Properties

Label 325.2.n.b.101.2
Level 325325
Weight 22
Character 325.101
Analytic conductor 2.5952.595
Analytic rank 00
Dimension 44
Inner twists 22

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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] = [325,2,Mod(101,325)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(325, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) 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("325.101"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 325=5213 325 = 5^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 325.n (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,-3,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.595138065692.59513806569
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(3,7)\Q(\sqrt{-3}, \sqrt{-7})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4x3x22x+4 x^{4} - x^{3} - x^{2} - 2x + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 65)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 101.2
Root 1.39564+0.228425i1.39564 + 0.228425i of defining polynomial
Character χ\chi == 325.101
Dual form 325.2.n.b.251.2

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+(0.3956440.228425i)q2+(0.500000+0.866025i)q3+(0.895644+1.55130i)q4+(0.395644+0.228425i)q6+(1.50000+0.866025i)q7+1.73205iq8+(1.000001.73205i)q9+(2.29129+1.32288i)q111.79129q12+(1.00000+3.46410i)q13+0.791288q14+(1.395642.41733i)q16+(2.29129+3.96863i)q170.913701iq18+(1.50000+0.866025i)q19+1.73205iq21+(0.604356+1.04678i)q22+(2.29129+3.96863i)q23+(1.50000+0.866025i)q24+(1.18693+1.14213i)q26+5.00000q27+(2.68693+1.55130i)q28+(2.291293.96863i)q296.20520iq31+(4.104362.36965i)q32+(2.291291.32288i)q33+2.09355iq34+(1.79129+3.10260i)q36+(6.873863.96863i)q37+0.791288q38+(2.50000+2.59808i)q39+(2.291291.32288i)q41+(0.395644+0.685275i)q42+(5.291299.16478i)q434.73930iq44+(1.81307+1.04678i)q461.82740iq47+(1.395642.41733i)q48+(2.000003.46410i)q494.58258q51+(6.269511.55130i)q527.58258q53+(1.978221.14213i)q54+(1.50000+2.59808i)q56+1.73205iq57+(1.813071.04678i)q58+(12.0826+6.97588i)q59+(0.7087121.22753i)q61+(1.417422.45505i)q62+(3.000001.73205i)q63+3.41742q641.20871q66+(0.873864+0.504525i)q67+(4.104367.10895i)q68+(2.29129+3.96863i)q69+(6.08258+3.51178i)q71+(3.00000+1.73205i)q72+(1.813073.14033i)q74+(2.68693+1.55130i)q764.58258q77+(0.395644+1.59898i)q786.00000q79+(0.5000000.866025i)q81+(0.6043561.04678i)q826.01450iq83+(2.686931.55130i)q844.83465iq86+(2.291293.96863i)q87+(2.291293.96863i)q88+(8.29129+4.78698i)q89+(1.50000+6.06218i)q918.20871q92+(5.373863.10260i)q93+(0.4174240.723000i)q944.73930iq96+(9.87386+5.70068i)q97+(1.582580.913701i)q98+5.29150iq99+O(q100)q+(0.395644 - 0.228425i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.895644 + 1.55130i) q^{4} +(0.395644 + 0.228425i) q^{6} +(1.50000 + 0.866025i) q^{7} +1.73205i q^{8} +(1.00000 - 1.73205i) q^{9} +(-2.29129 + 1.32288i) q^{11} -1.79129 q^{12} +(1.00000 + 3.46410i) q^{13} +0.791288 q^{14} +(-1.39564 - 2.41733i) q^{16} +(-2.29129 + 3.96863i) q^{17} -0.913701i q^{18} +(1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(-0.604356 + 1.04678i) q^{22} +(2.29129 + 3.96863i) q^{23} +(-1.50000 + 0.866025i) q^{24} +(1.18693 + 1.14213i) q^{26} +5.00000 q^{27} +(-2.68693 + 1.55130i) q^{28} +(-2.29129 - 3.96863i) q^{29} -6.20520i q^{31} +(-4.10436 - 2.36965i) q^{32} +(-2.29129 - 1.32288i) q^{33} +2.09355i q^{34} +(1.79129 + 3.10260i) q^{36} +(6.87386 - 3.96863i) q^{37} +0.791288 q^{38} +(-2.50000 + 2.59808i) q^{39} +(2.29129 - 1.32288i) q^{41} +(0.395644 + 0.685275i) q^{42} +(5.29129 - 9.16478i) q^{43} -4.73930i q^{44} +(1.81307 + 1.04678i) q^{46} -1.82740i q^{47} +(1.39564 - 2.41733i) q^{48} +(-2.00000 - 3.46410i) q^{49} -4.58258 q^{51} +(-6.26951 - 1.55130i) q^{52} -7.58258 q^{53} +(1.97822 - 1.14213i) q^{54} +(-1.50000 + 2.59808i) q^{56} +1.73205i q^{57} +(-1.81307 - 1.04678i) q^{58} +(12.0826 + 6.97588i) q^{59} +(0.708712 - 1.22753i) q^{61} +(-1.41742 - 2.45505i) q^{62} +(3.00000 - 1.73205i) q^{63} +3.41742 q^{64} -1.20871 q^{66} +(-0.873864 + 0.504525i) q^{67} +(-4.10436 - 7.10895i) q^{68} +(-2.29129 + 3.96863i) q^{69} +(6.08258 + 3.51178i) q^{71} +(3.00000 + 1.73205i) q^{72} +(1.81307 - 3.14033i) q^{74} +(-2.68693 + 1.55130i) q^{76} -4.58258 q^{77} +(-0.395644 + 1.59898i) q^{78} -6.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.604356 - 1.04678i) q^{82} -6.01450i q^{83} +(-2.68693 - 1.55130i) q^{84} -4.83465i q^{86} +(2.29129 - 3.96863i) q^{87} +(-2.29129 - 3.96863i) q^{88} +(-8.29129 + 4.78698i) q^{89} +(-1.50000 + 6.06218i) q^{91} -8.20871 q^{92} +(5.37386 - 3.10260i) q^{93} +(-0.417424 - 0.723000i) q^{94} -4.73930i q^{96} +(9.87386 + 5.70068i) q^{97} +(-1.58258 - 0.913701i) q^{98} +5.29150i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q3q2+2q3+q43q6+6q7+4q9+2q12+4q136q14q16+6q197q226q249q26+20q27+3q2821q322q366q38++12q98+O(q100) 4 q - 3 q^{2} + 2 q^{3} + q^{4} - 3 q^{6} + 6 q^{7} + 4 q^{9} + 2 q^{12} + 4 q^{13} - 6 q^{14} - q^{16} + 6 q^{19} - 7 q^{22} - 6 q^{24} - 9 q^{26} + 20 q^{27} + 3 q^{28} - 21 q^{32} - 2 q^{36} - 6 q^{38}+ \cdots + 12 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/325Z)×\left(\mathbb{Z}/325\mathbb{Z}\right)^\times.

nn 2727 301301
χ(n)\chi(n) 11 e(56)e\left(\frac{5}{6}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.395644 0.228425i 0.279763 0.161521i −0.353553 0.935414i 0.615027π-0.615027\pi
0.633316 + 0.773893i 0.281693π0.281693\pi
33 0.500000 + 0.866025i 0.288675 + 0.500000i 0.973494 0.228714i 0.0734519π-0.0734519\pi
−0.684819 + 0.728714i 0.740119π0.740119\pi
44 −0.895644 + 1.55130i −0.447822 + 0.775650i
55 0 0
66 0.395644 + 0.228425i 0.161521 + 0.0932542i
77 1.50000 + 0.866025i 0.566947 + 0.327327i 0.755929 0.654654i 0.227186π-0.227186\pi
−0.188982 + 0.981981i 0.560519π0.560519\pi
88 1.73205i 0.612372i
99 1.00000 1.73205i 0.333333 0.577350i
1010 0 0
1111 −2.29129 + 1.32288i −0.690849 + 0.398862i −0.803930 0.594724i 0.797261π-0.797261\pi
0.113081 + 0.993586i 0.463928π0.463928\pi
1212 −1.79129 −0.517100
1313 1.00000 + 3.46410i 0.277350 + 0.960769i
1414 0.791288 0.211481
1515 0 0
1616 −1.39564 2.41733i −0.348911 0.604332i
1717 −2.29129 + 3.96863i −0.555719 + 0.962533i 0.442128 + 0.896952i 0.354224π0.354224\pi
−0.997847 + 0.0655816i 0.979110π0.979110\pi
1818 0.913701i 0.215361i
1919 1.50000 + 0.866025i 0.344124 + 0.198680i 0.662094 0.749421i 0.269668π-0.269668\pi
−0.317970 + 0.948101i 0.603001π0.603001\pi
2020 0 0
2121 1.73205i 0.377964i
2222 −0.604356 + 1.04678i −0.128849 + 0.223173i
2323 2.29129 + 3.96863i 0.477767 + 0.827516i 0.999675 0.0254855i 0.00811315π-0.00811315\pi
−0.521909 + 0.853001i 0.674780π0.674780\pi
2424 −1.50000 + 0.866025i −0.306186 + 0.176777i
2525 0 0
2626 1.18693 + 1.14213i 0.232776 + 0.223989i
2727 5.00000 0.962250
2828 −2.68693 + 1.55130i −0.507782 + 0.293168i
2929 −2.29129 3.96863i −0.425481 0.736956i 0.570984 0.820961i 0.306562π-0.306562\pi
−0.996465 + 0.0840058i 0.973229π0.973229\pi
3030 0 0
3131 6.20520i 1.11449i −0.830349 0.557244i 0.811859π-0.811859\pi
0.830349 0.557244i 0.188141π-0.188141\pi
3232 −4.10436 2.36965i −0.725555 0.418899i
3333 −2.29129 1.32288i −0.398862 0.230283i
3434 2.09355i 0.359041i
3535 0 0
3636 1.79129 + 3.10260i 0.298548 + 0.517100i
3737 6.87386 3.96863i 1.13006 0.652438i 0.186107 0.982529i 0.440413π-0.440413\pi
0.943949 + 0.330091i 0.107080π0.107080\pi
3838 0.791288 0.128364
3939 −2.50000 + 2.59808i −0.400320 + 0.416025i
4040 0 0
4141 2.29129 1.32288i 0.357839 0.206598i −0.310293 0.950641i 0.600427π-0.600427\pi
0.668132 + 0.744042i 0.267094π0.267094\pi
4242 0.395644 + 0.685275i 0.0610492 + 0.105740i
4343 5.29129 9.16478i 0.806914 1.39762i −0.108078 0.994142i 0.534469π-0.534469\pi
0.914991 0.403473i 0.132197π-0.132197\pi
4444 4.73930i 0.714477i
4545 0 0
4646 1.81307 + 1.04678i 0.267322 + 0.154339i
4747 1.82740i 0.266554i −0.991079 0.133277i 0.957450π-0.957450\pi
0.991079 0.133277i 0.0425500π-0.0425500\pi
4848 1.39564 2.41733i 0.201444 0.348911i
4949 −2.00000 3.46410i −0.285714 0.494872i
5050 0 0
5151 −4.58258 −0.641689
5252 −6.26951 1.55130i −0.869424 0.215127i
5353 −7.58258 −1.04155 −0.520773 0.853695i 0.674356π-0.674356\pi
−0.520773 + 0.853695i 0.674356π0.674356\pi
5454 1.97822 1.14213i 0.269202 0.155424i
5555 0 0
5656 −1.50000 + 2.59808i −0.200446 + 0.347183i
5757 1.73205i 0.229416i
5858 −1.81307 1.04678i −0.238068 0.137448i
5959 12.0826 + 6.97588i 1.57302 + 0.908182i 0.995796 + 0.0915940i 0.0291962π0.0291962\pi
0.577221 + 0.816588i 0.304137π0.304137\pi
6060 0 0
6161 0.708712 1.22753i 0.0907413 0.157169i −0.817082 0.576522i 0.804410π-0.804410\pi
0.907823 + 0.419353i 0.137743π0.137743\pi
6262 −1.41742 2.45505i −0.180013 0.311792i
6363 3.00000 1.73205i 0.377964 0.218218i
6464 3.41742 0.427178
6565 0 0
6666 −1.20871 −0.148782
6767 −0.873864 + 0.504525i −0.106759 + 0.0616376i −0.552429 0.833560i 0.686299π-0.686299\pi
0.445670 + 0.895198i 0.352966π0.352966\pi
6868 −4.10436 7.10895i −0.497726 0.862087i
6969 −2.29129 + 3.96863i −0.275839 + 0.477767i
7070 0 0
7171 6.08258 + 3.51178i 0.721869 + 0.416771i 0.815440 0.578841i 0.196495π-0.196495\pi
−0.0935712 + 0.995613i 0.529828π0.529828\pi
7272 3.00000 + 1.73205i 0.353553 + 0.204124i
7373 0 0 1.00000 00
−1.00000 π\pi
7474 1.81307 3.14033i 0.210765 0.365056i
7575 0 0
7676 −2.68693 + 1.55130i −0.308212 + 0.177946i
7777 −4.58258 −0.522233
7878 −0.395644 + 1.59898i −0.0447979 + 0.181048i
7979 −6.00000 −0.675053 −0.337526 0.941316i 0.609590π-0.609590\pi
−0.337526 + 0.941316i 0.609590π0.609590\pi
8080 0 0
8181 −0.500000 0.866025i −0.0555556 0.0962250i
8282 0.604356 1.04678i 0.0667400 0.115597i
8383 6.01450i 0.660177i −0.943950 0.330089i 0.892921π-0.892921\pi
0.943950 0.330089i 0.107079π-0.107079\pi
8484 −2.68693 1.55130i −0.293168 0.169261i
8585 0 0
8686 4.83465i 0.521334i
8787 2.29129 3.96863i 0.245652 0.425481i
8888 −2.29129 3.96863i −0.244252 0.423057i
8989 −8.29129 + 4.78698i −0.878875 + 0.507419i −0.870287 0.492545i 0.836067π-0.836067\pi
−0.00858752 + 0.999963i 0.502734π0.502734\pi
9090 0 0
9191 −1.50000 + 6.06218i −0.157243 + 0.635489i
9292 −8.20871 −0.855817
9393 5.37386 3.10260i 0.557244 0.321725i
9494 −0.417424 0.723000i −0.0430540 0.0745718i
9595 0 0
9696 4.73930i 0.483703i
9797 9.87386 + 5.70068i 1.00254 + 0.578816i 0.908999 0.416799i 0.136848π-0.136848\pi
0.0935404 + 0.995615i 0.470182π0.470182\pi
9898 −1.58258 0.913701i −0.159864 0.0922977i
9999 5.29150i 0.531816i
100100 0 0
101101 −4.50000 7.79423i −0.447767 0.775555i 0.550474 0.834853i 0.314447π-0.314447\pi
−0.998240 + 0.0592978i 0.981114π0.981114\pi
102102 −1.81307 + 1.04678i −0.179521 + 0.103646i
103103 −3.16515 −0.311872 −0.155936 0.987767i 0.549839π-0.549839\pi
−0.155936 + 0.987767i 0.549839π0.549839\pi
104104 −6.00000 + 1.73205i −0.588348 + 0.169842i
105105 0 0
106106 −3.00000 + 1.73205i −0.291386 + 0.168232i
107107 −5.29129 9.16478i −0.511528 0.885993i −0.999911 0.0133631i 0.995746π-0.995746\pi
0.488383 0.872630i 0.337587π-0.337587\pi
108108 −4.47822 + 7.75650i −0.430917 + 0.746370i
109109 13.1334i 1.25795i −0.777425 0.628976i 0.783474π-0.783474\pi
0.777425 0.628976i 0.216526π-0.216526\pi
110110 0 0
111111 6.87386 + 3.96863i 0.652438 + 0.376685i
112112 4.83465i 0.456832i
113113 −3.70871 + 6.42368i −0.348886 + 0.604289i −0.986052 0.166438i 0.946773π-0.946773\pi
0.637166 + 0.770727i 0.280107π0.280107\pi
114114 0.395644 + 0.685275i 0.0370554 + 0.0641819i
115115 0 0
116116 8.20871 0.762160
117117 7.00000 + 1.73205i 0.647150 + 0.160128i
118118 6.37386 0.586762
119119 −6.87386 + 3.96863i −0.630126 + 0.363803i
120120 0 0
121121 −2.00000 + 3.46410i −0.181818 + 0.314918i
122122 0.647551i 0.0586265i
123123 2.29129 + 1.32288i 0.206598 + 0.119280i
124124 9.62614 + 5.55765i 0.864453 + 0.499092i
125125 0 0
126126 0.791288 1.37055i 0.0704935 0.122098i
127127 8.87386 + 15.3700i 0.787428 + 1.36387i 0.927538 + 0.373729i 0.121921π0.121921\pi
−0.140110 + 0.990136i 0.544746π0.544746\pi
128128 9.56080 5.51993i 0.845063 0.487897i
129129 10.5826 0.931744
130130 0 0
131131 −7.58258 −0.662493 −0.331246 0.943544i 0.607469π-0.607469\pi
−0.331246 + 0.943544i 0.607469π0.607469\pi
132132 4.10436 2.36965i 0.357238 0.206252i
133133 1.50000 + 2.59808i 0.130066 + 0.225282i
134134 −0.230493 + 0.399225i −0.0199115 + 0.0344878i
135135 0 0
136136 −6.87386 3.96863i −0.589429 0.340307i
137137 −9.08258 5.24383i −0.775977 0.448010i 0.0590258 0.998256i 0.481201π-0.481201\pi
−0.835003 + 0.550246i 0.814534π0.814534\pi
138138 2.09355i 0.178215i
139139 10.8739 18.8341i 0.922309 1.59749i 0.126476 0.991970i 0.459633π-0.459633\pi
0.795833 0.605517i 0.207033π-0.207033\pi
140140 0 0
141141 1.58258 0.913701i 0.133277 0.0769475i
142142 3.20871 0.269269
143143 −6.87386 6.61438i −0.574821 0.553122i
144144 −5.58258 −0.465215
145145 0 0
146146 0 0
147147 2.00000 3.46410i 0.164957 0.285714i
148148 14.2179i 1.16870i
149149 14.4564 + 8.34643i 1.18432 + 0.683766i 0.957009 0.290057i 0.0936742π-0.0936742\pi
0.227308 + 0.973823i 0.427008π0.427008\pi
150150 0 0
151151 9.66930i 0.786877i 0.919351 + 0.393438i 0.128715π0.128715\pi
−0.919351 + 0.393438i 0.871285π0.871285\pi
152152 −1.50000 + 2.59808i −0.121666 + 0.210732i
153153 4.58258 + 7.93725i 0.370479 + 0.641689i
154154 −1.81307 + 1.04678i −0.146101 + 0.0843516i
155155 0 0
156156 −1.79129 6.20520i −0.143418 0.496814i
157157 −9.16515 −0.731459 −0.365729 0.930721i 0.619180π-0.619180\pi
−0.365729 + 0.930721i 0.619180π0.619180\pi
158158 −2.37386 + 1.37055i −0.188854 + 0.109035i
159159 −3.79129 6.56670i −0.300669 0.520773i
160160 0 0
161161 7.93725i 0.625543i
162162 −0.395644 0.228425i −0.0310847 0.0179468i
163163 18.2477 + 10.5353i 1.42927 + 0.825191i 0.997063 0.0765827i 0.0244009π-0.0244009\pi
0.432209 + 0.901773i 0.357734π0.357734\pi
164164 4.73930i 0.370077i
165165 0 0
166166 −1.37386 2.37960i −0.106632 0.184693i
167167 −8.29129 + 4.78698i −0.641599 + 0.370427i −0.785230 0.619204i 0.787455π-0.787455\pi
0.143631 + 0.989631i 0.454122π0.454122\pi
168168 −3.00000 −0.231455
169169 −11.0000 + 6.92820i −0.846154 + 0.532939i
170170 0 0
171171 3.00000 1.73205i 0.229416 0.132453i
172172 9.47822 + 16.4168i 0.722707 + 1.25177i
173173 −8.29129 + 14.3609i −0.630375 + 1.09184i 0.357100 + 0.934066i 0.383766π0.383766\pi
−0.987475 + 0.157775i 0.949568π0.949568\pi
174174 2.09355i 0.158712i
175175 0 0
176176 6.39564 + 3.69253i 0.482090 + 0.278335i
177177 13.9518i 1.04868i
178178 −2.18693 + 3.78788i −0.163917 + 0.283913i
179179 −9.08258 15.7315i −0.678864 1.17583i −0.975323 0.220781i 0.929139π-0.929139\pi
0.296460 0.955045i 0.404194π-0.404194\pi
180180 0 0
181181 8.74773 0.650213 0.325107 0.945677i 0.394600π-0.394600\pi
0.325107 + 0.945677i 0.394600π0.394600\pi
182182 0.791288 + 2.74110i 0.0586542 + 0.203184i
183183 1.41742 0.104779
184184 −6.87386 + 3.96863i −0.506748 + 0.292571i
185185 0 0
186186 1.41742 2.45505i 0.103931 0.180013i
187187 12.1244i 0.886621i
188188 2.83485 + 1.63670i 0.206753 + 0.119369i
189189 7.50000 + 4.33013i 0.545545 + 0.314970i
190190 0 0
191191 8.29129 14.3609i 0.599937 1.03912i −0.392893 0.919584i 0.628526π-0.628526\pi
0.992830 0.119536i 0.0381408π-0.0381408\pi
192192 1.70871 + 2.95958i 0.123316 + 0.213589i
193193 −12.8739 + 7.43273i −0.926681 + 0.535020i −0.885760 0.464143i 0.846362π-0.846362\pi
−0.0409206 + 0.999162i 0.513029π0.513029\pi
194194 5.20871 0.373964
195195 0 0
196196 7.16515 0.511797
197197 −12.7087 + 7.33738i −0.905458 + 0.522767i −0.878967 0.476882i 0.841767π-0.841767\pi
−0.0264912 + 0.999649i 0.508433π0.508433\pi
198198 1.20871 + 2.09355i 0.0858994 + 0.148782i
199199 −5.29129 + 9.16478i −0.375089 + 0.649674i −0.990340 0.138657i 0.955721π-0.955721\pi
0.615251 + 0.788331i 0.289055π0.289055\pi
200200 0 0
201201 −0.873864 0.504525i −0.0616376 0.0355865i
202202 −3.56080 2.05583i −0.250537 0.144647i
203203 7.93725i 0.557086i
204204 4.10436 7.10895i 0.287362 0.497726i
205205 0 0
206206 −1.25227 + 0.723000i −0.0872500 + 0.0503738i
207207 9.16515 0.637022
208208 6.97822 7.25198i 0.483852 0.502834i
209209 −4.58258 −0.316983
210210 0 0
211211 0.0825757 + 0.143025i 0.00568475 + 0.00984627i 0.868854 0.495069i 0.164857π-0.164857\pi
−0.863169 + 0.504915i 0.831524π0.831524\pi
212212 6.79129 11.7629i 0.466428 0.807876i
213213 7.02355i 0.481246i
214214 −4.18693 2.41733i −0.286213 0.165245i
215215 0 0
216216 8.66025i 0.589256i
217217 5.37386 9.30780i 0.364802 0.631855i
218218 −3.00000 5.19615i −0.203186 0.351928i
219219 0 0
220220 0 0
221221 −16.0390 3.96863i −1.07890 0.266959i
222222 3.62614 0.243370
223223 7.50000 4.33013i 0.502237 0.289967i −0.227400 0.973801i 0.573022π-0.573022\pi
0.729637 + 0.683835i 0.239689π0.239689\pi
224224 −4.10436 7.10895i −0.274234 0.474987i
225225 0 0
226226 3.38865i 0.225410i
227227 −0.708712 0.409175i −0.0470389 0.0271579i 0.476296 0.879285i 0.341979π-0.341979\pi
−0.523335 + 0.852127i 0.675312π0.675312\pi
228228 −2.68693 1.55130i −0.177946 0.102737i
229229 26.2668i 1.73576i 0.496774 + 0.867880i 0.334518π0.334518\pi
−0.496774 + 0.867880i 0.665482π0.665482\pi
230230 0 0
231231 −2.29129 3.96863i −0.150756 0.261116i
232232 6.87386 3.96863i 0.451291 0.260553i
233233 −2.83485 −0.185717 −0.0928586 0.995679i 0.529600π-0.529600\pi
−0.0928586 + 0.995679i 0.529600π0.529600\pi
234234 3.16515 0.913701i 0.206912 0.0597305i
235235 0 0
236236 −21.6434 + 12.4958i −1.40886 + 0.813408i
237237 −3.00000 5.19615i −0.194871 0.337526i
238238 −1.81307 + 3.14033i −0.117524 + 0.203557i
239239 0.190700i 0.0123354i 0.999981 + 0.00616769i 0.00196325π0.00196325\pi
−0.999981 + 0.00616769i 0.998037π0.998037\pi
240240 0 0
241241 −1.50000 0.866025i −0.0966235 0.0557856i 0.450910 0.892570i 0.351100π-0.351100\pi
−0.547533 + 0.836784i 0.684433π0.684433\pi
242242 1.82740i 0.117470i
243243 8.00000 13.8564i 0.513200 0.888889i
244244 1.26951 + 2.19885i 0.0812719 + 0.140767i
245245 0 0
246246 1.20871 0.0770647
247247 −1.50000 + 6.06218i −0.0954427 + 0.385727i
248248 10.7477 0.682481
249249 5.20871 3.00725i 0.330089 0.190577i
250250 0 0
251251 0.0825757 0.143025i 0.00521213 0.00902768i −0.863408 0.504507i 0.831674π-0.831674\pi
0.868620 + 0.495479i 0.165008π0.165008\pi
252252 6.20520i 0.390891i
253253 −10.5000 6.06218i −0.660129 0.381126i
254254 7.02178 + 4.05403i 0.440586 + 0.254372i
255255 0 0
256256 −0.895644 + 1.55130i −0.0559777 + 0.0969563i
257257 −9.08258 15.7315i −0.566556 0.981303i −0.996903 0.0786397i 0.974942π-0.974942\pi
0.430348 0.902663i 0.358391π-0.358391\pi
258258 4.18693 2.41733i 0.260667 0.150496i
259259 13.7477 0.854242
260260 0 0
261261 −9.16515 −0.567309
262262 −3.00000 + 1.73205i −0.185341 + 0.107006i
263263 4.50000 + 7.79423i 0.277482 + 0.480613i 0.970758 0.240059i 0.0771668π-0.0771668\pi
−0.693276 + 0.720672i 0.743833π0.743833\pi
264264 2.29129 3.96863i 0.141019 0.244252i
265265 0 0
266266 1.18693 + 0.685275i 0.0727755 + 0.0420169i
267267 −8.29129 4.78698i −0.507419 0.292958i
268268 1.80750i 0.110411i
269269 7.50000 12.9904i 0.457283 0.792038i −0.541533 0.840679i 0.682156π-0.682156\pi
0.998816 + 0.0486418i 0.0154893π0.0154893\pi
270270 0 0
271271 7.50000 4.33013i 0.455593 0.263036i −0.254597 0.967047i 0.581943π-0.581943\pi
0.710189 + 0.704011i 0.248609π0.248609\pi
272272 12.7913 0.775586
273273 −6.00000 + 1.73205i −0.363137 + 0.104828i
274274 −4.79129 −0.289452
275275 0 0
276276 −4.10436 7.10895i −0.247053 0.427909i
277277 −3.70871 + 6.42368i −0.222835 + 0.385961i −0.955668 0.294447i 0.904864π-0.904864\pi
0.732833 + 0.680409i 0.238198π0.238198\pi
278278 9.93545i 0.595889i
279279 −10.7477 6.20520i −0.643450 0.371496i
280280 0 0
281281 3.65480i 0.218027i −0.994040 0.109014i 0.965231π-0.965231\pi
0.994040 0.109014i 0.0347692π-0.0347692\pi
282282 0.417424 0.723000i 0.0248573 0.0430540i
283283 −13.8739 24.0302i −0.824716 1.42845i −0.902136 0.431451i 0.858002π-0.858002\pi
0.0774209 0.996998i 0.475331π-0.475331\pi
284284 −10.8956 + 6.29060i −0.646538 + 0.373279i
285285 0 0
286286 −4.23049 1.04678i −0.250154 0.0618971i
287287 4.58258 0.270501
288288 −8.20871 + 4.73930i −0.483703 + 0.279266i
289289 −2.00000 3.46410i −0.117647 0.203771i
290290 0 0
291291 11.4014i 0.668359i
292292 0 0
293293 −15.7087 9.06943i −0.917713 0.529842i −0.0348081 0.999394i 0.511082π-0.511082\pi
−0.882905 + 0.469552i 0.844415π0.844415\pi
294294 1.82740i 0.106576i
295295 0 0
296296 6.87386 + 11.9059i 0.399535 + 0.692015i
297297 −11.4564 + 6.61438i −0.664770 + 0.383805i
298298 7.62614 0.441770
299299 −11.4564 + 11.9059i −0.662543 + 0.688535i
300300 0 0
301301 15.8739 9.16478i 0.914954 0.528249i
302302 2.20871 + 3.82560i 0.127097 + 0.220139i
303303 4.50000 7.79423i 0.258518 0.447767i
304304 4.83465i 0.277286i
305305 0 0
306306 3.62614 + 2.09355i 0.207292 + 0.119680i
307307 24.2487i 1.38395i −0.721923 0.691974i 0.756741π-0.756741\pi
0.721923 0.691974i 0.243259π-0.243259\pi
308308 4.10436 7.10895i 0.233867 0.405070i
309309 −1.58258 2.74110i −0.0900296 0.155936i
310310 0 0
311311 7.58258 0.429968 0.214984 0.976618i 0.431030π-0.431030\pi
0.214984 + 0.976618i 0.431030π0.431030\pi
312312 −4.50000 4.33013i −0.254762 0.245145i
313313 3.25227 0.183829 0.0919147 0.995767i 0.470701π-0.470701\pi
0.0919147 + 0.995767i 0.470701π0.470701\pi
314314 −3.62614 + 2.09355i −0.204635 + 0.118146i
315315 0 0
316316 5.37386 9.30780i 0.302303 0.523605i
317317 0.190700i 0.0107108i 0.999986 + 0.00535540i 0.00170469π0.00170469\pi
−0.999986 + 0.00535540i 0.998295π0.998295\pi
318318 −3.00000 1.73205i −0.168232 0.0971286i
319319 10.5000 + 6.06218i 0.587887 + 0.339417i
320320 0 0
321321 5.29129 9.16478i 0.295331 0.511528i
322322 1.81307 + 3.14033i 0.101038 + 0.175004i
323323 −6.87386 + 3.96863i −0.382472 + 0.220820i
324324 1.79129 0.0995160
325325 0 0
326326 9.62614 0.533142
327327 11.3739 6.56670i 0.628976 0.363140i
328328 2.29129 + 3.96863i 0.126515 + 0.219131i
329329 1.58258 2.74110i 0.0872502 0.151122i
330330 0 0
331331 −3.87386 2.23658i −0.212927 0.122933i 0.389744 0.920923i 0.372563π-0.372563\pi
−0.602671 + 0.797990i 0.705897π0.705897\pi
332332 9.33030 + 5.38685i 0.512067 + 0.295642i
333333 15.8745i 0.869918i
334334 −2.18693 + 3.78788i −0.119664 + 0.207263i
335335 0 0
336336 4.18693 2.41733i 0.228416 0.131876i
337337 −30.7477 −1.67494 −0.837468 0.546487i 0.815965π-0.815965\pi
−0.837468 + 0.546487i 0.815965π0.815965\pi
338338 −2.76951 + 5.25378i −0.150641 + 0.285768i
339339 −7.41742 −0.402859
340340 0 0
341341 8.20871 + 14.2179i 0.444527 + 0.769943i
342342 0.791288 1.37055i 0.0427879 0.0741109i
343343 19.0526i 1.02874i
344344 15.8739 + 9.16478i 0.855861 + 0.494132i
345345 0 0
346346 7.57575i 0.407275i
347347 −10.6652 + 18.4726i −0.572535 + 0.991660i 0.423769 + 0.905770i 0.360707π0.360707\pi
−0.996305 + 0.0858901i 0.972627π0.972627\pi
348348 4.10436 + 7.10895i 0.220017 + 0.381080i
349349 −2.12614 + 1.22753i −0.113809 + 0.0657079i −0.555824 0.831300i 0.687597π-0.687597\pi
0.442015 + 0.897008i 0.354264π0.354264\pi
350350 0 0
351351 5.00000 + 17.3205i 0.266880 + 0.924500i
352352 12.5390 0.668332
353353 −5.91742 + 3.41643i −0.314953 + 0.181838i −0.649141 0.760668i 0.724871π-0.724871\pi
0.334188 + 0.942506i 0.391538π0.391538\pi
354354 3.18693 + 5.51993i 0.169384 + 0.293381i
355355 0 0
356356 17.1497i 0.908933i
357357 −6.87386 3.96863i −0.363803 0.210042i
358358 −7.18693 4.14938i −0.379841 0.219301i
359359 19.5293i 1.03072i −0.856975 0.515359i 0.827659π-0.827659\pi
0.856975 0.515359i 0.172341π-0.172341\pi
360360 0 0
361361 −8.00000 13.8564i −0.421053 0.729285i
362362 3.46099 1.99820i 0.181905 0.105023i
363363 −4.00000 −0.209946
364364 −8.06080 7.75650i −0.422500 0.406551i
365365 0 0
366366 0.560795 0.323775i 0.0293132 0.0169240i
367367 −0.873864 1.51358i −0.0456153 0.0790080i 0.842316 0.538984i 0.181192π-0.181192\pi
−0.887932 + 0.459976i 0.847858π0.847858\pi
368368 6.39564 11.0776i 0.333396 0.577459i
369369 5.29150i 0.275465i
370370 0 0
371371 −11.3739 6.56670i −0.590502 0.340926i
372372 11.1153i 0.576302i
373373 −6.50000 + 11.2583i −0.336557 + 0.582934i −0.983783 0.179364i 0.942596π-0.942596\pi
0.647225 + 0.762299i 0.275929π0.275929\pi
374374 −2.76951 4.79693i −0.143208 0.248043i
375375 0 0
376376 3.16515 0.163230
377377 11.4564 11.9059i 0.590037 0.613184i
378378 3.95644 0.203497
379379 9.24773 5.33918i 0.475024 0.274255i −0.243317 0.969947i 0.578235π-0.578235\pi
0.718340 + 0.695692i 0.244902π0.244902\pi
380380 0 0
381381 −8.87386 + 15.3700i −0.454622 + 0.787428i
382382 7.57575i 0.387609i
383383 20.4564 + 11.8105i 1.04528 + 0.603490i 0.921323 0.388798i 0.127110π-0.127110\pi
0.123952 + 0.992288i 0.460443π0.460443\pi
384384 9.56080 + 5.51993i 0.487897 + 0.281688i
385385 0 0
386386 −3.39564 + 5.88143i −0.172834 + 0.299357i
387387 −10.5826 18.3296i −0.537943 0.931744i
388388 −17.6869 + 10.2116i −0.897918 + 0.518413i
389389 −3.16515 −0.160480 −0.0802398 0.996776i 0.525569π-0.525569\pi
−0.0802398 + 0.996776i 0.525569π0.525569\pi
390390 0 0
391391 −21.0000 −1.06202
392392 6.00000 3.46410i 0.303046 0.174964i
393393 −3.79129 6.56670i −0.191245 0.331246i
394394 −3.35208 + 5.80598i −0.168876 + 0.292501i
395395 0 0
396396 −8.20871 4.73930i −0.412503 0.238159i
397397 17.6216 + 10.1738i 0.884402 + 0.510610i 0.872107 0.489315i 0.162753π-0.162753\pi
0.0122949 + 0.999924i 0.496086π0.496086\pi
398398 4.83465i 0.242339i
399399 −1.50000 + 2.59808i −0.0750939 + 0.130066i
400400 0 0
401401 −25.8303 + 14.9131i −1.28990 + 0.744726i −0.978637 0.205596i 0.934087π-0.934087\pi
−0.311267 + 0.950323i 0.600753π0.600753\pi
402402 −0.460985 −0.0229918
403403 21.4955 6.20520i 1.07076 0.309103i
404404 16.1216 0.802079
405405 0 0
406406 −1.81307 3.14033i −0.0899811 0.155852i
407407 −10.5000 + 18.1865i −0.520466 + 0.901473i
408408 7.93725i 0.392953i
409409 −7.50000 4.33013i −0.370851 0.214111i 0.302979 0.952997i 0.402019π-0.402019\pi
−0.673830 + 0.738886i 0.735352π0.735352\pi
410410 0 0
411411 10.4877i 0.517318i
412412 2.83485 4.91010i 0.139663 0.241903i
413413 12.0826 + 20.9276i 0.594545 + 1.02978i
414414 3.62614 2.09355i 0.178215 0.102892i
415415 0 0
416416 4.10436 16.5876i 0.201233 0.813272i
417417 21.7477 1.06499
418418 −1.81307 + 1.04678i −0.0886801 + 0.0511995i
419419 2.91742 + 5.05313i 0.142526 + 0.246861i 0.928447 0.371465i 0.121144π-0.121144\pi
−0.785922 + 0.618326i 0.787811π0.787811\pi
420420 0 0
421421 5.48220i 0.267186i −0.991036 0.133593i 0.957348π-0.957348\pi
0.991036 0.133593i 0.0426515π-0.0426515\pi
422422 0.0653411 + 0.0377247i 0.00318076 + 0.00183641i
423423 −3.16515 1.82740i −0.153895 0.0888513i
424424 13.1334i 0.637815i
425425 0 0
426426 1.60436 + 2.77883i 0.0777313 + 0.134635i
427427 2.12614 1.22753i 0.102891 0.0594041i
428428 18.9564 0.916294
429429 2.29129 9.26013i 0.110624 0.447083i
430430 0 0
431431 7.33485 4.23478i 0.353307 0.203982i −0.312834 0.949808i 0.601278π-0.601278\pi
0.666141 + 0.745826i 0.267945π0.267945\pi
432432 −6.97822 12.0866i −0.335740 0.581518i
433433 4.87386 8.44178i 0.234223 0.405686i −0.724824 0.688934i 0.758079π-0.758079\pi
0.959047 + 0.283248i 0.0914121π0.0914121\pi
434434 4.91010i 0.235692i
435435 0 0
436436 20.3739 + 11.7629i 0.975731 + 0.563339i
437437 7.93725i 0.379690i
438438 0 0
439439 7.24773 + 12.5534i 0.345915 + 0.599143i 0.985520 0.169562i 0.0542352π-0.0542352\pi
−0.639604 + 0.768704i 0.720902π0.720902\pi
440440 0 0
441441 −8.00000 −0.380952
442442 −7.25227 + 2.09355i −0.344955 + 0.0995801i
443443 −19.9129 −0.946089 −0.473045 0.881038i 0.656845π-0.656845\pi
−0.473045 + 0.881038i 0.656845π0.656845\pi
444444 −12.3131 + 7.10895i −0.584352 + 0.337376i
445445 0 0
446446 1.97822 3.42638i 0.0936714 0.162244i
447447 16.6929i 0.789545i
448448 5.12614 + 2.95958i 0.242187 + 0.139827i
449449 −9.54356 5.50998i −0.450388 0.260032i 0.257606 0.966250i 0.417066π-0.417066\pi
−0.707994 + 0.706218i 0.750400π0.750400\pi
450450 0 0
451451 −3.50000 + 6.06218i −0.164809 + 0.285457i
452452 −6.64337 11.5067i −0.312478 0.541228i
453453 −8.37386 + 4.83465i −0.393438 + 0.227152i
454454 −0.373864 −0.0175463
455455 0 0
456456 −3.00000 −0.140488
457457 1.50000 0.866025i 0.0701670 0.0405110i −0.464506 0.885570i 0.653768π-0.653768\pi
0.534673 + 0.845059i 0.320435π0.320435\pi
458458 6.00000 + 10.3923i 0.280362 + 0.485601i
459459 −11.4564 + 19.8431i −0.534741 + 0.926198i
460460 0 0
461461 31.0390 + 17.9204i 1.44563 + 0.834635i 0.998217 0.0596914i 0.0190117π-0.0190117\pi
0.447414 + 0.894327i 0.352345π0.352345\pi
462462 −1.81307 1.04678i −0.0843516 0.0487004i
463463 39.4002i 1.83108i 0.402223 + 0.915542i 0.368238π0.368238\pi
−0.402223 + 0.915542i 0.631762π0.631762\pi
464464 −6.39564 + 11.0776i −0.296910 + 0.514264i
465465 0 0
466466 −1.12159 + 0.647551i −0.0519567 + 0.0299972i
467467 24.3303 1.12587 0.562936 0.826500i 0.309672π-0.309672\pi
0.562936 + 0.826500i 0.309672π0.309672\pi
468468 −8.95644 + 9.30780i −0.414012 + 0.430253i
469469 −1.74773 −0.0807025
470470 0 0
471471 −4.58258 7.93725i −0.211154 0.365729i
472472 −12.0826 + 20.9276i −0.556146 + 0.963272i
473473 27.9989i 1.28739i
474474 −2.37386 1.37055i −0.109035 0.0629515i
475475 0 0
476476 14.2179i 0.651677i
477477 −7.58258 + 13.1334i −0.347182 + 0.601337i
478478 0.0435608 + 0.0754495i 0.00199242 + 0.00345098i
479479 −4.03901 + 2.33193i −0.184547 + 0.106548i −0.589427 0.807821i 0.700647π-0.700647\pi
0.404880 + 0.914370i 0.367313π0.367313\pi
480480 0 0
481481 20.6216 + 19.8431i 0.940264 + 0.904769i
482482 −0.791288 −0.0360422
483483 −6.87386 + 3.96863i −0.312772 + 0.180579i
484484 −3.58258 6.20520i −0.162844 0.282055i
485485 0 0
486486 7.30960i 0.331570i
487487 −9.24773 5.33918i −0.419055 0.241941i 0.275618 0.961267i 0.411117π-0.411117\pi
−0.694673 + 0.719326i 0.744451π0.744451\pi
488488 2.12614 + 1.22753i 0.0962457 + 0.0555675i
489489 21.0707i 0.952848i
490490 0 0
491491 −9.70871 16.8160i −0.438148 0.758895i 0.559399 0.828899i 0.311032π-0.311032\pi
−0.997547 + 0.0700041i 0.977699π0.977699\pi
492492 −4.10436 + 2.36965i −0.185039 + 0.106832i
493493 21.0000 0.945792
494494 0.791288 + 2.74110i 0.0356017 + 0.123328i
495495 0 0
496496 −15.0000 + 8.66025i −0.673520 + 0.388857i
497497 6.08258 + 10.5353i 0.272841 + 0.472574i
498498 1.37386 2.37960i 0.0615643 0.106632i
499499 0.723000i 0.0323659i 0.999869 + 0.0161830i 0.00515142π0.00515142\pi
−0.999869 + 0.0161830i 0.994849π0.994849\pi
500500 0 0
501501 −8.29129 4.78698i −0.370427 0.213866i
502502 0.0754495i 0.00336747i
503503 0.0825757 0.143025i 0.00368187 0.00637718i −0.864179 0.503185i 0.832161π-0.832161\pi
0.867860 + 0.496808i 0.165495π0.165495\pi
504504 3.00000 + 5.19615i 0.133631 + 0.231455i
505505 0 0
506506 −5.53901 −0.246239
507507 −11.5000 6.06218i −0.510733 0.269231i
508508 −31.7913 −1.41051
509509 7.33485 4.23478i 0.325111 0.187703i −0.328557 0.944484i 0.606562π-0.606562\pi
0.653669 + 0.756781i 0.273229π0.273229\pi
510510 0 0
511511 0 0
512512 22.8981i 1.01196i
513513 7.50000 + 4.33013i 0.331133 + 0.191180i
514514 −7.18693 4.14938i −0.317002 0.183021i
515515 0 0
516516 −9.47822 + 16.4168i −0.417255 + 0.722707i
517517 2.41742 + 4.18710i 0.106318 + 0.184149i
518518 5.43920 3.14033i 0.238985 0.137978i
519519 −16.5826 −0.727894
520520 0 0
521521 27.4955 1.20460 0.602299 0.798271i 0.294252π-0.294252\pi
0.602299 + 0.798271i 0.294252π0.294252\pi
522522 −3.62614 + 2.09355i −0.158712 + 0.0916322i
523523 0.0825757 + 0.143025i 0.00361078 + 0.00625406i 0.867825 0.496870i 0.165517π-0.165517\pi
−0.864214 + 0.503124i 0.832184π0.832184\pi
524524 6.79129 11.7629i 0.296679 0.513863i
525525 0 0
526526 3.56080 + 2.05583i 0.155258 + 0.0896383i
527527 24.6261 + 14.2179i 1.07273 + 0.619342i
528528 7.38505i 0.321393i
529529 1.00000 1.73205i 0.0434783 0.0753066i
530530 0 0
531531 24.1652 13.9518i 1.04868 0.605455i
532532 −5.37386 −0.232987
533533 6.87386 + 6.61438i 0.297740 + 0.286501i
534534 −4.37386 −0.189276
535535 0 0
536536 −0.873864 1.51358i −0.0377452 0.0653765i
537537 9.08258 15.7315i 0.391942 0.678864i
538538 6.85275i 0.295443i
539539 9.16515 + 5.29150i 0.394771 + 0.227921i
540540 0 0
541541 10.3923i 0.446800i 0.974727 + 0.223400i 0.0717156π0.0717156\pi
−0.974727 + 0.223400i 0.928284π0.928284\pi
542542 1.97822 3.42638i 0.0849718 0.147175i
543543 4.37386 + 7.57575i 0.187700 + 0.325107i
544544 18.8085 10.8591i 0.806409 0.465580i
545545 0 0
546546 −1.97822 + 2.05583i −0.0846600 + 0.0879812i
547547 −28.7477 −1.22916 −0.614582 0.788853i 0.710675π-0.710675\pi
−0.614582 + 0.788853i 0.710675π0.710675\pi
548548 16.2695 9.39320i 0.694999 0.401258i
549549 −1.41742 2.45505i −0.0604942 0.104779i
550550 0 0
551551 7.93725i 0.338138i
552552 −6.87386 3.96863i −0.292571 0.168916i
553553 −9.00000 5.19615i −0.382719 0.220963i
554554 3.38865i 0.143970i
555555 0 0
556556 19.4782 + 33.7373i 0.826061 + 1.43078i
557557 6.70871 3.87328i 0.284257 0.164116i −0.351092 0.936341i 0.614190π-0.614190\pi
0.635349 + 0.772225i 0.280856π0.280856\pi
558558 −5.66970 −0.240017
559559 37.0390 + 9.16478i 1.56658 + 0.387629i
560560 0 0
561561 10.5000 6.06218i 0.443310 0.255945i
562562 −0.834849 1.44600i −0.0352160 0.0609958i
563563 −4.50000 + 7.79423i −0.189652 + 0.328488i −0.945134 0.326682i 0.894069π-0.894069\pi
0.755482 + 0.655169i 0.227403π0.227403\pi
564564 3.27340i 0.137835i
565565 0 0
566566 −10.9782 6.33828i −0.461449 0.266418i
567567 1.73205i 0.0727393i
568568 −6.08258 + 10.5353i −0.255219 + 0.442053i
569569 −3.87386 6.70973i −0.162401 0.281286i 0.773328 0.634006i 0.218590π-0.218590\pi
−0.935729 + 0.352719i 0.885257π0.885257\pi
570570 0 0
571571 −35.0780 −1.46797 −0.733985 0.679166i 0.762342π-0.762342\pi
−0.733985 + 0.679166i 0.762342π0.762342\pi
572572 16.4174 4.73930i 0.686447 0.198160i
573573 16.5826 0.692747
574574 1.81307 1.04678i 0.0756760 0.0436916i
575575 0 0
576576 3.41742 5.91915i 0.142393 0.246631i
577577 6.92820i 0.288425i 0.989547 + 0.144212i 0.0460649π0.0460649\pi
−0.989547 + 0.144212i 0.953935π0.953935\pi
578578 −1.58258 0.913701i −0.0658265 0.0380049i
579579 −12.8739 7.43273i −0.535020 0.308894i
580580 0 0
581581 5.20871 9.02175i 0.216094 0.374285i
582582 2.60436 + 4.51088i 0.107954 + 0.186982i
583583 17.3739 10.0308i 0.719552 0.415433i
584584 0 0
585585 0 0
586586 −8.28674 −0.342322
587587 34.2042 19.7478i 1.41176 0.815078i 0.416203 0.909272i 0.363361π-0.363361\pi
0.995554 + 0.0941934i 0.0300272π0.0300272\pi
588588 3.58258 + 6.20520i 0.147743 + 0.255898i
589589 5.37386 9.30780i 0.221426 0.383521i
590590 0 0
591591 −12.7087 7.33738i −0.522767 0.301819i
592592 −19.1869 11.0776i −0.788578 0.455286i
593593 21.1660i 0.869184i −0.900627 0.434592i 0.856893π-0.856893\pi
0.900627 0.434592i 0.143107π-0.143107\pi
594594 −3.02178 + 5.23388i −0.123985 + 0.214749i
595595 0 0
596596 −25.8956 + 14.9509i −1.06073 + 0.612411i
597597 −10.5826 −0.433116
598598 −1.81307 + 7.32743i −0.0741419 + 0.299641i
599599 15.4955 0.633127 0.316564 0.948571i 0.397471π-0.397471\pi
0.316564 + 0.948571i 0.397471π0.397471\pi
600600 0 0
601601 −8.45644 14.6470i −0.344945 0.597463i 0.640398 0.768043i 0.278769π-0.278769\pi
−0.985344 + 0.170580i 0.945436π0.945436\pi
602602 4.18693 7.25198i 0.170647 0.295569i
603603 2.01810i 0.0821834i
604604 −15.0000 8.66025i −0.610341 0.352381i
605605 0 0
606606 4.11165i 0.167024i
607607 3.87386 6.70973i 0.157235 0.272339i −0.776635 0.629950i 0.783075π-0.783075\pi
0.933871 + 0.357611i 0.116409π0.116409\pi
608608 −4.10436 7.10895i −0.166454 0.288306i
609609 6.87386 3.96863i 0.278543 0.160817i
610610 0 0
611611 6.33030 1.82740i 0.256097 0.0739287i
612612 −16.4174 −0.663635
613613 5.12614 2.95958i 0.207043 0.119536i −0.392894 0.919584i 0.628526π-0.628526\pi
0.599936 + 0.800048i 0.295193π0.295193\pi
614614 −5.53901 9.59386i −0.223536 0.387176i
615615 0 0
616616 7.93725i 0.319801i
617617 12.0826 + 6.97588i 0.486426 + 0.280838i 0.723091 0.690753i 0.242721π-0.242721\pi
−0.236664 + 0.971591i 0.576054π0.576054\pi
618618 −1.25227 0.723000i −0.0503738 0.0290833i
619619 29.7309i 1.19499i −0.801874 0.597493i 0.796164π-0.796164\pi
0.801874 0.597493i 0.203836π-0.203836\pi
620620 0 0
621621 11.4564 + 19.8431i 0.459731 + 0.796278i
622622 3.00000 1.73205i 0.120289 0.0694489i
623623 −16.5826 −0.664367
624624 9.76951 + 2.41733i 0.391093 + 0.0967705i
625625 0 0
626626 1.28674 0.742901i 0.0514286 0.0296923i
627627 −2.29129 3.96863i −0.0915052 0.158492i
628628 8.20871 14.2179i 0.327563 0.567356i
629629 36.3731i 1.45029i
630630 0 0
631631 −5.12614 2.95958i −0.204068 0.117819i 0.394483 0.918903i 0.370924π-0.370924\pi
−0.598552 + 0.801084i 0.704257π0.704257\pi
632632 10.3923i 0.413384i
633633 −0.0825757 + 0.143025i −0.00328209 + 0.00568475i
634634 0.0435608 + 0.0754495i 0.00173002 + 0.00299648i
635635 0 0
636636 13.5826 0.538584
637637 10.0000 10.3923i 0.396214 0.411758i
638638 5.53901 0.219292
639639 12.1652 7.02355i 0.481246 0.277847i
640640 0 0
641641 −9.08258 + 15.7315i −0.358740 + 0.621356i −0.987751 0.156041i 0.950127π-0.950127\pi
0.629010 + 0.777397i 0.283460π0.283460\pi
642642 4.83465i 0.190809i
643643 −18.8739 10.8968i −0.744313 0.429729i 0.0793227 0.996849i 0.474724π-0.474724\pi
−0.823635 + 0.567120i 0.808058π0.808058\pi
644644 −12.3131 7.10895i −0.485203 0.280132i
645645 0 0
646646 −1.81307 + 3.14033i −0.0713342 + 0.123554i
647647 13.5000 + 23.3827i 0.530740 + 0.919268i 0.999357 + 0.0358667i 0.0114192π0.0114192\pi
−0.468617 + 0.883402i 0.655247π0.655247\pi
648648 1.50000 0.866025i 0.0589256 0.0340207i
649649 −36.9129 −1.44896
650650 0 0
651651 10.7477 0.421237
652652 −32.6869 + 18.8718i −1.28012 + 0.739077i
653653 −21.4129 37.0882i −0.837951 1.45137i −0.891605 0.452814i 0.850420π-0.850420\pi
0.0536545 0.998560i 0.482913π-0.482913\pi
654654 3.00000 5.19615i 0.117309 0.203186i
655655 0 0
656656 −6.39564 3.69253i −0.249708 0.144169i
657657 0 0
658658 1.44600i 0.0563710i
659659 −15.2477 + 26.4098i −0.593967 + 1.02878i 0.399725 + 0.916635i 0.369106π0.369106\pi
−0.993692 + 0.112146i 0.964228π0.964228\pi
660660 0 0
661661 15.8739 9.16478i 0.617422 0.356469i −0.158443 0.987368i 0.550647π-0.550647\pi
0.775865 + 0.630900i 0.217314π0.217314\pi
662662 −2.04356 −0.0794252
663663 −4.58258 15.8745i −0.177972 0.616515i
664664 10.4174 0.404274
665665 0 0
666666 −3.62614 6.28065i −0.140510 0.243370i
667667 10.5000 18.1865i 0.406562 0.704185i
668668 17.1497i 0.663542i
669669 7.50000 + 4.33013i 0.289967 + 0.167412i
670670 0 0
671671 3.75015i 0.144773i
672672 4.10436 7.10895i 0.158329 0.274234i
673673 −12.0826 20.9276i −0.465749 0.806701i 0.533486 0.845809i 0.320882π-0.320882\pi
−0.999235 + 0.0391079i 0.987548π0.987548\pi
674674 −12.1652 + 7.02355i −0.468584 + 0.270537i
675675 0 0
676676 −0.895644 23.2695i −0.0344478 0.894981i
677677 2.83485 0.108952 0.0544760 0.998515i 0.482651π-0.482651\pi
0.0544760 + 0.998515i 0.482651π0.482651\pi
678678 −2.93466 + 1.69433i −0.112705 + 0.0650702i
679679 9.87386 + 17.1020i 0.378924 + 0.656316i
680680 0 0
681681 0.818350i 0.0313593i
682682 6.49545 + 3.75015i 0.248724 + 0.143601i
683683 28.6652 + 16.5498i 1.09684 + 0.633262i 0.935390 0.353619i 0.115049π-0.115049\pi
0.161452 + 0.986881i 0.448382π0.448382\pi
684684 6.20520i 0.237262i
685685 0 0
686686 −4.35208 7.53803i −0.166163 0.287803i
687687 −22.7477 + 13.1334i −0.867880 + 0.501071i
688688 −29.5390 −1.12616
689689 −7.58258 26.2668i −0.288873 1.00069i
690690 0 0
691691 17.1261 9.88778i 0.651509 0.376149i −0.137525 0.990498i 0.543915π-0.543915\pi
0.789034 + 0.614349i 0.210581π0.210581\pi
692692 −14.8521 25.7246i −0.564591 0.977901i
693693 −4.58258 + 7.93725i −0.174078 + 0.301511i
694694 9.74475i 0.369906i
695695 0 0
696696 6.87386 + 3.96863i 0.260553 + 0.150430i
697697 12.1244i 0.459243i
698698 −0.560795 + 0.971326i −0.0212264 + 0.0367652i
699699 −1.41742 2.45505i −0.0536119 0.0928586i
700700 0 0
701701 −21.1652 −0.799397 −0.399698 0.916647i 0.630885π-0.630885\pi
−0.399698 + 0.916647i 0.630885π0.630885\pi
702702 5.93466 + 5.71063i 0.223989 + 0.215534i
703703 13.7477 0.518505
704704 −7.83030 + 4.52083i −0.295116 + 0.170385i
705705 0 0
706706 −1.56080 + 2.70338i −0.0587413 + 0.101743i
707707 15.5885i 0.586264i
708708 −21.6434 12.4958i −0.813408 0.469621i
709709 −31.5000 18.1865i −1.18301 0.683010i −0.226299 0.974058i 0.572663π-0.572663\pi
−0.956708 + 0.291048i 0.905996π0.905996\pi
710710 0 0
711711 −6.00000 + 10.3923i −0.225018 + 0.389742i
712712 −8.29129 14.3609i −0.310729 0.538199i
713713 24.6261 14.2179i 0.922256 0.532465i
714714 −3.62614 −0.135705
715715 0 0
716716 32.5390 1.21604
717717 −0.165151 + 0.0953502i −0.00616769 + 0.00356092i
718718 −4.46099 7.72665i −0.166482 0.288356i
719719 12.2477 21.2137i 0.456763 0.791137i −0.542025 0.840363i 0.682342π-0.682342\pi
0.998788 + 0.0492257i 0.0156754π0.0156754\pi
720720 0 0
721721 −4.74773 2.74110i −0.176815 0.102084i
722722 −6.33030 3.65480i −0.235589 0.136018i
723723 1.73205i 0.0644157i
724724 −7.83485 + 13.5704i −0.291180 + 0.504338i
725725 0 0
726726 −1.58258 + 0.913701i −0.0587349 + 0.0339106i
727727 15.2523 0.565675 0.282838 0.959168i 0.408724π-0.408724\pi
0.282838 + 0.959168i 0.408724π0.408724\pi
728728 −10.5000 2.59808i −0.389156 0.0962911i
729729 13.0000 0.481481
730730 0 0
731731 24.2477 + 41.9983i 0.896835 + 1.55336i
732732 −1.26951 + 2.19885i −0.0469223 + 0.0812719i
733733 22.8027i 0.842237i 0.907006 + 0.421119i 0.138362π0.138362\pi
−0.907006 + 0.421119i 0.861638π0.861638\pi
734734 −0.691478 0.399225i −0.0255229 0.0147357i
735735 0 0
736736 21.7182i 0.800544i
737737 1.33485 2.31203i 0.0491698 0.0851646i
738738 −1.20871 2.09355i −0.0444933 0.0770647i
739739 14.7523 8.51723i 0.542671 0.313311i −0.203490 0.979077i 0.565228π-0.565228\pi
0.746161 + 0.665766i 0.231895π0.231895\pi
740740 0 0
741741 −6.00000 + 1.73205i −0.220416 + 0.0636285i
742742 −6.00000 −0.220267
743743 −4.96099 + 2.86423i −0.182001 + 0.105078i −0.588232 0.808692i 0.700176π-0.700176\pi
0.406232 + 0.913770i 0.366843π0.366843\pi
744744 5.37386 + 9.30780i 0.197015 + 0.341241i
745745 0 0
746746 5.93905i 0.217444i
747747 −10.4174 6.01450i −0.381154 0.220059i
748748 18.8085 + 10.8591i 0.687708 + 0.397048i
749749 18.3296i 0.669748i
750750 0 0
751751 −5.87386 10.1738i −0.214340 0.371248i 0.738728 0.674004i 0.235427π-0.235427\pi
−0.953068 + 0.302755i 0.902093π0.902093\pi
752752 −4.41742 + 2.55040i −0.161087 + 0.0930036i
753753 0.165151 0.00601845
754754 1.81307 7.32743i 0.0660281 0.266849i
755755 0 0
756756 −13.4347 + 7.75650i −0.488614 + 0.282101i
757757 4.87386 + 8.44178i 0.177144 + 0.306822i 0.940901 0.338682i 0.109981π-0.109981\pi
−0.763757 + 0.645503i 0.776648π0.776648\pi
758758 2.43920 4.22483i 0.0885959 0.153453i
759759 12.1244i 0.440086i
760760 0 0
761761 −30.7087 17.7297i −1.11319 0.642701i −0.173536 0.984827i 0.555519π-0.555519\pi
−0.939654 + 0.342127i 0.888853π0.888853\pi
762762 8.10805i 0.293724i
763763 11.3739 19.7001i 0.411762 0.713192i
764764 14.8521 + 25.7246i 0.537330 + 0.930682i
765765 0 0
766766 10.7913 0.389905
767767 −12.0826 + 48.8311i −0.436277 + 1.76319i
768768 −1.79129 −0.0646375
769769 13.5000 7.79423i 0.486822 0.281067i −0.236433 0.971648i 0.575978π-0.575978\pi
0.723255 + 0.690581i 0.242645π0.242645\pi
770770 0 0
771771 9.08258 15.7315i 0.327101 0.566556i
772772 26.6283i 0.958374i
773773 −20.9174 12.0767i −0.752347 0.434368i 0.0741940 0.997244i 0.476362π-0.476362\pi
−0.826541 + 0.562876i 0.809695π0.809695\pi
774774 −8.37386 4.83465i −0.300992 0.173778i
775775 0 0
776776 −9.87386 + 17.1020i −0.354451 + 0.613927i
777777 6.87386 + 11.9059i 0.246598 + 0.427121i
778778 −1.25227 + 0.723000i −0.0448962 + 0.0259208i
779779 4.58258 0.164188
780780 0 0
781781 −18.5826 −0.664937
782782 −8.30852 + 4.79693i −0.297112 + 0.171538i
783783 −11.4564 19.8431i −0.409420 0.709136i
784784 −5.58258 + 9.66930i −0.199378 + 0.345332i
785785 0 0
786786 −3.00000 1.73205i −0.107006 0.0617802i
787787 −14.1261 8.15573i −0.503542 0.290720i 0.226633 0.973980i 0.427228π-0.427228\pi
−0.730175 + 0.683260i 0.760562π0.760562\pi
788788 26.2867i 0.936425i
789789 −4.50000 + 7.79423i −0.160204 + 0.277482i
790790 0 0
791791 −11.1261 + 6.42368i −0.395600 + 0.228400i
792792 −9.16515 −0.325669
793793 4.96099 + 1.22753i 0.176170 + 0.0435907i
794794 9.29583 0.329897
795795 0 0
796796 −9.47822 16.4168i −0.335947 0.581877i
797797 22.0390 38.1727i 0.780662 1.35215i −0.150895 0.988550i 0.548215π-0.548215\pi
0.931557 0.363596i 0.118451π-0.118451\pi
798798 1.37055i 0.0485170i
799799 7.25227 + 4.18710i 0.256567 + 0.148129i
800800 0 0
801801 19.1479i 0.676558i
802802 −6.81307 + 11.8006i −0.240578 + 0.416693i
803803 0 0
804804 1.56534 0.903750i 0.0552053 0.0318728i
805805 0 0
806806 7.08712 7.36515i 0.249633 0.259426i
807807 15.0000 0.528025
808808 13.5000 7.79423i 0.474928 0.274200i
809809 27.4129 + 47.4805i 0.963785 + 1.66933i 0.712843 + 0.701323i 0.247407π0.247407\pi
0.250942 + 0.968002i 0.419260π0.419260\pi
810810 0 0
811811 50.5155i 1.77384i 0.461923 + 0.886920i 0.347160π0.347160\pi
−0.461923 + 0.886920i 0.652840π0.652840\pi
812812 12.3131 + 7.10895i 0.432104 + 0.249475i
813813 7.50000 + 4.33013i 0.263036 + 0.151864i
814814 9.59386i 0.336264i
815815 0 0
816816 6.39564 + 11.0776i 0.223892 + 0.387793i
817817 15.8739 9.16478i 0.555356 0.320635i
818818 −3.95644 −0.138334
819819 9.00000 + 8.66025i 0.314485 + 0.302614i
820820 0 0
821821 15.7087 9.06943i 0.548238 0.316525i −0.200173 0.979761i 0.564150π-0.564150\pi
0.748411 + 0.663235i 0.230817π0.230817\pi
822822 −2.39564 4.14938i −0.0835577 0.144726i
823823 −15.7087 + 27.2083i −0.547571 + 0.948421i 0.450869 + 0.892590i 0.351114π0.351114\pi
−0.998440 + 0.0558311i 0.982219π0.982219\pi
824824 5.48220i 0.190982i
825825 0 0
826826 9.56080 + 5.51993i 0.332663 + 0.192063i
827827 10.7737i 0.374638i −0.982299 0.187319i 0.940020π-0.940020\pi
0.982299 0.187319i 0.0599799π-0.0599799\pi
828828 −8.20871 + 14.2179i −0.285272 + 0.494106i
829829 16.6652 + 28.8649i 0.578805 + 1.00252i 0.995617 + 0.0935264i 0.0298139π0.0298139\pi
−0.416812 + 0.908993i 0.636853π0.636853\pi
830830 0 0
831831 −7.41742 −0.257308
832832 3.41742 + 11.8383i 0.118478 + 0.410419i
833833 18.3303 0.635107
834834 8.60436 4.96773i 0.297944 0.172018i
835835 0 0
836836 4.10436 7.10895i 0.141952 0.245868i
837837 31.0260i 1.07242i
838838 2.30852 + 1.33283i 0.0797466 + 0.0460417i
839839 −37.8303 21.8413i −1.30605 0.754047i −0.324613 0.945847i 0.605234π-0.605234\pi
−0.981434 + 0.191800i 0.938567π0.938567\pi
840840 0 0
841841 4.00000 6.92820i 0.137931 0.238904i
842842 −1.25227 2.16900i −0.0431562 0.0747487i
843843 3.16515 1.82740i 0.109014 0.0629390i
844844 −0.295834 −0.0101830
845845 0 0
846846 −1.66970 −0.0574054
847847 −6.00000 + 3.46410i −0.206162 + 0.119028i
848848 10.5826 + 18.3296i 0.363407 + 0.629440i
849849 13.8739 24.0302i 0.476150 0.824716i
850850 0 0
851851 31.5000 + 18.1865i 1.07981 + 0.623426i
852852 −10.8956 6.29060i −0.373279 0.215513i
853853 5.63310i 0.192874i −0.995339 0.0964369i 0.969255π-0.969255\pi
0.995339 0.0964369i 0.0307446π-0.0307446\pi
854854 0.560795 0.971326i 0.0191900 0.0332381i
855855 0 0
856856 15.8739 9.16478i 0.542557 0.313246i
857857 4.74773 0.162179 0.0810896 0.996707i 0.474160π-0.474160\pi
0.0810896 + 0.996707i 0.474160π0.474160\pi
858858 −1.20871 4.18710i −0.0412648 0.142945i
859859 −44.2432 −1.50956 −0.754779 0.655979i 0.772256π-0.772256\pi
−0.754779 + 0.655979i 0.772256π0.772256\pi
860860 0 0
861861 2.29129 + 3.96863i 0.0780869 + 0.135250i
862862 1.93466 3.35093i 0.0658947 0.114133i
863863 13.6657i 0.465186i 0.972574 + 0.232593i 0.0747210π0.0747210\pi
−0.972574 + 0.232593i 0.925279π0.925279\pi
864864 −20.5218 11.8483i −0.698165 0.403086i
865865 0 0
866866 4.45325i 0.151328i
867867 2.00000 3.46410i 0.0679236 0.117647i
868868 9.62614 + 16.6730i 0.326732 + 0.565917i
869869 13.7477 7.93725i 0.466360 0.269253i
870870 0 0
871871 −2.62159 2.52263i −0.0888292 0.0854759i
872872 22.7477 0.770335
873873 19.7477 11.4014i 0.668359 0.385877i
874874 1.81307 + 3.14033i 0.0613279 + 0.106223i
875875 0 0
876876 0 0
877877 6.87386 + 3.96863i 0.232114 + 0.134011i 0.611547 0.791208i 0.290548π-0.290548\pi
−0.379433 + 0.925219i 0.623881π0.623881\pi
878878 5.73504 + 3.31113i 0.193548 + 0.111745i
879879 18.1389i 0.611809i
880880 0 0
881881 −18.2477 31.6060i −0.614782 1.06483i −0.990423 0.138068i 0.955911π-0.955911\pi
0.375641 0.926765i 0.377422π-0.377422\pi
882882 −3.16515 + 1.82740i −0.106576 + 0.0615318i
883883 −36.2432 −1.21968 −0.609840 0.792524i 0.708766π-0.708766\pi
−0.609840 + 0.792524i 0.708766π0.708766\pi
884884 20.5218 21.3269i 0.690222 0.717300i
885885 0 0
886886 −7.87841 + 4.54860i −0.264680 + 0.152813i
887887 27.2477 + 47.1944i 0.914889 + 1.58463i 0.807064 + 0.590465i 0.201055π0.201055\pi
0.107826 + 0.994170i 0.465611π0.465611\pi
888888 −6.87386 + 11.9059i −0.230672 + 0.399535i
889889 30.7400i 1.03099i
890890 0 0
891891 2.29129 + 1.32288i 0.0767610 + 0.0443180i
892892 15.5130i 0.519414i
893893 1.58258 2.74110i 0.0529589 0.0917275i
894894 3.81307 + 6.60443i 0.127528 + 0.220885i
895895 0 0
896896 19.1216 0.638808
897897 −16.0390 3.96863i −0.535527 0.132509i
898898 −5.03447 −0.168002
899899 −24.6261 + 14.2179i −0.821328 + 0.474194i
900900 0 0
901901 17.3739 30.0924i 0.578807 1.00252i
902902 3.19795i 0.106480i
903903 15.8739 + 9.16478i 0.528249 + 0.304985i
904904 −11.1261 6.42368i −0.370050 0.213648i
905905 0 0
906906 −2.20871 + 3.82560i −0.0733795 + 0.127097i
907907 −3.12614 5.41463i −0.103802 0.179790i 0.809446 0.587194i 0.199767π-0.199767\pi
−0.913248 + 0.407404i 0.866434π0.866434\pi
908908 1.26951 0.732950i 0.0421301 0.0243238i
909909 −18.0000 −0.597022
910910 0 0
911911 −7.91288 −0.262165 −0.131083 0.991371i 0.541845π-0.541845\pi
−0.131083 + 0.991371i 0.541845π0.541845\pi
912912 4.18693 2.41733i 0.138643 0.0800457i
913913 7.95644 + 13.7810i 0.263320 + 0.456083i
914914 0.395644 0.685275i 0.0130867 0.0226669i
915915 0 0
916916 −40.7477 23.5257i −1.34634 0.777311i
917917 −11.3739 6.56670i −0.375598 0.216852i
918918 10.4678i 0.345487i
919919 −27.0826 + 46.9084i −0.893372 + 1.54737i −0.0575648 + 0.998342i 0.518334π0.518334\pi
−0.835807 + 0.549023i 0.815000π0.815000\pi
920920 0 0
921921 21.0000 12.1244i 0.691974 0.399511i
922922 16.3739 0.539244
923923 −6.08258 + 24.5824i −0.200210 + 0.809141i
924924 8.20871 0.270047
925925 0 0
926926 9.00000 + 15.5885i 0.295758 + 0.512268i
927927 −3.16515 + 5.48220i −0.103957 + 0.180059i
928928 21.7182i 0.712935i
929929 −22.8303 13.1811i −0.749038 0.432457i 0.0763082 0.997084i 0.475687π-0.475687\pi
−0.825346 + 0.564627i 0.809020π0.809020\pi
930930 0 0
931931 6.92820i 0.227063i
932932 2.53901 4.39770i 0.0831682 0.144052i
933933 3.79129 + 6.56670i 0.124121 + 0.214984i
934934 9.62614 5.55765i 0.314977 0.181852i
935935 0 0
936936 −3.00000 + 12.1244i −0.0980581 + 0.396297i
937937 −31.4955 −1.02891 −0.514456 0.857517i 0.672006π-0.672006\pi
−0.514456 + 0.857517i 0.672006π0.672006\pi
938938 −0.691478 + 0.399225i −0.0225775 + 0.0130352i
939939 1.62614 + 2.81655i 0.0530670 + 0.0919147i
940940 0 0
941941 26.4575i 0.862490i 0.902235 + 0.431245i 0.141926π0.141926\pi
−0.902235 + 0.431245i 0.858074π0.858074\pi
942942 −3.62614 2.09355i −0.118146 0.0682116i
943943 10.5000 + 6.06218i 0.341927 + 0.197412i
944944 38.9434i 1.26750i
945945 0 0
946946 6.39564 + 11.0776i 0.207940 + 0.360163i
947947 12.4129 7.16658i 0.403364 0.232883i −0.284570 0.958655i 0.591851π-0.591851\pi
0.687935 + 0.725773i 0.258518π0.258518\pi
948948 10.7477 0.349070
949949 0 0
950950 0 0
951951 −0.165151 + 0.0953502i −0.00535540 + 0.00309194i
952952 −6.87386 11.9059i −0.222783 0.385872i
953953 −4.03901 + 6.99578i −0.130837 + 0.226616i −0.923999 0.382394i 0.875100π-0.875100\pi
0.793163 + 0.609010i 0.208433π0.208433\pi
954954 6.92820i 0.224309i
955955 0 0
956956 −0.295834 0.170800i −0.00956794 0.00552406i
957957 12.1244i 0.391925i
958958 −1.06534 + 1.84522i −0.0344196 + 0.0596165i
959959 −9.08258 15.7315i −0.293292 0.507996i
960960 0 0
961961 −7.50455 −0.242082
962962 12.6915 + 3.14033i 0.409190 + 0.101248i
963963 −21.1652 −0.682037
964964 2.68693 1.55130i 0.0865402 0.0499640i
965965 0 0
966966 −1.81307 + 3.14033i −0.0583345 + 0.101038i
967967 37.3821i 1.20213i 0.799201 + 0.601064i 0.205256π0.205256\pi
−0.799201 + 0.601064i 0.794744π0.794744\pi
968968 −6.00000 3.46410i −0.192847 0.111340i
969969 −6.87386 3.96863i −0.220820 0.127491i
970970 0 0
971971 9.24773 16.0175i 0.296774 0.514027i −0.678622 0.734487i 0.737423π-0.737423\pi
0.975396 + 0.220460i 0.0707560π0.0707560\pi
972972 14.3303 + 24.8208i 0.459645 + 0.796128i
973973 32.6216 18.8341i 1.04580 0.603793i
974974 −4.87841 −0.156314
975975 0 0
976976 −3.95644 −0.126643
977977 −30.5780 + 17.6542i −0.978278 + 0.564809i −0.901750 0.432258i 0.857717π-0.857717\pi
−0.0765281 + 0.997067i 0.524383π0.524383\pi
978978 4.81307 + 8.33648i 0.153905 + 0.266571i
979979 12.6652 21.9367i 0.404780 0.701100i
980980 0 0
981981 −22.7477 13.1334i −0.726279 0.419317i
982982 −7.68239 4.43543i −0.245155 0.141540i
983983 55.0840i 1.75691i 0.477827 + 0.878454i 0.341424π0.341424\pi
−0.477827 + 0.878454i 0.658576π0.658576\pi
984984 −2.29129 + 3.96863i −0.0730436 + 0.126515i
985985 0 0
986986 8.30852 4.79693i 0.264597 0.152765i
987987 3.16515 0.100748
988988 −8.06080 7.75650i −0.256448 0.246767i
989989 48.4955 1.54207
990990 0 0
991991 6.50000 + 11.2583i 0.206479 + 0.357633i 0.950603 0.310409i 0.100466π-0.100466\pi
−0.744124 + 0.668042i 0.767133π0.767133\pi
992992 −14.7042 + 25.4684i −0.466858 + 0.808621i
993993 4.47315i 0.141951i
994994 4.81307 + 2.77883i 0.152661 + 0.0881390i
995995 0 0
996996 10.7737i 0.341378i
997997 0.0825757 0.143025i 0.00261520 0.00452966i −0.864715 0.502263i 0.832501π-0.832501\pi
0.867330 + 0.497733i 0.165834π0.165834\pi
998998 0.165151 + 0.286051i 0.00522778 + 0.00905477i
999999 34.3693 19.8431i 1.08740 0.627809i
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 325.2.n.b.101.2 4
5.2 odd 4 65.2.l.a.49.3 yes 8
5.3 odd 4 65.2.l.a.49.2 yes 8
5.4 even 2 325.2.n.c.101.1 4
13.2 odd 12 4225.2.a.bj.1.3 4
13.4 even 6 inner 325.2.n.b.251.2 4
13.11 odd 12 4225.2.a.bj.1.2 4
15.2 even 4 585.2.bf.a.244.2 8
15.8 even 4 585.2.bf.a.244.3 8
20.3 even 4 1040.2.df.b.49.4 8
20.7 even 4 1040.2.df.b.49.1 8
65.2 even 12 845.2.b.f.339.6 8
65.3 odd 12 845.2.d.c.844.5 8
65.4 even 6 325.2.n.c.251.1 4
65.7 even 12 845.2.n.c.529.3 8
65.8 even 4 845.2.n.c.484.3 8
65.12 odd 4 845.2.l.c.699.2 8
65.17 odd 12 65.2.l.a.4.2 8
65.18 even 4 845.2.n.d.484.1 8
65.22 odd 12 845.2.l.c.654.3 8
65.23 odd 12 845.2.d.c.844.3 8
65.24 odd 12 4225.2.a.bk.1.3 4
65.28 even 12 845.2.b.f.339.3 8
65.32 even 12 845.2.n.d.529.1 8
65.33 even 12 845.2.n.d.529.2 8
65.37 even 12 845.2.b.f.339.4 8
65.38 odd 4 845.2.l.c.699.3 8
65.42 odd 12 845.2.d.c.844.4 8
65.43 odd 12 65.2.l.a.4.3 yes 8
65.47 even 4 845.2.n.d.484.2 8
65.48 odd 12 845.2.l.c.654.2 8
65.54 odd 12 4225.2.a.bk.1.2 4
65.57 even 4 845.2.n.c.484.4 8
65.58 even 12 845.2.n.c.529.4 8
65.62 odd 12 845.2.d.c.844.6 8
65.63 even 12 845.2.b.f.339.5 8
195.17 even 12 585.2.bf.a.199.3 8
195.173 even 12 585.2.bf.a.199.2 8
260.43 even 12 1040.2.df.b.849.1 8
260.147 even 12 1040.2.df.b.849.4 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
65.2.l.a.4.2 8 65.17 odd 12
65.2.l.a.4.3 yes 8 65.43 odd 12
65.2.l.a.49.2 yes 8 5.3 odd 4
65.2.l.a.49.3 yes 8 5.2 odd 4
325.2.n.b.101.2 4 1.1 even 1 trivial
325.2.n.b.251.2 4 13.4 even 6 inner
325.2.n.c.101.1 4 5.4 even 2
325.2.n.c.251.1 4 65.4 even 6
585.2.bf.a.199.2 8 195.173 even 12
585.2.bf.a.199.3 8 195.17 even 12
585.2.bf.a.244.2 8 15.2 even 4
585.2.bf.a.244.3 8 15.8 even 4
845.2.b.f.339.3 8 65.28 even 12
845.2.b.f.339.4 8 65.37 even 12
845.2.b.f.339.5 8 65.63 even 12
845.2.b.f.339.6 8 65.2 even 12
845.2.d.c.844.3 8 65.23 odd 12
845.2.d.c.844.4 8 65.42 odd 12
845.2.d.c.844.5 8 65.3 odd 12
845.2.d.c.844.6 8 65.62 odd 12
845.2.l.c.654.2 8 65.48 odd 12
845.2.l.c.654.3 8 65.22 odd 12
845.2.l.c.699.2 8 65.12 odd 4
845.2.l.c.699.3 8 65.38 odd 4
845.2.n.c.484.3 8 65.8 even 4
845.2.n.c.484.4 8 65.57 even 4
845.2.n.c.529.3 8 65.7 even 12
845.2.n.c.529.4 8 65.58 even 12
845.2.n.d.484.1 8 65.18 even 4
845.2.n.d.484.2 8 65.47 even 4
845.2.n.d.529.1 8 65.32 even 12
845.2.n.d.529.2 8 65.33 even 12
1040.2.df.b.49.1 8 20.7 even 4
1040.2.df.b.49.4 8 20.3 even 4
1040.2.df.b.849.1 8 260.43 even 12
1040.2.df.b.849.4 8 260.147 even 12
4225.2.a.bj.1.2 4 13.11 odd 12
4225.2.a.bj.1.3 4 13.2 odd 12
4225.2.a.bk.1.2 4 65.54 odd 12
4225.2.a.bk.1.3 4 65.24 odd 12