Properties

Label 48.8.k.a.11.1
Level $48$
Weight $8$
Character 48.11
Analytic conductor $14.994$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,8,Mod(11,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.11");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 48.k (of order \(4\), 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: \(14.9944812232\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(54\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.1
Character \(\chi\) \(=\) 48.11
Dual form 48.8.k.a.35.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-11.3125 + 0.167474i) q^{2} +(4.08471 + 46.5866i) q^{3} +(127.944 - 3.78909i) q^{4} +(-280.037 + 280.037i) q^{5} +(-54.0103 - 526.326i) q^{6} -532.864 q^{7} +(-1446.73 + 64.2912i) q^{8} +(-2153.63 + 380.586i) q^{9} +O(q^{10})\) \(q+(-11.3125 + 0.167474i) q^{2} +(4.08471 + 46.5866i) q^{3} +(127.944 - 3.78909i) q^{4} +(-280.037 + 280.037i) q^{5} +(-54.0103 - 526.326i) q^{6} -532.864 q^{7} +(-1446.73 + 64.2912i) q^{8} +(-2153.63 + 380.586i) q^{9} +(3121.01 - 3214.81i) q^{10} +(4874.78 + 4874.78i) q^{11} +(699.135 + 5945.00i) q^{12} +(-6614.77 + 6614.77i) q^{13} +(6028.01 - 89.2408i) q^{14} +(-14189.9 - 11902.1i) q^{15} +(16355.3 - 969.582i) q^{16} -17690.5i q^{17} +(24299.1 - 4666.05i) q^{18} +(8933.09 + 8933.09i) q^{19} +(-34768.0 + 36890.1i) q^{20} +(-2176.60 - 24824.3i) q^{21} +(-55962.2 - 54329.4i) q^{22} -43376.1i q^{23} +(-8904.58 - 67135.5i) q^{24} -78716.6i q^{25} +(73721.6 - 75937.2i) q^{26} +(-26527.2 - 98775.8i) q^{27} +(-68176.7 + 2019.07i) q^{28} +(-62488.9 - 62488.9i) q^{29} +(162516. + 132266. i) q^{30} -146730. i q^{31} +(-184856. + 13707.4i) q^{32} +(-207188. + 247012. i) q^{33} +(2962.70 + 200124. i) q^{34} +(149222. - 149222. i) q^{35} +(-274102. + 56854.0i) q^{36} +(227020. + 227020. i) q^{37} +(-102551. - 99559.2i) q^{38} +(-335180. - 281141. i) q^{39} +(387133. - 423141. i) q^{40} +646374. q^{41} +(28780.1 + 280460. i) q^{42} +(-53791.8 + 53791.8i) q^{43} +(642170. + 605228. i) q^{44} +(496518. - 709675. i) q^{45} +(7264.36 + 490691. i) q^{46} -666787. q^{47} +(111976. + 757977. i) q^{48} -539599. q^{49} +(13183.0 + 890479. i) q^{50} +(824142. - 72260.8i) q^{51} +(-821256. + 871384. i) q^{52} +(819051. - 819051. i) q^{53} +(316630. + 1.11296e6i) q^{54} -2.73024e6 q^{55} +(770908. - 34258.5i) q^{56} +(-379674. + 452652. i) q^{57} +(717369. + 696439. i) q^{58} +(624777. + 624777. i) q^{59} +(-1.86060e6 - 1.46904e6i) q^{60} +(-2.09262e6 + 2.09262e6i) q^{61} +(24573.4 + 1.65987e6i) q^{62} +(1.14759e6 - 202801. i) q^{63} +(2.08889e6 - 186024. i) q^{64} -3.70476e6i q^{65} +(2.30244e6 - 2.82901e6i) q^{66} +(-2.12329e6 - 2.12329e6i) q^{67} +(-67031.0 - 2.26340e6i) q^{68} +(2.02075e6 - 177179. i) q^{69} +(-1.66307e6 + 1.71306e6i) q^{70} +3.60556e6i q^{71} +(3.09125e6 - 689064. i) q^{72} -4.50662e6i q^{73} +(-2.60618e6 - 2.53014e6i) q^{74} +(3.66714e6 - 321535. i) q^{75} +(1.17678e6 + 1.10909e6i) q^{76} +(-2.59760e6 - 2.59760e6i) q^{77} +(3.83879e6 + 3.12426e6i) q^{78} +2.96722e6i q^{79} +(-4.30857e6 + 4.85161e6i) q^{80} +(4.49328e6 - 1.63928e6i) q^{81} +(-7.31208e6 + 108251. i) q^{82} +(-6.95913e6 + 6.95913e6i) q^{83} +(-372544. - 3.16788e6i) q^{84} +(4.95401e6 + 4.95401e6i) q^{85} +(599509. - 617526. i) q^{86} +(2.65590e6 - 3.16640e6i) q^{87} +(-7.36588e6 - 6.73907e6i) q^{88} -2.66802e6 q^{89} +(-5.49799e6 + 8.11133e6i) q^{90} +(3.52477e6 - 3.52477e6i) q^{91} +(-164356. - 5.54971e6i) q^{92} +(6.83564e6 - 599348. i) q^{93} +(7.54300e6 - 111669. i) q^{94} -5.00319e6 q^{95} +(-1.39367e6 - 8.55584e6i) q^{96} +1.61896e7 q^{97} +(6.10420e6 - 90368.8i) q^{98} +(-1.23538e7 - 8.64320e6i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).

\(n\) \(17\) \(31\) \(37\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{1}{4}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −11.3125 + 0.167474i −0.999890 + 0.0148027i
\(3\) 4.08471 + 46.5866i 0.0873448 + 0.996178i
\(4\) 127.944 3.78909i 0.999562 0.0296023i
\(5\) −280.037 + 280.037i −1.00189 + 1.00189i −0.00189302 + 0.999998i \(0.500603\pi\)
−0.999998 + 0.00189302i \(0.999397\pi\)
\(6\) −54.0103 526.326i −0.102081 0.994776i
\(7\) −532.864 −0.587183 −0.293591 0.955931i \(-0.594850\pi\)
−0.293591 + 0.955931i \(0.594850\pi\)
\(8\) −1446.73 + 64.2912i −0.999014 + 0.0443953i
\(9\) −2153.63 + 380.586i −0.984742 + 0.174022i
\(10\) 3121.01 3214.81i 0.986951 1.01661i
\(11\) 4874.78 + 4874.78i 1.10428 + 1.10428i 0.993888 + 0.110396i \(0.0352120\pi\)
0.110396 + 0.993888i \(0.464788\pi\)
\(12\) 699.135 + 5945.00i 0.116796 + 0.993156i
\(13\) −6614.77 + 6614.77i −0.835052 + 0.835052i −0.988203 0.153151i \(-0.951058\pi\)
0.153151 + 0.988203i \(0.451058\pi\)
\(14\) 6028.01 89.2408i 0.587118 0.00869192i
\(15\) −14189.9 11902.1i −1.08557 0.910552i
\(16\) 16355.3 969.582i 0.998247 0.0591786i
\(17\) 17690.5i 0.873312i −0.899628 0.436656i \(-0.856163\pi\)
0.899628 0.436656i \(-0.143837\pi\)
\(18\) 24299.1 4666.05i 0.982058 0.188580i
\(19\) 8933.09 + 8933.09i 0.298789 + 0.298789i 0.840539 0.541751i \(-0.182238\pi\)
−0.541751 + 0.840539i \(0.682238\pi\)
\(20\) −34768.0 + 36890.1i −0.971794 + 1.03111i
\(21\) −2176.60 24824.3i −0.0512874 0.584938i
\(22\) −55962.2 54329.4i −1.12051 1.08782i
\(23\) 43376.1i 0.743366i −0.928360 0.371683i \(-0.878781\pi\)
0.928360 0.371683i \(-0.121219\pi\)
\(24\) −8904.58 67135.5i −0.131484 0.991318i
\(25\) 78716.6i 1.00757i
\(26\) 73721.6 75937.2i 0.822599 0.847321i
\(27\) −26527.2 98775.8i −0.259369 0.965778i
\(28\) −68176.7 + 2019.07i −0.586925 + 0.0173819i
\(29\) −62488.9 62488.9i −0.475784 0.475784i 0.427996 0.903781i \(-0.359220\pi\)
−0.903781 + 0.427996i \(0.859220\pi\)
\(30\) 162516. + 132266.i 1.09893 + 0.894383i
\(31\) 146730.i 0.884610i −0.896865 0.442305i \(-0.854161\pi\)
0.896865 0.442305i \(-0.145839\pi\)
\(32\) −184856. + 13707.4i −0.997262 + 0.0739489i
\(33\) −207188. + 247012.i −1.00361 + 1.19652i
\(34\) 2962.70 + 200124.i 0.0129274 + 0.873217i
\(35\) 149222. 149222.i 0.588293 0.588293i
\(36\) −274102. + 56854.0i −0.979159 + 0.203096i
\(37\) 227020. + 227020.i 0.736815 + 0.736815i 0.971960 0.235145i \(-0.0755566\pi\)
−0.235145 + 0.971960i \(0.575557\pi\)
\(38\) −102551. 99559.2i −0.303179 0.294333i
\(39\) −335180. 281141.i −0.904798 0.758923i
\(40\) 387133. 423141.i 0.956424 1.04538i
\(41\) 646374. 1.46467 0.732336 0.680944i \(-0.238430\pi\)
0.732336 + 0.680944i \(0.238430\pi\)
\(42\) 28780.1 + 280460.i 0.0599404 + 0.584115i
\(43\) −53791.8 + 53791.8i −0.103175 + 0.103175i −0.756810 0.653635i \(-0.773243\pi\)
0.653635 + 0.756810i \(0.273243\pi\)
\(44\) 642170. + 605228.i 1.13649 + 1.07111i
\(45\) 496518. 709675.i 0.812253 1.16096i
\(46\) 7264.36 + 490691.i 0.0110039 + 0.743285i
\(47\) −666787. −0.936795 −0.468397 0.883518i \(-0.655168\pi\)
−0.468397 + 0.883518i \(0.655168\pi\)
\(48\) 111976. + 757977.i 0.146144 + 0.989263i
\(49\) −539599. −0.655217
\(50\) 13183.0 + 890479.i 0.0149148 + 1.00746i
\(51\) 824142. 72260.8i 0.869975 0.0762793i
\(52\) −821256. + 871384.i −0.809966 + 0.859405i
\(53\) 819051. 819051.i 0.755693 0.755693i −0.219843 0.975535i \(-0.570554\pi\)
0.975535 + 0.219843i \(0.0705544\pi\)
\(54\) 316630. + 1.11296e6i 0.273637 + 0.961833i
\(55\) −2.73024e6 −2.21275
\(56\) 770908. 34258.5i 0.586604 0.0260681i
\(57\) −379674. + 452652.i −0.271549 + 0.323744i
\(58\) 717369. + 696439.i 0.482775 + 0.468689i
\(59\) 624777. + 624777.i 0.396044 + 0.396044i 0.876835 0.480791i \(-0.159651\pi\)
−0.480791 + 0.876835i \(0.659651\pi\)
\(60\) −1.86060e6 1.46904e6i −1.11205 0.878018i
\(61\) −2.09262e6 + 2.09262e6i −1.18042 + 1.18042i −0.200782 + 0.979636i \(0.564348\pi\)
−0.979636 + 0.200782i \(0.935652\pi\)
\(62\) 24573.4 + 1.65987e6i 0.0130947 + 0.884513i
\(63\) 1.14759e6 202801.i 0.578223 0.102183i
\(64\) 2.08889e6 186024.i 0.996058 0.0887030i
\(65\) 3.70476e6i 1.67326i
\(66\) 2.30244e6 2.82901e6i 0.985788 1.21124i
\(67\) −2.12329e6 2.12329e6i −0.862476 0.862476i 0.129149 0.991625i \(-0.458775\pi\)
−0.991625 + 0.129149i \(0.958775\pi\)
\(68\) −67031.0 2.26340e6i −0.0258520 0.872930i
\(69\) 2.02075e6 177179.i 0.740525 0.0649292i
\(70\) −1.66307e6 + 1.71306e6i −0.579520 + 0.596937i
\(71\) 3.60556e6i 1.19555i 0.801664 + 0.597775i \(0.203949\pi\)
−0.801664 + 0.597775i \(0.796051\pi\)
\(72\) 3.09125e6 689064.i 0.976045 0.217568i
\(73\) 4.50662e6i 1.35588i −0.735118 0.677939i \(-0.762873\pi\)
0.735118 0.677939i \(-0.237127\pi\)
\(74\) −2.60618e6 2.53014e6i −0.747641 0.725827i
\(75\) 3.66714e6 321535.i 1.00372 0.0880062i
\(76\) 1.17678e6 + 1.10909e6i 0.307503 + 0.289813i
\(77\) −2.59760e6 2.59760e6i −0.648416 0.648416i
\(78\) 3.83879e6 + 3.12426e6i 0.915933 + 0.745446i
\(79\) 2.96722e6i 0.677104i 0.940948 + 0.338552i \(0.109937\pi\)
−0.940948 + 0.338552i \(0.890063\pi\)
\(80\) −4.30857e6 + 4.85161e6i −0.940845 + 1.05943i
\(81\) 4.49328e6 1.63928e6i 0.939433 0.342734i
\(82\) −7.31208e6 + 108251.i −1.46451 + 0.0216812i
\(83\) −6.95913e6 + 6.95913e6i −1.33592 + 1.33592i −0.435956 + 0.899968i \(0.643590\pi\)
−0.899968 + 0.435956i \(0.856410\pi\)
\(84\) −372544. 3.16788e6i −0.0685804 0.583164i
\(85\) 4.95401e6 + 4.95401e6i 0.874964 + 0.874964i
\(86\) 599509. 617526.i 0.101637 0.104691i
\(87\) 2.65590e6 3.16640e6i 0.432409 0.515523i
\(88\) −7.36588e6 6.73907e6i −1.15222 1.05417i
\(89\) −2.66802e6 −0.401166 −0.200583 0.979677i \(-0.564284\pi\)
−0.200583 + 0.979677i \(0.564284\pi\)
\(90\) −5.49799e6 + 8.11133e6i −0.794979 + 1.17285i
\(91\) 3.52477e6 3.52477e6i 0.490328 0.490328i
\(92\) −164356. 5.54971e6i −0.0220053 0.743041i
\(93\) 6.83564e6 599348.i 0.881229 0.0772661i
\(94\) 7.54300e6 111669.i 0.936692 0.0138671i
\(95\) −5.00319e6 −0.598707
\(96\) −1.39367e6 8.55584e6i −0.160772 0.986992i
\(97\) 1.61896e7 1.80109 0.900543 0.434767i \(-0.143169\pi\)
0.900543 + 0.434767i \(0.143169\pi\)
\(98\) 6.10420e6 90368.8i 0.655145 0.00969901i
\(99\) −1.23538e7 8.64320e6i −1.27960 0.895265i
\(100\) −298264. 1.00713e7i −0.0298264 1.00713i
\(101\) −1.82308e6 + 1.82308e6i −0.176068 + 0.176068i −0.789639 0.613571i \(-0.789732\pi\)
0.613571 + 0.789639i \(0.289732\pi\)
\(102\) −9.31098e6 + 955470.i −0.868750 + 0.0891490i
\(103\) −2.05952e7 −1.85710 −0.928552 0.371202i \(-0.878946\pi\)
−0.928552 + 0.371202i \(0.878946\pi\)
\(104\) 9.14450e6 9.99504e6i 0.797156 0.871301i
\(105\) 7.56126e6 + 6.34221e6i 0.637429 + 0.534660i
\(106\) −9.12831e6 + 9.40265e6i −0.744424 + 0.766796i
\(107\) −2.03080e6 2.03080e6i −0.160259 0.160259i 0.622422 0.782682i \(-0.286149\pi\)
−0.782682 + 0.622422i \(0.786149\pi\)
\(108\) −3.76826e6 1.25372e7i −0.287845 0.957677i
\(109\) −3.58451e6 + 3.58451e6i −0.265117 + 0.265117i −0.827129 0.562012i \(-0.810027\pi\)
0.562012 + 0.827129i \(0.310027\pi\)
\(110\) 3.08858e7 457244.i 2.21250 0.0327547i
\(111\) −9.64879e6 + 1.15034e7i −0.669642 + 0.798356i
\(112\) −8.71514e6 + 516655.i −0.586153 + 0.0347486i
\(113\) 2.25513e7i 1.47027i 0.677920 + 0.735136i \(0.262881\pi\)
−0.677920 + 0.735136i \(0.737119\pi\)
\(114\) 4.21924e6 5.18419e6i 0.266727 0.327729i
\(115\) 1.21469e7 + 1.21469e7i 0.744772 + 0.744772i
\(116\) −8.23185e6 7.75830e6i −0.489660 0.461492i
\(117\) 1.17283e7 1.67633e7i 0.676993 0.967628i
\(118\) −7.17241e6 6.96314e6i −0.401863 0.390138i
\(119\) 9.42664e6i 0.512794i
\(120\) 2.12941e7 + 1.63068e7i 1.12493 + 0.861460i
\(121\) 2.80398e7i 1.43889i
\(122\) 2.33222e7 2.40232e7i 1.16282 1.19776i
\(123\) 2.64025e6 + 3.01124e7i 0.127931 + 1.45907i
\(124\) −555971. 1.87732e7i −0.0261864 0.884222i
\(125\) 165661. + 165661.i 0.00758639 + 0.00758639i
\(126\) −1.29481e7 + 2.48637e6i −0.576647 + 0.110731i
\(127\) 2.75160e7i 1.19199i −0.802989 0.595994i \(-0.796758\pi\)
0.802989 0.595994i \(-0.203242\pi\)
\(128\) −2.35993e7 + 2.45422e6i −0.994636 + 0.103438i
\(129\) −2.72570e6 2.28625e6i −0.111793 0.0937693i
\(130\) 620452. + 4.19100e7i 0.0247689 + 1.67308i
\(131\) 1.01111e7 1.01111e7i 0.392959 0.392959i −0.482781 0.875741i \(-0.660373\pi\)
0.875741 + 0.482781i \(0.160373\pi\)
\(132\) −2.55724e7 + 3.23887e7i −0.967751 + 1.22570i
\(133\) −4.76012e6 4.76012e6i −0.175443 0.175443i
\(134\) 2.43752e7 + 2.36640e7i 0.875149 + 0.849615i
\(135\) 3.50895e7 + 2.02323e7i 1.22746 + 0.707745i
\(136\) 1.13735e6 + 2.55934e7i 0.0387709 + 0.872451i
\(137\) −1.96189e7 −0.651857 −0.325929 0.945394i \(-0.605677\pi\)
−0.325929 + 0.945394i \(0.605677\pi\)
\(138\) −2.28300e7 + 2.34275e6i −0.739483 + 0.0758839i
\(139\) 6.05704e6 6.05704e6i 0.191297 0.191297i −0.604959 0.796256i \(-0.706811\pi\)
0.796256 + 0.604959i \(0.206811\pi\)
\(140\) 1.85266e7 1.96574e7i 0.570620 0.605450i
\(141\) −2.72363e6 3.10634e7i −0.0818242 0.933214i
\(142\) −603837. 4.07877e7i −0.0176974 1.19542i
\(143\) −6.44912e7 −1.84427
\(144\) −3.48542e7 + 8.31272e6i −0.972718 + 0.231993i
\(145\) 3.49984e7 0.953368
\(146\) 754741. + 5.09810e7i 0.0200707 + 1.35573i
\(147\) −2.20411e6 2.51381e7i −0.0572298 0.652713i
\(148\) 2.99060e7 + 2.81856e7i 0.758303 + 0.714680i
\(149\) 2.25230e7 2.25230e7i 0.557794 0.557794i −0.370885 0.928679i \(-0.620945\pi\)
0.928679 + 0.370885i \(0.120945\pi\)
\(150\) −4.14306e7 + 4.25150e6i −1.00231 + 0.102854i
\(151\) −7.78963e6 −0.184119 −0.0920593 0.995754i \(-0.529345\pi\)
−0.0920593 + 0.995754i \(0.529345\pi\)
\(152\) −1.34981e7 1.23494e7i −0.311759 0.285229i
\(153\) 6.73277e6 + 3.80989e7i 0.151976 + 0.859987i
\(154\) 2.98202e7 + 2.89502e7i 0.657944 + 0.638747i
\(155\) 4.10897e7 + 4.10897e7i 0.886283 + 0.886283i
\(156\) −4.39495e7 3.47002e7i −0.926867 0.731806i
\(157\) 6.08153e6 6.08153e6i 0.125419 0.125419i −0.641611 0.767030i \(-0.721734\pi\)
0.767030 + 0.641611i \(0.221734\pi\)
\(158\) −496933. 3.35666e7i −0.0100230 0.677030i
\(159\) 4.15024e7 + 3.48112e7i 0.818810 + 0.686799i
\(160\) 4.79280e7 5.56052e7i 0.925059 1.07324i
\(161\) 2.31135e7i 0.436492i
\(162\) −5.05555e7 + 1.92969e7i −0.934256 + 0.356602i
\(163\) −5.47976e7 5.47976e7i −0.991072 0.991072i 0.00888868 0.999960i \(-0.497171\pi\)
−0.999960 + 0.00888868i \(0.997171\pi\)
\(164\) 8.26996e7 2.44917e6i 1.46403 0.0433576i
\(165\) −1.11522e7 1.27193e8i −0.193272 2.20429i
\(166\) 7.75595e7 7.98904e7i 1.31600 1.35555i
\(167\) 6.22264e7i 1.03387i −0.856024 0.516937i \(-0.827072\pi\)
0.856024 0.516937i \(-0.172928\pi\)
\(168\) 4.74493e6 + 3.57741e7i 0.0772053 + 0.582085i
\(169\) 2.47620e7i 0.394622i
\(170\) −5.68717e7 5.52124e7i −0.887820 0.861916i
\(171\) −2.26384e7 1.58388e7i −0.346225 0.242234i
\(172\) −6.67851e6 + 7.08615e6i −0.100076 + 0.106184i
\(173\) −5.61944e7 5.61944e7i −0.825147 0.825147i 0.161694 0.986841i \(-0.448304\pi\)
−0.986841 + 0.161694i \(0.948304\pi\)
\(174\) −2.95145e7 + 3.62646e7i −0.424730 + 0.521868i
\(175\) 4.19452e7i 0.591629i
\(176\) 8.44550e7 + 7.50020e7i 1.16770 + 1.03700i
\(177\) −2.65542e7 + 3.16583e7i −0.359938 + 0.429123i
\(178\) 3.01819e7 446824.i 0.401122 0.00593836i
\(179\) −504953. + 504953.i −0.00658059 + 0.00658059i −0.710389 0.703809i \(-0.751481\pi\)
0.703809 + 0.710389i \(0.251481\pi\)
\(180\) 6.08374e7 9.26799e7i 0.777530 1.18449i
\(181\) −5.39182e7 5.39182e7i −0.675866 0.675866i 0.283196 0.959062i \(-0.408605\pi\)
−0.959062 + 0.283196i \(0.908605\pi\)
\(182\) −3.92836e7 + 4.04642e7i −0.483016 + 0.497532i
\(183\) −1.06036e8 8.89404e7i −1.27901 1.07280i
\(184\) 2.78870e6 + 6.27533e7i 0.0330019 + 0.742633i
\(185\) −1.27148e8 −1.47642
\(186\) −7.72276e7 + 7.92490e6i −0.879988 + 0.0903022i
\(187\) 8.62375e7 8.62375e7i 0.964385 0.964385i
\(188\) −8.53113e7 + 2.52651e6i −0.936384 + 0.0277312i
\(189\) 1.41354e7 + 5.26341e7i 0.152297 + 0.567088i
\(190\) 5.65985e7 837905.i 0.598642 0.00886252i
\(191\) −8.03957e7 −0.834865 −0.417432 0.908708i \(-0.637070\pi\)
−0.417432 + 0.908708i \(0.637070\pi\)
\(192\) 1.71987e7 + 9.65543e7i 0.175365 + 0.984504i
\(193\) 9.00026e7 0.901165 0.450583 0.892735i \(-0.351216\pi\)
0.450583 + 0.892735i \(0.351216\pi\)
\(194\) −1.83144e8 + 2.71133e6i −1.80089 + 0.0266610i
\(195\) 1.72593e8 1.51329e7i 1.66687 0.146151i
\(196\) −6.90384e7 + 2.04459e6i −0.654930 + 0.0193959i
\(197\) 3.98771e6 3.98771e6i 0.0371614 0.0371614i −0.688282 0.725443i \(-0.741635\pi\)
0.725443 + 0.688282i \(0.241635\pi\)
\(198\) 1.41199e8 + 9.57070e7i 1.29272 + 0.876225i
\(199\) 6.89098e7 0.619863 0.309931 0.950759i \(-0.399694\pi\)
0.309931 + 0.950759i \(0.399694\pi\)
\(200\) 5.06078e6 + 1.13881e8i 0.0447314 + 1.00658i
\(201\) 9.02438e7 1.07590e8i 0.783847 0.934513i
\(202\) 2.03182e7 2.09288e7i 0.173442 0.178655i
\(203\) 3.32981e7 + 3.32981e7i 0.279372 + 0.279372i
\(204\) 1.05170e8 1.23681e7i 0.867335 0.101999i
\(205\) −1.81009e8 + 1.81009e8i −1.46744 + 1.46744i
\(206\) 2.32983e8 3.44916e6i 1.85690 0.0274902i
\(207\) 1.65083e7 + 9.34160e7i 0.129362 + 0.732024i
\(208\) −1.01773e8 + 1.14600e8i −0.784171 + 0.883005i
\(209\) 8.70937e7i 0.659895i
\(210\) −8.65987e7 7.04797e7i −0.645274 0.525166i
\(211\) −5.69316e6 5.69316e6i −0.0417220 0.0417220i 0.685938 0.727660i \(-0.259392\pi\)
−0.727660 + 0.685938i \(0.759392\pi\)
\(212\) 1.01689e8 1.07896e8i 0.732991 0.777732i
\(213\) −1.67971e8 + 1.47277e7i −1.19098 + 0.104425i
\(214\) 2.33134e7 + 2.26332e7i 0.162614 + 0.157870i
\(215\) 3.01274e7i 0.206741i
\(216\) 4.47280e7 + 1.41196e8i 0.301989 + 0.953311i
\(217\) 7.81869e7i 0.519427i
\(218\) 3.99494e7 4.11500e7i 0.261163 0.269012i
\(219\) 2.09948e8 1.84082e7i 1.35070 0.118429i
\(220\) −3.49318e8 + 1.03451e7i −2.21178 + 0.0655022i
\(221\) 1.17019e8 + 1.17019e8i 0.729261 + 0.729261i
\(222\) 1.07225e8 1.31748e8i 0.657751 0.808181i
\(223\) 2.49955e8i 1.50937i 0.656090 + 0.754683i \(0.272209\pi\)
−0.656090 + 0.754683i \(0.727791\pi\)
\(224\) 9.85032e7 7.30420e6i 0.585575 0.0434215i
\(225\) 2.99584e7 + 1.69526e8i 0.175340 + 0.992198i
\(226\) −3.77676e6 2.55111e8i −0.0217641 1.47011i
\(227\) 1.04949e7 1.04949e7i 0.0595508 0.0595508i −0.676704 0.736255i \(-0.736592\pi\)
0.736255 + 0.676704i \(0.236592\pi\)
\(228\) −4.68618e7 + 5.93527e7i −0.261847 + 0.331641i
\(229\) 7.89367e6 + 7.89367e6i 0.0434365 + 0.0434365i 0.728491 0.685055i \(-0.240222\pi\)
−0.685055 + 0.728491i \(0.740222\pi\)
\(230\) −1.39446e8 1.35377e8i −0.755715 0.733666i
\(231\) 1.10403e8 1.31624e8i 0.589302 0.702574i
\(232\) 9.44219e7 + 8.63869e7i 0.496438 + 0.454193i
\(233\) 3.34430e7 0.173205 0.0866024 0.996243i \(-0.472399\pi\)
0.0866024 + 0.996243i \(0.472399\pi\)
\(234\) −1.29868e8 + 1.91598e8i −0.662595 + 0.977543i
\(235\) 1.86725e8 1.86725e8i 0.938566 0.938566i
\(236\) 8.23038e7 + 7.75691e7i 0.407594 + 0.384146i
\(237\) −1.38233e8 + 1.21203e7i −0.674516 + 0.0591415i
\(238\) −1.57872e6 1.06639e8i −0.00759076 0.512738i
\(239\) −8.85576e7 −0.419598 −0.209799 0.977745i \(-0.567281\pi\)
−0.209799 + 0.977745i \(0.567281\pi\)
\(240\) −2.43619e8 1.80904e8i −1.13755 0.844714i
\(241\) −1.54329e8 −0.710213 −0.355106 0.934826i \(-0.615555\pi\)
−0.355106 + 0.934826i \(0.615555\pi\)
\(242\) −4.69594e6 3.17200e8i −0.0212995 1.43873i
\(243\) 9.47225e7 + 2.02631e8i 0.423478 + 0.905906i
\(244\) −2.59809e8 + 2.75667e8i −1.14496 + 1.21484i
\(245\) 1.51108e8 1.51108e8i 0.656456 0.656456i
\(246\) −3.49108e7 3.40203e8i −0.149516 1.45702i
\(247\) −1.18181e8 −0.499008
\(248\) 9.43342e6 + 2.12278e8i 0.0392725 + 0.883737i
\(249\) −3.52629e8 2.95776e8i −1.44750 1.21413i
\(250\) −1.90178e6 1.84629e6i −0.00769786 0.00747326i
\(251\) 8.61580e7 + 8.61580e7i 0.343904 + 0.343904i 0.857833 0.513929i \(-0.171810\pi\)
−0.513929 + 0.857833i \(0.671810\pi\)
\(252\) 1.46059e8 3.02954e7i 0.574945 0.119255i
\(253\) 2.11449e8 2.11449e8i 0.820888 0.820888i
\(254\) 4.60821e6 + 3.11274e8i 0.0176447 + 1.19186i
\(255\) −2.10555e8 + 2.51026e8i −0.795196 + 0.948044i
\(256\) 2.66555e8 3.17156e7i 0.992996 0.118150i
\(257\) 5.02122e8i 1.84520i 0.385757 + 0.922600i \(0.373940\pi\)
−0.385757 + 0.922600i \(0.626060\pi\)
\(258\) 3.12173e7 + 2.54067e7i 0.113169 + 0.0921041i
\(259\) −1.20971e8 1.20971e8i −0.432645 0.432645i
\(260\) −1.40377e7 4.74002e8i −0.0495323 1.67253i
\(261\) 1.58360e8 + 1.10796e8i 0.551322 + 0.385728i
\(262\) −1.12688e8 + 1.16075e8i −0.387099 + 0.398733i
\(263\) 1.32867e8i 0.450372i −0.974316 0.225186i \(-0.927701\pi\)
0.974316 0.225186i \(-0.0722990\pi\)
\(264\) 2.83863e8 3.70679e8i 0.949501 1.23989i
\(265\) 4.58729e8i 1.51424i
\(266\) 5.46459e7 + 5.30515e7i 0.178021 + 0.172827i
\(267\) −1.08981e7 1.24294e8i −0.0350398 0.399633i
\(268\) −2.79707e8 2.63616e8i −0.887629 0.836567i
\(269\) −1.23584e8 1.23584e8i −0.387107 0.387107i 0.486547 0.873654i \(-0.338256\pi\)
−0.873654 + 0.486547i \(0.838256\pi\)
\(270\) −4.00337e8 2.23001e8i −1.23781 0.689498i
\(271\) 3.65542e8i 1.11569i −0.829944 0.557847i \(-0.811628\pi\)
0.829944 0.557847i \(-0.188372\pi\)
\(272\) −1.71524e7 2.89334e8i −0.0516814 0.871782i
\(273\) 1.78605e8 + 1.49810e8i 0.531281 + 0.445626i
\(274\) 2.21938e8 3.28565e6i 0.651786 0.00964928i
\(275\) 3.83726e8 3.83726e8i 1.11265 1.11265i
\(276\) 2.57871e8 3.03257e7i 0.738279 0.0868220i
\(277\) −2.90474e7 2.90474e7i −0.0821160 0.0821160i 0.664856 0.746972i \(-0.268493\pi\)
−0.746972 + 0.664856i \(0.768493\pi\)
\(278\) −6.75057e7 + 6.95345e7i −0.188444 + 0.194108i
\(279\) 5.58432e7 + 3.16001e8i 0.153942 + 0.871112i
\(280\) −2.06289e8 + 2.25477e8i −0.561596 + 0.613830i
\(281\) −2.09107e7 −0.0562208 −0.0281104 0.999605i \(-0.508949\pi\)
−0.0281104 + 0.999605i \(0.508949\pi\)
\(282\) 3.60133e7 + 3.50947e8i 0.0956294 + 0.931901i
\(283\) −2.12104e8 + 2.12104e8i −0.556284 + 0.556284i −0.928247 0.371964i \(-0.878685\pi\)
0.371964 + 0.928247i \(0.378685\pi\)
\(284\) 1.36618e7 + 4.61309e8i 0.0353910 + 1.19503i
\(285\) −2.04366e7 2.33082e8i −0.0522940 0.596419i
\(286\) 7.29554e8 1.08006e7i 1.84407 0.0273002i
\(287\) −3.44429e8 −0.860029
\(288\) 3.92895e8 9.98745e7i 0.969177 0.246366i
\(289\) 9.73838e7 0.237325
\(290\) −3.95919e8 + 5.86133e6i −0.953264 + 0.0141125i
\(291\) 6.61298e7 + 7.54218e8i 0.157316 + 1.79420i
\(292\) −1.70760e7 5.76594e8i −0.0401371 1.35528i
\(293\) −2.92417e8 + 2.92417e8i −0.679151 + 0.679151i −0.959808 0.280657i \(-0.909448\pi\)
0.280657 + 0.959808i \(0.409448\pi\)
\(294\) 2.91439e7 + 2.84005e8i 0.0668855 + 0.651794i
\(295\) −3.49922e8 −0.793586
\(296\) −3.43032e8 3.13841e8i −0.768799 0.703377i
\(297\) 3.52196e8 6.10825e8i 0.780076 1.35291i
\(298\) −2.51019e8 + 2.58563e8i −0.549476 + 0.565990i
\(299\) 2.86923e8 + 2.86923e8i 0.620749 + 0.620749i
\(300\) 4.67970e8 5.50335e7i 1.00068 0.117680i
\(301\) 2.86637e7 2.86637e7i 0.0605828 0.0605828i
\(302\) 8.81200e7 1.30456e6i 0.184098 0.00272546i
\(303\) −9.23779e7 7.74843e7i −0.190774 0.160016i
\(304\) 1.54765e8 + 1.37442e8i 0.315947 + 0.280583i
\(305\) 1.17202e9i 2.36530i
\(306\) −8.25448e7 4.29865e8i −0.164689 0.857643i
\(307\) −4.09109e8 4.09109e8i −0.806965 0.806965i 0.177208 0.984173i \(-0.443293\pi\)
−0.984173 + 0.177208i \(0.943293\pi\)
\(308\) −3.42189e8 3.22504e8i −0.667327 0.628938i
\(309\) −8.41256e7 9.59462e8i −0.162208 1.85001i
\(310\) −4.71708e8 4.57945e8i −0.899305 0.873066i
\(311\) 5.56969e8i 1.04995i 0.851117 + 0.524977i \(0.175926\pi\)
−0.851117 + 0.524977i \(0.824074\pi\)
\(312\) 5.02988e8 + 3.85185e8i 0.937598 + 0.718006i
\(313\) 9.34283e8i 1.72216i 0.508470 + 0.861080i \(0.330211\pi\)
−0.508470 + 0.861080i \(0.669789\pi\)
\(314\) −6.77786e7 + 6.98156e7i −0.123549 + 0.127262i
\(315\) −2.64577e8 + 3.78160e8i −0.476941 + 0.681693i
\(316\) 1.12431e7 + 3.79638e8i 0.0200438 + 0.676807i
\(317\) 6.98044e7 + 6.98044e7i 0.123077 + 0.123077i 0.765962 0.642886i \(-0.222263\pi\)
−0.642886 + 0.765962i \(0.722263\pi\)
\(318\) −4.75325e8 3.86850e8i −0.828887 0.674603i
\(319\) 6.09240e8i 1.05080i
\(320\) −5.32872e8 + 6.37059e8i −0.909071 + 1.08681i
\(321\) 8.63128e7 1.02903e8i 0.145649 0.173645i
\(322\) −3.87092e6 2.61471e8i −0.00646128 0.436444i
\(323\) 1.58031e8 1.58031e8i 0.260936 0.260936i
\(324\) 5.68676e8 2.26762e8i 0.928875 0.370393i
\(325\) 5.20692e8 + 5.20692e8i 0.841375 + 0.841375i
\(326\) 6.29074e8 + 6.10719e8i 1.00563 + 0.976293i
\(327\) −1.81632e8 1.52349e8i −0.287260 0.240947i
\(328\) −9.35126e8 + 4.15562e7i −1.46323 + 0.0650245i
\(329\) 3.55307e8 0.550069
\(330\) 1.47461e8 + 1.43700e9i 0.225880 + 2.20119i
\(331\) 1.83378e8 1.83378e8i 0.277938 0.277938i −0.554347 0.832286i \(-0.687032\pi\)
0.832286 + 0.554347i \(0.187032\pi\)
\(332\) −8.64010e8 + 9.16747e8i −1.29579 + 1.37488i
\(333\) −5.75318e8 4.02517e8i −0.853794 0.597350i
\(334\) 1.04213e7 + 7.03935e8i 0.0153042 + 1.03376i
\(335\) 1.18920e9 1.72821
\(336\) −5.96681e7 4.03899e8i −0.0858133 0.580878i
\(337\) 5.23664e8 0.745330 0.372665 0.927966i \(-0.378444\pi\)
0.372665 + 0.927966i \(0.378444\pi\)
\(338\) 4.14699e6 + 2.80119e8i 0.00584150 + 0.394579i
\(339\) −1.05059e9 + 9.21157e7i −1.46465 + 0.128421i
\(340\) 6.52606e8 + 6.15064e8i 0.900482 + 0.848680i
\(341\) 7.15275e8 7.15275e8i 0.976860 0.976860i
\(342\) 2.58749e8 + 1.75384e8i 0.349773 + 0.237082i
\(343\) 7.26369e8 0.971914
\(344\) 7.43637e7 8.12803e7i 0.0984932 0.107654i
\(345\) −5.16267e8 + 6.15501e8i −0.676874 + 0.806978i
\(346\) 6.45108e8 + 6.26286e8i 0.837271 + 0.812842i
\(347\) −3.76993e8 3.76993e8i −0.484373 0.484373i 0.422152 0.906525i \(-0.361275\pi\)
−0.906525 + 0.422152i \(0.861275\pi\)
\(348\) 3.27808e8 4.15185e8i 0.416958 0.528098i
\(349\) −2.64599e8 + 2.64599e8i −0.333195 + 0.333195i −0.853799 0.520603i \(-0.825707\pi\)
0.520603 + 0.853799i \(0.325707\pi\)
\(350\) −7.02473e6 4.74504e8i −0.00875773 0.591564i
\(351\) 8.28851e8 + 4.77908e8i 1.02306 + 0.589888i
\(352\) −9.67955e8 8.34313e8i −1.18292 1.01960i
\(353\) 4.70363e8i 0.569143i −0.958655 0.284571i \(-0.908149\pi\)
0.958655 0.284571i \(-0.0918513\pi\)
\(354\) 2.95092e8 3.62581e8i 0.353546 0.434404i
\(355\) −1.00969e9 1.00969e9i −1.19781 1.19781i
\(356\) −3.41357e8 + 1.01094e7i −0.400990 + 0.0118754i
\(357\) −4.39156e8 + 3.85051e7i −0.510834 + 0.0447899i
\(358\) 5.62770e6 5.79683e6i 0.00648246 0.00667728i
\(359\) 7.41464e8i 0.845785i −0.906180 0.422892i \(-0.861015\pi\)
0.906180 0.422892i \(-0.138985\pi\)
\(360\) −6.72700e8 + 1.05863e9i −0.759911 + 1.19587i
\(361\) 7.34272e8i 0.821451i
\(362\) 6.18978e8 + 6.00918e8i 0.685796 + 0.665787i
\(363\) −1.30628e9 + 1.14535e8i −1.43339 + 0.125679i
\(364\) 4.37618e8 4.64329e8i 0.475598 0.504628i
\(365\) 1.26202e9 + 1.26202e9i 1.35844 + 1.35844i
\(366\) 1.21442e9 + 9.88377e8i 1.29475 + 1.05375i
\(367\) 1.94756e8i 0.205665i 0.994699 + 0.102832i \(0.0327905\pi\)
−0.994699 + 0.102832i \(0.967209\pi\)
\(368\) −4.20566e7 7.09428e8i −0.0439913 0.742064i
\(369\) −1.39205e9 + 2.46001e8i −1.44232 + 0.254885i
\(370\) 1.43836e9 2.12940e7i 1.47625 0.0218550i
\(371\) −4.36442e8 + 4.36442e8i −0.443730 + 0.443730i
\(372\) 8.72307e8 1.02584e8i 0.878555 0.103319i
\(373\) 2.27250e8 + 2.27250e8i 0.226737 + 0.226737i 0.811328 0.584591i \(-0.198745\pi\)
−0.584591 + 0.811328i \(0.698745\pi\)
\(374\) −9.61116e8 + 9.90001e8i −0.950004 + 0.978555i
\(375\) −7.04091e6 + 8.39426e6i −0.00689476 + 0.00822003i
\(376\) 9.64658e8 4.28685e7i 0.935871 0.0415893i
\(377\) 8.26700e8 0.794609
\(378\) −1.68721e8 5.93054e8i −0.160675 0.564772i
\(379\) −9.77044e8 + 9.77044e8i −0.921885 + 0.921885i −0.997163 0.0752772i \(-0.976016\pi\)
0.0752772 + 0.997163i \(0.476016\pi\)
\(380\) −6.40128e8 + 1.89575e7i −0.598445 + 0.0177231i
\(381\) 1.28188e9 1.12395e8i 1.18743 0.104114i
\(382\) 9.09474e8 1.34642e7i 0.834773 0.0123583i
\(383\) −1.39271e9 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(384\) −2.10730e8 1.08939e9i −0.189919 0.981800i
\(385\) 1.45485e9 1.29929
\(386\) −1.01815e9 + 1.50731e7i −0.901066 + 0.0133397i
\(387\) 9.53752e7 1.36320e8i 0.0836463 0.119556i
\(388\) 2.07136e9 6.13437e7i 1.80030 0.0533162i
\(389\) −9.65687e8 + 9.65687e8i −0.831788 + 0.831788i −0.987761 0.155973i \(-0.950149\pi\)
0.155973 + 0.987761i \(0.450149\pi\)
\(390\) −1.94991e9 + 2.00095e8i −1.66452 + 0.170809i
\(391\) −7.67346e8 −0.649191
\(392\) 7.80653e8 3.46915e7i 0.654571 0.0290885i
\(393\) 5.12342e8 + 4.29740e8i 0.425781 + 0.357135i
\(394\) −4.44430e7 + 4.57787e7i −0.0366072 + 0.0377074i
\(395\) −8.30932e8 8.30932e8i −0.678384 0.678384i
\(396\) −1.61334e9 1.05904e9i −1.30555 0.856993i
\(397\) −3.86610e8 + 3.86610e8i −0.310103 + 0.310103i −0.844949 0.534846i \(-0.820369\pi\)
0.534846 + 0.844949i \(0.320369\pi\)
\(398\) −7.79540e8 + 1.15406e7i −0.619795 + 0.00917567i
\(399\) 2.02314e8 2.41202e8i 0.159449 0.190097i
\(400\) −7.63221e7 1.28743e9i −0.0596267 1.00581i
\(401\) 2.36223e9i 1.82944i −0.404090 0.914719i \(-0.632412\pi\)
0.404090 0.914719i \(-0.367588\pi\)
\(402\) −1.00286e9 + 1.23222e9i −0.769928 + 0.946013i
\(403\) 9.70583e8 + 9.70583e8i 0.738695 + 0.738695i
\(404\) −2.26344e8 + 2.40160e8i −0.170779 + 0.181203i
\(405\) −7.99224e8 + 1.71734e9i −0.597828 + 1.28459i
\(406\) −3.82260e8 3.71107e8i −0.283477 0.275206i
\(407\) 2.21335e9i 1.62731i
\(408\) −1.18766e9 + 1.57527e8i −0.865731 + 0.114827i
\(409\) 1.57545e9i 1.13861i −0.822127 0.569304i \(-0.807213\pi\)
0.822127 0.569304i \(-0.192787\pi\)
\(410\) 2.01734e9 2.07797e9i 1.44556 1.48900i
\(411\) −8.01376e7 9.13978e8i −0.0569364 0.649366i
\(412\) −2.63503e9 + 7.80371e7i −1.85629 + 0.0549745i
\(413\) −3.32921e8 3.32921e8i −0.232550 0.232550i
\(414\) −2.02395e8 1.05400e9i −0.140184 0.730029i
\(415\) 3.89763e9i 2.67690i
\(416\) 1.13211e9 1.31345e9i 0.771014 0.894516i
\(417\) 3.06918e8 + 2.57436e8i 0.207275 + 0.173857i
\(418\) −1.45859e7 9.85245e8i −0.00976826 0.659823i
\(419\) 8.92222e8 8.92222e8i 0.592549 0.592549i −0.345771 0.938319i \(-0.612382\pi\)
0.938319 + 0.345771i \(0.112382\pi\)
\(420\) 9.91449e8 + 7.82797e8i 0.652977 + 0.515557i
\(421\) 2.06046e9 + 2.06046e9i 1.34579 + 1.34579i 0.890183 + 0.455603i \(0.150576\pi\)
0.455603 + 0.890183i \(0.349424\pi\)
\(422\) 6.53572e7 + 6.34503e7i 0.0423350 + 0.0410998i
\(423\) 1.43601e9 2.53770e8i 0.922501 0.163023i
\(424\) −1.13228e9 + 1.23760e9i −0.721398 + 0.788497i
\(425\) −1.39254e9 −0.879925
\(426\) 1.89770e9 1.94737e8i 1.18931 0.122044i
\(427\) 1.11508e9 1.11508e9i 0.693121 0.693121i
\(428\) −2.67523e8 2.52133e8i −0.164933 0.155445i
\(429\) −2.63428e8 3.00443e9i −0.161087 1.83722i
\(430\) 5.04555e6 + 3.40815e8i 0.00306034 + 0.206718i
\(431\) 1.08406e9 0.652204 0.326102 0.945335i \(-0.394265\pi\)
0.326102 + 0.945335i \(0.394265\pi\)
\(432\) −5.29631e8 1.58979e9i −0.316068 0.948737i
\(433\) −3.10584e9 −1.83853 −0.919265 0.393639i \(-0.871216\pi\)
−0.919265 + 0.393639i \(0.871216\pi\)
\(434\) −1.30943e7 8.84487e8i −0.00768895 0.519370i
\(435\) 1.42959e8 + 1.63046e9i 0.0832718 + 0.949725i
\(436\) −4.45035e8 + 4.72199e8i −0.257153 + 0.272849i
\(437\) 3.87482e8 3.87482e8i 0.222109 0.222109i
\(438\) −2.37195e9 + 2.43404e8i −1.34880 + 0.138410i
\(439\) −1.07461e9 −0.606212 −0.303106 0.952957i \(-0.598024\pi\)
−0.303106 + 0.952957i \(0.598024\pi\)
\(440\) 3.94991e9 1.75530e8i 2.21056 0.0982354i
\(441\) 1.16210e9 2.05364e8i 0.645219 0.114022i
\(442\) −1.34337e9 1.30417e9i −0.739976 0.718386i
\(443\) 2.15347e9 + 2.15347e9i 1.17686 + 1.17686i 0.980539 + 0.196323i \(0.0629002\pi\)
0.196323 + 0.980539i \(0.437100\pi\)
\(444\) −1.19092e9 + 1.50835e9i −0.645715 + 0.817829i
\(445\) 7.47145e8 7.47145e8i 0.401925 0.401925i
\(446\) −4.18609e7 2.82761e9i −0.0223428 1.50920i
\(447\) 1.14127e9 + 9.57270e8i 0.604383 + 0.506942i
\(448\) −1.11309e9 + 9.91253e7i −0.584868 + 0.0520849i
\(449\) 6.24414e8i 0.325544i 0.986664 + 0.162772i \(0.0520435\pi\)
−0.986664 + 0.162772i \(0.947956\pi\)
\(450\) −3.67295e8 1.91274e9i −0.190008 0.989494i
\(451\) 3.15093e9 + 3.15093e9i 1.61741 + 1.61741i
\(452\) 8.54489e7 + 2.88530e9i 0.0435233 + 1.46963i
\(453\) −3.18184e7 3.62893e8i −0.0160818 0.183415i
\(454\) −1.16966e8 + 1.20481e8i −0.0586628 + 0.0604258i
\(455\) 1.97414e9i 0.982510i
\(456\) 5.20182e8 6.79273e8i 0.256909 0.335481i
\(457\) 4.78471e8i 0.234503i 0.993102 + 0.117252i \(0.0374084\pi\)
−0.993102 + 0.117252i \(0.962592\pi\)
\(458\) −9.06189e7 8.79749e7i −0.0440747 0.0427888i
\(459\) −1.74740e9 + 4.69280e8i −0.843426 + 0.226510i
\(460\) 1.60015e9 + 1.50810e9i 0.766493 + 0.722399i
\(461\) 1.57702e8 + 1.57702e8i 0.0749696 + 0.0749696i 0.743597 0.668628i \(-0.233118\pi\)
−0.668628 + 0.743597i \(0.733118\pi\)
\(462\) −1.22688e9 + 1.50748e9i −0.578838 + 0.711220i
\(463\) 1.92607e9i 0.901860i 0.892559 + 0.450930i \(0.148908\pi\)
−0.892559 + 0.450930i \(0.851092\pi\)
\(464\) −1.08261e9 9.61436e8i −0.503107 0.446794i
\(465\) −1.74639e9 + 2.08207e9i −0.805483 + 0.960308i
\(466\) −3.78323e8 + 5.60083e6i −0.173186 + 0.00256391i
\(467\) −1.93250e9 + 1.93250e9i −0.878031 + 0.878031i −0.993331 0.115300i \(-0.963217\pi\)
0.115300 + 0.993331i \(0.463217\pi\)
\(468\) 1.43705e9 2.18920e9i 0.648052 0.987244i
\(469\) 1.13142e9 + 1.13142e9i 0.506431 + 0.506431i
\(470\) −2.08105e9 + 2.14359e9i −0.924570 + 0.952357i
\(471\) 3.08159e8 + 2.58477e8i 0.135895 + 0.113985i
\(472\) −9.44050e8 8.63714e8i −0.413236 0.378071i
\(473\) −5.24446e8 −0.227870
\(474\) 1.56173e9 1.60260e8i 0.673567 0.0691197i
\(475\) 7.03182e8 7.03182e8i 0.301051 0.301051i
\(476\) 3.57184e7 + 1.20608e9i 0.0151799 + 0.512569i
\(477\) −1.45221e9 + 2.07565e9i −0.612655 + 0.875669i
\(478\) 1.00180e9 1.48311e7i 0.419552 0.00621120i
\(479\) −1.79615e9 −0.746738 −0.373369 0.927683i \(-0.621797\pi\)
−0.373369 + 0.927683i \(0.621797\pi\)
\(480\) 2.78623e9 + 2.00567e9i 1.14993 + 0.827782i
\(481\) −3.00337e9 −1.23056
\(482\) 1.74584e9 2.58461e7i 0.710135 0.0105131i
\(483\) −1.07678e9 + 9.44122e7i −0.434824 + 0.0381253i
\(484\) 1.06245e8 + 3.58753e9i 0.0425943 + 1.43826i
\(485\) −4.53368e9 + 4.53368e9i −1.80449 + 1.80449i
\(486\) −1.10548e9 2.27639e9i −0.436842 0.899538i
\(487\) 3.50227e8 0.137404 0.0687018 0.997637i \(-0.478114\pi\)
0.0687018 + 0.997637i \(0.478114\pi\)
\(488\) 2.89291e9 3.16199e9i 1.12685 1.23166i
\(489\) 2.32900e9 2.77667e9i 0.900719 1.07385i
\(490\) −1.68410e9 + 1.73471e9i −0.646667 + 0.666101i
\(491\) −2.16242e9 2.16242e9i −0.824433 0.824433i 0.162307 0.986740i \(-0.448107\pi\)
−0.986740 + 0.162307i \(0.948107\pi\)
\(492\) 4.51903e8 + 3.84269e9i 0.171067 + 1.45465i
\(493\) −1.10546e9 + 1.10546e9i −0.415508 + 0.415508i
\(494\) 1.33692e9 1.97922e7i 0.498953 0.00738669i
\(495\) 5.87993e9 1.03909e9i 2.17898 0.385066i
\(496\) −1.42266e8 2.39980e9i −0.0523499 0.883059i
\(497\) 1.92127e9i 0.702007i
\(498\) 4.03863e9 + 3.28691e9i 1.46532 + 1.19257i
\(499\) −1.89630e8 1.89630e8i −0.0683213 0.0683213i 0.672121 0.740442i \(-0.265384\pi\)
−0.740442 + 0.672121i \(0.765384\pi\)
\(500\) 2.18230e7 + 2.05676e7i 0.00780764 + 0.00735849i
\(501\) 2.89892e9 2.54177e8i 1.02992 0.0903035i
\(502\) −9.89089e8 9.60230e8i −0.348957 0.338776i
\(503\) 4.17355e9i 1.46224i −0.682251 0.731118i \(-0.738999\pi\)
0.682251 0.731118i \(-0.261001\pi\)
\(504\) −1.64721e9 + 3.67177e8i −0.573117 + 0.127752i
\(505\) 1.02106e9i 0.352802i
\(506\) −2.35660e9 + 2.42742e9i −0.808646 + 0.832949i
\(507\) 1.15358e9 1.01146e8i 0.393114 0.0344682i
\(508\) −1.04260e8 3.52050e9i −0.0352855 1.19147i
\(509\) 3.30226e9 + 3.30226e9i 1.10994 + 1.10994i 0.993158 + 0.116781i \(0.0372575\pi\)
0.116781 + 0.993158i \(0.462743\pi\)
\(510\) 2.33985e9 2.87499e9i 0.781076 0.959711i
\(511\) 2.40141e9i 0.796148i
\(512\) −3.01009e9 + 4.03422e8i −0.991138 + 0.132836i
\(513\) 6.45403e8 1.11934e9i 0.211067 0.366060i
\(514\) −8.40924e7 5.68024e9i −0.0273140 1.84500i
\(515\) 5.76743e9 5.76743e9i 1.86062 1.86062i
\(516\) −3.57400e8 2.82184e8i −0.114520 0.0904188i
\(517\) −3.25044e9 3.25044e9i −1.03449 1.03449i
\(518\) 1.38874e9 + 1.34822e9i 0.439002 + 0.426193i
\(519\) 2.38837e9 2.84744e9i 0.749921 0.894066i
\(520\) 2.38184e8 + 5.35978e9i 0.0742849 + 1.67161i
\(521\) −1.67425e9 −0.518666 −0.259333 0.965788i \(-0.583503\pi\)
−0.259333 + 0.965788i \(0.583503\pi\)
\(522\) −1.81000e9 1.22685e9i −0.556971 0.377524i
\(523\) −3.73056e9 + 3.73056e9i −1.14030 + 1.14030i −0.151903 + 0.988395i \(0.548540\pi\)
−0.988395 + 0.151903i \(0.951460\pi\)
\(524\) 1.25534e9 1.33196e9i 0.381155 0.404420i
\(525\) −1.95409e9 + 1.71334e8i −0.589368 + 0.0516757i
\(526\) 2.22517e7 + 1.50305e9i 0.00666674 + 0.450323i
\(527\) −2.59572e9 −0.772541
\(528\) −3.14911e9 + 4.24083e9i −0.931043 + 1.25381i
\(529\) 1.52334e9 0.447407
\(530\) −7.68252e7 5.18936e9i −0.0224150 1.51408i
\(531\) −1.58332e9 1.10776e9i −0.458921 0.321081i
\(532\) −6.27065e8 5.90992e8i −0.180560 0.170173i
\(533\) −4.27562e9 + 4.27562e9i −1.22308 + 1.22308i
\(534\) 1.44101e8 + 1.40425e9i 0.0409516 + 0.399070i
\(535\) 1.13740e9 0.321125
\(536\) 3.20833e9 + 2.93531e9i 0.899916 + 0.823336i
\(537\) −2.55866e7 2.14615e7i −0.00713023 0.00598066i
\(538\) 1.41874e9 + 1.37735e9i 0.392795 + 0.381334i
\(539\) −2.63043e9 2.63043e9i −0.723545 0.723545i
\(540\) 4.56615e9 + 2.45564e9i 1.24788 + 0.671099i
\(541\) 3.25585e8 3.25585e8i 0.0884044 0.0884044i −0.661522 0.749926i \(-0.730089\pi\)
0.749926 + 0.661522i \(0.230089\pi\)
\(542\) 6.12188e7 + 4.13518e9i 0.0165153 + 1.11557i
\(543\) 2.29163e9 2.73211e9i 0.614249 0.732316i
\(544\) 2.42492e8 + 3.27021e9i 0.0645805 + 0.870921i
\(545\) 2.00759e9i 0.531237i
\(546\) −2.04555e9 1.66481e9i −0.537820 0.437713i
\(547\) −1.62782e9 1.62782e9i −0.425256 0.425256i 0.461753 0.887009i \(-0.347221\pi\)
−0.887009 + 0.461753i \(0.847221\pi\)
\(548\) −2.51012e9 + 7.43377e7i −0.651572 + 0.0192964i
\(549\) 3.71031e9 5.30315e9i 0.956988 1.36783i
\(550\) −4.27663e9 + 4.40515e9i −1.09605 + 1.12899i
\(551\) 1.11644e9i 0.284318i
\(552\) −2.91208e9 + 3.86246e8i −0.736913 + 0.0977410i
\(553\) 1.58113e9i 0.397584i
\(554\) 3.33462e8 + 3.23733e8i 0.0833226 + 0.0808915i
\(555\) −5.19364e8 5.92340e9i −0.128957 1.47077i
\(556\) 7.52010e8 7.97912e8i 0.185550 0.196876i
\(557\) 4.72376e9 + 4.72376e9i 1.15823 + 1.15823i 0.984856 + 0.173373i \(0.0554665\pi\)
0.173373 + 0.984856i \(0.444534\pi\)
\(558\) −6.84647e8 3.56540e9i −0.166820 0.868738i
\(559\) 7.11641e8i 0.172314i
\(560\) 2.29588e9 2.58525e9i 0.552448 0.622076i
\(561\) 4.36977e9 + 3.66526e9i 1.04493 + 0.876465i
\(562\) 2.36552e8 3.50200e6i 0.0562146 0.000832222i
\(563\) −1.05595e9 + 1.05595e9i −0.249381 + 0.249381i −0.820717 0.571335i \(-0.806426\pi\)
0.571335 + 0.820717i \(0.306426\pi\)
\(564\) −4.66174e8 3.96405e9i −0.109414 0.930383i
\(565\) −6.31521e9 6.31521e9i −1.47305 1.47305i
\(566\) 2.36390e9 2.43494e9i 0.547988 0.564457i
\(567\) −2.39431e9 + 8.73515e8i −0.551618 + 0.201247i
\(568\) −2.31806e8 5.21626e9i −0.0530768 1.19437i
\(569\) −3.53716e9 −0.804937 −0.402469 0.915434i \(-0.631848\pi\)
−0.402469 + 0.915434i \(0.631848\pi\)
\(570\) 2.70224e8 + 2.63331e9i 0.0611169 + 0.595580i
\(571\) 1.10635e9 1.10635e9i 0.248696 0.248696i −0.571740 0.820435i \(-0.693731\pi\)
0.820435 + 0.571740i \(0.193731\pi\)
\(572\) −8.25125e9 + 2.44363e8i −1.84346 + 0.0545945i
\(573\) −3.28393e8 3.74537e9i −0.0729211 0.831674i
\(574\) 3.89634e9 5.76829e7i 0.859935 0.0127308i
\(575\) −3.41442e9 −0.748995
\(576\) −4.42789e9 + 1.19563e9i −0.965424 + 0.260686i
\(577\) −4.31286e9 −0.934652 −0.467326 0.884085i \(-0.654782\pi\)
−0.467326 + 0.884085i \(0.654782\pi\)
\(578\) −1.10165e9 + 1.63092e7i −0.237299 + 0.00351307i
\(579\) 3.67635e8 + 4.19292e9i 0.0787121 + 0.897721i
\(580\) 4.47784e9 1.32612e8i 0.952950 0.0282218i
\(581\) 3.70827e9 3.70827e9i 0.784431 0.784431i
\(582\) −8.74403e8 8.52099e9i −0.183857 1.79168i
\(583\) 7.98539e9 1.66900
\(584\) 2.89736e8 + 6.51985e9i 0.0601946 + 1.35454i
\(585\) 1.40998e9 + 7.97869e9i 0.291184 + 1.64773i
\(586\) 3.25899e9 3.35694e9i 0.669024 0.689130i
\(587\) 1.95206e9 + 1.95206e9i 0.398345 + 0.398345i 0.877649 0.479304i \(-0.159111\pi\)
−0.479304 + 0.877649i \(0.659111\pi\)
\(588\) −3.77253e8 3.20792e9i −0.0765265 0.650732i
\(589\) 1.31075e9 1.31075e9i 0.264311 0.264311i
\(590\) 3.95848e9 5.86028e7i 0.793499 0.0117472i
\(591\) 2.02063e8 + 1.69485e8i 0.0402652 + 0.0337735i
\(592\) 3.93309e9 + 3.49286e9i 0.779127 + 0.691920i
\(593\) 4.52044e8i 0.0890204i −0.999009 0.0445102i \(-0.985827\pi\)
0.999009 0.0445102i \(-0.0141727\pi\)
\(594\) −3.88191e9 + 6.96892e9i −0.759964 + 1.36431i
\(595\) −2.63981e9 2.63981e9i −0.513764 0.513764i
\(596\) 2.79634e9 2.96702e9i 0.541038 0.574062i
\(597\) 2.81477e8 + 3.21028e9i 0.0541418 + 0.617493i
\(598\) −3.29386e9 3.19776e9i −0.629870 0.611492i
\(599\) 5.87175e9i 1.11628i 0.829746 + 0.558141i \(0.188485\pi\)
−0.829746 + 0.558141i \(0.811515\pi\)
\(600\) −5.28468e9 + 7.00938e8i −0.998825 + 0.132480i
\(601\) 2.05570e9i 0.386276i 0.981172 + 0.193138i \(0.0618666\pi\)
−0.981172 + 0.193138i \(0.938133\pi\)
\(602\) −3.19457e8 + 3.29058e8i −0.0596794 + 0.0614730i
\(603\) 5.38087e9 + 3.76468e9i 0.999406 + 0.699226i
\(604\) −9.96636e8 + 2.95156e7i −0.184038 + 0.00545032i
\(605\) −7.85219e9 7.85219e9i −1.44161 1.44161i
\(606\) 1.05800e9 + 8.61068e8i 0.193122 + 0.157175i
\(607\) 5.45104e9i 0.989278i 0.869098 + 0.494639i \(0.164700\pi\)
−0.869098 + 0.494639i \(0.835300\pi\)
\(608\) −1.77379e9 1.52889e9i −0.320066 0.275875i
\(609\) −1.41523e9 + 1.68726e9i −0.253903 + 0.302706i
\(610\) 1.96283e8 + 1.32585e10i 0.0350130 + 2.36504i
\(611\) 4.41064e9 4.41064e9i 0.782272 0.782272i
\(612\) 1.00578e9 + 4.84901e9i 0.177367 + 0.855112i
\(613\) −2.12529e9 2.12529e9i −0.372654 0.372654i 0.495789 0.868443i \(-0.334879\pi\)
−0.868443 + 0.495789i \(0.834879\pi\)
\(614\) 4.69655e9 + 4.55952e9i 0.818822 + 0.794931i
\(615\) −9.17195e9 7.69322e9i −1.59001 1.33366i
\(616\) 3.92501e9 + 3.59101e9i 0.676564 + 0.618990i
\(617\) 1.13540e8 0.0194604 0.00973020 0.999953i \(-0.496903\pi\)
0.00973020 + 0.999953i \(0.496903\pi\)
\(618\) 1.11235e9 + 1.08398e10i 0.189576 + 1.84740i
\(619\) −2.55765e9 + 2.55765e9i −0.433435 + 0.433435i −0.889795 0.456360i \(-0.849153\pi\)
0.456360 + 0.889795i \(0.349153\pi\)
\(620\) 5.41287e9 + 5.10149e9i 0.912130 + 0.859658i
\(621\) −4.28451e9 + 1.15065e9i −0.717927 + 0.192806i
\(622\) −9.32779e7 6.30070e9i −0.0155422 1.04984i
\(623\) 1.42169e9 0.235558
\(624\) −5.75455e9 4.27315e9i −0.948124 0.704048i
\(625\) 6.05695e9 0.992371
\(626\) −1.56468e8 1.05691e10i −0.0254927 1.72197i
\(627\) −4.05740e9 + 3.55753e8i −0.657373 + 0.0576384i
\(628\) 7.55051e8 8.01138e8i 0.121651 0.129077i
\(629\) 4.01611e9 4.01611e9i 0.643469 0.643469i
\(630\) 2.92968e9 4.32223e9i 0.466798 0.688678i
\(631\) 2.74424e9 0.434830 0.217415 0.976079i \(-0.430237\pi\)
0.217415 + 0.976079i \(0.430237\pi\)
\(632\) −1.90766e8 4.29276e9i −0.0300602 0.676436i
\(633\) 2.41970e8 2.88480e8i 0.0379183 0.0452067i
\(634\) −8.01351e8 7.77970e8i −0.124885 0.121241i
\(635\) 7.70550e9 + 7.70550e9i 1.19424 + 1.19424i
\(636\) 5.44188e9 + 4.29663e9i 0.838782 + 0.662259i
\(637\) 3.56933e9 3.56933e9i 0.547140 0.547140i
\(638\) 1.02032e8 + 6.89201e9i 0.0155548 + 1.05069i
\(639\) −1.37223e9 7.76504e9i −0.208052 1.17731i
\(640\) 5.92141e9 7.29595e9i 0.892884 1.10015i
\(641\) 6.26005e9i 0.938803i −0.882985 0.469402i \(-0.844470\pi\)
0.882985 0.469402i \(-0.155530\pi\)
\(642\) −9.59177e8 + 1.17855e9i −0.143063 + 0.175782i
\(643\) −1.01424e9 1.01424e9i −0.150454 0.150454i 0.627867 0.778321i \(-0.283928\pi\)
−0.778321 + 0.627867i \(0.783928\pi\)
\(644\) 8.75793e7 + 2.95724e9i 0.0129211 + 0.436300i
\(645\) 1.40353e9 1.23062e8i 0.205951 0.0180578i
\(646\) −1.76126e9 + 1.81419e9i −0.257045 + 0.264770i
\(647\) 7.73864e9i 1.12331i 0.827371 + 0.561655i \(0.189835\pi\)
−0.827371 + 0.561655i \(0.810165\pi\)
\(648\) −6.39515e9 + 2.66047e9i −0.923291 + 0.384102i
\(649\) 6.09131e9i 0.874690i
\(650\) −5.97752e9 5.80311e9i −0.853737 0.828828i
\(651\) −3.64246e9 + 3.19371e8i −0.517442 + 0.0453693i
\(652\) −7.21866e9 6.80339e9i −1.01998 0.961300i
\(653\) 3.04674e9 + 3.04674e9i 0.428193 + 0.428193i 0.888013 0.459819i \(-0.152086\pi\)
−0.459819 + 0.888013i \(0.652086\pi\)
\(654\) 2.08022e9 + 1.69302e9i 0.290795 + 0.236668i
\(655\) 5.66295e9i 0.787405i
\(656\) 1.05716e10 6.26712e8i 1.46210 0.0866771i
\(657\) 1.71516e9 + 9.70559e9i 0.235953 + 1.33519i
\(658\) −4.01939e9 + 5.95046e7i −0.550009 + 0.00814254i
\(659\) −8.50044e8 + 8.50044e8i −0.115702 + 0.115702i −0.762588 0.646885i \(-0.776071\pi\)
0.646885 + 0.762588i \(0.276071\pi\)
\(660\) −1.90881e9 1.62313e10i −0.258439 2.19760i
\(661\) 7.19491e9 + 7.19491e9i 0.968992 + 0.968992i 0.999534 0.0305413i \(-0.00972312\pi\)
−0.0305413 + 0.999534i \(0.509723\pi\)
\(662\) −2.04374e9 + 2.10517e9i −0.273794 + 0.282022i
\(663\) −4.97353e9 + 5.92951e9i −0.662777 + 0.790171i
\(664\) 9.62055e9 1.05154e10i 1.27530 1.39392i
\(665\) 2.66602e9 0.351551
\(666\) 6.57568e9 + 4.45711e9i 0.862543 + 0.584646i
\(667\) −2.71053e9 + 2.71053e9i −0.353682 + 0.353682i
\(668\) −2.35782e8 7.96149e9i −0.0306050 1.03342i
\(669\) −1.16446e10 + 1.02099e9i −1.50360 + 0.131835i
\(670\) −1.34528e10 + 1.99160e8i −1.72803 + 0.0255823i
\(671\) −2.04021e10 −2.60703
\(672\) 7.42636e8 + 4.55910e9i 0.0944025 + 0.579544i
\(673\) 9.03391e9 1.14241 0.571206 0.820806i \(-0.306476\pi\)
0.571206 + 0.820806i \(0.306476\pi\)
\(674\) −5.92394e9 + 8.77002e7i −0.745248 + 0.0110329i
\(675\) −7.77529e9 + 2.08813e9i −0.973091 + 0.261333i
\(676\) −9.38253e7 3.16814e9i −0.0116817 0.394449i
\(677\) 8.12168e9 8.12168e9i 1.00597 1.00597i 0.00598859 0.999982i \(-0.498094\pi\)
0.999982 0.00598859i \(-0.00190624\pi\)
\(678\) 1.18693e10 1.21800e9i 1.46259 0.150087i
\(679\) −8.62684e9 −1.05757
\(680\) −7.48559e9 6.84859e9i −0.912946 0.835257i
\(681\) 5.31790e8 + 4.46053e8i 0.0645247 + 0.0541217i
\(682\) −7.97173e9 + 8.21131e9i −0.962293 + 0.991213i
\(683\) 7.13889e9 + 7.13889e9i 0.857350 + 0.857350i 0.991025 0.133675i \(-0.0426778\pi\)
−0.133675 + 0.991025i \(0.542678\pi\)
\(684\) −2.95646e9 1.94069e9i −0.353244 0.231879i
\(685\) 5.49402e9 5.49402e9i 0.653090 0.653090i
\(686\) −8.21703e9 + 1.21648e8i −0.971808 + 0.0143870i
\(687\) −3.35496e8 + 3.99983e8i −0.0394765 + 0.0470644i
\(688\) −8.27624e8 + 9.31935e8i −0.0968888 + 0.109100i
\(689\) 1.08357e10i 1.26208i
\(690\) 5.73718e9 7.04929e9i 0.664854 0.816909i
\(691\) 7.92433e9 + 7.92433e9i 0.913670 + 0.913670i 0.996559 0.0828893i \(-0.0264148\pi\)
−0.0828893 + 0.996559i \(0.526415\pi\)
\(692\) −7.40265e9 6.97680e9i −0.849212 0.800359i
\(693\) 6.58287e9 + 4.60565e9i 0.751361 + 0.525684i
\(694\) 4.32785e9 + 4.20158e9i 0.491490 + 0.477150i
\(695\) 3.39239e9i 0.383318i
\(696\) −3.63879e9 + 4.75167e9i −0.409096 + 0.534212i
\(697\) 1.14347e10i 1.27912i
\(698\) 2.94895e9 3.03758e9i 0.328227 0.338091i
\(699\) 1.36605e8 + 1.55800e9i 0.0151285 + 0.172543i
\(700\) 1.58934e8 + 5.36663e9i 0.0175135 + 0.591369i
\(701\) 6.73311e9 + 6.73311e9i 0.738248 + 0.738248i 0.972239 0.233991i \(-0.0751785\pi\)
−0.233991 + 0.972239i \(0.575179\pi\)
\(702\) −9.45639e9 5.26751e9i −1.03168 0.574679i
\(703\) 4.05598e9i 0.440304i
\(704\) 1.10897e10 + 9.27604e9i 1.19788 + 1.00198i
\(705\) 9.46161e9 + 7.93617e9i 1.01696 + 0.853000i
\(706\) 7.87735e7 + 5.32096e9i 0.00842488 + 0.569081i
\(707\) 9.71453e8 9.71453e8i 0.103384 0.103384i
\(708\) −3.27750e9 + 4.15110e9i −0.347077 + 0.439589i
\(709\) −2.91121e9 2.91121e9i −0.306769 0.306769i 0.536886 0.843655i \(-0.319601\pi\)
−0.843655 + 0.536886i \(0.819601\pi\)
\(710\) 1.15912e10 + 1.12530e10i 1.21541 + 1.17995i
\(711\) −1.12928e9 6.39030e9i −0.117831 0.666772i
\(712\) 3.85990e9 1.71530e8i 0.400771 0.0178099i
\(713\) −6.36455e9 −0.657589
\(714\) 4.96149e9 5.09135e8i 0.510115 0.0523467i
\(715\) 1.80599e10 1.80599e10i 1.84776 1.84776i
\(716\) −6.26923e7 + 6.65189e7i −0.00638291 + 0.00677251i
\(717\) −3.61732e8 4.12560e9i −0.0366497 0.417994i
\(718\) 1.24176e8 + 8.38779e9i 0.0125199 + 0.845692i
\(719\) −6.86830e9 −0.689126 −0.344563 0.938763i \(-0.611973\pi\)
−0.344563 + 0.938763i \(0.611973\pi\)
\(720\) 7.43261e9 1.20883e10i 0.742126 1.20699i
\(721\) 1.09745e10 1.09046
\(722\) 1.22971e8 + 8.30642e9i 0.0121597 + 0.821361i
\(723\) −6.30391e8 7.18968e9i −0.0620334 0.707498i
\(724\) −7.10281e9 6.69421e9i −0.695577 0.655562i
\(725\) −4.91891e9 + 4.91891e9i −0.479387 + 0.479387i
\(726\) 1.47581e10 1.51444e9i 1.43137 0.146884i
\(727\) −5.72289e9 −0.552389 −0.276194 0.961102i \(-0.589073\pi\)
−0.276194 + 0.961102i \(0.589073\pi\)
\(728\) −4.87277e9 + 5.32600e9i −0.468076 + 0.511613i
\(729\) −9.05297e9 + 5.24049e9i −0.865455 + 0.500986i
\(730\) −1.44879e10 1.40652e10i −1.37840 1.33819i
\(731\) 9.51605e8 + 9.51605e8i 0.0901044 + 0.0901044i
\(732\) −1.39036e10 1.09776e10i −1.31021 1.03447i
\(733\) 3.47201e7 3.47201e7i 0.00325625 0.00325625i −0.705477 0.708733i \(-0.749267\pi\)
0.708733 + 0.705477i \(0.249267\pi\)
\(734\) −3.26166e7 2.20317e9i −0.00304440 0.205642i
\(735\) 7.65684e9 + 6.42237e9i 0.711285 + 0.596609i
\(736\) 5.94575e8 + 8.01834e9i 0.0549711 + 0.741331i
\(737\) 2.07011e10i 1.90484i
\(738\) 1.57063e10 3.01601e9i 1.43839 0.276208i
\(739\) 5.02403e8 + 5.02403e8i 0.0457927 + 0.0457927i 0.729632 0.683840i \(-0.239691\pi\)
−0.683840 + 0.729632i \(0.739691\pi\)
\(740\) −1.62678e10 + 4.81775e8i −1.47577 + 0.0437053i
\(741\) −4.82735e8 5.50564e9i −0.0435858 0.497101i
\(742\) 4.86415e9 5.01033e9i 0.437112 0.450249i
\(743\) 1.36889e10i 1.22436i −0.790719 0.612179i \(-0.790293\pi\)
0.790719 0.612179i \(-0.209707\pi\)
\(744\) −9.85077e9 + 1.30656e9i −0.876930 + 0.116312i
\(745\) 1.26145e10i 1.11770i
\(746\) −2.60882e9 2.53270e9i −0.230069 0.223356i
\(747\) 1.23388e10 1.76359e10i 1.08306 1.54802i
\(748\) 1.07068e10 1.13603e10i 0.935414 0.992510i
\(749\) 1.08214e9 + 1.08214e9i 0.0941015 + 0.0941015i
\(750\) 7.82442e7 9.61390e7i 0.00677233 0.00832119i
\(751\) 6.06516e8i 0.0522519i 0.999659 + 0.0261260i \(0.00831710\pi\)
−0.999659 + 0.0261260i \(0.991683\pi\)
\(752\) −1.09055e10 + 6.46504e8i −0.935153 + 0.0554382i
\(753\) −3.66188e9 + 4.36574e9i −0.312552 + 0.372628i
\(754\) −9.35202e9 + 1.38451e8i −0.794522 + 0.0117624i
\(755\) 2.18139e9 2.18139e9i 0.184467 0.184467i
\(756\) 2.00797e9 + 6.68065e9i 0.169017 + 0.562331i
\(757\) −6.08954e9 6.08954e9i −0.510210 0.510210i 0.404381 0.914591i \(-0.367487\pi\)
−0.914591 + 0.404381i \(0.867487\pi\)
\(758\) 1.08892e10 1.12164e10i 0.908138 0.935431i
\(759\) 1.07144e10 + 8.98699e9i 0.889451 + 0.746050i
\(760\) 7.23825e9 3.21661e8i 0.598117 0.0265798i
\(761\) 6.17438e9 0.507863 0.253932 0.967222i \(-0.418276\pi\)
0.253932 + 0.967222i \(0.418276\pi\)
\(762\) −1.44824e10 + 1.48615e9i −1.18576 + 0.121680i
\(763\) 1.91006e9 1.91006e9i 0.155672 0.155672i
\(764\) −1.02861e10 + 3.04626e8i −0.834499 + 0.0247139i
\(765\) −1.25545e10 8.78367e9i −1.01388 0.709351i
\(766\) 1.57549e10 2.33242e8i 1.26653 0.0187502i
\(767\) −8.26552e9 −0.661434
\(768\) 2.56632e9 + 1.22884e10i 0.204431 + 0.978881i
\(769\) −2.10357e10 −1.66807 −0.834036 0.551710i \(-0.813975\pi\)
−0.834036 + 0.551710i \(0.813975\pi\)
\(770\) −1.64579e10 + 2.43649e8i −1.29914 + 0.0192330i
\(771\) −2.33922e10 + 2.05103e9i −1.83815 + 0.161169i
\(772\) 1.15153e10 3.41028e8i 0.900770 0.0266765i
\(773\) 1.83080e9 1.83080e9i 0.142565 0.142565i −0.632222 0.774787i \(-0.717857\pi\)
0.774787 + 0.632222i \(0.217857\pi\)
\(774\) −1.05610e9 + 1.55809e9i −0.0818674 + 0.120781i
\(775\) −1.15500e10 −0.891308
\(776\) −2.34219e10 + 1.04085e9i −1.79931 + 0.0799597i
\(777\) 5.14149e9 6.12976e9i 0.393202 0.468781i
\(778\) 1.07626e10 1.10860e10i 0.819384 0.844010i
\(779\) 5.77411e9 + 5.77411e9i 0.437627 + 0.437627i
\(780\) 2.20248e10 2.59013e9i 1.66181 0.195430i
\(781\) −1.75763e10 + 1.75763e10i −1.32023 + 1.32023i
\(782\) 8.68058e9 1.28510e8i 0.649120 0.00960981i
\(783\) −4.51474e9 + 7.83005e9i −0.336098 + 0.582906i
\(784\) −8.82530e9 + 5.23185e8i −0.654068 + 0.0387748i
\(785\) 3.40611e9i 0.251313i
\(786\) −5.86782e9 4.77562e9i −0.431020 0.350793i
\(787\) −8.83906e9 8.83906e9i −0.646390 0.646390i 0.305729 0.952119i \(-0.401100\pi\)
−0.952119 + 0.305729i \(0.901100\pi\)
\(788\) 4.95094e8 5.25313e8i 0.0360451 0.0382452i
\(789\) 6.18982e9 5.42723e8i 0.448651 0.0393377i
\(790\) 9.53906e9 + 9.26074e9i 0.688352 + 0.668268i
\(791\) 1.20168e10i 0.863317i
\(792\) 1.84282e10 + 1.17101e10i 1.31809 + 0.837574i
\(793\) 2.76844e10i 1.97142i
\(794\) 4.30876e9 4.43826e9i 0.305479 0.314659i
\(795\) −2.13706e10 + 1.87378e9i −1.50846 + 0.132261i
\(796\) 8.81659e9 2.61105e8i 0.619591 0.0183493i
\(797\) 5.23597e9 + 5.23597e9i 0.366347 + 0.366347i 0.866143 0.499796i \(-0.166592\pi\)
−0.499796 + 0.866143i \(0.666592\pi\)
\(798\) −2.24828e9 + 2.76247e9i −0.156617 + 0.192436i
\(799\) 1.17958e10i 0.818114i
\(800\) 1.07900e9 + 1.45513e10i 0.0745088 + 1.00481i
\(801\) 5.74593e9 1.01541e9i 0.395045 0.0698118i
\(802\) 3.95613e8 + 2.67227e10i 0.0270807 + 1.82924i
\(803\) 2.19688e10 2.19688e10i 1.49727 1.49727i
\(804\) 1.11385e10 1.41074e10i 0.755840 0.957307i
\(805\) −6.47265e9 6.47265e9i −0.437317 0.437317i
\(806\) −1.11422e10 1.08171e10i −0.749548 0.727679i
\(807\) 5.25258e9 6.26219e9i 0.351816 0.419439i
\(808\) 2.52029e9 2.75470e9i 0.168078 0.183711i
\(809\) −9.36137e9 −0.621612 −0.310806 0.950473i \(-0.600599\pi\)
−0.310806 + 0.950473i \(0.600599\pi\)
\(810\) 8.75359e9 1.95613e10i 0.578747 1.29330i
\(811\) −9.48370e9 + 9.48370e9i −0.624317 + 0.624317i −0.946632 0.322316i \(-0.895539\pi\)
0.322316 + 0.946632i \(0.395539\pi\)
\(812\) 4.38646e9 + 4.13412e9i 0.287520 + 0.270980i
\(813\) 1.70294e10 1.49313e9i 1.11143 0.0974500i
\(814\) −3.70678e8 2.50384e10i −0.0240886 1.62713i
\(815\) 3.06907e10 1.98589
\(816\) 1.34090e10 1.98092e9i 0.863936 0.127630i
\(817\) −9.61053e8 −0.0616553
\(818\) 2.63848e8 + 1.78223e10i 0.0168545 + 1.13848i
\(819\) −6.24958e9 + 8.93254e9i −0.397518 + 0.568174i
\(820\) −2.24731e10 + 2.38448e10i −1.42336 + 1.51024i
\(821\) 9.18151e9 9.18151e9i 0.579046 0.579046i −0.355594 0.934640i \(-0.615722\pi\)
0.934640 + 0.355594i \(0.115722\pi\)
\(822\) 1.05962e9 + 1.03259e10i 0.0665425 + 0.648452i
\(823\) −1.65417e10 −1.03438 −0.517191 0.855870i \(-0.673022\pi\)
−0.517191 + 0.855870i \(0.673022\pi\)
\(824\) 2.97957e10 1.32409e9i 1.85527 0.0824466i
\(825\) 1.94439e10 + 1.63091e10i 1.20558 + 1.01121i
\(826\) 3.82192e9 + 3.71041e9i 0.235967 + 0.229082i
\(827\) −4.53923e8 4.53923e8i −0.0279070 0.0279070i 0.693016 0.720923i \(-0.256282\pi\)
−0.720923 + 0.693016i \(0.756282\pi\)
\(828\) 2.46610e9 + 1.18895e10i 0.150975 + 0.727874i
\(829\) −1.27711e10 + 1.27711e10i −0.778554 + 0.778554i −0.979585 0.201031i \(-0.935571\pi\)
0.201031 + 0.979585i \(0.435571\pi\)
\(830\) 6.52752e8 + 4.40918e10i 0.0396255 + 2.67661i
\(831\) 1.23457e9 1.47187e9i 0.0746298 0.0889746i
\(832\) −1.25870e10 + 1.50480e10i −0.757688 + 0.905832i
\(833\) 9.54579e9i 0.572209i
\(834\) −3.51512e9 2.86083e9i −0.209826 0.170770i
\(835\) 1.74257e10 + 1.74257e10i 1.03583 + 1.03583i
\(836\) 3.30006e8 + 1.11431e10i 0.0195344 + 0.659606i
\(837\) −1.44933e10 + 3.89232e9i −0.854337 + 0.229440i
\(838\) −9.94381e9 + 1.02427e10i −0.583712 + 0.601255i
\(839\) 9.08084e8i 0.0530835i −0.999648 0.0265417i \(-0.991551\pi\)
0.999648 0.0265417i \(-0.00844949\pi\)
\(840\) −1.13468e10 8.68932e9i −0.660537 0.505834i
\(841\) 9.44014e9i 0.547259i
\(842\) −2.36539e10 2.29638e10i −1.36556 1.32572i
\(843\) −8.54143e7 9.74160e8i −0.00491060 0.0560059i
\(844\) −7.49977e8 7.06834e8i −0.0429388 0.0404686i
\(845\) 6.93427e9 + 6.93427e9i 0.395369 + 0.395369i
\(846\) −1.62023e10 + 3.11126e9i −0.919987 + 0.176661i
\(847\) 1.49414e10i 0.844889i
\(848\) 1.26017e10 1.41899e10i 0.709647 0.799089i
\(849\) −1.07476e10 9.01483e9i −0.602746 0.505569i
\(850\) 1.57530e10 2.33214e8i 0.879829 0.0130253i
\(851\) 9.84724e9 9.84724e9i 0.547723 0.547723i
\(852\) −2.14350e10 + 2.52077e9i −1.18737 + 0.139635i
\(853\) 5.94001e9 + 5.94001e9i 0.327692 + 0.327692i 0.851708 0.524017i \(-0.175567\pi\)
−0.524017 + 0.851708i \(0.675567\pi\)
\(854\) −1.24276e10 + 1.28011e10i −0.682785 + 0.703305i
\(855\) 1.07750e10 1.90415e9i 0.589572 0.104188i
\(856\) 3.06857e9 + 2.80745e9i 0.167216 + 0.152987i
\(857\) −4.67588e9 −0.253764 −0.126882 0.991918i \(-0.540497\pi\)
−0.126882 + 0.991918i \(0.540497\pi\)
\(858\) 3.48318e9 + 3.39434e10i 0.188266 + 1.83463i
\(859\) 3.42573e8 3.42573e8i 0.0184407 0.0184407i −0.697826 0.716267i \(-0.745849\pi\)
0.716267 + 0.697826i \(0.245849\pi\)
\(860\) −1.14155e8 3.85462e9i −0.00612000 0.206650i
\(861\) −1.40689e9 1.60458e10i −0.0751191 0.856743i
\(862\) −1.22634e10 + 1.81552e8i −0.652133 + 0.00965442i
\(863\) 2.75375e9 0.145843 0.0729216 0.997338i \(-0.476768\pi\)
0.0729216 + 0.997338i \(0.476768\pi\)
\(864\) 6.25768e9 + 1.78957e10i 0.330077 + 0.943954i
\(865\) 3.14730e10 1.65342
\(866\) 3.51347e10 5.20147e8i 1.83833 0.0272153i
\(867\) 3.97785e8 + 4.53678e9i 0.0207291 + 0.236418i
\(868\) 2.96257e8 + 1.00035e10i 0.0153762 + 0.519200i
\(869\) −1.44646e10 + 1.44646e10i −0.747715 + 0.747715i
\(870\) −1.89027e9 1.84206e10i −0.0973212 0.948388i
\(871\) 2.80901e10 1.44042
\(872\) 4.95536e9 5.41626e9i 0.253086 0.276625i
\(873\) −3.48664e10 + 6.16153e9i −1.77360 + 0.313429i
\(874\) −4.31849e9 + 4.44828e9i −0.218797 + 0.225373i
\(875\) −8.82747e7 8.82747e7i −0.00445459 0.00445459i
\(876\) 2.67918e10 3.15074e9i 1.34660 0.158361i
\(877\) 5.52325e9 5.52325e9i 0.276501 0.276501i −0.555210 0.831710i \(-0.687362\pi\)
0.831710 + 0.555210i \(0.187362\pi\)
\(878\) 1.21565e10 1.79969e8i 0.606146 0.00897361i
\(879\) −1.48172e10 1.24283e10i −0.735876 0.617235i
\(880\) −4.46539e10 + 2.64719e9i −2.20887 + 0.130947i
\(881\) 2.69323e9i 0.132696i −0.997797 0.0663480i \(-0.978865\pi\)
0.997797 0.0663480i \(-0.0211347\pi\)
\(882\) −1.31118e10 + 2.51779e9i −0.643461 + 0.123561i
\(883\) 3.24221e9 + 3.24221e9i 0.158482 + 0.158482i 0.781894 0.623412i \(-0.214254\pi\)
−0.623412 + 0.781894i \(0.714254\pi\)
\(884\) 1.54152e10 + 1.45285e10i 0.750529 + 0.707354i
\(885\) −1.42933e9 1.63017e10i −0.0693156 0.790553i
\(886\) −2.47217e10 2.40004e10i −1.19415 1.15931i
\(887\) 4.69795e9i 0.226035i −0.993593 0.113017i \(-0.963948\pi\)
0.993593 0.113017i \(-0.0360516\pi\)
\(888\) 1.32196e10 1.72626e10i 0.633538 0.827297i
\(889\) 1.46623e10i 0.699915i
\(890\) −8.32693e9 + 8.57718e9i −0.395931 + 0.407830i
\(891\) 2.98949e10 + 1.39126e10i 1.41588 + 0.658925i
\(892\) 9.47101e8 + 3.19802e10i 0.0446806 + 1.50870i
\(893\) −5.95647e9 5.95647e9i −0.279904 0.279904i
\(894\) −1.30709e10 1.06380e10i −0.611821 0.497940i
\(895\) 2.82811e8i 0.0131861i
\(896\) 1.25752e10 1.30777e9i 0.584033 0.0607368i
\(897\) −1.21948e10 + 1.45388e10i −0.564158 + 0.672596i
\(898\) −1.04573e8 7.06366e9i −0.00481895 0.325509i
\(899\) −9.16897e9 + 9.16897e9i −0.420883 + 0.420883i
\(900\) 4.47535e9 + 2.15764e10i 0.204634 + 0.986573i
\(901\) −1.44894e10 1.44894e10i −0.659956 0.659956i
\(902\) −3.61725e10 3.51171e10i −1.64118 1.59329i
\(903\) 1.45243e9 + 1.21826e9i 0.0656429 + 0.0550597i
\(904\) −1.44985e9 3.26256e10i −0.0652731 1.46882i
\(905\) 3.01982e10 1.35429
\(906\) 4.20720e8 + 4.09988e9i 0.0187951 + 0.183157i
\(907\) −2.62666e10 + 2.62666e10i −1.16890 + 1.16890i −0.186433 + 0.982468i \(0.559693\pi\)
−0.982468 + 0.186433i \(0.940307\pi\)
\(908\) 1.30299e9 1.38252e9i 0.0577619 0.0612875i
\(909\) 3.23240e9 4.62008e9i 0.142742 0.204021i
\(910\) −3.30616e8 2.23323e10i −0.0145438 0.982402i
\(911\) −1.83902e10 −0.805882 −0.402941 0.915226i \(-0.632012\pi\)
−0.402941 + 0.915226i \(0.632012\pi\)
\(912\) −5.77079e9 + 7.77137e9i −0.251914 + 0.339247i
\(913\) −6.78485e10 −2.95048
\(914\) −8.01314e7 5.41269e9i −0.00347129 0.234478i
\(915\) 5.46006e10 4.78738e9i 2.35626 0.206597i
\(916\) 1.03986e9 + 9.80037e8i 0.0447033 + 0.0421316i
\(917\) −5.38783e9 + 5.38783e9i −0.230739 + 0.230739i
\(918\) 1.96888e10 5.60136e9i 0.839981 0.238970i
\(919\) 2.04767e10 0.870272 0.435136 0.900365i \(-0.356700\pi\)
0.435136 + 0.900365i \(0.356700\pi\)
\(920\) −1.83542e10 1.67923e10i −0.777102 0.710974i
\(921\) 1.73879e10 2.07301e10i 0.733397 0.874365i
\(922\) −1.81041e9 1.75759e9i −0.0760711 0.0738516i
\(923\) −2.38499e10 2.38499e10i −0.998347 0.998347i
\(924\) 1.36266e10 1.72588e10i 0.568246 0.719711i
\(925\) 1.78702e10 1.78702e10i 0.742394 0.742394i
\(926\) −3.22567e8 2.17886e10i −0.0133500 0.901761i
\(927\) 4.43545e10 7.83826e9i 1.82877 0.323177i
\(928\) 1.24080e10 + 1.06949e10i 0.509665 + 0.439298i
\(929\) 4.17877e9i 0.170999i −0.996338 0.0854994i \(-0.972751\pi\)
0.996338 0.0854994i \(-0.0272486\pi\)
\(930\) 1.94073e10 2.38458e10i 0.791180 0.972126i
\(931\) −4.82029e9 4.82029e9i −0.195771 0.195771i
\(932\) 4.27883e9 1.26719e8i 0.173129 0.00512725i
\(933\) −2.59473e10 + 2.27506e9i −1.04594 + 0.0917080i
\(934\) 2.15377e10 2.21849e10i 0.864937 0.890932i
\(935\) 4.82994e10i 1.93242i
\(936\) −1.58899e10 + 2.50059e10i −0.633367 + 0.996729i
\(937\) 3.07879e10i 1.22262i 0.791392 + 0.611309i \(0.209357\pi\)
−0.791392 + 0.611309i \(0.790643\pi\)
\(938\) −1.29887e10 1.26097e10i −0.513872 0.498879i
\(939\) −4.35251e10 + 3.81628e9i −1.71558 + 0.150422i
\(940\) 2.31828e10 2.45978e10i 0.910371 0.965939i
\(941\) −1.22077e10 1.22077e10i −0.477606 0.477606i 0.426760 0.904365i \(-0.359655\pi\)
−0.904365 + 0.426760i \(0.859655\pi\)
\(942\) −3.52933e9 2.87240e9i −0.137567 0.111961i
\(943\) 2.80372e10i 1.08879i
\(944\) 1.08242e10 + 9.61264e9i 0.418787 + 0.371912i
\(945\) −1.86979e10 1.07811e10i −0.720746 0.415576i
\(946\) 5.93278e9 8.78311e7i 0.227845 0.00337310i
\(947\) −2.18974e10 + 2.18974e10i −0.837852 + 0.837852i −0.988576 0.150724i \(-0.951840\pi\)
0.150724 + 0.988576i \(0.451840\pi\)
\(948\) −1.76401e10 + 2.07449e9i −0.672470 + 0.0790828i
\(949\) 2.98103e10 + 2.98103e10i 1.13223 + 1.13223i
\(950\) −7.83696e9 + 8.07249e9i −0.296562 + 0.305474i
\(951\) −2.96682e9 + 3.53708e9i −0.111856 + 0.133356i
\(952\) −6.06050e8 1.36378e10i −0.0227656 0.512288i
\(953\) −4.29136e10 −1.60609 −0.803045 0.595918i \(-0.796788\pi\)
−0.803045 + 0.595918i \(0.796788\pi\)
\(954\) 1.60805e10 2.37240e10i 0.599625 0.884642i
\(955\) 2.25138e10 2.25138e10i 0.836443 0.836443i
\(956\) −1.13304e10 + 3.35552e8i −0.419414 + 0.0124210i
\(957\) 2.83824e10 2.48857e9i 1.04679 0.0917821i
\(958\) 2.03189e10 3.00808e8i 0.746656 0.0110538i
\(959\) 1.04542e10 0.382759
\(960\) −3.18551e10 2.22225e10i −1.16206 0.810669i
\(961\) 5.98305e9 0.217466
\(962\) 3.39756e10 5.02987e8i 1.23042 0.0182156i
\(963\) 5.14648e9 + 3.60069e9i 0.185703 + 0.129925i
\(964\) −1.97455e10 + 5.84767e8i −0.709902 + 0.0210239i
\(965\) −2.52041e10 + 2.52041e10i −0.902870 + 0.902870i
\(966\) 1.21653e10 1.24837e9i 0.434212 0.0445577i
\(967\) 3.78183e10 1.34496 0.672480 0.740116i \(-0.265229\pi\)
0.672480 + 0.740116i \(0.265229\pi\)
\(968\) −1.80271e9 4.05660e10i −0.0638798 1.43747i
\(969\) 8.00765e9 + 6.71663e9i 0.282730 + 0.237147i
\(970\) 5.05279e10 5.20464e10i 1.77758 1.83101i
\(971\) −1.84442e10 1.84442e10i −0.646537 0.646537i 0.305617 0.952155i \(-0.401137\pi\)
−0.952155 + 0.305617i \(0.901137\pi\)
\(972\) 1.28870e10 + 2.55664e10i 0.450110 + 0.892973i
\(973\) −3.22758e9 + 3.22758e9i −0.112326 + 0.112326i
\(974\) −3.96193e9 + 5.86539e7i −0.137389 + 0.00203395i
\(975\) −2.21304e10 + 2.63842e10i −0.764669 + 0.911649i
\(976\) −3.21964e10 + 3.62544e10i −1.10849 + 1.24820i
\(977\) 1.84798e10i 0.633968i 0.948431 + 0.316984i \(0.102670\pi\)
−0.948431 + 0.316984i \(0.897330\pi\)
\(978\) −2.58818e10 + 3.18010e10i −0.884724 + 1.08706i
\(979\) −1.30060e10 1.30060e10i −0.443001 0.443001i
\(980\) 1.87608e10 1.99059e10i 0.636736 0.675601i
\(981\) 6.35550e9 9.08393e9i 0.214935 0.307208i
\(982\) 2.48245e10 + 2.41002e10i 0.836547 + 0.812139i
\(983\) 1.10126e10i 0.369788i −0.982758 0.184894i \(-0.940806\pi\)
0.982758 0.184894i \(-0.0591942\pi\)
\(984\) −5.75569e9 4.33946e10i −0.192581 1.45196i
\(985\) 2.23342e9i 0.0744634i
\(986\) 1.23204e10 1.26906e10i 0.409312 0.421614i
\(987\) 1.45133e9 + 1.65525e10i 0.0480457 + 0.547967i
\(988\) −1.51205e10 + 4.47797e8i −0.498789 + 0.0147718i
\(989\) 2.33328e9 + 2.33328e9i 0.0766971 + 0.0766971i
\(990\) −6.63425e10 + 1.27394e10i −2.17304 + 0.417279i
\(991\) 4.11588e10i 1.34340i −0.740824 0.671700i \(-0.765565\pi\)
0.740824 0.671700i \(-0.234435\pi\)
\(992\) 2.01129e9 + 2.71239e10i 0.0654159 + 0.882188i
\(993\) 9.29200e9 + 7.79391e9i 0.301153 + 0.252600i
\(994\) 3.21763e8 + 2.17343e10i 0.0103916 + 0.701930i
\(995\) −1.92973e10 + 1.92973e10i −0.621035 + 0.621035i
\(996\) −4.62374e10 3.65067e10i −1.48281 1.17075i
\(997\) 3.46173e10 + 3.46173e10i 1.10627 + 1.10627i 0.993637 + 0.112629i \(0.0359272\pi\)
0.112629 + 0.993637i \(0.464073\pi\)
\(998\) 2.17695e9 + 2.11343e9i 0.0693251 + 0.0673024i
\(999\) 1.64019e10 2.84463e10i 0.520493 0.902707i
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 48.8.k.a.11.1 108
3.2 odd 2 inner 48.8.k.a.11.54 yes 108
16.3 odd 4 inner 48.8.k.a.35.54 yes 108
48.35 even 4 inner 48.8.k.a.35.1 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.8.k.a.11.1 108 1.1 even 1 trivial
48.8.k.a.11.54 yes 108 3.2 odd 2 inner
48.8.k.a.35.1 yes 108 48.35 even 4 inner
48.8.k.a.35.54 yes 108 16.3 odd 4 inner