Properties

Label 37.10.c.a.26.23
Level $37$
Weight $10$
Character 37.26
Analytic conductor $19.056$
Analytic rank $0$
Dimension $54$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [37,10,Mod(10,37)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(37, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("37.10");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 37 \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 37.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: \(19.0563259381\)
Analytic rank: \(0\)
Dimension: \(54\)
Relative dimension: \(27\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 26.23
Character \(\chi\) \(=\) 37.26
Dual form 37.10.c.a.10.23

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(15.6613 + 27.1261i) q^{2} +(119.437 - 206.872i) q^{3} +(-234.552 + 406.256i) q^{4} +(-908.086 + 1572.85i) q^{5} +7482.17 q^{6} +(-4896.80 + 8481.51i) q^{7} +1343.62 q^{8} +(-18689.1 - 32370.4i) q^{9} +O(q^{10})\) \(q+(15.6613 + 27.1261i) q^{2} +(119.437 - 206.872i) q^{3} +(-234.552 + 406.256i) q^{4} +(-908.086 + 1572.85i) q^{5} +7482.17 q^{6} +(-4896.80 + 8481.51i) q^{7} +1343.62 q^{8} +(-18689.1 - 32370.4i) q^{9} -56887.2 q^{10} +60900.9 q^{11} +(56028.5 + 97044.2i) q^{12} +(-66666.9 + 115470. i) q^{13} -306761. q^{14} +(216919. + 375714. i) q^{15} +(141133. + 244450. i) q^{16} +(130058. + 225267. i) q^{17} +(585389. - 1.01392e6i) q^{18} +(11868.3 - 20556.5i) q^{19} +(-425987. - 737831. i) q^{20} +(1.16972e6 + 2.02602e6i) q^{21} +(953786. + 1.65201e6i) q^{22} -533831. q^{23} +(160478. - 277956. i) q^{24} +(-672679. - 1.16511e6i) q^{25} -4.17636e6 q^{26} -4.22691e6 q^{27} +(-2.29711e6 - 3.97871e6i) q^{28} -3.49933e6 q^{29} +(-6.79446e6 + 1.17683e7i) q^{30} +3.89327e6 q^{31} +(-4.07669e6 + 7.06104e6i) q^{32} +(7.27384e6 - 1.25987e7i) q^{33} +(-4.07375e6 + 7.05594e6i) q^{34} +(-8.89344e6 - 1.54039e7i) q^{35} +1.75342e7 q^{36} +(1.13109e7 - 1.42346e6i) q^{37} +743492. q^{38} +(1.59250e7 + 2.75830e7i) q^{39} +(-1.22012e6 + 2.11331e6i) q^{40} +(1.57435e7 - 2.72686e7i) q^{41} +(-3.66387e7 + 6.34601e7i) q^{42} -2.67263e7 q^{43} +(-1.42844e7 + 2.47413e7i) q^{44} +6.78851e7 q^{45} +(-8.36048e6 - 1.44808e7i) q^{46} -1.62723e7 q^{47} +6.74264e7 q^{48} +(-2.77805e7 - 4.81173e7i) q^{49} +(2.10700e7 - 3.64944e7i) q^{50} +6.21351e7 q^{51} +(-3.12737e7 - 5.41676e7i) q^{52} +(2.33216e7 + 4.03941e7i) q^{53} +(-6.61989e7 - 1.14660e8i) q^{54} +(-5.53033e7 + 9.57881e7i) q^{55} +(-6.57943e6 + 1.13959e7i) q^{56} +(-2.83504e6 - 4.91043e6i) q^{57} +(-5.48040e7 - 9.49234e7i) q^{58} +(-6.73613e7 - 1.16673e8i) q^{59} -2.03515e8 q^{60} +(1.50644e7 - 2.60923e7i) q^{61} +(6.09737e7 + 1.05610e8i) q^{62} +3.66066e8 q^{63} -1.10865e8 q^{64} +(-1.21079e8 - 2.09714e8i) q^{65} +4.55671e8 q^{66} +(-1.03138e8 + 1.78640e8i) q^{67} -1.22021e8 q^{68} +(-6.37593e7 + 1.10434e8i) q^{69} +(2.78565e8 - 4.82489e8i) q^{70} +(1.82178e8 - 3.15541e8i) q^{71} +(-2.51110e7 - 4.34934e7i) q^{72} +3.57977e8 q^{73} +(2.15756e8 + 2.84527e8i) q^{74} -3.21372e8 q^{75} +(5.56747e6 + 9.64314e6i) q^{76} +(-2.98220e8 + 5.16531e8i) q^{77} +(-4.98813e8 + 8.63970e8i) q^{78} +(7.56682e7 - 1.31061e8i) q^{79} -5.12645e8 q^{80} +(-1.36995e8 + 2.37282e8i) q^{81} +9.86257e8 q^{82} +(2.74010e8 + 4.74599e8i) q^{83} -1.09744e9 q^{84} -4.72415e8 q^{85} +(-4.18569e8 - 7.24982e8i) q^{86} +(-4.17951e8 + 7.23912e8i) q^{87} +8.18275e7 q^{88} +(3.99786e6 + 6.92449e6i) q^{89} +(1.06317e9 + 1.84146e9i) q^{90} +(-6.52909e8 - 1.13087e9i) q^{91} +(1.25211e8 - 2.16872e8i) q^{92} +(4.65002e8 - 8.05408e8i) q^{93} +(-2.54845e8 - 4.41404e8i) q^{94} +(2.15549e7 + 3.73342e7i) q^{95} +(9.73819e8 + 1.68670e9i) q^{96} +7.48996e8 q^{97} +(8.70157e8 - 1.50716e9i) q^{98} +(-1.13818e9 - 1.97139e9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 54 q + 32 q^{2} + 73 q^{3} - 6486 q^{4} + 2729 q^{5} + 1020 q^{6} + 4231 q^{7} - 7848 q^{8} - 140840 q^{9} - 82404 q^{10} - 108196 q^{11} + 45492 q^{12} - 29827 q^{13} - 504992 q^{14} + 87135 q^{15} - 1561814 q^{16} + 116991 q^{17} + 1767678 q^{18} - 599677 q^{19} + 4122556 q^{20} - 221017 q^{21} - 257914 q^{22} + 1752736 q^{23} + 1149408 q^{24} - 6037260 q^{25} - 16731604 q^{26} - 1916582 q^{27} + 1917318 q^{28} - 11336100 q^{29} - 20390006 q^{30} + 14447580 q^{31} - 873740 q^{32} - 4494200 q^{33} + 13736524 q^{34} - 8546699 q^{35} + 61692836 q^{36} - 1919410 q^{37} - 85447920 q^{38} - 14035313 q^{39} + 3210182 q^{40} + 28676571 q^{41} - 101904850 q^{42} + 56602028 q^{43} + 153011074 q^{44} + 104234980 q^{45} + 99535572 q^{46} - 147509100 q^{47} - 203670880 q^{48} - 201857540 q^{49} - 91421384 q^{50} + 328228338 q^{51} - 69374156 q^{52} + 59137361 q^{53} + 201615042 q^{54} - 219079762 q^{55} + 202573590 q^{56} - 5989161 q^{57} - 157098688 q^{58} + 137993791 q^{59} + 413427232 q^{60} - 244884419 q^{61} + 109345558 q^{62} - 995908592 q^{63} + 184008092 q^{64} + 248745395 q^{65} + 1965122248 q^{66} - 130143913 q^{67} + 667610796 q^{68} + 246927272 q^{69} - 291173360 q^{70} + 473387559 q^{71} + 366188748 q^{72} + 923638972 q^{73} - 885443390 q^{74} - 2185997392 q^{75} - 337459826 q^{76} - 586609928 q^{77} - 261025842 q^{78} + 563110723 q^{79} - 4210381784 q^{80} + 713813329 q^{81} + 3458576264 q^{82} - 663594441 q^{83} - 2635249016 q^{84} - 1417287750 q^{85} - 2269028474 q^{86} + 314944482 q^{87} - 7714172 q^{88} + 655027619 q^{89} + 588021376 q^{90} - 1833870961 q^{91} - 2384055268 q^{92} - 90092600 q^{93} - 1449940302 q^{94} + 2787158841 q^{95} + 2383567424 q^{96} - 2751583248 q^{97} + 4970876154 q^{98} + 2668760954 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 15.6613 + 27.1261i 0.692138 + 1.19882i 0.971136 + 0.238526i \(0.0766643\pi\)
−0.278998 + 0.960292i \(0.590002\pi\)
\(3\) 119.437 206.872i 0.851323 1.47454i −0.0286913 0.999588i \(-0.509134\pi\)
0.880015 0.474947i \(-0.157533\pi\)
\(4\) −234.552 + 406.256i −0.458109 + 0.793468i
\(5\) −908.086 + 1572.85i −0.649774 + 1.12544i 0.333403 + 0.942784i \(0.391803\pi\)
−0.983177 + 0.182657i \(0.941530\pi\)
\(6\) 7482.17 2.35693
\(7\) −4896.80 + 8481.51i −0.770853 + 1.33516i 0.166244 + 0.986085i \(0.446836\pi\)
−0.937096 + 0.349071i \(0.886497\pi\)
\(8\) 1343.62 0.115977
\(9\) −18689.1 32370.4i −0.949502 1.64459i
\(10\) −56887.2 −1.79893
\(11\) 60900.9 1.25417 0.627085 0.778951i \(-0.284248\pi\)
0.627085 + 0.778951i \(0.284248\pi\)
\(12\) 56028.5 + 97044.2i 0.779998 + 1.35100i
\(13\) −66666.9 + 115470.i −0.647389 + 1.12131i 0.336355 + 0.941735i \(0.390806\pi\)
−0.983744 + 0.179575i \(0.942528\pi\)
\(14\) −306761. −2.13414
\(15\) 216919. + 375714.i 1.10633 + 1.91623i
\(16\) 141133. + 244450.i 0.538381 + 0.932503i
\(17\) 130058. + 225267.i 0.377674 + 0.654150i 0.990723 0.135895i \(-0.0433908\pi\)
−0.613050 + 0.790044i \(0.710058\pi\)
\(18\) 585389. 1.01392e6i 1.31437 2.27656i
\(19\) 11868.3 20556.5i 0.0208928 0.0361875i −0.855390 0.517985i \(-0.826682\pi\)
0.876283 + 0.481797i \(0.160016\pi\)
\(20\) −425987. 737831.i −0.595335 1.03115i
\(21\) 1.16972e6 + 2.02602e6i 1.31249 + 2.27330i
\(22\) 953786. + 1.65201e6i 0.868059 + 1.50352i
\(23\) −533831. −0.397767 −0.198883 0.980023i \(-0.563731\pi\)
−0.198883 + 0.980023i \(0.563731\pi\)
\(24\) 160478. 277956.i 0.0987337 0.171012i
\(25\) −672679. 1.16511e6i −0.344412 0.596538i
\(26\) −4.17636e6 −1.79233
\(27\) −4.22691e6 −1.53069
\(28\) −2.29711e6 3.97871e6i −0.706269 1.22329i
\(29\) −3.49933e6 −0.918743 −0.459372 0.888244i \(-0.651925\pi\)
−0.459372 + 0.888244i \(0.651925\pi\)
\(30\) −6.79446e6 + 1.17683e7i −1.53147 + 2.65259i
\(31\) 3.89327e6 0.757159 0.378580 0.925569i \(-0.376413\pi\)
0.378580 + 0.925569i \(0.376413\pi\)
\(32\) −4.07669e6 + 7.06104e6i −0.687279 + 1.19040i
\(33\) 7.27384e6 1.25987e7i 1.06770 1.84932i
\(34\) −4.07375e6 + 7.05594e6i −0.522804 + 0.905523i
\(35\) −8.89344e6 1.54039e7i −1.00176 1.73510i
\(36\) 1.75342e7 1.73990
\(37\) 1.13109e7 1.42346e6i 0.992174 0.124864i
\(38\) 743492. 0.0578429
\(39\) 1.59250e7 + 2.75830e7i 1.10227 + 1.90919i
\(40\) −1.22012e6 + 2.11331e6i −0.0753586 + 0.130525i
\(41\) 1.57435e7 2.72686e7i 0.870112 1.50708i 0.00823225 0.999966i \(-0.497380\pi\)
0.861880 0.507112i \(-0.169287\pi\)
\(42\) −3.66387e7 + 6.34601e7i −1.81685 + 3.14687i
\(43\) −2.67263e7 −1.19215 −0.596075 0.802929i \(-0.703274\pi\)
−0.596075 + 0.802929i \(0.703274\pi\)
\(44\) −1.42844e7 + 2.47413e7i −0.574547 + 0.995145i
\(45\) 6.78851e7 2.46785
\(46\) −8.36048e6 1.44808e7i −0.275309 0.476850i
\(47\) −1.62723e7 −0.486416 −0.243208 0.969974i \(-0.578200\pi\)
−0.243208 + 0.969974i \(0.578200\pi\)
\(48\) 6.74264e7 1.83335
\(49\) −2.77805e7 4.81173e7i −0.688427 1.19239i
\(50\) 2.10700e7 3.64944e7i 0.476761 0.825774i
\(51\) 6.21351e7 1.28609
\(52\) −3.12737e7 5.41676e7i −0.593150 1.02737i
\(53\) 2.33216e7 + 4.03941e7i 0.405991 + 0.703197i 0.994436 0.105340i \(-0.0335932\pi\)
−0.588446 + 0.808537i \(0.700260\pi\)
\(54\) −6.61989e7 1.14660e8i −1.05945 1.83502i
\(55\) −5.53033e7 + 9.57881e7i −0.814927 + 1.41149i
\(56\) −6.57943e6 + 1.13959e7i −0.0894010 + 0.154847i
\(57\) −2.83504e6 4.91043e6i −0.0355731 0.0616145i
\(58\) −5.48040e7 9.49234e7i −0.635897 1.10141i
\(59\) −6.73613e7 1.16673e8i −0.723730 1.25354i −0.959495 0.281727i \(-0.909093\pi\)
0.235765 0.971810i \(-0.424241\pi\)
\(60\) −2.03515e8 −2.02729
\(61\) 1.50644e7 2.60923e7i 0.139305 0.241284i −0.787929 0.615767i \(-0.788846\pi\)
0.927234 + 0.374483i \(0.122180\pi\)
\(62\) 6.09737e7 + 1.05610e8i 0.524059 + 0.907696i
\(63\) 3.66066e8 2.92771
\(64\) −1.10865e8 −0.826006
\(65\) −1.21079e8 2.09714e8i −0.841312 1.45720i
\(66\) 4.55671e8 2.95599
\(67\) −1.03138e8 + 1.78640e8i −0.625290 + 1.08303i 0.363194 + 0.931713i \(0.381686\pi\)
−0.988485 + 0.151321i \(0.951647\pi\)
\(68\) −1.22021e8 −0.692063
\(69\) −6.37593e7 + 1.10434e8i −0.338628 + 0.586521i
\(70\) 2.78565e8 4.82489e8i 1.38671 2.40185i
\(71\) 1.82178e8 3.15541e8i 0.850811 1.47365i −0.0296674 0.999560i \(-0.509445\pi\)
0.880478 0.474087i \(-0.157222\pi\)
\(72\) −2.51110e7 4.34934e7i −0.110120 0.190734i
\(73\) 3.57977e8 1.47538 0.737688 0.675142i \(-0.235918\pi\)
0.737688 + 0.675142i \(0.235918\pi\)
\(74\) 2.15756e8 + 2.84527e8i 0.836410 + 1.10301i
\(75\) −3.21372e8 −1.17282
\(76\) 5.56747e6 + 9.64314e6i 0.0191424 + 0.0331556i
\(77\) −2.98220e8 + 5.16531e8i −0.966780 + 1.67451i
\(78\) −4.98813e8 + 8.63970e8i −1.52585 + 2.64285i
\(79\) 7.56682e7 1.31061e8i 0.218570 0.378575i −0.735801 0.677198i \(-0.763194\pi\)
0.954371 + 0.298623i \(0.0965273\pi\)
\(80\) −5.12645e8 −1.39930
\(81\) −1.36995e8 + 2.37282e8i −0.353607 + 0.612466i
\(82\) 9.86257e8 2.40895
\(83\) 2.74010e8 + 4.74599e8i 0.633745 + 1.09768i 0.986779 + 0.162069i \(0.0518167\pi\)
−0.353034 + 0.935610i \(0.614850\pi\)
\(84\) −1.09744e9 −2.40505
\(85\) −4.72415e8 −0.981609
\(86\) −4.18569e8 7.24982e8i −0.825132 1.42917i
\(87\) −4.17951e8 + 7.23912e8i −0.782147 + 1.35472i
\(88\) 8.18275e7 0.145455
\(89\) 3.99786e6 + 6.92449e6i 0.00675417 + 0.0116986i 0.869383 0.494139i \(-0.164517\pi\)
−0.862629 + 0.505838i \(0.831183\pi\)
\(90\) 1.06317e9 + 1.84146e9i 1.70809 + 2.95850i
\(91\) −6.52909e8 1.13087e9i −0.998083 1.72873i
\(92\) 1.25211e8 2.16872e8i 0.182221 0.315615i
\(93\) 4.65002e8 8.05408e8i 0.644587 1.11646i
\(94\) −2.54845e8 4.41404e8i −0.336667 0.583124i
\(95\) 2.15549e7 + 3.73342e7i 0.0271512 + 0.0470273i
\(96\) 9.73819e8 + 1.68670e9i 1.17019 + 2.02684i
\(97\) 7.48996e8 0.859027 0.429513 0.903060i \(-0.358685\pi\)
0.429513 + 0.903060i \(0.358685\pi\)
\(98\) 8.70157e8 1.50716e9i 0.952973 1.65060i
\(99\) −1.13818e9 1.97139e9i −1.19084 2.06259i
\(100\) 6.31113e8 0.631113
\(101\) 7.27127e8 0.695287 0.347643 0.937627i \(-0.386982\pi\)
0.347643 + 0.937627i \(0.386982\pi\)
\(102\) 9.73115e8 + 1.68549e9i 0.890151 + 1.54179i
\(103\) −7.54258e8 −0.660317 −0.330158 0.943926i \(-0.607102\pi\)
−0.330158 + 0.943926i \(0.607102\pi\)
\(104\) −8.95749e7 + 1.55148e8i −0.0750820 + 0.130046i
\(105\) −4.24883e9 −3.41128
\(106\) −7.30491e8 + 1.26525e9i −0.562003 + 0.973418i
\(107\) 5.46867e8 9.47201e8i 0.403324 0.698578i −0.590801 0.806818i \(-0.701188\pi\)
0.994125 + 0.108239i \(0.0345213\pi\)
\(108\) 9.91431e8 1.71721e9i 0.701222 1.21455i
\(109\) 8.90950e8 + 1.54317e9i 0.604552 + 1.04712i 0.992122 + 0.125275i \(0.0399813\pi\)
−0.387570 + 0.921840i \(0.626685\pi\)
\(110\) −3.46448e9 −2.25617
\(111\) 1.05647e9 2.50991e9i 0.660545 1.56929i
\(112\) −2.76441e9 −1.66005
\(113\) 1.61775e9 + 2.80202e9i 0.933377 + 1.61666i 0.777503 + 0.628880i \(0.216486\pi\)
0.155875 + 0.987777i \(0.450180\pi\)
\(114\) 8.88007e7 1.53807e8i 0.0492430 0.0852914i
\(115\) 4.84765e8 8.39637e8i 0.258458 0.447663i
\(116\) 8.20775e8 1.42162e9i 0.420885 0.728994i
\(117\) 4.98377e9 2.45879
\(118\) 2.10993e9 3.65451e9i 1.00184 1.73524i
\(119\) −2.54747e9 −1.16452
\(120\) 2.91456e8 + 5.04817e8i 0.128309 + 0.222238i
\(121\) 1.35097e9 0.572943
\(122\) 9.43712e8 0.385674
\(123\) −3.76073e9 6.51378e9i −1.48149 2.56602i
\(124\) −9.13175e8 + 1.58167e9i −0.346862 + 0.600782i
\(125\) −1.10381e9 −0.404389
\(126\) 5.73307e9 + 9.92997e9i 2.02638 + 3.50978i
\(127\) −1.29253e9 2.23873e9i −0.440884 0.763633i 0.556871 0.830599i \(-0.312002\pi\)
−0.997755 + 0.0669653i \(0.978668\pi\)
\(128\) 3.50985e8 + 6.07924e8i 0.115570 + 0.200173i
\(129\) −3.19212e9 + 5.52891e9i −1.01491 + 1.75787i
\(130\) 3.79249e9 6.56879e9i 1.16461 2.01716i
\(131\) 9.06552e8 + 1.57019e9i 0.268950 + 0.465835i 0.968591 0.248659i \(-0.0799900\pi\)
−0.699641 + 0.714495i \(0.746657\pi\)
\(132\) 3.41219e9 + 5.91008e9i 0.978250 + 1.69438i
\(133\) 1.16234e8 + 2.01322e8i 0.0322106 + 0.0557904i
\(134\) −6.46109e9 −1.73115
\(135\) 3.83840e9 6.64831e9i 0.994600 1.72270i
\(136\) 1.74748e8 + 3.02673e8i 0.0438013 + 0.0758662i
\(137\) −4.38312e9 −1.06302 −0.531509 0.847052i \(-0.678375\pi\)
−0.531509 + 0.847052i \(0.678375\pi\)
\(138\) −3.99421e9 −0.937509
\(139\) −3.15778e9 5.46944e9i −0.717490 1.24273i −0.961991 0.273080i \(-0.911958\pi\)
0.244501 0.969649i \(-0.421376\pi\)
\(140\) 8.34389e9 1.83566
\(141\) −1.94352e9 + 3.36627e9i −0.414097 + 0.717238i
\(142\) 1.14126e10 2.35551
\(143\) −4.06007e9 + 7.03225e9i −0.811936 + 1.40631i
\(144\) 5.27530e9 9.13709e9i 1.02239 1.77083i
\(145\) 3.17769e9 5.50393e9i 0.596975 1.03399i
\(146\) 5.60639e9 + 9.71054e9i 1.02116 + 1.76871i
\(147\) −1.32721e10 −2.34430
\(148\) −2.07470e9 + 4.92898e9i −0.355449 + 0.844460i
\(149\) 6.36037e9 1.05717 0.528585 0.848881i \(-0.322723\pi\)
0.528585 + 0.848881i \(0.322723\pi\)
\(150\) −5.03310e9 8.71758e9i −0.811755 1.40600i
\(151\) −5.59268e8 + 9.68681e8i −0.0875435 + 0.151630i −0.906472 0.422265i \(-0.861235\pi\)
0.818929 + 0.573895i \(0.194568\pi\)
\(152\) 1.59465e7 2.76201e7i 0.00242308 0.00419691i
\(153\) 4.86132e9 8.42005e9i 0.717204 1.24223i
\(154\) −1.86820e10 −2.67658
\(155\) −3.53543e9 + 6.12354e9i −0.491982 + 0.852138i
\(156\) −1.49410e10 −2.01985
\(157\) −2.19717e9 3.80561e9i −0.288613 0.499892i 0.684866 0.728669i \(-0.259861\pi\)
−0.973479 + 0.228777i \(0.926527\pi\)
\(158\) 4.74025e9 0.605124
\(159\) 1.11419e10 1.38252
\(160\) −7.40398e9 1.28241e10i −0.893152 1.54698i
\(161\) 2.61406e9 4.52769e9i 0.306620 0.531081i
\(162\) −8.58206e9 −0.978980
\(163\) 5.27299e9 + 9.13309e9i 0.585077 + 1.01338i 0.994866 + 0.101202i \(0.0322689\pi\)
−0.409789 + 0.912180i \(0.634398\pi\)
\(164\) 7.38536e9 + 1.27918e10i 0.797213 + 1.38081i
\(165\) 1.32105e10 + 2.28813e10i 1.38753 + 2.40328i
\(166\) −8.58270e9 + 1.48657e10i −0.877278 + 1.51949i
\(167\) −2.59855e9 + 4.50083e9i −0.258528 + 0.447784i −0.965848 0.259110i \(-0.916571\pi\)
0.707320 + 0.706894i \(0.249904\pi\)
\(168\) 1.57166e9 + 2.72219e9i 0.152218 + 0.263650i
\(169\) −3.58670e9 6.21235e9i −0.338224 0.585822i
\(170\) −7.39863e9 1.28148e10i −0.679409 1.17677i
\(171\) −8.87230e8 −0.0793512
\(172\) 6.26871e9 1.08577e10i 0.546135 0.945934i
\(173\) 5.28311e9 + 9.15062e9i 0.448417 + 0.776682i 0.998283 0.0585713i \(-0.0186545\pi\)
−0.549866 + 0.835253i \(0.685321\pi\)
\(174\) −2.61826e10 −2.16541
\(175\) 1.31759e10 1.06196
\(176\) 8.59515e9 + 1.48872e10i 0.675222 + 1.16952i
\(177\) −3.21818e10 −2.46451
\(178\) −1.25223e8 + 2.16893e8i −0.00934963 + 0.0161940i
\(179\) 1.71466e10 1.24836 0.624180 0.781281i \(-0.285433\pi\)
0.624180 + 0.781281i \(0.285433\pi\)
\(180\) −1.59226e10 + 2.75787e10i −1.13054 + 1.95816i
\(181\) 6.69075e9 1.15887e10i 0.463363 0.802568i −0.535763 0.844368i \(-0.679976\pi\)
0.999126 + 0.0418002i \(0.0133093\pi\)
\(182\) 2.04508e10 3.54218e10i 1.38162 2.39304i
\(183\) −3.59850e9 6.23279e9i −0.237188 0.410821i
\(184\) −7.17265e8 −0.0461317
\(185\) −8.03235e9 + 1.90829e10i −0.504162 + 1.19777i
\(186\) 2.91301e10 1.78457
\(187\) 7.92064e9 + 1.37190e10i 0.473667 + 0.820415i
\(188\) 3.81669e9 6.61071e9i 0.222832 0.385956i
\(189\) 2.06984e10 3.58506e10i 1.17993 2.04371i
\(190\) −6.75155e8 + 1.16940e9i −0.0375848 + 0.0650988i
\(191\) 1.45570e10 0.791449 0.395724 0.918369i \(-0.370494\pi\)
0.395724 + 0.918369i \(0.370494\pi\)
\(192\) −1.32414e10 + 2.29347e10i −0.703198 + 1.21797i
\(193\) 2.64433e8 0.0137186 0.00685928 0.999976i \(-0.497817\pi\)
0.00685928 + 0.999976i \(0.497817\pi\)
\(194\) 1.17302e10 + 2.03174e10i 0.594565 + 1.02982i
\(195\) −5.78452e10 −2.86491
\(196\) 2.60639e10 1.26150
\(197\) −1.05599e10 1.82903e10i −0.499531 0.865213i 0.500469 0.865754i \(-0.333161\pi\)
−1.00000 0.000541832i \(0.999828\pi\)
\(198\) 3.56507e10 6.17489e10i 1.64845 2.85519i
\(199\) 1.48954e10 0.673306 0.336653 0.941629i \(-0.390705\pi\)
0.336653 + 0.941629i \(0.390705\pi\)
\(200\) −9.03824e8 1.56547e9i −0.0399437 0.0691846i
\(201\) 2.46370e10 + 4.26726e10i 1.06465 + 1.84403i
\(202\) 1.13877e10 + 1.97242e10i 0.481234 + 0.833522i
\(203\) 1.71355e10 2.96796e10i 0.708215 1.22667i
\(204\) −1.45739e10 + 2.52427e10i −0.589169 + 1.02047i
\(205\) 2.85930e10 + 4.95245e10i 1.13075 + 1.95852i
\(206\) −1.18127e10 2.04601e10i −0.457030 0.791600i
\(207\) 9.97680e9 + 1.72803e10i 0.377681 + 0.654162i
\(208\) −3.76357e10 −1.39417
\(209\) 7.22791e8 1.25191e9i 0.0262032 0.0453853i
\(210\) −6.65422e10 1.15254e11i −2.36108 4.08951i
\(211\) −3.06013e10 −1.06284 −0.531422 0.847107i \(-0.678342\pi\)
−0.531422 + 0.847107i \(0.678342\pi\)
\(212\) −2.18805e10 −0.743952
\(213\) −4.35177e10 7.53748e10i −1.44863 2.50910i
\(214\) 3.42585e10 1.11662
\(215\) 2.42698e10 4.20365e10i 0.774628 1.34170i
\(216\) −5.67936e9 −0.177524
\(217\) −1.90646e10 + 3.30208e10i −0.583658 + 1.01093i
\(218\) −2.79068e10 + 4.83361e10i −0.836867 + 1.44950i
\(219\) 4.27559e10 7.40553e10i 1.25602 2.17549i
\(220\) −2.59430e10 4.49345e10i −0.746651 1.29324i
\(221\) −3.46822e10 −0.978006
\(222\) 8.46298e10 1.06505e10i 2.33849 0.294295i
\(223\) −2.51407e10 −0.680779 −0.340390 0.940285i \(-0.610559\pi\)
−0.340390 + 0.940285i \(0.610559\pi\)
\(224\) −3.99255e10 6.91530e10i −1.05958 1.83525i
\(225\) −2.51435e10 + 4.35498e10i −0.654039 + 1.13283i
\(226\) −5.06720e10 + 8.77664e10i −1.29205 + 2.23790i
\(227\) 9.80838e9 1.69886e10i 0.245178 0.424660i −0.717004 0.697069i \(-0.754487\pi\)
0.962182 + 0.272409i \(0.0878203\pi\)
\(228\) 2.65986e9 0.0651855
\(229\) −1.28957e10 + 2.23360e10i −0.309874 + 0.536717i −0.978335 0.207030i \(-0.933620\pi\)
0.668461 + 0.743748i \(0.266954\pi\)
\(230\) 3.03682e10 0.715555
\(231\) 7.12371e10 + 1.23386e11i 1.64609 + 2.85110i
\(232\) −4.70176e9 −0.106553
\(233\) −1.48666e9 −0.0330453 −0.0165227 0.999863i \(-0.505260\pi\)
−0.0165227 + 0.999863i \(0.505260\pi\)
\(234\) 7.80522e10 + 1.35190e11i 1.70182 + 2.94764i
\(235\) 1.47766e10 2.55939e10i 0.316060 0.547433i
\(236\) 6.31989e10 1.32619
\(237\) −1.80752e10 3.13072e10i −0.372148 0.644580i
\(238\) −3.98967e10 6.91031e10i −0.806010 1.39605i
\(239\) 2.56967e10 + 4.45079e10i 0.509432 + 0.882362i 0.999940 + 0.0109254i \(0.00347774\pi\)
−0.490508 + 0.871436i \(0.663189\pi\)
\(240\) −6.12290e10 + 1.06052e11i −1.19126 + 2.06332i
\(241\) 3.34126e8 5.78724e8i 0.00638020 0.0110508i −0.862818 0.505515i \(-0.831302\pi\)
0.869198 + 0.494464i \(0.164636\pi\)
\(242\) 2.11579e10 + 3.66466e10i 0.396555 + 0.686854i
\(243\) −8.87461e9 1.53713e10i −0.163275 0.282801i
\(244\) 7.06677e9 + 1.22400e10i 0.127634 + 0.221069i
\(245\) 1.00908e11 1.78929
\(246\) 1.17796e11 2.04029e11i 2.05079 3.55208i
\(247\) 1.58245e9 + 2.74088e9i 0.0270516 + 0.0468547i
\(248\) 5.23107e9 0.0878129
\(249\) 1.30908e11 2.15809
\(250\) −1.72871e10 2.99421e10i −0.279893 0.484789i
\(251\) −8.44682e10 −1.34326 −0.671632 0.740885i \(-0.734406\pi\)
−0.671632 + 0.740885i \(0.734406\pi\)
\(252\) −8.58616e10 + 1.48717e11i −1.34121 + 2.32304i
\(253\) −3.25108e10 −0.498867
\(254\) 4.04854e10 7.01228e10i 0.610305 1.05708i
\(255\) −5.64240e10 + 9.77292e10i −0.835667 + 1.44742i
\(256\) −3.93751e10 + 6.81997e10i −0.572983 + 0.992436i
\(257\) −5.29897e10 9.17808e10i −0.757691 1.31236i −0.944025 0.329873i \(-0.892994\pi\)
0.186334 0.982486i \(-0.440339\pi\)
\(258\) −1.99971e11 −2.80982
\(259\) −4.33140e10 + 1.02904e11i −0.598107 + 1.42096i
\(260\) 1.13597e11 1.54165
\(261\) 6.53992e10 + 1.13275e11i 0.872349 + 1.51095i
\(262\) −2.83955e10 + 4.91825e10i −0.372301 + 0.644844i
\(263\) −2.93439e10 + 5.08252e10i −0.378196 + 0.655056i −0.990800 0.135335i \(-0.956789\pi\)
0.612603 + 0.790390i \(0.290122\pi\)
\(264\) 9.77326e9 1.69278e10i 0.123829 0.214478i
\(265\) −8.47119e10 −1.05521
\(266\) −3.64073e9 + 6.30593e9i −0.0445884 + 0.0772293i
\(267\) 1.90997e9 0.0229999
\(268\) −4.83824e10 8.38008e10i −0.572903 0.992296i
\(269\) 3.22133e10 0.375102 0.187551 0.982255i \(-0.439945\pi\)
0.187551 + 0.982255i \(0.439945\pi\)
\(270\) 2.40457e11 2.75360
\(271\) −3.61356e10 6.25886e10i −0.406980 0.704910i 0.587570 0.809174i \(-0.300085\pi\)
−0.994550 + 0.104264i \(0.966751\pi\)
\(272\) −3.67110e10 + 6.35853e10i −0.406665 + 0.704364i
\(273\) −3.11927e11 −3.39876
\(274\) −6.86453e10 1.18897e11i −0.735755 1.27437i
\(275\) −4.09667e10 7.09565e10i −0.431951 0.748161i
\(276\) −2.99098e10 5.18052e10i −0.310257 0.537381i
\(277\) 5.96303e8 1.03283e9i 0.00608566 0.0105407i −0.862967 0.505261i \(-0.831396\pi\)
0.869052 + 0.494720i \(0.164730\pi\)
\(278\) 9.89099e10 1.71317e11i 0.993204 1.72028i
\(279\) −7.27616e10 1.26027e11i −0.718925 1.24521i
\(280\) −1.19494e10 2.06969e10i −0.116181 0.201231i
\(281\) 7.41261e10 + 1.28390e11i 0.709239 + 1.22844i 0.965140 + 0.261736i \(0.0842948\pi\)
−0.255900 + 0.966703i \(0.582372\pi\)
\(282\) −1.21752e11 −1.14645
\(283\) 4.24977e9 7.36082e9i 0.0393846 0.0682162i −0.845661 0.533720i \(-0.820794\pi\)
0.885046 + 0.465504i \(0.154127\pi\)
\(284\) 8.54603e10 + 1.48022e11i 0.779528 + 1.35018i
\(285\) 1.02978e10 0.0924579
\(286\) −2.54344e11 −2.24789
\(287\) 1.54186e11 + 2.67058e11i 1.34146 + 2.32347i
\(288\) 3.04758e11 2.61029
\(289\) 2.54638e10 4.41047e10i 0.214725 0.371915i
\(290\) 1.99067e11 1.65276
\(291\) 8.94581e10 1.54946e11i 0.731309 1.26667i
\(292\) −8.39643e10 + 1.45430e11i −0.675883 + 1.17066i
\(293\) 6.77191e10 1.17293e11i 0.536793 0.929753i −0.462281 0.886733i \(-0.652969\pi\)
0.999074 0.0430194i \(-0.0136977\pi\)
\(294\) −2.07859e11 3.60022e11i −1.62258 2.81038i
\(295\) 2.44680e11 1.88104
\(296\) 1.51975e10 1.91258e9i 0.115069 0.0144813i
\(297\) −2.57423e11 −1.91974
\(298\) 9.96116e10 + 1.72532e11i 0.731707 + 1.26735i
\(299\) 3.55889e10 6.16417e10i 0.257510 0.446020i
\(300\) 7.53784e10 1.30559e11i 0.537281 0.930598i
\(301\) 1.30873e11 2.26679e11i 0.918972 1.59171i
\(302\) −3.50354e10 −0.242369
\(303\) 8.68461e10 1.50422e11i 0.591914 1.02522i
\(304\) 6.70006e9 0.0449933
\(305\) 2.73596e10 + 4.73881e10i 0.181034 + 0.313560i
\(306\) 3.04538e11 1.98562
\(307\) 1.11087e11 0.713739 0.356869 0.934154i \(-0.383844\pi\)
0.356869 + 0.934154i \(0.383844\pi\)
\(308\) −1.39896e11 2.42307e11i −0.885782 1.53422i
\(309\) −9.00866e10 + 1.56035e11i −0.562143 + 0.973660i
\(310\) −2.21477e11 −1.36208
\(311\) 1.29734e10 + 2.24706e10i 0.0786381 + 0.136205i 0.902663 0.430349i \(-0.141610\pi\)
−0.824024 + 0.566554i \(0.808276\pi\)
\(312\) 2.13972e10 + 3.70610e10i 0.127838 + 0.221422i
\(313\) 9.25069e9 + 1.60227e10i 0.0544784 + 0.0943594i 0.891979 0.452078i \(-0.149317\pi\)
−0.837500 + 0.546437i \(0.815984\pi\)
\(314\) 6.88211e10 1.19202e11i 0.399519 0.691988i
\(315\) −3.32420e11 + 5.75768e11i −1.90235 + 3.29496i
\(316\) 3.54962e10 + 6.14813e10i 0.200258 + 0.346858i
\(317\) 8.92040e10 + 1.54506e11i 0.496155 + 0.859366i 0.999990 0.00443391i \(-0.00141136\pi\)
−0.503835 + 0.863800i \(0.668078\pi\)
\(318\) 1.74496e11 + 3.02236e11i 0.956892 + 1.65739i
\(319\) −2.13112e11 −1.15226
\(320\) 1.00675e11 1.74374e11i 0.536717 0.929621i
\(321\) −1.30633e11 2.26262e11i −0.686719 1.18943i
\(322\) 1.63758e11 0.848892
\(323\) 6.17427e9 0.0315627
\(324\) −6.42648e10 1.11310e11i −0.323982 0.561153i
\(325\) 1.79382e11 0.891873
\(326\) −1.65164e11 + 2.86072e11i −0.809907 + 1.40280i
\(327\) 4.25651e11 2.05868
\(328\) 2.11533e10 3.66386e10i 0.100913 0.174786i
\(329\) 7.96821e10 1.38013e11i 0.374955 0.649441i
\(330\) −4.13788e11 + 7.16703e11i −1.92073 + 3.32680i
\(331\) −1.26874e11 2.19751e11i −0.580958 1.00625i −0.995366 0.0961582i \(-0.969345\pi\)
0.414408 0.910091i \(-0.363989\pi\)
\(332\) −2.57078e11 −1.16130
\(333\) −2.57467e11 3.39534e11i −1.14742 1.51316i
\(334\) −1.62787e11 −0.715748
\(335\) −1.87316e11 3.24441e11i −0.812594 1.40745i
\(336\) −3.30174e11 + 5.71877e11i −1.41324 + 2.44780i
\(337\) 7.08524e10 1.22720e11i 0.299240 0.518299i −0.676722 0.736239i \(-0.736600\pi\)
0.975962 + 0.217939i \(0.0699334\pi\)
\(338\) 1.12345e11 1.94587e11i 0.468196 0.810939i
\(339\) 7.72877e11 3.17842
\(340\) 1.10806e11 1.91921e11i 0.449684 0.778876i
\(341\) 2.37104e11 0.949607
\(342\) −1.38952e10 2.40671e10i −0.0549220 0.0951277i
\(343\) 1.48936e11 0.580998
\(344\) −3.59100e10 −0.138262
\(345\) −1.15798e11 2.00568e11i −0.440063 0.762212i
\(346\) −1.65481e11 + 2.86621e11i −0.620733 + 1.07514i
\(347\) −1.58026e11 −0.585120 −0.292560 0.956247i \(-0.594507\pi\)
−0.292560 + 0.956247i \(0.594507\pi\)
\(348\) −1.96062e11 3.39590e11i −0.716618 1.24122i
\(349\) −1.30393e11 2.25847e11i −0.470478 0.814892i 0.528952 0.848652i \(-0.322585\pi\)
−0.999430 + 0.0337598i \(0.989252\pi\)
\(350\) 2.06352e11 + 3.57411e11i 0.735024 + 1.27310i
\(351\) 2.81795e11 4.88084e11i 0.990950 1.71638i
\(352\) −2.48274e11 + 4.30024e11i −0.861965 + 1.49297i
\(353\) −1.05396e11 1.82551e11i −0.361274 0.625745i 0.626897 0.779102i \(-0.284325\pi\)
−0.988171 + 0.153357i \(0.950991\pi\)
\(354\) −5.04009e11 8.72969e11i −1.70578 2.95450i
\(355\) 3.30866e11 + 5.73077e11i 1.10567 + 1.91507i
\(356\) −3.75082e9 −0.0123766
\(357\) −3.04263e11 + 5.26999e11i −0.991385 + 1.71713i
\(358\) 2.68538e11 + 4.65121e11i 0.864036 + 1.49656i
\(359\) 1.15745e11 0.367772 0.183886 0.982948i \(-0.441132\pi\)
0.183886 + 0.982948i \(0.441132\pi\)
\(360\) 9.12117e10 0.286213
\(361\) 1.61062e11 + 2.78968e11i 0.499127 + 0.864513i
\(362\) 4.19143e11 1.28284
\(363\) 1.61356e11 2.79477e11i 0.487760 0.844825i
\(364\) 6.12564e11 1.82892
\(365\) −3.25074e11 + 5.63045e11i −0.958660 + 1.66045i
\(366\) 1.12714e11 1.95227e11i 0.328333 0.568690i
\(367\) 7.35591e10 1.27408e11i 0.211660 0.366606i −0.740574 0.671975i \(-0.765446\pi\)
0.952234 + 0.305369i \(0.0987797\pi\)
\(368\) −7.53414e10 1.30495e11i −0.214150 0.370919i
\(369\) −1.17693e12 −3.30469
\(370\) −6.43443e11 + 8.09765e10i −1.78485 + 0.224621i
\(371\) −4.56804e11 −1.25184
\(372\) 2.18134e11 + 3.77820e11i 0.590583 + 1.02292i
\(373\) 1.77752e11 3.07875e11i 0.475471 0.823540i −0.524134 0.851636i \(-0.675611\pi\)
0.999605 + 0.0280959i \(0.00894439\pi\)
\(374\) −2.48095e11 + 4.29713e11i −0.655685 + 1.13568i
\(375\) −1.31836e11 + 2.28347e11i −0.344266 + 0.596286i
\(376\) −2.18637e10 −0.0564130
\(377\) 2.33290e11 4.04069e11i 0.594784 1.03020i
\(378\) 1.29665e12 3.26671
\(379\) −1.68244e11 2.91408e11i −0.418855 0.725479i 0.576969 0.816766i \(-0.304235\pi\)
−0.995825 + 0.0912872i \(0.970902\pi\)
\(380\) −2.02230e10 −0.0497529
\(381\) −6.17506e11 −1.50134
\(382\) 2.27982e11 + 3.94876e11i 0.547791 + 0.948802i
\(383\) −1.14647e11 + 1.98574e11i −0.272250 + 0.471551i −0.969438 0.245338i \(-0.921101\pi\)
0.697188 + 0.716889i \(0.254434\pi\)
\(384\) 1.67683e11 0.393549
\(385\) −5.41618e11 9.38110e11i −1.25638 2.17611i
\(386\) 4.14137e9 + 7.17306e9i 0.00949513 + 0.0164461i
\(387\) 4.99490e11 + 8.65141e11i 1.13195 + 1.96059i
\(388\) −1.75678e11 + 3.04284e11i −0.393528 + 0.681611i
\(389\) −1.05714e11 + 1.83102e11i −0.234077 + 0.405433i −0.959004 0.283392i \(-0.908540\pi\)
0.724927 + 0.688826i \(0.241873\pi\)
\(390\) −9.05931e11 1.56912e12i −1.98292 3.43451i
\(391\) −6.94289e10 1.20254e11i −0.150226 0.260199i
\(392\) −3.73264e10 6.46512e10i −0.0798415 0.138290i
\(393\) 4.33105e11 0.915854
\(394\) 3.30764e11 5.72899e11i 0.691488 1.19769i
\(395\) 1.37427e11 + 2.38030e11i 0.284043 + 0.491976i
\(396\) 1.06785e12 2.18213
\(397\) −2.32323e11 −0.469391 −0.234696 0.972069i \(-0.575409\pi\)
−0.234696 + 0.972069i \(0.575409\pi\)
\(398\) 2.33281e11 + 4.04054e11i 0.466021 + 0.807172i
\(399\) 5.55305e10 0.109687
\(400\) 1.89875e11 3.28873e11i 0.370849 0.642330i
\(401\) −1.12406e11 −0.217089 −0.108545 0.994092i \(-0.534619\pi\)
−0.108545 + 0.994092i \(0.534619\pi\)
\(402\) −7.71695e11 + 1.33662e12i −1.47377 + 2.55264i
\(403\) −2.59553e11 + 4.49558e11i −0.490177 + 0.849011i
\(404\) −1.70549e11 + 2.95400e11i −0.318517 + 0.551688i
\(405\) −2.48806e11 4.30945e11i −0.459529 0.795928i
\(406\) 1.07346e12 1.96073
\(407\) 6.88841e11 8.66898e10i 1.24435 0.156600i
\(408\) 8.34858e10 0.149156
\(409\) −2.27483e11 3.94013e11i −0.401971 0.696234i 0.591993 0.805943i \(-0.298341\pi\)
−0.993964 + 0.109709i \(0.965008\pi\)
\(410\) −8.95606e11 + 1.55124e12i −1.56527 + 2.71113i
\(411\) −5.23508e11 + 9.06743e11i −0.904973 + 1.56746i
\(412\) 1.76913e11 3.06422e11i 0.302497 0.523941i
\(413\) 1.31942e12 2.23156
\(414\) −3.12499e11 + 5.41264e11i −0.522814 + 0.905540i
\(415\) −9.95299e11 −1.64716
\(416\) −5.43561e11 9.41476e11i −0.889874 1.54131i
\(417\) −1.50863e12 −2.44326
\(418\) 4.52793e10 0.0725449
\(419\) 3.34560e11 + 5.79475e11i 0.530287 + 0.918484i 0.999376 + 0.0353332i \(0.0112492\pi\)
−0.469088 + 0.883151i \(0.655417\pi\)
\(420\) 9.96572e11 1.72611e12i 1.56274 2.70675i
\(421\) 4.25674e11 0.660401 0.330201 0.943911i \(-0.392884\pi\)
0.330201 + 0.943911i \(0.392884\pi\)
\(422\) −4.79256e11 8.30096e11i −0.735634 1.27416i
\(423\) 3.04114e11 + 5.26740e11i 0.461853 + 0.799954i
\(424\) 3.13353e10 + 5.42743e10i 0.0470855 + 0.0815544i
\(425\) 1.74974e11 3.03065e11i 0.260150 0.450594i
\(426\) 1.36309e12 2.36093e12i 2.00530 3.47329i
\(427\) 1.47535e11 + 2.55538e11i 0.214768 + 0.371989i
\(428\) 2.56537e11 + 4.44336e11i 0.369533 + 0.640050i
\(429\) 9.69849e11 + 1.67983e12i 1.38244 + 2.39446i
\(430\) 1.52039e12 2.14460
\(431\) 6.29780e11 1.09081e12i 0.879105 1.52266i 0.0267811 0.999641i \(-0.491474\pi\)
0.852324 0.523014i \(-0.175192\pi\)
\(432\) −5.96559e11 1.03327e12i −0.824093 1.42737i
\(433\) 4.98286e11 0.681213 0.340606 0.940206i \(-0.389368\pi\)
0.340606 + 0.940206i \(0.389368\pi\)
\(434\) −1.19430e12 −1.61589
\(435\) −7.59071e11 1.31475e12i −1.01644 1.76052i
\(436\) −8.35896e11 −1.10780
\(437\) −6.33567e9 + 1.09737e10i −0.00831048 + 0.0143942i
\(438\) 2.67845e12 3.47736
\(439\) 2.45357e11 4.24971e11i 0.315289 0.546096i −0.664210 0.747546i \(-0.731232\pi\)
0.979499 + 0.201450i \(0.0645653\pi\)
\(440\) −7.43065e10 + 1.28703e11i −0.0945126 + 0.163701i
\(441\) −1.03838e12 + 1.79853e12i −1.30733 + 2.26436i
\(442\) −5.43168e11 9.40795e11i −0.676915 1.17245i
\(443\) −1.10501e12 −1.36317 −0.681584 0.731740i \(-0.738709\pi\)
−0.681584 + 0.731740i \(0.738709\pi\)
\(444\) 7.71869e11 + 1.01790e12i 0.942584 + 1.24303i
\(445\) −1.45216e10 −0.0175547
\(446\) −3.93736e11 6.81971e11i −0.471193 0.816130i
\(447\) 7.59666e11 1.31578e12i 0.899993 1.55883i
\(448\) 5.42882e11 9.40299e11i 0.636729 1.10285i
\(449\) −5.96871e11 + 1.03381e12i −0.693062 + 1.20042i 0.277767 + 0.960648i \(0.410406\pi\)
−0.970830 + 0.239771i \(0.922928\pi\)
\(450\) −1.57512e12 −1.81074
\(451\) 9.58796e11 1.66068e12i 1.09127 1.89013i
\(452\) −1.51778e12 −1.71035
\(453\) 1.33595e11 + 2.31393e11i 0.149056 + 0.258172i
\(454\) 6.14448e11 0.678787
\(455\) 2.37159e12 2.59411
\(456\) −3.80921e9 6.59774e9i −0.00412566 0.00714585i
\(457\) 2.93982e11 5.09192e11i 0.315281 0.546083i −0.664216 0.747541i \(-0.731235\pi\)
0.979497 + 0.201458i \(0.0645679\pi\)
\(458\) −8.07853e11 −0.857902
\(459\) −5.49744e11 9.52184e11i −0.578100 1.00130i
\(460\) 2.27405e11 + 3.93877e11i 0.236804 + 0.410157i
\(461\) −1.93574e11 3.35280e11i −0.199615 0.345743i 0.748789 0.662809i \(-0.230636\pi\)
−0.948404 + 0.317065i \(0.897302\pi\)
\(462\) −2.23133e12 + 3.86478e12i −2.27864 + 3.94671i
\(463\) −7.79047e11 + 1.34935e12i −0.787860 + 1.36461i 0.139415 + 0.990234i \(0.455478\pi\)
−0.927275 + 0.374380i \(0.877855\pi\)
\(464\) −4.93872e11 8.55412e11i −0.494634 0.856731i
\(465\) 8.44524e11 + 1.46276e12i 0.837672 + 1.45089i
\(466\) −2.32830e10 4.03273e10i −0.0228719 0.0396153i
\(467\) −1.61740e11 −0.157359 −0.0786793 0.996900i \(-0.525070\pi\)
−0.0786793 + 0.996900i \(0.525070\pi\)
\(468\) −1.16895e12 + 2.02468e12i −1.12639 + 1.95097i
\(469\) −1.01009e12 1.74953e12i −0.964013 1.66972i
\(470\) 9.25685e11 0.875029
\(471\) −1.04970e12 −0.982811
\(472\) −9.05079e10 1.56764e11i −0.0839359 0.145381i
\(473\) −1.62766e12 −1.49516
\(474\) 5.66162e11 9.80622e11i 0.515156 0.892276i
\(475\) −3.19343e10 −0.0287830
\(476\) 5.97514e11 1.03492e12i 0.533478 0.924012i
\(477\) 8.71716e11 1.50986e12i 0.770978 1.33537i
\(478\) −8.04886e11 + 1.39410e12i −0.705194 + 1.22143i
\(479\) 2.76000e11 + 4.78045e11i 0.239551 + 0.414915i 0.960586 0.277984i \(-0.0896663\pi\)
−0.721034 + 0.692899i \(0.756333\pi\)
\(480\) −3.53725e12 −3.04144
\(481\) −5.89693e11 + 1.40097e12i −0.502311 + 1.19337i
\(482\) 2.09314e10 0.0176639
\(483\) −6.24434e11 1.08155e12i −0.522065 0.904242i
\(484\) −3.16873e11 + 5.48839e11i −0.262470 + 0.454612i
\(485\) −6.80153e11 + 1.17806e12i −0.558173 + 0.966784i
\(486\) 2.77976e11 4.81468e11i 0.226018 0.391475i
\(487\) −6.48192e11 −0.522183 −0.261092 0.965314i \(-0.584082\pi\)
−0.261092 + 0.965314i \(0.584082\pi\)
\(488\) 2.02408e10 3.50581e10i 0.0161562 0.0279833i
\(489\) 2.51917e12 1.99236
\(490\) 1.58036e12 + 2.73726e12i 1.23843 + 2.14503i
\(491\) 1.49807e12 1.16323 0.581615 0.813464i \(-0.302421\pi\)
0.581615 + 0.813464i \(0.302421\pi\)
\(492\) 3.52835e12 2.71474
\(493\) −4.55116e11 7.88283e11i −0.346985 0.600996i
\(494\) −4.95663e10 + 8.58514e10i −0.0374469 + 0.0648599i
\(495\) 4.13426e12 3.09510
\(496\) 5.49471e11 + 9.51712e11i 0.407640 + 0.706054i
\(497\) 1.78418e12 + 3.09028e12i 1.31170 + 2.27193i
\(498\) 2.05019e12 + 3.55103e12i 1.49369 + 2.58716i
\(499\) 9.78301e11 1.69447e12i 0.706350 1.22343i −0.259852 0.965648i \(-0.583674\pi\)
0.966202 0.257786i \(-0.0829929\pi\)
\(500\) 2.58901e11 4.48429e11i 0.185254 0.320870i
\(501\) 6.20729e11 + 1.07513e12i 0.440182 + 0.762417i
\(502\) −1.32288e12 2.29130e12i −0.929724 1.61033i
\(503\) −1.20677e12 2.09019e12i −0.840560 1.45589i −0.889422 0.457087i \(-0.848893\pi\)
0.0488620 0.998806i \(-0.484441\pi\)
\(504\) 4.91853e11 0.339546
\(505\) −6.60294e11 + 1.14366e12i −0.451779 + 0.782504i
\(506\) −5.09161e11 8.81892e11i −0.345285 0.598051i
\(507\) −1.71354e12 −1.15175
\(508\) 1.21266e12 0.807892
\(509\) 7.12353e11 + 1.23383e12i 0.470398 + 0.814752i 0.999427 0.0338511i \(-0.0107772\pi\)
−0.529029 + 0.848604i \(0.677444\pi\)
\(510\) −3.53469e12 −2.31359
\(511\) −1.75294e12 + 3.03619e12i −1.13730 + 1.96986i
\(512\) −2.10725e12 −1.35519
\(513\) −5.01663e10 + 8.68906e10i −0.0319804 + 0.0553917i
\(514\) 1.65977e12 2.87481e12i 1.04885 1.81667i
\(515\) 6.84931e11 1.18634e12i 0.429057 0.743148i
\(516\) −1.49744e12 2.59364e12i −0.929875 1.61059i
\(517\) −9.90996e11 −0.610049
\(518\) −3.46973e12 + 4.36661e11i −2.11744 + 0.266477i
\(519\) 2.52400e12 1.52699
\(520\) −1.62683e11 2.81776e11i −0.0975727 0.169001i
\(521\) 7.31064e9 1.26624e10i 0.00434696 0.00752916i −0.863844 0.503760i \(-0.831950\pi\)
0.868191 + 0.496231i \(0.165283\pi\)
\(522\) −2.04847e12 + 3.54806e12i −1.20757 + 2.09157i
\(523\) 1.31885e11 2.28431e11i 0.0770793 0.133505i −0.824909 0.565265i \(-0.808774\pi\)
0.901989 + 0.431760i \(0.142107\pi\)
\(524\) −8.50534e11 −0.492834
\(525\) 1.57369e12 2.72572e12i 0.904073 1.56590i
\(526\) −1.83826e12 −1.04706
\(527\) 5.06351e11 + 8.77026e11i 0.285959 + 0.495296i
\(528\) 4.10633e12 2.29933
\(529\) −1.51618e12 −0.841782
\(530\) −1.32670e12 2.29791e12i −0.730349 1.26500i
\(531\) −2.51784e12 + 4.36103e12i −1.37437 + 2.38047i
\(532\) −1.09051e11 −0.0590239
\(533\) 2.09915e12 + 3.63583e12i 1.12660 + 1.95133i
\(534\) 2.99126e10 + 5.18102e10i 0.0159191 + 0.0275727i
\(535\) 9.93204e11 + 1.72028e12i 0.524139 + 0.907835i
\(536\) −1.38578e11 + 2.40024e11i −0.0725191 + 0.125607i
\(537\) 2.04795e12 3.54715e12i 1.06276 1.84075i
\(538\) 5.04502e11 + 8.73823e11i 0.259623 + 0.449679i
\(539\) −1.69186e12 2.93038e12i −0.863405 1.49546i
\(540\) 1.80061e12 + 3.11875e12i 0.911271 + 1.57837i
\(541\) 2.27036e12 1.13948 0.569740 0.821825i \(-0.307044\pi\)
0.569740 + 0.821825i \(0.307044\pi\)
\(542\) 1.13186e12 1.96044e12i 0.563372 0.975790i
\(543\) −1.59825e12 2.76825e12i −0.788943 1.36649i
\(544\) −2.12083e12 −1.03827
\(545\) −3.23624e12 −1.57129
\(546\) −4.88518e12 8.46138e12i −2.35241 4.07450i
\(547\) 2.10168e12 1.00375 0.501873 0.864941i \(-0.332644\pi\)
0.501873 + 0.864941i \(0.332644\pi\)
\(548\) 1.02807e12 1.78067e12i 0.486979 0.843472i
\(549\) −1.12616e12 −0.529083
\(550\) 1.28318e12 2.22254e12i 0.597939 1.03566i
\(551\) −4.15311e10 + 7.19341e10i −0.0191952 + 0.0332470i
\(552\) −8.56682e10 + 1.48382e11i −0.0392730 + 0.0680228i
\(553\) 7.41064e11 + 1.28356e12i 0.336971 + 0.583651i
\(554\) 3.73555e10 0.0168485
\(555\) 2.98835e12 + 3.94088e12i 1.33694 + 1.76309i
\(556\) 2.96266e12 1.31476
\(557\) −1.12939e12 1.95616e12i −0.497160 0.861106i 0.502835 0.864382i \(-0.332290\pi\)
−0.999995 + 0.00327673i \(0.998957\pi\)
\(558\) 2.27908e12 3.94748e12i 0.995190 1.72372i
\(559\) 1.78176e12 3.08610e12i 0.771785 1.33677i
\(560\) 2.51032e12 4.34800e12i 1.07866 1.86829i
\(561\) 3.78408e12 1.61297
\(562\) −2.32182e12 + 4.02151e12i −0.981783 + 1.70050i
\(563\) −1.22229e12 −0.512728 −0.256364 0.966580i \(-0.582525\pi\)
−0.256364 + 0.966580i \(0.582525\pi\)
\(564\) −9.11712e11 1.57913e12i −0.379404 0.657147i
\(565\) −5.87621e12 −2.42594
\(566\) 2.66228e11 0.109038
\(567\) −1.34167e12 2.32384e12i −0.545158 0.944242i
\(568\) 2.44777e11 4.23967e11i 0.0986742 0.170909i
\(569\) −2.99440e12 −1.19758 −0.598790 0.800906i \(-0.704352\pi\)
−0.598790 + 0.800906i \(0.704352\pi\)
\(570\) 1.61277e11 + 2.79341e11i 0.0639936 + 0.110840i
\(571\) 2.07737e12 + 3.59810e12i 0.817807 + 1.41648i 0.907295 + 0.420495i \(0.138144\pi\)
−0.0894883 + 0.995988i \(0.528523\pi\)
\(572\) −1.90460e12 3.29886e12i −0.743911 1.28849i
\(573\) 1.73865e12 3.01144e12i 0.673779 1.16702i
\(574\) −4.82950e12 + 8.36495e12i −1.85695 + 3.21632i
\(575\) 3.59097e11 + 6.21974e11i 0.136996 + 0.237283i
\(576\) 2.07195e12 + 3.58873e12i 0.784294 + 1.35844i
\(577\) −8.42250e10 1.45882e11i −0.0316337 0.0547912i 0.849775 0.527145i \(-0.176738\pi\)
−0.881409 + 0.472354i \(0.843404\pi\)
\(578\) 1.59519e12 0.594478
\(579\) 3.15832e10 5.47038e10i 0.0116789 0.0202285i
\(580\) 1.49067e12 + 2.58191e12i 0.546960 + 0.947362i
\(581\) −5.36709e12 −1.95410
\(582\) 5.60412e12 2.02467
\(583\) 1.42030e12 + 2.46004e12i 0.509181 + 0.881928i
\(584\) 4.80985e11 0.171109
\(585\) −4.52569e12 + 7.83872e12i −1.59766 + 2.76722i
\(586\) 4.24227e12 1.48614
\(587\) 2.71354e11 4.69999e11i 0.0943332 0.163390i −0.814997 0.579465i \(-0.803261\pi\)
0.909330 + 0.416075i \(0.136595\pi\)
\(588\) 3.11300e12 5.39188e12i 1.07394 1.86013i
\(589\) 4.62066e10 8.00321e10i 0.0158192 0.0273997i
\(590\) 3.83200e12 + 6.63722e12i 1.30194 + 2.25503i
\(591\) −5.04499e12 −1.70105
\(592\) 1.94430e12 + 2.56404e12i 0.650604 + 0.857981i
\(593\) −5.55744e12 −1.84556 −0.922781 0.385324i \(-0.874090\pi\)
−0.922781 + 0.385324i \(0.874090\pi\)
\(594\) −4.03157e12 6.98289e12i −1.32873 2.30142i
\(595\) 2.31332e12 4.00679e12i 0.756676 1.31060i
\(596\) −1.49184e12 + 2.58394e12i −0.484299 + 0.838830i
\(597\) 1.77906e12 3.08143e12i 0.573201 0.992814i
\(598\) 2.22947e12 0.712929
\(599\) −2.03257e12 + 3.52051e12i −0.645095 + 1.11734i 0.339184 + 0.940720i \(0.389849\pi\)
−0.984280 + 0.176618i \(0.943484\pi\)
\(600\) −4.31801e11 −0.136020
\(601\) −2.22272e12 3.84986e12i −0.694943 1.20368i −0.970200 0.242305i \(-0.922096\pi\)
0.275257 0.961371i \(-0.411237\pi\)
\(602\) 8.19859e12 2.54422
\(603\) 7.71020e12 2.37486
\(604\) −2.62355e11 4.54412e11i −0.0802089 0.138926i
\(605\) −1.22680e12 + 2.12487e12i −0.372283 + 0.644814i
\(606\) 5.44049e12 1.63874
\(607\) −2.25283e12 3.90202e12i −0.673566 1.16665i −0.976886 0.213762i \(-0.931428\pi\)
0.303320 0.952889i \(-0.401905\pi\)
\(608\) 9.67670e10 + 1.67605e11i 0.0287184 + 0.0497418i
\(609\) −4.09324e12 7.08971e12i −1.20584 2.08858i
\(610\) −8.56972e11 + 1.48432e12i −0.250601 + 0.434053i
\(611\) 1.08482e12 1.87897e12i 0.314900 0.545424i
\(612\) 2.28046e12 + 3.94988e12i 0.657115 + 1.13816i
\(613\) 1.73864e12 + 3.01141e12i 0.497321 + 0.861386i 0.999995 0.00309025i \(-0.000983659\pi\)
−0.502674 + 0.864476i \(0.667650\pi\)
\(614\) 1.73976e12 + 3.01335e12i 0.494006 + 0.855643i
\(615\) 1.36603e13 3.85054
\(616\) −4.00693e11 + 6.94021e11i −0.112124 + 0.194205i
\(617\) −5.31689e11 9.20912e11i −0.147698 0.255820i 0.782678 0.622426i \(-0.213853\pi\)
−0.930376 + 0.366606i \(0.880520\pi\)
\(618\) −5.64349e12 −1.55632
\(619\) −4.73794e12 −1.29712 −0.648562 0.761162i \(-0.724629\pi\)
−0.648562 + 0.761162i \(0.724629\pi\)
\(620\) −1.65848e12 2.87258e12i −0.450763 0.780745i
\(621\) 2.25646e12 0.608857
\(622\) −4.06361e11 + 7.03839e11i −0.108857 + 0.188546i
\(623\) −7.83068e10 −0.0208259
\(624\) −4.49511e12 + 7.78575e12i −1.18689 + 2.05575i
\(625\) 2.31618e12 4.01174e12i 0.607173 1.05165i
\(626\) −2.89756e11 + 5.01871e11i −0.0754132 + 0.130619i
\(627\) −1.72656e11 2.99050e11i −0.0446148 0.0772750i
\(628\) 2.06140e12 0.528865
\(629\) 1.79172e12 + 2.36283e12i 0.456397 + 0.601873i
\(630\) −2.08245e13 −5.26674
\(631\) 2.23611e12 + 3.87306e12i 0.561515 + 0.972573i 0.997365 + 0.0725534i \(0.0231148\pi\)
−0.435849 + 0.900020i \(0.643552\pi\)
\(632\) 1.01669e11 1.76096e11i 0.0253491 0.0439059i
\(633\) −3.65494e12 + 6.33054e12i −0.904823 + 1.56720i
\(634\) −2.79410e12 + 4.83952e12i −0.686815 + 1.18960i
\(635\) 4.69492e12 1.14590
\(636\) −2.61334e12 + 4.52644e12i −0.633344 + 1.09698i
\(637\) 7.40816e12 1.78272
\(638\) −3.33761e12 5.78092e12i −0.797523 1.38135i
\(639\) −1.36189e13 −3.23139
\(640\) −1.27490e12 −0.300377
\(641\) 1.32947e12 + 2.30271e12i 0.311041 + 0.538739i 0.978588 0.205829i \(-0.0659891\pi\)
−0.667547 + 0.744568i \(0.732656\pi\)
\(642\) 4.09175e12 7.08712e12i 0.950608 1.64650i
\(643\) −7.89447e12 −1.82127 −0.910633 0.413215i \(-0.864406\pi\)
−0.910633 + 0.413215i \(0.864406\pi\)
\(644\) 1.22627e12 + 2.12396e12i 0.280930 + 0.486586i
\(645\) −5.79744e12 1.00415e13i −1.31892 2.28443i
\(646\) 9.66970e10 + 1.67484e11i 0.0218457 + 0.0378379i
\(647\) −1.08139e12 + 1.87302e12i −0.242612 + 0.420217i −0.961458 0.274953i \(-0.911338\pi\)
0.718845 + 0.695170i \(0.244671\pi\)
\(648\) −1.84069e11 + 3.18816e11i −0.0410102 + 0.0710318i
\(649\) −4.10236e12 7.10550e12i −0.907681 1.57215i
\(650\) 2.80935e12 + 4.86593e12i 0.617299 + 1.06919i
\(651\) 4.55405e12 + 7.88784e12i 0.993764 + 1.72125i
\(652\) −4.94716e12 −1.07212
\(653\) −7.14480e11 + 1.23751e12i −0.153773 + 0.266343i −0.932612 0.360882i \(-0.882476\pi\)
0.778838 + 0.627225i \(0.215809\pi\)
\(654\) 6.66624e12 + 1.15463e13i 1.42489 + 2.46798i
\(655\) −3.29291e12 −0.699027
\(656\) 8.88776e12 1.87381
\(657\) −6.69026e12 1.15879e13i −1.40087 2.42638i
\(658\) 4.99170e12 1.03808
\(659\) 3.43271e12 5.94563e12i 0.709011 1.22804i −0.256213 0.966620i \(-0.582475\pi\)
0.965224 0.261423i \(-0.0841919\pi\)
\(660\) −1.23942e13 −2.54257
\(661\) 8.99717e11 1.55836e12i 0.183316 0.317512i −0.759692 0.650283i \(-0.774650\pi\)
0.943008 + 0.332771i \(0.107984\pi\)
\(662\) 3.97401e12 6.88318e12i 0.804207 1.39293i
\(663\) −4.14235e12 + 7.17476e12i −0.832600 + 1.44210i
\(664\) 3.68165e11 + 6.37680e11i 0.0734997 + 0.127305i
\(665\) −4.22200e11 −0.0837184
\(666\) 5.17798e12 1.23016e13i 1.01983 2.42286i
\(667\) 1.86805e12 0.365445
\(668\) −1.21899e12 2.11135e12i −0.236868 0.410268i
\(669\) −3.00274e12 + 5.20090e12i −0.579563 + 1.00383i
\(670\) 5.86723e12 1.01623e13i 1.12485 1.94831i
\(671\) 9.17435e11 1.58904e12i 0.174713 0.302611i
\(672\) −1.90744e13 −3.60819
\(673\) 4.13775e12 7.16679e12i 0.777493 1.34666i −0.155889 0.987775i \(-0.549824\pi\)
0.933383 0.358883i \(-0.116842\pi\)
\(674\) 4.43856e12 0.828462
\(675\) 2.84336e12 + 4.92484e12i 0.527187 + 0.913114i
\(676\) 3.36507e12 0.619775
\(677\) −4.28628e12 −0.784209 −0.392104 0.919921i \(-0.628253\pi\)
−0.392104 + 0.919921i \(0.628253\pi\)
\(678\) 1.21042e13 + 2.09652e13i 2.19991 + 3.81035i
\(679\) −3.66768e12 + 6.35262e12i −0.662183 + 1.14693i
\(680\) −6.34746e11 −0.113844
\(681\) −2.34297e12 4.05815e12i −0.417451 0.723046i
\(682\) 3.71335e12 + 6.43171e12i 0.657259 + 1.13841i
\(683\) 1.77583e12 + 3.07584e12i 0.312255 + 0.540841i 0.978850 0.204578i \(-0.0655823\pi\)
−0.666595 + 0.745420i \(0.732249\pi\)
\(684\) 2.08102e11 3.60442e11i 0.0363515 0.0629627i
\(685\) 3.98025e12 6.89400e12i 0.690722 1.19637i
\(686\) 2.33252e12 + 4.04005e12i 0.402131 + 0.696511i
\(687\) 3.08045e12 + 5.33550e12i 0.527606 + 0.913840i
\(688\) −3.77198e12 6.53325e12i −0.641831 1.11168i
\(689\) −6.21910e12 −1.05134
\(690\) 3.62709e12 6.28231e12i 0.609169 1.05511i
\(691\) 1.44784e12 + 2.50773e12i 0.241585 + 0.418437i 0.961166 0.275971i \(-0.0889995\pi\)
−0.719581 + 0.694408i \(0.755666\pi\)
\(692\) −4.95666e12 −0.821697
\(693\) 2.22938e13 3.67184
\(694\) −2.47489e12 4.28663e12i −0.404984 0.701452i
\(695\) 1.14702e13 1.86482
\(696\) −5.61566e11 + 9.72661e11i −0.0907109 + 0.157116i
\(697\) 8.19029e12 1.31447
\(698\) 4.08424e12 7.07411e12i 0.651271 1.12804i
\(699\) −1.77563e11 + 3.07547e11i −0.0281322 + 0.0487265i
\(700\) −3.09043e12 + 5.35279e12i −0.486495 + 0.842634i
\(701\) 2.13383e12 + 3.69589e12i 0.333755 + 0.578081i 0.983245 0.182290i \(-0.0583508\pi\)
−0.649490 + 0.760370i \(0.725018\pi\)
\(702\) 1.76531e13 2.74350
\(703\) 1.04979e11 2.49406e11i 0.0162108 0.0385130i
\(704\) −6.75175e12 −1.03595
\(705\) −3.52976e12 6.11373e12i −0.538139 0.932085i
\(706\) 3.30127e12 5.71796e12i 0.500103 0.866204i
\(707\) −3.56060e12 + 6.16713e12i −0.535964 + 0.928316i
\(708\) 7.54831e12 1.30741e13i 1.12902 1.95551i
\(709\) −7.45059e12 −1.10734 −0.553672 0.832735i \(-0.686774\pi\)
−0.553672 + 0.832735i \(0.686774\pi\)
\(710\) −1.03636e13 + 1.79503e13i −1.53055 + 2.65099i
\(711\) −5.65667e12 −0.830133
\(712\) 5.37159e9 + 9.30387e9i 0.000783327 + 0.00135676i
\(713\) −2.07835e12 −0.301173
\(714\) −1.90606e13 −2.74470
\(715\) −7.37379e12 1.27718e13i −1.05515 1.82757i
\(716\) −4.02177e12 + 6.96591e12i −0.571885 + 0.990534i
\(717\) 1.22766e13 1.73476
\(718\) 1.81272e12 + 3.13972e12i 0.254549 + 0.440891i
\(719\) −1.07666e12 1.86483e12i −0.150245 0.260232i 0.781073 0.624440i \(-0.214673\pi\)
−0.931317 + 0.364209i \(0.881339\pi\)
\(720\) 9.58085e12 + 1.65945e13i 1.32864 + 2.30128i
\(721\) 3.69345e12 6.39725e12i 0.509007 0.881626i
\(722\) −5.04488e12 + 8.73799e12i −0.690929 + 1.19672i
\(723\) −7.98144e10 1.38243e11i −0.0108632 0.0188157i
\(724\) 3.13866e12 + 5.43631e12i 0.424542 + 0.735328i
\(725\) 2.35393e12 + 4.07712e12i 0.316426 + 0.548066i
\(726\) 1.01082e13 1.35039
\(727\) −3.65789e12 + 6.33565e12i −0.485653 + 0.841175i −0.999864 0.0164885i \(-0.994751\pi\)
0.514211 + 0.857663i \(0.328085\pi\)
\(728\) −8.77260e11 1.51946e12i −0.115754 0.200492i
\(729\) −9.63277e12 −1.26322
\(730\) −2.03643e13 −2.65410
\(731\) −3.47597e12 6.02055e12i −0.450244 0.779845i
\(732\) 3.37614e12 0.434632
\(733\) 2.25726e12 3.90969e12i 0.288811 0.500235i −0.684715 0.728811i \(-0.740073\pi\)
0.973526 + 0.228576i \(0.0734068\pi\)
\(734\) 4.60812e12 0.585992
\(735\) 1.20522e13 2.08751e13i 1.52326 2.63837i
\(736\) 2.17627e12 3.76940e12i 0.273377 0.473503i
\(737\) −6.28119e12 + 1.08793e13i −0.784221 + 1.35831i
\(738\) −1.84322e13 3.19255e13i −2.28730 3.96173i
\(739\) 1.30653e13 1.61146 0.805730 0.592283i \(-0.201773\pi\)
0.805730 + 0.592283i \(0.201773\pi\)
\(740\) −5.86855e12 7.73913e12i −0.719429 0.948744i
\(741\) 7.56013e11 0.0921186
\(742\) −7.15414e12 1.23913e13i −0.866443 1.50072i
\(743\) 3.91044e12 6.77309e12i 0.470735 0.815337i −0.528705 0.848806i \(-0.677322\pi\)
0.999440 + 0.0334691i \(0.0106555\pi\)
\(744\) 6.24786e11 1.08216e12i 0.0747572 0.129483i
\(745\) −5.77577e12 + 1.00039e13i −0.686921 + 1.18978i
\(746\) 1.11353e13 1.31637
\(747\) 1.02420e13 1.77396e13i 1.20349 2.08450i
\(748\) −7.43121e12 −0.867965
\(749\) 5.35579e12 + 9.27651e12i 0.621807 + 1.07700i
\(750\) −8.25889e12 −0.953117
\(751\) −5.76638e12 −0.661490 −0.330745 0.943720i \(-0.607300\pi\)
−0.330745 + 0.943720i \(0.607300\pi\)
\(752\) −2.29656e12 3.97776e12i −0.261877 0.453585i
\(753\) −1.00887e13 + 1.74741e13i −1.14355 + 1.98069i
\(754\) 1.46145e13 1.64669
\(755\) −1.01573e12 1.75929e12i −0.113767 0.197050i
\(756\) 9.70968e12 + 1.68177e13i 1.08108 + 1.87248i
\(757\) 1.29682e12 + 2.24615e12i 0.143531 + 0.248603i 0.928824 0.370521i \(-0.120821\pi\)
−0.785293 + 0.619125i \(0.787488\pi\)
\(758\) 5.26985e12 9.12764e12i 0.579811 1.00426i
\(759\) −3.88300e12 + 6.72555e12i −0.424697 + 0.735597i
\(760\) 2.89616e10 + 5.01629e10i 0.00314891 + 0.00545408i
\(761\) −3.45772e12 5.98895e12i −0.373731 0.647321i 0.616405 0.787429i \(-0.288588\pi\)
−0.990136 + 0.140108i \(0.955255\pi\)
\(762\) −9.67094e12 1.67506e13i −1.03913 1.79983i
\(763\) −1.74512e13 −1.86408
\(764\) −3.41438e12 + 5.91388e12i −0.362570 + 0.627989i
\(765\) 8.82899e12 + 1.52923e13i 0.932040 + 1.61434i
\(766\) −7.18208e12 −0.753738
\(767\) 1.79631e13 1.87414
\(768\) 9.40571e12 + 1.62912e13i 0.975588 + 1.68977i
\(769\) −2.08441e12 −0.214938 −0.107469 0.994208i \(-0.534275\pi\)
−0.107469 + 0.994208i \(0.534275\pi\)
\(770\) 1.69649e13 2.93840e13i 1.73917 3.01233i
\(771\) −2.53158e13 −2.58016
\(772\) −6.20234e10 + 1.07428e11i −0.00628460 + 0.0108852i
\(773\) −5.56384e12 + 9.63686e12i −0.560489 + 0.970796i 0.436965 + 0.899479i \(0.356053\pi\)
−0.997454 + 0.0713169i \(0.977280\pi\)
\(774\) −1.56453e13 + 2.70985e13i −1.56693 + 2.71400i
\(775\) −2.61892e12 4.53611e12i −0.260775 0.451675i
\(776\) 1.00636e12 0.0996271
\(777\) 1.61145e13 + 2.12509e13i 1.58607 + 2.09162i
\(778\) −6.62246e12 −0.648054
\(779\) −3.73699e11 6.47265e11i −0.0363582 0.0629743i
\(780\) 1.35677e13 2.35000e13i 1.31244 2.27322i
\(781\) 1.10948e13 1.92167e13i 1.06706 1.84820i
\(782\) 2.17469e12 3.76668e12i 0.207954 0.360187i
\(783\) 1.47914e13 1.40631
\(784\) 7.84152e12 1.35819e13i 0.741272 1.28392i
\(785\) 7.98088e12 0.750132
\(786\) 6.78298e12 + 1.17485e13i 0.633897 + 1.09794i
\(787\) 7.33263e12 0.681355 0.340677 0.940180i \(-0.389344\pi\)
0.340677 + 0.940180i \(0.389344\pi\)
\(788\) 9.90739e12 0.915358
\(789\) 7.00952e12 + 1.21409e13i 0.643935 + 1.11533i
\(790\) −4.30455e12 + 7.45570e12i −0.393193 + 0.681031i
\(791\) −3.16871e13 −2.87798
\(792\) −1.52928e12 2.64879e12i −0.138109 0.239213i
\(793\) 2.00859e12 + 3.47899e12i 0.180369 + 0.312409i
\(794\) −3.63848e12 6.30203e12i −0.324883 0.562714i
\(795\) −1.01178e13 + 1.75245e13i −0.898323 + 1.55594i
\(796\) −3.49374e12 + 6.05134e12i −0.308448 + 0.534247i
\(797\) −4.12284e12 7.14097e12i −0.361938 0.626895i 0.626342 0.779549i \(-0.284551\pi\)
−0.988280 + 0.152654i \(0.951218\pi\)
\(798\) 8.69679e11 + 1.50633e12i 0.0759182 + 0.131494i
\(799\) −2.11634e12 3.66561e12i −0.183707 0.318189i
\(800\) 1.09692e13 0.946828
\(801\) 1.49432e11 2.58824e11i 0.0128262 0.0222156i
\(802\) −1.76042e12 3.04913e12i −0.150256 0.260250i
\(803\) 2.18011e13 1.85037
\(804\) −2.31147e13 −1.95090
\(805\) 4.74759e12 + 8.22307e12i 0.398467 + 0.690164i
\(806\) −1.62597e13 −1.35708
\(807\) 3.84747e12 6.66401e12i 0.319333 0.553102i
\(808\) 9.76981e11 0.0806371
\(809\) 8.81098e11 1.52611e12i 0.0723196 0.125261i −0.827598 0.561321i \(-0.810293\pi\)
0.899918 + 0.436060i \(0.143627\pi\)
\(810\) 7.79325e12 1.34983e13i 0.636115 1.10178i
\(811\) 7.36646e12 1.27591e13i 0.597950 1.03568i −0.395173 0.918607i \(-0.629315\pi\)
0.993123 0.117074i \(-0.0373514\pi\)
\(812\) 8.03834e12 + 1.39228e13i 0.648880 + 1.12389i
\(813\) −1.72637e13 −1.38589
\(814\) 1.31397e13 + 1.73279e13i 1.04900 + 1.38337i
\(815\) −1.91533e13 −1.52067
\(816\) 8.76933e12 + 1.51889e13i 0.692406 + 1.19928i
\(817\) −3.17196e11 + 5.49400e11i −0.0249074 + 0.0431409i
\(818\) 7.12536e12 1.23415e13i 0.556438 0.963780i
\(819\) −2.44045e13 + 4.22699e13i −1.89536 + 3.28287i
\(820\) −2.68262e13 −2.07203
\(821\) 3.49325e12 6.05049e12i 0.268340 0.464779i −0.700093 0.714051i \(-0.746858\pi\)
0.968433 + 0.249273i \(0.0801916\pi\)
\(822\) −3.27953e13 −2.50546
\(823\) 9.09161e12 + 1.57471e13i 0.690783 + 1.19647i 0.971582 + 0.236704i \(0.0760673\pi\)
−0.280799 + 0.959767i \(0.590599\pi\)
\(824\) −1.01343e12 −0.0765814
\(825\) −1.95718e13 −1.47092
\(826\) 2.06638e13 + 3.57908e13i 1.54454 + 2.67523i
\(827\) −5.16189e11 + 8.94065e11i −0.0383737 + 0.0664652i −0.884574 0.466399i \(-0.845551\pi\)
0.846201 + 0.532864i \(0.178884\pi\)
\(828\) −9.36031e12 −0.692076
\(829\) 1.17134e13 + 2.02881e13i 0.861363 + 1.49192i 0.870614 + 0.491966i \(0.163722\pi\)
−0.00925168 + 0.999957i \(0.502945\pi\)
\(830\) −1.55877e13 2.69986e13i −1.14006 1.97465i
\(831\) −1.42442e11 2.46716e11i −0.0103617 0.0179470i
\(832\) 7.39100e12 1.28016e13i 0.534747 0.926209i
\(833\) 7.22615e12 1.25161e13i 0.520001 0.900669i
\(834\) −2.36271e13 4.09233e13i −1.69107 2.92903i
\(835\) −4.71942e12 8.17428e12i −0.335969 0.581916i
\(836\) 3.39064e11 + 5.87276e11i 0.0240078 + 0.0415828i
\(837\) −1.64565e13 −1.15897
\(838\) −1.04793e13 + 1.81507e13i −0.734064 + 1.27144i
\(839\) 2.45310e12 + 4.24889e12i 0.170917 + 0.296037i 0.938741 0.344624i \(-0.111994\pi\)
−0.767824 + 0.640661i \(0.778660\pi\)
\(840\) −5.70881e12 −0.395630
\(841\) −2.26183e12 −0.155911
\(842\) 6.66661e12 + 1.15469e13i 0.457089 + 0.791701i
\(843\) 3.54137e13 2.41517
\(844\) 7.17760e12 1.24320e13i 0.486898 0.843333i
\(845\) 1.30281e13 0.879077
\(846\) −9.52562e12 + 1.64989e13i −0.639332 + 1.10736i
\(847\) −6.61543e12 + 1.14583e13i −0.441655 + 0.764968i
\(848\) −6.58290e12 + 1.14019e13i −0.437155 + 0.757175i
\(849\) −1.01516e12 1.75831e12i −0.0670581 0.116148i
\(850\) 1.09613e13 0.720239
\(851\) −6.03809e12 + 7.59885e11i −0.394654 + 0.0496667i
\(852\) 4.08286e13 2.65452
\(853\) −5.53051e12 9.57912e12i −0.357680 0.619520i 0.629893 0.776682i \(-0.283099\pi\)
−0.987573 + 0.157162i \(0.949765\pi\)
\(854\) −4.62117e12 + 8.00410e12i −0.297298 + 0.514935i
\(855\) 8.05681e11 1.39548e12i 0.0515603 0.0893051i
\(856\) 7.34780e11 1.27268e12i 0.0467762 0.0810188i
\(857\) 2.76224e13 1.74924 0.874618 0.484812i \(-0.161112\pi\)
0.874618 + 0.484812i \(0.161112\pi\)
\(858\) −3.03782e13 + 5.26165e13i −1.91368 + 3.31459i
\(859\) −7.70481e12 −0.482829 −0.241414 0.970422i \(-0.577611\pi\)
−0.241414 + 0.970422i \(0.577611\pi\)
\(860\) 1.13851e13 + 1.97195e13i 0.709728 + 1.22929i
\(861\) 7.36623e13 4.56805
\(862\) 3.94526e13 2.43385
\(863\) −1.10877e13 1.92044e13i −0.680443 1.17856i −0.974846 0.222881i \(-0.928454\pi\)
0.294402 0.955682i \(-0.404879\pi\)
\(864\) 1.72318e13 2.98464e13i 1.05201 1.82213i
\(865\) −1.91901e13 −1.16548
\(866\) 7.80379e12 + 1.35166e13i 0.471493 + 0.816650i
\(867\) −6.08266e12 1.05355e13i −0.365601 0.633240i
\(868\) −8.94327e12 1.54902e13i −0.534758 0.926229i
\(869\) 4.60826e12 7.98174e12i 0.274125 0.474798i
\(870\) 2.37761e13 4.11813e13i 1.40703 2.43705i
\(871\) −1.37518e13 2.38188e13i −0.809612 1.40229i
\(872\) 1.19710e12 + 2.07343e12i 0.0701140 + 0.121441i
\(873\) −1.39980e13 2.42453e13i −0.815648 1.41274i
\(874\) −3.96899e11 −0.0230080
\(875\) 5.40514e12 9.36197e12i 0.311724 0.539922i
\(876\) 2.00569e13 + 3.47396e13i 1.15079 + 1.99323i
\(877\) −8.44321e12 −0.481958 −0.240979 0.970530i \(-0.577469\pi\)
−0.240979 + 0.970530i \(0.577469\pi\)
\(878\) 1.53704e13 0.872893
\(879\) −1.61764e13 2.80183e13i −0.913969 1.58304i
\(880\) −3.12205e13 −1.75496
\(881\) −7.92527e12 + 1.37270e13i −0.443223 + 0.767685i −0.997927 0.0643631i \(-0.979498\pi\)
0.554703 + 0.832048i \(0.312832\pi\)
\(882\) −6.50497e13 −3.61940
\(883\) −1.32003e12 + 2.28636e12i −0.0730735 + 0.126567i −0.900247 0.435380i \(-0.856614\pi\)
0.827173 + 0.561947i \(0.189947\pi\)
\(884\) 8.13478e12 1.40899e13i 0.448034 0.776017i
\(885\) 2.92239e13 5.06172e13i 1.60138 2.77366i
\(886\) −1.73059e13 2.99747e13i −0.943500 1.63419i
\(887\) −1.42799e13 −0.774583 −0.387291 0.921957i \(-0.626589\pi\)
−0.387291 + 0.921957i \(0.626589\pi\)
\(888\) 1.41949e12 3.37236e12i 0.0766078 0.182002i
\(889\) 2.53171e13 1.35943
\(890\) −2.27427e11 3.93915e11i −0.0121503 0.0210449i
\(891\) −8.34310e12 + 1.44507e13i −0.443484 + 0.768136i
\(892\) 5.89681e12 1.02136e13i 0.311871 0.540177i
\(893\) −1.93124e11 + 3.34501e11i −0.0101626 + 0.0176022i
\(894\) 4.75894e13 2.49168
\(895\) −1.55706e13 + 2.69691e13i −0.811151 + 1.40495i
\(896\) −6.87482e12 −0.356349
\(897\) −8.50128e12 1.47246e13i −0.438448 0.759414i
\(898\) −3.73911e13 −1.91878
\(899\) −1.36239e13 −0.695635
\(900\) −1.17949e13 2.04294e13i −0.599243 1.03792i
\(901\) −6.06630e12 + 1.05071e13i −0.306664 + 0.531157i
\(902\) 6.00639e13 3.02123
\(903\) −3.12624e13 5.41480e13i −1.56468 2.71011i
\(904\) 2.17363e12 + 3.76484e12i 0.108250 + 0.187495i
\(905\) 1.21516e13 + 2.10471e13i 0.602162 + 1.04298i
\(906\) −4.18454e12 + 7.24783e12i −0.206334 + 0.357381i
\(907\) 7.38324e11 1.27882e12i 0.0362255 0.0627444i −0.847344 0.531044i \(-0.821800\pi\)
0.883570 + 0.468300i \(0.155133\pi\)
\(908\) 4.60115e12 + 7.96943e12i 0.224636 + 0.389082i
\(909\) −1.35893e13 2.35374e13i −0.660177 1.14346i
\(910\) 3.71422e13 + 6.43321e13i 1.79548 + 3.10987i
\(911\) 5.01114e12 0.241048 0.120524 0.992710i \(-0.461542\pi\)
0.120524 + 0.992710i \(0.461542\pi\)
\(912\) 8.00237e11 1.38605e12i 0.0383038 0.0663441i
\(913\) 1.66874e13 + 2.89035e13i 0.794825 + 1.37668i
\(914\) 1.84166e13 0.872872
\(915\) 1.30710e13 0.616473
\(916\) −6.04942e12 1.04779e13i −0.283912 0.491750i
\(917\) −1.77568e13 −0.829284
\(918\) 1.72194e13 2.98248e13i 0.800250 1.38607i
\(919\) −2.06488e13 −0.954939 −0.477470 0.878648i \(-0.658446\pi\)
−0.477470 + 0.878648i \(0.658446\pi\)
\(920\) 6.51338e11 1.12815e12i 0.0299752 0.0519185i
\(921\) 1.32679e13 2.29807e13i 0.607622 1.05243i
\(922\) 6.06324e12 1.05018e13i 0.276322 0.478604i
\(923\) 2.42905e13 + 4.20723e13i 1.10161 + 1.90805i
\(924\) −6.68352e13 −3.01635
\(925\) −9.26707e12 1.22209e13i −0.416202 0.548865i
\(926\) −4.88035e13 −2.18123
\(927\) 1.40964e13 + 2.44156e13i 0.626972 + 1.08595i
\(928\) 1.42657e13 2.47089e13i 0.631433 1.09367i
\(929\) −1.70735e13 + 2.95721e13i −0.752057 + 1.30260i 0.194767 + 0.980849i \(0.437605\pi\)
−0.946824 + 0.321751i \(0.895728\pi\)
\(930\) −2.64527e13 + 4.58174e13i −1.15957 + 2.00843i
\(931\) −1.31883e12 −0.0575328
\(932\) 3.48699e11 6.03964e11i 0.0151384 0.0262204i
\(933\) 6.19805e12 0.267786
\(934\) −2.53305e12 4.38737e12i −0.108914 0.188644i
\(935\) −2.87705e13 −1.23111
\(936\) 6.69628e12 0.285162
\(937\) −8.07621e12 1.39884e13i −0.342278 0.592843i 0.642577 0.766221i \(-0.277865\pi\)
−0.984855 + 0.173378i \(0.944532\pi\)
\(938\) 3.16387e13 5.47998e13i 1.33446 2.31135i
\(939\) 4.41951e12 0.185515
\(940\) 6.93178e12 + 1.20062e13i 0.289580 + 0.501568i
\(941\) 9.07396e12 + 1.57166e13i 0.377263 + 0.653438i 0.990663 0.136334i \(-0.0435321\pi\)
−0.613400 + 0.789772i \(0.710199\pi\)
\(942\) −1.64396e13 2.84742e13i −0.680240 1.17821i
\(943\) −8.40439e12 + 1.45568e13i −0.346102 + 0.599466i
\(944\) 1.90139e13 3.29330e13i 0.779285 1.34976i
\(945\) 3.75918e13 + 6.51109e13i 1.53338 + 2.65589i
\(946\) −2.54912e13 4.41520e13i −1.03486 1.79242i
\(947\) 1.32150e13 + 2.28891e13i 0.533941 + 0.924813i 0.999214 + 0.0396455i \(0.0126229\pi\)
−0.465273 + 0.885167i \(0.654044\pi\)
\(948\) 1.69583e13 0.681938
\(949\) −2.38652e13 + 4.13358e13i −0.955142 + 1.65435i
\(950\) −5.00132e11 8.66253e11i −0.0199218 0.0345055i
\(951\) 4.26171e13 1.68955
\(952\) −3.42283e12 −0.135058
\(953\) 2.47010e13 + 4.27834e13i 0.970056 + 1.68019i 0.695370 + 0.718652i \(0.255241\pi\)
0.274686 + 0.961534i \(0.411426\pi\)
\(954\) 5.46088e13 2.13449
\(955\) −1.32190e13 + 2.28961e13i −0.514262 + 0.890729i
\(956\) −2.41088e13 −0.933502
\(957\) −2.54536e13 + 4.40869e13i −0.980946 + 1.69905i
\(958\) −8.64502e12 + 1.49736e13i −0.331605 + 0.574357i
\(959\) 2.14633e13 3.71755e13i 0.819431 1.41930i
\(960\) −2.40486e13 4.16534e13i −0.913839 1.58282i
\(961\) −1.12820e13 −0.426710
\(962\) −4.72382e13 + 5.94487e12i −1.77830 + 0.223797i
\(963\) −4.08817e13 −1.53183
\(964\) 1.56740e11 + 2.71482e11i 0.00584566 + 0.0101250i
\(965\) −2.40128e11 + 4.15915e11i −0.00891396 + 0.0154394i
\(966\) 1.95589e13 3.38770e13i 0.722681 1.25172i
\(967\) 4.58120e12 7.93488e12i 0.168485 0.291824i −0.769403 0.638764i \(-0.779446\pi\)
0.937887 + 0.346940i \(0.112779\pi\)
\(968\) 1.81519e12 0.0664481
\(969\) 7.37438e11 1.27728e12i 0.0268701 0.0465403i
\(970\) −4.26083e13 −1.54533
\(971\) −9.80680e12 1.69859e13i −0.354031 0.613199i 0.632921 0.774216i \(-0.281856\pi\)
−0.986952 + 0.161017i \(0.948522\pi\)
\(972\) 8.32623e12 0.299192
\(973\) 6.18522e13 2.21232
\(974\) −1.01515e13 1.75829e13i −0.361423 0.626003i
\(975\) 2.14249e13 3.71090e13i 0.759272 1.31510i
\(976\) 8.50436e12 0.299997
\(977\) 1.68629e13 + 2.92074e13i 0.592116 + 1.02557i 0.993947 + 0.109861i \(0.0350406\pi\)
−0.401831 + 0.915714i \(0.631626\pi\)
\(978\) 3.94534e13 + 6.83353e13i 1.37899 + 2.38847i
\(979\) 2.43473e11 + 4.21707e11i 0.00847088 + 0.0146720i
\(980\) −2.36683e13 + 4.09946e13i −0.819689 + 1.41974i
\(981\) 3.33020e13 5.76808e13i 1.14805 1.98848i
\(982\) 2.34617e13 + 4.06369e13i 0.805115 + 1.39450i
\(983\) −3.31428e12 5.74050e12i −0.113214 0.196092i 0.803851 0.594831i \(-0.202781\pi\)
−0.917064 + 0.398739i \(0.869448\pi\)
\(984\) −5.05299e12 8.75204e12i −0.171819 0.297599i
\(985\) 3.83572e13 1.29833
\(986\) 1.42554e13 2.46911e13i 0.480323 0.831943i
\(987\) −1.90340e13 3.29679e13i −0.638416 1.10577i
\(988\) −1.48466e12 −0.0495703
\(989\) 1.42673e13 0.474198
\(990\) 6.47479e13 + 1.12147e14i 2.14224 + 3.71046i
\(991\) 2.12936e13 0.701321 0.350661 0.936503i \(-0.385957\pi\)
0.350661 + 0.936503i \(0.385957\pi\)
\(992\) −1.58717e13 + 2.74906e13i −0.520380 + 0.901325i
\(993\) −6.06138e13 −1.97833
\(994\) −5.58850e13 + 9.67957e13i −1.81575 + 3.14498i
\(995\) −1.35263e13 + 2.34282e13i −0.437497 + 0.757767i
\(996\) −3.07047e13 + 5.31822e13i −0.988640 + 1.71238i
\(997\) 2.68694e12 + 4.65391e12i 0.0861250 + 0.149173i 0.905870 0.423556i \(-0.139218\pi\)
−0.819745 + 0.572729i \(0.805885\pi\)
\(998\) 6.12858e13 1.95557
\(999\) −4.78100e13 + 6.01683e12i −1.51871 + 0.191127i
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 37.10.c.a.26.23 yes 54
37.10 even 3 inner 37.10.c.a.10.23 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.10.c.a.10.23 54 37.10 even 3 inner
37.10.c.a.26.23 yes 54 1.1 even 1 trivial