Properties

Label 50.6.d.b.21.1
Level $50$
Weight $6$
Character 50.21
Analytic conductor $8.019$
Analytic rank $0$
Dimension $28$
CM no
Inner twists $2$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [50,6,Mod(11,50)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(50, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("50.11");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 50 = 2 \cdot 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 50.d (of order \(5\), degree \(4\), 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: \(8.01919099065\)
Analytic rank: \(0\)
Dimension: \(28\)
Relative dimension: \(7\) over \(\Q(\zeta_{5})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label 21.1
Character \(\chi\) \(=\) 50.21
Dual form 50.6.d.b.31.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-1.23607 + 3.80423i) q^{2} +(-23.0554 - 16.7507i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-50.3632 - 24.2601i) q^{5} +(92.2216 - 67.0029i) q^{6} +20.3938 q^{7} +(51.7771 - 37.6183i) q^{8} +(175.874 + 541.284i) q^{9} +O(q^{10})\) \(q+(-1.23607 + 3.80423i) q^{2} +(-23.0554 - 16.7507i) q^{3} +(-12.9443 - 9.40456i) q^{4} +(-50.3632 - 24.2601i) q^{5} +(92.2216 - 67.0029i) q^{6} +20.3938 q^{7} +(51.7771 - 37.6183i) q^{8} +(175.874 + 541.284i) q^{9} +(154.543 - 161.606i) q^{10} +(-57.1025 + 175.743i) q^{11} +(140.902 + 433.652i) q^{12} +(-42.6701 - 131.325i) q^{13} +(-25.2082 + 77.5828i) q^{14} +(754.768 + 1402.95i) q^{15} +(79.1084 + 243.470i) q^{16} +(1758.93 - 1277.94i) q^{17} -2276.56 q^{18} +(-1883.38 + 1368.36i) q^{19} +(423.759 + 787.673i) q^{20} +(-470.188 - 341.612i) q^{21} +(-597.985 - 434.462i) q^{22} +(-627.573 + 1931.47i) q^{23} -1823.88 q^{24} +(1947.89 + 2443.63i) q^{25} +552.333 q^{26} +(2872.11 - 8839.44i) q^{27} +(-263.983 - 191.795i) q^{28} +(1243.88 + 903.731i) q^{29} +(-6270.07 + 1137.17i) q^{30} +(5987.07 - 4349.86i) q^{31} -1024.00 q^{32} +(4260.35 - 3095.33i) q^{33} +(2687.41 + 8271.00i) q^{34} +(-1027.10 - 494.757i) q^{35} +(2813.98 - 8660.54i) q^{36} +(-268.579 - 826.601i) q^{37} +(-2877.55 - 8856.18i) q^{38} +(-1216.01 + 3742.50i) q^{39} +(-3520.28 + 638.456i) q^{40} +(4845.54 + 14913.0i) q^{41} +(1880.75 - 1366.45i) q^{42} -15841.8 q^{43} +(2391.94 - 1737.85i) q^{44} +(4274.05 - 31527.5i) q^{45} +(-6572.02 - 4774.86i) q^{46} +(-1359.77 - 987.932i) q^{47} +(2254.43 - 6938.43i) q^{48} -16391.1 q^{49} +(-11703.9 + 4389.73i) q^{50} -61959.3 q^{51} +(-682.721 + 2101.20i) q^{52} +(28712.8 + 20861.1i) q^{53} +(30077.1 + 21852.3i) q^{54} +(7139.42 - 7465.68i) q^{55} +(1055.93 - 767.181i) q^{56} +66343.0 q^{57} +(-4975.52 + 3614.92i) q^{58} +(5738.77 + 17662.1i) q^{59} +(3424.18 - 25258.4i) q^{60} +(-14687.6 + 45203.7i) q^{61} +(9147.43 + 28152.9i) q^{62} +(3586.74 + 11038.8i) q^{63} +(1265.73 - 3895.53i) q^{64} +(-1036.96 + 7649.12i) q^{65} +(6509.24 + 20033.4i) q^{66} +(-25841.2 + 18774.7i) q^{67} -34786.6 q^{68} +(46822.5 - 34018.5i) q^{69} +(3151.73 - 3295.76i) q^{70} +(-1106.48 - 803.906i) q^{71} +(29468.4 + 21410.0i) q^{72} +(13331.8 - 41031.0i) q^{73} +3476.56 q^{74} +(-3976.86 - 88967.6i) q^{75} +37247.8 q^{76} +(-1164.54 + 3584.08i) q^{77} +(-12734.3 - 9251.98i) q^{78} +(35739.0 + 25965.9i) q^{79} +(1922.48 - 14181.1i) q^{80} +(-102397. + 74395.7i) q^{81} -62722.0 q^{82} +(-4785.42 + 3476.81i) q^{83} +(2873.54 + 8843.83i) q^{84} +(-119588. + 21689.1i) q^{85} +(19581.6 - 60266.0i) q^{86} +(-13540.0 - 41671.8i) q^{87} +(3654.56 + 11247.6i) q^{88} +(-439.415 + 1352.38i) q^{89} +(114655. + 55229.5i) q^{90} +(-870.206 - 2678.22i) q^{91} +(26288.1 - 19099.4i) q^{92} -210898. q^{93} +(5439.09 - 3951.73i) q^{94} +(128049. - 23223.7i) q^{95} +(23608.7 + 17152.8i) q^{96} +(90485.8 + 65741.8i) q^{97} +(20260.5 - 62355.4i) q^{98} -105170. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 28 q + 28 q^{2} + 7 q^{3} - 112 q^{4} - 145 q^{5} - 28 q^{6} - 236 q^{7} + 448 q^{8} - 446 q^{9} - 220 q^{10} - 389 q^{11} + 192 q^{12} + 1047 q^{13} + 164 q^{14} - 640 q^{15} - 1792 q^{16} + 909 q^{17} - 11576 q^{18} + 260 q^{19} - 1040 q^{20} - 1849 q^{21} + 556 q^{22} + 817 q^{23} + 2432 q^{24} + 16055 q^{25} - 4528 q^{26} + 1675 q^{27} + 2544 q^{28} - 2445 q^{29} - 5440 q^{30} + 16731 q^{31} - 28672 q^{32} + 29629 q^{33} - 7576 q^{34} - 825 q^{35} - 7136 q^{36} + 39819 q^{37} + 3100 q^{38} + 26008 q^{39} + 10231 q^{41} + 7396 q^{42} - 86148 q^{43} - 2224 q^{44} - 7870 q^{45} - 11708 q^{46} + 10019 q^{47} + 3072 q^{48} + 147076 q^{49} + 16520 q^{50} - 108074 q^{51} + 16752 q^{52} + 74512 q^{53} + 4260 q^{54} + 2735 q^{55} - 10176 q^{56} - 176840 q^{57} + 9780 q^{58} - 13430 q^{59} + 5760 q^{60} - 29774 q^{61} + 63956 q^{62} - 206818 q^{63} - 28672 q^{64} + 51235 q^{65} + 23264 q^{66} - 85061 q^{67} - 89696 q^{68} - 185227 q^{69} - 25260 q^{70} + 148501 q^{71} + 64064 q^{72} + 189082 q^{73} + 305304 q^{74} + 93630 q^{75} + 16480 q^{76} + 127243 q^{77} + 32028 q^{78} + 46930 q^{79} + 39680 q^{80} - 179812 q^{81} - 338864 q^{82} + 66807 q^{83} - 34464 q^{84} - 877380 q^{85} + 121332 q^{86} - 226000 q^{87} + 24896 q^{88} - 347190 q^{89} + 628660 q^{90} + 197001 q^{91} + 46832 q^{92} - 64906 q^{93} - 40076 q^{94} + 85970 q^{95} - 7168 q^{96} + 502364 q^{97} + 185056 q^{98} + 1151018 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/50\mathbb{Z}\right)^\times\).

\(n\) \(27\)
\(\chi(n)\) \(e\left(\frac{3}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.23607 + 3.80423i −0.218508 + 0.672499i
\(3\) −23.0554 16.7507i −1.47901 1.07456i −0.977875 0.209188i \(-0.932918\pi\)
−0.501130 0.865372i \(-0.667082\pi\)
\(4\) −12.9443 9.40456i −0.404508 0.293893i
\(5\) −50.3632 24.2601i −0.900923 0.433978i
\(6\) 92.2216 67.0029i 1.04581 0.759829i
\(7\) 20.3938 0.157309 0.0786546 0.996902i \(-0.474938\pi\)
0.0786546 + 0.996902i \(0.474938\pi\)
\(8\) 51.7771 37.6183i 0.286031 0.207813i
\(9\) 175.874 + 541.284i 0.723760 + 2.22750i
\(10\) 154.543 161.606i 0.488709 0.511042i
\(11\) −57.1025 + 175.743i −0.142290 + 0.437923i −0.996653 0.0817544i \(-0.973948\pi\)
0.854363 + 0.519677i \(0.173948\pi\)
\(12\) 140.902 + 433.652i 0.282465 + 0.869338i
\(13\) −42.6701 131.325i −0.0700269 0.215521i 0.909918 0.414787i \(-0.136144\pi\)
−0.979945 + 0.199267i \(0.936144\pi\)
\(14\) −25.2082 + 77.5828i −0.0343733 + 0.105790i
\(15\) 754.768 + 1402.95i 0.866135 + 1.60995i
\(16\) 79.1084 + 243.470i 0.0772542 + 0.237764i
\(17\) 1758.93 1277.94i 1.47614 1.07248i 0.497362 0.867543i \(-0.334302\pi\)
0.978776 0.204934i \(-0.0656978\pi\)
\(18\) −2276.56 −1.65614
\(19\) −1883.38 + 1368.36i −1.19689 + 0.869591i −0.993975 0.109606i \(-0.965041\pi\)
−0.202914 + 0.979197i \(0.565041\pi\)
\(20\) 423.759 + 787.673i 0.236888 + 0.440323i
\(21\) −470.188 341.612i −0.232661 0.169038i
\(22\) −597.985 434.462i −0.263411 0.191379i
\(23\) −627.573 + 1931.47i −0.247368 + 0.761322i 0.747869 + 0.663846i \(0.231077\pi\)
−0.995238 + 0.0974760i \(0.968923\pi\)
\(24\) −1823.88 −0.646349
\(25\) 1947.89 + 2443.63i 0.623326 + 0.781962i
\(26\) 552.333 0.160239
\(27\) 2872.11 8839.44i 0.758213 2.33354i
\(28\) −263.983 191.795i −0.0636329 0.0462320i
\(29\) 1243.88 + 903.731i 0.274652 + 0.199547i 0.716582 0.697503i \(-0.245706\pi\)
−0.441929 + 0.897050i \(0.645706\pi\)
\(30\) −6270.07 + 1137.17i −1.27195 + 0.230687i
\(31\) 5987.07 4349.86i 1.11895 0.812964i 0.134899 0.990859i \(-0.456929\pi\)
0.984049 + 0.177895i \(0.0569289\pi\)
\(32\) −1024.00 −0.176777
\(33\) 4260.35 3095.33i 0.681021 0.494791i
\(34\) 2687.41 + 8271.00i 0.398691 + 1.22705i
\(35\) −1027.10 494.757i −0.141723 0.0682687i
\(36\) 2813.98 8660.54i 0.361880 1.11375i
\(37\) −268.579 826.601i −0.0322528 0.0992639i 0.933634 0.358228i \(-0.116619\pi\)
−0.965887 + 0.258964i \(0.916619\pi\)
\(38\) −2877.55 8856.18i −0.323269 0.994919i
\(39\) −1216.01 + 3742.50i −0.128020 + 0.394004i
\(40\) −3520.28 + 638.456i −0.347878 + 0.0630930i
\(41\) 4845.54 + 14913.0i 0.450176 + 1.38550i 0.876706 + 0.481027i \(0.159736\pi\)
−0.426530 + 0.904474i \(0.640264\pi\)
\(42\) 1880.75 1366.45i 0.164516 0.119528i
\(43\) −15841.8 −1.30658 −0.653288 0.757110i \(-0.726611\pi\)
−0.653288 + 0.757110i \(0.726611\pi\)
\(44\) 2391.94 1737.85i 0.186260 0.135326i
\(45\) 4274.05 31527.5i 0.314636 2.32091i
\(46\) −6572.02 4774.86i −0.457936 0.332710i
\(47\) −1359.77 987.932i −0.0897886 0.0652353i 0.541985 0.840388i \(-0.317673\pi\)
−0.631774 + 0.775153i \(0.717673\pi\)
\(48\) 2254.43 6938.43i 0.141232 0.434669i
\(49\) −16391.1 −0.975254
\(50\) −11703.9 + 4389.73i −0.662070 + 0.248321i
\(51\) −61959.3 −3.33566
\(52\) −682.721 + 2101.20i −0.0350134 + 0.107760i
\(53\) 28712.8 + 20861.1i 1.40406 + 1.02011i 0.994153 + 0.107985i \(0.0344397\pi\)
0.409910 + 0.912126i \(0.365560\pi\)
\(54\) 30077.1 + 21852.3i 1.40363 + 1.01979i
\(55\) 7139.42 7465.68i 0.318241 0.332784i
\(56\) 1055.93 767.181i 0.0449952 0.0326910i
\(57\) 66343.0 2.70463
\(58\) −4975.52 + 3614.92i −0.194208 + 0.141101i
\(59\) 5738.77 + 17662.1i 0.214629 + 0.660560i 0.999180 + 0.0404956i \(0.0128937\pi\)
−0.784551 + 0.620065i \(0.787106\pi\)
\(60\) 3424.18 25258.4i 0.122794 0.905790i
\(61\) −14687.6 + 45203.7i −0.505388 + 1.55542i 0.294729 + 0.955581i \(0.404771\pi\)
−0.800117 + 0.599844i \(0.795229\pi\)
\(62\) 9147.43 + 28152.9i 0.302218 + 0.930130i
\(63\) 3586.74 + 11038.8i 0.113854 + 0.350407i
\(64\) 1265.73 3895.53i 0.0386271 0.118882i
\(65\) −1036.96 + 7649.12i −0.0304424 + 0.224558i
\(66\) 6509.24 + 20033.4i 0.183938 + 0.566102i
\(67\) −25841.2 + 18774.7i −0.703275 + 0.510959i −0.880997 0.473122i \(-0.843127\pi\)
0.177722 + 0.984081i \(0.443127\pi\)
\(68\) −34786.6 −0.912303
\(69\) 46822.5 34018.5i 1.18395 0.860187i
\(70\) 3151.73 3295.76i 0.0768783 0.0803916i
\(71\) −1106.48 803.906i −0.0260494 0.0189260i 0.574684 0.818375i \(-0.305125\pi\)
−0.600734 + 0.799449i \(0.705125\pi\)
\(72\) 29468.4 + 21410.0i 0.669923 + 0.486728i
\(73\) 13331.8 41031.0i 0.292807 0.901166i −0.691143 0.722718i \(-0.742892\pi\)
0.983949 0.178448i \(-0.0571075\pi\)
\(74\) 3476.56 0.0738023
\(75\) −3976.86 88967.6i −0.0816371 1.82633i
\(76\) 37247.8 0.739718
\(77\) −1164.54 + 3584.08i −0.0223835 + 0.0688892i
\(78\) −12734.3 9251.98i −0.236994 0.172186i
\(79\) 35739.0 + 25965.9i 0.644280 + 0.468097i 0.861318 0.508066i \(-0.169639\pi\)
−0.217038 + 0.976163i \(0.569639\pi\)
\(80\) 1922.48 14181.1i 0.0335843 0.247734i
\(81\) −102397. + 74395.7i −1.73410 + 1.25990i
\(82\) −62722.0 −1.03011
\(83\) −4785.42 + 3476.81i −0.0762474 + 0.0553970i −0.625256 0.780420i \(-0.715005\pi\)
0.549009 + 0.835817i \(0.315005\pi\)
\(84\) 2873.54 + 8843.83i 0.0444343 + 0.136755i
\(85\) −119588. + 21689.1i −1.79532 + 0.325608i
\(86\) 19581.6 60266.0i 0.285497 0.878670i
\(87\) −13540.0 41671.8i −0.191787 0.590261i
\(88\) 3654.56 + 11247.6i 0.0503070 + 0.154829i
\(89\) −439.415 + 1352.38i −0.00588031 + 0.0180977i −0.953954 0.299954i \(-0.903029\pi\)
0.948073 + 0.318052i \(0.103029\pi\)
\(90\) 114655. + 55229.5i 1.49206 + 0.718729i
\(91\) −870.206 2678.22i −0.0110159 0.0339034i
\(92\) 26288.1 19099.4i 0.323810 0.235261i
\(93\) −210898. −2.52851
\(94\) 5439.09 3951.73i 0.0634901 0.0461283i
\(95\) 128049. 23223.7i 1.45569 0.264011i
\(96\) 23608.7 + 17152.8i 0.261454 + 0.189957i
\(97\) 90485.8 + 65741.8i 0.976453 + 0.709435i 0.956913 0.290375i \(-0.0937799\pi\)
0.0195398 + 0.999809i \(0.493780\pi\)
\(98\) 20260.5 62355.4i 0.213101 0.655857i
\(99\) −105170. −1.07846
\(100\) −2232.78 49950.1i −0.0223278 0.499501i
\(101\) 142078. 1.38587 0.692936 0.721000i \(-0.256317\pi\)
0.692936 + 0.721000i \(0.256317\pi\)
\(102\) 76586.0 235707.i 0.728868 2.24322i
\(103\) −65630.7 47683.5i −0.609557 0.442869i 0.239702 0.970847i \(-0.422950\pi\)
−0.849258 + 0.527978i \(0.822950\pi\)
\(104\) −7149.55 5194.45i −0.0648179 0.0470930i
\(105\) 15392.6 + 28611.5i 0.136251 + 0.253260i
\(106\) −114851. + 83444.4i −0.992822 + 0.721327i
\(107\) 40399.5 0.341128 0.170564 0.985347i \(-0.445441\pi\)
0.170564 + 0.985347i \(0.445441\pi\)
\(108\) −120308. + 87409.1i −0.992514 + 0.721103i
\(109\) −27206.9 83734.4i −0.219338 0.675052i −0.998817 0.0486244i \(-0.984516\pi\)
0.779479 0.626428i \(-0.215484\pi\)
\(110\) 19576.3 + 36388.0i 0.154259 + 0.286733i
\(111\) −7653.97 + 23556.5i −0.0589630 + 0.181469i
\(112\) 1613.32 + 4965.30i 0.0121528 + 0.0374025i
\(113\) −16723.0 51468.1i −0.123202 0.379177i 0.870367 0.492403i \(-0.163882\pi\)
−0.993569 + 0.113226i \(0.963882\pi\)
\(114\) −82004.5 + 252384.i −0.590984 + 1.81886i
\(115\) 78464.2 82049.9i 0.553257 0.578540i
\(116\) −7601.91 23396.3i −0.0524539 0.161437i
\(117\) 63579.5 46193.2i 0.429390 0.311970i
\(118\) −74284.2 −0.491124
\(119\) 35871.4 26062.1i 0.232210 0.168710i
\(120\) 91856.1 + 44247.4i 0.582311 + 0.280501i
\(121\) 102668. + 74592.6i 0.637487 + 0.463162i
\(122\) −153810. 111750.i −0.935590 0.679746i
\(123\) 138089. 424993.i 0.822990 2.53290i
\(124\) −118407. −0.691548
\(125\) −38819.3 170325.i −0.222215 0.974998i
\(126\) −46427.7 −0.260526
\(127\) −85822.6 + 264135.i −0.472164 + 1.45317i 0.377581 + 0.925976i \(0.376756\pi\)
−0.849745 + 0.527194i \(0.823244\pi\)
\(128\) 13254.9 + 9630.27i 0.0715077 + 0.0519534i
\(129\) 365240. + 265363.i 1.93243 + 1.40399i
\(130\) −27817.2 13399.7i −0.144363 0.0695401i
\(131\) 148822. 108126.i 0.757686 0.550491i −0.140514 0.990079i \(-0.544875\pi\)
0.898200 + 0.439588i \(0.144875\pi\)
\(132\) −84257.4 −0.420894
\(133\) −38409.3 + 27906.0i −0.188282 + 0.136795i
\(134\) −39481.8 121512.i −0.189948 0.584600i
\(135\) −359094. + 375504.i −1.69580 + 1.77329i
\(136\) 42998.6 132336.i 0.199346 0.613523i
\(137\) 2876.77 + 8853.79i 0.0130949 + 0.0403021i 0.957390 0.288797i \(-0.0932551\pi\)
−0.944296 + 0.329099i \(0.893255\pi\)
\(138\) 71538.4 + 220173.i 0.319773 + 0.984159i
\(139\) −53716.6 + 165323.i −0.235815 + 0.725764i 0.761197 + 0.648520i \(0.224612\pi\)
−0.997012 + 0.0772434i \(0.975388\pi\)
\(140\) 8642.06 + 16063.7i 0.0372647 + 0.0692668i
\(141\) 14801.5 + 45554.4i 0.0626986 + 0.192967i
\(142\) 4425.93 3215.62i 0.0184197 0.0133827i
\(143\) 25516.1 0.104345
\(144\) −117873. + 85640.1i −0.473707 + 0.344168i
\(145\) −40721.0 75691.4i −0.160842 0.298969i
\(146\) 139612. + 101434.i 0.542052 + 0.393824i
\(147\) 377903. + 274563.i 1.44241 + 1.04797i
\(148\) −4297.26 + 13225.6i −0.0161264 + 0.0496320i
\(149\) 175030. 0.645873 0.322936 0.946421i \(-0.395330\pi\)
0.322936 + 0.946421i \(0.395330\pi\)
\(150\) 343368. + 94841.1i 1.24604 + 0.344166i
\(151\) −239990. −0.856544 −0.428272 0.903650i \(-0.640878\pi\)
−0.428272 + 0.903650i \(0.640878\pi\)
\(152\) −46040.8 + 141699.i −0.161634 + 0.497459i
\(153\) 1.00108e6 + 727325.i 3.45732 + 2.51189i
\(154\) −12195.2 8860.34i −0.0414369 0.0301057i
\(155\) −407056. + 73825.7i −1.36090 + 0.246819i
\(156\) 50937.0 37007.9i 0.167580 0.121754i
\(157\) −435244. −1.40924 −0.704619 0.709586i \(-0.748882\pi\)
−0.704619 + 0.709586i \(0.748882\pi\)
\(158\) −142956. + 103864.i −0.455575 + 0.330995i
\(159\) −312547. 961922.i −0.980445 3.01750i
\(160\) 51571.9 + 24842.4i 0.159262 + 0.0767172i
\(161\) −12798.6 + 39390.1i −0.0389133 + 0.119763i
\(162\) −156449. 481499.i −0.468365 1.44148i
\(163\) 88376.3 + 271994.i 0.260535 + 0.801845i 0.992688 + 0.120705i \(0.0385156\pi\)
−0.732153 + 0.681140i \(0.761484\pi\)
\(164\) 77528.7 238609.i 0.225088 0.692750i
\(165\) −289658. + 52533.8i −0.828277 + 0.150220i
\(166\) −7311.48 22502.4i −0.0205937 0.0633810i
\(167\) −291585. + 211849.i −0.809048 + 0.587808i −0.913554 0.406717i \(-0.866674\pi\)
0.104507 + 0.994524i \(0.466674\pi\)
\(168\) −37195.8 −0.101677
\(169\) 284957. 207033.i 0.767472 0.557601i
\(170\) 65308.9 481750.i 0.173321 1.27850i
\(171\) −1.07191e6 778785.i −2.80328 2.03670i
\(172\) 205061. + 148986.i 0.528521 + 0.383993i
\(173\) −61589.8 + 189554.i −0.156457 + 0.481524i −0.998306 0.0581894i \(-0.981467\pi\)
0.841849 + 0.539713i \(0.181467\pi\)
\(174\) 175265. 0.438857
\(175\) 39725.0 + 49835.0i 0.0980549 + 0.123010i
\(176\) −47305.6 −0.115115
\(177\) 163544. 503336.i 0.392374 1.20760i
\(178\) −4601.62 3343.27i −0.0108858 0.00790900i
\(179\) −347716. 252630.i −0.811132 0.589322i 0.103026 0.994679i \(-0.467147\pi\)
−0.914159 + 0.405356i \(0.867147\pi\)
\(180\) −351826. + 367904.i −0.809370 + 0.846357i
\(181\) 50269.3 36522.8i 0.114053 0.0828643i −0.529297 0.848437i \(-0.677544\pi\)
0.643350 + 0.765573i \(0.277544\pi\)
\(182\) 11264.2 0.0252070
\(183\) 1.09582e6 796162.i 2.41887 1.75741i
\(184\) 40164.6 + 123614.i 0.0874580 + 0.269168i
\(185\) −6526.95 + 48146.0i −0.0140211 + 0.103426i
\(186\) 260684. 802303.i 0.552500 1.70042i
\(187\) 124150. + 382094.i 0.259623 + 0.799036i
\(188\) 8310.18 + 25576.1i 0.0171481 + 0.0527764i
\(189\) 58573.3 180270.i 0.119274 0.367087i
\(190\) −69929.6 + 515835.i −0.140533 + 1.03664i
\(191\) 223329. + 687335.i 0.442957 + 1.36328i 0.884709 + 0.466143i \(0.154357\pi\)
−0.441753 + 0.897137i \(0.645643\pi\)
\(192\) −94435.0 + 68611.0i −0.184876 + 0.134320i
\(193\) −680494. −1.31502 −0.657508 0.753448i \(-0.728389\pi\)
−0.657508 + 0.753448i \(0.728389\pi\)
\(194\) −361943. + 262967.i −0.690456 + 0.501646i
\(195\) 152036. 158984.i 0.286325 0.299410i
\(196\) 212171. + 154151.i 0.394498 + 0.286620i
\(197\) 280647. + 203902.i 0.515223 + 0.374331i 0.814801 0.579740i \(-0.196846\pi\)
−0.299579 + 0.954072i \(0.596846\pi\)
\(198\) 129997. 400090.i 0.235652 0.725261i
\(199\) −410968. −0.735657 −0.367829 0.929894i \(-0.619899\pi\)
−0.367829 + 0.929894i \(0.619899\pi\)
\(200\) 192781. + 53247.8i 0.340793 + 0.0941296i
\(201\) 910269. 1.58920
\(202\) −175618. + 540496.i −0.302824 + 0.931996i
\(203\) 25367.5 + 18430.5i 0.0432053 + 0.0313905i
\(204\) 802018. + 582701.i 1.34930 + 0.980325i
\(205\) 117755. 868621.i 0.195702 1.44360i
\(206\) 262523. 190734.i 0.431022 0.313156i
\(207\) −1.15585e6 −1.87488
\(208\) 28598.2 20777.8i 0.0458332 0.0332998i
\(209\) −132934. 409128.i −0.210508 0.647878i
\(210\) −127871. + 23191.3i −0.200089 + 0.0362892i
\(211\) −55639.7 + 171242.i −0.0860357 + 0.264791i −0.984814 0.173613i \(-0.944456\pi\)
0.898778 + 0.438404i \(0.144456\pi\)
\(212\) −175477. 540063.i −0.268152 0.825287i
\(213\) 12044.4 + 37068.8i 0.0181901 + 0.0559834i
\(214\) −49936.6 + 153689.i −0.0745391 + 0.229408i
\(215\) 797845. + 384325.i 1.17712 + 0.567025i
\(216\) −183815. 565724.i −0.268069 0.825031i
\(217\) 122099. 88710.4i 0.176021 0.127887i
\(218\) 352174. 0.501899
\(219\) −994669. + 722669.i −1.40142 + 1.01819i
\(220\) −162626. + 29494.7i −0.226534 + 0.0410853i
\(221\) −242879. 176462.i −0.334510 0.243036i
\(222\) −80153.5 58234.9i −0.109154 0.0793051i
\(223\) −183023. + 563288.i −0.246459 + 0.758522i 0.748934 + 0.662644i \(0.230566\pi\)
−0.995393 + 0.0958777i \(0.969434\pi\)
\(224\) −20883.3 −0.0278086
\(225\) −980114. + 1.48413e6i −1.29069 + 1.95441i
\(226\) 216467. 0.281917
\(227\) 99287.3 305575.i 0.127888 0.393598i −0.866528 0.499128i \(-0.833654\pi\)
0.994416 + 0.105530i \(0.0336538\pi\)
\(228\) −858762. 623927.i −1.09405 0.794872i
\(229\) −551981. 401037.i −0.695561 0.505355i 0.182922 0.983127i \(-0.441444\pi\)
−0.878484 + 0.477773i \(0.841444\pi\)
\(230\) 215149. + 399915.i 0.268176 + 0.498480i
\(231\) 86885.0 63125.6i 0.107131 0.0778351i
\(232\) 98401.2 0.120027
\(233\) −1.13042e6 + 821300.i −1.36411 + 0.991087i −0.365943 + 0.930637i \(0.619254\pi\)
−0.998171 + 0.0604499i \(0.980746\pi\)
\(234\) 97140.8 + 298969.i 0.115974 + 0.356932i
\(235\) 44515.0 + 82743.6i 0.0525820 + 0.0977383i
\(236\) 91820.3 282594.i 0.107315 0.330280i
\(237\) −389029. 1.19731e6i −0.449895 1.38464i
\(238\) 54806.6 + 168677.i 0.0627178 + 0.193025i
\(239\) 206420. 635295.i 0.233753 0.719417i −0.763532 0.645770i \(-0.776536\pi\)
0.997284 0.0736463i \(-0.0234636\pi\)
\(240\) −281868. + 294749.i −0.315876 + 0.330311i
\(241\) 311809. + 959648.i 0.345816 + 1.06431i 0.961145 + 0.276043i \(0.0890231\pi\)
−0.615329 + 0.788270i \(0.710977\pi\)
\(242\) −410672. + 298371.i −0.450771 + 0.327505i
\(243\) 1.34846e6 1.46495
\(244\) 615241. 446998.i 0.661562 0.480653i
\(245\) 825507. + 397650.i 0.878629 + 0.423239i
\(246\) 1.44608e6 + 1.05064e6i 1.52354 + 1.10692i
\(247\) 260063. + 188947.i 0.271229 + 0.197059i
\(248\) 146359. 450446.i 0.151109 0.465065i
\(249\) 168569. 0.172298
\(250\) 695938. + 62856.0i 0.704240 + 0.0636058i
\(251\) 1.55659e6 1.55952 0.779759 0.626080i \(-0.215342\pi\)
0.779759 + 0.626080i \(0.215342\pi\)
\(252\) 57387.8 176622.i 0.0569270 0.175203i
\(253\) −303607. 220583.i −0.298202 0.216656i
\(254\) −898746. 652977.i −0.874083 0.635059i
\(255\) 3.12047e6 + 1.50314e6i 3.00517 + 1.44760i
\(256\) −53019.7 + 38521.1i −0.0505636 + 0.0367366i
\(257\) −73027.3 −0.0689688 −0.0344844 0.999405i \(-0.510979\pi\)
−0.0344844 + 0.999405i \(0.510979\pi\)
\(258\) −1.46096e6 + 1.06145e6i −1.36644 + 0.992774i
\(259\) −5477.35 16857.6i −0.00507366 0.0156151i
\(260\) 85359.3 89260.1i 0.0783100 0.0818887i
\(261\) −270409. + 832234.i −0.245708 + 0.756213i
\(262\) 227380. + 699804.i 0.204644 + 0.629830i
\(263\) −219037. 674125.i −0.195266 0.600968i −0.999973 0.00729575i \(-0.997678\pi\)
0.804707 0.593672i \(-0.202322\pi\)
\(264\) 104148. 320534.i 0.0919688 0.283051i
\(265\) −939976. 1.74721e6i −0.822247 1.52837i
\(266\) −58684.3 180612.i −0.0508531 0.156510i
\(267\) 32784.3 23819.2i 0.0281441 0.0204479i
\(268\) 511063. 0.434648
\(269\) −1.23525e6 + 897460.i −1.04081 + 0.756196i −0.970444 0.241325i \(-0.922418\pi\)
−0.0703702 + 0.997521i \(0.522418\pi\)
\(270\) −984638. 1.83022e6i −0.821991 1.52790i
\(271\) −743553. 540223.i −0.615019 0.446838i 0.236159 0.971714i \(-0.424111\pi\)
−0.851178 + 0.524877i \(0.824111\pi\)
\(272\) 450287. + 327152.i 0.369034 + 0.268119i
\(273\) −24799.2 + 76324.0i −0.0201387 + 0.0619805i
\(274\) −37237.7 −0.0299644
\(275\) −540682. + 202792.i −0.431132 + 0.161703i
\(276\) −926012. −0.731719
\(277\) −105783. + 325568.i −0.0828357 + 0.254942i −0.983893 0.178758i \(-0.942792\pi\)
0.901057 + 0.433700i \(0.142792\pi\)
\(278\) −562527. 408700.i −0.436548 0.317170i
\(279\) 3.40748e6 + 2.47568e6i 2.62073 + 1.90407i
\(280\) −71792.0 + 13020.6i −0.0547244 + 0.00992510i
\(281\) −537725. + 390680.i −0.406251 + 0.295159i −0.772082 0.635522i \(-0.780785\pi\)
0.365831 + 0.930681i \(0.380785\pi\)
\(282\) −191595. −0.143470
\(283\) 1.41644e6 1.02910e6i 1.05131 0.763822i 0.0788500 0.996886i \(-0.474875\pi\)
0.972461 + 0.233064i \(0.0748752\pi\)
\(284\) 6762.22 + 20812.0i 0.00497500 + 0.0153115i
\(285\) −3.34124e6 1.60949e6i −2.43667 1.17375i
\(286\) −31539.6 + 97068.8i −0.0228003 + 0.0701721i
\(287\) 98819.2 + 304134.i 0.0708168 + 0.217952i
\(288\) −180095. 554274.i −0.127944 0.393771i
\(289\) 1.02195e6 3.14525e6i 0.719759 2.21519i
\(290\) 338281. 61352.4i 0.236202 0.0428387i
\(291\) −984965. 3.03141e6i −0.681849 2.09852i
\(292\) −558449. + 405737.i −0.383289 + 0.278476i
\(293\) 55451.9 0.0377352 0.0188676 0.999822i \(-0.493994\pi\)
0.0188676 + 0.999822i \(0.493994\pi\)
\(294\) −1.51161e6 + 1.09825e6i −1.01993 + 0.741026i
\(295\) 139462. 1.02874e6i 0.0933044 0.688259i
\(296\) −45001.5 32695.5i −0.0298537 0.0216900i
\(297\) 1.38947e6 + 1.00951e6i 0.914024 + 0.664077i
\(298\) −216349. + 665854.i −0.141128 + 0.434348i
\(299\) 280429. 0.181403
\(300\) −785224. + 1.18902e6i −0.503721 + 0.762758i
\(301\) −323076. −0.205536
\(302\) 296643. 912974.i 0.187162 0.576025i
\(303\) −3.27566e6 2.37991e6i −2.04971 1.48920i
\(304\) −482145. 350299.i −0.299222 0.217398i
\(305\) 1.83636e6 1.92028e6i 1.13034 1.18199i
\(306\) −4.00431e6 + 2.90930e6i −2.44469 + 1.77617i
\(307\) 1.29467e6 0.783994 0.391997 0.919966i \(-0.371784\pi\)
0.391997 + 0.919966i \(0.371784\pi\)
\(308\) 48780.9 35441.4i 0.0293003 0.0212879i
\(309\) 714409. + 2.19873e6i 0.425648 + 1.31001i
\(310\) 222299. 1.63979e6i 0.131381 0.969132i
\(311\) −961268. + 2.95848e6i −0.563564 + 1.73447i 0.108615 + 0.994084i \(0.465358\pi\)
−0.672179 + 0.740388i \(0.734642\pi\)
\(312\) 77824.9 + 239520.i 0.0452618 + 0.139302i
\(313\) −270648. 832969.i −0.156151 0.480582i 0.842125 0.539282i \(-0.181304\pi\)
−0.998276 + 0.0587000i \(0.981304\pi\)
\(314\) 537992. 1.65577e6i 0.307930 0.947710i
\(315\) 87164.2 642966.i 0.0494951 0.365100i
\(316\) −218417. 672220.i −0.123047 0.378698i
\(317\) 1.79653e6 1.30526e6i 1.00412 0.729537i 0.0411540 0.999153i \(-0.486897\pi\)
0.962968 + 0.269615i \(0.0868966\pi\)
\(318\) 4.04570e6 2.24350
\(319\) −229853. + 166998.i −0.126466 + 0.0918830i
\(320\) −158252. + 165484.i −0.0863923 + 0.0903403i
\(321\) −931428. 676722.i −0.504530 0.366562i
\(322\) −134029. 97377.6i −0.0720375 0.0523383i
\(323\) −1.56406e6 + 4.81369e6i −0.834157 + 2.56727i
\(324\) 2.02511e6 1.07173
\(325\) 237793. 360077.i 0.124879 0.189098i
\(326\) −1.14397e6 −0.596169
\(327\) −775345. + 2.38627e6i −0.400983 + 1.23410i
\(328\) 811891. + 589873.i 0.416690 + 0.302743i
\(329\) −27731.0 20147.7i −0.0141246 0.0102621i
\(330\) 158186. 1.16686e6i 0.0799621 0.589839i
\(331\) 1.02772e6 746680.i 0.515589 0.374597i −0.299351 0.954143i \(-0.596770\pi\)
0.814939 + 0.579546i \(0.196770\pi\)
\(332\) 94641.7 0.0471235
\(333\) 400189. 290755.i 0.197768 0.143687i
\(334\) −445502. 1.37112e6i −0.218516 0.672524i
\(335\) 1.75692e6 318644.i 0.855342 0.155129i
\(336\) 45976.6 141501.i 0.0222172 0.0683774i
\(337\) 130520. + 401698.i 0.0626039 + 0.192675i 0.977467 0.211090i \(-0.0677013\pi\)
−0.914863 + 0.403765i \(0.867701\pi\)
\(338\) 435375. + 1.33995e6i 0.207287 + 0.637964i
\(339\) −476573. + 1.46674e6i −0.225232 + 0.693194i
\(340\) 1.75196e6 + 843926.i 0.821915 + 0.395920i
\(341\) 422583. + 1.30058e6i 0.196800 + 0.605689i
\(342\) 4.28762e6 3.11514e6i 1.98222 1.44016i
\(343\) −677037. −0.310725
\(344\) −820244. + 595942.i −0.373721 + 0.271524i
\(345\) −3.18342e6 + 577361.i −1.43995 + 0.261156i
\(346\) −644977. 468603.i −0.289637 0.210434i
\(347\) −618684. 449500.i −0.275832 0.200404i 0.441265 0.897377i \(-0.354530\pi\)
−0.717097 + 0.696973i \(0.754530\pi\)
\(348\) −216640. + 666748.i −0.0958937 + 0.295130i
\(349\) 3.97091e6 1.74513 0.872563 0.488501i \(-0.162456\pi\)
0.872563 + 0.488501i \(0.162456\pi\)
\(350\) −238687. + 89523.5i −0.104150 + 0.0390631i
\(351\) −1.28339e6 −0.556021
\(352\) 58473.0 179961.i 0.0251535 0.0774145i
\(353\) −341915. 248416.i −0.146043 0.106107i 0.512364 0.858768i \(-0.328770\pi\)
−0.658408 + 0.752662i \(0.728770\pi\)
\(354\) 1.71265e6 + 1.24431e6i 0.726375 + 0.527742i
\(355\) 36223.1 + 67330.6i 0.0152551 + 0.0283558i
\(356\) 18406.5 13373.1i 0.00769743 0.00559251i
\(357\) −1.26359e6 −0.524729
\(358\) 1.39086e6 1.01052e6i 0.573557 0.416714i
\(359\) 77077.4 + 237220.i 0.0315639 + 0.0971437i 0.965597 0.260042i \(-0.0837364\pi\)
−0.934033 + 0.357186i \(0.883736\pi\)
\(360\) −964710. 1.79318e6i −0.392320 0.729236i
\(361\) 909565. 2.79935e6i 0.367338 1.13055i
\(362\) 76804.6 + 236380.i 0.0308046 + 0.0948069i
\(363\) −1.11757e6 3.43953e6i −0.445152 1.37004i
\(364\) −13923.3 + 42851.5i −0.00550793 + 0.0169517i
\(365\) −1.66685e6 + 1.74302e6i −0.654882 + 0.684810i
\(366\) 1.67427e6 + 5.15287e6i 0.653314 + 2.01069i
\(367\) 143863. 104522.i 0.0557549 0.0405083i −0.559559 0.828791i \(-0.689029\pi\)
0.615314 + 0.788282i \(0.289029\pi\)
\(368\) −519902. −0.200125
\(369\) −7.21998e6 + 5.24562e6i −2.76039 + 2.00554i
\(370\) −175090. 84341.7i −0.0664902 0.0320286i
\(371\) 585565. + 425438.i 0.220872 + 0.160473i
\(372\) 2.72992e6 + 1.98340e6i 1.02280 + 0.743110i
\(373\) −433346. + 1.33370e6i −0.161273 + 0.496348i −0.998742 0.0501365i \(-0.984034\pi\)
0.837469 + 0.546485i \(0.184034\pi\)
\(374\) −1.60703e6 −0.594080
\(375\) −1.95808e6 + 4.57717e6i −0.719037 + 1.68081i
\(376\) −107569. −0.0392391
\(377\) 65606.0 201915.i 0.0237733 0.0731668i
\(378\) 613387. + 445652.i 0.220803 + 0.160423i
\(379\) 3.44927e6 + 2.50604e6i 1.23347 + 0.896169i 0.997145 0.0755051i \(-0.0240569\pi\)
0.236325 + 0.971674i \(0.424057\pi\)
\(380\) −1.87591e6 903635.i −0.666429 0.321021i
\(381\) 6.40313e6 4.65215e6i 2.25985 1.64188i
\(382\) −2.89083e6 −1.01359
\(383\) 1.71459e6 1.24572e6i 0.597258 0.433934i −0.247646 0.968851i \(-0.579657\pi\)
0.844905 + 0.534917i \(0.179657\pi\)
\(384\) −144284. 444060.i −0.0499332 0.153679i
\(385\) 145600. 152254.i 0.0500622 0.0523500i
\(386\) 841137. 2.58875e6i 0.287342 0.884346i
\(387\) −2.78616e6 8.57493e6i −0.945647 2.91040i
\(388\) −553000. 1.70196e6i −0.186486 0.573945i
\(389\) −1.37005e6 + 4.21657e6i −0.459052 + 1.41282i 0.407260 + 0.913312i \(0.366484\pi\)
−0.866312 + 0.499504i \(0.833516\pi\)
\(390\) 416883. + 774893.i 0.138788 + 0.257977i
\(391\) 1.36444e6 + 4.19932e6i 0.451350 + 1.38911i
\(392\) −848683. + 616604.i −0.278953 + 0.202671i
\(393\) −5.24234e6 −1.71216
\(394\) −1.12259e6 + 815608.i −0.364317 + 0.264692i
\(395\) −1.16999e6 2.17476e6i −0.377303 0.701323i
\(396\) 1.36135e6 + 989077.i 0.436245 + 0.316951i
\(397\) 1.65341e6 + 1.20127e6i 0.526508 + 0.382530i 0.819050 0.573722i \(-0.194501\pi\)
−0.292542 + 0.956253i \(0.594501\pi\)
\(398\) 507985. 1.56342e6i 0.160747 0.494728i
\(399\) 1.35299e6 0.425463
\(400\) −440857. + 667566.i −0.137768 + 0.208614i
\(401\) −2.68419e6 −0.833591 −0.416796 0.909000i \(-0.636847\pi\)
−0.416796 + 0.909000i \(0.636847\pi\)
\(402\) −1.12515e6 + 3.46287e6i −0.347254 + 1.06874i
\(403\) −826714. 600643.i −0.253567 0.184227i
\(404\) −1.83909e6 1.33618e6i −0.560597 0.407297i
\(405\) 6.96188e6 1.26264e6i 2.10906 0.382510i
\(406\) −101470. + 73722.2i −0.0305508 + 0.0221964i
\(407\) 160606. 0.0480592
\(408\) −3.20807e6 + 2.33080e6i −0.954100 + 0.693194i
\(409\) −762946. 2.34811e6i −0.225520 0.694080i −0.998238 0.0593307i \(-0.981103\pi\)
0.772718 0.634749i \(-0.218897\pi\)
\(410\) 3.15888e6 + 1.52164e6i 0.928054 + 0.447047i
\(411\) 81982.3 252316.i 0.0239395 0.0736783i
\(412\) 401099. + 1.23446e6i 0.116415 + 0.358288i
\(413\) 117035. + 360198.i 0.0337631 + 0.103912i
\(414\) 1.42870e6 4.39710e6i 0.409677 1.26086i
\(415\) 325357. 59008.4i 0.0927342 0.0168187i
\(416\) 43694.1 + 134477.i 0.0123791 + 0.0380990i
\(417\) 4.00773e6 2.91179e6i 1.12865 0.820011i
\(418\) 1.72073e6 0.481695
\(419\) 81032.6 58873.7i 0.0225489 0.0163827i −0.576454 0.817130i \(-0.695564\pi\)
0.599003 + 0.800747i \(0.295564\pi\)
\(420\) 69832.1 515116.i 0.0193167 0.142489i
\(421\) −278.928 202.653i −7.66985e−5 5.57247e-5i 0.587747 0.809045i \(-0.300015\pi\)
−0.587824 + 0.808989i \(0.700015\pi\)
\(422\) −582667. 423332.i −0.159272 0.115718i
\(423\) 295603. 909773.i 0.0803264 0.247219i
\(424\) 2.27142e6 0.613598
\(425\) 6.54903e6 + 1.80889e6i 1.75875 + 0.485781i
\(426\) −155906. −0.0416234
\(427\) −299536. + 921876.i −0.0795022 + 0.244683i
\(428\) −522943. 379940.i −0.137989 0.100255i
\(429\) −588283. 427413.i −0.154327 0.112125i
\(430\) −2.44825e6 + 2.56013e6i −0.638535 + 0.667715i
\(431\) −2.51117e6 + 1.82447e6i −0.651153 + 0.473090i −0.863664 0.504069i \(-0.831836\pi\)
0.212511 + 0.977159i \(0.431836\pi\)
\(432\) 2.37935e6 0.613407
\(433\) −1.26813e6 + 921348.i −0.325044 + 0.236159i −0.738325 0.674445i \(-0.764383\pi\)
0.413281 + 0.910604i \(0.364383\pi\)
\(434\) 186551. + 574146.i 0.0475416 + 0.146318i
\(435\) −329046. + 2.42720e6i −0.0833745 + 0.615011i
\(436\) −435311. + 1.33975e6i −0.109669 + 0.337526i
\(437\) −1.46098e6 4.49643e6i −0.365966 1.12633i
\(438\) −1.51972e6 4.67721e6i −0.378510 1.16494i
\(439\) −272215. + 837792.i −0.0674141 + 0.207479i −0.979089 0.203434i \(-0.934790\pi\)
0.911675 + 0.410913i \(0.134790\pi\)
\(440\) 88812.4 655124.i 0.0218697 0.161321i
\(441\) −2.88276e6 8.87223e6i −0.705850 2.17238i
\(442\) 971516. 705848.i 0.236534 0.171852i
\(443\) −2.04343e6 −0.494710 −0.247355 0.968925i \(-0.579561\pi\)
−0.247355 + 0.968925i \(0.579561\pi\)
\(444\) 320614. 232940.i 0.0771836 0.0560771i
\(445\) 54939.3 57449.9i 0.0131517 0.0137527i
\(446\) −1.91664e6 1.39252e6i −0.456252 0.331486i
\(447\) −4.03539e6 2.93188e6i −0.955249 0.694029i
\(448\) 25813.2 79444.8i 0.00607640 0.0187012i
\(449\) −6.11924e6 −1.43246 −0.716229 0.697866i \(-0.754133\pi\)
−0.716229 + 0.697866i \(0.754133\pi\)
\(450\) −4.43449e6 5.56307e6i −1.03232 1.29504i
\(451\) −2.89756e6 −0.670797
\(452\) −267568. + 823490.i −0.0616011 + 0.189589i
\(453\) 5.53306e6 + 4.02000e6i 1.26683 + 0.920409i
\(454\) 1.03975e6 + 755422.i 0.236750 + 0.172009i
\(455\) −21147.6 + 155995.i −0.00478886 + 0.0353250i
\(456\) 3.43505e6 2.49571e6i 0.773608 0.562059i
\(457\) −3.06337e6 −0.686134 −0.343067 0.939311i \(-0.611466\pi\)
−0.343067 + 0.939311i \(0.611466\pi\)
\(458\) 2.20792e6 1.60415e6i 0.491836 0.357340i
\(459\) −6.24442e6 1.92183e7i −1.38344 4.25779i
\(460\) −1.78731e6 + 324155.i −0.393826 + 0.0714263i
\(461\) −376162. + 1.15771e6i −0.0824371 + 0.253715i −0.983777 0.179398i \(-0.942585\pi\)
0.901339 + 0.433113i \(0.142585\pi\)
\(462\) 132748. + 408558.i 0.0289351 + 0.0890530i
\(463\) 1.76829e6 + 5.44224e6i 0.383355 + 1.17984i 0.937667 + 0.347536i \(0.112981\pi\)
−0.554312 + 0.832309i \(0.687019\pi\)
\(464\) −121631. + 374340.i −0.0262270 + 0.0807183i
\(465\) 1.06215e7 + 5.11640e6i 2.27799 + 1.09732i
\(466\) −1.72713e6 5.31556e6i −0.368435 1.13393i
\(467\) 2.32686e6 1.69056e6i 0.493717 0.358706i −0.312895 0.949788i \(-0.601299\pi\)
0.806612 + 0.591082i \(0.201299\pi\)
\(468\) −1.25742e6 −0.265378
\(469\) −527001. + 382888.i −0.110632 + 0.0803785i
\(470\) −369799. + 67068.6i −0.0772184 + 0.0140047i
\(471\) 1.00347e7 + 7.29066e6i 2.08427 + 1.51431i
\(472\) 961554. + 698610.i 0.198664 + 0.144338i
\(473\) 904609. 2.78410e6i 0.185912 0.572179i
\(474\) 5.03570e6 1.02947
\(475\) −7.01238e6 1.93687e6i −1.42604 0.393883i
\(476\) −709432. −0.143514
\(477\) −6.24193e6 + 1.92107e7i −1.25610 + 3.86587i
\(478\) 2.16166e6 + 1.57053e6i 0.432730 + 0.314397i
\(479\) 4.03748e6 + 2.93340e6i 0.804028 + 0.584161i 0.912093 0.409983i \(-0.134465\pi\)
−0.108065 + 0.994144i \(0.534465\pi\)
\(480\) −772883. 1.43662e6i −0.153112 0.284602i
\(481\) −97093.0 + 70542.2i −0.0191349 + 0.0139023i
\(482\) −4.03613e6 −0.791312
\(483\) 954890. 693768.i 0.186245 0.135315i
\(484\) −627451. 1.93109e6i −0.121749 0.374706i
\(485\) −2.96225e6 5.50616e6i −0.571830 1.06291i
\(486\) −1.66679e6 + 5.12986e6i −0.320104 + 0.985179i
\(487\) 1.66511e6 + 5.12469e6i 0.318142 + 0.979141i 0.974442 + 0.224641i \(0.0721208\pi\)
−0.656299 + 0.754501i \(0.727879\pi\)
\(488\) 940004. + 2.89303e6i 0.178682 + 0.549926i
\(489\) 2.51855e6 7.75131e6i 0.476298 1.46589i
\(490\) −2.53313e6 + 2.64889e6i −0.476615 + 0.498396i
\(491\) 807808. + 2.48618e6i 0.151218 + 0.465402i 0.997758 0.0669234i \(-0.0213183\pi\)
−0.846540 + 0.532325i \(0.821318\pi\)
\(492\) −5.78433e6 + 4.20256e6i −1.07731 + 0.782710i
\(493\) 3.34281e6 0.619434
\(494\) −1.04025e6 + 755787.i −0.191788 + 0.139342i
\(495\) 5.29668e6 + 2.55143e6i 0.971608 + 0.468027i
\(496\) 1.53269e6 + 1.11356e6i 0.279737 + 0.203241i
\(497\) −22565.4 16394.7i −0.00409782 0.00297724i
\(498\) −208363. + 641275.i −0.0376484 + 0.115870i
\(499\) 6.11661e6 1.09966 0.549831 0.835276i \(-0.314692\pi\)
0.549831 + 0.835276i \(0.314692\pi\)
\(500\) −1.09935e6 + 2.56981e6i −0.196657 + 0.459702i
\(501\) 1.02712e7 1.82822
\(502\) −1.92405e6 + 5.92162e6i −0.340767 + 1.04877i
\(503\) 2.77290e6 + 2.01463e6i 0.488669 + 0.355039i 0.804672 0.593719i \(-0.202341\pi\)
−0.316003 + 0.948758i \(0.602341\pi\)
\(504\) 600973. + 436633.i 0.105385 + 0.0765667i
\(505\) −7.15549e6 3.44682e6i −1.24856 0.601438i
\(506\) 1.21443e6 882334.i 0.210861 0.153199i
\(507\) −1.00378e7 −1.73427
\(508\) 3.59498e6 2.61191e6i 0.618070 0.449054i
\(509\) 411852. + 1.26755e6i 0.0704606 + 0.216855i 0.980086 0.198574i \(-0.0636312\pi\)
−0.909625 + 0.415430i \(0.863631\pi\)
\(510\) −9.57540e6 + 1.00130e7i −1.63016 + 1.70466i
\(511\) 271886. 836779.i 0.0460611 0.141762i
\(512\) −81007.0 249314.i −0.0136568 0.0420312i
\(513\) 6.68622e6 + 2.05781e7i 1.12173 + 3.45232i
\(514\) 90266.8 277813.i 0.0150702 0.0463814i
\(515\) 2.14856e6 + 3.99370e6i 0.356968 + 0.663525i
\(516\) −2.23215e6 6.86985e6i −0.369062 1.13586i
\(517\) 251269. 182558.i 0.0413440 0.0300382i
\(518\) 70900.3 0.0116098
\(519\) 4.59515e6 3.33857e6i 0.748826 0.544054i
\(520\) 234056. + 435058.i 0.0379587 + 0.0705567i
\(521\) −4.84681e6 3.52141e6i −0.782279 0.568359i 0.123383 0.992359i \(-0.460626\pi\)
−0.905662 + 0.424000i \(0.860626\pi\)
\(522\) −2.83176e6 2.05739e6i −0.454863 0.330477i
\(523\) 3.64868e6 1.12295e7i 0.583286 1.79517i −0.0227597 0.999741i \(-0.507245\pi\)
0.606046 0.795430i \(-0.292755\pi\)
\(524\) −2.94327e6 −0.468276
\(525\) −81103.5 1.81439e6i −0.0128423 0.287298i
\(526\) 2.83527e6 0.446817
\(527\) 4.97199e6 1.53022e7i 0.779837 2.40009i
\(528\) 1.09065e6 + 792404.i 0.170255 + 0.123698i
\(529\) 1.87038e6 + 1.35891e6i 0.290597 + 0.211131i
\(530\) 7.80864e6 1.41622e6i 1.20750 0.218998i
\(531\) −8.55091e6 + 6.21260e6i −1.31606 + 0.956174i
\(532\) 759625. 0.116364
\(533\) 1.75169e6 1.27268e6i 0.267079 0.194045i
\(534\) 50089.9 + 154161.i 0.00760147 + 0.0233949i
\(535\) −2.03465e6 980098.i −0.307330 0.148042i
\(536\) −631709. + 1.94420e6i −0.0949740 + 0.292300i
\(537\) 3.78499e6 + 1.16490e7i 0.566407 + 1.74322i
\(538\) −1.88729e6 5.80848e6i −0.281114 0.865181i
\(539\) 935972. 2.88063e6i 0.138769 0.427086i
\(540\) 8.17966e6 1.48351e6i 1.20712 0.218930i
\(541\) −583703. 1.79645e6i −0.0857430 0.263890i 0.898988 0.437974i \(-0.144304\pi\)
−0.984731 + 0.174084i \(0.944304\pi\)
\(542\) 2.97421e6 2.16089e6i 0.434884 0.315962i
\(543\) −1.77076e6 −0.257727
\(544\) −1.80115e6 + 1.30861e6i −0.260947 + 0.189589i
\(545\) −661178. + 4.87717e6i −0.0953514 + 0.703358i
\(546\) −259700. 188683.i −0.0372813 0.0270865i
\(547\) −3.62033e6 2.63032e6i −0.517345 0.375873i 0.298258 0.954485i \(-0.403594\pi\)
−0.815603 + 0.578612i \(0.803594\pi\)
\(548\) 46028.3 141661.i 0.00654747 0.0201510i
\(549\) −2.70512e7 −3.83050
\(550\) −103147. 2.30754e6i −0.0145396 0.325269i
\(551\) −3.57932e6 −0.502252
\(552\) 1.14461e6 3.52276e6i 0.159886 0.492080i
\(553\) 728856. + 529545.i 0.101351 + 0.0736359i
\(554\) −1.10778e6 804847.i −0.153348 0.111414i
\(555\) 956962. 1.00069e6i 0.131875 0.137901i
\(556\) 2.25011e6 1.63480e6i 0.308686 0.224273i
\(557\) 2.36298e6 0.322717 0.161359 0.986896i \(-0.448412\pi\)
0.161359 + 0.986896i \(0.448412\pi\)
\(558\) −1.36299e7 + 9.90271e6i −1.85314 + 1.34638i
\(559\) 675972. + 2.08043e6i 0.0914954 + 0.281594i
\(560\) 39206.7 289207.i 0.00528311 0.0389708i
\(561\) 3.53803e6 1.08889e7i 0.474629 1.46076i
\(562\) −821571. 2.52854e6i −0.109725 0.337698i
\(563\) 1.66314e6 + 5.11862e6i 0.221135 + 0.680584i 0.998661 + 0.0517329i \(0.0164744\pi\)
−0.777526 + 0.628851i \(0.783526\pi\)
\(564\) 236824. 728870.i 0.0313493 0.0964833i
\(565\) −406399. + 2.99780e6i −0.0535589 + 0.395077i
\(566\) 2.16412e6 + 6.66049e6i 0.283949 + 0.873907i
\(567\) −2.08827e6 + 1.51721e6i −0.272790 + 0.198194i
\(568\) −87532.0 −0.0113840
\(569\) 5.07710e6 3.68873e6i 0.657409 0.477635i −0.208378 0.978048i \(-0.566818\pi\)
0.865787 + 0.500413i \(0.166818\pi\)
\(570\) 1.02529e7 1.07214e7i 1.32178 1.38218i
\(571\) −2.97396e6 2.16071e6i −0.381721 0.277336i 0.380334 0.924849i \(-0.375809\pi\)
−0.762054 + 0.647513i \(0.775809\pi\)
\(572\) −330287. 239967.i −0.0422086 0.0306664i
\(573\) 6.36443e6 1.95877e7i 0.809792 2.49228i
\(574\) −1.27914e6 −0.162046
\(575\) −5.94224e6 + 2.22874e6i −0.749516 + 0.281119i
\(576\) 2.33119e6 0.292767
\(577\) 1.69378e6 5.21292e6i 0.211796 0.651841i −0.787570 0.616226i \(-0.788661\pi\)
0.999366 0.0356152i \(-0.0113391\pi\)
\(578\) 1.07020e7 + 7.77549e6i 1.33244 + 0.968074i
\(579\) 1.56891e7 + 1.13988e7i 1.94492 + 1.41306i
\(580\) −184740. + 1.36273e6i −0.0228030 + 0.168206i
\(581\) −97593.1 + 70905.6i −0.0119944 + 0.00871445i
\(582\) 1.27496e7 1.56024
\(583\) −5.30577e6 + 3.85487e6i −0.646513 + 0.469719i
\(584\) −853233. 2.62598e6i −0.103523 0.318610i
\(585\) −4.32271e6 + 783989.i −0.522236 + 0.0947154i
\(586\) −68542.3 + 210951.i −0.00824545 + 0.0253769i
\(587\) −2.73802e6 8.42676e6i −0.327976 1.00941i −0.970080 0.242787i \(-0.921938\pi\)
0.642104 0.766618i \(-0.278062\pi\)
\(588\) −2.30954e6 7.10803e6i −0.275475 0.847825i
\(589\) −5.32377e6 + 1.63849e7i −0.632312 + 1.94605i
\(590\) 3.74118e6 + 1.80214e6i 0.442465 + 0.213137i
\(591\) −3.05492e6 9.40209e6i −0.359776 1.10728i
\(592\) 180006. 130782.i 0.0211097 0.0153371i
\(593\) −1.17718e6 −0.137469 −0.0687346 0.997635i \(-0.521896\pi\)
−0.0687346 + 0.997635i \(0.521896\pi\)
\(594\) −5.55787e6 + 4.03803e6i −0.646312 + 0.469573i
\(595\) −2.43887e6 + 442325.i −0.282420 + 0.0512211i
\(596\) −2.26564e6 1.64608e6i −0.261261 0.189817i
\(597\) 9.47504e6 + 6.88402e6i 1.08804 + 0.790508i
\(598\) −346629. + 1.06681e6i −0.0396380 + 0.121993i
\(599\) −1.72066e6 −0.195942 −0.0979709 0.995189i \(-0.531235\pi\)
−0.0979709 + 0.995189i \(0.531235\pi\)
\(600\) −3.55272e6 4.45688e6i −0.402886 0.505420i
\(601\) −2.93282e6 −0.331207 −0.165604 0.986192i \(-0.552957\pi\)
−0.165604 + 0.986192i \(0.552957\pi\)
\(602\) 399344. 1.22905e6i 0.0449113 0.138223i
\(603\) −1.47072e7 1.06854e7i −1.64717 1.19674i
\(604\) 3.10649e6 + 2.25700e6i 0.346479 + 0.251732i
\(605\) −3.36106e6 6.24746e6i −0.373325 0.693929i
\(606\) 1.31027e7 9.51963e6i 1.44936 1.05302i
\(607\) −3.93464e6 −0.433444 −0.216722 0.976233i \(-0.569537\pi\)
−0.216722 + 0.976233i \(0.569537\pi\)
\(608\) 1.92858e6 1.40120e6i 0.211582 0.153723i
\(609\) −276132. 849848.i −0.0301699 0.0928534i
\(610\) 5.03530e6 + 9.35951e6i 0.547900 + 1.01842i
\(611\) −71718.5 + 220727.i −0.00777192 + 0.0239195i
\(612\) −6.11804e6 1.88294e7i −0.660289 2.03216i
\(613\) −3.75739e6 1.15641e7i −0.403864 1.24297i −0.921840 0.387571i \(-0.873314\pi\)
0.517976 0.855395i \(-0.326686\pi\)
\(614\) −1.60030e6 + 4.92521e6i −0.171309 + 0.527235i
\(615\) −1.72649e7 + 1.80539e7i −1.84068 + 1.92479i
\(616\) 74530.5 + 229381.i 0.00791375 + 0.0243560i
\(617\) 6.16800e6 4.48132e6i 0.652276 0.473907i −0.211769 0.977320i \(-0.567923\pi\)
0.864046 + 0.503413i \(0.167923\pi\)
\(618\) −9.24751e6 −0.973988
\(619\) −490963. + 356706.i −0.0515018 + 0.0374182i −0.613238 0.789898i \(-0.710133\pi\)
0.561737 + 0.827316i \(0.310133\pi\)
\(620\) 5.96334e6 + 2.87256e6i 0.623032 + 0.300117i
\(621\) 1.52706e7 + 1.10948e7i 1.58902 + 1.15449i
\(622\) −1.00665e7 7.31376e6i −1.04329 0.757992i
\(623\) −8961.37 + 27580.3i −0.000925027 + 0.00284694i
\(624\) −1.00739e6 −0.103570
\(625\) −2.17704e6 + 9.51987e6i −0.222929 + 0.974835i
\(626\) 3.50334e6 0.357311
\(627\) −3.78835e6 + 1.16594e7i −0.384841 + 1.18442i
\(628\) 5.63392e6 + 4.09328e6i 0.570048 + 0.414164i
\(629\) −1.52876e6 1.11071e6i −0.154068 0.111937i
\(630\) 2.33825e6 + 1.12634e6i 0.234714 + 0.113063i
\(631\) 5.70294e6 4.14343e6i 0.570197 0.414272i −0.264980 0.964254i \(-0.585365\pi\)
0.835177 + 0.549982i \(0.185365\pi\)
\(632\) 2.82725e6 0.281561
\(633\) 4.15122e6 3.01604e6i 0.411781 0.299176i
\(634\) 2.74485e6 + 8.44779e6i 0.271204 + 0.834680i
\(635\) 1.07302e7 1.12206e7i 1.05603 1.10429i
\(636\) −5.00076e6 + 1.53908e7i −0.490222 + 1.50875i
\(637\) 699409. + 2.15256e6i 0.0682940 + 0.210187i
\(638\) −351185. 1.08084e6i −0.0341573 0.105125i
\(639\) 240540. 740306.i 0.0233043 0.0717232i
\(640\) −433929. 806577.i −0.0418763 0.0778388i
\(641\) 3.03380e6 + 9.33708e6i 0.291636 + 0.897565i 0.984331 + 0.176333i \(0.0564236\pi\)
−0.692694 + 0.721232i \(0.743576\pi\)
\(642\) 3.72571e6 2.70689e6i 0.356756 0.259199i
\(643\) −1.90985e7 −1.82168 −0.910838 0.412763i \(-0.864564\pi\)
−0.910838 + 0.412763i \(0.864564\pi\)
\(644\) 536115. 389511.i 0.0509382 0.0370088i
\(645\) −1.19569e7 2.22253e7i −1.13167 2.10352i
\(646\) −1.63791e7 1.19001e7i −1.54422 1.12194i
\(647\) −8.30601e6 6.03467e6i −0.780067 0.566752i 0.124932 0.992165i \(-0.460129\pi\)
−0.904999 + 0.425414i \(0.860129\pi\)
\(648\) −2.50318e6 + 7.70399e6i −0.234182 + 0.720739i
\(649\) −3.43170e6 −0.319814
\(650\) 1.07589e6 + 1.34970e6i 0.0998810 + 0.125301i
\(651\) −4.30102e6 −0.397758
\(652\) 1.41402e6 4.35191e6i 0.130268 0.400923i
\(653\) 7.33044e6 + 5.32587e6i 0.672739 + 0.488774i 0.870941 0.491387i \(-0.163510\pi\)
−0.198202 + 0.980161i \(0.563510\pi\)
\(654\) −8.11952e6 5.89918e6i −0.742311 0.539321i
\(655\) −1.01183e7 + 1.83510e6i −0.921518 + 0.167131i
\(656\) −3.24756e6 + 2.35949e6i −0.294644 + 0.214072i
\(657\) 2.45541e7 2.21927
\(658\) 110924. 80590.9i 0.00998758 0.00725640i
\(659\) −2.95964e6 9.10883e6i −0.265476 0.817051i −0.991583 0.129470i \(-0.958672\pi\)
0.726107 0.687581i \(-0.241328\pi\)
\(660\) 4.24347e6 + 2.04409e6i 0.379194 + 0.182659i
\(661\) 1.98226e6 6.10077e6i 0.176464 0.543101i −0.823233 0.567704i \(-0.807832\pi\)
0.999697 + 0.0246023i \(0.00783194\pi\)
\(662\) 1.57021e6 + 4.83261e6i 0.139256 + 0.428585i
\(663\) 2.64381e6 + 8.13680e6i 0.233586 + 0.718903i
\(664\) −116984. + 360039.i −0.0102969 + 0.0316905i
\(665\) 2.61142e6 473620.i 0.228993 0.0415313i
\(666\) 611435. + 1.88180e6i 0.0534152 + 0.164395i
\(667\) −2.52615e6 + 1.83536e6i −0.219859 + 0.159737i
\(668\) 5.76670e6 0.500019
\(669\) 1.36552e7 9.92105e6i 1.17959 0.857023i
\(670\) −959479. + 7.07758e6i −0.0825749 + 0.609113i
\(671\) −7.10555e6 5.16248e6i −0.609244 0.442642i
\(672\) 481473. + 349811.i 0.0411290 + 0.0298820i
\(673\) −5.78623e6 + 1.78082e7i −0.492445 + 1.51559i 0.328456 + 0.944519i \(0.393472\pi\)
−0.820901 + 0.571070i \(0.806528\pi\)
\(674\) −1.68948e6 −0.143253
\(675\) 2.71949e7 1.01999e7i 2.29735 0.861662i
\(676\) −5.63562e6 −0.474324
\(677\) 1.07274e6 3.30155e6i 0.0899543 0.276851i −0.895952 0.444152i \(-0.853505\pi\)
0.985906 + 0.167301i \(0.0535051\pi\)
\(678\) −4.99074e6 3.62599e6i −0.416957 0.302937i
\(679\) 1.84535e6 + 1.34073e6i 0.153605 + 0.111601i
\(680\) −5.37603e6 + 5.62171e6i −0.445850 + 0.466225i
\(681\) −7.40771e6 + 5.38202e6i −0.612091 + 0.444710i
\(682\) −5.47003e6 −0.450328
\(683\) 1.32784e7 9.64736e6i 1.08917 0.791328i 0.109911 0.993941i \(-0.464943\pi\)
0.979259 + 0.202613i \(0.0649435\pi\)
\(684\) 6.55090e6 + 2.01616e7i 0.535378 + 1.64773i
\(685\) 69910.7 515695.i 0.00569268 0.0419920i
\(686\) 836863. 2.57560e6i 0.0678960 0.208962i
\(687\) 6.00847e6 + 1.84922e7i 0.485704 + 1.49484i
\(688\) −1.25322e6 3.85702e6i −0.100939 0.310657i
\(689\) 1.51440e6 4.66085e6i 0.121533 0.374039i
\(690\) 1.73851e6 1.28241e7i 0.139013 1.02543i
\(691\) 7.08711e6 + 2.18119e7i 0.564643 + 1.73779i 0.669009 + 0.743254i \(0.266719\pi\)
−0.104365 + 0.994539i \(0.533281\pi\)
\(692\) 2.57991e6 1.87441e6i 0.204804 0.148799i
\(693\) −2.14482e6 −0.169651
\(694\) 2.47473e6 1.79800e6i 0.195043 0.141707i
\(695\) 6.71608e6 7.02300e6i 0.527417 0.551519i
\(696\) −2.26868e6 1.64829e6i −0.177521 0.128977i
\(697\) 2.75809e7 + 2.00387e7i 2.15044 + 1.56239i
\(698\) −4.90832e6 + 1.51063e7i −0.381324 + 1.17359i
\(699\) 3.98197e7 3.08252
\(700\) −45534.9 1.01867e6i −0.00351236 0.0785761i
\(701\) −2.13181e7 −1.63852 −0.819262 0.573419i \(-0.805617\pi\)
−0.819262 + 0.573419i \(0.805617\pi\)
\(702\) 1.58636e6 4.88231e6i 0.121495 0.373923i
\(703\) 1.63692e6 + 1.18929e6i 0.124922 + 0.0907611i
\(704\) 612337. + 444889.i 0.0465649 + 0.0338314i
\(705\) 359703. 2.65335e6i 0.0272566 0.201058i
\(706\) 1.36766e6 993663.i 0.103268 0.0750287i
\(707\) 2.89751e6 0.218010
\(708\) −6.85061e6 + 4.97726e6i −0.513625 + 0.373170i
\(709\) 1.34134e6 + 4.12821e6i 0.100213 + 0.308423i 0.988577 0.150716i \(-0.0481580\pi\)
−0.888364 + 0.459139i \(0.848158\pi\)
\(710\) −300915. + 54575.5i −0.0224026 + 0.00406305i
\(711\) −7.76937e6 + 2.39117e7i −0.576384 + 1.77393i
\(712\) 28122.6 + 86552.4i 0.00207900 + 0.00639852i
\(713\) 4.64430e6 + 1.42937e7i 0.342134 + 1.05298i
\(714\) 1.56188e6 4.80698e6i 0.114658 0.352880i
\(715\) −1.28507e6 619022.i −0.0940072 0.0452836i
\(716\) 2.12505e6 + 6.54023e6i 0.154913 + 0.476772i
\(717\) −1.54007e7 + 1.11893e7i −1.11878 + 0.812840i
\(718\) −997710. −0.0722260
\(719\) −1.11830e7 + 8.12492e6i −0.806744 + 0.586134i −0.912885 0.408217i \(-0.866151\pi\)
0.106141 + 0.994351i \(0.466151\pi\)
\(720\) 8.01412e6 1.45348e6i 0.576135 0.104491i
\(721\) −1.33846e6 972450.i −0.0958888 0.0696673i
\(722\) 9.52509e6 + 6.92039e6i 0.680027 + 0.494069i
\(723\) 8.88594e6 2.73481e7i 0.632204 1.94572i
\(724\) −994180. −0.0704886
\(725\) 214559. + 4.79995e6i 0.0151601 + 0.339150i
\(726\) 1.44661e7 1.01862
\(727\) 1.18007e6 3.63188e6i 0.0828078 0.254856i −0.901077 0.433659i \(-0.857222\pi\)
0.983885 + 0.178803i \(0.0572223\pi\)
\(728\) −145807. 105935.i −0.0101964 0.00740815i
\(729\) −6.20694e6 4.50961e6i −0.432573 0.314282i
\(730\) −4.57050e6 8.49555e6i −0.317436 0.590044i
\(731\) −2.78647e7 + 2.02449e7i −1.92869 + 1.40127i
\(732\) −2.16722e7 −1.49494
\(733\) 3.27348e6 2.37832e6i 0.225035 0.163497i −0.469555 0.882903i \(-0.655586\pi\)
0.694590 + 0.719406i \(0.255586\pi\)
\(734\) 219803. + 676483.i 0.0150589 + 0.0463465i
\(735\) −1.23715e7 2.29958e7i −0.844701 1.57011i
\(736\) 642634. 1.97782e6i 0.0437290 0.134584i
\(737\) −1.82394e6 5.61350e6i −0.123692 0.380684i
\(738\) −1.10311e7 3.39504e7i −0.745555 2.29458i
\(739\) −1.78914e6 + 5.50642e6i −0.120513 + 0.370901i −0.993057 0.117635i \(-0.962469\pi\)
0.872544 + 0.488536i \(0.162469\pi\)
\(740\) 537278. 561831.i 0.0360678 0.0377161i
\(741\) −2.83086e6 8.71250e6i −0.189397 0.582904i
\(742\) −2.34226e6 + 1.70175e6i −0.156180 + 0.113471i
\(743\) 2.33348e7 1.55071 0.775357 0.631524i \(-0.217570\pi\)
0.775357 + 0.631524i \(0.217570\pi\)
\(744\) −1.09197e7 + 7.93361e6i −0.723231 + 0.525458i
\(745\) −8.81506e6 4.24625e6i −0.581882 0.280295i
\(746\) −4.53806e6 3.29709e6i −0.298554 0.216912i
\(747\) −2.72357e6 1.97879e6i −0.178582 0.129747i
\(748\) 1.98640e6 6.11351e6i 0.129811 0.399518i
\(749\) 823902. 0.0536625
\(750\) −1.49923e7 1.31067e7i −0.973227 0.850822i
\(751\) 6.10432e6 0.394946 0.197473 0.980308i \(-0.436727\pi\)
0.197473 + 0.980308i \(0.436727\pi\)
\(752\) 132963. 409218.i 0.00857405 0.0263882i
\(753\) −3.58878e7 2.60740e7i −2.30653 1.67580i
\(754\) 687035. + 499160.i 0.0440099 + 0.0319751i
\(755\) 1.20866e7 + 5.82217e6i 0.771681 + 0.371722i
\(756\) −2.45355e6 + 1.78261e6i −0.156131 + 0.113436i
\(757\) −1.88277e7 −1.19415 −0.597073 0.802187i \(-0.703670\pi\)
−0.597073 + 0.802187i \(0.703670\pi\)
\(758\) −1.37971e7 + 1.00242e7i −0.872196 + 0.633687i
\(759\) 3.30485e6 + 1.01713e7i 0.208232 + 0.640872i
\(760\) 5.75639e6 6.01945e6i 0.361507 0.378027i
\(761\) 512547. 1.57746e6i 0.0320828 0.0987406i −0.933733 0.357971i \(-0.883469\pi\)
0.965816 + 0.259230i \(0.0834688\pi\)
\(762\) 9.78311e6 + 3.01093e7i 0.610365 + 1.87851i
\(763\) −554854. 1.70767e6i −0.0345038 0.106192i
\(764\) 3.57326e6 1.09974e7i 0.221478 0.681640i
\(765\) −3.27724e7 6.09166e7i −2.02467 3.76342i
\(766\) 2.61965e6 + 8.06247e6i 0.161314 + 0.496473i
\(767\) 2.07460e6 1.50729e6i 0.127335 0.0925140i
\(768\) 1.86765e6 0.114259
\(769\) 2.15592e7 1.56637e7i 1.31467 0.955164i 0.314688 0.949195i \(-0.398100\pi\)
0.999982 0.00596883i \(-0.00189995\pi\)
\(770\) 399236. + 742092.i 0.0242663 + 0.0451056i
\(771\) 1.68368e6 + 1.22326e6i 0.102005 + 0.0741111i
\(772\) 8.80850e6 + 6.39975e6i 0.531935 + 0.386474i
\(773\) −8.84764e6 + 2.72302e7i −0.532573 + 1.63909i 0.216263 + 0.976335i \(0.430613\pi\)
−0.748836 + 0.662755i \(0.769387\pi\)
\(774\) 3.60649e7 2.16387
\(775\) 2.22916e7 + 6.15713e6i 1.33318 + 0.368234i
\(776\) 7.15819e6 0.426726
\(777\) −156094. + 480408.i −0.00927542 + 0.0285468i
\(778\) −1.43473e7 1.04239e7i −0.849810 0.617423i
\(779\) −2.95323e7 2.14565e7i −1.74363 1.26682i
\(780\) −3.46317e6 + 628097.i −0.203815 + 0.0369650i
\(781\) 204464. 148552.i 0.0119947 0.00871466i
\(782\) −1.76617e7 −1.03280
\(783\) 1.15610e7 8.39958e6i 0.673895 0.489613i
\(784\) −1.29667e6 3.99075e6i −0.0753425 0.231880i
\(785\) 2.19203e7 + 1.05591e7i 1.26961 + 0.611578i
\(786\) 6.47989e6 1.99430e7i 0.374120 1.15142i
\(787\) 2.06465e6 + 6.35435e6i 0.118826 + 0.365708i 0.992726 0.120398i \(-0.0384170\pi\)
−0.873900 + 0.486106i \(0.838417\pi\)
\(788\) −1.71516e6 5.27873e6i −0.0983988 0.302840i
\(789\) −6.24212e6 + 1.92113e7i −0.356976 + 1.09866i
\(790\) 9.71946e6 1.76277e6i 0.554083 0.100491i
\(791\) −341046. 1.04963e6i −0.0193808 0.0596481i
\(792\) −5.44539e6 + 3.95631e6i −0.308472 + 0.224118i
\(793\) 6.56309e6 0.370617
\(794\) −6.61365e6 + 4.80509e6i −0.372297 + 0.270490i
\(795\) −7.59547e6 + 5.60279e7i −0.426223 + 3.14403i
\(796\) 5.31968e6 + 3.86498e6i 0.297580 + 0.216204i
\(797\) −2.19107e7 1.59190e7i −1.22183 0.887709i −0.225576 0.974226i \(-0.572426\pi\)
−0.996250 + 0.0865166i \(0.972426\pi\)
\(798\) −1.67239e6 + 5.14708e6i −0.0929672 + 0.286123i
\(799\) −3.65426e6 −0.202504
\(800\) −1.99464e6 2.50228e6i −0.110190 0.138233i
\(801\) −809304. −0.0445687
\(802\) 3.31785e6 1.02113e7i 0.182146 0.560589i
\(803\) 6.44965e6 + 4.68594e6i 0.352978 + 0.256453i
\(804\) −1.17828e7 8.56068e6i −0.642846 0.467055i
\(805\) 1.60019e6 1.67331e6i 0.0870324 0.0910096i
\(806\) 3.30686e6 2.40257e6i 0.179299 0.130268i
\(807\) 4.35123e7 2.35195
\(808\) 7.35638e6 5.34472e6i 0.396402 0.288003i
\(809\) −1.06330e6 3.27251e6i −0.0571197 0.175796i 0.918426 0.395593i \(-0.129461\pi\)
−0.975546 + 0.219796i \(0.929461\pi\)
\(810\) −3.80198e6 + 2.80453e7i −0.203609 + 1.50192i
\(811\) 3.36152e6 1.03457e7i 0.179466 0.552341i −0.820343 0.571872i \(-0.806217\pi\)
0.999809 + 0.0195313i \(0.00621742\pi\)
\(812\) −155032. 477140.i −0.00825148 0.0253954i
\(813\) 8.09379e6 + 2.49101e7i 0.429463 + 1.32175i
\(814\) −198520. + 610982.i −0.0105013 + 0.0323197i
\(815\) 2.14770e6 1.58425e7i 0.113261 0.835468i
\(816\) −4.90150e6 1.50853e7i −0.257694 0.793099i
\(817\) 2.98362e7 2.16773e7i 1.56383 1.13619i
\(818\) 9.87578e6 0.516046
\(819\) 1.29663e6 942057.i 0.0675470 0.0490758i
\(820\) −9.69326e6 + 1.01362e7i −0.503426 + 0.526431i
\(821\) 2.33494e7 + 1.69643e7i 1.20898 + 0.878372i 0.995137 0.0984970i \(-0.0314035\pi\)
0.213838 + 0.976869i \(0.431403\pi\)
\(822\) 858530. + 623759.i 0.0443176 + 0.0321986i
\(823\) 1.80161e6 5.54478e6i 0.0927173 0.285355i −0.893935 0.448197i \(-0.852066\pi\)
0.986652 + 0.162843i \(0.0520663\pi\)
\(824\) −5.19194e6 −0.266386
\(825\) 1.58626e7 + 4.38136e6i 0.811406 + 0.224117i
\(826\) −1.51494e6 −0.0772583
\(827\) 9.65589e6 2.97178e7i 0.490940 1.51096i −0.332250 0.943191i \(-0.607808\pi\)
0.823190 0.567766i \(-0.192192\pi\)
\(828\) 1.49616e7 + 1.08702e7i 0.758406 + 0.551014i
\(829\) −8.47306e6 6.15604e6i −0.428207 0.311111i 0.352724 0.935727i \(-0.385255\pi\)
−0.780932 + 0.624616i \(0.785255\pi\)
\(830\) −177682. + 1.31067e6i −0.00895258 + 0.0660386i
\(831\) 7.89237e6 5.73414e6i 0.396465 0.288049i
\(832\) −565589. −0.0283265
\(833\) −2.88308e7 + 2.09468e7i −1.43961 + 1.04594i
\(834\) 6.12327e6 + 1.88455e7i 0.304838 + 0.938193i
\(835\) 1.98246e7 3.59549e6i 0.983986 0.178461i
\(836\) −2.12694e6 + 6.54605e6i −0.105254 + 0.323939i
\(837\) −2.12548e7 6.54156e7i −1.04868 3.22751i
\(838\) 123807. + 381038.i 0.00609024 + 0.0187438i
\(839\) 4.32545e6 1.33124e7i 0.212142 0.652906i −0.787202 0.616695i \(-0.788471\pi\)
0.999344 0.0362107i \(-0.0115287\pi\)
\(840\) 1.87330e6 + 902375.i 0.0916028 + 0.0441254i
\(841\) −5.60779e6 1.72590e7i −0.273402 0.841445i
\(842\) 1115.71 810.612i 5.42340e−5 3.94033e-5i
\(843\) 1.89417e7 0.918013
\(844\) 2.33067e6 1.69333e6i 0.112622 0.0818249i
\(845\) −1.93740e7 + 3.51376e6i −0.933420 + 0.169290i
\(846\) 3.09560e6 + 2.24908e6i 0.148703 + 0.108039i
\(847\) 2.09379e6 + 1.52123e6i 0.100283 + 0.0728595i
\(848\) −2.80764e6 + 8.64101e6i −0.134076 + 0.412644i
\(849\) −4.98948e7 −2.37567
\(850\) −1.49765e7 + 2.26781e7i −0.710988 + 1.07661i
\(851\) 1.76511e6 0.0835501
\(852\) 192710. 593100.i 0.00909505 0.0279917i
\(853\) −2.62112e7 1.90436e7i −1.23343 0.896140i −0.236289 0.971683i \(-0.575931\pi\)
−0.997143 + 0.0755424i \(0.975931\pi\)
\(854\) −3.13678e6 2.27900e6i −0.147177 0.106930i
\(855\) 3.50911e7 + 6.52266e7i 1.64165 + 3.05147i
\(856\) 2.09177e6 1.51976e6i 0.0975730 0.0708909i
\(857\) −1.32612e7 −0.616783 −0.308391 0.951260i \(-0.599791\pi\)
−0.308391 + 0.951260i \(0.599791\pi\)
\(858\) 2.35313e6 1.70965e6i 0.109126 0.0792847i
\(859\) −4.56574e6 1.40519e7i −0.211120 0.649759i −0.999406 0.0344512i \(-0.989032\pi\)
0.788287 0.615308i \(-0.210968\pi\)
\(860\) −6.71312e6 1.24782e7i −0.309512 0.575315i
\(861\) 2.81615e6 8.66723e6i 0.129464 0.398449i
\(862\) −3.83673e6 1.18082e7i −0.175870 0.541273i
\(863\) −8.77704e6 2.70129e7i −0.401163 1.23465i −0.924057 0.382255i \(-0.875148\pi\)
0.522894 0.852398i \(-0.324852\pi\)
\(864\) −2.94104e6 + 9.05158e6i −0.134034 + 0.412515i
\(865\) 7.70046e6 8.05236e6i 0.349926 0.365917i
\(866\) −1.93752e6 5.96309e6i −0.0877915 0.270194i
\(867\) −7.62469e7 + 5.53966e7i −3.44488 + 2.50285i
\(868\) −2.41477e6 −0.108787
\(869\) −6.60413e6 + 4.79818e6i −0.296665 + 0.215540i
\(870\) −8.82691e6 4.25195e6i −0.395376 0.190454i
\(871\) 3.56823e6 + 2.59247e6i 0.159370 + 0.115789i
\(872\) −4.55864e6 3.31204e6i −0.203022 0.147504i
\(873\) −1.96709e7 + 6.05408e7i −0.873551 + 2.68851i
\(874\) 1.89113e7 0.837420
\(875\) −791674. 3.47358e6i −0.0349564 0.153376i
\(876\) 1.96716e7 0.866125
\(877\) −5.45527e6 + 1.67896e7i −0.239507 + 0.737126i 0.756985 + 0.653432i \(0.226672\pi\)
−0.996492 + 0.0836934i \(0.973328\pi\)
\(878\) −2.85067e6 2.07113e6i −0.124799 0.0906718i
\(879\) −1.27847e6 928860.i −0.0558106 0.0405488i
\(880\) 2.38246e6 + 1.14764e6i 0.103710 + 0.0499573i
\(881\) −1.12530e7 + 8.17581e6i −0.488461 + 0.354888i −0.804592 0.593828i \(-0.797616\pi\)
0.316131 + 0.948715i \(0.397616\pi\)
\(882\) 3.73152e7 1.61516
\(883\) 2.00474e6 1.45653e6i 0.0865279 0.0628662i −0.543680 0.839292i \(-0.682970\pi\)
0.630208 + 0.776426i \(0.282970\pi\)
\(884\) 1.48434e6 + 4.56834e6i 0.0638858 + 0.196620i
\(885\) −2.04476e7 + 2.13820e7i −0.877573 + 0.917677i
\(886\) 2.52582e6 7.77367e6i 0.108098 0.332692i
\(887\) 1.10657e7 + 3.40568e7i 0.472249 + 1.45343i 0.849632 + 0.527376i \(0.176824\pi\)
−0.377383 + 0.926057i \(0.623176\pi\)
\(888\) 489854. + 1.50762e6i 0.0208466 + 0.0641591i
\(889\) −1.75025e6 + 5.38672e6i −0.0742756 + 0.228597i
\(890\) 150644. + 280013.i 0.00637494 + 0.0118496i
\(891\) −7.22744e6 2.22438e7i −0.304993 0.938673i
\(892\) 7.66658e6 5.57009e6i 0.322619 0.234396i
\(893\) 3.91281e6 0.164195
\(894\) 1.61416e7 1.17275e7i 0.675463 0.490753i
\(895\) 1.13832e7 + 2.11589e7i 0.475015 + 0.882948i
\(896\) 270319. + 196398.i 0.0112488 + 0.00817274i
\(897\) −6.46540e6 4.69739e6i −0.268296 0.194928i
\(898\) 7.56380e6 2.32790e7i 0.313003 0.963326i
\(899\) 1.13783e7 0.469546
\(900\) 2.66445e7 9.99348e6i 1.09648 0.411254i
\(901\) 7.71631e7 3.16663
\(902\) 3.58158e6 1.10230e7i 0.146575 0.451110i
\(903\) 7.44865e6 + 5.41176e6i 0.303989 + 0.220861i
\(904\) −2.80201e6 2.03578e6i −0.114038 0.0828533i
\(905\) −3.41777e6 + 619863.i −0.138714 + 0.0251579i
\(906\) −2.21322e7 + 1.60800e7i −0.895787 + 0.650827i
\(907\) −7.66605e6 −0.309424 −0.154712 0.987960i \(-0.549445\pi\)
−0.154712 + 0.987960i \(0.549445\pi\)
\(908\) −4.15900e6 + 3.02169e6i −0.167407 + 0.121628i
\(909\) 2.49877e7 + 7.69044e7i 1.00304 + 3.08703i
\(910\) −567300. 273270.i −0.0227096 0.0109393i
\(911\) 6.98768e6 2.15059e7i 0.278957 0.858541i −0.709188 0.705019i \(-0.750938\pi\)
0.988145 0.153522i \(-0.0490616\pi\)
\(912\) 5.24829e6 + 1.61526e7i 0.208944 + 0.643065i
\(913\) −337767. 1.03954e6i −0.0134104 0.0412729i
\(914\) 3.78654e6 1.16538e7i 0.149926 0.461424i
\(915\) −7.45040e7 + 1.35124e7i −2.94189 + 0.533557i
\(916\) 3.37341e6 + 1.03823e7i 0.132840 + 0.408841i
\(917\) 3.03506e6 2.20510e6i 0.119191 0.0865973i
\(918\) 8.08295e7 3.16565
\(919\) −3.18549e7 + 2.31439e7i −1.24419 + 0.903958i −0.997870 0.0652297i \(-0.979222\pi\)
−0.246322 + 0.969188i \(0.579222\pi\)
\(920\) 976073. 7.19999e6i 0.0380201 0.280455i
\(921\) −2.98491e7 2.16867e7i −1.15953 0.842449i
\(922\) −3.93922e6 2.86201e6i −0.152610 0.110878i
\(923\) −58359.3 + 179611.i −0.00225479 + 0.00693952i
\(924\) −1.71833e6 −0.0662105
\(925\) 1.49674e6 2.26644e6i 0.0575166 0.0870942i
\(926\) −2.28892e7 −0.877210
\(927\) 1.42676e7 4.39111e7i 0.545319 1.67832i
\(928\) −1.27373e6 925421.i −0.0485521 0.0352752i
\(929\) −1.69630e7 1.23243e7i −0.644857 0.468516i 0.216658 0.976247i \(-0.430484\pi\)
−0.861515 + 0.507732i \(0.830484\pi\)
\(930\) −3.25928e7 + 3.40823e7i −1.23570 + 1.29217i
\(931\) 3.08706e7 2.24288e7i 1.16727 0.848072i
\(932\) 2.23565e7 0.843069
\(933\) 7.17191e7 5.21070e7i 2.69731 1.95971i
\(934\) 3.55512e6 + 1.09415e7i 0.133348 + 0.410404i
\(935\) 3.01707e6 2.22554e7i 0.112864 0.832541i
\(936\) 1.55425e6 4.78350e6i 0.0579872 0.178466i
\(937\) 5.35716e6 + 1.64876e7i 0.199336 + 0.613493i 0.999899 + 0.0142439i \(0.00453413\pi\)
−0.800563 + 0.599249i \(0.795466\pi\)
\(938\) −805185. 2.47811e6i −0.0298806 0.0919629i
\(939\) −7.71294e6 + 2.37380e7i −0.285467 + 0.878577i
\(940\) 201952. 1.48970e6i 0.00745469 0.0549894i
\(941\) 1.29761e7 + 3.99363e7i 0.477716 + 1.47026i 0.842259 + 0.539072i \(0.181225\pi\)
−0.364543 + 0.931186i \(0.618775\pi\)
\(942\) −4.01390e7 + 2.91627e7i −1.47380 + 1.07078i
\(943\) −3.18450e7 −1.16617
\(944\) −3.84622e6 + 2.79444e6i −0.140477 + 0.102062i
\(945\) −7.32331e6 + 7.65797e6i −0.266764 + 0.278955i
\(946\) 9.47319e6 + 6.88267e6i 0.344166 + 0.250051i
\(947\) 1.29854e7 + 9.43446e6i 0.470523 + 0.341855i 0.797645 0.603127i \(-0.206079\pi\)
−0.327122 + 0.944982i \(0.606079\pi\)
\(948\) −6.22447e6 + 1.91570e7i −0.224948 + 0.692318i
\(949\) −5.95726e6 −0.214724
\(950\) 1.60361e7 2.42826e7i 0.576487 0.872942i
\(951\) −6.32838e7 −2.26903
\(952\) 876906. 2.69884e6i 0.0313589 0.0965127i
\(953\) 1.59402e7 + 1.15812e7i 0.568539 + 0.413068i 0.834574 0.550895i \(-0.185714\pi\)
−0.266035 + 0.963963i \(0.585714\pi\)
\(954\) −6.53664e7 4.74915e7i −2.32532 1.68945i
\(955\) 5.42729e6 4.00343e7i 0.192564 1.42044i
\(956\) −8.64662e6 + 6.28214e6i −0.305986 + 0.222312i
\(957\) 8.09671e6 0.285778
\(958\) −1.61499e7 + 1.17336e7i −0.568534 + 0.413064i
\(959\) 58668.4 + 180563.i 0.00205995 + 0.00633989i
\(960\) 6.42055e6 1.16446e6i 0.224851 0.0407801i
\(961\) 8.07683e6 2.48579e7i 0.282119 0.868273i
\(962\) −148345. 456559.i −0.00516815 0.0159059i
\(963\) 7.10522e6 + 2.18676e7i 0.246895 + 0.759864i
\(964\) 4.98894e6 1.53544e7i 0.172908 0.532156i
\(965\) 3.42718e7 + 1.65089e7i 1.18473 + 0.570688i
\(966\) 1.45894e6 + 4.49016e6i 0.0503032 + 0.154817i
\(967\) −2.03154e7 + 1.47600e7i −0.698649 + 0.507598i −0.879492 0.475914i \(-0.842117\pi\)
0.180843 + 0.983512i \(0.442117\pi\)
\(968\) 8.12189e6 0.278592
\(969\) 1.16693e8 8.47824e7i 3.99241 2.90066i
\(970\) 2.46082e7 4.46307e6i 0.839752 0.152302i
\(971\) −4.15419e7 3.01819e7i −1.41396 1.02730i −0.992732 0.120350i \(-0.961598\pi\)
−0.421231 0.906954i \(-0.638402\pi\)
\(972\) −1.74549e7 1.26817e7i −0.592586 0.430539i
\(973\) −1.09549e6 + 3.37156e6i −0.0370958 + 0.114169i
\(974\) −2.15537e7 −0.727988
\(975\) −1.15140e7 + 4.31851e6i −0.387894 + 0.145486i
\(976\) −1.21677e7 −0.408868
\(977\) 4.54099e6 1.39757e7i 0.152200 0.468423i −0.845667 0.533712i \(-0.820797\pi\)
0.997866 + 0.0652886i \(0.0207968\pi\)
\(978\) 2.63746e7 + 1.91623e7i 0.881737 + 0.640619i
\(979\) −212580. 154449.i −0.00708870 0.00515024i
\(980\) −6.94586e6 1.29108e7i −0.231026 0.429426i
\(981\) 4.05390e7 2.94533e7i 1.34493 0.977152i
\(982\) −1.04565e7 −0.346025
\(983\) 1.75667e7 1.27629e7i 0.579836 0.421276i −0.258829 0.965923i \(-0.583337\pi\)
0.838665 + 0.544648i \(0.183337\pi\)
\(984\) −8.83766e6 2.71995e7i −0.290971 0.895517i
\(985\) −9.18758e6 1.70777e7i −0.301725 0.560839i
\(986\) −4.13194e6 + 1.27168e7i −0.135351 + 0.416568i
\(987\) 301860. + 929028.i 0.00986307 + 0.0303554i
\(988\) −1.58936e6 4.89156e6i −0.0518001 0.159424i
\(989\) 9.94190e6 3.05980e7i 0.323206 0.994725i
\(990\) −1.62533e7 + 1.69960e7i −0.527052 + 0.551137i
\(991\) 529145. + 1.62854e6i 0.0171156 + 0.0526763i 0.959250 0.282560i \(-0.0911837\pi\)
−0.942134 + 0.335237i \(0.891184\pi\)
\(992\) −6.13076e6 + 4.45426e6i −0.197804 + 0.143713i
\(993\) −3.62019e7 −1.16509
\(994\) 90261.7 65578.9i 0.00289759 0.00210522i
\(995\) 2.06977e7 + 9.97013e6i 0.662771 + 0.319259i
\(996\) −2.18200e6 1.58532e6i −0.0696959 0.0506370i
\(997\) −7.33221e6 5.32716e6i −0.233613 0.169730i 0.464820 0.885405i \(-0.346119\pi\)
−0.698433 + 0.715675i \(0.746119\pi\)
\(998\) −7.56054e6 + 2.32690e7i −0.240285 + 0.739521i
\(999\) −8.07807e6 −0.256091
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 50.6.d.b.21.1 28
25.6 even 5 inner 50.6.d.b.31.1 yes 28
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.6.d.b.21.1 28 1.1 even 1 trivial
50.6.d.b.31.1 yes 28 25.6 even 5 inner