Properties

Label 25.6.e.a.4.6
Level $25$
Weight $6$
Character 25.4
Analytic conductor $4.010$
Analytic rank $0$
Dimension $48$
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] = [25,6,Mod(4,25)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(25, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("25.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 25 = 5^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 25.e (of order \(10\), 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: \(4.00959549532\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(12\) over \(\Q(\zeta_{10})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label 4.6
Character \(\chi\) \(=\) 25.4
Dual form 25.6.e.a.19.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.580095 - 0.188484i) q^{2} +(15.1807 - 20.8945i) q^{3} +(-25.5876 - 18.5905i) q^{4} +(-52.0512 + 20.3881i) q^{5} +(-12.7445 + 9.25945i) q^{6} +10.2303i q^{7} +(22.8118 + 31.3978i) q^{8} +(-131.033 - 403.279i) q^{9} +O(q^{10})\) \(q+(-0.580095 - 0.188484i) q^{2} +(15.1807 - 20.8945i) q^{3} +(-25.5876 - 18.5905i) q^{4} +(-52.0512 + 20.3881i) q^{5} +(-12.7445 + 9.25945i) q^{6} +10.2303i q^{7} +(22.8118 + 31.3978i) q^{8} +(-131.033 - 403.279i) q^{9} +(34.0375 - 2.01618i) q^{10} +(150.440 - 463.006i) q^{11} +(-776.875 + 252.422i) q^{12} +(868.080 - 282.056i) q^{13} +(1.92825 - 5.93455i) q^{14} +(-364.177 + 1397.09i) q^{15} +(305.439 + 940.046i) q^{16} +(111.270 + 153.150i) q^{17} +258.638i q^{18} +(433.060 - 314.636i) q^{19} +(1710.89 + 445.975i) q^{20} +(213.757 + 155.303i) q^{21} +(-174.539 + 240.232i) q^{22} +(-2826.19 - 918.286i) q^{23} +1002.34 q^{24} +(2293.65 - 2122.45i) q^{25} -556.732 q^{26} +(-4446.68 - 1444.81i) q^{27} +(190.186 - 261.769i) q^{28} +(5587.39 + 4059.48i) q^{29} +(474.586 - 741.802i) q^{30} +(-4536.49 + 3295.95i) q^{31} -1844.80i q^{32} +(-7390.47 - 10172.1i) q^{33} +(-35.6808 - 109.814i) q^{34} +(-208.576 - 532.500i) q^{35} +(-4144.31 + 12754.9i) q^{36} +(5692.75 - 1849.69i) q^{37} +(-310.520 + 100.894i) q^{38} +(7284.66 - 22419.9i) q^{39} +(-1827.52 - 1169.20i) q^{40} +(927.964 + 2855.98i) q^{41} +(-94.7270 - 130.380i) q^{42} -13831.0i q^{43} +(-12456.9 + 9050.45i) q^{44} +(15042.5 + 18319.6i) q^{45} +(1466.38 + 1065.39i) q^{46} +(-16043.3 + 22081.8i) q^{47} +(24278.5 + 7888.58i) q^{48} +16702.3 q^{49} +(-1730.59 + 798.902i) q^{50} +4889.15 q^{51} +(-27455.6 - 8920.87i) q^{52} +(-10251.9 + 14110.6i) q^{53} +(2307.17 + 1676.26i) q^{54} +(1609.22 + 27167.2i) q^{55} +(-321.209 + 233.372i) q^{56} -13825.0i q^{57} +(-2476.07 - 3408.02i) q^{58} +(-5608.17 - 17260.2i) q^{59} +(35290.9 - 28977.8i) q^{60} +(11412.8 - 35125.0i) q^{61} +(3252.83 - 1056.91i) q^{62} +(4125.67 - 1340.51i) q^{63} +(9426.35 - 29011.3i) q^{64} +(-39434.0 + 32379.8i) q^{65} +(2369.89 + 7293.78i) q^{66} +(8964.83 + 12339.0i) q^{67} -5987.30i q^{68} +(-62090.7 + 45111.5i) q^{69} +(20.6261 + 348.214i) q^{70} +(-4506.39 - 3274.09i) q^{71} +(9672.94 - 13313.7i) q^{72} +(-26400.2 - 8577.96i) q^{73} -3650.97 q^{74} +(-9528.04 - 80144.9i) q^{75} -16930.2 q^{76} +(4736.69 + 1539.04i) q^{77} +(-8451.59 + 11632.6i) q^{78} +(79695.5 + 57902.2i) q^{79} +(-35064.2 - 42703.2i) q^{80} +(-14331.4 + 10412.4i) q^{81} -1831.65i q^{82} +(3239.71 + 4459.08i) q^{83} +(-2582.35 - 7947.67i) q^{84} +(-8914.17 - 5703.06i) q^{85} +(-2606.92 + 8023.29i) q^{86} +(169641. - 55119.8i) q^{87} +(17969.1 - 5838.53i) q^{88} +(-15733.3 + 48422.2i) q^{89} +(-5273.12 - 13462.4i) q^{90} +(2885.52 + 8880.73i) q^{91} +(55244.0 + 76036.9i) q^{92} +144822. i q^{93} +(13468.7 - 9785.61i) q^{94} +(-16126.5 + 25206.5i) q^{95} +(-38546.1 - 28005.4i) q^{96} +(-24878.4 + 34242.2i) q^{97} +(-9688.95 - 3148.13i) q^{98} -206433. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48 q - 5 q^{2} - 5 q^{3} + 189 q^{4} - 60 q^{5} - 139 q^{6} + 610 q^{8} + 1031 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 48 q - 5 q^{2} - 5 q^{3} + 189 q^{4} - 60 q^{5} - 139 q^{6} + 610 q^{8} + 1031 q^{9} + 435 q^{10} - 724 q^{11} + 315 q^{12} - 5 q^{13} - 497 q^{14} - 105 q^{15} - 6967 q^{16} - 960 q^{17} + 4075 q^{19} + 9155 q^{20} + 2016 q^{21} - 5450 q^{22} - 10995 q^{23} - 20720 q^{24} - 16610 q^{25} + 21666 q^{26} - 13805 q^{27} + 14235 q^{28} + 17195 q^{29} + 39595 q^{30} + 8631 q^{31} + 28460 q^{33} - 24067 q^{34} - 4145 q^{35} - 43827 q^{36} + 19980 q^{37} - 77385 q^{38} + 6037 q^{39} + 93210 q^{40} - 26514 q^{41} + 182885 q^{42} + 26748 q^{44} - 94185 q^{45} - 14559 q^{46} - 7700 q^{47} - 127830 q^{48} - 130126 q^{49} - 231115 q^{50} + 121116 q^{51} - 189260 q^{52} + 45840 q^{53} + 19985 q^{54} + 79370 q^{55} - 43280 q^{56} + 337370 q^{58} + 47640 q^{59} + 71480 q^{60} + 7791 q^{61} + 135320 q^{62} - 35790 q^{63} + 68204 q^{64} + 197485 q^{65} - 14798 q^{66} - 66180 q^{67} + 17957 q^{69} - 129930 q^{70} - 46694 q^{71} - 50545 q^{72} - 18985 q^{73} - 183292 q^{74} - 202210 q^{75} + 273360 q^{76} - 132990 q^{77} - 665225 q^{78} - 54065 q^{79} + 362810 q^{80} - 382452 q^{81} + 161155 q^{83} + 474258 q^{84} - 83075 q^{85} + 74691 q^{86} + 897680 q^{87} + 578430 q^{88} + 436475 q^{89} + 775655 q^{90} + 181046 q^{91} - 1412870 q^{92} - 336327 q^{94} - 362785 q^{95} - 766024 q^{96} - 475210 q^{97} - 361660 q^{98} - 451848 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{1}{10}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.580095 0.188484i −0.102547 0.0333196i 0.257294 0.966333i \(-0.417169\pi\)
−0.359841 + 0.933014i \(0.617169\pi\)
\(3\) 15.1807 20.8945i 0.973843 1.34038i 0.0337618 0.999430i \(-0.489251\pi\)
0.940081 0.340950i \(-0.110749\pi\)
\(4\) −25.5876 18.5905i −0.799611 0.580952i
\(5\) −52.0512 + 20.3881i −0.931120 + 0.364713i
\(6\) −12.7445 + 9.25945i −0.144526 + 0.105004i
\(7\) 10.2303i 0.0789121i 0.999221 + 0.0394560i \(0.0125625\pi\)
−0.999221 + 0.0394560i \(0.987437\pi\)
\(8\) 22.8118 + 31.3978i 0.126019 + 0.173450i
\(9\) −131.033 403.279i −0.539231 1.65958i
\(10\) 34.0375 2.01618i 0.107636 0.00637571i
\(11\) 150.440 463.006i 0.374870 1.15373i −0.568696 0.822548i \(-0.692552\pi\)
0.943566 0.331184i \(-0.107448\pi\)
\(12\) −776.875 + 252.422i −1.55739 + 0.506027i
\(13\) 868.080 282.056i 1.42463 0.462890i 0.507559 0.861617i \(-0.330548\pi\)
0.917069 + 0.398728i \(0.130548\pi\)
\(14\) 1.92825 5.93455i 0.00262932 0.00809222i
\(15\) −364.177 + 1397.09i −0.417911 + 1.60323i
\(16\) 305.439 + 940.046i 0.298281 + 0.918014i
\(17\) 111.270 + 153.150i 0.0933804 + 0.128527i 0.853151 0.521664i \(-0.174689\pi\)
−0.759770 + 0.650191i \(0.774689\pi\)
\(18\) 258.638i 0.188153i
\(19\) 433.060 314.636i 0.275210 0.199952i −0.441616 0.897204i \(-0.645594\pi\)
0.716825 + 0.697253i \(0.245594\pi\)
\(20\) 1710.89 + 445.975i 0.956415 + 0.249307i
\(21\) 213.757 + 155.303i 0.105772 + 0.0768480i
\(22\) −174.539 + 240.232i −0.0768838 + 0.105822i
\(23\) −2826.19 918.286i −1.11399 0.361958i −0.306520 0.951864i \(-0.599165\pi\)
−0.807472 + 0.589906i \(0.799165\pi\)
\(24\) 1002.34 0.355211
\(25\) 2293.65 2122.45i 0.733969 0.679183i
\(26\) −556.732 −0.161515
\(27\) −4446.68 1444.81i −1.17389 0.381419i
\(28\) 190.186 261.769i 0.0458441 0.0630990i
\(29\) 5587.39 + 4059.48i 1.23371 + 0.896345i 0.997163 0.0752744i \(-0.0239833\pi\)
0.236550 + 0.971619i \(0.423983\pi\)
\(30\) 474.586 741.802i 0.0962747 0.150482i
\(31\) −4536.49 + 3295.95i −0.847843 + 0.615994i −0.924550 0.381060i \(-0.875559\pi\)
0.0767074 + 0.997054i \(0.475559\pi\)
\(32\) 1844.80i 0.318474i
\(33\) −7390.47 10172.1i −1.18137 1.62602i
\(34\) −35.6808 109.814i −0.00529343 0.0162915i
\(35\) −208.576 532.500i −0.0287802 0.0734766i
\(36\) −4144.31 + 12754.9i −0.532962 + 1.64029i
\(37\) 5692.75 1849.69i 0.683625 0.222123i 0.0534431 0.998571i \(-0.482980\pi\)
0.630182 + 0.776448i \(0.282980\pi\)
\(38\) −310.520 + 100.894i −0.0348843 + 0.0113346i
\(39\) 7284.66 22419.9i 0.766916 2.36032i
\(40\) −1827.52 1169.20i −0.180598 0.115542i
\(41\) 927.964 + 2855.98i 0.0862128 + 0.265336i 0.984864 0.173328i \(-0.0554520\pi\)
−0.898651 + 0.438663i \(0.855452\pi\)
\(42\) −94.7270 130.380i −0.00828611 0.0114048i
\(43\) 13831.0i 1.14073i −0.821392 0.570364i \(-0.806802\pi\)
0.821392 0.570364i \(-0.193198\pi\)
\(44\) −12456.9 + 9050.45i −0.970012 + 0.704755i
\(45\) 15042.5 + 18319.6i 1.10736 + 1.34861i
\(46\) 1466.38 + 1065.39i 0.102177 + 0.0742356i
\(47\) −16043.3 + 22081.8i −1.05938 + 1.45811i −0.178990 + 0.983851i \(0.557283\pi\)
−0.880387 + 0.474256i \(0.842717\pi\)
\(48\) 24278.5 + 7888.58i 1.52097 + 0.494192i
\(49\) 16702.3 0.993773
\(50\) −1730.59 + 798.902i −0.0978967 + 0.0451927i
\(51\) 4889.15 0.263213
\(52\) −27455.6 8920.87i −1.40806 0.457508i
\(53\) −10251.9 + 14110.6i −0.501322 + 0.690010i −0.982426 0.186653i \(-0.940236\pi\)
0.481104 + 0.876664i \(0.340236\pi\)
\(54\) 2307.17 + 1676.26i 0.107670 + 0.0782270i
\(55\) 1609.22 + 27167.2i 0.0717314 + 1.21098i
\(56\) −321.209 + 233.372i −0.0136873 + 0.00994439i
\(57\) 13825.0i 0.563607i
\(58\) −2476.07 3408.02i −0.0966480 0.133025i
\(59\) −5608.17 17260.2i −0.209745 0.645528i −0.999485 0.0320865i \(-0.989785\pi\)
0.789740 0.613441i \(-0.210215\pi\)
\(60\) 35290.9 28977.8i 1.26556 1.03917i
\(61\) 11412.8 35125.0i 0.392706 1.20862i −0.538028 0.842927i \(-0.680831\pi\)
0.930734 0.365697i \(-0.119169\pi\)
\(62\) 3252.83 1056.91i 0.107469 0.0349187i
\(63\) 4125.67 1340.51i 0.130961 0.0425519i
\(64\) 9426.35 29011.3i 0.287669 0.885355i
\(65\) −39434.0 + 32379.8i −1.15768 + 0.950586i
\(66\) 2369.89 + 7293.78i 0.0669683 + 0.206107i
\(67\) 8964.83 + 12339.0i 0.243981 + 0.335810i 0.913392 0.407082i \(-0.133454\pi\)
−0.669411 + 0.742892i \(0.733454\pi\)
\(68\) 5987.30i 0.157021i
\(69\) −62090.7 + 45111.5i −1.57001 + 1.14068i
\(70\) 20.6261 + 348.214i 0.000503121 + 0.00849378i
\(71\) −4506.39 3274.09i −0.106092 0.0770805i 0.533474 0.845816i \(-0.320886\pi\)
−0.639566 + 0.768736i \(0.720886\pi\)
\(72\) 9672.94 13313.7i 0.219901 0.302668i
\(73\) −26400.2 8577.96i −0.579830 0.188398i 0.00439445 0.999990i \(-0.498601\pi\)
−0.584224 + 0.811592i \(0.698601\pi\)
\(74\) −3650.97 −0.0775049
\(75\) −9528.04 80144.9i −0.195592 1.64522i
\(76\) −16930.2 −0.336223
\(77\) 4736.69 + 1539.04i 0.0910433 + 0.0295818i
\(78\) −8451.59 + 11632.6i −0.157290 + 0.216492i
\(79\) 79695.5 + 57902.2i 1.43670 + 1.04382i 0.988719 + 0.149780i \(0.0478566\pi\)
0.447981 + 0.894043i \(0.352143\pi\)
\(80\) −35064.2 42703.2i −0.612546 0.745994i
\(81\) −14331.4 + 10412.4i −0.242704 + 0.176335i
\(82\) 1831.65i 0.0300820i
\(83\) 3239.71 + 4459.08i 0.0516192 + 0.0710477i 0.834046 0.551694i \(-0.186019\pi\)
−0.782427 + 0.622742i \(0.786019\pi\)
\(84\) −2582.35 7947.67i −0.0399317 0.122897i
\(85\) −8914.17 5703.06i −0.133824 0.0856172i
\(86\) −2606.92 + 8023.29i −0.0380086 + 0.116979i
\(87\) 169641. 55119.8i 2.40289 0.780745i
\(88\) 17969.1 5838.53i 0.247355 0.0803705i
\(89\) −15733.3 + 48422.2i −0.210545 + 0.647992i 0.788895 + 0.614529i \(0.210654\pi\)
−0.999440 + 0.0334634i \(0.989346\pi\)
\(90\) −5273.12 13462.4i −0.0686217 0.175193i
\(91\) 2885.52 + 8880.73i 0.0365276 + 0.112420i
\(92\) 55244.0 + 76036.9i 0.680481 + 0.936601i
\(93\) 144822.i 1.73631i
\(94\) 13468.7 9785.61i 0.157220 0.114227i
\(95\) −16126.5 + 25206.5i −0.183329 + 0.286552i
\(96\) −38546.1 28005.4i −0.426876 0.310144i
\(97\) −24878.4 + 34242.2i −0.268468 + 0.369515i −0.921872 0.387495i \(-0.873340\pi\)
0.653404 + 0.757010i \(0.273340\pi\)
\(98\) −9688.95 3148.13i −0.101909 0.0331122i
\(99\) −206433. −2.11686
\(100\) −98146.2 + 11668.1i −0.981462 + 0.116681i
\(101\) 158775. 1.54874 0.774370 0.632733i \(-0.218067\pi\)
0.774370 + 0.632733i \(0.218067\pi\)
\(102\) −2836.17 921.527i −0.0269918 0.00877017i
\(103\) 79762.6 109784.i 0.740809 1.01964i −0.257762 0.966208i \(-0.582985\pi\)
0.998572 0.0534283i \(-0.0170149\pi\)
\(104\) 28658.4 + 20821.6i 0.259818 + 0.188769i
\(105\) −14292.6 3725.64i −0.126514 0.0329783i
\(106\) 8606.73 6253.16i 0.0744001 0.0540548i
\(107\) 61513.7i 0.519413i 0.965688 + 0.259706i \(0.0836258\pi\)
−0.965688 + 0.259706i \(0.916374\pi\)
\(108\) 86920.0 + 119635.i 0.717068 + 0.986959i
\(109\) −10287.6 31661.9i −0.0829368 0.255253i 0.900986 0.433849i \(-0.142845\pi\)
−0.983923 + 0.178595i \(0.942845\pi\)
\(110\) 4187.09 16062.9i 0.0329936 0.126573i
\(111\) 47771.8 147026.i 0.368014 1.13263i
\(112\) −9616.96 + 3124.74i −0.0724424 + 0.0235380i
\(113\) −99978.6 + 32485.0i −0.736565 + 0.239324i −0.653190 0.757194i \(-0.726570\pi\)
−0.0833745 + 0.996518i \(0.526570\pi\)
\(114\) −2605.79 + 8019.79i −0.0187792 + 0.0577964i
\(115\) 165829. 9822.71i 1.16927 0.0692607i
\(116\) −67500.2 207744.i −0.465758 1.43345i
\(117\) −227495. 313120.i −1.53641 2.11468i
\(118\) 11069.6i 0.0731857i
\(119\) −1566.77 + 1138.33i −0.0101423 + 0.00736884i
\(120\) −52172.9 + 20435.7i −0.330744 + 0.129550i
\(121\) −61449.3 44645.5i −0.381552 0.277213i
\(122\) −13241.0 + 18224.7i −0.0805419 + 0.110856i
\(123\) 73761.3 + 23966.5i 0.439608 + 0.142837i
\(124\) 177351. 1.03581
\(125\) −76114.9 + 157239.i −0.435707 + 0.900088i
\(126\) −2645.94 −0.0148475
\(127\) −53274.7 17310.0i −0.293097 0.0952330i 0.158778 0.987314i \(-0.449245\pi\)
−0.451875 + 0.892081i \(0.649245\pi\)
\(128\) −45635.4 + 62811.8i −0.246194 + 0.338857i
\(129\) −288991. 209964.i −1.52901 1.11089i
\(130\) 28978.6 11350.7i 0.150390 0.0589066i
\(131\) −10112.9 + 7347.47i −0.0514871 + 0.0374076i −0.613231 0.789904i \(-0.710131\pi\)
0.561744 + 0.827311i \(0.310131\pi\)
\(132\) 397672.i 1.98651i
\(133\) 3218.83 + 4430.34i 0.0157786 + 0.0217174i
\(134\) −2874.74 8847.55i −0.0138305 0.0425658i
\(135\) 260912. 15454.9i 1.23214 0.0729846i
\(136\) −2270.30 + 6987.26i −0.0105253 + 0.0323936i
\(137\) 87123.6 28308.2i 0.396583 0.128858i −0.103934 0.994584i \(-0.533143\pi\)
0.500517 + 0.865726i \(0.333143\pi\)
\(138\) 44521.3 14465.9i 0.199008 0.0646616i
\(139\) −83333.2 + 256473.i −0.365831 + 1.12591i 0.583627 + 0.812022i \(0.301633\pi\)
−0.949459 + 0.313892i \(0.898367\pi\)
\(140\) −4562.46 + 17502.9i −0.0196734 + 0.0754727i
\(141\) 217837. + 670434.i 0.922751 + 2.83993i
\(142\) 1997.02 + 2748.67i 0.00831117 + 0.0114393i
\(143\) 444359.i 1.81716i
\(144\) 339078. 246355.i 1.36268 0.990044i
\(145\) −373595. 97384.6i −1.47564 0.384654i
\(146\) 13697.8 + 9952.06i 0.0531826 + 0.0386394i
\(147\) 253553. 348986.i 0.967779 1.33203i
\(148\) −180050. 58501.8i −0.675677 0.219541i
\(149\) 262709. 0.969415 0.484707 0.874676i \(-0.338926\pi\)
0.484707 + 0.874676i \(0.338926\pi\)
\(150\) −9578.89 + 48287.6i −0.0347606 + 0.175229i
\(151\) −102301. −0.365121 −0.182560 0.983195i \(-0.558439\pi\)
−0.182560 + 0.983195i \(0.558439\pi\)
\(152\) 19757.8 + 6419.68i 0.0693631 + 0.0225374i
\(153\) 47182.1 64940.6i 0.162948 0.224278i
\(154\) −2457.65 1785.58i −0.00835060 0.00606706i
\(155\) 168932. 264048.i 0.564783 0.882783i
\(156\) −603192. + 438245.i −1.98447 + 1.44180i
\(157\) 342002.i 1.10734i 0.832737 + 0.553668i \(0.186772\pi\)
−0.832737 + 0.553668i \(0.813228\pi\)
\(158\) −35317.3 48610.1i −0.112550 0.154912i
\(159\) 139201. + 428418.i 0.436667 + 1.34392i
\(160\) 37611.9 + 96024.0i 0.116152 + 0.296538i
\(161\) 9394.34 28912.8i 0.0285629 0.0879074i
\(162\) 10276.2 3338.92i 0.0307640 0.00999583i
\(163\) −309013. + 100404.i −0.910977 + 0.295994i −0.726760 0.686891i \(-0.758975\pi\)
−0.184217 + 0.982886i \(0.558975\pi\)
\(164\) 29349.6 90328.8i 0.0852104 0.262251i
\(165\) 592073. + 378793.i 1.69303 + 1.08316i
\(166\) −1038.87 3197.33i −0.00292612 0.00900568i
\(167\) −252162. 347071.i −0.699663 0.963003i −0.999958 0.00915693i \(-0.997085\pi\)
0.300295 0.953846i \(-0.402915\pi\)
\(168\) 10254.2i 0.0280304i
\(169\) 373625. 271454.i 1.00628 0.731106i
\(170\) 4096.13 + 4988.50i 0.0108705 + 0.0132388i
\(171\) −183631. 133416.i −0.480238 0.348914i
\(172\) −257124. + 353901.i −0.662707 + 0.912138i
\(173\) −58227.4 18919.2i −0.147915 0.0480605i 0.234124 0.972207i \(-0.424778\pi\)
−0.382039 + 0.924146i \(0.624778\pi\)
\(174\) −108797. −0.272424
\(175\) 21713.3 + 23464.8i 0.0535957 + 0.0579191i
\(176\) 481197. 1.17096
\(177\) −445778. 144842.i −1.06951 0.347505i
\(178\) 18253.7 25124.0i 0.0431817 0.0594345i
\(179\) −262497. 190715.i −0.612339 0.444891i 0.237898 0.971290i \(-0.423542\pi\)
−0.850237 + 0.526400i \(0.823542\pi\)
\(180\) −44330.9 748402.i −0.101982 1.72168i
\(181\) 197793. 143705.i 0.448760 0.326044i −0.340346 0.940300i \(-0.610544\pi\)
0.789106 + 0.614257i \(0.210544\pi\)
\(182\) 5695.54i 0.0127455i
\(183\) −560663. 771686.i −1.23758 1.70339i
\(184\) −35638.4 109684.i −0.0776022 0.238835i
\(185\) −258603. + 212342.i −0.555526 + 0.456150i
\(186\) 27296.7 84010.7i 0.0578533 0.178054i
\(187\) 87648.8 28478.8i 0.183291 0.0595550i
\(188\) 821020. 266766.i 1.69418 0.550472i
\(189\) 14780.9 45490.9i 0.0300986 0.0926339i
\(190\) 14105.9 11582.6i 0.0283476 0.0232766i
\(191\) 56407.6 + 173605.i 0.111880 + 0.344333i 0.991284 0.131745i \(-0.0420581\pi\)
−0.879403 + 0.476078i \(0.842058\pi\)
\(192\) −463077. 637371.i −0.906568 1.24778i
\(193\) 625397.i 1.20854i 0.796778 + 0.604272i \(0.206536\pi\)
−0.796778 + 0.604272i \(0.793464\pi\)
\(194\) 20885.9 15174.5i 0.0398428 0.0289475i
\(195\) 77922.5 + 1.31550e6i 0.146749 + 2.47745i
\(196\) −427372. 310504.i −0.794632 0.577334i
\(197\) −54003.7 + 74329.7i −0.0991420 + 0.136457i −0.855706 0.517463i \(-0.826877\pi\)
0.756564 + 0.653920i \(0.226877\pi\)
\(198\) 119751. + 38909.4i 0.217078 + 0.0705328i
\(199\) −36116.8 −0.0646512 −0.0323256 0.999477i \(-0.510291\pi\)
−0.0323256 + 0.999477i \(0.510291\pi\)
\(200\) 118962. + 23598.8i 0.210298 + 0.0417171i
\(201\) 393910. 0.687712
\(202\) −92104.6 29926.6i −0.158819 0.0516035i
\(203\) −41529.7 + 57160.7i −0.0707324 + 0.0973549i
\(204\) −125101. 90891.4i −0.210468 0.152914i
\(205\) −106530. 129738.i −0.177046 0.215616i
\(206\) −66962.5 + 48651.1i −0.109942 + 0.0798775i
\(207\) 1.26007e6i 2.04394i
\(208\) 530292. + 729884.i 0.849878 + 1.16976i
\(209\) −80529.1 247843.i −0.127523 0.392474i
\(210\) 7588.86 + 4855.16i 0.0118749 + 0.00759723i
\(211\) 165545. 509496.i 0.255983 0.787833i −0.737652 0.675181i \(-0.764065\pi\)
0.993634 0.112652i \(-0.0359346\pi\)
\(212\) 524645. 170467.i 0.801725 0.260496i
\(213\) −136821. + 44455.7i −0.206634 + 0.0671395i
\(214\) 11594.4 35683.8i 0.0173066 0.0532644i
\(215\) 281987. + 719919.i 0.416038 + 1.06215i
\(216\) −56072.9 172575.i −0.0817746 0.251676i
\(217\) −33718.6 46409.7i −0.0486094 0.0669051i
\(218\) 20306.0i 0.0289390i
\(219\) −580006. + 421399.i −0.817189 + 0.593722i
\(220\) 463874. 725058.i 0.646165 1.00999i
\(221\) 139788. + 101562.i 0.192526 + 0.139879i
\(222\) −55424.4 + 76285.1i −0.0754776 + 0.103886i
\(223\) 564952. + 183564.i 0.760763 + 0.247187i 0.663606 0.748082i \(-0.269025\pi\)
0.0971567 + 0.995269i \(0.469025\pi\)
\(224\) 18872.9 0.0251315
\(225\) −1.15648e6 646871.i −1.52294 0.851847i
\(226\) 64120.0 0.0835069
\(227\) 277719. + 90236.4i 0.357718 + 0.116230i 0.482362 0.875972i \(-0.339779\pi\)
−0.124644 + 0.992202i \(0.539779\pi\)
\(228\) −257012. + 353747.i −0.327429 + 0.450667i
\(229\) 369812. + 268684.i 0.466007 + 0.338574i 0.795883 0.605451i \(-0.207007\pi\)
−0.329876 + 0.944024i \(0.607007\pi\)
\(230\) −98047.9 25558.0i −0.122213 0.0318572i
\(231\) 104064. 75606.8i 0.128313 0.0932247i
\(232\) 268036.i 0.326943i
\(233\) −215364. 296422.i −0.259886 0.357702i 0.659057 0.752093i \(-0.270956\pi\)
−0.918943 + 0.394391i \(0.870956\pi\)
\(234\) 72950.4 + 224518.i 0.0870940 + 0.268048i
\(235\) 384871. 1.47648e6i 0.454617 1.74404i
\(236\) −177375. + 545904.i −0.207306 + 0.638023i
\(237\) 2.41967e6 786198.i 2.79824 0.909204i
\(238\) 1123.43 365.026i 0.00128560 0.000417716i
\(239\) −3590.22 + 11049.6i −0.00406561 + 0.0125127i −0.953069 0.302754i \(-0.902094\pi\)
0.949003 + 0.315267i \(0.102094\pi\)
\(240\) −1.42456e6 + 84382.4i −1.59644 + 0.0945636i
\(241\) 196652. + 605232.i 0.218100 + 0.671242i 0.998919 + 0.0464851i \(0.0148020\pi\)
−0.780819 + 0.624757i \(0.785198\pi\)
\(242\) 27231.4 + 37480.9i 0.0298904 + 0.0411406i
\(243\) 678637.i 0.737262i
\(244\) −945014. + 686593.i −1.01616 + 0.738287i
\(245\) −869377. + 340528.i −0.925322 + 0.362442i
\(246\) −38271.3 27805.7i −0.0403213 0.0292952i
\(247\) 287186. 395277.i 0.299516 0.412249i
\(248\) −206971. 67248.9i −0.213688 0.0694314i
\(249\) 142351. 0.145500
\(250\) 73791.0 76867.1i 0.0746712 0.0777840i
\(251\) −1.14164e6 −1.14379 −0.571894 0.820327i \(-0.693791\pi\)
−0.571894 + 0.820327i \(0.693791\pi\)
\(252\) −130486. 42397.6i −0.129439 0.0420572i
\(253\) −850343. + 1.17040e6i −0.835205 + 1.14956i
\(254\) 27641.7 + 20082.9i 0.0268832 + 0.0195318i
\(255\) −254486. + 99680.2i −0.245083 + 0.0959971i
\(256\) −751400. + 545924.i −0.716591 + 0.520634i
\(257\) 1.07615e6i 1.01634i −0.861257 0.508169i \(-0.830323\pi\)
0.861257 0.508169i \(-0.169677\pi\)
\(258\) 128067. + 176269.i 0.119781 + 0.164865i
\(259\) 18922.9 + 58238.6i 0.0175282 + 0.0539462i
\(260\) 1.61098e6 95424.6i 1.47794 0.0875442i
\(261\) 904967. 2.78520e6i 0.822302 2.53079i
\(262\) 7251.34 2356.10i 0.00652627 0.00212051i
\(263\) −603693. + 196152.i −0.538179 + 0.174865i −0.565480 0.824762i \(-0.691309\pi\)
0.0273006 + 0.999627i \(0.491309\pi\)
\(264\) 150791. 464089.i 0.133158 0.409818i
\(265\) 245938. 943490.i 0.215135 0.825321i
\(266\) −1032.18 3176.71i −0.000894438 0.00275280i
\(267\) 772913. + 1.06382e6i 0.663517 + 0.913253i
\(268\) 482386.i 0.410259i
\(269\) −1.46636e6 + 1.06538e6i −1.23555 + 0.897681i −0.997294 0.0735202i \(-0.976577\pi\)
−0.238259 + 0.971202i \(0.576577\pi\)
\(270\) −154267. 40212.5i −0.128784 0.0335701i
\(271\) −1.39034e6 1.01014e6i −1.15000 0.835524i −0.161520 0.986869i \(-0.551640\pi\)
−0.988481 + 0.151345i \(0.951640\pi\)
\(272\) −109982. + 151377.i −0.0901361 + 0.124062i
\(273\) 229362. + 74524.3i 0.186258 + 0.0605189i
\(274\) −55875.6 −0.0449620
\(275\) −637648. 1.38128e6i −0.508451 1.10141i
\(276\) 2.42739e6 1.91808
\(277\) −1.76346e6 572983.i −1.38091 0.448686i −0.477943 0.878391i \(-0.658618\pi\)
−0.902969 + 0.429705i \(0.858618\pi\)
\(278\) 96682.4 133072.i 0.0750301 0.103270i
\(279\) 1.92362e6 + 1.39759e6i 1.47948 + 1.07490i
\(280\) 11961.3 18696.1i 0.00911766 0.0142513i
\(281\) 789897. 573894.i 0.596767 0.433576i −0.247963 0.968769i \(-0.579761\pi\)
0.844730 + 0.535193i \(0.179761\pi\)
\(282\) 429975.i 0.321973i
\(283\) 1.18036e6 + 1.62463e6i 0.876093 + 1.20584i 0.977488 + 0.210992i \(0.0676693\pi\)
−0.101395 + 0.994846i \(0.532331\pi\)
\(284\) 54440.9 + 167552.i 0.0400525 + 0.123269i
\(285\) 281864. + 719606.i 0.205555 + 0.524786i
\(286\) −83754.6 + 257770.i −0.0605472 + 0.186345i
\(287\) −29217.5 + 9493.36i −0.0209382 + 0.00680323i
\(288\) −743968. + 241730.i −0.528534 + 0.171731i
\(289\) 427686. 1.31628e6i 0.301218 0.927053i
\(290\) 198365. + 126909.i 0.138507 + 0.0886131i
\(291\) 337800. + 1.03964e6i 0.233844 + 0.719699i
\(292\) 516050. + 710281.i 0.354188 + 0.487498i
\(293\) 1.82689e6i 1.24320i 0.783333 + 0.621602i \(0.213518\pi\)
−0.783333 + 0.621602i \(0.786482\pi\)
\(294\) −212864. + 154654.i −0.143626 + 0.104350i
\(295\) 643813. + 784072.i 0.430730 + 0.524567i
\(296\) 187938. + 136545.i 0.124677 + 0.0905829i
\(297\) −1.33791e6 + 1.84148e6i −0.880111 + 1.21137i
\(298\) −152396. 49516.6i −0.0994109 0.0323005i
\(299\) −2.71237e6 −1.75457
\(300\) −1.24613e6 + 2.22784e6i −0.799393 + 1.42916i
\(301\) 141495. 0.0900172
\(302\) 59344.2 + 19282.1i 0.0374422 + 0.0121657i
\(303\) 2.41032e6 3.31752e6i 1.50823 2.07590i
\(304\) 428046. + 310994.i 0.265648 + 0.193005i
\(305\) 122080. + 2.06098e6i 0.0751443 + 1.26860i
\(306\) −39610.4 + 28778.6i −0.0241827 + 0.0175698i
\(307\) 728846.i 0.441357i 0.975347 + 0.220678i \(0.0708271\pi\)
−0.975347 + 0.220678i \(0.929173\pi\)
\(308\) −92588.8 127438.i −0.0556137 0.0765457i
\(309\) −1.08302e6 3.33319e6i −0.645269 1.98593i
\(310\) −147765. + 121332.i −0.0873310 + 0.0717087i
\(311\) −803693. + 2.47351e6i −0.471183 + 1.45015i 0.379855 + 0.925046i \(0.375974\pi\)
−0.851037 + 0.525105i \(0.824026\pi\)
\(312\) 870110. 282716.i 0.506043 0.164423i
\(313\) 1.66255e6 540195.i 0.959211 0.311666i 0.212758 0.977105i \(-0.431755\pi\)
0.746453 + 0.665438i \(0.231755\pi\)
\(314\) 64462.0 198394.i 0.0368961 0.113554i
\(315\) −187415. + 153889.i −0.106421 + 0.0873841i
\(316\) −962786. 2.96315e6i −0.542390 1.66931i
\(317\) −987747. 1.35952e6i −0.552075 0.759866i 0.438217 0.898869i \(-0.355610\pi\)
−0.990292 + 0.139004i \(0.955610\pi\)
\(318\) 274760.i 0.152365i
\(319\) 2.72013e6 1.97629e6i 1.49662 1.08736i
\(320\) 100832. + 1.70226e6i 0.0550455 + 0.929289i
\(321\) 1.28530e6 + 933822.i 0.696211 + 0.505827i
\(322\) −10899.2 + 15001.5i −0.00585809 + 0.00806297i
\(323\) 96373.2 + 31313.5i 0.0513984 + 0.0167004i
\(324\) 560277. 0.296510
\(325\) 1.39243e6 2.48939e6i 0.731247 1.30733i
\(326\) 198182. 0.103281
\(327\) −817732. 265697.i −0.422904 0.137410i
\(328\) −68502.8 + 94286.0i −0.0351580 + 0.0483908i
\(329\) −225903. 164128.i −0.115062 0.0835976i
\(330\) −272062. 331333.i −0.137525 0.167486i
\(331\) −1.37144e6 + 996410.i −0.688030 + 0.499883i −0.876012 0.482290i \(-0.839805\pi\)
0.187982 + 0.982172i \(0.439805\pi\)
\(332\) 174325.i 0.0867988i
\(333\) −1.49188e6 2.05339e6i −0.737264 1.01476i
\(334\) 80860.5 + 248863.i 0.0396616 + 0.122066i
\(335\) −718199. 459486.i −0.349650 0.223697i
\(336\) −80702.5 + 248377.i −0.0389977 + 0.120023i
\(337\) −1.95988e6 + 636803.i −0.940058 + 0.305443i −0.738669 0.674068i \(-0.764545\pi\)
−0.201389 + 0.979511i \(0.564545\pi\)
\(338\) −267903. + 87047.0i −0.127552 + 0.0414440i
\(339\) −838989. + 2.58214e6i −0.396513 + 1.22034i
\(340\) 122069. + 311646.i 0.0572676 + 0.146206i
\(341\) 843577. + 2.59626e6i 0.392861 + 1.20910i
\(342\) 81376.9 + 112006.i 0.0376215 + 0.0517815i
\(343\) 342811.i 0.157333i
\(344\) 434262. 315510.i 0.197859 0.143753i
\(345\) 2.31216e6 3.61402e6i 1.04585 1.63472i
\(346\) 30211.5 + 21949.9i 0.0135669 + 0.00985695i
\(347\) 4487.38 6176.34i 0.00200064 0.00275364i −0.808016 0.589161i \(-0.799458\pi\)
0.810016 + 0.586408i \(0.199458\pi\)
\(348\) −5.36540e6 1.74333e6i −2.37495 0.771668i
\(349\) 3.48086e6 1.52976 0.764879 0.644174i \(-0.222799\pi\)
0.764879 + 0.644174i \(0.222799\pi\)
\(350\) −8173.02 17704.4i −0.00356625 0.00772523i
\(351\) −4.26760e6 −1.84891
\(352\) −854153. 277531.i −0.367434 0.119386i
\(353\) 24975.3 34375.6i 0.0106678 0.0146829i −0.803650 0.595103i \(-0.797111\pi\)
0.814318 + 0.580420i \(0.197111\pi\)
\(354\) 231293. + 168044.i 0.0980967 + 0.0712714i
\(355\) 301315. + 78543.5i 0.126897 + 0.0330780i
\(356\) 1.30277e6 946517.i 0.544806 0.395825i
\(357\) 50017.5i 0.0207707i
\(358\) 116327. + 160110.i 0.0479702 + 0.0660253i
\(359\) 99161.8 + 305188.i 0.0406077 + 0.124978i 0.969305 0.245860i \(-0.0790705\pi\)
−0.928698 + 0.370838i \(0.879071\pi\)
\(360\) −232049. + 890205.i −0.0943675 + 0.362021i
\(361\) −676612. + 2.08240e6i −0.273257 + 0.840999i
\(362\) −141825. + 46081.7i −0.0568828 + 0.0184823i
\(363\) −1.86569e6 + 606198.i −0.743143 + 0.241462i
\(364\) 91263.2 280879.i 0.0361029 0.111113i
\(365\) 1.54905e6 91756.6i 0.608603 0.0360500i
\(366\) 179787. + 553328.i 0.0701545 + 0.215913i
\(367\) −1.64755e6 2.26766e6i −0.638519 0.878846i 0.360017 0.932946i \(-0.382771\pi\)
−0.998536 + 0.0540999i \(0.982771\pi\)
\(368\) 2.93723e6i 1.13063i
\(369\) 1.03016e6 748456.i 0.393858 0.286155i
\(370\) 190038. 74436.2i 0.0721664 0.0282670i
\(371\) −144356. 104881.i −0.0544502 0.0395604i
\(372\) 2.69231e6 3.70565e6i 1.00871 1.38838i
\(373\) 1.78747e6 + 580784.i 0.665221 + 0.216144i 0.622114 0.782927i \(-0.286274\pi\)
0.0431077 + 0.999070i \(0.486274\pi\)
\(374\) −56212.4 −0.0207804
\(375\) 2.12994e6 + 3.97738e6i 0.782150 + 1.46056i
\(376\) −1.05930e6 −0.386409
\(377\) 5.99531e6 + 1.94799e6i 2.17249 + 0.705885i
\(378\) −17148.7 + 23603.1i −0.00617306 + 0.00849649i
\(379\) 346402. + 251676.i 0.123875 + 0.0900002i 0.647997 0.761642i \(-0.275607\pi\)
−0.524123 + 0.851643i \(0.675607\pi\)
\(380\) 881236. 345173.i 0.313064 0.122625i
\(381\) −1.17043e6 + 850367.i −0.413079 + 0.300119i
\(382\) 111339.i 0.0390382i
\(383\) 30192.5 + 41556.4i 0.0105172 + 0.0144757i 0.814243 0.580524i \(-0.197152\pi\)
−0.803726 + 0.595000i \(0.797152\pi\)
\(384\) 619640. + 1.90705e6i 0.214443 + 0.659987i
\(385\) −277929. + 16462.8i −0.0955611 + 0.00566047i
\(386\) 117878. 362790.i 0.0402683 0.123933i
\(387\) −5.57774e6 + 1.81232e6i −1.89313 + 0.615116i
\(388\) 1.27315e6 413673.i 0.429340 0.139501i
\(389\) −108392. + 333596.i −0.0363181 + 0.111776i −0.967572 0.252595i \(-0.918716\pi\)
0.931254 + 0.364371i \(0.118716\pi\)
\(390\) 202749. 777803.i 0.0674990 0.258945i
\(391\) −173835. 535009.i −0.0575036 0.176978i
\(392\) 381011. + 524416.i 0.125234 + 0.172370i
\(393\) 322844.i 0.105441i
\(394\) 45337.2 32939.4i 0.0147135 0.0106899i
\(395\) −5.32876e6 1.38904e6i −1.71844 0.447943i
\(396\) 5.28212e6 + 3.83768e6i 1.69266 + 1.22979i
\(397\) −1.45664e6 + 2.00489e6i −0.463847 + 0.638431i −0.975301 0.220880i \(-0.929107\pi\)
0.511454 + 0.859311i \(0.329107\pi\)
\(398\) 20951.2 + 6807.45i 0.00662980 + 0.00215415i
\(399\) 141434. 0.0444754
\(400\) 2.69577e6 + 1.50786e6i 0.842428 + 0.471207i
\(401\) 1.60933e6 0.499785 0.249892 0.968274i \(-0.419605\pi\)
0.249892 + 0.968274i \(0.419605\pi\)
\(402\) −228505. 74245.9i −0.0705231 0.0229143i
\(403\) −3.00839e6 + 4.14069e6i −0.922724 + 1.27002i
\(404\) −4.06266e6 2.95170e6i −1.23839 0.899743i
\(405\) 533679. 834166.i 0.161675 0.252706i
\(406\) 34865.1 25331.0i 0.0104973 0.00762670i
\(407\) 2.91404e6i 0.871987i
\(408\) 111530. + 153508.i 0.0331697 + 0.0456542i
\(409\) 1.70184e6 + 5.23773e6i 0.503050 + 1.54823i 0.804024 + 0.594597i \(0.202688\pi\)
−0.300974 + 0.953632i \(0.597312\pi\)
\(410\) 37343.7 + 95339.4i 0.0109713 + 0.0280100i
\(411\) 731114. 2.25014e6i 0.213492 0.657060i
\(412\) −4.08186e6 + 1.32628e6i −1.18472 + 0.384939i
\(413\) 176577. 57373.3i 0.0509399 0.0165514i
\(414\) 237503. 730960.i 0.0681034 0.209601i
\(415\) −259543. 166049.i −0.0739757 0.0473278i
\(416\) −520337. 1.60143e6i −0.147418 0.453707i
\(417\) 4.09381e6 + 5.63465e6i 1.15289 + 1.58682i
\(418\) 158951.i 0.0444962i
\(419\) 3.41741e6 2.48290e6i 0.950960 0.690913i −7.35452e−5 1.00000i \(-0.500023\pi\)
0.951034 + 0.309087i \(0.100023\pi\)
\(420\) 296452. + 361036.i 0.0820033 + 0.0998683i
\(421\) −4.86824e6 3.53699e6i −1.33865 0.972586i −0.999492 0.0318568i \(-0.989858\pi\)
−0.339158 0.940730i \(-0.610142\pi\)
\(422\) −192064. + 264353.i −0.0525007 + 0.0722610i
\(423\) 1.10073e7 + 3.57650e6i 2.99110 + 0.971867i
\(424\) −676906. −0.182858
\(425\) 580268. + 115109.i 0.155832 + 0.0309126i
\(426\) 87748.1 0.0234268
\(427\) 359339. + 116756.i 0.0953751 + 0.0309892i
\(428\) 1.14357e6 1.57399e6i 0.301754 0.415328i
\(429\) −9.28463e6 6.74568e6i −2.43569 1.76963i
\(430\) −27885.7 470772.i −0.00727295 0.122783i
\(431\) 4.40903e6 3.20335e6i 1.14327 0.830636i 0.155701 0.987804i \(-0.450237\pi\)
0.987572 + 0.157168i \(0.0502365\pi\)
\(432\) 4.62139e6i 1.19142i
\(433\) −674101. 927820.i −0.172785 0.237818i 0.713838 0.700310i \(-0.246955\pi\)
−0.886623 + 0.462493i \(0.846955\pi\)
\(434\) 10812.5 + 33277.4i 0.00275551 + 0.00848058i
\(435\) −7.70624e6 + 6.32770e6i −1.95263 + 1.60333i
\(436\) −325375. + 1.00140e6i −0.0819726 + 0.252286i
\(437\) −1.51284e6 + 491550.i −0.378956 + 0.123130i
\(438\) 415886. 135130.i 0.103583 0.0336562i
\(439\) 886129. 2.72722e6i 0.219450 0.675398i −0.779358 0.626579i \(-0.784454\pi\)
0.998808 0.0488184i \(-0.0155456\pi\)
\(440\) −816279. + 670258.i −0.201005 + 0.165048i
\(441\) −2.18856e6 6.73570e6i −0.535873 1.64925i
\(442\) −61947.6 85263.6i −0.0150823 0.0207591i
\(443\) 4.85790e6i 1.17609i −0.808829 0.588043i \(-0.799898\pi\)
0.808829 0.588043i \(-0.200102\pi\)
\(444\) −3.95565e6 + 2.87395e6i −0.952271 + 0.691865i
\(445\) −168296. 2.84121e6i −0.0402878 0.680147i
\(446\) −293127. 212969.i −0.0697780 0.0506967i
\(447\) 3.98811e6 5.48917e6i 0.944058 1.29938i
\(448\) 296795. + 96434.4i 0.0698652 + 0.0227006i
\(449\) −547286. −0.128115 −0.0640573 0.997946i \(-0.520404\pi\)
−0.0640573 + 0.997946i \(0.520404\pi\)
\(450\) 548945. + 593226.i 0.127790 + 0.138098i
\(451\) 1.46194e6 0.338445
\(452\) 3.16212e6 + 1.02743e6i 0.728001 + 0.236542i
\(453\) −1.55300e6 + 2.13752e6i −0.355571 + 0.489401i
\(454\) −144095. 104691.i −0.0328103 0.0238381i
\(455\) −331256. 403422.i −0.0750127 0.0913548i
\(456\) 434073. 315372.i 0.0977575 0.0710250i
\(457\) 5.65806e6i 1.26729i 0.773622 + 0.633647i \(0.218443\pi\)
−0.773622 + 0.633647i \(0.781557\pi\)
\(458\) −163883. 225566.i −0.0365066 0.0502470i
\(459\) −273509. 841774.i −0.0605954 0.186494i
\(460\) −4.42576e6 2.83149e6i −0.975199 0.623908i
\(461\) −1.33954e6 + 4.12269e6i −0.293565 + 0.903500i 0.690135 + 0.723681i \(0.257551\pi\)
−0.983700 + 0.179819i \(0.942449\pi\)
\(462\) −74617.6 + 24244.7i −0.0162643 + 0.00528460i
\(463\) −124221. + 40361.8i −0.0269303 + 0.00875020i −0.322451 0.946586i \(-0.604507\pi\)
0.295521 + 0.955336i \(0.404507\pi\)
\(464\) −2.10949e6 + 6.49233e6i −0.454864 + 1.39993i
\(465\) −2.95265e6 7.53818e6i −0.633255 1.61672i
\(466\) 69060.3 + 212546.i 0.0147321 + 0.0453407i
\(467\) −722711. 994727.i −0.153346 0.211063i 0.725431 0.688294i \(-0.241640\pi\)
−0.878778 + 0.477232i \(0.841640\pi\)
\(468\) 1.22412e7i 2.58350i
\(469\) −126232. + 91713.0i −0.0264995 + 0.0192530i
\(470\) −501554. + 783954.i −0.104731 + 0.163699i
\(471\) 7.14595e6 + 5.19184e6i 1.48425 + 1.07837i
\(472\) 413998. 569819.i 0.0855349 0.117729i
\(473\) −6.40382e6 2.08073e6i −1.31609 0.427625i
\(474\) −1.55182e6 −0.317246
\(475\) 325491. 1.64081e6i 0.0661919 0.333676i
\(476\) 61251.9 0.0123909
\(477\) 7.03385e6 + 2.28544e6i 1.41546 + 0.459910i
\(478\) 4165.34 5733.09i 0.000833836 0.00114768i
\(479\) 7.92954e6 + 5.76115e6i 1.57910 + 1.14728i 0.917718 + 0.397234i \(0.130030\pi\)
0.661382 + 0.750049i \(0.269970\pi\)
\(480\) 2.57734e6 + 671833.i 0.510587 + 0.133094i
\(481\) 4.42005e6 3.21135e6i 0.871092 0.632886i
\(482\) 388158.i 0.0761011i
\(483\) −461505. 635207.i −0.0900136 0.123893i
\(484\) 742357. + 2.28474e6i 0.144045 + 0.443326i
\(485\) 596819. 2.28957e6i 0.115209 0.441976i
\(486\) −127912. + 393674.i −0.0245653 + 0.0756042i
\(487\) 122118. 39678.5i 0.0233323 0.00758112i −0.297328 0.954776i \(-0.596095\pi\)
0.320660 + 0.947194i \(0.396095\pi\)
\(488\) 1.36319e6 442928.i 0.259124 0.0841944i
\(489\) −2.59314e6 + 7.98087e6i −0.490404 + 1.50931i
\(490\) 568506. 33674.9i 0.106966 0.00633601i
\(491\) −3.02348e6 9.30531e6i −0.565983 1.74192i −0.665014 0.746831i \(-0.731574\pi\)
0.0990312 0.995084i \(-0.468426\pi\)
\(492\) −1.44182e6 1.98450e6i −0.268534 0.369605i
\(493\) 1.30741e6i 0.242267i
\(494\) −241098. + 175168.i −0.0444505 + 0.0322952i
\(495\) 1.07451e7 4.20877e6i 1.97105 0.772044i
\(496\) −4.48397e6 3.25779e6i −0.818386 0.594592i
\(497\) 33494.9 46101.8i 0.00608258 0.00837195i
\(498\) −82577.3 26831.0i −0.0149206 0.00484801i
\(499\) 5.82128e6 1.04657 0.523284 0.852158i \(-0.324707\pi\)
0.523284 + 0.852158i \(0.324707\pi\)
\(500\) 4.87074e6 2.60835e6i 0.871304 0.466596i
\(501\) −1.10799e7 −1.97215
\(502\) 662261. + 215182.i 0.117292 + 0.0381106i
\(503\) −3.29001e6 + 4.52831e6i −0.579799 + 0.798024i −0.993673 0.112309i \(-0.964175\pi\)
0.413875 + 0.910334i \(0.364175\pi\)
\(504\) 136203. + 98957.2i 0.0238842 + 0.0173529i
\(505\) −8.26443e6 + 3.23711e6i −1.44206 + 0.564845i
\(506\) 713881. 518665.i 0.123951 0.0900556i
\(507\) 1.19276e7i 2.06078i
\(508\) 1.04137e6 + 1.43332e6i 0.179038 + 0.246425i
\(509\) −994701. 3.06138e6i −0.170176 0.523748i 0.829204 0.558945i \(-0.188794\pi\)
−0.999380 + 0.0351978i \(0.988794\pi\)
\(510\) 166414. 9857.38i 0.0283312 0.00167817i
\(511\) 87755.1 270082.i 0.0148669 0.0457556i
\(512\) 2.90165e6 942803.i 0.489182 0.158945i
\(513\) −2.38027e6 + 773397.i −0.399331 + 0.129751i
\(514\) −202837. + 624267.i −0.0338640 + 0.104223i
\(515\) −1.91346e6 + 7.34059e6i −0.317908 + 1.21959i
\(516\) 3.49124e6 + 1.07449e7i 0.577239 + 1.77656i
\(517\) 7.81043e6 + 1.07501e7i 1.28514 + 1.76884i
\(518\) 37350.6i 0.00611608i
\(519\) −1.27924e6 + 929423.i −0.208465 + 0.151459i
\(520\) −1.91622e6 499498.i −0.310768 0.0810075i
\(521\) 6.38085e6 + 4.63596e6i 1.02987 + 0.748248i 0.968284 0.249854i \(-0.0803826\pi\)
0.0615910 + 0.998101i \(0.480383\pi\)
\(522\) −1.04993e6 + 1.44511e6i −0.168650 + 0.232127i
\(523\) −4.83632e6 1.57141e6i −0.773144 0.251210i −0.104234 0.994553i \(-0.533239\pi\)
−0.668910 + 0.743343i \(0.733239\pi\)
\(524\) 395358. 0.0629017
\(525\) 819907. 97474.8i 0.129827 0.0154346i
\(526\) 387171. 0.0610152
\(527\) −1.00955e6 328023.i −0.158344 0.0514490i
\(528\) 7.30491e6 1.00543e7i 1.14033 1.56953i
\(529\) 1.93700e6 + 1.40732e6i 0.300948 + 0.218651i
\(530\) −320501. + 500959.i −0.0495609 + 0.0774662i
\(531\) −6.22580e6 + 4.52331e6i −0.958206 + 0.696177i
\(532\) 173201.i 0.0265321i
\(533\) 1.61109e6 + 2.21748e6i 0.245642 + 0.338097i
\(534\) −247849. 762801.i −0.0376126 0.115760i
\(535\) −1.25415e6 3.20186e6i −0.189436 0.483636i
\(536\) −182914. + 562951.i −0.0275001 + 0.0846367i
\(537\) −7.96979e6 + 2.58954e6i −1.19264 + 0.387514i
\(538\) 1.05144e6 341633.i 0.156613 0.0508867i
\(539\) 2.51270e6 7.73328e6i 0.372536 1.14655i
\(540\) −6.96342e6 4.45502e6i −1.02763 0.657454i
\(541\) −259049. 797270.i −0.0380530 0.117115i 0.930226 0.366988i \(-0.119611\pi\)
−0.968279 + 0.249873i \(0.919611\pi\)
\(542\) 616134. + 848036.i 0.0900901 + 0.123998i
\(543\) 6.31432e6i 0.919025i
\(544\) 282531. 205271.i 0.0409326 0.0297392i
\(545\) 1.18101e6 + 1.43830e6i 0.170318 + 0.207423i
\(546\) −119005. 86462.4i −0.0170838 0.0124121i
\(547\) 28284.1 38929.8i 0.00404180 0.00556306i −0.806991 0.590563i \(-0.798906\pi\)
0.811033 + 0.585000i \(0.198906\pi\)
\(548\) −2.75554e6 895330.i −0.391973 0.127360i
\(549\) −1.56606e7 −2.21757
\(550\) 109548. + 921458.i 0.0154418 + 0.129888i
\(551\) 3.69694e6 0.518756
\(552\) −2.83280e6 920433.i −0.395702 0.128571i
\(553\) −592357. + 815309.i −0.0823703 + 0.113373i
\(554\) 914977. + 664769.i 0.126659 + 0.0920230i
\(555\) 511005. + 8.62688e6i 0.0704194 + 1.18883i
\(556\) 6.90025e6 5.01332e6i 0.946624 0.687763i
\(557\) 7.77800e6i 1.06226i −0.847291 0.531129i \(-0.821768\pi\)
0.847291 0.531129i \(-0.178232\pi\)
\(558\) −852457. 1.17331e6i −0.115901 0.159524i
\(559\) −3.90112e6 1.20064e7i −0.528031 1.62511i
\(560\) 436867. 358718.i 0.0588680 0.0483373i
\(561\) 735522. 2.26370e6i 0.0986707 0.303677i
\(562\) −566385. + 184030.i −0.0756434 + 0.0245780i
\(563\) 1.14167e7 3.70950e6i 1.51799 0.493224i 0.572784 0.819707i \(-0.305863\pi\)
0.945203 + 0.326483i \(0.105863\pi\)
\(564\) 6.88975e6 2.12045e7i 0.912023 2.80692i
\(565\) 4.54170e6 3.72925e6i 0.598545 0.491474i
\(566\) −378506. 1.16492e6i −0.0496628 0.152847i
\(567\) −106522. 146615.i −0.0139149 0.0191523i
\(568\) 216178.i 0.0281152i
\(569\) −2.55438e6 + 1.85586e6i −0.330753 + 0.240306i −0.740750 0.671781i \(-0.765530\pi\)
0.409997 + 0.912087i \(0.365530\pi\)
\(570\) −27873.6 470567.i −0.00359340 0.0606644i
\(571\) −907011. 658982.i −0.116419 0.0845830i 0.528053 0.849212i \(-0.322922\pi\)
−0.644471 + 0.764629i \(0.722922\pi\)
\(572\) −8.26083e6 + 1.13701e7i −1.05568 + 1.45302i
\(573\) 4.48369e6 + 1.45684e6i 0.570491 + 0.185364i
\(574\) 18738.3 0.00237384
\(575\) −8.43132e6 + 3.89221e6i −1.06347 + 0.490938i
\(576\) −1.29348e7 −1.62444
\(577\) −1.40905e7 4.57827e6i −1.76192 0.572481i −0.764521 0.644599i \(-0.777024\pi\)
−0.997396 + 0.0721176i \(0.977024\pi\)
\(578\) −496197. + 682957.i −0.0617781 + 0.0850303i
\(579\) 1.30673e7 + 9.49397e6i 1.61991 + 1.17693i
\(580\) 7.74897e6 + 9.43714e6i 0.956476 + 1.16485i
\(581\) −45617.8 + 33143.2i −0.00560652 + 0.00407338i
\(582\) 666761.i 0.0815948i
\(583\) 4.99099e6 + 6.86950e6i 0.608156 + 0.837055i
\(584\) −332908. 1.02459e6i −0.0403917 0.124313i
\(585\) 1.82253e7 + 1.16601e7i 2.20183 + 1.40868i
\(586\) 344339. 1.05977e6i 0.0414231 0.127487i
\(587\) −5.98357e6 + 1.94418e6i −0.716746 + 0.232885i −0.644612 0.764510i \(-0.722981\pi\)
−0.0721343 + 0.997395i \(0.522981\pi\)
\(588\) −1.29756e7 + 4.21604e6i −1.54769 + 0.502876i
\(589\) −927545. + 2.85469e6i −0.110166 + 0.339055i
\(590\) −225687. 576185.i −0.0266918 0.0681447i
\(591\) 733264. + 2.25675e6i 0.0863558 + 0.265776i
\(592\) 3.47758e6 + 4.78648e6i 0.407824 + 0.561322i
\(593\) 9.95947e6i 1.16305i −0.813527 0.581527i \(-0.802456\pi\)
0.813527 0.581527i \(-0.197544\pi\)
\(594\) 1.12321e6 816059.i 0.130615 0.0948976i
\(595\) 58344.1 91194.7i 0.00675623 0.0105603i
\(596\) −6.72209e6 4.88388e6i −0.775155 0.563183i
\(597\) −548278. + 754641.i −0.0629601 + 0.0866571i
\(598\) 1.57343e6 + 511239.i 0.179927 + 0.0584617i
\(599\) 2.32355e6 0.264597 0.132298 0.991210i \(-0.457764\pi\)
0.132298 + 0.991210i \(0.457764\pi\)
\(600\) 2.29902e6 2.12741e6i 0.260714 0.241253i
\(601\) 1.73058e7 1.95436 0.977181 0.212409i \(-0.0681310\pi\)
0.977181 + 0.212409i \(0.0681310\pi\)
\(602\) −82080.7 26669.6i −0.00923102 0.00299934i
\(603\) 3.80138e6 5.23215e6i 0.425743 0.585986i
\(604\) 2.61763e6 + 1.90182e6i 0.291955 + 0.212118i
\(605\) 4.10874e6 + 1.07102e6i 0.456374 + 0.118962i
\(606\) −2.02351e6 + 1.47017e6i −0.223833 + 0.162624i
\(607\) 7.85985e6i 0.865850i −0.901430 0.432925i \(-0.857482\pi\)
0.901430 0.432925i \(-0.142518\pi\)
\(608\) −580441. 798909.i −0.0636794 0.0876472i
\(609\) 563892. + 1.73548e6i 0.0616102 + 0.189617i
\(610\) 317645. 1.21858e6i 0.0345634 0.132595i
\(611\) −7.69861e6 + 2.36939e7i −0.834275 + 2.56763i
\(612\) −2.41455e6 + 784535.i −0.260590 + 0.0846708i
\(613\) −1.17373e7 + 3.81368e6i −1.26159 + 0.409914i −0.862059 0.506808i \(-0.830825\pi\)
−0.399526 + 0.916722i \(0.630825\pi\)
\(614\) 137376. 422800.i 0.0147059 0.0452600i
\(615\) −4.32799e6 + 256365.i −0.461423 + 0.0273319i
\(616\) 59729.9 + 183830.i 0.00634220 + 0.0195193i
\(617\) 802084. + 1.10397e6i 0.0848216 + 0.116747i 0.849319 0.527880i \(-0.177013\pi\)
−0.764497 + 0.644627i \(0.777013\pi\)
\(618\) 2.13770e6i 0.225152i
\(619\) −9.65516e6 + 7.01488e6i −1.01282 + 0.735858i −0.964799 0.262988i \(-0.915292\pi\)
−0.0480224 + 0.998846i \(0.515292\pi\)
\(620\) −9.23132e6 + 3.61584e6i −0.964461 + 0.377772i
\(621\) 1.12404e7 + 8.16665e6i 1.16964 + 0.849796i
\(622\) 932437. 1.28339e6i 0.0966370 0.133009i
\(623\) −495374. 160957.i −0.0511344 0.0166146i
\(624\) 2.33007e7 2.39557
\(625\) 756075. 9.73631e6i 0.0774221 0.996998i
\(626\) −1.06626e6 −0.108749
\(627\) −6.40104e6 2.07982e6i −0.650252 0.211280i
\(628\) 6.35797e6 8.75100e6i 0.643309 0.885439i
\(629\) 916712. + 666030.i 0.0923860 + 0.0671224i
\(630\) 137725. 53945.6i 0.0138248 0.00541508i
\(631\) −6.38974e6 + 4.64242e6i −0.638866 + 0.464163i −0.859460 0.511202i \(-0.829200\pi\)
0.220595 + 0.975366i \(0.429200\pi\)
\(632\) 3.82311e6i 0.380736i
\(633\) −8.13254e6 1.11935e7i −0.806709 1.11034i
\(634\) 316740. + 974825.i 0.0312953 + 0.0963171i
\(635\) 3.12593e6 185161.i 0.307641 0.0182228i
\(636\) 4.40265e6 1.35500e7i 0.431590 1.32830i
\(637\) 1.44990e7 4.71100e6i 1.41576 0.460007i
\(638\) −1.95043e6 + 633734.i −0.189705 + 0.0616389i
\(639\) −729882. + 2.24635e6i −0.0707132 + 0.217633i
\(640\) 1.09477e6 4.19984e6i 0.105651 0.405306i
\(641\) −821787. 2.52920e6i −0.0789976 0.243130i 0.903756 0.428047i \(-0.140798\pi\)
−0.982754 + 0.184917i \(0.940798\pi\)
\(642\) −569583. 783964.i −0.0545406 0.0750686i
\(643\) 7.75171e6i 0.739384i −0.929154 0.369692i \(-0.879463\pi\)
0.929154 0.369692i \(-0.120537\pi\)
\(644\) −777880. + 565163.i −0.0739091 + 0.0536981i
\(645\) 1.93231e7 + 5.03692e6i 1.82885 + 0.476723i
\(646\) −50003.5 36329.7i −0.00471432 0.00342515i
\(647\) 935013. 1.28694e6i 0.0878126 0.120864i −0.762850 0.646575i \(-0.776201\pi\)
0.850663 + 0.525711i \(0.176201\pi\)
\(648\) −653851. 212449.i −0.0611704 0.0198755i
\(649\) −8.83525e6 −0.823392
\(650\) −1.27695e6 + 1.18163e6i −0.118547 + 0.109698i
\(651\) −1.48158e6 −0.137016
\(652\) 9.77345e6 + 3.17559e6i 0.900386 + 0.292553i
\(653\) −1.10113e7 + 1.51558e7i −1.01055 + 1.39090i −0.0919206 + 0.995766i \(0.529301\pi\)
−0.918625 + 0.395130i \(0.870699\pi\)
\(654\) 424283. + 308259.i 0.0387892 + 0.0281820i
\(655\) 376589. 588628.i 0.0342977 0.0536090i
\(656\) −2.40132e6 + 1.74466e6i −0.217866 + 0.158289i
\(657\) 1.17707e7i 1.06387i
\(658\) 100110. + 137789.i 0.00901388 + 0.0124065i
\(659\) 301055. + 926553.i 0.0270043 + 0.0831106i 0.963650 0.267167i \(-0.0860874\pi\)
−0.936646 + 0.350277i \(0.886087\pi\)
\(660\) −8.10775e6 2.06993e7i −0.724504 1.84968i
\(661\) −3.72239e6 + 1.14563e7i −0.331374 + 1.01986i 0.637107 + 0.770775i \(0.280131\pi\)
−0.968481 + 0.249088i \(0.919869\pi\)
\(662\) 983374. 319518.i 0.0872115 0.0283367i
\(663\) 4.24417e6 1.37901e6i 0.374981 0.121839i
\(664\) −66101.5 + 203439.i −0.00581823 + 0.0179067i
\(665\) −257870. 164979.i −0.0226124 0.0144668i
\(666\) 478399. + 1.47236e6i 0.0417931 + 0.128626i
\(667\) −1.20633e7 1.66037e7i −1.04991 1.44507i
\(668\) 1.35685e7i 1.17650i
\(669\) 1.24118e7 9.01773e6i 1.07219 0.778990i
\(670\) 330018. + 401915.i 0.0284021 + 0.0345897i
\(671\) −1.45461e7 1.05684e7i −1.24721 0.906154i
\(672\) 286503. 394338.i 0.0244741 0.0336857i
\(673\) −1.26584e7 4.11296e6i −1.07731 0.350039i −0.283980 0.958830i \(-0.591655\pi\)
−0.793331 + 0.608791i \(0.791655\pi\)
\(674\) 1.25694e6 0.106578
\(675\) −1.32657e7 + 6.12394e6i −1.12065 + 0.517334i
\(676\) −1.46066e7 −1.22937
\(677\) 1.96185e6 + 637444.i 0.164511 + 0.0534528i 0.390114 0.920766i \(-0.372435\pi\)
−0.225604 + 0.974219i \(0.572435\pi\)
\(678\) 973387. 1.33975e6i 0.0813226 0.111931i
\(679\) −350308. 254514.i −0.0291592 0.0211854i
\(680\) −24284.9 409982.i −0.00201402 0.0340011i
\(681\) 6.10141e6 4.43294e6i 0.504153 0.366289i
\(682\) 1.66508e6i 0.137080i
\(683\) −2.52350e6 3.47329e6i −0.206991 0.284898i 0.692882 0.721051i \(-0.256341\pi\)
−0.899873 + 0.436153i \(0.856341\pi\)
\(684\) 2.21842e6 + 6.82758e6i 0.181302 + 0.557990i
\(685\) −3.95774e6 + 3.24976e6i −0.322271 + 0.264621i
\(686\) 64614.5 198863.i 0.00524227 0.0161341i
\(687\) 1.12280e7 3.64820e6i 0.907635 0.294908i
\(688\) 1.30018e7 4.22453e6i 1.04720 0.340257i
\(689\) −4.91953e6 + 1.51408e7i −0.394798 + 1.21506i
\(690\) −2.02246e6 + 1.66067e6i −0.161717 + 0.132788i
\(691\) 2.11737e6 + 6.51660e6i 0.168695 + 0.519190i 0.999290 0.0376877i \(-0.0119992\pi\)
−0.830595 + 0.556878i \(0.811999\pi\)
\(692\) 1.13818e6 + 1.56657e6i 0.0903537 + 0.124361i
\(693\) 2.11187e6i 0.167045i
\(694\) −3767.25 + 2737.07i −0.000296911 + 0.000215718i
\(695\) −891398. 1.50487e7i −0.0700019 1.18178i
\(696\) 5.60046e6 + 4.06897e6i 0.438228 + 0.318391i
\(697\) −334139. + 459903.i −0.0260522 + 0.0358578i
\(698\) −2.01923e6 656087.i −0.156873 0.0509710i
\(699\) −9.46296e6 −0.732544
\(700\) −119369. 1.00407e6i −0.00920757 0.0774492i
\(701\) 1.07149e7 0.823554 0.411777 0.911285i \(-0.364908\pi\)
0.411777 + 0.911285i \(0.364908\pi\)
\(702\) 2.47561e6 + 804375.i 0.189601 + 0.0616050i
\(703\) 1.88332e6 2.59217e6i 0.143726 0.197822i
\(704\) −1.20143e7 8.72891e6i −0.913623 0.663786i
\(705\) −2.50075e7 3.04556e7i −1.89495 2.30778i
\(706\) −20967.3 + 15233.6i −0.00158318 + 0.00115025i
\(707\) 1.62432e6i 0.122214i
\(708\) 8.71369e6 + 1.19934e7i 0.653309 + 0.899203i
\(709\) −5.38490e6 1.65730e7i −0.402311 1.23819i −0.923120 0.384513i \(-0.874369\pi\)
0.520808 0.853674i \(-0.325631\pi\)
\(710\) −159987. 102356.i −0.0119108 0.00762022i
\(711\) 1.29080e7 3.97266e7i 0.957599 2.94719i
\(712\) −1.87925e6 + 610607.i −0.138927 + 0.0451400i
\(713\) 1.58476e7 5.14920e6i 1.16745 0.379329i
\(714\) 9427.51 29014.9i 0.000692072 0.00212998i
\(715\) 9.05961e6 + 2.31294e7i 0.662742 + 1.69200i
\(716\) 3.17118e6 + 9.75988e6i 0.231174 + 0.711479i
\(717\) 176372. + 242756.i 0.0128125 + 0.0176348i
\(718\) 195729.i 0.0141691i
\(719\) −1.47635e6 + 1.07263e6i −0.106504 + 0.0773797i −0.639763 0.768573i \(-0.720967\pi\)
0.533259 + 0.845952i \(0.320967\pi\)
\(720\) −1.26267e7 + 1.97362e7i −0.907736 + 1.41884i
\(721\) 1.12312e6 + 815996.i 0.0804617 + 0.0584588i
\(722\) 784999. 1.08046e6i 0.0560436 0.0771374i
\(723\) 1.56313e7 + 5.07892e6i 1.11211 + 0.361348i
\(724\) −7.73258e6 −0.548249
\(725\) 2.14316e7 2.54790e6i 1.51429 0.180027i
\(726\) 1.19653e6 0.0842527
\(727\) 1.57665e7 + 5.12286e6i 1.10637 + 0.359481i 0.804551 0.593884i \(-0.202406\pi\)
0.301819 + 0.953365i \(0.402406\pi\)
\(728\) −213011. + 293184.i −0.0148961 + 0.0205028i
\(729\) −1.76623e7 1.28324e7i −1.23091 0.894312i
\(730\) −915892. 238744.i −0.0636117 0.0165816i
\(731\) 2.11822e6 1.53897e6i 0.146614 0.106522i
\(732\) 3.01685e7i 2.08102i
\(733\) 6.50068e6 + 8.94742e6i 0.446888 + 0.615089i 0.971725 0.236114i \(-0.0758738\pi\)
−0.524837 + 0.851203i \(0.675874\pi\)
\(734\) 528318. + 1.62600e6i 0.0361956 + 0.111399i
\(735\) −6.08261e6 + 2.33346e7i −0.415309 + 1.59324i
\(736\) −1.69405e6 + 5.21376e6i −0.115274 + 0.354778i
\(737\) 7.06171e6 2.29449e6i 0.478896 0.155603i
\(738\) −738664. + 240007.i −0.0499236 + 0.0162212i
\(739\) −1.79983e6 + 5.53930e6i −0.121233 + 0.373116i −0.993196 0.116456i \(-0.962847\pi\)
0.871963 + 0.489571i \(0.162847\pi\)
\(740\) 1.05646e7 625782.i 0.709205 0.0420091i
\(741\) −3.89942e6 1.20012e7i −0.260888 0.802931i
\(742\) 63971.7 + 88049.5i 0.00426558 + 0.00587107i
\(743\) 1.93219e7i 1.28404i 0.766688 + 0.642019i \(0.221903\pi\)
−0.766688 + 0.642019i \(0.778097\pi\)
\(744\) −4.54710e6 + 3.30366e6i −0.301163 + 0.218808i
\(745\) −1.36743e7 + 5.35613e6i −0.902641 + 0.353558i
\(746\) −927433. 673819.i −0.0610148 0.0443299i
\(747\) 1.37374e6 1.89079e6i 0.0900749 0.123978i
\(748\) −2.77215e6 900727.i −0.181160 0.0588626i
\(749\) −629304. −0.0409879
\(750\) −485897. 2.70872e6i −0.0315421 0.175837i
\(751\) 2.01167e7 1.30154 0.650769 0.759276i \(-0.274447\pi\)
0.650769 + 0.759276i \(0.274447\pi\)
\(752\) −2.56582e7 8.33684e6i −1.65455 0.537597i
\(753\) −1.73309e7 + 2.38540e7i −1.11387 + 1.53311i
\(754\) −3.11068e6 2.26004e6i −0.199263 0.144773i
\(755\) 5.32488e6 2.08571e6i 0.339971 0.133164i
\(756\) −1.22390e6 + 889218.i −0.0778830 + 0.0565853i
\(757\) 2.30556e6i 0.146230i 0.997324 + 0.0731150i \(0.0232940\pi\)
−0.997324 + 0.0731150i \(0.976706\pi\)
\(758\) −153509. 211287.i −0.00970424 0.0133567i
\(759\) 1.15460e7 + 3.55349e7i 0.727490 + 2.23898i
\(760\) −1.15930e6 + 68670.0i −0.0728051 + 0.00431254i
\(761\) 7.73300e6 2.37997e7i 0.484046 1.48974i −0.349312 0.937006i \(-0.613585\pi\)
0.833358 0.552734i \(-0.186415\pi\)
\(762\) 839242. 272686.i 0.0523600 0.0170128i
\(763\) 323911. 105245.i 0.0201426 0.00654472i
\(764\) 1.78406e6 5.49077e6i 0.110580 0.340329i
\(765\) −1.13187e6 + 4.34219e6i −0.0699268 + 0.268259i
\(766\) −9681.78 29797.5i −0.000596188 0.00183488i
\(767\) −9.73668e6 1.34014e7i −0.597616 0.822548i
\(768\) 2.39876e7i 1.46752i
\(769\) 1.09568e7 7.96056e6i 0.668139 0.485431i −0.201263 0.979537i \(-0.564504\pi\)
0.869402 + 0.494106i \(0.164504\pi\)
\(770\) 164328. + 42835.2i 0.00998814 + 0.00260360i
\(771\) −2.24855e7 1.63367e7i −1.36228 0.989754i
\(772\) 1.16264e7 1.60024e7i 0.702106 0.966366i
\(773\) 2.98451e7 + 9.69726e6i 1.79649 + 0.583714i 0.999787 0.0206598i \(-0.00657668\pi\)
0.796701 + 0.604374i \(0.206577\pi\)
\(774\) 3.57721e6 0.214631
\(775\) −3.40966e6 + 1.71882e7i −0.203918 + 1.02796i
\(776\) −1.64265e6 −0.0979242
\(777\) 1.50413e6 + 488720.i 0.0893782 + 0.0290407i
\(778\) 125755. 173087.i 0.00744864 0.0102522i
\(779\) 1.30046e6 + 944839.i 0.0767809 + 0.0557846i
\(780\) 2.24619e7 3.51091e7i 1.32194 2.06625i
\(781\) −2.19386e6 + 1.59393e6i −0.128701 + 0.0935067i
\(782\) 343121.i 0.0200646i
\(783\) −1.89802e7 2.61240e7i −1.10636 1.52277i
\(784\) 5.10155e6 + 1.57010e7i 0.296423 + 0.912297i
\(785\) −6.97276e6 1.78016e7i −0.403860 1.03106i
\(786\) 60851.0 187280.i 0.00351327 0.0108127i
\(787\) 6.90320e6 2.24299e6i 0.397295 0.129089i −0.103553 0.994624i \(-0.533021\pi\)
0.500849 + 0.865535i \(0.333021\pi\)
\(788\) 2.76364e6 897962.i 0.158550 0.0515161i
\(789\) −5.06600e6 + 1.55916e7i −0.289716 + 0.891655i
\(790\) 2.82937e6 + 1.81016e6i 0.161296 + 0.103193i
\(791\) −332332. 1.02281e6i −0.0188856 0.0581238i
\(792\) −4.70911e6 6.48153e6i −0.266763 0.367168i
\(793\) 3.37103e7i 1.90362i
\(794\) 1.22288e6 888473.i 0.0688386 0.0500141i
\(795\) −1.59802e7 1.94616e7i −0.896736 1.09210i
\(796\) 924140. + 671427.i 0.0516958 + 0.0375592i
\(797\) 8.03646e6 1.10612e7i 0.448145 0.616819i −0.523852 0.851809i \(-0.675506\pi\)
0.971998 + 0.234990i \(0.0755057\pi\)
\(798\) −82044.9 26658.0i −0.00456084 0.00148191i
\(799\) −5.16697e6 −0.286331
\(800\) −3.91549e6 4.23133e6i −0.216302 0.233750i
\(801\) 2.15892e7 1.18893
\(802\) −933562. 303333.i −0.0512516 0.0166527i
\(803\) −7.94329e6 + 1.09330e7i −0.434722 + 0.598343i
\(804\) −1.00792e7 7.32296e6i −0.549903 0.399528i
\(805\) 100489. + 1.69648e6i 0.00546550 + 0.0922696i
\(806\) 2.52561e6 1.83496e6i 0.136939 0.0994923i
\(807\) 4.68121e7i 2.53031i
\(808\) 3.62194e6 + 4.98518e6i 0.195170 + 0.268629i
\(809\) −2.55585e6 7.86611e6i −0.137298 0.422560i 0.858642 0.512575i \(-0.171308\pi\)
−0.995940 + 0.0900150i \(0.971308\pi\)
\(810\) −466812. + 383306.i −0.0249994 + 0.0205273i
\(811\) −5.46738e6 + 1.68269e7i −0.291895 + 0.898362i 0.692351 + 0.721561i \(0.256575\pi\)
−0.984247 + 0.176801i \(0.943425\pi\)
\(812\) 2.12529e6 690548.i 0.113117 0.0367539i
\(813\) −4.22127e7 + 1.37157e7i −2.23984 + 0.727768i
\(814\) −549251. + 1.69042e6i −0.0290543 + 0.0894199i
\(815\) 1.40374e7 1.15263e7i 0.740276 0.607851i
\(816\) 1.49334e6 + 4.59602e6i 0.0785114 + 0.241633i
\(817\) −4.35173e6 5.98964e6i −0.228090 0.313939i
\(818\) 3.35915e6i 0.175528i
\(819\) 3.20331e6 2.32734e6i 0.166874 0.121241i
\(820\) 313947. + 5.30010e6i 0.0163050 + 0.275264i
\(821\) −5.81242e6 4.22297e6i −0.300953 0.218655i 0.427052 0.904227i \(-0.359552\pi\)
−0.728005 + 0.685572i \(0.759552\pi\)
\(822\) −848232. + 1.16749e6i −0.0437860 + 0.0602662i
\(823\) −1.11178e7 3.61240e6i −0.572163 0.185907i 0.00862362 0.999963i \(-0.497255\pi\)
−0.580787 + 0.814056i \(0.697255\pi\)
\(824\) 5.26650e6 0.270211
\(825\) −3.85409e7 7.64544e6i −1.97146 0.391082i
\(826\) −113245. −0.00577524
\(827\) 2.44443e7 + 7.94242e6i 1.24283 + 0.403821i 0.855348 0.518055i \(-0.173344\pi\)
0.387486 + 0.921876i \(0.373344\pi\)
\(828\) 2.34253e7 3.22421e7i 1.18743 1.63436i
\(829\) −2.64197e7 1.91951e7i −1.33519 0.970070i −0.999606 0.0280591i \(-0.991067\pi\)
−0.335581 0.942011i \(-0.608933\pi\)
\(830\) 119262. + 145244.i 0.00600906 + 0.00731818i
\(831\) −3.87428e7 + 2.81483e7i −1.94620 + 1.41400i
\(832\) 2.78429e7i 1.39446i
\(833\) 1.85847e6 + 2.55796e6i 0.0927989 + 0.127727i
\(834\) −1.31276e6 4.04025e6i −0.0653536 0.201138i
\(835\) 2.02015e7 + 1.29244e7i 1.00269 + 0.641496i
\(836\) −2.54697e6 + 7.83877e6i −0.126040 + 0.387911i
\(837\) 2.49344e7 8.10166e6i 1.23022 0.399724i
\(838\) −2.45041e6 + 796187.i −0.120539 + 0.0391656i
\(839\) 2.08425e6 6.41467e6i 0.102222 0.314608i −0.886846 0.462065i \(-0.847109\pi\)
0.989068 + 0.147457i \(0.0471088\pi\)
\(840\) −209064. 533745.i −0.0102231 0.0260997i
\(841\) 8.40129e6 + 2.58565e7i 0.409596 + 1.26061i
\(842\) 2.15738e6 + 2.96938e6i 0.104869 + 0.144339i
\(843\) 2.52166e7i 1.22213i
\(844\) −1.37077e7 + 9.95919e6i −0.662380 + 0.481247i
\(845\) −1.39132e7 + 2.17470e7i −0.670325 + 1.04775i
\(846\) −5.71118e6 4.14942e6i −0.274347 0.199325i
\(847\) 456737. 628645.i 0.0218755 0.0301090i
\(848\) −1.63960e7 5.32737e6i −0.782974 0.254404i
\(849\) 5.18646e7 2.46946
\(850\) −314914. 176145.i −0.0149501 0.00836226i
\(851\) −1.77873e7 −0.841952
\(852\) 4.32735e6 + 1.40604e6i 0.204232 + 0.0663590i
\(853\) −2.24918e6 + 3.09573e6i −0.105840 + 0.145677i −0.858652 0.512560i \(-0.828697\pi\)
0.752811 + 0.658236i \(0.228697\pi\)
\(854\) −186444. 135460.i −0.00874791 0.00635573i
\(855\) 1.22783e7 + 3.20058e6i 0.574413 + 0.149731i
\(856\) −1.93139e6 + 1.40324e6i −0.0900920 + 0.0654557i
\(857\) 2.45516e7i 1.14190i 0.820985 + 0.570950i \(0.193425\pi\)
−0.820985 + 0.570950i \(0.806575\pi\)
\(858\) 4.11452e6 + 5.66314e6i 0.190810 + 0.262627i
\(859\) 4.32888e6 + 1.33229e7i 0.200167 + 0.616051i 0.999877 + 0.0156649i \(0.00498651\pi\)
−0.799710 + 0.600386i \(0.795013\pi\)
\(860\) 6.16827e6 2.36632e7i 0.284392 1.09101i
\(861\) −245185. + 754601.i −0.0112716 + 0.0346904i
\(862\) −3.16144e6 + 1.02721e6i −0.144916 + 0.0470861i
\(863\) 1.50438e7 4.88804e6i 0.687593 0.223413i 0.0556765 0.998449i \(-0.482268\pi\)
0.631917 + 0.775036i \(0.282268\pi\)
\(864\) −2.66539e6 + 8.20323e6i −0.121472 + 0.373853i
\(865\) 3.41653e6 202375.i 0.155255 0.00919638i
\(866\) 216163. + 665281.i 0.00979460 + 0.0301447i
\(867\) −2.10104e7 2.89184e7i −0.949264 1.30655i
\(868\) 1.81435e6i 0.0817377i
\(869\) 3.87984e7 2.81887e7i 1.74287 1.26627i
\(870\) 5.66303e6 2.21816e6i 0.253659 0.0993563i
\(871\) 1.12625e7 + 8.18268e6i 0.503025 + 0.365469i
\(872\) 759435. 1.04527e6i 0.0338220 0.0465520i
\(873\) 1.70690e7 + 5.54606e6i 0.758007 + 0.246291i
\(874\) 970239. 0.0429635
\(875\) −1.60860e6 778679.i −0.0710279 0.0343826i
\(876\) 2.26749e7 0.998357
\(877\) −2.84130e7 9.23194e6i −1.24743 0.405316i −0.390434 0.920631i \(-0.627675\pi\)
−0.857001 + 0.515315i \(0.827675\pi\)
\(878\) −1.02808e6 + 1.41503e6i −0.0450080 + 0.0619482i
\(879\) 3.81718e7 + 2.77334e7i 1.66637 + 1.21069i
\(880\) −2.50469e7 + 9.81067e6i −1.09030 + 0.427063i
\(881\) 1.49934e6 1.08934e6i 0.0650821 0.0472849i −0.554769 0.832005i \(-0.687193\pi\)
0.619851 + 0.784720i \(0.287193\pi\)
\(882\) 4.31986e6i 0.186981i
\(883\) −1.27854e7 1.75975e7i −0.551837 0.759539i 0.438423 0.898769i \(-0.355537\pi\)
−0.990260 + 0.139230i \(0.955537\pi\)
\(884\) −1.68875e6 5.19745e6i −0.0726835 0.223697i
\(885\) 2.61563e7 1.54934e6i 1.12258 0.0664951i
\(886\) −915638. + 2.81805e6i −0.0391868 + 0.120605i
\(887\) −1.77823e7 + 5.77781e6i −0.758889 + 0.246578i −0.662802 0.748795i \(-0.730633\pi\)
−0.0960871 + 0.995373i \(0.530633\pi\)
\(888\) 5.70606e6 1.85401e6i 0.242831 0.0789006i
\(889\) 177086. 545016.i 0.00751503 0.0231289i
\(890\) −437895. + 1.67989e6i −0.0185308 + 0.0710896i
\(891\) 2.66498e6 + 8.20196e6i 0.112460 + 0.346117i
\(892\) −1.10432e7 1.51997e7i −0.464711 0.639620i
\(893\) 1.46106e7i 0.613110i
\(894\) −3.34811e6 + 2.43254e6i −0.140106 + 0.101793i
\(895\) 1.75516e7 + 4.57516e6i 0.732419 + 0.190919i
\(896\) −642584. 466864.i −0.0267399 0.0194277i
\(897\) −4.11757e7 + 5.66735e7i −1.70868 + 2.35179i
\(898\) 317478. + 103155.i 0.0131378 + 0.00426873i
\(899\) −3.87270e7 −1.59814
\(900\) 1.75659e7 + 3.80514e7i 0.722878 + 1.56590i
\(901\) −3.30177e6 −0.135499
\(902\) −848063. 275552.i −0.0347066 0.0112769i
\(903\) 2.14800e6 2.95646e6i 0.0876626 0.120657i
\(904\) −3.30065e6 2.39806e6i −0.134332 0.0975976i
\(905\) −7.36550e6 + 1.15126e7i −0.298938 + 0.467254i
\(906\) 1.30378e6 947249.i 0.0527695 0.0383393i
\(907\) 2.53652e7i 1.02381i 0.859041 + 0.511906i \(0.171060\pi\)
−0.859041 + 0.511906i \(0.828940\pi\)
\(908\) −5.42862e6 7.47185e6i −0.218512 0.300756i
\(909\) −2.08048e7 6.40306e7i −0.835129 2.57026i
\(910\) 116121. + 296460.i 0.00464844 + 0.0118676i
\(911\) 5.87458e6 1.80801e7i 0.234521 0.721780i −0.762664 0.646795i \(-0.776109\pi\)
0.997185 0.0749853i \(-0.0238910\pi\)
\(912\) 1.29961e7 4.22269e6i 0.517399 0.168113i
\(913\) 2.55196e6 829183.i 0.101320 0.0329210i
\(914\) 1.06646e6 3.28222e6i 0.0422258 0.129958i
\(915\) 4.49164e7 + 2.87364e7i 1.77358 + 1.13469i
\(916\) −4.46763e6 1.37499e7i −0.175929 0.541455i
\(917\) −75166.9 103458.i −0.00295191 0.00406296i
\(918\) 539861.i 0.0211434i
\(919\) −2.34824e7 + 1.70610e7i −0.917179 + 0.666370i −0.942820 0.333302i \(-0.891837\pi\)
0.0256412 + 0.999671i \(0.491837\pi\)
\(920\) 4.09126e6 + 4.98258e6i 0.159363 + 0.194082i
\(921\) 1.52288e7 + 1.10644e7i 0.591586 + 0.429812i
\(922\) 1.55412e6 2.13907e6i 0.0602086 0.0828700i
\(923\) −4.83539e6 1.57111e6i −0.186822 0.0607020i
\(924\) −4.06830e6 −0.156759
\(925\) 9.13134e6 1.63251e7i 0.350897 0.627338i
\(926\) 79667.5 0.00305319
\(927\) −5.47251e7 1.77812e7i −2.09164 0.679615i
\(928\) 7.48892e6 1.03076e7i 0.285463 0.392906i
\(929\) 3.63789e7 + 2.64308e7i 1.38296 + 1.00478i 0.996596 + 0.0824362i \(0.0262701\pi\)
0.386367 + 0.922345i \(0.373730\pi\)
\(930\) 291987. + 4.92939e6i 0.0110702 + 0.186890i
\(931\) 7.23311e6 5.25517e6i 0.273496 0.198707i
\(932\) 1.15884e7i 0.437003i
\(933\) 3.94821e7 + 5.43424e7i 1.48490 + 2.04378i
\(934\) 231751. + 713256.i 0.00869269 + 0.0267534i
\(935\) −3.98160e6 + 3.26934e6i −0.148946 + 0.122301i
\(936\) 4.64169e6 1.42856e7i 0.173175 0.532979i
\(937\) 2.63288e7 8.55476e6i 0.979676 0.318316i 0.224960 0.974368i \(-0.427775\pi\)
0.754716 + 0.656052i \(0.227775\pi\)
\(938\) 90513.1 29409.5i 0.00335896 0.00109139i
\(939\) 1.39516e7 4.29386e7i 0.516369 1.58922i
\(940\) −3.72963e7 + 3.06245e7i −1.37672 + 1.13044i
\(941\) 6.88171e6 + 2.11797e7i 0.253351 + 0.779733i 0.994150 + 0.108007i \(0.0344469\pi\)
−0.740799 + 0.671726i \(0.765553\pi\)
\(942\) −3.16675e6 4.35866e6i −0.116275 0.160039i
\(943\) 8.92368e6i 0.326787i
\(944\) 1.45124e7 1.05439e7i 0.530040 0.385097i
\(945\) 158108. + 2.66921e6i 0.00575937 + 0.0972307i
\(946\) 3.32264e6 + 2.41404e6i 0.120713 + 0.0877035i
\(947\) 5.05765e6 6.96126e6i 0.183263 0.252239i −0.707495 0.706719i \(-0.750175\pi\)
0.890757 + 0.454479i \(0.150175\pi\)
\(948\) −7.65292e7 2.48658e7i −2.76571 0.898633i
\(949\) −2.53370e7 −0.913249
\(950\) −498083. + 890478.i −0.0179058 + 0.0320121i
\(951\) −4.34011e7 −1.55614
\(952\) −71481.8 23225.8i −0.00255625 0.000830575i
\(953\) 2.26445e7 3.11674e7i 0.807662 1.11165i −0.184018 0.982923i \(-0.558910\pi\)
0.991680 0.128728i \(-0.0410895\pi\)
\(954\) −3.64953e6 2.65154e6i −0.129827 0.0943251i
\(955\) −6.47555e6 7.88629e6i −0.229757 0.279811i
\(956\) 297281. 215987.i 0.0105202 0.00764335i
\(957\) 8.68370e7i 3.06496i
\(958\) −3.51400e6 4.83661e6i −0.123705 0.170266i
\(959\) 289601. + 891301.i 0.0101684 + 0.0312952i
\(960\) 3.70985e7 + 2.37347e7i 1.29921 + 0.831199i
\(961\) 869529. 2.67614e6i 0.0303722 0.0934759i
\(962\) −3.16934e6 + 1.02978e6i −0.110416 + 0.0358762i
\(963\) 2.48072e7 8.06034e6i 0.862009 0.280084i
\(964\) 6.21969e6 1.91423e7i 0.215564 0.663438i
\(965\) −1.27506e7 3.25527e7i −0.440771 1.12530i
\(966\) 147990. + 455467.i 0.00510258 + 0.0157041i
\(967\) 2.73456e7 + 3.76380e7i 0.940420 + 1.29438i 0.955654 + 0.294493i \(0.0951506\pi\)
−0.0152342 + 0.999884i \(0.504849\pi\)
\(968\) 2.94781e6i 0.101114i
\(969\) 2.11729e6 1.53830e6i 0.0724388 0.0526299i
\(970\) −777759. + 1.21568e6i −0.0265409 + 0.0414848i
\(971\) −2.67019e7 1.94001e7i −0.908854 0.660321i 0.0318711 0.999492i \(-0.489853\pi\)
−0.940725 + 0.339171i \(0.889853\pi\)
\(972\) −1.26162e7 + 1.73647e7i −0.428313 + 0.589523i
\(973\) −2.62380e6 852524.i −0.0888482 0.0288685i
\(974\) −78318.8 −0.00264526
\(975\) −3.08765e7 6.68848e7i −1.04020 2.25328i
\(976\) 3.65050e7 1.22667
\(977\) −5.29689e7 1.72106e7i −1.77535 0.576846i −0.776754 0.629804i \(-0.783135\pi\)
−0.998597 + 0.0529575i \(0.983135\pi\)
\(978\) 3.00854e6 4.14090e6i 0.100579 0.138435i
\(979\) 2.00528e7 + 1.45692e7i 0.668681 + 0.485826i
\(980\) 2.85758e7 + 7.44882e6i 0.950459 + 0.247755i
\(981\) −1.14206e7 + 8.29753e6i −0.378892 + 0.275281i
\(982\) 5.96784e6i 0.197487i
\(983\) −1.08279e7 1.49033e7i −0.357405 0.491926i 0.592018 0.805925i \(-0.298331\pi\)
−0.949423 + 0.313998i \(0.898331\pi\)
\(984\) 930134. + 2.86266e6i 0.0306237 + 0.0942501i
\(985\) 1.29552e6 4.96998e6i 0.0425454 0.163216i
\(986\) 246426. 758421.i 0.00807224 0.0248438i
\(987\) −6.85875e6 + 2.22854e6i −0.224105 + 0.0728162i
\(988\) −1.46968e7 + 4.77526e6i −0.478993 + 0.155634i
\(989\) −1.27008e7 + 3.90890e7i −0.412895 + 1.27076i
\(990\) −7.02646e6 + 416206.i −0.227850 + 0.0134965i
\(991\) −1.97903e6 6.09084e6i −0.0640132 0.197012i 0.913935 0.405861i \(-0.133028\pi\)
−0.977948 + 0.208849i \(0.933028\pi\)
\(992\) 6.08037e6 + 8.36891e6i 0.196178 + 0.270016i
\(993\) 4.37817e7i 1.40903i
\(994\) −28119.7 + 20430.2i −0.000902703 + 0.000655852i
\(995\) 1.87992e6 736351.i 0.0601980 0.0235791i
\(996\) −3.64242e6 2.64637e6i −0.116343 0.0845284i
\(997\) −3.23734e6 + 4.45582e6i −0.103146 + 0.141968i −0.857470 0.514534i \(-0.827965\pi\)
0.754324 + 0.656502i \(0.227965\pi\)
\(998\) −3.37690e6 1.09722e6i −0.107323 0.0348713i
\(999\) −2.79863e7 −0.887221
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 25.6.e.a.4.6 48
25.12 odd 20 625.6.a.g.1.26 48
25.13 odd 20 625.6.a.g.1.23 48
25.19 even 10 inner 25.6.e.a.19.6 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
25.6.e.a.4.6 48 1.1 even 1 trivial
25.6.e.a.19.6 yes 48 25.19 even 10 inner
625.6.a.g.1.23 48 25.13 odd 20
625.6.a.g.1.26 48 25.12 odd 20