Properties

Label 48.8.k.a.11.18
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 11.18
Character \(\chi\) \(=\) 48.11
Dual form 48.8.k.a.35.18

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-6.30926 - 9.39113i) q^{2} +(-45.6917 - 9.96321i) q^{3} +(-48.3865 + 118.502i) q^{4} +(-316.866 + 316.866i) q^{5} +(194.715 + 491.957i) q^{6} -1511.21 q^{7} +(1418.15 - 293.257i) q^{8} +(1988.47 + 910.472i) q^{9} +O(q^{10})\) \(q+(-6.30926 - 9.39113i) q^{2} +(-45.6917 - 9.96321i) q^{3} +(-48.3865 + 118.502i) q^{4} +(-316.866 + 316.866i) q^{5} +(194.715 + 491.957i) q^{6} -1511.21 q^{7} +(1418.15 - 293.257i) q^{8} +(1988.47 + 910.472i) q^{9} +(4974.91 + 976.537i) q^{10} +(-997.776 - 997.776i) q^{11} +(3391.52 - 4932.48i) q^{12} +(-8214.45 + 8214.45i) q^{13} +(9534.59 + 14191.9i) q^{14} +(17635.1 - 11321.1i) q^{15} +(-11701.5 - 11467.8i) q^{16} -2084.84i q^{17} +(-3995.41 - 24418.4i) q^{18} +(-31568.8 - 31568.8i) q^{19} +(-22217.2 - 52881.2i) q^{20} +(69049.6 + 15056.5i) q^{21} +(-3075.01 + 15665.5i) q^{22} +61890.6i q^{23} +(-67719.6 - 729.896i) q^{24} -122683. i q^{25} +(128970. + 25315.8i) q^{26} +(-81785.4 - 61412.6i) q^{27} +(73121.9 - 179081. i) q^{28} +(-7310.95 - 7310.95i) q^{29} +(-217583. - 94185.7i) q^{30} -32731.1i q^{31} +(-33867.7 + 182244. i) q^{32} +(35649.1 + 55531.2i) q^{33} +(-19579.0 + 13153.8i) q^{34} +(478849. - 478849. i) q^{35} +(-204108. + 191583. i) q^{36} +(122355. + 122355. i) q^{37} +(-97290.8 + 495643. i) q^{38} +(457175. - 293490. i) q^{39} +(-356440. + 542286. i) q^{40} -83043.4 q^{41} +(-294255. - 743449. i) q^{42} +(-159561. + 159561. i) q^{43} +(166517. - 69959.7i) q^{44} +(-918575. + 341580. i) q^{45} +(581222. - 390484. i) q^{46} +991040. q^{47} +(420406. + 640568. i) q^{48} +1.46020e6 q^{49} +(-1.15213e6 + 774036. i) q^{50} +(-20771.7 + 95260.0i) q^{51} +(-575962. - 1.37090e6i) q^{52} +(-1.01135e6 + 1.01135e6i) q^{53} +(-60728.0 + 1.15552e6i) q^{54} +632322. q^{55} +(-2.14312e6 + 443172. i) q^{56} +(1.12791e6 + 1.75696e6i) q^{57} +(-22531.3 + 114785. i) q^{58} +(692364. + 692364. i) q^{59} +(488277. + 2.63759e6i) q^{60} +(-528329. + 528329. i) q^{61} +(-307382. + 206509. i) q^{62} +(-3.00499e6 - 1.37591e6i) q^{63} +(1.92515e6 - 831766. i) q^{64} -5.20576e6i q^{65} +(296581. - 685146. i) q^{66} +(559587. + 559587. i) q^{67} +(247058. + 100878. i) q^{68} +(616628. - 2.82789e6i) q^{69} +(-7.51812e6 - 1.47575e6i) q^{70} -1.71256e6i q^{71} +(3.08695e6 + 708054. i) q^{72} +1.46382e6i q^{73} +(377081. - 1.92102e6i) q^{74} +(-1.22231e6 + 5.60558e6i) q^{75} +(5.26848e6 - 2.21347e6i) q^{76} +(1.50785e6 + 1.50785e6i) q^{77} +(-5.64064e6 - 2.44168e6i) q^{78} -7.53603e6i q^{79} +(7.34155e6 - 74052.3i) q^{80} +(3.12505e6 + 3.62089e6i) q^{81} +(523942. + 779871. i) q^{82} +(-1.84269e6 + 1.84269e6i) q^{83} +(-5.12529e6 + 7.45400e6i) q^{84} +(660615. + 660615. i) q^{85} +(2.50517e6 + 491746. i) q^{86} +(261209. + 406890. i) q^{87} +(-1.70760e6 - 1.12239e6i) q^{88} -5.79970e6 q^{89} +(9.00335e6 + 6.47133e6i) q^{90} +(1.24137e7 - 1.24137e7i) q^{91} +(-7.33416e6 - 2.99467e6i) q^{92} +(-326107. + 1.49554e6i) q^{93} +(-6.25273e6 - 9.30698e6i) q^{94} +2.00061e7 q^{95} +(3.36320e6 - 7.98959e6i) q^{96} -5.91455e6 q^{97} +(-9.21278e6 - 1.37129e7i) q^{98} +(-1.07560e6 - 2.89249e6i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −6.30926 9.39113i −0.557665 0.830066i
\(3\) −45.6917 9.96321i −0.977042 0.213047i
\(4\) −48.3865 + 118.502i −0.378019 + 0.925798i
\(5\) −316.866 + 316.866i −1.13365 + 1.13365i −0.144088 + 0.989565i \(0.546025\pi\)
−0.989565 + 0.144088i \(0.953975\pi\)
\(6\) 194.715 + 491.957i 0.368019 + 0.929818i
\(7\) −1511.21 −1.66525 −0.832627 0.553834i \(-0.813164\pi\)
−0.832627 + 0.553834i \(0.813164\pi\)
\(8\) 1418.15 293.257i 0.979281 0.202504i
\(9\) 1988.47 + 910.472i 0.909222 + 0.416311i
\(10\) 4974.91 + 976.537i 1.57321 + 0.308808i
\(11\) −997.776 997.776i −0.226026 0.226026i 0.585004 0.811030i \(-0.301093\pi\)
−0.811030 + 0.585004i \(0.801093\pi\)
\(12\) 3391.52 4932.48i 0.566579 0.824008i
\(13\) −8214.45 + 8214.45i −1.03700 + 1.03700i −0.0377070 + 0.999289i \(0.512005\pi\)
−0.999289 + 0.0377070i \(0.987995\pi\)
\(14\) 9534.59 + 14191.9i 0.928654 + 1.38227i
\(15\) 17635.1 11321.1i 1.34915 0.866106i
\(16\) −11701.5 11467.8i −0.714203 0.699939i
\(17\) 2084.84i 0.102920i −0.998675 0.0514602i \(-0.983612\pi\)
0.998675 0.0514602i \(-0.0163875\pi\)
\(18\) −3995.41 24418.4i −0.161476 0.986877i
\(19\) −31568.8 31568.8i −1.05590 1.05590i −0.998342 0.0575527i \(-0.981670\pi\)
−0.0575527 0.998342i \(-0.518330\pi\)
\(20\) −22217.2 52881.2i −0.620991 1.47808i
\(21\) 69049.6 + 15056.5i 1.62702 + 0.354777i
\(22\) −3075.01 + 15665.5i −0.0615698 + 0.313664i
\(23\) 61890.6i 1.06066i 0.847791 + 0.530331i \(0.177932\pi\)
−0.847791 + 0.530331i \(0.822068\pi\)
\(24\) −67719.6 729.896i −0.999942 0.0107776i
\(25\) 122683.i 1.57034i
\(26\) 128970. + 25315.8i 1.43907 + 0.282479i
\(27\) −81785.4 61412.6i −0.799655 0.600460i
\(28\) 73121.9 179081.i 0.629498 1.54169i
\(29\) −7310.95 7310.95i −0.0556648 0.0556648i 0.678726 0.734391i \(-0.262532\pi\)
−0.734391 + 0.678726i \(0.762532\pi\)
\(30\) −217583. 94185.7i −1.47130 0.636885i
\(31\) 32731.1i 0.197331i −0.995121 0.0986655i \(-0.968543\pi\)
0.995121 0.0986655i \(-0.0314574\pi\)
\(32\) −33867.7 + 182244.i −0.182709 + 0.983167i
\(33\) 35649.1 + 55531.2i 0.172683 + 0.268991i
\(34\) −19579.0 + 13153.8i −0.0854308 + 0.0573952i
\(35\) 478849. 478849.i 1.88782 1.88782i
\(36\) −204108. + 191583.i −0.729123 + 0.684382i
\(37\) 122355. + 122355.i 0.397114 + 0.397114i 0.877214 0.480100i \(-0.159400\pi\)
−0.480100 + 0.877214i \(0.659400\pi\)
\(38\) −97290.8 + 495643.i −0.287627 + 1.46530i
\(39\) 457175. 293490.i 1.23412 0.792260i
\(40\) −356440. + 542286.i −0.880596 + 1.33973i
\(41\) −83043.4 −0.188175 −0.0940874 0.995564i \(-0.529993\pi\)
−0.0940874 + 0.995564i \(0.529993\pi\)
\(42\) −294255. 743449.i −0.612846 1.54838i
\(43\) −159561. + 159561.i −0.306047 + 0.306047i −0.843374 0.537327i \(-0.819434\pi\)
0.537327 + 0.843374i \(0.319434\pi\)
\(44\) 166517. 69959.7i 0.294697 0.123812i
\(45\) −918575. + 341580.i −1.50269 + 0.558790i
\(46\) 581222. 390484.i 0.880419 0.591494i
\(47\) 991040. 1.39235 0.696176 0.717872i \(-0.254884\pi\)
0.696176 + 0.717872i \(0.254884\pi\)
\(48\) 420406. + 640568.i 0.548687 + 0.836028i
\(49\) 1.46020e6 1.77307
\(50\) −1.15213e6 + 774036.i −1.30348 + 0.875722i
\(51\) −20771.7 + 95260.0i −0.0219269 + 0.100558i
\(52\) −575962. 1.37090e6i −0.568044 1.35205i
\(53\) −1.01135e6 + 1.01135e6i −0.933117 + 0.933117i −0.997899 0.0647822i \(-0.979365\pi\)
0.0647822 + 0.997899i \(0.479365\pi\)
\(54\) −60728.0 + 1.15552e6i −0.0524821 + 0.998622i
\(55\) 632322. 0.512470
\(56\) −2.14312e6 + 443172.i −1.63075 + 0.337221i
\(57\) 1.12791e6 + 1.75696e6i 0.806699 + 1.25661i
\(58\) −22531.3 + 114785.i −0.0151631 + 0.0772478i
\(59\) 692364. + 692364.i 0.438887 + 0.438887i 0.891637 0.452751i \(-0.149557\pi\)
−0.452751 + 0.891637i \(0.649557\pi\)
\(60\) 488277. + 2.63759e6i 0.291835 + 1.57644i
\(61\) −528329. + 528329.i −0.298023 + 0.298023i −0.840239 0.542216i \(-0.817586\pi\)
0.542216 + 0.840239i \(0.317586\pi\)
\(62\) −307382. + 206509.i −0.163798 + 0.110045i
\(63\) −3.00499e6 1.37591e6i −1.51409 0.693264i
\(64\) 1.92515e6 831766.i 0.917984 0.396617i
\(65\) 5.20576e6i 2.35119i
\(66\) 296581. 685146.i 0.126981 0.293345i
\(67\) 559587. + 559587.i 0.227303 + 0.227303i 0.811565 0.584262i \(-0.198616\pi\)
−0.584262 + 0.811565i \(0.698616\pi\)
\(68\) 247058. + 100878.i 0.0952836 + 0.0389059i
\(69\) 616628. 2.82789e6i 0.225970 1.03631i
\(70\) −7.51812e6 1.47575e6i −2.61979 0.514244i
\(71\) 1.71256e6i 0.567861i −0.958845 0.283931i \(-0.908361\pi\)
0.958845 0.283931i \(-0.0916386\pi\)
\(72\) 3.08695e6 + 708054.i 0.974689 + 0.223564i
\(73\) 1.46382e6i 0.440410i 0.975454 + 0.220205i \(0.0706727\pi\)
−0.975454 + 0.220205i \(0.929327\pi\)
\(74\) 377081. 1.92102e6i 0.108174 0.551087i
\(75\) −1.22231e6 + 5.60558e6i −0.334555 + 1.53429i
\(76\) 5.26848e6 2.21347e6i 1.37669 0.578397i
\(77\) 1.50785e6 + 1.50785e6i 0.376391 + 0.376391i
\(78\) −5.64064e6 2.44168e6i −1.34585 0.582583i
\(79\) 7.53603e6i 1.71968i −0.510563 0.859840i \(-0.670563\pi\)
0.510563 0.859840i \(-0.329437\pi\)
\(80\) 7.34155e6 74052.3i 1.60315 0.0161705i
\(81\) 3.12505e6 + 3.62089e6i 0.653370 + 0.757039i
\(82\) 523942. + 779871.i 0.104939 + 0.156198i
\(83\) −1.84269e6 + 1.84269e6i −0.353736 + 0.353736i −0.861498 0.507762i \(-0.830473\pi\)
0.507762 + 0.861498i \(0.330473\pi\)
\(84\) −5.12529e6 + 7.45400e6i −0.943498 + 1.37218i
\(85\) 660615. + 660615.i 0.116676 + 0.116676i
\(86\) 2.50517e6 + 491746.i 0.424711 + 0.0833675i
\(87\) 261209. + 406890.i 0.0425276 + 0.0662460i
\(88\) −1.70760e6 1.12239e6i −0.267114 0.175572i
\(89\) −5.79970e6 −0.872049 −0.436024 0.899935i \(-0.643614\pi\)
−0.436024 + 0.899935i \(0.643614\pi\)
\(90\) 9.00335e6 + 6.47133e6i 1.30183 + 0.935718i
\(91\) 1.24137e7 1.24137e7i 1.72686 1.72686i
\(92\) −7.33416e6 2.99467e6i −0.981958 0.400951i
\(93\) −326107. + 1.49554e6i −0.0420407 + 0.192801i
\(94\) −6.25273e6 9.30698e6i −0.776466 1.15574i
\(95\) 2.00061e7 2.39404
\(96\) 3.36320e6 7.98959e6i 0.387975 0.921670i
\(97\) −5.91455e6 −0.657992 −0.328996 0.944331i \(-0.606710\pi\)
−0.328996 + 0.944331i \(0.606710\pi\)
\(98\) −9.21278e6 1.37129e7i −0.988780 1.47177i
\(99\) −1.07560e6 2.89249e6i −0.111411 0.299605i
\(100\) 1.45381e7 + 5.93618e6i 1.45381 + 0.593618i
\(101\) −5.25028e6 + 5.25028e6i −0.507058 + 0.507058i −0.913622 0.406564i \(-0.866727\pi\)
0.406564 + 0.913622i \(0.366727\pi\)
\(102\) 1.02565e6 405951.i 0.0956973 0.0378767i
\(103\) −1.49130e7 −1.34473 −0.672365 0.740219i \(-0.734722\pi\)
−0.672365 + 0.740219i \(0.734722\pi\)
\(104\) −9.24039e6 + 1.40583e7i −0.805515 + 1.22551i
\(105\) −2.66503e7 + 1.71086e7i −2.24667 + 1.44229i
\(106\) 1.58786e7 + 3.11685e6i 1.29492 + 0.254182i
\(107\) −2.88012e6 2.88012e6i −0.227283 0.227283i 0.584273 0.811557i \(-0.301380\pi\)
−0.811557 + 0.584273i \(0.801380\pi\)
\(108\) 1.12348e7 6.72020e6i 0.858190 0.513333i
\(109\) −1.11967e7 + 1.11967e7i −0.828129 + 0.828129i −0.987258 0.159129i \(-0.949131\pi\)
0.159129 + 0.987258i \(0.449131\pi\)
\(110\) −3.98948e6 5.93821e6i −0.285787 0.425384i
\(111\) −4.37156e6 6.80965e6i −0.303393 0.472601i
\(112\) 1.76834e7 + 1.73302e7i 1.18933 + 1.16558i
\(113\) 6.48206e6i 0.422609i 0.977420 + 0.211304i \(0.0677711\pi\)
−0.977420 + 0.211304i \(0.932229\pi\)
\(114\) 9.38358e6 2.16774e7i 0.593200 1.37038i
\(115\) −1.96110e7 1.96110e7i −1.20242 1.20242i
\(116\) 1.22011e6 512612.i 0.0725767 0.0304920i
\(117\) −2.38132e7 + 8.85516e6i −1.37457 + 0.511147i
\(118\) 2.13377e6 1.08704e7i 0.119553 0.609057i
\(119\) 3.15063e6i 0.171389i
\(120\) 2.16893e7 2.12267e7i 1.14580 1.12137i
\(121\) 1.74961e7i 0.897824i
\(122\) 8.29498e6 + 1.62824e6i 0.413576 + 0.0811819i
\(123\) 3.79440e6 + 827378.i 0.183855 + 0.0400900i
\(124\) 3.87871e6 + 1.58374e6i 0.182689 + 0.0745949i
\(125\) 1.41188e7 + 1.41188e7i 0.646564 + 0.646564i
\(126\) 6.03789e6 + 3.69012e7i 0.268898 + 1.64340i
\(127\) 2.82756e7i 1.22489i 0.790512 + 0.612447i \(0.209815\pi\)
−0.790512 + 0.612447i \(0.790185\pi\)
\(128\) −1.99575e7 1.28315e7i −0.841146 0.540808i
\(129\) 8.88038e6 5.70089e6i 0.364223 0.233818i
\(130\) −4.88879e7 + 3.28445e7i −1.95164 + 1.31117i
\(131\) −1.00935e7 + 1.00935e7i −0.392278 + 0.392278i −0.875499 0.483221i \(-0.839467\pi\)
0.483221 + 0.875499i \(0.339467\pi\)
\(132\) −8.30549e6 + 1.53753e6i −0.314309 + 0.0581856i
\(133\) 4.77070e7 + 4.77070e7i 1.75833 + 1.75833i
\(134\) 1.72457e6 8.78574e6i 0.0619177 0.315436i
\(135\) 4.53745e7 6.45544e6i 1.58724 0.225817i
\(136\) −611395. 2.95662e6i −0.0208418 0.100788i
\(137\) 2.74239e7 0.911188 0.455594 0.890188i \(-0.349427\pi\)
0.455594 + 0.890188i \(0.349427\pi\)
\(138\) −3.04475e7 + 1.20510e7i −0.986223 + 0.390344i
\(139\) −3.07201e6 + 3.07201e6i −0.0970223 + 0.0970223i −0.753952 0.656930i \(-0.771855\pi\)
0.656930 + 0.753952i \(0.271855\pi\)
\(140\) 3.35748e7 + 7.99144e7i 1.03411 + 2.46137i
\(141\) −4.52823e7 9.87394e6i −1.36039 0.296636i
\(142\) −1.60829e7 + 1.08050e7i −0.471362 + 0.316676i
\(143\) 1.63924e7 0.468776
\(144\) −1.28270e7 3.34573e7i −0.357977 0.933730i
\(145\) 4.63317e6 0.126209
\(146\) 1.37469e7 9.23561e6i 0.365569 0.245601i
\(147\) −6.67191e7 1.45483e7i −1.73236 0.377747i
\(148\) −2.04196e7 + 8.57899e6i −0.517764 + 0.217530i
\(149\) 2.20595e7 2.20595e7i 0.546315 0.546315i −0.379058 0.925373i \(-0.623752\pi\)
0.925373 + 0.379058i \(0.123752\pi\)
\(150\) 6.03546e7 2.38882e7i 1.46013 0.577915i
\(151\) 2.26818e7 0.536115 0.268058 0.963403i \(-0.413618\pi\)
0.268058 + 0.963403i \(0.413618\pi\)
\(152\) −5.40271e7 3.55116e7i −1.24784 0.820195i
\(153\) 1.89819e6 4.14564e6i 0.0428469 0.0935776i
\(154\) 4.64698e6 2.36738e7i 0.102529 0.522330i
\(155\) 1.03714e7 + 1.03714e7i 0.223705 + 0.223705i
\(156\) 1.26581e7 + 6.83772e7i 0.266953 + 1.44203i
\(157\) −2.39977e6 + 2.39977e6i −0.0494903 + 0.0494903i −0.731419 0.681929i \(-0.761142\pi\)
0.681929 + 0.731419i \(0.261142\pi\)
\(158\) −7.07718e7 + 4.75468e7i −1.42745 + 0.959006i
\(159\) 5.62867e7 3.61341e7i 1.11049 0.712897i
\(160\) −4.70152e7 6.84782e7i −0.907441 1.32170i
\(161\) 9.35294e7i 1.76627i
\(162\) 1.42875e7 5.21929e7i 0.264030 0.964514i
\(163\) 1.43447e6 + 1.43447e6i 0.0259439 + 0.0259439i 0.719960 0.694016i \(-0.244160\pi\)
−0.694016 + 0.719960i \(0.744160\pi\)
\(164\) 4.01818e6 9.84082e6i 0.0711337 0.174212i
\(165\) −2.88919e7 6.29995e6i −0.500705 0.109180i
\(166\) 2.89310e7 + 5.67892e6i 0.490890 + 0.0963580i
\(167\) 6.17509e7i 1.02597i −0.858397 0.512986i \(-0.828539\pi\)
0.858397 0.512986i \(-0.171461\pi\)
\(168\) 1.02338e8 + 1.10302e6i 1.66516 + 0.0179474i
\(169\) 7.22060e7i 1.15072i
\(170\) 2.03593e6 1.03719e7i 0.0317827 0.161915i
\(171\) −3.40311e7 9.15162e7i −0.520463 1.39962i
\(172\) −1.11877e7 2.66290e7i −0.167646 0.399029i
\(173\) 7.54742e7 + 7.54742e7i 1.10825 + 1.10825i 0.993381 + 0.114868i \(0.0366446\pi\)
0.114868 + 0.993381i \(0.463355\pi\)
\(174\) 2.17312e6 5.02023e6i 0.0312724 0.0722438i
\(175\) 1.85399e8i 2.61501i
\(176\) 233183. + 2.31178e7i 0.00322405 + 0.319633i
\(177\) −2.47371e7 3.85335e7i −0.335307 0.522314i
\(178\) 3.65918e7 + 5.44657e7i 0.486311 + 0.723858i
\(179\) 2.70955e7 2.70955e7i 0.353111 0.353111i −0.508155 0.861266i \(-0.669672\pi\)
0.861266 + 0.508155i \(0.169672\pi\)
\(180\) 3.96863e6 1.25381e8i 0.0507208 1.60242i
\(181\) −6.87870e7 6.87870e7i −0.862247 0.862247i 0.129352 0.991599i \(-0.458710\pi\)
−0.991599 + 0.129352i \(0.958710\pi\)
\(182\) −1.94900e8 3.82574e7i −2.39642 0.470399i
\(183\) 2.94041e7 1.88764e7i 0.354674 0.227689i
\(184\) 1.81499e7 + 8.77702e7i 0.214788 + 1.03869i
\(185\) −7.75401e7 −0.900379
\(186\) 1.61023e7 6.37325e6i 0.183482 0.0726216i
\(187\) −2.08021e6 + 2.08021e6i −0.0232627 + 0.0232627i
\(188\) −4.79529e7 + 1.17440e8i −0.526336 + 1.28904i
\(189\) 1.23595e8 + 9.28070e7i 1.33163 + 0.999919i
\(190\) −1.26224e8 1.87880e8i −1.33507 1.98721i
\(191\) 1.02497e8 1.06437 0.532187 0.846627i \(-0.321370\pi\)
0.532187 + 0.846627i \(0.321370\pi\)
\(192\) −9.62506e7 + 1.88242e7i −0.981407 + 0.191938i
\(193\) 1.01174e8 1.01302 0.506510 0.862234i \(-0.330935\pi\)
0.506510 + 0.862234i \(0.330935\pi\)
\(194\) 3.73164e7 + 5.55443e7i 0.366939 + 0.546177i
\(195\) −5.18660e7 + 2.37860e8i −0.500912 + 2.29721i
\(196\) −7.06539e7 + 1.73037e8i −0.670255 + 1.64150i
\(197\) 1.45920e8 1.45920e8i 1.35982 1.35982i 0.485690 0.874131i \(-0.338568\pi\)
0.874131 0.485690i \(-0.161432\pi\)
\(198\) −2.03775e7 + 2.83506e7i −0.186562 + 0.259558i
\(199\) −1.37812e8 −1.23965 −0.619827 0.784739i \(-0.712797\pi\)
−0.619827 + 0.784739i \(0.712797\pi\)
\(200\) −3.59776e7 1.73982e8i −0.318000 1.53780i
\(201\) −1.99932e7 3.11438e7i −0.173659 0.270511i
\(202\) 8.24315e7 + 1.61807e7i 0.703661 + 0.138123i
\(203\) 1.10483e7 + 1.10483e7i 0.0926960 + 0.0926960i
\(204\) −1.02834e7 7.07079e6i −0.0848073 0.0583126i
\(205\) 2.63136e7 2.63136e7i 0.213325 0.213325i
\(206\) 9.40901e7 + 1.40050e8i 0.749909 + 1.11622i
\(207\) −5.63496e7 + 1.23067e8i −0.441565 + 0.964377i
\(208\) 1.90323e8 1.91974e6i 1.46646 0.0147918i
\(209\) 6.29972e7i 0.477320i
\(210\) 3.28813e8 + 1.42334e8i 2.45008 + 1.06057i
\(211\) 2.56400e7 + 2.56400e7i 0.187901 + 0.187901i 0.794788 0.606887i \(-0.207582\pi\)
−0.606887 + 0.794788i \(0.707582\pi\)
\(212\) −7.09115e7 1.68783e8i −0.511141 1.21661i
\(213\) −1.70626e7 + 7.82500e7i −0.120981 + 0.554824i
\(214\) −8.87615e6 + 4.52190e7i −0.0619122 + 0.315408i
\(215\) 1.01119e8i 0.693902i
\(216\) −1.33994e8 6.31082e7i −0.904683 0.426086i
\(217\) 4.94635e7i 0.328606i
\(218\) 1.75793e8 + 3.45068e7i 1.14922 + 0.225583i
\(219\) 1.45843e7 6.68844e7i 0.0938279 0.430299i
\(220\) −3.05958e7 + 7.49315e7i −0.193724 + 0.474444i
\(221\) 1.71258e7 + 1.71258e7i 0.106728 + 0.106728i
\(222\) −3.63690e7 + 8.40177e7i −0.223098 + 0.515389i
\(223\) 1.72177e8i 1.03970i −0.854258 0.519849i \(-0.825988\pi\)
0.854258 0.519849i \(-0.174012\pi\)
\(224\) 5.11811e7 2.75408e8i 0.304258 1.63722i
\(225\) 1.11699e8 2.43951e8i 0.653749 1.42779i
\(226\) 6.08738e7 4.08970e7i 0.350793 0.235674i
\(227\) −1.90552e8 + 1.90552e8i −1.08125 + 1.08125i −0.0848515 + 0.996394i \(0.527042\pi\)
−0.996394 + 0.0848515i \(0.972958\pi\)
\(228\) −2.62779e8 + 4.86463e7i −1.46831 + 0.271818i
\(229\) −1.55895e8 1.55895e8i −0.857844 0.857844i 0.133240 0.991084i \(-0.457462\pi\)
−0.991084 + 0.133240i \(0.957462\pi\)
\(230\) −6.04384e7 + 3.07900e8i −0.327541 + 1.66864i
\(231\) −5.38731e7 8.39190e7i −0.287561 0.447939i
\(232\) −1.25120e7 8.22404e6i −0.0657838 0.0432391i
\(233\) −1.29313e8 −0.669725 −0.334862 0.942267i \(-0.608690\pi\)
−0.334862 + 0.942267i \(0.608690\pi\)
\(234\) 2.33404e8 + 1.67763e8i 1.19084 + 0.855937i
\(235\) −3.14027e8 + 3.14027e8i −1.57844 + 1.57844i
\(236\) −1.15548e8 + 4.85455e7i −0.572228 + 0.240413i
\(237\) −7.50830e7 + 3.44334e8i −0.366372 + 1.68020i
\(238\) 2.95879e7 1.98781e7i 0.142264 0.0955775i
\(239\) −5.31235e7 −0.251706 −0.125853 0.992049i \(-0.540167\pi\)
−0.125853 + 0.992049i \(0.540167\pi\)
\(240\) −3.36186e8 6.97618e7i −1.56979 0.325746i
\(241\) 3.47041e8 1.59706 0.798529 0.601956i \(-0.205612\pi\)
0.798529 + 0.601956i \(0.205612\pi\)
\(242\) −1.64308e8 + 1.10387e8i −0.745253 + 0.500685i
\(243\) −1.06713e8 1.96580e8i −0.477086 0.878857i
\(244\) −3.70442e7 8.81722e7i −0.163251 0.388568i
\(245\) −4.62687e8 + 4.62687e8i −2.01005 + 2.01005i
\(246\) −1.61698e7 4.08538e7i −0.0692520 0.174968i
\(247\) 5.18641e8 2.18992
\(248\) −9.59864e6 4.64177e7i −0.0399603 0.193243i
\(249\) 1.02555e8 6.58366e7i 0.420977 0.270253i
\(250\) 4.35121e7 2.21670e8i 0.176125 0.897258i
\(251\) −1.85712e7 1.85712e7i −0.0741281 0.0741281i 0.669071 0.743199i \(-0.266692\pi\)
−0.743199 + 0.669071i \(0.766692\pi\)
\(252\) 3.08449e8 2.89522e8i 1.21418 1.13967i
\(253\) 6.17529e7 6.17529e7i 0.239737 0.239737i
\(254\) 2.65539e8 1.78398e8i 1.01674 0.683080i
\(255\) −2.36028e7 3.67665e7i −0.0891400 0.138855i
\(256\) 5.41472e6 + 2.68381e8i 0.0201714 + 0.999797i
\(257\) 2.88995e8i 1.06200i −0.847372 0.531000i \(-0.821816\pi\)
0.847372 0.531000i \(-0.178184\pi\)
\(258\) −1.09566e8 4.74283e7i −0.397199 0.171937i
\(259\) −1.84903e8 1.84903e8i −0.661296 0.661296i
\(260\) 6.16893e8 + 2.51888e8i 2.17672 + 0.888794i
\(261\) −7.88118e6 2.11940e7i −0.0274378 0.0737855i
\(262\) 1.58473e8 + 3.11069e7i 0.544377 + 0.106857i
\(263\) 1.59344e8i 0.540120i 0.962844 + 0.270060i \(0.0870435\pi\)
−0.962844 + 0.270060i \(0.912956\pi\)
\(264\) 6.68407e7 + 6.82972e7i 0.223577 + 0.228449i
\(265\) 6.40924e8i 2.11566i
\(266\) 1.47026e8 7.49018e8i 0.478972 2.44009i
\(267\) 2.64998e8 + 5.77836e7i 0.852028 + 0.185787i
\(268\) −9.33887e7 + 3.92358e7i −0.296362 + 0.124512i
\(269\) 4.06306e8 + 4.06306e8i 1.27268 + 1.27268i 0.944675 + 0.328007i \(0.106377\pi\)
0.328007 + 0.944675i \(0.393623\pi\)
\(270\) −3.46903e8 3.85389e8i −1.07259 1.19159i
\(271\) 3.35239e8i 1.02320i 0.859223 + 0.511601i \(0.170947\pi\)
−0.859223 + 0.511601i \(0.829053\pi\)
\(272\) −2.39085e7 + 2.43958e7i −0.0720380 + 0.0735061i
\(273\) −6.90885e8 + 4.43524e8i −2.05512 + 1.31931i
\(274\) −1.73025e8 2.57542e8i −0.508138 0.756346i
\(275\) −1.22410e8 + 1.22410e8i −0.354937 + 0.354937i
\(276\) 3.05274e8 + 2.09903e8i 0.873993 + 0.600949i
\(277\) −3.11994e8 3.11994e8i −0.881997 0.881997i 0.111740 0.993737i \(-0.464358\pi\)
−0.993737 + 0.111740i \(0.964358\pi\)
\(278\) 4.82318e7 + 9.46753e6i 0.134641 + 0.0264290i
\(279\) 2.98008e7 6.50849e7i 0.0821510 0.179418i
\(280\) 5.38654e8 8.19506e8i 1.46642 2.23100i
\(281\) 2.68024e8 0.720611 0.360306 0.932834i \(-0.382672\pi\)
0.360306 + 0.932834i \(0.382672\pi\)
\(282\) 1.92971e8 + 4.87549e8i 0.512412 + 1.29463i
\(283\) −2.85261e8 + 2.85261e8i −0.748153 + 0.748153i −0.974132 0.225979i \(-0.927442\pi\)
0.225979 + 0.974132i \(0.427442\pi\)
\(284\) 2.02942e8 + 8.28649e7i 0.525725 + 0.214663i
\(285\) −9.14116e8 1.99325e8i −2.33907 0.510042i
\(286\) −1.03424e8 1.53943e8i −0.261420 0.389115i
\(287\) 1.25496e8 0.313359
\(288\) −2.33273e8 + 3.31550e8i −0.575427 + 0.817853i
\(289\) 4.05992e8 0.989407
\(290\) −2.92319e7 4.35107e7i −0.0703824 0.104762i
\(291\) 2.70246e8 + 5.89279e7i 0.642886 + 0.140183i
\(292\) −1.73466e8 7.08290e7i −0.407731 0.166484i
\(293\) 4.12499e8 4.12499e8i 0.958045 0.958045i −0.0411100 0.999155i \(-0.513089\pi\)
0.999155 + 0.0411100i \(0.0130894\pi\)
\(294\) 2.84323e8 + 7.18356e8i 0.652524 + 1.64863i
\(295\) −4.38773e8 −0.995090
\(296\) 2.09399e8 + 1.37636e8i 0.469304 + 0.308469i
\(297\) 2.03275e7 + 1.42880e8i 0.0450232 + 0.316463i
\(298\) −3.46342e8 6.79843e7i −0.758138 0.148817i
\(299\) −5.08397e8 5.08397e8i −1.09990 1.09990i
\(300\) −6.05130e8 4.16081e8i −1.29397 0.889720i
\(301\) 2.41130e8 2.41130e8i 0.509646 0.509646i
\(302\) −1.43105e8 2.13008e8i −0.298973 0.445011i
\(303\) 2.92204e8 1.87585e8i 0.603444 0.387390i
\(304\) 7.37772e6 + 7.31427e8i 0.0150614 + 1.49319i
\(305\) 3.34819e8i 0.675710i
\(306\) −5.09084e7 + 8.32980e6i −0.101570 + 0.0166192i
\(307\) −2.25856e8 2.25856e8i −0.445499 0.445499i 0.448356 0.893855i \(-0.352010\pi\)
−0.893855 + 0.448356i \(0.852010\pi\)
\(308\) −2.51642e8 + 1.05724e8i −0.490745 + 0.206179i
\(309\) 6.81402e8 + 1.48581e8i 1.31386 + 0.286490i
\(310\) 3.19632e7 1.62835e8i 0.0609374 0.310442i
\(311\) 5.16381e8i 0.973439i 0.873558 + 0.486719i \(0.161807\pi\)
−0.873558 + 0.486719i \(0.838193\pi\)
\(312\) 5.62275e8 5.50284e8i 1.04811 1.02576i
\(313\) 4.53248e8i 0.835470i 0.908569 + 0.417735i \(0.137176\pi\)
−0.908569 + 0.417735i \(0.862824\pi\)
\(314\) 3.76773e7 + 7.39576e6i 0.0686793 + 0.0134812i
\(315\) 1.38816e9 5.16198e8i 2.50237 0.930528i
\(316\) 8.93036e8 + 3.64642e8i 1.59208 + 0.650073i
\(317\) −2.20515e8 2.20515e8i −0.388803 0.388803i 0.485457 0.874260i \(-0.338653\pi\)
−0.874260 + 0.485457i \(0.838653\pi\)
\(318\) −6.94467e8 3.00616e8i −1.21103 0.524224i
\(319\) 1.45894e7i 0.0251634i
\(320\) −3.46456e8 + 8.73573e8i −0.591049 + 1.49030i
\(321\) 1.02903e8 + 1.60293e8i 0.173644 + 0.270487i
\(322\) −8.78346e8 + 5.90101e8i −1.46612 + 0.984988i
\(323\) −6.58160e7 + 6.58160e7i −0.108673 + 0.108673i
\(324\) −5.80293e8 + 1.95123e8i −0.947851 + 0.318714i
\(325\) 1.00777e9 + 1.00777e9i 1.62843 + 1.62843i
\(326\) 4.42084e6 2.25217e7i 0.00706714 0.0360031i
\(327\) 6.23152e8 4.00042e8i 0.985546 0.632686i
\(328\) −1.17768e8 + 2.43531e7i −0.184276 + 0.0381062i
\(329\) −1.49767e9 −2.31862
\(330\) 1.23123e8 + 3.11075e8i 0.188599 + 0.476504i
\(331\) 5.33443e8 5.33443e8i 0.808519 0.808519i −0.175890 0.984410i \(-0.556280\pi\)
0.984410 + 0.175890i \(0.0562804\pi\)
\(332\) −1.29201e8 3.07524e8i −0.193769 0.461207i
\(333\) 1.31898e8 + 3.54700e8i 0.195742 + 0.526388i
\(334\) −5.79911e8 + 3.89603e8i −0.851625 + 0.572149i
\(335\) −3.54628e8 −0.515366
\(336\) −6.35320e8 9.68030e8i −0.913703 1.39220i
\(337\) −6.08348e8 −0.865860 −0.432930 0.901428i \(-0.642520\pi\)
−0.432930 + 0.901428i \(0.642520\pi\)
\(338\) −6.78096e8 + 4.55567e8i −0.955174 + 0.641717i
\(339\) 6.45821e7 2.96177e8i 0.0900354 0.412907i
\(340\) −1.10249e8 + 4.63194e7i −0.152124 + 0.0639127i
\(341\) −3.26584e7 + 3.26584e7i −0.0446020 + 0.0446020i
\(342\) −6.44729e8 + 8.96990e8i −0.871537 + 1.21254i
\(343\) −9.62120e8 −1.28736
\(344\) −1.79490e8 + 2.73075e8i −0.237730 + 0.361682i
\(345\) 7.00672e8 + 1.09145e9i 0.918645 + 1.43099i
\(346\) 2.32601e8 1.18497e9i 0.301888 1.53795i
\(347\) −5.33079e8 5.33079e8i −0.684917 0.684917i 0.276187 0.961104i \(-0.410929\pi\)
−0.961104 + 0.276187i \(0.910929\pi\)
\(348\) −6.08563e7 + 1.12659e7i −0.0774067 + 0.0143297i
\(349\) 5.92520e8 5.92520e8i 0.746130 0.746130i −0.227620 0.973750i \(-0.573095\pi\)
0.973750 + 0.227620i \(0.0730945\pi\)
\(350\) 1.74110e9 1.16973e9i 2.17063 1.45830i
\(351\) 1.17629e9 1.67351e8i 1.45191 0.206564i
\(352\) 2.15631e8 1.48046e8i 0.263519 0.180924i
\(353\) 3.01802e8i 0.365183i 0.983189 + 0.182591i \(0.0584485\pi\)
−0.983189 + 0.182591i \(0.941551\pi\)
\(354\) −2.05800e8 + 4.75427e8i −0.246566 + 0.569604i
\(355\) 5.42652e8 + 5.42652e8i 0.643758 + 0.643758i
\(356\) 2.80627e8 6.87277e8i 0.329651 0.807341i
\(357\) 3.13903e7 1.43958e8i 0.0365138 0.167454i
\(358\) −4.25410e8 8.35046e7i −0.490023 0.0961878i
\(359\) 6.80496e6i 0.00776238i −0.999992 0.00388119i \(-0.998765\pi\)
0.999992 0.00388119i \(-0.00123542\pi\)
\(360\) −1.20251e9 + 7.53791e8i −1.35840 + 0.851515i
\(361\) 1.09931e9i 1.22983i
\(362\) −2.11992e8 + 1.07998e9i −0.234877 + 1.19657i
\(363\) −1.74317e8 + 7.99425e8i −0.191278 + 0.877212i
\(364\) 8.70397e8 + 2.07171e9i 0.945937 + 2.25151i
\(365\) −4.63834e8 4.63834e8i −0.499272 0.499272i
\(366\) −3.62789e8 1.57042e8i −0.386786 0.167429i
\(367\) 2.37968e8i 0.251297i 0.992075 + 0.125649i \(0.0401012\pi\)
−0.992075 + 0.125649i \(0.959899\pi\)
\(368\) 7.09748e8 7.24212e8i 0.742398 0.757528i
\(369\) −1.65129e8 7.56087e7i −0.171093 0.0783393i
\(370\) 4.89221e8 + 7.28189e8i 0.502110 + 0.747374i
\(371\) 1.52836e9 1.52836e9i 1.55388 1.55388i
\(372\) −1.61446e8 1.11008e8i −0.162602 0.111804i
\(373\) −5.45034e7 5.45034e7i −0.0543804 0.0543804i 0.679394 0.733774i \(-0.262243\pi\)
−0.733774 + 0.679394i \(0.762243\pi\)
\(374\) 3.26600e7 + 6.41091e6i 0.0322824 + 0.00633679i
\(375\) −5.04443e8 7.85779e8i −0.493972 0.769469i
\(376\) 1.40544e9 2.90630e8i 1.36350 0.281957i
\(377\) 1.20111e8 0.115448
\(378\) 9.17725e7 1.74624e9i 0.0873959 1.66296i
\(379\) −2.63889e8 + 2.63889e8i −0.248991 + 0.248991i −0.820556 0.571565i \(-0.806336\pi\)
0.571565 + 0.820556i \(0.306336\pi\)
\(380\) −9.68027e8 + 2.37077e9i −0.904992 + 2.21639i
\(381\) 2.81715e8 1.29196e9i 0.260959 1.19677i
\(382\) −6.46681e8 9.62563e8i −0.593565 0.883501i
\(383\) 9.41312e7 0.0856126 0.0428063 0.999083i \(-0.486370\pi\)
0.0428063 + 0.999083i \(0.486370\pi\)
\(384\) 7.84050e8 + 7.85135e8i 0.706618 + 0.707596i
\(385\) −9.55569e8 −0.853393
\(386\) −6.38333e8 9.50137e8i −0.564926 0.840874i
\(387\) −4.62559e8 + 1.72007e8i −0.405675 + 0.150854i
\(388\) 2.86184e8 7.00887e8i 0.248734 0.609168i
\(389\) −7.16086e8 + 7.16086e8i −0.616796 + 0.616796i −0.944708 0.327912i \(-0.893655\pi\)
0.327912 + 0.944708i \(0.393655\pi\)
\(390\) 2.56101e9 1.01364e9i 2.18618 0.865282i
\(391\) 1.29032e8 0.109164
\(392\) 2.07078e9 4.28214e8i 1.73634 0.359054i
\(393\) 5.61756e8 3.60627e8i 0.466846 0.299699i
\(394\) −2.29099e9 4.49704e8i −1.88707 0.370417i
\(395\) 2.38791e9 + 2.38791e9i 1.94952 + 1.94952i
\(396\) 3.94811e8 + 1.24968e7i 0.319489 + 0.0101127i
\(397\) −1.03641e9 + 1.03641e9i −0.831312 + 0.831312i −0.987696 0.156385i \(-0.950016\pi\)
0.156385 + 0.987696i \(0.450016\pi\)
\(398\) 8.69490e8 + 1.29421e9i 0.691311 + 1.02899i
\(399\) −1.70450e9 2.65513e9i −1.34336 2.09257i
\(400\) −1.40690e9 + 1.43557e9i −1.09914 + 1.12154i
\(401\) 2.41358e9i 1.86920i 0.355699 + 0.934601i \(0.384243\pi\)
−0.355699 + 0.934601i \(0.615757\pi\)
\(402\) −1.66333e8 + 3.84253e8i −0.127699 + 0.295003i
\(403\) 2.68868e8 + 2.68868e8i 0.204631 + 0.204631i
\(404\) −3.68127e8 8.76212e8i −0.277756 0.661111i
\(405\) −2.13756e9 1.57115e8i −1.59891 0.117524i
\(406\) 3.40495e7 1.73463e8i 0.0252505 0.128637i
\(407\) 2.44166e8i 0.179516i
\(408\) −1.52172e6 + 1.41185e8i −0.00110923 + 0.102915i
\(409\) 8.38522e8i 0.606014i −0.952988 0.303007i \(-0.902009\pi\)
0.952988 0.303007i \(-0.0979906\pi\)
\(410\) −4.13133e8 8.10949e7i −0.296038 0.0581099i
\(411\) −1.25305e9 2.73230e8i −0.890269 0.194125i
\(412\) 7.21588e8 1.76722e9i 0.508334 1.24495i
\(413\) −1.04630e9 1.04630e9i −0.730858 0.730858i
\(414\) 1.51127e9 2.47278e8i 1.04674 0.171271i
\(415\) 1.16777e9i 0.802027i
\(416\) −1.21883e9 1.77524e9i −0.830071 1.20901i
\(417\) 1.70973e8 1.09759e8i 0.115465 0.0741246i
\(418\) 5.91615e8 3.97466e8i 0.396207 0.266185i
\(419\) 1.00640e9 1.00640e9i 0.668375 0.668375i −0.288964 0.957340i \(-0.593311\pi\)
0.957340 + 0.288964i \(0.0933109\pi\)
\(420\) −7.37887e8 3.98594e9i −0.485979 2.62518i
\(421\) 6.80423e8 + 6.80423e8i 0.444418 + 0.444418i 0.893494 0.449076i \(-0.148247\pi\)
−0.449076 + 0.893494i \(0.648247\pi\)
\(422\) 7.90191e7 4.02558e8i 0.0511845 0.260757i
\(423\) 1.97065e9 + 9.02315e8i 1.26596 + 0.579651i
\(424\) −1.13766e9 + 1.73083e9i −0.724824 + 1.10274i
\(425\) −2.55774e8 −0.161620
\(426\) 8.42508e8 3.33462e8i 0.528008 0.208984i
\(427\) 7.98415e8 7.98415e8i 0.496285 0.496285i
\(428\) 4.80660e8 2.01942e8i 0.296336 0.124501i
\(429\) −7.48996e8 1.63321e8i −0.458014 0.0998712i
\(430\) −9.49621e8 + 6.37986e8i −0.575984 + 0.386965i
\(431\) −1.91227e9 −1.15048 −0.575241 0.817984i \(-0.695092\pi\)
−0.575241 + 0.817984i \(0.695092\pi\)
\(432\) 2.52745e8 + 1.65652e9i 0.150830 + 0.988560i
\(433\) 1.31602e9 0.779032 0.389516 0.921020i \(-0.372642\pi\)
0.389516 + 0.921020i \(0.372642\pi\)
\(434\) 4.64518e8 3.12078e8i 0.272765 0.183252i
\(435\) −2.11698e8 4.61613e7i −0.123312 0.0268884i
\(436\) −7.85065e8 1.86860e9i −0.453631 1.07973i
\(437\) 1.95381e9 1.95381e9i 1.11995 1.11995i
\(438\) −7.20136e8 + 2.85028e8i −0.409501 + 0.162079i
\(439\) −2.63233e9 −1.48496 −0.742480 0.669868i \(-0.766351\pi\)
−0.742480 + 0.669868i \(0.766351\pi\)
\(440\) 8.96728e8 1.85433e8i 0.501853 0.103777i
\(441\) 2.90356e9 + 1.32947e9i 1.61212 + 0.738149i
\(442\) 5.27795e7 2.68882e8i 0.0290728 0.148110i
\(443\) −1.88393e9 1.88393e9i −1.02956 1.02956i −0.999550 0.0300083i \(-0.990447\pi\)
−0.0300083 0.999550i \(-0.509553\pi\)
\(444\) 1.01848e9 1.88544e8i 0.552221 0.102229i
\(445\) 1.83773e9 1.83773e9i 0.988600 0.988600i
\(446\) −1.61693e9 + 1.08631e9i −0.863018 + 0.579803i
\(447\) −1.22772e9 + 7.88153e8i −0.650163 + 0.417382i
\(448\) −2.90930e9 + 1.25697e9i −1.52868 + 0.660468i
\(449\) 4.51150e8i 0.235212i −0.993060 0.117606i \(-0.962478\pi\)
0.993060 0.117606i \(-0.0375220\pi\)
\(450\) −2.99571e9 + 4.90167e8i −1.54973 + 0.253572i
\(451\) 8.28587e7 + 8.28587e7i 0.0425324 + 0.0425324i
\(452\) −7.68138e8 3.13644e8i −0.391250 0.159754i
\(453\) −1.03637e9 2.25983e8i −0.523807 0.114218i
\(454\) 2.99175e9 + 5.87257e8i 1.50048 + 0.294532i
\(455\) 7.86697e9i 3.91532i
\(456\) 2.11478e9 + 2.16087e9i 1.04445 + 1.06721i
\(457\) 2.65297e9i 1.30025i −0.759829 0.650123i \(-0.774717\pi\)
0.759829 0.650123i \(-0.225283\pi\)
\(458\) −4.80448e8 + 2.44761e9i −0.233677 + 1.19046i
\(459\) −1.28036e8 + 1.70510e8i −0.0617997 + 0.0823009i
\(460\) 3.27285e9 1.37504e9i 1.56774 0.658661i
\(461\) 8.95901e8 + 8.95901e8i 0.425899 + 0.425899i 0.887229 0.461330i \(-0.152628\pi\)
−0.461330 + 0.887229i \(0.652628\pi\)
\(462\) −4.48195e8 + 1.03540e9i −0.211456 + 0.488494i
\(463\) 1.79839e9i 0.842074i 0.907043 + 0.421037i \(0.138334\pi\)
−0.907043 + 0.421037i \(0.861666\pi\)
\(464\) 1.70859e6 + 1.69389e8i 0.000794007 + 0.0787179i
\(465\) −3.70554e8 5.77218e8i −0.170909 0.266229i
\(466\) 8.15869e8 + 1.21439e9i 0.373482 + 0.555916i
\(467\) 4.10614e8 4.10614e8i 0.186563 0.186563i −0.607646 0.794208i \(-0.707886\pi\)
0.794208 + 0.607646i \(0.207886\pi\)
\(468\) 1.02883e8 3.25039e9i 0.0463963 1.46580i
\(469\) −8.45652e8 8.45652e8i −0.378518 0.378518i
\(470\) 4.93034e9 + 9.67787e8i 2.19045 + 0.429969i
\(471\) 1.33559e8 8.57402e7i 0.0588979 0.0378104i
\(472\) 1.18492e9 + 7.78836e8i 0.518670 + 0.340917i
\(473\) 3.18413e8 0.138349
\(474\) 3.70741e9 1.46738e9i 1.59899 0.632876i
\(475\) −3.87295e9 + 3.87295e9i −1.65811 + 1.65811i
\(476\) −3.73356e8 1.52448e8i −0.158671 0.0647883i
\(477\) −2.93185e9 + 1.09023e9i −1.23688 + 0.459944i
\(478\) 3.35170e8 + 4.98890e8i 0.140368 + 0.208933i
\(479\) −4.12493e9 −1.71491 −0.857456 0.514557i \(-0.827957\pi\)
−0.857456 + 0.514557i \(0.827957\pi\)
\(480\) 1.46594e9 + 3.59731e9i 0.605024 + 1.48468i
\(481\) −2.01016e9 −0.823611
\(482\) −2.18957e9 3.25910e9i −0.890624 1.32566i
\(483\) −9.31852e8 + 4.27352e9i −0.376298 + 1.72572i
\(484\) 2.07332e9 + 8.46572e8i 0.831204 + 0.339395i
\(485\) 1.87412e9 1.87412e9i 0.745935 0.745935i
\(486\) −1.17283e9 + 2.24243e9i −0.463455 + 0.886120i
\(487\) 1.41285e9 0.554299 0.277149 0.960827i \(-0.410610\pi\)
0.277149 + 0.960827i \(0.410610\pi\)
\(488\) −5.94314e8 + 9.04187e8i −0.231498 + 0.352200i
\(489\) −5.12515e7 7.98353e7i −0.0198210 0.0308755i
\(490\) 7.26437e9 + 1.42594e9i 2.78940 + 0.547539i
\(491\) −2.08950e8 2.08950e8i −0.0796630 0.0796630i 0.666153 0.745816i \(-0.267940\pi\)
−0.745816 + 0.666153i \(0.767940\pi\)
\(492\) −2.81643e8 + 4.09610e8i −0.106616 + 0.155057i
\(493\) −1.52422e7 + 1.52422e7i −0.00572905 + 0.00572905i
\(494\) −3.27224e9 4.87063e9i −1.22124 1.81778i
\(495\) 1.25735e9 + 5.75712e8i 0.465950 + 0.213347i
\(496\) −3.75354e8 + 3.83003e8i −0.138120 + 0.140934i
\(497\) 2.58804e9i 0.945633i
\(498\) −1.26533e9 5.47725e8i −0.459092 0.198728i
\(499\) 2.83335e9 + 2.83335e9i 1.02082 + 1.02082i 0.999779 + 0.0210380i \(0.00669711\pi\)
0.0210380 + 0.999779i \(0.493303\pi\)
\(500\) −2.35626e9 + 9.89947e8i −0.843002 + 0.354174i
\(501\) −6.15237e8 + 2.82151e9i −0.218580 + 1.00242i
\(502\) −5.72340e7 + 2.91575e8i −0.0201926 + 0.102870i
\(503\) 4.30020e9i 1.50661i −0.657671 0.753305i \(-0.728458\pi\)
0.657671 0.753305i \(-0.271542\pi\)
\(504\) −4.66502e9 1.07002e9i −1.62310 0.372292i
\(505\) 3.32727e9i 1.14966i
\(506\) −9.69545e8 1.90314e8i −0.332691 0.0653047i
\(507\) −7.19403e8 + 3.29922e9i −0.245157 + 1.12430i
\(508\) −3.35071e9 1.36816e9i −1.13400 0.463033i
\(509\) 1.79218e9 + 1.79218e9i 0.602380 + 0.602380i 0.940943 0.338564i \(-0.109941\pi\)
−0.338564 + 0.940943i \(0.609941\pi\)
\(510\) −1.96362e8 + 4.53626e8i −0.0655485 + 0.151427i
\(511\) 2.21213e9i 0.733395i
\(512\) 2.48624e9 1.74413e9i 0.818648 0.574295i
\(513\) 6.43145e8 + 4.52059e9i 0.210329 + 1.47837i
\(514\) −2.71399e9 + 1.82335e9i −0.881530 + 0.592240i
\(515\) 4.72542e9 4.72542e9i 1.52446 1.52446i
\(516\) 2.45878e8 + 1.32819e9i 0.0787853 + 0.425585i
\(517\) −9.88836e8 9.88836e8i −0.314708 0.314708i
\(518\) −5.69847e8 + 2.90305e9i −0.180138 + 0.917700i
\(519\) −2.69658e9 4.20051e9i −0.846697 1.31891i
\(520\) −1.52663e9 7.38255e9i −0.476125 2.30247i
\(521\) 1.42418e9 0.441197 0.220598 0.975365i \(-0.429199\pi\)
0.220598 + 0.975365i \(0.429199\pi\)
\(522\) −1.49311e8 + 2.07732e8i −0.0459458 + 0.0639228i
\(523\) 3.21371e9 3.21371e9i 0.982314 0.982314i −0.0175319 0.999846i \(-0.505581\pi\)
0.999846 + 0.0175319i \(0.00558085\pi\)
\(524\) −7.07715e8 1.68450e9i −0.214882 0.511459i
\(525\) 1.84716e9 8.47119e9i 0.557119 2.55498i
\(526\) 1.49642e9 1.00534e9i 0.448335 0.301206i
\(527\) −6.82392e7 −0.0203094
\(528\) 2.19673e8 1.05861e9i 0.0649467 0.312982i
\(529\) −4.25615e8 −0.125004
\(530\) −6.01900e9 + 4.04376e9i −1.75614 + 1.17983i
\(531\) 7.46366e8 + 2.00712e9i 0.216332 + 0.581759i
\(532\) −7.96175e9 + 3.34501e9i −2.29255 + 0.963177i
\(533\) 6.82156e8 6.82156e8i 0.195136 0.195136i
\(534\) −1.12929e9 2.85321e9i −0.320931 0.810847i
\(535\) 1.82522e9 0.515321
\(536\) 9.57682e8 + 6.29476e8i 0.268624 + 0.176564i
\(537\) −1.50800e9 + 9.68082e8i −0.420233 + 0.269775i
\(538\) 1.25218e9 6.37916e9i 0.346680 1.76614i
\(539\) −1.45695e9 1.45695e9i −0.400760 0.400760i
\(540\) −1.43053e9 + 5.68933e9i −0.390948 + 1.55483i
\(541\) 2.40850e9 2.40850e9i 0.653969 0.653969i −0.299978 0.953946i \(-0.596979\pi\)
0.953946 + 0.299978i \(0.0969792\pi\)
\(542\) 3.14827e9 2.11511e9i 0.849326 0.570604i
\(543\) 2.45766e9 + 3.82834e9i 0.658752 + 1.02615i
\(544\) 3.79949e8 + 7.06088e7i 0.101188 + 0.0188045i
\(545\) 7.09570e9i 1.87762i
\(546\) 8.52417e9 + 3.68988e9i 2.24119 + 0.970148i
\(547\) −9.78391e8 9.78391e8i −0.255598 0.255598i 0.567663 0.823261i \(-0.307848\pi\)
−0.823261 + 0.567663i \(0.807848\pi\)
\(548\) −1.32695e9 + 3.24979e9i −0.344447 + 0.843576i
\(549\) −1.53160e9 + 5.69537e8i −0.395040 + 0.146899i
\(550\) 1.92188e9 + 3.77250e8i 0.492558 + 0.0966853i
\(551\) 4.61596e8i 0.117552i
\(552\) 4.51737e7 4.19120e9i 0.0114314 1.06060i
\(553\) 1.13885e10i 2.86371i
\(554\) −9.61524e8 + 4.89843e9i −0.240257 + 1.22398i
\(555\) 3.54294e9 + 7.72548e8i 0.879708 + 0.191823i
\(556\) −2.15396e8 5.12684e8i −0.0531467 0.126499i
\(557\) 4.61818e9 + 4.61818e9i 1.13234 + 1.13234i 0.989787 + 0.142556i \(0.0455322\pi\)
0.142556 + 0.989787i \(0.454468\pi\)
\(558\) −7.99241e8 + 1.30774e8i −0.194741 + 0.0318642i
\(559\) 2.62142e9i 0.634739i
\(560\) −1.10946e10 + 1.11908e8i −2.66964 + 0.0269280i
\(561\) 1.15774e8 7.43227e7i 0.0276847 0.0177726i
\(562\) −1.69103e9 2.51704e9i −0.401860 0.598155i
\(563\) 7.41388e8 7.41388e8i 0.175092 0.175092i −0.614120 0.789212i \(-0.710489\pi\)
0.789212 + 0.614120i \(0.210489\pi\)
\(564\) 3.36114e9 4.88829e9i 0.788877 1.14731i
\(565\) −2.05394e9 2.05394e9i −0.479092 0.479092i
\(566\) 4.47872e9 + 8.79137e8i 1.03824 + 0.203798i
\(567\) −4.72259e9 5.47191e9i −1.08803 1.26066i
\(568\) −5.02222e8 2.42867e9i −0.114994 0.556096i
\(569\) −1.77637e9 −0.404240 −0.202120 0.979361i \(-0.564783\pi\)
−0.202120 + 0.979361i \(0.564783\pi\)
\(570\) 3.89550e9 + 9.84217e9i 0.881052 + 2.22602i
\(571\) 2.91820e9 2.91820e9i 0.655977 0.655977i −0.298448 0.954426i \(-0.596469\pi\)
0.954426 + 0.298448i \(0.0964691\pi\)
\(572\) −7.93169e8 + 1.94253e9i −0.177207 + 0.433992i
\(573\) −4.68327e9 1.02120e9i −1.03994 0.226761i
\(574\) −7.91785e8 1.17855e9i −0.174749 0.260109i
\(575\) 7.59289e9 1.66560
\(576\) 4.58541e9 + 9.88564e7i 0.999768 + 0.0215539i
\(577\) 1.27582e9 0.276487 0.138243 0.990398i \(-0.455854\pi\)
0.138243 + 0.990398i \(0.455854\pi\)
\(578\) −2.56151e9 3.81272e9i −0.551758 0.821273i
\(579\) −4.62281e9 1.00802e9i −0.989764 0.215821i
\(580\) −2.24183e8 + 5.49041e8i −0.0477095 + 0.116844i
\(581\) 2.78468e9 2.78468e9i 0.589060 0.589060i
\(582\) −1.15165e9 2.90971e9i −0.242154 0.611813i
\(583\) 2.01820e9 0.421818
\(584\) 4.29276e8 + 2.07592e9i 0.0891849 + 0.431285i
\(585\) 4.73970e9 1.03515e10i 0.978825 2.13775i
\(586\) −6.47639e9 1.27126e9i −1.32951 0.260972i
\(587\) −8.28532e8 8.28532e8i −0.169074 0.169074i 0.617499 0.786572i \(-0.288146\pi\)
−0.786572 + 0.617499i \(0.788146\pi\)
\(588\) 4.95230e9 7.20241e9i 1.00458 1.46102i
\(589\) −1.03328e9 + 1.03328e9i −0.208361 + 0.208361i
\(590\) 2.76833e9 + 4.12057e9i 0.554927 + 0.825990i
\(591\) −8.12115e9 + 5.21349e9i −1.61831 + 1.03890i
\(592\) −2.85946e7 2.83488e9i −0.00566446 0.561575i
\(593\) 6.23217e9i 1.22729i −0.789582 0.613646i \(-0.789702\pi\)
0.789582 0.613646i \(-0.210298\pi\)
\(594\) 1.21355e9 1.09236e9i 0.237577 0.213852i
\(595\) −9.98325e8 9.98325e8i −0.194295 0.194295i
\(596\) 1.54671e9 + 3.68147e9i 0.299260 + 0.712295i
\(597\) 6.29685e9 + 1.37305e9i 1.21119 + 0.264104i
\(598\) −1.56681e9 + 7.98203e9i −0.299614 + 1.52637i
\(599\) 2.86565e9i 0.544790i 0.962185 + 0.272395i \(0.0878158\pi\)
−0.962185 + 0.272395i \(0.912184\pi\)
\(600\) −8.95455e7 + 8.30801e9i −0.0169244 + 1.57025i
\(601\) 1.10087e9i 0.206859i 0.994637 + 0.103430i \(0.0329816\pi\)
−0.994637 + 0.103430i \(0.967018\pi\)
\(602\) −3.78583e9 7.43130e8i −0.707251 0.138828i
\(603\) 6.03233e8 + 1.62221e9i 0.112040 + 0.301298i
\(604\) −1.09749e9 + 2.68784e9i −0.202662 + 0.496334i
\(605\) 5.54390e9 + 5.54390e9i 1.01782 + 1.01782i
\(606\) −3.60523e9 1.56060e9i −0.658079 0.284865i
\(607\) 6.43120e9i 1.16716i 0.812054 + 0.583582i \(0.198349\pi\)
−0.812054 + 0.583582i \(0.801651\pi\)
\(608\) 6.82238e9 4.68405e9i 1.23104 0.845199i
\(609\) −3.94741e8 6.14895e8i −0.0708193 0.110316i
\(610\) −3.14433e9 + 2.11246e9i −0.560884 + 0.376820i
\(611\) −8.14085e9 + 8.14085e9i −1.44386 + 1.44386i
\(612\) 3.99421e8 + 4.25533e8i 0.0704370 + 0.0750417i
\(613\) 1.97742e9 + 1.97742e9i 0.346726 + 0.346726i 0.858888 0.512163i \(-0.171156\pi\)
−0.512163 + 0.858888i \(0.671156\pi\)
\(614\) −6.96057e8 + 3.54602e9i −0.121354 + 0.618233i
\(615\) −1.46448e9 + 9.40146e8i −0.253876 + 0.162979i
\(616\) 2.58054e9 + 1.69617e9i 0.444813 + 0.292372i
\(617\) −1.14463e8 −0.0196186 −0.00980931 0.999952i \(-0.503122\pi\)
−0.00980931 + 0.999952i \(0.503122\pi\)
\(618\) −2.90379e9 7.33657e9i −0.494887 1.25035i
\(619\) −3.05207e8 + 3.05207e8i −0.0517223 + 0.0517223i −0.732495 0.680773i \(-0.761644\pi\)
0.680773 + 0.732495i \(0.261644\pi\)
\(620\) −1.73086e9 + 7.27195e8i −0.291670 + 0.122541i
\(621\) 3.80086e9 5.06174e9i 0.636885 0.848163i
\(622\) 4.84940e9 3.25798e9i 0.808018 0.542853i
\(623\) 8.76454e9 1.45218
\(624\) −8.71532e9 1.80851e9i −1.43594 0.297972i
\(625\) 6.37073e8 0.104378
\(626\) 4.25651e9 2.85966e9i 0.693496 0.465913i
\(627\) 6.27655e8 2.87845e9i 0.101691 0.466362i
\(628\) −1.68261e8 4.00494e8i −0.0271097 0.0645263i
\(629\) 2.55091e8 2.55091e8i 0.0408712 0.0408712i
\(630\) −1.36059e10 9.77952e9i −2.16788 1.55821i
\(631\) 7.46141e9 1.18227 0.591137 0.806571i \(-0.298679\pi\)
0.591137 + 0.806571i \(0.298679\pi\)
\(632\) −2.21000e9 1.06872e10i −0.348242 1.68405i
\(633\) −9.16080e8 1.42699e9i −0.143556 0.223619i
\(634\) −6.79596e8 + 3.46216e9i −0.105910 + 0.539554i
\(635\) −8.95956e9 8.95956e9i −1.38860 1.38860i
\(636\) 1.55845e9 + 8.41849e9i 0.240211 + 1.29758i
\(637\) −1.19947e10 + 1.19947e10i −1.83867 + 1.83867i
\(638\) 1.37011e8 9.20482e7i 0.0208873 0.0140327i
\(639\) 1.55924e9 3.40538e9i 0.236407 0.516312i
\(640\) 1.03897e10 2.25798e9i 1.56666 0.340479i
\(641\) 1.30471e10i 1.95664i 0.207109 + 0.978318i \(0.433595\pi\)
−0.207109 + 0.978318i \(0.566405\pi\)
\(642\) 8.56093e8 1.97770e9i 0.127688 0.294977i
\(643\) −5.89846e9 5.89846e9i −0.874984 0.874984i 0.118026 0.993011i \(-0.462343\pi\)
−0.993011 + 0.118026i \(0.962343\pi\)
\(644\) 1.10834e10 + 4.52556e9i 1.63521 + 0.667685i
\(645\) −1.00747e9 + 4.62030e9i −0.147833 + 0.677971i
\(646\) 1.03334e9 + 2.02836e8i 0.150809 + 0.0296027i
\(647\) 1.20673e10i 1.75164i 0.482638 + 0.875820i \(0.339679\pi\)
−0.482638 + 0.875820i \(0.660321\pi\)
\(648\) 5.49364e9 + 4.21853e9i 0.793137 + 0.609044i
\(649\) 1.38165e9i 0.198400i
\(650\) 3.10581e9 1.58224e10i 0.443587 2.25983i
\(651\) 4.92815e8 2.26007e9i 0.0700084 0.321062i
\(652\) −2.39397e8 + 1.00579e8i −0.0338261 + 0.0142115i
\(653\) −8.78108e9 8.78108e9i −1.23410 1.23410i −0.962373 0.271731i \(-0.912404\pi\)
−0.271731 0.962373i \(-0.587596\pi\)
\(654\) −7.68847e9 3.32813e9i −1.07478 0.465241i
\(655\) 6.39659e9i 0.889415i
\(656\) 9.71732e8 + 9.52325e8i 0.134395 + 0.131711i
\(657\) −1.33277e9 + 2.91076e9i −0.183348 + 0.400431i
\(658\) 9.44916e9 + 1.40648e10i 1.29301 + 1.92461i
\(659\) 3.93222e9 3.93222e9i 0.535228 0.535228i −0.386896 0.922123i \(-0.626453\pi\)
0.922123 + 0.386896i \(0.126453\pi\)
\(660\) 2.14453e9 3.11892e9i 0.290355 0.422280i
\(661\) 3.59193e9 + 3.59193e9i 0.483752 + 0.483752i 0.906328 0.422576i \(-0.138874\pi\)
−0.422576 + 0.906328i \(0.638874\pi\)
\(662\) −8.37527e9 1.64400e9i −1.12201 0.220241i
\(663\) −6.11881e8 9.53137e8i −0.0815398 0.127016i
\(664\) −2.07283e9 + 3.15360e9i −0.274774 + 0.418040i
\(665\) −3.02334e10 −3.98668
\(666\) 2.49885e9 3.47656e9i 0.327778 0.456027i
\(667\) 4.52478e8 4.52478e8i 0.0590415 0.0590415i
\(668\) 7.31761e9 + 2.98791e9i 0.949843 + 0.387837i
\(669\) −1.71543e9 + 7.86705e9i −0.221504 + 1.01583i
\(670\) 2.23744e9 + 3.33036e9i 0.287402 + 0.427788i
\(671\) 1.05431e9 0.134722
\(672\) −5.08249e9 + 1.20739e10i −0.646077 + 1.53481i
\(673\) −1.26829e10 −1.60386 −0.801929 0.597419i \(-0.796193\pi\)
−0.801929 + 0.597419i \(0.796193\pi\)
\(674\) 3.83823e9 + 5.71307e9i 0.482860 + 0.718721i
\(675\) −7.53426e9 + 1.00336e10i −0.942925 + 1.25573i
\(676\) 8.55656e9 + 3.49379e9i 1.06533 + 0.434995i
\(677\) −9.61552e9 + 9.61552e9i −1.19100 + 1.19100i −0.214216 + 0.976786i \(0.568720\pi\)
−0.976786 + 0.214216i \(0.931280\pi\)
\(678\) −3.18890e9 + 1.26216e9i −0.392949 + 0.155528i
\(679\) 8.93810e9 1.09572
\(680\) 1.13058e9 + 7.43121e8i 0.137886 + 0.0906314i
\(681\) 1.06052e10 6.80816e9i 1.28678 0.826066i
\(682\) 5.12749e8 + 1.00649e8i 0.0618955 + 0.0121496i
\(683\) 8.26144e9 + 8.26144e9i 0.992163 + 0.992163i 0.999970 0.00780614i \(-0.00248480\pi\)
−0.00780614 + 0.999970i \(0.502485\pi\)
\(684\) 1.24915e10 + 3.95388e8i 1.49251 + 0.0472419i
\(685\) −8.68970e9 + 8.68970e9i −1.03297 + 1.03297i
\(686\) 6.07026e9 + 9.03539e9i 0.717915 + 1.06859i
\(687\) 5.56990e9 + 8.67633e9i 0.655389 + 1.02091i
\(688\) 3.69692e9 3.72899e7i 0.432794 0.00436548i
\(689\) 1.66154e10i 1.93528i
\(690\) 5.82921e9 1.34663e10i 0.675519 1.56055i
\(691\) −9.55815e9 9.55815e9i −1.10205 1.10205i −0.994163 0.107885i \(-0.965592\pi\)
−0.107885 0.994163i \(-0.534408\pi\)
\(692\) −1.25958e10 + 5.29192e9i −1.44495 + 0.607075i
\(693\) 1.62545e9 + 4.37116e9i 0.185527 + 0.498919i
\(694\) −1.64288e9 + 8.36954e9i −0.186572 + 0.950481i
\(695\) 1.94683e9i 0.219979i
\(696\) 4.89758e8 + 5.00430e8i 0.0550616 + 0.0562615i
\(697\) 1.73132e8i 0.0193670i
\(698\) −9.30280e9 1.82607e9i −1.03543 0.203246i
\(699\) 5.90853e9 + 1.28837e9i 0.654349 + 0.142683i
\(700\) −2.19701e10 8.97079e9i −2.42097 0.988524i
\(701\) 1.23899e10 + 1.23899e10i 1.35848 + 1.35848i 0.875790 + 0.482692i \(0.160341\pi\)
0.482692 + 0.875790i \(0.339659\pi\)
\(702\) −8.99316e9 9.99085e9i −0.981143 1.08999i
\(703\) 7.72520e9i 0.838621i
\(704\) −2.75079e9 1.09095e9i −0.297134 0.117843i
\(705\) 1.74771e10 1.12197e10i 1.87849 1.20592i
\(706\) 2.83426e9 1.90415e9i 0.303126 0.203650i
\(707\) 7.93426e9 7.93426e9i 0.844381 0.844381i
\(708\) 5.76324e9 1.06691e9i 0.610310 0.112982i
\(709\) −5.87439e9 5.87439e9i −0.619014 0.619014i 0.326264 0.945279i \(-0.394210\pi\)
−0.945279 + 0.326264i \(0.894210\pi\)
\(710\) 1.67238e9 8.51985e9i 0.175360 0.893363i
\(711\) 6.86135e9 1.49852e10i 0.715922 1.56357i
\(712\) −8.22485e9 + 1.70080e9i −0.853981 + 0.176593i
\(713\) 2.02575e9 0.209301
\(714\) −1.54997e9 + 6.13475e8i −0.159360 + 0.0630744i
\(715\) −5.19418e9 + 5.19418e9i −0.531430 + 0.531430i
\(716\) 1.89982e9 + 4.52193e9i 0.193427 + 0.460392i
\(717\) 2.42731e9 + 5.29280e8i 0.245928 + 0.0536252i
\(718\) −6.39062e7 + 4.29343e7i −0.00644329 + 0.00432881i
\(719\) −1.07192e10 −1.07550 −0.537752 0.843103i \(-0.680726\pi\)
−0.537752 + 0.843103i \(0.680726\pi\)
\(720\) 1.46659e10 + 6.53703e9i 1.46435 + 0.652705i
\(721\) 2.25366e10 2.23932
\(722\) 1.03238e10 6.93583e9i 1.02084 0.685833i
\(723\) −1.58569e10 3.45764e9i −1.56039 0.340248i
\(724\) 1.14798e10 4.82305e9i 1.12421 0.472320i
\(725\) −8.96926e8 + 8.96926e8i −0.0874125 + 0.0874125i
\(726\) 8.60731e9 3.40675e9i 0.834813 0.330417i
\(727\) −1.33447e10 −1.28807 −0.644035 0.764996i \(-0.722741\pi\)
−0.644035 + 0.764996i \(0.722741\pi\)
\(728\) 1.39641e10 2.12450e10i 1.34139 2.04078i
\(729\) 2.91734e9 + 1.00453e10i 0.278895 + 0.960322i
\(730\) −1.42947e9 + 7.28237e9i −0.136002 + 0.692856i
\(731\) 3.32660e8 + 3.32660e8i 0.0314985 + 0.0314985i
\(732\) 8.14135e8 + 4.39782e9i 0.0767198 + 0.414427i
\(733\) 5.08063e9 5.08063e9i 0.476490 0.476490i −0.427517 0.904007i \(-0.640612\pi\)
0.904007 + 0.427517i \(0.140612\pi\)
\(734\) 2.23479e9 1.50140e9i 0.208593 0.140140i
\(735\) 2.57508e10 1.65311e10i 2.39213 1.53567i
\(736\) −1.12792e10 2.09609e9i −1.04281 0.193793i
\(737\) 1.11669e9i 0.102753i
\(738\) 3.31792e8 + 2.02778e9i 0.0303857 + 0.185705i
\(739\) 1.47179e10 + 1.47179e10i 1.34150 + 1.34150i 0.894573 + 0.446923i \(0.147480\pi\)
0.446923 + 0.894573i \(0.352520\pi\)
\(740\) 3.75189e9 9.18866e9i 0.340361 0.833569i
\(741\) −2.36976e10 5.16733e9i −2.13964 0.466555i
\(742\) −2.39958e10 4.71020e9i −2.15636 0.423278i
\(743\) 8.51607e9i 0.761690i −0.924639 0.380845i \(-0.875633\pi\)
0.924639 0.380845i \(-0.124367\pi\)
\(744\) −2.38903e7 + 2.21654e9i −0.00212675 + 0.197319i
\(745\) 1.39798e10i 1.23866i
\(746\) −1.67972e8 + 8.55724e8i −0.0148133 + 0.0754654i
\(747\) −5.34185e9 + 1.98641e9i −0.468889 + 0.174360i
\(748\) −1.45855e8 3.47163e8i −0.0127428 0.0303303i
\(749\) 4.35246e9 + 4.35246e9i 0.378485 + 0.378485i
\(750\) −4.19669e9 + 9.69497e9i −0.363239 + 0.839136i
\(751\) 9.07887e8i 0.0782154i 0.999235 + 0.0391077i \(0.0124515\pi\)
−0.999235 + 0.0391077i \(0.987548\pi\)
\(752\) −1.15967e10 1.13650e10i −0.994421 0.974561i
\(753\) 6.63523e8 + 1.03358e9i 0.0566335 + 0.0882190i
\(754\) −7.57811e8 1.12798e9i −0.0643815 0.0958297i
\(755\) −7.18708e9 + 7.18708e9i −0.607769 + 0.607769i
\(756\) −1.69781e10 + 1.01556e10i −1.42910 + 0.854830i
\(757\) −9.50445e9 9.50445e9i −0.796327 0.796327i 0.186187 0.982514i \(-0.440387\pi\)
−0.982514 + 0.186187i \(0.940387\pi\)
\(758\) 4.14315e9 + 8.13269e8i 0.345532 + 0.0678254i
\(759\) −3.43686e9 + 2.20634e9i −0.285309 + 0.183158i
\(760\) 2.83717e10 5.86695e9i 2.34444 0.484802i
\(761\) −5.98321e9 −0.492139 −0.246070 0.969252i \(-0.579139\pi\)
−0.246070 + 0.969252i \(0.579139\pi\)
\(762\) −1.39104e10 + 5.50569e9i −1.13893 + 0.450785i
\(763\) 1.69205e10 1.69205e10i 1.37904 1.37904i
\(764\) −4.95947e9 + 1.21461e10i −0.402354 + 0.985396i
\(765\) 7.12140e8 + 1.91508e9i 0.0575110 + 0.154658i
\(766\) −5.93898e8 8.83997e8i −0.0477432 0.0710641i
\(767\) −1.13748e10 −0.910247
\(768\) 2.42653e9 1.23167e10i 0.193295 0.981141i
\(769\) −4.50714e9 −0.357404 −0.178702 0.983903i \(-0.557190\pi\)
−0.178702 + 0.983903i \(0.557190\pi\)
\(770\) 6.02893e9 + 8.97386e9i 0.475908 + 0.708373i
\(771\) −2.87932e9 + 1.32047e10i −0.226256 + 1.03762i
\(772\) −4.89545e9 + 1.19893e10i −0.382941 + 0.937852i
\(773\) 7.16450e9 7.16450e9i 0.557901 0.557901i −0.370808 0.928709i \(-0.620919\pi\)
0.928709 + 0.370808i \(0.120919\pi\)
\(774\) 4.53374e9 + 3.25871e9i 0.351450 + 0.252611i
\(775\) −4.01554e9 −0.309876
\(776\) −8.38773e9 + 1.73449e9i −0.644359 + 0.133246i
\(777\) 6.60632e9 + 1.02908e10i 0.505227 + 0.787000i
\(778\) 1.12428e10 + 2.20688e9i 0.855947 + 0.168016i
\(779\) 2.62158e9 + 2.62158e9i 0.198693 + 0.198693i
\(780\) −2.56773e10 1.76554e10i −1.93740 1.33213i
\(781\) −1.70875e9 + 1.70875e9i −0.128352 + 0.128352i
\(782\) −8.14097e8 1.21176e9i −0.0608769 0.0906132i
\(783\) 1.48944e8 + 1.04691e9i 0.0110881 + 0.0779371i
\(784\) −1.70865e10 1.67453e10i −1.26633 1.24104i
\(785\) 1.52081e9i 0.112210i
\(786\) −6.93096e9 3.00022e9i −0.509113 0.220381i
\(787\) −1.38937e10 1.38937e10i −1.01603 1.01603i −0.999869 0.0161617i \(-0.994855\pi\)
−0.0161617 0.999869i \(-0.505145\pi\)
\(788\) 1.02312e10 + 2.43523e10i 0.744881 + 1.77296i
\(789\) 1.58758e9 7.28070e9i 0.115071 0.527720i
\(790\) 7.35921e9 3.74911e10i 0.531051 2.70541i
\(791\) 9.79573e9i 0.703751i
\(792\) −2.37361e9 3.78657e9i −0.169774 0.270837i
\(793\) 8.67988e9i 0.618098i
\(794\) 1.62720e10 + 3.19407e9i 1.15364 + 0.226450i
\(795\) −6.38566e9 + 2.92849e10i −0.450735 + 2.06709i
\(796\) 6.66822e9 1.63310e10i 0.468613 1.14767i
\(797\) −1.90624e9 1.90624e9i −0.133375 0.133375i 0.637268 0.770642i \(-0.280065\pi\)
−0.770642 + 0.637268i \(0.780065\pi\)
\(798\) −1.41805e10 + 3.27591e10i −0.987829 + 2.28203i
\(799\) 2.06616e9i 0.143301i
\(800\) 2.23581e10 + 4.15498e9i 1.54390 + 0.286915i
\(801\) −1.15325e10 5.28047e9i −0.792886 0.363043i
\(802\) 2.26662e10 1.52279e10i 1.55156 1.04239i
\(803\) 1.46056e9 1.46056e9i 0.0995442 0.0995442i
\(804\) 4.65801e9 8.62302e8i 0.316085 0.0585144i
\(805\) 2.96362e10 + 2.96362e10i 2.00234 + 2.00234i
\(806\) 8.28616e8 4.22134e9i 0.0557418 0.283973i
\(807\) −1.45167e10 2.26129e10i −0.972323 1.51460i
\(808\) −5.90601e9 + 8.98538e9i −0.393871 + 0.599234i
\(809\) −2.64210e10 −1.75440 −0.877202 0.480121i \(-0.840593\pi\)
−0.877202 + 0.480121i \(0.840593\pi\)
\(810\) 1.20109e10 + 2.10653e10i 0.794106 + 1.39274i
\(811\) 1.12769e9 1.12769e9i 0.0742361 0.0742361i −0.669014 0.743250i \(-0.733283\pi\)
0.743250 + 0.669014i \(0.233283\pi\)
\(812\) −1.84384e9 + 7.74662e8i −0.120859 + 0.0507769i
\(813\) 3.34005e9 1.53176e10i 0.217990 0.999712i
\(814\) −2.29299e9 + 1.54050e9i −0.149010 + 0.100110i
\(815\) −9.09068e8 −0.0588227
\(816\) 1.33548e9 8.76480e8i 0.0860444 0.0564711i
\(817\) 1.00743e10 0.646307
\(818\) −7.87467e9 + 5.29045e9i −0.503032 + 0.337953i
\(819\) 3.59867e10 1.33820e10i 2.28901 0.851189i
\(820\) 1.84499e9 + 4.39144e9i 0.116855 + 0.278137i
\(821\) 1.72292e10 1.72292e10i 1.08658 1.08658i 0.0907063 0.995878i \(-0.471088\pi\)
0.995878 0.0907063i \(-0.0289124\pi\)
\(822\) 5.33986e9 + 1.34914e10i 0.335335 + 0.847239i
\(823\) 1.77668e10 1.11099 0.555493 0.831521i \(-0.312529\pi\)
0.555493 + 0.831521i \(0.312529\pi\)
\(824\) −2.11489e10 + 4.37335e9i −1.31687 + 0.272313i
\(825\) 6.81271e9 4.37352e9i 0.422407 0.271171i
\(826\) −3.22457e9 + 1.64274e10i −0.199086 + 1.01423i
\(827\) −1.48933e10 1.48933e10i −0.915631 0.915631i 0.0810766 0.996708i \(-0.474164\pi\)
−0.996708 + 0.0810766i \(0.974164\pi\)
\(828\) −1.18572e10 1.26323e10i −0.725898 0.773353i
\(829\) −8.76714e9 + 8.76714e9i −0.534462 + 0.534462i −0.921897 0.387435i \(-0.873361\pi\)
0.387435 + 0.921897i \(0.373361\pi\)
\(830\) −1.09667e10 + 7.36777e9i −0.665736 + 0.447263i
\(831\) 1.11471e10 + 1.73640e10i 0.673842 + 1.04966i
\(832\) −8.98157e9 + 2.26466e10i −0.540656 + 1.36324i
\(833\) 3.04429e9i 0.182485i
\(834\) −2.10947e9 9.13131e8i −0.125919 0.0545070i
\(835\) 1.95667e10 + 1.95667e10i 1.16310 + 1.16310i
\(836\) −7.46531e9 3.04821e9i −0.441902 0.180436i
\(837\) −2.01010e9 + 2.67693e9i −0.118489 + 0.157797i
\(838\) −1.58008e10 3.10158e9i −0.927525 0.182066i
\(839\) 3.27205e10i 1.91273i 0.292181 + 0.956363i \(0.405619\pi\)
−0.292181 + 0.956363i \(0.594381\pi\)
\(840\) −3.27770e10 + 3.20779e10i −1.90806 + 1.86736i
\(841\) 1.71430e10i 0.993803i
\(842\) 2.09697e9 1.06829e10i 0.121060 0.616733i
\(843\) −1.22465e10 2.67037e9i −0.704067 0.153524i
\(844\) −4.27903e9 + 1.79777e9i −0.244989 + 0.102928i
\(845\) 2.28796e10 + 2.28796e10i 1.30452 + 1.30452i
\(846\) −3.95961e9 2.41996e10i −0.224831 1.37408i
\(847\) 2.64401e10i 1.49511i
\(848\) 2.34323e10 2.36355e8i 1.31956 0.0133101i
\(849\) 1.58762e10 1.01920e10i 0.890369 0.571586i
\(850\) 1.61374e9 + 2.40200e9i 0.0901298 + 0.134155i
\(851\) −7.57261e9 + 7.57261e9i −0.421204 + 0.421204i
\(852\) −8.44719e9 5.80820e9i −0.467922 0.321738i
\(853\) −1.21022e10 1.21022e10i −0.667640 0.667640i 0.289529 0.957169i \(-0.406501\pi\)
−0.957169 + 0.289529i \(0.906501\pi\)
\(854\) −1.25354e10 2.46061e9i −0.688710 0.135188i
\(855\) 3.97816e10 + 1.82150e10i 2.17671 + 0.996664i
\(856\) −4.92907e9 3.23983e9i −0.268600 0.176549i
\(857\) 3.22325e10 1.74929 0.874643 0.484768i \(-0.161096\pi\)
0.874643 + 0.484768i \(0.161096\pi\)
\(858\) 3.19185e9 + 8.06435e9i 0.172519 + 0.435877i
\(859\) 1.39418e10 1.39418e10i 0.750485 0.750485i −0.224085 0.974570i \(-0.571939\pi\)
0.974570 + 0.224085i \(0.0719393\pi\)
\(860\) 1.19828e10 + 4.89279e9i 0.642413 + 0.262308i
\(861\) −5.73411e9 1.25034e9i −0.306165 0.0667601i
\(862\) 1.20650e10 + 1.79584e10i 0.641583 + 0.954975i
\(863\) −1.72765e9 −0.0914995 −0.0457498 0.998953i \(-0.514568\pi\)
−0.0457498 + 0.998953i \(0.514568\pi\)
\(864\) 1.39619e10 1.28250e10i 0.736457 0.676484i
\(865\) −4.78304e10 −2.51274
\(866\) −8.30313e9 1.23589e10i −0.434439 0.646648i
\(867\) −1.85505e10 4.04498e9i −0.966693 0.210790i
\(868\) −5.86153e9 2.39336e9i −0.304223 0.124219i
\(869\) −7.51927e9 + 7.51927e9i −0.388693 + 0.388693i
\(870\) 9.02150e8 + 2.27932e9i 0.0464474 + 0.117351i
\(871\) −9.19341e9 −0.471425
\(872\) −1.25951e10 + 1.91621e10i −0.643271 + 0.978670i
\(873\) −1.17609e10 5.38503e9i −0.598261 0.273929i
\(874\) −3.06756e10 6.02138e9i −1.55419 0.305075i
\(875\) −2.13364e10 2.13364e10i −1.07669 1.07669i
\(876\) 7.22026e9 + 4.96457e9i 0.362901 + 0.249527i
\(877\) 2.51720e10 2.51720e10i 1.26014 1.26014i 0.309116 0.951024i \(-0.399967\pi\)
0.951024 0.309116i \(-0.100033\pi\)
\(878\) 1.66081e10 + 2.47206e10i 0.828111 + 1.23262i
\(879\) −2.29576e10 + 1.47380e10i −1.14016 + 0.731942i
\(880\) −7.39911e9 7.25134e9i −0.366008 0.358698i
\(881\) 2.74080e10i 1.35040i 0.737635 + 0.675199i \(0.235942\pi\)
−0.737635 + 0.675199i \(0.764058\pi\)
\(882\) −5.83410e9 3.56557e10i −0.286308 1.74980i
\(883\) 1.69764e10 + 1.69764e10i 0.829817 + 0.829817i 0.987491 0.157674i \(-0.0503995\pi\)
−0.157674 + 0.987491i \(0.550399\pi\)
\(884\) −2.85811e9 + 1.20079e9i −0.139154 + 0.0584634i
\(885\) 2.00483e10 + 4.37158e9i 0.972245 + 0.212001i
\(886\) −5.80601e9 + 2.95784e10i −0.280453 + 1.42875i
\(887\) 2.45295e9i 0.118020i −0.998257 0.0590099i \(-0.981206\pi\)
0.998257 0.0590099i \(-0.0187944\pi\)
\(888\) −8.19651e9 8.37512e9i −0.392811 0.401371i
\(889\) 4.27302e10i 2.03976i
\(890\) −2.88530e10 5.66362e9i −1.37191 0.269296i
\(891\) 4.94740e8 6.73094e9i 0.0234318 0.318789i
\(892\) 2.04033e10 + 8.33102e9i 0.962550 + 0.393026i
\(893\) −3.12860e10 3.12860e10i −1.47018 1.47018i
\(894\) 1.51476e10 + 6.55700e9i 0.709028 + 0.306919i
\(895\) 1.71713e10i 0.800611i
\(896\) 3.01599e10 + 1.93911e10i 1.40072 + 0.900583i
\(897\) 1.81643e10 + 2.82948e10i 0.840320 + 1.30898i
\(898\) −4.23681e9 + 2.84642e9i −0.195241 + 0.131169i
\(899\) −2.39296e8 + 2.39296e8i −0.0109844 + 0.0109844i
\(900\) 2.35039e10 + 2.50405e10i 1.07471 + 1.14497i
\(901\) 2.10851e9 + 2.10851e9i 0.0960369 + 0.0960369i
\(902\) 2.55359e8 1.30091e9i 0.0115859 0.0590236i
\(903\) −1.34201e10 + 8.61522e9i −0.606524 + 0.389367i
\(904\) 1.90091e9 + 9.19254e9i 0.0855800 + 0.413853i
\(905\) 4.35925e10 1.95498
\(906\) 4.41649e9 + 1.11585e10i 0.197301 + 0.498490i
\(907\) −1.88847e10 + 1.88847e10i −0.840395 + 0.840395i −0.988910 0.148515i \(-0.952551\pi\)
0.148515 + 0.988910i \(0.452551\pi\)
\(908\) −1.33607e10 3.18010e10i −0.592283 1.40975i
\(909\) −1.52203e10 + 5.65979e9i −0.672123 + 0.249935i
\(910\) 7.38797e10 4.96348e10i 3.24998 2.18344i
\(911\) 1.63226e10 0.715278 0.357639 0.933860i \(-0.383582\pi\)
0.357639 + 0.933860i \(0.383582\pi\)
\(912\) 6.95026e9 3.34937e10i 0.303403 1.46211i
\(913\) 3.67719e9 0.159907
\(914\) −2.49144e10 + 1.67383e10i −1.07929 + 0.725102i
\(915\) −3.33587e9 + 1.52985e10i −0.143958 + 0.660197i
\(916\) 2.60171e10 1.09307e10i 1.11847 0.469908i
\(917\) 1.52534e10 1.52534e10i 0.653243 0.653243i
\(918\) 2.40909e9 + 1.26608e8i 0.102779 + 0.00540148i
\(919\) −2.57371e10 −1.09384 −0.546922 0.837183i \(-0.684201\pi\)
−0.546922 + 0.837183i \(0.684201\pi\)
\(920\) −3.35624e10 2.20603e10i −1.42101 0.934014i
\(921\) 8.06950e9 + 1.25700e10i 0.340359 + 0.530184i
\(922\) 2.76104e9 1.40660e10i 0.116015 0.591033i
\(923\) 1.40678e10 + 1.40678e10i 0.588870 + 0.588870i
\(924\) 1.25513e10 2.32353e9i 0.523404 0.0968939i
\(925\) 1.50108e10 1.50108e10i 0.623603 0.623603i
\(926\) 1.68889e10 1.13465e10i 0.698977 0.469595i
\(927\) −2.96541e10 1.35779e10i −1.22266 0.559826i
\(928\) 1.57998e9 1.08477e9i 0.0648983 0.0445573i
\(929\) 1.94199e10i 0.794680i −0.917671 0.397340i \(-0.869933\pi\)
0.917671 0.397340i \(-0.130067\pi\)
\(930\) −3.08281e9 + 7.12174e9i −0.125677 + 0.290332i
\(931\) −4.60968e10 4.60968e10i −1.87218 1.87218i
\(932\) 6.25700e9 1.53239e10i 0.253169 0.620030i
\(933\) 5.14481e9 2.35943e10i 0.207388 0.951091i
\(934\) −6.44680e9 1.26546e9i −0.258899 0.0508199i
\(935\) 1.31829e9i 0.0527437i
\(936\) −3.11739e10 + 1.95413e10i −1.24258 + 0.778913i
\(937\) 1.61086e10i 0.639689i −0.947470 0.319845i \(-0.896369\pi\)
0.947470 0.319845i \(-0.103631\pi\)
\(938\) −2.60618e9 + 1.32771e10i −0.103109 + 0.525281i
\(939\) 4.51581e9 2.07097e10i 0.177994 0.816290i
\(940\) −2.20182e10 5.24074e10i −0.864637 2.05800i
\(941\) −5.75312e9 5.75312e9i −0.225082 0.225082i 0.585553 0.810634i \(-0.300878\pi\)
−0.810634 + 0.585553i \(0.800878\pi\)
\(942\) −1.64785e9 7.13311e8i −0.0642304 0.0278036i
\(943\) 5.13960e9i 0.199590i
\(944\) −1.61807e8 1.60416e10i −0.00626031 0.620648i
\(945\) −6.85702e10 + 9.75550e9i −2.64316 + 0.376043i
\(946\) −2.00895e9 2.99026e9i −0.0771526 0.114839i
\(947\) 9.82385e9 9.82385e9i 0.375887 0.375887i −0.493729 0.869616i \(-0.664367\pi\)
0.869616 + 0.493729i \(0.164367\pi\)
\(948\) −3.71713e10 2.55586e10i −1.41703 0.974335i
\(949\) −1.20245e10 1.20245e10i −0.456703 0.456703i
\(950\) 6.08067e10 + 1.19359e10i 2.30101 + 0.451671i
\(951\) 7.87866e9 + 1.22727e10i 0.297044 + 0.462710i
\(952\) 9.23944e8 + 4.46806e9i 0.0347069 + 0.167838i
\(953\) −7.68624e8 −0.0287666 −0.0143833 0.999897i \(-0.504579\pi\)
−0.0143833 + 0.999897i \(0.504579\pi\)
\(954\) 2.87363e10 + 2.06548e10i 1.07155 + 0.770196i
\(955\) −3.24778e10 + 3.24778e10i −1.20663 + 1.20663i
\(956\) 2.57046e9 6.29525e9i 0.0951498 0.233029i
\(957\) 1.45357e8 6.66614e8i 0.00536098 0.0245857i
\(958\) 2.60252e10 + 3.87377e10i 0.956347 + 1.42349i
\(959\) −4.14432e10 −1.51736
\(960\) 2.45338e10 3.64632e10i 0.894984 1.33017i
\(961\) 2.64413e10 0.961061
\(962\) 1.26826e10 + 1.88776e10i 0.459299 + 0.683652i
\(963\) −3.10476e9 8.34931e9i −0.112031 0.301272i
\(964\) −1.67921e10 + 4.11250e10i −0.603719 + 1.47855i
\(965\) −3.20585e10 + 3.20585e10i −1.14841 + 1.14841i
\(966\) 4.60124e10 1.82116e10i 1.64231 0.650022i
\(967\) −1.34957e10 −0.479957 −0.239979 0.970778i \(-0.577140\pi\)
−0.239979 + 0.970778i \(0.577140\pi\)
\(968\) −5.13085e9 2.48120e10i −0.181813 0.879223i
\(969\) 3.66299e9 2.35151e9i 0.129331 0.0830259i
\(970\) −2.94244e10 5.77578e9i −1.03516 0.203193i
\(971\) 2.76593e10 + 2.76593e10i 0.969557 + 0.969557i 0.999550 0.0299927i \(-0.00954841\pi\)
−0.0299927 + 0.999550i \(0.509548\pi\)
\(972\) 2.84587e10 3.13392e9i 0.993991 0.109460i
\(973\) 4.64245e9 4.64245e9i 0.161567 0.161567i
\(974\) −8.91403e9 1.32682e10i −0.309113 0.460105i
\(975\) −3.60062e10 5.60874e10i −1.24412 1.93798i
\(976\) 1.22410e10 1.23472e8i 0.421447 0.00425103i
\(977\) 2.41000e10i 0.826773i 0.910556 + 0.413387i \(0.135654\pi\)
−0.910556 + 0.413387i \(0.864346\pi\)
\(978\) −4.26385e8 + 9.85011e8i −0.0145752 + 0.0336709i
\(979\) 5.78681e9 + 5.78681e9i 0.197106 + 0.197106i
\(980\) −3.24416e10 7.72172e10i −1.10106 2.62073i
\(981\) −3.24586e10 + 1.20700e10i −1.09771 + 0.408194i
\(982\) −6.43955e8 + 3.28059e9i −0.0217003 + 0.110551i
\(983\) 3.06695e10i 1.02984i 0.857239 + 0.514919i \(0.172178\pi\)
−0.857239 + 0.514919i \(0.827822\pi\)
\(984\) 5.62366e9 + 6.06130e7i 0.188164 + 0.00202807i
\(985\) 9.24738e10i 3.08313i
\(986\) 2.39308e8 + 4.69743e7i 0.00795038 + 0.00156060i
\(987\) 6.84309e10 + 1.49216e10i 2.26539 + 0.493974i
\(988\) −2.50952e10 + 6.14601e10i −0.827831 + 2.02742i
\(989\) −9.87534e9 9.87534e9i −0.324612 0.324612i
\(990\) −2.52639e9 1.54403e10i −0.0827516 0.505745i
\(991\) 7.67545e9i 0.250522i −0.992124 0.125261i \(-0.960023\pi\)
0.992124 0.125261i \(-0.0399768\pi\)
\(992\) 5.96504e9 + 1.10853e9i 0.194009 + 0.0360542i
\(993\) −2.96888e10 + 1.90592e10i −0.962210 + 0.617705i
\(994\) 2.43046e10 1.63286e10i 0.784938 0.527347i
\(995\) 4.36678e10 4.36678e10i 1.40534 1.40534i
\(996\) 2.83951e9 + 1.53386e10i 0.0910618 + 0.491900i
\(997\) 9.39856e9 + 9.39856e9i 0.300350 + 0.300350i 0.841151 0.540800i \(-0.181879\pi\)
−0.540800 + 0.841151i \(0.681879\pi\)
\(998\) 8.73199e9 4.44846e10i 0.278071 1.41662i
\(999\) −2.49271e9 1.75210e10i −0.0791029 0.556005i
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.11.18 108
3.2 odd 2 inner 48.8.k.a.11.37 yes 108
16.3 odd 4 inner 48.8.k.a.35.37 yes 108
48.35 even 4 inner 48.8.k.a.35.18 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.8.k.a.11.18 108 1.1 even 1 trivial
48.8.k.a.11.37 yes 108 3.2 odd 2 inner
48.8.k.a.35.18 yes 108 48.35 even 4 inner
48.8.k.a.35.37 yes 108 16.3 odd 4 inner