Properties

Label 43.7.f.a.2.5
Level $43$
Weight $7$
Character 43.2
Analytic conductor $9.892$
Analytic rank $0$
Dimension $126$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [43,7,Mod(2,43)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(43, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([9]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("43.2");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 43 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 43.f (of order \(14\), degree \(6\), 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: \(9.89232559565\)
Analytic rank: \(0\)
Dimension: \(126\)
Relative dimension: \(21\) over \(\Q(\zeta_{14})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label 2.5
Character \(\chi\) \(=\) 43.2
Dual form 43.7.f.a.22.5

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-4.79242 - 9.95156i) q^{2} +(-6.97408 + 14.4818i) q^{3} +(-36.1629 + 45.3469i) q^{4} +(117.045 + 26.7147i) q^{5} +177.540 q^{6} -466.480i q^{7} +(-64.6015 - 14.7449i) q^{8} +(293.438 + 367.960i) q^{9} +O(q^{10})\) \(q+(-4.79242 - 9.95156i) q^{2} +(-6.97408 + 14.4818i) q^{3} +(-36.1629 + 45.3469i) q^{4} +(117.045 + 26.7147i) q^{5} +177.540 q^{6} -466.480i q^{7} +(-64.6015 - 14.7449i) q^{8} +(293.438 + 367.960i) q^{9} +(-295.075 - 1292.81i) q^{10} +(-1084.84 - 1360.35i) q^{11} +(-404.503 - 839.959i) q^{12} +(211.677 - 927.416i) q^{13} +(-4642.21 + 2235.57i) q^{14} +(-1203.16 + 1508.71i) q^{15} +(988.873 + 4332.54i) q^{16} +(1085.44 + 4755.64i) q^{17} +(2255.50 - 4683.59i) q^{18} +(-9694.59 - 7731.18i) q^{19} +(-5444.12 + 4341.54i) q^{20} +(6755.49 + 3253.27i) q^{21} +(-8338.59 + 17315.3i) q^{22} +(-6838.48 - 8575.18i) q^{23} +(664.069 - 832.716i) q^{24} +(-1091.80 - 525.782i) q^{25} +(-10243.7 + 2338.05i) q^{26} +(-18799.1 + 4290.77i) q^{27} +(21153.4 + 16869.3i) q^{28} +(-17403.5 - 36138.8i) q^{29} +(20780.1 + 4742.93i) q^{30} +(14896.9 - 7173.99i) q^{31} +(35060.8 - 27960.1i) q^{32} +(27266.2 - 6223.32i) q^{33} +(42124.1 - 33592.9i) q^{34} +(12461.9 - 54599.2i) q^{35} -27297.4 q^{36} +30453.6i q^{37} +(-30476.7 + 133527. i) q^{38} +(11954.4 + 9533.35i) q^{39} +(-7167.37 - 3451.62i) q^{40} +(108345. - 52176.4i) q^{41} -82818.7i q^{42} +(-66487.8 + 43597.4i) q^{43} +100919. q^{44} +(24515.5 + 50907.0i) q^{45} +(-52563.6 + 109149. i) q^{46} +(46855.2 - 58754.5i) q^{47} +(-69639.6 - 15894.8i) q^{48} -99954.8 q^{49} +13384.9i q^{50} +(-76440.3 - 17447.0i) q^{51} +(34400.6 + 43137.0i) q^{52} +(32796.4 + 143690. i) q^{53} +(132793. + 166517. i) q^{54} +(-90634.0 - 188203. i) q^{55} +(-6878.19 + 30135.3i) q^{56} +(179573. - 86477.6i) q^{57} +(-276233. + 346385. i) q^{58} +(-19083.1 - 83608.5i) q^{59} +(-24905.7 - 109119. i) q^{60} +(45072.3 - 93593.6i) q^{61} +(-142785. - 113867. i) q^{62} +(171646. - 136883. i) q^{63} +(-190025. - 91511.1i) q^{64} +(49551.4 - 102895. i) q^{65} +(-192603. - 241516. i) q^{66} +(96851.3 - 121448. i) q^{67} +(-254906. - 122756. i) q^{68} +(171877. - 39229.7i) q^{69} +(-603070. + 137647. i) q^{70} +(413448. + 329714. i) q^{71} +(-13531.0 - 28097.5i) q^{72} +(-444210. - 101388. i) q^{73} +(303060. - 145946. i) q^{74} +(15228.6 - 12144.4i) q^{75} +(701170. - 160037. i) q^{76} +(-634576. + 506058. i) q^{77} +(37581.0 - 164653. i) q^{78} +267187. q^{79} +533519. i q^{80} +(-7377.72 + 32323.9i) q^{81} +(-1.03847e6 - 828155. i) q^{82} +(707833. + 340875. i) q^{83} +(-391824. + 188693. i) q^{84} +585621. i q^{85} +(752500. + 452720. i) q^{86} +644730. q^{87} +(50024.3 + 103877. i) q^{88} +(-265904. + 552155. i) q^{89} +(389115. - 487935. i) q^{90} +(-432621. - 98743.0i) q^{91} +636158. q^{92} +265767. i q^{93} +(-809249. - 184706. i) q^{94} +(-928166. - 1.16388e6i) q^{95} +(160396. + 702740. i) q^{96} +(-322686. - 404636. i) q^{97} +(479026. + 994707. i) q^{98} +(182220. - 798358. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 126 q - 7 q^{2} - 7 q^{3} + 725 q^{4} - 7 q^{5} + 244 q^{6} + 2233 q^{8} + 6312 q^{9} + 1955 q^{10} - 985 q^{11} - 455 q^{12} - 4485 q^{13} - 6771 q^{14} + 5017 q^{15} - 41935 q^{16} - 10409 q^{17} - 5110 q^{18} - 33397 q^{19} - 24507 q^{20} - 5448 q^{21} + 25193 q^{22} - 29017 q^{23} - 1885 q^{24} - 2080 q^{25} + 34713 q^{26} - 7 q^{27} + 28665 q^{28} + 17353 q^{29} - 290052 q^{30} + 13547 q^{31} + 458283 q^{32} - 94801 q^{33} - 191527 q^{34} + 183008 q^{35} + 956352 q^{36} + 304607 q^{38} - 381031 q^{39} + 66419 q^{40} + 313447 q^{41} - 323228 q^{43} + 281588 q^{44} - 1237551 q^{45} + 80948 q^{46} - 180133 q^{47} - 762055 q^{48} - 1861754 q^{49} + 999215 q^{51} + 471797 q^{52} + 1030011 q^{53} - 92099 q^{54} + 324233 q^{55} - 842713 q^{56} + 331037 q^{57} + 849461 q^{58} - 369609 q^{59} + 553323 q^{60} - 594727 q^{61} - 886711 q^{62} + 1914136 q^{63} - 3250219 q^{64} + 1473521 q^{65} - 427559 q^{66} + 122535 q^{67} - 602346 q^{68} + 4320057 q^{69} - 1694994 q^{70} - 770707 q^{71} - 391202 q^{72} + 476945 q^{73} - 3943812 q^{74} + 2061367 q^{75} - 2044462 q^{76} + 3016216 q^{77} + 239350 q^{78} + 5077268 q^{79} + 2388946 q^{81} + 5820437 q^{82} - 1324235 q^{83} + 3759618 q^{84} - 4967947 q^{86} - 3537894 q^{87} - 7289555 q^{88} - 4331495 q^{89} - 12825206 q^{90} + 1802976 q^{91} - 12038260 q^{92} + 6249341 q^{94} - 5313259 q^{95} + 7069598 q^{96} + 788975 q^{97} + 4724783 q^{98} - 2216971 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{9}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −4.79242 9.95156i −0.599052 1.24395i −0.951366 0.308063i \(-0.900319\pi\)
0.352313 0.935882i \(-0.385395\pi\)
\(3\) −6.97408 + 14.4818i −0.258299 + 0.536364i −0.989279 0.146035i \(-0.953349\pi\)
0.730980 + 0.682399i \(0.239063\pi\)
\(4\) −36.1629 + 45.3469i −0.565046 + 0.708545i
\(5\) 117.045 + 26.7147i 0.936360 + 0.213718i 0.663364 0.748297i \(-0.269128\pi\)
0.272996 + 0.962015i \(0.411985\pi\)
\(6\) 177.540 0.821943
\(7\) 466.480i 1.36000i −0.733212 0.680000i \(-0.761980\pi\)
0.733212 0.680000i \(-0.238020\pi\)
\(8\) −64.6015 14.7449i −0.126175 0.0287986i
\(9\) 293.438 + 367.960i 0.402522 + 0.504746i
\(10\) −295.075 1292.81i −0.295075 1.29281i
\(11\) −1084.84 1360.35i −0.815059 1.02205i −0.999233 0.0391576i \(-0.987533\pi\)
0.184174 0.982894i \(-0.441039\pi\)
\(12\) −404.503 839.959i −0.234087 0.486087i
\(13\) 211.677 927.416i 0.0963481 0.422129i −0.903633 0.428308i \(-0.859110\pi\)
0.999981 + 0.00617944i \(0.00196699\pi\)
\(14\) −4642.21 + 2235.57i −1.69177 + 0.814712i
\(15\) −1203.16 + 1508.71i −0.356492 + 0.447027i
\(16\) 988.873 + 4332.54i 0.241424 + 1.05775i
\(17\) 1085.44 + 4755.64i 0.220933 + 0.967970i 0.956778 + 0.290820i \(0.0939281\pi\)
−0.735845 + 0.677150i \(0.763215\pi\)
\(18\) 2255.50 4683.59i 0.386745 0.803085i
\(19\) −9694.59 7731.18i −1.41341 1.12716i −0.973386 0.229173i \(-0.926398\pi\)
−0.440026 0.897985i \(-0.645031\pi\)
\(20\) −5444.12 + 4341.54i −0.680515 + 0.542693i
\(21\) 6755.49 + 3253.27i 0.729456 + 0.351287i
\(22\) −8338.59 + 17315.3i −0.783113 + 1.62615i
\(23\) −6838.48 8575.18i −0.562052 0.704790i 0.416884 0.908960i \(-0.363122\pi\)
−0.978936 + 0.204169i \(0.934551\pi\)
\(24\) 664.069 832.716i 0.0480374 0.0602370i
\(25\) −1091.80 525.782i −0.0698751 0.0336501i
\(26\) −10243.7 + 2338.05i −0.582822 + 0.133025i
\(27\) −18799.1 + 4290.77i −0.955093 + 0.217994i
\(28\) 21153.4 + 16869.3i 0.963622 + 0.768463i
\(29\) −17403.5 36138.8i −0.713582 1.48177i −0.869466 0.493992i \(-0.835537\pi\)
0.155885 0.987775i \(-0.450177\pi\)
\(30\) 20780.1 + 4742.93i 0.769634 + 0.175664i
\(31\) 14896.9 7173.99i 0.500048 0.240811i −0.166818 0.985988i \(-0.553349\pi\)
0.666867 + 0.745177i \(0.267635\pi\)
\(32\) 35060.8 27960.1i 1.06997 0.853273i
\(33\) 27266.2 6223.32i 0.758721 0.173173i
\(34\) 42124.1 33592.9i 1.07175 0.854693i
\(35\) 12461.9 54599.2i 0.290657 1.27345i
\(36\) −27297.4 −0.585079
\(37\) 30453.6i 0.601219i 0.953747 + 0.300610i \(0.0971901\pi\)
−0.953747 + 0.300610i \(0.902810\pi\)
\(38\) −30476.7 + 133527.i −0.555415 + 2.43343i
\(39\) 11954.4 + 9533.35i 0.201528 + 0.160713i
\(40\) −7167.37 3451.62i −0.111990 0.0539316i
\(41\) 108345. 52176.4i 1.57202 0.757047i 0.573939 0.818898i \(-0.305415\pi\)
0.998085 + 0.0618511i \(0.0197004\pi\)
\(42\) 82818.7i 1.11784i
\(43\) −66487.8 + 43597.4i −0.836251 + 0.548347i
\(44\) 100919. 1.18472
\(45\) 24515.5 + 50907.0i 0.269032 + 0.558650i
\(46\) −52563.6 + 109149.i −0.540022 + 1.12137i
\(47\) 46855.2 58754.5i 0.451299 0.565911i −0.503183 0.864180i \(-0.667838\pi\)
0.954482 + 0.298269i \(0.0964093\pi\)
\(48\) −69639.6 15894.8i −0.629698 0.143724i
\(49\) −99954.8 −0.849602
\(50\) 13384.9i 0.107079i
\(51\) −76440.3 17447.0i −0.576252 0.131526i
\(52\) 34400.6 + 43137.0i 0.244656 + 0.306789i
\(53\) 32796.4 + 143690.i 0.220292 + 0.965162i 0.957259 + 0.289233i \(0.0934003\pi\)
−0.736967 + 0.675929i \(0.763743\pi\)
\(54\) 132793. + 166517.i 0.843323 + 1.05749i
\(55\) −90634.0 188203.i −0.544757 1.13120i
\(56\) −6878.19 + 30135.3i −0.0391661 + 0.171598i
\(57\) 179573. 86477.6i 0.969651 0.466959i
\(58\) −276233. + 346385.i −1.41576 + 1.77531i
\(59\) −19083.1 83608.5i −0.0929164 0.407094i 0.906985 0.421164i \(-0.138378\pi\)
−0.999901 + 0.0140703i \(0.995521\pi\)
\(60\) −24905.7 109119.i −0.115304 0.505181i
\(61\) 45072.3 93593.6i 0.198573 0.412341i −0.777776 0.628542i \(-0.783652\pi\)
0.976349 + 0.216201i \(0.0693665\pi\)
\(62\) −142785. 113867.i −0.599110 0.477774i
\(63\) 171646. 136883.i 0.686455 0.547430i
\(64\) −190025. 91511.1i −0.724887 0.349087i
\(65\) 49551.4 102895.i 0.180433 0.374673i
\(66\) −192603. 241516.i −0.669931 0.840067i
\(67\) 96851.3 121448.i 0.322019 0.403798i −0.594303 0.804241i \(-0.702572\pi\)
0.916322 + 0.400442i \(0.131144\pi\)
\(68\) −254906. 122756.i −0.810688 0.390407i
\(69\) 171877. 39229.7i 0.523202 0.119417i
\(70\) −603070. + 137647.i −1.75822 + 0.401302i
\(71\) 413448. + 329714.i 1.15517 + 0.921218i 0.997798 0.0663212i \(-0.0211262\pi\)
0.157373 + 0.987539i \(0.449698\pi\)
\(72\) −13531.0 28097.5i −0.0362521 0.0752783i
\(73\) −444210. 101388.i −1.14188 0.260626i −0.390567 0.920574i \(-0.627721\pi\)
−0.751311 + 0.659948i \(0.770578\pi\)
\(74\) 303060. 145946.i 0.747884 0.360162i
\(75\) 15228.6 12144.4i 0.0360974 0.0287867i
\(76\) 701170. 160037.i 1.59729 0.364570i
\(77\) −634576. + 506058.i −1.38999 + 1.10848i
\(78\) 37581.0 164653.i 0.0791926 0.346965i
\(79\) 267187. 0.541919 0.270960 0.962591i \(-0.412659\pi\)
0.270960 + 0.962591i \(0.412659\pi\)
\(80\) 533519.i 1.04203i
\(81\) −7377.72 + 32323.9i −0.0138825 + 0.0608232i
\(82\) −1.03847e6 828155.i −1.88345 1.50200i
\(83\) 707833. + 340875.i 1.23793 + 0.596157i 0.934251 0.356617i \(-0.116070\pi\)
0.303681 + 0.952774i \(0.401784\pi\)
\(84\) −391824. + 188693.i −0.661079 + 0.318359i
\(85\) 585621.i 0.953586i
\(86\) 752500. + 452720.i 1.18307 + 0.711762i
\(87\) 644730. 0.979085
\(88\) 50024.3 + 103877.i 0.0734062 + 0.152430i
\(89\) −265904. + 552155.i −0.377185 + 0.783233i 0.622814 + 0.782370i \(0.285989\pi\)
−1.00000 0.000863685i \(0.999725\pi\)
\(90\) 389115. 487935.i 0.533766 0.669321i
\(91\) −432621. 98743.0i −0.574095 0.131033i
\(92\) 636158. 0.816961
\(93\) 265767.i 0.330409i
\(94\) −809249. 184706.i −0.974313 0.222381i
\(95\) −928166. 1.16388e6i −1.08257 1.35750i
\(96\) 160396. + 702740.i 0.181292 + 0.794294i
\(97\) −322686. 404636.i −0.353562 0.443353i 0.572966 0.819579i \(-0.305793\pi\)
−0.926528 + 0.376227i \(0.877221\pi\)
\(98\) 479026. + 994707.i 0.508956 + 1.05686i
\(99\) 182220. 798358.i 0.187798 0.822796i
\(100\) 63325.3 30495.8i 0.0633253 0.0304958i
\(101\) 935541. 1.17313e6i 0.908027 1.13863i −0.0818416 0.996645i \(-0.526080\pi\)
0.989869 0.141985i \(-0.0453484\pi\)
\(102\) 192709. + 844314.i 0.181594 + 0.795616i
\(103\) 182854. + 801134.i 0.167337 + 0.733151i 0.987055 + 0.160383i \(0.0512731\pi\)
−0.819718 + 0.572768i \(0.805870\pi\)
\(104\) −27349.3 + 56791.3i −0.0243134 + 0.0504873i
\(105\) 703786. + 561250.i 0.607956 + 0.484829i
\(106\) 1.27277e6 1.01500e6i 1.06864 0.852214i
\(107\) −150510. 72481.8i −0.122861 0.0591668i 0.371443 0.928456i \(-0.378863\pi\)
−0.494305 + 0.869289i \(0.664577\pi\)
\(108\) 485257. 1.00765e6i 0.385213 0.799903i
\(109\) −343364. 430565.i −0.265140 0.332475i 0.631384 0.775470i \(-0.282487\pi\)
−0.896524 + 0.442996i \(0.853916\pi\)
\(110\) −1.43856e6 + 1.80390e6i −1.08081 + 1.35530i
\(111\) −441023. 212386.i −0.322473 0.155295i
\(112\) 2.02104e6 461290.i 1.43854 0.328337i
\(113\) 1.33990e6 305822.i 0.928615 0.211950i 0.268642 0.963240i \(-0.413425\pi\)
0.659972 + 0.751290i \(0.270568\pi\)
\(114\) −1.72117e6 1.37259e6i −1.16174 0.926459i
\(115\) −571326. 1.18637e6i −0.375656 0.780058i
\(116\) 2.26815e6 + 517690.i 1.45311 + 0.331662i
\(117\) 403366. 194251.i 0.251850 0.121285i
\(118\) −740581. + 590593.i −0.450740 + 0.359453i
\(119\) 2.21841e6 506338.i 1.31644 0.300469i
\(120\) 99971.7 79724.8i 0.0578540 0.0461370i
\(121\) −279459. + 1.22439e6i −0.157747 + 0.691135i
\(122\) −1.14741e6 −0.631885
\(123\) 1.93292e6i 1.03872i
\(124\) −213399. + 934962.i −0.111925 + 0.490376i
\(125\) −1.58035e6 1.26029e6i −0.809139 0.645267i
\(126\) −2.18480e6 1.05215e6i −1.09220 0.525974i
\(127\) 470905. 226776.i 0.229891 0.110710i −0.315393 0.948961i \(-0.602136\pi\)
0.545284 + 0.838252i \(0.316422\pi\)
\(128\) 540440.i 0.257702i
\(129\) −167679. 1.26692e6i −0.0781106 0.590173i
\(130\) −1.26143e6 −0.574161
\(131\) −352252. 731460.i −0.156690 0.325369i 0.807815 0.589437i \(-0.200650\pi\)
−0.964504 + 0.264067i \(0.914936\pi\)
\(132\) −703816. + 1.46149e6i −0.306011 + 0.635439i
\(133\) −3.60644e6 + 4.52233e6i −1.53294 + 1.92224i
\(134\) −1.67275e6 381793.i −0.695209 0.158677i
\(135\) −2.31496e6 −0.940899
\(136\) 323226.i 0.128496i
\(137\) 350593. + 80020.5i 0.136346 + 0.0311200i 0.290149 0.956981i \(-0.406295\pi\)
−0.153803 + 0.988101i \(0.549152\pi\)
\(138\) −1.21410e6 1.52244e6i −0.461974 0.579297i
\(139\) −43987.3 192721.i −0.0163788 0.0717603i 0.966078 0.258250i \(-0.0831459\pi\)
−0.982457 + 0.186490i \(0.940289\pi\)
\(140\) 2.02524e6 + 2.53957e6i 0.738062 + 0.925501i
\(141\) 524102. + 1.08831e6i 0.186964 + 0.388235i
\(142\) 1.29975e6 5.69459e6i 0.453937 1.98883i
\(143\) −1.49125e6 + 718147.i −0.509966 + 0.245587i
\(144\) −1.30403e6 + 1.63520e6i −0.436716 + 0.547624i
\(145\) −1.07156e6 4.69480e6i −0.351489 1.53997i
\(146\) 1.11987e6 + 4.90648e6i 0.359840 + 1.57656i
\(147\) 697093. 1.44753e6i 0.219452 0.455696i
\(148\) −1.38097e6 1.10129e6i −0.425991 0.339717i
\(149\) 2.24736e6 1.79221e6i 0.679382 0.541789i −0.221874 0.975075i \(-0.571217\pi\)
0.901257 + 0.433286i \(0.142646\pi\)
\(150\) −193837. 93347.2i −0.0574333 0.0276584i
\(151\) −2.76551e6 + 5.74264e6i −0.803238 + 1.66794i −0.0606804 + 0.998157i \(0.519327\pi\)
−0.742557 + 0.669783i \(0.766387\pi\)
\(152\) 512290. + 642391.i 0.145876 + 0.182923i
\(153\) −1.43137e6 + 1.79489e6i −0.399649 + 0.501144i
\(154\) 8.07722e6 + 3.88979e6i 2.21157 + 1.06503i
\(155\) 1.93526e6 441711.i 0.519690 0.118616i
\(156\) −864616. + 197343.i −0.227745 + 0.0519814i
\(157\) −909102. 724985.i −0.234917 0.187340i 0.498955 0.866628i \(-0.333717\pi\)
−0.733872 + 0.679288i \(0.762289\pi\)
\(158\) −1.28047e6 2.65893e6i −0.324638 0.674118i
\(159\) −2.30963e6 527157.i −0.574580 0.131144i
\(160\) 4.85063e6 2.33594e6i 1.18424 0.570298i
\(161\) −4.00015e6 + 3.19002e6i −0.958515 + 0.764391i
\(162\) 357031. 81489.9i 0.0839770 0.0191672i
\(163\) 351947. 280668.i 0.0812670 0.0648083i −0.582014 0.813179i \(-0.697735\pi\)
0.663281 + 0.748371i \(0.269164\pi\)
\(164\) −1.55205e6 + 6.79999e6i −0.351864 + 1.54162i
\(165\) 3.35762e6 0.747446
\(166\) 8.67766e6i 1.89705i
\(167\) −1.14880e6 + 5.03322e6i −0.246658 + 1.08068i 0.688163 + 0.725557i \(0.258418\pi\)
−0.934820 + 0.355121i \(0.884440\pi\)
\(168\) −388446. 309775.i −0.0819224 0.0653309i
\(169\) 3.53351e6 + 1.70165e6i 0.732059 + 0.352541i
\(170\) 5.82784e6 2.80654e6i 1.18621 0.571248i
\(171\) 5.83585e6i 1.16712i
\(172\) 427387. 4.59163e6i 0.0839916 0.902363i
\(173\) 332436. 0.0642052 0.0321026 0.999485i \(-0.489780\pi\)
0.0321026 + 0.999485i \(0.489780\pi\)
\(174\) −3.08982e6 6.41607e6i −0.586523 1.21793i
\(175\) −245267. + 509302.i −0.0457641 + 0.0950302i
\(176\) 4.82099e6 6.04533e6i 0.884298 1.10887i
\(177\) 1.34389e6 + 306734.i 0.242351 + 0.0553150i
\(178\) 6.76913e6 1.20025
\(179\) 1.00560e7i 1.75334i −0.481091 0.876671i \(-0.659759\pi\)
0.481091 0.876671i \(-0.340241\pi\)
\(180\) −3.19503e6 729244.i −0.547844 0.125042i
\(181\) 1.44998e6 + 1.81822e6i 0.244527 + 0.306627i 0.888915 0.458071i \(-0.151460\pi\)
−0.644389 + 0.764698i \(0.722888\pi\)
\(182\) 1.09066e6 + 4.77848e6i 0.180915 + 0.792639i
\(183\) 1.04107e6 + 1.30546e6i 0.169874 + 0.213015i
\(184\) 315336. + 654802.i 0.0506198 + 0.105113i
\(185\) −813559. + 3.56443e6i −0.128491 + 0.562957i
\(186\) 2.64480e6 1.27367e6i 0.411011 0.197932i
\(187\) 5.29180e6 6.63570e6i 0.809242 1.01476i
\(188\) 969915. + 4.24947e6i 0.145969 + 0.639531i
\(189\) 2.00156e6 + 8.76940e6i 0.296472 + 1.29893i
\(190\) −7.13430e6 + 1.48145e7i −1.04014 + 2.15987i
\(191\) 3.62830e6 + 2.89347e6i 0.520718 + 0.415259i 0.848262 0.529577i \(-0.177649\pi\)
−0.327543 + 0.944836i \(0.606221\pi\)
\(192\) 2.65050e6 2.11370e6i 0.374476 0.298635i
\(193\) −8.49762e6 4.09224e6i −1.18202 0.569232i −0.263522 0.964653i \(-0.584884\pi\)
−0.918500 + 0.395422i \(0.870598\pi\)
\(194\) −2.48031e6 + 5.15042e6i −0.339704 + 0.705403i
\(195\) 1.14453e6 + 1.43519e6i 0.154355 + 0.193556i
\(196\) 3.61466e6 4.53264e6i 0.480064 0.601982i
\(197\) 7.79538e6 + 3.75406e6i 1.01962 + 0.491023i 0.867552 0.497347i \(-0.165692\pi\)
0.152068 + 0.988370i \(0.451407\pi\)
\(198\) −8.81818e6 + 2.01269e6i −1.13601 + 0.259288i
\(199\) −1.03045e7 + 2.35193e6i −1.30758 + 0.298445i −0.818858 0.573997i \(-0.805392\pi\)
−0.488717 + 0.872442i \(0.662535\pi\)
\(200\) 62779.2 + 50064.8i 0.00784740 + 0.00625809i
\(201\) 1.08334e6 + 2.24957e6i 0.133406 + 0.277020i
\(202\) −1.61580e7 3.68796e6i −1.96035 0.447437i
\(203\) −1.68580e7 + 8.11841e6i −2.01520 + 0.970471i
\(204\) 3.55548e6 2.83540e6i 0.418801 0.333982i
\(205\) 1.40752e7 3.21257e6i 1.63377 0.372898i
\(206\) 7.09622e6 5.65905e6i 0.811756 0.647354i
\(207\) 1.14865e6 5.03258e6i 0.129502 0.567387i
\(208\) 4.22739e6 0.469766
\(209\) 2.15751e7i 2.36328i
\(210\) 2.21248e6 9.69351e6i 0.238903 1.04670i
\(211\) 4.53902e6 + 3.61975e6i 0.483186 + 0.385328i 0.834569 0.550904i \(-0.185717\pi\)
−0.351383 + 0.936232i \(0.614288\pi\)
\(212\) −7.70193e6 3.70906e6i −0.808336 0.389274i
\(213\) −7.65829e6 + 3.68804e6i −0.792488 + 0.381642i
\(214\) 1.84517e6i 0.188276i
\(215\) −8.94675e6 + 3.32665e6i −0.900223 + 0.334728i
\(216\) 1.27772e6 0.126787
\(217\) −3.34652e6 6.94913e6i −0.327503 0.680066i
\(218\) −2.63925e6 + 5.48045e6i −0.254748 + 0.528989i
\(219\) 4.56625e6 5.72589e6i 0.434737 0.545143i
\(220\) 1.18120e7 + 2.69602e6i 1.10932 + 0.253195i
\(221\) 4.64022e6 0.429894
\(222\) 5.40671e6i 0.494168i
\(223\) 4.60253e6 + 1.05050e6i 0.415032 + 0.0947284i 0.424938 0.905223i \(-0.360296\pi\)
−0.00990558 + 0.999951i \(0.503153\pi\)
\(224\) −1.30428e7 1.63552e7i −1.16045 1.45516i
\(225\) −126909. 556023.i −0.0111415 0.0488141i
\(226\) −9.46475e6 1.18684e7i −0.819943 1.02818i
\(227\) −5.20887e6 1.08163e7i −0.445314 0.924704i −0.995946 0.0899556i \(-0.971327\pi\)
0.550632 0.834748i \(-0.314387\pi\)
\(228\) −2.57238e6 + 1.12703e7i −0.217036 + 0.950895i
\(229\) 7.31547e6 3.52294e6i 0.609166 0.293359i −0.103755 0.994603i \(-0.533086\pi\)
0.712921 + 0.701244i \(0.247372\pi\)
\(230\) −9.06820e6 + 1.13712e7i −0.745311 + 0.934591i
\(231\) −2.90306e6 1.27191e7i −0.235516 1.03186i
\(232\) 591432. + 2.59123e6i 0.0473632 + 0.207512i
\(233\) −2.94911e6 + 6.12389e6i −0.233143 + 0.484127i −0.984414 0.175867i \(-0.943727\pi\)
0.751270 + 0.659994i \(0.229441\pi\)
\(234\) −3.86620e6 3.08319e6i −0.301743 0.240632i
\(235\) 7.05377e6 5.62520e6i 0.543523 0.433445i
\(236\) 4.48149e6 + 2.15817e6i 0.340946 + 0.164191i
\(237\) −1.86339e6 + 3.86936e6i −0.139977 + 0.290666i
\(238\) −1.56704e7 1.96501e7i −1.16238 1.45758i
\(239\) 1.25595e7 1.57491e7i 0.919981 1.15362i −0.0677891 0.997700i \(-0.521594\pi\)
0.987770 0.155920i \(-0.0498341\pi\)
\(240\) −7.72633e6 3.72081e6i −0.558907 0.269156i
\(241\) 9.12278e6 2.08221e6i 0.651742 0.148756i 0.116149 0.993232i \(-0.462945\pi\)
0.535594 + 0.844476i \(0.320088\pi\)
\(242\) 1.35239e7 3.08673e6i 0.954233 0.217798i
\(243\) −1.14068e7 9.09665e6i −0.794962 0.633961i
\(244\) 2.61423e6 + 5.42851e6i 0.179959 + 0.373690i
\(245\) −1.16992e7 2.67027e6i −0.795533 0.181575i
\(246\) 1.92356e7 9.26338e6i 1.29211 0.622249i
\(247\) −9.22214e6 + 7.35441e6i −0.611985 + 0.488042i
\(248\) −1.06814e6 + 243797.i −0.0700285 + 0.0159835i
\(249\) −9.87298e6 + 7.87344e6i −0.639514 + 0.509996i
\(250\) −4.96812e6 + 2.17668e7i −0.317960 + 1.39307i
\(251\) 2.56090e7 1.61946 0.809732 0.586800i \(-0.199613\pi\)
0.809732 + 0.586800i \(0.199613\pi\)
\(252\) 1.27337e7i 0.795708i
\(253\) −4.24657e6 + 1.86055e7i −0.262227 + 1.14889i
\(254\) −4.51355e6 3.59943e6i −0.275433 0.219651i
\(255\) −8.48086e6 4.08417e6i −0.511469 0.246311i
\(256\) −1.75398e7 + 8.44673e6i −1.04545 + 0.503464i
\(257\) 2.84340e7i 1.67509i −0.546367 0.837546i \(-0.683990\pi\)
0.546367 0.837546i \(-0.316010\pi\)
\(258\) −1.18042e7 + 7.74027e6i −0.687350 + 0.450710i
\(259\) 1.42060e7 0.817659
\(260\) 2.87402e6 + 5.96797e6i 0.163520 + 0.339552i
\(261\) 8.19078e6 1.70083e7i 0.460685 0.956621i
\(262\) −5.59102e6 + 7.01092e6i −0.310876 + 0.389826i
\(263\) 2.20115e7 + 5.02398e6i 1.20999 + 0.276173i 0.779488 0.626417i \(-0.215479\pi\)
0.430503 + 0.902589i \(0.358336\pi\)
\(264\) −1.85320e6 −0.100719
\(265\) 1.76944e7i 0.950819i
\(266\) 6.22879e7 + 1.42168e7i 3.30947 + 0.755365i
\(267\) −6.14178e6 7.70155e6i −0.322672 0.404617i
\(268\) 2.00485e6 + 8.78381e6i 0.104154 + 0.456329i
\(269\) 1.98298e6 + 2.48657e6i 0.101873 + 0.127745i 0.830155 0.557533i \(-0.188252\pi\)
−0.728281 + 0.685278i \(0.759681\pi\)
\(270\) 1.10943e7 + 2.30375e7i 0.563648 + 1.17043i
\(271\) 1.88759e6 8.27006e6i 0.0948417 0.415528i −0.905112 0.425174i \(-0.860213\pi\)
0.999953 + 0.00964512i \(0.00307019\pi\)
\(272\) −1.95306e7 + 9.40544e6i −0.970530 + 0.467383i
\(273\) 4.44712e6 5.57651e6i 0.218570 0.274078i
\(274\) −883859. 3.87244e6i −0.0429666 0.188249i
\(275\) 469182. + 2.05562e6i 0.0225602 + 0.0988427i
\(276\) −4.43662e6 + 9.21273e6i −0.211021 + 0.438189i
\(277\) −4.50580e6 3.59326e6i −0.211999 0.169063i 0.511734 0.859144i \(-0.329003\pi\)
−0.723732 + 0.690081i \(0.757575\pi\)
\(278\) −1.70707e6 + 1.36134e6i −0.0794541 + 0.0633625i
\(279\) 7.01107e6 + 3.37635e6i 0.322829 + 0.155466i
\(280\) −1.61011e6 + 3.34344e6i −0.0733471 + 0.152307i
\(281\) −5.34936e6 6.70788e6i −0.241092 0.302320i 0.646534 0.762885i \(-0.276218\pi\)
−0.887626 + 0.460566i \(0.847647\pi\)
\(282\) 8.31865e6 1.04313e7i 0.370942 0.465146i
\(283\) −2.01394e7 9.69864e6i −0.888563 0.427909i −0.0668180 0.997765i \(-0.521285\pi\)
−0.821745 + 0.569856i \(0.806999\pi\)
\(284\) −2.99030e7 + 6.82517e6i −1.30545 + 0.297960i
\(285\) 2.33283e7 5.32453e6i 1.00774 0.230010i
\(286\) 1.42934e7 + 1.13986e7i 0.610993 + 0.487251i
\(287\) −2.43393e7 5.05410e7i −1.02958 2.13795i
\(288\) 2.05764e7 + 4.69642e6i 0.861373 + 0.196603i
\(289\) 309293. 148947.i 0.0128137 0.00617077i
\(290\) −4.15852e7 + 3.31631e7i −1.70508 + 1.35976i
\(291\) 8.11032e6 1.85113e6i 0.329123 0.0751203i
\(292\) 2.06616e7 1.64771e7i 0.829880 0.661807i
\(293\) −2.65231e6 + 1.16205e7i −0.105444 + 0.461980i 0.894446 + 0.447175i \(0.147570\pi\)
−0.999890 + 0.0148052i \(0.995287\pi\)
\(294\) −1.77459e7 −0.698324
\(295\) 1.02957e7i 0.401044i
\(296\) 449034. 1.96735e6i 0.0173143 0.0758587i
\(297\) 2.62310e7 + 2.09185e7i 1.00126 + 0.798476i
\(298\) −2.86056e7 1.37757e7i −1.08094 0.520554i
\(299\) −9.40031e6 + 4.52695e6i −0.351665 + 0.169353i
\(300\) 1.12975e6i 0.0418425i
\(301\) 2.03373e7 + 3.10152e7i 0.745752 + 1.13730i
\(302\) 7.04017e7 2.55601
\(303\) 1.04646e7 + 2.17299e7i 0.376178 + 0.781141i
\(304\) 2.39089e7 4.96473e7i 0.851018 1.76716i
\(305\) 7.77581e6 9.75056e6i 0.274060 0.343661i
\(306\) 2.47217e7 + 5.64256e6i 0.862807 + 0.196930i
\(307\) −3.47232e7 −1.20006 −0.600032 0.799976i \(-0.704846\pi\)
−0.600032 + 0.799976i \(0.704846\pi\)
\(308\) 4.70766e7i 1.61121i
\(309\) −1.28771e7 2.93912e6i −0.436459 0.0996189i
\(310\) −1.36703e7 1.71420e7i −0.458874 0.575409i
\(311\) −1.93516e6 8.47848e6i −0.0643332 0.281862i 0.932521 0.361115i \(-0.117604\pi\)
−0.996855 + 0.0792527i \(0.974747\pi\)
\(312\) −631707. 792135.i −0.0207994 0.0260817i
\(313\) −1.29371e7 2.68641e7i −0.421893 0.876071i −0.998265 0.0588830i \(-0.981246\pi\)
0.576371 0.817188i \(-0.304468\pi\)
\(314\) −2.85793e6 + 1.25214e7i −0.0923130 + 0.404450i
\(315\) 2.37471e7 1.14360e7i 0.759765 0.365883i
\(316\) −9.66228e6 + 1.21161e7i −0.306209 + 0.383974i
\(317\) 2.42845e6 + 1.06397e7i 0.0762344 + 0.334005i 0.998635 0.0522295i \(-0.0166327\pi\)
−0.922401 + 0.386234i \(0.873776\pi\)
\(318\) 5.82266e6 + 2.55108e7i 0.181067 + 0.793308i
\(319\) −3.02813e7 + 6.28799e7i −0.932831 + 1.93704i
\(320\) −1.97967e7 1.57874e7i −0.604149 0.481793i
\(321\) 2.09934e6 1.67417e6i 0.0634699 0.0506155i
\(322\) 5.09161e7 + 2.45199e7i 1.52506 + 0.734431i
\(323\) 2.62438e7 5.44957e7i 0.778786 1.61717i
\(324\) −1.19899e6 1.50349e6i −0.0352517 0.0442043i
\(325\) −718728. + 901256.i −0.0209370 + 0.0262542i
\(326\) −4.47976e6 2.15734e6i −0.129301 0.0622682i
\(327\) 8.63001e6 1.96974e6i 0.246813 0.0563335i
\(328\) −7.76861e6 + 1.77314e6i −0.220152 + 0.0502482i
\(329\) −2.74078e7 2.18570e7i −0.769639 0.613766i
\(330\) −1.60911e7 3.34136e7i −0.447759 0.929782i
\(331\) −5.21922e7 1.19125e7i −1.43920 0.328488i −0.569469 0.822013i \(-0.692851\pi\)
−0.869732 + 0.493525i \(0.835708\pi\)
\(332\) −4.10549e7 + 1.97710e7i −1.12189 + 0.540275i
\(333\) −1.12057e7 + 8.93624e6i −0.303463 + 0.242004i
\(334\) 5.55939e7 1.26889e7i 1.49207 0.340554i
\(335\) 1.45804e7 1.16275e7i 0.387824 0.309279i
\(336\) −7.41460e6 + 3.24855e7i −0.195465 + 0.856390i
\(337\) −5.39446e7 −1.40948 −0.704740 0.709466i \(-0.748936\pi\)
−0.704740 + 0.709466i \(0.748936\pi\)
\(338\) 4.33190e7i 1.12183i
\(339\) −4.91567e6 + 2.15370e7i −0.126178 + 0.552822i
\(340\) −2.65561e7 2.11778e7i −0.675659 0.538820i
\(341\) −2.59200e7 1.24824e7i −0.653689 0.314800i
\(342\) −5.80758e7 + 2.79678e7i −1.45183 + 0.699166i
\(343\) 8.25398e6i 0.204541i
\(344\) 4.93805e6 1.83610e6i 0.121305 0.0451047i
\(345\) 2.11653e7 0.515427
\(346\) −1.59317e6 3.30826e6i −0.0384623 0.0798678i
\(347\) −1.78157e7 + 3.69947e7i −0.426398 + 0.885424i 0.571499 + 0.820603i \(0.306362\pi\)
−0.997897 + 0.0648215i \(0.979352\pi\)
\(348\) −2.33153e7 + 2.92365e7i −0.553228 + 0.693726i
\(349\) 6.28606e7 + 1.43475e7i 1.47877 + 0.337521i 0.884424 0.466685i \(-0.154552\pi\)
0.594351 + 0.804206i \(0.297409\pi\)
\(350\) 6.24378e6 0.145627
\(351\) 1.83428e7i 0.424175i
\(352\) −7.60709e7 1.73627e7i −1.74418 0.398097i
\(353\) 5.00239e7 + 6.27279e7i 1.13724 + 1.42606i 0.889325 + 0.457276i \(0.151175\pi\)
0.247918 + 0.968781i \(0.420254\pi\)
\(354\) −3.38800e6 1.48438e7i −0.0763720 0.334608i
\(355\) 3.95838e7 + 4.96365e7i 0.884774 + 1.10947i
\(356\) −1.54227e7 3.20255e7i −0.341829 0.709816i
\(357\) −8.13869e6 + 3.56579e7i −0.178875 + 0.783703i
\(358\) −1.00073e8 + 4.81926e7i −2.18106 + 1.05034i
\(359\) 8.74314e6 1.09635e7i 0.188966 0.236956i −0.678319 0.734767i \(-0.737291\pi\)
0.867285 + 0.497811i \(0.165863\pi\)
\(360\) −833122. 3.65015e6i −0.0178567 0.0782353i
\(361\) 2.37453e7 + 1.04035e8i 0.504726 + 2.21135i
\(362\) 1.11452e7 2.31432e7i 0.234943 0.487863i
\(363\) −1.57824e7 1.25861e7i −0.329954 0.263130i
\(364\) 2.01226e7 1.60472e7i 0.417233 0.332732i
\(365\) −4.92840e7 2.37339e7i −1.01351 0.488080i
\(366\) 8.00212e6 1.66166e7i 0.163216 0.338921i
\(367\) 8.27589e6 + 1.03776e7i 0.167424 + 0.209943i 0.858464 0.512873i \(-0.171419\pi\)
−0.691041 + 0.722816i \(0.742848\pi\)
\(368\) 3.03899e7 3.81077e7i 0.609798 0.764662i
\(369\) 5.09916e7 + 2.45562e7i 1.01489 + 0.488746i
\(370\) 3.93706e7 8.98608e6i 0.777261 0.177405i
\(371\) 6.70288e7 1.52989e7i 1.31262 0.299597i
\(372\) −1.20517e7 9.61092e6i −0.234110 0.186696i
\(373\) 1.44550e6 + 3.00160e6i 0.0278542 + 0.0578398i 0.914432 0.404740i \(-0.132638\pi\)
−0.886578 + 0.462580i \(0.846924\pi\)
\(374\) −9.13961e7 2.08606e7i −1.74708 0.398760i
\(375\) 2.92727e7 1.40970e7i 0.555098 0.267321i
\(376\) −3.89324e6 + 3.10476e6i −0.0732399 + 0.0584069i
\(377\) −3.71997e7 + 8.49058e6i −0.694249 + 0.158458i
\(378\) 7.76769e7 6.19453e7i 1.43819 1.14692i
\(379\) 8.06707e6 3.53442e7i 0.148183 0.649232i −0.845207 0.534440i \(-0.820523\pi\)
0.993390 0.114792i \(-0.0366202\pi\)
\(380\) 8.63437e7 1.57355
\(381\) 8.40112e6i 0.151902i
\(382\) 1.14062e7 4.99740e7i 0.204622 0.896507i
\(383\) −3.07130e7 2.44928e7i −0.546670 0.435955i 0.310810 0.950472i \(-0.399400\pi\)
−0.857480 + 0.514517i \(0.827971\pi\)
\(384\) 7.82657e6 + 3.76908e6i 0.138222 + 0.0665643i
\(385\) −8.77932e7 + 4.22790e7i −1.53843 + 0.740870i
\(386\) 1.04176e8i 1.81137i
\(387\) −3.55522e7 1.16717e7i −0.613385 0.201373i
\(388\) 3.00183e7 0.513914
\(389\) −4.31579e7 8.96183e7i −0.733181 1.52247i −0.848533 0.529142i \(-0.822514\pi\)
0.115352 0.993325i \(-0.463200\pi\)
\(390\) 8.79733e6 1.82679e7i 0.148305 0.307960i
\(391\) 3.33577e7 4.18292e7i 0.558040 0.699761i
\(392\) 6.45723e6 + 1.47382e6i 0.107198 + 0.0244673i
\(393\) 1.30495e7 0.214989
\(394\) 9.55672e7i 1.56250i
\(395\) 3.12729e7 + 7.13784e6i 0.507431 + 0.115818i
\(396\) 2.96134e7 + 3.71341e7i 0.476874 + 0.597981i
\(397\) 1.89296e7 + 8.29358e7i 0.302530 + 1.32547i 0.866294 + 0.499535i \(0.166496\pi\)
−0.563763 + 0.825936i \(0.690647\pi\)
\(398\) 7.27887e7 + 9.12742e7i 1.15456 + 1.44777i
\(399\) −4.03401e7 8.37670e7i −0.635065 1.31873i
\(400\) 1.19832e6 5.25019e6i 0.0187238 0.0820342i
\(401\) −4.80377e7 + 2.31337e7i −0.744987 + 0.358767i −0.767559 0.640978i \(-0.778529\pi\)
0.0225717 + 0.999745i \(0.492815\pi\)
\(402\) 1.71949e7 2.15618e7i 0.264681 0.331899i
\(403\) −3.49994e6 1.53342e7i −0.0534743 0.234286i
\(404\) 1.93660e7 + 8.48478e7i 0.293694 + 1.28676i
\(405\) −1.72705e6 + 3.58626e6i −0.0259980 + 0.0539854i
\(406\) 1.61582e8 + 1.28857e8i 2.41443 + 1.92544i
\(407\) 4.14275e7 3.30373e7i 0.614477 0.490029i
\(408\) 4.68091e6 + 2.25421e6i 0.0689207 + 0.0331904i
\(409\) 2.53934e7 5.27300e7i 0.371151 0.770704i −0.628825 0.777547i \(-0.716464\pi\)
0.999977 + 0.00684294i \(0.00217819\pi\)
\(410\) −9.94242e7 1.24674e8i −1.44258 1.80894i
\(411\) −3.60391e6 + 4.51916e6i −0.0519097 + 0.0650927i
\(412\) −4.29415e7 2.06795e7i −0.614024 0.295698i
\(413\) −3.90017e7 + 8.90188e6i −0.553647 + 0.126366i
\(414\) −5.55868e7 + 1.26873e7i −0.783377 + 0.178801i
\(415\) 7.37419e7 + 5.88072e7i 1.03174 + 0.822785i
\(416\) −1.85091e7 3.84344e7i −0.257101 0.533876i
\(417\) 3.09772e6 + 707035.i 0.0427203 + 0.00975063i
\(418\) 2.14706e8 1.03397e8i 2.93979 1.41573i
\(419\) −9.39160e7 + 7.48955e7i −1.27673 + 1.01815i −0.278391 + 0.960468i \(0.589801\pi\)
−0.998335 + 0.0576870i \(0.981627\pi\)
\(420\) −5.09019e7 + 1.16180e7i −0.687047 + 0.156814i
\(421\) 1.00708e8 8.03122e7i 1.34964 1.07631i 0.359971 0.932963i \(-0.382787\pi\)
0.989673 0.143342i \(-0.0457848\pi\)
\(422\) 1.42692e7 6.25176e7i 0.189873 0.831889i
\(423\) 3.53684e7 0.467299
\(424\) 9.76620e6i 0.128123i
\(425\) 1.31535e6 5.76291e6i 0.0171346 0.0750714i
\(426\) 7.34035e7 + 5.85373e7i 0.949484 + 0.757188i
\(427\) −4.36596e7 2.10253e7i −0.560784 0.270059i
\(428\) 8.72972e6 4.20401e6i 0.111344 0.0536207i
\(429\) 2.66044e7i 0.336963i
\(430\) 7.59820e7 + 7.30915e7i 0.955664 + 0.919309i
\(431\) −7.45728e7 −0.931426 −0.465713 0.884936i \(-0.654202\pi\)
−0.465713 + 0.884936i \(0.654202\pi\)
\(432\) −3.71798e7 7.72047e7i −0.461165 0.957618i
\(433\) −2.98942e7 + 6.20759e7i −0.368233 + 0.764644i −0.999944 0.0105598i \(-0.996639\pi\)
0.631711 + 0.775204i \(0.282353\pi\)
\(434\) −5.31167e7 + 6.66063e7i −0.649774 + 0.814790i
\(435\) 7.54624e7 + 1.72238e7i 0.916775 + 0.209248i
\(436\) 3.19418e7 0.385390
\(437\) 1.36002e8i 1.62968i
\(438\) −7.88649e7 1.80004e7i −0.938559 0.214220i
\(439\) 2.08724e7 + 2.61731e7i 0.246705 + 0.309359i 0.889730 0.456486i \(-0.150892\pi\)
−0.643025 + 0.765845i \(0.722321\pi\)
\(440\) 3.08006e6 + 1.34946e7i 0.0361577 + 0.158417i
\(441\) −2.93306e7 3.67794e7i −0.341983 0.428834i
\(442\) −2.22379e7 4.61774e7i −0.257529 0.534765i
\(443\) −3.23401e7 + 1.41691e8i −0.371989 + 1.62979i 0.349196 + 0.937050i \(0.386455\pi\)
−0.721185 + 0.692743i \(0.756402\pi\)
\(444\) 2.55797e7 1.23186e7i 0.292245 0.140738i
\(445\) −4.58734e7 + 5.75234e7i −0.520572 + 0.652777i
\(446\) −1.16032e7 5.08368e7i −0.130789 0.573025i
\(447\) 1.02812e7 + 4.50450e7i 0.115112 + 0.504340i
\(448\) −4.26881e7 + 8.86428e7i −0.474759 + 0.985847i
\(449\) −6.76179e7 5.39235e7i −0.747004 0.595716i 0.174239 0.984703i \(-0.444253\pi\)
−0.921243 + 0.388988i \(0.872825\pi\)
\(450\) −4.92510e6 + 3.92763e6i −0.0540477 + 0.0431016i
\(451\) −1.88516e8 9.07846e7i −2.05503 0.989652i
\(452\) −3.45865e7 + 7.18195e7i −0.374534 + 0.777727i
\(453\) −6.38770e7 8.00993e7i −0.687148 0.861656i
\(454\) −8.26763e7 + 1.03673e8i −0.883515 + 1.10789i
\(455\) −4.79983e7 2.31147e7i −0.509555 0.245389i
\(456\) −1.28758e7 + 2.93881e6i −0.135793 + 0.0309939i
\(457\) 1.52324e8 3.47669e7i 1.59595 0.364265i 0.670133 0.742241i \(-0.266237\pi\)
0.925815 + 0.377976i \(0.123380\pi\)
\(458\) −7.01176e7 5.59169e7i −0.729845 0.582032i
\(459\) −4.08107e7 8.47443e7i −0.422023 0.876339i
\(460\) 7.44590e7 + 1.69948e7i 0.764969 + 0.174599i
\(461\) −9.87036e7 + 4.75331e7i −1.00747 + 0.485170i −0.863465 0.504408i \(-0.831711\pi\)
−0.144000 + 0.989578i \(0.545996\pi\)
\(462\) −1.12662e8 + 8.98453e7i −1.14249 + 0.911107i
\(463\) 1.12409e8 2.56566e7i 1.13255 0.258498i 0.385140 0.922858i \(-0.374153\pi\)
0.747412 + 0.664361i \(0.231296\pi\)
\(464\) 1.39363e8 1.11138e8i 1.39506 1.11252i
\(465\) −7.09990e6 + 3.11067e7i −0.0706144 + 0.309382i
\(466\) 7.50756e7 0.741893
\(467\) 9.25263e7i 0.908478i −0.890880 0.454239i \(-0.849911\pi\)
0.890880 0.454239i \(-0.150089\pi\)
\(468\) −5.77823e6 + 2.53161e7i −0.0563712 + 0.246979i
\(469\) −5.66529e7 4.51792e7i −0.549166 0.437945i
\(470\) −8.97841e7 4.32378e7i −0.864781 0.416456i
\(471\) 1.68393e7 8.10936e6i 0.161161 0.0776111i
\(472\) 5.68261e6i 0.0540408i
\(473\) 1.31437e8 + 4.31503e7i 1.24203 + 0.407756i
\(474\) 4.74363e7 0.445426
\(475\) 6.51962e6 + 1.35381e7i 0.0608333 + 0.126322i
\(476\) −5.72634e7 + 1.18909e8i −0.530954 + 1.10254i
\(477\) −4.32486e7 + 5.42321e7i −0.398490 + 0.499690i
\(478\) −2.16919e8 4.95103e7i −1.98616 0.453327i
\(479\) 6.83869e7 0.622252 0.311126 0.950369i \(-0.399294\pi\)
0.311126 + 0.950369i \(0.399294\pi\)
\(480\) 8.65371e7i 0.782490i
\(481\) 2.82431e7 + 6.44631e6i 0.253792 + 0.0579263i
\(482\) −6.44414e7 8.08070e7i −0.575472 0.721619i
\(483\) −1.82999e7 8.01770e7i −0.162408 0.711555i
\(484\) −4.54162e7 5.69501e7i −0.400566 0.502294i
\(485\) −2.69591e7 5.59811e7i −0.236309 0.490700i
\(486\) −3.58595e7 + 1.57111e8i −0.312389 + 1.36867i
\(487\) −1.63767e8 + 7.88662e7i −1.41788 + 0.682817i −0.976702 0.214601i \(-0.931155\pi\)
−0.441182 + 0.897418i \(0.645441\pi\)
\(488\) −4.29176e6 + 5.38170e6i −0.0369297 + 0.0463084i
\(489\) 1.61008e6 + 7.05424e6i 0.0137696 + 0.0603287i
\(490\) 2.94942e7 + 1.29222e8i 0.250696 + 1.09837i
\(491\) 3.66823e7 7.61715e7i 0.309893 0.643499i −0.686613 0.727023i \(-0.740903\pi\)
0.996506 + 0.0835239i \(0.0266175\pi\)
\(492\) −8.76521e7 6.99002e7i −0.735982 0.586926i
\(493\) 1.52973e8 1.21992e8i 1.27665 1.01810i
\(494\) 1.17384e8 + 5.65293e7i 0.973708 + 0.468913i
\(495\) 4.26558e7 8.85758e7i 0.351692 0.730297i
\(496\) 4.58127e7 + 5.74473e7i 0.375441 + 0.470788i
\(497\) 1.53805e8 1.92866e8i 1.25286 1.57103i
\(498\) 1.25668e8 + 6.05187e7i 1.01751 + 0.490006i
\(499\) 6.20080e7 1.41529e7i 0.499052 0.113905i 0.0344169 0.999408i \(-0.489043\pi\)
0.464635 + 0.885502i \(0.346185\pi\)
\(500\) 1.14300e8 2.60883e7i 0.914401 0.208706i
\(501\) −6.48784e7 5.17388e7i −0.515926 0.411437i
\(502\) −1.22729e8 2.54849e8i −0.970144 2.01452i
\(503\) −4.72745e7 1.07901e7i −0.371469 0.0847854i 0.0327109 0.999465i \(-0.489586\pi\)
−0.404180 + 0.914679i \(0.632443\pi\)
\(504\) −1.31069e7 + 6.31196e6i −0.102379 + 0.0493029i
\(505\) 1.40840e8 1.12316e8i 1.09359 0.872105i
\(506\) 2.05505e8 4.69051e7i 1.58625 0.362050i
\(507\) −4.92860e7 + 3.93043e7i −0.378181 + 0.301589i
\(508\) −6.74573e6 + 2.95550e7i −0.0514562 + 0.225444i
\(509\) −1.21771e8 −0.923401 −0.461701 0.887036i \(-0.652761\pi\)
−0.461701 + 0.887036i \(0.652761\pi\)
\(510\) 1.03971e8i 0.783793i
\(511\) −4.72955e7 + 2.07215e8i −0.354452 + 1.55296i
\(512\) 1.41074e8 + 1.12503e8i 1.05108 + 0.838212i
\(513\) 2.15422e8 + 1.03742e8i 1.59565 + 0.768426i
\(514\) −2.82963e8 + 1.36268e8i −2.08372 + 1.00347i
\(515\) 9.86536e7i 0.722256i
\(516\) 6.35146e7 + 3.82117e7i 0.462300 + 0.278130i
\(517\) −1.30757e8 −0.946224
\(518\) −6.80810e7 1.41372e8i −0.489820 1.01712i
\(519\) −2.31844e6 + 4.81429e6i −0.0165842 + 0.0344374i
\(520\) −4.71826e6 + 5.91651e6i −0.0335561 + 0.0420780i
\(521\) 4.23410e7 + 9.66405e6i 0.299397 + 0.0683355i 0.369581 0.929199i \(-0.379501\pi\)
−0.0701835 + 0.997534i \(0.522358\pi\)
\(522\) −2.08513e8 −1.46596
\(523\) 7.70056e7i 0.538291i −0.963100 0.269146i \(-0.913259\pi\)
0.963100 0.269146i \(-0.0867413\pi\)
\(524\) 4.59079e7 + 1.04782e7i 0.319076 + 0.0728269i
\(525\) −5.66512e6 7.10384e6i −0.0391500 0.0490925i
\(526\) −5.54918e7 2.43126e8i −0.381304 1.67060i
\(527\) 5.02867e7 + 6.30575e7i 0.343575 + 0.430829i
\(528\) 5.39255e7 + 1.11978e8i 0.366347 + 0.760727i
\(529\) 6.17212e6 2.70418e7i 0.0416934 0.182671i
\(530\) 1.76087e8 8.47989e7i 1.18277 0.569591i
\(531\) 2.51649e7 3.15557e7i 0.168078 0.210763i
\(532\) −7.46543e7 3.27082e8i −0.495815 2.17231i
\(533\) −2.54551e7 1.11526e8i −0.168110 0.736536i
\(534\) −4.72085e7 + 9.80294e7i −0.310025 + 0.643773i
\(535\) −1.56801e7 1.25045e7i −0.102397 0.0816590i
\(536\) −8.04747e6 + 6.41764e6i −0.0522594 + 0.0416755i
\(537\) 1.45629e8 + 7.01314e7i 0.940430 + 0.452887i
\(538\) 1.52420e7 3.16504e7i 0.0978805 0.203251i
\(539\) 1.08435e8 + 1.35974e8i 0.692475 + 0.868337i
\(540\) 8.37160e7 1.04976e8i 0.531651 0.666670i
\(541\) −3.94404e7 1.89935e7i −0.249086 0.119953i 0.305175 0.952296i \(-0.401285\pi\)
−0.554261 + 0.832343i \(0.686999\pi\)
\(542\) −9.13461e7 + 2.08492e7i −0.573710 + 0.130946i
\(543\) −3.64434e7 + 8.31797e6i −0.227625 + 0.0519539i
\(544\) 1.71024e8 + 1.36387e8i 1.06233 + 0.847184i
\(545\) −2.86866e7 5.95683e7i −0.177210 0.367981i
\(546\) −7.68074e7 1.75308e7i −0.471873 0.107702i
\(547\) 7.60888e7 3.66424e7i 0.464899 0.223884i −0.186745 0.982408i \(-0.559794\pi\)
0.651644 + 0.758525i \(0.274080\pi\)
\(548\) −1.63072e7 + 1.30045e7i −0.0990915 + 0.0790229i
\(549\) 4.76646e7 1.08791e7i 0.288058 0.0657473i
\(550\) 1.82081e7 1.45205e7i 0.109440 0.0872756i
\(551\) −1.10675e8 + 4.84901e8i −0.661602 + 2.89867i
\(552\) −1.16819e7 −0.0694540
\(553\) 1.24638e8i 0.737010i
\(554\) −1.41648e7 + 6.20602e7i −0.0833071 + 0.364992i
\(555\) −4.59457e7 3.66405e7i −0.268761 0.214330i
\(556\) 1.03300e7 + 4.97466e6i 0.0601002 + 0.0289427i
\(557\) −5.24999e7 + 2.52826e7i −0.303804 + 0.146304i −0.579574 0.814919i \(-0.696781\pi\)
0.275771 + 0.961223i \(0.411067\pi\)
\(558\) 8.59520e7i 0.494713i
\(559\) 2.63590e7 + 7.08904e7i 0.150902 + 0.405838i
\(560\) 2.48876e8 1.41716
\(561\) 5.91917e7 + 1.22913e8i 0.335253 + 0.696160i
\(562\) −4.11175e7 + 8.53814e7i −0.231642 + 0.481010i
\(563\) 2.48614e7 3.11753e7i 0.139316 0.174697i −0.707279 0.706935i \(-0.750077\pi\)
0.846595 + 0.532238i \(0.178649\pi\)
\(564\) −6.83045e7 1.55900e7i −0.380725 0.0868981i
\(565\) 1.64998e8 0.914815
\(566\) 2.46899e8i 1.36166i
\(567\) 1.50785e7 + 3.44156e6i 0.0827196 + 0.0188802i
\(568\) −2.18478e7 2.73963e7i −0.119224 0.149502i
\(569\) −9.51543e6 4.16898e7i −0.0516526 0.226305i 0.942513 0.334169i \(-0.108456\pi\)
−0.994166 + 0.107865i \(0.965599\pi\)
\(570\) −1.64786e8 2.06635e8i −0.889808 1.11578i
\(571\) 1.39651e8 + 2.89988e8i 0.750127 + 1.55765i 0.828024 + 0.560693i \(0.189465\pi\)
−0.0778967 + 0.996961i \(0.524820\pi\)
\(572\) 2.13622e7 9.35937e7i 0.114145 0.500102i
\(573\) −6.72068e7 + 3.23651e7i −0.357231 + 0.172034i
\(574\) −3.86318e8 + 4.84428e8i −2.04272 + 2.56149i
\(575\) 2.95756e6 + 1.29579e7i 0.0155572 + 0.0681604i
\(576\) −2.20881e7 9.67744e7i −0.115582 0.506399i
\(577\) −1.25213e8 + 2.60008e8i −0.651812 + 1.35350i 0.268865 + 0.963178i \(0.413351\pi\)
−0.920678 + 0.390324i \(0.872363\pi\)
\(578\) −2.96452e6 2.36412e6i −0.0153522 0.0122430i
\(579\) 1.18526e8 9.45215e7i 0.610631 0.486962i
\(580\) 2.51645e8 + 1.21186e8i 1.28975 + 0.621110i
\(581\) 1.59011e8 3.30190e8i 0.810773 1.68359i
\(582\) −5.72896e7 7.18389e7i −0.290608 0.364411i
\(583\) 1.59890e8 2.00496e8i 0.806894 1.01181i
\(584\) 2.72017e7 + 1.30996e7i 0.136571 + 0.0657690i
\(585\) 5.24013e7 1.19603e7i 0.261743 0.0597411i
\(586\) 1.28354e8 2.92959e7i 0.637845 0.145584i
\(587\) 2.00940e8 + 1.60244e8i 0.993462 + 0.792260i 0.978209 0.207624i \(-0.0665730\pi\)
0.0152536 + 0.999884i \(0.495144\pi\)
\(588\) 4.04320e7 + 8.39580e7i 0.198881 + 0.412981i
\(589\) −1.99883e8 4.56220e7i −0.978205 0.223269i
\(590\) −1.02459e8 + 4.93415e7i −0.498877 + 0.240246i
\(591\) −1.08731e8 + 8.67103e7i −0.526735 + 0.420057i
\(592\) −1.31941e8 + 3.01147e7i −0.635938 + 0.145149i
\(593\) −1.94849e7 + 1.55387e7i −0.0934404 + 0.0745162i −0.669096 0.743176i \(-0.733318\pi\)
0.575655 + 0.817692i \(0.304747\pi\)
\(594\) 8.24620e7 3.61290e8i 0.393455 1.72384i
\(595\) 2.73180e8 1.29688
\(596\) 1.66723e8i 0.787509i
\(597\) 3.78040e7 1.65630e8i 0.177670 0.778425i
\(598\) 9.01005e7 + 7.18528e7i 0.421331 + 0.336000i
\(599\) −2.39010e8 1.15101e8i −1.11208 0.535550i −0.214643 0.976692i \(-0.568859\pi\)
−0.897437 + 0.441143i \(0.854573\pi\)
\(600\) −1.16286e6 + 560002.i −0.00538360 + 0.00259260i
\(601\) 2.51018e8i 1.15633i −0.815920 0.578165i \(-0.803769\pi\)
0.815920 0.578165i \(-0.196231\pi\)
\(602\) 2.11185e8 3.51026e8i 0.967996 1.60898i
\(603\) 7.31078e7 0.333435
\(604\) −1.60402e8 3.33078e8i −0.727945 1.51159i
\(605\) −6.54184e7 + 1.35843e8i −0.295416 + 0.613438i
\(606\) 1.66096e8 2.08277e8i 0.746346 0.935889i
\(607\) −3.56339e8 8.13321e7i −1.59330 0.363660i −0.668380 0.743820i \(-0.733012\pi\)
−0.924921 + 0.380160i \(0.875869\pi\)
\(608\) −5.56064e8 −2.47408
\(609\) 3.00754e8i 1.33156i
\(610\) −1.34298e8 3.06527e7i −0.591672 0.135045i
\(611\) −4.45718e7 5.58912e7i −0.195405 0.245030i
\(612\) −2.96298e7 1.29817e8i −0.129263 0.566339i
\(613\) −1.95238e8 2.44820e8i −0.847583 1.06284i −0.997251 0.0740992i \(-0.976392\pi\)
0.149668 0.988736i \(-0.452180\pi\)
\(614\) 1.66408e8 + 3.45550e8i 0.718902 + 1.49281i
\(615\) −5.16376e7 + 2.26239e8i −0.221994 + 0.972618i
\(616\) 4.84563e7 2.33353e7i 0.207304 0.0998325i
\(617\) −4.32076e7 + 5.41807e7i −0.183952 + 0.230669i −0.865254 0.501334i \(-0.832843\pi\)
0.681302 + 0.732003i \(0.261414\pi\)
\(618\) 3.24638e7 + 1.42233e8i 0.137541 + 0.602608i
\(619\) 2.32643e7 + 1.01928e8i 0.0980885 + 0.429754i 0.999998 0.00217203i \(-0.000691380\pi\)
−0.901909 + 0.431926i \(0.857834\pi\)
\(620\) −4.99546e7 + 1.03732e8i −0.209604 + 0.435248i
\(621\) 1.65351e8 + 1.31863e8i 0.690451 + 0.550616i
\(622\) −7.51000e7 + 5.98903e7i −0.312082 + 0.248877i
\(623\) 2.57570e8 + 1.24039e8i 1.06520 + 0.512972i
\(624\) −2.94821e7 + 6.12203e7i −0.121340 + 0.251966i
\(625\) −1.39498e8 1.74925e8i −0.571385 0.716494i
\(626\) −2.05340e8 + 2.57488e8i −0.837048 + 1.04962i
\(627\) −3.12448e8 1.50467e8i −1.26758 0.610434i
\(628\) 6.57516e7 1.50074e7i 0.265477 0.0605935i
\(629\) −1.44826e8 + 3.30556e7i −0.581962 + 0.132829i
\(630\) −2.27612e8 1.81515e8i −0.910278 0.725922i
\(631\) −3.76065e7 7.80907e7i −0.149684 0.310822i 0.812622 0.582791i \(-0.198039\pi\)
−0.962306 + 0.271969i \(0.912325\pi\)
\(632\) −1.72607e7 3.93964e6i −0.0683765 0.0156065i
\(633\) −8.40760e7 + 4.04889e7i −0.331483 + 0.159634i
\(634\) 9.42438e7 7.51569e7i 0.369815 0.294918i
\(635\) 6.11753e7 1.39629e7i 0.238921 0.0545322i
\(636\) 1.07428e8 8.56709e7i 0.417586 0.333013i
\(637\) −2.11581e7 + 9.26998e7i −0.0818575 + 0.358641i
\(638\) 7.70874e8 2.96839
\(639\) 2.48883e8i 0.953879i
\(640\) 1.44377e7 6.32558e7i 0.0550756 0.241302i
\(641\) 3.26319e7 + 2.60231e7i 0.123899 + 0.0988064i 0.683479 0.729970i \(-0.260466\pi\)
−0.559580 + 0.828776i \(0.689037\pi\)
\(642\) −2.67215e7 1.28684e7i −0.100985 0.0486317i
\(643\) 2.76104e8 1.32965e8i 1.03858 0.500153i 0.164724 0.986340i \(-0.447327\pi\)
0.873855 + 0.486187i \(0.161613\pi\)
\(644\) 2.96755e8i 1.11107i
\(645\) 1.42194e7 1.52766e8i 0.0529909 0.569308i
\(646\) −6.68089e8 −2.47820
\(647\) −7.44597e7 1.54617e8i −0.274921 0.570880i 0.717097 0.696973i \(-0.245470\pi\)
−0.992018 + 0.126093i \(0.959756\pi\)
\(648\) 953224. 1.97939e6i 0.00350324 0.00727455i
\(649\) −9.30346e7 + 1.16662e8i −0.340338 + 0.426770i
\(650\) 1.24133e7 + 2.83327e6i 0.0452011 + 0.0103169i
\(651\) 1.23975e8 0.449357
\(652\) 2.61095e7i 0.0942010i
\(653\) −3.98575e7 9.09721e6i −0.143143 0.0326715i 0.150349 0.988633i \(-0.451960\pi\)
−0.293492 + 0.955962i \(0.594817\pi\)
\(654\) −6.09607e7 7.64423e7i −0.217930 0.273275i
\(655\) −2.16886e7 9.50240e7i −0.0771805 0.338150i
\(656\) 3.33196e8 + 4.17815e8i 1.18029 + 1.48004i
\(657\) −9.30416e7 1.93203e8i −0.328081 0.681267i
\(658\) −8.61616e7 + 3.77499e8i −0.302438 + 1.32507i
\(659\) 3.13982e8 1.51206e8i 1.09711 0.528338i 0.204358 0.978896i \(-0.434489\pi\)
0.892747 + 0.450558i \(0.148775\pi\)
\(660\) −1.21421e8 + 1.52258e8i −0.422341 + 0.529599i
\(661\) −6.05169e7 2.65142e8i −0.209543 0.918066i −0.964872 0.262721i \(-0.915380\pi\)
0.755329 0.655345i \(-0.227477\pi\)
\(662\) 1.31579e8 + 5.76483e8i 0.453535 + 1.98707i
\(663\) −3.23613e7 + 6.71989e7i −0.111041 + 0.230580i
\(664\) −4.07009e7 3.24579e7i −0.139027 0.110871i
\(665\) −5.42929e8 + 4.32971e8i −1.84620 + 1.47229i
\(666\) 1.42632e8 + 6.86879e7i 0.482830 + 0.232519i
\(667\) −1.90883e8 + 3.96373e8i −0.643266 + 1.33576i
\(668\) −1.86697e8 2.34110e8i −0.626336 0.785401i
\(669\) −4.73115e7 + 5.93268e7i −0.158012 + 0.198140i
\(670\) −1.85587e8 8.93739e7i −0.617054 0.297157i
\(671\) −1.76216e8 + 4.02202e7i −0.583282 + 0.133130i
\(672\) 3.27815e8 7.48215e7i 1.08024 0.246558i
\(673\) 1.00191e7 + 7.98998e6i 0.0328688 + 0.0262120i 0.639786 0.768553i \(-0.279023\pi\)
−0.606918 + 0.794765i \(0.707594\pi\)
\(674\) 2.58525e8 + 5.36833e8i 0.844352 + 1.75331i
\(675\) 2.27808e7 + 5.19957e6i 0.0740727 + 0.0169066i
\(676\) −2.04947e8 + 9.86971e7i −0.663439 + 0.319495i
\(677\) 1.69999e8 1.35569e8i 0.547873 0.436914i −0.310029 0.950727i \(-0.600339\pi\)
0.857902 + 0.513813i \(0.171767\pi\)
\(678\) 2.37885e8 5.42956e7i 0.763268 0.174211i
\(679\) −1.88755e8 + 1.50527e8i −0.602960 + 0.480845i
\(680\) 8.63490e6 3.78320e7i 0.0274619 0.120318i
\(681\) 1.92968e8 0.611002
\(682\) 3.17765e8i 1.00174i
\(683\) −1.08748e6 + 4.76457e6i −0.00341319 + 0.0149541i −0.976606 0.215037i \(-0.931013\pi\)
0.973193 + 0.229991i \(0.0738698\pi\)
\(684\) 2.64638e8 + 2.11041e8i 0.826957 + 0.659477i
\(685\) 3.88974e7 + 1.87320e7i 0.121018 + 0.0582790i
\(686\) −8.21400e7 + 3.95565e7i −0.254438 + 0.122531i
\(687\) 1.30511e8i 0.402509i
\(688\) −2.54635e8 2.44948e8i −0.781904 0.752159i
\(689\) 1.40203e8 0.428647
\(690\) −1.01433e8 2.10628e8i −0.308768 0.641163i
\(691\) 1.68980e7 3.50890e7i 0.0512153 0.106350i −0.873791 0.486302i \(-0.838345\pi\)
0.925006 + 0.379953i \(0.124060\pi\)
\(692\) −1.20219e7 + 1.50750e7i −0.0362789 + 0.0454923i
\(693\) −3.72418e8 8.50020e7i −1.11900 0.255405i
\(694\) 4.53536e8 1.35685
\(695\) 2.37321e7i 0.0706939i
\(696\) −4.16505e7 9.50646e6i −0.123536 0.0281962i
\(697\) 3.65735e8 + 4.58617e8i 1.08011 + 1.35442i
\(698\) −1.58474e8 6.94320e8i −0.466006 2.04171i
\(699\) −6.81178e7 8.54171e7i −0.199448 0.250100i
\(700\) −1.42257e7 2.95400e7i −0.0414744 0.0861224i
\(701\) 3.83165e6 1.67875e7i 0.0111232 0.0487341i −0.969062 0.246818i \(-0.920615\pi\)
0.980185 + 0.198084i \(0.0634720\pi\)
\(702\) 1.82540e8 8.79066e7i 0.527651 0.254103i
\(703\) 2.35442e8 2.95235e8i 0.677669 0.849770i
\(704\) 8.16599e7 + 3.57776e8i 0.234041 + 1.02540i
\(705\) 3.22696e7 + 1.41382e8i 0.0920928 + 0.403485i
\(706\) 3.84506e8 7.98434e8i 1.09267 2.26895i
\(707\) −5.47243e8 4.36412e8i −1.54854 1.23492i
\(708\) −6.25085e7 + 4.98489e7i −0.176132 + 0.140461i
\(709\) −2.69780e8 1.29919e8i −0.756957 0.364531i 0.0152657 0.999883i \(-0.495141\pi\)
−0.772222 + 0.635352i \(0.780855\pi\)
\(710\) 3.04259e8 6.31800e8i 0.850096 1.76524i
\(711\) 7.84030e7 + 9.83142e7i 0.218134 + 0.273532i
\(712\) 2.53192e7 3.17493e7i 0.0701473 0.0879619i
\(713\) −1.63391e8 7.86848e7i −0.450774 0.217081i
\(714\) 3.93856e8 8.98950e7i 1.08204 0.246968i
\(715\) −1.93728e8 + 4.42172e7i −0.529998 + 0.120969i
\(716\) 4.56009e8 + 3.63655e8i 1.24232 + 0.990719i
\(717\) 1.40485e8 + 2.91720e8i 0.381130 + 0.791424i
\(718\) −1.51005e8 3.44659e7i −0.407961 0.0931144i
\(719\) 1.28455e8 6.18608e7i 0.345593 0.166429i −0.253033 0.967458i \(-0.581428\pi\)
0.598626 + 0.801029i \(0.295714\pi\)
\(720\) −1.96314e8 + 1.56555e8i −0.525960 + 0.419439i
\(721\) 3.73713e8 8.52976e7i 0.997086 0.227578i
\(722\) 9.21512e8 7.34881e8i 2.44844 1.95257i
\(723\) −3.34687e7 + 1.46636e8i −0.0885573 + 0.387995i
\(724\) −1.34886e8 −0.355428
\(725\) 4.86068e7i 0.127551i
\(726\) −4.96150e7 + 2.17377e8i −0.129659 + 0.568074i
\(727\) 3.70724e8 + 2.95643e8i 0.964823 + 0.769420i 0.973062 0.230546i \(-0.0740511\pi\)
−0.00823874 + 0.999966i \(0.502623\pi\)
\(728\) 2.64920e7 + 1.27579e7i 0.0686628 + 0.0330662i
\(729\) 1.89512e8 9.12641e7i 0.489163 0.235569i
\(730\) 6.04196e8i 1.55313i
\(731\) −2.79502e8 2.68869e8i −0.715539 0.688318i
\(732\) −9.68466e7 −0.246917
\(733\) 5.50159e7 + 1.14242e8i 0.139694 + 0.290077i 0.959065 0.283186i \(-0.0913915\pi\)
−0.819371 + 0.573263i \(0.805677\pi\)
\(734\) 6.36122e7 1.32092e8i 0.160861 0.334032i
\(735\) 1.20262e8 1.50803e8i 0.302876 0.379795i
\(736\) −4.79525e8 1.09448e8i −1.20276 0.274522i
\(737\) −2.70280e8 −0.675167
\(738\) 6.25130e8i 1.55525i
\(739\) 6.04048e8 + 1.37870e8i 1.49671 + 0.341615i 0.890976 0.454051i \(-0.150022\pi\)
0.605736 + 0.795665i \(0.292879\pi\)
\(740\) −1.32215e8 1.65793e8i −0.326277 0.409139i
\(741\) −4.21894e7 1.84844e8i −0.103693 0.454308i
\(742\) −4.73478e8 5.93722e8i −1.15901 1.45335i
\(743\) 1.42975e8 + 2.96890e8i 0.348572 + 0.723818i 0.999372 0.0354316i \(-0.0112806\pi\)
−0.650800 + 0.759249i \(0.725566\pi\)
\(744\) 3.91870e6 1.71689e7i 0.00951531 0.0416893i
\(745\) 3.10921e8 1.49732e8i 0.751936 0.362113i
\(746\) 2.29432e7 2.87699e7i 0.0552634 0.0692981i
\(747\) 8.22772e7 + 3.60480e8i 0.197387 + 0.864807i
\(748\) 1.09542e8 + 4.79933e8i 0.261743 + 1.14677i
\(749\) −3.38113e7 + 7.02100e7i −0.0804668 + 0.167091i
\(750\) −2.80575e8 2.23751e8i −0.665066 0.530372i
\(751\) 4.25445e8 3.39281e8i 1.00444 0.801014i 0.0243772 0.999703i \(-0.492240\pi\)
0.980063 + 0.198689i \(0.0636683\pi\)
\(752\) 3.00890e8 + 1.44901e8i 0.707545 + 0.340736i
\(753\) −1.78599e8 + 3.70865e8i −0.418306 + 0.868622i
\(754\) 2.62771e8 + 3.29504e8i 0.613004 + 0.768683i
\(755\) −4.77102e8 + 5.98267e8i −1.10859 + 1.39013i
\(756\) −4.70048e8 2.26363e8i −1.08787 0.523890i
\(757\) 4.42524e8 1.01003e8i 1.02012 0.232835i 0.320420 0.947276i \(-0.396176\pi\)
0.699696 + 0.714441i \(0.253319\pi\)
\(758\) −3.90390e8 + 8.91041e7i −0.896379 + 0.204593i
\(759\) −2.39825e8 1.91254e8i −0.548491 0.437407i
\(760\) 4.27996e7 + 8.88743e7i 0.0974988 + 0.202458i
\(761\) −1.52658e8 3.48432e7i −0.346391 0.0790614i 0.0457861 0.998951i \(-0.485421\pi\)
−0.392177 + 0.919890i \(0.628278\pi\)
\(762\) 8.36043e7 4.02617e7i 0.188957 0.0909970i
\(763\) −2.00850e8 + 1.60172e8i −0.452166 + 0.360590i
\(764\) −2.62420e8 + 5.98956e7i −0.588460 + 0.134312i
\(765\) −2.15485e8 + 1.71844e8i −0.481319 + 0.383839i
\(766\) −9.65519e7 + 4.23022e8i −0.214820 + 0.941188i
\(767\) −8.15793e7 −0.180798
\(768\) 3.12917e8i 0.690789i
\(769\) 1.40354e8 6.14933e8i 0.308636 1.35222i −0.548075 0.836429i \(-0.684639\pi\)
0.856712 0.515796i \(-0.172504\pi\)
\(770\) 8.41483e8 + 6.71061e8i 1.84320 + 1.46991i
\(771\) 4.11776e8 + 1.98301e8i 0.898459 + 0.432675i
\(772\) 4.92869e8 2.37353e8i 1.07122 0.515874i
\(773\) 1.26755e8i 0.274427i 0.990541 + 0.137214i \(0.0438147\pi\)
−0.990541 + 0.137214i \(0.956185\pi\)
\(774\) 5.42293e7 + 4.09735e8i 0.116953 + 0.883651i
\(775\) −2.00364e7 −0.0430442
\(776\) 1.48797e7 + 3.08981e7i 0.0318427 + 0.0661220i
\(777\) −9.90737e7 + 2.05729e8i −0.211201 + 0.438563i
\(778\) −6.85011e8 + 8.58977e8i −1.45465 + 1.82407i
\(779\) −1.45375e9 3.31809e8i −3.07523 0.701901i
\(780\) −1.06471e8 −0.224361
\(781\) 9.20123e8i 1.93149i
\(782\) −5.76130e8 1.31498e8i −1.20476 0.274978i
\(783\) 4.82234e8 + 6.04702e8i 1.00455 + 1.25967i
\(784\) −9.88426e7 4.33058e8i −0.205114 0.898665i
\(785\) −8.70380e7 1.09142e8i −0.179928 0.225623i
\(786\) −6.25388e7 1.29863e8i −0.128790 0.267435i
\(787\) −1.81312e7 + 7.94380e7i −0.0371965 + 0.162969i −0.990115 0.140258i \(-0.955207\pi\)
0.952918 + 0.303227i \(0.0980639\pi\)
\(788\) −4.52139e8 + 2.17739e8i −0.924045 + 0.444996i
\(789\) −2.26266e8 + 2.83729e8i −0.460669 + 0.577661i
\(790\) −7.88403e7 3.45422e8i −0.159907 0.700597i
\(791\) −1.42660e8 6.25035e8i −0.288252 1.26292i
\(792\) −2.35434e7 + 4.88883e7i −0.0473907 + 0.0984078i
\(793\) −7.72595e7 6.16124e7i −0.154929 0.123552i
\(794\) 7.34622e8 5.85842e8i 1.46758 1.17036i
\(795\) −2.56247e8 1.23402e8i −0.509985 0.245596i
\(796\) 2.65988e8 5.52329e8i 0.527378 1.09511i
\(797\) 7.46652e7 + 9.36272e7i 0.147483 + 0.184938i 0.850086 0.526644i \(-0.176550\pi\)
−0.702602 + 0.711583i \(0.747979\pi\)
\(798\) −6.40286e8 + 8.02894e8i −1.25999 + 1.57997i
\(799\) 3.30274e8 + 1.59052e8i 0.647491 + 0.311815i
\(800\) −5.29802e7 + 1.20924e7i −0.103477 + 0.0236180i
\(801\) −2.81197e8 + 6.41815e7i −0.547159 + 0.124886i
\(802\) 4.60433e8 + 3.67183e8i 0.892573 + 0.711803i
\(803\) 3.43975e8 + 7.14272e8i 0.664325 + 1.37948i
\(804\) −1.41188e8 3.22252e7i −0.271662 0.0620050i
\(805\) −5.53418e8 + 2.66512e8i −1.06088 + 0.510892i
\(806\) −1.35826e8 + 1.08318e8i −0.259405 + 0.206869i
\(807\) −4.98396e7 + 1.13756e7i −0.0948318 + 0.0216447i
\(808\) −7.77350e7 + 6.19916e7i −0.147361 + 0.117517i
\(809\) −8.87065e7 + 3.88649e8i −0.167537 + 0.734026i 0.819440 + 0.573165i \(0.194284\pi\)
−0.986977 + 0.160862i \(0.948573\pi\)
\(810\) 4.39656e7 0.0827291
\(811\) 3.64474e7i 0.0683288i −0.999416 0.0341644i \(-0.989123\pi\)
0.999416 0.0341644i \(-0.0108770\pi\)
\(812\) 2.41492e8 1.05805e9i 0.451060 1.97623i
\(813\) 1.06601e8 + 8.50118e7i 0.198377 + 0.158200i
\(814\) −5.27311e8 2.53940e8i −0.977673 0.470822i
\(815\) 4.86916e7 2.34486e7i 0.0899458 0.0433156i
\(816\) 3.48433e8i 0.641282i
\(817\) 9.81631e8 + 9.13699e7i 1.80004 + 0.167547i
\(818\) −6.46441e8 −1.18105
\(819\) −9.06142e7 1.88162e8i −0.164947 0.342516i
\(820\) −3.63320e8 + 7.54441e8i −0.658942 + 1.36831i
\(821\) −2.60032e8 + 3.26070e8i −0.469891 + 0.589225i −0.959144 0.282917i \(-0.908698\pi\)
0.489253 + 0.872142i \(0.337269\pi\)
\(822\) 6.22441e7 + 1.42068e7i 0.112068 + 0.0255789i
\(823\) −2.17155e8 −0.389556 −0.194778 0.980847i \(-0.562399\pi\)
−0.194778 + 0.980847i \(0.562399\pi\)
\(824\) 5.44506e7i 0.0973242i
\(825\) −3.30413e7 7.54145e6i −0.0588430 0.0134305i
\(826\) 2.75500e8 + 3.45466e8i 0.488857 + 0.613007i
\(827\) 1.34282e8 + 5.88327e8i 0.237411 + 1.04016i 0.943326 + 0.331868i \(0.107679\pi\)
−0.705915 + 0.708297i \(0.749464\pi\)
\(828\) 1.86673e8 + 2.34081e8i 0.328845 + 0.412358i
\(829\) −2.49813e8 5.18742e8i −0.438482 0.910517i −0.996727 0.0808412i \(-0.974239\pi\)
0.558245 0.829676i \(-0.311475\pi\)
\(830\) 2.31821e8 1.01568e9i 0.405433 1.77632i
\(831\) 8.34609e7 4.01926e7i 0.145439 0.0700396i
\(832\) −1.25093e8 + 1.56861e8i −0.217201 + 0.272362i
\(833\) −1.08495e8 4.75349e8i −0.187705 0.822390i
\(834\) −7.80948e6 3.42156e7i −0.0134624 0.0589828i
\(835\) −2.68922e8 + 5.58423e8i −0.461921 + 0.959188i
\(836\) −9.78366e8 7.80221e8i −1.67449 1.33536i
\(837\) −2.49267e8 + 1.98784e8i −0.425097 + 0.339004i
\(838\) 1.19541e9 + 5.75680e8i 2.03135 + 0.978249i
\(839\) 3.30069e8 6.85396e8i 0.558881 1.16053i −0.409790 0.912180i \(-0.634398\pi\)
0.968671 0.248348i \(-0.0798876\pi\)
\(840\) −3.71900e7 4.66348e7i −0.0627464 0.0786815i
\(841\) −6.32265e8 + 7.92835e8i −1.06295 + 1.33289i
\(842\) −1.28187e9 6.17316e8i −2.14737 1.03412i
\(843\) 1.34449e8 3.06872e7i 0.224427 0.0512241i
\(844\) −3.28288e8 + 7.49297e7i −0.546045 + 0.124631i
\(845\) 3.68120e8 + 2.93566e8i 0.610126 + 0.486560i
\(846\) −1.69500e8 3.51971e8i −0.279936 0.581294i
\(847\) 5.71153e8 + 1.30362e8i 0.939945 + 0.214536i
\(848\) −5.90113e8 + 2.84183e8i −0.967715 + 0.466027i
\(849\) 2.80908e8 2.24017e8i 0.459030 0.366065i
\(850\) −6.36536e7 + 1.45285e7i −0.103649 + 0.0236573i
\(851\) 2.61145e8 2.08256e8i 0.423734 0.337916i
\(852\) 1.09705e8 4.80650e8i 0.177382 0.777160i
\(853\) 6.49440e8 1.04639 0.523193 0.852214i \(-0.324741\pi\)
0.523193 + 0.852214i \(0.324741\pi\)
\(854\) 5.35243e8i 0.859364i
\(855\) 1.55903e8 6.83056e8i 0.249434 1.09284i
\(856\) 8.65444e6 + 6.90169e6i 0.0137980 + 0.0110036i
\(857\) 8.13781e8 + 3.91896e8i 1.29290 + 0.622628i 0.948673 0.316258i \(-0.102427\pi\)
0.344227 + 0.938886i \(0.388141\pi\)
\(858\) −2.64755e8 + 1.27499e8i −0.419163 + 0.201858i
\(859\) 3.64291e8i 0.574737i −0.957820 0.287368i \(-0.907220\pi\)
0.957820 0.287368i \(-0.0927804\pi\)
\(860\) 1.72688e8 5.26009e8i 0.271497 0.826986i
\(861\) 9.01671e8 1.41266
\(862\) 3.57384e8 + 7.42116e8i 0.557973 + 1.15864i
\(863\) 2.28260e8 4.73987e8i 0.355139 0.737453i −0.644492 0.764611i \(-0.722931\pi\)
0.999631 + 0.0271576i \(0.00864559\pi\)
\(864\) −5.39141e8 + 6.76061e8i −0.835913 + 1.04820i
\(865\) 3.89100e7 + 8.88095e6i 0.0601192 + 0.0137218i
\(866\) 7.61018e8 1.17177
\(867\) 5.51790e6i 0.00846674i
\(868\) 4.36142e8 + 9.95465e7i 0.666912 + 0.152218i
\(869\) −2.89856e8 3.63468e8i −0.441696 0.553869i
\(870\) −1.90244e8 8.33513e8i −0.288903 1.26577i
\(871\) −9.21314e7 1.15529e8i −0.139429 0.174838i
\(872\) 1.58332e7 + 3.28780e7i 0.0238792 + 0.0495856i
\(873\) 5.42013e7 2.37471e8i 0.0814643 0.356918i
\(874\) 1.35344e9 6.51781e8i 2.02723 0.976264i
\(875\) −5.87899e8 + 7.37202e8i −0.877563 + 1.10043i
\(876\) 9.45225e7 + 4.14130e8i 0.140612 + 0.616062i
\(877\) −2.47502e8 1.08438e9i −0.366927 1.60761i −0.735170 0.677883i \(-0.762898\pi\)
0.368243 0.929730i \(-0.379959\pi\)
\(878\) 1.60434e8 3.33146e8i 0.237036 0.492210i
\(879\) −1.49789e8 1.19453e8i −0.220554 0.175886i
\(880\) 7.25772e8 5.78784e8i 1.06501 0.849315i
\(881\) 5.02557e8 + 2.42019e8i 0.734950 + 0.353933i 0.763629 0.645655i \(-0.223416\pi\)
−0.0286788 + 0.999589i \(0.509130\pi\)
\(882\) −2.25448e8 + 4.68147e8i −0.328579 + 0.682302i
\(883\) 1.08959e8 + 1.36630e8i 0.158264 + 0.198456i 0.854641 0.519220i \(-0.173777\pi\)
−0.696377 + 0.717676i \(0.745206\pi\)
\(884\) −1.67804e8 + 2.10420e8i −0.242910 + 0.304600i
\(885\) 1.49101e8 + 7.18034e7i 0.215106 + 0.103589i
\(886\) 1.56504e9 3.57210e8i 2.25021 0.513597i
\(887\) −6.60003e7 + 1.50641e7i −0.0945747 + 0.0215861i −0.269546 0.962987i \(-0.586874\pi\)
0.174972 + 0.984573i \(0.444017\pi\)
\(888\) 2.53592e7 + 2.02233e7i 0.0362156 + 0.0288810i
\(889\) −1.05786e8 2.19668e8i −0.150565 0.312652i
\(890\) 7.92292e8 + 1.80836e8i 1.12387 + 0.256516i
\(891\) 5.19755e7 2.50301e7i 0.0734794 0.0353858i
\(892\) −2.14078e8 + 1.70721e8i −0.301632 + 0.240543i
\(893\) −9.08483e8 + 2.07355e8i −1.27574 + 0.291180i
\(894\) 3.98996e8 3.18189e8i 0.558413 0.445320i
\(895\) 2.68644e8 1.17700e9i 0.374720 1.64176i
\(896\) −2.52105e8 −0.350475
\(897\) 1.67705e8i 0.232364i
\(898\) −2.12570e8 + 9.31328e8i −0.293543 + 1.28610i
\(899\) −5.18519e8 4.13505e8i −0.713650 0.569117i
\(900\) 2.98033e7 + 1.43525e7i 0.0408825 + 0.0196880i
\(901\) −6.47741e8 + 3.11936e8i −0.885579 + 0.426472i
\(902\) 2.31111e9i 3.14920i
\(903\) −5.90992e8 + 7.82190e7i −0.802636 + 0.106230i
\(904\) −9.10685e7 −0.123272
\(905\) 1.21140e8 + 2.51549e8i 0.163433 + 0.339373i
\(906\) −4.90987e8 + 1.01955e9i −0.660215 + 1.37095i
\(907\) 2.29711e8 2.88048e8i 0.307864 0.386050i −0.603697 0.797214i \(-0.706306\pi\)
0.911561 + 0.411164i \(0.134878\pi\)
\(908\) 6.78856e8 + 1.54944e8i 0.906817 + 0.206975i
\(909\) 7.06189e8 0.940220
\(910\) 5.88433e8i 0.780860i
\(911\) −7.34899e8 1.67736e8i −0.972014 0.221856i −0.293107 0.956080i \(-0.594689\pi\)
−0.678907 + 0.734224i \(0.737546\pi\)
\(912\) 5.52242e8 + 6.92489e8i 0.728022 + 0.912911i
\(913\) −3.04179e8 1.33270e9i −0.399684 1.75113i
\(914\) −1.07598e9 1.34924e9i −1.40918 1.76706i
\(915\) 8.69768e7 + 1.80609e8i 0.113538 + 0.235764i
\(916\) −1.04794e8 + 4.59134e8i −0.136349 + 0.597383i
\(917\) −3.41211e8 + 1.64319e8i −0.442502 + 0.213098i
\(918\) −6.47756e8 + 8.12260e8i −0.837304 + 1.04995i
\(919\) 2.35757e8 + 1.03292e9i 0.303752 + 1.33082i 0.864415 + 0.502780i \(0.167689\pi\)
−0.560663 + 0.828044i \(0.689454\pi\)
\(920\) 1.94156e7 + 8.50654e7i 0.0249338 + 0.109242i
\(921\) 2.42163e8 5.02856e8i 0.309976 0.643672i
\(922\) 9.46058e8 + 7.54456e8i 1.20705 + 0.962589i
\(923\) 3.93300e8 3.13646e8i 0.500171 0.398873i
\(924\) 6.81756e8 + 3.28316e8i 0.864197 + 0.416176i
\(925\) 1.60119e7 3.32491e7i 0.0202311 0.0420103i
\(926\) −7.94034e8 9.95688e8i −1.00001 1.25398i
\(927\) −2.41129e8 + 3.02366e8i −0.302699 + 0.379572i
\(928\) −1.62063e9 7.80452e8i −2.02786 0.976568i
\(929\) 7.74510e8 1.76777e8i 0.966006 0.220484i 0.289710 0.957115i \(-0.406441\pi\)
0.676296 + 0.736630i \(0.263584\pi\)
\(930\) 3.43586e8 7.84212e7i 0.427156 0.0974955i
\(931\) 9.69021e8 + 7.72769e8i 1.20084 + 0.957636i
\(932\) −1.71051e8 3.55191e8i −0.211289 0.438747i
\(933\) 1.36280e8 + 3.11050e7i 0.167798 + 0.0382988i
\(934\) −9.20781e8 + 4.43425e8i −1.13010 + 0.544226i
\(935\) 7.96649e8 6.35307e8i 0.974613 0.777228i
\(936\) −2.89223e7 + 6.60132e6i −0.0352699 + 0.00805013i
\(937\) −5.59425e8 + 4.46126e8i −0.680022 + 0.542299i −0.901453 0.432877i \(-0.857499\pi\)
0.221431 + 0.975176i \(0.428927\pi\)
\(938\) −1.78099e8 + 7.80303e8i −0.215801 + 0.945485i
\(939\) 4.79266e8 0.578868
\(940\) 5.23290e8i 0.630027i
\(941\) 2.53431e8 1.11035e9i 0.304152 1.33258i −0.559643 0.828734i \(-0.689062\pi\)
0.863795 0.503843i \(-0.168081\pi\)
\(942\) −1.61402e8 1.28713e8i −0.193088 0.153982i
\(943\) −1.18834e9 5.72275e8i −1.41712 0.682448i
\(944\) 3.43366e8 1.65356e8i 0.408170 0.196564i
\(945\) 1.07989e9i 1.27962i
\(946\) −2.00486e8 1.51479e9i −0.236816 1.78929i
\(947\) 5.73994e8 0.675860 0.337930 0.941171i \(-0.390273\pi\)
0.337930 + 0.941171i \(0.390273\pi\)
\(948\) −1.08078e8 2.24426e8i −0.126856 0.263420i
\(949\) −1.88058e8 + 3.90506e8i −0.220036 + 0.456909i
\(950\) 1.03481e8 1.29761e8i 0.120695 0.151347i
\(951\) −1.71019e8 3.90340e7i −0.198840 0.0453838i
\(952\) −1.50779e8 −0.174755
\(953\) 3.16830e8i 0.366056i 0.983108 + 0.183028i \(0.0585900\pi\)
−0.983108 + 0.183028i \(0.941410\pi\)
\(954\) 7.46959e8 + 1.70489e8i 0.860304 + 0.196359i
\(955\) 3.47376e8 + 4.35595e8i 0.398831 + 0.500119i
\(956\) 2.59985e8 + 1.13907e9i 0.297560 + 1.30370i
\(957\) −6.99431e8 8.77059e8i −0.798012 1.00067i
\(958\) −3.27739e8 6.80557e8i −0.372762 0.774048i
\(959\) 3.73280e7 1.63545e8i 0.0423232 0.185430i
\(960\) 3.66694e8 1.76591e8i 0.414468 0.199597i
\(961\) −3.82897e8 + 4.80137e8i −0.431431 + 0.540998i
\(962\) −7.12021e7 3.11957e8i −0.0799774 0.350404i
\(963\) −1.74950e7 7.66506e7i −0.0195900 0.0858296i
\(964\) −2.35485e8 + 4.88989e8i −0.262864 + 0.545843i
\(965\) −8.85280e8 7.05987e8i −0.985142 0.785625i
\(966\) −7.10186e8 + 5.66354e8i −0.787845 + 0.628285i
\(967\) −2.85218e8 1.37354e8i −0.315426 0.151901i 0.269471 0.963008i \(-0.413151\pi\)
−0.584898 + 0.811107i \(0.698865\pi\)
\(968\) 3.61069e7 7.49767e7i 0.0398074 0.0826610i
\(969\) 6.06172e8 + 7.60115e8i 0.666230 + 0.835426i
\(970\) −4.27900e8 + 5.36570e8i −0.468843 + 0.587910i
\(971\) 5.46924e7 + 2.63385e7i 0.0597405 + 0.0287695i 0.463515 0.886089i \(-0.346588\pi\)
−0.403775 + 0.914858i \(0.632302\pi\)
\(972\) 8.25010e8 1.88303e8i 0.898381 0.205050i
\(973\) −8.99004e7 + 2.05192e7i −0.0975940 + 0.0222752i
\(974\) 1.56968e9 + 1.25178e9i 1.69877 + 1.35473i
\(975\) −8.03937e6 1.66939e7i −0.00867378 0.0180113i
\(976\) 4.50068e8 + 1.02725e8i 0.484093 + 0.110491i
\(977\) 3.57902e8 1.72357e8i 0.383778 0.184818i −0.232040 0.972706i \(-0.574540\pi\)
0.615818 + 0.787888i \(0.288826\pi\)
\(978\) 6.24845e7 4.98297e7i 0.0667968 0.0532687i
\(979\) 1.03959e9 2.37279e8i 1.10793 0.252878i
\(980\) 5.44166e8 4.33958e8i 0.578167 0.461073i
\(981\) 5.76745e7 2.52688e8i 0.0610909 0.267657i
\(982\) −9.33822e8 −0.986120
\(983\) 1.14803e9i 1.20862i 0.796748 + 0.604312i \(0.206552\pi\)
−0.796748 + 0.604312i \(0.793448\pi\)
\(984\) 2.85007e7 1.24870e8i 0.0299137 0.131061i
\(985\) 8.12121e8 + 6.47645e8i 0.849791 + 0.677685i
\(986\) −1.94712e9 9.37682e8i −2.03124 0.978193i
\(987\) 5.07674e8 2.44483e8i 0.528000 0.254271i
\(988\) 6.84153e8i 0.709385i
\(989\) 8.28532e8 + 2.72005e8i 0.856486 + 0.281182i
\(990\) −1.08589e9 −1.11913
\(991\) −5.44390e8 1.13044e9i −0.559358 1.16152i −0.968492 0.249044i \(-0.919884\pi\)
0.409135 0.912474i \(-0.365831\pi\)
\(992\) 3.21713e8 6.68045e8i 0.329560 0.684338i
\(993\) 5.36508e8 6.72760e8i 0.547934 0.687088i
\(994\) −2.65641e9 6.06309e8i −2.70481 0.617354i
\(995\) −1.26892e9 −1.28814
\(996\) 7.32436e8i 0.741296i
\(997\) −1.69254e9 3.86312e8i −1.70787 0.389810i −0.746567 0.665310i \(-0.768299\pi\)
−0.961301 + 0.275500i \(0.911157\pi\)
\(998\) −4.38012e8 5.49249e8i −0.440650 0.552558i
\(999\) −1.30669e8 5.72499e8i −0.131062 0.574220i
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 43.7.f.a.2.5 126
43.22 odd 14 inner 43.7.f.a.22.5 yes 126
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
43.7.f.a.2.5 126 1.1 even 1 trivial
43.7.f.a.22.5 yes 126 43.22 odd 14 inner