Properties

Label 450.2.h.e.361.1
Level 450450
Weight 22
Character 450.361
Analytic conductor 3.5933.593
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [450,2,Mod(91,450)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(450, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("450.91");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 450=23252 450 = 2 \cdot 3^{2} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 450.h (of order 55, degree 44, 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: 3.593268090963.59326809096
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ5)\Q(\zeta_{5})
Coefficient field: 8.0.58140625.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x83x7+4x67x5+11x4+5x310x225x+25 x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 5 5
Twist minimal: no (minimal twist has level 50)
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 361.1
Root 1.666370.917186i1.66637 - 0.917186i of defining polynomial
Character χ\chi == 450.361
Dual form 450.2.h.e.91.1

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+(0.8090170.587785i)q2+(0.3090170.951057i)q4+(2.023730.951057i)q52.77447q7+(0.3090170.951057i)q8+(2.19625+0.420099i)q10+(2.244591.63079i)q11+(4.593433.33732i)q13+(2.24459+1.63079i)q14+(0.8090170.587785i)q16+(1.593434.90406i)q17+(0.436451+1.34326i)q19+(1.52988+1.63079i)q20+(0.8573582.63868i)q22+(0.529876+0.384978i)q23+(3.19098+3.84937i)q255.67779q26+(0.857358+2.63868i)q28+(1.26594+3.89618i)q29+(2.202396.77827i)q311.00000q32+(4.171643.03088i)q34+(5.61478+2.63868i)q35+(0.847416+0.615684i)q37+(1.14264+0.830178i)q38+(0.279141+2.21858i)q40+(7.36789+5.35309i)q41+9.24660q43+(0.8573582.63868i)q44+(0.202395+0.622907i)q46+(0.8573582.63868i)q47+0.697669q49+(4.84416+1.23859i)q50+(4.59343+3.33732i)q52+(0.1625770.500362i)q53+(6.09343+1.16555i)q55+(0.857358+2.63868i)q56+(1.26594+3.89618i)q58+(3.059752.22304i)q59+(8.763656.36716i)q61+(5.765944.18920i)q62+(0.809017+0.587785i)q64+(6.12188+11.1224i)q65+(1.336004.11180i)q675.15643q68+(6.093431.16555i)q70+(4.0934312.5983i)q71+(3.40859+2.47648i)q73+1.04746q74+1.41238q76+(6.22754+4.52458i)q77+(3.05975+9.41695i)q79+(1.07822+1.95894i)q80+9.10722q82+(1.444974.44717i)q83+(1.43937+11.4399i)q85+(7.480665.43502i)q86+(2.244591.63079i)q88+(7.43002+5.39823i)q89+(12.7443+9.25928i)q91+(0.202395+0.622907i)q92+(0.8573582.63868i)q94+(0.3942543.13348i)q95+(0.0278640+0.0857567i)q97+(0.5644260.410079i)q98+O(q100)q+(0.809017 - 0.587785i) q^{2} +(0.309017 - 0.951057i) q^{4} +(-2.02373 - 0.951057i) q^{5} -2.77447 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-2.19625 + 0.420099i) q^{10} +(2.24459 - 1.63079i) q^{11} +(-4.59343 - 3.33732i) q^{13} +(-2.24459 + 1.63079i) q^{14} +(-0.809017 - 0.587785i) q^{16} +(-1.59343 - 4.90406i) q^{17} +(0.436451 + 1.34326i) q^{19} +(-1.52988 + 1.63079i) q^{20} +(0.857358 - 2.63868i) q^{22} +(-0.529876 + 0.384978i) q^{23} +(3.19098 + 3.84937i) q^{25} -5.67779 q^{26} +(-0.857358 + 2.63868i) q^{28} +(-1.26594 + 3.89618i) q^{29} +(-2.20239 - 6.77827i) q^{31} -1.00000 q^{32} +(-4.17164 - 3.03088i) q^{34} +(5.61478 + 2.63868i) q^{35} +(0.847416 + 0.615684i) q^{37} +(1.14264 + 0.830178i) q^{38} +(-0.279141 + 2.21858i) q^{40} +(7.36789 + 5.35309i) q^{41} +9.24660 q^{43} +(-0.857358 - 2.63868i) q^{44} +(-0.202395 + 0.622907i) q^{46} +(0.857358 - 2.63868i) q^{47} +0.697669 q^{49} +(4.84416 + 1.23859i) q^{50} +(-4.59343 + 3.33732i) q^{52} +(0.162577 - 0.500362i) q^{53} +(-6.09343 + 1.16555i) q^{55} +(0.857358 + 2.63868i) q^{56} +(1.26594 + 3.89618i) q^{58} +(-3.05975 - 2.22304i) q^{59} +(8.76365 - 6.36716i) q^{61} +(-5.76594 - 4.18920i) q^{62} +(-0.809017 + 0.587785i) q^{64} +(6.12188 + 11.1224i) q^{65} +(-1.33600 - 4.11180i) q^{67} -5.15643 q^{68} +(6.09343 - 1.16555i) q^{70} +(4.09343 - 12.5983i) q^{71} +(-3.40859 + 2.47648i) q^{73} +1.04746 q^{74} +1.41238 q^{76} +(-6.22754 + 4.52458i) q^{77} +(-3.05975 + 9.41695i) q^{79} +(1.07822 + 1.95894i) q^{80} +9.10722 q^{82} +(-1.44497 - 4.44717i) q^{83} +(-1.43937 + 11.4399i) q^{85} +(7.48066 - 5.43502i) q^{86} +(-2.24459 - 1.63079i) q^{88} +(-7.43002 + 5.39823i) q^{89} +(12.7443 + 9.25928i) q^{91} +(0.202395 + 0.622907i) q^{92} +(-0.857358 - 2.63868i) q^{94} +(0.394254 - 3.13348i) q^{95} +(-0.0278640 + 0.0857567i) q^{97} +(0.564426 - 0.410079i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+2q22q4+4q7+2q8q1113q13+q142q16+11q17+20q195q20+q22+3q23+30q2522q26q28+15q299q318q32++19q98+O(q100) 8 q + 2 q^{2} - 2 q^{4} + 4 q^{7} + 2 q^{8} - q^{11} - 13 q^{13} + q^{14} - 2 q^{16} + 11 q^{17} + 20 q^{19} - 5 q^{20} + q^{22} + 3 q^{23} + 30 q^{25} - 22 q^{26} - q^{28} + 15 q^{29} - 9 q^{31} - 8 q^{32}+ \cdots + 19 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/450Z)×\left(\mathbb{Z}/450\mathbb{Z}\right)^\times.

nn 101101 127127
χ(n)\chi(n) 11 e(45)e\left(\frac{4}{5}\right)

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0.809017 0.587785i 0.572061 0.415627i
33 0 0
44 0.309017 0.951057i 0.154508 0.475528i
55 −2.02373 0.951057i −0.905040 0.425325i
66 0 0
77 −2.77447 −1.04865 −0.524325 0.851518i 0.675682π-0.675682\pi
−0.524325 + 0.851518i 0.675682π0.675682\pi
88 −0.309017 0.951057i −0.109254 0.336249i
99 0 0
1010 −2.19625 + 0.420099i −0.694515 + 0.132847i
1111 2.24459 1.63079i 0.676770 0.491702i −0.195515 0.980701i 0.562638π-0.562638\pi
0.872284 + 0.488999i 0.162638π0.162638\pi
1212 0 0
1313 −4.59343 3.33732i −1.27399 0.925606i −0.274633 0.961549i 0.588556π-0.588556\pi
−0.999354 + 0.0359433i 0.988556π0.988556\pi
1414 −2.24459 + 1.63079i −0.599892 + 0.435847i
1515 0 0
1616 −0.809017 0.587785i −0.202254 0.146946i
1717 −1.59343 4.90406i −0.386462 1.18941i −0.935414 0.353555i 0.884973π-0.884973\pi
0.548951 0.835854i 0.315027π-0.315027\pi
1818 0 0
1919 0.436451 + 1.34326i 0.100129 + 0.308164i 0.988556 0.150852i 0.0482018π-0.0482018\pi
−0.888428 + 0.459017i 0.848202π0.848202\pi
2020 −1.52988 + 1.63079i −0.342091 + 0.364656i
2121 0 0
2222 0.857358 2.63868i 0.182789 0.562567i
2323 −0.529876 + 0.384978i −0.110487 + 0.0802734i −0.641657 0.766992i 0.721753π-0.721753\pi
0.531170 + 0.847265i 0.321753π0.321753\pi
2424 0 0
2525 3.19098 + 3.84937i 0.638197 + 0.769873i
2626 −5.67779 −1.11351
2727 0 0
2828 −0.857358 + 2.63868i −0.162025 + 0.498663i
2929 −1.26594 + 3.89618i −0.235080 + 0.723502i 0.762031 + 0.647541i 0.224202π0.224202\pi
−0.997111 + 0.0759609i 0.975798π0.975798\pi
3030 0 0
3131 −2.20239 6.77827i −0.395562 1.21741i −0.928523 0.371274i 0.878921π-0.878921\pi
0.532961 0.846140i 0.321079π-0.321079\pi
3232 −1.00000 −0.176777
3333 0 0
3434 −4.17164 3.03088i −0.715431 0.519791i
3535 5.61478 + 2.63868i 0.949071 + 0.446018i
3636 0 0
3737 0.847416 + 0.615684i 0.139314 + 0.101218i 0.655260 0.755404i 0.272559π-0.272559\pi
−0.515945 + 0.856622i 0.672559π0.672559\pi
3838 1.14264 + 0.830178i 0.185361 + 0.134673i
3939 0 0
4040 −0.279141 + 2.21858i −0.0441361 + 0.350788i
4141 7.36789 + 5.35309i 1.15067 + 0.836012i 0.988570 0.150762i 0.0481728π-0.0481728\pi
0.162101 + 0.986774i 0.448173π0.448173\pi
4242 0 0
4343 9.24660 1.41009 0.705047 0.709161i 0.250926π-0.250926\pi
0.705047 + 0.709161i 0.250926π0.250926\pi
4444 −0.857358 2.63868i −0.129252 0.397795i
4545 0 0
4646 −0.202395 + 0.622907i −0.0298415 + 0.0918426i
4747 0.857358 2.63868i 0.125058 0.384890i −0.868853 0.495070i 0.835143π-0.835143\pi
0.993912 + 0.110179i 0.0351425π0.0351425\pi
4848 0 0
4949 0.697669 0.0996670
5050 4.84416 + 1.23859i 0.685068 + 0.175163i
5151 0 0
5252 −4.59343 + 3.33732i −0.636994 + 0.462803i
5353 0.162577 0.500362i 0.0223317 0.0687299i −0.939270 0.343180i 0.888496π-0.888496\pi
0.961601 + 0.274450i 0.0884959π0.0884959\pi
5454 0 0
5555 −6.09343 + 1.16555i −0.821637 + 0.157163i
5656 0.857358 + 2.63868i 0.114569 + 0.352608i
5757 0 0
5858 1.26594 + 3.89618i 0.166227 + 0.511593i
5959 −3.05975 2.22304i −0.398346 0.289415i 0.370521 0.928824i 0.379179π-0.379179\pi
−0.768867 + 0.639409i 0.779179π0.779179\pi
6060 0 0
6161 8.76365 6.36716i 1.12207 0.815232i 0.137549 0.990495i 0.456078π-0.456078\pi
0.984522 + 0.175263i 0.0560776π0.0560776\pi
6262 −5.76594 4.18920i −0.732276 0.532029i
6363 0 0
6464 −0.809017 + 0.587785i −0.101127 + 0.0734732i
6565 6.12188 + 11.1224i 0.759326 + 1.37957i
6666 0 0
6767 −1.33600 4.11180i −0.163219 0.502336i 0.835682 0.549214i 0.185073π-0.185073\pi
−0.998901 + 0.0468778i 0.985073π0.985073\pi
6868 −5.15643 −0.625309
6969 0 0
7070 6.09343 1.16555i 0.728304 0.139310i
7171 4.09343 12.5983i 0.485800 1.49514i −0.345018 0.938596i 0.612127π-0.612127\pi
0.830819 0.556543i 0.187873π-0.187873\pi
7272 0 0
7373 −3.40859 + 2.47648i −0.398945 + 0.289850i −0.769111 0.639115i 0.779301π-0.779301\pi
0.370166 + 0.928966i 0.379301π0.379301\pi
7474 1.04746 0.121765
7575 0 0
7676 1.41238 0.162012
7777 −6.22754 + 4.52458i −0.709695 + 0.515623i
7878 0 0
7979 −3.05975 + 9.41695i −0.344249 + 1.05949i 0.617736 + 0.786386i 0.288050π0.288050\pi
−0.961985 + 0.273104i 0.911950π0.911950\pi
8080 1.07822 + 1.95894i 0.120548 + 0.219016i
8181 0 0
8282 9.10722 1.00572
8383 −1.44497 4.44717i −0.158606 0.488141i 0.839902 0.542738i 0.182612π-0.182612\pi
−0.998508 + 0.0545976i 0.982612π0.982612\pi
8484 0 0
8585 −1.43937 + 11.4399i −0.156122 + 1.24084i
8686 7.48066 5.43502i 0.806660 0.586073i
8787 0 0
8888 −2.24459 1.63079i −0.239274 0.173843i
8989 −7.43002 + 5.39823i −0.787581 + 0.572211i −0.907245 0.420603i 0.861818π-0.861818\pi
0.119664 + 0.992814i 0.461818π0.461818\pi
9090 0 0
9191 12.7443 + 9.25928i 1.33597 + 0.970637i
9292 0.202395 + 0.622907i 0.0211011 + 0.0649425i
9393 0 0
9494 −0.857358 2.63868i −0.0884297 0.272159i
9595 0.394254 3.13348i 0.0404496 0.321488i
9696 0 0
9797 −0.0278640 + 0.0857567i −0.00282917 + 0.00870727i −0.952461 0.304660i 0.901457π-0.901457\pi
0.949632 + 0.313367i 0.101457π0.101457\pi
9898 0.564426 0.410079i 0.0570156 0.0414243i
9999 0 0
100100 4.64703 1.84529i 0.464703 0.184529i
101101 7.90632 0.786709 0.393354 0.919387i 0.371315π-0.371315\pi
0.393354 + 0.919387i 0.371315π0.371315\pi
102102 0 0
103103 2.42091 7.45079i 0.238539 0.734148i −0.758093 0.652146i 0.773869π-0.773869\pi
0.996632 0.0820014i 0.0261312π-0.0261312\pi
104104 −1.75453 + 5.39990i −0.172046 + 0.529503i
105105 0 0
106106 −0.162577 0.500362i −0.0157909 0.0485994i
107107 10.2220 0.988194 0.494097 0.869407i 0.335499π-0.335499\pi
0.494097 + 0.869407i 0.335499π0.335499\pi
108108 0 0
109109 −3.16400 2.29878i −0.303056 0.220183i 0.425855 0.904791i 0.359973π-0.359973\pi
−0.728911 + 0.684608i 0.759973π0.759973\pi
110110 −4.24459 + 4.52458i −0.404706 + 0.431401i
111111 0 0
112112 2.24459 + 1.63079i 0.212094 + 0.154095i
113113 −5.15785 3.74740i −0.485210 0.352526i 0.318129 0.948047i 0.396945π-0.396945\pi
−0.803339 + 0.595522i 0.796945π0.796945\pi
114114 0 0
115115 1.43846 0.275149i 0.134137 0.0256578i
116116 3.31428 + 2.40797i 0.307724 + 0.223574i
117117 0 0
118118 −3.78206 −0.348167
119119 4.42091 + 13.6062i 0.405264 + 1.24727i
120120 0 0
121121 −1.02048 + 3.14070i −0.0927706 + 0.285519i
122122 3.34742 10.3023i 0.303061 0.932725i
123123 0 0
124124 −7.12710 −0.640032
125125 −2.79673 10.8249i −0.250147 0.968208i
126126 0 0
127127 −7.72525 + 5.61272i −0.685505 + 0.498049i −0.875179 0.483798i 0.839257π-0.839257\pi
0.189674 + 0.981847i 0.439257π0.439257\pi
128128 −0.309017 + 0.951057i −0.0273135 + 0.0840623i
129129 0 0
130130 11.4903 + 5.39990i 1.00777 + 0.473602i
131131 −1.73026 5.32519i −0.151173 0.465264i 0.846580 0.532262i 0.178658π-0.178658\pi
−0.997753 + 0.0669981i 0.978658π0.978658\pi
132132 0 0
133133 −1.21092 3.72682i −0.105000 0.323156i
134134 −3.49771 2.54123i −0.302156 0.219529i
135135 0 0
136136 −4.17164 + 3.03088i −0.357715 + 0.259895i
137137 6.45931 + 4.69296i 0.551856 + 0.400947i 0.828469 0.560035i 0.189212π-0.189212\pi
−0.276613 + 0.960981i 0.589212π0.589212\pi
138138 0 0
139139 17.8699 12.9832i 1.51571 1.10122i 0.552140 0.833751i 0.313811π-0.313811\pi
0.963565 0.267473i 0.0861887π-0.0861887\pi
140140 4.24459 4.52458i 0.358733 0.382396i
141141 0 0
142142 −4.09343 12.5983i −0.343513 1.05722i
143143 −15.7528 −1.31732
144144 0 0
145145 6.26741 6.68083i 0.520480 0.554813i
146146 −1.30196 + 4.00703i −0.107751 + 0.331624i
147147 0 0
148148 0.847416 0.615684i 0.0696572 0.0506089i
149149 −4.18401 −0.342768 −0.171384 0.985204i 0.554824π-0.554824\pi
−0.171384 + 0.985204i 0.554824π0.554824\pi
150150 0 0
151151 −0.331561 −0.0269821 −0.0134910 0.999909i 0.504294π-0.504294\pi
−0.0134910 + 0.999909i 0.504294π0.504294\pi
152152 1.14264 0.830178i 0.0926805 0.0673364i
153153 0 0
154154 −2.37871 + 7.32092i −0.191682 + 0.589936i
155155 −1.98946 + 15.8120i −0.159798 + 1.27005i
156156 0 0
157157 3.60750 0.287910 0.143955 0.989584i 0.454018π-0.454018\pi
0.143955 + 0.989584i 0.454018π0.454018\pi
158158 3.05975 + 9.41695i 0.243421 + 0.749172i
159159 0 0
160160 2.02373 + 0.951057i 0.159990 + 0.0751876i
161161 1.47012 1.06811i 0.115862 0.0841787i
162162 0 0
163163 −4.12101 2.99409i −0.322782 0.234515i 0.414580 0.910013i 0.363929π-0.363929\pi
−0.737362 + 0.675498i 0.763929π0.763929\pi
164164 7.36789 5.35309i 0.575336 0.418006i
165165 0 0
166166 −3.78299 2.74850i −0.293617 0.213325i
167167 −6.44699 19.8418i −0.498883 1.53540i −0.810817 0.585300i 0.800977π-0.800977\pi
0.311934 0.950104i 0.399023π-0.399023\pi
168168 0 0
169169 5.94464 + 18.2957i 0.457280 + 1.40736i
170170 5.55975 + 10.1011i 0.426414 + 0.774723i
171171 0 0
172172 2.85736 8.79404i 0.217871 0.670539i
173173 −9.69826 + 7.04620i −0.737345 + 0.535713i −0.891879 0.452275i 0.850613π-0.850613\pi
0.154533 + 0.987988i 0.450613π0.450613\pi
174174 0 0
175175 −8.85328 10.6799i −0.669245 0.807328i
176176 −2.77447 −0.209133
177177 0 0
178178 −2.83802 + 8.73452i −0.212718 + 0.654680i
179179 2.63942 8.12330i 0.197279 0.607164i −0.802663 0.596433i 0.796584π-0.796584\pi
0.999942 0.0107309i 0.00341581π-0.00341581\pi
180180 0 0
181181 2.41912 + 7.44529i 0.179812 + 0.553404i 0.999820 0.0189471i 0.00603140π-0.00603140\pi
−0.820009 + 0.572351i 0.806031π0.806031\pi
182182 15.7528 1.16768
183183 0 0
184184 0.529876 + 0.384978i 0.0390630 + 0.0283809i
185185 −1.12939 2.05192i −0.0830346 0.150860i
186186 0 0
187187 −11.5741 8.40906i −0.846381 0.614932i
188188 −2.24459 1.63079i −0.163704 0.118938i
189189 0 0
190190 −1.52286 2.76678i −0.110480 0.200723i
191191 2.72324 + 1.97855i 0.197047 + 0.143163i 0.681934 0.731414i 0.261139π-0.261139\pi
−0.484887 + 0.874577i 0.661139π0.661139\pi
192192 0 0
193193 −15.4211 −1.11004 −0.555018 0.831839i 0.687288π-0.687288\pi
−0.555018 + 0.831839i 0.687288π0.687288\pi
194194 0.0278640 + 0.0857567i 0.00200052 + 0.00615697i
195195 0 0
196196 0.215591 0.663522i 0.0153994 0.0473945i
197197 −2.72086 + 8.37394i −0.193853 + 0.596619i 0.806135 + 0.591732i 0.201556π0.201556\pi
−0.999988 + 0.00488692i 0.998444π0.998444\pi
198198 0 0
199199 −17.6222 −1.24920 −0.624601 0.780944i 0.714738π-0.714738\pi
−0.624601 + 0.780944i 0.714738π0.714738\pi
200200 2.67490 4.22433i 0.189144 0.298705i
201201 0 0
202202 6.39635 4.64722i 0.450046 0.326977i
203203 3.51232 10.8098i 0.246517 0.758700i
204204 0 0
205205 −9.81955 17.8405i −0.685827 1.24603i
206206 −2.42091 7.45079i −0.168673 0.519121i
207207 0 0
208208 1.75453 + 5.39990i 0.121655 + 0.374415i
209209 3.17022 + 2.30330i 0.219289 + 0.159323i
210210 0 0
211211 −4.93617 + 3.58634i −0.339820 + 0.246894i −0.744586 0.667527i 0.767353π-0.767353\pi
0.404766 + 0.914420i 0.367353π0.367353\pi
212212 −0.425633 0.309240i −0.0292326 0.0212387i
213213 0 0
214214 8.26974 6.00832i 0.565308 0.410720i
215215 −18.7126 8.79404i −1.27619 0.599749i
216216 0 0
217217 6.11047 + 18.8061i 0.414806 + 1.27664i
218218 −3.91091 −0.264880
219219 0 0
220220 −0.774467 + 6.15537i −0.0522146 + 0.414995i
221221 −9.04713 + 27.8442i −0.608576 + 1.87300i
222222 0 0
223223 4.06828 2.95578i 0.272432 0.197933i −0.443178 0.896434i 0.646149π-0.646149\pi
0.715610 + 0.698500i 0.246149π0.246149\pi
224224 2.77447 0.185377
225225 0 0
226226 −6.37545 −0.424089
227227 −14.4314 + 10.4851i −0.957848 + 0.695918i −0.952650 0.304069i 0.901655π-0.901655\pi
−0.00519840 + 0.999986i 0.501655π0.501655\pi
228228 0 0
229229 −6.66137 + 20.5016i −0.440195 + 1.35478i 0.447472 + 0.894298i 0.352324π0.352324\pi
−0.887668 + 0.460485i 0.847676π0.847676\pi
230230 1.00201 1.06811i 0.0660707 0.0704289i
231231 0 0
232232 4.09668 0.268960
233233 −4.54454 13.9867i −0.297723 0.916297i −0.982293 0.187350i 0.940010π-0.940010\pi
0.684570 0.728947i 0.259990π-0.259990\pi
234234 0 0
235235 −4.24459 + 4.52458i −0.276887 + 0.295151i
236236 −3.05975 + 2.22304i −0.199173 + 0.144708i
237237 0 0
238238 11.5741 + 8.40906i 0.750236 + 0.545079i
239239 5.61478 4.07938i 0.363190 0.263873i −0.391192 0.920309i 0.627937π-0.627937\pi
0.754381 + 0.656436i 0.227937π0.227937\pi
240240 0 0
241241 −2.67787 1.94559i −0.172497 0.125326i 0.498187 0.867070i 0.333999π-0.333999\pi
−0.670684 + 0.741743i 0.733999π0.733999\pi
242242 1.02048 + 3.14070i 0.0655987 + 0.201892i
243243 0 0
244244 −3.34742 10.3023i −0.214296 0.659536i
245245 −1.41189 0.663522i −0.0902026 0.0423909i
246246 0 0
247247 2.47807 7.62672i 0.157676 0.485277i
248248 −5.76594 + 4.18920i −0.366138 + 0.266015i
249249 0 0
250250 −8.62531 7.11365i −0.545513 0.449906i
251251 9.46454 0.597397 0.298698 0.954348i 0.403448π-0.403448\pi
0.298698 + 0.954348i 0.403448π0.403448\pi
252252 0 0
253253 −0.561537 + 1.72823i −0.0353036 + 0.108653i
254254 −2.95078 + 9.08158i −0.185149 + 0.569829i
255255 0 0
256256 0.309017 + 0.951057i 0.0193136 + 0.0594410i
257257 7.07963 0.441615 0.220808 0.975317i 0.429131π-0.429131\pi
0.220808 + 0.975317i 0.429131π0.429131\pi
258258 0 0
259259 −2.35113 1.70820i −0.146092 0.106142i
260260 12.4698 2.38523i 0.773347 0.147926i
261261 0 0
262262 −4.52988 3.29115i −0.279857 0.203328i
263263 1.15969 + 0.842563i 0.0715095 + 0.0519547i 0.622966 0.782249i 0.285928π-0.285928\pi
−0.551456 + 0.834204i 0.685928π0.685928\pi
264264 0 0
265265 −0.804885 + 0.857977i −0.0494437 + 0.0527051i
266266 −3.17022 2.30330i −0.194379 0.141225i
267267 0 0
268268 −4.32340 −0.264094
269269 4.41368 + 13.5839i 0.269107 + 0.828226i 0.990719 + 0.135928i 0.0434015π0.0434015\pi
−0.721612 + 0.692298i 0.756598π0.756598\pi
270270 0 0
271271 9.51325 29.2788i 0.577889 1.77856i −0.0482363 0.998836i 0.515360π-0.515360\pi
0.626125 0.779723i 0.284640π-0.284640\pi
272272 −1.59343 + 4.90406i −0.0966156 + 0.297352i
273273 0 0
274274 7.98414 0.482340
275275 13.4400 + 3.43643i 0.810460 + 0.207224i
276276 0 0
277277 −2.58051 + 1.87485i −0.155048 + 0.112649i −0.662604 0.748970i 0.730549π-0.730549\pi
0.507556 + 0.861619i 0.330549π0.330549\pi
278278 6.82570 21.0073i 0.409378 1.25994i
279279 0 0
280280 0.774467 6.15537i 0.0462833 0.367854i
281281 −6.30053 19.3910i −0.375858 1.15677i −0.942898 0.333081i 0.891912π-0.891912\pi
0.567040 0.823690i 0.308088π-0.308088\pi
282282 0 0
283283 −4.10897 12.6461i −0.244253 0.751733i −0.995758 0.0920063i 0.970672π-0.970672\pi
0.751506 0.659727i 0.229328π-0.229328\pi
284284 −10.7167 7.78616i −0.635921 0.462023i
285285 0 0
286286 −12.7443 + 9.25928i −0.753587 + 0.547513i
287287 −20.4420 14.8520i −1.20665 0.876684i
288288 0 0
289289 −7.75751 + 5.63616i −0.456324 + 0.331539i
290290 1.14355 9.08880i 0.0671516 0.533713i
291291 0 0
292292 1.30196 + 4.00703i 0.0761917 + 0.234494i
293293 26.0420 1.52139 0.760696 0.649108i 0.224858π-0.224858\pi
0.760696 + 0.649108i 0.224858π0.224858\pi
294294 0 0
295295 4.07788 + 7.40883i 0.237423 + 0.431359i
296296 0.323684 0.996198i 0.0188138 0.0579028i
297297 0 0
298298 −3.38494 + 2.45930i −0.196084 + 0.142464i
299299 3.71874 0.215060
300300 0 0
301301 −25.6544 −1.47869
302302 −0.268239 + 0.194887i −0.0154354 + 0.0112145i
303303 0 0
304304 0.436451 1.34326i 0.0250322 0.0770411i
305305 −23.7908 + 4.55071i −1.36226 + 0.260573i
306306 0 0
307307 25.1000 1.43253 0.716267 0.697826i 0.245849π-0.245849\pi
0.716267 + 0.697826i 0.245849π0.245849\pi
308308 2.37871 + 7.32092i 0.135540 + 0.417148i
309309 0 0
310310 7.68456 + 13.9616i 0.436453 + 0.792964i
311311 0.585185 0.425162i 0.0331828 0.0241087i −0.571070 0.820901i 0.693472π-0.693472\pi
0.604253 + 0.796792i 0.293472π0.293472\pi
312312 0 0
313313 −17.4879 12.7057i −0.988477 0.718170i −0.0288898 0.999583i 0.509197π-0.509197\pi
−0.959587 + 0.281412i 0.909197π0.909197\pi
314314 2.91853 2.12043i 0.164702 0.119663i
315315 0 0
316316 8.01054 + 5.81999i 0.450628 + 0.327400i
317317 5.81992 + 17.9119i 0.326879 + 1.00603i 0.970585 + 0.240758i 0.0773960π0.0773960\pi
−0.643706 + 0.765273i 0.722604π0.722604\pi
318318 0 0
319319 3.51232 + 10.8098i 0.196652 + 0.605233i
320320 2.19625 0.420099i 0.122774 0.0234842i
321321 0 0
322322 0.561537 1.72823i 0.0312933 0.0963107i
323323 5.89196 4.28076i 0.327837 0.238188i
324324 0 0
325325 −1.81098 28.3311i −0.100455 1.57153i
326326 −5.09385 −0.282122
327327 0 0
328328 2.81428 8.66148i 0.155393 0.478250i
329329 −2.37871 + 7.32092i −0.131143 + 0.403615i
330330 0 0
331331 5.21494 + 16.0499i 0.286639 + 0.882185i 0.985903 + 0.167320i 0.0535115π0.0535115\pi
−0.699263 + 0.714864i 0.746489π0.746489\pi
332332 −4.67603 −0.256631
333333 0 0
334334 −16.8784 12.2629i −0.923546 0.670996i
335335 −1.20684 + 9.59180i −0.0659366 + 0.524056i
336336 0 0
337337 −15.6562 11.3749i −0.852845 0.619628i 0.0730841 0.997326i 0.476716π-0.476716\pi
−0.925929 + 0.377698i 0.876716π0.876716\pi
338338 15.5633 + 11.3074i 0.846530 + 0.615040i
339339 0 0
340340 10.4352 + 4.90406i 0.565930 + 0.265960i
341341 −15.9974 11.6228i −0.866309 0.629410i
342342 0 0
343343 17.4856 0.944134
344344 −2.85736 8.79404i −0.154058 0.474143i
345345 0 0
346346 −3.70441 + 11.4010i −0.199150 + 0.612921i
347347 2.79311 8.59630i 0.149942 0.461473i −0.847672 0.530521i 0.821996π-0.821996\pi
0.997613 + 0.0690480i 0.0219962π0.0219962\pi
348348 0 0
349349 36.7305 1.96614 0.983068 0.183240i 0.0586584π-0.0586584\pi
0.983068 + 0.183240i 0.0586584π0.0586584\pi
350350 −13.4400 3.43643i −0.718396 0.183685i
351351 0 0
352352 −2.24459 + 1.63079i −0.119637 + 0.0869214i
353353 −5.67779 + 17.4744i −0.302198 + 0.930070i 0.678510 + 0.734591i 0.262626π0.262626\pi
−0.980708 + 0.195479i 0.937374π0.937374\pi
354354 0 0
355355 −20.2657 + 21.6024i −1.07559 + 1.14654i
356356 2.83802 + 8.73452i 0.150415 + 0.462928i
357357 0 0
358358 −2.63942 8.12330i −0.139498 0.429330i
359359 −19.7609 14.3572i −1.04294 0.757742i −0.0720846 0.997399i 0.522965π-0.522965\pi
−0.970858 + 0.239657i 0.922965π0.922965\pi
360360 0 0
361361 13.7575 9.99539i 0.724078 0.526073i
362362 6.33334 + 4.60144i 0.332873 + 0.241846i
363363 0 0
364364 12.7443 9.25928i 0.667983 0.485318i
365365 9.25334 1.76998i 0.484342 0.0926450i
366366 0 0
367367 4.48768 + 13.8117i 0.234255 + 0.720963i 0.997219 + 0.0745221i 0.0237431π0.0237431\pi
−0.762964 + 0.646441i 0.776257π0.776257\pi
368368 0.654963 0.0341423
369369 0 0
370370 −2.11979 0.996198i −0.110202 0.0517898i
371371 −0.451065 + 1.38824i −0.0234182 + 0.0720737i
372372 0 0
373373 18.8410 13.6888i 0.975549 0.708778i 0.0188399 0.999823i 0.494003π-0.494003\pi
0.956710 + 0.291044i 0.0940027π0.0940027\pi
374374 −14.3064 −0.739764
375375 0 0
376376 −2.77447 −0.143082
377377 18.8178 13.6719i 0.969166 0.704140i
378378 0 0
379379 8.84332 27.2169i 0.454251 1.39804i −0.417762 0.908556i 0.637185π-0.637185\pi
0.872013 0.489483i 0.162815π-0.162815\pi
380380 −2.85829 1.34326i −0.146627 0.0689076i
381381 0 0
382382 3.36611 0.172225
383383 5.13454 + 15.8025i 0.262363 + 0.807469i 0.992289 + 0.123944i 0.0395542π0.0395542\pi
−0.729927 + 0.683526i 0.760446π0.760446\pi
384384 0 0
385385 16.9060 3.23378i 0.861610 0.164809i
386386 −12.4759 + 9.06430i −0.635008 + 0.461361i
387387 0 0
388388 0.0729490 + 0.0530006i 0.00370343 + 0.00269070i
389389 21.3392 15.5039i 1.08194 0.786077i 0.103922 0.994585i 0.466861π-0.466861\pi
0.978021 + 0.208508i 0.0668609π0.0668609\pi
390390 0 0
391391 2.73227 + 1.98511i 0.138177 + 0.100391i
392392 −0.215591 0.663522i −0.0108890 0.0335129i
393393 0 0
394394 2.72086 + 8.37394i 0.137075 + 0.421873i
395395 15.1482 16.1474i 0.762187 0.812463i
396396 0 0
397397 −5.53406 + 17.0321i −0.277747 + 0.854816i 0.710733 + 0.703462i 0.248363π0.248363\pi
−0.988480 + 0.151354i 0.951637π0.951637\pi
398398 −14.2566 + 10.3580i −0.714620 + 0.519202i
399399 0 0
400400 −0.318958 4.98982i −0.0159479 0.249491i
401401 −32.0164 −1.59882 −0.799411 0.600785i 0.794855π-0.794855\pi
−0.799411 + 0.600785i 0.794855π0.794855\pi
402402 0 0
403403 −12.5047 + 38.4856i −0.622905 + 1.91710i
404404 2.44319 7.51936i 0.121553 0.374102i
405405 0 0
406406 −3.51232 10.8098i −0.174314 0.536482i
407407 2.90615 0.144053
408408 0 0
409409 −14.5901 10.6003i −0.721435 0.524153i 0.165407 0.986225i 0.447106π-0.447106\pi
−0.886842 + 0.462072i 0.847106π0.847106\pi
410410 −18.4306 8.66148i −0.910221 0.427760i
411411 0 0
412412 −6.33802 4.60484i −0.312252 0.226864i
413413 8.48918 + 6.16775i 0.417725 + 0.303495i
414414 0 0
415415 −1.30527 + 10.3741i −0.0640733 + 0.509246i
416416 4.59343 + 3.33732i 0.225211 + 0.163626i
417417 0 0
418418 3.91861 0.191666
419419 6.03511 + 18.5742i 0.294834 + 0.907407i 0.983277 + 0.182116i 0.0582947π0.0582947\pi
−0.688443 + 0.725291i 0.741705π0.741705\pi
420420 0 0
421421 −6.04242 + 18.5967i −0.294490 + 0.906346i 0.688903 + 0.724854i 0.258093π0.258093\pi
−0.983392 + 0.181492i 0.941907π0.941907\pi
422422 −1.88545 + 5.80281i −0.0917822 + 0.282477i
423423 0 0
424424 −0.526111 −0.0255502
425425 13.7929 21.7825i 0.669055 1.05660i
426426 0 0
427427 −24.3145 + 17.6655i −1.17666 + 0.854893i
428428 3.15876 9.72166i 0.152684 0.469914i
429429 0 0
430430 −20.3079 + 3.88449i −0.979332 + 0.187327i
431431 6.55002 + 20.1589i 0.315503 + 0.971019i 0.975547 + 0.219792i 0.0705378π0.0705378\pi
−0.660044 + 0.751227i 0.729462π0.729462\pi
432432 0 0
433433 2.64199 + 8.13122i 0.126966 + 0.390761i 0.994254 0.107045i 0.0341389π-0.0341389\pi
−0.867288 + 0.497807i 0.834139π0.834139\pi
434434 15.9974 + 11.6228i 0.767901 + 0.557913i
435435 0 0
436436 −3.16400 + 2.29878i −0.151528 + 0.110091i
437437 −0.748388 0.543736i −0.0358003 0.0260104i
438438 0 0
439439 22.7102 16.4999i 1.08390 0.787499i 0.105541 0.994415i 0.466343π-0.466343\pi
0.978359 + 0.206916i 0.0663427π0.0663427\pi
440440 2.99148 + 5.43502i 0.142613 + 0.259104i
441441 0 0
442442 9.04713 + 27.8442i 0.430328 + 1.32441i
443443 33.0546 1.57047 0.785236 0.619197i 0.212542π-0.212542\pi
0.785236 + 0.619197i 0.212542π0.212542\pi
444444 0 0
445445 20.1704 3.85820i 0.956169 0.182896i
446446 1.55394 4.78254i 0.0735813 0.226460i
447447 0 0
448448 2.24459 1.63079i 0.106047 0.0770476i
449449 37.1628 1.75382 0.876911 0.480652i 0.159600π-0.159600\pi
0.876911 + 0.480652i 0.159600π0.159600\pi
450450 0 0
451451 25.2677 1.18981
452452 −5.15785 + 3.74740i −0.242605 + 0.176263i
453453 0 0
454454 −5.51232 + 16.9652i −0.258706 + 0.796215i
455455 −16.9850 30.8589i −0.796267 1.44669i
456456 0 0
457457 29.3139 1.37125 0.685624 0.727956i 0.259529π-0.259529\pi
0.685624 + 0.727956i 0.259529π0.259529\pi
458458 6.66137 + 20.5016i 0.311265 + 0.957976i
459459 0 0
460460 0.182827 1.45309i 0.00852435 0.0677504i
461461 7.20624 5.23564i 0.335628 0.243848i −0.407187 0.913345i 0.633490π-0.633490\pi
0.742815 + 0.669497i 0.233490π0.233490\pi
462462 0 0
463463 14.7865 + 10.7430i 0.687187 + 0.499271i 0.875734 0.482793i 0.160378π-0.160378\pi
−0.188547 + 0.982064i 0.560378π0.560378\pi
464464 3.31428 2.40797i 0.153862 0.111787i
465465 0 0
466466 −11.8978 8.64424i −0.551154 0.400436i
467467 11.3360 + 34.8886i 0.524568 + 1.61445i 0.765169 + 0.643829i 0.222655π0.222655\pi
−0.240601 + 0.970624i 0.577345π0.577345\pi
468468 0 0
469469 3.70670 + 11.4081i 0.171160 + 0.526775i
470470 −0.774467 + 6.15537i −0.0357235 + 0.283926i
471471 0 0
472472 −1.16872 + 3.59695i −0.0537948 + 0.165563i
473473 20.7548 15.0793i 0.954309 0.693346i
474474 0 0
475475 −3.77798 + 5.96637i −0.173346 + 0.273756i
476476 14.3064 0.655731
477477 0 0
478478 2.14465 6.60057i 0.0980942 0.301903i
479479 3.89046 11.9736i 0.177760 0.547088i −0.821989 0.569503i 0.807136π-0.807136\pi
0.999749 + 0.0224155i 0.00713568π0.00713568\pi
480480 0 0
481481 −1.83781 5.65620i −0.0837969 0.257900i
482482 −3.31003 −0.150768
483483 0 0
484484 2.67164 + 1.94106i 0.121438 + 0.0882301i
485485 0.137949 0.147048i 0.00626393 0.00667712i
486486 0 0
487487 14.8257 + 10.7715i 0.671816 + 0.488103i 0.870633 0.491934i 0.163710π-0.163710\pi
−0.198816 + 0.980037i 0.563710π0.563710\pi
488488 −8.76365 6.36716i −0.396712 0.288228i
489489 0 0
490490 −1.53226 + 0.293090i −0.0692202 + 0.0132405i
491491 17.5595 + 12.7577i 0.792448 + 0.575747i 0.908689 0.417474i 0.137085π-0.137085\pi
−0.116241 + 0.993221i 0.537085π0.537085\pi
492492 0 0
493493 21.1243 0.951389
494494 −2.47807 7.62672i −0.111494 0.343143i
495495 0 0
496496 −2.20239 + 6.77827i −0.0988904 + 0.304353i
497497 −11.3571 + 34.9535i −0.509434 + 1.56788i
498498 0 0
499499 15.8391 0.709055 0.354527 0.935046i 0.384642π-0.384642\pi
0.354527 + 0.935046i 0.384642π0.384642\pi
500500 −11.1593 0.685229i −0.499060 0.0306444i
501501 0 0
502502 7.65697 5.56312i 0.341748 0.248294i
503503 −8.51433 + 26.2044i −0.379635 + 1.16840i 0.560662 + 0.828044i 0.310547π0.310547\pi
−0.940298 + 0.340353i 0.889453π0.889453\pi
504504 0 0
505505 −16.0003 7.51936i −0.712003 0.334607i
506506 0.561537 + 1.72823i 0.0249634 + 0.0768294i
507507 0 0
508508 2.95078 + 9.08158i 0.130920 + 0.402930i
509509 −22.3386 16.2300i −0.990142 0.719380i −0.0301894 0.999544i 0.509611π-0.509611\pi
−0.959952 + 0.280164i 0.909611π0.909611\pi
510510 0 0
511511 9.45701 6.87092i 0.418354 0.303952i
512512 0.809017 + 0.587785i 0.0357538 + 0.0259767i
513513 0 0
514514 5.72754 4.16130i 0.252631 0.183547i
515515 −11.9854 + 12.7760i −0.528139 + 0.562977i
516516 0 0
517517 −2.37871 7.32092i −0.104616 0.321974i
518518 −2.90615 −0.127689
519519 0 0
520520 8.68631 9.25928i 0.380920 0.406046i
521521 −5.28084 + 16.2527i −0.231358 + 0.712046i 0.766226 + 0.642571i 0.222132π0.222132\pi
−0.997584 + 0.0694747i 0.977868π0.977868\pi
522522 0 0
523523 −29.3796 + 21.3456i −1.28468 + 0.933376i −0.999684 0.0251516i 0.991993π-0.991993\pi
−0.284999 + 0.958528i 0.591993π0.591993\pi
524524 −5.59923 −0.244604
525525 0 0
526526 1.43345 0.0625016
527527 −29.7317 + 21.6013i −1.29513 + 0.940970i
528528 0 0
529529 −6.97483 + 21.4663i −0.303253 + 0.933318i
530530 −0.146859 + 1.16722i −0.00637915 + 0.0507007i
531531 0 0
532532 −3.91861 −0.169893
533533 −15.9789 49.1780i −0.692123 2.13014i
534534 0 0
535535 −20.6865 9.72166i −0.894356 0.420304i
536536 −3.49771 + 2.54123i −0.151078 + 0.109764i
537537 0 0
538538 11.5552 + 8.39532i 0.498178 + 0.361948i
539539 1.56598 1.13775i 0.0674516 0.0490064i
540540 0 0
541541 −20.1742 14.6574i −0.867355 0.630170i 0.0625209 0.998044i 0.480086π-0.480086\pi
−0.929876 + 0.367873i 0.880086π0.880086\pi
542542 −9.51325 29.2788i −0.408629 1.25763i
543543 0 0
544544 1.59343 + 4.90406i 0.0683176 + 0.210260i
545545 4.21681 + 7.66125i 0.180628 + 0.328172i
546546 0 0
547547 2.06176 6.34546i 0.0881547 0.271312i −0.897255 0.441513i 0.854442π-0.854442\pi
0.985409 + 0.170201i 0.0544418π0.0544418\pi
548548 6.45931 4.69296i 0.275928 0.200473i
549549 0 0
550550 12.8930 5.11968i 0.549761 0.218304i
551551 −5.78609 −0.246496
552552 0 0
553553 8.48918 26.1270i 0.360997 1.11103i
554554 −0.985668 + 3.03357i −0.0418770 + 0.128884i
555555 0 0
556556 −6.82570 21.0073i −0.289474 0.890909i
557557 20.4328 0.865765 0.432882 0.901450i 0.357497π-0.357497\pi
0.432882 + 0.901450i 0.357497π0.357497\pi
558558 0 0
559559 −42.4736 30.8589i −1.79644 1.30519i
560560 −2.99148 5.43502i −0.126413 0.229671i
561561 0 0
562562 −16.4950 11.9843i −0.695799 0.505528i
563563 −0.487680 0.354320i −0.0205532 0.0149328i 0.577461 0.816418i 0.304043π-0.304043\pi
−0.598014 + 0.801485i 0.704043π0.704043\pi
564564 0 0
565565 6.87412 + 12.4891i 0.289196 + 0.525422i
566566 −10.7574 7.81572i −0.452168 0.328519i
567567 0 0
568568 −13.2466 −0.555815
569569 −10.4688 32.2195i −0.438873 1.35071i −0.889065 0.457781i 0.848644π-0.848644\pi
0.450192 0.892932i 0.351356π-0.351356\pi
570570 0 0
571571 −1.92521 + 5.92520i −0.0805677 + 0.247962i −0.983225 0.182399i 0.941614π-0.941614\pi
0.902657 + 0.430361i 0.141614π0.141614\pi
572572 −4.86789 + 14.9818i −0.203537 + 0.626422i
573573 0 0
574574 −25.2677 −1.05465
575575 −3.17275 0.811231i −0.132313 0.0338307i
576576 0 0
577577 −3.05893 + 2.22244i −0.127345 + 0.0925214i −0.649634 0.760247i 0.725078π-0.725078\pi
0.522290 + 0.852768i 0.325078π0.325078\pi
578578 −2.96310 + 9.11949i −0.123249 + 0.379321i
579579 0 0
580580 −4.41711 8.02516i −0.183410 0.333226i
581581 4.00903 + 12.3385i 0.166323 + 0.511889i
582582 0 0
583583 −0.451065 1.38824i −0.0186812 0.0574949i
584584 3.40859 + 2.47648i 0.141048 + 0.102478i
585585 0 0
586586 21.0684 15.3071i 0.870330 0.632332i
587587 13.2296 + 9.61184i 0.546042 + 0.396723i 0.826324 0.563195i 0.190428π-0.190428\pi
−0.280282 + 0.959918i 0.590428π0.590428\pi
588588 0 0
589589 8.14373 5.91676i 0.335556 0.243796i
590590 7.65388 + 3.59695i 0.315105 + 0.148084i
591591 0 0
592592 −0.323684 0.996198i −0.0133033 0.0409435i
593593 −9.53314 −0.391479 −0.195740 0.980656i 0.562711π-0.562711\pi
−0.195740 + 0.980656i 0.562711π0.562711\pi
594594 0 0
595595 3.99349 31.7397i 0.163717 1.30120i
596596 −1.29293 + 3.97923i −0.0529605 + 0.162996i
597597 0 0
598598 3.00852 2.18582i 0.123028 0.0893848i
599599 16.0682 0.656528 0.328264 0.944586i 0.393536π-0.393536\pi
0.328264 + 0.944586i 0.393536π0.393536\pi
600600 0 0
601601 15.0380 0.613413 0.306707 0.951804i 0.400773π-0.400773\pi
0.306707 + 0.951804i 0.400773π0.400773\pi
602602 −20.7548 + 15.0793i −0.845904 + 0.614585i
603603 0 0
604604 −0.102458 + 0.315333i −0.00416896 + 0.0128307i
605605 5.05216 5.38541i 0.205399 0.218948i
606606 0 0
607607 −44.8348 −1.81979 −0.909894 0.414840i 0.863837π-0.863837\pi
−0.909894 + 0.414840i 0.863837π0.863837\pi
608608 −0.436451 1.34326i −0.0177004 0.0544763i
609609 0 0
610610 −16.5723 + 17.6655i −0.670994 + 0.715255i
611611 −12.7443 + 9.25928i −0.515580 + 0.374590i
612612 0 0
613613 12.5793 + 9.13937i 0.508072 + 0.369136i 0.812092 0.583530i 0.198329π-0.198329\pi
−0.304020 + 0.952666i 0.598329π0.598329\pi
614614 20.3064 14.7534i 0.819498 0.595400i
615615 0 0
616616 6.22754 + 4.52458i 0.250915 + 0.182300i
617617 −5.43852 16.7380i −0.218946 0.673848i −0.998850 0.0479478i 0.984732π-0.984732\pi
0.779903 0.625900i 0.215268π-0.215268\pi
618618 0 0
619619 −11.5229 35.4637i −0.463143 1.42541i −0.861303 0.508091i 0.830351π-0.830351\pi
0.398161 0.917316i 0.369649π-0.369649\pi
620620 14.4233 + 6.77827i 0.579255 + 0.272222i
621621 0 0
622622 0.223521 0.687926i 0.00896236 0.0275833i
623623 20.6144 14.9772i 0.825897 0.600049i
624624 0 0
625625 −4.63525 + 24.5665i −0.185410 + 0.982661i
626626 −21.6163 −0.863960
627627 0 0
628628 1.11478 3.43094i 0.0444845 0.136909i
629629 1.66906 5.13683i 0.0665496 0.204819i
630630 0 0
631631 2.64380 + 8.13677i 0.105248 + 0.323920i 0.989789 0.142543i 0.0455280π-0.0455280\pi
−0.884541 + 0.466463i 0.845528π0.845528\pi
632632 9.90157 0.393863
633633 0 0
634634 15.2367 + 11.0701i 0.605129 + 0.439652i
635635 20.9719 4.01150i 0.832243 0.159191i
636636 0 0
637637 −3.20469 2.32834i −0.126974 0.0922523i
638638 9.19537 + 6.68083i 0.364048 + 0.264497i
639639 0 0
640640 1.52988 1.63079i 0.0604737 0.0644627i
641641 −18.4582 13.4107i −0.729055 0.529690i 0.160209 0.987083i 0.448783π-0.448783\pi
−0.889264 + 0.457394i 0.848783π0.848783\pi
642642 0 0
643643 34.7745 1.37137 0.685686 0.727898i 0.259503π-0.259503\pi
0.685686 + 0.727898i 0.259503π0.259503\pi
644644 −0.561537 1.72823i −0.0221277 0.0681020i
645645 0 0
646646 2.25053 6.92641i 0.0885459 0.272516i
647647 5.08583 15.6526i 0.199945 0.615366i −0.799939 0.600082i 0.795135π-0.795135\pi
0.999883 0.0152844i 0.00486537π-0.00486537\pi
648648 0 0
649649 −10.4932 −0.411894
650650 −18.1177 21.8559i −0.710635 0.857258i
651651 0 0
652652 −4.12101 + 2.99409i −0.161391 + 0.117257i
653653 −9.33515 + 28.7306i −0.365313 + 1.12432i 0.584473 + 0.811414i 0.301301π0.301301\pi
−0.949785 + 0.312903i 0.898699π0.898699\pi
654654 0 0
655655 −1.56298 + 12.4223i −0.0610705 + 0.485381i
656656 −2.81428 8.66148i −0.109879 0.338174i
657657 0 0
658658 2.37871 + 7.32092i 0.0927318 + 0.285399i
659659 −23.0523 16.7485i −0.897991 0.652428i 0.0399585 0.999201i 0.487277π-0.487277\pi
−0.937949 + 0.346773i 0.887277π0.887277\pi
660660 0 0
661661 −41.0448 + 29.8208i −1.59646 + 1.15990i −0.702562 + 0.711622i 0.747961π0.747961\pi
−0.893897 + 0.448273i 0.852039π0.852039\pi
662662 13.6529 + 9.91941i 0.530635 + 0.385529i
663663 0 0
664664 −3.78299 + 2.74850i −0.146809 + 0.106663i
665665 −1.09385 + 8.69374i −0.0424175 + 0.337129i
666666 0 0
667667 −0.829146 2.55185i −0.0321047 0.0988080i
668668 −20.8629 −0.807209
669669 0 0
670670 4.66156 + 8.46929i 0.180092 + 0.327197i
671671 9.28730 28.5834i 0.358532 1.10345i
672672 0 0
673673 16.5401 12.0171i 0.637573 0.463224i −0.221442 0.975173i 0.571077π-0.571077\pi
0.859016 + 0.511949i 0.171077π0.171077\pi
674674 −19.3521 −0.745414
675675 0 0
676676 19.2373 0.739894
677677 6.90383 5.01592i 0.265336 0.192778i −0.447160 0.894454i 0.647565π-0.647565\pi
0.712496 + 0.701676i 0.247565π0.247565\pi
678678 0 0
679679 0.0773079 0.237929i 0.00296680 0.00913088i
680680 11.3248 2.16621i 0.434287 0.0830705i
681681 0 0
682682 −19.7739 −0.757182
683683 15.0085 + 46.1913i 0.574283 + 1.76746i 0.638608 + 0.769532i 0.279511π0.279511\pi
−0.0643246 + 0.997929i 0.520489π0.520489\pi
684684 0 0
685685 −8.60863 15.6405i −0.328919 0.597591i
686686 14.1462 10.2778i 0.540103 0.392408i
687687 0 0
688688 −7.48066 5.43502i −0.285197 0.207208i
689689 −2.41665 + 1.75580i −0.0920671 + 0.0668907i
690690 0 0
691691 −36.2501 26.3373i −1.37902 1.00192i −0.996971 0.0777740i 0.975219π-0.975219\pi
−0.382048 0.924142i 0.624781π-0.624781\pi
692692 3.70441 + 11.4010i 0.140820 + 0.433401i
693693 0 0
694694 −2.79311 8.59630i −0.106025 0.326311i
695695 −48.5117 + 9.27932i −1.84015 + 0.351985i
696696 0 0
697697 14.5117 44.6623i 0.549669 1.69171i
698698 29.7156 21.5896i 1.12475 0.817179i
699699 0 0
700700 −12.8930 + 5.11968i −0.487311 + 0.193506i
701701 −2.21913 −0.0838152 −0.0419076 0.999121i 0.513344π-0.513344\pi
−0.0419076 + 0.999121i 0.513344π0.513344\pi
702702 0 0
703703 −0.457166 + 1.40701i −0.0172424 + 0.0530665i
704704 −0.857358 + 2.63868i −0.0323129 + 0.0994488i
705705 0 0
706706 5.67779 + 17.4744i 0.213686 + 0.657659i
707707 −21.9358 −0.824982
708708 0 0
709709 −27.7968 20.1955i −1.04393 0.758459i −0.0728805 0.997341i 0.523219π-0.523219\pi
−0.971049 + 0.238882i 0.923219π0.923219\pi
710710 −3.69767 + 29.3886i −0.138771 + 1.10293i
711711 0 0
712712 7.43002 + 5.39823i 0.278452 + 0.202307i
713713 3.77648 + 2.74377i 0.141430 + 0.102755i
714714 0 0
715715 31.8795 + 14.9818i 1.19223 + 0.560289i
716716 −6.91009 5.02047i −0.258242 0.187624i
717717 0 0
718718 −24.4259 −0.911565
719719 −3.70511 11.4032i −0.138177 0.425266i 0.857893 0.513828i 0.171773π-0.171773\pi
−0.996071 + 0.0885618i 0.971773π0.971773\pi
720720 0 0
721721 −6.71673 + 20.6720i −0.250144 + 0.769864i
722722 5.25489 16.1729i 0.195567 0.601892i
723723 0 0
724724 7.82844 0.290942
725725 −19.0374 + 7.55955i −0.707032 + 0.280754i
726726 0 0
727727 −34.1265 + 24.7944i −1.26568 + 0.919573i −0.999022 0.0442177i 0.985920π-0.985920\pi
−0.266661 + 0.963790i 0.585920π0.585920\pi
728728 4.86789 14.9818i 0.180416 0.555264i
729729 0 0
730730 6.44574 6.87092i 0.238568 0.254304i
731731 −14.7338 45.3459i −0.544948 1.67718i
732732 0 0
733733 −0.0996219 0.306605i −0.00367962 0.0113247i 0.949200 0.314674i 0.101895π-0.101895\pi
−0.952879 + 0.303349i 0.901895π0.901895\pi
734734 11.7489 + 8.53607i 0.433660 + 0.315072i
735735 0 0
736736 0.529876 0.384978i 0.0195315 0.0141905i
737737 −9.70427 7.05056i −0.357461 0.259711i
738738 0 0
739739 4.44942 3.23269i 0.163674 0.118916i −0.502933 0.864325i 0.667746π-0.667746\pi
0.666607 + 0.745409i 0.267746π0.267746\pi
740740 −2.30049 + 0.440039i −0.0845678 + 0.0161761i
741741 0 0
742742 0.451065 + 1.38824i 0.0165591 + 0.0509638i
743743 6.03812 0.221517 0.110759 0.993847i 0.464672π-0.464672\pi
0.110759 + 0.993847i 0.464672π0.464672\pi
744744 0 0
745745 8.46733 + 3.97923i 0.310219 + 0.145788i
746746 7.19662 22.1489i 0.263487 0.810929i
747747 0 0
748748 −11.5741 + 8.40906i −0.423190 + 0.307466i
749749 −28.3605 −1.03627
750750 0 0
751751 −13.5719 −0.495244 −0.247622 0.968857i 0.579649π-0.579649\pi
−0.247622 + 0.968857i 0.579649π0.579649\pi
752752 −2.24459 + 1.63079i −0.0818518 + 0.0594688i
753753 0 0
754754 7.18776 22.1216i 0.261763 0.805623i
755755 0.670991 + 0.315333i 0.0244199 + 0.0114762i
756756 0 0
757757 33.0661 1.20181 0.600904 0.799321i 0.294807π-0.294807\pi
0.600904 + 0.799321i 0.294807π0.294807\pi
758758 −8.84332 27.2169i −0.321204 0.988563i
759759 0 0
760760 −3.10195 + 0.593341i −0.112520 + 0.0215227i
761761 4.19767 3.04978i 0.152165 0.110555i −0.509098 0.860709i 0.670021π-0.670021\pi
0.661263 + 0.750154i 0.270021π0.270021\pi
762762 0 0
763763 8.77840 + 6.37788i 0.317799 + 0.230895i
764764 2.72324 1.97855i 0.0985233 0.0715814i
765765 0 0
766766 13.4424 + 9.76647i 0.485694 + 0.352877i
767767 6.63575 + 20.4227i 0.239603 + 0.737422i
768768 0 0
769769 10.2191 + 31.4512i 0.368511 + 1.13416i 0.947753 + 0.319005i 0.103349π0.103349\pi
−0.579242 + 0.815156i 0.696651π0.696651\pi
770770 11.7765 12.5533i 0.424395 0.452389i
771771 0 0
772772 −4.76538 + 14.6663i −0.171510 + 0.527853i
773773 −0.914961 + 0.664758i −0.0329088 + 0.0239097i −0.604118 0.796895i 0.706474π-0.706474\pi
0.571209 + 0.820804i 0.306474π0.306474\pi
774774 0 0
775775 19.0643 30.1072i 0.684808 1.08148i
776776 0.0901699 0.00323691
777777 0 0
778778 8.15086 25.0858i 0.292223 0.899369i
779779 −3.97485 + 12.2333i −0.142414 + 0.438305i
780780 0 0
781781 −11.3571 34.9535i −0.406388 1.25073i
782782 3.37727 0.120771
783783 0 0
784784 −0.564426 0.410079i −0.0201581 0.0146457i
785785 −7.30061 3.43094i −0.260570 0.122455i
786786 0 0
787787 −12.7509 9.26408i −0.454521 0.330229i 0.336857 0.941556i 0.390636π-0.390636\pi
−0.791378 + 0.611327i 0.790636π0.790636\pi
788788 7.12330 + 5.17538i 0.253757 + 0.184365i
789789 0 0
790790 2.76393 21.9674i 0.0983363 0.781564i
791791 14.3103 + 10.3970i 0.508815 + 0.369676i
792792 0 0
793793 −61.5044 −2.18409
794794 5.53406 + 17.0321i 0.196396 + 0.604446i
795795 0 0
796796 −5.44555 + 16.7597i −0.193012 + 0.594031i
797797 7.15055 22.0071i 0.253285 0.779532i −0.740877 0.671640i 0.765590π-0.765590\pi
0.994163 0.107892i 0.0344100π-0.0344100\pi
798798 0 0
799799 −14.3064 −0.506122
800800 −3.19098 3.84937i −0.112818 0.136096i
801801 0 0
802802 −25.9018 + 18.8188i −0.914624 + 0.664513i
803803 −3.61226 + 11.1174i −0.127474 + 0.392324i
804804 0 0
805805 −3.99097 + 0.763393i −0.140663 + 0.0269061i
806806 12.5047 + 38.4856i 0.440460 + 1.35560i
807807 0 0
808808 −2.44319 7.51936i −0.0859511 0.264530i
809809 27.1345 + 19.7143i 0.953997 + 0.693119i 0.951749 0.306878i 0.0992844π-0.0992844\pi
0.00224811 + 0.999997i 0.499284π0.499284\pi
810810 0 0
811811 9.67796 7.03145i 0.339839 0.246907i −0.404755 0.914425i 0.632643π-0.632643\pi
0.744594 + 0.667518i 0.232643π0.232643\pi
812812 −9.19537 6.68083i −0.322694 0.234451i
813813 0 0
814814 2.35113 1.70820i 0.0824070 0.0598722i
815815 5.49227 + 9.97854i 0.192386 + 0.349533i
816816 0 0
817817 4.03569 + 12.4206i 0.141191 + 0.434540i
818818 −18.0344 −0.630557
819819 0 0
820820 −20.0017 + 3.82593i −0.698491 + 0.133607i
821821 3.30466 10.1707i 0.115333 0.354960i −0.876683 0.481068i 0.840249π-0.840249\pi
0.992016 + 0.126109i 0.0402489π0.0402489\pi
822822 0 0
823823 9.72525 7.06581i 0.339001 0.246299i −0.405239 0.914211i 0.632812π-0.632812\pi
0.744240 + 0.667912i 0.232812π0.232812\pi
824824 −7.83422 −0.272918
825825 0 0
826826 10.4932 0.365105
827827 −3.34912 + 2.43328i −0.116460 + 0.0846133i −0.644491 0.764612i 0.722931π-0.722931\pi
0.528031 + 0.849225i 0.322931π0.322931\pi
828828 0 0
829829 −6.28859 + 19.3543i −0.218412 + 0.672203i 0.780482 + 0.625178i 0.214974π0.214974\pi
−0.998894 + 0.0470242i 0.985026π0.985026\pi
830830 5.04178 + 9.16007i 0.175003 + 0.317951i
831831 0 0
832832 5.67779 0.196842
833833 −1.11168 3.42141i −0.0385175 0.118545i
834834 0 0
835835 −5.82368 + 46.2859i −0.201537 + 1.60179i
836836 3.17022 2.30330i 0.109644 0.0796614i
837837 0 0
838838 15.8001 + 11.4795i 0.545806 + 0.396552i
839839 2.53639 1.84279i 0.0875658 0.0636203i −0.543141 0.839642i 0.682765π-0.682765\pi
0.630707 + 0.776021i 0.282765π0.282765\pi
840840 0 0
841841 9.88393 + 7.18109i 0.340825 + 0.247624i
842842 6.04242 + 18.5967i 0.208236 + 0.640883i
843843 0 0
844844 1.88545 + 5.80281i 0.0648998 + 0.199741i
845845 5.36990 42.6793i 0.184730 1.46821i
846846 0 0
847847 2.83128 8.71378i 0.0972839 0.299409i
848848 −0.425633 + 0.309240i −0.0146163 + 0.0106194i
849849 0 0
850850 −1.64469 25.7297i −0.0564123 0.882520i
851851 −0.686050 −0.0235175
852852 0 0
853853 7.21464 22.2044i 0.247025 0.760263i −0.748272 0.663392i 0.769116π-0.769116\pi
0.995297 0.0968717i 0.0308837π-0.0308837\pi
854854 −9.28730 + 28.5834i −0.317805 + 0.978102i
855855 0 0
856856 −3.15876 9.72166i −0.107964 0.332280i
857857 −15.3036 −0.522762 −0.261381 0.965236i 0.584178π-0.584178\pi
−0.261381 + 0.965236i 0.584178π0.584178\pi
858858 0 0
859859 2.39576 + 1.74062i 0.0817422 + 0.0593892i 0.627906 0.778289i 0.283912π-0.283912\pi
−0.546164 + 0.837679i 0.683912π0.683912\pi
860860 −14.1462 + 15.0793i −0.482380 + 0.514199i
861861 0 0
862862 17.1482 + 12.4589i 0.584069 + 0.424351i
863863 −30.5987 22.2312i −1.04159 0.756760i −0.0709954 0.997477i 0.522618π-0.522618\pi
−0.970595 + 0.240717i 0.922618π0.922618\pi
864864 0 0
865865 26.3280 5.03603i 0.895180 0.171230i
866866 6.91683 + 5.02537i 0.235043 + 0.170769i
867867 0 0
868868 19.7739 0.671170
869869 8.48918 + 26.1270i 0.287976 + 0.886298i
870870 0 0
871871 −7.58555 + 23.3459i −0.257027 + 0.791046i
872872 −1.20854 + 3.71950i −0.0409263 + 0.125958i
873873 0 0
874874 −0.925059 −0.0312906
875875 7.75943 + 30.0333i 0.262317 + 1.01531i
876876 0 0
877877 12.6215 9.17007i 0.426198 0.309651i −0.353929 0.935272i 0.615154π-0.615154\pi
0.780127 + 0.625621i 0.215154π0.215154\pi
878878 8.67453 26.6975i 0.292751 0.900996i
879879 0 0
880880 5.61478 + 2.63868i 0.189274 + 0.0889497i
881881 −0.359812 1.10739i −0.0121224 0.0373089i 0.944812 0.327612i 0.106244π-0.106244\pi
−0.956935 + 0.290303i 0.906244π0.906244\pi
882882 0 0
883883 15.1063 + 46.4925i 0.508368 + 1.56460i 0.795033 + 0.606566i 0.207453π0.207453\pi
−0.286665 + 0.958031i 0.592547π0.592547\pi
884884 23.6857 + 17.2087i 0.796636 + 0.578790i
885885 0 0
886886 26.7417 19.4290i 0.898406 0.652730i
887887 6.98094 + 5.07195i 0.234397 + 0.170299i 0.698783 0.715333i 0.253725π-0.253725\pi
−0.464386 + 0.885633i 0.653725π0.653725\pi
888888 0 0
889889 21.4335 15.5723i 0.718855 0.522279i
890890 14.0504 14.9772i 0.470971 0.502037i
891891 0 0
892892 −1.55394 4.78254i −0.0520299 0.160131i
893893 3.91861 0.131131
894894 0 0
895895 −13.0672 + 13.9291i −0.436788 + 0.465600i
896896 0.857358 2.63868i 0.0286423 0.0881520i
897897 0 0
898898 30.0654 21.8438i 1.00329 0.728936i
899899 29.1975 0.973790
900900 0 0
901901 −2.71286 −0.0903784
902902 20.4420 14.8520i 0.680643 0.494516i
903903 0 0
904904 −1.97012 + 6.06342i −0.0655253 + 0.201666i
905905 2.18524 17.3680i 0.0726398 0.577332i
906906 0 0
907907 29.5085 0.979815 0.489907 0.871774i 0.337031π-0.337031\pi
0.489907 + 0.871774i 0.337031π0.337031\pi
908908 5.51232 + 16.9652i 0.182933 + 0.563009i
909909 0 0
910910 −31.8795 14.9818i −1.05680 0.496643i
911911 −31.0734 + 22.5761i −1.02951 + 0.747981i −0.968210 0.250139i 0.919524π-0.919524\pi
−0.0612971 + 0.998120i 0.519524π0.519524\pi
912912 0 0
913913 −10.4958 7.62563i −0.347360 0.252372i
914914 23.7155 17.2303i 0.784438 0.569928i
915915 0 0
916916 17.4397 + 12.6707i 0.576223 + 0.418651i
917917 4.80055 + 14.7746i 0.158528 + 0.487899i
918918 0 0
919919 12.8831 + 39.6500i 0.424974 + 1.30793i 0.903020 + 0.429600i 0.141345π0.141345\pi
−0.478046 + 0.878335i 0.658655π0.658655\pi
920920 −0.706192 1.28303i −0.0232825 0.0423004i
921921 0 0
922922 2.75254 8.47145i 0.0906501 0.278992i
923923 −60.8473 + 44.2081i −2.00281 + 1.45513i
924924 0 0
925925 0.334097 + 5.22665i 0.0109851 + 0.171851i
926926 18.2771 0.600624
927927 0 0
928928 1.26594 3.89618i 0.0415567 0.127898i
929929 −8.68484 + 26.7292i −0.284940 + 0.876956i 0.701476 + 0.712693i 0.252525π0.252525\pi
−0.986417 + 0.164263i 0.947475π0.947475\pi
930930 0 0
931931 0.304498 + 0.937148i 0.00997952 + 0.0307138i
932932 −14.7065 −0.481726
933933 0 0
934934 29.6780 + 21.5624i 0.971095 + 0.705542i
935935 15.4254 + 28.0253i 0.504463 + 0.916525i
936936 0 0
937937 10.4164 + 7.56796i 0.340289 + 0.247234i 0.744784 0.667306i 0.232553π-0.232553\pi
−0.404495 + 0.914540i 0.632553π0.632553\pi
938938 9.70427 + 7.05056i 0.316856 + 0.230209i
939939 0 0
940940 2.99148 + 5.43502i 0.0975712 + 0.177271i
941941 8.21234 + 5.96661i 0.267714 + 0.194506i 0.713541 0.700613i 0.247090π-0.247090\pi
−0.445827 + 0.895119i 0.647090π0.647090\pi
942942 0 0
943943 −5.96489 −0.194243
944944 1.16872 + 3.59695i 0.0380386 + 0.117071i
945945 0 0
946946 7.92764 24.3988i 0.257750 0.793273i
947947 17.7298 54.5669i 0.576143 1.77318i −0.0561124 0.998424i 0.517871π-0.517871\pi
0.632255 0.774760i 0.282129π-0.282129\pi
948948 0 0
949949 23.9219 0.776538
950950 0.450491 + 7.04754i 0.0146159 + 0.228652i
951951 0 0
952952 11.5741 8.40906i 0.375118 0.272539i
953953 −1.59843 + 4.91947i −0.0517784 + 0.159357i −0.973602 0.228252i 0.926699π-0.926699\pi
0.921824 + 0.387609i 0.126699π0.126699\pi
954954 0 0
955955 −3.62939 6.59401i −0.117444 0.213377i
956956 −2.14465 6.60057i −0.0693631 0.213478i
957957 0 0
958958 −3.89046 11.9736i −0.125695 0.386849i
959959 −17.9211 13.0205i −0.578704 0.420453i
960960 0 0
961961 −16.0149 + 11.6355i −0.516611 + 0.375340i
962962 −4.81145 3.49572i −0.155127 0.112707i
963963 0 0
964964 −2.67787 + 1.94559i −0.0862484 + 0.0626631i
965965 31.2082 + 14.6663i 1.00463 + 0.472126i
966966 0 0
967967 −12.7927 39.3718i −0.411384 1.26611i −0.915445 0.402443i 0.868161π-0.868161\pi
0.504061 0.863668i 0.331839π-0.331839\pi
968968 3.30233 0.106141
969969 0 0
970970 0.0251701 0.200049i 0.000808164 0.00642318i
971971 −13.3139 + 40.9761i −0.427265 + 1.31499i 0.473544 + 0.880770i 0.342975π0.342975\pi
−0.900809 + 0.434216i 0.857025π0.857025\pi
972972 0 0
973973 −49.5795 + 36.0216i −1.58944 + 1.15480i
974974 18.3256 0.587189
975975 0 0
976976 −10.8325 −0.346739
977977 32.7340 23.7826i 1.04725 0.760874i 0.0755652 0.997141i 0.475924π-0.475924\pi
0.971688 + 0.236267i 0.0759239π0.0759239\pi
978978 0 0
979979 −7.87398 + 24.2336i −0.251654 + 0.774510i
980980 −1.06735 + 1.13775i −0.0340951 + 0.0363441i
981981 0 0
982982 21.7047 0.692625
983983 −12.4777 38.4023i −0.397976 1.22484i −0.926620 0.376000i 0.877299π-0.877299\pi
0.528644 0.848844i 0.322701π-0.322701\pi
984984 0 0
985985 13.4704 14.3589i 0.429202 0.457513i
986986 17.0899 12.4165i 0.544253 0.395423i
987987 0 0
988988 −6.48768 4.71358i −0.206401 0.149959i
989989 −4.89955 + 3.55973i −0.155797 + 0.113193i
990990 0 0
991991 47.0391 + 34.1759i 1.49424 + 1.08563i 0.972604 + 0.232467i 0.0746798π0.0746798\pi
0.521641 + 0.853165i 0.325320π0.325320\pi
992992 2.20239 + 6.77827i 0.0699261 + 0.215210i
993993 0 0
994994 11.3571 + 34.9535i 0.360225 + 1.10866i
995995 35.6625 + 16.7597i 1.13058 + 0.531317i
996996 0 0
997997 12.1434 37.3735i 0.384585 1.18363i −0.552197 0.833714i 0.686210π-0.686210\pi
0.936781 0.349916i 0.113790π-0.113790\pi
998998 12.8141 9.30998i 0.405623 0.294702i
999999 0 0
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 450.2.h.e.361.1 8
3.2 odd 2 50.2.d.b.11.2 8
12.11 even 2 400.2.u.d.161.1 8
15.2 even 4 250.2.e.c.199.1 16
15.8 even 4 250.2.e.c.199.4 16
15.14 odd 2 250.2.d.d.51.1 8
25.16 even 5 inner 450.2.h.e.91.1 8
75.29 odd 10 1250.2.a.f.1.2 4
75.38 even 20 250.2.e.c.49.1 16
75.41 odd 10 50.2.d.b.41.2 yes 8
75.47 even 20 1250.2.b.e.1249.6 8
75.53 even 20 1250.2.b.e.1249.3 8
75.59 odd 10 250.2.d.d.201.1 8
75.62 even 20 250.2.e.c.49.4 16
75.71 odd 10 1250.2.a.l.1.3 4
300.71 even 10 10000.2.a.t.1.2 4
300.179 even 10 10000.2.a.x.1.3 4
300.191 even 10 400.2.u.d.241.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
50.2.d.b.11.2 8 3.2 odd 2
50.2.d.b.41.2 yes 8 75.41 odd 10
250.2.d.d.51.1 8 15.14 odd 2
250.2.d.d.201.1 8 75.59 odd 10
250.2.e.c.49.1 16 75.38 even 20
250.2.e.c.49.4 16 75.62 even 20
250.2.e.c.199.1 16 15.2 even 4
250.2.e.c.199.4 16 15.8 even 4
400.2.u.d.161.1 8 12.11 even 2
400.2.u.d.241.1 8 300.191 even 10
450.2.h.e.91.1 8 25.16 even 5 inner
450.2.h.e.361.1 8 1.1 even 1 trivial
1250.2.a.f.1.2 4 75.29 odd 10
1250.2.a.l.1.3 4 75.71 odd 10
1250.2.b.e.1249.3 8 75.53 even 20
1250.2.b.e.1249.6 8 75.47 even 20
10000.2.a.t.1.2 4 300.71 even 10
10000.2.a.x.1.3 4 300.179 even 10