Properties

Label 110.5.h.a.51.4
Level 110110
Weight 55
Character 110.51
Analytic conductor 11.37111.371
Analytic rank 00
Dimension 3232
Inner twists 22

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [110,5,Mod(41,110)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(110, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 3]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("110.41");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: N N == 110=2511 110 = 2 \cdot 5 \cdot 11
Weight: k k == 5 5
Character orbit: [χ][\chi] == 110.h (of order 1010, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 11.370695939211.3706959392
Analytic rank: 00
Dimension: 3232
Relative dimension: 88 over Q(ζ10)\Q(\zeta_{10})
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 51.4
Character χ\chi == 110.51
Dual form 110.5.h.a.41.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.66251+2.28825i)q2+(4.8939815.0621i)q3+(2.472147.60845i)q4+(9.04508+6.57164i)q5+(26.3296+36.2396i)q6+(75.4276+24.5079i)q7+(21.5200+6.99226i)q8+(137.38699.8171i)q931.6228iq10+(116.546+32.5265i)q11126.698q12+(109.181+150.275i)q13+(69.3189213.342i)q14+(54.7164+168.400i)q15+(51.7771+37.6183i)q16+(199.384+274.428i)q17+(456.812148.427i)q18+(7.65733+2.48802i)q19+(72.3607+52.5731i)q20+1256.04iq21+(268.188+212.611i)q22+473.434q23+(210.637289.916i)q24+(38.6271118.882i)q25+(162.352499.668i)q26+(1138.00+826.808i)q27+(372.935+513.301i)q28+(1312.91+426.591i)q29+(476.307154.761i)q30+(1342.21975.170i)q31181.019iq32+(1060.291596.25i)q33959.436q34+(521.192717.359i)q35+(419.816+1292.06i)q36+(124.180+382.188i)q37+(18.4236+13.3855i)q38+(1729.14+2379.95i)q39+(240.600+78.1758i)q40+(2871.98933.163i)q41+(2874.132088.18i)q42+2574.67iq43+(40.6421967.146i)q44+1898.63q45+(787.088+1083.33i)q46+(705.352+2170.85i)q47+(313.215+963.977i)q48+(3146.242285.88i)q49+(207.813+286.031i)q50+(5109.261660.10i)q51+(1413.27+459.201i)q52+(2648.051923.92i)q533978.61iq54+(1267.92+471.695i)q551794.56q56+(74.9497103.159i)q57+(1206.583713.48i)q58+(218.082+671.187i)q59+(1146.00832.614i)q60+(338.369+465.725i)q61+(4462.861450.07i)q62+(12809.0+4161.91i)q63+(414.217+300.946i)q642076.75iq65+(1889.87+5079.99i)q661985.60q67+(1595.072195.43i)q68+(2316.987130.93i)q69+(775.009+2385.23i)q70+(1710.82+1242.99i)q71+(2258.603108.70i)q72+(1025.58333.230i)q73+(1080.99351.235i)q74+(1601.581163.61i)q7564.4112iq76+(9587.96+402.912i)q778320.61q78+(2287.683148.72i)q79+(221.115680.521i)q80+(2633.49+8105.05i)q81+(6910.005020.41i)q82+(5341.447351.87i)q83+(9556.543105.11i)q84+(3606.891171.95i)q85+(5891.474280.41i)q86+21863.0iq87+(2280.64+1514.89i)q88593.105q89+(3156.49+4344.54i)q90+(4552.3614010.7i)q91+(1170.393602.10i)q92+(21256.9+15444.0i)q93+(3794.795223.07i)q94+(85.6116+27.8169i)q95+(2726.54885.906i)q96+(79.017257.4093i)q97+10999.7iq98+(12765.216102.0i)q99+O(q100)q+(-1.66251 + 2.28825i) q^{2} +(4.89398 - 15.0621i) q^{3} +(-2.47214 - 7.60845i) q^{4} +(-9.04508 + 6.57164i) q^{5} +(26.3296 + 36.2396i) q^{6} +(-75.4276 + 24.5079i) q^{7} +(21.5200 + 6.99226i) q^{8} +(-137.386 - 99.8171i) q^{9} -31.6228i q^{10} +(116.546 + 32.5265i) q^{11} -126.698 q^{12} +(-109.181 + 150.275i) q^{13} +(69.3189 - 213.342i) q^{14} +(54.7164 + 168.400i) q^{15} +(-51.7771 + 37.6183i) q^{16} +(199.384 + 274.428i) q^{17} +(456.812 - 148.427i) q^{18} +(7.65733 + 2.48802i) q^{19} +(72.3607 + 52.5731i) q^{20} +1256.04i q^{21} +(-268.188 + 212.611i) q^{22} +473.434 q^{23} +(210.637 - 289.916i) q^{24} +(38.6271 - 118.882i) q^{25} +(-162.352 - 499.668i) q^{26} +(-1138.00 + 826.808i) q^{27} +(372.935 + 513.301i) q^{28} +(-1312.91 + 426.591i) q^{29} +(-476.307 - 154.761i) q^{30} +(-1342.21 - 975.170i) q^{31} -181.019i q^{32} +(1060.29 - 1596.25i) q^{33} -959.436 q^{34} +(521.192 - 717.359i) q^{35} +(-419.816 + 1292.06i) q^{36} +(124.180 + 382.188i) q^{37} +(-18.4236 + 13.3855i) q^{38} +(1729.14 + 2379.95i) q^{39} +(-240.600 + 78.1758i) q^{40} +(-2871.98 - 933.163i) q^{41} +(-2874.13 - 2088.18i) q^{42} +2574.67i q^{43} +(-40.6421 - 967.146i) q^{44} +1898.63 q^{45} +(-787.088 + 1083.33i) q^{46} +(-705.352 + 2170.85i) q^{47} +(313.215 + 963.977i) q^{48} +(3146.24 - 2285.88i) q^{49} +(207.813 + 286.031i) q^{50} +(5109.26 - 1660.10i) q^{51} +(1413.27 + 459.201i) q^{52} +(-2648.05 - 1923.92i) q^{53} -3978.61i q^{54} +(-1267.92 + 471.695i) q^{55} -1794.56 q^{56} +(74.9497 - 103.159i) q^{57} +(1206.58 - 3713.48i) q^{58} +(218.082 + 671.187i) q^{59} +(1146.00 - 832.614i) q^{60} +(338.369 + 465.725i) q^{61} +(4462.86 - 1450.07i) q^{62} +(12809.0 + 4161.91i) q^{63} +(414.217 + 300.946i) q^{64} -2076.75i q^{65} +(1889.87 + 5079.99i) q^{66} -1985.60 q^{67} +(1595.07 - 2195.43i) q^{68} +(2316.98 - 7130.93i) q^{69} +(775.009 + 2385.23i) q^{70} +(-1710.82 + 1242.99i) q^{71} +(-2258.60 - 3108.70i) q^{72} +(1025.58 - 333.230i) q^{73} +(-1080.99 - 351.235i) q^{74} +(-1601.58 - 1163.61i) q^{75} -64.4112i q^{76} +(-9587.96 + 402.912i) q^{77} -8320.61 q^{78} +(2287.68 - 3148.72i) q^{79} +(221.115 - 680.521i) q^{80} +(2633.49 + 8105.05i) q^{81} +(6910.00 - 5020.41i) q^{82} +(-5341.44 - 7351.87i) q^{83} +(9556.54 - 3105.11i) q^{84} +(-3606.89 - 1171.95i) q^{85} +(-5891.47 - 4280.41i) q^{86} +21863.0i q^{87} +(2280.64 + 1514.89i) q^{88} -593.105 q^{89} +(-3156.49 + 4344.54i) q^{90} +(4552.36 - 14010.7i) q^{91} +(-1170.39 - 3602.10i) q^{92} +(-21256.9 + 15444.0i) q^{93} +(-3794.79 - 5223.07i) q^{94} +(-85.6116 + 27.8169i) q^{95} +(-2726.54 - 885.906i) q^{96} +(-79.0172 - 57.4093i) q^{97} +10999.7i q^{98} +(-12765.2 - 16102.0i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q18q3+64q4200q5+80q660q7262q9258q1196q12570q1348q14+150q15512q16+150q17480q181020q19+1600q20++65268q99+O(q100) 32 q - 18 q^{3} + 64 q^{4} - 200 q^{5} + 80 q^{6} - 60 q^{7} - 262 q^{9} - 258 q^{11} - 96 q^{12} - 570 q^{13} - 48 q^{14} + 150 q^{15} - 512 q^{16} + 150 q^{17} - 480 q^{18} - 1020 q^{19} + 1600 q^{20}+ \cdots + 65268 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/110Z)×\left(\mathbb{Z}/110\mathbb{Z}\right)^\times.

nn 6767 101101
χ(n)\chi(n) 11 e(710)e\left(\frac{7}{10}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.66251 + 2.28825i −0.415627 + 0.572061i
33 4.89398 15.0621i 0.543776 1.67357i −0.180106 0.983647i 0.557644π-0.557644\pi
0.723882 0.689923i 0.242356π-0.242356\pi
44 −2.47214 7.60845i −0.154508 0.475528i
55 −9.04508 + 6.57164i −0.361803 + 0.262866i
66 26.3296 + 36.2396i 0.731377 + 1.00665i
77 −75.4276 + 24.5079i −1.53934 + 0.500162i −0.951194 0.308593i 0.900142π-0.900142\pi
−0.588146 + 0.808755i 0.700142π0.700142\pi
88 21.5200 + 6.99226i 0.336249 + 0.109254i
99 −137.386 99.8171i −1.69613 1.23231i
1010 31.6228i 0.316228i
1111 116.546 + 32.5265i 0.963192 + 0.268814i
1212 −126.698 −0.879848
1313 −109.181 + 150.275i −0.646044 + 0.889203i −0.998920 0.0464667i 0.985204π-0.985204\pi
0.352876 + 0.935670i 0.385204π0.385204\pi
1414 69.3189 213.342i 0.353668 1.08848i
1515 54.7164 + 168.400i 0.243184 + 0.748444i
1616 −51.7771 + 37.6183i −0.202254 + 0.146946i
1717 199.384 + 274.428i 0.689909 + 0.949579i 0.999999 0.00112843i 0.000359191π-0.000359191\pi
−0.310090 + 0.950707i 0.600359π0.600359\pi
1818 456.812 148.427i 1.40991 0.458109i
1919 7.65733 + 2.48802i 0.0212114 + 0.00689202i 0.319604 0.947551i 0.396450π-0.396450\pi
−0.298392 + 0.954443i 0.596450π0.596450\pi
2020 72.3607 + 52.5731i 0.180902 + 0.131433i
2121 1256.04i 2.84817i
2222 −268.188 + 212.611i −0.554107 + 0.439279i
2323 473.434 0.894960 0.447480 0.894294i 0.352321π-0.352321\pi
0.447480 + 0.894294i 0.352321π0.352321\pi
2424 210.637 289.916i 0.365689 0.503327i
2525 38.6271 118.882i 0.0618034 0.190211i
2626 −162.352 499.668i −0.240166 0.739154i
2727 −1138.00 + 826.808i −1.56105 + 1.13417i
2828 372.935 + 513.301i 0.475682 + 0.654720i
2929 −1312.91 + 426.591i −1.56113 + 0.507243i −0.957110 0.289724i 0.906436π-0.906436\pi
−0.604023 + 0.796967i 0.706436π0.706436\pi
3030 −476.307 154.761i −0.529229 0.171957i
3131 −1342.21 975.170i −1.39668 1.01474i −0.995095 0.0989211i 0.968461π-0.968461\pi
−0.401581 0.915824i 0.631539π-0.631539\pi
3232 181.019i 0.176777i
3333 1060.29 1596.25i 0.973640 1.46580i
3434 −959.436 −0.829962
3535 521.192 717.359i 0.425463 0.585600i
3636 −419.816 + 1292.06i −0.323932 + 0.996960i
3737 124.180 + 382.188i 0.0907089 + 0.279173i 0.986112 0.166084i 0.0531123π-0.0531123\pi
−0.895403 + 0.445257i 0.853112π0.853112\pi
3838 −18.4236 + 13.3855i −0.0127587 + 0.00926974i
3939 1729.14 + 2379.95i 1.13684 + 1.56473i
4040 −240.600 + 78.1758i −0.150375 + 0.0488599i
4141 −2871.98 933.163i −1.70850 0.555124i −0.718414 0.695616i 0.755131π-0.755131\pi
−0.990082 + 0.140492i 0.955131π0.955131\pi
4242 −2874.13 2088.18i −1.62933 1.18378i
4343 2574.67i 1.39247i 0.717816 + 0.696233i 0.245142π0.245142\pi
−0.717816 + 0.696233i 0.754858π0.754858\pi
4444 −40.6421 967.146i −0.0209928 0.499559i
4545 1898.63 0.937597
4646 −787.088 + 1083.33i −0.371970 + 0.511972i
4747 −705.352 + 2170.85i −0.319308 + 0.982730i 0.654636 + 0.755944i 0.272822π0.272822\pi
−0.973945 + 0.226786i 0.927178π0.927178\pi
4848 313.215 + 963.977i 0.135944 + 0.418393i
4949 3146.24 2285.88i 1.31039 0.952052i
5050 207.813 + 286.031i 0.0831254 + 0.114412i
5151 5109.26 1660.10i 1.96434 0.638254i
5252 1413.27 + 459.201i 0.522661 + 0.169823i
5353 −2648.05 1923.92i −0.942702 0.684913i 0.00636735 0.999980i 0.497973π-0.497973\pi
−0.949070 + 0.315066i 0.897973π0.897973\pi
5454 3978.61i 1.36441i
5555 −1267.92 + 471.695i −0.419148 + 0.155932i
5656 −1794.56 −0.572246
5757 74.9497 103.159i 0.0230686 0.0317511i
5858 1206.58 3713.48i 0.358675 1.10389i
5959 218.082 + 671.187i 0.0626492 + 0.192814i 0.977482 0.211018i 0.0676779π-0.0676779\pi
−0.914833 + 0.403832i 0.867678π0.867678\pi
6060 1146.00 832.614i 0.318332 0.231282i
6161 338.369 + 465.725i 0.0909350 + 0.125161i 0.852060 0.523443i 0.175353π-0.175353\pi
−0.761125 + 0.648605i 0.775353π0.775353\pi
6262 4462.86 1450.07i 1.16099 0.377229i
6363 12809.0 + 4161.91i 3.22727 + 1.04860i
6464 414.217 + 300.946i 0.101127 + 0.0734732i
6565 2076.75i 0.491540i
6666 1889.87 + 5079.99i 0.433854 + 1.16621i
6767 −1985.60 −0.442326 −0.221163 0.975237i 0.570985π-0.570985\pi
−0.221163 + 0.975237i 0.570985π0.570985\pi
6868 1595.07 2195.43i 0.344955 0.474789i
6969 2316.98 7130.93i 0.486658 1.49778i
7070 775.009 + 2385.23i 0.158165 + 0.486782i
7171 −1710.82 + 1242.99i −0.339382 + 0.246575i −0.744401 0.667733i 0.767265π-0.767265\pi
0.405019 + 0.914308i 0.367265π0.367265\pi
7272 −2258.60 3108.70i −0.435687 0.599672i
7373 1025.58 333.230i 0.192452 0.0625315i −0.211205 0.977442i 0.567739π-0.567739\pi
0.403657 + 0.914910i 0.367739π0.367739\pi
7474 −1080.99 351.235i −0.197405 0.0641409i
7575 −1601.58 1163.61i −0.284725 0.206865i
7676 64.4112i 0.0111515i
7777 −9587.96 + 402.912i −1.61713 + 0.0679561i
7878 −8320.61 −1.36762
7979 2287.68 3148.72i 0.366557 0.504522i −0.585404 0.810741i 0.699064π-0.699064\pi
0.951961 + 0.306220i 0.0990642π0.0990642\pi
8080 221.115 680.521i 0.0345492 0.106331i
8181 2633.49 + 8105.05i 0.401385 + 1.23534i
8282 6910.00 5020.41i 1.02766 0.746640i
8383 −5341.44 7351.87i −0.775358 1.06719i −0.995779 0.0917844i 0.970743π-0.970743\pi
0.220420 0.975405i 0.429257π-0.429257\pi
8484 9556.54 3105.11i 1.35439 0.440066i
8585 −3606.89 1171.95i −0.499223 0.162207i
8686 −5891.47 4280.41i −0.796576 0.578746i
8787 21863.0i 2.88849i
8888 2280.64 + 1514.89i 0.294504 + 0.195621i
8989 −593.105 −0.0748776 −0.0374388 0.999299i 0.511920π-0.511920\pi
−0.0374388 + 0.999299i 0.511920π0.511920\pi
9090 −3156.49 + 4344.54i −0.389691 + 0.536363i
9191 4552.36 14010.7i 0.549736 1.69191i
9292 −1170.39 3602.10i −0.138279 0.425579i
9393 −21256.9 + 15444.0i −2.45773 + 1.78564i
9494 −3794.79 5223.07i −0.429469 0.591113i
9595 −85.6116 + 27.8169i −0.00948605 + 0.00308220i
9696 −2726.54 885.906i −0.295848 0.0961269i
9797 −79.0172 57.4093i −0.00839804 0.00610154i 0.583578 0.812057i 0.301652π-0.301652\pi
−0.591976 + 0.805955i 0.701652π0.701652\pi
9898 10999.7i 1.14532i
9999 −12765.2 16102.0i −1.30244 1.64289i
100100 −1000.00 −0.100000
101101 3849.12 5297.86i 0.377328 0.519347i −0.577546 0.816358i 0.695990π-0.695990\pi
0.954874 + 0.297011i 0.0959898π0.0959898\pi
102102 −4695.47 + 14451.2i −0.451314 + 1.38900i
103103 4639.97 + 14280.4i 0.437362 + 1.34606i 0.890647 + 0.454696i 0.150252π0.150252\pi
−0.453285 + 0.891366i 0.649748π0.649748\pi
104104 −3400.34 + 2470.49i −0.314381 + 0.228411i
105105 −8254.26 11361.0i −0.748686 1.03048i
106106 8804.81 2860.86i 0.783625 0.254615i
107107 8188.80 + 2660.70i 0.715242 + 0.232396i 0.643959 0.765060i 0.277291π-0.277291\pi
0.0712828 + 0.997456i 0.477291π0.477291\pi
108108 9104.03 + 6614.47i 0.780524 + 0.567084i
109109 6056.07i 0.509728i −0.966977 0.254864i 0.917969π-0.917969\pi
0.966977 0.254864i 0.0820306π-0.0820306\pi
110110 1028.58 3685.52i 0.0850064 0.304588i
111111 6364.31 0.516541
112112 2983.48 4106.41i 0.237841 0.327360i
113113 2258.58 6951.20i 0.176880 0.544381i −0.822834 0.568281i 0.807608π-0.807608\pi
0.999714 + 0.0239005i 0.00760850π0.00760850\pi
114114 111.450 + 343.007i 0.00857569 + 0.0263933i
115115 −4282.25 + 3111.24i −0.323800 + 0.235254i
116116 6491.40 + 8934.64i 0.482417 + 0.663989i
117117 30000.1 9747.63i 2.19155 0.712077i
118118 −1898.40 616.828i −0.136340 0.0442997i
119119 −21764.7 15813.0i −1.53695 1.11666i
120120 4006.55i 0.278232i
121121 12525.1 + 7581.68i 0.855478 + 0.517839i
122122 −1628.23 −0.109395
123123 −28110.9 + 38691.3i −1.85808 + 2.55742i
124124 −4101.42 + 12622.9i −0.266741 + 0.820946i
125125 431.864 + 1329.14i 0.0276393 + 0.0850651i
126126 −30818.6 + 22391.0i −1.94121 + 1.41037i
127127 4179.71 + 5752.88i 0.259142 + 0.356679i 0.918687 0.394987i 0.129251π-0.129251\pi
−0.659544 + 0.751666i 0.729251π0.729251\pi
128128 −1377.28 + 447.504i −0.0840623 + 0.0273135i
129129 38780.0 + 12600.4i 2.33039 + 0.757189i
130130 4752.12 + 3452.62i 0.281191 + 0.204297i
131131 4271.99i 0.248936i −0.992224 0.124468i 0.960278π-0.960278\pi
0.992224 0.124468i 0.0397224π-0.0397224\pi
132132 −14766.2 4121.04i −0.847463 0.236515i
133133 −638.551 −0.0360987
134134 3301.08 4543.55i 0.183843 0.253038i
135135 4859.86 14957.1i 0.266659 0.820691i
136136 2371.86 + 7299.83i 0.128236 + 0.394671i
137137 4256.22 3092.33i 0.226769 0.164757i −0.468600 0.883411i 0.655241π-0.655241\pi
0.695368 + 0.718654i 0.255241π0.255241\pi
138138 12465.3 + 17157.0i 0.654554 + 0.900916i
139139 −7985.47 + 2594.64i −0.413305 + 0.134291i −0.508286 0.861188i 0.669721π-0.669721\pi
0.0949814 + 0.995479i 0.469721π0.469721\pi
140140 −6746.45 2192.06i −0.344207 0.111840i
141141 29245.7 + 21248.2i 1.47104 + 1.06877i
142142 5981.26i 0.296631i
143143 −17612.6 + 13962.7i −0.861295 + 0.682808i
144144 10868.4 0.524133
145145 9072.00 12486.5i 0.431487 0.593890i
146146 −942.518 + 2900.77i −0.0442164 + 0.136084i
147147 −19032.5 58576.1i −0.880769 2.71073i
148148 2600.87 1889.64i 0.118739 0.0862693i
149149 −9698.99 13349.5i −0.436872 0.601302i 0.532642 0.846341i 0.321199π-0.321199\pi
−0.969513 + 0.245039i 0.921199π0.921199\pi
150150 5325.27 1730.28i 0.236679 0.0769015i
151151 −6137.80 1994.29i −0.269190 0.0874651i 0.171312 0.985217i 0.445199π-0.445199\pi
−0.440502 + 0.897752i 0.645199π0.645199\pi
152152 147.389 + 107.084i 0.00637935 + 0.00463487i
153153 57604.6i 2.46079i
154154 15018.1 22609.5i 0.633248 0.953342i
155155 18548.8 0.772064
156156 13833.1 19039.6i 0.568421 0.782364i
157157 2488.58 7659.06i 0.100961 0.310725i −0.887801 0.460228i 0.847768π-0.847768\pi
0.988761 + 0.149504i 0.0477675π0.0477675\pi
158158 3401.76 + 10469.5i 0.136267 + 0.419386i
159159 −41937.9 + 30469.7i −1.65887 + 1.20524i
160160 1189.59 + 1637.34i 0.0464685 + 0.0639584i
161161 −35710.0 + 11602.9i −1.37765 + 0.447625i
162162 −22924.5 7448.63i −0.873515 0.283822i
163163 −24463.6 17773.9i −0.920758 0.668970i 0.0229546 0.999737i 0.492693π-0.492693\pi
−0.943713 + 0.330767i 0.892693π0.892693\pi
164164 24158.2i 0.898209i
165165 899.541 + 21406.1i 0.0330410 + 0.786266i
166166 25703.1 0.932758
167167 −19175.6 + 26392.9i −0.687567 + 0.946355i −0.999994 0.00358666i 0.998858π-0.998858\pi
0.312426 + 0.949942i 0.398858π0.398858\pi
168168 −8782.57 + 27030.0i −0.311174 + 0.957695i
169169 −1836.27 5651.45i −0.0642928 0.197873i
170170 8678.18 6305.07i 0.300283 0.218168i
171171 −803.667 1106.15i −0.0274842 0.0378288i
172172 19589.2 6364.93i 0.662157 0.215148i
173173 20432.8 + 6639.01i 0.682709 + 0.221825i 0.629781 0.776773i 0.283145π-0.283145\pi
0.0529278 + 0.998598i 0.483145π0.483145\pi
174174 −50027.9 36347.4i −1.65240 1.20054i
175175 9913.66i 0.323711i
176176 −7258.01 + 2700.14i −0.234311 + 0.0871688i
177177 11176.8 0.356756
178178 986.042 1357.17i 0.0311211 0.0428346i
179179 −6223.61 + 19154.3i −0.194239 + 0.597806i 0.805746 + 0.592262i 0.201765π0.201765\pi
−0.999985 + 0.00554457i 0.998235π0.998235\pi
180180 −4693.68 14445.7i −0.144867 0.445854i
181181 −29614.9 + 21516.5i −0.903967 + 0.656771i −0.939482 0.342598i 0.888693π-0.888693\pi
0.0355146 + 0.999369i 0.488693π0.488693\pi
182182 24491.7 + 33709.9i 0.739393 + 1.01769i
183183 8670.79 2817.31i 0.258914 0.0841264i
184184 10188.3 + 3310.37i 0.300930 + 0.0977780i
185185 −3634.83 2640.86i −0.106204 0.0771616i
186186 74316.7i 2.14813i
187187 14311.3 + 38468.8i 0.409255 + 1.10008i
188188 18260.5 0.516652
189189 65573.6 90254.3i 1.83572 2.52665i
190190 78.6780 242.146i 0.00217945 0.00670765i
191191 9645.48 + 29685.7i 0.264397 + 0.813731i 0.991832 + 0.127554i 0.0407126π0.0407126\pi
−0.727434 + 0.686177i 0.759287π0.759287\pi
192192 6560.06 4766.16i 0.177953 0.129290i
193193 −8084.08 11126.8i −0.217028 0.298713i 0.686597 0.727039i 0.259104π-0.259104\pi
−0.903625 + 0.428325i 0.859104π0.859104\pi
194194 262.733 85.3673i 0.00698091 0.00226823i
195195 −31280.4 10163.6i −0.822626 0.267287i
196196 −25169.9 18287.0i −0.655194 0.476026i
197197 6804.30i 0.175328i 0.996150 + 0.0876639i 0.0279402π0.0279402\pi
−0.996150 + 0.0876639i 0.972060π0.972060\pi
198198 58067.6 2440.15i 1.48116 0.0622425i
199199 42627.8 1.07643 0.538216 0.842807i 0.319099π-0.319099\pi
0.538216 + 0.842807i 0.319099π0.319099\pi
200200 1662.51 2288.25i 0.0415627 0.0572061i
201201 −9717.51 + 29907.4i −0.240527 + 0.740265i
202202 5723.61 + 17615.5i 0.140271 + 0.431709i
203203 88575.0 64353.5i 2.14941 1.56164i
204204 −25261.6 34769.5i −0.607015 0.835485i
205205 32109.7 10433.1i 0.764062 0.248259i
206206 −40391.0 13123.8i −0.951810 0.309262i
207207 −65043.4 47256.8i −1.51797 1.10287i
208208 11888.0i 0.274779i
209209 811.507 + 539.035i 0.0185780 + 0.0123403i
210210 39719.6 0.900670
211211 34454.8 47422.9i 0.773899 1.06518i −0.222030 0.975040i 0.571268π-0.571268\pi
0.995929 0.0901411i 0.0287318π-0.0287318\pi
212212 −8091.72 + 24903.8i −0.180040 + 0.554106i
213213 10349.3 + 31851.8i 0.228113 + 0.702061i
214214 −19702.3 + 14314.6i −0.430219 + 0.312572i
215215 −16919.8 23288.1i −0.366031 0.503799i
216216 −30271.0 + 9835.66i −0.648813 + 0.210812i
217217 125139. + 40660.1i 2.65750 + 0.863473i
218218 13857.8 + 10068.3i 0.291595 + 0.211856i
219219 17078.2i 0.356085i
220220 6723.35 + 8480.84i 0.138912 + 0.175224i
221221 −63008.8 −1.29008
222222 −10580.7 + 14563.1i −0.214689 + 0.295493i
223223 −5698.33 + 17537.7i −0.114588 + 0.352665i −0.991861 0.127327i 0.959360π-0.959360\pi
0.877273 + 0.479992i 0.159360π0.159360\pi
224224 4436.41 + 13653.9i 0.0884169 + 0.272119i
225225 −17173.3 + 12477.1i −0.339226 + 0.246462i
226226 12151.1 + 16724.6i 0.237903 + 0.327446i
227227 6106.78 1984.21i 0.118511 0.0385067i −0.249161 0.968462i 0.580155π-0.580155\pi
0.367672 + 0.929955i 0.380155π0.380155\pi
228228 −970.170 315.227i −0.0186628 0.00606393i
229229 82077.4 + 59632.7i 1.56514 + 1.13714i 0.931633 + 0.363401i 0.118384π0.118384\pi
0.633505 + 0.773739i 0.281616π0.281616\pi
230230 14971.3i 0.283011i
231231 −40854.6 + 146387.i −0.765627 + 2.74333i
232232 −31236.7 −0.580348
233233 −35041.2 + 48230.0i −0.645456 + 0.888394i −0.998892 0.0470645i 0.985013π-0.985013\pi
0.353436 + 0.935459i 0.385013π0.385013\pi
234234 −27570.4 + 84853.1i −0.503515 + 1.54966i
235235 −7886.08 24270.8i −0.142799 0.439490i
236236 4567.56 3318.53i 0.0820088 0.0595829i
237237 −36230.6 49867.1i −0.645028 0.887805i
238238 72368.0 23513.8i 1.27759 0.415115i
239239 −99182.8 32226.5i −1.73636 0.564179i −0.742019 0.670379i 0.766132π-0.766132\pi
−0.994345 + 0.106200i 0.966132π0.966132\pi
240240 −9167.96 6660.91i −0.159166 0.115641i
241241 51292.2i 0.883116i −0.897233 0.441558i 0.854426π-0.854426\pi
0.897233 0.441558i 0.145574π-0.145574\pi
242242 −38171.7 + 16055.8i −0.651795 + 0.274158i
243243 21028.9 0.356127
244244 2706.95 3725.80i 0.0454675 0.0625806i
245245 −13436.1 + 41351.9i −0.223841 + 0.688912i
246246 −41800.6 128649.i −0.690737 2.12587i
247247 −1209.93 + 879.063i −0.0198319 + 0.0144087i
248248 −22065.6 30370.7i −0.358766 0.493800i
249249 −136876. + 44473.6i −2.20764 + 0.717305i
250250 −3759.38 1221.50i −0.0601501 0.0195440i
251251 55459.4 + 40293.6i 0.880295 + 0.639572i 0.933329 0.359021i 0.116889π-0.116889\pi
−0.0530347 + 0.998593i 0.516889π0.516889\pi
252252 107746.i 1.69668i
253253 55177.0 + 15399.1i 0.862019 + 0.240578i
254254 −20112.8 −0.311749
255255 −35304.1 + 48591.9i −0.542931 + 0.747281i
256256 1265.73 3895.53i 0.0193136 0.0594410i
257257 −23012.1 70823.9i −0.348409 1.07229i −0.959733 0.280913i 0.909363π-0.909363\pi
0.611324 0.791380i 0.290637π-0.290637\pi
258258 −93304.8 + 67789.9i −1.40173 + 1.01842i
259259 −18733.3 25784.1i −0.279264 0.384373i
260260 −15800.9 + 5134.02i −0.233741 + 0.0759470i
261261 222958. + 72443.3i 3.27296 + 1.06345i
262262 9775.36 + 7102.22i 0.142407 + 0.103464i
263263 29697.8i 0.429352i −0.976685 0.214676i 0.931130π-0.931130\pi
0.976685 0.214676i 0.0688696π-0.0688696\pi
264264 33978.9 26937.4i 0.487530 0.386499i
265265 36595.2 0.521113
266266 1061.60 1461.16i 0.0150036 0.0206507i
267267 −2902.65 + 8933.43i −0.0407166 + 0.125313i
268268 4908.68 + 15107.4i 0.0683432 + 0.210339i
269269 76848.3 55833.6i 1.06201 0.771597i 0.0875530 0.996160i 0.472095π-0.472095\pi
0.974460 + 0.224562i 0.0720953π0.0720953\pi
270270 26146.0 + 35986.8i 0.358655 + 0.493647i
271271 −27600.9 + 8968.09i −0.375825 + 0.122113i −0.490838 0.871251i 0.663309π-0.663309\pi
0.115013 + 0.993364i 0.463309π0.463309\pi
272272 −20647.0 6708.63i −0.279074 0.0906767i
273273 −188752. 137137.i −2.53260 1.84004i
274274 14880.3i 0.198203i
275275 8368.66 12598.9i 0.110660 0.166596i
276276 −59983.2 −0.787429
277277 −36853.9 + 50725.1i −0.480313 + 0.661094i −0.978565 0.205938i 0.933975π-0.933975\pi
0.498252 + 0.867032i 0.333975π0.333975\pi
278278 7338.74 22586.3i 0.0949580 0.292251i
279279 87062.3 + 267950.i 1.11846 + 3.44228i
280280 16232.0 11793.2i 0.207041 0.150424i
281281 11738.0 + 16156.0i 0.148656 + 0.204608i 0.876851 0.480763i 0.159640π-0.159640\pi
−0.728194 + 0.685371i 0.759640π0.759640\pi
282282 −97242.3 + 31595.9i −1.22280 + 0.397313i
283283 −56112.1 18231.9i −0.700622 0.227646i −0.0630203 0.998012i 0.520073π-0.520073\pi
−0.637601 + 0.770366i 0.720073π0.720073\pi
284284 13686.6 + 9943.89i 0.169691 + 0.123288i
285285 1425.63i 0.0175516i
286286 −2669.08 63515.2i −0.0326309 0.776507i
287287 239497. 2.90761
288288 −18068.8 + 24869.6i −0.217844 + 0.299836i
289289 −9747.56 + 29999.9i −0.116708 + 0.359190i
290290 13490.0 + 41517.9i 0.160404 + 0.493674i
291291 −1251.42 + 909.207i −0.0147780 + 0.0107368i
292292 −5070.73 6979.27i −0.0594710 0.0818548i
293293 −139410. + 45297.1i −1.62390 + 0.527636i −0.972857 0.231407i 0.925667π-0.925667\pi
−0.651041 + 0.759043i 0.725667π0.725667\pi
294294 165678. + 53832.2i 1.91678 + 0.622798i
295295 −6383.37 4637.79i −0.0733509 0.0532926i
296296 9092.97i 0.103782i
297297 −159523. + 59346.1i −1.80847 + 0.672790i
298298 46671.6 0.525557
299299 −51690.2 + 71145.5i −0.578184 + 0.795802i
300300 −4893.98 + 15062.1i −0.0543776 + 0.167357i
301301 −63099.8 194201.i −0.696458 2.14348i
302302 14767.6 10729.3i 0.161918 0.117640i
303303 −60959.5 83903.6i −0.663982 0.913893i
304304 −490.069 + 159.233i −0.00530286 + 0.00172300i
305305 −6121.15 1988.88i −0.0658012 0.0213801i
306306 131814. + 95768.2i 1.40772 + 1.02277i
307307 92349.8i 0.979849i 0.871765 + 0.489925i 0.162976π0.162976\pi
−0.871765 + 0.489925i 0.837024π0.837024\pi
308308 26768.3 + 71953.5i 0.282175 + 0.758491i
309309 237801. 2.49056
310310 −30837.6 + 42444.3i −0.320890 + 0.441668i
311311 −40126.6 + 123497.i −0.414870 + 1.27684i 0.497497 + 0.867465i 0.334252π0.334252\pi
−0.912367 + 0.409373i 0.865748π0.865748\pi
312312 20569.7 + 63307.0i 0.211309 + 0.650343i
313313 48991.0 35594.0i 0.500066 0.363319i −0.308976 0.951070i 0.599986π-0.599986\pi
0.809042 + 0.587751i 0.199986π0.199986\pi
314314 13388.5 + 18427.7i 0.135792 + 0.186901i
315315 −143209. + 46531.6i −1.44328 + 0.468950i
316316 −29612.3 9621.63i −0.296550 0.0963551i
317317 49792.9 + 36176.7i 0.495506 + 0.360006i 0.807298 0.590144i 0.200929π-0.200929\pi
−0.311792 + 0.950150i 0.600929π0.600929\pi
318318 146620.i 1.44991i
319319 −166891. + 7013.19i −1.64002 + 0.0689182i
320320 −5724.33 −0.0559017
321321 80151.8 110319.i 0.777863 1.07064i
322322 32817.9 101003.i 0.316519 0.974144i
323323 843.965 + 2597.46i 0.00808946 + 0.0248968i
324324 55156.5 40073.6i 0.525420 0.381740i
325325 13647.7 + 18784.4i 0.129209 + 0.177841i
326326 81341.9 26429.6i 0.765384 0.248688i
327327 −91217.4 29638.3i −0.853065 0.277178i
328328 −55280.0 40163.2i −0.513831 0.373320i
329329 181029.i 1.67246i
330330 −50477.9 33529.4i −0.463525 0.307892i
331331 161058. 1.47003 0.735013 0.678053i 0.237176π-0.237176\pi
0.735013 + 0.678053i 0.237176π0.237176\pi
332332 −42731.6 + 58814.9i −0.387679 + 0.533595i
333333 21088.2 64902.8i 0.190174 0.585295i
334334 −28513.9 87756.8i −0.255602 0.786662i
335335 17960.0 13048.7i 0.160035 0.116272i
336336 −47250.1 65034.2i −0.418528 0.576054i
337337 145390. 47240.1i 1.28019 0.415959i 0.411544 0.911390i 0.364990π-0.364990\pi
0.868648 + 0.495431i 0.164990π0.164990\pi
338338 15984.7 + 5193.75i 0.139917 + 0.0454619i
339339 −93646.4 68038.1i −0.814877 0.592043i
340340 30340.0i 0.262457i
341341 −124710. 157310.i −1.07249 1.35284i
342342 3867.25 0.0330636
343343 −69364.3 + 95471.8i −0.589587 + 0.811497i
344344 −18002.7 + 55406.7i −0.152132 + 0.468215i
345345 25904.6 + 79726.2i 0.217640 + 0.669827i
346346 −49161.4 + 35717.8i −0.410650 + 0.298355i
347347 77459.2 + 106613.i 0.643301 + 0.885427i 0.998786 0.0492544i 0.0156845π-0.0156845\pi
−0.355486 + 0.934682i 0.615685π0.615685\pi
348348 166344. 54048.3i 1.37356 0.446297i
349349 −85603.5 27814.3i −0.702814 0.228358i −0.0642580 0.997933i 0.520468π-0.520468\pi
−0.638556 + 0.769575i 0.720468π0.720468\pi
350350 −22684.9 16481.5i −0.185183 0.134543i
351351 261286.i 2.12081i
352352 5887.92 21097.1i 0.0475200 0.170270i
353353 −136929. −1.09887 −0.549436 0.835536i 0.685158π-0.685158\pi
−0.549436 + 0.835536i 0.685158π0.685158\pi
354354 −18581.5 + 25575.3i −0.148277 + 0.204086i
355355 7306.09 22485.8i 0.0579733 0.178424i
356356 1466.24 + 4512.61i 0.0115692 + 0.0356064i
357357 −344694. + 250435.i −2.70456 + 1.96498i
358358 −33483.0 46085.4i −0.261251 0.359581i
359359 182984. 59455.2i 1.41979 0.461319i 0.504257 0.863554i 0.331766π-0.331766\pi
0.915537 + 0.402235i 0.131766π0.131766\pi
360360 40858.5 + 13275.7i 0.315266 + 0.102436i
361361 −105379. 76562.7i −0.808615 0.587493i
362362 103537.i 0.790096i
363363 175494. 151550.i 1.33183 1.15011i
364364 −117854. −0.889491
365365 −7086.57 + 9753.82i −0.0531925 + 0.0732131i
366366 −7968.55 + 24524.7i −0.0594864 + 0.183080i
367367 −31877.4 98108.5i −0.236674 0.728407i −0.996895 0.0787429i 0.974909π-0.974909\pi
0.760221 0.649664i 0.225091π-0.225091\pi
368368 −24513.0 + 17809.8i −0.181010 + 0.131511i
369369 301426. + 414877.i 2.21374 + 3.04696i
370370 12085.9 3926.93i 0.0882823 0.0286847i
371371 246888. + 80218.6i 1.79371 + 0.582811i
372372 170055. + 123552.i 1.22886 + 0.892821i
373373 158342.i 1.13809i −0.822305 0.569047i 0.807312π-0.807312\pi
0.822305 0.569047i 0.192688π-0.192688\pi
374374 −111819. 31207.1i −0.799413 0.223105i
375375 22133.3 0.157392
376376 −30358.3 + 41784.6i −0.214734 + 0.295557i
377377 79239.6 243874.i 0.557519 1.71587i
378378 97507.4 + 300097.i 0.682424 + 2.10028i
379379 −82118.6 + 59662.6i −0.571693 + 0.415359i −0.835720 0.549156i 0.814949π-0.814949\pi
0.264027 + 0.964515i 0.414949π0.414949\pi
380380 423.287 + 582.604i 0.00293135 + 0.00403466i
381381 107106. 34800.9i 0.737843 0.239740i
382382 −83963.9 27281.5i −0.575395 0.186957i
383383 −121897. 88563.2i −0.830988 0.603748i 0.0888508 0.996045i 0.471681π-0.471681\pi
−0.919839 + 0.392297i 0.871681π0.871681\pi
384384 22934.8i 0.155537i
385385 84076.2 66653.0i 0.567220 0.449675i
386386 38900.6 0.261085
387387 256996. 353725.i 1.71595 2.36180i
388388 −241.455 + 743.122i −0.00160388 + 0.00493625i
389389 −27838.1 85676.7i −0.183967 0.566192i 0.815962 0.578105i 0.196208π-0.196208\pi
−0.999929 + 0.0119134i 0.996208π0.996208\pi
390390 75260.7 54680.1i 0.494810 0.359501i
391391 94395.1 + 129924.i 0.617442 + 0.849835i
392392 83690.4 27192.7i 0.544632 0.176962i
393393 −64345.3 20907.1i −0.416612 0.135365i
394394 −15569.9 11312.2i −0.100298 0.0728710i
395395 43514.2i 0.278893i
396396 −90954.1 + 136930.i −0.580005 + 0.873186i
397397 −267884. −1.69968 −0.849839 0.527043i 0.823301π-0.823301\pi
−0.849839 + 0.527043i 0.823301π0.823301\pi
398398 −70869.0 + 97542.8i −0.447394 + 0.615785i
399399 −3125.06 + 9617.94i −0.0196296 + 0.0604138i
400400 2472.14 + 7608.45i 0.0154508 + 0.0475528i
401401 180960. 131475.i 1.12537 0.817627i 0.140353 0.990102i 0.455176π-0.455176\pi
0.985014 + 0.172475i 0.0551763π0.0551763\pi
402402 −52280.1 71957.4i −0.323507 0.445270i
403403 293088. 95230.1i 1.80463 0.586359i
404404 −49824.0 16188.8i −0.305264 0.0991864i
405405 −77083.6 56004.5i −0.469950 0.341439i
406406 309670.i 1.87865i
407407 2041.54 + 48581.7i 0.0123245 + 0.293281i
408408 121559. 0.730241
409409 21795.0 29998.3i 0.130290 0.179329i −0.738888 0.673828i 0.764649π-0.764649\pi
0.869178 + 0.494500i 0.164649π0.164649\pi
410410 −29509.2 + 90820.0i −0.175546 + 0.540274i
411411 −25747.1 79241.6i −0.152421 0.469104i
412412 97180.9 70606.0i 0.572514 0.415956i
413413 −32898.8 45281.3i −0.192877 0.265472i
414414 216270. 70270.5i 1.26182 0.409989i
415415 96627.6 + 31396.2i 0.561055 + 0.182298i
416416 27202.8 + 19764.0i 0.157190 + 0.114206i
417417 132976.i 0.764719i
418418 −2582.58 + 960.777i −0.0147809 + 0.00549883i
419419 −254975. −1.45234 −0.726171 0.687514i 0.758702π-0.758702\pi
−0.726171 + 0.687514i 0.758702π0.758702\pi
420420 −66034.1 + 90888.1i −0.374343 + 0.515239i
421421 −105341. + 324206.i −0.594337 + 1.82918i −0.0363359 + 0.999340i 0.511569π0.511569\pi
−0.558001 + 0.829840i 0.688431π0.688431\pi
422422 51234.0 + 157682.i 0.287696 + 0.885436i
423423 313594. 227839.i 1.75262 1.27335i
424424 −43533.4 59918.5i −0.242153 0.333296i
425425 40326.2 13102.8i 0.223259 0.0725414i
426426 −90090.5 29272.2i −0.496432 0.161301i
427427 −36936.3 26835.8i −0.202581 0.147183i
428428 68881.7i 0.376025i
429429 124113. + 333617.i 0.674376 + 1.81273i
430430 81418.2 0.440336
431431 51918.6 71459.8i 0.279491 0.384687i −0.646074 0.763275i 0.723590π-0.723590\pi
0.925565 + 0.378588i 0.123590π0.123590\pi
432432 27819.4 85619.4i 0.149067 0.458780i
433433 87917.2 + 270581.i 0.468920 + 1.44319i 0.853985 + 0.520297i 0.174179π0.174179\pi
−0.385066 + 0.922889i 0.625821π0.625821\pi
434434 −301084. + 218751.i −1.59849 + 1.16137i
435435 −143676. 197753.i −0.759285 1.04507i
436436 −46077.3 + 14971.4i −0.242390 + 0.0787572i
437437 3625.24 + 1177.91i 0.0189834 + 0.00616808i
438438 39079.1 + 28392.7i 0.203703 + 0.147999i
439439 145989.i 0.757517i 0.925496 + 0.378758i 0.123649π0.123649\pi
−0.925496 + 0.378758i 0.876351π0.876351\pi
440440 −30583.9 + 1285.22i −0.157974 + 0.00663851i
441441 −660420. −3.39581
442442 104753. 144180.i 0.536192 0.738005i
443443 1141.72 3513.84i 0.00581769 0.0179050i −0.948106 0.317956i 0.897004π-0.897004\pi
0.953923 + 0.300051i 0.0970036π0.0970036\pi
444444 −15733.4 48422.5i −0.0798100 0.245630i
445445 5364.69 3897.67i 0.0270910 0.0196827i
446446 −30657.0 42195.7i −0.154120 0.212128i
447447 −248539. + 80755.2i −1.24388 + 0.404162i
448448 −38619.0 12548.1i −0.192417 0.0625202i
449449 −134699. 97864.7i −0.668147 0.485437i 0.201257 0.979538i 0.435497π-0.435497\pi
−0.869404 + 0.494101i 0.835497π0.835497\pi
450450 60040.1i 0.296494i
451451 −304366. 202172.i −1.49638 0.993958i
452452 −58471.4 −0.286198
453453 −60076.6 + 82688.3i −0.292758 + 0.402947i
454454 −5612.20 + 17272.6i −0.0272284 + 0.0838003i
455455 50897.0 + 156645.i 0.245849 + 0.756646i
456456 2334.23 1695.92i 0.0112257 0.00815596i
457457 90738.0 + 124890.i 0.434467 + 0.597992i 0.968971 0.247173i 0.0795017π-0.0795017\pi
−0.534504 + 0.845166i 0.679502π0.679502\pi
458458 −272909. + 88673.4i −1.30103 + 0.422729i
459459 −453799. 147448.i −2.15396 0.699865i
460460 34258.0 + 24889.9i 0.161900 + 0.117627i
461461 53007.3i 0.249421i 0.992193 + 0.124711i 0.0398003π0.0398003\pi
−0.992193 + 0.124711i 0.960200π0.960200\pi
462462 −267048. 336855.i −1.25114 1.57819i
463463 176639. 0.823995 0.411998 0.911185i 0.364831π-0.364831\pi
0.411998 + 0.911185i 0.364831π0.364831\pi
464464 51931.2 71477.1i 0.241208 0.331995i
465465 90777.7 279385.i 0.419830 1.29210i
466466 −52106.0 160366.i −0.239947 0.738481i
467467 174511. 126789.i 0.800181 0.581366i −0.110786 0.993844i 0.535337π-0.535337\pi
0.910967 + 0.412479i 0.135337π0.135337\pi
468468 −148329. 204157.i −0.677226 0.932121i
469469 149769. 48663.0i 0.680891 0.221235i
470470 68648.3 + 22305.2i 0.310767 + 0.100974i
471471 −103183. 74966.6i −0.465120 0.337929i
472472 15968.8i 0.0716784i
473473 −83744.9 + 300068.i −0.374314 + 1.34121i
474474 174342. 0.775970
475475 591.561 814.214i 0.00262188 0.00360871i
476476 −66507.1 + 204688.i −0.293531 + 0.903395i
477477 171766. + 528641.i 0.754919 + 2.32340i
478478 238634. 173378.i 1.04442 0.758819i
479479 193242. + 265975.i 0.842231 + 1.15923i 0.985522 + 0.169550i 0.0542315π0.0542315\pi
−0.143291 + 0.989681i 0.545768π0.545768\pi
480480 30483.6 9904.73i 0.132307 0.0429893i
481481 −70991.7 23066.6i −0.306844 0.0996996i
482482 117369. + 85273.7i 0.505196 + 0.367047i
483483 594653.i 2.54900i
484484 26721.2 114039.i 0.114068 0.486815i
485485 1091.99 0.00464232
486486 −34960.8 + 48119.4i −0.148016 + 0.203727i
487487 −69972.0 + 215352.i −0.295030 + 0.908010i 0.688181 + 0.725539i 0.258409π0.258409\pi
−0.983211 + 0.182471i 0.941591π0.941591\pi
488488 4025.22 + 12388.3i 0.0169025 + 0.0520204i
489489 −387437. + 281489.i −1.62025 + 1.17718i
490490 −72285.8 99492.9i −0.301065 0.414381i
491491 −274974. + 89344.6i −1.14059 + 0.370600i −0.817591 0.575799i 0.804691π-0.804691\pi
−0.322999 + 0.946399i 0.604691π0.604691\pi
492492 363875. + 118230.i 1.50322 + 0.488425i
493493 −378842. 275245.i −1.55871 1.13247i
494494 4230.06i 0.0173337i
495495 221279. + 61755.9i 0.903086 + 0.252039i
496496 106180. 0.431597
497497 98580.4 135684.i 0.399096 0.549309i
498498 125790. 387143.i 0.507211 1.56104i
499499 −18146.5 55849.2i −0.0728773 0.224293i 0.907983 0.419008i 0.137622π-0.137622\pi
−0.980860 + 0.194714i 0.937622π0.937622\pi
500500 9045.08 6571.64i 0.0361803 0.0262866i
501501 303689. + 417991.i 1.20991 + 1.66530i
502502 −184404. + 59916.3i −0.731748 + 0.237759i
503503 −241937. 78610.2i −0.956240 0.310701i −0.210991 0.977488i 0.567669π-0.567669\pi
−0.745248 + 0.666787i 0.767669π0.767669\pi
504504 246549. + 179128.i 0.970604 + 0.705185i
505505 73214.6i 0.287088i
506506 −126969. + 100657.i −0.495904 + 0.393137i
507507 −94109.5 −0.366115
508508 33437.7 46023.0i 0.129571 0.178340i
509509 138608. 426592.i 0.534999 1.64656i −0.208652 0.977990i 0.566908π-0.566908\pi
0.743651 0.668568i 0.233092π-0.233092\pi
510510 −52496.9 161569.i −0.201834 0.621180i
511511 −69190.1 + 50269.6i −0.264973 + 0.192514i
512512 6809.63 + 9372.65i 0.0259767 + 0.0357538i
513513 −10771.2 + 3499.77i −0.0409288 + 0.0132986i
514514 200320. + 65088.0i 0.758226 + 0.246363i
515515 −135814. 98674.9i −0.512072 0.372042i
516516 326206.i 1.22516i
517517 −152816. + 230062.i −0.571727 + 0.860723i
518518 90144.7 0.335955
519519 199995. 275270.i 0.742481 1.02194i
520520 14521.2 44691.7i 0.0537027 0.165280i
521521 −26747.6 82320.5i −0.0985391 0.303272i 0.889621 0.456700i 0.150969π-0.150969\pi
−0.988160 + 0.153428i 0.950969π0.950969\pi
522522 −536437. + 389744.i −1.96869 + 1.43034i
523523 174188. + 239749.i 0.636817 + 0.876503i 0.998441 0.0558208i 0.0177776π-0.0177776\pi
−0.361624 + 0.932324i 0.617778π0.617778\pi
524524 −32503.2 + 10560.9i −0.118376 + 0.0384627i
525525 149321. + 48517.3i 0.541754 + 0.176027i
526526 67956.0 + 49372.9i 0.245616 + 0.178450i
527527 562772.i 2.02634i
528528 5149.28 + 122536.i 0.0184705 + 0.439536i
529529 −55701.2 −0.199046
530530 −60839.7 + 83738.7i −0.216589 + 0.298109i
531531 37034.4 113980.i 0.131346 0.404241i
532532 1578.58 + 4858.38i 0.00557756 + 0.0171660i
533533 453798. 329704.i 1.59738 1.16057i
534534 −15616.2 21493.9i −0.0547637 0.0753758i
535535 −91553.6 + 29747.6i −0.319866 + 0.103931i
536536 −42730.1 13883.8i −0.148732 0.0483259i
537537 258047. + 187482.i 0.894849 + 0.650146i
538538 268672.i 0.928233i
539539 441034. 164074.i 1.51808 0.564759i
540540 −125815. −0.431463
541541 112033. 154200.i 0.382781 0.526853i −0.573537 0.819179i 0.694429π-0.694429\pi
0.956319 + 0.292326i 0.0944293π0.0944293\pi
542542 25365.6 78067.3i 0.0863468 0.265748i
543543 179149. + 551364.i 0.607596 + 1.86999i
544544 49676.8 36092.3i 0.167863 0.121960i
545545 39798.3 + 54777.7i 0.133990 + 0.184421i
546546 627604. 203921.i 2.10524 0.684032i
547547 450105. + 146248.i 1.50432 + 0.488782i 0.941273 0.337645i 0.109630π-0.109630\pi
0.563043 + 0.826427i 0.309630π0.309630\pi
548548 −34049.8 24738.6i −0.113384 0.0823785i
549549 97759.3i 0.324350i
550550 14916.3 + 40095.2i 0.0493101 + 0.132546i
551551 −11114.8 −0.0366098
552552 99722.6 137256.i 0.327277 0.450458i
553553 −95385.6 + 293567.i −0.311912 + 0.959968i
554554 −54801.5 168662.i −0.178555 0.549537i
555555 −57565.7 + 41823.9i −0.186886 + 0.135781i
556556 39482.3 + 54342.7i 0.127718 + 0.175789i
557557 283002. 91952.9i 0.912177 0.296384i 0.184923 0.982753i 0.440796π-0.440796\pi
0.727254 + 0.686369i 0.240796π0.240796\pi
558558 −757878. 246249.i −2.43406 0.790873i
559559 −386909. 281106.i −1.23818 0.899594i
560560 56749.1i 0.180960i
561561 649462. 27292.1i 2.06361 0.0867185i
562562 −56483.6 −0.178834
563563 −167187. + 230113.i −0.527455 + 0.725980i −0.986740 0.162309i 0.948106π-0.948106\pi
0.459285 + 0.888289i 0.348106π0.348106\pi
564564 89366.8 275043.i 0.280943 0.864653i
565565 25251.7 + 77716.8i 0.0791032 + 0.243455i
566566 135006. 98087.5i 0.421425 0.306183i
567567 −397276. 546803.i −1.23574 1.70085i
568568 −45508.1 + 14786.5i −0.141056 + 0.0458319i
569569 −56742.4 18436.7i −0.175260 0.0569455i 0.220072 0.975484i 0.429371π-0.429371\pi
−0.395333 + 0.918538i 0.629371π0.629371\pi
570570 −3262.19 2370.12i −0.0100406 0.00729492i
571571 445717.i 1.36706i 0.729923 + 0.683529i 0.239556π0.239556\pi
−0.729923 + 0.683529i 0.760444π0.760444\pi
572572 149776. + 99487.0i 0.457772 + 0.304070i
573573 494335. 1.50561
574574 −398165. + 548027.i −1.20848 + 1.66333i
575575 18287.4 56282.8i 0.0553116 0.170232i
576576 −26868.2 82691.8i −0.0809830 0.249240i
577577 −107665. + 78223.6i −0.323389 + 0.234956i −0.737620 0.675216i 0.764050π-0.764050\pi
0.414231 + 0.910172i 0.364050π0.364050\pi
578578 −52441.8 72179.9i −0.156972 0.216053i
579579 −207156. + 67309.2i −0.617933 + 0.200779i
580580 −117430. 38155.5i −0.349080 0.113423i
581581 583072. + 423626.i 1.72731 + 1.25496i
582582 4375.11i 0.0129165i
583583 −246042. 310358.i −0.723889 0.913114i
584584 24400.4 0.0715437
585585 −207296. + 285318.i −0.605729 + 0.833715i
586586 128119. 394311.i 0.373095 1.14827i
587587 −137518. 423238.i −0.399102 1.22831i −0.925720 0.378208i 0.876540π-0.876540\pi
0.526618 0.850102i 0.323460π-0.323460\pi
588588 −398623. + 289616.i −1.15294 + 0.837661i
589589 −7851.48 10806.6i −0.0226319 0.0311501i
590590 21224.8 6896.35i 0.0609733 0.0198114i
591591 102487. + 33300.1i 0.293423 + 0.0953391i
592592 −20807.0 15117.1i −0.0593697 0.0431346i
593593 511499.i 1.45457i 0.686334 + 0.727286i 0.259219π0.259219\pi
−0.686334 + 0.727286i 0.740781π0.740781\pi
594594 129410. 463692.i 0.366771 1.31418i
595595 300781. 0.849604
596596 −77591.9 + 106796.i −0.218436 + 0.300651i
597597 208620. 642065.i 0.585338 1.80148i
598598 −76863.0 236560.i −0.214939 0.661513i
599599 487583. 354250.i 1.35892 0.987315i 0.360410 0.932794i 0.382637π-0.382637\pi
0.998513 0.0545208i 0.0173631π-0.0173631\pi
600600 −26329.6 36239.6i −0.0731377 0.100665i
601601 −454526. + 147685.i −1.25837 + 0.408871i −0.860915 0.508749i 0.830108π-0.830108\pi
−0.397460 + 0.917620i 0.630108π0.630108\pi
602602 549284. + 178473.i 1.51567 + 0.492470i
603603 272795. + 198197.i 0.750243 + 0.545083i
604604 51629.3i 0.141522i
605605 −163114. + 13733.2i −0.445637 + 0.0375200i
606606 293338. 0.798772
607607 80389.5 110647.i 0.218183 0.300304i −0.685869 0.727725i 0.740578π-0.740578\pi
0.904053 + 0.427421i 0.140578π0.140578\pi
608608 450.379 1386.13i 0.00121835 0.00374969i
609609 −535817. 1.64907e6i −1.44471 4.44637i
610610 14727.5 10700.2i 0.0395795 0.0287562i
611611 −249214. 343014.i −0.667560 0.918817i
612612 −438282. + 142407.i −1.17018 + 0.380213i
613613 110540. + 35916.6i 0.294170 + 0.0955815i 0.452384 0.891823i 0.350574π-0.350574\pi
−0.158214 + 0.987405i 0.550574π0.550574\pi
614614 −211319. 153532.i −0.560534 0.407252i
615615 534700.i 1.41371i
616616 −209150. 58370.9i −0.551183 0.153828i
617617 −626094. −1.64463 −0.822317 0.569030i 0.807319π-0.807319\pi
−0.822317 + 0.569030i 0.807319π0.807319\pi
618618 −395346. + 544147.i −1.03514 + 1.42475i
619619 −7784.19 + 23957.3i −0.0203157 + 0.0625253i −0.960700 0.277587i 0.910465π-0.910465\pi
0.940385 + 0.340113i 0.110465π0.110465\pi
620620 −45855.2 141128.i −0.119290 0.367138i
621621 −538770. + 391439.i −1.39708 + 1.01504i
622622 −215881. 297134.i −0.557999 0.768019i
623623 44736.5 14535.8i 0.115262 0.0374509i
624624 −179059. 58179.9i −0.459862 0.149418i
625625 −12640.9 9184.14i −0.0323607 0.0235114i
626626 171279.i 0.437074i
627627 12090.5 9585.00i 0.0307546 0.0243813i
628628 −64425.7 −0.163358
629629 −80123.7 + 110281.i −0.202516 + 0.278739i
630630 131611. 405058.i 0.331598 1.02055i
631631 160364. + 493548.i 0.402760 + 1.23957i 0.922751 + 0.385397i 0.125936π0.125936\pi
−0.519990 + 0.854172i 0.674064π0.674064\pi
632632 71247.4 51764.3i 0.178375 0.129597i
633633 −545669. 751049.i −1.36183 1.87439i
634634 −165562. + 53794.4i −0.411891 + 0.133832i
635635 −75611.6 24567.7i −0.187517 0.0609280i
636636 335503. + 243757.i 0.829435 + 0.602620i
637637 722378.i 1.78027i
638638 261409. 393546.i 0.642213 0.966839i
639639 359115. 0.879492
640640 9516.75 13098.7i 0.0232343 0.0319792i
641641 −147680. + 454514.i −0.359424 + 1.10619i 0.593976 + 0.804483i 0.297557π0.297557\pi
−0.953400 + 0.301710i 0.902443π0.902443\pi
642642 119185. + 366814.i 0.289169 + 0.889970i
643643 −386078. + 280502.i −0.933798 + 0.678444i −0.946920 0.321470i 0.895823π-0.895823\pi
0.0131219 + 0.999914i 0.495823π0.495823\pi
644644 176560. + 243014.i 0.425717 + 0.585949i
645645 −433574. + 140877.i −1.04218 + 0.338625i
646646 −7346.72 2387.09i −0.0176047 0.00572011i
647647 286054. + 207831.i 0.683345 + 0.496479i 0.874466 0.485087i 0.161212π-0.161212\pi
−0.191121 + 0.981567i 0.561212π0.561212\pi
648648 192834.i 0.459234i
649649 3585.28 + 85317.7i 0.00851204 + 0.202558i
650650 −65672.8 −0.155438
651651 1.22485e6 1.68587e6i 2.89016 3.97797i
652652 −74754.2 + 230070.i −0.175849 + 0.541208i
653653 −69709.4 214544.i −0.163480 0.503140i 0.835441 0.549580i 0.185212π-0.185212\pi
−0.998921 + 0.0464400i 0.985212π0.985212\pi
654654 219469. 159454.i 0.513119 0.372803i
655655 28074.0 + 38640.5i 0.0654367 + 0.0900659i
656656 183807. 59722.4i 0.427124 0.138781i
657657 −174163. 56588.8i −0.403482 0.131099i
658658 414238. + 300962.i 0.956750 + 0.695120i
659659 524030.i 1.20666i 0.797491 + 0.603331i 0.206160π0.206160\pi
−0.797491 + 0.603331i 0.793840π0.793840\pi
660660 160643. 59762.9i 0.368787 0.137197i
661661 −322127. −0.737265 −0.368633 0.929575i 0.620174π-0.620174\pi
−0.368633 + 0.929575i 0.620174π0.620174\pi
662662 −267759. + 368539.i −0.610983 + 0.840945i
663663 −308364. + 949047.i −0.701515 + 2.15904i
664664 −63541.5 195561.i −0.144119 0.443553i
665665 5775.74 4196.32i 0.0130606 0.00948912i
666666 113454. + 156156.i 0.255783 + 0.352056i
667667 −621578. + 201963.i −1.39715 + 0.453962i
668668 248214. + 80649.5i 0.556254 + 0.180738i
669669 236267. + 171658.i 0.527899 + 0.383541i
670670 62790.3i 0.139876i
671671 24287.3 + 65284.5i 0.0539428 + 0.144999i
672672 227368. 0.503490
673673 −75463.9 + 103867.i −0.166613 + 0.229323i −0.884157 0.467190i 0.845266π-0.845266\pi
0.717544 + 0.696513i 0.245266π0.245266\pi
674674 −133615. + 411225.i −0.294128 + 0.905232i
675675 54334.8 + 167225.i 0.119253 + 0.367024i
676676 −38459.3 + 27942.3i −0.0841603 + 0.0611461i
677677 −52364.9 72074.1i −0.114252 0.157254i 0.748061 0.663630i 0.230985π-0.230985\pi
−0.862313 + 0.506376i 0.830985π0.830985\pi
678678 311376. 101172.i 0.677369 0.220091i
679679 7367.06 + 2393.70i 0.0159792 + 0.00519196i
680680 −69425.5 50440.6i −0.150142 0.109084i
681681 101692.i 0.219276i
682682 567295. 23839.2i 1.21966 0.0512535i
683683 535111. 1.14710 0.573552 0.819169i 0.305565π-0.305565\pi
0.573552 + 0.819169i 0.305565π0.305565\pi
684684 −6429.34 + 8849.22i −0.0137421 + 0.0189144i
685685 −18176.2 + 55940.7i −0.0387367 + 0.119219i
686686 −103144. 317445.i −0.219178 0.674560i
687687 1.29988e6 944419.i 2.75417 2.00102i
688688 −96854.5 133309.i −0.204618 0.281632i
689689 578236. 187880.i 1.21805 0.395770i
690690 −225500. 73269.3i −0.473639 0.153895i
691691 145982. + 106062.i 0.305733 + 0.222128i 0.730063 0.683380i 0.239491π-0.239491\pi
−0.424331 + 0.905507i 0.639491π0.639491\pi
692692 171874.i 0.358921i
693693 1.35747e6 + 901688.i 2.82660 + 1.87754i
694694 −372734. −0.773892
695695 55178.2 75946.3i 0.114235 0.157231i
696696 −152872. + 470491.i −0.315579 + 0.971253i
697697 −316540. 974210.i −0.651573 2.00534i
698698 205962. 149640.i 0.422743 0.307141i
699699 554956. + 763832.i 1.13581 + 1.56330i
700700 75427.6 24507.9i 0.153934 0.0500162i
701701 −320482. 104131.i −0.652181 0.211907i −0.0358055 0.999359i 0.511400π-0.511400\pi
−0.616376 + 0.787452i 0.711400π0.711400\pi
702702 597887. + 434390.i 1.21323 + 0.881466i
703703 3235.50i 0.00654683i
704704 38486.7 + 48547.1i 0.0776543 + 0.0979531i
705705 −404165. −0.813169
706706 227646. 313328.i 0.456721 0.628623i
707707 −160490. + 493939.i −0.321078 + 0.988176i
708708 −27630.6 85038.1i −0.0551218 0.169647i
709709 574225. 417199.i 1.14232 0.829948i 0.154883 0.987933i 0.450500π-0.450500\pi
0.987441 + 0.157985i 0.0504998π0.0504998\pi
710710 39306.7 + 54101.0i 0.0779739 + 0.107322i
711711 −628592. + 204242.i −1.24345 + 0.404023i
712712 −12763.6 4147.14i −0.0251775 0.00818067i
713713 −635446. 461679.i −1.24997 0.908156i
714714 1.20509e6i 2.36387i
715715 67549.5 242038.i 0.132133 0.473447i
716716 161120. 0.314285
717717 −970798. + 1.33619e6i −1.88839 + 2.59914i
718718 −168165. + 517558.i −0.326202 + 1.00395i
719719 9151.06 + 28164.1i 0.0177016 + 0.0544800i 0.959517 0.281650i 0.0908818π-0.0908818\pi
−0.941816 + 0.336130i 0.890882π0.890882\pi
720720 −98305.7 + 71423.3i −0.189633 + 0.137776i
721721 −699965. 963419.i −1.34650 1.85329i
722722 350388. 113848.i 0.672164 0.218399i
723723 −772571. 251023.i −1.47796 0.480217i
724724 236919. + 172132.i 0.451984 + 0.328385i
725725 172560.i 0.328294i
726726 55022.9 + 653525.i 0.104393 + 1.23991i
727727 −200557. −0.379463 −0.189732 0.981836i 0.560762π-0.560762\pi
−0.189732 + 0.981836i 0.560762π0.560762\pi
728728 195933. 269679.i 0.369696 0.508844i
729729 −110397. + 339768.i −0.207732 + 0.639334i
730730 −10537.7 32431.6i −0.0197742 0.0608587i
731731 −706562. + 513347.i −1.32226 + 0.960675i
732732 −42870.7 59006.5i −0.0800090 0.110123i
733733 89057.4 28936.5i 0.165753 0.0538565i −0.224965 0.974367i 0.572227π-0.572227\pi
0.390718 + 0.920510i 0.372227π0.372227\pi
734734 277493. + 90162.8i 0.515062 + 0.167354i
735735 557092. + 404751.i 1.03122 + 0.749227i
736736 85700.7i 0.158208i
737737 −231415. 64584.7i −0.426045 0.118903i
738738 −1.45046e6 −2.66314
739739 −150274. + 206835.i −0.275167 + 0.378735i −0.924126 0.382089i 0.875205π-0.875205\pi
0.648959 + 0.760824i 0.275205π0.275205\pi
740740 −11107.0 + 34183.9i −0.0202831 + 0.0624250i
741741 7319.20 + 22526.2i 0.0133299 + 0.0410253i
742742 −594012. + 431575.i −1.07892 + 0.783878i
743743 −390015. 536809.i −0.706486 0.972394i −0.999866 0.0163980i 0.994780π-0.994780\pi
0.293380 0.955996i 0.405220π-0.405220\pi
744744 −565435. + 183721.i −1.02150 + 0.331905i
745745 175456. + 57009.2i 0.316123 + 0.102715i
746746 362325. + 263245.i 0.651060 + 0.473023i
747747 1.54321e6i 2.76557i
748748 257309. 203987.i 0.459888 0.364585i
749749 −682870. −1.21724
750750 −36796.7 + 50646.3i −0.0654164 + 0.0900379i
751751 145739. 448538.i 0.258402 0.795279i −0.734739 0.678350i 0.762695π-0.762695\pi
0.993140 0.116928i 0.0373048π-0.0373048\pi
752752 −45142.5 138934.i −0.0798271 0.245682i
753753 878326. 638141.i 1.54905 1.12545i
754754 426308. + 586763.i 0.749861 + 1.03210i
755755 68622.7 22296.9i 0.120385 0.0391156i
756756 −848802. 275793.i −1.48512 0.482546i
757757 −296813. 215647.i −0.517954 0.376315i 0.297879 0.954604i 0.403721π-0.403721\pi
−0.815833 + 0.578288i 0.803721π0.803721\pi
758758 287097.i 0.499678i
759759 501979. 755720.i 0.871369 1.31183i
760760 −2036.86 −0.00352642
761761 −598122. + 823245.i −1.03281 + 1.42154i −0.129995 + 0.991515i 0.541496π0.541496\pi
−0.902816 + 0.430027i 0.858504π0.858504\pi
762762 −98431.7 + 302942.i −0.169522 + 0.521734i
763763 148422. + 456795.i 0.254946 + 0.784644i
764764 202017. 146774.i 0.346100 0.251457i
765765 378557. + 521039.i 0.646857 + 0.890322i
766766 405309. 131693.i 0.690762 0.224442i
767767 −124673. 40508.8i −0.211925 0.0688587i
768768 −52480.5 38129.3i −0.0889765 0.0646452i
769769 1.10968e6i 1.87648i −0.345983 0.938241i 0.612454π-0.612454\pi
0.345983 0.938241i 0.387546π-0.387546\pi
770770 12741.2 + 303198.i 0.0214896 + 0.511381i
771771 −1.17938e6 −1.98402
772772 −64672.6 + 89014.2i −0.108514 + 0.149357i
773773 109830. 338023.i 0.183807 0.565701i −0.816118 0.577885i 0.803878π-0.803878\pi
0.999926 + 0.0121836i 0.00387827π0.00387827\pi
774774 382151. + 1.17614e6i 0.637901 + 1.96326i
775775 −167776. + 121896.i −0.279335 + 0.202949i
776776 −1299.03 1787.95i −0.00215722 0.00296916i
777777 −480045. + 155976.i −0.795133 + 0.258354i
778778 242330. + 78737.9i 0.400358 + 0.130084i
779779 −19670.0 14291.1i −0.0324137 0.0235500i
780780 263121.i 0.432480i
781781 −239820. + 89218.3i −0.393173 + 0.146269i
782782 −454230. −0.742783
783783 1.14139e6 1.57099e6i 1.86170 2.56242i
784784 −76912.4 + 236712.i −0.125131 + 0.385113i
785785 27823.2 + 85630.9i 0.0451510 + 0.138960i
786786 154815. 112480.i 0.250592 0.182066i
787787 70476.9 + 97003.1i 0.113788 + 0.156616i 0.862112 0.506717i 0.169141π-0.169141\pi
−0.748324 + 0.663333i 0.769141π0.769141\pi
788788 51770.2 16821.1i 0.0833733 0.0270896i
789789 −447313. 145341.i −0.718551 0.233471i
790790 −99571.3 72342.8i −0.159544 0.115915i
791791 579666.i 0.926456i
792792 −162117. 435772.i −0.258450 0.694718i
793793 −106931. −0.170042
794794 445360. 612985.i 0.706432 0.972320i
795795 179096. 551201.i 0.283369 0.872119i
796796 −105382. 324331.i −0.166318 0.511874i
797797 743265. 540014.i 1.17011 0.850135i 0.179089 0.983833i 0.442685π-0.442685\pi
0.991022 + 0.133698i 0.0426851π0.0426851\pi
798798 −16812.8 23140.8i −0.0264018 0.0363390i
799799 −736379. + 239264.i −1.15347 + 0.374786i
800800 −21520.0 6992.26i −0.0336249 0.0109254i
801801 81484.6 + 59202.0i 0.127002 + 0.0922724i
802802 632660.i 0.983607i
803803 130366. 5478.33i 0.202178 0.00849605i
804804 251572. 0.389180
805805 246750. 339622.i 0.380773 0.524088i
806806 −269351. + 828978.i −0.414619 + 1.27607i
807807 −464878. 1.43075e6i −0.713826 2.19693i
808808 119877. 87095.6i 0.183617 0.133405i
809809 −236470. 325474.i −0.361310 0.497300i 0.589203 0.807985i 0.299442π-0.299442\pi
−0.950513 + 0.310684i 0.899442π0.899442\pi
810810 256304. 83278.3i 0.390648 0.126929i
811811 −10379.5 3372.50i −0.0157810 0.00512755i 0.301116 0.953588i 0.402641π-0.402641\pi
−0.316897 + 0.948460i 0.602641π0.602641\pi
812812 −708600. 514828.i −1.07471 0.780819i
813813 459619.i 0.695371i
814814 −114561. 76096.0i −0.172897 0.114845i
815815 338079. 0.508982
816816 −202092. + 278156.i −0.303508 + 0.417743i
817817 −6405.82 + 19715.1i −0.00959689 + 0.0295362i
818818 32409.1 + 99744.8i 0.0484351 + 0.149068i
819819 −2.02394e6 + 1.47048e6i −3.01738 + 2.19226i
820820 −158759. 218513.i −0.236108 0.324975i
821821 115263. 37451.3i 0.171004 0.0555624i −0.222264 0.974987i 0.571345π-0.571345\pi
0.393267 + 0.919424i 0.371345π0.371345\pi
822822 224129. + 72823.9i 0.331707 + 0.107778i
823823 523952. + 380674.i 0.773557 + 0.562022i 0.903038 0.429560i 0.141331π-0.141331\pi
−0.129482 + 0.991582i 0.541331π0.541331\pi
824824 339757.i 0.500396i
825825 −148810. 187708.i −0.218637 0.275788i
826826 158309. 0.232031
827827 31437.7 43270.3i 0.0459663 0.0632672i −0.785415 0.618969i 0.787550π-0.787550\pi
0.831381 + 0.555702i 0.187550π0.187550\pi
828828 −198755. + 611705.i −0.289906 + 0.892239i
829829 13213.4 + 40666.8i 0.0192268 + 0.0591740i 0.960210 0.279280i 0.0900959π-0.0900959\pi
−0.940983 + 0.338454i 0.890096π0.890096\pi
830830 −232486. + 168911.i −0.337475 + 0.245190i
831831 583665. + 803347.i 0.845205 + 1.16332i
832832 −90449.6 + 29388.8i −0.130665 + 0.0424557i
833833 1.25462e6 + 407650.i 1.80810 + 0.587486i
834834 −304282. 221074.i −0.437466 0.317838i
835835 364741.i 0.523132i
836836 2095.07 7506.88i 0.00299768 0.0107411i
837837 2.33371e6 3.33117
838838 423897. 583444.i 0.603632 0.830829i
839839 114652. 352863.i 0.162876 0.501282i −0.835997 0.548734i 0.815110π-0.815110\pi
0.998874 + 0.0474520i 0.0151101π0.0151101\pi
840840 −98192.1 302204.i −0.139161 0.428294i
841841 969557. 704425.i 1.37082 0.995962i
842842 −566732. 780040.i −0.799381 1.10025i
843843 300790. 97732.7i 0.423261 0.137526i
844844 −445992. 144912.i −0.626098 0.203431i
845845 53748.4 + 39050.5i 0.0752753 + 0.0546907i
846846 1.09636e6i 1.53184i
847847 −1.13055e6 264905.i −1.57587 0.369252i
848848 209483. 0.291311
849849 −549223. + 755941.i −0.761963 + 1.04875i
850850 −37060.3 + 114060.i −0.0512945 + 0.157868i
851851 58791.3 + 180941.i 0.0811809 + 0.249849i
852852 216758. 157484.i 0.298604 0.216949i
853853 520557. + 716485.i 0.715434 + 0.984711i 0.999663 + 0.0259545i 0.00826250π0.00826250\pi
−0.284229 + 0.958757i 0.591737π0.591737\pi
854854 122814. 39904.7i 0.168396 0.0547152i
855855 14538.5 + 4723.84i 0.0198878 + 0.00646193i
856856 157618. + 114516.i 0.215109 + 0.156286i
857857 534294.i 0.727476i −0.931501 0.363738i 0.881500π-0.881500\pi
0.931501 0.363738i 0.118500π-0.118500\pi
858858 −969736. 270640.i −1.31728 0.367636i
859859 724471. 0.981827 0.490914 0.871208i 0.336663π-0.336663\pi
0.490914 + 0.871208i 0.336663π0.336663\pi
860860 −135358. + 186305.i −0.183016 + 0.251899i
861861 1.17209e6 3.60733e6i 1.58109 4.86608i
862862 77202.5 + 237605.i 0.103900 + 0.319772i
863863 −201547. + 146432.i −0.270616 + 0.196614i −0.714814 0.699314i 0.753489π-0.753489\pi
0.444198 + 0.895929i 0.353489π0.353489\pi
864864 149668. + 206001.i 0.200494 + 0.275957i
865865 −228446. + 74226.4i −0.305317 + 0.0992034i
866866 −765320. 248668.i −1.02049 0.331576i
867867 404158. + 293638.i 0.537667 + 0.390638i
868868 1.05263e6i 1.39713i
869869 369037. 292561.i 0.488687 0.387416i
870870 691369. 0.913422
871871 216791. 298387.i 0.285762 0.393318i
872872 42345.6 130326.i 0.0556898 0.171396i
873873 5125.46 + 15774.5i 0.00672518 + 0.0206980i
874874 −8722.35 + 6337.16i −0.0114185 + 0.00829605i
875875 −65149.0 89669.9i −0.0850926 0.117120i
876876 −129939. + 42219.7i −0.169329 + 0.0550182i
877877 261333. + 84912.3i 0.339778 + 0.110401i 0.473936 0.880559i 0.342833π-0.342833\pi
−0.134158 + 0.990960i 0.542833π0.542833\pi
878878 −334060. 242708.i −0.433346 0.314844i
879879 2.32150e6i 3.00462i
880880 47905.0 72120.1i 0.0618608 0.0931302i
881881 −264167. −0.340351 −0.170175 0.985414i 0.554433π-0.554433\pi
−0.170175 + 0.985414i 0.554433π0.554433\pi
882882 1.09795e6 1.51120e6i 1.41139 1.94261i
883883 −79926.4 + 245988.i −0.102511 + 0.315495i −0.989138 0.146989i 0.953042π-0.953042\pi
0.886627 + 0.462484i 0.153042π0.153042\pi
884884 155766. + 479400.i 0.199328 + 0.613470i
885885 −101095. + 73449.9i −0.129075 + 0.0937787i
886886 6142.42 + 8454.32i 0.00782478 + 0.0107699i
887887 −300034. + 97487.1i −0.381350 + 0.123908i −0.493418 0.869792i 0.664253π-0.664253\pi
0.112068 + 0.993701i 0.464253π0.464253\pi
888888 136960. + 44500.9i 0.173687 + 0.0564342i
889889 −456257. 331490.i −0.577305 0.419437i
890890 18755.6i 0.0236784i
891891 43294.8 + 1.03027e6i 0.0545356 + 1.29777i
892892 147522. 0.185407
893893 −10802.2 + 14868.0i −0.0135460 + 0.0186444i
894894 228410. 702974.i 0.285786 0.879558i
895895 −69582.1 214152.i −0.0868664 0.267347i
896896 92917.3 67508.4i 0.115739 0.0840895i
897897 818632. + 1.12675e6i 1.01743 + 1.40037i
898898 447877. 145524.i 0.555400 0.180460i
899899 2.17820e6 + 707739.i 2.69512 + 0.875697i
900900 137386. + 99817.1i 0.169613 + 0.123231i
901901 1.11030e6i 1.36770i
902902 968630. 360352.i 1.19054 0.442908i
903903 −3.23389e6 −3.96598
904904 97209.1 133797.i 0.118952 0.163723i
905905 126471. 389237.i 0.154416 0.475244i
906906 −89333.4 274940.i −0.108832 0.334951i
907907 83861.2 60928.7i 0.101940 0.0740641i −0.535647 0.844442i 0.679932π-0.679932\pi
0.637588 + 0.770378i 0.279932π0.279932\pi
908908 −30193.6 41557.9i −0.0366221 0.0504060i
909909 −1.05763e6 + 343646.i −1.27999 + 0.415895i
910910 −443058. 143958.i −0.535030 0.173842i
911911 −1.10533e6 803071.i −1.33185 0.967647i −0.999702 0.0244211i 0.992226π-0.992226\pi
−0.332151 0.943226i 0.607774π-0.607774\pi
912912 8160.77i 0.00981164i
913913 −383395. 1.03057e6i −0.459944 1.23634i
914914 −436632. −0.522664
915915 −59913.7 + 82464.1i −0.0715622 + 0.0984969i
916916 250806. 771902.i 0.298915 0.919965i
917917 104698. + 322226.i 0.124508 + 0.383197i
918918 1.09184e6 793270.i 1.29561 0.941316i
919919 555794. + 764984.i 0.658086 + 0.905778i 0.999416 0.0341659i 0.0108775π-0.0108775\pi
−0.341330 + 0.939943i 0.610877π0.610877\pi
920920 −113908. + 37011.1i −0.134580 + 0.0437277i
921921 1.39099e6 + 451959.i 1.63985 + 0.532819i
922922 −121294. 88125.0i −0.142684 0.103666i
923923 392806.i 0.461078i
924924 1.21478e6 51048.2i 1.42283 0.0597911i
925925 50232.1 0.0587080
926926 −293664. + 404194.i −0.342475 + 0.471376i
927927 787956. 2.42508e6i 0.916943 2.82206i
928928 77221.3 + 237663.i 0.0896687 + 0.275972i
929929 −591734. + 429920.i −0.685639 + 0.498146i −0.875223 0.483719i 0.839286π-0.839286\pi
0.189585 + 0.981864i 0.439286π0.439286\pi
930930 488383. + 672201.i 0.564670 + 0.777201i
931931 29779.1 9675.82i 0.0343568 0.0111632i
932932 453583. + 147378.i 0.522185 + 0.169668i
933933 1.66375e6 + 1.20879e6i 1.91128 + 1.38863i
934934 610112.i 0.699384i
935935 −382250. 253906.i −0.437244 0.290435i
936936 713759. 0.814704
937937 −765154. + 1.05314e6i −0.871505 + 1.19952i 0.107197 + 0.994238i 0.465812π0.465812\pi
−0.978702 + 0.205286i 0.934188π0.934188\pi
938938 −137640. + 423612.i −0.156437 + 0.481462i
939939 −296361. 912105.i −0.336116 1.03446i
940940 −165168. + 120002.i −0.186926 + 0.135810i
941941 −268909. 370121.i −0.303687 0.417989i 0.629713 0.776828i 0.283173π-0.283173\pi
−0.933399 + 0.358839i 0.883173π0.883173\pi
942942 343084. 111475.i 0.386633 0.125625i
943943 −1.35969e6 441791.i −1.52904 0.496814i
944944 −36540.5 26548.2i −0.0410044 0.0297915i
945945 1.24728e6i 1.39670i
946946 −547403. 690494.i −0.611680 0.771574i
947947 1.27039e6 1.41656 0.708282 0.705930i 0.249471π-0.249471\pi
0.708282 + 0.705930i 0.249471π0.249471\pi
948948 −289845. + 398937.i −0.322514 + 0.443903i
949949 −61897.7 + 190502.i −0.0687294 + 0.211527i
950950 879.647 + 2707.28i 0.000974678 + 0.00299975i
951951 788584. 572940.i 0.871940 0.633502i
952952 −357807. 492479.i −0.394798 0.543393i
953953 −409152. + 132942.i −0.450505 + 0.146378i −0.525477 0.850808i 0.676113π-0.676113\pi
0.0749724 + 0.997186i 0.476113π0.476113\pi
954954 −1.49522e6 485828.i −1.64289 0.533809i
955955 −282328. 205123.i −0.309562 0.224910i
956956 834296.i 0.912860i
957957 −711126. + 2.54805e6i −0.776467 + 2.78217i
958958 −929883. −1.01321
959959 −245250. + 337558.i −0.266669 + 0.367038i
960960 −28014.8 + 86220.7i −0.0303980 + 0.0935554i
961961 565177. + 1.73944e6i 0.611981 + 1.88348i
962962 170806. 124098.i 0.184567 0.134096i
963963 −859447. 1.18293e6i −0.926758 1.27557i
964964 −390255. + 126801.i −0.419946 + 0.136449i
965965 146242. + 47517.0i 0.157043 + 0.0510264i
966966 −1.36071e6 988616.i −1.45818 1.05943i
967967 266832.i 0.285354i 0.989769 + 0.142677i 0.0455711π0.0455711\pi
−0.989769 + 0.142677i 0.954429π0.954429\pi
968968 216526. + 250736.i 0.231078 + 0.267587i
969969 43253.6 0.0460654
970970 −1815.44 + 2498.74i −0.00192947 + 0.00265569i
971971 −426622. + 1.31301e6i −0.452486 + 1.39261i 0.421576 + 0.906793i 0.361477π0.361477\pi
−0.874062 + 0.485815i 0.838523π0.838523\pi
972972 −51986.4 159998.i −0.0550246 0.169348i
973973 538736. 391414.i 0.569050 0.413439i
974974 −376449. 518137.i −0.396815 0.546169i
975975 349725. 113633.i 0.367890 0.119535i
976976 −35039.5 11385.0i −0.0367840 0.0119518i
977977 −77747.2 56486.7i −0.0814509 0.0591775i 0.546315 0.837580i 0.316030π-0.316030\pi
−0.627765 + 0.778403i 0.716030π0.716030\pi
978978 1.35453e6i 1.41615i
979979 −69124.2 19291.6i −0.0721215 0.0201281i
980980 347840. 0.362182
981981 −604500. + 832022.i −0.628142 + 0.864564i
982982 252705. 777745.i 0.262054 0.806519i
983983 21031.5 + 64728.4i 0.0217653 + 0.0669866i 0.961349 0.275332i 0.0887878π-0.0887878\pi
−0.939584 + 0.342319i 0.888788π0.888788\pi
984984 −875484. + 636076.i −0.904186 + 0.656930i
985985 −44715.4 61545.5i −0.0460876 0.0634342i
986986 1.25966e6 409287.i 1.29568 0.420992i
987987 −2.72668e6 885952.i −2.79898 0.909444i
988988 9679.41 + 7032.50i 0.00991597 + 0.00720437i
989989 1.21894e6i 1.24620i
990990 −509190. + 403670.i −0.519529 + 0.411867i
991991 336596. 0.342738 0.171369 0.985207i 0.445181π-0.445181\pi
0.171369 + 0.985207i 0.445181π0.445181\pi
992992 −176525. + 242965.i −0.179383 + 0.246900i
993993 788213. 2.42587e6i 0.799365 2.46019i
994994 146588. + 451152.i 0.148363 + 0.456615i
995995 −385572. + 280134.i −0.389457 + 0.282957i
996996 676751. + 931468.i 0.682198 + 0.938965i
997997 920987. 299247.i 0.926538 0.301050i 0.193392 0.981122i 0.438051π-0.438051\pi
0.733146 + 0.680071i 0.238051π0.238051\pi
998998 157966. + 51326.1i 0.158599 + 0.0515320i
999999 −457314. 332258.i −0.458230 0.332924i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 110.5.h.a.51.4 yes 32
11.8 odd 10 inner 110.5.h.a.41.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
110.5.h.a.41.4 32 11.8 odd 10 inner
110.5.h.a.51.4 yes 32 1.1 even 1 trivial