Properties

Label 700.2.t.d.299.1
Level 700700
Weight 22
Character 700.299
Analytic conductor 5.5905.590
Analytic rank 00
Dimension 3232
Inner twists 44

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [700,2,Mod(199,700)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(700, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 3, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("700.199"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 700=22527 700 = 2^{2} \cdot 5^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 700.t (of order 66, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [32,0,0,2,0,0,0,0,16,0,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(12)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.589528141495.58952814149
Analytic rank: 00
Dimension: 3232
Relative dimension: 1616 over Q(ζ6)\Q(\zeta_{6})
Twist minimal: no (minimal twist has level 140)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 299.1
Character χ\chi == 700.299
Dual form 700.2.t.d.199.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.41125+0.0915727i)q2+(2.596471.49907i)q3+(1.983230.258463i)q4+(3.52698+2.35332i)q6+(1.65899+2.06101i)q7+(2.77516+0.546365i)q8+(2.994435.18651i)q9+(1.936931.11828i)q11+(4.761943.64409i)q123.17109q13+(2.529972.75667i)q14+(3.866391.02518i)q16+(1.722752.98390i)q17+(3.75094+7.59365i)q18+(1.026181.77739i)q19+(7.39711+2.86441i)q21+(2.63107+1.75554i)q22+(1.330682.30481i)q23+(6.38656+5.57878i)q24+(4.475190.290385i)q268.96105iq27+(3.82285+3.65867i)q28+7.38092q29+(2.44599+4.23658i)q31+(5.36255+1.80084i)q32+(3.352785.80718i)q33+(2.70447+4.05325i)q34+(4.5981211.0600i)q36+(9.69410+5.59689i)q37+(1.28543+2.60230i)q38+(8.23364+4.75369i)q391.46011iq41+(10.70143.36501i)q429.95752q43+(3.552332.71844i)q44+(1.66686+3.37451i)q46+(5.306013.06343i)q47+(8.502158.45786i)q48+(1.49553+6.83838i)q49+(8.946155.16506i)q51+(6.28900+0.819610i)q52+(4.03374+2.32888i)q53+(0.820587+12.6462i)q54+(5.730014.81321i)q566.15325iq57+(10.4163+0.675891i)q58+(3.559386.16503i)q59+(2.196811.26833i)q61+(3.839855.75488i)q62+(15.65722.43279i)q63+(7.402973.03249i)q64+(4.19981+8.50238i)q66+(0.0263848+0.0456998i)q67+(4.187845.47248i)q687.97917iq690.212347iq71+(5.47629+16.0294i)q72+(7.43720+12.8816i)q73+(14.19337.01088i)q74+(1.575753.79020i)q76+(5.51813+2.13680i)q77+(11.18447.46261i)q78+(0.399413+0.230601i)q79+(4.449957.70755i)q81+(0.133707+2.06058i)q82+10.9174iq83+(15.4105+3.76890i)q84+(14.05250.911837i)q86+(19.164311.0645i)q87+(4.76428+4.16168i)q88+(6.079923.51024i)q89+(5.260806.53565i)q91+(2.043344.91490i)q92+(12.7019+7.33344i)q93+(7.76862+3.83736i)q94+(11.2241+12.7147i)q960.185459q97+(1.484359.78758i)q9813.3945iq99+O(q100)q+(-1.41125 + 0.0915727i) q^{2} +(2.59647 - 1.49907i) q^{3} +(1.98323 - 0.258463i) q^{4} +(-3.52698 + 2.35332i) q^{6} +(1.65899 + 2.06101i) q^{7} +(-2.77516 + 0.546365i) q^{8} +(2.99443 - 5.18651i) q^{9} +(1.93693 - 1.11828i) q^{11} +(4.76194 - 3.64409i) q^{12} -3.17109 q^{13} +(-2.52997 - 2.75667i) q^{14} +(3.86639 - 1.02518i) q^{16} +(-1.72275 - 2.98390i) q^{17} +(-3.75094 + 7.59365i) q^{18} +(1.02618 - 1.77739i) q^{19} +(7.39711 + 2.86441i) q^{21} +(-2.63107 + 1.75554i) q^{22} +(1.33068 - 2.30481i) q^{23} +(-6.38656 + 5.57878i) q^{24} +(4.47519 - 0.290385i) q^{26} -8.96105i q^{27} +(3.82285 + 3.65867i) q^{28} +7.38092 q^{29} +(2.44599 + 4.23658i) q^{31} +(-5.36255 + 1.80084i) q^{32} +(3.35278 - 5.80718i) q^{33} +(2.70447 + 4.05325i) q^{34} +(4.59812 - 11.0600i) q^{36} +(9.69410 + 5.59689i) q^{37} +(-1.28543 + 2.60230i) q^{38} +(-8.23364 + 4.75369i) q^{39} -1.46011i q^{41} +(-10.7014 - 3.36501i) q^{42} -9.95752 q^{43} +(3.55233 - 2.71844i) q^{44} +(-1.66686 + 3.37451i) q^{46} +(-5.30601 - 3.06343i) q^{47} +(8.50215 - 8.45786i) q^{48} +(-1.49553 + 6.83838i) q^{49} +(-8.94615 - 5.16506i) q^{51} +(-6.28900 + 0.819610i) q^{52} +(-4.03374 + 2.32888i) q^{53} +(0.820587 + 12.6462i) q^{54} +(-5.73001 - 4.81321i) q^{56} -6.15325i q^{57} +(-10.4163 + 0.675891i) q^{58} +(-3.55938 - 6.16503i) q^{59} +(-2.19681 - 1.26833i) q^{61} +(-3.83985 - 5.75488i) q^{62} +(15.6572 - 2.43279i) q^{63} +(7.40297 - 3.03249i) q^{64} +(-4.19981 + 8.50238i) q^{66} +(0.0263848 + 0.0456998i) q^{67} +(-4.18784 - 5.47248i) q^{68} -7.97917i q^{69} -0.212347i q^{71} +(-5.47629 + 16.0294i) q^{72} +(7.43720 + 12.8816i) q^{73} +(-14.1933 - 7.01088i) q^{74} +(1.57575 - 3.79020i) q^{76} +(5.51813 + 2.13680i) q^{77} +(11.1844 - 7.46261i) q^{78} +(0.399413 + 0.230601i) q^{79} +(-4.44995 - 7.70755i) q^{81} +(0.133707 + 2.06058i) q^{82} +10.9174i q^{83} +(15.4105 + 3.76890i) q^{84} +(14.0525 - 0.911837i) q^{86} +(19.1643 - 11.0645i) q^{87} +(-4.76428 + 4.16168i) q^{88} +(-6.07992 - 3.51024i) q^{89} +(-5.26080 - 6.53565i) q^{91} +(2.04334 - 4.91490i) q^{92} +(12.7019 + 7.33344i) q^{93} +(7.76862 + 3.83736i) q^{94} +(-11.2241 + 12.7147i) q^{96} -0.185459 q^{97} +(1.48435 - 9.78758i) q^{98} -13.3945i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 32q+2q4+16q9+14q12+8q132q1414q1654q1812q2136q24+30q2632q28+40q2960q32+24q33+60q36+60q37+46q38++124q98+O(q100) 32 q + 2 q^{4} + 16 q^{9} + 14 q^{12} + 8 q^{13} - 2 q^{14} - 14 q^{16} - 54 q^{18} - 12 q^{21} - 36 q^{24} + 30 q^{26} - 32 q^{28} + 40 q^{29} - 60 q^{32} + 24 q^{33} + 60 q^{36} + 60 q^{37} + 46 q^{38}+ \cdots + 124 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/700Z)×\left(\mathbb{Z}/700\mathbb{Z}\right)^\times.

nn 101101 351351 477477
χ(n)\chi(n) e(56)e\left(\frac{5}{6}\right) 1-1 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.41125 + 0.0915727i −0.997901 + 0.0647517i
33 2.59647 1.49907i 1.49907 0.865490i 0.499072 0.866560i 0.333674π-0.333674\pi
0.999999 + 0.00107081i 0.000340849π0.000340849\pi
44 1.98323 0.258463i 0.991614 0.129232i
55 0 0
66 −3.52698 + 2.35332i −1.43988 + 0.960741i
77 1.65899 + 2.06101i 0.627038 + 0.778989i
88 −2.77516 + 0.546365i −0.981165 + 0.193169i
99 2.99443 5.18651i 0.998144 1.72884i
1010 0 0
1111 1.93693 1.11828i 0.584005 0.337175i −0.178718 0.983900i 0.557195π-0.557195\pi
0.762723 + 0.646725i 0.223862π0.223862\pi
1212 4.76194 3.64409i 1.37465 1.05196i
1313 −3.17109 −0.879502 −0.439751 0.898120i 0.644933π-0.644933\pi
−0.439751 + 0.898120i 0.644933π0.644933\pi
1414 −2.52997 2.75667i −0.676163 0.736752i
1515 0 0
1616 3.86639 1.02518i 0.966598 0.256296i
1717 −1.72275 2.98390i −0.417829 0.723701i 0.577892 0.816113i 0.303876π-0.303876\pi
−0.995721 + 0.0924124i 0.970542π0.970542\pi
1818 −3.75094 + 7.59365i −0.884104 + 1.78984i
1919 1.02618 1.77739i 0.235421 0.407761i −0.723974 0.689827i 0.757686π-0.757686\pi
0.959395 + 0.282066i 0.0910198π0.0910198\pi
2020 0 0
2121 7.39711 + 2.86441i 1.61418 + 0.625065i
2222 −2.63107 + 1.75554i −0.560947 + 0.374283i
2323 1.33068 2.30481i 0.277467 0.480587i −0.693288 0.720661i 0.743838π-0.743838\pi
0.970755 + 0.240074i 0.0771718π0.0771718\pi
2424 −6.38656 + 5.57878i −1.30365 + 1.13876i
2525 0 0
2626 4.47519 0.290385i 0.877657 0.0569493i
2727 8.96105i 1.72455i
2828 3.82285 + 3.65867i 0.722450 + 0.691423i
2929 7.38092 1.37060 0.685301 0.728260i 0.259671π-0.259671\pi
0.685301 + 0.728260i 0.259671π0.259671\pi
3030 0 0
3131 2.44599 + 4.23658i 0.439313 + 0.760913i 0.997637 0.0687104i 0.0218884π-0.0218884\pi
−0.558323 + 0.829623i 0.688555π0.688555\pi
3232 −5.36255 + 1.80084i −0.947974 + 0.318347i
3333 3.35278 5.80718i 0.583643 1.01090i
3434 2.70447 + 4.05325i 0.463813 + 0.695127i
3535 0 0
3636 4.59812 11.0600i 0.766354 1.84333i
3737 9.69410 + 5.59689i 1.59370 + 0.920123i 0.992664 + 0.120902i 0.0385785π0.0385785\pi
0.601036 + 0.799222i 0.294755π0.294755\pi
3838 −1.28543 + 2.60230i −0.208524 + 0.422149i
3939 −8.23364 + 4.75369i −1.31844 + 0.761200i
4040 0 0
4141 1.46011i 0.228031i −0.993479 0.114016i 0.963629π-0.963629\pi
0.993479 0.114016i 0.0363714π-0.0363714\pi
4242 −10.7014 3.36501i −1.65127 0.519233i
4343 −9.95752 −1.51851 −0.759254 0.650794i 0.774436π-0.774436\pi
−0.759254 + 0.650794i 0.774436π0.774436\pi
4444 3.55233 2.71844i 0.535534 0.409820i
4545 0 0
4646 −1.66686 + 3.37451i −0.245766 + 0.497545i
4747 −5.30601 3.06343i −0.773962 0.446847i 0.0603243 0.998179i 0.480787π-0.480787\pi
−0.834286 + 0.551332i 0.814120π0.814120\pi
4848 8.50215 8.45786i 1.22718 1.22079i
4949 −1.49553 + 6.83838i −0.213647 + 0.976911i
5050 0 0
5151 −8.94615 5.16506i −1.25271 0.723253i
5252 −6.28900 + 0.819610i −0.872127 + 0.113659i
5353 −4.03374 + 2.32888i −0.554077 + 0.319897i −0.750765 0.660570i 0.770315π-0.770315\pi
0.196688 + 0.980466i 0.436982π0.436982\pi
5454 0.820587 + 12.6462i 0.111668 + 1.72094i
5555 0 0
5656 −5.73001 4.81321i −0.765705 0.643193i
5757 6.15325i 0.815018i
5858 −10.4163 + 0.675891i −1.36773 + 0.0887488i
5959 −3.55938 6.16503i −0.463392 0.802619i 0.535735 0.844386i 0.320035π-0.320035\pi
−0.999127 + 0.0417674i 0.986701π0.986701\pi
6060 0 0
6161 −2.19681 1.26833i −0.281272 0.162393i 0.352727 0.935726i 0.385254π-0.385254\pi
−0.633999 + 0.773334i 0.718588π0.718588\pi
6262 −3.83985 5.75488i −0.487662 0.730870i
6363 15.6572 2.43279i 1.97262 0.306503i
6464 7.40297 3.03249i 0.925371 0.379062i
6565 0 0
6666 −4.19981 + 8.50238i −0.516961 + 1.04657i
6767 0.0263848 + 0.0456998i 0.00322341 + 0.00558311i 0.867633 0.497206i 0.165641π-0.165641\pi
−0.864409 + 0.502789i 0.832307π0.832307\pi
6868 −4.18784 5.47248i −0.507850 0.663636i
6969 7.97917i 0.960579i
7070 0 0
7171 0.212347i 0.0252009i −0.999921 0.0126005i 0.995989π-0.995989\pi
0.999921 0.0126005i 0.00401095π-0.00401095\pi
7272 −5.47629 + 16.0294i −0.645387 + 1.88909i
7373 7.43720 + 12.8816i 0.870459 + 1.50768i 0.861523 + 0.507719i 0.169511π0.169511\pi
0.00893589 + 0.999960i 0.497156π0.497156\pi
7474 −14.1933 7.01088i −1.64994 0.814998i
7575 0 0
7676 1.57575 3.79020i 0.180751 0.434766i
7777 5.51813 + 2.13680i 0.628849 + 0.243511i
7878 11.1844 7.46261i 1.26638 0.844974i
7979 0.399413 + 0.230601i 0.0449375 + 0.0259447i 0.522300 0.852762i 0.325074π-0.325074\pi
−0.477363 + 0.878706i 0.658407π0.658407\pi
8080 0 0
8181 −4.44995 7.70755i −0.494439 0.856394i
8282 0.133707 + 2.06058i 0.0147654 + 0.227553i
8383 10.9174i 1.19834i 0.800624 + 0.599168i 0.204502π0.204502\pi
−0.800624 + 0.599168i 0.795498π0.795498\pi
8484 15.4105 + 3.76890i 1.68142 + 0.411221i
8585 0 0
8686 14.0525 0.911837i 1.51532 0.0983259i
8787 19.1643 11.0645i 2.05463 1.18624i
8888 −4.76428 + 4.16168i −0.507874 + 0.443637i
8989 −6.07992 3.51024i −0.644470 0.372085i 0.141864 0.989886i 0.454690π-0.454690\pi
−0.786334 + 0.617801i 0.788024π0.788024\pi
9090 0 0
9191 −5.26080 6.53565i −0.551481 0.685122i
9292 2.04334 4.91490i 0.213033 0.512414i
9393 12.7019 + 7.33344i 1.31712 + 0.760442i
9494 7.76862 + 3.83736i 0.801272 + 0.395794i
9595 0 0
9696 −11.2241 + 12.7147i −1.14556 + 1.29769i
9797 −0.185459 −0.0188305 −0.00941523 0.999956i 0.502997π-0.502997\pi
−0.00941523 + 0.999956i 0.502997π0.502997\pi
9898 1.48435 9.78758i 0.149942 0.988695i
9999 13.3945i 1.34620i
100100 0 0
101101 −5.41172 + 3.12446i −0.538486 + 0.310895i −0.744465 0.667661i 0.767295π-0.767295\pi
0.205979 + 0.978556i 0.433962π0.433962\pi
102102 13.0982 + 6.46995i 1.29691 + 0.640620i
103103 −9.88858 5.70918i −0.974351 0.562542i −0.0737911 0.997274i 0.523510π-0.523510\pi
−0.900560 + 0.434732i 0.856843π0.856843\pi
104104 8.80027 1.73257i 0.862937 0.169893i
105105 0 0
106106 5.47934 3.65601i 0.532201 0.355103i
107107 1.30194 2.25502i 0.125863 0.218001i −0.796207 0.605024i 0.793163π-0.793163\pi
0.922070 + 0.387023i 0.126497π0.126497\pi
108108 −2.31610 17.7718i −0.222867 1.71009i
109109 0.500946 + 0.867663i 0.0479819 + 0.0831071i 0.889019 0.457871i 0.151388π-0.151388\pi
−0.841037 + 0.540978i 0.818054π0.818054\pi
110110 0 0
111111 33.5606 3.18543
112112 8.52721 + 6.26791i 0.805745 + 0.592262i
113113 14.8588i 1.39780i −0.715220 0.698899i 0.753674π-0.753674\pi
0.715220 0.698899i 0.246326π-0.246326\pi
114114 0.563470 + 8.68375i 0.0527738 + 0.813307i
115115 0 0
116116 14.6381 1.90770i 1.35911 0.177125i
117117 −9.49562 + 16.4469i −0.877870 + 1.52052i
118118 5.58771 + 8.37443i 0.514391 + 0.770929i
119119 3.29182 8.50085i 0.301760 0.779272i
120120 0 0
121121 −2.99888 + 5.19421i −0.272626 + 0.472201i
122122 3.21638 + 1.58875i 0.291197 + 0.143839i
123123 −2.18882 3.79114i −0.197359 0.341836i
124124 5.94597 + 7.76992i 0.533963 + 0.697759i
125125 0 0
126126 −21.8733 + 4.86704i −1.94863 + 0.433590i
127127 −3.02360 −0.268301 −0.134151 0.990961i 0.542831π-0.542831\pi
−0.134151 + 0.990961i 0.542831π0.542831\pi
128128 −10.1697 + 4.95750i −0.898885 + 0.438186i
129129 −25.8544 + 14.9270i −2.27635 + 1.31425i
130130 0 0
131131 −7.85267 + 13.6012i −0.686091 + 1.18834i 0.287002 + 0.957930i 0.407341π0.407341\pi
−0.973093 + 0.230414i 0.925992π0.925992\pi
132132 5.14838 12.3835i 0.448109 1.07785i
133133 5.36563 0.833705i 0.465259 0.0722914i
134134 −0.0414202 0.0620775i −0.00357816 0.00536268i
135135 0 0
136136 6.41120 + 7.33952i 0.549756 + 0.629359i
137137 8.32628 4.80718i 0.711362 0.410705i −0.100203 0.994967i 0.531949π-0.531949\pi
0.811565 + 0.584262i 0.198616π0.198616\pi
138138 0.730674 + 11.2606i 0.0621991 + 0.958563i
139139 −7.49745 −0.635925 −0.317963 0.948103i 0.602999π-0.602999\pi
−0.317963 + 0.948103i 0.602999π0.602999\pi
140140 0 0
141141 −18.3692 −1.54697
142142 0.0194451 + 0.299673i 0.00163180 + 0.0251480i
143143 −6.14217 + 3.54618i −0.513634 + 0.296547i
144144 6.26053 23.1229i 0.521711 1.92691i
145145 0 0
146146 −11.6753 17.4981i −0.966257 1.44815i
147147 6.36813 + 19.9975i 0.525234 + 1.64937i
148148 20.6722 + 8.59435i 1.69925 + 0.706451i
149149 3.25066 5.63031i 0.266305 0.461253i −0.701600 0.712571i 0.747531π-0.747531\pi
0.967905 + 0.251318i 0.0808640π0.0808640\pi
150150 0 0
151151 −20.5029 + 11.8373i −1.66850 + 0.963309i −0.700052 + 0.714092i 0.746840π0.746840\pi
−0.968448 + 0.249217i 0.919827π0.919827\pi
152152 −1.87670 + 5.49320i −0.152220 + 0.445557i
153153 −20.6347 −1.66821
154154 −7.98311 2.51025i −0.643297 0.202281i
155155 0 0
156156 −15.1005 + 11.5558i −1.20901 + 0.925201i
157157 3.91624 + 6.78313i 0.312550 + 0.541353i 0.978914 0.204274i 0.0654834π-0.0654834\pi
−0.666363 + 0.745627i 0.732150π0.732150\pi
158158 −0.584787 0.288860i −0.0465232 0.0229805i
159159 −6.98233 + 12.0937i −0.553734 + 0.959096i
160160 0 0
161161 6.95783 1.08110i 0.548354 0.0852026i
162162 6.98578 + 10.4697i 0.548855 + 0.822581i
163163 5.42579 9.39774i 0.424980 0.736088i −0.571438 0.820645i 0.693614π-0.693614\pi
0.996419 + 0.0845574i 0.0269476π0.0269476\pi
164164 −0.377386 2.89574i −0.0294689 0.226119i
165165 0 0
166166 −0.999731 15.4071i −0.0775942 1.19582i
167167 11.7476i 0.909058i 0.890732 + 0.454529i 0.150192π0.150192\pi
−0.890732 + 0.454529i 0.849808π0.849808\pi
168168 −22.0931 3.90766i −1.70452 0.301483i
169169 −2.94418 −0.226476
170170 0 0
171171 −6.14563 10.6445i −0.469968 0.814009i
172172 −19.7480 + 2.57365i −1.50577 + 0.196239i
173173 −8.24371 + 14.2785i −0.626758 + 1.08558i 0.361440 + 0.932395i 0.382285π0.382285\pi
−0.988198 + 0.153181i 0.951048π0.951048\pi
174174 −26.0324 + 17.3697i −1.97351 + 1.31679i
175175 0 0
176176 6.34247 6.30943i 0.478082 0.475591i
177177 −18.4836 10.6715i −1.38932 0.802122i
178178 8.90170 + 4.39706i 0.667211 + 0.329574i
179179 −7.88914 + 4.55480i −0.589662 + 0.340441i −0.764964 0.644073i 0.777243π-0.777243\pi
0.175302 + 0.984515i 0.443910π0.443910\pi
180180 0 0
181181 16.5755i 1.23205i 0.787728 + 0.616023i 0.211257π0.211257\pi
−0.787728 + 0.616023i 0.788743π0.788743\pi
182182 8.02276 + 8.74166i 0.594687 + 0.647975i
183183 −7.60525 −0.562196
184184 −2.43359 + 7.12325i −0.179406 + 0.525133i
185185 0 0
186186 −18.5970 9.18614i −1.36360 0.673560i
187187 −6.67369 3.85305i −0.488028 0.281763i
188188 −11.3148 4.70407i −0.825218 0.343080i
189189 18.4688 14.8663i 1.34341 1.08136i
190190 0 0
191191 2.59197 + 1.49648i 0.187549 + 0.108281i 0.590834 0.806793i 0.298799π-0.298799\pi
−0.403286 + 0.915074i 0.632132π0.632132\pi
192192 14.6757 18.9714i 1.05912 1.36914i
193193 12.7382 7.35442i 0.916918 0.529383i 0.0342676 0.999413i 0.489090π-0.489090\pi
0.882651 + 0.470030i 0.155757π0.155757\pi
194194 0.261728 0.0169829i 0.0187909 0.00121930i
195195 0 0
196196 −1.19851 + 13.9486i −0.0856075 + 0.996329i
197197 4.81748i 0.343231i 0.985164 + 0.171616i 0.0548987π0.0548987\pi
−0.985164 + 0.171616i 0.945101π0.945101\pi
198198 1.22657 + 18.9029i 0.0871686 + 1.34337i
199199 −0.637180 1.10363i −0.0451685 0.0782342i 0.842557 0.538607i 0.181049π-0.181049\pi
−0.887726 + 0.460373i 0.847716π0.847716\pi
200200 0 0
201201 0.137014 + 0.0791053i 0.00966425 + 0.00557966i
202202 7.35115 4.90494i 0.517225 0.345110i
203203 12.2448 + 15.2122i 0.859420 + 1.06768i
204204 −19.0772 7.93125i −1.33567 0.555298i
205205 0 0
206206 14.4780 + 7.15153i 1.00873 + 0.498270i
207207 −7.96929 13.8032i −0.553904 0.959390i
208208 −12.2607 + 3.25095i −0.850126 + 0.225413i
209209 4.59023i 0.317513i
210210 0 0
211211 3.70986i 0.255397i 0.991813 + 0.127698i 0.0407590π0.0407590\pi
−0.991813 + 0.127698i 0.959241π0.959241\pi
212212 −7.39791 + 5.66128i −0.508090 + 0.388818i
213213 −0.318323 0.551351i −0.0218111 0.0377780i
214214 −1.63085 + 3.30161i −0.111483 + 0.225693i
215215 0 0
216216 4.89600 + 24.8683i 0.333131 + 1.69207i
217217 −4.67378 + 12.0697i −0.317277 + 0.819342i
218218 −0.786412 1.17861i −0.0532625 0.0798258i
219219 38.6209 + 22.2978i 2.60976 + 1.50675i
220220 0 0
221221 5.46301 + 9.46220i 0.367482 + 0.636497i
222222 −47.3622 + 3.07323i −3.17874 + 0.206262i
223223 12.9581i 0.867737i −0.900976 0.433869i 0.857148π-0.857148\pi
0.900976 0.433869i 0.142852π-0.142852\pi
224224 −12.6080 8.06471i −0.842404 0.538846i
225225 0 0
226226 1.36066 + 20.9694i 0.0905098 + 1.39487i
227227 −7.70115 + 4.44626i −0.511143 + 0.295109i −0.733304 0.679901i 0.762023π-0.762023\pi
0.222160 + 0.975010i 0.428689π0.428689\pi
228228 −1.59039 12.2033i −0.105326 0.808183i
229229 11.2113 + 6.47287i 0.740866 + 0.427739i 0.822384 0.568933i 0.192643π-0.192643\pi
−0.0815180 + 0.996672i 0.525977π0.525977\pi
230230 0 0
231231 17.5309 2.72392i 1.15345 0.179221i
232232 −20.4832 + 4.03267i −1.34479 + 0.264758i
233233 −13.1776 7.60809i −0.863294 0.498423i 0.00182020 0.999998i 0.499421π-0.499421\pi
−0.865114 + 0.501576i 0.832754π0.832754\pi
234234 11.8946 24.0801i 0.777572 1.57417i
235235 0 0
236236 −8.65250 11.3067i −0.563230 0.736003i
237237 1.38275 0.0898194
238238 −3.86712 + 12.2982i −0.250668 + 0.797176i
239239 0.0438513i 0.00283650i 0.999999 + 0.00141825i 0.000451444π0.000451444\pi
−0.999999 + 0.00141825i 0.999549π0.999549\pi
240240 0 0
241241 1.99236 1.15029i 0.128339 0.0740968i −0.434456 0.900693i 0.643059π-0.643059\pi
0.562795 + 0.826596i 0.309726π0.309726\pi
242242 3.75651 7.60493i 0.241478 0.488863i
243243 0.173149 + 0.0999675i 0.0111075 + 0.00641292i
244244 −4.68458 1.94759i −0.299900 0.124682i
245245 0 0
246246 3.43612 + 5.14979i 0.219079 + 0.328339i
247247 −3.25410 + 5.63627i −0.207053 + 0.358627i
248248 −9.10273 10.4208i −0.578024 0.661720i
249249 16.3659 + 28.3466i 1.03715 + 1.79639i
250250 0 0
251251 −6.32409 −0.399173 −0.199587 0.979880i 0.563960π-0.563960\pi
−0.199587 + 0.979880i 0.563960π0.563960\pi
252252 30.4230 8.87159i 1.91647 0.558857i
253253 5.95233i 0.374220i
254254 4.26704 0.276879i 0.267738 0.0173729i
255255 0 0
256256 13.8980 7.92752i 0.868625 0.495470i
257257 7.12068 12.3334i 0.444176 0.769335i −0.553819 0.832637i 0.686830π-0.686830\pi
0.997994 + 0.0633025i 0.0201633π0.0201633\pi
258258 35.1200 23.4333i 2.18648 1.45889i
259259 4.54713 + 29.2648i 0.282545 + 1.81843i
260260 0 0
261261 22.1017 38.2812i 1.36806 2.36955i
262262 9.83654 19.9138i 0.607704 1.23028i
263263 5.87421 + 10.1744i 0.362219 + 0.627382i 0.988326 0.152355i 0.0486858π-0.0486858\pi
−0.626107 + 0.779738i 0.715353π0.715353\pi
264264 −6.13164 + 17.9477i −0.377376 + 1.10460i
265265 0 0
266266 −7.49588 + 1.66791i −0.459602 + 0.102266i
267267 −21.0484 −1.28814
268268 0.0641387 + 0.0838136i 0.00391790 + 0.00511973i
269269 7.35196 4.24466i 0.448257 0.258801i −0.258837 0.965921i 0.583339π-0.583339\pi
0.707094 + 0.707120i 0.250006π0.250006\pi
270270 0 0
271271 3.98686 6.90544i 0.242184 0.419476i −0.719152 0.694853i 0.755469π-0.755469\pi
0.961336 + 0.275377i 0.0888028π0.0888028\pi
272272 −9.71988 9.77078i −0.589354 0.592440i
273273 −23.4569 9.08330i −1.41968 0.549746i
274274 −11.3102 + 7.54657i −0.683275 + 0.455905i
275275 0 0
276276 −2.06232 15.8245i −0.124137 0.952524i
277277 −11.7737 + 6.79754i −0.707412 + 0.408425i −0.810102 0.586289i 0.800588π-0.800588\pi
0.102690 + 0.994713i 0.467255π0.467255\pi
278278 10.5807 0.686562i 0.634591 0.0411772i
279279 29.2974 1.75399
280280 0 0
281281 9.48286 0.565700 0.282850 0.959164i 0.408720π-0.408720\pi
0.282850 + 0.959164i 0.408720π0.408720\pi
282282 25.9235 1.68212i 1.54372 0.100169i
283283 18.6621 10.7746i 1.10935 0.640483i 0.170689 0.985325i 0.445401π-0.445401\pi
0.938661 + 0.344842i 0.112067π0.112067\pi
284284 −0.0548838 0.421132i −0.00325675 0.0249896i
285285 0 0
286286 8.34337 5.56699i 0.493354 0.329183i
287287 3.00931 2.42231i 0.177634 0.142984i
288288 −6.71772 + 33.2054i −0.395845 + 1.95665i
289289 2.56424 4.44140i 0.150838 0.261259i
290290 0 0
291291 −0.481537 + 0.278016i −0.0282282 + 0.0162976i
292292 18.0791 + 23.6249i 1.05800 + 1.38255i
293293 −28.9496 −1.69125 −0.845626 0.533776i 0.820773π-0.820773\pi
−0.845626 + 0.533776i 0.820773π0.820773\pi
294294 −10.8182 27.6383i −0.630931 1.61190i
295295 0 0
296296 −29.9606 10.2357i −1.74142 0.594940i
297297 −10.0210 17.3569i −0.581477 1.00715i
298298 −4.07190 + 8.24342i −0.235879 + 0.477529i
299299 −4.21972 + 7.30877i −0.244033 + 0.422677i
300300 0 0
301301 −16.5194 20.5226i −0.952162 1.18290i
302302 27.8506 18.5829i 1.60262 1.06933i
303303 −9.36757 + 16.2251i −0.538153 + 0.932108i
304304 2.14545 7.92411i 0.123050 0.454479i
305305 0 0
306306 29.1206 1.88957i 1.66471 0.108020i
307307 8.00589i 0.456920i 0.973553 + 0.228460i 0.0733690π0.0733690\pi
−0.973553 + 0.228460i 0.926631π0.926631\pi
308308 11.4960 + 2.81154i 0.655045 + 0.160202i
309309 −34.2339 −1.94750
310310 0 0
311311 −6.87633 11.9101i −0.389921 0.675363i 0.602518 0.798105i 0.294164π-0.294164\pi
−0.992438 + 0.122743i 0.960831π0.960831\pi
312312 20.2524 17.6908i 1.14656 1.00154i
313313 5.31792 9.21091i 0.300587 0.520631i −0.675682 0.737193i 0.736151π-0.736151\pi
0.976269 + 0.216562i 0.0694842π0.0694842\pi
314314 −6.14793 9.21404i −0.346948 0.519979i
315315 0 0
316316 0.851730 + 0.354102i 0.0479136 + 0.0199198i
317317 14.7081 + 8.49175i 0.826091 + 0.476944i 0.852513 0.522707i 0.175078π-0.175078\pi
−0.0264211 + 0.999651i 0.508411π0.508411\pi
318318 8.74632 17.7066i 0.490469 0.992939i
319319 14.2963 8.25397i 0.800439 0.462133i
320320 0 0
321321 7.80679i 0.435732i
322322 −9.72021 + 2.16284i −0.541686 + 0.120531i
323323 −7.07140 −0.393463
324324 −10.8174 14.1357i −0.600966 0.785316i
325325 0 0
326326 −6.79654 + 13.7594i −0.376426 + 0.762061i
327327 2.60138 + 1.50191i 0.143857 + 0.0830557i
328328 0.797755 + 4.05204i 0.0440486 + 0.223737i
329329 −2.48885 16.0179i −0.137215 0.883097i
330330 0 0
331331 −7.21415 4.16509i −0.396525 0.228934i 0.288458 0.957492i 0.406857π-0.406857\pi
−0.684984 + 0.728558i 0.740191π0.740191\pi
332332 2.82173 + 21.6516i 0.154863 + 1.18829i
333333 58.0567 33.5190i 3.18149 1.83683i
334334 −1.07576 16.5788i −0.0588630 0.907150i
335335 0 0
336336 31.5367 + 3.49154i 1.72047 + 0.190479i
337337 27.0772i 1.47499i −0.675353 0.737495i 0.736009π-0.736009\pi
0.675353 0.737495i 0.263991π-0.263991\pi
338338 4.15496 0.269607i 0.226000 0.0146647i
339339 −22.2744 38.5804i −1.20978 2.09540i
340340 0 0
341341 9.47541 + 5.47063i 0.513122 + 0.296251i
342342 9.64775 + 14.4593i 0.521690 + 0.781870i
343343 −16.5750 + 8.26248i −0.894967 + 0.446132i
344344 27.6337 5.44044i 1.48991 0.293329i
345345 0 0
346346 10.3264 20.9054i 0.555150 1.12388i
347347 13.8861 + 24.0514i 0.745443 + 1.29115i 0.949987 + 0.312288i 0.101095π0.101095\pi
−0.204544 + 0.978857i 0.565571π0.565571\pi
348348 35.1475 26.8968i 1.88410 1.44182i
349349 9.64063i 0.516051i 0.966138 + 0.258026i 0.0830719π0.0830719\pi
−0.966138 + 0.258026i 0.916928π0.916928\pi
350350 0 0
351351 28.4163i 1.51675i
352352 −8.37301 + 9.48495i −0.446283 + 0.505550i
353353 8.15697 + 14.1283i 0.434152 + 0.751973i 0.997226 0.0744333i 0.0237148π-0.0237148\pi
−0.563074 + 0.826406i 0.690381π0.690381\pi
354354 27.0622 + 13.3676i 1.43834 + 0.710478i
355355 0 0
356356 −12.9651 5.39018i −0.687151 0.285679i
357357 −4.19629 27.0069i −0.222091 1.42936i
358358 10.7164 7.15037i 0.566380 0.377909i
359359 1.38744 + 0.801040i 0.0732264 + 0.0422773i 0.536166 0.844112i 0.319872π-0.319872\pi
−0.462940 + 0.886390i 0.653205π0.653205\pi
360360 0 0
361361 7.39392 + 12.8067i 0.389154 + 0.674034i
362362 −1.51786 23.3921i −0.0797771 1.22946i
363363 17.9822i 0.943818i
364364 −12.1226 11.6020i −0.635396 0.608108i
365365 0 0
366366 10.7329 0.696433i 0.561016 0.0364031i
367367 −1.09164 + 0.630259i −0.0569832 + 0.0328993i −0.528221 0.849107i 0.677141π-0.677141\pi
0.471238 + 0.882006i 0.343807π0.343807\pi
368368 2.78209 10.2755i 0.145027 0.535648i
369369 −7.57289 4.37221i −0.394229 0.227608i
370370 0 0
371371 −11.4918 4.45000i −0.596623 0.231033i
372372 27.0862 + 11.2609i 1.40435 + 0.583851i
373373 7.99120 + 4.61372i 0.413768 + 0.238889i 0.692408 0.721507i 0.256550π-0.256550\pi
−0.278639 + 0.960396i 0.589883π0.589883\pi
374374 9.77105 + 4.82648i 0.505249 + 0.249571i
375375 0 0
376376 16.3988 + 5.60247i 0.845702 + 0.288925i
377377 −23.4056 −1.20545
378378 −24.7027 + 22.6712i −1.27057 + 1.16608i
379379 2.53516i 0.130223i −0.997878 0.0651113i 0.979260π-0.979260\pi
0.997878 0.0651113i 0.0207403π-0.0207403\pi
380380 0 0
381381 −7.85068 + 4.53259i −0.402203 + 0.232212i
382382 −3.79495 1.87454i −0.194166 0.0959099i
383383 −1.14737 0.662435i −0.0586279 0.0338489i 0.470400 0.882454i 0.344110π-0.344110\pi
−0.529027 + 0.848605i 0.677443π0.677443\pi
384384 −18.9737 + 28.1171i −0.968248 + 1.43485i
385385 0 0
386386 −17.3033 + 11.5454i −0.880715 + 0.587644i
387387 −29.8171 + 51.6448i −1.51569 + 2.62525i
388388 −0.367807 + 0.0479342i −0.0186726 + 0.00243349i
389389 16.1134 + 27.9093i 0.816983 + 1.41506i 0.907895 + 0.419197i 0.137688π0.137688\pi
−0.0909120 + 0.995859i 0.528978π0.528978\pi
390390 0 0
391391 −9.16976 −0.463735
392392 0.414074 19.7947i 0.0209139 0.999781i
393393 47.0869i 2.37522i
394394 −0.441150 6.79865i −0.0222248 0.342511i
395395 0 0
396396 −3.46199 26.5644i −0.173971 1.33491i
397397 17.5871 30.4617i 0.882670 1.52883i 0.0343095 0.999411i 0.489077π-0.489077\pi
0.848361 0.529419i 0.177590π-0.177590\pi
398398 1.00028 + 1.49914i 0.0501395 + 0.0751452i
399399 12.6819 10.2082i 0.634890 0.511047i
400400 0 0
401401 −15.9623 + 27.6476i −0.797120 + 1.38065i 0.124364 + 0.992237i 0.460311π0.460311\pi
−0.921484 + 0.388416i 0.873022π0.873022\pi
402402 −0.200605 0.0990903i −0.0100053 0.00494217i
403403 −7.75647 13.4346i −0.386377 0.669225i
404404 −9.92512 + 7.59524i −0.493793 + 0.377877i
405405 0 0
406406 −18.6735 20.3468i −0.926751 1.00979i
407407 25.0357 1.24097
408408 27.6490 + 9.44599i 1.36883 + 0.467646i
409409 −14.2151 + 8.20712i −0.702894 + 0.405816i −0.808424 0.588600i 0.799679π-0.799679\pi
0.105530 + 0.994416i 0.466346π0.466346\pi
410410 0 0
411411 14.4126 24.9634i 0.710922 1.23135i
412412 −21.0869 8.76677i −1.03888 0.431908i
413413 6.80123 17.5636i 0.334666 0.864250i
414414 12.5106 + 18.7500i 0.614864 + 0.921510i
415415 0 0
416416 17.0051 5.71063i 0.833746 0.279987i
417417 −19.4669 + 11.2392i −0.953298 + 0.550387i
418418 0.420340 + 6.47794i 0.0205595 + 0.316846i
419419 −11.8654 −0.579665 −0.289832 0.957077i 0.593600π-0.593600\pi
−0.289832 + 0.957077i 0.593600π0.593600\pi
420420 0 0
421421 10.3433 0.504101 0.252051 0.967714i 0.418895π-0.418895\pi
0.252051 + 0.967714i 0.418895π0.418895\pi
422422 −0.339721 5.23552i −0.0165374 0.254861i
423423 −31.7770 + 18.3465i −1.54505 + 0.892035i
424424 9.92185 8.66691i 0.481847 0.420902i
425425 0 0
426426 0.499720 + 0.748942i 0.0242115 + 0.0362864i
427427 −1.03044 6.63178i −0.0498663 0.320934i
428428 1.99920 4.80873i 0.0966349 0.232439i
429429 −10.6320 + 18.4151i −0.513316 + 0.889089i
430430 0 0
431431 25.6838 14.8286i 1.23715 0.714267i 0.268636 0.963242i 0.413427π-0.413427\pi
0.968510 + 0.248975i 0.0800937π0.0800937\pi
432432 −9.18671 34.6469i −0.441996 1.66695i
433433 29.4107 1.41339 0.706693 0.707520i 0.250186π-0.250186\pi
0.706693 + 0.707520i 0.250186π0.250186\pi
434434 5.49059 17.4612i 0.263557 0.838166i
435435 0 0
436436 1.21775 + 1.59130i 0.0583196 + 0.0762094i
437437 −2.73103 4.73029i −0.130643 0.226280i
438438 −56.5455 27.9311i −2.70185 1.33460i
439439 4.41191 7.64165i 0.210569 0.364716i −0.741324 0.671147i 0.765802π-0.765802\pi
0.951893 + 0.306432i 0.0991351π0.0991351\pi
440440 0 0
441441 30.9890 + 28.2336i 1.47567 + 1.34446i
442442 −8.57612 12.8532i −0.407925 0.611366i
443443 9.78342 16.9454i 0.464824 0.805099i −0.534369 0.845251i 0.679451π-0.679451\pi
0.999194 + 0.0401518i 0.0127842π0.0127842\pi
444444 66.5583 8.67417i 3.15872 0.411658i
445445 0 0
446446 1.18661 + 18.2870i 0.0561874 + 0.865916i
447447 19.4919i 0.921935i
448448 18.5314 + 10.2267i 0.875528 + 0.483168i
449449 −5.02309 −0.237054 −0.118527 0.992951i 0.537817π-0.537817\pi
−0.118527 + 0.992951i 0.537817π0.537817\pi
450450 0 0
451451 −1.63282 2.82813i −0.0768866 0.133171i
452452 −3.84045 29.4684i −0.180640 1.38608i
453453 −35.4900 + 61.4705i −1.66747 + 2.88814i
454454 10.4611 6.97998i 0.490962 0.327587i
455455 0 0
456456 3.36192 + 17.0762i 0.157436 + 0.799667i
457457 24.1144 + 13.9225i 1.12802 + 0.651265i 0.943437 0.331551i 0.107572π-0.107572\pi
0.184587 + 0.982816i 0.440905π0.440905\pi
458458 −16.4147 8.10816i −0.767008 0.378869i
459459 −26.7388 + 15.4377i −1.24806 + 0.720569i
460460 0 0
461461 19.8494i 0.924481i −0.886755 0.462240i 0.847046π-0.847046\pi
0.886755 0.462240i 0.152954π-0.152954\pi
462462 −24.4909 + 5.44948i −1.13942 + 0.253533i
463463 35.7118 1.65967 0.829833 0.558012i 0.188436π-0.188436\pi
0.829833 + 0.558012i 0.188436π0.188436\pi
464464 28.5375 7.56680i 1.32482 0.351280i
465465 0 0
466466 19.2935 + 9.53018i 0.893756 + 0.441477i
467467 −19.5818 11.3055i −0.906136 0.523158i −0.0269503 0.999637i 0.508580π-0.508580\pi
−0.879186 + 0.476479i 0.841913π0.841913\pi
468468 −14.5811 + 35.0722i −0.674010 + 1.62121i
469469 −0.0504157 + 0.130195i −0.00232798 + 0.00601183i
470470 0 0
471471 20.3368 + 11.7415i 0.937070 + 0.541018i
472472 13.2462 + 15.1642i 0.609705 + 0.697989i
473473 −19.2870 + 11.1353i −0.886816 + 0.512003i
474474 −1.95140 + 0.126622i −0.0896309 + 0.00581596i
475475 0 0
476476 4.33127 17.7100i 0.198523 0.811734i
477477 27.8947i 1.27721i
478478 −0.00401558 0.0618849i −0.000183668 0.00283055i
479479 −4.28200 7.41664i −0.195649 0.338875i 0.751464 0.659774i 0.229348π-0.229348\pi
−0.947113 + 0.320900i 0.896015π0.896015\pi
480480 0 0
481481 −30.7409 17.7483i −1.40166 0.809251i
482482 −2.70638 + 1.80579i −0.123272 + 0.0822515i
483483 16.4451 13.2373i 0.748280 0.602319i
484484 −4.60495 + 11.0764i −0.209316 + 0.503473i
485485 0 0
486486 −0.253510 0.125223i −0.0114994 0.00568023i
487487 −15.8225 27.4054i −0.716987 1.24186i −0.962188 0.272386i 0.912187π-0.912187\pi
0.245201 0.969472i 0.421146π-0.421146\pi
488488 6.78945 + 2.31955i 0.307344 + 0.105001i
489489 32.5346i 1.47126i
490490 0 0
491491 35.7781i 1.61464i −0.590113 0.807321i 0.700917π-0.700917\pi
0.590113 0.807321i 0.299083π-0.299083\pi
492492 −5.32079 6.95297i −0.239880 0.313464i
493493 −12.7155 22.0239i −0.572677 0.991906i
494494 4.07621 8.25214i 0.183397 0.371281i
495495 0 0
496496 13.8004 + 13.8727i 0.619658 + 0.622903i
497497 0.437649 0.352280i 0.0196312 0.0158019i
498498 −25.6921 38.5053i −1.15129 1.72546i
499499 −35.7797 20.6574i −1.60172 0.924752i −0.991144 0.132793i 0.957605π-0.957605\pi
−0.610574 0.791959i 0.709061π-0.709061\pi
500500 0 0
501501 17.6105 + 30.5023i 0.786780 + 1.36274i
502502 8.92485 0.579114i 0.398336 0.0258471i
503503 29.0170i 1.29381i −0.762572 0.646903i 0.776064π-0.776064\pi
0.762572 0.646903i 0.223936π-0.223936\pi
504504 −42.1219 + 15.3059i −1.87626 + 0.681779i
505505 0 0
506506 0.545071 + 8.40021i 0.0242314 + 0.373435i
507507 −7.64448 + 4.41354i −0.339503 + 0.196012i
508508 −5.99649 + 0.781489i −0.266051 + 0.0346730i
509509 −17.3474 10.0155i −0.768910 0.443931i 0.0635754 0.997977i 0.479750π-0.479750\pi
−0.832486 + 0.554046i 0.813083π0.813083\pi
510510 0 0
511511 −14.2109 + 36.6986i −0.628654 + 1.62345i
512512 −18.8875 + 12.4604i −0.834720 + 0.550675i
513513 −15.9273 9.19562i −0.703206 0.405996i
514514 −8.91962 + 18.0575i −0.393428 + 0.796481i
515515 0 0
516516 −47.4171 + 36.2861i −2.08742 + 1.59741i
517517 −13.7031 −0.602663
518518 −9.09698 40.8835i −0.399698 1.79632i
519519 49.4317i 2.16981i
520520 0 0
521521 18.5712 10.7221i 0.813620 0.469743i −0.0345917 0.999402i 0.511013π-0.511013\pi
0.848211 + 0.529658i 0.177680π0.177680\pi
522522 −27.6854 + 56.0481i −1.21176 + 2.45316i
523523 −35.5105 20.5020i −1.55277 0.896491i −0.997915 0.0645418i 0.979441π-0.979441\pi
−0.554852 0.831949i 0.687225π-0.687225\pi
524524 −12.0582 + 29.0040i −0.526766 + 1.26704i
525525 0 0
526526 −9.22165 13.8207i −0.402083 0.602611i
527527 8.42768 14.5972i 0.367116 0.635863i
528528 7.00973 25.8901i 0.305059 1.12672i
529529 7.95856 + 13.7846i 0.346024 + 0.599332i
530530 0 0
531531 −42.6333 −1.85013
532532 10.4258 3.04025i 0.452016 0.131811i
533533 4.63015i 0.200554i
534534 29.7045 1.92746i 1.28544 0.0834094i
535535 0 0
536536 −0.0981906 0.112408i −0.00424119 0.00485530i
537537 −13.6559 + 23.6528i −0.589297 + 1.02069i
538538 −9.98673 + 6.66349i −0.430559 + 0.287284i
539539 4.75052 + 14.9178i 0.204620 + 0.642557i
540540 0 0
541541 −1.72641 + 2.99023i −0.0742242 + 0.128560i −0.900749 0.434341i 0.856981π-0.856981\pi
0.826524 + 0.562901i 0.190315π0.190315\pi
542542 −4.99409 + 10.1104i −0.214514 + 0.434277i
543543 24.8479 + 43.0377i 1.06632 + 1.84693i
544544 14.6119 + 12.8989i 0.626479 + 0.553035i
545545 0 0
546546 33.9352 + 10.6708i 1.45229 + 0.456666i
547547 28.2607 1.20834 0.604170 0.796855i 0.293505π-0.293505\pi
0.604170 + 0.796855i 0.293505π0.293505\pi
548548 15.2704 11.6858i 0.652321 0.499191i
549549 −13.1564 + 7.59584i −0.561500 + 0.324182i
550550 0 0
551551 7.57413 13.1188i 0.322669 0.558879i
552552 4.35953 + 22.1434i 0.185554 + 0.942487i
553553 0.187349 + 1.20576i 0.00796691 + 0.0512741i
554554 15.9931 10.6711i 0.679481 0.453374i
555555 0 0
556556 −14.8692 + 1.93781i −0.630593 + 0.0821816i
557557 1.79833 1.03826i 0.0761976 0.0439927i −0.461417 0.887183i 0.652659π-0.652659\pi
0.537615 + 0.843191i 0.319326π0.319326\pi
558558 −41.3459 + 2.68285i −1.75031 + 0.113574i
559559 31.5762 1.33553
560560 0 0
561561 −23.1040 −0.975453
562562 −13.3826 + 0.868371i −0.564513 + 0.0366300i
563563 −39.7588 + 22.9547i −1.67563 + 0.967426i −0.711240 + 0.702949i 0.751866π0.751866\pi
−0.964392 + 0.264477i 0.914801π0.914801\pi
564564 −36.4303 + 4.74776i −1.53399 + 0.199917i
565565 0 0
566566 −25.3502 + 16.9145i −1.06555 + 0.710971i
567567 8.50292 21.9581i 0.357089 0.922154i
568568 0.116019 + 0.589295i 0.00486803 + 0.0247263i
569569 3.96413 6.86607i 0.166185 0.287840i −0.770891 0.636968i 0.780189π-0.780189\pi
0.937075 + 0.349127i 0.113522π0.113522\pi
570570 0 0
571571 −18.3314 + 10.5837i −0.767147 + 0.442912i −0.831856 0.554992i 0.812721π-0.812721\pi
0.0647092 + 0.997904i 0.479388π0.479388\pi
572572 −11.2648 + 8.62041i −0.471003 + 0.360438i
573573 8.97330 0.374865
574574 −4.02506 + 3.69404i −0.168003 + 0.154186i
575575 0 0
576576 6.43964 47.4762i 0.268318 1.97817i
577577 5.16573 + 8.94731i 0.215052 + 0.372481i 0.953289 0.302061i 0.0976745π-0.0976745\pi
−0.738237 + 0.674542i 0.764341π0.764341\pi
578578 −3.21207 + 6.50272i −0.133604 + 0.270478i
579579 22.0496 38.1911i 0.916351 1.58717i
580580 0 0
581581 −22.5008 + 18.1117i −0.933490 + 0.751402i
582582 0.654109 0.436444i 0.0271137 0.0180912i
583583 −5.20871 + 9.02174i −0.215723 + 0.373642i
584584 −27.6774 31.6851i −1.14530 1.31114i
585585 0 0
586586 40.8550 2.65099i 1.68770 0.109511i
587587 20.4660i 0.844722i 0.906428 + 0.422361i 0.138799π0.138799\pi
−0.906428 + 0.422361i 0.861201π0.861201\pi
588588 17.7981 + 38.0138i 0.733980 + 1.56766i
589589 10.0401 0.413694
590590 0 0
591591 7.22175 + 12.5084i 0.297063 + 0.514529i
592592 43.2191 + 11.7016i 1.77629 + 0.480931i
593593 22.4236 38.8389i 0.920828 1.59492i 0.122692 0.992445i 0.460847π-0.460847\pi
0.798136 0.602477i 0.205819π-0.205819\pi
594594 15.7315 + 23.5772i 0.645471 + 0.967383i
595595 0 0
596596 4.99158 12.0064i 0.204463 0.491800i
597597 −3.30884 1.91036i −0.135422 0.0781857i
598598 5.28578 10.7009i 0.216152 0.437592i
599599 −14.1499 + 8.16942i −0.578147 + 0.333793i −0.760397 0.649459i 0.774995π-0.774995\pi
0.182250 + 0.983252i 0.441662π0.441662\pi
600600 0 0
601601 39.8029i 1.62359i −0.583941 0.811796i 0.698490π-0.698490\pi
0.583941 0.811796i 0.301510π-0.301510\pi
602602 25.1922 + 27.4496i 1.02676 + 1.11876i
603603 0.316030 0.0128697
604604 −37.6024 + 28.7754i −1.53002 + 1.17085i
605605 0 0
606606 11.7342 23.7554i 0.476668 0.964998i
607607 −8.14710 4.70373i −0.330681 0.190919i 0.325463 0.945555i 0.394480π-0.394480\pi
−0.656143 + 0.754636i 0.727813π0.727813\pi
608608 −2.30213 + 11.3793i −0.0933636 + 0.461493i
609609 54.5975 + 21.1420i 2.21240 + 0.856716i
610610 0 0
611611 16.8259 + 9.71441i 0.680701 + 0.393003i
612612 −40.9233 + 5.33330i −1.65423 + 0.215586i
613613 −11.8091 + 6.81796i −0.476963 + 0.275375i −0.719150 0.694855i 0.755469π-0.755469\pi
0.242187 + 0.970230i 0.422135π0.422135\pi
614614 −0.733121 11.2983i −0.0295863 0.455961i
615615 0 0
616616 −16.4811 2.91505i −0.664044 0.117451i
617617 39.1144i 1.57469i 0.616515 + 0.787343i 0.288544π0.288544\pi
−0.616515 + 0.787343i 0.711456π0.711456\pi
618618 48.3124 3.13489i 1.94341 0.126104i
619619 9.50950 + 16.4709i 0.382219 + 0.662023i 0.991379 0.131024i 0.0418266π-0.0418266\pi
−0.609160 + 0.793047i 0.708493π0.708493\pi
620620 0 0
621621 −20.6535 11.9243i −0.828798 0.478507i
622622 10.7948 + 16.1785i 0.432833 + 0.648697i
623623 −2.85186 18.3542i −0.114257 0.735347i
624624 −26.9611 + 26.8206i −1.07931 + 1.07368i
625625 0 0
626626 −6.66143 + 13.4858i −0.266244 + 0.539002i
627627 −6.88108 11.9184i −0.274804 0.475974i
628628 9.52000 + 12.4403i 0.379889 + 0.496422i
629629 38.5683i 1.53782i
630630 0 0
631631 16.4987i 0.656802i 0.944538 + 0.328401i 0.106510π0.106510\pi
−0.944538 + 0.328401i 0.893490π0.893490\pi
632632 −1.23443 0.421729i −0.0491028 0.0167755i
633633 5.56134 + 9.63252i 0.221043 + 0.382858i
634634 −21.5344 10.6371i −0.855241 0.422452i
635635 0 0
636636 −10.7218 + 25.7893i −0.425146 + 1.02261i
637637 4.74245 21.6851i 0.187903 0.859196i
638638 −19.4197 + 12.9575i −0.768835 + 0.512993i
639639 −1.10134 0.635857i −0.0435682 0.0251541i
640640 0 0
641641 −13.4723 23.3347i −0.532124 0.921665i −0.999297 0.0374991i 0.988061π-0.988061\pi
0.467173 0.884166i 0.345272π-0.345272\pi
642642 0.714889 + 11.0173i 0.0282144 + 0.434818i
643643 43.6730i 1.72229i −0.508355 0.861147i 0.669746π-0.669746\pi
0.508355 0.861147i 0.330254π-0.330254\pi
644644 13.5195 3.94241i 0.532745 0.155353i
645645 0 0
646646 9.97948 0.647547i 0.392637 0.0254774i
647647 24.3422 14.0540i 0.956989 0.552518i 0.0617443 0.998092i 0.480334π-0.480334\pi
0.895245 + 0.445574i 0.147000π0.147000\pi
648648 16.5604 + 18.9583i 0.650556 + 0.744754i
649649 −13.7885 7.96080i −0.541246 0.312489i
650650 0 0
651651 5.95797 + 38.3448i 0.233511 + 1.50285i
652652 8.33161 20.0402i 0.326291 0.784836i
653653 −36.0902 20.8367i −1.41232 0.815403i −0.416713 0.909038i 0.636818π-0.636818\pi
−0.995607 + 0.0936346i 0.970151π0.970151\pi
654654 −3.80872 1.88134i −0.148933 0.0735664i
655655 0 0
656656 −1.49688 5.64538i −0.0584435 0.220415i
657657 89.0808 3.47537
658658 4.97918 + 22.3773i 0.194109 + 0.872359i
659659 47.0951i 1.83457i −0.398236 0.917283i 0.630378π-0.630378\pi
0.398236 0.917283i 0.369622π-0.369622\pi
660660 0 0
661661 −10.0792 + 5.81924i −0.392036 + 0.226342i −0.683042 0.730379i 0.739343π-0.739343\pi
0.291006 + 0.956721i 0.406010π0.406010\pi
662662 10.5623 + 5.21735i 0.410517 + 0.202778i
663663 28.3690 + 16.3789i 1.10176 + 0.636103i
664664 −5.96486 30.2973i −0.231481 1.17577i
665665 0 0
666666 −78.8628 + 52.6200i −3.05587 + 2.03898i
667667 9.82168 17.0116i 0.380297 0.658693i
668668 3.03633 + 23.2982i 0.117479 + 0.901435i
669669 −19.4251 33.6452i −0.751017 1.30080i
670670 0 0
671671 −5.67340 −0.219019
672672 −44.8257 2.03952i −1.72919 0.0786763i
673673 14.9849i 0.577626i −0.957385 0.288813i 0.906739π-0.906739\pi
0.957385 0.288813i 0.0932606π-0.0932606\pi
674674 2.47953 + 38.2126i 0.0955080 + 1.47189i
675675 0 0
676676 −5.83899 + 0.760963i −0.224576 + 0.0292678i
677677 −11.5093 + 19.9347i −0.442339 + 0.766154i −0.997863 0.0653470i 0.979185π-0.979185\pi
0.555524 + 0.831501i 0.312518π0.312518\pi
678678 34.9676 + 52.4067i 1.34292 + 2.01267i
679679 −0.307673 0.382232i −0.0118074 0.0146687i
680680 0 0
681681 −13.3305 + 23.0892i −0.510827 + 0.884779i
682682 −13.8731 6.85272i −0.531228 0.262404i
683683 18.6347 + 32.2762i 0.713037 + 1.23502i 0.963712 + 0.266945i 0.0860142π0.0860142\pi
−0.250675 + 0.968071i 0.580652π0.580652\pi
684684 −14.9394 19.5222i −0.571223 0.746448i
685685 0 0
686686 22.6348 13.1782i 0.864201 0.503146i
687687 38.8132 1.48082
688688 −38.4997 + 10.2083i −1.46779 + 0.389187i
689689 12.7914 7.38510i 0.487312 0.281350i
690690 0 0
691691 13.9969 24.2433i 0.532467 0.922260i −0.466815 0.884355i 0.654598π-0.654598\pi
0.999281 0.0379044i 0.0120682π-0.0120682\pi
692692 −12.6587 + 30.4483i −0.481211 + 1.15747i
693693 27.6062 22.2213i 1.04867 0.844118i
694694 −21.7991 32.6708i −0.827483 1.24017i
695695 0 0
696696 −47.1387 + 41.1765i −1.78679 + 1.56079i
697697 −4.35683 + 2.51542i −0.165027 + 0.0952782i
698698 −0.882819 13.6053i −0.0334152 0.514968i
699699 −45.6203 −1.72552
700700 0 0
701701 29.2334 1.10413 0.552065 0.833801i 0.313840π-0.313840\pi
0.552065 + 0.833801i 0.313840π0.313840\pi
702702 −2.60216 40.1024i −0.0982121 1.51357i
703703 19.8957 11.4868i 0.750381 0.433233i
704704 10.9478 14.1523i 0.412611 0.533386i
705705 0 0
706706 −12.8053 19.1915i −0.481932 0.722283i
707707 −15.4175 5.97017i −0.579835 0.224532i
708708 −39.4155 16.3868i −1.48133 0.615852i
709709 −2.08074 + 3.60395i −0.0781440 + 0.135349i −0.902449 0.430796i 0.858233π-0.858233\pi
0.824305 + 0.566146i 0.191566π0.191566\pi
710710 0 0
711711 2.39203 1.38104i 0.0897082 0.0517931i
712712 18.7906 + 6.41962i 0.704207 + 0.240585i
713713 13.0194 0.487580
714714 8.39509 + 37.7291i 0.314178 + 1.41197i
715715 0 0
716716 −14.4687 + 11.0723i −0.540722 + 0.413790i
717717 0.0657362 + 0.113858i 0.00245496 + 0.00425212i
718718 −2.03137 1.00341i −0.0758102 0.0374470i
719719 −21.1113 + 36.5658i −0.787318 + 1.36368i 0.140286 + 0.990111i 0.455198π0.455198\pi
−0.927604 + 0.373564i 0.878135π0.878135\pi
720720 0 0
721721 −4.63835 29.8519i −0.172741 1.11174i
722722 −11.6074 17.3962i −0.431982 0.647421i
723723 3.44874 5.97339i 0.128260 0.222153i
724724 4.28415 + 32.8730i 0.159219 + 1.22172i
725725 0 0
726726 −1.64667 25.3772i −0.0611138 0.941837i
727727 27.2605i 1.01104i −0.862816 0.505519i 0.831301π-0.831301\pi
0.862816 0.505519i 0.168699π-0.168699\pi
728728 18.1704 + 15.2631i 0.673439 + 0.565689i
729729 27.2992 1.01108
730730 0 0
731731 17.1544 + 29.7122i 0.634477 + 1.09895i
732732 −15.0830 + 1.96568i −0.557482 + 0.0726535i
733733 7.65300 13.2554i 0.282670 0.489599i −0.689372 0.724408i 0.742113π-0.742113\pi
0.972041 + 0.234809i 0.0754466π0.0754466\pi
734734 1.48286 0.989415i 0.0547333 0.0365200i
735735 0 0
736736 −2.98526 + 14.7560i −0.110038 + 0.543915i
737737 0.102211 + 0.0590113i 0.00376498 + 0.00217371i
738738 11.0876 + 5.47680i 0.408140 + 0.201604i
739739 42.5694 24.5774i 1.56594 0.904096i 0.569305 0.822126i 0.307212π-0.307212\pi
0.996635 0.0819692i 0.0261209π-0.0261209\pi
740740 0 0
741741 19.5125i 0.716810i
742742 16.6252 + 5.22771i 0.610331 + 0.191915i
743743 35.2067 1.29161 0.645805 0.763503i 0.276522π-0.276522\pi
0.645805 + 0.763503i 0.276522π0.276522\pi
744744 −39.2564 13.4116i −1.43921 0.491692i
745745 0 0
746746 −11.7000 5.77932i −0.428369 0.211596i
747747 56.6229 + 32.6913i 2.07173 + 1.19611i
748748 −14.2313 5.91659i −0.520349 0.216332i
749749 6.80752 1.05774i 0.248741 0.0386491i
750750 0 0
751751 −0.584292 0.337341i −0.0213211 0.0123098i 0.489302 0.872115i 0.337252π-0.337252\pi
−0.510623 + 0.859805i 0.670585π0.670585\pi
752752 −23.6557 6.40478i −0.862635 0.233558i
753753 −16.4203 + 9.48027i −0.598389 + 0.345480i
754754 33.0310 2.14331i 1.20292 0.0780548i
755755 0 0
756756 32.7855 34.2567i 1.19240 1.24590i
757757 45.8640i 1.66695i −0.552553 0.833477i 0.686346π-0.686346\pi
0.552553 0.833477i 0.313654π-0.313654\pi
758758 0.232152 + 3.57774i 0.00843214 + 0.129949i
759759 −8.92298 15.4550i −0.323883 0.560983i
760760 0 0
761761 18.9229 + 10.9252i 0.685956 + 0.396037i 0.802095 0.597196i 0.203719π-0.203719\pi
−0.116139 + 0.993233i 0.537052π0.537052\pi
762762 10.6642 7.11551i 0.386322 0.257768i
763763 −0.957201 + 2.47190i −0.0346530 + 0.0894886i
764764 5.52726 + 2.29793i 0.199969 + 0.0831360i
765765 0 0
766766 1.67988 + 0.829791i 0.0606967 + 0.0299816i
767767 11.2871 + 19.5499i 0.407554 + 0.705905i
768768 24.2018 41.4177i 0.873307 1.49453i
769769 16.0214i 0.577745i −0.957368 0.288872i 0.906720π-0.906720\pi
0.957368 0.288872i 0.0932803π-0.0932803\pi
770770 0 0
771771 42.6976i 1.53772i
772772 23.3620 17.8779i 0.840816 0.643439i
773773 21.1707 + 36.6688i 0.761458 + 1.31888i 0.942099 + 0.335335i 0.108850π0.108850\pi
−0.180641 + 0.983549i 0.557817π0.557817\pi
774774 37.3500 75.6139i 1.34252 2.71789i
775775 0 0
776776 0.514676 0.101328i 0.0184758 0.00363746i
777777 55.6765 + 69.1687i 1.99738 + 2.48141i
778778 −25.2957 37.9113i −0.906896 1.35919i
779779 −2.59519 1.49833i −0.0929824 0.0536834i
780780 0 0
781781 −0.237464 0.411299i −0.00849712 0.0147174i
782782 12.9408 0.839700i 0.462762 0.0300276i
783783 66.1408i 2.36368i
784784 1.22829 + 27.9730i 0.0438675 + 0.999037i
785785 0 0
786786 −4.31187 66.4511i −0.153799 2.37023i
787787 −3.79528 + 2.19121i −0.135287 + 0.0781081i −0.566116 0.824326i 0.691555π-0.691555\pi
0.430829 + 0.902434i 0.358221π0.358221\pi
788788 1.24514 + 9.55417i 0.0443563 + 0.340353i
789789 30.5044 + 17.6117i 1.08599 + 0.626994i
790790 0 0
791791 30.6241 24.6506i 1.08887 0.876473i
792792 7.31828 + 37.1718i 0.260044 + 1.32084i
793793 6.96627 + 4.02198i 0.247380 + 0.142825i
794794 −22.0302 + 44.5995i −0.781824 + 1.58278i
795795 0 0
796796 −1.54892 2.02406i −0.0549001 0.0717409i
797797 −53.6019 −1.89868 −0.949339 0.314255i 0.898245π-0.898245\pi
−0.949339 + 0.314255i 0.898245π0.898245\pi
798798 −16.9625 + 15.5675i −0.600466 + 0.551085i
799799 21.1101i 0.746822i
800800 0 0
801801 −36.4118 + 21.0224i −1.28655 + 0.742789i
802802 19.9950 40.4792i 0.706048 1.42937i
803803 28.8106 + 16.6338i 1.01670 + 0.586995i
804804 0.292177 + 0.121471i 0.0103043 + 0.00428394i
805805 0 0
806806 12.1765 + 18.2492i 0.428900 + 0.642802i
807807 12.7261 22.0422i 0.447980 0.775924i
808808 13.3113 11.6276i 0.468289 0.409058i
809809 −0.754693 1.30717i −0.0265336 0.0459575i 0.852454 0.522803i 0.175114π-0.175114\pi
−0.878987 + 0.476845i 0.841780π0.841780\pi
810810 0 0
811811 −43.1894 −1.51658 −0.758292 0.651915i 0.773966π-0.773966\pi
−0.758292 + 0.651915i 0.773966π0.773966\pi
812812 28.2161 + 27.0043i 0.990192 + 0.947667i
813813 23.9063i 0.838432i
814814 −35.3315 + 2.29258i −1.23837 + 0.0803550i
815815 0 0
816816 −39.8845 10.7987i −1.39624 0.378031i
817817 −10.2182 + 17.6984i −0.357489 + 0.619189i
818818 19.3095 12.8840i 0.675142 0.450478i
819819 −49.6503 + 7.71460i −1.73492 + 0.269570i
820820 0 0
821821 4.56478 7.90644i 0.159312 0.275937i −0.775309 0.631582i 0.782406π-0.782406\pi
0.934621 + 0.355646i 0.115739π0.115739\pi
822822 −18.0538 + 36.5493i −0.629698 + 1.27480i
823823 −0.190193 0.329424i −0.00662972 0.0114830i 0.862692 0.505731i 0.168777π-0.168777\pi
−0.869321 + 0.494248i 0.835444π0.835444\pi
824824 30.5616 + 10.4411i 1.06467 + 0.363732i
825825 0 0
826826 −7.98985 + 25.4094i −0.278003 + 0.884106i
827827 −23.9044 −0.831236 −0.415618 0.909539i 0.636435π-0.636435\pi
−0.415618 + 0.909539i 0.636435π0.636435\pi
828828 −19.3725 25.3152i −0.673243 0.879763i
829829 −35.8241 + 20.6830i −1.24422 + 0.718352i −0.969951 0.243301i 0.921770π-0.921770\pi
−0.274271 + 0.961653i 0.588436π0.588436\pi
830830 0 0
831831 −20.3800 + 35.2992i −0.706974 + 1.22452i
832832 −23.4755 + 9.61631i −0.813866 + 0.333386i
833833 22.9814 7.31833i 0.796259 0.253565i
834834 26.4434 17.6439i 0.915659 0.610959i
835835 0 0
836836 −1.18640 9.10347i −0.0410327 0.314850i
837837 37.9642 21.9187i 1.31224 0.757620i
838838 16.7451 1.08655i 0.578448 0.0375343i
839839 46.4174 1.60251 0.801253 0.598326i 0.204167π-0.204167\pi
0.801253 + 0.598326i 0.204167π0.204167\pi
840840 0 0
841841 25.4780 0.878551
842842 −14.5969 + 0.947163i −0.503043 + 0.0326414i
843843 24.6219 14.2155i 0.848025 0.489607i
844844 0.958861 + 7.35749i 0.0330054 + 0.253255i
845845 0 0
846846 43.1651 28.8013i 1.48405 0.990208i
847847 −15.6804 + 2.43641i −0.538786 + 0.0837159i
848848 −13.2085 + 13.1397i −0.453582 + 0.451219i
849849 32.3038 55.9518i 1.10866 1.92026i
850850 0 0
851851 25.7996 14.8954i 0.884398 0.510608i
852852 −0.773811 1.01118i −0.0265103 0.0346425i
853853 10.5928 0.362692 0.181346 0.983419i 0.441955π-0.441955\pi
0.181346 + 0.983419i 0.441955π0.441955\pi
854854 2.06149 + 9.26471i 0.0705427 + 0.317032i
855855 0 0
856856 −2.38101 + 6.96937i −0.0813814 + 0.238208i
857857 −0.141688 0.245410i −0.00483996 0.00838305i 0.863595 0.504186i 0.168207π-0.168207\pi
−0.868435 + 0.495803i 0.834874π0.834874\pi
858858 13.3180 26.9618i 0.454669 0.920461i
859859 4.93861 8.55393i 0.168503 0.291856i −0.769391 0.638779i 0.779440π-0.779440\pi
0.937894 + 0.346922i 0.112773π0.112773\pi
860860 0 0
861861 4.18236 10.8006i 0.142535 0.368084i
862862 −34.8883 + 23.2787i −1.18830 + 0.792875i
863863 −16.2817 + 28.2007i −0.554235 + 0.959963i 0.443728 + 0.896162i 0.353656π0.353656\pi
−0.997963 + 0.0638012i 0.979678π0.979678\pi
864864 16.1374 + 48.0541i 0.549006 + 1.63483i
865865 0 0
866866 −41.5057 + 2.69321i −1.41042 + 0.0915192i
867867 15.3759i 0.522195i
868868 −6.14961 + 25.1449i −0.208731 + 0.853473i
869869 1.03151 0.0349916
870870 0 0
871871 −0.0836685 0.144918i −0.00283500 0.00491036i
872872 −1.86426 2.13420i −0.0631319 0.0722732i
873873 −0.555343 + 0.961883i −0.0187955 + 0.0325548i
874874 4.28733 + 6.42551i 0.145021 + 0.217346i
875875 0 0
876876 82.3573 + 34.2396i 2.78260 + 1.15685i
877877 −32.9700 19.0353i −1.11332 0.642775i −0.173632 0.984811i 0.555550π-0.555550\pi
−0.939687 + 0.342036i 0.888884π0.888884\pi
878878 −5.52652 + 11.1883i −0.186511 + 0.377585i
879879 −75.1666 + 43.3975i −2.53531 + 1.46376i
880880 0 0
881881 27.7529i 0.935019i −0.883988 0.467509i 0.845151π-0.845151\pi
0.883988 0.467509i 0.154849π-0.154849\pi
882882 −46.3186 37.0068i −1.55963 1.24608i
883883 −44.1707 −1.48646 −0.743232 0.669034i 0.766708π-0.766708\pi
−0.743232 + 0.669034i 0.766708π0.766708\pi
884884 13.2800 + 17.3537i 0.446656 + 0.583669i
885885 0 0
886886 −12.2551 + 24.8100i −0.411717 + 0.833508i
887887 −17.4310 10.0638i −0.585275 0.337909i 0.177952 0.984039i 0.443053π-0.443053\pi
−0.763227 + 0.646130i 0.776386π0.776386\pi
888888 −93.1358 + 18.3363i −3.12543 + 0.615326i
889889 −5.01611 6.23167i −0.168235 0.209003i
890890 0 0
891891 −17.2385 9.95263i −0.577510 0.333426i
892892 −3.34919 25.6988i −0.112139 0.860461i
893893 −10.8898 + 6.28724i −0.364414 + 0.210394i
894894 1.78493 + 27.5079i 0.0596968 + 0.920000i
895895 0 0
896896 −27.0889 12.7355i −0.904976 0.425462i
897897 25.3027i 0.844831i
898898 7.08882 0.459978i 0.236557 0.0153497i
899899 18.0537 + 31.2699i 0.602124 + 1.04291i
900900 0 0
901901 13.8983 + 8.02418i 0.463019 + 0.267324i
902902 2.56329 + 3.84167i 0.0853483 + 0.127913i
903903 −73.6569 28.5224i −2.45115 0.949167i
904904 8.11832 + 41.2355i 0.270011 + 1.37147i
905905 0 0
906906 44.4561 90.0000i 1.47696 2.99005i
907907 7.50854 + 13.0052i 0.249317 + 0.431830i 0.963336 0.268296i 0.0864606π-0.0864606\pi
−0.714020 + 0.700126i 0.753127π0.753127\pi
908908 −14.1240 + 10.8084i −0.468720 + 0.358690i
909909 37.4239i 1.24127i
910910 0 0
911911 24.0198i 0.795811i 0.917426 + 0.397906i 0.130263π0.130263\pi
−0.917426 + 0.397906i 0.869737π0.869737\pi
912912 −6.30821 23.7909i −0.208886 0.787795i
913913 12.2087 + 21.1461i 0.404049 + 0.699834i
914914 −35.3063 17.4398i −1.16783 0.576857i
915915 0 0
916916 23.9076 + 9.93946i 0.789931 + 0.328409i
917917 −41.0597 + 6.37981i −1.35591 + 0.210680i
918918 36.3214 24.2349i 1.19878 0.799871i
919919 −49.7575 28.7275i −1.64135 0.947632i −0.980355 0.197239i 0.936802π-0.936802\pi
−0.660992 0.750393i 0.729864π-0.729864\pi
920920 0 0
921921 12.0014 + 20.7870i 0.395459 + 0.684956i
922922 1.81767 + 28.0124i 0.0598617 + 0.922541i
923923 0.673370i 0.0221643i
924924 34.0637 9.93325i 1.12061 0.326780i
925925 0 0
926926 −50.3981 + 3.27022i −1.65618 + 0.107466i
927927 −59.2214 + 34.1915i −1.94509 + 1.12300i
928928 −39.5806 + 13.2919i −1.29930 + 0.436327i
929929 −3.45964 1.99743i −0.113507 0.0655334i 0.442172 0.896930i 0.354208π-0.354208\pi
−0.555679 + 0.831397i 0.687542π0.687542\pi
930930 0 0
931931 10.6198 + 9.67552i 0.348049 + 0.317102i
932932 −28.1006 11.6827i −0.920466 0.382678i
933933 −35.7083 20.6162i −1.16904 0.674945i
934934 28.6700 + 14.1617i 0.938110 + 0.463386i
935935 0 0
936936 17.3658 50.8307i 0.567619 1.66145i
937937 43.2204 1.41195 0.705975 0.708237i 0.250509π-0.250509\pi
0.705975 + 0.708237i 0.250509π0.250509\pi
938938 0.0592267 0.188353i 0.00193382 0.00614995i
939939 31.8878i 1.04062i
940940 0 0
941941 −30.6731 + 17.7091i −0.999915 + 0.577301i −0.908223 0.418486i 0.862561π-0.862561\pi
−0.0916918 + 0.995787i 0.529227π0.529227\pi
942942 −29.7754 14.7078i −0.970136 0.479206i
943943 −3.36529 1.94295i −0.109589 0.0632712i
944944 −20.0823 20.1874i −0.653622 0.657044i
945945 0 0
946946 26.1990 17.4809i 0.851802 0.568352i
947947 24.3466 42.1696i 0.791159 1.37033i −0.134091 0.990969i 0.542812π-0.542812\pi
0.925250 0.379358i 0.123855π-0.123855\pi
948948 2.74231 0.357390i 0.0890662 0.0116075i
949949 −23.5840 40.8488i −0.765571 1.32601i
950950 0 0
951951 50.9190 1.65116
952952 −4.49073 + 25.3897i −0.145546 + 0.822886i
953953 47.5308i 1.53967i 0.638241 + 0.769837i 0.279662π0.279662\pi
−0.638241 + 0.769837i 0.720338π0.720338\pi
954954 −2.55440 39.3663i −0.0827016 1.27453i
955955 0 0
956956 0.0113339 + 0.0869671i 0.000366566 + 0.00281272i
957957 24.7466 42.8623i 0.799943 1.38554i
958958 6.72211 + 10.0746i 0.217182 + 0.325495i
959959 23.7208 + 9.18550i 0.765986 + 0.296615i
960960 0 0
961961 3.53423 6.12147i 0.114008 0.197467i
962962 45.0082 + 22.2321i 1.45112 + 0.716792i
963963 −7.79713 13.5050i −0.251259 0.435193i
964964 3.65400 2.79624i 0.117688 0.0900609i
965965 0 0
966966 −21.9960 + 20.1870i −0.707708 + 0.649508i
967967 −29.3643 −0.944292 −0.472146 0.881520i 0.656521π-0.656521\pi
−0.472146 + 0.881520i 0.656521π0.656521\pi
968968 5.48442 16.0532i 0.176276 0.515970i
969969 −18.3607 + 10.6005i −0.589829 + 0.340538i
970970 0 0
971971 −13.3188 + 23.0688i −0.427419 + 0.740312i −0.996643 0.0818708i 0.973911π-0.973911\pi
0.569224 + 0.822183i 0.307244π0.307244\pi
972972 0.369231 + 0.153506i 0.0118431 + 0.00492370i
973973 −12.4382 15.4523i −0.398749 0.495379i
974974 24.8391 + 37.2269i 0.795895 + 1.19283i
975975 0 0
976976 −9.79398 2.65172i −0.313498 0.0848795i
977977 13.3970 7.73476i 0.428608 0.247457i −0.270146 0.962819i 0.587072π-0.587072\pi
0.698753 + 0.715363i 0.253739π0.253739\pi
978978 2.97928 + 45.9143i 0.0952668 + 1.46818i
979979 −15.7018 −0.501832
980980 0 0
981981 6.00019 0.191571
982982 3.27629 + 50.4916i 0.104551 + 1.61125i
983983 −38.1277 + 22.0131i −1.21609 + 0.702107i −0.964078 0.265618i 0.914424π-0.914424\pi
−0.252007 + 0.967725i 0.581091π0.581091\pi
984984 8.14565 + 9.32511i 0.259674 + 0.297274i
985985 0 0
986986 19.9615 + 29.9167i 0.635703 + 0.952743i
987987 −30.4743 37.8591i −0.970006 1.20507i
988988 −4.99686 + 12.0191i −0.158971 + 0.382378i
989989 −13.2503 + 22.9502i −0.421336 + 0.729775i
990990 0 0
991991 14.4776 8.35865i 0.459896 0.265521i −0.252104 0.967700i 0.581123π-0.581123\pi
0.712001 + 0.702179i 0.247789π0.247789\pi
992992 −20.7462 18.3141i −0.658692 0.581472i
993993 −24.9751 −0.792560
994994 −0.585370 + 0.537230i −0.0185668 + 0.0170399i
995995 0 0
996996 39.7839 + 51.9877i 1.26060 + 1.64729i
997997 13.7897 + 23.8844i 0.436723 + 0.756427i 0.997435 0.0715845i 0.0228056π-0.0228056\pi
−0.560711 + 0.828011i 0.689472π0.689472\pi
998998 52.3856 + 25.8762i 1.65824 + 0.819098i
999999 50.1540 86.8693i 1.58680 2.74842i
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 700.2.t.d.299.1 32
4.3 odd 2 inner 700.2.t.d.299.6 32
5.2 odd 4 700.2.p.c.551.9 32
5.3 odd 4 140.2.o.a.131.8 yes 32
5.4 even 2 700.2.t.c.299.16 32
7.3 odd 6 700.2.t.c.199.11 32
20.3 even 4 140.2.o.a.131.3 yes 32
20.7 even 4 700.2.p.c.551.14 32
20.19 odd 2 700.2.t.c.299.11 32
28.3 even 6 700.2.t.c.199.16 32
35.3 even 12 140.2.o.a.31.3 32
35.13 even 4 980.2.o.f.411.8 32
35.17 even 12 700.2.p.c.451.14 32
35.18 odd 12 980.2.o.f.31.3 32
35.23 odd 12 980.2.g.a.391.25 32
35.24 odd 6 inner 700.2.t.d.199.6 32
35.33 even 12 980.2.g.a.391.26 32
140.3 odd 12 140.2.o.a.31.8 yes 32
140.23 even 12 980.2.g.a.391.28 32
140.59 even 6 inner 700.2.t.d.199.1 32
140.83 odd 4 980.2.o.f.411.3 32
140.87 odd 12 700.2.p.c.451.9 32
140.103 odd 12 980.2.g.a.391.27 32
140.123 even 12 980.2.o.f.31.8 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
140.2.o.a.31.3 32 35.3 even 12
140.2.o.a.31.8 yes 32 140.3 odd 12
140.2.o.a.131.3 yes 32 20.3 even 4
140.2.o.a.131.8 yes 32 5.3 odd 4
700.2.p.c.451.9 32 140.87 odd 12
700.2.p.c.451.14 32 35.17 even 12
700.2.p.c.551.9 32 5.2 odd 4
700.2.p.c.551.14 32 20.7 even 4
700.2.t.c.199.11 32 7.3 odd 6
700.2.t.c.199.16 32 28.3 even 6
700.2.t.c.299.11 32 20.19 odd 2
700.2.t.c.299.16 32 5.4 even 2
700.2.t.d.199.1 32 140.59 even 6 inner
700.2.t.d.199.6 32 35.24 odd 6 inner
700.2.t.d.299.1 32 1.1 even 1 trivial
700.2.t.d.299.6 32 4.3 odd 2 inner
980.2.g.a.391.25 32 35.23 odd 12
980.2.g.a.391.26 32 35.33 even 12
980.2.g.a.391.27 32 140.103 odd 12
980.2.g.a.391.28 32 140.23 even 12
980.2.o.f.31.3 32 35.18 odd 12
980.2.o.f.31.8 32 140.123 even 12
980.2.o.f.411.3 32 140.83 odd 4
980.2.o.f.411.8 32 35.13 even 4