Properties

Label 15.5.d.c.14.2
Level $15$
Weight $5$
Character 15.14
Analytic conductor $1.551$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [15,5,Mod(14,15)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(15, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("15.14");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 15 = 3 \cdot 5 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 15.d (of order \(2\), degree \(1\), 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: \(1.55054944626\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\sqrt{10}, \sqrt{-26})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} + 8x^{2} + 81 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 3^{2} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 14.2
Root \(-1.58114 + 2.54951i\) of defining polynomial
Character \(\chi\) \(=\) 15.14
Dual form 15.5.d.c.14.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-3.16228 q^{2} +(-4.74342 + 7.64853i) q^{3} -6.00000 q^{4} +(-6.32456 + 24.1868i) q^{5} +(15.0000 - 24.1868i) q^{6} -15.2971i q^{7} +69.5701 q^{8} +(-36.0000 - 72.5603i) q^{9} +O(q^{10})\) \(q-3.16228 q^{2} +(-4.74342 + 7.64853i) q^{3} -6.00000 q^{4} +(-6.32456 + 24.1868i) q^{5} +(15.0000 - 24.1868i) q^{6} -15.2971i q^{7} +69.5701 q^{8} +(-36.0000 - 72.5603i) q^{9} +(20.0000 - 76.4853i) q^{10} +96.7471i q^{11} +(28.4605 - 45.8912i) q^{12} +244.753i q^{13} +48.3735i q^{14} +(-154.993 - 163.101i) q^{15} -124.000 q^{16} -278.280 q^{17} +(113.842 + 229.456i) q^{18} +308.000 q^{19} +(37.9473 - 145.121i) q^{20} +(117.000 + 72.5603i) q^{21} -305.941i q^{22} +414.258 q^{23} +(-330.000 + 532.109i) q^{24} +(-545.000 - 305.941i) q^{25} -773.977i q^{26} +(725.743 + 68.8368i) q^{27} +91.7824i q^{28} -193.494i q^{29} +(490.132 + 515.772i) q^{30} +32.0000 q^{31} -720.999 q^{32} +(-739.973 - 458.912i) q^{33} +880.000 q^{34} +(369.986 + 96.7471i) q^{35} +(216.000 + 435.362i) q^{36} +1284.95i q^{37} -973.982 q^{38} +(-1872.00 - 1160.97i) q^{39} +(-440.000 + 1682.68i) q^{40} +2080.06i q^{41} +(-369.986 - 229.456i) q^{42} -2585.20i q^{43} -580.483i q^{44} +(1982.68 - 411.812i) q^{45} -1310.00 q^{46} +2444.44 q^{47} +(588.184 - 948.418i) q^{48} +2167.00 q^{49} +(1723.44 + 967.471i) q^{50} +(1320.00 - 2128.44i) q^{51} -1468.52i q^{52} -1416.70 q^{53} +(-2295.00 - 217.681i) q^{54} +(-2340.00 - 611.882i) q^{55} -1064.22i q^{56} +(-1460.97 + 2355.75i) q^{57} +611.882i q^{58} +3966.63i q^{59} +(929.959 + 978.609i) q^{60} -928.000 q^{61} -101.193 q^{62} +(-1109.96 + 550.694i) q^{63} +4264.00 q^{64} +(-5919.78 - 1547.95i) q^{65} +(2340.00 + 1451.21i) q^{66} +2585.20i q^{67} +1669.68 q^{68} +(-1965.00 + 3168.47i) q^{69} +(-1170.00 - 305.941i) q^{70} -4643.86i q^{71} +(-2504.52 - 5048.03i) q^{72} +4221.99i q^{73} -4063.38i q^{74} +(4925.16 - 2717.24i) q^{75} -1848.00 q^{76} +1479.95 q^{77} +(5919.78 + 3671.29i) q^{78} +8.00000 q^{79} +(784.245 - 2999.16i) q^{80} +(-3969.00 + 5224.34i) q^{81} -6577.74i q^{82} +4436.68 q^{83} +(-702.000 - 435.362i) q^{84} +(1760.00 - 6730.71i) q^{85} +8175.13i q^{86} +(1479.95 + 917.824i) q^{87} +6730.71i q^{88} -9287.72i q^{89} +(-6269.80 + 1302.26i) q^{90} +3744.00 q^{91} -2485.55 q^{92} +(-151.789 + 244.753i) q^{93} -7730.00 q^{94} +(-1947.96 + 7449.53i) q^{95} +(3420.00 - 5514.58i) q^{96} +2508.72i q^{97} -6852.66 q^{98} +(7020.00 - 3482.90i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 24 q^{4} + 60 q^{6} - 144 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 24 q^{4} + 60 q^{6} - 144 q^{9} + 80 q^{10} + 120 q^{15} - 496 q^{16} + 1232 q^{19} + 468 q^{21} - 1320 q^{24} - 2180 q^{25} + 2340 q^{30} + 128 q^{31} + 3520 q^{34} + 864 q^{36} - 7488 q^{39} - 1760 q^{40} + 7020 q^{45} - 5240 q^{46} + 8668 q^{49} + 5280 q^{51} - 9180 q^{54} - 9360 q^{55} - 720 q^{60} - 3712 q^{61} + 17056 q^{64} + 9360 q^{66} - 7860 q^{69} - 4680 q^{70} + 9360 q^{75} - 7392 q^{76} + 32 q^{79} - 15876 q^{81} - 2808 q^{84} + 7040 q^{85} - 2880 q^{90} + 14976 q^{91} - 30920 q^{94} + 13680 q^{96} + 28080 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).

\(n\) \(7\) \(11\)
\(\chi(n)\) \(-1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −3.16228 −0.790569 −0.395285 0.918559i \(-0.629354\pi\)
−0.395285 + 0.918559i \(0.629354\pi\)
\(3\) −4.74342 + 7.64853i −0.527046 + 0.849837i
\(4\) −6.00000 −0.375000
\(5\) −6.32456 + 24.1868i −0.252982 + 0.967471i
\(6\) 15.0000 24.1868i 0.416667 0.671855i
\(7\) 15.2971i 0.312185i −0.987742 0.156092i \(-0.950110\pi\)
0.987742 0.156092i \(-0.0498898\pi\)
\(8\) 69.5701 1.08703
\(9\) −36.0000 72.5603i −0.444444 0.895806i
\(10\) 20.0000 76.4853i 0.200000 0.764853i
\(11\) 96.7471i 0.799563i 0.916611 + 0.399781i \(0.130914\pi\)
−0.916611 + 0.399781i \(0.869086\pi\)
\(12\) 28.4605 45.8912i 0.197642 0.318689i
\(13\) 244.753i 1.44824i 0.689673 + 0.724121i \(0.257754\pi\)
−0.689673 + 0.724121i \(0.742246\pi\)
\(14\) 48.3735i 0.246804i
\(15\) −154.993 163.101i −0.688859 0.724895i
\(16\) −124.000 −0.484375
\(17\) −278.280 −0.962908 −0.481454 0.876471i \(-0.659891\pi\)
−0.481454 + 0.876471i \(0.659891\pi\)
\(18\) 113.842 + 229.456i 0.351364 + 0.708197i
\(19\) 308.000 0.853186 0.426593 0.904444i \(-0.359714\pi\)
0.426593 + 0.904444i \(0.359714\pi\)
\(20\) 37.9473 145.121i 0.0948683 0.362802i
\(21\) 117.000 + 72.5603i 0.265306 + 0.164536i
\(22\) 305.941i 0.632110i
\(23\) 414.258 0.783097 0.391549 0.920157i \(-0.371940\pi\)
0.391549 + 0.920157i \(0.371940\pi\)
\(24\) −330.000 + 532.109i −0.572917 + 0.923800i
\(25\) −545.000 305.941i −0.872000 0.489506i
\(26\) 773.977i 1.14494i
\(27\) 725.743 + 68.8368i 0.995532 + 0.0944263i
\(28\) 91.7824i 0.117069i
\(29\) 193.494i 0.230076i −0.993361 0.115038i \(-0.963301\pi\)
0.993361 0.115038i \(-0.0366990\pi\)
\(30\) 490.132 + 515.772i 0.544591 + 0.573080i
\(31\) 32.0000 0.0332986 0.0166493 0.999861i \(-0.494700\pi\)
0.0166493 + 0.999861i \(0.494700\pi\)
\(32\) −720.999 −0.704101
\(33\) −739.973 458.912i −0.679498 0.421407i
\(34\) 880.000 0.761246
\(35\) 369.986 + 96.7471i 0.302030 + 0.0789772i
\(36\) 216.000 + 435.362i 0.166667 + 0.335927i
\(37\) 1284.95i 0.938607i 0.883037 + 0.469303i \(0.155495\pi\)
−0.883037 + 0.469303i \(0.844505\pi\)
\(38\) −973.982 −0.674502
\(39\) −1872.00 1160.97i −1.23077 0.763291i
\(40\) −440.000 + 1682.68i −0.275000 + 1.05167i
\(41\) 2080.06i 1.23740i 0.785629 + 0.618698i \(0.212340\pi\)
−0.785629 + 0.618698i \(0.787660\pi\)
\(42\) −369.986 229.456i −0.209743 0.130077i
\(43\) 2585.20i 1.39816i −0.715042 0.699081i \(-0.753593\pi\)
0.715042 0.699081i \(-0.246407\pi\)
\(44\) 580.483i 0.299836i
\(45\) 1982.68 411.812i 0.979103 0.203364i
\(46\) −1310.00 −0.619093
\(47\) 2444.44 1.10658 0.553291 0.832988i \(-0.313372\pi\)
0.553291 + 0.832988i \(0.313372\pi\)
\(48\) 588.184 948.418i 0.255288 0.411640i
\(49\) 2167.00 0.902541
\(50\) 1723.44 + 967.471i 0.689377 + 0.386988i
\(51\) 1320.00 2128.44i 0.507497 0.818315i
\(52\) 1468.52i 0.543091i
\(53\) −1416.70 −0.504343 −0.252172 0.967683i \(-0.581145\pi\)
−0.252172 + 0.967683i \(0.581145\pi\)
\(54\) −2295.00 217.681i −0.787037 0.0746505i
\(55\) −2340.00 611.882i −0.773554 0.202275i
\(56\) 1064.22i 0.339355i
\(57\) −1460.97 + 2355.75i −0.449668 + 0.725068i
\(58\) 611.882i 0.181891i
\(59\) 3966.63i 1.13951i 0.821815 + 0.569754i \(0.192962\pi\)
−0.821815 + 0.569754i \(0.807038\pi\)
\(60\) 929.959 + 978.609i 0.258322 + 0.271836i
\(61\) −928.000 −0.249395 −0.124698 0.992195i \(-0.539796\pi\)
−0.124698 + 0.992195i \(0.539796\pi\)
\(62\) −101.193 −0.0263249
\(63\) −1109.96 + 550.694i −0.279657 + 0.138749i
\(64\) 4264.00 1.04102
\(65\) −5919.78 1547.95i −1.40113 0.366380i
\(66\) 2340.00 + 1451.21i 0.537190 + 0.333151i
\(67\) 2585.20i 0.575897i 0.957646 + 0.287949i \(0.0929732\pi\)
−0.957646 + 0.287949i \(0.907027\pi\)
\(68\) 1669.68 0.361091
\(69\) −1965.00 + 3168.47i −0.412728 + 0.665505i
\(70\) −1170.00 305.941i −0.238776 0.0624370i
\(71\) 4643.86i 0.921218i −0.887603 0.460609i \(-0.847631\pi\)
0.887603 0.460609i \(-0.152369\pi\)
\(72\) −2504.52 5048.03i −0.483126 0.973771i
\(73\) 4221.99i 0.792266i 0.918193 + 0.396133i \(0.129648\pi\)
−0.918193 + 0.396133i \(0.870352\pi\)
\(74\) 4063.38i 0.742034i
\(75\) 4925.16 2717.24i 0.875584 0.483065i
\(76\) −1848.00 −0.319945
\(77\) 1479.95 0.249611
\(78\) 5919.78 + 3671.29i 0.973009 + 0.603434i
\(79\) 8.00000 0.00128185 0.000640923 1.00000i \(-0.499796\pi\)
0.000640923 1.00000i \(0.499796\pi\)
\(80\) 784.245 2999.16i 0.122538 0.468619i
\(81\) −3969.00 + 5224.34i −0.604938 + 0.796272i
\(82\) 6577.74i 0.978247i
\(83\) 4436.68 0.644023 0.322012 0.946736i \(-0.395641\pi\)
0.322012 + 0.946736i \(0.395641\pi\)
\(84\) −702.000 435.362i −0.0994898 0.0617010i
\(85\) 1760.00 6730.71i 0.243599 0.931586i
\(86\) 8175.13i 1.10534i
\(87\) 1479.95 + 917.824i 0.195527 + 0.121261i
\(88\) 6730.71i 0.869151i
\(89\) 9287.72i 1.17254i −0.810114 0.586272i \(-0.800595\pi\)
0.810114 0.586272i \(-0.199405\pi\)
\(90\) −6269.80 + 1302.26i −0.774049 + 0.160773i
\(91\) 3744.00 0.452119
\(92\) −2485.55 −0.293661
\(93\) −151.789 + 244.753i −0.0175499 + 0.0282984i
\(94\) −7730.00 −0.874830
\(95\) −1947.96 + 7449.53i −0.215841 + 0.825432i
\(96\) 3420.00 5514.58i 0.371094 0.598371i
\(97\) 2508.72i 0.266630i 0.991074 + 0.133315i \(0.0425621\pi\)
−0.991074 + 0.133315i \(0.957438\pi\)
\(98\) −6852.66 −0.713521
\(99\) 7020.00 3482.90i 0.716253 0.355361i
\(100\) 3270.00 + 1835.65i 0.327000 + 0.183565i
\(101\) 4837.35i 0.474204i −0.971485 0.237102i \(-0.923802\pi\)
0.971485 0.237102i \(-0.0761976\pi\)
\(102\) −4174.21 + 6730.71i −0.401212 + 0.646934i
\(103\) 5491.64i 0.517640i −0.965926 0.258820i \(-0.916666\pi\)
0.965926 0.258820i \(-0.0833337\pi\)
\(104\) 17027.5i 1.57429i
\(105\) −2494.97 + 2370.94i −0.226301 + 0.215051i
\(106\) 4480.00 0.398718
\(107\) −2925.11 −0.255490 −0.127745 0.991807i \(-0.540774\pi\)
−0.127745 + 0.991807i \(0.540774\pi\)
\(108\) −4354.46 413.021i −0.373324 0.0354099i
\(109\) −6352.00 −0.534635 −0.267318 0.963608i \(-0.586137\pi\)
−0.267318 + 0.963608i \(0.586137\pi\)
\(110\) 7399.73 + 1934.94i 0.611548 + 0.159913i
\(111\) −9828.00 6095.07i −0.797663 0.494689i
\(112\) 1896.84i 0.151215i
\(113\) 8867.03 0.694418 0.347209 0.937788i \(-0.387129\pi\)
0.347209 + 0.937788i \(0.387129\pi\)
\(114\) 4620.00 7449.53i 0.355494 0.573217i
\(115\) −2620.00 + 10019.6i −0.198110 + 0.757624i
\(116\) 1160.97i 0.0862786i
\(117\) 17759.4 8811.11i 1.29734 0.643663i
\(118\) 12543.6i 0.900861i
\(119\) 4256.87i 0.300605i
\(120\) −10782.9 11347.0i −0.748812 0.787985i
\(121\) 5281.00 0.360699
\(122\) 2934.59 0.197164
\(123\) −15909.4 9866.60i −1.05158 0.652165i
\(124\) −192.000 −0.0124870
\(125\) 10846.6 11246.8i 0.694183 0.719798i
\(126\) 3510.00 1741.45i 0.221088 0.109691i
\(127\) 3808.97i 0.236156i 0.993004 + 0.118078i \(0.0376734\pi\)
−0.993004 + 0.118078i \(0.962327\pi\)
\(128\) −1947.96 −0.118894
\(129\) 19773.0 + 12262.7i 1.18821 + 0.736896i
\(130\) 18720.0 + 4895.06i 1.10769 + 0.289648i
\(131\) 8030.01i 0.467922i 0.972246 + 0.233961i \(0.0751688\pi\)
−0.972246 + 0.233961i \(0.924831\pi\)
\(132\) 4439.84 + 2753.47i 0.254812 + 0.158027i
\(133\) 4711.49i 0.266352i
\(134\) 8175.13i 0.455287i
\(135\) −6254.94 + 17118.0i −0.343207 + 0.939260i
\(136\) −19360.0 −1.04671
\(137\) −21263.2 −1.13289 −0.566443 0.824101i \(-0.691681\pi\)
−0.566443 + 0.824101i \(0.691681\pi\)
\(138\) 6213.88 10019.6i 0.326290 0.526128i
\(139\) −19372.0 −1.00264 −0.501320 0.865262i \(-0.667152\pi\)
−0.501320 + 0.865262i \(0.667152\pi\)
\(140\) −2219.92 580.483i −0.113261 0.0296165i
\(141\) −11595.0 + 18696.4i −0.583220 + 0.940414i
\(142\) 14685.2i 0.728287i
\(143\) −23679.1 −1.15796
\(144\) 4464.00 + 8997.48i 0.215278 + 0.433906i
\(145\) 4680.00 + 1223.76i 0.222592 + 0.0582052i
\(146\) 13351.1i 0.626342i
\(147\) −10279.0 + 16574.4i −0.475681 + 0.767012i
\(148\) 7709.72i 0.351978i
\(149\) 16205.1i 0.729928i −0.931022 0.364964i \(-0.881081\pi\)
0.931022 0.364964i \(-0.118919\pi\)
\(150\) −15574.7 + 8592.67i −0.692210 + 0.381897i
\(151\) 33272.0 1.45923 0.729617 0.683856i \(-0.239698\pi\)
0.729617 + 0.683856i \(0.239698\pi\)
\(152\) 21427.6 0.927441
\(153\) 10018.1 + 20192.1i 0.427959 + 0.862579i
\(154\) −4680.00 −0.197335
\(155\) −202.386 + 773.977i −0.00842397 + 0.0322155i
\(156\) 11232.0 + 6965.79i 0.461538 + 0.286234i
\(157\) 29309.2i 1.18906i −0.804073 0.594530i \(-0.797338\pi\)
0.804073 0.594530i \(-0.202662\pi\)
\(158\) −25.2982 −0.00101339
\(159\) 6720.00 10835.7i 0.265812 0.428609i
\(160\) 4560.00 17438.6i 0.178125 0.681197i
\(161\) 6336.93i 0.244471i
\(162\) 12551.1 16520.8i 0.478246 0.629509i
\(163\) 12252.9i 0.461174i 0.973052 + 0.230587i \(0.0740647\pi\)
−0.973052 + 0.230587i \(0.925935\pi\)
\(164\) 12480.4i 0.464023i
\(165\) 15779.6 14995.1i 0.579599 0.550786i
\(166\) −14030.0 −0.509145
\(167\) 2520.34 0.0903702 0.0451851 0.998979i \(-0.485612\pi\)
0.0451851 + 0.998979i \(0.485612\pi\)
\(168\) 8139.70 + 5048.03i 0.288396 + 0.178856i
\(169\) −31343.0 −1.09741
\(170\) −5565.61 + 21284.4i −0.192582 + 0.736483i
\(171\) −11088.0 22348.6i −0.379194 0.764289i
\(172\) 15511.2i 0.524311i
\(173\) 49318.9 1.64786 0.823931 0.566690i \(-0.191776\pi\)
0.823931 + 0.566690i \(0.191776\pi\)
\(174\) −4680.00 2902.41i −0.154578 0.0958651i
\(175\) −4680.00 + 8336.90i −0.152816 + 0.272225i
\(176\) 11996.6i 0.387288i
\(177\) −30338.9 18815.4i −0.968396 0.600574i
\(178\) 29370.4i 0.926977i
\(179\) 38021.6i 1.18665i 0.804961 + 0.593327i \(0.202186\pi\)
−0.804961 + 0.593327i \(0.797814\pi\)
\(180\) −11896.1 + 2470.87i −0.367164 + 0.0762615i
\(181\) 20342.0 0.620921 0.310461 0.950586i \(-0.399517\pi\)
0.310461 + 0.950586i \(0.399517\pi\)
\(182\) −11839.6 −0.357432
\(183\) 4401.89 7097.84i 0.131443 0.211945i
\(184\) 28820.0 0.851252
\(185\) −31078.9 8126.76i −0.908075 0.237451i
\(186\) 480.000 773.977i 0.0138744 0.0223719i
\(187\) 26922.8i 0.769905i
\(188\) −14666.6 −0.414968
\(189\) 1053.00 11101.7i 0.0294785 0.310790i
\(190\) 6160.00 23557.5i 0.170637 0.652562i
\(191\) 55532.8i 1.52224i 0.648611 + 0.761120i \(0.275350\pi\)
−0.648611 + 0.761120i \(0.724650\pi\)
\(192\) −20225.9 + 32613.3i −0.548663 + 0.884693i
\(193\) 50725.0i 1.36178i 0.732384 + 0.680891i \(0.238407\pi\)
−0.732384 + 0.680891i \(0.761593\pi\)
\(194\) 7933.26i 0.210789i
\(195\) 39919.6 37935.1i 1.04982 0.997634i
\(196\) −13002.0 −0.338453
\(197\) 28865.3 0.743778 0.371889 0.928277i \(-0.378710\pi\)
0.371889 + 0.928277i \(0.378710\pi\)
\(198\) −22199.2 + 11013.9i −0.566248 + 0.280938i
\(199\) 34328.0 0.866847 0.433423 0.901190i \(-0.357305\pi\)
0.433423 + 0.901190i \(0.357305\pi\)
\(200\) −37915.7 21284.4i −0.947893 0.532109i
\(201\) −19773.0 12262.7i −0.489419 0.303525i
\(202\) 15297.1i 0.374891i
\(203\) −2959.89 −0.0718263
\(204\) −7920.00 + 12770.6i −0.190311 + 0.306868i
\(205\) −50310.0 13155.5i −1.19714 0.313039i
\(206\) 17366.1i 0.409230i
\(207\) −14913.3 30058.7i −0.348043 0.701503i
\(208\) 30349.4i 0.701492i
\(209\) 29798.1i 0.682175i
\(210\) 7889.80 7497.57i 0.178907 0.170013i
\(211\) −33268.0 −0.747243 −0.373621 0.927581i \(-0.621884\pi\)
−0.373621 + 0.927581i \(0.621884\pi\)
\(212\) 8500.20 0.189129
\(213\) 35518.7 + 22027.8i 0.782885 + 0.485525i
\(214\) 9250.00 0.201983
\(215\) 62527.7 + 16350.3i 1.35268 + 0.353710i
\(216\) 50490.0 + 4788.98i 1.08218 + 0.102644i
\(217\) 489.506i 0.0103953i
\(218\) 20086.8 0.422666
\(219\) −32292.0 20026.6i −0.673297 0.417561i
\(220\) 14040.0 + 3671.29i 0.290083 + 0.0758532i
\(221\) 68110.0i 1.39452i
\(222\) 31078.9 + 19274.3i 0.630608 + 0.391086i
\(223\) 76011.1i 1.52851i −0.644916 0.764253i \(-0.723108\pi\)
0.644916 0.764253i \(-0.276892\pi\)
\(224\) 11029.2i 0.219810i
\(225\) −2579.19 + 50559.3i −0.0509469 + 0.998701i
\(226\) −28040.0 −0.548986
\(227\) 16788.5 0.325807 0.162904 0.986642i \(-0.447914\pi\)
0.162904 + 0.986642i \(0.447914\pi\)
\(228\) 8765.83 14134.5i 0.168626 0.271901i
\(229\) 40298.0 0.768445 0.384222 0.923241i \(-0.374470\pi\)
0.384222 + 0.923241i \(0.374470\pi\)
\(230\) 8285.17 31684.7i 0.156619 0.598954i
\(231\) −7020.00 + 11319.4i −0.131557 + 0.212129i
\(232\) 13461.4i 0.250101i
\(233\) −87253.6 −1.60721 −0.803603 0.595166i \(-0.797086\pi\)
−0.803603 + 0.595166i \(0.797086\pi\)
\(234\) −56160.0 + 27863.2i −1.02564 + 0.508860i
\(235\) −15460.0 + 59123.1i −0.279946 + 1.07059i
\(236\) 23799.8i 0.427316i
\(237\) −37.9473 + 61.1882i −0.000675592 + 0.00108936i
\(238\) 13461.4i 0.237649i
\(239\) 88620.3i 1.55145i −0.631072 0.775725i \(-0.717385\pi\)
0.631072 0.775725i \(-0.282615\pi\)
\(240\) 19219.2 + 20224.6i 0.333666 + 0.351121i
\(241\) 72152.0 1.24227 0.621133 0.783706i \(-0.286673\pi\)
0.621133 + 0.783706i \(0.286673\pi\)
\(242\) −16700.0 −0.285158
\(243\) −21131.9 55138.2i −0.357871 0.933771i
\(244\) 5568.00 0.0935232
\(245\) −13705.3 + 52412.7i −0.228327 + 0.873182i
\(246\) 50310.0 + 31200.9i 0.831350 + 0.515582i
\(247\) 75383.9i 1.23562i
\(248\) 2226.24 0.0361967
\(249\) −21045.0 + 33934.0i −0.339430 + 0.547314i
\(250\) −34300.0 + 35565.7i −0.548800 + 0.569051i
\(251\) 15963.3i 0.253381i 0.991942 + 0.126691i \(0.0404355\pi\)
−0.991942 + 0.126691i \(0.959564\pi\)
\(252\) 6659.76 3304.16i 0.104871 0.0520308i
\(253\) 40078.3i 0.626135i
\(254\) 12045.0i 0.186698i
\(255\) 43131.6 + 45388.0i 0.663308 + 0.698008i
\(256\) −62064.0 −0.947021
\(257\) −84938.8 −1.28600 −0.642998 0.765868i \(-0.722310\pi\)
−0.642998 + 0.765868i \(0.722310\pi\)
\(258\) −62527.7 38778.0i −0.939362 0.582568i
\(259\) 19656.0 0.293019
\(260\) 35518.7 + 9287.72i 0.525425 + 0.137392i
\(261\) −14040.0 + 6965.79i −0.206104 + 0.102256i
\(262\) 25393.1i 0.369925i
\(263\) −2849.21 −0.0411920 −0.0205960 0.999788i \(-0.506556\pi\)
−0.0205960 + 0.999788i \(0.506556\pi\)
\(264\) −51480.0 31926.5i −0.738636 0.458083i
\(265\) 8960.00 34265.4i 0.127590 0.487938i
\(266\) 14899.1i 0.210569i
\(267\) 71037.4 + 44055.5i 0.996471 + 0.617985i
\(268\) 15511.2i 0.215961i
\(269\) 3918.26i 0.0541487i −0.999633 0.0270744i \(-0.991381\pi\)
0.999633 0.0270744i \(-0.00861909\pi\)
\(270\) 19779.9 54131.9i 0.271329 0.742550i
\(271\) −67048.0 −0.912951 −0.456475 0.889736i \(-0.650888\pi\)
−0.456475 + 0.889736i \(0.650888\pi\)
\(272\) 34506.8 0.466409
\(273\) −17759.4 + 28636.1i −0.238288 + 0.384228i
\(274\) 67240.0 0.895626
\(275\) 29598.9 52727.2i 0.391391 0.697219i
\(276\) 11790.0 19010.8i 0.154773 0.249564i
\(277\) 10340.8i 0.134771i −0.997727 0.0673853i \(-0.978534\pi\)
0.997727 0.0673853i \(-0.0214657\pi\)
\(278\) 61259.6 0.792656
\(279\) −1152.00 2321.93i −0.0147994 0.0298291i
\(280\) 25740.0 + 6730.71i 0.328316 + 0.0858508i
\(281\) 22300.2i 0.282420i 0.989980 + 0.141210i \(0.0450994\pi\)
−0.989980 + 0.141210i \(0.954901\pi\)
\(282\) 36666.6 59123.1i 0.461076 0.743463i
\(283\) 117466.i 1.46669i −0.679854 0.733347i \(-0.737957\pi\)
0.679854 0.733347i \(-0.262043\pi\)
\(284\) 27863.2i 0.345457i
\(285\) −47737.9 50235.3i −0.587724 0.618470i
\(286\) 74880.0 0.915448
\(287\) 31818.8 0.386296
\(288\) 25956.0 + 52315.9i 0.312934 + 0.630738i
\(289\) −6081.00 −0.0728080
\(290\) −14799.5 3869.88i −0.175975 0.0460153i
\(291\) −19188.0 11899.9i −0.226592 0.140526i
\(292\) 25331.9i 0.297100i
\(293\) 57363.7 0.668193 0.334097 0.942539i \(-0.391569\pi\)
0.334097 + 0.942539i \(0.391569\pi\)
\(294\) 32505.0 52412.7i 0.376059 0.606376i
\(295\) −95940.0 25087.2i −1.10244 0.288276i
\(296\) 89394.3i 1.02030i
\(297\) −6659.76 + 70213.5i −0.0754997 + 0.795990i
\(298\) 51245.1i 0.577059i
\(299\) 101391.i 1.13411i
\(300\) −29551.0 + 16303.5i −0.328344 + 0.181149i
\(301\) −39546.0 −0.436485
\(302\) −105215. −1.15363
\(303\) 36998.6 + 22945.6i 0.402996 + 0.249927i
\(304\) −38192.0 −0.413262
\(305\) 5869.19 22445.3i 0.0630926 0.241283i
\(306\) −31680.0 63853.1i −0.338331 0.681929i
\(307\) 10417.3i 0.110530i −0.998472 0.0552648i \(-0.982400\pi\)
0.998472 0.0552648i \(-0.0176003\pi\)
\(308\) −8879.68 −0.0936043
\(309\) 42003.0 + 26049.2i 0.439910 + 0.272820i
\(310\) 640.000 2447.53i 0.00665973 0.0254686i
\(311\) 101971.i 1.05428i −0.849777 0.527142i \(-0.823264\pi\)
0.849777 0.527142i \(-0.176736\pi\)
\(312\) −130235. 80768.5i −1.33789 0.829722i
\(313\) 182586.i 1.86371i 0.362832 + 0.931854i \(0.381810\pi\)
−0.362832 + 0.931854i \(0.618190\pi\)
\(314\) 92683.7i 0.940035i
\(315\) −6299.51 30329.2i −0.0634872 0.305661i
\(316\) −48.0000 −0.000480692
\(317\) 33494.8 0.333319 0.166659 0.986015i \(-0.446702\pi\)
0.166659 + 0.986015i \(0.446702\pi\)
\(318\) −21250.5 + 34265.4i −0.210143 + 0.338845i
\(319\) 18720.0 0.183960
\(320\) −26967.9 + 103132.i −0.263358 + 1.00715i
\(321\) 13875.0 22372.8i 0.134655 0.217125i
\(322\) 20039.1i 0.193271i
\(323\) −85710.4 −0.821539
\(324\) 23814.0 31346.1i 0.226852 0.298602i
\(325\) 74880.0 133390.i 0.708923 1.26287i
\(326\) 38747.2i 0.364590i
\(327\) 30130.2 48583.5i 0.281777 0.454352i
\(328\) 144710.i 1.34509i
\(329\) 37392.8i 0.345458i
\(330\) −49899.5 + 47418.8i −0.458214 + 0.435434i
\(331\) 204092. 1.86282 0.931408 0.363977i \(-0.118581\pi\)
0.931408 + 0.363977i \(0.118581\pi\)
\(332\) −26620.1 −0.241509
\(333\) 93236.6 46258.3i 0.840810 0.417159i
\(334\) −7970.00 −0.0714439
\(335\) −62527.7 16350.3i −0.557164 0.145692i
\(336\) −14508.0 8997.48i −0.128508 0.0796971i
\(337\) 44912.2i 0.395461i −0.980256 0.197731i \(-0.936643\pi\)
0.980256 0.197731i \(-0.0633572\pi\)
\(338\) 99115.3 0.867575
\(339\) −42060.0 + 67819.7i −0.365991 + 0.590142i
\(340\) −10560.0 + 40384.2i −0.0913495 + 0.349345i
\(341\) 3095.91i 0.0266244i
\(342\) 35063.3 + 70672.4i 0.299779 + 0.604224i
\(343\) 69877.0i 0.593944i
\(344\) 179853.i 1.51985i
\(345\) −64207.2 67566.2i −0.539443 0.567664i
\(346\) −155960. −1.30275
\(347\) 135260. 1.12334 0.561669 0.827362i \(-0.310159\pi\)
0.561669 + 0.827362i \(0.310159\pi\)
\(348\) −8879.68 5506.94i −0.0733227 0.0454728i
\(349\) −228682. −1.87751 −0.938753 0.344592i \(-0.888017\pi\)
−0.938753 + 0.344592i \(0.888017\pi\)
\(350\) 14799.5 26363.6i 0.120812 0.215213i
\(351\) −16848.0 + 177628.i −0.136752 + 1.44177i
\(352\) 69754.6i 0.562973i
\(353\) 106923. 0.858067 0.429034 0.903288i \(-0.358854\pi\)
0.429034 + 0.903288i \(0.358854\pi\)
\(354\) 95940.0 + 59499.5i 0.765585 + 0.474795i
\(355\) 112320. + 29370.4i 0.891252 + 0.233052i
\(356\) 55726.3i 0.439704i
\(357\) −32558.8 20192.1i −0.255465 0.158433i
\(358\) 120235.i 0.938133i
\(359\) 176467.i 1.36922i −0.728909 0.684611i \(-0.759972\pi\)
0.728909 0.684611i \(-0.240028\pi\)
\(360\) 137936. 28649.8i 1.06432 0.221063i
\(361\) −35457.0 −0.272074
\(362\) −64327.1 −0.490881
\(363\) −25050.0 + 40391.9i −0.190105 + 0.306536i
\(364\) −22464.0 −0.169545
\(365\) −102116. 26702.2i −0.766495 0.200429i
\(366\) −13920.0 + 22445.3i −0.103915 + 0.167557i
\(367\) 178042.i 1.32188i 0.750440 + 0.660939i \(0.229842\pi\)
−0.750440 + 0.660939i \(0.770158\pi\)
\(368\) −51368.0 −0.379313
\(369\) 150930. 74882.2i 1.10847 0.549954i
\(370\) 98280.0 + 25699.1i 0.717896 + 0.187721i
\(371\) 21671.3i 0.157448i
\(372\) 910.736 1468.52i 0.00658122 0.0106119i
\(373\) 77770.2i 0.558979i −0.960149 0.279490i \(-0.909835\pi\)
0.960149 0.279490i \(-0.0901653\pi\)
\(374\) 85137.4i 0.608664i
\(375\) 34571.9 + 136309.i 0.245844 + 0.969309i
\(376\) 170060. 1.20289
\(377\) 47358.3 0.333206
\(378\) −3329.88 + 35106.7i −0.0233048 + 0.245701i
\(379\) −12292.0 −0.0855745 −0.0427872 0.999084i \(-0.513624\pi\)
−0.0427872 + 0.999084i \(0.513624\pi\)
\(380\) 11687.8 44697.2i 0.0809403 0.309537i
\(381\) −29133.0 18067.5i −0.200694 0.124465i
\(382\) 175610.i 1.20344i
\(383\) −246111. −1.67777 −0.838886 0.544308i \(-0.816792\pi\)
−0.838886 + 0.544308i \(0.816792\pi\)
\(384\) 9240.00 14899.1i 0.0626628 0.101041i
\(385\) −9360.00 + 35795.1i −0.0631472 + 0.241492i
\(386\) 160407.i 1.07658i
\(387\) −187583. + 93067.3i −1.25248 + 0.621406i
\(388\) 15052.3i 0.0999861i
\(389\) 99794.6i 0.659490i 0.944070 + 0.329745i \(0.106963\pi\)
−0.944070 + 0.329745i \(0.893037\pi\)
\(390\) −126237. + 119961.i −0.829959 + 0.788699i
\(391\) −115280. −0.754051
\(392\) 150758. 0.981091
\(393\) −61417.8 38089.7i −0.397657 0.246617i
\(394\) −91280.0 −0.588008
\(395\) −50.5964 + 193.494i −0.000324284 + 0.00124015i
\(396\) −42120.0 + 20897.4i −0.268595 + 0.133260i
\(397\) 143548.i 0.910783i 0.890291 + 0.455391i \(0.150501\pi\)
−0.890291 + 0.455391i \(0.849499\pi\)
\(398\) −108555. −0.685303
\(399\) 36036.0 + 22348.6i 0.226355 + 0.140380i
\(400\) 67580.0 + 37936.7i 0.422375 + 0.237104i
\(401\) 245738.i 1.52821i 0.645092 + 0.764105i \(0.276819\pi\)
−0.645092 + 0.764105i \(0.723181\pi\)
\(402\) 62527.7 + 38778.0i 0.386919 + 0.239957i
\(403\) 7832.09i 0.0482245i
\(404\) 29024.1i 0.177826i
\(405\) −101258. 129039.i −0.617332 0.786703i
\(406\) 9360.00 0.0567837
\(407\) −124315. −0.750475
\(408\) 91832.5 148076.i 0.551666 0.889535i
\(409\) 34808.0 0.208081 0.104041 0.994573i \(-0.466823\pi\)
0.104041 + 0.994573i \(0.466823\pi\)
\(410\) 159094. + 41601.2i 0.946426 + 0.247479i
\(411\) 100860. 162632.i 0.597084 0.962769i
\(412\) 32949.9i 0.194115i
\(413\) 60677.8 0.355737
\(414\) 47160.0 + 95054.0i 0.275152 + 0.554587i
\(415\) −28060.0 + 107309.i −0.162926 + 0.623074i
\(416\) 176467.i 1.01971i
\(417\) 91889.5 148167.i 0.528437 0.852080i
\(418\) 94229.9i 0.539307i
\(419\) 219326.i 1.24928i 0.780911 + 0.624642i \(0.214755\pi\)
−0.780911 + 0.624642i \(0.785245\pi\)
\(420\) 14969.8 14225.6i 0.0848630 0.0806442i
\(421\) 168992. 0.953459 0.476729 0.879050i \(-0.341822\pi\)
0.476729 + 0.879050i \(0.341822\pi\)
\(422\) 105203. 0.590747
\(423\) −87999.9 177369.i −0.491814 0.991284i
\(424\) −98560.0 −0.548238
\(425\) 151663. + 85137.4i 0.839656 + 0.471349i
\(426\) −112320. 69657.9i −0.618925 0.383841i
\(427\) 14195.7i 0.0778574i
\(428\) 17550.6 0.0958088
\(429\) 112320. 181111.i 0.610299 0.984077i
\(430\) −197730. 51704.1i −1.06939 0.279633i
\(431\) 154989.i 0.834345i −0.908827 0.417173i \(-0.863021\pi\)
0.908827 0.417173i \(-0.136979\pi\)
\(432\) −89992.1 8535.76i −0.482211 0.0457377i
\(433\) 153644.i 0.819481i −0.912202 0.409740i \(-0.865619\pi\)
0.912202 0.409740i \(-0.134381\pi\)
\(434\) 1547.95i 0.00821823i
\(435\) −31559.2 + 29990.3i −0.166781 + 0.158490i
\(436\) 38112.0 0.200488
\(437\) 127592. 0.668127
\(438\) 102116. + 63329.8i 0.532288 + 0.330111i
\(439\) 65168.0 0.338147 0.169073 0.985603i \(-0.445922\pi\)
0.169073 + 0.985603i \(0.445922\pi\)
\(440\) −162794. 42568.7i −0.840878 0.219880i
\(441\) −78012.0 157238.i −0.401129 0.808502i
\(442\) 215383.i 1.10247i
\(443\) 116514. 0.593706 0.296853 0.954923i \(-0.404063\pi\)
0.296853 + 0.954923i \(0.404063\pi\)
\(444\) 58968.0 + 36570.4i 0.299123 + 0.185508i
\(445\) 224640. + 58740.7i 1.13440 + 0.296633i
\(446\) 240368.i 1.20839i
\(447\) 123945. + 76867.7i 0.620320 + 0.384706i
\(448\) 65226.7i 0.324989i
\(449\) 79090.7i 0.392313i −0.980573 0.196157i \(-0.937154\pi\)
0.980573 0.196157i \(-0.0628461\pi\)
\(450\) 8156.11 159882.i 0.0402771 0.789543i
\(451\) −201240. −0.989376
\(452\) −53202.2 −0.260407
\(453\) −157823. + 254482.i −0.769084 + 1.24011i
\(454\) −53090.0 −0.257573
\(455\) −23679.1 + 90555.3i −0.114378 + 0.437412i
\(456\) −101640. + 163890.i −0.488804 + 0.788173i
\(457\) 389402.i 1.86451i −0.361797 0.932257i \(-0.617836\pi\)
0.361797 0.932257i \(-0.382164\pi\)
\(458\) −127433. −0.607509
\(459\) −201960. 19155.9i −0.958606 0.0909238i
\(460\) 15720.0 60117.4i 0.0742911 0.284109i
\(461\) 236643.i 1.11351i 0.830678 + 0.556753i \(0.187953\pi\)
−0.830678 + 0.556753i \(0.812047\pi\)
\(462\) 22199.2 35795.1i 0.104005 0.167703i
\(463\) 253793.i 1.18391i 0.805971 + 0.591955i \(0.201644\pi\)
−0.805971 + 0.591955i \(0.798356\pi\)
\(464\) 23993.3i 0.111443i
\(465\) −4959.78 5219.25i −0.0229381 0.0241380i
\(466\) 275920. 1.27061
\(467\) −365853. −1.67754 −0.838771 0.544485i \(-0.816725\pi\)
−0.838771 + 0.544485i \(0.816725\pi\)
\(468\) −106556. + 52866.6i −0.486504 + 0.241374i
\(469\) 39546.0 0.179786
\(470\) 48888.8 186964.i 0.221316 0.846373i
\(471\) 224172. + 139026.i 1.01051 + 0.626690i
\(472\) 275959.i 1.23868i
\(473\) 250111. 1.11792
\(474\) 120.000 193.494i 0.000534102 0.000861214i
\(475\) −167860. 94229.9i −0.743978 0.417639i
\(476\) 25541.2i 0.112727i
\(477\) 51001.2 + 102796.i 0.224153 + 0.451794i
\(478\) 280242.i 1.22653i
\(479\) 255606.i 1.11404i −0.830500 0.557019i \(-0.811945\pi\)
0.830500 0.557019i \(-0.188055\pi\)
\(480\) 111750. + 117596.i 0.485026 + 0.510400i
\(481\) −314496. −1.35933
\(482\) −228165. −0.982097
\(483\) 48468.2 + 30058.7i 0.207760 + 0.128848i
\(484\) −31686.0 −0.135262
\(485\) −60677.8 15866.5i −0.257956 0.0674525i
\(486\) 66825.0 + 174362.i 0.282922 + 0.738211i
\(487\) 445925.i 1.88020i −0.340902 0.940099i \(-0.610733\pi\)
0.340902 0.940099i \(-0.389267\pi\)
\(488\) −64561.1 −0.271101
\(489\) −93717.0 58120.8i −0.391923 0.243060i
\(490\) 43340.0 165744.i 0.180508 0.690311i
\(491\) 229387.i 0.951495i −0.879582 0.475747i \(-0.842178\pi\)
0.879582 0.475747i \(-0.157822\pi\)
\(492\) 95456.5 + 59199.6i 0.394344 + 0.244562i
\(493\) 53845.6i 0.221542i
\(494\) 238385.i 0.976843i
\(495\) 39841.6 + 191819.i 0.162602 + 0.782854i
\(496\) −3968.00 −0.0161290
\(497\) −71037.4 −0.287590
\(498\) 66550.1 107309.i 0.268343 0.432690i
\(499\) 157748. 0.633524 0.316762 0.948505i \(-0.397404\pi\)
0.316762 + 0.948505i \(0.397404\pi\)
\(500\) −65079.7 + 67481.1i −0.260319 + 0.269924i
\(501\) −11955.0 + 19276.9i −0.0476293 + 0.0767999i
\(502\) 50480.3i 0.200315i
\(503\) 499630. 1.97475 0.987377 0.158390i \(-0.0506302\pi\)
0.987377 + 0.158390i \(0.0506302\pi\)
\(504\) −77220.0 + 38311.8i −0.303997 + 0.150825i
\(505\) 117000. + 30594.1i 0.458779 + 0.119965i
\(506\) 126739.i 0.495003i
\(507\) 148673. 239728.i 0.578384 0.932615i
\(508\) 22853.8i 0.0885587i
\(509\) 153441.i 0.592251i 0.955149 + 0.296125i \(0.0956946\pi\)
−0.955149 + 0.296125i \(0.904305\pi\)
\(510\) −136394. 143529.i −0.524391 0.551824i
\(511\) 64584.0 0.247334
\(512\) 227431. 0.867580
\(513\) 223529. + 21201.7i 0.849373 + 0.0805631i
\(514\) 268600. 1.01667
\(515\) 132825. + 34732.2i 0.500802 + 0.130954i
\(516\) −118638. 73576.2i −0.445579 0.276336i
\(517\) 236493.i 0.884782i
\(518\) −62157.7 −0.231652
\(519\) −233940. + 377217.i −0.868500 + 1.40041i
\(520\) −411840. 107691.i −1.52308 0.398267i
\(521\) 242642.i 0.893902i −0.894558 0.446951i \(-0.852510\pi\)
0.894558 0.446951i \(-0.147490\pi\)
\(522\) 44398.4 22027.8i 0.162939 0.0808406i
\(523\) 133865.i 0.489398i 0.969599 + 0.244699i \(0.0786892\pi\)
−0.969599 + 0.244699i \(0.921311\pi\)
\(524\) 48180.1i 0.175471i
\(525\) −41565.8 75340.5i −0.150806 0.273344i
\(526\) 9010.00 0.0325652
\(527\) −8904.97 −0.0320635
\(528\) 91756.6 + 56905.1i 0.329132 + 0.204119i
\(529\) −108231. −0.386759
\(530\) −28334.0 + 108357.i −0.100869 + 0.385748i
\(531\) 287820. 142799.i 1.02078 0.506448i
\(532\) 28269.0i 0.0998819i
\(533\) −509101. −1.79205
\(534\) −224640. 139316.i −0.787779 0.488560i
\(535\) 18500.0 70748.9i 0.0646345 0.247179i
\(536\) 179853.i 0.626019i
\(537\) −290809. 180352.i −1.00846 0.625422i
\(538\) 12390.6i 0.0428083i
\(539\) 209651.i 0.721638i
\(540\) 37529.6 102708.i 0.128702 0.352222i
\(541\) −195478. −0.667888 −0.333944 0.942593i \(-0.608380\pi\)
−0.333944 + 0.942593i \(0.608380\pi\)
\(542\) 212024. 0.721751
\(543\) −96490.6 + 155586.i −0.327254 + 0.527682i
\(544\) 200640. 0.677984
\(545\) 40173.6 153634.i 0.135253 0.517244i
\(546\) 56160.0 90555.3i 0.188383 0.303759i
\(547\) 143165.i 0.478479i 0.970961 + 0.239239i \(0.0768981\pi\)
−0.970961 + 0.239239i \(0.923102\pi\)
\(548\) 127579. 0.424833
\(549\) 33408.0 + 67336.0i 0.110842 + 0.223410i
\(550\) −93600.0 + 166738.i −0.309421 + 0.551200i
\(551\) 59596.2i 0.196298i
\(552\) −136705. + 220431.i −0.448649 + 0.723425i
\(553\) 122.376i 0.000400173i
\(554\) 32700.5i 0.106545i
\(555\) 209578. 199159.i 0.680392 0.646568i
\(556\) 116232. 0.375990
\(557\) −401799. −1.29509 −0.647543 0.762029i \(-0.724203\pi\)
−0.647543 + 0.762029i \(0.724203\pi\)
\(558\) 3642.94 + 7342.59i 0.0117000 + 0.0235820i
\(559\) 632736. 2.02488
\(560\) −45878.3 11996.6i −0.146296 0.0382546i
\(561\) 205920. + 127706.i 0.654294 + 0.405776i
\(562\) 70519.4i 0.223273i
\(563\) −126178. −0.398077 −0.199038 0.979992i \(-0.563782\pi\)
−0.199038 + 0.979992i \(0.563782\pi\)
\(564\) 69570.0 112178.i 0.218708 0.352655i
\(565\) −56080.0 + 214465.i −0.175675 + 0.671829i
\(566\) 371460.i 1.15952i
\(567\) 79917.1 + 60714.0i 0.248584 + 0.188853i
\(568\) 323074.i 1.00139i
\(569\) 355497.i 1.09802i 0.835815 + 0.549012i \(0.184996\pi\)
−0.835815 + 0.549012i \(0.815004\pi\)
\(570\) 150961. + 158858.i 0.464637 + 0.488944i
\(571\) −454108. −1.39279 −0.696397 0.717657i \(-0.745215\pi\)
−0.696397 + 0.717657i \(0.745215\pi\)
\(572\) 142075. 0.434235
\(573\) −424744. 263415.i −1.29366 0.802291i
\(574\) −100620. −0.305394
\(575\) −225771. 126739.i −0.682861 0.383331i
\(576\) −153504. 309397.i −0.462674 0.932548i
\(577\) 103163.i 0.309866i 0.987925 + 0.154933i \(0.0495162\pi\)
−0.987925 + 0.154933i \(0.950484\pi\)
\(578\) 19229.8 0.0575598
\(579\) −387972. 240610.i −1.15729 0.717723i
\(580\) −28080.0 7342.59i −0.0834721 0.0218270i
\(581\) 67868.1i 0.201054i
\(582\) 60677.8 + 37630.8i 0.179136 + 0.111096i
\(583\) 137062.i 0.403254i
\(584\) 293724.i 0.861220i
\(585\) 100792. + 485268.i 0.294520 + 1.41798i
\(586\) −181400. −0.528253
\(587\) 474661. 1.37755 0.688775 0.724975i \(-0.258149\pi\)
0.688775 + 0.724975i \(0.258149\pi\)
\(588\) 61673.9 99446.2i 0.178380 0.287630i
\(589\) 9856.00 0.0284099
\(590\) 303389. + 79332.6i 0.871557 + 0.227902i
\(591\) −136920. + 220777.i −0.392005 + 0.632090i
\(592\) 159334.i 0.454638i
\(593\) 173103. 0.492261 0.246130 0.969237i \(-0.420841\pi\)
0.246130 + 0.969237i \(0.420841\pi\)
\(594\) 21060.0 222035.i 0.0596878 0.629285i
\(595\) −102960. 26922.8i −0.290827 0.0760478i
\(596\) 97230.8i 0.273723i
\(597\) −162832. + 262559.i −0.456868 + 0.736678i
\(598\) 320626.i 0.896596i
\(599\) 587255.i 1.63671i −0.574710 0.818357i \(-0.694885\pi\)
0.574710 0.818357i \(-0.305115\pi\)
\(600\) 342644. 189039.i 0.951789 0.525108i
\(601\) 475352. 1.31603 0.658016 0.753004i \(-0.271396\pi\)
0.658016 + 0.753004i \(0.271396\pi\)
\(602\) 125055. 0.345072
\(603\) 187583. 93067.3i 0.515892 0.255954i
\(604\) −199632. −0.547213
\(605\) −33400.0 + 127730.i −0.0912505 + 0.348966i
\(606\) −117000. 72560.3i −0.318596 0.197585i
\(607\) 311310.i 0.844921i −0.906381 0.422461i \(-0.861166\pi\)
0.906381 0.422461i \(-0.138834\pi\)
\(608\) −222068. −0.600729
\(609\) 14040.0 22638.8i 0.0378558 0.0610407i
\(610\) −18560.0 + 70978.4i −0.0498791 + 0.190751i
\(611\) 598284.i 1.60260i
\(612\) −60108.6 121153.i −0.160485 0.323467i
\(613\) 224316.i 0.596952i −0.954417 0.298476i \(-0.903522\pi\)
0.954417 0.298476i \(-0.0964783\pi\)
\(614\) 32942.4i 0.0873813i
\(615\) 339261. 322396.i 0.896983 0.852391i
\(616\) 102960. 0.271336
\(617\) 200463. 0.526580 0.263290 0.964717i \(-0.415192\pi\)
0.263290 + 0.964717i \(0.415192\pi\)
\(618\) −132825. 82374.7i −0.347779 0.215683i
\(619\) 22508.0 0.0587429 0.0293715 0.999569i \(-0.490649\pi\)
0.0293715 + 0.999569i \(0.490649\pi\)
\(620\) 1214.31 4643.86i 0.00315899 0.0120808i
\(621\) 300645. + 28516.2i 0.779598 + 0.0739450i
\(622\) 322462.i 0.833485i
\(623\) −142075. −0.366050
\(624\) 232128. + 143960.i 0.596154 + 0.369719i
\(625\) 203425. + 333476.i 0.520768 + 0.853698i
\(626\) 577387.i 1.47339i
\(627\) −227912. 141345.i −0.579738 0.359538i
\(628\) 175855.i 0.445898i
\(629\) 357577.i 0.903792i
\(630\) 19920.8 + 95909.5i 0.0501910 + 0.241646i
\(631\) −157408. −0.395338 −0.197669 0.980269i \(-0.563337\pi\)
−0.197669 + 0.980269i \(0.563337\pi\)
\(632\) 556.561 0.00139341
\(633\) 157804. 254451.i 0.393832 0.635034i
\(634\) −105920. −0.263511
\(635\) −92126.6 24090.0i −0.228475 0.0597434i
\(636\) −40320.0 + 65014.0i −0.0996796 + 0.160729i
\(637\) 530380.i 1.30710i
\(638\) −59197.8 −0.145434
\(639\) −336960. + 167179.i −0.825233 + 0.409430i
\(640\) 12320.0 47114.9i 0.0300781 0.115027i
\(641\) 297836.i 0.724871i −0.932009 0.362436i \(-0.881945\pi\)
0.932009 0.362436i \(-0.118055\pi\)
\(642\) −43876.6 + 70748.9i −0.106454 + 0.171652i
\(643\) 130805.i 0.316376i 0.987409 + 0.158188i \(0.0505651\pi\)
−0.987409 + 0.158188i \(0.949435\pi\)
\(644\) 38021.6i 0.0916767i
\(645\) −421650. + 400689.i −1.01352 + 0.963137i
\(646\) 271040. 0.649484
\(647\) 117520. 0.280739 0.140369 0.990099i \(-0.455171\pi\)
0.140369 + 0.990099i \(0.455171\pi\)
\(648\) −276124. + 363458.i −0.657588 + 0.865574i
\(649\) −383760. −0.911109
\(650\) −236791. + 421817.i −0.560453 + 0.998384i
\(651\) 3744.00 + 2321.93i 0.00883433 + 0.00547882i
\(652\) 73517.7i 0.172940i
\(653\) −640829. −1.50285 −0.751426 0.659818i \(-0.770633\pi\)
−0.751426 + 0.659818i \(0.770633\pi\)
\(654\) −95280.0 + 153634.i −0.222765 + 0.359197i
\(655\) −194220. 50786.2i −0.452701 0.118376i
\(656\) 257928.i 0.599364i
\(657\) 306349. 151992.i 0.709717 0.352118i
\(658\) 118246.i 0.273109i
\(659\) 121805.i 0.280474i −0.990118 0.140237i \(-0.955214\pi\)
0.990118 0.140237i \(-0.0447865\pi\)
\(660\) −94677.6 + 89970.9i −0.217350 + 0.206545i
\(661\) 5072.00 0.0116085 0.00580425 0.999983i \(-0.498152\pi\)
0.00580425 + 0.999983i \(0.498152\pi\)
\(662\) −645396. −1.47269
\(663\) 520941. + 323074.i 1.18512 + 0.734979i
\(664\) 308660. 0.700074
\(665\) 113956. + 29798.1i 0.257687 + 0.0673822i
\(666\) −294840. + 146282.i −0.664719 + 0.329793i
\(667\) 80156.6i 0.180172i
\(668\) −15122.0 −0.0338888
\(669\) 581373. + 360552.i 1.29898 + 0.805593i
\(670\) 197730. + 51704.1i 0.440477 + 0.115179i
\(671\) 89781.3i 0.199407i
\(672\) −84356.9 52315.9i −0.186802 0.115850i
\(673\) 181790.i 0.401366i −0.979656 0.200683i \(-0.935684\pi\)
0.979656 0.200683i \(-0.0643161\pi\)
\(674\) 142025.i 0.312640i
\(675\) −374470. 259551.i −0.821882 0.569658i
\(676\) 188058. 0.411527
\(677\) 304666. 0.664733 0.332367 0.943150i \(-0.392153\pi\)
0.332367 + 0.943150i \(0.392153\pi\)
\(678\) 133005. 214465.i 0.289341 0.466548i
\(679\) 38376.0 0.0832377
\(680\) 122443. 468256.i 0.264800 1.01266i
\(681\) −79635.0 + 128408.i −0.171716 + 0.276883i
\(682\) 9790.12i 0.0210484i
\(683\) 627816. 1.34583 0.672917 0.739718i \(-0.265041\pi\)
0.672917 + 0.739718i \(0.265041\pi\)
\(684\) 66528.0 + 134091.i 0.142198 + 0.286608i
\(685\) 134480. 514287.i 0.286600 1.09604i
\(686\) 220970.i 0.469554i
\(687\) −191150. + 308220.i −0.405006 + 0.653052i
\(688\) 320565.i 0.677235i
\(689\) 346742.i 0.730411i
\(690\) 203041. + 213663.i 0.426467 + 0.448777i
\(691\) −17308.0 −0.0362486 −0.0181243 0.999836i \(-0.505769\pi\)
−0.0181243 + 0.999836i \(0.505769\pi\)
\(692\) −295913. −0.617949
\(693\) −53278.1 107385.i −0.110938 0.223603i
\(694\) −427730. −0.888077
\(695\) 122519. 468546.i 0.253650 0.970025i
\(696\) 102960. + 63853.1i 0.212545 + 0.131815i
\(697\) 578841.i 1.19150i
\(698\) 723156. 1.48430
\(699\) 413880. 667361.i 0.847072 1.36586i
\(700\) 28080.0 50021.4i 0.0573061 0.102084i
\(701\) 23944.9i 0.0487278i 0.999703 + 0.0243639i \(0.00775604\pi\)
−0.999703 + 0.0243639i \(0.992244\pi\)
\(702\) 53278.1 561708.i 0.108112 1.13982i
\(703\) 395765.i 0.800806i
\(704\) 412530.i 0.832357i
\(705\) −378872. 398692.i −0.762279 0.802157i
\(706\) −338120. −0.678362
\(707\) −73997.3 −0.148039
\(708\) 182033. + 112892.i 0.363149 + 0.225215i
\(709\) −381322. −0.758577 −0.379288 0.925279i \(-0.623831\pi\)
−0.379288 + 0.925279i \(0.623831\pi\)
\(710\) −355187. 92877.2i −0.704596 0.184244i
\(711\) −288.000 580.483i −0.000569709 0.00114829i
\(712\) 646148.i 1.27459i
\(713\) 13256.3 0.0260761
\(714\) 102960. + 63853.1i 0.201963 + 0.125252i
\(715\) 149760. 572722.i 0.292943 1.12029i
\(716\) 228130.i 0.444996i
\(717\) 677815. + 420363.i 1.31848 + 0.817686i
\(718\) 558037.i 1.08247i
\(719\) 927031.i 1.79323i 0.442810 + 0.896616i \(0.353982\pi\)
−0.442810 + 0.896616i \(0.646018\pi\)
\(720\) −245853. + 51064.7i −0.474253 + 0.0985044i
\(721\) −84006.0 −0.161599
\(722\) 112125. 0.215094
\(723\) −342247. + 551857.i −0.654731 + 1.05572i
\(724\) −122052. −0.232845
\(725\) −59197.8 + 105454.i −0.112624 + 0.200627i
\(726\) 79215.0 127730.i 0.150291 0.242338i
\(727\) 373998.i 0.707620i 0.935317 + 0.353810i \(0.115114\pi\)
−0.935317 + 0.353810i \(0.884886\pi\)
\(728\) 260470. 0.491469
\(729\) 521964. + 99915.6i 0.982167 + 0.188009i
\(730\) 322920. + 84439.8i 0.605967 + 0.158453i
\(731\) 719411.i 1.34630i
\(732\) −26411.3 + 42587.0i −0.0492911 + 0.0794795i
\(733\) 318240.i 0.592307i −0.955140 0.296153i \(-0.904296\pi\)
0.955140 0.296153i \(-0.0957040\pi\)
\(734\) 563020.i 1.04504i
\(735\) −335870. 353441.i −0.621723 0.654248i
\(736\) −298680. −0.551379
\(737\) −250111. −0.460466
\(738\) −477283. + 236798.i −0.876320 + 0.434777i
\(739\) 409268. 0.749409 0.374705 0.927144i \(-0.377744\pi\)
0.374705 + 0.927144i \(0.377744\pi\)
\(740\) 186473. + 48760.5i 0.340528 + 0.0890441i
\(741\) −576576. 357577.i −1.05007 0.651229i
\(742\) 68530.8i 0.124474i
\(743\) 11400.0 0.0206504 0.0103252 0.999947i \(-0.496713\pi\)
0.0103252 + 0.999947i \(0.496713\pi\)
\(744\) −10560.0 + 17027.5i −0.0190773 + 0.0307613i
\(745\) 391950. + 102490.i 0.706184 + 0.184659i
\(746\) 245931.i 0.441912i
\(747\) −159720. 321927.i −0.286233 0.576920i
\(748\) 161537.i 0.288715i
\(749\) 44745.5i 0.0797602i
\(750\) −109326. 431047.i −0.194357 0.766306i
\(751\) 347432. 0.616013 0.308007 0.951384i \(-0.400338\pi\)
0.308007 + 0.951384i \(0.400338\pi\)
\(752\) −303111. −0.536001
\(753\) −122096. 75720.4i −0.215333 0.133544i
\(754\) −149760. −0.263423
\(755\) −210431. + 804742.i −0.369160 + 1.41177i
\(756\) −6318.00 + 66610.4i −0.0110544 + 0.116546i
\(757\) 886067.i 1.54623i 0.634265 + 0.773116i \(0.281303\pi\)
−0.634265 + 0.773116i \(0.718697\pi\)
\(758\) 38870.7 0.0676525
\(759\) −306540. 190108.i −0.532113 0.330002i
\(760\) −135520. + 518264.i −0.234626 + 0.897272i
\(761\) 261604.i 0.451726i −0.974159 0.225863i \(-0.927480\pi\)
0.974159 0.225863i \(-0.0725202\pi\)
\(762\) 92126.6 + 57134.5i 0.158663 + 0.0983985i
\(763\) 97166.9i 0.166905i
\(764\) 333197.i 0.570840i
\(765\) −551742. + 114599.i −0.942786 + 0.195821i
\(766\) 778270. 1.32639
\(767\) −970845. −1.65029
\(768\) 294395. 474698.i 0.499124 0.804814i
\(769\) −832882. −1.40842 −0.704208 0.709994i \(-0.748698\pi\)
−0.704208 + 0.709994i \(0.748698\pi\)
\(770\) 29598.9 113194.i 0.0499223 0.190916i
\(771\) 402900. 649657.i 0.677780 1.09289i
\(772\) 304350.i 0.510669i
\(773\) −38529.2 −0.0644809 −0.0322404 0.999480i \(-0.510264\pi\)
−0.0322404 + 0.999480i \(0.510264\pi\)
\(774\) 593190. 294305.i 0.990175 0.491264i
\(775\) −17440.0 9790.12i −0.0290364 0.0162999i
\(776\) 174532.i 0.289835i
\(777\) −93236.6 + 150339.i −0.154435 + 0.249018i
\(778\) 315578.i 0.521372i
\(779\) 640659.i 1.05573i
\(780\) −239517. + 227610.i −0.393684 + 0.374113i
\(781\) 449280. 0.736572
\(782\) 364547. 0.596129
\(783\) 13319.5 140427.i 0.0217253 0.229048i
\(784\) −268708. −0.437168
\(785\) 708894. + 185367.i 1.15038 + 0.300811i
\(786\) 194220. + 120450.i 0.314376 + 0.194967i
\(787\) 627164.i 1.01259i 0.862362 + 0.506293i \(0.168984\pi\)
−0.862362 + 0.506293i \(0.831016\pi\)
\(788\) −173192. −0.278917
\(789\) 13515.0 21792.3i 0.0217101 0.0350065i
\(790\) 160.000 611.882i 0.000256369 0.000980424i
\(791\) 135639.i 0.216787i
\(792\) 488382. 242305.i 0.778591 0.386289i
\(793\) 227131.i 0.361185i
\(794\) 453937.i 0.720037i
\(795\) 219579. + 231066.i 0.347421 + 0.365596i
\(796\) −205968. −0.325068
\(797\) 1.09025e6 1.71637 0.858184 0.513343i \(-0.171593\pi\)
0.858184 + 0.513343i \(0.171593\pi\)
\(798\) −113956. 70672.4i −0.178950 0.110980i
\(799\) −680240. −1.06554
\(800\) 392945. + 220583.i 0.613976 + 0.344662i
\(801\) −673920. + 334358.i −1.05037 + 0.521131i
\(802\) 777091.i 1.20816i
\(803\) −408465. −0.633467
\(804\) 118638. + 73576.2i 0.183532 + 0.113822i
\(805\) 153270. + 40078.3i 0.236519 + 0.0618468i
\(806\) 24767.3i 0.0381248i
\(807\) 29968.9 + 18585.9i 0.0460176 + 0.0285389i
\(808\) 336535.i 0.515475i
\(809\) 101004.i 0.154327i −0.997018 0.0771634i \(-0.975414\pi\)
0.997018 0.0771634i \(-0.0245863\pi\)
\(810\) 320205. + 408057.i 0.488044 + 0.621943i
\(811\) −400948. −0.609602 −0.304801 0.952416i \(-0.598590\pi\)
−0.304801 + 0.952416i \(0.598590\pi\)
\(812\) 17759.4 0.0269349
\(813\) 318037. 512819.i 0.481167 0.775859i
\(814\) 393120. 0.593303
\(815\) −296359. 77494.4i −0.446173 0.116669i
\(816\) −163680. + 263926.i −0.245819 + 0.396371i
\(817\) 796242.i 1.19289i
\(818\) −110073. −0.164502
\(819\) −134784. 271666.i −0.200942 0.405011i
\(820\) 301860. + 78932.8i 0.448929 + 0.117390i
\(821\) 777895.i 1.15408i −0.816717 0.577038i \(-0.804208\pi\)
0.816717 0.577038i \(-0.195792\pi\)
\(822\) −318947. + 514287.i −0.472036 + 0.761136i
\(823\) 218457.i 0.322528i 0.986911 + 0.161264i \(0.0515570\pi\)
−0.986911 + 0.161264i \(0.948443\pi\)
\(824\) 382054.i 0.562692i
\(825\) 262885. + 476495.i 0.386241 + 0.700085i
\(826\) −191880. −0.281235
\(827\) 460867. 0.673852 0.336926 0.941531i \(-0.390613\pi\)
0.336926 + 0.941531i \(0.390613\pi\)
\(828\) 89479.8 + 180352.i 0.130516 + 0.263064i
\(829\) −60352.0 −0.0878178 −0.0439089 0.999036i \(-0.513981\pi\)
−0.0439089 + 0.999036i \(0.513981\pi\)
\(830\) 88733.5 339340.i 0.128805 0.492583i
\(831\) 79092.0 + 49050.8i 0.114533 + 0.0710303i
\(832\) 1.04363e6i 1.50764i
\(833\) −603034. −0.869064
\(834\) −290580. + 468546.i −0.417767 + 0.673628i
\(835\) −15940.0 + 60958.8i −0.0228621 + 0.0874306i
\(836\) 178789.i 0.255816i
\(837\) 23223.8 + 2202.78i 0.0331499 + 0.00314427i
\(838\) 693569.i 0.987646i
\(839\) 162148.i 0.230350i −0.993345 0.115175i \(-0.963257\pi\)
0.993345 0.115175i \(-0.0367429\pi\)
\(840\) −173576. + 164947.i −0.245997 + 0.233768i
\(841\) 669841. 0.947065
\(842\) −534400. −0.753775
\(843\) −170564. 105779.i −0.240011 0.148849i
\(844\) 199608. 0.280216
\(845\) 198231. 758086.i 0.277624 1.06171i
\(846\) 278280. + 560891.i 0.388813 + 0.783679i
\(847\) 80783.8i 0.112605i
\(848\) 175671. 0.244291
\(849\) 898443. + 557191.i 1.24645 + 0.773016i
\(850\) −479600. 269228.i −0.663806 0.372634i
\(851\) 532303.i 0.735020i
\(852\) −213112. 132167.i −0.293582 0.182072i
\(853\) 1.27675e6i 1.75472i −0.479828 0.877362i \(-0.659301\pi\)
0.479828 0.877362i \(-0.340699\pi\)
\(854\) 44890.7i 0.0615517i
\(855\) 610667. 126838.i 0.835357 0.173507i
\(856\) −203500. −0.277726
\(857\) −311105. −0.423589 −0.211795 0.977314i \(-0.567931\pi\)
−0.211795 + 0.977314i \(0.567931\pi\)
\(858\) −355187. + 572722.i −0.482484 + 0.777981i
\(859\) 1.14631e6 1.55351 0.776757 0.629801i \(-0.216863\pi\)
0.776757 + 0.629801i \(0.216863\pi\)
\(860\) −375166. 98101.6i −0.507256 0.132641i
\(861\) −150930. + 243367.i −0.203596 + 0.328289i
\(862\) 490118.i 0.659608i
\(863\) −640839. −0.860453 −0.430227 0.902721i \(-0.641566\pi\)
−0.430227 + 0.902721i \(0.641566\pi\)
\(864\) −523260. 49631.3i −0.700955 0.0664856i
\(865\) −311920. + 1.19286e6i −0.416880 + 1.59426i
\(866\) 485864.i 0.647857i
\(867\) 28844.7 46510.7i 0.0383732 0.0618749i
\(868\) 2937.04i 0.00389825i
\(869\) 773.977i 0.00102492i
\(870\) 99798.9 94837.6i 0.131852 0.125297i
\(871\) −632736. −0.834039
\(872\) −441909. −0.581166
\(873\) 182033. 90313.8i 0.238848 0.118502i
\(874\) −403480. −0.528201
\(875\) −172044. 165921.i −0.224710 0.216713i
\(876\) 193752. + 120160.i 0.252486 + 0.156585i
\(877\) 447959.i 0.582424i 0.956659 + 0.291212i \(0.0940585\pi\)
−0.956659 + 0.291212i \(0.905942\pi\)
\(878\) −206079. −0.267329
\(879\) −272100. + 438748.i −0.352169 + 0.567855i
\(880\) 290160. + 75873.4i 0.374690 + 0.0979770i
\(881\) 72995.7i 0.0940471i −0.998894 0.0470235i \(-0.985026\pi\)
0.998894 0.0470235i \(-0.0149736\pi\)
\(882\) 246696. + 497231.i 0.317120 + 0.639177i
\(883\) 797910.i 1.02337i 0.859173 + 0.511685i \(0.170978\pi\)
−0.859173 + 0.511685i \(0.829022\pi\)
\(884\) 408660.i 0.522947i
\(885\) 646963. 614801.i 0.826025 0.784961i
\(886\) −368450. −0.469365
\(887\) 1.04890e6 1.33317 0.666586 0.745428i \(-0.267755\pi\)
0.666586 + 0.745428i \(0.267755\pi\)
\(888\) −683735. 424034.i −0.867085 0.537744i
\(889\) 58266.0 0.0737245
\(890\) −710374. 185754.i −0.896824 0.234509i
\(891\) −505440. 383989.i −0.636670 0.483686i
\(892\) 456067.i 0.573190i
\(893\) 752888. 0.944120
\(894\) −391950. 243077.i −0.490406 0.304137i
\(895\) −919620. 240470.i −1.14805 0.300203i
\(896\) 29798.1i 0.0371170i
\(897\) −775492. 480940.i −0.963812 0.597731i
\(898\) 250107.i 0.310151i
\(899\) 6191.81i 0.00766123i
\(900\) 15475.1 303356.i 0.0191051 0.374513i
\(901\) 394240. 0.485636
\(902\) 636377. 0.782170
\(903\) 187583. 302469.i 0.230048 0.370941i
\(904\) 616880. 0.754856
\(905\) −128654. + 492007.i −0.157082 + 0.600723i
\(906\) 499080. 804742.i 0.608014 0.980394i
\(907\) 1.06515e6i 1.29478i −0.762159 0.647390i \(-0.775861\pi\)
0.762159 0.647390i \(-0.224139\pi\)
\(908\) −100731. −0.122178
\(909\) −351000. + 174145.i −0.424795 + 0.210757i
\(910\) 74880.0 286361.i 0.0904239 0.345805i
\(911\) 1.25520e6i 1.51243i −0.654324 0.756215i \(-0.727047\pi\)
0.654324 0.756215i \(-0.272953\pi\)
\(912\) 181161. 292113.i 0.217808 0.351205i
\(913\) 429235.i 0.514937i
\(914\) 1.23140e6i 1.47403i
\(915\) 143834. + 151358.i 0.171798 + 0.180786i
\(916\) −241788. −0.288167
\(917\) 122836. 0.146078
\(918\) 638654. + 60576.4i 0.757844 + 0.0718816i
\(919\) 552368. 0.654030 0.327015 0.945019i \(-0.393957\pi\)
0.327015 + 0.945019i \(0.393957\pi\)
\(920\) −182274. + 697063.i −0.215352 + 0.823562i
\(921\) 79677.0 + 49413.6i 0.0939320 + 0.0582542i
\(922\) 748332.i 0.880304i
\(923\) 1.13660e6 1.33415
\(924\) 42120.0 67916.5i 0.0493338 0.0795483i
\(925\) 393120. 700299.i 0.459454 0.818465i
\(926\) 802566.i 0.935963i
\(927\) −398475. + 197699.i −0.463705 + 0.230062i
\(928\) 139509.i 0.161997i
\(929\) 748290.i 0.867039i −0.901144 0.433520i \(-0.857271\pi\)
0.901144 0.433520i \(-0.142729\pi\)
\(930\) 15684.2 + 16504.7i 0.0181341 + 0.0190828i
\(931\) 667436. 0.770035
\(932\) 523521. 0.602702
\(933\) 779932. + 483693.i 0.895969 + 0.555657i
\(934\) 1.15693e6 1.32621
\(935\) 651176. + 170275.i 0.744861 + 0.194772i
\(936\) 1.23552e6 612990.i 1.41026 0.699683i
\(937\) 173102.i 0.197161i −0.995129 0.0985807i \(-0.968570\pi\)
0.995129 0.0985807i \(-0.0314302\pi\)
\(938\) −125055. −0.142134
\(939\) −1.39651e6 866080.i −1.58385 0.982261i
\(940\) 92760.0 354739.i 0.104980 0.401470i
\(941\) 1.74861e6i 1.97475i 0.158388 + 0.987377i \(0.449370\pi\)
−0.158388 + 0.987377i \(0.550630\pi\)
\(942\) −708894. 439637.i −0.798876 0.495442i
\(943\) 861683.i 0.969001i
\(944\) 491862.i 0.551950i
\(945\) 261855. + 95682.2i 0.293223 + 0.107144i
\(946\) −790920. −0.883792
\(947\) −983427. −1.09658 −0.548292 0.836287i \(-0.684722\pi\)
−0.548292 + 0.836287i \(0.684722\pi\)
\(948\) 227.684 367.129i 0.000253347 0.000408510i
\(949\) −1.03334e6 −1.14739
\(950\) 530820. + 297981.i 0.588166 + 0.330173i
\(951\) −158880. + 256186.i −0.175674 + 0.283266i
\(952\) 296151.i 0.326768i
\(953\) −894507. −0.984913 −0.492457 0.870337i \(-0.663901\pi\)
−0.492457 + 0.870337i \(0.663901\pi\)
\(954\) −161280. 325070.i −0.177208 0.357175i
\(955\) −1.34316e6 351220.i −1.47272 0.385100i
\(956\) 531722.i 0.581793i
\(957\) −88796.8 + 143180.i −0.0969557 + 0.156336i
\(958\) 808297.i 0.880724i
\(959\) 325264.i 0.353670i
\(960\) −660891. 695465.i −0.717113 0.754628i
\(961\) −922497. −0.998891
\(962\) 994524. 1.07464
\(963\) 105304. + 212247.i 0.113551 + 0.228870i
\(964\) −432912. −0.465849
\(965\) −1.22688e6 320813.i −1.31749 0.344507i
\(966\) −153270. 95054.0i −0.164249 0.101863i
\(967\) 811983.i 0.868349i −0.900829 0.434174i \(-0.857040\pi\)
0.900829 0.434174i \(-0.142960\pi\)
\(968\) 367400. 0.392092
\(969\) 406560. 655558.i 0.432989 0.698174i
\(970\) 191880. + 50174.4i 0.203932 + 0.0533259i
\(971\) 333487.i 0.353705i 0.984237 + 0.176852i \(0.0565915\pi\)
−0.984237 + 0.176852i \(0.943409\pi\)
\(972\) 126792. + 330829.i 0.134202 + 0.350164i
\(973\) 296335.i 0.313009i
\(974\) 1.41014e6i 1.48643i
\(975\) 665053. + 1.20545e6i 0.699596 + 1.26806i
\(976\) 115072. 0.120801
\(977\) −1.32479e6 −1.38790 −0.693951 0.720023i \(-0.744131\pi\)
−0.693951 + 0.720023i \(0.744131\pi\)
\(978\) 296359. + 183794.i 0.309842 + 0.192156i
\(979\) 898560. 0.937522
\(980\) 82231.9 314476.i 0.0856225 0.327443i
\(981\) 228672. + 460903.i 0.237616 + 0.478930i
\(982\) 725387.i 0.752223i
\(983\) 815276. 0.843719 0.421859 0.906661i \(-0.361378\pi\)
0.421859 + 0.906661i \(0.361378\pi\)
\(984\) −1.10682e6 686421.i −1.14311 0.708925i
\(985\) −182560. + 698158.i −0.188163 + 0.719583i
\(986\) 170275.i 0.175145i
\(987\) 286000. + 177369.i 0.293583 + 0.182073i
\(988\) 452303.i 0.463357i
\(989\) 1.07094e6i 1.09490i
\(990\) −125990. 606585.i −0.128548 0.618901i
\(991\) 1.57635e6 1.60511 0.802557 0.596575i \(-0.203472\pi\)
0.802557 + 0.596575i \(0.203472\pi\)
\(992\) −23072.0 −0.0234456
\(993\) −968093. + 1.56100e6i −0.981790 + 1.58309i
\(994\) 224640. 0.227360
\(995\) −217109. + 830284.i −0.219297 + 0.838649i
\(996\) 126270. 203604.i 0.127286 0.205243i
\(997\) 128251.i 0.129024i 0.997917 + 0.0645118i \(0.0205490\pi\)
−0.997917 + 0.0645118i \(0.979451\pi\)
\(998\) −498843. −0.500844
\(999\) −88452.0 + 932545.i −0.0886292 + 0.934413i
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 15.5.d.c.14.2 yes 4
3.2 odd 2 inner 15.5.d.c.14.4 yes 4
4.3 odd 2 240.5.c.c.209.3 4
5.2 odd 4 75.5.c.h.26.2 4
5.3 odd 4 75.5.c.h.26.3 4
5.4 even 2 inner 15.5.d.c.14.3 yes 4
12.11 even 2 240.5.c.c.209.1 4
15.2 even 4 75.5.c.h.26.4 4
15.8 even 4 75.5.c.h.26.1 4
15.14 odd 2 inner 15.5.d.c.14.1 4
20.19 odd 2 240.5.c.c.209.2 4
60.59 even 2 240.5.c.c.209.4 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.5.d.c.14.1 4 15.14 odd 2 inner
15.5.d.c.14.2 yes 4 1.1 even 1 trivial
15.5.d.c.14.3 yes 4 5.4 even 2 inner
15.5.d.c.14.4 yes 4 3.2 odd 2 inner
75.5.c.h.26.1 4 15.8 even 4
75.5.c.h.26.2 4 5.2 odd 4
75.5.c.h.26.3 4 5.3 odd 4
75.5.c.h.26.4 4 15.2 even 4
240.5.c.c.209.1 4 12.11 even 2
240.5.c.c.209.2 4 20.19 odd 2
240.5.c.c.209.3 4 4.3 odd 2
240.5.c.c.209.4 4 60.59 even 2