Properties

Label 40.2.k.a.3.4
Level 4040
Weight 22
Character 40.3
Analytic conductor 0.3190.319
Analytic rank 00
Dimension 88
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] = [40,2,Mod(3,40)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(40, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 2, 3])) 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("40.3"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 40=235 40 = 2^{3} \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 40.k (of order 44, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 0.3194016080850.319401608085
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(i)\Q(i)
Coefficient field: Q(ζ20)\Q(\zeta_{20})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x8x6+x4x2+1 x^{8} - x^{6} + x^{4} - x^{2} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 24 2^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 3.4
Root 0.587785+0.809017i0.587785 + 0.809017i of defining polynomial
Character χ\chi == 40.3
Dual form 40.2.k.a.27.4

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+(1.26007+0.642040i)q2+(1.618031.61803i)q3+(1.17557+1.61803i)q4+(1.90211+1.17557i)q5+(1.000003.07768i)q6+(1.175571.17557i)q7+(0.442463+2.79360i)q8+2.23607iq9+(3.15156+0.260074i)q10+1.23607q11+(0.7159214.52015i)q12+(3.077683.07768i)q13+(0.7265432.23607i)q14+(4.97980+1.17557i)q15+(1.23607+3.80423i)q16+(1.00000+1.00000i)q17+(1.43564+2.81761i)q18+2.00000iq19+(4.138181.69572i)q20+3.80423iq21+(1.55754+0.793604i)q22+(2.62866+2.62866i)q23+(3.804235.23607i)q24+(2.236074.47214i)q25+(5.854101.90211i)q26+(1.23607+1.23607i)q27+(0.5201473.28408i)q28+1.45309q29+(5.52015+4.67853i)q305.25731iq31+(4.00000+4.00000i)q32+(2.000002.00000i)q33+(1.90211+0.618034i)q34+(3.61803+0.854102i)q35+(3.61803+2.62866i)q36+(3.077683.07768i)q37+(1.28408+2.52015i)q389.95959q39+(4.125694.79360i)q407.70820q41+(2.44246+4.79360i)q42+(2.38197+2.38197i)q43+(1.45309+2.00000i)q44+(2.628664.25325i)q45+(5.00000+1.62460i)q46+(7.33094+7.33094i)q47+(8.155374.15537i)q484.23607iq49+(5.688904.19958i)q50+3.23607q51+(8.59783+1.36176i)q52+(0.7265430.726543i)q53+(2.35114+0.763932i)q54+(2.35114+1.45309i)q55+(2.763933.80423i)q56+(3.236073.23607i)q57+(1.83099+0.932938i)q588.47214iq59+(3.95199+9.43945i)q60+9.95959iq61+(3.375406.62460i)q62+(2.628662.62866i)q63+(7.60845+2.47214i)q64+(2.23607+9.47214i)q65+(1.236073.80423i)q66+(2.38197+2.38197i)q67+(2.793600.442463i)q68+8.50651q69+(4.01062+3.39915i)q707.05342iq71+(6.24669+0.989378i)q72+(8.70820+8.70820i)q73+(1.902115.85410i)q74+(10.8541+3.61803i)q75+(3.23607+2.35114i)q76+(1.453091.45309i)q77+(12.54986.39445i)q78+12.3107q79+(2.120998.68915i)q80+10.7082q81+(9.712904.94897i)q82+(4.381974.38197i)q83+(6.15537+4.47214i)q84+(0.7265433.07768i)q85+(1.47214+4.53077i)q86+(2.351142.35114i)q87+(0.546915+3.45309i)q88+6.47214iq89+(0.5815427.04711i)q907.23607q91+(7.343421.16308i)q92+(8.50651+8.50651i)q93+(4.53077+13.9443i)q94+(2.351143.80423i)q95+12.9443q96+(0.236068+0.236068i)q97+(2.719725.33776i)q98+2.76393iq99+O(q100)q+(1.26007 + 0.642040i) q^{2} +(-1.61803 - 1.61803i) q^{3} +(1.17557 + 1.61803i) q^{4} +(-1.90211 + 1.17557i) q^{5} +(-1.00000 - 3.07768i) q^{6} +(-1.17557 - 1.17557i) q^{7} +(0.442463 + 2.79360i) q^{8} +2.23607i q^{9} +(-3.15156 + 0.260074i) q^{10} +1.23607 q^{11} +(0.715921 - 4.52015i) q^{12} +(3.07768 - 3.07768i) q^{13} +(-0.726543 - 2.23607i) q^{14} +(4.97980 + 1.17557i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-1.00000 + 1.00000i) q^{17} +(-1.43564 + 2.81761i) q^{18} +2.00000i q^{19} +(-4.13818 - 1.69572i) q^{20} +3.80423i q^{21} +(1.55754 + 0.793604i) q^{22} +(-2.62866 + 2.62866i) q^{23} +(3.80423 - 5.23607i) q^{24} +(2.23607 - 4.47214i) q^{25} +(5.85410 - 1.90211i) q^{26} +(-1.23607 + 1.23607i) q^{27} +(0.520147 - 3.28408i) q^{28} +1.45309 q^{29} +(5.52015 + 4.67853i) q^{30} -5.25731i q^{31} +(-4.00000 + 4.00000i) q^{32} +(-2.00000 - 2.00000i) q^{33} +(-1.90211 + 0.618034i) q^{34} +(3.61803 + 0.854102i) q^{35} +(-3.61803 + 2.62866i) q^{36} +(-3.07768 - 3.07768i) q^{37} +(-1.28408 + 2.52015i) q^{38} -9.95959 q^{39} +(-4.12569 - 4.79360i) q^{40} -7.70820 q^{41} +(-2.44246 + 4.79360i) q^{42} +(2.38197 + 2.38197i) q^{43} +(1.45309 + 2.00000i) q^{44} +(-2.62866 - 4.25325i) q^{45} +(-5.00000 + 1.62460i) q^{46} +(7.33094 + 7.33094i) q^{47} +(8.15537 - 4.15537i) q^{48} -4.23607i q^{49} +(5.68890 - 4.19958i) q^{50} +3.23607 q^{51} +(8.59783 + 1.36176i) q^{52} +(0.726543 - 0.726543i) q^{53} +(-2.35114 + 0.763932i) q^{54} +(-2.35114 + 1.45309i) q^{55} +(2.76393 - 3.80423i) q^{56} +(3.23607 - 3.23607i) q^{57} +(1.83099 + 0.932938i) q^{58} -8.47214i q^{59} +(3.95199 + 9.43945i) q^{60} +9.95959i q^{61} +(3.37540 - 6.62460i) q^{62} +(2.62866 - 2.62866i) q^{63} +(-7.60845 + 2.47214i) q^{64} +(-2.23607 + 9.47214i) q^{65} +(-1.23607 - 3.80423i) q^{66} +(-2.38197 + 2.38197i) q^{67} +(-2.79360 - 0.442463i) q^{68} +8.50651 q^{69} +(4.01062 + 3.39915i) q^{70} -7.05342i q^{71} +(-6.24669 + 0.989378i) q^{72} +(8.70820 + 8.70820i) q^{73} +(-1.90211 - 5.85410i) q^{74} +(-10.8541 + 3.61803i) q^{75} +(-3.23607 + 2.35114i) q^{76} +(-1.45309 - 1.45309i) q^{77} +(-12.5498 - 6.39445i) q^{78} +12.3107 q^{79} +(-2.12099 - 8.68915i) q^{80} +10.7082 q^{81} +(-9.71290 - 4.94897i) q^{82} +(-4.38197 - 4.38197i) q^{83} +(-6.15537 + 4.47214i) q^{84} +(0.726543 - 3.07768i) q^{85} +(1.47214 + 4.53077i) q^{86} +(-2.35114 - 2.35114i) q^{87} +(0.546915 + 3.45309i) q^{88} +6.47214i q^{89} +(-0.581542 - 7.04711i) q^{90} -7.23607 q^{91} +(-7.34342 - 1.16308i) q^{92} +(-8.50651 + 8.50651i) q^{93} +(4.53077 + 13.9443i) q^{94} +(-2.35114 - 3.80423i) q^{95} +12.9443 q^{96} +(-0.236068 + 0.236068i) q^{97} +(2.71972 - 5.33776i) q^{98} +2.76393i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q2q24q38q6+4q810q108q11+12q12+8q168q17+10q18+12q22+20q26+8q2720q28+20q3032q3216q33+20q35+6q98+O(q100) 8 q - 2 q^{2} - 4 q^{3} - 8 q^{6} + 4 q^{8} - 10 q^{10} - 8 q^{11} + 12 q^{12} + 8 q^{16} - 8 q^{17} + 10 q^{18} + 12 q^{22} + 20 q^{26} + 8 q^{27} - 20 q^{28} + 20 q^{30} - 32 q^{32} - 16 q^{33} + 20 q^{35}+ \cdots - 6 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

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

nn 1717 2121 3131
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 1-1 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 1.26007 + 0.642040i 0.891007 + 0.453990i
33 −1.61803 1.61803i −0.934172 0.934172i 0.0637909 0.997963i 0.479681π-0.479681\pi
−0.997963 + 0.0637909i 0.979681π0.979681\pi
44 1.17557 + 1.61803i 0.587785 + 0.809017i
55 −1.90211 + 1.17557i −0.850651 + 0.525731i
66 −1.00000 3.07768i −0.408248 1.25646i
77 −1.17557 1.17557i −0.444324 0.444324i 0.449138 0.893462i 0.351731π-0.351731\pi
−0.893462 + 0.449138i 0.851731π0.851731\pi
88 0.442463 + 2.79360i 0.156434 + 0.987688i
99 2.23607i 0.745356i
1010 −3.15156 + 0.260074i −0.996612 + 0.0822425i
1111 1.23607 0.372689 0.186344 0.982485i 0.440336π-0.440336\pi
0.186344 + 0.982485i 0.440336π0.440336\pi
1212 0.715921 4.52015i 0.206669 1.30485i
1313 3.07768 3.07768i 0.853596 0.853596i −0.136978 0.990574i 0.543739π-0.543739\pi
0.990574 + 0.136978i 0.0437390π0.0437390\pi
1414 −0.726543 2.23607i −0.194177 0.597614i
1515 4.97980 + 1.17557i 1.28578 + 0.303531i
1616 −1.23607 + 3.80423i −0.309017 + 0.951057i
1717 −1.00000 + 1.00000i −0.242536 + 0.242536i −0.817898 0.575363i 0.804861π-0.804861\pi
0.575363 + 0.817898i 0.304861π0.304861\pi
1818 −1.43564 + 2.81761i −0.338385 + 0.664117i
1919 2.00000i 0.458831i 0.973329 + 0.229416i 0.0736815π0.0736815\pi
−0.973329 + 0.229416i 0.926318π0.926318\pi
2020 −4.13818 1.69572i −0.925325 0.379174i
2121 3.80423i 0.830150i
2222 1.55754 + 0.793604i 0.332068 + 0.169197i
2323 −2.62866 + 2.62866i −0.548113 + 0.548113i −0.925895 0.377782i 0.876687π-0.876687\pi
0.377782 + 0.925895i 0.376687π0.376687\pi
2424 3.80423 5.23607i 0.776534 1.06881i
2525 2.23607 4.47214i 0.447214 0.894427i
2626 5.85410 1.90211i 1.14808 0.373035i
2727 −1.23607 + 1.23607i −0.237881 + 0.237881i
2828 0.520147 3.28408i 0.0982985 0.620633i
2929 1.45309 0.269831 0.134916 0.990857i 0.456924π-0.456924\pi
0.134916 + 0.990857i 0.456924π0.456924\pi
3030 5.52015 + 4.67853i 1.00784 + 0.854179i
3131 5.25731i 0.944241i −0.881534 0.472120i 0.843489π-0.843489\pi
0.881534 0.472120i 0.156511π-0.156511\pi
3232 −4.00000 + 4.00000i −0.707107 + 0.707107i
3333 −2.00000 2.00000i −0.348155 0.348155i
3434 −1.90211 + 0.618034i −0.326210 + 0.105992i
3535 3.61803 + 0.854102i 0.611559 + 0.144370i
3636 −3.61803 + 2.62866i −0.603006 + 0.438109i
3737 −3.07768 3.07768i −0.505968 0.505968i 0.407318 0.913286i 0.366464π-0.366464\pi
−0.913286 + 0.407318i 0.866464π0.866464\pi
3838 −1.28408 + 2.52015i −0.208305 + 0.408822i
3939 −9.95959 −1.59481
4040 −4.12569 4.79360i −0.652330 0.757935i
4141 −7.70820 −1.20382 −0.601910 0.798564i 0.705593π-0.705593\pi
−0.601910 + 0.798564i 0.705593π0.705593\pi
4242 −2.44246 + 4.79360i −0.376880 + 0.739669i
4343 2.38197 + 2.38197i 0.363246 + 0.363246i 0.865007 0.501760i 0.167314π-0.167314\pi
−0.501760 + 0.865007i 0.667314π0.667314\pi
4444 1.45309 + 2.00000i 0.219061 + 0.301511i
4545 −2.62866 4.25325i −0.391857 0.634038i
4646 −5.00000 + 1.62460i −0.737210 + 0.239534i
4747 7.33094 + 7.33094i 1.06933 + 1.06933i 0.997411 + 0.0719165i 0.0229115π0.0229115\pi
0.0719165 + 0.997411i 0.477088π0.477088\pi
4848 8.15537 4.15537i 1.17713 0.599776i
4949 4.23607i 0.605153i
5050 5.68890 4.19958i 0.804532 0.593910i
5151 3.23607 0.453140
5252 8.59783 + 1.36176i 1.19230 + 0.188842i
5353 0.726543 0.726543i 0.0997983 0.0997983i −0.655445 0.755243i 0.727519π-0.727519\pi
0.755243 + 0.655445i 0.227519π0.227519\pi
5454 −2.35114 + 0.763932i −0.319950 + 0.103958i
5555 −2.35114 + 1.45309i −0.317028 + 0.195934i
5656 2.76393 3.80423i 0.369346 0.508361i
5757 3.23607 3.23607i 0.428628 0.428628i
5858 1.83099 + 0.932938i 0.240421 + 0.122501i
5959 8.47214i 1.10298i −0.834182 0.551489i 0.814060π-0.814060\pi
0.834182 0.551489i 0.185940π-0.185940\pi
6060 3.95199 + 9.43945i 0.510200 + 1.21863i
6161 9.95959i 1.27520i 0.770370 + 0.637598i 0.220072π0.220072\pi
−0.770370 + 0.637598i 0.779928π0.779928\pi
6262 3.37540 6.62460i 0.428676 0.841325i
6363 2.62866 2.62866i 0.331179 0.331179i
6464 −7.60845 + 2.47214i −0.951057 + 0.309017i
6565 −2.23607 + 9.47214i −0.277350 + 1.17487i
6666 −1.23607 3.80423i −0.152149 0.468268i
6767 −2.38197 + 2.38197i −0.291003 + 0.291003i −0.837477 0.546473i 0.815970π-0.815970\pi
0.546473 + 0.837477i 0.315970π0.315970\pi
6868 −2.79360 0.442463i −0.338774 0.0536566i
6969 8.50651 1.02406
7070 4.01062 + 3.39915i 0.479361 + 0.406276i
7171 7.05342i 0.837087i −0.908197 0.418544i 0.862541π-0.862541\pi
0.908197 0.418544i 0.137459π-0.137459\pi
7272 −6.24669 + 0.989378i −0.736179 + 0.116599i
7373 8.70820 + 8.70820i 1.01922 + 1.01922i 0.999812 + 0.0194065i 0.00617767π0.00617767\pi
0.0194065 + 0.999812i 0.493822π0.493822\pi
7474 −1.90211 5.85410i −0.221116 0.680526i
7575 −10.8541 + 3.61803i −1.25332 + 0.417775i
7676 −3.23607 + 2.35114i −0.371202 + 0.269694i
7777 −1.45309 1.45309i −0.165594 0.165594i
7878 −12.5498 6.39445i −1.42099 0.724029i
7979 12.3107 1.38507 0.692533 0.721386i 0.256495π-0.256495\pi
0.692533 + 0.721386i 0.256495π0.256495\pi
8080 −2.12099 8.68915i −0.237134 0.971477i
8181 10.7082 1.18980
8282 −9.71290 4.94897i −1.07261 0.546522i
8383 −4.38197 4.38197i −0.480983 0.480983i 0.424462 0.905446i 0.360463π-0.360463\pi
−0.905446 + 0.424462i 0.860463π0.860463\pi
8484 −6.15537 + 4.47214i −0.671606 + 0.487950i
8585 0.726543 3.07768i 0.0788046 0.333822i
8686 1.47214 + 4.53077i 0.158745 + 0.488565i
8787 −2.35114 2.35114i −0.252069 0.252069i
8888 0.546915 + 3.45309i 0.0583013 + 0.368100i
8989 6.47214i 0.686045i 0.939327 + 0.343023i 0.111451π0.111451\pi
−0.939327 + 0.343023i 0.888549π0.888549\pi
9090 −0.581542 7.04711i −0.0612999 0.742831i
9191 −7.23607 −0.758546
9292 −7.34342 1.16308i −0.765605 0.121260i
9393 −8.50651 + 8.50651i −0.882084 + 0.882084i
9494 4.53077 + 13.9443i 0.467313 + 1.43824i
9595 −2.35114 3.80423i −0.241222 0.390305i
9696 12.9443 1.32112
9797 −0.236068 + 0.236068i −0.0239691 + 0.0239691i −0.718990 0.695021i 0.755395π-0.755395\pi
0.695021 + 0.718990i 0.255395π0.255395\pi
9898 2.71972 5.33776i 0.274734 0.539195i
9999 2.76393i 0.277786i
100100 9.86472 1.63928i 0.986472 0.163928i
101101 12.3107i 1.22496i −0.790485 0.612482i 0.790171π-0.790171\pi
0.790485 0.612482i 0.209829π-0.209829\pi
102102 4.07768 + 2.07768i 0.403751 + 0.205721i
103103 −7.33094 + 7.33094i −0.722339 + 0.722339i −0.969081 0.246742i 0.920640π-0.920640\pi
0.246742 + 0.969081i 0.420640π0.420640\pi
104104 9.95959 + 7.23607i 0.976618 + 0.709555i
105105 −4.47214 7.23607i −0.436436 0.706168i
106106 1.38197 0.449028i 0.134228 0.0436135i
107107 12.0902 12.0902i 1.16880 1.16880i 0.186310 0.982491i 0.440347π-0.440347\pi
0.982491 0.186310i 0.0596528π-0.0596528\pi
108108 −3.45309 0.546915i −0.332273 0.0526269i
109109 −6.71040 −0.642739 −0.321370 0.946954i 0.604143π-0.604143\pi
−0.321370 + 0.946954i 0.604143π0.604143\pi
110110 −3.89555 + 0.321469i −0.371426 + 0.0306508i
111111 9.95959i 0.945323i
112112 5.92522 3.01905i 0.559881 0.285273i
113113 −4.70820 4.70820i −0.442911 0.442911i 0.450078 0.892989i 0.351396π-0.351396\pi
−0.892989 + 0.450078i 0.851396π0.851396\pi
114114 6.15537 2.00000i 0.576503 0.187317i
115115 1.90983 8.09017i 0.178093 0.754412i
116116 1.70820 + 2.35114i 0.158603 + 0.218298i
117117 6.88191 + 6.88191i 0.636233 + 0.636233i
118118 5.43945 10.6755i 0.500742 0.982761i
119119 2.35114 0.215529
120120 −1.08070 + 14.4317i −0.0986540 + 1.31743i
121121 −9.47214 −0.861103
122122 −6.39445 + 12.5498i −0.578927 + 1.13621i
123123 12.4721 + 12.4721i 1.12457 + 1.12457i
124124 8.50651 6.18034i 0.763907 0.555011i
125125 1.00406 + 11.1352i 0.0898056 + 0.995959i
126126 5.00000 1.62460i 0.445435 0.144731i
127127 −8.78402 8.78402i −0.779456 0.779456i 0.200282 0.979738i 0.435814π-0.435814\pi
−0.979738 + 0.200282i 0.935814π0.935814\pi
128128 −11.1744 1.76985i −0.987688 0.156434i
129129 7.70820i 0.678670i
130130 −8.89910 + 10.4999i −0.780502 + 0.920906i
131131 0.291796 0.0254943 0.0127472 0.999919i 0.495942π-0.495942\pi
0.0127472 + 0.999919i 0.495942π0.495942\pi
132132 0.884927 5.58721i 0.0770230 0.486304i
133133 2.35114 2.35114i 0.203870 0.203870i
134134 −4.53077 + 1.47214i −0.391399 + 0.127173i
135135 0.898056 3.80423i 0.0772924 0.327416i
136136 −3.23607 2.35114i −0.277491 0.201609i
137137 3.47214 3.47214i 0.296645 0.296645i −0.543054 0.839698i 0.682732π-0.682732\pi
0.839698 + 0.543054i 0.182732π0.182732\pi
138138 10.7188 + 5.46151i 0.912447 + 0.464915i
139139 5.41641i 0.459414i 0.973260 + 0.229707i 0.0737767π0.0737767\pi
−0.973260 + 0.229707i 0.926223π0.926223\pi
140140 2.87129 + 6.85816i 0.242668 + 0.579620i
141141 23.7234i 1.99787i
142142 4.52858 8.88783i 0.380030 0.745850i
143143 3.80423 3.80423i 0.318125 0.318125i
144144 −8.50651 2.76393i −0.708876 0.230328i
145145 −2.76393 + 1.70820i −0.229532 + 0.141859i
146146 5.38197 + 16.5640i 0.445415 + 1.37085i
147147 −6.85410 + 6.85410i −0.565317 + 0.565317i
148148 1.36176 8.59783i 0.111936 0.706737i
149149 −13.2088 −1.08211 −0.541053 0.840988i 0.681974π-0.681974\pi
−0.541053 + 0.840988i 0.681974π0.681974\pi
150150 −15.9999 2.40977i −1.30639 0.196757i
151151 14.6619i 1.19317i 0.802551 + 0.596583i 0.203475π0.203475\pi
−0.802551 + 0.596583i 0.796525π0.796525\pi
152152 −5.58721 + 0.884927i −0.453182 + 0.0717771i
153153 −2.23607 2.23607i −0.180775 0.180775i
154154 −0.898056 2.76393i −0.0723674 0.222724i
155155 6.18034 + 10.0000i 0.496417 + 0.803219i
156156 −11.7082 16.1150i −0.937407 1.29023i
157157 9.78808 + 9.78808i 0.781174 + 0.781174i 0.980029 0.198855i 0.0637223π-0.0637223\pi
−0.198855 + 0.980029i 0.563722π0.563722\pi
158158 15.5124 + 7.90398i 1.23410 + 0.628807i
159159 −2.35114 −0.186458
160160 2.90617 12.3107i 0.229753 0.973249i
161161 6.18034 0.487079
162162 13.4931 + 6.87509i 1.06012 + 0.540158i
163163 −7.14590 7.14590i −0.559710 0.559710i 0.369515 0.929225i 0.379524π-0.379524\pi
−0.929225 + 0.369515i 0.879524π0.879524\pi
164164 −9.06154 12.4721i −0.707587 0.973910i
165165 6.15537 + 1.45309i 0.479195 + 0.113123i
166166 −2.70820 8.33499i −0.210197 0.646921i
167167 −0.277515 0.277515i −0.0214747 0.0214747i 0.696288 0.717763i 0.254834π-0.254834\pi
−0.717763 + 0.696288i 0.754834π0.754834\pi
168168 −10.6275 + 1.68323i −0.819930 + 0.129864i
169169 5.94427i 0.457252i
170170 2.89149 3.41164i 0.221767 0.261661i
171171 −4.47214 −0.341993
172172 −1.05393 + 6.65427i −0.0803616 + 0.507383i
173173 6.32688 6.32688i 0.481024 0.481024i −0.424435 0.905459i 0.639527π-0.639527\pi
0.905459 + 0.424435i 0.139527π0.139527\pi
174174 −1.45309 4.47214i −0.110158 0.339032i
175175 −7.88597 + 2.62866i −0.596123 + 0.198708i
176176 −1.52786 + 4.70228i −0.115167 + 0.354448i
177177 −13.7082 + 13.7082i −1.03037 + 1.03037i
178178 −4.15537 + 8.15537i −0.311458 + 0.611271i
179179 16.4721i 1.23119i 0.788065 + 0.615593i 0.211083π0.211083\pi
−0.788065 + 0.615593i 0.788917π0.788917\pi
180180 3.79174 9.25325i 0.282620 0.689697i
181181 9.40456i 0.699036i 0.936930 + 0.349518i 0.113655π0.113655\pi
−0.936930 + 0.349518i 0.886345π0.886345\pi
182182 −9.11798 4.64584i −0.675869 0.344373i
183183 16.1150 16.1150i 1.19125 1.19125i
184184 −8.50651 6.18034i −0.627108 0.455621i
185185 9.47214 + 2.23607i 0.696405 + 0.164399i
186186 −16.1803 + 5.25731i −1.18640 + 0.385485i
187187 −1.23607 + 1.23607i −0.0903902 + 0.0903902i
188188 −3.24367 + 20.4797i −0.236569 + 1.49364i
189189 2.90617 0.211393
190190 −0.520147 6.30313i −0.0377354 0.457277i
191191 12.8658i 0.930934i 0.885065 + 0.465467i 0.154114π0.154114\pi
−0.885065 + 0.465467i 0.845886π0.845886\pi
192192 16.3107 + 8.31073i 1.17713 + 0.599776i
193193 −7.47214 7.47214i −0.537856 0.537856i 0.385043 0.922899i 0.374187π-0.374187\pi
−0.922899 + 0.385043i 0.874187π0.874187\pi
194194 −0.449028 + 0.145898i −0.0322383 + 0.0104749i
195195 18.9443 11.7082i 1.35663 0.838442i
196196 6.85410 4.97980i 0.489579 0.355700i
197197 −2.17963 2.17963i −0.155292 0.155292i 0.625185 0.780477i 0.285024π-0.285024\pi
−0.780477 + 0.625185i 0.785024π0.785024\pi
198198 −1.77455 + 3.48276i −0.126112 + 0.247509i
199199 18.1231 1.28471 0.642355 0.766407i 0.277957π-0.277957\pi
0.642355 + 0.766407i 0.277957π0.277957\pi
200200 13.4828 + 4.26793i 0.953375 + 0.301788i
201201 7.70820 0.543695
202202 7.90398 15.5124i 0.556122 1.09145i
203203 −1.70820 1.70820i −0.119892 0.119892i
204204 3.80423 + 5.23607i 0.266349 + 0.366598i
205205 14.6619 9.06154i 1.02403 0.632885i
206206 −13.9443 + 4.53077i −0.971543 + 0.315674i
207207 −5.87785 5.87785i −0.408539 0.408539i
208208 7.90398 + 15.5124i 0.548042 + 1.07559i
209209 2.47214i 0.171001i
210210 −0.989378 11.9893i −0.0682736 0.827338i
211211 15.7082 1.08140 0.540699 0.841216i 0.318160π-0.318160\pi
0.540699 + 0.841216i 0.318160π0.318160\pi
212212 2.02967 + 0.321469i 0.139398 + 0.0220785i
213213 −11.4127 + 11.4127i −0.781984 + 0.781984i
214214 22.9969 7.47214i 1.57203 0.510785i
215215 −7.33094 1.73060i −0.499966 0.118026i
216216 −4.00000 2.90617i −0.272166 0.197740i
217217 −6.18034 + 6.18034i −0.419549 + 0.419549i
218218 −8.45559 4.30834i −0.572685 0.291798i
219219 28.1803i 1.90425i
220220 −5.11507 2.09602i −0.344858 0.141314i
221221 6.15537i 0.414055i
222222 −6.39445 + 12.5498i −0.429168 + 0.842289i
223223 −1.73060 + 1.73060i −0.115890 + 0.115890i −0.762673 0.646784i 0.776114π-0.776114\pi
0.646784 + 0.762673i 0.276114π0.276114\pi
224224 9.40456 0.628369
225225 10.0000 + 5.00000i 0.666667 + 0.333333i
226226 −2.90983 8.95554i −0.193559 0.595713i
227227 −11.6180 + 11.6180i −0.771116 + 0.771116i −0.978302 0.207186i 0.933570π-0.933570\pi
0.207186 + 0.978302i 0.433570π0.433570\pi
228228 9.04029 + 1.43184i 0.598708 + 0.0948260i
229229 −21.3723 −1.41232 −0.706160 0.708053i 0.749574π-0.749574\pi
−0.706160 + 0.708053i 0.749574π0.749574\pi
230230 7.60074 8.96802i 0.501178 0.591334i
231231 4.70228i 0.309387i
232232 0.642937 + 4.05934i 0.0422109 + 0.266509i
233233 −3.47214 3.47214i −0.227467 0.227467i 0.584167 0.811634i 0.301421π-0.301421\pi
−0.811634 + 0.584167i 0.801421π0.801421\pi
234234 4.25325 + 13.0902i 0.278044 + 0.855731i
235235 −22.5623 5.32624i −1.47180 0.347445i
236236 13.7082 9.95959i 0.892328 0.648314i
237237 −19.9192 19.9192i −1.29389 1.29389i
238238 2.96261 + 1.50953i 0.192038 + 0.0978480i
239239 −29.3238 −1.89680 −0.948398 0.317083i 0.897297π-0.897297\pi
−0.948398 + 0.317083i 0.897297π0.897297\pi
240240 −10.6275 + 17.4912i −0.686002 + 1.12905i
241241 6.76393 0.435703 0.217852 0.975982i 0.430095π-0.430095\pi
0.217852 + 0.975982i 0.430095π0.430095\pi
242242 −11.9356 6.08149i −0.767249 0.390933i
243243 −13.6180 13.6180i −0.873597 0.873597i
244244 −16.1150 + 11.7082i −1.03165 + 0.749541i
245245 4.97980 + 8.05748i 0.318148 + 0.514774i
246246 7.70820 + 23.7234i 0.491457 + 1.51255i
247247 6.15537 + 6.15537i 0.391657 + 0.391657i
248248 14.6868 2.32617i 0.932616 0.147712i
249249 14.1803i 0.898643i
250250 −5.88403 + 14.6758i −0.372139 + 0.928177i
251251 −22.1803 −1.40001 −0.700005 0.714138i 0.746819π-0.746819\pi
−0.700005 + 0.714138i 0.746819π0.746819\pi
252252 7.34342 + 1.16308i 0.462592 + 0.0732674i
253253 −3.24920 + 3.24920i −0.204275 + 0.204275i
254254 −5.42882 16.7082i −0.340635 1.04837i
255255 −6.15537 + 3.80423i −0.385464 + 0.238230i
256256 −12.9443 9.40456i −0.809017 0.587785i
257257 18.7082 18.7082i 1.16699 1.16699i 0.184073 0.982913i 0.441072π-0.441072\pi
0.982913 0.184073i 0.0589283π-0.0589283\pi
258258 4.94897 9.71290i 0.308110 0.604699i
259259 7.23607i 0.449627i
260260 −17.9549 + 7.51713i −1.11352 + 0.466193i
261261 3.24920i 0.201120i
262262 0.367684 + 0.187345i 0.0227156 + 0.0115742i
263263 16.3925 16.3925i 1.01080 1.01080i 0.0108623 0.999941i 0.496542π-0.496542\pi
0.999941 0.0108623i 0.00345764π-0.00345764\pi
264264 4.70228 6.47214i 0.289405 0.398332i
265265 −0.527864 + 2.23607i −0.0324264 + 0.137361i
266266 4.47214 1.45309i 0.274204 0.0890944i
267267 10.4721 10.4721i 0.640884 0.640884i
268268 −6.65427 1.05393i −0.406474 0.0643792i
269269 17.9111 1.09206 0.546029 0.837766i 0.316139π-0.316139\pi
0.546029 + 0.837766i 0.316139π0.316139\pi
270270 3.57408 4.21702i 0.217512 0.256639i
271271 31.6749i 1.92411i −0.272851 0.962056i 0.587967π-0.587967\pi
0.272851 0.962056i 0.412033π-0.412033\pi
272272 −2.56816 5.04029i −0.155717 0.305613i
273273 11.7082 + 11.7082i 0.708613 + 0.708613i
274274 6.60440 2.14590i 0.398986 0.129638i
275275 2.76393 5.52786i 0.166671 0.333343i
276276 10.0000 + 13.7638i 0.601929 + 0.828485i
277277 2.17963 + 2.17963i 0.130961 + 0.130961i 0.769549 0.638588i 0.220481π-0.220481\pi
−0.638588 + 0.769549i 0.720481π0.720481\pi
278278 −3.47755 + 6.82507i −0.208569 + 0.409341i
279279 11.7557 0.703796
280280 −0.785175 + 10.4853i −0.0469232 + 0.626614i
281281 3.70820 0.221213 0.110606 0.993864i 0.464721π-0.464721\pi
0.110606 + 0.993864i 0.464721π0.464721\pi
282282 15.2314 29.8932i 0.907015 1.78012i
283283 15.6180 + 15.6180i 0.928396 + 0.928396i 0.997602 0.0692066i 0.0220468π-0.0220468\pi
−0.0692066 + 0.997602i 0.522047π0.522047\pi
284284 11.4127 8.29180i 0.677218 0.492028i
285285 −2.35114 + 9.95959i −0.139270 + 0.589955i
286286 7.23607 2.35114i 0.427878 0.139026i
287287 9.06154 + 9.06154i 0.534886 + 0.534886i
288288 −8.94427 8.94427i −0.527046 0.527046i
289289 15.0000i 0.882353i
290290 −4.57949 + 0.377909i −0.268917 + 0.0221916i
291291 0.763932 0.0447825
292292 −3.85306 + 24.3273i −0.225483 + 1.42365i
293293 −0.726543 + 0.726543i −0.0424451 + 0.0424451i −0.728011 0.685566i 0.759555π-0.759555\pi
0.685566 + 0.728011i 0.259555π0.259555\pi
294294 −13.0373 + 4.23607i −0.760349 + 0.247053i
295295 9.95959 + 16.1150i 0.579870 + 0.938249i
296296 7.23607 9.95959i 0.420588 0.578890i
297297 −1.52786 + 1.52786i −0.0886557 + 0.0886557i
298298 −16.6440 8.48057i −0.964164 0.491266i
299299 16.1803i 0.935733i
300300 −18.6139 13.3091i −1.07467 0.768398i
301301 5.60034i 0.322798i
302302 −9.41350 + 18.4750i −0.541686 + 1.06312i
303303 −19.9192 + 19.9192i −1.14433 + 1.14433i
304304 −7.60845 2.47214i −0.436375 0.141787i
305305 −11.7082 18.9443i −0.670410 1.08475i
306306 −1.38197 4.25325i −0.0790017 0.243142i
307307 6.56231 6.56231i 0.374531 0.374531i −0.494594 0.869124i 0.664683π-0.664683\pi
0.869124 + 0.494594i 0.164683π0.164683\pi
308308 0.642937 4.05934i 0.0366347 0.231303i
309309 23.7234 1.34958
310310 1.36729 + 16.5688i 0.0776567 + 0.941042i
311311 8.16348i 0.462909i −0.972846 0.231454i 0.925652π-0.925652\pi
0.972846 0.231454i 0.0743484π-0.0743484\pi
312312 −4.40676 27.8232i −0.249483 1.57518i
313313 −6.23607 6.23607i −0.352483 0.352483i 0.508549 0.861033i 0.330182π-0.330182\pi
−0.861033 + 0.508549i 0.830182π0.830182\pi
314314 6.04937 + 18.6180i 0.341385 + 1.05068i
315315 −1.90983 + 8.09017i −0.107607 + 0.455829i
316316 14.4721 + 19.9192i 0.814121 + 1.12054i
317317 10.6861 + 10.6861i 0.600193 + 0.600193i 0.940364 0.340171i 0.110485π-0.110485\pi
−0.340171 + 0.940364i 0.610485π0.610485\pi
318318 −2.96261 1.50953i −0.166135 0.0846500i
319319 1.79611 0.100563
320320 11.5660 13.6466i 0.646557 0.762866i
321321 −39.1246 −2.18372
322322 7.78768 + 3.96802i 0.433991 + 0.221129i
323323 −2.00000 2.00000i −0.111283 0.111283i
324324 12.5882 + 17.3262i 0.699347 + 0.962569i
325325 −6.88191 20.6457i −0.381740 1.14522i
326326 −4.41641 13.5923i −0.244602 0.752808i
327327 10.8576 + 10.8576i 0.600429 + 0.600429i
328328 −3.41060 21.5337i −0.188319 1.18900i
329329 17.2361i 0.950255i
330330 6.82328 + 5.78298i 0.375609 + 0.318343i
331331 28.0689 1.54281 0.771403 0.636347i 0.219555π-0.219555\pi
0.771403 + 0.636347i 0.219555π0.219555\pi
332332 1.93886 12.2415i 0.106409 0.671838i
333333 6.88191 6.88191i 0.377126 0.377126i
334334 −0.171513 0.527864i −0.00938480 0.0288834i
335335 1.73060 7.33094i 0.0945528 0.400532i
336336 −14.4721 4.70228i −0.789520 0.256531i
337337 −2.05573 + 2.05573i −0.111983 + 0.111983i −0.760878 0.648895i 0.775231π-0.775231\pi
0.648895 + 0.760878i 0.275231π0.275231\pi
338338 3.81646 7.49022i 0.207588 0.407414i
339339 15.2361i 0.827510i
340340 5.83390 2.44246i 0.316388 0.132461i
341341 6.49839i 0.351908i
342342 −5.63522 2.87129i −0.304718 0.155261i
343343 −13.2088 + 13.2088i −0.713208 + 0.713208i
344344 −5.60034 + 7.70820i −0.301950 + 0.415599i
345345 −16.1803 + 10.0000i −0.871120 + 0.538382i
346346 12.0344 3.91023i 0.646976 0.210215i
347347 −3.03444 + 3.03444i −0.162897 + 0.162897i −0.783849 0.620952i 0.786746π-0.786746\pi
0.620952 + 0.783849i 0.286746π0.286746\pi
348348 1.04029 6.56816i 0.0557656 0.352090i
349349 −15.5599 −0.832904 −0.416452 0.909158i 0.636727π-0.636727\pi
−0.416452 + 0.909158i 0.636727π0.636727\pi
350350 −11.6246 1.75080i −0.621361 0.0935844i
351351 7.60845i 0.406109i
352352 −4.94427 + 4.94427i −0.263531 + 0.263531i
353353 4.41641 + 4.41641i 0.235062 + 0.235062i 0.814802 0.579740i 0.196846π-0.196846\pi
−0.579740 + 0.814802i 0.696846π0.696846\pi
354354 −26.0746 + 8.47214i −1.38585 + 0.450289i
355355 8.29180 + 13.4164i 0.440083 + 0.712069i
356356 −10.4721 + 7.60845i −0.555022 + 0.403247i
357357 −3.80423 3.80423i −0.201341 0.201341i
358358 −10.5758 + 20.7561i −0.558946 + 1.09699i
359359 1.79611 0.0947952 0.0473976 0.998876i 0.484907π-0.484907\pi
0.0473976 + 0.998876i 0.484907π0.484907\pi
360360 10.7188 9.22533i 0.564932 0.486218i
361361 15.0000 0.789474
362362 −6.03810 + 11.8504i −0.317356 + 0.622845i
363363 15.3262 + 15.3262i 0.804419 + 0.804419i
364364 −8.50651 11.7082i −0.445862 0.613677i
365365 −26.8011 6.32688i −1.40283 0.331164i
366366 30.6525 9.95959i 1.60223 0.520596i
367367 −24.0009 24.0009i −1.25284 1.25284i −0.954442 0.298396i 0.903548π-0.903548\pi
−0.298396 0.954442i 0.596452π-0.596452\pi
368368 −6.75080 13.2492i −0.351910 0.690662i
369369 17.2361i 0.897274i
370370 10.4999 + 8.89910i 0.545866 + 0.462642i
371371 −1.70820 −0.0886855
372372 −23.7638 3.76382i −1.23210 0.195145i
373373 15.0454 15.0454i 0.779021 0.779021i −0.200644 0.979664i 0.564303π-0.564303\pi
0.979664 + 0.200644i 0.0643033π0.0643033\pi
374374 −2.35114 + 0.763932i −0.121575 + 0.0395020i
375375 16.3925 19.6417i 0.846504 1.01429i
376376 −17.2361 + 23.7234i −0.888882 + 1.22344i
377377 4.47214 4.47214i 0.230327 0.230327i
378378 3.66199 + 1.86588i 0.188352 + 0.0959703i
379379 35.8885i 1.84347i −0.387820 0.921735i 0.626772π-0.626772\pi
0.387820 0.921735i 0.373228π-0.373228\pi
380380 3.39144 8.27636i 0.173977 0.424568i
381381 28.4257i 1.45629i
382382 −8.26033 + 16.2118i −0.422635 + 0.829468i
383383 −11.1352 + 11.1352i −0.568980 + 0.568980i −0.931843 0.362862i 0.881799π-0.881799\pi
0.362862 + 0.931843i 0.381799π0.381799\pi
384384 15.2169 + 20.9443i 0.776534 + 1.06881i
385385 4.47214 + 1.05573i 0.227921 + 0.0538049i
386386 −4.61803 14.2128i −0.235052 0.723415i
387387 −5.32624 + 5.32624i −0.270748 + 0.270748i
388388 −0.659481 0.104451i −0.0334801 0.00530272i
389389 23.7234 1.20282 0.601412 0.798939i 0.294605π-0.294605\pi
0.601412 + 0.798939i 0.294605π0.294605\pi
390390 31.3883 2.59023i 1.58941 0.131161i
391391 5.25731i 0.265874i
392392 11.8339 1.87431i 0.597702 0.0946667i
393393 −0.472136 0.472136i −0.0238161 0.0238161i
394394 −1.34708 4.14590i −0.0678651 0.208867i
395395 −23.4164 + 14.4721i −1.17821 + 0.728172i
396396 −4.47214 + 3.24920i −0.224733 + 0.163278i
397397 7.22494 + 7.22494i 0.362609 + 0.362609i 0.864773 0.502164i 0.167462π-0.167462\pi
−0.502164 + 0.864773i 0.667462π0.667462\pi
398398 22.8364 + 11.6357i 1.14469 + 0.583246i
399399 −7.60845 −0.380899
400400 14.2491 + 14.0344i 0.712454 + 0.701719i
401401 −3.88854 −0.194185 −0.0970923 0.995275i 0.530954π-0.530954\pi
−0.0970923 + 0.995275i 0.530954π0.530954\pi
402402 9.71290 + 4.94897i 0.484436 + 0.246832i
403403 −16.1803 16.1803i −0.806000 0.806000i
404404 19.9192 14.4721i 0.991017 0.720016i
405405 −20.3682 + 12.5882i −1.01210 + 0.625515i
406406 −1.05573 3.24920i −0.0523949 0.161255i
407407 −3.80423 3.80423i −0.188568 0.188568i
408408 1.43184 + 9.04029i 0.0708867 + 0.447561i
409409 27.5967i 1.36457i −0.731086 0.682286i 0.760986π-0.760986\pi
0.731086 0.682286i 0.239014π-0.239014\pi
410410 24.2929 2.00470i 1.19974 0.0990051i
411411 −11.2361 −0.554234
412412 −20.4797 3.24367i −1.00896 0.159804i
413413 −9.95959 + 9.95959i −0.490080 + 0.490080i
414414 −3.63271 11.1803i −0.178538 0.549484i
415415 13.4863 + 3.18368i 0.662017 + 0.156281i
416416 24.6215i 1.20717i
417417 8.76393 8.76393i 0.429172 0.429172i
418418 −1.58721 + 3.11507i −0.0776329 + 0.152363i
419419 24.8328i 1.21316i −0.795022 0.606581i 0.792540π-0.792540\pi
0.795022 0.606581i 0.207460π-0.207460\pi
420420 6.45089 15.7426i 0.314771 0.768159i
421421 3.46120i 0.168689i 0.996437 + 0.0843443i 0.0268795π0.0268795\pi
−0.996437 + 0.0843443i 0.973120π0.973120\pi
422422 19.7935 + 10.0853i 0.963532 + 0.490944i
423423 −16.3925 + 16.3925i −0.797029 + 0.797029i
424424 2.35114 + 1.70820i 0.114182 + 0.0829577i
425425 2.23607 + 6.70820i 0.108465 + 0.325396i
426426 −21.7082 + 7.05342i −1.05177 + 0.341739i
427427 11.7082 11.7082i 0.566600 0.566600i
428428 33.7752 + 5.34946i 1.63258 + 0.258576i
429429 −12.3107 −0.594368
430430 −8.12641 6.88743i −0.391890 0.332142i
431431 11.7557i 0.566252i 0.959083 + 0.283126i 0.0913715π0.0913715\pi
−0.959083 + 0.283126i 0.908628π0.908628\pi
432432 −3.17442 6.23015i −0.152729 0.299748i
433433 23.1803 + 23.1803i 1.11398 + 1.11398i 0.992608 + 0.121369i 0.0387283π0.0387283\pi
0.121369 + 0.992608i 0.461272π0.461272\pi
434434 −11.7557 + 3.81966i −0.564292 + 0.183350i
435435 7.23607 + 1.70820i 0.346943 + 0.0819021i
436436 −7.88854 10.8576i −0.377793 0.519987i
437437 −5.25731 5.25731i −0.251491 0.251491i
438438 18.0929 35.5093i 0.864512 1.69670i
439439 −11.2007 −0.534579 −0.267290 0.963616i 0.586128π-0.586128\pi
−0.267290 + 0.963616i 0.586128π0.586128\pi
440440 −5.09964 5.92522i −0.243116 0.282474i
441441 9.47214 0.451054
442442 −3.95199 + 7.75621i −0.187977 + 0.368926i
443443 10.0902 + 10.0902i 0.479398 + 0.479398i 0.904939 0.425541i 0.139916π-0.139916\pi
−0.425541 + 0.904939i 0.639916π0.639916\pi
444444 −16.1150 + 11.7082i −0.764782 + 0.555647i
445445 −7.60845 12.3107i −0.360675 0.583585i
446446 −3.29180 + 1.06957i −0.155871 + 0.0506456i
447447 21.3723 + 21.3723i 1.01087 + 1.01087i
448448 11.8504 + 6.03810i 0.559881 + 0.285273i
449449 31.5967i 1.49114i 0.666426 + 0.745571i 0.267823π0.267823\pi
−0.666426 + 0.745571i 0.732177π0.732177\pi
450450 9.39054 + 12.7208i 0.442674 + 0.599663i
451451 −9.52786 −0.448650
452452 2.08321 13.1529i 0.0979859 0.618658i
453453 23.7234 23.7234i 1.11462 1.11462i
454454 −22.0988 + 7.18034i −1.03715 + 0.336990i
455455 13.7638 8.50651i 0.645258 0.398791i
456456 10.4721 + 7.60845i 0.490403 + 0.356298i
457457 −21.6525 + 21.6525i −1.01286 + 1.01286i −0.0129439 + 0.999916i 0.504120π0.504120\pi
−0.999916 + 0.0129439i 0.995880π0.995880\pi
458458 −26.9306 13.7218i −1.25839 0.641180i
459459 2.47214i 0.115389i
460460 15.3353 6.42040i 0.715013 0.299352i
461461 6.49839i 0.302660i 0.988483 + 0.151330i 0.0483557π0.0483557\pi
−0.988483 + 0.151330i 0.951644π0.951644\pi
462462 −3.01905 + 5.92522i −0.140459 + 0.275666i
463463 17.2905 17.2905i 0.803559 0.803559i −0.180091 0.983650i 0.557639π-0.557639\pi
0.983650 + 0.180091i 0.0576392π0.0576392\pi
464464 −1.79611 + 5.52786i −0.0833824 + 0.256625i
465465 6.18034 26.1803i 0.286606 1.21408i
466466 −2.14590 6.60440i −0.0994068 0.305943i
467467 −2.67376 + 2.67376i −0.123727 + 0.123727i −0.766259 0.642532i 0.777884π-0.777884\pi
0.642532 + 0.766259i 0.277884π0.277884\pi
468468 −3.04499 + 19.2253i −0.140755 + 0.888691i
469469 5.60034 0.258600
470470 −25.0105 21.1973i −1.15365 0.977761i
471471 31.6749i 1.45950i
472472 23.6678 3.74861i 1.08940 0.172544i
473473 2.94427 + 2.94427i 0.135378 + 0.135378i
474474 −12.3107 37.8885i −0.565451 1.74028i
475475 8.94427 + 4.47214i 0.410391 + 0.205196i
476476 2.76393 + 3.80423i 0.126685 + 0.174366i
477477 1.62460 + 1.62460i 0.0743853 + 0.0743853i
478478 −36.9501 18.8270i −1.69006 0.861127i
479479 7.60845 0.347639 0.173820 0.984778i 0.444389π-0.444389\pi
0.173820 + 0.984778i 0.444389π0.444389\pi
480480 −24.6215 + 15.2169i −1.12381 + 0.694553i
481481 −18.9443 −0.863784
482482 8.52305 + 4.34271i 0.388214 + 0.197805i
483483 −10.0000 10.0000i −0.455016 0.455016i
484484 −11.1352 15.3262i −0.506144 0.696647i
485485 0.171513 0.726543i 0.00778802 0.0329906i
486486 −8.41641 25.9030i −0.381776 1.17499i
487487 9.33905 + 9.33905i 0.423193 + 0.423193i 0.886302 0.463109i 0.153266π-0.153266\pi
−0.463109 + 0.886302i 0.653266π0.653266\pi
488488 −27.8232 + 4.40676i −1.25950 + 0.199484i
489489 23.1246i 1.04573i
490490 1.10169 + 13.3502i 0.0497692 + 0.603103i
491491 −10.7639 −0.485769 −0.242885 0.970055i 0.578094π-0.578094\pi
−0.242885 + 0.970055i 0.578094π0.578094\pi
492492 −5.51846 + 34.8422i −0.248792 + 1.57081i
493493 −1.45309 + 1.45309i −0.0654437 + 0.0654437i
494494 3.80423 + 11.7082i 0.171160 + 0.526777i
495495 −3.24920 5.25731i −0.146041 0.236299i
496496 20.0000 + 6.49839i 0.898027 + 0.291787i
497497 −8.29180 + 8.29180i −0.371938 + 0.371938i
498498 −9.10434 + 17.8683i −0.407975 + 0.800696i
499499 23.8885i 1.06940i 0.845043 + 0.534699i 0.179575π0.179575\pi
−0.845043 + 0.534699i 0.820425π0.820425\pi
500500 −16.8367 + 14.7148i −0.752962 + 0.658064i
501501 0.898056i 0.0401222i
502502 −27.9489 14.2407i −1.24742 0.635592i
503503 −5.53483 + 5.53483i −0.246786 + 0.246786i −0.819650 0.572864i 0.805832π-0.805832\pi
0.572864 + 0.819650i 0.305832π0.305832\pi
504504 8.50651 + 6.18034i 0.378910 + 0.275294i
505505 14.4721 + 23.4164i 0.644002 + 1.04202i
506506 −6.18034 + 2.00811i −0.274750 + 0.0892716i
507507 −9.61803 + 9.61803i −0.427152 + 0.427152i
508508 3.88661 24.5391i 0.172440 1.08875i
509509 9.06154 0.401646 0.200823 0.979628i 0.435638π-0.435638\pi
0.200823 + 0.979628i 0.435638π0.435638\pi
510510 −10.1987 + 0.841616i −0.451605 + 0.0372674i
511511 20.4742i 0.905726i
512512 −10.2726 20.1612i −0.453990 0.891007i
513513 −2.47214 2.47214i −0.109147 0.109147i
514514 35.5851 11.5623i 1.56959 0.509991i
515515 5.32624 22.5623i 0.234702 0.994214i
516516 12.4721 9.06154i 0.549055 0.398912i
517517 9.06154 + 9.06154i 0.398526 + 0.398526i
518518 −4.64584 + 9.11798i −0.204127 + 0.400621i
519519 −20.4742 −0.898718
520520 −27.4508 2.05562i −1.20380 0.0901447i
521521 8.47214 0.371171 0.185586 0.982628i 0.440582π-0.440582\pi
0.185586 + 0.982628i 0.440582π0.440582\pi
522522 −2.08611 + 4.09423i −0.0913067 + 0.179199i
523523 −16.7426 16.7426i −0.732105 0.732105i 0.238932 0.971036i 0.423203π-0.423203\pi
−0.971036 + 0.238932i 0.923203π0.923203\pi
524524 0.343027 + 0.472136i 0.0149852 + 0.0206254i
525525 17.0130 + 8.50651i 0.742509 + 0.371254i
526526 31.1803 10.1311i 1.35953 0.441737i
527527 5.25731 + 5.25731i 0.229012 + 0.229012i
528528 10.0806 5.13632i 0.438701 0.223529i
529529 9.18034i 0.399145i
530530 −2.10079 + 2.47870i −0.0912526 + 0.107668i
531531 18.9443 0.822111
532532 6.56816 + 1.04029i 0.284766 + 0.0451025i
533533 −23.7234 + 23.7234i −1.02758 + 1.02758i
534534 19.9192 6.47214i 0.861987 0.280077i
535535 −8.78402 + 37.2097i −0.379766 + 1.60872i
536536 −7.70820 5.60034i −0.332944 0.241898i
537537 26.6525 26.6525i 1.15014 1.15014i
538538 22.5693 + 11.4996i 0.973030 + 0.495784i
539539 5.23607i 0.225533i
540540 7.21110 3.01905i 0.310316 0.129919i
541541 2.90617i 0.124946i 0.998047 + 0.0624730i 0.0198987π0.0198987\pi
−0.998047 + 0.0624730i 0.980101π0.980101\pi
542542 20.3365 39.9127i 0.873529 1.71440i
543543 15.2169 15.2169i 0.653020 0.653020i
544544 8.00000i 0.342997i
545545 12.7639 7.88854i 0.546747 0.337908i
546546 7.23607 + 22.2703i 0.309675 + 0.953082i
547547 −8.56231 + 8.56231i −0.366098 + 0.366098i −0.866052 0.499954i 0.833350π-0.833350\pi
0.499954 + 0.866052i 0.333350π0.333350\pi
548548 9.69977 + 1.53629i 0.414354 + 0.0656272i
549549 −22.2703 −0.950474
550550 7.03186 5.19096i 0.299840 0.221343i
551551 2.90617i 0.123807i
552552 3.76382 + 23.7638i 0.160199 + 1.01146i
553553 −14.4721 14.4721i −0.615418 0.615418i
554554 1.34708 + 4.14590i 0.0572321 + 0.176142i
555555 −11.7082 18.9443i −0.496986 0.804140i
556556 −8.76393 + 6.36737i −0.371674 + 0.270037i
557557 −17.1845 17.1845i −0.728132 0.728132i 0.242116 0.970247i 0.422159π-0.422159\pi
−0.970247 + 0.242116i 0.922159π0.922159\pi
558558 14.8131 + 7.54763i 0.627087 + 0.319517i
559559 14.6619 0.620131
560560 −7.72133 + 12.7081i −0.326286 + 0.537015i
561561 4.00000 0.168880
562562 4.67261 + 2.38081i 0.197102 + 0.100429i
563563 11.3262 + 11.3262i 0.477344 + 0.477344i 0.904281 0.426937i 0.140407π-0.140407\pi
−0.426937 + 0.904281i 0.640407π0.640407\pi
564564 38.3853 27.8885i 1.61631 1.17432i
565565 14.4904 + 3.42071i 0.609614 + 0.143910i
566566 9.65248 + 29.7073i 0.405724 + 1.24869i
567567 −12.5882 12.5882i −0.528657 0.528657i
568568 19.7045 3.12088i 0.826781 0.130949i
569569 13.1246i 0.550212i −0.961414 0.275106i 0.911287π-0.911287\pi
0.961414 0.275106i 0.0887130π-0.0887130\pi
570570 −9.35706 + 11.0403i −0.391924 + 0.462427i
571571 −8.65248 −0.362095 −0.181047 0.983474i 0.557949π-0.557949\pi
−0.181047 + 0.983474i 0.557949π0.557949\pi
572572 10.6275 + 1.68323i 0.444358 + 0.0703794i
573573 20.8172 20.8172i 0.869653 0.869653i
574574 5.60034 + 17.2361i 0.233754 + 0.719420i
575575 5.87785 + 17.6336i 0.245123 + 0.735370i
576576 −5.52786 17.0130i −0.230328 0.708876i
577577 21.7639 21.7639i 0.906044 0.906044i −0.0899059 0.995950i 0.528657π-0.528657\pi
0.995950 + 0.0899059i 0.0286566π0.0286566\pi
578578 −9.63059 + 18.9011i −0.400580 + 0.786182i
579579 24.1803i 1.00490i
580580 −6.01313 2.46402i −0.249682 0.102313i
581581 10.3026i 0.427425i
582582 0.962611 + 0.490475i 0.0399015 + 0.0203308i
583583 0.898056 0.898056i 0.0371937 0.0371937i
584584 −20.4742 + 28.1803i −0.847229 + 1.16611i
585585 −21.1803 5.00000i −0.875699 0.206725i
586586 −1.38197 + 0.449028i −0.0570885 + 0.0185492i
587587 5.90983 5.90983i 0.243925 0.243925i −0.574547 0.818472i 0.694822π-0.694822\pi
0.818472 + 0.574547i 0.194822π0.194822\pi
588588 −19.1477 3.03269i −0.789636 0.125066i
589589 10.5146 0.433247
590590 2.20338 + 26.7005i 0.0907116 + 1.09924i
591591 7.05342i 0.290139i
592592 15.5124 7.90398i 0.637557 0.324851i
593593 −6.41641 6.41641i −0.263490 0.263490i 0.562980 0.826470i 0.309655π-0.309655\pi
−0.826470 + 0.562980i 0.809655π0.809655\pi
594594 −2.90617 + 0.944272i −0.119242 + 0.0387439i
595595 −4.47214 + 2.76393i −0.183340 + 0.113310i
596596 −15.5279 21.3723i −0.636046 0.875442i
597597 −29.3238 29.3238i −1.20014 1.20014i
598598 −10.3884 + 20.3884i −0.424814 + 0.833744i
599599 −27.5276 −1.12475 −0.562374 0.826883i 0.690112π-0.690112\pi
−0.562374 + 0.826883i 0.690112π0.690112\pi
600600 −14.9099 28.7212i −0.608694 1.17254i
601601 −4.29180 −0.175066 −0.0875330 0.996162i 0.527898π-0.527898\pi
−0.0875330 + 0.996162i 0.527898π0.527898\pi
602602 3.59564 7.05684i 0.146547 0.287615i
603603 −5.32624 5.32624i −0.216901 0.216901i
604604 −23.7234 + 17.2361i −0.965292 + 0.701326i
605605 18.0171 11.1352i 0.732498 0.452709i
606606 −37.8885 + 12.3107i −1.53912 + 0.500089i
607607 −6.08985 6.08985i −0.247180 0.247180i 0.572633 0.819812i 0.305922π-0.305922\pi
−0.819812 + 0.572633i 0.805922π0.805922\pi
608608 −8.00000 8.00000i −0.324443 0.324443i
609609 5.52786i 0.224000i
610610 −2.59023 31.3883i −0.104875 1.27088i
611611 45.1246 1.82555
612612 0.989378 6.24669i 0.0399933 0.252507i
613613 −27.3561 + 27.3561i −1.10490 + 1.10490i −0.111094 + 0.993810i 0.535435π0.535435\pi
−0.993810 + 0.111094i 0.964565π0.964565\pi
614614 12.4822 4.05573i 0.503743 0.163676i
615615 −38.3853 9.06154i −1.54784 0.365396i
616616 3.41641 4.70228i 0.137651 0.189460i
617617 −30.8885 + 30.8885i −1.24353 + 1.24353i −0.284998 + 0.958528i 0.591993π0.591993\pi
−0.958528 + 0.284998i 0.908007π0.908007\pi
618618 29.8932 + 15.2314i 1.20248 + 0.612695i
619619 27.3050i 1.09748i 0.835994 + 0.548739i 0.184892π0.184892\pi
−0.835994 + 0.548739i 0.815108π0.815108\pi
620620 −8.91491 + 21.7557i −0.358032 + 0.873730i
621621 6.49839i 0.260772i
622622 5.24128 10.2866i 0.210156 0.412455i
623623 7.60845 7.60845i 0.304826 0.304826i
624624 12.3107 37.8885i 0.492824 1.51676i
625625 −15.0000 20.0000i −0.600000 0.800000i
626626 −3.85410 11.8617i −0.154041 0.474089i
627627 4.00000 4.00000i 0.159745 0.159745i
628628 −4.33087 + 27.3440i −0.172820 + 1.09115i
629629 6.15537 0.245431
630630 −7.60074 + 8.96802i −0.302821 + 0.357295i
631631 28.0827i 1.11795i 0.829183 + 0.558977i 0.188806π0.188806\pi
−0.829183 + 0.558977i 0.811194π0.811194\pi
632632 5.44705 + 34.3913i 0.216672 + 1.36801i
633633 −25.4164 25.4164i −1.01021 1.01021i
634634 6.60440 + 20.3262i 0.262294 + 0.807258i
635635 27.0344 + 6.38197i 1.07283 + 0.253261i
636636 −2.76393 3.80423i −0.109597 0.150847i
637637 −13.0373 13.0373i −0.516556 0.516556i
638638 2.26323 + 1.15317i 0.0896023 + 0.0456546i
639639 15.7719 0.623928
640640 23.3356 9.76985i 0.922420 0.386187i
641641 −7.34752 −0.290210 −0.145105 0.989416i 0.546352π-0.546352\pi
−0.145105 + 0.989416i 0.546352π0.546352\pi
642642 −49.2999 25.1195i −1.94571 0.991389i
643643 8.56231 + 8.56231i 0.337664 + 0.337664i 0.855488 0.517823i 0.173258π-0.173258\pi
−0.517823 + 0.855488i 0.673258π0.673258\pi
644644 7.26543 + 10.0000i 0.286298 + 0.394055i
645645 9.06154 + 14.6619i 0.356798 + 0.577311i
646646 −1.23607 3.80423i −0.0486324 0.149675i
647647 −22.8909 22.8909i −0.899933 0.899933i 0.0954968 0.995430i 0.469556π-0.469556\pi
−0.995430 + 0.0954968i 0.969556π0.969556\pi
648648 4.73799 + 29.9145i 0.186126 + 1.17515i
649649 10.4721i 0.411067i
650650 4.58366 30.4336i 0.179786 1.19370i
651651 20.0000 0.783862
652652 3.16180 19.9628i 0.123826 0.781804i
653653 11.2412 11.2412i 0.439901 0.439901i −0.452078 0.891979i 0.649317π-0.649317\pi
0.891979 + 0.452078i 0.149317π0.149317\pi
654654 6.71040 + 20.6525i 0.262397 + 0.807576i
655655 −0.555029 + 0.343027i −0.0216868 + 0.0134032i
656656 9.52786 29.3238i 0.372001 1.14490i
657657 −19.4721 + 19.4721i −0.759680 + 0.759680i
658658 11.0662 21.7187i 0.431407 0.846684i
659659 18.0000i 0.701180i −0.936529 0.350590i 0.885981π-0.885981\pi
0.936529 0.350590i 0.114019π-0.114019\pi
660660 4.88493 + 11.6678i 0.190146 + 0.454168i
661661 2.35114i 0.0914488i 0.998954 + 0.0457244i 0.0145596π0.0145596\pi
−0.998954 + 0.0457244i 0.985440π0.985440\pi
662662 35.3689 + 18.0213i 1.37465 + 0.700419i
663663 9.95959 9.95959i 0.386799 0.386799i
664664 10.3026 14.1803i 0.399819 0.550304i
665665 −1.70820 + 7.23607i −0.0662413 + 0.280603i
666666 13.0902 4.25325i 0.507234 0.164810i
667667 −3.81966 + 3.81966i −0.147898 + 0.147898i
668668 0.122790 0.775266i 0.00475089 0.0299959i
669669 5.60034 0.216522
670670 6.88743 8.12641i 0.266085 0.313950i
671671 12.3107i 0.475251i
672672 −15.2169 15.2169i −0.587005 0.587005i
673673 −30.7082 30.7082i −1.18371 1.18371i −0.978775 0.204940i 0.934300π-0.934300\pi
−0.204940 0.978775i 0.565700π-0.565700\pi
674674 −3.91023 + 1.27051i −0.150616 + 0.0489382i
675675 2.76393 + 8.29180i 0.106384 + 0.319151i
676676 9.61803 6.98791i 0.369924 0.268766i
677677 8.33499 + 8.33499i 0.320340 + 0.320340i 0.848897 0.528558i 0.177267π-0.177267\pi
−0.528558 + 0.848897i 0.677267π0.677267\pi
678678 −9.78216 + 19.1986i −0.375682 + 0.737316i
679679 0.555029 0.0213001
680680 8.91930 + 0.667910i 0.342040 + 0.0256132i
681681 37.5967 1.44071
682682 4.17223 8.18845i 0.159763 0.313552i
683683 1.79837 + 1.79837i 0.0688129 + 0.0688129i 0.740676 0.671863i 0.234506π-0.234506\pi
−0.671863 + 0.740676i 0.734506π0.734506\pi
684684 −5.25731 7.23607i −0.201018 0.276678i
685685 −2.52265 + 10.6861i −0.0963857 + 0.408296i
686686 −25.1246 + 8.16348i −0.959262 + 0.311683i
687687 34.5811 + 34.5811i 1.31935 + 1.31935i
688688 −12.0058 + 6.11727i −0.457717 + 0.233219i
689689 4.47214i 0.170375i
690690 −26.8088 + 2.21232i −1.02059 + 0.0842215i
691691 −31.1246 −1.18404 −0.592018 0.805925i 0.701669π-0.701669\pi
−0.592018 + 0.805925i 0.701669π0.701669\pi
692692 17.6748 + 2.79941i 0.671895 + 0.106418i
693693 3.24920 3.24920i 0.123427 0.123427i
694694 −5.77185 + 1.87539i −0.219096 + 0.0711888i
695695 −6.36737 10.3026i −0.241528 0.390801i
696696 5.52786 7.60845i 0.209533 0.288398i
697697 7.70820 7.70820i 0.291969 0.291969i
698698 −19.6067 9.99009i −0.742123 0.378131i
699699 11.2361i 0.424987i
700700 −13.5238 9.66959i −0.511150 0.365476i
701701 40.3934i 1.52564i −0.646612 0.762819i 0.723815π-0.723815\pi
0.646612 0.762819i 0.276185π-0.276185\pi
702702 −4.88493 + 9.58721i −0.184370 + 0.361846i
703703 6.15537 6.15537i 0.232154 0.232154i
704704 −9.40456 + 3.05573i −0.354448 + 0.115167i
705705 27.8885 + 45.1246i 1.05034 + 1.69949i
706706 2.72949 + 8.40051i 0.102726 + 0.316157i
707707 −14.4721 + 14.4721i −0.544281 + 0.544281i
708708 −38.2953 6.06538i −1.43923 0.227951i
709709 −13.7638 −0.516911 −0.258456 0.966023i 0.583214π-0.583214\pi
−0.258456 + 0.966023i 0.583214π0.583214\pi
710710 1.83441 + 22.2293i 0.0688441 + 0.834252i
711711 27.5276i 1.03237i
712712 −18.0806 + 2.86368i −0.677599 + 0.107321i
713713 13.8197 + 13.8197i 0.517550 + 0.517550i
714714 −2.35114 7.23607i −0.0879892 0.270803i
715715 −2.76393 + 11.7082i −0.103365 + 0.437862i
716716 −26.6525 + 19.3642i −0.996050 + 0.723673i
717717 47.4468 + 47.4468i 1.77193 + 1.77193i
718718 2.26323 + 1.15317i 0.0844631 + 0.0430361i
719719 44.5407 1.66109 0.830543 0.556954i 0.188030π-0.188030\pi
0.830543 + 0.556954i 0.188030π0.188030\pi
720720 19.4295 4.74269i 0.724096 0.176750i
721721 17.2361 0.641905
722722 18.9011 + 9.63059i 0.703426 + 0.358414i
723723 −10.9443 10.9443i −0.407022 0.407022i
724724 −15.2169 + 11.0557i −0.565532 + 0.410883i
725725 3.24920 6.49839i 0.120672 0.241344i
726726 9.47214 + 29.1522i 0.351544 + 1.08194i
727727 −5.87785 5.87785i −0.217997 0.217997i 0.589657 0.807654i 0.299263π-0.299263\pi
−0.807654 + 0.589657i 0.799263π0.799263\pi
728728 −3.20170 20.2147i −0.118663 0.749207i
729729 11.9443i 0.442380i
730730 −29.7092 25.1797i −1.09959 0.931942i
731731 −4.76393 −0.176200
732732 45.0188 + 7.13028i 1.66394 + 0.263543i
733733 −1.28157 + 1.28157i −0.0473359 + 0.0473359i −0.730379 0.683043i 0.760656π-0.760656\pi
0.683043 + 0.730379i 0.260656π0.260656\pi
734734 −14.8334 45.6525i −0.547510 1.68506i
735735 4.97980 21.0948i 0.183683 0.778092i
736736 21.0292i 0.775148i
737737 −2.94427 + 2.94427i −0.108454 + 0.108454i
738738 11.0662 21.7187i 0.407354 0.799477i
739739 17.4164i 0.640673i −0.947304 0.320336i 0.896204π-0.896204\pi
0.947304 0.320336i 0.103796π-0.103796\pi
740740 7.51713 + 17.9549i 0.276335 + 0.660035i
741741 19.9192i 0.731750i
742742 −2.15246 1.09673i −0.0790194 0.0402624i
743743 13.4863 13.4863i 0.494765 0.494765i −0.415039 0.909804i 0.636232π-0.636232\pi
0.909804 + 0.415039i 0.136232π0.136232\pi
744744 −27.5276 20.0000i −1.00921 0.733236i
745745 25.1246 15.5279i 0.920495 0.568897i
746746 28.6180 9.29856i 1.04778 0.340445i
747747 9.79837 9.79837i 0.358504 0.358504i
748748 −3.45309 0.546915i −0.126257 0.0199972i
749749 −28.4257 −1.03865
750750 33.2665 14.2253i 1.21472 0.519436i
751751 7.05342i 0.257383i 0.991685 + 0.128692i 0.0410777π0.0410777\pi
−0.991685 + 0.128692i 0.958922π0.958922\pi
752752 −36.9501 + 18.8270i −1.34743 + 0.686550i
753753 35.8885 + 35.8885i 1.30785 + 1.30785i
754754 8.50651 2.76393i 0.309789 0.100656i
755755 −17.2361 27.8885i −0.627285 1.01497i
756756 3.41641 + 4.70228i 0.124254 + 0.171020i
757757 38.0018 + 38.0018i 1.38120 + 1.38120i 0.842497 + 0.538701i 0.181085π0.181085\pi
0.538701 + 0.842497i 0.318915π0.318915\pi
758758 23.0419 45.2222i 0.836918 1.64254i
759759 10.5146 0.381657
760760 9.58721 8.25139i 0.347765 0.299309i
761761 −14.9443 −0.541729 −0.270865 0.962617i 0.587310π-0.587310\pi
−0.270865 + 0.962617i 0.587310π0.587310\pi
762762 −18.2504 + 35.8185i −0.661143 + 1.29757i
763763 7.88854 + 7.88854i 0.285584 + 0.285584i
764764 −20.8172 + 15.1246i −0.753141 + 0.547189i
765765 6.88191 + 1.62460i 0.248816 + 0.0587375i
766766 −21.1803 + 6.88191i −0.765277 + 0.248654i
767767 −26.0746 26.0746i −0.941498 0.941498i
768768 5.72737 + 36.1612i 0.206669 + 1.30485i
769769 2.47214i 0.0891475i −0.999006 0.0445738i 0.985807π-0.985807\pi
0.999006 0.0445738i 0.0141930π-0.0141930\pi
770770 4.95740 + 4.20158i 0.178652 + 0.151415i
771771 −60.5410 −2.18033
772772 3.30615 20.8742i 0.118991 0.751279i
773773 4.18774 4.18774i 0.150623 0.150623i −0.627773 0.778396i 0.716034π-0.716034\pi
0.778396 + 0.627773i 0.216034π0.216034\pi
774774 −10.1311 + 3.29180i −0.364155 + 0.118321i
775775 −23.5114 11.7557i −0.844555 0.422277i
776776 −0.763932 0.555029i −0.0274236 0.0199244i
777777 11.7082 11.7082i 0.420029 0.420029i
778778 29.8932 + 15.2314i 1.07172 + 0.546071i
779779 15.4164i 0.552350i
780780 41.2146 + 16.8887i 1.47572 + 0.604711i
781781 8.71851i 0.311973i
782782 3.37540 6.62460i 0.120704 0.236895i
783783 −1.79611 + 1.79611i −0.0641878 + 0.0641878i
784784 16.1150 + 5.23607i 0.575534 + 0.187002i
785785 −30.1246 7.11146i −1.07519 0.253819i
786786 −0.291796 0.898056i −0.0104080 0.0320326i
787787 11.1459 11.1459i 0.397308 0.397308i −0.479974 0.877283i 0.659354π-0.659354\pi
0.877283 + 0.479974i 0.159354π0.159354\pi
788788 0.964406 6.08902i 0.0343555 0.216912i
789789 −53.0472 −1.88853
790790 −38.7981 + 3.20170i −1.38037 + 0.113911i
791791 11.0697i 0.393591i
792792 −7.72133 + 1.22294i −0.274366 + 0.0434552i
793793 30.6525 + 30.6525i 1.08850 + 1.08850i
794794 4.46526 + 13.7426i 0.158466 + 0.487708i
795795 4.47214 2.76393i 0.158610 0.0980266i
796796 21.3050 + 29.3238i 0.755134 + 1.03935i
797797 −19.7477 19.7477i −0.699498 0.699498i 0.264804 0.964302i 0.414693π-0.414693\pi
−0.964302 + 0.264804i 0.914693π0.914693\pi
798798 −9.58721 4.88493i −0.339384 0.172925i
799799 −14.6619 −0.518700
800800 8.94427 + 26.8328i 0.316228 + 0.948683i
801801 −14.4721 −0.511348
802802 −4.89985 2.49660i −0.173020 0.0881580i
803803 10.7639 + 10.7639i 0.379851 + 0.379851i
804804 9.06154 + 12.4721i 0.319576 + 0.439858i
805805 −11.7557 + 7.26543i −0.414334 + 0.256073i
806806 −10.0000 30.7768i −0.352235 1.08407i
807807 −28.9807 28.9807i −1.02017 1.02017i
808808 34.3913 5.44705i 1.20988 0.191627i
809809 12.9443i 0.455096i −0.973767 0.227548i 0.926929π-0.926929\pi
0.973767 0.227548i 0.0730709π-0.0730709\pi
810810 −33.7476 + 2.78492i −1.18577 + 0.0978521i
811811 −32.0689 −1.12609 −0.563045 0.826426i 0.690370π-0.690370\pi
−0.563045 + 0.826426i 0.690370π0.690370\pi
812812 0.755818 4.77205i 0.0265240 0.167466i
813813 −51.2511 + 51.2511i −1.79745 + 1.79745i
814814 −2.35114 7.23607i −0.0824074 0.253624i
815815 21.9928 + 5.19180i 0.770375 + 0.181861i
816816 −4.00000 + 12.3107i −0.140028 + 0.430962i
817817 −4.76393 + 4.76393i −0.166669 + 0.166669i
818818 17.7182 34.7739i 0.619502 1.21584i
819819 16.1803i 0.565387i
820820 31.8979 + 13.0709i 1.11392 + 0.456457i
821821 20.4742i 0.714555i −0.933998 0.357278i 0.883705π-0.883705\pi
0.933998 0.357278i 0.116295π-0.116295\pi
822822 −14.1583 7.21400i −0.493826 0.251617i
823823 −24.3440 + 24.3440i −0.848577 + 0.848577i −0.989956 0.141379i 0.954846π-0.954846\pi
0.141379 + 0.989956i 0.454846π0.454846\pi
824824 −23.7234 17.2361i −0.826444 0.600447i
825825 −13.4164 + 4.47214i −0.467099 + 0.155700i
826826 −18.9443 + 6.15537i −0.659156 + 0.214173i
827827 14.8541 14.8541i 0.516528 0.516528i −0.399991 0.916519i 0.630987π-0.630987\pi
0.916519 + 0.399991i 0.130987π0.130987\pi
828828 2.60074 16.4204i 0.0903818 0.570648i
829829 −3.11817 −0.108299 −0.0541493 0.998533i 0.517245π-0.517245\pi
−0.0541493 + 0.998533i 0.517245π0.517245\pi
830830 14.9497 + 12.6704i 0.518911 + 0.439797i
831831 7.05342i 0.244681i
832832 −15.8080 + 31.0249i −0.548042 + 1.07559i
833833 4.23607 + 4.23607i 0.146771 + 0.146771i
834834 16.6700 5.41641i 0.577235 0.187555i
835835 0.854102 + 0.201626i 0.0295574 + 0.00697756i
836836 −4.00000 + 2.90617i −0.138343 + 0.100512i
837837 6.49839 + 6.49839i 0.224617 + 0.224617i
838838 15.9436 31.2912i 0.550764 1.08094i
839839 9.40456 0.324682 0.162341 0.986735i 0.448096π-0.448096\pi
0.162341 + 0.986735i 0.448096π0.448096\pi
840840 18.2360 15.6951i 0.629200 0.541532i
841841 −26.8885 −0.927191
842842 −2.22223 + 4.36137i −0.0765830 + 0.150303i
843843 −6.00000 6.00000i −0.206651 0.206651i
844844 18.4661 + 25.4164i 0.635629 + 0.874869i
845845 6.98791 + 11.3067i 0.240391 + 0.388962i
846846 −31.1803 + 10.1311i −1.07200 + 0.348315i
847847 11.1352 + 11.1352i 0.382609 + 0.382609i
848848 1.86588 + 3.66199i 0.0640744 + 0.125753i
849849 50.5410i 1.73456i
850850 −1.48932 + 9.88847i −0.0510833 + 0.339172i
851851 16.1803 0.554655
852852 −31.8825 5.04969i −1.09228 0.173000i
853853 24.7930 24.7930i 0.848896 0.848896i −0.141100 0.989995i 0.545064π-0.545064\pi
0.989995 + 0.141100i 0.0450639π0.0450639\pi
854854 22.2703 7.23607i 0.762075 0.247613i
855855 8.50651 5.25731i 0.290916 0.179796i
856856 39.1246 + 28.4257i 1.33725 + 0.971570i
857857 −17.8328 + 17.8328i −0.609157 + 0.609157i −0.942726 0.333568i 0.891747π-0.891747\pi
0.333568 + 0.942726i 0.391747π0.391747\pi
858858 −15.5124 7.90398i −0.529586 0.269837i
859859 7.52786i 0.256847i 0.991719 + 0.128424i 0.0409917π0.0409917\pi
−0.991719 + 0.128424i 0.959008π0.959008\pi
860860 −5.81787 13.8961i −0.198388 0.473855i
861861 29.3238i 0.999351i
862862 −7.54763 + 14.8131i −0.257073 + 0.504535i
863863 −6.22088 + 6.22088i −0.211761 + 0.211761i −0.805015 0.593254i 0.797843π-0.797843\pi
0.593254 + 0.805015i 0.297843π0.297843\pi
864864 9.88854i 0.336415i
865865 −4.59675 + 19.4721i −0.156294 + 0.662072i
866866 14.3262 + 44.0916i 0.486825 + 1.49829i
867867 24.2705 24.2705i 0.824270 0.824270i
868868 −17.2654 2.73457i −0.586027 0.0928175i
869869 15.2169 0.516198
870870 8.02124 + 6.79830i 0.271946 + 0.230484i
871871 14.6619i 0.496799i
872872 −2.96911 18.7462i −0.100547 0.634826i
873873 −0.527864 0.527864i −0.0178655 0.0178655i
874874 −3.24920 10.0000i −0.109906 0.338255i
875875 11.9098 14.2705i 0.402626 0.482431i
876876 45.5967 33.1280i 1.54057 1.11929i
877877 5.08580 + 5.08580i 0.171735 + 0.171735i 0.787741 0.616006i 0.211250π-0.211250\pi
−0.616006 + 0.787741i 0.711250π0.711250\pi
878878 −14.1137 7.19128i −0.476313 0.242694i
879879 2.35114 0.0793020
880880 −2.62169 10.7404i −0.0883773 0.362058i
881881 47.1246 1.58767 0.793834 0.608134i 0.208082π-0.208082\pi
0.793834 + 0.608134i 0.208082π0.208082\pi
882882 11.9356 + 6.08149i 0.401892 + 0.204774i
883883 21.7984 + 21.7984i 0.733574 + 0.733574i 0.971326 0.237752i 0.0764106π-0.0764106\pi
−0.237752 + 0.971326i 0.576411π0.576411\pi
884884 −9.95959 + 7.23607i −0.334977 + 0.243375i
885885 9.95959 42.1895i 0.334788 1.41818i
886886 6.23607 + 19.1926i 0.209505 + 0.644789i
887887 28.1482 + 28.1482i 0.945123 + 0.945123i 0.998571 0.0534473i 0.0170209π-0.0170209\pi
−0.0534473 + 0.998571i 0.517021π0.517021\pi
888888 −27.8232 + 4.40676i −0.933684 + 0.147881i
889889 20.6525i 0.692662i
890890 −1.68323 20.3974i −0.0564220 0.683721i
891891 13.2361 0.443425
892892 −4.83461 0.765727i −0.161875 0.0256384i
893893 −14.6619 + 14.6619i −0.490641 + 0.490641i
894894 13.2088 + 40.6525i 0.441768 + 1.35962i
895895 −19.3642 31.3319i −0.647272 1.04731i
896896 11.0557 + 15.2169i 0.369346 + 0.508361i
897897 26.1803 26.1803i 0.874136 0.874136i
898898 −20.2864 + 39.8142i −0.676965 + 1.32862i
899899 7.63932i 0.254786i
900900 3.66554 + 22.0582i 0.122185 + 0.735273i
901901 1.45309i 0.0484093i
902902 −12.0058 6.11727i −0.399750 0.203683i
903903 −9.06154 + 9.06154i −0.301549 + 0.301549i
904904 11.0697 15.2361i 0.368171 0.506744i
905905 −11.0557 17.8885i −0.367505 0.594635i
906906 45.1246 14.6619i 1.49916 0.487108i
907907 −23.3262 + 23.3262i −0.774535 + 0.774535i −0.978896 0.204361i 0.934488π-0.934488\pi
0.204361 + 0.978896i 0.434488π0.434488\pi
908908 −32.4562 5.14056i −1.07710 0.170595i
909909 27.5276 0.913034
910910 22.8049 1.88191i 0.755976 0.0623847i
911911 25.1765i 0.834135i 0.908876 + 0.417067i 0.136942π0.136942\pi
−0.908876 + 0.417067i 0.863058π0.863058\pi
912912 8.31073 + 16.3107i 0.275196 + 0.540102i
913913 −5.41641 5.41641i −0.179257 0.179257i
914914 −41.1855 + 13.3820i −1.36229 + 0.442636i
915915 −11.7082 + 49.5967i −0.387061 + 1.63962i
916916 −25.1246 34.5811i −0.830141 1.14259i
917917 −0.343027 0.343027i −0.0113277 0.0113277i
918918 1.58721 3.11507i 0.0523857 0.102813i
919919 21.7153 0.716322 0.358161 0.933660i 0.383404π-0.383404\pi
0.358161 + 0.933660i 0.383404π0.383404\pi
920920 23.4458 + 1.75571i 0.772984 + 0.0578839i
921921 −21.2361 −0.699752
922922 −4.17223 + 8.18845i −0.137405 + 0.269672i
923923 −21.7082 21.7082i −0.714534 0.714534i
924924 −7.60845 + 5.52786i −0.250300 + 0.181853i
925925 −20.6457 + 6.88191i −0.678827 + 0.226276i
926926 32.8885 10.6861i 1.08078 0.351168i
927927 −16.3925 16.3925i −0.538400 0.538400i
928928 −5.81234 + 5.81234i −0.190799 + 0.190799i
929929 5.34752i 0.175447i 0.996145 + 0.0877233i 0.0279591π0.0279591\pi
−0.996145 + 0.0877233i 0.972041π0.972041\pi
930930 24.5965 29.0211i 0.806551 0.951640i
931931 8.47214 0.277663
932932 1.53629 9.69977i 0.0503230 0.317727i
933933 −13.2088 + 13.2088i −0.432436 + 0.432436i
934934 −5.08580 + 1.65248i −0.166412 + 0.0540707i
935935 0.898056 3.80423i 0.0293696 0.124411i
936936 −16.1803 + 22.2703i −0.528871 + 0.727928i
937937 20.3050 20.3050i 0.663334 0.663334i −0.292831 0.956164i 0.594597π-0.594597\pi
0.956164 + 0.292831i 0.0945972π0.0945972\pi
938938 7.05684 + 3.59564i 0.230414 + 0.117402i
939939 20.1803i 0.658561i
940940 −17.9055 42.7679i −0.584015 1.39494i
941941 60.8676i 1.98423i 0.125340 + 0.992114i 0.459998π0.459998\pi
−0.125340 + 0.992114i 0.540002π0.540002\pi
942942 20.3365 39.9127i 0.662600 1.30043i
943943 20.2622 20.2622i 0.659828 0.659828i
944944 32.2299 + 10.4721i 1.04899 + 0.340839i
945945 −5.52786 + 3.41641i −0.179821 + 0.111136i
946946 1.81966 + 5.60034i 0.0591623 + 0.182083i
947947 −8.85410 + 8.85410i −0.287720 + 0.287720i −0.836178 0.548458i 0.815215π-0.815215\pi
0.548458 + 0.836178i 0.315215π0.315215\pi
948948 8.81351 55.6463i 0.286250 1.80731i
949949 53.6022 1.74000
950950 8.39915 + 11.3778i 0.272504 + 0.369144i
951951 34.5811i 1.12137i
952952 1.04029 + 6.56816i 0.0337161 + 0.212875i
953953 −6.81966 6.81966i −0.220910 0.220910i 0.587971 0.808882i 0.299927π-0.299927\pi
−0.808882 + 0.587971i 0.799927π0.799927\pi
954954 1.00406 + 3.09017i 0.0325075 + 0.100048i
955955 −15.1246 24.4721i −0.489421 0.791900i
956956 −34.4721 47.4468i −1.11491 1.53454i
957957 −2.90617 2.90617i −0.0939431 0.0939431i
958958 9.58721 + 4.88493i 0.309749 + 0.157825i
959959 −8.16348 −0.263613
960960 −40.7947 + 3.36646i −1.31664 + 0.108652i
961961 3.36068 0.108409
962962 −23.8712 12.1630i −0.769638 0.392150i
963963 27.0344 + 27.0344i 0.871173 + 0.871173i
964964 7.95148 + 10.9443i 0.256100 + 0.352491i
965965 22.9969 + 5.42882i 0.740295 + 0.174760i
966966 −6.18034 19.0211i −0.198849 0.611995i
967967 12.0332 + 12.0332i 0.386962 + 0.386962i 0.873602 0.486640i 0.161778π-0.161778\pi
−0.486640 + 0.873602i 0.661778π0.661778\pi
968968 −4.19107 26.4614i −0.134706 0.850502i
969969 6.47214i 0.207915i
970970 0.682589 0.805379i 0.0219166 0.0258591i
971971 33.5967 1.07817 0.539085 0.842251i 0.318770π-0.318770\pi
0.539085 + 0.842251i 0.318770π0.318770\pi
972972 6.02548 38.0434i 0.193267 1.22024i
973973 6.36737 6.36737i 0.204128 0.204128i
974974 5.77185 + 17.7639i 0.184942 + 0.569193i
975975 −22.2703 + 44.5407i −0.713221 + 1.42644i
976976 −37.8885 12.3107i −1.21278 0.394057i
977977 −28.2361 + 28.2361i −0.903352 + 0.903352i −0.995725 0.0923727i 0.970555π-0.970555\pi
0.0923727 + 0.995725i 0.470555π0.470555\pi
978978 −14.8469 + 29.1387i −0.474752 + 0.931753i
979979 8.00000i 0.255681i
980980 −7.18317 + 17.5296i −0.229458 + 0.559963i
981981 15.0049i 0.479070i
982982 −13.5633 6.91087i −0.432824 0.220535i
983983 −0.620541 + 0.620541i −0.0197922 + 0.0197922i −0.716934 0.697141i 0.754455π-0.754455\pi
0.697141 + 0.716934i 0.254455π0.254455\pi
984984 −29.3238 + 40.3607i −0.934807 + 1.28665i
985985 6.70820 + 1.58359i 0.213741 + 0.0504574i
986986 −2.76393 + 0.898056i −0.0880215 + 0.0285999i
987987 −27.8885 + 27.8885i −0.887702 + 0.887702i
988988 −2.72353 + 17.1957i −0.0866469 + 0.547067i
989989 −12.5227 −0.398200
990990 −0.718826 8.71071i −0.0228458 0.276845i
991991 19.3642i 0.615123i −0.951528 0.307561i 0.900487π-0.900487\pi
0.951528 0.307561i 0.0995129π-0.0995129\pi
992992 21.0292 + 21.0292i 0.667679 + 0.667679i
993993 −45.4164 45.4164i −1.44125 1.44125i
994994 −15.7719 + 5.12461i −0.500255 + 0.162543i
995995 −34.4721 + 21.3050i −1.09284 + 0.675412i
996996 −22.9443 + 16.6700i −0.727017 + 0.528209i
997997 −35.6506 35.6506i −1.12907 1.12907i −0.990329 0.138738i 0.955696π-0.955696\pi
−0.138738 0.990329i 0.544304π-0.544304\pi
998998 −15.3374 + 30.1013i −0.485497 + 0.952841i
999999 7.60845 0.240721
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 40.2.k.a.3.4 yes 8
3.2 odd 2 360.2.w.c.163.1 8
4.3 odd 2 160.2.o.a.143.3 8
5.2 odd 4 inner 40.2.k.a.27.2 yes 8
5.3 odd 4 200.2.k.h.107.3 8
5.4 even 2 200.2.k.h.43.1 8
8.3 odd 2 inner 40.2.k.a.3.2 8
8.5 even 2 160.2.o.a.143.4 8
12.11 even 2 1440.2.bi.c.1423.4 8
15.2 even 4 360.2.w.c.307.3 8
16.3 odd 4 1280.2.n.m.1023.2 8
16.5 even 4 1280.2.n.m.1023.1 8
16.11 odd 4 1280.2.n.q.1023.3 8
16.13 even 4 1280.2.n.q.1023.4 8
20.3 even 4 800.2.o.g.207.2 8
20.7 even 4 160.2.o.a.47.4 8
20.19 odd 2 800.2.o.g.143.1 8
24.5 odd 2 1440.2.bi.c.1423.1 8
24.11 even 2 360.2.w.c.163.3 8
40.3 even 4 200.2.k.h.107.1 8
40.13 odd 4 800.2.o.g.207.1 8
40.19 odd 2 200.2.k.h.43.3 8
40.27 even 4 inner 40.2.k.a.27.4 yes 8
40.29 even 2 800.2.o.g.143.2 8
40.37 odd 4 160.2.o.a.47.3 8
60.47 odd 4 1440.2.bi.c.847.1 8
80.27 even 4 1280.2.n.m.767.1 8
80.37 odd 4 1280.2.n.q.767.3 8
80.67 even 4 1280.2.n.q.767.4 8
80.77 odd 4 1280.2.n.m.767.2 8
120.77 even 4 1440.2.bi.c.847.4 8
120.107 odd 4 360.2.w.c.307.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
40.2.k.a.3.2 8 8.3 odd 2 inner
40.2.k.a.3.4 yes 8 1.1 even 1 trivial
40.2.k.a.27.2 yes 8 5.2 odd 4 inner
40.2.k.a.27.4 yes 8 40.27 even 4 inner
160.2.o.a.47.3 8 40.37 odd 4
160.2.o.a.47.4 8 20.7 even 4
160.2.o.a.143.3 8 4.3 odd 2
160.2.o.a.143.4 8 8.5 even 2
200.2.k.h.43.1 8 5.4 even 2
200.2.k.h.43.3 8 40.19 odd 2
200.2.k.h.107.1 8 40.3 even 4
200.2.k.h.107.3 8 5.3 odd 4
360.2.w.c.163.1 8 3.2 odd 2
360.2.w.c.163.3 8 24.11 even 2
360.2.w.c.307.1 8 120.107 odd 4
360.2.w.c.307.3 8 15.2 even 4
800.2.o.g.143.1 8 20.19 odd 2
800.2.o.g.143.2 8 40.29 even 2
800.2.o.g.207.1 8 40.13 odd 4
800.2.o.g.207.2 8 20.3 even 4
1280.2.n.m.767.1 8 80.27 even 4
1280.2.n.m.767.2 8 80.77 odd 4
1280.2.n.m.1023.1 8 16.5 even 4
1280.2.n.m.1023.2 8 16.3 odd 4
1280.2.n.q.767.3 8 80.37 odd 4
1280.2.n.q.767.4 8 80.67 even 4
1280.2.n.q.1023.3 8 16.11 odd 4
1280.2.n.q.1023.4 8 16.13 even 4
1440.2.bi.c.847.1 8 60.47 odd 4
1440.2.bi.c.847.4 8 120.77 even 4
1440.2.bi.c.1423.1 8 24.5 odd 2
1440.2.bi.c.1423.4 8 12.11 even 2