Properties

Label 40.5.e.c.19.9
Level 4040
Weight 55
Character 40.19
Analytic conductor 4.1354.135
Analytic rank 00
Dimension 2020
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [40,5,Mod(19,40)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(40, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([1, 1, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("40.19");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: N N == 40=235 40 = 2^{3} \cdot 5
Weight: k k == 5 5
Character orbit: [χ][\chi] == 40.e (of order 22, degree 11, 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: 4.134798523354.13479852335
Analytic rank: 00
Dimension: 2020
Coefficient field: Q[x]/(x20+)\mathbb{Q}[x]/(x^{20} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20+10x1820x16+2640x14+22400x12652288x10+5734400x8++1099511627776 x^{20} + 10 x^{18} - 20 x^{16} + 2640 x^{14} + 22400 x^{12} - 652288 x^{10} + 5734400 x^{8} + \cdots + 1099511627776 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 23355 2^{33}\cdot 5^{5}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 19.9
Root 0.4956913.96917i-0.495691 - 3.96917i of defining polynomial
Character χ\chi == 40.19
Dual form 40.5.e.c.19.10

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+(0.4956913.96917i)q2+10.2033iq3+(15.5086+3.93496i)q4+(17.914117.4381i)q5+(40.49865.05768i)q6+84.8600q7+(23.3060+59.6056i)q823.1073q9+(78.094462.4601i)q10+71.3055q11+(40.1496158.239i)q12109.279q13+(42.0643336.824i)q14+(177.926+182.783i)q15+(225.032122.051i)q16+151.344iq17+(11.4541+91.7167i)q18368.470q19+(209.204+340.931i)q20+865.852iq21+(35.3455283.023i)q22+358.031q23+(608.174+237.798i)q24+(16.8280624.773i)q25+(54.1687+433.748i)q26+590.697iq27+(1316.06+333.921i)q28+387.610iq29+(637.299796.821i)q301687.73iq31+(595.988832.691i)q32+727.551iq33+(600.70975.0197i)q34+(1520.191479.79i)q35+(358.36190.9262i)q361158.77q37+(182.647+1462.52i)q381115.01iq39+(1456.91+661.369i)q402545.99q41+(3436.71429.195i)q42+1354.04iq43+(1105.85+280.584i)q44+(413.946+402.946i)q45+(177.4731421.08i)q46+901.424q47+(1245.33+2296.07i)q48+4800.23q49+(2488.17+242.901i)q501544.21q51+(1694.77430.009i)q523409.47q53+(2344.57292.803i)q54+(1277.371243.43i)q55+(1977.75+5058.14i)q563759.61iq57+(1538.49192.135i)q581454.37q59+(3478.622134.57i)q605324.84iq61+(6698.88+836.592i)q621960.88q63+(3009.66+2778.33i)q64+(1957.64+1905.62i)q65+(2887.77360.640i)q66657.048iq67+(595.5322347.13i)q68+3653.09iq69+(6627.105300.36i)q70+6741.79iq71+(538.5381377.32i)q72+4130.26iq73+(574.391+4599.34i)q74+(6374.75+171.701i)q75+(5714.451449.91i)q76+6050.98q77+(4425.66+552.700i)q78+2307.14iq79+(1902.906110.56i)q807898.74q81+(1262.03+10105.5i)q822146.14iq83+(3407.0913428.1i)q84+(2639.14+2711.18i)q85+(5374.41671.184i)q863954.90q87+(1661.84+4250.21i)q88+5117.03q89+(1804.55+1443.28i)q909273.44q91+(5552.55+1408.84i)q92+17220.4q93+(446.8273577.90i)q94+(6600.80+6425.40i)q95+(8496.196081.05i)q969169.66iq97+(2379.4319052.9i)q981647.68q99+O(q100)q+(-0.495691 - 3.96917i) q^{2} +10.2033i q^{3} +(-15.5086 + 3.93496i) q^{4} +(17.9141 - 17.4381i) q^{5} +(40.4986 - 5.05768i) q^{6} +84.8600 q^{7} +(23.3060 + 59.6056i) q^{8} -23.1073 q^{9} +(-78.0944 - 62.4601i) q^{10} +71.3055 q^{11} +(-40.1496 - 158.239i) q^{12} -109.279 q^{13} +(-42.0643 - 336.824i) q^{14} +(177.926 + 182.783i) q^{15} +(225.032 - 122.051i) q^{16} +151.344i q^{17} +(11.4541 + 91.7167i) q^{18} -368.470 q^{19} +(-209.204 + 340.931i) q^{20} +865.852i q^{21} +(-35.3455 - 283.023i) q^{22} +358.031 q^{23} +(-608.174 + 237.798i) q^{24} +(16.8280 - 624.773i) q^{25} +(54.1687 + 433.748i) q^{26} +590.697i q^{27} +(-1316.06 + 333.921i) q^{28} +387.610i q^{29} +(637.299 - 796.821i) q^{30} -1687.73i q^{31} +(-595.988 - 832.691i) q^{32} +727.551i q^{33} +(600.709 - 75.0197i) q^{34} +(1520.19 - 1479.79i) q^{35} +(358.361 - 90.9262i) q^{36} -1158.77 q^{37} +(182.647 + 1462.52i) q^{38} -1115.01i q^{39} +(1456.91 + 661.369i) q^{40} -2545.99 q^{41} +(3436.71 - 429.195i) q^{42} +1354.04i q^{43} +(-1105.85 + 280.584i) q^{44} +(-413.946 + 402.946i) q^{45} +(-177.473 - 1421.08i) q^{46} +901.424 q^{47} +(1245.33 + 2296.07i) q^{48} +4800.23 q^{49} +(-2488.17 + 242.901i) q^{50} -1544.21 q^{51} +(1694.77 - 430.009i) q^{52} -3409.47 q^{53} +(2344.57 - 292.803i) q^{54} +(1277.37 - 1243.43i) q^{55} +(1977.75 + 5058.14i) q^{56} -3759.61i q^{57} +(1538.49 - 192.135i) q^{58} -1454.37 q^{59} +(-3478.62 - 2134.57i) q^{60} -5324.84i q^{61} +(-6698.88 + 836.592i) q^{62} -1960.88 q^{63} +(-3009.66 + 2778.33i) q^{64} +(-1957.64 + 1905.62i) q^{65} +(2887.77 - 360.640i) q^{66} -657.048i q^{67} +(-595.532 - 2347.13i) q^{68} +3653.09i q^{69} +(-6627.10 - 5300.36i) q^{70} +6741.79i q^{71} +(-538.538 - 1377.32i) q^{72} +4130.26i q^{73} +(574.391 + 4599.34i) q^{74} +(6374.75 + 171.701i) q^{75} +(5714.45 - 1449.91i) q^{76} +6050.98 q^{77} +(-4425.66 + 552.700i) q^{78} +2307.14i q^{79} +(1902.90 - 6110.56i) q^{80} -7898.74 q^{81} +(1262.03 + 10105.5i) q^{82} -2146.14i q^{83} +(-3407.09 - 13428.1i) q^{84} +(2639.14 + 2711.18i) q^{85} +(5374.41 - 671.184i) q^{86} -3954.90 q^{87} +(1661.84 + 4250.21i) q^{88} +5117.03 q^{89} +(1804.55 + 1443.28i) q^{90} -9273.44 q^{91} +(-5552.55 + 1408.84i) q^{92} +17220.4 q^{93} +(-446.827 - 3577.90i) q^{94} +(-6600.80 + 6425.40i) q^{95} +(8496.19 - 6081.05i) q^{96} -9169.66i q^{97} +(-2379.43 - 19052.9i) q^{98} -1647.68 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q20q4+12q6652q9240q10168q11+660q14+280q16+728q19+900q201232q241420q25+4680q26+1540q302312q34+4440q357868q36+62504q99+O(q100) 20 q - 20 q^{4} + 12 q^{6} - 652 q^{9} - 240 q^{10} - 168 q^{11} + 660 q^{14} + 280 q^{16} + 728 q^{19} + 900 q^{20} - 1232 q^{24} - 1420 q^{25} + 4680 q^{26} + 1540 q^{30} - 2312 q^{34} + 4440 q^{35} - 7868 q^{36}+ \cdots - 62504 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/40Z)×\left(\mathbb{Z}/40\mathbb{Z}\right)^\times.

nn 1717 2121 3131
χ(n)\chi(n) 1-1 1-1 1-1

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 −0.495691 3.96917i −0.123923 0.992292i
33 10.2033i 1.13370i 0.823821 + 0.566850i 0.191838π0.191838\pi
−0.823821 + 0.566850i 0.808162π0.808162\pi
44 −15.5086 + 3.93496i −0.969286 + 0.245935i
55 17.9141 17.4381i 0.716563 0.697522i
66 40.4986 5.05768i 1.12496 0.140491i
77 84.8600 1.73184 0.865919 0.500185i 0.166735π-0.166735\pi
0.865919 + 0.500185i 0.166735π0.166735\pi
88 23.3060 + 59.6056i 0.364156 + 0.931338i
99 −23.1073 −0.285275
1010 −78.0944 62.4601i −0.780944 0.624601i
1111 71.3055 0.589301 0.294651 0.955605i 0.404797π-0.404797\pi
0.294651 + 0.955605i 0.404797π0.404797\pi
1212 −40.1496 158.239i −0.278816 1.09888i
1313 −109.279 −0.646623 −0.323311 0.946293i 0.604796π-0.604796\pi
−0.323311 + 0.946293i 0.604796π0.604796\pi
1414 −42.0643 336.824i −0.214614 1.71849i
1515 177.926 + 182.783i 0.790781 + 0.812367i
1616 225.032 122.051i 0.879032 0.476763i
1717 151.344i 0.523681i 0.965111 + 0.261840i 0.0843294π0.0843294\pi
−0.965111 + 0.261840i 0.915671π0.915671\pi
1818 11.4541 + 91.7167i 0.0353521 + 0.283076i
1919 −368.470 −1.02069 −0.510346 0.859969i 0.670483π-0.670483\pi
−0.510346 + 0.859969i 0.670483π0.670483\pi
2020 −209.204 + 340.931i −0.523009 + 0.852327i
2121 865.852i 1.96338i
2222 −35.3455 283.023i −0.0730278 0.584759i
2323 358.031 0.676807 0.338403 0.941001i 0.390113π-0.390113\pi
0.338403 + 0.941001i 0.390113π0.390113\pi
2424 −608.174 + 237.798i −1.05586 + 0.412843i
2525 16.8280 624.773i 0.0269248 0.999637i
2626 54.1687 + 433.748i 0.0801312 + 0.641639i
2727 590.697i 0.810283i
2828 −1316.06 + 333.921i −1.67865 + 0.425919i
2929 387.610i 0.460892i 0.973085 + 0.230446i 0.0740185π0.0740185\pi
−0.973085 + 0.230446i 0.925982π0.925982\pi
3030 637.299 796.821i 0.708110 0.885356i
3131 1687.73i 1.75622i −0.478457 0.878111i 0.658804π-0.658804\pi
0.478457 0.878111i 0.341196π-0.341196\pi
3232 −595.988 832.691i −0.582020 0.813175i
3333 727.551i 0.668091i
3434 600.709 75.0197i 0.519644 0.0648960i
3535 1520.19 1479.79i 1.24097 1.20800i
3636 358.361 90.9262i 0.276513 0.0701591i
3737 −1158.77 −0.846434 −0.423217 0.906028i 0.639099π-0.639099\pi
−0.423217 + 0.906028i 0.639099π0.639099\pi
3838 182.647 + 1462.52i 0.126487 + 1.01283i
3939 1115.01i 0.733076i
4040 1456.91 + 661.369i 0.910570 + 0.413355i
4141 −2545.99 −1.51457 −0.757285 0.653084i 0.773475π-0.773475\pi
−0.757285 + 0.653084i 0.773475π0.773475\pi
4242 3436.71 429.195i 1.94825 0.243308i
4343 1354.04i 0.732308i 0.930554 + 0.366154i 0.119326π0.119326\pi
−0.930554 + 0.366154i 0.880674π0.880674\pi
4444 −1105.85 + 280.584i −0.571202 + 0.144930i
4545 −413.946 + 402.946i −0.204418 + 0.198986i
4646 −177.473 1421.08i −0.0838717 0.671590i
4747 901.424 0.408069 0.204034 0.978964i 0.434595π-0.434595\pi
0.204034 + 0.978964i 0.434595π0.434595\pi
4848 1245.33 + 2296.07i 0.540506 + 0.996558i
4949 4800.23 1.99926
5050 −2488.17 + 242.901i −0.995269 + 0.0971605i
5151 −1544.21 −0.593697
5252 1694.77 430.009i 0.626763 0.159027i
5353 −3409.47 −1.21377 −0.606883 0.794791i 0.707580π-0.707580\pi
−0.606883 + 0.794791i 0.707580π0.707580\pi
5454 2344.57 292.803i 0.804038 0.100413i
5555 1277.37 1243.43i 0.422271 0.411051i
5656 1977.75 + 5058.14i 0.630659 + 1.61293i
5757 3759.61i 1.15716i
5858 1538.49 192.135i 0.457339 0.0571150i
5959 −1454.37 −0.417803 −0.208902 0.977937i 0.566989π-0.566989\pi
−0.208902 + 0.977937i 0.566989π0.566989\pi
6060 −3478.62 2134.57i −0.966283 0.592936i
6161 5324.84i 1.43102i −0.698601 0.715512i 0.746194π-0.746194\pi
0.698601 0.715512i 0.253806π-0.253806\pi
6262 −6698.88 + 836.592i −1.74268 + 0.217636i
6363 −1960.88 −0.494050
6464 −3009.66 + 2778.33i −0.734781 + 0.678304i
6565 −1957.64 + 1905.62i −0.463346 + 0.451034i
6666 2887.77 360.640i 0.662941 0.0827916i
6767 657.048i 0.146368i −0.997318 0.0731842i 0.976684π-0.976684\pi
0.997318 0.0731842i 0.0233161π-0.0233161\pi
6868 −595.532 2347.13i −0.128791 0.507597i
6969 3653.09i 0.767295i
7070 −6627.10 5300.36i −1.35247 1.08171i
7171 6741.79i 1.33739i 0.743536 + 0.668696i 0.233147π0.233147\pi
−0.743536 + 0.668696i 0.766853π0.766853\pi
7272 −538.538 1377.32i −0.103885 0.265688i
7373 4130.26i 0.775054i 0.921858 + 0.387527i 0.126671π0.126671\pi
−0.921858 + 0.387527i 0.873329π0.873329\pi
7474 574.391 + 4599.34i 0.104892 + 0.839909i
7575 6374.75 + 171.701i 1.13329 + 0.0305246i
7676 5714.45 1449.91i 0.989344 0.251024i
7777 6050.98 1.02057
7878 −4425.66 + 552.700i −0.727425 + 0.0908448i
7979 2307.14i 0.369675i 0.982769 + 0.184837i 0.0591758π0.0591758\pi
−0.982769 + 0.184837i 0.940824π0.940824\pi
8080 1902.90 6110.56i 0.297329 0.954775i
8181 −7898.74 −1.20389
8282 1262.03 + 10105.5i 0.187690 + 1.50290i
8383 2146.14i 0.311532i −0.987794 0.155766i 0.950215π-0.950215\pi
0.987794 0.155766i 0.0497846π-0.0497846\pi
8484 −3407.09 13428.1i −0.482865 1.90308i
8585 2639.14 + 2711.18i 0.365279 + 0.375250i
8686 5374.41 671.184i 0.726664 0.0907497i
8787 −3954.90 −0.522513
8888 1661.84 + 4250.21i 0.214598 + 0.548839i
8989 5117.03 0.646008 0.323004 0.946398i 0.395307π-0.395307\pi
0.323004 + 0.946398i 0.395307π0.395307\pi
9090 1804.55 + 1443.28i 0.222784 + 0.178183i
9191 −9273.44 −1.11985
9292 −5552.55 + 1408.84i −0.656019 + 0.166450i
9393 17220.4 1.99103
9494 −446.827 3577.90i −0.0505690 0.404923i
9595 −6600.80 + 6425.40i −0.731391 + 0.711956i
9696 8496.19 6081.05i 0.921896 0.659836i
9797 9169.66i 0.974563i −0.873245 0.487281i 0.837989π-0.837989\pi
0.873245 0.487281i 0.162011π-0.162011\pi
9898 −2379.43 19052.9i −0.247754 1.98385i
9999 −1647.68 −0.168113
100100 2197.48 + 9755.57i 0.219748 + 0.975557i
101101 536.675i 0.0526100i −0.999654 0.0263050i 0.991626π-0.991626\pi
0.999654 0.0263050i 0.00837411π-0.00837411\pi
102102 765.449 + 6129.21i 0.0735725 + 0.589121i
103103 3140.33 0.296007 0.148003 0.988987i 0.452715π-0.452715\pi
0.148003 + 0.988987i 0.452715π0.452715\pi
104104 −2546.86 6513.66i −0.235471 0.602224i
105105 15098.8 + 15510.9i 1.36950 + 1.40689i
106106 1690.04 + 13532.8i 0.150413 + 1.20441i
107107 16703.3i 1.45893i 0.684017 + 0.729466i 0.260231π0.260231\pi
−0.684017 + 0.729466i 0.739769π0.739769\pi
108108 −2324.37 9160.87i −0.199277 0.785397i
109109 15790.1i 1.32902i −0.747279 0.664510i 0.768640π-0.768640\pi
0.747279 0.664510i 0.231360π-0.231360\pi
110110 −5568.56 4453.74i −0.460212 0.368078i
111111 11823.3i 0.959602i
112112 19096.2 10357.3i 1.52234 0.825676i
113113 4460.76i 0.349343i −0.984627 0.174672i 0.944114π-0.944114\pi
0.984627 0.174672i 0.0558864π-0.0558864\pi
114114 −14922.5 + 1863.60i −1.14824 + 0.143398i
115115 6413.79 6243.36i 0.484974 0.472088i
116116 −1525.23 6011.28i −0.113349 0.446736i
117117 2525.15 0.184465
118118 720.920 + 5772.65i 0.0517753 + 0.414583i
119119 12843.0i 0.906930i
120120 −6748.14 + 14865.3i −0.468621 + 1.03231i
121121 −9556.53 −0.652724
122122 −21135.2 + 2639.47i −1.41999 + 0.177336i
123123 25977.5i 1.71707i
124124 6641.15 + 26174.3i 0.431916 + 1.70228i
125125 −10593.4 11485.7i −0.677976 0.735084i
126126 971.993 + 7783.08i 0.0612240 + 0.490242i
127127 −10888.2 −0.675070 −0.337535 0.941313i 0.609593π-0.609593\pi
−0.337535 + 0.941313i 0.609593π0.609593\pi
128128 12519.5 + 10568.7i 0.764132 + 0.645060i
129129 −13815.7 −0.830218
130130 8534.10 + 6825.59i 0.504976 + 0.403881i
131131 −9105.25 −0.530578 −0.265289 0.964169i 0.585467π-0.585467\pi
−0.265289 + 0.964169i 0.585467π0.585467\pi
132132 −2862.88 11283.3i −0.164307 0.647571i
133133 −31268.4 −1.76767
134134 −2607.93 + 325.693i −0.145240 + 0.0181384i
135135 10300.6 + 10581.8i 0.565191 + 0.580619i
136136 −9020.94 + 3527.21i −0.487724 + 0.190701i
137137 14976.2i 0.797921i −0.916968 0.398960i 0.869371π-0.869371\pi
0.916968 0.398960i 0.130629π-0.130629\pi
138138 14499.7 1810.81i 0.761381 0.0950853i
139139 25598.6 1.32491 0.662456 0.749101i 0.269514π-0.269514\pi
0.662456 + 0.749101i 0.269514π0.269514\pi
140140 −17753.0 + 28931.4i −0.905767 + 1.47609i
141141 9197.49i 0.462627i
142142 26759.3 3341.84i 1.32708 0.165733i
143143 −7792.21 −0.381056
144144 −5199.88 + 2820.27i −0.250766 + 0.136009i
145145 6759.17 + 6943.68i 0.321482 + 0.330258i
146146 16393.7 2047.33i 0.769080 0.0960468i
147147 48978.1i 2.26656i
148148 17970.8 4559.70i 0.820437 0.208168i
149149 10269.8i 0.462585i 0.972884 + 0.231292i 0.0742954π0.0742954\pi
−0.972884 + 0.231292i 0.925705π0.925705\pi
150150 −2478.39 25387.6i −0.110151 1.12834i
151151 14739.4i 0.646435i −0.946325 0.323217i 0.895236π-0.895236\pi
0.946325 0.323217i 0.104764π-0.104764\pi
152152 −8587.55 21962.9i −0.371691 0.950610i
153153 3497.14i 0.149393i
154154 −2999.42 24017.4i −0.126472 1.01271i
155155 −29430.7 30234.1i −1.22500 1.25844i
156156 4387.51 + 17292.2i 0.180289 + 0.710561i
157157 −27740.2 −1.12541 −0.562705 0.826658i 0.690239π-0.690239\pi
−0.562705 + 0.826658i 0.690239π0.690239\pi
158158 9157.42 1143.63i 0.366825 0.0458111i
159159 34787.8i 1.37605i
160160 −25197.1 4524.00i −0.984261 0.176719i
161161 30382.5 1.17212
162162 3915.33 + 31351.4i 0.149190 + 1.19461i
163163 3732.97i 0.140501i −0.997529 0.0702505i 0.977620π-0.977620\pi
0.997529 0.0702505i 0.0223799π-0.0223799\pi
164164 39484.7 10018.4i 1.46805 0.372486i
165165 12687.1 + 13033.4i 0.466008 + 0.478729i
166166 −8518.41 + 1063.82i −0.309131 + 0.0386059i
167167 20717.4 0.742853 0.371427 0.928462i 0.378869π-0.378869\pi
0.371427 + 0.928462i 0.378869π0.378869\pi
168168 −51609.7 + 20179.5i −1.82857 + 0.714978i
169169 −16619.0 −0.581879
170170 9452.94 11819.1i 0.327091 0.408966i
171171 8514.34 0.291178
172172 −5328.09 20999.2i −0.180100 0.709817i
173173 35335.7 1.18065 0.590326 0.807165i 0.298999π-0.298999\pi
0.590326 + 0.807165i 0.298999π0.298999\pi
174174 1960.41 + 15697.7i 0.0647512 + 0.518485i
175175 1428.02 53018.3i 0.0466293 1.73121i
176176 16046.0 8702.92i 0.518015 0.280957i
177177 14839.4i 0.473664i
178178 −2536.46 20310.3i −0.0800551 0.641028i
179179 23669.8 0.738734 0.369367 0.929284i 0.379575π-0.379575\pi
0.369367 + 0.929284i 0.379575π0.379575\pi
180180 4834.13 7877.98i 0.149202 0.243148i
181181 7525.59i 0.229712i 0.993382 + 0.114856i 0.0366406π0.0366406\pi
−0.993382 + 0.114856i 0.963359π0.963359\pi
182182 4596.76 + 36807.8i 0.138774 + 1.11121i
183183 54330.9 1.62235
184184 8344.25 + 21340.6i 0.246463 + 0.630336i
185185 −20758.2 + 20206.7i −0.606523 + 0.590407i
186186 −8535.99 68350.7i −0.246734 1.97568i
187187 10791.6i 0.308606i
188188 −13979.8 + 3547.07i −0.395535 + 0.100358i
189189 50126.5i 1.40328i
190190 28775.5 + 23014.7i 0.797104 + 0.637525i
191191 28925.8i 0.792901i 0.918056 + 0.396450i 0.129758π0.129758\pi
−0.918056 + 0.396450i 0.870242π0.870242\pi
192192 −28348.2 30708.5i −0.768994 0.833021i
193193 48944.4i 1.31398i 0.753900 + 0.656990i 0.228171π0.228171\pi
−0.753900 + 0.656990i 0.771829π0.771829\pi
194194 −36395.9 + 4545.32i −0.967051 + 0.120770i
195195 −19443.6 19974.3i −0.511337 0.525295i
196196 −74444.7 + 18888.7i −1.93786 + 0.491688i
197197 47883.5 1.23382 0.616912 0.787032i 0.288383π-0.288383\pi
0.616912 + 0.787032i 0.288383π0.288383\pi
198198 816.738 + 6539.90i 0.0208330 + 0.166817i
199199 29644.2i 0.748573i 0.927313 + 0.374286i 0.122112π0.122112\pi
−0.927313 + 0.374286i 0.877888π0.877888\pi
200200 37632.2 13557.9i 0.940805 0.338948i
201201 6704.06 0.165938
202202 −2130.15 + 266.025i −0.0522045 + 0.00651958i
203203 32892.6i 0.798190i
204204 23948.4 6076.39i 0.575462 0.146011i
205205 −45609.1 + 44397.2i −1.08529 + 1.05645i
206206 −1556.63 12464.5i −0.0366819 0.293725i
207207 −8273.12 −0.193076
208208 −24591.3 + 13337.7i −0.568402 + 0.308286i
209209 −26273.9 −0.601496
210210 54081.2 67618.2i 1.22633 1.53329i
211211 19653.5 0.441444 0.220722 0.975337i 0.429159π-0.429159\pi
0.220722 + 0.975337i 0.429159π0.429159\pi
212212 52876.1 13416.1i 1.17649 0.298508i
213213 −68788.5 −1.51620
214214 66298.2 8279.68i 1.44769 0.180795i
215215 23611.8 + 24256.3i 0.510802 + 0.524745i
216216 −35208.8 + 13766.8i −0.754648 + 0.295069i
217217 143221.i 3.04149i
218218 −62673.5 + 7827.00i −1.31878 + 0.164696i
219219 −42142.3 −0.878678
220220 −14917.4 + 24310.2i −0.308210 + 0.502277i
221221 16538.7i 0.338624i
222222 −46928.5 + 5860.68i −0.952205 + 0.118916i
223223 −60977.7 −1.22620 −0.613100 0.790005i 0.710078π-0.710078\pi
−0.613100 + 0.790005i 0.710078π0.710078\pi
224224 −50575.6 70662.2i −1.00796 1.40829i
225225 −388.849 + 14436.8i −0.00768097 + 0.285172i
226226 −17705.5 + 2211.16i −0.346650 + 0.0432915i
227227 2698.14i 0.0523616i 0.999657 + 0.0261808i 0.00833456π0.00833456\pi
−0.999657 + 0.0261808i 0.991665π0.991665\pi
228228 14793.9 + 58306.2i 0.284586 + 1.12162i
229229 68901.3i 1.31388i −0.753942 0.656941i 0.771850π-0.771850\pi
0.753942 0.656941i 0.228150π-0.228150\pi
230230 −27960.2 22362.6i −0.528548 0.422734i
231231 61740.0i 1.15702i
232232 −23103.7 + 9033.63i −0.429246 + 0.167837i
233233 83770.9i 1.54305i 0.636196 + 0.771527i 0.280507π0.280507\pi
−0.636196 + 0.771527i 0.719493π0.719493\pi
234234 −1251.69 10022.7i −0.0228595 0.183044i
235235 16148.2 15719.1i 0.292407 0.284637i
236236 22555.3 5722.90i 0.404971 0.102752i
237237 −23540.4 −0.419100
238238 50976.2 6366.18i 0.899939 0.112389i
239239 36602.8i 0.640795i −0.947283 0.320397i 0.896184π-0.896184\pi
0.947283 0.320397i 0.103816π-0.103816\pi
240240 62347.9 + 19415.9i 1.08243 + 0.337082i
241241 48755.9 0.839447 0.419724 0.907652i 0.362127π-0.362127\pi
0.419724 + 0.907652i 0.362127π0.362127\pi
242242 4737.09 + 37931.5i 0.0808873 + 0.647693i
243243 32746.8i 0.554570i
244244 20953.0 + 82580.7i 0.351939 + 1.38707i
245245 85991.6 83706.6i 1.43260 1.39453i
246246 −103109. + 12876.8i −1.70383 + 0.212784i
247247 40266.1 0.660003
248248 100598. 39334.2i 1.63564 0.639538i
249249 21897.8 0.353184
250250 −40337.6 + 47740.2i −0.645401 + 0.763844i
251251 75319.3 1.19553 0.597763 0.801673i 0.296056π-0.296056\pi
0.597763 + 0.801673i 0.296056π0.296056\pi
252252 30410.5 7716.00i 0.478876 0.121504i
253253 25529.5 0.398843
254254 5397.19 + 43217.1i 0.0836566 + 0.669867i
255255 −27663.0 + 26928.0i −0.425421 + 0.414117i
256256 35743.0 54930.9i 0.545394 0.838180i
257257 27190.5i 0.411672i 0.978587 + 0.205836i 0.0659913π0.0659913\pi
−0.978587 + 0.205836i 0.934009π0.934009\pi
258258 6848.29 + 54836.7i 0.102883 + 0.823819i
259259 −98333.1 −1.46589
260260 22861.6 37256.7i 0.338190 0.551134i
261261 8956.62i 0.131481i
262262 4513.39 + 36140.3i 0.0657507 + 0.526488i
263263 −48135.0 −0.695905 −0.347952 0.937512i 0.613123π-0.613123\pi
−0.347952 + 0.937512i 0.613123π0.613123\pi
264264 −43366.1 + 16956.3i −0.622218 + 0.243289i
265265 −61077.5 + 59454.6i −0.869740 + 0.846630i
266266 15499.5 + 124109.i 0.219055 + 1.75405i
267267 52210.6i 0.732379i
268268 2585.46 + 10189.9i 0.0359971 + 0.141873i
269269 57856.4i 0.799553i −0.916613 0.399776i 0.869088π-0.869088\pi
0.916613 0.399776i 0.130912π-0.130912\pi
270270 36894.9 46130.1i 0.506104 0.632786i
271271 135141.i 1.84013i −0.391765 0.920065i 0.628136π-0.628136\pi
0.391765 0.920065i 0.371864π-0.371864\pi
272272 18471.7 + 34057.2i 0.249672 + 0.460332i
273273 94619.7i 1.26957i
274274 −59443.0 + 7423.55i −0.791770 + 0.0988805i
275275 1199.93 44549.8i 0.0158668 0.589088i
276276 −14374.8 56654.3i −0.188705 0.743729i
277277 66626.3 0.868333 0.434166 0.900833i 0.357043π-0.357043\pi
0.434166 + 0.900833i 0.357043π0.357043\pi
278278 −12689.0 101605.i −0.164187 1.31470i
279279 38998.8i 0.501006i
280280 123634. + 56123.8i 1.57696 + 0.715864i
281281 70518.3 0.893078 0.446539 0.894764i 0.352656π-0.352656\pi
0.446539 + 0.894764i 0.352656π0.352656\pi
282282 36506.4 4559.11i 0.459061 0.0573300i
283283 5580.69i 0.0696811i 0.999393 + 0.0348406i 0.0110923π0.0110923\pi
−0.999393 + 0.0348406i 0.988908π0.988908\pi
284284 −26528.7 104556.i −0.328911 1.29632i
285285 −65560.3 67349.9i −0.807144 0.829177i
286286 3862.53 + 30928.6i 0.0472214 + 0.378118i
287287 −216053. −2.62299
288288 13771.7 + 19241.2i 0.166036 + 0.231978i
289289 60616.1 0.725758
290290 24210.2 30270.2i 0.287873 0.359931i
291291 93560.8 1.10486
292292 −16252.4 64054.5i −0.190613 0.751249i
293293 85817.1 0.999628 0.499814 0.866133i 0.333402π-0.333402\pi
0.499814 + 0.866133i 0.333402π0.333402\pi
294294 194402. 24278.0i 2.24909 0.280878i
295295 −26053.8 + 25361.5i −0.299382 + 0.291427i
296296 −27006.2 69069.1i −0.308234 0.788316i
297297 42119.9i 0.477501i
298298 40762.7 5090.67i 0.459019 0.0573248i
299299 −39125.3 −0.437639
300300 −99539.0 + 22421.5i −1.10599 + 0.249128i
301301 114904.i 1.26824i
302302 −58503.0 + 7306.16i −0.641452 + 0.0801079i
303303 5475.85 0.0596440
304304 −82917.6 + 44972.2i −0.897222 + 0.486628i
305305 −92854.9 95389.5i −0.998171 1.02542i
306306 −13880.7 + 1733.50i −0.148242 + 0.0185132i
307307 24380.3i 0.258680i −0.991600 0.129340i 0.958714π-0.958714\pi
0.991600 0.129340i 0.0412858π-0.0412858\pi
308308 −93842.2 + 23810.4i −0.989228 + 0.250995i
309309 32041.8i 0.335583i
310310 −105416. + 131802.i −1.09694 + 1.37151i
311311 145304.i 1.50230i 0.660133 + 0.751149i 0.270500π0.270500\pi
−0.660133 + 0.751149i 0.729500π0.729500\pi
312312 66460.8 25986.4i 0.682742 0.266954i
313313 15.3803i 0.000156991i 1.00000 7.84956e-5i 2.49859e5π2.49859e-5\pi
−1.00000 7.84956e-5i 0.999975π0.999975\pi
314314 13750.6 + 110106.i 0.139464 + 1.11673i
315315 −35127.4 + 34194.0i −0.354018 + 0.344611i
316316 −9078.50 35780.5i −0.0909159 0.358320i
317317 −19873.1 −0.197764 −0.0988819 0.995099i 0.531527π-0.531527\pi
−0.0988819 + 0.995099i 0.531527π0.531527\pi
318318 −138079. + 17244.0i −1.36544 + 0.170523i
319319 27638.7i 0.271604i
320320 −5466.54 + 102254.i −0.0533842 + 0.998574i
321321 −170429. −1.65399
322322 −15060.3 120593.i −0.145252 1.16308i
323323 55765.7i 0.534517i
324324 122498. 31081.2i 1.16692 0.296079i
325325 −1838.95 + 68274.8i −0.0174102 + 0.646388i
326326 −14816.8 + 1850.40i −0.139418 + 0.0174113i
327327 161111. 1.50671
328328 −59336.9 151756.i −0.551540 1.41058i
329329 76494.8 0.706708
330330 45442.9 56817.7i 0.417290 0.521742i
331331 −55183.9 −0.503682 −0.251841 0.967769i 0.581036π-0.581036\pi
−0.251841 + 0.967769i 0.581036π0.581036\pi
332332 8444.99 + 33283.7i 0.0766167 + 0.301964i
333333 26776.0 0.241466
334334 −10269.4 82231.0i −0.0920564 0.737127i
335335 −11457.6 11770.4i −0.102095 0.104882i
336336 105678. + 194845.i 0.936068 + 1.72588i
337337 172509.i 1.51898i 0.650520 + 0.759489i 0.274551π0.274551\pi
−0.650520 + 0.759489i 0.725449π0.725449\pi
338338 8237.91 + 65963.8i 0.0721080 + 0.577394i
339339 45514.5 0.396050
340340 −51597.8 31661.7i −0.446347 0.273890i
341341 120344.i 1.03494i
342342 −4220.48 33794.9i −0.0360836 0.288934i
343343 203598. 1.73056
344344 −80708.3 + 31557.2i −0.682027 + 0.266674i
345345 63702.9 + 65441.8i 0.535206 + 0.549815i
346346 −17515.6 140253.i −0.146310 1.17155i
347347 53756.2i 0.446447i 0.974767 + 0.223223i 0.0716579π0.0716579\pi
−0.974767 + 0.223223i 0.928342π0.928342\pi
348348 61334.9 15562.4i 0.506465 0.128504i
349349 101720.i 0.835136i 0.908646 + 0.417568i 0.137117π0.137117\pi
−0.908646 + 0.417568i 0.862883π0.862883\pi
350350 −211146. + 20612.6i −1.72364 + 0.168266i
351351 64550.9i 0.523948i
352352 −42497.2 59375.4i −0.342985 0.479205i
353353 119472.i 0.958778i −0.877603 0.479389i 0.840858π-0.840858\pi
0.877603 0.479389i 0.159142π-0.159142\pi
354354 −58900.1 + 7355.76i −0.470013 + 0.0586977i
355355 117564. + 120773.i 0.932861 + 0.958325i
356356 −79357.9 + 20135.3i −0.626167 + 0.158876i
357357 −131041. −1.02819
358358 −11732.9 93949.3i −0.0915459 0.733039i
359359 66348.7i 0.514806i 0.966304 + 0.257403i 0.0828668π0.0828668\pi
−0.966304 + 0.257403i 0.917133π0.917133\pi
360360 −33665.3 15282.4i −0.259763 0.117920i
361361 5449.20 0.0418137
362362 29870.3 3730.37i 0.227941 0.0284665i
363363 97508.1i 0.739993i
364364 143818. 36490.6i 1.08545 0.275409i
365365 72023.8 + 73989.8i 0.540618 + 0.555375i
366366 −26931.3 215648.i −0.201046 1.60985i
367367 146492. 1.08763 0.543817 0.839204i 0.316979π-0.316979\pi
0.543817 + 0.839204i 0.316979π0.316979\pi
368368 80568.4 43698.1i 0.594935 0.322676i
369369 58831.0 0.432069
370370 90493.3 + 72376.7i 0.661018 + 0.528683i
371371 −289328. −2.10205
372372 −267064. + 67761.6i −1.92988 + 0.489663i
373373 −113125. −0.813092 −0.406546 0.913630i 0.633267π-0.633267\pi
−0.406546 + 0.913630i 0.633267π0.633267\pi
374374 42833.8 5349.32i 0.306227 0.0382433i
375375 117192. 108087.i 0.833364 0.768622i
376376 21008.6 + 53729.9i 0.148601 + 0.380050i
377377 42357.7i 0.298023i
378378 198961. 24847.3i 1.39246 0.173898i
379379 43592.1 0.303480 0.151740 0.988420i 0.451512π-0.451512\pi
0.151740 + 0.988420i 0.451512π0.451512\pi
380380 77085.3 125623.i 0.533832 0.869964i
381381 111096.i 0.765327i
382382 114811. 14338.3i 0.786789 0.0982584i
383383 −99396.2 −0.677598 −0.338799 0.940859i 0.610021π-0.610021\pi
−0.338799 + 0.940859i 0.610021π0.610021\pi
384384 −107835. + 127741.i −0.731304 + 0.866296i
385385 108398. 105517.i 0.731306 0.711873i
386386 194269. 24261.3i 1.30385 0.162832i
387387 31288.2i 0.208909i
388388 36082.2 + 142208.i 0.239679 + 0.944630i
389389 99896.0i 0.660159i 0.943953 + 0.330080i 0.107076π0.107076\pi
−0.943953 + 0.330080i 0.892924π0.892924\pi
390390 −69643.5 + 87076.0i −0.457880 + 0.572492i
391391 54185.7i 0.354431i
392392 111874. + 286120.i 0.728043 + 1.86199i
393393 92903.6i 0.601516i
394394 −23735.4 190058.i −0.152899 1.22431i
395395 40232.0 + 41330.3i 0.257856 + 0.264895i
396396 25553.1 6483.54i 0.162950 0.0413449i
397397 55234.5 0.350453 0.175226 0.984528i 0.443934π-0.443934\pi
0.175226 + 0.984528i 0.443934π0.443934\pi
398398 117663. 14694.4i 0.742803 0.0927652i
399399 319041.i 2.00401i
400400 −72467.6 142648.i −0.452922 0.891550i
401401 −40688.8 −0.253038 −0.126519 0.991964i 0.540380π-0.540380\pi
−0.126519 + 0.991964i 0.540380π0.540380\pi
402402 −3323.14 26609.5i −0.0205635 0.164659i
403403 184434.i 1.13561i
404404 2111.79 + 8323.07i 0.0129386 + 0.0509942i
405405 −141499. + 137739.i −0.862665 + 0.839743i
406406 130556. 16304.6i 0.792037 0.0989139i
407407 −82626.5 −0.498804
408408 −35989.2 92043.4i −0.216198 0.552933i
409409 −313804. −1.87591 −0.937955 0.346757i 0.887283π-0.887283\pi
−0.937955 + 0.346757i 0.887283π0.887283\pi
410410 198828. + 159023.i 1.18280 + 0.946002i
411411 152806. 0.904603
412412 −48702.1 + 12357.1i −0.286915 + 0.0727984i
413413 −123418. −0.723567
414414 4100.91 + 32837.4i 0.0239265 + 0.191588i
415415 −37424.6 38446.2i −0.217301 0.223232i
416416 65129.2 + 90995.8i 0.376347 + 0.525817i
417417 261190.i 1.50205i
418418 13023.7 + 104286.i 0.0745390 + 0.596859i
419419 264287. 1.50538 0.752692 0.658373i 0.228755π-0.228755\pi
0.752692 + 0.658373i 0.228755π0.228755\pi
420420 −295196. 181140.i −1.67344 1.02687i
421421 179764.i 1.01424i 0.861877 + 0.507118i 0.169289π0.169289\pi
−0.861877 + 0.507118i 0.830711π0.830711\pi
422422 −9742.08 78008.2i −0.0547050 0.438042i
423423 −20829.4 −0.116412
424424 −79461.0 203224.i −0.442000 1.13043i
425425 94555.6 + 2546.81i 0.523491 + 0.0141000i
426426 34097.8 + 273033.i 0.187892 + 1.50451i
427427 451866.i 2.47830i
428428 −65726.8 259045.i −0.358802 1.41412i
429429 79506.2i 0.432003i
430430 84573.3 105743.i 0.457400 0.571892i
431431 151073.i 0.813266i −0.913592 0.406633i 0.866703π-0.866703\pi
0.913592 0.406633i 0.133297π-0.133297\pi
432432 72095.3 + 132926.i 0.386313 + 0.712265i
433433 133641.i 0.712796i 0.934334 + 0.356398i 0.115995π0.115995\pi
−0.934334 + 0.356398i 0.884005π0.884005\pi
434434 −568467. + 70993.2i −3.01805 + 0.376910i
435435 −70848.4 + 68965.8i −0.374413 + 0.364465i
436436 62133.3 + 244882.i 0.326852 + 1.28820i
437437 −131924. −0.690812
438438 20889.5 + 167270.i 0.108888 + 0.871905i
439439 74613.0i 0.387156i −0.981085 0.193578i 0.937991π-0.937991\pi
0.981085 0.193578i 0.0620092π-0.0620092\pi
440440 103886. + 47159.2i 0.536600 + 0.243591i
441441 −110920. −0.570339
442442 −65645.0 + 8198.10i −0.336014 + 0.0419632i
443443 110554.i 0.563334i 0.959512 + 0.281667i 0.0908874π0.0908874\pi
−0.959512 + 0.281667i 0.909113π0.909113\pi
444444 46524.0 + 183362.i 0.236000 + 0.930129i
445445 91666.8 89231.1i 0.462905 0.450605i
446446 30226.1 + 242031.i 0.151954 + 1.21675i
447447 −104786. −0.524432
448448 −255400. + 235770.i −1.27252 + 1.17471i
449449 9722.73 0.0482276 0.0241138 0.999709i 0.492324π-0.492324\pi
0.0241138 + 0.999709i 0.492324π0.492324\pi
450450 57494.9 5612.79i 0.283925 0.0277175i
451451 −181543. −0.892539
452452 17552.9 + 69180.1i 0.0859157 + 0.338613i
453453 150390. 0.732863
454454 10709.4 1337.44i 0.0519580 0.00648879i
455455 −166125. + 161711.i −0.802440 + 0.781117i
456456 224094. 87621.4i 1.07771 0.421386i
457457 331629.i 1.58789i −0.607990 0.793945i 0.708024π-0.708024\pi
0.607990 0.793945i 0.291976π-0.291976\pi
458458 −273481. + 34153.7i −1.30375 + 0.162820i
459459 −89398.3 −0.424330
460460 −74901.4 + 122064.i −0.353976 + 0.576860i
461461 86774.7i 0.408311i −0.978938 0.204156i 0.934555π-0.934555\pi
0.978938 0.204156i 0.0654449π-0.0654449\pi
462462 245056. 30603.9i 1.14811 0.143382i
463463 −35664.8 −0.166371 −0.0831856 0.996534i 0.526509π-0.526509\pi
−0.0831856 + 0.996534i 0.526509π0.526509\pi
464464 47308.3 + 87224.7i 0.219736 + 0.405139i
465465 308487. 300290.i 1.42670 1.38879i
466466 332501. 41524.5i 1.53116 0.191220i
467467 293718.i 1.34678i −0.739288 0.673389i 0.764838π-0.764838\pi
0.739288 0.673389i 0.235162π-0.235162\pi
468468 −39161.4 + 9936.35i −0.178800 + 0.0453665i
469469 55757.1i 0.253486i
470470 −70396.2 56303.0i −0.318679 0.254880i
471471 283042.i 1.27588i
472472 −33895.6 86688.9i −0.152146 0.389116i
473473 96550.3i 0.431550i
474474 11668.8 + 93435.9i 0.0519360 + 0.415869i
475475 −6200.61 + 230210.i −0.0274819 + 1.02032i
476476 −50536.8 199177.i −0.223046 0.879075i
477477 78783.6 0.346257
478478 −145283. + 18143.7i −0.635855 + 0.0794090i
479479 435529.i 1.89822i 0.314945 + 0.949110i 0.398014π0.398014\pi
−0.314945 + 0.949110i 0.601986π0.601986\pi
480480 46159.7 257093.i 0.200346 1.11586i
481481 126629. 0.547323
482482 −24167.9 193520.i −0.104027 0.832977i
483483 310002.i 1.32883i
484484 148208. 37604.6i 0.632676 0.160528i
485485 −159901. 164266.i −0.679779 0.698335i
486486 −129978. + 16232.3i −0.550295 + 0.0687238i
487487 187286. 0.789672 0.394836 0.918752i 0.370801π-0.370801\pi
0.394836 + 0.918752i 0.370801π0.370801\pi
488488 317390. 124101.i 1.33277 0.521116i
489489 38088.6 0.159286
490490 −374871. 299822.i −1.56131 1.24874i
491491 −287674. −1.19327 −0.596634 0.802513i 0.703496π-0.703496\pi
−0.596634 + 0.802513i 0.703496π0.703496\pi
492492 102221. + 402875.i 0.422287 + 1.66433i
493493 −58662.4 −0.241360
494494 −19959.6 159823.i −0.0817894 0.654916i
495495 −29516.6 + 28732.3i −0.120464 + 0.117263i
496496 −205989. 379793.i −0.837301 1.54377i
497497 572109.i 2.31615i
498498 −10854.5 86915.9i −0.0437675 0.350462i
499499 175430. 0.704537 0.352268 0.935899i 0.385410π-0.385410\pi
0.352268 + 0.935899i 0.385410π0.385410\pi
500500 209484. + 136442.i 0.837936 + 0.545769i
501501 211386.i 0.842172i
502502 −37335.1 298955.i −0.148153 1.18631i
503503 −95682.5 −0.378178 −0.189089 0.981960i 0.560553π-0.560553\pi
−0.189089 + 0.981960i 0.560553π0.560553\pi
504504 −45700.3 116880.i −0.179911 0.460128i
505505 −9358.57 9614.03i −0.0366967 0.0376984i
506506 −12654.8 101331.i −0.0494257 0.395769i
507507 169569.i 0.659676i
508508 168861. 42844.7i 0.654336 0.166023i
509509 370388.i 1.42962i −0.699318 0.714811i 0.746513π-0.746513\pi
0.699318 0.714811i 0.253487π-0.253487\pi
510510 120594. + 96451.2i 0.463644 + 0.370823i
511511 350494.i 1.34227i
512512 −235748. 114641.i −0.899306 0.437321i
513513 217654.i 0.827050i
514514 107924. 13478.1i 0.408499 0.0510155i
515515 56256.2 54761.3i 0.212107 0.206471i
516516 214261. 54364.1i 0.804719 0.204180i
517517 64276.4 0.240475
518518 48742.8 + 390300.i 0.181656 + 1.45459i
519519 360541.i 1.33850i
520520 −159210. 72273.9i −0.588795 0.267285i
521521 −259622. −0.956458 −0.478229 0.878235i 0.658721π-0.658721\pi
−0.478229 + 0.878235i 0.658721π0.658721\pi
522522 −35550.3 + 4439.71i −0.130468 + 0.0162935i
523523 108562.i 0.396895i 0.980111 + 0.198448i 0.0635900π0.0635900\pi
−0.980111 + 0.198448i 0.936410π0.936410\pi
524524 141209. 35828.8i 0.514282 0.130488i
525525 540961. + 14570.5i 1.96267 + 0.0528637i
526526 23860.1 + 191056.i 0.0862384 + 0.690541i
527527 255427. 0.919700
528528 88798.5 + 163722.i 0.318521 + 0.587273i
529529 −151655. −0.541933
530530 266261. + 212956.i 0.947884 + 0.758119i
531531 33606.6 0.119189
532532 484928. 123040.i 1.71338 0.434733i
533533 278224. 0.979356
534534 207233. 25880.3i 0.726734 0.0907584i
535535 291273. + 299224.i 1.01764 + 1.04542i
536536 39163.8 15313.1i 0.136319 0.0533009i
537537 241510.i 0.837502i
538538 −229642. + 28678.9i −0.793390 + 0.0990827i
539539 342282. 1.17817
540540 −201387. 123576.i −0.690626 0.423786i
541541 280006.i 0.956694i −0.878171 0.478347i 0.841236π-0.841236\pi
0.878171 0.478347i 0.158764π-0.158764\pi
542542 −536397. + 66988.2i −1.82595 + 0.228034i
543543 −76785.8 −0.260424
544544 126023. 90199.1i 0.425844 0.304793i
545545 −275348. 282865.i −0.927021 0.952326i
546546 −375561. + 46902.1i −1.25978 + 0.157328i
547547 72377.7i 0.241897i 0.992659 + 0.120948i 0.0385936π0.0385936\pi
−0.992659 + 0.120948i 0.961406π0.961406\pi
548548 58930.7 + 232259.i 0.196237 + 0.773414i
549549 123043.i 0.408235i
550550 −177420. + 17320.2i −0.586513 + 0.0572568i
551551 142823.i 0.470429i
552552 −217745. + 85138.9i −0.714611 + 0.279415i
553553 195784.i 0.640216i
554554 −33026.0 264451.i −0.107606 0.861640i
555555 −206175. 211803.i −0.669344 0.687615i
556556 −396998. + 100730.i −1.28422 + 0.325842i
557557 402974. 1.29887 0.649437 0.760416i 0.275005π-0.275005\pi
0.649437 + 0.760416i 0.275005π0.275005\pi
558558 154793. 19331.4i 0.497144 0.0620861i
559559 147968.i 0.473527i
560560 161481. 518542.i 0.514925 1.65352i
561561 −110110. −0.349866
562562 −34955.3 279899.i −0.110673 0.886194i
563563 244892.i 0.772606i −0.922372 0.386303i 0.873752π-0.873752\pi
0.922372 0.386303i 0.126248π-0.126248\pi
564564 −36191.8 142640.i −0.113776 0.448418i
565565 −77787.0 79910.4i −0.243675 0.250326i
566566 22150.7 2766.30i 0.0691440 0.00863508i
567567 −670288. −2.08495
568568 −401849. + 157124.i −1.24556 + 0.487019i
569569 644997. 1.99220 0.996100 0.0882331i 0.0281220π-0.0281220\pi
0.996100 + 0.0882331i 0.0281220π0.0281220\pi
570570 −234825. + 293605.i −0.722762 + 0.903677i
571571 198216. 0.607947 0.303973 0.952681i 0.401687π-0.401687\pi
0.303973 + 0.952681i 0.401687π0.401687\pi
572572 120846. 30662.0i 0.369352 0.0937149i
573573 −295139. −0.898911
574574 107096. + 857551.i 0.325048 + 2.60277i
575575 6024.94 223688.i 0.0182229 0.676561i
576576 69545.1 64199.8i 0.209615 0.193503i
577577 218459.i 0.656172i 0.944648 + 0.328086i 0.106404π0.106404\pi
−0.944648 + 0.328086i 0.893596π0.893596\pi
578578 −30046.8 240595.i −0.0899379 0.720164i
579579 −499394. −1.48966
580580 −132148. 81089.5i −0.392831 0.241051i
581581 182122.i 0.539523i
582582 −46377.2 371358.i −0.136917 1.09634i
583583 −243114. −0.715274
584584 −246187. + 96259.8i −0.721837 + 0.282240i
585585 45235.7 44033.7i 0.132181 0.128669i
586586 −42538.7 340622.i −0.123877 0.991923i
587587 330673.i 0.959673i 0.877358 + 0.479836i 0.159304π0.159304\pi
−0.877358 + 0.479836i 0.840696π0.840696\pi
588588 −192727. 759581.i −0.557427 2.19695i
589589 621878.i 1.79256i
590590 113578. + 90840.3i 0.326281 + 0.260960i
591591 488569.i 1.39879i
592592 −260760. + 141429.i −0.744042 + 0.403548i
593593 499960.i 1.42176i −0.703314 0.710879i 0.748297π-0.748297\pi
0.703314 0.710879i 0.251703π-0.251703\pi
594594 167181. 20878.4i 0.473820 0.0591732i
595595 223958. + 230071.i 0.632604 + 0.649873i
596596 −40411.4 159271.i −0.113766 0.448377i
597597 −302469. −0.848657
598598 19394.1 + 155295.i 0.0542334 + 0.434265i
599599 407848.i 1.13670i −0.822788 0.568348i 0.807583π-0.807583\pi
0.822788 0.568348i 0.192417π-0.192417\pi
600600 138335. + 383973.i 0.384265 + 1.06659i
601601 441217. 1.22153 0.610763 0.791813i 0.290863π-0.290863\pi
0.610763 + 0.791813i 0.290863π0.290863\pi
602602 456072. 56956.7i 1.25846 0.157164i
603603 15182.6i 0.0417553i
604604 57998.8 + 228587.i 0.158981 + 0.626580i
605605 −171196. + 166647.i −0.467718 + 0.455290i
606606 −2714.33 21734.6i −0.00739124 0.0591842i
607607 −71921.7 −0.195201 −0.0976006 0.995226i 0.531117π-0.531117\pi
−0.0976006 + 0.995226i 0.531117π0.531117\pi
608608 219604. + 306822.i 0.594064 + 0.830001i
609609 −335613. −0.904908
610610 −332590. + 415840.i −0.893818 + 1.11755i
611611 −98506.9 −0.263866
612612 13761.1 + 54235.7i 0.0367410 + 0.144805i
613613 527274. 1.40319 0.701593 0.712577i 0.252472π-0.252472\pi
0.701593 + 0.712577i 0.252472π0.252472\pi
614614 −96769.6 + 12085.1i −0.256686 + 0.0320563i
615615 −452998. 465363.i −1.19769 1.23039i
616616 141024. + 360673.i 0.371648 + 0.950499i
617617 91867.0i 0.241318i −0.992694 0.120659i 0.961499π-0.961499\pi
0.992694 0.120659i 0.0385007π-0.0385007\pi
618618 127179. 15882.8i 0.332996 0.0415863i
619619 −633381. −1.65304 −0.826521 0.562906i 0.809683π-0.809683\pi
−0.826521 + 0.562906i 0.809683π0.809683\pi
620620 575399. + 353079.i 1.49687 + 0.918520i
621621 211488.i 0.548405i
622622 576735. 72025.7i 1.49072 0.186169i
623623 434231. 1.11878
624624 −136088. 250913.i −0.349503 0.644397i
625625 −390059. 21027.4i −0.998550 0.0538300i
626626 61.0469 7.62386i 0.000155781 1.94548e-5i
627627 268081.i 0.681915i
628628 430211. 109157.i 1.09084 0.276777i
629629 175372.i 0.443261i
630630 153134. + 122477.i 0.385826 + 0.308584i
631631 128753.i 0.323368i 0.986843 + 0.161684i 0.0516926π0.0516926\pi
−0.986843 + 0.161684i 0.948307π0.948307\pi
632632 −137518. + 53770.1i −0.344292 + 0.134619i
633633 200531.i 0.500465i
634634 9850.91 + 78879.6i 0.0245074 + 0.196239i
635635 −195052. + 189869.i −0.483730 + 0.470877i
636636 136889. + 539510.i 0.338418 + 1.33378i
637637 −524565. −1.29277
638638 109703. 13700.3i 0.269511 0.0336579i
639639 155785.i 0.381525i
640640 408573. 28988.7i 0.997492 0.0707733i
641641 391151. 0.951980 0.475990 0.879451i 0.342090π-0.342090\pi
0.475990 + 0.879451i 0.342090π0.342090\pi
642642 84480.0 + 676461.i 0.204967 + 1.64124i
643643 720581.i 1.74285i −0.490525 0.871427i 0.663195π-0.663195\pi
0.490525 0.871427i 0.336805π-0.336805\pi
644644 −471189. + 119554.i −1.13612 + 0.288265i
645645 −247495. + 240918.i −0.594903 + 0.579096i
646646 −221343. + 27642.5i −0.530397 + 0.0662388i
647647 403682. 0.964341 0.482171 0.876077i 0.339849π-0.339849\pi
0.482171 + 0.876077i 0.339849π0.339849\pi
648648 −184088. 470810.i −0.438405 1.12123i
649649 −103705. −0.246212
650650 271906. 26544.1i 0.643563 0.0628262i
651651 1.46132e6 3.44814
652652 14689.1 + 57893.1i 0.0345541 + 0.136186i
653653 −404377. −0.948332 −0.474166 0.880436i 0.657250π-0.657250\pi
−0.474166 + 0.880436i 0.657250π0.657250\pi
654654 −79861.2 639476.i −0.186716 1.49510i
655655 −163112. + 158778.i −0.380192 + 0.370090i
656656 −572930. + 310742.i −1.33136 + 0.722091i
657657 95439.1i 0.221104i
658658 −37917.8 303621.i −0.0875772 0.701261i
659659 179720. 0.413834 0.206917 0.978359i 0.433657π-0.433657\pi
0.206917 + 0.978359i 0.433657π0.433657\pi
660660 −248044. 152206.i −0.569432 0.349418i
661661 512413.i 1.17278i −0.810028 0.586391i 0.800548π-0.800548\pi
0.810028 0.586391i 0.199452π-0.199452\pi
662662 27354.1 + 219034.i 0.0624176 + 0.499799i
663663 168750. 0.383898
664664 127922. 50018.0i 0.290142 0.113446i
665665 −560144. + 545260.i −1.26665 + 1.23299i
666666 −13272.6 106278.i −0.0299232 0.239605i
667667 138776.i 0.311935i
668668 −321298. + 81522.3i −0.720037 + 0.182694i
669669 622174.i 1.39014i
670670 −41039.3 + 51311.8i −0.0914218 + 0.114306i
671671 379690.i 0.843304i
672672 720987. 516038.i 1.59657 1.14273i
673673 136431.i 0.301220i −0.988593 0.150610i 0.951876π-0.951876\pi
0.988593 0.150610i 0.0481238π-0.0481238\pi
674674 684716. 85511.0i 1.50727 0.188236i
675675 369052. + 9940.24i 0.809990 + 0.0218167i
676676 257738. 65395.3i 0.564007 0.143104i
677677 −185710. −0.405190 −0.202595 0.979263i 0.564937π-0.564937\pi
−0.202595 + 0.979263i 0.564937π0.564937\pi
678678 −22561.1 180655.i −0.0490796 0.392997i
679679 778138.i 1.68778i
680680 −100094. + 220495.i −0.216466 + 0.476848i
681681 −27529.9 −0.0593623
682682 −477667. + 59653.6i −1.02697 + 0.128253i
683683 521505.i 1.11794i 0.829189 + 0.558968i 0.188802π0.188802\pi
−0.829189 + 0.558968i 0.811198π0.811198\pi
684684 −132045. + 33503.6i −0.282235 + 0.0716109i
685685 −261156. 268284.i −0.556568 0.571761i
686686 −100922. 808116.i −0.214455 1.71722i
687687 703020. 1.48955
688688 165262. + 304702.i 0.349137 + 0.643723i
689689 372584. 0.784849
690690 228172. 285286.i 0.479253 0.599215i
691691 −159485. −0.334012 −0.167006 0.985956i 0.553410π-0.553410\pi
−0.167006 + 0.985956i 0.553410π0.553410\pi
692692 −548007. + 139045.i −1.14439 + 0.290363i
693693 −139822. −0.291144
694694 213367. 26646.5i 0.443005 0.0553249i
695695 458576. 446391.i 0.949383 0.924156i
696696 −92172.8 235734.i −0.190276 0.486636i
697697 385320.i 0.793152i
698698 403745. 50421.8i 0.828698 0.103492i
699699 −854739. −1.74936
700700 186478. + 827858.i 0.380568 + 1.68951i
701701 924458.i 1.88127i 0.339418 + 0.940635i 0.389770π0.389770\pi
−0.339418 + 0.940635i 0.610230π0.610230\pi
702702 −256213. + 31997.3i −0.519909 + 0.0649290i
703703 426971. 0.863949
704704 −214605. + 198110.i −0.433007 + 0.399726i
705705 160386. + 164765.i 0.322693 + 0.331502i
706706 −474206. + 59221.3i −0.951387 + 0.118814i
707707 45542.2i 0.0911120i
708708 58392.5 + 230138.i 0.116490 + 0.459116i
709709 49979.9i 0.0994267i 0.998764 + 0.0497134i 0.0158308π0.0158308\pi
−0.998764 + 0.0497134i 0.984169π0.984169\pi
710710 421093. 526496.i 0.835336 1.04443i
711711 53311.7i 0.105459i
712712 119257. + 305004.i 0.235248 + 0.601652i
713713 604259.i 1.18862i
714714 64956.0 + 520125.i 0.127416 + 1.02026i
715715 −139590. + 135881.i −0.273050 + 0.265795i
716716 −367084. + 93139.6i −0.716044 + 0.181680i
717717 373470. 0.726469
718718 263349. 32888.4i 0.510838 0.0637961i
719719 823502.i 1.59297i 0.604659 + 0.796484i 0.293309π0.293309\pi
−0.604659 + 0.796484i 0.706691π0.706691\pi
720720 −43971.0 + 141198.i −0.0848205 + 0.272374i
721721 266489. 0.512635
722722 −2701.12 21628.8i −0.00518166 0.0414914i
723723 497471.i 0.951681i
724724 −29612.9 116711.i −0.0564942 0.222657i
725725 242168. + 6522.70i 0.460725 + 0.0124094i
726726 −387026. + 48333.9i −0.734289 + 0.0917019i
727727 −791865. −1.49824 −0.749122 0.662432i 0.769524π-0.769524\pi
−0.749122 + 0.662432i 0.769524π0.769524\pi
728728 −216127. 552749.i −0.407798 1.04295i
729729 −305673. −0.575177
730730 257976. 322550.i 0.484099 0.605274i
731731 −204925. −0.383496
732732 −842595. + 213790.i −1.57252 + 0.398993i
733733 −586208. −1.09105 −0.545524 0.838095i 0.683669π-0.683669\pi
−0.545524 + 0.838095i 0.683669π0.683669\pi
734734 −72614.9 581452.i −0.134782 1.07925i
735735 854084. + 877398.i 1.58098 + 1.62413i
736736 −213382. 298129.i −0.393915 0.550362i
737737 46851.1i 0.0862551i
738738 −29162.0 233510.i −0.0535432 0.428739i
739739 51496.3 0.0942947 0.0471474 0.998888i 0.484987π-0.484987\pi
0.0471474 + 0.998888i 0.484987π0.484987\pi
740740 242419. 395060.i 0.442693 0.721438i
741741 410847.i 0.748245i
742742 143417. + 1.14839e6i 0.260491 + 2.08584i
743743 −333510. −0.604132 −0.302066 0.953287i 0.597676π-0.597676\pi
−0.302066 + 0.953287i 0.597676π0.597676\pi
744744 401338. + 1.02643e6i 0.725044 + 1.85432i
745745 179086. + 183975.i 0.322663 + 0.331471i
746746 56074.9 + 449011.i 0.100761 + 0.806825i
747747 49591.6i 0.0888724i
748748 −42464.7 167363.i −0.0758970 0.299127i
749749 1.41744e6i 2.52663i
750750 −487108. 411576.i −0.865970 0.731691i
751751 315513.i 0.559419i −0.960085 0.279710i 0.909762π-0.909762\pi
0.960085 0.279710i 0.0902382π-0.0902382\pi
752752 202849. 110020.i 0.358705 0.194552i
753753 768505.i 1.35537i
754754 −168125. + 20996.3i −0.295726 + 0.0369318i
755755 −257026. 264042.i −0.450903 0.463211i
756756 −197246. 777391.i −0.345115 1.36018i
757757 559184. 0.975806 0.487903 0.872898i 0.337762π-0.337762\pi
0.487903 + 0.872898i 0.337762π0.337762\pi
758758 −21608.2 173024.i −0.0376080 0.301140i
759759 260486.i 0.452168i
760760 −536828. 243695.i −0.929412 0.421909i
761761 −432702. −0.747170 −0.373585 0.927596i 0.621872π-0.621872\pi
−0.373585 + 0.927596i 0.621872π0.621872\pi
762762 −440957. + 55069.1i −0.759428 + 0.0948414i
763763 1.33995e6i 2.30165i
764764 −113822. 448598.i −0.195002 0.768548i
765765 −60983.4 62648.1i −0.104205 0.107050i
766766 49269.8 + 394520.i 0.0839698 + 0.672375i
767767 158933. 0.270161
768768 560477. + 364696.i 0.950244 + 0.618313i
769769 258310. 0.436805 0.218403 0.975859i 0.429915π-0.429915\pi
0.218403 + 0.975859i 0.429915π0.429915\pi
770770 −472548. 377945.i −0.797011 0.637451i
771771 −277433. −0.466712
772772 −192594. 759059.i −0.323154 1.27362i
773773 280428. 0.469312 0.234656 0.972078i 0.424604π-0.424604\pi
0.234656 + 0.972078i 0.424604π0.424604\pi
774774 −124188. + 15509.2i −0.207299 + 0.0258886i
775775 −1.05445e6 28401.1i −1.75558 0.0472859i
776776 546563. 213708.i 0.907647 0.354893i
777777 1.00332e6i 1.66187i
778778 396504. 49517.5i 0.655071 0.0818087i
779779 938122. 1.54591
780780 380141. + 233264.i 0.624820 + 0.383406i
781781 480727.i 0.788127i
782782 215072. 26859.4i 0.351699 0.0439220i
783783 −228960. −0.373453
784784 1.08021e6 585874.i 1.75741 0.953173i
785785 −496940. + 483735.i −0.806426 + 0.784998i
786786 −368750. + 46051.4i −0.596880 + 0.0745415i
787787 1.17964e6i 1.90459i 0.305177 + 0.952296i 0.401284π0.401284\pi
−0.305177 + 0.952296i 0.598716π0.598716\pi
788788 −742605. + 188420.i −1.19593 + 0.303440i
789789 491136.i 0.788947i
790790 144104. 180175.i 0.230899 0.288695i
791791 378540.i 0.605005i
792792 −38400.7 98210.7i −0.0612193 0.156570i
793793 581894.i 0.925332i
794794 −27379.2 219235.i −0.0434291 0.347751i
795795 −606633. 623192.i −0.959824 0.986024i
796796 −116649. 459740.i −0.184100 0.725582i
797797 −627511. −0.987881 −0.493940 0.869496i 0.664444π-0.664444\pi
−0.493940 + 0.869496i 0.664444π0.664444\pi
798798 −1.26633e6 + 158146.i −1.98856 + 0.248343i
799799 136425.i 0.213698i
800800 −530272. + 358345.i −0.828550 + 0.559914i
801801 −118241. −0.184290
802802 20169.1 + 161501.i 0.0313572 + 0.251088i
803803 294510.i 0.456740i
804804 −103970. + 26380.2i −0.160841 + 0.0408099i
805805 544274. 529812.i 0.839897 0.817579i
806806 732048. 91422.1i 1.12686 0.140728i
807807 590326. 0.906453
808808 31988.8 12507.7i 0.0489977 0.0191582i
809809 −328656. −0.502163 −0.251081 0.967966i 0.580786π-0.580786\pi
−0.251081 + 0.967966i 0.580786π0.580786\pi
810810 616848. + 493356.i 0.940174 + 0.751953i
811811 510808. 0.776634 0.388317 0.921526i 0.373057π-0.373057\pi
0.388317 + 0.921526i 0.373057π0.373057\pi
812812 −129431. 510118.i −0.196303 0.773675i
813813 1.37888e6 2.08616
814814 40957.2 + 327958.i 0.0618132 + 0.494960i
815815 −65095.8 66872.7i −0.0980026 0.100678i
816816 −347496. + 188472.i −0.521879 + 0.283053i
817817 498923.i 0.747462i
818818 155550. + 1.24554e6i 0.232468 + 1.86145i
819819 214284. 0.319464
820820 532631. 868007.i 0.792135 1.29091i
821821 37920.6i 0.0562586i 0.999604 + 0.0281293i 0.00895502π0.00895502\pi
−0.999604 + 0.0281293i 0.991045π0.991045\pi
822822 −75744.7 606514.i −0.112101 0.897630i
823823 −449975. −0.664337 −0.332168 0.943220i 0.607780π-0.607780\pi
−0.332168 + 0.943220i 0.607780π0.607780\pi
824824 73188.5 + 187182.i 0.107793 + 0.275682i
825825 454554. + 12243.2i 0.667849 + 0.0179882i
826826 61177.3 + 489867.i 0.0896664 + 0.717990i
827827 41920.8i 0.0612940i 0.999530 + 0.0306470i 0.00975678π0.00975678\pi
−0.999530 + 0.0306470i 0.990243π0.990243\pi
828828 128304. 32554.4i 0.187146 0.0474842i
829829 1.28858e6i 1.87500i −0.347985 0.937500i 0.613134π-0.613134\pi
0.347985 0.937500i 0.386866π-0.386866\pi
830830 −134048. + 167602.i −0.194583 + 0.243289i
831831 679808.i 0.984429i
832832 328894. 303614.i 0.475126 0.438607i
833833 726484.i 1.04697i
834834 1.03671e6 129470.i 1.49047 0.186138i
835835 371134. 361272.i 0.532301 0.518157i
836836 407471. 103387.i 0.583021 0.147929i
837837 996936. 1.42304
838838 −131004. 1.04900e6i −0.186551 1.49378i
839839 506198.i 0.719112i −0.933124 0.359556i 0.882928π-0.882928\pi
0.933124 0.359556i 0.117072π-0.117072\pi
840840 −572647. + 1.26147e6i −0.811575 + 1.78780i
841841 557039. 0.787579
842842 713514. 89107.4i 1.00642 0.125687i
843843 719519.i 1.01248i
844844 −304799. + 77335.9i −0.427886 + 0.108567i
845845 −297715. + 289804.i −0.416953 + 0.405874i
846846 10325.0 + 82675.6i 0.0144261 + 0.115514i
847847 −810968. −1.13041
848848 −767241. + 416130.i −1.06694 + 0.578679i
849849 −56941.5 −0.0789975
850850 −36761.6 376569.i −0.0508811 0.521203i
851851 −414874. −0.572872
852852 1.06681e6 270680.i 1.46963 0.372887i
853853 −656590. −0.902395 −0.451197 0.892424i 0.649003π-0.649003\pi
−0.451197 + 0.892424i 0.649003π0.649003\pi
854854 −1.79353e6 + 223986.i −2.45920 + 0.307118i
855855 152527. 148474.i 0.208648 0.203103i
856856 −995611. + 389287.i −1.35876 + 0.531279i
857857 388067.i 0.528379i −0.964471 0.264189i 0.914896π-0.914896\pi
0.964471 0.264189i 0.0851044π-0.0851044\pi
858858 −315573. + 39410.5i −0.428673 + 0.0535349i
859859 282145. 0.382372 0.191186 0.981554i 0.438767π-0.438767\pi
0.191186 + 0.981554i 0.438767π0.438767\pi
860860 −461633. 283270.i −0.624166 0.383004i
861861 2.20445e6i 2.97368i
862862 −599634. + 74885.5i −0.806997 + 0.100782i
863863 1.01110e6 1.35761 0.678804 0.734320i 0.262499π-0.262499\pi
0.678804 + 0.734320i 0.262499π0.262499\pi
864864 491868. 352048.i 0.658902 0.471601i
865865 633007. 616186.i 0.846011 0.823531i
866866 530445. 66244.8i 0.707301 0.0883316i
867867 618484.i 0.822792i
868868 563568. + 2.22115e6i 0.748009 + 2.94807i
869869 164512.i 0.217850i
870870 308856. + 247023.i 0.408054 + 0.326362i
871871 71801.7i 0.0946452i
872872 941178. 368003.i 1.23777 0.483970i
873873 211886.i 0.278018i
874874 65393.3 + 523627.i 0.0856072 + 0.685487i
875875 −898955. 974676.i −1.17414 1.27305i
876876 653567. 165828.i 0.851691 0.216098i
877877 190192. 0.247283 0.123641 0.992327i 0.460543π-0.460543\pi
0.123641 + 0.992327i 0.460543π0.460543\pi
878878 −296152. + 36985.0i −0.384172 + 0.0479774i
879879 875617.i 1.13328i
880880 135688. 435716.i 0.175216 0.562650i
881881 237801. 0.306380 0.153190 0.988197i 0.451045π-0.451045\pi
0.153190 + 0.988197i 0.451045π0.451045\pi
882882 54982.1 + 440261.i 0.0706780 + 0.565943i
883883 175861.i 0.225552i −0.993620 0.112776i 0.964026π-0.964026\pi
0.993620 0.112776i 0.0359743π-0.0359743\pi
884884 65079.3 + 256492.i 0.0832795 + 0.328224i
885885 −258770. 265834.i −0.330391 0.339410i
886886 438807. 54800.5i 0.558992 0.0698099i
887887 −1.36691e6 −1.73738 −0.868688 0.495360i 0.835036π-0.835036\pi
−0.868688 + 0.495360i 0.835036π0.835036\pi
888888 704732. 275552.i 0.893713 0.349445i
889889 −923974. −1.16911
890890 −399611. 319610.i −0.504496 0.403497i
891891 −563224. −0.709456
892892 945678. 239945.i 1.18854 0.301566i
893893 −332148. −0.416513
894894 51941.6 + 415914.i 0.0649891 + 0.520390i
895895 424022. 412755.i 0.529349 0.515283i
896896 1.06241e6 + 896857.i 1.32335 + 1.11714i
897897 399207.i 0.496151i
898898 −4819.47 38591.2i −0.00597650 0.0478559i
899899 654181. 0.809428
900900 −50777.8 225425.i −0.0626886 0.278302i
901901 516002.i 0.635626i
902902 89989.3 + 720575.i 0.110606 + 0.885659i
903903 −1.17240e6 −1.43780
904904 265887. 103962.i 0.325356 0.127215i
905905 131232. + 134814.i 0.160229 + 0.164603i
906906 −74547.0 596923.i −0.0908183 0.727214i
907907 699123.i 0.849843i 0.905230 + 0.424922i 0.139698π0.139698\pi
−0.905230 + 0.424922i 0.860302π0.860302\pi
908908 −10617.1 41844.3i −0.0128775 0.0507534i
909909 12401.1i 0.0150083i
910910 724204. + 579220.i 0.874537 + 0.699456i
911911 1.27217e6i 1.53288i 0.642315 + 0.766441i 0.277974π0.277974\pi
−0.642315 + 0.766441i 0.722026π0.722026\pi
912912 −458865. 846033.i −0.551690 1.01718i
913913 153032.i 0.183586i
914914 −1.31629e6 + 164386.i −1.57565 + 0.196776i
915915 973288. 947426.i 1.16252 1.13163i
916916 271124. + 1.06856e6i 0.323130 + 1.27353i
917917 −772672. −0.918875
918918 44313.9 + 354837.i 0.0525841 + 0.421059i
919919 507149.i 0.600488i 0.953862 + 0.300244i 0.0970681π0.0970681\pi
−0.953862 + 0.300244i 0.902932π0.902932\pi
920920 521619. + 236790.i 0.616280 + 0.279762i
921921 248760. 0.293265
922922 −344424. + 43013.4i −0.405164 + 0.0505991i
923923 736738.i 0.864788i
924924 −242944. 957500.i −0.284553 1.12149i
925925 −19499.7 + 723967.i −0.0227900 + 0.846127i
926926 17678.7 + 141560.i 0.0206172 + 0.165089i
927927 −72564.6 −0.0844433
928928 322759. 231011.i 0.374786 0.268248i
929929 −31736.2 −0.0367725 −0.0183862 0.999831i 0.505853π-0.505853\pi
−0.0183862 + 0.999831i 0.505853π0.505853\pi
930930 −1.34482e6 1.07559e6i −1.55488 1.24360i
931931 −1.76874e6 −2.04063
932932 −329635. 1.29917e6i −0.379491 1.49566i
933933 −1.48258e6 −1.70315
934934 −1.16581e6 + 145593.i −1.33640 + 0.166896i
935935 188185. + 193322.i 0.215260 + 0.221135i
936936 58851.0 + 150513.i 0.0671742 + 0.171800i
937937 1.23459e6i 1.40619i 0.711096 + 0.703094i 0.248199π0.248199\pi
−0.711096 + 0.703094i 0.751801π0.751801\pi
938938 −221309. + 27638.3i −0.251532 + 0.0314127i
939939 −156.930 −0.000177981
940940 −188581. + 307323.i −0.213424 + 0.347808i
941941 126651.i 0.143031i 0.997439 + 0.0715156i 0.0227836π0.0227836\pi
−0.997439 + 0.0715156i 0.977216π0.977216\pi
942942 −1.12344e6 + 140301.i −1.26604 + 0.158110i
943943 −911544. −1.02507
944944 −327281. + 177508.i −0.367263 + 0.199193i
945945 874110. + 897970.i 0.978819 + 1.00554i
946946 383224. 47859.1i 0.428224 0.0534789i
947947 213933.i 0.238549i 0.992861 + 0.119275i 0.0380569π0.0380569\pi
−0.992861 + 0.119275i 0.961943π0.961943\pi
948948 365079. 92630.6i 0.406228 0.103071i
949949 451352.i 0.501168i
950950 916817. 89501.9i 1.01586 0.0991711i
951951 202771.i 0.224205i
952952 −765517. + 299320.i −0.844659 + 0.330264i
953953 281174.i 0.309592i −0.987946 0.154796i 0.950528π-0.950528\pi
0.987946 0.154796i 0.0494720π-0.0494720\pi
954954 −39052.3 312705.i −0.0429092 0.343588i
955955 504410. + 518179.i 0.553066 + 0.568163i
956956 144031. + 567658.i 0.157594 + 0.621113i
957957 −282006. −0.307918
958958 1.72869e6 215888.i 1.88359 0.235233i
959959 1.27088e6i 1.38187i
960960 −1.04333e6 55776.8i −1.13208 0.0605217i
961961 −1.92491e6 −2.08431
962962 −62769.0 502613.i −0.0678258 0.543104i
963963 385968.i 0.416197i
964964 −756135. + 191853.i −0.813665 + 0.206449i
965965 853496. + 876794.i 0.916530 + 0.941549i
966966 1.23045e6 153665.i 1.31859 0.164672i
967967 1.15290e6 1.23293 0.616467 0.787381i 0.288563π-0.288563\pi
0.616467 + 0.787381i 0.288563π0.288563\pi
968968 −222724. 569623.i −0.237693 0.607907i
969969 568994. 0.605982
970970 −572738. + 716099.i −0.608712 + 0.761079i
971971 857201. 0.909169 0.454584 0.890704i 0.349788π-0.349788\pi
0.454584 + 0.890704i 0.349788π0.349788\pi
972972 128857. + 507856.i 0.136388 + 0.537537i
973973 2.17230e6 2.29453
974974 −92835.8 743368.i −0.0978583 0.783585i
975975 −696628. 18763.4i −0.732810 0.0197379i
976976 −649903. 1.19826e6i −0.682259 1.25792i
977977 1.68459e6i 1.76484i −0.470464 0.882419i 0.655914π-0.655914\pi
0.470464 0.882419i 0.344086π-0.344086\pi
978978 −18880.2 151180.i −0.0197391 0.158058i
979979 364872. 0.380693
980980 −1.00423e6 + 1.63654e6i −1.04563 + 1.70402i
981981 364866.i 0.379136i
982982 142597. + 1.14183e6i 0.147873 + 1.18407i
983983 501269. 0.518756 0.259378 0.965776i 0.416482π-0.416482\pi
0.259378 + 0.965776i 0.416482π0.416482\pi
984984 1.54841e6 605432.i 1.59917 0.625281i
985985 857788. 834995.i 0.884112 0.860620i
986986 29078.4 + 232841.i 0.0299100 + 0.239500i
987987 780500.i 0.801195i
988988 −624471. + 158446.i −0.639732 + 0.162318i
989989 484787.i 0.495631i
990990 128674. + 102914.i 0.131287 + 0.105003i
991991 650776.i 0.662650i −0.943517 0.331325i 0.892504π-0.892504\pi
0.943517 0.331325i 0.107496π-0.107496\pi
992992 −1.40536e6 + 1.00587e6i −1.42811 + 1.02216i
993993 563058.i 0.571024i
994994 2.27080e6 283589.i 2.29829 0.287023i
995995 516938. + 531049.i 0.522146 + 0.536400i
996996 −339603. + 86166.8i −0.342336 + 0.0868603i
997997 724549. 0.728916 0.364458 0.931220i 0.381254π-0.381254\pi
0.364458 + 0.931220i 0.381254π0.381254\pi
998998 −86959.2 696313.i −0.0873081 0.699106i
999999 684480.i 0.685851i
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 40.5.e.c.19.9 20
4.3 odd 2 160.5.e.c.79.6 20
5.2 odd 4 200.5.g.i.51.19 20
5.3 odd 4 200.5.g.i.51.2 20
5.4 even 2 inner 40.5.e.c.19.12 yes 20
8.3 odd 2 inner 40.5.e.c.19.11 yes 20
8.5 even 2 160.5.e.c.79.5 20
20.3 even 4 800.5.g.i.751.16 20
20.7 even 4 800.5.g.i.751.5 20
20.19 odd 2 160.5.e.c.79.15 20
40.3 even 4 200.5.g.i.51.1 20
40.13 odd 4 800.5.g.i.751.15 20
40.19 odd 2 inner 40.5.e.c.19.10 yes 20
40.27 even 4 200.5.g.i.51.20 20
40.29 even 2 160.5.e.c.79.16 20
40.37 odd 4 800.5.g.i.751.6 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.5.e.c.19.9 20 1.1 even 1 trivial
40.5.e.c.19.10 yes 20 40.19 odd 2 inner
40.5.e.c.19.11 yes 20 8.3 odd 2 inner
40.5.e.c.19.12 yes 20 5.4 even 2 inner
160.5.e.c.79.5 20 8.5 even 2
160.5.e.c.79.6 20 4.3 odd 2
160.5.e.c.79.15 20 20.19 odd 2
160.5.e.c.79.16 20 40.29 even 2
200.5.g.i.51.1 20 40.3 even 4
200.5.g.i.51.2 20 5.3 odd 4
200.5.g.i.51.19 20 5.2 odd 4
200.5.g.i.51.20 20 40.27 even 4
800.5.g.i.751.5 20 20.7 even 4
800.5.g.i.751.6 20 40.37 odd 4
800.5.g.i.751.15 20 40.13 odd 4
800.5.g.i.751.16 20 20.3 even 4