Properties

Label 38.10.e.a.5.5
Level $38$
Weight $10$
Character 38.5
Analytic conductor $19.571$
Analytic rank $0$
Dimension $42$
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] = [38,10,Mod(5,38)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(38, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([16]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("38.5");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 38 = 2 \cdot 19 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 38.e (of order \(9\), degree \(6\), 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: \(19.5713617742\)
Analytic rank: \(0\)
Dimension: \(42\)
Relative dimension: \(7\) over \(\Q(\zeta_{9})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label 5.5
Character \(\chi\) \(=\) 38.5
Dual form 38.10.e.a.23.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(15.0351 - 5.47232i) q^{2} +(10.6794 - 60.5660i) q^{3} +(196.107 - 164.554i) q^{4} +(1283.65 + 1077.11i) q^{5} +(-170.871 - 969.056i) q^{6} +(-13.1166 - 22.7186i) q^{7} +(2048.00 - 3547.24i) q^{8} +(14941.8 + 5438.36i) q^{9} +O(q^{10})\) \(q+(15.0351 - 5.47232i) q^{2} +(10.6794 - 60.5660i) q^{3} +(196.107 - 164.554i) q^{4} +(1283.65 + 1077.11i) q^{5} +(-170.871 - 969.056i) q^{6} +(-13.1166 - 22.7186i) q^{7} +(2048.00 - 3547.24i) q^{8} +(14941.8 + 5438.36i) q^{9} +(25194.1 + 9169.91i) q^{10} +(-16305.0 + 28241.1i) q^{11} +(-7872.04 - 13634.8i) q^{12} +(13730.4 + 77868.8i) q^{13} +(-321.533 - 269.798i) q^{14} +(78945.0 - 66242.7i) q^{15} +(11380.2 - 64540.4i) q^{16} +(273208. - 99439.6i) q^{17} +254411. q^{18} +(312091. - 474644. i) q^{19} +428976. q^{20} +(-1516.06 + 551.799i) q^{21} +(-90602.7 + 513833. i) q^{22} +(340527. - 285736. i) q^{23} +(-192971. - 161922. i) q^{24} +(148436. + 841821. i) q^{25} +(632560. + 1.09563e6i) q^{26} +(1.09421e6 - 1.89522e6i) q^{27} +(-6310.70 - 2296.91i) q^{28} +(1.94759e6 + 708864. i) q^{29} +(824443. - 1.42798e6i) q^{30} +(-279915. - 484827. i) q^{31} +(-182083. - 1.03265e6i) q^{32} +(1.53632e6 + 1.28913e6i) q^{33} +(3.56354e6 - 2.99016e6i) q^{34} +(7633.35 - 43290.9i) q^{35} +(3.82510e6 - 1.39222e6i) q^{36} +2.80119e6 q^{37} +(2.09490e6 - 8.84418e6i) q^{38} +4.86284e6 q^{39} +(6.44969e6 - 2.34750e6i) q^{40} +(-2.71007e6 + 1.53695e7i) q^{41} +(-19774.4 + 16592.7i) q^{42} +(1.39214e6 + 1.16814e6i) q^{43} +(1.44964e6 + 8.22133e6i) q^{44} +(1.33223e7 + 2.30749e7i) q^{45} +(3.55621e6 - 6.15954e6i) q^{46} +(-3.83193e7 - 1.39471e7i) q^{47} +(-3.78742e6 - 1.37851e6i) q^{48} +(2.01765e7 - 3.49467e7i) q^{49} +(6.83846e6 + 1.18446e7i) q^{50} +(-3.10495e6 - 1.76091e7i) q^{51} +(1.55062e7 + 1.30113e7i) q^{52} +(-4.17144e7 + 3.50025e7i) q^{53} +(6.08021e6 - 3.44826e7i) q^{54} +(-5.13488e7 + 1.86894e7i) q^{55} -107451. q^{56} +(-2.54144e7 - 2.39710e7i) q^{57} +3.31613e7 q^{58} +(-1.47375e8 + 5.36400e7i) q^{59} +(4.58122e6 - 2.59814e7i) q^{60} +(-1.20789e8 + 1.01354e8i) q^{61} +(-6.86168e6 - 5.75763e6i) q^{62} +(-72433.3 - 410790. i) q^{63} +(-8.38861e6 - 1.45295e7i) q^{64} +(-6.62484e7 + 1.14746e8i) q^{65} +(3.01532e7 + 1.09749e7i) q^{66} +(-1.17008e8 - 4.25873e7i) q^{67} +(3.72150e7 - 6.44582e7i) q^{68} +(-1.36693e7 - 2.36759e7i) q^{69} +(-122134. - 692654. i) q^{70} +(-1.56035e6 - 1.30929e6i) q^{71} +(4.98919e7 - 4.18643e7i) q^{72} +(2.14505e7 - 1.21652e8i) q^{73} +(4.21162e7 - 1.53290e7i) q^{74} +5.25710e7 q^{75} +(-1.69012e7 - 1.44437e8i) q^{76} +855466. q^{77} +(7.31131e7 - 2.66110e7i) q^{78} +(4.73359e7 - 2.68455e8i) q^{79} +(8.41254e7 - 7.05896e7i) q^{80} +(1.36651e8 + 1.14664e8i) q^{81} +(4.33611e7 + 2.45913e8i) q^{82} +(3.09912e8 + 5.36783e8i) q^{83} +(-206509. + 357684. i) q^{84} +(4.57812e8 + 1.66630e8i) q^{85} +(2.73234e7 + 9.94489e6i) q^{86} +(6.37322e7 - 1.10387e8i) q^{87} +(6.67853e7 + 1.15676e8i) q^{88} +(-4.30242e7 - 2.44003e8i) q^{89} +(3.26576e8 + 2.74029e8i) q^{90} +(1.58898e6 - 1.33331e6i) q^{91} +(1.97610e7 - 1.12070e8i) q^{92} +(-3.23534e7 + 1.17757e7i) q^{93} -6.52458e8 q^{94} +(9.11861e8 - 2.73122e8i) q^{95} -6.44878e7 q^{96} +(1.29307e9 - 4.70640e8i) q^{97} +(1.12115e8 - 6.35838e8i) q^{98} +(-3.97211e8 + 3.33300e8i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 42 q - 252 q^{3} + 4032 q^{6} + 14373 q^{7} + 86016 q^{8} + 12852 q^{9} + 32625 q^{11} - 62208 q^{12} + 351237 q^{13} + 165264 q^{14} - 834165 q^{15} + 1075035 q^{17} - 3364608 q^{18} + 696762 q^{19} - 1396224 q^{20} - 3148065 q^{21} - 1462656 q^{22} - 4882824 q^{23} + 1032192 q^{24} - 483270 q^{25} - 70176 q^{26} + 2570400 q^{27} + 1519104 q^{28} + 13670499 q^{29} - 2263968 q^{31} - 5777733 q^{33} - 9526080 q^{34} + 43019613 q^{35} + 3290112 q^{36} - 50105184 q^{37} - 692160 q^{38} - 89820600 q^{39} - 94033860 q^{41} - 43526160 q^{42} + 30524217 q^{43} + 23402496 q^{44} + 39789630 q^{45} - 18312576 q^{46} + 81865791 q^{47} + 33030144 q^{48} + 40421580 q^{49} - 16761600 q^{50} - 28132314 q^{51} - 91666176 q^{52} + 126049077 q^{53} - 106214544 q^{54} + 553870071 q^{55} + 117743616 q^{56} + 384197394 q^{57} - 63148512 q^{58} + 135312639 q^{59} - 129611520 q^{60} + 132517452 q^{61} - 419324112 q^{62} + 577860735 q^{63} - 352321536 q^{64} - 184218951 q^{65} + 413765760 q^{66} + 229749621 q^{67} + 152743680 q^{68} - 517946637 q^{69} - 688313808 q^{70} - 2107934406 q^{71} + 105283584 q^{72} - 26577420 q^{73} + 322027248 q^{74} + 941894730 q^{75} - 107163648 q^{76} + 620006124 q^{77} + 122597280 q^{78} - 624601023 q^{79} - 1037387736 q^{81} + 1504541760 q^{82} + 907729401 q^{83} - 604998912 q^{84} + 1462808898 q^{85} + 222950208 q^{86} + 63648732 q^{87} - 133632000 q^{88} - 847590846 q^{89} - 4481693280 q^{90} + 957045924 q^{91} + 648163584 q^{92} + 2438307564 q^{93} + 2205393024 q^{94} - 208077987 q^{95} - 509607936 q^{96} + 535342599 q^{97} + 1861154832 q^{98} - 11757151095 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(21\)
\(\chi(n)\) \(e\left(\frac{8}{9}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.0351 5.47232i 0.664463 0.241845i
\(3\) 10.6794 60.5660i 0.0761206 0.431701i −0.922801 0.385276i \(-0.874106\pi\)
0.998922 0.0464248i \(-0.0147828\pi\)
\(4\) 196.107 164.554i 0.383022 0.321394i
\(5\) 1283.65 + 1077.11i 0.918507 + 0.770719i 0.973718 0.227756i \(-0.0731389\pi\)
−0.0552116 + 0.998475i \(0.517583\pi\)
\(6\) −170.871 969.056i −0.0538254 0.305259i
\(7\) −13.1166 22.7186i −0.00206481 0.00357636i 0.864991 0.501787i \(-0.167324\pi\)
−0.867056 + 0.498211i \(0.833991\pi\)
\(8\) 2048.00 3547.24i 0.176777 0.306186i
\(9\) 14941.8 + 5438.36i 0.759121 + 0.276297i
\(10\) 25194.1 + 9169.91i 0.796708 + 0.289978i
\(11\) −16305.0 + 28241.1i −0.335779 + 0.581587i −0.983634 0.180177i \(-0.942333\pi\)
0.647855 + 0.761764i \(0.275666\pi\)
\(12\) −7872.04 13634.8i −0.109590 0.189816i
\(13\) 13730.4 + 77868.8i 0.133333 + 0.756168i 0.976006 + 0.217743i \(0.0698695\pi\)
−0.842673 + 0.538425i \(0.819019\pi\)
\(14\) −321.533 269.798i −0.00223692 0.00187699i
\(15\) 78945.0 66242.7i 0.402637 0.337853i
\(16\) 11380.2 64540.4i 0.0434120 0.246202i
\(17\) 273208. 99439.6i 0.793365 0.288761i 0.0866311 0.996240i \(-0.472390\pi\)
0.706734 + 0.707479i \(0.250168\pi\)
\(18\) 254411. 0.571229
\(19\) 312091. 474644.i 0.549401 0.835559i
\(20\) 428976. 0.599513
\(21\) −1516.06 + 551.799i −0.00170109 + 0.000619148i
\(22\) −90602.7 + 513833.i −0.0824592 + 0.467649i
\(23\) 340527. 285736.i 0.253733 0.212907i −0.507045 0.861920i \(-0.669262\pi\)
0.760778 + 0.649013i \(0.224818\pi\)
\(24\) −192971. 161922.i −0.118725 0.0996218i
\(25\) 148436. + 841821.i 0.0759991 + 0.431012i
\(26\) 632560. + 1.09563e6i 0.271470 + 0.470200i
\(27\) 1.09421e6 1.89522e6i 0.396243 0.686313i
\(28\) −6310.70 2296.91i −0.00194029 0.000706207i
\(29\) 1.94759e6 + 708864.i 0.511336 + 0.186111i 0.584785 0.811188i \(-0.301179\pi\)
−0.0734499 + 0.997299i \(0.523401\pi\)
\(30\) 824443. 1.42798e6i 0.185830 0.321867i
\(31\) −279915. 484827.i −0.0544376 0.0942886i 0.837522 0.546403i \(-0.184003\pi\)
−0.891960 + 0.452114i \(0.850670\pi\)
\(32\) −182083. 1.03265e6i −0.0306970 0.174091i
\(33\) 1.53632e6 + 1.28913e6i 0.225512 + 0.189227i
\(34\) 3.56354e6 2.99016e6i 0.457327 0.383743i
\(35\) 7633.35 43290.9i 0.000859823 0.00487630i
\(36\) 3.82510e6 1.39222e6i 0.379560 0.138149i
\(37\) 2.80119e6 0.245717 0.122859 0.992424i \(-0.460794\pi\)
0.122859 + 0.992424i \(0.460794\pi\)
\(38\) 2.09490e6 8.84418e6i 0.162981 0.688068i
\(39\) 4.86284e6 0.336588
\(40\) 6.44969e6 2.34750e6i 0.398354 0.144989i
\(41\) −2.71007e6 + 1.53695e7i −0.149780 + 0.849442i 0.813625 + 0.581390i \(0.197491\pi\)
−0.963404 + 0.268052i \(0.913620\pi\)
\(42\) −19774.4 + 16592.7i −0.000980576 + 0.000822801i
\(43\) 1.39214e6 + 1.16814e6i 0.0620975 + 0.0521060i 0.673308 0.739362i \(-0.264873\pi\)
−0.611211 + 0.791468i \(0.709317\pi\)
\(44\) 1.44964e6 + 8.22133e6i 0.0583074 + 0.330678i
\(45\) 1.33223e7 + 2.30749e7i 0.484310 + 0.838850i
\(46\) 3.55621e6 6.15954e6i 0.117106 0.202833i
\(47\) −3.83193e7 1.39471e7i −1.14545 0.416911i −0.301574 0.953443i \(-0.597512\pi\)
−0.843880 + 0.536532i \(0.819734\pi\)
\(48\) −3.78742e6 1.37851e6i −0.102981 0.0374821i
\(49\) 2.01765e7 3.49467e7i 0.499991 0.866011i
\(50\) 6.83846e6 + 1.18446e7i 0.154737 + 0.268012i
\(51\) −3.10495e6 1.76091e7i −0.0642672 0.364478i
\(52\) 1.55062e7 + 1.30113e7i 0.294097 + 0.246777i
\(53\) −4.17144e7 + 3.50025e7i −0.726181 + 0.609338i −0.929087 0.369860i \(-0.879406\pi\)
0.202907 + 0.979198i \(0.434961\pi\)
\(54\) 6.08021e6 3.44826e7i 0.0973077 0.551859i
\(55\) −5.13488e7 + 1.86894e7i −0.756655 + 0.275400i
\(56\) −107451. −0.00146004
\(57\) −2.54144e7 2.39710e7i −0.318891 0.300780i
\(58\) 3.31613e7 0.384774
\(59\) −1.47375e8 + 5.36400e7i −1.58339 + 0.576308i −0.975938 0.218046i \(-0.930032\pi\)
−0.607455 + 0.794354i \(0.707809\pi\)
\(60\) 4.58122e6 2.59814e7i 0.0456352 0.258810i
\(61\) −1.20789e8 + 1.01354e8i −1.11698 + 0.937254i −0.998448 0.0556966i \(-0.982262\pi\)
−0.118528 + 0.992951i \(0.537818\pi\)
\(62\) −6.86168e6 5.75763e6i −0.0589750 0.0494859i
\(63\) −72433.3 410790.i −0.000579303 0.00328539i
\(64\) −8.38861e6 1.45295e7i −0.0625000 0.108253i
\(65\) −6.62484e7 + 1.14746e8i −0.460326 + 0.797308i
\(66\) 3.01532e7 + 1.09749e7i 0.195608 + 0.0711955i
\(67\) −1.17008e8 4.25873e7i −0.709378 0.258192i −0.0379682 0.999279i \(-0.512089\pi\)
−0.671409 + 0.741087i \(0.734311\pi\)
\(68\) 3.72150e7 6.44582e7i 0.211070 0.365585i
\(69\) −1.36693e7 2.36759e7i −0.0725980 0.125743i
\(70\) −122134. 692654.i −0.000607987 0.00344806i
\(71\) −1.56035e6 1.30929e6i −0.00728719 0.00611468i 0.639137 0.769093i \(-0.279292\pi\)
−0.646424 + 0.762978i \(0.723736\pi\)
\(72\) 4.98919e7 4.18643e7i 0.218793 0.183589i
\(73\) 2.14505e7 1.21652e8i 0.0884064 0.501378i −0.908163 0.418617i \(-0.862515\pi\)
0.996569 0.0827609i \(-0.0263738\pi\)
\(74\) 4.21162e7 1.53290e7i 0.163270 0.0594254i
\(75\) 5.25710e7 0.191854
\(76\) −1.69012e7 1.44437e8i −0.0581106 0.496612i
\(77\) 855466. 0.00277328
\(78\) 7.31131e7 2.66110e7i 0.223650 0.0814021i
\(79\) 4.73359e7 2.68455e8i 0.136731 0.775443i −0.836907 0.547345i \(-0.815638\pi\)
0.973638 0.228097i \(-0.0732504\pi\)
\(80\) 8.41254e7 7.05896e7i 0.229627 0.192680i
\(81\) 1.36651e8 + 1.14664e8i 0.352721 + 0.295968i
\(82\) 4.33611e7 + 2.45913e8i 0.105910 + 0.600646i
\(83\) 3.09912e8 + 5.36783e8i 0.716781 + 1.24150i 0.962268 + 0.272102i \(0.0877188\pi\)
−0.245487 + 0.969400i \(0.578948\pi\)
\(84\) −206509. + 357684.i −0.000452567 + 0.000783868i
\(85\) 4.57812e8 + 1.66630e8i 0.951265 + 0.346232i
\(86\) 2.73234e7 + 9.94489e6i 0.0538631 + 0.0196046i
\(87\) 6.37322e7 1.10387e8i 0.119267 0.206577i
\(88\) 6.67853e7 + 1.15676e8i 0.118716 + 0.205622i
\(89\) −4.30242e7 2.44003e8i −0.0726872 0.412230i −0.999340 0.0363126i \(-0.988439\pi\)
0.926653 0.375917i \(-0.122672\pi\)
\(90\) 3.26576e8 + 2.74029e8i 0.524678 + 0.440257i
\(91\) 1.58898e6 1.33331e6i 0.00242902 0.00203819i
\(92\) 1.97610e7 1.12070e8i 0.0287583 0.163096i
\(93\) −3.23534e7 + 1.17757e7i −0.0448483 + 0.0163235i
\(94\) −6.52458e8 −0.861940
\(95\) 9.11861e8 2.73122e8i 1.14861 0.344033i
\(96\) −6.44878e7 −0.0774920
\(97\) 1.29307e9 4.70640e8i 1.48303 0.539780i 0.531427 0.847104i \(-0.321656\pi\)
0.951605 + 0.307324i \(0.0994337\pi\)
\(98\) 1.12115e8 6.35838e8i 0.122786 0.696352i
\(99\) −3.97211e8 + 3.33300e8i −0.415588 + 0.348720i
\(100\) 1.67634e8 + 1.40662e8i 0.167634 + 0.140662i
\(101\) −1.28205e8 7.27085e8i −0.122591 0.695247i −0.982710 0.185153i \(-0.940722\pi\)
0.860119 0.510094i \(-0.170389\pi\)
\(102\) −1.43046e8 2.47763e8i −0.130850 0.226639i
\(103\) −5.43629e8 + 9.41593e8i −0.475921 + 0.824319i −0.999619 0.0275843i \(-0.991219\pi\)
0.523698 + 0.851904i \(0.324552\pi\)
\(104\) 3.04339e8 + 1.10770e8i 0.255098 + 0.0928482i
\(105\) −2.54044e6 924643.i −0.00203965 0.000742373i
\(106\) −4.35634e8 + 7.54541e8i −0.335155 + 0.580506i
\(107\) −7.22970e8 1.25222e9i −0.533204 0.923536i −0.999248 0.0387744i \(-0.987655\pi\)
0.466044 0.884761i \(-0.345679\pi\)
\(108\) −9.72834e7 5.51722e8i −0.0688069 0.390223i
\(109\) −4.60761e8 3.86624e8i −0.312649 0.262343i 0.472937 0.881096i \(-0.343194\pi\)
−0.785586 + 0.618753i \(0.787638\pi\)
\(110\) −6.69758e8 + 5.61994e8i −0.436165 + 0.365986i
\(111\) 2.99151e7 1.69657e8i 0.0187041 0.106076i
\(112\) −1.61554e6 + 588008.i −0.000970144 + 0.000353104i
\(113\) −1.96043e9 −1.13110 −0.565548 0.824715i \(-0.691335\pi\)
−0.565548 + 0.824715i \(0.691335\pi\)
\(114\) −5.13284e8 2.21330e8i −0.284633 0.122735i
\(115\) 7.44889e8 0.397147
\(116\) 4.98582e8 1.81469e8i 0.255668 0.0930555i
\(117\) −2.18323e8 + 1.23817e9i −0.107712 + 0.610863i
\(118\) −1.92226e9 + 1.61296e9i −0.912729 + 0.765871i
\(119\) −5.84270e6 4.90260e6i −0.00267087 0.00224112i
\(120\) −7.32995e7 4.15702e8i −0.0322690 0.183007i
\(121\) 6.47268e8 + 1.12110e9i 0.274505 + 0.475456i
\(122\) −1.26143e9 + 2.18487e9i −0.515519 + 0.892905i
\(123\) 9.01930e8 + 3.28276e8i 0.355304 + 0.129320i
\(124\) −1.34673e8 4.90171e7i −0.0511546 0.0186187i
\(125\) 9.20219e8 1.59387e9i 0.337129 0.583925i
\(126\) −3.33702e6 5.77988e6i −0.00117948 0.00204292i
\(127\) −3.13580e8 1.77840e9i −0.106962 0.606614i −0.990418 0.138100i \(-0.955900\pi\)
0.883456 0.468515i \(-0.155211\pi\)
\(128\) −2.05633e8 1.72547e8i −0.0677094 0.0568149i
\(129\) 8.56170e7 7.18412e7i 0.0272211 0.0228412i
\(130\) −3.68125e8 + 2.08774e9i −0.113045 + 0.641109i
\(131\) 1.64965e9 6.00424e8i 0.489408 0.178130i −0.0855159 0.996337i \(-0.527254\pi\)
0.574924 + 0.818207i \(0.305032\pi\)
\(132\) 5.13415e8 0.147192
\(133\) −1.48768e7 864549.i −0.00412267 0.000239584i
\(134\) −1.99227e9 −0.533798
\(135\) 3.44594e9 1.25422e9i 0.892906 0.324991i
\(136\) 2.06794e8 1.17279e9i 0.0518338 0.293964i
\(137\) −3.38412e9 + 2.83961e9i −0.820735 + 0.688679i −0.953144 0.302517i \(-0.902173\pi\)
0.132409 + 0.991195i \(0.457729\pi\)
\(138\) −3.35081e8 2.81166e8i −0.0786491 0.0659944i
\(139\) −3.65663e8 2.07378e9i −0.0830835 0.471190i −0.997754 0.0669891i \(-0.978661\pi\)
0.914670 0.404201i \(-0.132450\pi\)
\(140\) −5.62672e6 9.74576e6i −0.00123788 0.00214407i
\(141\) −1.25395e9 + 2.17190e9i −0.267174 + 0.462758i
\(142\) −3.06249e7 1.11465e7i −0.00632087 0.00230061i
\(143\) −2.42297e9 8.81890e8i −0.484548 0.176361i
\(144\) 5.21034e8 9.02458e8i 0.100980 0.174902i
\(145\) 1.73650e9 + 3.00770e9i 0.326226 + 0.565040i
\(146\) −3.43207e8 1.94643e9i −0.0625128 0.354527i
\(147\) −1.90111e9 1.59522e9i −0.335798 0.281768i
\(148\) 5.49335e8 4.60947e8i 0.0941152 0.0789720i
\(149\) −5.52432e8 + 3.13300e9i −0.0918208 + 0.520741i 0.903855 + 0.427840i \(0.140725\pi\)
−0.995675 + 0.0929015i \(0.970386\pi\)
\(150\) 7.90409e8 2.87685e8i 0.127480 0.0463988i
\(151\) −6.56833e9 −1.02816 −0.514078 0.857744i \(-0.671866\pi\)
−0.514078 + 0.857744i \(0.671866\pi\)
\(152\) −1.04452e9 2.07913e9i −0.158715 0.315926i
\(153\) 4.62300e9 0.682044
\(154\) 1.28620e7 4.68138e6i 0.00184274 0.000670704i
\(155\) 1.62900e8 9.23849e8i 0.0226687 0.128561i
\(156\) 9.53638e8 8.00197e8i 0.128921 0.108177i
\(157\) 1.47279e9 + 1.23582e9i 0.193461 + 0.162333i 0.734373 0.678746i \(-0.237476\pi\)
−0.540912 + 0.841079i \(0.681921\pi\)
\(158\) −7.57374e8 4.29528e9i −0.0966837 0.548321i
\(159\) 1.67448e9 + 2.90028e9i 0.207775 + 0.359876i
\(160\) 8.78543e8 1.52168e9i 0.105980 0.183562i
\(161\) −1.09581e7 3.98843e6i −0.00128534 0.000467827i
\(162\) 2.68204e9 + 9.76184e8i 0.305948 + 0.111356i
\(163\) 5.18875e9 8.98717e9i 0.575729 0.997192i −0.420233 0.907416i \(-0.638052\pi\)
0.995962 0.0897760i \(-0.0286151\pi\)
\(164\) 1.99765e9 + 3.46003e9i 0.215637 + 0.373493i
\(165\) 5.83569e8 + 3.30958e9i 0.0612935 + 0.347612i
\(166\) 7.59700e9 + 6.37464e9i 0.776526 + 0.651582i
\(167\) 4.70146e9 3.94499e9i 0.467744 0.392484i −0.378227 0.925713i \(-0.623466\pi\)
0.845971 + 0.533229i \(0.179022\pi\)
\(168\) −1.14752e6 + 6.50790e6i −0.000111139 + 0.000630302i
\(169\) 4.08994e9 1.48862e9i 0.385680 0.140376i
\(170\) 7.79509e9 0.715815
\(171\) 7.24448e9 5.39477e9i 0.647925 0.482492i
\(172\) 4.65231e8 0.0405313
\(173\) −1.16236e10 + 4.23064e9i −0.986581 + 0.359086i −0.784395 0.620261i \(-0.787027\pi\)
−0.202185 + 0.979347i \(0.564804\pi\)
\(174\) 3.54143e8 2.00845e9i 0.0292892 0.166107i
\(175\) 1.71781e7 1.44141e7i 0.00138453 0.00116176i
\(176\) 1.63714e9 + 1.37372e9i 0.128611 + 0.107917i
\(177\) 1.67488e9 + 9.49874e9i 0.128264 + 0.727422i
\(178\) −1.98213e9 3.43316e9i −0.147994 0.256332i
\(179\) 2.48419e9 4.30275e9i 0.180862 0.313262i −0.761313 0.648385i \(-0.775445\pi\)
0.942174 + 0.335123i \(0.108778\pi\)
\(180\) 6.40967e9 + 2.33293e9i 0.455103 + 0.165644i
\(181\) −1.92031e10 6.98934e9i −1.32989 0.484042i −0.423278 0.906000i \(-0.639121\pi\)
−0.906615 + 0.421958i \(0.861343\pi\)
\(182\) 1.65941e7 2.87418e7i 0.00112107 0.00194175i
\(183\) 4.84866e9 + 8.39812e9i 0.319589 + 0.553544i
\(184\) −3.16175e8 1.79312e9i −0.0203352 0.115327i
\(185\) 3.59576e9 + 3.01720e9i 0.225693 + 0.189379i
\(186\) −4.21995e8 + 3.54096e8i −0.0258523 + 0.0216927i
\(187\) −1.64637e9 + 9.33705e9i −0.0984558 + 0.558371i
\(188\) −9.80975e9 + 3.57046e9i −0.572727 + 0.208456i
\(189\) −5.74091e7 −0.00327267
\(190\) 1.22153e10 9.09640e9i 0.680006 0.506382i
\(191\) 4.46855e9 0.242950 0.121475 0.992595i \(-0.461238\pi\)
0.121475 + 0.992595i \(0.461238\pi\)
\(192\) −9.69579e8 + 3.52898e8i −0.0514906 + 0.0187410i
\(193\) −1.97541e9 + 1.12031e10i −0.102483 + 0.581208i 0.889713 + 0.456520i \(0.150904\pi\)
−0.992196 + 0.124688i \(0.960207\pi\)
\(194\) 1.68660e10 1.41522e10i 0.854877 0.717327i
\(195\) 6.24219e9 + 5.23782e9i 0.309158 + 0.259415i
\(196\) −1.79385e9 1.01734e10i −0.0868226 0.492395i
\(197\) −1.67566e10 2.90232e10i −0.792660 1.37293i −0.924314 0.381632i \(-0.875362\pi\)
0.131654 0.991296i \(-0.457971\pi\)
\(198\) −4.14818e9 + 7.18485e9i −0.191807 + 0.332219i
\(199\) −1.73492e10 6.31458e9i −0.784224 0.285434i −0.0812910 0.996690i \(-0.525904\pi\)
−0.702933 + 0.711256i \(0.748127\pi\)
\(200\) 3.29014e9 + 1.19751e9i 0.145405 + 0.0529231i
\(201\) −3.82892e9 + 6.63188e9i −0.165460 + 0.286585i
\(202\) −5.90641e9 1.02302e10i −0.249599 0.432318i
\(203\) −9.44133e6 5.35444e7i −0.000390212 0.00221300i
\(204\) −3.50654e9 2.94234e9i −0.141757 0.118948i
\(205\) −2.00335e10 + 1.68101e10i −0.792254 + 0.664780i
\(206\) −3.02080e9 + 1.71318e10i −0.116875 + 0.662829i
\(207\) 6.64202e9 2.41750e9i 0.251440 0.0915165i
\(208\) 5.18194e9 0.191958
\(209\) 8.31583e9 + 1.65529e10i 0.301472 + 0.600087i
\(210\) −4.32556e7 −0.00153481
\(211\) −2.73813e10 + 9.96598e9i −0.951006 + 0.346138i −0.770503 0.637437i \(-0.779995\pi\)
−0.180503 + 0.983574i \(0.557773\pi\)
\(212\) −2.42071e9 + 1.37285e10i −0.0823059 + 0.466780i
\(213\) −9.59622e7 + 8.05218e7i −0.00319442 + 0.00268044i
\(214\) −1.77225e10 1.48709e10i −0.577646 0.484703i
\(215\) 5.28801e8 + 2.99898e9i 0.0168779 + 0.0957194i
\(216\) −4.48186e9 7.76282e9i −0.140093 0.242648i
\(217\) −7.34308e6 + 1.27186e7i −0.000224807 + 0.000389377i
\(218\) −9.04331e9 3.29150e9i −0.271190 0.0987050i
\(219\) −7.13887e9 2.59834e9i −0.209716 0.0763303i
\(220\) −6.99446e9 + 1.21148e10i −0.201304 + 0.348668i
\(221\) 1.14945e10 + 1.99090e10i 0.324134 + 0.561416i
\(222\) −4.78642e8 2.71452e9i −0.0132258 0.0750074i
\(223\) −4.30529e10 3.61257e10i −1.16582 0.978238i −0.165850 0.986151i \(-0.553037\pi\)
−0.999969 + 0.00791300i \(0.997481\pi\)
\(224\) −2.10720e7 + 1.76815e7i −0.000559229 + 0.000469249i
\(225\) −2.36023e9 + 1.33856e10i −0.0613951 + 0.348189i
\(226\) −2.94753e10 + 1.07281e10i −0.751571 + 0.273550i
\(227\) 3.87327e10 0.968193 0.484096 0.875015i \(-0.339148\pi\)
0.484096 + 0.875015i \(0.339148\pi\)
\(228\) −8.92846e9 5.18866e8i −0.218811 0.0127159i
\(229\) −6.16514e10 −1.48144 −0.740719 0.671815i \(-0.765515\pi\)
−0.740719 + 0.671815i \(0.765515\pi\)
\(230\) 1.11995e10 4.07627e9i 0.263889 0.0960479i
\(231\) 9.13588e6 5.18121e7i 0.000211104 0.00119723i
\(232\) 6.50317e9 5.45681e9i 0.147377 0.123664i
\(233\) 4.24653e10 + 3.56326e10i 0.943915 + 0.792039i 0.978262 0.207371i \(-0.0664908\pi\)
−0.0343473 + 0.999410i \(0.510935\pi\)
\(234\) 3.49316e9 + 1.98107e10i 0.0761636 + 0.431945i
\(235\) −3.41661e10 5.91774e10i −0.730786 1.26576i
\(236\) −2.00746e10 + 3.47702e10i −0.421253 + 0.729632i
\(237\) −1.57537e10 5.73389e9i −0.324351 0.118054i
\(238\) −1.14674e8 4.17379e7i −0.00231669 0.000843208i
\(239\) 4.11203e10 7.12224e10i 0.815202 1.41197i −0.0939804 0.995574i \(-0.529959\pi\)
0.909183 0.416398i \(-0.136708\pi\)
\(240\) −3.37692e9 5.84900e9i −0.0657007 0.113797i
\(241\) 6.19016e9 + 3.51062e10i 0.118202 + 0.670358i 0.985115 + 0.171898i \(0.0549898\pi\)
−0.866913 + 0.498460i \(0.833899\pi\)
\(242\) 1.58667e10 + 1.33138e10i 0.297385 + 0.249535i
\(243\) 4.14011e10 3.47396e10i 0.761699 0.639141i
\(244\) −7.00946e9 + 3.97526e10i −0.126599 + 0.717978i
\(245\) 6.35410e10 2.31270e10i 1.12670 0.410084i
\(246\) 1.53570e10 0.267362
\(247\) 4.12451e10 + 1.77851e10i 0.705076 + 0.304032i
\(248\) −2.29306e9 −0.0384932
\(249\) 3.58205e10 1.30376e10i 0.590520 0.214932i
\(250\) 5.11342e9 2.89996e10i 0.0827907 0.469529i
\(251\) 4.71037e10 3.95247e10i 0.749071 0.628545i −0.186186 0.982515i \(-0.559613\pi\)
0.935257 + 0.353969i \(0.115168\pi\)
\(252\) −8.18017e7 6.86398e7i −0.00127779 0.00107219i
\(253\) 2.51721e9 + 1.42758e10i 0.0386257 + 0.219057i
\(254\) −1.44467e10 2.50224e10i −0.217779 0.377205i
\(255\) 1.49813e10 2.59483e10i 0.221880 0.384307i
\(256\) −4.03595e9 1.46897e9i −0.0587308 0.0213763i
\(257\) 1.06240e11 + 3.86683e10i 1.51911 + 0.552912i 0.960927 0.276803i \(-0.0892749\pi\)
0.558187 + 0.829715i \(0.311497\pi\)
\(258\) 8.94120e8 1.54866e9i 0.0125634 0.0217604i
\(259\) −3.67422e7 6.36394e7i −0.000507360 0.000878773i
\(260\) 5.89000e9 + 3.34039e10i 0.0799347 + 0.453332i
\(261\) 2.52454e10 + 2.11834e10i 0.336744 + 0.282561i
\(262\) 2.15169e10 1.80548e10i 0.282114 0.236722i
\(263\) 4.02224e9 2.28113e10i 0.0518403 0.294001i −0.947855 0.318703i \(-0.896753\pi\)
0.999695 + 0.0247024i \(0.00786381\pi\)
\(264\) 7.71923e9 2.80957e9i 0.0978040 0.0355977i
\(265\) −9.12485e10 −1.13663
\(266\) −2.28406e8 + 6.84123e7i −0.00279730 + 0.000837851i
\(267\) −1.52377e10 −0.183493
\(268\) −2.99539e10 + 1.09023e10i −0.354689 + 0.129096i
\(269\) −2.17587e10 + 1.23400e11i −0.253366 + 1.43691i 0.546867 + 0.837220i \(0.315820\pi\)
−0.800233 + 0.599690i \(0.795291\pi\)
\(270\) 4.49465e10 3.77146e10i 0.514706 0.431889i
\(271\) 3.94022e10 + 3.30624e10i 0.443771 + 0.372368i 0.837118 0.547022i \(-0.184239\pi\)
−0.393347 + 0.919390i \(0.628683\pi\)
\(272\) −3.30870e9 1.87646e10i −0.0366520 0.207864i
\(273\) −6.37839e7 1.10477e8i −0.000694991 0.00120376i
\(274\) −3.53412e10 + 6.12128e10i −0.378795 + 0.656092i
\(275\) −2.61942e10 9.53391e9i −0.276190 0.100525i
\(276\) −6.57660e9 2.39369e9i −0.0682198 0.0248300i
\(277\) 1.73507e10 3.00523e10i 0.177075 0.306703i −0.763802 0.645450i \(-0.776670\pi\)
0.940877 + 0.338747i \(0.110003\pi\)
\(278\) −1.68462e10 2.91784e10i −0.169161 0.292995i
\(279\) −1.54576e9 8.76646e9i −0.0152730 0.0866174i
\(280\) −1.37930e8 1.15737e8i −0.00134106 0.00112528i
\(281\) 3.04142e10 2.55205e10i 0.291003 0.244181i −0.485585 0.874190i \(-0.661393\pi\)
0.776588 + 0.630009i \(0.216949\pi\)
\(282\) −6.96787e9 + 3.95167e10i −0.0656114 + 0.372100i
\(283\) 1.18861e11 4.32618e10i 1.10154 0.400928i 0.273656 0.961828i \(-0.411767\pi\)
0.827884 + 0.560900i \(0.189545\pi\)
\(284\) −5.21445e8 −0.00475638
\(285\) −6.80374e9 5.81445e10i −0.0610866 0.522044i
\(286\) −4.12556e10 −0.364616
\(287\) 3.84722e8 1.40027e8i 0.00334718 0.00121827i
\(288\) 2.89525e9 1.64198e10i 0.0247982 0.140638i
\(289\) −2.60892e10 + 2.18914e10i −0.219999 + 0.184601i
\(290\) 4.25675e10 + 3.57184e10i 0.353417 + 0.296552i
\(291\) −1.46955e10 8.33425e10i −0.120134 0.681315i
\(292\) −1.58116e10 2.73865e10i −0.127278 0.220452i
\(293\) −2.40964e10 + 4.17362e10i −0.191006 + 0.330833i −0.945584 0.325378i \(-0.894508\pi\)
0.754578 + 0.656211i \(0.227842\pi\)
\(294\) −3.73128e10 1.35808e10i −0.291270 0.106013i
\(295\) −2.46954e11 8.98839e10i −1.89853 0.691008i
\(296\) 5.73685e9 9.93651e9i 0.0434371 0.0752352i
\(297\) 3.56820e10 + 6.18031e10i 0.266100 + 0.460899i
\(298\) 8.83892e9 + 5.01280e10i 0.0649271 + 0.368220i
\(299\) 2.69255e10 + 2.25932e10i 0.194825 + 0.163477i
\(300\) 1.03096e10 8.65074e9i 0.0734842 0.0616606i
\(301\) 8.27848e6 4.69496e7i 5.81301e−5 0.000329672i
\(302\) −9.87554e10 + 3.59440e10i −0.683171 + 0.248654i
\(303\) −4.54058e10 −0.309471
\(304\) −2.70821e10 2.55440e10i −0.181866 0.171537i
\(305\) −2.64221e11 −1.74831
\(306\) 6.95072e10 2.52986e10i 0.453193 0.164949i
\(307\) 1.46529e10 8.31005e10i 0.0941455 0.533926i −0.900860 0.434109i \(-0.857063\pi\)
0.995006 0.0998167i \(-0.0318256\pi\)
\(308\) 1.67763e8 1.40770e8i 0.00106223 0.000891316i
\(309\) 5.12229e10 + 4.29811e10i 0.319632 + 0.268203i
\(310\) −2.60639e9 1.47816e10i −0.0160292 0.0909062i
\(311\) 1.22012e11 + 2.11330e11i 0.739570 + 1.28097i 0.952689 + 0.303947i \(0.0983046\pi\)
−0.213119 + 0.977026i \(0.568362\pi\)
\(312\) 9.95909e9 1.72496e10i 0.0595009 0.103059i
\(313\) −2.16929e11 7.89556e10i −1.27752 0.464979i −0.387908 0.921698i \(-0.626802\pi\)
−0.889611 + 0.456719i \(0.849024\pi\)
\(314\) 2.89064e10 + 1.05211e10i 0.167807 + 0.0610768i
\(315\) 3.49487e8 6.05330e8i 0.00200002 0.00346413i
\(316\) −3.48923e10 6.04353e10i −0.196851 0.340956i
\(317\) 4.86638e10 + 2.75986e11i 0.270669 + 1.53504i 0.752390 + 0.658718i \(0.228901\pi\)
−0.481721 + 0.876325i \(0.659988\pi\)
\(318\) 4.10472e10 + 3.44427e10i 0.225093 + 0.188875i
\(319\) −5.17745e10 + 4.34440e10i −0.279935 + 0.234894i
\(320\) 4.88184e9 2.76863e10i 0.0260261 0.147601i
\(321\) −8.35629e10 + 3.04144e10i −0.439279 + 0.159885i
\(322\) −1.86582e8 −0.000967205
\(323\) 3.80672e10 1.60711e11i 0.194599 0.821549i
\(324\) 4.56667e10 0.230222
\(325\) −6.35135e10 + 2.31170e10i −0.315785 + 0.114936i
\(326\) 2.88325e10 1.63517e11i 0.141385 0.801835i
\(327\) −2.83370e10 + 2.37775e10i −0.137053 + 0.115001i
\(328\) 4.89693e10 + 4.10901e10i 0.233610 + 0.196022i
\(329\) 1.85761e8 + 1.05350e9i 0.000874123 + 0.00495740i
\(330\) 2.68851e10 + 4.65664e10i 0.124795 + 0.216152i
\(331\) −1.50680e11 + 2.60985e11i −0.689967 + 1.19506i 0.281880 + 0.959450i \(0.409042\pi\)
−0.971848 + 0.235609i \(0.924291\pi\)
\(332\) 1.49106e11 + 5.42700e10i 0.673554 + 0.245154i
\(333\) 4.18548e10 + 1.52339e10i 0.186529 + 0.0678910i
\(334\) 4.90985e10 8.50412e10i 0.215879 0.373913i
\(335\) −1.04326e11 1.80698e11i −0.452574 0.783882i
\(336\) 1.83603e7 + 1.04126e8i 7.85874e−5 + 0.000445691i
\(337\) −1.89621e11 1.59111e11i −0.800851 0.671994i 0.147554 0.989054i \(-0.452860\pi\)
−0.948405 + 0.317060i \(0.897304\pi\)
\(338\) 5.33464e10 4.47630e10i 0.222321 0.186549i
\(339\) −2.09363e10 + 1.18736e11i −0.0860997 + 0.488295i
\(340\) 1.17200e11 4.26572e10i 0.475633 0.173116i
\(341\) 1.82561e10 0.0731160
\(342\) 7.93994e10 1.20755e11i 0.313834 0.477295i
\(343\) −2.11719e9 −0.00825918
\(344\) 6.99478e9 2.54589e9i 0.0269315 0.00980228i
\(345\) 7.95498e9 4.51149e10i 0.0302310 0.171449i
\(346\) −1.51610e11 + 1.27216e11i −0.568703 + 0.477199i
\(347\) 1.25316e11 + 1.05152e11i 0.464005 + 0.389347i 0.844602 0.535394i \(-0.179837\pi\)
−0.380597 + 0.924741i \(0.624281\pi\)
\(348\) −5.66629e9 3.21351e10i −0.0207106 0.117456i
\(349\) 1.09349e11 + 1.89398e11i 0.394548 + 0.683377i 0.993043 0.117749i \(-0.0375680\pi\)
−0.598496 + 0.801126i \(0.704235\pi\)
\(350\) 1.79395e8 3.10721e8i 0.000639004 0.00110679i
\(351\) 1.62602e11 + 5.91824e10i 0.571801 + 0.208118i
\(352\) 3.21319e10 + 1.16951e10i 0.111556 + 0.0406032i
\(353\) 1.56760e11 2.71516e11i 0.537340 0.930700i −0.461706 0.887033i \(-0.652762\pi\)
0.999046 0.0436674i \(-0.0139042\pi\)
\(354\) 7.71622e10 + 1.33649e11i 0.261150 + 0.452325i
\(355\) −5.92696e8 3.36135e9i −0.00198064 0.0112327i
\(356\) −4.85889e10 4.07709e10i −0.160329 0.134532i
\(357\) −3.59328e8 + 3.01512e8i −0.00117080 + 0.000982420i
\(358\) 1.38040e10 7.82865e10i 0.0444152 0.251891i
\(359\) 1.01482e11 3.69364e10i 0.322451 0.117362i −0.175723 0.984440i \(-0.556226\pi\)
0.498174 + 0.867077i \(0.334004\pi\)
\(360\) 1.09136e11 0.342459
\(361\) −1.27887e11 2.96264e11i −0.396317 0.918114i
\(362\) −3.26968e11 −1.00073
\(363\) 7.48130e10 2.72297e10i 0.226150 0.0823120i
\(364\) 9.22091e7 5.22944e8i 0.000275307 0.00156135i
\(365\) 1.58567e11 1.33054e11i 0.467623 0.392382i
\(366\) 1.18857e11 + 9.97330e10i 0.346227 + 0.290519i
\(367\) 6.05669e10 + 3.43492e11i 0.174276 + 0.988369i 0.938976 + 0.343982i \(0.111776\pi\)
−0.764700 + 0.644386i \(0.777113\pi\)
\(368\) −1.45663e10 2.52295e10i −0.0414031 0.0717123i
\(369\) −1.24078e11 + 2.14910e11i −0.348399 + 0.603446i
\(370\) 7.05736e10 + 2.56867e10i 0.195765 + 0.0712526i
\(371\) 1.34236e9 + 4.88580e8i 0.00367864 + 0.00133892i
\(372\) −4.40701e9 + 7.63316e9i −0.0119316 + 0.0206662i
\(373\) −1.82441e11 3.15998e11i −0.488015 0.845267i 0.511890 0.859051i \(-0.328946\pi\)
−0.999905 + 0.0137838i \(0.995612\pi\)
\(374\) 2.63420e10 + 1.49393e11i 0.0696188 + 0.394828i
\(375\) −8.67067e10 7.27556e10i −0.226419 0.189988i
\(376\) −1.27952e11 + 1.07364e11i −0.330142 + 0.277022i
\(377\) −2.84573e10 + 1.61389e11i −0.0725533 + 0.411470i
\(378\) −8.63150e8 + 3.14161e8i −0.00217457 + 0.000791478i
\(379\) 1.49237e11 0.371534 0.185767 0.982594i \(-0.440523\pi\)
0.185767 + 0.982594i \(0.440523\pi\)
\(380\) 1.33879e11 2.03611e11i 0.329373 0.500928i
\(381\) −1.11059e11 −0.270018
\(382\) 6.71850e10 2.44533e10i 0.161431 0.0587561i
\(383\) 4.56507e10 2.58898e11i 0.108406 0.614800i −0.881399 0.472372i \(-0.843398\pi\)
0.989805 0.142428i \(-0.0454910\pi\)
\(384\) −1.26465e10 + 1.06117e10i −0.0296812 + 0.0249054i
\(385\) 1.09812e9 + 9.21432e8i 0.00254728 + 0.00213742i
\(386\) 3.16066e10 + 1.79250e11i 0.0724661 + 0.410976i
\(387\) 1.44482e10 + 2.50251e10i 0.0327428 + 0.0567122i
\(388\) 1.76136e11 3.05076e11i 0.394552 0.683385i
\(389\) 4.50220e11 + 1.63867e11i 0.996900 + 0.362842i 0.788388 0.615178i \(-0.210916\pi\)
0.208512 + 0.978020i \(0.433138\pi\)
\(390\) 1.22515e11 + 4.45918e10i 0.268162 + 0.0976031i
\(391\) 6.46213e10 1.11927e11i 0.139824 0.242181i
\(392\) −8.26428e10 1.43141e11i −0.176774 0.306181i
\(393\) −1.87480e10 1.06325e11i −0.0396449 0.224837i
\(394\) −4.10761e11 3.44669e11i −0.858729 0.720559i
\(395\) 3.49919e11 2.93617e11i 0.723237 0.606868i
\(396\) −2.30503e10 + 1.30725e11i −0.0471031 + 0.267135i
\(397\) 5.51906e11 2.00877e11i 1.11508 0.405858i 0.282229 0.959347i \(-0.408926\pi\)
0.832856 + 0.553490i \(0.186704\pi\)
\(398\) −2.95402e11 −0.590118
\(399\) −2.11238e8 + 8.91798e8i −0.000417249 + 0.00176152i
\(400\) 5.60207e10 0.109415
\(401\) 2.56705e11 9.34329e10i 0.495775 0.180447i −0.0820180 0.996631i \(-0.526137\pi\)
0.577793 + 0.816184i \(0.303914\pi\)
\(402\) −2.12763e10 + 1.20664e11i −0.0406330 + 0.230441i
\(403\) 3.39096e10 2.84535e10i 0.0640397 0.0537357i
\(404\) −1.44786e11 1.21490e11i −0.270403 0.226895i
\(405\) 5.19067e10 + 2.94378e11i 0.0958685 + 0.543697i
\(406\) −4.34964e8 7.53379e8i −0.000794485 0.00137609i
\(407\) −4.56735e10 + 7.91088e10i −0.0825067 + 0.142906i
\(408\) −6.88226e10 2.50494e10i −0.122959 0.0447534i
\(409\) 2.08652e11 + 7.59431e10i 0.368695 + 0.134194i 0.519722 0.854336i \(-0.326036\pi\)
−0.151027 + 0.988530i \(0.548258\pi\)
\(410\) −2.09215e11 + 3.62371e11i −0.365650 + 0.633324i
\(411\) 1.35844e11 + 2.35288e11i 0.234829 + 0.406735i
\(412\) 4.83329e10 + 2.74109e11i 0.0826428 + 0.468691i
\(413\) 3.15169e9 + 2.64458e9i 0.00533050 + 0.00447282i
\(414\) 8.66340e10 7.26946e10i 0.144940 0.121619i
\(415\) −1.80356e11 + 1.02285e12i −0.298480 + 1.69276i
\(416\) 7.79108e10 2.83572e10i 0.127549 0.0464241i
\(417\) −1.29506e11 −0.209738
\(418\) 2.15612e11 + 2.03367e11i 0.345445 + 0.325826i
\(419\) −8.05265e11 −1.27637 −0.638184 0.769884i \(-0.720314\pi\)
−0.638184 + 0.769884i \(0.720314\pi\)
\(420\) −6.50352e8 + 2.36709e8i −0.00101983 + 0.000371187i
\(421\) 1.73524e10 9.84103e10i 0.0269209 0.152676i −0.968384 0.249464i \(-0.919746\pi\)
0.995305 + 0.0967876i \(0.0308568\pi\)
\(422\) −3.57143e11 + 2.99679e11i −0.548196 + 0.459991i
\(423\) −4.96710e11 4.16789e11i −0.754347 0.632972i
\(424\) 3.87313e10 + 2.19656e11i 0.0581991 + 0.330063i
\(425\) 1.24264e11 + 2.15232e11i 0.184755 + 0.320005i
\(426\) −1.00216e9 + 1.73579e9i −0.00147432 + 0.00255360i
\(427\) 3.88697e9 + 1.41474e9i 0.00565830 + 0.00205945i
\(428\) −3.47837e11 1.26602e11i −0.501048 0.182366i
\(429\) −7.92885e10 + 1.37332e11i −0.113019 + 0.195755i
\(430\) 2.43619e10 + 4.21961e10i 0.0343640 + 0.0595202i
\(431\) −4.78240e10 2.71223e11i −0.0667572 0.378599i −0.999822 0.0188895i \(-0.993987\pi\)
0.933064 0.359709i \(-0.117124\pi\)
\(432\) −1.09866e11 9.21884e10i −0.151770 0.127350i
\(433\) 7.17243e11 6.01838e11i 0.980552 0.822781i −0.00362043 0.999993i \(-0.501152\pi\)
0.984173 + 0.177212i \(0.0567080\pi\)
\(434\) −4.08036e7 + 2.31409e8i −5.52070e−5 + 0.000313095i
\(435\) 2.00709e11 7.30523e10i 0.268761 0.0978210i
\(436\) −1.53979e11 −0.204067
\(437\) −2.93477e10 2.50805e11i −0.0384953 0.328980i
\(438\) −1.21552e11 −0.157808
\(439\) −1.36514e12 + 4.96871e11i −1.75423 + 0.638489i −0.999839 0.0179317i \(-0.994292\pi\)
−0.754395 + 0.656421i \(0.772070\pi\)
\(440\) −3.88664e10 + 2.20422e11i −0.0494353 + 0.280362i
\(441\) 4.91525e11 4.12438e11i 0.618831 0.519260i
\(442\) 2.81769e11 + 2.36432e11i 0.351151 + 0.294650i
\(443\) −5.72133e10 3.24473e11i −0.0705797 0.400278i −0.999546 0.0301143i \(-0.990413\pi\)
0.928967 0.370163i \(-0.120698\pi\)
\(444\) −2.20511e10 3.81937e10i −0.0269282 0.0466410i
\(445\) 2.07590e11 3.59556e11i 0.250949 0.434657i
\(446\) −8.44996e11 3.07553e11i −1.01123 0.368056i
\(447\) 1.83854e11 + 6.69172e10i 0.217815 + 0.0792783i
\(448\) −2.20060e8 + 3.81156e8i −0.000258102 + 0.000447045i
\(449\) −2.28767e11 3.96236e11i −0.265634 0.460092i 0.702095 0.712083i \(-0.252248\pi\)
−0.967730 + 0.251991i \(0.918915\pi\)
\(450\) 3.77637e10 + 2.14169e11i 0.0434129 + 0.246207i
\(451\) −3.89865e11 3.27136e11i −0.443731 0.372335i
\(452\) −3.84456e11 + 3.22597e11i −0.433235 + 0.363527i
\(453\) −7.01460e10 + 3.97818e11i −0.0782638 + 0.443856i
\(454\) 5.82350e11 2.11958e11i 0.643328 0.234152i
\(455\) 3.47582e9 0.00380195
\(456\) −1.37080e11 + 4.10582e10i −0.148467 + 0.0444691i
\(457\) −7.59705e11 −0.814746 −0.407373 0.913262i \(-0.633555\pi\)
−0.407373 + 0.913262i \(0.633555\pi\)
\(458\) −9.26934e11 + 3.37377e11i −0.984361 + 0.358278i
\(459\) 1.10486e11 6.26596e11i 0.116185 0.658917i
\(460\) 1.46078e11 1.22574e11i 0.152116 0.127641i
\(461\) −1.20312e12 1.00953e12i −1.24066 1.04104i −0.997472 0.0710603i \(-0.977362\pi\)
−0.243190 0.969979i \(-0.578194\pi\)
\(462\) −1.46174e8 8.28994e8i −0.000149273 0.000846570i
\(463\) 4.85010e11 + 8.40062e11i 0.490497 + 0.849565i 0.999940 0.0109388i \(-0.00348199\pi\)
−0.509443 + 0.860504i \(0.670149\pi\)
\(464\) 6.79143e10 1.17631e11i 0.0680190 0.117812i
\(465\) −5.42142e10 1.97323e10i −0.0537743 0.0195722i
\(466\) 8.33463e11 + 3.03356e11i 0.818747 + 0.298000i
\(467\) −5.21834e11 + 9.03843e11i −0.507699 + 0.879361i 0.492261 + 0.870448i \(0.336170\pi\)
−0.999960 + 0.00891308i \(0.997163\pi\)
\(468\) 1.60931e11 + 2.78740e11i 0.155072 + 0.268592i
\(469\) 5.67218e8 + 3.21686e9i 0.000541343 + 0.00307011i
\(470\) −8.37528e11 7.02770e11i −0.791697 0.664313i
\(471\) 9.05773e10 7.60033e10i 0.0848057 0.0711604i
\(472\) −1.11549e11 + 6.32628e11i −0.103449 + 0.586691i
\(473\) −5.56884e10 + 2.02689e10i −0.0511552 + 0.0186190i
\(474\) −2.68236e11 −0.244070
\(475\) 4.45891e11 + 1.92270e11i 0.401890 + 0.173297i
\(476\) −1.95254e9 −0.00174328
\(477\) −8.13644e11 + 2.96142e11i −0.719618 + 0.261919i
\(478\) 2.28495e11 1.29586e12i 0.200194 1.13536i
\(479\) 8.21287e11 6.89142e11i 0.712829 0.598134i −0.212563 0.977147i \(-0.568181\pi\)
0.925391 + 0.379013i \(0.123736\pi\)
\(480\) −8.27799e10 6.94606e10i −0.0711769 0.0597245i
\(481\) 3.84614e10 + 2.18126e11i 0.0327622 + 0.185804i
\(482\) 2.85182e11 + 4.93949e11i 0.240663 + 0.416841i
\(483\) −3.58589e8 + 6.21095e8i −0.000299802 + 0.000519273i
\(484\) 3.11415e11 + 1.13346e11i 0.257950 + 0.0938861i
\(485\) 2.16679e12 + 7.88647e11i 1.77819 + 0.647209i
\(486\) 4.32362e11 7.48873e11i 0.351548 0.608899i
\(487\) 7.61690e11 + 1.31929e12i 0.613618 + 1.06282i 0.990625 + 0.136607i \(0.0436198\pi\)
−0.377008 + 0.926210i \(0.623047\pi\)
\(488\) 1.12151e11 + 6.36042e11i 0.0895190 + 0.507687i
\(489\) −4.88904e11 4.10240e11i −0.386664 0.324450i
\(490\) 8.28786e11 6.95434e11i 0.649471 0.544971i
\(491\) −3.89885e11 + 2.21115e12i −0.302740 + 1.71692i 0.331216 + 0.943555i \(0.392541\pi\)
−0.633956 + 0.773369i \(0.718570\pi\)
\(492\) 2.30894e11 8.40386e10i 0.177652 0.0646600i
\(493\) 6.02586e11 0.459418
\(494\) 7.17449e11 + 4.16936e10i 0.542026 + 0.0314991i
\(495\) −8.68882e11 −0.650485
\(496\) −3.44764e10 + 1.25484e10i −0.0255773 + 0.00930937i
\(497\) −9.27878e6 + 5.26226e7i −6.82161e−6 + 3.86873e-5i
\(498\) 4.67218e11 3.92043e11i 0.340398 0.285628i
\(499\) 9.62651e11 + 8.07760e11i 0.695050 + 0.583217i 0.920361 0.391070i \(-0.127895\pi\)
−0.225310 + 0.974287i \(0.572340\pi\)
\(500\) −8.18147e10 4.63994e11i −0.0585418 0.332007i
\(501\) −1.88724e11 3.26879e11i −0.133831 0.231802i
\(502\) 4.91916e11 8.52023e11i 0.345720 0.598804i
\(503\) 3.67792e11 + 1.33865e11i 0.256181 + 0.0932422i 0.466918 0.884301i \(-0.345364\pi\)
−0.210737 + 0.977543i \(0.567586\pi\)
\(504\) −1.60551e9 5.84359e8i −0.00110835 0.000403406i
\(505\) 6.18582e11 1.07142e12i 0.423239 0.733072i
\(506\) 1.15968e11 + 2.00863e11i 0.0786433 + 0.136214i
\(507\) −4.64814e10 2.63609e11i −0.0312423 0.177184i
\(508\) −3.54138e11 2.97157e11i −0.235931 0.197970i
\(509\) 1.25817e12 1.05573e12i 0.830825 0.697145i −0.124655 0.992200i \(-0.539783\pi\)
0.955480 + 0.295055i \(0.0953381\pi\)
\(510\) 8.32470e10 4.72117e11i 0.0544882 0.309018i
\(511\) −3.04512e9 + 1.10833e9i −0.00197565 + 0.000719078i
\(512\) −6.87195e10 −0.0441942
\(513\) −5.58064e11 1.11084e12i −0.355759 0.708146i
\(514\) 1.80894e12 1.14311
\(515\) −1.71203e12 + 6.23128e11i −1.07245 + 0.390342i
\(516\) 4.96839e9 2.81772e10i 0.00308526 0.0174974i
\(517\) 1.01868e12 8.54773e11i 0.627090 0.526191i
\(518\) −9.00677e8 7.55758e8i −0.000549649 0.000461210i
\(519\) 1.32100e11 + 7.49175e11i 0.0799188 + 0.453242i
\(520\) 2.71353e11 + 4.69998e11i 0.162750 + 0.281891i
\(521\) 1.27879e12 2.21493e12i 0.760378 1.31701i −0.182277 0.983247i \(-0.558347\pi\)
0.942656 0.333767i \(-0.108320\pi\)
\(522\) 4.95488e11 + 1.80343e11i 0.292090 + 0.106312i
\(523\) 2.43103e12 + 8.84822e11i 1.42080 + 0.517128i 0.934279 0.356542i \(-0.116044\pi\)
0.486518 + 0.873670i \(0.338267\pi\)
\(524\) 2.24707e11 3.89204e11i 0.130204 0.225520i
\(525\) −6.89553e8 1.19434e9i −0.000396142 0.000686138i
\(526\) −6.43559e10 3.64980e11i −0.0366566 0.207890i
\(527\) −1.24686e11 1.04624e11i −0.0704158 0.0590859i
\(528\) 1.00684e11 8.44842e10i 0.0563780 0.0473067i
\(529\) −2.78453e11 + 1.57919e12i −0.154597 + 0.876765i
\(530\) −1.37193e12 + 4.99341e11i −0.755249 + 0.274888i
\(531\) −2.49375e12 −1.36122
\(532\) −3.05972e9 + 2.27849e9i −0.00165607 + 0.00123323i
\(533\) −1.23402e12 −0.662292
\(534\) −2.29101e11 + 8.33858e10i −0.121924 + 0.0443768i
\(535\) 4.20740e11 2.38613e12i 0.222035 1.25922i
\(536\) −3.90699e11 + 3.27835e11i −0.204456 + 0.171559i
\(537\) −2.34071e11 1.96409e11i −0.121468 0.101924i
\(538\) 3.48140e11 + 1.97440e12i 0.179157 + 1.01605i
\(539\) 6.57954e11 + 1.13961e12i 0.335773 + 0.581577i
\(540\) 4.69388e11 8.13004e11i 0.237553 0.411453i
\(541\) −1.08264e12 3.94047e11i −0.543369 0.197770i 0.0557289 0.998446i \(-0.482252\pi\)
−0.599098 + 0.800676i \(0.704474\pi\)
\(542\) 7.73343e11 + 2.81474e11i 0.384924 + 0.140101i
\(543\) −6.28394e11 + 1.08841e12i −0.310194 + 0.537271i
\(544\) −1.52432e11 2.64021e11i −0.0746247 0.129254i
\(545\) −1.75019e11 9.92582e11i −0.0849769 0.481928i
\(546\) −1.56356e9 1.31198e9i −0.000752919 0.000631774i
\(547\) −2.57022e12 + 2.15667e12i −1.22752 + 1.03001i −0.229119 + 0.973399i \(0.573584\pi\)
−0.998396 + 0.0566089i \(0.981971\pi\)
\(548\) −1.96382e11 + 1.11374e12i −0.0930228 + 0.527558i
\(549\) −2.35601e12 + 8.57516e11i −1.10688 + 0.402872i
\(550\) −4.46004e11 −0.207829
\(551\) 9.44282e11 7.03182e11i 0.436435 0.325001i
\(552\) −1.11979e11 −0.0513345
\(553\) −6.71982e9 + 2.44581e9i −0.00305559 + 0.00111214i
\(554\) 9.64132e10 5.46787e11i 0.0434853 0.246618i
\(555\) 2.21140e11 1.85559e11i 0.0989349 0.0830163i
\(556\) −4.12957e11 3.46512e11i −0.183260 0.153774i
\(557\) 5.44872e11 + 3.09012e12i 0.239854 + 1.36028i 0.832147 + 0.554555i \(0.187112\pi\)
−0.592293 + 0.805723i \(0.701777\pi\)
\(558\) −7.12136e10 1.23346e11i −0.0310963 0.0538604i
\(559\) −7.18473e10 + 1.24443e11i −0.0311213 + 0.0539036i
\(560\) −2.70714e9 9.85319e8i −0.00116323 0.000423380i
\(561\) 5.47926e11 + 1.99429e11i 0.233555 + 0.0850070i
\(562\) 3.17623e11 5.50139e11i 0.134307 0.232627i
\(563\) −1.17795e12 2.04027e12i −0.494129 0.855856i 0.505848 0.862622i \(-0.331180\pi\)
−0.999977 + 0.00676634i \(0.997846\pi\)
\(564\) 1.11486e11 + 6.32268e11i 0.0463942 + 0.263115i
\(565\) −2.51652e12 2.11161e12i −1.03892 0.871756i
\(566\) 1.55034e12 1.30089e12i 0.634970 0.532803i
\(567\) 8.12610e8 4.60854e9i 0.000330186 0.00187258i
\(568\) −7.83997e9 + 2.85352e9i −0.00316044 + 0.00115030i
\(569\) −1.92424e12 −0.769581 −0.384790 0.923004i \(-0.625726\pi\)
−0.384790 + 0.923004i \(0.625726\pi\)
\(570\) −4.20480e11 8.36976e11i −0.166843 0.332105i
\(571\) −1.57461e12 −0.619884 −0.309942 0.950755i \(-0.600310\pi\)
−0.309942 + 0.950755i \(0.600310\pi\)
\(572\) −6.20281e11 + 2.25764e11i −0.242274 + 0.0881805i
\(573\) 4.77215e10 2.70642e11i 0.0184935 0.104882i
\(574\) 5.01805e9 4.21065e9i 0.00192944 0.00161899i
\(575\) 2.91085e11 + 2.44250e11i 0.111049 + 0.0931813i
\(576\) −4.63241e10 2.62717e11i −0.0175350 0.0994458i
\(577\) 1.88649e12 + 3.26749e12i 0.708537 + 1.22722i 0.965400 + 0.260774i \(0.0839778\pi\)
−0.256863 + 0.966448i \(0.582689\pi\)
\(578\) −2.72456e11 + 4.71908e11i −0.101536 + 0.175866i
\(579\) 6.57432e11 + 2.39286e11i 0.243107 + 0.0884837i
\(580\) 8.35469e11 + 3.04086e11i 0.306552 + 0.111576i
\(581\) 8.12999e9 1.40816e10i 0.00296004 0.00512694i
\(582\) −6.77026e11 1.17264e12i −0.244597 0.423655i
\(583\) −3.08357e11 1.74878e12i −0.110546 0.626940i
\(584\) −3.87597e11 3.25232e11i −0.137887 0.115701i
\(585\) −1.61390e12 + 1.35422e12i −0.569737 + 0.478066i
\(586\) −1.33898e11 + 7.59370e11i −0.0469065 + 0.266020i
\(587\) 3.86378e12 1.40630e12i 1.34320 0.488885i 0.432382 0.901690i \(-0.357673\pi\)
0.910819 + 0.412805i \(0.135451\pi\)
\(588\) −6.35320e11 −0.219177
\(589\) −3.17479e11 1.84499e10i −0.108692 0.00631648i
\(590\) −4.20485e12 −1.42862
\(591\) −1.93677e12 + 7.04927e11i −0.653033 + 0.237684i
\(592\) 3.18782e10 1.80790e11i 0.0106671 0.0604961i
\(593\) −5.09094e11 + 4.27181e11i −0.169064 + 0.141862i −0.723394 0.690435i \(-0.757419\pi\)
0.554330 + 0.832297i \(0.312975\pi\)
\(594\) 8.74689e11 + 7.33951e11i 0.288280 + 0.241896i
\(595\) −2.21934e9 1.25865e10i −0.000725933 0.00411697i
\(596\) 4.07210e11 + 7.05309e11i 0.132194 + 0.228966i
\(597\) −5.67728e11 + 9.83334e11i −0.182918 + 0.316823i
\(598\) 5.28465e11 + 1.92345e11i 0.168990 + 0.0615073i
\(599\) 4.00019e12 + 1.45595e12i 1.26958 + 0.462089i 0.886972 0.461822i \(-0.152804\pi\)
0.382607 + 0.923911i \(0.375026\pi\)
\(600\) 1.07665e11 1.86482e11i 0.0339153 0.0587430i
\(601\) −1.70211e12 2.94814e12i −0.532173 0.921751i −0.999294 0.0375576i \(-0.988042\pi\)
0.467121 0.884193i \(-0.345291\pi\)
\(602\) −1.32456e8 7.51193e8i −4.11042e−5 0.000233113i
\(603\) −1.51670e12 1.27266e12i −0.467166 0.391998i
\(604\) −1.28810e12 + 1.08084e12i −0.393806 + 0.330443i
\(605\) −3.76684e11 + 2.13628e12i −0.114308 + 0.648275i
\(606\) −6.82680e11 + 2.48475e11i −0.205632 + 0.0748439i
\(607\) −5.82226e12 −1.74078 −0.870388 0.492367i \(-0.836132\pi\)
−0.870388 + 0.492367i \(0.836132\pi\)
\(608\) −5.46966e11 2.35854e11i −0.162328 0.0699967i
\(609\) −3.34380e9 −0.000985060
\(610\) −3.97259e12 + 1.44590e12i −1.16169 + 0.422819i
\(611\) 5.59905e11 3.17538e12i 0.162528 0.921744i
\(612\) 9.06605e11 7.60732e11i 0.261238 0.219205i
\(613\) 2.57496e12 + 2.16065e12i 0.736544 + 0.618033i 0.931907 0.362697i \(-0.118144\pi\)
−0.195363 + 0.980731i \(0.562589\pi\)
\(614\) −2.34446e11 1.32961e12i −0.0665709 0.377542i
\(615\) 8.04175e11 + 1.39287e12i 0.226680 + 0.392621i
\(616\) 1.75199e9 3.03454e9i 0.000490252 0.000849141i
\(617\) 5.82933e12 + 2.12170e12i 1.61933 + 0.589388i 0.983254 0.182238i \(-0.0583341\pi\)
0.636076 + 0.771626i \(0.280556\pi\)
\(618\) 1.00535e12 + 3.65916e11i 0.277247 + 0.100910i
\(619\) 2.20898e12 3.82606e12i 0.604761 1.04748i −0.387329 0.921942i \(-0.626602\pi\)
0.992089 0.125534i \(-0.0400646\pi\)
\(620\) −1.20077e11 2.07979e11i −0.0326360 0.0565272i
\(621\) −1.68926e11 9.58028e11i −0.0455811 0.258503i
\(622\) 2.99092e12 + 2.50968e12i 0.801214 + 0.672298i
\(623\) −4.97907e9 + 4.17794e9i −0.00132420 + 0.00111113i
\(624\) 5.53401e10 3.13849e11i 0.0146120 0.0828687i
\(625\) 4.46687e12 1.62581e12i 1.17096 0.426196i
\(626\) −3.69361e12 −0.961317
\(627\) 1.09135e12 3.26882e11i 0.282007 0.0844670i
\(628\) 4.92184e11 0.126273
\(629\) 7.65309e11 2.78550e11i 0.194944 0.0709536i
\(630\) 1.94201e9 1.10137e10i 0.000491156 0.00278548i
\(631\) 4.40580e12 3.69690e12i 1.10635 0.928337i 0.108514 0.994095i \(-0.465391\pi\)
0.997836 + 0.0657574i \(0.0209464\pi\)
\(632\) −8.55331e11 7.17708e11i −0.213259 0.178945i
\(633\) 3.11183e11 + 1.76481e12i 0.0770370 + 0.436899i
\(634\) 2.24195e12 + 3.88317e12i 0.551092 + 0.954519i
\(635\) 1.51301e12 2.62061e12i 0.369283 0.639617i
\(636\) 8.05630e11 + 2.93225e11i 0.195244 + 0.0710631i
\(637\) 2.99828e12 + 1.09129e12i 0.721515 + 0.262610i
\(638\) −5.40695e11 + 9.36510e11i −0.129199 + 0.223779i
\(639\) −1.61940e10 2.80489e10i −0.00384239 0.00665521i
\(640\) −7.81094e10 4.42981e11i −0.0184032 0.104370i
\(641\) −5.08746e12 4.26888e12i −1.19025 0.998742i −0.999855 0.0170348i \(-0.994577\pi\)
−0.190399 0.981707i \(-0.560978\pi\)
\(642\) −1.08994e12 + 9.14566e11i −0.253218 + 0.212475i
\(643\) −4.75446e11 + 2.69639e12i −0.109686 + 0.622061i 0.879559 + 0.475791i \(0.157838\pi\)
−0.989245 + 0.146270i \(0.953273\pi\)
\(644\) −2.80528e9 + 1.02104e9i −0.000642672 + 0.000233913i
\(645\) 1.87283e11 0.0426070
\(646\) −3.07117e11 2.62462e12i −0.0693838 0.592952i
\(647\) −5.81279e11 −0.130411 −0.0652057 0.997872i \(-0.520770\pi\)
−0.0652057 + 0.997872i \(0.520770\pi\)
\(648\) 6.86603e11 2.49903e11i 0.152974 0.0556781i
\(649\) 8.88092e11 5.03662e12i 0.196497 1.11439i
\(650\) −8.28427e11 + 6.95133e11i −0.182031 + 0.152742i
\(651\) 6.91894e8 + 5.80568e8i 0.000150982 + 0.000126689i
\(652\) −4.61320e11 2.61628e12i −0.0999743 0.566983i
\(653\) 3.43620e12 + 5.95168e12i 0.739553 + 1.28094i 0.952697 + 0.303923i \(0.0982965\pi\)
−0.213143 + 0.977021i \(0.568370\pi\)
\(654\) −2.95930e11 + 5.12566e11i −0.0632542 + 0.109559i
\(655\) 2.76430e12 + 1.00612e12i 0.586813 + 0.213582i
\(656\) 9.61115e11 + 3.49817e11i 0.202632 + 0.0737520i
\(657\) 9.82093e11 1.70104e12i 0.205640 0.356180i
\(658\) 8.55803e9 + 1.48230e10i 0.00177974 + 0.00308261i
\(659\) 8.54346e11 + 4.84524e12i 0.176461 + 1.00076i 0.936444 + 0.350818i \(0.114096\pi\)
−0.759982 + 0.649944i \(0.774792\pi\)
\(660\) 6.59046e11 + 5.53005e11i 0.135197 + 0.113444i
\(661\) 1.72575e12 1.44808e12i 0.351618 0.295043i −0.449821 0.893119i \(-0.648512\pi\)
0.801440 + 0.598076i \(0.204068\pi\)
\(662\) −8.37288e11 + 4.74850e12i −0.169439 + 0.960937i
\(663\) 1.32857e12 4.83558e11i 0.267037 0.0971937i
\(664\) 2.53880e12 0.506841
\(665\) −1.81655e10 1.71338e10i −0.00360205 0.00339748i
\(666\) 7.12656e11 0.140361
\(667\) 8.65755e11 3.15109e11i 0.169367 0.0616445i
\(668\) 2.72828e11 1.54728e12i 0.0530145 0.300660i
\(669\) −2.64777e12 + 2.22174e12i −0.511049 + 0.428821i
\(670\) −2.55738e12 2.14590e12i −0.490297 0.411408i
\(671\) −8.92884e11 5.06380e12i −0.170037 0.964329i
\(672\) 8.45861e8 + 1.46507e9i 0.000160006 + 0.000277139i
\(673\) −1.18131e12 + 2.04609e12i −0.221971 + 0.384465i −0.955406 0.295294i \(-0.904582\pi\)
0.733435 + 0.679759i \(0.237916\pi\)
\(674\) −3.72167e12 1.35458e12i −0.694654 0.252833i
\(675\) 1.75785e12 + 6.39807e11i 0.325924 + 0.118627i
\(676\) 5.57110e11 9.64944e11i 0.102608 0.177722i
\(677\) 4.09727e11 + 7.09668e11i 0.0749628 + 0.129839i 0.901070 0.433673i \(-0.142783\pi\)
−0.826107 + 0.563513i \(0.809450\pi\)
\(678\) 3.34981e11 + 1.89977e12i 0.0608817 + 0.345277i
\(679\) −2.76531e10 2.32037e10i −0.00499263 0.00418931i
\(680\) 1.52867e12 1.28271e12i 0.274173 0.230058i
\(681\) 4.13643e11 2.34589e12i 0.0736994 0.417970i
\(682\) 2.74481e11 9.99030e10i 0.0485829 0.0176827i
\(683\) −7.57557e12 −1.33205 −0.666027 0.745928i \(-0.732006\pi\)
−0.666027 + 0.745928i \(0.732006\pi\)
\(684\) 5.32967e11 2.25006e12i 0.0930995 0.393044i
\(685\) −7.40261e12 −1.28463
\(686\) −3.18322e10 + 1.15860e10i −0.00548792 + 0.00199744i
\(687\) −6.58402e11 + 3.73398e12i −0.112768 + 0.639539i
\(688\) 9.12352e10 7.65554e10i 0.0155244 0.0130265i
\(689\) −3.29836e12 2.76765e12i −0.557586 0.467870i
\(690\) −1.27280e11 7.21839e11i −0.0213766 0.121233i
\(691\) −8.21486e11 1.42286e12i −0.137072 0.237416i 0.789315 0.613988i \(-0.210436\pi\)
−0.926387 + 0.376573i \(0.877103\pi\)
\(692\) −1.58330e12 + 2.74236e12i −0.262474 + 0.454619i
\(693\) 1.27822e10 + 4.65233e9i 0.00210526 + 0.000766251i
\(694\) 2.45956e12 + 8.95206e11i 0.402476 + 0.146489i
\(695\) 1.76431e12 3.05587e12i 0.286842 0.496825i
\(696\) −2.61047e11 4.52147e11i −0.0421674 0.0730361i
\(697\) 7.87930e11 + 4.46857e12i 0.126456 + 0.717168i
\(698\) 2.68051e12 + 2.24922e12i 0.427433 + 0.358659i
\(699\) 2.61163e12 2.19142e12i 0.413775 0.347199i
\(700\) 9.96851e8 5.65342e9i 0.000156924 0.000889960i
\(701\) 4.49933e12 1.63762e12i 0.703747 0.256143i 0.0347372 0.999396i \(-0.488941\pi\)
0.669010 + 0.743253i \(0.266718\pi\)
\(702\) 2.76860e12 0.430273
\(703\) 8.74227e11 1.32957e12i 0.134997 0.205311i
\(704\) 5.47105e11 0.0839448
\(705\) −3.94902e12 + 1.43732e12i −0.602057 + 0.219131i
\(706\) 8.71075e11 4.94011e12i 0.131958 0.748369i
\(707\) −1.48368e10 + 1.24495e10i −0.00223333 + 0.00187398i
\(708\) 1.89151e12 + 1.58716e12i 0.282917 + 0.237395i
\(709\) 1.56313e12 + 8.86496e12i 0.232320 + 1.31755i 0.848184 + 0.529702i \(0.177696\pi\)
−0.615863 + 0.787853i \(0.711193\pi\)
\(710\) −2.73056e10 4.72947e10i −0.00403264 0.00698474i
\(711\) 2.16724e12 3.75377e12i 0.318049 0.550876i
\(712\) −9.53649e11 3.47100e11i −0.139068 0.0506168i
\(713\) −2.33851e11 8.51150e10i −0.0338873 0.0123340i
\(714\) −3.75255e9 + 6.49961e9i −0.000540362 + 0.000935935i
\(715\) −2.16036e12 3.74185e12i −0.309136 0.535439i
\(716\) −2.20864e11 1.25258e12i −0.0314063 0.178114i
\(717\) −3.87452e12 3.25110e12i −0.547496 0.459404i
\(718\) 1.32366e12 1.11068e12i 0.185873 0.155966i
\(719\) −6.82274e11 + 3.86937e12i −0.0952092 + 0.539958i 0.899474 + 0.436975i \(0.143950\pi\)
−0.994683 + 0.102984i \(0.967161\pi\)
\(720\) 1.64088e12 5.97230e11i 0.227551 0.0828219i
\(721\) 2.85223e10 0.00393075
\(722\) −3.54404e12 3.75452e12i −0.485379 0.514205i
\(723\) 2.19235e12 0.298392
\(724\) −4.91598e12 + 1.78927e12i −0.664947 + 0.242021i
\(725\) −3.07645e11 + 1.74474e12i −0.0413551 + 0.234536i
\(726\) 9.75810e11 8.18802e11i 0.130362 0.109387i
\(727\) 3.67381e12 + 3.08269e12i 0.487766 + 0.409285i 0.853225 0.521543i \(-0.174643\pi\)
−0.365459 + 0.930828i \(0.619088\pi\)
\(728\) −1.47535e9 8.36711e9i −0.000194672 0.00110404i
\(729\) 9.36820e10 + 1.62262e11i 0.0122852 + 0.0212786i
\(730\) 1.65596e12 2.86821e12i 0.215823 0.373816i
\(731\) 4.96503e11 + 1.80712e11i 0.0643122 + 0.0234077i
\(732\) 2.33280e12 + 8.49069e11i 0.300315 + 0.109306i
\(733\) −5.58530e12 + 9.67403e12i −0.714626 + 1.23777i 0.248478 + 0.968638i \(0.420070\pi\)
−0.963104 + 0.269131i \(0.913264\pi\)
\(734\) 2.79032e12 + 4.83298e12i 0.354832 + 0.614587i
\(735\) −7.22131e11 4.09541e12i −0.0912689 0.517612i
\(736\) −3.57069e11 2.99616e11i −0.0448541 0.0376370i
\(737\) 3.11052e12 2.61004e12i 0.388355 0.325869i
\(738\) −6.89472e11 + 3.91019e12i −0.0855584 + 0.485226i
\(739\) −1.17481e13 + 4.27596e12i −1.44900 + 0.527392i −0.942311 0.334739i \(-0.891352\pi\)
−0.506686 + 0.862131i \(0.669130\pi\)
\(740\) 1.20165e12 0.147311
\(741\) 1.51765e12 2.30812e12i 0.184922 0.281239i
\(742\) 2.28562e10 0.00276813
\(743\) 3.01450e12 1.09719e12i 0.362883 0.132078i −0.154143 0.988049i \(-0.549262\pi\)
0.517025 + 0.855970i \(0.327039\pi\)
\(744\) −2.44886e10 + 1.38882e11i −0.00293012 + 0.0166175i
\(745\) −4.08372e12 + 3.42665e12i −0.485683 + 0.407536i
\(746\) −4.47226e12 3.75267e12i −0.528692 0.443625i
\(747\) 1.71141e12 + 9.70591e12i 0.201100 + 1.14050i
\(748\) 1.21358e12 + 2.10198e12i 0.141746 + 0.245511i
\(749\) −1.89658e10 + 3.28498e10i −0.00220193 + 0.00381386i
\(750\) −1.70178e12 6.19399e11i −0.196394 0.0714817i
\(751\) −9.28439e12 3.37924e12i −1.06506 0.387650i −0.250733 0.968056i \(-0.580671\pi\)
−0.814327 + 0.580406i \(0.802894\pi\)
\(752\) −1.33623e12 + 2.31442e12i −0.152371 + 0.263914i
\(753\) −1.89081e12 3.27498e12i −0.214324 0.371220i
\(754\) 4.55317e11 + 2.58223e12i 0.0513030 + 0.290954i
\(755\) −8.43145e12 7.07483e12i −0.944367 0.792418i
\(756\) −1.12583e10 + 9.44687e9i −0.00125351 + 0.00105182i
\(757\) −2.59273e12 + 1.47041e13i −0.286963 + 1.62745i 0.411225 + 0.911534i \(0.365101\pi\)
−0.698188 + 0.715914i \(0.746010\pi\)
\(758\) 2.24379e12 8.16671e11i 0.246871 0.0898536i
\(759\) 8.91510e11 0.0975076
\(760\) 8.98663e11 3.79394e12i 0.0977093 0.412505i
\(761\) −1.26232e13 −1.36439 −0.682193 0.731172i \(-0.738974\pi\)
−0.682193 + 0.731172i \(0.738974\pi\)
\(762\) −1.66979e12 + 6.07753e11i −0.179417 + 0.0653025i
\(763\) −2.73996e9 + 1.55391e10i −0.000292673 + 0.00165983i
\(764\) 8.76315e11 7.35316e11i 0.0930551 0.0780825i
\(765\) 5.93433e12 + 4.97949e12i 0.626462 + 0.525664i
\(766\) −7.30411e11 4.14237e12i −0.0766545 0.434729i
\(767\) −6.20039e12 1.07394e13i −0.646904 1.12047i
\(768\) −1.32071e11 + 2.28754e11i −0.0136988 + 0.0237270i
\(769\) −8.74434e12 3.18268e12i −0.901692 0.328189i −0.150762 0.988570i \(-0.548173\pi\)
−0.750931 + 0.660381i \(0.770395\pi\)
\(770\) 2.15527e10 + 7.84454e9i 0.00220950 + 0.000804191i
\(771\) 3.47657e12 6.02160e12i 0.354329 0.613715i
\(772\) 1.45612e12 + 2.52208e12i 0.147543 + 0.255553i
\(773\) 2.14558e12 + 1.21682e13i 0.216141 + 1.22580i 0.878916 + 0.476977i \(0.158268\pi\)
−0.662775 + 0.748819i \(0.730621\pi\)
\(774\) 3.54176e11 + 2.97189e11i 0.0354719 + 0.0297645i
\(775\) 3.66588e11 3.07604e11i 0.0365024 0.0306291i
\(776\) 9.78741e11 5.55072e12i 0.0968925 0.549504i
\(777\) −4.24677e9 + 1.54570e9i −0.000417988 + 0.000152135i
\(778\) 7.66583e12 0.750155
\(779\) 6.44928e12 + 6.08301e12i 0.627470 + 0.591834i
\(780\) 2.08604e12 0.201789
\(781\) 6.24173e10 2.27181e10i 0.00600310 0.00218495i
\(782\) 3.59084e11 2.03647e12i 0.0343372 0.194736i
\(783\) 3.47451e12 2.91546e12i 0.330344 0.277191i
\(784\) −2.02586e12 1.69990e12i −0.191508 0.160694i
\(785\) 5.59437e11 + 3.17273e12i 0.0525821 + 0.298208i
\(786\) −8.63721e11 1.49601e12i −0.0807183 0.139808i
\(787\) 5.44818e11 9.43652e11i 0.0506250 0.0876850i −0.839602 0.543201i \(-0.817212\pi\)
0.890227 + 0.455516i \(0.150545\pi\)
\(788\) −8.06197e12 2.93432e12i −0.744857 0.271106i
\(789\) −1.33863e12 4.87222e11i −0.122974 0.0447590i
\(790\) 3.65429e12 6.32942e12i 0.333796 0.578152i
\(791\) 2.57143e10 + 4.45384e10i 0.00233550 + 0.00404521i
\(792\) 3.68806e11 + 2.09160e12i 0.0333069 + 0.188893i
\(793\) −9.55081e12 8.01408e12i −0.857651 0.719655i
\(794\) 7.19869e12 6.04042e12i 0.642778 0.539355i
\(795\) −9.74481e11 + 5.52655e12i −0.0865209 + 0.490685i
\(796\) −4.44139e12 + 1.61653e12i −0.392112 + 0.142717i
\(797\) 1.84217e13 1.61721 0.808606 0.588350i \(-0.200222\pi\)
0.808606 + 0.588350i \(0.200222\pi\)
\(798\) 1.70422e9 + 1.45642e10i 0.000148769 + 0.00127138i
\(799\) −1.18560e13 −1.02915
\(800\) 8.42275e11 3.06563e11i 0.0727025 0.0264615i
\(801\) 6.84116e11 3.87981e12i 0.0587196 0.333016i
\(802\) 3.34828e12 2.80954e12i 0.285784 0.239801i
\(803\) 3.08582e12 + 2.58931e12i 0.261909 + 0.219768i
\(804\) 3.40421e11 + 1.93062e12i 0.0287319 + 0.162946i
\(805\) −9.77042e9 1.69229e10i −0.000820034 0.00142034i
\(806\) 3.54126e11 6.13365e11i 0.0295563 0.0511931i
\(807\) 7.24147e12 + 2.63568e12i 0.601029 + 0.218757i
\(808\) −2.84171e12 1.03430e12i −0.234546 0.0853679i
\(809\) −5.66933e12 + 9.81957e12i −0.465333 + 0.805980i −0.999216 0.0395780i \(-0.987399\pi\)
0.533884 + 0.845558i \(0.320732\pi\)
\(810\) 2.39135e12 + 4.14194e12i 0.195191 + 0.338081i
\(811\) −4.07898e12 2.31330e13i −0.331099 1.87775i −0.462798 0.886464i \(-0.653155\pi\)
0.131700 0.991290i \(-0.457957\pi\)
\(812\) −1.06624e10 8.94686e9i −0.000860706 0.000722218i
\(813\) 2.42325e12 2.03335e12i 0.194532 0.163232i
\(814\) −2.53796e11 + 1.43935e12i −0.0202616 + 0.114909i
\(815\) 1.63407e13 5.94754e12i 1.29737 0.472203i
\(816\) −1.17183e12 −0.0925250
\(817\) 9.88925e11 2.96204e11i 0.0776541 0.0232590i
\(818\) 3.55268e12 0.277438
\(819\) 3.09932e10 1.12806e10i 0.00240707 0.000876101i
\(820\) −1.16255e12 + 6.59317e12i −0.0897947 + 0.509251i
\(821\) 7.93812e12 6.66088e12i 0.609781 0.511667i −0.284792 0.958589i \(-0.591925\pi\)
0.894573 + 0.446923i \(0.147480\pi\)
\(822\) 3.32999e12 + 2.79419e12i 0.254402 + 0.213468i
\(823\) 5.16386e11 + 2.92857e12i 0.0392352 + 0.222514i 0.998121 0.0612796i \(-0.0195181\pi\)
−0.958885 + 0.283793i \(0.908407\pi\)
\(824\) 2.22670e12 + 3.85676e12i 0.168264 + 0.291441i
\(825\) −8.57169e11 + 1.48466e12i −0.0644205 + 0.111580i
\(826\) 6.18578e10 + 2.25144e10i 0.00462364 + 0.00168287i
\(827\) 7.02649e12 + 2.55743e12i 0.522353 + 0.190121i 0.589721 0.807607i \(-0.299238\pi\)
−0.0673678 + 0.997728i \(0.521460\pi\)
\(828\) 9.04741e11 1.56706e12i 0.0668941 0.115864i
\(829\) 9.45818e12 + 1.63820e13i 0.695524 + 1.20468i 0.970004 + 0.243090i \(0.0781609\pi\)
−0.274480 + 0.961593i \(0.588506\pi\)
\(830\) 2.88570e12 + 1.63656e13i 0.211057 + 1.19697i
\(831\) −1.63485e12 1.37180e12i −0.118925 0.0997899i
\(832\) 1.01622e12 8.52706e11i 0.0735243 0.0616942i
\(833\) 2.03729e12 1.15540e13i 0.146605 0.831441i
\(834\) −1.94713e12 + 7.08697e11i −0.139363 + 0.0507240i
\(835\) 1.02842e13 0.732121
\(836\) 4.35463e12 + 1.87774e12i 0.308335 + 0.132955i
\(837\) −1.22514e12 −0.0862820
\(838\) −1.21072e13 + 4.40667e12i −0.848099 + 0.308683i
\(839\) −3.21604e11 + 1.82391e12i −0.0224075 + 0.127079i −0.993960 0.109747i \(-0.964996\pi\)
0.971552 + 0.236826i \(0.0761071\pi\)
\(840\) −8.48275e9 + 7.11787e9i −0.000587868 + 0.000493280i
\(841\) −7.82251e12 6.56386e12i −0.539218 0.452457i
\(842\) −2.77638e11 1.57457e12i −0.0190360 0.107958i
\(843\) −1.22087e12 2.11461e12i −0.0832617 0.144214i
\(844\) −3.72974e12 + 6.46010e12i −0.253010 + 0.438226i
\(845\) 6.85347e12 + 2.49446e12i 0.462440 + 0.168314i
\(846\) −9.74888e12 3.54830e12i −0.654317 0.238152i
\(847\) 1.69799e10 2.94101e10i 0.00113360 0.00196346i
\(848\) 1.78436e12 + 3.09060e12i 0.118495 + 0.205240i
\(849\) −1.35083e12 7.66094e12i −0.0892311 0.506055i
\(850\) 3.04614e12 + 2.55602e12i 0.200154 + 0.167949i
\(851\) 9.53883e11 8.00403e11i 0.0623465 0.0523150i
\(852\) −5.56873e9 + 3.15819e10i −0.000362058 + 0.00205333i
\(853\) 1.34731e13 4.90380e12i 0.871357 0.317148i 0.132641 0.991164i \(-0.457654\pi\)
0.738717 + 0.674016i \(0.235432\pi\)
\(854\) 6.61829e10 0.00425780
\(855\) 1.51102e13 + 8.78107e11i 0.966989 + 0.0561953i
\(856\) −5.92257e12 −0.377032
\(857\) 2.09877e13 7.63890e12i 1.32908 0.483746i 0.422724 0.906259i \(-0.361074\pi\)
0.906357 + 0.422513i \(0.138852\pi\)
\(858\) −4.40586e11 + 2.49869e12i −0.0277548 + 0.157405i
\(859\) 1.67657e13 1.40681e13i 1.05063 0.881587i 0.0574740 0.998347i \(-0.481695\pi\)
0.993160 + 0.116760i \(0.0372509\pi\)
\(860\) 5.97194e11 + 5.01105e11i 0.0372282 + 0.0312382i
\(861\) −4.37229e9 2.47965e10i −0.000271141 0.00153772i
\(862\) −2.20326e12 3.81616e12i −0.135920 0.235420i
\(863\) −1.26522e13 + 2.19143e13i −0.776457 + 1.34486i 0.157515 + 0.987517i \(0.449652\pi\)
−0.933972 + 0.357346i \(0.883682\pi\)
\(864\) −2.15633e12 7.84839e11i −0.131644 0.0479147i
\(865\) −1.94775e13 7.08923e12i −1.18294 0.430553i
\(866\) 7.49035e12 1.29737e13i 0.452555 0.783849i
\(867\) 1.04726e12 + 1.81391e12i 0.0629461 + 0.109026i
\(868\) 6.52857e8 + 3.70254e9i 3.90373e−5 + 0.000221391i
\(869\) 6.80965e12 + 5.71398e12i 0.405075 + 0.339899i
\(870\) 2.61792e12 2.19669e12i 0.154924 0.129997i
\(871\) 1.70966e12 9.69598e12i 0.100653 0.570834i
\(872\) −2.31509e12 + 8.42623e11i −0.135595 + 0.0493525i
\(873\) 2.18803e13 1.27494
\(874\) −1.81373e12 3.61027e12i −0.105141 0.209285i
\(875\) −4.82806e10 −0.00278443
\(876\) −1.82755e12 + 6.65174e11i −0.104858 + 0.0381652i
\(877\) −1.77940e12 + 1.00915e13i −0.101572 + 0.576045i 0.890962 + 0.454078i \(0.150031\pi\)
−0.992534 + 0.121967i \(0.961080\pi\)
\(878\) −1.78060e13 + 1.49410e13i −1.01121 + 0.848505i
\(879\) 2.27046e12 + 1.90514e12i 0.128281 + 0.107641i
\(880\) 6.21862e11 + 3.52676e12i 0.0349560 + 0.198246i
\(881\) −9.30646e12 1.61193e13i −0.520467 0.901475i −0.999717 0.0237963i \(-0.992425\pi\)
0.479250 0.877678i \(-0.340909\pi\)
\(882\) 5.13312e12 8.89082e12i 0.285610 0.494690i
\(883\) −4.46579e12 1.62541e12i −0.247215 0.0899790i 0.215441 0.976517i \(-0.430881\pi\)
−0.462656 + 0.886538i \(0.653103\pi\)
\(884\) 5.53026e12 + 2.01285e12i 0.304586 + 0.110860i
\(885\) −8.08124e12 + 1.39971e13i −0.442826 + 0.766997i
\(886\) −2.63582e12 4.56538e12i −0.143703 0.248900i
\(887\) 2.06796e12 + 1.17280e13i 0.112172 + 0.636161i 0.988111 + 0.153739i \(0.0491316\pi\)
−0.875939 + 0.482422i \(0.839757\pi\)
\(888\) −5.40549e11 4.53574e11i −0.0291727 0.0244788i
\(889\) −3.62897e10 + 3.04507e10i −0.00194861 + 0.00163508i
\(890\) 1.15352e12 6.54196e12i 0.0616271 0.349504i
\(891\) −5.46634e12 + 1.98959e12i −0.290567 + 0.105758i
\(892\) −1.43876e13 −0.760934
\(893\) −1.85790e13 + 1.38353e13i −0.977668 + 0.728043i
\(894\) 3.13045e12 0.163903
\(895\) 7.82338e12 2.84748e12i 0.407559 0.148339i
\(896\) −1.22282e9 + 6.93495e9i −6.33834e−5 + 0.000359465i
\(897\) 1.65593e12 1.38949e12i 0.0854035 0.0716620i
\(898\) −5.60786e12 4.70555e12i −0.287775 0.241472i
\(899\) −2.01483e11 1.14267e12i −0.0102877 0.0583446i
\(900\) 1.73978e12 + 3.01339e12i 0.0883901 + 0.153096i
\(901\) −7.91607e12 + 1.37110e13i −0.400173 + 0.693121i
\(902\) −7.65185e12 2.78504e12i −0.384890 0.140089i
\(903\) −2.75514e9 1.00279e9i −0.000137895 5.01897e-5i
\(904\) −4.01497e12 + 6.95413e12i −0.199951 + 0.346326i
\(905\) −1.71217e13 2.96557e13i −0.848456 1.46957i
\(906\) 1.12234e12 + 6.36508e12i 0.0553408 + 0.313854i
\(907\) 1.25188e13 + 1.05045e13i 0.614230 + 0.515400i 0.895984 0.444087i \(-0.146472\pi\)
−0.281754 + 0.959487i \(0.590916\pi\)
\(908\) 7.59578e12 6.37361e12i 0.370839 0.311171i
\(909\) 2.03855e12 1.15612e13i 0.0990337 0.561648i
\(910\) 5.22592e10 1.90208e10i 0.00252625 0.000919481i
\(911\) −3.63134e13 −1.74676 −0.873381 0.487037i \(-0.838078\pi\)
−0.873381 + 0.487037i \(0.838078\pi\)
\(912\) −1.83632e12 + 1.36746e12i −0.0878964 + 0.0654541i
\(913\) −2.02125e13 −0.962721
\(914\) −1.14222e13 + 4.15735e12i −0.541369 + 0.197042i
\(915\) −2.82173e12 + 1.60028e13i −0.133082 + 0.754747i
\(916\) −1.20903e13 + 1.01450e13i −0.567424 + 0.476125i
\(917\) −3.52786e10 2.96023e10i −0.00164759 0.00138249i
\(918\) −1.76777e12 1.00255e13i −0.0821551 0.465925i
\(919\) −7.65155e12 1.32529e13i −0.353858 0.612901i 0.633064 0.774100i \(-0.281797\pi\)
−0.986922 + 0.161199i \(0.948464\pi\)
\(920\) 1.52553e12 2.64230e12i 0.0702063 0.121601i
\(921\) −4.87658e12 1.77493e12i −0.223330 0.0812855i
\(922\) −2.36135e13 8.59459e12i −1.07614 0.391684i
\(923\) 8.05287e10 1.39480e11i 0.00365210 0.00632563i
\(924\) −6.73426e9 1.16641e10i −0.000303925 0.000526413i
\(925\) 4.15798e11 + 2.35811e12i 0.0186743 + 0.105907i
\(926\) 1.18893e13 + 9.97627e12i 0.531380 + 0.445881i
\(927\) −1.32435e13 + 1.11126e13i −0.589039 + 0.494262i
\(928\) 3.77382e11 2.14024e12i 0.0167038 0.0947320i
\(929\) 1.01842e13 3.70674e12i 0.448596 0.163276i −0.107836 0.994169i \(-0.534392\pi\)
0.556432 + 0.830893i \(0.312170\pi\)
\(930\) −9.23096e11 −0.0404645
\(931\) −1.02903e13 2.04832e13i −0.448907 0.893559i
\(932\) 1.41912e13 0.616097
\(933\) 1.41024e13 5.13287e12i 0.609294 0.221765i
\(934\) −2.89970e12 + 1.64450e13i −0.124679 + 0.707087i
\(935\) −1.21704e13 + 1.02122e13i −0.520779 + 0.436985i
\(936\) 3.94496e12 + 3.31021e12i 0.167997 + 0.140966i
\(937\) −3.25435e12 1.84563e13i −0.137923 0.782199i −0.972780 0.231732i \(-0.925561\pi\)
0.834857 0.550467i \(-0.185550\pi\)
\(938\) 2.61318e10 + 4.52617e10i 0.00110219 + 0.00190905i
\(939\) −7.09870e12 + 1.22953e13i −0.297977 + 0.516112i
\(940\) −1.64381e13 5.98298e12i −0.686714 0.249944i
\(941\) 4.48178e12 + 1.63123e12i 0.186336 + 0.0678208i 0.433503 0.901152i \(-0.357277\pi\)
−0.247167 + 0.968973i \(0.579500\pi\)
\(942\) 9.45922e11 1.63838e12i 0.0391405 0.0677933i
\(943\) 3.46879e12 + 6.00812e12i 0.142848 + 0.247421i
\(944\) 1.78479e12 + 1.01220e13i 0.0731498 + 0.414853i
\(945\) −7.36933e10 6.18360e10i −0.00300597 0.00252231i
\(946\) −7.26362e11 + 6.09490e11i −0.0294878 + 0.0247432i
\(947\) −7.29799e12 + 4.13889e13i −0.294868 + 1.67228i 0.372869 + 0.927884i \(0.378374\pi\)
−0.667737 + 0.744397i \(0.732737\pi\)
\(948\) −4.03296e12 + 1.46788e12i −0.162176 + 0.0590271i
\(949\) 9.76739e12 0.390913
\(950\) 7.75617e12 + 4.50740e11i 0.308952 + 0.0179544i
\(951\) 1.72351e13 0.683283
\(952\) −2.93566e10 + 1.06849e10i −0.00115835 + 0.000421604i
\(953\) 4.68433e12 2.65661e13i 0.183962 1.04330i −0.743319 0.668937i \(-0.766750\pi\)
0.927281 0.374365i \(-0.122139\pi\)
\(954\) −1.06126e13 + 8.90505e12i −0.414815 + 0.348071i
\(955\) 5.73606e12 + 4.81312e12i 0.223151 + 0.187246i
\(956\) −3.65592e12 2.07337e13i −0.141558 0.802817i
\(957\) 2.07831e12 + 3.59973e12i 0.0800951 + 0.138729i
\(958\) 8.57691e12 1.48557e13i 0.328993 0.569832i
\(959\) 1.08900e11 + 3.96365e10i 0.00415763 + 0.00151325i
\(960\) −1.62471e12 5.91347e11i −0.0617385 0.0224710i
\(961\) 1.30631e13 2.26260e13i 0.494073 0.855760i
\(962\) 1.77193e12 + 3.06906e12i 0.0667049 + 0.115536i
\(963\) −3.99243e12 2.26422e13i −0.149595 0.848398i
\(964\) 6.99078e12 + 5.86596e12i 0.260723 + 0.218772i
\(965\) −1.46028e13 + 1.22532e13i −0.542078 + 0.454858i
\(966\) −1.99259e9 + 1.13005e10i −7.36242e−5 + 0.000417543i
\(967\) −2.95541e13 + 1.07568e13i −1.08692 + 0.395608i −0.822480 0.568794i \(-0.807410\pi\)
−0.264443 + 0.964401i \(0.585188\pi\)
\(968\) 5.30242e12 0.194104
\(969\) −9.32707e12 4.02188e12i −0.339851 0.146545i
\(970\) 3.68936e13 1.33807
\(971\) 2.96951e13 1.08081e13i 1.07201 0.390179i 0.255080 0.966920i \(-0.417898\pi\)
0.816927 + 0.576741i \(0.195676\pi\)
\(972\) 2.40252e12 1.36254e13i 0.0863316 0.489611i
\(973\) −4.23172e10 + 3.55084e10i −0.00151359 + 0.00127006i
\(974\) 1.86716e13 + 1.56674e13i 0.664763 + 0.557802i
\(975\) 7.21819e11 + 4.09364e12i 0.0255804 + 0.145074i
\(976\) 5.16683e12 + 8.94921e12i 0.182264 + 0.315690i
\(977\) −1.16884e13 + 2.02450e13i −0.410423 + 0.710873i −0.994936 0.100511i \(-0.967952\pi\)
0.584513 + 0.811384i \(0.301285\pi\)
\(978\) −9.59568e12 3.49254e12i −0.335391 0.122072i
\(979\) 7.59241e12 + 2.76341e12i 0.264154 + 0.0961442i
\(980\) 8.65522e12 1.49913e13i 0.299751 0.519184i
\(981\) −4.78198e12 8.28264e12i −0.164853 0.285534i
\(982\) 6.23816e12 + 3.53784e13i 0.214070 + 1.21405i
\(983\) 2.62894e13 + 2.20595e13i 0.898029 + 0.753536i 0.969804 0.243885i \(-0.0784220\pi\)
−0.0717752 + 0.997421i \(0.522866\pi\)
\(984\) 3.01163e12 2.52705e12i 0.102405 0.0859284i
\(985\) 9.75166e12 5.53044e13i 0.330077 1.87196i
\(986\) 9.05992e12 3.29754e12i 0.305266 0.111108i
\(987\) 6.57903e10 0.00220665
\(988\) 1.10151e13 3.29925e12i 0.367774 0.110156i
\(989\) 8.07842e11 0.0268499
\(990\) −1.30637e13 + 4.75480e12i −0.432223 + 0.157316i
\(991\) −7.51635e12 + 4.26273e13i −0.247557 + 1.40397i 0.566921 + 0.823772i \(0.308134\pi\)
−0.814478 + 0.580194i \(0.802977\pi\)
\(992\) −4.49687e11 + 3.77332e11i −0.0147437 + 0.0123715i
\(993\) 1.41976e13 + 1.19132e13i 0.463388 + 0.388828i
\(994\) 1.48460e8 + 8.41961e8i 4.82361e−6 + 2.73560e-5i
\(995\) −1.54688e13 2.67927e13i −0.500325 0.866589i
\(996\) 4.87928e12 8.45116e12i 0.157104 0.272113i
\(997\) 5.78370e13 + 2.10509e13i 1.85386 + 0.674751i 0.983106 + 0.183037i \(0.0585927\pi\)
0.870757 + 0.491714i \(0.163629\pi\)
\(998\) 1.88939e13 + 6.87680e12i 0.602883 + 0.219432i
\(999\) 3.06508e12 5.30888e12i 0.0973638 0.168639i
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 38.10.e.a.5.5 42
19.4 even 9 inner 38.10.e.a.23.5 yes 42
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
38.10.e.a.5.5 42 1.1 even 1 trivial
38.10.e.a.23.5 yes 42 19.4 even 9 inner