Properties

Label 784.2.m.k.197.8
Level 784784
Weight 22
Character 784.197
Analytic conductor 6.2606.260
Analytic rank 00
Dimension 2424
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [784,2,Mod(197,784)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(784, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("784.197");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 784=2472 784 = 2^{4} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 784.m (of order 44, degree 22, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 6.260271518476.26027151847
Analytic rank: 00
Dimension: 2424
Relative dimension: 1212 over Q(i)\Q(i)
Twist minimal: no (minimal twist has level 112)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 197.8
Character χ\chi == 784.197
Dual form 784.2.m.k.589.8

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.844695+1.13424i)q2+(0.614312+0.614312i)q3+(0.572980+1.91617i)q4+(2.315622.31562i)q5+(1.215680.177868i)q6+(2.65738+0.968682i)q8+2.24524iq9+(0.6704664.58245i)q10+(2.101282.10128i)q11+(0.8251351.52911i)q12+(3.632933.63293i)q13+2.84503q15+(3.343392.19585i)q163.63712q17+(2.54663+1.89654i)q18+(1.173401.17340i)q19+(5.763923.11031i)q20+(0.6084054.15828i)q226.16261iq23+(1.037392.22753i)q24+5.72420iq25+(7.18931+1.05188i)q26+(3.222213.22221i)q27+(5.102665.10266i)q29+(2.40318+3.22693i)q302.01521q31+(0.3335305.64701i)q32+2.58168q33+(3.072264.12535i)q34+(4.302261.28648i)q36+(4.07871+4.07871i)q37+(2.32209+0.339748i)q38+4.46350iq39+(8.39658+3.91038i)q403.71244iq41+(2.916402.91640i)q43+(5.230392.82241i)q44+(5.199135.19913i)q45+(6.989865.20553i)q4610.1313q47+(3.402820.704944i)q48+(6.49259+4.83520i)q50+(2.234332.23433i)q51+(4.87970+9.04289i)q52+(2.696092.69609i)q53+(0.9329616.37654i)q54+9.73153iq55+1.44167iq57+(10.0978+1.47743i)q58+(2.671842.67184i)q59+(1.63014+5.45154i)q60+(4.79291+4.79291i)q61+(1.702242.28573i)q62+(6.123315.14831i)q6416.8250q65+(2.18073+2.92823i)q66+(4.30731+4.30731i)q67+(2.084006.96933i)q68+(3.78577+3.78577i)q69+9.55168iq71+(2.174925.96646i)q721.14315iq73+(1.18095+8.07148i)q74+(3.516443.51644i)q75+(1.57610+2.92078i)q76+(5.06266+3.77030i)q780.241393q79+(2.65726+12.8268i)q802.77684q81+(4.210793.13588i)q82+(0.4591830.459183i)q83+(8.42219+8.42219i)q85+(0.8444165.77135i)q86+6.26924iq87+(7.61936+3.54842i)q884.35118iq89+(10.2887+1.50536i)q90+(11.8086+3.53106i)q92+(1.237971.23797i)q93+(8.5578511.4913i)q945.43432q95+(3.67392+3.26414i)q966.80176q97+(4.717884.71788i)q99+O(q100)q+(0.844695 + 1.13424i) q^{2} +(-0.614312 + 0.614312i) q^{3} +(-0.572980 + 1.91617i) q^{4} +(-2.31562 - 2.31562i) q^{5} +(-1.21568 - 0.177868i) q^{6} +(-2.65738 + 0.968682i) q^{8} +2.24524i q^{9} +(0.670466 - 4.58245i) q^{10} +(-2.10128 - 2.10128i) q^{11} +(-0.825135 - 1.52911i) q^{12} +(3.63293 - 3.63293i) q^{13} +2.84503 q^{15} +(-3.34339 - 2.19585i) q^{16} -3.63712 q^{17} +(-2.54663 + 1.89654i) q^{18} +(1.17340 - 1.17340i) q^{19} +(5.76392 - 3.11031i) q^{20} +(0.608405 - 4.15828i) q^{22} -6.16261i q^{23} +(1.03739 - 2.22753i) q^{24} +5.72420i q^{25} +(7.18931 + 1.05188i) q^{26} +(-3.22221 - 3.22221i) q^{27} +(5.10266 - 5.10266i) q^{29} +(2.40318 + 3.22693i) q^{30} -2.01521 q^{31} +(-0.333530 - 5.64701i) q^{32} +2.58168 q^{33} +(-3.07226 - 4.12535i) q^{34} +(-4.30226 - 1.28648i) q^{36} +(4.07871 + 4.07871i) q^{37} +(2.32209 + 0.339748i) q^{38} +4.46350i q^{39} +(8.39658 + 3.91038i) q^{40} -3.71244i q^{41} +(-2.91640 - 2.91640i) q^{43} +(5.23039 - 2.82241i) q^{44} +(5.19913 - 5.19913i) q^{45} +(6.98986 - 5.20553i) q^{46} -10.1313 q^{47} +(3.40282 - 0.704944i) q^{48} +(-6.49259 + 4.83520i) q^{50} +(2.23433 - 2.23433i) q^{51} +(4.87970 + 9.04289i) q^{52} +(-2.69609 - 2.69609i) q^{53} +(0.932961 - 6.37654i) q^{54} +9.73153i q^{55} +1.44167i q^{57} +(10.0978 + 1.47743i) q^{58} +(-2.67184 - 2.67184i) q^{59} +(-1.63014 + 5.45154i) q^{60} +(-4.79291 + 4.79291i) q^{61} +(-1.70224 - 2.28573i) q^{62} +(6.12331 - 5.14831i) q^{64} -16.8250 q^{65} +(2.18073 + 2.92823i) q^{66} +(-4.30731 + 4.30731i) q^{67} +(2.08400 - 6.96933i) q^{68} +(3.78577 + 3.78577i) q^{69} +9.55168i q^{71} +(-2.17492 - 5.96646i) q^{72} -1.14315i q^{73} +(-1.18095 + 8.07148i) q^{74} +(-3.51644 - 3.51644i) q^{75} +(1.57610 + 2.92078i) q^{76} +(-5.06266 + 3.77030i) q^{78} -0.241393 q^{79} +(2.65726 + 12.8268i) q^{80} -2.77684 q^{81} +(4.21079 - 3.13588i) q^{82} +(0.459183 - 0.459183i) q^{83} +(8.42219 + 8.42219i) q^{85} +(0.844416 - 5.77135i) q^{86} +6.26924i q^{87} +(7.61936 + 3.54842i) q^{88} -4.35118i q^{89} +(10.2887 + 1.50536i) q^{90} +(11.8086 + 3.53106i) q^{92} +(1.23797 - 1.23797i) q^{93} +(-8.55785 - 11.4913i) q^{94} -5.43432 q^{95} +(3.67392 + 3.26414i) q^{96} -6.80176 q^{97} +(4.71788 - 4.71788i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q+4q2+4q4+4q5+2q62q82q10+4q11+2q12+12q1320q1516q16+8q1718q184q19+8q20+18q2410q26+12q27+12q99+O(q100) 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/784Z)×\left(\mathbb{Z}/784\mathbb{Z}\right)^\times.

nn 197197 687687 689689
χ(n)\chi(n) e(14)e\left(\frac{1}{4}\right) 11 11

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 0.844695 + 1.13424i 0.597290 + 0.802026i
33 −0.614312 + 0.614312i −0.354673 + 0.354673i −0.861845 0.507172i 0.830691π-0.830691\pi
0.507172 + 0.861845i 0.330691π0.330691\pi
44 −0.572980 + 1.91617i −0.286490 + 0.958083i
55 −2.31562 2.31562i −1.03558 1.03558i −0.999343 0.0362338i 0.988464π-0.988464\pi
−0.0362338 0.999343i 0.511536π-0.511536\pi
66 −1.21568 0.177868i −0.496299 0.0726143i
77 0 0
88 −2.65738 + 0.968682i −0.939525 + 0.342481i
99 2.24524i 0.748414i
1010 0.670466 4.58245i 0.212020 1.44910i
1111 −2.10128 2.10128i −0.633559 0.633559i 0.315400 0.948959i 0.397861π-0.397861\pi
−0.948959 + 0.315400i 0.897861π0.897861\pi
1212 −0.825135 1.52911i −0.238196 0.441417i
1313 3.63293 3.63293i 1.00759 1.00759i 0.00762179 0.999971i 0.497574π-0.497574\pi
0.999971 0.00762179i 0.00242611π-0.00242611\pi
1414 0 0
1515 2.84503 0.734583
1616 −3.34339 2.19585i −0.835847 0.548963i
1717 −3.63712 −0.882131 −0.441066 0.897475i 0.645399π-0.645399\pi
−0.441066 + 0.897475i 0.645399π0.645399\pi
1818 −2.54663 + 1.89654i −0.600247 + 0.447020i
1919 1.17340 1.17340i 0.269197 0.269197i −0.559579 0.828777i 0.689037π-0.689037\pi
0.828777 + 0.559579i 0.189037π0.189037\pi
2020 5.76392 3.11031i 1.28885 0.695486i
2121 0 0
2222 0.608405 4.15828i 0.129712 0.886549i
2323 6.16261i 1.28499i −0.766288 0.642497i 0.777899π-0.777899\pi
0.766288 0.642497i 0.222101π-0.222101\pi
2424 1.03739 2.22753i 0.211756 0.454693i
2525 5.72420i 1.14484i
2626 7.18931 + 1.05188i 1.40994 + 0.206291i
2727 −3.22221 3.22221i −0.620115 0.620115i
2828 0 0
2929 5.10266 5.10266i 0.947539 0.947539i −0.0511514 0.998691i 0.516289π-0.516289\pi
0.998691 + 0.0511514i 0.0162891π0.0162891\pi
3030 2.40318 + 3.22693i 0.438759 + 0.589154i
3131 −2.01521 −0.361943 −0.180972 0.983488i 0.557924π-0.557924\pi
−0.180972 + 0.983488i 0.557924π0.557924\pi
3232 −0.333530 5.64701i −0.0589603 0.998260i
3333 2.58168 0.449413
3434 −3.07226 4.12535i −0.526888 0.707492i
3535 0 0
3636 −4.30226 1.28648i −0.717043 0.214413i
3737 4.07871 + 4.07871i 0.670536 + 0.670536i 0.957839 0.287304i 0.0927590π-0.0927590\pi
−0.287304 + 0.957839i 0.592759π0.592759\pi
3838 2.32209 + 0.339748i 0.376692 + 0.0551144i
3939 4.46350i 0.714732i
4040 8.39658 + 3.91038i 1.32762 + 0.618285i
4141 3.71244i 0.579786i −0.957059 0.289893i 0.906380π-0.906380\pi
0.957059 0.289893i 0.0936198π-0.0936198\pi
4242 0 0
4343 −2.91640 2.91640i −0.444747 0.444747i 0.448857 0.893604i 0.351831π-0.351831\pi
−0.893604 + 0.448857i 0.851831π0.851831\pi
4444 5.23039 2.82241i 0.788511 0.425494i
4545 5.19913 5.19913i 0.775040 0.775040i
4646 6.98986 5.20553i 1.03060 0.767513i
4747 −10.1313 −1.47780 −0.738900 0.673815i 0.764655π-0.764655\pi
−0.738900 + 0.673815i 0.764655π0.764655\pi
4848 3.40282 0.704944i 0.491155 0.101750i
4949 0 0
5050 −6.49259 + 4.83520i −0.918191 + 0.683801i
5151 2.23433 2.23433i 0.312868 0.312868i
5252 4.87970 + 9.04289i 0.676692 + 1.25402i
5353 −2.69609 2.69609i −0.370336 0.370336i 0.497264 0.867600i 0.334338π-0.334338\pi
−0.867600 + 0.497264i 0.834338π0.834338\pi
5454 0.932961 6.37654i 0.126960 0.867737i
5555 9.73153i 1.31220i
5656 0 0
5757 1.44167i 0.190954i
5858 10.0978 + 1.47743i 1.32591 + 0.193995i
5959 −2.67184 2.67184i −0.347845 0.347845i 0.511462 0.859306i 0.329104π-0.329104\pi
−0.859306 + 0.511462i 0.829104π0.829104\pi
6060 −1.63014 + 5.45154i −0.210451 + 0.703791i
6161 −4.79291 + 4.79291i −0.613670 + 0.613670i −0.943900 0.330231i 0.892873π-0.892873\pi
0.330231 + 0.943900i 0.392873π0.392873\pi
6262 −1.70224 2.28573i −0.216185 0.290288i
6363 0 0
6464 6.12331 5.14831i 0.765414 0.643538i
6565 −16.8250 −2.08688
6666 2.18073 + 2.92823i 0.268430 + 0.360441i
6767 −4.30731 + 4.30731i −0.526222 + 0.526222i −0.919444 0.393222i 0.871361π-0.871361\pi
0.393222 + 0.919444i 0.371361π0.371361\pi
6868 2.08400 6.96933i 0.252722 0.845155i
6969 3.78577 + 3.78577i 0.455753 + 0.455753i
7070 0 0
7171 9.55168i 1.13358i 0.823864 + 0.566788i 0.191814π0.191814\pi
−0.823864 + 0.566788i 0.808186π0.808186\pi
7272 −2.17492 5.96646i −0.256317 0.703154i
7373 1.14315i 0.133796i −0.997760 0.0668980i 0.978690π-0.978690\pi
0.997760 0.0668980i 0.0213102π-0.0213102\pi
7474 −1.18095 + 8.07148i −0.137283 + 0.938291i
7575 −3.51644 3.51644i −0.406044 0.406044i
7676 1.57610 + 2.92078i 0.180791 + 0.335036i
7777 0 0
7878 −5.06266 + 3.77030i −0.573233 + 0.426902i
7979 −0.241393 −0.0271588 −0.0135794 0.999908i 0.504323π-0.504323\pi
−0.0135794 + 0.999908i 0.504323π0.504323\pi
8080 2.65726 + 12.8268i 0.297090 + 1.43408i
8181 −2.77684 −0.308538
8282 4.21079 3.13588i 0.465004 0.346300i
8383 0.459183 0.459183i 0.0504018 0.0504018i −0.681457 0.731858i 0.738653π-0.738653\pi
0.731858 + 0.681457i 0.238653π0.238653\pi
8484 0 0
8585 8.42219 + 8.42219i 0.913515 + 0.913515i
8686 0.844416 5.77135i 0.0910557 0.622341i
8787 6.26924i 0.672133i
8888 7.61936 + 3.54842i 0.812226 + 0.378263i
8989 4.35118i 0.461224i −0.973046 0.230612i 0.925927π-0.925927\pi
0.973046 0.230612i 0.0740728π-0.0740728\pi
9090 10.2887 + 1.50536i 1.08453 + 0.158679i
9191 0 0
9292 11.8086 + 3.53106i 1.23113 + 0.368138i
9393 1.23797 1.23797i 0.128371 0.128371i
9494 −8.55785 11.4913i −0.882675 1.18523i
9595 −5.43432 −0.557549
9696 3.67392 + 3.26414i 0.374968 + 0.333144i
9797 −6.80176 −0.690614 −0.345307 0.938490i 0.612225π-0.612225\pi
−0.345307 + 0.938490i 0.612225π0.612225\pi
9898 0 0
9999 4.71788 4.71788i 0.474165 0.474165i
100100 −10.9685 3.27985i −1.09685 0.327985i
101101 2.25232 + 2.25232i 0.224114 + 0.224114i 0.810229 0.586114i 0.199343π-0.199343\pi
−0.586114 + 0.810229i 0.699343π0.699343\pi
102102 4.42158 + 0.646928i 0.437801 + 0.0640554i
103103 3.75921i 0.370406i 0.982700 + 0.185203i 0.0592942π0.0592942\pi
−0.982700 + 0.185203i 0.940706π0.940706\pi
104104 −6.13491 + 13.1732i −0.601577 + 1.29174i
105105 0 0
106106 0.780626 5.33537i 0.0758211 0.518217i
107107 0.268184 + 0.268184i 0.0259263 + 0.0259263i 0.719951 0.694025i 0.244164π-0.244164\pi
−0.694025 + 0.719951i 0.744164π0.744164\pi
108108 8.02056 4.32803i 0.771779 0.416465i
109109 7.06908 7.06908i 0.677095 0.677095i −0.282247 0.959342i 0.591080π-0.591080\pi
0.959342 + 0.282247i 0.0910796π0.0910796\pi
110110 −11.0378 + 8.22017i −1.05242 + 0.783763i
111111 −5.01120 −0.475642
112112 0 0
113113 2.62015 0.246483 0.123242 0.992377i 0.460671π-0.460671\pi
0.123242 + 0.992377i 0.460671π0.460671\pi
114114 −1.63520 + 1.21777i −0.153150 + 0.114055i
115115 −14.2703 + 14.2703i −1.33071 + 1.33071i
116116 6.85382 + 12.7013i 0.636361 + 1.17928i
117117 8.15680 + 8.15680i 0.754097 + 0.754097i
118118 0.773607 5.28739i 0.0712163 0.486744i
119119 0 0
120120 −7.56031 + 2.75592i −0.690159 + 0.251580i
121121 2.16926i 0.197205i
122122 −9.48484 1.38774i −0.858717 0.125640i
123123 2.28060 + 2.28060i 0.205635 + 0.205635i
124124 1.15468 3.86148i 0.103693 0.346772i
125125 1.67697 1.67697i 0.149993 0.149993i
126126 0 0
127127 −12.8840 −1.14327 −0.571635 0.820508i 0.693691π-0.693691\pi
−0.571635 + 0.820508i 0.693691π0.693691\pi
128128 11.0117 + 2.59653i 0.973308 + 0.229503i
129129 3.58316 0.315479
130130 −14.2120 19.0835i −1.24647 1.67373i
131131 −6.57048 + 6.57048i −0.574065 + 0.574065i −0.933262 0.359197i 0.883051π-0.883051\pi
0.359197 + 0.933262i 0.383051π0.383051\pi
132132 −1.47925 + 4.94693i −0.128752 + 0.430575i
133133 0 0
134134 −8.52388 1.24714i −0.736351 0.107737i
135135 14.9229i 1.28435i
136136 9.66520 3.52321i 0.828784 0.302113i
137137 11.8024i 1.00834i −0.863604 0.504172i 0.831798π-0.831798\pi
0.863604 0.504172i 0.168202π-0.168202\pi
138138 −1.09613 + 7.49177i −0.0933090 + 0.637742i
139139 −8.15708 8.15708i −0.691874 0.691874i 0.270770 0.962644i 0.412722π-0.412722\pi
−0.962644 + 0.270770i 0.912722π0.912722\pi
140140 0 0
141141 6.22377 6.22377i 0.524136 0.524136i
142142 −10.8339 + 8.06825i −0.909157 + 0.677073i
143143 −15.2676 −1.27674
144144 4.93022 7.50671i 0.410852 0.625559i
145145 −23.6316 −1.96250
146146 1.29660 0.965616i 0.107308 0.0799149i
147147 0 0
148148 −10.1525 + 5.47846i −0.834531 + 0.450327i
149149 −8.30787 8.30787i −0.680607 0.680607i 0.279530 0.960137i 0.409821π-0.409821\pi
−0.960137 + 0.279530i 0.909821π0.909821\pi
150150 1.01815 6.95880i 0.0831318 0.568184i
151151 19.6074i 1.59563i −0.602903 0.797815i 0.705989π-0.705989\pi
0.602903 0.797815i 0.294011π-0.294011\pi
152152 −1.98152 + 4.25483i −0.160723 + 0.345113i
153153 8.16622i 0.660199i
154154 0 0
155155 4.66647 + 4.66647i 0.374820 + 0.374820i
156156 −8.55281 2.55750i −0.684773 0.204764i
157157 3.82384 3.82384i 0.305176 0.305176i −0.537859 0.843035i 0.680767π-0.680767\pi
0.843035 + 0.537859i 0.180767π0.180767\pi
158158 −0.203903 0.273796i −0.0162217 0.0217821i
159159 3.31248 0.262696
160160 −12.3040 + 13.8487i −0.972718 + 1.09483i
161161 0 0
162162 −2.34558 3.14959i −0.184286 0.247455i
163163 7.97599 7.97599i 0.624727 0.624727i −0.322009 0.946737i 0.604358π-0.604358\pi
0.946737 + 0.322009i 0.104358π0.104358\pi
164164 7.11366 + 2.12716i 0.555484 + 0.166103i
165165 −5.97819 5.97819i −0.465402 0.465402i
166166 0.908690 + 0.132952i 0.0705280 + 0.0103191i
167167 21.8111i 1.68779i 0.536508 + 0.843895i 0.319743π0.319743\pi
−0.536508 + 0.843895i 0.680257π0.680257\pi
168168 0 0
169169 13.3963i 1.03049i
170170 −2.43857 + 16.6669i −0.187029 + 1.27830i
171171 2.63458 + 2.63458i 0.201471 + 0.201471i
172172 7.25935 3.91727i 0.553520 0.298689i
173173 16.0601 16.0601i 1.22103 1.22103i 0.253759 0.967267i 0.418333π-0.418333\pi
0.967267 0.253759i 0.0816671π-0.0816671\pi
174174 −7.11080 + 5.29560i −0.539068 + 0.401458i
175175 0 0
176176 2.41129 + 11.6395i 0.181758 + 0.877359i
177177 3.28269 0.246742
178178 4.93526 3.67542i 0.369913 0.275484i
179179 −15.2220 + 15.2220i −1.13774 + 1.13774i −0.148888 + 0.988854i 0.547569π0.547569\pi
−0.988854 + 0.148888i 0.952431π0.952431\pi
180180 6.98340 + 12.9414i 0.520512 + 0.964595i
181181 11.8484 + 11.8484i 0.880684 + 0.880684i 0.993604 0.112920i 0.0360205π-0.0360205\pi
−0.112920 + 0.993604i 0.536020π0.536020\pi
182182 0 0
183183 5.88869i 0.435304i
184184 5.96961 + 16.3764i 0.440086 + 1.20728i
185185 18.8895i 1.38878i
186186 2.44986 + 0.358442i 0.179632 + 0.0262823i
187187 7.64260 + 7.64260i 0.558882 + 0.558882i
188188 5.80503 19.4132i 0.423375 1.41586i
189189 0 0
190190 −4.59034 6.16380i −0.333018 0.447169i
191191 7.88799 0.570755 0.285377 0.958415i 0.407881π-0.407881\pi
0.285377 + 0.958415i 0.407881π0.407881\pi
192192 −0.598958 + 6.92429i −0.0432261 + 0.499717i
193193 24.8808 1.79096 0.895478 0.445105i 0.146834π-0.146834\pi
0.895478 + 0.445105i 0.146834π0.146834\pi
194194 −5.74541 7.71480i −0.412497 0.553890i
195195 10.3358 10.3358i 0.740160 0.740160i
196196 0 0
197197 −7.75408 7.75408i −0.552455 0.552455i 0.374694 0.927149i 0.377748π-0.377748\pi
−0.927149 + 0.374694i 0.877748π0.877748\pi
198198 9.33635 + 1.36602i 0.663506 + 0.0970786i
199199 11.4472i 0.811469i 0.913991 + 0.405734i 0.132984π0.132984\pi
−0.913991 + 0.405734i 0.867016π0.867016\pi
200200 −5.54493 15.2114i −0.392086 1.07561i
201201 5.29207i 0.373274i
202202 −0.652139 + 4.45719i −0.0458843 + 0.313607i
203203 0 0
204204 3.00112 + 5.56157i 0.210120 + 0.389387i
205205 −8.59661 + 8.59661i −0.600414 + 0.600414i
206206 −4.26383 + 3.17539i −0.297075 + 0.221240i
207207 13.8366 0.961707
208208 −20.1237 + 4.16891i −1.39532 + 0.289062i
209209 −4.93130 −0.341105
210210 0 0
211211 −8.69524 + 8.69524i −0.598605 + 0.598605i −0.939941 0.341336i 0.889120π-0.889120\pi
0.341336 + 0.939941i 0.389120π0.389120\pi
212212 6.71096 3.62135i 0.460910 0.248715i
213213 −5.86771 5.86771i −0.402049 0.402049i
214214 −0.0776500 + 0.530717i −0.00530805 + 0.0362791i
215215 13.5066i 0.921139i
216216 11.6839 + 5.44134i 0.794991 + 0.370236i
217217 0 0
218218 13.9892 + 2.04679i 0.947470 + 0.138626i
219219 0.702252 + 0.702252i 0.0474538 + 0.0474538i
220220 −18.6472 5.57597i −1.25720 0.375932i
221221 −13.2134 + 13.2134i −0.888829 + 0.888829i
222222 −4.23293 5.68388i −0.284096 0.381477i
223223 −21.9483 −1.46976 −0.734882 0.678195i 0.762762π-0.762762\pi
−0.734882 + 0.678195i 0.762762π0.762762\pi
224224 0 0
225225 −12.8522 −0.856814
226226 2.21323 + 2.97187i 0.147222 + 0.197686i
227227 17.4436 17.4436i 1.15777 1.15777i 0.172820 0.984953i 0.444712π-0.444712\pi
0.984953 0.172820i 0.0552878π-0.0552878\pi
228228 −2.76248 0.826050i −0.182950 0.0547065i
229229 6.72768 + 6.72768i 0.444578 + 0.444578i 0.893547 0.448969i 0.148209π-0.148209\pi
−0.448969 + 0.893547i 0.648209π0.648209\pi
230230 −28.2399 4.13182i −1.86208 0.272444i
231231 0 0
232232 −8.61684 + 18.5025i −0.565723 + 1.21475i
233233 22.2376i 1.45684i 0.685133 + 0.728418i 0.259744π0.259744\pi
−0.685133 + 0.728418i 0.740256π0.740256\pi
234234 −2.36172 + 16.1417i −0.154391 + 1.05522i
235235 23.4602 + 23.4602i 1.53038 + 1.53038i
236236 6.65061 3.58878i 0.432918 0.233610i
237237 0.148290 0.148290i 0.00963250 0.00963250i
238238 0 0
239239 14.9579 0.967548 0.483774 0.875193i 0.339266π-0.339266\pi
0.483774 + 0.875193i 0.339266π0.339266\pi
240240 −9.51202 6.24726i −0.613999 0.403259i
241241 24.3500 1.56852 0.784262 0.620430i 0.213042π-0.213042\pi
0.784262 + 0.620430i 0.213042π0.213042\pi
242242 2.46045 1.83236i 0.158164 0.117789i
243243 11.3725 11.3725i 0.729545 0.729545i
244244 −6.43777 11.9303i −0.412136 0.763757i
245245 0 0
246246 −0.660325 + 4.51315i −0.0421008 + 0.287748i
247247 8.52578i 0.542483i
248248 5.35518 1.95210i 0.340055 0.123958i
249249 0.564162i 0.0357523i
250250 3.31862 + 0.485552i 0.209888 + 0.0307090i
251251 3.50509 + 3.50509i 0.221239 + 0.221239i 0.809020 0.587781i 0.199998π-0.199998\pi
−0.587781 + 0.809020i 0.699998π0.699998\pi
252252 0 0
253253 −12.9494 + 12.9494i −0.814120 + 0.814120i
254254 −10.8831 14.6135i −0.682863 0.916932i
255255 −10.3477 −0.647998
256256 6.35647 + 14.6832i 0.397279 + 0.917698i
257257 −6.49705 −0.405275 −0.202638 0.979254i 0.564951π-0.564951\pi
−0.202638 + 0.979254i 0.564951π0.564951\pi
258258 3.02668 + 4.06415i 0.188433 + 0.253023i
259259 0 0
260260 9.64038 32.2394i 0.597871 1.99940i
261261 11.4567 + 11.4567i 0.709152 + 0.709152i
262262 −13.0025 1.90242i −0.803298 0.117532i
263263 24.7362i 1.52530i −0.646811 0.762650i 0.723898π-0.723898\pi
0.646811 0.762650i 0.276102π-0.276102\pi
264264 −6.86050 + 2.50083i −0.422235 + 0.153915i
265265 12.4862i 0.767023i
266266 0 0
267267 2.67298 + 2.67298i 0.163584 + 0.163584i
268268 −5.78552 10.7215i −0.353407 0.654922i
269269 1.05961 1.05961i 0.0646055 0.0646055i −0.674066 0.738671i 0.735454π-0.735454\pi
0.738671 + 0.674066i 0.235454π0.235454\pi
270270 −16.9260 + 12.6053i −1.03009 + 0.767132i
271271 7.36247 0.447238 0.223619 0.974677i 0.428213π-0.428213\pi
0.223619 + 0.974677i 0.428213π0.428213\pi
272272 12.1603 + 7.98658i 0.737327 + 0.484257i
273273 0 0
274274 13.3866 9.96939i 0.808717 0.602273i
275275 12.0281 12.0281i 0.725324 0.725324i
276276 −9.42333 + 5.08499i −0.567218 + 0.306080i
277277 −3.20233 3.20233i −0.192410 0.192410i 0.604327 0.796737i 0.293442π-0.293442\pi
−0.796737 + 0.604327i 0.793442π0.793442\pi
278278 2.36180 16.1423i 0.141652 0.968151i
279279 4.52464i 0.270883i
280280 0 0
281281 9.72875i 0.580369i 0.956971 + 0.290184i 0.0937166π0.0937166\pi
−0.956971 + 0.290184i 0.906283π0.906283\pi
282282 12.3164 + 1.80203i 0.733432 + 0.107310i
283283 −2.84445 2.84445i −0.169085 0.169085i 0.617492 0.786577i 0.288149π-0.288149\pi
−0.786577 + 0.617492i 0.788149π0.788149\pi
284284 −18.3026 5.47292i −1.08606 0.324758i
285285 3.33837 3.33837i 0.197748 0.197748i
286286 −12.8965 17.3170i −0.762583 1.02398i
287287 0 0
288288 12.6789 0.748855i 0.747112 0.0441267i
289289 −3.77136 −0.221844
290290 −19.9615 26.8038i −1.17218 1.57398i
291291 4.17840 4.17840i 0.244942 0.244942i
292292 2.19047 + 0.655004i 0.128188 + 0.0383312i
293293 −1.88131 1.88131i −0.109908 0.109908i 0.650014 0.759922i 0.274763π-0.274763\pi
−0.759922 + 0.650014i 0.774763π0.774763\pi
294294 0 0
295295 12.3740i 0.720440i
296296 −14.7896 6.88770i −0.859630 0.400339i
297297 13.5415i 0.785760i
298298 2.40546 16.4407i 0.139345 0.952384i
299299 −22.3883 22.3883i −1.29475 1.29475i
300300 8.75295 4.72324i 0.505352 0.272696i
301301 0 0
302302 22.2394 16.5623i 1.27974 0.953053i
303303 −2.76726 −0.158975
304304 −6.49977 + 1.34652i −0.372787 + 0.0772284i
305305 22.1971 1.27100
306306 9.26241 6.89796i 0.529497 0.394330i
307307 −3.98977 + 3.98977i −0.227708 + 0.227708i −0.811735 0.584026i 0.801476π-0.801476\pi
0.584026 + 0.811735i 0.301476π0.301476\pi
308308 0 0
309309 −2.30933 2.30933i −0.131373 0.131373i
310310 −1.35113 + 9.23462i −0.0767391 + 0.524491i
311311 0.808093i 0.0458228i 0.999737 + 0.0229114i 0.00729356π0.00729356\pi
−0.999737 + 0.0229114i 0.992706π0.992706\pi
312312 −4.32371 11.8612i −0.244782 0.671509i
313313 23.2955i 1.31674i 0.752694 + 0.658371i 0.228754π0.228754\pi
−0.752694 + 0.658371i 0.771246π0.771246\pi
314314 7.56712 + 1.10716i 0.427037 + 0.0624805i
315315 0 0
316316 0.138313 0.462549i 0.00778073 0.0260204i
317317 −2.20803 + 2.20803i −0.124015 + 0.124015i −0.766390 0.642375i 0.777949π-0.777949\pi
0.642375 + 0.766390i 0.277949π0.277949\pi
318318 2.79803 + 3.75713i 0.156906 + 0.210689i
319319 −21.4442 −1.20064
320320 −26.1008 2.25775i −1.45908 0.126212i
321321 −0.329497 −0.0183907
322322 0 0
323323 −4.26781 + 4.26781i −0.237467 + 0.237467i
324324 1.59107 5.32088i 0.0883930 0.295605i
325325 20.7956 + 20.7956i 1.15353 + 1.15353i
326326 15.7839 + 2.30937i 0.874191 + 0.127904i
327327 8.68524i 0.480295i
328328 3.59618 + 9.86537i 0.198566 + 0.544724i
329329 0 0
330330 1.73093 11.8304i 0.0952845 0.651244i
331331 −11.1391 11.1391i −0.612258 0.612258i 0.331276 0.943534i 0.392521π-0.392521\pi
−0.943534 + 0.331276i 0.892521π0.892521\pi
332332 0.616767 + 1.14297i 0.0338495 + 0.0627288i
333333 −9.15769 + 9.15769i −0.501838 + 0.501838i
334334 −24.7389 + 18.4237i −1.35365 + 1.00810i
335335 19.9482 1.08989
336336 0 0
337337 −5.36065 −0.292013 −0.146007 0.989284i 0.546642π-0.546642\pi
−0.146007 + 0.989284i 0.546642π0.546642\pi
338338 15.1946 11.3158i 0.826476 0.615499i
339339 −1.60959 + 1.60959i −0.0874210 + 0.0874210i
340340 −20.9641 + 11.3126i −1.13694 + 0.613510i
341341 4.23452 + 4.23452i 0.229312 + 0.229312i
342342 −0.762816 + 5.21364i −0.0412484 + 0.281922i
343343 0 0
344344 10.5750 + 4.92491i 0.570168 + 0.265534i
345345 17.5328i 0.943934i
346346 31.7818 + 4.65005i 1.70860 + 0.249988i
347347 −11.7410 11.7410i −0.630292 0.630292i 0.317849 0.948141i 0.397039π-0.397039\pi
−0.948141 + 0.317849i 0.897039π0.897039\pi
348348 −12.0129 3.59215i −0.643960 0.192560i
349349 22.2799 22.2799i 1.19262 1.19262i 0.216286 0.976330i 0.430606π-0.430606\pi
0.976330 0.216286i 0.0693943π-0.0693943\pi
350350 0 0
351351 −23.4121 −1.24965
352352 −11.1651 + 12.5668i −0.595102 + 0.669812i
353353 −13.6875 −0.728510 −0.364255 0.931299i 0.618676π-0.618676\pi
−0.364255 + 0.931299i 0.618676π0.618676\pi
354354 2.77287 + 3.72334i 0.147377 + 0.197894i
355355 22.1181 22.1181i 1.17390 1.17390i
356356 8.33758 + 2.49314i 0.441891 + 0.132136i
357357 0 0
358358 −30.1232 4.40737i −1.59206 0.232937i
359359 6.32231i 0.333679i 0.985984 + 0.166840i 0.0533562π0.0533562\pi
−0.985984 + 0.166840i 0.946644π0.946644\pi
360360 −8.77975 + 18.8524i −0.462733 + 0.993606i
361361 16.2462i 0.855066i
362362 −3.43059 + 23.4471i −0.180308 + 1.23235i
363363 1.33260 + 1.33260i 0.0699434 + 0.0699434i
364364 0 0
365365 −2.64711 + 2.64711i −0.138556 + 0.138556i
366366 6.67916 4.97414i 0.349125 0.260003i
367367 37.2328 1.94354 0.971768 0.235939i 0.0758165π-0.0758165\pi
0.971768 + 0.235939i 0.0758165π0.0758165\pi
368368 −13.5322 + 20.6040i −0.705414 + 1.07406i
369369 8.33534 0.433920
370370 21.4251 15.9559i 1.11384 0.829505i
371371 0 0
372372 1.66282 + 3.08149i 0.0862134 + 0.159768i
373373 3.05659 + 3.05659i 0.158264 + 0.158264i 0.781797 0.623533i 0.214303π-0.214303\pi
−0.623533 + 0.781797i 0.714303π0.714303\pi
374374 −2.21284 + 15.1242i −0.114423 + 0.782053i
375375 2.06037i 0.106397i
376376 26.9227 9.81400i 1.38843 0.506118i
377377 37.0752i 1.90947i
378378 0 0
379379 −11.5118 11.5118i −0.591323 0.591323i 0.346666 0.937989i 0.387314π-0.387314\pi
−0.937989 + 0.346666i 0.887314π0.887314\pi
380380 3.11376 10.4131i 0.159732 0.534179i
381381 7.91479 7.91479i 0.405487 0.405487i
382382 6.66295 + 8.94684i 0.340906 + 0.457760i
383383 19.7267 1.00799 0.503993 0.863708i 0.331864π-0.331864\pi
0.503993 + 0.863708i 0.331864π0.331864\pi
384384 −8.35971 + 5.16955i −0.426605 + 0.263808i
385385 0 0
386386 21.0167 + 28.2206i 1.06972 + 1.43639i
387387 6.54802 6.54802i 0.332855 0.332855i
388388 3.89728 13.0333i 0.197854 0.661666i
389389 −4.19887 4.19887i −0.212891 0.212891i 0.592603 0.805494i 0.298100π-0.298100\pi
−0.805494 + 0.592603i 0.798100π0.798100\pi
390390 20.4538 + 2.99262i 1.03572 + 0.151537i
391391 22.4142i 1.13353i
392392 0 0
393393 8.07264i 0.407211i
394394 2.24512 15.3448i 0.113107 0.773059i
395395 0.558974 + 0.558974i 0.0281250 + 0.0281250i
396396 6.33699 + 11.7435i 0.318446 + 0.590133i
397397 18.0822 18.0822i 0.907520 0.907520i −0.0885515 0.996072i 0.528224π-0.528224\pi
0.996072 + 0.0885515i 0.0282238π0.0282238\pi
398398 −12.9838 + 9.66937i −0.650819 + 0.484682i
399399 0 0
400400 12.5695 19.1382i 0.628475 0.956911i
401401 3.60293 0.179922 0.0899610 0.995945i 0.471326π-0.471326\pi
0.0899610 + 0.995945i 0.471326π0.471326\pi
402402 6.00245 4.47018i 0.299375 0.222952i
403403 −7.32112 + 7.32112i −0.364691 + 0.364691i
404404 −5.60636 + 3.02529i −0.278927 + 0.150514i
405405 6.43010 + 6.43010i 0.319514 + 0.319514i
406406 0 0
407407 17.1410i 0.849648i
408408 −3.77310 + 8.10180i −0.186796 + 0.401099i
409409 15.3319i 0.758114i 0.925373 + 0.379057i 0.123751π0.123751\pi
−0.925373 + 0.379057i 0.876249π0.876249\pi
410410 −17.0121 2.48907i −0.840168 0.122926i
411411 7.25032 + 7.25032i 0.357632 + 0.357632i
412412 −7.20327 2.15395i −0.354880 0.106118i
413413 0 0
414414 11.6877 + 15.6939i 0.574418 + 0.771314i
415415 −2.12659 −0.104390
416416 −21.7269 19.3035i −1.06525 0.946432i
417417 10.0220 0.490778
418418 −4.16544 5.59325i −0.203738 0.273575i
419419 17.2949 17.2949i 0.844910 0.844910i −0.144583 0.989493i 0.546184π-0.546184\pi
0.989493 + 0.144583i 0.0461841π0.0461841\pi
420420 0 0
421421 18.2430 + 18.2430i 0.889111 + 0.889111i 0.994438 0.105327i 0.0335888π-0.0335888\pi
−0.105327 + 0.994438i 0.533589π0.533589\pi
422422 −17.2073 2.51762i −0.837637 0.122556i
423423 22.7472i 1.10601i
424424 9.77617 + 4.55287i 0.474773 + 0.221107i
425425 20.8196i 1.00990i
426426 1.69894 11.6118i 0.0823138 0.562593i
427427 0 0
428428 −0.667549 + 0.360221i −0.0322672 + 0.0174119i
429429 9.37906 9.37906i 0.452825 0.452825i
430430 −15.3196 + 11.4089i −0.738777 + 0.550187i
431431 33.6195 1.61940 0.809698 0.586846i 0.199631π-0.199631\pi
0.809698 + 0.586846i 0.199631π0.199631\pi
432432 3.69760 + 17.8486i 0.177901 + 0.858742i
433433 −26.5511 −1.27596 −0.637982 0.770051i 0.720231π-0.720231\pi
−0.637982 + 0.770051i 0.720231π0.720231\pi
434434 0 0
435435 14.5172 14.5172i 0.696046 0.696046i
436436 9.49509 + 17.5960i 0.454732 + 0.842695i
437437 −7.23124 7.23124i −0.345917 0.345917i
438438 −0.203330 + 1.38971i −0.00971550 + 0.0664028i
439439 19.6106i 0.935962i 0.883739 + 0.467981i 0.155018π0.155018\pi
−0.883739 + 0.467981i 0.844982π0.844982\pi
440440 −9.42675 25.8603i −0.449403 1.23284i
441441 0 0
442442 −26.1484 3.82581i −1.24375 0.181975i
443443 4.82383 + 4.82383i 0.229187 + 0.229187i 0.812353 0.583166i 0.198186π-0.198186\pi
−0.583166 + 0.812353i 0.698186π0.698186\pi
444444 2.87132 9.60229i 0.136267 0.455704i
445445 −10.0757 + 10.0757i −0.477633 + 0.477633i
446446 −18.5396 24.8945i −0.877875 1.17879i
447447 10.2072 0.482786
448448 0 0
449449 6.32412 0.298454 0.149227 0.988803i 0.452322π-0.452322\pi
0.149227 + 0.988803i 0.452322π0.452322\pi
450450 −10.8562 14.5774i −0.511766 0.687187i
451451 −7.80088 + 7.80088i −0.367329 + 0.367329i
452452 −1.50130 + 5.02065i −0.0706151 + 0.236152i
453453 12.0451 + 12.0451i 0.565927 + 0.565927i
454454 34.5197 + 5.05063i 1.62009 + 0.237038i
455455 0 0
456456 −1.39652 3.83107i −0.0653981 0.179406i
457457 39.4984i 1.84766i −0.382805 0.923829i 0.625042π-0.625042\pi
0.382805 0.923829i 0.374958π-0.374958\pi
458458 −1.94794 + 13.3136i −0.0910211 + 0.622104i
459459 11.7196 + 11.7196i 0.547023 + 0.547023i
460460 −19.1676 35.5208i −0.893696 1.65617i
461461 1.26773 1.26773i 0.0590440 0.0590440i −0.676968 0.736012i 0.736707π-0.736707\pi
0.736012 + 0.676968i 0.236707π0.236707\pi
462462 0 0
463463 −14.4427 −0.671208 −0.335604 0.942003i 0.608940π-0.608940\pi
−0.335604 + 0.942003i 0.608940π0.608940\pi
464464 −28.2648 + 5.85548i −1.31216 + 0.271834i
465465 −5.73334 −0.265877
466466 −25.2227 + 18.7840i −1.16842 + 0.870153i
467467 12.2835 12.2835i 0.568412 0.568412i −0.363271 0.931683i 0.618340π-0.618340\pi
0.931683 + 0.363271i 0.118340π0.118340\pi
468468 −20.3035 + 10.9561i −0.938528 + 0.506446i
469469 0 0
470470 −6.79269 + 46.4262i −0.313323 + 2.14148i
471471 4.69806i 0.216475i
472472 9.68827 + 4.51193i 0.445939 + 0.207679i
473473 12.2563i 0.563547i
474474 0.293456 + 0.0429361i 0.0134789 + 0.00197212i
475475 6.71680 + 6.71680i 0.308188 + 0.308188i
476476 0 0
477477 6.05337 6.05337i 0.277165 0.277165i
478478 12.6349 + 16.9658i 0.577907 + 0.775999i
479479 4.78688 0.218718 0.109359 0.994002i 0.465120π-0.465120\pi
0.109359 + 0.994002i 0.465120π0.465120\pi
480480 −0.948901 16.0659i −0.0433112 0.733305i
481481 29.6353 1.35125
482482 20.5684 + 27.6187i 0.936863 + 1.25800i
483483 0 0
484484 4.15666 + 1.24294i 0.188939 + 0.0564974i
485485 15.7503 + 15.7503i 0.715184 + 0.715184i
486486 22.5054 + 3.29279i 1.02086 + 0.149364i
487487 26.8699i 1.21759i 0.793328 + 0.608795i 0.208347π0.208347\pi
−0.793328 + 0.608795i 0.791653π0.791653\pi
488488 8.09377 17.3794i 0.366388 0.786728i
489489 9.79948i 0.443148i
490490 0 0
491491 −11.7576 11.7576i −0.530611 0.530611i 0.390143 0.920754i 0.372426π-0.372426\pi
−0.920754 + 0.390143i 0.872426π0.872426\pi
492492 −5.67674 + 3.06327i −0.255927 + 0.138103i
493493 −18.5590 + 18.5590i −0.835854 + 0.835854i
494494 9.67025 7.20169i 0.435085 0.324019i
495495 −21.8496 −0.982068
496496 6.73764 + 4.42511i 0.302529 + 0.198693i
497497 0 0
498498 −0.639893 + 0.476545i −0.0286743 + 0.0213545i
499499 −13.9362 + 13.9362i −0.623868 + 0.623868i −0.946518 0.322650i 0.895426π-0.895426\pi
0.322650 + 0.946518i 0.395426π0.395426\pi
500500 2.25249 + 4.17424i 0.100734 + 0.186677i
501501 −13.3988 13.3988i −0.598614 0.598614i
502502 −1.01487 + 6.93633i −0.0452957 + 0.309584i
503503 23.6387i 1.05400i −0.849866 0.526999i 0.823317π-0.823317\pi
0.849866 0.526999i 0.176683π-0.176683\pi
504504 0 0
505505 10.4311i 0.464176i
506506 −25.6259 3.74937i −1.13921 0.166680i
507507 8.22952 + 8.22952i 0.365486 + 0.365486i
508508 7.38228 24.6879i 0.327536 1.09535i
509509 −24.0695 + 24.0695i −1.06686 + 1.06686i −0.0692630 + 0.997598i 0.522065π0.522065\pi
−0.997598 + 0.0692630i 0.977935π0.977935\pi
510510 −8.74065 11.7367i −0.387043 0.519711i
511511 0 0
512512 −11.2849 + 19.6125i −0.498726 + 0.866760i
513513 −7.56192 −0.333867
514514 −5.48803 7.36919i −0.242067 0.325041i
515515 8.70490 8.70490i 0.383584 0.383584i
516516 −2.05308 + 6.86593i −0.0903818 + 0.302256i
517517 21.2887 + 21.2887i 0.936274 + 0.936274i
518518 0 0
519519 19.7318i 0.866131i
520520 44.7103 16.2980i 1.96068 0.714716i
521521 17.6401i 0.772828i −0.922325 0.386414i 0.873714π-0.873714\pi
0.922325 0.386414i 0.126286π-0.126286\pi
522522 −3.31718 + 22.6720i −0.145189 + 0.992327i
523523 −10.1679 10.1679i −0.444612 0.444612i 0.448946 0.893559i 0.351799π-0.351799\pi
−0.893559 + 0.448946i 0.851799π0.851799\pi
524524 −8.82537 16.3549i −0.385538 0.714466i
525525 0 0
526526 28.0567 20.8946i 1.22333 0.911046i
527527 7.32957 0.319281
528528 −8.63155 5.66899i −0.375640 0.246711i
529529 −14.9778 −0.651209
530530 −14.1623 + 10.5471i −0.615172 + 0.458135i
531531 5.99894 5.99894i 0.260332 0.260332i
532532 0 0
533533 −13.4870 13.4870i −0.584189 0.584189i
534534 −0.773936 + 5.28964i −0.0334915 + 0.228905i
535535 1.24202i 0.0536974i
536536 7.27374 15.6186i 0.314178 0.674620i
537537 18.7020i 0.807053i
538538 2.09689 + 0.306800i 0.0904035 + 0.0132271i
539539 0 0
540540 −28.5947 8.55050i −1.23052 0.367955i
541541 21.0200 21.0200i 0.903721 0.903721i −0.0920350 0.995756i 0.529337π-0.529337\pi
0.995756 + 0.0920350i 0.0293372π0.0293372\pi
542542 6.21904 + 8.35077i 0.267131 + 0.358696i
543543 −14.5572 −0.624710
544544 1.21309 + 20.5389i 0.0520107 + 0.880597i
545545 −32.7386 −1.40237
546546 0 0
547547 27.6503 27.6503i 1.18224 1.18224i 0.203076 0.979163i 0.434906π-0.434906\pi
0.979163 0.203076i 0.0650940π-0.0650940\pi
548548 22.6153 + 6.76252i 0.966077 + 0.288880i
549549 −10.7613 10.7613i −0.459279 0.459279i
550550 23.8029 + 3.48263i 1.01496 + 0.148500i
551551 11.9750i 0.510150i
552552 −13.7274 6.39301i −0.584277 0.272105i
553553 0 0
554554 0.927205 6.33720i 0.0393932 0.269242i
555555 11.6040 + 11.6040i 0.492564 + 0.492564i
556556 20.3042 10.9565i 0.861089 0.464658i
557557 4.65226 4.65226i 0.197123 0.197123i −0.601643 0.798765i 0.705487π-0.705487\pi
0.798765 + 0.601643i 0.205487π0.205487\pi
558558 5.13201 3.82194i 0.217255 0.161796i
559559 −21.1901 −0.896247
560560 0 0
561561 −9.38988 −0.396441
562562 −11.0347 + 8.21783i −0.465471 + 0.346648i
563563 18.8252 18.8252i 0.793386 0.793386i −0.188657 0.982043i 0.560413π-0.560413\pi
0.982043 + 0.188657i 0.0604134π0.0604134\pi
564564 8.35968 + 15.4919i 0.352006 + 0.652326i
565565 −6.06728 6.06728i −0.255253 0.255253i
566566 0.823582 5.62896i 0.0346178 0.236603i
567567 0 0
568568 −9.25253 25.3824i −0.388228 1.06502i
569569 2.54263i 0.106593i 0.998579 + 0.0532963i 0.0169728π0.0169728\pi
−0.998579 + 0.0532963i 0.983027π0.983027\pi
570570 6.60639 + 0.966592i 0.276711 + 0.0404861i
571571 −28.3705 28.3705i −1.18727 1.18727i −0.977819 0.209450i 0.932833π-0.932833\pi
−0.209450 0.977819i 0.567167π-0.567167\pi
572572 8.74803 29.2552i 0.365773 1.22322i
573573 −4.84569 + 4.84569i −0.202431 + 0.202431i
574574 0 0
575575 35.2760 1.47111
576576 11.5592 + 13.7483i 0.481633 + 0.572847i
577577 −34.7511 −1.44671 −0.723354 0.690478i 0.757400π-0.757400\pi
−0.723354 + 0.690478i 0.757400π0.757400\pi
578578 −3.18565 4.27760i −0.132505 0.177925i
579579 −15.2845 + 15.2845i −0.635204 + 0.635204i
580580 13.5405 45.2821i 0.562237 1.88024i
581581 0 0
582582 8.26877 + 1.20982i 0.342751 + 0.0501485i
583583 11.3305i 0.469260i
584584 1.10735 + 3.03779i 0.0458225 + 0.125705i
585585 37.7761i 1.56185i
586586 0.544717 3.72299i 0.0225020 0.153795i
587587 −20.1643 20.1643i −0.832268 0.832268i 0.155559 0.987827i 0.450282π-0.450282\pi
−0.987827 + 0.155559i 0.950282π0.950282\pi
588588 0 0
589589 −2.36466 + 2.36466i −0.0974341 + 0.0974341i
590590 −14.0350 + 10.4522i −0.577811 + 0.430311i
591591 9.52684 0.391882
592592 −4.68046 22.5929i −0.192366 0.928564i
593593 −8.40923 −0.345326 −0.172663 0.984981i 0.555237π-0.555237\pi
−0.172663 + 0.984981i 0.555237π0.555237\pi
594594 −15.3593 + 11.4385i −0.630199 + 0.469326i
595595 0 0
596596 20.6795 11.1590i 0.847065 0.457091i
597597 −7.03213 7.03213i −0.287806 0.287806i
598598 6.48233 44.3049i 0.265082 1.81176i
599599 3.56073i 0.145488i −0.997351 0.0727438i 0.976824π-0.976824\pi
0.997351 0.0727438i 0.0231755π-0.0231755\pi
600600 12.7508 + 5.93821i 0.520551 + 0.242426i
601601 45.3712i 1.85073i 0.379076 + 0.925365i 0.376242π0.376242\pi
−0.379076 + 0.925365i 0.623758π0.623758\pi
602602 0 0
603603 −9.67096 9.67096i −0.393832 0.393832i
604604 37.5711 + 11.2347i 1.52875 + 0.457132i
605605 −5.02318 + 5.02318i −0.204221 + 0.204221i
606606 −2.33749 3.13872i −0.0949540 0.127502i
607607 4.90180 0.198958 0.0994789 0.995040i 0.468282π-0.468282\pi
0.0994789 + 0.995040i 0.468282π0.468282\pi
608608 −7.01759 6.23486i −0.284601 0.252857i
609609 0 0
610610 18.7498 + 25.1768i 0.759158 + 1.01938i
611611 −36.8062 + 36.8062i −1.48902 + 1.48902i
612612 15.6478 + 4.67908i 0.632526 + 0.189141i
613613 −5.64844 5.64844i −0.228138 0.228138i 0.583776 0.811915i 0.301575π-0.301575\pi
−0.811915 + 0.583776i 0.801575π0.801575\pi
614614 −7.89548 1.15520i −0.318635 0.0466201i
615615 10.5620i 0.425901i
616616 0 0
617617 40.2966i 1.62228i 0.584852 + 0.811140i 0.301153π0.301153\pi
−0.584852 + 0.811140i 0.698847π0.698847\pi
618618 0.668643 4.57000i 0.0268968 0.183832i
619619 −14.2321 14.2321i −0.572038 0.572038i 0.360660 0.932698i 0.382552π-0.382552\pi
−0.932698 + 0.360660i 0.882552π0.882552\pi
620620 −11.6155 + 6.26794i −0.466491 + 0.251726i
621621 −19.8573 + 19.8573i −0.796844 + 0.796844i
622622 −0.916568 + 0.682592i −0.0367510 + 0.0273695i
623623 0 0
624624 9.80118 14.9232i 0.392361 0.597406i
625625 20.8545 0.834181
626626 −26.4226 + 19.6776i −1.05606 + 0.786476i
627627 3.02935 3.02935i 0.120981 0.120981i
628628 5.13613 + 9.51810i 0.204954 + 0.379814i
629629 −14.8348 14.8348i −0.591500 0.591500i
630630 0 0
631631 15.2886i 0.608631i 0.952571 + 0.304315i 0.0984277π0.0984277\pi
−0.952571 + 0.304315i 0.901572π0.901572\pi
632632 0.641472 0.233833i 0.0255164 0.00930137i
633633 10.6832i 0.424618i
634634 −4.36953 0.639313i −0.173536 0.0253904i
635635 29.8345 + 29.8345i 1.18394 + 1.18394i
636636 −1.89798 + 6.34725i −0.0752599 + 0.251685i
637637 0 0
638638 −18.1138 24.3228i −0.717133 0.962948i
639639 −21.4458 −0.848384
640640 −19.4864 31.5116i −0.770267 1.24560i
641641 −12.3673 −0.488480 −0.244240 0.969715i 0.578538π-0.578538\pi
−0.244240 + 0.969715i 0.578538π0.578538\pi
642642 −0.278324 0.373727i −0.0109846 0.0147498i
643643 29.2082 29.2082i 1.15186 1.15186i 0.165677 0.986180i 0.447019π-0.447019\pi
0.986180 0.165677i 0.0529809π-0.0529809\pi
644644 0 0
645645 −8.29724 8.29724i −0.326703 0.326703i
646646 −8.44570 1.23570i −0.332292 0.0486181i
647647 14.3708i 0.564975i 0.959271 + 0.282487i 0.0911595π0.0911595\pi
−0.959271 + 0.282487i 0.908841π0.908841\pi
648648 7.37911 2.68987i 0.289879 0.105668i
649649 11.2286i 0.440760i
650650 −6.02117 + 41.1531i −0.236170 + 1.61416i
651651 0 0
652652 10.7132 + 19.8534i 0.419563 + 0.777519i
653653 10.3709 10.3709i 0.405844 0.405844i −0.474442 0.880287i 0.657350π-0.657350\pi
0.880287 + 0.474442i 0.157350π0.157350\pi
654654 −9.85111 + 7.33638i −0.385209 + 0.286875i
655655 30.4295 1.18898
656656 −8.15198 + 12.4121i −0.318281 + 0.484613i
657657 2.56666 0.100135
658658 0 0
659659 −30.0445 + 30.0445i −1.17037 + 1.17037i −0.188248 + 0.982122i 0.560281π0.560281\pi
−0.982122 + 0.188248i 0.939719π0.939719\pi
660660 14.8806 8.02982i 0.579226 0.312560i
661661 1.95989 + 1.95989i 0.0762309 + 0.0762309i 0.744194 0.667963i 0.232834π-0.232834\pi
−0.667963 + 0.744194i 0.732834π0.732834\pi
662662 3.22521 22.0434i 0.125351 0.856742i
663663 16.2343i 0.630487i
664664 −0.775420 + 1.66502i −0.0300921 + 0.0646154i
665665 0 0
666666 −18.1224 2.65152i −0.702230 0.102744i
667667 −31.4457 31.4457i −1.21758 1.21758i
668668 −41.7936 12.4973i −1.61704 0.483535i
669669 13.4831 13.4831i 0.521286 0.521286i
670670 16.8502 + 22.6260i 0.650978 + 0.874118i
671671 20.1425 0.777592
672672 0 0
673673 −4.79538 −0.184848 −0.0924242 0.995720i 0.529462π-0.529462\pi
−0.0924242 + 0.995720i 0.529462π0.529462\pi
674674 −4.52811 6.08024i −0.174416 0.234202i
675675 18.4446 18.4446i 0.709933 0.709933i
676676 25.6696 + 7.67583i 0.987292 + 0.295224i
677677 −35.1646 35.1646i −1.35149 1.35149i −0.884000 0.467486i 0.845160π-0.845160\pi
−0.467486 0.884000i 0.654840π-0.654840\pi
678678 −3.18527 0.466042i −0.122330 0.0178982i
679679 0 0
680680 −30.5394 14.2225i −1.17113 0.545409i
681681 21.4316i 0.821262i
682682 −1.22607 + 8.37983i −0.0469485 + 0.320880i
683683 −2.91144 2.91144i −0.111403 0.111403i 0.649208 0.760611i 0.275101π-0.275101\pi
−0.760611 + 0.649208i 0.775101π0.775101\pi
684684 −6.55785 + 3.53873i −0.250746 + 0.135307i
685685 −27.3298 + 27.3298i −1.04422 + 1.04422i
686686 0 0
687687 −8.26579 −0.315360
688688 3.34667 + 16.1546i 0.127591 + 0.615890i
689689 −19.5894 −0.746296
690690 19.8863 14.8099i 0.757059 0.563802i
691691 −25.1130 + 25.1130i −0.955342 + 0.955342i −0.999045 0.0437029i 0.986085π-0.986085\pi
0.0437029 + 0.999045i 0.486085π0.486085\pi
692692 21.5717 + 39.9759i 0.820033 + 1.51966i
693693 0 0
694694 3.39951 23.2347i 0.129043 0.881977i
695695 37.7774i 1.43298i
696696 −6.07290 16.6597i −0.230193 0.631486i
697697 13.5026i 0.511448i
698698 44.0904 + 6.45093i 1.66885 + 0.244171i
699699 −13.6608 13.6608i −0.516701 0.516701i
700700 0 0
701701 15.7687 15.7687i 0.595575 0.595575i −0.343557 0.939132i 0.611632π-0.611632\pi
0.939132 + 0.343557i 0.111632π0.111632\pi
702702 −19.7761 26.5549i −0.746401 1.00225i
703703 9.57195 0.361013
704704 −23.6848 2.04876i −0.892655 0.0772156i
705705 −28.8238 −1.08557
706706 −11.5617 15.5248i −0.435131 0.584283i
707707 0 0
708708 −1.88092 + 6.29018i −0.0706892 + 0.236400i
709709 −8.16940 8.16940i −0.306808 0.306808i 0.536862 0.843670i 0.319610π-0.319610\pi
−0.843670 + 0.536862i 0.819610π0.819610\pi
710710 43.7701 + 6.40407i 1.64266 + 0.240341i
711711 0.541985i 0.0203260i
712712 4.21491 + 11.5627i 0.157960 + 0.433331i
713713 12.4190i 0.465095i
714714 0 0
715715 35.3539 + 35.3539i 1.32216 + 1.32216i
716716 −20.4459 37.8897i −0.764100 1.41600i
717717 −9.18884 + 9.18884i −0.343163 + 0.343163i
718718 −7.17099 + 5.34043i −0.267619 + 0.199303i
719719 −28.8526 −1.07602 −0.538011 0.842938i 0.680824π-0.680824\pi
−0.538011 + 0.842938i 0.680824π0.680824\pi
720720 −28.7992 + 5.96618i −1.07328 + 0.222347i
721721 0 0
722722 −18.4271 + 13.7231i −0.685784 + 0.510722i
723723 −14.9585 + 14.9585i −0.556313 + 0.556313i
724724 −29.4924 + 15.9146i −1.09608 + 0.591461i
725725 29.2086 + 29.2086i 1.08478 + 1.08478i
726726 −0.385842 + 2.63713i −0.0143199 + 0.0978729i
727727 19.1342i 0.709648i −0.934933 0.354824i 0.884541π-0.884541\pi
0.934933 0.354824i 0.115459π-0.115459\pi
728728 0 0
729729 5.64199i 0.208963i
730730 −5.23845 0.766445i −0.193884 0.0283674i
731731 10.6073 + 10.6073i 0.392325 + 0.392325i
732732 11.2837 + 3.37410i 0.417058 + 0.124710i
733733 8.17266 8.17266i 0.301864 0.301864i −0.539879 0.841743i 0.681530π-0.681530\pi
0.841743 + 0.539879i 0.181530π0.181530\pi
734734 31.4504 + 42.2308i 1.16085 + 1.55877i
735735 0 0
736736 −34.8004 + 2.05541i −1.28276 + 0.0757636i
737737 18.1017 0.666786
738738 7.04082 + 9.45423i 0.259176 + 0.348015i
739739 −5.86541 + 5.86541i −0.215763 + 0.215763i −0.806710 0.590947i 0.798754π-0.798754\pi
0.590947 + 0.806710i 0.298754π0.298754\pi
740740 36.1954 + 10.8233i 1.33057 + 0.397873i
741741 5.23749 + 5.23749i 0.192404 + 0.192404i
742742 0 0
743743 9.24326i 0.339102i −0.985521 0.169551i 0.945768π-0.945768\pi
0.985521 0.169551i 0.0542318π-0.0542318\pi
744744 −2.09055 + 4.48895i −0.0766434 + 0.164573i
745745 38.4757i 1.40964i
746746 −0.885006 + 6.04878i −0.0324024 + 0.221462i
747747 1.03098 + 1.03098i 0.0377214 + 0.0377214i
748748 −19.0236 + 10.2654i −0.695570 + 0.375341i
749749 0 0
750750 −2.33695 + 1.74038i −0.0853332 + 0.0635499i
751751 −20.6757 −0.754467 −0.377234 0.926118i 0.623125π-0.623125\pi
−0.377234 + 0.926118i 0.623125π0.623125\pi
752752 33.8728 + 22.2468i 1.23522 + 0.811258i
753753 −4.30644 −0.156935
754754 42.0520 31.3172i 1.53144 1.14051i
755755 −45.4034 + 45.4034i −1.65240 + 1.65240i
756756 0 0
757757 19.3612 + 19.3612i 0.703694 + 0.703694i 0.965201 0.261508i 0.0842197π-0.0842197\pi
−0.261508 + 0.965201i 0.584220π0.584220\pi
758758 3.33314 22.7811i 0.121065 0.827447i
759759 15.9099i 0.577493i
760760 14.4410 5.26412i 0.523831 0.190950i
761761 17.6413i 0.639497i 0.947502 + 0.319748i 0.103598π0.103598\pi
−0.947502 + 0.319748i 0.896402π0.896402\pi
762762 15.6628 + 2.29165i 0.567404 + 0.0830178i
763763 0 0
764764 −4.51966 + 15.1147i −0.163516 + 0.546831i
765765 −18.9099 + 18.9099i −0.683687 + 0.683687i
766766 16.6630 + 22.3747i 0.602060 + 0.808431i
767767 −19.4132 −0.700971
768768 −12.9249 5.11518i −0.466387 0.184578i
769769 33.4127 1.20489 0.602447 0.798159i 0.294193π-0.294193\pi
0.602447 + 0.798159i 0.294193π0.294193\pi
770770 0 0
771771 3.99122 3.99122i 0.143740 0.143740i
772772 −14.2562 + 47.6757i −0.513091 + 1.71589i
773773 9.47365 + 9.47365i 0.340744 + 0.340744i 0.856647 0.515903i 0.172544π-0.172544\pi
−0.515903 + 0.856647i 0.672544π0.672544\pi
774774 12.9581 + 1.89592i 0.465769 + 0.0681474i
775775 11.5355i 0.414367i
776776 18.0748 6.58874i 0.648849 0.236522i
777777 0 0
778778 1.21574 8.30927i 0.0435865 0.297902i
779779 −4.35620 4.35620i −0.156077 0.156077i
780780 13.8829 + 25.7273i 0.497086 + 0.921184i
781781 20.0707 20.0707i 0.718187 0.718187i
782782 −25.4229 + 18.9331i −0.909123 + 0.677048i
783783 −32.8837 −1.17517
784784 0 0
785785 −17.7091 −0.632066
786786 9.15628 6.81892i 0.326594 0.243223i
787787 6.81141 6.81141i 0.242801 0.242801i −0.575207 0.818008i 0.695079π-0.695079\pi
0.818008 + 0.575207i 0.195079π0.195079\pi
788788 19.3010 10.4152i 0.687571 0.371025i
789789 15.1958 + 15.1958i 0.540983 + 0.540983i
790790 −0.161846 + 1.10617i −0.00575821 + 0.0393558i
791791 0 0
792792 −7.96706 + 17.1073i −0.283097 + 0.607882i
793793 34.8246i 1.23666i
794794 35.7834 + 5.23553i 1.26991 + 0.185802i
795795 −7.67044 7.67044i −0.272042 0.272042i
796796 −21.9347 6.55901i −0.777455 0.232478i
797797 −3.47475 + 3.47475i −0.123082 + 0.123082i −0.765965 0.642883i 0.777738π-0.777738\pi
0.642883 + 0.765965i 0.277738π0.277738\pi
798798 0 0
799799 36.8487 1.30361
800800 32.3246 1.90919i 1.14285 0.0675001i
801801 9.76945 0.345186
802802 3.04338 + 4.08658i 0.107466 + 0.144302i
803803 −2.40208 + 2.40208i −0.0847677 + 0.0847677i
804804 10.1405 + 3.03225i 0.357627 + 0.106939i
805805 0 0
806806 −14.4880 2.11976i −0.510318 0.0746654i
807807 1.30186i 0.0458277i
808808 −8.16706 3.80349i −0.287316 0.133806i
809809 44.9480i 1.58029i 0.612921 + 0.790144i 0.289994π0.289994\pi
−0.612921 + 0.790144i 0.710006π0.710006\pi
810810 −1.86178 + 12.7247i −0.0654161 + 0.447101i
811811 23.3543 + 23.3543i 0.820080 + 0.820080i 0.986119 0.166039i 0.0530978π-0.0530978\pi
−0.166039 + 0.986119i 0.553098π0.553098\pi
812812 0 0
813813 −4.52285 + 4.52285i −0.158623 + 0.158623i
814814 19.4419 14.4789i 0.681439 0.507486i
815815 −36.9387 −1.29391
816816 −12.3765 + 2.56397i −0.433263 + 0.0897568i
817817 −6.84423 −0.239449
818818 −17.3900 + 12.9508i −0.608026 + 0.452813i
819819 0 0
820820 −11.5468 21.3982i −0.403233 0.747259i
821821 −22.7441 22.7441i −0.793774 0.793774i 0.188332 0.982105i 0.439692π-0.439692\pi
−0.982105 + 0.188332i 0.939692π0.939692\pi
822822 −2.09926 + 14.3479i −0.0732202 + 0.500440i
823823 6.46922i 0.225503i 0.993623 + 0.112751i 0.0359664π0.0359664\pi
−0.993623 + 0.112751i 0.964034π0.964034\pi
824824 −3.64148 9.98964i −0.126857 0.348006i
825825 14.7781i 0.514506i
826826 0 0
827827 0.313180 + 0.313180i 0.0108903 + 0.0108903i 0.712531 0.701641i 0.247549π-0.247549\pi
−0.701641 + 0.712531i 0.747549π0.747549\pi
828828 −7.92808 + 26.5132i −0.275520 + 0.921396i
829829 −20.1834 + 20.1834i −0.700998 + 0.700998i −0.964625 0.263627i 0.915081π-0.915081\pi
0.263627 + 0.964625i 0.415081π0.415081\pi
830830 −1.79632 2.41205i −0.0623510 0.0837234i
831831 3.93446 0.136485
832832 3.54213 40.9490i 0.122801 1.41965i
833833 0 0
834834 8.46552 + 11.3673i 0.293137 + 0.393617i
835835 50.5061 50.5061i 1.74784 1.74784i
836836 2.82554 9.44919i 0.0977232 0.326807i
837837 6.49345 + 6.49345i 0.224446 + 0.224446i
838838 34.2253 + 5.00756i 1.18229 + 0.172983i
839839 49.1079i 1.69539i 0.530482 + 0.847696i 0.322011π0.322011\pi
−0.530482 + 0.847696i 0.677989π0.677989\pi
840840 0 0
841841 23.0742i 0.795662i
842842 −5.28210 + 36.1017i −0.182033 + 1.24415i
843843 −5.97649 5.97649i −0.205841 0.205841i
844844 −11.6793 21.6437i −0.402019 0.745008i
845845 −31.0208 + 31.0208i −1.06715 + 1.06715i
846846 25.8007 19.2145i 0.887046 0.660606i
847847 0 0
848848 3.09385 + 14.9343i 0.106243 + 0.512845i
849849 3.49475 0.119940
850850 23.6143 17.5862i 0.809965 0.603202i
851851 25.1355 25.1355i 0.861634 0.861634i
852852 14.6056 7.88142i 0.500379 0.270013i
853853 −4.33966 4.33966i −0.148587 0.148587i 0.628899 0.777487i 0.283506π-0.283506\pi
−0.777487 + 0.628899i 0.783506π0.783506\pi
854854 0 0
855855 12.2014i 0.417278i
856856 −0.972450 0.452881i −0.0332377 0.0154791i
857857 16.1733i 0.552471i 0.961090 + 0.276235i 0.0890870π0.0890870\pi
−0.961090 + 0.276235i 0.910913π0.910913\pi
858858 18.5605 + 2.71562i 0.633645 + 0.0927096i
859859 −31.4890 31.4890i −1.07439 1.07439i −0.997001 0.0773900i 0.975341π-0.975341\pi
−0.0773900 0.997001i 0.524659π-0.524659\pi
860860 −25.8808 7.73899i −0.882528 0.263897i
861861 0 0
862862 28.3983 + 38.1325i 0.967249 + 1.29880i
863863 5.70353 0.194150 0.0970752 0.995277i 0.469051π-0.469051\pi
0.0970752 + 0.995277i 0.469051π0.469051\pi
864864 −17.1212 + 19.2706i −0.582474 + 0.655599i
865865 −74.3782 −2.52893
866866 −22.4276 30.1152i −0.762121 1.02336i
867867 2.31679 2.31679i 0.0786822 0.0786822i
868868 0 0
869869 0.507233 + 0.507233i 0.0172067 + 0.0172067i
870870 28.7285 + 4.20331i 0.973988 + 0.142506i
871871 31.2963i 1.06044i
872872 −11.9375 + 25.6329i −0.404256 + 0.868040i
873873 15.2716i 0.516865i
874874 2.09374 14.3101i 0.0708217 0.484047i
875875 0 0
876876 −1.74801 + 0.943255i −0.0590598 + 0.0318696i
877877 11.1824 11.1824i 0.377602 0.377602i −0.492634 0.870236i 0.663966π-0.663966\pi
0.870236 + 0.492634i 0.163966π0.163966\pi
878878 −22.2430 + 16.5650i −0.750665 + 0.559040i
879879 2.31143 0.0779625
880880 21.3690 32.5363i 0.720349 1.09680i
881881 −20.6047 −0.694190 −0.347095 0.937830i 0.612832π-0.612832\pi
−0.347095 + 0.937830i 0.612832π0.612832\pi
882882 0 0
883883 3.92964 3.92964i 0.132243 0.132243i −0.637887 0.770130i 0.720191π-0.720191\pi
0.770130 + 0.637887i 0.220191π0.220191\pi
884884 −17.7480 32.8901i −0.596931 1.10621i
885885 −7.60147 7.60147i −0.255521 0.255521i
886886 −1.39669 + 9.54603i −0.0469229 + 0.320705i
887887 18.5762i 0.623726i −0.950127 0.311863i 0.899047π-0.899047\pi
0.950127 0.311863i 0.100953π-0.100953\pi
888888 13.3166 4.85425i 0.446877 0.162898i
889889 0 0
890890 −19.9391 2.91732i −0.668359 0.0977887i
891891 5.83491 + 5.83491i 0.195477 + 0.195477i
892892 12.5759 42.0565i 0.421073 1.40816i
893893 −11.8881 + 11.8881i −0.397820 + 0.397820i
894894 8.62201 + 11.5774i 0.288363 + 0.387207i
895895 70.4965 2.35644
896896 0 0
897897 27.5068 0.918426
898898 5.34195 + 7.17304i 0.178263 + 0.239367i
899899 −10.2829 + 10.2829i −0.342955 + 0.342955i
900900 7.36407 24.6270i 0.245469 0.820899i
901901 9.80599 + 9.80599i 0.326685 + 0.326685i
902902 −15.4374 2.25867i −0.514009 0.0752055i
903903 0 0
904904 −6.96274 + 2.53810i −0.231577 + 0.0844158i
905905 54.8727i 1.82403i
906906 −3.48753 + 23.8364i −0.115866 + 0.791910i
907907 20.1706 + 20.1706i 0.669753 + 0.669753i 0.957659 0.287905i 0.0929589π-0.0929589\pi
−0.287905 + 0.957659i 0.592959π0.592959\pi
908908 23.4300 + 43.4197i 0.777552 + 1.44093i
909909 −5.05701 + 5.05701i −0.167730 + 0.167730i
910910 0 0
911911 40.6520 1.34686 0.673431 0.739250i 0.264820π-0.264820\pi
0.673431 + 0.739250i 0.264820π0.264820\pi
912912 3.16570 4.82007i 0.104827 0.159608i
913913 −1.92974 −0.0638651
914914 44.8005 33.3641i 1.48187 1.10359i
915915 −13.6360 + 13.6360i −0.450791 + 0.450791i
916916 −16.7462 + 9.03653i −0.553310 + 0.298575i
917917 0 0
918918 −3.39329 + 23.1922i −0.111995 + 0.765458i
919919 26.9677i 0.889581i −0.895635 0.444790i 0.853278π-0.853278\pi
0.895635 0.444790i 0.146722π-0.146722\pi
920920 24.0982 51.7449i 0.794493 1.70598i
921921 4.90192i 0.161524i
922922 2.50875 + 0.367058i 0.0826211 + 0.0120884i
923923 34.7005 + 34.7005i 1.14218 + 1.14218i
924924 0 0
925925 −23.3473 + 23.3473i −0.767656 + 0.767656i
926926 −12.1997 16.3814i −0.400905 0.538326i
927927 −8.44033 −0.277217
928928 −30.5167 27.1129i −1.00176 0.890024i
929929 −15.6320 −0.512870 −0.256435 0.966561i 0.582548π-0.582548\pi
−0.256435 + 0.966561i 0.582548π0.582548\pi
930930 −4.84292 6.50295i −0.158806 0.213240i
931931 0 0
932932 −42.6110 12.7417i −1.39577 0.417369i
933933 −0.496421 0.496421i −0.0162521 0.0162521i
934934 24.3082 + 3.55657i 0.795388 + 0.116374i
935935 35.3947i 1.15753i
936936 −29.5770 13.7744i −0.966756 0.450229i
937937 47.9244i 1.56562i −0.622260 0.782811i 0.713785π-0.713785\pi
0.622260 0.782811i 0.286215π-0.286215\pi
938938 0 0
939939 −14.3107 14.3107i −0.467013 0.467013i
940940 −58.3960 + 31.5115i −1.90467 + 1.02779i
941941 −7.62070 + 7.62070i −0.248428 + 0.248428i −0.820325 0.571897i 0.806208π-0.806208\pi
0.571897 + 0.820325i 0.306208π0.306208\pi
942942 −5.32871 + 3.96843i −0.173619 + 0.129298i
943943 −22.8784 −0.745022
944944 3.06604 + 14.8000i 0.0997910 + 0.481698i
945945 0 0
946946 −13.9016 + 10.3529i −0.451979 + 0.336601i
947947 −19.6254 + 19.6254i −0.637739 + 0.637739i −0.949997 0.312258i 0.898915π-0.898915\pi
0.312258 + 0.949997i 0.398915π0.398915\pi
948948 0.199182 + 0.369117i 0.00646912 + 0.0119884i
949949 −4.15299 4.15299i −0.134812 0.134812i
950950 −1.94479 + 13.2921i −0.0630972 + 0.431252i
951951 2.71283i 0.0879696i
952952 0 0
953953 3.58597i 0.116161i −0.998312 0.0580805i 0.981502π-0.981502\pi
0.998312 0.0580805i 0.0184980π-0.0184980\pi
954954 11.9792 + 1.75269i 0.387841 + 0.0567456i
955955 −18.2656 18.2656i −0.591061 0.591061i
956956 −8.57060 + 28.6619i −0.277193 + 0.926992i
957957 13.1734 13.1734i 0.425836 0.425836i
958958 4.04346 + 5.42945i 0.130638 + 0.175418i
959959 0 0
960960 17.4210 14.6471i 0.562260 0.472732i
961961 −26.9389 −0.868997
962962 25.0328 + 33.6134i 0.807090 + 1.08374i
963963 −0.602137 + 0.602137i −0.0194036 + 0.0194036i
964964 −13.9521 + 46.6587i −0.449367 + 1.50278i
965965 −57.6144 57.6144i −1.85467 1.85467i
966966 0 0
967967 51.9947i 1.67204i −0.548703 0.836018i 0.684878π-0.684878\pi
0.548703 0.836018i 0.315122π-0.315122\pi
968968 2.10132 + 5.76454i 0.0675390 + 0.185279i
969969 5.24354i 0.168447i
970970 −4.56035 + 31.1688i −0.146424 + 1.00077i
971971 35.0803 + 35.0803i 1.12578 + 1.12578i 0.990856 + 0.134925i 0.0430795π0.0430795\pi
0.134925 + 0.990856i 0.456921π0.456921\pi
972972 15.2754 + 28.3078i 0.489958 + 0.907973i
973973 0 0
974974 −30.4768 + 22.6968i −0.976538 + 0.727254i
975975 −25.5500 −0.818254
976976 26.5491 5.50004i 0.849816 0.176052i
977977 5.67083 0.181426 0.0907129 0.995877i 0.471085π-0.471085\pi
0.0907129 + 0.995877i 0.471085π0.471085\pi
978978 −11.1149 + 8.27758i −0.355416 + 0.264688i
979979 −9.14303 + 9.14303i −0.292213 + 0.292213i
980980 0 0
981981 15.8718 + 15.8718i 0.506748 + 0.506748i
982982 3.40429 23.2674i 0.108635 0.742492i
983983 46.7462i 1.49097i −0.666522 0.745486i 0.732218π-0.732218\pi
0.666522 0.745486i 0.267782π-0.267782\pi
984984 −8.26958 3.85124i −0.263625 0.122773i
985985 35.9110i 1.14422i
986986 −36.7269 5.37357i −1.16962 0.171129i
987987 0 0
988988 16.3368 + 4.88511i 0.519744 + 0.155416i
989989 −17.9726 + 17.9726i −0.571497 + 0.571497i
990990 −18.4563 24.7826i −0.586579 0.787644i
991991 14.4138 0.457870 0.228935 0.973442i 0.426476π-0.426476\pi
0.228935 + 0.973442i 0.426476π0.426476\pi
992992 0.672133 + 11.3799i 0.0213403 + 0.361313i
993993 13.6857 0.434303
994994 0 0
995995 26.5073 26.5073i 0.840339 0.840339i
996996 −1.08103 0.323254i −0.0342537 0.0102427i
997997 −40.2131 40.2131i −1.27356 1.27356i −0.944205 0.329357i 0.893168π-0.893168\pi
−0.329357 0.944205i 0.606832π-0.606832\pi
998998 −27.5787 4.03508i −0.872988 0.127728i
999999 26.2849i 0.831619i
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 784.2.m.k.197.8 24
7.2 even 3 784.2.x.o.165.9 48
7.3 odd 6 112.2.w.c.37.1 48
7.4 even 3 784.2.x.o.373.1 48
7.5 odd 6 112.2.w.c.53.9 yes 48
7.6 odd 2 784.2.m.j.197.8 24
16.13 even 4 inner 784.2.m.k.589.8 24
28.3 even 6 448.2.ba.c.177.8 48
28.19 even 6 448.2.ba.c.305.5 48
56.3 even 6 896.2.ba.e.737.5 48
56.5 odd 6 896.2.ba.f.865.5 48
56.19 even 6 896.2.ba.e.865.8 48
56.45 odd 6 896.2.ba.f.737.8 48
112.3 even 12 448.2.ba.c.401.5 48
112.5 odd 12 896.2.ba.f.417.8 48
112.13 odd 4 784.2.m.j.589.8 24
112.19 even 12 448.2.ba.c.81.8 48
112.45 odd 12 112.2.w.c.93.9 yes 48
112.59 even 12 896.2.ba.e.289.8 48
112.61 odd 12 112.2.w.c.109.1 yes 48
112.75 even 12 896.2.ba.e.417.5 48
112.93 even 12 784.2.x.o.557.1 48
112.101 odd 12 896.2.ba.f.289.5 48
112.109 even 12 784.2.x.o.765.9 48
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
112.2.w.c.37.1 48 7.3 odd 6
112.2.w.c.53.9 yes 48 7.5 odd 6
112.2.w.c.93.9 yes 48 112.45 odd 12
112.2.w.c.109.1 yes 48 112.61 odd 12
448.2.ba.c.81.8 48 112.19 even 12
448.2.ba.c.177.8 48 28.3 even 6
448.2.ba.c.305.5 48 28.19 even 6
448.2.ba.c.401.5 48 112.3 even 12
784.2.m.j.197.8 24 7.6 odd 2
784.2.m.j.589.8 24 112.13 odd 4
784.2.m.k.197.8 24 1.1 even 1 trivial
784.2.m.k.589.8 24 16.13 even 4 inner
784.2.x.o.165.9 48 7.2 even 3
784.2.x.o.373.1 48 7.4 even 3
784.2.x.o.557.1 48 112.93 even 12
784.2.x.o.765.9 48 112.109 even 12
896.2.ba.e.289.8 48 112.59 even 12
896.2.ba.e.417.5 48 112.75 even 12
896.2.ba.e.737.5 48 56.3 even 6
896.2.ba.e.865.8 48 56.19 even 6
896.2.ba.f.289.5 48 112.101 odd 12
896.2.ba.f.417.8 48 112.5 odd 12
896.2.ba.f.737.8 48 56.45 odd 6
896.2.ba.f.865.5 48 56.5 odd 6