Properties

Label 91.8.h.a.16.9
Level $91$
Weight $8$
Character 91.16
Analytic conductor $28.427$
Analytic rank $0$
Dimension $126$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,8,Mod(16,91)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(91, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.16");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.h (of order \(3\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(28.4270373191\)
Analytic rank: \(0\)
Dimension: \(126\)
Relative dimension: \(63\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 16.9
Character \(\chi\) \(=\) 91.16
Dual form 91.8.h.a.74.9

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-18.0124 q^{2} +(2.20243 - 3.81472i) q^{3} +196.447 q^{4} +(111.005 - 192.267i) q^{5} +(-39.6710 + 68.7122i) q^{6} +(-798.622 - 430.983i) q^{7} -1232.89 q^{8} +(1083.80 + 1877.19i) q^{9} +O(q^{10})\) \(q-18.0124 q^{2} +(2.20243 - 3.81472i) q^{3} +196.447 q^{4} +(111.005 - 192.267i) q^{5} +(-39.6710 + 68.7122i) q^{6} +(-798.622 - 430.983i) q^{7} -1232.89 q^{8} +(1083.80 + 1877.19i) q^{9} +(-1999.47 + 3463.19i) q^{10} +(-797.940 + 1382.07i) q^{11} +(432.660 - 749.388i) q^{12} +(7377.37 + 2884.95i) q^{13} +(14385.1 + 7763.05i) q^{14} +(-488.962 - 846.908i) q^{15} -2937.89 q^{16} -17576.0 q^{17} +(-19521.8 - 33812.8i) q^{18} +(-19154.3 - 33176.2i) q^{19} +(21806.6 - 37770.2i) q^{20} +(-3402.99 + 2097.31i) q^{21} +(14372.8 - 24894.4i) q^{22} -18356.7 q^{23} +(-2715.35 + 4703.12i) q^{24} +(14418.1 + 24973.0i) q^{25} +(-132884. - 51964.9i) q^{26} +19181.4 q^{27} +(-156887. - 84665.2i) q^{28} +(-51542.4 - 89274.1i) q^{29} +(8807.39 + 15254.8i) q^{30} +(-6473.60 - 11212.6i) q^{31} +210728. q^{32} +(3514.81 + 6087.83i) q^{33} +316586. q^{34} +(-171515. + 105707. i) q^{35} +(212909. + 368769. i) q^{36} +84650.2 q^{37} +(345015. + 597584. i) q^{38} +(27253.4 - 21788.7i) q^{39} +(-136857. + 237044. i) q^{40} +(70051.3 + 121332. i) q^{41} +(61295.9 - 37777.5i) q^{42} +(-364236. + 630875. i) q^{43} +(-156753. + 271503. i) q^{44} +481230. q^{45} +330649. q^{46} +(23191.6 - 40169.0i) q^{47} +(-6470.49 + 11207.2i) q^{48} +(452050. + 688385. i) q^{49} +(-259705. - 449823. i) q^{50} +(-38709.9 + 67047.5i) q^{51} +(1.44926e6 + 566739. i) q^{52} +(640099. + 1.10868e6i) q^{53} -345503. q^{54} +(177151. + 306835. i) q^{55} +(984611. + 531354. i) q^{56} -168744. q^{57} +(928403. + 1.60804e6i) q^{58} -105425. q^{59} +(-96055.0 - 166372. i) q^{60} +(552960. + 957755. i) q^{61} +(116605. + 201966. i) q^{62} +(-56505.4 - 1.96627e6i) q^{63} -3.41967e6 q^{64} +(1.37361e6 - 1.09818e6i) q^{65} +(-63310.1 - 109656. i) q^{66} +(-1.56688e6 + 2.71392e6i) q^{67} -3.45275e6 q^{68} +(-40429.3 + 70025.7i) q^{69} +(3.08940e6 - 1.90404e6i) q^{70} +(30963.0 - 53629.5i) q^{71} +(-1.33620e6 - 2.31437e6i) q^{72} +(2.24168e6 + 3.88271e6i) q^{73} -1.52475e6 q^{74} +127020. q^{75} +(-3.76280e6 - 6.51736e6i) q^{76} +(1.23290e6 - 759854. i) q^{77} +(-490899. + 392466. i) q^{78} +(2.28994e6 - 3.96629e6i) q^{79} +(-326121. + 564858. i) q^{80} +(-2.32802e6 + 4.03225e6i) q^{81} +(-1.26179e6 - 2.18549e6i) q^{82} +6.30798e6 q^{83} +(-668505. + 412009. i) q^{84} +(-1.95103e6 + 3.37928e6i) q^{85} +(6.56077e6 - 1.13636e7i) q^{86} -454074. q^{87} +(983770. - 1.70394e6i) q^{88} +4.06406e6 q^{89} -8.66810e6 q^{90} +(-4.64836e6 - 5.48351e6i) q^{91} -3.60612e6 q^{92} -57030.6 q^{93} +(-417736. + 723540. i) q^{94} -8.50492e6 q^{95} +(464114. - 803868. i) q^{96} +(14469.3 - 25061.5i) q^{97} +(-8.14250e6 - 1.23995e7i) q^{98} -3.45922e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 126 q - 2 q^{2} - 80 q^{3} + 7678 q^{4} - 2 q^{5} - 258 q^{6} + 953 q^{7} - 264 q^{8} - 41707 q^{9} - 4255 q^{10} + 7423 q^{11} - 18072 q^{12} - 1824 q^{13} - 15916 q^{14} + 11047 q^{15} + 410294 q^{16} + 99274 q^{17} - 21111 q^{18} - 4844 q^{19} + 36626 q^{20} + 73198 q^{21} - 43360 q^{22} + 34130 q^{23} - 130304 q^{24} - 810669 q^{25} + 390708 q^{26} + 416614 q^{27} + 69267 q^{28} + 191096 q^{29} + 70666 q^{30} + 183609 q^{31} + 695346 q^{32} + 178591 q^{33} - 742000 q^{34} + 579437 q^{35} - 1732409 q^{36} - 1362898 q^{37} - 877438 q^{38} + 459227 q^{39} - 1502882 q^{40} + 593701 q^{41} + 1442877 q^{42} - 592188 q^{43} + 1254066 q^{44} + 1954226 q^{45} - 1385452 q^{46} + 98278 q^{47} - 374916 q^{48} - 1497637 q^{49} + 289562 q^{50} - 281250 q^{51} - 8455 q^{52} - 1256681 q^{53} - 293814 q^{54} - 3015554 q^{55} - 1646151 q^{56} + 2743072 q^{57} + 1851469 q^{58} - 2279458 q^{59} + 1031485 q^{60} - 1127636 q^{61} - 7724680 q^{62} + 5142530 q^{63} + 11827496 q^{64} - 2789048 q^{65} + 435059 q^{66} + 4373348 q^{67} + 8737122 q^{68} - 7610377 q^{69} - 8084578 q^{70} - 60067 q^{71} - 11660951 q^{72} - 5060877 q^{73} + 1184002 q^{74} + 22637254 q^{75} + 637438 q^{76} + 21469082 q^{77} - 7230943 q^{78} - 2446486 q^{79} - 123568 q^{80} - 30756895 q^{81} + 8626952 q^{82} - 18679806 q^{83} + 11302461 q^{84} + 5330093 q^{85} - 8512356 q^{86} - 16508762 q^{87} - 6438219 q^{88} - 6176684 q^{89} + 53481084 q^{90} + 29236777 q^{91} + 2460546 q^{92} + 27682404 q^{93} - 17421794 q^{94} + 39553398 q^{95} + 26667066 q^{96} + 7705262 q^{97} + 14093080 q^{98} - 60531432 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/91\mathbb{Z}\right)^\times\).

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{1}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −18.0124 −1.59209 −0.796043 0.605240i \(-0.793077\pi\)
−0.796043 + 0.605240i \(0.793077\pi\)
\(3\) 2.20243 3.81472i 0.0470953 0.0815714i −0.841517 0.540231i \(-0.818337\pi\)
0.888612 + 0.458659i \(0.151670\pi\)
\(4\) 196.447 1.53474
\(5\) 111.005 192.267i 0.397145 0.687875i −0.596228 0.802815i \(-0.703334\pi\)
0.993372 + 0.114941i \(0.0366678\pi\)
\(6\) −39.6710 + 68.7122i −0.0749797 + 0.129869i
\(7\) −798.622 430.983i −0.880031 0.474917i
\(8\) −1232.89 −0.851351
\(9\) 1083.80 + 1877.19i 0.495564 + 0.858342i
\(10\) −1999.47 + 3463.19i −0.632289 + 1.09516i
\(11\) −797.940 + 1382.07i −0.180757 + 0.313081i −0.942139 0.335224i \(-0.891188\pi\)
0.761381 + 0.648304i \(0.224521\pi\)
\(12\) 432.660 749.388i 0.0722790 0.125191i
\(13\) 7377.37 + 2884.95i 0.931322 + 0.364197i
\(14\) 14385.1 + 7763.05i 1.40109 + 0.756108i
\(15\) −488.962 846.908i −0.0374073 0.0647913i
\(16\) −2937.89 −0.179314
\(17\) −17576.0 −0.867658 −0.433829 0.900995i \(-0.642838\pi\)
−0.433829 + 0.900995i \(0.642838\pi\)
\(18\) −19521.8 33812.8i −0.788981 1.36655i
\(19\) −19154.3 33176.2i −0.640662 1.10966i −0.985285 0.170918i \(-0.945327\pi\)
0.344623 0.938741i \(-0.388007\pi\)
\(20\) 21806.6 37770.2i 0.609514 1.05571i
\(21\) −3402.99 + 2097.31i −0.0801849 + 0.0494190i
\(22\) 14372.8 24894.4i 0.287781 0.498451i
\(23\) −18356.7 −0.314592 −0.157296 0.987552i \(-0.550278\pi\)
−0.157296 + 0.987552i \(0.550278\pi\)
\(24\) −2715.35 + 4703.12i −0.0400946 + 0.0694459i
\(25\) 14418.1 + 24973.0i 0.184552 + 0.319654i
\(26\) −132884. 51964.9i −1.48274 0.579833i
\(27\) 19181.4 0.187545
\(28\) −156887. 84665.2i −1.35062 0.728873i
\(29\) −51542.4 89274.1i −0.392439 0.679724i 0.600332 0.799751i \(-0.295035\pi\)
−0.992771 + 0.120027i \(0.961702\pi\)
\(30\) 8807.39 + 15254.8i 0.0595556 + 0.103153i
\(31\) −6473.60 11212.6i −0.0390283 0.0675991i 0.845851 0.533419i \(-0.179093\pi\)
−0.884880 + 0.465820i \(0.845760\pi\)
\(32\) 210728. 1.13684
\(33\) 3514.81 + 6087.83i 0.0170256 + 0.0294892i
\(34\) 316586. 1.38139
\(35\) −171515. + 105707.i −0.676183 + 0.416740i
\(36\) 212909. + 368769.i 0.760562 + 1.31733i
\(37\) 84650.2 0.274740 0.137370 0.990520i \(-0.456135\pi\)
0.137370 + 0.990520i \(0.456135\pi\)
\(38\) 345015. + 597584.i 1.01999 + 1.76667i
\(39\) 27253.4 21788.7i 0.0735689 0.0588173i
\(40\) −136857. + 237044.i −0.338110 + 0.585623i
\(41\) 70051.3 + 121332.i 0.158735 + 0.274937i 0.934413 0.356192i \(-0.115925\pi\)
−0.775678 + 0.631129i \(0.782592\pi\)
\(42\) 61295.9 37777.5i 0.127661 0.0786794i
\(43\) −364236. + 630875.i −0.698624 + 1.21005i 0.270320 + 0.962771i \(0.412871\pi\)
−0.968944 + 0.247281i \(0.920463\pi\)
\(44\) −156753. + 271503.i −0.277415 + 0.480497i
\(45\) 481230. 0.787242
\(46\) 330649. 0.500858
\(47\) 23191.6 40169.0i 0.0325827 0.0564350i −0.849274 0.527952i \(-0.822960\pi\)
0.881857 + 0.471517i \(0.156293\pi\)
\(48\) −6470.49 + 11207.2i −0.00844486 + 0.0146269i
\(49\) 452050. + 688385.i 0.548908 + 0.835882i
\(50\) −259705. 449823.i −0.293823 0.508917i
\(51\) −38709.9 + 67047.5i −0.0408626 + 0.0707761i
\(52\) 1.44926e6 + 566739.i 1.42934 + 0.558948i
\(53\) 640099. + 1.10868e6i 0.590584 + 1.02292i 0.994154 + 0.107972i \(0.0344358\pi\)
−0.403570 + 0.914949i \(0.632231\pi\)
\(54\) −345503. −0.298589
\(55\) 177151. + 306835.i 0.143574 + 0.248677i
\(56\) 984611. + 531354.i 0.749215 + 0.404321i
\(57\) −168744. −0.120689
\(58\) 928403. + 1.60804e6i 0.624797 + 1.08218i
\(59\) −105425. −0.0668282 −0.0334141 0.999442i \(-0.510638\pi\)
−0.0334141 + 0.999442i \(0.510638\pi\)
\(60\) −96055.0 166372.i −0.0574104 0.0994377i
\(61\) 552960. + 957755.i 0.311917 + 0.540256i 0.978777 0.204926i \(-0.0656955\pi\)
−0.666860 + 0.745183i \(0.732362\pi\)
\(62\) 116605. + 201966.i 0.0621365 + 0.107624i
\(63\) −56505.4 1.96627e6i −0.0284707 0.990719i
\(64\) −3.41967e6 −1.63063
\(65\) 1.37361e6 1.09818e6i 0.620392 0.495994i
\(66\) −63310.1 109656.i −0.0271063 0.0469494i
\(67\) −1.56688e6 + 2.71392e6i −0.636465 + 1.10239i 0.349738 + 0.936848i \(0.386271\pi\)
−0.986203 + 0.165542i \(0.947063\pi\)
\(68\) −3.45275e6 −1.33163
\(69\) −40429.3 + 70025.7i −0.0148158 + 0.0256617i
\(70\) 3.08940e6 1.90404e6i 1.07654 0.663487i
\(71\) 30963.0 53629.5i 0.0102669 0.0177828i −0.860846 0.508865i \(-0.830065\pi\)
0.871113 + 0.491082i \(0.163399\pi\)
\(72\) −1.33620e6 2.31437e6i −0.421899 0.730751i
\(73\) 2.24168e6 + 3.88271e6i 0.674441 + 1.16817i 0.976632 + 0.214919i \(0.0689486\pi\)
−0.302191 + 0.953247i \(0.597718\pi\)
\(74\) −1.52475e6 −0.437410
\(75\) 127020. 0.0347662
\(76\) −3.76280e6 6.51736e6i −0.983249 1.70304i
\(77\) 1.23290e6 759854.i 0.307759 0.189676i
\(78\) −490899. + 392466.i −0.117128 + 0.0936422i
\(79\) 2.28994e6 3.96629e6i 0.522552 0.905087i −0.477104 0.878847i \(-0.658313\pi\)
0.999656 0.0262395i \(-0.00835326\pi\)
\(80\) −326121. + 564858.i −0.0712138 + 0.123346i
\(81\) −2.32802e6 + 4.03225e6i −0.486732 + 0.843044i
\(82\) −1.26179e6 2.18549e6i −0.252720 0.437724i
\(83\) 6.30798e6 1.21092 0.605462 0.795874i \(-0.292988\pi\)
0.605462 + 0.795874i \(0.292988\pi\)
\(84\) −668505. + 412009.i −0.123063 + 0.0758453i
\(85\) −1.95103e6 + 3.37928e6i −0.344586 + 0.596840i
\(86\) 6.56077e6 1.13636e7i 1.11227 1.92651i
\(87\) −454074. −0.0739280
\(88\) 983770. 1.70394e6i 0.153888 0.266542i
\(89\) 4.06406e6 0.611076 0.305538 0.952180i \(-0.401164\pi\)
0.305538 + 0.952180i \(0.401164\pi\)
\(90\) −8.66810e6 −1.25336
\(91\) −4.64836e6 5.48351e6i −0.646629 0.762805i
\(92\) −3.60612e6 −0.482817
\(93\) −57030.6 −0.00735220
\(94\) −417736. + 723540.i −0.0518746 + 0.0898494i
\(95\) −8.50492e6 −1.01774
\(96\) 464114. 803868.i 0.0535396 0.0927333i
\(97\) 14469.3 25061.5i 0.00160970 0.00278809i −0.865219 0.501393i \(-0.832821\pi\)
0.866829 + 0.498605i \(0.166154\pi\)
\(98\) −8.14250e6 1.23995e7i −0.873910 1.33080i
\(99\) −3.45922e6 −0.358307
\(100\) 2.83240e6 + 4.90585e6i 0.283240 + 0.490585i
\(101\) 8.91117e6 1.54346e7i 0.860617 1.49063i −0.0107171 0.999943i \(-0.503411\pi\)
0.871334 0.490690i \(-0.163255\pi\)
\(102\) 697258. 1.20769e6i 0.0650568 0.112682i
\(103\) −7.29444e6 + 1.26343e7i −0.657751 + 1.13926i 0.323445 + 0.946247i \(0.395159\pi\)
−0.981196 + 0.193012i \(0.938174\pi\)
\(104\) −9.09547e6 3.55682e6i −0.792882 0.310060i
\(105\) 25492.8 + 887093.i 0.00214909 + 0.0747837i
\(106\) −1.15297e7 1.99701e7i −0.940260 1.62858i
\(107\) 1.29583e7 1.02260 0.511301 0.859402i \(-0.329164\pi\)
0.511301 + 0.859402i \(0.329164\pi\)
\(108\) 3.76812e6 0.287833
\(109\) 5.72032e6 + 9.90788e6i 0.423085 + 0.732805i 0.996239 0.0866427i \(-0.0276139\pi\)
−0.573155 + 0.819447i \(0.694281\pi\)
\(110\) −3.19092e6 5.52683e6i −0.228581 0.395915i
\(111\) 186436. 322917.i 0.0129390 0.0224109i
\(112\) 2.34626e6 + 1.26618e6i 0.157802 + 0.0851594i
\(113\) −1.22808e7 + 2.12710e7i −0.800669 + 1.38680i 0.118508 + 0.992953i \(0.462189\pi\)
−0.919177 + 0.393846i \(0.871144\pi\)
\(114\) 3.03948e6 0.192147
\(115\) −2.03769e6 + 3.52939e6i −0.124939 + 0.216400i
\(116\) −1.01253e7 1.75376e7i −0.602291 1.04320i
\(117\) 2.57997e6 + 1.69755e7i 0.148924 + 0.979876i
\(118\) 1.89895e6 0.106396
\(119\) 1.40366e7 + 7.57496e6i 0.763566 + 0.412065i
\(120\) 602836. + 1.04414e6i 0.0318467 + 0.0551601i
\(121\) 8.47017e6 + 1.46708e7i 0.434654 + 0.752842i
\(122\) −9.96014e6 1.72515e7i −0.496599 0.860135i
\(123\) 617132. 0.0299027
\(124\) −1.27172e6 2.20268e6i −0.0598983 0.103747i
\(125\) 2.37465e7 1.08747
\(126\) 1.01780e6 + 3.54172e7i 0.0453278 + 1.57731i
\(127\) 1.12338e6 + 1.94575e6i 0.0486646 + 0.0842895i 0.889332 0.457263i \(-0.151170\pi\)
−0.840667 + 0.541552i \(0.817837\pi\)
\(128\) 3.46233e7 1.45926
\(129\) 1.60441e6 + 2.77892e6i 0.0658038 + 0.113975i
\(130\) −2.47420e7 + 1.97808e7i −0.987717 + 0.789665i
\(131\) 9.14894e6 1.58464e7i 0.355567 0.615860i −0.631648 0.775255i \(-0.717621\pi\)
0.987215 + 0.159396i \(0.0509545\pi\)
\(132\) 690472. + 1.19593e6i 0.0261299 + 0.0452583i
\(133\) 998638. + 3.47504e7i 0.0368067 + 1.28079i
\(134\) 2.82233e7 4.88842e7i 1.01331 1.75510i
\(135\) 2.12923e6 3.68794e6i 0.0744827 0.129008i
\(136\) 2.16692e7 0.738682
\(137\) 2.39793e7 0.796735 0.398367 0.917226i \(-0.369577\pi\)
0.398367 + 0.917226i \(0.369577\pi\)
\(138\) 728230. 1.26133e6i 0.0235880 0.0408557i
\(139\) −1.64364e7 + 2.84688e7i −0.519106 + 0.899118i 0.480647 + 0.876914i \(0.340402\pi\)
−0.999753 + 0.0222040i \(0.992932\pi\)
\(140\) −3.36935e7 + 2.07658e7i −1.03776 + 0.639588i
\(141\) −102156. 176939.i −0.00306899 0.00531564i
\(142\) −557718. + 965997.i −0.0163458 + 0.0283117i
\(143\) −9.87390e6 + 7.89404e6i −0.282366 + 0.225748i
\(144\) −3.18408e6 5.51499e6i −0.0888618 0.153913i
\(145\) −2.28859e7 −0.623420
\(146\) −4.03781e7 6.99369e7i −1.07377 1.85982i
\(147\) 3.62160e6 208323.i 0.0940351 0.00540912i
\(148\) 1.66292e7 0.421654
\(149\) −1.14569e7 1.98440e7i −0.283737 0.491447i 0.688565 0.725174i \(-0.258241\pi\)
−0.972302 + 0.233728i \(0.924908\pi\)
\(150\) −2.28793e6 −0.0553507
\(151\) 2.30274e7 + 3.98847e7i 0.544285 + 0.942729i 0.998652 + 0.0519141i \(0.0165322\pi\)
−0.454367 + 0.890815i \(0.650134\pi\)
\(152\) 2.36151e7 + 4.09026e7i 0.545428 + 0.944709i
\(153\) −1.90488e7 3.29936e7i −0.429980 0.744748i
\(154\) −2.22075e7 + 1.36868e7i −0.489979 + 0.301981i
\(155\) −2.87442e6 −0.0619996
\(156\) 5.35384e6 4.28031e6i 0.112909 0.0902692i
\(157\) −2.37581e7 4.11503e7i −0.489963 0.848641i 0.509970 0.860192i \(-0.329656\pi\)
−0.999933 + 0.0115513i \(0.996323\pi\)
\(158\) −4.12473e7 + 7.14425e7i −0.831948 + 1.44098i
\(159\) 5.63909e6 0.111255
\(160\) 2.33919e7 4.05160e7i 0.451488 0.782000i
\(161\) 1.46601e7 + 7.91144e6i 0.276851 + 0.149405i
\(162\) 4.19333e7 7.26306e7i 0.774919 1.34220i
\(163\) 3.42519e7 + 5.93259e7i 0.619480 + 1.07297i 0.989581 + 0.143979i \(0.0459899\pi\)
−0.370100 + 0.928992i \(0.620677\pi\)
\(164\) 1.37613e7 + 2.38353e7i 0.243617 + 0.421957i
\(165\) 1.56065e6 0.0270465
\(166\) −1.13622e8 −1.92790
\(167\) −5.56232e7 9.63422e7i −0.924162 1.60070i −0.792903 0.609348i \(-0.791431\pi\)
−0.131260 0.991348i \(-0.541902\pi\)
\(168\) 4.19550e6 2.58574e6i 0.0682655 0.0420729i
\(169\) 4.61026e7 + 4.25667e7i 0.734721 + 0.678370i
\(170\) 3.51427e7 6.08690e7i 0.548611 0.950221i
\(171\) 4.15188e7 7.19127e7i 0.634978 1.09981i
\(172\) −7.15530e7 + 1.23933e8i −1.07221 + 1.85711i
\(173\) 8.06196e6 + 1.39637e7i 0.118380 + 0.205041i 0.919126 0.393964i \(-0.128896\pi\)
−0.800746 + 0.599004i \(0.795563\pi\)
\(174\) 8.17896e6 0.117700
\(175\) −751711. 2.61579e7i −0.0106027 0.368952i
\(176\) 2.34426e6 4.06037e6i 0.0324124 0.0561399i
\(177\) −232190. + 402165.i −0.00314729 + 0.00545127i
\(178\) −7.32035e7 −0.972886
\(179\) 3.40550e7 5.89850e7i 0.443809 0.768699i −0.554160 0.832410i \(-0.686960\pi\)
0.997968 + 0.0637113i \(0.0202937\pi\)
\(180\) 9.45359e7 1.20821
\(181\) −1.19823e8 −1.50198 −0.750990 0.660314i \(-0.770423\pi\)
−0.750990 + 0.660314i \(0.770423\pi\)
\(182\) 8.37281e7 + 9.87711e7i 1.02949 + 1.21445i
\(183\) 4.87142e6 0.0587593
\(184\) 2.26318e7 0.267828
\(185\) 9.39662e6 1.62754e7i 0.109112 0.188987i
\(186\) 1.02726e6 0.0117053
\(187\) 1.40246e7 2.42913e7i 0.156836 0.271647i
\(188\) 4.55591e6 7.89106e6i 0.0500060 0.0866130i
\(189\) −1.53187e7 8.26685e6i −0.165046 0.0890684i
\(190\) 1.53194e8 1.62033
\(191\) 8.09539e7 + 1.40216e8i 0.840661 + 1.45607i 0.889337 + 0.457253i \(0.151167\pi\)
−0.0486757 + 0.998815i \(0.515500\pi\)
\(192\) −7.53158e6 + 1.30451e7i −0.0767948 + 0.133012i
\(193\) −7.01859e7 + 1.21566e8i −0.702747 + 1.21719i 0.264751 + 0.964317i \(0.414710\pi\)
−0.967498 + 0.252877i \(0.918623\pi\)
\(194\) −260626. + 451418.i −0.00256279 + 0.00443888i
\(195\) −1.16397e6 7.65858e6i −0.0112414 0.0739652i
\(196\) 8.88036e7 + 1.35231e8i 0.842431 + 1.28286i
\(197\) −1.52064e7 2.63383e7i −0.141708 0.245446i 0.786432 0.617677i \(-0.211926\pi\)
−0.928140 + 0.372231i \(0.878593\pi\)
\(198\) 6.23089e7 0.570456
\(199\) 5.61153e6 0.0504772 0.0252386 0.999681i \(-0.491965\pi\)
0.0252386 + 0.999681i \(0.491965\pi\)
\(200\) −1.77760e7 3.07889e7i −0.157119 0.272138i
\(201\) 6.90189e6 + 1.19544e7i 0.0599490 + 0.103835i
\(202\) −1.60512e8 + 2.78014e8i −1.37018 + 2.37322i
\(203\) 2.68724e6 + 9.35102e7i 0.0225460 + 0.784554i
\(204\) −7.60442e6 + 1.31712e7i −0.0627135 + 0.108623i
\(205\) 3.11043e7 0.252163
\(206\) 1.31390e8 2.27575e8i 1.04720 1.81380i
\(207\) −1.98950e7 3.44591e7i −0.155900 0.270028i
\(208\) −2.16739e7 8.47566e6i −0.166999 0.0653058i
\(209\) 6.11359e7 0.463217
\(210\) −459186. 1.59787e7i −0.00342154 0.119062i
\(211\) −7.03763e7 1.21895e8i −0.515748 0.893302i −0.999833 0.0182808i \(-0.994181\pi\)
0.484085 0.875021i \(-0.339153\pi\)
\(212\) 1.25745e8 + 2.17797e8i 0.906392 + 1.56992i
\(213\) −136388. 236230.i −0.000967044 0.00167497i
\(214\) −2.33411e8 −1.62807
\(215\) 8.08643e7 + 1.40061e8i 0.554909 + 0.961131i
\(216\) −2.36485e7 −0.159667
\(217\) 337511. + 1.17446e7i 0.00224222 + 0.0780245i
\(218\) −1.03037e8 1.78465e8i −0.673588 1.16669i
\(219\) 1.97486e7 0.127052
\(220\) 3.48007e7 + 6.02766e7i 0.220348 + 0.381654i
\(221\) −1.29665e8 5.07059e7i −0.808069 0.315999i
\(222\) −3.35816e6 + 5.81650e6i −0.0205999 + 0.0356801i
\(223\) −7.24812e7 1.25541e8i −0.437682 0.758087i 0.559829 0.828608i \(-0.310867\pi\)
−0.997510 + 0.0705216i \(0.977534\pi\)
\(224\) −1.68292e8 9.08203e7i −1.00045 0.539902i
\(225\) −3.12527e7 + 5.41313e7i −0.182915 + 0.316818i
\(226\) 2.21207e8 3.83142e8i 1.27473 2.20790i
\(227\) 8.83975e7 0.501591 0.250795 0.968040i \(-0.419308\pi\)
0.250795 + 0.968040i \(0.419308\pi\)
\(228\) −3.31492e7 −0.185225
\(229\) 388866. 673535.i 0.00213981 0.00370626i −0.864954 0.501852i \(-0.832652\pi\)
0.867093 + 0.498146i \(0.165986\pi\)
\(230\) 3.67037e7 6.35727e7i 0.198913 0.344527i
\(231\) −183250. 6.37669e6i −0.000978141 0.0340372i
\(232\) 6.35461e7 + 1.10065e8i 0.334103 + 0.578684i
\(233\) −8.29339e7 + 1.43646e8i −0.429523 + 0.743956i −0.996831 0.0795500i \(-0.974652\pi\)
0.567308 + 0.823506i \(0.307985\pi\)
\(234\) −4.64715e7 3.05769e8i −0.237100 1.56005i
\(235\) −5.14878e6 8.91794e6i −0.0258801 0.0448257i
\(236\) −2.07103e7 −0.102564
\(237\) −1.00869e7 1.74710e7i −0.0492195 0.0852506i
\(238\) −2.52832e8 1.36443e8i −1.21566 0.656044i
\(239\) −4.67511e7 −0.221513 −0.110757 0.993848i \(-0.535327\pi\)
−0.110757 + 0.993848i \(0.535327\pi\)
\(240\) 1.43652e6 + 2.48812e6i 0.00670766 + 0.0116180i
\(241\) 2.72314e8 1.25317 0.626587 0.779352i \(-0.284452\pi\)
0.626587 + 0.779352i \(0.284452\pi\)
\(242\) −1.52568e8 2.64256e8i −0.692006 1.19859i
\(243\) 3.12294e7 + 5.40910e7i 0.139618 + 0.241826i
\(244\) 1.08627e8 + 1.88148e8i 0.478712 + 0.829153i
\(245\) 1.82534e8 1.04998e7i 0.792978 0.0456140i
\(246\) −1.11160e7 −0.0476076
\(247\) −4.55966e7 3.00013e8i −0.192528 1.26678i
\(248\) 7.98123e6 + 1.38239e7i 0.0332268 + 0.0575505i
\(249\) 1.38929e7 2.40632e7i 0.0570288 0.0987768i
\(250\) −4.27732e8 −1.73134
\(251\) −9.47312e7 + 1.64079e8i −0.378125 + 0.654931i −0.990789 0.135412i \(-0.956764\pi\)
0.612665 + 0.790343i \(0.290098\pi\)
\(252\) −1.11003e7 3.86267e8i −0.0436951 1.52050i
\(253\) 1.46476e7 2.53703e7i 0.0568648 0.0984926i
\(254\) −2.02347e7 3.50476e7i −0.0774782 0.134196i
\(255\) 8.59400e6 + 1.48852e7i 0.0324567 + 0.0562167i
\(256\) −1.85931e8 −0.692645
\(257\) −1.49557e8 −0.549594 −0.274797 0.961502i \(-0.588611\pi\)
−0.274797 + 0.961502i \(0.588611\pi\)
\(258\) −2.88992e7 5.00549e7i −0.104765 0.181459i
\(259\) −6.76035e7 3.64828e7i −0.241780 0.130479i
\(260\) 2.69841e8 2.15733e8i 0.952139 0.761221i
\(261\) 1.11723e8 1.93510e8i 0.388957 0.673694i
\(262\) −1.64794e8 + 2.85432e8i −0.566093 + 0.980502i
\(263\) −1.28348e8 + 2.22304e8i −0.435053 + 0.753534i −0.997300 0.0734352i \(-0.976604\pi\)
0.562247 + 0.826970i \(0.309937\pi\)
\(264\) −4.33337e6 7.50561e6i −0.0144948 0.0251057i
\(265\) 2.84217e8 0.938189
\(266\) −1.79879e7 6.25939e8i −0.0585995 2.03914i
\(267\) 8.95081e6 1.55033e7i 0.0287788 0.0498463i
\(268\) −3.07809e8 + 5.33140e8i −0.976808 + 1.69188i
\(269\) 1.04290e7 0.0326671 0.0163336 0.999867i \(-0.494801\pi\)
0.0163336 + 0.999867i \(0.494801\pi\)
\(270\) −3.83526e7 + 6.64287e7i −0.118583 + 0.205392i
\(271\) 5.80041e8 1.77038 0.885189 0.465232i \(-0.154029\pi\)
0.885189 + 0.465232i \(0.154029\pi\)
\(272\) 5.16363e7 0.155584
\(273\) −3.11557e7 + 5.65515e6i −0.0926762 + 0.0168219i
\(274\) −4.31924e8 −1.26847
\(275\) −4.60192e7 −0.133437
\(276\) −7.94221e6 + 1.37563e7i −0.0227384 + 0.0393840i
\(277\) −1.82117e8 −0.514839 −0.257420 0.966300i \(-0.582872\pi\)
−0.257420 + 0.966300i \(0.582872\pi\)
\(278\) 2.96060e8 5.12791e8i 0.826462 1.43147i
\(279\) 1.40322e7 2.43044e7i 0.0386821 0.0669993i
\(280\) 2.11459e8 1.30325e8i 0.575669 0.354792i
\(281\) −6.01056e8 −1.61601 −0.808003 0.589178i \(-0.799452\pi\)
−0.808003 + 0.589178i \(0.799452\pi\)
\(282\) 1.84007e6 + 3.18709e6i 0.00488609 + 0.00846296i
\(283\) −3.75201e8 + 6.49867e8i −0.984037 + 1.70440i −0.337895 + 0.941184i \(0.609715\pi\)
−0.646142 + 0.763217i \(0.723619\pi\)
\(284\) 6.08258e6 1.05353e7i 0.0157570 0.0272919i
\(285\) −1.87315e7 + 3.24439e7i −0.0479308 + 0.0830186i
\(286\) 1.77853e8 1.42191e8i 0.449551 0.359410i
\(287\) −3.65223e6 1.27090e8i −0.00911950 0.317339i
\(288\) 2.28387e8 + 3.95578e8i 0.563375 + 0.975794i
\(289\) −1.01423e8 −0.247169
\(290\) 4.12231e8 0.992538
\(291\) −63735.1 110392.i −0.000151619 0.000262611i
\(292\) 4.40371e8 + 7.62745e8i 1.03509 + 1.79283i
\(293\) −1.20909e7 + 2.09420e7i −0.0280815 + 0.0486386i −0.879725 0.475484i \(-0.842273\pi\)
0.851643 + 0.524122i \(0.175606\pi\)
\(294\) −6.52337e7 + 3.75240e6i −0.149712 + 0.00861178i
\(295\) −1.17027e7 + 2.02697e7i −0.0265405 + 0.0459694i
\(296\) −1.04364e8 −0.233900
\(297\) −1.53056e7 + 2.65100e7i −0.0339002 + 0.0587168i
\(298\) 2.06367e8 + 3.57437e8i 0.451734 + 0.782426i
\(299\) −1.35424e8 5.29582e7i −0.292986 0.114574i
\(300\) 2.49526e7 0.0533570
\(301\) 5.62784e8 3.46851e8i 1.18948 0.733095i
\(302\) −4.14779e8 7.18419e8i −0.866548 1.50091i
\(303\) −3.92524e7 6.79872e7i −0.0810620 0.140403i
\(304\) 5.62732e7 + 9.74681e7i 0.114880 + 0.198978i
\(305\) 2.45526e8 0.495505
\(306\) 3.43115e8 + 5.94293e8i 0.684566 + 1.18570i
\(307\) −4.60518e8 −0.908369 −0.454185 0.890908i \(-0.650069\pi\)
−0.454185 + 0.890908i \(0.650069\pi\)
\(308\) 2.42199e8 1.49271e8i 0.472330 0.291103i
\(309\) 3.21310e7 + 5.56525e7i 0.0619540 + 0.107307i
\(310\) 5.17751e7 0.0987087
\(311\) 3.03719e8 + 5.26056e8i 0.572545 + 0.991678i 0.996304 + 0.0859024i \(0.0273773\pi\)
−0.423758 + 0.905775i \(0.639289\pi\)
\(312\) −3.36004e7 + 2.68630e7i −0.0626330 + 0.0500742i
\(313\) −1.34739e8 + 2.33375e8i −0.248364 + 0.430179i −0.963072 0.269244i \(-0.913226\pi\)
0.714708 + 0.699423i \(0.246560\pi\)
\(314\) 4.27941e8 + 7.41215e8i 0.780063 + 1.35111i
\(315\) −3.84320e8 2.07402e8i −0.692798 0.373875i
\(316\) 4.49851e8 7.79165e8i 0.801981 1.38907i
\(317\) 2.76540e8 4.78982e8i 0.487585 0.844523i −0.512313 0.858799i \(-0.671211\pi\)
0.999898 + 0.0142762i \(0.00454441\pi\)
\(318\) −1.01573e8 −0.177127
\(319\) 1.64511e8 0.283745
\(320\) −3.79602e8 + 6.57489e8i −0.647594 + 1.12167i
\(321\) 2.85398e7 4.94324e7i 0.0481597 0.0834150i
\(322\) −2.64063e8 1.42504e8i −0.440770 0.237866i
\(323\) 3.36656e8 + 5.83105e8i 0.555876 + 0.962805i
\(324\) −4.57332e8 + 7.92122e8i −0.747006 + 1.29385i
\(325\) 3.43222e7 + 2.25830e8i 0.0554605 + 0.364914i
\(326\) −6.16958e8 1.06860e9i −0.986266 1.70826i
\(327\) 5.03944e7 0.0797012
\(328\) −8.63654e7 1.49589e8i −0.135139 0.234068i
\(329\) −3.58335e7 + 2.20846e7i −0.0554757 + 0.0341904i
\(330\) −2.81110e7 −0.0430604
\(331\) −1.68423e7 2.91717e7i −0.0255272 0.0442144i 0.852980 0.521944i \(-0.174793\pi\)
−0.878507 + 0.477730i \(0.841460\pi\)
\(332\) 1.23918e9 1.85845
\(333\) 9.17438e7 + 1.58905e8i 0.136151 + 0.235821i
\(334\) 1.00191e9 + 1.73535e9i 1.47135 + 2.54845i
\(335\) 3.47865e8 + 6.02519e8i 0.505537 + 0.875616i
\(336\) 9.99759e6 6.16165e6i 0.0143783 0.00886155i
\(337\) 7.63688e8 1.08695 0.543477 0.839424i \(-0.317107\pi\)
0.543477 + 0.839424i \(0.317107\pi\)
\(338\) −8.30419e8 7.66728e8i −1.16974 1.08002i
\(339\) 5.40952e7 + 9.36957e7i 0.0754154 + 0.130623i
\(340\) −3.83273e8 + 6.63849e8i −0.528850 + 0.915994i
\(341\) 2.06622e7 0.0282186
\(342\) −7.47854e8 + 1.29532e9i −1.01094 + 1.75100i
\(343\) −6.43341e7 7.44585e8i −0.0860818 0.996288i
\(344\) 4.49062e8 7.77799e8i 0.594774 1.03018i
\(345\) 8.97574e6 + 1.55464e7i 0.0117680 + 0.0203828i
\(346\) −1.45215e8 2.51520e8i −0.188472 0.326442i
\(347\) 1.38433e8 0.177863 0.0889314 0.996038i \(-0.471655\pi\)
0.0889314 + 0.996038i \(0.471655\pi\)
\(348\) −8.92013e7 −0.113460
\(349\) 6.95055e8 + 1.20387e9i 0.875246 + 1.51597i 0.856501 + 0.516146i \(0.172634\pi\)
0.0187451 + 0.999824i \(0.494033\pi\)
\(350\) 1.35401e7 + 4.71167e8i 0.0168805 + 0.587404i
\(351\) 1.41508e8 + 5.53373e7i 0.174665 + 0.0683035i
\(352\) −1.68148e8 + 2.91241e8i −0.205491 + 0.355921i
\(353\) 2.01637e8 3.49246e8i 0.243983 0.422591i −0.717862 0.696185i \(-0.754879\pi\)
0.961845 + 0.273594i \(0.0882126\pi\)
\(354\) 4.18230e6 7.24396e6i 0.00501076 0.00867890i
\(355\) −6.87412e6 1.19063e7i −0.00815488 0.0141247i
\(356\) 7.98372e8 0.937843
\(357\) 5.98109e7 3.68622e7i 0.0695731 0.0428788i
\(358\) −6.13413e8 + 1.06246e9i −0.706582 + 1.22384i
\(359\) −3.63378e8 + 6.29389e8i −0.414503 + 0.717941i −0.995376 0.0960537i \(-0.969378\pi\)
0.580873 + 0.813994i \(0.302711\pi\)
\(360\) −5.93302e8 −0.670220
\(361\) −2.86839e8 + 4.96820e8i −0.320895 + 0.555807i
\(362\) 2.15829e9 2.39128
\(363\) 7.46198e7 0.0818805
\(364\) −9.13155e8 1.07722e9i −0.992406 1.17071i
\(365\) 9.95354e8 1.07140
\(366\) −8.77460e7 −0.0935499
\(367\) −2.61154e8 + 4.52332e8i −0.275782 + 0.477668i −0.970332 0.241776i \(-0.922270\pi\)
0.694550 + 0.719444i \(0.255603\pi\)
\(368\) 5.39300e7 0.0564109
\(369\) −1.51843e8 + 2.63000e8i −0.157327 + 0.272498i
\(370\) −1.69256e8 + 2.93160e8i −0.173715 + 0.300883i
\(371\) −3.33725e7 1.16129e9i −0.0339297 1.18068i
\(372\) −1.12035e7 −0.0112837
\(373\) 1.23244e8 + 2.13465e8i 0.122966 + 0.212983i 0.920936 0.389714i \(-0.127426\pi\)
−0.797970 + 0.602697i \(0.794093\pi\)
\(374\) −2.52616e8 + 4.37545e8i −0.249696 + 0.432486i
\(375\) 5.23000e7 9.05863e7i 0.0512145 0.0887061i
\(376\) −2.85926e7 + 4.95239e7i −0.0277394 + 0.0480460i
\(377\) −1.22696e8 8.07305e8i −0.117933 0.775967i
\(378\) 2.75926e8 + 1.48906e8i 0.262767 + 0.141805i
\(379\) −9.62038e8 1.66630e9i −0.907726 1.57223i −0.817215 0.576333i \(-0.804483\pi\)
−0.0905115 0.995895i \(-0.528850\pi\)
\(380\) −1.67076e9 −1.56197
\(381\) 9.89664e6 0.00916748
\(382\) −1.45817e9 2.52563e9i −1.33841 2.31819i
\(383\) −6.76573e8 1.17186e9i −0.615345 1.06581i −0.990324 0.138776i \(-0.955683\pi\)
0.374979 0.927033i \(-0.377650\pi\)
\(384\) 7.62553e7 1.32078e8i 0.0687243 0.119034i
\(385\) −9.23603e6 3.21394e8i −0.00824846 0.287029i
\(386\) 1.26422e9 2.18969e9i 1.11883 1.93788i
\(387\) −1.57903e9 −1.38485
\(388\) 2.84244e6 4.92325e6i 0.00247047 0.00427899i
\(389\) −8.48379e8 1.46944e9i −0.730746 1.26569i −0.956565 0.291519i \(-0.905839\pi\)
0.225819 0.974169i \(-0.427494\pi\)
\(390\) 2.09659e7 + 1.37949e8i 0.0178973 + 0.117759i
\(391\) 3.22638e8 0.272958
\(392\) −5.57327e8 8.48702e8i −0.467314 0.711630i
\(393\) −4.02998e7 6.98012e7i −0.0334910 0.0580082i
\(394\) 2.73904e8 + 4.74416e8i 0.225612 + 0.390771i
\(395\) −5.08391e8 8.80559e8i −0.415057 0.718901i
\(396\) −6.79553e8 −0.549908
\(397\) 2.45074e8 + 4.24481e8i 0.196576 + 0.340480i 0.947416 0.320004i \(-0.103684\pi\)
−0.750840 + 0.660484i \(0.770351\pi\)
\(398\) −1.01077e8 −0.0803641
\(399\) 1.34763e8 + 7.27258e7i 0.106210 + 0.0573170i
\(400\) −4.23589e7 7.33678e7i −0.0330929 0.0573186i
\(401\) −9.57815e8 −0.741782 −0.370891 0.928676i \(-0.620948\pi\)
−0.370891 + 0.928676i \(0.620948\pi\)
\(402\) −1.24320e8 2.15328e8i −0.0954440 0.165314i
\(403\) −1.54103e7 1.01396e8i −0.0117285 0.0771705i
\(404\) 1.75057e9 3.03208e9i 1.32082 2.28773i
\(405\) 5.16846e8 + 8.95203e8i 0.386606 + 0.669621i
\(406\) −4.84036e7 1.68434e9i −0.0358952 1.24908i
\(407\) −6.75458e7 + 1.16993e8i −0.0496612 + 0.0860158i
\(408\) 4.77249e7 8.26620e7i 0.0347884 0.0602553i
\(409\) −1.78719e9 −1.29163 −0.645817 0.763492i \(-0.723483\pi\)
−0.645817 + 0.763492i \(0.723483\pi\)
\(410\) −5.60263e8 −0.401465
\(411\) 5.28126e7 9.14741e7i 0.0375224 0.0649908i
\(412\) −1.43297e9 + 2.48197e9i −1.00948 + 1.74847i
\(413\) 8.41944e7 + 4.54362e7i 0.0588109 + 0.0317378i
\(414\) 3.58356e8 + 6.20692e8i 0.248207 + 0.429907i
\(415\) 7.00219e8 1.21282e9i 0.480912 0.832964i
\(416\) 1.55462e9 + 6.07940e8i 1.05876 + 0.414032i
\(417\) 7.24002e7 + 1.25401e8i 0.0488949 + 0.0846884i
\(418\) −1.10120e9 −0.737481
\(419\) −4.62881e8 8.01733e8i −0.307411 0.532452i 0.670384 0.742014i \(-0.266129\pi\)
−0.977795 + 0.209562i \(0.932796\pi\)
\(420\) 5.00797e6 + 1.74266e8i 0.00329829 + 0.114773i
\(421\) 4.54758e8 0.297025 0.148513 0.988911i \(-0.452551\pi\)
0.148513 + 0.988911i \(0.452551\pi\)
\(422\) 1.26765e9 + 2.19563e9i 0.821116 + 1.42221i
\(423\) 1.00540e8 0.0645874
\(424\) −7.89170e8 1.36688e9i −0.502794 0.870865i
\(425\) −2.53413e8 4.38925e8i −0.160128 0.277350i
\(426\) 2.45667e6 + 4.25508e6i 0.00153962 + 0.00266670i
\(427\) −2.88294e7 1.00320e9i −0.0179200 0.623577i
\(428\) 2.54562e9 1.56943
\(429\) 8.36696e6 + 5.50522e7i 0.00511643 + 0.0336647i
\(430\) −1.45656e9 2.52284e9i −0.883464 1.53020i
\(431\) −3.95876e8 + 6.85678e8i −0.238171 + 0.412525i −0.960190 0.279349i \(-0.909881\pi\)
0.722018 + 0.691874i \(0.243215\pi\)
\(432\) −5.63527e7 −0.0336296
\(433\) −6.48227e7 + 1.12276e8i −0.0383724 + 0.0664630i −0.884574 0.466400i \(-0.845551\pi\)
0.846201 + 0.532863i \(0.178884\pi\)
\(434\) −6.07938e6 2.11549e8i −0.00356981 0.124222i
\(435\) −5.04046e7 + 8.73034e7i −0.0293601 + 0.0508532i
\(436\) 1.12374e9 + 1.94637e9i 0.649325 + 1.12466i
\(437\) 3.51610e8 + 6.09007e8i 0.201547 + 0.349090i
\(438\) −3.55719e8 −0.202278
\(439\) 1.35223e9 0.762822 0.381411 0.924406i \(-0.375438\pi\)
0.381411 + 0.924406i \(0.375438\pi\)
\(440\) −2.18407e8 3.78293e8i −0.122231 0.211711i
\(441\) −8.02302e8 + 1.59466e9i −0.445454 + 0.885385i
\(442\) 2.33557e9 + 9.13335e8i 1.28652 + 0.503097i
\(443\) −6.23175e8 + 1.07937e9i −0.340563 + 0.589872i −0.984537 0.175175i \(-0.943951\pi\)
0.643975 + 0.765047i \(0.277284\pi\)
\(444\) 3.66247e7 6.34359e7i 0.0198579 0.0343949i
\(445\) 4.51133e8 7.81384e8i 0.242686 0.420344i
\(446\) 1.30556e9 + 2.26130e9i 0.696827 + 1.20694i
\(447\) −1.00932e8 −0.0534507
\(448\) 2.73102e9 + 1.47382e9i 1.43500 + 0.774411i
\(449\) −1.14902e9 + 1.99017e9i −0.599056 + 1.03759i 0.393905 + 0.919151i \(0.371124\pi\)
−0.992961 + 0.118444i \(0.962209\pi\)
\(450\) 5.62937e8 9.75035e8i 0.291216 0.504402i
\(451\) −2.23587e8 −0.114770
\(452\) −2.41253e9 + 4.17862e9i −1.22882 + 2.12837i
\(453\) 2.02865e8 0.102533
\(454\) −1.59225e9 −0.798576
\(455\) −1.57029e9 + 2.85027e8i −0.781519 + 0.141856i
\(456\) 2.08042e8 0.102748
\(457\) −1.34355e9 −0.658485 −0.329242 0.944245i \(-0.606793\pi\)
−0.329242 + 0.944245i \(0.606793\pi\)
\(458\) −7.00440e6 + 1.21320e7i −0.00340676 + 0.00590069i
\(459\) −3.37132e8 −0.162725
\(460\) −4.00298e8 + 6.93336e8i −0.191748 + 0.332117i
\(461\) 1.94242e9 3.36436e9i 0.923399 1.59937i 0.129282 0.991608i \(-0.458733\pi\)
0.794117 0.607765i \(-0.207934\pi\)
\(462\) 3.30077e6 + 1.14860e8i 0.00155728 + 0.0541901i
\(463\) −2.02725e9 −0.949234 −0.474617 0.880192i \(-0.657413\pi\)
−0.474617 + 0.880192i \(0.657413\pi\)
\(464\) 1.51426e8 + 2.62277e8i 0.0703700 + 0.121884i
\(465\) −6.33069e6 + 1.09651e7i −0.00291989 + 0.00505739i
\(466\) 1.49384e9 2.58741e9i 0.683838 1.18444i
\(467\) −4.36129e8 + 7.55397e8i −0.198155 + 0.343215i −0.947930 0.318478i \(-0.896828\pi\)
0.749775 + 0.661693i \(0.230162\pi\)
\(468\) 5.06826e8 + 3.33477e9i 0.228559 + 1.50385i
\(469\) 2.42100e9 1.49209e9i 1.08365 0.667869i
\(470\) 9.27418e7 + 1.60634e8i 0.0412034 + 0.0713664i
\(471\) −2.09302e8 −0.0922997
\(472\) 1.29977e8 0.0568943
\(473\) −5.81277e8 1.00680e9i −0.252563 0.437451i
\(474\) 1.81689e8 + 3.14694e8i 0.0783616 + 0.135726i
\(475\) 5.52339e8 9.56680e8i 0.236471 0.409580i
\(476\) 2.75744e9 + 1.48808e9i 1.17188 + 0.632413i
\(477\) −1.38748e9 + 2.40318e9i −0.585344 + 1.01385i
\(478\) 8.42100e8 0.352668
\(479\) 1.30515e9 2.26059e9i 0.542610 0.939827i −0.456144 0.889906i \(-0.650770\pi\)
0.998753 0.0499212i \(-0.0158970\pi\)
\(480\) −1.03038e8 1.78467e8i −0.0425259 0.0736570i
\(481\) 6.24496e8 + 2.44212e8i 0.255871 + 0.100060i
\(482\) −4.90504e9 −1.99516
\(483\) 6.24676e7 3.84996e7i 0.0252255 0.0155468i
\(484\) 1.66394e9 + 2.88202e9i 0.667080 + 1.15542i
\(485\) −3.21233e6 5.56392e6i −0.00127857 0.00221455i
\(486\) −5.62517e8 9.74308e8i −0.222284 0.385008i
\(487\) 3.87084e9 1.51864 0.759319 0.650718i \(-0.225532\pi\)
0.759319 + 0.650718i \(0.225532\pi\)
\(488\) −6.81738e8 1.18080e9i −0.265551 0.459948i
\(489\) 3.01749e8 0.116698
\(490\) −3.28787e9 + 1.89126e8i −1.26249 + 0.0726214i
\(491\) −2.47951e9 4.29464e9i −0.945325 1.63735i −0.755098 0.655612i \(-0.772411\pi\)
−0.190227 0.981740i \(-0.560922\pi\)
\(492\) 1.21233e8 0.0458928
\(493\) 9.05910e8 + 1.56908e9i 0.340503 + 0.589768i
\(494\) 8.21304e8 + 5.40395e9i 0.306521 + 2.01682i
\(495\) −3.83992e8 + 6.65094e8i −0.142300 + 0.246470i
\(496\) 1.90187e7 + 3.29414e7i 0.00699835 + 0.0121215i
\(497\) −4.78412e7 + 2.94851e7i −0.0174805 + 0.0107735i
\(498\) −2.50244e8 + 4.33435e8i −0.0907948 + 0.157261i
\(499\) 2.33202e9 4.03917e9i 0.840194 1.45526i −0.0495356 0.998772i \(-0.515774\pi\)
0.889730 0.456487i \(-0.150893\pi\)
\(500\) 4.66493e9 1.66898
\(501\) −4.90024e8 −0.174095
\(502\) 1.70634e9 2.95546e9i 0.602007 1.04271i
\(503\) 2.18225e8 3.77977e8i 0.0764568 0.132427i −0.825262 0.564750i \(-0.808973\pi\)
0.901719 + 0.432323i \(0.142306\pi\)
\(504\) 6.96649e7 + 2.42419e9i 0.0242386 + 0.843450i
\(505\) −1.97837e9 3.42665e9i −0.683579 1.18399i
\(506\) −2.63838e8 + 4.56980e8i −0.0905336 + 0.156809i
\(507\) 2.63918e8 8.21184e7i 0.0899374 0.0279842i
\(508\) 2.20684e8 + 3.82236e8i 0.0746874 + 0.129362i
\(509\) −4.79285e9 −1.61095 −0.805474 0.592631i \(-0.798089\pi\)
−0.805474 + 0.592631i \(0.798089\pi\)
\(510\) −1.54799e8 2.68119e8i −0.0516739 0.0895019i
\(511\) −1.16873e8 4.06694e9i −0.0387474 1.34833i
\(512\) −1.08272e9 −0.356511
\(513\) −3.67406e8 6.36366e8i −0.120153 0.208111i
\(514\) 2.69389e9 0.875001
\(515\) 1.61944e9 + 2.80496e9i 0.522445 + 0.904901i
\(516\) 3.15180e8 + 5.45909e8i 0.100992 + 0.174923i
\(517\) 3.70109e7 + 6.41048e7i 0.0117791 + 0.0204021i
\(518\) 1.21770e9 + 6.57143e8i 0.384934 + 0.207733i
\(519\) 7.10236e7 0.0223006
\(520\) −1.69350e9 + 1.35393e9i −0.528171 + 0.422265i
\(521\) 1.00631e9 + 1.74299e9i 0.311746 + 0.539960i 0.978740 0.205103i \(-0.0657528\pi\)
−0.666994 + 0.745063i \(0.732419\pi\)
\(522\) −2.01240e9 + 3.48559e9i −0.619253 + 1.07258i
\(523\) 1.03729e9 0.317062 0.158531 0.987354i \(-0.449324\pi\)
0.158531 + 0.987354i \(0.449324\pi\)
\(524\) 1.79728e9 3.11298e9i 0.545702 0.945184i
\(525\) −1.01441e8 5.47434e7i −0.0305953 0.0165110i
\(526\) 2.31185e9 4.00424e9i 0.692642 1.19969i
\(527\) 1.13780e8 + 1.97073e8i 0.0338633 + 0.0586529i
\(528\) −1.03261e7 1.78854e7i −0.00305294 0.00528785i
\(529\) −3.06786e9 −0.901032
\(530\) −5.11944e9 −1.49368
\(531\) −1.14259e8 1.97902e8i −0.0331177 0.0573615i
\(532\) 1.96179e8 + 6.82661e9i 0.0564887 + 1.96569i
\(533\) 1.66756e8 + 1.09721e9i 0.0477020 + 0.313866i
\(534\) −1.61226e8 + 2.79251e8i −0.0458183 + 0.0793597i
\(535\) 1.43844e9 2.49146e9i 0.406121 0.703421i
\(536\) 1.93179e9 3.34596e9i 0.541855 0.938521i
\(537\) −1.50008e8 2.59821e8i −0.0418026 0.0724042i
\(538\) −1.87852e8 −0.0520089
\(539\) −1.31211e9 + 7.54754e7i −0.360918 + 0.0207608i
\(540\) 4.18281e8 7.24484e8i 0.114311 0.197993i
\(541\) 2.32572e9 4.02827e9i 0.631492 1.09378i −0.355755 0.934579i \(-0.615776\pi\)
0.987247 0.159196i \(-0.0508903\pi\)
\(542\) −1.04479e10 −2.81859
\(543\) −2.63901e8 + 4.57090e8i −0.0707361 + 0.122519i
\(544\) −3.70376e9 −0.986385
\(545\) 2.53994e9 0.672104
\(546\) 5.61189e8 1.01863e8i 0.147549 0.0267819i
\(547\) −4.70401e9 −1.22889 −0.614445 0.788960i \(-0.710620\pi\)
−0.614445 + 0.788960i \(0.710620\pi\)
\(548\) 4.71064e9 1.22278
\(549\) −1.19859e9 + 2.07603e9i −0.309150 + 0.535463i
\(550\) 8.28917e8 0.212443
\(551\) −1.97452e9 + 3.41997e9i −0.502841 + 0.870946i
\(552\) 4.98449e7 8.63338e7i 0.0126134 0.0218471i
\(553\) −3.53820e9 + 2.18064e9i −0.889702 + 0.548335i
\(554\) 3.28037e9 0.819669
\(555\) −4.13908e7 7.16909e7i −0.0102773 0.0178008i
\(556\) −3.22888e9 + 5.59259e9i −0.796692 + 1.37991i
\(557\) −1.75779e9 + 3.04458e9i −0.430997 + 0.746508i −0.996959 0.0779228i \(-0.975171\pi\)
0.565963 + 0.824431i \(0.308505\pi\)
\(558\) −2.52753e8 + 4.37781e8i −0.0615852 + 0.106669i
\(559\) −4.50715e9 + 3.60340e9i −1.09134 + 0.872511i
\(560\) 5.03892e8 3.10555e8i 0.121249 0.0747276i
\(561\) −6.17763e7 1.07000e8i −0.0147724 0.0255866i
\(562\) 1.08265e10 2.57282
\(563\) 6.71569e9 1.58603 0.793014 0.609203i \(-0.208511\pi\)
0.793014 + 0.609203i \(0.208511\pi\)
\(564\) −2.00681e7 3.47590e7i −0.00471009 0.00815812i
\(565\) 2.72647e9 + 4.72239e9i 0.635963 + 1.10152i
\(566\) 6.75827e9 1.17057e10i 1.56667 2.71355i
\(567\) 3.59704e9 2.21690e9i 0.828714 0.510748i
\(568\) −3.81739e7 + 6.61192e7i −0.00874073 + 0.0151394i
\(569\) 6.73366e9 1.53235 0.766176 0.642631i \(-0.222157\pi\)
0.766176 + 0.642631i \(0.222157\pi\)
\(570\) 3.37399e8 5.84392e8i 0.0763100 0.132173i
\(571\) −6.63971e8 1.15003e9i −0.149253 0.258514i 0.781699 0.623656i \(-0.214354\pi\)
−0.930952 + 0.365143i \(0.881020\pi\)
\(572\) −1.93970e9 + 1.55076e9i −0.433359 + 0.346464i
\(573\) 7.13180e8 0.158365
\(574\) 6.57854e7 + 2.28919e9i 0.0145190 + 0.505231i
\(575\) −2.64670e8 4.58422e8i −0.0580587 0.100561i
\(576\) −3.70623e9 6.41939e9i −0.808080 1.39963i
\(577\) 4.18890e9 + 7.25539e9i 0.907788 + 1.57234i 0.817130 + 0.576454i \(0.195564\pi\)
0.0906585 + 0.995882i \(0.471103\pi\)
\(578\) 1.82687e9 0.393514
\(579\) 3.09159e8 + 5.35479e8i 0.0661921 + 0.114648i
\(580\) −4.49586e9 −0.956787
\(581\) −5.03769e9 2.71863e9i −1.06565 0.575088i
\(582\) 1.14802e6 + 1.98843e6i 0.000241390 + 0.000418100i
\(583\) −2.04304e9 −0.427009
\(584\) −2.76374e9 4.78694e9i −0.574186 0.994520i
\(585\) 3.55021e9 + 1.38832e9i 0.733176 + 0.286712i
\(586\) 2.17785e8 3.77215e8i 0.0447082 0.0774368i
\(587\) 2.65036e9 + 4.59057e9i 0.540844 + 0.936770i 0.998856 + 0.0478235i \(0.0152285\pi\)
−0.458012 + 0.888946i \(0.651438\pi\)
\(588\) 7.11451e8 4.09243e7i 0.144319 0.00830159i
\(589\) −2.47995e8 + 4.29539e8i −0.0500079 + 0.0866163i
\(590\) 2.10794e8 3.65105e8i 0.0422547 0.0731873i
\(591\) −1.33964e8 −0.0266952
\(592\) −2.48693e8 −0.0492649
\(593\) −2.96231e8 + 5.13087e8i −0.0583363 + 0.101041i −0.893719 0.448628i \(-0.851913\pi\)
0.835382 + 0.549669i \(0.185246\pi\)
\(594\) 2.75690e8 4.77509e8i 0.0539720 0.0934823i
\(595\) 3.01455e9 1.85791e9i 0.586696 0.361588i
\(596\) −2.25067e9 3.89828e9i −0.435462 0.754243i
\(597\) 1.23590e7 2.14064e7i 0.00237724 0.00411750i
\(598\) 2.43932e9 + 9.53905e8i 0.466460 + 0.182411i
\(599\) 3.59532e8 + 6.22727e8i 0.0683508 + 0.118387i 0.898175 0.439637i \(-0.144893\pi\)
−0.829825 + 0.558024i \(0.811560\pi\)
\(600\) −1.56601e8 −0.0295982
\(601\) 1.83017e9 + 3.16995e9i 0.343899 + 0.595650i 0.985153 0.171678i \(-0.0549189\pi\)
−0.641254 + 0.767329i \(0.721586\pi\)
\(602\) −1.01371e10 + 6.24762e9i −1.89376 + 1.16715i
\(603\) −6.79274e9 −1.26164
\(604\) 4.52366e9 + 7.83521e9i 0.835335 + 1.44684i
\(605\) 3.76094e9 0.690482
\(606\) 7.07030e8 + 1.22461e9i 0.129058 + 0.223534i
\(607\) −2.50069e7 4.33132e7i −0.00453836 0.00786068i 0.863747 0.503925i \(-0.168111\pi\)
−0.868286 + 0.496065i \(0.834778\pi\)
\(608\) −4.03635e9 6.99117e9i −0.728327 1.26150i
\(609\) 3.62633e8 + 1.95698e8i 0.0650590 + 0.0351097i
\(610\) −4.42251e9 −0.788887
\(611\) 2.86978e8 2.29435e8i 0.0508985 0.0406926i
\(612\) −3.74208e9 6.48148e9i −0.659908 1.14299i
\(613\) 2.40739e9 4.16973e9i 0.422120 0.731133i −0.574027 0.818836i \(-0.694620\pi\)
0.996147 + 0.0877036i \(0.0279528\pi\)
\(614\) 8.29504e9 1.44620
\(615\) 6.85049e7 1.18654e8i 0.0118757 0.0205693i
\(616\) −1.52003e9 + 9.36815e8i −0.262011 + 0.161481i
\(617\) −4.66117e9 + 8.07338e9i −0.798908 + 1.38375i 0.121420 + 0.992601i \(0.461255\pi\)
−0.920328 + 0.391148i \(0.872078\pi\)
\(618\) −5.78756e8 1.00243e9i −0.0986361 0.170843i
\(619\) −1.37973e9 2.38976e9i −0.233817 0.404984i 0.725111 0.688632i \(-0.241788\pi\)
−0.958928 + 0.283648i \(0.908455\pi\)
\(620\) −5.64669e8 −0.0951532
\(621\) −3.52107e8 −0.0590003
\(622\) −5.47070e9 9.47553e9i −0.911542 1.57884i
\(623\) −3.24565e9 1.75154e9i −0.537766 0.290210i
\(624\) −8.00674e7 + 6.40127e7i −0.0131920 + 0.0105468i
\(625\) 1.50957e9 2.61466e9i 0.247329 0.428386i
\(626\) 2.42698e9 4.20365e9i 0.395417 0.684883i
\(627\) 1.34647e8 2.33216e8i 0.0218153 0.0377853i
\(628\) −4.66720e9 8.08383e9i −0.751965 1.30244i
\(629\) −1.48781e9 −0.238381
\(630\) 6.92253e9 + 3.73581e9i 1.10299 + 0.595241i
\(631\) −2.07754e9 + 3.59840e9i −0.329190 + 0.570173i −0.982351 0.187045i \(-0.940109\pi\)
0.653162 + 0.757218i \(0.273442\pi\)
\(632\) −2.82324e9 + 4.89000e9i −0.444875 + 0.770547i
\(633\) −6.19995e8 −0.0971572
\(634\) −4.98115e9 + 8.62761e9i −0.776278 + 1.34455i
\(635\) 4.98804e8 0.0773075
\(636\) 1.10778e9 0.170747
\(637\) 1.34898e9 + 6.38261e9i 0.206784 + 0.978387i
\(638\) −2.96324e9 −0.451746
\(639\) 1.34231e8 0.0203516
\(640\) 3.84337e9 6.65691e9i 0.579538 1.00379i
\(641\) 7.92485e9 1.18847 0.594235 0.804292i \(-0.297455\pi\)
0.594235 + 0.804292i \(0.297455\pi\)
\(642\) −5.14071e8 + 8.90396e8i −0.0766744 + 0.132804i
\(643\) 4.90970e9 8.50384e9i 0.728310 1.26147i −0.229287 0.973359i \(-0.573639\pi\)
0.957597 0.288111i \(-0.0930272\pi\)
\(644\) 2.87992e9 + 1.55418e9i 0.424893 + 0.229298i
\(645\) 7.12391e8 0.104534
\(646\) −6.06398e9 1.05031e10i −0.885002 1.53287i
\(647\) −3.08684e9 + 5.34657e9i −0.448074 + 0.776086i −0.998261 0.0589551i \(-0.981223\pi\)
0.550187 + 0.835042i \(0.314556\pi\)
\(648\) 2.87019e9 4.97132e9i 0.414380 0.717726i
\(649\) 8.41225e7 1.45704e8i 0.0120797 0.0209226i
\(650\) −6.18226e8 4.06775e9i −0.0882979 0.580975i
\(651\) 4.55458e7 + 2.45792e7i 0.00647016 + 0.00349168i
\(652\) 6.72866e9 + 1.16544e10i 0.950741 + 1.64673i
\(653\) 1.23202e10 1.73150 0.865751 0.500474i \(-0.166841\pi\)
0.865751 + 0.500474i \(0.166841\pi\)
\(654\) −9.07724e8 −0.126891
\(655\) −2.03116e9 3.51808e9i −0.282423 0.489171i
\(656\) −2.05803e8 3.56461e8i −0.0284635 0.0493002i
\(657\) −4.85906e9 + 8.41614e9i −0.668457 + 1.15780i
\(658\) 6.45447e8 3.97797e8i 0.0883222 0.0544341i
\(659\) 2.32896e9 4.03388e9i 0.317003 0.549066i −0.662858 0.748745i \(-0.730657\pi\)
0.979861 + 0.199679i \(0.0639901\pi\)
\(660\) 3.06584e8 0.0415094
\(661\) −4.94569e9 + 8.56618e9i −0.666073 + 1.15367i 0.312921 + 0.949779i \(0.398693\pi\)
−0.978993 + 0.203892i \(0.934641\pi\)
\(662\) 3.03370e8 + 5.25452e8i 0.0406415 + 0.0703931i
\(663\) −4.79006e8 + 3.82958e8i −0.0638327 + 0.0510333i
\(664\) −7.77703e9 −1.03092
\(665\) 6.79221e9 + 3.66548e9i 0.895644 + 0.483342i
\(666\) −1.65253e9 2.86226e9i −0.216765 0.375447i
\(667\) 9.46150e8 + 1.63878e9i 0.123458 + 0.213836i
\(668\) −1.09270e10 1.89261e10i −1.41835 2.45665i
\(669\) −6.38538e8 −0.0824509
\(670\) −6.26588e9 1.08528e10i −0.804859 1.39406i
\(671\) −1.76491e9 −0.225525
\(672\) −7.17105e8 + 4.41961e8i −0.0911570 + 0.0561813i
\(673\) 6.31202e9 + 1.09327e10i 0.798207 + 1.38253i 0.920783 + 0.390076i \(0.127551\pi\)
−0.122576 + 0.992459i \(0.539116\pi\)
\(674\) −1.37559e10 −1.73053
\(675\) 2.76560e8 + 4.79016e8i 0.0346119 + 0.0599496i
\(676\) 9.05671e9 + 8.36208e9i 1.12760 + 1.04112i
\(677\) −3.25321e8 + 5.63472e8i −0.0402950 + 0.0697931i −0.885470 0.464697i \(-0.846163\pi\)
0.845175 + 0.534490i \(0.179496\pi\)
\(678\) −9.74385e8 1.68768e9i −0.120068 0.207964i
\(679\) −2.23566e7 + 1.37787e7i −0.00274070 + 0.00168913i
\(680\) 2.40540e9 4.16628e9i 0.293364 0.508121i
\(681\) 1.94689e8 3.37211e8i 0.0236226 0.0409155i
\(682\) −3.72175e8 −0.0449265
\(683\) −4.68549e9 −0.562707 −0.281353 0.959604i \(-0.590783\pi\)
−0.281353 + 0.959604i \(0.590783\pi\)
\(684\) 8.15623e9 1.41270e10i 0.974526 1.68793i
\(685\) 2.66182e9 4.61041e9i 0.316419 0.548054i
\(686\) 1.15881e9 + 1.34118e10i 0.137050 + 1.58618i
\(687\) −1.71290e6 2.96682e6i −0.000201550 0.000349095i
\(688\) 1.07008e9 1.85344e9i 0.125273 0.216980i
\(689\) 1.52375e9 + 1.00258e10i 0.177478 + 1.16776i
\(690\) −1.61675e8 2.80029e8i −0.0187357 0.0324512i
\(691\) −8.32107e9 −0.959414 −0.479707 0.877429i \(-0.659257\pi\)
−0.479707 + 0.877429i \(0.659257\pi\)
\(692\) 1.58375e9 + 2.74313e9i 0.181683 + 0.314684i
\(693\) 2.76261e9 + 1.49087e9i 0.315321 + 0.170166i
\(694\) −2.49350e9 −0.283173
\(695\) 3.64906e9 + 6.32037e9i 0.412320 + 0.714160i
\(696\) 5.59823e8 0.0629387
\(697\) −1.23122e9 2.13254e9i −0.137728 0.238552i
\(698\) −1.25196e10 2.16846e10i −1.39347 2.41356i
\(699\) 3.65312e8 + 6.32739e8i 0.0404570 + 0.0700736i
\(700\) −1.47671e8 5.13864e9i −0.0162724 0.566245i
\(701\) 1.25111e10 1.37177 0.685884 0.727710i \(-0.259416\pi\)
0.685884 + 0.727710i \(0.259416\pi\)
\(702\) −2.54890e9 9.96758e8i −0.278082 0.108745i
\(703\) −1.62142e9 2.80838e9i −0.176015 0.304868i
\(704\) 2.72869e9 4.72623e9i 0.294747 0.510517i
\(705\) −4.53592e7 −0.00487533
\(706\) −3.63197e9 + 6.29076e9i −0.388442 + 0.672801i
\(707\) −1.37687e10 + 8.48584e9i −1.46530 + 0.903081i
\(708\) −4.56130e7 + 7.90040e7i −0.00483027 + 0.00836628i
\(709\) −2.11298e9 3.65979e9i −0.222656 0.385651i 0.732958 0.680274i \(-0.238139\pi\)
−0.955613 + 0.294623i \(0.904806\pi\)
\(710\) 1.23819e8 + 2.14461e8i 0.0129833 + 0.0224877i
\(711\) 9.92734e9 1.03583
\(712\) −5.01054e9 −0.520241
\(713\) 1.18834e8 + 2.05827e8i 0.0122780 + 0.0212661i
\(714\) −1.07734e9 + 6.63977e8i −0.110766 + 0.0682668i
\(715\) 4.21706e8 + 2.77470e9i 0.0431458 + 0.283887i
\(716\) 6.69000e9 1.15874e10i 0.681131 1.17975i
\(717\) −1.02966e8 + 1.78342e8i −0.0104322 + 0.0180691i
\(718\) 6.54531e9 1.13368e10i 0.659925 1.14302i
\(719\) −2.88932e9 5.00445e9i −0.289898 0.502118i 0.683887 0.729588i \(-0.260288\pi\)
−0.973785 + 0.227470i \(0.926955\pi\)
\(720\) −1.41380e9 −0.141164
\(721\) 1.12707e10 6.94628e9i 1.11989 0.690206i
\(722\) 5.16666e9 8.94892e9i 0.510893 0.884892i
\(723\) 5.99753e8 1.03880e9i 0.0590185 0.102223i
\(724\) −2.35388e10 −2.30515
\(725\) 1.48629e9 2.57433e9i 0.144851 0.250889i
\(726\) −1.34408e9 −0.130361
\(727\) 6.88165e9 0.664236 0.332118 0.943238i \(-0.392237\pi\)
0.332118 + 0.943238i \(0.392237\pi\)
\(728\) 5.73091e9 + 6.76055e9i 0.550508 + 0.649415i
\(729\) −9.90765e9 −0.947162
\(730\) −1.79287e10 −1.70577
\(731\) 6.40181e9 1.10883e10i 0.606167 1.04991i
\(732\) 9.56974e8 0.0901802
\(733\) −4.72023e8 + 8.17568e8i −0.0442690 + 0.0766761i −0.887311 0.461172i \(-0.847429\pi\)
0.843042 + 0.537848i \(0.180763\pi\)
\(734\) 4.70402e9 8.14759e9i 0.439069 0.760489i
\(735\) 3.61963e8 7.19439e8i 0.0336247 0.0668326i
\(736\) −3.86828e9 −0.357639
\(737\) −2.50055e9 4.33109e9i −0.230091 0.398530i
\(738\) 2.73506e9 4.73726e9i 0.250478 0.433840i
\(739\) −3.51818e9 + 6.09367e9i −0.320673 + 0.555422i −0.980627 0.195884i \(-0.937242\pi\)
0.659954 + 0.751306i \(0.270576\pi\)
\(740\) 1.84593e9 3.19725e9i 0.167458 0.290045i
\(741\) −1.24489e9 4.86818e8i −0.112400 0.0439544i
\(742\) 6.01119e8 + 2.09176e10i 0.0540190 + 1.87974i
\(743\) −6.12173e9 1.06032e10i −0.547537 0.948362i −0.998443 0.0557904i \(-0.982232\pi\)
0.450905 0.892572i \(-0.351101\pi\)
\(744\) 7.03123e7 0.00625930
\(745\) −5.08711e9 −0.450738
\(746\) −2.21992e9 3.84501e9i −0.195772 0.339087i
\(747\) 6.83658e9 + 1.18413e10i 0.600090 + 1.03939i
\(748\) 2.75508e9 4.77194e9i 0.240702 0.416907i
\(749\) −1.03488e10 5.58483e9i −0.899920 0.485650i
\(750\) −9.42049e8 + 1.63168e9i −0.0815379 + 0.141228i
\(751\) −1.60176e10 −1.37993 −0.689966 0.723842i \(-0.742374\pi\)
−0.689966 + 0.723842i \(0.742374\pi\)
\(752\) −6.81343e7 + 1.18012e8i −0.00584256 + 0.0101196i
\(753\) 4.17277e8 + 7.22745e8i 0.0356158 + 0.0616883i
\(754\) 2.21005e9 + 1.45415e10i 0.187760 + 1.23541i
\(755\) 1.02247e10 0.864639
\(756\) −3.00930e9 1.62400e9i −0.253302 0.136697i
\(757\) 1.94628e9 + 3.37105e9i 0.163068 + 0.282442i 0.935968 0.352086i \(-0.114528\pi\)
−0.772899 + 0.634529i \(0.781194\pi\)
\(758\) 1.73286e10 + 3.00140e10i 1.44518 + 2.50312i
\(759\) −6.45203e7 1.11753e8i −0.00535612 0.00927708i
\(760\) 1.04856e10 0.866456
\(761\) −9.07476e8 1.57179e9i −0.0746430 0.129285i 0.826288 0.563248i \(-0.190448\pi\)
−0.900931 + 0.433962i \(0.857115\pi\)
\(762\) −1.78262e8 −0.0145954
\(763\) −2.98237e8 1.03780e10i −0.0243067 0.845821i
\(764\) 1.59031e10 + 2.75450e10i 1.29020 + 2.23468i
\(765\) −8.45809e9 −0.683058
\(766\) 1.21867e10 + 2.11080e10i 0.979683 + 1.69686i
\(767\) −7.77756e8 3.04145e8i −0.0622386 0.0243387i
\(768\) −4.09499e8 + 7.09272e8i −0.0326203 + 0.0565001i
\(769\) 6.12444e9 + 1.06078e10i 0.485651 + 0.841172i 0.999864 0.0164901i \(-0.00524921\pi\)
−0.514213 + 0.857663i \(0.671916\pi\)
\(770\) 1.66363e8 + 5.78908e9i 0.0131323 + 0.456974i
\(771\) −3.29389e8 + 5.70519e8i −0.0258833 + 0.0448311i
\(772\) −1.37878e10 + 2.38811e10i −1.07853 + 1.86808i
\(773\) 1.78900e9 0.139310 0.0696552 0.997571i \(-0.477810\pi\)
0.0696552 + 0.997571i \(0.477810\pi\)
\(774\) 2.84422e10 2.20480
\(775\) 1.86675e8 3.23330e8i 0.0144055 0.0249511i
\(776\) −1.78390e7 + 3.08981e7i −0.00137042 + 0.00237364i
\(777\) −2.88063e8 + 1.77537e8i −0.0220300 + 0.0135774i
\(778\) 1.52813e10 + 2.64681e10i 1.16341 + 2.01509i
\(779\) 2.68357e9 4.64808e9i 0.203391 0.352283i
\(780\) −2.28658e8 1.50450e9i −0.0172526 0.113517i
\(781\) 4.94132e7 + 8.55862e7i 0.00371163 + 0.00642873i
\(782\) −5.81148e9 −0.434573
\(783\) −9.88655e8 1.71240e9i −0.0736001 0.127479i
\(784\) −1.32807e9 2.02240e9i −0.0984272 0.149886i
\(785\) −1.05491e10 −0.778345
\(786\) 7.25895e8 + 1.25729e9i 0.0533206 + 0.0923540i
\(787\) −7.12083e9 −0.520738 −0.260369 0.965509i \(-0.583844\pi\)
−0.260369 + 0.965509i \(0.583844\pi\)
\(788\) −2.98725e9 5.17407e9i −0.217485 0.376696i
\(789\) 5.65352e8 + 9.79219e8i 0.0409779 + 0.0709758i
\(790\) 9.15735e9 + 1.58610e10i 0.660807 + 1.14455i
\(791\) 1.89752e10 1.16947e10i 1.36323 0.840175i
\(792\) 4.26484e9 0.305045
\(793\) 1.31631e9 + 8.66097e9i 0.0937354 + 0.616752i
\(794\) −4.41438e9 7.64592e9i −0.312966 0.542073i
\(795\) 6.25968e8 1.08421e9i 0.0441842 0.0765294i
\(796\) 1.10237e9 0.0774694
\(797\) −1.11489e10 + 1.93105e10i −0.780062 + 1.35111i 0.151844 + 0.988405i \(0.451479\pi\)
−0.931905 + 0.362702i \(0.881854\pi\)
\(798\) −2.42740e9 1.30997e9i −0.169095 0.0912536i
\(799\) −4.07615e8 + 7.06010e8i −0.0282707 + 0.0489663i
\(800\) 3.03831e9 + 5.26251e9i 0.209806 + 0.363394i
\(801\) 4.40463e9 + 7.62904e9i 0.302827 + 0.524513i
\(802\) 1.72526e10 1.18098
\(803\) −7.15491e9 −0.487640
\(804\) 1.35585e9 + 2.34841e9i 0.0920061 + 0.159359i
\(805\) 3.14845e9 1.94043e9i 0.212722 0.131103i
\(806\) 2.77577e8 + 1.82638e9i 0.0186729 + 0.122862i
\(807\) 2.29692e7 3.97838e7i 0.00153847 0.00266470i
\(808\) −1.09865e10 + 1.90291e10i −0.732687 + 1.26905i
\(809\) 5.37821e9 9.31534e9i 0.357123 0.618556i −0.630356 0.776307i \(-0.717091\pi\)
0.987479 + 0.157751i \(0.0504242\pi\)
\(810\) −9.30963e9 1.61248e10i −0.615510 1.06609i
\(811\) 9.11605e9 0.600114 0.300057 0.953921i \(-0.402994\pi\)
0.300057 + 0.953921i \(0.402994\pi\)
\(812\) 5.27899e8 + 1.83698e10i 0.0346023 + 1.20409i
\(813\) 1.27750e9 2.21269e9i 0.0833764 0.144412i
\(814\) 1.21666e9 2.10732e9i 0.0790650 0.136945i
\(815\) 1.52085e10 0.984093
\(816\) 1.13725e8 1.96978e8i 0.00732726 0.0126912i
\(817\) 2.79068e10 1.79033
\(818\) 3.21916e10 2.05639
\(819\) 5.25572e9 1.46689e10i 0.334302 0.933047i
\(820\) 6.11033e9 0.387005
\(821\) −7.86608e9 −0.496087 −0.248043 0.968749i \(-0.579788\pi\)
−0.248043 + 0.968749i \(0.579788\pi\)
\(822\) −9.51281e8 + 1.64767e9i −0.0597390 + 0.103471i
\(823\) −1.27526e9 −0.0797445 −0.0398722 0.999205i \(-0.512695\pi\)
−0.0398722 + 0.999205i \(0.512695\pi\)
\(824\) 8.99323e9 1.55767e10i 0.559978 0.969910i
\(825\) −1.01354e8 + 1.75550e8i −0.00628423 + 0.0108846i
\(826\) −1.51654e9 8.18416e8i −0.0936320 0.0505294i
\(827\) −1.95992e10 −1.20495 −0.602476 0.798137i \(-0.705819\pi\)
−0.602476 + 0.798137i \(0.705819\pi\)
\(828\) −3.90830e9 6.76938e9i −0.239267 0.414422i
\(829\) 7.49393e8 1.29799e9i 0.0456845 0.0791279i −0.842279 0.539042i \(-0.818786\pi\)
0.887963 + 0.459914i \(0.152120\pi\)
\(830\) −1.26126e10 + 2.18457e10i −0.765653 + 1.32615i
\(831\) −4.01100e8 + 6.94726e8i −0.0242465 + 0.0419962i
\(832\) −2.52282e10 9.86558e9i −1.51864 0.593869i
\(833\) −7.94523e9 1.20991e10i −0.476265 0.725261i
\(834\) −1.30410e9 2.25877e9i −0.0778449 0.134831i
\(835\) −2.46979e10 −1.46810
\(836\) 1.20099e10 0.710917
\(837\) −1.24173e8 2.15073e8i −0.00731959 0.0126779i
\(838\) 8.33759e9 + 1.44411e10i 0.489426 + 0.847710i
\(839\) −6.48836e8 + 1.12382e9i −0.0379287 + 0.0656944i −0.884367 0.466793i \(-0.845409\pi\)
0.846438 + 0.532487i \(0.178743\pi\)
\(840\) −3.14297e7 1.09369e9i −0.00182963 0.0636672i
\(841\) 3.31169e9 5.73602e9i 0.191984 0.332525i
\(842\) −8.19129e9 −0.472890
\(843\) −1.32378e9 + 2.29286e9i −0.0761063 + 0.131820i
\(844\) −1.38252e10 2.39459e10i −0.791539 1.37099i
\(845\) 1.33018e10 4.13888e9i 0.758424 0.235985i
\(846\) −1.81097e9 −0.102829
\(847\) −4.41605e8 1.53669e10i −0.0249713 0.868949i
\(848\) −1.88054e9 3.25719e9i −0.105900 0.183425i
\(849\) 1.65271e9 + 2.86257e9i 0.0926869 + 0.160538i
\(850\) 4.56458e9 + 7.90609e9i 0.254938 + 0.441566i
\(851\) −1.55390e9 −0.0864310
\(852\) −2.67929e7 4.64067e7i −0.00148416 0.00257064i
\(853\) −1.63173e9 −0.0900173 −0.0450087 0.998987i \(-0.514332\pi\)
−0.0450087 + 0.998987i \(0.514332\pi\)
\(854\) 5.19286e8 + 1.80700e10i 0.0285302 + 0.992789i
\(855\) −9.21762e9 1.59654e10i −0.504356 0.873571i
\(856\) −1.59762e10 −0.870593
\(857\) 1.12607e10 + 1.95041e10i 0.611127 + 1.05850i 0.991051 + 0.133485i \(0.0426169\pi\)
−0.379924 + 0.925018i \(0.624050\pi\)
\(858\) −1.50709e8 9.91622e8i −0.00814580 0.0535970i
\(859\) −1.51118e9 + 2.61745e9i −0.0813470 + 0.140897i −0.903829 0.427894i \(-0.859256\pi\)
0.822482 + 0.568791i \(0.192589\pi\)
\(860\) 1.58855e10 + 2.75145e10i 0.851641 + 1.47509i
\(861\) −4.92855e8 2.65974e8i −0.0263153 0.0142013i
\(862\) 7.13069e9 1.23507e10i 0.379189 0.656775i
\(863\) −2.30905e9 + 3.99939e9i −0.122291 + 0.211815i −0.920671 0.390340i \(-0.872358\pi\)
0.798380 + 0.602154i \(0.205691\pi\)
\(864\) 4.04205e9 0.213208
\(865\) 3.57968e9 0.188056
\(866\) 1.16761e9 2.02236e9i 0.0610922 0.105815i
\(867\) −2.23377e8 + 3.86900e8i −0.0116405 + 0.0201619i
\(868\) 6.63028e7 + 2.30720e9i 0.00344122 + 0.119747i
\(869\) 3.65447e9 + 6.32973e9i 0.188910 + 0.327202i
\(870\) 9.07908e8 1.57254e9i 0.0467439 0.0809627i
\(871\) −1.93890e10 + 1.55012e10i −0.994241 + 0.794881i
\(872\) −7.05252e9 1.22153e10i −0.360194 0.623874i
\(873\) 6.27271e7 0.00319084
\(874\) −6.33334e9 1.09697e10i −0.320880 0.555781i
\(875\) −1.89645e10 1.02344e10i −0.957003 0.516455i
\(876\) 3.87954e9 0.194992
\(877\) −1.92051e10 3.32642e10i −0.961431 1.66525i −0.718912 0.695101i \(-0.755360\pi\)
−0.242519 0.970147i \(-0.577974\pi\)
\(878\) −2.43568e10 −1.21448
\(879\) 5.32585e7 + 9.22463e7i 0.00264501 + 0.00458129i
\(880\) −5.20450e8 9.01446e8i −0.0257448 0.0445913i
\(881\) −1.22756e10 2.12620e10i −0.604822 1.04758i −0.992080 0.125611i \(-0.959911\pi\)
0.387257 0.921972i \(-0.373422\pi\)
\(882\) 1.44514e10 2.87236e10i 0.709201 1.40961i
\(883\) −5.51635e9 −0.269643 −0.134822 0.990870i \(-0.543046\pi\)
−0.134822 + 0.990870i \(0.543046\pi\)
\(884\) −2.54722e10 9.96100e9i −1.24018 0.484976i
\(885\) 5.15487e7 + 8.92849e7i 0.00249986 + 0.00432989i
\(886\) 1.12249e10 1.94421e10i 0.542205 0.939127i
\(887\) −3.35871e9 −0.161599 −0.0807997 0.996730i \(-0.525747\pi\)
−0.0807997 + 0.996730i \(0.525747\pi\)
\(888\) −2.29855e8 + 3.98120e8i −0.0110156 + 0.0190796i
\(889\) −5.85690e7 2.03807e9i −0.00279583 0.0972890i
\(890\) −8.12598e9 + 1.40746e10i −0.386377 + 0.669224i
\(891\) −3.71524e9 6.43499e9i −0.175960 0.304772i
\(892\) −1.42387e10 2.46621e10i −0.671727 1.16347i
\(893\) −1.77687e9 −0.0834981
\(894\) 1.81803e9 0.0850981
\(895\) −7.56058e9 1.30953e10i −0.352512 0.610569i
\(896\) −2.76509e10 1.49221e10i −1.28420 0.693028i
\(897\) −5.00283e8 + 3.99969e8i −0.0231442 + 0.0185034i
\(898\) 2.06967e10 3.58477e10i 0.953748 1.65194i
\(899\) −6.67330e8 + 1.15585e9i −0.0306325 + 0.0530570i
\(900\) −6.13949e9 + 1.06339e10i −0.280727 + 0.486233i
\(901\) −1.12504e10 1.94862e10i −0.512425 0.887546i
\(902\) 4.02734e9 0.182724
\(903\) −8.36481e7 2.91077e9i −0.00378050 0.131553i
\(904\) 1.51409e10 2.62248e10i 0.681650 1.18065i
\(905\) −1.33010e10 + 2.30379e10i −0.596503 + 1.03317i
\(906\) −3.65409e9 −0.163241
\(907\) 1.33660e10 2.31506e10i 0.594807 1.03024i −0.398767 0.917052i \(-0.630562\pi\)
0.993574 0.113184i \(-0.0361049\pi\)
\(908\) 1.73654e10 0.769811
\(909\) 3.86317e10 1.70596
\(910\) 2.82847e10 5.13402e9i 1.24425 0.225846i
\(911\) −3.33269e10 −1.46043 −0.730216 0.683217i \(-0.760580\pi\)
−0.730216 + 0.683217i \(0.760580\pi\)
\(912\) 4.95751e8 0.0216412
\(913\) −5.03339e9 + 8.71808e9i −0.218883 + 0.379117i
\(914\) 2.42005e10 1.04836
\(915\) 5.40753e8 9.36612e8i 0.0233359 0.0404190i
\(916\) 7.63913e7 1.32314e8i 0.00328405 0.00568814i
\(917\) −1.41361e10 + 8.71226e9i −0.605392 + 0.373111i
\(918\) 6.07255e9 0.259073
\(919\) −1.15778e10 2.00533e10i −0.492063 0.852278i 0.507895 0.861419i \(-0.330424\pi\)
−0.999958 + 0.00914063i \(0.997090\pi\)
\(920\) 2.51225e9 4.35134e9i 0.106367 0.184232i
\(921\) −1.01426e9 + 1.75675e9i −0.0427799 + 0.0740970i
\(922\) −3.49876e10 + 6.06003e10i −1.47013 + 2.54634i
\(923\) 3.83144e8 3.06318e8i 0.0160382 0.0128223i
\(924\) −3.59988e7 1.25268e9i −0.00150119 0.0522382i
\(925\) 1.22050e9 + 2.11397e9i 0.0507039 + 0.0878217i
\(926\) 3.65156e10 1.51126
\(927\) −3.16228e10 −1.30383
\(928\) −1.08614e10 1.88126e10i −0.446138 0.772734i
\(929\) −1.11470e10 1.93072e10i −0.456147 0.790069i 0.542607 0.839987i \(-0.317437\pi\)
−0.998753 + 0.0499177i \(0.984104\pi\)
\(930\) 1.14031e8 1.97508e8i 0.00464871 0.00805181i
\(931\) 1.41793e10 2.81828e10i 0.575880 1.14462i
\(932\) −1.62921e10 + 2.82187e10i −0.659206 + 1.14178i
\(933\) 2.67567e9 0.107857
\(934\) 7.85573e9 1.36065e10i 0.315480 0.546428i
\(935\) −3.11361e9 5.39292e9i −0.124573 0.215766i
\(936\) −3.18081e9 2.09288e10i −0.126786 0.834219i
\(937\) 2.91339e10 1.15694 0.578469 0.815705i \(-0.303651\pi\)
0.578469 + 0.815705i \(0.303651\pi\)
\(938\) −4.36080e10 + 2.68762e10i −1.72527 + 1.06331i
\(939\) 5.93507e8 + 1.02798e9i 0.0233936 + 0.0405188i
\(940\) −1.01146e9 1.75190e9i −0.0397192 0.0687958i
\(941\) −4.62060e8 8.00312e8i −0.0180774 0.0313109i 0.856845 0.515574i \(-0.172421\pi\)
−0.874923 + 0.484263i \(0.839088\pi\)
\(942\) 3.77003e9 0.146949
\(943\) −1.28591e9 2.22726e9i −0.0499368 0.0864930i
\(944\) 3.09726e8 0.0119833
\(945\) −3.28989e9 + 2.02761e9i −0.126815 + 0.0781577i
\(946\) 1.04702e10 + 1.81349e10i 0.402101 + 0.696460i
\(947\) −7.49425e9 −0.286750 −0.143375 0.989668i \(-0.545795\pi\)
−0.143375 + 0.989668i \(0.545795\pi\)
\(948\) −1.98153e9 3.43211e9i −0.0755390 0.130837i
\(949\) 5.33630e9 + 3.51113e10i 0.202679 + 1.33357i
\(950\) −9.94896e9 + 1.72321e10i −0.376483 + 0.652087i
\(951\) −1.21812e9 2.10984e9i −0.0459259 0.0795461i
\(952\) −1.73055e10 9.33908e9i −0.650063 0.350812i
\(953\) −7.55645e9 + 1.30882e10i −0.282809 + 0.489839i −0.972075 0.234669i \(-0.924600\pi\)
0.689267 + 0.724508i \(0.257933\pi\)
\(954\) 2.49918e10 4.32870e10i 0.931918 1.61413i
\(955\) 3.59452e10 1.33546
\(956\) −9.18410e9 −0.339965
\(957\) 3.62324e8 6.27563e8i 0.0133630 0.0231454i
\(958\) −2.35090e10 + 4.07187e10i −0.863881 + 1.49629i
\(959\) −1.91503e10 1.03347e10i −0.701151 0.378382i
\(960\) 1.67209e9 + 2.89614e9i 0.0609973 + 0.105650i
\(961\) 1.36725e10 2.36815e10i 0.496954 0.860749i
\(962\) −1.12487e10 4.39884e9i −0.407369 0.159303i
\(963\) 1.40442e10 + 2.43253e10i 0.506764 + 0.877742i
\(964\) 5.34953e10 1.92329
\(965\) 1.55820e10 + 2.69888e10i 0.558185 + 0.966804i
\(966\) −1.12519e9 + 6.93471e8i −0.0401612 + 0.0247519i
\(967\) −7.82699e9 −0.278357 −0.139179 0.990267i \(-0.544446\pi\)
−0.139179 + 0.990267i \(0.544446\pi\)
\(968\) −1.04428e10 1.80874e10i −0.370043 0.640933i
\(969\) 2.96584e9 0.104716
\(970\) 5.78618e7 + 1.00220e8i 0.00203559 + 0.00352575i
\(971\) 2.32937e10 + 4.03459e10i 0.816529 + 1.41427i 0.908225 + 0.418482i \(0.137438\pi\)
−0.0916962 + 0.995787i \(0.529229\pi\)
\(972\) 6.13492e9 + 1.06260e10i 0.214278 + 0.371140i
\(973\) 2.53961e10 1.56519e10i 0.883835 0.544719i
\(974\) −6.97232e10 −2.41780
\(975\) 9.37071e8 + 3.66446e8i 0.0323785 + 0.0126617i
\(976\) −1.62453e9 2.81378e9i −0.0559313 0.0968758i
\(977\) 1.09282e10 1.89283e10i 0.374903 0.649352i −0.615409 0.788208i \(-0.711009\pi\)
0.990313 + 0.138856i \(0.0443425\pi\)
\(978\) −5.43522e9 −0.185794
\(979\) −3.24288e9 + 5.61683e9i −0.110456 + 0.191316i
\(980\) 3.58581e10 2.06264e9i 1.21702 0.0700055i
\(981\) −1.23993e10 + 2.14763e10i −0.419331 + 0.726303i
\(982\) 4.46620e10 + 7.73569e10i 1.50504 + 2.60681i
\(983\) 2.07444e10 + 3.59304e10i 0.696568 + 1.20649i 0.969649 + 0.244500i \(0.0786240\pi\)
−0.273081 + 0.961991i \(0.588043\pi\)
\(984\) −7.60855e8 −0.0254577
\(985\) −6.75198e9 −0.225115
\(986\) −1.63176e10 2.82629e10i −0.542110 0.938962i
\(987\) 5.32603e6 + 1.85334e8i 0.000176317 + 0.00613544i
\(988\) −8.95730e9 5.89365e10i −0.295480 1.94417i
\(989\) 6.68618e9 1.15808e10i 0.219781 0.380673i
\(990\) 6.91662e9 1.19799e10i 0.226553 0.392402i
\(991\) 2.26375e10 3.92093e10i 0.738875 1.27977i −0.214128 0.976806i \(-0.568691\pi\)
0.953002 0.302963i \(-0.0979758\pi\)
\(992\) −1.36417e9 2.36281e9i −0.0443688 0.0768490i
\(993\) −1.48376e8 −0.00480884
\(994\) 8.61734e8 5.31098e8i 0.0278305 0.0171523i
\(995\) 6.22910e8 1.07891e9i 0.0200468 0.0347220i
\(996\) 2.72921e9 4.72713e9i 0.0875243 0.151597i
\(997\) 1.38073e10 0.441241 0.220621 0.975360i \(-0.429192\pi\)
0.220621 + 0.975360i \(0.429192\pi\)
\(998\) −4.20052e10 + 7.27552e10i −1.33766 + 2.31690i
\(999\) 1.62371e9 0.0515262
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 91.8.h.a.16.9 yes 126
7.4 even 3 91.8.g.a.81.55 yes 126
13.9 even 3 91.8.g.a.9.55 126
91.74 even 3 inner 91.8.h.a.74.9 yes 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.8.g.a.9.55 126 13.9 even 3
91.8.g.a.81.55 yes 126 7.4 even 3
91.8.h.a.16.9 yes 126 1.1 even 1 trivial
91.8.h.a.74.9 yes 126 91.74 even 3 inner