Properties

Label 48.8.k.a.11.11
Level $48$
Weight $8$
Character 48.11
Analytic conductor $14.994$
Analytic rank $0$
Dimension $108$
CM no
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [48,8,Mod(11,48)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(48, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 1, 2]))
 
N = Newforms(chi, 8, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("48.11");
 
S:= CuspForms(chi, 8);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 48 = 2^{4} \cdot 3 \)
Weight: \( k \) \(=\) \( 8 \)
Character orbit: \([\chi]\) \(=\) 48.k (of order \(4\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(14.9944812232\)
Analytic rank: \(0\)
Dimension: \(108\)
Relative dimension: \(54\) over \(\Q(i)\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label 11.11
Character \(\chi\) \(=\) 48.11
Dual form 48.8.k.a.35.11

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-9.27322 - 6.48131i) q^{2} +(27.2746 - 37.9881i) q^{3} +(43.9852 + 120.205i) q^{4} +(-379.549 + 379.549i) q^{5} +(-499.136 + 175.497i) q^{6} +864.981 q^{7} +(371.203 - 1399.77i) q^{8} +(-699.194 - 2072.22i) q^{9} +O(q^{10})\) \(q+(-9.27322 - 6.48131i) q^{2} +(27.2746 - 37.9881i) q^{3} +(43.9852 + 120.205i) q^{4} +(-379.549 + 379.549i) q^{5} +(-499.136 + 175.497i) q^{6} +864.981 q^{7} +(371.203 - 1399.77i) q^{8} +(-699.194 - 2072.22i) q^{9} +(5979.61 - 1059.67i) q^{10} +(-285.623 - 285.623i) q^{11} +(5766.05 + 1607.63i) q^{12} +(4742.77 - 4742.77i) q^{13} +(-8021.16 - 5606.21i) q^{14} +(4066.31 + 24770.4i) q^{15} +(-12514.6 + 10574.5i) q^{16} -23420.2i q^{17} +(-6946.93 + 23747.8i) q^{18} +(14837.1 + 14837.1i) q^{19} +(-62318.3 - 28929.2i) q^{20} +(23592.0 - 32859.0i) q^{21} +(797.433 + 4499.86i) q^{22} -59037.2i q^{23} +(-43050.3 - 52279.5i) q^{24} -209990. i q^{25} +(-74720.2 + 13241.4i) q^{26} +(-97790.0 - 29957.9i) q^{27} +(38046.4 + 103975. i) q^{28} +(53858.0 + 53858.0i) q^{29} +(122837. - 256056. i) q^{30} -79079.0i q^{31} +(184587. - 16948.6i) q^{32} +(-18640.5 + 3060.03i) q^{33} +(-151794. + 217181. i) q^{34} +(-328303. + 328303. i) q^{35} +(218338. - 175194. i) q^{36} +(-24070.3 - 24070.3i) q^{37} +(-41423.7 - 233751. i) q^{38} +(-50811.9 - 309526. i) q^{39} +(390392. + 672171. i) q^{40} -703269. q^{41} +(-431743. + 151802. i) q^{42} +(569708. - 569708. i) q^{43} +(21770.2 - 46896.6i) q^{44} +(1.05189e6 + 521131. i) q^{45} +(-382638. + 547465. i) q^{46} +1.06175e6 q^{47} +(60374.8 + 763821. i) q^{48} -75350.6 q^{49} +(-1.36101e6 + 1.94728e6i) q^{50} +(-889690. - 638777. i) q^{51} +(778718. + 361495. i) q^{52} +(1.16855e6 - 1.16855e6i) q^{53} +(712661. + 911613. i) q^{54} +216816. q^{55} +(321084. - 1.21078e6i) q^{56} +(968306. - 158957. i) q^{57} +(-150367. - 848508. i) q^{58} +(-138554. - 138554. i) q^{59} +(-2.79867e6 + 1.57832e6i) q^{60} +(406144. - 406144. i) q^{61} +(-512535. + 733317. i) q^{62} +(-604790. - 1.79243e6i) q^{63} +(-1.82157e6 - 1.03920e6i) q^{64} +3.60023e6i q^{65} +(192691. + 92438.8i) q^{66} +(840959. + 840959. i) q^{67} +(2.81523e6 - 1.03014e6i) q^{68} +(-2.24271e6 - 1.61021e6i) q^{69} +(5.17225e6 - 916591. i) q^{70} +1.70865e6i q^{71} +(-3.16018e6 + 209497. i) q^{72} -496669. i q^{73} +(67201.9 + 379216. i) q^{74} +(-7.97711e6 - 5.72738e6i) q^{75} +(-1.13088e6 + 2.43610e6i) q^{76} +(-247059. - 247059. i) q^{77} +(-1.53495e6 + 3.19963e6i) q^{78} -305230. i q^{79} +(736363. - 8.76344e6i) q^{80} +(-3.80522e6 + 2.89777e6i) q^{81} +(6.52157e6 + 4.55811e6i) q^{82} +(3.74938e6 - 3.74938e6i) q^{83} +(4.98752e6 + 1.39057e6i) q^{84} +(8.88912e6 + 8.88912e6i) q^{85} +(-8.97549e6 + 1.59057e6i) q^{86} +(3.51492e6 - 577010. i) q^{87} +(-505831. + 293783. i) q^{88} +7.69964e6 q^{89} +(-6.37677e6 - 1.16502e7i) q^{90} +(4.10241e6 - 4.10241e6i) q^{91} +(7.09658e6 - 2.59676e6i) q^{92} +(-3.00406e6 - 2.15685e6i) q^{93} +(-9.84587e6 - 6.88155e6i) q^{94} -1.12628e7 q^{95} +(4.39070e6 - 7.47439e6i) q^{96} -4.94267e6 q^{97} +(698743. + 488371. i) q^{98} +(-392168. + 791580. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 108 q - 2 q^{3} - 4 q^{4} + 172 q^{6} - 8 q^{7} - 6504 q^{10} + 12016 q^{12} - 4 q^{13} - 55280 q^{16} + 21172 q^{18} - 60588 q^{19} - 4376 q^{21} - 212744 q^{22} - 317304 q^{24} + 238042 q^{27} + 219736 q^{28} - 503852 q^{30} - 4 q^{33} - 364856 q^{34} + 867620 q^{36} - 4 q^{37} - 283948 q^{39} + 390392 q^{40} - 3022344 q^{42} + 752844 q^{43} - 156252 q^{45} - 1166824 q^{46} + 358320 q^{48} + 9882508 q^{49} + 1121592 q^{51} - 4458688 q^{52} + 203816 q^{54} + 4191000 q^{55} + 4975544 q^{58} - 4390240 q^{60} - 2279892 q^{61} + 4781432 q^{64} + 1457476 q^{66} + 1552540 q^{67} + 4372 q^{69} - 9366152 q^{70} - 1660280 q^{72} - 886066 q^{75} - 6569272 q^{76} - 13616772 q^{78} - 4 q^{81} + 11560256 q^{82} - 10944176 q^{84} + 7846496 q^{85} - 40789116 q^{87} + 24614816 q^{88} + 25746032 q^{90} - 1590680 q^{91} - 14495396 q^{93} - 6995856 q^{94} - 13927736 q^{96} - 8 q^{97} - 4701076 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

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

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −9.27322 6.48131i −0.819645 0.572872i
\(3\) 27.2746 37.9881i 0.583222 0.812313i
\(4\) 43.9852 + 120.205i 0.343634 + 0.939104i
\(5\) −379.549 + 379.549i −1.35792 + 1.35792i −0.481432 + 0.876484i \(0.659883\pi\)
−0.876484 + 0.481432i \(0.840117\pi\)
\(6\) −499.136 + 175.497i −0.943386 + 0.331696i
\(7\) 864.981 0.953155 0.476577 0.879132i \(-0.341877\pi\)
0.476577 + 0.879132i \(0.341877\pi\)
\(8\) 371.203 1399.77i 0.256328 0.966590i
\(9\) −699.194 2072.22i −0.319705 0.947517i
\(10\) 5979.61 1059.67i 1.89092 0.335096i
\(11\) −285.623 285.623i −0.0647022 0.0647022i 0.674015 0.738717i \(-0.264568\pi\)
−0.738717 + 0.674015i \(0.764568\pi\)
\(12\) 5766.05 + 1607.63i 0.963261 + 0.268567i
\(13\) 4742.77 4742.77i 0.598730 0.598730i −0.341245 0.939974i \(-0.610849\pi\)
0.939974 + 0.341245i \(0.110849\pi\)
\(14\) −8021.16 5606.21i −0.781248 0.546036i
\(15\) 4066.31 + 24770.4i 0.311086 + 1.89502i
\(16\) −12514.6 + 10574.5i −0.763831 + 0.645416i
\(17\) 23420.2i 1.15616i −0.815978 0.578082i \(-0.803801\pi\)
0.815978 0.578082i \(-0.196199\pi\)
\(18\) −6946.93 + 23747.8i −0.280762 + 0.959777i
\(19\) 14837.1 + 14837.1i 0.496261 + 0.496261i 0.910272 0.414011i \(-0.135872\pi\)
−0.414011 + 0.910272i \(0.635872\pi\)
\(20\) −62318.3 28929.2i −1.74185 0.808597i
\(21\) 23592.0 32859.0i 0.555901 0.774260i
\(22\) 797.433 + 4499.86i 0.0159667 + 0.0900989i
\(23\) 59037.2i 1.01176i −0.862604 0.505881i \(-0.831168\pi\)
0.862604 0.505881i \(-0.168832\pi\)
\(24\) −43050.3 52279.5i −0.635677 0.771955i
\(25\) 209990.i 2.68787i
\(26\) −74720.2 + 13241.4i −0.833741 + 0.147750i
\(27\) −97790.0 29957.9i −0.956139 0.292913i
\(28\) 38046.4 + 103975.i 0.327537 + 0.895111i
\(29\) 53858.0 + 53858.0i 0.410070 + 0.410070i 0.881763 0.471693i \(-0.156357\pi\)
−0.471693 + 0.881763i \(0.656357\pi\)
\(30\) 122837. 256056.i 0.830623 1.73145i
\(31\) 79079.0i 0.476755i −0.971173 0.238377i \(-0.923384\pi\)
0.971173 0.238377i \(-0.0766155\pi\)
\(32\) 184587. 16948.6i 0.995811 0.0914345i
\(33\) −18640.5 + 3060.03i −0.0902941 + 0.0148227i
\(34\) −151794. + 217181.i −0.662335 + 0.947644i
\(35\) −328303. + 328303.i −1.29430 + 1.29430i
\(36\) 218338. 175194.i 0.779955 0.625835i
\(37\) −24070.3 24070.3i −0.0781222 0.0781222i 0.666966 0.745088i \(-0.267593\pi\)
−0.745088 + 0.666966i \(0.767593\pi\)
\(38\) −41423.7 233751.i −0.122463 0.691052i
\(39\) −50811.9 309526.i −0.137164 0.835548i
\(40\) 390392. + 672171.i 0.964475 + 1.66062i
\(41\) −703269. −1.59360 −0.796798 0.604246i \(-0.793474\pi\)
−0.796798 + 0.604246i \(0.793474\pi\)
\(42\) −431743. + 151802.i −0.899193 + 0.316158i
\(43\) 569708. 569708.i 1.09273 1.09273i 0.0974942 0.995236i \(-0.468917\pi\)
0.995236 0.0974942i \(-0.0310827\pi\)
\(44\) 21770.2 46896.6i 0.0385282 0.0829959i
\(45\) 1.05189e6 + 521131.i 1.72078 + 0.852516i
\(46\) −382638. + 547465.i −0.579610 + 0.829285i
\(47\) 1.06175e6 1.49170 0.745849 0.666115i \(-0.232044\pi\)
0.745849 + 0.666115i \(0.232044\pi\)
\(48\) 60374.8 + 763821.i 0.0787974 + 0.996891i
\(49\) −75350.6 −0.0914956
\(50\) −1.36101e6 + 1.94728e6i −1.53981 + 2.20310i
\(51\) −889690. 638777.i −0.939168 0.674300i
\(52\) 778718. + 361495.i 0.768013 + 0.356525i
\(53\) 1.16855e6 1.16855e6i 1.07816 1.07816i 0.0814833 0.996675i \(-0.474034\pi\)
0.996675 0.0814833i \(-0.0259657\pi\)
\(54\) 712661. + 911613.i 0.615893 + 0.787830i
\(55\) 216816. 0.175720
\(56\) 321084. 1.21078e6i 0.244321 0.921310i
\(57\) 968306. 158957.i 0.692549 0.113689i
\(58\) −150367. 848508.i −0.101194 0.571029i
\(59\) −138554. 138554.i −0.0878285 0.0878285i 0.661828 0.749656i \(-0.269781\pi\)
−0.749656 + 0.661828i \(0.769781\pi\)
\(60\) −2.79867e6 + 1.57832e6i −1.67272 + 0.943336i
\(61\) 406144. 406144.i 0.229101 0.229101i −0.583216 0.812317i \(-0.698206\pi\)
0.812317 + 0.583216i \(0.198206\pi\)
\(62\) −512535. + 733317.i −0.273120 + 0.390769i
\(63\) −604790. 1.79243e6i −0.304728 0.903131i
\(64\) −1.82157e6 1.03920e6i −0.868591 0.495529i
\(65\) 3.60023e6i 1.62605i
\(66\) 192691. + 92438.8i 0.0825006 + 0.0395777i
\(67\) 840959. + 840959.i 0.341596 + 0.341596i 0.856967 0.515371i \(-0.172346\pi\)
−0.515371 + 0.856967i \(0.672346\pi\)
\(68\) 2.81523e6 1.03014e6i 1.08576 0.397298i
\(69\) −2.24271e6 1.61021e6i −0.821867 0.590081i
\(70\) 5.17225e6 916591.i 1.80234 0.319398i
\(71\) 1.70865e6i 0.566563i 0.959037 + 0.283282i \(0.0914231\pi\)
−0.959037 + 0.283282i \(0.908577\pi\)
\(72\) −3.16018e6 + 209497.i −0.997810 + 0.0661475i
\(73\) 496669.i 0.149430i −0.997205 0.0747149i \(-0.976195\pi\)
0.997205 0.0747149i \(-0.0238047\pi\)
\(74\) 67201.9 + 379216.i 0.0192784 + 0.108787i
\(75\) −7.97711e6 5.72738e6i −2.18339 1.56762i
\(76\) −1.13088e6 + 2.43610e6i −0.295508 + 0.636573i
\(77\) −247059. 247059.i −0.0616712 0.0616712i
\(78\) −1.53495e6 + 3.19963e6i −0.366237 + 0.763430i
\(79\) 305230.i 0.0696519i −0.999393 0.0348260i \(-0.988912\pi\)
0.999393 0.0348260i \(-0.0110877\pi\)
\(80\) 736363. 8.76344e6i 0.160797 1.91364i
\(81\) −3.80522e6 + 2.89777e6i −0.795578 + 0.605851i
\(82\) 6.52157e6 + 4.55811e6i 1.30618 + 0.912927i
\(83\) 3.74938e6 3.74938e6i 0.719758 0.719758i −0.248797 0.968556i \(-0.580035\pi\)
0.968556 + 0.248797i \(0.0800353\pi\)
\(84\) 4.98752e6 + 1.39057e6i 0.918137 + 0.255986i
\(85\) 8.88912e6 + 8.88912e6i 1.56997 + 1.56997i
\(86\) −8.97549e6 + 1.59057e6i −1.52165 + 0.269655i
\(87\) 3.51492e6 577010.i 0.572266 0.0939433i
\(88\) −505831. + 293783.i −0.0791255 + 0.0459555i
\(89\) 7.69964e6 1.15773 0.578863 0.815425i \(-0.303497\pi\)
0.578863 + 0.815425i \(0.303497\pi\)
\(90\) −6.37677e6 1.16502e7i −0.922045 1.68455i
\(91\) 4.10241e6 4.10241e6i 0.570682 0.570682i
\(92\) 7.09658e6 2.59676e6i 0.950148 0.347676i
\(93\) −3.00406e6 2.15685e6i −0.387274 0.278054i
\(94\) −9.84587e6 6.88155e6i −1.22266 0.854553i
\(95\) −1.12628e7 −1.34776
\(96\) 4.39070e6 7.47439e6i 0.506505 0.862237i
\(97\) −4.94267e6 −0.549871 −0.274935 0.961463i \(-0.588656\pi\)
−0.274935 + 0.961463i \(0.588656\pi\)
\(98\) 698743. + 488371.i 0.0749939 + 0.0524153i
\(99\) −392168. + 791580.i −0.0406208 + 0.0819920i
\(100\) 2.52419e7 9.23644e6i 2.52419 0.923644i
\(101\) 1.59492e6 1.59492e6i 0.154033 0.154033i −0.625883 0.779917i \(-0.715261\pi\)
0.779917 + 0.625883i \(0.215261\pi\)
\(102\) 4.11018e6 + 1.16899e7i 0.383495 + 1.09071i
\(103\) −1.77794e7 −1.60320 −0.801600 0.597861i \(-0.796017\pi\)
−0.801600 + 0.597861i \(0.796017\pi\)
\(104\) −4.87827e6 8.39933e6i −0.425254 0.732197i
\(105\) 3.51728e6 + 2.14259e7i 0.296513 + 1.80625i
\(106\) −1.84100e7 + 3.26249e6i −1.50135 + 0.266059i
\(107\) −6.93843e6 6.93843e6i −0.547543 0.547543i 0.378186 0.925729i \(-0.376548\pi\)
−0.925729 + 0.378186i \(0.876548\pi\)
\(108\) −700216. 1.30726e7i −0.0534871 0.998569i
\(109\) −2.51694e6 + 2.51694e6i −0.186158 + 0.186158i −0.794033 0.607875i \(-0.792022\pi\)
0.607875 + 0.794033i \(0.292022\pi\)
\(110\) −2.01058e6 1.40525e6i −0.144028 0.100665i
\(111\) −1.57089e6 + 257877.i −0.109022 + 0.0178971i
\(112\) −1.08249e7 + 9.14675e6i −0.728049 + 0.615182i
\(113\) 1.92987e7i 1.25821i 0.777321 + 0.629105i \(0.216578\pi\)
−0.777321 + 0.629105i \(0.783422\pi\)
\(114\) −1.00096e7 4.80185e6i −0.632774 0.303558i
\(115\) 2.24075e7 + 2.24075e7i 1.37389 + 1.37389i
\(116\) −4.10506e6 + 8.84298e6i −0.244184 + 0.526012i
\(117\) −1.31442e7 6.51195e6i −0.758723 0.375890i
\(118\) 386829. + 2.18285e6i 0.0216736 + 0.122303i
\(119\) 2.02580e7i 1.10200i
\(120\) 3.61823e7 + 3.50295e6i 1.91145 + 0.185054i
\(121\) 1.93240e7i 0.991627i
\(122\) −6.39862e6 + 1.13392e6i −0.319026 + 0.0565356i
\(123\) −1.91814e7 + 2.67159e7i −0.929420 + 1.29450i
\(124\) 9.50571e6 3.47830e6i 0.447722 0.163829i
\(125\) 5.00491e7 + 5.00491e7i 2.29198 + 2.29198i
\(126\) −6.00896e6 + 2.05414e7i −0.267610 + 0.914817i
\(127\) 5.60477e6i 0.242798i −0.992604 0.121399i \(-0.961262\pi\)
0.992604 0.121399i \(-0.0387380\pi\)
\(128\) 1.01564e7 + 2.14429e7i 0.428061 + 0.903750i
\(129\) −6.10359e6 3.71807e7i −0.250335 1.52494i
\(130\) 2.33342e7 3.33857e7i 0.931518 1.33278i
\(131\) −2.51498e7 + 2.51498e7i −0.977430 + 0.977430i −0.999751 0.0223212i \(-0.992894\pi\)
0.0223212 + 0.999751i \(0.492894\pi\)
\(132\) −1.18774e6 2.10609e6i −0.0449482 0.0797020i
\(133\) 1.28338e7 + 1.28338e7i 0.473014 + 0.473014i
\(134\) −2.34788e6 1.32489e7i −0.0842964 0.475678i
\(135\) 4.84866e7 2.57456e7i 1.69611 0.900606i
\(136\) −3.27830e7 8.69366e6i −1.11754 0.296358i
\(137\) 1.91722e7 0.637016 0.318508 0.947920i \(-0.396818\pi\)
0.318508 + 0.947920i \(0.396818\pi\)
\(138\) 1.03608e7 + 2.94676e7i 0.335597 + 0.954482i
\(139\) −1.59862e7 + 1.59862e7i −0.504885 + 0.504885i −0.912952 0.408067i \(-0.866203\pi\)
0.408067 + 0.912952i \(0.366203\pi\)
\(140\) −5.39042e7 2.50232e7i −1.66025 0.770718i
\(141\) 2.89589e7 4.03340e7i 0.869991 1.21173i
\(142\) 1.10743e7 1.58447e7i 0.324568 0.464380i
\(143\) −2.70929e6 −0.0774782
\(144\) 3.06628e7 + 1.85394e7i 0.855744 + 0.517400i
\(145\) −4.08835e7 −1.11368
\(146\) −3.21907e6 + 4.60572e6i −0.0856042 + 0.122479i
\(147\) −2.05516e6 + 2.86243e6i −0.0533622 + 0.0743231i
\(148\) 1.83464e6 3.95211e6i 0.0465194 0.100210i
\(149\) −3.06647e7 + 3.06647e7i −0.759428 + 0.759428i −0.976218 0.216790i \(-0.930441\pi\)
0.216790 + 0.976218i \(0.430441\pi\)
\(150\) 3.68526e7 + 1.04813e8i 0.891555 + 2.53570i
\(151\) −3.15631e7 −0.746038 −0.373019 0.927824i \(-0.621677\pi\)
−0.373019 + 0.927824i \(0.621677\pi\)
\(152\) 2.62760e7 1.52609e7i 0.606886 0.352475i
\(153\) −4.85318e7 + 1.63753e7i −1.09549 + 0.369631i
\(154\) 689765. + 3.89229e6i 0.0152187 + 0.0858782i
\(155\) 3.00143e7 + 3.00143e7i 0.647393 + 0.647393i
\(156\) 3.49717e7 1.97224e7i 0.737532 0.415934i
\(157\) 1.46347e7 1.46347e7i 0.301810 0.301810i −0.539911 0.841722i \(-0.681542\pi\)
0.841722 + 0.539911i \(0.181542\pi\)
\(158\) −1.97829e6 + 2.83047e6i −0.0399017 + 0.0570898i
\(159\) −1.25193e7 7.62628e7i −0.246996 1.50461i
\(160\) −6.36271e7 + 7.64927e7i −1.22807 + 1.47639i
\(161\) 5.10660e7i 0.964365i
\(162\) 5.40680e7 2.20879e6i 0.999167 0.0408180i
\(163\) −1.16825e7 1.16825e7i −0.211291 0.211291i 0.593525 0.804816i \(-0.297736\pi\)
−0.804816 + 0.593525i \(0.797736\pi\)
\(164\) −3.09334e7 8.45366e7i −0.547614 1.49655i
\(165\) 5.91356e6 8.23642e6i 0.102484 0.142740i
\(166\) −5.90698e7 + 1.04679e7i −1.00228 + 0.177616i
\(167\) 1.99434e7i 0.331354i 0.986180 + 0.165677i \(0.0529809\pi\)
−0.986180 + 0.165677i \(0.947019\pi\)
\(168\) −3.72377e7 4.52208e7i −0.605899 0.735793i
\(169\) 1.77607e7i 0.283046i
\(170\) −2.48176e7 1.40044e8i −0.387426 2.18622i
\(171\) 2.03717e7 4.11196e7i 0.311559 0.628873i
\(172\) 9.35407e7 + 4.34232e7i 1.40169 + 0.650687i
\(173\) −3.80258e7 3.80258e7i −0.558363 0.558363i 0.370478 0.928841i \(-0.379194\pi\)
−0.928841 + 0.370478i \(0.879194\pi\)
\(174\) −3.63344e7 1.74306e7i −0.522873 0.250836i
\(175\) 1.81637e8i 2.56195i
\(176\) 6.59478e6 + 554137.i 0.0911814 + 0.00766167i
\(177\) −9.04238e6 + 1.48440e6i −0.122568 + 0.0201207i
\(178\) −7.14005e7 4.99038e7i −0.948923 0.663229i
\(179\) 5.05679e7 5.05679e7i 0.659006 0.659006i −0.296139 0.955145i \(-0.595699\pi\)
0.955145 + 0.296139i \(0.0956992\pi\)
\(180\) −1.63752e7 + 1.49364e8i −0.209282 + 1.90894i
\(181\) 5.43327e7 + 5.43327e7i 0.681062 + 0.681062i 0.960239 0.279178i \(-0.0900619\pi\)
−0.279178 + 0.960239i \(0.590062\pi\)
\(182\) −6.46316e7 + 1.14536e7i −0.794684 + 0.140828i
\(183\) −4.35124e6 2.65061e7i −0.0524849 0.319718i
\(184\) −8.26385e7 2.19148e7i −0.977958 0.259343i
\(185\) 1.82717e7 0.212167
\(186\) 1.38781e7 + 3.94712e7i 0.158138 + 0.449764i
\(187\) −6.68935e6 + 6.68935e6i −0.0748064 + 0.0748064i
\(188\) 4.67014e7 + 1.27628e8i 0.512599 + 1.40086i
\(189\) −8.45865e7 2.59130e7i −0.911349 0.279191i
\(190\) 1.04442e8 + 7.29975e7i 1.10468 + 0.772095i
\(191\) 1.81090e8 1.88052 0.940260 0.340458i \(-0.110582\pi\)
0.940260 + 0.340458i \(0.110582\pi\)
\(192\) −8.91598e7 + 4.08542e7i −0.909106 + 0.416565i
\(193\) −9.72967e7 −0.974199 −0.487099 0.873347i \(-0.661945\pi\)
−0.487099 + 0.873347i \(0.661945\pi\)
\(194\) 4.58345e7 + 3.20350e7i 0.450698 + 0.315006i
\(195\) 1.36766e8 + 9.81948e7i 1.32086 + 0.948347i
\(196\) −3.31431e6 9.05754e6i −0.0314410 0.0859239i
\(197\) 1.00223e7 1.00223e7i 0.0933974 0.0933974i −0.658864 0.752262i \(-0.728963\pi\)
0.752262 + 0.658864i \(0.228963\pi\)
\(198\) 8.76714e6 4.79873e6i 0.0802656 0.0439337i
\(199\) −1.42971e8 −1.28607 −0.643033 0.765838i \(-0.722324\pi\)
−0.643033 + 0.765838i \(0.722324\pi\)
\(200\) −2.93938e8 7.79489e7i −2.59807 0.688977i
\(201\) 5.48832e7 9.00964e6i 0.476709 0.0782566i
\(202\) −2.51272e7 + 4.45287e6i −0.214494 + 0.0380111i
\(203\) 4.65862e7 + 4.65862e7i 0.390860 + 0.390860i
\(204\) 3.76511e7 1.35042e8i 0.310508 1.11369i
\(205\) 2.66925e8 2.66925e8i 2.16397 2.16397i
\(206\) 1.64873e8 + 1.15234e8i 1.31405 + 0.918429i
\(207\) −1.22338e8 + 4.12784e7i −0.958661 + 0.323465i
\(208\) −9.20146e6 + 1.09506e8i −0.0708982 + 0.843758i
\(209\) 8.47561e6i 0.0642183i
\(210\) 1.06252e8 2.21484e8i 0.791713 1.65034i
\(211\) 9.10976e7 + 9.10976e7i 0.667603 + 0.667603i 0.957161 0.289557i \(-0.0935081\pi\)
−0.289557 + 0.957161i \(0.593508\pi\)
\(212\) 1.91865e8 + 8.90671e7i 1.38299 + 0.642010i
\(213\) 6.49083e7 + 4.66027e7i 0.460227 + 0.330432i
\(214\) 1.93715e7 + 1.09312e8i 0.135118 + 0.762463i
\(215\) 4.32464e8i 2.96767i
\(216\) −7.82342e7 + 1.25763e8i −0.528212 + 0.849113i
\(217\) 6.84018e7i 0.454421i
\(218\) 3.96533e7 7.02708e6i 0.259228 0.0459385i
\(219\) −1.88675e7 1.35464e7i −0.121384 0.0871507i
\(220\) 9.53669e6 + 2.60624e7i 0.0603835 + 0.165019i
\(221\) −1.11077e8 1.11077e8i −0.692230 0.692230i
\(222\) 1.62386e7 + 7.79007e6i 0.0996123 + 0.0477866i
\(223\) 9.12546e7i 0.551046i 0.961294 + 0.275523i \(0.0888510\pi\)
−0.961294 + 0.275523i \(0.911149\pi\)
\(224\) 1.59665e8 1.46603e7i 0.949162 0.0871512i
\(225\) −4.35145e8 + 1.46824e8i −2.54680 + 0.859324i
\(226\) 1.25081e8 1.78961e8i 0.720793 1.03128i
\(227\) −4.22896e7 + 4.22896e7i −0.239963 + 0.239963i −0.816835 0.576872i \(-0.804273\pi\)
0.576872 + 0.816835i \(0.304273\pi\)
\(228\) 6.16986e7 + 1.09404e8i 0.344749 + 0.611308i
\(229\) 819829. + 819829.i 0.00451127 + 0.00451127i 0.709359 0.704848i \(-0.248985\pi\)
−0.704848 + 0.709359i \(0.748985\pi\)
\(230\) −6.25596e7 3.53019e8i −0.339037 1.91316i
\(231\) −1.61237e7 + 2.64687e6i −0.0860643 + 0.0141283i
\(232\) 9.53812e7 5.53967e7i 0.501482 0.291257i
\(233\) −2.91586e8 −1.51016 −0.755078 0.655635i \(-0.772401\pi\)
−0.755078 + 0.655635i \(0.772401\pi\)
\(234\) 7.96830e7 + 1.45578e8i 0.406546 + 0.742748i
\(235\) −4.02987e8 + 4.02987e8i −2.02560 + 2.02560i
\(236\) 1.05606e7 2.27492e7i 0.0522992 0.112661i
\(237\) −1.15951e7 8.32503e6i −0.0565791 0.0406225i
\(238\) −1.31299e8 + 1.87857e8i −0.631308 + 0.903252i
\(239\) 1.15744e8 0.548409 0.274205 0.961671i \(-0.411585\pi\)
0.274205 + 0.961671i \(0.411585\pi\)
\(240\) −3.12823e8 2.66992e8i −1.46069 1.24669i
\(241\) 2.04934e8 0.943093 0.471546 0.881841i \(-0.343696\pi\)
0.471546 + 0.881841i \(0.343696\pi\)
\(242\) −1.25245e8 + 1.79196e8i −0.568076 + 0.812782i
\(243\) 6.29482e6 + 2.23589e8i 0.0281424 + 0.999604i
\(244\) 6.66850e7 + 3.09564e7i 0.293876 + 0.136422i
\(245\) 2.85992e7 2.85992e7i 0.124243 0.124243i
\(246\) 3.51027e8 1.23422e8i 1.50338 0.528589i
\(247\) 1.40738e8 0.594252
\(248\) −1.10692e8 2.93544e7i −0.460826 0.122206i
\(249\) −4.01691e7 2.44695e8i −0.164890 1.00445i
\(250\) −1.39732e8 7.88500e8i −0.565597 3.19162i
\(251\) −2.65133e7 2.65133e7i −0.105829 0.105829i 0.652210 0.758039i \(-0.273842\pi\)
−0.758039 + 0.652210i \(0.773842\pi\)
\(252\) 1.88858e8 1.51539e8i 0.743418 0.596518i
\(253\) −1.68624e7 + 1.68624e7i −0.0654632 + 0.0654632i
\(254\) −3.63262e7 + 5.19742e7i −0.139092 + 0.199008i
\(255\) 5.80128e8 9.52338e7i 2.19095 0.359667i
\(256\) 4.47952e7 2.64671e8i 0.166875 0.985978i
\(257\) 2.68830e8i 0.987896i −0.869492 0.493948i \(-0.835553\pi\)
0.869492 0.493948i \(-0.164447\pi\)
\(258\) −1.84380e8 + 3.84344e8i −0.668412 + 1.39332i
\(259\) −2.08203e7 2.08203e7i −0.0744626 0.0744626i
\(260\) −4.32766e8 + 1.58357e8i −1.52703 + 0.558766i
\(261\) 7.39485e7 1.49263e8i 0.257447 0.519649i
\(262\) 3.96224e8 7.02160e7i 1.36109 0.241202i
\(263\) 5.79933e8i 1.96577i −0.184218 0.982885i \(-0.558975\pi\)
0.184218 0.982885i \(-0.441025\pi\)
\(264\) −2.63608e6 + 2.72284e7i −0.00881749 + 0.0910769i
\(265\) 8.87045e8i 2.92809i
\(266\) −3.58307e7 2.02190e8i −0.116727 0.658679i
\(267\) 2.10005e8 2.92495e8i 0.675211 0.940435i
\(268\) −6.40979e7 + 1.38077e8i −0.203410 + 0.438178i
\(269\) 2.20500e8 + 2.20500e8i 0.690677 + 0.690677i 0.962381 0.271704i \(-0.0875871\pi\)
−0.271704 + 0.962381i \(0.587587\pi\)
\(270\) −6.16492e8 7.55120e7i −1.90614 0.233476i
\(271\) 2.87271e8i 0.876799i −0.898780 0.438399i \(-0.855546\pi\)
0.898780 0.438399i \(-0.144454\pi\)
\(272\) 2.47657e8 + 2.93095e8i 0.746208 + 0.883114i
\(273\) −4.39513e7 2.67734e8i −0.130738 0.796407i
\(274\) −1.77788e8 1.24261e8i −0.522127 0.364929i
\(275\) −5.99779e7 + 5.99779e7i −0.173911 + 0.173911i
\(276\) 9.49101e7 3.40411e8i 0.271726 0.974590i
\(277\) 4.76350e8 + 4.76350e8i 1.34663 + 1.34663i 0.889299 + 0.457326i \(0.151193\pi\)
0.457326 + 0.889299i \(0.348807\pi\)
\(278\) 2.51854e8 4.46319e7i 0.703060 0.124591i
\(279\) −1.63869e8 + 5.52915e7i −0.451733 + 0.152421i
\(280\) 3.37682e8 + 5.81416e8i 0.919294 + 1.58283i
\(281\) −3.31808e8 −0.892104 −0.446052 0.895007i \(-0.647170\pi\)
−0.446052 + 0.895007i \(0.647170\pi\)
\(282\) −5.29959e8 + 1.86335e8i −1.40725 + 0.494791i
\(283\) −5.55023e7 + 5.55023e7i −0.145566 + 0.145566i −0.776134 0.630568i \(-0.782822\pi\)
0.630568 + 0.776134i \(0.282822\pi\)
\(284\) −2.05388e8 + 7.51552e7i −0.532061 + 0.194691i
\(285\) −3.07187e8 + 4.27852e8i −0.786043 + 1.09480i
\(286\) 2.51239e7 + 1.75598e7i 0.0635046 + 0.0443851i
\(287\) −6.08314e8 −1.51894
\(288\) −1.64184e8 3.70655e8i −0.405001 0.914316i
\(289\) −1.38168e8 −0.336717
\(290\) 3.79122e8 + 2.64979e8i 0.912821 + 0.637996i
\(291\) −1.34809e8 + 1.87763e8i −0.320696 + 0.446667i
\(292\) 5.97022e7 2.18461e7i 0.140330 0.0513492i
\(293\) 1.49536e8 1.49536e8i 0.347303 0.347303i −0.511801 0.859104i \(-0.671021\pi\)
0.859104 + 0.511801i \(0.171021\pi\)
\(294\) 3.76102e7 1.32238e7i 0.0863157 0.0303487i
\(295\) 1.05176e8 0.238527
\(296\) −4.26278e7 + 2.47579e7i −0.0955371 + 0.0554872i
\(297\) 1.93744e7 + 3.64877e7i 0.0429122 + 0.0808164i
\(298\) 4.83108e8 8.56130e7i 1.05752 0.187406i
\(299\) −2.80000e8 2.80000e8i −0.605771 0.605771i
\(300\) 3.37586e8 1.21081e9i 0.721873 2.58912i
\(301\) 4.92787e8 4.92787e8i 1.04154 1.04154i
\(302\) 2.92692e8 + 2.04571e8i 0.611486 + 0.427385i
\(303\) −1.70872e7 1.04089e8i −0.0352877 0.214959i
\(304\) −3.42574e8 2.87854e7i −0.699354 0.0587644i
\(305\) 3.08303e8i 0.622198i
\(306\) 5.56180e8 + 1.62699e8i 1.10966 + 0.324608i
\(307\) −2.60008e8 2.60008e8i −0.512865 0.512865i 0.402538 0.915403i \(-0.368128\pi\)
−0.915403 + 0.402538i \(0.868128\pi\)
\(308\) 1.88308e7 4.05647e7i 0.0367233 0.0791080i
\(309\) −4.84927e8 + 6.75407e8i −0.935021 + 1.30230i
\(310\) −8.37973e7 4.72862e8i −0.159758 0.901505i
\(311\) 4.12887e8i 0.778340i −0.921166 0.389170i \(-0.872762\pi\)
0.921166 0.389170i \(-0.127238\pi\)
\(312\) −4.52128e8 4.37722e7i −0.842791 0.0815938i
\(313\) 8.30539e8i 1.53093i −0.643479 0.765464i \(-0.722509\pi\)
0.643479 0.765464i \(-0.277491\pi\)
\(314\) −2.30562e8 + 4.08587e7i −0.420276 + 0.0744784i
\(315\) 9.09863e8 + 4.50768e8i 1.64017 + 0.812580i
\(316\) 3.66903e7 1.34256e7i 0.0654104 0.0239348i
\(317\) 2.06944e8 + 2.06944e8i 0.364875 + 0.364875i 0.865604 0.500729i \(-0.166935\pi\)
−0.500729 + 0.865604i \(0.666935\pi\)
\(318\) −3.78189e8 + 7.88344e8i −0.659499 + 1.37474i
\(319\) 3.07662e7i 0.0530648i
\(320\) 1.08580e9 2.96947e8i 1.85236 0.506587i
\(321\) −4.52821e8 + 7.43351e7i −0.764115 + 0.125437i
\(322\) −3.30975e8 + 4.73546e8i −0.552458 + 0.790437i
\(323\) 3.47487e8 3.47487e8i 0.573759 0.573759i
\(324\) −5.15700e8 3.29949e8i −0.842345 0.538939i
\(325\) −9.95934e8 9.95934e8i −1.60931 1.60931i
\(326\) 3.26166e7 + 1.84053e8i 0.0521407 + 0.294226i
\(327\) 2.69654e7 + 1.64263e8i 0.0426471 + 0.259789i
\(328\) −2.61056e8 + 9.84416e8i −0.408484 + 1.54035i
\(329\) 9.18396e8 1.42182
\(330\) −1.08221e8 + 3.80505e7i −0.165772 + 0.0582857i
\(331\) 1.04208e8 1.04208e8i 0.157944 0.157944i −0.623711 0.781655i \(-0.714376\pi\)
0.781655 + 0.623711i \(0.214376\pi\)
\(332\) 6.15613e8 + 2.85778e8i 0.923261 + 0.428594i
\(333\) −3.30491e7 + 6.67087e7i −0.0490461 + 0.0989982i
\(334\) 1.29259e8 1.84940e8i 0.189823 0.271592i
\(335\) −6.38370e8 −0.927717
\(336\) 5.22231e7 + 6.60691e8i 0.0751061 + 0.950191i
\(337\) 1.19265e9 1.69749 0.848746 0.528800i \(-0.177358\pi\)
0.848746 + 0.528800i \(0.177358\pi\)
\(338\) 1.15113e8 1.64699e8i 0.162149 0.231997i
\(339\) 7.33120e8 + 5.26363e8i 1.02206 + 0.733815i
\(340\) −6.77529e8 + 1.45951e9i −0.934871 + 2.01386i
\(341\) −2.25868e7 + 2.25868e7i −0.0308471 + 0.0308471i
\(342\) −4.55420e8 + 2.49276e8i −0.615631 + 0.336969i
\(343\) −7.77526e8 −1.04036
\(344\) −5.85984e8 1.00894e9i −0.776124 1.33632i
\(345\) 1.46237e9 2.40063e8i 1.91731 0.314745i
\(346\) 1.06164e8 + 5.99078e8i 0.137788 + 0.777530i
\(347\) −3.77988e8 3.77988e8i −0.485652 0.485652i 0.421279 0.906931i \(-0.361581\pi\)
−0.906931 + 0.421279i \(0.861581\pi\)
\(348\) 2.23964e8 + 3.97132e8i 0.284873 + 0.505135i
\(349\) −3.18472e8 + 3.18472e8i −0.401035 + 0.401035i −0.878598 0.477562i \(-0.841520\pi\)
0.477562 + 0.878598i \(0.341520\pi\)
\(350\) −1.17725e9 + 1.68436e9i −1.46767 + 2.09989i
\(351\) −6.05879e8 + 3.21712e8i −0.747844 + 0.397093i
\(352\) −5.75633e7 4.78815e7i −0.0703472 0.0585151i
\(353\) 2.24711e8i 0.271902i 0.990716 + 0.135951i \(0.0434090\pi\)
−0.990716 + 0.135951i \(0.956591\pi\)
\(354\) 9.34728e7 + 4.48413e7i 0.111989 + 0.0537238i
\(355\) −6.48515e8 6.48515e8i −0.769345 0.769345i
\(356\) 3.38670e8 + 9.25537e8i 0.397834 + 1.08722i
\(357\) −7.69565e8 5.52530e8i −0.895172 0.642713i
\(358\) −7.96673e8 + 1.41181e8i −0.917676 + 0.162624i
\(359\) 7.52967e8i 0.858905i 0.903089 + 0.429452i \(0.141293\pi\)
−0.903089 + 0.429452i \(0.858707\pi\)
\(360\) 1.11993e9 1.27896e9i 1.26512 1.44476i
\(361\) 4.53595e8i 0.507450i
\(362\) −1.51692e8 8.55987e8i −0.168067 0.948390i
\(363\) −7.34083e8 5.27054e8i −0.805512 0.578339i
\(364\) 6.73577e8 + 3.12686e8i 0.732036 + 0.339824i
\(365\) 1.88510e8 + 1.88510e8i 0.202913 + 0.202913i
\(366\) −1.31444e8 + 2.73998e8i −0.140139 + 0.292122i
\(367\) 6.85984e7i 0.0724407i 0.999344 + 0.0362204i \(0.0115318\pi\)
−0.999344 + 0.0362204i \(0.988468\pi\)
\(368\) 6.24289e8 + 7.38827e8i 0.653007 + 0.772814i
\(369\) 4.91721e8 + 1.45733e9i 0.509480 + 1.50996i
\(370\) −1.69437e8 1.18424e8i −0.173901 0.121544i
\(371\) 1.01078e9 1.01078e9i 1.02765 1.02765i
\(372\) 1.27130e8 4.55973e8i 0.128041 0.459239i
\(373\) 1.01373e9 + 1.01373e9i 1.01145 + 1.01145i 0.999934 + 0.0115128i \(0.00366470\pi\)
0.0115128 + 0.999934i \(0.496335\pi\)
\(374\) 1.05388e8 1.86761e7i 0.104169 0.0184601i
\(375\) 3.26634e9 5.36202e8i 3.19854 0.525073i
\(376\) 3.94126e8 1.48621e9i 0.382365 1.44186i
\(377\) 5.10873e8 0.491042
\(378\) 6.16439e8 + 7.88528e8i 0.587041 + 0.750924i
\(379\) 1.88686e8 1.88686e8i 0.178034 0.178034i −0.612464 0.790498i \(-0.709822\pi\)
0.790498 + 0.612464i \(0.209822\pi\)
\(380\) −4.95395e8 1.35384e9i −0.463137 1.26569i
\(381\) −2.12915e8 1.52868e8i −0.197228 0.141605i
\(382\) −1.67929e9 1.17370e9i −1.54136 1.07730i
\(383\) −1.62776e9 −1.48045 −0.740227 0.672357i \(-0.765282\pi\)
−0.740227 + 0.672357i \(0.765282\pi\)
\(384\) 1.09159e9 + 1.99022e8i 0.983782 + 0.179367i
\(385\) 1.87542e8 0.167489
\(386\) 9.02254e8 + 6.30610e8i 0.798497 + 0.558092i
\(387\) −1.57890e9 7.82225e8i −1.38473 0.686030i
\(388\) −2.17404e8 5.94135e8i −0.188954 0.516385i
\(389\) −5.29200e8 + 5.29200e8i −0.455823 + 0.455823i −0.897282 0.441459i \(-0.854461\pi\)
0.441459 + 0.897282i \(0.354461\pi\)
\(390\) −6.31830e8 1.79700e9i −0.539354 1.53399i
\(391\) −1.38266e9 −1.16976
\(392\) −2.79704e7 + 1.05474e8i −0.0234529 + 0.0884387i
\(393\) 2.69443e8 + 1.64135e9i 0.223920 + 1.36404i
\(394\) −1.57896e8 + 2.79813e7i −0.130058 + 0.0230479i
\(395\) 1.15850e8 + 1.15850e8i 0.0945814 + 0.0945814i
\(396\) −1.12402e8 1.23229e7i −0.0909577 0.00997190i
\(397\) −6.11235e8 + 6.11235e8i −0.490277 + 0.490277i −0.908393 0.418117i \(-0.862690\pi\)
0.418117 + 0.908393i \(0.362690\pi\)
\(398\) 1.32580e9 + 9.26642e8i 1.05412 + 0.736752i
\(399\) 8.37567e8 1.37495e8i 0.660107 0.108363i
\(400\) 2.22054e9 + 2.62794e9i 1.73479 + 2.05308i
\(401\) 2.13943e9i 1.65689i −0.560073 0.828443i \(-0.689227\pi\)
0.560073 0.828443i \(-0.310773\pi\)
\(402\) −5.67338e8 2.72167e8i −0.435563 0.208951i
\(403\) −3.75054e8 3.75054e8i −0.285447 0.285447i
\(404\) 2.61871e8 + 1.21565e8i 0.197584 + 0.0917221i
\(405\) 3.44424e8 2.54411e9i 0.257633 1.90302i
\(406\) −1.30064e8 7.33944e8i −0.0964533 0.544279i
\(407\) 1.37500e7i 0.0101094i
\(408\) −1.22440e9 + 1.00825e9i −0.892507 + 0.734947i
\(409\) 2.76146e8i 0.199576i −0.995009 0.0997878i \(-0.968184\pi\)
0.995009 0.0997878i \(-0.0318164\pi\)
\(410\) −4.20528e9 + 7.45230e8i −3.01336 + 0.534007i
\(411\) 5.22914e8 7.28317e8i 0.371522 0.517456i
\(412\) −7.82032e8 2.13718e9i −0.550914 1.50557i
\(413\) −1.19846e8 1.19846e8i −0.0837142 0.0837142i
\(414\) 1.40201e9 + 4.10127e8i 0.971065 + 0.284064i
\(415\) 2.84615e9i 1.95474i
\(416\) 7.95072e8 9.55840e8i 0.541477 0.650966i
\(417\) 1.71268e8 + 1.04330e9i 0.115665 + 0.704584i
\(418\) −5.49331e7 + 7.85962e7i −0.0367889 + 0.0526362i
\(419\) −1.35442e8 + 1.35442e8i −0.0899507 + 0.0899507i −0.750650 0.660700i \(-0.770260\pi\)
0.660700 + 0.750650i \(0.270260\pi\)
\(420\) −2.42080e9 + 1.36522e9i −1.59436 + 0.899145i
\(421\) −1.22939e8 1.22939e8i −0.0802973 0.0802973i 0.665817 0.746115i \(-0.268083\pi\)
−0.746115 + 0.665817i \(0.768083\pi\)
\(422\) −2.54336e8 1.43520e9i −0.164746 0.929649i
\(423\) −7.42371e8 2.20019e9i −0.476903 1.41341i
\(424\) −1.20194e9 2.06948e9i −0.765774 1.31850i
\(425\) −4.91800e9 −3.10762
\(426\) −2.99863e8 8.52848e8i −0.187927 0.534488i
\(427\) 3.51307e8 3.51307e8i 0.218368 0.218368i
\(428\) 5.28848e8 1.13922e9i 0.326045 0.702354i
\(429\) −7.38948e7 + 1.02921e8i −0.0451870 + 0.0629366i
\(430\) 2.80294e9 4.01034e9i 1.70010 2.43243i
\(431\) 2.41161e9 1.45090 0.725450 0.688275i \(-0.241632\pi\)
0.725450 + 0.688275i \(0.241632\pi\)
\(432\) 1.54059e9 6.59169e8i 0.919379 0.393372i
\(433\) 1.89903e9 1.12415 0.562073 0.827087i \(-0.310004\pi\)
0.562073 + 0.827087i \(0.310004\pi\)
\(434\) −4.43334e8 + 6.34305e8i −0.260325 + 0.372464i
\(435\) −1.11508e9 + 1.55309e9i −0.649522 + 0.904656i
\(436\) −4.13258e8 1.91842e8i −0.238791 0.110851i
\(437\) 8.75937e8 8.75937e8i 0.502097 0.502097i
\(438\) 8.71639e7 + 2.47905e8i 0.0495653 + 0.140970i
\(439\) −5.16004e8 −0.291090 −0.145545 0.989352i \(-0.546494\pi\)
−0.145545 + 0.989352i \(0.546494\pi\)
\(440\) 8.04827e7 3.03493e8i 0.0450421 0.169849i
\(441\) 5.26847e7 + 1.56143e8i 0.0292516 + 0.0866937i
\(442\) 3.10116e8 + 1.74996e9i 0.170823 + 0.963942i
\(443\) −4.70668e8 4.70668e8i −0.257218 0.257218i 0.566703 0.823922i \(-0.308219\pi\)
−0.823922 + 0.566703i \(0.808219\pi\)
\(444\) −1.00094e8 1.77486e8i −0.0542710 0.0962332i
\(445\) −2.92239e9 + 2.92239e9i −1.57209 + 1.57209i
\(446\) 5.91450e8 8.46224e8i 0.315679 0.451662i
\(447\) 3.28527e8 + 2.00126e9i 0.173978 + 1.05981i
\(448\) −1.57562e9 8.98888e8i −0.827902 0.472316i
\(449\) 4.79872e8i 0.250186i 0.992145 + 0.125093i \(0.0399230\pi\)
−0.992145 + 0.125093i \(0.960077\pi\)
\(450\) 4.98680e9 + 1.45878e9i 2.57975 + 0.754652i
\(451\) 2.00870e8 + 2.00870e8i 0.103109 + 0.103109i
\(452\) −2.31980e9 + 8.48856e8i −1.18159 + 0.432364i
\(453\) −8.60872e8 + 1.19902e9i −0.435106 + 0.606016i
\(454\) 6.66254e8 1.18069e8i 0.334152 0.0592161i
\(455\) 3.11413e9i 1.54988i
\(456\) 1.36935e8 1.41441e9i 0.0676295 0.698553i
\(457\) 1.91025e9i 0.936233i −0.883667 0.468116i \(-0.844933\pi\)
0.883667 0.468116i \(-0.155067\pi\)
\(458\) −2.28889e6 1.29160e7i −0.00111326 0.00628202i
\(459\) −7.01620e8 + 2.29026e9i −0.338655 + 1.10545i
\(460\) −1.70790e9 + 3.67910e9i −0.818107 + 1.76234i
\(461\) 1.37257e9 + 1.37257e9i 0.652503 + 0.652503i 0.953595 0.301092i \(-0.0973511\pi\)
−0.301092 + 0.953595i \(0.597351\pi\)
\(462\) 1.66674e8 + 7.99578e7i 0.0786359 + 0.0377237i
\(463\) 2.30752e9i 1.08047i 0.841515 + 0.540234i \(0.181664\pi\)
−0.841515 + 0.540234i \(0.818336\pi\)
\(464\) −1.24353e9 1.04490e8i −0.577890 0.0485581i
\(465\) 1.95882e9 3.21559e8i 0.903459 0.148312i
\(466\) 2.70395e9 + 1.88986e9i 1.23779 + 0.865126i
\(467\) −1.54704e9 + 1.54704e9i −0.702899 + 0.702899i −0.965032 0.262133i \(-0.915574\pi\)
0.262133 + 0.965032i \(0.415574\pi\)
\(468\) 2.04621e8 1.86643e9i 0.0922763 0.841688i
\(469\) 7.27413e8 + 7.27413e8i 0.325594 + 0.325594i
\(470\) 6.34887e9 1.12510e9i 2.82068 0.499862i
\(471\) −1.56789e8 9.55098e8i −0.0691421 0.421187i
\(472\) −2.45375e8 + 1.42512e8i −0.107407 + 0.0623812i
\(473\) −3.25444e8 −0.141404
\(474\) 5.35670e7 + 1.52352e8i 0.0231033 + 0.0657087i
\(475\) 3.11563e9 3.11563e9i 1.33388 1.33388i
\(476\) 2.43512e9 8.91054e8i 1.03490 0.378686i
\(477\) −3.23854e9 1.60445e9i −1.36627 0.676881i
\(478\) −1.07332e9 7.50171e8i −0.449501 0.314169i
\(479\) 2.40866e9 1.00138 0.500692 0.865626i \(-0.333079\pi\)
0.500692 + 0.865626i \(0.333079\pi\)
\(480\) 1.17041e9 + 4.50338e9i 0.483053 + 1.85864i
\(481\) −2.28320e8 −0.0935482
\(482\) −1.90040e9 1.32824e9i −0.773001 0.540272i
\(483\) −1.93990e9 1.39280e9i −0.783366 0.562439i
\(484\) 2.32285e9 8.49970e8i 0.931241 0.340757i
\(485\) 1.87598e9 1.87598e9i 0.746678 0.746678i
\(486\) 1.39077e9 2.11419e9i 0.549579 0.835442i
\(487\) 1.13646e9 0.445866 0.222933 0.974834i \(-0.428437\pi\)
0.222933 + 0.974834i \(0.428437\pi\)
\(488\) −4.17747e8 7.19272e8i −0.162721 0.280171i
\(489\) −7.62434e8 + 1.25161e8i −0.294864 + 0.0484048i
\(490\) −4.50567e8 + 7.98464e7i −0.173011 + 0.0306598i
\(491\) 1.76149e9 + 1.76149e9i 0.671575 + 0.671575i 0.958079 0.286504i \(-0.0924933\pi\)
−0.286504 + 0.958079i \(0.592493\pi\)
\(492\) −4.05508e9 1.13060e9i −1.53505 0.427987i
\(493\) 1.26137e9 1.26137e9i 0.474108 0.474108i
\(494\) −1.30509e9 9.12164e8i −0.487076 0.340431i
\(495\) −1.51596e8 4.49290e8i −0.0561785 0.166498i
\(496\) 8.36221e8 + 9.89642e8i 0.307705 + 0.364160i
\(497\) 1.47795e9i 0.540022i
\(498\) −1.21345e9 + 2.52946e9i −0.440269 + 0.917751i
\(499\) −1.04410e9 1.04410e9i −0.376174 0.376174i 0.493546 0.869720i \(-0.335700\pi\)
−0.869720 + 0.493546i \(0.835700\pi\)
\(500\) −3.81474e9 + 8.21758e9i −1.36480 + 2.94001i
\(501\) 7.57613e8 + 5.43948e8i 0.269163 + 0.193253i
\(502\) 7.40226e7 + 4.17704e8i 0.0261157 + 0.147369i
\(503\) 3.69751e9i 1.29545i 0.761873 + 0.647726i \(0.224280\pi\)
−0.761873 + 0.647726i \(0.775720\pi\)
\(504\) −2.73349e9 + 1.81211e8i −0.951067 + 0.0630489i
\(505\) 1.21070e9i 0.418328i
\(506\) 2.65659e8 4.70782e7i 0.0911586 0.0161545i
\(507\) 6.74696e8 + 4.84416e8i 0.229922 + 0.165078i
\(508\) 6.73722e8 2.46527e8i 0.228012 0.0834336i
\(509\) 1.43787e9 + 1.43787e9i 0.483288 + 0.483288i 0.906180 0.422892i \(-0.138985\pi\)
−0.422892 + 0.906180i \(0.638985\pi\)
\(510\) −5.99689e9 2.87686e9i −2.00185 0.960337i
\(511\) 4.29609e8i 0.142430i
\(512\) −2.13081e9 + 2.16403e9i −0.701618 + 0.712553i
\(513\) −1.00643e9 1.89540e9i −0.329133 0.619856i
\(514\) −1.74237e9 + 2.49292e9i −0.565938 + 0.809723i
\(515\) 6.74816e9 6.74816e9i 2.17701 2.17701i
\(516\) 4.20085e9 2.36908e9i 1.34606 0.759113i
\(517\) −3.03261e8 3.03261e8i −0.0965161 0.0965161i
\(518\) 5.81284e7 + 3.28014e8i 0.0183753 + 0.103690i
\(519\) −2.48167e9 + 4.07390e8i −0.779215 + 0.127916i
\(520\) 5.03950e9 + 1.33642e9i 1.57172 + 0.416802i
\(521\) 3.74977e9 1.16164 0.580821 0.814031i \(-0.302731\pi\)
0.580821 + 0.814031i \(0.302731\pi\)
\(522\) −1.65316e9 + 9.04865e8i −0.508708 + 0.278443i
\(523\) −1.96251e9 + 1.96251e9i −0.599868 + 0.599868i −0.940277 0.340409i \(-0.889434\pi\)
0.340409 + 0.940277i \(0.389434\pi\)
\(524\) −4.12936e9 1.91692e9i −1.25379 0.582029i
\(525\) −6.90005e9 4.95408e9i −2.08111 1.49419i
\(526\) −3.75873e9 + 5.37785e9i −1.12614 + 1.61123i
\(527\) −1.85205e9 −0.551207
\(528\) 2.00921e8 2.35409e8i 0.0594026 0.0695994i
\(529\) −8.05605e7 −0.0236607
\(530\) 5.74921e9 8.22576e9i 1.67742 2.40000i
\(531\) −1.90238e8 + 3.83989e8i −0.0551399 + 0.111298i
\(532\) −9.78191e8 + 2.10718e9i −0.281665 + 0.606752i
\(533\) −3.33545e9 + 3.33545e9i −0.954133 + 0.954133i
\(534\) −3.84317e9 + 1.35126e9i −1.09218 + 0.384013i
\(535\) 5.26695e9 1.48703
\(536\) 1.48932e9 8.64983e8i 0.417744 0.242622i
\(537\) −5.41760e8 3.30020e9i −0.150972 0.919665i
\(538\) −6.15615e8 3.47387e9i −0.170440 0.961780i
\(539\) 2.15219e7 + 2.15219e7i 0.00591997 + 0.00591997i
\(540\) 5.22745e9 + 4.69591e9i 1.42860 + 1.28334i
\(541\) 1.72885e9 1.72885e9i 0.469426 0.469426i −0.432303 0.901728i \(-0.642299\pi\)
0.901728 + 0.432303i \(0.142299\pi\)
\(542\) −1.86190e9 + 2.66393e9i −0.502294 + 0.718663i
\(543\) 3.54590e9 5.82095e8i 0.950445 0.156025i
\(544\) −3.96941e8 4.32308e9i −0.105713 1.15132i
\(545\) 1.91061e9i 0.505573i
\(546\) −1.32770e9 + 2.76762e9i −0.349081 + 0.727667i
\(547\) −7.94068e8 7.94068e8i −0.207445 0.207445i 0.595736 0.803180i \(-0.296861\pi\)
−0.803180 + 0.595736i \(0.796861\pi\)
\(548\) 8.43294e8 + 2.30460e9i 0.218901 + 0.598224i
\(549\) −1.12559e9 5.57647e8i −0.290321 0.143832i
\(550\) 9.44924e8 1.67453e8i 0.242174 0.0429164i
\(551\) 1.59819e9i 0.407003i
\(552\) −3.08643e9 + 2.54157e9i −0.781034 + 0.643153i
\(553\) 2.64019e8i 0.0663891i
\(554\) −1.32992e9 7.50467e9i −0.332310 1.87520i
\(555\) 4.98352e8 6.94107e8i 0.123740 0.172346i
\(556\) −2.62477e9 1.21847e9i −0.647635 0.300643i
\(557\) −1.24382e9 1.24382e9i −0.304974 0.304974i 0.537982 0.842956i \(-0.319187\pi\)
−0.842956 + 0.537982i \(0.819187\pi\)
\(558\) 1.87796e9 + 5.49356e8i 0.457578 + 0.133855i
\(559\) 5.40400e9i 1.30850i
\(560\) 6.36940e8 7.58021e9i 0.153264 1.82399i
\(561\) 7.16666e7 + 4.36565e8i 0.0171375 + 0.104395i
\(562\) 3.07693e9 + 2.15055e9i 0.731208 + 0.511062i
\(563\) −1.51669e9 + 1.51669e9i −0.358194 + 0.358194i −0.863147 0.504953i \(-0.831510\pi\)
0.504953 + 0.863147i \(0.331510\pi\)
\(564\) 6.12212e9 + 1.70691e9i 1.43689 + 0.400621i
\(565\) −7.32479e9 7.32479e9i −1.70854 1.70854i
\(566\) 8.74413e8 1.54957e8i 0.202703 0.0359215i
\(567\) −3.29145e9 + 2.50651e9i −0.758309 + 0.577470i
\(568\) 2.39172e9 + 6.34256e8i 0.547634 + 0.145226i
\(569\) −3.99792e9 −0.909790 −0.454895 0.890545i \(-0.650323\pi\)
−0.454895 + 0.890545i \(0.650323\pi\)
\(570\) 5.62166e9 1.97658e9i 1.27146 0.447047i
\(571\) −2.85797e8 + 2.85797e8i −0.0642438 + 0.0642438i −0.738499 0.674255i \(-0.764465\pi\)
0.674255 + 0.738499i \(0.264465\pi\)
\(572\) −1.19169e8 3.25671e8i −0.0266242 0.0727601i
\(573\) 4.93916e9 6.87927e9i 1.09676 1.52757i
\(574\) 5.64103e9 + 3.94268e9i 1.24499 + 0.870161i
\(575\) −1.23972e10 −2.71948
\(576\) −8.79821e8 + 4.50129e9i −0.191830 + 0.981428i
\(577\) 5.79824e9 1.25655 0.628276 0.777990i \(-0.283761\pi\)
0.628276 + 0.777990i \(0.283761\pi\)
\(578\) 1.28126e9 + 8.95509e8i 0.275988 + 0.192896i
\(579\) −2.65373e9 + 3.69612e9i −0.568174 + 0.791354i
\(580\) −1.79827e9 4.91441e9i −0.382699 1.04586i
\(581\) 3.24315e9 3.24315e9i 0.686041 0.686041i
\(582\) 2.46706e9 8.67424e8i 0.518740 0.182390i
\(583\) −6.67531e8 −0.139518
\(584\) −6.95223e8 1.84365e8i −0.144437 0.0383031i
\(585\) 7.46047e9 2.51726e9i 1.54071 0.519855i
\(586\) −2.35587e9 + 4.17491e8i −0.483626 + 0.0857048i
\(587\) 1.91942e9 + 1.91942e9i 0.391686 + 0.391686i 0.875288 0.483602i \(-0.160672\pi\)
−0.483602 + 0.875288i \(0.660672\pi\)
\(588\) −4.34475e8 1.21136e8i −0.0881342 0.0245727i
\(589\) 1.17330e9 1.17330e9i 0.236595 0.236595i
\(590\) −9.75317e8 6.81676e8i −0.195508 0.136646i
\(591\) −1.07374e8 6.54081e8i −0.0213965 0.130339i
\(592\) 5.55761e8 + 4.66987e7i 0.110094 + 0.00925079i
\(593\) 2.03450e9i 0.400652i −0.979729 0.200326i \(-0.935800\pi\)
0.979729 0.200326i \(-0.0642001\pi\)
\(594\) 5.68252e7 4.63930e8i 0.0111247 0.0908239i
\(595\) 7.68892e9 + 7.68892e9i 1.49643 + 1.49643i
\(596\) −5.03485e9 2.33726e9i −0.974147 0.452216i
\(597\) −3.89948e9 + 5.43121e9i −0.750062 + 1.04469i
\(598\) 7.81734e8 + 4.41127e9i 0.149487 + 0.843547i
\(599\) 2.22251e9i 0.422522i −0.977430 0.211261i \(-0.932243\pi\)
0.977430 0.211261i \(-0.0677571\pi\)
\(600\) −1.09782e10 + 9.04011e9i −2.07491 + 1.70862i
\(601\) 6.17762e9i 1.16081i 0.814328 + 0.580405i \(0.197106\pi\)
−0.814328 + 0.580405i \(0.802894\pi\)
\(602\) −7.76363e9 + 1.37582e9i −1.45036 + 0.257023i
\(603\) 1.15466e9 2.33064e9i 0.214458 0.432878i
\(604\) −1.38831e9 3.79406e9i −0.256364 0.700607i
\(605\) 7.33441e9 + 7.33441e9i 1.34655 + 1.34655i
\(606\) −5.16179e8 + 1.07599e9i −0.0942206 + 0.196405i
\(607\) 4.76558e9i 0.864878i 0.901663 + 0.432439i \(0.142347\pi\)
−0.901663 + 0.432439i \(0.857653\pi\)
\(608\) 2.99020e9 + 2.48726e9i 0.539557 + 0.448807i
\(609\) 3.04034e9 4.99103e8i 0.545459 0.0895425i
\(610\) 1.99821e9 2.85896e9i 0.356440 0.509981i
\(611\) 5.03566e9 5.03566e9i 0.893124 0.893124i
\(612\) −4.10308e9 5.11351e9i −0.723569 0.901757i
\(613\) 2.49971e9 + 2.49971e9i 0.438307 + 0.438307i 0.891442 0.453135i \(-0.149695\pi\)
−0.453135 + 0.891442i \(0.649695\pi\)
\(614\) 7.25919e8 + 4.09631e9i 0.126561 + 0.714173i
\(615\) −2.85971e9 1.74202e10i −0.495746 3.01989i
\(616\) −4.37535e8 + 2.54117e8i −0.0754188 + 0.0438027i
\(617\) −2.98038e9 −0.510827 −0.255414 0.966832i \(-0.582212\pi\)
−0.255414 + 0.966832i \(0.582212\pi\)
\(618\) 8.87435e9 3.12024e9i 1.51244 0.531775i
\(619\) −5.34568e9 + 5.34568e9i −0.905912 + 0.905912i −0.995939 0.0900274i \(-0.971305\pi\)
0.0900274 + 0.995939i \(0.471305\pi\)
\(620\) −2.28769e9 + 4.92807e9i −0.385502 + 0.830435i
\(621\) −1.76863e9 + 5.77324e9i −0.296358 + 0.967385i
\(622\) −2.67605e9 + 3.82879e9i −0.445890 + 0.637963i
\(623\) 6.66004e9 1.10349
\(624\) 3.90898e9 + 3.33629e9i 0.644046 + 0.549690i
\(625\) −2.15867e10 −3.53677
\(626\) −5.38298e9 + 7.70177e9i −0.877026 + 1.25482i
\(627\) −3.21972e8 2.31169e8i −0.0521654 0.0374535i
\(628\) 2.40287e9 + 1.11546e9i 0.387144 + 0.179719i
\(629\) −5.63731e8 + 5.63731e8i −0.0903222 + 0.0903222i
\(630\) −5.51579e9 1.00772e10i −0.878852 1.60564i
\(631\) 8.39547e9 1.33028 0.665139 0.746720i \(-0.268372\pi\)
0.665139 + 0.746720i \(0.268372\pi\)
\(632\) −4.27253e8 1.13303e8i −0.0673248 0.0178538i
\(633\) 5.94528e9 9.75977e8i 0.931663 0.152942i
\(634\) −5.77767e8 3.26030e9i −0.0900410 0.508095i
\(635\) 2.12728e9 + 2.12728e9i 0.329699 + 0.329699i
\(636\) 8.61653e9 4.85932e9i 1.32811 0.748990i
\(637\) −3.57371e8 + 3.57371e8i −0.0547811 + 0.0547811i
\(638\) −1.99405e8 + 2.85302e8i −0.0303994 + 0.0434943i
\(639\) 3.54069e9 1.19468e9i 0.536828 0.181133i
\(640\) −1.19935e10 4.28376e9i −1.80849 0.645944i
\(641\) 7.18143e8i 0.107698i −0.998549 0.0538490i \(-0.982851\pi\)
0.998549 0.0538490i \(-0.0171490\pi\)
\(642\) 4.68090e9 + 2.24555e9i 0.698163 + 0.334927i
\(643\) −7.16100e9 7.16100e9i −1.06227 1.06227i −0.997928 0.0643437i \(-0.979505\pi\)
−0.0643437 0.997928i \(-0.520495\pi\)
\(644\) 6.13840e9 2.24615e9i 0.905639 0.331389i
\(645\) 1.64285e10 + 1.17953e10i 2.41068 + 1.73081i
\(646\) −5.47449e9 + 9.70152e8i −0.798970 + 0.141588i
\(647\) 7.88616e9i 1.14472i 0.820001 + 0.572362i \(0.193973\pi\)
−0.820001 + 0.572362i \(0.806027\pi\)
\(648\) 2.64370e9 + 6.40211e9i 0.381680 + 0.924294i
\(649\) 7.91482e7i 0.0113654i
\(650\) 2.78055e9 + 1.56905e10i 0.397132 + 2.24099i
\(651\) −2.59846e9 1.86563e9i −0.369132 0.265028i
\(652\) 8.90443e8 1.91816e9i 0.125817 0.271031i
\(653\) 6.09780e9 + 6.09780e9i 0.856993 + 0.856993i 0.990983 0.133990i \(-0.0427790\pi\)
−0.133990 + 0.990983i \(0.542779\pi\)
\(654\) 8.14581e8 1.69801e9i 0.113871 0.237366i
\(655\) 1.90912e10i 2.65453i
\(656\) 8.80113e9 7.43672e9i 1.21724 1.02853i
\(657\) −1.02921e9 + 3.47268e8i −0.141587 + 0.0477734i
\(658\) −8.51649e9 5.95241e9i −1.16539 0.814521i
\(659\) −4.02156e9 + 4.02156e9i −0.547388 + 0.547388i −0.925684 0.378297i \(-0.876510\pi\)
0.378297 + 0.925684i \(0.376510\pi\)
\(660\) 1.25017e9 + 3.48560e8i 0.169264 + 0.0471926i
\(661\) 2.04154e9 + 2.04154e9i 0.274950 + 0.274950i 0.831089 0.556139i \(-0.187718\pi\)
−0.556139 + 0.831089i \(0.687718\pi\)
\(662\) −1.64175e9 + 2.90940e8i −0.219940 + 0.0389762i
\(663\) −7.24917e9 + 1.19002e9i −0.966031 + 0.158584i
\(664\) −3.85650e9 6.64007e9i −0.511216 0.880205i
\(665\) −9.74209e9 −1.28462
\(666\) 7.38831e8 4.04402e8i 0.0969137 0.0530462i
\(667\) 3.17963e9 3.17963e9i 0.414893 0.414893i
\(668\) −2.39730e9 + 8.77215e8i −0.311175 + 0.113865i
\(669\) 3.46659e9 + 2.48893e9i 0.447622 + 0.321382i
\(670\) 5.91974e9 + 4.13747e9i 0.760398 + 0.531463i
\(671\) −2.32008e8 −0.0296466
\(672\) 3.79787e9 6.46521e9i 0.482778 0.821845i
\(673\) 5.02685e8 0.0635687 0.0317843 0.999495i \(-0.489881\pi\)
0.0317843 + 0.999495i \(0.489881\pi\)
\(674\) −1.10597e10 7.72993e9i −1.39134 0.972447i
\(675\) −6.29085e9 + 2.05349e10i −0.787310 + 2.56998i
\(676\) −2.13493e9 + 7.81208e8i −0.265809 + 0.0972642i
\(677\) −4.92963e9 + 4.92963e9i −0.610596 + 0.610596i −0.943101 0.332505i \(-0.892106\pi\)
0.332505 + 0.943101i \(0.392106\pi\)
\(678\) −3.38686e9 9.63266e9i −0.417343 1.18698i
\(679\) −4.27532e9 −0.524112
\(680\) 1.57424e10 9.14306e9i 1.91995 1.11509i
\(681\) 4.53071e8 + 2.75994e9i 0.0549733 + 0.334876i
\(682\) 3.55844e8 6.30602e7i 0.0429551 0.00761220i
\(683\) −7.74114e9 7.74114e9i −0.929678 0.929678i 0.0680069 0.997685i \(-0.478336\pi\)
−0.997685 + 0.0680069i \(0.978336\pi\)
\(684\) 5.83885e9 + 6.40126e8i 0.697639 + 0.0764838i
\(685\) −7.27679e9 + 7.27679e9i −0.865014 + 0.865014i
\(686\) 7.21017e9 + 5.03939e9i 0.852729 + 0.595996i
\(687\) 5.35042e7 8.78326e6i 0.00629564 0.00103349i
\(688\) −1.10529e9 + 1.31541e10i −0.129395 + 1.53993i
\(689\) 1.10844e10i 1.29105i
\(690\) −1.51168e10 7.25194e9i −1.75182 0.840392i
\(691\) 6.55081e9 + 6.55081e9i 0.755304 + 0.755304i 0.975464 0.220160i \(-0.0706579\pi\)
−0.220160 + 0.975464i \(0.570658\pi\)
\(692\) 2.89833e9 6.24347e9i 0.332488 0.716234i
\(693\) −3.39218e8 + 6.84702e8i −0.0387180 + 0.0781511i
\(694\) 1.05531e9 + 5.95503e9i 0.119845 + 0.676279i
\(695\) 1.21351e10i 1.37118i
\(696\) 4.97068e8 5.13427e9i 0.0558835 0.577227i
\(697\) 1.64707e10i 1.84246i
\(698\) 5.01738e9 8.89145e8i 0.558449 0.0989644i
\(699\) −7.95290e9 + 1.10768e10i −0.880756 + 1.22672i
\(700\) 2.18337e10 7.98934e9i 2.40594 0.880376i
\(701\) 1.99853e9 + 1.99853e9i 0.219128 + 0.219128i 0.808131 0.589003i \(-0.200479\pi\)
−0.589003 + 0.808131i \(0.700479\pi\)
\(702\) 7.70357e9 + 9.43584e8i 0.840450 + 0.102944i
\(703\) 7.14263e8i 0.0775380i
\(704\) 2.23463e8 + 8.17101e8i 0.0241380 + 0.0882616i
\(705\) 4.31742e9 + 2.63000e10i 0.464047 + 2.82680i
\(706\) 1.45642e9 2.08379e9i 0.155765 0.222863i
\(707\) 1.37958e9 1.37958e9i 0.146818 0.146818i
\(708\) −5.76163e8 1.02165e9i −0.0610140 0.108190i
\(709\) −2.22347e9 2.22347e9i −0.234299 0.234299i 0.580186 0.814484i \(-0.302980\pi\)
−0.814484 + 0.580186i \(0.802980\pi\)
\(710\) 1.81059e9 + 1.02171e10i 0.189853 + 1.07133i
\(711\) −6.32505e8 + 2.13415e8i −0.0659964 + 0.0222680i
\(712\) 2.85813e9 1.07777e10i 0.296758 1.11905i
\(713\) −4.66860e9 −0.482362
\(714\) 3.55523e9 + 1.01115e10i 0.365531 + 1.03962i
\(715\) 1.02831e9 1.02831e9i 0.105209 0.105209i
\(716\) 8.30276e9 + 3.85429e9i 0.845331 + 0.392417i
\(717\) 3.15686e9 4.39689e9i 0.319844 0.445480i
\(718\) 4.88021e9 6.98242e9i 0.492043 0.703997i
\(719\) −6.96861e9 −0.699189 −0.349595 0.936901i \(-0.613681\pi\)
−0.349595 + 0.936901i \(0.613681\pi\)
\(720\) −1.86746e10 + 4.60144e9i −1.86461 + 0.459441i
\(721\) −1.53789e10 −1.52810
\(722\) −2.93989e9 + 4.20629e9i −0.290704 + 0.415929i
\(723\) 5.58949e9 7.78506e9i 0.550032 0.766087i
\(724\) −4.14124e9 + 8.92091e9i −0.405551 + 0.873624i
\(725\) 1.13096e10 1.13096e10i 1.10221 1.10221i
\(726\) 3.39131e9 + 9.64531e9i 0.328919 + 0.935488i
\(727\) 9.65672e9 0.932093 0.466047 0.884760i \(-0.345678\pi\)
0.466047 + 0.884760i \(0.345678\pi\)
\(728\) −4.21961e9 7.26527e9i −0.405333 0.697898i
\(729\) 8.66540e9 + 5.85916e9i 0.828404 + 0.560130i
\(730\) −5.26303e8 2.96989e9i −0.0500733 0.282560i
\(731\) −1.33427e10 1.33427e10i −1.26338 1.26338i
\(732\) 2.99478e9 1.68892e9i 0.282212 0.159155i
\(733\) 1.48172e10 1.48172e10i 1.38964 1.38964i 0.563561 0.826075i \(-0.309431\pi\)
0.826075 0.563561i \(-0.190569\pi\)
\(734\) 4.44608e8 6.36128e8i 0.0414993 0.0593757i
\(735\) −3.06399e8 1.86646e9i −0.0284630 0.173386i
\(736\) −1.00060e9 1.08975e10i −0.0925099 1.00752i
\(737\) 4.80394e8i 0.0442040i
\(738\) 4.88556e9 1.67011e10i 0.447422 1.52950i
\(739\) 1.17557e10 + 1.17557e10i 1.07150 + 1.07150i 0.997239 + 0.0742612i \(0.0236599\pi\)
0.0742612 + 0.997239i \(0.476340\pi\)
\(740\) 8.03683e8 + 2.19635e9i 0.0729078 + 0.199247i
\(741\) 3.83856e9 5.34636e9i 0.346581 0.482719i
\(742\) −1.59243e10 + 2.82199e9i −1.43102 + 0.253596i
\(743\) 9.46323e9i 0.846406i 0.906035 + 0.423203i \(0.139094\pi\)
−0.906035 + 0.423203i \(0.860906\pi\)
\(744\) −4.13421e9 + 3.40437e9i −0.368033 + 0.303062i
\(745\) 2.32775e10i 2.06248i
\(746\) −2.83025e9 1.59709e10i −0.249597 1.40846i
\(747\) −1.03911e10 5.14800e9i −0.912093 0.451873i
\(748\) −1.09833e9 5.09863e8i −0.0959570 0.0445449i
\(749\) −6.00162e9 6.00162e9i −0.521893 0.521893i
\(750\) −3.37648e10 1.61978e10i −2.92247 1.40198i
\(751\) 2.05325e10i 1.76889i 0.466641 + 0.884447i \(0.345464\pi\)
−0.466641 + 0.884447i \(0.654536\pi\)
\(752\) −1.32874e10 + 1.12275e10i −1.13941 + 0.962767i
\(753\) −1.73033e9 + 2.84051e8i −0.147688 + 0.0242445i
\(754\) −4.73744e9 3.31113e9i −0.402480 0.281304i
\(755\) 1.19798e10 1.19798e10i 1.01306 1.01306i
\(756\) −6.05674e8 1.13075e10i −0.0509815 0.951791i
\(757\) −1.78178e9 1.78178e9i −0.149286 0.149286i 0.628513 0.777799i \(-0.283664\pi\)
−0.777799 + 0.628513i \(0.783664\pi\)
\(758\) −2.97267e9 + 5.26795e8i −0.247916 + 0.0439339i
\(759\) 1.80656e8 + 1.10048e9i 0.0149970 + 0.0913561i
\(760\) −4.18078e9 + 1.57653e10i −0.345469 + 1.30273i
\(761\) 1.53743e10 1.26459 0.632294 0.774729i \(-0.282114\pi\)
0.632294 + 0.774729i \(0.282114\pi\)
\(762\) 9.83620e8 + 2.79754e9i 0.0805351 + 0.229052i
\(763\) −2.17711e9 + 2.17711e9i −0.177437 + 0.177437i
\(764\) 7.96528e9 + 2.17680e10i 0.646211 + 1.76600i
\(765\) 1.22050e10 2.46354e10i 0.985649 1.98951i
\(766\) 1.50946e10 + 1.05500e10i 1.21345 + 0.848112i
\(767\) −1.31426e9 −0.105171
\(768\) −8.83260e9 8.92049e9i −0.703598 0.710599i
\(769\) −1.44722e10 −1.14761 −0.573804 0.818992i \(-0.694533\pi\)
−0.573804 + 0.818992i \(0.694533\pi\)
\(770\) −1.73911e9 1.21552e9i −0.137281 0.0959496i
\(771\) −1.02123e10 7.33222e9i −0.802480 0.576162i
\(772\) −4.27961e9 1.16956e10i −0.334768 0.914873i
\(773\) 6.14800e8 6.14800e8i 0.0478747 0.0478747i −0.682764 0.730639i \(-0.739222\pi\)
0.730639 + 0.682764i \(0.239222\pi\)
\(774\) 9.57163e9 + 1.74871e10i 0.741980 + 1.35558i
\(775\) −1.66058e10 −1.28145
\(776\) −1.83473e9 + 6.91861e9i −0.140947 + 0.531499i
\(777\) −1.35879e9 + 2.23059e8i −0.103915 + 0.0170587i
\(778\) 8.33729e9 1.47748e9i 0.634741 0.112484i
\(779\) −1.04344e10 1.04344e10i −0.790839 0.790839i
\(780\) −5.78785e9 + 2.07591e10i −0.436703 + 1.56631i
\(781\) 4.88029e8 4.88029e8i 0.0366579 0.0366579i
\(782\) 1.28217e10 + 8.96147e9i 0.958790 + 0.670125i
\(783\) −3.65330e9 6.88025e9i −0.271969 0.512198i
\(784\) 9.42983e8 7.96795e8i 0.0698872 0.0590528i
\(785\) 1.11091e10i 0.819666i
\(786\) 8.13947e9 1.69669e10i 0.597884 1.24630i
\(787\) 1.25091e10 + 1.25091e10i 0.914772 + 0.914772i 0.996643 0.0818710i \(-0.0260896\pi\)
−0.0818710 + 0.996643i \(0.526090\pi\)
\(788\) 1.64556e9 + 7.63899e8i 0.119804 + 0.0556153i
\(789\) −2.20306e10 1.58174e10i −1.59682 1.14648i
\(790\) −3.23442e8 1.82516e9i −0.0233401 0.131706i
\(791\) 1.66930e10i 1.19927i
\(792\) 9.62457e8 + 8.42783e8i 0.0688404 + 0.0602806i
\(793\) 3.85250e9i 0.274339i
\(794\) 9.62972e9 1.70651e9i 0.682719 0.120987i
\(795\) 3.36972e10 + 2.41938e10i 2.37853 + 1.70773i
\(796\) −6.28862e9 1.71859e10i −0.441937 1.20775i
\(797\) 3.62593e9 + 3.62593e9i 0.253697 + 0.253697i 0.822484 0.568788i \(-0.192587\pi\)
−0.568788 + 0.822484i \(0.692587\pi\)
\(798\) −8.65809e9 4.15351e9i −0.603131 0.289338i
\(799\) 2.48665e10i 1.72465i
\(800\) −3.55904e9 3.87614e10i −0.245764 2.67661i
\(801\) −5.38354e9 1.59554e10i −0.370130 1.09696i
\(802\) −1.38663e10 + 1.98394e10i −0.949184 + 1.35806i
\(803\) −1.41860e8 + 1.41860e8i −0.00966843 + 0.00966843i
\(804\) 3.49706e9 + 6.20096e9i 0.237305 + 0.420788i
\(805\) 1.93821e10 + 1.93821e10i 1.30953 + 1.30953i
\(806\) 1.04712e9 + 5.90880e9i 0.0704404 + 0.397490i
\(807\) 1.43904e10 2.36233e9i 0.963864 0.158228i
\(808\) −1.64049e9 2.82457e9i −0.109404 0.188370i
\(809\) −8.97245e9 −0.595787 −0.297894 0.954599i \(-0.596284\pi\)
−0.297894 + 0.954599i \(0.596284\pi\)
\(810\) −1.96831e10 + 2.13598e10i −1.30136 + 1.41221i
\(811\) 4.56809e9 4.56809e9i 0.300720 0.300720i −0.540576 0.841295i \(-0.681794\pi\)
0.841295 + 0.540576i \(0.181794\pi\)
\(812\) −3.55080e9 + 7.64901e9i −0.232745 + 0.501371i
\(813\) −1.09129e10 7.83521e9i −0.712235 0.511368i
\(814\) 8.91183e7 1.27507e8i 0.00579137 0.00828608i
\(815\) 8.86819e9 0.573830
\(816\) 1.78889e10 1.41399e9i 1.15257 0.0911027i
\(817\) 1.69056e10 1.08456
\(818\) −1.78979e9 + 2.56076e9i −0.114331 + 0.163581i
\(819\) −1.13695e10 5.63272e9i −0.723181 0.358281i
\(820\) 4.38265e10 + 2.03450e10i 2.77580 + 1.28858i
\(821\) −6.85603e9 + 6.85603e9i −0.432386 + 0.432386i −0.889439 0.457053i \(-0.848905\pi\)
0.457053 + 0.889439i \(0.348905\pi\)
\(822\) −9.56955e9 + 3.36467e9i −0.600952 + 0.211296i
\(823\) −1.30667e10 −0.817082 −0.408541 0.912740i \(-0.633962\pi\)
−0.408541 + 0.912740i \(0.633962\pi\)
\(824\) −6.59978e9 + 2.48871e10i −0.410946 + 1.54964i
\(825\) 6.42575e8 + 3.91432e9i 0.0398414 + 0.242699i
\(826\) 3.34600e8 + 1.88812e9i 0.0206583 + 0.116573i
\(827\) −4.65003e9 4.65003e9i −0.285881 0.285881i 0.549568 0.835449i \(-0.314792\pi\)
−0.835449 + 0.549568i \(0.814792\pi\)
\(828\) −1.03429e10 1.28900e10i −0.633196 0.789128i
\(829\) −1.79452e10 + 1.79452e10i −1.09398 + 1.09398i −0.0988778 + 0.995100i \(0.531525\pi\)
−0.995100 + 0.0988778i \(0.968475\pi\)
\(830\) 1.84468e10 2.63930e10i 1.11982 1.60219i
\(831\) 3.10879e10 5.10339e9i 1.87926 0.308500i
\(832\) −1.35680e10 + 3.71060e9i −0.816739 + 0.223364i
\(833\) 1.76473e9i 0.105784i
\(834\) 5.17374e9 1.07848e10i 0.308833 0.643770i
\(835\) −7.56950e9 7.56950e9i −0.449950 0.449950i
\(836\) 1.01881e9 3.72801e8i 0.0603077 0.0220676i
\(837\) −2.36904e9 + 7.73313e9i −0.139647 + 0.455844i
\(838\) 2.13383e9 3.78142e8i 0.125258 0.0221973i
\(839\) 3.63912e8i 0.0212730i 0.999943 + 0.0106365i \(0.00338577\pi\)
−0.999943 + 0.0106365i \(0.996614\pi\)
\(840\) 3.12970e10 + 3.02998e9i 1.82190 + 0.176385i
\(841\) 1.14485e10i 0.663686i
\(842\) 3.43233e8 + 1.93684e9i 0.0198151 + 0.111815i
\(843\) −9.04994e9 + 1.26048e10i −0.520294 + 0.724667i
\(844\) −6.94346e9 + 1.49574e10i −0.397537 + 0.856360i
\(845\) −6.74105e9 6.74105e9i −0.384352 0.384352i
\(846\) −7.37592e9 + 2.52144e10i −0.418813 + 1.43170i
\(847\) 1.67149e10i 0.945174i
\(848\) −2.26711e9 + 2.69808e10i −0.127669 + 1.51939i
\(849\) 5.94626e8 + 3.62223e9i 0.0333478 + 0.203142i
\(850\) 4.56057e10 + 3.18751e10i 2.54714 + 1.78027i
\(851\) −1.42104e9 + 1.42104e9i −0.0790410 + 0.0790410i
\(852\) −2.74688e9 + 9.85215e9i −0.152160 + 0.545748i
\(853\) 1.45667e10 + 1.45667e10i 0.803598 + 0.803598i 0.983656 0.180058i \(-0.0576285\pi\)
−0.180058 + 0.983656i \(0.557628\pi\)
\(854\) −5.53468e9 + 9.80818e8i −0.304082 + 0.0538872i
\(855\) 7.87486e9 + 2.33389e10i 0.430885 + 1.27703i
\(856\) −1.22878e10 + 7.13665e9i −0.669600 + 0.388899i
\(857\) −7.23133e9 −0.392451 −0.196225 0.980559i \(-0.562868\pi\)
−0.196225 + 0.980559i \(0.562868\pi\)
\(858\) 1.35231e9 4.75473e8i 0.0730919 0.0256992i
\(859\) 1.81480e10 1.81480e10i 0.976906 0.976906i −0.0228336 0.999739i \(-0.507269\pi\)
0.999739 + 0.0228336i \(0.00726879\pi\)
\(860\) −5.19845e10 + 1.90220e10i −2.78695 + 1.01979i
\(861\) −1.65915e10 + 2.31087e10i −0.885881 + 1.23386i
\(862\) −2.23634e10 1.56304e10i −1.18922 0.831181i
\(863\) −1.94578e10 −1.03052 −0.515259 0.857035i \(-0.672304\pi\)
−0.515259 + 0.857035i \(0.672304\pi\)
\(864\) −1.85585e10 3.87244e9i −0.978916 0.204261i
\(865\) 2.88653e10 1.51642
\(866\) −1.76101e10 1.23082e10i −0.921401 0.643993i
\(867\) −3.76847e9 + 5.24874e9i −0.196381 + 0.273519i
\(868\) 8.22226e9 3.00867e9i 0.426749 0.156155i
\(869\) −8.71809e7 + 8.71809e7i −0.00450663 + 0.00450663i
\(870\) 2.04064e10 7.17494e9i 1.05063 0.369403i
\(871\) 7.97695e9 0.409047
\(872\) 2.58885e9 + 4.45745e9i 0.132221 + 0.227656i
\(873\) 3.45588e9 + 1.02423e10i 0.175796 + 0.521012i
\(874\) −1.38000e10 + 2.44554e9i −0.699179 + 0.123904i
\(875\) 4.32915e10 + 4.32915e10i 2.18461 + 2.18461i
\(876\) 7.98462e8 2.86382e9i 0.0401319 0.143940i
\(877\) 1.47073e10 1.47073e10i 0.736266 0.736266i −0.235587 0.971853i \(-0.575701\pi\)
0.971853 + 0.235587i \(0.0757014\pi\)
\(878\) 4.78502e9 + 3.34438e9i 0.238590 + 0.166757i
\(879\) −1.60206e9 9.75912e9i −0.0795641 0.484674i
\(880\) −2.71336e9 + 2.29272e9i −0.134220 + 0.113413i
\(881\) 3.79505e10i 1.86983i −0.354875 0.934914i \(-0.615477\pi\)
0.354875 0.934914i \(-0.384523\pi\)
\(882\) 5.23455e8 1.78941e9i 0.0256885 0.0878154i
\(883\) −2.30991e10 2.30991e10i −1.12910 1.12910i −0.990324 0.138776i \(-0.955683\pi\)
−0.138776 0.990324i \(-0.544317\pi\)
\(884\) 8.46628e9 1.82378e10i 0.412202 0.887950i
\(885\) 2.86862e9 3.99543e9i 0.139114 0.193759i
\(886\) 1.31406e9 + 7.41516e9i 0.0634743 + 0.358181i
\(887\) 2.25109e10i 1.08308i −0.840676 0.541539i \(-0.817842\pi\)
0.840676 0.541539i \(-0.182158\pi\)
\(888\) −2.22150e8 + 2.29461e9i −0.0106464 + 0.109967i
\(889\) 4.84802e9i 0.231424i
\(890\) 4.60409e10 8.15904e9i 2.18917 0.387949i
\(891\) 1.91453e9 + 2.59191e8i 0.0906755 + 0.0122757i
\(892\) −1.09693e10 + 4.01385e9i −0.517489 + 0.189358i
\(893\) 1.57533e10 + 1.57533e10i 0.740272 + 0.740272i
\(894\) 9.92428e9 2.06874e10i 0.464534 0.968333i
\(895\) 3.83860e10i 1.78975i
\(896\) 8.78512e9 + 1.85477e10i 0.408009 + 0.861413i
\(897\) −1.82736e10 + 2.99979e9i −0.845375 + 0.138777i
\(898\) 3.11020e9 4.44996e9i 0.143325 0.205064i
\(899\) 4.25904e9 4.25904e9i 0.195503 0.195503i
\(900\) −3.67889e10 4.58486e10i −1.68216 2.09642i
\(901\) −2.73677e10 2.73677e10i −1.24653 1.24653i
\(902\) −5.60810e8 3.16461e9i −0.0254444 0.143581i
\(903\) −5.27949e9 3.21606e10i −0.238608 1.45351i
\(904\) 2.70137e10 + 7.16373e9i 1.21617 + 0.322515i
\(905\) −4.12438e10 −1.84965
\(906\) 1.57543e10 5.53924e9i 0.703802 0.247458i
\(907\) 1.81420e10 1.81420e10i 0.807344 0.807344i −0.176887 0.984231i \(-0.556603\pi\)
0.984231 + 0.176887i \(0.0566028\pi\)
\(908\) −6.94356e9 3.22332e9i −0.307809 0.142890i
\(909\) −4.42019e9 2.18987e9i −0.195194 0.0967040i
\(910\) 2.01836e10 2.88780e10i 0.887881 1.27035i
\(911\) 1.51339e9 0.0663189 0.0331595 0.999450i \(-0.489443\pi\)
0.0331595 + 0.999450i \(0.489443\pi\)
\(912\) −1.04371e10 + 1.22286e10i −0.455614 + 0.533822i
\(913\) −2.14182e9 −0.0931399
\(914\) −1.23809e10 + 1.77142e10i −0.536342 + 0.767378i
\(915\) 1.17119e10 + 8.40885e9i 0.505420 + 0.362880i
\(916\) −6.24874e7 + 1.34608e8i −0.00268632 + 0.00578678i
\(917\) −2.17541e10 + 2.17541e10i −0.931642 + 0.931642i
\(918\) 2.13502e10 1.66907e10i 0.910861 0.712073i
\(919\) −1.96115e10 −0.833502 −0.416751 0.909021i \(-0.636831\pi\)
−0.416751 + 0.909021i \(0.636831\pi\)
\(920\) 3.96831e10 2.30476e10i 1.68015 0.975818i
\(921\) −1.69688e10 + 2.78561e9i −0.715721 + 0.117493i
\(922\) −3.83210e9 2.16243e10i −0.161020 0.908622i
\(923\) 8.10373e9 + 8.10373e9i 0.339218 + 0.339218i
\(924\) −1.02737e9 1.82173e9i −0.0428426 0.0759683i
\(925\) −5.05451e9 + 5.05451e9i −0.209982 + 0.209982i
\(926\) 1.49558e10 2.13981e10i 0.618970 0.885600i
\(927\) 1.24313e10 + 3.68429e10i 0.512550 + 1.51906i
\(928\) 1.08543e10 + 9.02869e9i 0.445846 + 0.370857i
\(929\) 2.16188e10i 0.884660i −0.896852 0.442330i \(-0.854152\pi\)
0.896852 0.442330i \(-0.145848\pi\)
\(930\) −2.02487e10 9.71381e9i −0.825479 0.396004i
\(931\) −1.11798e9 1.11798e9i −0.0454057 0.0454057i
\(932\) −1.28255e10 3.50502e10i −0.518941 1.41819i
\(933\) −1.56848e10 1.12613e10i −0.632256 0.453945i
\(934\) 2.43729e10 4.31920e9i 0.978799 0.173456i
\(935\) 5.07787e9i 0.203161i
\(936\) −1.39944e10 + 1.59816e10i −0.557814 + 0.637023i
\(937\) 1.51515e10i 0.601682i 0.953674 + 0.300841i \(0.0972673\pi\)
−0.953674 + 0.300841i \(0.902733\pi\)
\(938\) −2.03087e9 1.14601e10i −0.0803475 0.453395i
\(939\) −3.15506e10 2.26526e10i −1.24359 0.892871i
\(940\) −6.61666e10 3.07157e10i −2.59831 1.20618i
\(941\) −3.51178e9 3.51178e9i −0.137393 0.137393i 0.635066 0.772458i \(-0.280973\pi\)
−0.772458 + 0.635066i \(0.780973\pi\)
\(942\) −4.73635e9 + 9.87303e9i −0.184614 + 0.384833i
\(943\) 4.15190e10i 1.61234i
\(944\) 3.19908e9 + 2.68808e8i 0.123772 + 0.0104002i
\(945\) 4.19400e10 2.22695e10i 1.61665 0.858417i
\(946\) 3.01791e9 + 2.10930e9i 0.115901 + 0.0810065i
\(947\) −3.02280e10 + 3.02280e10i −1.15660 + 1.15660i −0.171402 + 0.985201i \(0.554830\pi\)
−0.985201 + 0.171402i \(0.945170\pi\)
\(948\) 4.90699e8 1.75997e9i 0.0187062 0.0670930i
\(949\) −2.35559e9 2.35559e9i −0.0894680 0.0894680i
\(950\) −4.90853e10 + 8.69855e9i −1.85746 + 0.329165i
\(951\) 1.35057e10 2.21710e9i 0.509196 0.0835897i
\(952\) −2.83566e10 7.51985e9i −1.06519 0.282475i
\(953\) 3.27290e10 1.22492 0.612461 0.790501i \(-0.290180\pi\)
0.612461 + 0.790501i \(0.290180\pi\)
\(954\) 1.96327e10 + 3.58684e10i 0.732085 + 1.33750i
\(955\) −6.87325e10 + 6.87325e10i −2.55359 + 2.55359i
\(956\) 5.09101e9 + 1.39130e10i 0.188452 + 0.515013i
\(957\) −1.16875e9 8.39135e8i −0.0431052 0.0309485i
\(958\) −2.23360e10 1.56112e10i −0.820778 0.573665i
\(959\) 1.65836e10 0.607175
\(960\) 1.83343e10 4.93467e10i 0.668829 1.80015i
\(961\) 2.12591e10 0.772705
\(962\) 2.11726e9 + 1.47981e9i 0.0766763 + 0.0535912i
\(963\) −9.52665e9 + 1.92293e10i −0.343754 + 0.693859i
\(964\) 9.01407e9 + 2.46341e10i 0.324079 + 0.885662i
\(965\) 3.69288e10 3.69288e10i 1.32288 1.32288i
\(966\) 8.96194e9 + 2.54889e10i 0.319876 + 0.909769i
\(967\) 4.75540e10 1.69120 0.845600 0.533818i \(-0.179243\pi\)
0.845600 + 0.533818i \(0.179243\pi\)
\(968\) −2.70492e10 7.17314e9i −0.958497 0.254182i
\(969\) −3.72281e9 2.26779e10i −0.131443 0.800701i
\(970\) −2.95553e10 + 5.23758e9i −1.03976 + 0.184259i
\(971\) 3.10181e10 + 3.10181e10i 1.08730 + 1.08730i 0.995806 + 0.0914900i \(0.0291630\pi\)
0.0914900 + 0.995806i \(0.470837\pi\)
\(972\) −2.65997e10 + 1.05913e10i −0.929061 + 0.369927i
\(973\) −1.38277e10 + 1.38277e10i −0.481233 + 0.481233i
\(974\) −1.05387e10 7.36578e9i −0.365451 0.255424i
\(975\) −6.49973e10 + 1.06700e10i −2.24584 + 0.368678i
\(976\) −7.87961e8 + 9.37751e9i −0.0271288 + 0.322859i
\(977\) 3.53964e9i 0.121430i −0.998155 0.0607152i \(-0.980662\pi\)
0.998155 0.0607152i \(-0.0193382\pi\)
\(978\) 7.88142e9 + 3.78092e9i 0.269413 + 0.129244i
\(979\) −2.19920e9 2.19920e9i −0.0749073 0.0749073i
\(980\) 4.69572e9 + 2.17983e9i 0.159372 + 0.0739831i
\(981\) 6.97550e9 + 3.45583e9i 0.235903 + 0.116872i
\(982\) −4.91791e9 2.77514e10i −0.165726 0.935179i
\(983\) 2.17172e10i 0.729233i 0.931158 + 0.364616i \(0.118800\pi\)
−0.931158 + 0.364616i \(0.881200\pi\)
\(984\) 3.02759e10 + 3.67666e10i 1.01301 + 1.23018i
\(985\) 7.60789e9i 0.253652i
\(986\) −1.98722e10 + 3.52162e9i −0.660203 + 0.116997i
\(987\) 2.50489e10 3.48882e10i 0.829236 1.15496i
\(988\) 6.19037e9 + 1.69174e10i 0.204205 + 0.558064i
\(989\) −3.36340e10 3.36340e10i −1.10558 1.10558i
\(990\) −1.50620e9 + 5.14891e9i −0.0493356 + 0.168652i
\(991\) 2.19631e10i 0.716863i −0.933556 0.358432i \(-0.883312\pi\)
0.933556 0.358432i \(-0.116688\pi\)
\(992\) −1.34028e9 1.45970e10i −0.0435918 0.474758i
\(993\) −1.11644e9 6.80090e9i −0.0361836 0.220417i
\(994\) 9.57904e9 1.37053e10i 0.309364 0.442626i
\(995\) 5.42646e10 5.42646e10i 1.74637 1.74637i
\(996\) 2.76468e10 1.55915e10i 0.886618 0.500012i
\(997\) −1.74874e10 1.74874e10i −0.558847 0.558847i 0.370132 0.928979i \(-0.379312\pi\)
−0.928979 + 0.370132i \(0.879312\pi\)
\(998\) 2.91502e9 + 1.64492e10i 0.0928292 + 0.523828i
\(999\) 1.63274e9 + 3.07492e9i 0.0518128 + 0.0975787i
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 48.8.k.a.11.11 108
3.2 odd 2 inner 48.8.k.a.11.44 yes 108
16.3 odd 4 inner 48.8.k.a.35.44 yes 108
48.35 even 4 inner 48.8.k.a.35.11 yes 108
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
48.8.k.a.11.11 108 1.1 even 1 trivial
48.8.k.a.11.44 yes 108 3.2 odd 2 inner
48.8.k.a.35.11 yes 108 48.35 even 4 inner
48.8.k.a.35.44 yes 108 16.3 odd 4 inner