e9i 0.129873 0.224946i
\(587\) −9.93977e8 + 1.72162e9i −0.202835 + 0.351320i −0.949441 0.313946i \(-0.898349\pi\)
0.746606 + 0.665267i \(0.231682\pi\)
\(588\) −9.15295e9 −1.85669
\(589\) 3.30307e9 + 3.18148e9i 0.666061 + 0.641542i
\(590\) −1.76363e9 −0.353530
\(591\) 8.39864e7 1.45469e8i 0.0167360 0.0289877i
\(592\) 9.88020e7 1.71130e8i 0.0195722 0.0339001i
\(593\) 3.18893e9 + 5.52339e9i 0.627991 + 1.08771i 0.987954 + 0.154746i \(0.0494561\pi\)
−0.359963 + 0.932967i \(0.617211\pi\)
\(594\) −4.96910e8 + 8.60673e8i −0.0972803 + 0.168494i
\(595\) −7.45660e9 1.29152e10i −1.45121 2.51358i
\(596\) −1.02065e9 −0.197477
\(597\) 1.01312e10 1.94872
\(598\) 6.69459e8 + 1.15954e9i 0.128018 + 0.221733i
\(599\) 2.44848e9 + 4.24088e9i 0.465481 + 0.806237i 0.999223 0.0394107i \(-0.0125481\pi\)
−0.533742 + 0.845647i \(0.679215\pi\)
\(600\) 1.42228e9 0.268817
\(601\) −4.36013e9 −0.819292 −0.409646 0.912245i \(-0.634348\pi\)
−0.409646 + 0.912245i \(0.634348\pi\)
\(602\) −2.06637e9 3.57906e9i −0.386030 0.668623i
\(603\) −3.83091e9 + 6.63534e9i −0.711528 + 1.23240i
\(604\) 5.41549e8 + 9.37991e8i 0.100002 + 0.173209i
\(605\) 2.77600e9 4.80818e9i 0.509655 0.882748i
\(606\) 9.61673e8 1.66567e9i 0.175539 0.304042i
\(607\) 6.41174e9 1.16363 0.581816 0.813321i \(-0.302343\pi\)
0.581816 + 0.813321i \(0.302343\pi\)
\(608\) 2.35776e8 9.50893e8i 0.0425439 0.171581i
\(609\) −2.28042e10 −4.09123
\(610\) 1.08625e9 1.88144e9i 0.193765 0.335611i
\(611\) −1.00416e9 + 1.73926e9i −0.178098 + 0.308475i
\(612\) 2.63397e9 + 4.56217e9i 0.464495 + 0.804528i
\(613\) 2.07978e9 3.60228e9i 0.364674 0.631634i −0.624050 0.781385i \(-0.714514\pi\)
0.988724 + 0.149751i \(0.0478471\pi\)
\(614\) 3.92281e9 + 6.79450e9i 0.683923 + 1.18459i
\(615\) 1.52667e10 2.64656
\(616\) 1.52782e9 0.263354
\(617\) −2.70933e7 4.69270e7i −0.00464370 0.00804312i 0.863694 0.504016i \(-0.168145\pi\)
−0.868338 + 0.495973i \(0.834811\pi\)
\(618\) −2.11330e9 3.66034e9i −0.360164 0.623823i
\(619\) −6.39443e8 −0.108364 −0.0541819 0.998531i \(-0.517255\pi\)
−0.0541819 + 0.998531i \(0.517255\pi\)
\(620\) −3.34632e9 −0.563893
\(621\) 2.92548e9 + 5.06707e9i 0.490203 + 0.849056i
\(622\) 7.29353e8 1.26328e9i 0.121527 0.210490i
\(623\) −9.05439e9 1.56827e10i −1.50021 2.59843i
\(624\) 2.96926e8 5.14291e8i 0.0489218 0.0847350i
\(625\) 3.81420e9 6.60639e9i 0.624919 1.08239i
\(626\) −4.24273e9 −0.691251
\(627\) −3.75000e9 + 1.08056e9i −0.607568 + 0.175070i
\(628\) −3.06231e9 −0.493390
\(629\) −6.32581e8 + 1.09566e9i −0.101353 + 0.175549i
\(630\) −7.13957e9 + 1.23661e10i −1.13757 + 1.97034i
\(631\) 3.76343e9 + 6.51844e9i 0.596322 + 1.03286i 0.993359 + 0.115057i \(0.0367050\pi\)
−0.397037 + 0.917802i \(0.629962\pi\)
\(632\) −1.95607e9 + 3.38801e9i −0.308230 + 0.533870i
\(633\) 2.38186e9 + 4.12550e9i 0.373252 + 0.646492i
\(634\) 6.81750e9 1.06246
\(635\) −1.02787e10 −1.59305
\(636\) −1.61047e9 2.78941e9i −0.248229 0.429945i
\(637\) −1.94667e9 3.37173e9i −0.298404 0.516850i
\(638\) 2.68019e9 0.408594
\(639\) 9.09267e9 1.37860
\(640\) 3.57425e8 + 6.19078e8i 0.0538958 + 0.0933502i
\(641\) 4.35523e9 7.54348e9i 0.653143 1.13128i −0.329213 0.944256i \(-0.606784\pi\)
0.982356 0.187021i \(-0.0598831\pi\)
\(642\) 4.02547e9 + 6.97231e9i 0.600404 + 1.03993i
\(643\) 6.64828e8 1.15152e9i 0.0986213 0.170817i −0.812493 0.582971i \(-0.801890\pi\)
0.911114 + 0.412154i \(0.135223\pi\)
\(644\) 4.49739e9 7.78972e9i 0.663530 1.14927i
\(645\) −7.70274e9 −1.13028
\(646\) −1.50956e9 + 6.08810e9i −0.220311 + 0.888521i
\(647\) 1.16976e10 1.69798 0.848988 0.528413i \(-0.177213\pi\)
0.848988 + 0.528413i \(0.177213\pi\)
\(648\) −4.59735e8 + 7.96284e8i −0.0663735 + 0.114962i
\(649\) −5.78401e8 + 1.00182e9i −0.0830564 + 0.143858i
\(650\) 3.02494e8 + 5.23935e8i 0.0432036 + 0.0748308i
\(651\) 9.33767e9 1.61733e10i 1.32649 2.29755i
\(652\) −1.11418e8 1.92982e8i −0.0157430 0.0272678i
\(653\) −1.65914e9 −0.233177 −0.116588 0.993180i \(-0.537196\pi\)
−0.116588 + 0.993180i \(0.537196\pi\)
\(654\) −8.68794e8 −0.121449
\(655\) 2.89239e9 + 5.00976e9i 0.402172 + 0.696582i
\(656\) 1.25690e9 + 2.17702e9i 0.173835 + 0.301092i
\(657\) 5.67117e9 0.780178
\(658\) 1.34918e10 1.84620
\(659\) 1.05598e9 + 1.82902e9i 0.143734 + 0.248954i 0.928900 0.370331i \(-0.120756\pi\)
−0.785166 + 0.619285i \(0.787423\pi\)
\(660\) 1.42380e9 2.46609e9i 0.192772 0.333892i
\(661\) 1.38493e9 + 2.39877e9i 0.186519 + 0.323060i 0.944087 0.329696i \(-0.106946\pi\)
−0.757568 + 0.652756i \(0.773613\pi\)
\(662\) 2.19564e9 3.80296e9i 0.294143 0.509471i
\(663\) −1.90107e9 + 3.29275e9i −0.253338 + 0.438795i
\(664\) 1.15319e9 0.152866
\(665\) −1.63372e10 + 4.70754e9i −2.15428 + 0.620753i
\(666\) 1.21137e9 0.158897
\(667\) 7.88958e9 1.36652e10i 1.02947 1.78309i
\(668\) −2.92126e9 + 5.05976e9i −0.379186 + 0.656769i
\(669\) −8.42323e9 1.45895e10i −1.08765 1.88386i
\(670\) 3.32833e9 5.76483e9i 0.427528 0.740500i
\(671\) −7.12493e8 1.23407e9i −0.0910441 0.157693i
\(672\) −3.98947e9 −0.507134
\(673\) 2.12430e9 0.268636 0.134318 0.990938i \(-0.457116\pi\)
0.134318 + 0.990938i \(0.457116\pi\)
\(674\) 3.05785e8 + 5.29635e8i 0.0384686 + 0.0666295i
\(675\) 1.32187e9 + 2.28955e9i 0.165434 + 0.286541i
\(676\) −3.76330e9 −0.468550
\(677\) 1.20120e10 1.48783 0.743915 0.668274i \(-0.232967\pi\)
0.743915 + 0.668274i \(0.232967\pi\)
\(678\) −1.28565e9 2.22682e9i −0.158424 0.274398i
\(679\) −7.62006e9 + 1.31983e10i −0.934145 + 1.61799i
\(680\) −2.28841e9 3.96365e9i −0.279096 0.483408i
\(681\) −3.39846e9 + 5.88631e9i −0.412351 + 0.714214i
\(682\) −1.09746e9 + 1.90086e9i −0.132478 + 0.229458i
\(683\) 6.25738e9 0.751485 0.375742 0.926724i \(-0.377388\pi\)
0.375742 + 0.926724i \(0.377388\pi\)
\(684\) 5.77096e9 1.66289e9i 0.689528 0.198686i
\(685\) 1.27964e10 1.52115
\(686\) −7.58193e9 + 1.31323e10i −0.896696 + 1.55312i
\(687\) −6.49000e9 + 1.12410e10i −0.763653 + 1.32269i
\(688\) −6.34164e8 1.09841e9i −0.0742407 0.128589i
\(689\) 6.85036e8 1.18652e9i 0.0797896 0.138200i
\(690\) −8.38239e9 1.45187e10i −0.971395 1.68251i
\(691\) 1.21622e10 1.40229 0.701146 0.713018i \(-0.252672\pi\)
0.701146 + 0.713018i \(0.252672\pi\)
\(692\) 4.46149e9 0.511810
\(693\) 4.68299e9 + 8.11117e9i 0.534511 + 0.925800i
\(694\) 2.61672e9 + 4.53229e9i 0.297166 + 0.514707i
\(695\) −1.97779e10 −2.23477
\(696\) −6.99855e9 −0.786821
\(697\) −8.04732e9 1.39384e10i −0.900195 1.55918i
\(698\) 4.44810e9 7.70434e9i 0.495086 0.857515i
\(699\) −6.81403e9 1.18022e10i −0.754630 1.30706i
\(700\) 2.03214e9 3.51977e9i 0.223929 0.387856i
\(701\) −3.38467e9 + 5.86242e9i −0.371111 + 0.642782i −0.989737 0.142903i \(-0.954356\pi\)
0.618626 + 0.785686i \(0.287690\pi\)
\(702\) 1.10385e9 0.120429
\(703\) 1.03884e9 + 1.00060e9i 0.112773 + 0.108622i
\(704\) 4.68884e8 0.0506478
\(705\) 1.25732e10 2.17775e10i 1.35140 2.34070i
\(706\) −1.04392e9 + 1.80812e9i −0.111648 + 0.193379i
\(707\) −2.74805e9 4.75977e9i −0.292454 0.506545i
\(708\) 1.51033e9 2.61597e9i 0.159940 0.277024i
\(709\) −2.39107e9 4.14146e9i −0.251960 0.436407i 0.712106 0.702072i \(-0.247742\pi\)
−0.964065 + 0.265665i \(0.914408\pi\)
\(710\) −7.89978e9 −0.828344
\(711\) −2.39825e10 −2.50237
\(712\) −2.77877e9 4.81297e9i −0.288518 0.499727i
\(713\) 6.46112e9 + 1.11910e10i 0.667566 + 1.15626i
\(714\) 2.55426e10 2.62616
\(715\) 1.21127e9 0.123928
\(716\) −2.68583e8 4.65199e8i −0.0273453 0.0473634i
\(717\) −8.52848e9 + 1.47718e10i −0.864081 + 1.49663i
\(718\) −2.22480e9 3.85346e9i −0.224313 0.388522i
\(719\) 4.39238e9 7.60783e9i 0.440706 0.763325i −0.557036 0.830488i \(-0.688062\pi\)
0.997742 + 0.0671633i \(0.0213948\pi\)
\(720\) −2.19112e9 + 3.79512e9i −0.218777 + 0.378933i
\(721\) −1.20778e10 −1.20009
\(722\) 6.32261e9 + 3.34081e9i 0.625196 + 0.330348i
\(723\) 5.83599e9 0.574289
\(724\) −2.76561e9 + 4.79018e9i −0.270836 + 0.469101i
\(725\) 3.56489e9 6.17457e9i 0.347427 0.601761i
\(726\) 4.75460e9 + 8.23520e9i 0.461143 + 0.798723i
\(727\) −5.17575e9 + 8.96466e9i −0.499577 + 0.865293i −1.00000 0.000487869i \(-0.999845\pi\)
0.500422 + 0.865781i \(0.333178\pi\)
\(728\) −8.48489e8 1.46963e9i −0.0815054 0.141171i
\(729\) −1.67215e10 −1.59856
\(730\) −4.92715e9 −0.468777
\(731\) 4.06024e9 + 7.03254e9i 0.384451 + 0.665889i
\(732\) 1.86048e9 + 3.22244e9i 0.175321 + 0.303666i
\(733\) 6.10462e9 0.572525 0.286263 0.958151i \(-0.407587\pi\)
0.286263 + 0.958151i \(0.407587\pi\)
\(734\) −1.02615e10 −0.957799
\(735\) 2.43745e10 + 4.22179e10i 2.26428 + 3.92185i
\(736\) 1.38024e9 2.39064e9i 0.127609 0.221026i
\(737\) −2.18312e9 3.78127e9i −0.200882 0.347938i
\(738\) −7.70517e9 + 1.33458e10i −0.705643 + 1.22221i
\(739\) −6.10665e9 + 1.05770e10i −0.556606 + 0.964069i 0.441171 + 0.897423i \(0.354563\pi\)
−0.997777 + 0.0666463i \(0.978770\pi\)
\(740\) −1.05245e9 −0.0954750
\(741\) 3.12200e9 + 3.00707e9i 0.281883 + 0.271506i
\(742\) −9.20408e9 −0.827116
\(743\) 7.73643e9 1.33999e10i 0.691958 1.19851i −0.279237 0.960222i \(-0.590082\pi\)
0.971195 0.238285i \(-0.0765851\pi\)
\(744\) 2.86571e9 4.96355e9i 0.255110 0.441863i
\(745\) 2.71802e9 + 4.70774e9i 0.240827 + 0.417124i
\(746\) −7.34240e8 + 1.27174e9i −0.0647519 + 0.112153i
\(747\) 3.53468e9 + 6.12225e9i 0.310262 + 0.537389i
\(748\) −3.00203e9 −0.262277
\(749\) 2.30062e10 2.00059
\(750\) 3.98605e9 + 6.90405e9i 0.345008 + 0.597571i
\(751\) −7.52271e9 1.30297e10i −0.648089 1.12252i −0.983579 0.180479i \(-0.942235\pi\)
0.335490 0.942044i \(-0.391098\pi\)
\(752\) 4.14061e9 0.355060
\(753\) −1.15353e10 −0.984573
\(754\) −1.48847e9 2.57810e9i −0.126456 0.219028i
\(755\) 2.88432e9 4.99578e9i 0.243909 0.422463i
\(756\) −3.70782e9 6.42213e9i −0.312099 0.540571i
\(757\) −9.52906e9 + 1.65048e10i −0.798389 + 1.38285i 0.122276 + 0.992496i \(0.460981\pi\)
−0.920665 + 0.390354i \(0.872353\pi\)
\(758\) 3.83188e9 6.63700e9i 0.319572 0.553516i
\(759\) −1.09963e10 −0.912856
\(760\) −5.01386e9 + 1.44473e9i −0.414309 + 0.119382i
\(761\) 9.48311e9 0.780018 0.390009 0.920811i \(-0.372472\pi\)
0.390009 + 0.920811i \(0.372472\pi\)
\(762\) 8.80239e9 1.52462e10i 0.720706 1.24830i
\(763\) −1.24132e9 + 2.15004e9i −0.101169 + 0.175230i
\(764\) −8.54008e8 1.47919e9i −0.0692844 0.120004i
\(765\) 1.40286e10 2.42983e10i 1.13292 1.96228i
\(766\) −4.63680e9 8.03118e9i −0.372750 0.645622i
\(767\) 1.28488e9 0.102821
\(768\) −1.22436e9 −0.0975314
\(769\) 8.19532e9 + 1.41947e10i 0.649866 + 1.12560i 0.983155 + 0.182775i \(0.0585081\pi\)
−0.333289 + 0.942825i \(0.608159\pi\)
\(770\) −4.06861e9 7.04705e9i −0.321166 0.556275i
\(771\) −2.94495e9 −0.231413
\(772\) 8.40950e8 0.0657824
\(773\) 3.66406e8 + 6.34633e8i 0.0285321 + 0.0494191i 0.879939 0.475087i \(-0.157583\pi\)
−0.851407 + 0.524506i \(0.824250\pi\)
\(774\) 3.88761e9 6.73354e9i 0.301363 0.521975i
\(775\) 2.91945e9 + 5.05663e9i 0.225291 + 0.390216i
\(776\) −2.33858e9 + 4.05053e9i −0.179653 + 0.311169i
\(777\) 2.93678e9 5.08665e9i 0.224594 0.389008i
\(778\) −1.09351e10 −0.832516
\(779\) −1.76315e10 + 5.08048e9i −1.33631 + 0.385056i
\(780\) −3.16288e9 −0.238645
\(781\) −2.59081e9 + 4.48742e9i −0.194606 + 0.337068i
\(782\) −8.83699e9 + 1.53061e10i −0.660816 + 1.14457i
\(783\) −6.50446e9 1.12661e10i −0.484223 0.838699i
\(784\) −4.01349e9 + 6.95157e9i −0.297452 + 0.515201i
\(785\) 8.15499e9 + 1.41249e10i 0.601699 + 1.04217i
\(786\) −9.90788e9 −0.727783
\(787\) 1.56506e9 0.114451 0.0572255 0.998361i \(-0.481775\pi\)
0.0572255 + 0.998361i \(0.481775\pi\)
\(788\) −7.36546e7 1.27574e8i −0.00536239 0.00928793i
\(789\) −5.10479e9 8.84176e9i −0.370006 0.640869i
\(790\) 2.08362e10 1.50357
\(791\) −7.34771e9 −0.527879
\(792\) 1.43720e9 + 2.48930e9i 0.102796 + 0.178049i
\(793\) −7.91380e8 + 1.37071e9i −0.0563545 + 0.0976089i
\(794\) −5.68157e9 9.84076e9i −0.402806 0.697681i
\(795\) −8.57743e9 + 1.48565e10i −0.605441 + 1.04866i
\(796\) 4.44243e9 7.69451e9i 0.312194 0.540736i
\(797\) 3.24169e9 0.226813 0.113406 0.993549i \(-0.463824\pi\)
0.113406 + 0.993549i \(0.463824\pi\)
\(798\) 7.00817e9 2.82642e10i 0.488197 1.96891i
\(799\) −2.65102e10 −1.83865
\(800\) 6.23659e8 1.08021e9i 0.0430657 0.0745920i
\(801\) 1.70347e10 2.95049e10i 1.17117 2.02852i
\(802\) 4.94961e9 + 8.57297e9i 0.338813 + 0.586842i
\(803\) −1.61591e9 + 2.79884e9i −0.110132 + 0.190754i
\(804\) 5.70059e9 + 9.87372e9i 0.386833 + 0.670015i
\(805\) −4.79066e10 −3.23676
\(806\) 2.43794e9 0.164002
\(807\) 2.17150e9 + 3.76114e9i 0.145446 + 0.251920i
\(808\) −8.43371e8 1.46076e9i −0.0562444 0.0974181i
\(809\) −2.16746e9 −0.143923 −0.0719616 0.997407i \(-0.522926\pi\)
−0.0719616 + 0.997407i \(0.522926\pi\)
\(810\) 4.89713e9 0.323776
\(811\) −7.51987e9 1.30248e10i −0.495036 0.857428i 0.504947 0.863150i \(-0.331512\pi\)
−0.999984 + 0.00572206i \(0.998179\pi\)
\(812\) −9.99945e9 + 1.73196e10i −0.655435 + 1.13525i
\(813\) 7.50065e9 + 1.29915e10i 0.489533 + 0.847896i
\(814\) −3.45161e8 + 5.97836e8i −0.0224303 + 0.0388505i
\(815\) −5.93417e8 + 1.02783e9i −0.0383980 + 0.0665073i
\(816\) 7.83896e9 0.505060
\(817\) 8.89589e9 2.56333e9i 0.570706 0.164448i
\(818\) −8.03452e9 −0.513243
\(819\) 5.20148e9 9.00923e9i 0.330852 0.573052i
\(820\) 6.69431e9 1.15949e10i 0.423992 0.734376i
\(821\) −5.98292e9 1.03627e10i −0.377322 0.653541i 0.613350 0.789811i \(-0.289822\pi\)
−0.990672 + 0.136271i \(0.956488\pi\)
\(822\) −1.09585e10 + 1.89807e10i −0.688178 + 1.19196i
\(823\) 1.57234e10 + 2.72338e10i 0.983213 + 1.70297i 0.649624 + 0.760255i \(0.274926\pi\)
0.333588 + 0.942719i \(0.391741\pi\)
\(824\) −3.70665e9 −0.230800
\(825\) −4.96868e9 −0.308072
\(826\) −4.31589e9 7.47534e9i −0.266465 0.461531i
\(827\) −2.87110e8 4.97289e8i −0.0176514 0.0305731i 0.857065 0.515209i \(-0.172286\pi\)
−0.874716 + 0.484636i \(0.838952\pi\)
\(828\) 1.69225e10 1.03600
\(829\) 3.08401e10 1.88007 0.940036 0.341075i \(-0.110791\pi\)
0.940036 + 0.341075i \(0.110791\pi\)
\(830\) −3.07096e9 5.31906e9i −0.186424 0.322895i
\(831\) −1.37408e9 + 2.37998e9i −0.0830633 + 0.143870i
\(832\) −2.60399e8 4.51025e8i −0.0156750 0.0271499i
\(833\) 2.56964e10 4.45075e10i 1.54033 2.66794i
\(834\) 1.69373e10 2.93362e10i 1.01103 1.75115i
\(835\) 3.11175e10 1.84970
\(836\) −8.23673e8 + 3.32190e9i −0.0487566 + 0.196637i
\(837\) 1.06536e10 0.627995
\(838\) 9.14103e9 1.58327e10i 0.536588 0.929398i
\(839\) 5.66018e9 9.80372e9i 0.330875 0.573092i −0.651809 0.758383i \(-0.725990\pi\)
0.982684 + 0.185291i \(0.0593229\pi\)
\(840\) 1.06240e10 + 1.84014e10i 0.618461 + 1.07121i
\(841\) −8.91665e9 + 1.54441e10i −0.516911 + 0.895316i
\(842\) −6.31316e8 1.09347e9i −0.0364464 0.0631270i
\(843\) −2.26006e10 −1.29934
\(844\) 4.17770e9 0.239187
\(845\) 1.00218e10 + 1.73582e10i 0.571406 + 0.989705i
\(846\) 1.26916e10 + 2.19824e10i 0.720640 + 1.24819i
\(847\) 2.71733e10 1.53656
\(848\) −2.82471e9 −0.159070
\(849\) −1.53655e10 2.66138e10i −0.861728 1.49256i
\(850\) −3.99298e9 + 6.91604e9i −0.223013 + 0.386270i
\(851\) 2.03208e9 + 3.51966e9i 0.113028 + 0.195771i
\(852\) 6.76518e9 1.17176e10i 0.374749 0.649084i
\(853\) 3.64179e9 6.30776e9i 0.200906 0.347980i −0.747915 0.663795i \(-0.768945\pi\)
0.948821 + 0.315815i \(0.102278\pi\)
\(854\) 1.06329e10 0.584184
\(855\) −2.30383e10 2.21902e10i −1.26057 1.21417i
\(856\) 7.06054e9 0.384751
\(857\) −5.34697e9 + 9.26122e9i −0.290185 + 0.502615i −0.973853 0.227178i \(-0.927050\pi\)
0.683669 + 0.729793i \(0.260383\pi\)
\(858\) −1.03730e9 + 1.79665e9i −0.0560658 + 0.0971088i
\(859\) 1.73570e10 + 3.00632e10i 0.934326 + 1.61830i 0.775831 + 0.630941i \(0.217331\pi\)
0.158495 + 0.987360i \(0.449336\pi\)
\(860\) −3.37759e9 + 5.85015e9i −0.181076 + 0.313634i
\(861\) 3.73600e10 + 6.47094e10i 1.99478 + 3.45507i
\(862\) −1.80393e10 −0.959278
\(863\) 6.11220e9 0.323713 0.161856 0.986814i \(-0.448252\pi\)
0.161856 + 0.986814i \(0.448252\pi\)
\(864\) −1.13792e9 1.97094e9i −0.0600225 0.103962i
\(865\) −1.18810e10 2.05786e10i −0.624163 1.08108i
\(866\) 8.40744e9 0.439897
\(867\) −2.02435e10 −1.05492
\(868\) −8.18898e9 1.41837e10i −0.425021 0.736159i
\(869\) 6.83345e9 1.18359e10i 0.353241 0.611831i
\(870\) 1.86373e10 + 3.22807e10i 0.959545 + 1.66198i
\(871\) −2.42483e9 + 4.19993e9i −0.124342 + 0.215367i
\(872\) −3.80959e8 + 6.59840e8i −0.0194568 + 0.0337001i
\(873\) −2.86723e10 −1.45852
\(874\) 1.45124e10 + 1.39782e10i 0.735273 + 0.708206i
\(875\) 2.27809e10 1.14959
\(876\) 4.21949e9 7.30838e9i 0.212078 0.367330i
\(877\) 4.43397e9 7.67985e9i 0.221970 0.384463i −0.733436 0.679758i \(-0.762085\pi\)
0.955406 + 0.295295i \(0.0954181\pi\)
\(878\) −7.00364e9 1.21307e10i −0.349215 0.604858i
\(879\) 5.77110e9 9.99584e9i 0.286614 0.496430i
\(880\) −1.24865e9 2.16272e9i −0.0617662 0.106982i
\(881\) 5.64381e9 0.278072 0.139036 0.990287i \(-0.455600\pi\)
0.139036 + 0.990287i \(0.455600\pi\)
\(882\) −4.92077e10 −2.41487
\(883\) −1.09258e10 1.89241e10i −0.534063 0.925024i −0.999208 0.0397899i \(-0.987331\pi\)
0.465145 0.885235i \(-0.346002\pi\)
\(884\) 1.66721e9 + 2.88769e9i 0.0811721 + 0.140594i
\(885\) −1.60882e10 −0.780199
\(886\) −1.29181e10 −0.623994
\(887\) −3.74723e9 6.49039e9i −0.180292 0.312276i 0.761688 0.647944i \(-0.224371\pi\)
−0.941980 + 0.335669i \(0.891038\pi\)
\(888\) 9.01290e8 1.56108e9i 0.0431936 0.0748135i
\(889\) −2.51535e10 4.35671e10i −1.20072 2.07971i
\(890\) −1.47998e10 + 2.56341e10i −0.703707 + 1.21886i
\(891\) 1.60606e9 2.78178e9i 0.0760660 0.131750i
\(892\) −1.47741e10 −0.696984
\(893\) −7.27367e9 + 2.93350e10i −0.341801 + 1.37850i
\(894\) −9.31057e9 −0.435808
\(895\) −1.43048e9 + 2.47767e9i −0.0666963 + 0.115521i
\(896\) −1.74935e9 + 3.02996e9i −0.0812453 + 0.140721i
\(897\) 6.10693e9 + 1.05775e10i 0.282520 + 0.489339i
\(898\) −9.11806e9 + 1.57929e10i −0.420180 + 0.727773i
\(899\) −1.43656e10 2.48819e10i −0.659423 1.14215i
\(900\) 7.64641e9 0.349630
\(901\) 1.80852e10 0.823734
\(902\) −4.39093e9 7.60532e9i −0.199221 0.345060i
\(903\) −1.88498e10 3.26488e10i −0.851922 1.47557i
\(904\) −2.25499e9 −0.101521
\(905\) 2.94595e10 1.32116
\(906\) 4.94011e9 + 8.55652e9i 0.220693 + 0.382251i
\(907\) 3.07428e9 5.32481e9i 0.136810 0.236962i −0.789477 0.613780i \(-0.789648\pi\)
0.926287 + 0.376818i \(0.122982\pi\)
\(908\) 2.98039e9 + 5.16219e9i 0.132121 + 0.228841i
\(909\) 5.17011e9 8.95489e9i 0.228311 0.395446i
\(910\) −4.51909e9 + 7.82729e9i −0.198795 + 0.344323i
\(911\) −2.28020e9 −0.0999215 −0.0499608 0.998751i \(-0.515910\pi\)
−0.0499608 + 0.998751i \(0.515910\pi\)
\(912\) 2.15079e9 8.67422e9i 0.0938893 0.378659i
\(913\) −4.02861e9 −0.175189
\(914\) −6.48758e9 + 1.12368e10i −0.281042 + 0.486779i
\(915\) 9.90897e9 1.71628e10i 0.427617 0.740654i
\(916\) 5.69162e9 + 9.85818e9i 0.244682 + 0.423802i
\(917\) −1.41563e10 + 2.45194e10i −0.606256 + 1.05007i
\(918\) 7.28554e9 + 1.26189e10i 0.310823 + 0.538360i
\(919\) −4.01517e10 −1.70647 −0.853237 0.521524i \(-0.825364\pi\)
−0.853237 + 0.521524i \(0.825364\pi\)
\(920\) −1.47024e10 −0.622489
\(921\) 3.57845e10 + 6.19806e10i 1.50934 + 2.61425i
\(922\) 1.20793e10 + 2.09220e10i 0.507555 + 0.879112i
\(923\) 5.75533e9 0.240915
\(924\) 1.39370e10 0.581191
\(925\) 9.18191e8 + 1.59035e9i 0.0381449 + 0.0660690i
\(926\) −5.81561e8 + 1.00729e9i −0.0240689 + 0.0416886i
\(927\) −1.13614e10 1.96786e10i −0.468439 0.811361i
\(928\) −3.06881e9 + 5.31533e9i −0.126053 + 0.218329i
\(929\) 1.75288e10 3.03608e10i 0.717295 1.24239i −0.244773 0.969580i \(-0.578713\pi\)
0.962068 0.272811i \(-0.0879532\pi\)
\(930\) −3.05258e10 −1.24445
\(931\) −4.21995e10 4.06460e10i −1.71389 1.65080i
\(932\) −1.19516e10 −0.483581
\(933\) 6.65329e9 1.15238e10i 0.268195 0.464527i
\(934\) 1.70939e10 2.96076e10i 0.686480 1.18902i
\(935\) 7.99447e9 + 1.38468e10i 0.319852 + 0.554000i
\(936\) 1.59632e9 2.76491e9i 0.0636290 0.110209i
\(937\) −1.45738e10 2.52426e10i −0.578743 1.00241i −0.995624 0.0934511i \(-0.970210\pi\)
0.416881 0.908961i \(-0.363123\pi\)
\(938\) 3.25798e10 1.28896
\(939\) −3.87030e10 −1.52551
\(940\) −1.10265e10 1.90985e10i −0.433003 0.749983i
\(941\) 3.17285e9 + 5.49554e9i 0.124133 + 0.215004i 0.921394 0.388631i \(-0.127052\pi\)
−0.797261 + 0.603635i \(0.793718\pi\)
\(942\) −2.79349e10 −1.08885
\(943\) −5.17018e10 −2.00778
\(944\) −1.32454e9 2.29416e9i −0.0512462 0.0887611i
\(945\) −1.97480e10 + 3.42045e10i −0.761223 + 1.31848i
\(946\) 2.21543e9 + 3.83723e9i 0.0850821 + 0.147367i
\(947\) −2.32891e10 + 4.03380e10i −0.891104 + 1.54344i −0.0525499 + 0.998618i \(0.516735\pi\)
−0.838554 + 0.544819i \(0.816598\pi\)
\(948\) −1.78436e10 + 3.09061e10i −0.680227 + 1.17819i
\(949\) 3.58964e9 0.136339
\(950\) 6.55739e9 + 6.31600e9i 0.248141 + 0.239006i
\(951\) 6.21905e10 2.34473
\(952\) 1.12002e10 1.93993e10i 0.420724 0.728715i
\(953\) −5.04381e9 + 8.73614e9i −0.188770 + 0.326960i −0.944841 0.327531i \(-0.893784\pi\)
0.756070 + 0.654491i \(0.227117\pi\)
\(954\) −8.65814e9 1.49963e10i −0.322853 0.559198i
\(955\) −4.54848e9 + 7.87820e9i −0.168988 + 0.292695i
\(956\) 7.47934e9 + 1.29546e10i 0.276860 + 0.479536i
\(957\) 2.44491e10 0.901720
\(958\) −7.60749e9 −0.279552
\(959\) 3.13148e10 + 5.42389e10i 1.14653 + 1.98585i
\(960\) 3.26049e9 + 5.64734e9i 0.118942 + 0.206013i
\(961\) −3.98344e9 −0.144786
\(962\) 7.66753e8 0.0277679
\(963\) 2.16416e10 + 3.74843e10i 0.780902 + 1.35256i
\(964\) 2.55903e9 4.43237e9i 0.0920038 0.159355i
\(965\) −2.23947e9 3.87887e9i −0.0802231 0.138950i
\(966\) 4.10260e10 7.10592e10i 1.46433 2.53630i
\(967\) 1.90554e9 3.30049e9i 0.0677680 0.117378i −0.830150 0.557539i \(-0.811746\pi\)
0.897919 + 0.440162i \(0.145079\pi\)
\(968\) 8.33941e9 0.295509
\(969\) −1.37705e10 + 5.55367e10i −0.486200 + 1.96086i
\(970\) 2.49107e10 0.876365
\(971\) −6.56614e9 + 1.13729e10i −0.230167 + 0.398661i −0.957857 0.287245i \(-0.907261\pi\)
0.727690 + 0.685906i \(0.240594\pi\)
\(972\) −9.05439e9 + 1.56827e10i −0.316248 + 0.547757i
\(973\) −4.83996e10 8.38306e10i −1.68441 2.91748i
\(974\) 1.28360e10 2.22327e10i 0.445117 0.770966i
\(975\) 2.75940e9 + 4.77943e9i 0.0953452 + 0.165143i
\(976\) 3.26321e9 0.112349
\(977\) −3.67732e10 −1.26154 −0.630769 0.775971i \(-0.717260\pi\)
−0.630769 + 0.775971i \(0.717260\pi\)
\(978\) −1.01638e9 1.76041e9i −0.0347431 0.0601767i
\(979\) 9.70751e9 + 1.68139e10i 0.330650 + 0.572703i
\(980\) 4.27521e10 1.45099
\(981\) −4.67078e9 −0.157960
\(982\) 1.08799e10 + 1.88446e10i 0.366637 + 0.635034i
\(983\) −5.16863e9 + 8.95232e9i −0.173555 + 0.300607i −0.939660 0.342109i \(-0.888859\pi\)
0.766105 + 0.642715i \(0.222192\pi\)
\(984\) 1.14657e10 + 1.98592e10i 0.383634 + 0.664474i
\(985\) −3.92288e8 + 6.79462e8i −0.0130791 + 0.0226537i
\(986\) 1.96480e10 3.40314e10i 0.652755 1.13060i
\(987\) 1.23075e11 4.07436
\(988\) 3.65281e9 1.05255e9i 0.120497 0.0347211i
\(989\) 2.60859e10 0.857471
\(990\) 7.65457e9 1.32581e10i 0.250725 0.434268i
\(991\) −2.32044e10 + 4.01911e10i −0.757376 + 1.31181i 0.186808 + 0.982396i \(0.440186\pi\)
−0.944184 + 0.329418i \(0.893148\pi\)
\(992\) −2.51318e9 4.35295e9i −0.0817396 0.141577i
\(993\) 2.00290e10 3.46913e10i 0.649139 1.12434i
\(994\) −1.93320e10 3.34840e10i −0.624345 1.08140i
\(995\) −4.73211e10 −1.52291
\(996\) 1.05196e10 0.337358
\(997\) −1.55674e10 2.69636e10i −0.497489 0.861677i 0.502506 0.864574i \(-0.332411\pi\)
−0.999996 + 0.00289645i \(0.999078\pi\)
\(998\) −1.25521e9 2.17408e9i −0.0399723 0.0692340i
\(999\) 3.35064e9 0.106328
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 38.8.c.b.11.6 yes 14
19.7 even 3 inner 38.8.c.b.7.6 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.8.c.b.7.6 14 19.7 even 3 inner
38.8.c.b.11.6 yes 14 1.1 even 1 trivial