Properties

Label 363.2.e.l.148.1
Level 363363
Weight 22
Character 363.148
Analytic conductor 2.8992.899
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] = [363,2,Mod(124,363)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(363, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 8])) 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("363.124"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 363=3112 363 = 3 \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 363.e (of order 55, degree 44, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,5,-1,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.898569593372.89856959337
Analytic rank: 00
Dimension: 44
Coefficient field: Q(ζ10)\Q(\zeta_{10})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4x3+x2x+1 x^{4} - x^{3} + x^{2} - x + 1 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)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 148.1
Root 0.309017+0.951057i-0.309017 + 0.951057i of defining polynomial
Character χ\chi == 363.148
Dual form 363.2.e.l.130.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(0.690983+2.12663i)q2+(0.8090170.587785i)q3+(2.42705+1.76336i)q4+(0.6180341.90211i)q5+(0.6909832.12663i)q6+(3.618032.62866i)q7+(1.809021.31433i)q8+(0.309017+0.951057i)q9+4.47214q10+3.00000q12+(8.09017+5.87785i)q14+(1.61803+1.17557i)q15+(0.309017+0.951057i)q16+(1.381974.25325i)q17+(1.80902+1.31433i)q18+(3.61803+2.62866i)q19+(1.85410+5.70634i)q204.47214q214.00000q23+(0.690983+2.12663i)q24+(0.809017+0.587785i)q25+(0.3090170.951057i)q27+(4.14590+12.7598i)q28+(3.61803+2.62866i)q29+(3.618032.62866i)q306.70820q32+10.0000q34+(2.763938.50651i)q35+(2.427051.76336i)q36+(1.61803+1.17557i)q37+(3.09017+9.51057i)q38+(3.61803+2.62866i)q40+(3.61803+2.62866i)q41+(3.090179.51057i)q42+4.47214q43+2.00000q45+(2.763938.50651i)q46+(6.472144.70228i)q47+(0.8090170.587785i)q48+(4.0172212.3637i)q49+(0.690983+2.12663i)q50+(3.61803+2.62866i)q51+(1.85410+5.70634i)q53+2.23607q5410.0000q56+(1.381974.25325i)q57+(8.090175.87785i)q58+(1.854105.70634i)q60+(2.763938.50651i)q61+(3.61803+2.62866i)q63+(4.0172212.3637i)q6412.0000q67+(4.14590+12.7598i)q68+(3.23607+2.35114i)q69+(16.180311.7557i)q70+(2.47214+7.60845i)q71+(0.6909832.12663i)q72+(7.236075.25731i)q73+(3.618032.62866i)q74+(0.3090170.951057i)q7513.4164q76+(4.14590+12.7598i)q79+(1.61803+1.17557i)q80+(0.809017+0.587785i)q81+(3.09017+9.51057i)q82+(2.76393+8.50651i)q83+(10.85417.88597i)q84+(7.236075.25731i)q85+(3.09017+9.51057i)q86+4.47214q8714.0000q89+(1.38197+4.25325i)q90+(9.708207.05342i)q92+(5.5278617.0130i)q94+(7.236075.25731i)q95+(5.42705+3.94298i)q96+(0.618034+1.90211i)q97+29.0689q98+O(q100)q+(0.690983 + 2.12663i) q^{2} +(-0.809017 - 0.587785i) q^{3} +(-2.42705 + 1.76336i) q^{4} +(0.618034 - 1.90211i) q^{5} +(0.690983 - 2.12663i) q^{6} +(3.61803 - 2.62866i) q^{7} +(-1.80902 - 1.31433i) q^{8} +(0.309017 + 0.951057i) q^{9} +4.47214 q^{10} +3.00000 q^{12} +(8.09017 + 5.87785i) q^{14} +(-1.61803 + 1.17557i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(1.38197 - 4.25325i) q^{17} +(-1.80902 + 1.31433i) q^{18} +(3.61803 + 2.62866i) q^{19} +(1.85410 + 5.70634i) q^{20} -4.47214 q^{21} -4.00000 q^{23} +(0.690983 + 2.12663i) q^{24} +(0.809017 + 0.587785i) q^{25} +(0.309017 - 0.951057i) q^{27} +(-4.14590 + 12.7598i) q^{28} +(-3.61803 + 2.62866i) q^{29} +(-3.61803 - 2.62866i) q^{30} -6.70820 q^{32} +10.0000 q^{34} +(-2.76393 - 8.50651i) q^{35} +(-2.42705 - 1.76336i) q^{36} +(-1.61803 + 1.17557i) q^{37} +(-3.09017 + 9.51057i) q^{38} +(-3.61803 + 2.62866i) q^{40} +(3.61803 + 2.62866i) q^{41} +(-3.09017 - 9.51057i) q^{42} +4.47214 q^{43} +2.00000 q^{45} +(-2.76393 - 8.50651i) q^{46} +(-6.47214 - 4.70228i) q^{47} +(0.809017 - 0.587785i) q^{48} +(4.01722 - 12.3637i) q^{49} +(-0.690983 + 2.12663i) q^{50} +(-3.61803 + 2.62866i) q^{51} +(1.85410 + 5.70634i) q^{53} +2.23607 q^{54} -10.0000 q^{56} +(-1.38197 - 4.25325i) q^{57} +(-8.09017 - 5.87785i) q^{58} +(1.85410 - 5.70634i) q^{60} +(2.76393 - 8.50651i) q^{61} +(3.61803 + 2.62866i) q^{63} +(-4.01722 - 12.3637i) q^{64} -12.0000 q^{67} +(4.14590 + 12.7598i) q^{68} +(3.23607 + 2.35114i) q^{69} +(16.1803 - 11.7557i) q^{70} +(-2.47214 + 7.60845i) q^{71} +(0.690983 - 2.12663i) q^{72} +(7.23607 - 5.25731i) q^{73} +(-3.61803 - 2.62866i) q^{74} +(-0.309017 - 0.951057i) q^{75} -13.4164 q^{76} +(4.14590 + 12.7598i) q^{79} +(1.61803 + 1.17557i) q^{80} +(-0.809017 + 0.587785i) q^{81} +(-3.09017 + 9.51057i) q^{82} +(-2.76393 + 8.50651i) q^{83} +(10.8541 - 7.88597i) q^{84} +(-7.23607 - 5.25731i) q^{85} +(3.09017 + 9.51057i) q^{86} +4.47214 q^{87} -14.0000 q^{89} +(1.38197 + 4.25325i) q^{90} +(9.70820 - 7.05342i) q^{92} +(5.52786 - 17.0130i) q^{94} +(7.23607 - 5.25731i) q^{95} +(5.42705 + 3.94298i) q^{96} +(0.618034 + 1.90211i) q^{97} +29.0689 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+5q2q33q42q5+5q6+10q75q8q9+12q12+10q142q15+q16+10q175q18+10q196q2016q23+5q24+q25+2q97+O(q100) 4 q + 5 q^{2} - q^{3} - 3 q^{4} - 2 q^{5} + 5 q^{6} + 10 q^{7} - 5 q^{8} - q^{9} + 12 q^{12} + 10 q^{14} - 2 q^{15} + q^{16} + 10 q^{17} - 5 q^{18} + 10 q^{19} - 6 q^{20} - 16 q^{23} + 5 q^{24} + q^{25}+ \cdots - 2 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/363Z)×\left(\mathbb{Z}/363\mathbb{Z}\right)^\times.

nn 122122 244244
χ(n)\chi(n) 11 e(25)e\left(\frac{2}{5}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.690983 + 2.12663i 0.488599 + 1.50375i 0.826700 + 0.562643i 0.190215π0.190215\pi
−0.338101 + 0.941110i 0.609785π0.609785\pi
33 −0.809017 0.587785i −0.467086 0.339358i
44 −2.42705 + 1.76336i −1.21353 + 0.881678i
55 0.618034 1.90211i 0.276393 0.850651i −0.712454 0.701719i 0.752416π-0.752416\pi
0.988847 0.148932i 0.0475836π-0.0475836\pi
66 0.690983 2.12663i 0.282093 0.868192i
77 3.61803 2.62866i 1.36749 0.993538i 0.369560 0.929207i 0.379509π-0.379509\pi
0.997929 0.0643314i 0.0204915π-0.0204915\pi
88 −1.80902 1.31433i −0.639584 0.464685i
99 0.309017 + 0.951057i 0.103006 + 0.317019i
1010 4.47214 1.41421
1111 0 0
1212 3.00000 0.866025
1313 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
1414 8.09017 + 5.87785i 2.16219 + 1.57092i
1515 −1.61803 + 1.17557i −0.417775 + 0.303531i
1616 −0.309017 + 0.951057i −0.0772542 + 0.237764i
1717 1.38197 4.25325i 0.335176 1.03157i −0.631459 0.775409i 0.717544π-0.717544\pi
0.966635 0.256157i 0.0824563π-0.0824563\pi
1818 −1.80902 + 1.31433i −0.426389 + 0.309790i
1919 3.61803 + 2.62866i 0.830034 + 0.603055i 0.919569 0.392929i 0.128538π-0.128538\pi
−0.0895350 + 0.995984i 0.528538π0.528538\pi
2020 1.85410 + 5.70634i 0.414590 + 1.27598i
2121 −4.47214 −0.975900
2222 0 0
2323 −4.00000 −0.834058 −0.417029 0.908893i 0.636929π-0.636929\pi
−0.417029 + 0.908893i 0.636929π0.636929\pi
2424 0.690983 + 2.12663i 0.141046 + 0.434096i
2525 0.809017 + 0.587785i 0.161803 + 0.117557i
2626 0 0
2727 0.309017 0.951057i 0.0594703 0.183031i
2828 −4.14590 + 12.7598i −0.783501 + 2.41137i
2929 −3.61803 + 2.62866i −0.671852 + 0.488129i −0.870645 0.491912i 0.836298π-0.836298\pi
0.198793 + 0.980042i 0.436298π0.436298\pi
3030 −3.61803 2.62866i −0.660560 0.479925i
3131 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
3232 −6.70820 −1.18585
3333 0 0
3434 10.0000 1.71499
3535 −2.76393 8.50651i −0.467190 1.43786i
3636 −2.42705 1.76336i −0.404508 0.293893i
3737 −1.61803 + 1.17557i −0.266003 + 0.193263i −0.712789 0.701378i 0.752568π-0.752568\pi
0.446786 + 0.894641i 0.352568π0.352568\pi
3838 −3.09017 + 9.51057i −0.501292 + 1.54282i
3939 0 0
4040 −3.61803 + 2.62866i −0.572061 + 0.415627i
4141 3.61803 + 2.62866i 0.565042 + 0.410527i 0.833301 0.552820i 0.186448π-0.186448\pi
−0.268259 + 0.963347i 0.586448π0.586448\pi
4242 −3.09017 9.51057i −0.476824 1.46751i
4343 4.47214 0.681994 0.340997 0.940064i 0.389235π-0.389235\pi
0.340997 + 0.940064i 0.389235π0.389235\pi
4444 0 0
4545 2.00000 0.298142
4646 −2.76393 8.50651i −0.407520 1.25422i
4747 −6.47214 4.70228i −0.944058 0.685898i 0.00533600 0.999986i 0.498301π-0.498301\pi
−0.949394 + 0.314087i 0.898301π0.898301\pi
4848 0.809017 0.587785i 0.116772 0.0848395i
4949 4.01722 12.3637i 0.573889 1.76625i
5050 −0.690983 + 2.12663i −0.0977198 + 0.300750i
5151 −3.61803 + 2.62866i −0.506626 + 0.368085i
5252 0 0
5353 1.85410 + 5.70634i 0.254680 + 0.783826i 0.993892 + 0.110353i 0.0351982π0.0351982\pi
−0.739212 + 0.673473i 0.764802π0.764802\pi
5454 2.23607 0.304290
5555 0 0
5656 −10.0000 −1.33631
5757 −1.38197 4.25325i −0.183046 0.563357i
5858 −8.09017 5.87785i −1.06229 0.771800i
5959 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
6060 1.85410 5.70634i 0.239364 0.736685i
6161 2.76393 8.50651i 0.353885 1.08915i −0.602768 0.797917i 0.705935π-0.705935\pi
0.956653 0.291230i 0.0940645π-0.0940645\pi
6262 0 0
6363 3.61803 + 2.62866i 0.455829 + 0.331179i
6464 −4.01722 12.3637i −0.502153 1.54547i
6565 0 0
6666 0 0
6767 −12.0000 −1.46603 −0.733017 0.680211i 0.761888π-0.761888\pi
−0.733017 + 0.680211i 0.761888π0.761888\pi
6868 4.14590 + 12.7598i 0.502764 + 1.54735i
6969 3.23607 + 2.35114i 0.389577 + 0.283044i
7070 16.1803 11.7557i 1.93392 1.40508i
7171 −2.47214 + 7.60845i −0.293389 + 0.902957i 0.690369 + 0.723457i 0.257448π0.257448\pi
−0.983758 + 0.179500i 0.942552π0.942552\pi
7272 0.690983 2.12663i 0.0814331 0.250625i
7373 7.23607 5.25731i 0.846918 0.615322i −0.0773767 0.997002i 0.524654π-0.524654\pi
0.924294 + 0.381680i 0.124654π0.124654\pi
7474 −3.61803 2.62866i −0.420588 0.305575i
7575 −0.309017 0.951057i −0.0356822 0.109819i
7676 −13.4164 −1.53897
7777 0 0
7878 0 0
7979 4.14590 + 12.7598i 0.466450 + 1.43559i 0.857150 + 0.515067i 0.172233π0.172233\pi
−0.390700 + 0.920518i 0.627767π0.627767\pi
8080 1.61803 + 1.17557i 0.180902 + 0.131433i
8181 −0.809017 + 0.587785i −0.0898908 + 0.0653095i
8282 −3.09017 + 9.51057i −0.341252 + 1.05027i
8383 −2.76393 + 8.50651i −0.303381 + 0.933711i 0.676895 + 0.736079i 0.263325π0.263325\pi
−0.980276 + 0.197631i 0.936675π0.936675\pi
8484 10.8541 7.88597i 1.18428 0.860430i
8585 −7.23607 5.25731i −0.784862 0.570235i
8686 3.09017 + 9.51057i 0.333222 + 1.02555i
8787 4.47214 0.479463
8888 0 0
8989 −14.0000 −1.48400 −0.741999 0.670402i 0.766122π-0.766122\pi
−0.741999 + 0.670402i 0.766122π0.766122\pi
9090 1.38197 + 4.25325i 0.145672 + 0.448332i
9191 0 0
9292 9.70820 7.05342i 1.01215 0.735370i
9393 0 0
9494 5.52786 17.0130i 0.570156 1.75476i
9595 7.23607 5.25731i 0.742405 0.539389i
9696 5.42705 + 3.94298i 0.553896 + 0.402429i
9797 0.618034 + 1.90211i 0.0627518 + 0.193130i 0.977517 0.210855i 0.0676247π-0.0676247\pi
−0.914766 + 0.403985i 0.867625π0.867625\pi
9898 29.0689 2.93640
9999 0 0
100100 −3.00000 −0.300000
101101 1.38197 + 4.25325i 0.137511 + 0.423215i 0.995972 0.0896637i 0.0285792π-0.0285792\pi
−0.858461 + 0.512878i 0.828579π0.828579\pi
102102 −8.09017 5.87785i −0.801046 0.581994i
103103 −12.9443 + 9.40456i −1.27544 + 0.926659i −0.999405 0.0344892i 0.989020π-0.989020\pi
−0.276032 + 0.961148i 0.589020π0.589020\pi
104104 0 0
105105 −2.76393 + 8.50651i −0.269732 + 0.830150i
106106 −10.8541 + 7.88597i −1.05424 + 0.765953i
107107 −7.23607 5.25731i −0.699537 0.508243i 0.180244 0.983622i 0.442311π-0.442311\pi
−0.879781 + 0.475378i 0.842311π0.842311\pi
108108 0.927051 + 2.85317i 0.0892055 + 0.274546i
109109 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
110110 0 0
111111 2.00000 0.189832
112112 1.38197 + 4.25325i 0.130584 + 0.401895i
113113 −4.85410 3.52671i −0.456636 0.331765i 0.335575 0.942014i 0.391070π-0.391070\pi
−0.792210 + 0.610249i 0.791070π0.791070\pi
114114 8.09017 5.87785i 0.757714 0.550511i
115115 −2.47214 + 7.60845i −0.230528 + 0.709492i
116116 4.14590 12.7598i 0.384937 1.18471i
117117 0 0
118118 0 0
119119 −6.18034 19.0211i −0.566551 1.74366i
120120 4.47214 0.408248
121121 0 0
122122 20.0000 1.81071
123123 −1.38197 4.25325i −0.124608 0.383503i
124124 0 0
125125 9.70820 7.05342i 0.868328 0.630877i
126126 −3.09017 + 9.51057i −0.275294 + 0.847268i
127127 4.14590 12.7598i 0.367889 1.13225i −0.580263 0.814429i 0.697050π-0.697050\pi
0.948152 0.317817i 0.102950π-0.102950\pi
128128 12.6631 9.20029i 1.11927 0.813199i
129129 −3.61803 2.62866i −0.318550 0.231440i
130130 0 0
131131 −17.8885 −1.56293 −0.781465 0.623949i 0.785527π-0.785527\pi
−0.781465 + 0.623949i 0.785527π0.785527\pi
132132 0 0
133133 20.0000 1.73422
134134 −8.29180 25.5195i −0.716302 2.20455i
135135 −1.61803 1.17557i −0.139258 0.101177i
136136 −8.09017 + 5.87785i −0.693726 + 0.504022i
137137 6.79837 20.9232i 0.580824 1.78759i −0.0346048 0.999401i 0.511017π-0.511017\pi
0.615429 0.788192i 0.288983π-0.288983\pi
138138 −2.76393 + 8.50651i −0.235282 + 0.724122i
139139 −10.8541 + 7.88597i −0.920633 + 0.668879i −0.943681 0.330855i 0.892663π-0.892663\pi
0.0230486 + 0.999734i 0.492663π0.492663\pi
140140 21.7082 + 15.7719i 1.83468 + 1.33297i
141141 2.47214 + 7.60845i 0.208191 + 0.640747i
142142 −17.8885 −1.50117
143143 0 0
144144 −1.00000 −0.0833333
145145 2.76393 + 8.50651i 0.229532 + 0.706427i
146146 16.1803 + 11.7557i 1.33909 + 0.972909i
147147 −10.5172 + 7.64121i −0.867446 + 0.630236i
148148 1.85410 5.70634i 0.152406 0.469058i
149149 −6.90983 + 21.2663i −0.566075 + 1.74220i 0.0986594 + 0.995121i 0.468545π0.468545\pi
−0.664735 + 0.747079i 0.731455π0.731455\pi
150150 1.80902 1.31433i 0.147706 0.107314i
151151 −10.8541 7.88597i −0.883294 0.641751i 0.0508267 0.998707i 0.483814π-0.483814\pi
−0.934121 + 0.356957i 0.883814π0.883814\pi
152152 −3.09017 9.51057i −0.250646 0.771409i
153153 4.47214 0.361551
154154 0 0
155155 0 0
156156 0 0
157157 −1.61803 1.17557i −0.129133 0.0938207i 0.521344 0.853347i 0.325431π-0.325431\pi
−0.650477 + 0.759526i 0.725431π0.725431\pi
158158 −24.2705 + 17.6336i −1.93086 + 1.40285i
159159 1.85410 5.70634i 0.147040 0.452542i
160160 −4.14590 + 12.7598i −0.327762 + 1.00875i
161161 −14.4721 + 10.5146i −1.14056 + 0.828668i
162162 −1.80902 1.31433i −0.142130 0.103263i
163163 1.23607 + 3.80423i 0.0968163 + 0.297970i 0.987723 0.156217i 0.0499299π-0.0499299\pi
−0.890906 + 0.454187i 0.849930π0.849930\pi
164164 −13.4164 −1.04765
165165 0 0
166166 −20.0000 −1.55230
167167 2.76393 + 8.50651i 0.213879 + 0.658253i 0.999231 + 0.0392036i 0.0124821π0.0124821\pi
−0.785352 + 0.619050i 0.787518π0.787518\pi
168168 8.09017 + 5.87785i 0.624170 + 0.453486i
169169 10.5172 7.64121i 0.809017 0.587785i
170170 6.18034 19.0211i 0.474010 1.45885i
171171 −1.38197 + 4.25325i −0.105682 + 0.325254i
172172 −10.8541 + 7.88597i −0.827618 + 0.601299i
173173 10.8541 + 7.88597i 0.825222 + 0.599559i 0.918204 0.396109i 0.129640π-0.129640\pi
−0.0929814 + 0.995668i 0.529640π0.529640\pi
174174 3.09017 + 9.51057i 0.234265 + 0.720994i
175175 4.47214 0.338062
176176 0 0
177177 0 0
178178 −9.67376 29.7728i −0.725079 2.23156i
179179 3.23607 + 2.35114i 0.241875 + 0.175733i 0.702118 0.712060i 0.252238π-0.252238\pi
−0.460243 + 0.887793i 0.652238π0.652238\pi
180180 −4.85410 + 3.52671i −0.361803 + 0.262866i
181181 −3.09017 + 9.51057i −0.229691 + 0.706915i 0.768091 + 0.640341i 0.221207π0.221207\pi
−0.997781 + 0.0665740i 0.978793π0.978793\pi
182182 0 0
183183 −7.23607 + 5.25731i −0.534906 + 0.388632i
184184 7.23607 + 5.25731i 0.533450 + 0.387574i
185185 1.23607 + 3.80423i 0.0908775 + 0.279692i
186186 0 0
187187 0 0
188188 24.0000 1.75038
189189 −1.38197 4.25325i −0.100523 0.309379i
190190 16.1803 + 11.7557i 1.17385 + 0.852848i
191191 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
192192 −4.01722 + 12.3637i −0.289918 + 0.892276i
193193 −5.52786 + 17.0130i −0.397904 + 1.22462i 0.528772 + 0.848764i 0.322653π0.322653\pi
−0.926677 + 0.375860i 0.877347π0.877347\pi
194194 −3.61803 + 2.62866i −0.259760 + 0.188726i
195195 0 0
196196 12.0517 + 37.0912i 0.860833 + 2.64937i
197197 22.3607 1.59313 0.796566 0.604551i 0.206648π-0.206648\pi
0.796566 + 0.604551i 0.206648π0.206648\pi
198198 0 0
199199 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
200200 −0.690983 2.12663i −0.0488599 0.150375i
201201 9.70820 + 7.05342i 0.684764 + 0.497510i
202202 −8.09017 + 5.87785i −0.569222 + 0.413564i
203203 −6.18034 + 19.0211i −0.433775 + 1.33502i
204204 4.14590 12.7598i 0.290271 0.893362i
205205 7.23607 5.25731i 0.505389 0.367187i
206206 −28.9443 21.0292i −2.01664 1.46518i
207207 −1.23607 3.80423i −0.0859127 0.264412i
208208 0 0
209209 0 0
210210 −20.0000 −1.38013
211211 −1.38197 4.25325i −0.0951385 0.292806i 0.892151 0.451737i 0.149195π-0.149195\pi
−0.987290 + 0.158931i 0.949195π0.949195\pi
212212 −14.5623 10.5801i −1.00014 0.726647i
213213 6.47214 4.70228i 0.443463 0.322195i
214214 6.18034 19.0211i 0.422479 1.30026i
215215 2.76393 8.50651i 0.188499 0.580139i
216216 −1.80902 + 1.31433i −0.123088 + 0.0894287i
217217 0 0
218218 0 0
219219 −8.94427 −0.604398
220220 0 0
221221 0 0
222222 1.38197 + 4.25325i 0.0927515 + 0.285460i
223223 12.9443 + 9.40456i 0.866813 + 0.629776i 0.929730 0.368243i 0.120040π-0.120040\pi
−0.0629172 + 0.998019i 0.520040π0.520040\pi
224224 −24.2705 + 17.6336i −1.62164 + 1.17819i
225225 −0.309017 + 0.951057i −0.0206011 + 0.0634038i
226226 4.14590 12.7598i 0.275781 0.848767i
227227 −7.23607 + 5.25731i −0.480275 + 0.348940i −0.801432 0.598086i 0.795928π-0.795928\pi
0.321157 + 0.947026i 0.395928π0.395928\pi
228228 10.8541 + 7.88597i 0.718830 + 0.522261i
229229 3.09017 + 9.51057i 0.204204 + 0.628476i 0.999745 + 0.0225760i 0.00718678π0.00718678\pi
−0.795541 + 0.605900i 0.792813π0.792813\pi
230230 −17.8885 −1.17954
231231 0 0
232232 10.0000 0.656532
233233 −1.38197 4.25325i −0.0905356 0.278640i 0.895529 0.445003i 0.146798π-0.146798\pi
−0.986065 + 0.166363i 0.946798π0.946798\pi
234234 0 0
235235 −12.9443 + 9.40456i −0.844391 + 0.613486i
236236 0 0
237237 4.14590 12.7598i 0.269305 0.828836i
238238 36.1803 26.2866i 2.34522 1.70390i
239239 −7.23607 5.25731i −0.468062 0.340067i 0.328623 0.944461i 0.393415π-0.393415\pi
−0.796686 + 0.604394i 0.793415π0.793415\pi
240240 −0.618034 1.90211i −0.0398939 0.122781i
241241 8.94427 0.576151 0.288076 0.957608i 0.406985π-0.406985\pi
0.288076 + 0.957608i 0.406985π0.406985\pi
242242 0 0
243243 1.00000 0.0641500
244244 8.29180 + 25.5195i 0.530828 + 1.63372i
245245 −21.0344 15.2824i −1.34384 0.976358i
246246 8.09017 5.87785i 0.515810 0.374758i
247247 0 0
248248 0 0
249249 7.23607 5.25731i 0.458567 0.333169i
250250 21.7082 + 15.7719i 1.37295 + 0.997505i
251251 −3.70820 11.4127i −0.234060 0.720362i −0.997245 0.0741818i 0.976365π-0.976365\pi
0.763185 0.646180i 0.223635π-0.223635\pi
252252 −13.4164 −0.845154
253253 0 0
254254 30.0000 1.88237
255255 2.76393 + 8.50651i 0.173084 + 0.532698i
256256 7.28115 + 5.29007i 0.455072 + 0.330629i
257257 17.7984 12.9313i 1.11023 0.806631i 0.127532 0.991834i 0.459294π-0.459294\pi
0.982700 + 0.185204i 0.0592945π0.0592945\pi
258258 3.09017 9.51057i 0.192386 0.592102i
259259 −2.76393 + 8.50651i −0.171742 + 0.528569i
260260 0 0
261261 −3.61803 2.62866i −0.223951 0.162710i
262262 −12.3607 38.0423i −0.763645 2.35026i
263263 8.94427 0.551527 0.275764 0.961225i 0.411069π-0.411069\pi
0.275764 + 0.961225i 0.411069π0.411069\pi
264264 0 0
265265 12.0000 0.737154
266266 13.8197 + 42.5325i 0.847338 + 2.60784i
267267 11.3262 + 8.22899i 0.693155 + 0.503606i
268268 29.1246 21.1603i 1.77907 1.29257i
269269 −3.09017 + 9.51057i −0.188411 + 0.579869i −0.999990 0.00437267i 0.998608π-0.998608\pi
0.811579 + 0.584242i 0.198608π0.198608\pi
270270 1.38197 4.25325i 0.0841038 0.258845i
271271 10.8541 7.88597i 0.659340 0.479038i −0.207100 0.978320i 0.566403π-0.566403\pi
0.866440 + 0.499281i 0.166403π0.166403\pi
272272 3.61803 + 2.62866i 0.219376 + 0.159386i
273273 0 0
274274 49.1935 2.97189
275275 0 0
276276 −12.0000 −0.722315
277277 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
278278 −24.2705 17.6336i −1.45565 1.05759i
279279 0 0
280280 −6.18034 + 19.0211i −0.369346 + 1.13673i
281281 9.67376 29.7728i 0.577088 1.77610i −0.0518675 0.998654i 0.516517π-0.516517\pi
0.628956 0.777441i 0.283483π-0.283483\pi
282282 −14.4721 + 10.5146i −0.861803 + 0.626137i
283283 10.8541 + 7.88597i 0.645209 + 0.468772i 0.861636 0.507527i 0.169440π-0.169440\pi
−0.216427 + 0.976299i 0.569440π0.569440\pi
284284 −7.41641 22.8254i −0.440083 1.35444i
285285 −8.94427 −0.529813
286286 0 0
287287 20.0000 1.18056
288288 −2.07295 6.37988i −0.122150 0.375938i
289289 −2.42705 1.76336i −0.142768 0.103727i
290290 −16.1803 + 11.7557i −0.950142 + 0.690319i
291291 0.618034 1.90211i 0.0362298 0.111504i
292292 −8.29180 + 25.5195i −0.485241 + 1.49342i
293293 18.0902 13.1433i 1.05684 0.767838i 0.0833380 0.996521i 0.473442π-0.473442\pi
0.973501 + 0.228683i 0.0734419π0.0734419\pi
294294 −23.5172 17.0863i −1.37155 0.996491i
295295 0 0
296296 4.47214 0.259938
297297 0 0
298298 −50.0000 −2.89642
299299 0 0
300300 2.42705 + 1.76336i 0.140126 + 0.101807i
301301 16.1803 11.7557i 0.932619 0.677588i
302302 9.27051 28.5317i 0.533458 1.64181i
303303 1.38197 4.25325i 0.0793919 0.244343i
304304 −3.61803 + 2.62866i −0.207508 + 0.150764i
305305 −14.4721 10.5146i −0.828672 0.602066i
306306 3.09017 + 9.51057i 0.176653 + 0.543683i
307307 −4.47214 −0.255238 −0.127619 0.991823i 0.540734π-0.540734\pi
−0.127619 + 0.991823i 0.540734π0.540734\pi
308308 0 0
309309 16.0000 0.910208
310310 0 0
311311 9.70820 + 7.05342i 0.550502 + 0.399963i 0.827970 0.560772i 0.189495π-0.189495\pi
−0.277469 + 0.960735i 0.589495π0.589495\pi
312312 0 0
313313 4.32624 13.3148i 0.244533 0.752596i −0.751179 0.660098i 0.770515π-0.770515\pi
0.995713 0.0924984i 0.0294853π-0.0294853\pi
314314 1.38197 4.25325i 0.0779889 0.240025i
315315 7.23607 5.25731i 0.407706 0.296216i
316316 −32.5623 23.6579i −1.83177 1.33086i
317317 5.56231 + 17.1190i 0.312410 + 0.961500i 0.976807 + 0.214120i 0.0686884π0.0686884\pi
−0.664397 + 0.747380i 0.731312π0.731312\pi
318318 13.4164 0.752355
319319 0 0
320320 −26.0000 −1.45344
321321 2.76393 + 8.50651i 0.154268 + 0.474787i
322322 −32.3607 23.5114i −1.80339 1.31024i
323323 16.1803 11.7557i 0.900298 0.654105i
324324 0.927051 2.85317i 0.0515028 0.158509i
325325 0 0
326326 −7.23607 + 5.25731i −0.400769 + 0.291176i
327327 0 0
328328 −3.09017 9.51057i −0.170626 0.525133i
329329 −35.7771 −1.97245
330330 0 0
331331 −20.0000 −1.09930 −0.549650 0.835395i 0.685239π-0.685239\pi
−0.549650 + 0.835395i 0.685239π0.685239\pi
332332 −8.29180 25.5195i −0.455071 1.40057i
333333 −1.61803 1.17557i −0.0886677 0.0644209i
334334 −16.1803 + 11.7557i −0.885349 + 0.643244i
335335 −7.41641 + 22.8254i −0.405202 + 1.24708i
336336 1.38197 4.25325i 0.0753924 0.232034i
337337 −7.23607 + 5.25731i −0.394174 + 0.286384i −0.767164 0.641451i 0.778333π-0.778333\pi
0.372990 + 0.927835i 0.378333π0.378333\pi
338338 23.5172 + 17.0863i 1.27917 + 0.929370i
339339 1.85410 + 5.70634i 0.100701 + 0.309926i
340340 26.8328 1.45521
341341 0 0
342342 −10.0000 −0.540738
343343 −8.29180 25.5195i −0.447715 1.37792i
344344 −8.09017 5.87785i −0.436193 0.316913i
345345 6.47214 4.70228i 0.348448 0.253162i
346346 −9.27051 + 28.5317i −0.498386 + 1.53387i
347347 2.76393 8.50651i 0.148376 0.456653i −0.849054 0.528306i 0.822827π-0.822827\pi
0.997430 + 0.0716528i 0.0228274π0.0228274\pi
348348 −10.8541 + 7.88597i −0.581841 + 0.422732i
349349 21.7082 + 15.7719i 1.16201 + 0.844252i 0.990031 0.140848i 0.0449828π-0.0449828\pi
0.171982 + 0.985100i 0.444983π0.444983\pi
350350 3.09017 + 9.51057i 0.165177 + 0.508361i
351351 0 0
352352 0 0
353353 −14.0000 −0.745145 −0.372572 0.928003i 0.621524π-0.621524\pi
−0.372572 + 0.928003i 0.621524π0.621524\pi
354354 0 0
355355 12.9443 + 9.40456i 0.687011 + 0.499142i
356356 33.9787 24.6870i 1.80087 1.30841i
357357 −6.18034 + 19.0211i −0.327098 + 1.00670i
358358 −2.76393 + 8.50651i −0.146078 + 0.449583i
359359 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
360360 −3.61803 2.62866i −0.190687 0.138542i
361361 0.309017 + 0.951057i 0.0162641 + 0.0500556i
362362 −22.3607 −1.17525
363363 0 0
364364 0 0
365365 −5.52786 17.0130i −0.289342 0.890502i
366366 −16.1803 11.7557i −0.845760 0.614481i
367367 −6.47214 + 4.70228i −0.337843 + 0.245457i −0.743751 0.668457i 0.766955π-0.766955\pi
0.405908 + 0.913914i 0.366955π0.366955\pi
368368 1.23607 3.80423i 0.0644345 0.198309i
369369 −1.38197 + 4.25325i −0.0719423 + 0.221416i
370370 −7.23607 + 5.25731i −0.376185 + 0.273315i
371371 21.7082 + 15.7719i 1.12703 + 0.818838i
372372 0 0
373373 −26.8328 −1.38935 −0.694675 0.719323i 0.744452π-0.744452\pi
−0.694675 + 0.719323i 0.744452π0.744452\pi
374374 0 0
375375 −12.0000 −0.619677
376376 5.52786 + 17.0130i 0.285078 + 0.877379i
377377 0 0
378378 8.09017 5.87785i 0.416113 0.302324i
379379 −6.18034 + 19.0211i −0.317463 + 0.977050i 0.657266 + 0.753659i 0.271713π0.271713\pi
−0.974729 + 0.223391i 0.928287π0.928287\pi
380380 −8.29180 + 25.5195i −0.425360 + 1.30912i
381381 −10.8541 + 7.88597i −0.556072 + 0.404010i
382382 0 0
383383 −11.1246 34.2380i −0.568441 1.74948i −0.657499 0.753455i 0.728386π-0.728386\pi
0.0890579 0.996026i 0.471614π-0.471614\pi
384384 −15.6525 −0.798762
385385 0 0
386386 −40.0000 −2.03595
387387 1.38197 + 4.25325i 0.0702493 + 0.216205i
388388 −4.85410 3.52671i −0.246430 0.179042i
389389 −8.09017 + 5.87785i −0.410188 + 0.298019i −0.773678 0.633579i 0.781585π-0.781585\pi
0.363490 + 0.931598i 0.381585π0.381585\pi
390390 0 0
391391 −5.52786 + 17.0130i −0.279556 + 0.860385i
392392 −23.5172 + 17.0863i −1.18780 + 0.862987i
393393 14.4721 + 10.5146i 0.730023 + 0.530393i
394394 15.4508 + 47.5528i 0.778403 + 2.39568i
395395 26.8328 1.35011
396396 0 0
397397 22.0000 1.10415 0.552074 0.833795i 0.313837π-0.313837\pi
0.552074 + 0.833795i 0.313837π0.313837\pi
398398 0 0
399399 −16.1803 11.7557i −0.810030 0.588521i
400400 −0.809017 + 0.587785i −0.0404508 + 0.0293893i
401401 9.27051 28.5317i 0.462947 1.42480i −0.398599 0.917125i 0.630503π-0.630503\pi
0.861546 0.507679i 0.169497π-0.169497\pi
402402 −8.29180 + 25.5195i −0.413557 + 1.27280i
403403 0 0
404404 −10.8541 7.88597i −0.540012 0.392342i
405405 0.618034 + 1.90211i 0.0307104 + 0.0945168i
406406 −44.7214 −2.21948
407407 0 0
408408 10.0000 0.495074
409409 −8.29180 25.5195i −0.410003 1.26186i −0.916645 0.399703i 0.869113π-0.869113\pi
0.506642 0.862157i 0.330887π-0.330887\pi
410410 16.1803 + 11.7557i 0.799090 + 0.580573i
411411 −17.7984 + 12.9313i −0.877929 + 0.637853i
412412 14.8328 45.6507i 0.730760 2.24905i
413413 0 0
414414 7.23607 5.25731i 0.355633 0.258383i
415415 14.4721 + 10.5146i 0.710409 + 0.516143i
416416 0 0
417417 13.4164 0.657004
418418 0 0
419419 4.00000 0.195413 0.0977064 0.995215i 0.468849π-0.468849\pi
0.0977064 + 0.995215i 0.468849π0.468849\pi
420420 −8.29180 25.5195i −0.404598 1.24523i
421421 −8.09017 5.87785i −0.394291 0.286469i 0.372921 0.927863i 0.378356π-0.378356\pi
−0.767211 + 0.641394i 0.778356π0.778356\pi
422422 8.09017 5.87785i 0.393823 0.286129i
423423 2.47214 7.60845i 0.120199 0.369936i
424424 4.14590 12.7598i 0.201343 0.619669i
425425 3.61803 2.62866i 0.175500 0.127509i
426426 14.4721 + 10.5146i 0.701177 + 0.509435i
427427 −12.3607 38.0423i −0.598175 1.84099i
428428 26.8328 1.29701
429429 0 0
430430 20.0000 0.964486
431431 −2.76393 8.50651i −0.133134 0.409744i 0.862161 0.506634i 0.169110π-0.169110\pi
−0.995295 + 0.0968900i 0.969110π0.969110\pi
432432 0.809017 + 0.587785i 0.0389238 + 0.0282798i
433433 4.85410 3.52671i 0.233273 0.169483i −0.465008 0.885307i 0.653949π-0.653949\pi
0.698281 + 0.715824i 0.253949π0.253949\pi
434434 0 0
435435 2.76393 8.50651i 0.132520 0.407856i
436436 0 0
437437 −14.4721 10.5146i −0.692296 0.502983i
438438 −6.18034 19.0211i −0.295308 0.908865i
439439 −13.4164 −0.640330 −0.320165 0.947362i 0.603738π-0.603738\pi
−0.320165 + 0.947362i 0.603738π0.603738\pi
440440 0 0
441441 13.0000 0.619048
442442 0 0
443443 19.4164 + 14.1068i 0.922501 + 0.670236i 0.944145 0.329529i 0.106890π-0.106890\pi
−0.0216440 + 0.999766i 0.506890π0.506890\pi
444444 −4.85410 + 3.52671i −0.230365 + 0.167370i
445445 −8.65248 + 26.6296i −0.410167 + 1.26236i
446446 −11.0557 + 34.0260i −0.523504 + 1.61118i
447447 18.0902 13.1433i 0.855636 0.621656i
448448 −47.0344 34.1725i −2.22217 1.61450i
449449 −1.85410 5.70634i −0.0875005 0.269299i 0.897726 0.440554i 0.145218π-0.145218\pi
−0.985227 + 0.171255i 0.945218π0.945218\pi
450450 −2.23607 −0.105409
451451 0 0
452452 18.0000 0.846649
453453 4.14590 + 12.7598i 0.194791 + 0.599506i
454454 −16.1803 11.7557i −0.759381 0.551723i
455455 0 0
456456 −3.09017 + 9.51057i −0.144710 + 0.445373i
457457 8.29180 25.5195i 0.387874 1.19375i −0.546500 0.837459i 0.684040π-0.684040\pi
0.934374 0.356294i 0.115960π-0.115960\pi
458458 −18.0902 + 13.1433i −0.845298 + 0.614145i
459459 −3.61803 2.62866i −0.168875 0.122695i
460460 −7.41641 22.8254i −0.345792 1.06424i
461461 13.4164 0.624864 0.312432 0.949940i 0.398856π-0.398856\pi
0.312432 + 0.949940i 0.398856π0.398856\pi
462462 0 0
463463 24.0000 1.11537 0.557687 0.830051i 0.311689π-0.311689\pi
0.557687 + 0.830051i 0.311689π0.311689\pi
464464 −1.38197 4.25325i −0.0641562 0.197452i
465465 0 0
466466 8.09017 5.87785i 0.374770 0.272286i
467467 −2.47214 + 7.60845i −0.114397 + 0.352077i −0.991821 0.127639i 0.959260π-0.959260\pi
0.877424 + 0.479716i 0.159260π0.159260\pi
468468 0 0
469469 −43.4164 + 31.5439i −2.00478 + 1.45656i
470470 −28.9443 21.0292i −1.33510 0.970007i
471471 0.618034 + 1.90211i 0.0284775 + 0.0876447i
472472 0 0
473473 0 0
474474 30.0000 1.37795
475475 1.38197 + 4.25325i 0.0634089 + 0.195153i
476476 48.5410 + 35.2671i 2.22487 + 1.61647i
477477 −4.85410 + 3.52671i −0.222254 + 0.161477i
478478 6.18034 19.0211i 0.282682 0.870006i
479479 −2.76393 + 8.50651i −0.126287 + 0.388672i −0.994133 0.108161i 0.965504π-0.965504\pi
0.867846 + 0.496833i 0.165504π0.165504\pi
480480 10.8541 7.88597i 0.495420 0.359943i
481481 0 0
482482 6.18034 + 19.0211i 0.281507 + 0.866389i
483483 17.8885 0.813957
484484 0 0
485485 4.00000 0.181631
486486 0.690983 + 2.12663i 0.0313436 + 0.0964658i
487487 −6.47214 4.70228i −0.293280 0.213081i 0.431409 0.902157i 0.358017π-0.358017\pi
−0.724689 + 0.689076i 0.758017π0.758017\pi
488488 −16.1803 + 11.7557i −0.732450 + 0.532156i
489489 1.23607 3.80423i 0.0558969 0.172033i
490490 17.9656 55.2923i 0.811601 2.49785i
491491 21.7082 15.7719i 0.979678 0.711777i 0.0220410 0.999757i 0.492984π-0.492984\pi
0.957637 + 0.287980i 0.0929836π0.0929836\pi
492492 10.8541 + 7.88597i 0.489341 + 0.355527i
493493 6.18034 + 19.0211i 0.278349 + 0.856669i
494494 0 0
495495 0 0
496496 0 0
497497 11.0557 + 34.0260i 0.495917 + 1.52628i
498498 16.1803 + 11.7557i 0.725058 + 0.526786i
499499 16.1803 11.7557i 0.724331 0.526258i −0.163434 0.986554i 0.552257π-0.552257\pi
0.887765 + 0.460297i 0.152257π0.152257\pi
500500 −11.1246 + 34.2380i −0.497508 + 1.53117i
501501 2.76393 8.50651i 0.123483 0.380043i
502502 21.7082 15.7719i 0.968885 0.703936i
503503 21.7082 + 15.7719i 0.967921 + 0.703236i 0.954977 0.296680i 0.0958796π-0.0958796\pi
0.0129442 + 0.999916i 0.495880π0.495880\pi
504504 −3.09017 9.51057i −0.137647 0.423634i
505505 8.94427 0.398015
506506 0 0
507507 −13.0000 −0.577350
508508 12.4377 + 38.2793i 0.551833 + 1.69837i
509509 −24.2705 17.6336i −1.07577 0.781594i −0.0988307 0.995104i 0.531510π-0.531510\pi
−0.976941 + 0.213511i 0.931510π0.931510\pi
510510 −16.1803 + 11.7557i −0.716477 + 0.520551i
511511 12.3607 38.0423i 0.546804 1.68289i
512512 3.45492 10.6331i 0.152687 0.469923i
513513 3.61803 2.62866i 0.159740 0.116058i
514514 39.7984 + 28.9152i 1.75543 + 1.27540i
515515 9.88854 + 30.4338i 0.435741 + 1.34107i
516516 13.4164 0.590624
517517 0 0
518518 −20.0000 −0.878750
519519 −4.14590 12.7598i −0.181985 0.560091i
520520 0 0
521521 −24.2705 + 17.6336i −1.06331 + 0.772540i −0.974698 0.223526i 0.928243π-0.928243\pi
−0.0886124 + 0.996066i 0.528243π0.528243\pi
522522 3.09017 9.51057i 0.135253 0.416266i
523523 1.38197 4.25325i 0.0604292 0.185982i −0.916285 0.400527i 0.868827π-0.868827\pi
0.976714 + 0.214545i 0.0688270π0.0688270\pi
524524 43.4164 31.5439i 1.89665 1.37800i
525525 −3.61803 2.62866i −0.157904 0.114724i
526526 6.18034 + 19.0211i 0.269476 + 0.829361i
527527 0 0
528528 0 0
529529 −7.00000 −0.304348
530530 8.29180 + 25.5195i 0.360173 + 1.10850i
531531 0 0
532532 −48.5410 + 35.2671i −2.10452 + 1.52902i
533533 0 0
534534 −9.67376 + 29.7728i −0.418625 + 1.28839i
535535 −14.4721 + 10.5146i −0.625685 + 0.454587i
536536 21.7082 + 15.7719i 0.937652 + 0.681244i
537537 −1.23607 3.80423i −0.0533403 0.164164i
538538 −22.3607 −0.964037
539539 0 0
540540 6.00000 0.258199
541541 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
542542 24.2705 + 17.6336i 1.04251 + 0.757426i
543543 8.09017 5.87785i 0.347182 0.252243i
544544 −9.27051 + 28.5317i −0.397470 + 1.22329i
545545 0 0
546546 0 0
547547 −32.5623 23.6579i −1.39226 1.01154i −0.995613 0.0935692i 0.970172π-0.970172\pi
−0.396651 0.917970i 0.629828π-0.629828\pi
548548 20.3951 + 62.7697i 0.871236 + 2.68139i
549549 8.94427 0.381732
550550 0 0
551551 −20.0000 −0.852029
552552 −2.76393 8.50651i −0.117641 0.362061i
553553 48.5410 + 35.2671i 2.06417 + 1.49971i
554554 0 0
555555 1.23607 3.80423i 0.0524682 0.161480i
556556 12.4377 38.2793i 0.527476 1.62340i
557557 32.5623 23.6579i 1.37971 1.00242i 0.382802 0.923830i 0.374959π-0.374959\pi
0.996907 0.0785870i 0.0250408π-0.0250408\pi
558558 0 0
559559 0 0
560560 8.94427 0.377964
561561 0 0
562562 70.0000 2.95277
563563 5.52786 + 17.0130i 0.232972 + 0.717013i 0.997384 + 0.0722854i 0.0230292π0.0230292\pi
−0.764412 + 0.644728i 0.776971π0.776971\pi
564564 −19.4164 14.1068i −0.817578 0.594005i
565565 −9.70820 + 7.05342i −0.408427 + 0.296740i
566566 −9.27051 + 28.5317i −0.389669 + 1.19928i
567567 −1.38197 + 4.25325i −0.0580371 + 0.178620i
568568 14.4721 10.5146i 0.607237 0.441184i
569569 −3.61803 2.62866i −0.151676 0.110199i 0.509359 0.860554i 0.329883π-0.329883\pi
−0.661035 + 0.750355i 0.729883π0.729883\pi
570570 −6.18034 19.0211i −0.258866 0.796707i
571571 −13.4164 −0.561459 −0.280730 0.959787i 0.590576π-0.590576\pi
−0.280730 + 0.959787i 0.590576π0.590576\pi
572572 0 0
573573 0 0
574574 13.8197 + 42.5325i 0.576821 + 1.77527i
575575 −3.23607 2.35114i −0.134953 0.0980494i
576576 10.5172 7.64121i 0.438218 0.318384i
577577 −0.618034 + 1.90211i −0.0257291 + 0.0791860i −0.963097 0.269156i 0.913255π-0.913255\pi
0.937367 + 0.348342i 0.113255π0.113255\pi
578578 2.07295 6.37988i 0.0862233 0.265368i
579579 14.4721 10.5146i 0.601441 0.436973i
580580 −21.7082 15.7719i −0.901384 0.654894i
581581 12.3607 + 38.0423i 0.512807 + 1.57826i
582582 4.47214 0.185376
583583 0 0
584584 −20.0000 −0.827606
585585 0 0
586586 40.4508 + 29.3893i 1.67101 + 1.21406i
587587 6.47214 4.70228i 0.267134 0.194084i −0.446152 0.894957i 0.647206π-0.647206\pi
0.713286 + 0.700873i 0.247206π0.247206\pi
588588 12.0517 37.0912i 0.497002 1.52962i
589589 0 0
590590 0 0
591591 −18.0902 13.1433i −0.744130 0.540642i
592592 −0.618034 1.90211i −0.0254010 0.0781764i
593593 −22.3607 −0.918243 −0.459122 0.888373i 0.651836π-0.651836\pi
−0.459122 + 0.888373i 0.651836π0.651836\pi
594594 0 0
595595 −40.0000 −1.63984
596596 −20.7295 63.7988i −0.849113 2.61330i
597597 0 0
598598 0 0
599599 −11.1246 + 34.2380i −0.454539 + 1.39893i 0.417136 + 0.908844i 0.363034π0.363034\pi
−0.871675 + 0.490084i 0.836966π0.836966\pi
600600 −0.690983 + 2.12663i −0.0282093 + 0.0868192i
601601 0 0 −0.587785 0.809017i 0.700000π-0.700000\pi
0.587785 + 0.809017i 0.300000π0.300000\pi
602602 36.1803 + 26.2866i 1.47460 + 1.07136i
603603 −3.70820 11.4127i −0.151010 0.464760i
604604 40.2492 1.63772
605605 0 0
606606 10.0000 0.406222
607607 −1.38197 4.25325i −0.0560923 0.172634i 0.919085 0.394059i 0.128929π-0.128929\pi
−0.975178 + 0.221425i 0.928929π0.928929\pi
608608 −24.2705 17.6336i −0.984299 0.715135i
609609 16.1803 11.7557i 0.655660 0.476365i
610610 12.3607 38.0423i 0.500469 1.54029i
611611 0 0
612612 −10.8541 + 7.88597i −0.438751 + 0.318771i
613613 −36.1803 26.2866i −1.46131 1.06170i −0.983019 0.183503i 0.941256π-0.941256\pi
−0.478291 0.878201i 0.658744π-0.658744\pi
614614 −3.09017 9.51057i −0.124709 0.383815i
615615 −8.94427 −0.360668
616616 0 0
617617 −2.00000 −0.0805170 −0.0402585 0.999189i 0.512818π-0.512818\pi
−0.0402585 + 0.999189i 0.512818π0.512818\pi
618618 11.0557 + 34.0260i 0.444727 + 1.36873i
619619 −35.5967 25.8626i −1.43075 1.03950i −0.989876 0.141937i 0.954667π-0.954667\pi
−0.440878 0.897567i 0.645333π-0.645333\pi
620620 0 0
621621 −1.23607 + 3.80423i −0.0496017 + 0.152658i
622622 −8.29180 + 25.5195i −0.332471 + 1.02324i
623623 −50.6525 + 36.8012i −2.02935 + 1.47441i
624624 0 0
625625 −5.87132 18.0701i −0.234853 0.722803i
626626 31.3050 1.25120
627627 0 0
628628 6.00000 0.239426
629629 2.76393 + 8.50651i 0.110205 + 0.339177i
630630 16.1803 + 11.7557i 0.644640 + 0.468358i
631631 −25.8885 + 18.8091i −1.03061 + 0.748780i −0.968430 0.249286i 0.919804π-0.919804\pi
−0.0621766 + 0.998065i 0.519804π0.519804\pi
632632 9.27051 28.5317i 0.368761 1.13493i
633633 −1.38197 + 4.25325i −0.0549282 + 0.169052i
634634 −32.5623 + 23.6579i −1.29321 + 0.939575i
635635 −21.7082 15.7719i −0.861464 0.625890i
636636 5.56231 + 17.1190i 0.220560 + 0.678813i
637637 0 0
638638 0 0
639639 −8.00000 −0.316475
640640 −9.67376 29.7728i −0.382389 1.17687i
641641 24.2705 + 17.6336i 0.958628 + 0.696484i 0.952832 0.303500i 0.0981551π-0.0981551\pi
0.00579592 + 0.999983i 0.498155π0.498155\pi
642642 −16.1803 + 11.7557i −0.638587 + 0.463961i
643643 11.1246 34.2380i 0.438712 1.35022i −0.450523 0.892765i 0.648762π-0.648762\pi
0.889235 0.457451i 0.151238π-0.151238\pi
644644 16.5836 51.0390i 0.653485 2.01122i
645645 −7.23607 + 5.25731i −0.284920 + 0.207006i
646646 36.1803 + 26.2866i 1.42350 + 1.03423i
647647 −3.70820 11.4127i −0.145785 0.448679i 0.851327 0.524636i 0.175799π-0.175799\pi
−0.997111 + 0.0759575i 0.975799π0.975799\pi
648648 2.23607 0.0878410
649649 0 0
650650 0 0
651651 0 0
652652 −9.70820 7.05342i −0.380203 0.276233i
653653 −37.2148 + 27.0381i −1.45633 + 1.05808i −0.472026 + 0.881585i 0.656477π0.656477\pi
−0.984301 + 0.176499i 0.943523π0.943523\pi
654654 0 0
655655 −11.0557 + 34.0260i −0.431983 + 1.32951i
656656 −3.61803 + 2.62866i −0.141260 + 0.102632i
657657 7.23607 + 5.25731i 0.282306 + 0.205107i
658658 −24.7214 76.0845i −0.963739 2.96608i
659659 17.8885 0.696839 0.348419 0.937339i 0.386719π-0.386719\pi
0.348419 + 0.937339i 0.386719π0.386719\pi
660660 0 0
661661 −22.0000 −0.855701 −0.427850 0.903850i 0.640729π-0.640729\pi
−0.427850 + 0.903850i 0.640729π0.640729\pi
662662 −13.8197 42.5325i −0.537116 1.65307i
663663 0 0
664664 16.1803 11.7557i 0.627919 0.456210i
665665 12.3607 38.0423i 0.479327 1.47522i
666666 1.38197 4.25325i 0.0535501 0.164810i
667667 14.4721 10.5146i 0.560363 0.407128i
668668 −21.7082 15.7719i −0.839916 0.610234i
669669 −4.94427 15.2169i −0.191157 0.588320i
670670 −53.6656 −2.07328
671671 0 0
672672 30.0000 1.15728
673673 −5.52786 17.0130i −0.213083 0.655804i −0.999284 0.0378322i 0.987955π-0.987955\pi
0.786201 0.617971i 0.212045π-0.212045\pi
674674 −16.1803 11.7557i −0.623243 0.452813i
675675 0.809017 0.587785i 0.0311391 0.0226239i
676676 −12.0517 + 37.0912i −0.463525 + 1.42658i
677677 −9.67376 + 29.7728i −0.371793 + 1.14426i 0.573824 + 0.818979i 0.305459π0.305459\pi
−0.945617 + 0.325282i 0.894541π0.894541\pi
678678 −10.8541 + 7.88597i −0.416849 + 0.302859i
679679 7.23607 + 5.25731i 0.277695 + 0.201757i
680680 6.18034 + 19.0211i 0.237005 + 0.729427i
681681 8.94427 0.342745
682682 0 0
683683 44.0000 1.68361 0.841807 0.539779i 0.181492π-0.181492\pi
0.841807 + 0.539779i 0.181492π0.181492\pi
684684 −4.14590 12.7598i −0.158522 0.487882i
685685 −35.5967 25.8626i −1.36008 0.988157i
686686 48.5410 35.2671i 1.85330 1.34650i
687687 3.09017 9.51057i 0.117897 0.362851i
688688 −1.38197 + 4.25325i −0.0526870 + 0.162154i
689689 0 0
690690 14.4721 + 10.5146i 0.550945 + 0.400285i
691691 3.70820 + 11.4127i 0.141067 + 0.434159i 0.996484 0.0837803i 0.0266994π-0.0266994\pi
−0.855418 + 0.517939i 0.826699π0.826699\pi
692692 −40.2492 −1.53005
693693 0 0
694694 20.0000 0.759190
695695 8.29180 + 25.5195i 0.314526 + 0.968011i
696696 −8.09017 5.87785i −0.306657 0.222799i
697697 16.1803 11.7557i 0.612874 0.445279i
698698 −18.5410 + 57.0634i −0.701788 + 2.15988i
699699 −1.38197 + 4.25325i −0.0522708 + 0.160873i
700700 −10.8541 + 7.88597i −0.410246 + 0.298062i
701701 18.0902 + 13.1433i 0.683256 + 0.496415i 0.874436 0.485140i 0.161231π-0.161231\pi
−0.191180 + 0.981555i 0.561231π0.561231\pi
702702 0 0
703703 −8.94427 −0.337340
704704 0 0
705705 16.0000 0.602595
706706 −9.67376 29.7728i −0.364077 1.12051i
707707 16.1803 + 11.7557i 0.608524 + 0.442119i
708708 0 0
709709 −1.85410 + 5.70634i −0.0696323 + 0.214306i −0.979817 0.199896i 0.935939π-0.935939\pi
0.910185 + 0.414202i 0.135939π0.135939\pi
710710 −11.0557 + 34.0260i −0.414914 + 1.27697i
711711 −10.8541 + 7.88597i −0.407061 + 0.295747i
712712 25.3262 + 18.4006i 0.949141 + 0.689591i
713713 0 0
714714 −44.7214 −1.67365
715715 0 0
716716 −12.0000 −0.448461
717717 2.76393 + 8.50651i 0.103221 + 0.317681i
718718 0 0
719719 19.4164 14.1068i 0.724110 0.526097i −0.163585 0.986529i 0.552306π-0.552306\pi
0.887695 + 0.460433i 0.152306π0.152306\pi
720720 −0.618034 + 1.90211i −0.0230328 + 0.0708876i
721721 −22.1115 + 68.0521i −0.823474 + 2.53439i
722722 −1.80902 + 1.31433i −0.0673246 + 0.0489142i
723723 −7.23607 5.25731i −0.269112 0.195522i
724724 −9.27051 28.5317i −0.344536 1.06037i
725725 −4.47214 −0.166091
726726 0 0
727727 −8.00000 −0.296704 −0.148352 0.988935i 0.547397π-0.547397\pi
−0.148352 + 0.988935i 0.547397π0.547397\pi
728728 0 0
729729 −0.809017 0.587785i −0.0299636 0.0217698i
730730 32.3607 23.5114i 1.19772 0.870196i
731731 6.18034 19.0211i 0.228588 0.703522i
732732 8.29180 25.5195i 0.306474 0.943229i
733733 14.4721 10.5146i 0.534541 0.388366i −0.287513 0.957777i 0.592828π-0.592828\pi
0.822053 + 0.569410i 0.192828π0.192828\pi
734734 −14.4721 10.5146i −0.534176 0.388102i
735735 8.03444 + 24.7275i 0.296355 + 0.912086i
736736 26.8328 0.989071
737737 0 0
738738 −10.0000 −0.368105
739739 1.38197 + 4.25325i 0.0508364 + 0.156458i 0.973252 0.229741i 0.0737878π-0.0737878\pi
−0.922415 + 0.386199i 0.873788π0.873788\pi
740740 −9.70820 7.05342i −0.356881 0.259289i
741741 0 0
742742 −18.5410 + 57.0634i −0.680662 + 2.09486i
743743 0 0 −0.951057 0.309017i 0.900000π-0.900000\pi
0.951057 + 0.309017i 0.100000π0.100000\pi
744744 0 0
745745 36.1803 + 26.2866i 1.32555 + 0.963065i
746746 −18.5410 57.0634i −0.678835 2.08924i
747747 −8.94427 −0.327254
748748 0 0
749749 −40.0000 −1.46157
750750 −8.29180 25.5195i −0.302774 0.931841i
751751 −25.8885 18.8091i −0.944686 0.686355i 0.00485778 0.999988i 0.498454π-0.498454\pi
−0.949544 + 0.313633i 0.898454π0.898454\pi
752752 6.47214 4.70228i 0.236015 0.171475i
753753 −3.70820 + 11.4127i −0.135134 + 0.415901i
754754 0 0
755755 −21.7082 + 15.7719i −0.790042 + 0.573999i
756756 10.8541 + 7.88597i 0.394760 + 0.286810i
757757 12.9787 + 39.9444i 0.471719 + 1.45180i 0.850331 + 0.526248i 0.176401π0.176401\pi
−0.378612 + 0.925555i 0.623599π0.623599\pi
758758 −44.7214 −1.62435
759759 0 0
760760 −20.0000 −0.725476
761761 −9.67376 29.7728i −0.350674 1.07926i −0.958476 0.285174i 0.907949π-0.907949\pi
0.607802 0.794088i 0.292051π-0.292051\pi
762762 −24.2705 17.6336i −0.879228 0.638796i
763763 0 0
764764 0 0
765765 2.76393 8.50651i 0.0999302 0.307553i
766766 65.1246 47.3158i 2.35305 1.70959i
767767 0 0
768768 −2.78115 8.55951i −0.100356 0.308865i
769769 35.7771 1.29015 0.645077 0.764117i 0.276825π-0.276825\pi
0.645077 + 0.764117i 0.276825π0.276825\pi
770770 0 0
771771 −22.0000 −0.792311
772772 −16.5836 51.0390i −0.596857 1.83694i
773773 −11.3262 8.22899i −0.407376 0.295976i 0.365162 0.930944i 0.381013π-0.381013\pi
−0.772539 + 0.634968i 0.781013π0.781013\pi
774774 −8.09017 + 5.87785i −0.290795 + 0.211275i
775775 0 0
776776 1.38197 4.25325i 0.0496097 0.152683i
777777 7.23607 5.25731i 0.259592 0.188605i
778778 −18.0902 13.1433i −0.648564 0.471209i
779779 6.18034 + 19.0211i 0.221434 + 0.681503i
780780 0 0
781781 0 0
782782 −40.0000 −1.43040
783783 1.38197 + 4.25325i 0.0493874 + 0.151999i
784784 10.5172 + 7.64121i 0.375615 + 0.272900i
785785 −3.23607 + 2.35114i −0.115500 + 0.0839158i
786786 −12.3607 + 38.0423i −0.440891 + 1.35692i
787787 12.4377 38.2793i 0.443356 1.36451i −0.440921 0.897546i 0.645348π-0.645348\pi
0.884277 0.466963i 0.154652π-0.154652\pi
788788 −54.2705 + 39.4298i −1.93331 + 1.40463i
789789 −7.23607 5.25731i −0.257611 0.187165i
790790 18.5410 + 57.0634i 0.659660 + 2.03022i
791791 −26.8328 −0.954065
792792 0 0
793793 0 0
794794 15.2016 + 46.7858i 0.539486 + 1.66037i
795795 −9.70820 7.05342i −0.344315 0.250159i
796796 0 0
797797 12.9787 39.9444i 0.459730 1.41490i −0.405762 0.913979i 0.632994π-0.632994\pi
0.865492 0.500924i 0.167006π-0.167006\pi
798798 13.8197 42.5325i 0.489211 1.50564i
799799 −28.9443 + 21.0292i −1.02397 + 0.743961i
800800 −5.42705 3.94298i −0.191875 0.139406i
801801 −4.32624 13.3148i −0.152860 0.470455i
802802 67.0820 2.36875
803803 0 0
804804 −36.0000 −1.26962
805805 11.0557 + 34.0260i 0.389663 + 1.19926i
806806 0 0
807807 8.09017 5.87785i 0.284787 0.206910i
808808 3.09017 9.51057i 0.108712 0.334581i
809809 −4.14590 + 12.7598i −0.145762 + 0.448609i −0.997108 0.0759949i 0.975787π-0.975787\pi
0.851346 + 0.524604i 0.175787π0.175787\pi
810810 −3.61803 + 2.62866i −0.127125 + 0.0923615i
811811 3.61803 + 2.62866i 0.127046 + 0.0923046i 0.649494 0.760367i 0.274981π-0.274981\pi
−0.522447 + 0.852672i 0.674981π0.674981\pi
812812 −18.5410 57.0634i −0.650662 2.00253i
813813 −13.4164 −0.470534
814814 0 0
815815 8.00000 0.280228
816816 −1.38197 4.25325i −0.0483785 0.148894i
817817 16.1803 + 11.7557i 0.566078 + 0.411280i
818818 48.5410 35.2671i 1.69720 1.23309i
819819 0 0
820820 −8.29180 + 25.5195i −0.289562 + 0.891180i
821821 −18.0902 + 13.1433i −0.631351 + 0.458704i −0.856868 0.515536i 0.827593π-0.827593\pi
0.225517 + 0.974239i 0.427593π0.427593\pi
822822 −39.7984 28.9152i −1.38813 1.00853i
823823 4.94427 + 15.2169i 0.172346 + 0.530428i 0.999502 0.0315446i 0.0100426π-0.0100426\pi
−0.827156 + 0.561973i 0.810043π0.810043\pi
824824 35.7771 1.24635
825825 0 0
826826 0 0
827827 13.8197 + 42.5325i 0.480557 + 1.47900i 0.838314 + 0.545187i 0.183541π0.183541\pi
−0.357758 + 0.933814i 0.616459π0.616459\pi
828828 9.70820 + 7.05342i 0.337383 + 0.245123i
829829 −11.3262 + 8.22899i −0.393377 + 0.285805i −0.766838 0.641841i 0.778171π-0.778171\pi
0.373461 + 0.927646i 0.378171π0.378171\pi
830830 −12.3607 + 38.0423i −0.429045 + 1.32047i
831831 0 0
832832 0 0
833833 −47.0344 34.1725i −1.62965 1.18401i
834834 9.27051 + 28.5317i 0.321012 + 0.987972i
835835 17.8885 0.619059
836836 0 0
837837 0 0
838838 2.76393 + 8.50651i 0.0954784 + 0.293852i
839839 16.1803 + 11.7557i 0.558607 + 0.405852i 0.830949 0.556349i 0.187798π-0.187798\pi
−0.272342 + 0.962201i 0.587798π0.587798\pi
840840 16.1803 11.7557i 0.558275 0.405610i
841841 −2.78115 + 8.55951i −0.0959018 + 0.295155i
842842 6.90983 21.2663i 0.238128 0.732884i
843843 −25.3262 + 18.4006i −0.872282 + 0.633750i
844844 10.8541 + 7.88597i 0.373614 + 0.271446i
845845 −8.03444 24.7275i −0.276393 0.850651i
846846 17.8885 0.615021
847847 0 0
848848 −6.00000 −0.206041
849849 −4.14590 12.7598i −0.142287 0.437914i
850850 8.09017 + 5.87785i 0.277491 + 0.201609i
851851 6.47214 4.70228i 0.221862 0.161192i
852852 −7.41641 + 22.8254i −0.254082 + 0.781984i
853853 2.76393 8.50651i 0.0946352 0.291257i −0.892523 0.451001i 0.851067π-0.851067\pi
0.987158 + 0.159744i 0.0510669π0.0510669\pi
854854 72.3607 52.5731i 2.47613 1.79901i
855855 7.23607 + 5.25731i 0.247468 + 0.179796i
856856 6.18034 + 19.0211i 0.211240 + 0.650129i
857857 40.2492 1.37489 0.687444 0.726238i 0.258733π-0.258733\pi
0.687444 + 0.726238i 0.258733π0.258733\pi
858858 0 0
859859 4.00000 0.136478 0.0682391 0.997669i 0.478262π-0.478262\pi
0.0682391 + 0.997669i 0.478262π0.478262\pi
860860 8.29180 + 25.5195i 0.282748 + 0.870209i
861861 −16.1803 11.7557i −0.551425 0.400633i
862862 16.1803 11.7557i 0.551105 0.400401i
863863 1.23607 3.80423i 0.0420762 0.129497i −0.927812 0.373049i 0.878312π-0.878312\pi
0.969888 + 0.243551i 0.0783124π0.0783124\pi
864864 −2.07295 + 6.37988i −0.0705232 + 0.217048i
865865 21.7082 15.7719i 0.738101 0.536262i
866866 10.8541 + 7.88597i 0.368837 + 0.267976i
867867 0.927051 + 2.85317i 0.0314843 + 0.0968987i
868868 0 0
869869 0 0
870870 20.0000 0.678064
871871 0 0
872872 0 0
873873 −1.61803 + 1.17557i −0.0547622 + 0.0397870i
874874 12.3607 38.0423i 0.418106 1.28680i
875875 16.5836 51.0390i 0.560628 1.72543i
876876 21.7082 15.7719i 0.733452 0.532884i
877877 7.23607 + 5.25731i 0.244345 + 0.177527i 0.703217 0.710976i 0.251746π-0.251746\pi
−0.458872 + 0.888502i 0.651746π0.651746\pi
878878 −9.27051 28.5317i −0.312865 0.962898i
879879 −22.3607 −0.754207
880880 0 0
881881 −18.0000 −0.606435 −0.303218 0.952921i 0.598061π-0.598061\pi
−0.303218 + 0.952921i 0.598061π0.598061\pi
882882 8.98278 + 27.6462i 0.302466 + 0.930894i
883883 −35.5967 25.8626i −1.19793 0.870344i −0.203847 0.979003i 0.565344π-0.565344\pi
−0.994079 + 0.108659i 0.965344π0.965344\pi
884884 0 0
885885 0 0
886886 −16.5836 + 51.0390i −0.557137 + 1.71469i
887887 43.4164 31.5439i 1.45778 1.05914i 0.473846 0.880608i 0.342865π-0.342865\pi
0.983934 0.178532i 0.0571347π-0.0571347\pi
888888 −3.61803 2.62866i −0.121413 0.0882119i
889889 −18.5410 57.0634i −0.621846 1.91384i
890890 −62.6099 −2.09869
891891 0 0
892892 −48.0000 −1.60716
893893 −11.0557 34.0260i −0.369966 1.13864i
894894 40.4508 + 29.3893i 1.35288 + 0.982924i
895895 6.47214 4.70228i 0.216340 0.157180i
896896 21.6312 66.5740i 0.722647 2.22408i
897897 0 0
898898 10.8541 7.88597i 0.362206 0.263158i
899899 0 0
900900 −0.927051 2.85317i −0.0309017 0.0951057i
901901 26.8328 0.893931
902902 0 0
903903 −20.0000 −0.665558
904904 4.14590 + 12.7598i 0.137891 + 0.424383i
905905 16.1803 + 11.7557i 0.537853 + 0.390773i
906906 −24.2705 + 17.6336i −0.806334 + 0.585836i
907907 −3.70820 + 11.4127i −0.123129 + 0.378952i −0.993556 0.113346i 0.963843π-0.963843\pi
0.870427 + 0.492298i 0.163843π0.163843\pi
908908 8.29180 25.5195i 0.275173 0.846895i
909909 −3.61803 + 2.62866i −0.120003 + 0.0871870i
910910 0 0
911911 0 0 0.951057 0.309017i 0.100000π-0.100000\pi
−0.951057 + 0.309017i 0.900000π0.900000\pi
912912 4.47214 0.148087
913913 0 0
914914 60.0000 1.98462
915915 5.52786 + 17.0130i 0.182746 + 0.562433i
916916 −24.2705 17.6336i −0.801920 0.582629i
917917 −64.7214 + 47.0228i −2.13729 + 1.55283i
918918 3.09017 9.51057i 0.101991 0.313895i
919919 6.90983 21.2663i 0.227934 0.701510i −0.770046 0.637988i 0.779767π-0.779767\pi
0.997980 0.0635214i 0.0202331π-0.0202331\pi
920920 14.4721 10.5146i 0.477132 0.346657i
921921 3.61803 + 2.62866i 0.119218 + 0.0866171i
922922 9.27051 + 28.5317i 0.305308 + 0.939641i
923923 0 0
924924 0 0
925925 −2.00000 −0.0657596
926926 16.5836 + 51.0390i 0.544971 + 1.67725i
927927 −12.9443 9.40456i −0.425146 0.308886i
928928 24.2705 17.6336i 0.796719 0.578850i
929929 9.27051 28.5317i 0.304156 0.936095i −0.675835 0.737053i 0.736217π-0.736217\pi
0.979991 0.199042i 0.0637830π-0.0637830\pi
930930 0 0
931931 47.0344 34.1725i 1.54149 1.11996i
932932 10.8541 + 7.88597i 0.355538 + 0.258313i
933933 −3.70820 11.4127i −0.121401 0.373634i
934934 −17.8885 −0.585331
935935 0 0
936936 0 0
937937 16.5836 + 51.0390i 0.541762 + 1.66737i 0.728566 + 0.684976i 0.240187π0.240187\pi
−0.186804 + 0.982397i 0.559813π0.559813\pi
938938 −97.0820 70.5342i −3.16984 2.30302i
939939 −11.3262 + 8.22899i −0.369618 + 0.268543i
940940 14.8328 45.6507i 0.483793 1.48896i
941941 6.90983 21.2663i 0.225254 0.693261i −0.773012 0.634392i 0.781251π-0.781251\pi
0.998266 0.0588688i 0.0187494π-0.0187494\pi
942942 −3.61803 + 2.62866i −0.117882 + 0.0856462i
943943 −14.4721 10.5146i −0.471278 0.342403i
944944 0 0
945945 −8.94427 −0.290957
946946 0 0
947947 52.0000 1.68977 0.844886 0.534946i 0.179668π-0.179668\pi
0.844886 + 0.534946i 0.179668π0.179668\pi
948948 12.4377 + 38.2793i 0.403958 + 1.24325i
949949 0 0
950950 −8.09017 + 5.87785i −0.262480 + 0.190703i
951951 5.56231 17.1190i 0.180370 0.555122i
952952 −13.8197 + 42.5325i −0.447898 + 1.37849i
953953 −18.0902 + 13.1433i −0.585998 + 0.425753i −0.840882 0.541219i 0.817963π-0.817963\pi
0.254883 + 0.966972i 0.417963π0.417963\pi
954954 −10.8541 7.88597i −0.351415 0.255318i
955955 0 0
956956 26.8328 0.867835
957957 0 0
958958 −20.0000 −0.646171
959959 −30.4033 93.5716i −0.981772 3.02158i
960960 21.0344 + 15.2824i 0.678884 + 0.493238i
961961 25.0795 18.2213i 0.809017 0.587785i
962962 0 0
963963 2.76393 8.50651i 0.0890665 0.274118i
964964 −21.7082 + 15.7719i −0.699174 + 0.507980i
965965 28.9443 + 21.0292i 0.931749 + 0.676955i
966966 12.3607 + 38.0423i 0.397698 + 1.22399i
967967 13.4164 0.431443 0.215721 0.976455i 0.430790π-0.430790\pi
0.215721 + 0.976455i 0.430790π0.430790\pi
968968 0 0
969969 −20.0000 −0.642493
970970 2.76393 + 8.50651i 0.0887445 + 0.273128i
971971 0 0 0.587785 0.809017i 0.300000π-0.300000\pi
−0.587785 + 0.809017i 0.700000π0.700000\pi
972972 −2.42705 + 1.76336i −0.0778477 + 0.0565597i
973973 −18.5410 + 57.0634i −0.594398 + 1.82937i
974974 5.52786 17.0130i 0.177124 0.545132i
975975 0 0
976976 7.23607 + 5.25731i 0.231621 + 0.168282i
977977 −12.9787 39.9444i −0.415226 1.27793i −0.912049 0.410082i 0.865500π-0.865500\pi
0.496823 0.867852i 0.334500π-0.334500\pi
978978 8.94427 0.286006
979979 0 0
980980 78.0000 2.49162
981981 0 0
982982 48.5410 + 35.2671i 1.54901 + 1.12542i
983983 −29.1246 + 21.1603i −0.928931 + 0.674908i −0.945731 0.324951i 0.894652π-0.894652\pi
0.0168000 + 0.999859i 0.494652π0.494652\pi
984984 −3.09017 + 9.51057i −0.0985110 + 0.303186i
985985 13.8197 42.5325i 0.440331 1.35520i
986986 −36.1803 + 26.2866i −1.15222 + 0.837134i
987987 28.9443 + 21.0292i 0.921306 + 0.669368i
988988 0 0
989989 −17.8885 −0.568823
990990 0 0
991991 40.0000 1.27064 0.635321 0.772248i 0.280868π-0.280868\pi
0.635321 + 0.772248i 0.280868π0.280868\pi
992992 0 0
993993 16.1803 + 11.7557i 0.513468 + 0.373056i
994994 −64.7214 + 47.0228i −2.05284 + 1.49147i
995995 0 0
996996 −8.29180 + 25.5195i −0.262736 + 0.808617i
997997 21.7082 15.7719i 0.687506 0.499502i −0.188334 0.982105i 0.560309π-0.560309\pi
0.875839 + 0.482603i 0.160309π0.160309\pi
998998 36.1803 + 26.2866i 1.14527 + 0.832086i
999999 0.618034 + 1.90211i 0.0195537 + 0.0601802i
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 363.2.e.l.148.1 4
11.2 odd 10 363.2.e.a.130.1 4
11.3 even 5 363.2.a.g.1.2 yes 2
11.4 even 5 363.2.e.a.124.1 4
11.5 even 5 363.2.e.a.202.1 4
11.6 odd 10 inner 363.2.e.l.202.1 4
11.7 odd 10 inner 363.2.e.l.124.1 4
11.8 odd 10 363.2.a.g.1.1 2
11.9 even 5 inner 363.2.e.l.130.1 4
11.10 odd 2 363.2.e.a.148.1 4
33.8 even 10 1089.2.a.p.1.2 2
33.14 odd 10 1089.2.a.p.1.1 2
44.3 odd 10 5808.2.a.bx.1.2 2
44.19 even 10 5808.2.a.bx.1.1 2
55.14 even 10 9075.2.a.bi.1.1 2
55.19 odd 10 9075.2.a.bi.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
363.2.a.g.1.1 2 11.8 odd 10
363.2.a.g.1.2 yes 2 11.3 even 5
363.2.e.a.124.1 4 11.4 even 5
363.2.e.a.130.1 4 11.2 odd 10
363.2.e.a.148.1 4 11.10 odd 2
363.2.e.a.202.1 4 11.5 even 5
363.2.e.l.124.1 4 11.7 odd 10 inner
363.2.e.l.130.1 4 11.9 even 5 inner
363.2.e.l.148.1 4 1.1 even 1 trivial
363.2.e.l.202.1 4 11.6 odd 10 inner
1089.2.a.p.1.1 2 33.14 odd 10
1089.2.a.p.1.2 2 33.8 even 10
5808.2.a.bx.1.1 2 44.19 even 10
5808.2.a.bx.1.2 2 44.3 odd 10
9075.2.a.bi.1.1 2 55.14 even 10
9075.2.a.bi.1.2 2 55.19 odd 10