Properties

Label 27.5.f.a.5.7
Level $27$
Weight $5$
Character 27.5
Analytic conductor $2.791$
Analytic rank $0$
Dimension $66$
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [27,5,Mod(2,27)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(27, base_ring=CyclotomicField(18))
 
chi = DirichletCharacter(H, H._module([1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("27.2");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 27 = 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 27.f (of order \(18\), degree \(6\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(2.79098900326\)
Analytic rank: \(0\)
Dimension: \(66\)
Relative dimension: \(11\) over \(\Q(\zeta_{18})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label 5.7
Character \(\chi\) \(=\) 27.5
Dual form 27.5.f.a.11.7

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.868224 + 1.03471i) q^{2} +(-7.41018 - 5.10776i) q^{3} +(2.46156 - 13.9602i) q^{4} +(-3.20330 - 8.80100i) q^{5} +(-1.14866 - 12.1021i) q^{6} +(-7.41386 - 42.0461i) q^{7} +(35.2980 - 20.3793i) q^{8} +(28.8216 + 75.6988i) q^{9} +(6.32529 - 10.9557i) q^{10} +(-6.44259 + 17.7009i) q^{11} +(-89.5460 + 90.8746i) q^{12} +(-37.7989 - 31.7171i) q^{13} +(37.0686 - 44.1766i) q^{14} +(-21.2163 + 81.5787i) q^{15} +(-161.398 - 58.7439i) q^{16} +(390.443 + 225.422i) q^{17} +(-53.3026 + 95.5455i) q^{18} +(-57.0245 - 98.7692i) q^{19} +(-130.749 + 23.0546i) q^{20} +(-159.823 + 349.437i) q^{21} +(-23.9089 + 8.70211i) q^{22} +(608.929 + 107.371i) q^{23} +(-365.657 - 29.2792i) q^{24} +(411.581 - 345.358i) q^{25} -66.6484i q^{26} +(173.078 - 708.156i) q^{27} -605.222 q^{28} +(-179.539 - 213.967i) q^{29} +(-102.831 + 48.8759i) q^{30} +(211.710 - 1200.67i) q^{31} +(-302.391 - 830.812i) q^{32} +(138.152 - 98.2595i) q^{33} +(105.745 + 599.712i) q^{34} +(-346.299 + 199.936i) q^{35} +(1127.72 - 216.019i) q^{36} +(-1105.90 + 1915.47i) q^{37} +(52.6874 - 144.758i) q^{38} +(118.094 + 428.097i) q^{39} +(-292.429 - 245.377i) q^{40} +(-348.778 + 415.658i) q^{41} +(-500.328 + 138.019i) q^{42} +(3152.26 + 1147.33i) q^{43} +(231.249 + 133.512i) q^{44} +(573.901 - 496.145i) q^{45} +(417.590 + 723.286i) q^{46} +(-3962.16 + 698.636i) q^{47} +(895.936 + 1259.68i) q^{48} +(543.294 - 197.743i) q^{49} +(714.690 + 126.019i) q^{50} +(-1741.85 - 3664.71i) q^{51} +(-535.821 + 449.607i) q^{52} +3918.45i q^{53} +(883.006 - 435.753i) q^{54} +176.423 q^{55} +(-1118.57 - 1333.05i) q^{56} +(-81.9277 + 1023.17i) q^{57} +(65.5128 - 371.542i) q^{58} +(-1539.61 - 4230.04i) q^{59} +(1086.63 + 496.995i) q^{60} +(208.280 + 1181.21i) q^{61} +(1426.15 - 823.390i) q^{62} +(2969.16 - 1773.06i) q^{63} +(-776.940 + 1345.70i) q^{64} +(-158.060 + 434.267i) q^{65} +(221.617 + 57.6364i) q^{66} +(-2416.30 - 2027.52i) q^{67} +(4108.04 - 4895.77i) q^{68} +(-3963.85 - 3905.90i) q^{69} +(-507.540 - 184.729i) q^{70} +(2478.15 + 1430.76i) q^{71} +(2560.04 + 2084.65i) q^{72} +(-1176.80 - 2038.28i) q^{73} +(-2942.13 + 518.776i) q^{74} +(-4813.90 + 456.907i) q^{75} +(-1519.21 + 552.947i) q^{76} +(792.017 + 139.654i) q^{77} +(-340.424 + 493.877i) q^{78} +(3852.86 - 3232.93i) q^{79} +1608.63i q^{80} +(-4899.63 + 4363.53i) q^{81} -732.903 q^{82} +(7265.33 + 8658.48i) q^{83} +(4484.80 + 3091.33i) q^{84} +(733.235 - 4158.38i) q^{85} +(1549.72 + 4257.81i) q^{86} +(237.530 + 2502.57i) q^{87} +(133.321 + 756.101i) q^{88} +(-982.504 + 567.249i) q^{89} +(1011.64 + 163.055i) q^{90} +(-1053.34 + 1824.44i) q^{91} +(2997.83 - 8236.48i) q^{92} +(-7701.53 + 7815.80i) q^{93} +(-4162.93 - 3493.11i) q^{94} +(-686.601 + 818.260i) q^{95} +(-2002.81 + 7701.01i) q^{96} +(1751.37 + 637.447i) q^{97} +(676.307 + 390.466i) q^{98} +(-1525.62 + 22.4713i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 66 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 3 q^{5} + 90 q^{6} - 6 q^{7} - 9 q^{8} - 108 q^{9} - 3 q^{10} - 492 q^{11} - 339 q^{12} - 6 q^{13} + 1137 q^{14} + 1017 q^{15} - 54 q^{16} - 9 q^{17} + 603 q^{18} - 3 q^{19}+ \cdots - 162405 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).

\(n\) \(2\)
\(\chi(n)\) \(e\left(\frac{5}{18}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.868224 + 1.03471i 0.217056 + 0.258677i 0.863575 0.504221i \(-0.168220\pi\)
−0.646519 + 0.762898i \(0.723776\pi\)
\(3\) −7.41018 5.10776i −0.823354 0.567529i
\(4\) 2.46156 13.9602i 0.153848 0.872513i
\(5\) −3.20330 8.80100i −0.128132 0.352040i 0.858994 0.511986i \(-0.171090\pi\)
−0.987126 + 0.159946i \(0.948868\pi\)
\(6\) −1.14866 12.1021i −0.0319071 0.336168i
\(7\) −7.41386 42.0461i −0.151303 0.858083i −0.962088 0.272739i \(-0.912070\pi\)
0.810785 0.585344i \(-0.199041\pi\)
\(8\) 35.2980 20.3793i 0.551531 0.318427i
\(9\) 28.8216 + 75.6988i 0.355823 + 0.934554i
\(10\) 6.32529 10.9557i 0.0632529 0.109557i
\(11\) −6.44259 + 17.7009i −0.0532445 + 0.146288i −0.963464 0.267838i \(-0.913691\pi\)
0.910219 + 0.414127i \(0.135913\pi\)
\(12\) −89.5460 + 90.8746i −0.621847 + 0.631074i
\(13\) −37.7989 31.7171i −0.223662 0.187675i 0.524070 0.851675i \(-0.324413\pi\)
−0.747732 + 0.664000i \(0.768857\pi\)
\(14\) 37.0686 44.1766i 0.189125 0.225391i
\(15\) −21.2163 + 81.5787i −0.0942947 + 0.362572i
\(16\) −161.398 58.7439i −0.630459 0.229468i
\(17\) 390.443 + 225.422i 1.35101 + 0.780008i 0.988391 0.151929i \(-0.0485484\pi\)
0.362622 + 0.931936i \(0.381882\pi\)
\(18\) −53.3026 + 95.5455i −0.164514 + 0.294894i
\(19\) −57.0245 98.7692i −0.157962 0.273599i 0.776171 0.630522i \(-0.217159\pi\)
−0.934134 + 0.356923i \(0.883826\pi\)
\(20\) −130.749 + 23.0546i −0.326872 + 0.0576364i
\(21\) −159.823 + 349.437i −0.362411 + 0.792375i
\(22\) −23.9089 + 8.70211i −0.0493985 + 0.0179796i
\(23\) 608.929 + 107.371i 1.15109 + 0.202969i 0.716454 0.697635i \(-0.245764\pi\)
0.434641 + 0.900604i \(0.356875\pi\)
\(24\) −365.657 29.2792i −0.634822 0.0508320i
\(25\) 411.581 345.358i 0.658530 0.552572i
\(26\) 66.6484i 0.0985923i
\(27\) 173.078 708.156i 0.237418 0.971408i
\(28\) −605.222 −0.771967
\(29\) −179.539 213.967i −0.213483 0.254419i 0.648667 0.761072i \(-0.275327\pi\)
−0.862150 + 0.506653i \(0.830882\pi\)
\(30\) −102.831 + 48.8759i −0.114256 + 0.0543065i
\(31\) 211.710 1200.67i 0.220302 1.24939i −0.651164 0.758937i \(-0.725719\pi\)
0.871465 0.490457i \(-0.163170\pi\)
\(32\) −302.391 830.812i −0.295303 0.811340i
\(33\) 138.152 98.2595i 0.126862 0.0902291i
\(34\) 105.745 + 599.712i 0.0914752 + 0.518782i
\(35\) −346.299 + 199.936i −0.282693 + 0.163213i
\(36\) 1127.72 216.019i 0.870152 0.166681i
\(37\) −1105.90 + 1915.47i −0.807816 + 1.39918i 0.106558 + 0.994306i \(0.466017\pi\)
−0.914374 + 0.404871i \(0.867316\pi\)
\(38\) 52.6874 144.758i 0.0364871 0.100248i
\(39\) 118.094 + 428.097i 0.0776422 + 0.281458i
\(40\) −292.429 245.377i −0.182768 0.153360i
\(41\) −348.778 + 415.658i −0.207483 + 0.247268i −0.859743 0.510727i \(-0.829376\pi\)
0.652260 + 0.757995i \(0.273821\pi\)
\(42\) −500.328 + 138.019i −0.283633 + 0.0782423i
\(43\) 3152.26 + 1147.33i 1.70485 + 0.620513i 0.996363 0.0852133i \(-0.0271572\pi\)
0.708484 + 0.705727i \(0.249379\pi\)
\(44\) 231.249 + 133.512i 0.119447 + 0.0689626i
\(45\) 573.901 496.145i 0.283408 0.245010i
\(46\) 417.590 + 723.286i 0.197349 + 0.341818i
\(47\) −3962.16 + 698.636i −1.79364 + 0.316268i −0.968567 0.248752i \(-0.919980\pi\)
−0.825077 + 0.565020i \(0.808868\pi\)
\(48\) 895.936 + 1259.68i 0.388861 + 0.546737i
\(49\) 543.294 197.743i 0.226278 0.0823585i
\(50\) 714.690 + 126.019i 0.285876 + 0.0504076i
\(51\) −1741.85 3664.71i −0.669685 1.40896i
\(52\) −535.821 + 449.607i −0.198159 + 0.166275i
\(53\) 3918.45i 1.39496i 0.716603 + 0.697482i \(0.245696\pi\)
−0.716603 + 0.697482i \(0.754304\pi\)
\(54\) 883.006 435.753i 0.302814 0.149435i
\(55\) 176.423 0.0583216
\(56\) −1118.57 1333.05i −0.356685 0.425081i
\(57\) −81.9277 + 1023.17i −0.0252163 + 0.314917i
\(58\) 65.5128 371.542i 0.0194747 0.110446i
\(59\) −1539.61 4230.04i −0.442290 1.21518i −0.937982 0.346683i \(-0.887308\pi\)
0.495693 0.868498i \(-0.334914\pi\)
\(60\) 1086.63 + 496.995i 0.301842 + 0.138054i
\(61\) 208.280 + 1181.21i 0.0559742 + 0.317446i 0.999920 0.0126552i \(-0.00402839\pi\)
−0.943946 + 0.330101i \(0.892917\pi\)
\(62\) 1426.15 823.390i 0.371008 0.214201i
\(63\) 2969.16 1773.06i 0.748088 0.446726i
\(64\) −776.940 + 1345.70i −0.189683 + 0.328540i
\(65\) −158.060 + 434.267i −0.0374108 + 0.102785i
\(66\) 221.617 + 57.6364i 0.0508763 + 0.0132315i
\(67\) −2416.30 2027.52i −0.538271 0.451663i 0.332675 0.943042i \(-0.392049\pi\)
−0.870946 + 0.491378i \(0.836493\pi\)
\(68\) 4108.04 4895.77i 0.888417 1.05877i
\(69\) −3963.85 3905.90i −0.832567 0.820395i
\(70\) −507.540 184.729i −0.103580 0.0376999i
\(71\) 2478.15 + 1430.76i 0.491599 + 0.283825i 0.725237 0.688499i \(-0.241730\pi\)
−0.233639 + 0.972323i \(0.575063\pi\)
\(72\) 2560.04 + 2084.65i 0.493834 + 0.402132i
\(73\) −1176.80 2038.28i −0.220830 0.382488i 0.734231 0.678900i \(-0.237543\pi\)
−0.955060 + 0.296412i \(0.904210\pi\)
\(74\) −2942.13 + 518.776i −0.537277 + 0.0947364i
\(75\) −4813.90 + 456.907i −0.855804 + 0.0812278i
\(76\) −1519.21 + 552.947i −0.263021 + 0.0957317i
\(77\) 792.017 + 139.654i 0.133584 + 0.0235544i
\(78\) −340.424 + 493.877i −0.0559539 + 0.0811763i
\(79\) 3852.86 3232.93i 0.617347 0.518015i −0.279622 0.960110i \(-0.590209\pi\)
0.896968 + 0.442095i \(0.145765\pi\)
\(80\) 1608.63i 0.251349i
\(81\) −4899.63 + 4363.53i −0.746781 + 0.665070i
\(82\) −732.903 −0.108998
\(83\) 7265.33 + 8658.48i 1.05463 + 1.25686i 0.965380 + 0.260846i \(0.0840016\pi\)
0.0892470 + 0.996010i \(0.471554\pi\)
\(84\) 4484.80 + 3091.33i 0.635601 + 0.438113i
\(85\) 733.235 4158.38i 0.101486 0.575555i
\(86\) 1549.72 + 4257.81i 0.209534 + 0.575691i
\(87\) 237.530 + 2502.57i 0.0313819 + 0.330635i
\(88\) 133.321 + 756.101i 0.0172160 + 0.0976370i
\(89\) −982.504 + 567.249i −0.124038 + 0.0716133i −0.560735 0.827995i \(-0.689481\pi\)
0.436697 + 0.899609i \(0.356148\pi\)
\(90\) 1011.64 + 163.055i 0.124894 + 0.0201303i
\(91\) −1053.34 + 1824.44i −0.127200 + 0.220317i
\(92\) 2997.83 8236.48i 0.354186 0.973119i
\(93\) −7701.53 + 7815.80i −0.890453 + 0.903666i
\(94\) −4162.93 3493.11i −0.471133 0.395327i
\(95\) −686.601 + 818.260i −0.0760777 + 0.0906659i
\(96\) −2002.81 + 7701.01i −0.217319 + 0.835613i
\(97\) 1751.37 + 637.447i 0.186138 + 0.0677486i 0.433407 0.901198i \(-0.357311\pi\)
−0.247270 + 0.968947i \(0.579533\pi\)
\(98\) 676.307 + 390.466i 0.0704193 + 0.0406566i
\(99\) −1525.62 + 22.4713i −0.155660 + 0.00229276i
\(100\) −3808.13 6595.88i −0.380813 0.659588i
\(101\) −845.823 + 149.141i −0.0829157 + 0.0146203i −0.214952 0.976625i \(-0.568960\pi\)
0.132036 + 0.991245i \(0.457848\pi\)
\(102\) 2279.59 4984.09i 0.219107 0.479056i
\(103\) 4752.33 1729.71i 0.447952 0.163041i −0.108187 0.994131i \(-0.534504\pi\)
0.556139 + 0.831089i \(0.312282\pi\)
\(104\) −1980.60 349.233i −0.183117 0.0322886i
\(105\) 3587.36 + 287.250i 0.325384 + 0.0260544i
\(106\) −4054.46 + 3402.09i −0.360845 + 0.302785i
\(107\) 10768.0i 0.940518i −0.882529 0.470259i \(-0.844161\pi\)
0.882529 0.470259i \(-0.155839\pi\)
\(108\) −9459.96 4159.37i −0.811039 0.356599i
\(109\) 2700.53 0.227298 0.113649 0.993521i \(-0.463746\pi\)
0.113649 + 0.993521i \(0.463746\pi\)
\(110\) 153.175 + 182.546i 0.0126591 + 0.0150865i
\(111\) 17978.7 8545.35i 1.45919 0.693560i
\(112\) −1273.37 + 7221.65i −0.101512 + 0.575706i
\(113\) 4381.95 + 12039.3i 0.343171 + 0.942855i 0.984468 + 0.175562i \(0.0561744\pi\)
−0.641297 + 0.767293i \(0.721603\pi\)
\(114\) −1129.81 + 803.565i −0.0869352 + 0.0618317i
\(115\) −1005.61 5703.13i −0.0760389 0.431238i
\(116\) −3428.96 + 1979.71i −0.254828 + 0.147125i
\(117\) 1311.52 3775.47i 0.0958082 0.275803i
\(118\) 3040.14 5265.67i 0.218338 0.378173i
\(119\) 6583.44 18087.8i 0.464899 1.27730i
\(120\) 913.624 + 3311.94i 0.0634461 + 0.229996i
\(121\) 10943.8 + 9182.97i 0.747479 + 0.627210i
\(122\) −1041.38 + 1241.07i −0.0699664 + 0.0833827i
\(123\) 4707.59 1298.63i 0.311163 0.0858368i
\(124\) −16240.4 5911.03i −1.05622 0.384433i
\(125\) −9427.31 5442.86i −0.603348 0.348343i
\(126\) 4412.49 + 1532.81i 0.277935 + 0.0965486i
\(127\) 5755.85 + 9969.42i 0.356863 + 0.618105i 0.987435 0.158026i \(-0.0505129\pi\)
−0.630572 + 0.776131i \(0.717180\pi\)
\(128\) −15998.2 + 2820.91i −0.976450 + 0.172174i
\(129\) −17498.6 24602.9i −1.05153 1.47845i
\(130\) −586.572 + 213.495i −0.0347084 + 0.0126328i
\(131\) −20719.2 3653.35i −1.20734 0.212887i −0.466471 0.884536i \(-0.654475\pi\)
−0.740869 + 0.671650i \(0.765586\pi\)
\(132\) −1031.65 2170.51i −0.0592087 0.124570i
\(133\) −3730.09 + 3129.92i −0.210871 + 0.176941i
\(134\) 4260.51i 0.237275i
\(135\) −6786.90 + 745.180i −0.372395 + 0.0408878i
\(136\) 18375.8 0.993502
\(137\) 21898.4 + 26097.6i 1.16673 + 1.39046i 0.905049 + 0.425307i \(0.139834\pi\)
0.261686 + 0.965153i \(0.415722\pi\)
\(138\) 599.956 7492.63i 0.0315037 0.393438i
\(139\) −2943.24 + 16692.0i −0.152334 + 0.863928i 0.808849 + 0.588016i \(0.200091\pi\)
−0.961183 + 0.275912i \(0.911020\pi\)
\(140\) 1938.71 + 5326.56i 0.0989136 + 0.271763i
\(141\) 32928.8 + 15060.7i 1.65629 + 0.757544i
\(142\) 671.168 + 3806.38i 0.0332855 + 0.188771i
\(143\) 804.942 464.734i 0.0393634 0.0227265i
\(144\) −204.895 13910.7i −0.00988112 0.670848i
\(145\) −1308.00 + 2265.52i −0.0622117 + 0.107754i
\(146\) 1087.30 2987.33i 0.0510086 0.140145i
\(147\) −5035.93 1309.70i −0.233048 0.0606091i
\(148\) 24018.2 + 20153.6i 1.09652 + 0.920090i
\(149\) −17955.5 + 21398.5i −0.808768 + 0.963852i −0.999843 0.0177231i \(-0.994358\pi\)
0.191075 + 0.981575i \(0.438803\pi\)
\(150\) −4652.31 4584.29i −0.206769 0.203746i
\(151\) −3119.16 1135.28i −0.136799 0.0497908i 0.272713 0.962095i \(-0.412079\pi\)
−0.409512 + 0.912305i \(0.634301\pi\)
\(152\) −4025.70 2324.24i −0.174243 0.100599i
\(153\) −5811.01 + 36053.1i −0.248238 + 1.54014i
\(154\) 543.147 + 940.758i 0.0229021 + 0.0396676i
\(155\) −11245.2 + 1982.84i −0.468064 + 0.0825324i
\(156\) 6267.02 594.828i 0.257520 0.0244423i
\(157\) −20046.5 + 7296.35i −0.813280 + 0.296010i −0.714978 0.699147i \(-0.753563\pi\)
−0.0983021 + 0.995157i \(0.531341\pi\)
\(158\) 6690.29 + 1179.68i 0.267998 + 0.0472552i
\(159\) 20014.5 29036.4i 0.791681 1.14855i
\(160\) −6343.32 + 5322.68i −0.247786 + 0.207917i
\(161\) 26399.1i 1.01845i
\(162\) −8768.95 1281.17i −0.334132 0.0488176i
\(163\) −3741.11 −0.140807 −0.0704036 0.997519i \(-0.522429\pi\)
−0.0704036 + 0.997519i \(0.522429\pi\)
\(164\) 4944.13 + 5892.18i 0.183824 + 0.219073i
\(165\) −1307.33 901.125i −0.0480193 0.0330992i
\(166\) −2651.08 + 15035.0i −0.0962069 + 0.545616i
\(167\) −4391.73 12066.2i −0.157472 0.432650i 0.835718 0.549159i \(-0.185052\pi\)
−0.993190 + 0.116509i \(0.962830\pi\)
\(168\) 1479.86 + 15591.5i 0.0524325 + 0.552421i
\(169\) −4536.78 25729.4i −0.158845 0.900856i
\(170\) 4939.33 2851.72i 0.170911 0.0986755i
\(171\) 5833.18 7163.37i 0.199486 0.244977i
\(172\) 23776.4 41182.0i 0.803693 1.39204i
\(173\) 14623.8 40178.7i 0.488618 1.34247i −0.413314 0.910588i \(-0.635629\pi\)
0.901932 0.431878i \(-0.142149\pi\)
\(174\) −2383.21 + 2418.57i −0.0787161 + 0.0798840i
\(175\) −17572.4 14745.0i −0.573791 0.481468i
\(176\) 2079.64 2478.41i 0.0671370 0.0800108i
\(177\) −10197.2 + 39209.4i −0.325489 + 1.25154i
\(178\) −1439.97 524.107i −0.0454479 0.0165417i
\(179\) −23006.7 13282.9i −0.718040 0.414561i 0.0959908 0.995382i \(-0.469398\pi\)
−0.814031 + 0.580822i \(0.802731\pi\)
\(180\) −5513.60 9233.07i −0.170173 0.284971i
\(181\) −8497.75 14718.5i −0.259386 0.449270i 0.706692 0.707522i \(-0.250187\pi\)
−0.966078 + 0.258252i \(0.916854\pi\)
\(182\) −2802.30 + 494.122i −0.0846004 + 0.0149173i
\(183\) 4489.97 9816.86i 0.134073 0.293137i
\(184\) 23682.1 8619.59i 0.699496 0.254596i
\(185\) 20400.6 + 3597.18i 0.596074 + 0.105104i
\(186\) −14773.7 1182.97i −0.427036 0.0341940i
\(187\) −6505.63 + 5458.87i −0.186040 + 0.156106i
\(188\) 57032.3i 1.61363i
\(189\) −31058.4 2027.07i −0.869471 0.0567474i
\(190\) −1442.78 −0.0399663
\(191\) 33917.8 + 40421.7i 0.929739 + 1.10802i 0.993923 + 0.110082i \(0.0351113\pi\)
−0.0641834 + 0.997938i \(0.520444\pi\)
\(192\) 12630.8 6003.46i 0.342632 0.162854i
\(193\) 8157.94 46266.0i 0.219011 1.24207i −0.654798 0.755804i \(-0.727246\pi\)
0.873809 0.486269i \(-0.161643\pi\)
\(194\) 861.010 + 2365.61i 0.0228773 + 0.0628549i
\(195\) 3389.39 2410.67i 0.0891358 0.0633969i
\(196\) −1423.18 8071.25i −0.0370465 0.210101i
\(197\) 20705.7 11954.4i 0.533528 0.308032i −0.208924 0.977932i \(-0.566996\pi\)
0.742452 + 0.669899i \(0.233663\pi\)
\(198\) −1347.83 1559.06i −0.0343800 0.0397680i
\(199\) −9654.27 + 16721.7i −0.243789 + 0.422254i −0.961790 0.273787i \(-0.911724\pi\)
0.718002 + 0.696041i \(0.245057\pi\)
\(200\) 7489.85 20578.2i 0.187246 0.514455i
\(201\) 7549.16 + 27366.1i 0.186856 + 0.677363i
\(202\) −888.682 745.693i −0.0217793 0.0182750i
\(203\) −7665.38 + 9135.24i −0.186012 + 0.221681i
\(204\) −55447.7 + 15295.7i −1.33237 + 0.367544i
\(205\) 4775.45 + 1738.12i 0.113633 + 0.0413592i
\(206\) 5915.83 + 3415.50i 0.139406 + 0.0804860i
\(207\) 9422.50 + 49189.8i 0.219900 + 1.14798i
\(208\) 4237.47 + 7339.51i 0.0979444 + 0.169645i
\(209\) 2115.69 373.053i 0.0484349 0.00854038i
\(210\) 2817.41 + 3961.27i 0.0638869 + 0.0898247i
\(211\) −27331.4 + 9947.83i −0.613900 + 0.223441i −0.630209 0.776426i \(-0.717031\pi\)
0.0163089 + 0.999867i \(0.494808\pi\)
\(212\) 54702.4 + 9645.51i 1.21712 + 0.214612i
\(213\) −11055.6 23260.0i −0.243681 0.512684i
\(214\) 11141.7 9349.02i 0.243291 0.204145i
\(215\) 31418.3i 0.679682i
\(216\) −8322.44 28523.7i −0.178379 0.611362i
\(217\) −52053.0 −1.10542
\(218\) 2344.67 + 2794.26i 0.0493365 + 0.0587969i
\(219\) −1690.72 + 21114.8i −0.0352521 + 0.440250i
\(220\) 434.276 2462.90i 0.00897263 0.0508863i
\(221\) −7608.58 20904.4i −0.155783 0.428010i
\(222\) 24451.5 + 11183.4i 0.496134 + 0.226918i
\(223\) 14655.3 + 83114.6i 0.294704 + 1.67135i 0.668403 + 0.743800i \(0.266978\pi\)
−0.373699 + 0.927550i \(0.621911\pi\)
\(224\) −32690.5 + 18873.9i −0.651517 + 0.376153i
\(225\) 38005.6 + 21202.5i 0.750728 + 0.418814i
\(226\) −8652.67 + 14986.9i −0.169408 + 0.293423i
\(227\) 1755.16 4822.25i 0.0340615 0.0935832i −0.921496 0.388387i \(-0.873032\pi\)
0.955558 + 0.294804i \(0.0952544\pi\)
\(228\) 14081.9 + 3662.31i 0.270890 + 0.0704507i
\(229\) −46872.0 39330.2i −0.893804 0.749990i 0.0751658 0.997171i \(-0.476051\pi\)
−0.968969 + 0.247181i \(0.920496\pi\)
\(230\) 5027.98 5992.11i 0.0950468 0.113272i
\(231\) −5155.67 5080.29i −0.0966187 0.0952060i
\(232\) −10697.9 3893.71i −0.198757 0.0723415i
\(233\) 65323.4 + 37714.5i 1.20325 + 0.694699i 0.961277 0.275584i \(-0.0888711\pi\)
0.241976 + 0.970282i \(0.422204\pi\)
\(234\) 5045.21 1920.91i 0.0921398 0.0350814i
\(235\) 18840.7 + 32633.0i 0.341162 + 0.590910i
\(236\) −62842.1 + 11080.8i −1.12831 + 0.198951i
\(237\) −45063.5 + 4277.16i −0.802283 + 0.0761480i
\(238\) 24431.5 8892.36i 0.431318 0.156987i
\(239\) −57194.9 10085.0i −1.00129 0.176555i −0.351112 0.936334i \(-0.614196\pi\)
−0.650182 + 0.759778i \(0.725307\pi\)
\(240\) 8216.51 11920.3i 0.142648 0.206949i
\(241\) 54221.6 45497.3i 0.933552 0.783343i −0.0428999 0.999079i \(-0.513660\pi\)
0.976452 + 0.215736i \(0.0692152\pi\)
\(242\) 19296.6i 0.329495i
\(243\) 58595.0 7308.43i 0.992311 0.123769i
\(244\) 17002.7 0.285587
\(245\) −3480.67 4148.10i −0.0579869 0.0691061i
\(246\) 5430.94 + 3743.49i 0.0897439 + 0.0618595i
\(247\) −977.207 + 5542.02i −0.0160174 + 0.0908394i
\(248\) −16995.8 46695.7i −0.276337 0.759230i
\(249\) −9611.99 101270.i −0.155030 1.63337i
\(250\) −2553.24 14480.1i −0.0408519 0.231682i
\(251\) −8013.71 + 4626.72i −0.127200 + 0.0734388i −0.562250 0.826967i \(-0.690064\pi\)
0.435050 + 0.900406i \(0.356731\pi\)
\(252\) −17443.5 45814.6i −0.274683 0.721444i
\(253\) −5823.63 + 10086.8i −0.0909815 + 0.157585i
\(254\) −5318.09 + 14611.3i −0.0824305 + 0.226476i
\(255\) −26673.4 + 27069.2i −0.410202 + 0.416289i
\(256\) 2236.65 + 1876.78i 0.0341286 + 0.0286373i
\(257\) 51197.8 61015.2i 0.775149 0.923787i −0.223554 0.974692i \(-0.571766\pi\)
0.998704 + 0.0509044i \(0.0162104\pi\)
\(258\) 10264.2 39466.7i 0.154200 0.592914i
\(259\) 88737.2 + 32297.7i 1.32284 + 0.481473i
\(260\) 5673.39 + 3275.53i 0.0839259 + 0.0484546i
\(261\) 11022.4 19757.8i 0.161806 0.290039i
\(262\) −14208.7 24610.2i −0.206992 0.358520i
\(263\) −112009. + 19750.3i −1.61936 + 0.285537i −0.908527 0.417826i \(-0.862792\pi\)
−0.710831 + 0.703363i \(0.751681\pi\)
\(264\) 2874.05 6283.82i 0.0412369 0.0901604i
\(265\) 34486.3 12552.0i 0.491083 0.178739i
\(266\) −6477.11 1142.09i −0.0915414 0.0161412i
\(267\) 10177.9 + 814.974i 0.142770 + 0.0114320i
\(268\) −34252.4 + 28741.2i −0.476894 + 0.400161i
\(269\) 225.820i 0.00312074i 0.999999 + 0.00156037i \(0.000496682\pi\)
−0.999999 + 0.00156037i \(0.999503\pi\)
\(270\) −6663.59 6375.48i −0.0914073 0.0874552i
\(271\) −23425.8 −0.318974 −0.159487 0.987200i \(-0.550984\pi\)
−0.159487 + 0.987200i \(0.550984\pi\)
\(272\) −49774.3 59318.7i −0.672771 0.801778i
\(273\) 17124.3 8139.24i 0.229767 0.109209i
\(274\) −7990.62 + 45317.0i −0.106434 + 0.603616i
\(275\) 3461.48 + 9510.34i 0.0457717 + 0.125757i
\(276\) −64284.4 + 45721.6i −0.843893 + 0.600210i
\(277\) −5680.28 32214.5i −0.0740304 0.419847i −0.999189 0.0402664i \(-0.987179\pi\)
0.925159 0.379581i \(-0.123932\pi\)
\(278\) −19826.7 + 11447.0i −0.256544 + 0.148115i
\(279\) 96991.0 18579.0i 1.24601 0.238679i
\(280\) −8149.10 + 14114.7i −0.103943 + 0.180034i
\(281\) −18690.8 + 51352.6i −0.236710 + 0.650355i 0.763281 + 0.646067i \(0.223587\pi\)
−0.999991 + 0.00428802i \(0.998635\pi\)
\(282\) 13006.1 + 47147.8i 0.163549 + 0.592875i
\(283\) 39160.2 + 32859.3i 0.488959 + 0.410285i 0.853653 0.520842i \(-0.174382\pi\)
−0.364694 + 0.931127i \(0.618827\pi\)
\(284\) 26073.8 31073.6i 0.323272 0.385260i
\(285\) 9267.31 2556.46i 0.114094 0.0314738i
\(286\) 1179.73 + 429.388i 0.0144229 + 0.00524950i
\(287\) 20062.6 + 11583.1i 0.243570 + 0.140625i
\(288\) 54176.1 46836.0i 0.653165 0.564670i
\(289\) 59869.9 + 103698.i 0.716824 + 1.24158i
\(290\) −3479.80 + 613.582i −0.0413769 + 0.00729586i
\(291\) −9722.06 13669.2i −0.114808 0.161420i
\(292\) −31351.6 + 11411.0i −0.367700 + 0.133832i
\(293\) −16271.7 2869.13i −0.189538 0.0334207i 0.0780733 0.996948i \(-0.475123\pi\)
−0.267611 + 0.963527i \(0.586234\pi\)
\(294\) −3017.15 6347.83i −0.0349062 0.0734397i
\(295\) −32296.8 + 27100.2i −0.371121 + 0.311407i
\(296\) 90149.9i 1.02892i
\(297\) 11419.9 + 7625.98i 0.129464 + 0.0864536i
\(298\) −37730.6 −0.424875
\(299\) −19611.4 23371.9i −0.219364 0.261428i
\(300\) −5471.19 + 68327.7i −0.0607910 + 0.759197i
\(301\) 24870.3 141046.i 0.274503 1.55679i
\(302\) −1533.44 4213.09i −0.0168133 0.0461942i
\(303\) 7029.48 + 3215.09i 0.0765664 + 0.0350194i
\(304\) 3401.52 + 19291.0i 0.0368066 + 0.208740i
\(305\) 9728.68 5616.86i 0.104581 0.0603801i
\(306\) −42349.7 + 25289.5i −0.452280 + 0.270083i
\(307\) −51266.0 + 88795.3i −0.543942 + 0.942135i 0.454731 + 0.890629i \(0.349735\pi\)
−0.998673 + 0.0515059i \(0.983598\pi\)
\(308\) 3899.19 10712.9i 0.0411030 0.112930i
\(309\) −44050.5 11456.3i −0.461354 0.119985i
\(310\) −11815.1 9914.01i −0.122945 0.103163i
\(311\) −19903.6 + 23720.2i −0.205784 + 0.245243i −0.859058 0.511877i \(-0.828950\pi\)
0.653275 + 0.757121i \(0.273395\pi\)
\(312\) 12892.8 + 12704.3i 0.132446 + 0.130509i
\(313\) 60314.9 + 21952.8i 0.615652 + 0.224079i 0.630975 0.775803i \(-0.282655\pi\)
−0.0153222 + 0.999883i \(0.504877\pi\)
\(314\) −24954.5 14407.5i −0.253098 0.146126i
\(315\) −25115.8 20451.9i −0.253120 0.206117i
\(316\) −35648.4 61744.8i −0.356998 0.618338i
\(317\) 99398.3 17526.6i 0.989146 0.174413i 0.344411 0.938819i \(-0.388079\pi\)
0.644735 + 0.764406i \(0.276968\pi\)
\(318\) 47421.3 4500.95i 0.468942 0.0445092i
\(319\) 4944.09 1799.50i 0.0485853 0.0176836i
\(320\) 14332.3 + 2527.17i 0.139964 + 0.0246794i
\(321\) −55000.3 + 79792.8i −0.533771 + 0.774379i
\(322\) 27315.4 22920.4i 0.263449 0.221060i
\(323\) 51418.3i 0.492848i
\(324\) 48855.0 + 79140.9i 0.465392 + 0.753895i
\(325\) −26511.1 −0.250992
\(326\) −3248.12 3870.96i −0.0305630 0.0364236i
\(327\) −20011.4 13793.7i −0.187147 0.128998i
\(328\) −3840.36 + 21779.8i −0.0356964 + 0.202444i
\(329\) 58749.8 + 161414.i 0.542769 + 1.49124i
\(330\) −202.649 2135.08i −0.00186087 0.0196059i
\(331\) −194.082 1100.69i −0.00177145 0.0100464i 0.983909 0.178669i \(-0.0571792\pi\)
−0.985681 + 0.168623i \(0.946068\pi\)
\(332\) 138758. 80112.1i 1.25887 0.726812i
\(333\) −176873. 28508.2i −1.59505 0.257088i
\(334\) 8671.99 15020.3i 0.0777366 0.134644i
\(335\) −10104.0 + 27760.6i −0.0900337 + 0.247366i
\(336\) 46322.4 47009.7i 0.410310 0.416398i
\(337\) −93620.4 78556.9i −0.824349 0.691711i 0.129637 0.991561i \(-0.458619\pi\)
−0.953986 + 0.299851i \(0.903063\pi\)
\(338\) 22683.5 27033.1i 0.198553 0.236626i
\(339\) 29022.8 111595.i 0.252546 0.971062i
\(340\) −56247.0 20472.2i −0.486565 0.177095i
\(341\) 19888.9 + 11482.9i 0.171042 + 0.0987510i
\(342\) 12476.5 183.770i 0.106670 0.00157117i
\(343\) −63597.2 110154.i −0.540567 0.936290i
\(344\) 134650. 23742.5i 1.13786 0.200636i
\(345\) −21678.4 + 47397.6i −0.182133 + 0.398216i
\(346\) 54270.0 19752.7i 0.453323 0.164996i
\(347\) −18668.4 3291.75i −0.155042 0.0273381i 0.0955884 0.995421i \(-0.469527\pi\)
−0.250630 + 0.968083i \(0.580638\pi\)
\(348\) 35521.1 + 2844.28i 0.293311 + 0.0234862i
\(349\) 95678.3 80283.6i 0.785530 0.659138i −0.159105 0.987262i \(-0.550861\pi\)
0.944635 + 0.328124i \(0.106416\pi\)
\(350\) 30984.2i 0.252932i
\(351\) −29002.8 + 21278.0i −0.235410 + 0.172710i
\(352\) 16654.3 0.134413
\(353\) −25396.8 30266.7i −0.203812 0.242893i 0.654450 0.756105i \(-0.272900\pi\)
−0.858262 + 0.513212i \(0.828456\pi\)
\(354\) −49423.8 + 23491.3i −0.394393 + 0.187457i
\(355\) 4653.86 26393.3i 0.0369281 0.209429i
\(356\) 5500.42 + 15112.3i 0.0434006 + 0.119242i
\(357\) −141173. + 100408.i −1.10768 + 0.787826i
\(358\) −6231.01 35337.8i −0.0486175 0.275723i
\(359\) −89204.5 + 51502.2i −0.692146 + 0.399611i −0.804415 0.594067i \(-0.797521\pi\)
0.112269 + 0.993678i \(0.464188\pi\)
\(360\) 10146.5 29208.7i 0.0782906 0.225375i
\(361\) 58656.9 101597.i 0.450096 0.779589i
\(362\) 7851.45 21571.7i 0.0599146 0.164614i
\(363\) −34191.5 123946.i −0.259480 0.940631i
\(364\) 22876.7 + 19195.9i 0.172660 + 0.144879i
\(365\) −14169.2 + 16886.2i −0.106356 + 0.126750i
\(366\) 14055.9 3877.43i 0.104929 0.0289455i
\(367\) −189399. 68935.5i −1.40619 0.511812i −0.476183 0.879346i \(-0.657980\pi\)
−0.930010 + 0.367534i \(0.880202\pi\)
\(368\) −91972.3 53100.2i −0.679143 0.392104i
\(369\) −41517.2 14422.2i −0.304912 0.105920i
\(370\) 13990.3 + 24231.9i 0.102193 + 0.177004i
\(371\) 164756. 29050.8i 1.19699 0.211062i
\(372\) 90152.5 + 126754.i 0.651466 + 0.915959i
\(373\) −100938. + 36738.3i −0.725497 + 0.264059i −0.678257 0.734824i \(-0.737265\pi\)
−0.0472394 + 0.998884i \(0.515042\pi\)
\(374\) −11296.7 1991.91i −0.0807622 0.0142405i
\(375\) 42057.3 + 88485.0i 0.299074 + 0.629227i
\(376\) −125619. + 105407.i −0.888543 + 0.745576i
\(377\) 13782.2i 0.0969694i
\(378\) −24868.2 33896.3i −0.174045 0.237230i
\(379\) 221758. 1.54384 0.771918 0.635722i \(-0.219297\pi\)
0.771918 + 0.635722i \(0.219297\pi\)
\(380\) 9732.96 + 11599.3i 0.0674028 + 0.0803275i
\(381\) 8269.50 103275.i 0.0569678 0.711450i
\(382\) −12376.4 + 70190.1i −0.0848141 + 0.481005i
\(383\) −42635.0 117139.i −0.290649 0.798552i −0.995972 0.0896658i \(-0.971420\pi\)
0.705323 0.708886i \(-0.250802\pi\)
\(384\) 132958. + 60811.3i 0.901678 + 0.412403i
\(385\) −1307.97 7417.89i −0.00882425 0.0500448i
\(386\) 54954.8 31728.1i 0.368834 0.212946i
\(387\) 4001.81 + 271690.i 0.0267199 + 1.81406i
\(388\) 13210.0 22880.4i 0.0877484 0.151985i
\(389\) −74280.1 + 204083.i −0.490877 + 1.34867i 0.409001 + 0.912534i \(0.365877\pi\)
−0.899878 + 0.436141i \(0.856345\pi\)
\(390\) 5437.09 + 1414.03i 0.0357468 + 0.00929673i
\(391\) 213548. + 179188.i 1.39683 + 1.17208i
\(392\) 15147.3 18051.9i 0.0985743 0.117476i
\(393\) 134872. + 132900.i 0.873249 + 0.860481i
\(394\) 30346.5 + 11045.2i 0.195486 + 0.0711512i
\(395\) −40794.9 23553.0i −0.261464 0.150956i
\(396\) −3441.70 + 21353.3i −0.0219474 + 0.136168i
\(397\) −59824.4 103619.i −0.379575 0.657443i 0.611426 0.791302i \(-0.290596\pi\)
−0.991000 + 0.133859i \(0.957263\pi\)
\(398\) −25684.2 + 4528.81i −0.162143 + 0.0285903i
\(399\) 43627.5 4140.86i 0.274040 0.0260103i
\(400\) −86715.9 + 31562.0i −0.541974 + 0.197262i
\(401\) 78697.1 + 13876.4i 0.489407 + 0.0862956i 0.412906 0.910774i \(-0.364514\pi\)
0.0765013 + 0.997069i \(0.475625\pi\)
\(402\) −21761.6 + 31571.1i −0.134660 + 0.195361i
\(403\) −46084.1 + 38669.1i −0.283753 + 0.238097i
\(404\) 12175.0i 0.0745943i
\(405\) 54098.4 + 29143.9i 0.329818 + 0.177680i
\(406\) −16107.6 −0.0977188
\(407\) −26780.7 31916.0i −0.161671 0.192672i
\(408\) −136168. 93859.2i −0.818003 0.563841i
\(409\) −44493.9 + 252337.i −0.265983 + 1.50846i 0.500239 + 0.865887i \(0.333245\pi\)
−0.766222 + 0.642576i \(0.777866\pi\)
\(410\) 2347.71 + 6450.27i 0.0139661 + 0.0383716i
\(411\) −28971.5 305240.i −0.171509 1.80700i
\(412\) −12448.9 70601.2i −0.0733393 0.415928i
\(413\) −166442. + 96095.6i −0.975807 + 0.563382i
\(414\) −42716.3 + 52457.3i −0.249226 + 0.306059i
\(415\) 52930.2 91677.9i 0.307332 0.532314i
\(416\) −14920.9 + 40994.7i −0.0862198 + 0.236887i
\(417\) 107068. 108657.i 0.615729 0.624865i
\(418\) 2222.89 + 1865.23i 0.0127223 + 0.0106753i
\(419\) −194699. + 232033.i −1.10901 + 1.32167i −0.167048 + 0.985949i \(0.553423\pi\)
−0.941962 + 0.335718i \(0.891021\pi\)
\(420\) 12840.6 49373.2i 0.0727924 0.279893i
\(421\) −61184.4 22269.3i −0.345205 0.125644i 0.163599 0.986527i \(-0.447690\pi\)
−0.508803 + 0.860883i \(0.669912\pi\)
\(422\) −34022.9 19643.1i −0.191050 0.110303i
\(423\) −167082. 279795.i −0.933788 1.56372i
\(424\) 79855.4 + 138314.i 0.444194 + 0.769366i
\(425\) 238550. 42062.9i 1.32069 0.232874i
\(426\) 14468.6 31634.2i 0.0797274 0.174316i
\(427\) 48121.3 17514.7i 0.263926 0.0960611i
\(428\) −150323. 26506.1i −0.820614 0.144696i
\(429\) −8338.52 667.688i −0.0453079 0.00362793i
\(430\) 32508.8 27278.1i 0.175818 0.147529i
\(431\) 247253.i 1.33103i −0.746385 0.665514i \(-0.768212\pi\)
0.746385 0.665514i \(-0.231788\pi\)
\(432\) −69534.2 + 104127.i −0.372590 + 0.557953i
\(433\) 229960. 1.22652 0.613262 0.789880i \(-0.289857\pi\)
0.613262 + 0.789880i \(0.289857\pi\)
\(434\) −45193.6 53859.7i −0.239937 0.285946i
\(435\) 21264.3 10107.0i 0.112376 0.0534126i
\(436\) 6647.52 37700.0i 0.0349693 0.198321i
\(437\) −24118.9 66266.2i −0.126298 0.347000i
\(438\) −23315.6 + 16583.0i −0.121534 + 0.0864400i
\(439\) 13862.8 + 78620.1i 0.0719322 + 0.407948i 0.999419 + 0.0340912i \(0.0108537\pi\)
−0.927487 + 0.373857i \(0.878035\pi\)
\(440\) 6227.38 3595.38i 0.0321662 0.0185712i
\(441\) 30627.5 + 35427.4i 0.157483 + 0.182164i
\(442\) 15024.0 26022.4i 0.0769028 0.133199i
\(443\) −37093.8 + 101914.i −0.189014 + 0.519312i −0.997613 0.0690480i \(-0.978004\pi\)
0.808599 + 0.588360i \(0.200226\pi\)
\(444\) −75039.2 272021.i −0.380647 1.37987i
\(445\) 8139.62 + 6829.95i 0.0411040 + 0.0344903i
\(446\) −73275.3 + 87326.1i −0.368373 + 0.439010i
\(447\) 242352. 66854.6i 1.21292 0.334592i
\(448\) 62341.5 + 22690.5i 0.310614 + 0.113054i
\(449\) 26892.6 + 15526.5i 0.133395 + 0.0770158i 0.565213 0.824945i \(-0.308794\pi\)
−0.431817 + 0.901961i \(0.642127\pi\)
\(450\) 11059.0 + 57733.2i 0.0546124 + 0.285102i
\(451\) −5110.47 8851.59i −0.0251251 0.0435179i
\(452\) 178858. 31537.4i 0.875449 0.154365i
\(453\) 17314.8 + 24344.5i 0.0843763 + 0.118633i
\(454\) 6513.49 2370.72i 0.0316011 0.0115019i
\(455\) 19431.1 + 3426.22i 0.0938586 + 0.0165498i
\(456\) 17959.5 + 37785.3i 0.0863704 + 0.181716i
\(457\) −126339. + 106011.i −0.604930 + 0.507597i −0.893026 0.450005i \(-0.851422\pi\)
0.288096 + 0.957602i \(0.406978\pi\)
\(458\) 82646.3i 0.393996i
\(459\) 227211. 237479.i 1.07846 1.12720i
\(460\) −82092.2 −0.387959
\(461\) −188614. 224781.i −0.887507 1.05769i −0.997962 0.0638087i \(-0.979675\pi\)
0.110455 0.993881i \(-0.464769\pi\)
\(462\) 780.345 9745.45i 0.00365597 0.0456581i
\(463\) −12545.1 + 71146.6i −0.0585209 + 0.331889i −0.999986 0.00522092i \(-0.998338\pi\)
0.941465 + 0.337109i \(0.109449\pi\)
\(464\) 16408.0 + 45080.5i 0.0762112 + 0.209389i
\(465\) 93457.2 + 42744.8i 0.432222 + 0.197687i
\(466\) 17691.8 + 100335.i 0.0814706 + 0.462043i
\(467\) 35163.8 20301.9i 0.161236 0.0930898i −0.417211 0.908810i \(-0.636992\pi\)
0.578447 + 0.815720i \(0.303659\pi\)
\(468\) −49478.0 27602.6i −0.225902 0.126026i
\(469\) −67335.0 + 116628.i −0.306123 + 0.530220i
\(470\) −17407.7 + 47827.4i −0.0788038 + 0.216512i
\(471\) 185817. + 48325.6i 0.837611 + 0.217839i
\(472\) −140551. 117936.i −0.630883 0.529374i
\(473\) −40617.4 + 48406.0i −0.181548 + 0.216360i
\(474\) −43550.8 42914.0i −0.193838 0.191004i
\(475\) −57580.9 20957.7i −0.255206 0.0928875i
\(476\) −236304. 136430.i −1.04294 0.602140i
\(477\) −296622. + 112936.i −1.30367 + 0.496359i
\(478\) −39222.9 67936.1i −0.171666 0.297334i
\(479\) 54719.7 9648.55i 0.238491 0.0420524i −0.0531249 0.998588i \(-0.516918\pi\)
0.291616 + 0.956535i \(0.405807\pi\)
\(480\) 74192.2 7041.88i 0.322015 0.0305637i
\(481\) 102555. 37327.0i 0.443268 0.161337i
\(482\) 94153.0 + 16601.7i 0.405266 + 0.0714593i
\(483\) −134840. + 195622.i −0.577997 + 0.838541i
\(484\) 155135. 130174.i 0.662246 0.555691i
\(485\) 17455.7i 0.0742087i
\(486\) 58435.7 + 54283.4i 0.247403 + 0.229824i
\(487\) −138957. −0.585898 −0.292949 0.956128i \(-0.594637\pi\)
−0.292949 + 0.956128i \(0.594637\pi\)
\(488\) 31424.2 + 37449.9i 0.131955 + 0.157258i
\(489\) 27722.3 + 19108.7i 0.115934 + 0.0799121i
\(490\) 1270.07 7202.95i 0.00528977 0.0299998i
\(491\) −4504.33 12375.5i −0.0186839 0.0513335i 0.930000 0.367559i \(-0.119807\pi\)
−0.948684 + 0.316226i \(0.897584\pi\)
\(492\) −6541.06 68915.6i −0.0270220 0.284700i
\(493\) −21867.0 124014.i −0.0899695 0.510242i
\(494\) −6582.81 + 3800.59i −0.0269748 + 0.0155739i
\(495\) 5084.79 + 13355.0i 0.0207521 + 0.0545046i
\(496\) −104701. + 181348.i −0.425588 + 0.737140i
\(497\) 41785.2 114804.i 0.169165 0.464776i
\(498\) 96440.1 97871.0i 0.388865 0.394635i
\(499\) 134809. + 113118.i 0.541398 + 0.454287i 0.872016 0.489478i \(-0.162813\pi\)
−0.330618 + 0.943765i \(0.607257\pi\)
\(500\) −99189.4 + 118209.i −0.396758 + 0.472837i
\(501\) −29087.6 + 111845.i −0.115886 + 0.445594i
\(502\) −11745.0 4274.83i −0.0466064 0.0169633i
\(503\) 293462. + 169430.i 1.15989 + 0.669661i 0.951277 0.308338i \(-0.0997728\pi\)
0.208610 + 0.977999i \(0.433106\pi\)
\(504\) 68671.8 123095.i 0.270344 0.484595i
\(505\) 4022.02 + 6966.34i 0.0157711 + 0.0273163i
\(506\) −15493.1 + 2731.86i −0.0605116 + 0.0106698i
\(507\) −97800.9 + 213832.i −0.380476 + 0.831872i
\(508\) 153344. 55812.5i 0.594207 0.216274i
\(509\) 267722. + 47206.7i 1.03335 + 0.182208i 0.664507 0.747282i \(-0.268642\pi\)
0.368847 + 0.929490i \(0.379753\pi\)
\(510\) −51167.2 4097.10i −0.196721 0.0157520i
\(511\) −76977.0 + 64591.4i −0.294794 + 0.247362i
\(512\) 263863.i 1.00656i
\(513\) −79813.7 + 23287.5i −0.303279 + 0.0884886i
\(514\) 107584. 0.407214
\(515\) −30446.3 36284.4i −0.114794 0.136806i
\(516\) −386535. + 183722.i −1.45174 + 0.690020i
\(517\) 13160.1 74634.7i 0.0492355 0.279228i
\(518\) 43625.0 + 119859.i 0.162583 + 0.446694i
\(519\) −313588. + 223036.i −1.16419 + 0.828020i
\(520\) 3270.86 + 18549.9i 0.0120964 + 0.0686019i
\(521\) −212819. + 122871.i −0.784035 + 0.452663i −0.837858 0.545888i \(-0.816192\pi\)
0.0538237 + 0.998550i \(0.482859\pi\)
\(522\) 30013.5 5749.19i 0.110148 0.0210992i
\(523\) 145495. 252005.i 0.531920 0.921312i −0.467386 0.884053i \(-0.654804\pi\)
0.999306 0.0372584i \(-0.0118625\pi\)
\(524\) −102003. + 280251.i −0.371493 + 1.02067i
\(525\) 54900.7 + 199018.i 0.199186 + 0.722061i
\(526\) −117685. 98749.4i −0.425353 0.356914i
\(527\) 353318. 421068.i 1.27217 1.51611i
\(528\) −28069.6 + 7743.22i −0.100686 + 0.0277750i
\(529\) 96301.8 + 35051.0i 0.344130 + 0.125253i
\(530\) 42929.5 + 24785.3i 0.152828 + 0.0882354i
\(531\) 275835. 238463.i 0.978275 0.845732i
\(532\) 34512.4 + 59777.3i 0.121942 + 0.211209i
\(533\) 26366.9 4649.19i 0.0928121 0.0163653i
\(534\) 7993.44 + 11238.8i 0.0280318 + 0.0394127i
\(535\) −94769.0 + 34493.1i −0.331100 + 0.120510i
\(536\) −126610. 22324.8i −0.440695 0.0777065i
\(537\) 102638. + 215942.i 0.355926 + 0.748838i
\(538\) −233.658 + 196.062i −0.000807266 + 0.000677376i
\(539\) 10890.7i 0.0374869i
\(540\) −6303.50 + 96580.8i −0.0216169 + 0.331210i
\(541\) −462829. −1.58134 −0.790671 0.612241i \(-0.790268\pi\)
−0.790671 + 0.612241i \(0.790268\pi\)
\(542\) −20338.8 24238.9i −0.0692353 0.0825114i
\(543\) −12208.8 + 152471.i −0.0414070 + 0.517117i
\(544\) 69217.2 392550.i 0.233892 1.32647i
\(545\) −8650.61 23767.4i −0.0291242 0.0800181i
\(546\) 23289.4 + 10652.0i 0.0781221 + 0.0357309i
\(547\) −65549.2 371748.i −0.219075 1.24244i −0.873693 0.486477i \(-0.838282\pi\)
0.654618 0.755960i \(-0.272829\pi\)
\(548\) 418232. 241466.i 1.39269 0.804072i
\(549\) −83413.6 + 49811.1i −0.276753 + 0.165265i
\(550\) −6835.10 + 11838.7i −0.0225954 + 0.0391363i
\(551\) −10895.2 + 29934.3i −0.0358865 + 0.0985974i
\(552\) −219516. 57089.8i −0.720423 0.187362i
\(553\) −164497. 138029.i −0.537907 0.451358i
\(554\) 28400.8 33846.8i 0.0925362 0.110280i
\(555\) −132799. 130857.i −0.431130 0.424826i
\(556\) 225778. + 82176.5i 0.730352 + 0.265826i
\(557\) 153585. + 88672.5i 0.495039 + 0.285811i 0.726662 0.686995i \(-0.241070\pi\)
−0.231624 + 0.972805i \(0.574404\pi\)
\(558\) 103434. + 84226.7i 0.332196 + 0.270509i
\(559\) −82762.2 143348.i −0.264855 0.458742i
\(560\) 67636.8 11926.2i 0.215678 0.0380299i
\(561\) 76090.5 7222.06i 0.241771 0.0229475i
\(562\) −69362.9 + 25246.0i −0.219611 + 0.0799319i
\(563\) −134655. 23743.4i −0.424822 0.0749076i −0.0428501 0.999082i \(-0.513644\pi\)
−0.381972 + 0.924174i \(0.624755\pi\)
\(564\) 291307. 422620.i 0.915784 1.32859i
\(565\) 91921.3 77131.1i 0.287951 0.241620i
\(566\) 69048.7i 0.215537i
\(567\) 219794. + 173660.i 0.683676 + 0.540173i
\(568\) 116632. 0.361510
\(569\) −301401. 359196.i −0.930938 1.10945i −0.993773 0.111425i \(-0.964459\pi\)
0.0628350 0.998024i \(-0.479986\pi\)
\(570\) 10691.3 + 7369.39i 0.0329064 + 0.0226820i
\(571\) −16388.9 + 92946.2i −0.0502664 + 0.285075i −0.999571 0.0292821i \(-0.990678\pi\)
0.949305 + 0.314357i \(0.101789\pi\)
\(572\) −4506.36 12381.1i −0.0137732 0.0378415i
\(573\) −44873.1 472776.i −0.136671 1.43995i
\(574\) 5433.64 + 30815.7i 0.0164918 + 0.0935294i
\(575\) 287705. 166107.i 0.870186 0.502402i
\(576\) −124261. 20028.2i −0.374531 0.0603666i
\(577\) −151696. + 262746.i −0.455641 + 0.789194i −0.998725 0.0504846i \(-0.983923\pi\)
0.543083 + 0.839679i \(0.317257\pi\)
\(578\) −55316.5 + 151981.i −0.165577 + 0.454918i
\(579\) −296767. + 301171.i −0.885236 + 0.898371i
\(580\) 28407.5 + 23836.7i 0.0844455 + 0.0708582i
\(581\) 310191. 369671.i 0.918919 1.09512i
\(582\) 5702.70 21927.4i 0.0168358 0.0647353i
\(583\) −69360.0 25245.0i −0.204067 0.0742741i
\(584\) −83077.5 47964.8i −0.243589 0.140636i
\(585\) −37429.1 + 551.304i −0.109370 + 0.00161094i
\(586\) −11158.7 19327.5i −0.0324952 0.0562833i
\(587\) −498455. + 87891.1i −1.44661 + 0.255076i −0.841149 0.540803i \(-0.818120\pi\)
−0.605456 + 0.795879i \(0.707009\pi\)
\(588\) −30680.0 + 67078.7i −0.0887360 + 0.194013i
\(589\) −130662. + 47557.0i −0.376632 + 0.137083i
\(590\) −56081.7 9888.71i −0.161108 0.0284077i
\(591\) −214493. 17175.1i −0.614099 0.0491727i
\(592\) 291012. 244188.i 0.830362 0.696756i
\(593\) 382244.i 1.08701i 0.839407 + 0.543503i \(0.182902\pi\)
−0.839407 + 0.543503i \(0.817098\pi\)
\(594\) 2024.36 + 18437.3i 0.00573740 + 0.0522547i
\(595\) −180280. −0.509229
\(596\) 254529. + 303336.i 0.716547 + 0.853947i
\(597\) 156950. 74599.1i 0.440366 0.209308i
\(598\) 7156.08 40584.1i 0.0200112 0.113489i
\(599\) −99670.1 273841.i −0.277787 0.763213i −0.997613 0.0690580i \(-0.978001\pi\)
0.719826 0.694155i \(-0.244222\pi\)
\(600\) −160610. + 114232.i −0.446138 + 0.317311i
\(601\) 95074.7 + 539196.i 0.263218 + 1.49279i 0.774061 + 0.633111i \(0.218222\pi\)
−0.510843 + 0.859674i \(0.670667\pi\)
\(602\) 167535. 96726.4i 0.462288 0.266902i
\(603\) 83838.9 241347.i 0.230574 0.663755i
\(604\) −23526.7 + 40749.5i −0.0644893 + 0.111699i
\(605\) 45762.9 125733.i 0.125027 0.343508i
\(606\) 2776.48 + 10064.9i 0.00756048 + 0.0274072i
\(607\) −172994. 145159.i −0.469519 0.393973i 0.377100 0.926173i \(-0.376921\pi\)
−0.846619 + 0.532199i \(0.821366\pi\)
\(608\) −64815.0 + 77243.5i −0.175335 + 0.208956i
\(609\) 103462. 28540.9i 0.278964 0.0769544i
\(610\) 14258.5 + 5189.67i 0.0383190 + 0.0139470i
\(611\) 171924. + 99260.4i 0.460526 + 0.265885i
\(612\) 489005. + 169870.i 1.30560 + 0.453537i
\(613\) 295834. + 512400.i 0.787277 + 1.36360i 0.927629 + 0.373502i \(0.121843\pi\)
−0.140352 + 0.990102i \(0.544823\pi\)
\(614\) −136388. + 24048.8i −0.361775 + 0.0637906i
\(615\) −26509.0 37271.6i −0.0700880 0.0985435i
\(616\) 30802.7 11211.3i 0.0811759 0.0295456i
\(617\) 111685. + 19693.0i 0.293375 + 0.0517300i 0.318399 0.947957i \(-0.396855\pi\)
−0.0250234 + 0.999687i \(0.507966\pi\)
\(618\) −26391.8 55526.1i −0.0691022 0.145385i
\(619\) −171675. + 144052.i −0.448049 + 0.375958i −0.838711 0.544576i \(-0.816690\pi\)
0.390662 + 0.920534i \(0.372246\pi\)
\(620\) 161867.i 0.421090i
\(621\) 181427. 412633.i 0.470456 1.06999i
\(622\) −41824.3 −0.108105
\(623\) 31134.8 + 37105.0i 0.0802176 + 0.0955996i
\(624\) 6088.02 76031.1i 0.0156353 0.195264i
\(625\) 40607.1 230294.i 0.103954 0.589554i
\(626\) 29652.0 + 81468.3i 0.0756669 + 0.207893i
\(627\) −17583.1 8042.02i −0.0447260 0.0204564i
\(628\) 52512.7 + 297814.i 0.133151 + 0.755138i
\(629\) −863581. + 498589.i −2.18274 + 1.26021i
\(630\) −644.324 43744.4i −0.00162339 0.110215i
\(631\) 36775.4 63696.9i 0.0923633 0.159978i −0.816142 0.577852i \(-0.803891\pi\)
0.908505 + 0.417874i \(0.137225\pi\)
\(632\) 70113.4 192635.i 0.175536 0.482282i
\(633\) 253342. + 65887.1i 0.632266 + 0.164435i
\(634\) 104435. + 87631.3i 0.259817 + 0.218012i
\(635\) 69303.1 82592.3i 0.171872 0.204829i
\(636\) −356088. 350881.i −0.880325 0.867454i
\(637\) −26807.7 9757.21i −0.0660665 0.0240462i
\(638\) 6154.54 + 3553.32i 0.0151201 + 0.00872958i
\(639\) −36882.6 + 228830.i −0.0903274 + 0.560416i
\(640\) 76073.7 + 131764.i 0.185727 + 0.321688i
\(641\) −337744. + 59553.3i −0.821999 + 0.144941i −0.568802 0.822474i \(-0.692593\pi\)
−0.253197 + 0.967415i \(0.581482\pi\)
\(642\) −130315. + 12368.7i −0.316172 + 0.0300092i
\(643\) 201474. 73330.5i 0.487300 0.177363i −0.0866731 0.996237i \(-0.527624\pi\)
0.573973 + 0.818874i \(0.305401\pi\)
\(644\) −368537. 64983.1i −0.888607 0.156685i
\(645\) −160477. + 232815.i −0.385739 + 0.559618i
\(646\) 53203.0 44642.6i 0.127489 0.106976i
\(647\) 20926.3i 0.0499902i −0.999688 0.0249951i \(-0.992043\pi\)
0.999688 0.0249951i \(-0.00795701\pi\)
\(648\) −84021.4 + 253875.i −0.200097 + 0.604602i
\(649\) 84794.5 0.201316
\(650\) −23017.5 27431.2i −0.0544794 0.0649260i
\(651\) 385722. + 265874.i 0.910149 + 0.627356i
\(652\) −9208.96 + 52226.6i −0.0216628 + 0.122856i
\(653\) 64062.7 + 176011.i 0.150238 + 0.412774i 0.991867 0.127282i \(-0.0406252\pi\)
−0.841629 + 0.540056i \(0.818403\pi\)
\(654\) −3101.98 32682.0i −0.00725243 0.0764105i
\(655\) 34216.6 + 194052.i 0.0797544 + 0.452310i
\(656\) 80709.3 46597.5i 0.187550 0.108282i
\(657\) 120378. 147829.i 0.278879 0.342475i
\(658\) −116008. + 200932.i −0.267940 + 0.464085i
\(659\) −34435.2 + 94610.0i −0.0792925 + 0.217854i −0.973004 0.230787i \(-0.925870\pi\)
0.893712 + 0.448642i \(0.148092\pi\)
\(660\) −15798.0 + 16032.4i −0.0362671 + 0.0368052i
\(661\) 377130. + 316450.i 0.863154 + 0.724272i 0.962645 0.270766i \(-0.0872770\pi\)
−0.0994911 + 0.995038i \(0.531721\pi\)
\(662\) 970.390 1156.47i 0.00221427 0.00263886i
\(663\) −50393.7 + 193768.i −0.114643 + 0.440814i
\(664\) 432906. + 157565.i 0.981877 + 0.357374i
\(665\) 39495.0 + 22802.4i 0.0893097 + 0.0515630i
\(666\) −124068. 207764.i −0.279711 0.468405i
\(667\) −86353.0 149568.i −0.194100 0.336191i
\(668\) −179257. + 31607.8i −0.401720 + 0.0708340i
\(669\) 315930. 690750.i 0.705893 1.54337i
\(670\) −37496.7 + 13647.7i −0.0835302 + 0.0304025i
\(671\) −22250.4 3923.34i −0.0494188 0.00871387i
\(672\) 338646. + 27116.3i 0.749906 + 0.0600471i
\(673\) 133890. 112347.i 0.295609 0.248045i −0.482905 0.875673i \(-0.660418\pi\)
0.778514 + 0.627628i \(0.215974\pi\)
\(674\) 165075.i 0.363380i
\(675\) −173332. 351238.i −0.380426 0.770892i
\(676\) −370355. −0.810447
\(677\) −66906.1 79735.6i −0.145978 0.173970i 0.688101 0.725615i \(-0.258445\pi\)
−0.834079 + 0.551645i \(0.814000\pi\)
\(678\) 140667. 66859.7i 0.306008 0.145447i
\(679\) 13817.7 78364.3i 0.0299707 0.169972i
\(680\) −58863.2 161725.i −0.127299 0.349752i
\(681\) −37636.9 + 26768.9i −0.0811558 + 0.0577212i
\(682\) 5386.60 + 30548.9i 0.0115810 + 0.0656791i
\(683\) −316965. + 183000.i −0.679469 + 0.392292i −0.799655 0.600460i \(-0.794984\pi\)
0.120186 + 0.992751i \(0.461651\pi\)
\(684\) −85643.5 99065.5i −0.183055 0.211744i
\(685\) 159537. 276327.i 0.340001 0.588900i
\(686\) 58760.3 161443.i 0.124864 0.343060i
\(687\) 146440. + 530855.i 0.310276 + 1.12477i
\(688\) −441369. 370352.i −0.932448 0.782417i
\(689\) 124282. 148113.i 0.261800 0.312001i
\(690\) −67864.5 + 18720.9i −0.142542 + 0.0393214i
\(691\) 126437. + 46019.3i 0.264800 + 0.0963793i 0.471008 0.882129i \(-0.343890\pi\)
−0.206208 + 0.978508i \(0.566112\pi\)
\(692\) −524905. 303054.i −1.09615 0.632860i
\(693\) 12255.6 + 63979.8i 0.0255192 + 0.133222i
\(694\) −12802.4 22174.4i −0.0265810 0.0460397i
\(695\) 156334. 27565.9i 0.323656 0.0570693i
\(696\) 59385.1 + 83495.2i 0.122591 + 0.172363i
\(697\) −229877. + 83668.2i −0.473183 + 0.172224i
\(698\) 166140. + 29295.0i 0.341008 + 0.0601289i
\(699\) −291422. 613127.i −0.596442 1.25486i
\(700\) −249098. + 209018.i −0.508363 + 0.426567i
\(701\) 730976.i 1.48753i −0.668439 0.743767i \(-0.733037\pi\)
0.668439 0.743767i \(-0.266963\pi\)
\(702\) −47197.5 11535.4i −0.0957733 0.0234076i
\(703\) 252253. 0.510418
\(704\) −18814.5 22422.3i −0.0379619 0.0452413i
\(705\) 27068.6 338050.i 0.0544613 0.680148i
\(706\) 9267.14 52556.5i 0.0185924 0.105443i
\(707\) 12541.6 + 34457.8i 0.0250908 + 0.0689365i
\(708\) 522270. + 238872.i 1.04191 + 0.476539i
\(709\) −84369.5 478483.i −0.167839 0.951863i −0.946089 0.323908i \(-0.895003\pi\)
0.778250 0.627955i \(-0.216108\pi\)
\(710\) 31350.0 18099.9i 0.0621901 0.0359055i
\(711\) 355775. + 198479.i 0.703779 + 0.392622i
\(712\) −23120.3 + 40045.5i −0.0456072 + 0.0789940i
\(713\) 257833. 708390.i 0.507177 1.39346i
\(714\) −226462. 58896.4i −0.444221 0.115529i
\(715\) −6668.59 5595.61i −0.0130443 0.0109455i
\(716\) −242065. + 288482.i −0.472178 + 0.562720i
\(717\) 372313. + 366870.i 0.724219 + 0.713630i
\(718\) −130739. 47585.2i −0.253605 0.0923045i
\(719\) 555622. + 320788.i 1.07479 + 0.620527i 0.929485 0.368860i \(-0.120252\pi\)
0.145300 + 0.989388i \(0.453585\pi\)
\(720\) −121772. + 46363.4i −0.234899 + 0.0894356i
\(721\) −107960. 186993.i −0.207680 0.359712i
\(722\) 156050. 27515.9i 0.299358 0.0527849i
\(723\) −634181. + 60192.7i −1.21321 + 0.115151i
\(724\) −226391. + 82399.7i −0.431900 + 0.157199i
\(725\) −147790. 26059.4i −0.281170 0.0495779i
\(726\) 98562.2 142991.i 0.186998 0.271291i
\(727\) −204709. + 171771.i −0.387318 + 0.324999i −0.815567 0.578662i \(-0.803575\pi\)
0.428249 + 0.903661i \(0.359131\pi\)
\(728\) 85865.6i 0.162015i
\(729\) −471529. 245132.i −0.887265 0.461259i
\(730\) −29774.4 −0.0558724
\(731\) 972144. + 1.15856e6i 1.81927 + 2.16812i
\(732\) −125993. 86845.6i −0.235139 0.162079i
\(733\) −68087.6 + 386144.i −0.126724 + 0.718690i 0.853544 + 0.521020i \(0.174448\pi\)
−0.980269 + 0.197670i \(0.936663\pi\)
\(734\) −93112.3 255824.i −0.172828 0.474842i
\(735\) 4604.90 + 48516.6i 0.00852405 + 0.0898080i
\(736\) −94929.8 538373.i −0.175245 0.993866i
\(737\) 51456.0 29708.1i 0.0947330 0.0546941i
\(738\) −21123.4 55479.9i −0.0387839 0.101864i
\(739\) 169462. 293516.i 0.310301 0.537456i −0.668127 0.744047i \(-0.732904\pi\)
0.978427 + 0.206591i \(0.0662370\pi\)
\(740\) 100435. 275942.i 0.183409 0.503912i
\(741\) 35548.6 36076.0i 0.0647419 0.0657026i
\(742\) 173104. + 145251.i 0.314412 + 0.263823i
\(743\) −445339. + 530734.i −0.806701 + 0.961389i −0.999804 0.0197896i \(-0.993700\pi\)
0.193103 + 0.981178i \(0.438145\pi\)
\(744\) −112568. + 432834.i −0.203362 + 0.781944i
\(745\) 245845. + 89480.2i 0.442944 + 0.161218i
\(746\) −125650. 72544.0i −0.225780 0.130354i
\(747\) −446038. + 799528.i −0.799339 + 1.43282i
\(748\) 60193.0 + 104257.i 0.107583 + 0.186339i
\(749\) −452752. + 79832.4i −0.807043 + 0.142303i
\(750\) −55041.1 + 120342.i −0.0978509 + 0.213941i
\(751\) 688146. 250465.i 1.22012 0.444086i 0.349914 0.936782i \(-0.386211\pi\)
0.870201 + 0.492696i \(0.163989\pi\)
\(752\) 680524. + 119995.i 1.20339 + 0.212191i
\(753\) 83015.2 + 6647.26i 0.146409 + 0.0117234i
\(754\) −14260.5 + 11966.0i −0.0250838 + 0.0210478i
\(755\) 31088.3i 0.0545385i
\(756\) −104750. + 428591.i −0.183279 + 0.749894i
\(757\) 347674. 0.606709 0.303355 0.952878i \(-0.401893\pi\)
0.303355 + 0.952878i \(0.401893\pi\)
\(758\) 192536. + 229455.i 0.335099 + 0.399355i
\(759\) 94675.3 44999.5i 0.164344 0.0781132i
\(760\) −7560.09 + 42875.4i −0.0130888 + 0.0742303i
\(761\) 227751. + 625741.i 0.393270 + 1.08050i 0.965499 + 0.260407i \(0.0838566\pi\)
−0.572229 + 0.820094i \(0.693921\pi\)
\(762\) 114039. 81109.1i 0.196401 0.139688i
\(763\) −20021.4 113547.i −0.0343910 0.195041i
\(764\) 647786. 373999.i 1.10980 0.640743i
\(765\) 335918. 64346.3i 0.573997 0.109951i
\(766\) 84187.8 145818.i 0.143480 0.248515i
\(767\) −75969.0 + 208723.i −0.129135 + 0.354797i
\(768\) −6987.90 25331.5i −0.0118474 0.0429476i
\(769\) −69815.7 58582.4i −0.118059 0.0990636i 0.581847 0.813299i \(-0.302330\pi\)
−0.699906 + 0.714235i \(0.746775\pi\)
\(770\) 6539.74 7793.76i 0.0110301 0.0131452i
\(771\) −691036. + 190628.i −1.16250 + 0.320684i
\(772\) −625802. 227773.i −1.05003 0.382180i
\(773\) −75723.2 43718.8i −0.126727 0.0731660i 0.435296 0.900287i \(-0.356644\pi\)
−0.562024 + 0.827121i \(0.689977\pi\)
\(774\) −277646. + 240029.i −0.463457 + 0.400665i
\(775\) −327524. 567288.i −0.545305 0.944497i
\(776\) 74810.7 13191.1i 0.124234 0.0219058i
\(777\) −492590. 692580.i −0.815913 1.14717i
\(778\) −275658. + 100331.i −0.455419 + 0.165759i
\(779\) 60943.1 + 10745.9i 0.100427 + 0.0177080i
\(780\) −25310.2 53250.6i −0.0416013 0.0875256i
\(781\) −41291.4 + 34647.6i −0.0676951 + 0.0568029i
\(782\) 376536.i 0.615734i
\(783\) −182596. + 90109.0i −0.297829 + 0.146975i
\(784\) −99302.4 −0.161558
\(785\) 128430. + 153057.i 0.208415 + 0.248379i
\(786\) −20413.9 + 254941.i −0.0330430 + 0.412662i
\(787\) −152733. + 866190.i −0.246594 + 1.39850i 0.570168 + 0.821528i \(0.306878\pi\)
−0.816762 + 0.576975i \(0.804233\pi\)
\(788\) −115918. 318482.i −0.186680 0.512900i
\(789\) 930890. + 425764.i 1.49535 + 0.683934i
\(790\) −11048.7 62660.1i −0.0177034 0.100401i
\(791\) 473719. 273502.i 0.757125 0.437126i
\(792\) −53393.4 + 31884.3i −0.0851211 + 0.0508308i
\(793\) 29591.9 51254.7i 0.0470572 0.0815055i
\(794\) 55274.4 151865.i 0.0876765 0.240889i
\(795\) −319662. 83135.1i −0.505774 0.131538i
\(796\) 209674. + 175937.i 0.330916 + 0.277672i
\(797\) −123272. + 146910.i −0.194065 + 0.231278i −0.854299 0.519783i \(-0.826013\pi\)
0.660233 + 0.751061i \(0.270457\pi\)
\(798\) 42163.0 + 41546.6i 0.0662104 + 0.0652423i
\(799\) −1.70449e6 620382.i −2.66993 0.971775i
\(800\) −411386. 237514.i −0.642790 0.371115i
\(801\) −71257.5 58025.4i −0.111062 0.0904384i
\(802\) 53968.7 + 93476.4i 0.0839060 + 0.145329i
\(803\) 43660.9 7698.60i 0.0677114 0.0119393i
\(804\) 400620. 38024.4i 0.619755 0.0588235i
\(805\) −232339. + 84564.3i −0.358533 + 0.130495i
\(806\) −80022.6 14110.1i −0.123181 0.0217201i
\(807\) 1153.43 1673.37i 0.00177111 0.00256948i
\(808\) −26816.5 + 22501.7i −0.0410751 + 0.0344661i
\(809\) 342800.i 0.523774i −0.965099 0.261887i \(-0.915655\pi\)
0.965099 0.261887i \(-0.0843447\pi\)
\(810\) 16814.0 + 81279.5i 0.0256272 + 0.123883i
\(811\) 1.12925e6 1.71691 0.858453 0.512892i \(-0.171426\pi\)
0.858453 + 0.512892i \(0.171426\pi\)
\(812\) 108661. + 129497.i 0.164802 + 0.196403i
\(813\) 173589. + 119653.i 0.262629 + 0.181027i
\(814\) 9772.12 55420.5i 0.0147482 0.0836414i
\(815\) 11983.9 + 32925.5i 0.0180419 + 0.0495697i
\(816\) 65851.2 + 693798.i 0.0988970 + 1.04196i
\(817\) −66435.1 376772.i −0.0995299 0.564462i
\(818\) −299726. + 173047.i −0.447938 + 0.258617i
\(819\) −168467. 27153.4i −0.251158 0.0404815i
\(820\) 36019.6 62387.7i 0.0535687 0.0927836i
\(821\) 391161. 1.07471e6i 0.580323 1.59442i −0.207308 0.978276i \(-0.566470\pi\)
0.787631 0.616148i \(-0.211308\pi\)
\(822\) 290680. 294993.i 0.430202 0.436585i
\(823\) 474071. + 397792.i 0.699912 + 0.587296i 0.921749 0.387788i \(-0.126761\pi\)
−0.221837 + 0.975084i \(0.571205\pi\)
\(824\) 132497. 157904.i 0.195143 0.232562i
\(825\) 22926.3 88153.8i 0.0336842 0.129519i
\(826\) −243940. 88787.0i −0.357539 0.130134i
\(827\) 106515. + 61496.6i 0.155740 + 0.0899167i 0.575845 0.817559i \(-0.304673\pi\)
−0.420104 + 0.907476i \(0.638007\pi\)
\(828\) 709894. 10456.2i 1.03546 0.0152516i
\(829\) 235237. + 407442.i 0.342291 + 0.592866i 0.984858 0.173364i \(-0.0554637\pi\)
−0.642567 + 0.766230i \(0.722130\pi\)
\(830\) 140815. 24829.5i 0.204406 0.0360423i
\(831\) −122452. + 267729.i −0.177322 + 0.387697i
\(832\) 72049.1 26223.7i 0.104084 0.0378833i
\(833\) 256701. + 45263.3i 0.369945 + 0.0652313i
\(834\) 205388. + 16446.0i 0.295286 + 0.0236444i
\(835\) −92126.5 + 77303.3i −0.132133 + 0.110873i
\(836\) 30453.7i 0.0435740i
\(837\) −813618. 357733.i −1.16137 0.510632i
\(838\) −409129. −0.582602
\(839\) 42223.1 + 50319.5i 0.0599827 + 0.0714846i 0.795202 0.606345i \(-0.207365\pi\)
−0.735219 + 0.677830i \(0.762921\pi\)
\(840\) 132481. 62968.6i 0.187756 0.0892412i
\(841\) 109271. 619705.i 0.154494 0.876179i
\(842\) −30079.5 82642.8i −0.0424274 0.116568i
\(843\) 400799. 285064.i 0.563991 0.401132i
\(844\) 71595.7 + 406040.i 0.100508 + 0.570011i
\(845\) −211911. + 122347.i −0.296784 + 0.171348i
\(846\) 144442. 415806.i 0.201815 0.580965i
\(847\) 304972. 528227.i 0.425102 0.736298i
\(848\) 230185. 632428.i 0.320100 0.879467i
\(849\) −122347. 443514.i −0.169737 0.615308i
\(850\) 250638. + 210310.i 0.346904 + 0.291087i
\(851\) −879080. + 1.04765e6i −1.21386 + 1.44662i
\(852\) −351928. + 97082.1i −0.484813 + 0.133740i
\(853\) 913792. + 332593.i 1.25588 + 0.457104i 0.882386 0.470527i \(-0.155936\pi\)
0.373498 + 0.927631i \(0.378158\pi\)
\(854\) 59902.7 + 34584.8i 0.0821355 + 0.0474209i
\(855\) −81730.3 28391.4i −0.111802 0.0388377i
\(856\) −219444. 380089.i −0.299486 0.518725i
\(857\) −1.09569e6 + 193200.i −1.49185 + 0.263054i −0.859304 0.511465i \(-0.829103\pi\)
−0.632550 + 0.774519i \(0.717992\pi\)
\(858\) −6548.84 9207.64i −0.00889589 0.0125076i
\(859\) 507014. 184538.i 0.687122 0.250092i 0.0252197 0.999682i \(-0.491971\pi\)
0.661903 + 0.749590i \(0.269749\pi\)
\(860\) −438606. 77338.0i −0.593031 0.104567i
\(861\) −89503.5 188308.i −0.120735 0.254017i
\(862\) 255835. 214671.i 0.344307 0.288908i
\(863\) 924852.i 1.24180i −0.783891 0.620899i \(-0.786768\pi\)
0.783891 0.620899i \(-0.213232\pi\)
\(864\) −640682. + 70344.8i −0.858252 + 0.0942334i
\(865\) −400457. −0.535209
\(866\) 199656. + 237941.i 0.266224 + 0.317274i
\(867\) 86015.8 1.07422e6i 0.114430 1.42907i
\(868\) −128132. + 726670.i −0.170066 + 0.964491i
\(869\) 32403.3 + 89027.4i 0.0429092 + 0.117892i
\(870\) 28919.9 + 13227.2i 0.0382084 + 0.0174755i
\(871\) 27026.7 + 153276.i 0.0356251 + 0.202040i
\(872\) 95323.4 55035.0i 0.125362 0.0723779i
\(873\) 2223.37 + 150949.i 0.00291732 + 0.198062i
\(874\) 47625.6 82490.0i 0.0623473 0.107989i
\(875\) −158958. + 436734.i −0.207619 + 0.570428i
\(876\) 290606. + 75578.3i 0.378700 + 0.0984893i
\(877\) −732255. 614435.i −0.952057 0.798871i 0.0275855 0.999619i \(-0.491218\pi\)
−0.979643 + 0.200748i \(0.935663\pi\)
\(878\) −69312.9 + 82603.9i −0.0899135 + 0.107155i
\(879\) 105921. + 104372.i 0.137090 + 0.135085i
\(880\) −28474.2 10363.8i −0.0367694 0.0133830i
\(881\) −1.16480e6 672499.i −1.50072 0.866443i −1.00000 0.000835760i \(-0.999734\pi\)
−0.500724 0.865607i \(-0.666933\pi\)
\(882\) −10065.6 + 62449.5i −0.0129390 + 0.0802771i
\(883\) −195760. 339066.i −0.251074 0.434873i 0.712748 0.701421i \(-0.247450\pi\)
−0.963822 + 0.266547i \(0.914117\pi\)
\(884\) −310559. + 54759.9i −0.397411 + 0.0700742i
\(885\) 377746. 35853.4i 0.482296 0.0457767i
\(886\) −137657. + 50103.2i −0.175361 + 0.0638261i
\(887\) −163507. 28830.7i −0.207821 0.0366444i 0.0687684 0.997633i \(-0.478093\pi\)
−0.276589 + 0.960988i \(0.589204\pi\)
\(888\) 460464. 668027.i 0.583942 0.847166i
\(889\) 376502. 315923.i 0.476391 0.399740i
\(890\) 14352.1i 0.0181190i
\(891\) −45671.9 114840.i −0.0575299 0.144657i
\(892\) 1.19637e6 1.50361
\(893\) 294944. + 351500.i 0.369859 + 0.440781i
\(894\) 279590. + 192719.i 0.349822 + 0.241129i
\(895\) −43205.6 + 245031.i −0.0539379 + 0.305897i
\(896\) 237216. + 651746.i 0.295480 + 0.811825i
\(897\) 25945.8 + 273361.i 0.0322464 + 0.339743i
\(898\) 7283.44 + 41306.5i 0.00903200 + 0.0512230i
\(899\) −294913. + 170268.i −0.364901 + 0.210675i
\(900\) 389544. 478375.i 0.480918 0.590587i
\(901\) −883306. + 1.52993e6i −1.08808 + 1.88461i
\(902\) 4721.79 12973.0i 0.00580355 0.0159451i
\(903\) −904724. + 918148.i −1.10953 + 1.12600i
\(904\) 400027. + 335663.i 0.489500 + 0.410739i
\(905\) −102317. + 121937.i −0.124925 + 0.148880i
\(906\) −10156.4 + 39052.2i −0.0123732 + 0.0475762i
\(907\) 1.28533e6 + 467822.i 1.56243 + 0.568678i 0.971292 0.237892i \(-0.0764565\pi\)
0.591138 + 0.806570i \(0.298679\pi\)
\(908\) −62999.2 36372.6i −0.0764123 0.0441167i
\(909\) −35667.8 59729.3i −0.0431667 0.0722870i
\(910\) 13325.4 + 23080.2i 0.0160915 + 0.0278713i
\(911\) 950257. 167556.i 1.14500 0.201894i 0.431207 0.902253i \(-0.358088\pi\)
0.713791 + 0.700359i \(0.246977\pi\)
\(912\) 73327.6 160324.i 0.0881613 0.192756i
\(913\) −200070. + 72819.6i −0.240016 + 0.0873588i
\(914\) −219381. 38682.8i −0.262607 0.0463048i
\(915\) −100781. 8069.81i −0.120375 0.00963876i
\(916\) −664436. + 557528.i −0.791886 + 0.664471i
\(917\) 898246.i 1.06821i
\(918\) 442992. + 28912.5i 0.525666 + 0.0343084i
\(919\) −1.00521e6 −1.19021 −0.595107 0.803647i \(-0.702890\pi\)
−0.595107 + 0.803647i \(0.702890\pi\)
\(920\) −151722. 180815.i −0.179256 0.213629i
\(921\) 833435. 396135.i 0.982545 0.467008i
\(922\) 68824.1 390321.i 0.0809616 0.459156i
\(923\) −48291.9 132681.i −0.0566853 0.155742i
\(924\) −83612.9 + 59468.8i −0.0979330 + 0.0696538i
\(925\) 206356. + 1.17030e6i 0.241176 + 1.36778i
\(926\) −84508.0 + 48790.7i −0.0985543 + 0.0569004i
\(927\) 267906. + 309893.i 0.311762 + 0.360622i
\(928\) −123475. + 213865.i −0.143378 + 0.248338i
\(929\) 100931. 277305.i 0.116948 0.321312i −0.867383 0.497641i \(-0.834200\pi\)
0.984331 + 0.176328i \(0.0564221\pi\)
\(930\) 36913.4 + 133813.i 0.0426793 + 0.154715i
\(931\) −50511.9 42384.5i −0.0582766 0.0488999i
\(932\) 687300. 819092.i 0.791251 0.942976i
\(933\) 268646. 74108.2i 0.308615 0.0851339i
\(934\) 51536.6 + 18757.8i 0.0590775 + 0.0215024i
\(935\) 68883.0 + 39769.6i 0.0787932 + 0.0454913i
\(936\) −30647.5 159994.i −0.0349820 0.182622i
\(937\) 848848. + 1.47025e6i 0.966831 + 1.67460i 0.704612 + 0.709592i \(0.251121\pi\)
0.262219 + 0.965008i \(0.415546\pi\)
\(938\) −179138. + 31586.8i −0.203602 + 0.0359004i
\(939\) −334814. 470748.i −0.379728 0.533897i
\(940\) 501941. 182692.i 0.568064 0.206758i
\(941\) −921233. 162438.i −1.04038 0.183446i −0.372741 0.927935i \(-0.621582\pi\)
−0.667635 + 0.744489i \(0.732693\pi\)
\(942\) 111327. + 234224.i 0.125459 + 0.263954i
\(943\) −257011. + 215658.i −0.289020 + 0.242517i
\(944\) 773162.i 0.867613i
\(945\) 81649.1 + 279838.i 0.0914297 + 0.313360i
\(946\) −85351.1 −0.0953734
\(947\) 3750.59 + 4469.77i 0.00418215 + 0.00498409i 0.768131 0.640292i \(-0.221187\pi\)
−0.763949 + 0.645276i \(0.776742\pi\)
\(948\) −51216.5 + 639624.i −0.0569892 + 0.711718i
\(949\) −20166.4 + 114369.i −0.0223922 + 0.126992i
\(950\) −28308.0 77775.5i −0.0313662 0.0861779i
\(951\) −826081. 377827.i −0.913401 0.417765i
\(952\) −136236. 772631.i −0.150320 0.852507i
\(953\) −532595. + 307494.i −0.586423 + 0.338571i −0.763682 0.645593i \(-0.776610\pi\)
0.177259 + 0.984164i \(0.443277\pi\)
\(954\) −374391. 208864.i −0.411366 0.229491i
\(955\) 247102. 427993.i 0.270938 0.469278i
\(956\) −281578. + 773628.i −0.308093 + 0.846479i
\(957\) −45828.0 11918.6i −0.0500389 0.0130137i
\(958\) 57492.4 + 48241.8i 0.0626440 + 0.0525645i
\(959\) 934948. 1.11423e6i 1.01660 1.21154i
\(960\) −93296.6 91932.5i −0.101233 0.0997532i
\(961\) −528956. 192524.i −0.572760 0.208468i
\(962\) 127663. + 73706.4i 0.137948 + 0.0796444i
\(963\) 815124. 310351.i 0.878964 0.334657i
\(964\) −501682. 868939.i −0.539852 0.935051i
\(965\) −433319. + 76405.9i −0.465322 + 0.0820488i
\(966\) −319484. + 30323.5i −0.342369 + 0.0324956i
\(967\) −1.36323e6 + 496176.i −1.45786 + 0.530619i −0.944776 0.327718i \(-0.893720\pi\)
−0.513087 + 0.858337i \(0.671498\pi\)
\(968\) 573439. + 101113.i 0.611979 + 0.107908i
\(969\) −262632. + 381019.i −0.279705 + 0.405788i
\(970\) 18061.6 15155.5i 0.0191961 0.0161074i
\(971\) 1.14407e6i 1.21343i −0.794921 0.606713i \(-0.792488\pi\)
0.794921 0.606713i \(-0.207512\pi\)
\(972\) 42208.0 835988.i 0.0446747 0.884846i
\(973\) 723652. 0.764371
\(974\) −120646. 143780.i −0.127173 0.151559i
\(975\) 196452. + 135412.i 0.206655 + 0.142445i
\(976\) 35773.3 202880.i 0.0375542 0.212981i
\(977\) −87019.9 239085.i −0.0911653 0.250474i 0.885727 0.464206i \(-0.153660\pi\)
−0.976892 + 0.213732i \(0.931438\pi\)
\(978\) 4297.24 + 45275.1i 0.00449275 + 0.0473349i
\(979\) −3710.93 21045.7i −0.00387184 0.0219583i
\(980\) −66476.2 + 38380.0i −0.0692172 + 0.0399625i
\(981\) 77833.7 + 204427.i 0.0808779 + 0.212422i
\(982\) 8894.31 15405.4i 0.00922336 0.0159753i
\(983\) 80074.8 220004.i 0.0828684 0.227679i −0.891337 0.453341i \(-0.850232\pi\)
0.974206 + 0.225662i \(0.0724543\pi\)
\(984\) 139703. 141776.i 0.144284 0.146424i
\(985\) −171537. 143937.i −0.176802 0.148354i
\(986\) 109333. 130298.i 0.112460 0.134024i
\(987\) 389116. 1.49619e6i 0.399433 1.53586i
\(988\) 74962.3 + 27284.0i 0.0767943 + 0.0279508i
\(989\) 1.79631e6 + 1.03710e6i 1.83650 + 1.06030i
\(990\) −9403.80 + 16856.4i −0.00959474 + 0.0171987i
\(991\) −638655. 1.10618e6i −0.650308 1.12637i −0.983048 0.183348i \(-0.941306\pi\)
0.332740 0.943019i \(-0.392027\pi\)
\(992\) −1.06155e6 + 187180.i −1.07874 + 0.190211i
\(993\) −4183.89 + 9147.66i −0.00424309 + 0.00927708i
\(994\) 155068. 56440.0i 0.156945 0.0571234i
\(995\) 178093. + 31402.6i 0.179888 + 0.0317190i
\(996\) −1.43742e6 115098.i −1.44899 0.116024i
\(997\) 1.09814e6 921445.i 1.10475 0.926999i 0.107018 0.994257i \(-0.465870\pi\)
0.997736 + 0.0672585i \(0.0214252\pi\)
\(998\) 237699.i 0.238653i
\(999\) 1.16505e6 + 1.11468e6i 1.16738 + 1.11691i
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 27.5.f.a.5.7 66
3.2 odd 2 81.5.f.a.44.5 66
27.11 odd 18 inner 27.5.f.a.11.7 yes 66
27.16 even 9 81.5.f.a.35.5 66
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
27.5.f.a.5.7 66 1.1 even 1 trivial
27.5.f.a.11.7 yes 66 27.11 odd 18 inner
81.5.f.a.35.5 66 27.16 even 9
81.5.f.a.44.5 66 3.2 odd 2