Properties

Label 49.6.e.a.8.16
Level $49$
Weight $6$
Character 49.8
Analytic conductor $7.859$
Analytic rank $0$
Dimension $138$
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] = [49,6,Mod(8,49)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(49, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([12]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("49.8");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 49 = 7^{2} \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 49.e (of order \(7\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(7.85880717084\)
Analytic rank: \(0\)
Dimension: \(138\)
Relative dimension: \(23\) over \(\Q(\zeta_{7})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label 8.16
Character \(\chi\) \(=\) 49.8
Dual form 49.6.e.a.43.16

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.96579 + 3.71898i) q^{2} +(-21.3031 + 10.2591i) q^{3} +(2.08576 - 9.13830i) q^{4} +(-47.1674 + 22.7146i) q^{5} +(-101.334 - 48.7998i) q^{6} +(76.1422 - 104.925i) q^{7} +(177.313 - 85.3894i) q^{8} +(197.068 - 247.115i) q^{9} +O(q^{10})\) \(q+(2.96579 + 3.71898i) q^{2} +(-21.3031 + 10.2591i) q^{3} +(2.08576 - 9.13830i) q^{4} +(-47.1674 + 22.7146i) q^{5} +(-101.334 - 48.7998i) q^{6} +(76.1422 - 104.925i) q^{7} +(177.313 - 85.3894i) q^{8} +(197.068 - 247.115i) q^{9} +(-224.364 - 108.048i) q^{10} +(-36.0209 - 45.1687i) q^{11} +(49.3171 + 216.072i) q^{12} +(-251.057 - 314.816i) q^{13} +(616.037 - 28.0152i) q^{14} +(771.783 - 967.785i) q^{15} +(573.192 + 276.035i) q^{16} +(-305.919 - 1340.32i) q^{17} +1503.48 q^{18} -1353.35 q^{19} +(109.193 + 478.407i) q^{20} +(-545.633 + 3016.39i) q^{21} +(61.1514 - 267.922i) q^{22} +(358.676 - 1571.46i) q^{23} +(-2901.31 + 3638.13i) q^{24} +(-239.598 + 300.446i) q^{25} +(426.211 - 1867.35i) q^{26} +(-384.465 + 1684.45i) q^{27} +(-800.026 - 914.660i) q^{28} +(-1224.78 - 5366.13i) q^{29} +5888.12 q^{30} -3747.05 q^{31} +(-727.968 - 3189.44i) q^{32} +(1230.75 + 592.696i) q^{33} +(4077.33 - 5112.81i) q^{34} +(-1208.09 + 6678.60i) q^{35} +(-1847.18 - 2316.29i) q^{36} +(3321.97 + 14554.5i) q^{37} +(-4013.74 - 5033.07i) q^{38} +(8578.02 + 4130.96i) q^{39} +(-6423.80 + 8055.19i) q^{40} +(2329.35 - 1121.76i) q^{41} +(-12836.1 + 6916.77i) q^{42} +(-14161.8 - 6819.98i) q^{43} +(-487.896 + 234.958i) q^{44} +(-3682.04 + 16132.1i) q^{45} +(6907.98 - 3326.71i) q^{46} +(10028.5 + 12575.3i) q^{47} -15042.6 q^{48} +(-5211.72 - 15978.5i) q^{49} -1827.95 q^{50} +(20267.4 + 25414.6i) q^{51} +(-3400.53 + 1637.61i) q^{52} +(2253.39 - 9872.73i) q^{53} +(-7404.68 + 3565.91i) q^{54} +(2725.00 + 1312.29i) q^{55} +(4541.48 - 25106.4i) q^{56} +(28830.6 - 13884.1i) q^{57} +(16324.1 - 20469.7i) q^{58} +(31818.2 + 15322.9i) q^{59} +(-7234.16 - 9071.35i) q^{60} +(-1467.62 - 6430.07i) q^{61} +(-11113.0 - 13935.2i) q^{62} +(-10923.5 - 39493.3i) q^{63} +(22395.6 - 28083.2i) q^{64} +(18992.6 + 9146.37i) q^{65} +(1445.91 + 6334.93i) q^{66} -48864.5 q^{67} -12886.3 q^{68} +(8480.78 + 37156.7i) q^{69} +(-28420.5 + 15314.5i) q^{70} +(14863.5 - 65121.1i) q^{71} +(13841.7 - 60644.2i) q^{72} +(33619.5 - 42157.5i) q^{73} +(-44275.6 + 55519.8i) q^{74} +(2021.90 - 8858.50i) q^{75} +(-2822.75 + 12367.3i) q^{76} +(-7482.06 + 340.258i) q^{77} +(10077.6 + 44153.0i) q^{78} -51393.3 q^{79} -33306.0 q^{80} +(8000.28 + 35051.5i) q^{81} +(11080.2 + 5335.92i) q^{82} +(-52764.2 + 66164.2i) q^{83} +(26426.6 + 11277.6i) q^{84} +(44874.2 + 56270.5i) q^{85} +(-16637.6 - 72894.2i) q^{86} +(81143.2 + 101750. i) q^{87} +(-10243.9 - 4933.20i) q^{88} +(45615.4 - 57199.9i) q^{89} +(-70915.1 + 34150.9i) q^{90} +(-52148.3 + 2371.52i) q^{91} +(-13612.4 - 6555.37i) q^{92} +(79824.0 - 38441.2i) q^{93} +(-17025.0 + 74591.4i) q^{94} +(63833.8 - 30740.8i) q^{95} +(48228.6 + 60476.8i) q^{96} -10722.3 q^{97} +(43967.0 - 66771.2i) q^{98} -18260.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 138 q - 5 q^{2} + 13 q^{3} - 389 q^{4} + 67 q^{5} + 331 q^{6} - 56 q^{7} + 305 q^{8} - 918 q^{9} - 771 q^{10} + 410 q^{11} - 1316 q^{12} + 483 q^{13} + 2597 q^{14} + 2557 q^{15} - 7357 q^{16} - 1422 q^{17} - 2480 q^{18} - 6758 q^{19} - 3647 q^{20} - 399 q^{21} - 857 q^{22} - 2392 q^{23} - 3571 q^{24} - 8066 q^{25} - 343 q^{26} + 16396 q^{27} + 32102 q^{28} + 30341 q^{29} + 13716 q^{30} - 32712 q^{31} - 26993 q^{32} - 16775 q^{33} + 35163 q^{34} - 12019 q^{35} + 35461 q^{36} - 34872 q^{37} + 13383 q^{38} - 20671 q^{39} + 165169 q^{40} + 51233 q^{41} - 13741 q^{42} - 17203 q^{43} - 4267 q^{44} + 30777 q^{45} - 74611 q^{46} + 64264 q^{47} - 247084 q^{48} - 70350 q^{49} - 263036 q^{50} - 57453 q^{51} - 36043 q^{52} + 124590 q^{53} + 144840 q^{54} + 90977 q^{55} + 404404 q^{56} - 103899 q^{57} + 24861 q^{58} - 8079 q^{59} + 72065 q^{60} - 236659 q^{61} - 173227 q^{62} - 119805 q^{63} + 105381 q^{64} - 33383 q^{65} + 536577 q^{66} + 19716 q^{67} - 256340 q^{68} - 202795 q^{69} + 194803 q^{70} + 61778 q^{71} - 392108 q^{72} - 157760 q^{73} - 328319 q^{74} + 355167 q^{75} - 61334 q^{76} - 24402 q^{77} + 497217 q^{78} - 73876 q^{79} - 1340760 q^{80} - 815116 q^{81} + 248976 q^{82} + 303107 q^{83} + 1250354 q^{84} + 205487 q^{85} + 1083219 q^{86} + 197027 q^{87} + 1052915 q^{88} + 219783 q^{89} + 82170 q^{90} - 837235 q^{91} + 35936 q^{92} + 138365 q^{93} - 571908 q^{94} - 610016 q^{95} - 1054494 q^{96} + 762020 q^{97} - 2160767 q^{98} - 1090772 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).

\(n\) \(3\)
\(\chi(n)\) \(e\left(\frac{6}{7}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.96579 + 3.71898i 0.524282 + 0.657429i 0.971512 0.236990i \(-0.0761609\pi\)
−0.447230 + 0.894419i \(0.647589\pi\)
\(3\) −21.3031 + 10.2591i −1.36660 + 0.658119i −0.966097 0.258178i \(-0.916878\pi\)
−0.400500 + 0.916297i \(0.631164\pi\)
\(4\) 2.08576 9.13830i 0.0651799 0.285572i
\(5\) −47.1674 + 22.7146i −0.843756 + 0.406331i −0.805256 0.592927i \(-0.797972\pi\)
−0.0384996 + 0.999259i \(0.512258\pi\)
\(6\) −101.334 48.7998i −1.14915 0.553401i
\(7\) 76.1422 104.925i 0.587328 0.809349i
\(8\) 177.313 85.3894i 0.979525 0.471714i
\(9\) 197.068 247.115i 0.810978 1.01693i
\(10\) −224.364 108.048i −0.709500 0.341677i
\(11\) −36.0209 45.1687i −0.0897579 0.112553i 0.734925 0.678149i \(-0.237218\pi\)
−0.824682 + 0.565596i \(0.808646\pi\)
\(12\) 49.3171 + 216.072i 0.0988655 + 0.433158i
\(13\) −251.057 314.816i −0.412016 0.516652i 0.531913 0.846799i \(-0.321473\pi\)
−0.943930 + 0.330147i \(0.892902\pi\)
\(14\) 616.037 28.0152i 0.840015 0.0382009i
\(15\) 771.783 967.785i 0.885660 1.11058i
\(16\) 573.192 + 276.035i 0.559758 + 0.269565i
\(17\) −305.919 1340.32i −0.256735 1.12483i −0.924718 0.380652i \(-0.875700\pi\)
0.667984 0.744176i \(-0.267158\pi\)
\(18\) 1503.48 1.09374
\(19\) −1353.35 −0.860053 −0.430027 0.902816i \(-0.641496\pi\)
−0.430027 + 0.902816i \(0.641496\pi\)
\(20\) 109.193 + 478.407i 0.0610409 + 0.267438i
\(21\) −545.633 + 3016.39i −0.269993 + 1.49259i
\(22\) 61.1514 267.922i 0.0269370 0.118019i
\(23\) 358.676 1571.46i 0.141378 0.619418i −0.853738 0.520703i \(-0.825670\pi\)
0.995116 0.0987147i \(-0.0314731\pi\)
\(24\) −2901.31 + 3638.13i −1.02817 + 1.28929i
\(25\) −239.598 + 300.446i −0.0766714 + 0.0961429i
\(26\) 426.211 1867.35i 0.123649 0.541743i
\(27\) −384.465 + 1684.45i −0.101496 + 0.444681i
\(28\) −800.026 914.660i −0.192845 0.220478i
\(29\) −1224.78 5366.13i −0.270436 1.18486i −0.909500 0.415704i \(-0.863535\pi\)
0.639064 0.769154i \(-0.279322\pi\)
\(30\) 5888.12 1.19446
\(31\) −3747.05 −0.700302 −0.350151 0.936693i \(-0.613870\pi\)
−0.350151 + 0.936693i \(0.613870\pi\)
\(32\) −727.968 3189.44i −0.125672 0.550604i
\(33\) 1230.75 + 592.696i 0.196736 + 0.0947430i
\(34\) 4077.33 5112.81i 0.604893 0.758511i
\(35\) −1208.09 + 6678.60i −0.166697 + 0.921543i
\(36\) −1847.18 2316.29i −0.237548 0.297876i
\(37\) 3321.97 + 14554.5i 0.398925 + 1.74780i 0.631644 + 0.775259i \(0.282380\pi\)
−0.232719 + 0.972544i \(0.574762\pi\)
\(38\) −4013.74 5033.07i −0.450910 0.565424i
\(39\) 8578.02 + 4130.96i 0.903079 + 0.434900i
\(40\) −6423.80 + 8055.19i −0.634808 + 0.796023i
\(41\) 2329.35 1121.76i 0.216409 0.104217i −0.322539 0.946556i \(-0.604536\pi\)
0.538948 + 0.842339i \(0.318822\pi\)
\(42\) −12836.1 + 6916.77i −1.12282 + 0.605035i
\(43\) −14161.8 6819.98i −1.16802 0.562487i −0.253618 0.967304i \(-0.581621\pi\)
−0.914397 + 0.404818i \(0.867335\pi\)
\(44\) −487.896 + 234.958i −0.0379923 + 0.0182961i
\(45\) −3682.04 + 16132.1i −0.271055 + 1.18757i
\(46\) 6907.98 3326.71i 0.481345 0.231804i
\(47\) 10028.5 + 12575.3i 0.662202 + 0.830375i 0.993581 0.113123i \(-0.0360854\pi\)
−0.331379 + 0.943498i \(0.607514\pi\)
\(48\) −15042.6 −0.942370
\(49\) −5211.72 15978.5i −0.310092 0.950707i
\(50\) −1827.95 −0.103405
\(51\) 20267.4 + 25414.6i 1.09112 + 1.36822i
\(52\) −3400.53 + 1637.61i −0.174396 + 0.0839849i
\(53\) 2253.39 9872.73i 0.110191 0.482778i −0.889476 0.456981i \(-0.848931\pi\)
0.999667 0.0257968i \(-0.00821229\pi\)
\(54\) −7404.68 + 3565.91i −0.345559 + 0.166412i
\(55\) 2725.00 + 1312.29i 0.121467 + 0.0584956i
\(56\) 4541.48 25106.4i 0.193521 1.06983i
\(57\) 28830.6 13884.1i 1.17535 0.566017i
\(58\) 16324.1 20469.7i 0.637175 0.798992i
\(59\) 31818.2 + 15322.9i 1.19000 + 0.573073i 0.920809 0.390015i \(-0.127530\pi\)
0.269189 + 0.963087i \(0.413244\pi\)
\(60\) −7234.16 9071.35i −0.259424 0.325307i
\(61\) −1467.62 6430.07i −0.0504998 0.221254i 0.943381 0.331711i \(-0.107626\pi\)
−0.993881 + 0.110457i \(0.964769\pi\)
\(62\) −11113.0 13935.2i −0.367156 0.460399i
\(63\) −10923.5 39493.3i −0.346745 1.25364i
\(64\) 22395.6 28083.2i 0.683460 0.857031i
\(65\) 18992.6 + 9146.37i 0.557573 + 0.268513i
\(66\) 1445.91 + 6334.93i 0.0408583 + 0.179012i
\(67\) −48864.5 −1.32986 −0.664930 0.746905i \(-0.731539\pi\)
−0.664930 + 0.746905i \(0.731539\pi\)
\(68\) −12886.3 −0.337953
\(69\) 8480.78 + 37156.7i 0.214444 + 0.939539i
\(70\) −28420.5 + 15314.5i −0.693245 + 0.373557i
\(71\) 14863.5 65121.1i 0.349924 1.53312i −0.427426 0.904050i \(-0.640580\pi\)
0.777350 0.629068i \(-0.216563\pi\)
\(72\) 13841.7 60644.2i 0.314671 1.37866i
\(73\) 33619.5 42157.5i 0.738387 0.925908i −0.260833 0.965384i \(-0.583997\pi\)
0.999221 + 0.0394755i \(0.0125687\pi\)
\(74\) −44275.6 + 55519.8i −0.939907 + 1.17861i
\(75\) 2021.90 8858.50i 0.0415055 0.181847i
\(76\) −2822.75 + 12367.3i −0.0560582 + 0.245607i
\(77\) −7482.06 + 340.258i −0.143812 + 0.00654006i
\(78\) 10077.6 + 44153.0i 0.187552 + 0.821720i
\(79\) −51393.3 −0.926485 −0.463243 0.886232i \(-0.653314\pi\)
−0.463243 + 0.886232i \(0.653314\pi\)
\(80\) −33306.0 −0.581832
\(81\) 8000.28 + 35051.5i 0.135485 + 0.593600i
\(82\) 11080.2 + 5335.92i 0.181975 + 0.0876344i
\(83\) −52764.2 + 66164.2i −0.840706 + 1.05421i 0.157072 + 0.987587i \(0.449795\pi\)
−0.997778 + 0.0666251i \(0.978777\pi\)
\(84\) 26426.6 + 11277.6i 0.408642 + 0.174389i
\(85\) 44874.2 + 56270.5i 0.673674 + 0.844760i
\(86\) −16637.6 72894.2i −0.242575 1.06279i
\(87\) 81143.2 + 101750.i 1.14935 + 1.44124i
\(88\) −10243.9 4933.20i −0.141013 0.0679082i
\(89\) 45615.4 57199.9i 0.610431 0.765456i −0.376532 0.926404i \(-0.622884\pi\)
0.986963 + 0.160947i \(0.0514549\pi\)
\(90\) −70915.1 + 34150.9i −0.922852 + 0.444422i
\(91\) −52148.3 + 2371.52i −0.660140 + 0.0300209i
\(92\) −13612.4 6555.37i −0.167673 0.0807473i
\(93\) 79824.0 38441.2i 0.957031 0.460882i
\(94\) −17025.0 + 74591.4i −0.198732 + 0.870701i
\(95\) 63833.8 30740.8i 0.725675 0.349466i
\(96\) 48228.6 + 60476.8i 0.534105 + 0.669747i
\(97\) −10722.3 −0.115707 −0.0578533 0.998325i \(-0.518426\pi\)
−0.0578533 + 0.998325i \(0.518426\pi\)
\(98\) 43967.0 66771.2i 0.462446 0.702302i
\(99\) −18260.4 −0.187251
\(100\) 2245.83 + 2816.18i 0.0224583 + 0.0281618i
\(101\) 105112. 50619.5i 1.02530 0.493758i 0.155850 0.987781i \(-0.450188\pi\)
0.869449 + 0.494023i \(0.164474\pi\)
\(102\) −34407.3 + 150748.i −0.327454 + 1.43467i
\(103\) −170795. + 82250.4i −1.58629 + 0.763915i −0.998967 0.0454416i \(-0.985531\pi\)
−0.587318 + 0.809356i \(0.699816\pi\)
\(104\) −71397.7 34383.3i −0.647293 0.311720i
\(105\) −42780.1 154669.i −0.378676 1.36908i
\(106\) 43399.5 20900.1i 0.375163 0.180669i
\(107\) −126461. + 158577.i −1.06781 + 1.33900i −0.130135 + 0.991496i \(0.541541\pi\)
−0.937680 + 0.347501i \(0.887030\pi\)
\(108\) 14591.1 + 7026.71i 0.120373 + 0.0579686i
\(109\) 130390. + 163503.i 1.05118 + 1.31814i 0.946171 + 0.323666i \(0.104915\pi\)
0.105008 + 0.994471i \(0.466513\pi\)
\(110\) 3201.39 + 14026.2i 0.0252265 + 0.110524i
\(111\) −220083. 275976.i −1.69543 2.12600i
\(112\) 72607.2 39124.6i 0.546934 0.294716i
\(113\) −39122.6 + 49058.2i −0.288225 + 0.361423i −0.904773 0.425895i \(-0.859959\pi\)
0.616547 + 0.787318i \(0.288531\pi\)
\(114\) 137140. + 66043.0i 0.988329 + 0.475954i
\(115\) 18777.3 + 82268.9i 0.132400 + 0.580084i
\(116\) −51591.9 −0.355989
\(117\) −127271. −0.859538
\(118\) 37380.7 + 163776.i 0.247140 + 1.08279i
\(119\) −163927. 69956.2i −1.06117 0.452855i
\(120\) 54208.5 237503.i 0.343648 1.50562i
\(121\) 35094.5 153759.i 0.217909 0.954723i
\(122\) 19560.6 24528.3i 0.118983 0.149199i
\(123\) −38114.4 + 47793.9i −0.227157 + 0.284846i
\(124\) −7815.44 + 34241.7i −0.0456456 + 0.199987i
\(125\) 40881.0 179111.i 0.234016 1.02529i
\(126\) 114478. 157753.i 0.642386 0.885220i
\(127\) 43210.7 + 189318.i 0.237729 + 1.04156i 0.943045 + 0.332665i \(0.107948\pi\)
−0.705316 + 0.708893i \(0.749195\pi\)
\(128\) 66174.7 0.356999
\(129\) 371658. 1.96639
\(130\) 22312.9 + 97759.3i 0.115797 + 0.507341i
\(131\) −237125. 114193.i −1.20725 0.581382i −0.281518 0.959556i \(-0.590838\pi\)
−0.925735 + 0.378173i \(0.876552\pi\)
\(132\) 7983.27 10010.7i 0.0398792 0.0500069i
\(133\) −103047. + 142001.i −0.505133 + 0.696083i
\(134\) −144922. 181726.i −0.697222 0.874289i
\(135\) −20127.4 88184.1i −0.0950505 0.416443i
\(136\) −168693. 211534.i −0.782075 0.980692i
\(137\) 139736. + 67293.3i 0.636073 + 0.306317i 0.723989 0.689811i \(-0.242307\pi\)
−0.0879163 + 0.996128i \(0.528021\pi\)
\(138\) −113033. + 141739.i −0.505251 + 0.633565i
\(139\) 253970. 122306.i 1.11492 0.536920i 0.216604 0.976260i \(-0.430502\pi\)
0.898321 + 0.439340i \(0.144788\pi\)
\(140\) 58511.3 + 24969.8i 0.252301 + 0.107670i
\(141\) −342649. 165011.i −1.45145 0.698981i
\(142\) 286266. 137858.i 1.19138 0.573736i
\(143\) −5176.53 + 22679.9i −0.0211689 + 0.0927472i
\(144\) 181170. 87246.9i 0.728082 0.350626i
\(145\) 179659. + 225286.i 0.709627 + 0.889844i
\(146\) 256491. 0.995842
\(147\) 274951. + 286926.i 1.04945 + 1.09516i
\(148\) 139932. 0.525125
\(149\) 103263. + 129487.i 0.381047 + 0.477817i 0.934958 0.354758i \(-0.115437\pi\)
−0.553912 + 0.832576i \(0.686865\pi\)
\(150\) 38941.1 18753.0i 0.141312 0.0680524i
\(151\) 15526.0 68023.6i 0.0554135 0.242783i −0.939634 0.342181i \(-0.888835\pi\)
0.995048 + 0.0993980i \(0.0316917\pi\)
\(152\) −239966. + 115562.i −0.842444 + 0.405699i
\(153\) −391500. 188536.i −1.35208 0.651129i
\(154\) −23455.6 26816.5i −0.0796975 0.0911172i
\(155\) 176739. 85112.8i 0.590884 0.284555i
\(156\) 55641.6 69772.4i 0.183058 0.229547i
\(157\) −284938. 137219.i −0.922576 0.444289i −0.0885856 0.996069i \(-0.528235\pi\)
−0.833990 + 0.551780i \(0.813949\pi\)
\(158\) −152421. 191130.i −0.485739 0.609098i
\(159\) 53280.7 + 233438.i 0.167139 + 0.732282i
\(160\) 106783. + 133902.i 0.329764 + 0.413511i
\(161\) −137576. 157289.i −0.418290 0.478226i
\(162\) −106629. + 133708.i −0.319217 + 0.400286i
\(163\) 225509. + 108599.i 0.664806 + 0.320154i 0.735678 0.677332i \(-0.236864\pi\)
−0.0708717 + 0.997485i \(0.522578\pi\)
\(164\) −5392.49 23626.0i −0.0156560 0.0685932i
\(165\) −71513.9 −0.204494
\(166\) −402551. −1.13384
\(167\) −114262. 500617.i −0.317039 1.38904i −0.842718 0.538355i \(-0.819046\pi\)
0.525679 0.850683i \(-0.323811\pi\)
\(168\) 160820. + 581436.i 0.439609 + 1.58938i
\(169\) 46541.2 203910.i 0.125349 0.549190i
\(170\) −76181.4 + 333773.i −0.202175 + 0.885785i
\(171\) −266701. + 334433.i −0.697485 + 0.874618i
\(172\) −91861.2 + 115190.i −0.236762 + 0.296890i
\(173\) 25638.1 112328.i 0.0651283 0.285346i −0.931868 0.362798i \(-0.881821\pi\)
0.996996 + 0.0774524i \(0.0246786\pi\)
\(174\) −137754. + 603539.i −0.344930 + 1.51124i
\(175\) 13281.0 + 48016.6i 0.0327819 + 0.118521i
\(176\) −8178.73 35833.4i −0.0199024 0.0871979i
\(177\) −835026. −2.00340
\(178\) 348011. 0.823271
\(179\) 4749.12 + 20807.3i 0.0110785 + 0.0485380i 0.980165 0.198183i \(-0.0635040\pi\)
−0.969087 + 0.246721i \(0.920647\pi\)
\(180\) 139740. + 67295.3i 0.321469 + 0.154811i
\(181\) −28850.0 + 36176.7i −0.0654560 + 0.0820792i −0.813482 0.581591i \(-0.802431\pi\)
0.748026 + 0.663670i \(0.231002\pi\)
\(182\) −163480. 186905.i −0.365836 0.418256i
\(183\) 97231.3 + 121924.i 0.214624 + 0.269130i
\(184\) −70588.3 309268.i −0.153705 0.673426i
\(185\) −487288. 611039.i −1.04678 1.31262i
\(186\) 379703. + 182855.i 0.804751 + 0.387548i
\(187\) −49521.1 + 62097.4i −0.103559 + 0.129858i
\(188\) 135834. 65414.2i 0.280294 0.134982i
\(189\) 147468. + 168598.i 0.300291 + 0.343319i
\(190\) 303642. + 146226.i 0.610207 + 0.293860i
\(191\) 342692. 165032.i 0.679706 0.327329i −0.0619791 0.998077i \(-0.519741\pi\)
0.741685 + 0.670748i \(0.234027\pi\)
\(192\) −188990. + 828018.i −0.369986 + 1.62101i
\(193\) 460840. 221929.i 0.890547 0.428865i 0.0680817 0.997680i \(-0.478312\pi\)
0.822466 + 0.568815i \(0.192598\pi\)
\(194\) −31800.0 39876.0i −0.0606629 0.0760688i
\(195\) −498436. −0.938691
\(196\) −156887. + 14298.9i −0.291707 + 0.0265866i
\(197\) 112791. 0.207065 0.103533 0.994626i \(-0.466985\pi\)
0.103533 + 0.994626i \(0.466985\pi\)
\(198\) −54156.5 67910.2i −0.0981721 0.123104i
\(199\) 582046. 280299.i 1.04190 0.501751i 0.166948 0.985966i \(-0.446609\pi\)
0.874949 + 0.484215i \(0.160895\pi\)
\(200\) −16828.9 + 73732.2i −0.0297496 + 0.130341i
\(201\) 1.04097e6 501303.i 1.81738 0.875206i
\(202\) 499994. + 240784.i 0.862156 + 0.415193i
\(203\) −656302. 280078.i −1.11780 0.477023i
\(204\) 274519. 132201.i 0.461846 0.222413i
\(205\) −84389.2 + 105821.i −0.140250 + 0.175868i
\(206\) −812428. 391245.i −1.33388 0.642363i
\(207\) −317648. 398318.i −0.515253 0.646107i
\(208\) −57003.9 249750.i −0.0913579 0.400265i
\(209\) 48748.7 + 61129.0i 0.0771965 + 0.0968014i
\(210\) 448334. 617813.i 0.701542 0.966739i
\(211\) −244778. + 306942.i −0.378500 + 0.474625i −0.934195 0.356762i \(-0.883881\pi\)
0.555695 + 0.831386i \(0.312452\pi\)
\(212\) −85520.0 41184.3i −0.130686 0.0629349i
\(213\) 351442. + 1.53977e6i 0.530768 + 2.32545i
\(214\) −964798. −1.44013
\(215\) 822890. 1.21408
\(216\) 75663.7 + 331504.i 0.110345 + 0.483454i
\(217\) −285309. + 393161.i −0.411307 + 0.566789i
\(218\) −221358. + 969833.i −0.315467 + 1.38215i
\(219\) −283705. + 1.24299e6i −0.399721 + 1.75129i
\(220\) 17675.8 22164.7i 0.0246219 0.0308749i
\(221\) −345150. + 432805.i −0.475366 + 0.596090i
\(222\) 373628. 1.63697e6i 0.508812 2.22925i
\(223\) −111473. + 488397.i −0.150110 + 0.657674i 0.842742 + 0.538318i \(0.180940\pi\)
−0.992852 + 0.119356i \(0.961917\pi\)
\(224\) −390082. 166468.i −0.519441 0.221673i
\(225\) 27027.8 + 118417.i 0.0355922 + 0.155940i
\(226\) −298476. −0.388721
\(227\) 1.28641e6 1.65697 0.828487 0.560008i \(-0.189202\pi\)
0.828487 + 0.560008i \(0.189202\pi\)
\(228\) −66743.2 292421.i −0.0850295 0.372539i
\(229\) 714265. + 343972.i 0.900058 + 0.433445i 0.825910 0.563802i \(-0.190662\pi\)
0.0741484 + 0.997247i \(0.476376\pi\)
\(230\) −250267. + 313824.i −0.311949 + 0.391171i
\(231\) 155901. 84007.4i 0.192229 0.103583i
\(232\) −675381. 846901.i −0.823813 1.03303i
\(233\) −224278. 982625.i −0.270643 1.18576i −0.909257 0.416236i \(-0.863349\pi\)
0.638614 0.769527i \(-0.279508\pi\)
\(234\) −377459. 473318.i −0.450640 0.565085i
\(235\) −758660. 365352.i −0.896144 0.431560i
\(236\) 206390. 258805.i 0.241217 0.302477i
\(237\) 1.09484e6 527246.i 1.26613 0.609737i
\(238\) −226007. 817116.i −0.258630 0.935064i
\(239\) 365223. + 175882.i 0.413583 + 0.199171i 0.629092 0.777331i \(-0.283427\pi\)
−0.215509 + 0.976502i \(0.569141\pi\)
\(240\) 709522. 341688.i 0.795130 0.382914i
\(241\) 155347. 680619.i 0.172290 0.754851i −0.812762 0.582595i \(-0.802037\pi\)
0.985052 0.172256i \(-0.0551056\pi\)
\(242\) 675910. 325501.i 0.741908 0.357284i
\(243\) −791797. 992883.i −0.860198 1.07865i
\(244\) −61821.0 −0.0664755
\(245\) 608769. + 635283.i 0.647944 + 0.676164i
\(246\) −290784. −0.306360
\(247\) 339768. + 426055.i 0.354356 + 0.444348i
\(248\) −664401. + 319959.i −0.685963 + 0.330343i
\(249\) 445261. 1.95082e6i 0.455110 1.99397i
\(250\) 787356. 379170.i 0.796748 0.383694i
\(251\) 709295. + 341578.i 0.710628 + 0.342221i 0.754033 0.656837i \(-0.228106\pi\)
−0.0434043 + 0.999058i \(0.513820\pi\)
\(252\) −383686. + 17448.7i −0.380605 + 0.0173086i
\(253\) −83900.7 + 40404.5i −0.0824070 + 0.0396851i
\(254\) −575917. + 722177.i −0.560113 + 0.702360i
\(255\) −1.53324e6 738372.i −1.47659 0.711090i
\(256\) −520399. 652560.i −0.496292 0.622330i
\(257\) 128581. + 563351.i 0.121435 + 0.532043i 0.998650 + 0.0519444i \(0.0165419\pi\)
−0.877215 + 0.480098i \(0.840601\pi\)
\(258\) 1.10226e6 + 1.38219e6i 1.03094 + 1.29276i
\(259\) 1.78008e6 + 759652.i 1.64888 + 0.703664i
\(260\) 123196. 154483.i 0.113022 0.141725i
\(261\) −1.56742e6 754828.i −1.42424 0.685878i
\(262\) −278579. 1.22053e6i −0.250723 1.09849i
\(263\) −651073. −0.580417 −0.290209 0.956963i \(-0.593725\pi\)
−0.290209 + 0.956963i \(0.593725\pi\)
\(264\) 268837. 0.237399
\(265\) 117969. + 516856.i 0.103194 + 0.452121i
\(266\) −833712. + 37914.3i −0.722457 + 0.0328548i
\(267\) −384935. + 1.68651e6i −0.330452 + 1.44781i
\(268\) −101919. + 446538.i −0.0866802 + 0.379771i
\(269\) 161031. 201927.i 0.135684 0.170143i −0.709347 0.704859i \(-0.751010\pi\)
0.845032 + 0.534716i \(0.179582\pi\)
\(270\) 268261. 336389.i 0.223949 0.280823i
\(271\) −310733. + 1.36141e6i −0.257018 + 1.12607i 0.667402 + 0.744697i \(0.267406\pi\)
−0.924421 + 0.381374i \(0.875451\pi\)
\(272\) 194624. 852705.i 0.159505 0.698838i
\(273\) 1.08659e6 585513.i 0.882389 0.475477i
\(274\) 164165. + 719253.i 0.132100 + 0.578769i
\(275\) 22201.3 0.0177030
\(276\) 357238. 0.282283
\(277\) 133192. + 583552.i 0.104299 + 0.456962i 0.999926 + 0.0121571i \(0.00386982\pi\)
−0.895628 + 0.444805i \(0.853273\pi\)
\(278\) 1.20807e6 + 581777.i 0.937521 + 0.451486i
\(279\) −738423. + 925953.i −0.567930 + 0.712162i
\(280\) 356072. + 1.28736e6i 0.271421 + 0.981308i
\(281\) 1.06979e6 + 1.34148e6i 0.808228 + 1.01349i 0.999490 + 0.0319473i \(0.0101709\pi\)
−0.191261 + 0.981539i \(0.561258\pi\)
\(282\) −402551. 1.76369e6i −0.301438 1.32069i
\(283\) −1.14459e6 1.43527e6i −0.849539 1.06529i −0.997090 0.0762342i \(-0.975710\pi\)
0.147551 0.989055i \(-0.452861\pi\)
\(284\) −564094. 271654.i −0.415007 0.199857i
\(285\) −1.04449e6 + 1.30975e6i −0.761715 + 0.955160i
\(286\) −99698.5 + 48012.3i −0.0720731 + 0.0347086i
\(287\) 59661.2 329822.i 0.0427551 0.236360i
\(288\) −931617. 448643.i −0.661845 0.318728i
\(289\) −423622. + 204006.i −0.298356 + 0.143680i
\(290\) −305001. + 1.33630e6i −0.212964 + 0.933058i
\(291\) 228418. 110001.i 0.158124 0.0761487i
\(292\) −315126. 395156.i −0.216285 0.271213i
\(293\) 592296. 0.403060 0.201530 0.979482i \(-0.435409\pi\)
0.201530 + 0.979482i \(0.435409\pi\)
\(294\) −251625. + 1.87349e6i −0.169780 + 1.26411i
\(295\) −1.84884e6 −1.23692
\(296\) 1.83183e6 + 2.29704e6i 1.21522 + 1.52384i
\(297\) 89933.3 43309.6i 0.0591602 0.0284900i
\(298\) −175306. + 768064.i −0.114355 + 0.501022i
\(299\) −584769. + 281610.i −0.378274 + 0.182167i
\(300\) −76734.5 36953.4i −0.0492252 0.0237056i
\(301\) −1.79390e6 + 966649.i −1.14126 + 0.614968i
\(302\) 299025. 144003.i 0.188665 0.0908561i
\(303\) −1.71992e6 + 2.15671e6i −1.07622 + 1.34954i
\(304\) −775728. 373571.i −0.481421 0.231840i
\(305\) 215280. + 269953.i 0.132512 + 0.166165i
\(306\) −459942. 2.01514e6i −0.280802 1.23027i
\(307\) −442293. 554618.i −0.267833 0.335852i 0.629668 0.776864i \(-0.283191\pi\)
−0.897501 + 0.441012i \(0.854620\pi\)
\(308\) −12496.4 + 69083.0i −0.00750598 + 0.0414949i
\(309\) 2.79465e6 3.50438e6i 1.66507 2.08793i
\(310\) 840701. + 404860.i 0.496864 + 0.239277i
\(311\) 241623. + 1.05862e6i 0.141657 + 0.620639i 0.995050 + 0.0993718i \(0.0316833\pi\)
−0.853394 + 0.521267i \(0.825460\pi\)
\(312\) 1.87373e6 1.08974
\(313\) 531682. 0.306755 0.153377 0.988168i \(-0.450985\pi\)
0.153377 + 0.988168i \(0.450985\pi\)
\(314\) −334752. 1.46664e6i −0.191601 0.839460i
\(315\) 1.41231e6 + 1.61467e6i 0.801961 + 0.916871i
\(316\) −107194. + 469647.i −0.0603882 + 0.264578i
\(317\) 41482.5 181747.i 0.0231855 0.101582i −0.962011 0.273010i \(-0.911981\pi\)
0.985197 + 0.171428i \(0.0548379\pi\)
\(318\) −710131. + 890477.i −0.393796 + 0.493804i
\(319\) −198264. + 248615.i −0.109085 + 0.136789i
\(320\) −418443. + 1.83332e6i −0.228434 + 1.00084i
\(321\) 1.06716e6 4.67555e6i 0.578054 2.53262i
\(322\) 176933. 978127.i 0.0950974 0.525721i
\(323\) 414015. + 1.81392e6i 0.220805 + 0.967411i
\(324\) 336998. 0.178346
\(325\) 154738. 0.0812623
\(326\) 264933. + 1.16075e6i 0.138068 + 0.604913i
\(327\) −4.45510e6 2.14546e6i −2.30403 1.10956i
\(328\) 317238. 397804.i 0.162817 0.204167i
\(329\) 2.08306e6 94730.4i 1.06099 0.0482502i
\(330\) −212095. 265959.i −0.107213 0.134440i
\(331\) −749294. 3.28287e6i −0.375909 1.64696i −0.709838 0.704365i \(-0.751232\pi\)
0.333929 0.942598i \(-0.391625\pi\)
\(332\) 494575. + 620178.i 0.246256 + 0.308796i
\(333\) 4.25129e6 + 2.04731e6i 2.10092 + 1.01175i
\(334\) 1.52290e6 1.90966e6i 0.746976 0.936678i
\(335\) 2.30481e6 1.10994e6i 1.12208 0.540364i
\(336\) −1.14538e6 + 1.57836e6i −0.553480 + 0.762706i
\(337\) −2.99637e6 1.44297e6i −1.43721 0.692123i −0.456886 0.889525i \(-0.651035\pi\)
−0.980323 + 0.197402i \(0.936750\pi\)
\(338\) 896369. 431669.i 0.426771 0.205522i
\(339\) 330144. 1.44646e6i 0.156029 0.683606i
\(340\) 607814. 292708.i 0.285150 0.137321i
\(341\) 134972. + 169250.i 0.0628576 + 0.0788209i
\(342\) −2.03473e6 −0.940678
\(343\) −2.07339e6 669799.i −0.951579 0.307404i
\(344\) −3.09343e6 −1.40943
\(345\) −1.24402e6 1.55995e6i −0.562702 0.705606i
\(346\) 493781. 237792.i 0.221740 0.106784i
\(347\) 594962. 2.60670e6i 0.265256 1.16216i −0.650206 0.759758i \(-0.725317\pi\)
0.915462 0.402405i \(-0.131825\pi\)
\(348\) 1.09907e6 529284.i 0.486494 0.234283i
\(349\) −559069. 269233.i −0.245698 0.118322i 0.306982 0.951715i \(-0.400681\pi\)
−0.552680 + 0.833393i \(0.686395\pi\)
\(350\) −139184. + 191799.i −0.0607323 + 0.0836904i
\(351\) 626815. 301858.i 0.271563 0.130778i
\(352\) −117841. + 147768.i −0.0506920 + 0.0635657i
\(353\) −826707. 398121.i −0.353114 0.170051i 0.248914 0.968526i \(-0.419926\pi\)
−0.602028 + 0.798475i \(0.705641\pi\)
\(354\) −2.47651e6 3.10545e6i −1.05034 1.31709i
\(355\) 778129. + 3.40921e6i 0.327703 + 1.43576i
\(356\) −427567. 536153.i −0.178805 0.224214i
\(357\) 4.20985e6 191449.i 1.74822 0.0795029i
\(358\) −63296.8 + 79371.7i −0.0261020 + 0.0327309i
\(359\) 706106. + 340043.i 0.289157 + 0.139251i 0.572839 0.819668i \(-0.305842\pi\)
−0.283682 + 0.958918i \(0.591556\pi\)
\(360\) 724636. + 3.17484e6i 0.294689 + 1.29112i
\(361\) −644550. −0.260309
\(362\) −220103. −0.0882786
\(363\) 829799. + 3.63559e6i 0.330527 + 1.44813i
\(364\) −87097.0 + 481493.i −0.0344548 + 0.190474i
\(365\) −628152. + 2.75211e6i −0.246793 + 1.08127i
\(366\) −165066. + 723203.i −0.0644103 + 0.282200i
\(367\) 2.10949e6 2.64522e6i 0.817548 1.02517i −0.181578 0.983376i \(-0.558121\pi\)
0.999126 0.0417961i \(-0.0133080\pi\)
\(368\) 639368. 801742.i 0.246111 0.308614i
\(369\) 181837. 796681.i 0.0695211 0.304592i
\(370\) 827251. 3.62442e6i 0.314147 1.37637i
\(371\) −864323. 988170.i −0.326018 0.372732i
\(372\) −184794. 809634.i −0.0692357 0.303341i
\(373\) 608993. 0.226642 0.113321 0.993558i \(-0.463851\pi\)
0.113321 + 0.993558i \(0.463851\pi\)
\(374\) −377808. −0.139666
\(375\) 966619. + 4.23504e6i 0.354958 + 1.55517i
\(376\) 2.85198e6 + 1.37344e6i 1.04034 + 0.501003i
\(377\) −1.38185e6 + 1.73279e6i −0.500735 + 0.627902i
\(378\) −189654. + 1.04846e6i −0.0682706 + 0.377416i
\(379\) −446650. 560082.i −0.159724 0.200287i 0.695529 0.718498i \(-0.255170\pi\)
−0.855253 + 0.518210i \(0.826598\pi\)
\(380\) −147776. 647451.i −0.0524984 0.230010i
\(381\) −2.86275e6 3.58978e6i −1.01035 1.26694i
\(382\) 1.63010e6 + 785016.i 0.571553 + 0.275245i
\(383\) −2.84865e6 + 3.57210e6i −0.992298 + 1.24430i −0.0226642 + 0.999743i \(0.507215\pi\)
−0.969634 + 0.244560i \(0.921357\pi\)
\(384\) −1.40973e6 + 678890.i −0.487874 + 0.234948i
\(385\) 345180. 186001.i 0.118685 0.0639534i
\(386\) 2.19210e6 + 1.05566e6i 0.748846 + 0.360625i
\(387\) −4.47616e6 + 2.15561e6i −1.51925 + 0.731631i
\(388\) −22364.1 + 97983.5i −0.00754175 + 0.0330426i
\(389\) −3.39420e6 + 1.63456e6i −1.13727 + 0.547680i −0.905186 0.425016i \(-0.860269\pi\)
−0.232083 + 0.972696i \(0.574554\pi\)
\(390\) −1.47825e6 1.85367e6i −0.492139 0.617122i
\(391\) −2.21598e6 −0.733035
\(392\) −2.28850e6 2.38817e6i −0.752205 0.784966i
\(393\) 6.22301e6 2.03245
\(394\) 334513. + 419466.i 0.108561 + 0.136131i
\(395\) 2.42408e6 1.16738e6i 0.781727 0.376460i
\(396\) −38086.8 + 166869.i −0.0122050 + 0.0534735i
\(397\) 523640. 252172.i 0.166746 0.0803008i −0.348649 0.937253i \(-0.613359\pi\)
0.515395 + 0.856953i \(0.327645\pi\)
\(398\) 2.76865e6 + 1.33331e6i 0.876113 + 0.421914i
\(399\) 738431. 4.08222e6i 0.232208 1.28370i
\(400\) −220269. + 106076.i −0.0688342 + 0.0331488i
\(401\) 1.58664e6 1.98958e6i 0.492740 0.617876i −0.471835 0.881687i \(-0.656408\pi\)
0.964574 + 0.263811i \(0.0849795\pi\)
\(402\) 4.95162e6 + 2.38457e6i 1.52821 + 0.735946i
\(403\) 940724. + 1.17963e6i 0.288536 + 0.361812i
\(404\) −243337. 1.06613e6i −0.0741745 0.324980i
\(405\) −1.17353e6 1.47156e6i −0.355515 0.445802i
\(406\) −904846. 3.27142e6i −0.272433 0.984967i
\(407\) 537747. 674314.i 0.160913 0.201779i
\(408\) 5.76382e6 + 2.77571e6i 1.71419 + 0.825512i
\(409\) −183660. 804665.i −0.0542882 0.237852i 0.940503 0.339785i \(-0.110354\pi\)
−0.994791 + 0.101933i \(0.967497\pi\)
\(410\) −643825. −0.189151
\(411\) −3.66718e6 −1.07085
\(412\) 395392. + 1.73233e6i 0.114759 + 0.502790i
\(413\) 4.03047e6 2.17183e6i 1.16273 0.626542i
\(414\) 539261. 2.36266e6i 0.154631 0.677485i
\(415\) 985855. 4.31931e6i 0.280991 1.23110i
\(416\) −821324. + 1.02991e6i −0.232692 + 0.291786i
\(417\) −4.15562e6 + 5.21099e6i −1.17030 + 1.46751i
\(418\) −82759.0 + 362591.i −0.0231673 + 0.101502i
\(419\) −727475. + 3.18728e6i −0.202434 + 0.886921i 0.767015 + 0.641629i \(0.221741\pi\)
−0.969449 + 0.245292i \(0.921116\pi\)
\(420\) −1.50264e6 + 68334.9i −0.415654 + 0.0189025i
\(421\) 1.06569e6 + 4.66909e6i 0.293039 + 1.28389i 0.880272 + 0.474470i \(0.157360\pi\)
−0.587233 + 0.809418i \(0.699783\pi\)
\(422\) −1.86747e6 −0.510473
\(423\) 5.08384e6 1.38147
\(424\) −443472. 1.94298e6i −0.119799 0.524872i
\(425\) 475992. + 229226.i 0.127828 + 0.0615589i
\(426\) −4.68406e6 + 5.87363e6i −1.25054 + 1.56813i
\(427\) −786426. 335609.i −0.208732 0.0890766i
\(428\) 1.18535e6 + 1.48639e6i 0.312780 + 0.392213i
\(429\) −122398. 536259.i −0.0321092 0.140680i
\(430\) 2.44052e6 + 3.06031e6i 0.636518 + 0.798168i
\(431\) −4.88006e6 2.35011e6i −1.26541 0.609391i −0.323812 0.946122i \(-0.604964\pi\)
−0.941601 + 0.336731i \(0.890679\pi\)
\(432\) −685339. + 859388.i −0.176684 + 0.221554i
\(433\) −2.83828e6 + 1.36684e6i −0.727504 + 0.350347i −0.760702 0.649101i \(-0.775145\pi\)
0.0331979 + 0.999449i \(0.489431\pi\)
\(434\) −2.30832e6 + 104974.i −0.588264 + 0.0267522i
\(435\) −6.13853e6 2.95616e6i −1.55540 0.749039i
\(436\) 1.76610e6 850511.i 0.444939 0.214271i
\(437\) −485413. + 2.12673e6i −0.121593 + 0.532732i
\(438\) −5.46407e6 + 2.63136e6i −1.36091 + 0.655382i
\(439\) 802834. + 1.00672e6i 0.198822 + 0.249315i 0.871241 0.490856i \(-0.163316\pi\)
−0.672419 + 0.740171i \(0.734745\pi\)
\(440\) 595234. 0.146574
\(441\) −4.97560e6 1.86096e6i −1.21828 0.455659i
\(442\) −2.63324e6 −0.641112
\(443\) −285572. 358097.i −0.0691364 0.0866944i 0.746061 0.665878i \(-0.231943\pi\)
−0.815197 + 0.579184i \(0.803371\pi\)
\(444\) −2.98099e6 + 1.43557e6i −0.717635 + 0.345595i
\(445\) −852285. + 3.73411e6i −0.204026 + 0.893895i
\(446\) −2.14694e6 + 1.03391e6i −0.511074 + 0.246120i
\(447\) −3.52824e6 1.69911e6i −0.835198 0.402210i
\(448\) −1.24139e6 4.48819e6i −0.292223 1.05652i
\(449\) 3.97512e6 1.91432e6i 0.930539 0.448124i 0.0937167 0.995599i \(-0.470125\pi\)
0.836822 + 0.547475i \(0.184411\pi\)
\(450\) −360230. + 451714.i −0.0838588 + 0.105156i
\(451\) −134574. 64807.3i −0.0311544 0.0150031i
\(452\) 366709. + 459838.i 0.0844258 + 0.105867i
\(453\) 367107. + 1.60840e6i 0.0840517 + 0.368255i
\(454\) 3.81523e6 + 4.78414e6i 0.868722 + 1.08934i
\(455\) 2.40583e6 1.29639e6i 0.544799 0.293566i
\(456\) 3.92648e6 4.92365e6i 0.884283 1.10886i
\(457\) 1.62445e6 + 782296.i 0.363846 + 0.175219i 0.606869 0.794802i \(-0.292425\pi\)
−0.243024 + 0.970020i \(0.578139\pi\)
\(458\) 839133. + 3.67648e6i 0.186925 + 0.818972i
\(459\) 2.37532e6 0.526247
\(460\) 790962. 0.174286
\(461\) −1.37257e6 6.01361e6i −0.300802 1.31790i −0.868920 0.494953i \(-0.835185\pi\)
0.568117 0.822948i \(-0.307672\pi\)
\(462\) 774790. + 330643.i 0.168880 + 0.0720700i
\(463\) 13406.5 58737.9i 0.00290646 0.0127340i −0.973454 0.228883i \(-0.926493\pi\)
0.976360 + 0.216149i \(0.0693498\pi\)
\(464\) 779202. 3.41391e6i 0.168018 0.736133i
\(465\) −2.89191e6 + 3.62634e6i −0.620229 + 0.777743i
\(466\) 2.98920e6 3.74834e6i 0.637662 0.799603i
\(467\) 919166. 4.02713e6i 0.195030 0.854483i −0.778812 0.627258i \(-0.784177\pi\)
0.973842 0.227226i \(-0.0729655\pi\)
\(468\) −265457. + 1.16304e6i −0.0560246 + 0.245460i
\(469\) −3.72065e6 + 5.12713e6i −0.781064 + 1.07632i
\(470\) −891290. 3.90500e6i −0.186112 0.815410i
\(471\) 7.47782e6 1.55318
\(472\) 6.95020e6 1.43596
\(473\) 202072. + 885334.i 0.0415291 + 0.181951i
\(474\) 5.20787e6 + 2.50798e6i 1.06467 + 0.512717i
\(475\) 324259. 406608.i 0.0659415 0.0826880i
\(476\) −981193. + 1.35210e6i −0.198489 + 0.273522i
\(477\) −1.99563e6 2.50244e6i −0.401592 0.503580i
\(478\) 429071. + 1.87988e6i 0.0858934 + 0.376323i
\(479\) 1.41926e6 + 1.77969e6i 0.282633 + 0.354411i 0.902801 0.430058i \(-0.141507\pi\)
−0.620168 + 0.784469i \(0.712936\pi\)
\(480\) −3.64852e6 1.75704e6i −0.722793 0.348079i
\(481\) 3.74798e6 4.69981e6i 0.738642 0.926228i
\(482\) 2.99193e6 1.44084e6i 0.586589 0.282487i
\(483\) 4.54443e6 + 1.93935e6i 0.886364 + 0.378258i
\(484\) −1.33190e6 641408.i −0.258439 0.124458i
\(485\) 505742. 243553.i 0.0976281 0.0470152i
\(486\) 1.34421e6 5.88936e6i 0.258152 1.13104i
\(487\) 7.00300e6 3.37246e6i 1.33802 0.644355i 0.378394 0.925645i \(-0.376477\pi\)
0.959623 + 0.281290i \(0.0907623\pi\)
\(488\) −809288. 1.01482e6i −0.153834 0.192902i
\(489\) −5.91818e6 −1.11922
\(490\) −557125. + 4.14811e6i −0.104824 + 0.780477i
\(491\) 4.57843e6 0.857063 0.428531 0.903527i \(-0.359031\pi\)
0.428531 + 0.903527i \(0.359031\pi\)
\(492\) 357258. + 447987.i 0.0665379 + 0.0834359i
\(493\) −6.81764e6 + 3.28320e6i −1.26333 + 0.608388i
\(494\) −576812. + 2.52718e6i −0.106345 + 0.465927i
\(495\) 861297. 414779.i 0.157994 0.0760858i
\(496\) −2.14778e6 1.03432e6i −0.392000 0.188777i
\(497\) −5.70112e6 6.51802e6i −1.03531 1.18365i
\(498\) 8.57560e6 4.12979e6i 1.54950 0.746199i
\(499\) −2.96462e6 + 3.71752e6i −0.532989 + 0.668347i −0.973310 0.229494i \(-0.926293\pi\)
0.440322 + 0.897840i \(0.354864\pi\)
\(500\) −1.55151e6 747166.i −0.277542 0.133657i
\(501\) 7.57000e6 + 9.49248e6i 1.34742 + 1.68961i
\(502\) 833294. + 3.65090e6i 0.147584 + 0.646607i
\(503\) 288083. + 361245.i 0.0507689 + 0.0636622i 0.806568 0.591142i \(-0.201323\pi\)
−0.755799 + 0.654804i \(0.772751\pi\)
\(504\) −5.30919e6 6.06993e6i −0.931005 1.06441i
\(505\) −3.80807e6 + 4.77517e6i −0.664472 + 0.833222i
\(506\) −399095. 192194.i −0.0692947 0.0333706i
\(507\) 1.10045e6 + 4.82140e6i 0.190130 + 0.833016i
\(508\) 1.82017e6 0.312935
\(509\) −7.83801e6 −1.34095 −0.670473 0.741934i \(-0.733909\pi\)
−0.670473 + 0.741934i \(0.733909\pi\)
\(510\) −1.80129e6 7.89196e6i −0.306660 1.34357i
\(511\) −1.86353e6 6.73751e6i −0.315708 1.14142i
\(512\) 1.35467e6 5.93521e6i 0.228381 1.00060i
\(513\) 520315. 2.27965e6i 0.0872916 0.382450i
\(514\) −1.71375e6 + 2.14897e6i −0.286114 + 0.358775i
\(515\) 6.18765e6 7.75907e6i 1.02803 1.28911i
\(516\) 775189. 3.39633e6i 0.128169 0.561546i
\(517\) 206777. 905947.i 0.0340232 0.149065i
\(518\) 2.45420e6 + 8.87304e6i 0.401870 + 1.45294i
\(519\) 606204. + 2.65595e6i 0.0987872 + 0.432815i
\(520\) 4.14864e6 0.672818
\(521\) −4.36566e6 −0.704622 −0.352311 0.935883i \(-0.614604\pi\)
−0.352311 + 0.935883i \(0.614604\pi\)
\(522\) −1.84143e6 8.06785e6i −0.295788 1.29593i
\(523\) 3.86256e6 + 1.86011e6i 0.617477 + 0.297361i 0.716353 0.697738i \(-0.245810\pi\)
−0.0988753 + 0.995100i \(0.531524\pi\)
\(524\) −1.53812e6 + 1.92874e6i −0.244715 + 0.306863i
\(525\) −775531. 886655.i −0.122801 0.140397i
\(526\) −1.93094e6 2.42133e6i −0.304302 0.381583i
\(527\) 1.14629e6 + 5.02224e6i 0.179792 + 0.787719i
\(528\) 541849. + 679457.i 0.0845851 + 0.106066i
\(529\) 3.45810e6 + 1.66534e6i 0.537278 + 0.258739i
\(530\) −1.57230e6 + 1.97161e6i −0.243135 + 0.304881i
\(531\) 1.00569e7 4.84313e6i 1.54784 0.745400i
\(532\) 1.08271e6 + 1.23785e6i 0.165857 + 0.189622i
\(533\) −937948. 451692.i −0.143008 0.0688691i
\(534\) −7.41373e6 + 3.57026e6i −1.12508 + 0.541810i
\(535\) 2.36281e6 1.03521e7i 0.356898 1.56367i
\(536\) −8.66430e6 + 4.17251e6i −1.30263 + 0.627314i
\(537\) −314634. 394538.i −0.0470836 0.0590410i
\(538\) 1.22855e6 0.182994
\(539\) −533999. + 810967.i −0.0791715 + 0.120235i
\(540\) −847834. −0.125120
\(541\) −6.46247e6 8.10369e6i −0.949305 1.19039i −0.981607 0.190912i \(-0.938855\pi\)
0.0323022 0.999478i \(-0.489716\pi\)
\(542\) −5.98462e6 + 2.88204e6i −0.875062 + 0.421407i
\(543\) 243456. 1.06665e6i 0.0354341 0.155247i
\(544\) −4.05216e6 + 1.95142e6i −0.587070 + 0.282718i
\(545\) −9.86405e6 4.75028e6i −1.42254 0.685059i
\(546\) 5.40011e6 + 2.30451e6i 0.775213 + 0.330824i
\(547\) −6.05595e6 + 2.91639e6i −0.865395 + 0.416752i −0.813269 0.581888i \(-0.802314\pi\)
−0.0521262 + 0.998641i \(0.516600\pi\)
\(548\) 906402. 1.13659e6i 0.128935 0.161679i
\(549\) −1.87819e6 904488.i −0.265955 0.128077i
\(550\) 65844.4 + 82566.2i 0.00928137 + 0.0116385i
\(551\) 1.65756e6 + 7.26224e6i 0.232589 + 1.01904i
\(552\) 4.67654e6 + 5.86420e6i 0.653247 + 0.819146i
\(553\) −3.91320e6 + 5.39246e6i −0.544150 + 0.749850i
\(554\) −1.77520e6 + 2.22603e6i −0.245738 + 0.308146i
\(555\) 1.66494e7 + 8.01795e6i 2.29439 + 1.10492i
\(556\) −587945. 2.57596e6i −0.0806584 0.353388i
\(557\) 5.38379e6 0.735275 0.367638 0.929969i \(-0.380167\pi\)
0.367638 + 0.929969i \(0.380167\pi\)
\(558\) −5.63360e6 −0.765951
\(559\) 1.40839e6 + 6.17058e6i 0.190632 + 0.835211i
\(560\) −2.53599e6 + 3.49465e6i −0.341726 + 0.470905i
\(561\) 417893. 1.83091e6i 0.0560607 0.245618i
\(562\) −1.81615e6 + 7.95708e6i −0.242556 + 1.06271i
\(563\) 4.87191e6 6.10919e6i 0.647782 0.812292i −0.344170 0.938907i \(-0.611840\pi\)
0.991952 + 0.126615i \(0.0404112\pi\)
\(564\) −2.22260e6 + 2.78706e6i −0.294215 + 0.368933i
\(565\) 730973. 3.20260e6i 0.0963342 0.422068i
\(566\) 1.94313e6 8.51341e6i 0.254953 1.11702i
\(567\) 4.28696e6 + 1.82947e6i 0.560004 + 0.238983i
\(568\) −2.92517e6 1.28160e7i −0.380434 1.66679i
\(569\) 7.88101e6 1.02047 0.510236 0.860034i \(-0.329558\pi\)
0.510236 + 0.860034i \(0.329558\pi\)
\(570\) −7.96867e6 −1.02730
\(571\) −1.32282e6 5.79564e6i −0.169789 0.743894i −0.986082 0.166257i \(-0.946832\pi\)
0.816293 0.577637i \(-0.196025\pi\)
\(572\) 196459. + 94609.4i 0.0251062 + 0.0120905i
\(573\) −5.60735e6 + 7.03140e6i −0.713463 + 0.894654i
\(574\) 1.40354e6 756302.i 0.177806 0.0958110i
\(575\) 386202. + 484282.i 0.0487130 + 0.0610842i
\(576\) −2.52633e6 1.10686e7i −0.317274 1.39007i
\(577\) 5.71609e6 + 7.16775e6i 0.714759 + 0.896279i 0.998029 0.0627612i \(-0.0199907\pi\)
−0.283270 + 0.959040i \(0.591419\pi\)
\(578\) −2.01507e6 970405.i −0.250882 0.120818i
\(579\) −7.54056e6 + 9.45557e6i −0.934776 + 1.17217i
\(580\) 2.43345e6 1.17189e6i 0.300368 0.144649i
\(581\) 2.92473e6 + 1.05742e7i 0.359456 + 1.29959i
\(582\) 1.08653e6 + 523245.i 0.132964 + 0.0640321i
\(583\) −527108. + 253842.i −0.0642286 + 0.0309308i
\(584\) 2.36137e6 1.03458e7i 0.286505 1.25526i
\(585\) 6.00304e6 2.89091e6i 0.725240 0.349257i
\(586\) 1.75662e6 + 2.20274e6i 0.211317 + 0.264983i
\(587\) 8.05448e6 0.964811 0.482405 0.875948i \(-0.339763\pi\)
0.482405 + 0.875948i \(0.339763\pi\)
\(588\) 3.19549e6 1.91412e6i 0.381149 0.228311i
\(589\) 5.07106e6 0.602297
\(590\) −5.48325e6 6.87578e6i −0.648497 0.813190i
\(591\) −2.40280e6 + 1.15713e6i −0.282975 + 0.136274i
\(592\) −2.11342e6 + 9.25949e6i −0.247846 + 1.08588i
\(593\) −2.50372e6 + 1.20573e6i −0.292380 + 0.140803i −0.574324 0.818628i \(-0.694735\pi\)
0.281944 + 0.959431i \(0.409021\pi\)
\(594\) 427790. + 206013.i 0.0497468 + 0.0239568i
\(595\) 9.32104e6 423888.i 1.07937 0.0490861i
\(596\) 1.39868e6 673567.i 0.161288 0.0776721i
\(597\) −9.52382e6 + 1.19425e7i −1.09364 + 1.37138i
\(598\) −2.78160e6 1.33955e6i −0.318084 0.153181i
\(599\) −1.59639e6 2.00182e6i −0.181791 0.227959i 0.682583 0.730808i \(-0.260857\pi\)
−0.864374 + 0.502849i \(0.832285\pi\)
\(600\) −397914. 1.74338e6i −0.0451244 0.197703i
\(601\) 3.02017e6 + 3.78717e6i 0.341071 + 0.427689i 0.922553 0.385870i \(-0.126099\pi\)
−0.581483 + 0.813559i \(0.697527\pi\)
\(602\) −8.91529e6 3.80462e6i −1.00264 0.427878i
\(603\) −9.62961e6 + 1.20751e7i −1.07849 + 1.35238i
\(604\) −589237. 283762.i −0.0657200 0.0316491i
\(605\) 1.83726e6 + 8.04957e6i 0.204072 + 0.894096i
\(606\) −1.31217e7 −1.45147
\(607\) −9.53447e6 −1.05033 −0.525164 0.851001i \(-0.675996\pi\)
−0.525164 + 0.851001i \(0.675996\pi\)
\(608\) 985194. + 4.31642e6i 0.108084 + 0.473548i
\(609\) 1.68546e7 766489.i 1.84152 0.0837458i
\(610\) −365474. + 1.60125e6i −0.0397678 + 0.174234i
\(611\) 1.44119e6 6.31425e6i 0.156177 0.684256i
\(612\) −2.53948e6 + 3.18440e6i −0.274073 + 0.343676i
\(613\) −5.38935e6 + 6.75803e6i −0.579276 + 0.726389i −0.981989 0.188938i \(-0.939496\pi\)
0.402714 + 0.915326i \(0.368067\pi\)
\(614\) 750866. 3.28976e6i 0.0803788 0.352163i
\(615\) 712135. 3.12007e6i 0.0759232 0.332641i
\(616\) −1.29761e6 + 699221.i −0.137782 + 0.0742443i
\(617\) 2.90362e6 + 1.27216e7i 0.307063 + 1.34533i 0.859227 + 0.511595i \(0.170945\pi\)
−0.552164 + 0.833736i \(0.686198\pi\)
\(618\) 2.13211e7 2.24563
\(619\) −2.27745e6 −0.238903 −0.119452 0.992840i \(-0.538114\pi\)
−0.119452 + 0.992840i \(0.538114\pi\)
\(620\) −409153. 1.79261e6i −0.0427470 0.187287i
\(621\) 2.50915e6 + 1.20834e6i 0.261095 + 0.125736i
\(622\) −3.22038e6 + 4.03823e6i −0.333758 + 0.418519i
\(623\) −2.52847e6 9.14155e6i −0.260998 0.943626i
\(624\) 3.77657e6 + 4.73566e6i 0.388272 + 0.486877i
\(625\) 1.87297e6 + 8.20602e6i 0.191792 + 0.840297i
\(626\) 1.57686e6 + 1.97731e6i 0.160826 + 0.201669i
\(627\) −1.66563e6 802124.i −0.169203 0.0814840i
\(628\) −1.84826e6 + 2.31765e6i −0.187010 + 0.234503i
\(629\) 1.84914e7 8.90499e6i 1.86356 0.897443i
\(630\) −1.81633e6 + 1.00411e7i −0.182324 + 1.00793i
\(631\) −5.36679e6 2.58451e6i −0.536588 0.258407i 0.145906 0.989298i \(-0.453390\pi\)
−0.682494 + 0.730891i \(0.739105\pi\)
\(632\) −9.11269e6 + 4.38844e6i −0.907515 + 0.437036i
\(633\) 2.06561e6 9.05002e6i 0.204898 0.897719i
\(634\) 798941. 384750.i 0.0789390 0.0380150i
\(635\) −6.33843e6 7.94813e6i −0.623802 0.782224i
\(636\) 2.24436e6 0.220013
\(637\) −3.72185e6 + 5.65226e6i −0.363421 + 0.551916i
\(638\) −1.51260e6 −0.147120
\(639\) −1.31633e7 1.65063e7i −1.27530 1.59918i
\(640\) −3.12129e6 + 1.50313e6i −0.301220 + 0.145060i
\(641\) 349144. 1.52970e6i 0.0335629 0.147049i −0.955370 0.295412i \(-0.904543\pi\)
0.988933 + 0.148363i \(0.0474004\pi\)
\(642\) 2.05532e7 9.89791e6i 1.96808 0.947777i
\(643\) −1.08558e7 5.22789e6i −1.03546 0.498653i −0.162639 0.986686i \(-0.552000\pi\)
−0.872825 + 0.488032i \(0.837715\pi\)
\(644\) −1.72430e6 + 929144.i −0.163832 + 0.0882812i
\(645\) −1.75302e7 + 8.44208e6i −1.65915 + 0.799006i
\(646\) −5.51804e6 + 6.91940e6i −0.520240 + 0.652360i
\(647\) 1.01071e7 + 4.86732e6i 0.949218 + 0.457119i 0.843412 0.537268i \(-0.180543\pi\)
0.105806 + 0.994387i \(0.466258\pi\)
\(648\) 4.41158e6 + 5.53195e6i 0.412721 + 0.517536i
\(649\) −454006. 1.98913e6i −0.0423107 0.185375i
\(650\) 458920. + 575468.i 0.0426043 + 0.0534242i
\(651\) 2.04451e6 1.13026e7i 0.189077 1.04526i
\(652\) 1.46277e6 1.83426e6i 0.134759 0.168982i
\(653\) −1.51055e7 7.27441e6i −1.38628 0.667598i −0.415952 0.909387i \(-0.636552\pi\)
−0.970329 + 0.241789i \(0.922266\pi\)
\(654\) −5.23394e6 2.29314e7i −0.478503 2.09646i
\(655\) 1.37784e7 1.25486
\(656\) 1.64481e6 0.149230
\(657\) −3.79244e6 1.66158e7i −0.342772 1.50178i
\(658\) 6.53022e6 + 7.46591e6i 0.587980 + 0.672230i
\(659\) −1.49197e6 + 6.53675e6i −0.133828 + 0.586338i 0.862891 + 0.505391i \(0.168652\pi\)
−0.996718 + 0.0809473i \(0.974205\pi\)
\(660\) −149161. + 653516.i −0.0133289 + 0.0583978i
\(661\) 1.17822e7 1.47744e7i 1.04888 1.31525i 0.101600 0.994825i \(-0.467604\pi\)
0.947275 0.320423i \(-0.103825\pi\)
\(662\) 9.98669e6 1.25229e7i 0.885679 1.11061i
\(663\) 2.91262e6 1.27610e7i 0.257336 1.12746i
\(664\) −3.70605e6 + 1.62373e7i −0.326206 + 1.42920i
\(665\) 1.63496e6 9.03847e6i 0.143368 0.792575i
\(666\) 4.99450e6 + 2.18823e7i 0.436321 + 1.91165i
\(667\) −8.87196e6 −0.772156
\(668\) −4.81311e6 −0.417335
\(669\) −2.63576e6 1.15480e7i −0.227688 0.997566i
\(670\) 1.09634e7 + 5.27970e6i 0.943536 + 0.454383i
\(671\) −237573. + 297907.i −0.0203700 + 0.0255432i
\(672\) 1.00178e7 455574.i 0.855754 0.0389167i
\(673\) 3.00366e6 + 3.76648e6i 0.255631 + 0.320551i 0.893042 0.449972i \(-0.148566\pi\)
−0.637411 + 0.770524i \(0.719995\pi\)
\(674\) −3.52019e6 1.54230e7i −0.298481 1.30773i
\(675\) −413970. 519102.i −0.0349711 0.0438524i
\(676\) −1.76632e6 850615.i −0.148663 0.0715923i
\(677\) 1.06593e7 1.33663e7i 0.893832 1.12083i −0.0982409 0.995163i \(-0.531322\pi\)
0.992073 0.125667i \(-0.0401070\pi\)
\(678\) 6.35848e6 3.06208e6i 0.531225 0.255825i
\(679\) −816419. + 1.12504e6i −0.0679577 + 0.0936470i
\(680\) 1.27617e7 + 6.14571e6i 1.05837 + 0.509682i
\(681\) −2.74046e7 + 1.31974e7i −2.26442 + 1.09049i
\(682\) −229137. + 1.00392e6i −0.0188640 + 0.0826488i
\(683\) 743824. 358207.i 0.0610125 0.0293821i −0.403129 0.915143i \(-0.632077\pi\)
0.464141 + 0.885761i \(0.346363\pi\)
\(684\) 2.49987e6 + 3.13474e6i 0.204304 + 0.256190i
\(685\) −8.11952e6 −0.661156
\(686\) −3.65825e6 9.69736e6i −0.296800 0.786762i
\(687\) −1.87449e7 −1.51528
\(688\) −6.23490e6 7.81832e6i −0.502179 0.629713i
\(689\) −3.67382e6 + 1.76922e6i −0.294829 + 0.141982i
\(690\) 2.11192e6 9.25294e6i 0.168871 0.739873i
\(691\) 2.12352e7 1.02263e7i 1.69185 0.814752i 0.696593 0.717466i \(-0.254698\pi\)
0.995257 0.0972855i \(-0.0310160\pi\)
\(692\) −973009. 468577.i −0.0772417 0.0371976i
\(693\) −1.39039e6 + 1.91598e6i −0.109977 + 0.151551i
\(694\) 1.14588e7 5.51826e6i 0.903108 0.434914i
\(695\) −9.20098e6 + 1.15377e7i −0.722557 + 0.906058i
\(696\) 2.30761e7 + 1.11129e7i 1.80568 + 0.869568i
\(697\) −2.21611e6 2.77891e6i −0.172786 0.216667i
\(698\) −656806. 2.87765e6i −0.0510268 0.223563i
\(699\) 1.48586e7 + 1.86321e7i 1.15023 + 1.44235i
\(700\) 466491. 21214.4i 0.0359831 0.00163638i
\(701\) 7.96376e6 9.98624e6i 0.612101 0.767551i −0.375108 0.926981i \(-0.622394\pi\)
0.987209 + 0.159431i \(0.0509658\pi\)
\(702\) 2.98160e6 + 1.43586e6i 0.228353 + 0.109969i
\(703\) −4.49577e6 1.96973e7i −0.343096 1.50320i
\(704\) −2.07519e6 −0.157807
\(705\) 1.99100e7 1.50869
\(706\) −971233. 4.25525e6i −0.0733351 0.321302i
\(707\) 2.69222e6 1.48832e7i 0.202564 1.11982i
\(708\) −1.74166e6 + 7.63072e6i −0.130581 + 0.572114i
\(709\) 4.71700e6 2.06665e7i 0.352411 1.54402i −0.419184 0.907901i \(-0.637684\pi\)
0.771595 0.636114i \(-0.219459\pi\)
\(710\) −1.03710e7 + 1.30048e7i −0.772103 + 0.968186i
\(711\) −1.01280e7 + 1.27001e7i −0.751359 + 0.942175i
\(712\) 3.20394e6 1.40374e7i 0.236856 1.03773i
\(713\) −1.34398e6 + 5.88834e6i −0.0990074 + 0.433780i
\(714\) 1.31975e7 + 1.50885e7i 0.968827 + 1.10765i
\(715\) −271001. 1.18733e6i −0.0198247 0.0868575i
\(716\) 200048. 0.0145832
\(717\) −9.58477e6 −0.696280
\(718\) 829548. + 3.63449e6i 0.0600524 + 0.263107i
\(719\) −2.04376e7 9.84224e6i −1.47437 0.710022i −0.487743 0.872987i \(-0.662180\pi\)
−0.986632 + 0.162966i \(0.947894\pi\)
\(720\) −6.56354e6 + 8.23041e6i −0.471853 + 0.591685i
\(721\) −4.37453e6 + 2.41834e7i −0.313396 + 1.73253i
\(722\) −1.91160e6 2.39707e6i −0.136475 0.171134i
\(723\) 3.67313e6 + 1.60930e7i 0.261331 + 1.14497i
\(724\) 270420. + 339096.i 0.0191731 + 0.0240423i
\(725\) 1.90569e6 + 917732.i 0.134650 + 0.0648442i
\(726\) −1.10597e7 + 1.38684e7i −0.778754 + 0.976527i
\(727\) 1.08584e7 5.22914e6i 0.761957 0.366939i −0.0122061 0.999926i \(-0.503885\pi\)
0.774163 + 0.632986i \(0.218171\pi\)
\(728\) −9.04406e6 + 4.87341e6i −0.632463 + 0.340804i
\(729\) 1.91824e7 + 9.23778e6i 1.33686 + 0.643797i
\(730\) −1.20980e7 + 5.82610e6i −0.840247 + 0.404642i
\(731\) −4.80858e6 + 2.10678e7i −0.332831 + 1.45823i
\(732\) 1.31698e6 634225.i 0.0908452 0.0437487i
\(733\) −1.37273e7 1.72134e7i −0.943678 1.18333i −0.982907 0.184105i \(-0.941061\pi\)
0.0392286 0.999230i \(-0.487510\pi\)
\(734\) 1.60938e7 1.10260
\(735\) −1.94861e7 7.28813e6i −1.33047 0.497620i
\(736\) −5.27318e6 −0.358821
\(737\) 1.76014e6 + 2.20715e6i 0.119365 + 0.149680i
\(738\) 3.50213e6 1.68654e6i 0.236696 0.113987i
\(739\) −3.07704e6 + 1.34814e7i −0.207263 + 0.908080i 0.759115 + 0.650956i \(0.225632\pi\)
−0.966379 + 0.257124i \(0.917225\pi\)
\(740\) −6.60023e6 + 3.17850e6i −0.443077 + 0.213375i
\(741\) −1.16090e7 5.59062e6i −0.776696 0.374037i
\(742\) 1.11158e6 6.14510e6i 0.0741195 0.409750i
\(743\) 682932. 328883.i 0.0453843 0.0218559i −0.411054 0.911611i \(-0.634839\pi\)
0.456438 + 0.889755i \(0.349125\pi\)
\(744\) 1.08714e7 1.36322e7i 0.720031 0.902891i
\(745\) −7.81189e6 3.76201e6i −0.515662 0.248330i
\(746\) 1.80614e6 + 2.26483e6i 0.118824 + 0.149001i
\(747\) 5.95206e6 + 2.60777e7i 0.390271 + 1.70989i
\(748\) 464176. + 582059.i 0.0303339 + 0.0380376i
\(749\) 7.00973e6 + 2.53433e7i 0.456559 + 1.65066i
\(750\) −1.28832e7 + 1.61550e7i −0.836318 + 1.04871i
\(751\) 1.11436e7 + 5.36649e6i 0.720986 + 0.347209i 0.758132 0.652101i \(-0.226112\pi\)
−0.0371457 + 0.999310i \(0.511827\pi\)
\(752\) 2.27702e6 + 9.97628e6i 0.146833 + 0.643315i
\(753\) −1.86145e7 −1.19636
\(754\) −1.05425e7 −0.675327
\(755\) 812812. + 3.56116e6i 0.0518947 + 0.227365i
\(756\) 1.84828e6 995951.i 0.117615 0.0633772i
\(757\) 2.14575e6 9.40114e6i 0.136094 0.596267i −0.860178 0.509995i \(-0.829647\pi\)
0.996272 0.0862722i \(-0.0274955\pi\)
\(758\) 758263. 3.32217e6i 0.0479343 0.210014i
\(759\) 1.37284e6 1.72148e6i 0.0864997 0.108467i
\(760\) 8.69363e6 1.09015e7i 0.545968 0.684622i
\(761\) −5.57331e6 + 2.44183e7i −0.348860 + 1.52846i 0.430912 + 0.902394i \(0.358192\pi\)
−0.779773 + 0.626063i \(0.784665\pi\)
\(762\) 4.85999e6 2.12930e7i 0.303213 1.32846i
\(763\) 2.70838e7 1.23168e6i 1.68422 0.0765925i
\(764\) −793338. 3.47584e6i −0.0491728 0.215440i
\(765\) 2.27486e7 1.40540
\(766\) −2.17330e7 −1.33828
\(767\) −3.16432e6 1.38638e7i −0.194219 0.850930i
\(768\) 1.77808e7 + 8.56278e6i 1.08780 + 0.523856i
\(769\) −1.52252e7 + 1.90918e7i −0.928425 + 1.16421i 0.0577212 + 0.998333i \(0.481617\pi\)
−0.986147 + 0.165876i \(0.946955\pi\)
\(770\) 1.71547e6 + 732079.i 0.104269 + 0.0444970i
\(771\) −8.51864e6 1.06820e7i −0.516100 0.647169i
\(772\) −1.06685e6 4.67419e6i −0.0644260 0.282269i
\(773\) 8.97241e6 + 1.12510e7i 0.540083 + 0.677242i 0.974737 0.223355i \(-0.0717010\pi\)
−0.434655 + 0.900597i \(0.643130\pi\)
\(774\) −2.12920e7 1.02537e7i −1.27751 0.615216i
\(775\) 897786. 1.12579e6i 0.0536931 0.0673290i
\(776\) −1.90120e6 + 915570.i −0.113338 + 0.0545805i
\(777\) −4.57146e7 + 2.07894e6i −2.71645 + 0.123535i
\(778\) −1.61454e7 7.77520e6i −0.956310 0.460535i
\(779\) −3.15242e6 + 1.51813e6i −0.186123 + 0.0896323i
\(780\) −1.03962e6 + 4.55486e6i −0.0611838 + 0.268064i
\(781\) −3.47683e6 + 1.67435e6i −0.203965 + 0.0982245i
\(782\) −6.57214e6 8.24120e6i −0.384317 0.481918i
\(783\) 9.50987e6 0.554332
\(784\) 1.42331e6 1.05974e7i 0.0827009 0.615755i
\(785\) 1.65567e7 0.958957
\(786\) 1.84561e7 + 2.31433e7i 1.06558 + 1.33619i
\(787\) −4.50923e6 + 2.17153e6i −0.259517 + 0.124977i −0.559119 0.829088i \(-0.688860\pi\)
0.299602 + 0.954064i \(0.403146\pi\)
\(788\) 235254. 1.03072e6i 0.0134965 0.0591321i
\(789\) 1.38699e7 6.67939e6i 0.793197 0.381983i
\(790\) 1.15308e7 + 5.55293e6i 0.657341 + 0.316559i
\(791\) 2.16857e6 + 7.84037e6i 0.123235 + 0.445549i
\(792\) −3.23781e6 + 1.55925e6i −0.183417 + 0.0883288i
\(793\) −1.65583e6 + 2.07635e6i −0.0935046 + 0.117251i
\(794\) 2.49083e6 + 1.19952e6i 0.140214 + 0.0675236i
\(795\) −7.81556e6 9.80040e6i −0.438573 0.549954i
\(796\) −1.34745e6 5.90355e6i −0.0753753 0.330241i
\(797\) 939145. + 1.17765e6i 0.0523705 + 0.0656705i 0.807327 0.590104i \(-0.200913\pi\)
−0.754956 + 0.655775i \(0.772342\pi\)
\(798\) 1.73717e7 9.36079e6i 0.965686 0.520362i
\(799\) 1.37870e7 1.72884e7i 0.764018 0.958049i
\(800\) 1.13268e6 + 545468.i 0.0625720 + 0.0301331i
\(801\) −5.14564e6 2.25445e7i −0.283373 1.24154i
\(802\) 1.21049e7 0.664544
\(803\) −3.11521e6 −0.170490
\(804\) −2.40985e6 1.05583e7i −0.131477 0.576040i
\(805\) 1.00618e7 + 4.29391e6i 0.547253 + 0.233541i
\(806\) −1.59703e6 + 6.99707e6i −0.0865918 + 0.379383i
\(807\) −1.35890e6 + 5.95371e6i −0.0734518 + 0.321813i
\(808\) 1.43154e7 1.79510e7i 0.771393 0.967297i
\(809\) 1.57180e7 1.97097e7i 0.844354 1.05879i −0.153152 0.988203i \(-0.548942\pi\)
0.997506 0.0705840i \(-0.0224863\pi\)
\(810\) 1.99227e6 8.72869e6i 0.106693 0.467452i
\(811\) −1.29696e6 + 5.68235e6i −0.0692427 + 0.303372i −0.997677 0.0681251i \(-0.978298\pi\)
0.928434 + 0.371497i \(0.121155\pi\)
\(812\) −3.92832e6 + 5.41331e6i −0.209082 + 0.288119i
\(813\) −7.34719e6 3.21901e7i −0.389848 1.70803i
\(814\) 4.10260e6 0.217019
\(815\) −1.31035e7 −0.691022
\(816\) 4.60183e6 + 2.01620e7i 0.241939 + 1.06000i
\(817\) 1.91659e7 + 9.22981e6i 1.00456 + 0.483768i
\(818\) 2.44784e6 3.06949e6i 0.127908 0.160392i
\(819\) −9.69070e6 + 1.33540e7i −0.504830 + 0.695666i
\(820\) 791006. + 991890.i 0.0410814 + 0.0515144i
\(821\) −8.03624e6 3.52091e7i −0.416097 1.82304i −0.553901 0.832583i \(-0.686861\pi\)
0.137804 0.990460i \(-0.455996\pi\)
\(822\) −1.08761e7 1.36382e7i −0.561426 0.704006i
\(823\) −1.85534e7 8.93486e6i −0.954827 0.459821i −0.109451 0.993992i \(-0.534909\pi\)
−0.845376 + 0.534172i \(0.820624\pi\)
\(824\) −2.32608e7 + 2.91681e7i −1.19346 + 1.49655i
\(825\) −472958. + 227765.i −0.0241929 + 0.0116507i
\(826\) 2.00305e7 + 8.54805e6i 1.02151 + 0.435930i
\(827\) 2.18207e7 + 1.05083e7i 1.10944 + 0.534280i 0.896615 0.442810i \(-0.146018\pi\)
0.212828 + 0.977090i \(0.431733\pi\)
\(828\) −4.30249e6 + 2.07197e6i −0.218094 + 0.105029i
\(829\) −1.42760e6 + 6.25473e6i −0.0721474 + 0.316098i −0.998105 0.0615283i \(-0.980403\pi\)
0.925958 + 0.377627i \(0.123260\pi\)
\(830\) 1.89873e7 9.14378e6i 0.956681 0.460713i
\(831\) −8.82410e6 1.10651e7i −0.443269 0.555842i
\(832\) −1.44636e7 −0.724384
\(833\) −1.98220e7 + 1.18735e7i −0.989770 + 0.592879i
\(834\) −3.17042e7 −1.57835
\(835\) 1.67608e7 + 2.10173e7i 0.831913 + 1.04319i
\(836\) 660293. 317980.i 0.0326754 0.0157356i
\(837\) 1.44061e6 6.31172e6i 0.0710776 0.311411i
\(838\) −1.40110e7 + 6.74732e6i −0.689220 + 0.331911i
\(839\) 2.02056e7 + 9.73048e6i 0.990982 + 0.477232i 0.857869 0.513869i \(-0.171788\pi\)
0.133114 + 0.991101i \(0.457503\pi\)
\(840\) −2.07926e7 2.37719e7i −1.01674 1.16243i
\(841\) −8.81534e6 + 4.24525e6i −0.429783 + 0.206973i
\(842\) −1.42036e7 + 1.78108e7i −0.690430 + 0.865772i
\(843\) −3.65523e7 1.76026e7i −1.77152 0.853118i
\(844\) 2.29438e6 + 2.87706e6i 0.110869 + 0.139025i
\(845\) 2.43652e6 + 1.06751e7i 0.117389 + 0.514315i
\(846\) 1.50776e7 + 1.89067e7i 0.724279 + 0.908217i
\(847\) −1.34611e7 1.53899e7i −0.644720 0.737100i
\(848\) 4.01684e6 5.03696e6i 0.191821 0.240535i
\(849\) 3.91079e7 + 1.88334e7i 1.86206 + 0.896723i
\(850\) 559205. + 2.45004e6i 0.0265475 + 0.116312i
\(851\) 2.40633e7 1.13902
\(852\) 1.48039e7 0.698678
\(853\) −601136. 2.63375e6i −0.0282879 0.123937i 0.958813 0.284040i \(-0.0916747\pi\)
−0.987100 + 0.160102i \(0.948818\pi\)
\(854\) −1.08425e6 3.92005e6i −0.0508726 0.183927i
\(855\) 4.98308e6 2.18323e7i 0.233122 1.02137i
\(856\) −8.88234e6 + 3.89161e7i −0.414327 + 1.81528i
\(857\) −1.03178e7 + 1.29381e7i −0.479883 + 0.601754i −0.961560 0.274595i \(-0.911456\pi\)
0.481677 + 0.876349i \(0.340028\pi\)
\(858\) 1.63133e6 2.04562e6i 0.0756526 0.0948653i
\(859\) −2.82397e6 + 1.23726e7i −0.130580 + 0.572108i 0.866728 + 0.498781i \(0.166219\pi\)
−0.997308 + 0.0733271i \(0.976638\pi\)
\(860\) 1.71635e6 7.51982e6i 0.0791334 0.346706i
\(861\) 2.11269e6 + 7.63831e6i 0.0971241 + 0.351147i
\(862\) −5.73320e6 2.51188e7i −0.262802 1.15141i
\(863\) −3.66266e6 −0.167405 −0.0837026 0.996491i \(-0.526675\pi\)
−0.0837026 + 0.996491i \(0.526675\pi\)
\(864\) 5.65233e6 0.257598
\(865\) 1.34220e6 + 5.88056e6i 0.0609925 + 0.267226i
\(866\) −1.35010e7 6.50174e6i −0.611746 0.294601i
\(867\) 6.93158e6 8.69193e6i 0.313173 0.392707i
\(868\) 2.99774e6 + 3.42728e6i 0.135050 + 0.154401i
\(869\) 1.85123e6 + 2.32137e6i 0.0831593 + 0.104278i
\(870\) −7.21167e6 3.15964e7i −0.323026 1.41527i
\(871\) 1.22678e7 + 1.53833e7i 0.547924 + 0.687075i
\(872\) 3.70812e7 + 1.78574e7i 1.65144 + 0.795292i
\(873\) −2.11302e6 + 2.64964e6i −0.0938356 + 0.117666i
\(874\) −9.34890e6 + 4.50219e6i −0.413983 + 0.199363i
\(875\) −1.56806e7 1.79274e7i −0.692376 0.791584i
\(876\) 1.07671e7 + 5.18516e6i 0.474066 + 0.228298i
\(877\) 2.17244e7 1.04619e7i 0.953779 0.459316i 0.108770 0.994067i \(-0.465309\pi\)
0.845010 + 0.534751i \(0.179595\pi\)
\(878\) −1.36294e6 + 5.97144e6i −0.0596680 + 0.261423i
\(879\) −1.26178e7 + 6.07640e6i −0.550821 + 0.265261i
\(880\) 1.19971e6 + 1.50439e6i 0.0522240 + 0.0654868i
\(881\) 1.83991e7 0.798650 0.399325 0.916809i \(-0.369244\pi\)
0.399325 + 0.916809i \(0.369244\pi\)
\(882\) −7.83570e6 2.40233e7i −0.339161 1.03983i
\(883\) 1.58794e7 0.685383 0.342691 0.939448i \(-0.388661\pi\)
0.342691 + 0.939448i \(0.388661\pi\)
\(884\) 3.23520e6 + 4.05682e6i 0.139242 + 0.174604i
\(885\) 3.93860e7 1.89673e7i 1.69038 0.814043i
\(886\) 484806. 2.12408e6i 0.0207484 0.0909046i
\(887\) 2.08665e7 1.00488e7i 0.890512 0.428848i 0.0680594 0.997681i \(-0.478319\pi\)
0.822453 + 0.568833i \(0.192605\pi\)
\(888\) −6.25891e7 3.01413e7i −2.66358 1.28271i
\(889\) 2.31545e7 + 9.88122e6i 0.982609 + 0.419330i
\(890\) −1.64148e7 + 7.90493e6i −0.694639 + 0.334521i
\(891\) 1.29506e6 1.62395e6i 0.0546505 0.0685296i
\(892\) 4.23061e6 + 2.03736e6i 0.178029 + 0.0857343i
\(893\) −1.35720e7 1.70188e7i −0.569529 0.714166i
\(894\) −4.14505e6 1.81606e7i −0.173455 0.759954i
\(895\) −696632. 873549.i −0.0290701 0.0364527i
\(896\) 5.03869e6 6.94342e6i 0.209676 0.288937i
\(897\) 9.56836e6 1.19983e7i 0.397060 0.497898i
\(898\) 1.89087e7 + 9.10593e6i 0.782474 + 0.376820i
\(899\) 4.58933e6 + 2.01072e7i 0.189387 + 0.829758i
\(900\) 1.13850e6 0.0468519
\(901\) −1.39220e7 −0.571332
\(902\) −158100. 692681.i −0.00647017 0.0283476i
\(903\) 2.82989e7 3.89964e7i 1.15492 1.59150i
\(904\) −2.74790e6 + 1.20393e7i −0.111835 + 0.489983i
\(905\) 539038. 2.36168e6i 0.0218775 0.0958516i
\(906\) −4.89284e6 + 6.13543e6i −0.198034 + 0.248327i
\(907\) −2.22229e7 + 2.78666e7i −0.896978 + 1.12477i 0.0946325 + 0.995512i \(0.469832\pi\)
−0.991610 + 0.129262i \(0.958739\pi\)
\(908\) 2.68315e6 1.17556e7i 0.108001 0.473185i
\(909\) 8.20543e6 3.59503e7i 0.329376 1.44309i
\(910\) 1.19564e7 + 5.10242e6i 0.478627 + 0.204255i
\(911\) −2.79437e6 1.22429e7i −0.111555 0.488754i −0.999581 0.0289600i \(-0.990780\pi\)
0.888026 0.459794i \(-0.152077\pi\)
\(912\) 2.03579e7 0.810488
\(913\) 4.88917e6 0.194115
\(914\) 1.90844e6 + 8.36143e6i 0.0755638 + 0.331067i
\(915\) −7.35561e6 3.54227e6i −0.290446 0.139872i
\(916\) 4.63310e6 5.80973e6i 0.182446 0.228779i
\(917\) −3.00370e7 + 1.61855e7i −1.17959 + 0.635627i
\(918\) 7.04468e6 + 8.83376e6i 0.275902 + 0.345970i
\(919\) −1.10489e7 4.84082e7i −0.431547 1.89073i −0.454032 0.890985i \(-0.650015\pi\)
0.0224850 0.999747i \(-0.492842\pi\)
\(920\) 1.03544e7 + 1.29840e7i 0.403323 + 0.505752i
\(921\) 1.51121e7 + 7.27761e6i 0.587051 + 0.282709i
\(922\) 1.82937e7 2.29396e7i 0.708721 0.888708i
\(923\) −2.42327e7 + 1.16699e7i −0.936263 + 0.450881i
\(924\) −442514. 1.59989e6i −0.0170509 0.0616466i
\(925\) −5.16878e6 2.48915e6i −0.198625 0.0956527i
\(926\) 258206. 124345.i 0.00989553 0.00476544i
\(927\) −1.33328e7 + 5.84149e7i −0.509592 + 2.23267i
\(928\) −1.62233e7 + 7.81274e6i −0.618401 + 0.297806i
\(929\) 2.13828e7 + 2.68132e7i 0.812879 + 1.01932i 0.999321 + 0.0368524i \(0.0117331\pi\)
−0.186441 + 0.982466i \(0.559695\pi\)
\(930\) −2.20631e7 −0.836486
\(931\) 7.05326e6 + 2.16245e7i 0.266696 + 0.817658i
\(932\) −9.44731e6 −0.356261
\(933\) −1.60078e7 2.00731e7i −0.602042 0.754936i
\(934\) 1.77029e7 8.52525e6i 0.664013 0.319772i
\(935\) 925259. 4.05382e6i 0.0346126 0.151648i
\(936\) −2.25668e7 + 1.08676e7i −0.841939 + 0.405456i
\(937\) −3.35146e7 1.61398e7i −1.24706 0.600550i −0.310334 0.950627i \(-0.600441\pi\)
−0.936721 + 0.350077i \(0.886155\pi\)
\(938\) −3.01023e7 + 1.36895e6i −1.11710 + 0.0508019i
\(939\) −1.13265e7 + 5.45455e6i −0.419210 + 0.201881i
\(940\) −4.92107e6 + 6.17083e6i −0.181652 + 0.227784i
\(941\) 3.79058e7 + 1.82545e7i 1.39550 + 0.672040i 0.972244 0.233968i \(-0.0751712\pi\)
0.423261 + 0.906008i \(0.360885\pi\)
\(942\) 2.21776e7 + 2.78099e7i 0.814306 + 1.02111i
\(943\) −927315. 4.06283e6i −0.0339585 0.148782i
\(944\) 1.40083e7 + 1.75659e7i 0.511630 + 0.641564i
\(945\) −1.07853e7 4.60265e6i −0.392874 0.167660i
\(946\) −2.69324e6 + 3.37721e6i −0.0978469 + 0.122696i
\(947\) 2.26756e7 + 1.09200e7i 0.821643 + 0.395682i 0.796974 0.604013i \(-0.206433\pi\)
0.0246688 + 0.999696i \(0.492147\pi\)
\(948\) −2.53457e6 1.11047e7i −0.0915974 0.401314i
\(949\) −2.17123e7 −0.782600
\(950\) 2.47385e6 0.0889334
\(951\) 980843. + 4.29735e6i 0.0351680 + 0.154081i
\(952\) −3.50399e7 + 1.59349e6i −1.25306 + 0.0569846i
\(953\) 5.87021e6 2.57191e7i 0.209373 0.917324i −0.755612 0.655020i \(-0.772660\pi\)
0.964985 0.262305i \(-0.0844826\pi\)
\(954\) 3.38792e6 1.48434e7i 0.120521 0.528036i
\(955\) −1.24153e7 + 1.55682e7i −0.440502 + 0.552372i
\(956\) 2.36903e6 2.97067e6i 0.0838350 0.105126i
\(957\) 1.67309e6 7.33027e6i 0.0590525 0.258726i
\(958\) −2.40943e6 + 1.05564e7i −0.0848203 + 0.371622i
\(959\) 1.77006e7 9.53801e6i 0.621500 0.334897i
\(960\) −9.89396e6 4.33483e7i −0.346491 1.51808i
\(961\) −1.45888e7 −0.509577
\(962\) 2.85942e7 0.996186
\(963\) 1.42654e7 + 6.25007e7i 0.495698 + 2.17180i
\(964\) −5.89568e6 2.83921e6i −0.204334 0.0984023i
\(965\) −1.66956e7 + 2.09356e7i −0.577143 + 0.723714i
\(966\) 6.26543e6 + 2.26523e7i 0.216027 + 0.781035i
\(967\) 4.95026e6 + 6.20743e6i 0.170240 + 0.213474i 0.859631 0.510915i \(-0.170693\pi\)
−0.689391 + 0.724389i \(0.742122\pi\)
\(968\) −6.90669e6 3.02602e7i −0.236909 1.03797i
\(969\) −2.74289e7 3.43947e7i −0.938423 1.17675i
\(970\) 2.40569e6 + 1.15852e6i 0.0820938 + 0.0395343i
\(971\) −3.29511e7 + 4.13194e7i −1.12156 + 1.40639i −0.219053 + 0.975713i \(0.570297\pi\)
−0.902506 + 0.430678i \(0.858275\pi\)
\(972\) −1.07248e7 + 5.16477e6i −0.364101 + 0.175342i
\(973\) 6.50488e6 3.59606e7i 0.220271 1.21771i
\(974\) 3.33115e7 + 1.60420e7i 1.12512 + 0.541827i
\(975\) −3.29641e6 + 1.58747e6i −0.111053 + 0.0534802i
\(976\) 933693. 4.09078e6i 0.0313747 0.137462i
\(977\) −1.30611e7 + 6.28990e6i −0.437768 + 0.210818i −0.639769 0.768567i \(-0.720970\pi\)
0.202001 + 0.979385i \(0.435256\pi\)
\(978\) −1.75521e7 2.20096e7i −0.586787 0.735808i
\(979\) −4.22676e6 −0.140945
\(980\) 7.07515e6 4.23807e6i 0.235326 0.140962i
\(981\) 6.60998e7 2.19294
\(982\) 1.35786e7 + 1.70271e7i 0.449342 + 0.563458i
\(983\) 2.35523e6 1.13422e6i 0.0777408 0.0374380i −0.394609 0.918849i \(-0.629120\pi\)
0.472350 + 0.881411i \(0.343406\pi\)
\(984\) −2.67708e6 + 1.17290e7i −0.0881401 + 0.386167i
\(985\) −5.32004e6 + 2.56200e6i −0.174713 + 0.0841372i
\(986\) −3.24298e7 1.56174e7i −1.06231 0.511583i
\(987\) −4.34039e7 + 2.33883e7i −1.41820 + 0.764198i
\(988\) 4.60209e6 2.21625e6i 0.149990 0.0722315i
\(989\) −1.57968e7 + 1.98086e7i −0.513546 + 0.643967i
\(990\) 4.09697e6 + 1.97300e6i 0.132854 + 0.0639792i
\(991\) −2.75347e7 3.45274e7i −0.890627 1.11681i −0.992528 0.122016i \(-0.961064\pi\)
0.101902 0.994794i \(-0.467507\pi\)
\(992\) 2.72773e6 + 1.19510e7i 0.0880081 + 0.385589i
\(993\) 4.96415e7 + 6.22485e7i 1.59761 + 2.00334i
\(994\) 7.33206e6 4.05334e7i 0.235375 1.30121i
\(995\) −2.10867e7 + 2.64419e7i −0.675229 + 0.846711i
\(996\) −1.68984e7 8.13786e6i −0.539757 0.259933i
\(997\) 5.65935e6 + 2.47952e7i 0.180314 + 0.790006i 0.981480 + 0.191564i \(0.0613560\pi\)
−0.801166 + 0.598442i \(0.795787\pi\)
\(998\) −2.26178e7 −0.718827
\(999\) −2.57935e7 −0.817705
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 49.6.e.a.8.16 138
49.43 even 7 inner 49.6.e.a.43.16 yes 138
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
49.6.e.a.8.16 138 1.1 even 1 trivial
49.6.e.a.43.16 yes 138 49.43 even 7 inner