Properties

Label 14.7.d.a.3.4
Level $14$
Weight $7$
Character 14.3
Analytic conductor $3.221$
Analytic rank $0$
Dimension $8$
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] = [14,7,Mod(3,14)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(14, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 7, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("14.3");
 
S:= CuspForms(chi, 7);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 14 = 2 \cdot 7 \)
Weight: \( k \) \(=\) \( 7 \)
Character orbit: \([\chi]\) \(=\) 14.d (of order \(6\), degree \(2\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(3.22075717068\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - 2x^{7} + 285x^{6} + 282x^{5} + 62091x^{4} + 29260x^{3} + 4838750x^{2} + 2401000x + 294122500 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{6}\cdot 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 3.4
Root \(7.51287 - 13.0127i\) of defining polynomial
Character \(\chi\) \(=\) 14.3
Dual form 14.7.d.a.5.4

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.82843 + 4.89898i) q^{2} +(21.8891 + 12.6377i) q^{3} +(-16.0000 + 27.7128i) q^{4} +(-10.7486 + 6.20573i) q^{5} +142.979i q^{6} +(195.705 + 281.689i) q^{7} -181.019 q^{8} +(-45.0775 - 78.0766i) q^{9} +O(q^{10})\) \(q+(2.82843 + 4.89898i) q^{2} +(21.8891 + 12.6377i) q^{3} +(-16.0000 + 27.7128i) q^{4} +(-10.7486 + 6.20573i) q^{5} +142.979i q^{6} +(195.705 + 281.689i) q^{7} -181.019 q^{8} +(-45.0775 - 78.0766i) q^{9} +(-60.8035 - 35.1049i) q^{10} +(774.831 - 1342.05i) q^{11} +(-700.452 + 404.406i) q^{12} -2770.09i q^{13} +(-826.452 + 1755.49i) q^{14} -313.705 q^{15} +(-512.000 - 886.810i) q^{16} +(-109.615 - 63.2864i) q^{17} +(254.997 - 441.668i) q^{18} +(-1147.81 + 662.687i) q^{19} -397.167i q^{20} +(723.904 + 8639.18i) q^{21} +8766.21 q^{22} +(7119.76 + 12331.8i) q^{23} +(-3962.35 - 2287.67i) q^{24} +(-7735.48 + 13398.2i) q^{25} +(13570.6 - 7835.01i) q^{26} -20704.5i q^{27} +(-10937.7 + 916.501i) q^{28} -7479.03 q^{29} +(-887.290 - 1536.83i) q^{30} +(-49241.9 - 28429.8i) q^{31} +(2896.31 - 5016.55i) q^{32} +(33920.8 - 19584.2i) q^{33} -716.004i q^{34} +(-3851.65 - 1813.28i) q^{35} +2884.96 q^{36} +(45005.7 + 77952.2i) q^{37} +(-6492.98 - 3748.72i) q^{38} +(35007.6 - 60634.9i) q^{39} +(1945.71 - 1123.36i) q^{40} +35783.9i q^{41} +(-40275.7 + 27981.7i) q^{42} -79422.8 q^{43} +(24794.6 + 42945.5i) q^{44} +(969.044 + 559.478i) q^{45} +(-40275.4 + 69759.1i) q^{46} +(126334. - 72939.0i) q^{47} -25882.0i q^{48} +(-41048.4 + 110256. i) q^{49} -87516.9 q^{50} +(-1599.59 - 2770.57i) q^{51} +(76767.1 + 44321.5i) q^{52} +(85090.3 - 147381. i) q^{53} +(101431. - 58561.0i) q^{54} +19233.6i q^{55} +(-35426.3 - 50991.2i) q^{56} -33499.3 q^{57} +(-21153.9 - 36639.6i) q^{58} +(-187919. - 108495. i) q^{59} +(5019.27 - 8693.64i) q^{60} +(-172492. + 99588.5i) q^{61} -321647. i q^{62} +(13171.4 - 27977.8i) q^{63} +32768.0 q^{64} +(17190.5 + 29774.8i) q^{65} +(191885. + 110785. i) q^{66} +(-72219.0 + 125087. i) q^{67} +(3507.69 - 2025.16i) q^{68} +359909. i q^{69} +(-2010.86 - 23997.9i) q^{70} +407591. q^{71} +(8159.90 + 14133.4i) q^{72} +(-161733. - 93376.3i) q^{73} +(-254591. + 440964. i) q^{74} +(-338646. + 195517. i) q^{75} -42411.9i q^{76} +(529678. - 44383.4i) q^{77} +396066. q^{78} +(-41929.3 - 72623.6i) q^{79} +(11006.6 + 6354.67i) q^{80} +(228795. - 396285. i) q^{81} +(-175305. + 101212. i) q^{82} +162495. i q^{83} +(-250998. - 118165. i) q^{84} +1570.95 q^{85} +(-224642. - 389091. i) q^{86} +(-163709. - 94517.7i) q^{87} +(-140259. + 242936. i) q^{88} +(-439806. + 253922. i) q^{89} +6329.77i q^{90} +(780305. - 542120. i) q^{91} -455665. q^{92} +(-718575. - 1.24461e6i) q^{93} +(714653. + 412605. i) q^{94} +(8224.91 - 14246.0i) q^{95} +(126795. - 73205.3i) q^{96} -509740. i q^{97} +(-656243. + 110755. i) q^{98} -139710. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 128 q^{4} - 336 q^{5} + 652 q^{7} + 756 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 128 q^{4} - 336 q^{5} + 652 q^{7} + 756 q^{9} - 2016 q^{10} - 1356 q^{11} + 2064 q^{14} + 27144 q^{15} - 4096 q^{16} - 17304 q^{17} - 6816 q^{18} - 32004 q^{19} + 9756 q^{21} + 25248 q^{22} - 4128 q^{23} + 10752 q^{24} + 4664 q^{25} - 4704 q^{26} - 7552 q^{28} - 30312 q^{29} + 9648 q^{30} - 3108 q^{31} + 3276 q^{33} + 98028 q^{35} - 48384 q^{36} - 6124 q^{37} + 155568 q^{38} + 100764 q^{39} + 64512 q^{40} - 315936 q^{42} - 297376 q^{43} - 43392 q^{44} - 172116 q^{45} - 194064 q^{46} + 313908 q^{47} + 32432 q^{49} + 38784 q^{50} + 253692 q^{51} + 255360 q^{52} + 278484 q^{53} + 386064 q^{54} - 125952 q^{56} - 81288 q^{57} - 169824 q^{58} - 835464 q^{59} - 434304 q^{60} - 995316 q^{61} + 1216188 q^{63} + 262144 q^{64} + 8316 q^{65} + 1673280 q^{66} + 648808 q^{67} + 553728 q^{68} - 1572816 q^{70} + 190128 q^{71} - 218112 q^{72} - 1617084 q^{73} - 1158144 q^{74} - 2042208 q^{75} + 1456224 q^{77} + 1122432 q^{78} + 70096 q^{79} + 344064 q^{80} + 1177920 q^{81} + 66528 q^{82} - 1133568 q^{84} + 2190984 q^{85} - 573024 q^{86} - 2057076 q^{87} - 403968 q^{88} + 739116 q^{89} + 2233752 q^{91} + 264192 q^{92} - 23364 q^{93} + 3795120 q^{94} + 725640 q^{95} - 344064 q^{96} - 3532320 q^{98} - 4625928 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/14\mathbb{Z}\right)^\times\).

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.82843 + 4.89898i 0.353553 + 0.612372i
\(3\) 21.8891 + 12.6377i 0.810708 + 0.468063i 0.847202 0.531271i \(-0.178285\pi\)
−0.0364935 + 0.999334i \(0.511619\pi\)
\(4\) −16.0000 + 27.7128i −0.250000 + 0.433013i
\(5\) −10.7486 + 6.20573i −0.0859892 + 0.0496459i −0.542378 0.840135i \(-0.682476\pi\)
0.456389 + 0.889780i \(0.349143\pi\)
\(6\) 142.979i 0.661941i
\(7\) 195.705 + 281.689i 0.570567 + 0.821251i
\(8\) −181.019 −0.353553
\(9\) −45.0775 78.0766i −0.0618347 0.107101i
\(10\) −60.8035 35.1049i −0.0608035 0.0351049i
\(11\) 774.831 1342.05i 0.582142 1.00830i −0.413083 0.910693i \(-0.635548\pi\)
0.995225 0.0976064i \(-0.0311186\pi\)
\(12\) −700.452 + 404.406i −0.405354 + 0.234031i
\(13\) 2770.09i 1.26085i −0.776249 0.630427i \(-0.782880\pi\)
0.776249 0.630427i \(-0.217120\pi\)
\(14\) −826.452 + 1755.49i −0.301185 + 0.639756i
\(15\) −313.705 −0.0929495
\(16\) −512.000 886.810i −0.125000 0.216506i
\(17\) −109.615 63.2864i −0.0223113 0.0128814i 0.488803 0.872394i \(-0.337434\pi\)
−0.511114 + 0.859513i \(0.670767\pi\)
\(18\) 254.997 441.668i 0.0437238 0.0757318i
\(19\) −1147.81 + 662.687i −0.167343 + 0.0966156i −0.581332 0.813666i \(-0.697468\pi\)
0.413989 + 0.910282i \(0.364135\pi\)
\(20\) 397.167i 0.0496459i
\(21\) 723.904 + 8639.18i 0.0781669 + 0.932856i
\(22\) 8766.21 0.823273
\(23\) 7119.76 + 12331.8i 0.585170 + 1.01354i 0.994854 + 0.101316i \(0.0323055\pi\)
−0.409685 + 0.912227i \(0.634361\pi\)
\(24\) −3962.35 2287.67i −0.286629 0.165485i
\(25\) −7735.48 + 13398.2i −0.495071 + 0.857487i
\(26\) 13570.6 7835.01i 0.772112 0.445779i
\(27\) 20704.5i 1.05190i
\(28\) −10937.7 + 916.501i −0.498254 + 0.0417502i
\(29\) −7479.03 −0.306656 −0.153328 0.988175i \(-0.548999\pi\)
−0.153328 + 0.988175i \(0.548999\pi\)
\(30\) −887.290 1536.83i −0.0328626 0.0569197i
\(31\) −49241.9 28429.8i −1.65291 0.954309i −0.975866 0.218369i \(-0.929927\pi\)
−0.677046 0.735941i \(-0.736740\pi\)
\(32\) 2896.31 5016.55i 0.0883883 0.153093i
\(33\) 33920.8 19584.2i 0.943895 0.544958i
\(34\) 716.004i 0.0182171i
\(35\) −3851.65 1813.28i −0.0898343 0.0422924i
\(36\) 2884.96 0.0618347
\(37\) 45005.7 + 77952.2i 0.888511 + 1.53895i 0.841636 + 0.540046i \(0.181593\pi\)
0.0468752 + 0.998901i \(0.485074\pi\)
\(38\) −6492.98 3748.72i −0.118329 0.0683176i
\(39\) 35007.6 60634.9i 0.590158 1.02218i
\(40\) 1945.71 1123.36i 0.0304018 0.0175525i
\(41\) 35783.9i 0.519202i 0.965716 + 0.259601i \(0.0835910\pi\)
−0.965716 + 0.259601i \(0.916409\pi\)
\(42\) −40275.7 + 27981.7i −0.543619 + 0.377682i
\(43\) −79422.8 −0.998942 −0.499471 0.866331i \(-0.666472\pi\)
−0.499471 + 0.866331i \(0.666472\pi\)
\(44\) 24794.6 + 42945.5i 0.291071 + 0.504150i
\(45\) 969.044 + 559.478i 0.0106342 + 0.00613968i
\(46\) −40275.4 + 69759.1i −0.413777 + 0.716684i
\(47\) 126334. 72939.0i 1.21682 0.702532i 0.252585 0.967575i \(-0.418719\pi\)
0.964237 + 0.265043i \(0.0853861\pi\)
\(48\) 25882.0i 0.234031i
\(49\) −41048.4 + 110256.i −0.348906 + 0.937158i
\(50\) −87516.9 −0.700136
\(51\) −1599.59 2770.57i −0.0120586 0.0208861i
\(52\) 76767.1 + 44321.5i 0.545966 + 0.315213i
\(53\) 85090.3 147381.i 0.571547 0.989949i −0.424860 0.905259i \(-0.639677\pi\)
0.996407 0.0846900i \(-0.0269900\pi\)
\(54\) 101431. 58561.0i 0.644152 0.371901i
\(55\) 19233.6i 0.115604i
\(56\) −35426.3 50991.2i −0.201726 0.290356i
\(57\) −33499.3 −0.180889
\(58\) −21153.9 36639.6i −0.108419 0.187788i
\(59\) −187919. 108495.i −0.914989 0.528269i −0.0329557 0.999457i \(-0.510492\pi\)
−0.882033 + 0.471188i \(0.843825\pi\)
\(60\) 5019.27 8693.64i 0.0232374 0.0402483i
\(61\) −172492. + 99588.5i −0.759942 + 0.438753i −0.829275 0.558841i \(-0.811246\pi\)
0.0693329 + 0.997594i \(0.477913\pi\)
\(62\) 321647.i 1.34960i
\(63\) 13171.4 27977.8i 0.0526758 0.111890i
\(64\) 32768.0 0.125000
\(65\) 17190.5 + 29774.8i 0.0625962 + 0.108420i
\(66\) 191885. + 110785.i 0.667434 + 0.385343i
\(67\) −72219.0 + 125087.i −0.240119 + 0.415899i −0.960748 0.277422i \(-0.910520\pi\)
0.720629 + 0.693321i \(0.243853\pi\)
\(68\) 3507.69 2025.16i 0.0111556 0.00644071i
\(69\) 359909.i 1.09558i
\(70\) −2010.86 23997.9i −0.00586255 0.0699647i
\(71\) 407591. 1.13880 0.569402 0.822059i \(-0.307175\pi\)
0.569402 + 0.822059i \(0.307175\pi\)
\(72\) 8159.90 + 14133.4i 0.0218619 + 0.0378659i
\(73\) −161733. 93376.3i −0.415747 0.240032i 0.277509 0.960723i \(-0.410491\pi\)
−0.693256 + 0.720691i \(0.743824\pi\)
\(74\) −254591. + 440964.i −0.628272 + 1.08820i
\(75\) −338646. + 195517.i −0.802716 + 0.463448i
\(76\) 42411.9i 0.0966156i
\(77\) 529678. 44383.4i 1.16022 0.0972183i
\(78\) 396066. 0.834610
\(79\) −41929.3 72623.6i −0.0850425 0.147298i 0.820367 0.571838i \(-0.193769\pi\)
−0.905409 + 0.424540i \(0.860436\pi\)
\(80\) 11006.6 + 6354.67i 0.0214973 + 0.0124115i
\(81\) 228795. 396285.i 0.430518 0.745679i
\(82\) −175305. + 101212.i −0.317945 + 0.183565i
\(83\) 162495.i 0.284188i 0.989853 + 0.142094i \(0.0453836\pi\)
−0.989853 + 0.142094i \(0.954616\pi\)
\(84\) −250998. 118165.i −0.423480 0.199367i
\(85\) 1570.95 0.00255804
\(86\) −224642. 389091.i −0.353179 0.611724i
\(87\) −163709. 94517.7i −0.248609 0.143534i
\(88\) −140259. + 242936.i −0.205818 + 0.356488i
\(89\) −439806. + 253922.i −0.623866 + 0.360189i −0.778373 0.627803i \(-0.783954\pi\)
0.154507 + 0.987992i \(0.450621\pi\)
\(90\) 6329.77i 0.00868281i
\(91\) 780305. 542120.i 1.03548 0.719402i
\(92\) −455665. −0.585170
\(93\) −718575. 1.24461e6i −0.893353 1.54733i
\(94\) 714653. + 412605.i 0.860423 + 0.496765i
\(95\) 8224.91 14246.0i 0.00959313 0.0166158i
\(96\) 126795. 73205.3i 0.143314 0.0827426i
\(97\) 509740.i 0.558514i −0.960216 0.279257i \(-0.909912\pi\)
0.960216 0.279257i \(-0.0900881\pi\)
\(98\) −656243. + 110755.i −0.697246 + 0.117675i
\(99\) −139710. −0.143986
\(100\) −247535. 428744.i −0.247535 0.428744i
\(101\) 1.35057e6 + 779754.i 1.31085 + 0.756821i 0.982237 0.187642i \(-0.0600846\pi\)
0.328616 + 0.944464i \(0.393418\pi\)
\(102\) 9048.63 15672.7i 0.00852673 0.0147687i
\(103\) −629819. + 363626.i −0.576374 + 0.332769i −0.759691 0.650284i \(-0.774650\pi\)
0.183317 + 0.983054i \(0.441316\pi\)
\(104\) 501441.i 0.445779i
\(105\) −61393.4 88367.1i −0.0530339 0.0763348i
\(106\) 962686. 0.808290
\(107\) 874822. + 1.51524e6i 0.714116 + 1.23688i 0.963300 + 0.268428i \(0.0865043\pi\)
−0.249184 + 0.968456i \(0.580162\pi\)
\(108\) 573779. + 331271.i 0.455484 + 0.262974i
\(109\) 386426. 669309.i 0.298392 0.516830i −0.677376 0.735637i \(-0.736883\pi\)
0.975768 + 0.218807i \(0.0702165\pi\)
\(110\) −94224.9 + 54400.8i −0.0707926 + 0.0408721i
\(111\) 2.27508e6i 1.66352i
\(112\) 149604. 317778.i 0.106485 0.226188i
\(113\) −2.26586e6 −1.57035 −0.785176 0.619273i \(-0.787428\pi\)
−0.785176 + 0.619273i \(0.787428\pi\)
\(114\) −94750.4 164112.i −0.0639538 0.110771i
\(115\) −153056. 88366.7i −0.100637 0.0581025i
\(116\) 119665. 207265.i 0.0766640 0.132786i
\(117\) −216279. + 124869.i −0.135039 + 0.0779645i
\(118\) 1.22748e6i 0.747085i
\(119\) −3625.13 43262.8i −0.00215121 0.0256729i
\(120\) 56786.6 0.0328626
\(121\) −314946. 545503.i −0.177779 0.307922i
\(122\) −975764. 563358.i −0.537360 0.310245i
\(123\) −452226. + 783278.i −0.243019 + 0.420921i
\(124\) 1.57574e6 909755.i 0.826456 0.477155i
\(125\) 385946.i 0.197605i
\(126\) 174317. 14606.6i 0.0871421 0.00730191i
\(127\) 813391. 0.397089 0.198545 0.980092i \(-0.436379\pi\)
0.198545 + 0.980092i \(0.436379\pi\)
\(128\) 92681.9 + 160530.i 0.0441942 + 0.0765466i
\(129\) −1.73850e6 1.00372e6i −0.809850 0.467567i
\(130\) −97244.0 + 168432.i −0.0442622 + 0.0766643i
\(131\) 2.65677e6 1.53389e6i 1.18179 0.682307i 0.225362 0.974275i \(-0.427643\pi\)
0.956428 + 0.291968i \(0.0943101\pi\)
\(132\) 1.25339e6i 0.544958i
\(133\) −411303. 193634.i −0.174826 0.0823050i
\(134\) −817064. −0.339580
\(135\) 128486. + 222545.i 0.0522223 + 0.0904516i
\(136\) 19842.5 + 11456.1i 0.00788822 + 0.00455427i
\(137\) 314000. 543865.i 0.122115 0.211509i −0.798487 0.602013i \(-0.794366\pi\)
0.920601 + 0.390503i \(0.127699\pi\)
\(138\) −1.76319e6 + 1.01798e6i −0.670906 + 0.387348i
\(139\) 2.79572e6i 1.04100i −0.853863 0.520498i \(-0.825746\pi\)
0.853863 0.520498i \(-0.174254\pi\)
\(140\) 111878. 77727.4i 0.0407717 0.0283263i
\(141\) 3.68712e6 1.31532
\(142\) 1.15284e6 + 1.99678e6i 0.402628 + 0.697373i
\(143\) −3.71760e6 2.14636e6i −1.27132 0.733996i
\(144\) −46159.4 + 79950.4i −0.0154587 + 0.0267752i
\(145\) 80389.5 46412.9i 0.0263691 0.0152242i
\(146\) 1.05643e6i 0.339456i
\(147\) −2.29189e6 + 1.89464e6i −0.721509 + 0.596452i
\(148\) −2.88037e6 −0.888511
\(149\) 2.04538e6 + 3.54271e6i 0.618324 + 1.07097i 0.989792 + 0.142522i \(0.0455212\pi\)
−0.371468 + 0.928446i \(0.621145\pi\)
\(150\) −1.91567e6 1.10601e6i −0.567606 0.327707i
\(151\) −819369. + 1.41919e6i −0.237985 + 0.412201i −0.960136 0.279534i \(-0.909820\pi\)
0.722151 + 0.691735i \(0.243153\pi\)
\(152\) 207775. 119959.i 0.0591647 0.0341588i
\(153\) 11411.2i 0.00318607i
\(154\) 1.71559e6 + 2.46935e6i 0.469733 + 0.676114i
\(155\) 705712. 0.189510
\(156\) 1.12024e6 + 1.94032e6i 0.295079 + 0.511092i
\(157\) 4.98347e6 + 2.87721e6i 1.28775 + 0.743485i 0.978253 0.207414i \(-0.0665046\pi\)
0.309501 + 0.950899i \(0.399838\pi\)
\(158\) 237188. 410821.i 0.0601341 0.104155i
\(159\) 3.72510e6 2.15069e6i 0.926716 0.535040i
\(160\) 71894.9i 0.0175525i
\(161\) −2.08036e6 + 4.41895e6i −0.498495 + 1.05887i
\(162\) 2.58852e6 0.608845
\(163\) −478970. 829600.i −0.110597 0.191560i 0.805414 0.592713i \(-0.201943\pi\)
−0.916011 + 0.401152i \(0.868610\pi\)
\(164\) −991672. 572542.i −0.224821 0.129800i
\(165\) −243068. + 421006.i −0.0541098 + 0.0937210i
\(166\) −796061. + 459606.i −0.174029 + 0.100476i
\(167\) 6.70923e6i 1.44053i −0.693698 0.720266i \(-0.744020\pi\)
0.693698 0.720266i \(-0.255980\pi\)
\(168\) −131041. 1.56386e6i −0.0276362 0.329814i
\(169\) −2.84662e6 −0.589751
\(170\) 4443.33 + 7696.07i 0.000904402 + 0.00156647i
\(171\) 103481. + 59744.5i 0.0206952 + 0.0119484i
\(172\) 1.27077e6 2.20103e6i 0.249735 0.432554i
\(173\) −300592. + 173547.i −0.0580550 + 0.0335181i −0.528747 0.848780i \(-0.677338\pi\)
0.470692 + 0.882298i \(0.344004\pi\)
\(174\) 1.06935e6i 0.202988i
\(175\) −5.28801e6 + 443098.i −0.986683 + 0.0826772i
\(176\) −1.58685e6 −0.291071
\(177\) −2.74226e6 4.74974e6i −0.494526 0.856544i
\(178\) −2.48792e6 1.43640e6i −0.441140 0.254692i
\(179\) 1.47270e6 2.55079e6i 0.256777 0.444750i −0.708600 0.705611i \(-0.750673\pi\)
0.965377 + 0.260860i \(0.0840062\pi\)
\(180\) −31009.4 + 17903.3i −0.00531712 + 0.00306984i
\(181\) 2.88805e6i 0.487046i 0.969895 + 0.243523i \(0.0783031\pi\)
−0.969895 + 0.243523i \(0.921697\pi\)
\(182\) 4.86287e6 + 2.28935e6i 0.806638 + 0.379751i
\(183\) −5.03428e6 −0.821455
\(184\) −1.28881e6 2.23229e6i −0.206889 0.358342i
\(185\) −967502. 558587.i −0.152805 0.0882218i
\(186\) 4.06487e6 7.04057e6i 0.631696 1.09413i
\(187\) −169867. + 98072.5i −0.0259767 + 0.0149976i
\(188\) 4.66810e6i 0.702532i
\(189\) 5.83222e6 4.05196e6i 0.863870 0.600177i
\(190\) 93054.3 0.0135667
\(191\) 2.83365e6 + 4.90802e6i 0.406674 + 0.704379i 0.994515 0.104597i \(-0.0333553\pi\)
−0.587841 + 0.808976i \(0.700022\pi\)
\(192\) 717263. + 414112.i 0.101339 + 0.0585078i
\(193\) −6.54313e6 + 1.13330e7i −0.910152 + 1.57643i −0.0963038 + 0.995352i \(0.530702\pi\)
−0.813848 + 0.581078i \(0.802631\pi\)
\(194\) 2.49721e6 1.44176e6i 0.342018 0.197464i
\(195\) 868991.i 0.117196i
\(196\) −2.39872e6 2.90166e6i −0.318575 0.385370i
\(197\) 4.47088e6 0.584783 0.292391 0.956299i \(-0.405549\pi\)
0.292391 + 0.956299i \(0.405549\pi\)
\(198\) −395159. 684436.i −0.0509069 0.0881733i
\(199\) 6.97809e6 + 4.02880e6i 0.885477 + 0.511230i 0.872460 0.488685i \(-0.162523\pi\)
0.0130165 + 0.999915i \(0.495857\pi\)
\(200\) 1.40027e6 2.42534e6i 0.175034 0.303168i
\(201\) −3.16162e6 + 1.82536e6i −0.389333 + 0.224782i
\(202\) 8.82191e6i 1.07031i
\(203\) −1.46368e6 2.10676e6i −0.174968 0.251841i
\(204\) 102374. 0.0120586
\(205\) −222065. 384628.i −0.0257762 0.0446457i
\(206\) −3.56279e6 2.05698e6i −0.407558 0.235304i
\(207\) 641882. 1.11177e6i 0.0723676 0.125344i
\(208\) −2.45655e6 + 1.41829e6i −0.272983 + 0.157607i
\(209\) 2.05388e6i 0.224976i
\(210\) 259262. 550705.i 0.0279950 0.0594650i
\(211\) 421809. 0.0449023 0.0224511 0.999748i \(-0.492853\pi\)
0.0224511 + 0.999748i \(0.492853\pi\)
\(212\) 2.72289e6 + 4.71618e6i 0.285774 + 0.494975i
\(213\) 8.92180e6 + 5.15101e6i 0.923238 + 0.533032i
\(214\) −4.94874e6 + 8.57147e6i −0.504956 + 0.874610i
\(215\) 853688. 492877.i 0.0858981 0.0495933i
\(216\) 3.74791e6i 0.371901i
\(217\) −1.62850e6 1.94348e7i −0.159371 1.90195i
\(218\) 4.37191e6 0.421990
\(219\) −2.36012e6 4.08785e6i −0.224700 0.389191i
\(220\) −533017. 307737.i −0.0500579 0.0289009i
\(221\) −175309. + 303645.i −0.0162416 + 0.0281312i
\(222\) −1.11455e7 + 6.43488e6i −1.01869 + 0.588141i
\(223\) 4.49399e6i 0.405245i −0.979257 0.202622i \(-0.935054\pi\)
0.979257 0.202622i \(-0.0649464\pi\)
\(224\) 1.97993e6 165904.i 0.176159 0.0147609i
\(225\) 1.39478e6 0.122450
\(226\) −6.40881e6 1.11004e7i −0.555203 0.961640i
\(227\) −3.37074e6 1.94610e6i −0.288169 0.166375i 0.348947 0.937143i \(-0.386539\pi\)
−0.637116 + 0.770768i \(0.719873\pi\)
\(228\) 535989. 928360.i 0.0452222 0.0783271i
\(229\) −2.13533e6 + 1.23283e6i −0.177811 + 0.102659i −0.586264 0.810120i \(-0.699402\pi\)
0.408453 + 0.912779i \(0.366068\pi\)
\(230\) 999755.i 0.0821694i
\(231\) 1.21551e7 + 5.72239e6i 0.986103 + 0.464239i
\(232\) 1.35385e6 0.108419
\(233\) −1.13486e7 1.96564e7i −0.897170 1.55394i −0.831095 0.556130i \(-0.812286\pi\)
−0.0660751 0.997815i \(-0.521048\pi\)
\(234\) −1.22346e6 706366.i −0.0954867 0.0551293i
\(235\) −905280. + 1.56799e6i −0.0697556 + 0.120820i
\(236\) 6.01342e6 3.47185e6i 0.457494 0.264134i
\(237\) 2.11956e6i 0.159221i
\(238\) 201690. 140125.i 0.0149608 0.0103941i
\(239\) −3.91448e6 −0.286734 −0.143367 0.989670i \(-0.545793\pi\)
−0.143367 + 0.989670i \(0.545793\pi\)
\(240\) 160617. + 278196.i 0.0116187 + 0.0201242i
\(241\) 8.50987e6 + 4.91317e6i 0.607955 + 0.351003i 0.772165 0.635422i \(-0.219174\pi\)
−0.164209 + 0.986425i \(0.552507\pi\)
\(242\) 1.78161e6 3.08583e6i 0.125709 0.217734i
\(243\) −3.05515e6 + 1.76389e6i −0.212919 + 0.122929i
\(244\) 6.37367e6i 0.438753i
\(245\) −243003. 1.43983e6i −0.0165239 0.0979071i
\(246\) −5.11635e6 −0.343681
\(247\) 1.83570e6 + 3.17953e6i 0.121818 + 0.210995i
\(248\) 8.91374e6 + 5.14635e6i 0.584393 + 0.337399i
\(249\) −2.05356e6 + 3.55688e6i −0.133018 + 0.230394i
\(250\) 1.89074e6 1.09162e6i 0.121008 0.0698638i
\(251\) 1.12666e7i 0.712477i 0.934395 + 0.356238i \(0.115941\pi\)
−0.934395 + 0.356238i \(0.884059\pi\)
\(252\) 564600. + 812662.i 0.0352809 + 0.0507818i
\(253\) 2.20664e7 1.36261
\(254\) 2.30062e6 + 3.98479e6i 0.140392 + 0.243167i
\(255\) 34386.8 + 19853.2i 0.00207382 + 0.00119732i
\(256\) −524288. + 908093.i −0.0312500 + 0.0541266i
\(257\) −2.70095e7 + 1.55940e7i −1.59117 + 0.918665i −0.598067 + 0.801446i \(0.704065\pi\)
−0.993106 + 0.117219i \(0.962602\pi\)
\(258\) 1.13558e7i 0.661240i
\(259\) −1.31505e7 + 2.79332e7i −0.756905 + 1.60776i
\(260\) −1.10019e6 −0.0625962
\(261\) 337136. + 583937.i 0.0189620 + 0.0328431i
\(262\) 1.50290e7 + 8.67698e6i 0.835652 + 0.482464i
\(263\) 6.75928e6 1.17074e7i 0.371564 0.643567i −0.618243 0.785987i \(-0.712155\pi\)
0.989806 + 0.142420i \(0.0454884\pi\)
\(264\) −6.14031e6 + 3.54511e6i −0.333717 + 0.192672i
\(265\) 2.11219e6i 0.113500i
\(266\) −214732. 2.56264e6i −0.0114091 0.136158i
\(267\) −1.28360e7 −0.674364
\(268\) −2.31101e6 4.00278e6i −0.120060 0.207949i
\(269\) −2.25818e7 1.30376e7i −1.16011 0.669792i −0.208783 0.977962i \(-0.566950\pi\)
−0.951331 + 0.308170i \(0.900284\pi\)
\(270\) −726828. + 1.25890e6i −0.0369267 + 0.0639589i
\(271\) 9.56566e6 5.52274e6i 0.480626 0.277490i −0.240051 0.970760i \(-0.577164\pi\)
0.720677 + 0.693271i \(0.243831\pi\)
\(272\) 129611.i 0.00644071i
\(273\) 2.39313e7 2.00528e6i 1.17619 0.0985570i
\(274\) 3.55251e6 0.172696
\(275\) 1.19874e7 + 2.07627e7i 0.576403 + 0.998359i
\(276\) −9.97410e6 5.75855e6i −0.474402 0.273896i
\(277\) 7.97353e6 1.38106e7i 0.375155 0.649788i −0.615195 0.788375i \(-0.710923\pi\)
0.990350 + 0.138587i \(0.0442560\pi\)
\(278\) 1.36962e7 7.90748e6i 0.637477 0.368047i
\(279\) 5.12618e6i 0.236038i
\(280\) 697222. + 328240.i 0.0317612 + 0.0149526i
\(281\) −1.25628e6 −0.0566198 −0.0283099 0.999599i \(-0.509013\pi\)
−0.0283099 + 0.999599i \(0.509013\pi\)
\(282\) 1.04288e7 + 1.80631e7i 0.465034 + 0.805463i
\(283\) 292144. + 168669.i 0.0128896 + 0.00744179i 0.506431 0.862281i \(-0.330965\pi\)
−0.493541 + 0.869722i \(0.664298\pi\)
\(284\) −6.52145e6 + 1.12955e7i −0.284701 + 0.493117i
\(285\) 360072. 207888.i 0.0155545 0.00898037i
\(286\) 2.42832e7i 1.03803i
\(287\) −1.00799e7 + 7.00307e6i −0.426395 + 0.296239i
\(288\) −522234. −0.0218619
\(289\) −1.20608e7 2.08899e7i −0.499668 0.865451i
\(290\) 454751. + 262551.i 0.0186458 + 0.0107651i
\(291\) 6.44194e6 1.11578e7i 0.261419 0.452792i
\(292\) 5.17544e6 2.98804e6i 0.207873 0.120016i
\(293\) 1.30355e7i 0.518233i 0.965846 + 0.259117i \(0.0834314\pi\)
−0.965846 + 0.259117i \(0.916569\pi\)
\(294\) −1.57643e7 5.86907e6i −0.620343 0.230955i
\(295\) 2.69317e6 0.104905
\(296\) −8.14691e6 1.41109e7i −0.314136 0.544100i
\(297\) −2.77864e7 1.60425e7i −1.06063 0.612353i
\(298\) −1.15704e7 + 2.00406e7i −0.437221 + 0.757289i
\(299\) 3.41602e7 1.97224e7i 1.27793 0.737813i
\(300\) 1.25131e7i 0.463448i
\(301\) −1.55434e7 2.23725e7i −0.569963 0.820382i
\(302\) −9.27010e6 −0.336561
\(303\) 1.97086e7 + 3.41363e7i 0.708480 + 1.22712i
\(304\) 1.17535e6 + 678591.i 0.0418358 + 0.0241539i
\(305\) 1.23604e6 2.14088e6i 0.0435645 0.0754560i
\(306\) −55903.1 + 32275.7i −0.00195106 + 0.00112645i
\(307\) 3.48621e7i 1.20487i −0.798170 0.602433i \(-0.794198\pi\)
0.798170 0.602433i \(-0.205802\pi\)
\(308\) −7.24486e6 + 1.53890e7i −0.247958 + 0.526694i
\(309\) −1.83816e7 −0.623028
\(310\) 1.99605e6 + 3.45727e6i 0.0670019 + 0.116051i
\(311\) −3.81969e7 2.20530e7i −1.26983 0.733139i −0.294877 0.955535i \(-0.595279\pi\)
−0.974956 + 0.222397i \(0.928612\pi\)
\(312\) −6.33705e6 + 1.09761e7i −0.208652 + 0.361397i
\(313\) 3.77077e7 2.17706e7i 1.22970 0.709965i 0.262729 0.964870i \(-0.415377\pi\)
0.966966 + 0.254905i \(0.0820441\pi\)
\(314\) 3.25519e7i 1.05145i
\(315\) 32047.6 + 382462.i 0.00102533 + 0.0122365i
\(316\) 2.68347e6 0.0850425
\(317\) 1.63697e7 + 2.83531e7i 0.513880 + 0.890067i 0.999870 + 0.0161023i \(0.00512574\pi\)
−0.485990 + 0.873964i \(0.661541\pi\)
\(318\) 2.10724e7 + 1.21661e7i 0.655287 + 0.378330i
\(319\) −5.79499e6 + 1.00372e7i −0.178517 + 0.309201i
\(320\) −352212. + 203349.i −0.0107486 + 0.00620573i
\(321\) 4.42229e7i 1.33700i
\(322\) −2.75325e7 + 2.30703e6i −0.824665 + 0.0691012i
\(323\) 167756. 0.00497818
\(324\) 7.32144e6 + 1.26811e7i 0.215259 + 0.372840i
\(325\) 3.71144e7 + 2.14280e7i 1.08117 + 0.624211i
\(326\) 2.70946e6 4.69293e6i 0.0782042 0.135454i
\(327\) 1.69170e7 9.76706e6i 0.483817 0.279332i
\(328\) 6.47758e6i 0.183565i
\(329\) 4.52703e7 + 2.13124e7i 1.27123 + 0.598474i
\(330\) −2.75000e6 −0.0765228
\(331\) 1.58127e7 + 2.73884e7i 0.436036 + 0.755236i 0.997380 0.0723465i \(-0.0230487\pi\)
−0.561344 + 0.827583i \(0.689715\pi\)
\(332\) −4.50320e6 2.59992e6i −0.123057 0.0710471i
\(333\) 4.05750e6 7.02779e6i 0.109882 0.190321i
\(334\) 3.28684e7 1.89766e7i 0.882143 0.509305i
\(335\) 1.79269e6i 0.0476837i
\(336\) 7.29067e6 5.06523e6i 0.192198 0.133531i
\(337\) −8.23591e6 −0.215190 −0.107595 0.994195i \(-0.534315\pi\)
−0.107595 + 0.994195i \(0.534315\pi\)
\(338\) −8.05145e6 1.39455e7i −0.208509 0.361147i
\(339\) −4.95976e7 2.86352e7i −1.27310 0.735023i
\(340\) −25135.3 + 43535.5i −0.000639509 + 0.00110766i
\(341\) −7.63083e7 + 4.40566e7i −1.92446 + 1.11109i
\(342\) 675932.i 0.0168976i
\(343\) −3.90912e7 + 1.00147e7i −0.968716 + 0.248173i
\(344\) 1.43771e7 0.353179
\(345\) −2.23350e6 3.86854e6i −0.0543912 0.0942084i
\(346\) −1.70041e6 981731.i −0.0410511 0.0237009i
\(347\) 3.12505e7 5.41274e7i 0.747943 1.29547i −0.200864 0.979619i \(-0.564375\pi\)
0.948807 0.315856i \(-0.102292\pi\)
\(348\) 5.23870e6 3.02457e6i 0.124304 0.0717671i
\(349\) 2.49010e7i 0.585788i −0.956145 0.292894i \(-0.905382\pi\)
0.956145 0.292894i \(-0.0946183\pi\)
\(350\) −1.71275e7 2.46526e7i −0.399474 0.574987i
\(351\) −5.73533e7 −1.32629
\(352\) −4.48830e6 7.77397e6i −0.102909 0.178244i
\(353\) 5.99767e7 + 3.46276e7i 1.36351 + 0.787224i 0.990089 0.140438i \(-0.0448511\pi\)
0.373422 + 0.927662i \(0.378184\pi\)
\(354\) 1.55126e7 2.68686e7i 0.349683 0.605668i
\(355\) −4.38105e6 + 2.52940e6i −0.0979249 + 0.0565369i
\(356\) 1.62510e7i 0.360189i
\(357\) 467392. 992799.i 0.0102725 0.0218201i
\(358\) 1.66617e7 0.363137
\(359\) −1.50466e7 2.60615e7i −0.325204 0.563270i 0.656350 0.754457i \(-0.272100\pi\)
−0.981554 + 0.191187i \(0.938766\pi\)
\(360\) −175416. 101276.i −0.00375977 0.00217070i
\(361\) −2.26446e7 + 3.92217e7i −0.481331 + 0.833689i
\(362\) −1.41485e7 + 8.16865e6i −0.298253 + 0.172197i
\(363\) 1.59208e7i 0.332847i
\(364\) 2.53879e6 + 3.02984e7i 0.0526409 + 0.628225i
\(365\) 2.31787e6 0.0476663
\(366\) −1.42391e7 2.46628e7i −0.290428 0.503036i
\(367\) −1.83705e7 1.06062e7i −0.371640 0.214566i 0.302535 0.953138i \(-0.402167\pi\)
−0.674175 + 0.738572i \(0.735500\pi\)
\(368\) 7.29063e6 1.26277e7i 0.146292 0.253386i
\(369\) 2.79388e6 1.61305e6i 0.0556070 0.0321047i
\(370\) 6.31969e6i 0.124764i
\(371\) 5.81681e7 4.87408e6i 1.13910 0.0954489i
\(372\) 4.59888e7 0.893353
\(373\) −2.44206e7 4.22977e7i −0.470575 0.815060i 0.528858 0.848710i \(-0.322620\pi\)
−0.999434 + 0.0336496i \(0.989287\pi\)
\(374\) −960911. 554782.i −0.0183683 0.0106049i
\(375\) 4.87747e6 8.44803e6i 0.0924913 0.160200i
\(376\) −2.28689e7 + 1.32034e7i −0.430211 + 0.248383i
\(377\) 2.07176e7i 0.386648i
\(378\) 3.63465e7 + 1.71112e7i 0.672956 + 0.316815i
\(379\) 8.40563e6 0.154402 0.0772009 0.997016i \(-0.475402\pi\)
0.0772009 + 0.997016i \(0.475402\pi\)
\(380\) 263197. + 455871.i 0.00479657 + 0.00830790i
\(381\) 1.78044e7 + 1.02794e7i 0.321924 + 0.185863i
\(382\) −1.60295e7 + 2.77640e7i −0.287562 + 0.498071i
\(383\) 1.47384e7 8.50922e6i 0.262334 0.151458i −0.363065 0.931764i \(-0.618270\pi\)
0.625399 + 0.780305i \(0.284936\pi\)
\(384\) 4.68514e6i 0.0827426i
\(385\) −5.41789e6 + 3.76410e6i −0.0949397 + 0.0659598i
\(386\) −7.40271e7 −1.28715
\(387\) 3.58019e6 + 6.20106e6i 0.0617693 + 0.106988i
\(388\) 1.41263e7 + 8.15585e6i 0.241844 + 0.139628i
\(389\) −2.99145e6 + 5.18135e6i −0.0508199 + 0.0880226i −0.890316 0.455343i \(-0.849517\pi\)
0.839496 + 0.543365i \(0.182850\pi\)
\(390\) −4.25717e6 + 2.45788e6i −0.0717674 + 0.0414349i
\(391\) 1.80234e6i 0.0301513i
\(392\) 7.43056e6 1.99584e7i 0.123357 0.331335i
\(393\) 7.75392e7 1.27745
\(394\) 1.26456e7 + 2.19028e7i 0.206752 + 0.358105i
\(395\) 901366. + 520404.i 0.0146255 + 0.00844402i
\(396\) 2.23536e6 3.87175e6i 0.0359966 0.0623479i
\(397\) −9.15067e7 + 5.28314e7i −1.46245 + 0.844346i −0.999124 0.0418414i \(-0.986678\pi\)
−0.463326 + 0.886188i \(0.653344\pi\)
\(398\) 4.55807e7i 0.722989i
\(399\) −6.55597e6 9.43639e6i −0.103209 0.148555i
\(400\) 1.58423e7 0.247535
\(401\) −3.06343e7 5.30601e7i −0.475089 0.822877i 0.524504 0.851408i \(-0.324251\pi\)
−0.999593 + 0.0285303i \(0.990917\pi\)
\(402\) −1.78848e7 1.03258e7i −0.275300 0.158945i
\(403\) −7.87533e7 + 1.36405e8i −1.20324 + 2.08408i
\(404\) −4.32183e7 + 2.49521e7i −0.655427 + 0.378411i
\(405\) 5.67936e6i 0.0854938i
\(406\) 6.18107e6 1.31294e7i 0.0923603 0.196185i
\(407\) 1.39487e8 2.06896
\(408\) 289556. + 501526.i 0.00426336 + 0.00738436i
\(409\) 9.47417e7 + 5.46991e7i 1.38475 + 0.799486i 0.992717 0.120466i \(-0.0384388\pi\)
0.392032 + 0.919951i \(0.371772\pi\)
\(410\) 1.25619e6 2.17579e6i 0.0182265 0.0315693i
\(411\) 1.37464e7 7.93648e6i 0.197999 0.114315i
\(412\) 2.32721e7i 0.332769i
\(413\) −6.21476e6 7.41679e7i −0.0882214 1.05285i
\(414\) 7.26207e6 0.102343
\(415\) −1.00840e6 1.74660e6i −0.0141088 0.0244371i
\(416\) −1.38963e7 8.02305e6i −0.193028 0.111445i
\(417\) 3.53314e7 6.11958e7i 0.487251 0.843943i
\(418\) −1.00619e7 + 5.80925e6i −0.137769 + 0.0795411i
\(419\) 2.04457e7i 0.277946i −0.990296 0.138973i \(-0.955620\pi\)
0.990296 0.138973i \(-0.0443802\pi\)
\(420\) 3.43120e6 287511.i 0.0463124 0.00388066i
\(421\) −3.19255e7 −0.427850 −0.213925 0.976850i \(-0.568625\pi\)
−0.213925 + 0.976850i \(0.568625\pi\)
\(422\) 1.19306e6 + 2.06643e6i 0.0158754 + 0.0274969i
\(423\) −1.13897e7 6.57582e6i −0.150484 0.0868818i
\(424\) −1.54030e7 + 2.66787e7i −0.202073 + 0.350000i
\(425\) 1.69585e6 979101.i 0.0220913 0.0127544i
\(426\) 5.82770e7i 0.753821i
\(427\) −6.18106e7 2.90993e7i −0.793924 0.373765i
\(428\) −5.59886e7 −0.714116
\(429\) −5.42500e7 9.39637e7i −0.687112 1.19011i
\(430\) 4.82919e6 + 2.78813e6i 0.0607392 + 0.0350678i
\(431\) −155642. + 269579.i −0.00194399 + 0.00336709i −0.866996 0.498316i \(-0.833952\pi\)
0.865052 + 0.501683i \(0.167285\pi\)
\(432\) −1.83609e7 + 1.06007e7i −0.227742 + 0.131487i
\(433\) 5.06252e7i 0.623596i −0.950148 0.311798i \(-0.899069\pi\)
0.950148 0.311798i \(-0.100931\pi\)
\(434\) 9.06044e7 6.29478e7i 1.10836 0.770036i
\(435\) 2.34621e6 0.0285035
\(436\) 1.23656e7 + 2.14179e7i 0.149196 + 0.258415i
\(437\) −1.63442e7 9.43634e6i −0.195848 0.113073i
\(438\) 1.33509e7 2.31244e7i 0.158887 0.275200i
\(439\) 7.01109e7 4.04786e7i 0.828690 0.478445i −0.0247137 0.999695i \(-0.507867\pi\)
0.853404 + 0.521250i \(0.174534\pi\)
\(440\) 3.48165e6i 0.0408721i
\(441\) 1.04587e7 1.76513e6i 0.121945 0.0205808i
\(442\) −1.98340e6 −0.0229691
\(443\) 1.28372e6 + 2.22346e6i 0.0147658 + 0.0255752i 0.873314 0.487158i \(-0.161966\pi\)
−0.858548 + 0.512733i \(0.828633\pi\)
\(444\) −6.30487e7 3.64012e7i −0.720323 0.415879i
\(445\) 3.15155e6 5.45864e6i 0.0357638 0.0619447i
\(446\) 2.20160e7 1.27109e7i 0.248161 0.143276i
\(447\) 1.03396e8i 1.15766i
\(448\) 6.41285e6 + 9.23039e6i 0.0713209 + 0.102656i
\(449\) −6.11330e7 −0.675362 −0.337681 0.941261i \(-0.609643\pi\)
−0.337681 + 0.941261i \(0.609643\pi\)
\(450\) 3.94505e6 + 6.83302e6i 0.0432927 + 0.0749851i
\(451\) 4.80237e7 + 2.77265e7i 0.523511 + 0.302249i
\(452\) 3.62537e7 6.27932e7i 0.392588 0.679982i
\(453\) −3.58705e7 + 2.07099e7i −0.385872 + 0.222783i
\(454\) 2.20176e7i 0.235289i
\(455\) −5.02297e6 + 1.06694e7i −0.0533245 + 0.113268i
\(456\) 6.06402e6 0.0639538
\(457\) −4.79859e6 8.31141e6i −0.0502765 0.0870815i 0.839792 0.542908i \(-0.182677\pi\)
−0.890068 + 0.455827i \(0.849344\pi\)
\(458\) −1.20792e7 6.97395e6i −0.125731 0.0725910i
\(459\) −1.31031e6 + 2.26952e6i −0.0135499 + 0.0234691i
\(460\) 4.89778e6 2.82773e6i 0.0503183 0.0290513i
\(461\) 6.04509e7i 0.617021i 0.951221 + 0.308510i \(0.0998304\pi\)
−0.951221 + 0.308510i \(0.900170\pi\)
\(462\) 6.34589e6 + 7.57329e7i 0.0643527 + 0.767996i
\(463\) −1.14757e8 −1.15621 −0.578104 0.815963i \(-0.696207\pi\)
−0.578104 + 0.815963i \(0.696207\pi\)
\(464\) 3.82926e6 + 6.63248e6i 0.0383320 + 0.0663930i
\(465\) 1.54474e7 + 8.91857e6i 0.153637 + 0.0887026i
\(466\) 6.41974e7 1.11193e8i 0.634395 1.09880i
\(467\) −5.93604e7 + 3.42717e7i −0.582836 + 0.336500i −0.762259 0.647272i \(-0.775910\pi\)
0.179424 + 0.983772i \(0.442577\pi\)
\(468\) 7.99162e6i 0.0779645i
\(469\) −4.93692e7 + 4.13680e6i −0.478561 + 0.0401001i
\(470\) −1.02421e7 −0.0986493
\(471\) 7.27226e7 + 1.25959e8i 0.695995 + 1.20550i
\(472\) 3.40171e7 + 1.96398e7i 0.323497 + 0.186771i
\(473\) −6.15393e7 + 1.06589e8i −0.581526 + 1.00723i
\(474\) 1.03837e7 5.99501e6i 0.0975025 0.0562931i
\(475\) 2.05048e7i 0.191326i
\(476\) 1.25694e6 + 591743.i 0.0116545 + 0.00548671i
\(477\) −1.53426e7 −0.141366
\(478\) −1.10718e7 1.91769e7i −0.101376 0.175588i
\(479\) 8.46880e7 + 4.88946e7i 0.770576 + 0.444892i 0.833080 0.553153i \(-0.186575\pi\)
−0.0625041 + 0.998045i \(0.519909\pi\)
\(480\) −908585. + 1.57372e6i −0.00821565 + 0.0142299i
\(481\) 2.15935e8 1.24670e8i 1.94039 1.12028i
\(482\) 5.55862e7i 0.496393i
\(483\) −1.01383e8 + 7.04359e7i −0.899750 + 0.625105i
\(484\) 2.01566e7 0.177779
\(485\) 3.16331e6 + 5.47902e6i 0.0277279 + 0.0480261i
\(486\) −1.72826e7 9.97809e6i −0.150556 0.0869237i
\(487\) −1.14091e7 + 1.97612e7i −0.0987794 + 0.171091i −0.911180 0.412009i \(-0.864827\pi\)
0.812400 + 0.583100i \(0.198160\pi\)
\(488\) 3.12245e7 1.80275e7i 0.268680 0.155123i
\(489\) 2.42123e7i 0.207066i
\(490\) 6.36640e6 5.26293e6i 0.0541135 0.0447342i
\(491\) 1.11615e7 0.0942930 0.0471465 0.998888i \(-0.484987\pi\)
0.0471465 + 0.998888i \(0.484987\pi\)
\(492\) −1.44712e7 2.50649e7i −0.121509 0.210461i
\(493\) 819816. + 473321.i 0.00684188 + 0.00395016i
\(494\) −1.03843e7 + 1.79862e7i −0.0861384 + 0.149196i
\(495\) 1.50169e6 867002.i 0.0123813 0.00714833i
\(496\) 5.82243e7i 0.477155i
\(497\) 7.97674e7 + 1.14814e8i 0.649765 + 0.935244i
\(498\) −2.32334e7 −0.188116
\(499\) 2.16628e7 + 3.75211e7i 0.174347 + 0.301977i 0.939935 0.341354i \(-0.110885\pi\)
−0.765588 + 0.643331i \(0.777552\pi\)
\(500\) 1.06957e7 + 6.17514e6i 0.0855653 + 0.0494011i
\(501\) 8.47892e7 1.46859e8i 0.674260 1.16785i
\(502\) −5.51947e7 + 3.18667e7i −0.436301 + 0.251899i
\(503\) 2.32014e8i 1.82310i −0.411192 0.911549i \(-0.634887\pi\)
0.411192 0.911549i \(-0.365113\pi\)
\(504\) −2.38428e6 + 5.06452e6i −0.0186237 + 0.0395591i
\(505\) −1.93558e7 −0.150292
\(506\) 6.24133e7 + 1.08103e8i 0.481755 + 0.834424i
\(507\) −6.23100e7 3.59747e7i −0.478116 0.276041i
\(508\) −1.30143e7 + 2.25414e7i −0.0992723 + 0.171945i
\(509\) −1.02119e8 + 5.89587e7i −0.774382 + 0.447089i −0.834435 0.551106i \(-0.814206\pi\)
0.0600538 + 0.998195i \(0.480873\pi\)
\(510\) 224614.i 0.00169327i
\(511\) −5.34872e6 6.38325e7i −0.0400855 0.478387i
\(512\) −5.93164e6 −0.0441942
\(513\) 1.37206e7 + 2.37647e7i 0.101630 + 0.176028i
\(514\) −1.52789e8 8.82127e7i −1.12513 0.649594i
\(515\) 4.51313e6 7.81698e6i 0.0330412 0.0572291i
\(516\) 5.56319e7 3.21191e7i 0.404925 0.233784i
\(517\) 2.26062e8i 1.63589i
\(518\) −1.74039e8 + 1.45833e7i −1.25216 + 0.104922i
\(519\) −8.77294e6 −0.0627542
\(520\) −3.11181e6 5.38981e6i −0.0221311 0.0383322i
\(521\) −1.94107e8 1.12068e8i −1.37255 0.792443i −0.381303 0.924450i \(-0.624525\pi\)
−0.991249 + 0.132007i \(0.957858\pi\)
\(522\) −1.90713e6 + 3.30325e6i −0.0134082 + 0.0232236i
\(523\) 1.57711e8 9.10546e7i 1.10245 0.636497i 0.165584 0.986196i \(-0.447049\pi\)
0.936862 + 0.349698i \(0.113716\pi\)
\(524\) 9.81688e7i 0.682307i
\(525\) −1.21350e8 5.71292e7i −0.838610 0.394802i
\(526\) 7.64725e7 0.525470
\(527\) 3.59844e6 + 6.23268e6i 0.0245857 + 0.0425837i
\(528\) −3.47348e7 2.00542e7i −0.235974 0.136239i
\(529\) −2.73640e7 + 4.73959e7i −0.184847 + 0.320165i
\(530\) −1.03476e7 + 5.97417e6i −0.0695042 + 0.0401283i
\(531\) 1.95628e7i 0.130661i
\(532\) 1.19470e7 8.30021e6i 0.0793457 0.0551257i
\(533\) 9.91248e7 0.654637
\(534\) −3.63056e7 6.28831e7i −0.238424 0.412962i
\(535\) −1.88063e7 1.08578e7i −0.122812 0.0709058i
\(536\) 1.30730e7 2.26432e7i 0.0848950 0.147042i
\(537\) 6.44723e7 3.72231e7i 0.416342 0.240375i
\(538\) 1.47503e8i 0.947229i
\(539\) 1.16163e8 + 1.40518e8i 0.741823 + 0.897361i
\(540\) −8.22312e6 −0.0522223
\(541\) 1.22675e8 + 2.12480e8i 0.774756 + 1.34192i 0.934932 + 0.354828i \(0.115461\pi\)
−0.160176 + 0.987089i \(0.551206\pi\)
\(542\) 5.41116e7 + 3.12413e7i 0.339854 + 0.196215i
\(543\) −3.64983e7 + 6.32170e7i −0.227968 + 0.394852i
\(544\) −634959. + 366594.i −0.00394411 + 0.00227713i
\(545\) 9.59222e6i 0.0592556i
\(546\) 7.75119e7 + 1.11567e8i 0.476201 + 0.685424i
\(547\) 1.02069e8 0.623637 0.311819 0.950142i \(-0.399062\pi\)
0.311819 + 0.950142i \(0.399062\pi\)
\(548\) 1.00480e7 + 1.74037e7i 0.0610574 + 0.105755i
\(549\) 1.55511e7 + 8.97841e6i 0.0939816 + 0.0542603i
\(550\) −6.78109e7 + 1.17452e8i −0.407578 + 0.705947i
\(551\) 8.58449e6 4.95625e6i 0.0513168 0.0296278i
\(552\) 6.51505e7i 0.387348i
\(553\) 1.22515e7 2.60238e7i 0.0724461 0.153885i
\(554\) 9.02102e7 0.530550
\(555\) −1.41185e7 2.44540e7i −0.0825866 0.143044i
\(556\) 7.74772e7 + 4.47315e7i 0.450764 + 0.260249i
\(557\) −9.57059e7 + 1.65768e8i −0.553826 + 0.959255i 0.444168 + 0.895944i \(0.353499\pi\)
−0.997994 + 0.0633110i \(0.979834\pi\)
\(558\) −2.51131e7 + 1.44990e7i −0.144543 + 0.0834520i
\(559\) 2.20009e8i 1.25952i
\(560\) 364004. + 4.34408e6i 0.00207273 + 0.0247362i
\(561\) −4.95764e6 −0.0280793
\(562\) −3.55330e6 6.15450e6i −0.0200181 0.0346724i
\(563\) −1.66748e8 9.62718e7i −0.934403 0.539478i −0.0462018 0.998932i \(-0.514712\pi\)
−0.888202 + 0.459454i \(0.848045\pi\)
\(564\) −5.89939e7 + 1.02181e8i −0.328829 + 0.569549i
\(565\) 2.43549e7 1.40613e7i 0.135033 0.0779615i
\(566\) 1.90828e6i 0.0105243i
\(567\) 1.56405e8 1.31057e7i 0.858029 0.0718969i
\(568\) −7.37818e7 −0.402628
\(569\) 2.99208e7 + 5.18243e7i 0.162419 + 0.281317i 0.935736 0.352702i \(-0.114737\pi\)
−0.773317 + 0.634020i \(0.781404\pi\)
\(570\) 2.03688e6 + 1.17599e6i 0.0109987 + 0.00635008i
\(571\) 1.27846e8 2.21435e8i 0.686716 1.18943i −0.286178 0.958177i \(-0.592385\pi\)
0.972894 0.231251i \(-0.0742819\pi\)
\(572\) 1.18963e8 6.86834e7i 0.635659 0.366998i
\(573\) 1.43243e8i 0.761395i
\(574\) −6.28183e7 2.95737e7i −0.332162 0.156376i
\(575\) −2.20299e8 −1.15880
\(576\) −1.47710e6 2.55841e6i −0.00772934 0.0133876i
\(577\) −2.79824e7 1.61556e7i −0.145666 0.0841001i 0.425396 0.905007i \(-0.360135\pi\)
−0.571061 + 0.820907i \(0.693468\pi\)
\(578\) 6.82260e7 1.18171e8i 0.353319 0.611966i
\(579\) −2.86447e8 + 1.65380e8i −1.47574 + 0.852016i
\(580\) 2.97042e6i 0.0152242i
\(581\) −4.57731e7 + 3.18011e7i −0.233390 + 0.162149i
\(582\) 7.28822e7 0.369703
\(583\) −1.31861e8 2.28390e8i −0.665444 1.15258i
\(584\) 2.92767e7 + 1.69029e7i 0.146989 + 0.0848640i
\(585\) 1.54981e6 2.68435e6i 0.00774123 0.0134082i
\(586\) −6.38607e7 + 3.68700e7i −0.317352 + 0.183223i
\(587\) 9.56070e7i 0.472689i −0.971669 0.236344i \(-0.924051\pi\)
0.971669 0.236344i \(-0.0759493\pi\)
\(588\) −1.58356e7 9.38290e7i −0.0778939 0.461536i
\(589\) 7.53603e7 0.368805
\(590\) 7.61744e6 + 1.31938e7i 0.0370897 + 0.0642412i
\(591\) 9.78637e7 + 5.65016e7i 0.474088 + 0.273715i
\(592\) 4.60859e7 7.98231e7i 0.222128 0.384737i
\(593\) −1.00699e8 + 5.81386e7i −0.482905 + 0.278805i −0.721626 0.692283i \(-0.756605\pi\)
0.238722 + 0.971088i \(0.423272\pi\)
\(594\) 1.81500e8i 0.865997i
\(595\) 307443. + 442520.i 0.00145953 + 0.00210079i
\(596\) −1.30905e8 −0.618324
\(597\) 1.01829e8 + 1.76374e8i 0.478576 + 0.828917i
\(598\) 1.93239e8 + 1.11567e8i 0.903633 + 0.521713i
\(599\) 1.79992e8 3.11756e8i 0.837477 1.45055i −0.0545197 0.998513i \(-0.517363\pi\)
0.891997 0.452041i \(-0.149304\pi\)
\(600\) 6.13014e7 3.53924e7i 0.283803 0.163854i
\(601\) 3.47560e8i 1.60105i 0.599297 + 0.800527i \(0.295447\pi\)
−0.599297 + 0.800527i \(0.704553\pi\)
\(602\) 6.56392e7 1.39426e8i 0.300867 0.639079i
\(603\) 1.30218e7 0.0593908
\(604\) −2.62198e7 4.54140e7i −0.118992 0.206101i
\(605\) 6.77049e6 + 3.90895e6i 0.0305741 + 0.0176520i
\(606\) −1.11489e8 + 1.93104e8i −0.500971 + 0.867707i
\(607\) −1.84155e8 + 1.06322e8i −0.823414 + 0.475398i −0.851592 0.524205i \(-0.824363\pi\)
0.0281785 + 0.999603i \(0.491029\pi\)
\(608\) 7.67738e6i 0.0341588i
\(609\) −5.41410e6 6.46127e7i −0.0239703 0.286066i
\(610\) 1.39842e7 0.0616095
\(611\) −2.02048e8 3.49957e8i −0.885790 1.53423i
\(612\) −316236. 182579.i −0.00137961 0.000796519i
\(613\) 3.94274e7 6.82903e7i 0.171166 0.296468i −0.767662 0.640855i \(-0.778580\pi\)
0.938828 + 0.344387i \(0.111913\pi\)
\(614\) 1.70789e8 9.86049e7i 0.737826 0.425984i
\(615\) 1.12256e7i 0.0482595i
\(616\) −9.58820e7 + 8.03424e6i −0.410199 + 0.0343719i
\(617\) 4.19908e6 0.0178772 0.00893859 0.999960i \(-0.497155\pi\)
0.00893859 + 0.999960i \(0.497155\pi\)
\(618\) −5.19910e7 9.00510e7i −0.220274 0.381525i
\(619\) 2.30232e8 + 1.32925e8i 0.970721 + 0.560446i 0.899456 0.437011i \(-0.143963\pi\)
0.0712651 + 0.997457i \(0.477296\pi\)
\(620\) −1.12914e7 + 1.95573e7i −0.0473775 + 0.0820603i
\(621\) 2.55323e8 1.47411e8i 1.06614 0.615537i
\(622\) 2.49501e8i 1.03681i
\(623\) −1.57599e8 7.41948e7i −0.651763 0.306838i
\(624\) −7.16956e7 −0.295079
\(625\) −1.18472e8 2.05199e8i −0.485260 0.840496i
\(626\) 2.13307e8 + 1.23153e8i 0.869526 + 0.502021i
\(627\) −2.59563e7 + 4.49577e7i −0.105303 + 0.182390i
\(628\) −1.59471e8 + 9.20707e7i −0.643877 + 0.371743i
\(629\) 1.13930e7i 0.0457811i
\(630\) −1.78303e6 + 1.23877e6i −0.00713077 + 0.00495413i
\(631\) −2.02533e8 −0.806135 −0.403068 0.915170i \(-0.632056\pi\)
−0.403068 + 0.915170i \(0.632056\pi\)
\(632\) 7.59001e6 + 1.31463e7i 0.0300671 + 0.0520777i
\(633\) 9.23303e6 + 5.33069e6i 0.0364027 + 0.0210171i
\(634\) −9.26008e7 + 1.60389e8i −0.363368 + 0.629372i
\(635\) −8.74285e6 + 5.04769e6i −0.0341454 + 0.0197138i
\(636\) 1.37644e8i 0.535040i
\(637\) 3.05419e8 + 1.13708e8i 1.18162 + 0.439919i
\(638\) −6.55628e7 −0.252462
\(639\) −1.83732e7 3.18233e7i −0.0704177 0.121967i
\(640\) −1.99241e6 1.15032e6i −0.00760044 0.00438812i
\(641\) 1.15943e7 2.00819e7i 0.0440221 0.0762484i −0.843175 0.537640i \(-0.819316\pi\)
0.887197 + 0.461391i \(0.152649\pi\)
\(642\) −2.16647e8 + 1.25081e8i −0.818744 + 0.472702i
\(643\) 3.10031e8i 1.16620i 0.812401 + 0.583100i \(0.198160\pi\)
−0.812401 + 0.583100i \(0.801840\pi\)
\(644\) −8.91757e7 1.28356e8i −0.333879 0.480571i
\(645\) 2.49153e7 0.0928511
\(646\) 474486. + 821834.i 0.00176005 + 0.00304850i
\(647\) 1.29013e8 + 7.44859e7i 0.476345 + 0.275018i 0.718892 0.695122i \(-0.244650\pi\)
−0.242547 + 0.970140i \(0.577983\pi\)
\(648\) −4.14163e7 + 7.17352e7i −0.152211 + 0.263637i
\(649\) −2.91212e8 + 1.68131e8i −1.06531 + 0.615055i
\(650\) 2.42430e8i 0.882768i
\(651\) 2.09964e8 4.45990e8i 0.761030 1.61652i
\(652\) 3.06541e7 0.110597
\(653\) 1.15112e8 + 1.99379e8i 0.413408 + 0.716044i 0.995260 0.0972506i \(-0.0310048\pi\)
−0.581851 + 0.813295i \(0.697672\pi\)
\(654\) 9.56973e7 + 5.52508e7i 0.342110 + 0.197518i
\(655\) −1.90378e7 + 3.29744e7i −0.0677474 + 0.117342i
\(656\) 3.17335e7 1.83214e7i 0.112410 0.0649002i
\(657\) 1.68367e7i 0.0593691i
\(658\) 2.36346e7 + 2.82059e8i 0.0829602 + 0.990061i
\(659\) 4.63051e8 1.61798 0.808989 0.587824i \(-0.200015\pi\)
0.808989 + 0.587824i \(0.200015\pi\)
\(660\) −7.77818e6 1.34722e7i −0.0270549 0.0468605i
\(661\) −2.85316e8 1.64727e8i −0.987920 0.570376i −0.0832680 0.996527i \(-0.526536\pi\)
−0.904652 + 0.426151i \(0.859869\pi\)
\(662\) −8.94502e7 + 1.54932e8i −0.308324 + 0.534033i
\(663\) −7.67473e6 + 4.43101e6i −0.0263344 + 0.0152041i
\(664\) 2.94148e7i 0.100476i
\(665\) 5.62259e6 471134.i 0.0191193 0.00160206i
\(666\) 4.59053e7 0.155396
\(667\) −5.32489e7 9.22298e7i −0.179446 0.310809i
\(668\) 1.85932e8 + 1.07348e8i 0.623769 + 0.360133i
\(669\) 5.67936e7 9.83694e7i 0.189680 0.328535i
\(670\) 8.78233e6 5.07048e6i 0.0292002 0.0168587i
\(671\) 3.08657e8i 1.02167i
\(672\) 4.54356e7 + 2.13902e7i 0.149723 + 0.0704868i
\(673\) −8.50491e7 −0.279013 −0.139506 0.990221i \(-0.544552\pi\)
−0.139506 + 0.990221i \(0.544552\pi\)
\(674\) −2.32947e7 4.03476e7i −0.0760812 0.131776i
\(675\) 2.77403e8 + 1.60159e8i 0.901987 + 0.520762i
\(676\) 4.55459e7 7.88878e7i 0.147438 0.255370i
\(677\) 3.43079e8 1.98077e8i 1.10568 0.638362i 0.167970 0.985792i \(-0.446279\pi\)
0.937706 + 0.347430i \(0.112945\pi\)
\(678\) 3.23970e8i 1.03948i
\(679\) 1.43588e8 9.97585e7i 0.458680 0.318670i
\(680\) −284373. −0.000904402
\(681\) −4.91883e7 8.51967e7i −0.155747 0.269762i
\(682\) −4.31665e8 2.49222e8i −1.36080 0.785657i
\(683\) −1.61680e8 + 2.80039e8i −0.507452 + 0.878933i 0.492510 + 0.870307i \(0.336079\pi\)
−0.999963 + 0.00862666i \(0.997254\pi\)
\(684\) −3.31138e6 + 1.91183e6i −0.0103476 + 0.00597420i
\(685\) 7.79441e6i 0.0242500i
\(686\) −1.59628e8 1.63181e8i −0.494467 0.505473i
\(687\) −6.23206e7 −0.192204
\(688\) 4.06645e7 + 7.04330e7i 0.124868 + 0.216277i
\(689\) −4.08258e8 2.35708e8i −1.24818 0.720637i
\(690\) 1.26346e7 2.18838e7i 0.0384604 0.0666154i
\(691\) −4.13643e8 + 2.38817e8i −1.25369 + 0.723821i −0.971841 0.235637i \(-0.924282\pi\)
−0.281853 + 0.959458i \(0.590949\pi\)
\(692\) 1.11070e7i 0.0335181i
\(693\) −2.73419e7 3.93547e7i −0.0821540 0.118249i
\(694\) 3.53559e8 1.05775
\(695\) 1.73495e7 + 3.00502e7i 0.0516811 + 0.0895143i
\(696\) 2.96346e7 + 1.71095e7i 0.0878964 + 0.0507470i
\(697\) 2.26463e6 3.92246e6i 0.00668805 0.0115840i
\(698\) 1.21989e8 7.04306e7i 0.358720 0.207107i
\(699\) 5.73681e8i 1.67973i
\(700\) 7.23286e7 1.53635e8i 0.210871 0.447916i
\(701\) 1.25339e7 0.0363859 0.0181929 0.999834i \(-0.494209\pi\)
0.0181929 + 0.999834i \(0.494209\pi\)
\(702\) −1.62220e8 2.80973e8i −0.468913 0.812181i
\(703\) −1.03316e8 5.96494e7i −0.297373 0.171688i
\(704\) 2.53897e7 4.39762e7i 0.0727678 0.126037i
\(705\) −3.96316e7 + 2.28813e7i −0.113103 + 0.0653000i
\(706\) 3.91766e8i 1.11330i
\(707\) 4.46653e7 + 5.33043e8i 0.126390 + 1.50836i
\(708\) 1.75505e8 0.494526
\(709\) 9.71988e7 + 1.68353e8i 0.272723 + 0.472371i 0.969558 0.244861i \(-0.0787423\pi\)
−0.696835 + 0.717232i \(0.745409\pi\)
\(710\) −2.47829e7 1.43084e7i −0.0692433 0.0399777i
\(711\) −3.78013e6 + 6.54739e6i −0.0105172 + 0.0182163i
\(712\) 7.96134e7 4.59648e7i 0.220570 0.127346i
\(713\) 8.09654e8i 2.23373i
\(714\) 6.18568e6 518318.i 0.0169939 0.00142397i
\(715\) 5.32788e7 0.145759
\(716\) 4.71265e7 + 8.16254e7i 0.128388 + 0.222375i
\(717\) −8.56844e7 4.94699e7i −0.232458 0.134210i
\(718\) 8.51166e7 1.47426e8i 0.229954 0.398292i
\(719\) −2.09066e8 + 1.20704e8i −0.562467 + 0.324741i −0.754135 0.656719i \(-0.771944\pi\)
0.191668 + 0.981460i \(0.438610\pi\)
\(720\) 1.14581e6i 0.00306984i
\(721\) −2.25688e8 1.06250e8i −0.602147 0.283480i
\(722\) −2.56195e8 −0.680705
\(723\) 1.24182e8 + 2.15090e8i 0.328583 + 0.569122i
\(724\) −8.00361e7 4.62089e7i −0.210897 0.121761i
\(725\) 5.78539e7 1.00206e8i 0.151816 0.262954i
\(726\) 7.79956e7 4.50308e7i 0.203826 0.117679i
\(727\) 3.89703e8i 1.01422i 0.861882 + 0.507109i \(0.169286\pi\)
−0.861882 + 0.507109i \(0.830714\pi\)
\(728\) −1.41250e8 + 9.81343e7i −0.366096 + 0.254347i
\(729\) −4.22749e8 −1.09119
\(730\) 6.55594e6 + 1.13552e7i 0.0168526 + 0.0291895i
\(731\) 8.70595e6 + 5.02638e6i 0.0222876 + 0.0128678i
\(732\) 8.05484e7 1.39514e8i 0.205364 0.355700i
\(733\) 1.51751e8 8.76135e7i 0.385319 0.222464i −0.294811 0.955556i \(-0.595257\pi\)
0.680130 + 0.733092i \(0.261923\pi\)
\(734\) 1.19995e8i 0.303442i
\(735\) 1.28771e7 3.45877e7i 0.0324306 0.0871083i
\(736\) 8.24841e7 0.206889
\(737\) 1.11915e8 + 1.93843e8i 0.279567 + 0.484224i
\(738\) 1.58046e7 + 9.12478e6i 0.0393201 + 0.0227014i
\(739\) −3.83128e6 + 6.63597e6i −0.00949315 + 0.0164426i −0.870733 0.491756i \(-0.836355\pi\)
0.861240 + 0.508199i \(0.169688\pi\)
\(740\) 3.09601e7 1.78748e7i 0.0764023 0.0441109i
\(741\) 9.27963e7i 0.228074i
\(742\) 1.88402e8 + 2.71178e8i 0.461184 + 0.663809i
\(743\) 4.78399e8 1.16634 0.583169 0.812351i \(-0.301813\pi\)
0.583169 + 0.812351i \(0.301813\pi\)
\(744\) 1.30076e8 + 2.25298e8i 0.315848 + 0.547065i
\(745\) −4.39702e7 2.53862e7i −0.106338 0.0613944i
\(746\) 1.38144e8 2.39272e8i 0.332747 0.576335i
\(747\) 1.26871e7 7.32488e6i 0.0304368 0.0175727i
\(748\) 6.27664e6i 0.0149976i
\(749\) −2.55619e8 + 5.42967e8i −0.608341 + 1.29219i
\(750\) 5.51823e7 0.130802
\(751\) 3.50940e7 + 6.07847e7i 0.0828540 + 0.143507i 0.904475 0.426527i \(-0.140263\pi\)
−0.821621 + 0.570035i \(0.806930\pi\)
\(752\) −1.29366e8 7.46895e7i −0.304205 0.175633i
\(753\) −1.42384e8 + 2.46615e8i −0.333484 + 0.577611i
\(754\) −1.01495e8 + 5.85983e7i −0.236773 + 0.136701i
\(755\) 2.03391e7i 0.0472598i
\(756\) 1.89757e7 + 2.26458e8i 0.0439169 + 0.524111i
\(757\) −5.44271e7 −0.125466 −0.0627332 0.998030i \(-0.519982\pi\)
−0.0627332 + 0.998030i \(0.519982\pi\)
\(758\) 2.37747e7 + 4.11790e7i 0.0545893 + 0.0945514i
\(759\) 4.83015e8 + 2.78869e8i 1.10468 + 0.637786i
\(760\) −1.48887e6 + 2.57880e6i −0.00339168 + 0.00587457i
\(761\) 4.83017e8 2.78870e8i 1.09599 0.632773i 0.160829 0.986982i \(-0.448583\pi\)
0.935166 + 0.354210i \(0.115250\pi\)
\(762\) 1.16298e8i 0.262850i
\(763\) 2.64162e8 2.21350e7i 0.594699 0.0498317i
\(764\) −1.81354e8 −0.406674
\(765\) −70814.7 122655.i −0.000158175 0.000273968i
\(766\) 8.33729e7 + 4.81354e7i 0.185498 + 0.107097i
\(767\) −3.00542e8 + 5.20555e8i −0.666070 + 1.15367i
\(768\) −2.29524e7 + 1.32516e7i −0.0506693 + 0.0292539i
\(769\) 3.50325e8i 0.770356i −0.922842 0.385178i \(-0.874140\pi\)
0.922842 0.385178i \(-0.125860\pi\)
\(770\) −3.37644e7 1.58956e7i −0.0739582 0.0348182i
\(771\) −7.88286e8 −1.71997
\(772\) −2.09380e8 3.62657e8i −0.455076 0.788215i
\(773\) 4.94039e8 + 2.85234e8i 1.06960 + 0.617536i 0.928073 0.372398i \(-0.121464\pi\)
0.141530 + 0.989934i \(0.454798\pi\)
\(774\) −2.02526e7 + 3.50785e7i −0.0436775 + 0.0756516i
\(775\) 7.61819e8 4.39837e8i 1.63662 0.944901i
\(776\) 9.22729e7i 0.197464i
\(777\) −6.40864e8 + 4.45243e8i −1.36616 + 0.949148i
\(778\) −3.38444e7 −0.0718702
\(779\) −2.37135e7 4.10730e7i −0.0501630 0.0868848i
\(780\) −2.40822e7 1.39039e7i −0.0507472 0.0292989i
\(781\) 3.15814e8 5.47006e8i 0.662946 1.14826i
\(782\) 8.82960e6 5.09777e6i 0.0184638 0.0106601i
\(783\) 1.54849e8i 0.322570i
\(784\) 1.18793e8 2.00488e7i 0.246514 0.0416044i
\(785\) −7.14208e7 −0.147644
\(786\) 2.19314e8 + 3.79863e8i 0.451647 + 0.782275i
\(787\) −6.46413e8 3.73207e8i −1.32613 0.765641i −0.341431 0.939907i \(-0.610911\pi\)
−0.984699 + 0.174266i \(0.944245\pi\)
\(788\) −7.15341e7 + 1.23901e8i −0.146196 + 0.253218i
\(789\) 2.95909e8 1.70843e8i 0.602459 0.347830i
\(790\) 5.88770e6i 0.0119416i
\(791\) −4.43438e8 6.38267e8i −0.895992 1.28965i
\(792\) 2.52902e7 0.0509069
\(793\) 2.75870e8 + 4.77820e8i 0.553203 + 0.958175i
\(794\) −5.17640e8 2.98860e8i −1.03411 0.597043i
\(795\) −2.66932e7 + 4.62340e7i −0.0531250 + 0.0920153i
\(796\) −2.23299e8 + 1.28922e8i −0.442738 + 0.255615i
\(797\) 8.52897e8i 1.68470i −0.538934 0.842348i \(-0.681173\pi\)
0.538934 0.842348i \(-0.318827\pi\)
\(798\) 2.76856e7 5.88077e7i 0.0544810 0.115725i
\(799\) −1.84642e7 −0.0361984
\(800\) 4.48087e7 + 7.76109e7i 0.0875169 + 0.151584i
\(801\) 3.96507e7 + 2.28924e7i 0.0771532 + 0.0445444i
\(802\) 1.73294e8 3.00153e8i 0.335938 0.581862i
\(803\) −2.50631e8 + 1.44702e8i −0.484047 + 0.279465i
\(804\) 1.16823e8i 0.224782i
\(805\) −5.06176e6 6.04078e7i −0.00970317 0.115799i
\(806\) −8.90992e8 −1.70164
\(807\) −3.29530e8 5.70762e8i −0.627010 1.08601i
\(808\) −2.44480e8 1.41151e8i −0.463457 0.267577i
\(809\) 2.68931e8 4.65802e8i 0.507920 0.879744i −0.492038 0.870574i \(-0.663748\pi\)
0.999958 0.00916987i \(-0.00291890\pi\)
\(810\) −2.78231e7 + 1.60637e7i −0.0523540 + 0.0302266i
\(811\) 546840.i 0.00102517i −1.00000 0.000512587i \(-0.999837\pi\)
1.00000 0.000512587i \(-0.000163162\pi\)
\(812\) 8.18032e7 6.85454e6i 0.152793 0.0128030i
\(813\) 2.79179e8 0.519530
\(814\) 3.94530e8 + 6.83346e8i 0.731487 + 1.26697i
\(815\) 1.02965e7 + 5.94472e6i 0.0190204 + 0.0109814i
\(816\) −1.63798e6 + 2.83706e6i −0.00301465 + 0.00522153i
\(817\) 9.11621e7 5.26325e7i 0.167166 0.0965134i
\(818\) 6.18850e8i 1.13064i
\(819\) −7.75011e7 3.64861e7i −0.141077 0.0664165i
\(820\) 1.42122e7 0.0257762
\(821\) 2.66538e7 + 4.61657e7i 0.0481648 + 0.0834238i 0.889103 0.457708i \(-0.151329\pi\)
−0.840938 + 0.541132i \(0.817996\pi\)
\(822\) 7.77613e7 + 4.48955e7i 0.140006 + 0.0808328i
\(823\) 3.83179e8 6.63686e8i 0.687389 1.19059i −0.285291 0.958441i \(-0.592090\pi\)
0.972680 0.232151i \(-0.0745764\pi\)
\(824\) 1.14009e8 6.58234e7i 0.203779 0.117652i
\(825\) 6.05971e8i 1.07917i
\(826\) 3.45769e8 2.40224e8i 0.613544 0.426262i
\(827\) 1.00353e9 1.77425 0.887127 0.461526i \(-0.152698\pi\)
0.887127 + 0.461526i \(0.152698\pi\)
\(828\) 2.05402e7 + 3.55767e7i 0.0361838 + 0.0626722i
\(829\) −1.28437e8 7.41532e7i −0.225438 0.130157i 0.383028 0.923737i \(-0.374881\pi\)
−0.608466 + 0.793580i \(0.708215\pi\)
\(830\) 5.70438e6 9.88028e6i 0.00997641 0.0172796i
\(831\) 3.49067e8 2.01534e8i 0.608283 0.351192i
\(832\) 9.07705e7i 0.157607i
\(833\) 1.14772e7 9.48790e6i 0.0198564 0.0164148i
\(834\) 3.99729e8 0.689077
\(835\) 4.16357e7 + 7.21151e7i 0.0715165 + 0.123870i
\(836\) −5.69188e7 3.28621e7i −0.0974175 0.0562440i
\(837\) −5.88624e8 + 1.01953e9i −1.00383 + 1.73869i
\(838\) 1.00163e8 5.78293e7i 0.170207 0.0982688i
\(839\) 2.21066e8i 0.374315i 0.982330 + 0.187157i \(0.0599274\pi\)
−0.982330 + 0.187157i \(0.940073\pi\)
\(840\) 1.11134e7 + 1.59962e7i 0.0187503 + 0.0269884i
\(841\) −5.38887e8 −0.905962
\(842\) −9.02991e7 1.56403e8i −0.151268 0.262004i
\(843\) −2.74989e7 1.58765e7i −0.0459021 0.0265016i
\(844\) −6.74895e6 + 1.16895e7i −0.0112256 + 0.0194433i
\(845\) 3.05973e7 1.76653e7i 0.0507122 0.0292787i
\(846\) 7.43969e7i 0.122869i
\(847\) 9.20258e7 1.95474e8i 0.151446 0.321692i
\(848\) −1.74265e8 −0.285774
\(849\) 4.26319e6 + 7.38405e6i 0.00696645 + 0.0120662i
\(850\) 9.59319e6 + 5.53863e6i 0.0156209 + 0.00901873i
\(851\) −6.40860e8 + 1.11000e9i −1.03986 + 1.80109i
\(852\) −2.85498e8 + 1.64832e8i −0.461619 + 0.266516i
\(853\) 9.10570e8i 1.46712i 0.679624 + 0.733561i \(0.262143\pi\)
−0.679624 + 0.733561i \(0.737857\pi\)
\(854\) −3.22699e7 3.85114e8i −0.0518112 0.618323i
\(855\) −1.48303e6 −0.00237276
\(856\) −1.58360e8 2.74287e8i −0.252478 0.437305i
\(857\) 1.68169e8 + 9.70924e7i 0.267180 + 0.154256i 0.627605 0.778532i \(-0.284035\pi\)
−0.360426 + 0.932788i \(0.617369\pi\)
\(858\) 3.06884e8 5.31539e8i 0.485862 0.841537i
\(859\) −6.25498e8 + 3.61132e8i −0.986840 + 0.569752i −0.904328 0.426838i \(-0.859628\pi\)
−0.0825118 + 0.996590i \(0.526294\pi\)
\(860\) 3.15441e7i 0.0495933i
\(861\) −3.09143e8 + 2.59041e7i −0.484340 + 0.0405844i
\(862\) −1.76088e6 −0.00274922
\(863\) 9.71379e7 + 1.68248e8i 0.151132 + 0.261768i 0.931644 0.363373i \(-0.118375\pi\)
−0.780512 + 0.625141i \(0.785042\pi\)
\(864\) −1.03865e8 5.99665e7i −0.161038 0.0929753i
\(865\) 2.15397e6 3.73079e6i 0.00332807 0.00576438i
\(866\) 2.48012e8 1.43190e8i 0.381873 0.220475i
\(867\) 6.09681e8i 0.935504i
\(868\) 5.64648e8 + 2.65826e8i 0.863413 + 0.406479i
\(869\) −1.29952e8 −0.198027
\(870\) 6.63607e6 + 1.14940e7i 0.0100775 + 0.0174548i
\(871\) 3.46503e8 + 2.00053e8i 0.524387 + 0.302755i
\(872\) −6.99506e7 + 1.21158e8i −0.105497 + 0.182727i
\(873\) −3.97988e7 + 2.29778e7i −0.0598173 + 0.0345355i
\(874\) 1.06760e8i 0.159909i
\(875\) 1.08717e8 7.55315e7i 0.162283 0.112747i
\(876\) 1.51048e8 0.224700
\(877\) −2.48367e8 4.30184e8i −0.368210 0.637758i 0.621076 0.783750i \(-0.286696\pi\)
−0.989286 + 0.145992i \(0.953362\pi\)
\(878\) 3.96607e8 + 2.28981e8i 0.585973 + 0.338311i
\(879\) −1.64739e8 + 2.85336e8i −0.242566 + 0.420136i
\(880\) 1.70565e7 9.84759e6i 0.0250290 0.0144505i
\(881\) 8.63809e7i 0.126325i 0.998003 + 0.0631626i \(0.0201187\pi\)
−0.998003 + 0.0631626i \(0.979881\pi\)
\(882\) 3.82292e7 + 4.62446e7i 0.0557172 + 0.0673993i
\(883\) 6.49219e8 0.942994 0.471497 0.881868i \(-0.343714\pi\)
0.471497 + 0.881868i \(0.343714\pi\)
\(884\) −5.60990e6 9.71663e6i −0.00812079 0.0140656i
\(885\) 5.89512e7 + 3.40355e7i 0.0850477 + 0.0491023i
\(886\) −7.26180e6 + 1.25778e7i −0.0104410 + 0.0180844i
\(887\) −6.17373e8 + 3.56441e8i −0.884661 + 0.510759i −0.872192 0.489163i \(-0.837302\pi\)
−0.0124685 + 0.999922i \(0.503969\pi\)
\(888\) 4.11833e8i 0.588141i
\(889\) 1.59184e8 + 2.29123e8i 0.226566 + 0.326110i
\(890\) 3.56557e7 0.0505776
\(891\) −3.54555e8 6.14107e8i −0.501246 0.868183i
\(892\) 1.24541e8 + 7.19038e7i 0.175476 + 0.101311i
\(893\) −9.66714e7 + 1.67440e8i −0.135751 + 0.235128i
\(894\) −5.06533e8 + 2.92447e8i −0.708917 + 0.409293i
\(895\) 3.65568e7i 0.0509916i
\(896\) −2.70812e7 + 5.75239e7i −0.0376482 + 0.0799695i
\(897\) 9.96983e8 1.38137
\(898\) −1.72910e8 2.99489e8i −0.238777 0.413573i
\(899\) 3.68282e8 + 2.12628e8i 0.506875 + 0.292645i
\(900\) −2.23166e7 + 3.86534e7i −0.0306126 + 0.0530225i
\(901\) −1.86544e7 + 1.07701e7i −0.0255039 + 0.0147247i
\(902\) 3.13689e8i 0.427445i
\(903\) −5.74945e7 6.86148e8i −0.0780842 0.931869i
\(904\) 4.10164e8 0.555203
\(905\) −1.79225e7 3.10427e7i −0.0241798 0.0418806i
\(906\) −2.02914e8 1.17153e8i −0.272853 0.157532i
\(907\) 4.14206e8 7.17425e8i 0.555129 0.961512i −0.442764 0.896638i \(-0.646002\pi\)
0.997893 0.0648738i \(-0.0206645\pi\)
\(908\) 1.07864e8 6.22751e7i 0.144085 0.0831873i
\(909\) 1.40597e8i 0.187191i
\(910\) −6.64764e7 + 5.57026e6i −0.0882152 + 0.00739182i
\(911\) −1.17587e9 −1.55526 −0.777631 0.628721i \(-0.783579\pi\)
−0.777631 + 0.628721i \(0.783579\pi\)
\(912\) 1.71516e7 + 2.97075e7i 0.0226111 + 0.0391635i
\(913\) 2.18076e8 + 1.25906e8i 0.286547 + 0.165438i
\(914\) 2.71449e7 4.70164e7i 0.0355509 0.0615759i
\(915\) 5.41116e7 3.12414e7i 0.0706362 0.0407818i
\(916\) 7.89013e7i 0.102659i
\(917\) 9.52022e8 + 4.48195e8i 1.23464 + 0.581244i
\(918\) −1.48245e7 −0.0191625
\(919\) −2.25460e8 3.90508e8i −0.290485 0.503134i 0.683440 0.730007i \(-0.260483\pi\)
−0.973924 + 0.226873i \(0.927150\pi\)
\(920\) 2.77060e7 + 1.59961e7i 0.0355804 + 0.0205423i
\(921\) 4.40576e8 7.63101e8i 0.563952 0.976794i
\(922\) −2.96147e8 + 1.70981e8i −0.377846 + 0.218150i
\(923\) 1.12907e9i 1.43587i
\(924\) −3.53065e8 + 2.45293e8i −0.447547 + 0.310935i
\(925\) −1.39256e9 −1.75950
\(926\) −3.24582e8 5.62192e8i −0.408781 0.708030i
\(927\) 5.67813e7 + 3.27827e7i 0.0712798 + 0.0411534i
\(928\) −2.16616e7 + 3.75190e7i −0.0271048 + 0.0469469i
\(929\) −1.03420e9 + 5.97094e8i −1.28990 + 0.744725i −0.978636 0.205599i \(-0.934086\pi\)
−0.311264 + 0.950323i \(0.600752\pi\)
\(930\) 1.00902e8i 0.125444i
\(931\) −2.59493e7 1.53754e8i −0.0321571 0.190537i
\(932\) 7.26311e8 0.897170
\(933\) −5.57398e8 9.65441e8i −0.686310 1.18872i
\(934\) −3.35793e8 1.93870e8i −0.412127 0.237942i
\(935\) 1.21722e6 2.10829e6i 0.00148914 0.00257927i
\(936\) 3.91508e7 2.26037e7i 0.0477433 0.0275646i
\(937\) 5.57908e8i 0.678178i −0.940754 0.339089i \(-0.889881\pi\)
0.940754 0.339089i \(-0.110119\pi\)
\(938\) −1.59903e8 2.30158e8i −0.193753 0.278880i
\(939\) 1.10052e9 1.32923
\(940\) −2.89690e7 5.01757e7i −0.0348778 0.0604101i
\(941\) 9.18066e8 + 5.30046e8i 1.10181 + 0.636128i 0.936695 0.350147i \(-0.113868\pi\)
0.165111 + 0.986275i \(0.447202\pi\)
\(942\) −4.11381e8 + 7.12533e8i −0.492143 + 0.852417i
\(943\) −4.41279e8 + 2.54773e8i −0.526234 + 0.303821i
\(944\) 2.22198e8i 0.264134i
\(945\) −3.75431e7 + 7.97462e7i −0.0444871 + 0.0944963i
\(946\) −6.96238e8 −0.822402
\(947\) −4.08434e8 7.07429e8i −0.480919 0.832977i 0.518841 0.854871i \(-0.326364\pi\)
−0.999760 + 0.0218939i \(0.993030\pi\)
\(948\) 5.87389e7 + 3.39129e7i 0.0689447 + 0.0398052i
\(949\) −2.58661e8 + 4.48015e8i −0.302645 + 0.524196i
\(950\) 1.00453e8 5.79963e7i 0.117163 0.0676440i
\(951\) 8.27499e8i 0.962112i
\(952\) 656218. + 7.83141e6i 0.000760567 + 0.00907672i
\(953\) 1.23336e9 1.42499 0.712494 0.701678i \(-0.247565\pi\)
0.712494 + 0.701678i \(0.247565\pi\)
\(954\) −4.33955e7 7.51632e7i −0.0499804 0.0865686i
\(955\) −6.09158e7 3.51697e7i −0.0699390 0.0403793i
\(956\) 6.26316e7 1.08481e8i 0.0716836 0.124160i
\(957\) −2.53694e8 + 1.46471e8i −0.289451 + 0.167115i
\(958\) 5.53180e8i 0.629173i
\(959\) 2.14652e8 1.79864e7i 0.243377 0.0203933i
\(960\) −1.02795e7 −0.0116187
\(961\) 1.17276e9 + 2.03128e9i 1.32141 + 2.28875i
\(962\) 1.22151e9 + 7.05241e8i 1.37206 + 0.792159i
\(963\) 7.88697e7 1.36606e8i 0.0883143 0.152965i
\(964\) −2.72316e8 + 1.57222e8i −0.303978 + 0.175502i
\(965\) 1.62420e8i 0.180741i
\(966\) −6.31817e8 2.97448e8i −0.700906 0.329974i
\(967\) −5.82431e8 −0.644118 −0.322059 0.946720i \(-0.604375\pi\)
−0.322059 + 0.946720i \(0.604375\pi\)
\(968\) 5.70114e7 + 9.87466e7i 0.0628544 + 0.108867i
\(969\) 3.67203e6 + 2.12005e6i 0.00403585 + 0.00233010i
\(970\) −1.78944e7 + 3.09940e7i −0.0196066 + 0.0339596i
\(971\) 2.97824e7 1.71949e7i 0.0325314 0.0187820i −0.483646 0.875264i \(-0.660688\pi\)
0.516177 + 0.856482i \(0.327354\pi\)
\(972\) 1.12889e8i 0.122929i
\(973\) 7.87523e8 5.47135e8i 0.854918 0.593958i
\(974\) −1.29080e8 −0.139695
\(975\) 5.41601e8 + 9.38081e8i 0.584340 + 1.01211i
\(976\) 1.76632e8 + 1.01979e8i 0.189986 + 0.109688i
\(977\) 2.60603e8 4.51377e8i 0.279444 0.484012i −0.691802 0.722087i \(-0.743183\pi\)
0.971247 + 0.238075i \(0.0765164\pi\)
\(978\) 1.18615e8 6.84827e7i 0.126802 0.0732090i
\(979\) 7.86987e8i 0.838725i
\(980\) 4.37899e7 + 1.63031e7i 0.0465260 + 0.0173217i
\(981\) −6.96765e7 −0.0738039
\(982\) 3.15696e7 + 5.46802e7i 0.0333376 + 0.0577425i
\(983\) −5.40048e8 3.11797e8i −0.568554 0.328255i 0.188018 0.982166i \(-0.439794\pi\)
−0.756572 + 0.653911i \(0.773127\pi\)
\(984\) 8.18616e7 1.41788e8i 0.0859201 0.148818i
\(985\) −4.80559e7 + 2.77451e7i −0.0502850 + 0.0290320i
\(986\) 5.35501e6i 0.00558637i
\(987\) 7.21587e8 + 1.03862e9i 0.750476 + 1.08020i
\(988\) −1.17485e8 −0.121818
\(989\) −5.65472e8 9.79426e8i −0.584550 1.01247i
\(990\) 8.49485e6 + 4.90450e6i 0.00875488 + 0.00505463i
\(991\) −6.99332e7 + 1.21128e8i −0.0718559 + 0.124458i −0.899715 0.436478i \(-0.856226\pi\)
0.827859 + 0.560937i \(0.189559\pi\)
\(992\) −2.85240e8 + 1.64683e8i −0.292196 + 0.168700i
\(993\) 7.99344e8i 0.816368i
\(994\) −3.36854e8 + 7.15521e8i −0.342991 + 0.728557i
\(995\) −1.00007e8 −0.101522
\(996\) −6.57140e7 1.13820e8i −0.0665090 0.115197i
\(997\) −1.68279e9 9.71557e8i −1.69802 0.980353i −0.947636 0.319354i \(-0.896534\pi\)
−0.750386 0.661000i \(-0.770132\pi\)
\(998\) −1.22543e8 + 2.12252e8i −0.123282 + 0.213530i
\(999\) 1.61396e9 9.31820e8i 1.61881 0.934621i
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 14.7.d.a.3.4 8
3.2 odd 2 126.7.n.c.73.1 8
4.3 odd 2 112.7.s.c.17.2 8
7.2 even 3 98.7.d.c.19.3 8
7.3 odd 6 98.7.b.c.97.3 8
7.4 even 3 98.7.b.c.97.2 8
7.5 odd 6 inner 14.7.d.a.5.4 yes 8
7.6 odd 2 98.7.d.c.31.3 8
21.5 even 6 126.7.n.c.19.1 8
28.19 even 6 112.7.s.c.33.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
14.7.d.a.3.4 8 1.1 even 1 trivial
14.7.d.a.5.4 yes 8 7.5 odd 6 inner
98.7.b.c.97.2 8 7.4 even 3
98.7.b.c.97.3 8 7.3 odd 6
98.7.d.c.19.3 8 7.2 even 3
98.7.d.c.31.3 8 7.6 odd 2
112.7.s.c.17.2 8 4.3 odd 2
112.7.s.c.33.2 8 28.19 even 6
126.7.n.c.19.1 8 21.5 even 6
126.7.n.c.73.1 8 3.2 odd 2