Properties

Label 40.3.i.a.13.2
Level 4040
Weight 33
Character 40.13
Analytic conductor 1.0901.090
Analytic rank 00
Dimension 2020
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [40,3,Mod(13,40)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(40, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 2, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("40.13");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 40=235 40 = 2^{3} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 40.i (of order 44, degree 22, 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: 1.089921057441.08992105744
Analytic rank: 00
Dimension: 2020
Relative dimension: 1010 over Q(i)\Q(i)
Coefficient field: Q[x]/(x20)\mathbb{Q}[x]/(x^{20} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x20x183x16+11x14+x1240x10+4x8+176x6192x4256x2+1024 x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 220 2^{20}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 13.2
Root 1.39859+0.209644i1.39859 + 0.209644i of defining polynomial
Character χ\chi == 40.13
Dual form 40.3.i.a.37.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.608231.18894i)q2+(2.52630+2.52630i)q3+(1.17282+3.82420i)q4+(3.09141+3.92978i)q5+(7.066501.05925i)q6+(5.20520+5.20520i)q7+(2.660597.54462i)q83.76437iq9+(0.2994089.99552i)q102.49236iq11+(12.62406.69817i)q12+(6.65988+6.65988i)q13+(14.55992.18248i)q14+(17.73762.11798i)q15+(13.2490+8.97020i)q16+(21.942821.9428i)q17+(4.47563+6.05398i)q18+17.5567q19+(11.4026+16.4311i)q2026.2998iq21+(2.96328+4.00830i)q22+(20.1791+20.1791i)q23+(12.3385+25.7814i)q24+(5.88639+24.2971i)q25+(18.62892.79240i)q26+(13.226813.2268i)q27+(26.010513.8010i)q28+1.04754q29+(26.0081+24.4953i)q302.47263q31+(31.9725+1.32614i)q32+(6.29646+6.29646i)q33+(61.3780+9.20035i)q34+(36.54674.36391i)q35+(14.39574.41493i)q36+(19.2786+19.2786i)q37+(28.235320.8740i)q3833.6497iq39+(37.873712.8680i)q4043.9414q41+(31.2690+42.2962i)q42+(32.939432.9394i)q43+(9.531292.92310i)q44+(14.793211.6372i)q45+(8.4608656.4446i)q46+(33.707933.7079i)q47+(10.809556.1323i)q485.18827iq49+(38.354632.0768i)q50+110.868iq51+(33.279517.6578i)q52+(36.4034+36.4034i)q53+(5.54582+36.9976i)q54+(9.794457.70491i)q55+(25.4224+53.1202i)q56+(44.3536+44.3536i)q57+(1.684691.24547i)q58+30.5963q59+(12.703570.3162i)q6023.8366iq61+(3.97657+2.93982i)q62+(19.5943+19.5943i)q63+(49.842540.1463i)q64+(46.76035.58347i)q65+(2.6400317.6123i)q66+(19.9932+19.9932i)q67+(109.649+58.1787i)q68101.957q69+(53.5872+50.4702i)q7021.8350q71+(28.400710.0154i)q72+(32.6450+32.6450i)q73+(8.0832853.9257i)q74+(46.511076.2526i)q75+(20.5909+67.1405i)q76+(12.9733+12.9733i)q77+(40.0076+54.1165i)q78+16.4124iq79+(76.209024.3351i)q80+100.709q81+(70.6680+52.2439i)q82+(0.343799+0.343799i)q83+(100.57630.8450i)q84+(154.065+18.3963i)q85+(92.1373+13.8111i)q86+(2.64640+2.64640i)q87+(18.80396.63116i)q8884.4631iq89+(37.6268+1.12708i)q9069.3320iq91+(53.5025+100.836i)q92+(6.246616.24661i)q93+(94.2869+14.1333i)q94+(54.2751+68.9942i)q95+(84.1223+77.4219i)q96+(24.1311+24.1311i)q97+(6.16856+8.34394i)q989.38218q99+O(q100)q+(-1.60823 - 1.18894i) q^{2} +(-2.52630 + 2.52630i) q^{3} +(1.17282 + 3.82420i) q^{4} +(3.09141 + 3.92978i) q^{5} +(7.06650 - 1.05925i) q^{6} +(-5.20520 + 5.20520i) q^{7} +(2.66059 - 7.54462i) q^{8} -3.76437i q^{9} +(-0.299408 - 9.99552i) q^{10} -2.49236i q^{11} +(-12.6240 - 6.69817i) q^{12} +(-6.65988 + 6.65988i) q^{13} +(14.5599 - 2.18248i) q^{14} +(-17.7376 - 2.11798i) q^{15} +(-13.2490 + 8.97020i) q^{16} +(21.9428 - 21.9428i) q^{17} +(-4.47563 + 6.05398i) q^{18} +17.5567 q^{19} +(-11.4026 + 16.4311i) q^{20} -26.2998i q^{21} +(-2.96328 + 4.00830i) q^{22} +(20.1791 + 20.1791i) q^{23} +(12.3385 + 25.7814i) q^{24} +(-5.88639 + 24.2971i) q^{25} +(18.6289 - 2.79240i) q^{26} +(-13.2268 - 13.2268i) q^{27} +(-26.0105 - 13.8010i) q^{28} +1.04754 q^{29} +(26.0081 + 24.4953i) q^{30} -2.47263 q^{31} +(31.9725 + 1.32614i) q^{32} +(6.29646 + 6.29646i) q^{33} +(-61.3780 + 9.20035i) q^{34} +(-36.5467 - 4.36391i) q^{35} +(14.3957 - 4.41493i) q^{36} +(19.2786 + 19.2786i) q^{37} +(-28.2353 - 20.8740i) q^{38} -33.6497i q^{39} +(37.8737 - 12.8680i) q^{40} -43.9414 q^{41} +(-31.2690 + 42.2962i) q^{42} +(32.9394 - 32.9394i) q^{43} +(9.53129 - 2.92310i) q^{44} +(14.7932 - 11.6372i) q^{45} +(-8.46086 - 56.4446i) q^{46} +(33.7079 - 33.7079i) q^{47} +(10.8095 - 56.1323i) q^{48} -5.18827i q^{49} +(38.3546 - 32.0768i) q^{50} +110.868i q^{51} +(-33.2795 - 17.6578i) q^{52} +(-36.4034 + 36.4034i) q^{53} +(5.54582 + 36.9976i) q^{54} +(9.79445 - 7.70491i) q^{55} +(25.4224 + 53.1202i) q^{56} +(-44.3536 + 44.3536i) q^{57} +(-1.68469 - 1.24547i) q^{58} +30.5963 q^{59} +(-12.7035 - 70.3162i) q^{60} -23.8366i q^{61} +(3.97657 + 2.93982i) q^{62} +(19.5943 + 19.5943i) q^{63} +(-49.8425 - 40.1463i) q^{64} +(-46.7603 - 5.58347i) q^{65} +(-2.64003 - 17.6123i) q^{66} +(19.9932 + 19.9932i) q^{67} +(109.649 + 58.1787i) q^{68} -101.957 q^{69} +(53.5872 + 50.4702i) q^{70} -21.8350 q^{71} +(-28.4007 - 10.0154i) q^{72} +(32.6450 + 32.6450i) q^{73} +(-8.08328 - 53.9257i) q^{74} +(-46.5110 - 76.2526i) q^{75} +(20.5909 + 67.1405i) q^{76} +(12.9733 + 12.9733i) q^{77} +(-40.0076 + 54.1165i) q^{78} +16.4124i q^{79} +(-76.2090 - 24.3351i) q^{80} +100.709 q^{81} +(70.6680 + 52.2439i) q^{82} +(-0.343799 + 0.343799i) q^{83} +(100.576 - 30.8450i) q^{84} +(154.065 + 18.3963i) q^{85} +(-92.1373 + 13.8111i) q^{86} +(-2.64640 + 2.64640i) q^{87} +(-18.8039 - 6.63116i) q^{88} -84.4631i q^{89} +(-37.6268 + 1.12708i) q^{90} -69.3320i q^{91} +(-53.5025 + 100.836i) q^{92} +(6.24661 - 6.24661i) q^{93} +(-94.2869 + 14.1333i) q^{94} +(54.2751 + 68.9942i) q^{95} +(-84.1223 + 77.4219i) q^{96} +(-24.1311 + 24.1311i) q^{97} +(-6.16856 + 8.34394i) q^{98} -9.38218 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 20q2q216q64q7+4q8+6q1044q124q1556q1612q17+10q1824q20+92q224q2328q25+100q26+68q28+100q30136q31++546q98+O(q100) 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31}+ \cdots + 546 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

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

nn 1717 2121 3131
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 1-1 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.60823 1.18894i −0.804116 0.594472i
33 −2.52630 + 2.52630i −0.842100 + 0.842100i −0.989132 0.147032i 0.953028π-0.953028\pi
0.147032 + 0.989132i 0.453028π0.453028\pi
44 1.17282 + 3.82420i 0.293205 + 0.956049i
55 3.09141 + 3.92978i 0.618282 + 0.785957i
66 7.06650 1.05925i 1.17775 0.176541i
77 −5.20520 + 5.20520i −0.743600 + 0.743600i −0.973269 0.229669i 0.926236π-0.926236\pi
0.229669 + 0.973269i 0.426236π0.426236\pi
88 2.66059 7.54462i 0.332574 0.943077i
99 3.76437i 0.418263i
1010 −0.299408 9.99552i −0.0299408 0.999552i
1111 2.49236i 0.226579i −0.993562 0.113289i 0.963861π-0.963861\pi
0.993562 0.113289i 0.0361387π-0.0361387\pi
1212 −12.6240 6.69817i −1.05200 0.558181i
1313 −6.65988 + 6.65988i −0.512298 + 0.512298i −0.915230 0.402932i 0.867991π-0.867991\pi
0.402932 + 0.915230i 0.367991π0.367991\pi
1414 14.5599 2.18248i 1.03999 0.155891i
1515 −17.7376 2.11798i −1.18251 0.141199i
1616 −13.2490 + 8.97020i −0.828061 + 0.560638i
1717 21.9428 21.9428i 1.29075 1.29075i 0.356434 0.934320i 0.383992π-0.383992\pi
0.934320 0.356434i 0.116008π-0.116008\pi
1818 −4.47563 + 6.05398i −0.248646 + 0.336332i
1919 17.5567 0.924039 0.462020 0.886870i 0.347125π-0.347125\pi
0.462020 + 0.886870i 0.347125π0.347125\pi
2020 −11.4026 + 16.4311i −0.570130 + 0.821555i
2121 26.2998i 1.25237i
2222 −2.96328 + 4.00830i −0.134695 + 0.182195i
2323 20.1791 + 20.1791i 0.877354 + 0.877354i 0.993260 0.115906i 0.0369772π-0.0369772\pi
−0.115906 + 0.993260i 0.536977π0.536977\pi
2424 12.3385 + 25.7814i 0.514105 + 1.07423i
2525 −5.88639 + 24.2971i −0.235455 + 0.971885i
2626 18.6289 2.79240i 0.716495 0.107400i
2727 −13.2268 13.2268i −0.489880 0.489880i
2828 −26.0105 13.8010i −0.928946 0.492891i
2929 1.04754 0.0361220 0.0180610 0.999837i 0.494251π-0.494251\pi
0.0180610 + 0.999837i 0.494251π0.494251\pi
3030 26.0081 + 24.4953i 0.866935 + 0.816509i
3131 −2.47263 −0.0797623 −0.0398812 0.999204i 0.512698π-0.512698\pi
−0.0398812 + 0.999204i 0.512698π0.512698\pi
3232 31.9725 + 1.32614i 0.999141 + 0.0414418i
3333 6.29646 + 6.29646i 0.190802 + 0.190802i
3434 −61.3780 + 9.20035i −1.80523 + 0.270599i
3535 −36.5467 4.36391i −1.04419 0.124683i
3636 14.3957 4.41493i 0.399880 0.122637i
3737 19.2786 + 19.2786i 0.521043 + 0.521043i 0.917886 0.396843i 0.129894π-0.129894\pi
−0.396843 + 0.917886i 0.629894π0.629894\pi
3838 −28.2353 20.8740i −0.743035 0.549316i
3939 33.6497i 0.862813i
4040 37.8737 12.8680i 0.946842 0.321699i
4141 −43.9414 −1.07174 −0.535871 0.844300i 0.680017π-0.680017\pi
−0.535871 + 0.844300i 0.680017π0.680017\pi
4242 −31.2690 + 42.2962i −0.744500 + 1.00705i
4343 32.9394 32.9394i 0.766032 0.766032i −0.211373 0.977405i 0.567794π-0.567794\pi
0.977405 + 0.211373i 0.0677936π0.0677936\pi
4444 9.53129 2.92310i 0.216620 0.0664340i
4545 14.7932 11.6372i 0.328737 0.258604i
4646 −8.46086 56.4446i −0.183932 1.22706i
4747 33.7079 33.7079i 0.717189 0.717189i −0.250840 0.968029i 0.580707π-0.580707\pi
0.968029 + 0.250840i 0.0807067π0.0807067\pi
4848 10.8095 56.1323i 0.225197 1.16942i
4949 5.18827i 0.105883i
5050 38.3546 32.0768i 0.767092 0.641537i
5151 110.868i 2.17389i
5252 −33.2795 17.6578i −0.639991 0.339574i
5353 −36.4034 + 36.4034i −0.686856 + 0.686856i −0.961536 0.274679i 0.911428π-0.911428\pi
0.274679 + 0.961536i 0.411428π0.411428\pi
5454 5.54582 + 36.9976i 0.102700 + 0.685141i
5555 9.79445 7.70491i 0.178081 0.140089i
5656 25.4224 + 53.1202i 0.453971 + 0.948575i
5757 −44.3536 + 44.3536i −0.778133 + 0.778133i
5858 −1.68469 1.24547i −0.0290463 0.0214736i
5959 30.5963 0.518581 0.259291 0.965799i 0.416511π-0.416511\pi
0.259291 + 0.965799i 0.416511π0.416511\pi
6060 −12.7035 70.3162i −0.211725 1.17194i
6161 23.8366i 0.390764i −0.980727 0.195382i 0.937405π-0.937405\pi
0.980727 0.195382i 0.0625947π-0.0625947\pi
6262 3.97657 + 2.93982i 0.0641382 + 0.0474165i
6363 19.5943 + 19.5943i 0.311021 + 0.311021i
6464 −49.8425 40.1463i −0.778789 0.627286i
6565 −46.7603 5.58347i −0.719389 0.0858996i
6666 −2.64003 17.6123i −0.0400004 0.266853i
6767 19.9932 + 19.9932i 0.298407 + 0.298407i 0.840390 0.541983i 0.182326π-0.182326\pi
−0.541983 + 0.840390i 0.682326π0.682326\pi
6868 109.649 + 58.1787i 1.61248 + 0.855569i
6969 −101.957 −1.47764
7070 53.5872 + 50.4702i 0.765531 + 0.721003i
7171 −21.8350 −0.307535 −0.153767 0.988107i 0.549141π-0.549141\pi
−0.153767 + 0.988107i 0.549141π0.549141\pi
7272 −28.4007 10.0154i −0.394454 0.139103i
7373 32.6450 + 32.6450i 0.447191 + 0.447191i 0.894420 0.447228i 0.147589π-0.147589\pi
−0.447228 + 0.894420i 0.647589π0.647589\pi
7474 −8.08328 53.9257i −0.109233 0.728725i
7575 −46.5110 76.2526i −0.620147 1.01670i
7676 20.5909 + 67.1405i 0.270933 + 0.883427i
7777 12.9733 + 12.9733i 0.168484 + 0.168484i
7878 −40.0076 + 54.1165i −0.512918 + 0.693801i
7979 16.4124i 0.207753i 0.994590 + 0.103876i 0.0331246π0.0331246\pi
−0.994590 + 0.103876i 0.966875π0.966875\pi
8080 −76.2090 24.3351i −0.952612 0.304188i
8181 100.709 1.24332
8282 70.6680 + 52.2439i 0.861805 + 0.637121i
8383 −0.343799 + 0.343799i −0.00414216 + 0.00414216i −0.709175 0.705033i 0.750932π-0.750932\pi
0.705033 + 0.709175i 0.250932π0.250932\pi
8484 100.576 30.8450i 1.19733 0.367202i
8585 154.065 + 18.3963i 1.81253 + 0.216427i
8686 −92.1373 + 13.8111i −1.07136 + 0.160594i
8787 −2.64640 + 2.64640i −0.0304184 + 0.0304184i
8888 −18.8039 6.63116i −0.213681 0.0753541i
8989 84.4631i 0.949024i −0.880249 0.474512i 0.842625π-0.842625\pi
0.880249 0.474512i 0.157375π-0.157375\pi
9090 −37.6268 + 1.12708i −0.418076 + 0.0125232i
9191 69.3320i 0.761891i
9292 −53.5025 + 100.836i −0.581549 + 1.09604i
9393 6.24661 6.24661i 0.0671678 0.0671678i
9494 −94.2869 + 14.1333i −1.00305 + 0.150354i
9595 54.2751 + 68.9942i 0.571316 + 0.726255i
9696 −84.1223 + 77.4219i −0.876274 + 0.806478i
9797 −24.1311 + 24.1311i −0.248774 + 0.248774i −0.820467 0.571693i 0.806287π-0.806287\pi
0.571693 + 0.820467i 0.306287π0.306287\pi
9898 −6.16856 + 8.34394i −0.0629445 + 0.0851422i
9999 −9.38218 −0.0947695
100100 −99.8207 + 5.98548i −0.998207 + 0.0598548i
101101 152.095i 1.50589i −0.658085 0.752944i 0.728633π-0.728633\pi
0.658085 0.752944i 0.271367π-0.271367\pi
102102 131.816 178.302i 1.29232 1.74806i
103103 −120.657 120.657i −1.17143 1.17143i −0.981870 0.189558i 0.939295π-0.939295\pi
−0.189558 0.981870i 0.560705π-0.560705\pi
104104 32.5270 + 67.9655i 0.312760 + 0.653514i
105105 103.352 81.3034i 0.984309 0.774318i
106106 101.827 15.2635i 0.960629 0.143995i
107107 −75.2789 75.2789i −0.703541 0.703541i 0.261628 0.965169i 0.415741π-0.415741\pi
−0.965169 + 0.261628i 0.915741π0.915741\pi
108108 35.0691 66.0944i 0.324714 0.611985i
109109 11.8614 0.108820 0.0544100 0.998519i 0.482672π-0.482672\pi
0.0544100 + 0.998519i 0.482672π0.482672\pi
110110 −24.9125 + 0.746235i −0.226477 + 0.00678395i
111111 −97.4070 −0.877541
112112 22.2719 115.655i 0.198856 1.03264i
113113 −82.0090 82.0090i −0.725743 0.725743i 0.244025 0.969769i 0.421532π-0.421532\pi
−0.969769 + 0.244025i 0.921532π0.921532\pi
114114 124.065 18.5969i 1.08829 0.163131i
115115 −16.9177 + 141.682i −0.147110 + 1.23201i
116116 1.22858 + 4.00600i 0.0105912 + 0.0345345i
117117 25.0702 + 25.0702i 0.214276 + 0.214276i
118118 −49.2059 36.3773i −0.416999 0.308282i
119119 228.434i 1.91961i
120120 −63.1719 + 128.189i −0.526433 + 1.06824i
121121 114.788 0.948662
122122 −28.3404 + 38.3348i −0.232299 + 0.314220i
123123 111.009 111.009i 0.902513 0.902513i
124124 −2.89996 9.45584i −0.0233867 0.0762567i
125125 −113.680 + 51.9801i −0.909437 + 0.415841i
126126 −8.21565 54.8087i −0.0652035 0.434990i
127127 −55.8589 + 55.8589i −0.439834 + 0.439834i −0.891956 0.452122i 0.850667π-0.850667\pi
0.452122 + 0.891956i 0.350667π0.350667\pi
128128 32.4266 + 123.825i 0.253333 + 0.967379i
129129 166.429i 1.29015i
130130 68.5630 + 64.5749i 0.527407 + 0.496730i
131131 151.619i 1.15740i 0.815541 + 0.578700i 0.196440π0.196440\pi
−0.815541 + 0.578700i 0.803560π0.803560\pi
132132 −16.6943 + 31.4635i −0.126472 + 0.238360i
133133 −91.3864 + 91.3864i −0.687116 + 0.687116i
134134 −8.38292 55.9246i −0.0625591 0.417348i
135135 11.0890 92.8677i 0.0821406 0.687909i
136136 −107.169 223.931i −0.788010 1.64655i
137137 68.2473 68.2473i 0.498156 0.498156i −0.412708 0.910863i 0.635417π-0.635417\pi
0.910863 + 0.412708i 0.135417π0.135417\pi
138138 163.971 + 121.221i 1.18819 + 0.878415i
139139 69.7245 0.501615 0.250807 0.968037i 0.419304π-0.419304\pi
0.250807 + 0.968037i 0.419304π0.419304\pi
140140 −26.1743 144.880i −0.186959 1.03486i
141141 170.312i 1.20789i
142142 35.1157 + 25.9606i 0.247294 + 0.182821i
143143 16.5988 + 16.5988i 0.116076 + 0.116076i
144144 33.7671 + 49.8740i 0.234494 + 0.346348i
145145 3.23837 + 4.11660i 0.0223336 + 0.0283904i
146146 −13.6876 91.3138i −0.0937509 0.625437i
147147 13.1071 + 13.1071i 0.0891640 + 0.0891640i
148148 −51.1148 + 96.3355i −0.345370 + 0.650916i
149149 78.9012 0.529538 0.264769 0.964312i 0.414704π-0.414704\pi
0.264769 + 0.964312i 0.414704π0.414704\pi
150150 −15.8595 + 177.931i −0.105730 + 1.18621i
151151 197.562 1.30835 0.654177 0.756341i 0.273015π-0.273015\pi
0.654177 + 0.756341i 0.273015π0.273015\pi
152152 46.7113 132.459i 0.307311 0.871440i
153153 −82.6009 82.6009i −0.539875 0.539875i
154154 −5.43953 36.2885i −0.0353216 0.235640i
155155 −7.64392 9.71691i −0.0493156 0.0626897i
156156 128.683 39.4651i 0.824891 0.252981i
157157 −94.1106 94.1106i −0.599431 0.599431i 0.340730 0.940161i 0.389326π-0.389326\pi
−0.940161 + 0.340730i 0.889326π0.889326\pi
158158 19.5135 26.3950i 0.123503 0.167057i
159159 183.932i 1.15680i
160160 93.6287 + 129.745i 0.585179 + 0.810904i
161161 −210.073 −1.30480
162162 −161.963 119.737i −0.999773 0.739119i
163163 −132.980 + 132.980i −0.815827 + 0.815827i −0.985500 0.169673i 0.945729π-0.945729\pi
0.169673 + 0.985500i 0.445729π0.445729\pi
164164 −51.5354 168.041i −0.314240 1.02464i
165165 −5.27879 + 44.2086i −0.0319926 + 0.267931i
166166 0.961668 0.144151i 0.00579318 0.000868378i
167167 −51.4111 + 51.4111i −0.307851 + 0.307851i −0.844075 0.536225i 0.819850π-0.819850\pi
0.536225 + 0.844075i 0.319850π0.319850\pi
168168 −198.422 69.9730i −1.18108 0.416506i
169169 80.2920i 0.475101i
170170 −225.900 212.760i −1.32882 1.25153i
171171 66.0900i 0.386492i
172172 164.599 + 87.3347i 0.956969 + 0.507760i
173173 183.164 183.164i 1.05875 1.05875i 0.0605880 0.998163i 0.480702π-0.480702\pi
0.998163 0.0605880i 0.0192976π-0.0192976\pi
174174 7.40244 1.10960i 0.0425428 0.00637702i
175175 −95.8316 157.111i −0.547609 0.897779i
176176 22.3570 + 33.0213i 0.127028 + 0.187621i
177177 −77.2954 + 77.2954i −0.436697 + 0.436697i
178178 −100.422 + 135.836i −0.564168 + 0.763125i
179179 −31.3468 −0.175122 −0.0875610 0.996159i 0.527907π-0.527907\pi
−0.0875610 + 0.996159i 0.527907π0.527907\pi
180180 61.8527 + 42.9236i 0.343626 + 0.238464i
181181 57.4156i 0.317214i −0.987342 0.158607i 0.949300π-0.949300\pi
0.987342 0.158607i 0.0507002π-0.0507002\pi
182182 −82.4320 + 111.502i −0.452923 + 0.612648i
183183 60.2184 + 60.2184i 0.329063 + 0.329063i
184184 205.932 98.5555i 1.11920 0.535628i
185185 −16.1627 + 135.359i −0.0873659 + 0.731669i
186186 −17.4729 + 2.61912i −0.0939401 + 0.0140813i
187187 −54.6895 54.6895i −0.292457 0.292457i
188188 168.439 + 89.3723i 0.895952 + 0.475385i
189189 137.696 0.728550
190190 −5.25664 175.489i −0.0276665 0.923625i
191191 161.923 0.847767 0.423884 0.905717i 0.360667π-0.360667\pi
0.423884 + 0.905717i 0.360667π0.360667\pi
192192 227.339 24.4956i 1.18405 0.127581i
193193 63.0037 + 63.0037i 0.326444 + 0.326444i 0.851233 0.524789i 0.175856π-0.175856\pi
−0.524789 + 0.851233i 0.675856π0.675856\pi
194194 67.4989 10.1179i 0.347933 0.0521540i
195195 132.236 104.025i 0.678133 0.533461i
196196 19.8410 6.08491i 0.101229 0.0310455i
197197 −3.96178 3.96178i −0.0201106 0.0201106i 0.696980 0.717091i 0.254527π-0.254527\pi
−0.717091 + 0.696980i 0.754527π0.754527\pi
198198 15.0887 + 11.1549i 0.0762056 + 0.0563378i
199199 123.026i 0.618221i −0.951026 0.309110i 0.899969π-0.899969\pi
0.951026 0.309110i 0.100031π-0.100031\pi
200200 167.651 + 109.055i 0.838256 + 0.545276i
201201 −101.018 −0.502576
202202 −180.832 + 244.603i −0.895208 + 1.21091i
203203 −5.45265 + 5.45265i −0.0268604 + 0.0268604i
204204 −423.982 + 130.029i −2.07834 + 0.637395i
205205 −135.841 172.680i −0.662639 0.842343i
206206 50.5900 + 337.499i 0.245582 + 1.63834i
207207 75.9617 75.9617i 0.366965 0.366965i
208208 28.4961 147.977i 0.137001 0.711428i
209209 43.7578i 0.209367i
210210 −262.880 + 7.87438i −1.25181 + 0.0374970i
211211 273.854i 1.29789i −0.760837 0.648943i 0.775211π-0.775211\pi
0.760837 0.648943i 0.224789π-0.224789\pi
212212 −181.908 96.5191i −0.858059 0.455279i
213213 55.1617 55.1617i 0.258975 0.258975i
214214 31.5635 + 210.568i 0.147493 + 0.983964i
215215 231.274 + 27.6155i 1.07569 + 0.128444i
216216 −134.982 + 64.5999i −0.624916 + 0.299074i
217217 12.8706 12.8706i 0.0593113 0.0593113i
218218 −19.0759 14.1025i −0.0875040 0.0646905i
219219 −164.942 −0.753159
220220 40.9523 + 28.4194i 0.186147 + 0.129179i
221221 292.273i 1.32250i
222222 156.653 + 115.812i 0.705644 + 0.521674i
223223 128.870 + 128.870i 0.577894 + 0.577894i 0.934323 0.356429i 0.116006π-0.116006\pi
−0.356429 + 0.934323i 0.616006π0.616006\pi
224224 −173.326 + 159.521i −0.773778 + 0.712145i
225225 91.4634 + 22.1585i 0.406504 + 0.0984824i
226226 34.3854 + 229.394i 0.152148 + 1.01502i
227227 242.455 + 242.455i 1.06808 + 1.06808i 0.997506 + 0.0705768i 0.0224840π0.0224840\pi
0.0705768 + 0.997506i 0.477516π0.477516\pi
228228 −221.636 117.598i −0.972086 0.515781i
229229 −385.669 −1.68414 −0.842072 0.539365i 0.818664π-0.818664\pi
−0.842072 + 0.539365i 0.818664π0.818664\pi
230230 195.659 207.743i 0.850692 0.903229i
231231 −65.5487 −0.283760
232232 2.78707 7.90328i 0.0120132 0.0340659i
233233 9.90826 + 9.90826i 0.0425247 + 0.0425247i 0.728049 0.685525i 0.240427π-0.240427\pi
−0.685525 + 0.728049i 0.740427π0.740427\pi
234234 −10.5116 70.1259i −0.0449215 0.299683i
235235 236.669 + 28.2598i 1.00710 + 0.120255i
236236 35.8840 + 117.006i 0.152051 + 0.495789i
237237 −41.4627 41.4627i −0.174948 0.174948i
238238 271.595 367.374i 1.14116 1.54359i
239239 44.7391i 0.187193i −0.995610 0.0935965i 0.970164π-0.970164\pi
0.995610 0.0935965i 0.0298364π-0.0298364\pi
240240 254.004 131.049i 1.05835 0.546037i
241241 −21.4785 −0.0891223 −0.0445611 0.999007i 0.514189π-0.514189\pi
−0.0445611 + 0.999007i 0.514189π0.514189\pi
242242 −184.606 136.477i −0.762835 0.563953i
243243 −135.380 + 135.380i −0.557118 + 0.557118i
244244 91.1560 27.9561i 0.373590 0.114574i
245245 20.3888 16.0391i 0.0832194 0.0654655i
246246 −310.512 + 46.5448i −1.26224 + 0.189206i
247247 −116.926 + 116.926i −0.473384 + 0.473384i
248248 −6.57866 + 18.6551i −0.0265269 + 0.0752220i
249249 1.73708i 0.00697623i
250250 244.625 + 51.5627i 0.978499 + 0.206251i
251251 149.651i 0.596218i −0.954532 0.298109i 0.903644π-0.903644\pi
0.954532 0.298109i 0.0963560π-0.0963560\pi
252252 −51.9519 + 97.9131i −0.206158 + 0.388544i
253253 50.2938 50.2938i 0.198790 0.198790i
254254 156.247 23.4209i 0.615146 0.0922084i
255255 −435.688 + 342.739i −1.70858 + 1.34407i
256256 95.0710 237.692i 0.371371 0.928485i
257257 244.045 244.045i 0.949590 0.949590i −0.0491992 0.998789i 0.515667π-0.515667\pi
0.998789 + 0.0491992i 0.0156669π0.0156669\pi
258258 197.875 267.657i 0.766959 1.03743i
259259 −200.698 −0.774896
260260 −33.4892 185.369i −0.128804 0.712958i
261261 3.94332i 0.0151085i
262262 180.267 243.839i 0.688042 0.930683i
263263 −241.557 241.557i −0.918467 0.918467i 0.0784512 0.996918i 0.475003π-0.475003\pi
−0.996918 + 0.0784512i 0.975003π0.975003\pi
264264 64.2566 30.7521i 0.243396 0.116485i
265265 −255.595 30.5197i −0.964510 0.115169i
266266 255.624 38.3172i 0.960992 0.144050i
267267 213.379 + 213.379i 0.799172 + 0.799172i
268268 −53.0096 + 99.9066i −0.197797 + 0.372786i
269269 350.619 1.30342 0.651708 0.758470i 0.274053π-0.274053\pi
0.651708 + 0.758470i 0.274053π0.274053\pi
270270 −128.248 + 136.169i −0.474993 + 0.504328i
271271 −298.610 −1.10188 −0.550940 0.834545i 0.685731π-0.685731\pi
−0.550940 + 0.834545i 0.685731π0.685731\pi
272272 −93.8885 + 487.552i −0.345178 + 1.79247i
273273 175.153 + 175.153i 0.641588 + 0.641588i
274274 −190.900 + 28.6153i −0.696715 + 0.104435i
275275 60.5573 + 14.6710i 0.220208 + 0.0533492i
276276 −119.577 389.904i −0.433252 1.41270i
277277 275.798 + 275.798i 0.995660 + 0.995660i 0.999991 0.00433109i 0.00137863π-0.00137863\pi
−0.00433109 + 0.999991i 0.501379π0.501379\pi
278278 −112.133 82.8985i −0.403357 0.298196i
279279 9.30790i 0.0333617i
280280 −130.160 + 264.120i −0.464857 + 0.943287i
281281 13.2859 0.0472808 0.0236404 0.999721i 0.492474π-0.492474\pi
0.0236404 + 0.999721i 0.492474π0.492474\pi
282282 202.492 273.902i 0.718057 0.971283i
283283 −253.189 + 253.189i −0.894662 + 0.894662i −0.994958 0.100296i 0.968021π-0.968021\pi
0.100296 + 0.994958i 0.468021π0.468021\pi
284284 −25.6085 83.5013i −0.0901709 0.294019i
285285 −311.415 37.1849i −1.09268 0.130473i
286286 −6.95969 46.4299i −0.0243346 0.162342i
287287 228.724 228.724i 0.796948 0.796948i
288288 4.99207 120.356i 0.0173336 0.417904i
289289 673.975i 2.33209i
290290 −0.313642 10.4707i −0.00108152 0.0361058i
291291 121.925i 0.418985i
292292 −86.5541 + 163.128i −0.296418 + 0.558656i
293293 −143.408 + 143.408i −0.489447 + 0.489447i −0.908132 0.418685i 0.862491π-0.862491\pi
0.418685 + 0.908132i 0.362491π0.362491\pi
294294 −5.49565 36.6629i −0.0186927 0.124704i
295295 94.5856 + 120.237i 0.320629 + 0.407582i
296296 196.742 94.1572i 0.664669 0.318099i
297297 −32.9659 + 32.9659i −0.110996 + 0.110996i
298298 −126.891 93.8092i −0.425810 0.314796i
299299 −268.781 −0.898934
300300 237.056 267.298i 0.790186 0.890993i
301301 342.912i 1.13924i
302302 −317.725 234.890i −1.05207 0.777781i
303303 384.236 + 384.236i 1.26811 + 1.26811i
304304 −232.609 + 157.488i −0.765161 + 0.518051i
305305 93.6728 73.6888i 0.307124 0.241602i
306306 34.6335 + 231.049i 0.113181 + 0.755063i
307307 −357.761 357.761i −1.16535 1.16535i −0.983288 0.182059i 0.941724π-0.941724\pi
−0.182059 0.983288i 0.558276π-0.558276\pi
308308 −34.3970 + 64.8276i −0.111679 + 0.210479i
309309 609.631 1.97292
310310 0.740327 + 24.7152i 0.00238815 + 0.0797266i
311311 −380.204 −1.22252 −0.611261 0.791429i 0.709337π-0.709337\pi
−0.611261 + 0.791429i 0.709337π0.709337\pi
312312 −253.874 89.5280i −0.813699 0.286949i
313313 270.798 + 270.798i 0.865169 + 0.865169i 0.991933 0.126764i 0.0404591π-0.0404591\pi
−0.126764 + 0.991933i 0.540459π0.540459\pi
314314 39.4594 + 263.244i 0.125667 + 0.838357i
315315 −16.4274 + 137.575i −0.0521503 + 0.436747i
316316 −62.7645 + 19.2489i −0.198622 + 0.0609141i
317317 −238.939 238.939i −0.753752 0.753752i 0.221426 0.975177i 0.428929π-0.428929\pi
−0.975177 + 0.221426i 0.928929π0.928929\pi
318318 −218.685 + 295.805i −0.687687 + 0.930204i
319319 2.61085i 0.00818448i
320320 3.68258 319.979i 0.0115081 0.999934i
321321 380.354 1.18490
322322 337.846 + 249.765i 1.04921 + 0.775668i
323323 385.245 385.245i 1.19271 1.19271i
324324 118.113 + 385.131i 0.364548 + 1.18867i
325325 −122.613 201.019i −0.377272 0.618519i
326326 371.968 55.7568i 1.14101 0.171033i
327327 −29.9654 + 29.9654i −0.0916373 + 0.0916373i
328328 −116.910 + 331.521i −0.356433 + 1.01074i
329329 350.913i 1.06660i
330330 61.0511 64.8215i 0.185003 0.196429i
331331 73.0725i 0.220763i 0.993889 + 0.110381i 0.0352072π0.0352072\pi
−0.993889 + 0.110381i 0.964793π0.964793\pi
332332 −1.71797 0.911542i −0.00517462 0.00274561i
333333 72.5718 72.5718i 0.217933 0.217933i
334334 143.806 21.5560i 0.430557 0.0645390i
335335 −16.7618 + 140.376i −0.0500353 + 0.419034i
336336 235.914 + 348.445i 0.702126 + 1.03704i
337337 −207.932 + 207.932i −0.617008 + 0.617008i −0.944763 0.327755i 0.893708π-0.893708\pi
0.327755 + 0.944763i 0.393708π0.393708\pi
338338 95.4627 129.128i 0.282434 0.382036i
339339 414.358 1.22230
340340 110.339 + 610.750i 0.324528 + 1.79632i
341341 6.16270i 0.0180724i
342342 −78.5774 + 106.288i −0.229759 + 0.310784i
343343 −228.049 228.049i −0.664866 0.664866i
344344 −160.877 336.153i −0.467665 0.977189i
345345 −315.191 400.669i −0.913597 1.16136i
346346 −512.342 + 76.7983i −1.48076 + 0.221961i
347347 150.516 + 150.516i 0.433765 + 0.433765i 0.889907 0.456142i 0.150769π-0.150769\pi
−0.456142 + 0.889907i 0.650769π0.650769\pi
348348 −13.2241 7.01659i −0.0380003 0.0201626i
349349 −159.797 −0.457871 −0.228935 0.973442i 0.573524π-0.573524\pi
−0.228935 + 0.973442i 0.573524π0.573524\pi
350350 −32.6771 + 366.610i −0.0933632 + 1.04746i
351351 176.177 0.501930
352352 3.30521 79.6871i 0.00938981 0.226384i
353353 31.8920 + 31.8920i 0.0903455 + 0.0903455i 0.750835 0.660490i 0.229651π-0.229651\pi
−0.660490 + 0.750835i 0.729651π0.729651\pi
354354 216.209 32.4090i 0.610759 0.0915508i
355355 −67.5008 85.8067i −0.190143 0.241709i
356356 323.004 99.0601i 0.907314 0.278259i
357357 −577.092 577.092i −1.61650 1.61650i
358358 50.4130 + 37.2697i 0.140818 + 0.104105i
359359 374.114i 1.04210i 0.853526 + 0.521050i 0.174459π0.174459\pi
−0.853526 + 0.521050i 0.825541π0.825541\pi
360360 −48.4397 142.571i −0.134555 0.396029i
361361 −52.7608 −0.146152
362362 −68.2640 + 92.3377i −0.188575 + 0.255076i
363363 −289.989 + 289.989i −0.798868 + 0.798868i
364364 265.139 81.3141i 0.728405 0.223390i
365365 −27.3687 + 229.207i −0.0749828 + 0.627963i
366366 −25.2488 168.442i −0.0689859 0.460223i
367367 195.775 195.775i 0.533446 0.533446i −0.388150 0.921596i 0.626886π-0.626886\pi
0.921596 + 0.388150i 0.126886π0.126886\pi
368368 −448.364 86.3421i −1.21838 0.234625i
369369 165.412i 0.448270i
370370 186.927 198.472i 0.505209 0.536410i
371371 378.974i 1.02149i
372372 31.2144 + 16.5621i 0.0839097 + 0.0445218i
373373 342.423 342.423i 0.918023 0.918023i −0.0788627 0.996885i 0.525129π-0.525129\pi
0.996885 + 0.0788627i 0.0251289π0.0251289\pi
374374 22.9306 + 152.976i 0.0613118 + 0.409027i
375375 155.871 418.506i 0.415657 1.11602i
376376 −164.630 343.996i −0.437846 0.914883i
377377 −6.97649 + 6.97649i −0.0185053 + 0.0185053i
378378 −221.447 163.713i −0.585839 0.433103i
379379 607.050 1.60171 0.800857 0.598855i 0.204378π-0.204378\pi
0.800857 + 0.598855i 0.204378π0.204378\pi
380380 −200.192 + 288.476i −0.526822 + 0.759148i
381381 282.232i 0.740767i
382382 −260.411 192.518i −0.681703 0.503974i
383383 −154.687 154.687i −0.403882 0.403882i 0.475717 0.879599i 0.342189π-0.342189\pi
−0.879599 + 0.475717i 0.842189π0.842189\pi
384384 −394.737 230.898i −1.02796 0.601298i
385385 −10.8764 + 91.0877i −0.0282505 + 0.236592i
386386 −26.4167 176.233i −0.0684370 0.456561i
387387 −123.996 123.996i −0.320403 0.320403i
388388 −120.584 63.9806i −0.310782 0.164899i
389389 −323.730 −0.832210 −0.416105 0.909317i 0.636605π-0.636605\pi
−0.416105 + 0.909317i 0.636605π0.636605\pi
390390 −336.346 + 10.0750i −0.862426 + 0.0258333i
391391 885.575 2.26490
392392 −39.1435 13.8039i −0.0998559 0.0352139i
393393 −383.036 383.036i −0.974645 0.974645i
394394 1.66113 + 11.0818i 0.00421605 + 0.0281264i
395395 −64.4974 + 50.7376i −0.163284 + 0.128450i
396396 −11.0036 35.8793i −0.0277869 0.0906043i
397397 376.174 + 376.174i 0.947543 + 0.947543i 0.998691 0.0511485i 0.0162882π-0.0162882\pi
−0.0511485 + 0.998691i 0.516288π0.516288\pi
398398 −146.271 + 197.854i −0.367515 + 0.497121i
399399 461.739i 1.15724i
400400 −139.962 374.714i −0.349904 0.936786i
401401 −401.761 −1.00190 −0.500948 0.865477i 0.667015π-0.667015\pi
−0.500948 + 0.865477i 0.667015π0.667015\pi
402402 162.460 + 120.105i 0.404130 + 0.298768i
403403 16.4674 16.4674i 0.0408621 0.0408621i
404404 581.640 178.380i 1.43970 0.441534i
405405 311.332 + 395.764i 0.768721 + 0.977195i
406406 15.2520 2.28623i 0.0375666 0.00563111i
407407 48.0493 48.0493i 0.118057 0.118057i
408408 836.459 + 294.975i 2.05014 + 0.722978i
409409 166.880i 0.408020i 0.978969 + 0.204010i 0.0653974π0.0653974\pi
−0.978969 + 0.204010i 0.934603π0.934603\pi
410410 13.1564 + 439.217i 0.0320889 + 1.07126i
411411 344.826i 0.838993i
412412 319.907 602.925i 0.776474 1.46341i
413413 −159.260 + 159.260i −0.385617 + 0.385617i
414414 −212.478 + 31.8498i −0.513233 + 0.0769319i
415415 −2.41388 0.288233i −0.00581658 0.000694536i
416416 −221.765 + 204.101i −0.533089 + 0.490628i
417417 −176.145 + 176.145i −0.422410 + 0.422410i
418418 −52.0256 + 70.3727i −0.124463 + 0.168356i
419419 −533.694 −1.27373 −0.636866 0.770974i 0.719770π-0.719770\pi
−0.636866 + 0.770974i 0.719770π0.719770\pi
420420 432.134 + 299.886i 1.02889 + 0.714014i
421421 214.523i 0.509556i 0.967000 + 0.254778i 0.0820023π0.0820023\pi
−0.967000 + 0.254778i 0.917998π0.917998\pi
422422 −325.597 + 440.421i −0.771558 + 1.04365i
423423 −126.889 126.889i −0.299974 0.299974i
424424 177.795 + 371.504i 0.419328 + 0.876189i
425425 403.984 + 662.312i 0.950550 + 1.55838i
426426 −154.297 + 23.1286i −0.362199 + 0.0542925i
427427 124.074 + 124.074i 0.290573 + 0.290573i
428428 199.593 376.170i 0.466338 0.878902i
429429 −83.8673 −0.195495
430430 −339.108 319.384i −0.788624 0.742753i
431431 −525.371 −1.21896 −0.609479 0.792802i 0.708621π-0.708621\pi
−0.609479 + 0.792802i 0.708621π0.708621\pi
432432 293.888 + 56.5944i 0.680296 + 0.131006i
433433 −262.829 262.829i −0.606994 0.606994i 0.335165 0.942159i 0.391208π-0.391208\pi
−0.942159 + 0.335165i 0.891208π0.891208\pi
434434 −36.0012 + 5.39646i −0.0829521 + 0.0124342i
435435 −18.5809 2.21867i −0.0427146 0.00510039i
436436 13.9113 + 45.3603i 0.0319066 + 0.104037i
437437 354.280 + 354.280i 0.810709 + 0.810709i
438438 265.265 + 196.107i 0.605627 + 0.447732i
439439 419.145i 0.954771i 0.878694 + 0.477386i 0.158416π0.158416\pi
−0.878694 + 0.477386i 0.841584π0.841584\pi
440440 −32.0716 94.3950i −0.0728900 0.214534i
441441 −19.5306 −0.0442870
442442 347.497 470.043i 0.786191 1.06345i
443443 −119.234 + 119.234i −0.269152 + 0.269152i −0.828758 0.559606i 0.810952π-0.810952\pi
0.559606 + 0.828758i 0.310952π0.310952\pi
444444 −114.241 372.504i −0.257300 0.838972i
445445 331.922 261.110i 0.745891 0.586764i
446446 −54.0337 360.473i −0.121152 0.808236i
447447 −199.328 + 199.328i −0.445924 + 0.445924i
448448 468.410 50.4709i 1.04556 0.112658i
449449 596.070i 1.32755i 0.747932 + 0.663775i 0.231047π0.231047\pi
−0.747932 + 0.663775i 0.768953π0.768953\pi
450450 −120.749 144.381i −0.268331 0.320846i
451451 109.518i 0.242834i
452452 217.437 409.801i 0.481055 0.906639i
453453 −499.099 + 499.099i −1.10176 + 1.10176i
454454 −101.658 678.189i −0.223917 1.49381i
455455 272.460 214.334i 0.598813 0.471063i
456456 216.624 + 452.637i 0.475053 + 0.992626i
457457 144.279 144.279i 0.315708 0.315708i −0.531408 0.847116i 0.678337π-0.678337\pi
0.847116 + 0.531408i 0.178337π0.178337\pi
458458 620.245 + 458.539i 1.35425 + 1.00118i
459459 −580.465 −1.26463
460460 −561.660 + 101.471i −1.22100 + 0.220588i
461461 743.994i 1.61387i −0.590640 0.806935i 0.701125π-0.701125\pi
0.590640 0.806935i 0.298875π-0.298875\pi
462462 105.417 + 77.9337i 0.228176 + 0.168688i
463463 446.519 + 446.519i 0.964404 + 0.964404i 0.999388 0.0349842i 0.0111381π-0.0111381\pi
−0.0349842 + 0.999388i 0.511138π0.511138\pi
464464 −13.8788 + 9.39664i −0.0299113 + 0.0202514i
465465 43.8586 + 5.23700i 0.0943196 + 0.0112624i
466466 −4.15441 27.7152i −0.00891504 0.0594746i
467467 5.61916 + 5.61916i 0.0120325 + 0.0120325i 0.713097 0.701065i 0.247292π-0.247292\pi
−0.701065 + 0.713097i 0.747292π0.747292\pi
468468 −66.4707 + 125.276i −0.142031 + 0.267685i
469469 −208.138 −0.443791
470470 −347.020 326.835i −0.738341 0.695394i
471471 475.503 1.00956
472472 81.4042 230.837i 0.172467 0.489062i
473473 −82.0969 82.0969i −0.173566 0.173566i
474474 17.3848 + 115.979i 0.0366768 + 0.244681i
475475 −103.346 + 426.578i −0.217570 + 0.898060i
476476 −873.576 + 267.912i −1.83524 + 0.562840i
477477 137.036 + 137.036i 0.287287 + 0.287287i
478478 −53.1923 + 71.9509i −0.111281 + 0.150525i
479479 765.340i 1.59779i −0.601472 0.798894i 0.705419π-0.705419\pi
0.601472 0.798894i 0.294581π-0.294581\pi
480480 −564.308 91.2398i −1.17564 0.190083i
481481 −256.786 −0.533859
482482 34.5424 + 25.5367i 0.0716647 + 0.0529807i
483483 530.707 530.707i 1.09877 1.09877i
484484 134.626 + 438.973i 0.278153 + 0.906968i
485485 −169.429 20.2309i −0.349338 0.0417132i
486486 378.681 56.7630i 0.779179 0.116796i
487487 −611.323 + 611.323i −1.25528 + 1.25528i −0.301963 + 0.953320i 0.597642π0.597642\pi
−0.953320 + 0.301963i 0.902358π0.902358\pi
488488 −179.838 63.4195i −0.368521 0.129958i
489489 671.893i 1.37402i
490490 −51.8594 + 1.55341i −0.105836 + 0.00317023i
491491 899.211i 1.83139i 0.401877 + 0.915694i 0.368358π0.368358\pi
−0.401877 + 0.915694i 0.631642π0.631642\pi
492492 554.715 + 294.327i 1.12747 + 0.598226i
493493 22.9860 22.9860i 0.0466247 0.0466247i
494494 327.062 49.0255i 0.662069 0.0992419i
495495 −29.0041 36.8699i −0.0585942 0.0744847i
496496 32.7599 22.1800i 0.0660481 0.0447178i
497497 113.655 113.655i 0.228683 0.228683i
498498 −2.06529 + 2.79363i −0.00414717 + 0.00560969i
499499 755.350 1.51373 0.756864 0.653572i 0.226730π-0.226730\pi
0.756864 + 0.653572i 0.226730π0.226730\pi
500500 −332.108 373.770i −0.664216 0.747540i
501501 259.760i 0.518482i
502502 −177.927 + 240.673i −0.354435 + 0.479429i
503503 −505.226 505.226i −1.00443 1.00443i −0.999990 0.00443600i 0.998588π-0.998588\pi
−0.00443600 0.999990i 0.501412π-0.501412\pi
504504 199.964 95.6991i 0.396754 0.189879i
505505 597.699 470.187i 1.18356 0.931063i
506506 −140.681 + 21.0876i −0.278025 + 0.0416750i
507507 −202.842 202.842i −0.400082 0.400082i
508508 −279.128 148.103i −0.549464 0.291541i
509509 −594.029 −1.16705 −0.583526 0.812095i 0.698327π-0.698327\pi
−0.583526 + 0.812095i 0.698327π0.698327\pi
510510 1108.19 33.1949i 2.17291 0.0650880i
511511 −339.847 −0.665063
512512 −435.499 + 269.230i −0.850584 + 0.525840i
513513 −232.219 232.219i −0.452668 0.452668i
514514 −682.636 + 102.325i −1.32809 + 0.199076i
515515 101.156 847.156i 0.196419 1.64496i
516516 −636.459 + 195.192i −1.23345 + 0.378279i
517517 −84.0123 84.0123i −0.162500 0.162500i
518518 322.769 + 238.619i 0.623106 + 0.460654i
519519 925.453i 1.78315i
520520 −166.535 + 337.933i −0.320260 + 0.649871i
521521 871.615 1.67297 0.836483 0.547993i 0.184608π-0.184608\pi
0.836483 + 0.547993i 0.184608π0.184608\pi
522522 −4.68839 + 6.34178i −0.00898160 + 0.0121490i
523523 601.907 601.907i 1.15087 1.15087i 0.164497 0.986378i 0.447400π-0.447400\pi
0.986378 0.164497i 0.0526001π-0.0526001\pi
524524 −579.822 + 177.822i −1.10653 + 0.339356i
525525 639.009 + 154.811i 1.21716 + 0.294878i
526526 101.282 + 675.677i 0.192551 + 1.28456i
527527 −54.2566 + 54.2566i −0.102954 + 0.102954i
528528 −139.902 26.9411i −0.264966 0.0510249i
529529 285.396i 0.539500i
530530 374.770 + 352.971i 0.707114 + 0.665983i
531531 115.176i 0.216903i
532532 −456.660 242.300i −0.858383 0.455451i
533533 292.645 292.645i 0.549052 0.549052i
534534 −89.4672 596.859i −0.167542 1.11771i
535535 63.1119 528.547i 0.117966 0.987939i
536536 204.035 97.6475i 0.380663 0.182178i
537537 79.1915 79.1915i 0.147470 0.147470i
538538 −563.877 416.867i −1.04810 0.774845i
539539 −12.9311 −0.0239908
540540 368.150 66.5107i 0.681759 0.123168i
541541 109.548i 0.202492i 0.994861 + 0.101246i 0.0322830π0.0322830\pi
−0.994861 + 0.101246i 0.967717π0.967717\pi
542542 480.233 + 355.030i 0.886040 + 0.655037i
543543 145.049 + 145.049i 0.267125 + 0.267125i
544544 730.666 672.468i 1.34314 1.23615i
545545 36.6684 + 46.6127i 0.0672815 + 0.0855279i
546546 −73.4397 489.935i −0.134505 0.897317i
547547 −330.968 330.968i −0.605060 0.605060i 0.336591 0.941651i 0.390726π-0.390726\pi
−0.941651 + 0.336591i 0.890726π0.890726\pi
548548 341.033 + 180.949i 0.622323 + 0.330200i
549549 −89.7299 −0.163442
550550 −79.9471 95.5937i −0.145358 0.173807i
551551 18.3914 0.0333782
552552 −271.266 + 769.227i −0.491424 + 1.39353i
553553 −85.4301 85.4301i −0.154485 0.154485i
554554 −115.639 771.455i −0.208734 1.39252i
555555 −301.125 382.788i −0.542567 0.689709i
556556 81.7744 + 266.640i 0.147076 + 0.479569i
557557 −62.7080 62.7080i −0.112582 0.112582i 0.648572 0.761153i 0.275367π-0.275367\pi
−0.761153 + 0.648572i 0.775367π0.775367\pi
558558 11.0666 14.9693i 0.0198326 0.0268266i
559559 438.745i 0.784874i
560560 523.352 270.014i 0.934557 0.482168i
561561 276.324 0.492556
562562 −21.3668 15.7962i −0.0380193 0.0281071i
563563 −116.120 + 116.120i −0.206252 + 0.206252i −0.802672 0.596420i 0.796589π-0.796589\pi
0.596420 + 0.802672i 0.296589π0.296589\pi
564564 −651.308 + 199.746i −1.15480 + 0.354159i
565565 68.7543 575.801i 0.121689 1.01912i
566566 708.215 106.159i 1.25126 0.187560i
567567 −524.210 + 524.210i −0.924533 + 0.924533i
568568 −58.0939 + 164.737i −0.102278 + 0.290029i
569569 323.733i 0.568950i −0.958683 0.284475i 0.908181π-0.908181\pi
0.958683 0.284475i 0.0918193π-0.0918193\pi
570570 456.617 + 430.057i 0.801082 + 0.754486i
571571 433.708i 0.759558i 0.925077 + 0.379779i 0.124000π0.124000\pi
−0.925077 + 0.379779i 0.876000π0.876000\pi
572572 −44.0098 + 82.9447i −0.0769402 + 0.145008i
573573 −409.067 + 409.067i −0.713904 + 0.713904i
574574 −639.782 + 95.9011i −1.11460 + 0.167075i
575575 −609.078 + 371.513i −1.05927 + 0.646110i
576576 −151.125 + 187.626i −0.262370 + 0.325739i
577577 27.1282 27.1282i 0.0470159 0.0470159i −0.683208 0.730224i 0.739416π-0.739416\pi
0.730224 + 0.683208i 0.239416π0.239416\pi
578578 −801.319 + 1083.91i −1.38637 + 1.87527i
579579 −318.332 −0.549797
580580 −11.9447 + 17.2122i −0.0205943 + 0.0296762i
581581 3.57909i 0.00616023i
582582 −144.962 + 196.083i −0.249075 + 0.336913i
583583 90.7305 + 90.7305i 0.155627 + 0.155627i
584584 333.149 159.439i 0.570460 0.273012i
585585 −21.0182 + 176.023i −0.0359286 + 0.300894i
586586 401.137 60.1291i 0.684535 0.102609i
587587 −163.733 163.733i −0.278932 0.278932i 0.553751 0.832682i 0.313196π-0.313196\pi
−0.832682 + 0.553751i 0.813196π0.813196\pi
588588 −34.7519 + 65.4965i −0.0591019 + 0.111389i
589589 −43.4114 −0.0737035
590590 −9.16078 305.826i −0.0155268 0.518349i
591591 20.0173 0.0338702
592592 −428.355 82.4889i −0.723572 0.139339i
593593 280.606 + 280.606i 0.473198 + 0.473198i 0.902948 0.429750i 0.141398π-0.141398\pi
−0.429750 + 0.902948i 0.641398π0.641398\pi
594594 92.2115 13.8222i 0.155238 0.0232697i
595595 −897.695 + 706.182i −1.50873 + 1.18686i
596596 92.5370 + 301.734i 0.155263 + 0.506265i
597597 310.800 + 310.800i 0.520603 + 0.520603i
598598 432.263 + 319.566i 0.722848 + 0.534392i
599599 639.232i 1.06716i −0.845748 0.533582i 0.820845π-0.820845\pi
0.845748 0.533582i 0.179155π-0.179155\pi
600600 −699.043 + 148.031i −1.16507 + 0.246718i
601601 −332.979 −0.554041 −0.277021 0.960864i 0.589347π-0.589347\pi
−0.277021 + 0.960864i 0.589347π0.589347\pi
602602 407.704 551.482i 0.677249 0.916084i
603603 75.2619 75.2619i 0.124812 0.124812i
604604 231.704 + 755.514i 0.383617 + 1.25085i
605605 354.857 + 451.092i 0.586540 + 0.745607i
606606 −161.106 1074.78i −0.265851 1.77356i
607607 681.745 681.745i 1.12314 1.12314i 0.131873 0.991267i 0.457901π-0.457901\pi
0.991267 0.131873i 0.0420990π-0.0420990\pi
608608 561.333 + 23.2826i 0.923245 + 0.0382938i
609609 27.5501i 0.0452382i
610610 −238.259 + 7.13689i −0.390589 + 0.0116998i
611611 448.981i 0.734830i
612612 219.006 412.758i 0.357853 0.674442i
613613 378.926 378.926i 0.618150 0.618150i −0.326907 0.945057i 0.606006π-0.606006\pi
0.945057 + 0.326907i 0.106006π0.106006\pi
614614 150.005 + 1000.72i 0.244308 + 1.62984i
615615 779.417 + 93.0672i 1.26734 + 0.151329i
616616 132.395 63.3617i 0.214927 0.102860i
617617 −68.3041 + 68.3041i −0.110704 + 0.110704i −0.760289 0.649585i 0.774943π-0.774943\pi
0.649585 + 0.760289i 0.274943π0.274943\pi
618618 −980.429 724.818i −1.58645 1.17284i
619619 1009.69 1.63116 0.815580 0.578645i 0.196418π-0.196418\pi
0.815580 + 0.578645i 0.196418π0.196418\pi
620620 28.1944 40.6281i 0.0454749 0.0655291i
621621 533.810i 0.859597i
622622 611.456 + 452.042i 0.983049 + 0.726755i
623623 439.648 + 439.648i 0.705694 + 0.705694i
624624 301.845 + 445.824i 0.483725 + 0.714462i
625625 −555.701 286.045i −0.889121 0.457671i
626626 −113.542 757.470i −0.181377 1.21002i
627627 110.545 + 110.545i 0.176308 + 0.176308i
628628 249.523 470.273i 0.397329 0.748842i
629629 846.054 1.34508
630630 189.988 201.722i 0.301569 0.320193i
631631 −867.965 −1.37554 −0.687769 0.725929i 0.741410π-0.741410\pi
−0.687769 + 0.725929i 0.741410π0.741410\pi
632632 123.826 + 43.6668i 0.195927 + 0.0690930i
633633 691.837 + 691.837i 1.09295 + 1.09295i
634634 100.184 + 668.355i 0.158019 + 1.05419i
635635 −392.196 46.8307i −0.617631 0.0737491i
636636 703.391 215.719i 1.10596 0.339181i
637637 34.5532 + 34.5532i 0.0542437 + 0.0542437i
638638 −3.10415 + 4.19885i −0.00486545 + 0.00658127i
639639 82.1949i 0.128631i
640640 −386.360 + 510.222i −0.603687 + 0.797222i
641641 116.032 0.181017 0.0905083 0.995896i 0.471151π-0.471151\pi
0.0905083 + 0.995896i 0.471151π0.471151\pi
642642 −611.697 452.220i −0.952799 0.704392i
643643 −429.493 + 429.493i −0.667951 + 0.667951i −0.957241 0.289290i 0.906581π-0.906581\pi
0.289290 + 0.957241i 0.406581π0.406581\pi
644644 −246.378 803.361i −0.382575 1.24745i
645645 −654.031 + 514.501i −1.01400 + 0.797676i
646646 −1077.60 + 161.528i −1.66811 + 0.250044i
647647 511.695 511.695i 0.790873 0.790873i −0.190763 0.981636i 0.561096π-0.561096\pi
0.981636 + 0.190763i 0.0610963π0.0610963\pi
648648 267.945 759.810i 0.413495 1.17255i
649649 76.2571i 0.117499i
650650 −41.8093 + 469.065i −0.0643220 + 0.721638i
651651 65.0297i 0.0998920i
652652 −664.503 352.580i −1.01918 0.540766i
653653 −777.556 + 777.556i −1.19074 + 1.19074i −0.213886 + 0.976859i 0.568612π0.568612\pi
−0.976859 + 0.213886i 0.931388π0.931388\pi
654654 83.8186 12.5641i 0.128163 0.0192112i
655655 −595.831 + 468.717i −0.909666 + 0.715599i
656656 582.179 394.163i 0.887468 0.600859i
657657 122.888 122.888i 0.187044 0.187044i
658658 417.216 564.349i 0.634067 0.857673i
659659 734.265 1.11421 0.557105 0.830442i 0.311912π-0.311912\pi
0.557105 + 0.830442i 0.311912π0.311912\pi
660660 −175.254 + 31.6617i −0.265536 + 0.0479723i
661661 799.237i 1.20913i 0.796555 + 0.604567i 0.206654π0.206654\pi
−0.796555 + 0.604567i 0.793346π0.793346\pi
662662 86.8791 117.518i 0.131237 0.177519i
663663 −738.369 738.369i −1.11368 1.11368i
664664 1.67913 + 3.50855i 0.00252880 + 0.00528395i
665665 −641.641 76.6160i −0.964874 0.115212i
666666 −202.996 + 30.4284i −0.304799 + 0.0456883i
667667 21.1384 + 21.1384i 0.0316918 + 0.0316918i
668668 −256.902 136.310i −0.384584 0.204057i
669669 −651.130 −0.973288
670670 193.857 205.829i 0.289338 0.307207i
671671 −59.4096 −0.0885388
672672 34.8771 840.870i 0.0519005 1.25130i
673673 −185.806 185.806i −0.276087 0.276087i 0.555458 0.831545i 0.312543π-0.312543\pi
−0.831545 + 0.555458i 0.812543π0.812543\pi
674674 581.622 87.1832i 0.862940 0.129352i
675675 399.230 243.515i 0.591452 0.360762i
676676 −307.053 + 94.1682i −0.454220 + 0.139302i
677677 −448.763 448.763i −0.662870 0.662870i 0.293186 0.956055i 0.405285π-0.405285\pi
−0.956055 + 0.293186i 0.905285π0.905285\pi
678678 −666.385 492.649i −0.982868 0.726621i
679679 251.214i 0.369977i
680680 548.696 1113.41i 0.806907 1.63737i
681681 −1225.03 −1.79886
682682 7.32711 9.91105i 0.0107436 0.0145323i
683683 −67.1358 + 67.1358i −0.0982955 + 0.0982955i −0.754544 0.656249i 0.772142π-0.772142\pi
0.656249 + 0.754544i 0.272142π0.272142\pi
684684 252.741 77.5118i 0.369505 0.113321i
685685 479.178 + 57.2168i 0.699529 + 0.0835282i
686686 95.6181 + 637.893i 0.139385 + 0.929873i
687687 974.315 974.315i 1.41822 1.41822i
688688 −140.940 + 731.886i −0.204855 + 1.06379i
689689 484.884i 0.703751i
690690 30.5268 + 1019.11i 0.0442417 + 1.47698i
691691 533.282i 0.771753i −0.922550 0.385877i 0.873899π-0.873899\pi
0.922550 0.385877i 0.126101π-0.126101\pi
692692 915.274 + 485.636i 1.32265 + 0.701787i
693693 48.8361 48.8361i 0.0704706 0.0704706i
694694 −63.1097 421.021i −0.0909362 0.606659i
695695 215.547 + 274.002i 0.310139 + 0.394248i
696696 12.9251 + 27.0070i 0.0185705 + 0.0388032i
697697 −964.199 + 964.199i −1.38336 + 1.38336i
698698 256.991 + 189.990i 0.368181 + 0.272192i
699699 −50.0625 −0.0716201
700700 488.431 550.743i 0.697759 0.786775i
701701 1203.60i 1.71697i −0.512835 0.858487i 0.671405π-0.671405\pi
0.512835 0.858487i 0.328595π-0.328595\pi
702702 −283.334 209.465i −0.403610 0.298383i
703703 338.469 + 338.469i 0.481464 + 0.481464i
704704 −100.059 + 124.226i −0.142129 + 0.176457i
705705 −669.291 + 526.505i −0.949348 + 0.746816i
706706 −13.3719 89.2075i −0.0189404 0.126356i
707707 791.683 + 791.683i 1.11978 + 1.11978i
708708 −386.246 204.939i −0.545546 0.289462i
709709 −456.445 −0.643788 −0.321894 0.946776i 0.604319π-0.604319\pi
−0.321894 + 0.946776i 0.604319π0.604319\pi
710710 6.53757 + 218.252i 0.00920785 + 0.307397i
711711 61.7825 0.0868952
712712 −637.242 224.722i −0.895003 0.315620i
713713 −49.8956 49.8956i −0.0699798 0.0699798i
714714 241.967 + 1614.23i 0.338890 + 2.26082i
715715 −13.9160 + 116.544i −0.0194630 + 0.162998i
716716 −36.7642 119.877i −0.0513467 0.167425i
717717 113.024 + 113.024i 0.157635 + 0.157635i
718718 444.800 601.662i 0.619499 0.837969i
719719 63.2841i 0.0880168i 0.999031 + 0.0440084i 0.0140128π0.0140128\pi
−0.999031 + 0.0440084i 0.985987π0.985987\pi
720720 −91.6061 + 286.879i −0.127231 + 0.398443i
721721 1256.09 1.74215
722722 84.8517 + 62.7297i 0.117523 + 0.0868833i
723723 54.2610 54.2610i 0.0750498 0.0750498i
724724 219.569 67.3383i 0.303272 0.0930087i
725725 −6.16622 + 25.4522i −0.00850513 + 0.0351065i
726726 811.151 121.589i 1.11729 0.167478i
727727 408.139 408.139i 0.561401 0.561401i −0.368304 0.929705i 0.620061π-0.620061\pi
0.929705 + 0.368304i 0.120061π0.120061\pi
728728 −523.084 184.464i −0.718522 0.253385i
729729 222.361i 0.305021i
730730 316.529 336.078i 0.433602 0.460380i
731731 1445.57i 1.97752i
732732 −159.662 + 300.913i −0.218117 + 0.411083i
733733 −90.0317 + 90.0317i −0.122826 + 0.122826i −0.765848 0.643022i 0.777681π-0.777681\pi
0.643022 + 0.765848i 0.277681π0.277681\pi
734734 −547.616 + 82.0858i −0.746071 + 0.111834i
735735 −10.9887 + 92.0275i −0.0149506 + 0.125208i
736736 618.418 + 671.938i 0.840241 + 0.912959i
737737 49.8304 49.8304i 0.0676125 0.0676125i
738738 196.665 266.020i 0.266484 0.360461i
739739 −875.498 −1.18471 −0.592353 0.805679i 0.701801π-0.701801\pi
−0.592353 + 0.805679i 0.701801π0.701801\pi
740740 −536.595 + 96.9423i −0.725128 + 0.131003i
741741 590.779i 0.797272i
742742 −450.579 + 609.478i −0.607250 + 0.821399i
743743 282.061 + 282.061i 0.379624 + 0.379624i 0.870967 0.491342i 0.163494π-0.163494\pi
−0.491342 + 0.870967i 0.663494π0.663494\pi
744744 −30.5086 63.7479i −0.0410062 0.0856827i
745745 243.916 + 310.065i 0.327404 + 0.416194i
746746 −957.816 + 143.573i −1.28394 + 0.192458i
747747 1.29419 + 1.29419i 0.00173251 + 0.00173251i
748748 145.002 273.285i 0.193854 0.365354i
749749 783.683 1.04631
750750 −748.258 + 487.732i −0.997677 + 0.650310i
751751 606.986 0.808237 0.404119 0.914707i 0.367578π-0.367578\pi
0.404119 + 0.914707i 0.367578π0.367578\pi
752752 −144.229 + 748.962i −0.191793 + 0.995960i
753753 378.063 + 378.063i 0.502075 + 0.502075i
754754 19.5145 2.92515i 0.0258812 0.00387951i
755755 610.743 + 776.374i 0.808932 + 1.02831i
756756 161.493 + 526.577i 0.213615 + 0.696530i
757757 −173.075 173.075i −0.228633 0.228633i 0.583488 0.812121i 0.301687π-0.301687\pi
−0.812121 + 0.583488i 0.801687π0.801687\pi
758758 −976.277 721.749i −1.28796 0.952175i
759759 254.114i 0.334801i
760760 664.938 225.919i 0.874919 0.297262i
761761 100.678 0.132297 0.0661483 0.997810i 0.478929π-0.478929\pi
0.0661483 + 0.997810i 0.478929π0.478929\pi
762762 −335.559 + 453.895i −0.440366 + 0.595663i
763763 −61.7409 + 61.7409i −0.0809187 + 0.0809187i
764764 189.907 + 619.228i 0.248570 + 0.810507i
765765 69.2505 579.957i 0.0905235 0.758113i
766766 64.8582 + 432.686i 0.0846713 + 0.564864i
767767 −203.768 + 203.768i −0.265668 + 0.265668i
768768 360.303 + 840.659i 0.469145 + 1.09461i
769769 370.732i 0.482097i 0.970513 + 0.241048i 0.0774913π0.0774913\pi
−0.970513 + 0.241048i 0.922509π0.922509\pi
770770 125.790 133.559i 0.163364 0.173453i
771771 1233.06i 1.59930i
772772 −167.047 + 314.831i −0.216382 + 0.407812i
773773 −319.455 + 319.455i −0.413267 + 0.413267i −0.882875 0.469608i 0.844395π-0.844395\pi
0.469608 + 0.882875i 0.344395π0.344395\pi
774774 51.9900 + 346.839i 0.0671705 + 0.448112i
775775 14.5549 60.0779i 0.0187805 0.0775198i
776776 117.857 + 246.263i 0.151877 + 0.317349i
777777 507.023 507.023i 0.652539 0.652539i
778778 520.633 + 384.897i 0.669194 + 0.494726i
779779 −771.468 −0.990331
780780 552.901 + 383.694i 0.708848 + 0.491915i
781781 54.4207i 0.0696808i
782782 −1424.21 1052.90i −1.82124 1.34642i
783783 −13.8556 13.8556i −0.0176955 0.0176955i
784784 46.5398 + 68.7393i 0.0593620 + 0.0876776i
785785 78.8999 660.769i 0.100509 0.841744i
786786 160.602 + 1071.42i 0.204328 + 1.36313i
787787 −1104.16 1104.16i −1.40300 1.40300i −0.790372 0.612627i 0.790113π-0.790113\pi
−0.612627 0.790372i 0.709887π-0.709887\pi
788788 10.5042 19.7971i 0.0133302 0.0251232i
789789 1220.49 1.54688
790790 164.051 4.91402i 0.207659 0.00622028i
791791 853.747 1.07933
792792 −24.9621 + 70.7849i −0.0315178 + 0.0893749i
793793 158.749 + 158.749i 0.200188 + 0.200188i
794794 −157.725 1052.23i −0.198646 1.32522i
795795 722.811 568.608i 0.909197 0.715230i
796796 470.476 144.287i 0.591050 0.181266i
797797 434.605 + 434.605i 0.545301 + 0.545301i 0.925078 0.379777i 0.123999π-0.123999\pi
−0.379777 + 0.925078i 0.623999π0.623999\pi
798798 −548.982 + 742.583i −0.687947 + 0.930555i
799799 1479.29i 1.85143i
800800 −220.424 + 769.034i −0.275530 + 0.961293i
801801 −317.950 −0.396942
802802 646.124 + 477.671i 0.805641 + 0.595600i
803803 81.3631 81.3631i 0.101324 0.101324i
804804 −118.476 386.312i −0.147358 0.480488i
805805 −649.422 825.542i −0.806735 1.02552i
806806 −46.0623 + 6.90459i −0.0571493 + 0.00856649i
807807 −885.768 + 885.768i −1.09761 + 1.09761i
808808 −1147.50 404.662i −1.42017 0.500819i
809809 164.175i 0.202935i 0.994839 + 0.101468i 0.0323538π0.0323538\pi
−0.994839 + 0.101468i 0.967646π0.967646\pi
810810 −30.1531 1006.64i −0.0372260 1.24276i
811811 1283.08i 1.58210i −0.611752 0.791049i 0.709535π-0.709535\pi
0.611752 0.791049i 0.290465π-0.290465\pi
812812 −27.2470 14.4570i −0.0335554 0.0178042i
813813 754.377 754.377i 0.927893 0.927893i
814814 −134.402 + 20.1465i −0.165113 + 0.0247500i
815815 −933.677 111.487i −1.14562 0.136794i
816816 −994.511 1468.89i −1.21876 1.80011i
817817 578.308 578.308i 0.707843 0.707843i
818818 198.411 268.382i 0.242556 0.328095i
819819 −260.991 −0.318671
820820 501.046 722.006i 0.611032 0.880495i
821821 1292.43i 1.57421i 0.616817 + 0.787106i 0.288422π0.288422\pi
−0.616817 + 0.787106i 0.711578π0.711578\pi
822822 409.979 554.561i 0.498758 0.674648i
823823 38.6290 + 38.6290i 0.0469368 + 0.0469368i 0.730186 0.683249i 0.239434π-0.239434\pi
−0.683249 + 0.730186i 0.739434π0.739434\pi
824824 −1231.33 + 589.292i −1.49433 + 0.715160i
825825 −190.049 + 115.922i −0.230363 + 0.140512i
826826 445.478 66.7757i 0.539320 0.0808422i
827827 −432.150 432.150i −0.522552 0.522552i 0.395789 0.918341i 0.370471π-0.370471\pi
−0.918341 + 0.395789i 0.870471π0.870471\pi
828828 379.582 + 201.403i 0.458433 + 0.243241i
829829 −684.217 −0.825353 −0.412676 0.910878i 0.635406π-0.635406\pi
−0.412676 + 0.910878i 0.635406π0.635406\pi
830830 3.53939 + 3.33352i 0.00426432 + 0.00401629i
831831 −1393.49 −1.67689
832832 599.315 64.5758i 0.720330 0.0776151i
833833 −113.845 113.845i −0.136669 0.136669i
834834 492.708 73.8553i 0.590777 0.0885556i
835835 −360.967 43.1017i −0.432296 0.0516189i
836836 167.338 51.3201i 0.200166 0.0613876i
837837 32.7049 + 32.7049i 0.0390740 + 0.0390740i
838838 858.304 + 634.533i 1.02423 + 0.757199i
839839 579.065i 0.690184i 0.938569 + 0.345092i 0.112152π0.112152\pi
−0.938569 + 0.345092i 0.887848π0.887848\pi
840840 −338.424 996.070i −0.402886 1.18580i
841841 −839.903 −0.998695
842842 255.056 345.003i 0.302917 0.409742i
843843 −33.5642 + 33.5642i −0.0398151 + 0.0398151i
844844 1047.27 321.182i 1.24084 0.380547i
845845 −315.530 + 248.215i −0.373408 + 0.293746i
846846 53.2029 + 354.931i 0.0628876 + 0.419540i
847847 −597.495 + 597.495i −0.705426 + 0.705426i
848848 155.762 808.854i 0.183682 0.953837i
849849 1279.26i 1.50679i
850850 137.752 1545.47i 0.162062 1.81819i
851851 778.051i 0.914279i
852852 275.644 + 146.254i 0.323526 + 0.171660i
853853 89.6610 89.6610i 0.105113 0.105113i −0.652595 0.757707i 0.726320π-0.726320\pi
0.757707 + 0.652595i 0.226320π0.226320\pi
854854 −52.0229 347.058i −0.0609167 0.406391i
855855 259.720 204.311i 0.303766 0.238961i
856856 −768.237 + 367.664i −0.897473 + 0.429514i
857857 −409.705 + 409.705i −0.478069 + 0.478069i −0.904514 0.426445i 0.859766π-0.859766\pi
0.426445 + 0.904514i 0.359766π0.359766\pi
858858 134.878 + 99.7135i 0.157201 + 0.116216i
859859 799.305 0.930507 0.465253 0.885178i 0.345963π-0.345963\pi
0.465253 + 0.885178i 0.345963π0.345963\pi
860860 165.635 + 916.824i 0.192599 + 1.06607i
861861 1155.65i 1.34222i
862862 844.918 + 624.637i 0.980184 + 0.724637i
863863 1116.04 + 1116.04i 1.29321 + 1.29321i 0.932793 + 0.360414i 0.117364π0.117364\pi
0.360414 + 0.932793i 0.382636π0.382636\pi
864864 −405.352 440.433i −0.469158 0.509761i
865865 1286.03 + 153.560i 1.48674 + 0.177526i
866866 110.201 + 735.178i 0.127253 + 0.848935i
867867 1702.66 + 1702.66i 1.96386 + 1.96386i
868868 64.3144 + 34.1247i 0.0740949 + 0.0393142i
869869 40.9058 0.0470723
870870 27.2445 + 25.6598i 0.0313155 + 0.0294940i
871871 −266.305 −0.305746
872872 31.5583 89.4897i 0.0361907 0.102626i
873873 90.8383 + 90.8383i 0.104053 + 0.104053i
874874 −148.545 990.984i −0.169960 1.13385i
875875 321.159 862.293i 0.367038 0.985477i
876876 −193.447 630.770i −0.220830 0.720058i
877877 −98.3606 98.3606i −0.112156 0.112156i 0.648802 0.760957i 0.275270π-0.275270\pi
−0.760957 + 0.648802i 0.775270π0.775270\pi
878878 498.340 674.082i 0.567585 0.767747i
879879 724.582i 0.824326i
880880 −60.6518 + 189.940i −0.0689225 + 0.215841i
881881 −654.962 −0.743430 −0.371715 0.928347i 0.621230π-0.621230\pi
−0.371715 + 0.928347i 0.621230π0.621230\pi
882882 31.4097 + 23.2207i 0.0356119 + 0.0263274i
883883 −963.144 + 963.144i −1.09076 + 1.09076i −0.0953158 + 0.995447i 0.530386π0.530386\pi
−0.995447 + 0.0953158i 0.969614π0.969614\pi
884884 −1117.71 + 342.784i −1.26438 + 0.387765i
885885 −542.705 64.8024i −0.613227 0.0732231i
886886 333.520 49.9935i 0.376433 0.0564260i
887887 −588.066 + 588.066i −0.662983 + 0.662983i −0.956082 0.293099i 0.905313π-0.905313\pi
0.293099 + 0.956082i 0.405313π0.405313\pi
888888 −259.160 + 734.899i −0.291847 + 0.827588i
889889 581.514i 0.654121i
890890 −844.252 + 25.2890i −0.948598 + 0.0284146i
891891 251.003i 0.281709i
892892 −341.684 + 643.968i −0.383054 + 0.721937i
893893 591.801 591.801i 0.662711 0.662711i
894894 557.556 83.5758i 0.623664 0.0934852i
895895 −96.9059 123.186i −0.108275 0.137638i
896896 −813.319 475.745i −0.907722 0.530965i
897897 679.022 679.022i 0.756992 0.756992i
898898 708.694 958.619i 0.789192 1.06750i
899899 −2.59018 −0.00288118
900900 22.5316 + 375.762i 0.0250351 + 0.417513i
901901 1597.59i 1.77313i
902902 130.211 176.130i 0.144358 0.195267i
903903 −866.299 866.299i −0.959356 0.959356i
904904 −836.919 + 400.534i −0.925795 + 0.443069i
905905 225.631 177.495i 0.249316 0.196127i
906906 1396.07 209.266i 1.54092 0.230978i
907907 692.104 + 692.104i 0.763069 + 0.763069i 0.976876 0.213807i 0.0685863π-0.0685863\pi
−0.213807 + 0.976876i 0.568586π0.568586\pi
908908 −642.839 + 1211.55i −0.707973 + 1.33431i
909909 −572.540 −0.629857
910910 −693.010 + 20.7586i −0.761549 + 0.0228116i
911911 −45.1707 −0.0495836 −0.0247918 0.999693i 0.507892π-0.507892\pi
−0.0247918 + 0.999693i 0.507892π0.507892\pi
912912 189.779 985.500i 0.208091 1.08059i
913913 0.856873 + 0.856873i 0.000938525 + 0.000938525i
914914 −403.573 + 60.4943i −0.441546 + 0.0661863i
915915 −50.4856 + 422.805i −0.0551755 + 0.462082i
916916 −452.321 1474.87i −0.493800 1.61013i
917917 −789.209 789.209i −0.860643 0.860643i
918918 933.523 + 690.141i 1.01691 + 0.751788i
919919 1598.45i 1.73934i 0.493637 + 0.869668i 0.335667π0.335667\pi
−0.493637 + 0.869668i 0.664333π0.664333\pi
920920 1023.92 + 504.594i 1.11296 + 0.548472i
921921 1807.62 1.96268
922922 −884.568 + 1196.52i −0.959402 + 1.29774i
923923 145.418 145.418i 0.157550 0.157550i
924924 −76.8769 250.671i −0.0832001 0.271289i
925925 −581.896 + 354.933i −0.629077 + 0.383712i
926926 −187.220 1248.99i −0.202181 1.34880i
927927 −454.197 + 454.197i −0.489965 + 0.489965i
928928 33.4925 + 1.38918i 0.0360910 + 0.00149696i
929929 887.585i 0.955420i 0.878518 + 0.477710i 0.158533π0.158533\pi
−0.878518 + 0.477710i 0.841467π0.841467\pi
930930 −64.3084 60.5678i −0.0691488 0.0651267i
931931 91.0891i 0.0978400i
932932 −26.2705 + 49.5118i −0.0281873 + 0.0531242i
933933 960.509 960.509i 1.02948 1.02948i
934934 −2.35604 15.7178i −0.00252253 0.0168285i
935935 45.8503 383.986i 0.0490377 0.410680i
936936 255.847 122.444i 0.273341 0.130816i
937937 1241.34 1241.34i 1.32480 1.32480i 0.414958 0.909841i 0.363796π-0.363796\pi
0.909841 0.414958i 0.136204π-0.136204\pi
938938 334.734 + 247.464i 0.356859 + 0.263821i
939939 −1368.23 −1.45712
940940 169.500 + 938.215i 0.180319 + 0.998101i
941941 328.028i 0.348595i 0.984693 + 0.174298i 0.0557654π0.0557654\pi
−0.984693 + 0.174298i 0.944235π0.944235\pi
942942 −764.719 565.347i −0.811804 0.600156i
943943 −886.700 886.700i −0.940297 0.940297i
944944 −405.370 + 274.455i −0.429417 + 0.290736i
945945 425.675 + 541.115i 0.450449 + 0.572609i
946946 34.4222 + 229.640i 0.0363871 + 0.242748i
947947 −228.351 228.351i −0.241131 0.241131i 0.576187 0.817318i 0.304540π-0.304540\pi
−0.817318 + 0.576187i 0.804540π0.804540\pi
948948 109.933 207.190i 0.115963 0.218555i
949949 −434.823 −0.458191
950950 673.382 563.165i 0.708823 0.592805i
951951 1207.26 1.26947
952952 1723.45 + 607.769i 1.81034 + 0.638412i
953953 −1291.50 1291.50i −1.35519 1.35519i −0.879742 0.475451i 0.842285π-0.842285\pi
−0.475451 0.879742i 0.657715π-0.657715\pi
954954 −57.4574 383.313i −0.0602279 0.401796i
955955 500.572 + 636.324i 0.524159 + 0.666308i
956956 171.091 52.4710i 0.178966 0.0548860i
957957 6.59578 + 6.59578i 0.00689215 + 0.00689215i
958958 −909.947 + 1230.84i −0.949840 + 1.28481i
959959 710.482i 0.740857i
960960 799.059 + 817.665i 0.832353 + 0.851735i
961961 −954.886 −0.993638
962962 412.972 + 305.305i 0.429285 + 0.317365i
963963 −283.377 + 283.377i −0.294265 + 0.294265i
964964 −25.1904 82.1379i −0.0261311 0.0852053i
965965 −52.8207 + 442.361i −0.0547365 + 0.458405i
966966 −1484.48 + 222.519i −1.53673 + 0.230351i
967967 486.969 486.969i 0.503588 0.503588i −0.408963 0.912551i 0.634110π-0.634110\pi
0.912551 + 0.408963i 0.134110π0.134110\pi
968968 305.404 866.033i 0.315500 0.894662i
969969 1946.49i 2.00876i
970970 248.428 + 233.978i 0.256111 + 0.241214i
971971 361.550i 0.372348i −0.982517 0.186174i 0.940391π-0.940391\pi
0.982517 0.186174i 0.0596088π-0.0596088\pi
972972 −676.495 358.943i −0.695983 0.369282i
973973 −362.930 + 362.930i −0.373001 + 0.373001i
974974 1709.98 256.320i 1.75562 0.263162i
975975 817.591 + 198.075i 0.838555 + 0.203154i
976976 213.819 + 315.811i 0.219077 + 0.323577i
977977 −1073.65 + 1073.65i −1.09892 + 1.09892i −0.104387 + 0.994537i 0.533288π0.533288\pi
−0.994537 + 0.104387i 0.966712π0.966712\pi
978978 −798.844 + 1080.56i −0.816814 + 1.10487i
979979 −210.513 −0.215028
980980 85.2489 + 59.1597i 0.0869887 + 0.0603671i
981981 44.6506i 0.0455154i
982982 1069.11 1446.14i 1.08871 1.47265i
983983 122.156 + 122.156i 0.124269 + 0.124269i 0.766506 0.642237i 0.221994π-0.221994\pi
−0.642237 + 0.766506i 0.721994π0.721994\pi
984984 −542.172 1132.87i −0.550988 1.15129i
985985 3.32146 27.8164i 0.00337204 0.0282400i
986986 −64.2958 + 9.63773i −0.0652088 + 0.00977458i
987987 −886.510 886.510i −0.898187 0.898187i
988988 −584.280 310.014i −0.591377 0.313780i
989989 1329.38 1.34416
990990 2.80910 + 93.7797i 0.00283748 + 0.0947270i
991991 324.300 0.327245 0.163623 0.986523i 0.447682π-0.447682\pi
0.163623 + 0.986523i 0.447682π0.447682\pi
992992 −79.0563 3.27905i −0.0796938 0.00330549i
993993 −184.603 184.603i −0.185904 0.185904i
994994 −317.914 + 47.6543i −0.319833 + 0.0479420i
995995 483.465 380.323i 0.485895 0.382235i
996996 6.64294 2.03728i 0.00666962 0.00204547i
997997 743.909 + 743.909i 0.746148 + 0.746148i 0.973753 0.227606i 0.0730897π-0.0730897\pi
−0.227606 + 0.973753i 0.573090π0.573090\pi
998998 −1214.78 898.070i −1.21721 0.899869i
999999 509.987i 0.510498i
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 40.3.i.a.13.2 20
3.2 odd 2 360.3.u.b.253.9 20
4.3 odd 2 160.3.m.a.113.8 20
5.2 odd 4 inner 40.3.i.a.37.8 yes 20
5.3 odd 4 200.3.i.b.157.3 20
5.4 even 2 200.3.i.b.93.9 20
8.3 odd 2 160.3.m.a.113.3 20
8.5 even 2 inner 40.3.i.a.13.8 yes 20
15.2 even 4 360.3.u.b.37.3 20
20.3 even 4 800.3.m.b.657.8 20
20.7 even 4 160.3.m.a.17.3 20
20.19 odd 2 800.3.m.b.593.3 20
24.5 odd 2 360.3.u.b.253.3 20
40.3 even 4 800.3.m.b.657.3 20
40.13 odd 4 200.3.i.b.157.9 20
40.19 odd 2 800.3.m.b.593.8 20
40.27 even 4 160.3.m.a.17.8 20
40.29 even 2 200.3.i.b.93.3 20
40.37 odd 4 inner 40.3.i.a.37.2 yes 20
120.77 even 4 360.3.u.b.37.9 20
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.3.i.a.13.2 20 1.1 even 1 trivial
40.3.i.a.13.8 yes 20 8.5 even 2 inner
40.3.i.a.37.2 yes 20 40.37 odd 4 inner
40.3.i.a.37.8 yes 20 5.2 odd 4 inner
160.3.m.a.17.3 20 20.7 even 4
160.3.m.a.17.8 20 40.27 even 4
160.3.m.a.113.3 20 8.3 odd 2
160.3.m.a.113.8 20 4.3 odd 2
200.3.i.b.93.3 20 40.29 even 2
200.3.i.b.93.9 20 5.4 even 2
200.3.i.b.157.3 20 5.3 odd 4
200.3.i.b.157.9 20 40.13 odd 4
360.3.u.b.37.3 20 15.2 even 4
360.3.u.b.37.9 20 120.77 even 4
360.3.u.b.253.3 20 24.5 odd 2
360.3.u.b.253.9 20 3.2 odd 2
800.3.m.b.593.3 20 20.19 odd 2
800.3.m.b.593.8 20 40.19 odd 2
800.3.m.b.657.3 20 40.3 even 4
800.3.m.b.657.8 20 20.3 even 4