Properties

Label 69.6.e.b.13.6
Level $69$
Weight $6$
Character 69.13
Analytic conductor $11.066$
Analytic rank $0$
Dimension $100$
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] = [69,6,Mod(4,69)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(69, base_ring=CyclotomicField(22))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("69.4");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 69 = 3 \cdot 23 \)
Weight: \( k \) \(=\) \( 6 \)
Character orbit: \([\chi]\) \(=\) 69.e (of order \(11\), degree \(10\), 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: \(11.0664835671\)
Analytic rank: \(0\)
Dimension: \(100\)
Relative dimension: \(10\) over \(\Q(\zeta_{11})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label 13.6
Character \(\chi\) \(=\) 69.13
Dual form 69.6.e.b.16.6

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.18855 + 2.52572i) q^{2} +(7.57128 + 4.86577i) q^{3} +(2.96456 - 20.6189i) q^{4} +(-1.08863 + 2.38376i) q^{5} +(4.28056 + 29.7719i) q^{6} +(60.1265 + 17.6547i) q^{7} +(148.533 - 95.4564i) q^{8} +(33.6486 + 73.6802i) q^{9} +O(q^{10})\) \(q+(2.18855 + 2.52572i) q^{2} +(7.57128 + 4.86577i) q^{3} +(2.96456 - 20.6189i) q^{4} +(-1.08863 + 2.38376i) q^{5} +(4.28056 + 29.7719i) q^{6} +(60.1265 + 17.6547i) q^{7} +(148.533 - 95.4564i) q^{8} +(33.6486 + 73.6802i) q^{9} +(-8.40324 + 2.46741i) q^{10} +(66.0544 - 76.2309i) q^{11} +(122.772 - 141.687i) q^{12} +(980.347 - 287.856i) q^{13} +(86.9989 + 190.501i) q^{14} +(-19.8411 + 12.7511i) q^{15} +(-73.4212 - 21.5584i) q^{16} +(102.799 + 714.982i) q^{17} +(-112.454 + 246.240i) q^{18} +(118.644 - 825.185i) q^{19} +(45.9234 + 29.5132i) q^{20} +(369.331 + 426.230i) q^{21} +337.101 q^{22} +(-830.673 + 2397.15i) q^{23} +1589.05 q^{24} +(2041.94 + 2356.53i) q^{25} +(2872.58 + 1846.10i) q^{26} +(-103.748 + 721.580i) q^{27} +(542.270 - 1187.41i) q^{28} +(-366.071 - 2546.08i) q^{29} +(-75.6292 - 22.2067i) q^{30} +(332.765 - 213.855i) q^{31} +(-2453.32 - 5372.02i) q^{32} +(871.038 - 255.760i) q^{33} +(-1580.87 + 1824.42i) q^{34} +(-107.540 + 124.108i) q^{35} +(1618.96 - 475.370i) q^{36} +(-2448.54 - 5361.55i) q^{37} +(2343.85 - 1506.30i) q^{38} +(8823.12 + 2590.70i) q^{39} +(65.8482 + 457.984i) q^{40} +(-5068.58 + 11098.6i) q^{41} +(-268.240 + 1865.65i) q^{42} +(-14142.6 - 9088.90i) q^{43} +(-1375.98 - 1587.96i) q^{44} -212.267 q^{45} +(-7872.50 + 3148.23i) q^{46} +6572.62 q^{47} +(-450.994 - 520.475i) q^{48} +(-10835.4 - 6963.52i) q^{49} +(-1483.04 + 10314.8i) q^{50} +(-2700.62 + 5913.53i) q^{51} +(-3028.99 - 21067.1i) q^{52} +(-16145.4 - 4740.71i) q^{53} +(-2049.57 + 1317.18i) q^{54} +(109.808 + 240.445i) q^{55} +(10616.0 - 3117.15i) q^{56} +(4913.45 - 5670.42i) q^{57} +(5629.52 - 6496.82i) q^{58} +(-12062.6 + 3541.90i) q^{59} +(204.095 + 446.905i) q^{60} +(-29683.0 + 19076.1i) q^{61} +(1268.41 + 372.439i) q^{62} +(722.369 + 5024.19i) q^{63} +(7181.80 - 15725.9i) q^{64} +(-381.053 + 2650.28i) q^{65} +(2552.29 + 1640.26i) q^{66} +(-22906.4 - 26435.4i) q^{67} +15046.9 q^{68} +(-17953.2 + 14107.6i) q^{69} -548.819 q^{70} +(31589.1 + 36455.7i) q^{71} +(12031.2 + 7731.97i) q^{72} +(5659.59 - 39363.3i) q^{73} +(8183.03 - 17918.3i) q^{74} +(3993.81 + 27777.6i) q^{75} +(-16662.7 - 4892.62i) q^{76} +(5317.45 - 3417.32i) q^{77} +(12766.4 + 27954.6i) q^{78} +(-7875.41 + 2312.43i) q^{79} +(131.319 - 151.550i) q^{80} +(-4296.54 + 4958.47i) q^{81} +(-39124.9 + 11488.1i) q^{82} +(29990.0 + 65668.9i) q^{83} +(9883.32 - 6351.62i) q^{84} +(-1816.26 - 533.301i) q^{85} +(-7995.77 - 55611.8i) q^{86} +(9617.00 - 21058.3i) q^{87} +(2534.54 - 17628.1i) q^{88} +(97496.6 + 62657.2i) q^{89} +(-464.557 - 536.127i) q^{90} +64026.8 q^{91} +(46964.1 + 24234.1i) q^{92} +3560.02 q^{93} +(14384.5 + 16600.6i) q^{94} +(1837.89 + 1181.14i) q^{95} +(7564.22 - 52610.3i) q^{96} +(-44685.9 + 97848.4i) q^{97} +(-6126.01 - 42607.3i) q^{98} +(7839.34 + 2301.84i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 100 q + 12 q^{2} - 90 q^{3} - 148 q^{4} - 50 q^{5} + 9 q^{6} - 78 q^{7} - 1844 q^{8} - 810 q^{9} - 38 q^{10} + 404 q^{11} - 1332 q^{12} - 2850 q^{13} - 724 q^{14} + 639 q^{15} - 5556 q^{16} - 2519 q^{17} + 972 q^{18} + 1117 q^{19} - 22411 q^{20} - 702 q^{21} + 32798 q^{22} + 12040 q^{23} - 756 q^{24} - 5928 q^{25} - 788 q^{26} - 7290 q^{27} - 54024 q^{28} + 13774 q^{29} - 342 q^{30} + 12501 q^{31} + 37412 q^{32} - 4185 q^{33} + 9441 q^{34} + 28894 q^{35} - 21789 q^{36} - 38902 q^{37} - 15042 q^{38} - 25650 q^{39} - 133835 q^{40} - 19456 q^{41} + 85950 q^{42} - 8126 q^{43} + 120643 q^{44} + 40500 q^{45} + 90500 q^{46} + 60846 q^{47} + 62955 q^{48} - 25762 q^{49} - 110197 q^{50} - 51084 q^{51} + 91725 q^{52} - 83896 q^{53} - 31347 q^{54} + 190331 q^{55} - 358140 q^{56} - 40437 q^{57} + 150977 q^{58} + 248368 q^{59} + 122625 q^{60} - 81516 q^{61} + 82657 q^{62} - 6318 q^{63} - 298028 q^{64} - 25475 q^{65} - 6669 q^{66} + 51337 q^{67} + 491228 q^{68} + 17082 q^{69} + 395832 q^{70} - 206653 q^{71} - 149364 q^{72} - 121007 q^{73} + 716844 q^{74} - 59490 q^{75} + 171145 q^{76} + 71982 q^{77} + 11916 q^{78} - 661118 q^{79} - 1386592 q^{80} - 65610 q^{81} - 136394 q^{82} - 368400 q^{83} + 165204 q^{84} + 45505 q^{85} - 99668 q^{86} + 50112 q^{87} - 474416 q^{88} + 328408 q^{89} - 3078 q^{90} + 1042320 q^{91} + 1554071 q^{92} + 160722 q^{93} - 299081 q^{94} - 434011 q^{95} + 412740 q^{96} - 88136 q^{97} + 515807 q^{98} - 37665 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/69\mathbb{Z}\right)^\times\).

\(n\) \(28\) \(47\)
\(\chi(n)\) \(e\left(\frac{7}{11}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.18855 + 2.52572i 0.386885 + 0.446489i 0.915467 0.402393i \(-0.131822\pi\)
−0.528582 + 0.848882i \(0.677276\pi\)
\(3\) 7.57128 + 4.86577i 0.485698 + 0.312139i
\(4\) 2.96456 20.6189i 0.0926424 0.644342i
\(5\) −1.08863 + 2.38376i −0.0194740 + 0.0426420i −0.919119 0.393980i \(-0.871098\pi\)
0.899645 + 0.436622i \(0.143825\pi\)
\(6\) 4.28056 + 29.7719i 0.0485425 + 0.337621i
\(7\) 60.1265 + 17.6547i 0.463789 + 0.136181i 0.505275 0.862958i \(-0.331391\pi\)
−0.0414860 + 0.999139i \(0.513209\pi\)
\(8\) 148.533 95.4564i 0.820537 0.527327i
\(9\) 33.6486 + 73.6802i 0.138472 + 0.303211i
\(10\) −8.40324 + 2.46741i −0.0265734 + 0.00780265i
\(11\) 66.0544 76.2309i 0.164596 0.189954i −0.667460 0.744646i \(-0.732618\pi\)
0.832056 + 0.554692i \(0.187164\pi\)
\(12\) 122.772 141.687i 0.246121 0.284038i
\(13\) 980.347 287.856i 1.60887 0.472407i 0.650874 0.759186i \(-0.274403\pi\)
0.957997 + 0.286779i \(0.0925844\pi\)
\(14\) 86.9989 + 190.501i 0.118630 + 0.259763i
\(15\) −19.8411 + 12.7511i −0.0227687 + 0.0146326i
\(16\) −73.4212 21.5584i −0.0717004 0.0210531i
\(17\) 102.799 + 714.982i 0.0862713 + 0.600030i 0.986395 + 0.164395i \(0.0525671\pi\)
−0.900123 + 0.435635i \(0.856524\pi\)
\(18\) −112.454 + 246.240i −0.0818076 + 0.179134i
\(19\) 118.644 825.185i 0.0753982 0.524406i −0.916762 0.399434i \(-0.869207\pi\)
0.992160 0.124972i \(-0.0398841\pi\)
\(20\) 45.9234 + 29.5132i 0.0256720 + 0.0164984i
\(21\) 369.331 + 426.230i 0.182754 + 0.210909i
\(22\) 337.101 0.148492
\(23\) −830.673 + 2397.15i −0.327424 + 0.944878i
\(24\) 1589.05 0.563133
\(25\) 2041.94 + 2356.53i 0.653422 + 0.754089i
\(26\) 2872.58 + 1846.10i 0.833372 + 0.535576i
\(27\) −103.748 + 721.580i −0.0273885 + 0.190491i
\(28\) 542.270 1187.41i 0.130714 0.286223i
\(29\) −366.071 2546.08i −0.0808296 0.562182i −0.989485 0.144635i \(-0.953799\pi\)
0.908655 0.417547i \(-0.137110\pi\)
\(30\) −75.6292 22.2067i −0.0153421 0.00450486i
\(31\) 332.765 213.855i 0.0621918 0.0399682i −0.509175 0.860663i \(-0.670050\pi\)
0.571367 + 0.820695i \(0.306413\pi\)
\(32\) −2453.32 5372.02i −0.423525 0.927390i
\(33\) 871.038 255.760i 0.139236 0.0408835i
\(34\) −1580.87 + 1824.42i −0.234530 + 0.270662i
\(35\) −107.540 + 124.108i −0.0148388 + 0.0171249i
\(36\) 1618.96 475.370i 0.208200 0.0611330i
\(37\) −2448.54 5361.55i −0.294037 0.643852i 0.703742 0.710455i \(-0.251511\pi\)
−0.997780 + 0.0666037i \(0.978784\pi\)
\(38\) 2343.85 1506.30i 0.263312 0.169220i
\(39\) 8823.12 + 2590.70i 0.928882 + 0.272744i
\(40\) 65.8482 + 457.984i 0.00650719 + 0.0452585i
\(41\) −5068.58 + 11098.6i −0.470898 + 1.03112i 0.513969 + 0.857809i \(0.328175\pi\)
−0.984867 + 0.173313i \(0.944553\pi\)
\(42\) −268.240 + 1865.65i −0.0234639 + 0.163195i
\(43\) −14142.6 9088.90i −1.16643 0.749618i −0.193585 0.981083i \(-0.562012\pi\)
−0.972843 + 0.231466i \(0.925648\pi\)
\(44\) −1375.98 1587.96i −0.107147 0.123654i
\(45\) −212.267 −0.0156261
\(46\) −7872.50 + 3148.23i −0.548553 + 0.219368i
\(47\) 6572.62 0.434004 0.217002 0.976171i \(-0.430372\pi\)
0.217002 + 0.976171i \(0.430372\pi\)
\(48\) −450.994 520.475i −0.0282532 0.0326060i
\(49\) −10835.4 6963.52i −0.644698 0.414322i
\(50\) −1483.04 + 10314.8i −0.0838933 + 0.583491i
\(51\) −2700.62 + 5913.53i −0.145391 + 0.318362i
\(52\) −3028.99 21067.1i −0.155342 1.08043i
\(53\) −16145.4 4740.71i −0.789511 0.231821i −0.137972 0.990436i \(-0.544058\pi\)
−0.651539 + 0.758615i \(0.725876\pi\)
\(54\) −2049.57 + 1317.18i −0.0956484 + 0.0614695i
\(55\) 109.808 + 240.445i 0.00489470 + 0.0107179i
\(56\) 10616.0 3117.15i 0.452368 0.132827i
\(57\) 4913.45 5670.42i 0.200308 0.231168i
\(58\) 5629.52 6496.82i 0.219736 0.253589i
\(59\) −12062.6 + 3541.90i −0.451139 + 0.132466i −0.499406 0.866368i \(-0.666448\pi\)
0.0482668 + 0.998834i \(0.484630\pi\)
\(60\) 204.095 + 446.905i 0.00731903 + 0.0160264i
\(61\) −29683.0 + 19076.1i −1.02137 + 0.656395i −0.940312 0.340315i \(-0.889466\pi\)
−0.0810585 + 0.996709i \(0.525830\pi\)
\(62\) 1268.41 + 372.439i 0.0419064 + 0.0123048i
\(63\) 722.369 + 5024.19i 0.0229302 + 0.159483i
\(64\) 7181.80 15725.9i 0.219171 0.479918i
\(65\) −381.053 + 2650.28i −0.0111867 + 0.0778052i
\(66\) 2552.29 + 1640.26i 0.0721224 + 0.0463502i
\(67\) −22906.4 26435.4i −0.623403 0.719446i 0.352946 0.935644i \(-0.385180\pi\)
−0.976350 + 0.216198i \(0.930634\pi\)
\(68\) 15046.9 0.394617
\(69\) −17953.2 + 14107.6i −0.453962 + 0.356723i
\(70\) −548.819 −0.0133870
\(71\) 31589.1 + 36455.7i 0.743688 + 0.858262i 0.993941 0.109919i \(-0.0350591\pi\)
−0.250252 + 0.968181i \(0.580514\pi\)
\(72\) 12031.2 + 7731.97i 0.273512 + 0.175776i
\(73\) 5659.59 39363.3i 0.124302 0.864539i −0.828292 0.560296i \(-0.810687\pi\)
0.952594 0.304243i \(-0.0984036\pi\)
\(74\) 8183.03 17918.3i 0.173714 0.380381i
\(75\) 3993.81 + 27777.6i 0.0819849 + 0.570218i
\(76\) −16662.7 4892.62i −0.330912 0.0971644i
\(77\) 5317.45 3417.32i 0.102206 0.0656839i
\(78\) 12766.4 + 27954.6i 0.237593 + 0.520256i
\(79\) −7875.41 + 2312.43i −0.141973 + 0.0416870i −0.351947 0.936020i \(-0.614480\pi\)
0.209974 + 0.977707i \(0.432662\pi\)
\(80\) 131.319 151.550i 0.00229404 0.00264746i
\(81\) −4296.54 + 4958.47i −0.0727623 + 0.0839722i
\(82\) −39124.9 + 11488.1i −0.642568 + 0.188675i
\(83\) 29990.0 + 65668.9i 0.477838 + 1.04632i 0.983052 + 0.183326i \(0.0586863\pi\)
−0.505214 + 0.862994i \(0.668586\pi\)
\(84\) 9883.32 6351.62i 0.152829 0.0982170i
\(85\) −1816.26 533.301i −0.0272666 0.00800618i
\(86\) −7995.77 55611.8i −0.116577 0.810813i
\(87\) 9617.00 21058.3i 0.136220 0.298281i
\(88\) 2534.54 17628.1i 0.0348893 0.242661i
\(89\) 97496.6 + 62657.2i 1.30471 + 0.838487i 0.993717 0.111925i \(-0.0357017\pi\)
0.310994 + 0.950412i \(0.399338\pi\)
\(90\) −464.557 536.127i −0.00604551 0.00697689i
\(91\) 64026.8 0.810510
\(92\) 46964.1 + 24234.1i 0.578491 + 0.298509i
\(93\) 3560.02 0.0426821
\(94\) 14384.5 + 16600.6i 0.167910 + 0.193778i
\(95\) 1837.89 + 1181.14i 0.0208934 + 0.0134274i
\(96\) 7564.22 52610.3i 0.0837696 0.582630i
\(97\) −44685.9 + 97848.4i −0.482215 + 1.05590i 0.499633 + 0.866237i \(0.333468\pi\)
−0.981848 + 0.189667i \(0.939259\pi\)
\(98\) −6126.01 42607.3i −0.0644336 0.448146i
\(99\) 7839.34 + 2301.84i 0.0803881 + 0.0236041i
\(100\) 54642.6 35116.6i 0.546426 0.351166i
\(101\) −436.862 956.593i −0.00426128 0.00933091i 0.907489 0.420075i \(-0.137996\pi\)
−0.911751 + 0.410744i \(0.865269\pi\)
\(102\) −20846.4 + 6121.04i −0.198395 + 0.0582539i
\(103\) 69470.3 80173.0i 0.645217 0.744621i −0.335071 0.942193i \(-0.608760\pi\)
0.980288 + 0.197572i \(0.0633057\pi\)
\(104\) 118136. 136336.i 1.07103 1.23603i
\(105\) −1418.10 + 416.390i −0.0125526 + 0.00368576i
\(106\) −23361.2 51154.0i −0.201944 0.442196i
\(107\) −95615.2 + 61448.1i −0.807360 + 0.518859i −0.878010 0.478642i \(-0.841129\pi\)
0.0706498 + 0.997501i \(0.477493\pi\)
\(108\) 14570.7 + 4278.33i 0.120204 + 0.0352951i
\(109\) 11255.6 + 78284.5i 0.0907408 + 0.631116i 0.983544 + 0.180669i \(0.0578264\pi\)
−0.892803 + 0.450447i \(0.851265\pi\)
\(110\) −366.978 + 803.570i −0.00289173 + 0.00633201i
\(111\) 7549.48 52507.8i 0.0581580 0.404498i
\(112\) −4033.95 2592.46i −0.0303868 0.0195284i
\(113\) 15734.6 + 18158.7i 0.115920 + 0.133779i 0.810744 0.585401i \(-0.199063\pi\)
−0.694823 + 0.719180i \(0.744517\pi\)
\(114\) 25075.2 0.180710
\(115\) −4809.94 4589.73i −0.0339153 0.0323625i
\(116\) −53582.7 −0.369726
\(117\) 54196.6 + 62546.2i 0.366022 + 0.422412i
\(118\) −35345.4 22715.1i −0.233684 0.150179i
\(119\) −6441.88 + 44804.2i −0.0417009 + 0.290036i
\(120\) −1729.89 + 3787.93i −0.0109664 + 0.0240131i
\(121\) 21472.0 + 149341.i 0.133324 + 0.927290i
\(122\) −113144. 33222.0i −0.688225 0.202081i
\(123\) −92379.0 + 59368.4i −0.550568 + 0.353828i
\(124\) −3422.96 7495.24i −0.0199916 0.0437755i
\(125\) −15697.9 + 4609.32i −0.0898600 + 0.0263853i
\(126\) −11108.8 + 12820.2i −0.0623360 + 0.0719396i
\(127\) −64616.3 + 74571.2i −0.355495 + 0.410263i −0.905125 0.425145i \(-0.860223\pi\)
0.549631 + 0.835408i \(0.314769\pi\)
\(128\) −125890. + 36964.7i −0.679153 + 0.199417i
\(129\) −62853.1 137629.i −0.332547 0.728176i
\(130\) −7527.83 + 4837.84i −0.0390671 + 0.0251069i
\(131\) −283448. 83227.8i −1.44309 0.423731i −0.535842 0.844318i \(-0.680006\pi\)
−0.907252 + 0.420587i \(0.861824\pi\)
\(132\) −2691.26 18718.1i −0.0134437 0.0935033i
\(133\) 21702.0 47520.9i 0.106383 0.232946i
\(134\) 16636.6 115710.i 0.0800392 0.556685i
\(135\) −1607.13 1032.84i −0.00758957 0.00487752i
\(136\) 83518.7 + 96385.7i 0.387201 + 0.446854i
\(137\) −279972. −1.27442 −0.637211 0.770690i \(-0.719912\pi\)
−0.637211 + 0.770690i \(0.719912\pi\)
\(138\) −74923.5 14469.6i −0.334904 0.0646784i
\(139\) −67679.2 −0.297111 −0.148555 0.988904i \(-0.547462\pi\)
−0.148555 + 0.988904i \(0.547462\pi\)
\(140\) 2240.16 + 2585.29i 0.00965961 + 0.0111478i
\(141\) 49763.2 + 31980.9i 0.210795 + 0.135470i
\(142\) −22942.8 + 159570.i −0.0954827 + 0.664097i
\(143\) 42812.7 93746.8i 0.175078 0.383368i
\(144\) −882.094 6135.10i −0.00354494 0.0246556i
\(145\) 6467.76 + 1899.11i 0.0255467 + 0.00750118i
\(146\) 111807. 71854.1i 0.434098 0.278978i
\(147\) −48155.4 105446.i −0.183802 0.402471i
\(148\) −117808. + 34591.6i −0.442101 + 0.129813i
\(149\) −187948. + 216903.i −0.693540 + 0.800387i −0.987865 0.155318i \(-0.950360\pi\)
0.294325 + 0.955705i \(0.404905\pi\)
\(150\) −61417.7 + 70879.8i −0.222877 + 0.257214i
\(151\) 327152. 96060.4i 1.16763 0.342848i 0.360239 0.932860i \(-0.382695\pi\)
0.807395 + 0.590012i \(0.200877\pi\)
\(152\) −61146.7 133893.i −0.214666 0.470054i
\(153\) −49221.0 + 31632.4i −0.169989 + 0.109246i
\(154\) 20268.7 + 5951.43i 0.0688691 + 0.0202218i
\(155\) 147.522 + 1026.04i 0.000493206 + 0.00343032i
\(156\) 79574.2 174243.i 0.261795 0.573250i
\(157\) 74357.2 517166.i 0.240754 1.67448i −0.407612 0.913155i \(-0.633639\pi\)
0.648367 0.761328i \(-0.275452\pi\)
\(158\) −23076.3 14830.2i −0.0735399 0.0472612i
\(159\) −99173.9 114453.i −0.311103 0.359032i
\(160\) 15476.4 0.0477935
\(161\) −92266.4 + 129467.i −0.280530 + 0.393635i
\(162\) −21926.9 −0.0656433
\(163\) 218683. + 252374.i 0.644684 + 0.744005i 0.980196 0.198031i \(-0.0634548\pi\)
−0.335512 + 0.942036i \(0.608909\pi\)
\(164\) 213816. + 137411.i 0.620770 + 0.398945i
\(165\) −338.566 + 2354.78i −0.000968129 + 0.00673348i
\(166\) −100227. + 219466.i −0.282302 + 0.618155i
\(167\) −4662.44 32428.0i −0.0129367 0.0899765i 0.982330 0.187156i \(-0.0599270\pi\)
−0.995267 + 0.0971795i \(0.969018\pi\)
\(168\) 95544.2 + 28054.3i 0.261175 + 0.0766878i
\(169\) 565867. 363661.i 1.52404 0.979444i
\(170\) −2628.00 5754.52i −0.00697434 0.0152717i
\(171\) 64792.0 19024.7i 0.169446 0.0497538i
\(172\) −229330. + 264661.i −0.591071 + 0.682132i
\(173\) 299367. 345488.i 0.760482 0.877643i −0.235058 0.971981i \(-0.575528\pi\)
0.995540 + 0.0943385i \(0.0300736\pi\)
\(174\) 74234.7 21797.3i 0.185880 0.0545794i
\(175\) 81170.9 + 177740.i 0.200357 + 0.438722i
\(176\) −6493.21 + 4172.93i −0.0158008 + 0.0101545i
\(177\) −108563. 31877.1i −0.260465 0.0764795i
\(178\) 55121.4 + 383378.i 0.130398 + 0.906936i
\(179\) 169753. 371707.i 0.395990 0.867098i −0.601671 0.798744i \(-0.705498\pi\)
0.997661 0.0683536i \(-0.0217746\pi\)
\(180\) −629.277 + 4376.72i −0.00144764 + 0.0100686i
\(181\) 202085. + 129872.i 0.458498 + 0.294659i 0.749428 0.662085i \(-0.230328\pi\)
−0.290930 + 0.956744i \(0.593965\pi\)
\(182\) 140126. + 161714.i 0.313574 + 0.361883i
\(183\) −317558. −0.700964
\(184\) 105441. + 435349.i 0.229596 + 0.947967i
\(185\) 15446.2 0.0331812
\(186\) 7791.29 + 8991.63i 0.0165130 + 0.0190571i
\(187\) 61294.0 + 39391.3i 0.128178 + 0.0823751i
\(188\) 19484.9 135521.i 0.0402072 0.279647i
\(189\) −18977.3 + 41554.4i −0.0386437 + 0.0846180i
\(190\) 1039.08 + 7226.97i 0.00208817 + 0.0145235i
\(191\) −10648.6 3126.71i −0.0211207 0.00620161i 0.271155 0.962536i \(-0.412594\pi\)
−0.292276 + 0.956334i \(0.594413\pi\)
\(192\) 130894. 84120.6i 0.256252 0.164683i
\(193\) 60291.4 + 132020.i 0.116510 + 0.255121i 0.958898 0.283750i \(-0.0915785\pi\)
−0.842389 + 0.538870i \(0.818851\pi\)
\(194\) −344935. + 101282.i −0.658011 + 0.193209i
\(195\) −15780.7 + 18211.9i −0.0297194 + 0.0342980i
\(196\) −175703. + 202772.i −0.326692 + 0.377022i
\(197\) 143827. 42231.5i 0.264044 0.0775302i −0.147031 0.989132i \(-0.546972\pi\)
0.411075 + 0.911602i \(0.365154\pi\)
\(198\) 11343.0 + 24837.7i 0.0205620 + 0.0450244i
\(199\) −171948. + 110504.i −0.307797 + 0.197809i −0.685415 0.728152i \(-0.740379\pi\)
0.377619 + 0.925961i \(0.376743\pi\)
\(200\) 528242. + 155106.i 0.933808 + 0.274191i
\(201\) −44802.3 311607.i −0.0782185 0.544022i
\(202\) 1460.00 3196.94i 0.00251752 0.00551260i
\(203\) 22939.8 159550.i 0.0390705 0.271741i
\(204\) 113925. + 73214.9i 0.191665 + 0.123175i
\(205\) −20938.7 24164.6i −0.0347989 0.0401601i
\(206\) 354534. 0.582089
\(207\) −204573. + 19456.6i −0.331836 + 0.0315603i
\(208\) −78183.9 −0.125302
\(209\) −55067.6 63551.5i −0.0872029 0.100637i
\(210\) −4155.26 2670.42i −0.00650204 0.00417861i
\(211\) 140859. 979698.i 0.217811 1.51491i −0.528284 0.849068i \(-0.677164\pi\)
0.746095 0.665840i \(-0.231927\pi\)
\(212\) −145612. + 318846.i −0.222514 + 0.487239i
\(213\) 61784.6 + 429722.i 0.0933107 + 0.648990i
\(214\) −364460. 107015.i −0.544020 0.159739i
\(215\) 37061.8 23818.2i 0.0546802 0.0351409i
\(216\) 53469.5 + 117082.i 0.0779779 + 0.170748i
\(217\) 23783.5 6983.47i 0.0342868 0.0100675i
\(218\) −173091. + 199758.i −0.246680 + 0.284684i
\(219\) 234383. 270493.i 0.330230 0.381105i
\(220\) 5283.26 1551.30i 0.00735944 0.00216093i
\(221\) 306590. + 671339.i 0.422258 + 0.924616i
\(222\) 149142. 95848.1i 0.203104 0.130527i
\(223\) −804816. 236315.i −1.08376 0.318222i −0.309380 0.950938i \(-0.600122\pi\)
−0.774383 + 0.632717i \(0.781940\pi\)
\(224\) −52667.9 366313.i −0.0701335 0.487789i
\(225\) −104921. + 229745.i −0.138167 + 0.302544i
\(226\) −11427.9 + 79482.5i −0.0148831 + 0.103514i
\(227\) 87789.2 + 56418.7i 0.113078 + 0.0726705i 0.595957 0.803016i \(-0.296773\pi\)
−0.482880 + 0.875687i \(0.660409\pi\)
\(228\) −102352. 118120.i −0.130394 0.150483i
\(229\) 21417.9 0.0269891 0.0134945 0.999909i \(-0.495704\pi\)
0.0134945 + 0.999909i \(0.495704\pi\)
\(230\) 1065.59 22193.4i 0.00132822 0.0276634i
\(231\) 56887.8 0.0701438
\(232\) −297413. 343233.i −0.362777 0.418667i
\(233\) 866343. + 556765.i 1.04544 + 0.671865i 0.946327 0.323211i \(-0.104762\pi\)
0.0991155 + 0.995076i \(0.468399\pi\)
\(234\) −39362.3 + 273771.i −0.0469938 + 0.326849i
\(235\) −7155.14 + 15667.6i −0.00845179 + 0.0185068i
\(236\) 37269.9 + 259218.i 0.0435591 + 0.302960i
\(237\) −70878.7 20811.9i −0.0819681 0.0240680i
\(238\) −127261. + 81786.0i −0.145631 + 0.0935915i
\(239\) −45250.3 99084.3i −0.0512421 0.112204i 0.882279 0.470726i \(-0.156008\pi\)
−0.933521 + 0.358522i \(0.883281\pi\)
\(240\) 1731.65 508.460i 0.00194059 0.000569808i
\(241\) 602911. 695796.i 0.668668 0.771684i −0.315499 0.948926i \(-0.602172\pi\)
0.984167 + 0.177242i \(0.0567174\pi\)
\(242\) −330201. + 381072.i −0.362443 + 0.418282i
\(243\) −56657.1 + 16636.0i −0.0615515 + 0.0180732i
\(244\) 305332. + 668584.i 0.328321 + 0.718922i
\(245\) 28395.1 18248.5i 0.0302224 0.0194228i
\(246\) −352124. 103393.i −0.370987 0.108931i
\(247\) −121222. 843120.i −0.126427 0.879320i
\(248\) 29012.7 63529.0i 0.0299543 0.0655908i
\(249\) −92467.0 + 643122.i −0.0945123 + 0.657347i
\(250\) −45997.5 29560.8i −0.0465462 0.0299134i
\(251\) −1.19714e6 1.38157e6i −1.19939 1.38417i −0.903299 0.429012i \(-0.858862\pi\)
−0.296093 0.955159i \(-0.595684\pi\)
\(252\) 105735. 0.104886
\(253\) 127867. + 221665.i 0.125591 + 0.217719i
\(254\) −329762. −0.320713
\(255\) −11156.5 12875.3i −0.0107443 0.0123995i
\(256\) −834282. 536160.i −0.795633 0.511322i
\(257\) 157307. 1.09410e6i 0.148565 1.03329i −0.770006 0.638036i \(-0.779747\pi\)
0.918571 0.395256i \(-0.129344\pi\)
\(258\) 210056. 459958.i 0.196465 0.430198i
\(259\) −52565.2 365599.i −0.0486910 0.338654i
\(260\) 53516.4 + 15713.8i 0.0490968 + 0.0144161i
\(261\) 175278. 112644.i 0.159267 0.102355i
\(262\) −410129. 898058.i −0.369120 0.808260i
\(263\) −1.93541e6 + 568289.i −1.72538 + 0.506617i −0.986010 0.166684i \(-0.946694\pi\)
−0.739369 + 0.673301i \(0.764876\pi\)
\(264\) 104964. 121135.i 0.0926895 0.106969i
\(265\) 28877.0 33325.9i 0.0252603 0.0291519i
\(266\) 167520. 49188.5i 0.145166 0.0426245i
\(267\) 433298. + 948791.i 0.371971 + 0.814503i
\(268\) −612976. + 393936.i −0.521323 + 0.335034i
\(269\) 945045. + 277490.i 0.796291 + 0.233812i 0.654478 0.756081i \(-0.272889\pi\)
0.141813 + 0.989893i \(0.454707\pi\)
\(270\) −908.621 6319.60i −0.000758531 0.00527570i
\(271\) −116820. + 255801.i −0.0966263 + 0.211582i −0.951772 0.306805i \(-0.900740\pi\)
0.855146 + 0.518387i \(0.173467\pi\)
\(272\) 7866.26 54711.0i 0.00644683 0.0448387i
\(273\) 484765. + 311539.i 0.393663 + 0.252992i
\(274\) −612733. 707131.i −0.493054 0.569015i
\(275\) 314519. 0.250793
\(276\) 237661. + 412000.i 0.187796 + 0.325555i
\(277\) −615757. −0.482181 −0.241090 0.970503i \(-0.577505\pi\)
−0.241090 + 0.970503i \(0.577505\pi\)
\(278\) −148119. 170939.i −0.114948 0.132657i
\(279\) 26953.9 + 17322.2i 0.0207306 + 0.0133227i
\(280\) −4126.36 + 28699.5i −0.00314538 + 0.0218766i
\(281\) −745330. + 1.63205e6i −0.563097 + 1.23301i 0.387295 + 0.921956i \(0.373409\pi\)
−0.950392 + 0.311054i \(0.899318\pi\)
\(282\) 28134.5 + 195680.i 0.0210677 + 0.146529i
\(283\) −707854. 207845.i −0.525385 0.154267i 0.00827549 0.999966i \(-0.497366\pi\)
−0.533661 + 0.845699i \(0.679184\pi\)
\(284\) 845326. 543258.i 0.621911 0.399678i
\(285\) 8168.02 + 17885.5i 0.00595668 + 0.0130433i
\(286\) 330476. 97036.5i 0.238905 0.0701488i
\(287\) −500699. + 577838.i −0.358816 + 0.414096i
\(288\) 313261. 361522.i 0.222548 0.256835i
\(289\) 861711. 253021.i 0.606900 0.178202i
\(290\) 9358.41 + 20492.1i 0.00653442 + 0.0143084i
\(291\) −814437. + 523407.i −0.563800 + 0.362332i
\(292\) −794852. 233390.i −0.545543 0.160186i
\(293\) −470.325 3271.19i −0.000320059 0.00222606i 0.989661 0.143428i \(-0.0458125\pi\)
−0.989981 + 0.141202i \(0.954903\pi\)
\(294\) 160936. 352400.i 0.108589 0.237776i
\(295\) 4688.64 32610.2i 0.00313683 0.0218172i
\(296\) −875483. 562639.i −0.580789 0.373250i
\(297\) 48153.7 + 55572.3i 0.0316766 + 0.0365567i
\(298\) −959170. −0.625684
\(299\) −124314. + 2.58915e6i −0.0804161 + 1.67486i
\(300\) 584584. 0.375011
\(301\) −689882. 796167.i −0.438893 0.506510i
\(302\) 958609. + 616061.i 0.604817 + 0.388693i
\(303\) 1346.96 9368.31i 0.000842845 0.00586212i
\(304\) −26500.7 + 58028.3i −0.0164465 + 0.0360127i
\(305\) −13159.2 91524.0i −0.00809988 0.0563359i
\(306\) −187617. 55089.4i −0.114543 0.0336329i
\(307\) 855456. 549768.i 0.518026 0.332915i −0.255365 0.966845i \(-0.582196\pi\)
0.773391 + 0.633930i \(0.218559\pi\)
\(308\) −54697.6 119771.i −0.0328543 0.0719408i
\(309\) 916082. 268986.i 0.545806 0.160263i
\(310\) −2268.63 + 2618.14i −0.00134079 + 0.00154735i
\(311\) 57230.8 66047.9i 0.0335528 0.0387220i −0.738725 0.674007i \(-0.764572\pi\)
0.772278 + 0.635285i \(0.219117\pi\)
\(312\) 1.55782e6 457418.i 0.906008 0.266028i
\(313\) 1.22037e6 + 2.67225e6i 0.704097 + 1.54176i 0.834932 + 0.550353i \(0.185507\pi\)
−0.130835 + 0.991404i \(0.541766\pi\)
\(314\) 1.46895e6 944038.i 0.840782 0.540338i
\(315\) −12762.9 3747.51i −0.00724722 0.00212798i
\(316\) 24332.7 + 169238.i 0.0137080 + 0.0953411i
\(317\) 589115. 1.28998e6i 0.329270 0.721001i −0.670512 0.741899i \(-0.733925\pi\)
0.999782 + 0.0208984i \(0.00665264\pi\)
\(318\) 72028.8 500972.i 0.0399428 0.277808i
\(319\) −218270. 140274.i −0.120093 0.0771792i
\(320\) 29668.6 + 34239.4i 0.0161965 + 0.0186918i
\(321\) −1.02292e6 −0.554089
\(322\) −528927. + 50305.3i −0.284286 + 0.0270380i
\(323\) 602189. 0.321164
\(324\) 89501.2 + 103290.i 0.0473659 + 0.0546632i
\(325\) 2.68015e6 + 1.72243e6i 1.40751 + 0.904551i
\(326\) −158827. + 1.10467e6i −0.0827714 + 0.575688i
\(327\) −295695. + 647481.i −0.152923 + 0.334856i
\(328\) 306585. + 2.13234e6i 0.157350 + 1.09439i
\(329\) 395189. + 116038.i 0.201287 + 0.0591031i
\(330\) −6688.48 + 4298.42i −0.00338098 + 0.00217282i
\(331\) −1.14862e6 2.51513e6i −0.576244 1.26180i −0.943405 0.331642i \(-0.892397\pi\)
0.367161 0.930157i \(-0.380330\pi\)
\(332\) 1.44293e6 423683.i 0.718456 0.210958i
\(333\) 312650. 360817.i 0.154507 0.178310i
\(334\) 71700.1 82746.3i 0.0351685 0.0405866i
\(335\) 87952.1 25825.1i 0.0428188 0.0125727i
\(336\) −17927.9 39256.5i −0.00866323 0.0189698i
\(337\) 2.97546e6 1.91221e6i 1.42718 0.917196i 0.427270 0.904124i \(-0.359476\pi\)
0.999915 0.0130713i \(-0.00416084\pi\)
\(338\) 2.15693e6 + 633333.i 1.02694 + 0.301537i
\(339\) 30775.1 + 214046.i 0.0145446 + 0.101160i
\(340\) −16380.5 + 35868.3i −0.00768476 + 0.0168273i
\(341\) 5678.23 39493.0i 0.00264440 0.0183922i
\(342\) 189852. + 122010.i 0.0877706 + 0.0564067i
\(343\) −1.21826e6 1.40595e6i −0.559121 0.645260i
\(344\) −2.96824e6 −1.35239
\(345\) −14084.9 58154.2i −0.00637096 0.0263047i
\(346\) 1.52779e6 0.686076
\(347\) −1.25573e6 1.44919e6i −0.559852 0.646103i 0.403298 0.915069i \(-0.367864\pi\)
−0.963150 + 0.268965i \(0.913318\pi\)
\(348\) −405690. 260721.i −0.179575 0.115406i
\(349\) −325946. + 2.26700e6i −0.143246 + 0.996297i 0.783710 + 0.621127i \(0.213325\pi\)
−0.926956 + 0.375170i \(0.877584\pi\)
\(350\) −271274. + 594007.i −0.118369 + 0.259192i
\(351\) 106002. + 737263.i 0.0459248 + 0.319414i
\(352\) −571566. 167827.i −0.245872 0.0721946i
\(353\) 741805. 476729.i 0.316850 0.203627i −0.372543 0.928015i \(-0.621514\pi\)
0.689392 + 0.724388i \(0.257878\pi\)
\(354\) −157084. 343965.i −0.0666228 0.145884i
\(355\) −121291. + 35614.1i −0.0510806 + 0.0149986i
\(356\) 1.58096e6 1.82453e6i 0.661144 0.763001i
\(357\) −266780. + 307881.i −0.110786 + 0.127853i
\(358\) 1.31034e6 384751.i 0.540352 0.158662i
\(359\) 21171.5 + 46359.1i 0.00866993 + 0.0189845i 0.913917 0.405900i \(-0.133042\pi\)
−0.905248 + 0.424885i \(0.860315\pi\)
\(360\) −31528.7 + 20262.2i −0.0128218 + 0.00824008i
\(361\) 1.70894e6 + 501792.i 0.690176 + 0.202654i
\(362\) 114252. + 794642.i 0.0458240 + 0.318713i
\(363\) −564088. + 1.23518e6i −0.224688 + 0.491998i
\(364\) 189811. 1.32016e6i 0.0750876 0.522245i
\(365\) 87671.7 + 56343.2i 0.0344451 + 0.0221365i
\(366\) −694992. 802064.i −0.271192 0.312972i
\(367\) −1.77935e6 −0.689597 −0.344798 0.938677i \(-0.612053\pi\)
−0.344798 + 0.938677i \(0.612053\pi\)
\(368\) 112668. 158094.i 0.0433691 0.0608548i
\(369\) −988300. −0.377853
\(370\) 33804.8 + 39012.8i 0.0128373 + 0.0148150i
\(371\) −887068. 570084.i −0.334597 0.215032i
\(372\) 10553.9 73403.9i 0.00395417 0.0275018i
\(373\) −1.45587e6 + 3.18790e6i −0.541813 + 1.18640i 0.418689 + 0.908130i \(0.362490\pi\)
−0.960502 + 0.278275i \(0.910238\pi\)
\(374\) 34653.7 + 241021.i 0.0128106 + 0.0890998i
\(375\) −141281. 41483.9i −0.0518807 0.0152336i
\(376\) 976252. 627399.i 0.356117 0.228862i
\(377\) −1.09178e6 2.39066e6i −0.395623 0.866294i
\(378\) −146488. + 43012.6i −0.0527316 + 0.0154834i
\(379\) −292415. + 337465.i −0.104569 + 0.120679i −0.805621 0.592431i \(-0.798168\pi\)
0.701053 + 0.713110i \(0.252714\pi\)
\(380\) 29802.4 34393.8i 0.0105875 0.0122186i
\(381\) −852075. + 250192.i −0.300722 + 0.0883000i
\(382\) −15407.8 33738.4i −0.00540235 0.0118295i
\(383\) 696964. 447912.i 0.242780 0.156025i −0.413593 0.910462i \(-0.635726\pi\)
0.656373 + 0.754437i \(0.272090\pi\)
\(384\) −1.13301e6 332683.i −0.392109 0.115134i
\(385\) 2357.35 + 16395.7i 0.000810536 + 0.00563740i
\(386\) −201494. + 441211.i −0.0688327 + 0.150723i
\(387\) 193793. 1.34786e6i 0.0657749 0.457474i
\(388\) 1.88506e6 + 1.21145e6i 0.635690 + 0.408533i
\(389\) 2.97166e6 + 3.42948e6i 0.995693 + 1.14909i 0.988820 + 0.149115i \(0.0476424\pi\)
0.00687337 + 0.999976i \(0.497812\pi\)
\(390\) −80535.1 −0.0268117
\(391\) −1.79931e6 347492.i −0.595202 0.114948i
\(392\) −2.27413e6 −0.747482
\(393\) −1.74110e6 2.00933e6i −0.568645 0.656251i
\(394\) 421438. + 270842.i 0.136771 + 0.0878973i
\(395\) 3061.11 21290.5i 0.000987157 0.00686583i
\(396\) 70701.7 154815.i 0.0226564 0.0496107i
\(397\) 613680. + 4.26824e6i 0.195419 + 1.35917i 0.817371 + 0.576112i \(0.195431\pi\)
−0.621952 + 0.783055i \(0.713660\pi\)
\(398\) −655419. 192448.i −0.207401 0.0608985i
\(399\) 395538. 254197.i 0.124381 0.0799351i
\(400\) −99118.9 217040.i −0.0309747 0.0678250i
\(401\) −4.02530e6 + 1.18193e6i −1.25008 + 0.367056i −0.838793 0.544451i \(-0.816738\pi\)
−0.411285 + 0.911507i \(0.634920\pi\)
\(402\) 688979. 795125.i 0.212638 0.245397i
\(403\) 264665. 305440.i 0.0811773 0.0936835i
\(404\) −21019.1 + 6171.75i −0.00640707 + 0.00188129i
\(405\) −7142.49 15639.9i −0.00216377 0.00473801i
\(406\) 453183. 291243.i 0.136445 0.0876880i
\(407\) −570452. 167500.i −0.170700 0.0501220i
\(408\) 163353. + 1.13615e6i 0.0485822 + 0.337896i
\(409\) 553535. 1.21207e6i 0.163620 0.358278i −0.810008 0.586419i \(-0.800537\pi\)
0.973628 + 0.228141i \(0.0732646\pi\)
\(410\) 15207.5 105771.i 0.00446786 0.0310746i
\(411\) −2.11975e6 1.36228e6i −0.618984 0.397797i
\(412\) −1.44713e6 1.67008e6i −0.420016 0.484724i
\(413\) −787812. −0.227273
\(414\) −496861. 474114.i −0.142474 0.135951i
\(415\) −189187. −0.0539226
\(416\) −3.95147e6 4.56024e6i −1.11950 1.29197i
\(417\) −512418. 329311.i −0.144306 0.0927399i
\(418\) 39995.0 278171.i 0.0111960 0.0778702i
\(419\) −708307. + 1.55098e6i −0.197100 + 0.431589i −0.982215 0.187762i \(-0.939877\pi\)
0.785115 + 0.619350i \(0.212604\pi\)
\(420\) 4381.51 + 30474.1i 0.00121199 + 0.00842960i
\(421\) −1.35530e6 397953.i −0.372676 0.109428i 0.0900306 0.995939i \(-0.471304\pi\)
−0.462707 + 0.886511i \(0.653122\pi\)
\(422\) 2.78272e6 1.78835e6i 0.760657 0.488844i
\(423\) 221160. + 484272.i 0.0600973 + 0.131595i
\(424\) −2.85065e6 + 837027.i −0.770069 + 0.226113i
\(425\) −1.47497e6 + 1.70220e6i −0.396104 + 0.457129i
\(426\) −950138. + 1.09652e6i −0.253666 + 0.292747i
\(427\) −2.12152e6 + 622934.i −0.563089 + 0.165338i
\(428\) 983539. + 2.15365e6i 0.259527 + 0.568285i
\(429\) 780297. 501467.i 0.204700 0.131552i
\(430\) 141270. + 41480.5i 0.0368449 + 0.0108187i
\(431\) −1.06172e6 7.38444e6i −0.275307 1.91480i −0.388906 0.921277i \(-0.627147\pi\)
0.113599 0.993527i \(-0.463762\pi\)
\(432\) 23173.4 50742.6i 0.00597420 0.0130817i
\(433\) −136609. + 950134.i −0.0350154 + 0.243537i −0.999811 0.0194653i \(-0.993804\pi\)
0.964795 + 0.263002i \(0.0847127\pi\)
\(434\) 69689.7 + 44786.8i 0.0177601 + 0.0114137i
\(435\) 39728.6 + 45849.3i 0.0100665 + 0.0116174i
\(436\) 1.64751e6 0.415061
\(437\) 1.87954e6 + 969866.i 0.470812 + 0.242945i
\(438\) 1.19615e6 0.297920
\(439\) −695160. 802257.i −0.172156 0.198679i 0.663114 0.748518i \(-0.269234\pi\)
−0.835271 + 0.549839i \(0.814689\pi\)
\(440\) 39262.1 + 25232.2i 0.00966811 + 0.00621332i
\(441\) 148476. 1.03267e6i 0.0363545 0.252851i
\(442\) −1.02463e6 + 2.24362e6i −0.249465 + 0.546253i
\(443\) 897685. + 6.24353e6i 0.217327 + 1.51155i 0.747846 + 0.663872i \(0.231088\pi\)
−0.530519 + 0.847673i \(0.678003\pi\)
\(444\) −1.06027e6 311325.i −0.255247 0.0749473i
\(445\) −255497. + 164198.i −0.0611627 + 0.0393069i
\(446\) −1.16451e6 2.54993e6i −0.277209 0.607003i
\(447\) −2.47841e6 + 727726.i −0.586683 + 0.172266i
\(448\) 709453. 818753.i 0.167005 0.192734i
\(449\) 4.44724e6 5.13239e6i 1.04106 1.20144i 0.0619543 0.998079i \(-0.480267\pi\)
0.979103 0.203365i \(-0.0651878\pi\)
\(450\) −809896. + 237807.i −0.188537 + 0.0553596i
\(451\) 511257. + 1.11950e6i 0.118358 + 0.259168i
\(452\) 421060. 270599.i 0.0969388 0.0622988i
\(453\) 2.94436e6 + 864543.i 0.674134 + 0.197943i
\(454\) 49633.1 + 345206.i 0.0113014 + 0.0786029i
\(455\) −69701.4 + 152625.i −0.0157838 + 0.0345618i
\(456\) 188531. 1.31126e6i 0.0424592 0.295310i
\(457\) 6.83712e6 + 4.39395e6i 1.53138 + 0.984157i 0.989634 + 0.143614i \(0.0458723\pi\)
0.541744 + 0.840543i \(0.317764\pi\)
\(458\) 46874.1 + 54095.6i 0.0104417 + 0.0120503i
\(459\) −526582. −0.116663
\(460\) −108895. + 85569.4i −0.0239945 + 0.0188549i
\(461\) −4.11756e6 −0.902376 −0.451188 0.892429i \(-0.649000\pi\)
−0.451188 + 0.892429i \(0.649000\pi\)
\(462\) 124502. + 143683.i 0.0271376 + 0.0313184i
\(463\) 6.47954e6 + 4.16415e6i 1.40473 + 0.902763i 0.999932 0.0116440i \(-0.00370649\pi\)
0.404795 + 0.914407i \(0.367343\pi\)
\(464\) −28012.0 + 194828.i −0.00604018 + 0.0420104i
\(465\) −3875.54 + 8486.25i −0.000831189 + 0.00182005i
\(466\) 489802. + 3.40665e6i 0.104485 + 0.726713i
\(467\) −8.37996e6 2.46058e6i −1.77807 0.522090i −0.783070 0.621933i \(-0.786348\pi\)
−0.995003 + 0.0998435i \(0.968166\pi\)
\(468\) 1.45031e6 932054.i 0.306087 0.196710i
\(469\) −910570. 1.99387e6i −0.191153 0.418567i
\(470\) −55231.3 + 16217.4i −0.0115330 + 0.00338638i
\(471\) 3.07939e6 3.55380e6i 0.639606 0.738144i
\(472\) −1.45360e6 + 1.67754e6i −0.300323 + 0.346592i
\(473\) −1.62704e6 + 477741.i −0.334383 + 0.0981837i
\(474\) −102557. 224568.i −0.0209661 0.0459094i
\(475\) 2.18684e6 1.40539e6i 0.444715 0.285801i
\(476\) 904719. + 265649.i 0.183019 + 0.0537392i
\(477\) −193973. 1.34911e6i −0.0390342 0.271489i
\(478\) 151227. 331141.i 0.0302733 0.0662892i
\(479\) −258840. + 1.80027e6i −0.0515457 + 0.358508i 0.947682 + 0.319216i \(0.103420\pi\)
−0.999228 + 0.0392926i \(0.987490\pi\)
\(480\) 117176. + 75304.4i 0.0232132 + 0.0149182i
\(481\) −3.94377e6 4.55135e6i −0.777228 0.896969i
\(482\) 3.07689e6 0.603246
\(483\) −1.32853e6 + 531283.i −0.259122 + 0.103623i
\(484\) 3.14291e6 0.609843
\(485\) −184601. 213041.i −0.0356353 0.0411253i
\(486\) −166015. 106691.i −0.0318828 0.0204898i
\(487\) −382367. + 2.65942e6i −0.0730564 + 0.508119i 0.920133 + 0.391606i \(0.128080\pi\)
−0.993189 + 0.116512i \(0.962829\pi\)
\(488\) −2.58797e6 + 5.66686e6i −0.491937 + 1.07719i
\(489\) 427720. + 2.97486e6i 0.0808886 + 0.562592i
\(490\) 108235. + 31780.6i 0.0203646 + 0.00597959i
\(491\) 8.95633e6 5.75588e6i 1.67659 1.07748i 0.792983 0.609244i \(-0.208527\pi\)
0.883605 0.468234i \(-0.155109\pi\)
\(492\) 950251. + 2.08076e6i 0.176981 + 0.387533i
\(493\) 1.78277e6 523468.i 0.330353 0.0970003i
\(494\) 1.86419e6 2.15138e6i 0.343694 0.396644i
\(495\) −14021.2 + 16181.3i −0.00257200 + 0.00296825i
\(496\) −29042.3 + 8527.60i −0.00530063 + 0.00155641i
\(497\) 1.25572e6 + 2.74965e6i 0.228036 + 0.499329i
\(498\) −1.82672e6 + 1.17396e6i −0.330064 + 0.212119i
\(499\) 4.19948e6 + 1.23308e6i 0.754995 + 0.221687i 0.636509 0.771269i \(-0.280378\pi\)
0.118486 + 0.992956i \(0.462196\pi\)
\(500\) 48502.0 + 337339.i 0.00867630 + 0.0603450i
\(501\) 122486. 268208.i 0.0218019 0.0477394i
\(502\) 869469. 6.04729e6i 0.153991 1.07103i
\(503\) 7.77439e6 + 4.99630e6i 1.37008 + 0.880498i 0.998845 0.0480406i \(-0.0152977\pi\)
0.371236 + 0.928539i \(0.378934\pi\)
\(504\) 586886. + 677303.i 0.102915 + 0.118770i
\(505\) 2755.87 0.000480873
\(506\) −280021. + 808082.i −0.0486199 + 0.140307i
\(507\) 6.05382e6 1.04595
\(508\) 1.34602e6 + 1.55339e6i 0.231416 + 0.267068i
\(509\) −3.11654e6 2.00288e6i −0.533186 0.342658i 0.246183 0.969223i \(-0.420824\pi\)
−0.779369 + 0.626565i \(0.784460\pi\)
\(510\) 8102.82 56356.3i 0.00137946 0.00959439i
\(511\) 1.03524e6 2.26686e6i 0.175384 0.384036i
\(512\) 125842. + 875249.i 0.0212154 + 0.147556i
\(513\) 583128. + 171222.i 0.0978297 + 0.0287254i
\(514\) 3.10766e6 1.99717e6i 0.518831 0.333432i
\(515\) 115486. + 252879.i 0.0191872 + 0.0420141i
\(516\) −3.02410e6 + 887956.i −0.500002 + 0.146814i
\(517\) 434151. 501037.i 0.0714355 0.0824410i
\(518\) 808360. 932897.i 0.132367 0.152760i
\(519\) 3.94766e6 1.15914e6i 0.643311 0.188893i
\(520\) 196387. + 430028.i 0.0318497 + 0.0697411i
\(521\) 6.75456e6 4.34089e6i 1.09019 0.700624i 0.133302 0.991075i \(-0.457442\pi\)
0.956890 + 0.290452i \(0.0938056\pi\)
\(522\) 668112. + 196175.i 0.107318 + 0.0315115i
\(523\) −1.39261e6 9.68582e6i −0.222626 1.54840i −0.728049 0.685525i \(-0.759573\pi\)
0.505424 0.862871i \(-0.331336\pi\)
\(524\) −2.55637e6 + 5.59766e6i −0.406719 + 0.890591i
\(525\) −250271. + 1.74068e6i −0.0396290 + 0.275626i
\(526\) −5.67109e6 3.64459e6i −0.893722 0.574360i
\(527\) 187110. + 215937.i 0.0293475 + 0.0338688i
\(528\) −69466.4 −0.0108440
\(529\) −5.05631e6 3.98249e6i −0.785587 0.618751i
\(530\) 147371. 0.0227888
\(531\) −666857. 769594.i −0.102635 0.118447i
\(532\) −915493. 588352.i −0.140241 0.0901276i
\(533\) −1.77416e6 + 1.23395e7i −0.270504 + 1.88140i
\(534\) −1.44809e6 + 3.17087e6i −0.219756 + 0.481199i
\(535\) −42388.4 294818.i −0.00640270 0.0445317i
\(536\) −5.92578e6 1.73996e6i −0.890909 0.261594i
\(537\) 3.09389e6 1.98832e6i 0.462987 0.297544i
\(538\) 1.36741e6 + 2.99422e6i 0.203678 + 0.445993i
\(539\) −1.24656e6 + 366024.i −0.184817 + 0.0542673i
\(540\) −26060.5 + 30075.5i −0.00384591 + 0.00443842i
\(541\) −1.17929e6 + 1.36098e6i −0.173232 + 0.199921i −0.835726 0.549147i \(-0.814953\pi\)
0.662494 + 0.749068i \(0.269498\pi\)
\(542\) −901750. + 264778.i −0.131852 + 0.0387153i
\(543\) 898115. + 1.96660e6i 0.130717 + 0.286230i
\(544\) 3.58870e6 2.30632e6i 0.519924 0.334135i
\(545\) −198865. 58392.0i −0.0286792 0.00842097i
\(546\) 274070. + 1.90620e6i 0.0393442 + 0.273645i
\(547\) −3.30228e6 + 7.23099e6i −0.471896 + 1.03331i 0.512717 + 0.858558i \(0.328639\pi\)
−0.984613 + 0.174750i \(0.944088\pi\)
\(548\) −829993. + 5.77273e6i −0.118065 + 0.821163i
\(549\) −2.40432e6 1.54516e6i −0.340457 0.218798i
\(550\) 688342. + 794389.i 0.0970280 + 0.111976i
\(551\) −2.14442e6 −0.300906
\(552\) −1.31998e6 + 3.80920e6i −0.184383 + 0.532091i
\(553\) −514346. −0.0715224
\(554\) −1.34761e6 1.55523e6i −0.186548 0.215288i
\(555\) 116948. + 75157.6i 0.0161161 + 0.0103572i
\(556\) −200639. + 1.39547e6i −0.0275251 + 0.191441i
\(557\) 4.03607e6 8.83775e6i 0.551214 1.20699i −0.404999 0.914317i \(-0.632728\pi\)
0.956213 0.292673i \(-0.0945447\pi\)
\(558\) 15238.9 + 105989.i 0.00207189 + 0.0144103i
\(559\) −1.64809e7 4.83924e6i −2.23076 0.655010i
\(560\) 10571.3 6793.75i 0.00142448 0.000915460i
\(561\) 272406. + 596485.i 0.0365434 + 0.0800189i
\(562\) −5.75329e6 + 1.68932e6i −0.768379 + 0.225616i
\(563\) 1.14361e6 1.31979e6i 0.152057 0.175483i −0.674611 0.738174i \(-0.735688\pi\)
0.826667 + 0.562691i \(0.190234\pi\)
\(564\) 806938. 931256.i 0.106817 0.123274i
\(565\) −60415.2 + 17739.5i −0.00796205 + 0.00233787i
\(566\) −1.02422e6 2.24272e6i −0.134385 0.294262i
\(567\) −345876. + 222281.i −0.0451818 + 0.0290366i
\(568\) 8.17195e6 + 2.39950e6i 1.06281 + 0.312069i
\(569\) 821332. + 5.71249e6i 0.106350 + 0.739681i 0.971306 + 0.237833i \(0.0764372\pi\)
−0.864956 + 0.501848i \(0.832654\pi\)
\(570\) −27297.6 + 59773.4i −0.00351915 + 0.00770585i
\(571\) 319562. 2.22261e6i 0.0410172 0.285281i −0.958981 0.283470i \(-0.908514\pi\)
0.999998 0.00181092i \(-0.000576433\pi\)
\(572\) −1.80604e6 1.16067e6i −0.230801 0.148327i
\(573\) −65409.7 75486.9i −0.00832254 0.00960472i
\(574\) −2.55526e6 −0.323710
\(575\) −7.34513e6 + 2.93734e6i −0.926467 + 0.370497i
\(576\) 1.40035e6 0.175865
\(577\) −2.70556e6 3.12238e6i −0.338312 0.390432i 0.560946 0.827853i \(-0.310438\pi\)
−0.899257 + 0.437420i \(0.855892\pi\)
\(578\) 2.52496e6 + 1.62269e6i 0.314365 + 0.202030i
\(579\) −185894. + 1.29292e6i −0.0230446 + 0.160279i
\(580\) 58331.6 127728.i 0.00720003 0.0157659i
\(581\) 643825. + 4.47790e6i 0.0791275 + 0.550344i
\(582\) −3.10442e6 911539.i −0.379903 0.111550i
\(583\) −1.42786e6 + 917630.i −0.173986 + 0.111814i
\(584\) −2.91685e6 6.38700e6i −0.353901 0.774934i
\(585\) −208095. + 61102.2i −0.0251404 + 0.00738189i
\(586\) 7232.77 8347.06i 0.000870083 0.00100413i
\(587\) 473240. 546148.i 0.0566874 0.0654207i −0.726698 0.686957i \(-0.758946\pi\)
0.783385 + 0.621537i \(0.213491\pi\)
\(588\) −2.31693e6 + 680313.i −0.276357 + 0.0811457i
\(589\) −136989. 299965.i −0.0162704 0.0356273i
\(590\) 92625.5 59526.8i 0.0109547 0.00704016i
\(591\) 1.29445e6 + 380083.i 0.152446 + 0.0447621i
\(592\) 64188.1 + 446438.i 0.00752749 + 0.0523548i
\(593\) 5.19979e6 1.13859e7i 0.607224 1.32964i −0.317232 0.948348i \(-0.602754\pi\)
0.924457 0.381287i \(-0.124519\pi\)
\(594\) −34973.4 + 243246.i −0.00406698 + 0.0282865i
\(595\) −99789.9 64131.1i −0.0115556 0.00742636i
\(596\) 3.91513e6 + 4.51831e6i 0.451472 + 0.521027i
\(597\) −1.83955e6 −0.211240
\(598\) −6.81154e6 + 5.35250e6i −0.778919 + 0.612074i
\(599\) 3.90106e6 0.444238 0.222119 0.975020i \(-0.428703\pi\)
0.222119 + 0.975020i \(0.428703\pi\)
\(600\) 3.24476e6 + 3.74465e6i 0.367963 + 0.424652i
\(601\) −4.08525e6 2.62543e6i −0.461352 0.296493i 0.289243 0.957256i \(-0.406596\pi\)
−0.750595 + 0.660763i \(0.770233\pi\)
\(602\) 501053. 3.48490e6i 0.0563498 0.391922i
\(603\) 1.17699e6 2.57726e6i 0.131820 0.288645i
\(604\) −1.01080e6 7.03030e6i −0.112739 0.784118i
\(605\) −379368. 111393.i −0.0421379 0.0123728i
\(606\) 26609.6 17101.0i 0.00294345 0.00189164i
\(607\) −3.92508e6 8.59473e6i −0.432392 0.946805i −0.992933 0.118679i \(-0.962134\pi\)
0.560541 0.828127i \(-0.310593\pi\)
\(608\) −4.72398e6 + 1.38709e6i −0.518262 + 0.152175i
\(609\) 950015. 1.09638e6i 0.103798 0.119789i
\(610\) 202365. 233541.i 0.0220196 0.0254120i
\(611\) 6.44345e6 1.89197e6i 0.698257 0.205027i
\(612\) 506309. + 1.10866e6i 0.0546433 + 0.119652i
\(613\) 6.65938e6 4.27973e6i 0.715785 0.460007i −0.131383 0.991332i \(-0.541942\pi\)
0.847168 + 0.531324i \(0.178305\pi\)
\(614\) 3.26077e6 + 957448.i 0.349059 + 0.102493i
\(615\) −40953.8 284840.i −0.00436623 0.0303678i
\(616\) 463613. 1.01517e6i 0.0492270 0.107792i
\(617\) 1.25222e6 8.70940e6i 0.132425 0.921033i −0.809956 0.586491i \(-0.800509\pi\)
0.942381 0.334543i \(-0.108582\pi\)
\(618\) 2.68428e6 + 1.72508e6i 0.282720 + 0.181693i
\(619\) −1.15794e7 1.33634e7i −1.21468 1.40181i −0.889985 0.455990i \(-0.849285\pi\)
−0.324690 0.945820i \(-0.605260\pi\)
\(620\) 21593.2 0.00225599
\(621\) −1.64355e6 848095.i −0.171023 0.0882502i
\(622\) 292071. 0.0302700
\(623\) 4.75593e6 + 5.48863e6i 0.490925 + 0.566558i
\(624\) −591953. 380425.i −0.0608591 0.0391118i
\(625\) −1.38064e6 + 9.60254e6i −0.141377 + 0.983301i
\(626\) −4.07850e6 + 8.93068e6i −0.415973 + 0.910854i
\(627\) −107706. 749112.i −0.0109414 0.0760988i
\(628\) −1.04430e7 3.06634e6i −1.05664 0.310256i
\(629\) 3.58170e6 2.30182e6i 0.360963 0.231977i
\(630\) −18467.0 40437.1i −0.00185372 0.00405909i
\(631\) −5.82908e6 + 1.71157e6i −0.582810 + 0.171128i −0.559830 0.828608i \(-0.689134\pi\)
−0.0229797 + 0.999736i \(0.507315\pi\)
\(632\) −949022. + 1.09523e6i −0.0945113 + 0.109072i
\(633\) 5.83347e6 6.73218e6i 0.578652 0.667800i
\(634\) 4.54745e6 1.33525e6i 0.449308 0.131929i
\(635\) −107417. 235210.i −0.0105715 0.0231485i
\(636\) −2.65390e6 + 1.70556e6i −0.260161 + 0.167195i
\(637\) −1.26270e7 3.70762e6i −1.23297 0.362031i
\(638\) −123403. 858287.i −0.0120026 0.0834797i
\(639\) −1.62314e6 + 3.55417e6i −0.157254 + 0.344339i
\(640\) 48932.6 340334.i 0.00472224 0.0328439i
\(641\) 1.55140e6 + 997024.i 0.149135 + 0.0958430i 0.613080 0.790021i \(-0.289930\pi\)
−0.463945 + 0.885864i \(0.653567\pi\)
\(642\) −2.23872e6 2.58362e6i −0.214369 0.247395i
\(643\) 1.12056e7 1.06883 0.534416 0.845222i \(-0.320532\pi\)
0.534416 + 0.845222i \(0.320532\pi\)
\(644\) 2.39594e6 + 2.28625e6i 0.227647 + 0.217224i
\(645\) 396499. 0.0375269
\(646\) 1.31792e6 + 1.52096e6i 0.124253 + 0.143396i
\(647\) −5.91366e6 3.80048e6i −0.555387 0.356926i 0.232643 0.972562i \(-0.425263\pi\)
−0.788030 + 0.615636i \(0.788899\pi\)
\(648\) −164860. + 1.14663e6i −0.0154234 + 0.107272i
\(649\) −526786. + 1.15350e6i −0.0490933 + 0.107499i
\(650\) 1.51527e6 + 1.05389e7i 0.140672 + 0.978393i
\(651\) 214052. + 62851.2i 0.0197955 + 0.00581248i
\(652\) 5.85199e6 3.76084e6i 0.539119 0.346470i
\(653\) 2.52057e6 + 5.51928e6i 0.231321 + 0.506523i 0.989325 0.145727i \(-0.0465522\pi\)
−0.758003 + 0.652251i \(0.773825\pi\)
\(654\) −2.28250e6 + 670203.i −0.208673 + 0.0612719i
\(655\) 506964. 585068.i 0.0461715 0.0532848i
\(656\) 611410. 705605.i 0.0554719 0.0640180i
\(657\) 3.09074e6 907522.i 0.279350 0.0820245i
\(658\) 571811. + 1.25209e6i 0.0514858 + 0.112738i
\(659\) 1.93347e6 1.24256e6i 0.173430 0.111457i −0.451046 0.892501i \(-0.648949\pi\)
0.624476 + 0.781044i \(0.285313\pi\)
\(660\) 47549.3 + 13961.7i 0.00424898 + 0.00124761i
\(661\) 2.31223e6 + 1.60819e7i 0.205839 + 1.43164i 0.786548 + 0.617529i \(0.211866\pi\)
−0.580710 + 0.814111i \(0.697225\pi\)
\(662\) 3.83870e6 8.40558e6i 0.340439 0.745458i
\(663\) −945298. + 6.57469e6i −0.0835190 + 0.580887i
\(664\) 1.07230e7 + 6.89127e6i 0.943837 + 0.606567i
\(665\) 89653.0 + 103465.i 0.00786160 + 0.00907277i
\(666\) 1.59557e6 0.139390
\(667\) 6.40742e6 + 1.23743e6i 0.557659 + 0.107698i
\(668\) −682453. −0.0591741
\(669\) −4.94363e6 5.70526e6i −0.427052 0.492845i
\(670\) 257715. + 165623.i 0.0221795 + 0.0142539i
\(671\) −506505. + 3.52282e6i −0.0434288 + 0.302054i
\(672\) 1.38363e6 3.02973e6i 0.118194 0.258810i
\(673\) 2.81741e6 + 1.95955e7i 0.239780 + 1.66770i 0.653216 + 0.757172i \(0.273419\pi\)
−0.413436 + 0.910533i \(0.635672\pi\)
\(674\) 1.13417e7 + 3.33022e6i 0.961673 + 0.282373i
\(675\) −1.91227e6 + 1.22894e6i −0.161544 + 0.103818i
\(676\) −5.82075e6 1.27457e7i −0.489906 1.07274i
\(677\) −1.55402e7 + 4.56300e6i −1.30312 + 0.382630i −0.858372 0.513027i \(-0.828524\pi\)
−0.444745 + 0.895657i \(0.646706\pi\)
\(678\) −473267. + 546179.i −0.0395396 + 0.0456311i
\(679\) −4.41429e6 + 5.09436e6i −0.367440 + 0.424048i
\(680\) −320681. + 94160.6i −0.0265951 + 0.00780902i
\(681\) 390156. + 854323.i 0.0322382 + 0.0705918i
\(682\) 112175. 72090.7i 0.00923499 0.00593497i
\(683\) 9.10188e6 + 2.67255e6i 0.746585 + 0.219217i 0.632829 0.774291i \(-0.281894\pi\)
0.113756 + 0.993509i \(0.463712\pi\)
\(684\) −200189. 1.39234e6i −0.0163606 0.113790i
\(685\) 304785. 667387.i 0.0248180 0.0543439i
\(686\) 884809. 6.15398e6i 0.0717859 0.499282i
\(687\) 162161. + 104214.i 0.0131085 + 0.00842434i
\(688\) 842424. + 972209.i 0.0678516 + 0.0783049i
\(689\) −1.71927e7 −1.37974
\(690\) 116056. 162848.i 0.00927993 0.0130214i
\(691\) 6.11417e6 0.487127 0.243564 0.969885i \(-0.421683\pi\)
0.243564 + 0.969885i \(0.421683\pi\)
\(692\) −6.23611e6 7.19685e6i −0.495049 0.571317i
\(693\) 430714. + 276803.i 0.0340687 + 0.0218946i
\(694\) 912022. 6.34325e6i 0.0718798 0.499935i
\(695\) 73677.5 161331.i 0.00578593 0.0126694i
\(696\) −581707. 4.04586e6i −0.0455178 0.316583i
\(697\) −8.45637e6 2.48302e6i −0.659329 0.193596i
\(698\) −6.43917e6 + 4.13820e6i −0.500255 + 0.321494i
\(699\) 3.85024e6 + 8.43085e6i 0.298054 + 0.652647i
\(700\) 3.90544e6 1.14674e6i 0.301248 0.0884545i
\(701\) 7.81131e6 9.01473e6i 0.600383 0.692879i −0.371476 0.928443i \(-0.621148\pi\)
0.971859 + 0.235563i \(0.0756935\pi\)
\(702\) −1.63013e6 + 1.88127e6i −0.124847 + 0.144081i
\(703\) −4.71477e6 + 1.38438e6i −0.359809 + 0.105650i
\(704\) −724413. 1.58624e6i −0.0550877 0.120625i
\(705\) −130408. + 83808.4i −0.00988173 + 0.00635060i
\(706\) 2.82756e6 + 830248.i 0.213501 + 0.0626897i
\(707\) −9378.55 65229.3i −0.000705646 0.00490788i
\(708\) −979114. + 2.14396e6i −0.0734091 + 0.160744i
\(709\) 700585. 4.87268e6i 0.0523414 0.364042i −0.946771 0.321909i \(-0.895675\pi\)
0.999112 0.0421334i \(-0.0134154\pi\)
\(710\) −355402. 228403.i −0.0264590 0.0170042i
\(711\) −435377. 502452.i −0.0322992 0.0372752i
\(712\) 2.04625e7 1.51272
\(713\) 236223. + 975330.i 0.0174020 + 0.0718502i
\(714\) −1.36148e6 −0.0999463
\(715\) 176863. + 204111.i 0.0129381 + 0.0149314i
\(716\) −7.16096e6 4.60207e6i −0.522022 0.335483i
\(717\) 139519. 970373.i 0.0101352 0.0704921i
\(718\) −70755.3 + 154933.i −0.00512210 + 0.0112158i
\(719\) 2.75150e6 + 1.91371e7i 0.198494 + 1.38056i 0.808657 + 0.588280i \(0.200195\pi\)
−0.610163 + 0.792276i \(0.708896\pi\)
\(720\) 15584.9 + 4576.14i 0.00112040 + 0.000328979i
\(721\) 5.59244e6 3.59404e6i 0.400648 0.257481i
\(722\) 2.47273e6 + 5.41452e6i 0.176536 + 0.386560i
\(723\) 7.95039e6 2.33445e6i 0.565644 0.166088i
\(724\) 3.27692e6 3.78177e6i 0.232337 0.268132i
\(725\) 5.25241e6 6.06160e6i 0.371119 0.428294i
\(726\) −4.35426e6 + 1.27853e6i −0.306600 + 0.0900259i
\(727\) 9.92335e6 + 2.17291e7i 0.696342 + 1.52478i 0.844352 + 0.535790i \(0.179986\pi\)
−0.148010 + 0.988986i \(0.547287\pi\)
\(728\) 9.51009e6 6.11177e6i 0.665053 0.427404i
\(729\) −509914. 149724.i −0.0355368 0.0104345i
\(730\) 49566.7 + 344744.i 0.00344257 + 0.0239436i
\(731\) 5.04456e6 1.10460e7i 0.349164 0.764562i
\(732\) −941419. + 6.54772e6i −0.0649390 + 0.451660i
\(733\) 1.76808e7 + 1.13628e7i 1.21547 + 0.781133i 0.981565 0.191127i \(-0.0612143\pi\)
0.233902 + 0.972260i \(0.424851\pi\)
\(734\) −3.89419e6 4.49413e6i −0.266794 0.307897i
\(735\) 303780. 0.0207416
\(736\) 1.49154e7 1.41858e6i 1.01494 0.0965293i
\(737\) −3.52826e6 −0.239272
\(738\) −2.16295e6 2.49617e6i −0.146186 0.168707i
\(739\) −754677. 485002.i −0.0508335 0.0326687i 0.514977 0.857204i \(-0.327800\pi\)
−0.565811 + 0.824535i \(0.691437\pi\)
\(740\) 45791.1 318484.i 0.00307399 0.0213801i
\(741\) 3.18462e6 6.97334e6i 0.213065 0.466547i
\(742\) −501519. 3.48814e6i −0.0334409 0.232587i
\(743\) 1.54019e7 + 4.52240e6i 1.02353 + 0.300536i 0.750078 0.661349i \(-0.230016\pi\)
0.273454 + 0.961885i \(0.411834\pi\)
\(744\) 528781. 339827.i 0.0350222 0.0225074i
\(745\) −312441. 684150.i −0.0206242 0.0451607i
\(746\) −1.12380e7 + 3.29977e6i −0.739335 + 0.217088i
\(747\) −3.82938e6 + 4.41933e6i −0.251088 + 0.289771i
\(748\) 993916. 1.14704e6i 0.0649525 0.0749592i
\(749\) −6.83385e6 + 2.00660e6i −0.445104 + 0.130694i
\(750\) −204424. 447626.i −0.0132702 0.0290578i
\(751\) 4.94317e6 3.17678e6i 0.319820 0.205536i −0.370873 0.928683i \(-0.620942\pi\)
0.690694 + 0.723147i \(0.257305\pi\)
\(752\) −482570. 141695.i −0.0311183 0.00913715i
\(753\) −2.34147e6 1.62853e7i −0.150488 1.04667i
\(754\) 3.64874e6 7.98962e6i 0.233730 0.511797i
\(755\) −127161. + 884426.i −0.00811872 + 0.0564669i
\(756\) 800549. + 514482.i 0.0509429 + 0.0327390i
\(757\) 6.90199e6 + 7.96532e6i 0.437758 + 0.505200i 0.931165 0.364599i \(-0.118794\pi\)
−0.493406 + 0.869799i \(0.664248\pi\)
\(758\) −1.49231e6 −0.0943378
\(759\) −110453. + 2.30046e6i −0.00695944 + 0.144947i
\(760\) 385734. 0.0242245
\(761\) −1.33759e7 1.54367e7i −0.837265 0.966255i 0.162526 0.986704i \(-0.448036\pi\)
−0.999791 + 0.0204490i \(0.993490\pi\)
\(762\) −2.49672e6 1.60455e6i −0.155770 0.100107i
\(763\) −705331. + 4.90568e6i −0.0438613 + 0.305062i
\(764\) −96037.9 + 210294.i −0.00595264 + 0.0130345i
\(765\) −21820.8 151767.i −0.00134809 0.00937614i
\(766\) 2.65664e6 + 780060.i 0.163592 + 0.0480348i
\(767\) −1.08060e7 + 6.94457e6i −0.663247 + 0.426243i
\(768\) −3.70775e6 8.11884e6i −0.226834 0.496696i
\(769\) −6.07850e6 + 1.78481e6i −0.370664 + 0.108837i −0.461759 0.887005i \(-0.652781\pi\)
0.0910950 + 0.995842i \(0.470963\pi\)
\(770\) −36251.9 + 41836.9i −0.00220345 + 0.00254292i
\(771\) 6.51464e6 7.51830e6i 0.394688 0.455495i
\(772\) 2.90085e6 851765.i 0.175179 0.0514371i
\(773\) −1.17257e7 2.56756e7i −0.705812 1.54551i −0.832779 0.553605i \(-0.813252\pi\)
0.126968 0.991907i \(-0.459475\pi\)
\(774\) 3.82844e6 2.46039e6i 0.229704 0.147622i
\(775\) 1.18344e6 + 347490.i 0.0707770 + 0.0207820i
\(776\) 2.70293e6 + 1.87993e7i 0.161131 + 1.12069i
\(777\) 1.38093e6 3.02382e6i 0.0820579 0.179682i
\(778\) −2.15828e6 + 1.50112e7i −0.127838 + 0.889132i
\(779\) 8.55708e6 + 5.49930e6i 0.505222 + 0.324686i
\(780\) 328728. + 379372.i 0.0193464 + 0.0223269i
\(781\) 4.86565e6 0.285439
\(782\) −3.06022e6 5.30506e6i −0.178951 0.310223i
\(783\) 1.87518e6 0.109305
\(784\) 645429. + 744865.i 0.0375023 + 0.0432800i
\(785\) 1.15185e6 + 740251.i 0.0667149 + 0.0428751i
\(786\) 1.26454e6 8.79505e6i 0.0730088 0.507787i
\(787\) −107164. + 234656.i −0.00616754 + 0.0135050i −0.912691 0.408651i \(-0.865999\pi\)
0.906523 + 0.422156i \(0.138727\pi\)
\(788\) −444385. 3.09076e6i −0.0254943 0.177317i
\(789\) −1.74187e7 5.11460e6i −0.996148 0.292495i
\(790\) 60473.2 38863.8i 0.00344743 0.00221553i
\(791\) 625480. + 1.36961e6i 0.0355445 + 0.0778315i
\(792\) 1.38413e6 406416.i 0.0784085 0.0230228i
\(793\) −2.36085e7 + 2.72456e7i −1.33317 + 1.53856i
\(794\) −9.43732e6 + 1.08912e7i −0.531248 + 0.613093i
\(795\) 380792. 111811.i 0.0213683 0.00627430i
\(796\) 1.76873e6 + 3.87298e6i 0.0989416 + 0.216652i
\(797\) 742785. 477359.i 0.0414207 0.0266195i −0.519767 0.854308i \(-0.673981\pi\)
0.561187 + 0.827689i \(0.310345\pi\)
\(798\) 1.50768e6 + 442696.i 0.0838114 + 0.0246093i
\(799\) 675659. + 4.69931e6i 0.0374421 + 0.260416i
\(800\) 7.64977e6 1.67507e7i 0.422594 0.925352i
\(801\) −1.33597e6 + 9.29189e6i −0.0735726 + 0.511709i
\(802\) −1.17948e7 7.58006e6i −0.647522 0.416137i
\(803\) −2.62686e6 3.03156e6i −0.143763 0.165912i
\(804\) −6.55782e6 −0.357783
\(805\) −208174. 360883.i −0.0113224 0.0196280i
\(806\) 1.35069e6 0.0732349
\(807\) 5.80500e6 + 6.69932e6i 0.313775 + 0.362116i
\(808\) −156201. 100385.i −0.00841698 0.00540927i
\(809\) −1.72508e6 + 1.19982e7i −0.0926696 + 0.644531i 0.889556 + 0.456826i \(0.151014\pi\)
−0.982225 + 0.187705i \(0.939895\pi\)
\(810\) 23870.3 52268.6i 0.00127833 0.00279916i
\(811\) −4.57655e6 3.18306e7i −0.244335 1.69939i −0.629875 0.776697i \(-0.716894\pi\)
0.385539 0.922691i \(-0.374015\pi\)
\(812\) −3.22174e6 945988.i −0.171475 0.0503495i
\(813\) −2.12915e6 + 1.36832e6i −0.112974 + 0.0726042i
\(814\) −825405. 1.80738e6i −0.0436622 0.0956070i
\(815\) −839665. + 246548.i −0.0442804 + 0.0130019i
\(816\) 325769. 375957.i 0.0171271 0.0197657i
\(817\) −9.17796e6 + 1.05919e7i −0.481051 + 0.555162i
\(818\) 4.27280e6 1.25461e6i 0.223269 0.0655578i
\(819\) 2.15441e6 + 4.71751e6i 0.112233 + 0.245755i
\(820\) −560322. + 360097.i −0.0291007 + 0.0187019i
\(821\) −2.02967e7 5.95966e6i −1.05092 0.308577i −0.289729 0.957109i \(-0.593565\pi\)
−0.761188 + 0.648532i \(0.775383\pi\)
\(822\) −1.19844e6 8.33530e6i −0.0618636 0.430271i
\(823\) −8.78282e6 + 1.92317e7i −0.451996 + 0.989732i 0.537244 + 0.843427i \(0.319465\pi\)
−0.989239 + 0.146305i \(0.953262\pi\)
\(824\) 2.66561e6 1.85397e7i 0.136766 0.951229i
\(825\) 2.38132e6 + 1.53038e6i 0.121810 + 0.0782824i
\(826\) −1.72417e6 1.98979e6i −0.0879284 0.101475i
\(827\) −2.72099e7 −1.38345 −0.691725 0.722161i \(-0.743149\pi\)
−0.691725 + 0.722161i \(0.743149\pi\)
\(828\) −205295. + 4.27577e6i −0.0104064 + 0.216740i
\(829\) −1.05961e7 −0.535503 −0.267751 0.963488i \(-0.586281\pi\)
−0.267751 + 0.963488i \(0.586281\pi\)
\(830\) −414045. 477834.i −0.0208618 0.0240758i
\(831\) −4.66207e6 2.99613e6i −0.234194 0.150507i
\(832\) 2.51385e6 1.74842e7i 0.125901 0.875664i
\(833\) 3.86492e6 8.46299e6i 0.192987 0.422583i
\(834\) −289705. 2.01494e6i −0.0144225 0.100311i
\(835\) 82376.3 + 24187.9i 0.00408871 + 0.00120055i
\(836\) −1.47362e6 + 947035.i −0.0729237 + 0.0468652i
\(837\) 119790. + 262303.i 0.00591026 + 0.0129417i
\(838\) −5.46750e6 + 1.60540e6i −0.268954 + 0.0789721i
\(839\) −1.45226e7 + 1.67600e7i −0.712264 + 0.821996i −0.990354 0.138559i \(-0.955753\pi\)
0.278091 + 0.960555i \(0.410298\pi\)
\(840\) −170887. + 197214.i −0.00835624 + 0.00964361i
\(841\) 1.33318e7 3.91457e6i 0.649978 0.190851i
\(842\) −1.96103e6 4.29406e6i −0.0953245 0.208732i
\(843\) −1.35843e7 + 8.73007e6i −0.658366 + 0.423106i
\(844\) −1.97828e7 5.80874e6i −0.955940 0.280689i
\(845\) 250862. + 1.74478e6i 0.0120863 + 0.0840620i
\(846\) −739118. + 1.61844e6i −0.0355049 + 0.0777448i
\(847\) −1.34554e6 + 9.35843e6i −0.0644448 + 0.448223i
\(848\) 1.08321e6 + 696137.i 0.0517277 + 0.0332434i
\(849\) −4.34804e6 5.01790e6i −0.207026 0.238920i
\(850\) −7.52732e6 −0.357350
\(851\) 1.48864e7 1.41581e6i 0.704636 0.0670166i
\(852\) 9.04357e6 0.426816
\(853\) 1.66929e7 + 1.92646e7i 0.785524 + 0.906543i 0.997495 0.0707327i \(-0.0225337\pi\)
−0.211971 + 0.977276i \(0.567988\pi\)
\(854\) −6.21640e6 3.99504e6i −0.291672 0.187446i
\(855\) −25184.1 + 175160.i −0.00117818 + 0.00819443i
\(856\) −8.33640e6 + 1.82542e7i −0.388861 + 0.851486i
\(857\) −991093. 6.89320e6i −0.0460959 0.320604i −0.999803 0.0198659i \(-0.993676\pi\)
0.953707 0.300738i \(-0.0972330\pi\)
\(858\) 2.97429e6 + 873329.i 0.137932 + 0.0405004i
\(859\) 9.18906e6 5.90545e6i 0.424902 0.273068i −0.310666 0.950519i \(-0.600552\pi\)
0.735567 + 0.677452i \(0.236916\pi\)
\(860\) −381234. 834786.i −0.0175770 0.0384883i
\(861\) −6.60256e6 + 1.93869e6i −0.303532 + 0.0891250i
\(862\) 1.63274e7 1.88428e7i 0.748426 0.863730i
\(863\) 7.01014e6 8.09014e6i 0.320405 0.369768i −0.572583 0.819847i \(-0.694059\pi\)
0.892989 + 0.450079i \(0.148604\pi\)
\(864\) 4.13087e6 1.21293e6i 0.188259 0.0552779i
\(865\) 497662. + 1.08973e6i 0.0226149 + 0.0495197i
\(866\) −2.69875e6 + 1.73438e6i −0.122284 + 0.0785868i
\(867\) 7.75540e6 + 2.27719e6i 0.350394 + 0.102885i
\(868\) −73484.2 511094.i −0.00331051 0.0230251i
\(869\) −343927. + 753095.i −0.0154496 + 0.0338299i
\(870\) −28854.4 + 200687.i −0.00129245 + 0.00898920i
\(871\) −3.00657e7 1.93221e7i −1.34285 0.862995i
\(872\) 9.14459e6 + 1.05534e7i 0.407261 + 0.470004i
\(873\) −8.71311e6 −0.386935
\(874\) 1.66385e6 + 6.86979e6i 0.0736777 + 0.304204i
\(875\) −1.02524e6 −0.0452693
\(876\) −4.88243e6 5.63463e6i −0.214969 0.248087i
\(877\) 1.14743e7 + 7.37411e6i 0.503766 + 0.323751i 0.767721 0.640784i \(-0.221391\pi\)
−0.263955 + 0.964535i \(0.585027\pi\)
\(878\) 504886. 3.51156e6i 0.0221033 0.153732i
\(879\) 12355.9 27055.6i 0.000539387 0.00118109i
\(880\) −2878.59 20021.0i −0.000125306 0.000871525i
\(881\) 1.55015e7 + 4.55165e6i 0.672874 + 0.197574i 0.600283 0.799788i \(-0.295055\pi\)
0.0725918 + 0.997362i \(0.476873\pi\)
\(882\) 2.93318e6 1.88504e6i 0.126960 0.0815924i
\(883\) −4.98039e6 1.09055e7i −0.214962 0.470701i 0.771178 0.636620i \(-0.219668\pi\)
−0.986139 + 0.165920i \(0.946941\pi\)
\(884\) 1.47512e7 4.33135e6i 0.634888 0.186420i
\(885\) 194173. 224087.i 0.00833354 0.00961742i
\(886\) −1.38048e7 + 1.59316e7i −0.590807 + 0.681828i
\(887\) 1.81704e7 5.33530e6i 0.775452 0.227693i 0.130020 0.991511i \(-0.458496\pi\)
0.645432 + 0.763818i \(0.276678\pi\)
\(888\) −3.89086e6 8.51979e6i −0.165582 0.362574i
\(889\) −5.20169e6 + 3.34292e6i −0.220744 + 0.141864i
\(890\) −973888. 285959.i −0.0412130 0.0121012i
\(891\) 94183.1 + 655058.i 0.00397447 + 0.0276430i
\(892\) −7.25850e6 + 1.58939e7i −0.305446 + 0.668834i
\(893\) 779801. 5.42363e6i 0.0327231 0.227594i
\(894\) −7.26215e6 4.66710e6i −0.303893 0.195300i
\(895\) 701263. + 809301.i 0.0292633 + 0.0337717i
\(896\) −8.22194e6 −0.342140
\(897\) −1.35394e7 + 1.89983e7i −0.561848 + 0.788377i
\(898\) 2.26960e7 0.939200
\(899\) −666307. 768959.i −0.0274963 0.0317325i
\(900\) 4.42605e6 + 2.84445e6i 0.182142 + 0.117055i
\(901\) 1.72980e6 1.20310e7i 0.0709876 0.493730i
\(902\) −1.70862e6 + 3.74137e6i −0.0699247 + 0.153114i
\(903\) −1.34933e6 9.38481e6i −0.0550680 0.383006i
\(904\) 4.07048e6 + 1.19520e6i 0.165662 + 0.0486429i
\(905\) −529580. + 340340.i −0.0214936 + 0.0138131i
\(906\) 4.26029e6 + 9.32874e6i 0.172432 + 0.377574i
\(907\) 3.99085e7 1.17182e7i 1.61082 0.472979i 0.652290 0.757970i \(-0.273809\pi\)
0.958530 + 0.284990i \(0.0919904\pi\)
\(908\) 1.42355e6 1.64286e6i 0.0573004 0.0661282i
\(909\) 55782.2 64376.1i 0.00223916 0.00258413i
\(910\) −538032. + 157981.i −0.0215380 + 0.00632412i
\(911\) 1.44620e7 + 3.16674e7i 0.577341 + 1.26420i 0.942796 + 0.333371i \(0.108186\pi\)
−0.365455 + 0.930829i \(0.619087\pi\)
\(912\) −482996. + 310403.i −0.0192290 + 0.0123577i
\(913\) 6.98697e6 + 2.05156e6i 0.277403 + 0.0814530i
\(914\) 3.86548e6 + 2.68850e7i 0.153052 + 1.06450i
\(915\) 345703. 756983.i 0.0136505 0.0298905i
\(916\) 63494.5 441614.i 0.00250033 0.0173902i
\(917\) −1.55733e7 1.00084e7i −0.611588 0.393043i
\(918\) −1.15245e6 1.33000e6i −0.0451352 0.0520888i
\(919\) 4.00368e7 1.56376 0.781881 0.623428i \(-0.214261\pi\)
0.781881 + 0.623428i \(0.214261\pi\)
\(920\) −1.15255e6 222587.i −0.0448944 0.00867023i
\(921\) 9.15194e6 0.355520
\(922\) −9.01149e6 1.03998e7i −0.349116 0.402901i
\(923\) 4.14622e7 + 2.66461e7i 1.60195 + 1.02951i
\(924\) 168647. 1.17297e6i 0.00649829 0.0451966i
\(925\) 7.63486e6 1.67180e7i 0.293391 0.642437i
\(926\) 3.66332e6 + 2.54790e7i 0.140394 + 0.976460i
\(927\) 8.24474e6 + 2.42087e6i 0.315121 + 0.0925279i
\(928\) −1.27795e7 + 8.21288e6i −0.487129 + 0.313059i
\(929\) −1.11031e6 2.43124e6i −0.0422091 0.0924249i 0.887353 0.461091i \(-0.152542\pi\)
−0.929562 + 0.368666i \(0.879815\pi\)
\(930\) −29915.7 + 8784.05i −0.00113421 + 0.000333033i
\(931\) −7.03175e6 + 8.11507e6i −0.265882 + 0.306844i
\(932\) 1.40482e7 1.62125e7i 0.529763 0.611379i
\(933\) 754684. 221595.i 0.0283832 0.00833405i
\(934\) −1.21252e7 2.65505e7i −0.454802 0.995878i
\(935\) −160626. + 103228.i −0.00600878 + 0.00386161i
\(936\) 1.40204e7 + 4.11677e6i 0.523084 + 0.153591i
\(937\) −5.35770e6 3.72636e7i −0.199356 1.38655i −0.806159 0.591699i \(-0.798457\pi\)
0.606803 0.794852i \(-0.292452\pi\)
\(938\) 3.04313e6 6.66353e6i 0.112931 0.247285i
\(939\) −3.76274e6 + 2.61704e7i −0.139264 + 0.968604i
\(940\) 301837. + 193979.i 0.0111417 + 0.00716036i
\(941\) 1.82872e7 + 2.11045e7i 0.673244 + 0.776965i 0.984880 0.173236i \(-0.0554224\pi\)
−0.311636 + 0.950202i \(0.600877\pi\)
\(942\) 1.57153e7 0.577027
\(943\) −2.23948e7 2.13695e7i −0.820101 0.782555i
\(944\) 962008. 0.0351357
\(945\) −78396.7 90474.6i −0.00285574 0.00329570i
\(946\) −4.76749e6 3.06388e6i −0.173206 0.111312i
\(947\) −1.14649e6 + 7.97402e6i −0.0415428 + 0.288936i 0.958450 + 0.285259i \(0.0920796\pi\)
−0.999993 + 0.00367734i \(0.998829\pi\)
\(948\) −639242. + 1.39975e6i −0.0231017 + 0.0505858i
\(949\) −5.78260e6 4.02189e7i −0.208429 1.44965i
\(950\) 8.33563e6 + 2.44756e6i 0.299661 + 0.0879883i
\(951\) 1.07371e7 6.90032e6i 0.384978 0.247410i
\(952\) 3.32002e6 + 7.26983e6i 0.118727 + 0.259975i
\(953\) 2.57482e7 7.56035e6i 0.918363 0.269656i 0.211806 0.977312i \(-0.432066\pi\)
0.706557 + 0.707656i \(0.250247\pi\)
\(954\) 2.98296e6 3.44252e6i 0.106115 0.122463i
\(955\) 19045.7 21979.9i 0.000675754 0.000779862i
\(956\) −2.17716e6 + 639272.i −0.0770453 + 0.0226225i
\(957\) −970047. 2.12411e6i −0.0342383 0.0749715i
\(958\) −5.11347e6 + 3.28623e6i −0.180012 + 0.115687i
\(959\) −1.68337e7 4.94283e6i −0.591063 0.173552i
\(960\) 58028.5 + 403597.i 0.00203218 + 0.0141341i
\(961\) −1.18280e7 + 2.58997e7i −0.413145 + 0.904661i
\(962\) 2.86431e6 1.99217e7i 0.0997889 0.694047i
\(963\) −7.74483e6 4.97730e6i −0.269120 0.172953i
\(964\) −1.25592e7 1.44941e7i −0.435282 0.502342i
\(965\) −380339. −0.0131478
\(966\) −4.24943e6 2.19276e6i −0.146517 0.0756046i
\(967\) −2.16966e7 −0.746147 −0.373074 0.927802i \(-0.621696\pi\)
−0.373074 + 0.927802i \(0.621696\pi\)
\(968\) 1.74449e7 + 2.01324e7i 0.598383 + 0.690570i
\(969\) 4.55935e6 + 2.93011e6i 0.155989 + 0.100248i
\(970\) 134074. 932502.i 0.00457524 0.0318215i
\(971\) 6.26691e6 1.37226e7i 0.213307 0.467078i −0.772488 0.635029i \(-0.780988\pi\)
0.985795 + 0.167952i \(0.0537152\pi\)
\(972\) 175054. + 1.21753e6i 0.00594301 + 0.0413346i
\(973\) −4.06931e6 1.19486e6i −0.137797 0.0404608i
\(974\) −7.55379e6 + 4.85453e6i −0.255134 + 0.163964i
\(975\) 1.19112e7 + 2.60820e7i 0.401278 + 0.878677i
\(976\) 2.59061e6 760672.i 0.0870518 0.0255607i
\(977\) −3.15574e6 + 3.64191e6i −0.105770 + 0.122066i −0.806166 0.591689i \(-0.798461\pi\)
0.700396 + 0.713755i \(0.253007\pi\)
\(978\) −6.57757e6 + 7.59093e6i −0.219897 + 0.253774i
\(979\) 1.12165e7 3.29346e6i 0.374025 0.109824i
\(980\) −292085. 639577.i −0.00971502 0.0212729i
\(981\) −5.38928e6 + 3.46348e6i −0.178796 + 0.114905i
\(982\) 3.41391e7 + 1.00242e7i 1.12973 + 0.331718i
\(983\) −5.70229e6 3.96603e7i −0.188220 1.30910i −0.836614 0.547793i \(-0.815468\pi\)
0.648394 0.761305i \(-0.275441\pi\)
\(984\) −8.05425e6 + 1.76363e7i −0.265178 + 0.580658i
\(985\) −55904.5 + 388825.i −0.00183593 + 0.0127692i
\(986\) 5.22382e6 + 3.35714e6i 0.171118 + 0.109971i
\(987\) 2.42747e6 + 2.80145e6i 0.0793161 + 0.0915356i
\(988\) −1.77436e7 −0.578295
\(989\) 3.35353e7 2.63520e7i 1.09021 0.856689i
\(990\) −71555.5 −0.00232036
\(991\) 1.19840e7 + 1.38302e7i 0.387629 + 0.447348i 0.915706 0.401848i \(-0.131632\pi\)
−0.528077 + 0.849197i \(0.677087\pi\)
\(992\) −1.96521e6 1.26296e6i −0.0634059 0.0407485i
\(993\) 3.54150e6 2.46317e7i 0.113976 0.792722i
\(994\) −4.19664e6 + 9.18935e6i −0.134721 + 0.294998i
\(995\) −76228.5 530181.i −0.00244095 0.0169772i
\(996\) 1.29864e7 + 3.81314e6i 0.414801 + 0.121797i
\(997\) −1.23718e7 + 7.95087e6i −0.394180 + 0.253324i −0.722684 0.691178i \(-0.757092\pi\)
0.328504 + 0.944503i \(0.393456\pi\)
\(998\) 6.07636e6 + 1.33054e7i 0.193116 + 0.422864i
\(999\) 4.12281e6 1.21057e6i 0.130701 0.0383774i
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 69.6.e.b.13.6 100
23.16 even 11 inner 69.6.e.b.16.6 yes 100
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
69.6.e.b.13.6 100 1.1 even 1 trivial
69.6.e.b.16.6 yes 100 23.16 even 11 inner