Properties

Label 308.2.n.a.263.2
Level 308308
Weight 22
Character 308.263
Analytic conductor 2.4592.459
Analytic rank 00
Dimension 44
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] = [308,2,Mod(219,308)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(308, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 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("308.219"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 308=22711 308 = 2^{2} \cdot 7 \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 308.n (of order 66, degree 22, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.459392382262.45939238226
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: yes
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 263.2
Root 0.8956441.09445i-0.895644 - 1.09445i of defining polynomial
Character χ\chi == 308.263
Dual form 308.2.n.a.219.2

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+(0.8956441.09445i)q2+(2.29129+1.32288i)q3+(0.3956441.96048i)q4+(3.500001.32288i)q6+(0.500000+2.59808i)q7+(2.500001.32288i)q8+(2.00000+3.46410i)q9+(3.291290.409175i)q11+(1.686935.01540i)q122.64575iq13+(2.39564+2.87418i)q14+(3.68693+1.55130i)q16+(4.582582.64575i)q17+(5.58258+0.913701i)q18+(4.58258+5.29150i)q21+(2.500003.96863i)q22+(4.58258+2.64575i)q23+(3.978226.33828i)q24+(2.500004.33013i)q25+(2.895642.36965i)q26+2.64575iq27+(5.291290.0476751i)q28+7.93725iq29+(9.165155.29150i)q31+(1.60436+5.42458i)q32+(8.08258+3.41643i)q33+(7.00000+2.64575i)q34+(6.000005.29150i)q36+(4.00000+6.92820i)q37+(3.500006.06218i)q39+(1.68693+9.75470i)q42+2.00000q43+(2.104366.29060i)q44+(1.20871+7.38505i)q46+(10.50001.32288i)q48+(6.500002.59808i)q49+(2.500006.61438i)q50+(7.0000012.1244i)q51+(5.18693+1.04678i)q52+(2.000003.46410i)q53+(2.89564+2.36965i)q54+(4.686935.83375i)q56+(8.68693+7.10895i)q58+(2.291291.32288i)q59+(2.291291.32288i)q61+(14.0000+5.29150i)q62+(10.0000+3.46410i)q63+(4.50000+6.61438i)q64+(10.97825.78608i)q66+(2.291291.32288i)q67+(3.37386+10.0308i)q6814.0000q695.29150iq71+(0.41742411.3060i)q72+(9.16515+5.29150i)q73+(11.1652+1.82740i)q74+(11.45646.61438i)q75+(0.582576+8.75560i)q77+(3.500009.26013i)q78+(6.50000+11.2583i)q79+(2.500004.33013i)q81+(12.1869+6.89048i)q84+(1.791292.18890i)q86+(10.5000+18.1865i)q87+(8.769513.33103i)q88+(7.00000+12.1244i)q89+(6.87386+1.32288i)q91+(7.00000+7.93725i)q92+(14.000024.2487i)q93+(10.8521+10.3069i)q96+7.00000q97+(8.66515+4.78698i)q98+(8.00000+10.5830i)q99+O(q100)q+(0.895644 - 1.09445i) q^{2} +(2.29129 + 1.32288i) q^{3} +(-0.395644 - 1.96048i) q^{4} +(3.50000 - 1.32288i) q^{6} +(-0.500000 + 2.59808i) q^{7} +(-2.50000 - 1.32288i) q^{8} +(2.00000 + 3.46410i) q^{9} +(3.29129 - 0.409175i) q^{11} +(1.68693 - 5.01540i) q^{12} -2.64575i q^{13} +(2.39564 + 2.87418i) q^{14} +(-3.68693 + 1.55130i) q^{16} +(-4.58258 - 2.64575i) q^{17} +(5.58258 + 0.913701i) q^{18} +(-4.58258 + 5.29150i) q^{21} +(2.50000 - 3.96863i) q^{22} +(-4.58258 + 2.64575i) q^{23} +(-3.97822 - 6.33828i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-2.89564 - 2.36965i) q^{26} +2.64575i q^{27} +(5.29129 - 0.0476751i) q^{28} +7.93725i q^{29} +(-9.16515 - 5.29150i) q^{31} +(-1.60436 + 5.42458i) q^{32} +(8.08258 + 3.41643i) q^{33} +(-7.00000 + 2.64575i) q^{34} +(6.00000 - 5.29150i) q^{36} +(4.00000 + 6.92820i) q^{37} +(3.50000 - 6.06218i) q^{39} +(1.68693 + 9.75470i) q^{42} +2.00000 q^{43} +(-2.10436 - 6.29060i) q^{44} +(-1.20871 + 7.38505i) q^{46} +(-10.5000 - 1.32288i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(-2.50000 - 6.61438i) q^{50} +(-7.00000 - 12.1244i) q^{51} +(-5.18693 + 1.04678i) q^{52} +(2.00000 - 3.46410i) q^{53} +(2.89564 + 2.36965i) q^{54} +(4.68693 - 5.83375i) q^{56} +(8.68693 + 7.10895i) q^{58} +(-2.29129 - 1.32288i) q^{59} +(2.29129 - 1.32288i) q^{61} +(-14.0000 + 5.29150i) q^{62} +(-10.0000 + 3.46410i) q^{63} +(4.50000 + 6.61438i) q^{64} +(10.9782 - 5.78608i) q^{66} +(-2.29129 - 1.32288i) q^{67} +(-3.37386 + 10.0308i) q^{68} -14.0000 q^{69} -5.29150i q^{71} +(-0.417424 - 11.3060i) q^{72} +(9.16515 + 5.29150i) q^{73} +(11.1652 + 1.82740i) q^{74} +(11.4564 - 6.61438i) q^{75} +(-0.582576 + 8.75560i) q^{77} +(-3.50000 - 9.26013i) q^{78} +(6.50000 + 11.2583i) q^{79} +(2.50000 - 4.33013i) q^{81} +(12.1869 + 6.89048i) q^{84} +(1.79129 - 2.18890i) q^{86} +(-10.5000 + 18.1865i) q^{87} +(-8.76951 - 3.33103i) q^{88} +(7.00000 + 12.1244i) q^{89} +(6.87386 + 1.32288i) q^{91} +(7.00000 + 7.93725i) q^{92} +(-14.0000 - 24.2487i) q^{93} +(-10.8521 + 10.3069i) q^{96} +7.00000 q^{97} +(-8.66515 + 4.78698i) q^{98} +(8.00000 + 10.5830i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4qq2+3q4+14q62q710q8+8q9+4q117q12+5q14q16+4q18+10q22+7q24+10q257q26+12q2811q32+14q3328q34++32q99+O(q100) 4 q - q^{2} + 3 q^{4} + 14 q^{6} - 2 q^{7} - 10 q^{8} + 8 q^{9} + 4 q^{11} - 7 q^{12} + 5 q^{14} - q^{16} + 4 q^{18} + 10 q^{22} + 7 q^{24} + 10 q^{25} - 7 q^{26} + 12 q^{28} - 11 q^{32} + 14 q^{33} - 28 q^{34}+ \cdots + 32 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/308Z)×\left(\mathbb{Z}/308\mathbb{Z}\right)^\times.

nn 4545 5757 155155
χ(n)\chi(n) e(23)e\left(\frac{2}{3}\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 0.895644 1.09445i 0.633316 0.773893i
33 2.29129 + 1.32288i 1.32288 + 0.763763i 0.984186 0.177136i 0.0566831π-0.0566831\pi
0.338689 + 0.940898i 0.390016π0.390016\pi
44 −0.395644 1.96048i −0.197822 0.980238i
55 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
66 3.50000 1.32288i 1.42887 0.540062i
77 −0.500000 + 2.59808i −0.188982 + 0.981981i
88 −2.50000 1.32288i −0.883883 0.467707i
99 2.00000 + 3.46410i 0.666667 + 1.15470i
1010 0 0
1111 3.29129 0.409175i 0.992361 0.123371i
1212 1.68693 5.01540i 0.486975 1.44782i
1313 2.64575i 0.733799i −0.930261 0.366900i 0.880419π-0.880419\pi
0.930261 0.366900i 0.119581π-0.119581\pi
1414 2.39564 + 2.87418i 0.640263 + 0.768156i
1515 0 0
1616 −3.68693 + 1.55130i −0.921733 + 0.387825i
1717 −4.58258 2.64575i −1.11144 0.641689i −0.172236 0.985056i 0.555099π-0.555099\pi
−0.939201 + 0.343367i 0.888433π0.888433\pi
1818 5.58258 + 0.913701i 1.31583 + 0.215361i
1919 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
2020 0 0
2121 −4.58258 + 5.29150i −1.00000 + 1.15470i
2222 2.50000 3.96863i 0.533002 0.846114i
2323 −4.58258 + 2.64575i −0.955533 + 0.551677i −0.894795 0.446476i 0.852679π-0.852679\pi
−0.0607377 + 0.998154i 0.519345π0.519345\pi
2424 −3.97822 6.33828i −0.812051 1.29380i
2525 2.50000 4.33013i 0.500000 0.866025i
2626 −2.89564 2.36965i −0.567882 0.464727i
2727 2.64575i 0.509175i
2828 5.29129 0.0476751i 0.999959 0.00900975i
2929 7.93725i 1.47391i 0.675941 + 0.736956i 0.263737π0.263737\pi
−0.675941 + 0.736956i 0.736263π0.736263\pi
3030 0 0
3131 −9.16515 5.29150i −1.64611 0.950382i −0.978598 0.205783i 0.934026π-0.934026\pi
−0.667512 0.744599i 0.732641π-0.732641\pi
3232 −1.60436 + 5.42458i −0.283613 + 0.958939i
3333 8.08258 + 3.41643i 1.40700 + 0.594724i
3434 −7.00000 + 2.64575i −1.20049 + 0.453743i
3535 0 0
3636 6.00000 5.29150i 1.00000 0.881917i
3737 4.00000 + 6.92820i 0.657596 + 1.13899i 0.981236 + 0.192809i 0.0617599π0.0617599\pi
−0.323640 + 0.946180i 0.604907π0.604907\pi
3838 0 0
3939 3.50000 6.06218i 0.560449 0.970725i
4040 0 0
4141 0 0 1.00000 00
−1.00000 π\pi
4242 1.68693 + 9.75470i 0.260299 + 1.50518i
4343 2.00000 0.304997 0.152499 0.988304i 0.451268π-0.451268\pi
0.152499 + 0.988304i 0.451268π0.451268\pi
4444 −2.10436 6.29060i −0.317244 0.948344i
4545 0 0
4646 −1.20871 + 7.38505i −0.178215 + 1.08887i
4747 0 0 −0.500000 0.866025i 0.666667π-0.666667\pi
0.500000 + 0.866025i 0.333333π0.333333\pi
4848 −10.5000 1.32288i −1.51554 0.190941i
4949 −6.50000 2.59808i −0.928571 0.371154i
5050 −2.50000 6.61438i −0.353553 0.935414i
5151 −7.00000 12.1244i −0.980196 1.69775i
5252 −5.18693 + 1.04678i −0.719298 + 0.145162i
5353 2.00000 3.46410i 0.274721 0.475831i −0.695344 0.718677i 0.744748π-0.744748\pi
0.970065 + 0.242846i 0.0780811π0.0780811\pi
5454 2.89564 + 2.36965i 0.394047 + 0.322469i
5555 0 0
5656 4.68693 5.83375i 0.626318 0.779568i
5757 0 0
5858 8.68693 + 7.10895i 1.14065 + 0.933451i
5959 −2.29129 1.32288i −0.298300 0.172224i 0.343379 0.939197i 0.388429π-0.388429\pi
−0.641679 + 0.766973i 0.721762π0.721762\pi
6060 0 0
6161 2.29129 1.32288i 0.293369 0.169377i −0.346091 0.938201i 0.612491π-0.612491\pi
0.639460 + 0.768824i 0.279158π0.279158\pi
6262 −14.0000 + 5.29150i −1.77800 + 0.672022i
6363 −10.0000 + 3.46410i −1.25988 + 0.436436i
6464 4.50000 + 6.61438i 0.562500 + 0.826797i
6565 0 0
6666 10.9782 5.78608i 1.35133 0.712217i
6767 −2.29129 1.32288i −0.279925 0.161615i 0.353464 0.935448i 0.385004π-0.385004\pi
−0.633390 + 0.773833i 0.718337π0.718337\pi
6868 −3.37386 + 10.0308i −0.409141 + 1.21641i
6969 −14.0000 −1.68540
7070 0 0
7171 5.29150i 0.627986i −0.949425 0.313993i 0.898333π-0.898333\pi
0.949425 0.313993i 0.101667π-0.101667\pi
7272 −0.417424 11.3060i −0.0491939 1.33243i
7373 9.16515 + 5.29150i 1.07270 + 0.619324i 0.928918 0.370286i 0.120740π-0.120740\pi
0.143782 + 0.989609i 0.454074π0.454074\pi
7474 11.1652 + 1.82740i 1.29792 + 0.212431i
7575 11.4564 6.61438i 1.32288 0.763763i
7676 0 0
7777 −0.582576 + 8.75560i −0.0663907 + 0.997794i
7878 −3.50000 9.26013i −0.396297 1.04850i
7979 6.50000 + 11.2583i 0.731307 + 1.26666i 0.956325 + 0.292306i 0.0944227π0.0944227\pi
−0.225018 + 0.974355i 0.572244π0.572244\pi
8080 0 0
8181 2.50000 4.33013i 0.277778 0.481125i
8282 0 0
8383 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
8484 12.1869 + 6.89048i 1.32970 + 0.751813i
8585 0 0
8686 1.79129 2.18890i 0.193160 0.236035i
8787 −10.5000 + 18.1865i −1.12572 + 1.94980i
8888 −8.76951 3.33103i −0.934833 0.355089i
8989 7.00000 + 12.1244i 0.741999 + 1.28518i 0.951584 + 0.307389i 0.0994552π0.0994552\pi
−0.209585 + 0.977790i 0.567211π0.567211\pi
9090 0 0
9191 6.87386 + 1.32288i 0.720577 + 0.138675i
9292 7.00000 + 7.93725i 0.729800 + 0.827516i
9393 −14.0000 24.2487i −1.45173 2.51447i
9494 0 0
9595 0 0
9696 −10.8521 + 10.3069i −1.10759 + 1.05194i
9797 7.00000 0.710742 0.355371 0.934725i 0.384354π-0.384354\pi
0.355371 + 0.934725i 0.384354π0.384354\pi
9898 −8.66515 + 4.78698i −0.875312 + 0.483558i
9999 8.00000 + 10.5830i 0.804030 + 1.06363i
100100 −9.47822 3.18800i −0.947822 0.318800i
101101 −6.87386 3.96863i −0.683975 0.394893i 0.117376 0.993088i 0.462552π-0.462552\pi
−0.801351 + 0.598194i 0.795885π0.795885\pi
102102 −19.5390 3.19795i −1.93465 0.316644i
103103 4.58258 2.64575i 0.451535 0.260694i −0.256943 0.966426i 0.582715π-0.582715\pi
0.708478 + 0.705733i 0.249382π0.249382\pi
104104 −3.50000 + 6.61438i −0.343203 + 0.648593i
105105 0 0
106106 −2.00000 5.29150i −0.194257 0.513956i
107107 4.00000 + 6.92820i 0.386695 + 0.669775i 0.992003 0.126217i 0.0402834π-0.0402834\pi
−0.605308 + 0.795991i 0.706950π0.706950\pi
108108 5.18693 1.04678i 0.499113 0.100726i
109109 −9.16515 5.29150i −0.877862 0.506834i −0.00790932 0.999969i 0.502518π-0.502518\pi
−0.869953 + 0.493135i 0.835851π0.835851\pi
110110 0 0
111111 21.1660i 2.00899i
112112 −2.18693 10.3546i −0.206646 0.978416i
113113 −19.0000 −1.78737 −0.893685 0.448695i 0.851889π-0.851889\pi
−0.893685 + 0.448695i 0.851889π0.851889\pi
114114 0 0
115115 0 0
116116 15.5608 3.14033i 1.44478 0.291572i
117117 9.16515 5.29150i 0.847319 0.489200i
118118 −3.50000 + 1.32288i −0.322201 + 0.121781i
119119 9.16515 10.5830i 0.840168 0.970143i
120120 0 0
121121 10.6652 2.69343i 0.969559 0.244857i
122122 0.604356 3.69253i 0.0547158 0.334306i
123123 0 0
124124 −6.74773 + 20.0616i −0.605964 + 1.80159i
125125 0 0
126126 −5.16515 + 14.0471i −0.460148 + 1.25142i
127127 5.00000 0.443678 0.221839 0.975083i 0.428794π-0.428794\pi
0.221839 + 0.975083i 0.428794π0.428794\pi
128128 11.2695 + 0.999100i 0.996093 + 0.0883088i
129129 4.58258 + 2.64575i 0.403473 + 0.232945i
130130 0 0
131131 −7.00000 12.1244i −0.611593 1.05931i −0.990972 0.134069i 0.957196π-0.957196\pi
0.379379 0.925241i 0.376138π-0.376138\pi
132132 3.50000 17.1974i 0.304636 1.49684i
133133 0 0
134134 −3.50000 + 1.32288i −0.302354 + 0.114279i
135135 0 0
136136 7.95644 + 12.6766i 0.682259 + 1.08701i
137137 −1.50000 + 2.59808i −0.128154 + 0.221969i −0.922961 0.384893i 0.874238π-0.874238\pi
0.794808 + 0.606861i 0.207572π0.207572\pi
138138 −12.5390 + 15.3223i −1.06739 + 1.30432i
139139 14.0000 1.18746 0.593732 0.804663i 0.297654π-0.297654\pi
0.593732 + 0.804663i 0.297654π0.297654\pi
140140 0 0
141141 0 0
142142 −5.79129 4.73930i −0.485994 0.397713i
143143 −1.08258 8.70793i −0.0905295 0.728194i
144144 −12.7477 9.66930i −1.06231 0.805775i
145145 0 0
146146 14.0000 5.29150i 1.15865 0.437928i
147147 −11.4564 14.5516i −0.944911 1.20020i
148148 12.0000 10.5830i 0.986394 0.869918i
149149 9.16515 5.29150i 0.750838 0.433497i −0.0751583 0.997172i 0.523946π-0.523946\pi
0.825997 + 0.563675i 0.190613π0.190613\pi
150150 3.02178 18.4626i 0.246727 1.50747i
151151 8.50000 14.7224i 0.691720 1.19809i −0.279554 0.960130i 0.590186π-0.590186\pi
0.971274 0.237964i 0.0764802π-0.0764802\pi
152152 0 0
153153 21.1660i 1.71117i
154154 9.06080 + 8.47950i 0.730140 + 0.683298i
155155 0 0
156156 −13.2695 4.46320i −1.06241 0.357342i
157157 7.00000 12.1244i 0.558661 0.967629i −0.438948 0.898513i 0.644649π-0.644649\pi
0.997609 0.0691164i 0.0220180π-0.0220180\pi
158158 18.1434 + 2.96953i 1.44341 + 0.236243i
159159 9.16515 5.29150i 0.726844 0.419643i
160160 0 0
161161 −4.58258 13.2288i −0.361158 1.04257i
162162 −2.50000 6.61438i −0.196419 0.519675i
163163 2.29129 1.32288i 0.179468 0.103616i −0.407575 0.913172i 0.633625π-0.633625\pi
0.587042 + 0.809556i 0.300292π0.300292\pi
164164 0 0
165165 0 0
166166 0 0
167167 −21.0000 −1.62503 −0.812514 0.582941i 0.801902π-0.801902\pi
−0.812514 + 0.582941i 0.801902π0.801902\pi
168168 18.4564 7.16658i 1.42395 0.552914i
169169 6.00000 0.461538
170170 0 0
171171 0 0
172172 −0.791288 3.92095i −0.0603351 0.298970i
173173 −11.4564 + 6.61438i −0.871017 + 0.502882i −0.867686 0.497113i 0.834394π-0.834394\pi
−0.00333090 + 0.999994i 0.501060π0.501060\pi
174174 10.5000 + 27.7804i 0.796003 + 2.10603i
175175 10.0000 + 8.66025i 0.755929 + 0.654654i
176176 −11.5000 + 6.61438i −0.866845 + 0.498578i
177177 −3.50000 6.06218i −0.263076 0.455661i
178178 19.5390 + 3.19795i 1.46451 + 0.239697i
179179 6.87386 + 3.96863i 0.513777 + 0.296629i 0.734385 0.678733i 0.237471π-0.237471\pi
−0.220608 + 0.975363i 0.570804π0.570804\pi
180180 0 0
181181 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
182182 7.60436 6.33828i 0.563672 0.469824i
183183 7.00000 0.517455
184184 14.9564 0.552200i 1.10260 0.0407088i
185185 0 0
186186 −39.0780 6.39590i −2.86534 0.468970i
187187 −16.1652 6.83285i −1.18211 0.499668i
188188 0 0
189189 −6.87386 1.32288i −0.500000 0.0962250i
190190 0 0
191191 −9.16515 + 5.29150i −0.663167 + 0.382880i −0.793483 0.608593i 0.791734π-0.791734\pi
0.130316 + 0.991473i 0.458401π0.458401\pi
192192 1.56080 + 21.1084i 0.112641 + 1.52337i
193193 18.3303 + 10.5830i 1.31944 + 0.761781i 0.983639 0.180150i 0.0576584π-0.0576584\pi
0.335805 + 0.941932i 0.390992π0.390992\pi
194194 6.26951 7.66115i 0.450124 0.550039i
195195 0 0
196196 −2.52178 + 13.7710i −0.180127 + 0.983643i
197197 7.93725i 0.565506i 0.959193 + 0.282753i 0.0912477π0.0912477\pi
−0.959193 + 0.282753i 0.908752π0.908752\pi
198198 18.7477 + 0.723000i 1.33234 + 0.0513814i
199199 9.16515 + 5.29150i 0.649700 + 0.375105i 0.788341 0.615238i 0.210940π-0.210940\pi
−0.138641 + 0.990343i 0.544273π0.544273\pi
200200 −11.9782 + 7.51813i −0.846988 + 0.531612i
201201 −3.50000 6.06218i −0.246871 0.427593i
202202 −10.5000 + 3.96863i −0.738777 + 0.279232i
203203 −20.6216 3.96863i −1.44735 0.278543i
204204 −21.0000 + 18.5203i −1.47029 + 1.29668i
205205 0 0
206206 1.20871 7.38505i 0.0842150 0.514541i
207207 −18.3303 10.5830i −1.27404 0.735570i
208208 4.10436 + 9.75470i 0.284586 + 0.676367i
209209 0 0
210210 0 0
211211 −2.00000 −0.137686 −0.0688428 0.997628i 0.521931π-0.521931\pi
−0.0688428 + 0.997628i 0.521931π0.521931\pi
212212 −7.58258 2.55040i −0.520773 0.175162i
213213 7.00000 12.1244i 0.479632 0.830747i
214214 11.1652 + 1.82740i 0.763234 + 0.124919i
215215 0 0
216216 3.50000 6.61438i 0.238145 0.450051i
217217 18.3303 21.1660i 1.24434 1.43684i
218218 −14.0000 + 5.29150i −0.948200 + 0.358386i
219219 14.0000 + 24.2487i 0.946032 + 1.63858i
220220 0 0
221221 −7.00000 + 12.1244i −0.470871 + 0.815572i
222222 23.1652 + 18.9572i 1.55474 + 1.27232i
223223 15.8745i 1.06304i 0.847047 + 0.531518i 0.178378π0.178378\pi
−0.847047 + 0.531518i 0.821622π0.821622\pi
224224 −13.2913 6.88053i −0.888062 0.459725i
225225 20.0000 1.33333
226226 −17.0172 + 20.7946i −1.13197 + 1.38323i
227227 7.00000 12.1244i 0.464606 0.804722i −0.534577 0.845120i 0.679529π-0.679529\pi
0.999184 + 0.0403978i 0.0128625π0.0128625\pi
228228 0 0
229229 −7.00000 12.1244i −0.462573 0.801200i 0.536515 0.843891i 0.319740π-0.319740\pi
−0.999088 + 0.0426906i 0.986407π0.986407\pi
230230 0 0
231231 −12.9174 + 19.2909i −0.849904 + 1.26925i
232232 10.5000 19.8431i 0.689359 1.30277i
233233 −13.7477 + 7.93725i −0.900644 + 0.519987i −0.877409 0.479743i 0.840730π-0.840730\pi
−0.0232346 + 0.999730i 0.507396π0.507396\pi
234234 2.41742 14.7701i 0.158032 0.965552i
235235 0 0
236236 −1.68693 + 5.01540i −0.109810 + 0.326475i
237237 34.3948i 2.23418i
238238 −3.37386 19.5094i −0.218695 1.26461i
239239 19.0000 1.22901 0.614504 0.788914i 0.289356π-0.289356\pi
0.614504 + 0.788914i 0.289356π0.289356\pi
240240 0 0
241241 −4.58258 2.64575i −0.295190 0.170428i 0.345090 0.938570i 0.387848π-0.387848\pi
−0.640280 + 0.768142i 0.721182π0.721182\pi
242242 6.60436 14.0848i 0.424544 0.905407i
243243 18.3303 10.5830i 1.17589 0.678900i
244244 −3.50000 3.96863i −0.224065 0.254065i
245245 0 0
246246 0 0
247247 0 0
248248 15.9129 + 25.3531i 1.01047 + 1.60992i
249249 0 0
250250 0 0
251251 15.8745i 1.00199i −0.865450 0.500995i 0.832967π-0.832967\pi
0.865450 0.500995i 0.167033π-0.167033\pi
252252 10.7477 + 18.2342i 0.677043 + 1.14865i
253253 −14.0000 + 10.5830i −0.880172 + 0.665348i
254254 4.47822 5.47225i 0.280988 0.343360i
255255 0 0
256256 11.1869 11.4391i 0.699183 0.714943i
257257 3.50000 + 6.06218i 0.218324 + 0.378148i 0.954296 0.298864i 0.0966077π-0.0966077\pi
−0.735972 + 0.677012i 0.763274π0.763274\pi
258258 7.00000 2.64575i 0.435801 0.164717i
259259 −20.0000 + 6.92820i −1.24274 + 0.430498i
260260 0 0
261261 −27.4955 + 15.8745i −1.70193 + 0.982607i
262262 −19.5390 3.19795i −1.20712 0.197570i
263263 5.50000 9.52628i 0.339145 0.587416i −0.645128 0.764075i 0.723196π-0.723196\pi
0.984272 + 0.176659i 0.0565291π0.0565291\pi
264264 −15.6869 19.2333i −0.965464 1.18373i
265265 0 0
266266 0 0
267267 37.0405i 2.26684i
268268 −1.68693 + 5.01540i −0.103046 + 0.306364i
269269 −14.0000 + 24.2487i −0.853595 + 1.47847i 0.0243472 + 0.999704i 0.492249π0.492249\pi
−0.877942 + 0.478766i 0.841084π0.841084\pi
270270 0 0
271271 −3.50000 6.06218i −0.212610 0.368251i 0.739921 0.672694i 0.234863π-0.234863\pi
−0.952531 + 0.304443i 0.901530π0.901530\pi
272272 21.0000 + 2.64575i 1.27331 + 0.160422i
273273 14.0000 + 12.1244i 0.847319 + 0.733799i
274274 1.50000 + 3.96863i 0.0906183 + 0.239754i
275275 6.45644 15.2746i 0.389338 0.921095i
276276 5.53901 + 27.4467i 0.333410 + 1.65209i
277277 11.4564 + 6.61438i 0.688351 + 0.397419i 0.802994 0.595987i 0.203239π-0.203239\pi
−0.114643 + 0.993407i 0.536572π0.536572\pi
278278 12.5390 15.3223i 0.752040 0.918971i
279279 42.3320i 2.53435i
280280 0 0
281281 15.8745i 0.946994i −0.880795 0.473497i 0.842992π-0.842992\pi
0.880795 0.473497i 0.157008π-0.157008\pi
282282 0 0
283283 −14.0000 + 24.2487i −0.832214 + 1.44144i 0.0640654 + 0.997946i 0.479593π0.479593\pi
−0.896279 + 0.443491i 0.853740π0.853740\pi
284284 −10.3739 + 2.09355i −0.615576 + 0.124229i
285285 0 0
286286 −10.5000 6.61438i −0.620878 0.391116i
287287 0 0
288288 −22.0000 + 5.29150i −1.29636 + 0.311805i
289289 5.50000 + 9.52628i 0.323529 + 0.560369i
290290 0 0
291291 16.0390 + 9.26013i 0.940224 + 0.542838i
292292 6.74773 20.0616i 0.394881 1.17402i
293293 21.1660i 1.23653i −0.785969 0.618266i 0.787836π-0.787836\pi
0.785969 0.618266i 0.212164π-0.212164\pi
294294 −26.1869 0.494575i −1.52725 0.0288442i
295295 0 0
296296 −0.834849 22.6120i −0.0485246 1.31430i
297297 1.08258 + 8.70793i 0.0628174 + 0.505285i
298298 2.41742 14.7701i 0.140038 0.855609i
299299 7.00000 + 12.1244i 0.404820 + 0.701170i
300300 −17.5000 19.8431i −1.01036 1.14564i
301301 −1.00000 + 5.19615i −0.0576390 + 0.299501i
302302 −8.50000 22.4889i −0.489120 1.29409i
303303 −10.5000 18.1865i −0.603209 1.04479i
304304 0 0
305305 0 0
306306 −23.1652 18.9572i −1.32426 1.08371i
307307 −28.0000 −1.59804 −0.799022 0.601302i 0.794649π-0.794649\pi
−0.799022 + 0.601302i 0.794649π0.794649\pi
308308 17.3956 2.32198i 0.991209 0.132307i
309309 14.0000 0.796432
310310 0 0
311311 9.16515 + 5.29150i 0.519708 + 0.300054i 0.736815 0.676094i 0.236329π-0.236329\pi
−0.217107 + 0.976148i 0.569662π0.569662\pi
312312 −16.7695 + 10.5254i −0.949386 + 0.595882i
313313 10.5000 + 18.1865i 0.593495 + 1.02796i 0.993757 + 0.111563i 0.0355857π0.0355857\pi
−0.400262 + 0.916401i 0.631081π0.631081\pi
314314 −7.00000 18.5203i −0.395033 1.04516i
315315 0 0
316316 19.5000 17.1974i 1.09696 0.967428i
317317 3.00000 + 5.19615i 0.168497 + 0.291845i 0.937892 0.346929i 0.112775π-0.112775\pi
−0.769395 + 0.638774i 0.779442π0.779442\pi
318318 2.41742 14.7701i 0.135562 0.828266i
319319 3.24773 + 26.1238i 0.181838 + 1.46265i
320320 0 0
321321 21.1660i 1.18137i
322322 −18.5826 6.83285i −1.03557 0.380780i
323323 0 0
324324 −9.47822 3.18800i −0.526568 0.177111i
325325 −11.4564 6.61438i −0.635489 0.366900i
326326 0.604356 3.69253i 0.0334722 0.204510i
327327 −14.0000 24.2487i −0.774202 1.34096i
328328 0 0
329329 0 0
330330 0 0
331331 −20.6216 + 11.9059i −1.13347 + 0.654406i −0.944804 0.327636i 0.893748π-0.893748\pi
−0.188661 + 0.982042i 0.560415π0.560415\pi
332332 0 0
333333 −16.0000 + 27.7128i −0.876795 + 1.51865i
334334 −18.8085 + 22.9835i −1.02916 + 1.25760i
335335 0 0
336336 8.68693 26.6184i 0.473911 1.45215i
337337 15.8745i 0.864740i 0.901696 + 0.432370i 0.142322π0.142322\pi
−0.901696 + 0.432370i 0.857678π0.857678\pi
338338 5.37386 6.56670i 0.292300 0.357182i
339339 −43.5345 25.1346i −2.36447 1.36513i
340340 0 0
341341 −32.3303 13.6657i −1.75078 0.740039i
342342 0 0
343343 10.0000 15.5885i 0.539949 0.841698i
344344 −5.00000 2.64575i −0.269582 0.142649i
345345 0 0
346346 −3.02178 + 18.4626i −0.162452 + 0.992557i
347347 −9.00000 + 15.5885i −0.483145 + 0.836832i −0.999813 0.0193540i 0.993839π-0.993839\pi
0.516667 + 0.856186i 0.327172π0.327172\pi
348348 39.8085 + 13.3896i 2.13396 + 0.717758i
349349 10.5830i 0.566495i 0.959047 + 0.283248i 0.0914118π0.0914118\pi
−0.959047 + 0.283248i 0.908588π0.908588\pi
350350 18.4347 3.18800i 0.985374 0.170406i
351351 7.00000 0.373632
352352 −3.06080 + 18.5103i −0.163141 + 0.986603i
353353 −7.00000 + 12.1244i −0.372572 + 0.645314i −0.989960 0.141344i 0.954858π-0.954858\pi
0.617388 + 0.786659i 0.288191π0.288191\pi
354354 −9.76951 1.59898i −0.519243 0.0849846i
355355 0 0
356356 21.0000 18.5203i 1.11300 0.981572i
357357 35.0000 12.1244i 1.85240 0.641689i
358358 10.5000 3.96863i 0.554942 0.209748i
359359 −7.50000 12.9904i −0.395835 0.685606i 0.597372 0.801964i 0.296211π-0.296211\pi
−0.993207 + 0.116358i 0.962878π0.962878\pi
360360 0 0
361361 9.50000 16.4545i 0.500000 0.866025i
362362 0 0
363363 28.0000 + 7.93725i 1.46962 + 0.416598i
364364 −0.126136 13.9994i −0.00661135 0.733770i
365365 0 0
366366 6.26951 7.66115i 0.327712 0.400455i
367367 13.7477 + 7.93725i 0.717626 + 0.414321i 0.813878 0.581036i 0.197352π-0.197352\pi
−0.0962526 + 0.995357i 0.530686π0.530686\pi
368368 12.7913 16.8637i 0.666792 0.879079i
369369 0 0
370370 0 0
371371 8.00000 + 6.92820i 0.415339 + 0.359694i
372372 −42.0000 + 37.0405i −2.17760 + 1.92046i
373373 −20.6216 + 11.9059i −1.06775 + 0.616463i −0.927565 0.373663i 0.878102π-0.878102\pi
−0.140181 + 0.990126i 0.544768π0.544768\pi
374374 −21.9564 + 11.5722i −1.13534 + 0.598382i
375375 0 0
376376 0 0
377377 21.0000 1.08156
378378 −7.60436 + 6.33828i −0.391126 + 0.326006i
379379 18.5203i 0.951322i −0.879629 0.475661i 0.842209π-0.842209\pi
0.879629 0.475661i 0.157791π-0.157791\pi
380380 0 0
381381 11.4564 + 6.61438i 0.586931 + 0.338865i
382382 −2.41742 + 14.7701i −0.123686 + 0.755704i
383383 −13.7477 + 7.93725i −0.702476 + 0.405575i −0.808269 0.588813i 0.799595π-0.799595\pi
0.105793 + 0.994388i 0.466262π0.466262\pi
384384 24.5000 + 17.1974i 1.25026 + 0.877600i
385385 0 0
386386 28.0000 10.5830i 1.42516 0.538661i
387387 4.00000 + 6.92820i 0.203331 + 0.352180i
388388 −2.76951 13.7233i −0.140600 0.696697i
389389 −9.00000 + 15.5885i −0.456318 + 0.790366i −0.998763 0.0497253i 0.984165π-0.984165\pi
0.542445 + 0.840091i 0.317499π0.317499\pi
390390 0 0
391391 28.0000 1.41602
392392 12.8131 + 15.0939i 0.647158 + 0.762356i
393393 37.0405i 1.86845i
394394 8.68693 + 7.10895i 0.437641 + 0.358144i
395395 0 0
396396 17.5826 19.8709i 0.883558 0.998551i
397397 −14.0000 24.2487i −0.702640 1.21701i −0.967537 0.252731i 0.918671π-0.918671\pi
0.264897 0.964277i 0.414662π-0.414662\pi
398398 14.0000 5.29150i 0.701757 0.265239i
399399 0 0
400400 −2.50000 + 19.8431i −0.125000 + 0.992157i
401401 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i 0.0688266π0.0688266\pi
−0.302556 + 0.953131i 0.597840π0.597840\pi
402402 −9.76951 1.59898i −0.487259 0.0797497i
403403 −14.0000 + 24.2487i −0.697390 + 1.20791i
404404 −5.06080 + 15.0462i −0.251784 + 0.748577i
405405 0 0
406406 −22.8131 + 19.0148i −1.13219 + 0.943690i
407407 16.0000 + 21.1660i 0.793091 + 1.04916i
408408 1.46099 + 39.5710i 0.0723295 + 1.95906i
409409 −32.0780 18.5203i −1.58616 0.915768i −0.993932 0.109995i 0.964917π-0.964917\pi
−0.592224 0.805773i 0.701750π-0.701750\pi
410410 0 0
411411 −6.87386 + 3.96863i −0.339063 + 0.195758i
412412 −7.00000 7.93725i −0.344865 0.391040i
413413 4.58258 5.29150i 0.225494 0.260378i
414414 −28.0000 + 10.5830i −1.37612 + 0.520126i
415415 0 0
416416 14.3521 + 4.24473i 0.703669 + 0.208115i
417417 32.0780 + 18.5203i 1.57087 + 0.906941i
418418 0 0
419419 5.29150i 0.258507i 0.991612 + 0.129253i 0.0412581π0.0412581\pi
−0.991612 + 0.129253i 0.958742π0.958742\pi
420420 0 0
421421 12.0000 0.584844 0.292422 0.956289i 0.405539π-0.405539\pi
0.292422 + 0.956289i 0.405539π0.405539\pi
422422 −1.79129 + 2.18890i −0.0871985 + 0.106554i
423423 0 0
424424 −9.58258 + 6.01450i −0.465371 + 0.292090i
425425 −22.9129 + 13.2288i −1.11144 + 0.641689i
426426 −7.00000 18.5203i −0.339151 0.897309i
427427 2.29129 + 6.61438i 0.110883 + 0.320092i
428428 12.0000 10.5830i 0.580042 0.511549i
429429 9.03901 21.3845i 0.436408 1.03245i
430430 0 0
431431 1.50000 2.59808i 0.0722525 0.125145i −0.827636 0.561266i 0.810315π-0.810315\pi
0.899888 + 0.436121i 0.143648π0.143648\pi
432432 −4.10436 9.75470i −0.197471 0.469323i
433433 −14.0000 −0.672797 −0.336399 0.941720i 0.609209π-0.609209\pi
−0.336399 + 0.941720i 0.609209π0.609209\pi
434434 −6.74773 39.0188i −0.323901 1.87296i
435435 0 0
436436 −6.74773 + 20.0616i −0.323158 + 0.960777i
437437 0 0
438438 39.0780 + 6.39590i 1.86722 + 0.305608i
439439 −17.5000 30.3109i −0.835229 1.44666i −0.893843 0.448379i 0.852001π-0.852001\pi
0.0586141 0.998281i 0.481332π-0.481332\pi
440440 0 0
441441 −4.00000 27.7128i −0.190476 1.31966i
442442 7.00000 + 18.5203i 0.332956 + 0.880919i
443443 −32.0780 + 18.5203i −1.52407 + 0.879924i −0.524479 + 0.851423i 0.675740π0.675740\pi
−0.999594 + 0.0285009i 0.990927π0.990927\pi
444444 41.4955 8.37420i 1.96929 0.397422i
445445 0 0
446446 17.3739 + 14.2179i 0.822676 + 0.673237i
447447 28.0000 1.32435
448448 −19.4347 + 8.38415i −0.918201 + 0.396114i
449449 −30.0000 −1.41579 −0.707894 0.706319i 0.750354π-0.750354\pi
−0.707894 + 0.706319i 0.750354π0.750354\pi
450450 17.9129 21.8890i 0.844421 1.03186i
451451 0 0
452452 7.51723 + 37.2490i 0.353581 + 1.75205i
453453 38.9519 22.4889i 1.83012 1.05662i
454454 −7.00000 18.5203i −0.328526 0.869199i
455455 0 0
456456 0 0
457457 −4.58258 + 2.64575i −0.214364 + 0.123763i −0.603338 0.797486i 0.706163π-0.706163\pi
0.388974 + 0.921249i 0.372830π0.372830\pi
458458 −19.5390 3.19795i −0.912998 0.149430i
459459 7.00000 12.1244i 0.326732 0.565916i
460460 0 0
461461 7.93725i 0.369675i −0.982769 0.184837i 0.940824π-0.940824\pi
0.982769 0.184837i 0.0591758π-0.0591758\pi
462462 9.54356 + 31.4153i 0.444007 + 1.46157i
463463 21.1660i 0.983668i −0.870689 0.491834i 0.836327π-0.836327\pi
0.870689 0.491834i 0.163673π-0.163673\pi
464464 −12.3131 29.2641i −0.571620 1.35855i
465465 0 0
466466 −3.62614 + 22.1552i −0.167978 + 1.02632i
467467 13.7477 7.93725i 0.636169 0.367292i −0.146968 0.989141i 0.546952π-0.546952\pi
0.783137 + 0.621849i 0.213618π0.213618\pi
468468 −14.0000 15.8745i −0.647150 0.733799i
469469 4.58258 5.29150i 0.211604 0.244339i
470470 0 0
471471 32.0780 18.5203i 1.47808 0.853368i
472472 3.97822 + 6.33828i 0.183112 + 0.291743i
473473 6.58258 0.818350i 0.302667 0.0376278i
474474 37.6434 + 30.8055i 1.72902 + 1.41494i
475475 0 0
476476 −24.3739 13.7810i −1.11717 0.631649i
477477 16.0000 0.732590
478478 17.0172 20.7946i 0.778350 0.951121i
479479 10.5000 18.1865i 0.479757 0.830964i −0.519973 0.854183i 0.674058π-0.674058\pi
0.999730 + 0.0232187i 0.00739140π0.00739140\pi
480480 0 0
481481 18.3303 10.5830i 0.835790 0.482544i
482482 −7.00000 + 2.64575i −0.318841 + 0.120511i
483483 7.00000 36.3731i 0.318511 1.65503i
484484 −9.50000 19.8431i −0.431818 0.901961i
485485 0 0
486486 4.83485 29.5402i 0.219313 1.33997i
487487 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
488488 −7.47822 + 0.276100i −0.338523 + 0.0124985i
489489 7.00000 0.316551
490490 0 0
491491 −26.0000 −1.17336 −0.586682 0.809818i 0.699566π-0.699566\pi
−0.586682 + 0.809818i 0.699566π0.699566\pi
492492 0 0
493493 21.0000 36.3731i 0.945792 1.63816i
494494 0 0
495495 0 0
496496 42.0000 + 5.29150i 1.88586 + 0.237595i
497497 13.7477 + 2.64575i 0.616670 + 0.118678i
498498 0 0
499499 22.9129 13.2288i 1.02572 0.592200i 0.109965 0.993935i 0.464926π-0.464926\pi
0.915756 + 0.401735i 0.131593π0.131593\pi
500500 0 0
501501 −48.1170 27.7804i −2.14971 1.24114i
502502 −17.3739 14.2179i −0.775433 0.634576i
503503 −7.00000 −0.312115 −0.156057 0.987748i 0.549878π-0.549878\pi
−0.156057 + 0.987748i 0.549878π0.549878\pi
504504 29.5826 + 4.56850i 1.31771 + 0.203497i
505505 0 0
506506 −0.956439 + 24.8009i −0.0425189 + 1.10254i
507507 13.7477 + 7.93725i 0.610558 + 0.352506i
508508 −1.97822 9.80238i −0.0877693 0.434910i
509509 7.00000 + 12.1244i 0.310270 + 0.537403i 0.978421 0.206623i 0.0662474π-0.0662474\pi
−0.668151 + 0.744026i 0.732914π0.732914\pi
510510 0 0
511511 −18.3303 + 21.1660i −0.810885 + 0.936329i
512512 −2.50000 22.4889i −0.110485 0.993878i
513513 0 0
514514 9.76951 + 1.59898i 0.430915 + 0.0705278i
515515 0 0
516516 3.37386 10.0308i 0.148526 0.441582i
517517 0 0
518518 −10.3303 + 28.0942i −0.453887 + 1.23439i
519519 −35.0000 −1.53633
520520 0 0
521521 21.0000 36.3731i 0.920027 1.59353i 0.120656 0.992694i 0.461500π-0.461500\pi
0.799370 0.600839i 0.205167π-0.205167\pi
522522 −7.25227 + 44.3103i −0.317423 + 1.93941i
523523 7.00000 + 12.1244i 0.306089 + 0.530161i 0.977503 0.210921i 0.0676463π-0.0676463\pi
−0.671414 + 0.741082i 0.734313π0.734313\pi
524524 −21.0000 + 18.5203i −0.917389 + 0.809061i
525525 11.4564 + 33.0719i 0.500000 + 1.44338i
526526 −5.50000 14.5516i −0.239811 0.634481i
527527 28.0000 + 48.4974i 1.21970 + 2.11258i
528528 −35.0998 0.0576255i −1.52752 0.00250783i
529529 2.50000 4.33013i 0.108696 0.188266i
530530 0 0
531531 10.5830i 0.459263i
532532 0 0
533533 0 0
534534 40.5390 + 33.1751i 1.75429 + 1.43563i
535535 0 0
536536 3.97822 + 6.33828i 0.171833 + 0.273772i
537537 10.5000 + 18.1865i 0.453108 + 0.784807i
538538 14.0000 + 37.0405i 0.603583 + 1.59693i
539539 −22.4564 5.89138i −0.967267 0.253760i
540540 0 0
541541 20.6216 11.9059i 0.886591 0.511874i 0.0137654 0.999905i 0.495618π-0.495618\pi
0.872826 + 0.488031i 0.162285π0.162285\pi
542542 −9.76951 1.59898i −0.419636 0.0686819i
543543 0 0
544544 21.7042 20.6138i 0.930558 0.883810i
545545 0 0
546546 25.8085 4.46320i 1.10450 0.191007i
547547 −2.00000 −0.0855138 −0.0427569 0.999086i 0.513614π-0.513614\pi
−0.0427569 + 0.999086i 0.513614π0.513614\pi
548548 5.68693 + 1.91280i 0.242934 + 0.0817108i
549549 9.16515 + 5.29150i 0.391159 + 0.225836i
550550 −10.9347 20.7469i −0.466255 0.884650i
551551 0 0
552552 35.0000 + 18.5203i 1.48970 + 0.788275i
553553 −32.5000 + 11.2583i −1.38204 + 0.478753i
554554 17.5000 6.61438i 0.743504 0.281018i
555555 0 0
556556 −5.53901 27.4467i −0.234907 1.16400i
557557 −9.16515 5.29150i −0.388340 0.224208i 0.293101 0.956082i 0.405313π-0.405313\pi
−0.681441 + 0.731873i 0.738646π0.738646\pi
558558 −46.3303 37.9144i −1.96132 1.60505i
559559 5.29150i 0.223807i
560560 0 0
561561 −28.0000 37.0405i −1.18216 1.56385i
562562 −17.3739 14.2179i −0.732872 0.599746i
563563 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
564564 0 0
565565 0 0
566566 14.0000 + 37.0405i 0.588464 + 1.55693i
567567 10.0000 + 8.66025i 0.419961 + 0.363696i
568568 −7.00000 + 13.2288i −0.293713 + 0.555066i
569569 27.4955 15.8745i 1.15267 0.665494i 0.203133 0.979151i 0.434888π-0.434888\pi
0.949536 + 0.313657i 0.101554π0.101554\pi
570570 0 0
571571 9.00000 15.5885i 0.376638 0.652357i −0.613933 0.789359i 0.710413π-0.710413\pi
0.990571 + 0.137002i 0.0437466π0.0437466\pi
572572 −16.6434 + 5.56760i −0.695894 + 0.232793i
573573 −28.0000 −1.16972
574574 0 0
575575 26.4575i 1.10335i
576576 −13.9129 + 28.8172i −0.579703 + 1.20072i
577577 −17.5000 + 30.3109i −0.728535 + 1.26186i 0.228968 + 0.973434i 0.426465π0.426465\pi
−0.957503 + 0.288425i 0.906868π0.906868\pi
578578 15.3521 + 2.51268i 0.638562 + 0.104514i
579579 28.0000 + 48.4974i 1.16364 + 2.01548i
580580 0 0
581581 0 0
582582 24.5000 9.26013i 1.01556 0.383845i
583583 5.16515 12.2197i 0.213919 0.506089i
584584 −15.9129 25.3531i −0.658480 1.04912i
585585 0 0
586586 −23.1652 18.9572i −0.956944 0.783115i
587587 7.93725i 0.327606i −0.986493 0.163803i 0.947624π-0.947624\pi
0.986493 0.163803i 0.0523761π-0.0523761\pi
588588 −23.9955 + 28.2173i −0.989556 + 1.16366i
589589 0 0
590590 0 0
591591 −10.5000 + 18.1865i −0.431912 + 0.748094i
592592 −25.4955 19.3386i −1.04786 0.794812i
593593 −13.7477 + 7.93725i −0.564551 + 0.325944i −0.754970 0.655759i 0.772349π-0.772349\pi
0.190419 + 0.981703i 0.439015π0.439015\pi
594594 10.5000 + 6.61438i 0.430820 + 0.271391i
595595 0 0
596596 −14.0000 15.8745i −0.573462 0.650245i
597597 14.0000 + 24.2487i 0.572982 + 0.992434i
598598 19.5390 + 3.19795i 0.799010 + 0.130774i
599599 0 0 0.500000 0.866025i 0.333333π-0.333333\pi
−0.500000 + 0.866025i 0.666667π0.666667\pi
600600 −37.3911 + 1.38050i −1.52649 + 0.0563587i
601601 42.3320i 1.72676i 0.504555 + 0.863380i 0.331657π0.331657\pi
−0.504555 + 0.863380i 0.668343π0.668343\pi
602602 4.79129 + 5.74835i 0.195278 + 0.234285i
603603 10.5830i 0.430973i
604604 −32.2259 10.8392i −1.31126 0.441041i
605605 0 0
606606 −29.3085 4.79693i −1.19058 0.194862i
607607 0 0 0.866025 0.500000i 0.166667π-0.166667\pi
−0.866025 + 0.500000i 0.833333π0.833333\pi
608608 0 0
609609 −42.0000 36.3731i −1.70193 1.47391i
610610 0 0
611611 0 0
612612 −41.4955 + 8.37420i −1.67735 + 0.338507i
613613 −36.6606 21.1660i −1.48071 0.854887i −0.480947 0.876750i 0.659707π-0.659707\pi
−0.999761 + 0.0218626i 0.993040π0.993040\pi
614614 −25.0780 + 30.6446i −1.01207 + 1.23672i
615615 0 0
616616 13.0390 21.1183i 0.525357 0.850882i
617617 −23.0000 −0.925945 −0.462973 0.886373i 0.653217π-0.653217\pi
−0.462973 + 0.886373i 0.653217π0.653217\pi
618618 12.5390 15.3223i 0.504393 0.616354i
619619 4.58258 + 2.64575i 0.184189 + 0.106342i 0.589259 0.807944i 0.299420π-0.299420\pi
−0.405070 + 0.914286i 0.632753π0.632753\pi
620620 0 0
621621 −7.00000 12.1244i −0.280900 0.486534i
622622 14.0000 5.29150i 0.561349 0.212170i
623623 −35.0000 + 12.1244i −1.40225 + 0.485752i
624624 −3.50000 + 27.7804i −0.140112 + 1.11211i
625625 −12.5000 21.6506i −0.500000 0.866025i
626626 29.3085 + 4.79693i 1.17140 + 0.191724i
627627 0 0
628628 −26.5390 8.92640i −1.05902 0.356202i
629629 42.3320i 1.68789i
630630 0 0
631631 26.4575i 1.05326i −0.850096 0.526628i 0.823456π-0.823456\pi
0.850096 0.526628i 0.176544π-0.176544\pi
632632 −1.35663 36.7445i −0.0539638 1.46162i
633633 −4.58258 2.64575i −0.182141 0.105159i
634634 8.37386 + 1.37055i 0.332569 + 0.0544315i
635635 0 0
636636 −14.0000 15.8745i −0.555136 0.629465i
637637 −6.87386 + 17.1974i −0.272352 + 0.681385i
638638 31.5000 + 19.8431i 1.24710 + 0.785597i
639639 18.3303 10.5830i 0.725136 0.418657i
640640 0 0
641641 5.50000 9.52628i 0.217237 0.376265i −0.736725 0.676192i 0.763629π-0.763629\pi
0.953962 + 0.299927i 0.0969622π0.0969622\pi
642642 23.1652 + 18.9572i 0.914256 + 0.748181i
643643 18.5203i 0.730368i 0.930935 + 0.365184i 0.118994π0.118994\pi
−0.930935 + 0.365184i 0.881006π0.881006\pi
644644 −24.1216 + 14.2179i −0.950524 + 0.560264i
645645 0 0
646646 0 0
647647 27.4955 + 15.8745i 1.08096 + 0.624091i 0.931155 0.364625i 0.118803π-0.118803\pi
0.149803 + 0.988716i 0.452136π0.452136\pi
648648 −11.9782 + 7.51813i −0.470549 + 0.295340i
649649 −8.08258 3.41643i −0.317269 0.134106i
650650 −17.5000 + 6.61438i −0.686406 + 0.259437i
651651 70.0000 24.2487i 2.74352 0.950382i
652652 −3.50000 3.96863i −0.137071 0.155423i
653653 −4.00000 6.92820i −0.156532 0.271122i 0.777084 0.629397i 0.216698π-0.216698\pi
−0.933616 + 0.358276i 0.883365π0.883365\pi
654654 −39.0780 6.39590i −1.52807 0.250100i
655655 0 0
656656 0 0
657657 42.3320i 1.65153i
658658 0 0
659659 −26.0000 −1.01282 −0.506408 0.862294i 0.669027π-0.669027\pi
−0.506408 + 0.862294i 0.669027π0.669027\pi
660660 0 0
661661 0 0 −0.866025 0.500000i 0.833333π-0.833333\pi
0.866025 + 0.500000i 0.166667π0.166667\pi
662662 −5.43920 + 33.2327i −0.211401 + 1.29163i
663663 −32.0780 + 18.5203i −1.24581 + 0.719267i
664664 0 0
665665 0 0
666666 16.0000 + 42.3320i 0.619987 + 1.64033i
667667 −21.0000 36.3731i −0.813123 1.40837i
668668 8.30852 + 41.1700i 0.321466 + 1.59291i
669669 −21.0000 + 36.3731i −0.811907 + 1.40626i
670670 0 0
671671 7.00000 5.29150i 0.270232 0.204276i
672672 −21.3521 33.3480i −0.823674 1.28643i
673673 31.7490i 1.22383i 0.790922 + 0.611917i 0.209601π0.209601\pi
−0.790922 + 0.611917i 0.790399π0.790399\pi
674674 17.3739 + 14.2179i 0.669216 + 0.547653i
675675 11.4564 + 6.61438i 0.440959 + 0.254588i
676676 −2.37386 11.7629i −0.0913024 0.452418i
677677 27.4955 15.8745i 1.05674 0.610107i 0.132209 0.991222i 0.457793π-0.457793\pi
0.924528 + 0.381115i 0.124460π0.124460\pi
678678 −66.5000 + 25.1346i −2.55392 + 0.965290i
679679 −3.50000 + 18.1865i −0.134318 + 0.697935i
680680 0 0
681681 32.0780 18.5203i 1.22923 0.709698i
682682 −43.9129 + 23.1443i −1.68151 + 0.886241i
683683 20.6216 + 11.9059i 0.789063 + 0.455566i 0.839633 0.543155i 0.182770π-0.182770\pi
−0.0505694 + 0.998721i 0.516104π0.516104\pi
684684 0 0
685685 0 0
686686 −8.10436 24.9062i −0.309426 0.950924i
687687 37.0405i 1.41318i
688688 −7.37386 + 3.10260i −0.281126 + 0.118286i
689689 −9.16515 5.29150i −0.349164 0.201590i
690690 0 0
691691 −2.29129 + 1.32288i −0.0871647 + 0.0503246i −0.542949 0.839766i 0.682692π-0.682692\pi
0.455784 + 0.890090i 0.349359π0.349359\pi
692692 17.5000 + 19.8431i 0.665250 + 0.754323i
693693 −31.4955 + 15.4931i −1.19641 + 0.588534i
694694 9.00000 + 23.8118i 0.341635 + 0.903882i
695695 0 0
696696 50.3085 31.5761i 1.90694 1.19689i
697697 0 0
698698 11.5826 + 9.47860i 0.438407 + 0.358770i
699699 −42.0000 −1.58859
700700 13.0218 23.0311i 0.492177 0.870495i
701701 34.3948i 1.29907i 0.760331 + 0.649536i 0.225037π0.225037\pi
−0.760331 + 0.649536i 0.774963π0.774963\pi
702702 6.26951 7.66115i 0.236627 0.289152i
703703 0 0
704704 17.5172 + 19.9285i 0.660206 + 0.751085i
705705 0 0
706706 7.00000 + 18.5203i 0.263448 + 0.697019i
707707 13.7477 15.8745i 0.517036 0.597022i
708708 −10.5000 + 9.26013i −0.394614 + 0.348017i
709709 −4.00000 6.92820i −0.150223 0.260194i 0.781086 0.624423i 0.214666π-0.214666\pi
−0.931309 + 0.364229i 0.881333π0.881333\pi
710710 0 0
711711 −26.0000 + 45.0333i −0.975076 + 1.68888i
712712 −1.46099 39.5710i −0.0547527 1.48299i
713713 56.0000 2.09722
714714 18.0780 49.1649i 0.676553 1.83995i
715715 0 0
716716 5.06080 15.0462i 0.189131 0.562303i
717717 43.5345 + 25.1346i 1.62582 + 0.938670i
718718 −20.9347 3.42638i −0.781275 0.127871i
719719 −27.4955 + 15.8745i −1.02541 + 0.592019i −0.915666 0.401941i 0.868336π-0.868336\pi
−0.109742 + 0.993960i 0.535002π0.535002\pi
720720 0 0
721721 4.58258 + 13.2288i 0.170664 + 0.492665i
722722 −9.50000 25.1346i −0.353553 0.935414i
723723 −7.00000 12.1244i −0.260333 0.450910i
724724 0 0
725725 34.3693 + 19.8431i 1.27644 + 0.736956i
726726 33.7650 23.5357i 1.25314 0.873490i
727727 21.1660i 0.785004i −0.919751 0.392502i 0.871610π-0.871610\pi
0.919751 0.392502i 0.128390π-0.128390\pi
728728 −15.4347 12.4005i −0.572047 0.459591i
729729 41.0000 1.51852
730730 0 0
731731 −9.16515 5.29150i −0.338985 0.195713i
732732 −2.76951 13.7233i −0.102364 0.507229i
733733 11.4564 6.61438i 0.423153 0.244308i −0.273272 0.961937i 0.588106π-0.588106\pi
0.696426 + 0.717629i 0.254773π0.254773\pi
734734 21.0000 7.93725i 0.775124 0.292969i
735735 0 0
736736 −7.00000 29.1033i −0.258023 1.07276i
737737 −8.08258 3.41643i −0.297726 0.125846i
738738 0 0
739739 23.0000 39.8372i 0.846069 1.46543i −0.0386212 0.999254i 0.512297π-0.512297\pi
0.884690 0.466180i 0.154370π-0.154370\pi
740740 0 0
741741 0 0
742742 14.7477 2.55040i 0.541406 0.0936282i
743743 12.0000 0.440237 0.220119 0.975473i 0.429356π-0.429356\pi
0.220119 + 0.975473i 0.429356π0.429356\pi
744744 2.92197 + 79.1420i 0.107125 + 2.90149i
745745 0 0
746746 −5.43920 + 33.2327i −0.199143 + 1.21674i
747747 0 0
748748 −7.00000 + 34.3948i −0.255945 + 1.25760i
749749 −20.0000 + 6.92820i −0.730784 + 0.253151i
750750 0 0
751751 41.2432 23.8118i 1.50499 0.868904i 0.505002 0.863118i 0.331492π-0.331492\pi
0.999983 0.00578524i 0.00184151π-0.00184151\pi
752752 0 0
753753 21.0000 36.3731i 0.765283 1.32551i
754754 18.8085 22.9835i 0.684966 0.837008i
755755 0 0
756756 0.126136 + 13.9994i 0.00458754 + 0.509154i
757757 2.00000 0.0726912 0.0363456 0.999339i 0.488428π-0.488428\pi
0.0363456 + 0.999339i 0.488428π0.488428\pi
758758 −20.2695 16.5876i −0.736222 0.602487i
759759 −46.0780 + 5.72845i −1.67253 + 0.207930i
760760 0 0
761761 −13.7477 + 7.93725i −0.498355 + 0.287725i −0.728034 0.685541i 0.759566π-0.759566\pi
0.229679 + 0.973266i 0.426232π0.426232\pi
762762 17.5000 6.61438i 0.633958 0.239614i
763763 18.3303 21.1660i 0.663602 0.766261i
764764 14.0000 + 15.8745i 0.506502 + 0.574320i
765765 0 0
766766 −3.62614 + 22.1552i −0.131018 + 0.800498i
767767 −3.50000 + 6.06218i −0.126378 + 0.218893i
768768 40.7650 11.4113i 1.47098 0.411770i
769769 47.6235i 1.71735i −0.512522 0.858674i 0.671289π-0.671289\pi
0.512522 0.858674i 0.328711π-0.328711\pi
770770 0 0
771771 18.5203i 0.666991i
772772 13.4955 40.1232i 0.485712 1.44407i
773773 7.00000 12.1244i 0.251773 0.436083i −0.712241 0.701935i 0.752320π-0.752320\pi
0.964014 + 0.265852i 0.0856532π0.0856532\pi
774774 11.1652 + 1.82740i 0.401323 + 0.0656846i
775775 −45.8258 + 26.4575i −1.64611 + 0.950382i
776776 −17.5000 9.26013i −0.628213 0.332419i
777777 −54.9909 10.5830i −1.97279 0.379663i
778778 9.00000 + 23.8118i 0.322666 + 0.853693i
779779 0 0
780780 0 0
781781 −2.16515 17.4159i −0.0774752 0.623188i
782782 25.0780 30.6446i 0.896789 1.09585i
783783 −21.0000 −0.750479
784784 27.9955 0.504525i 0.999838 0.0180188i
785785 0 0
786786 −40.5390 33.1751i −1.44598 1.18332i
787787 7.00000 12.1244i 0.249523 0.432187i −0.713871 0.700278i 0.753059π-0.753059\pi
0.963394 + 0.268091i 0.0863928π0.0863928\pi
788788 15.5608 3.14033i 0.554330 0.111869i
789789 25.2042 14.5516i 0.897292 0.518052i
790790 0 0
791791 9.50000 49.3634i 0.337781 1.75516i
792792 −6.00000 37.0405i −0.213201 1.31618i
793793 −3.50000 6.06218i −0.124289 0.215274i
794794 −39.0780 6.39590i −1.38683 0.226982i
795795 0 0
796796 6.74773 20.0616i 0.239167 0.711065i
797797 14.0000 0.495905 0.247953 0.968772i 0.420242π-0.420242\pi
0.247953 + 0.968772i 0.420242π0.420242\pi
798798 0 0
799799 0 0
800800 19.4782 + 20.5085i 0.688659 + 0.725085i
801801 −28.0000 + 48.4974i −0.989331 + 1.71357i
802802 37.6824 + 6.16748i 1.33061 + 0.217781i
803803 32.3303 + 13.6657i 1.14091 + 0.482252i
804804 −10.5000 + 9.26013i −0.370306 + 0.326580i
805805 0 0
806806 14.0000 + 37.0405i 0.493129 + 1.30470i
807807 −64.1561 + 37.0405i −2.25840 + 1.30389i
808808 11.9347 + 19.0148i 0.419860 + 0.668940i
809809 −27.4955 15.8745i −0.966689 0.558118i −0.0684635 0.997654i 0.521810π-0.521810\pi
−0.898225 + 0.439536i 0.855143π0.855143\pi
810810 0 0
811811 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
812812 0.378409 + 41.9983i 0.0132796 + 1.47385i
813813 18.5203i 0.649534i
814814 37.4955 + 1.44600i 1.31421 + 0.0506823i
815815 0 0
816816 44.6170 + 33.8426i 1.56191 + 1.18473i
817817 0 0
818818 −49.0000 + 18.5203i −1.71324 + 0.647546i
819819 9.16515 + 26.4575i 0.320256 + 0.924500i
820820 0 0
821821 29.7867 17.1974i 1.03956 0.600193i 0.119855 0.992791i 0.461757π-0.461757\pi
0.919710 + 0.392599i 0.128424π0.128424\pi
822822 −1.81307 + 11.0776i −0.0632380 + 0.386375i
823823 −9.16515 5.29150i −0.319477 0.184450i 0.331682 0.943391i 0.392384π-0.392384\pi
−0.651159 + 0.758941i 0.725717π0.725717\pi
824824 −14.9564 + 0.552200i −0.521032 + 0.0192368i
825825 35.0000 26.4575i 1.21854 0.921132i
826826 −1.68693 9.75470i −0.0586959 0.339410i
827827 −26.0000 −0.904109 −0.452054 0.891990i 0.649309π-0.649309\pi
−0.452054 + 0.891990i 0.649309π0.649309\pi
828828 −13.4955 + 40.1232i −0.468999 + 1.39438i
829829 −21.0000 + 36.3731i −0.729360 + 1.26329i 0.227794 + 0.973709i 0.426849π0.426849\pi
−0.957154 + 0.289579i 0.906485π0.906485\pi
830830 0 0
831831 17.5000 + 30.3109i 0.607068 + 1.05147i
832832 17.5000 11.9059i 0.606703 0.412762i
833833 22.9129 + 29.1033i 0.793884 + 1.00837i
834834 49.0000 18.5203i 1.69673 0.641304i
835835 0 0
836836 0 0
837837 14.0000 24.2487i 0.483911 0.838158i
838838 5.79129 + 4.73930i 0.200057 + 0.163716i
839839 0 0 1.00000 00
−1.00000 π\pi
840840 0 0
841841 −34.0000 −1.17241
842842 10.7477 13.1334i 0.370391 0.452607i
843843 21.0000 36.3731i 0.723278 1.25275i
844844 0.791288 + 3.92095i 0.0272373 + 0.134965i
845845 0 0
846846 0 0
847847 1.66515 + 29.0556i 0.0572153 + 0.998362i
848848 −2.00000 + 15.8745i −0.0686803 + 0.545133i
849849 −64.1561 + 37.0405i −2.20183 + 1.27123i
850850 −6.04356 + 36.9253i −0.207292 + 1.26653i
851851 −36.6606 21.1660i −1.25671 0.725561i
852852 −26.5390 8.92640i −0.909212 0.305814i
853853 0 0 1.00000 00
−1.00000 π\pi
854854 9.29129 + 3.41643i 0.317941 + 0.116908i
855855 0 0
856856 −0.834849 22.6120i −0.0285345 0.772863i
857857 18.3303 + 10.5830i 0.626151 + 0.361509i 0.779260 0.626701i 0.215595π-0.215595\pi
−0.153109 + 0.988209i 0.548928π0.548928\pi
858858 −15.3085 29.0456i −0.522624 0.991602i
859859 −16.0390 + 9.26013i −0.547244 + 0.315952i −0.748010 0.663688i 0.768990π-0.768990\pi
0.200766 + 0.979639i 0.435657π0.435657\pi
860860 0 0
861861 0 0
862862 −1.50000 3.96863i −0.0510902 0.135172i
863863 13.7477 7.93725i 0.467978 0.270187i −0.247415 0.968910i 0.579581π-0.579581\pi
0.715393 + 0.698722i 0.246248π0.246248\pi
864864 −14.3521 4.24473i −0.488268 0.144409i
865865 0 0
866866 −12.5390 + 15.3223i −0.426093 + 0.520673i
867867 29.1033i 0.988399i
868868 −48.7477 27.5619i −1.65461 0.935512i
869869 26.0000 + 34.3948i 0.881990 + 1.16676i
870870 0 0
871871 −3.50000 + 6.06218i −0.118593 + 0.205409i
872872 15.9129 + 25.3531i 0.538878 + 0.858565i
873873 14.0000 + 24.2487i 0.473828 + 0.820695i
874874 0 0
875875 0 0
876876 42.0000 37.0405i 1.41905 1.25148i
877877 −11.4564 + 6.61438i −0.386856 + 0.223352i −0.680797 0.732472i 0.738367π-0.738367\pi
0.293941 + 0.955824i 0.405033π0.405033\pi
878878 −48.8475 7.99488i −1.64852 0.269814i
879879 28.0000 48.4974i 0.944417 1.63578i
880880 0 0
881881 7.00000 0.235836 0.117918 0.993023i 0.462378π-0.462378\pi
0.117918 + 0.993023i 0.462378π0.462378\pi
882882 −33.9129 20.4430i −1.14191 0.688352i
883883 34.3948i 1.15748i −0.815514 0.578738i 0.803545π-0.803545\pi
0.815514 0.578738i 0.196455π-0.196455\pi
884884 26.5390 + 8.92640i 0.892604 + 0.300227i
885885 0 0
886886 −8.46099 + 51.6954i −0.284252 + 1.73674i
887887 24.5000 + 42.4352i 0.822629 + 1.42484i 0.903718 + 0.428129i 0.140827π0.140827\pi
−0.0810881 + 0.996707i 0.525840π0.525840\pi
888888 28.0000 52.9150i 0.939618 1.77571i
889889 −2.50000 + 12.9904i −0.0838473 + 0.435683i
890890 0 0
891891 6.45644 15.2746i 0.216299 0.511719i
892892 31.1216 6.28065i 1.04203 0.210292i
893893 0 0
894894 25.0780 30.6446i 0.838735 1.02491i
895895 0 0
896896 −8.23049 + 28.7795i −0.274961 + 0.961455i
897897 37.0405i 1.23675i
898898 −26.8693 + 32.8335i −0.896641 + 1.09567i
899899 42.0000 72.7461i 1.40078 2.42622i
900900 −7.91288 39.2095i −0.263763 1.30698i
901901 −18.3303 + 10.5830i −0.610671 + 0.352571i
902902 0 0
903903 −9.16515 + 10.5830i −0.304997 + 0.352180i
904904 47.5000 + 25.1346i 1.57983 + 0.835966i
905905 0 0
906906 10.2741 62.7730i 0.341333 2.08549i
907907 −4.58258 2.64575i −0.152162 0.0878507i 0.421986 0.906602i 0.361333π-0.361333\pi
−0.574148 + 0.818752i 0.694667π0.694667\pi
908908 −26.5390 8.92640i −0.880728 0.296233i
909909 31.7490i 1.05305i
910910 0 0
911911 15.8745i 0.525946i −0.964803 0.262973i 0.915297π-0.915297\pi
0.964803 0.262973i 0.0847030π-0.0847030\pi
912912 0 0
913913 0 0
914914 −1.20871 + 7.38505i −0.0399806 + 0.244276i
915915 0 0
916916 −21.0000 + 18.5203i −0.693860 + 0.611927i
917917 35.0000 12.1244i 1.15580 0.400381i
918918 −7.00000 18.5203i −0.231034 0.611260i
919919 4.00000 + 6.92820i 0.131948 + 0.228540i 0.924427 0.381358i 0.124544π-0.124544\pi
−0.792480 + 0.609898i 0.791210π0.791210\pi
920920 0 0
921921 −64.1561 37.0405i −2.11401 1.22053i
922922 −8.68693 7.10895i −0.286089 0.234121i
923923 −14.0000 −0.460816
924924 42.9301 + 17.6920i 1.41230 + 0.582023i
925925 40.0000 1.31519
926926 −23.1652 18.9572i −0.761254 0.622973i
927927 18.3303 + 10.5830i 0.602046 + 0.347591i
928928 −43.0562 12.7342i −1.41339 0.418020i
929929 −17.5000 30.3109i −0.574156 0.994468i −0.996133 0.0878612i 0.971997π-0.971997\pi
0.421976 0.906607i 0.361337π-0.361337\pi
930930 0 0
931931 0 0
932932 21.0000 + 23.8118i 0.687878 + 0.779980i
933933 14.0000 + 24.2487i 0.458339 + 0.793867i
934934 3.62614 22.1552i 0.118651 0.724939i
935935 0 0
936936 −29.9129 + 1.10440i −0.977733 + 0.0360985i
937937 26.4575i 0.864329i 0.901795 + 0.432165i 0.142250π0.142250\pi
−0.901795 + 0.432165i 0.857750π0.857750\pi
938938 −1.68693 9.75470i −0.0550803 0.318502i
939939 55.5608i 1.81316i
940940 0 0
941941 48.1170 + 27.7804i 1.56857 + 0.905615i 0.996336 + 0.0855250i 0.0272567π0.0272567\pi
0.572235 + 0.820090i 0.306077π0.306077\pi
942942 8.46099 51.6954i 0.275674 1.68433i
943943 0 0
944944 10.5000 + 1.32288i 0.341746 + 0.0430559i
945945 0 0
946946 5.00000 7.93725i 0.162564 0.258062i
947947 −13.7477 + 7.93725i −0.446741 + 0.257926i −0.706453 0.707760i 0.749706π-0.749706\pi
0.259712 + 0.965686i 0.416372π0.416372\pi
948948 67.4301 13.6081i 2.19003 0.441970i
949949 14.0000 24.2487i 0.454459 0.787146i
950950 0 0
951951 15.8745i 0.514766i
952952 −36.9129 + 14.3332i −1.19635 + 0.464540i
953953 15.8745i 0.514226i −0.966381 0.257113i 0.917229π-0.917229\pi
0.966381 0.257113i 0.0827712π-0.0827712\pi
954954 14.3303 17.5112i 0.463961 0.566946i
955955 0 0
956956 −7.51723 37.2490i −0.243125 1.20472i
957957 −27.1170 + 64.1535i −0.876570 + 2.07379i
958958 −10.5000 27.7804i −0.339240 0.897544i
959959 −6.00000 5.19615i −0.193750 0.167793i
960960 0 0
961961 40.5000 + 70.1481i 1.30645 + 2.26284i
962962 4.83485 29.5402i 0.155882 0.952415i
963963 −16.0000 + 27.7128i −0.515593 + 0.893033i
964964 −3.37386 + 10.0308i −0.108665 + 0.323070i
965965 0 0
966966 −33.5390 40.2385i −1.07910 1.29465i
967967 16.0000 0.514525 0.257263 0.966342i 0.417179π-0.417179\pi
0.257263 + 0.966342i 0.417179π0.417179\pi
968968 −30.2259 7.37510i −0.971499 0.237045i
969969 0 0
970970 0 0
971971 25.2042 14.5516i 0.808840 0.466984i −0.0377128 0.999289i 0.512007π-0.512007\pi
0.846553 + 0.532305i 0.178674π0.178674\pi
972972 −28.0000 31.7490i −0.898100 1.01835i
973973 −7.00000 + 36.3731i −0.224410 + 1.16607i
974974 0 0
975975 −17.5000 30.3109i −0.560449 0.970725i
976976 −6.39564 + 8.43183i −0.204720 + 0.269896i
977977 19.0000 32.9090i 0.607864 1.05285i −0.383728 0.923446i 0.625360π-0.625360\pi
0.991592 0.129405i 0.0413067π-0.0413067\pi
978978 6.26951 7.66115i 0.200477 0.244977i
979979 28.0000 + 37.0405i 0.894884 + 1.18382i
980980 0 0
981981 42.3320i 1.35156i
982982 −23.2867 + 28.4557i −0.743110 + 0.908058i
983983 41.2432 + 23.8118i 1.31545 + 0.759477i 0.982994 0.183640i 0.0587881π-0.0587881\pi
0.332460 + 0.943117i 0.392121π0.392121\pi
984984 0 0
985985 0 0
986986 −21.0000 55.5608i −0.668776 1.76942i
987987 0 0
988988 0 0
989989 −9.16515 + 5.29150i −0.291435 + 0.168260i
990990 0 0
991991 −18.3303 10.5830i −0.582281 0.336180i 0.179758 0.983711i 0.442468π-0.442468\pi
−0.762039 + 0.647531i 0.775802π0.775802\pi
992992 43.4083 41.2276i 1.37822 1.30898i
993993 −63.0000 −1.99924
994994 15.2087 12.6766i 0.482391 0.402076i
995995 0 0
996996 0 0
997997 −45.8258 26.4575i −1.45132 0.837918i −0.452760 0.891632i 0.649561π-0.649561\pi
−0.998556 + 0.0537146i 0.982894π0.982894\pi
998998 6.04356 36.9253i 0.191306 1.16885i
999999 −18.3303 + 10.5830i −0.579945 + 0.334831i
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 308.2.n.a.263.2 yes 4
4.3 odd 2 308.2.n.b.263.2 yes 4
7.2 even 3 inner 308.2.n.a.219.1 4
11.10 odd 2 308.2.n.b.263.1 yes 4
28.23 odd 6 308.2.n.b.219.1 yes 4
44.43 even 2 inner 308.2.n.a.263.1 yes 4
77.65 odd 6 308.2.n.b.219.2 yes 4
308.219 even 6 inner 308.2.n.a.219.2 yes 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
308.2.n.a.219.1 4 7.2 even 3 inner
308.2.n.a.219.2 yes 4 308.219 even 6 inner
308.2.n.a.263.1 yes 4 44.43 even 2 inner
308.2.n.a.263.2 yes 4 1.1 even 1 trivial
308.2.n.b.219.1 yes 4 28.23 odd 6
308.2.n.b.219.2 yes 4 77.65 odd 6
308.2.n.b.263.1 yes 4 11.10 odd 2
308.2.n.b.263.2 yes 4 4.3 odd 2