Properties

Label 63.4.f.c.43.8
Level $63$
Weight $4$
Character 63.43
Analytic conductor $3.717$
Analytic rank $0$
Dimension $18$
CM no
Inner twists $2$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [63,4,Mod(22,63)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(63, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([2, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("63.22");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 63 = 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 63.f (of order \(3\), degree \(2\), 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: \(3.71712033036\)
Analytic rank: \(0\)
Dimension: \(18\)
Relative dimension: \(9\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{18} - 3 x^{17} + 6 x^{16} - 23 x^{15} - 6 x^{14} + 255 x^{13} - 56 x^{12} - 81 x^{11} + 5832 x^{10} - 32373 x^{9} + 52488 x^{8} - 6561 x^{7} - 40824 x^{6} + 1673055 x^{5} + \cdots + 387420489 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{10} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 43.8
Root \(-1.07135 + 2.80218i\) of defining polynomial
Character \(\chi\) \(=\) 63.43
Dual form 63.4.f.c.22.8

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(2.21232 - 3.83185i) q^{2} +(-4.03378 - 3.27546i) q^{3} +(-5.78871 - 10.0263i) q^{4} +(-1.92707 - 3.33779i) q^{5} +(-21.4751 + 8.21047i) q^{6} +(-3.50000 + 6.06218i) q^{7} -15.8288 q^{8} +(5.54273 + 26.4250i) q^{9} +O(q^{10})\) \(q+(2.21232 - 3.83185i) q^{2} +(-4.03378 - 3.27546i) q^{3} +(-5.78871 - 10.0263i) q^{4} +(-1.92707 - 3.33779i) q^{5} +(-21.4751 + 8.21047i) q^{6} +(-3.50000 + 6.06218i) q^{7} -15.8288 q^{8} +(5.54273 + 26.4250i) q^{9} -17.0532 q^{10} +(19.8164 - 34.3229i) q^{11} +(-9.49049 + 59.4047i) q^{12} +(-31.7297 - 54.9575i) q^{13} +(15.4862 + 26.8229i) q^{14} +(-3.15941 + 19.7760i) q^{15} +(11.2914 - 19.5573i) q^{16} +10.5049 q^{17} +(113.519 + 37.2215i) q^{18} -8.40311 q^{19} +(-22.3105 + 38.6430i) q^{20} +(33.9746 - 12.9894i) q^{21} +(-87.6802 - 151.867i) q^{22} +(87.2126 + 151.057i) q^{23} +(63.8497 + 51.8465i) q^{24} +(55.0728 - 95.3888i) q^{25} -280.785 q^{26} +(64.1957 - 124.747i) q^{27} +81.0419 q^{28} +(42.0688 - 72.8654i) q^{29} +(68.7889 + 55.8571i) q^{30} +(11.4889 + 19.8994i) q^{31} +(-113.275 - 196.199i) q^{32} +(-192.358 + 73.5434i) q^{33} +(23.2403 - 40.2534i) q^{34} +26.9790 q^{35} +(232.860 - 208.540i) q^{36} +302.219 q^{37} +(-18.5904 + 32.1995i) q^{38} +(-52.0203 + 325.616i) q^{39} +(30.5032 + 52.8331i) q^{40} +(179.082 + 310.180i) q^{41} +(25.3894 - 158.922i) q^{42} +(-170.966 + 296.121i) q^{43} -458.844 q^{44} +(77.5197 - 69.4233i) q^{45} +771.768 q^{46} +(-153.122 + 265.216i) q^{47} +(-109.606 + 41.9052i) q^{48} +(-24.5000 - 42.4352i) q^{49} +(-243.677 - 422.061i) q^{50} +(-42.3746 - 34.4085i) q^{51} +(-367.348 + 636.265i) q^{52} -192.951 q^{53} +(-335.992 - 521.969i) q^{54} -152.750 q^{55} +(55.4007 - 95.9567i) q^{56} +(33.8963 + 27.5241i) q^{57} +(-186.139 - 322.403i) q^{58} +(151.531 + 262.459i) q^{59} +(216.569 - 82.8000i) q^{60} +(204.728 - 354.599i) q^{61} +101.669 q^{62} +(-179.592 - 58.8863i) q^{63} -821.743 q^{64} +(-122.291 + 211.814i) q^{65} +(-143.750 + 899.789i) q^{66} +(-196.183 - 339.799i) q^{67} +(-60.8101 - 105.326i) q^{68} +(142.984 - 894.990i) q^{69} +(59.6862 - 103.380i) q^{70} +901.317 q^{71} +(-87.7346 - 418.274i) q^{72} -1139.05 q^{73} +(668.605 - 1158.06i) q^{74} +(-534.594 + 204.389i) q^{75} +(48.6432 + 84.2524i) q^{76} +(138.714 + 240.261i) q^{77} +(1132.62 + 919.700i) q^{78} +(-242.087 + 419.307i) q^{79} -87.0375 q^{80} +(-667.556 + 292.933i) q^{81} +1584.75 q^{82} +(-51.9270 + 89.9401i) q^{83} +(-326.905 - 265.449i) q^{84} +(-20.2438 - 35.0633i) q^{85} +(756.462 + 1310.23i) q^{86} +(-408.364 + 156.128i) q^{87} +(-313.668 + 543.289i) q^{88} +1424.71 q^{89} +(-94.5214 - 450.630i) q^{90} +444.216 q^{91} +(1009.70 - 1748.85i) q^{92} +(18.8359 - 117.901i) q^{93} +(677.511 + 1173.48i) q^{94} +(16.1934 + 28.0478i) q^{95} +(-185.713 + 1162.45i) q^{96} +(752.514 - 1303.39i) q^{97} -216.807 q^{98} +(1016.82 + 333.403i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 18 q + 6 q^{2} + 9 q^{3} - 36 q^{4} + 24 q^{5} - 63 q^{7} - 150 q^{8} + 63 q^{9} + 111 q^{11} - 18 q^{13} + 42 q^{14} - 36 q^{15} - 144 q^{16} - 546 q^{17} - 45 q^{18} + 90 q^{19} + 402 q^{20} - 63 q^{21} + 162 q^{22} + 312 q^{23} - 36 q^{24} - 279 q^{25} + 102 q^{26} + 432 q^{27} + 504 q^{28} + 378 q^{29} - 864 q^{30} - 18 q^{31} + 891 q^{32} + 513 q^{33} + 324 q^{34} - 336 q^{35} + 414 q^{36} - 72 q^{37} + 147 q^{38} - 810 q^{39} - 405 q^{40} + 477 q^{41} + 315 q^{42} + 171 q^{43} - 1896 q^{44} - 720 q^{45} - 756 q^{46} + 654 q^{47} - 2709 q^{48} - 441 q^{49} + 429 q^{50} + 1341 q^{51} - 747 q^{52} - 1896 q^{53} - 108 q^{54} - 432 q^{55} + 525 q^{56} - 1143 q^{57} - 297 q^{58} + 957 q^{59} + 5400 q^{60} + 198 q^{61} - 600 q^{62} - 504 q^{63} + 4770 q^{64} + 2478 q^{65} - 2646 q^{66} + 333 q^{67} + 1443 q^{68} + 3366 q^{69} - 5652 q^{71} - 3681 q^{72} + 306 q^{73} + 2100 q^{74} - 4113 q^{75} + 144 q^{76} + 777 q^{77} + 6336 q^{78} - 1152 q^{79} - 8418 q^{80} - 1917 q^{81} - 6048 q^{82} + 1890 q^{83} + 1008 q^{84} + 648 q^{85} + 3837 q^{86} + 4212 q^{87} + 2268 q^{88} - 2604 q^{89} - 135 q^{90} + 252 q^{91} + 987 q^{92} + 378 q^{93} - 324 q^{94} + 3144 q^{95} + 5643 q^{96} + 1737 q^{97} - 588 q^{98} + 720 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).

\(n\) \(10\) \(29\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

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



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.21232 3.83185i 0.782173 1.35476i −0.148501 0.988912i \(-0.547445\pi\)
0.930674 0.365851i \(-0.119222\pi\)
\(3\) −4.03378 3.27546i −0.776301 0.630362i
\(4\) −5.78871 10.0263i −0.723588 1.25329i
\(5\) −1.92707 3.33779i −0.172363 0.298541i 0.766883 0.641787i \(-0.221807\pi\)
−0.939245 + 0.343246i \(0.888473\pi\)
\(6\) −21.4751 + 8.21047i −1.46119 + 0.558651i
\(7\) −3.50000 + 6.06218i −0.188982 + 0.327327i
\(8\) −15.8288 −0.699539
\(9\) 5.54273 + 26.4250i 0.205286 + 0.978702i
\(10\) −17.0532 −0.539270
\(11\) 19.8164 34.3229i 0.543169 0.940796i −0.455551 0.890210i \(-0.650558\pi\)
0.998720 0.0505861i \(-0.0161089\pi\)
\(12\) −9.49049 + 59.4047i −0.228306 + 1.42905i
\(13\) −31.7297 54.9575i −0.676941 1.17250i −0.975897 0.218230i \(-0.929972\pi\)
0.298956 0.954267i \(-0.403362\pi\)
\(14\) 15.4862 + 26.8229i 0.295634 + 0.512052i
\(15\) −3.15941 + 19.7760i −0.0543837 + 0.340409i
\(16\) 11.2914 19.5573i 0.176428 0.305582i
\(17\) 10.5049 0.149872 0.0749360 0.997188i \(-0.476125\pi\)
0.0749360 + 0.997188i \(0.476125\pi\)
\(18\) 113.519 + 37.2215i 1.48648 + 0.487400i
\(19\) −8.40311 −0.101463 −0.0507317 0.998712i \(-0.516155\pi\)
−0.0507317 + 0.998712i \(0.516155\pi\)
\(20\) −22.3105 + 38.6430i −0.249439 + 0.432042i
\(21\) 33.9746 12.9894i 0.353042 0.134977i
\(22\) −87.6802 151.867i −0.849703 1.47173i
\(23\) 87.2126 + 151.057i 0.790656 + 1.36946i 0.925561 + 0.378598i \(0.123594\pi\)
−0.134905 + 0.990858i \(0.543073\pi\)
\(24\) 63.8497 + 51.8465i 0.543053 + 0.440963i
\(25\) 55.0728 95.3888i 0.440582 0.763111i
\(26\) −280.785 −2.11794
\(27\) 64.1957 124.747i 0.457573 0.889172i
\(28\) 81.0419 0.546981
\(29\) 42.0688 72.8654i 0.269379 0.466578i −0.699323 0.714806i \(-0.746515\pi\)
0.968702 + 0.248228i \(0.0798483\pi\)
\(30\) 68.7889 + 55.8571i 0.418636 + 0.339935i
\(31\) 11.4889 + 19.8994i 0.0665635 + 0.115291i 0.897386 0.441245i \(-0.145463\pi\)
−0.830823 + 0.556537i \(0.812130\pi\)
\(32\) −113.275 196.199i −0.625764 1.08386i
\(33\) −192.358 + 73.5434i −1.01470 + 0.387948i
\(34\) 23.2403 40.2534i 0.117226 0.203041i
\(35\) 26.9790 0.130294
\(36\) 232.860 208.540i 1.07806 0.965461i
\(37\) 302.219 1.34282 0.671412 0.741084i \(-0.265688\pi\)
0.671412 + 0.741084i \(0.265688\pi\)
\(38\) −18.5904 + 32.1995i −0.0793620 + 0.137459i
\(39\) −52.0203 + 325.616i −0.213588 + 1.33693i
\(40\) 30.5032 + 52.8331i 0.120574 + 0.208841i
\(41\) 179.082 + 310.180i 0.682146 + 1.18151i 0.974325 + 0.225148i \(0.0722865\pi\)
−0.292179 + 0.956364i \(0.594380\pi\)
\(42\) 25.3894 158.922i 0.0932779 0.583863i
\(43\) −170.966 + 296.121i −0.606326 + 1.05019i 0.385514 + 0.922702i \(0.374024\pi\)
−0.991840 + 0.127486i \(0.959309\pi\)
\(44\) −458.844 −1.57212
\(45\) 77.5197 69.4233i 0.256799 0.229978i
\(46\) 771.768 2.47372
\(47\) −153.122 + 265.216i −0.475217 + 0.823100i −0.999597 0.0283840i \(-0.990964\pi\)
0.524380 + 0.851484i \(0.324297\pi\)
\(48\) −109.606 + 41.9052i −0.329589 + 0.126010i
\(49\) −24.5000 42.4352i −0.0714286 0.123718i
\(50\) −243.677 422.061i −0.689223 1.19377i
\(51\) −42.3746 34.4085i −0.116346 0.0944737i
\(52\) −367.348 + 636.265i −0.979654 + 1.69681i
\(53\) −192.951 −0.500073 −0.250036 0.968236i \(-0.580443\pi\)
−0.250036 + 0.968236i \(0.580443\pi\)
\(54\) −335.992 521.969i −0.846716 1.31539i
\(55\) −152.750 −0.374488
\(56\) 55.4007 95.9567i 0.132200 0.228978i
\(57\) 33.8963 + 27.5241i 0.0787662 + 0.0639588i
\(58\) −186.139 322.403i −0.421402 0.729889i
\(59\) 151.531 + 262.459i 0.334366 + 0.579140i 0.983363 0.181652i \(-0.0581444\pi\)
−0.648997 + 0.760791i \(0.724811\pi\)
\(60\) 216.569 82.8000i 0.465983 0.178157i
\(61\) 204.728 354.599i 0.429716 0.744290i −0.567132 0.823627i \(-0.691947\pi\)
0.996848 + 0.0793371i \(0.0252803\pi\)
\(62\) 101.669 0.208257
\(63\) −179.592 58.8863i −0.359151 0.117762i
\(64\) −821.743 −1.60497
\(65\) −122.291 + 211.814i −0.233359 + 0.404190i
\(66\) −143.750 + 899.789i −0.268097 + 1.67813i
\(67\) −196.183 339.799i −0.357725 0.619598i 0.629855 0.776713i \(-0.283114\pi\)
−0.987580 + 0.157114i \(0.949781\pi\)
\(68\) −60.8101 105.326i −0.108446 0.187833i
\(69\) 142.984 894.990i 0.249467 1.56151i
\(70\) 59.6862 103.380i 0.101912 0.176518i
\(71\) 901.317 1.50657 0.753286 0.657693i \(-0.228467\pi\)
0.753286 + 0.657693i \(0.228467\pi\)
\(72\) −87.7346 418.274i −0.143606 0.684640i
\(73\) −1139.05 −1.82624 −0.913120 0.407691i \(-0.866334\pi\)
−0.913120 + 0.407691i \(0.866334\pi\)
\(74\) 668.605 1158.06i 1.05032 1.81921i
\(75\) −534.594 + 204.389i −0.823061 + 0.314677i
\(76\) 48.6432 + 84.2524i 0.0734178 + 0.127163i
\(77\) 138.714 + 240.261i 0.205298 + 0.355587i
\(78\) 1132.62 + 919.700i 1.64416 + 1.33507i
\(79\) −242.087 + 419.307i −0.344771 + 0.597161i −0.985312 0.170763i \(-0.945377\pi\)
0.640541 + 0.767924i \(0.278710\pi\)
\(80\) −87.0375 −0.121639
\(81\) −667.556 + 292.933i −0.915715 + 0.401828i
\(82\) 1584.75 2.13422
\(83\) −51.9270 + 89.9401i −0.0686714 + 0.118942i −0.898317 0.439349i \(-0.855209\pi\)
0.829645 + 0.558291i \(0.188543\pi\)
\(84\) −326.905 265.449i −0.424622 0.344797i
\(85\) −20.2438 35.0633i −0.0258324 0.0447430i
\(86\) 756.462 + 1310.23i 0.948504 + 1.64286i
\(87\) −408.364 + 156.128i −0.503232 + 0.192399i
\(88\) −313.668 + 543.289i −0.379968 + 0.658123i
\(89\) 1424.71 1.69684 0.848422 0.529321i \(-0.177553\pi\)
0.848422 + 0.529321i \(0.177553\pi\)
\(90\) −94.5214 450.630i −0.110705 0.527785i
\(91\) 444.216 0.511720
\(92\) 1009.70 1748.85i 1.14422 1.98185i
\(93\) 18.8359 117.901i 0.0210020 0.131460i
\(94\) 677.511 + 1173.48i 0.743404 + 1.28761i
\(95\) 16.1934 + 28.0478i 0.0174885 + 0.0302910i
\(96\) −185.713 + 1162.45i −0.197440 + 1.23586i
\(97\) 752.514 1303.39i 0.787693 1.36432i −0.139684 0.990196i \(-0.544609\pi\)
0.927377 0.374128i \(-0.122058\pi\)
\(98\) −216.807 −0.223478
\(99\) 1016.82 + 333.403i 1.03226 + 0.338468i
\(100\) −1275.20 −1.27520
\(101\) 769.021 1331.98i 0.757628 1.31225i −0.186429 0.982468i \(-0.559691\pi\)
0.944057 0.329782i \(-0.106975\pi\)
\(102\) −225.594 + 86.2505i −0.218992 + 0.0837262i
\(103\) 710.125 + 1229.97i 0.679327 + 1.17663i 0.975184 + 0.221396i \(0.0710614\pi\)
−0.295857 + 0.955232i \(0.595605\pi\)
\(104\) 502.242 + 869.908i 0.473547 + 0.820207i
\(105\) −108.827 88.3688i −0.101147 0.0821325i
\(106\) −426.869 + 739.359i −0.391143 + 0.677480i
\(107\) −1105.83 −0.999112 −0.499556 0.866282i \(-0.666504\pi\)
−0.499556 + 0.866282i \(0.666504\pi\)
\(108\) −1622.37 + 78.4785i −1.44549 + 0.0699222i
\(109\) −2138.26 −1.87898 −0.939488 0.342583i \(-0.888698\pi\)
−0.939488 + 0.342583i \(0.888698\pi\)
\(110\) −337.932 + 585.316i −0.292915 + 0.507343i
\(111\) −1219.08 989.906i −1.04244 0.846466i
\(112\) 79.0398 + 136.901i 0.0666836 + 0.115499i
\(113\) −216.248 374.553i −0.180026 0.311814i 0.761863 0.647738i \(-0.224285\pi\)
−0.941889 + 0.335924i \(0.890951\pi\)
\(114\) 180.457 68.9935i 0.148258 0.0566827i
\(115\) 336.130 582.195i 0.272559 0.472087i
\(116\) −974.097 −0.779678
\(117\) 1276.38 1143.07i 1.00856 0.903222i
\(118\) 1340.94 1.04613
\(119\) −36.7673 + 63.6829i −0.0283231 + 0.0490571i
\(120\) 50.0095 313.029i 0.0380435 0.238129i
\(121\) −119.876 207.631i −0.0900645 0.155996i
\(122\) −905.845 1568.97i −0.672224 1.16433i
\(123\) 293.603 1837.77i 0.215230 1.34721i
\(124\) 133.012 230.383i 0.0963292 0.166847i
\(125\) −906.286 −0.648485
\(126\) −622.959 + 557.895i −0.440457 + 0.394454i
\(127\) −489.245 −0.341839 −0.170919 0.985285i \(-0.554674\pi\)
−0.170919 + 0.985285i \(0.554674\pi\)
\(128\) −911.753 + 1579.20i −0.629597 + 1.09049i
\(129\) 1659.57 634.497i 1.13269 0.433057i
\(130\) 541.093 + 937.201i 0.365054 + 0.632292i
\(131\) 339.589 + 588.186i 0.226489 + 0.392291i 0.956765 0.290862i \(-0.0939419\pi\)
−0.730276 + 0.683152i \(0.760609\pi\)
\(132\) 1850.88 + 1502.93i 1.22044 + 0.991007i
\(133\) 29.4109 50.9412i 0.0191748 0.0332117i
\(134\) −1736.08 −1.11921
\(135\) −540.091 + 26.1257i −0.344323 + 0.0166559i
\(136\) −166.280 −0.104841
\(137\) 405.842 702.940i 0.253091 0.438366i −0.711284 0.702904i \(-0.751886\pi\)
0.964375 + 0.264538i \(0.0852195\pi\)
\(138\) −3113.14 2527.90i −1.92035 1.55934i
\(139\) 88.5339 + 153.345i 0.0540241 + 0.0935725i 0.891773 0.452484i \(-0.149462\pi\)
−0.837749 + 0.546056i \(0.816129\pi\)
\(140\) −156.174 270.501i −0.0942792 0.163296i
\(141\) 1486.37 568.276i 0.887763 0.339415i
\(142\) 1994.00 3453.71i 1.17840 2.04105i
\(143\) −2515.07 −1.47077
\(144\) 579.385 + 189.974i 0.335292 + 0.109939i
\(145\) −324.279 −0.185724
\(146\) −2519.94 + 4364.66i −1.42844 + 2.47412i
\(147\) −40.1674 + 251.423i −0.0225371 + 0.141068i
\(148\) −1749.46 3030.15i −0.971652 1.68295i
\(149\) 1493.35 + 2586.56i 0.821075 + 1.42214i 0.904882 + 0.425662i \(0.139959\pi\)
−0.0838066 + 0.996482i \(0.526708\pi\)
\(150\) −399.504 + 2500.65i −0.217463 + 1.36118i
\(151\) −698.478 + 1209.80i −0.376432 + 0.652000i −0.990540 0.137222i \(-0.956183\pi\)
0.614108 + 0.789222i \(0.289516\pi\)
\(152\) 133.011 0.0709777
\(153\) 58.2261 + 277.593i 0.0307667 + 0.146680i
\(154\) 1227.52 0.642315
\(155\) 44.2800 76.6952i 0.0229462 0.0397439i
\(156\) 3565.86 1363.32i 1.83011 0.699698i
\(157\) 1732.01 + 2999.93i 0.880443 + 1.52497i 0.850849 + 0.525410i \(0.176088\pi\)
0.0295941 + 0.999562i \(0.490579\pi\)
\(158\) 1071.15 + 1855.28i 0.539341 + 0.934165i
\(159\) 778.322 + 632.003i 0.388207 + 0.315227i
\(160\) −436.580 + 756.179i −0.215717 + 0.373633i
\(161\) −1220.98 −0.597680
\(162\) −354.373 + 3206.03i −0.171865 + 1.55488i
\(163\) −2922.25 −1.40422 −0.702111 0.712067i \(-0.747759\pi\)
−0.702111 + 0.712067i \(0.747759\pi\)
\(164\) 2073.31 3591.08i 0.987186 1.70986i
\(165\) 616.161 + 500.328i 0.290716 + 0.236063i
\(166\) 229.758 + 397.952i 0.107426 + 0.186067i
\(167\) −1315.23 2278.04i −0.609433 1.05557i −0.991334 0.131366i \(-0.958064\pi\)
0.381901 0.924203i \(-0.375270\pi\)
\(168\) −537.776 + 205.606i −0.246966 + 0.0944215i
\(169\) −915.049 + 1584.91i −0.416499 + 0.721398i
\(170\) −179.143 −0.0808215
\(171\) −46.5762 222.052i −0.0208291 0.0993025i
\(172\) 3958.68 1.75492
\(173\) −568.028 + 983.853i −0.249632 + 0.432376i −0.963424 0.267983i \(-0.913643\pi\)
0.713792 + 0.700358i \(0.246976\pi\)
\(174\) −305.173 + 1910.19i −0.132960 + 0.832250i
\(175\) 385.509 + 667.722i 0.166524 + 0.288429i
\(176\) −447.509 775.108i −0.191660 0.331966i
\(177\) 248.432 1555.03i 0.105499 0.660359i
\(178\) 3151.91 5459.28i 1.32722 2.29882i
\(179\) 2482.26 1.03650 0.518248 0.855230i \(-0.326584\pi\)
0.518248 + 0.855230i \(0.326584\pi\)
\(180\) −1144.80 375.367i −0.474047 0.155435i
\(181\) 147.725 0.0606648 0.0303324 0.999540i \(-0.490343\pi\)
0.0303324 + 0.999540i \(0.490343\pi\)
\(182\) 982.747 1702.17i 0.400253 0.693259i
\(183\) −1987.30 + 759.795i −0.802761 + 0.306916i
\(184\) −1380.47 2391.04i −0.553095 0.957988i
\(185\) −582.399 1008.74i −0.231453 0.400888i
\(186\) −410.108 333.011i −0.161670 0.131277i
\(187\) 208.170 360.561i 0.0814058 0.140999i
\(188\) 3545.52 1.37545
\(189\) 531.556 + 825.782i 0.204577 + 0.317814i
\(190\) 143.300 0.0547162
\(191\) 149.334 258.654i 0.0565730 0.0979873i −0.836352 0.548193i \(-0.815316\pi\)
0.892925 + 0.450206i \(0.148649\pi\)
\(192\) 3314.73 + 2691.58i 1.24594 + 1.01171i
\(193\) −1189.32 2059.97i −0.443572 0.768289i 0.554379 0.832264i \(-0.312956\pi\)
−0.997952 + 0.0639746i \(0.979622\pi\)
\(194\) −3329.60 5767.04i −1.23222 2.13427i
\(195\) 1187.08 453.853i 0.435943 0.166672i
\(196\) −283.647 + 491.290i −0.103370 + 0.179042i
\(197\) −281.450 −0.101789 −0.0508945 0.998704i \(-0.516207\pi\)
−0.0508945 + 0.998704i \(0.516207\pi\)
\(198\) 3527.08 3158.70i 1.26595 1.13373i
\(199\) 77.5836 0.0276370 0.0138185 0.999905i \(-0.495601\pi\)
0.0138185 + 0.999905i \(0.495601\pi\)
\(200\) −871.733 + 1509.89i −0.308204 + 0.533826i
\(201\) −321.639 + 2013.26i −0.112869 + 0.706491i
\(202\) −3402.64 5893.54i −1.18519 2.05281i
\(203\) 294.482 + 510.058i 0.101816 + 0.176350i
\(204\) −99.6971 + 624.043i −0.0342166 + 0.214175i
\(205\) 690.211 1195.48i 0.235153 0.407297i
\(206\) 6284.09 2.12540
\(207\) −3508.27 + 3141.86i −1.17798 + 1.05495i
\(208\) −1433.09 −0.477726
\(209\) −166.519 + 288.419i −0.0551118 + 0.0954564i
\(210\) −579.377 + 221.511i −0.190385 + 0.0727889i
\(211\) 1168.35 + 2023.65i 0.381198 + 0.660253i 0.991234 0.132120i \(-0.0421784\pi\)
−0.610036 + 0.792374i \(0.708845\pi\)
\(212\) 1116.94 + 1934.59i 0.361847 + 0.626737i
\(213\) −3635.71 2952.23i −1.16955 0.949687i
\(214\) −2446.46 + 4237.39i −0.781478 + 1.35356i
\(215\) 1317.86 0.418033
\(216\) −1016.14 + 1974.60i −0.320090 + 0.622010i
\(217\) −160.845 −0.0503173
\(218\) −4730.52 + 8193.49i −1.46968 + 2.54557i
\(219\) 4594.67 + 3730.91i 1.41771 + 1.15119i
\(220\) 884.227 + 1531.53i 0.270975 + 0.469343i
\(221\) −333.319 577.325i −0.101455 0.175724i
\(222\) −6490.17 + 2481.36i −1.96213 + 0.750171i
\(223\) −1157.33 + 2004.55i −0.347535 + 0.601948i −0.985811 0.167860i \(-0.946314\pi\)
0.638276 + 0.769807i \(0.279648\pi\)
\(224\) 1585.86 0.473033
\(225\) 2825.90 + 926.580i 0.837303 + 0.274542i
\(226\) −1913.64 −0.563245
\(227\) −529.952 + 917.904i −0.154952 + 0.268385i −0.933042 0.359768i \(-0.882856\pi\)
0.778089 + 0.628154i \(0.216189\pi\)
\(228\) 79.7497 499.184i 0.0231647 0.144997i
\(229\) −1171.23 2028.63i −0.337978 0.585395i 0.646074 0.763275i \(-0.276410\pi\)
−0.984052 + 0.177880i \(0.943076\pi\)
\(230\) −1487.26 2576.00i −0.426377 0.738506i
\(231\) 227.420 1423.51i 0.0647755 0.405455i
\(232\) −665.898 + 1153.37i −0.188441 + 0.326389i
\(233\) 502.705 0.141345 0.0706723 0.997500i \(-0.477486\pi\)
0.0706723 + 0.997500i \(0.477486\pi\)
\(234\) −1556.32 7419.73i −0.434784 2.07283i
\(235\) 1180.31 0.327639
\(236\) 1754.33 3038.60i 0.483887 0.838117i
\(237\) 2349.95 898.445i 0.644074 0.246246i
\(238\) 162.682 + 281.774i 0.0443072 + 0.0767423i
\(239\) 2022.28 + 3502.69i 0.547323 + 0.947992i 0.998457 + 0.0555351i \(0.0176865\pi\)
−0.451134 + 0.892456i \(0.648980\pi\)
\(240\) 351.090 + 285.088i 0.0944282 + 0.0766764i
\(241\) 296.441 513.451i 0.0792342 0.137238i −0.823686 0.567047i \(-0.808086\pi\)
0.902920 + 0.429809i \(0.141419\pi\)
\(242\) −1060.81 −0.281784
\(243\) 3652.26 + 1004.93i 0.964168 + 0.265293i
\(244\) −4740.43 −1.24375
\(245\) −94.4267 + 163.552i −0.0246233 + 0.0426487i
\(246\) −6392.53 5190.78i −1.65680 1.34533i
\(247\) 266.628 + 461.814i 0.0686848 + 0.118966i
\(248\) −181.855 314.982i −0.0465638 0.0806508i
\(249\) 504.057 192.714i 0.128286 0.0490472i
\(250\) −2004.99 + 3472.75i −0.507228 + 0.878544i
\(251\) −2663.71 −0.669848 −0.334924 0.942245i \(-0.608711\pi\)
−0.334924 + 0.942245i \(0.608711\pi\)
\(252\) 449.194 + 2141.53i 0.112288 + 0.535332i
\(253\) 6912.94 1.71784
\(254\) −1082.37 + 1874.71i −0.267377 + 0.463110i
\(255\) −33.1894 + 207.745i −0.00815059 + 0.0510178i
\(256\) 747.207 + 1294.20i 0.182424 + 0.315967i
\(257\) −819.857 1420.03i −0.198993 0.344667i 0.749209 0.662334i \(-0.230434\pi\)
−0.948202 + 0.317667i \(0.897101\pi\)
\(258\) 1240.21 7762.94i 0.299271 1.87325i
\(259\) −1057.77 + 1832.11i −0.253770 + 0.439543i
\(260\) 2831.63 0.675424
\(261\) 2158.64 + 707.794i 0.511941 + 0.167860i
\(262\) 3005.12 0.708614
\(263\) 1966.25 3405.64i 0.461004 0.798482i −0.538007 0.842940i \(-0.680823\pi\)
0.999011 + 0.0444579i \(0.0141561\pi\)
\(264\) 3044.79 1164.10i 0.709825 0.271384i
\(265\) 371.831 + 644.030i 0.0861940 + 0.149292i
\(266\) −130.133 225.396i −0.0299960 0.0519546i
\(267\) −5746.97 4666.58i −1.31726 1.06963i
\(268\) −2271.29 + 3934.00i −0.517691 + 0.896668i
\(269\) −859.514 −0.194816 −0.0974080 0.995245i \(-0.531055\pi\)
−0.0974080 + 0.995245i \(0.531055\pi\)
\(270\) −1094.74 + 2127.34i −0.246755 + 0.479504i
\(271\) 4260.30 0.954963 0.477482 0.878642i \(-0.341550\pi\)
0.477482 + 0.878642i \(0.341550\pi\)
\(272\) 118.616 205.448i 0.0264416 0.0457983i
\(273\) −1791.87 1455.01i −0.397248 0.322569i
\(274\) −1795.71 3110.25i −0.395922 0.685756i
\(275\) −2182.68 3780.52i −0.478621 0.828996i
\(276\) −9801.16 + 3747.24i −2.13754 + 0.817236i
\(277\) 2031.16 3518.07i 0.440579 0.763106i −0.557153 0.830410i \(-0.688106\pi\)
0.997733 + 0.0673041i \(0.0214398\pi\)
\(278\) 783.461 0.169025
\(279\) −462.160 + 413.891i −0.0991714 + 0.0888136i
\(280\) −427.045 −0.0911457
\(281\) −1535.16 + 2658.98i −0.325908 + 0.564490i −0.981696 0.190456i \(-0.939003\pi\)
0.655787 + 0.754946i \(0.272337\pi\)
\(282\) 1110.77 6952.74i 0.234558 1.46819i
\(283\) 2717.14 + 4706.23i 0.570733 + 0.988539i 0.996491 + 0.0837015i \(0.0266742\pi\)
−0.425758 + 0.904837i \(0.639992\pi\)
\(284\) −5217.46 9036.91i −1.09014 1.88818i
\(285\) 26.5489 166.180i 0.00551796 0.0345391i
\(286\) −5564.13 + 9637.36i −1.15040 + 1.99255i
\(287\) −2507.15 −0.515654
\(288\) 4556.69 4080.77i 0.932310 0.834937i
\(289\) −4802.65 −0.977538
\(290\) −717.409 + 1242.59i −0.145268 + 0.251611i
\(291\) −7304.68 + 2792.77i −1.47151 + 0.562594i
\(292\) 6593.62 + 11420.5i 1.32145 + 2.28881i
\(293\) 4472.88 + 7747.25i 0.891837 + 1.54471i 0.837670 + 0.546176i \(0.183917\pi\)
0.0541670 + 0.998532i \(0.482750\pi\)
\(294\) 874.552 + 710.143i 0.173486 + 0.140872i
\(295\) 584.022 1011.56i 0.115265 0.199644i
\(296\) −4783.75 −0.939358
\(297\) −3009.57 4675.42i −0.587990 0.913453i
\(298\) 13215.1 2.56889
\(299\) 5534.46 9585.97i 1.07046 1.85408i
\(300\) 5143.88 + 4176.87i 0.989939 + 0.803838i
\(301\) −1196.76 2072.85i −0.229170 0.396934i
\(302\) 3090.51 + 5352.92i 0.588870 + 1.01995i
\(303\) −7464.92 + 2854.03i −1.41534 + 0.541121i
\(304\) −94.8829 + 164.342i −0.0179010 + 0.0310055i
\(305\) −1578.10 −0.296268
\(306\) 1192.51 + 391.010i 0.222782 + 0.0730476i
\(307\) 3114.75 0.579050 0.289525 0.957170i \(-0.406503\pi\)
0.289525 + 0.957170i \(0.406503\pi\)
\(308\) 1605.95 2781.60i 0.297103 0.514598i
\(309\) 1164.24 7287.42i 0.214340 1.34164i
\(310\) −195.923 339.348i −0.0358957 0.0621732i
\(311\) 392.347 + 679.564i 0.0715368 + 0.123905i 0.899575 0.436766i \(-0.143876\pi\)
−0.828038 + 0.560672i \(0.810543\pi\)
\(312\) 823.417 5154.09i 0.149413 0.935234i
\(313\) 2295.78 3976.40i 0.414584 0.718081i −0.580800 0.814046i \(-0.697260\pi\)
0.995385 + 0.0959649i \(0.0305936\pi\)
\(314\) 15327.0 2.75463
\(315\) 149.538 + 712.920i 0.0267476 + 0.127519i
\(316\) 5605.48 0.997889
\(317\) 2097.90 3633.66i 0.371702 0.643807i −0.618125 0.786080i \(-0.712108\pi\)
0.989828 + 0.142272i \(0.0454409\pi\)
\(318\) 4143.64 1584.22i 0.730703 0.279366i
\(319\) −1667.30 2887.85i −0.292636 0.506861i
\(320\) 1583.56 + 2742.80i 0.276636 + 0.479148i
\(321\) 4460.69 + 3622.11i 0.775612 + 0.629803i
\(322\) −2701.19 + 4678.60i −0.467489 + 0.809714i
\(323\) −88.2743 −0.0152065
\(324\) 6801.33 + 4997.44i 1.16621 + 0.856900i
\(325\) −6989.77 −1.19299
\(326\) −6464.95 + 11197.6i −1.09834 + 1.90239i
\(327\) 8625.27 + 7003.79i 1.45865 + 1.18444i
\(328\) −2834.65 4909.76i −0.477188 0.826513i
\(329\) −1071.86 1856.51i −0.179615 0.311103i
\(330\) 3280.32 1254.15i 0.547200 0.209208i
\(331\) 3416.58 5917.69i 0.567348 0.982676i −0.429479 0.903077i \(-0.641303\pi\)
0.996827 0.0795989i \(-0.0253639\pi\)
\(332\) 1202.36 0.198759
\(333\) 1675.12 + 7986.12i 0.275664 + 1.31422i
\(334\) −11638.8 −1.90673
\(335\) −756.119 + 1309.64i −0.123317 + 0.213591i
\(336\) 129.584 811.120i 0.0210399 0.131697i
\(337\) −2594.16 4493.21i −0.419325 0.726293i 0.576546 0.817064i \(-0.304400\pi\)
−0.995872 + 0.0907716i \(0.971067\pi\)
\(338\) 4048.76 + 7012.66i 0.651549 + 1.12852i
\(339\) −354.535 + 2219.18i −0.0568015 + 0.355543i
\(340\) −234.371 + 405.943i −0.0373840 + 0.0647510i
\(341\) 910.674 0.144621
\(342\) −953.910 312.776i −0.150823 0.0494533i
\(343\) 343.000 0.0539949
\(344\) 2706.18 4687.23i 0.424149 0.734648i
\(345\) −3262.83 + 1247.46i −0.509174 + 0.194670i
\(346\) 2513.32 + 4353.19i 0.390511 + 0.676385i
\(347\) 2.25987 + 3.91421i 0.000349614 + 0.000605549i 0.866200 0.499697i \(-0.166555\pi\)
−0.865851 + 0.500303i \(0.833222\pi\)
\(348\) 3929.29 + 3190.61i 0.605265 + 0.491480i
\(349\) 276.840 479.501i 0.0424610 0.0735447i −0.844014 0.536321i \(-0.819814\pi\)
0.886475 + 0.462777i \(0.153147\pi\)
\(350\) 3411.48 0.521003
\(351\) −8892.71 + 430.165i −1.35230 + 0.0654146i
\(352\) −8978.82 −1.35958
\(353\) −5834.63 + 10105.9i −0.879734 + 1.52374i −0.0281006 + 0.999605i \(0.508946\pi\)
−0.851633 + 0.524138i \(0.824387\pi\)
\(354\) −5409.04 4392.18i −0.812111 0.659441i
\(355\) −1736.91 3008.41i −0.259677 0.449774i
\(356\) −8247.23 14284.6i −1.22782 2.12664i
\(357\) 356.902 136.453i 0.0529111 0.0202293i
\(358\) 5491.55 9511.64i 0.810719 1.40421i
\(359\) −4813.47 −0.707646 −0.353823 0.935312i \(-0.615119\pi\)
−0.353823 + 0.935312i \(0.615119\pi\)
\(360\) −1227.04 + 1098.89i −0.179641 + 0.160879i
\(361\) −6788.39 −0.989705
\(362\) 326.815 566.061i 0.0474504 0.0821864i
\(363\) −196.534 + 1230.19i −0.0284170 + 0.177873i
\(364\) −2571.44 4453.86i −0.370274 0.641334i
\(365\) 2195.03 + 3801.91i 0.314776 + 0.545208i
\(366\) −1485.12 + 9295.93i −0.212099 + 1.32761i
\(367\) 3263.41 5652.40i 0.464166 0.803959i −0.534998 0.844854i \(-0.679688\pi\)
0.999163 + 0.0408948i \(0.0130208\pi\)
\(368\) 3939.01 0.557976
\(369\) −7203.88 + 6451.49i −1.01631 + 0.910166i
\(370\) −5153.81 −0.724145
\(371\) 675.329 1169.70i 0.0945049 0.163687i
\(372\) −1291.15 + 493.640i −0.179955 + 0.0688012i
\(373\) −2602.17 4507.09i −0.361221 0.625652i 0.626941 0.779066i \(-0.284307\pi\)
−0.988162 + 0.153414i \(0.950973\pi\)
\(374\) −921.076 1595.35i −0.127347 0.220571i
\(375\) 3655.76 + 2968.50i 0.503420 + 0.408781i
\(376\) 2423.74 4198.04i 0.332433 0.575791i
\(377\) −5339.33 −0.729415
\(378\) 4340.24 209.950i 0.590576 0.0285678i
\(379\) 9918.32 1.34425 0.672124 0.740439i \(-0.265382\pi\)
0.672124 + 0.740439i \(0.265382\pi\)
\(380\) 187.478 324.721i 0.0253090 0.0438365i
\(381\) 1973.51 + 1602.50i 0.265370 + 0.215482i
\(382\) −660.750 1144.45i −0.0884997 0.153286i
\(383\) 964.048 + 1669.78i 0.128618 + 0.222772i 0.923141 0.384461i \(-0.125613\pi\)
−0.794524 + 0.607233i \(0.792279\pi\)
\(384\) 8850.42 3383.74i 1.17616 0.449677i
\(385\) 534.626 926.000i 0.0707716 0.122580i
\(386\) −10524.7 −1.38780
\(387\) −8772.61 2876.44i −1.15229 0.377824i
\(388\) −17424.3 −2.27986
\(389\) 1241.45 2150.25i 0.161810 0.280263i −0.773708 0.633542i \(-0.781600\pi\)
0.935518 + 0.353280i \(0.114934\pi\)
\(390\) 887.114 5552.79i 0.115181 0.720966i
\(391\) 916.164 + 1586.84i 0.118497 + 0.205243i
\(392\) 387.805 + 671.697i 0.0499671 + 0.0865455i
\(393\) 556.751 3484.92i 0.0714616 0.447306i
\(394\) −622.656 + 1078.47i −0.0796166 + 0.137900i
\(395\) 1866.08 0.237703
\(396\) −2543.25 12124.9i −0.322735 1.53864i
\(397\) −603.393 −0.0762806 −0.0381403 0.999272i \(-0.512143\pi\)
−0.0381403 + 0.999272i \(0.512143\pi\)
\(398\) 171.640 297.289i 0.0216169 0.0374415i
\(399\) −285.493 + 109.151i −0.0358208 + 0.0136952i
\(400\) −1243.70 2154.15i −0.155462 0.269268i
\(401\) −1325.70 2296.18i −0.165093 0.285949i 0.771595 0.636114i \(-0.219459\pi\)
−0.936688 + 0.350164i \(0.886126\pi\)
\(402\) 7002.95 + 5686.45i 0.868845 + 0.705509i
\(403\) 729.080 1262.80i 0.0901192 0.156091i
\(404\) −17806.5 −2.19284
\(405\) 2264.18 + 1663.66i 0.277797 + 0.204118i
\(406\) 2605.95 0.318550
\(407\) 5988.88 10373.0i 0.729380 1.26332i
\(408\) 670.738 + 544.644i 0.0813884 + 0.0660880i
\(409\) 4376.21 + 7579.82i 0.529070 + 0.916376i 0.999425 + 0.0338991i \(0.0107925\pi\)
−0.470355 + 0.882477i \(0.655874\pi\)
\(410\) −3053.93 5289.56i −0.367861 0.637154i
\(411\) −3939.53 + 1506.18i −0.472804 + 0.180765i
\(412\) 8221.41 14239.9i 0.983106 1.70279i
\(413\) −2121.43 −0.252757
\(414\) 4277.71 + 20393.9i 0.507821 + 2.42103i
\(415\) 400.269 0.0473456
\(416\) −7188.39 + 12450.7i −0.847211 + 1.46741i
\(417\) 145.150 908.550i 0.0170456 0.106695i
\(418\) 736.786 + 1276.15i 0.0862139 + 0.149327i
\(419\) −5712.54 9894.41i −0.666052 1.15364i −0.978999 0.203866i \(-0.934649\pi\)
0.312946 0.949771i \(-0.398684\pi\)
\(420\) −256.044 + 1602.68i −0.0297469 + 0.186197i
\(421\) −5436.83 + 9416.87i −0.629394 + 1.09014i 0.358279 + 0.933615i \(0.383364\pi\)
−0.987673 + 0.156528i \(0.949970\pi\)
\(422\) 10339.1 1.19265
\(423\) −7857.04 2576.23i −0.903126 0.296125i
\(424\) 3054.18 0.349820
\(425\) 578.537 1002.05i 0.0660309 0.114369i
\(426\) −19355.8 + 7400.23i −2.20139 + 0.841649i
\(427\) 1433.09 + 2482.19i 0.162417 + 0.281315i
\(428\) 6401.35 + 11087.5i 0.722946 + 1.25218i
\(429\) 10145.2 + 8238.01i 1.14176 + 0.927120i
\(430\) 2915.52 5049.82i 0.326974 0.566335i
\(431\) 15702.7 1.75493 0.877465 0.479641i \(-0.159233\pi\)
0.877465 + 0.479641i \(0.159233\pi\)
\(432\) −1714.86 2664.07i −0.190987 0.296701i
\(433\) 9870.43 1.09548 0.547739 0.836649i \(-0.315489\pi\)
0.547739 + 0.836649i \(0.315489\pi\)
\(434\) −355.840 + 616.333i −0.0393568 + 0.0681680i
\(435\) 1308.07 + 1062.16i 0.144177 + 0.117073i
\(436\) 12377.8 + 21438.9i 1.35960 + 2.35490i
\(437\) −732.857 1269.35i −0.0802227 0.138950i
\(438\) 24461.1 9352.12i 2.66849 1.02023i
\(439\) −1675.28 + 2901.67i −0.182134 + 0.315465i −0.942607 0.333904i \(-0.891634\pi\)
0.760473 + 0.649369i \(0.224967\pi\)
\(440\) 2417.85 0.261969
\(441\) 985.552 882.619i 0.106420 0.0953049i
\(442\) −2949.63 −0.317420
\(443\) −2841.43 + 4921.49i −0.304741 + 0.527827i −0.977204 0.212304i \(-0.931903\pi\)
0.672463 + 0.740131i \(0.265237\pi\)
\(444\) −2868.21 + 17953.2i −0.306575 + 1.91897i
\(445\) −2745.52 4755.39i −0.292473 0.506577i
\(446\) 5120.74 + 8869.39i 0.543664 + 0.941654i
\(447\) 2448.33 15325.0i 0.259065 1.62159i
\(448\) 2876.10 4981.55i 0.303310 0.525348i
\(449\) −12959.0 −1.36208 −0.681041 0.732245i \(-0.738473\pi\)
−0.681041 + 0.732245i \(0.738473\pi\)
\(450\) 9802.30 8778.52i 1.02686 0.919608i
\(451\) 14195.0 1.48208
\(452\) −2503.60 + 4336.35i −0.260529 + 0.451250i
\(453\) 6780.15 2592.22i 0.703221 0.268859i
\(454\) 2344.85 + 4061.39i 0.242399 + 0.419847i
\(455\) −856.037 1482.70i −0.0882014 0.152769i
\(456\) −536.536 435.672i −0.0551000 0.0447416i
\(457\) −1120.67 + 1941.07i −0.114711 + 0.198685i −0.917664 0.397357i \(-0.869928\pi\)
0.802953 + 0.596042i \(0.203261\pi\)
\(458\) −10364.5 −1.05743
\(459\) 674.373 1310.46i 0.0685774 0.133262i
\(460\) −7783.04 −0.788883
\(461\) −6238.22 + 10804.9i −0.630244 + 1.09162i 0.357257 + 0.934006i \(0.383712\pi\)
−0.987502 + 0.157609i \(0.949621\pi\)
\(462\) −4951.55 4020.70i −0.498630 0.404892i
\(463\) 4874.71 + 8443.24i 0.489302 + 0.847496i 0.999924 0.0123094i \(-0.00391830\pi\)
−0.510622 + 0.859805i \(0.670585\pi\)
\(464\) −950.032 1645.50i −0.0950520 0.164635i
\(465\) −429.828 + 164.334i −0.0428662 + 0.0163888i
\(466\) 1112.14 1926.29i 0.110556 0.191488i
\(467\) −5947.85 −0.589365 −0.294683 0.955595i \(-0.595214\pi\)
−0.294683 + 0.955595i \(0.595214\pi\)
\(468\) −18849.4 6180.50i −1.86178 0.610457i
\(469\) 2746.56 0.270415
\(470\) 2611.23 4522.78i 0.256270 0.443873i
\(471\) 2839.60 17774.2i 0.277796 1.73884i
\(472\) −2398.54 4154.40i −0.233902 0.405131i
\(473\) 6775.84 + 11736.1i 0.658675 + 1.14086i
\(474\) 1756.13 10992.3i 0.170172 1.06517i
\(475\) −462.783 + 801.563i −0.0447030 + 0.0774279i
\(476\) 851.341 0.0819772
\(477\) −1069.48 5098.72i −0.102658 0.489422i
\(478\) 17895.7 1.71240
\(479\) 5604.82 9707.83i 0.534636 0.926017i −0.464545 0.885550i \(-0.653782\pi\)
0.999181 0.0404673i \(-0.0128846\pi\)
\(480\) 4237.90 1620.26i 0.402985 0.154072i
\(481\) −9589.32 16609.2i −0.909014 1.57446i
\(482\) −1311.64 2271.83i −0.123950 0.214687i
\(483\) 4925.15 + 3999.26i 0.463979 + 0.376755i
\(484\) −1387.85 + 2403.83i −0.130339 + 0.225754i
\(485\) −5800.60 −0.543076
\(486\) 11930.7 11771.7i 1.11355 1.09871i
\(487\) −11643.7 −1.08342 −0.541709 0.840566i \(-0.682223\pi\)
−0.541709 + 0.840566i \(0.682223\pi\)
\(488\) −3240.58 + 5612.85i −0.300603 + 0.520660i
\(489\) 11787.7 + 9571.71i 1.09010 + 0.885169i
\(490\) 417.804 + 723.657i 0.0385193 + 0.0667173i
\(491\) −6256.33 10836.3i −0.575039 0.995997i −0.996037 0.0889358i \(-0.971653\pi\)
0.420998 0.907062i \(-0.361680\pi\)
\(492\) −20125.7 + 7694.58i −1.84418 + 0.705078i
\(493\) 441.931 765.447i 0.0403724 0.0699270i
\(494\) 2359.47 0.214894
\(495\) −846.655 4036.42i −0.0768774 0.366512i
\(496\) 518.904 0.0469747
\(497\) −3154.61 + 5463.94i −0.284715 + 0.493142i
\(498\) 376.684 2357.81i 0.0338948 0.212161i
\(499\) −334.598 579.541i −0.0300174 0.0519916i 0.850626 0.525771i \(-0.176223\pi\)
−0.880644 + 0.473779i \(0.842890\pi\)
\(500\) 5246.22 + 9086.73i 0.469237 + 0.812742i
\(501\) −2156.29 + 13497.1i −0.192288 + 1.20360i
\(502\) −5892.97 + 10206.9i −0.523937 + 0.907485i
\(503\) −7651.80 −0.678284 −0.339142 0.940735i \(-0.610137\pi\)
−0.339142 + 0.940735i \(0.610137\pi\)
\(504\) 2842.72 + 932.097i 0.251240 + 0.0823788i
\(505\) −5927.84 −0.522348
\(506\) 15293.6 26489.4i 1.34365 2.32726i
\(507\) 8882.42 3395.98i 0.778071 0.297476i
\(508\) 2832.10 + 4905.34i 0.247350 + 0.428424i
\(509\) 9999.11 + 17319.0i 0.870732 + 1.50815i 0.861240 + 0.508198i \(0.169688\pi\)
0.00949201 + 0.999955i \(0.496979\pi\)
\(510\) 722.624 + 586.776i 0.0627418 + 0.0509468i
\(511\) 3986.67 6905.11i 0.345127 0.597777i
\(512\) −7975.81 −0.688446
\(513\) −539.444 + 1048.27i −0.0464269 + 0.0902185i
\(514\) −7255.14 −0.622589
\(515\) 2736.93 4740.49i 0.234181 0.405614i
\(516\) −15968.5 12966.5i −1.36235 1.10624i
\(517\) 6068.66 + 10511.2i 0.516246 + 0.894165i
\(518\) 4680.23 + 8106.40i 0.396984 + 0.687596i
\(519\) 5513.87 2108.09i 0.466343 0.178295i
\(520\) 1935.72 3352.76i 0.163244 0.282746i
\(521\) 826.109 0.0694673 0.0347337 0.999397i \(-0.488942\pi\)
0.0347337 + 0.999397i \(0.488942\pi\)
\(522\) 7487.76 6705.72i 0.627836 0.562263i
\(523\) −5294.65 −0.442675 −0.221338 0.975197i \(-0.571042\pi\)
−0.221338 + 0.975197i \(0.571042\pi\)
\(524\) 3931.57 6809.68i 0.327770 0.567714i
\(525\) 632.036 3956.16i 0.0525416 0.328878i
\(526\) −8699.93 15068.7i −0.721169 1.24910i
\(527\) 120.690 + 209.042i 0.00997601 + 0.0172790i
\(528\) −733.683 + 4592.41i −0.0604725 + 0.378521i
\(529\) −9128.58 + 15811.2i −0.750273 + 1.29951i
\(530\) 3290.44 0.269674
\(531\) −6095.57 + 5458.93i −0.498164 + 0.446135i
\(532\) −681.004 −0.0554986
\(533\) 11364.5 19683.8i 0.923546 1.59963i
\(534\) −30595.8 + 11697.5i −2.47942 + 0.947944i
\(535\) 2131.02 + 3691.04i 0.172210 + 0.298276i
\(536\) 3105.34 + 5378.60i 0.250243 + 0.433433i
\(537\) −10012.9 8130.54i −0.804633 0.653368i
\(538\) −1901.52 + 3293.53i −0.152380 + 0.263929i
\(539\) −1942.00 −0.155191
\(540\) 3388.37 + 5263.90i 0.270023 + 0.419485i
\(541\) 5643.29 0.448473 0.224237 0.974535i \(-0.428011\pi\)
0.224237 + 0.974535i \(0.428011\pi\)
\(542\) 9425.15 16324.8i 0.746946 1.29375i
\(543\) −595.891 483.868i −0.0470942 0.0382408i
\(544\) −1189.95 2061.06i −0.0937845 0.162440i
\(545\) 4120.59 + 7137.07i 0.323865 + 0.560951i
\(546\) −9539.57 + 3647.22i −0.747721 + 0.285873i
\(547\) −9850.94 + 17062.3i −0.770010 + 1.33370i 0.167546 + 0.985864i \(0.446416\pi\)
−0.937557 + 0.347833i \(0.886918\pi\)
\(548\) −9397.21 −0.732534
\(549\) 10505.0 + 3444.47i 0.816653 + 0.267771i
\(550\) −19315.2 −1.49746
\(551\) −353.509 + 612.296i −0.0273321 + 0.0473406i
\(552\) −2263.25 + 14166.6i −0.174512 + 1.09234i
\(553\) −1694.61 2935.15i −0.130311 0.225705i
\(554\) −8987.14 15566.2i −0.689218 1.19376i
\(555\) −954.833 + 5976.67i −0.0730278 + 0.457109i
\(556\) 1024.99 1775.34i 0.0781824 0.135416i
\(557\) 4658.25 0.354356 0.177178 0.984179i \(-0.443303\pi\)
0.177178 + 0.984179i \(0.443303\pi\)
\(558\) 563.522 + 2686.59i 0.0427523 + 0.203821i
\(559\) 21698.8 1.64179
\(560\) 304.631 527.637i 0.0229875 0.0398156i
\(561\) −2020.71 + 772.570i −0.152076 + 0.0581425i
\(562\) 6792.55 + 11765.0i 0.509833 + 0.883057i
\(563\) −4467.06 7737.17i −0.334394 0.579188i 0.648974 0.760811i \(-0.275198\pi\)
−0.983368 + 0.181623i \(0.941865\pi\)
\(564\) −14301.9 11613.2i −1.06776 0.867030i
\(565\) −833.453 + 1443.58i −0.0620595 + 0.107490i
\(566\) 24044.8 1.78565
\(567\) 560.635 5072.11i 0.0415246 0.375677i
\(568\) −14266.7 −1.05391
\(569\) 517.761 896.788i 0.0381470 0.0660726i −0.846322 0.532672i \(-0.821188\pi\)
0.884469 + 0.466600i \(0.154521\pi\)
\(570\) −578.041 469.374i −0.0424762 0.0344910i
\(571\) −213.177 369.234i −0.0156238 0.0270612i 0.858108 0.513470i \(-0.171640\pi\)
−0.873732 + 0.486408i \(0.838307\pi\)
\(572\) 14559.0 + 25216.9i 1.06423 + 1.84331i
\(573\) −1449.59 + 554.217i −0.105685 + 0.0404062i
\(574\) −5546.63 + 9607.04i −0.403330 + 0.698589i
\(575\) 19212.2 1.39340
\(576\) −4554.70 21714.5i −0.329478 1.57078i
\(577\) −19507.3 −1.40745 −0.703726 0.710471i \(-0.748482\pi\)
−0.703726 + 0.710471i \(0.748482\pi\)
\(578\) −10625.0 + 18403.0i −0.764604 + 1.32433i
\(579\) −1949.88 + 12205.0i −0.139955 + 0.876035i
\(580\) 1877.16 + 3251.33i 0.134387 + 0.232766i
\(581\) −363.489 629.581i −0.0259553 0.0449560i
\(582\) −5458.83 + 34168.9i −0.388790 + 2.43359i
\(583\) −3823.59 + 6622.65i −0.271624 + 0.470467i
\(584\) 18029.7 1.27753
\(585\) −6275.01 2057.50i −0.443487 0.145414i
\(586\) 39581.7 2.79028
\(587\) −956.651 + 1656.97i −0.0672661 + 0.116508i −0.897697 0.440613i \(-0.854761\pi\)
0.830431 + 0.557122i \(0.188094\pi\)
\(588\) 2753.37 1052.68i 0.193107 0.0738298i
\(589\) −96.5426 167.217i −0.00675377 0.0116979i
\(590\) −2584.09 4475.77i −0.180314 0.312313i
\(591\) 1135.30 + 921.876i 0.0790190 + 0.0641640i
\(592\) 3412.48 5910.58i 0.236912 0.410344i
\(593\) −26311.5 −1.82206 −0.911031 0.412337i \(-0.864713\pi\)
−0.911031 + 0.412337i \(0.864713\pi\)
\(594\) −24573.6 + 1188.70i −1.69742 + 0.0821090i
\(595\) 283.413 0.0195274
\(596\) 17289.2 29945.7i 1.18824 2.05809i
\(597\) −312.955 254.122i −0.0214546 0.0174213i
\(598\) −24488.0 42414.4i −1.67456 2.90043i
\(599\) −5780.20 10011.6i −0.394278 0.682910i 0.598730 0.800951i \(-0.295672\pi\)
−0.993009 + 0.118040i \(0.962339\pi\)
\(600\) 8461.95 3235.22i 0.575763 0.220129i
\(601\) −5780.33 + 10011.8i −0.392320 + 0.679519i −0.992755 0.120155i \(-0.961661\pi\)
0.600435 + 0.799674i \(0.294994\pi\)
\(602\) −10590.5 −0.717002
\(603\) 7891.79 7067.55i 0.532966 0.477301i
\(604\) 16173.1 1.08953
\(605\) −462.019 + 800.241i −0.0310475 + 0.0537759i
\(606\) −5578.57 + 34918.4i −0.373950 + 2.34070i
\(607\) 2416.25 + 4185.06i 0.161569 + 0.279846i 0.935432 0.353508i \(-0.115011\pi\)
−0.773862 + 0.633354i \(0.781678\pi\)
\(608\) 951.866 + 1648.68i 0.0634922 + 0.109972i
\(609\) 482.798 3022.02i 0.0321248 0.201081i
\(610\) −3491.26 + 6047.04i −0.231733 + 0.401373i
\(611\) 19434.1 1.28678
\(612\) 2446.18 2190.70i 0.161570 0.144696i
\(613\) −1202.99 −0.0792631 −0.0396316 0.999214i \(-0.512618\pi\)
−0.0396316 + 0.999214i \(0.512618\pi\)
\(614\) 6890.83 11935.3i 0.452917 0.784475i
\(615\) −6699.90 + 2561.54i −0.439295 + 0.167954i
\(616\) −2195.68 3803.03i −0.143614 0.248747i
\(617\) 6269.06 + 10858.3i 0.409049 + 0.708493i 0.994783 0.102010i \(-0.0325273\pi\)
−0.585735 + 0.810503i \(0.699194\pi\)
\(618\) −25348.6 20583.3i −1.64995 1.33977i
\(619\) −13211.3 + 22882.6i −0.857847 + 1.48583i 0.0161321 + 0.999870i \(0.494865\pi\)
−0.873979 + 0.485964i \(0.838469\pi\)
\(620\) −1025.30 −0.0664143
\(621\) 24442.6 1182.36i 1.57946 0.0764031i
\(622\) 3471.98 0.223817
\(623\) −4986.49 + 8636.85i −0.320673 + 0.555422i
\(624\) 5780.77 + 4694.03i 0.370859 + 0.301141i
\(625\) −5137.62 8898.61i −0.328807 0.569511i
\(626\) −10158.0 17594.1i −0.648553 1.12333i
\(627\) 1616.41 617.994i 0.102955 0.0393625i
\(628\) 20052.2 34731.5i 1.27416 2.20690i
\(629\) 3174.80 0.201252
\(630\) 3062.63 + 1004.20i 0.193679 + 0.0635053i
\(631\) −10485.8 −0.661545 −0.330773 0.943711i \(-0.607309\pi\)
−0.330773 + 0.943711i \(0.607309\pi\)
\(632\) 3831.93 6637.10i 0.241181 0.417737i
\(633\) 1915.49 11989.8i 0.120275 0.752848i
\(634\) −9282.43 16077.6i −0.581471 1.00714i
\(635\) 942.812 + 1633.00i 0.0589203 + 0.102053i
\(636\) 1831.20 11462.2i 0.114170 0.714632i
\(637\) −1554.76 + 2692.92i −0.0967059 + 0.167500i
\(638\) −14754.4 −0.915569
\(639\) 4995.76 + 23817.3i 0.309279 + 1.47449i
\(640\) 7028.07 0.434076
\(641\) 2172.72 3763.25i 0.133880 0.231887i −0.791289 0.611442i \(-0.790590\pi\)
0.925169 + 0.379555i \(0.123923\pi\)
\(642\) 23747.9 9079.41i 1.45990 0.558155i
\(643\) −14240.9 24666.0i −0.873416 1.51280i −0.858440 0.512914i \(-0.828566\pi\)
−0.0149760 0.999888i \(-0.504767\pi\)
\(644\) 7067.87 + 12241.9i 0.432474 + 0.749067i
\(645\) −5315.94 4316.58i −0.324519 0.263512i
\(646\) −195.291 + 338.254i −0.0118941 + 0.0206013i
\(647\) 9196.04 0.558785 0.279392 0.960177i \(-0.409867\pi\)
0.279392 + 0.960177i \(0.409867\pi\)
\(648\) 10566.6 4636.76i 0.640578 0.281095i
\(649\) 12011.1 0.726470
\(650\) −15463.6 + 26783.7i −0.933127 + 1.61622i
\(651\) 648.812 + 526.841i 0.0390614 + 0.0317181i
\(652\) 16916.0 + 29299.4i 1.01608 + 1.75990i
\(653\) 7451.10 + 12905.7i 0.446530 + 0.773413i 0.998157 0.0606781i \(-0.0193263\pi\)
−0.551627 + 0.834091i \(0.685993\pi\)
\(654\) 45919.3 17556.1i 2.74555 1.04969i
\(655\) 1308.83 2266.96i 0.0780766 0.135233i
\(656\) 8088.37 0.481399
\(657\) −6313.44 30099.3i −0.374902 1.78734i
\(658\) −9485.16 −0.561961
\(659\) −9210.71 + 15953.4i −0.544459 + 0.943031i 0.454182 + 0.890909i \(0.349932\pi\)
−0.998641 + 0.0521216i \(0.983402\pi\)
\(660\) 1449.68 9074.09i 0.0854978 0.535164i
\(661\) −1583.27 2742.30i −0.0931649 0.161366i 0.815676 0.578509i \(-0.196365\pi\)
−0.908841 + 0.417142i \(0.863032\pi\)
\(662\) −15117.1 26183.6i −0.887528 1.53724i
\(663\) −546.471 + 3420.58i −0.0320108 + 0.200368i
\(664\) 821.939 1423.64i 0.0480383 0.0832048i
\(665\) −226.708 −0.0132201
\(666\) 34307.5 + 11249.0i 1.99608 + 0.654492i
\(667\) 14675.7 0.851944
\(668\) −15226.9 + 26373.8i −0.881958 + 1.52760i
\(669\) 11234.2 4295.12i 0.649237 0.248220i
\(670\) 3345.55 + 5794.67i 0.192910 + 0.334131i
\(671\) −8113.91 14053.7i −0.466817 0.808550i
\(672\) −6396.99 5194.40i −0.367216 0.298182i
\(673\) −7829.88 + 13561.7i −0.448469 + 0.776771i −0.998287 0.0585137i \(-0.981364\pi\)
0.549818 + 0.835285i \(0.314697\pi\)
\(674\) −22956.4 −1.31194
\(675\) −8364.07 12993.7i −0.476938 0.740932i
\(676\) 21187.8 1.20550
\(677\) −6337.73 + 10977.3i −0.359791 + 0.623177i −0.987926 0.154928i \(-0.950485\pi\)
0.628135 + 0.778105i \(0.283819\pi\)
\(678\) 7719.20 + 6268.05i 0.437248 + 0.355049i
\(679\) 5267.60 + 9123.75i 0.297720 + 0.515666i
\(680\) 320.435 + 555.009i 0.0180707 + 0.0312994i
\(681\) 5144.27 1966.78i 0.289469 0.110672i
\(682\) 2014.70 3489.56i 0.113119 0.195927i
\(683\) −21325.5 −1.19473 −0.597363 0.801971i \(-0.703785\pi\)
−0.597363 + 0.801971i \(0.703785\pi\)
\(684\) −1956.75 + 1752.38i −0.109383 + 0.0979591i
\(685\) −3128.35 −0.174494
\(686\) 758.825 1314.32i 0.0422334 0.0731503i
\(687\) −1920.21 + 12019.3i −0.106638 + 0.667491i
\(688\) 3860.89 + 6687.25i 0.213946 + 0.370566i
\(689\) 6122.28 + 10604.1i 0.338520 + 0.586334i
\(690\) −2438.33 + 15262.5i −0.134530 + 0.842075i
\(691\) 3743.95 6484.70i 0.206116 0.357004i −0.744372 0.667766i \(-0.767251\pi\)
0.950488 + 0.310762i \(0.100584\pi\)
\(692\) 13152.6 0.722524
\(693\) −5580.02 + 4997.22i −0.305869 + 0.273923i
\(694\) 19.9982 0.00109383
\(695\) 341.223 591.016i 0.0186235 0.0322568i
\(696\) 6463.89 2471.31i 0.352031 0.134590i
\(697\) 1881.25 + 3258.42i 0.102235 + 0.177076i
\(698\) −1224.92 2121.62i −0.0664237 0.115049i
\(699\) −2027.80 1646.59i −0.109726 0.0890983i
\(700\) 4463.20 7730.49i 0.240990 0.417407i
\(701\) 17119.4 0.922381 0.461191 0.887301i \(-0.347422\pi\)
0.461191 + 0.887301i \(0.347422\pi\)
\(702\) −18025.2 + 35027.2i −0.969112 + 1.88321i
\(703\) −2539.58 −0.136248
\(704\) −16283.9 + 28204.6i −0.871767 + 1.50995i
\(705\) −4761.12 3866.07i −0.254347 0.206531i
\(706\) 25816.1 + 44714.8i 1.37621 + 2.38366i
\(707\) 5383.15 + 9323.88i 0.286357 + 0.495984i
\(708\) −17029.4 + 6510.77i −0.903960 + 0.345607i
\(709\) 14829.8 25686.0i 0.785538 1.36059i −0.143140 0.989702i \(-0.545720\pi\)
0.928677 0.370889i \(-0.120947\pi\)
\(710\) −15370.4 −0.812449
\(711\) −12422.0 4073.03i −0.655219 0.214839i
\(712\) −22551.4 −1.18701
\(713\) −2003.96 + 3470.95i −0.105258 + 0.182312i
\(714\) 266.715 1669.47i 0.0139798 0.0875047i
\(715\) 4846.73 + 8394.77i 0.253507 + 0.439086i
\(716\) −14369.1 24888.0i −0.749996 1.29903i
\(717\) 3315.49 20752.9i 0.172691 1.08094i
\(718\) −10648.9 + 18444.5i −0.553502 + 0.958693i
\(719\) 10886.1 0.564649 0.282325 0.959319i \(-0.408895\pi\)
0.282325 + 0.959319i \(0.408895\pi\)
\(720\) −482.426 2299.96i −0.0249707 0.119048i
\(721\) −9941.74 −0.513523
\(722\) −15018.1 + 26012.1i −0.774120 + 1.34082i
\(723\) −2877.57 + 1100.17i −0.148019 + 0.0565915i
\(724\) −855.138 1481.14i −0.0438964 0.0760307i
\(725\) −4633.70 8025.80i −0.237367 0.411132i
\(726\) 4279.09 + 3474.65i 0.218749 + 0.177626i
\(727\) 9576.19 16586.4i 0.488530 0.846158i −0.511383 0.859353i \(-0.670867\pi\)
0.999913 + 0.0131946i \(0.00420008\pi\)
\(728\) −7031.39 −0.357968
\(729\) −11440.8 16016.5i −0.581254 0.813722i
\(730\) 19424.4 0.984836
\(731\) −1795.99 + 3110.74i −0.0908714 + 0.157394i
\(732\) 19121.8 + 15527.1i 0.965524 + 0.784013i
\(733\) −11109.0 19241.4i −0.559783 0.969572i −0.997514 0.0704661i \(-0.977551\pi\)
0.437732 0.899106i \(-0.355782\pi\)
\(734\) −14439.4 25009.8i −0.726116 1.25767i
\(735\) 916.603 350.441i 0.0459992 0.0175867i
\(736\) 19758.1 34222.0i 0.989528 1.71391i
\(737\) −15550.5 −0.777220
\(738\) 8783.85 + 41876.9i 0.438127 + 2.08877i
\(739\) 6173.20 0.307287 0.153643 0.988126i \(-0.450899\pi\)
0.153643 + 0.988126i \(0.450899\pi\)
\(740\) −6742.67 + 11678.6i −0.334953 + 0.580156i
\(741\) 437.133 2736.18i 0.0216714 0.135649i
\(742\) −2988.08 5175.51i −0.147838 0.256063i
\(743\) 1591.20 + 2756.05i 0.0785674 + 0.136083i 0.902632 0.430413i \(-0.141632\pi\)
−0.824065 + 0.566496i \(0.808299\pi\)
\(744\) −298.149 + 1866.23i −0.0146917 + 0.0919614i
\(745\) 5755.61 9969.00i 0.283046 0.490250i
\(746\) −23027.3 −1.13015
\(747\) −2664.48 873.653i −0.130506 0.0427916i
\(748\) −4820.14 −0.235617
\(749\) 3870.42 6703.76i 0.188814 0.327036i
\(750\) 19462.6 7441.03i 0.947562 0.362277i
\(751\) 11697.0 + 20259.7i 0.568347 + 0.984405i 0.996730 + 0.0808081i \(0.0257501\pi\)
−0.428383 + 0.903597i \(0.640917\pi\)
\(752\) 3457.93 + 5989.32i 0.167683 + 0.290436i
\(753\) 10744.8 + 8724.87i 0.520004 + 0.422247i
\(754\) −11812.3 + 20459.5i −0.570529 + 0.988184i
\(755\) 5384.07 0.259532
\(756\) 5202.54 10109.8i 0.250284 0.486361i
\(757\) −21168.6 −1.01636 −0.508182 0.861250i \(-0.669682\pi\)
−0.508182 + 0.861250i \(0.669682\pi\)
\(758\) 21942.5 38005.5i 1.05143 1.82114i
\(759\) −27885.3 22643.1i −1.33356 1.08286i
\(760\) −256.322 443.962i −0.0122339 0.0211897i
\(761\) −17753.7 30750.4i −0.845694 1.46478i −0.885018 0.465558i \(-0.845854\pi\)
0.0393241 0.999227i \(-0.487480\pi\)
\(762\) 10506.6 4016.93i 0.499492 0.190969i
\(763\) 7483.92 12962.5i 0.355093 0.615039i
\(764\) −3457.81 −0.163742
\(765\) 814.341 729.289i 0.0384870 0.0344673i
\(766\) 8531.13 0.402405
\(767\) 9616.05 16655.5i 0.452693 0.784087i
\(768\) 1225.03 7667.96i 0.0575581 0.360278i
\(769\) −14514.9 25140.6i −0.680653 1.17893i −0.974782 0.223160i \(-0.928363\pi\)
0.294129 0.955766i \(-0.404971\pi\)
\(770\) −2365.53 4097.21i −0.110711 0.191758i
\(771\) −1344.14 + 8413.51i −0.0627862 + 0.393003i
\(772\) −13769.3 + 23849.1i −0.641927 + 1.11185i
\(773\) 17176.5 0.799220 0.399610 0.916685i \(-0.369146\pi\)
0.399610 + 0.916685i \(0.369146\pi\)
\(774\) −30429.9 + 27251.7i −1.41315 + 1.26556i
\(775\) 2530.91 0.117307
\(776\) −11911.4 + 20631.1i −0.551022 + 0.954398i
\(777\) 10267.8 3925.64i 0.474073 0.181250i
\(778\) −5492.97 9514.10i −0.253126 0.438428i
\(779\) −1504.85 2606.48i −0.0692129 0.119880i
\(780\) −11422.2 9274.88i −0.524332 0.425762i
\(781\) 17860.8 30935.8i 0.818323 1.41738i
\(782\) 8107.39 0.370741
\(783\) −6389.13 9925.62i −0.291608 0.453018i
\(784\) −1106.56 −0.0504080
\(785\) 6675.43 11562.2i 0.303511 0.525697i
\(786\) −12122.0 9843.15i −0.550098 0.446684i
\(787\) −9166.30 15876.5i −0.415176 0.719105i 0.580271 0.814423i \(-0.302947\pi\)
−0.995447 + 0.0953181i \(0.969613\pi\)
\(788\) 1629.23 + 2821.91i 0.0736534 + 0.127571i
\(789\) −19086.4 + 7297.24i −0.861211 + 0.329263i
\(790\) 4128.36 7150.53i 0.185925 0.322031i
\(791\) 3027.48 0.136087
\(792\) −16095.0 5277.36i −0.722109 0.236771i
\(793\) −25983.8 −1.16357
\(794\) −1334.90 + 2312.11i −0.0596646 + 0.103342i
\(795\) 609.611 3815.79i 0.0271958 0.170229i
\(796\) −449.109 777.879i −0.0199978 0.0346372i
\(797\) 3577.12 + 6195.76i 0.158981 + 0.275364i 0.934502 0.355959i \(-0.115846\pi\)
−0.775520 + 0.631323i \(0.782512\pi\)
\(798\) −213.350 + 1335.44i −0.00946430 + 0.0592408i
\(799\) −1608.54 + 2786.08i −0.0712218 + 0.123360i
\(800\) −24953.6 −1.10280
\(801\) 7896.79 + 37647.9i 0.348339 + 1.66070i
\(802\) −11731.5 −0.516525
\(803\) −22571.8 + 39095.5i −0.991956 + 1.71812i
\(804\) 22047.5 8429.34i 0.967110 0.369751i
\(805\) 2352.91 + 4075.36i 0.103018 + 0.178432i
\(806\) −3225.91 5587.45i −0.140978 0.244180i
\(807\) 3467.09 + 2815.30i 0.151236 + 0.122805i
\(808\) −12172.6 + 21083.6i −0.529990 + 0.917970i
\(809\) 33931.9 1.47464 0.737318 0.675546i \(-0.236092\pi\)
0.737318 + 0.675546i \(0.236092\pi\)
\(810\) 11384.0 4995.45i 0.493818 0.216694i
\(811\) −41265.7 −1.78673 −0.893363 0.449336i \(-0.851660\pi\)
−0.893363 + 0.449336i \(0.851660\pi\)
\(812\) 3409.34 5905.15i 0.147345 0.255209i
\(813\) −17185.1 13954.5i −0.741339 0.601973i
\(814\) −26498.6 45897.0i −1.14100 1.97627i
\(815\) 5631.39 + 9753.86i 0.242036 + 0.419218i
\(816\) −1151.41 + 440.212i −0.0493962 + 0.0188854i
\(817\) 1436.64 2488.34i 0.0615200 0.106556i
\(818\) 38726.3 1.65530
\(819\) 2462.17 + 11738.4i 0.105049 + 0.500821i
\(820\) −15981.7 −0.680616
\(821\) 8273.49 14330.1i 0.351702 0.609165i −0.634846 0.772639i \(-0.718937\pi\)
0.986548 + 0.163474i \(0.0522699\pi\)
\(822\) −2944.03 + 18427.8i −0.124921 + 0.781927i
\(823\) 4178.02 + 7236.55i 0.176958 + 0.306501i 0.940837 0.338859i \(-0.110041\pi\)
−0.763879 + 0.645360i \(0.776708\pi\)
\(824\) −11240.4 19468.9i −0.475215 0.823097i
\(825\) −3578.47 + 22399.1i −0.151014 + 0.945255i
\(826\) −4693.28 + 8129.00i −0.197700 + 0.342426i
\(827\) −2525.94 −0.106210 −0.0531050 0.998589i \(-0.516912\pi\)
−0.0531050 + 0.998589i \(0.516912\pi\)
\(828\) 51809.6 + 16987.8i 2.17453 + 0.713003i
\(829\) 42284.4 1.77153 0.885764 0.464135i \(-0.153635\pi\)
0.885764 + 0.464135i \(0.153635\pi\)
\(830\) 885.522 1533.77i 0.0370324 0.0641420i
\(831\) −19716.5 + 7538.13i −0.823055 + 0.314675i
\(832\) 26073.7 + 45160.9i 1.08647 + 1.88182i
\(833\) −257.371 445.780i −0.0107051 0.0185419i
\(834\) −3160.31 2566.19i −0.131214 0.106547i
\(835\) −5069.08 + 8779.91i −0.210087 + 0.363882i
\(836\) 3855.72 0.159513
\(837\) 3219.93 155.757i 0.132972 0.00643221i
\(838\) −50551.9 −2.08387
\(839\) −5120.57 + 8869.09i −0.210705 + 0.364952i −0.951935 0.306299i \(-0.900909\pi\)
0.741230 + 0.671251i \(0.234243\pi\)
\(840\) 1722.60 + 1398.77i 0.0707565 + 0.0574548i
\(841\) 8654.92 + 14990.8i 0.354870 + 0.614653i
\(842\) 24056.0 + 41666.2i 0.984590 + 1.70536i
\(843\) 14901.9 5697.38i 0.608836 0.232774i
\(844\) 13526.5 23428.6i 0.551660 0.955503i
\(845\) 7053.47 0.287156
\(846\) −27254.0 + 24407.5i −1.10758 + 0.991900i
\(847\) 1678.26 0.0680823
\(848\) −2178.69 + 3773.60i −0.0882269 + 0.152814i
\(849\) 4454.71 27883.8i 0.180077 1.12717i
\(850\) −2559.81 4433.73i −0.103295 0.178913i
\(851\) 26357.3 + 45652.2i 1.06171 + 1.83894i
\(852\) −8553.94 + 53542.5i −0.343959 + 2.15297i
\(853\) −5091.41 + 8818.58i −0.204369 + 0.353977i −0.949931 0.312459i \(-0.898847\pi\)
0.745563 + 0.666435i \(0.232181\pi\)
\(854\) 12681.8 0.508154
\(855\) −651.407 + 583.372i −0.0260557 + 0.0233344i
\(856\) 17504.0 0.698918
\(857\) 457.041 791.619i 0.0182173 0.0315533i −0.856773 0.515694i \(-0.827534\pi\)
0.874990 + 0.484140i \(0.160868\pi\)
\(858\) 54011.3 20649.9i 2.14908 0.821650i
\(859\) −13430.7 23262.7i −0.533470 0.923997i −0.999236 0.0390890i \(-0.987554\pi\)
0.465766 0.884908i \(-0.345779\pi\)
\(860\) −7628.68 13213.3i −0.302483 0.523917i
\(861\) 10113.3 + 8212.08i 0.400303 + 0.325049i
\(862\) 34739.5 60170.5i 1.37266 2.37751i
\(863\) 33250.8 1.31155 0.655777 0.754954i \(-0.272341\pi\)
0.655777 + 0.754954i \(0.272341\pi\)
\(864\) −31747.1 + 1535.69i −1.25007 + 0.0604692i
\(865\) 4378.53 0.172109
\(866\) 21836.5 37822.0i 0.856854 1.48411i
\(867\) 19372.8 + 15730.9i 0.758864 + 0.616203i
\(868\) 931.083 + 1612.68i 0.0364090 + 0.0630623i
\(869\) 9594.56 + 16618.3i 0.374537 + 0.648718i
\(870\) 6963.92 2662.48i 0.271378 0.103755i
\(871\) −12449.7 + 21563.5i −0.484318 + 0.838863i
\(872\) 33846.0 1.31442
\(873\) 38613.1 + 12660.8i 1.49697 + 0.490839i
\(874\) −6485.26 −0.250992
\(875\) 3172.00 5494.07i 0.122552 0.212267i
\(876\) 10810.1 67664.8i 0.416941 2.60980i
\(877\) 11576.9 + 20051.7i 0.445750 + 0.772061i 0.998104 0.0615482i \(-0.0196038\pi\)
−0.552354 + 0.833609i \(0.686270\pi\)
\(878\) 7412.50 + 12838.8i 0.284920 + 0.493496i
\(879\) 7333.21 45901.4i 0.281391 1.76134i
\(880\) −1724.77 + 2987.38i −0.0660703 + 0.114437i
\(881\) −23462.3 −0.897236 −0.448618 0.893724i \(-0.648084\pi\)
−0.448618 + 0.893724i \(0.648084\pi\)
\(882\) −1201.70 5729.12i −0.0458770 0.218718i
\(883\) 1599.37 0.0609549 0.0304775 0.999535i \(-0.490297\pi\)
0.0304775 + 0.999535i \(0.490297\pi\)
\(884\) −3858.97 + 6683.93i −0.146823 + 0.254304i
\(885\) −5669.12 + 2167.45i −0.215328 + 0.0823255i
\(886\) 12572.3 + 21775.8i 0.476720 + 0.825703i
\(887\) −10238.6 17733.8i −0.387574 0.671298i 0.604549 0.796568i \(-0.293354\pi\)
−0.992123 + 0.125270i \(0.960020\pi\)
\(888\) 19296.6 + 15669.0i 0.729224 + 0.592136i
\(889\) 1712.36 2965.89i 0.0646014 0.111893i
\(890\) −24295.9 −0.915057
\(891\) −3174.21 + 28717.3i −0.119349 + 1.07976i
\(892\) 26797.7 1.00589
\(893\) 1286.71 2228.64i 0.0482172 0.0835146i
\(894\) −53306.7 43285.5i −1.99423 1.61933i
\(895\) −4783.50 8285.26i −0.178653 0.309437i
\(896\) −6382.27 11054.4i −0.237965 0.412168i
\(897\) −53723.2 + 20539.8i −1.99974 + 0.764552i
\(898\) −28669.5 + 49657.1i −1.06538 + 1.84530i
\(899\) 1933.30 0.0717233
\(900\) −7068.10 33697.1i −0.261781 1.24804i
\(901\) −2026.94 −0.0749469
\(902\) 31404.0 54393.3i 1.15924 2.00787i
\(903\) −1962.07 + 12281.4i −0.0723074 + 0.452600i
\(904\) 3422.94 + 5928.71i 0.125935 + 0.218126i
\(905\) −284.678 493.076i −0.0104564 0.0181109i
\(906\) 5066.84 31715.3i 0.185800 1.16299i
\(907\) 14862.7 25742.9i 0.544109 0.942424i −0.454554 0.890719i \(-0.650201\pi\)
0.998662 0.0517044i \(-0.0164654\pi\)
\(908\) 12270.9 0.448487
\(909\) 39460.1 + 12938.5i 1.43983 + 0.472105i
\(910\) −7575.31 −0.275955
\(911\) 1412.43 2446.40i 0.0513676 0.0889713i −0.839198 0.543826i \(-0.816975\pi\)
0.890566 + 0.454854i \(0.150309\pi\)
\(912\) 921.032 352.134i 0.0334413 0.0127854i
\(913\) 2058.01 + 3564.57i 0.0746003 + 0.129211i
\(914\) 4958.58 + 8588.51i 0.179448 + 0.310813i
\(915\) 6365.71 + 5169.01i 0.229993 + 0.186756i
\(916\) −13559.8 + 23486.3i −0.489114 + 0.847170i
\(917\) −4754.25 −0.171210
\(918\) −3529.58 5483.26i −0.126899 0.197140i
\(919\) 1150.69 0.0413034 0.0206517 0.999787i \(-0.493426\pi\)
0.0206517 + 0.999787i \(0.493426\pi\)
\(920\) −5320.53 + 9215.42i −0.190666 + 0.330243i
\(921\) −12564.2 10202.2i −0.449517 0.365011i
\(922\) 27601.8 + 47807.8i 0.985920 + 1.70766i
\(923\) −28598.5 49534.1i −1.01986 1.76645i
\(924\) −15589.1 + 5960.10i −0.555025 + 0.212200i
\(925\) 16644.0 28828.3i 0.591624 1.02472i
\(926\) 43137.6 1.53087
\(927\) −28565.9 + 25582.4i −1.01211 + 0.906404i
\(928\) −19061.5 −0.674271
\(929\) −8032.09 + 13912.0i −0.283664 + 0.491321i −0.972284 0.233801i \(-0.924884\pi\)
0.688620 + 0.725122i \(0.258217\pi\)
\(930\) −321.212 + 2010.59i −0.0113258 + 0.0708924i
\(931\) 205.876 + 356.588i 0.00724739 + 0.0125529i
\(932\) −2910.01 5040.29i −0.102275 0.177146i
\(933\) 643.246 4026.33i 0.0225712 0.141282i
\(934\) −13158.5 + 22791.3i −0.460985 + 0.798450i
\(935\) −1604.63 −0.0561253
\(936\) −20203.5 + 18093.4i −0.705526 + 0.631839i
\(937\) −7995.92 −0.278778 −0.139389 0.990238i \(-0.544514\pi\)
−0.139389 + 0.990238i \(0.544514\pi\)
\(938\) 6076.27 10524.4i 0.211511 0.366348i
\(939\) −22285.2 + 8520.20i −0.774494 + 0.296109i
\(940\) −6832.49 11834.2i −0.237076 0.410627i
\(941\) −9716.25 16829.0i −0.336600 0.583009i 0.647191 0.762328i \(-0.275944\pi\)
−0.983791 + 0.179320i \(0.942610\pi\)
\(942\) −61825.9 50203.1i −2.13843 1.73642i
\(943\) −31236.5 + 54103.2i −1.07869 + 1.86834i
\(944\) 6843.98 0.235967
\(945\) 1731.94 3365.57i 0.0596190 0.115854i
\(946\) 59961.2 2.06079
\(947\) −20478.3 + 35469.4i −0.702697 + 1.21711i 0.264819 + 0.964298i \(0.414688\pi\)
−0.967516 + 0.252809i \(0.918646\pi\)
\(948\) −22611.3 18360.5i −0.774662 0.629032i
\(949\) 36141.7 + 62599.2i 1.23626 + 2.14126i
\(950\) 2047.65 + 3546.63i 0.0699309 + 0.121124i
\(951\) −20364.4 + 7785.82i −0.694385 + 0.265481i
\(952\) 581.981 1008.02i 0.0198131 0.0343174i
\(953\) 7968.49 0.270855 0.135427 0.990787i \(-0.456759\pi\)
0.135427 + 0.990787i \(0.456759\pi\)
\(954\) −21903.6 7181.93i −0.743348 0.243735i
\(955\) −1151.11 −0.0390043
\(956\) 23412.7 40552.1i 0.792073 1.37191i
\(957\) −2733.52 + 17110.1i −0.0923323 + 0.577944i
\(958\) −24799.3 42953.6i −0.836356 1.44861i
\(959\) 2840.90 + 4920.58i 0.0956594 + 0.165687i
\(960\) 2596.22 16250.8i 0.0872840 0.546344i
\(961\) 14631.5 25342.5i 0.491139 0.850677i
\(962\) −84858.6 −2.84402
\(963\) −6129.34 29221.6i −0.205104 0.977833i
\(964\) −6864.04 −0.229332
\(965\) −4583.83 + 7939.43i −0.152911 + 0.264849i
\(966\) 26220.5 10024.8i 0.873325 0.333895i
\(967\) 21570.6 + 37361.4i 0.717337 + 1.24246i 0.962051 + 0.272869i \(0.0879725\pi\)
−0.244714 + 0.969595i \(0.578694\pi\)
\(968\) 1897.49 + 3286.54i 0.0630036 + 0.109125i
\(969\) 356.079 + 289.139i 0.0118048 + 0.00958563i
\(970\) −12832.8 + 22227.0i −0.424779 + 0.735739i
\(971\) 15809.2 0.522492 0.261246 0.965272i \(-0.415867\pi\)
0.261246 + 0.965272i \(0.415867\pi\)
\(972\) −11066.1 42436.0i −0.365172 1.40035i
\(973\) −1239.48 −0.0408384
\(974\) −25759.5 + 44616.8i −0.847420 + 1.46778i
\(975\) 28195.2 + 22894.7i 0.926122 + 0.752018i
\(976\) −4623.32 8007.83i −0.151628 0.262627i
\(977\) −5380.65 9319.55i −0.176195 0.305178i 0.764379 0.644767i \(-0.223045\pi\)
−0.940574 + 0.339589i \(0.889712\pi\)
\(978\) 62755.5 23993.0i 2.05184 0.784471i
\(979\) 28232.6 48900.3i 0.921672 1.59638i
\(980\) 2186.43 0.0712684
\(981\) −11851.8 56503.5i −0.385728 1.83896i
\(982\) −55364.0 −1.79912
\(983\) 88.2920 152.926i 0.00286478 0.00496194i −0.864589 0.502479i \(-0.832421\pi\)
0.867454 + 0.497517i \(0.165755\pi\)
\(984\) −4647.37 + 29089.7i −0.150562 + 0.942424i
\(985\) 542.374 + 939.420i 0.0175447 + 0.0303882i
\(986\) −1955.38 3386.83i −0.0631563 0.109390i
\(987\) −1757.29 + 10999.6i −0.0566720 + 0.354732i
\(988\) 3086.87 5346.61i 0.0993991 0.172164i
\(989\) −59641.5 −1.91758
\(990\) −17340.0 5685.60i −0.556669 0.182525i
\(991\) −60295.8 −1.93275 −0.966377 0.257129i \(-0.917224\pi\)
−0.966377 + 0.257129i \(0.917224\pi\)
\(992\) 2602.82 4508.22i 0.0833061 0.144290i
\(993\) −33164.9 + 12679.8i −1.05987 + 0.405217i
\(994\) 13958.0 + 24176.0i 0.445393 + 0.771444i
\(995\) −149.509 258.958i −0.00476358 0.00825077i
\(996\) −4850.05 3938.28i −0.154297 0.125290i
\(997\) −8722.95 + 15108.6i −0.277090 + 0.479934i −0.970660 0.240455i \(-0.922703\pi\)
0.693570 + 0.720389i \(0.256037\pi\)
\(998\) −2960.95 −0.0939151
\(999\) 19401.2 37701.0i 0.614440 1.19400i
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 63.4.f.c.43.8 yes 18
3.2 odd 2 189.4.f.c.127.2 18
9.2 odd 6 567.4.a.k.1.8 9
9.4 even 3 inner 63.4.f.c.22.8 18
9.5 odd 6 189.4.f.c.64.2 18
9.7 even 3 567.4.a.j.1.2 9
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
63.4.f.c.22.8 18 9.4 even 3 inner
63.4.f.c.43.8 yes 18 1.1 even 1 trivial
189.4.f.c.64.2 18 9.5 odd 6
189.4.f.c.127.2 18 3.2 odd 2
567.4.a.j.1.2 9 9.7 even 3
567.4.a.k.1.8 9 9.2 odd 6