Properties

Label 55.3.i.d.41.3
Level 5555
Weight 33
Character 55.41
Analytic conductor 1.4991.499
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [55,3,Mod(6,55)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(55, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 9]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("55.6");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 55=511 55 = 5 \cdot 11
Weight: k k == 3 3
Character orbit: [χ][\chi] == 55.i (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: 1.498641453981.49864145398
Analytic rank: 00
Dimension: 1212
Relative dimension: 33 over Q(ζ10)\Q(\zeta_{10})
Coefficient field: Q[x]/(x12+)\mathbb{Q}[x]/(x^{12} + \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12+25x10+235x8+1025x6+2090x4+1880x2+605 x^{12} + 25x^{10} + 235x^{8} + 1025x^{6} + 2090x^{4} + 1880x^{2} + 605 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 41.3
Root 2.63198i2.63198i of defining polynomial
Character χ\chi == 55.41
Dual form 55.3.i.d.51.3

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+(2.07416+2.85483i)q2+(0.2865580.881935i)q3+(2.61187+8.03851i)q4+(1.809021.31433i)q5+(1.923412.64735i)q6+(3.73363+1.21313i)q7+(14.9418+4.85489i)q8+(6.585464.78462i)q97.89056iq10+(2.8788010.6166i)q11+7.83789q12+(3.378494.65009i)q13+(4.28086+13.1751i)q14+(0.640763+1.97207i)q15+(17.499712.7143i)q16+(5.29106+7.28252i)q17+(27.3186+8.87634i)q18+(27.7487+9.01609i)q19+(15.290211.1090i)q203.64045iq21+(24.337630.2390i)q22+36.7936q23+(8.56339+11.7865i)q24+(1.54508+4.75528i)q25+(6.2677119.2900i)q26+(12.85889.34246i)q27+(19.5035+26.8443i)q28+(24.82748.06690i)q29+(6.95896+2.26110i)q30+(39.1642+28.4544i)q3113.4870iq32+(8.53822+5.58119i)q3331.7649q34+(5.159757.10179i)q35+(21.2608+65.4341i)q36+(6.7391920.7411i)q37+(83.294560.5170i)q38+(3.13294+4.31213i)q39+(33.4109+10.8559i)q40+(40.537113.1713i)q41+(10.39297.55087i)q42+70.3737iq43+(92.8608+4.58797i)q4418.2018q45+(76.3156+105.039i)q46+(5.4635116.8149i)q47+(6.19847+19.0769i)q48+(27.173519.7427i)q49+(10.3708+14.2742i)q50+(7.93890+2.57951i)q51+(46.204015.0126i)q52+(50.442336.6485i)q5356.0874iq54+(8.74592+22.9893i)q5561.6768q56+(15.9032+21.8889i)q57+(28.466287.6100i)q58+(12.0295+37.0230i)q59+(14.178910.3016i)q60+(26.416636.3594i)q61+(162.46552.7881i)q62+(30.39219.87498i)q63+(31.4956+22.8829i)q64+12.8525iq65+(33.643012.7989i)q66+36.2530q67+(44.721161.5533i)q68+(10.543532.4495i)q69+(9.5722929.4605i)q70+(1.98595+1.44287i)q71+(75.1699+103.462i)q72+(125.450+40.7610i)q73+(73.190523.7810i)q74+(3.751092.72533i)q75246.607iq76+(2.1309743.1309i)q7718.8086q78+(24.942734.3307i)q79+(14.9465+46.0006i)q80+(18.084155.6573i)q81+(121.682+88.4072i)q82+(45.3846+62.4666i)q83+(29.2638+9.50839i)q84+(19.14326.22001i)q85+(200.905+145.966i)q86+24.2077iq87+(94.5569+144.655i)q88+105.316q89+(37.753351.9630i)q90+(6.9728721.4603i)q91+(96.1001+295.766i)q92+(36.3177+26.3864i)q93+(36.671750.4742i)q94+(62.0479+20.1606i)q95+(11.8946+3.86481i)q96+(45.8248+33.2937i)q97118.525iq98+(69.754656.1413i)q99+O(q100)q+(2.07416 + 2.85483i) q^{2} +(-0.286558 - 0.881935i) q^{3} +(-2.61187 + 8.03851i) q^{4} +(-1.80902 - 1.31433i) q^{5} +(1.92341 - 2.64735i) q^{6} +(3.73363 + 1.21313i) q^{7} +(-14.9418 + 4.85489i) q^{8} +(6.58546 - 4.78462i) q^{9} -7.89056i q^{10} +(-2.87880 - 10.6166i) q^{11} +7.83789 q^{12} +(-3.37849 - 4.65009i) q^{13} +(4.28086 + 13.1751i) q^{14} +(-0.640763 + 1.97207i) q^{15} +(-17.4997 - 12.7143i) q^{16} +(-5.29106 + 7.28252i) q^{17} +(27.3186 + 8.87634i) q^{18} +(-27.7487 + 9.01609i) q^{19} +(15.2902 - 11.1090i) q^{20} -3.64045i q^{21} +(24.3376 - 30.2390i) q^{22} +36.7936 q^{23} +(8.56339 + 11.7865i) q^{24} +(1.54508 + 4.75528i) q^{25} +(6.26771 - 19.2900i) q^{26} +(-12.8588 - 9.34246i) q^{27} +(-19.5035 + 26.8443i) q^{28} +(-24.8274 - 8.06690i) q^{29} +(-6.95896 + 2.26110i) q^{30} +(-39.1642 + 28.4544i) q^{31} -13.4870i q^{32} +(-8.53822 + 5.58119i) q^{33} -31.7649 q^{34} +(-5.15975 - 7.10179i) q^{35} +(21.2608 + 65.4341i) q^{36} +(6.73919 - 20.7411i) q^{37} +(-83.2945 - 60.5170i) q^{38} +(-3.13294 + 4.31213i) q^{39} +(33.4109 + 10.8559i) q^{40} +(40.5371 - 13.1713i) q^{41} +(10.3929 - 7.55087i) q^{42} +70.3737i q^{43} +(92.8608 + 4.58797i) q^{44} -18.2018 q^{45} +(76.3156 + 105.039i) q^{46} +(-5.46351 - 16.8149i) q^{47} +(-6.19847 + 19.0769i) q^{48} +(-27.1735 - 19.7427i) q^{49} +(-10.3708 + 14.2742i) q^{50} +(7.93890 + 2.57951i) q^{51} +(46.2040 - 15.0126i) q^{52} +(50.4423 - 36.6485i) q^{53} -56.0874i q^{54} +(-8.74592 + 22.9893i) q^{55} -61.6768 q^{56} +(15.9032 + 21.8889i) q^{57} +(-28.4662 - 87.6100i) q^{58} +(-12.0295 + 37.0230i) q^{59} +(-14.1789 - 10.3016i) q^{60} +(26.4166 - 36.3594i) q^{61} +(-162.465 - 52.7881i) q^{62} +(30.3921 - 9.87498i) q^{63} +(-31.4956 + 22.8829i) q^{64} +12.8525i q^{65} +(-33.6430 - 12.7989i) q^{66} +36.2530 q^{67} +(-44.7211 - 61.5533i) q^{68} +(-10.5435 - 32.4495i) q^{69} +(9.57229 - 29.4605i) q^{70} +(1.98595 + 1.44287i) q^{71} +(-75.1699 + 103.462i) q^{72} +(125.450 + 40.7610i) q^{73} +(73.1905 - 23.7810i) q^{74} +(3.75109 - 2.72533i) q^{75} -246.607i q^{76} +(2.13097 - 43.1309i) q^{77} -18.8086 q^{78} +(-24.9427 - 34.3307i) q^{79} +(14.9465 + 46.0006i) q^{80} +(18.0841 - 55.6573i) q^{81} +(121.682 + 88.4072i) q^{82} +(-45.3846 + 62.4666i) q^{83} +(29.2638 + 9.50839i) q^{84} +(19.1432 - 6.22001i) q^{85} +(-200.905 + 145.966i) q^{86} +24.2077i q^{87} +(94.5569 + 144.655i) q^{88} +105.316 q^{89} +(-37.7533 - 51.9630i) q^{90} +(-6.97287 - 21.4603i) q^{91} +(-96.1001 + 295.766i) q^{92} +(36.3177 + 26.3864i) q^{93} +(36.6717 - 50.4742i) q^{94} +(62.0479 + 20.1606i) q^{95} +(-11.8946 + 3.86481i) q^{96} +(-45.8248 + 33.2937i) q^{97} -118.525i q^{98} +(-69.7546 - 56.1413i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+5q213q3+13q415q5+20q65q735q8+4q9+12q112q12+70q1360q14+35q1543q1615q1730q1880q19+20q20++669q99+O(q100) 12 q + 5 q^{2} - 13 q^{3} + 13 q^{4} - 15 q^{5} + 20 q^{6} - 5 q^{7} - 35 q^{8} + 4 q^{9} + 12 q^{11} - 2 q^{12} + 70 q^{13} - 60 q^{14} + 35 q^{15} - 43 q^{16} - 15 q^{17} - 30 q^{18} - 80 q^{19} + 20 q^{20}+ \cdots + 669 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/55Z)×\left(\mathbb{Z}/55\mathbb{Z}\right)^\times.

nn 1212 4646
χ(n)\chi(n) 11 e(310)e\left(\frac{3}{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 2.07416 + 2.85483i 1.03708 + 1.42742i 0.899498 + 0.436925i 0.143933π0.143933\pi
0.137581 + 0.990491i 0.456067π0.456067\pi
33 −0.286558 0.881935i −0.0955193 0.293978i 0.891869 0.452293i 0.149394π-0.149394\pi
−0.987389 + 0.158315i 0.949394π0.949394\pi
44 −2.61187 + 8.03851i −0.652968 + 2.00963i
55 −1.80902 1.31433i −0.361803 0.262866i
66 1.92341 2.64735i 0.320568 0.441224i
77 3.73363 + 1.21313i 0.533376 + 0.173304i 0.563307 0.826248i 0.309529π-0.309529\pi
−0.0299310 + 0.999552i 0.509529π0.509529\pi
88 −14.9418 + 4.85489i −1.86773 + 0.606861i
99 6.58546 4.78462i 0.731718 0.531624i
1010 7.89056i 0.789056i
1111 −2.87880 10.6166i −0.261709 0.965147i
1212 7.83789 0.653158
1313 −3.37849 4.65009i −0.259884 0.357699i 0.659058 0.752092i 0.270955π-0.270955\pi
−0.918942 + 0.394393i 0.870955π0.870955\pi
1414 4.28086 + 13.1751i 0.305775 + 0.941080i
1515 −0.640763 + 1.97207i −0.0427175 + 0.131471i
1616 −17.4997 12.7143i −1.09373 0.794641i
1717 −5.29106 + 7.28252i −0.311239 + 0.428383i −0.935767 0.352619i 0.885291π-0.885291\pi
0.624528 + 0.781002i 0.285291π0.285291\pi
1818 27.3186 + 8.87634i 1.51770 + 0.493130i
1919 −27.7487 + 9.01609i −1.46046 + 0.474531i −0.928210 0.372058i 0.878652π-0.878652\pi
−0.532247 + 0.846589i 0.678652π0.678652\pi
2020 15.2902 11.1090i 0.764508 0.555448i
2121 3.64045i 0.173355i
2222 24.3376 30.2390i 1.10625 1.37450i
2323 36.7936 1.59972 0.799860 0.600186i 0.204907π-0.204907\pi
0.799860 + 0.600186i 0.204907π0.204907\pi
2424 8.56339 + 11.7865i 0.356808 + 0.491104i
2525 1.54508 + 4.75528i 0.0618034 + 0.190211i
2626 6.26771 19.2900i 0.241066 0.741924i
2727 −12.8588 9.34246i −0.476252 0.346017i
2828 −19.5035 + 26.8443i −0.696555 + 0.958726i
2929 −24.8274 8.06690i −0.856116 0.278169i −0.152111 0.988363i 0.548607π-0.548607\pi
−0.704006 + 0.710195i 0.748607π0.748607\pi
3030 −6.95896 + 2.26110i −0.231965 + 0.0753701i
3131 −39.1642 + 28.4544i −1.26336 + 0.917885i −0.998918 0.0465167i 0.985188π-0.985188\pi
−0.264442 + 0.964401i 0.585188π0.585188\pi
3232 13.4870i 0.421469i
3333 −8.53822 + 5.58119i −0.258734 + 0.169127i
3434 −31.7649 −0.934261
3535 −5.15975 7.10179i −0.147422 0.202908i
3636 21.2608 + 65.4341i 0.590579 + 1.81761i
3737 6.73919 20.7411i 0.182140 0.560571i −0.817747 0.575578i 0.804777π-0.804777\pi
0.999887 + 0.0150073i 0.00477717π0.00477717\pi
3838 −83.2945 60.5170i −2.19196 1.59255i
3939 −3.13294 + 4.31213i −0.0803319 + 0.110567i
4040 33.4109 + 10.8559i 0.835272 + 0.271396i
4141 40.5371 13.1713i 0.988709 0.321251i 0.230364 0.973105i 0.426008π-0.426008\pi
0.758345 + 0.651854i 0.226008π0.226008\pi
4242 10.3929 7.55087i 0.247450 0.179783i
4343 70.3737i 1.63660i 0.574794 + 0.818298i 0.305082π0.305082\pi
−0.574794 + 0.818298i 0.694918π0.694918\pi
4444 92.8608 + 4.58797i 2.11047 + 0.104272i
4545 −18.2018 −0.404484
4646 76.3156 + 105.039i 1.65904 + 2.28347i
4747 −5.46351 16.8149i −0.116245 0.357765i 0.875960 0.482384i 0.160229π-0.160229\pi
−0.992205 + 0.124619i 0.960229π0.960229\pi
4848 −6.19847 + 19.0769i −0.129135 + 0.397436i
4949 −27.1735 19.7427i −0.554561 0.402912i
5050 −10.3708 + 14.2742i −0.207416 + 0.285483i
5151 7.93890 + 2.57951i 0.155665 + 0.0505785i
5252 46.2040 15.0126i 0.888538 0.288704i
5353 50.4423 36.6485i 0.951742 0.691481i 0.000523852 1.00000i 0.499833π-0.499833\pi
0.951218 + 0.308519i 0.0998333π0.0998333\pi
5454 56.0874i 1.03866i
5555 −8.74592 + 22.9893i −0.159017 + 0.417988i
5656 −61.6768 −1.10137
5757 15.9032 + 21.8889i 0.279004 + 0.384016i
5858 −28.4662 87.6100i −0.490797 1.51052i
5959 −12.0295 + 37.0230i −0.203890 + 0.627509i 0.795867 + 0.605471i 0.207015π0.207015\pi
−0.999757 + 0.0220376i 0.992985π0.992985\pi
6060 −14.1789 10.3016i −0.236315 0.171693i
6161 26.4166 36.3594i 0.433060 0.596055i −0.535593 0.844477i 0.679912π-0.679912\pi
0.968652 + 0.248421i 0.0799117π0.0799117\pi
6262 −162.465 52.7881i −2.62041 0.851422i
6363 30.3921 9.87498i 0.482414 0.156746i
6464 −31.4956 + 22.8829i −0.492118 + 0.357545i
6565 12.8525i 0.197731i
6666 −33.6430 12.7989i −0.509742 0.193923i
6767 36.2530 0.541090 0.270545 0.962707i 0.412796π-0.412796\pi
0.270545 + 0.962707i 0.412796π0.412796\pi
6868 −44.7211 61.5533i −0.657663 0.905195i
6969 −10.5435 32.4495i −0.152804 0.470283i
7070 9.57229 29.4605i 0.136747 0.420864i
7171 1.98595 + 1.44287i 0.0279711 + 0.0203222i 0.601683 0.798735i 0.294497π-0.294497\pi
−0.573712 + 0.819057i 0.694497π0.694497\pi
7272 −75.1699 + 103.462i −1.04403 + 1.43698i
7373 125.450 + 40.7610i 1.71849 + 0.558370i 0.991709 0.128503i 0.0410172π-0.0410172\pi
0.726777 + 0.686873i 0.241017π0.241017\pi
7474 73.1905 23.7810i 0.989061 0.321365i
7575 3.75109 2.72533i 0.0500146 0.0363377i
7676 246.607i 3.24483i
7777 2.13097 43.1309i 0.0276749 0.560142i
7878 −18.8086 −0.241136
7979 −24.9427 34.3307i −0.315730 0.434565i 0.621427 0.783472i 0.286553π-0.286553\pi
−0.937158 + 0.348907i 0.886553π0.886553\pi
8080 14.9465 + 46.0006i 0.186831 + 0.575008i
8181 18.0841 55.6573i 0.223261 0.687127i
8282 121.682 + 88.4072i 1.48393 + 1.07814i
8383 −45.3846 + 62.4666i −0.546803 + 0.752609i −0.989574 0.144025i 0.953995π-0.953995\pi
0.442771 + 0.896635i 0.353995π0.353995\pi
8484 29.2638 + 9.50839i 0.348379 + 0.113195i
8585 19.1432 6.22001i 0.225215 0.0731766i
8686 −200.905 + 145.966i −2.33610 + 1.69728i
8787 24.2077i 0.278250i
8888 94.5569 + 144.655i 1.07451 + 1.64381i
8989 105.316 1.18332 0.591661 0.806187i 0.298472π-0.298472\pi
0.591661 + 0.806187i 0.298472π0.298472\pi
9090 −37.7533 51.9630i −0.419481 0.577366i
9191 −6.97287 21.4603i −0.0766249 0.235827i
9292 −96.1001 + 295.766i −1.04457 + 3.21484i
9393 36.3177 + 26.3864i 0.390513 + 0.283725i
9494 36.6717 50.4742i 0.390124 0.536960i
9595 62.0479 + 20.1606i 0.653136 + 0.212217i
9696 −11.8946 + 3.86481i −0.123903 + 0.0402584i
9797 −45.8248 + 33.2937i −0.472421 + 0.343234i −0.798384 0.602149i 0.794311π-0.794311\pi
0.325963 + 0.945382i 0.394311π0.394311\pi
9898 118.525i 1.20944i
9999 −69.7546 56.1413i −0.704592 0.567084i
100100 −42.2610 −0.422610
101101 −54.3720 74.8367i −0.538337 0.740957i 0.450035 0.893011i 0.351411π-0.351411\pi
−0.988372 + 0.152054i 0.951411π0.951411\pi
102102 9.10247 + 28.0145i 0.0892399 + 0.274652i
103103 −13.5278 + 41.6344i −0.131338 + 0.404218i −0.995003 0.0998498i 0.968164π-0.968164\pi
0.863664 + 0.504068i 0.168164π0.168164\pi
104104 73.0564 + 53.0786i 0.702465 + 0.510371i
105105 −4.78475 + 6.58564i −0.0455690 + 0.0627204i
106106 209.251 + 67.9896i 1.97406 + 0.641412i
107107 60.5320 19.6680i 0.565719 0.183813i −0.0121737 0.999926i 0.503875π-0.503875\pi
0.577893 + 0.816113i 0.303875π0.303875\pi
108108 108.685 78.9643i 1.00634 0.731151i
109109 180.853i 1.65920i 0.558358 + 0.829600i 0.311432π0.311432\pi
−0.558358 + 0.829600i 0.688568π0.688568\pi
110110 −83.7711 + 22.7153i −0.761555 + 0.206503i
111111 −20.2235 −0.182193
112112 −49.9133 68.6998i −0.445654 0.613391i
113113 −22.4996 69.2468i −0.199112 0.612803i −0.999904 0.0138608i 0.995588π-0.995588\pi
0.800792 0.598942i 0.204412π-0.204412\pi
114114 −29.5033 + 90.8020i −0.258801 + 0.796508i
115115 −66.5602 48.3588i −0.578784 0.420511i
116116 129.692 178.505i 1.11803 1.53884i
117117 −44.4978 14.4582i −0.380323 0.123574i
118118 −130.646 + 42.4493i −1.10717 + 0.359740i
119119 −28.5895 + 20.7715i −0.240248 + 0.174551i
120120 32.5771i 0.271475i
121121 −104.425 + 61.1262i −0.863017 + 0.505175i
122122 158.592 1.29994
123123 −23.2324 31.9767i −0.188881 0.259973i
124124 −126.440 389.141i −1.01967 3.13823i
125125 3.45492 10.6331i 0.0276393 0.0850651i
126126 91.2293 + 66.2820i 0.724042 + 0.526047i
127127 −68.7276 + 94.5954i −0.541162 + 0.744846i −0.988780 0.149379i 0.952273π-0.952273\pi
0.447618 + 0.894225i 0.352273π0.352273\pi
128128 −181.961 59.1227i −1.42157 0.461896i
129129 62.0650 20.1661i 0.481124 0.156327i
130130 −36.6918 + 26.6582i −0.282245 + 0.205063i
131131 41.6464i 0.317912i −0.987286 0.158956i 0.949187π-0.949187\pi
0.987286 0.158956i 0.0508127π-0.0508127\pi
132132 −22.5637 83.2119i −0.170937 0.630393i
133133 −114.541 −0.861211
134134 75.1945 + 103.496i 0.561153 + 0.772360i
135135 10.9827 + 33.8014i 0.0813535 + 0.250380i
136136 43.7022 134.502i 0.321340 0.988982i
137137 −85.7502 62.3011i −0.625914 0.454753i 0.229069 0.973410i 0.426432π-0.426432\pi
−0.854982 + 0.518657i 0.826432π0.826432\pi
138138 70.7691 97.4053i 0.512819 0.705835i
139139 31.5601 + 10.2545i 0.227051 + 0.0737733i 0.420333 0.907370i 0.361913π-0.361913\pi
−0.193282 + 0.981143i 0.561913π0.561913\pi
140140 70.5645 22.9278i 0.504032 0.163770i
141141 −13.2641 + 9.63691i −0.0940714 + 0.0683469i
142142 8.66229i 0.0610020i
143143 −39.6422 + 49.2548i −0.277218 + 0.344439i
144144 −176.076 −1.22275
145145 34.3106 + 47.2245i 0.236625 + 0.325686i
146146 143.836 + 442.682i 0.985179 + 3.03207i
147147 −9.62499 + 29.6227i −0.0654761 + 0.201515i
148148 149.126 + 108.346i 1.00761 + 0.732069i
149149 70.8877 97.5686i 0.475757 0.654823i −0.501926 0.864911i 0.667375π-0.667375\pi
0.977683 + 0.210088i 0.0673750π0.0673750\pi
150150 15.5607 + 5.05598i 0.103738 + 0.0337065i
151151 −65.2872 + 21.2131i −0.432366 + 0.140484i −0.517111 0.855919i 0.672992π-0.672992\pi
0.0847449 + 0.996403i 0.472992π0.472992\pi
152152 370.843 269.433i 2.43976 1.77259i
153153 73.2744i 0.478918i
154154 127.551 83.3767i 0.828256 0.541407i
155155 108.247 0.698368
156156 −26.4802 36.4469i −0.169745 0.233634i
157157 −57.8493 178.042i −0.368467 1.13402i −0.947782 0.318920i 0.896680π-0.896680\pi
0.579315 0.815104i 0.303320π-0.303320\pi
158158 46.2732 142.414i 0.292868 0.901356i
159159 −46.7762 33.9849i −0.294190 0.213742i
160160 −17.7263 + 24.3982i −0.110790 + 0.152489i
161161 137.374 + 44.6354i 0.853253 + 0.277239i
162162 196.402 63.8147i 1.21236 0.393918i
163163 −29.2151 + 21.2260i −0.179234 + 0.130221i −0.673785 0.738928i 0.735333π-0.735333\pi
0.494551 + 0.869149i 0.335333π0.335333\pi
164164 360.259i 2.19670i
165165 22.7813 + 1.12555i 0.138068 + 0.00682154i
166166 −272.466 −1.64136
167167 −90.2211 124.179i −0.540246 0.743585i 0.448403 0.893832i 0.351993π-0.351993\pi
−0.988648 + 0.150247i 0.951993π0.951993\pi
168168 17.6740 + 54.3949i 0.105202 + 0.323779i
169169 42.0147 129.308i 0.248608 0.765136i
170170 57.4632 + 41.7494i 0.338019 + 0.245585i
171171 −139.599 + 192.142i −0.816370 + 1.12364i
172172 −565.700 183.807i −3.28895 1.06864i
173173 −1.64642 + 0.534955i −0.00951689 + 0.00309223i −0.313772 0.949498i 0.601593π-0.601593\pi
0.304255 + 0.952591i 0.401593π0.401593\pi
174174 −69.1090 + 50.2107i −0.397178 + 0.288567i
175175 19.6289i 0.112165i
176176 −84.6043 + 222.389i −0.480706 + 1.26357i
177177 36.0990 0.203949
178178 218.441 + 300.659i 1.22720 + 1.68909i
179179 26.7282 + 82.2609i 0.149320 + 0.459558i 0.997541 0.0700832i 0.0223265π-0.0223265\pi
−0.848222 + 0.529641i 0.822326π0.822326\pi
180180 47.5407 146.315i 0.264115 0.812862i
181181 −144.912 105.285i −0.800619 0.581684i 0.110477 0.993879i 0.464762π-0.464762\pi
−0.911096 + 0.412195i 0.864762π0.864762\pi
182182 46.8027 64.4184i 0.257158 0.353947i
183183 −39.6365 12.8787i −0.216593 0.0703753i
184184 −549.762 + 178.629i −2.98784 + 0.970808i
185185 −39.4519 + 28.6635i −0.213254 + 0.154938i
186186 158.411i 0.851670i
187187 92.5476 + 35.2082i 0.494907 + 0.188279i
188188 149.437 0.794878
189189 −36.6764 50.4807i −0.194055 0.267094i
190190 71.1420 + 218.953i 0.374432 + 1.15238i
191191 104.623 321.997i 0.547765 1.68585i −0.166559 0.986032i 0.553266π-0.553266\pi
0.714324 0.699815i 0.246734π-0.246734\pi
192192 29.2065 + 21.2198i 0.152117 + 0.110520i
193193 −5.22978 + 7.19818i −0.0270973 + 0.0372963i −0.822351 0.568981i 0.807338π-0.807338\pi
0.795253 + 0.606277i 0.207338π0.207338\pi
194194 −190.096 61.7658i −0.979874 0.318381i
195195 11.3351 3.68300i 0.0581287 0.0188872i
196196 229.676 166.869i 1.17181 0.851373i
197197 199.660i 1.01350i 0.862093 + 0.506751i 0.169154π0.169154\pi
−0.862093 + 0.506751i 0.830846π0.830846\pi
198198 15.5920 315.584i 0.0787477 1.59386i
199199 182.624 0.917706 0.458853 0.888512i 0.348260π-0.348260\pi
0.458853 + 0.888512i 0.348260π0.348260\pi
200200 −46.1727 63.5513i −0.230864 0.317757i
201201 −10.3886 31.9728i −0.0516845 0.159069i
202202 100.870 310.446i 0.499356 1.53686i
203203 −82.9101 60.2377i −0.408424 0.296737i
204204 −41.4708 + 57.0796i −0.203288 + 0.279802i
205205 −90.6436 29.4519i −0.442164 0.143668i
206206 −146.918 + 47.7366i −0.713195 + 0.231731i
207207 242.303 176.043i 1.17054 0.850450i
208208 124.330i 0.597740i
209209 175.603 + 268.642i 0.840207 + 1.28537i
210210 −28.7252 −0.136787
211211 80.0829 + 110.225i 0.379540 + 0.522392i 0.955463 0.295112i 0.0953571π-0.0953571\pi
−0.575923 + 0.817504i 0.695357π0.695357\pi
212212 162.851 + 501.202i 0.768163 + 2.36416i
213213 0.703432 2.16494i 0.00330250 0.0101640i
214214 181.702 + 132.014i 0.849073 + 0.616888i
215215 92.4941 127.307i 0.430205 0.592126i
216216 237.490 + 77.1653i 1.09949 + 0.357247i
217217 −180.744 + 58.7271i −0.832920 + 0.270632i
218218 −516.305 + 375.117i −2.36837 + 1.72072i
219219 122.319i 0.558533i
220220 −161.957 130.349i −0.736167 0.592497i
221221 51.7402 0.234118
222222 −41.9466 57.7346i −0.188949 0.260066i
223223 −12.5350 38.5788i −0.0562108 0.172999i 0.919009 0.394236i 0.128991π-0.128991\pi
−0.975220 + 0.221237i 0.928991π0.928991\pi
224224 16.3615 50.3555i 0.0730424 0.224801i
225225 32.9273 + 23.9231i 0.146344 + 0.106325i
226226 151.020 207.861i 0.668230 0.919740i
227227 181.180 + 58.8689i 0.798148 + 0.259334i 0.679570 0.733611i 0.262166π-0.262166\pi
0.118578 + 0.992945i 0.462166π0.462166\pi
228228 −217.491 + 70.6672i −0.953909 + 0.309944i
229229 185.982 135.124i 0.812148 0.590060i −0.102304 0.994753i 0.532622π-0.532622\pi
0.914453 + 0.404693i 0.132622π0.132622\pi
230230 290.322i 1.26227i
231231 −38.6493 + 10.4801i −0.167313 + 0.0453685i
232232 410.130 1.76780
233233 111.299 + 153.190i 0.477678 + 0.657467i 0.978057 0.208340i 0.0668059π-0.0668059\pi
−0.500379 + 0.865807i 0.666806π0.666806\pi
234234 −51.0197 157.022i −0.218033 0.671036i
235235 −12.2168 + 37.5994i −0.0519863 + 0.159997i
236236 −266.191 193.399i −1.12793 0.819486i
237237 −23.1299 + 31.8355i −0.0975944 + 0.134327i
238238 −118.598 38.5349i −0.498312 0.161912i
239239 −106.671 + 34.6595i −0.446322 + 0.145019i −0.523551 0.851994i 0.675393π-0.675393\pi
0.0772283 + 0.997013i 0.475393π0.475393\pi
240240 36.2865 26.3637i 0.151194 0.109849i
241241 118.124i 0.490141i 0.969505 + 0.245070i 0.0788110π0.0788110\pi
−0.969505 + 0.245070i 0.921189π0.921189\pi
242242 −391.099 171.331i −1.61611 0.707978i
243243 −197.317 −0.812006
244244 223.278 + 307.316i 0.915076 + 1.25949i
245245 23.2089 + 71.4298i 0.0947304 + 0.291550i
246246 43.1004 132.649i 0.175205 0.539225i
247247 135.674 + 98.5731i 0.549288 + 0.399081i
248248 447.040 615.298i 1.80258 2.48104i
249249 68.0967 + 22.1260i 0.273481 + 0.0888593i
250250 37.5218 12.1916i 0.150087 0.0487664i
251251 148.903 108.184i 0.593240 0.431014i −0.250233 0.968186i 0.580507π-0.580507\pi
0.843473 + 0.537172i 0.180507π0.180507\pi
252252 270.099i 1.07182i
253253 −105.921 390.623i −0.418661 1.54397i
254254 −412.606 −1.62443
255255 −10.9713 15.1007i −0.0430247 0.0592184i
256256 −160.509 493.997i −0.626990 1.92968i
257257 −124.017 + 381.685i −0.482557 + 1.48516i 0.352932 + 0.935649i 0.385185π0.385185\pi
−0.835489 + 0.549507i 0.814815π0.814815\pi
258258 186.303 + 135.357i 0.722106 + 0.524641i
259259 50.3234 69.2642i 0.194299 0.267429i
260260 −103.315 33.5692i −0.397366 0.129112i
261261 −202.097 + 65.6652i −0.774317 + 0.251591i
262262 118.894 86.3812i 0.453792 0.329699i
263263 72.9866i 0.277516i 0.990326 + 0.138758i 0.0443110π0.0443110\pi
−0.990326 + 0.138758i 0.955689π0.955689\pi
264264 100.480 124.845i 0.380607 0.472898i
265265 −139.419 −0.526110
266266 −237.576 326.996i −0.893144 1.22931i
267267 −30.1791 92.8816i −0.113030 0.347871i
268268 −94.6882 + 291.420i −0.353314 + 1.08739i
269269 −161.917 117.640i −0.601923 0.437322i 0.244638 0.969614i 0.421331π-0.421331\pi
−0.846561 + 0.532292i 0.821331π0.821331\pi
270270 −73.7173 + 101.463i −0.273027 + 0.375789i
271271 144.974 + 47.1049i 0.534959 + 0.173819i 0.564023 0.825759i 0.309253π-0.309253\pi
−0.0290645 + 0.999578i 0.509253π0.509253\pi
272272 185.184 60.1698i 0.680822 0.221213i
273273 −16.9284 + 12.2992i −0.0620089 + 0.0450521i
274274 374.025i 1.36505i
275275 46.0370 30.0931i 0.167407 0.109429i
276276 288.384 1.04487
277277 −121.855 167.719i −0.439911 0.605485i 0.530281 0.847822i 0.322086π-0.322086\pi
−0.970192 + 0.242336i 0.922086π0.922086\pi
278278 36.1857 + 111.368i 0.130164 + 0.400605i
279279 −121.770 + 374.771i −0.436453 + 1.34327i
280280 111.574 + 81.0636i 0.398480 + 0.289513i
281281 −72.0371 + 99.1506i −0.256360 + 0.352849i −0.917726 0.397214i 0.869977π-0.869977\pi
0.661366 + 0.750063i 0.269977π0.269977\pi
282282 −55.0235 17.8782i −0.195119 0.0633980i
283283 158.184 51.3970i 0.558953 0.181615i −0.0158971 0.999874i 0.505060π-0.505060\pi
0.574850 + 0.818259i 0.305060π0.305060\pi
284284 −16.7856 + 12.1954i −0.0591042 + 0.0429417i
285285 60.4994i 0.212279i
286286 −222.838 11.0098i −0.779155 0.0384957i
287287 167.329 0.583028
288288 −64.5301 88.8181i −0.224063 0.308396i
289289 64.2661 + 197.791i 0.222374 + 0.684397i
290290 −63.6524 + 195.902i −0.219491 + 0.675524i
291291 42.4943 + 30.8739i 0.146028 + 0.106096i
292292 −655.316 + 901.965i −2.24423 + 3.08892i
293293 48.4902 + 15.7554i 0.165496 + 0.0537728i 0.390593 0.920564i 0.372270π-0.372270\pi
−0.225097 + 0.974336i 0.572270π0.572270\pi
294294 −104.531 + 33.9643i −0.355549 + 0.115525i
295295 70.4220 51.1646i 0.238719 0.173439i
296296 342.628i 1.15753i
297297 −62.1675 + 163.412i −0.209318 + 0.550209i
298298 425.574 1.42810
299299 −124.307 171.093i −0.415741 0.572219i
300300 12.1102 + 37.2714i 0.0403674 + 0.124238i
301301 −85.3725 + 262.749i −0.283629 + 0.872922i
302302 −195.976 142.385i −0.648927 0.471473i
303303 −50.4203 + 69.3976i −0.166404 + 0.229035i
304304 600.226 + 195.025i 1.97443 + 0.641530i
305305 −95.5763 + 31.0546i −0.313365 + 0.101818i
306306 −209.186 + 151.983i −0.683615 + 0.496675i
307307 388.897i 1.26676i −0.773839 0.633382i 0.781666π-0.781666\pi
0.773839 0.633382i 0.218334π-0.218334\pi
308308 341.143 + 129.782i 1.10761 + 0.421371i
309309 40.5954 0.131377
310310 224.521 + 309.027i 0.724263 + 0.996862i
311311 −12.6147 38.8239i −0.0405616 0.124836i 0.928725 0.370769i 0.120906π-0.120906\pi
−0.969287 + 0.245933i 0.920906π0.920906\pi
312312 25.8769 79.6410i 0.0829389 0.255260i
313313 414.787 + 301.360i 1.32520 + 0.962812i 0.999852 + 0.0172161i 0.00548034π0.00548034\pi
0.325345 + 0.945595i 0.394520π0.394520\pi
314314 388.291 534.437i 1.23660 1.70203i
315315 −67.9587 22.0811i −0.215742 0.0700988i
316316 341.114 110.835i 1.07948 0.350743i
317317 −142.274 + 103.368i −0.448814 + 0.326083i −0.789127 0.614230i 0.789467π-0.789467\pi
0.340313 + 0.940312i 0.389467π0.389467\pi
318318 204.028i 0.641598i
319319 −14.1702 + 286.806i −0.0444207 + 0.899077i
320320 87.0516 0.272036
321321 −34.6918 47.7492i −0.108074 0.148751i
322322 157.508 + 484.760i 0.489155 + 1.50547i
323323 81.1601 249.785i 0.251270 0.773328i
324324 400.168 + 290.739i 1.23509 + 0.897343i
325325 16.8924 23.2505i 0.0519767 0.0715399i
326326 −121.193 39.3781i −0.371759 0.120792i
327327 159.500 51.8248i 0.487769 0.158486i
328328 −541.752 + 393.606i −1.65168 + 1.20002i
329329 69.4088i 0.210969i
330330 44.0387 + 67.3713i 0.133451 + 0.204156i
331331 −97.5050 −0.294577 −0.147289 0.989094i 0.547055π-0.547055\pi
−0.147289 + 0.989094i 0.547055π0.547055\pi
332332 −383.600 527.979i −1.15542 1.59030i
333333 −54.8576 168.834i −0.164737 0.507010i
334334 167.377 515.132i 0.501127 1.54231i
335335 −65.5823 47.6484i −0.195768 0.142234i
336336 −46.2856 + 63.7067i −0.137755 + 0.189603i
337337 147.559 + 47.9448i 0.437860 + 0.142269i 0.519648 0.854380i 0.326063π-0.326063\pi
−0.0817878 + 0.996650i 0.526063π0.526063\pi
338338 456.298 148.260i 1.34999 0.438639i
339339 −54.6237 + 39.6864i −0.161132 + 0.117069i
340340 170.129i 0.500379i
341341 414.835 + 333.876i 1.21653 + 0.979109i
342342 −838.084 −2.45054
343343 −190.574 262.302i −0.555608 0.764729i
344344 −341.656 1051.51i −0.993187 3.05671i
345345 −23.5760 + 72.5593i −0.0683361 + 0.210317i
346346 −4.94214 3.59068i −0.0142837 0.0103777i
347347 29.5186 40.6288i 0.0850680 0.117086i −0.764362 0.644787i 0.776946π-0.776946\pi
0.849430 + 0.527701i 0.176946π0.176946\pi
348348 −194.594 63.2275i −0.559179 0.181688i
349349 −146.948 + 47.7462i −0.421053 + 0.136809i −0.511878 0.859058i 0.671050π-0.671050\pi
0.0908242 + 0.995867i 0.471050π0.471050\pi
350350 −56.0371 + 40.7134i −0.160106 + 0.116324i
351351 91.3580i 0.260279i
352352 −143.186 + 38.8263i −0.406779 + 0.110302i
353353 −559.143 −1.58397 −0.791987 0.610538i 0.790953π-0.790953\pi
−0.791987 + 0.610538i 0.790953π0.790953\pi
354354 74.8751 + 103.057i 0.211511 + 0.291121i
355355 −1.69620 5.22037i −0.00477803 0.0147053i
356356 −275.071 + 846.582i −0.772672 + 2.37804i
357357 26.5117 + 19.2619i 0.0742624 + 0.0539548i
358358 −179.403 + 246.927i −0.501125 + 0.689739i
359359 −646.648 210.109i −1.80125 0.585261i −0.801331 0.598221i 0.795874π-0.795874\pi
−0.999916 + 0.0129603i 0.995874π0.995874\pi
360360 271.967 88.3675i 0.755465 0.245465i
361361 396.644 288.179i 1.09874 0.798279i
362362 632.077i 1.74607i
363363 83.8331 + 74.5799i 0.230945 + 0.205454i
364364 190.721 0.523959
365365 −173.367 238.619i −0.474978 0.653751i
366366 −45.4458 139.868i −0.124169 0.382153i
367367 139.082 428.051i 0.378970 1.16635i −0.561791 0.827279i 0.689887π-0.689887\pi
0.940761 0.339071i 0.110113π-0.110113\pi
368368 −643.875 467.803i −1.74966 1.27120i
369369 203.936 280.693i 0.552671 0.760686i
370370 −163.659 53.1760i −0.442322 0.143719i
371371 232.793 75.6389i 0.627473 0.203878i
372372 −306.965 + 223.023i −0.825173 + 0.599524i
373373 396.273i 1.06239i −0.847248 0.531197i 0.821742π-0.821742\pi
0.847248 0.531197i 0.178258π-0.178258\pi
374374 91.4446 + 337.235i 0.244504 + 0.901699i
375375 −10.3678 −0.0276474
376376 163.269 + 224.721i 0.434227 + 0.597662i
377377 46.3672 + 142.703i 0.122990 + 0.378524i
378378 68.0414 209.410i 0.180004 0.553995i
379379 −429.812 312.277i −1.13407 0.823950i −0.147787 0.989019i 0.547215π-0.547215\pi
−0.986282 + 0.165069i 0.947215π0.947215\pi
380380 −324.122 + 446.116i −0.852954 + 1.17399i
381381 103.121 + 33.5062i 0.270660 + 0.0879427i
382382 1136.25 369.190i 2.97448 0.966467i
383383 500.006 363.276i 1.30550 0.948500i 0.305506 0.952190i 0.401175π-0.401175\pi
0.999993 + 0.00368998i 0.00117456π0.00117456\pi
384384 177.420i 0.462031i
385385 −60.5431 + 75.2238i −0.157255 + 0.195386i
386386 −31.3970 −0.0813393
387387 336.711 + 463.443i 0.870054 + 1.19753i
388388 −147.943 455.322i −0.381297 1.17351i
389389 3.92137 12.0687i 0.0100806 0.0310250i −0.945890 0.324488i 0.894808π-0.894808\pi
0.955970 + 0.293463i 0.0948079π0.0948079\pi
390390 34.0251 + 24.7207i 0.0872438 + 0.0633864i
391391 −194.677 + 267.950i −0.497895 + 0.685294i
392392 501.870 + 163.067i 1.28028 + 0.415988i
393393 −36.7294 + 11.9341i −0.0934591 + 0.0303667i
394394 −569.995 + 414.126i −1.44669 + 1.05108i
395395 94.8876i 0.240222i
396396 633.483 414.090i 1.59970 1.04568i
397397 −240.779 −0.606497 −0.303249 0.952911i 0.598071π-0.598071\pi
−0.303249 + 0.952911i 0.598071π0.598071\pi
398398 378.790 + 521.359i 0.951733 + 1.30995i
399399 32.8227 + 101.018i 0.0822623 + 0.253177i
400400 33.4214 102.860i 0.0835535 0.257151i
401401 581.860 + 422.746i 1.45102 + 1.05423i 0.985591 + 0.169145i 0.0541008π0.0541008\pi
0.465431 + 0.885084i 0.345899π0.345899\pi
402402 69.7294 95.9743i 0.173456 0.238742i
403403 264.631 + 85.9839i 0.656653 + 0.213360i
404404 743.588 241.606i 1.84056 0.598036i
405405 −105.866 + 76.9165i −0.261399 + 0.189917i
406406 361.637i 0.890731i
407407 −239.601 11.8380i −0.588701 0.0290859i
408408 −131.145 −0.321433
409409 −62.9642 86.6628i −0.153947 0.211890i 0.725077 0.688668i 0.241804π-0.241804\pi
−0.879023 + 0.476779i 0.841804π0.841804\pi
410410 −103.929 319.860i −0.253485 0.780147i
411411 −30.3731 + 93.4789i −0.0739006 + 0.227443i
412412 −299.346 217.488i −0.726568 0.527882i
413413 −89.8276 + 123.637i −0.217500 + 0.299363i
414414 1005.15 + 326.592i 2.42789 + 0.788870i
415415 164.203 53.3528i 0.395670 0.128561i
416416 −62.7158 + 45.5657i −0.150759 + 0.109533i
417417 30.7724i 0.0737948i
418418 −402.698 + 1058.52i −0.963392 + 2.53235i
419419 29.4752 0.0703464 0.0351732 0.999381i 0.488802π-0.488802\pi
0.0351732 + 0.999381i 0.488802π0.488802\pi
420420 −40.4416 55.6631i −0.0962895 0.132531i
421421 −127.694 393.002i −0.303311 0.933496i −0.980302 0.197504i 0.936716π-0.936716\pi
0.676991 0.735991i 0.263284π-0.263284\pi
422422 −148.568 + 457.247i −0.352058 + 1.08352i
423423 −116.433 84.5934i −0.275255 0.199984i
424424 −575.775 + 792.487i −1.35796 + 1.86907i
425425 −42.8056 13.9084i −0.100719 0.0327256i
426426 7.63957 2.48225i 0.0179333 0.00582687i
427427 142.739 103.706i 0.334283 0.242871i
428428 537.957i 1.25691i
429429 54.7993 + 20.8475i 0.127737 + 0.0485956i
430430 555.288 1.29137
431431 115.324 + 158.730i 0.267574 + 0.368284i 0.921569 0.388215i 0.126908π-0.126908\pi
−0.653995 + 0.756499i 0.726908π0.726908\pi
432432 106.242 + 326.980i 0.245931 + 0.756898i
433433 −25.9577 + 79.8895i −0.0599484 + 0.184502i −0.976546 0.215309i 0.930924π-0.930924\pi
0.916598 + 0.399811i 0.130924π0.130924\pi
434434 −542.547 394.183i −1.25011 0.908256i
435435 31.8169 43.7922i 0.0731423 0.100672i
436436 −1453.79 472.364i −3.33438 1.08340i
437437 −1020.97 + 331.734i −2.33632 + 0.759117i
438438 349.199 253.708i 0.797258 0.579242i
439439 139.738i 0.318309i −0.987254 0.159154i 0.949123π-0.949123\pi
0.987254 0.159154i 0.0508768π-0.0508768\pi
440440 19.0692 385.962i 0.0433392 0.877187i
441441 −273.411 −0.619980
442442 107.317 + 147.709i 0.242799 + 0.334184i
443443 91.4047 + 281.315i 0.206331 + 0.635022i 0.999656 + 0.0262237i 0.00834822π0.00834822\pi
−0.793325 + 0.608799i 0.791652π0.791652\pi
444444 52.8211 162.567i 0.118966 0.366141i
445445 −190.518 138.419i −0.428130 0.311055i
446446 84.1364 115.804i 0.188647 0.259650i
447447 −106.363 34.5593i −0.237948 0.0773139i
448448 −145.353 + 47.2280i −0.324448 + 0.105420i
449449 −532.550 + 386.920i −1.18608 + 0.861737i −0.992844 0.119415i 0.961898π-0.961898\pi
−0.193235 + 0.981153i 0.561898π0.561898\pi
450450 143.622i 0.319160i
451451 −256.532 392.449i −0.568808 0.870175i
452452 615.407 1.36152
453453 37.4171 + 51.5003i 0.0825986 + 0.113687i
454454 207.734 + 639.341i 0.457565 + 1.40824i
455455 −15.5918 + 47.9867i −0.0342677 + 0.105465i
456456 −343.891 249.851i −0.754146 0.547919i
457457 87.2258 120.056i 0.190866 0.262705i −0.702849 0.711339i 0.748089π-0.748089\pi
0.893716 + 0.448634i 0.148089π0.148089\pi
458458 771.512 + 250.679i 1.68452 + 0.547335i
459459 136.073 44.2129i 0.296456 0.0963244i
460460 562.580 408.738i 1.22300 0.888561i
461461 500.817i 1.08637i −0.839613 0.543185i 0.817218π-0.817218\pi
0.839613 0.543185i 0.182782π-0.182782\pi
462462 −110.084 88.5998i −0.238276 0.191774i
463463 −398.770 −0.861275 −0.430638 0.902525i 0.641711π-0.641711\pi
−0.430638 + 0.902525i 0.641711π0.641711\pi
464464 331.906 + 456.830i 0.715315 + 0.984547i
465465 −31.0191 95.4668i −0.0667076 0.205305i
466466 −206.480 + 635.479i −0.443090 + 1.36369i
467467 508.794 + 369.661i 1.08949 + 0.791564i 0.979314 0.202347i 0.0648569π-0.0648569\pi
0.110181 + 0.993912i 0.464857π0.464857\pi
468468 232.445 319.933i 0.496677 0.683618i
469469 135.356 + 43.9797i 0.288604 + 0.0937733i
470470 −132.679 + 43.1101i −0.282297 + 0.0917237i
471471 −140.444 + 102.039i −0.298183 + 0.216642i
472472 611.593i 1.29575i
473473 747.130 202.592i 1.57956 0.428312i
474474 −138.860 −0.292954
475475 −85.7481 118.022i −0.180522 0.248468i
476476 −92.2999 284.070i −0.193907 0.596785i
477477 156.837 482.694i 0.328799 1.01194i
478478 −320.200 232.639i −0.669874 0.486692i
479479 −56.6925 + 78.0306i −0.118356 + 0.162903i −0.864084 0.503347i 0.832102π-0.832102\pi
0.745728 + 0.666250i 0.232102π0.232102\pi
480480 26.5972 + 8.64197i 0.0554109 + 0.0180041i
481481 −119.216 + 38.7357i −0.247851 + 0.0805317i
482482 −337.224 + 245.007i −0.699634 + 0.508314i
483483 133.945i 0.277319i
484484 −218.619 999.076i −0.451692 2.06421i
485485 126.657 0.261148
486486 −409.267 563.308i −0.842114 1.15907i
487487 247.215 + 760.849i 0.507628 + 1.56232i 0.796307 + 0.604892i 0.206784π0.206784\pi
−0.288680 + 0.957426i 0.593216π0.593216\pi
488488 −218.192 + 671.525i −0.447114 + 1.37607i
489489 27.0918 + 19.6833i 0.0554024 + 0.0402522i
490490 −155.781 + 214.414i −0.317920 + 0.437580i
491491 −800.353 260.050i −1.63005 0.529634i −0.655764 0.754966i 0.727653π-0.727653\pi
−0.974282 + 0.225332i 0.927653π0.927653\pi
492492 317.725 103.235i 0.645783 0.209828i
493493 190.110 138.123i 0.385620 0.280169i
494494 591.783i 1.19794i
495495 52.3992 + 193.241i 0.105857 + 0.390386i
496496 1047.14 2.11116
497497 5.66440 + 7.79638i 0.0113972 + 0.0156869i
498498 78.0774 + 240.298i 0.156782 + 0.482525i
499499 −220.886 + 679.818i −0.442658 + 1.36236i 0.442374 + 0.896830i 0.354136π0.354136\pi
−0.885032 + 0.465530i 0.845864π0.845864\pi
500500 76.4508 + 55.5448i 0.152902 + 0.111090i
501501 −83.6639 + 115.153i −0.166994 + 0.229847i
502502 617.697 + 200.702i 1.23047 + 0.399805i
503503 −660.549 + 214.625i −1.31322 + 0.426690i −0.880161 0.474676i 0.842565π-0.842565\pi
−0.433057 + 0.901366i 0.642565π0.642565\pi
504504 −406.170 + 295.100i −0.805894 + 0.585516i
505505 206.843i 0.409591i
506506 895.466 1112.60i 1.76970 2.19882i
507507 −126.081 −0.248680
508508 −580.899 799.539i −1.14350 1.57390i
509509 −7.78172 23.9497i −0.0152883 0.0470524i 0.943121 0.332449i 0.107875π-0.107875\pi
−0.958410 + 0.285396i 0.907875π0.907875\pi
510510 20.3537 62.6424i 0.0399093 0.122828i
511511 418.934 + 304.373i 0.819832 + 0.595643i
512512 627.525 863.714i 1.22563 1.68694i
513513 441.047 + 143.305i 0.859741 + 0.279347i
514514 −1346.88 + 437.627i −2.62038 + 0.851415i
515515 79.1934 57.5374i 0.153774 0.111723i
516516 551.581i 1.06896i
517517 −162.789 + 106.411i −0.314873 + 0.205824i
518518 302.116 0.583236
519519 0.943590 + 1.29874i 0.00181809 + 0.00250239i
520520 −62.3976 192.040i −0.119995 0.369308i
521521 144.330 444.202i 0.277025 0.852596i −0.711651 0.702533i 0.752052π-0.752052\pi
0.988676 0.150063i 0.0479476π-0.0479476\pi
522522 −606.643 440.752i −1.16215 0.844353i
523523 −469.788 + 646.608i −0.898257 + 1.23634i 0.0727642 + 0.997349i 0.476818π0.476818\pi
−0.971021 + 0.238995i 0.923182π0.923182\pi
524524 334.775 + 108.775i 0.638884 + 0.207586i
525525 17.3114 5.62481i 0.0329741 0.0107139i
526526 −208.365 + 151.386i −0.396130 + 0.287806i
527527 435.768i 0.826884i
528528 220.377 + 10.8881i 0.417380 + 0.0206215i
529529 824.767 1.55911
530530 −289.177 398.018i −0.545617 0.750978i
531531 97.9211 + 301.370i 0.184409 + 0.567552i
532532 299.167 920.740i 0.562343 1.73071i
533533 −198.202 144.002i −0.371860 0.270172i
534534 202.565 278.807i 0.379336 0.522111i
535535 −135.354 43.9790i −0.252997 0.0822038i
536536 −541.686 + 176.004i −1.01061 + 0.328366i
537537 64.8896 47.1450i 0.120837 0.0877934i
538538 706.250i 1.31273i
539539 −131.374 + 345.326i −0.243736 + 0.640679i
540540 −300.398 −0.556293
541541 631.800 + 869.598i 1.16784 + 1.60739i 0.676564 + 0.736383i 0.263468π0.263468\pi
0.491272 + 0.871006i 0.336532π0.336532\pi
542542 166.222 + 511.579i 0.306683 + 0.943872i
543543 −51.3286 + 157.973i −0.0945278 + 0.290927i
544544 98.2193 + 71.3605i 0.180550 + 0.131177i
545545 237.700 327.166i 0.436147 0.600304i
546546 −70.2245 22.8173i −0.128616 0.0417899i
547547 322.941 104.930i 0.590386 0.191828i 0.00143823 0.999999i 0.499542π-0.499542\pi
0.588948 + 0.808171i 0.299542π0.299542\pi
548548 724.777 526.581i 1.32259 0.960915i
549549 365.837i 0.666369i
550550 181.399 + 69.0102i 0.329816 + 0.125473i
551551 761.659 1.38232
552552 315.078 + 433.667i 0.570793 + 0.785629i
553553 −51.4792 158.437i −0.0930909 0.286504i
554554 226.064 695.753i 0.408057 1.25587i
555555 36.5846 + 26.5803i 0.0659182 + 0.0478924i
556556 −164.862 + 226.913i −0.296514 + 0.408116i
557557 393.990 + 128.015i 0.707344 + 0.229830i 0.640527 0.767935i 0.278716π-0.278716\pi
0.0668164 + 0.997765i 0.478716π0.478716\pi
558558 −1322.48 + 429.700i −2.37003 + 0.770071i
559559 327.244 237.757i 0.585409 0.425325i
560560 189.881i 0.339074i
561561 4.53112 91.7101i 0.00807686 0.163476i
562562 −432.475 −0.769528
563563 −471.902 649.518i −0.838193 1.15367i −0.986342 0.164708i 0.947332π-0.947332\pi
0.148150 0.988965i 0.452668π-0.452668\pi
564564 −42.8224 131.794i −0.0759262 0.233677i
565565 −50.3107 + 154.840i −0.0890455 + 0.274054i
566566 474.827 + 344.982i 0.838918 + 0.609509i
567567 135.039 185.865i 0.238164 0.327805i
568568 −36.6786 11.9176i −0.0645750 0.0209817i
569569 436.517 141.833i 0.767165 0.249267i 0.100814 0.994905i 0.467855π-0.467855\pi
0.666351 + 0.745638i 0.267855π0.267855\pi
570570 172.716 125.485i 0.303010 0.220150i
571571 203.201i 0.355869i −0.984042 0.177935i 0.943058π-0.943058\pi
0.984042 0.177935i 0.0569416π-0.0569416\pi
572572 −292.395 447.312i −0.511180 0.782014i
573573 −313.961 −0.547924
574574 347.067 + 477.696i 0.604646 + 0.832223i
575575 56.8492 + 174.964i 0.0988682 + 0.304285i
576576 −97.9271 + 301.388i −0.170012 + 0.523244i
577577 −655.994 476.608i −1.13690 0.826010i −0.150220 0.988653i 0.547998π-0.547998\pi
−0.986685 + 0.162643i 0.947998π0.947998\pi
578578 −431.362 + 593.718i −0.746300 + 1.02719i
579579 7.84696 + 2.54963i 0.0135526 + 0.00440351i
580580 −469.229 + 152.462i −0.809016 + 0.262865i
581581 −245.230 + 178.170i −0.422082 + 0.306661i
582582 185.351i 0.318473i
583583 −534.296 430.023i −0.916460 0.737604i
584584 −2072.33 −3.54851
585585 61.4944 + 84.6398i 0.105119 + 0.144684i
586586 55.5972 + 171.111i 0.0948758 + 0.291998i
587587 18.3545 56.4895i 0.0312684 0.0962342i −0.934204 0.356738i 0.883889π-0.883889\pi
0.965473 + 0.260504i 0.0838888π0.0838888\pi
588588 −212.983 154.741i −0.362216 0.263165i
589589 830.206 1142.68i 1.40952 1.94003i
590590 292.132 + 94.9196i 0.495140 + 0.160881i
591591 176.087 57.2141i 0.297947 0.0968090i
592592 −381.641 + 277.279i −0.644665 + 0.468376i
593593 1164.75i 1.96416i 0.188457 + 0.982081i 0.439651π0.439651\pi
−0.188457 + 0.982081i 0.560349π0.560349\pi
594594 −595.459 + 161.464i −1.00246 + 0.271826i
595595 79.0195 0.132806
596596 599.157 + 824.669i 1.00530 + 1.38367i
597597 −52.3322 161.062i −0.0876586 0.269786i
598598 230.612 709.749i 0.385638 1.18687i
599599 −196.571 142.817i −0.328165 0.238426i 0.411487 0.911416i 0.365010π-0.365010\pi
−0.739651 + 0.672990i 0.765010π0.765010\pi
600600 −42.8169 + 58.9324i −0.0713615 + 0.0982207i
601601 −572.415 185.989i −0.952438 0.309466i −0.208732 0.977973i 0.566934π-0.566934\pi
−0.743706 + 0.668507i 0.766934π0.766934\pi
602602 −927.181 + 301.260i −1.54017 + 0.500431i
603603 238.743 173.457i 0.395925 0.287656i
604604 580.218i 0.960626i
605605 269.247 + 26.6704i 0.445036 + 0.0440833i
606606 −302.698 −0.499502
607607 135.753 + 186.849i 0.223646 + 0.307823i 0.906065 0.423139i 0.139072π-0.139072\pi
−0.682418 + 0.730962i 0.739072π0.739072\pi
608608 121.600 + 374.246i 0.200000 + 0.615537i
609609 −29.3672 + 90.3829i −0.0482220 + 0.148412i
610610 −286.896 208.442i −0.470321 0.341708i
611611 −59.7326 + 82.2149i −0.0977621 + 0.134558i
612612 −589.017 191.383i −0.962447 0.312718i
613613 670.628 217.900i 1.09401 0.355465i 0.294215 0.955739i 0.404942π-0.404942\pi
0.799794 + 0.600274i 0.204942π0.204942\pi
614614 1110.23 806.633i 1.80820 1.31373i
615615 88.3814i 0.143710i
616616 177.555 + 654.799i 0.288239 + 1.06299i
617617 −181.458 −0.294097 −0.147049 0.989129i 0.546977π-0.546977\pi
−0.147049 + 0.989129i 0.546977π0.546977\pi
618618 84.2011 + 115.893i 0.136248 + 0.187529i
619619 323.645 + 996.077i 0.522852 + 1.60917i 0.768526 + 0.639819i 0.220991π0.220991\pi
−0.245674 + 0.969352i 0.579009π0.579009\pi
620620 −282.727 + 870.145i −0.456012 + 1.40346i
621621 −473.121 343.743i −0.761870 0.553531i
622622 84.6710 116.540i 0.136127 0.187363i
623623 393.210 + 127.762i 0.631156 + 0.205075i
624624 109.651 35.6277i 0.175723 0.0570958i
625625 −20.2254 + 14.6946i −0.0323607 + 0.0235114i
626626 1809.21i 2.89012i
627627 186.604 231.852i 0.297614 0.369780i
628628 1582.29 2.51956
629629 115.390 + 158.821i 0.183450 + 0.252497i
630630 −77.9191 239.810i −0.123681 0.380651i
631631 −104.631 + 322.020i −0.165817 + 0.510333i −0.999096 0.0425205i 0.986461π-0.986461\pi
0.833278 + 0.552854i 0.186461π0.186461\pi
632632 539.360 + 391.868i 0.853418 + 0.620044i
633633 74.2626 102.214i 0.117318 0.161475i
634634 −590.197 191.767i −0.930911 0.302471i
635635 248.659 80.7941i 0.391589 0.127235i
636636 395.362 287.247i 0.621638 0.451646i
637637 193.060i 0.303076i
638638 −848.173 + 554.426i −1.32942 + 0.869007i
639639 19.9820 0.0312707
640640 251.464 + 346.111i 0.392913 + 0.540798i
641641 −218.541 672.600i −0.340937 1.04930i −0.963723 0.266905i 0.913999π-0.913999\pi
0.622786 0.782393i 0.286001π-0.286001\pi
642642 64.3596 198.079i 0.100249 0.308534i
643643 793.754 + 576.696i 1.23445 + 0.896884i 0.997216 0.0745679i 0.0237578π-0.0237578\pi
0.237238 + 0.971451i 0.423758π0.423758\pi
644644 −717.605 + 987.698i −1.11429 + 1.53369i
645645 −138.781 45.0928i −0.215165 0.0699114i
646646 881.433 286.395i 1.36445 0.443336i
647647 −280.736 + 203.966i −0.433904 + 0.315250i −0.783208 0.621760i 0.786418π-0.786418\pi
0.349304 + 0.937009i 0.386418π0.386418\pi
648648 919.417i 1.41885i
649649 427.690 + 21.1309i 0.658998 + 0.0325591i
650650 101.414 0.156021
651651 103.587 + 142.575i 0.159120 + 0.219010i
652652 −94.3195 290.286i −0.144662 0.445223i
653653 344.696 1060.87i 0.527866 1.62460i −0.230712 0.973022i 0.574106π-0.574106\pi
0.758578 0.651582i 0.225894π-0.225894\pi
654654 478.780 + 347.854i 0.732079 + 0.531887i
655655 −54.7371 + 75.3391i −0.0835680 + 0.115022i
656656 −876.848 284.905i −1.33666 0.434307i
657657 1021.17 331.798i 1.55429 0.505019i
658658 198.150 143.965i 0.301141 0.218791i
659659 68.8178i 0.104428i −0.998636 0.0522138i 0.983372π-0.983372\pi
0.998636 0.0522138i 0.0166277π-0.0166277\pi
660660 −68.5496 + 180.188i −0.103863 + 0.273012i
661661 −56.9620 −0.0861754 −0.0430877 0.999071i 0.513719π-0.513719\pi
−0.0430877 + 0.999071i 0.513719π0.513719\pi
662662 −202.241 278.360i −0.305500 0.420484i
663663 −14.8266 45.6314i −0.0223628 0.0688257i
664664 374.860 1153.70i 0.564548 1.73750i
665665 207.207 + 150.545i 0.311589 + 0.226383i
666666 368.210 506.798i 0.552868 0.760958i
667667 −913.487 296.810i −1.36955 0.444993i
668668 1233.86 400.905i 1.84709 0.600157i
669669 −30.4320 + 22.1101i −0.0454888 + 0.0330495i
670670 286.057i 0.426950i
671671 −462.062 175.784i −0.688617 0.261973i
672672 −49.0988 −0.0730637
673673 220.445 + 303.417i 0.327556 + 0.450842i 0.940755 0.339086i 0.110118π-0.110118\pi
−0.613199 + 0.789928i 0.710118π0.710118\pi
674674 169.186 + 520.701i 0.251018 + 0.772554i
675675 24.5581 75.5821i 0.0363824 0.111974i
676676 929.707 + 675.472i 1.37531 + 0.999218i
677677 −341.663 + 470.259i −0.504672 + 0.694621i −0.983009 0.183555i 0.941240π-0.941240\pi
0.478338 + 0.878176i 0.341240π0.341240\pi
678678 −226.596 73.6255i −0.334212 0.108592i
679679 −211.483 + 68.7149i −0.311462 + 0.101200i
680680 −255.837 + 185.877i −0.376231 + 0.273348i
681681 176.658i 0.259410i
682682 −92.7269 + 1876.80i −0.135963 + 2.75190i
683683 −688.418 −1.00793 −0.503966 0.863723i 0.668126π-0.668126\pi
−0.503966 + 0.863723i 0.668126π0.668126\pi
684684 −1179.92 1624.02i −1.72503 2.37430i
685685 73.2394 + 225.408i 0.106919 + 0.329062i
686686 353.549 1088.11i 0.515377 1.58617i
687687 −172.465 125.303i −0.251041 0.182392i
688688 894.749 1231.52i 1.30051 1.78999i
689689 −340.838 110.745i −0.494685 0.160733i
690690 −256.045 + 83.1940i −0.371080 + 0.120571i
691691 −479.696 + 348.519i −0.694205 + 0.504369i −0.878040 0.478588i 0.841149π-0.841149\pi
0.183835 + 0.982957i 0.441149π0.441149\pi
692692 14.6320i 0.0211445i
693693 −192.331 294.233i −0.277535 0.424578i
694694 177.215 0.255353
695695 −43.6150 60.0308i −0.0627553 0.0863753i
696696 −117.526 361.707i −0.168859 0.519695i
697697 −118.564 + 364.902i −0.170106 + 0.523532i
698698 −441.100 320.478i −0.631948 0.459137i
699699 103.210 142.056i 0.147654 0.203228i
700700 −157.787 51.2681i −0.225410 0.0732401i
701701 −563.333 + 183.038i −0.803613 + 0.261110i −0.681890 0.731455i 0.738842π-0.738842\pi
−0.121723 + 0.992564i 0.538842π0.538842\pi
702702 −260.812 + 189.491i −0.371527 + 0.269930i
703703 636.300i 0.905120i
704704 333.608 + 268.501i 0.473875 + 0.381394i
705705 36.6610 0.0520014
706706 −1159.75 1596.26i −1.64270 2.26099i
707707 −112.219 345.373i −0.158725 0.488505i
708708 −94.2860 + 290.183i −0.133172 + 0.409862i
709709 238.019 + 172.931i 0.335711 + 0.243909i 0.742850 0.669458i 0.233473π-0.233473\pi
−0.407139 + 0.913366i 0.633473π0.633473\pi
710710 11.3851 15.6702i 0.0160353 0.0220707i
711711 −328.518 106.742i −0.462051 0.150129i
712712 −1573.61 + 511.296i −2.21012 + 0.718112i
713713 −1440.99 + 1046.94i −2.02102 + 1.46836i
714714 115.638i 0.161959i
715715 136.450 36.9999i 0.190840 0.0517480i
716716 −731.066 −1.02104
717717 61.1349 + 84.1449i 0.0852648 + 0.117357i
718718 −741.424 2281.87i −1.03262 3.17809i
719719 184.687 568.407i 0.256866 0.790552i −0.736590 0.676339i 0.763565π-0.763565\pi
0.993456 0.114213i 0.0364346π-0.0364346\pi
720720 318.525 + 231.422i 0.442396 + 0.321419i
721721 −101.016 + 139.037i −0.140105 + 0.192839i
722722 1645.40 + 534.624i 2.27895 + 0.740477i
723723 104.178 33.8493i 0.144091 0.0468179i
724724 1224.82 889.887i 1.69175 1.22913i
725725 130.525i 0.180035i
726726 −39.0299 + 394.020i −0.0537602 + 0.542727i
727727 165.031 0.227003 0.113502 0.993538i 0.463793π-0.463793\pi
0.113502 + 0.993538i 0.463793π0.463793\pi
728728 208.375 + 286.803i 0.286229 + 0.393960i
729729 −106.214 326.894i −0.145699 0.448415i
730730 321.627 989.867i 0.440585 1.35598i
731731 −512.498 372.351i −0.701091 0.509372i
732732 207.051 284.981i 0.282856 0.389318i
733733 −35.3224 11.4769i −0.0481888 0.0156575i 0.284823 0.958580i 0.408065π-0.408065\pi
−0.333012 + 0.942923i 0.608065π0.608065\pi
734734 1510.49 490.788i 2.05789 0.668649i
735735 56.3457 40.9375i 0.0766608 0.0556973i
736736 496.235i 0.674232i
737737 −104.365 384.884i −0.141608 0.522231i
738738 1224.33 1.65898
739739 −152.133 209.393i −0.205864 0.283347i 0.693584 0.720376i 0.256031π-0.256031\pi
−0.899447 + 0.437029i 0.856031π0.856031\pi
740740 −127.369 392.000i −0.172120 0.529730i
741741 48.0565 147.903i 0.0648536 0.199599i
742742 698.785 + 507.697i 0.941758 + 0.684228i
743743 −329.255 + 453.181i −0.443143 + 0.609933i −0.970907 0.239457i 0.923030π-0.923030\pi
0.527764 + 0.849391i 0.323030π0.323030\pi
744744 −670.756 217.942i −0.901553 0.292932i
745745 −256.474 + 83.3335i −0.344261 + 0.111857i
746746 1131.29 821.932i 1.51648 1.10179i
747747 628.519i 0.841391i
748748 −524.744 + 651.986i −0.701530 + 0.871639i
749749 249.864 0.333597
750750 −21.5044 29.5982i −0.0286725 0.0394643i
751751 −231.599 712.788i −0.308387 0.949119i −0.978391 0.206761i 0.933708π-0.933708\pi
0.670004 0.742358i 0.266292π-0.266292\pi
752752 −118.180 + 363.720i −0.157154 + 0.483671i
753753 −138.081 100.322i −0.183374 0.133229i
754754 −311.222 + 428.360i −0.412761 + 0.568116i
755755 145.987 + 47.4340i 0.193360 + 0.0628264i
756756 501.584 162.975i 0.663471 0.215575i
757757 −692.859 + 503.392i −0.915270 + 0.664982i −0.942342 0.334651i 0.891382π-0.891382\pi
0.0270725 + 0.999633i 0.491382π0.491382\pi
758758 1874.75i 2.47329i
759759 −314.151 + 205.352i −0.413902 + 0.270556i
760760 −1024.99 −1.34867
761761 −94.4945 130.061i −0.124172 0.170907i 0.742405 0.669951i 0.233685π-0.233685\pi
−0.866577 + 0.499043i 0.833685π0.833685\pi
762762 118.235 + 363.891i 0.155165 + 0.477548i
763763 −219.398 + 675.238i −0.287547 + 0.884978i
764764 2315.11 + 1682.03i 3.03025 + 2.20161i
765765 96.3066 132.555i 0.125891 0.173274i
766766 2074.18 + 673.942i 2.70781 + 0.879820i
767767 212.802 69.1436i 0.277447 0.0901481i
768768 −389.678 + 283.118i −0.507393 + 0.368643i
769769 81.4227i 0.105881i −0.998598 0.0529407i 0.983141π-0.983141\pi
0.998598 0.0529407i 0.0168594π-0.0168594\pi
770770 −340.327 16.8145i −0.441983 0.0218371i
771771 372.159 0.482697
772772 −44.2031 60.8404i −0.0572579 0.0788088i
773773 140.758 + 433.209i 0.182094 + 0.560426i 0.999886 0.0150867i 0.00480244π-0.00480244\pi
−0.817793 + 0.575513i 0.804802π0.804802\pi
774774 −624.660 + 1922.51i −0.807055 + 2.48386i
775775 −195.821 142.272i −0.252672 0.183577i
776776 523.068 719.942i 0.674057 0.927760i
777777 −75.5070 24.5337i −0.0971776 0.0315749i
778778 42.5877 13.8376i 0.0547400 0.0177861i
779779 −1006.10 + 730.972i −1.29152 + 0.938346i
780780 100.737i 0.129150i
781781 9.60130 25.2378i 0.0122936 0.0323147i
782782 −1168.74 −1.49456
783783 243.885 + 335.679i 0.311476 + 0.428709i
784784 224.514 + 690.982i 0.286369 + 0.881354i
785785 −129.355 + 398.113i −0.164783 + 0.507151i
786786 −110.252 80.1031i −0.140270 0.101912i
787787 70.2003 96.6224i 0.0891999 0.122773i −0.762085 0.647477i 0.775824π-0.775824\pi
0.851285 + 0.524704i 0.175824π0.175824\pi
788788 −1604.97 521.486i −2.03676 0.661784i
789789 64.3694 20.9149i 0.0815836 0.0265081i
790790 −270.888 + 196.812i −0.342896 + 0.249129i
791791 285.837i 0.361362i
792792 1314.82 + 500.202i 1.66013 + 0.631568i
793793 −258.323 −0.325754
794794 −499.414 687.385i −0.628985 0.865724i
795795 39.9517 + 122.959i 0.0502537 + 0.154665i
796796 −476.989 + 1468.02i −0.599233 + 1.84425i
797797 1109.47 + 806.080i 1.39206 + 1.01139i 0.995636 + 0.0933265i 0.0297500π0.0297500\pi
0.396427 + 0.918066i 0.370250π0.370250\pi
798798 −220.309 + 303.230i −0.276077 + 0.379987i
799799 151.363 + 49.1808i 0.189440 + 0.0615529i
800800 64.1345 20.8386i 0.0801681 0.0260482i
801801 693.553 503.895i 0.865858 0.629083i
802802 2537.95i 3.16453i
803803 71.6002 1449.19i 0.0891659 1.80472i
804804 284.147 0.353417
805805 −189.846 261.300i −0.235833 0.324597i
806806 303.417 + 933.822i 0.376448 + 1.15859i
807807 −57.3519 + 176.511i −0.0710680 + 0.218725i
808808 1175.74 + 854.225i 1.45512 + 1.05721i
809809 −7.99326 + 11.0018i −0.00988042 + 0.0135992i −0.813929 0.580965i 0.802675π-0.802675\pi
0.804048 + 0.594564i 0.202675π0.202675\pi
810810 −439.167 142.694i −0.542182 0.176166i
811811 −203.261 + 66.0435i −0.250630 + 0.0814346i −0.431638 0.902047i 0.642064π-0.642064\pi
0.181008 + 0.983482i 0.442064π0.442064\pi
812812 700.772 509.141i 0.863020 0.627020i
813813 141.356i 0.173869i
814814 −463.175 708.575i −0.569011 0.870485i
815815 80.7486 0.0990780
816816 −106.132 146.078i −0.130063 0.179017i
817817 −634.495 1952.78i −0.776616 2.39018i
818818 116.810 359.505i 0.142800 0.439492i
819819 −148.599 107.963i −0.181439 0.131823i
820820 473.499 651.715i 0.577438 0.794775i
821821 1240.59 + 403.092i 1.51107 + 0.490977i 0.943224 0.332157i 0.107776π-0.107776\pi
0.567848 + 0.823134i 0.307776π0.307776\pi
822822 −329.865 + 107.180i −0.401296 + 0.130389i
823823 −231.338 + 168.077i −0.281091 + 0.204225i −0.719393 0.694603i 0.755580π-0.755580\pi
0.438302 + 0.898828i 0.355580π0.355580\pi
824824 687.770i 0.834672i
825825 −39.7324 31.9782i −0.0481605 0.0387615i
826826 −539.279 −0.652881
827827 −328.834 452.602i −0.397623 0.547282i 0.562522 0.826782i 0.309831π-0.309831\pi
−0.960146 + 0.279501i 0.909831π0.909831\pi
828828 782.262 + 2407.55i 0.944761 + 2.90767i
829829 −279.385 + 859.857i −0.337014 + 1.03722i 0.628707 + 0.777642i 0.283584π0.283584\pi
−0.965721 + 0.259580i 0.916416π0.916416\pi
830830 492.896 + 358.110i 0.593851 + 0.431458i
831831 −112.999 + 155.530i −0.135980 + 0.187160i
832832 212.815 + 69.1477i 0.255787 + 0.0831103i
833833 287.553 93.4317i 0.345202 0.112163i
834834 87.8501 63.8268i 0.105336 0.0765310i
835835 343.221i 0.411044i
836836 −2618.13 + 709.932i −3.13174 + 0.849201i
837837 769.439 0.919281
838838 61.1361 + 84.1466i 0.0729548 + 0.100414i
839839 −49.7340 153.066i −0.0592778 0.182438i 0.917033 0.398811i 0.130577π-0.130577\pi
−0.976311 + 0.216373i 0.930577π0.930577\pi
840840 39.5202 121.631i 0.0470479 0.144799i
841841 −129.060 93.7676i −0.153460 0.111495i
842842 857.096 1179.69i 1.01793 1.40106i
843843 108.087 + 35.1196i 0.128217 + 0.0416603i
844844 −1095.21 + 355.855i −1.29764 + 0.421629i
845845 −245.958 + 178.699i −0.291075 + 0.211478i
846846 507.856i 0.600303i
847847 −464.039 + 101.542i −0.547862 + 0.119884i
848848 −1348.68 −1.59043
849849 −90.6575 124.779i −0.106782 0.146972i
850850 −49.0794 151.051i −0.0577405 0.177707i
851851 247.959 763.139i 0.291374 0.896756i
852852 15.5656 + 11.3091i 0.0182695 + 0.0132736i
853853 859.656 1183.22i 1.00780 1.38712i 0.0873903 0.996174i 0.472147π-0.472147\pi
0.920413 0.390948i 0.127853π-0.127853\pi
854854 592.125 + 192.393i 0.693355 + 0.225285i
855855 505.075 164.109i 0.590731 0.191940i
856856 −808.971 + 587.752i −0.945059 + 0.686626i
857857 874.204i 1.02007i −0.860152 0.510037i 0.829632π-0.829632\pi
0.860152 0.510037i 0.170368π-0.170368\pi
858858 54.1462 + 199.684i 0.0631075 + 0.232732i
859859 984.004 1.14552 0.572761 0.819722i 0.305872π-0.305872\pi
0.572761 + 0.819722i 0.305872π0.305872\pi
860860 781.778 + 1076.02i 0.909044 + 1.25119i
861861 −47.9494 147.573i −0.0556904 0.171397i
862862 −213.948 + 658.463i −0.248199 + 0.763878i
863863 1110.66 + 806.939i 1.28697 + 0.935039i 0.999740 0.0228217i 0.00726500π-0.00726500\pi
0.287232 + 0.957861i 0.407265π0.407265\pi
864864 −126.002 + 173.427i −0.145835 + 0.200725i
865865 3.68151 + 1.19620i 0.00425608 + 0.00138289i
866866 −281.911 + 91.5985i −0.325533 + 0.105772i
867867 156.023 113.357i 0.179957 0.130746i
868868 1606.30i 1.85057i
869869 −292.670 + 363.638i −0.336790 + 0.418456i
870870 191.013 0.219555
871871 −122.480 168.580i −0.140620 0.193547i
872872 −878.020 2702.27i −1.00690 3.09893i
873873 −142.480 + 438.508i −0.163207 + 0.502300i
874874 −3064.70 2226.64i −3.50653 2.54764i
875875 25.7988 35.5090i 0.0294843 0.0405817i
876876 983.260 + 319.481i 1.12244 + 0.364704i
877877 −771.335 + 250.622i −0.879516 + 0.285772i −0.713756 0.700394i 0.753008π-0.753008\pi
−0.165760 + 0.986166i 0.553008π0.553008\pi
878878 398.927 289.838i 0.454359 0.330111i
879879 47.2800i 0.0537884i
880880 445.343 291.108i 0.506071 0.330804i
881881 −348.997 −0.396137 −0.198069 0.980188i 0.563467π-0.563467\pi
−0.198069 + 0.980188i 0.563467π0.563467\pi
882882 −567.098 780.543i −0.642968 0.884970i
883883 302.060 + 929.644i 0.342084 + 1.05282i 0.963127 + 0.269049i 0.0867092π0.0867092\pi
−0.621043 + 0.783776i 0.713291π0.713291\pi
884884 −135.139 + 415.914i −0.152872 + 0.470491i
885885 −65.3038 47.4460i −0.0737896 0.0536113i
886886 −613.519 + 844.436i −0.692459 + 0.953088i
887887 14.4247 + 4.68686i 0.0162623 + 0.00528395i 0.317137 0.948380i 0.397279π-0.397279\pi
−0.300875 + 0.953664i 0.597279π0.597279\pi
888888 302.175 98.1827i 0.340287 0.110566i
889889 −371.360 + 269.809i −0.417728 + 0.303497i
890890 831.000i 0.933708i
891891 −642.952 31.7663i −0.721608 0.0356525i
892892 342.856 0.384368
893893 303.210 + 417.333i 0.339541 + 0.467338i
894894 −121.952 375.329i −0.136411 0.419831i
895895 59.7661 183.941i 0.0667777 0.205521i
896896 −607.652 441.485i −0.678184 0.492729i
897897 −115.272 + 158.659i −0.128509 + 0.176877i
898898 −2209.18 717.807i −2.46011 0.799340i
899899 1201.88 390.515i 1.33691 0.434388i
900900 −278.308 + 202.202i −0.309231 + 0.224669i
901901 561.257i 0.622926i
902902 588.287 1546.36i 0.652203 1.71437i
903903 256.192 0.283712
904904 672.370 + 925.438i 0.743773 + 1.02372i
905905 123.770 + 380.924i 0.136762 + 0.420910i
906906 −69.4156 + 213.639i −0.0766177 + 0.235805i
907907 −450.207 327.095i −0.496369 0.360634i 0.311259 0.950325i 0.399249π-0.399249\pi
−0.807629 + 0.589692i 0.799249π0.799249\pi
908908 −946.436 + 1302.66i −1.04233 + 1.43464i
909909 −716.130 232.685i −0.787821 0.255979i
910910 −169.334 + 55.0199i −0.186081 + 0.0604614i
911911 264.619 192.257i 0.290471 0.211039i −0.433001 0.901394i 0.642545π-0.642545\pi
0.723472 + 0.690354i 0.242545π0.242545\pi
912912 585.246i 0.641717i
913913 793.837 + 302.002i 0.869482 + 0.330780i
914914 523.660 0.572932
915915 54.7763 + 75.3931i 0.0598648 + 0.0823968i
916916 600.434 + 1847.94i 0.655495 + 2.01741i
917917 50.5226 155.492i 0.0550955 0.169567i
918918 408.458 + 296.762i 0.444943 + 0.323270i
919919 312.999 430.806i 0.340586 0.468776i −0.604026 0.796964i 0.706438π-0.706438\pi
0.944612 + 0.328188i 0.106438π0.106438\pi
920920 1229.31 + 399.426i 1.33620 + 0.434158i
921921 −342.981 + 111.441i −0.372401 + 0.121000i
922922 1429.75 1038.77i 1.55070 1.12665i
923923 14.1096i 0.0152866i
924924 16.7023 338.056i 0.0180761 0.365861i
925925 109.042 0.117884
926926 −827.113 1138.42i −0.893210 1.22940i
927927 110.118 + 338.907i 0.118789 + 0.365596i
928928 −108.798 + 334.847i −0.117240 + 0.360826i
929929 −617.340 448.524i −0.664521 0.482803i 0.203666 0.979041i 0.434714π-0.434714\pi
−0.868187 + 0.496238i 0.834714π0.834714\pi
930930 208.203 286.567i 0.223875 0.308137i
931931 932.031 + 302.835i 1.00111 + 0.325279i
932932 −1522.12 + 494.566i −1.63317 + 0.530650i
933933 −30.6253 + 22.2506i −0.0328246 + 0.0238484i
934934 2219.26i 2.37608i
935935 −121.145 185.330i −0.129567 0.198214i
936936 735.071 0.785332
937937 930.495 + 1280.72i 0.993058 + 1.36683i 0.929489 + 0.368850i 0.120248π0.120248\pi
0.0635691 + 0.997977i 0.479752π0.479752\pi
938938 155.194 + 477.638i 0.165452 + 0.509209i
939939 146.919 452.172i 0.156464 0.481546i
940940 −270.334 196.409i −0.287590 0.208946i
941941 −325.495 + 448.005i −0.345903 + 0.476094i −0.946154 0.323717i 0.895067π-0.895067\pi
0.600251 + 0.799812i 0.295067π0.295067\pi
942942 −582.606 189.300i −0.618477 0.200956i
943943 1491.50 484.619i 1.58166 0.513912i
944944 681.233 494.945i 0.721645 0.524306i
945945 139.525i 0.147646i
946946 2128.03 + 1712.72i 2.24950 + 1.81049i
947947 945.630 0.998553 0.499276 0.866443i 0.333599π-0.333599\pi
0.499276 + 0.866443i 0.333599π0.333599\pi
948948 −195.498 269.080i −0.206222 0.283840i
949949 −234.287 721.062i −0.246878 0.759813i
950950 159.078 489.593i 0.167451 0.515361i
951951 131.934 + 95.8555i 0.138732 + 0.100794i
952952 326.336 449.163i 0.342790 0.471810i
953953 −602.472 195.755i −0.632185 0.205409i −0.0246421 0.999696i 0.507845π-0.507845\pi
−0.607543 + 0.794287i 0.707845π0.707845\pi
954954 1703.32 553.441i 1.78545 0.580127i
955955 −612.474 + 444.989i −0.641334 + 0.465957i
956956 948.003i 0.991635i
957957 257.004 69.6892i 0.268552 0.0728205i
958958 −340.353 −0.355275
959959 −244.580 336.636i −0.255037 0.351028i
960960 −24.9453 76.7738i −0.0259847 0.0799727i
961961 427.212 1314.82i 0.444549 1.36818i
962962 −357.857 259.999i −0.371993 0.270269i
963963 304.527 419.145i 0.316227 0.435249i
964964 −949.540 308.524i −0.985000 0.320046i
965965 18.9215 6.14798i 0.0196078 0.00637096i
966966 382.391 277.823i 0.395850 0.287602i
967967 855.136i 0.884318i −0.896937 0.442159i 0.854213π-0.854213\pi
0.896937 0.442159i 0.145787π-0.145787\pi
968968 1263.54 1420.31i 1.30531 1.46726i
969969 −243.551 −0.251343
970970 262.706 + 361.583i 0.270831 + 0.372766i
971971 306.329 + 942.784i 0.315478 + 0.970942i 0.975557 + 0.219746i 0.0705227π0.0705227\pi
−0.660079 + 0.751196i 0.729477π0.729477\pi
972972 515.368 1586.14i 0.530214 1.63183i
973973 105.394 + 76.5730i 0.108318 + 0.0786979i
974974 −1659.33 + 2283.88i −1.70363 + 2.34484i
975975 −25.3460 8.23543i −0.0259959 0.00844659i
976976 −924.565 + 300.409i −0.947300 + 0.307796i
977977 −46.4848 + 33.7732i −0.0475791 + 0.0345682i −0.611321 0.791383i 0.709361π-0.709361\pi
0.563742 + 0.825951i 0.309361π0.309361\pi
978978 118.169i 0.120827i
979979 −303.183 1118.10i −0.309686 1.14208i
980980 −634.808 −0.647763
981981 865.312 + 1191.00i 0.882071 + 1.21407i
982982 −917.657 2824.26i −0.934477 2.87603i
983983 218.826 673.476i 0.222610 0.685123i −0.775915 0.630837i 0.782712π-0.782712\pi
0.998525 0.0542862i 0.0172883π-0.0172883\pi
984984 502.378 + 364.999i 0.510546 + 0.370934i
985985 262.418 361.188i 0.266415 0.366688i
986986 788.638 + 256.244i 0.799835 + 0.259882i
987987 −61.2140 + 19.8896i −0.0620203 + 0.0201516i
988988 −1146.74 + 833.159i −1.16067 + 0.843278i
989989 2589.30i 2.61810i
990990 −442.987 + 550.403i −0.447461 + 0.555963i
991991 1006.83 1.01598 0.507989 0.861363i 0.330389π-0.330389\pi
0.507989 + 0.861363i 0.330389π0.330389\pi
992992 383.765 + 528.207i 0.386860 + 0.532467i
993993 27.9408 + 85.9930i 0.0281378 + 0.0865992i
994994 −10.5085 + 32.3418i −0.0105719 + 0.0325370i
995995 −330.369 240.027i −0.332029 0.241233i
996996 −355.720 + 489.606i −0.357148 + 0.491573i
997997 537.627 + 174.686i 0.539245 + 0.175211i 0.565961 0.824432i 0.308505π-0.308505\pi
−0.0267164 + 0.999643i 0.508505π0.508505\pi
998998 −2398.92 + 779.456i −2.40373 + 0.781018i
999999 −280.431 + 203.745i −0.280712 + 0.203949i
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 55.3.i.d.41.3 12
5.2 odd 4 275.3.q.f.74.1 24
5.3 odd 4 275.3.q.f.74.6 24
5.4 even 2 275.3.x.f.151.1 12
11.2 odd 10 605.3.c.d.241.11 12
11.7 odd 10 inner 55.3.i.d.51.3 yes 12
11.9 even 5 605.3.c.d.241.2 12
55.7 even 20 275.3.q.f.249.6 24
55.18 even 20 275.3.q.f.249.1 24
55.29 odd 10 275.3.x.f.51.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
55.3.i.d.41.3 12 1.1 even 1 trivial
55.3.i.d.51.3 yes 12 11.7 odd 10 inner
275.3.q.f.74.1 24 5.2 odd 4
275.3.q.f.74.6 24 5.3 odd 4
275.3.q.f.249.1 24 55.18 even 20
275.3.q.f.249.6 24 55.7 even 20
275.3.x.f.51.1 12 55.29 odd 10
275.3.x.f.151.1 12 5.4 even 2
605.3.c.d.241.2 12 11.9 even 5
605.3.c.d.241.11 12 11.2 odd 10