Properties

Label 37.10.c.a.10.17
Level $37$
Weight $10$
Character 37.10
Analytic conductor $19.056$
Analytic rank $0$
Dimension $54$
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] = [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 10.17
Character \(\chi\) \(=\) 37.10
Dual form 37.10.c.a.26.17

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(4.81916 - 8.34702i) q^{2} +(-93.7353 - 162.354i) q^{3} +(209.551 + 362.954i) q^{4} +(-535.707 - 927.872i) q^{5} -1806.90 q^{6} +(5666.05 + 9813.89i) q^{7} +8974.26 q^{8} +(-7731.11 + 13390.7i) q^{9} +O(q^{10})\) \(q+(4.81916 - 8.34702i) q^{2} +(-93.7353 - 162.354i) q^{3} +(209.551 + 362.954i) q^{4} +(-535.707 - 927.872i) q^{5} -1806.90 q^{6} +(5666.05 + 9813.89i) q^{7} +8974.26 q^{8} +(-7731.11 + 13390.7i) q^{9} -10326.6 q^{10} +18602.9 q^{11} +(39284.7 - 68043.2i) q^{12} +(32706.8 + 56649.8i) q^{13} +109222. q^{14} +(-100429. + 173949. i) q^{15} +(-64042.0 + 110924. i) q^{16} +(178999. - 310035. i) q^{17} +(74514.8 + 129063. i) q^{18} +(-82505.0 - 142903. i) q^{19} +(224516. - 388874. i) q^{20} +(1.06222e6 - 1.83982e6i) q^{21} +(89650.2 - 155279. i) q^{22} -129062. q^{23} +(-841205. - 1.45701e6i) q^{24} +(402599. - 697321. i) q^{25} +630476. q^{26} -791273. q^{27} +(-2.37466e6 + 4.11303e6i) q^{28} +5.59872e6 q^{29} +(967969. + 1.67657e6i) q^{30} +5.01231e6 q^{31} +(2.91467e6 + 5.04835e6i) q^{32} +(-1.74375e6 - 3.02026e6i) q^{33} +(-1.72524e6 - 2.98821e6i) q^{34} +(6.07069e6 - 1.05147e7i) q^{35} -6.48026e6 q^{36} +(4.12592e6 - 1.06273e7i) q^{37} -1.59042e6 q^{38} +(6.13155e6 - 1.06202e7i) q^{39} +(-4.80757e6 - 8.32696e6i) q^{40} +(8.84591e6 + 1.53216e7i) q^{41} +(-1.02380e7 - 1.77327e7i) q^{42} -2.70734e7 q^{43} +(3.89826e6 + 6.75199e6i) q^{44} +1.65664e7 q^{45} +(-621971. + 1.07728e6i) q^{46} +5.87524e7 q^{47} +2.40120e7 q^{48} +(-4.40315e7 + 7.62648e7i) q^{49} +(-3.88037e6 - 6.72100e6i) q^{50} -6.71140e7 q^{51} +(-1.37075e7 + 2.37421e7i) q^{52} +(-1.74077e7 + 3.01509e7i) q^{53} +(-3.81327e6 + 6.60477e6i) q^{54} +(-9.96569e6 - 1.72611e7i) q^{55} +(5.08486e7 + 8.80724e7i) q^{56} +(-1.54673e7 + 2.67901e7i) q^{57} +(2.69811e7 - 4.67326e7i) q^{58} +(-4.63688e7 + 8.03131e7i) q^{59} -8.41804e7 q^{60} +(-1.47381e7 - 2.55272e7i) q^{61} +(2.41551e7 - 4.18379e7i) q^{62} -1.75219e8 q^{63} -9.39408e6 q^{64} +(3.50425e7 - 6.06953e7i) q^{65} -3.36135e7 q^{66} +(-6.09016e7 - 1.05485e8i) q^{67} +1.50038e8 q^{68} +(1.20977e7 + 2.09538e7i) q^{69} +(-5.85112e7 - 1.01344e8i) q^{70} +(-8.65406e7 - 1.49893e8i) q^{71} +(-6.93810e7 + 1.20171e8i) q^{72} +3.22643e8 q^{73} +(-6.88224e7 - 8.56536e7i) q^{74} -1.50951e8 q^{75} +(3.45781e7 - 5.98910e7i) q^{76} +(1.05405e8 + 1.82567e8i) q^{77} +(-5.90978e7 - 1.02360e8i) q^{78} +(2.62049e8 + 4.53882e8i) q^{79} +1.37231e8 q^{80} +(2.26342e8 + 3.92035e8i) q^{81} +1.70519e8 q^{82} +(2.35790e7 - 4.08401e7i) q^{83} +8.90357e8 q^{84} -3.83563e8 q^{85} +(-1.30471e8 + 2.25982e8i) q^{86} +(-5.24798e8 - 9.08976e8i) q^{87} +1.66947e8 q^{88} +(4.58496e8 - 7.94139e8i) q^{89} +(7.98362e7 - 1.38280e8i) q^{90} +(-3.70636e8 + 6.41961e8i) q^{91} +(-2.70452e7 - 4.68436e7i) q^{92} +(-4.69830e8 - 8.13770e8i) q^{93} +(2.83137e8 - 4.90408e8i) q^{94} +(-8.83970e7 + 1.53108e8i) q^{95} +(5.46414e8 - 9.46417e8i) q^{96} +5.93854e7 q^{97} +(4.24389e8 + 7.35064e8i) q^{98} +(-1.43821e8 + 2.49105e8i) 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 \(\left(\mathbb{Z}/37\mathbb{Z}\right)^\times\).

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.81916 8.34702i 0.212979 0.368890i −0.739667 0.672973i \(-0.765017\pi\)
0.952645 + 0.304084i \(0.0983502\pi\)
\(3\) −93.7353 162.354i −0.668125 1.15723i −0.978428 0.206588i \(-0.933764\pi\)
0.310303 0.950638i \(-0.399569\pi\)
\(4\) 209.551 + 362.954i 0.409280 + 0.708894i
\(5\) −535.707 927.872i −0.383321 0.663931i 0.608214 0.793773i \(-0.291886\pi\)
−0.991535 + 0.129842i \(0.958553\pi\)
\(6\) −1806.90 −0.569185
\(7\) 5666.05 + 9813.89i 0.891948 + 1.54490i 0.837537 + 0.546380i \(0.183995\pi\)
0.0544104 + 0.998519i \(0.482672\pi\)
\(8\) 8974.26 0.774629
\(9\) −7731.11 + 13390.7i −0.392781 + 0.680317i
\(10\) −10326.6 −0.326556
\(11\) 18602.9 0.383101 0.191550 0.981483i \(-0.438648\pi\)
0.191550 + 0.981483i \(0.438648\pi\)
\(12\) 39284.7 68043.2i 0.546900 0.947259i
\(13\) 32706.8 + 56649.8i 0.317609 + 0.550114i 0.979989 0.199054i \(-0.0637868\pi\)
−0.662380 + 0.749168i \(0.730454\pi\)
\(14\) 109222. 0.759863
\(15\) −100429. + 173949.i −0.512212 + 0.887177i
\(16\) −64042.0 + 110924.i −0.244301 + 0.423142i
\(17\) 178999. 310035.i 0.519792 0.900306i −0.479943 0.877300i \(-0.659343\pi\)
0.999735 0.0230067i \(-0.00732389\pi\)
\(18\) 74514.8 + 129063.i 0.167308 + 0.289786i
\(19\) −82505.0 142903.i −0.145241 0.251565i 0.784222 0.620481i \(-0.213062\pi\)
−0.929463 + 0.368916i \(0.879729\pi\)
\(20\) 224516. 388874.i 0.313771 0.543468i
\(21\) 1.06222e6 1.83982e6i 1.19186 2.06437i
\(22\) 89650.2 155279.i 0.0815923 0.141322i
\(23\) −129062. −0.0961665 −0.0480832 0.998843i \(-0.515311\pi\)
−0.0480832 + 0.998843i \(0.515311\pi\)
\(24\) −841205. 1.45701e6i −0.517549 0.896420i
\(25\) 402599. 697321.i 0.206131 0.357029i
\(26\) 630476. 0.270575
\(27\) −791273. −0.286543
\(28\) −2.37466e6 + 4.11303e6i −0.730113 + 1.26459i
\(29\) 5.59872e6 1.46993 0.734967 0.678103i \(-0.237198\pi\)
0.734967 + 0.678103i \(0.237198\pi\)
\(30\) 967969. + 1.67657e6i 0.218180 + 0.377899i
\(31\) 5.01231e6 0.974788 0.487394 0.873182i \(-0.337947\pi\)
0.487394 + 0.873182i \(0.337947\pi\)
\(32\) 2.91467e6 + 5.04835e6i 0.491376 + 0.851088i
\(33\) −1.74375e6 3.02026e6i −0.255959 0.443334i
\(34\) −1.72524e6 2.98821e6i −0.221409 0.383492i
\(35\) 6.07069e6 1.05147e7i 0.683804 1.18438i
\(36\) −6.48026e6 −0.643030
\(37\) 4.12592e6 1.06273e7i 0.361921 0.932209i
\(38\) −1.59042e6 −0.123733
\(39\) 6.13155e6 1.06202e7i 0.424404 0.735090i
\(40\) −4.80757e6 8.32696e6i −0.296931 0.514300i
\(41\) 8.84591e6 + 1.53216e7i 0.488894 + 0.846790i 0.999918 0.0127764i \(-0.00406697\pi\)
−0.511024 + 0.859567i \(0.670734\pi\)
\(42\) −1.02380e7 1.77327e7i −0.507683 0.879333i
\(43\) −2.70734e7 −1.20763 −0.603816 0.797124i \(-0.706354\pi\)
−0.603816 + 0.797124i \(0.706354\pi\)
\(44\) 3.89826e6 + 6.75199e6i 0.156796 + 0.271578i
\(45\) 1.65664e7 0.602244
\(46\) −621971. + 1.07728e6i −0.0204814 + 0.0354748i
\(47\) 5.87524e7 1.75625 0.878123 0.478435i \(-0.158796\pi\)
0.878123 + 0.478435i \(0.158796\pi\)
\(48\) 2.40120e7 0.652894
\(49\) −4.40315e7 + 7.62648e7i −1.09114 + 1.88991i
\(50\) −3.88037e6 6.72100e6i −0.0878028 0.152079i
\(51\) −6.71140e7 −1.38914
\(52\) −1.37075e7 + 2.37421e7i −0.259982 + 0.450302i
\(53\) −1.74077e7 + 3.01509e7i −0.303039 + 0.524879i −0.976823 0.214049i \(-0.931335\pi\)
0.673784 + 0.738929i \(0.264668\pi\)
\(54\) −3.81327e6 + 6.60477e6i −0.0610275 + 0.105703i
\(55\) −9.96569e6 1.72611e7i −0.146850 0.254352i
\(56\) 5.08486e7 + 8.80724e7i 0.690928 + 1.19672i
\(57\) −1.54673e7 + 2.67901e7i −0.194078 + 0.336153i
\(58\) 2.69811e7 4.67326e7i 0.313064 0.542243i
\(59\) −4.63688e7 + 8.03131e7i −0.498186 + 0.862884i −0.999998 0.00209289i \(-0.999334\pi\)
0.501811 + 0.864977i \(0.332667\pi\)
\(60\) −8.41804e7 −0.838553
\(61\) −1.47381e7 2.55272e7i −0.136288 0.236058i 0.789801 0.613363i \(-0.210184\pi\)
−0.926089 + 0.377306i \(0.876851\pi\)
\(62\) 2.41551e7 4.18379e7i 0.207609 0.359589i
\(63\) −1.75219e8 −1.40136
\(64\) −9.39408e6 −0.0699914
\(65\) 3.50425e7 6.06953e7i 0.243492 0.421740i
\(66\) −3.36135e7 −0.218055
\(67\) −6.09016e7 1.05485e8i −0.369226 0.639518i 0.620219 0.784429i \(-0.287044\pi\)
−0.989445 + 0.144911i \(0.953710\pi\)
\(68\) 1.50038e8 0.850962
\(69\) 1.20977e7 + 2.09538e7i 0.0642512 + 0.111286i
\(70\) −5.85112e7 1.01344e8i −0.291271 0.504497i
\(71\) −8.65406e7 1.49893e8i −0.404164 0.700032i 0.590060 0.807360i \(-0.299104\pi\)
−0.994224 + 0.107327i \(0.965771\pi\)
\(72\) −6.93810e7 + 1.20171e8i −0.304259 + 0.526993i
\(73\) 3.22643e8 1.32975 0.664874 0.746956i \(-0.268485\pi\)
0.664874 + 0.746956i \(0.268485\pi\)
\(74\) −6.88224e7 8.56536e7i −0.266801 0.332049i
\(75\) −1.50951e8 −0.550884
\(76\) 3.45781e7 5.98910e7i 0.118889 0.205921i
\(77\) 1.05405e8 + 1.82567e8i 0.341706 + 0.591852i
\(78\) −5.90978e7 1.02360e8i −0.180778 0.313117i
\(79\) 2.62049e8 + 4.53882e8i 0.756939 + 1.31106i 0.944405 + 0.328786i \(0.106639\pi\)
−0.187466 + 0.982271i \(0.560027\pi\)
\(80\) 1.37231e8 0.374582
\(81\) 2.26342e8 + 3.92035e8i 0.584227 + 1.01191i
\(82\) 1.70519e8 0.416496
\(83\) 2.35790e7 4.08401e7i 0.0545349 0.0944572i −0.837469 0.546485i \(-0.815966\pi\)
0.892004 + 0.452027i \(0.149299\pi\)
\(84\) 8.90357e8 1.95123
\(85\) −3.83563e8 −0.796988
\(86\) −1.30471e8 + 2.25982e8i −0.257200 + 0.445483i
\(87\) −5.24798e8 9.08976e8i −0.982099 1.70105i
\(88\) 1.66947e8 0.296761
\(89\) 4.58496e8 7.94139e8i 0.774606 1.34166i −0.160410 0.987050i \(-0.551282\pi\)
0.935016 0.354606i \(-0.115385\pi\)
\(90\) 7.98362e7 1.38280e8i 0.128265 0.222162i
\(91\) −3.70636e8 + 6.41961e8i −0.566581 + 0.981346i
\(92\) −2.70452e7 4.68436e7i −0.0393590 0.0681718i
\(93\) −4.69830e8 8.13770e8i −0.651280 1.12805i
\(94\) 2.83137e8 4.90408e8i 0.374043 0.647861i
\(95\) −8.83970e7 + 1.53108e8i −0.111348 + 0.192860i
\(96\) 5.46414e8 9.46417e8i 0.656601 1.13727i
\(97\) 5.93854e7 0.0681094 0.0340547 0.999420i \(-0.489158\pi\)
0.0340547 + 0.999420i \(0.489158\pi\)
\(98\) 4.24389e8 + 7.35064e8i 0.464780 + 0.805022i
\(99\) −1.43821e8 + 2.49105e8i −0.150475 + 0.260630i
\(100\) 3.37461e8 0.337461
\(101\) 7.90766e7 0.0756140 0.0378070 0.999285i \(-0.487963\pi\)
0.0378070 + 0.999285i \(0.487963\pi\)
\(102\) −3.23433e8 + 5.60202e8i −0.295858 + 0.512441i
\(103\) 1.11243e9 0.973878 0.486939 0.873436i \(-0.338113\pi\)
0.486939 + 0.873436i \(0.338113\pi\)
\(104\) 2.93519e8 + 5.08390e8i 0.246029 + 0.426134i
\(105\) −2.27615e9 −1.82746
\(106\) 1.67780e8 + 2.90604e8i 0.129082 + 0.223576i
\(107\) −5.25982e8 9.11028e8i −0.387922 0.671900i 0.604248 0.796796i \(-0.293474\pi\)
−0.992170 + 0.124896i \(0.960140\pi\)
\(108\) −1.65812e8 2.87196e8i −0.117276 0.203129i
\(109\) 1.15140e8 1.99428e8i 0.0781278 0.135321i −0.824314 0.566132i \(-0.808439\pi\)
0.902442 + 0.430811i \(0.141772\pi\)
\(110\) −1.92105e8 −0.125104
\(111\) −2.11212e9 + 3.26287e8i −1.32058 + 0.204008i
\(112\) −1.45146e9 −0.871614
\(113\) 5.27678e8 9.13966e8i 0.304450 0.527323i −0.672688 0.739926i \(-0.734861\pi\)
0.977139 + 0.212602i \(0.0681939\pi\)
\(114\) 1.49078e8 + 2.58211e8i 0.0826690 + 0.143187i
\(115\) 6.91395e7 + 1.19753e8i 0.0368626 + 0.0638479i
\(116\) 1.17322e9 + 2.03208e9i 0.601615 + 1.04203i
\(117\) −1.01144e9 −0.499002
\(118\) 4.46917e8 + 7.74083e8i 0.212206 + 0.367552i
\(119\) 4.05686e9 1.85451
\(120\) −9.01278e8 + 1.56106e9i −0.396774 + 0.687233i
\(121\) −2.01188e9 −0.853234
\(122\) −2.84101e8 −0.116106
\(123\) 1.65835e9 2.87234e9i 0.653285 1.13152i
\(124\) 1.05034e9 + 1.81924e9i 0.398962 + 0.691022i
\(125\) −2.95530e9 −1.08270
\(126\) −8.44410e8 + 1.46256e9i −0.298460 + 0.516947i
\(127\) −1.06948e9 + 1.85239e9i −0.364800 + 0.631851i −0.988744 0.149617i \(-0.952196\pi\)
0.623944 + 0.781469i \(0.285529\pi\)
\(128\) −1.53758e9 + 2.66317e9i −0.506283 + 0.876908i
\(129\) 2.53773e9 + 4.39548e9i 0.806848 + 1.39750i
\(130\) −3.37750e8 5.85000e8i −0.103717 0.179643i
\(131\) −3.10446e8 + 5.37709e8i −0.0921012 + 0.159524i −0.908395 0.418113i \(-0.862692\pi\)
0.816294 + 0.577637i \(0.196025\pi\)
\(132\) 7.30809e8 1.26580e9i 0.209518 0.362896i
\(133\) 9.34955e8 1.61939e9i 0.259095 0.448765i
\(134\) −1.17398e9 −0.314549
\(135\) 4.23891e8 + 7.34200e8i 0.109838 + 0.190245i
\(136\) 1.60638e9 2.78233e9i 0.402646 0.697403i
\(137\) −4.37991e9 −1.06224 −0.531120 0.847297i \(-0.678229\pi\)
−0.531120 + 0.847297i \(0.678229\pi\)
\(138\) 2.33202e8 0.0547365
\(139\) −2.36158e9 + 4.09037e9i −0.536581 + 0.929386i 0.462504 + 0.886617i \(0.346951\pi\)
−0.999085 + 0.0427684i \(0.986382\pi\)
\(140\) 5.08849e9 1.11947
\(141\) −5.50717e9 9.53870e9i −1.17339 2.03237i
\(142\) −1.66821e9 −0.344313
\(143\) 6.08440e8 + 1.05385e9i 0.121676 + 0.210749i
\(144\) −9.90231e8 1.71513e9i −0.191913 0.332404i
\(145\) −2.99927e9 5.19489e9i −0.563456 0.975934i
\(146\) 1.55487e9 2.69311e9i 0.283208 0.490530i
\(147\) 1.65092e10 2.91607
\(148\) 4.72180e9 7.29436e8i 0.808964 0.124971i
\(149\) −1.00150e10 −1.66460 −0.832301 0.554323i \(-0.812977\pi\)
−0.832301 + 0.554323i \(0.812977\pi\)
\(150\) −7.27456e8 + 1.25999e9i −0.117326 + 0.203215i
\(151\) −3.37590e9 5.84724e9i −0.528438 0.915281i −0.999450 0.0331543i \(-0.989445\pi\)
0.471013 0.882126i \(-0.343889\pi\)
\(152\) −7.40421e8 1.28245e9i −0.112508 0.194869i
\(153\) 2.76772e9 + 4.79382e9i 0.408329 + 0.707246i
\(154\) 2.03185e9 0.291104
\(155\) −2.68513e9 4.65078e9i −0.373657 0.647192i
\(156\) 5.13950e9 0.694801
\(157\) −6.18312e9 + 1.07095e10i −0.812193 + 1.40676i 0.0991328 + 0.995074i \(0.468393\pi\)
−0.911326 + 0.411686i \(0.864940\pi\)
\(158\) 5.05142e9 0.644847
\(159\) 6.52685e9 0.809872
\(160\) 3.12281e9 5.40887e9i 0.376709 0.652480i
\(161\) −7.31273e8 1.26660e9i −0.0857755 0.148567i
\(162\) 4.36310e9 0.497712
\(163\) −7.18809e9 + 1.24501e10i −0.797571 + 1.38143i 0.123623 + 0.992329i \(0.460549\pi\)
−0.921194 + 0.389104i \(0.872785\pi\)
\(164\) −3.70735e9 + 6.42131e9i −0.400190 + 0.693149i
\(165\) −1.86827e9 + 3.23595e9i −0.196229 + 0.339878i
\(166\) −2.27262e8 3.93629e8i −0.0232295 0.0402347i
\(167\) 4.35845e8 + 7.54905e8i 0.0433618 + 0.0751049i 0.886892 0.461977i \(-0.152860\pi\)
−0.843530 + 0.537082i \(0.819527\pi\)
\(168\) 9.53262e9 1.65110e10i 0.923253 1.59912i
\(169\) 3.16279e9 5.47811e9i 0.298249 0.516583i
\(170\) −1.84845e9 + 3.20161e9i −0.169741 + 0.294001i
\(171\) 2.55142e9 0.228192
\(172\) −5.67327e9 9.82639e9i −0.494260 0.856083i
\(173\) 2.25233e9 3.90115e9i 0.191172 0.331120i −0.754467 0.656338i \(-0.772104\pi\)
0.945639 + 0.325218i \(0.105438\pi\)
\(174\) −1.01163e10 −0.836664
\(175\) 9.12458e9 0.735431
\(176\) −1.19137e9 + 2.06351e9i −0.0935919 + 0.162106i
\(177\) 1.73856e10 1.33140
\(178\) −4.41913e9 7.65416e9i −0.329949 0.571488i
\(179\) 1.48739e10 1.08289 0.541447 0.840735i \(-0.317877\pi\)
0.541447 + 0.840735i \(0.317877\pi\)
\(180\) 3.47152e9 + 6.01285e9i 0.246487 + 0.426927i
\(181\) −2.99989e9 5.19596e9i −0.207755 0.359842i 0.743252 0.669011i \(-0.233282\pi\)
−0.951007 + 0.309169i \(0.899949\pi\)
\(182\) 3.57231e9 + 6.18742e9i 0.241339 + 0.418012i
\(183\) −2.76296e9 + 4.78559e9i −0.182115 + 0.315432i
\(184\) −1.15824e9 −0.0744933
\(185\) −1.20710e10 + 1.86476e9i −0.757654 + 0.117045i
\(186\) −9.05674e9 −0.554835
\(187\) 3.32989e9 5.76754e9i 0.199133 0.344908i
\(188\) 1.23117e10 + 2.13244e10i 0.718797 + 1.24499i
\(189\) −4.48340e9 7.76547e9i −0.255581 0.442680i
\(190\) 8.51998e8 + 1.47570e9i 0.0474294 + 0.0821501i
\(191\) −1.51894e10 −0.825832 −0.412916 0.910769i \(-0.635490\pi\)
−0.412916 + 0.910769i \(0.635490\pi\)
\(192\) 8.80557e8 + 1.52517e9i 0.0467630 + 0.0809958i
\(193\) −1.31175e10 −0.680522 −0.340261 0.940331i \(-0.610515\pi\)
−0.340261 + 0.940331i \(0.610515\pi\)
\(194\) 2.86187e8 4.95691e8i 0.0145058 0.0251248i
\(195\) −1.31389e10 −0.650732
\(196\) −3.69075e10 −1.78633
\(197\) 1.30980e10 2.26865e10i 0.619596 1.07317i −0.369964 0.929046i \(-0.620630\pi\)
0.989559 0.144125i \(-0.0460368\pi\)
\(198\) 1.38619e9 + 2.40095e9i 0.0640958 + 0.111017i
\(199\) 1.55156e10 0.701342 0.350671 0.936499i \(-0.385953\pi\)
0.350671 + 0.936499i \(0.385953\pi\)
\(200\) 3.61303e9 6.25794e9i 0.159675 0.276565i
\(201\) −1.14173e10 + 1.97753e10i −0.493378 + 0.854555i
\(202\) 3.81083e8 6.60054e8i 0.0161042 0.0278932i
\(203\) 3.17226e10 + 5.49452e10i 1.31110 + 2.27090i
\(204\) −1.40638e10 2.43593e10i −0.568549 0.984756i
\(205\) 9.47763e9 1.64157e10i 0.374807 0.649184i
\(206\) 5.36096e9 9.28546e9i 0.207415 0.359254i
\(207\) 9.97793e8 1.72823e9i 0.0377723 0.0654236i
\(208\) −8.37842e9 −0.310368
\(209\) −1.53483e9 2.65840e9i −0.0556419 0.0963747i
\(210\) −1.09691e10 + 1.89991e10i −0.389211 + 0.674133i
\(211\) −4.95087e10 −1.71953 −0.859766 0.510689i \(-0.829391\pi\)
−0.859766 + 0.510689i \(0.829391\pi\)
\(212\) −1.45912e10 −0.496112
\(213\) −1.62238e10 + 2.81005e10i −0.540064 + 0.935418i
\(214\) −1.01392e10 −0.330476
\(215\) 1.45034e10 + 2.51206e10i 0.462910 + 0.801784i
\(216\) −7.10109e9 −0.221964
\(217\) 2.84000e10 + 4.91903e10i 0.869460 + 1.50595i
\(218\) −1.10975e9 1.92215e9i −0.0332791 0.0576411i
\(219\) −3.02430e10 5.23824e10i −0.888437 1.53882i
\(220\) 4.17665e9 7.23417e9i 0.120206 0.208203i
\(221\) 2.34179e10 0.660362
\(222\) −7.45513e9 + 1.92024e10i −0.206000 + 0.530599i
\(223\) 6.70641e10 1.81601 0.908005 0.418959i \(-0.137605\pi\)
0.908005 + 0.418959i \(0.137605\pi\)
\(224\) −3.30293e10 + 5.72085e10i −0.876564 + 1.51825i
\(225\) 6.22507e9 + 1.07821e10i 0.161928 + 0.280468i
\(226\) −5.08593e9 8.80909e9i −0.129683 0.224617i
\(227\) 1.75101e10 + 3.03284e10i 0.437695 + 0.758111i 0.997511 0.0705063i \(-0.0224615\pi\)
−0.559816 + 0.828617i \(0.689128\pi\)
\(228\) −1.29647e10 −0.317729
\(229\) −2.18914e10 3.79169e10i −0.526033 0.911116i −0.999540 0.0303260i \(-0.990345\pi\)
0.473507 0.880790i \(-0.342988\pi\)
\(230\) 1.33278e9 0.0314038
\(231\) 1.97603e10 3.42259e10i 0.456604 0.790862i
\(232\) 5.02444e10 1.13865
\(233\) −2.48727e10 −0.552867 −0.276433 0.961033i \(-0.589153\pi\)
−0.276433 + 0.961033i \(0.589153\pi\)
\(234\) −4.87427e9 + 8.44249e9i −0.106277 + 0.184077i
\(235\) −3.14741e10 5.45147e10i −0.673205 1.16603i
\(236\) −3.88666e10 −0.815591
\(237\) 4.91265e10 8.50896e10i 1.01146 1.75190i
\(238\) 1.95507e10 3.38627e10i 0.394971 0.684109i
\(239\) −2.85026e10 + 4.93680e10i −0.565060 + 0.978712i 0.431985 + 0.901881i \(0.357813\pi\)
−0.997044 + 0.0768309i \(0.975520\pi\)
\(240\) −1.28634e10 2.22800e10i −0.250268 0.433476i
\(241\) 5.41590e9 + 9.38061e9i 0.103417 + 0.179124i 0.913091 0.407757i \(-0.133689\pi\)
−0.809673 + 0.586881i \(0.800356\pi\)
\(242\) −9.69556e9 + 1.67932e10i −0.181721 + 0.314749i
\(243\) 3.46451e10 6.00070e10i 0.637402 1.10401i
\(244\) 6.17678e9 1.06985e10i 0.111560 0.193227i
\(245\) 9.43519e10 1.67303
\(246\) −1.59837e10 2.76845e10i −0.278271 0.481980i
\(247\) 5.39694e9 9.34778e9i 0.0922596 0.159798i
\(248\) 4.49818e10 0.755099
\(249\) −8.84074e9 −0.145744
\(250\) −1.42421e10 + 2.46680e10i −0.230591 + 0.399396i
\(251\) −6.49736e10 −1.03325 −0.516625 0.856212i \(-0.672812\pi\)
−0.516625 + 0.856212i \(0.672812\pi\)
\(252\) −3.67175e10 6.35966e10i −0.573549 0.993416i
\(253\) −2.40093e9 −0.0368415
\(254\) 1.03079e10 + 1.78539e10i 0.155389 + 0.269142i
\(255\) 3.59534e10 + 6.22731e10i 0.532487 + 0.922295i
\(256\) 1.24148e10 + 2.15031e10i 0.180659 + 0.312911i
\(257\) 3.92835e10 6.80411e10i 0.561709 0.972909i −0.435638 0.900122i \(-0.643477\pi\)
0.997348 0.0727871i \(-0.0231893\pi\)
\(258\) 4.89189e10 0.687366
\(259\) 1.27672e11 1.97232e10i 1.76298 0.272351i
\(260\) 2.93728e10 0.398626
\(261\) −4.32843e10 + 7.49706e10i −0.577362 + 1.00002i
\(262\) 2.99218e9 + 5.18260e9i 0.0392312 + 0.0679504i
\(263\) 2.73207e10 + 4.73208e10i 0.352120 + 0.609889i 0.986621 0.163033i \(-0.0521277\pi\)
−0.634501 + 0.772922i \(0.718794\pi\)
\(264\) −1.56488e10 2.71046e10i −0.198273 0.343419i
\(265\) 3.73016e10 0.464645
\(266\) −9.01139e9 1.56082e10i −0.110363 0.191155i
\(267\) −1.71909e11 −2.07013
\(268\) 2.55240e10 4.42089e10i 0.302234 0.523484i
\(269\) −5.73847e10 −0.668207 −0.334103 0.942536i \(-0.608433\pi\)
−0.334103 + 0.942536i \(0.608433\pi\)
\(270\) 8.17118e9 0.0935724
\(271\) −7.90061e9 + 1.36843e10i −0.0889813 + 0.154120i −0.907081 0.420957i \(-0.861694\pi\)
0.818099 + 0.575077i \(0.195028\pi\)
\(272\) 2.29269e10 + 3.97105e10i 0.253971 + 0.439891i
\(273\) 1.38967e11 1.51419
\(274\) −2.11074e10 + 3.65592e10i −0.226234 + 0.391849i
\(275\) 7.48950e9 1.29722e10i 0.0789688 0.136778i
\(276\) −5.07017e9 + 8.78180e9i −0.0525935 + 0.0910946i
\(277\) −5.24754e10 9.08900e10i −0.535546 0.927592i −0.999137 0.0415429i \(-0.986773\pi\)
0.463591 0.886049i \(-0.346561\pi\)
\(278\) 2.27616e10 + 3.94243e10i 0.228561 + 0.395878i
\(279\) −3.87507e10 + 6.71182e10i −0.382878 + 0.663165i
\(280\) 5.44799e10 9.43620e10i 0.529694 0.917457i
\(281\) −8.11097e10 + 1.40486e11i −0.776058 + 1.34417i 0.158140 + 0.987417i \(0.449450\pi\)
−0.934198 + 0.356755i \(0.883883\pi\)
\(282\) −1.06160e11 −0.999628
\(283\) −1.19731e10 2.07380e10i −0.110960 0.192189i 0.805197 0.593007i \(-0.202059\pi\)
−0.916158 + 0.400818i \(0.868726\pi\)
\(284\) 3.62694e10 6.28205e10i 0.330833 0.573019i
\(285\) 3.31437e10 0.297577
\(286\) 1.17287e10 0.103658
\(287\) −1.00243e11 + 1.73626e11i −0.872137 + 1.51059i
\(288\) −9.01344e10 −0.772013
\(289\) −4.78709e9 8.29149e9i −0.0403675 0.0699185i
\(290\) −5.78158e10 −0.480016
\(291\) −5.56651e9 9.64147e9i −0.0455055 0.0788179i
\(292\) 6.76103e10 + 1.17104e11i 0.544239 + 0.942650i
\(293\) 3.15434e10 + 5.46347e10i 0.250037 + 0.433076i 0.963536 0.267580i \(-0.0862240\pi\)
−0.713499 + 0.700656i \(0.752891\pi\)
\(294\) 7.95605e10 1.37803e11i 0.621061 1.07571i
\(295\) 9.93604e10 0.763861
\(296\) 3.70271e10 9.53717e10i 0.280354 0.722116i
\(297\) −1.47200e10 −0.109775
\(298\) −4.82636e10 + 8.35950e10i −0.354525 + 0.614055i
\(299\) −4.22120e9 7.31134e9i −0.0305433 0.0529025i
\(300\) −3.16320e10 5.47882e10i −0.225466 0.390518i
\(301\) −1.53399e11 2.65695e11i −1.07714 1.86567i
\(302\) −6.50760e10 −0.450184
\(303\) −7.41227e9 1.28384e10i −0.0505195 0.0875024i
\(304\) 2.11351e10 0.141930
\(305\) −1.57906e10 + 2.73501e10i −0.104484 + 0.180972i
\(306\) 5.33522e10 0.347861
\(307\) −2.03297e11 −1.30620 −0.653098 0.757274i \(-0.726531\pi\)
−0.653098 + 0.757274i \(0.726531\pi\)
\(308\) −4.41755e10 + 7.65142e10i −0.279707 + 0.484467i
\(309\) −1.04274e11 1.80607e11i −0.650672 1.12700i
\(310\) −5.17602e10 −0.318323
\(311\) 7.74660e10 1.34175e11i 0.469558 0.813299i −0.529836 0.848100i \(-0.677746\pi\)
0.999394 + 0.0348013i \(0.0110798\pi\)
\(312\) 5.50262e10 9.53081e10i 0.328756 0.569422i
\(313\) −8.48918e10 + 1.47037e11i −0.499938 + 0.865919i −1.00000 7.11850e-5i \(-0.999977\pi\)
0.500062 + 0.865990i \(0.333311\pi\)
\(314\) 5.95948e10 + 1.03221e11i 0.345960 + 0.599219i
\(315\) 9.38663e10 + 1.62581e11i 0.537170 + 0.930406i
\(316\) −1.09826e11 + 1.90223e11i −0.619600 + 1.07318i
\(317\) 4.76530e10 8.25374e10i 0.265047 0.459075i −0.702529 0.711655i \(-0.747946\pi\)
0.967576 + 0.252580i \(0.0812791\pi\)
\(318\) 3.14539e10 5.44797e10i 0.172485 0.298753i
\(319\) 1.04152e11 0.563133
\(320\) 5.03247e9 + 8.71650e9i 0.0268291 + 0.0464694i
\(321\) −9.86062e10 + 1.70791e11i −0.518360 + 0.897826i
\(322\) −1.40965e10 −0.0730733
\(323\) −5.90731e10 −0.301980
\(324\) −9.48604e10 + 1.64303e11i −0.478225 + 0.828311i
\(325\) 5.26708e10 0.261875
\(326\) 6.92811e10 + 1.19998e11i 0.339731 + 0.588432i
\(327\) −4.31706e10 −0.208797
\(328\) 7.93855e10 + 1.37500e11i 0.378712 + 0.655948i
\(329\) 3.32894e11 + 5.76590e11i 1.56648 + 2.71322i
\(330\) 1.80070e10 + 3.11890e10i 0.0835851 + 0.144774i
\(331\) 1.65562e11 2.86762e11i 0.758114 1.31309i −0.185697 0.982607i \(-0.559454\pi\)
0.943811 0.330485i \(-0.107212\pi\)
\(332\) 1.97641e10 0.0892802
\(333\) 1.10408e11 + 1.37409e11i 0.492041 + 0.612375i
\(334\) 8.40161e9 0.0369406
\(335\) −6.52508e10 + 1.13018e11i −0.283064 + 0.490281i
\(336\) 1.36053e11 + 2.35651e11i 0.582347 + 1.00865i
\(337\) −1.27910e11 2.21547e11i −0.540221 0.935690i −0.998891 0.0470832i \(-0.985007\pi\)
0.458670 0.888607i \(-0.348326\pi\)
\(338\) −3.04839e10 5.27997e10i −0.127042 0.220042i
\(339\) −1.97848e11 −0.813643
\(340\) −8.03762e10 1.39216e11i −0.326191 0.564980i
\(341\) 9.32434e10 0.373442
\(342\) 1.22957e10 2.12968e10i 0.0485999 0.0841775i
\(343\) −5.40648e11 −2.10907
\(344\) −2.42964e11 −0.935466
\(345\) 1.29616e10 2.24502e10i 0.0492576 0.0853167i
\(346\) −2.17087e10 3.76005e10i −0.0814312 0.141043i
\(347\) 3.83370e11 1.41950 0.709751 0.704453i \(-0.248807\pi\)
0.709751 + 0.704453i \(0.248807\pi\)
\(348\) 2.19944e11 3.80955e11i 0.803907 1.39241i
\(349\) 2.29448e11 3.97415e11i 0.827883 1.43394i −0.0718122 0.997418i \(-0.522878\pi\)
0.899696 0.436518i \(-0.143788\pi\)
\(350\) 4.39728e10 7.61631e10i 0.156631 0.271293i
\(351\) −2.58800e10 4.48254e10i −0.0910085 0.157631i
\(352\) 5.42212e10 + 9.39139e10i 0.188247 + 0.326053i
\(353\) 2.41120e11 4.17632e11i 0.826508 1.43155i −0.0742536 0.997239i \(-0.523657\pi\)
0.900761 0.434314i \(-0.143009\pi\)
\(354\) 8.37838e10 1.45118e11i 0.283560 0.491141i
\(355\) −9.27208e10 + 1.60597e11i −0.309849 + 0.536674i
\(356\) 3.84314e11 1.26812
\(357\) −3.80271e11 6.58649e11i −1.23904 2.14609i
\(358\) 7.16796e10 1.24153e11i 0.230633 0.399468i
\(359\) −3.93437e11 −1.25012 −0.625058 0.780578i \(-0.714925\pi\)
−0.625058 + 0.780578i \(0.714925\pi\)
\(360\) 1.48671e11 0.466516
\(361\) 1.47730e11 2.55875e11i 0.457810 0.792950i
\(362\) −5.78277e10 −0.176989
\(363\) 1.88584e11 + 3.26637e11i 0.570066 + 0.987384i
\(364\) −3.10670e11 −0.927561
\(365\) −1.72842e11 2.99371e11i −0.509720 0.882860i
\(366\) 2.66303e10 + 4.61250e10i 0.0775730 + 0.134360i
\(367\) −1.98049e11 3.43031e11i −0.569869 0.987042i −0.996578 0.0826531i \(-0.973661\pi\)
0.426710 0.904389i \(-0.359673\pi\)
\(368\) 8.26540e9 1.43161e10i 0.0234935 0.0406920i
\(369\) −2.73555e11 −0.768114
\(370\) −4.26069e10 + 1.09744e11i −0.118188 + 0.304419i
\(371\) −3.94531e11 −1.08118
\(372\) 1.96907e11 3.41053e11i 0.533112 0.923377i
\(373\) 3.16679e11 + 5.48503e11i 0.847089 + 1.46720i 0.883795 + 0.467875i \(0.154980\pi\)
−0.0367059 + 0.999326i \(0.511686\pi\)
\(374\) −3.20945e10 5.55893e10i −0.0848220 0.146916i
\(375\) 2.77016e11 + 4.79806e11i 0.723377 + 1.25293i
\(376\) 5.27259e11 1.36044
\(377\) 1.83116e11 + 3.17166e11i 0.466864 + 0.808632i
\(378\) −8.64247e10 −0.217733
\(379\) −2.81240e11 + 4.87122e11i −0.700165 + 1.21272i 0.268243 + 0.963351i \(0.413557\pi\)
−0.968408 + 0.249370i \(0.919776\pi\)
\(380\) −7.40949e10 −0.182290
\(381\) 4.00991e11 0.974926
\(382\) −7.32003e10 + 1.26787e11i −0.175885 + 0.304641i
\(383\) 9.69745e10 + 1.67965e11i 0.230284 + 0.398863i 0.957892 0.287130i \(-0.0927012\pi\)
−0.727608 + 0.685993i \(0.759368\pi\)
\(384\) 5.76502e11 1.35304
\(385\) 1.12932e11 1.95604e11i 0.261966 0.453738i
\(386\) −6.32151e10 + 1.09492e11i −0.144937 + 0.251038i
\(387\) 2.09307e11 3.62531e11i 0.474335 0.821572i
\(388\) 1.24443e10 + 2.15542e10i 0.0278758 + 0.0482823i
\(389\) −1.60026e11 2.77174e11i −0.354339 0.613733i 0.632666 0.774425i \(-0.281961\pi\)
−0.987005 + 0.160692i \(0.948627\pi\)
\(390\) −6.33182e10 + 1.09670e11i −0.138592 + 0.240048i
\(391\) −2.31019e10 + 4.00137e10i −0.0499866 + 0.0865793i
\(392\) −3.95150e11 + 6.84420e11i −0.845230 + 1.46398i
\(393\) 1.16399e11 0.246140
\(394\) −1.26243e11 2.18659e11i −0.263921 0.457125i
\(395\) 2.80763e11 4.86296e11i 0.580301 1.00511i
\(396\) −1.20551e11 −0.246345
\(397\) 2.35049e10 0.0474898 0.0237449 0.999718i \(-0.492441\pi\)
0.0237449 + 0.999718i \(0.492441\pi\)
\(398\) 7.47722e10 1.29509e11i 0.149371 0.258718i
\(399\) −3.50553e11 −0.692430
\(400\) 5.15665e10 + 8.93157e10i 0.100716 + 0.174445i
\(401\) −5.67046e11 −1.09514 −0.547569 0.836761i \(-0.684447\pi\)
−0.547569 + 0.836761i \(0.684447\pi\)
\(402\) 1.10043e11 + 1.90600e11i 0.210158 + 0.364004i
\(403\) 1.63936e11 + 2.83946e11i 0.309601 + 0.536245i
\(404\) 1.65706e10 + 2.87012e10i 0.0309473 + 0.0536023i
\(405\) 2.42506e11 4.20032e11i 0.447893 0.775773i
\(406\) 6.11505e11 1.11695
\(407\) 7.67541e10 1.97697e11i 0.138652 0.357130i
\(408\) −6.02298e11 −1.07607
\(409\) −3.53567e11 + 6.12396e11i −0.624765 + 1.08212i 0.363821 + 0.931469i \(0.381472\pi\)
−0.988586 + 0.150656i \(0.951861\pi\)
\(410\) −9.13483e10 1.58220e11i −0.159652 0.276525i
\(411\) 4.10552e11 + 7.11097e11i 0.709708 + 1.22925i
\(412\) 2.33111e11 + 4.03760e11i 0.398589 + 0.690376i
\(413\) −1.05091e12 −1.77742
\(414\) −9.61704e9 1.66572e10i −0.0160894 0.0278677i
\(415\) −5.05258e10 −0.0836174
\(416\) −1.90659e11 + 3.30230e11i −0.312131 + 0.540626i
\(417\) 8.85452e11 1.43401
\(418\) −2.95864e10 −0.0474022
\(419\) 4.92379e11 8.52825e11i 0.780434 1.35175i −0.151255 0.988495i \(-0.548331\pi\)
0.931689 0.363257i \(-0.118335\pi\)
\(420\) −4.76971e11 8.26137e11i −0.747945 1.29548i
\(421\) −1.08991e12 −1.69092 −0.845458 0.534042i \(-0.820673\pi\)
−0.845458 + 0.534042i \(0.820673\pi\)
\(422\) −2.38590e11 + 4.13250e11i −0.366223 + 0.634318i
\(423\) −4.54221e11 + 7.86734e11i −0.689820 + 1.19480i
\(424\) −1.56221e11 + 2.70582e11i −0.234743 + 0.406587i
\(425\) −1.44129e11 2.49639e11i −0.214290 0.371161i
\(426\) 1.56370e11 + 2.70841e11i 0.230044 + 0.398448i
\(427\) 1.67014e11 2.89276e11i 0.243123 0.421102i
\(428\) 2.20441e11 3.81815e11i 0.317537 0.549991i
\(429\) 1.14065e11 1.97566e11i 0.162590 0.281614i
\(430\) 2.79576e11 0.394360
\(431\) 1.40443e11 + 2.43254e11i 0.196043 + 0.339556i 0.947242 0.320520i \(-0.103858\pi\)
−0.751199 + 0.660076i \(0.770524\pi\)
\(432\) 5.06747e10 8.77712e10i 0.0700027 0.121248i
\(433\) −7.33467e11 −1.00273 −0.501366 0.865235i \(-0.667169\pi\)
−0.501366 + 0.865235i \(0.667169\pi\)
\(434\) 5.47456e11 0.740706
\(435\) −5.62275e11 + 9.73890e11i −0.752918 + 1.30409i
\(436\) 9.65108e10 0.127905
\(437\) 1.06483e10 + 1.84434e10i 0.0139673 + 0.0241921i
\(438\) −5.82983e11 −0.756872
\(439\) 3.00979e11 + 5.21311e11i 0.386764 + 0.669894i 0.992012 0.126142i \(-0.0402596\pi\)
−0.605249 + 0.796037i \(0.706926\pi\)
\(440\) −8.94347e10 1.54905e11i −0.113755 0.197029i
\(441\) −6.80824e11 1.17922e12i −0.857159 1.48464i
\(442\) 1.12854e11 1.95469e11i 0.140643 0.243601i
\(443\) 7.81777e11 0.964419 0.482210 0.876056i \(-0.339834\pi\)
0.482210 + 0.876056i \(0.339834\pi\)
\(444\) −5.61026e11 6.98230e11i −0.685109 0.852658i
\(445\) −9.82478e11 −1.18769
\(446\) 3.23192e11 5.59786e11i 0.386771 0.669907i
\(447\) 9.38754e11 + 1.62597e12i 1.11216 + 1.92632i
\(448\) −5.32274e10 9.21925e10i −0.0624286 0.108130i
\(449\) −7.61750e11 1.31939e12i −0.884513 1.53202i −0.846271 0.532753i \(-0.821158\pi\)
−0.0382420 0.999269i \(-0.512176\pi\)
\(450\) 1.19998e11 0.137949
\(451\) 1.64559e11 + 2.85025e11i 0.187296 + 0.324406i
\(452\) 4.42303e11 0.498422
\(453\) −6.32882e11 + 1.09618e12i −0.706124 + 1.22304i
\(454\) 3.37535e11 0.372879
\(455\) 7.94210e11 0.868728
\(456\) −1.38807e11 + 2.40421e11i −0.150339 + 0.260394i
\(457\) 8.28939e10 + 1.43576e11i 0.0888995 + 0.153979i 0.907046 0.421031i \(-0.138332\pi\)
−0.818147 + 0.575010i \(0.804998\pi\)
\(458\) −4.21991e11 −0.448135
\(459\) −1.41637e11 + 2.45322e11i −0.148943 + 0.257976i
\(460\) −2.89766e10 + 5.01889e10i −0.0301743 + 0.0522633i
\(461\) 1.04783e10 1.81489e10i 0.0108053 0.0187153i −0.860572 0.509328i \(-0.829894\pi\)
0.871377 + 0.490613i \(0.163227\pi\)
\(462\) −1.90456e11 3.29880e11i −0.194494 0.336873i
\(463\) −3.84857e11 6.66592e11i −0.389211 0.674133i 0.603133 0.797641i \(-0.293919\pi\)
−0.992344 + 0.123508i \(0.960586\pi\)
\(464\) −3.58553e11 + 6.21032e11i −0.359106 + 0.621990i
\(465\) −5.03383e11 + 8.71884e11i −0.499298 + 0.864810i
\(466\) −1.19865e11 + 2.07613e11i −0.117749 + 0.203947i
\(467\) 1.43152e12 1.39274 0.696371 0.717682i \(-0.254797\pi\)
0.696371 + 0.717682i \(0.254797\pi\)
\(468\) −2.11948e11 3.67105e11i −0.204232 0.353740i
\(469\) 6.90143e11 1.19536e12i 0.658660 1.14083i
\(470\) −6.06714e11 −0.573513
\(471\) 2.31831e12 2.17058
\(472\) −4.16126e11 + 7.20751e11i −0.385910 + 0.668415i
\(473\) −5.03643e11 −0.462645
\(474\) −4.73496e11 8.20120e11i −0.430838 0.746234i
\(475\) −1.32866e11 −0.119754
\(476\) 8.50122e11 + 1.47245e12i 0.759014 + 1.31465i
\(477\) −2.69161e11 4.66200e11i −0.238056 0.412325i
\(478\) 2.74717e11 + 4.75824e11i 0.240691 + 0.416889i
\(479\) −1.41612e11 + 2.45280e11i −0.122911 + 0.212888i −0.920915 0.389765i \(-0.872556\pi\)
0.798003 + 0.602653i \(0.205890\pi\)
\(480\) −1.17087e12 −1.00675
\(481\) 7.36977e11 1.13850e11i 0.627771 0.0969798i
\(482\) 1.04400e11 0.0881028
\(483\) −1.37092e11 + 2.37451e11i −0.114617 + 0.198523i
\(484\) −4.21593e11 7.30220e11i −0.349212 0.604852i
\(485\) −3.18132e10 5.51020e10i −0.0261077 0.0452199i
\(486\) −3.33920e11 5.78366e11i −0.271506 0.470262i
\(487\) 1.25802e12 1.01347 0.506733 0.862103i \(-0.330853\pi\)
0.506733 + 0.862103i \(0.330853\pi\)
\(488\) −1.32264e11 2.29087e11i −0.105573 0.182857i
\(489\) 2.69511e12 2.13151
\(490\) 4.54696e11 7.87557e11i 0.356319 0.617163i
\(491\) −3.36416e11 −0.261222 −0.130611 0.991434i \(-0.541694\pi\)
−0.130611 + 0.991434i \(0.541694\pi\)
\(492\) 1.39004e12 1.06951
\(493\) 1.00216e12 1.73580e12i 0.764060 1.32339i
\(494\) −5.20174e10 9.00968e10i −0.0392986 0.0680672i
\(495\) 3.08183e11 0.230720
\(496\) −3.20998e11 + 5.55986e11i −0.238142 + 0.412473i
\(497\) 9.80688e11 1.69860e12i 0.720986 1.24878i
\(498\) −4.26049e10 + 7.37939e10i −0.0310404 + 0.0537636i
\(499\) 9.00566e10 + 1.55983e11i 0.0650224 + 0.112622i 0.896704 0.442631i \(-0.145955\pi\)
−0.831682 + 0.555253i \(0.812621\pi\)
\(500\) −6.19288e11 1.07264e12i −0.443127 0.767518i
\(501\) 8.17080e10 1.41522e11i 0.0579422 0.100359i
\(502\) −3.13118e11 + 5.42336e11i −0.220060 + 0.381155i
\(503\) 4.69517e11 8.13228e11i 0.327036 0.566443i −0.654886 0.755727i \(-0.727283\pi\)
0.981922 + 0.189284i \(0.0606168\pi\)
\(504\) −1.57246e12 −1.08553
\(505\) −4.23619e10 7.33730e10i −0.0289844 0.0502024i
\(506\) −1.15704e10 + 2.00406e10i −0.00784644 + 0.0135904i
\(507\) −1.18586e12 −0.797071
\(508\) −8.96441e11 −0.597221
\(509\) 4.11770e11 7.13206e11i 0.271909 0.470961i −0.697441 0.716642i \(-0.745678\pi\)
0.969351 + 0.245681i \(0.0790116\pi\)
\(510\) 6.93060e11 0.453634
\(511\) 1.82811e12 + 3.16638e12i 1.18606 + 2.05432i
\(512\) −1.33517e12 −0.858660
\(513\) 6.52840e10 + 1.13075e11i 0.0416178 + 0.0720841i
\(514\) −3.78627e11 6.55801e11i −0.239264 0.414418i
\(515\) −5.95936e11 1.03219e12i −0.373308 0.646588i
\(516\) −1.06357e12 + 1.84216e12i −0.660454 + 1.14394i
\(517\) 1.09296e12 0.672819
\(518\) 4.50643e11 1.16073e12i 0.275010 0.708351i
\(519\) −8.44492e11 −0.510907
\(520\) 3.14480e11 5.44696e11i 0.188616 0.326692i
\(521\) 4.05631e11 + 7.02573e11i 0.241191 + 0.417755i 0.961054 0.276361i \(-0.0891286\pi\)
−0.719863 + 0.694116i \(0.755795\pi\)
\(522\) 4.17188e11 + 7.22590e11i 0.245931 + 0.425966i
\(523\) 1.01275e12 + 1.75414e12i 0.591897 + 1.02520i 0.993977 + 0.109592i \(0.0349543\pi\)
−0.402079 + 0.915605i \(0.631712\pi\)
\(524\) −2.60218e11 −0.150781
\(525\) −8.55295e11 1.48141e12i −0.491359 0.851059i
\(526\) 5.26650e11 0.299976
\(527\) 8.97197e11 1.55399e12i 0.506687 0.877608i
\(528\) 4.46692e11 0.250124
\(529\) −1.78450e12 −0.990752
\(530\) 1.79762e11 3.11357e11i 0.0989594 0.171403i
\(531\) −7.16964e11 1.24182e12i −0.391356 0.677849i
\(532\) 7.83685e11 0.424169
\(533\) −5.78642e11 + 1.00224e12i −0.310554 + 0.537896i
\(534\) −8.28457e11 + 1.43493e12i −0.440894 + 0.763651i
\(535\) −5.63545e11 + 9.76088e11i −0.297397 + 0.515107i
\(536\) −5.46547e11 9.46646e11i −0.286013 0.495389i
\(537\) −1.39421e12 2.41484e12i −0.723508 1.25315i
\(538\) −2.76546e11 + 4.78991e11i −0.142314 + 0.246495i
\(539\) −8.19113e11 + 1.41874e12i −0.418017 + 0.724027i
\(540\) −1.77654e11 + 3.07705e11i −0.0899089 + 0.155727i
\(541\) 2.91793e12 1.46449 0.732247 0.681039i \(-0.238471\pi\)
0.732247 + 0.681039i \(0.238471\pi\)
\(542\) 7.61485e10 + 1.31893e11i 0.0379022 + 0.0656486i
\(543\) −5.62390e11 + 9.74089e11i −0.277612 + 0.480839i
\(544\) 2.08689e12 1.02165
\(545\) −2.46724e11 −0.119792
\(546\) 6.69703e11 1.15996e12i 0.322489 0.558568i
\(547\) 1.14338e11 0.0546071 0.0273036 0.999627i \(-0.491308\pi\)
0.0273036 + 0.999627i \(0.491308\pi\)
\(548\) −9.17816e11 1.58970e12i −0.434753 0.753015i
\(549\) 4.55768e11 0.214125
\(550\) −7.21861e10 1.25030e11i −0.0336373 0.0582616i
\(551\) −4.61922e11 8.00073e11i −0.213495 0.369783i
\(552\) 1.08568e11 + 1.88045e11i 0.0497708 + 0.0862056i
\(553\) −2.96957e12 + 5.14344e12i −1.35030 + 2.33879i
\(554\) −1.01155e12 −0.456239
\(555\) 1.43423e12 + 1.78499e12i 0.641654 + 0.798576i
\(556\) −1.97949e12 −0.878448
\(557\) −1.12197e12 + 1.94331e12i −0.493894 + 0.855449i −0.999975 0.00703682i \(-0.997760\pi\)
0.506082 + 0.862486i \(0.331093\pi\)
\(558\) 3.73491e11 + 6.46906e11i 0.163090 + 0.282480i
\(559\) −8.85482e11 1.53370e12i −0.383554 0.664335i
\(560\) 7.77558e11 + 1.34677e12i 0.334108 + 0.578692i
\(561\) −1.24851e12 −0.532182
\(562\) 7.81760e11 + 1.35405e12i 0.330567 + 0.572560i
\(563\) −2.84085e12 −1.19168 −0.595840 0.803103i \(-0.703181\pi\)
−0.595840 + 0.803103i \(0.703181\pi\)
\(564\) 2.30807e12 3.99770e12i 0.960491 1.66362i
\(565\) −1.13072e12 −0.466808
\(566\) −2.30801e11 −0.0945286
\(567\) −2.56493e12 + 4.44258e12i −1.04220 + 1.80514i
\(568\) −7.76638e11 1.34518e12i −0.313077 0.542265i
\(569\) −5.97926e11 −0.239135 −0.119567 0.992826i \(-0.538151\pi\)
−0.119567 + 0.992826i \(0.538151\pi\)
\(570\) 1.59725e11 2.76651e11i 0.0633774 0.109773i
\(571\) −4.62531e11 + 8.01127e11i −0.182087 + 0.315383i −0.942591 0.333950i \(-0.891618\pi\)
0.760504 + 0.649333i \(0.224952\pi\)
\(572\) −2.54999e11 + 4.41671e11i −0.0995993 + 0.172511i
\(573\) 1.42379e12 + 2.46607e12i 0.551759 + 0.955674i
\(574\) 9.66171e11 + 1.67346e12i 0.371493 + 0.643445i
\(575\) −5.19603e10 + 8.99978e10i −0.0198228 + 0.0343342i
\(576\) 7.26267e10 1.25793e11i 0.0274913 0.0476163i
\(577\) 1.61463e12 2.79662e12i 0.606432 1.05037i −0.385391 0.922753i \(-0.625934\pi\)
0.991823 0.127618i \(-0.0407331\pi\)
\(578\) −9.22790e10 −0.0343896
\(579\) 1.22957e12 + 2.12968e12i 0.454674 + 0.787518i
\(580\) 1.25700e12 2.17720e12i 0.461223 0.798861i
\(581\) 5.34400e11 0.194569
\(582\) −1.07303e11 −0.0387668
\(583\) −3.23833e11 + 5.60894e11i −0.116095 + 0.201082i
\(584\) 2.89548e12 1.03006
\(585\) 5.41834e11 + 9.38484e11i 0.191278 + 0.331303i
\(586\) 6.08049e11 0.213010
\(587\) −1.15072e12 1.99311e12i −0.400036 0.692882i 0.593694 0.804691i \(-0.297669\pi\)
−0.993730 + 0.111809i \(0.964336\pi\)
\(588\) 3.45953e12 + 5.99208e12i 1.19349 + 2.06719i
\(589\) −4.13541e11 7.16274e11i −0.141579 0.245222i
\(590\) 4.78833e11 8.29363e11i 0.162686 0.281780i
\(591\) −4.91100e12 −1.65587
\(592\) 9.14585e11 + 1.13825e12i 0.306039 + 0.380883i
\(593\) 1.29875e12 0.431301 0.215651 0.976471i \(-0.430813\pi\)
0.215651 + 0.976471i \(0.430813\pi\)
\(594\) −7.09378e10 + 1.22868e11i −0.0233797 + 0.0404948i
\(595\) −2.17329e12 3.76425e12i −0.710872 1.23127i
\(596\) −2.09865e12 3.63496e12i −0.681289 1.18003i
\(597\) −1.45436e12 2.51903e12i −0.468584 0.811612i
\(598\) −8.13705e10 −0.0260203
\(599\) −2.13870e12 3.70433e12i −0.678779 1.17568i −0.975349 0.220669i \(-0.929176\pi\)
0.296569 0.955011i \(-0.404157\pi\)
\(600\) −1.35467e12 −0.426730
\(601\) −7.45593e11 + 1.29140e12i −0.233113 + 0.403764i −0.958723 0.284343i \(-0.908225\pi\)
0.725610 + 0.688107i \(0.241558\pi\)
\(602\) −2.95702e12 −0.917634
\(603\) 1.88335e12 0.580099
\(604\) 1.41485e12 2.45059e12i 0.432558 0.749213i
\(605\) 1.07778e12 + 1.86677e12i 0.327062 + 0.566488i
\(606\) −1.42884e11 −0.0430383
\(607\) −1.52565e12 + 2.64250e12i −0.456147 + 0.790069i −0.998753 0.0499178i \(-0.984104\pi\)
0.542607 + 0.839987i \(0.317437\pi\)
\(608\) 4.80949e11 8.33029e11i 0.142736 0.247226i
\(609\) 5.94706e12 1.03006e13i 1.75196 3.03449i
\(610\) 1.52195e11 + 2.63609e11i 0.0445057 + 0.0770861i
\(611\) 1.92160e12 + 3.32831e12i 0.557799 + 0.966136i
\(612\) −1.15996e12 + 2.00911e12i −0.334242 + 0.578924i
\(613\) 3.17282e12 5.49549e12i 0.907556 1.57193i 0.0901063 0.995932i \(-0.471279\pi\)
0.817449 0.576000i \(-0.195387\pi\)
\(614\) −9.79719e11 + 1.69692e12i −0.278192 + 0.481842i
\(615\) −3.55355e12 −1.00167
\(616\) 9.45931e11 + 1.63840e12i 0.264695 + 0.458466i
\(617\) −6.20020e10 + 1.07391e11i −0.0172236 + 0.0298321i −0.874509 0.485010i \(-0.838816\pi\)
0.857285 + 0.514842i \(0.172149\pi\)
\(618\) −2.01005e12 −0.554317
\(619\) 6.04119e10 0.0165392 0.00826961 0.999966i \(-0.497368\pi\)
0.00826961 + 0.999966i \(0.497368\pi\)
\(620\) 1.12535e12 1.94916e12i 0.305860 0.529766i
\(621\) 1.02123e11 0.0275558
\(622\) −7.46642e11 1.29322e12i −0.200012 0.346430i
\(623\) 1.03915e13 2.76363
\(624\) 7.85354e11 + 1.36027e12i 0.207365 + 0.359166i
\(625\) 7.96851e11 + 1.38019e12i 0.208890 + 0.361808i
\(626\) 8.18214e11 + 1.41719e12i 0.212952 + 0.368844i
\(627\) −2.87736e11 + 4.98373e11i −0.0743515 + 0.128781i
\(628\) −5.18273e12 −1.32966
\(629\) −2.55628e12 3.18144e12i −0.651150 0.810394i
\(630\) 1.80942e12 0.457623
\(631\) −2.10183e11 + 3.64047e11i −0.0527795 + 0.0914167i −0.891208 0.453595i \(-0.850141\pi\)
0.838429 + 0.545011i \(0.183475\pi\)
\(632\) 2.35170e12 + 4.07326e12i 0.586347 + 1.01558i
\(633\) 4.64071e12 + 8.03794e12i 1.14886 + 1.98989i
\(634\) −4.59294e11 7.95521e11i −0.112899 0.195546i
\(635\) 2.29170e12 0.559341
\(636\) 1.36771e12 + 2.36894e12i 0.331465 + 0.574113i
\(637\) −5.76051e12 −1.38622
\(638\) 5.01926e11 8.69362e11i 0.119935 0.207734i
\(639\) 2.67622e12 0.634992
\(640\) 3.29477e12 0.776275
\(641\) −1.47699e12 + 2.55823e12i −0.345555 + 0.598519i −0.985454 0.169940i \(-0.945643\pi\)
0.639899 + 0.768459i \(0.278976\pi\)
\(642\) 9.50397e11 + 1.64614e12i 0.220799 + 0.382436i
\(643\) −5.61065e12 −1.29439 −0.647194 0.762326i \(-0.724057\pi\)
−0.647194 + 0.762326i \(0.724057\pi\)
\(644\) 3.06479e11 5.30837e11i 0.0702124 0.121611i
\(645\) 2.71896e12 4.70938e12i 0.618563 1.07138i
\(646\) −2.84683e11 + 4.93085e11i −0.0643153 + 0.111397i
\(647\) −3.77531e12 6.53902e12i −0.846999 1.46705i −0.883874 0.467726i \(-0.845073\pi\)
0.0368744 0.999320i \(-0.488260\pi\)
\(648\) 2.03125e12 + 3.51823e12i 0.452559 + 0.783856i
\(649\) −8.62593e11 + 1.49406e12i −0.190856 + 0.330572i
\(650\) 2.53829e11 4.39644e11i 0.0557739 0.0966031i
\(651\) 5.32417e12 9.22173e12i 1.16182 2.01232i
\(652\) −6.02510e12 −1.30572
\(653\) 2.31391e12 + 4.00782e12i 0.498010 + 0.862578i 0.999997 0.00229674i \(-0.000731075\pi\)
−0.501988 + 0.864875i \(0.667398\pi\)
\(654\) −2.08046e11 + 3.60346e11i −0.0444692 + 0.0770229i
\(655\) 6.65233e11 0.141217
\(656\) −2.26604e12 −0.477749
\(657\) −2.49439e12 + 4.32040e12i −0.522299 + 0.904649i
\(658\) 6.41707e12 1.33451
\(659\) 1.91578e12 + 3.31823e12i 0.395696 + 0.685365i 0.993190 0.116508i \(-0.0371701\pi\)
−0.597494 + 0.801873i \(0.703837\pi\)
\(660\) −1.56600e12 −0.321250
\(661\) −4.08766e12 7.08003e12i −0.832852 1.44254i −0.895767 0.444524i \(-0.853373\pi\)
0.0629146 0.998019i \(-0.479960\pi\)
\(662\) −1.59574e12 2.76390e12i −0.322924 0.559321i
\(663\) −2.19508e12 3.80199e12i −0.441204 0.764188i
\(664\) 2.11604e11 3.66509e11i 0.0422443 0.0731693i
\(665\) −2.00345e12 −0.397265
\(666\) 1.67903e12 2.59382e11i 0.330693 0.0510864i
\(667\) −7.22583e11 −0.141358
\(668\) −1.82664e11 + 3.16383e11i −0.0354943 + 0.0614779i
\(669\) −6.28627e12 1.08881e13i −1.21332 2.10153i
\(670\) 6.28907e11 + 1.08930e12i 0.120573 + 0.208839i
\(671\) −2.74171e11 4.74879e11i −0.0522120 0.0904339i
\(672\) 1.23840e13 2.34261
\(673\) 3.97493e11 + 6.88478e11i 0.0746899 + 0.129367i 0.900951 0.433920i \(-0.142870\pi\)
−0.826261 + 0.563287i \(0.809537\pi\)
\(674\) −2.46568e12 −0.460222
\(675\) −3.18566e11 + 5.51772e11i −0.0590652 + 0.102304i
\(676\) 2.65107e12 0.488270
\(677\) 3.35699e11 0.0614187 0.0307094 0.999528i \(-0.490223\pi\)
0.0307094 + 0.999528i \(0.490223\pi\)
\(678\) −9.53462e11 + 1.65144e12i −0.173289 + 0.300145i
\(679\) 3.36481e11 + 5.82802e11i 0.0607500 + 0.105222i
\(680\) −3.44220e12 −0.617370
\(681\) 3.28263e12 5.68568e12i 0.584870 1.01302i
\(682\) 4.49354e11 7.78305e11i 0.0795352 0.137759i
\(683\) 1.44257e12 2.49861e12i 0.253655 0.439344i −0.710874 0.703319i \(-0.751700\pi\)
0.964529 + 0.263975i \(0.0850338\pi\)
\(684\) 5.34654e11 + 9.26048e11i 0.0933943 + 0.161764i
\(685\) 2.34635e12 + 4.06399e12i 0.407178 + 0.705253i
\(686\) −2.60547e12 + 4.51280e12i −0.449187 + 0.778014i
\(687\) −4.10399e12 + 7.10831e12i −0.702911 + 1.21748i
\(688\) 1.73383e12 3.00309e12i 0.295025 0.510999i
\(689\) −2.27739e12 −0.384992
\(690\) −1.24928e11 2.16382e11i −0.0209816 0.0363412i
\(691\) −2.21505e12 + 3.83657e12i −0.369600 + 0.640165i −0.989503 0.144513i \(-0.953838\pi\)
0.619903 + 0.784678i \(0.287172\pi\)
\(692\) 1.88792e12 0.312972
\(693\) −3.25959e12 −0.536862
\(694\) 1.84752e12 3.20000e12i 0.302323 0.523640i
\(695\) 5.06045e12 0.822730
\(696\) −4.70967e12 8.15739e12i −0.760762 1.31768i
\(697\) 6.33362e12 1.01649
\(698\) −2.21149e12 3.83041e12i −0.352643 0.610795i
\(699\) 2.33145e12 + 4.03818e12i 0.369384 + 0.639792i
\(700\) 1.91207e12 + 3.31180e12i 0.300997 + 0.521343i
\(701\) −4.14845e12 + 7.18532e12i −0.648865 + 1.12387i 0.334529 + 0.942386i \(0.391423\pi\)
−0.983394 + 0.181482i \(0.941911\pi\)
\(702\) −4.98879e11 −0.0775314
\(703\) −1.85907e12 + 2.87195e11i −0.287077 + 0.0443484i
\(704\) −1.74757e11 −0.0268138
\(705\) −5.90046e12 + 1.02199e13i −0.899570 + 1.55810i
\(706\) −2.32399e12 4.02527e12i −0.352057 0.609781i
\(707\) 4.48052e11 + 7.76049e11i 0.0674437 + 0.116816i
\(708\) 3.64317e12 + 6.31016e12i 0.544917 + 0.943823i
\(709\) −1.16500e13 −1.73148 −0.865739 0.500496i \(-0.833151\pi\)
−0.865739 + 0.500496i \(0.833151\pi\)
\(710\) 8.93672e11 + 1.54789e12i 0.131982 + 0.228600i
\(711\) −8.10372e12 −1.18924
\(712\) 4.11466e12 7.12681e12i 0.600032 1.03929i
\(713\) −6.46900e11 −0.0937419
\(714\) −7.33034e12 −1.05556
\(715\) 6.51891e11 1.12911e12i 0.0932820 0.161569i
\(716\) 3.11685e12 + 5.39854e12i 0.443207 + 0.767657i
\(717\) 1.06868e13 1.51012
\(718\) −1.89604e12 + 3.28403e12i −0.266248 + 0.461155i
\(719\) 2.71012e12 4.69406e12i 0.378188 0.655041i −0.612610 0.790385i \(-0.709881\pi\)
0.990799 + 0.135344i \(0.0432138\pi\)
\(720\) −1.06095e12 + 1.83761e12i −0.147129 + 0.254835i
\(721\) 6.30308e12 + 1.09172e13i 0.868648 + 1.50454i
\(722\) −1.42386e12 2.46621e12i −0.195008 0.337763i
\(723\) 1.01532e12 1.75859e12i 0.138191 0.239355i
\(724\) 1.25726e12 2.17764e12i 0.170060 0.294552i
\(725\) 2.25404e12 3.90411e12i 0.302998 0.524808i
\(726\) 3.63527e12 0.485648
\(727\) 3.47196e12 + 6.01361e12i 0.460967 + 0.798418i 0.999009 0.0444998i \(-0.0141694\pi\)
−0.538043 + 0.842918i \(0.680836\pi\)
\(728\) −3.32619e12 + 5.76112e12i −0.438890 + 0.760179i
\(729\) −4.07970e12 −0.535001
\(730\) −3.33181e12 −0.434237
\(731\) −4.84610e12 + 8.39369e12i −0.627717 + 1.08724i
\(732\) −2.31593e12 −0.298144
\(733\) 9.87880e11 + 1.71106e12i 0.126397 + 0.218926i 0.922278 0.386527i \(-0.126325\pi\)
−0.795881 + 0.605453i \(0.792992\pi\)
\(734\) −3.81771e12 −0.485479
\(735\) −8.84410e12 1.53184e13i −1.11779 1.93607i
\(736\) −3.76173e11 6.51551e11i −0.0472539 0.0818462i
\(737\) −1.13294e12 1.96232e12i −0.141451 0.245000i
\(738\) −1.31830e12 + 2.28337e12i −0.163592 + 0.283349i
\(739\) −2.96842e12 −0.366122 −0.183061 0.983102i \(-0.558601\pi\)
−0.183061 + 0.983102i \(0.558601\pi\)
\(740\) −3.20632e12 3.99046e12i −0.393065 0.489192i
\(741\) −2.02354e12 −0.246564
\(742\) −1.90130e12 + 3.29316e12i −0.230268 + 0.398836i
\(743\) 5.90091e12 + 1.02207e13i 0.710345 + 1.23035i 0.964727 + 0.263251i \(0.0847946\pi\)
−0.254382 + 0.967104i \(0.581872\pi\)
\(744\) −4.21638e12 7.30298e12i −0.504500 0.873820i
\(745\) 5.36508e12 + 9.29259e12i 0.638077 + 1.10518i
\(746\) 6.10449e12 0.721647
\(747\) 3.64584e11 + 6.31478e11i 0.0428405 + 0.0742020i
\(748\) 2.79113e12 0.326004
\(749\) 5.96049e12 1.03239e13i 0.692012 1.19860i
\(750\) 5.33994e12 0.616255
\(751\) 3.52704e12 0.404605 0.202302 0.979323i \(-0.435158\pi\)
0.202302 + 0.979323i \(0.435158\pi\)
\(752\) −3.76262e12 + 6.51705e12i −0.429052 + 0.743140i
\(753\) 6.09032e12 + 1.05487e13i 0.690340 + 1.19570i
\(754\) 3.52986e12 0.397728
\(755\) −3.61699e12 + 6.26481e12i −0.405122 + 0.701692i
\(756\) 1.87900e12 3.25453e12i 0.209209 0.362360i
\(757\) 1.40260e11 2.42937e11i 0.0155239 0.0268882i −0.858159 0.513384i \(-0.828392\pi\)
0.873683 + 0.486496i \(0.161725\pi\)
\(758\) 2.71068e12 + 4.69503e12i 0.298240 + 0.516567i
\(759\) 2.25052e11 + 3.89801e11i 0.0246147 + 0.0426339i
\(760\) −7.93298e11 + 1.37403e12i −0.0862532 + 0.149395i
\(761\) −7.42700e12 + 1.28639e13i −0.802754 + 1.39041i 0.115043 + 0.993361i \(0.463299\pi\)
−0.917797 + 0.397050i \(0.870034\pi\)
\(762\) 1.93244e12 3.34708e12i 0.207638 0.359640i
\(763\) 2.60955e12 0.278744
\(764\) −3.18297e12 5.51307e12i −0.337997 0.585427i
\(765\) 2.96537e12 5.13617e12i 0.313042 0.542204i
\(766\) 1.86934e12 0.196182
\(767\) −6.06629e12 −0.632913
\(768\) 2.32741e12 4.03119e12i 0.241406 0.418127i
\(769\) −1.08389e12 −0.111767 −0.0558837 0.998437i \(-0.517798\pi\)
−0.0558837 + 0.998437i \(0.517798\pi\)
\(770\) −1.08848e12 1.88530e12i −0.111586 0.193273i
\(771\) −1.47290e13 −1.50117
\(772\) −2.74879e12 4.76104e12i −0.278524 0.482418i
\(773\) −3.11933e12 5.40284e12i −0.314234 0.544270i 0.665040 0.746808i \(-0.268414\pi\)
−0.979274 + 0.202538i \(0.935081\pi\)
\(774\) −2.01737e12 3.49418e12i −0.202046 0.349954i
\(775\) 2.01795e12 3.49519e12i 0.200934 0.348027i
\(776\) 5.32940e11 0.0527595
\(777\) −1.51696e13 1.88794e13i −1.49306 1.85820i
\(778\) −3.08477e12 −0.301866
\(779\) 1.45966e12 2.52821e12i 0.142015 0.245977i
\(780\) −2.75327e12 4.76880e12i −0.266332 0.461300i
\(781\) −1.60991e12 2.78844e12i −0.154836 0.268183i
\(782\) 2.22664e11 + 3.85665e11i 0.0212921 + 0.0368791i
\(783\) −4.43012e12 −0.421199
\(784\) −5.63973e12 9.76830e12i −0.533134 0.923415i
\(785\) 1.32494e13 1.24532
\(786\) 5.60945e11 9.71585e11i 0.0524226 0.0907987i
\(787\) 5.56854e12 0.517434 0.258717 0.965953i \(-0.416700\pi\)
0.258717 + 0.965953i \(0.416700\pi\)
\(788\) 1.09789e13 1.01435
\(789\) 5.12182e12 8.87125e12i 0.470520 0.814964i
\(790\) −2.70608e12 4.68707e12i −0.247183 0.428134i
\(791\) 1.19594e13 1.08621
\(792\) −1.29069e12 + 2.23553e12i −0.116562 + 0.201891i
\(793\) 9.64071e11 1.66982e12i 0.0865725 0.149948i
\(794\) 1.13274e11 1.96196e11i 0.0101143 0.0175185i
\(795\) −3.49648e12 6.05607e12i −0.310441 0.537699i
\(796\) 3.25132e12 + 5.63145e12i 0.287046 + 0.497178i
\(797\) 7.61799e12 1.31947e13i 0.668772 1.15835i −0.309476 0.950907i \(-0.600154\pi\)
0.978248 0.207439i \(-0.0665129\pi\)
\(798\) −1.68937e12 + 2.92608e12i −0.147473 + 0.255430i
\(799\) 1.05166e13 1.82153e13i 0.912882 1.58116i
\(800\) 4.69377e12 0.405151
\(801\) 7.08937e12 + 1.22791e13i 0.608501 + 1.05395i
\(802\) −2.73268e12 + 4.73315e12i −0.233241 + 0.403985i
\(803\) 6.00209e12 0.509427
\(804\) −9.57001e12 −0.807719
\(805\) −7.83496e11 + 1.35705e12i −0.0657590 + 0.113898i
\(806\) 3.16014e12 0.263754
\(807\) 5.37897e12 + 9.31665e12i 0.446445 + 0.773266i
\(808\) 7.09654e11 0.0585728
\(809\) 6.20448e12 + 1.07465e13i 0.509257 + 0.882059i 0.999943 + 0.0107221i \(0.00341303\pi\)
−0.490686 + 0.871337i \(0.663254\pi\)
\(810\) −2.33734e12 4.04840e12i −0.190783 0.330446i
\(811\) −1.10090e13 1.90681e13i −0.893621 1.54780i −0.835502 0.549488i \(-0.814823\pi\)
−0.0581193 0.998310i \(-0.518510\pi\)
\(812\) −1.32951e13 + 2.30277e13i −1.07322 + 1.85887i
\(813\) 2.96226e12 0.237802
\(814\) −1.28030e12 1.59340e12i −0.102212 0.127208i
\(815\) 1.54028e13 1.22290
\(816\) 4.29811e12 7.44455e12i 0.339369 0.587804i
\(817\) 2.23369e12 + 3.86886e12i 0.175398 + 0.303797i
\(818\) 3.40779e12 + 5.90246e12i 0.266123 + 0.460939i
\(819\) −5.73086e12 9.92614e12i −0.445084 0.770908i
\(820\) 7.94421e12 0.613604
\(821\) 1.59638e12 + 2.76500e12i 0.122628 + 0.212398i 0.920803 0.390027i \(-0.127534\pi\)
−0.798175 + 0.602426i \(0.794201\pi\)
\(822\) 7.91405e12 0.604610
\(823\) 2.25658e12 3.90851e12i 0.171456 0.296970i −0.767473 0.641081i \(-0.778486\pi\)
0.938929 + 0.344111i \(0.111820\pi\)
\(824\) 9.98322e12 0.754394
\(825\) −2.80812e12 −0.211044
\(826\) −5.06451e12 + 8.77199e12i −0.378553 + 0.655674i
\(827\) 8.86846e12 + 1.53606e13i 0.659285 + 1.14192i 0.980801 + 0.195011i \(0.0624744\pi\)
−0.321516 + 0.946904i \(0.604192\pi\)
\(828\) 8.36356e11 0.0618379
\(829\) −7.48689e12 + 1.29677e13i −0.550562 + 0.953601i 0.447673 + 0.894198i \(0.352253\pi\)
−0.998234 + 0.0594030i \(0.981080\pi\)
\(830\) −2.43492e11 + 4.21740e11i −0.0178087 + 0.0308456i
\(831\) −9.83758e12 + 1.70392e13i −0.715622 + 1.23949i
\(832\) −3.07250e11 5.32172e11i −0.0222299 0.0385033i
\(833\) 1.57632e13 + 2.73026e13i 1.13433 + 1.96472i
\(834\) 4.26713e12 7.39089e12i 0.305414 0.528992i
\(835\) 4.66970e11 8.08816e11i 0.0332430 0.0575785i
\(836\) 6.43252e11 1.11415e12i 0.0455463 0.0788885i
\(837\) −3.96611e12 −0.279319
\(838\) −4.74570e12 8.21979e12i −0.332432 0.575788i
\(839\) 1.48430e12 2.57089e12i 0.103417 0.179124i −0.809673 0.586881i \(-0.800356\pi\)
0.913090 + 0.407757i \(0.133689\pi\)
\(840\) −2.04268e13 −1.41561
\(841\) 1.68385e13 1.16071
\(842\) −5.25246e12 + 9.09752e12i −0.360129 + 0.623762i
\(843\) 3.04113e13 2.07401
\(844\) −1.03746e13 1.79694e13i −0.703770 1.21897i
\(845\) −6.77731e12 −0.457301
\(846\) 4.37792e12 + 7.58279e12i 0.293834 + 0.508935i
\(847\) −1.13994e13 1.97444e13i −0.761040 1.31816i
\(848\) −2.22964e12 3.86185e12i −0.148066 0.256457i
\(849\) −2.24460e12 + 3.88776e12i −0.148270 + 0.256812i
\(850\) −2.77833e12 −0.182557
\(851\) −5.32501e11 + 1.37158e12i −0.0348046 + 0.0896472i
\(852\) −1.35989e13 −0.884150
\(853\) −3.50331e12 + 6.06791e12i −0.226573 + 0.392436i −0.956790 0.290779i \(-0.906085\pi\)
0.730217 + 0.683215i \(0.239419\pi\)
\(854\) −1.60973e12 2.78814e12i −0.103560 0.179371i
\(855\) −1.36681e12 2.36739e12i −0.0874705 0.151503i
\(856\) −4.72030e12 8.17580e12i −0.300495 0.520473i
\(857\) −1.59639e13 −1.01094 −0.505468 0.862845i \(-0.668680\pi\)
−0.505468 + 0.862845i \(0.668680\pi\)
\(858\) −1.09939e12 1.90420e12i −0.0692562 0.119955i
\(859\) −1.20102e13 −0.752628 −0.376314 0.926492i \(-0.622809\pi\)
−0.376314 + 0.926492i \(0.622809\pi\)
\(860\) −6.07842e12 + 1.05281e13i −0.378920 + 0.656308i
\(861\) 3.75851e13 2.33078
\(862\) 2.70726e12 0.167012
\(863\) 1.41294e13 2.44728e13i 0.867112 1.50188i 0.00217741 0.999998i \(-0.499307\pi\)
0.864935 0.501885i \(-0.167360\pi\)
\(864\) −2.30630e12 3.99463e12i −0.140800 0.243873i
\(865\) −4.82636e12 −0.293121
\(866\) −3.53469e12 + 6.12227e12i −0.213561 + 0.369898i
\(867\) −8.97439e11 + 1.55441e12i −0.0539410 + 0.0934285i
\(868\) −1.19025e13 + 2.06158e13i −0.711706 + 1.23271i
\(869\) 4.87487e12 + 8.44352e12i 0.289984 + 0.502267i
\(870\) 5.41938e12 + 9.38665e12i 0.320711 + 0.555487i
\(871\) 3.98379e12 6.90012e12i 0.234539 0.406233i
\(872\) 1.03329e12 1.78972e12i 0.0605201 0.104824i
\(873\) −4.59115e11 + 7.95210e11i −0.0267521 + 0.0463359i
\(874\) 2.05263e11 0.0118990
\(875\) −1.67449e13 2.90030e13i −0.965710 1.67266i
\(876\) 1.26749e13 2.19536e13i 0.727239 1.25962i
\(877\) −5.42980e12 −0.309946 −0.154973 0.987919i \(-0.549529\pi\)
−0.154973 + 0.987919i \(0.549529\pi\)
\(878\) 5.80185e12 0.329489
\(879\) 5.91345e12 1.02424e13i 0.334111 0.578698i
\(880\) 2.55289e12 0.143503
\(881\) −1.14083e13 1.97597e13i −0.638011 1.10507i −0.985869 0.167520i \(-0.946424\pi\)
0.347858 0.937547i \(-0.386909\pi\)
\(882\) −1.31240e13 −0.730226
\(883\) 8.88814e12 + 1.53947e13i 0.492026 + 0.852214i 0.999958 0.00918338i \(-0.00292320\pi\)
−0.507932 + 0.861397i \(0.669590\pi\)
\(884\) 4.90725e12 + 8.49960e12i 0.270273 + 0.468127i
\(885\) −9.31357e12 1.61316e13i −0.510354 0.883959i
\(886\) 3.76750e12 6.52551e12i 0.205401 0.355764i
\(887\) −2.38636e13 −1.29444 −0.647218 0.762305i \(-0.724068\pi\)
−0.647218 + 0.762305i \(0.724068\pi\)
\(888\) −1.89548e13 + 2.92818e12i −1.02296 + 0.158030i
\(889\) −2.42388e13 −1.30153
\(890\) −4.73472e12 + 8.20077e12i −0.252952 + 0.438126i
\(891\) 4.21061e12 + 7.29298e12i 0.223818 + 0.387664i
\(892\) 1.40534e13 + 2.43412e13i 0.743257 + 1.28736i
\(893\) −4.84737e12 8.39589e12i −0.255079 0.441809i
\(894\) 1.80960e13 0.947467
\(895\) −7.96805e12 1.38011e13i −0.415096 0.718967i
\(896\) −3.48481e13 −1.80631
\(897\) −7.91351e11 + 1.37066e12i −0.0408135 + 0.0706910i
\(898\) −1.46840e13 −0.753529
\(899\) 2.80625e13 1.43287
\(900\) −2.60894e12 + 4.51882e12i −0.132548 + 0.229580i
\(901\) 6.23189e12 + 1.07940e13i 0.315035 + 0.545656i
\(902\) 3.17215e12 0.159560
\(903\) −2.87578e13 + 4.98100e13i −1.43933 + 2.49300i
\(904\) 4.73552e12 8.20217e12i 0.235836 0.408480i
\(905\) −3.21412e12 + 5.56702e12i −0.159273 + 0.275870i
\(906\) 6.09992e12 + 1.05654e13i 0.300779 + 0.520964i
\(907\) 3.83983e12 + 6.65078e12i 0.188399 + 0.326317i 0.944717 0.327888i \(-0.106337\pi\)
−0.756317 + 0.654205i \(0.773003\pi\)
\(908\) −7.33853e12 + 1.27107e13i −0.358280 + 0.620559i
\(909\) −6.11350e11 + 1.05889e12i −0.0296997 + 0.0514414i
\(910\) 3.82742e12 6.62929e12i 0.185021 0.320465i
\(911\) −7.08628e12 −0.340868 −0.170434 0.985369i \(-0.554517\pi\)
−0.170434 + 0.985369i \(0.554517\pi\)
\(912\) −1.98111e12 3.43138e12i −0.0948269 0.164245i
\(913\) 4.38638e11 7.59743e11i 0.0208924 0.0361866i
\(914\) 1.59791e12 0.0757348
\(915\) 5.92055e12 0.279233
\(916\) 9.17473e12 1.58911e13i 0.430590 0.745804i
\(917\) −7.03602e12 −0.328598
\(918\) 1.36514e12 + 2.36449e12i 0.0634432 + 0.109887i
\(919\) −1.39199e13 −0.643749 −0.321874 0.946782i \(-0.604313\pi\)
−0.321874 + 0.946782i \(0.604313\pi\)
\(920\) 6.20476e11 + 1.07470e12i 0.0285548 + 0.0494584i
\(921\) 1.90561e13 + 3.30061e13i 0.872701 + 1.51156i
\(922\) −1.00993e11 1.74925e11i −0.00460258 0.00797191i
\(923\) 5.66093e12 9.80501e12i 0.256732 0.444673i
\(924\) 1.65632e13 0.747516
\(925\) −5.74952e12 7.15561e12i −0.258222 0.321373i
\(926\) −7.41874e12 −0.331574
\(927\) −8.60030e12 + 1.48962e13i −0.382521 + 0.662545i
\(928\) 1.63184e13 + 2.82643e13i 0.722290 + 1.25104i
\(929\) 9.80949e12 + 1.69905e13i 0.432092 + 0.748405i 0.997053 0.0767124i \(-0.0244423\pi\)
−0.564962 + 0.825117i \(0.691109\pi\)
\(930\) 4.85176e12 + 8.40349e12i 0.212680 + 0.368372i
\(931\) 1.45313e13 0.633914
\(932\) −5.21210e12 9.02763e12i −0.226277 0.391924i
\(933\) −2.90452e13 −1.25489
\(934\) 6.89871e12 1.19489e13i 0.296624 0.513768i
\(935\) −7.13538e12 −0.305327
\(936\) −9.07690e12 −0.386542
\(937\) 6.00269e12 1.03970e13i 0.254400 0.440634i −0.710332 0.703867i \(-0.751455\pi\)
0.964732 + 0.263232i \(0.0847886\pi\)
\(938\) −6.65181e12 1.15213e13i −0.280561 0.485946i
\(939\) 3.18294e13 1.33608
\(940\) 1.31909e13 2.28473e13i 0.551059 0.954462i
\(941\) −1.89335e13 + 3.27938e13i −0.787186 + 1.36345i 0.140498 + 0.990081i \(0.455130\pi\)
−0.927684 + 0.373366i \(0.878204\pi\)
\(942\) 1.11723e13 1.93510e13i 0.462288 0.800706i
\(943\) −1.14167e12 1.97743e12i −0.0470153 0.0814328i
\(944\) −5.93910e12 1.02868e13i −0.243415 0.421607i
\(945\) −4.80357e12 + 8.32003e12i −0.195939 + 0.339376i
\(946\) −2.42713e12 + 4.20392e12i −0.0985334 + 0.170665i
\(947\) −1.53479e13 + 2.65834e13i −0.620119 + 1.07408i 0.369344 + 0.929293i \(0.379582\pi\)
−0.989463 + 0.144785i \(0.953751\pi\)
\(948\) 4.11781e13 1.65588
\(949\) 1.05526e13 + 1.82776e13i 0.422339 + 0.731513i
\(950\) −6.40300e11 + 1.10903e12i −0.0255051 + 0.0441762i
\(951\) −1.78671e13 −0.708338
\(952\) 3.64073e13 1.43656
\(953\) 1.43046e13 2.47763e13i 0.561768 0.973011i −0.435574 0.900153i \(-0.643455\pi\)
0.997342 0.0728583i \(-0.0232121\pi\)
\(954\) −5.18851e12 −0.202803
\(955\) 8.13709e12 + 1.40939e13i 0.316558 + 0.548295i
\(956\) −2.38911e13 −0.925071
\(957\) −9.76275e12 1.69096e13i −0.376243 0.651672i
\(958\) 1.36490e12 + 2.36408e12i 0.0523549 + 0.0906813i
\(959\) −2.48168e13 4.29839e13i −0.947462 1.64105i
\(960\) 9.43441e11 1.63409e12i 0.0358504 0.0620947i
\(961\) −1.31636e12 −0.0497875
\(962\) 2.60130e12 6.70022e12i 0.0979269 0.252233i
\(963\) 1.62657e13 0.609473
\(964\) −2.26982e12 + 3.93144e12i −0.0846534 + 0.146624i
\(965\) 7.02712e12 + 1.21713e13i 0.260858 + 0.451820i
\(966\) 1.32134e12 + 2.28862e12i 0.0488221 + 0.0845623i
\(967\) 5.22499e12 + 9.04994e12i 0.192161 + 0.332833i 0.945966 0.324265i \(-0.105117\pi\)
−0.753805 + 0.657098i \(0.771784\pi\)
\(968\) −1.80551e13 −0.660940
\(969\) 5.53724e12 + 9.59078e12i 0.201761 + 0.349459i
\(970\) −6.13250e11 −0.0222415
\(971\) 1.87037e13 3.23957e13i 0.675212 1.16950i −0.301195 0.953562i \(-0.597386\pi\)
0.976407 0.215939i \(-0.0692811\pi\)
\(972\) 2.90397e13 1.04350
\(973\) −5.35232e13 −1.91441
\(974\) 6.06262e12 1.05008e13i 0.215846 0.373857i
\(975\) −4.93711e12 8.55133e12i −0.174965 0.303049i
\(976\) 3.77543e12 0.133181
\(977\) 2.17111e13 3.76048e13i 0.762354 1.32044i −0.179280 0.983798i \(-0.557377\pi\)
0.941634 0.336638i \(-0.109290\pi\)
\(978\) 1.29882e13 2.24962e13i 0.453965 0.786291i
\(979\) 8.52935e12 1.47733e13i 0.296752 0.513990i
\(980\) 1.97716e13 + 3.42454e13i 0.684737 + 1.18600i
\(981\) 1.78031e12 + 3.08359e12i 0.0613742 + 0.106303i
\(982\) −1.62124e12 + 2.80808e12i −0.0556348 + 0.0963623i
\(983\) −1.46738e13 + 2.54158e13i −0.501247 + 0.868185i 0.498752 + 0.866745i \(0.333792\pi\)
−0.999999 + 0.00144059i \(0.999541\pi\)
\(984\) 1.48824e13 2.57771e13i 0.506053 0.876510i
\(985\) −2.80669e13 −0.950016
\(986\) −9.65916e12 1.67302e13i −0.325457 0.563708i
\(987\) 6.24079e13 1.08094e14i 2.09321 3.62554i
\(988\) 4.52375e12 0.151040
\(989\) 3.49415e12 0.116134
\(990\) 1.48518e12 2.57241e12i 0.0491385 0.0851103i
\(991\) 4.05032e13 1.33401 0.667003 0.745055i \(-0.267577\pi\)
0.667003 + 0.745055i \(0.267577\pi\)
\(992\) 1.46092e13 + 2.53039e13i 0.478988 + 0.829631i
\(993\) −6.20760e13 −2.02606
\(994\) −9.45217e12 1.63716e13i −0.307109 0.531929i
\(995\) −8.31182e12 1.43965e13i −0.268839 0.465643i
\(996\) −1.85259e12 3.20878e12i −0.0596503 0.103317i
\(997\) −5.47070e11 + 9.47552e11i −0.0175353 + 0.0303721i −0.874660 0.484737i \(-0.838915\pi\)
0.857125 + 0.515109i \(0.172249\pi\)
\(998\) 1.73599e12 0.0553935
\(999\) −3.26473e12 + 8.40906e12i −0.103706 + 0.267118i
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.10.17 54
37.26 even 3 inner 37.10.c.a.26.17 yes 54
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
37.10.c.a.10.17 54 1.1 even 1 trivial
37.10.c.a.26.17 yes 54 37.26 even 3 inner