Properties

Label 980.2.c.e.979.14
Level 980980
Weight 22
Character 980.979
Analytic conductor 7.8257.825
Analytic rank 00
Dimension 4848
Inner twists 88

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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] = [980,2,Mod(979,980)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(980, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 1])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("980.979"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 980=22572 980 = 2^{2} \cdot 5 \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 980.c (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [48,0,0,16] 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: 7.825339398097.82533939809
Analytic rank: 00
Dimension: 4848
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 979.14
Character χ\chi == 980.979
Dual form 980.2.c.e.979.15

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+(1.147300.826865i)q2+1.52335iq3+(0.632590+1.89732i)q4+(0.0967363+2.23397i)q5+(1.259611.74774i)q6+(0.8430592.69986i)q8+0.679393q9+(1.958182.48305i)q10+4.56056iq11+(2.89029+0.963658i)q12+2.19514q13+(3.403130.147364i)q15+(3.19966+2.40045i)q16+6.22202q17+(0.7794670.561766i)q18+3.83396q19+(4.29976+1.22965i)q20+(3.770975.23233i)q220.430261q23+(4.11284+1.28428i)q24+(4.981280.432213i)q25+(2.518481.81508i)q26+5.60502iq270.473706q29+(3.78256+2.98300i)q30+7.59779q31+(5.655820.108351i)q326.94735q33+(7.138515.14477i)q34+(0.429777+1.28903i)q368.44308iq37+(4.398703.17017i)q38+3.34397iq39+(5.94987+2.14455i)q40+1.45831iq418.58232q43+(8.65285+2.88496i)q44+(0.0657220+1.51775i)q45+(0.493638+0.355767i)q464.48893iq47+(3.656744.87421i)q48+(5.35764+4.61473i)q50+9.47833iq51+(1.38862+4.16488i)q52+9.23911iq53+(4.634596.43063i)q54+(10.18820.441172i)q55+5.84048iq57+(0.543482+0.391691i)q583.13601q59+(1.873196.55006i)q60+5.71165iq61+(8.716946.28235i)q62+(6.578504.55228i)q64+(0.212349+4.90388i)q65+(7.97068+5.74451i)q6614.9459q67+(3.93598+11.8052i)q680.655439iq694.57799iq71+(0.5727681.83427i)q7212.2715q73+(6.98128+9.68674i)q74+(0.6584137.58826i)q75+(2.42532+7.27425i)q76+(2.765013.83653i)q786.20417iq79+(5.053037.38017i)q806.50025q81+(1.205831.67312i)q82+7.69966iq83+(0.601895+13.8998i)q85+(9.84648+7.09641i)q860.721622iq87+(12.3129+3.84482i)q889.32432iq89+(1.330371.68697i)q90+(0.2721780.816343i)q92+11.5741iq93+(3.71174+5.15014i)q94+(0.370883+8.56497i)q95+(0.165057+8.61581i)q96+9.05280q97+3.09841iq99+O(q100)q+(-1.14730 - 0.826865i) q^{2} +1.52335i q^{3} +(0.632590 + 1.89732i) q^{4} +(-0.0967363 + 2.23397i) q^{5} +(1.25961 - 1.74774i) q^{6} +(0.843059 - 2.69986i) q^{8} +0.679393 q^{9} +(1.95818 - 2.48305i) q^{10} +4.56056i q^{11} +(-2.89029 + 0.963658i) q^{12} +2.19514 q^{13} +(-3.40313 - 0.147364i) q^{15} +(-3.19966 + 2.40045i) q^{16} +6.22202 q^{17} +(-0.779467 - 0.561766i) q^{18} +3.83396 q^{19} +(-4.29976 + 1.22965i) q^{20} +(3.77097 - 5.23233i) q^{22} -0.430261 q^{23} +(4.11284 + 1.28428i) q^{24} +(-4.98128 - 0.432213i) q^{25} +(-2.51848 - 1.81508i) q^{26} +5.60502i q^{27} -0.473706 q^{29} +(3.78256 + 2.98300i) q^{30} +7.59779 q^{31} +(5.65582 - 0.108351i) q^{32} -6.94735 q^{33} +(-7.13851 - 5.14477i) q^{34} +(0.429777 + 1.28903i) q^{36} -8.44308i q^{37} +(-4.39870 - 3.17017i) q^{38} +3.34397i q^{39} +(5.94987 + 2.14455i) q^{40} +1.45831i q^{41} -8.58232 q^{43} +(-8.65285 + 2.88496i) q^{44} +(-0.0657220 + 1.51775i) q^{45} +(0.493638 + 0.355767i) q^{46} -4.48893i q^{47} +(-3.65674 - 4.87421i) q^{48} +(5.35764 + 4.61473i) q^{50} +9.47833i q^{51} +(1.38862 + 4.16488i) q^{52} +9.23911i q^{53} +(4.63459 - 6.43063i) q^{54} +(-10.1882 - 0.441172i) q^{55} +5.84048i q^{57} +(0.543482 + 0.391691i) q^{58} -3.13601 q^{59} +(-1.87319 - 6.55006i) q^{60} +5.71165i q^{61} +(-8.71694 - 6.28235i) q^{62} +(-6.57850 - 4.55228i) q^{64} +(-0.212349 + 4.90388i) q^{65} +(7.97068 + 5.74451i) q^{66} -14.9459 q^{67} +(3.93598 + 11.8052i) q^{68} -0.655439i q^{69} -4.57799i q^{71} +(0.572768 - 1.83427i) q^{72} -12.2715 q^{73} +(-6.98128 + 9.68674i) q^{74} +(0.658413 - 7.58826i) q^{75} +(2.42532 + 7.27425i) q^{76} +(2.76501 - 3.83653i) q^{78} -6.20417i q^{79} +(-5.05303 - 7.38017i) q^{80} -6.50025 q^{81} +(1.20583 - 1.67312i) q^{82} +7.69966i q^{83} +(-0.601895 + 13.8998i) q^{85} +(9.84648 + 7.09641i) q^{86} -0.721622i q^{87} +(12.3129 + 3.84482i) q^{88} -9.32432i q^{89} +(1.33037 - 1.68697i) q^{90} +(-0.272178 - 0.816343i) q^{92} +11.5741i q^{93} +(-3.71174 + 5.15014i) q^{94} +(-0.370883 + 8.56497i) q^{95} +(0.165057 + 8.61581i) q^{96} +9.05280 q^{97} +3.09841i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 48q+16q464q9+16q1616q2548q298q30+176q3648q4432q46+32q50+24q6080q6416q65112q7448q8164q85112q86+O(q100) 48 q + 16 q^{4} - 64 q^{9} + 16 q^{16} - 16 q^{25} - 48 q^{29} - 8 q^{30} + 176 q^{36} - 48 q^{44} - 32 q^{46} + 32 q^{50} + 24 q^{60} - 80 q^{64} - 16 q^{65} - 112 q^{74} - 48 q^{81} - 64 q^{85} - 112 q^{86}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/980Z)×\left(\mathbb{Z}/980\mathbb{Z}\right)^\times.

nn 101101 197197 491491
χ(n)\chi(n) 1-1 1-1 1-1

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.14730 0.826865i −0.811263 0.584682i
33 1.52335i 0.879509i 0.898118 + 0.439754i 0.144935π0.144935\pi
−0.898118 + 0.439754i 0.855065π0.855065\pi
44 0.632590 + 1.89732i 0.316295 + 0.948661i
55 −0.0967363 + 2.23397i −0.0432618 + 0.999064i
66 1.25961 1.74774i 0.514233 0.713513i
77 0 0
88 0.843059 2.69986i 0.298066 0.954545i
99 0.679393 0.226464
1010 1.95818 2.48305i 0.619231 0.785209i
1111 4.56056i 1.37506i 0.726156 + 0.687530i 0.241305π0.241305\pi
−0.726156 + 0.687530i 0.758695π0.758695\pi
1212 −2.89029 + 0.963658i −0.834356 + 0.278184i
1313 2.19514 0.608822 0.304411 0.952541i 0.401540π-0.401540\pi
0.304411 + 0.952541i 0.401540π0.401540\pi
1414 0 0
1515 −3.40313 0.147364i −0.878685 0.0380491i
1616 −3.19966 + 2.40045i −0.799915 + 0.600113i
1717 6.22202 1.50906 0.754530 0.656265i 0.227865π-0.227865\pi
0.754530 + 0.656265i 0.227865π0.227865\pi
1818 −0.779467 0.561766i −0.183722 0.132410i
1919 3.83396 0.879571 0.439785 0.898103i 0.355055π-0.355055\pi
0.439785 + 0.898103i 0.355055π0.355055\pi
2020 −4.29976 + 1.22965i −0.961456 + 0.274958i
2121 0 0
2222 3.77097 5.23233i 0.803973 1.11554i
2323 −0.430261 −0.0897155 −0.0448578 0.998993i 0.514283π-0.514283\pi
−0.0448578 + 0.998993i 0.514283π0.514283\pi
2424 4.11284 + 1.28428i 0.839531 + 0.262152i
2525 −4.98128 0.432213i −0.996257 0.0864426i
2626 −2.51848 1.81508i −0.493914 0.355967i
2727 5.60502i 1.07869i
2828 0 0
2929 −0.473706 −0.0879650 −0.0439825 0.999032i 0.514005π-0.514005\pi
−0.0439825 + 0.999032i 0.514005π0.514005\pi
3030 3.78256 + 2.98300i 0.690598 + 0.544619i
3131 7.59779 1.36460 0.682302 0.731070i 0.260979π-0.260979\pi
0.682302 + 0.731070i 0.260979π0.260979\pi
3232 5.65582 0.108351i 0.999817 0.0191539i
3333 −6.94735 −1.20938
3434 −7.13851 5.14477i −1.22424 0.882320i
3535 0 0
3636 0.429777 + 1.28903i 0.0716295 + 0.214838i
3737 8.44308i 1.38803i −0.719959 0.694017i 0.755839π-0.755839\pi
0.719959 0.694017i 0.244161π-0.244161\pi
3838 −4.39870 3.17017i −0.713563 0.514269i
3939 3.34397i 0.535464i
4040 5.94987 + 2.14455i 0.940757 + 0.339083i
4141 1.45831i 0.227750i 0.993495 + 0.113875i 0.0363264π0.0363264\pi
−0.993495 + 0.113875i 0.963674π0.963674\pi
4242 0 0
4343 −8.58232 −1.30879 −0.654396 0.756152i 0.727077π-0.727077\pi
−0.654396 + 0.756152i 0.727077π0.727077\pi
4444 −8.65285 + 2.88496i −1.30447 + 0.434925i
4545 −0.0657220 + 1.51775i −0.00979725 + 0.226252i
4646 0.493638 + 0.355767i 0.0727829 + 0.0524550i
4747 4.48893i 0.654778i −0.944890 0.327389i 0.893831π-0.893831\pi
0.944890 0.327389i 0.106169π-0.106169\pi
4848 −3.65674 4.87421i −0.527805 0.703532i
4949 0 0
5050 5.35764 + 4.61473i 0.757685 + 0.652621i
5151 9.47833i 1.32723i
5252 1.38862 + 4.16488i 0.192567 + 0.577565i
5353 9.23911i 1.26909i 0.772886 + 0.634544i 0.218812π0.218812\pi
−0.772886 + 0.634544i 0.781188π0.781188\pi
5454 4.63459 6.43063i 0.630688 0.875098i
5555 −10.1882 0.441172i −1.37377 0.0594876i
5656 0 0
5757 5.84048i 0.773590i
5858 0.543482 + 0.391691i 0.0713627 + 0.0514315i
5959 −3.13601 −0.408273 −0.204137 0.978942i 0.565439π-0.565439\pi
−0.204137 + 0.978942i 0.565439π0.565439\pi
6060 −1.87319 6.55006i −0.241828 0.845609i
6161 5.71165i 0.731302i 0.930752 + 0.365651i 0.119154π0.119154\pi
−0.930752 + 0.365651i 0.880846π0.880846\pi
6262 −8.71694 6.28235i −1.10705 0.797859i
6363 0 0
6464 −6.57850 4.55228i −0.822313 0.569035i
6565 −0.212349 + 4.90388i −0.0263387 + 0.608252i
6666 7.97068 + 5.74451i 0.981123 + 0.707101i
6767 −14.9459 −1.82593 −0.912967 0.408033i 0.866215π-0.866215\pi
−0.912967 + 0.408033i 0.866215π0.866215\pi
6868 3.93598 + 11.8052i 0.477308 + 1.43159i
6969 0.655439i 0.0789056i
7070 0 0
7171 4.57799i 0.543308i −0.962395 0.271654i 0.912429π-0.912429\pi
0.962395 0.271654i 0.0875706π-0.0875706\pi
7272 0.572768 1.83427i 0.0675014 0.216170i
7373 −12.2715 −1.43627 −0.718134 0.695905i 0.755003π-0.755003\pi
−0.718134 + 0.695905i 0.755003π0.755003\pi
7474 −6.98128 + 9.68674i −0.811558 + 1.12606i
7575 0.658413 7.58826i 0.0760270 0.876217i
7676 2.42532 + 7.27425i 0.278204 + 0.834414i
7777 0 0
7878 2.76501 3.83653i 0.313076 0.434402i
7979 6.20417i 0.698024i −0.937118 0.349012i 0.886517π-0.886517\pi
0.937118 0.349012i 0.113483π-0.113483\pi
8080 −5.05303 7.38017i −0.564946 0.825128i
8181 −6.50025 −0.722250
8282 1.20583 1.67312i 0.133161 0.184765i
8383 7.69966i 0.845148i 0.906329 + 0.422574i 0.138873π0.138873\pi
−0.906329 + 0.422574i 0.861127π0.861127\pi
8484 0 0
8585 −0.601895 + 13.8998i −0.0652847 + 1.50765i
8686 9.84648 + 7.09641i 1.06177 + 0.765226i
8787 0.721622i 0.0773660i
8888 12.3129 + 3.84482i 1.31256 + 0.409859i
8989 9.32432i 0.988376i −0.869355 0.494188i 0.835466π-0.835466\pi
0.869355 0.494188i 0.164534π-0.164534\pi
9090 1.33037 1.68697i 0.140234 0.177822i
9191 0 0
9292 −0.272178 0.816343i −0.0283766 0.0851096i
9393 11.5741i 1.20018i
9494 −3.71174 + 5.15014i −0.382836 + 0.531197i
9595 −0.370883 + 8.56497i −0.0380518 + 0.878747i
9696 0.165057 + 8.61581i 0.0168460 + 0.879347i
9797 9.05280 0.919172 0.459586 0.888133i 0.347998π-0.347998\pi
0.459586 + 0.888133i 0.347998π0.347998\pi
9898 0 0
9999 3.09841i 0.311402i
100100 −2.33106 9.72451i −0.233106 0.972451i
101101 7.99802i 0.795832i 0.917422 + 0.397916i 0.130267π0.130267\pi
−0.917422 + 0.397916i 0.869733π0.869733\pi
102102 7.83730 10.8745i 0.776008 1.07673i
103103 12.5017i 1.23183i −0.787813 0.615914i 0.788787π-0.788787\pi
0.787813 0.615914i 0.211213π-0.211213\pi
104104 1.85063 5.92657i 0.181469 0.581148i
105105 0 0
106106 7.63949 10.6000i 0.742013 1.02956i
107107 14.4668 1.39855 0.699277 0.714851i 0.253505π-0.253505\pi
0.699277 + 0.714851i 0.253505π0.253505\pi
108108 −10.6345 + 3.54568i −1.02331 + 0.341183i
109109 18.2962 1.75246 0.876230 0.481892i 0.160050π-0.160050\pi
0.876230 + 0.481892i 0.160050π0.160050\pi
110110 11.3241 + 8.93040i 1.07971 + 0.851480i
111111 12.8618 1.22079
112112 0 0
113113 1.13588i 0.106854i 0.998572 + 0.0534272i 0.0170145π0.0170145\pi
−0.998572 + 0.0534272i 0.982986π0.982986\pi
114114 4.82928 6.70077i 0.452304 0.627585i
115115 0.0416218 0.961191i 0.00388126 0.0896315i
116116 −0.299662 0.898773i −0.0278229 0.0834490i
117117 1.49136 0.137876
118118 3.59794 + 2.59305i 0.331217 + 0.238710i
119119 0 0
120120 −3.26690 + 9.06375i −0.298226 + 0.827404i
121121 −9.79871 −0.890791
122122 4.72277 6.55298i 0.427579 0.593278i
123123 −2.22153 −0.200309
124124 4.80629 + 14.4155i 0.431617 + 1.29455i
125125 1.44742 11.0863i 0.129462 0.991584i
126126 0 0
127127 −8.33473 −0.739588 −0.369794 0.929114i 0.620572π-0.620572\pi
−0.369794 + 0.929114i 0.620572π0.620572\pi
128128 3.78339 + 10.6624i 0.334407 + 0.942429i
129129 13.0739i 1.15109i
130130 4.29847 5.45063i 0.377001 0.478052i
131131 −5.68203 −0.496441 −0.248220 0.968704i 0.579846π-0.579846\pi
−0.248220 + 0.968704i 0.579846π0.579846\pi
132132 −4.39482 13.1814i −0.382520 1.14729i
133133 0 0
134134 17.1474 + 12.3583i 1.48131 + 1.06759i
135135 −12.5215 0.542209i −1.07768 0.0466659i
136136 5.24553 16.7986i 0.449800 1.44047i
137137 14.7846i 1.26313i 0.775321 + 0.631567i 0.217588π0.217588\pi
−0.775321 + 0.631567i 0.782412π0.782412\pi
138138 −0.541959 + 0.751985i −0.0461347 + 0.0640132i
139139 −1.11362 −0.0944558 −0.0472279 0.998884i 0.515039π-0.515039\pi
−0.0472279 + 0.998884i 0.515039π0.515039\pi
140140 0 0
141141 6.83823 0.575883
142142 −3.78538 + 5.25233i −0.317662 + 0.440766i
143143 10.0111i 0.837166i
144144 −2.17383 + 1.63085i −0.181152 + 0.135904i
145145 0.0458246 1.05825i 0.00380552 0.0878826i
146146 14.0790 + 10.1468i 1.16519 + 0.839759i
147147 0 0
148148 16.0192 5.34101i 1.31677 0.439028i
149149 6.87811 0.563476 0.281738 0.959491i 0.409089π-0.409089\pi
0.281738 + 0.959491i 0.409089π0.409089\pi
150150 −7.02986 + 8.16158i −0.573986 + 0.666390i
151151 21.2380i 1.72832i −0.503215 0.864161i 0.667850π-0.667850\pi
0.503215 0.864161i 0.332150π-0.332150\pi
152152 3.23225 10.3512i 0.262170 0.839590i
153153 4.22720 0.341748
154154 0 0
155155 −0.734983 + 16.9733i −0.0590352 + 1.36333i
156156 −6.34459 + 2.11536i −0.507974 + 0.169364i
157157 2.32742 0.185748 0.0928741 0.995678i 0.470395π-0.470395\pi
0.0928741 + 0.995678i 0.470395π0.470395\pi
158158 −5.13001 + 7.11804i −0.408122 + 0.566281i
159159 −14.0744 −1.11617
160160 −0.305070 + 12.6454i −0.0241179 + 0.999709i
161161 0 0
162162 7.45773 + 5.37482i 0.585934 + 0.422286i
163163 −3.06683 −0.240213 −0.120106 0.992761i 0.538324π-0.538324\pi
−0.120106 + 0.992761i 0.538324π0.538324\pi
164164 −2.76689 + 0.922515i −0.216058 + 0.0720363i
165165 0.672061 15.5202i 0.0523199 1.20825i
166166 6.36658 8.83381i 0.494142 0.685637i
167167 13.0431i 1.00930i 0.863323 + 0.504652i 0.168379π0.168379\pi
−0.863323 + 0.504652i 0.831621π0.831621\pi
168168 0 0
169169 −8.18137 −0.629336
170170 12.1838 15.4496i 0.934457 1.18493i
171171 2.60477 0.199191
172172 −5.42909 16.2834i −0.413964 1.24160i
173173 −11.0602 −0.840895 −0.420448 0.907317i 0.638127π-0.638127\pi
−0.420448 + 0.907317i 0.638127π0.638127\pi
174174 −0.596684 + 0.827916i −0.0452345 + 0.0627642i
175175 0 0
176176 −10.9474 14.5922i −0.825192 1.09993i
177177 4.77725i 0.359080i
178178 −7.70995 + 10.6978i −0.577885 + 0.801832i
179179 22.0450i 1.64772i −0.566794 0.823860i 0.691816π-0.691816\pi
0.566794 0.823860i 0.308184π-0.308184\pi
180180 −2.92123 + 0.835415i −0.217736 + 0.0622682i
181181 2.49964i 0.185797i −0.995676 0.0928984i 0.970387π-0.970387\pi
0.995676 0.0928984i 0.0296132π-0.0296132\pi
182182 0 0
183183 −8.70087 −0.643187
184184 −0.362735 + 1.16164i −0.0267412 + 0.0856375i
185185 18.8616 + 0.816752i 1.38673 + 0.0600488i
186186 9.57024 13.2790i 0.701724 0.973662i
187187 28.3759i 2.07505i
188188 8.51694 2.83965i 0.621162 0.207103i
189189 0 0
190190 7.50758 9.51991i 0.544657 0.690647i
191191 7.76066i 0.561542i 0.959775 + 0.280771i 0.0905901π0.0905901\pi
−0.959775 + 0.280771i 0.909410π0.909410\pi
192192 6.93474 10.0214i 0.500472 0.723231i
193193 6.03714i 0.434563i −0.976109 0.217281i 0.930281π-0.930281\pi
0.976109 0.217281i 0.0697189π-0.0697189\pi
194194 −10.3863 7.48544i −0.745690 0.537423i
195195 −7.47035 0.323483i −0.534963 0.0231651i
196196 0 0
197197 9.74467i 0.694279i −0.937813 0.347140i 0.887153π-0.887153\pi
0.937813 0.347140i 0.112847π-0.112847\pi
198198 2.56197 3.55481i 0.182071 0.252629i
199199 −17.2535 −1.22307 −0.611535 0.791217i 0.709448π-0.709448\pi
−0.611535 + 0.791217i 0.709448π0.709448\pi
200200 −5.36643 + 13.0844i −0.379464 + 0.925207i
201201 22.7679i 1.60593i
202202 6.61328 9.17612i 0.465309 0.645629i
203203 0 0
204204 −17.9834 + 5.99590i −1.25909 + 0.419797i
205205 −3.25784 0.141072i −0.227537 0.00985289i
206206 −10.3372 + 14.3432i −0.720227 + 0.999336i
207207 −0.292316 −0.0203174
208208 −7.02369 + 5.26932i −0.487006 + 0.365362i
209209 17.4850i 1.20946i
210210 0 0
211211 26.8147i 1.84600i −0.384796 0.923002i 0.625728π-0.625728\pi
0.384796 0.923002i 0.374272π-0.374272\pi
212212 −17.5296 + 5.84456i −1.20393 + 0.401406i
213213 6.97391 0.477844
214214 −16.5977 11.9620i −1.13459 0.817709i
215215 0.830222 19.1727i 0.0566207 1.30757i
216216 15.1328 + 4.72536i 1.02965 + 0.321520i
217217 0 0
218218 −20.9912 15.1285i −1.42171 1.02463i
219219 18.6938i 1.26321i
220220 −5.60789 19.6093i −0.378084 1.32206i
221221 13.6582 0.918749
222222 −14.7563 10.6350i −0.990380 0.713772i
223223 17.6054i 1.17894i −0.807789 0.589472i 0.799336π-0.799336\pi
0.807789 0.589472i 0.200664π-0.200664\pi
224224 0 0
225225 −3.38425 0.293642i −0.225617 0.0195762i
226226 0.939217 1.30319i 0.0624758 0.0866870i
227227 8.79143i 0.583508i 0.956493 + 0.291754i 0.0942388π0.0942388\pi
−0.956493 + 0.291754i 0.905761π0.905761\pi
228228 −11.0813 + 3.69463i −0.733875 + 0.244683i
229229 17.0838i 1.12893i 0.825457 + 0.564466i 0.190918π0.190918\pi
−0.825457 + 0.564466i 0.809082π0.809082\pi
230230 −0.842528 + 1.06836i −0.0555546 + 0.0704454i
231231 0 0
232232 −0.399362 + 1.27894i −0.0262194 + 0.0839666i
233233 14.1823i 0.929114i −0.885543 0.464557i 0.846214π-0.846214\pi
0.885543 0.464557i 0.153786π-0.153786\pi
234234 −1.71104 1.23315i −0.111854 0.0806138i
235235 10.0282 + 0.434242i 0.654164 + 0.0283269i
236236 −1.98381 5.95001i −0.129135 0.387313i
237237 9.45115 0.613918
238238 0 0
239239 13.6734i 0.884456i 0.896903 + 0.442228i 0.145812π0.145812\pi
−0.896903 + 0.442228i 0.854188π0.854188\pi
240240 11.2426 7.69755i 0.725707 0.496875i
241241 3.35937i 0.216396i 0.994129 + 0.108198i 0.0345080π0.0345080\pi
−0.994129 + 0.108198i 0.965492π0.965492\pi
242242 11.2420 + 8.10220i 0.722666 + 0.520829i
243243 6.91288i 0.443461i
244244 −10.8368 + 3.61313i −0.693758 + 0.231307i
245245 0 0
246246 2.54876 + 1.83690i 0.162503 + 0.117117i
247247 8.41607 0.535502
248248 6.40539 20.5130i 0.406742 1.30258i
249249 −11.7293 −0.743315
250250 −10.8275 + 11.5224i −0.684788 + 0.728742i
251251 26.2007 1.65377 0.826887 0.562368i 0.190110π-0.190110\pi
0.826887 + 0.562368i 0.190110π0.190110\pi
252252 0 0
253253 1.96223i 0.123364i
254254 9.56243 + 6.89170i 0.600000 + 0.432423i
255255 −21.1744 0.916899i −1.32599 0.0574184i
256256 4.47565 15.3613i 0.279728 0.960079i
257257 22.2810 1.38985 0.694926 0.719081i 0.255437π-0.255437\pi
0.694926 + 0.719081i 0.255437π0.255437\pi
258258 −10.8104 + 14.9997i −0.673023 + 0.933839i
259259 0 0
260260 −9.43857 + 2.69925i −0.585355 + 0.167400i
261261 −0.321833 −0.0199209
262262 6.51898 + 4.69827i 0.402744 + 0.290260i
263263 13.7838 0.849944 0.424972 0.905207i 0.360284π-0.360284\pi
0.424972 + 0.905207i 0.360284π0.360284\pi
264264 −5.85702 + 18.7569i −0.360475 + 1.15441i
265265 −20.6399 0.893757i −1.26790 0.0549031i
266266 0 0
267267 14.2042 0.869285
268268 −9.45463 28.3572i −0.577534 1.73219i
269269 5.86157i 0.357386i −0.983905 0.178693i 0.942813π-0.942813\pi
0.983905 0.178693i 0.0571869π-0.0571869\pi
270270 13.9175 + 10.9756i 0.846994 + 0.667956i
271271 17.3982 1.05687 0.528433 0.848975i 0.322780π-0.322780\pi
0.528433 + 0.848975i 0.322780π0.322780\pi
272272 −19.9083 + 14.9357i −1.20712 + 0.905607i
273273 0 0
274274 12.2249 16.9624i 0.738532 1.02473i
275275 1.97113 22.7174i 0.118864 1.36991i
276276 1.24358 0.414624i 0.0748547 0.0249574i
277277 4.01044i 0.240964i 0.992716 + 0.120482i 0.0384440π0.0384440\pi
−0.992716 + 0.120482i 0.961556π0.961556\pi
278278 1.27765 + 0.920811i 0.0766285 + 0.0552266i
279279 5.16189 0.309034
280280 0 0
281281 −11.7101 −0.698566 −0.349283 0.937017i 0.613575π-0.613575\pi
−0.349283 + 0.937017i 0.613575π0.613575\pi
282282 −7.84549 5.65429i −0.467192 0.336708i
283283 17.6039i 1.04644i −0.852197 0.523221i 0.824730π-0.824730\pi
0.852197 0.523221i 0.175270π-0.175270\pi
284284 8.68593 2.89599i 0.515415 0.171846i
285285 −13.0475 0.564986i −0.772866 0.0334669i
286286 8.27779 11.4857i 0.489476 0.679162i
287287 0 0
288288 3.84252 0.0736129i 0.226423 0.00433768i
289289 21.7135 1.27726
290290 −0.927602 + 1.17624i −0.0544706 + 0.0690709i
291291 13.7906i 0.808420i
292292 −7.76281 23.2829i −0.454284 1.36253i
293293 −23.5436 −1.37543 −0.687715 0.725980i 0.741386π-0.741386\pi
−0.687715 + 0.725980i 0.741386π0.741386\pi
294294 0 0
295295 0.303366 7.00576i 0.0176626 0.407891i
296296 −22.7951 7.11801i −1.32494 0.413726i
297297 −25.5620 −1.48326
298298 −7.89124 5.68726i −0.457127 0.329454i
299299 −0.944481 −0.0546208
300300 14.8139 3.55103i 0.855279 0.205019i
301301 0 0
302302 −17.5609 + 24.3663i −1.01052 + 1.40212i
303303 −12.1838 −0.699941
304304 −12.2674 + 9.20324i −0.703582 + 0.527842i
305305 −12.7597 0.552524i −0.730618 0.0316375i
306306 −4.84986 3.49532i −0.277248 0.199814i
307307 11.0383i 0.629989i 0.949093 + 0.314995i 0.102003π0.102003\pi
−0.949093 + 0.314995i 0.897997π0.897997\pi
308308 0 0
309309 19.0445 1.08340
310310 14.8778 18.8657i 0.845005 1.07150i
311311 21.6665 1.22859 0.614297 0.789075i 0.289440π-0.289440\pi
0.614297 + 0.789075i 0.289440π0.289440\pi
312312 9.02826 + 2.81916i 0.511124 + 0.159604i
313313 −3.82369 −0.216128 −0.108064 0.994144i 0.534465π-0.534465\pi
−0.108064 + 0.994144i 0.534465π0.534465\pi
314314 −2.67025 1.92446i −0.150691 0.108604i
315315 0 0
316316 11.7713 3.92469i 0.662188 0.220781i
317317 8.73885i 0.490823i −0.969419 0.245411i 0.921077π-0.921077\pi
0.969419 0.245411i 0.0789230π-0.0789230\pi
318318 16.1476 + 11.6376i 0.905511 + 0.652607i
319319 2.16036i 0.120957i
320320 10.8061 14.2558i 0.604077 0.796926i
321321 22.0380i 1.23004i
322322 0 0
323323 23.8550 1.32733
324324 −4.11199 12.3331i −0.228444 0.685170i
325325 −10.9346 0.948767i −0.606543 0.0526281i
326326 3.51857 + 2.53585i 0.194876 + 0.140448i
327327 27.8716i 1.54130i
328328 3.93725 + 1.22944i 0.217398 + 0.0678847i
329329 0 0
330330 −13.6042 + 17.2506i −0.748884 + 0.949614i
331331 9.68144i 0.532140i 0.963954 + 0.266070i 0.0857252π0.0857252\pi
−0.963954 + 0.266070i 0.914275π0.914275\pi
332332 −14.6087 + 4.87073i −0.801758 + 0.267316i
333333 5.73617i 0.314340i
334334 10.7849 14.9643i 0.590121 0.818810i
335335 1.44581 33.3888i 0.0789932 1.82422i
336336 0 0
337337 9.54187i 0.519779i −0.965638 0.259889i 0.916314π-0.916314\pi
0.965638 0.259889i 0.0836861π-0.0836861\pi
338338 9.38648 + 6.76489i 0.510557 + 0.367961i
339339 −1.73034 −0.0939793
340340 −26.7532 + 7.65090i −1.45090 + 0.414928i
341341 34.6502i 1.87641i
342342 −2.98844 2.15379i −0.161597 0.116464i
343343 0 0
344344 −7.23540 + 23.1711i −0.390106 + 1.24930i
345345 1.46423 + 0.0634048i 0.0788317 + 0.00341360i
346346 12.6894 + 9.14533i 0.682187 + 0.491656i
347347 −24.1787 −1.29798 −0.648991 0.760796i 0.724809π-0.724809\pi
−0.648991 + 0.760796i 0.724809π0.724809\pi
348348 1.36915 0.456491i 0.0733941 0.0244705i
349349 8.31416i 0.445047i −0.974927 0.222523i 0.928571π-0.928571\pi
0.974927 0.222523i 0.0714294π-0.0714294\pi
350350 0 0
351351 12.3038i 0.656727i
352352 0.494141 + 25.7937i 0.0263378 + 1.37481i
353353 10.5285 0.560377 0.280189 0.959945i 0.409603π-0.409603\pi
0.280189 + 0.959945i 0.409603π0.409603\pi
354354 −3.95014 + 5.48093i −0.209947 + 0.291308i
355355 10.2271 + 0.442858i 0.542799 + 0.0235045i
356356 17.6912 5.89847i 0.937633 0.312618i
357357 0 0
358358 −18.2282 + 25.2922i −0.963391 + 1.33673i
359359 11.1046i 0.586080i 0.956100 + 0.293040i 0.0946669π0.0946669\pi
−0.956100 + 0.293040i 0.905333π0.905333\pi
360360 4.04230 + 1.45699i 0.213048 + 0.0767901i
361361 −4.30076 −0.226356
362362 −2.06686 + 2.86783i −0.108632 + 0.150730i
363363 14.9269i 0.783459i
364364 0 0
365365 1.18710 27.4142i 0.0621355 1.43492i
366366 9.98250 + 7.19444i 0.521794 + 0.376060i
367367 23.3837i 1.22062i −0.792164 0.610309i 0.791045π-0.791045\pi
0.792164 0.610309i 0.208955π-0.208955\pi
368368 1.37669 1.03282i 0.0717648 0.0538395i
369369 0.990769i 0.0515774i
370370 −20.9646 16.5331i −1.08990 0.859513i
371371 0 0
372372 −21.9598 + 7.32168i −1.13857 + 0.379611i
373373 8.59223i 0.444889i 0.974945 + 0.222444i 0.0714035π0.0714035\pi
−0.974945 + 0.222444i 0.928596π0.928596\pi
374374 23.4630 32.5556i 1.21324 1.68341i
375375 16.8883 + 2.20494i 0.872107 + 0.113863i
376376 −12.1195 3.78443i −0.625015 0.195167i
377377 −1.03985 −0.0535550
378378 0 0
379379 5.57279i 0.286255i −0.989704 0.143128i 0.954284π-0.954284\pi
0.989704 0.143128i 0.0457159π-0.0457159\pi
380380 −16.4851 + 4.71443i −0.845669 + 0.241845i
381381 12.6967i 0.650474i
382382 6.41701 8.90380i 0.328323 0.455558i
383383 12.2341i 0.625135i −0.949896 0.312567i 0.898811π-0.898811\pi
0.949896 0.312567i 0.101189π-0.101189\pi
384384 −16.2426 + 5.76344i −0.828874 + 0.294114i
385385 0 0
386386 −4.99190 + 6.92640i −0.254081 + 0.352545i
387387 −5.83077 −0.296395
388388 5.72671 + 17.1761i 0.290730 + 0.871983i
389389 −3.98430 −0.202012 −0.101006 0.994886i 0.532206π-0.532206\pi
−0.101006 + 0.994886i 0.532206π0.532206\pi
390390 8.30324 + 6.54810i 0.420451 + 0.331576i
391391 −2.67709 −0.135386
392392 0 0
393393 8.65574i 0.436624i
394394 −8.05753 + 11.1801i −0.405932 + 0.563243i
395395 13.8600 + 0.600168i 0.697370 + 0.0301978i
396396 −5.87869 + 1.96002i −0.295415 + 0.0984949i
397397 39.7805 1.99653 0.998263 0.0589121i 0.0187632π-0.0187632\pi
0.998263 + 0.0589121i 0.0187632π0.0187632\pi
398398 19.7950 + 14.2663i 0.992231 + 0.715107i
399399 0 0
400400 16.9759 10.5744i 0.848796 0.528720i
401401 0.431925 0.0215693 0.0107847 0.999942i 0.496567π-0.496567\pi
0.0107847 + 0.999942i 0.496567π0.496567\pi
402402 −18.8260 + 26.1216i −0.938955 + 1.30283i
403403 16.6782 0.830800
404404 −15.1748 + 5.05946i −0.754975 + 0.251718i
405405 0.628810 14.5214i 0.0312458 0.721573i
406406 0 0
407407 38.5052 1.90863
408408 25.5902 + 7.99079i 1.26690 + 0.395603i
409409 18.3685i 0.908263i 0.890935 + 0.454132i 0.150050π0.150050\pi
−0.890935 + 0.454132i 0.849950π0.849950\pi
410410 3.62107 + 2.85564i 0.178832 + 0.141030i
411411 −22.5222 −1.11094
412412 23.7197 7.90844i 1.16859 0.389621i
413413 0 0
414414 0.335374 + 0.241706i 0.0164827 + 0.0118792i
415415 −17.2008 0.744837i −0.844356 0.0365626i
416416 12.4153 0.237845i 0.608710 0.0116613i
417417 1.69643i 0.0830747i
418418 14.4577 20.0605i 0.707151 0.981192i
419419 −23.3512 −1.14078 −0.570389 0.821375i 0.693208π-0.693208\pi
−0.570389 + 0.821375i 0.693208π0.693208\pi
420420 0 0
421421 35.7600 1.74283 0.871417 0.490543i 0.163201π-0.163201\pi
0.871417 + 0.490543i 0.163201π0.163201\pi
422422 −22.1722 + 30.7645i −1.07932 + 1.49759i
423423 3.04975i 0.148284i
424424 24.9443 + 7.78911i 1.21140 + 0.378273i
425425 −30.9936 2.68924i −1.50341 0.130447i
426426 −8.00116 5.76648i −0.387657 0.279387i
427427 0 0
428428 9.15152 + 27.4481i 0.442355 + 1.32675i
429429 −15.2504 −0.736295
430430 −16.8057 + 21.3103i −0.810444 + 1.02767i
431431 14.6244i 0.704430i 0.935919 + 0.352215i 0.114571π0.114571\pi
−0.935919 + 0.352215i 0.885429π0.885429\pi
432432 −13.4546 17.9342i −0.647334 0.862857i
433433 −2.12837 −0.102283 −0.0511414 0.998691i 0.516286π-0.516286\pi
−0.0511414 + 0.998691i 0.516286π0.516286\pi
434434 0 0
435435 1.61208 + 0.0698070i 0.0772936 + 0.00334699i
436436 11.5740 + 34.7138i 0.554294 + 1.66249i
437437 −1.64960 −0.0789111
438438 −15.4572 + 21.4474i −0.738575 + 1.02480i
439439 24.6770 1.17777 0.588884 0.808217i 0.299567π-0.299567\pi
0.588884 + 0.808217i 0.299567π0.299567\pi
440440 −9.78033 + 27.1347i −0.466259 + 1.29360i
441441 0 0
442442 −15.6700 11.2935i −0.745347 0.537175i
443443 16.1404 0.766855 0.383427 0.923571i 0.374744π-0.374744\pi
0.383427 + 0.923571i 0.374744π0.374744\pi
444444 8.13624 + 24.4030i 0.386129 + 1.15811i
445445 20.8303 + 0.902000i 0.987450 + 0.0427589i
446446 −14.5573 + 20.1987i −0.689307 + 0.956434i
447447 10.4778i 0.495582i
448448 0 0
449449 −28.5162 −1.34576 −0.672882 0.739750i 0.734944π-0.734944\pi
−0.672882 + 0.739750i 0.734944π0.734944\pi
450450 3.63994 + 3.13521i 0.171589 + 0.147795i
451451 −6.65073 −0.313171
452452 −2.15512 + 0.718544i −0.101369 + 0.0337975i
453453 32.3530 1.52007
454454 7.26932 10.0864i 0.341166 0.473378i
455455 0 0
456456 15.7685 + 4.92386i 0.738427 + 0.230581i
457457 23.3827i 1.09380i 0.837199 + 0.546899i 0.184192π0.184192\pi
−0.837199 + 0.546899i 0.815808π0.815808\pi
458458 14.1260 19.6003i 0.660065 0.915860i
459459 34.8745i 1.62780i
460460 1.85002 0.529070i 0.0862576 0.0246680i
461461 9.92550i 0.462277i −0.972921 0.231138i 0.925755π-0.925755\pi
0.972921 0.231138i 0.0742450π-0.0742450\pi
462462 0 0
463463 16.8887 0.784887 0.392443 0.919776i 0.371630π-0.371630\pi
0.392443 + 0.919776i 0.371630π0.371630\pi
464464 1.51570 1.13711i 0.0703645 0.0527890i
465465 −25.8563 1.11964i −1.19906 0.0519220i
466466 −11.7269 + 16.2714i −0.543236 + 0.753756i
467467 30.7573i 1.42328i 0.702546 + 0.711638i 0.252046π0.252046\pi
−0.702546 + 0.711638i 0.747954π0.747954\pi
468468 0.943420 + 2.82959i 0.0436096 + 0.130798i
469469 0 0
470470 −11.1462 8.79013i −0.514137 0.405458i
471471 3.54548i 0.163367i
472472 −2.64384 + 8.46678i −0.121692 + 0.389715i
473473 39.1402i 1.79967i
474474 −10.8433 7.81482i −0.498049 0.358946i
475475 −19.0980 1.65709i −0.876278 0.0760324i
476476 0 0
477477 6.27698i 0.287403i
478478 11.3060 15.6874i 0.517125 0.717526i
479479 15.7534 0.719792 0.359896 0.932992i 0.382812π-0.382812\pi
0.359896 + 0.932992i 0.382812π0.382812\pi
480480 −19.2635 0.464729i −0.879253 0.0212119i
481481 18.5337i 0.845065i
482482 2.77774 3.85420i 0.126523 0.175554i
483483 0 0
484484 −6.19856 18.5913i −0.281753 0.845059i
485485 −0.875734 + 20.2237i −0.0397650 + 0.918312i
486486 5.71601 7.93114i 0.259284 0.359764i
487487 13.5048 0.611963 0.305981 0.952038i 0.401015π-0.401015\pi
0.305981 + 0.952038i 0.401015π0.401015\pi
488488 15.4207 + 4.81526i 0.698061 + 0.217977i
489489 4.67187i 0.211269i
490490 0 0
491491 3.87067i 0.174681i −0.996179 0.0873404i 0.972163π-0.972163\pi
0.996179 0.0873404i 0.0278368π-0.0278368\pi
492492 −1.40532 4.21496i −0.0633566 0.190025i
493493 −2.94741 −0.132745
494494 −9.65574 6.95895i −0.434432 0.313098i
495495 −6.92178 0.299729i −0.311111 0.0134718i
496496 −24.3104 + 18.2381i −1.09157 + 0.818917i
497497 0 0
498498 13.4570 + 9.69855i 0.603024 + 0.434602i
499499 24.3694i 1.09092i 0.838136 + 0.545462i 0.183646π0.183646\pi
−0.838136 + 0.545462i 0.816354π0.816354\pi
500500 21.9498 4.26682i 0.981625 0.190818i
501501 −19.8692 −0.887691
502502 −30.0600 21.6644i −1.34165 0.966931i
503503 11.2245i 0.500475i −0.968184 0.250238i 0.919491π-0.919491\pi
0.968184 0.250238i 0.0805087π-0.0805087\pi
504504 0 0
505505 −17.8674 0.773699i −0.795087 0.0344291i
506506 −1.62250 + 2.25126i −0.0721288 + 0.100081i
507507 12.4631i 0.553507i
508508 −5.27247 15.8137i −0.233928 0.701618i
509509 14.3783i 0.637308i −0.947871 0.318654i 0.896769π-0.896769\pi
0.947871 0.318654i 0.103231π-0.103231\pi
510510 23.5352 + 18.5603i 1.04215 + 0.821863i
511511 0 0
512512 −17.8366 + 13.9232i −0.788274 + 0.615325i
513513 21.4894i 0.948781i
514514 −25.5630 18.4234i −1.12754 0.812621i
515515 27.9284 + 1.20937i 1.23067 + 0.0532911i
516516 24.8054 8.27042i 1.09200 0.364085i
517517 20.4720 0.900359
518518 0 0
519519 16.8487i 0.739575i
520520 13.0608 + 4.70757i 0.572753 + 0.206441i
521521 25.8122i 1.13085i 0.824799 + 0.565426i 0.191288π0.191288\pi
−0.824799 + 0.565426i 0.808712π0.808712\pi
522522 0.369238 + 0.266112i 0.0161611 + 0.0116474i
523523 4.42548i 0.193513i −0.995308 0.0967563i 0.969153π-0.969153\pi
0.995308 0.0967563i 0.0308468π-0.0308468\pi
524524 −3.59439 10.7806i −0.157022 0.470954i
525525 0 0
526526 −15.8141 11.3973i −0.689528 0.496946i
527527 47.2736 2.05927
528528 22.2291 16.6768i 0.967400 0.725764i
529529 −22.8149 −0.991951
530530 22.9412 + 18.0918i 0.996500 + 0.785859i
531531 −2.13058 −0.0924593
532532 0 0
533533 3.20120i 0.138659i
534534 −16.2965 11.7450i −0.705219 0.508255i
535535 −1.39946 + 32.3184i −0.0605039 + 1.39724i
536536 −12.6003 + 40.3519i −0.544249 + 1.74294i
537537 33.5823 1.44918
538538 −4.84672 + 6.72497i −0.208957 + 0.289934i
539539 0 0
540540 −6.89221 24.1002i −0.296593 1.03711i
541541 4.10160 0.176342 0.0881708 0.996105i 0.471898π-0.471898\pi
0.0881708 + 0.996105i 0.471898π0.471898\pi
542542 −19.9610 14.3860i −0.857396 0.617930i
543543 3.80784 0.163410
544544 35.1906 0.674161i 1.50878 0.0289044i
545545 −1.76991 + 40.8733i −0.0758146 + 1.75082i
546546 0 0
547547 4.16833 0.178225 0.0891125 0.996022i 0.471597π-0.471597\pi
0.0891125 + 0.996022i 0.471597π0.471597\pi
548548 −28.0512 + 9.35259i −1.19829 + 0.399523i
549549 3.88046i 0.165614i
550550 −21.0457 + 24.4338i −0.897393 + 1.04186i
551551 −1.81617 −0.0773714
552552 −1.76959 0.552574i −0.0753190 0.0235191i
553553 0 0
554554 3.31609 4.60117i 0.140887 0.195485i
555555 −1.24420 + 28.7329i −0.0528135 + 1.21964i
556556 −0.704463 2.11289i −0.0298759 0.0896065i
557557 12.1574i 0.515124i 0.966262 + 0.257562i 0.0829192π0.0829192\pi
−0.966262 + 0.257562i 0.917081π0.917081\pi
558558 −5.92223 4.26818i −0.250708 0.180687i
559559 −18.8394 −0.796820
560560 0 0
561561 −43.2265 −1.82502
562562 13.4350 + 9.68267i 0.566721 + 0.408439i
563563 24.9027i 1.04952i 0.851249 + 0.524762i 0.175846π0.175846\pi
−0.851249 + 0.524762i 0.824154π0.824154\pi
564564 4.32579 + 12.9743i 0.182149 + 0.546317i
565565 −2.53752 0.109881i −0.106754 0.00462271i
566566 −14.5560 + 20.1969i −0.611835 + 0.848939i
567567 0 0
568568 −12.3600 3.85952i −0.518612 0.161942i
569569 −29.5875 −1.24037 −0.620187 0.784454i 0.712943π-0.712943\pi
−0.620187 + 0.784454i 0.712943π0.712943\pi
570570 14.5022 + 11.4367i 0.607430 + 0.479031i
571571 24.5175i 1.02603i −0.858381 0.513013i 0.828529π-0.828529\pi
0.858381 0.513013i 0.171471π-0.171471\pi
572572 −18.9942 + 6.33289i −0.794187 + 0.264791i
573573 −11.8222 −0.493881
574574 0 0
575575 2.14325 + 0.185964i 0.0893797 + 0.00775524i
576576 −4.46939 3.09279i −0.186225 0.128866i
577577 13.5476 0.563993 0.281997 0.959415i 0.409003π-0.409003\pi
0.281997 + 0.959415i 0.409003π0.409003\pi
578578 −24.9119 17.9541i −1.03620 0.746793i
579579 9.19670 0.382202
580580 2.03682 0.582492i 0.0845745 0.0241867i
581581 0 0
582582 11.4030 15.8220i 0.472668 0.655841i
583583 −42.1355 −1.74507
584584 −10.3456 + 33.1313i −0.428103 + 1.37098i
585585 −0.144269 + 3.33166i −0.00596478 + 0.137747i
586586 27.0115 + 19.4674i 1.11584 + 0.804189i
587587 26.8772i 1.10934i −0.832070 0.554671i 0.812844π-0.812844\pi
0.832070 0.554671i 0.187156π-0.187156\pi
588588 0 0
589589 29.1296 1.20027
590590 −6.14086 + 7.78686i −0.252815 + 0.320580i
591591 14.8446 0.610625
592592 20.2672 + 27.0150i 0.832977 + 1.11031i
593593 0.947148 0.0388947 0.0194473 0.999811i 0.493809π-0.493809\pi
0.0194473 + 0.999811i 0.493809π0.493809\pi
594594 29.3273 + 21.1363i 1.20331 + 0.867234i
595595 0 0
596596 4.35102 + 13.0500i 0.178225 + 0.534548i
597597 26.2832i 1.07570i
598598 1.08360 + 0.780958i 0.0443118 + 0.0319357i
599599 22.0707i 0.901786i 0.892578 + 0.450893i 0.148894π0.148894\pi
−0.892578 + 0.450893i 0.851106π0.851106\pi
600600 −19.9322 8.17497i −0.813727 0.333742i
601601 20.5283i 0.837367i −0.908132 0.418684i 0.862492π-0.862492\pi
0.908132 0.418684i 0.137508π-0.137508\pi
602602 0 0
603603 −10.1542 −0.413509
604604 40.2953 13.4349i 1.63959 0.546660i
605605 0.947891 21.8901i 0.0385372 0.889957i
606606 13.9785 + 10.0744i 0.567837 + 0.409243i
607607 25.0474i 1.01664i 0.861168 + 0.508321i 0.169734π0.169734\pi
−0.861168 + 0.508321i 0.830266π0.830266\pi
608608 21.6842 0.415413i 0.879409 0.0168472i
609609 0 0
610610 14.1823 + 11.1844i 0.574225 + 0.452845i
611611 9.85381i 0.398643i
612612 2.67408 + 8.02035i 0.108093 + 0.324203i
613613 23.4199i 0.945921i −0.881084 0.472961i 0.843185π-0.843185\pi
0.881084 0.472961i 0.156815π-0.156815\pi
614614 9.12718 12.6642i 0.368343 0.511087i
615615 0.214903 4.96284i 0.00866571 0.200121i
616616 0 0
617617 16.7405i 0.673948i −0.941514 0.336974i 0.890597π-0.890597\pi
0.941514 0.336974i 0.109403π-0.109403\pi
618618 −21.8497 15.7472i −0.878925 0.633446i
619619 27.3839 1.10065 0.550326 0.834950i 0.314504π-0.314504\pi
0.550326 + 0.834950i 0.314504π0.314504\pi
620620 −32.6687 + 9.34262i −1.31201 + 0.375209i
621621 2.41162i 0.0967749i
622622 −24.8579 17.9153i −0.996712 0.718336i
623623 0 0
624624 −8.02704 10.6996i −0.321339 0.428326i
625625 24.6264 + 4.30595i 0.985055 + 0.172238i
626626 4.38691 + 3.16167i 0.175336 + 0.126366i
627627 −26.6358 −1.06373
628628 1.47230 + 4.41586i 0.0587512 + 0.176212i
629629 52.5330i 2.09463i
630630 0 0
631631 3.77099i 0.150121i 0.997179 + 0.0750604i 0.0239150π0.0239150\pi
−0.997179 + 0.0750604i 0.976085π0.976085\pi
632632 −16.7504 5.23048i −0.666295 0.208057i
633633 40.8483 1.62358
634634 −7.22585 + 10.0261i −0.286975 + 0.398186i
635635 0.806271 18.6196i 0.0319959 0.738896i
636636 −8.90334 26.7037i −0.353040 1.05887i
637637 0 0
638638 −1.78633 + 2.47858i −0.0707214 + 0.0981281i
639639 3.11026i 0.123040i
640640 −24.1854 + 7.42056i −0.956013 + 0.293323i
641641 25.1167 0.992051 0.496026 0.868308i 0.334792π-0.334792\pi
0.496026 + 0.868308i 0.334792π0.334792\pi
642642 18.2224 25.2842i 0.719182 0.997886i
643643 12.8390i 0.506319i 0.967424 + 0.253160i 0.0814698π0.0814698\pi
−0.967424 + 0.253160i 0.918530π0.918530\pi
644644 0 0
645645 29.2068 + 1.26472i 1.15002 + 0.0497984i
646646 −27.3688 19.7248i −1.07681 0.776063i
647647 4.44061i 0.174578i 0.996183 + 0.0872892i 0.0278204π0.0278204\pi
−0.996183 + 0.0872892i 0.972180π0.972180\pi
648648 −5.48009 + 17.5498i −0.215278 + 0.689420i
649649 14.3019i 0.561400i
650650 11.7608 + 10.1300i 0.461295 + 0.397330i
651651 0 0
652652 −1.94005 5.81877i −0.0759781 0.227880i
653653 37.9879i 1.48658i −0.668968 0.743291i 0.733264π-0.733264\pi
0.668968 0.743291i 0.266736π-0.266736\pi
654654 23.0461 31.9771i 0.901172 1.25040i
655655 0.549658 12.6935i 0.0214769 0.495976i
656656 −3.50061 4.66611i −0.136676 0.182181i
657657 −8.33715 −0.325263
658658 0 0
659659 19.5420i 0.761248i 0.924730 + 0.380624i 0.124291π0.124291\pi
−0.924730 + 0.380624i 0.875709π0.875709\pi
660660 29.8719 8.54280i 1.16276 0.332528i
661661 22.8705i 0.889560i −0.895640 0.444780i 0.853282π-0.853282\pi
0.895640 0.444780i 0.146718π-0.146718\pi
662662 8.00524 11.1075i 0.311132 0.431705i
663663 20.8062i 0.808048i
664664 20.7880 + 6.49127i 0.806731 + 0.251910i
665665 0 0
666666 −4.74304 + 6.58110i −0.183789 + 0.255013i
667667 0.203817 0.00789183
668668 −24.7469 + 8.25092i −0.957487 + 0.319238i
669669 26.8193 1.03689
670670 −29.2668 + 37.1114i −1.13068 + 1.43374i
671671 −26.0483 −1.00559
672672 0 0
673673 23.0022i 0.886670i 0.896356 + 0.443335i 0.146205π0.146205\pi
−0.896356 + 0.443335i 0.853795π0.853795\pi
674674 −7.88983 + 10.9474i −0.303905 + 0.421677i
675675 2.42256 27.9202i 0.0932444 1.07465i
676676 −5.17545 15.5227i −0.199056 0.597027i
677677 −40.7663 −1.56678 −0.783388 0.621533i 0.786510π-0.786510\pi
−0.783388 + 0.621533i 0.786510π0.786510\pi
678678 1.98522 + 1.43076i 0.0762419 + 0.0549480i
679679 0 0
680680 37.0202 + 13.3434i 1.41966 + 0.511696i
681681 −13.3925 −0.513200
682682 28.6510 39.7541i 1.09710 1.52226i
683683 10.9004 0.417092 0.208546 0.978013i 0.433127π-0.433127\pi
0.208546 + 0.978013i 0.433127π0.433127\pi
684684 1.64775 + 4.94208i 0.0630032 + 0.188965i
685685 −33.0284 1.43021i −1.26195 0.0546455i
686686 0 0
687687 −26.0247 −0.992905
688688 27.4605 20.6014i 1.04692 0.785423i
689689 20.2811i 0.772649i
690690 −1.62749 1.28347i −0.0619574 0.0488608i
691691 16.0135 0.609183 0.304591 0.952483i 0.401480π-0.401480\pi
0.304591 + 0.952483i 0.401480π0.401480\pi
692692 −6.99660 20.9849i −0.265971 0.797724i
693693 0 0
694694 27.7402 + 19.9925i 1.05301 + 0.758907i
695695 0.107727 2.48779i 0.00408633 0.0943674i
696696 −1.94828 0.608370i −0.0738493 0.0230602i
697697 9.07366i 0.343689i
698698 −6.87468 + 9.53882i −0.260211 + 0.361050i
699699 21.6047 0.817164
700700 0 0
701701 22.0640 0.833346 0.416673 0.909057i 0.363196π-0.363196\pi
0.416673 + 0.909057i 0.363196π0.363196\pi
702702 10.1736 14.1161i 0.383976 0.532779i
703703 32.3704i 1.22087i
704704 20.7610 30.0017i 0.782458 1.13073i
705705 −0.661505 + 15.2764i −0.0249137 + 0.575343i
706706 −12.0794 8.70567i −0.454613 0.327642i
707707 0 0
708708 9.06398 3.02204i 0.340645 0.113575i
709709 −37.1908 −1.39673 −0.698364 0.715743i 0.746088π-0.746088\pi
−0.698364 + 0.715743i 0.746088π0.746088\pi
710710 −11.3674 8.96454i −0.426610 0.336433i
711711 4.21507i 0.158077i
712712 −25.1744 7.86095i −0.943449 0.294601i
713713 −3.26903 −0.122426
714714 0 0
715715 −22.3644 0.968433i −0.836383 0.0362173i
716716 41.8264 13.9454i 1.56313 0.521165i
717717 −20.8294 −0.777887
718718 9.18203 12.7403i 0.342670 0.475465i
719719 −36.3717 −1.35644 −0.678218 0.734861i 0.737247π-0.737247\pi
−0.678218 + 0.734861i 0.737247π0.737247\pi
720720 −3.43299 5.01404i −0.127940 0.186862i
721721 0 0
722722 4.93425 + 3.55614i 0.183634 + 0.132346i
723723 −5.11751 −0.190322
724724 4.74262 1.58125i 0.176258 0.0587666i
725725 2.35966 + 0.204742i 0.0876357 + 0.00760392i
726726 −12.3425 + 17.1256i −0.458074 + 0.635591i
727727 34.1872i 1.26793i 0.773360 + 0.633967i 0.218575π0.218575\pi
−0.773360 + 0.633967i 0.781425π0.781425\pi
728728 0 0
729729 −30.0315 −1.11228
730730 −24.0298 + 30.4707i −0.889381 + 1.12777i
731731 −53.3993 −1.97505
732732 −5.50408 16.5084i −0.203437 0.610166i
733733 −22.5349 −0.832345 −0.416172 0.909286i 0.636629π-0.636629\pi
−0.416172 + 0.909286i 0.636629π0.636629\pi
734734 −19.3351 + 26.8281i −0.713673 + 0.990242i
735735 0 0
736736 −2.43348 + 0.0466191i −0.0896991 + 0.00171840i
737737 68.1618i 2.51077i
738738 0.819232 1.13671i 0.0301563 0.0418428i
739739 7.02861i 0.258552i 0.991609 + 0.129276i 0.0412652π0.0412652\pi
−0.991609 + 0.129276i 0.958735π0.958735\pi
740740 10.3820 + 36.3032i 0.381651 + 1.33453i
741741 12.8206i 0.470978i
742742 0 0
743743 0.0257779 0.000945701 0.000472850 1.00000i 0.499849π-0.499849\pi
0.000472850 1.00000i 0.499849π0.499849\pi
744744 31.2485 + 9.75767i 1.14563 + 0.357734i
745745 −0.665363 + 15.3655i −0.0243770 + 0.562949i
746746 7.10461 9.85785i 0.260118 0.360922i
747747 5.23110i 0.191396i
748748 −53.8382 + 17.9503i −1.96852 + 0.656328i
749749 0 0
750750 −17.5527 16.4940i −0.640935 0.602277i
751751 10.3551i 0.377865i −0.981990 0.188932i 0.939497π-0.939497\pi
0.981990 0.188932i 0.0605027π-0.0605027\pi
752752 10.7755 + 14.3630i 0.392941 + 0.523766i
753753 39.9129i 1.45451i
754754 1.19302 + 0.859815i 0.0434472 + 0.0313126i
755755 47.4451 + 2.05448i 1.72670 + 0.0747703i
756756 0 0
757757 36.2159i 1.31629i −0.752892 0.658145i 0.771342π-0.771342\pi
0.752892 0.658145i 0.228658π-0.228658\pi
758758 −4.60795 + 6.39366i −0.167368 + 0.232228i
759759 2.98917 0.108500
760760 22.8115 + 8.22210i 0.827462 + 0.298247i
761761 25.8142i 0.935765i −0.883791 0.467883i 0.845017π-0.845017\pi
0.883791 0.467883i 0.154983π-0.154983\pi
762762 −10.4985 + 14.5670i −0.380320 + 0.527706i
763763 0 0
764764 −14.7245 + 4.90931i −0.532713 + 0.177613i
765765 −0.408923 + 9.44345i −0.0147847 + 0.341429i
766766 −10.1160 + 14.0362i −0.365505 + 0.507149i
767767 −6.88396 −0.248566
768768 23.4006 + 6.81800i 0.844398 + 0.246023i
769769 17.9643i 0.647810i 0.946090 + 0.323905i 0.104996π0.104996\pi
−0.946090 + 0.323905i 0.895004π0.895004\pi
770770 0 0
771771 33.9419i 1.22239i
772772 11.4544 3.81903i 0.412253 0.137450i
773773 4.26473 0.153392 0.0766958 0.997055i 0.475563π-0.475563\pi
0.0766958 + 0.997055i 0.475563π0.475563\pi
774774 6.68963 + 4.82125i 0.240454 + 0.173296i
775775 −37.8468 3.28386i −1.35950 0.117960i
776776 7.63204 24.4413i 0.273974 0.877392i
777777 0 0
778778 4.57118 + 3.29448i 0.163885 + 0.118113i
779779 5.59112i 0.200323i
780780 −4.11191 14.3783i −0.147230 0.514825i
781781 20.8782 0.747081
782782 3.07142 + 2.21359i 0.109834 + 0.0791578i
783783 2.65513i 0.0948866i
784784 0 0
785785 −0.225146 + 5.19939i −0.00803580 + 0.185574i
786786 −7.15712 + 9.93072i −0.255286 + 0.354217i
787787 37.6885i 1.34345i 0.740801 + 0.671725i 0.234446π0.234446\pi
−0.740801 + 0.671725i 0.765554π0.765554\pi
788788 18.4888 6.16438i 0.658636 0.219597i
789789 20.9976i 0.747533i
790790 −15.4053 12.1489i −0.548094 0.432238i
791791 0 0
792792 8.36529 + 2.61214i 0.297247 + 0.0928185i
793793 12.5379i 0.445233i
794794 −45.6401 32.8931i −1.61971 1.16733i
795795 1.36151 31.4419i 0.0482877 1.11513i
796796 −10.9144 32.7355i −0.386851 1.16028i
797797 −12.2918 −0.435398 −0.217699 0.976016i 0.569855π-0.569855\pi
−0.217699 + 0.976016i 0.569855π0.569855\pi
798798 0 0
799799 27.9302i 0.988099i
800800 −28.2201 1.90479i −0.997730 0.0673445i
801801 6.33488i 0.223832i
802802 −0.495547 0.357144i −0.0174984 0.0126112i
803803 55.9648i 1.97495i
804804 43.1981 14.4028i 1.52348 0.507946i
805805 0 0
806806 −19.1349 13.7906i −0.673997 0.485754i
807807 8.92924 0.314324
808808 21.5935 + 6.74280i 0.759658 + 0.237211i
809809 −27.1048 −0.952952 −0.476476 0.879187i 0.658086π-0.658086\pi
−0.476476 + 0.879187i 0.658086π0.658086\pi
810810 −12.7287 + 16.1404i −0.447239 + 0.567117i
811811 −41.9273 −1.47227 −0.736133 0.676837i 0.763350π-0.763350\pi
−0.736133 + 0.676837i 0.763350π0.763350\pi
812812 0 0
813813 26.5036i 0.929523i
814814 −44.1769 31.8386i −1.54840 1.11594i
815815 0.296674 6.85122i 0.0103920 0.239988i
816816 −22.7523 30.3274i −0.796489 1.06167i
817817 −32.9043 −1.15117
818818 15.1882 21.0741i 0.531045 0.736840i
819819 0 0
820820 −1.79322 6.27041i −0.0626218 0.218972i
821821 36.4251 1.27125 0.635623 0.771999i 0.280743π-0.280743\pi
0.635623 + 0.771999i 0.280743π0.280743\pi
822822 25.8397 + 18.6228i 0.901263 + 0.649545i
823823 −39.7814 −1.38669 −0.693346 0.720604i 0.743864π-0.743864\pi
−0.693346 + 0.720604i 0.743864π0.743864\pi
824824 −33.7528 10.5397i −1.17584 0.367166i
825825 34.6067 + 3.00273i 1.20485 + 0.104542i
826826 0 0
827827 −1.33392 −0.0463851 −0.0231925 0.999731i 0.507383π-0.507383\pi
−0.0231925 + 0.999731i 0.507383π0.507383\pi
828828 −0.184916 0.554618i −0.00642628 0.0192743i
829829 13.4098i 0.465743i −0.972508 0.232872i 0.925188π-0.925188\pi
0.972508 0.232872i 0.0748122π-0.0748122\pi
830830 19.1186 + 15.0773i 0.663617 + 0.523341i
831831 −6.10931 −0.211930
832832 −14.4407 9.99289i −0.500642 0.346441i
833833 0 0
834834 −1.40272 + 1.94632i −0.0485722 + 0.0673954i
835835 −29.1379 1.26174i −1.00836 0.0436643i
836836 −33.1747 + 11.0608i −1.14737 + 0.382547i
837837 42.5858i 1.47198i
838838 26.7908 + 19.3082i 0.925471 + 0.666992i
839839 14.3910 0.496834 0.248417 0.968653i 0.420090π-0.420090\pi
0.248417 + 0.968653i 0.420090π0.420090\pi
840840 0 0
841841 −28.7756 −0.992262
842842 −41.0274 29.5687i −1.41390 1.01900i
843843 17.8386i 0.614395i
844844 50.8762 16.9627i 1.75123 0.583881i
845845 0.791436 18.2770i 0.0272262 0.628747i
846846 −2.52173 + 3.49897i −0.0866988 + 0.120297i
847847 0 0
848848 −22.1780 29.5620i −0.761597 1.01516i
849849 26.8169 0.920355
850850 33.3353 + 28.7129i 1.14339 + 0.984844i
851851 3.63272i 0.124528i
852852 4.41162 + 13.2317i 0.151140 + 0.453312i
853853 33.2591 1.13877 0.569385 0.822071i 0.307181π-0.307181\pi
0.569385 + 0.822071i 0.307181π0.307181\pi
854854 0 0
855855 −0.251975 + 5.81898i −0.00861738 + 0.199005i
856856 12.1963 39.0582i 0.416862 1.33498i
857857 1.72832 0.0590384 0.0295192 0.999564i 0.490602π-0.490602\pi
0.0295192 + 0.999564i 0.490602π0.490602\pi
858858 17.4967 + 12.6100i 0.597329 + 0.430498i
859859 17.5725 0.599565 0.299783 0.954008i 0.403086π-0.403086\pi
0.299783 + 0.954008i 0.403086π0.403086\pi
860860 36.9019 10.5532i 1.25835 0.359863i
861861 0 0
862862 12.0924 16.7785i 0.411867 0.571478i
863863 41.6307 1.41713 0.708563 0.705648i 0.249344π-0.249344\pi
0.708563 + 0.705648i 0.249344π0.249344\pi
864864 0.607309 + 31.7010i 0.0206611 + 1.07849i
865865 1.06993 24.7083i 0.0363786 0.840108i
866866 2.44187 + 1.75987i 0.0829783 + 0.0598029i
867867 33.0773i 1.12337i
868868 0 0
869869 28.2945 0.959825
870870 −1.79182 1.41307i −0.0607485 0.0479074i
871871 −32.8083 −1.11167
872872 15.4248 49.3973i 0.522349 1.67280i
873873 6.15041 0.208160
874874 1.89259 + 1.36400i 0.0640177 + 0.0461379i
875875 0 0
876876 35.4681 11.8255i 1.19836 0.399547i
877877 44.4208i 1.49998i 0.661448 + 0.749991i 0.269942π0.269942\pi
−0.661448 + 0.749991i 0.730058π0.730058\pi
878878 −28.3119 20.4045i −0.955480 0.688620i
879879 35.8652i 1.20970i
880880 33.6577 23.0446i 1.13460 0.776834i
881881 25.0886i 0.845257i 0.906303 + 0.422628i 0.138892π0.138892\pi
−0.906303 + 0.422628i 0.861108π0.861108\pi
882882 0 0
883883 −7.23066 −0.243331 −0.121666 0.992571i 0.538824π-0.538824\pi
−0.121666 + 0.992571i 0.538824π0.538824\pi
884884 8.64003 + 25.9140i 0.290596 + 0.871581i
885885 10.6722 + 0.462133i 0.358744 + 0.0155344i
886886 −18.5179 13.3460i −0.622121 0.448366i
887887 38.2195i 1.28328i −0.767004 0.641642i 0.778253π-0.778253\pi
0.767004 0.641642i 0.221747π-0.221747\pi
888888 10.8433 34.7251i 0.363876 1.16530i
889889 0 0
890890 −23.1527 18.2587i −0.776081 0.612033i
891891 29.6448i 0.993137i
892892 33.4031 11.1370i 1.11842 0.372894i
893893 17.2104i 0.575923i
894894 8.66371 12.0212i 0.289758 0.402048i
895895 49.2479 + 2.13255i 1.64618 + 0.0712833i
896896 0 0
897897 1.43878i 0.0480394i
898898 32.7166 + 23.5791i 1.09177 + 0.786843i
899899 −3.59912 −0.120037
900900 −1.58371 6.60677i −0.0527903 0.220226i
901901 57.4859i 1.91513i
902902 7.63038 + 5.49925i 0.254064 + 0.183105i
903903 0 0
904904 3.06671 + 0.957611i 0.101997 + 0.0318497i
905905 5.58413 + 0.241806i 0.185623 + 0.00803790i
906906 −37.1185 26.7515i −1.23318 0.888760i
907907 −18.4940 −0.614085 −0.307042 0.951696i 0.599339π-0.599339\pi
−0.307042 + 0.951696i 0.599339π0.599339\pi
908908 −16.6802 + 5.56137i −0.553551 + 0.184561i
909909 5.43380i 0.180228i
910910 0 0
911911 14.7738i 0.489477i −0.969589 0.244739i 0.921298π-0.921298\pi
0.969589 0.244739i 0.0787022π-0.0787022\pi
912912 −14.0198 18.6875i −0.464242 0.618806i
913913 −35.1148 −1.16213
914914 19.3343 26.8270i 0.639523 0.887357i
915915 0.841690 19.4375i 0.0278254 0.642585i
916916 −32.4135 + 10.8071i −1.07097 + 0.357075i
917917 0 0
918918 28.8365 40.0115i 0.951746 1.32058i
919919 28.1692i 0.929217i −0.885516 0.464609i 0.846195π-0.846195\pi
0.885516 0.464609i 0.153805π-0.153805\pi
920920 −2.55999 0.922714i −0.0844005 0.0304210i
921921 −16.8152 −0.554081
922922 −8.20704 + 11.3875i −0.270285 + 0.375028i
923923 10.0493i 0.330778i
924924 0 0
925925 −3.64921 + 42.0574i −0.119985 + 1.38284i
926926 −19.3764 13.9647i −0.636749 0.458909i
927927 8.49356i 0.278965i
928928 −2.67919 + 0.0513265i −0.0879489 + 0.00168487i
929929 10.6309i 0.348787i 0.984676 + 0.174394i 0.0557965π0.0557965\pi
−0.984676 + 0.174394i 0.944203π0.944203\pi
930930 28.7391 + 22.6642i 0.942393 + 0.743189i
931931 0 0
932932 26.9084 8.97159i 0.881414 0.293874i
933933 33.0057i 1.08056i
934934 25.4321 35.2878i 0.832163 1.15465i
935935 −63.3910 2.74498i −2.07311 0.0897704i
936936 1.25731 4.02647i 0.0410963 0.131609i
937937 58.4711 1.91017 0.955084 0.296334i 0.0957641π-0.0957641\pi
0.955084 + 0.296334i 0.0957641π0.0957641\pi
938938 0 0
939939 5.82483i 0.190086i
940940 5.51981 + 19.3013i 0.180036 + 0.629540i
941941 44.8301i 1.46142i −0.682688 0.730710i 0.739189π-0.739189\pi
0.682688 0.730710i 0.260811π-0.260811\pi
942942 2.93163 4.06773i 0.0955178 0.132534i
943943 0.627455i 0.0204328i
944944 10.0342 7.52783i 0.326584 0.245010i
945945 0 0
946946 −32.3636 + 44.9055i −1.05223 + 1.46000i
947947 −14.4192 −0.468560 −0.234280 0.972169i 0.575273π-0.575273\pi
−0.234280 + 0.972169i 0.575273π0.575273\pi
948948 5.97870 + 17.9319i 0.194179 + 0.582400i
949949 −26.9376 −0.874430
950950 20.5410 + 17.6927i 0.666437 + 0.574026i
951951 13.3124 0.431683
952952 0 0
953953 3.56629i 0.115523i 0.998330 + 0.0577617i 0.0183964π0.0183964\pi
−0.998330 + 0.0577617i 0.981604π0.981604\pi
954954 5.19022 7.20158i 0.168039 0.233160i
955955 −17.3371 0.750737i −0.561016 0.0242933i
956956 −25.9428 + 8.64962i −0.839049 + 0.279749i
957957 3.29100 0.106383
958958 −18.0739 13.0259i −0.583941 0.420849i
959959 0 0
960960 21.7167 + 16.4615i 0.700903 + 0.531291i
961961 26.7265 0.862144
962962 −15.3249 + 21.2637i −0.494094 + 0.685570i
963963 9.82861 0.316723
964964 −6.37380 + 2.12510i −0.205286 + 0.0684449i
965965 13.4868 + 0.584011i 0.434156 + 0.0188000i
966966 0 0
967967 −17.8167 −0.572946 −0.286473 0.958088i 0.592483π-0.592483\pi
−0.286473 + 0.958088i 0.592483π0.592483\pi
968968 −8.26088 + 26.4551i −0.265515 + 0.850301i
969969 36.3395i 1.16739i
970970 17.7270 22.4785i 0.569180 0.721742i
971971 26.4818 0.849842 0.424921 0.905231i 0.360302π-0.360302\pi
0.424921 + 0.905231i 0.360302π0.360302\pi
972972 −13.1160 + 4.37302i −0.420694 + 0.140265i
973973 0 0
974974 −15.4941 11.1667i −0.496463 0.357803i
975975 1.44531 16.6573i 0.0462869 0.533460i
976976 −13.7106 18.2754i −0.438864 0.584980i
977977 9.22921i 0.295269i 0.989042 + 0.147634i 0.0471659π0.0471659\pi
−0.989042 + 0.147634i 0.952834π0.952834\pi
978978 −3.86300 + 5.36003i −0.123525 + 0.171395i
979979 42.5241 1.35908
980980 0 0
981981 12.4303 0.396870
982982 −3.20052 + 4.44081i −0.102133 + 0.141712i
983983 46.1255i 1.47117i 0.677430 + 0.735587i 0.263094π0.263094\pi
−0.677430 + 0.735587i 0.736906π0.736906\pi
984984 −1.87288 + 5.99782i −0.0597052 + 0.191204i
985985 21.7694 + 0.942664i 0.693629 + 0.0300358i
986986 3.38156 + 2.43711i 0.107691 + 0.0776133i
987987 0 0
988988 5.32392 + 15.9680i 0.169376 + 0.508009i
989989 3.69263 0.117419
990990 7.69351 + 6.06725i 0.244516 + 0.192830i
991991 8.81233i 0.279933i 0.990156 + 0.139966i 0.0446995π0.0446995\pi
−0.990156 + 0.139966i 0.955301π0.955301\pi
992992 42.9717 0.823228i 1.36435 0.0261375i
993993 −14.7483 −0.468022
994994 0 0
995995 1.66904 38.5439i 0.0529122 1.22193i
996996 −7.41984 22.2543i −0.235107 0.705154i
997997 33.9240 1.07438 0.537192 0.843460i 0.319485π-0.319485\pi
0.537192 + 0.843460i 0.319485π0.319485\pi
998998 20.1502 27.9590i 0.637843 0.885026i
999999 47.3236 1.49725
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 980.2.c.e.979.14 yes 48
4.3 odd 2 inner 980.2.c.e.979.33 yes 48
5.4 even 2 inner 980.2.c.e.979.35 yes 48
7.2 even 3 980.2.s.g.619.21 96
7.3 odd 6 980.2.s.g.19.43 96
7.4 even 3 980.2.s.g.19.44 96
7.5 odd 6 980.2.s.g.619.22 96
7.6 odd 2 inner 980.2.c.e.979.13 48
20.19 odd 2 inner 980.2.c.e.979.16 yes 48
28.3 even 6 980.2.s.g.19.28 96
28.11 odd 6 980.2.s.g.19.27 96
28.19 even 6 980.2.s.g.619.5 96
28.23 odd 6 980.2.s.g.619.6 96
28.27 even 2 inner 980.2.c.e.979.34 yes 48
35.4 even 6 980.2.s.g.19.5 96
35.9 even 6 980.2.s.g.619.28 96
35.19 odd 6 980.2.s.g.619.27 96
35.24 odd 6 980.2.s.g.19.6 96
35.34 odd 2 inner 980.2.c.e.979.36 yes 48
140.19 even 6 980.2.s.g.619.44 96
140.39 odd 6 980.2.s.g.19.22 96
140.59 even 6 980.2.s.g.19.21 96
140.79 odd 6 980.2.s.g.619.43 96
140.139 even 2 inner 980.2.c.e.979.15 yes 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
980.2.c.e.979.13 48 7.6 odd 2 inner
980.2.c.e.979.14 yes 48 1.1 even 1 trivial
980.2.c.e.979.15 yes 48 140.139 even 2 inner
980.2.c.e.979.16 yes 48 20.19 odd 2 inner
980.2.c.e.979.33 yes 48 4.3 odd 2 inner
980.2.c.e.979.34 yes 48 28.27 even 2 inner
980.2.c.e.979.35 yes 48 5.4 even 2 inner
980.2.c.e.979.36 yes 48 35.34 odd 2 inner
980.2.s.g.19.5 96 35.4 even 6
980.2.s.g.19.6 96 35.24 odd 6
980.2.s.g.19.21 96 140.59 even 6
980.2.s.g.19.22 96 140.39 odd 6
980.2.s.g.19.27 96 28.11 odd 6
980.2.s.g.19.28 96 28.3 even 6
980.2.s.g.19.43 96 7.3 odd 6
980.2.s.g.19.44 96 7.4 even 3
980.2.s.g.619.5 96 28.19 even 6
980.2.s.g.619.6 96 28.23 odd 6
980.2.s.g.619.21 96 7.2 even 3
980.2.s.g.619.22 96 7.5 odd 6
980.2.s.g.619.27 96 35.19 odd 6
980.2.s.g.619.28 96 35.9 even 6
980.2.s.g.619.43 96 140.79 odd 6
980.2.s.g.619.44 96 140.19 even 6