Properties

Label 91.8.u.a.30.20
Level $91$
Weight $8$
Character 91.30
Analytic conductor $28.427$
Analytic rank $0$
Dimension $126$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [91,8,Mod(30,91)]
 
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, 1]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("91.30");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 91 = 7 \cdot 13 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 91.u (of order \(6\), 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 \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 30.20
Character \(\chi\) \(=\) 91.30
Dual form 91.8.u.a.88.20

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-8.37044 + 4.83268i) q^{2} +37.7504 q^{3} +(-17.2905 + 29.9480i) q^{4} +(377.122 + 217.731i) q^{5} +(-315.987 + 182.435i) q^{6} +(-808.021 + 413.093i) q^{7} -1571.40i q^{8} -761.911 q^{9} +O(q^{10})\) \(q+(-8.37044 + 4.83268i) q^{2} +37.7504 q^{3} +(-17.2905 + 29.9480i) q^{4} +(377.122 + 217.731i) q^{5} +(-315.987 + 182.435i) q^{6} +(-808.021 + 413.093i) q^{7} -1571.40i q^{8} -761.911 q^{9} -4208.90 q^{10} -7210.27i q^{11} +(-652.722 + 1130.55i) q^{12} +(-4259.79 - 6678.53i) q^{13} +(4767.15 - 7362.67i) q^{14} +(14236.5 + 8219.43i) q^{15} +(5380.89 + 9319.98i) q^{16} +(-15071.9 + 26105.2i) q^{17} +(6377.53 - 3682.07i) q^{18} -42938.2i q^{19} +(-13041.2 + 7529.36i) q^{20} +(-30503.1 + 15594.4i) q^{21} +(34844.9 + 60353.1i) q^{22} +(-28824.1 - 49924.8i) q^{23} -59321.0i q^{24} +(55751.4 + 96564.2i) q^{25} +(67931.5 + 35316.0i) q^{26} -111322. q^{27} +(1599.77 - 31341.2i) q^{28} +(-49998.0 + 86599.0i) q^{29} -158887. q^{30} +(49670.5 - 28677.3i) q^{31} +(84111.0 + 48561.5i) q^{32} -272190. i q^{33} -291350. i q^{34} +(-394665. - 20145.2i) q^{35} +(13173.8 - 22817.7i) q^{36} +(27673.0 - 15977.0i) q^{37} +(207507. + 359412. i) q^{38} +(-160809. - 252117. i) q^{39} +(342144. - 592610. i) q^{40} +(643220. + 371363. i) q^{41} +(179961. - 277943. i) q^{42} +(-232943. - 403469. i) q^{43} +(215933. + 124669. i) q^{44} +(-287333. - 165892. i) q^{45} +(482541. + 278595. i) q^{46} +(-822662. - 474964. i) q^{47} +(203131. + 351833. i) q^{48} +(482252. - 667575. i) q^{49} +(-933327. - 538856. i) q^{50} +(-568968. + 985481. i) q^{51} +(273662. - 12097.2i) q^{52} +(-241116. - 417626. i) q^{53} +(931818. - 537985. i) q^{54} +(1.56990e6 - 2.71915e6i) q^{55} +(649135. + 1.26973e6i) q^{56} -1.62093e6i q^{57} -966496. i q^{58} +(-1.44985e6 - 837069. i) q^{59} +(-492311. + 284236. i) q^{60} +1.43978e6 q^{61} +(-277176. + 480082. i) q^{62} +(615640. - 314740. i) q^{63} -2.31624e6 q^{64} +(-152335. - 3.44611e6i) q^{65} +(1.31541e6 + 2.27835e6i) q^{66} -2.52182e6i q^{67} +(-521200. - 902744. i) q^{68} +(-1.08812e6 - 1.88468e6i) q^{69} +(3.40088e6 - 1.73867e6i) q^{70} +(-906768. + 523523. i) q^{71} +1.19727e6i q^{72} +(-3.86146e6 + 2.22941e6i) q^{73} +(-154424. + 267470. i) q^{74} +(2.10463e6 + 3.64533e6i) q^{75} +(1.28591e6 + 742423. i) q^{76} +(2.97851e6 + 5.82604e6i) q^{77} +(2.56444e6 + 1.33319e6i) q^{78} +(-1.93303e6 + 3.34811e6i) q^{79} +4.68636e6i q^{80} -2.53616e6 q^{81} -7.17871e6 q^{82} +5.42351e6i q^{83} +(60392.1 - 1.18314e6i) q^{84} +(-1.13678e7 + 6.56323e6i) q^{85} +(3.89966e6 + 2.25147e6i) q^{86} +(-1.88744e6 + 3.26914e6i) q^{87} -1.13302e7 q^{88} +(2.39248e6 - 1.38130e6i) q^{89} +3.20681e6 q^{90} +(6.20085e6 + 3.63670e6i) q^{91} +1.99353e6 q^{92} +(1.87508e6 - 1.08258e6i) q^{93} +9.18139e6 q^{94} +(9.34900e6 - 1.61929e7i) q^{95} +(3.17522e6 + 1.83321e6i) q^{96} +(2.67492e6 - 1.54436e6i) q^{97} +(-810489. + 7.91846e6i) q^{98} +5.49358e6i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 126 q - 3 q^{2} - 164 q^{3} + 3841 q^{4} - 6 q^{6} + 754 q^{7} + 85710 q^{9} + 7486 q^{10} - 18328 q^{12} + 1816 q^{13} - 6668 q^{14} - 11817 q^{15} - 237219 q^{16} - 28969 q^{17} + 75423 q^{18} + 12342 q^{20} - 54000 q^{21} + 51388 q^{22} + 17067 q^{23} + 810665 q^{25} + 144300 q^{26} - 528170 q^{27} + 18464 q^{28} + 191096 q^{29} - 432160 q^{30} - 259995 q^{31} + 49149 q^{32} + 87303 q^{35} + 1965131 q^{36} - 571857 q^{37} - 1061954 q^{38} - 1352875 q^{39} + 345362 q^{40} - 636567 q^{41} - 3473694 q^{42} - 659976 q^{43} + 2519268 q^{44} + 1980717 q^{45} - 4068600 q^{46} - 294840 q^{47} + 4726652 q^{48} + 541120 q^{49} - 2908992 q^{50} - 502094 q^{51} + 7809224 q^{52} - 434723 q^{53} + 2119563 q^{54} + 2152196 q^{55} - 858015 q^{56} + 1376949 q^{59} - 3768141 q^{60} - 4854916 q^{61} - 1713436 q^{62} + 10091940 q^{63} - 40270472 q^{64} - 4876182 q^{65} + 8270835 q^{66} + 531379 q^{68} - 311689 q^{69} + 5298534 q^{70} + 1505877 q^{71} - 13207461 q^{73} + 3730527 q^{74} + 5624951 q^{75} + 25297146 q^{76} + 11107478 q^{77} - 9362803 q^{78} + 5012226 q^{79} + 45989766 q^{81} - 34046788 q^{82} - 35428032 q^{84} + 19854117 q^{85} + 5226210 q^{86} + 17331733 q^{87} + 24348310 q^{88} - 43738596 q^{89} + 90517324 q^{90} + 9582031 q^{91} - 8502078 q^{92} - 30517344 q^{93} - 7710416 q^{94} + 14810909 q^{95} + 41499936 q^{96} - 60232128 q^{97} - 65830509 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(15\) \(66\)
\(\chi(n)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{1}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −8.37044 + 4.83268i −0.739849 + 0.427152i −0.822015 0.569467i \(-0.807150\pi\)
0.0821652 + 0.996619i \(0.473816\pi\)
\(3\) 37.7504 0.807229 0.403614 0.914929i \(-0.367754\pi\)
0.403614 + 0.914929i \(0.367754\pi\)
\(4\) −17.2905 + 29.9480i −0.135082 + 0.233969i
\(5\) 377.122 + 217.731i 1.34923 + 0.778979i 0.988141 0.153551i \(-0.0490711\pi\)
0.361091 + 0.932531i \(0.382404\pi\)
\(6\) −315.987 + 182.435i −0.597228 + 0.344810i
\(7\) −808.021 + 413.093i −0.890388 + 0.455202i
\(8\) 1571.40i 1.08511i
\(9\) −761.911 −0.348382
\(10\) −4208.90 −1.33097
\(11\) 7210.27i 1.63334i −0.577104 0.816671i \(-0.695817\pi\)
0.577104 0.816671i \(-0.304183\pi\)
\(12\) −652.722 + 1130.55i −0.109042 + 0.188866i
\(13\) −4259.79 6678.53i −0.537757 0.843100i
\(14\) 4767.15 7362.67i 0.464312 0.717112i
\(15\) 14236.5 + 8219.43i 1.08914 + 0.628814i
\(16\) 5380.89 + 9319.98i 0.328424 + 0.568847i
\(17\) −15071.9 + 26105.2i −0.744039 + 1.28871i 0.206604 + 0.978425i \(0.433759\pi\)
−0.950643 + 0.310288i \(0.899575\pi\)
\(18\) 6377.53 3682.07i 0.257750 0.148812i
\(19\) 42938.2i 1.43617i −0.695954 0.718086i \(-0.745018\pi\)
0.695954 0.718086i \(-0.254982\pi\)
\(20\) −13041.2 + 7529.36i −0.364514 + 0.210452i
\(21\) −30503.1 + 15594.4i −0.718747 + 0.367452i
\(22\) 34844.9 + 60353.1i 0.697685 + 1.20843i
\(23\) −28824.1 49924.8i −0.493979 0.855597i 0.505997 0.862535i \(-0.331125\pi\)
−0.999976 + 0.00693831i \(0.997791\pi\)
\(24\) 59321.0i 0.875929i
\(25\) 55751.4 + 96564.2i 0.713617 + 1.23602i
\(26\) 67931.5 + 35316.0i 0.757991 + 0.394062i
\(27\) −111322. −1.08845
\(28\) 1599.77 31341.2i 0.0137723 0.269813i
\(29\) −49998.0 + 86599.0i −0.380679 + 0.659356i −0.991160 0.132676i \(-0.957643\pi\)
0.610480 + 0.792032i \(0.290977\pi\)
\(30\) −158887. −1.07440
\(31\) 49670.5 28677.3i 0.299455 0.172891i −0.342743 0.939429i \(-0.611356\pi\)
0.642198 + 0.766539i \(0.278023\pi\)
\(32\) 84111.0 + 48561.5i 0.453762 + 0.261979i
\(33\) 272190.i 1.31848i
\(34\) 291350.i 1.27127i
\(35\) −394665. 20145.2i −1.55593 0.0794208i
\(36\) 13173.8 22817.7i 0.0470601 0.0815105i
\(37\) 27673.0 15977.0i 0.0898154 0.0518549i −0.454420 0.890788i \(-0.650153\pi\)
0.544235 + 0.838933i \(0.316820\pi\)
\(38\) 207507. + 359412.i 0.613464 + 1.06255i
\(39\) −160809. 252117.i −0.434093 0.680574i
\(40\) 342144. 592610.i 0.845276 1.46406i
\(41\) 643220. + 371363.i 1.45753 + 0.841503i 0.998889 0.0471216i \(-0.0150048\pi\)
0.458636 + 0.888624i \(0.348338\pi\)
\(42\) 179961. 277943.i 0.374806 0.578874i
\(43\) −232943. 403469.i −0.446796 0.773874i 0.551379 0.834255i \(-0.314102\pi\)
−0.998175 + 0.0603811i \(0.980768\pi\)
\(44\) 215933. + 124669.i 0.382151 + 0.220635i
\(45\) −287333. 165892.i −0.470048 0.271382i
\(46\) 482541. + 278595.i 0.730940 + 0.422009i
\(47\) −822662. 474964.i −1.15579 0.667296i −0.205499 0.978657i \(-0.565882\pi\)
−0.950291 + 0.311362i \(0.899215\pi\)
\(48\) 203131. + 351833.i 0.265113 + 0.459189i
\(49\) 482252. 667575.i 0.585582 0.810613i
\(50\) −933327. 538856.i −1.05594 0.609646i
\(51\) −568968. + 985481.i −0.600609 + 1.04029i
\(52\) 273662. 12097.2i 0.269900 0.0119309i
\(53\) −241116. 417626.i −0.222465 0.385320i 0.733091 0.680130i \(-0.238077\pi\)
−0.955556 + 0.294810i \(0.904744\pi\)
\(54\) 931818. 537985.i 0.805291 0.464935i
\(55\) 1.56990e6 2.71915e6i 1.27234 2.20376i
\(56\) 649135. + 1.26973e6i 0.493943 + 0.966166i
\(57\) 1.62093e6i 1.15932i
\(58\) 966496.i 0.650432i
\(59\) −1.44985e6 837069.i −0.919051 0.530614i −0.0357189 0.999362i \(-0.511372\pi\)
−0.883332 + 0.468747i \(0.844705\pi\)
\(60\) −492311. + 284236.i −0.294246 + 0.169883i
\(61\) 1.43978e6 0.812159 0.406080 0.913838i \(-0.366896\pi\)
0.406080 + 0.913838i \(0.366896\pi\)
\(62\) −277176. + 480082.i −0.147701 + 0.255826i
\(63\) 615640. 314740.i 0.310195 0.158584i
\(64\) −2.31624e6 −1.10447
\(65\) −152335. 3.44611e6i −0.0688021 1.55644i
\(66\) 1.31541e6 + 2.27835e6i 0.563192 + 0.975476i
\(67\) 2.52182e6i 1.02436i −0.858878 0.512180i \(-0.828838\pi\)
0.858878 0.512180i \(-0.171162\pi\)
\(68\) −521200. 902744.i −0.201012 0.348164i
\(69\) −1.08812e6 1.88468e6i −0.398754 0.690663i
\(70\) 3.40088e6 1.73867e6i 1.18508 0.605861i
\(71\) −906768. + 523523.i −0.300671 + 0.173593i −0.642744 0.766081i \(-0.722204\pi\)
0.342073 + 0.939673i \(0.388871\pi\)
\(72\) 1.19727e6i 0.378031i
\(73\) −3.86146e6 + 2.22941e6i −1.16177 + 0.670750i −0.951728 0.306942i \(-0.900694\pi\)
−0.210045 + 0.977692i \(0.567361\pi\)
\(74\) −154424. + 267470.i −0.0442999 + 0.0767297i
\(75\) 2.10463e6 + 3.64533e6i 0.576052 + 0.997752i
\(76\) 1.28591e6 + 742423.i 0.336020 + 0.194001i
\(77\) 2.97851e6 + 5.82604e6i 0.743500 + 1.45431i
\(78\) 2.56444e6 + 1.33319e6i 0.611872 + 0.318099i
\(79\) −1.93303e6 + 3.34811e6i −0.441107 + 0.764020i −0.997772 0.0667174i \(-0.978747\pi\)
0.556665 + 0.830737i \(0.312081\pi\)
\(80\) 4.68636e6i 1.02334i
\(81\) −2.53616e6 −0.530248
\(82\) −7.17871e6 −1.43780
\(83\) 5.42351e6i 1.04113i 0.853821 + 0.520567i \(0.174280\pi\)
−0.853821 + 0.520567i \(0.825720\pi\)
\(84\) 60392.1 1.18314e6i 0.0111174 0.217801i
\(85\) −1.13678e7 + 6.56323e6i −2.00776 + 1.15918i
\(86\) 3.89966e6 + 2.25147e6i 0.661124 + 0.381700i
\(87\) −1.88744e6 + 3.26914e6i −0.307295 + 0.532251i
\(88\) −1.13302e7 −1.77235
\(89\) 2.39248e6 1.38130e6i 0.359735 0.207693i −0.309229 0.950988i \(-0.600071\pi\)
0.668965 + 0.743294i \(0.266738\pi\)
\(90\) 3.20681e6 0.463686
\(91\) 6.20085e6 + 3.63670e6i 0.862594 + 0.505898i
\(92\) 1.99353e6 0.266911
\(93\) 1.87508e6 1.08258e6i 0.241729 0.139562i
\(94\) 9.18139e6 1.14015
\(95\) 9.34900e6 1.61929e7i 1.11875 1.93773i
\(96\) 3.17522e6 + 1.83321e6i 0.366290 + 0.211477i
\(97\) 2.67492e6 1.54436e6i 0.297584 0.171810i −0.343773 0.939053i \(-0.611705\pi\)
0.641357 + 0.767243i \(0.278372\pi\)
\(98\) −810489. + 7.91846e6i −0.0869873 + 0.849864i
\(99\) 5.49358e6i 0.569026i
\(100\) −3.85587e6 −0.385587
\(101\) 2.97138e6 0.286968 0.143484 0.989653i \(-0.454169\pi\)
0.143484 + 0.989653i \(0.454169\pi\)
\(102\) 1.09985e7i 1.02621i
\(103\) 3.50148e6 6.06474e6i 0.315734 0.546867i −0.663859 0.747857i \(-0.731083\pi\)
0.979593 + 0.200990i \(0.0644160\pi\)
\(104\) −1.04947e7 + 6.69384e6i −0.914853 + 0.583524i
\(105\) −1.48988e7 760490.i −1.25599 0.0641107i
\(106\) 4.03650e6 + 2.33047e6i 0.329181 + 0.190053i
\(107\) −6.62358e6 1.14724e7i −0.522697 0.905337i −0.999651 0.0264091i \(-0.991593\pi\)
0.476955 0.878928i \(-0.341741\pi\)
\(108\) 1.92482e6 3.33389e6i 0.147030 0.254664i
\(109\) −6.49605e6 + 3.75050e6i −0.480459 + 0.277393i −0.720608 0.693343i \(-0.756137\pi\)
0.240149 + 0.970736i \(0.422804\pi\)
\(110\) 3.03473e7i 2.17393i
\(111\) 1.04467e6 603138.i 0.0725015 0.0418588i
\(112\) −8.19789e6 5.30793e6i −0.551365 0.356995i
\(113\) 4.43308e6 + 7.67832e6i 0.289022 + 0.500601i 0.973577 0.228361i \(-0.0733366\pi\)
−0.684555 + 0.728962i \(0.740003\pi\)
\(114\) 7.83345e6 + 1.35679e7i 0.495206 + 0.857722i
\(115\) 2.51037e7i 1.53920i
\(116\) −1.72898e6 2.99468e6i −0.102846 0.178134i
\(117\) 3.24558e6 + 5.08844e6i 0.187345 + 0.293721i
\(118\) 1.61811e7 0.906612
\(119\) 1.39450e6 2.73196e7i 0.0758584 1.48614i
\(120\) 1.29160e7 2.23712e7i 0.682331 1.18183i
\(121\) −3.25008e7 −1.66780
\(122\) −1.20516e7 + 6.95798e6i −0.600875 + 0.346916i
\(123\) 2.42818e7 + 1.40191e7i 1.17656 + 0.679285i
\(124\) 1.98338e6i 0.0934177i
\(125\) 1.45347e7i 0.665614i
\(126\) −3.63214e6 + 5.60970e6i −0.161758 + 0.249829i
\(127\) −2.35264e6 + 4.07490e6i −0.101916 + 0.176524i −0.912474 0.409134i \(-0.865831\pi\)
0.810558 + 0.585659i \(0.199164\pi\)
\(128\) 8.62171e6 4.97775e6i 0.363378 0.209796i
\(129\) −8.79367e6 1.52311e7i −0.360667 0.624693i
\(130\) 1.79290e7 + 2.81092e7i 0.715739 + 1.12214i
\(131\) 1.30027e7 2.25213e7i 0.505340 0.875275i −0.494641 0.869098i \(-0.664700\pi\)
0.999981 0.00617756i \(-0.00196639\pi\)
\(132\) 8.15155e6 + 4.70630e6i 0.308483 + 0.178103i
\(133\) 1.77375e7 + 3.46950e7i 0.653749 + 1.27875i
\(134\) 1.21871e7 + 2.11088e7i 0.437558 + 0.757872i
\(135\) −4.19821e7 2.42384e7i −1.46857 0.847882i
\(136\) 4.10218e7 + 2.36839e7i 1.39839 + 0.807361i
\(137\) 381748. + 220402.i 0.0126840 + 0.00732308i 0.506329 0.862341i \(-0.331002\pi\)
−0.493645 + 0.869664i \(0.664336\pi\)
\(138\) 1.82161e7 + 1.05171e7i 0.590036 + 0.340657i
\(139\) 7.52791e6 + 1.30387e7i 0.237751 + 0.411797i 0.960069 0.279765i \(-0.0902564\pi\)
−0.722318 + 0.691562i \(0.756923\pi\)
\(140\) 7.42727e6 1.14711e7i 0.228760 0.353312i
\(141\) −3.10558e7 1.79301e7i −0.932987 0.538660i
\(142\) 5.06003e6 8.76423e6i 0.148301 0.256865i
\(143\) −4.81540e7 + 3.07142e7i −1.37707 + 0.878341i
\(144\) −4.09976e6 7.10100e6i −0.114417 0.198176i
\(145\) −3.77106e7 + 2.17722e7i −1.02725 + 0.593083i
\(146\) 2.15481e7 3.73223e7i 0.573025 0.992508i
\(147\) 1.82052e7 2.52012e7i 0.472699 0.654350i
\(148\) 1.10500e6i 0.0280187i
\(149\) 2.28935e7i 0.566970i −0.958977 0.283485i \(-0.908509\pi\)
0.958977 0.283485i \(-0.0914906\pi\)
\(150\) −3.52334e7 2.03420e7i −0.852384 0.492124i
\(151\) −1.60506e7 + 9.26684e6i −0.379379 + 0.219035i −0.677548 0.735479i \(-0.736957\pi\)
0.298169 + 0.954513i \(0.403624\pi\)
\(152\) −6.74732e7 −1.55840
\(153\) 1.14834e7 1.98899e7i 0.259210 0.448964i
\(154\) −5.30868e7 3.43724e7i −1.17129 0.758381i
\(155\) 2.49757e7 0.538713
\(156\) 1.03309e7 456674.i 0.217871 0.00963097i
\(157\) −1.51988e7 2.63251e7i −0.313445 0.542902i 0.665661 0.746254i \(-0.268150\pi\)
−0.979106 + 0.203352i \(0.934816\pi\)
\(158\) 3.73668e7i 0.753679i
\(159\) −9.10222e6 1.57655e7i −0.179580 0.311041i
\(160\) 2.11467e7 + 3.66272e7i 0.408153 + 0.706942i
\(161\) 4.39141e7 + 2.84333e7i 0.829303 + 0.536953i
\(162\) 2.12288e7 1.22564e7i 0.392304 0.226497i
\(163\) 3.46429e7i 0.626553i 0.949662 + 0.313276i \(0.101427\pi\)
−0.949662 + 0.313276i \(0.898573\pi\)
\(164\) −2.22432e7 + 1.28421e7i −0.393771 + 0.227344i
\(165\) 5.92643e7 1.02649e8i 1.02707 1.77893i
\(166\) −2.62101e7 4.53972e7i −0.444723 0.770283i
\(167\) 6.78834e7 + 3.91925e7i 1.12786 + 0.651171i 0.943396 0.331668i \(-0.107611\pi\)
0.184466 + 0.982839i \(0.440945\pi\)
\(168\) 2.45051e7 + 4.79326e7i 0.398725 + 0.779917i
\(169\) −2.64569e7 + 5.68982e7i −0.421634 + 0.906766i
\(170\) 6.34359e7 1.09874e8i 0.990294 1.71524i
\(171\) 3.27151e7i 0.500336i
\(172\) 1.61108e7 0.241416
\(173\) −4.85137e7 −0.712366 −0.356183 0.934416i \(-0.615922\pi\)
−0.356183 + 0.934416i \(0.615922\pi\)
\(174\) 3.64856e7i 0.525048i
\(175\) −8.49382e7 5.49954e7i −1.19804 0.775699i
\(176\) 6.71996e7 3.87977e7i 0.929121 0.536428i
\(177\) −5.47322e7 3.15996e7i −0.741884 0.428327i
\(178\) −1.33507e7 + 2.31242e7i −0.177433 + 0.307324i
\(179\) −4.18849e7 −0.545848 −0.272924 0.962036i \(-0.587991\pi\)
−0.272924 + 0.962036i \(0.587991\pi\)
\(180\) 9.93627e6 5.73671e6i 0.126990 0.0733177i
\(181\) 4.01125e7 0.502812 0.251406 0.967882i \(-0.419107\pi\)
0.251406 + 0.967882i \(0.419107\pi\)
\(182\) −6.94788e7 474097.i −0.854285 0.00582931i
\(183\) 5.43521e7 0.655598
\(184\) −7.84520e7 + 4.52943e7i −0.928414 + 0.536020i
\(185\) 1.39148e7 0.161576
\(186\) −1.04635e7 + 1.81233e7i −0.119229 + 0.206510i
\(187\) 1.88226e8 + 1.08672e8i 2.10491 + 1.21527i
\(188\) 2.84485e7 1.64247e7i 0.312253 0.180279i
\(189\) 8.99508e7 4.59865e7i 0.969145 0.495466i
\(190\) 1.80723e8i 1.91150i
\(191\) −1.87927e8 −1.95152 −0.975759 0.218846i \(-0.929771\pi\)
−0.975759 + 0.218846i \(0.929771\pi\)
\(192\) −8.74388e7 −0.891558
\(193\) 2.19599e7i 0.219877i −0.993938 0.109938i \(-0.964935\pi\)
0.993938 0.109938i \(-0.0350654\pi\)
\(194\) −1.49268e7 + 2.58540e7i −0.146778 + 0.254227i
\(195\) −5.75068e6 1.30092e8i −0.0555390 1.25640i
\(196\) 1.16542e7 + 2.59852e7i 0.110557 + 0.246507i
\(197\) −5.34766e7 3.08748e7i −0.498348 0.287721i 0.229683 0.973265i \(-0.426231\pi\)
−0.728031 + 0.685544i \(0.759564\pi\)
\(198\) −2.65487e7 4.59837e7i −0.243061 0.420994i
\(199\) 6.80970e7 1.17947e8i 0.612551 1.06097i −0.378258 0.925700i \(-0.623477\pi\)
0.990809 0.135269i \(-0.0431900\pi\)
\(200\) 1.51741e8 8.76078e7i 1.34122 0.774351i
\(201\) 9.51997e7i 0.826893i
\(202\) −2.48717e7 + 1.43597e7i −0.212313 + 0.122579i
\(203\) 4.62598e6 9.06276e7i 0.0388122 0.760369i
\(204\) −1.96755e7 3.40789e7i −0.162263 0.281048i
\(205\) 1.61715e8 + 2.80098e8i 1.31103 + 2.27076i
\(206\) 6.76860e7i 0.539466i
\(207\) 2.19614e7 + 3.80383e7i 0.172093 + 0.298074i
\(208\) 3.93223e7 7.56376e7i 0.302982 0.582795i
\(209\) −3.09596e8 −2.34576
\(210\) 1.28384e8 6.56352e7i 0.956631 0.489068i
\(211\) −4.75998e7 + 8.24453e7i −0.348832 + 0.604195i −0.986042 0.166495i \(-0.946755\pi\)
0.637210 + 0.770690i \(0.280088\pi\)
\(212\) 1.66761e7 0.120204
\(213\) −3.42308e7 + 1.97632e7i −0.242711 + 0.140129i
\(214\) 1.10885e8 + 6.40192e7i 0.773433 + 0.446542i
\(215\) 2.02876e8i 1.39218i
\(216\) 1.74932e8i 1.18109i
\(217\) −2.82884e7 + 4.36903e7i −0.187931 + 0.290253i
\(218\) 3.62499e7 6.27866e7i 0.236978 0.410459i
\(219\) −1.45771e8 + 8.41612e7i −0.937817 + 0.541449i
\(220\) 5.42887e7 + 9.40308e7i 0.343740 + 0.595375i
\(221\) 2.38547e8 1.05449e7i 1.48663 0.0657160i
\(222\) −5.82955e6 + 1.00971e7i −0.0357601 + 0.0619384i
\(223\) −2.50980e8 1.44904e8i −1.51556 0.875009i −0.999833 0.0182549i \(-0.994189\pi\)
−0.515726 0.856754i \(-0.672478\pi\)
\(224\) −8.80238e7 4.49308e6i −0.523278 0.0267101i
\(225\) −4.24776e7 7.35733e7i −0.248611 0.430607i
\(226\) −7.42136e7 4.28472e7i −0.427665 0.246913i
\(227\) 1.06089e8 + 6.12506e7i 0.601978 + 0.347552i 0.769819 0.638262i \(-0.220346\pi\)
−0.167842 + 0.985814i \(0.553680\pi\)
\(228\) 4.85437e7 + 2.80267e7i 0.271245 + 0.156603i
\(229\) −1.78644e8 1.03140e8i −0.983022 0.567548i −0.0798410 0.996808i \(-0.525441\pi\)
−0.903181 + 0.429259i \(0.858775\pi\)
\(230\) 1.21318e8 + 2.10129e8i 0.657472 + 1.13877i
\(231\) 1.12440e8 + 2.19935e8i 0.600175 + 1.17396i
\(232\) 1.36082e8 + 7.85669e7i 0.715472 + 0.413078i
\(233\) 4.21300e6 7.29713e6i 0.0218195 0.0377925i −0.854909 0.518777i \(-0.826387\pi\)
0.876729 + 0.480985i \(0.159721\pi\)
\(234\) −5.17577e7 2.69077e7i −0.264070 0.137284i
\(235\) −2.06829e8 3.58239e8i −1.03962 1.80067i
\(236\) 5.01371e7 2.89467e7i 0.248294 0.143353i
\(237\) −7.29726e7 + 1.26392e8i −0.356074 + 0.616739i
\(238\) 1.20354e8 + 2.35416e8i 0.578685 + 1.13192i
\(239\) 3.25389e8i 1.54174i 0.636994 + 0.770868i \(0.280177\pi\)
−0.636994 + 0.770868i \(0.719823\pi\)
\(240\) 1.76912e8i 0.826070i
\(241\) 2.54936e8 + 1.47187e8i 1.17320 + 0.677347i 0.954431 0.298430i \(-0.0964630\pi\)
0.218768 + 0.975777i \(0.429796\pi\)
\(242\) 2.72046e8 1.57066e8i 1.23392 0.712406i
\(243\) 1.47721e8 0.660421
\(244\) −2.48945e7 + 4.31185e7i −0.109708 + 0.190020i
\(245\) 3.27220e8 1.46756e8i 1.42154 0.637549i
\(246\) −2.70999e8 −1.16063
\(247\) −2.86764e8 + 1.82908e8i −1.21084 + 0.772312i
\(248\) −4.50635e7 7.80523e7i −0.187605 0.324941i
\(249\) 2.04739e8i 0.840434i
\(250\) −7.02417e7 1.21662e8i −0.284318 0.492454i
\(251\) 6.33053e7 + 1.09648e8i 0.252687 + 0.437666i 0.964265 0.264941i \(-0.0853525\pi\)
−0.711578 + 0.702607i \(0.752019\pi\)
\(252\) −1.21889e6 + 2.38792e7i −0.00479801 + 0.0939978i
\(253\) −3.59971e8 + 2.07830e8i −1.39748 + 0.806837i
\(254\) 4.54783e7i 0.174135i
\(255\) −4.29140e8 + 2.47764e8i −1.62072 + 0.935724i
\(256\) 1.00127e8 1.73426e8i 0.373004 0.646062i
\(257\) −3.30253e7 5.72016e7i −0.121362 0.210204i 0.798943 0.601406i \(-0.205393\pi\)
−0.920305 + 0.391202i \(0.872059\pi\)
\(258\) 1.47214e8 + 8.49939e7i 0.533678 + 0.308119i
\(259\) −1.57604e7 + 2.43413e7i −0.0563661 + 0.0870552i
\(260\) 1.05838e8 + 5.50228e7i 0.373452 + 0.194149i
\(261\) 3.80940e7 6.59807e7i 0.132622 0.229708i
\(262\) 2.51351e8i 0.863429i
\(263\) −2.49131e8 −0.844466 −0.422233 0.906487i \(-0.638754\pi\)
−0.422233 + 0.906487i \(0.638754\pi\)
\(264\) −4.27720e8 −1.43069
\(265\) 2.09994e8i 0.693181i
\(266\) −3.16140e8 2.04693e8i −1.02990 0.666833i
\(267\) 9.03169e7 5.21445e7i 0.290389 0.167656i
\(268\) 7.55236e7 + 4.36035e7i 0.239668 + 0.138373i
\(269\) 3.00364e7 5.20246e7i 0.0940838 0.162958i −0.815142 0.579261i \(-0.803341\pi\)
0.909226 + 0.416303i \(0.136675\pi\)
\(270\) 4.68545e8 1.44870
\(271\) −7.25904e7 + 4.19101e7i −0.221558 + 0.127916i −0.606671 0.794953i \(-0.707496\pi\)
0.385114 + 0.922869i \(0.374162\pi\)
\(272\) −3.24400e8 −0.977440
\(273\) 2.34084e8 + 1.37287e8i 0.696310 + 0.408375i
\(274\) −4.26053e6 −0.0125123
\(275\) 6.96253e8 4.01982e8i 2.01884 1.16558i
\(276\) 7.52566e7 0.215458
\(277\) −9.30040e7 + 1.61088e8i −0.262919 + 0.455390i −0.967016 0.254714i \(-0.918019\pi\)
0.704097 + 0.710104i \(0.251352\pi\)
\(278\) −1.26024e8 7.27599e7i −0.351800 0.203112i
\(279\) −3.78445e7 + 2.18495e7i −0.104325 + 0.0602320i
\(280\) −3.16563e7 + 6.20178e8i −0.0861800 + 1.68835i
\(281\) 8.43156e7i 0.226692i 0.993556 + 0.113346i \(0.0361568\pi\)
−0.993556 + 0.113346i \(0.963843\pi\)
\(282\) 3.46601e8 0.920360
\(283\) −5.95085e8 −1.56073 −0.780363 0.625326i \(-0.784966\pi\)
−0.780363 + 0.625326i \(0.784966\pi\)
\(284\) 3.62079e7i 0.0937970i
\(285\) 3.52928e8 6.11289e8i 0.903086 1.56419i
\(286\) 2.54638e8 4.89804e8i 0.643638 1.23806i
\(287\) −6.73143e8 3.43598e7i −1.68082 0.0857954i
\(288\) −6.40851e7 3.69996e7i −0.158082 0.0912689i
\(289\) −2.49152e8 4.31544e8i −0.607187 1.05168i
\(290\) 2.10436e8 3.64487e8i 0.506673 0.877584i
\(291\) 1.00979e8 5.83003e7i 0.240218 0.138690i
\(292\) 1.54191e8i 0.362425i
\(293\) 3.46128e8 1.99837e8i 0.803896 0.464130i −0.0409356 0.999162i \(-0.513034\pi\)
0.844832 + 0.535032i \(0.179701\pi\)
\(294\) −3.05963e7 + 2.98925e8i −0.0702187 + 0.686035i
\(295\) −3.64512e8 6.31354e8i −0.826675 1.43184i
\(296\) −2.51063e7 4.34855e7i −0.0562681 0.0974593i
\(297\) 8.02664e8i 1.77781i
\(298\) 1.10637e8 + 1.91629e8i 0.242183 + 0.419472i
\(299\) −2.10640e8 + 4.05172e8i −0.455713 + 0.876577i
\(300\) −1.45561e8 −0.311257
\(301\) 3.54892e8 + 2.29784e8i 0.750091 + 0.485665i
\(302\) 8.95673e7 1.55135e8i 0.187122 0.324105i
\(303\) 1.12171e8 0.231649
\(304\) 4.00184e8 2.31046e8i 0.816962 0.471673i
\(305\) 5.42972e8 + 3.13485e8i 1.09579 + 0.632655i
\(306\) 2.21982e8i 0.442888i
\(307\) 5.29588e7i 0.104461i 0.998635 + 0.0522305i \(0.0166330\pi\)
−0.998635 + 0.0522305i \(0.983367\pi\)
\(308\) −2.25978e8 1.15348e7i −0.440696 0.0224948i
\(309\) 1.32182e8 2.28946e8i 0.254869 0.441447i
\(310\) −2.09058e8 + 1.20700e8i −0.398566 + 0.230112i
\(311\) −4.33303e8 7.50503e8i −0.816828 1.41479i −0.908008 0.418953i \(-0.862397\pi\)
0.0911803 0.995834i \(-0.470936\pi\)
\(312\) −3.96177e8 + 2.52695e8i −0.738496 + 0.471037i
\(313\) −1.96260e8 + 3.39932e8i −0.361765 + 0.626595i −0.988251 0.152837i \(-0.951159\pi\)
0.626487 + 0.779432i \(0.284492\pi\)
\(314\) 2.54442e8 + 1.46902e8i 0.463804 + 0.267777i
\(315\) 3.00700e8 + 1.53489e7i 0.542059 + 0.0276688i
\(316\) −6.68461e7 1.15781e8i −0.119171 0.206411i
\(317\) −5.26947e8 3.04233e8i −0.929093 0.536412i −0.0425687 0.999094i \(-0.513554\pi\)
−0.886525 + 0.462681i \(0.846887\pi\)
\(318\) 1.52379e8 + 8.79762e7i 0.265724 + 0.153416i
\(319\) 6.24402e8 + 3.60499e8i 1.07695 + 0.621779i
\(320\) −8.73503e8 5.04317e8i −1.49018 0.860358i
\(321\) −2.50043e8 4.33086e8i −0.421936 0.730814i
\(322\) −5.04989e8 2.57766e7i −0.842920 0.0430259i
\(323\) 1.12091e9 + 6.47159e8i 1.85081 + 1.06857i
\(324\) 4.38515e7 7.59530e7i 0.0716270 0.124062i
\(325\) 4.07417e8 7.83680e8i 0.658336 1.26633i
\(326\) −1.67418e8 2.89976e8i −0.267633 0.463555i
\(327\) −2.45228e8 + 1.41583e8i −0.387841 + 0.223920i
\(328\) 5.83561e8 1.01076e9i 0.913120 1.58157i
\(329\) 8.60932e8 + 4.39453e7i 1.33286 + 0.0680341i
\(330\) 1.14562e9i 1.75486i
\(331\) 6.13243e8i 0.929468i 0.885450 + 0.464734i \(0.153850\pi\)
−0.885450 + 0.464734i \(0.846150\pi\)
\(332\) −1.62423e8 9.37751e7i −0.243593 0.140639i
\(333\) −2.10844e7 + 1.21731e7i −0.0312900 + 0.0180653i
\(334\) −7.57619e8 −1.11260
\(335\) 5.49080e8 9.51034e8i 0.797955 1.38210i
\(336\) −3.09473e8 2.00376e8i −0.445077 0.288177i
\(337\) 1.29241e9 1.83949 0.919743 0.392521i \(-0.128397\pi\)
0.919743 + 0.392521i \(0.128397\pi\)
\(338\) −5.35147e7 6.04121e8i −0.0753815 0.850972i
\(339\) 1.67350e8 + 2.89859e8i 0.233307 + 0.404099i
\(340\) 4.53926e8i 0.626338i
\(341\) −2.06771e8 3.58137e8i −0.282389 0.489113i
\(342\) −1.58102e8 2.73840e8i −0.213720 0.370174i
\(343\) −1.13899e8 + 7.38629e8i −0.152403 + 0.988319i
\(344\) −6.34011e8 + 3.66047e8i −0.839735 + 0.484822i
\(345\) 9.47672e8i 1.24248i
\(346\) 4.06081e8 2.34451e8i 0.527044 0.304289i
\(347\) 6.32120e8 1.09486e9i 0.812168 1.40672i −0.0991749 0.995070i \(-0.531620\pi\)
0.911343 0.411647i \(-0.135046\pi\)
\(348\) −6.52696e7 1.13050e8i −0.0830201 0.143795i
\(349\) −1.04945e9 6.05901e8i −1.32152 0.762979i −0.337547 0.941309i \(-0.609597\pi\)
−0.983971 + 0.178330i \(0.942931\pi\)
\(350\) 9.76745e8 + 4.98568e7i 1.21771 + 0.0621565i
\(351\) 4.74210e8 + 7.43470e8i 0.585323 + 0.917674i
\(352\) 3.50141e8 6.06463e8i 0.427902 0.741148i
\(353\) 1.14243e9i 1.38235i −0.722686 0.691177i \(-0.757093\pi\)
0.722686 0.691177i \(-0.242907\pi\)
\(354\) 6.10843e8 0.731844
\(355\) −4.55949e8 −0.540900
\(356\) 9.55334e7i 0.112223i
\(357\) 5.26428e7 1.03133e9i 0.0612351 1.19966i
\(358\) 3.50595e8 2.02416e8i 0.403845 0.233160i
\(359\) 1.34290e9 + 7.75323e8i 1.53184 + 0.884407i 0.999277 + 0.0380161i \(0.0121038\pi\)
0.532561 + 0.846391i \(0.321230\pi\)
\(360\) −2.60683e8 + 4.51516e8i −0.294479 + 0.510052i
\(361\) −9.49820e8 −1.06259
\(362\) −3.35760e8 + 1.93851e8i −0.372005 + 0.214777i
\(363\) −1.22692e9 −1.34630
\(364\) −2.16128e8 + 1.22823e8i −0.234885 + 0.133482i
\(365\) −1.94165e9 −2.09000
\(366\) −4.54951e8 + 2.62666e8i −0.485044 + 0.280040i
\(367\) −5.93915e8 −0.627181 −0.313591 0.949558i \(-0.601532\pi\)
−0.313591 + 0.949558i \(0.601532\pi\)
\(368\) 3.10199e8 5.37281e8i 0.324469 0.561997i
\(369\) −4.90076e8 2.82946e8i −0.507775 0.293164i
\(370\) −1.16473e8 + 6.72457e7i −0.119542 + 0.0690174i
\(371\) 3.67345e8 + 2.37847e8i 0.373478 + 0.241818i
\(372\) 7.48731e7i 0.0754094i
\(373\) −7.14874e8 −0.713261 −0.356631 0.934245i \(-0.616075\pi\)
−0.356631 + 0.934245i \(0.616075\pi\)
\(374\) −2.10071e9 −2.07642
\(375\) 5.48692e8i 0.537303i
\(376\) −7.46360e8 + 1.29273e9i −0.724087 + 1.25416i
\(377\) 7.91335e8 3.49808e7i 0.760616 0.0336229i
\(378\) −5.30690e8 + 8.19630e8i −0.505382 + 0.780543i
\(379\) 2.73947e8 + 1.58163e8i 0.258481 + 0.149234i 0.623641 0.781711i \(-0.285653\pi\)
−0.365160 + 0.930945i \(0.618986\pi\)
\(380\) 3.23298e8 + 5.59968e8i 0.302246 + 0.523505i
\(381\) −8.88132e7 + 1.53829e8i −0.0822697 + 0.142495i
\(382\) 1.57303e9 9.08191e8i 1.44383 0.833596i
\(383\) 1.11724e7i 0.0101614i 0.999987 + 0.00508068i \(0.00161724\pi\)
−0.999987 + 0.00508068i \(0.998383\pi\)
\(384\) 3.25473e8 1.87912e8i 0.293329 0.169354i
\(385\) −1.45253e8 + 2.84564e9i −0.129721 + 2.54137i
\(386\) 1.06125e8 + 1.83814e8i 0.0939209 + 0.162676i
\(387\) 1.77482e8 + 3.07407e8i 0.155656 + 0.269604i
\(388\) 1.06811e8i 0.0928338i
\(389\) 8.72641e8 + 1.51146e9i 0.751644 + 1.30189i 0.947026 + 0.321158i \(0.104072\pi\)
−0.195382 + 0.980727i \(0.562595\pi\)
\(390\) 6.76827e8 + 1.06113e9i 0.577765 + 0.905824i
\(391\) 1.73773e9 1.47016
\(392\) −1.04903e9 7.57812e8i −0.879602 0.635419i
\(393\) 4.90856e8 8.50188e8i 0.407925 0.706547i
\(394\) 5.96831e8 0.491603
\(395\) −1.45798e9 + 8.41763e8i −1.19031 + 0.687226i
\(396\) −1.64522e8 9.49867e7i −0.133134 0.0768652i
\(397\) 5.37764e8i 0.431345i −0.976466 0.215673i \(-0.930806\pi\)
0.976466 0.215673i \(-0.0691944\pi\)
\(398\) 1.31636e9i 1.04661i
\(399\) 6.69596e8 + 1.30975e9i 0.527725 + 1.03224i
\(400\) −5.99984e8 + 1.03920e9i −0.468738 + 0.811878i
\(401\) 1.41748e9 8.18384e8i 1.09777 0.633799i 0.162138 0.986768i \(-0.448161\pi\)
0.935635 + 0.352969i \(0.114828\pi\)
\(402\) 4.60069e8 + 7.96863e8i 0.353209 + 0.611776i
\(403\) −4.03107e8 2.09566e8i −0.306798 0.159498i
\(404\) −5.13766e7 + 8.89869e7i −0.0387642 + 0.0671415i
\(405\) −9.56441e8 5.52202e8i −0.715428 0.413052i
\(406\) 3.99252e8 + 7.80949e8i 0.296078 + 0.579137i
\(407\) −1.15199e8 1.99530e8i −0.0846968 0.146699i
\(408\) 1.54859e9 + 8.94077e8i 1.12882 + 0.651725i
\(409\) 9.66202e8 + 5.57837e8i 0.698291 + 0.403159i 0.806711 0.590947i \(-0.201246\pi\)
−0.108419 + 0.994105i \(0.534579\pi\)
\(410\) −2.70725e9 1.56303e9i −1.93992 1.12002i
\(411\) 1.44111e7 + 8.32026e6i 0.0102389 + 0.00591140i
\(412\) 1.21085e8 + 2.09725e8i 0.0852999 + 0.147744i
\(413\) 1.51729e9 + 7.74484e7i 1.05985 + 0.0540988i
\(414\) −3.67653e8 2.12265e8i −0.254646 0.147020i
\(415\) −1.18087e9 + 2.04532e9i −0.811023 + 1.40473i
\(416\) −3.39758e7 7.68599e8i −0.0231389 0.523448i
\(417\) 2.84181e8 + 4.92216e8i 0.191919 + 0.332414i
\(418\) 2.59146e9 1.49618e9i 1.73551 1.00200i
\(419\) 9.23500e8 1.59955e9i 0.613321 1.06230i −0.377356 0.926068i \(-0.623167\pi\)
0.990677 0.136235i \(-0.0435001\pi\)
\(420\) 2.80382e8 4.33039e8i 0.184662 0.285203i
\(421\) 5.49442e8i 0.358868i 0.983770 + 0.179434i \(0.0574266\pi\)
−0.983770 + 0.179434i \(0.942573\pi\)
\(422\) 9.20138e8i 0.596018i
\(423\) 6.26795e8 + 3.61880e8i 0.402656 + 0.232474i
\(424\) −6.56258e8 + 3.78891e8i −0.418113 + 0.241398i
\(425\) −3.36111e9 −2.12384
\(426\) 1.91018e8 3.30853e8i 0.119713 0.207349i
\(427\) −1.16337e9 + 5.94762e8i −0.723137 + 0.369697i
\(428\) 4.58100e8 0.282428
\(429\) −1.81783e9 + 1.15947e9i −1.11161 + 0.709022i
\(430\) 9.80432e8 + 1.69816e9i 0.594673 + 1.03000i
\(431\) 6.48635e8i 0.390238i 0.980780 + 0.195119i \(0.0625094\pi\)
−0.980780 + 0.195119i \(0.937491\pi\)
\(432\) −5.99014e8 1.03752e9i −0.357474 0.619162i
\(433\) 1.57745e9 + 2.73222e9i 0.933785 + 1.61736i 0.776786 + 0.629764i \(0.216849\pi\)
0.156999 + 0.987599i \(0.449818\pi\)
\(434\) 2.56452e7 5.02416e8i 0.0150589 0.295018i
\(435\) −1.42359e9 + 8.21910e8i −0.829225 + 0.478753i
\(436\) 2.59392e8i 0.149883i
\(437\) −2.14368e9 + 1.23766e9i −1.22879 + 0.709439i
\(438\) 8.13447e8 1.40893e9i 0.462562 0.801181i
\(439\) 1.77380e8 + 3.07231e8i 0.100064 + 0.173316i 0.911711 0.410832i \(-0.134762\pi\)
−0.811647 + 0.584149i \(0.801429\pi\)
\(440\) −4.27288e9 2.46695e9i −2.39131 1.38062i
\(441\) −3.67433e8 + 5.08633e8i −0.204006 + 0.282403i
\(442\) −1.94579e9 + 1.24109e9i −1.07181 + 0.683635i
\(443\) 6.28859e8 1.08922e9i 0.343669 0.595252i −0.641442 0.767171i \(-0.721664\pi\)
0.985111 + 0.171919i \(0.0549969\pi\)
\(444\) 4.17142e7i 0.0226175i
\(445\) 1.20301e9 0.647155
\(446\) 2.80109e9 1.49505
\(447\) 8.64238e8i 0.457675i
\(448\) 1.87157e9 9.56820e8i 0.983405 0.502756i
\(449\) −1.92367e9 + 1.11063e9i −1.00292 + 0.579039i −0.909112 0.416551i \(-0.863239\pi\)
−0.0938126 + 0.995590i \(0.529905\pi\)
\(450\) 7.11112e8 + 4.10561e8i 0.367870 + 0.212390i
\(451\) 2.67763e9 4.63779e9i 1.37446 2.38064i
\(452\) −3.06600e8 −0.156167
\(453\) −6.05917e8 + 3.49827e8i −0.306246 + 0.176811i
\(454\) −1.18402e9 −0.593830
\(455\) 1.54665e9 + 2.72160e9i 0.769755 + 1.35452i
\(456\) −2.54714e9 −1.25799
\(457\) −1.27448e8 + 7.35824e7i −0.0624637 + 0.0360634i −0.530907 0.847430i \(-0.678149\pi\)
0.468443 + 0.883494i \(0.344815\pi\)
\(458\) 1.99377e9 0.969718
\(459\) 1.67784e9 2.90610e9i 0.809851 1.40270i
\(460\) 7.51805e8 + 4.34055e8i 0.360124 + 0.207918i
\(461\) 5.44625e8 3.14439e8i 0.258907 0.149480i −0.364929 0.931035i \(-0.618907\pi\)
0.623836 + 0.781555i \(0.285573\pi\)
\(462\) −2.00405e9 1.29757e9i −0.945498 0.612187i
\(463\) 1.59516e9i 0.746914i −0.927647 0.373457i \(-0.878172\pi\)
0.927647 0.373457i \(-0.121828\pi\)
\(464\) −1.07614e9 −0.500097
\(465\) 9.42843e8 0.434865
\(466\) 8.14402e7i 0.0372810i
\(467\) 1.78015e9 3.08332e9i 0.808814 1.40091i −0.104872 0.994486i \(-0.533443\pi\)
0.913686 0.406421i \(-0.133223\pi\)
\(468\) −2.08506e8 + 9.21699e6i −0.0940284 + 0.00415651i
\(469\) 1.04175e9 + 2.03768e9i 0.466291 + 0.912078i
\(470\) 3.46250e9 + 1.99908e9i 1.53832 + 0.888151i
\(471\) −5.73761e8 9.93783e8i −0.253022 0.438246i
\(472\) −1.31537e9 + 2.27829e9i −0.575773 + 0.997268i
\(473\) −2.90912e9 + 1.67958e9i −1.26400 + 0.729771i
\(474\) 1.41061e9i 0.608392i
\(475\) 4.14630e9 2.39386e9i 1.77514 1.02488i
\(476\) 7.94057e8 + 5.14132e8i 0.337464 + 0.218500i
\(477\) 1.83709e8 + 3.18194e8i 0.0775026 + 0.134239i
\(478\) −1.57250e9 2.72365e9i −0.658556 1.14065i
\(479\) 1.21052e9i 0.503267i −0.967823 0.251633i \(-0.919032\pi\)
0.967823 0.251633i \(-0.0809677\pi\)
\(480\) 7.98296e8 + 1.38269e9i 0.329473 + 0.570664i
\(481\) −2.24584e8 1.16756e8i −0.0920177 0.0478379i
\(482\) −2.84524e9 −1.15732
\(483\) 1.65777e9 + 1.07337e9i 0.669437 + 0.433444i
\(484\) 5.61954e8 9.73334e8i 0.225290 0.390214i
\(485\) 1.34503e9 0.535346
\(486\) −1.23649e9 + 7.13888e8i −0.488612 + 0.282100i
\(487\) 5.69826e8 + 3.28989e8i 0.223558 + 0.129071i 0.607597 0.794246i \(-0.292134\pi\)
−0.384039 + 0.923317i \(0.625467\pi\)
\(488\) 2.26247e9i 0.881279i
\(489\) 1.30778e9i 0.505771i
\(490\) −2.02975e9 + 2.80975e9i −0.779393 + 1.07890i
\(491\) 8.04274e8 1.39304e9i 0.306633 0.531104i −0.670991 0.741466i \(-0.734131\pi\)
0.977624 + 0.210362i \(0.0674643\pi\)
\(492\) −8.39688e8 + 4.84794e8i −0.317863 + 0.183518i
\(493\) −1.50712e9 2.61042e9i −0.566480 0.981173i
\(494\) 1.51641e9 2.91686e9i 0.565942 1.08861i
\(495\) −1.19612e9 + 2.07175e9i −0.443260 + 0.767748i
\(496\) 5.34543e8 + 3.08619e8i 0.196697 + 0.113563i
\(497\) 5.16424e8 7.97596e8i 0.188694 0.291431i
\(498\) −9.89439e8 1.71376e9i −0.358993 0.621795i
\(499\) −3.15144e9 1.81948e9i −1.13542 0.655535i −0.190128 0.981759i \(-0.560890\pi\)
−0.945292 + 0.326224i \(0.894224\pi\)
\(500\) −4.35287e8 2.51313e8i −0.155733 0.0899124i
\(501\) 2.56262e9 + 1.47953e9i 0.910442 + 0.525644i
\(502\) −1.05979e9 6.11868e8i −0.373900 0.215871i
\(503\) 2.02696e9 + 3.51079e9i 0.710160 + 1.23003i 0.964797 + 0.262997i \(0.0847108\pi\)
−0.254637 + 0.967037i \(0.581956\pi\)
\(504\) −4.94583e8 9.67418e8i −0.172081 0.336595i
\(505\) 1.12057e9 + 6.46962e8i 0.387186 + 0.223542i
\(506\) 2.00875e9 3.47925e9i 0.689284 1.19388i
\(507\) −9.98758e8 + 2.14793e9i −0.340355 + 0.731968i
\(508\) −8.13568e7 1.40914e8i −0.0275341 0.0476904i
\(509\) 1.34977e8 7.79289e7i 0.0453677 0.0261931i −0.477145 0.878825i \(-0.658328\pi\)
0.522512 + 0.852632i \(0.324995\pi\)
\(510\) 2.39473e9 4.14779e9i 0.799393 1.38459i
\(511\) 2.19918e9 3.39655e9i 0.729102 1.12607i
\(512\) 3.20984e9i 1.05691i
\(513\) 4.77999e9i 1.56321i
\(514\) 5.52873e8 + 3.19201e8i 0.179579 + 0.103680i
\(515\) 2.64097e9 1.52476e9i 0.851996 0.491900i
\(516\) 6.08187e8 0.194878
\(517\) −3.42462e9 + 5.93161e9i −1.08992 + 1.88780i
\(518\) 1.42878e7 2.79912e8i 0.00451659 0.0884846i
\(519\) −1.83141e9 −0.575042
\(520\) −5.41522e9 + 2.39379e8i −1.68890 + 0.0746576i
\(521\) 2.63938e9 + 4.57155e9i 0.817656 + 1.41622i 0.907405 + 0.420257i \(0.138060\pi\)
−0.0897489 + 0.995964i \(0.528606\pi\)
\(522\) 7.36384e8i 0.226599i
\(523\) −2.27926e9 3.94780e9i −0.696688 1.20670i −0.969608 0.244662i \(-0.921323\pi\)
0.272920 0.962037i \(-0.412010\pi\)
\(524\) 4.49646e8 + 7.78810e8i 0.136525 + 0.236468i
\(525\) −3.20645e9 2.07610e9i −0.967089 0.626166i
\(526\) 2.08533e9 1.20397e9i 0.624778 0.360716i
\(527\) 1.72888e9i 0.514549i
\(528\) 2.53681e9 1.46463e9i 0.750013 0.433020i
\(529\) 4.07526e7 7.05856e7i 0.0119691 0.0207311i
\(530\) 1.01483e9 + 1.75774e9i 0.296094 + 0.512850i
\(531\) 1.10465e9 + 6.37772e8i 0.320181 + 0.184856i
\(532\) −1.34574e9 6.86915e7i −0.387498 0.0197794i
\(533\) −2.59822e8 5.87769e9i −0.0743244 1.68136i
\(534\) −5.03995e8 + 8.72945e8i −0.143229 + 0.248080i
\(535\) 5.76864e9i 1.62868i
\(536\) −3.96280e9 −1.11154
\(537\) −1.58117e9 −0.440624
\(538\) 5.80625e8i 0.160752i
\(539\) −4.81339e9 3.47717e9i −1.32401 0.956455i
\(540\) 1.45178e9 8.38187e8i 0.396756 0.229067i
\(541\) 1.19728e9 + 6.91248e8i 0.325091 + 0.187691i 0.653659 0.756789i \(-0.273233\pi\)
−0.328569 + 0.944480i \(0.606566\pi\)
\(542\) 4.05076e8 7.01612e8i 0.109279 0.189278i
\(543\) 1.51426e9 0.405884
\(544\) −2.53542e9 + 1.46382e9i −0.675233 + 0.389846i
\(545\) −3.26640e9 −0.864335
\(546\) −2.62285e9 1.78973e7i −0.689603 0.00470559i
\(547\) 3.70158e9 0.967010 0.483505 0.875342i \(-0.339363\pi\)
0.483505 + 0.875342i \(0.339363\pi\)
\(548\) −1.32012e7 + 7.62173e6i −0.00342675 + 0.00197843i
\(549\) −1.09698e9 −0.282941
\(550\) −3.88530e9 + 6.72953e9i −0.995761 + 1.72471i
\(551\) 3.71841e9 + 2.14682e9i 0.946949 + 0.546721i
\(552\) −2.96159e9 + 1.70988e9i −0.749443 + 0.432691i
\(553\) 1.78851e8 3.50386e9i 0.0449730 0.881067i
\(554\) 1.79783e9i 0.449226i
\(555\) 5.25289e8 0.130428
\(556\) −5.20645e8 −0.128464
\(557\) 6.65082e9i 1.63073i −0.578947 0.815365i \(-0.696536\pi\)
0.578947 0.815365i \(-0.303464\pi\)
\(558\) 2.11183e8 3.65780e8i 0.0514564 0.0891252i
\(559\) −1.70229e9 + 3.27440e9i −0.412185 + 0.792850i
\(560\) −1.93590e9 3.78667e9i −0.465827 0.911171i
\(561\) 7.10558e9 + 4.10241e9i 1.69914 + 0.981000i
\(562\) −4.07470e8 7.05758e8i −0.0968319 0.167718i
\(563\) −3.57164e9 + 6.18627e9i −0.843507 + 1.46100i 0.0434038 + 0.999058i \(0.486180\pi\)
−0.886911 + 0.461940i \(0.847154\pi\)
\(564\) 1.07394e9 6.20039e8i 0.252059 0.145527i
\(565\) 3.86088e9i 0.900568i
\(566\) 4.98113e9 2.87586e9i 1.15470 0.666668i
\(567\) 2.04927e9 1.04767e9i 0.472127 0.241370i
\(568\) 8.22665e8 + 1.42490e9i 0.188367 + 0.326260i
\(569\) −2.72316e9 4.71665e9i −0.619698 1.07335i −0.989541 0.144254i \(-0.953922\pi\)
0.369842 0.929094i \(-0.379412\pi\)
\(570\) 6.82235e9i 1.54302i
\(571\) 1.23038e9 + 2.13109e9i 0.276576 + 0.479043i 0.970531 0.240974i \(-0.0774670\pi\)
−0.693956 + 0.720018i \(0.744134\pi\)
\(572\) −8.72241e7 1.97318e9i −0.0194872 0.440839i
\(573\) −7.09432e9 −1.57532
\(574\) 5.80055e9 2.96547e9i 1.28020 0.654489i
\(575\) 3.21397e9 5.56676e9i 0.705024 1.22114i
\(576\) 1.76477e9 0.384777
\(577\) −6.82034e8 + 3.93773e8i −0.147806 + 0.0853356i −0.572079 0.820199i \(-0.693863\pi\)
0.424273 + 0.905534i \(0.360530\pi\)
\(578\) 4.17103e9 + 2.40814e9i 0.898454 + 0.518722i
\(579\) 8.28994e8i 0.177491i
\(580\) 1.50581e9i 0.320459i
\(581\) −2.24041e9 4.38231e9i −0.473927 0.927014i
\(582\) −5.63493e8 + 9.75998e8i −0.118484 + 0.205220i
\(583\) −3.01119e9 + 1.73851e9i −0.629359 + 0.363361i
\(584\) 3.50331e9 + 6.06790e9i 0.727835 + 1.26065i
\(585\) 1.16065e8 + 2.62563e9i 0.0239694 + 0.542235i
\(586\) −1.93149e9 + 3.34545e9i −0.396508 + 0.686772i
\(587\) 4.55609e9 + 2.63046e9i 0.929734 + 0.536782i 0.886727 0.462293i \(-0.152973\pi\)
0.0430064 + 0.999075i \(0.486306\pi\)
\(588\) 4.39949e8 + 9.80950e8i 0.0892445 + 0.198988i
\(589\) −1.23135e9 2.13276e9i −0.248301 0.430070i
\(590\) 6.10225e9 + 3.52314e9i 1.22323 + 0.706232i
\(591\) −2.01876e9 1.16553e9i −0.402280 0.232257i
\(592\) 2.97811e8 + 1.71941e8i 0.0589950 + 0.0340608i
\(593\) 3.44384e9 + 1.98830e9i 0.678190 + 0.391553i 0.799173 0.601102i \(-0.205271\pi\)
−0.120983 + 0.992655i \(0.538605\pi\)
\(594\) −3.87902e9 6.71865e9i −0.759397 1.31531i
\(595\) 6.47423e9 9.99920e9i 1.26002 1.94606i
\(596\) 6.85615e8 + 3.95840e8i 0.132653 + 0.0765875i
\(597\) 2.57069e9 4.45256e9i 0.494469 0.856445i
\(598\) −1.94918e8 4.40942e9i −0.0372732 0.843194i
\(599\) −2.91712e9 5.05259e9i −0.554574 0.960551i −0.997937 0.0642084i \(-0.979548\pi\)
0.443362 0.896343i \(-0.353786\pi\)
\(600\) 5.72828e9 3.30723e9i 1.08267 0.625078i
\(601\) −3.35333e9 + 5.80814e9i −0.630110 + 1.09138i 0.357419 + 0.933944i \(0.383657\pi\)
−0.987529 + 0.157438i \(0.949677\pi\)
\(602\) −4.08108e9 2.08314e8i −0.762407 0.0389162i
\(603\) 1.92140e9i 0.356868i
\(604\) 6.40913e8i 0.118350i
\(605\) −1.22567e10 7.07644e9i −2.25025 1.29918i
\(606\) −9.38917e8 + 5.42084e8i −0.171385 + 0.0989492i
\(607\) −3.51112e9 −0.637214 −0.318607 0.947887i \(-0.603215\pi\)
−0.318607 + 0.947887i \(0.603215\pi\)
\(608\) 2.08515e9 3.61158e9i 0.376248 0.651680i
\(609\) 1.74632e8 3.42122e9i 0.0313303 0.613792i
\(610\) −6.05988e9 −1.08096
\(611\) 3.32306e8 + 7.51742e9i 0.0589378 + 1.33329i
\(612\) 3.97108e8 + 6.87811e8i 0.0700291 + 0.121294i
\(613\) 6.64398e9i 1.16497i 0.812840 + 0.582487i \(0.197920\pi\)
−0.812840 + 0.582487i \(0.802080\pi\)
\(614\) −2.55933e8 4.43289e8i −0.0446207 0.0772854i
\(615\) 6.10479e9 + 1.05738e10i 1.05830 + 1.83303i
\(616\) 9.15506e9 4.68043e9i 1.57808 0.806777i
\(617\) −5.64237e9 + 3.25762e9i −0.967082 + 0.558345i −0.898345 0.439290i \(-0.855230\pi\)
−0.0687365 + 0.997635i \(0.521897\pi\)
\(618\) 2.55517e9i 0.435472i
\(619\) 7.52657e9 4.34547e9i 1.27550 0.736409i 0.299481 0.954102i \(-0.403187\pi\)
0.976017 + 0.217693i \(0.0698533\pi\)
\(620\) −4.31843e8 + 7.47974e8i −0.0727704 + 0.126042i
\(621\) 3.20877e9 + 5.55775e9i 0.537673 + 0.931277i
\(622\) 7.25388e9 + 4.18803e9i 1.20866 + 0.697820i
\(623\) −1.36257e9 + 2.10443e9i −0.225762 + 0.348680i
\(624\) 1.48443e9 2.85535e9i 0.244576 0.470449i
\(625\) 1.19091e9 2.06271e9i 0.195118 0.337954i
\(626\) 3.79384e9i 0.618114i
\(627\) −1.16874e10 −1.89356
\(628\) 1.05118e9 0.169363
\(629\) 9.63214e8i 0.154328i
\(630\) −2.59117e9 + 1.32471e9i −0.412861 + 0.211071i
\(631\) 1.84667e9 1.06617e9i 0.292608 0.168937i −0.346510 0.938046i \(-0.612633\pi\)
0.639117 + 0.769109i \(0.279300\pi\)
\(632\) 5.26122e9 + 3.03757e9i 0.829043 + 0.478648i
\(633\) −1.79691e9 + 3.11234e9i −0.281588 + 0.487724i
\(634\) 5.88104e9 0.916519
\(635\) −1.77447e9 + 1.02449e9i −0.275017 + 0.158781i
\(636\) 6.29528e8 0.0970320
\(637\) −6.51271e9 3.77005e8i −0.998329 0.0577909i
\(638\) −6.96869e9 −1.06238
\(639\) 6.90877e8 3.98878e8i 0.104748 0.0604765i
\(640\) 4.33525e9 0.653708
\(641\) 1.94107e9 3.36204e9i 0.291098 0.504196i −0.682972 0.730445i \(-0.739313\pi\)
0.974070 + 0.226249i \(0.0726462\pi\)
\(642\) 4.18593e9 + 2.41675e9i 0.624338 + 0.360462i
\(643\) −5.74185e9 + 3.31506e9i −0.851752 + 0.491759i −0.861242 0.508196i \(-0.830313\pi\)
0.00948948 + 0.999955i \(0.496979\pi\)
\(644\) −1.61082e9 + 8.23514e8i −0.237654 + 0.121498i
\(645\) 7.65863e9i 1.12381i
\(646\) −1.25100e10 −1.82576
\(647\) 3.38871e9 0.491892 0.245946 0.969284i \(-0.420901\pi\)
0.245946 + 0.969284i \(0.420901\pi\)
\(648\) 3.98533e9i 0.575376i
\(649\) −6.03549e9 + 1.04538e10i −0.866674 + 1.50112i
\(650\) 3.77008e8 + 8.52866e9i 0.0538461 + 1.21810i
\(651\) −1.06790e9 + 1.64932e9i −0.151704 + 0.234300i
\(652\) −1.03749e9 5.98993e8i −0.146594 0.0846360i
\(653\) −5.00089e9 8.66179e9i −0.702831 1.21734i −0.967469 0.252991i \(-0.918586\pi\)
0.264637 0.964348i \(-0.414748\pi\)
\(654\) 1.36845e9 2.37022e9i 0.191296 0.331334i
\(655\) 9.80720e9 5.66219e9i 1.36364 0.787299i
\(656\) 7.99307e9i 1.10548i
\(657\) 2.94209e9 1.69861e9i 0.404741 0.233677i
\(658\) −7.41875e9 + 3.79276e9i −1.01517 + 0.518998i
\(659\) 1.72641e9 + 2.99022e9i 0.234987 + 0.407010i 0.959269 0.282494i \(-0.0911618\pi\)
−0.724282 + 0.689504i \(0.757829\pi\)
\(660\) 2.04942e9 + 3.54970e9i 0.277477 + 0.480604i
\(661\) 2.23000e9i 0.300330i −0.988661 0.150165i \(-0.952019\pi\)
0.988661 0.150165i \(-0.0479805\pi\)
\(662\) −2.96360e9 5.13311e9i −0.397024 0.687666i
\(663\) 9.00524e9 3.98075e8i 1.20005 0.0530479i
\(664\) 8.52251e9 1.12974
\(665\) −8.65001e8 + 1.69462e10i −0.114062 + 2.23459i
\(666\) 1.17657e8 2.03788e8i 0.0154333 0.0267312i
\(667\) 5.76459e9 0.752191
\(668\) −2.34747e9 + 1.35532e9i −0.304708 + 0.175923i
\(669\) −9.47460e9 5.47016e9i −1.22340 0.706332i
\(670\) 1.06141e10i 1.36339i
\(671\) 1.03812e10i 1.32653i
\(672\) −3.32293e9 1.69615e8i −0.422405 0.0215612i
\(673\) 4.32462e9 7.49046e9i 0.546884 0.947231i −0.451601 0.892220i \(-0.649147\pi\)
0.998486 0.0550115i \(-0.0175196\pi\)
\(674\) −1.08181e10 + 6.24581e9i −1.36094 + 0.785741i
\(675\) −6.20638e9 1.07498e10i −0.776739 1.34535i
\(676\) −1.24654e9 1.77613e9i −0.155200 0.221137i
\(677\) 2.65858e9 4.60480e9i 0.329298 0.570361i −0.653075 0.757294i \(-0.726521\pi\)
0.982373 + 0.186932i \(0.0598545\pi\)
\(678\) −2.80159e9 1.61750e9i −0.345224 0.199315i
\(679\) −1.52342e9 + 2.35287e9i −0.186757 + 0.288439i
\(680\) 1.03135e10 + 1.78635e10i 1.25784 + 2.17863i
\(681\) 4.00490e9 + 2.31223e9i 0.485934 + 0.280554i
\(682\) 3.46152e9 + 1.99851e9i 0.417851 + 0.241247i
\(683\) 2.29805e7 + 1.32678e7i 0.00275986 + 0.00159341i 0.501379 0.865228i \(-0.332826\pi\)
−0.498619 + 0.866821i \(0.666159\pi\)
\(684\) −9.79753e8 5.65661e8i −0.117063 0.0675864i
\(685\) 9.59769e7 + 1.66237e8i 0.0114091 + 0.0197611i
\(686\) −2.61617e9 6.73309e9i −0.309408 0.796306i
\(687\) −6.74386e9 3.89357e9i −0.793524 0.458141i
\(688\) 2.50688e9 4.34204e9i 0.293477 0.508317i
\(689\) −1.76202e9 + 3.38930e9i −0.205231 + 0.394769i
\(690\) 4.57979e9 + 7.93243e9i 0.530730 + 0.919252i
\(691\) 9.78829e9 5.65127e9i 1.12858 0.651588i 0.185005 0.982737i \(-0.440770\pi\)
0.943578 + 0.331149i \(0.107436\pi\)
\(692\) 8.38826e8 1.45289e9i 0.0962278 0.166672i
\(693\) −2.26936e9 4.43893e9i −0.259022 0.506654i
\(694\) 1.22193e10i 1.38768i
\(695\) 6.55624e9i 0.740813i
\(696\) 5.13714e9 + 2.96593e9i 0.577549 + 0.333448i
\(697\) −1.93890e10 + 1.11943e10i −2.16891 + 1.25222i
\(698\) 1.17125e10 1.30363
\(699\) 1.59042e8 2.75469e8i 0.0176134 0.0305072i
\(700\) 3.11563e9 1.59283e9i 0.343322 0.175520i
\(701\) −2.61091e9 −0.286272 −0.143136 0.989703i \(-0.545719\pi\)
−0.143136 + 0.989703i \(0.545719\pi\)
\(702\) −7.56229e9 3.93147e9i −0.825038 0.428918i
\(703\) −6.86025e8 1.18823e9i −0.0744726 0.128990i
\(704\) 1.67007e10i 1.80397i
\(705\) −7.80787e9 1.35236e10i −0.839210 1.45355i
\(706\) 5.52101e9 + 9.56266e9i 0.590475 + 1.02273i
\(707\) −2.40094e9 + 1.22745e9i −0.255513 + 0.130628i
\(708\) 1.89269e9 1.09275e9i 0.200430 0.115719i
\(709\) 2.89089e9i 0.304628i 0.988332 + 0.152314i \(0.0486725\pi\)
−0.988332 + 0.152314i \(0.951328\pi\)
\(710\) 3.81650e9 2.20345e9i 0.400185 0.231047i
\(711\) 1.47280e9 2.55096e9i 0.153674 0.266171i
\(712\) −2.17058e9 3.75955e9i −0.225369 0.390351i
\(713\) −2.86341e9 1.65319e9i −0.295850 0.170809i
\(714\) 4.54342e9 + 8.88705e9i 0.467131 + 0.913722i
\(715\) −2.48473e10 + 1.09837e9i −2.54220 + 0.112377i
\(716\) 7.24210e8 1.25437e9i 0.0737342 0.127711i
\(717\) 1.22835e10i 1.24453i
\(718\) −1.49875e10 −1.51111
\(719\) 1.10411e10 1.10780 0.553900 0.832584i \(-0.313139\pi\)
0.553900 + 0.832584i \(0.313139\pi\)
\(720\) 3.57059e9i 0.356513i
\(721\) −3.23969e8 + 6.34687e9i −0.0321906 + 0.630647i
\(722\) 7.95041e9 4.59017e9i 0.786158 0.453888i
\(723\) 9.62393e9 + 5.55638e9i 0.947040 + 0.546774i
\(724\) −6.93566e8 + 1.20129e9i −0.0679208 + 0.117642i
\(725\) −1.11498e10 −1.08664
\(726\) 1.02698e10 5.92928e9i 0.996058 0.575075i
\(727\) −1.53295e10 −1.47965 −0.739823 0.672802i \(-0.765091\pi\)
−0.739823 + 0.672802i \(0.765091\pi\)
\(728\) 5.71472e9 9.74403e9i 0.548953 0.936006i
\(729\) 1.11231e10 1.06336
\(730\) 1.62525e10 9.38338e9i 1.54629 0.892749i
\(731\) 1.40435e10 1.32973
\(732\) −9.39775e8 + 1.62774e9i −0.0885595 + 0.153390i
\(733\) 3.16974e9 + 1.83005e9i 0.297276 + 0.171632i 0.641218 0.767358i \(-0.278429\pi\)
−0.343943 + 0.938991i \(0.611763\pi\)
\(734\) 4.97133e9 2.87020e9i 0.464020 0.267902i
\(735\) 1.23527e10 5.54007e9i 1.14751 0.514648i
\(736\) 5.59897e9i 0.517650i
\(737\) −1.81830e10 −1.67313
\(738\) 5.46954e9 0.500903
\(739\) 1.07137e10i 0.976530i −0.872695 0.488265i \(-0.837630\pi\)
0.872695 0.488265i \(-0.162370\pi\)
\(740\) −2.40594e8 + 4.16721e8i −0.0218260 + 0.0378037i
\(741\) −1.08254e10 + 6.90483e9i −0.977422 + 0.623433i
\(742\) −4.22428e9 2.15623e8i −0.379611 0.0193768i
\(743\) −1.89082e10 1.09167e10i −1.69118 0.976402i −0.953570 0.301172i \(-0.902622\pi\)
−0.737608 0.675229i \(-0.764045\pi\)
\(744\) −1.70116e9 2.94650e9i −0.151440 0.262302i
\(745\) 4.98463e9 8.63363e9i 0.441658 0.764974i
\(746\) 5.98381e9 3.45475e9i 0.527706 0.304671i
\(747\) 4.13223e9i 0.362712i
\(748\) −6.50903e9 + 3.75799e9i −0.568670 + 0.328322i
\(749\) 1.00911e10 + 6.53377e9i 0.877514 + 0.568169i
\(750\) −2.65165e9 4.59279e9i −0.229510 0.397523i
\(751\) 3.19921e9 + 5.54120e9i 0.275615 + 0.477380i 0.970290 0.241944i \(-0.0777850\pi\)
−0.694675 + 0.719324i \(0.744452\pi\)
\(752\) 1.02229e10i 0.876623i
\(753\) 2.38980e9 + 4.13925e9i 0.203976 + 0.353297i
\(754\) −6.45477e9 + 4.11707e9i −0.548379 + 0.349775i
\(755\) −8.07073e9 −0.682493
\(756\) −1.78091e8 + 3.48898e9i −0.0149905 + 0.293678i
\(757\) 1.08710e10 1.88291e10i 0.910824 1.57759i 0.0979207 0.995194i \(-0.468781\pi\)
0.812903 0.582399i \(-0.197886\pi\)
\(758\) −3.05740e9 −0.254983
\(759\) −1.35890e10 + 7.84564e9i −1.12809 + 0.651302i
\(760\) −2.54456e10 1.46910e10i −2.10264 1.21396i
\(761\) 2.20920e10i 1.81714i −0.417732 0.908570i \(-0.637175\pi\)
0.417732 0.908570i \(-0.362825\pi\)
\(762\) 1.71682e9i 0.140567i
\(763\) 3.69964e9 5.71395e9i 0.301525 0.465694i
\(764\) 3.24935e9 5.62805e9i 0.263615 0.456595i
\(765\) 8.66129e9 5.00060e9i 0.699467 0.403838i
\(766\) −5.39927e7 9.35182e7i −0.00434045 0.00751788i
\(767\) 5.85651e8 + 1.32486e10i 0.0468657 + 1.06019i
\(768\) 3.77985e9 6.54689e9i 0.301100 0.521520i
\(769\) 1.22152e10 + 7.05244e9i 0.968630 + 0.559239i 0.898818 0.438322i \(-0.144427\pi\)
0.0698116 + 0.997560i \(0.477760\pi\)
\(770\) −1.25362e10 2.45212e10i −0.989577 1.93564i
\(771\) −1.24672e9 2.15938e9i −0.0979666 0.169683i
\(772\) 6.57655e8 + 3.79697e8i 0.0514444 + 0.0297014i
\(773\) 1.71980e10 + 9.92928e9i 1.33922 + 0.773196i 0.986691 0.162607i \(-0.0519901\pi\)
0.352524 + 0.935803i \(0.385323\pi\)
\(774\) −2.97120e9 1.71542e9i −0.230323 0.132977i
\(775\) 5.53839e9 + 3.19759e9i 0.427393 + 0.246756i
\(776\) −2.42682e9 4.20337e9i −0.186432 0.322910i
\(777\) −5.94960e8 + 9.18892e8i −0.0455003 + 0.0702734i
\(778\) −1.46088e10 8.43438e9i −1.11221 0.642133i
\(779\) 1.59457e10 2.76187e10i 1.20854 2.09326i
\(780\) 3.99542e9 + 2.07713e9i 0.301461 + 0.156723i
\(781\) 3.77474e9 + 6.53804e9i 0.283536 + 0.491099i
\(782\) −1.45456e10 + 8.39789e9i −1.08770 + 0.627981i
\(783\) 5.56590e9 9.64041e9i 0.414351 0.717678i
\(784\) 8.81673e9 + 9.02431e8i 0.653434 + 0.0668818i
\(785\) 1.32370e10i 0.976668i
\(786\) 9.48860e9i 0.696985i
\(787\) −4.37572e9 2.52632e9i −0.319991 0.184747i 0.331397 0.943491i \(-0.392480\pi\)
−0.651389 + 0.758744i \(0.725813\pi\)
\(788\) 1.84927e9 1.06768e9i 0.134636 0.0777319i
\(789\) −9.40477e9 −0.681677
\(790\) 8.13593e9 1.40918e10i 0.587101 1.01689i
\(791\) −6.75387e9 4.37297e9i −0.485216 0.314165i
\(792\) 8.63263e9 0.617454
\(793\) −6.13315e9 9.61560e9i −0.436745 0.684731i
\(794\) 2.59884e9 + 4.50132e9i 0.184250 + 0.319131i
\(795\) 7.92736e9i 0.559556i
\(796\) 2.35486e9 + 4.07874e9i 0.165489 + 0.286636i
\(797\) −4.20985e9 7.29167e9i −0.294552 0.510179i 0.680329 0.732907i \(-0.261837\pi\)
−0.974881 + 0.222728i \(0.928504\pi\)
\(798\) −1.19344e10 7.72723e9i −0.831362 0.538287i
\(799\) 2.47981e10 1.43172e10i 1.71990 0.992988i
\(800\) 1.08295e10i 0.747812i
\(801\) −1.82286e9 + 1.05243e9i −0.125325 + 0.0723566i
\(802\) −7.90997e9 + 1.37005e10i −0.541458 + 0.937832i
\(803\) 1.60747e10 + 2.78421e10i 1.09556 + 1.89757i
\(804\) 2.85104e9 + 1.64605e9i 0.193467 + 0.111698i
\(805\) 1.03701e10 + 2.02843e10i 0.700646 + 1.37048i
\(806\) 4.38695e9 1.93925e8i 0.295114 0.0130455i
\(807\) 1.13388e9 1.96395e9i 0.0759471 0.131544i
\(808\) 4.66923e9i 0.311391i
\(809\) 1.35171e10 0.897561 0.448780 0.893642i \(-0.351859\pi\)
0.448780 + 0.893642i \(0.351859\pi\)
\(810\) 1.06744e10 0.705745
\(811\) 8.79108e9i 0.578721i 0.957220 + 0.289361i \(0.0934426\pi\)
−0.957220 + 0.289361i \(0.906557\pi\)
\(812\) 2.63413e9 + 1.70553e9i 0.172660 + 0.111793i
\(813\) −2.74031e9 + 1.58212e9i −0.178848 + 0.103258i
\(814\) 1.92853e9 + 1.11344e9i 0.125326 + 0.0723568i
\(815\) −7.54285e9 + 1.30646e10i −0.488072 + 0.845365i
\(816\) −1.22462e10 −0.789017
\(817\) −1.73242e10 + 1.00021e10i −1.11142 + 0.641676i
\(818\) −1.07834e10 −0.688840
\(819\) −4.72449e9 2.77084e9i −0.300512 0.176246i
\(820\) −1.11845e10 −0.708384
\(821\) 2.08038e10 1.20111e10i 1.31202 0.757497i 0.329592 0.944123i \(-0.393089\pi\)
0.982431 + 0.186627i \(0.0597555\pi\)
\(822\) −1.60837e8 −0.0101003
\(823\) −9.85789e9 + 1.70744e10i −0.616431 + 1.06769i 0.373701 + 0.927549i \(0.378089\pi\)
−0.990132 + 0.140140i \(0.955245\pi\)
\(824\) −9.53014e9 5.50223e9i −0.593409 0.342605i
\(825\) 2.62838e10 1.51750e10i 1.62967 0.940890i
\(826\) −1.30747e10 + 6.68430e9i −0.807237 + 0.412692i
\(827\) 2.21357e10i 1.36090i 0.732797 + 0.680448i \(0.238215\pi\)
−0.732797 + 0.680448i \(0.761785\pi\)
\(828\) −1.51889e9 −0.0929869
\(829\) 2.93886e9 0.179159 0.0895793 0.995980i \(-0.471448\pi\)
0.0895793 + 0.995980i \(0.471448\pi\)
\(830\) 2.28270e10i 1.38572i
\(831\) −3.51093e9 + 6.08112e9i −0.212236 + 0.367604i
\(832\) 9.86668e9 + 1.54691e10i 0.593936 + 0.931177i
\(833\) 1.01588e10 + 2.26509e10i 0.608952 + 1.35777i
\(834\) −4.75744e9 2.74671e9i −0.283983 0.163958i
\(835\) 1.70669e10 + 2.95607e10i 1.01450 + 1.75716i
\(836\) 5.35307e9 9.27179e9i 0.316870 0.548835i
\(837\) −5.52944e9 + 3.19242e9i −0.325943 + 0.188183i
\(838\) 1.78519e10i 1.04793i
\(839\) 6.37606e9 3.68122e9i 0.372723 0.215191i −0.301925 0.953332i \(-0.597629\pi\)
0.674647 + 0.738140i \(0.264296\pi\)
\(840\) −1.19504e9 + 2.34119e10i −0.0695670 + 1.36289i
\(841\) 3.62534e9 + 6.27928e9i 0.210166 + 0.364019i
\(842\) −2.65527e9 4.59907e9i −0.153291 0.265508i
\(843\) 3.18294e9i 0.182992i
\(844\) −1.64605e9 2.85104e9i −0.0942419 0.163232i
\(845\) −2.23660e10 + 1.56971e10i −1.27523 + 0.894993i
\(846\) −6.99540e9 −0.397207
\(847\) 2.62613e10 1.34258e10i 1.48499 0.759188i
\(848\) 2.59484e9 4.49440e9i 0.146125 0.253097i
\(849\) −2.24647e10 −1.25986
\(850\) 2.81339e10 1.62431e10i 1.57132 0.907201i
\(851\) −1.59530e9 9.21048e8i −0.0887338 0.0512305i
\(852\) 1.36686e9i 0.0757156i
\(853\) 1.73103e10i 0.954955i −0.878644 0.477477i \(-0.841551\pi\)
0.878644 0.477477i \(-0.158449\pi\)
\(854\) 6.86363e9 1.06006e10i 0.377096 0.582409i
\(855\) −7.12311e9 + 1.23376e10i −0.389752 + 0.675070i
\(856\) −1.80277e10 + 1.04083e10i −0.982387 + 0.567182i
\(857\) −1.70421e10 2.95178e10i −0.924890 1.60196i −0.791737 0.610862i \(-0.790823\pi\)
−0.133153 0.991095i \(-0.542510\pi\)
\(858\) 9.61267e9 1.84903e10i 0.519563 0.999396i
\(859\) 3.15343e9 5.46189e9i 0.169749 0.294013i −0.768583 0.639750i \(-0.779038\pi\)
0.938331 + 0.345737i \(0.112371\pi\)
\(860\) 6.07572e9 + 3.50782e9i 0.325727 + 0.188058i
\(861\) −2.54114e10 1.29709e9i −1.35680 0.0692565i
\(862\) −3.13464e9 5.42936e9i −0.166691 0.288718i
\(863\) 3.38609e9 + 1.95496e9i 0.179333 + 0.103538i 0.586979 0.809602i \(-0.300317\pi\)
−0.407646 + 0.913140i \(0.633650\pi\)
\(864\) −9.36344e9 5.40599e9i −0.493898 0.285152i
\(865\) −1.82956e10 1.05630e10i −0.961147 0.554918i
\(866\) −2.64078e10 1.52466e10i −1.38172 0.797737i
\(867\) −9.40559e9 1.62910e10i −0.490139 0.848945i
\(868\) −8.19318e8 1.60261e9i −0.0425239 0.0831780i
\(869\) 2.41407e10 + 1.39377e10i 1.24790 + 0.720478i
\(870\) 7.94405e9 1.37595e10i 0.409001 0.708411i
\(871\) −1.68421e10 + 1.07424e10i −0.863637 + 0.550857i
\(872\) 5.89354e9 + 1.02079e10i 0.301001 + 0.521350i
\(873\) −2.03805e9 + 1.17667e9i −0.103673 + 0.0598555i
\(874\) 1.19624e10 2.07195e10i 0.606077 1.04976i
\(875\) −6.00420e9 1.17444e10i −0.302989 0.592655i
\(876\) 5.82075e9i 0.292560i
\(877\) 4.23690e9i 0.212105i 0.994361 + 0.106052i \(0.0338211\pi\)
−0.994361 + 0.106052i \(0.966179\pi\)
\(878\) −2.96950e9 1.71444e9i −0.148065 0.0854853i
\(879\) 1.30664e10 7.54392e9i 0.648928 0.374659i
\(880\) 3.37899e10 1.67147
\(881\) −1.83214e10 + 3.17336e10i −0.902699 + 1.56352i −0.0787236 + 0.996896i \(0.525084\pi\)
−0.823976 + 0.566625i \(0.808249\pi\)
\(882\) 6.17521e8 6.03316e9i 0.0303048 0.296077i
\(883\) −6.04803e9 −0.295632 −0.147816 0.989015i \(-0.547224\pi\)
−0.147816 + 0.989015i \(0.547224\pi\)
\(884\) −3.80880e9 + 7.32635e9i −0.185441 + 0.356701i
\(885\) −1.37605e10 2.38338e10i −0.667316 1.15583i
\(886\) 1.21563e10i 0.587196i
\(887\) 3.75352e9 + 6.50128e9i 0.180595 + 0.312800i 0.942083 0.335379i \(-0.108864\pi\)
−0.761488 + 0.648179i \(0.775531\pi\)
\(888\) −9.47773e8 1.64159e9i −0.0454212 0.0786719i
\(889\) 2.17675e8 4.26446e9i 0.0103909 0.203567i
\(890\) −1.00697e10 + 5.81375e9i −0.478797 + 0.276434i
\(891\) 1.82864e10i 0.866076i
\(892\) 8.67915e9 5.01091e9i 0.409450 0.236396i
\(893\) −2.03941e10 + 3.53237e10i −0.958352 + 1.65991i
\(894\) 4.17658e9 + 7.23405e9i 0.195497 + 0.338610i
\(895\) −1.57957e10 9.11964e9i −0.736475 0.425204i
\(896\) −4.91025e9 + 7.58369e9i −0.228048 + 0.352211i
\(897\) −7.95172e9 + 1.52954e10i −0.367864 + 0.707598i
\(898\) 1.07346e10 1.85929e10i 0.494676 0.856803i
\(899\) 5.73522e9i 0.263264i
\(900\) 2.93783e9 0.134332
\(901\) 1.45363e10 0.662089
\(902\) 5.17604e10i 2.34842i
\(903\) 1.33973e10 + 8.67443e9i 0.605495 + 0.392043i
\(904\) 1.20657e10 6.96615e9i 0.543205 0.313620i
\(905\) 1.51273e10 + 8.73376e9i 0.678409 + 0.391680i
\(906\) 3.38120e9 5.85641e9i 0.151050 0.261627i
\(907\) −1.67691e10 −0.746249 −0.373124 0.927781i \(-0.621714\pi\)
−0.373124 + 0.927781i \(0.621714\pi\)
\(908\) −3.66867e9 + 2.11811e9i −0.162633 + 0.0938960i
\(909\) −2.26393e9 −0.0999744
\(910\) −2.60987e10 1.53065e10i −1.14809 0.673335i
\(911\) 4.60672e9 0.201873 0.100936 0.994893i \(-0.467816\pi\)
0.100936 + 0.994893i \(0.467816\pi\)
\(912\) 1.51071e10 8.72207e9i 0.659475 0.380748i
\(913\) 3.91049e10 1.70053
\(914\) 7.11200e8 1.23183e9i 0.0308092 0.0533630i
\(915\) 2.04974e10 + 1.18342e10i 0.884554 + 0.510697i
\(916\) 6.17767e9 3.56668e9i 0.265577 0.153331i
\(917\) −1.20305e9 + 2.35690e10i −0.0515220 + 1.00937i
\(918\) 3.24337e10i 1.38372i
\(919\) 2.50071e10 1.06282 0.531408 0.847116i \(-0.321663\pi\)
0.531408 + 0.847116i \(0.321663\pi\)
\(920\) −3.94479e10 −1.67019
\(921\) 1.99921e9i 0.0843239i
\(922\) −3.03917e9 + 5.26399e9i −0.127702 + 0.221186i
\(923\) 7.35900e9 + 3.82578e9i 0.308044 + 0.160145i
\(924\) −8.53076e9 4.35443e8i −0.355743 0.0181585i
\(925\) 3.08562e9 + 1.78148e9i 0.128188 + 0.0740091i
\(926\) 7.70889e9 + 1.33522e10i 0.319046 + 0.552604i
\(927\) −2.66781e9 + 4.62079e9i −0.109996 + 0.190519i
\(928\) −8.41076e9 + 4.85595e9i −0.345476 + 0.199460i
\(929\) 9.47547e9i 0.387744i −0.981027 0.193872i \(-0.937895\pi\)
0.981027 0.193872i \(-0.0621047\pi\)
\(930\) −7.89201e9 + 4.55645e9i −0.321734 + 0.185753i
\(931\) −2.86645e10 2.07071e10i −1.16418 0.840997i
\(932\) 1.45690e8 + 2.52342e8i 0.00589485 + 0.0102102i
\(933\) −1.63573e10 2.83318e10i −0.659367 1.14206i
\(934\) 3.44116e10i 1.38195i
\(935\) 4.73226e10 + 8.19652e10i 1.89334 + 3.27936i
\(936\) 7.99599e9 5.10011e9i 0.318718 0.203289i
\(937\) −3.22026e10 −1.27880 −0.639399 0.768875i \(-0.720817\pi\)
−0.639399 + 0.768875i \(0.720817\pi\)
\(938\) −1.85673e10 1.20219e10i −0.734581 0.475623i
\(939\) −7.40887e9 + 1.28325e10i −0.292027 + 0.505805i
\(940\) 1.43047e10 0.561735
\(941\) 1.99367e10 1.15105e10i 0.779991 0.450328i −0.0564362 0.998406i \(-0.517974\pi\)
0.836427 + 0.548078i \(0.184640\pi\)
\(942\) 9.60526e9 + 5.54560e9i 0.374396 + 0.216158i
\(943\) 4.28169e10i 1.66274i
\(944\) 1.80167e10i 0.697065i
\(945\) 4.39351e10 + 2.24262e9i 1.69356 + 0.0864458i
\(946\) 1.62337e10 2.81176e10i 0.623446 1.07984i
\(947\) 2.31814e9 1.33838e9i 0.0886980 0.0512098i −0.454995 0.890494i \(-0.650359\pi\)
0.543693 + 0.839284i \(0.317026\pi\)
\(948\) −2.52346e9 4.37077e9i −0.0961984 0.166621i
\(949\) 3.13382e10 + 1.62920e10i 1.19026 + 0.618790i
\(950\) −2.31375e10 + 4.00754e10i −0.875557 + 1.51651i
\(951\) −1.98924e10 1.14849e10i −0.749991 0.433007i
\(952\) −4.29301e10 2.19132e9i −1.61262 0.0823145i
\(953\) 3.15171e9 + 5.45892e9i 0.117956 + 0.204306i 0.918958 0.394356i \(-0.129032\pi\)
−0.801001 + 0.598663i \(0.795699\pi\)
\(954\) −3.07545e9 1.77561e9i −0.114681 0.0662108i
\(955\) −7.08714e10 4.09176e10i −2.63305 1.52019i
\(956\) −9.74475e9 5.62614e9i −0.360718 0.208261i
\(957\) 2.35714e10 + 1.36090e10i 0.869348 + 0.501918i
\(958\) 5.85006e9 + 1.01326e10i 0.214971 + 0.372341i
\(959\) −3.99507e8 2.03924e7i −0.0146271 0.000746625i
\(960\) −3.29751e10 1.90382e10i −1.20292 0.694505i
\(961\) −1.21115e10 + 2.09778e10i −0.440218 + 0.762479i
\(962\) 2.44411e9 1.08042e8i 0.0885133 0.00391272i
\(963\) 5.04658e9 + 8.74093e9i 0.182098 + 0.315403i
\(964\) −8.81594e9 + 5.08989e9i −0.316956 + 0.182995i
\(965\) 4.78136e9 8.28155e9i 0.171280 0.296665i
\(966\) −1.90635e10 9.73075e8i −0.680429 0.0347317i
\(967\) 3.20971e10i 1.14149i 0.821126 + 0.570747i \(0.193346\pi\)
−0.821126 + 0.570747i \(0.806654\pi\)
\(968\) 5.10718e10i 1.80974i
\(969\) 4.23148e10 + 2.44305e10i 1.49403 + 0.862579i
\(970\) −1.12585e10 + 6.50008e9i −0.396075 + 0.228674i
\(971\) −2.64500e10 −0.927169 −0.463584 0.886053i \(-0.653437\pi\)
−0.463584 + 0.886053i \(0.653437\pi\)
\(972\) −2.55417e9 + 4.42396e9i −0.0892110 + 0.154518i
\(973\) −1.14689e10 7.42583e9i −0.399142 0.258434i
\(974\) −6.35959e9 −0.220533
\(975\) 1.53801e10 2.95842e10i 0.531428 1.02222i
\(976\) 7.74729e9 + 1.34187e10i 0.266732 + 0.461994i
\(977\) 2.68843e9i 0.0922291i 0.998936 + 0.0461145i \(0.0146839\pi\)
−0.998936 + 0.0461145i \(0.985316\pi\)
\(978\) −6.32009e9 1.09467e10i −0.216041 0.374195i
\(979\) −9.95953e9 1.72504e10i −0.339234 0.587571i
\(980\) −1.26275e9 + 1.23371e10i −0.0428575 + 0.418717i
\(981\) 4.94941e9 2.85754e9i 0.167383 0.0966388i
\(982\) 1.55472e10i 0.523916i
\(983\) −2.01599e10 + 1.16393e10i −0.676941 + 0.390832i −0.798701 0.601728i \(-0.794479\pi\)
0.121761 + 0.992559i \(0.461146\pi\)
\(984\) 2.20296e10 3.81565e10i 0.737097 1.27669i
\(985\) −1.34448e10 2.32871e10i −0.448257 0.776405i
\(986\) 2.52306e10 + 1.45669e10i 0.838220 + 0.483947i
\(987\) 3.25005e10 + 1.65895e9i 1.07592 + 0.0549191i
\(988\) −5.19433e8 1.17506e10i −0.0171348 0.387624i
\(989\) −1.34287e10 + 2.32593e10i −0.441416 + 0.764555i
\(990\) 2.31219e10i 0.757357i
\(991\) 3.85889e10 1.25952 0.629760 0.776790i \(-0.283153\pi\)
0.629760 + 0.776790i \(0.283153\pi\)
\(992\) 5.57044e9 0.181175
\(993\) 2.31501e10i 0.750293i
\(994\) −4.68171e8 + 9.17194e9i −0.0151200 + 0.296216i
\(995\) 5.13617e10 2.96537e10i 1.65295 0.954329i
\(996\) −6.13154e9 3.54004e9i −0.196635 0.113527i
\(997\) −8.67125e9 + 1.50190e10i −0.277108 + 0.479965i −0.970665 0.240437i \(-0.922709\pi\)
0.693557 + 0.720402i \(0.256043\pi\)
\(998\) 3.51719e10 1.12005
\(999\) −3.08063e9 + 1.77860e9i −0.0977598 + 0.0564416i
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.u.a.30.20 yes 126
7.4 even 3 91.8.k.a.4.20 126
13.10 even 6 91.8.k.a.23.44 yes 126
91.88 even 6 inner 91.8.u.a.88.20 yes 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.8.k.a.4.20 126 7.4 even 3
91.8.k.a.23.44 yes 126 13.10 even 6
91.8.u.a.30.20 yes 126 1.1 even 1 trivial
91.8.u.a.88.20 yes 126 91.88 even 6 inner