Properties

Label 45.3.k.a.22.5
Level 4545
Weight 33
Character 45.22
Analytic conductor 1.2261.226
Analytic rank 00
Dimension 4040
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,3,Mod(7,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([8, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 45=325 45 = 3^{2} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 45.k (of order 1212, 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: 1.226161189621.22616118962
Analytic rank: 00
Dimension: 4040
Relative dimension: 1010 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 22.5
Character χ\chi == 45.22
Dual form 45.3.k.a.43.5

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+(0.04920770.183646i)q2+(2.37796+1.82902i)q3+(3.43280+1.98193i)q4+(4.906160.964151i)q5+(0.218877+0.526704i)q6+(2.33248+8.70492i)q7+(1.070641.07064i)q8+(2.309408.69866i)q9+(0.06435870.948439i)q10+(7.0411012.1955i)q11+(11.7880+1.56570i)q12+(3.4684512.9444i)q13+(1.48385+0.856699i)q14+(9.90321+11.2662i)q15+(7.78377+13.4819i)q16+(0.7406940.740694i)q17+(1.483830.852153i)q18+7.09073iq19+(18.7527+6.41391i)q20+(10.374924.9661i)q21+(2.58614+0.692953i)q22+(5.1044119.0499i)q23+(0.587726+4.50418i)q24+(23.14089.46056i)q252.54786q26+(10.4183+24.9090i)q27+(25.2594+25.2594i)q28+(6.18301+3.56976i)q29+(1.58167+2.37306i)q30+(13.078322.6522i)q31+(8.709022.33357i)q32+(39.0493+16.1223i)q33+(0.172473+0.0995774i)q34+(3.05064+44.9566i)q35+(25.167825.2837i)q36+(23.015123.0151i)q37+(1.30218+0.348919i)q38+(31.9234+24.4375i)q39+(4.220496.28502i)q40+(36.0387+62.4209i)q41+(5.09544+0.676780i)q42+(12.04843.22835i)q4355.8198iq44+(2.9434844.9036i)q453.74961q46+(13.9048+51.8935i)q47+(43.168117.8228i)q48+(27.900016.1081i)q49+(0.5986854.71525i)q50+(3.11608+0.406601i)q51+(13.748451.3098i)q52+(17.290717.2907i)q53+(5.087090.687563i)q54+(46.303153.0446i)q55+(6.82262+11.8171i)q56+(12.969116.8615i)q57+(0.351320+1.31114i)q58+(27.540715.9006i)q59+(56.3244+19.0470i)q60+(40.7317+70.5494i)q61+(3.516433.51643i)q62+(70.3345+40.3926i)q63+60.5560iq64+(29.497160.1633i)q65+(4.882316.37790i)q66+(64.140417.1864i)q67+(1.074654.01065i)q68+(46.9807+35.9639i)q69+(8.10597+2.77245i)q7036.3928q71+(6.8406211.7857i)q72+(2.909912.90991i)q73+(5.35915+3.09411i)q74+(37.7245+64.8218i)q75+(14.0533+24.3410i)q76+(122.58432.8464i)q77+(6.058724.66008i)q78+(71.8823+41.5012i)q79+(51.1870+58.6396i)q80+(70.333340.1774i)q81+(9.68994+9.68994i)q82+(51.3796+13.7671i)q83+(13.8661106.266i)q84+(4.348112.91982i)q85+(1.18574+2.05377i)q86+(8.1738119.7976i)q87+(20.59565.51857i)q88+22.5436iq89+(8.101522.75016i)q90+120.770q91+(20.233175.5111i)q92+(10.3316+77.7864i)q93+(8.84580+5.10712i)q94+(6.83654+34.7883i)q95+(16.4416+21.4781i)q96+(9.03502+33.7192i)q97+(4.33107+4.33107i)q98+(122.346+33.0837i)q99+O(q100)q+(0.0492077 - 0.183646i) q^{2} +(-2.37796 + 1.82902i) q^{3} +(3.43280 + 1.98193i) q^{4} +(4.90616 - 0.964151i) q^{5} +(0.218877 + 0.526704i) q^{6} +(-2.33248 + 8.70492i) q^{7} +(1.07064 - 1.07064i) q^{8} +(2.30940 - 8.69866i) q^{9} +(0.0643587 - 0.948439i) q^{10} +(-7.04110 - 12.1955i) q^{11} +(-11.7880 + 1.56570i) q^{12} +(-3.46845 - 12.9444i) q^{13} +(1.48385 + 0.856699i) q^{14} +(-9.90321 + 11.2662i) q^{15} +(7.78377 + 13.4819i) q^{16} +(-0.740694 - 0.740694i) q^{17} +(-1.48383 - 0.852153i) q^{18} +7.09073i q^{19} +(18.7527 + 6.41391i) q^{20} +(-10.3749 - 24.9661i) q^{21} +(-2.58614 + 0.692953i) q^{22} +(-5.10441 - 19.0499i) q^{23} +(-0.587726 + 4.50418i) q^{24} +(23.1408 - 9.46056i) q^{25} -2.54786 q^{26} +(10.4183 + 24.9090i) q^{27} +(-25.2594 + 25.2594i) q^{28} +(-6.18301 + 3.56976i) q^{29} +(1.58167 + 2.37306i) q^{30} +(13.0783 - 22.6522i) q^{31} +(8.70902 - 2.33357i) q^{32} +(39.0493 + 16.1223i) q^{33} +(-0.172473 + 0.0995774i) q^{34} +(-3.05064 + 44.9566i) q^{35} +(25.1678 - 25.2837i) q^{36} +(-23.0151 - 23.0151i) q^{37} +(1.30218 + 0.348919i) q^{38} +(31.9234 + 24.4375i) q^{39} +(4.22049 - 6.28502i) q^{40} +(-36.0387 + 62.4209i) q^{41} +(-5.09544 + 0.676780i) q^{42} +(-12.0484 - 3.22835i) q^{43} -55.8198i q^{44} +(2.94348 - 44.9036i) q^{45} -3.74961 q^{46} +(-13.9048 + 51.8935i) q^{47} +(-43.1681 - 17.8228i) q^{48} +(-27.9000 - 16.1081i) q^{49} +(-0.598685 - 4.71525i) q^{50} +(3.11608 + 0.406601i) q^{51} +(13.7484 - 51.3098i) q^{52} +(17.2907 - 17.2907i) q^{53} +(5.08709 - 0.687563i) q^{54} +(-46.3031 - 53.0446i) q^{55} +(6.82262 + 11.8171i) q^{56} +(-12.9691 - 16.8615i) q^{57} +(0.351320 + 1.31114i) q^{58} +(-27.5407 - 15.9006i) q^{59} +(-56.3244 + 19.0470i) q^{60} +(40.7317 + 70.5494i) q^{61} +(-3.51643 - 3.51643i) q^{62} +(70.3345 + 40.3926i) q^{63} +60.5560i q^{64} +(-29.4971 - 60.1633i) q^{65} +(4.88231 - 6.37790i) q^{66} +(64.1404 - 17.1864i) q^{67} +(-1.07465 - 4.01065i) q^{68} +(46.9807 + 35.9639i) q^{69} +(8.10597 + 2.77245i) q^{70} -36.3928 q^{71} +(-6.84062 - 11.7857i) q^{72} +(2.90991 - 2.90991i) q^{73} +(-5.35915 + 3.09411i) q^{74} +(-37.7245 + 64.8218i) q^{75} +(-14.0533 + 24.3410i) q^{76} +(122.584 - 32.8464i) q^{77} +(6.05872 - 4.66008i) q^{78} +(-71.8823 + 41.5012i) q^{79} +(51.1870 + 58.6396i) q^{80} +(-70.3333 - 40.1774i) q^{81} +(9.68994 + 9.68994i) q^{82} +(51.3796 + 13.7671i) q^{83} +(13.8661 - 106.266i) q^{84} +(-4.34811 - 2.91982i) q^{85} +(-1.18574 + 2.05377i) q^{86} +(8.17381 - 19.7976i) q^{87} +(-20.5956 - 5.51857i) q^{88} +22.5436i q^{89} +(-8.10152 - 2.75016i) q^{90} +120.770 q^{91} +(20.2331 - 75.5111i) q^{92} +(10.3316 + 77.7864i) q^{93} +(8.84580 + 5.10712i) q^{94} +(6.83654 + 34.7883i) q^{95} +(-16.4416 + 21.4781i) q^{96} +(-9.03502 + 33.7192i) q^{97} +(-4.33107 + 4.33107i) q^{98} +(-122.346 + 33.0837i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q2q26q32q524q62q724q88q10+8q1130q122q1330q15+28q16+28q17+48q18114q20+12q21+14q22+82q23+1876q98+O(q100) 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/45Z)×\left(\mathbb{Z}/45\mathbb{Z}\right)^\times.

nn 1111 3737
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) e(14)e\left(\frac{1}{4}\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 0.0492077 0.183646i 0.0246039 0.0918228i −0.952532 0.304438i 0.901531π-0.901531\pi
0.977136 + 0.212615i 0.0681980π0.0681980\pi
33 −2.37796 + 1.82902i −0.792654 + 0.609672i
44 3.43280 + 1.98193i 0.858199 + 0.495482i
55 4.90616 0.964151i 0.981232 0.192830i
66 0.218877 + 0.526704i 0.0364795 + 0.0877840i
77 −2.33248 + 8.70492i −0.333211 + 1.24356i 0.572585 + 0.819846i 0.305941π0.305941\pi
−0.905796 + 0.423715i 0.860726π0.860726\pi
88 1.07064 1.07064i 0.133831 0.133831i
99 2.30940 8.69866i 0.256600 0.966518i
1010 0.0643587 0.948439i 0.00643587 0.0948439i
1111 −7.04110 12.1955i −0.640100 1.10869i −0.985410 0.170197i 0.945560π-0.945560\pi
0.345310 0.938489i 0.387774π-0.387774\pi
1212 −11.7880 + 1.56570i −0.982336 + 0.130475i
1313 −3.46845 12.9444i −0.266804 0.995725i −0.961137 0.276071i 0.910967π-0.910967\pi
0.694333 0.719653i 0.255699π-0.255699\pi
1414 1.48385 + 0.856699i 0.105989 + 0.0611928i
1515 −9.90321 + 11.2662i −0.660214 + 0.751077i
1616 7.78377 + 13.4819i 0.486486 + 0.842618i
1717 −0.740694 0.740694i −0.0435702 0.0435702i 0.684986 0.728556i 0.259808π-0.259808\pi
−0.728556 + 0.684986i 0.759808π0.759808\pi
1818 −1.48383 0.852153i −0.0824350 0.0473418i
1919 7.09073i 0.373196i 0.982436 + 0.186598i 0.0597463π0.0597463\pi
−0.982436 + 0.186598i 0.940254π0.940254\pi
2020 18.7527 + 6.41391i 0.937637 + 0.320696i
2121 −10.3749 24.9661i −0.494043 1.18886i
2222 −2.58614 + 0.692953i −0.117552 + 0.0314979i
2323 −5.10441 19.0499i −0.221931 0.828257i −0.983611 0.180304i 0.942292π-0.942292\pi
0.761680 0.647953i 0.224375π-0.224375\pi
2424 −0.587726 + 4.50418i −0.0244886 + 0.187674i
2525 23.1408 9.46056i 0.925633 0.378423i
2626 −2.54786 −0.0979947
2727 10.4183 + 24.9090i 0.385863 + 0.922556i
2828 −25.2594 + 25.2594i −0.902123 + 0.902123i
2929 −6.18301 + 3.56976i −0.213207 + 0.123095i −0.602801 0.797892i 0.705949π-0.705949\pi
0.389594 + 0.920987i 0.372615π0.372615\pi
3030 1.58167 + 2.37306i 0.0527222 + 0.0791021i
3131 13.0783 22.6522i 0.421879 0.730716i −0.574244 0.818684i 0.694704π-0.694704\pi
0.996123 + 0.0879678i 0.0280373π0.0280373\pi
3232 8.70902 2.33357i 0.272157 0.0729242i
3333 39.0493 + 16.1223i 1.18331 + 0.488553i
3434 −0.172473 + 0.0995774i −0.00507274 + 0.00292875i
3535 −3.05064 + 44.9566i −0.0871612 + 1.28447i
3636 25.1678 25.2837i 0.699106 0.702324i
3737 −23.0151 23.0151i −0.622031 0.622031i 0.324020 0.946050i 0.394966π-0.394966\pi
−0.946050 + 0.324020i 0.894966π0.894966\pi
3838 1.30218 + 0.348919i 0.0342680 + 0.00918207i
3939 31.9234 + 24.4375i 0.818548 + 0.626602i
4040 4.22049 6.28502i 0.105512 0.157125i
4141 −36.0387 + 62.4209i −0.878993 + 1.52246i −0.0265459 + 0.999648i 0.508451π0.508451\pi
−0.852447 + 0.522813i 0.824883π0.824883\pi
4242 −5.09544 + 0.676780i −0.121320 + 0.0161138i
4343 −12.0484 3.22835i −0.280195 0.0750779i 0.115985 0.993251i 0.462998π-0.462998\pi
−0.396180 + 0.918173i 0.629664π0.629664\pi
4444 55.8198i 1.26863i
4545 2.94348 44.9036i 0.0654106 0.997858i
4646 −3.74961 −0.0815133
4747 −13.9048 + 51.8935i −0.295847 + 1.10412i 0.644695 + 0.764440i 0.276985π0.276985\pi
−0.940542 + 0.339677i 0.889682π0.889682\pi
4848 −43.1681 17.8228i −0.899335 0.371308i
4949 −27.9000 16.1081i −0.569388 0.328736i
5050 −0.598685 4.71525i −0.0119737 0.0943049i
5151 3.11608 + 0.406601i 0.0610997 + 0.00797257i
5252 13.7484 51.3098i 0.264393 0.986727i
5353 17.2907 17.2907i 0.326240 0.326240i −0.524915 0.851155i 0.675903π-0.675903\pi
0.851155 + 0.524915i 0.175903π0.175903\pi
5454 5.08709 0.687563i 0.0942054 0.0127326i
5555 −46.3031 53.0446i −0.841875 0.964447i
5656 6.82262 + 11.8171i 0.121833 + 0.211020i
5757 −12.9691 16.8615i −0.227527 0.295816i
5858 0.351320 + 1.31114i 0.00605724 + 0.0226059i
5959 −27.5407 15.9006i −0.466792 0.269502i 0.248104 0.968733i 0.420193π-0.420193\pi
−0.714896 + 0.699231i 0.753526π0.753526\pi
6060 −56.3244 + 19.0470i −0.938740 + 0.317450i
6161 40.7317 + 70.5494i 0.667733 + 1.15655i 0.978537 + 0.206073i 0.0660684π0.0660684\pi
−0.310804 + 0.950474i 0.600598π0.600598\pi
6262 −3.51643 3.51643i −0.0567166 0.0567166i
6363 70.3345 + 40.3926i 1.11642 + 0.641152i
6464 60.5560i 0.946187i
6565 −29.4971 60.1633i −0.453802 0.925589i
6666 4.88231 6.37790i 0.0739744 0.0966348i
6767 64.1404 17.1864i 0.957319 0.256513i 0.253854 0.967243i 0.418302π-0.418302\pi
0.703465 + 0.710730i 0.251635π0.251635\pi
6868 −1.07465 4.01065i −0.0158037 0.0589802i
6969 46.9807 + 35.9639i 0.680880 + 0.521216i
7070 8.10597 + 2.77245i 0.115800 + 0.0396064i
7171 −36.3928 −0.512574 −0.256287 0.966601i 0.582499π-0.582499\pi
−0.256287 + 0.966601i 0.582499π0.582499\pi
7272 −6.84062 11.7857i −0.0950086 0.163691i
7373 2.90991 2.90991i 0.0398617 0.0398617i −0.686895 0.726757i 0.741027π-0.741027\pi
0.726757 + 0.686895i 0.241027π0.241027\pi
7474 −5.35915 + 3.09411i −0.0724210 + 0.0418123i
7575 −37.7245 + 64.8218i −0.502993 + 0.864291i
7676 −14.0533 + 24.3410i −0.184912 + 0.320277i
7777 122.584 32.8464i 1.59201 0.426577i
7878 6.05872 4.66008i 0.0776759 0.0597446i
7979 −71.8823 + 41.5012i −0.909902 + 0.525332i −0.880400 0.474232i 0.842726π-0.842726\pi
−0.0295025 + 0.999565i 0.509392π0.509392\pi
8080 51.1870 + 58.6396i 0.639838 + 0.732995i
8181 −70.3333 40.1774i −0.868313 0.496017i
8282 9.68994 + 9.68994i 0.118170 + 0.118170i
8383 51.3796 + 13.7671i 0.619031 + 0.165869i 0.554687 0.832059i 0.312838π-0.312838\pi
0.0643438 + 0.997928i 0.479505π0.479505\pi
8484 13.8661 106.266i 0.165072 1.26507i
8585 −4.34811 2.91982i −0.0511542 0.0343509i
8686 −1.18574 + 2.05377i −0.0137877 + 0.0238811i
8787 8.17381 19.7976i 0.0939518 0.227558i
8888 −20.5956 5.51857i −0.234041 0.0627111i
8989 22.5436i 0.253299i 0.991948 + 0.126650i 0.0404224π0.0404224\pi
−0.991948 + 0.126650i 0.959578π0.959578\pi
9090 −8.10152 2.75016i −0.0900168 0.0305574i
9191 120.770 1.32715
9292 20.2331 75.5111i 0.219925 0.820773i
9393 10.3316 + 77.7864i 0.111093 + 0.836413i
9494 8.84580 + 5.10712i 0.0941042 + 0.0543311i
9595 6.83654 + 34.7883i 0.0719636 + 0.366192i
9696 −16.4416 + 21.4781i −0.171266 + 0.223730i
9797 −9.03502 + 33.7192i −0.0931446 + 0.347620i −0.996732 0.0807843i 0.974258π-0.974258\pi
0.903587 + 0.428405i 0.140924π0.140924\pi
9898 −4.33107 + 4.33107i −0.0441946 + 0.0441946i
9999 −122.346 + 33.0837i −1.23581 + 0.334179i
100100 98.1879 + 13.3872i 0.981879 + 0.133872i
101101 −29.7283 51.4909i −0.294340 0.509811i 0.680491 0.732756i 0.261766π-0.261766\pi
−0.974831 + 0.222945i 0.928433π0.928433\pi
102102 0.228006 0.552247i 0.00223535 0.00541419i
103103 20.3691 + 76.0184i 0.197758 + 0.738043i 0.991536 + 0.129835i 0.0414447π0.0414447\pi
−0.793778 + 0.608208i 0.791889π0.791889\pi
104104 −17.5723 10.1454i −0.168965 0.0975519i
105105 −74.9720 112.485i −0.714019 1.07128i
106106 −2.32453 4.02620i −0.0219295 0.0379830i
107107 −50.6865 50.6865i −0.473706 0.473706i 0.429406 0.903112i 0.358723π-0.358723\pi
−0.903112 + 0.429406i 0.858723π0.858723\pi
108108 −13.6039 + 106.156i −0.125962 + 0.982925i
109109 47.8364i 0.438866i −0.975628 0.219433i 0.929579π-0.929579\pi
0.975628 0.219433i 0.0704208π-0.0704208\pi
110110 −12.0199 + 5.89316i −0.109272 + 0.0535742i
111111 96.8241 + 12.6341i 0.872289 + 0.113820i
112112 −135.514 + 36.3109i −1.20995 + 0.324205i
113113 −45.1005 168.318i −0.399120 1.48954i −0.814648 0.579955i 0.803070π-0.803070\pi
0.415529 0.909580i 0.363597π-0.363597\pi
114114 −3.73472 + 1.55200i −0.0327607 + 0.0136140i
115115 −43.4101 88.5405i −0.377479 0.769918i
116116 −28.3000 −0.243966
117117 −120.609 + 0.276954i −1.03085 + 0.00236713i
118118 −4.27530 + 4.27530i −0.0362313 + 0.0362313i
119119 8.17534 4.72003i 0.0687003 0.0396641i
120120 1.45923 + 22.6649i 0.0121603 + 0.188874i
121121 −38.6542 + 66.9510i −0.319456 + 0.553314i
122122 14.9604 4.00863i 0.122626 0.0328576i
123123 −28.4701 214.350i −0.231464 1.74268i
124124 89.7900 51.8403i 0.724113 0.418067i
125125 104.411 68.7263i 0.835289 0.549810i
126126 10.8789 10.9290i 0.0863407 0.0867381i
127127 16.3333 + 16.3333i 0.128608 + 0.128608i 0.768481 0.639873i 0.221013π-0.221013\pi
−0.639873 + 0.768481i 0.721013π0.721013\pi
128128 45.9569 + 12.3141i 0.359038 + 0.0962041i
129129 34.5553 14.3598i 0.267870 0.111316i
130130 −12.5002 + 2.45652i −0.0961555 + 0.0188963i
131131 −27.6049 + 47.8130i −0.210724 + 0.364985i −0.951941 0.306280i 0.900916π-0.900916\pi
0.741217 + 0.671265i 0.234249π0.234249\pi
132132 102.095 + 132.737i 0.773449 + 1.00559i
133133 −61.7243 16.5390i −0.464092 0.124353i
134134 12.6248i 0.0942150i
135135 75.1300 + 112.163i 0.556518 + 0.830835i
136136 −1.58604 −0.0116621
137137 −50.7417 + 189.371i −0.370377 + 1.38227i 0.489606 + 0.871944i 0.337141π0.337141\pi
−0.859983 + 0.510323i 0.829526π0.829526\pi
138138 8.91643 6.85810i 0.0646118 0.0496964i
139139 82.5364 + 47.6524i 0.593787 + 0.342823i 0.766594 0.642133i 0.221950π-0.221950\pi
−0.172806 + 0.984956i 0.555283π0.555283\pi
140140 −99.5729 + 148.281i −0.711235 + 1.05915i
141141 −61.8489 148.833i −0.438645 1.05555i
142142 −1.79081 + 6.68338i −0.0126113 + 0.0470660i
143143 −133.443 + 133.443i −0.933165 + 0.933165i
144144 135.250 36.5733i 0.939237 0.253981i
145145 −26.8931 + 23.4752i −0.185469 + 0.161898i
146146 −0.391202 0.677581i −0.00267946 0.00464097i
147147 95.8070 12.7252i 0.651748 0.0865657i
148148 −33.3920 124.621i −0.225622 0.842031i
149149 225.341 + 130.101i 1.51235 + 0.873158i 0.999896 + 0.0144460i 0.00459846π0.00459846\pi
0.512458 + 0.858712i 0.328735π0.328735\pi
150150 10.0479 + 10.1177i 0.0669860 + 0.0674511i
151151 −128.914 223.285i −0.853735 1.47871i −0.877814 0.479002i 0.840999π-0.840999\pi
0.0240792 0.999710i 0.492335π-0.492335\pi
152152 7.59165 + 7.59165i 0.0499451 + 0.0499451i
153153 −8.15361 + 4.73248i −0.0532915 + 0.0309313i
154154 24.1284i 0.156678i
155155 42.3239 123.745i 0.273057 0.798353i
156156 61.1532 + 147.159i 0.392008 + 0.943325i
157157 44.8971 12.0301i 0.285969 0.0766251i −0.112983 0.993597i 0.536041π-0.536041\pi
0.398952 + 0.916972i 0.369374π0.369374\pi
158158 4.08436 + 15.2431i 0.0258504 + 0.0964750i
159159 −9.49166 + 72.7416i −0.0596960 + 0.457494i
160160 40.4779 19.8457i 0.252987 0.124036i
161161 177.734 1.10394
162162 −10.8393 + 10.9394i −0.0669096 + 0.0675270i
163163 76.8331 76.8331i 0.471369 0.471369i −0.430989 0.902357i 0.641835π-0.641835\pi
0.902357 + 0.430989i 0.141835π0.141835\pi
164164 −247.427 + 142.852i −1.50870 + 0.871050i
165165 207.126 + 41.4489i 1.25531 + 0.251206i
166166 5.05654 8.75819i 0.0304611 0.0527602i
167167 −301.256 + 80.7212i −1.80393 + 0.483360i −0.994580 0.103972i 0.966845π-0.966845\pi
−0.809346 + 0.587333i 0.800178π0.800178\pi
168168 −37.8376 15.6220i −0.225224 0.0929881i
169169 −9.16964 + 5.29409i −0.0542582 + 0.0313260i
170170 −0.750173 + 0.654833i −0.00441278 + 0.00385196i
171171 61.6799 + 16.3754i 0.360701 + 0.0957623i
172172 −34.9612 34.9612i −0.203263 0.203263i
173173 192.633 + 51.6158i 1.11348 + 0.298357i 0.768244 0.640157i 0.221131π-0.221131\pi
0.345240 + 0.938514i 0.387797π0.387797\pi
174174 −3.23353 2.47528i −0.0185835 0.0142257i
175175 28.3780 + 223.506i 0.162160 + 1.27718i
176176 109.613 189.855i 0.622799 1.07872i
177177 94.5733 12.5613i 0.534312 0.0709677i
178178 4.14004 + 1.10932i 0.0232587 + 0.00623214i
179179 254.120i 1.41967i −0.704370 0.709833i 0.748770π-0.748770\pi
0.704370 0.709833i 0.251230π-0.251230\pi
180180 99.1001 148.311i 0.550556 0.823952i
181181 −236.998 −1.30938 −0.654691 0.755896i 0.727201π-0.727201\pi
−0.654691 + 0.755896i 0.727201π0.727201\pi
182182 5.94283 22.1789i 0.0326529 0.121862i
183183 −225.894 93.2648i −1.23440 0.509644i
184184 −25.8607 14.9307i −0.140547 0.0811450i
185185 −135.106 90.7259i −0.730303 0.490410i
186186 14.7935 + 1.93033i 0.0795351 + 0.0103781i
187187 −3.81787 + 14.2485i −0.0204164 + 0.0761950i
188188 −150.582 + 150.582i −0.800966 + 0.800966i
189189 −241.131 + 32.5909i −1.27583 + 0.172439i
190190 6.72513 + 0.456350i 0.0353954 + 0.00240184i
191191 27.2962 + 47.2784i 0.142912 + 0.247531i 0.928592 0.371102i 0.121020π-0.121020\pi
−0.785680 + 0.618633i 0.787687π0.787687\pi
192192 −110.758 144.000i −0.576864 0.749999i
193193 51.8234 + 193.408i 0.268515 + 1.00211i 0.960063 + 0.279782i 0.0902623π0.0902623\pi
−0.691548 + 0.722330i 0.743071π0.743071\pi
194194 5.74779 + 3.31849i 0.0296278 + 0.0171056i
195195 180.183 + 89.1153i 0.924014 + 0.457001i
196196 −63.8500 110.591i −0.325765 0.564242i
197197 18.5367 + 18.5367i 0.0940948 + 0.0940948i 0.752587 0.658492i 0.228806π-0.228806\pi
−0.658492 + 0.752587i 0.728806π0.728806\pi
198198 0.0553320 + 24.0962i 0.000279454 + 0.121698i
199199 206.081i 1.03558i −0.855507 0.517792i 0.826754π-0.826754\pi
0.855507 0.517792i 0.173246π-0.173246\pi
200200 14.6467 34.9045i 0.0732335 0.174522i
201201 −121.089 + 158.182i −0.602434 + 0.786977i
202202 −10.9190 + 2.92572i −0.0540542 + 0.0144838i
203203 −16.6528 62.1490i −0.0820334 0.306153i
204204 9.89103 + 7.57163i 0.0484854 + 0.0371158i
205205 −116.629 + 340.994i −0.568920 + 1.66338i
206206 14.9628 0.0726348
207207 −177.497 + 0.407585i −0.857473 + 0.00196901i
208208 147.518 147.518i 0.709219 0.709219i
209209 86.4753 49.9266i 0.413758 0.238883i
210210 −24.3465 + 8.23317i −0.115936 + 0.0392056i
211211 121.373 210.225i 0.575230 0.996327i −0.420787 0.907159i 0.638246π-0.638246\pi
0.996017 0.0891675i 0.0284206π-0.0284206\pi
212212 93.6244 25.0866i 0.441625 0.118333i
213213 86.5406 66.5630i 0.406294 0.312502i
214214 −11.8025 + 6.81419i −0.0551520 + 0.0318420i
215215 −62.2238 4.22235i −0.289413 0.0196389i
216216 37.8230 + 15.5144i 0.175106 + 0.0718258i
217217 166.681 + 166.681i 0.768115 + 0.768115i
218218 −8.78496 2.35392i −0.0402980 0.0107978i
219219 −1.59738 + 12.2419i −0.00729397 + 0.0558991i
220220 −53.8187 273.861i −0.244631 1.24482i
221221 −7.01880 + 12.1569i −0.0317593 + 0.0550087i
222222 7.08468 17.1596i 0.0319130 0.0772957i
223223 198.758 + 53.2572i 0.891293 + 0.238821i 0.675273 0.737568i 0.264026π-0.264026\pi
0.216020 + 0.976389i 0.430692π0.430692\pi
224224 81.2544i 0.362743i
225225 −28.8527 223.142i −0.128234 0.991744i
226226 −33.1301 −0.146593
227227 48.1829 179.821i 0.212259 0.792163i −0.774854 0.632140i 0.782177π-0.782177\pi
0.987113 0.160022i 0.0511567π-0.0511567\pi
228228 −11.1019 83.5858i −0.0486927 0.366604i
229229 −156.704 90.4733i −0.684298 0.395080i 0.117174 0.993111i 0.462616π-0.462616\pi
−0.801473 + 0.598031i 0.795950π0.795950\pi
230230 −18.3962 + 3.61519i −0.0799835 + 0.0157182i
231231 −231.425 + 302.316i −1.00184 + 1.30873i
232232 −2.79786 + 10.4417i −0.0120597 + 0.0450075i
233233 −120.230 + 120.230i −0.516010 + 0.516010i −0.916362 0.400351i 0.868888π-0.868888\pi
0.400351 + 0.916362i 0.368888π0.368888\pi
234234 −5.88404 + 22.1630i −0.0251455 + 0.0947136i
235235 −18.1861 + 268.004i −0.0773877 + 1.14044i
236236 −63.0278 109.167i −0.267067 0.462573i
237237 95.0268 230.162i 0.400957 0.971148i
238238 −0.464524 1.73363i −0.00195178 0.00728415i
239239 332.123 + 191.751i 1.38963 + 0.802306i 0.993274 0.115790i 0.0369398π-0.0369398\pi
0.396360 + 0.918095i 0.370273π0.370273\pi
240240 −228.973 45.8208i −0.954056 0.190920i
241241 162.944 + 282.226i 0.676114 + 1.17106i 0.976142 + 0.217134i 0.0696708π0.0696708\pi
−0.300028 + 0.953931i 0.596996π0.596996\pi
242242 10.3932 + 10.3932i 0.0429470 + 0.0429470i
243243 240.735 33.1004i 0.990679 0.136216i
244244 322.909i 1.32340i
245245 −152.412 52.1289i −0.622092 0.212771i
246246 −40.7654 5.31925i −0.165713 0.0216230i
247247 91.7854 24.5938i 0.371601 0.0995702i
248248 −10.2503 38.2546i −0.0413318 0.154252i
249249 −147.359 + 61.2364i −0.591803 + 0.245929i
250250 −7.48345 22.5565i −0.0299338 0.0902261i
251251 428.941 1.70893 0.854465 0.519509i 0.173885π-0.173885\pi
0.854465 + 0.519509i 0.173885π0.173885\pi
252252 161.389 + 278.057i 0.640433 + 1.10340i
253253 −196.383 + 196.383i −0.776219 + 0.776219i
254254 3.80325 2.19581i 0.0149734 0.00864492i
255255 15.6800 1.00953i 0.0614903 0.00395893i
256256 −116.589 + 201.938i −0.455426 + 0.788821i
257257 355.861 95.3527i 1.38467 0.371022i 0.511857 0.859070i 0.328958π-0.328958\pi
0.872817 + 0.488048i 0.162291π0.162291\pi
258258 −0.936723 7.05253i −0.00363071 0.0273354i
259259 254.027 146.663i 0.980800 0.566265i
260260 17.9815 264.990i 0.0691597 1.01919i
261261 16.7731 + 62.0279i 0.0642647 + 0.237655i
262262 7.42228 + 7.42228i 0.0283293 + 0.0283293i
263263 −63.7296 17.0763i −0.242318 0.0649289i 0.135616 0.990761i 0.456699π-0.456699\pi
−0.377934 + 0.925833i 0.623365π0.623365\pi
264264 59.0691 24.5467i 0.223747 0.0929800i
265265 68.1601 101.502i 0.257208 0.383026i
266266 −6.07462 + 10.5216i −0.0228369 + 0.0395547i
267267 −41.2327 53.6079i −0.154429 0.200779i
268268 254.243 + 68.1242i 0.948668 + 0.254195i
269269 146.927i 0.546197i 0.961986 + 0.273099i 0.0880485π0.0880485\pi
−0.961986 + 0.273099i 0.911951π0.911951\pi
270270 24.2952 8.27802i 0.0899822 0.0306593i
271271 −45.0155 −0.166109 −0.0830544 0.996545i 0.526468π-0.526468\pi
−0.0830544 + 0.996545i 0.526468π0.526468\pi
272272 4.22056 15.7513i 0.0155168 0.0579094i
273273 −287.187 + 220.891i −1.05197 + 0.809124i
274274 32.2802 + 18.6370i 0.117811 + 0.0680182i
275275 −278.314 215.602i −1.01205 0.784008i
276276 89.9973 + 216.569i 0.326077 + 0.784671i
277277 −41.0870 + 153.339i −0.148329 + 0.553570i 0.851256 + 0.524751i 0.175841π0.175841\pi
−0.999585 + 0.0288193i 0.990825π0.990825\pi
278278 12.8126 12.8126i 0.0460885 0.0460885i
279279 −166.841 166.076i −0.597996 0.595256i
280280 44.8664 + 51.3987i 0.160237 + 0.183567i
281281 −33.0937 57.3199i −0.117771 0.203986i 0.801113 0.598513i 0.204242π-0.204242\pi
−0.918884 + 0.394528i 0.870908π0.870908\pi
282282 −30.3760 + 4.03456i −0.107716 + 0.0143069i
283283 −104.177 388.793i −0.368116 1.37383i −0.863148 0.504952i 0.831510π-0.831510\pi
0.495032 0.868875i 0.335156π-0.335156\pi
284284 −124.929 72.1278i −0.439891 0.253971i
285285 −79.8853 70.2210i −0.280299 0.246390i
286286 17.9397 + 31.0726i 0.0627264 + 0.108645i
287287 −459.310 459.310i −1.60038 1.60038i
288288 −0.186335 81.1460i −0.000646996 0.281757i
289289 287.903i 0.996203i
290290 2.98777 + 6.09395i 0.0103027 + 0.0210136i
291291 −40.1880 96.7081i −0.138103 0.332330i
292292 15.7563 4.22190i 0.0539600 0.0144586i
293293 56.1985 + 209.736i 0.191804 + 0.715821i 0.993071 + 0.117515i 0.0374927π0.0374927\pi
−0.801267 + 0.598306i 0.795841π0.795841\pi
294294 2.37752 18.2207i 0.00808682 0.0619752i
295295 −150.450 51.4577i −0.509999 0.174433i
296296 −49.2820 −0.166493
297297 230.423 302.444i 0.775833 1.01833i
298298 34.9809 34.9809i 0.117386 0.117386i
299299 −228.886 + 132.147i −0.765504 + 0.441964i
300300 −257.972 + 147.753i −0.859908 + 0.492510i
301301 56.2051 97.3500i 0.186728 0.323422i
302302 −47.3490 + 12.6871i −0.156785 + 0.0420103i
303303 164.871 + 68.0699i 0.544127 + 0.224653i
304304 −95.5965 + 55.1926i −0.314462 + 0.181555i
305305 267.857 + 306.855i 0.878218 + 1.00608i
306306 0.467880 + 1.73025i 0.00152902 + 0.00565441i
307307 −219.096 219.096i −0.713666 0.713666i 0.253634 0.967300i 0.418374π-0.418374\pi
−0.967300 + 0.253634i 0.918374π0.918374\pi
308308 485.907 + 130.198i 1.57762 + 0.422722i
309309 −187.476 143.513i −0.606717 0.464445i
310310 −20.6425 13.8618i −0.0665888 0.0447155i
311311 −68.8478 + 119.248i −0.221376 + 0.383434i −0.955226 0.295877i 0.904388π-0.904388\pi
0.733850 + 0.679311i 0.237721π0.237721\pi
312312 60.3424 8.01473i 0.193405 0.0256882i
313313 −6.37451 1.70804i −0.0203658 0.00545701i 0.248622 0.968601i 0.420022π-0.420022\pi
−0.268988 + 0.963144i 0.586689π0.586689\pi
314314 8.83713i 0.0281437i
315315 384.017 + 130.359i 1.21910 + 0.413839i
316316 −329.010 −1.04117
317317 −114.489 + 427.280i −0.361165 + 1.34789i 0.511381 + 0.859354i 0.329134π0.329134\pi
−0.872546 + 0.488532i 0.837533π0.837533\pi
318318 12.8916 + 5.32255i 0.0405397 + 0.0167376i
319319 87.0704 + 50.2701i 0.272948 + 0.157587i
320320 58.3851 + 297.097i 0.182453 + 0.928429i
321321 213.237 + 27.8241i 0.664290 + 0.0866796i
322322 8.74588 32.6401i 0.0271611 0.101367i
323323 5.25206 5.25206i 0.0162603 0.0162603i
324324 −161.811 277.316i −0.499418 0.855915i
325325 −202.724 266.731i −0.623767 0.820711i
326326 −10.3293 17.8909i −0.0316849 0.0548799i
327327 87.4936 + 113.753i 0.267565 + 0.347869i
328328 28.2459 + 105.415i 0.0861156 + 0.321388i
329329 −419.296 242.081i −1.27446 0.735808i
330330 17.8041 35.9983i 0.0539519 0.109086i
331331 −130.851 226.641i −0.395321 0.684716i 0.597821 0.801630i 0.296033π-0.296033\pi
−0.993142 + 0.116913i 0.962700π0.962700\pi
332332 149.090 + 149.090i 0.449067 + 0.449067i
333333 −253.352 + 147.050i −0.760817 + 0.441590i
334334 59.2964i 0.177534i
335335 298.113 146.160i 0.889889 0.436299i
336336 255.834 334.204i 0.761412 0.994654i
337337 140.831 37.7355i 0.417895 0.111975i −0.0437433 0.999043i 0.513928π-0.513928\pi
0.461639 + 0.887068i 0.347262π0.347262\pi
338338 0.521020 + 1.94447i 0.00154148 + 0.00575288i
339339 415.103 + 317.763i 1.22449 + 0.937354i
340340 −9.13929 18.6408i −0.0268803 0.0548258i
341341 −368.341 −1.08018
342342 6.04239 10.5214i 0.0176678 0.0307645i
343343 −106.954 + 106.954i −0.311820 + 0.311820i
344344 −16.3559 + 9.44310i −0.0475463 + 0.0274509i
345345 265.170 + 131.148i 0.768607 + 0.380140i
346346 18.9580 32.8363i 0.0547920 0.0949025i
347347 9.77990 2.62052i 0.0281842 0.00755192i −0.244699 0.969599i 0.578689π-0.578689\pi
0.272884 + 0.962047i 0.412023π0.412023\pi
348348 67.2964 51.7612i 0.193380 0.148739i
349349 −94.1070 + 54.3327i −0.269648 + 0.155681i −0.628727 0.777626i 0.716424π-0.716424\pi
0.359080 + 0.933307i 0.383091π0.383091\pi
350350 42.4423 + 5.78670i 0.121264 + 0.0165334i
351351 286.297 221.255i 0.815662 0.630355i
352352 −89.7803 89.7803i −0.255058 0.255058i
353353 −467.133 125.168i −1.32332 0.354583i −0.473101 0.881008i 0.656865π-0.656865\pi
−0.850221 + 0.526425i 0.823532π0.823532\pi
354354 2.34691 17.9861i 0.00662968 0.0508082i
355355 −178.549 + 35.0881i −0.502954 + 0.0988399i
356356 −44.6798 + 77.3877i −0.125505 + 0.217381i
357357 −10.8076 + 26.1769i −0.0302735 + 0.0733246i
358358 −46.6681 12.5047i −0.130358 0.0349293i
359359 279.063i 0.777333i 0.921378 + 0.388667i 0.127064π0.127064\pi
−0.921378 + 0.388667i 0.872936π0.872936\pi
360360 −44.9244 51.2272i −0.124790 0.142298i
361361 310.722 0.860724
362362 −11.6621 + 43.5237i −0.0322159 + 0.120231i
363363 −30.5363 229.906i −0.0841220 0.633350i
364364 414.580 + 239.358i 1.13896 + 0.657576i
365365 11.4709 17.0821i 0.0314271 0.0468001i
366366 −28.2434 + 36.8952i −0.0771678 + 0.100806i
367367 46.2339 172.547i 0.125978 0.470156i −0.873895 0.486115i 0.838414π-0.838414\pi
0.999873 + 0.0159593i 0.00508022π0.00508022\pi
368368 217.097 217.097i 0.589938 0.589938i
369369 459.750 + 457.643i 1.24594 + 1.24023i
370370 −23.3097 + 20.3472i −0.0629991 + 0.0549925i
371371 110.184 + 190.844i 0.296992 + 0.514406i
372372 −118.701 + 287.502i −0.319087 + 0.772854i
373373 −22.7204 84.7938i −0.0609127 0.227329i 0.928758 0.370685i 0.120877π-0.120877\pi
−0.989671 + 0.143356i 0.954211π0.954211\pi
374374 2.42880 + 1.40227i 0.00649412 + 0.00374938i
375375 −122.584 + 354.398i −0.326891 + 0.945062i
376376 40.6724 + 70.4466i 0.108171 + 0.187358i
377377 67.6540 + 67.6540i 0.179453 + 0.179453i
378378 −5.88035 + 45.8865i −0.0155565 + 0.121393i
379379 10.3793i 0.0273860i 0.999906 + 0.0136930i 0.00435875π0.00435875\pi
−0.999906 + 0.0136930i 0.995641π0.995641\pi
380380 −45.4793 + 132.971i −0.119682 + 0.349923i
381381 −68.7136 8.96607i −0.180351 0.0235330i
382382 10.0257 2.68637i 0.0262452 0.00703238i
383383 −33.3422 124.435i −0.0870554 0.324895i 0.908640 0.417580i 0.137122π-0.137122\pi
−0.995695 + 0.0926850i 0.970455π0.970455\pi
384384 −131.807 + 54.7734i −0.343246 + 0.142639i
385385 569.750 279.340i 1.47987 0.725558i
386386 38.0686 0.0986233
387387 −55.9068 + 97.3490i −0.144462 + 0.251548i
388388 −97.8443 + 97.8443i −0.252176 + 0.252176i
389389 635.357 366.824i 1.63331 0.942991i 0.650245 0.759724i 0.274666π-0.274666\pi
0.983063 0.183267i 0.0586673π-0.0586673\pi
390390 25.2320 28.7046i 0.0646975 0.0736016i
391391 −10.3294 + 17.8910i −0.0264178 + 0.0457570i
392392 −47.1170 + 12.6250i −0.120196 + 0.0322065i
393393 −21.8075 164.187i −0.0554898 0.417779i
394394 4.31633 2.49203i 0.0109552 0.00632496i
395395 −312.652 + 272.917i −0.791525 + 0.690930i
396396 −485.557 128.910i −1.22615 0.325531i
397397 151.257 + 151.257i 0.381000 + 0.381000i 0.871462 0.490463i 0.163172π-0.163172\pi
−0.490463 + 0.871462i 0.663172π0.663172\pi
398398 −37.8459 10.1408i −0.0950903 0.0254794i
399399 177.028 73.5656i 0.443679 0.184375i
400400 307.669 + 238.343i 0.769173 + 0.595858i
401401 −3.27254 + 5.66821i −0.00816096 + 0.0141352i −0.870077 0.492916i 0.835931π-0.835931\pi
0.861916 + 0.507051i 0.169264π0.169264\pi
402402 23.0910 + 30.0213i 0.0574402 + 0.0746799i
403403 −338.581 90.7225i −0.840151 0.225118i
404404 235.677i 0.583360i
405405 −383.804 129.305i −0.947663 0.319271i
406406 −12.2328 −0.0301302
407407 −118.630 + 442.734i −0.291475 + 1.08780i
408408 3.77154 2.90089i 0.00924397 0.00711003i
409409 −639.259 369.076i −1.56298 0.902387i −0.996953 0.0779993i 0.975147π-0.975147\pi
−0.566026 0.824387i 0.691520π-0.691520\pi
410410 56.8830 + 38.1978i 0.138739 + 0.0931655i
411411 −225.700 543.123i −0.549148 1.32147i
412412 −80.7400 + 301.326i −0.195971 + 0.731373i
413413 202.652 202.652i 0.490683 0.490683i
414414 −8.65937 + 32.6166i −0.0209163 + 0.0787840i
415415 265.350 + 18.0060i 0.639398 + 0.0433879i
416416 −60.4136 104.639i −0.145225 0.251537i
417417 −283.426 + 37.6448i −0.679678 + 0.0902753i
418418 −4.91354 18.3376i −0.0117549 0.0438698i
419419 235.376 + 135.894i 0.561756 + 0.324330i 0.753850 0.657047i 0.228195π-0.228195\pi
−0.192094 + 0.981377i 0.561528π0.561528\pi
420420 −34.4273 534.726i −0.0819697 1.27316i
421421 102.996 + 178.395i 0.244647 + 0.423741i 0.962032 0.272936i 0.0879947π-0.0879947\pi
−0.717386 + 0.696676i 0.754661π0.754661\pi
422422 −32.6344 32.6344i −0.0773327 0.0773327i
423423 419.292 + 240.796i 0.991235 + 0.569259i
424424 37.0244i 0.0873217i
425425 −24.1477 10.1329i −0.0568180 0.0238421i
426426 −7.96553 19.1682i −0.0186984 0.0449958i
427427 −709.133 + 190.011i −1.66073 + 0.444992i
428428 −73.5396 274.453i −0.171821 0.641246i
429429 73.2528 561.390i 0.170752 1.30860i
430430 −3.83731 + 11.2194i −0.00892397 + 0.0260915i
431431 −238.470 −0.553294 −0.276647 0.960972i 0.589223π-0.589223\pi
−0.276647 + 0.960972i 0.589223π0.589223\pi
432432 −254.727 + 334.345i −0.589645 + 0.773946i
433433 79.6977 79.6977i 0.184059 0.184059i −0.609063 0.793122i 0.708454π-0.708454\pi
0.793122 + 0.609063i 0.208454π0.208454\pi
434434 38.8122 22.4083i 0.0894291 0.0516319i
435435 21.0142 105.011i 0.0483084 0.241404i
436436 94.8083 164.213i 0.217450 0.376635i
437437 135.078 36.1940i 0.309103 0.0828238i
438438 2.16957 + 0.895748i 0.00495336 + 0.00204509i
439439 −280.123 + 161.729i −0.638094 + 0.368404i −0.783880 0.620912i 0.786762π-0.786762\pi
0.145786 + 0.989316i 0.453429π0.453429\pi
440440 −106.366 7.21774i −0.241741 0.0164039i
441441 −204.551 + 205.492i −0.463834 + 0.465969i
442442 1.88719 + 1.88719i 0.00426965 + 0.00426965i
443443 −729.682 195.518i −1.64714 0.441349i −0.688328 0.725400i 0.741655π-0.741655\pi
−0.958809 + 0.284051i 0.908322π0.908322\pi
444444 307.338 + 235.268i 0.692202 + 0.529884i
445445 21.7355 + 110.603i 0.0488438 + 0.248545i
446446 19.5609 33.8805i 0.0438585 0.0759652i
447447 −773.808 + 102.778i −1.73111 + 0.229928i
448448 −527.135 141.245i −1.17664 0.315280i
449449 514.733i 1.14640i −0.819416 0.573199i 0.805702π-0.805702\pi
0.819416 0.573199i 0.194298π-0.194298\pi
450450 −42.3989 5.68165i −0.0942198 0.0126259i
451451 1015.01 2.25057
452452 178.772 667.186i 0.395513 1.47607i
453453 714.945 + 295.179i 1.57825 + 0.651609i
454454 −30.6524 17.6972i −0.0675162 0.0389805i
455455 592.518 116.441i 1.30224 0.255914i
456456 −31.9379 4.16741i −0.0700393 0.00913905i
457457 147.494 550.455i 0.322744 1.20450i −0.593816 0.804601i 0.702379π-0.702379\pi
0.916560 0.399897i 0.130954π-0.130954\pi
458458 −24.3261 + 24.3261i −0.0531137 + 0.0531137i
459459 10.7332 26.1667i 0.0233838 0.0570081i
460460 26.4629 389.977i 0.0575280 0.847777i
461461 −119.334 206.693i −0.258860 0.448358i 0.707077 0.707137i 0.250013π-0.250013\pi
−0.965937 + 0.258778i 0.916680π0.916680\pi
462462 44.1312 + 57.3764i 0.0955222 + 0.124191i
463463 213.508 + 796.822i 0.461140 + 1.72100i 0.669380 + 0.742921i 0.266560π0.266560\pi
−0.208239 + 0.978078i 0.566773π0.566773\pi
464464 −96.2543 55.5724i −0.207445 0.119768i
465465 125.687 + 371.671i 0.270294 + 0.799293i
466466 16.1635 + 27.9961i 0.0346857 + 0.0600774i
467467 489.265 + 489.265i 1.04768 + 1.04768i 0.998805 + 0.0488707i 0.0155622π0.0155622\pi
0.0488707 + 0.998805i 0.484438π0.484438\pi
468468 −414.576 238.088i −0.885845 0.508734i
469469 598.424i 1.27596i
470470 48.3229 + 16.5277i 0.102815 + 0.0351653i
471471 −84.7602 + 110.725i −0.179958 + 0.235084i
472472 −46.5102 + 12.4624i −0.0985386 + 0.0264033i
473473 45.4623 + 169.667i 0.0961147 + 0.358705i
474474 −37.5922 28.7770i −0.0793085 0.0607110i
475475 67.0823 + 164.085i 0.141226 + 0.345443i
476476 37.4190 0.0786114
477477 −110.475 190.337i −0.231603 0.399030i
478478 51.5572 51.5572i 0.107860 0.107860i
479479 −142.795 + 82.4426i −0.298110 + 0.172114i −0.641594 0.767045i 0.721726π-0.721726\pi
0.343483 + 0.939159i 0.388393π0.388393\pi
480480 −59.9569 + 121.227i −0.124910 + 0.252556i
481481 −218.091 + 377.744i −0.453411 + 0.785331i
482482 59.8478 16.0362i 0.124165 0.0332700i
483483 −422.645 + 325.078i −0.875041 + 0.673040i
484484 −265.384 + 153.220i −0.548314 + 0.316569i
485485 −11.8169 + 174.143i −0.0243647 + 0.359057i
486486 5.76728 45.8387i 0.0118668 0.0943184i
487487 326.960 + 326.960i 0.671376 + 0.671376i 0.958033 0.286657i 0.0925441π-0.0925441\pi
−0.286657 + 0.958033i 0.592544π0.592544\pi
488488 119.142 + 31.9241i 0.244144 + 0.0654183i
489489 −42.1772 + 323.235i −0.0862520 + 0.661013i
490490 −17.0731 + 25.4247i −0.0348431 + 0.0518872i
491491 −182.011 + 315.253i −0.370695 + 0.642063i −0.989673 0.143346i 0.954214π-0.954214\pi
0.618977 + 0.785409i 0.287547π0.287547\pi
492492 327.094 792.245i 0.664824 1.61025i
493493 7.22382 + 1.93562i 0.0146528 + 0.00392620i
494494 18.0662i 0.0365713i
495495 −568.350 + 280.274i −1.14818 + 0.566209i
496496 407.193 0.820953
497497 84.8853 316.796i 0.170795 0.637417i
498498 3.99460 + 30.0751i 0.00802129 + 0.0603918i
499499 353.578 + 204.138i 0.708573 + 0.409095i 0.810532 0.585694i 0.199178π-0.199178\pi
−0.101960 + 0.994789i 0.532511π0.532511\pi
500500 494.633 28.9882i 0.989266 0.0579764i
501501 568.734 742.953i 1.13520 1.48294i
502502 21.1072 78.7732i 0.0420463 0.156919i
503503 555.921 555.921i 1.10521 1.10521i 0.111440 0.993771i 0.464454π-0.464454\pi
0.993771 0.111440i 0.0355462π-0.0355462\pi
504504 118.549 32.0571i 0.235217 0.0636055i
505505 −195.497 223.960i −0.387123 0.443486i
506506 26.4014 + 45.7286i 0.0521767 + 0.0903726i
507507 12.1221 29.3606i 0.0239094 0.0579104i
508508 23.6974 + 88.4400i 0.0466485 + 0.174095i
509509 −453.968 262.098i −0.891882 0.514928i −0.0173243 0.999850i 0.505515π-0.505515\pi
−0.874558 + 0.484922i 0.838848π0.838848\pi
510510 0.586183 2.92925i 0.00114938 0.00574362i
511511 18.5432 + 32.1178i 0.0362881 + 0.0628528i
512512 165.919 + 165.919i 0.324061 + 0.324061i
513513 −176.623 + 73.8735i −0.344295 + 0.144003i
514514 70.0445i 0.136273i
515515 173.227 + 353.320i 0.336363 + 0.686057i
516516 147.081 + 19.1918i 0.285041 + 0.0371935i
517517 730.775 195.811i 1.41349 0.378744i
518518 −14.4339 53.8679i −0.0278646 0.103992i
519519 −552.479 + 229.588i −1.06451 + 0.442366i
520520 −95.9944 32.8325i −0.184605 0.0631395i
521521 −694.042 −1.33213 −0.666067 0.745892i 0.732023π-0.732023\pi
−0.666067 + 0.745892i 0.732023π0.732023\pi
522522 12.2165 0.0280527i 0.0234033 5.37408e-5i
523523 244.233 244.233i 0.466985 0.466985i −0.433951 0.900936i 0.642881π-0.642881\pi
0.900936 + 0.433951i 0.142881π0.142881\pi
524524 −189.524 + 109.422i −0.361687 + 0.208820i
525525 −476.277 479.584i −0.907195 0.913493i
526526 −6.27198 + 10.8634i −0.0119239 + 0.0206528i
527527 −26.4653 + 7.09137i −0.0502189 + 0.0134561i
528528 86.5925 + 651.950i 0.164001 + 1.23475i
529529 121.283 70.0227i 0.229268 0.132368i
530530 −15.2864 17.5120i −0.0288422 0.0330415i
531531 −201.917 + 202.846i −0.380258 + 0.382008i
532532 −179.108 179.108i −0.336669 0.336669i
533533 933.001 + 249.997i 1.75047 + 0.469037i
534534 −11.8738 + 4.93428i −0.0222356 + 0.00924022i
535535 −297.546 199.807i −0.556160 0.373470i
536536 50.2711 87.0720i 0.0937893 0.162448i
537537 464.790 + 604.288i 0.865531 + 1.12530i
538538 26.9825 + 7.22994i 0.0501534 + 0.0134386i
539539 453.674i 0.841696i
540540 35.6076 + 533.934i 0.0659400 + 0.988767i
541541 −682.588 −1.26172 −0.630858 0.775899i 0.717297π-0.717297\pi
−0.630858 + 0.775899i 0.717297π0.717297\pi
542542 −2.21511 + 8.26689i −0.00408691 + 0.0152526i
543543 563.573 433.474i 1.03789 0.798294i
544544 −8.17918 4.72225i −0.0150353 0.00868061i
545545 −46.1216 234.693i −0.0846267 0.430630i
546546 26.4338 + 63.6102i 0.0484136 + 0.116502i
547547 −16.7386 + 62.4694i −0.0306008 + 0.114204i −0.979537 0.201265i 0.935495π-0.935495\pi
0.948936 + 0.315468i 0.102162π0.102162\pi
548548 −549.504 + 549.504i −1.00275 + 1.00275i
549549 707.751 191.384i 1.28916 0.348605i
550550 −53.2896 + 40.5018i −0.0968901 + 0.0736396i
551551 −25.3122 43.8421i −0.0459387 0.0795682i
552552 88.8042 11.7950i 0.160877 0.0213678i
553553 −193.601 722.530i −0.350093 1.30656i
554554 26.1382 + 15.0909i 0.0471809 + 0.0272399i
555555 487.216 31.3684i 0.877866 0.0565196i
556556 188.887 + 327.162i 0.339725 + 0.588421i
557557 −66.9124 66.9124i −0.120130 0.120130i 0.644486 0.764616i 0.277071π-0.277071\pi
−0.764616 + 0.644486i 0.777071π0.777071\pi
558558 −38.7091 + 22.4674i −0.0693711 + 0.0402641i
559559 167.156i 0.299028i
560560 −629.845 + 308.804i −1.12472 + 0.551435i
561561 −16.9819 40.8652i −0.0302708 0.0728436i
562562 −12.1550 + 3.25693i −0.0216282 + 0.00579525i
563563 36.8258 + 137.436i 0.0654099 + 0.244113i 0.990888 0.134688i 0.0430032π-0.0430032\pi
−0.925478 + 0.378801i 0.876337π0.876337\pi
564564 82.6612 633.493i 0.146562 1.12322i
565565 −383.554 782.309i −0.678857 1.38462i
566566 −76.5264 −0.135206
567567 513.792 518.533i 0.906159 0.914521i
568568 −38.9637 + 38.9637i −0.0685981 + 0.0685981i
569569 −276.828 + 159.827i −0.486517 + 0.280891i −0.723128 0.690714i 0.757297π-0.757297\pi
0.236611 + 0.971604i 0.423963π0.423963\pi
570570 −16.8268 + 11.2152i −0.0295206 + 0.0196758i
571571 −324.309 + 561.720i −0.567967 + 0.983748i 0.428800 + 0.903400i 0.358937π0.358937\pi
−0.996767 + 0.0803483i 0.974397π0.974397\pi
572572 −722.555 + 193.608i −1.26321 + 0.338475i
573573 −151.382 62.5011i −0.264193 0.109077i
574574 −106.952 + 61.7486i −0.186327 + 0.107576i
575575 −298.343 392.540i −0.518858 0.682679i
576576 526.756 + 139.848i 0.914506 + 0.242792i
577577 −519.616 519.616i −0.900548 0.900548i 0.0949353 0.995483i 0.469736π-0.469736\pi
−0.995483 + 0.0949353i 0.969736π0.969736\pi
578578 −52.8721 14.1670i −0.0914742 0.0245104i
579579 −476.980 365.130i −0.823800 0.630622i
580580 −138.844 + 27.2855i −0.239387 + 0.0470440i
581581 −239.683 + 415.144i −0.412536 + 0.714533i
582582 −19.7376 + 2.62156i −0.0339134 + 0.00450440i
583583 −332.615 89.1240i −0.570523 0.152871i
584584 6.23095i 0.0106694i
585585 −591.461 + 117.644i −1.01104 + 0.201101i
586586 41.2824 0.0704478
587587 213.739 797.684i 0.364120 1.35892i −0.504489 0.863418i 0.668319π-0.668319\pi
0.868609 0.495498i 0.165014π-0.165014\pi
588588 354.106 + 146.200i 0.602222 + 0.248639i
589589 160.621 + 92.7344i 0.272701 + 0.157444i
590590 −16.8533 + 25.0973i −0.0285649 + 0.0425379i
591591 −77.9834 10.1756i −0.131952 0.0172177i
592592 131.143 489.432i 0.221525 0.826743i
593593 329.014 329.014i 0.554829 0.554829i −0.373002 0.927831i 0.621671π-0.621671\pi
0.927831 + 0.373002i 0.121671π0.121671\pi
594594 −44.2039 57.1987i −0.0744174 0.0962941i
595595 35.5587 31.0395i 0.0597625 0.0521672i
596596 515.699 + 893.218i 0.865267 + 1.49869i
597597 376.926 + 490.053i 0.631366 + 0.820860i
598598 13.0053 + 48.5366i 0.0217480 + 0.0811648i
599599 −445.587 257.260i −0.743885 0.429482i 0.0795952 0.996827i 0.474637π-0.474637\pi
−0.823480 + 0.567345i 0.807971π0.807971\pi
600600 29.0116 + 109.791i 0.0483526 + 0.182984i
601601 −19.7478 34.2041i −0.0328582 0.0569121i 0.849129 0.528186i 0.177128π-0.177128\pi
−0.881987 + 0.471274i 0.843794π0.843794\pi
602602 −15.1122 15.1122i −0.0251033 0.0251033i
603603 −1.37232 597.626i −0.00227583 0.991087i
604604 1021.99i 1.69204i
605605 −125.093 + 365.741i −0.206765 + 0.604531i
606606 20.6137 26.9282i 0.0340159 0.0444360i
607607 −390.594 + 104.659i −0.643483 + 0.172421i −0.565781 0.824556i 0.691425π-0.691425\pi
−0.0777026 + 0.996977i 0.524758π0.524758\pi
608608 16.5468 + 61.7533i 0.0272151 + 0.101568i
609609 153.271 + 117.330i 0.251677 + 0.192660i
610610 69.5332 34.0911i 0.113989 0.0558870i
611611 719.960 1.17833
612612 −37.3691 + 0.0858104i −0.0610606 + 0.000140213i
613613 −559.593 + 559.593i −0.912876 + 0.912876i −0.996498 0.0836213i 0.973351π-0.973351\pi
0.0836213 + 0.996498i 0.473351π0.473351\pi
614614 −51.0172 + 29.4548i −0.0830898 + 0.0479719i
615615 −346.345 1024.19i −0.563162 1.66534i
616616 96.0775 166.411i 0.155970 0.270148i
617617 −337.484 + 90.4285i −0.546976 + 0.146562i −0.521716 0.853119i 0.674708π-0.674708\pi
−0.0252596 + 0.999681i 0.508041π0.508041\pi
618618 −35.5809 + 27.3671i −0.0575742 + 0.0442834i
619619 384.591 222.044i 0.621311 0.358714i −0.156068 0.987746i 0.549882π-0.549882\pi
0.777379 + 0.629032i 0.216549π0.216549\pi
620620 390.542 340.908i 0.629907 0.549852i
621621 421.335 325.614i 0.678479 0.524338i
622622 18.5115 + 18.5115i 0.0297613 + 0.0297613i
623623 −196.241 52.5825i −0.314993 0.0844021i
624624 −80.9792 + 620.603i −0.129774 + 0.994557i
625625 445.995 437.850i 0.713593 0.700561i
626626 −0.627350 + 1.08660i −0.00100216 + 0.00173579i
627627 −114.319 + 276.888i −0.182326 + 0.441608i
628628 177.965 + 47.6857i 0.283384 + 0.0759326i
629629 34.0943i 0.0542040i
630630 42.8365 64.1084i 0.0679945 0.101759i
631631 −181.428 −0.287524 −0.143762 0.989612i 0.545920π-0.545920\pi
−0.143762 + 0.989612i 0.545920π0.545920\pi
632632 −32.5273 + 121.393i −0.0514672 + 0.192078i
633633 95.8834 + 721.901i 0.151475 + 1.14044i
634634 72.8343 + 42.0509i 0.114881 + 0.0663264i
635635 95.8813 + 64.3858i 0.150994 + 0.101395i
636636 −176.751 + 230.895i −0.277911 + 0.363043i
637637 −111.740 + 417.019i −0.175416 + 0.654661i
638638 13.5164 13.5164i 0.0211856 0.0211856i
639639 −84.0456 + 316.568i −0.131527 + 0.495412i
640640 237.345 + 16.1056i 0.370851 + 0.0251650i
641641 44.3645 + 76.8416i 0.0692114 + 0.119878i 0.898554 0.438862i 0.144618π-0.144618\pi
−0.829343 + 0.558740i 0.811285π0.811285\pi
642642 15.6027 37.7909i 0.0243032 0.0588643i
643643 111.166 + 414.879i 0.172887 + 0.645224i 0.996902 + 0.0786553i 0.0250626π0.0250626\pi
−0.824015 + 0.566568i 0.808271π0.808271\pi
644644 610.125 + 352.256i 0.947399 + 0.546981i
645645 155.689 103.768i 0.241378 0.160880i
646646 −0.706077 1.22296i −0.00109300 0.00189313i
647647 237.290 + 237.290i 0.366755 + 0.366755i 0.866292 0.499537i 0.166497π-0.166497\pi
−0.499537 + 0.866292i 0.666497π0.666497\pi
648648 −118.318 + 32.2862i −0.182589 + 0.0498244i
649649 447.832i 0.690034i
650650 −58.9596 + 24.1042i −0.0907071 + 0.0370834i
651651 −701.223 91.4988i −1.07715 0.140551i
652652 416.030 111.475i 0.638083 0.170974i
653653 208.275 + 777.291i 0.318950 + 1.19034i 0.920255 + 0.391319i 0.127981π0.127981\pi
−0.601305 + 0.799020i 0.705352π0.705352\pi
654654 25.1956 10.4703i 0.0385255 0.0160096i
655655 −89.3349 + 261.194i −0.136389 + 0.398769i
656656 −1122.07 −1.71047
657657 −18.5921 32.0324i −0.0282985 0.0487556i
658658 −65.0897 + 65.0897i −0.0989206 + 0.0989206i
659659 407.245 235.123i 0.617974 0.356787i −0.158106 0.987422i 0.550539π-0.550539\pi
0.776080 + 0.630635i 0.217205π0.217205\pi
660660 628.875 + 552.795i 0.952840 + 0.837568i
661661 379.580 657.451i 0.574251 0.994631i −0.421872 0.906655i 0.638627π-0.638627\pi
0.996123 0.0879760i 0.0280399π-0.0280399\pi
662662 −48.0606 + 12.8778i −0.0725990 + 0.0194528i
663663 −5.54476 41.7462i −0.00836313 0.0629656i
664664 69.7489 40.2696i 0.105044 0.0606469i
665665 −318.775 21.6313i −0.479361 0.0325283i
666666 14.5381 + 53.7630i 0.0218290 + 0.0807252i
667667 99.5643 + 99.5643i 0.149272 + 0.149272i
668668 −1194.13 319.967i −1.78762 0.478992i
669669 −570.048 + 236.889i −0.852090 + 0.354094i
670670 −12.1722 61.9393i −0.0181675 0.0924468i
671671 573.592 993.490i 0.854832 1.48061i
672672 −148.616 193.220i −0.221154 0.287529i
673673 1217.91 + 326.337i 1.80967 + 0.484899i 0.995418 0.0956152i 0.0304818π-0.0304818\pi
0.814250 + 0.580514i 0.197148π0.197148\pi
674674 27.7198i 0.0411273i
675675 476.742 + 477.852i 0.706284 + 0.707929i
676676 −41.9700 −0.0620858
677677 25.8294 96.3967i 0.0381528 0.142388i −0.944222 0.329309i 0.893184π-0.893184\pi
0.982375 + 0.186921i 0.0598509π0.0598509\pi
678678 78.7820 60.5954i 0.116198 0.0893738i
679679 −272.449 157.298i −0.401250 0.231662i
680680 −7.78136 + 1.52918i −0.0114432 + 0.00224880i
681681 214.318 + 515.734i 0.314711 + 0.757319i
682682 −18.1252 + 67.6443i −0.0265766 + 0.0991852i
683683 366.381 366.381i 0.536430 0.536430i −0.386049 0.922478i 0.626160π-0.626160\pi
0.922478 + 0.386049i 0.126160π0.126160\pi
684684 179.280 + 178.458i 0.262105 + 0.260904i
685685 −66.3650 + 978.005i −0.0968832 + 1.42774i
686686 14.3787 + 24.9047i 0.0209602 + 0.0363042i
687687 538.114 71.4727i 0.783281 0.104036i
688688 −50.2575 187.563i −0.0730486 0.272621i
689689 −283.790 163.846i −0.411887 0.237803i
690690 37.1332 42.2437i 0.0538162 0.0612228i
691691 −298.133 516.381i −0.431451 0.747296i 0.565547 0.824716i 0.308665π-0.308665\pi
−0.996999 + 0.0774204i 0.975332π0.975332\pi
692692 558.971 + 558.971i 0.807761 + 0.807761i
693693 −2.62277 1142.18i −0.00378466 1.64816i
694694 1.92499i 0.00277376i
695695 450.881 + 154.213i 0.648750 + 0.221889i
696696 −12.4449 29.9474i −0.0178806 0.0430279i
697697 72.9284 19.5411i 0.104632 0.0280360i
698698 5.34718 + 19.9559i 0.00766071 + 0.0285902i
699699 66.0000 505.806i 0.0944206 0.723614i
700700 −345.556 + 823.493i −0.493651 + 1.17642i
701701 147.235 0.210036 0.105018 0.994470i 0.466510π-0.466510\pi
0.105018 + 0.994470i 0.466510π0.466510\pi
702702 −26.5444 63.4647i −0.0378126 0.0904056i
703703 163.194 163.194i 0.232140 0.232140i
704704 738.513 426.381i 1.04902 0.605654i
705705 −446.938 670.567i −0.633955 0.951159i
706706 −45.9731 + 79.6277i −0.0651177 + 0.112787i
707707 517.565 138.681i 0.732058 0.196154i
708708 349.546 + 144.317i 0.493710 + 0.203837i
709709 123.232 71.1480i 0.173811 0.100350i −0.410571 0.911829i 0.634670π-0.634670\pi
0.584382 + 0.811479i 0.301337π0.301337\pi
710710 −2.34219 + 34.5163i −0.00329886 + 0.0486145i
711711 195.000 + 721.122i 0.274262 + 1.01424i
712712 24.1362 + 24.1362i 0.0338992 + 0.0338992i
713713 −498.280 133.514i −0.698849 0.187256i
714714 4.27545 + 3.27288i 0.00598803 + 0.00458386i
715715 −526.032 + 783.350i −0.735709 + 1.09559i
716716 503.648 872.343i 0.703418 1.21836i
717717 −1140.49 + 151.481i −1.59064 + 0.211270i
718718 51.2486 + 13.7320i 0.0713769 + 0.0191254i
719719 1075.81i 1.49626i 0.663555 + 0.748128i 0.269047π0.269047\pi
−0.663555 + 0.748128i 0.730953π0.730953\pi
720720 628.297 309.836i 0.872635 0.430328i
721721 −709.245 −0.983696
722722 15.2899 57.0627i 0.0211771 0.0790342i
723723 −903.670 373.097i −1.24989 0.516041i
724724 −813.567 469.713i −1.12371 0.648775i
725725 −109.308 + 141.102i −0.150770 + 0.194623i
726726 −43.7239 5.70530i −0.0602257 0.00785853i
727727 −186.556 + 696.238i −0.256611 + 0.957687i 0.710576 + 0.703621i 0.248435π0.248435\pi
−0.967187 + 0.254066i 0.918232π0.918232\pi
728728 129.302 129.302i 0.177613 0.177613i
729729 −511.918 + 519.020i −0.702219 + 0.711961i
730730 −2.57259 2.94715i −0.00352410 0.00403718i
731731 6.53293 + 11.3154i 0.00893698 + 0.0154793i
732732 −590.605 767.865i −0.806838 1.04900i
733733 −316.043 1179.49i −0.431164 1.60913i −0.750082 0.661345i 0.769986π-0.769986\pi
0.318918 0.947782i 0.396681π-0.396681\pi
734734 −29.4125 16.9813i −0.0400715 0.0231353i
735735 457.776 154.804i 0.622824 0.210618i
736736 −88.9088 153.995i −0.120800 0.209232i
737737 −661.216 661.216i −0.897173 0.897173i
738738 106.668 61.9115i 0.144536 0.0838910i
739739 683.603i 0.925038i 0.886609 + 0.462519i 0.153054π0.153054\pi
−0.886609 + 0.462519i 0.846946π0.846946\pi
740740 −283.980 579.214i −0.383756 0.782721i
741741 −173.280 + 226.360i −0.233846 + 0.305479i
742742 40.4697 10.8438i 0.0545413 0.0146143i
743743 204.636 + 763.713i 0.275419 + 1.02788i 0.955560 + 0.294797i 0.0952519π0.0952519\pi
−0.680141 + 0.733081i 0.738081π0.738081\pi
744744 94.3431 + 72.2201i 0.126805 + 0.0970700i
745745 1230.99 + 421.032i 1.65234 + 0.565143i
746746 −16.6900 −0.0223727
747747 238.412 415.140i 0.319159 0.555742i
748748 −41.3454 + 41.3454i −0.0552746 + 0.0552746i
749749 559.447 322.997i 0.746925 0.431238i
750750 59.0516 + 39.9512i 0.0787355 + 0.0532683i
751751 326.862 566.142i 0.435236 0.753851i −0.562079 0.827084i 0.689998π-0.689998\pi
0.997315 + 0.0732329i 0.0233317π0.0233317\pi
752752 −807.855 + 216.464i −1.07427 + 0.287851i
753753 −1020.01 + 784.541i −1.35459 + 1.04189i
754754 15.7535 9.09526i 0.0208932 0.0120627i
755755 −847.754 971.182i −1.12285 1.28633i
756756 −892.348 366.027i −1.18035 0.484163i
757757 668.868 + 668.868i 0.883577 + 0.883577i 0.993896 0.110319i 0.0351874π-0.0351874\pi
−0.110319 + 0.993896i 0.535187π0.535187\pi
758758 1.90611 + 0.510741i 0.00251466 + 0.000673800i
759759 107.804 826.181i 0.142034 1.08851i
760760 44.5654 + 29.9264i 0.0586386 + 0.0393768i
761761 478.705 829.141i 0.629047 1.08954i −0.358696 0.933454i 0.616779π-0.616779\pi
0.987743 0.156087i 0.0498881π-0.0498881\pi
762762 −5.02782 + 12.1778i −0.00659819 + 0.0159813i
763763 416.413 + 111.577i 0.545757 + 0.146235i
764764 216.396i 0.283241i
765765 −35.4401 + 31.0796i −0.0463269 + 0.0406270i
766766 −24.4926 −0.0319747
767767 −110.301 + 411.649i −0.143808 + 0.536700i
768768 −92.1038 693.444i −0.119927 0.902922i
769769 435.970 + 251.708i 0.566932 + 0.327318i 0.755923 0.654661i 0.227188π-0.227188\pi
−0.188991 + 0.981979i 0.560522π0.560522\pi
770770 −23.2634 118.378i −0.0302123 0.153737i
771771 −671.823 + 877.621i −0.871365 + 1.13829i
772772 −205.421 + 766.640i −0.266089 + 0.993057i
773773 −362.267 + 362.267i −0.468651 + 0.468651i −0.901477 0.432827i 0.857516π-0.857516\pi
0.432827 + 0.901477i 0.357516π0.357516\pi
774774 15.1267 + 15.0574i 0.0195435 + 0.0194540i
775775 88.3390 647.918i 0.113986 0.836024i
776776 26.4279 + 45.7745i 0.0340566 + 0.0589878i
777777 −335.819 + 813.378i −0.432199 + 1.04682i
778778 −36.1011 134.731i −0.0464024 0.173176i
779779 −442.610 255.541i −0.568177 0.328037i
780780 441.911 + 663.024i 0.566552 + 0.850030i
781781 256.245 + 443.830i 0.328099 + 0.568284i
782782 2.77732 + 2.77732i 0.00355155 + 0.00355155i
783783 −153.336 116.822i −0.195831 0.149198i
784784 501.526i 0.639701i
785785 208.673 102.309i 0.265826 0.130330i
786786 −31.2254 4.07443i −0.0397270 0.00518376i
787787 −502.205 + 134.565i −0.638126 + 0.170985i −0.563354 0.826215i 0.690489π-0.690489\pi
−0.0747716 + 0.997201i 0.523823π0.523823\pi
788788 26.8943 + 100.371i 0.0341299 + 0.127374i
789789 182.779 75.9557i 0.231659 0.0962683i
790790 34.7351 + 70.8469i 0.0439685 + 0.0896796i
791791 1570.39 1.98532
792792 −95.5677 + 166.409i −0.120666 + 0.210113i
793793 771.945 771.945i 0.973449 0.973449i
794794 35.2207 20.3347i 0.0443585 0.0256104i
795795 23.5663 + 366.033i 0.0296432 + 0.460419i
796796 408.438 707.435i 0.513113 0.888737i
797797 −269.356 + 72.1737i −0.337962 + 0.0905567i −0.423809 0.905752i 0.639307π-0.639307\pi
0.0858466 + 0.996308i 0.472640π0.472640\pi
798798 −4.79887 36.1304i −0.00601362 0.0452762i
799799 48.7365 28.1380i 0.0609968 0.0352165i
800800 179.457 136.393i 0.224321 0.170491i
801801 196.099 + 52.0623i 0.244818 + 0.0649967i
802802 0.879908 + 0.879908i 0.00109714 + 0.00109714i
803803 −55.9768 14.9989i −0.0697096 0.0186786i
804804 −729.181 + 303.018i −0.906941 + 0.376888i
805805 871.992 171.363i 1.08322 0.212873i
806806 −33.3216 + 57.7147i −0.0413419 + 0.0716063i
807807 −268.732 349.387i −0.333001 0.432945i
808808 −86.9569 23.3000i −0.107620 0.0288367i
809809 423.966i 0.524062i 0.965060 + 0.262031i 0.0843922π0.0843922\pi
−0.965060 + 0.262031i 0.915608π0.915608\pi
810810 −42.6324 + 64.1211i −0.0526326 + 0.0791618i
811811 −1163.79 −1.43501 −0.717506 0.696552i 0.754716π-0.754716\pi
−0.717506 + 0.696552i 0.754716π0.754716\pi
812812 66.0092 246.350i 0.0812921 0.303386i
813813 107.045 82.3340i 0.131667 0.101272i
814814 75.4686 + 43.5718i 0.0927133 + 0.0535281i
815815 302.877 451.034i 0.371628 0.553416i
816816 18.7731 + 45.1756i 0.0230063 + 0.0553622i
817817 22.8914 85.4317i 0.0280188 0.104568i
818818 −99.2357 + 99.2357i −0.121315 + 0.121315i
819819 278.907 1050.54i 0.340546 1.28271i
820820 −1076.19 + 939.413i −1.31242 + 1.14563i
821821 −382.915 663.228i −0.466400 0.807829i 0.532863 0.846202i 0.321116π-0.321116\pi
−0.999264 + 0.0383722i 0.987783π0.987783\pi
822822 −110.848 + 14.7230i −0.134852 + 0.0179112i
823823 256.028 + 955.510i 0.311091 + 1.16101i 0.927574 + 0.373640i 0.121891π0.121891\pi
−0.616482 + 0.787369i 0.711443π0.711443\pi
824824 103.197 + 59.5806i 0.125239 + 0.0723066i
825825 1056.16 + 3.65372i 1.28019 + 0.00442876i
826826 −27.2441 47.1882i −0.0329832 0.0571286i
827827 −260.100 260.100i −0.314510 0.314510i 0.532144 0.846654i 0.321387π-0.321387\pi
−0.846654 + 0.532144i 0.821387π0.821387\pi
828828 −610.119 350.387i −0.736858 0.423172i
829829 325.275i 0.392370i −0.980567 0.196185i 0.937145π-0.937145\pi
0.980567 0.196185i 0.0628553π-0.0628553\pi
830830 16.3640 47.8444i 0.0197157 0.0576438i
831831 −182.756 439.783i −0.219923 0.529221i
832832 783.862 210.035i 0.942142 0.252446i
833833 8.73421 + 32.5965i 0.0104852 + 0.0391315i
834834 −7.03342 + 53.9023i −0.00843336 + 0.0646310i
835835 −1400.18 + 686.487i −1.67686 + 0.822140i
836836 395.803 0.473449
837837 700.497 + 89.7687i 0.836914 + 0.107251i
838838 36.5387 36.5387i 0.0436022 0.0436022i
839839 81.4767 47.0406i 0.0971116 0.0560674i −0.450658 0.892697i 0.648810π-0.648810\pi
0.547769 + 0.836629i 0.315477π0.315477\pi
840840 −200.700 40.1628i −0.238928 0.0478128i
841841 −395.014 + 684.184i −0.469695 + 0.813536i
842842 37.8296 10.1364i 0.0449283 0.0120385i
843843 183.535 + 75.7757i 0.217716 + 0.0898882i
844844 833.301 481.107i 0.987323 0.570031i
845845 −39.8834 + 34.8146i −0.0471993 + 0.0412007i
846846 64.8536 65.1522i 0.0766591 0.0770120i
847847 −492.644 492.644i −0.581633 0.581633i
848848 367.698 + 98.5244i 0.433606 + 0.116184i
849849 958.837 + 733.994i 1.12937 + 0.864539i
850850 −3.04911 + 3.93600i −0.00358719 + 0.00463058i
851851 −320.958 + 555.915i −0.377154 + 0.653249i
852852 428.999 56.9800i 0.503520 0.0668779i
853853 −984.979 263.924i −1.15472 0.309407i −0.369867 0.929085i 0.620597π-0.620597\pi
−0.784856 + 0.619678i 0.787263π0.787263\pi
854854 139.579i 0.163442i
855855 318.400 + 20.8714i 0.372397 + 0.0244110i
856856 −108.534 −0.126793
857857 −408.073 + 1522.95i −0.476164 + 1.77707i 0.140756 + 0.990044i 0.455047π0.455047\pi
−0.616920 + 0.787026i 0.711620π0.711620\pi
858858 −99.4922 41.0773i −0.115958 0.0478756i
859859 507.067 + 292.755i 0.590299 + 0.340809i 0.765216 0.643774i 0.222632π-0.222632\pi
−0.174917 + 0.984583i 0.555966π0.555966\pi
860860 −205.233 137.818i −0.238643 0.160253i
861861 1932.30 + 252.136i 2.24426 + 0.292841i
862862 −11.7345 + 43.7939i −0.0136132 + 0.0508050i
863863 −550.423 + 550.423i −0.637802 + 0.637802i −0.950013 0.312211i 0.898930π-0.898930\pi
0.312211 + 0.950013i 0.398930π0.398930\pi
864864 148.860 + 192.621i 0.172292 + 0.222941i
865865 994.853 + 67.5082i 1.15012 + 0.0780442i
866866 −10.7144 18.5579i −0.0123723 0.0214294i
867867 526.579 + 684.622i 0.607357 + 0.789644i
868868 241.833 + 902.531i 0.278609 + 1.03978i
869869 1012.26 + 584.429i 1.16486 + 0.672530i
870870 −18.2507 9.02650i −0.0209779 0.0103753i
871871 −444.935 770.650i −0.510833 0.884788i
872872 −51.2158 51.2158i −0.0587337 0.0587337i
873873 272.446 + 156.464i 0.312080 + 0.179225i
874874 26.5875i 0.0304205i
875875 354.720 + 1069.19i 0.405395 + 1.22194i
876876 −29.7460 + 38.8581i −0.0339567 + 0.0443585i
877877 −882.630 + 236.500i −1.00642 + 0.269669i −0.724133 0.689661i 0.757760π-0.757760\pi
−0.282287 + 0.959330i 0.591093π0.591093\pi
878878 15.9166 + 59.4017i 0.0181283 + 0.0676557i
879879 −517.247 395.955i −0.588450 0.450461i
880880 354.729 1037.14i 0.403101 1.17857i
881881 −459.689 −0.521781 −0.260891 0.965368i 0.584016π-0.584016\pi
−0.260891 + 0.965368i 0.584016π0.584016\pi
882882 27.6723 + 47.6767i 0.0313745 + 0.0540552i
883883 107.163 107.163i 0.121362 0.121362i −0.643817 0.765179i 0.722650π-0.722650\pi
0.765179 + 0.643817i 0.222650π0.222650\pi
884884 −48.1882 + 27.8215i −0.0545116 + 0.0314723i
885885 451.881 152.811i 0.510600 0.172667i
886886 −71.8119 + 124.382i −0.0810519 + 0.140386i
887887 642.507 172.159i 0.724360 0.194092i 0.122244 0.992500i 0.460991π-0.460991\pi
0.602116 + 0.798408i 0.294324π0.294324\pi
888888 117.191 90.1376i 0.131972 0.101506i
889889 −180.277 + 104.083i −0.202786 + 0.117078i
890890 21.3813 + 1.45088i 0.0240239 + 0.00163020i
891891 5.23854 + 1140.65i 0.00587940 + 1.28019i
892892 576.746 + 576.746i 0.646576 + 0.646576i
893893 −367.963 98.5954i −0.412053 0.110409i
894894 −19.2026 + 147.164i −0.0214794 + 0.164613i
895895 −245.010 1246.75i −0.273755 1.39302i
896896 −214.387 + 371.329i −0.239271 + 0.414430i
897897 302.582 732.877i 0.337327 0.817031i
898898 −94.5284 25.3288i −0.105266 0.0282058i
899899 186.745i 0.207725i
900900 343.206 823.187i 0.381340 0.914652i
901901 −25.6142 −0.0284287
902902 49.9463 186.402i 0.0553728 0.206654i
903903 44.4012 + 334.295i 0.0491708 + 0.370204i
904904 −228.495 131.922i −0.252760 0.145931i
905905 −1162.75 + 228.502i −1.28481 + 0.252489i
906906 89.3891 116.772i 0.0986635 0.128887i
907907 215.603 804.640i 0.237710 0.887144i −0.739199 0.673487i 0.764796π-0.764796\pi
0.976909 0.213657i 0.0685376π-0.0685376\pi
908908 521.794 521.794i 0.574663 0.574663i
909909 −516.557 + 139.683i −0.568269 + 0.153667i
910910 7.77262 114.543i 0.00854134 0.125872i
911911 −38.7954 67.1955i −0.0425855 0.0737602i 0.843947 0.536427i 0.180226π-0.180226\pi
−0.886533 + 0.462666i 0.846893π0.846893\pi
912912 126.376 306.093i 0.138571 0.335629i
913913 −193.871 723.538i −0.212345 0.792484i
914914 −93.8309 54.1733i −0.102660 0.0592706i
915915 −1198.20 239.776i −1.30950 0.262050i
916916 −358.623 621.153i −0.391510 0.678115i
917917 −351.821 351.821i −0.383665 0.383665i
918918 −4.27725 3.25871i −0.00465932 0.00354979i
919919 1478.95i 1.60930i −0.593750 0.804650i 0.702353π-0.702353\pi
0.593750 0.804650i 0.297647π-0.297647\pi
920920 −141.272 48.3187i −0.153557 0.0525203i
921921 921.730 + 120.272i 1.00079 + 0.130588i
922922 −43.8305 + 11.7443i −0.0475385 + 0.0127379i
923923 126.226 + 471.083i 0.136757 + 0.510383i
924924 −1393.60 + 579.125i −1.50823 + 0.626758i
925925 −750.325 314.853i −0.811162 0.340382i
926926 156.839 0.169373
927927 708.298 1.62646i 0.764076 0.00175454i
928928 −45.5177 + 45.5177i −0.0490492 + 0.0490492i
929929 −1381.56 + 797.643i −1.48715 + 0.858604i −0.999893 0.0146572i 0.995334π-0.995334\pi
−0.487253 + 0.873261i 0.662001π0.662001\pi
930930 74.4406 4.79270i 0.0800436 0.00515345i
931931 114.218 197.831i 0.122683 0.212493i
932932 −651.014 + 174.439i −0.698513 + 0.187166i
933933 −54.3888 409.491i −0.0582946 0.438897i
934934 113.927 65.7757i 0.121977 0.0704237i
935935 −4.99338 + 73.5863i −0.00534051 + 0.0787019i
936936 −128.833 + 129.426i −0.137642 + 0.138276i
937937 −921.265 921.265i −0.983207 0.983207i 0.0166542 0.999861i 0.494699π-0.494699\pi
−0.999861 + 0.0166542i 0.994699π0.994699\pi
938938 109.898 + 29.4471i 0.117162 + 0.0313935i
939939 18.2824 7.59741i 0.0194700 0.00809096i
940940 −593.594 + 883.961i −0.631483 + 0.940384i
941941 −618.185 + 1070.73i −0.656945 + 1.13786i 0.324458 + 0.945900i 0.394818π0.394818\pi
−0.981402 + 0.191961i 0.938515π0.938515\pi
942942 16.1632 + 21.0144i 0.0171584 + 0.0223082i
943943 1373.07 + 367.913i 1.45607 + 0.390152i
944944 495.068i 0.524436i
945945 −1151.61 + 392.383i −1.21863 + 0.415221i
946946 33.3958 0.0353021
947947 418.272 1561.01i 0.441681 1.64838i −0.282872 0.959158i 0.591287π-0.591287\pi
0.724553 0.689219i 0.242046π-0.242046\pi
948948 782.372 601.764i 0.825287 0.634772i
949949 −47.7599 27.5742i −0.0503265 0.0290560i
950950 33.4345 4.24511i 0.0351943 0.00446854i
951951 −509.250 1225.46i −0.535489 1.28860i
952952 3.69940 13.8064i 0.00388593 0.0145025i
953953 1074.57 1074.57i 1.12756 1.12756i 0.136988 0.990573i 0.456258π-0.456258\pi
0.990573 0.136988i 0.0437421π-0.0437421\pi
954954 −40.3908 + 10.9222i −0.0423384 + 0.0114488i
955955 179.503 + 205.638i 0.187961 + 0.215328i
956956 760.073 + 1316.48i 0.795055 + 1.37708i
957957 −298.995 + 39.7127i −0.312429 + 0.0414971i
958958 8.11362 + 30.2804i 0.00846933 + 0.0316080i
959959 −1530.10 883.405i −1.59552 0.921173i
960960 −682.233 599.699i −0.710660 0.624686i
961961 138.418 + 239.748i 0.144036 + 0.249477i
962962 58.6394 + 58.6394i 0.0609557 + 0.0609557i
963963 −557.960 + 323.849i −0.579398 + 0.336292i
964964 1291.77i 1.34001i
965965 440.729 + 898.924i 0.456713 + 0.931527i
966966 38.9019 + 93.6132i 0.0402711 + 0.0969081i
967967 174.037 46.6332i 0.179977 0.0482246i −0.167705 0.985837i 0.553636π-0.553636\pi
0.347682 + 0.937613i 0.386969π0.386969\pi
968968 30.2958 + 113.066i 0.0312974 + 0.116803i
969969 −2.88310 + 22.0953i −0.00297533 + 0.0228022i
970970 31.3991 + 10.7393i 0.0323702 + 0.0110714i
971971 −40.8568 −0.0420770 −0.0210385 0.999779i 0.506697π-0.506697\pi
−0.0210385 + 0.999779i 0.506697π0.506697\pi
972972 891.997 + 363.492i 0.917693 + 0.373963i
973973 −607.325 + 607.325i −0.624178 + 0.624178i
974974 76.1338 43.9558i 0.0781661 0.0451292i
975975 969.926 + 263.491i 0.994796 + 0.270247i
976976 −634.092 + 1098.28i −0.649685 + 1.12529i
977977 754.152 202.074i 0.771906 0.206832i 0.148693 0.988883i 0.452494π-0.452494\pi
0.623213 + 0.782052i 0.285827π0.285827\pi
978978 57.2853 + 23.6513i 0.0585739 + 0.0241834i
979979 274.932 158.732i 0.280829 0.162137i
980980 −419.885 481.018i −0.428454 0.490835i
981981 −416.113 110.474i −0.424172 0.112613i
982982 48.9385 + 48.9385i 0.0498355 + 0.0498355i
983983 −496.515 133.041i −0.505101 0.135341i −0.00273477 0.999996i 0.500871π-0.500871\pi
−0.502367 + 0.864655i 0.667537π0.667537\pi
984984 −259.974 199.011i −0.264201 0.202247i
985985 108.816 + 73.0718i 0.110473 + 0.0741845i
986986 0.710935 1.23138i 0.000721030 0.00124886i
987987 1439.84 191.241i 1.45881 0.193760i
988988 363.824 + 97.4863i 0.368243 + 0.0986704i
989989 245.999i 0.248735i
990990 23.5039 + 118.167i 0.0237413 + 0.119360i
991991 941.294 0.949843 0.474922 0.880028i 0.342476π-0.342476\pi
0.474922 + 0.880028i 0.342476π0.342476\pi
992992 61.0382 227.798i 0.0615304 0.229635i
993993 725.690 + 299.615i 0.730805 + 0.301727i
994994 −54.0013 31.1776i −0.0543272 0.0313658i
995995 −198.693 1011.07i −0.199692 1.01615i
996996 −627.219 81.8425i −0.629738 0.0821712i
997997 344.990 1287.52i 0.346029 1.29140i −0.545377 0.838191i 0.683614π-0.683614\pi
0.891406 0.453206i 0.149720π-0.149720\pi
998998 54.8879 54.8879i 0.0549979 0.0549979i
999999 333.505 813.063i 0.333839 0.813877i
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 45.3.k.a.22.5 yes 40
3.2 odd 2 135.3.l.a.37.6 40
5.2 odd 4 225.3.o.b.193.5 40
5.3 odd 4 inner 45.3.k.a.13.6 yes 40
5.4 even 2 225.3.o.b.157.6 40
9.2 odd 6 135.3.l.a.127.5 40
9.4 even 3 405.3.g.h.82.5 20
9.5 odd 6 405.3.g.g.82.6 20
9.7 even 3 inner 45.3.k.a.7.6 40
15.8 even 4 135.3.l.a.118.5 40
45.7 odd 12 225.3.o.b.43.6 40
45.13 odd 12 405.3.g.h.163.5 20
45.23 even 12 405.3.g.g.163.6 20
45.34 even 6 225.3.o.b.7.5 40
45.38 even 12 135.3.l.a.73.6 40
45.43 odd 12 inner 45.3.k.a.43.5 yes 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.3.k.a.7.6 40 9.7 even 3 inner
45.3.k.a.13.6 yes 40 5.3 odd 4 inner
45.3.k.a.22.5 yes 40 1.1 even 1 trivial
45.3.k.a.43.5 yes 40 45.43 odd 12 inner
135.3.l.a.37.6 40 3.2 odd 2
135.3.l.a.73.6 40 45.38 even 12
135.3.l.a.118.5 40 15.8 even 4
135.3.l.a.127.5 40 9.2 odd 6
225.3.o.b.7.5 40 45.34 even 6
225.3.o.b.43.6 40 45.7 odd 12
225.3.o.b.157.6 40 5.4 even 2
225.3.o.b.193.5 40 5.2 odd 4
405.3.g.g.82.6 20 9.5 odd 6
405.3.g.g.163.6 20 45.23 even 12
405.3.g.h.82.5 20 9.4 even 3
405.3.g.h.163.5 20 45.13 odd 12