Properties

Label 855.2.n.c.818.4
Level 855855
Weight 22
Character 855.818
Analytic conductor 6.8276.827
Analytic rank 00
Dimension 88
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [855,2,Mod(647,855)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(855, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 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("855.647");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 855=32519 855 = 3^{2} \cdot 5 \cdot 19
Weight: k k == 2 2
Character orbit: [χ][\chi] == 855.n (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: 6.827209372826.82720937282
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(i)\Q(i)
Coefficient field: Q(ζ24)\Q(\zeta_{24})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8x4+1 x^{8} - x^{4} + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 818.4
Root 0.258819+0.965926i-0.258819 + 0.965926i of defining polynomial
Character χ\chi == 855.818
Dual form 855.2.n.c.647.4

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+(1.41421+1.41421i)q2+2.00000iq4+(0.448288+2.19067i)q5+(2.366032.36603i)q7+(3.73205+2.46410i)q10+1.55291iq11+(0.732051+0.732051i)q13+6.69213q14+4.00000q16+(4.57081+4.57081i)q17+1.00000iq19+(4.381340.896575i)q20+(2.19615+2.19615i)q22+(2.44949+2.44949i)q23+(4.598081.96410i)q25+2.07055iq26+(4.73205+4.73205i)q288.76268q290.535898q31+(5.65685+5.65685i)q32+12.9282iq34+(4.12252+6.24384i)q35+(3.464103.46410i)q37+(1.41421+1.41421i)q382.82843iq41+(3.098083.09808i)q433.10583q446.92820q46+(2.638962.63896i)q474.19615iq49+(3.725009.28032i)q50+(1.46410+1.46410i)q52+(4.242644.24264i)q53+(3.401920.696152i)q55+(12.392312.3923i)q58+13.3843q5912.8564q61+(0.7578750.757875i)q62+8.00000iq64+(1.93185+1.27551i)q65+(9.464109.46410i)q67+(9.14162+9.14162i)q68+(3.00000+14.6603i)q700.757875iq71+(3.901923.90192i)q73+9.79796q742.00000q76+(3.67423+3.67423i)q77+13.4641iq79+(1.79315+8.76268i)q80+(4.000004.00000i)q82+(0.757875+0.757875i)q83+(12.0622+7.96410i)q858.76268iq86+8.76268q89+3.46410q91+(4.898984.89898i)q927.46410iq94+(2.190670.448288i)q95+(5.66025+5.66025i)q97+(5.934265.93426i)q98+O(q100)q+(1.41421 + 1.41421i) q^{2} +2.00000i q^{4} +(-0.448288 + 2.19067i) q^{5} +(2.36603 - 2.36603i) q^{7} +(-3.73205 + 2.46410i) q^{10} +1.55291i q^{11} +(0.732051 + 0.732051i) q^{13} +6.69213 q^{14} +4.00000 q^{16} +(4.57081 + 4.57081i) q^{17} +1.00000i q^{19} +(-4.38134 - 0.896575i) q^{20} +(-2.19615 + 2.19615i) q^{22} +(-2.44949 + 2.44949i) q^{23} +(-4.59808 - 1.96410i) q^{25} +2.07055i q^{26} +(4.73205 + 4.73205i) q^{28} -8.76268 q^{29} -0.535898 q^{31} +(5.65685 + 5.65685i) q^{32} +12.9282i q^{34} +(4.12252 + 6.24384i) q^{35} +(3.46410 - 3.46410i) q^{37} +(-1.41421 + 1.41421i) q^{38} -2.82843i q^{41} +(-3.09808 - 3.09808i) q^{43} -3.10583 q^{44} -6.92820 q^{46} +(-2.63896 - 2.63896i) q^{47} -4.19615i q^{49} +(-3.72500 - 9.28032i) q^{50} +(-1.46410 + 1.46410i) q^{52} +(4.24264 - 4.24264i) q^{53} +(-3.40192 - 0.696152i) q^{55} +(-12.3923 - 12.3923i) q^{58} +13.3843 q^{59} -12.8564 q^{61} +(-0.757875 - 0.757875i) q^{62} +8.00000i q^{64} +(-1.93185 + 1.27551i) q^{65} +(9.46410 - 9.46410i) q^{67} +(-9.14162 + 9.14162i) q^{68} +(-3.00000 + 14.6603i) q^{70} -0.757875i q^{71} +(-3.90192 - 3.90192i) q^{73} +9.79796 q^{74} -2.00000 q^{76} +(3.67423 + 3.67423i) q^{77} +13.4641i q^{79} +(-1.79315 + 8.76268i) q^{80} +(4.00000 - 4.00000i) q^{82} +(-0.757875 + 0.757875i) q^{83} +(-12.0622 + 7.96410i) q^{85} -8.76268i q^{86} +8.76268 q^{89} +3.46410 q^{91} +(-4.89898 - 4.89898i) q^{92} -7.46410i q^{94} +(-2.19067 - 0.448288i) q^{95} +(-5.66025 + 5.66025i) q^{97} +(5.93426 - 5.93426i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+12q716q108q13+32q16+24q2216q25+24q2832q314q43+16q5248q5516q58+8q61+48q6724q7052q7316q76++24q97+O(q100) 8 q + 12 q^{7} - 16 q^{10} - 8 q^{13} + 32 q^{16} + 24 q^{22} - 16 q^{25} + 24 q^{28} - 32 q^{31} - 4 q^{43} + 16 q^{52} - 48 q^{55} - 16 q^{58} + 8 q^{61} + 48 q^{67} - 24 q^{70} - 52 q^{73} - 16 q^{76}+ \cdots + 24 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/855Z)×\left(\mathbb{Z}/855\mathbb{Z}\right)^\times.

nn 172172 191191 496496
χ(n)\chi(n) e(34)e\left(\frac{3}{4}\right) 1-1 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 1.41421 + 1.41421i 1.00000 + 1.00000i 1.00000 00
1.00000i 0.5π0.5\pi
33 0 0
44 2.00000i 1.00000i
55 −0.448288 + 2.19067i −0.200480 + 0.979698i
66 0 0
77 2.36603 2.36603i 0.894274 0.894274i −0.100649 0.994922i 0.532092π-0.532092\pi
0.994922 + 0.100649i 0.0320918π0.0320918\pi
88 0 0
99 0 0
1010 −3.73205 + 2.46410i −1.18018 + 0.779217i
1111 1.55291i 0.468221i 0.972210 + 0.234111i 0.0752178π0.0752178\pi
−0.972210 + 0.234111i 0.924782π0.924782\pi
1212 0 0
1313 0.732051 + 0.732051i 0.203034 + 0.203034i 0.801299 0.598264i 0.204143π-0.204143\pi
−0.598264 + 0.801299i 0.704143π0.704143\pi
1414 6.69213 1.78855
1515 0 0
1616 4.00000 1.00000
1717 4.57081 + 4.57081i 1.10858 + 1.10858i 0.993337 + 0.115247i 0.0367661π0.0367661\pi
0.115247 + 0.993337i 0.463234π0.463234\pi
1818 0 0
1919 1.00000i 0.229416i
2020 −4.38134 0.896575i −0.979698 0.200480i
2121 0 0
2222 −2.19615 + 2.19615i −0.468221 + 0.468221i
2323 −2.44949 + 2.44949i −0.510754 + 0.510754i −0.914757 0.404004i 0.867618π-0.867618\pi
0.404004 + 0.914757i 0.367618π0.367618\pi
2424 0 0
2525 −4.59808 1.96410i −0.919615 0.392820i
2626 2.07055i 0.406069i
2727 0 0
2828 4.73205 + 4.73205i 0.894274 + 0.894274i
2929 −8.76268 −1.62719 −0.813595 0.581432i 0.802492π-0.802492\pi
−0.813595 + 0.581432i 0.802492π0.802492\pi
3030 0 0
3131 −0.535898 −0.0962502 −0.0481251 0.998841i 0.515325π-0.515325\pi
−0.0481251 + 0.998841i 0.515325π0.515325\pi
3232 5.65685 + 5.65685i 1.00000 + 1.00000i
3333 0 0
3434 12.9282i 2.21717i
3535 4.12252 + 6.24384i 0.696833 + 1.05540i
3636 0 0
3737 3.46410 3.46410i 0.569495 0.569495i −0.362492 0.931987i 0.618074π-0.618074\pi
0.931987 + 0.362492i 0.118074π0.118074\pi
3838 −1.41421 + 1.41421i −0.229416 + 0.229416i
3939 0 0
4040 0 0
4141 2.82843i 0.441726i −0.975305 0.220863i 0.929113π-0.929113\pi
0.975305 0.220863i 0.0708874π-0.0708874\pi
4242 0 0
4343 −3.09808 3.09808i −0.472452 0.472452i 0.430255 0.902707i 0.358424π-0.358424\pi
−0.902707 + 0.430255i 0.858424π0.858424\pi
4444 −3.10583 −0.468221
4545 0 0
4646 −6.92820 −1.02151
4747 −2.63896 2.63896i −0.384932 0.384932i 0.487944 0.872875i 0.337747π-0.337747\pi
−0.872875 + 0.487944i 0.837747π0.837747\pi
4848 0 0
4949 4.19615i 0.599450i
5050 −3.72500 9.28032i −0.526795 1.31244i
5151 0 0
5252 −1.46410 + 1.46410i −0.203034 + 0.203034i
5353 4.24264 4.24264i 0.582772 0.582772i −0.352892 0.935664i 0.614802π-0.614802\pi
0.935664 + 0.352892i 0.114802π0.114802\pi
5454 0 0
5555 −3.40192 0.696152i −0.458715 0.0938692i
5656 0 0
5757 0 0
5858 −12.3923 12.3923i −1.62719 1.62719i
5959 13.3843 1.74248 0.871241 0.490855i 0.163316π-0.163316\pi
0.871241 + 0.490855i 0.163316π0.163316\pi
6060 0 0
6161 −12.8564 −1.64609 −0.823047 0.567973i 0.807728π-0.807728\pi
−0.823047 + 0.567973i 0.807728π0.807728\pi
6262 −0.757875 0.757875i −0.0962502 0.0962502i
6363 0 0
6464 8.00000i 1.00000i
6565 −1.93185 + 1.27551i −0.239617 + 0.158208i
6666 0 0
6767 9.46410 9.46410i 1.15622 1.15622i 0.170943 0.985281i 0.445319π-0.445319\pi
0.985281 0.170943i 0.0546814π-0.0546814\pi
6868 −9.14162 + 9.14162i −1.10858 + 1.10858i
6969 0 0
7070 −3.00000 + 14.6603i −0.358569 + 1.75224i
7171 0.757875i 0.0899432i −0.998988 0.0449716i 0.985680π-0.985680\pi
0.998988 0.0449716i 0.0143197π-0.0143197\pi
7272 0 0
7373 −3.90192 3.90192i −0.456686 0.456686i 0.440880 0.897566i 0.354666π-0.354666\pi
−0.897566 + 0.440880i 0.854666π0.854666\pi
7474 9.79796 1.13899
7575 0 0
7676 −2.00000 −0.229416
7777 3.67423 + 3.67423i 0.418718 + 0.418718i
7878 0 0
7979 13.4641i 1.51483i 0.652934 + 0.757415i 0.273538π0.273538\pi
−0.652934 + 0.757415i 0.726462π0.726462\pi
8080 −1.79315 + 8.76268i −0.200480 + 0.979698i
8181 0 0
8282 4.00000 4.00000i 0.441726 0.441726i
8383 −0.757875 + 0.757875i −0.0831876 + 0.0831876i −0.747476 0.664289i 0.768735π-0.768735\pi
0.664289 + 0.747476i 0.268735π0.268735\pi
8484 0 0
8585 −12.0622 + 7.96410i −1.30833 + 0.863828i
8686 8.76268i 0.944904i
8787 0 0
8888 0 0
8989 8.76268 0.928843 0.464421 0.885614i 0.346262π-0.346262\pi
0.464421 + 0.885614i 0.346262π0.346262\pi
9090 0 0
9191 3.46410 0.363137
9292 −4.89898 4.89898i −0.510754 0.510754i
9393 0 0
9494 7.46410i 0.769863i
9595 −2.19067 0.448288i −0.224758 0.0459934i
9696 0 0
9797 −5.66025 + 5.66025i −0.574712 + 0.574712i −0.933441 0.358730i 0.883210π-0.883210\pi
0.358730 + 0.933441i 0.383210π0.383210\pi
9898 5.93426 5.93426i 0.599450 0.599450i
9999 0 0
100100 3.92820 9.19615i 0.392820 0.919615i
101101 18.9396i 1.88456i −0.334828 0.942279i 0.608678π-0.608678\pi
0.334828 0.942279i 0.391322π-0.391322\pi
102102 0 0
103103 1.80385 + 1.80385i 0.177738 + 0.177738i 0.790369 0.612631i 0.209889π-0.209889\pi
−0.612631 + 0.790369i 0.709889π0.709889\pi
104104 0 0
105105 0 0
106106 12.0000 1.16554
107107 −0.378937 0.378937i −0.0366333 0.0366333i 0.688553 0.725186i 0.258246π-0.258246\pi
−0.725186 + 0.688553i 0.758246π0.758246\pi
108108 0 0
109109 8.39230i 0.803837i −0.915675 0.401919i 0.868344π-0.868344\pi
0.915675 0.401919i 0.131656π-0.131656\pi
110110 −3.82654 5.79555i −0.364846 0.552584i
111111 0 0
112112 9.46410 9.46410i 0.894274 0.894274i
113113 −10.9348 + 10.9348i −1.02866 + 1.02866i −0.0290796 + 0.999577i 0.509258π0.509258\pi
−0.999577 + 0.0290796i 0.990742π0.990742\pi
114114 0 0
115115 −4.26795 6.46410i −0.397988 0.602781i
116116 17.5254i 1.62719i
117117 0 0
118118 18.9282 + 18.9282i 1.74248 + 1.74248i
119119 21.6293 1.98276
120120 0 0
121121 8.58846 0.780769
122122 −18.1817 18.1817i −1.64609 1.64609i
123123 0 0
124124 1.07180i 0.0962502i
125125 6.36396 9.19239i 0.569210 0.822192i
126126 0 0
127127 −1.26795 + 1.26795i −0.112512 + 0.112512i −0.761122 0.648609i 0.775351π-0.775351\pi
0.648609 + 0.761122i 0.275351π0.275351\pi
128128 0 0
129129 0 0
130130 −4.53590 0.928203i −0.397825 0.0814088i
131131 12.8666i 1.12416i −0.827082 0.562081i 0.810001π-0.810001\pi
0.827082 0.562081i 0.189999π-0.189999\pi
132132 0 0
133133 2.36603 + 2.36603i 0.205160 + 0.205160i
134134 26.7685 2.31245
135135 0 0
136136 0 0
137137 −1.08604 1.08604i −0.0927870 0.0927870i 0.659190 0.751977i 0.270899π-0.270899\pi
−0.751977 + 0.659190i 0.770899π0.770899\pi
138138 0 0
139139 9.73205i 0.825462i −0.910853 0.412731i 0.864575π-0.864575\pi
0.910853 0.412731i 0.135425π-0.135425\pi
140140 −12.4877 + 8.24504i −1.05540 + 0.696833i
141141 0 0
142142 1.07180 1.07180i 0.0899432 0.0899432i
143143 −1.13681 + 1.13681i −0.0950650 + 0.0950650i
144144 0 0
145145 3.92820 19.1962i 0.326220 1.59415i
146146 11.0363i 0.913371i
147147 0 0
148148 6.92820 + 6.92820i 0.569495 + 0.569495i
149149 −24.3562 −1.99534 −0.997669 0.0682436i 0.978261π-0.978261\pi
−0.997669 + 0.0682436i 0.978261π0.978261\pi
150150 0 0
151151 1.07180 0.0872216 0.0436108 0.999049i 0.486114π-0.486114\pi
0.0436108 + 0.999049i 0.486114π0.486114\pi
152152 0 0
153153 0 0
154154 10.3923i 0.837436i
155155 0.240237 1.17398i 0.0192963 0.0942961i
156156 0 0
157157 −0.0717968 + 0.0717968i −0.00573001 + 0.00573001i −0.709966 0.704236i 0.751290π-0.751290\pi
0.704236 + 0.709966i 0.251290π0.251290\pi
158158 −19.0411 + 19.0411i −1.51483 + 1.51483i
159159 0 0
160160 −14.9282 + 9.85641i −1.18018 + 0.779217i
161161 11.5911i 0.913507i
162162 0 0
163163 −9.19615 9.19615i −0.720298 0.720298i 0.248368 0.968666i 0.420106π-0.420106\pi
−0.968666 + 0.248368i 0.920106π0.920106\pi
164164 5.65685 0.441726
165165 0 0
166166 −2.14359 −0.166375
167167 14.0406 + 14.0406i 1.08649 + 1.08649i 0.995887 + 0.0906075i 0.0288809π0.0288809\pi
0.0906075 + 0.995887i 0.471119π0.471119\pi
168168 0 0
169169 11.9282i 0.917554i
170170 −28.3214 5.79555i −2.17215 0.444499i
171171 0 0
172172 6.19615 6.19615i 0.472452 0.472452i
173173 −8.10634 + 8.10634i −0.616314 + 0.616314i −0.944584 0.328270i 0.893534π-0.893534\pi
0.328270 + 0.944584i 0.393534π0.393534\pi
174174 0 0
175175 −15.5263 + 6.23205i −1.17368 + 0.471099i
176176 6.21166i 0.468221i
177177 0 0
178178 12.3923 + 12.3923i 0.928843 + 0.928843i
179179 −5.17638 −0.386901 −0.193450 0.981110i 0.561968π-0.561968\pi
−0.193450 + 0.981110i 0.561968π0.561968\pi
180180 0 0
181181 18.3923 1.36709 0.683545 0.729909i 0.260437π-0.260437\pi
0.683545 + 0.729909i 0.260437π0.260437\pi
182182 4.89898 + 4.89898i 0.363137 + 0.363137i
183183 0 0
184184 0 0
185185 6.03579 + 9.14162i 0.443760 + 0.672105i
186186 0 0
187187 −7.09808 + 7.09808i −0.519063 + 0.519063i
188188 5.27792 5.27792i 0.384932 0.384932i
189189 0 0
190190 −2.46410 3.73205i −0.178765 0.270751i
191191 2.58819i 0.187275i 0.995606 + 0.0936374i 0.0298495π0.0298495\pi
−0.995606 + 0.0936374i 0.970151π0.970151\pi
192192 0 0
193193 −11.4641 11.4641i −0.825204 0.825204i 0.161645 0.986849i 0.448320π-0.448320\pi
−0.986849 + 0.161645i 0.948320π0.948320\pi
194194 −16.0096 −1.14942
195195 0 0
196196 8.39230 0.599450
197197 −9.79796 9.79796i −0.698076 0.698076i 0.265920 0.963995i 0.414324π-0.414324\pi
−0.963995 + 0.265920i 0.914324π0.914324\pi
198198 0 0
199199 9.73205i 0.689887i −0.938623 0.344943i 0.887898π-0.887898\pi
0.938623 0.344943i 0.112102π-0.112102\pi
200200 0 0
201201 0 0
202202 26.7846 26.7846i 1.88456 1.88456i
203203 −20.7327 + 20.7327i −1.45515 + 1.45515i
204204 0 0
205205 6.19615 + 1.26795i 0.432758 + 0.0885574i
206206 5.10205i 0.355477i
207207 0 0
208208 2.92820 + 2.92820i 0.203034 + 0.203034i
209209 −1.55291 −0.107417
210210 0 0
211211 −5.85641 −0.403172 −0.201586 0.979471i 0.564609π-0.564609\pi
−0.201586 + 0.979471i 0.564609π0.564609\pi
212212 8.48528 + 8.48528i 0.582772 + 0.582772i
213213 0 0
214214 1.07180i 0.0732665i
215215 8.17569 5.39804i 0.557578 0.368143i
216216 0 0
217217 −1.26795 + 1.26795i −0.0860740 + 0.0860740i
218218 11.8685 11.8685i 0.803837 0.803837i
219219 0 0
220220 1.39230 6.80385i 0.0938692 0.458715i
221221 6.69213i 0.450161i
222222 0 0
223223 −4.92820 4.92820i −0.330017 0.330017i 0.522576 0.852593i 0.324971π-0.324971\pi
−0.852593 + 0.522576i 0.824971π0.824971\pi
224224 26.7685 1.78855
225225 0 0
226226 −30.9282 −2.05731
227227 −17.1464 17.1464i −1.13805 1.13805i −0.988800 0.149249i 0.952314π-0.952314\pi
−0.149249 0.988800i 0.547686π-0.547686\pi
228228 0 0
229229 12.6603i 0.836613i −0.908306 0.418307i 0.862624π-0.862624\pi
0.908306 0.418307i 0.137376π-0.137376\pi
230230 3.10583 15.1774i 0.204792 1.00077i
231231 0 0
232232 0 0
233233 −5.46739 + 5.46739i −0.358180 + 0.358180i −0.863142 0.504962i 0.831507π-0.831507\pi
0.504962 + 0.863142i 0.331507π0.331507\pi
234234 0 0
235235 6.96410 4.59808i 0.454288 0.299945i
236236 26.7685i 1.74248i
237237 0 0
238238 30.5885 + 30.5885i 1.98276 + 1.98276i
239239 8.14351 0.526760 0.263380 0.964692i 0.415163π-0.415163\pi
0.263380 + 0.964692i 0.415163π0.415163\pi
240240 0 0
241241 28.3923 1.82891 0.914455 0.404689i 0.132620π-0.132620\pi
0.914455 + 0.404689i 0.132620π0.132620\pi
242242 12.1459 + 12.1459i 0.780769 + 0.780769i
243243 0 0
244244 25.7128i 1.64609i
245245 9.19239 + 1.88108i 0.587280 + 0.120178i
246246 0 0
247247 −0.732051 + 0.732051i −0.0465793 + 0.0465793i
248248 0 0
249249 0 0
250250 22.0000 4.00000i 1.39140 0.252982i
251251 15.0387i 0.949235i 0.880192 + 0.474618i 0.157414π0.157414\pi
−0.880192 + 0.474618i 0.842586π0.842586\pi
252252 0 0
253253 −3.80385 3.80385i −0.239146 0.239146i
254254 −3.58630 −0.225025
255255 0 0
256256 16.0000 1.00000
257257 −18.5606 18.5606i −1.15778 1.15778i −0.984952 0.172829i 0.944709π-0.944709\pi
−0.172829 0.984952i 0.555291π-0.555291\pi
258258 0 0
259259 16.3923i 1.01857i
260260 −2.55103 3.86370i −0.158208 0.239617i
261261 0 0
262262 18.1962 18.1962i 1.12416 1.12416i
263263 −12.9546 + 12.9546i −0.798812 + 0.798812i −0.982908 0.184096i 0.941064π-0.941064\pi
0.184096 + 0.982908i 0.441064π0.441064\pi
264264 0 0
265265 7.39230 + 11.1962i 0.454106 + 0.687774i
266266 6.69213i 0.410321i
267267 0 0
268268 18.9282 + 18.9282i 1.15622 + 1.15622i
269269 −16.4901 −1.00542 −0.502709 0.864456i 0.667663π-0.667663\pi
−0.502709 + 0.864456i 0.667663π0.667663\pi
270270 0 0
271271 19.4641 1.18236 0.591180 0.806540i 0.298662π-0.298662\pi
0.591180 + 0.806540i 0.298662π0.298662\pi
272272 18.2832 + 18.2832i 1.10858 + 1.10858i
273273 0 0
274274 3.07180i 0.185574i
275275 3.05008 7.14042i 0.183927 0.430583i
276276 0 0
277277 −9.16987 + 9.16987i −0.550964 + 0.550964i −0.926719 0.375755i 0.877383π-0.877383\pi
0.375755 + 0.926719i 0.377383π0.377383\pi
278278 13.7632 13.7632i 0.825462 0.825462i
279279 0 0
280280 0 0
281281 3.10583i 0.185278i 0.995700 + 0.0926391i 0.0295303π0.0295303\pi
−0.995700 + 0.0926391i 0.970470π0.970470\pi
282282 0 0
283283 0.633975 + 0.633975i 0.0376859 + 0.0376859i 0.725699 0.688013i 0.241517π-0.241517\pi
−0.688013 + 0.725699i 0.741517π0.741517\pi
284284 1.51575 0.0899432
285285 0 0
286286 −3.21539 −0.190130
287287 −6.69213 6.69213i −0.395024 0.395024i
288288 0 0
289289 24.7846i 1.45792i
290290 32.7028 21.5921i 1.92037 1.26793i
291291 0 0
292292 7.80385 7.80385i 0.456686 0.456686i
293293 −10.2784 + 10.2784i −0.600472 + 0.600472i −0.940438 0.339965i 0.889585π-0.889585\pi
0.339965 + 0.940438i 0.389585π0.389585\pi
294294 0 0
295295 −6.00000 + 29.3205i −0.349334 + 1.70711i
296296 0 0
297297 0 0
298298 −34.4449 34.4449i −1.99534 1.99534i
299299 −3.58630 −0.207401
300300 0 0
301301 −14.6603 −0.845003
302302 1.51575 + 1.51575i 0.0872216 + 0.0872216i
303303 0 0
304304 4.00000i 0.229416i
305305 5.76337 28.1642i 0.330010 1.61267i
306306 0 0
307307 −18.3923 + 18.3923i −1.04970 + 1.04970i −0.0510059 + 0.998698i 0.516243π0.516243\pi
−0.998698 + 0.0510059i 0.983757π0.983757\pi
308308 −7.34847 + 7.34847i −0.418718 + 0.418718i
309309 0 0
310310 2.00000 1.32051i 0.113592 0.0749998i
311311 9.65926i 0.547726i −0.961769 0.273863i 0.911698π-0.911698\pi
0.961769 0.273863i 0.0883015π-0.0883015\pi
312312 0 0
313313 22.3205 + 22.3205i 1.26163 + 1.26163i 0.950303 + 0.311327i 0.100773π0.100773\pi
0.311327 + 0.950303i 0.399227π0.399227\pi
314314 −0.203072 −0.0114600
315315 0 0
316316 −26.9282 −1.51483
317317 7.45001 + 7.45001i 0.418434 + 0.418434i 0.884664 0.466230i 0.154388π-0.154388\pi
−0.466230 + 0.884664i 0.654388π0.654388\pi
318318 0 0
319319 13.6077i 0.761885i
320320 −17.5254 3.58630i −0.979698 0.200480i
321321 0 0
322322 −16.3923 + 16.3923i −0.913507 + 0.913507i
323323 −4.57081 + 4.57081i −0.254327 + 0.254327i
324324 0 0
325325 −1.92820 4.80385i −0.106957 0.266470i
326326 26.0106i 1.44060i
327327 0 0
328328 0 0
329329 −12.4877 −0.688468
330330 0 0
331331 2.14359 0.117823 0.0589113 0.998263i 0.481237π-0.481237\pi
0.0589113 + 0.998263i 0.481237π0.481237\pi
332332 −1.51575 1.51575i −0.0831876 0.0831876i
333333 0 0
334334 39.7128i 2.17299i
335335 16.4901 + 24.9754i 0.900950 + 1.36455i
336336 0 0
337337 3.66025 3.66025i 0.199387 0.199387i −0.600350 0.799737i 0.704972π-0.704972\pi
0.799737 + 0.600350i 0.204972π0.204972\pi
338338 16.8690 16.8690i 0.917554 0.917554i
339339 0 0
340340 −15.9282 24.1244i −0.863828 1.30833i
341341 0.832204i 0.0450664i
342342 0 0
343343 6.63397 + 6.63397i 0.358201 + 0.358201i
344344 0 0
345345 0 0
346346 −22.9282 −1.23263
347347 24.1667 + 24.1667i 1.29734 + 1.29734i 0.930145 + 0.367193i 0.119681π0.119681\pi
0.367193 + 0.930145i 0.380319π0.380319\pi
348348 0 0
349349 11.3397i 0.607003i −0.952831 0.303501i 0.901844π-0.901844\pi
0.952831 0.303501i 0.0981557π-0.0981557\pi
350350 −30.7709 13.1440i −1.64478 0.702578i
351351 0 0
352352 −8.78461 + 8.78461i −0.468221 + 0.468221i
353353 12.6264 12.6264i 0.672035 0.672035i −0.286150 0.958185i 0.592376π-0.592376\pi
0.958185 + 0.286150i 0.0923756π0.0923756\pi
354354 0 0
355355 1.66025 + 0.339746i 0.0881171 + 0.0180318i
356356 17.5254i 0.928843i
357357 0 0
358358 −7.32051 7.32051i −0.386901 0.386901i
359359 0.517638 0.0273199 0.0136599 0.999907i 0.495652π-0.495652\pi
0.0136599 + 0.999907i 0.495652π0.495652\pi
360360 0 0
361361 −1.00000 −0.0526316
362362 26.0106 + 26.0106i 1.36709 + 1.36709i
363363 0 0
364364 6.92820i 0.363137i
365365 10.2970 6.79865i 0.538970 0.355857i
366366 0 0
367367 −13.7321 + 13.7321i −0.716807 + 0.716807i −0.967950 0.251143i 0.919194π-0.919194\pi
0.251143 + 0.967950i 0.419194π0.419194\pi
368368 −9.79796 + 9.79796i −0.510754 + 0.510754i
369369 0 0
370370 −4.39230 + 21.4641i −0.228345 + 1.11587i
371371 20.0764i 1.04231i
372372 0 0
373373 −3.46410 3.46410i −0.179364 0.179364i 0.611714 0.791079i 0.290480π-0.290480\pi
−0.791079 + 0.611714i 0.790480π0.790480\pi
374374 −20.0764 −1.03813
375375 0 0
376376 0 0
377377 −6.41473 6.41473i −0.330375 0.330375i
378378 0 0
379379 20.9282i 1.07501i 0.843261 + 0.537505i 0.180633π0.180633\pi
−0.843261 + 0.537505i 0.819367π0.819367\pi
380380 0.896575 4.38134i 0.0459934 0.224758i
381381 0 0
382382 −3.66025 + 3.66025i −0.187275 + 0.187275i
383383 −14.0406 + 14.0406i −0.717441 + 0.717441i −0.968081 0.250639i 0.919359π-0.919359\pi
0.250639 + 0.968081i 0.419359π0.419359\pi
384384 0 0
385385 −9.69615 + 6.40192i −0.494162 + 0.326272i
386386 32.4254i 1.65041i
387387 0 0
388388 −11.3205 11.3205i −0.574712 0.574712i
389389 −11.0735 −0.561447 −0.280724 0.959789i 0.590574π-0.590574\pi
−0.280724 + 0.959789i 0.590574π0.590574\pi
390390 0 0
391391 −22.3923 −1.13243
392392 0 0
393393 0 0
394394 27.7128i 1.39615i
395395 −29.4954 6.03579i −1.48408 0.303694i
396396 0 0
397397 23.2224 23.2224i 1.16550 1.16550i 0.182248 0.983253i 0.441663π-0.441663\pi
0.983253 0.182248i 0.0583373π-0.0583373\pi
398398 13.7632 13.7632i 0.689887 0.689887i
399399 0 0
400400 −18.3923 7.85641i −0.919615 0.392820i
401401 19.0411i 0.950868i 0.879751 + 0.475434i 0.157709π0.157709\pi
−0.879751 + 0.475434i 0.842291π0.842291\pi
402402 0 0
403403 −0.392305 0.392305i −0.0195421 0.0195421i
404404 37.8792 1.88456
405405 0 0
406406 −58.6410 −2.91030
407407 5.37945 + 5.37945i 0.266650 + 0.266650i
408408 0 0
409409 11.8564i 0.586262i 0.956072 + 0.293131i 0.0946971π0.0946971\pi
−0.956072 + 0.293131i 0.905303π0.905303\pi
410410 6.96953 + 10.5558i 0.344201 + 0.521315i
411411 0 0
412412 −3.60770 + 3.60770i −0.177738 + 0.177738i
413413 31.6675 31.6675i 1.55826 1.55826i
414414 0 0
415415 −1.32051 2.00000i −0.0648212 0.0981761i
416416 8.28221i 0.406069i
417417 0 0
418418 −2.19615 2.19615i −0.107417 0.107417i
419419 29.9759 1.46442 0.732209 0.681080i 0.238489π-0.238489\pi
0.732209 + 0.681080i 0.238489π0.238489\pi
420420 0 0
421421 9.60770 0.468250 0.234125 0.972206i 0.424777π-0.424777\pi
0.234125 + 0.972206i 0.424777π0.424777\pi
422422 −8.28221 8.28221i −0.403172 0.403172i
423423 0 0
424424 0 0
425425 −12.0394 29.9945i −0.583997 1.45495i
426426 0 0
427427 −30.4186 + 30.4186i −1.47206 + 1.47206i
428428 0.757875 0.757875i 0.0366333 0.0366333i
429429 0 0
430430 19.1962 + 3.92820i 0.925721 + 0.189435i
431431 8.76268i 0.422084i 0.977477 + 0.211042i 0.0676856π0.0676856\pi
−0.977477 + 0.211042i 0.932314π0.932314\pi
432432 0 0
433433 −4.73205 4.73205i −0.227408 0.227408i 0.584201 0.811609i 0.301408π-0.301408\pi
−0.811609 + 0.584201i 0.801408π0.801408\pi
434434 −3.58630 −0.172148
435435 0 0
436436 16.7846 0.803837
437437 −2.44949 2.44949i −0.117175 0.117175i
438438 0 0
439439 31.8564i 1.52042i 0.649675 + 0.760212i 0.274905π0.274905\pi
−0.649675 + 0.760212i 0.725095π0.725095\pi
440440 0 0
441441 0 0
442442 −9.46410 + 9.46410i −0.450161 + 0.450161i
443443 −22.4379 + 22.4379i −1.06606 + 1.06606i −0.0684012 + 0.997658i 0.521790π0.521790\pi
−0.997658 + 0.0684012i 0.978210π0.978210\pi
444444 0 0
445445 −3.92820 + 19.1962i −0.186215 + 0.909985i
446446 13.9391i 0.660034i
447447 0 0
448448 18.9282 + 18.9282i 0.894274 + 0.894274i
449449 −6.41473 −0.302730 −0.151365 0.988478i 0.548367π-0.548367\pi
−0.151365 + 0.988478i 0.548367π0.548367\pi
450450 0 0
451451 4.39230 0.206826
452452 −21.8695 21.8695i −1.02866 1.02866i
453453 0 0
454454 48.4974i 2.27610i
455455 −1.55291 + 7.58871i −0.0728017 + 0.355764i
456456 0 0
457457 0.0262794 0.0262794i 0.00122930 0.00122930i −0.706492 0.707721i 0.749723π-0.749723\pi
0.707721 + 0.706492i 0.249723π0.249723\pi
458458 17.9043 17.9043i 0.836613 0.836613i
459459 0 0
460460 12.9282 8.53590i 0.602781 0.397988i
461461 17.5897i 0.819236i −0.912257 0.409618i 0.865662π-0.865662\pi
0.912257 0.409618i 0.134338π-0.134338\pi
462462 0 0
463463 9.97372 + 9.97372i 0.463518 + 0.463518i 0.899807 0.436289i 0.143707π-0.143707\pi
−0.436289 + 0.899807i 0.643707π0.643707\pi
464464 −35.0507 −1.62719
465465 0 0
466466 −15.4641 −0.716361
467467 −7.91688 7.91688i −0.366349 0.366349i 0.499795 0.866144i 0.333409π-0.333409\pi
−0.866144 + 0.499795i 0.833409π0.833409\pi
468468 0 0
469469 44.7846i 2.06796i
470470 16.3514 + 3.34607i 0.754233 + 0.154342i
471471 0 0
472472 0 0
473473 4.81105 4.81105i 0.221212 0.221212i
474474 0 0
475475 1.96410 4.59808i 0.0901192 0.210974i
476476 43.2586i 1.98276i
477477 0 0
478478 11.5167 + 11.5167i 0.526760 + 0.526760i
479479 −23.7642 −1.08582 −0.542908 0.839792i 0.682677π-0.682677\pi
−0.542908 + 0.839792i 0.682677π0.682677\pi
480480 0 0
481481 5.07180 0.231254
482482 40.1528 + 40.1528i 1.82891 + 1.82891i
483483 0 0
484484 17.1769i 0.780769i
485485 −9.86233 14.9372i −0.447825 0.678262i
486486 0 0
487487 −26.9282 + 26.9282i −1.22023 + 1.22023i −0.252685 + 0.967549i 0.581314π0.581314\pi
−0.967549 + 0.252685i 0.918686π0.918686\pi
488488 0 0
489489 0 0
490490 10.3397 + 15.6603i 0.467102 + 0.707458i
491491 37.7033i 1.70153i 0.525550 + 0.850763i 0.323860π0.323860\pi
−0.525550 + 0.850763i 0.676140π0.676140\pi
492492 0 0
493493 −40.0526 40.0526i −1.80388 1.80388i
494494 −2.07055 −0.0931586
495495 0 0
496496 −2.14359 −0.0962502
497497 −1.79315 1.79315i −0.0804338 0.0804338i
498498 0 0
499499 41.7321i 1.86818i −0.357033 0.934092i 0.616212π-0.616212\pi
0.357033 0.934092i 0.383788π-0.383788\pi
500500 18.3848 + 12.7279i 0.822192 + 0.569210i
501501 0 0
502502 −21.2679 + 21.2679i −0.949235 + 0.949235i
503503 −2.07055 + 2.07055i −0.0923214 + 0.0923214i −0.751759 0.659438i 0.770794π-0.770794\pi
0.659438 + 0.751759i 0.270794π0.270794\pi
504504 0 0
505505 41.4904 + 8.49038i 1.84630 + 0.377817i
506506 10.7589i 0.478292i
507507 0 0
508508 −2.53590 2.53590i −0.112512 0.112512i
509509 −11.0363 −0.489176 −0.244588 0.969627i 0.578653π-0.578653\pi
−0.244588 + 0.969627i 0.578653π0.578653\pi
510510 0 0
511511 −18.4641 −0.816804
512512 22.6274 + 22.6274i 1.00000 + 1.00000i
513513 0 0
514514 52.4974i 2.31556i
515515 −4.76028 + 3.14299i −0.209763 + 0.138497i
516516 0 0
517517 4.09808 4.09808i 0.180233 0.180233i
518518 23.1822 23.1822i 1.01857 1.01857i
519519 0 0
520520 0 0
521521 5.65685i 0.247831i 0.992293 + 0.123916i 0.0395452π0.0395452\pi
−0.992293 + 0.123916i 0.960455π0.960455\pi
522522 0 0
523523 25.6603 + 25.6603i 1.12204 + 1.12204i 0.991434 + 0.130611i 0.0416938π0.0416938\pi
0.130611 + 0.991434i 0.458306π0.458306\pi
524524 25.7332 1.12416
525525 0 0
526526 −36.6410 −1.59762
527527 −2.44949 2.44949i −0.106701 0.106701i
528528 0 0
529529 11.0000i 0.478261i
530530 −5.37945 + 26.2880i −0.233668 + 1.14188i
531531 0 0
532532 −4.73205 + 4.73205i −0.205160 + 0.205160i
533533 2.07055 2.07055i 0.0896856 0.0896856i
534534 0 0
535535 1.00000 0.660254i 0.0432338 0.0285453i
536536 0 0
537537 0 0
538538 −23.3205 23.3205i −1.00542 1.00542i
539539 6.51626 0.280675
540540 0 0
541541 29.1962 1.25524 0.627620 0.778520i 0.284029π-0.284029\pi
0.627620 + 0.778520i 0.284029π0.284029\pi
542542 27.5264 + 27.5264i 1.18236 + 1.18236i
543543 0 0
544544 51.7128i 2.21717i
545545 18.3848 + 3.76217i 0.787517 + 0.161154i
546546 0 0
547547 −22.0526 + 22.0526i −0.942899 + 0.942899i −0.998456 0.0555562i 0.982307π-0.982307\pi
0.0555562 + 0.998456i 0.482307π0.482307\pi
548548 2.17209 2.17209i 0.0927870 0.0927870i
549549 0 0
550550 14.4115 5.78461i 0.614510 0.246657i
551551 8.76268i 0.373303i
552552 0 0
553553 31.8564 + 31.8564i 1.35467 + 1.35467i
554554 −25.9363 −1.10193
555555 0 0
556556 19.4641 0.825462
557557 15.0895 + 15.0895i 0.639362 + 0.639362i 0.950398 0.311036i 0.100676π-0.100676\pi
−0.311036 + 0.950398i 0.600676π0.600676\pi
558558 0 0
559559 4.53590i 0.191848i
560560 16.4901 + 24.9754i 0.696833 + 1.05540i
561561 0 0
562562 −4.39230 + 4.39230i −0.185278 + 0.185278i
563563 28.2843 28.2843i 1.19204 1.19204i 0.215546 0.976494i 0.430847π-0.430847\pi
0.976494 0.215546i 0.0691532π-0.0691532\pi
564564 0 0
565565 −19.0526 28.8564i −0.801547 1.21400i
566566 1.79315i 0.0753718i
567567 0 0
568568 0 0
569569 −17.4510 −0.731585 −0.365793 0.930696i 0.619202π-0.619202\pi
−0.365793 + 0.930696i 0.619202π0.619202\pi
570570 0 0
571571 −42.3923 −1.77406 −0.887031 0.461709i 0.847236π-0.847236\pi
−0.887031 + 0.461709i 0.847236π0.847236\pi
572572 −2.27362 2.27362i −0.0950650 0.0950650i
573573 0 0
574574 18.9282i 0.790048i
575575 16.0740 6.45189i 0.670332 0.269063i
576576 0 0
577577 14.8301 14.8301i 0.617386 0.617386i −0.327474 0.944860i 0.606197π-0.606197\pi
0.944860 + 0.327474i 0.106197π0.106197\pi
578578 −35.0507 + 35.0507i −1.45792 + 1.45792i
579579 0 0
580580 38.3923 + 7.85641i 1.59415 + 0.326220i
581581 3.58630i 0.148785i
582582 0 0
583583 6.58846 + 6.58846i 0.272866 + 0.272866i
584584 0 0
585585 0 0
586586 −29.0718 −1.20094
587587 24.6844 + 24.6844i 1.01883 + 1.01883i 0.999819 + 0.0190136i 0.00605258π0.00605258\pi
0.0190136 + 0.999819i 0.493947π0.493947\pi
588588 0 0
589589 0.535898i 0.0220813i
590590 −49.9507 + 32.9802i −2.05644 + 1.35777i
591591 0 0
592592 13.8564 13.8564i 0.569495 0.569495i
593593 −5.00052 + 5.00052i −0.205347 + 0.205347i −0.802286 0.596940i 0.796383π-0.796383\pi
0.596940 + 0.802286i 0.296383π0.296383\pi
594594 0 0
595595 −9.69615 + 47.3827i −0.397503 + 1.94250i
596596 48.7124i 1.99534i
597597 0 0
598598 −5.07180 5.07180i −0.207401 0.207401i
599599 23.3853 0.955497 0.477749 0.878497i 0.341453π-0.341453\pi
0.477749 + 0.878497i 0.341453π0.341453\pi
600600 0 0
601601 16.0000 0.652654 0.326327 0.945257i 0.394189π-0.394189\pi
0.326327 + 0.945257i 0.394189π0.394189\pi
602602 −20.7327 20.7327i −0.845003 0.845003i
603603 0 0
604604 2.14359i 0.0872216i
605605 −3.85010 + 18.8145i −0.156529 + 0.764917i
606606 0 0
607607 −11.5167 + 11.5167i −0.467447 + 0.467447i −0.901086 0.433640i 0.857229π-0.857229\pi
0.433640 + 0.901086i 0.357229π0.357229\pi
608608 −5.65685 + 5.65685i −0.229416 + 0.229416i
609609 0 0
610610 47.9808 31.6795i 1.94268 1.28267i
611611 3.86370i 0.156309i
612612 0 0
613613 13.1506 + 13.1506i 0.531149 + 0.531149i 0.920914 0.389765i 0.127444π-0.127444\pi
−0.389765 + 0.920914i 0.627444π0.627444\pi
614614 −52.0213 −2.09941
615615 0 0
616616 0 0
617617 −28.5109 28.5109i −1.14781 1.14781i −0.986983 0.160822i 0.948585π-0.948585\pi
−0.160822 0.986983i 0.551415π-0.551415\pi
618618 0 0
619619 36.2487i 1.45696i −0.685068 0.728479i 0.740227π-0.740227\pi
0.685068 0.728479i 0.259773π-0.259773\pi
620620 2.34795 + 0.480473i 0.0942961 + 0.0192963i
621621 0 0
622622 13.6603 13.6603i 0.547726 0.547726i
623623 20.7327 20.7327i 0.830639 0.830639i
624624 0 0
625625 17.2846 + 18.0622i 0.691384 + 0.722487i
626626 63.1319i 2.52326i
627627 0 0
628628 −0.143594 0.143594i −0.00573001 0.00573001i
629629 31.6675 1.26267
630630 0 0
631631 7.00000 0.278666 0.139333 0.990246i 0.455504π-0.455504\pi
0.139333 + 0.990246i 0.455504π0.455504\pi
632632 0 0
633633 0 0
634634 21.0718i 0.836868i
635635 −2.20925 3.34607i −0.0876715 0.132785i
636636 0 0
637637 3.07180 3.07180i 0.121709 0.121709i
638638 19.2442 19.2442i 0.761885 0.761885i
639639 0 0
640640 0 0
641641 12.5521i 0.495776i 0.968789 + 0.247888i 0.0797366π0.0797366\pi
−0.968789 + 0.247888i 0.920263π0.920263\pi
642642 0 0
643643 −8.24167 8.24167i −0.325020 0.325020i 0.525669 0.850689i 0.323815π-0.323815\pi
−0.850689 + 0.525669i 0.823815π0.823815\pi
644644 −23.1822 −0.913507
645645 0 0
646646 −12.9282 −0.508653
647647 −22.1977 22.1977i −0.872682 0.872682i 0.120082 0.992764i 0.461684π-0.461684\pi
−0.992764 + 0.120082i 0.961684π0.961684\pi
648648 0 0
649649 20.7846i 0.815867i
650650 4.06678 9.52056i 0.159512 0.373427i
651651 0 0
652652 18.3923 18.3923i 0.720298 0.720298i
653653 −13.7124 + 13.7124i −0.536609 + 0.536609i −0.922531 0.385922i 0.873883π-0.873883\pi
0.385922 + 0.922531i 0.373883π0.373883\pi
654654 0 0
655655 28.1865 + 5.76795i 1.10134 + 0.225372i
656656 11.3137i 0.441726i
657657 0 0
658658 −17.6603 17.6603i −0.688468 0.688468i
659659 −12.9038 −0.502660 −0.251330 0.967901i 0.580868π-0.580868\pi
−0.251330 + 0.967901i 0.580868π0.580868\pi
660660 0 0
661661 37.5692 1.46127 0.730637 0.682767i 0.239223π-0.239223\pi
0.730637 + 0.682767i 0.239223π0.239223\pi
662662 3.03150 + 3.03150i 0.117823 + 0.117823i
663663 0 0
664664 0 0
665665 −6.24384 + 4.12252i −0.242126 + 0.159865i
666666 0 0
667667 21.4641 21.4641i 0.831093 0.831093i
668668 −28.0812 + 28.0812i −1.08649 + 1.08649i
669669 0 0
670670 −12.0000 + 58.6410i −0.463600 + 2.26550i
671671 19.9649i 0.770736i
672672 0 0
673673 6.92820 + 6.92820i 0.267063 + 0.267063i 0.827915 0.560853i 0.189527π-0.189527\pi
−0.560853 + 0.827915i 0.689527π0.689527\pi
674674 10.3528 0.398773
675675 0 0
676676 23.8564 0.917554
677677 12.2474 + 12.2474i 0.470708 + 0.470708i 0.902144 0.431436i 0.141993π-0.141993\pi
−0.431436 + 0.902144i 0.641993π0.641993\pi
678678 0 0
679679 26.7846i 1.02790i
680680 0 0
681681 0 0
682682 1.17691 1.17691i 0.0450664 0.0450664i
683683 21.2132 21.2132i 0.811701 0.811701i −0.173188 0.984889i 0.555407π-0.555407\pi
0.984889 + 0.173188i 0.0554069π0.0554069\pi
684684 0 0
685685 2.86603 1.89230i 0.109505 0.0723013i
686686 18.7637i 0.716402i
687687 0 0
688688 −12.3923 12.3923i −0.472452 0.472452i
689689 6.21166 0.236645
690690 0 0
691691 30.5167 1.16091 0.580454 0.814293i 0.302875π-0.302875\pi
0.580454 + 0.814293i 0.302875π0.302875\pi
692692 −16.2127 16.2127i −0.616314 0.616314i
693693 0 0
694694 68.3538i 2.59468i
695695 21.3197 + 4.36276i 0.808703 + 0.165489i
696696 0 0
697697 12.9282 12.9282i 0.489691 0.489691i
698698 16.0368 16.0368i 0.607003 0.607003i
699699 0 0
700700 −12.4641 31.0526i −0.471099 1.17368i
701701 42.8797i 1.61954i 0.586745 + 0.809771i 0.300409π0.300409\pi
−0.586745 + 0.809771i 0.699591π0.699591\pi
702702 0 0
703703 3.46410 + 3.46410i 0.130651 + 0.130651i
704704 −12.4233 −0.468221
705705 0 0
706706 35.7128 1.34407
707707 −44.8115 44.8115i −1.68531 1.68531i
708708 0 0
709709 29.8564i 1.12128i −0.828059 0.560640i 0.810555π-0.810555\pi
0.828059 0.560640i 0.189445π-0.189445\pi
710710 1.86748 + 2.82843i 0.0700853 + 0.106149i
711711 0 0
712712 0 0
713713 1.31268 1.31268i 0.0491602 0.0491602i
714714 0 0
715715 −1.98076 3.00000i −0.0740763 0.112194i
716716 10.3528i 0.386901i
717717 0 0
718718 0.732051 + 0.732051i 0.0273199 + 0.0273199i
719719 20.4182 0.761469 0.380735 0.924684i 0.375671π-0.375671\pi
0.380735 + 0.924684i 0.375671π0.375671\pi
720720 0 0
721721 8.53590 0.317893
722722 −1.41421 1.41421i −0.0526316 0.0526316i
723723 0 0
724724 36.7846i 1.36709i
725725 40.2915 + 17.2108i 1.49639 + 0.639193i
726726 0 0
727727 8.95448 8.95448i 0.332103 0.332103i −0.521281 0.853385i 0.674546π-0.674546\pi
0.853385 + 0.521281i 0.174546π0.174546\pi
728728 0 0
729729 0 0
730730 24.1769 + 4.94744i 0.894828 + 0.183113i
731731 28.3214i 1.04751i
732732 0 0
733733 −3.00000 3.00000i −0.110808 0.110808i 0.649529 0.760337i 0.274966π-0.274966\pi
−0.760337 + 0.649529i 0.774966π0.774966\pi
734734 −38.8401 −1.43361
735735 0 0
736736 −27.7128 −1.02151
737737 14.6969 + 14.6969i 0.541369 + 0.541369i
738738 0 0
739739 3.78461i 0.139219i 0.997574 + 0.0696096i 0.0221753π0.0221753\pi
−0.997574 + 0.0696096i 0.977825π0.977825\pi
740740 −18.2832 + 12.0716i −0.672105 + 0.443760i
741741 0 0
742742 28.3923 28.3923i 1.04231 1.04231i
743743 −8.76268 + 8.76268i −0.321472 + 0.321472i −0.849331 0.527860i 0.822995π-0.822995\pi
0.527860 + 0.849331i 0.322995π0.322995\pi
744744 0 0
745745 10.9186 53.3564i 0.400026 1.95483i
746746 9.79796i 0.358729i
747747 0 0
748748 −14.1962 14.1962i −0.519063 0.519063i
749749 −1.79315 −0.0655203
750750 0 0
751751 −40.1051 −1.46346 −0.731728 0.681596i 0.761286π-0.761286\pi
−0.731728 + 0.681596i 0.761286π0.761286\pi
752752 −10.5558 10.5558i −0.384932 0.384932i
753753 0 0
754754 18.1436i 0.660751i
755755 −0.480473 + 2.34795i −0.0174862 + 0.0854508i
756756 0 0
757757 −5.43782 + 5.43782i −0.197641 + 0.197641i −0.798988 0.601347i 0.794631π-0.794631\pi
0.601347 + 0.798988i 0.294631π0.294631\pi
758758 −29.5969 + 29.5969i −1.07501 + 1.07501i
759759 0 0
760760 0 0
761761 17.7656i 0.644003i −0.946739 0.322001i 0.895644π-0.895644\pi
0.946739 0.322001i 0.104356π-0.104356\pi
762762 0 0
763763 −19.8564 19.8564i −0.718850 0.718850i
764764 −5.17638 −0.187275
765765 0 0
766766 −39.7128 −1.43488
767767 9.79796 + 9.79796i 0.353784 + 0.353784i
768768 0 0
769769 10.8038i 0.389597i −0.980843 0.194798i 0.937595π-0.937595\pi
0.980843 0.194798i 0.0624052π-0.0624052\pi
770770 −22.7661 4.65874i −0.820434 0.167889i
771771 0 0
772772 22.9282 22.9282i 0.825204 0.825204i
773773 21.6665 21.6665i 0.779289 0.779289i −0.200421 0.979710i 0.564231π-0.564231\pi
0.979710 + 0.200421i 0.0642310π0.0642310\pi
774774 0 0
775775 2.46410 + 1.05256i 0.0885131 + 0.0378090i
776776 0 0
777777 0 0
778778 −15.6603 15.6603i −0.561447 0.561447i
779779 2.82843 0.101339
780780 0 0
781781 1.17691 0.0421133
782782 −31.6675 31.6675i −1.13243 1.13243i
783783 0 0
784784 16.7846i 0.599450i
785785 −0.125097 0.189469i −0.00446492 0.00676243i
786786 0 0
787787 −9.46410 + 9.46410i −0.337359 + 0.337359i −0.855372 0.518014i 0.826672π-0.826672\pi
0.518014 + 0.855372i 0.326672π0.326672\pi
788788 19.5959 19.5959i 0.698076 0.698076i
789789 0 0
790790 −33.1769 50.2487i −1.18038 1.78777i
791791 51.7439i 1.83980i
792792 0 0
793793 −9.41154 9.41154i −0.334214 0.334214i
794794 65.6830 2.33100
795795 0 0
796796 19.4641 0.689887
797797 −15.6579 15.6579i −0.554631 0.554631i 0.373143 0.927774i 0.378280π-0.378280\pi
−0.927774 + 0.373143i 0.878280π0.878280\pi
798798 0 0
799799 24.1244i 0.853458i
800800 −14.9000 37.1213i −0.526795 1.31244i
801801 0 0
802802 −26.9282 + 26.9282i −0.950868 + 0.950868i
803803 6.05935 6.05935i 0.213830 0.213830i
804804 0 0
805805 −25.3923 5.19615i −0.894961 0.183140i
806806 1.10961i 0.0390842i
807807 0 0
808808 0 0
809809 0.314566 0.0110596 0.00552978 0.999985i 0.498240π-0.498240\pi
0.00552978 + 0.999985i 0.498240π0.498240\pi
810810 0 0
811811 39.8564 1.39955 0.699774 0.714364i 0.253284π-0.253284\pi
0.699774 + 0.714364i 0.253284π0.253284\pi
812812 −41.4655 41.4655i −1.45515 1.45515i
813813 0 0
814814 15.2154i 0.533299i
815815 24.2683 16.0232i 0.850080 0.561269i
816816 0 0
817817 3.09808 3.09808i 0.108388 0.108388i
818818 −16.7675 + 16.7675i −0.586262 + 0.586262i
819819 0 0
820820 −2.53590 + 12.3923i −0.0885574 + 0.432758i
821821 33.7752i 1.17876i −0.807855 0.589382i 0.799371π-0.799371\pi
0.807855 0.589382i 0.200629π-0.200629\pi
822822 0 0
823823 12.6340 + 12.6340i 0.440393 + 0.440393i 0.892144 0.451751i 0.149201π-0.149201\pi
−0.451751 + 0.892144i 0.649201π0.649201\pi
824824 0 0
825825 0 0
826826 89.5692 3.11651
827827 39.1918 + 39.1918i 1.36283 + 1.36283i 0.870285 + 0.492549i 0.163935π0.163935\pi
0.492549 + 0.870285i 0.336065π0.336065\pi
828828 0 0
829829 16.6795i 0.579303i 0.957132 + 0.289651i 0.0935394π0.0935394\pi
−0.957132 + 0.289651i 0.906461π0.906461\pi
830830 0.960947 4.69591i 0.0333549 0.162997i
831831 0 0
832832 −5.85641 + 5.85641i −0.203034 + 0.203034i
833833 19.1798 19.1798i 0.664541 0.664541i
834834 0 0
835835 −37.0526 + 24.4641i −1.28226 + 0.846615i
836836 3.10583i 0.107417i
837837 0 0
838838 42.3923 + 42.3923i 1.46442 + 1.46442i
839839 −21.5921 −0.745443 −0.372722 0.927943i 0.621575π-0.621575\pi
−0.372722 + 0.927943i 0.621575π0.621575\pi
840840 0 0
841841 47.7846 1.64775
842842 13.5873 + 13.5873i 0.468250 + 0.468250i
843843 0 0
844844 11.7128i 0.403172i
845845 26.1308 + 5.34727i 0.898926 + 0.183952i
846846 0 0
847847 20.3205 20.3205i 0.698221 0.698221i
848848 16.9706 16.9706i 0.582772 0.582772i
849849 0 0
850850 25.3923 59.4449i 0.870949 2.03894i
851851 16.9706i 0.581743i
852852 0 0
853853 −24.7128 24.7128i −0.846151 0.846151i 0.143500 0.989650i 0.454164π-0.454164\pi
−0.989650 + 0.143500i 0.954164π0.954164\pi
854854 −86.0367 −2.94412
855855 0 0
856856 0 0
857857 −4.62158 4.62158i −0.157870 0.157870i 0.623752 0.781622i 0.285607π-0.285607\pi
−0.781622 + 0.623752i 0.785607π0.785607\pi
858858 0 0
859859 28.5692i 0.974769i −0.873187 0.487385i 0.837951π-0.837951\pi
0.873187 0.487385i 0.162049π-0.162049\pi
860860 10.7961 + 16.3514i 0.368143 + 0.557578i
861861 0 0
862862 −12.3923 + 12.3923i −0.422084 + 0.422084i
863863 −11.5911 + 11.5911i −0.394566 + 0.394566i −0.876311 0.481745i 0.840003π-0.840003\pi
0.481745 + 0.876311i 0.340003π0.340003\pi
864864 0 0
865865 −14.1244 21.3923i −0.480242 0.727360i
866866 13.3843i 0.454816i
867867 0 0
868868 −2.53590 2.53590i −0.0860740 0.0860740i
869869 −20.9086 −0.709276
870870 0 0
871871 13.8564 0.469506
872872 0 0
873873 0 0
874874 6.92820i 0.234350i
875875 −6.69213 36.8067i −0.226235 1.24429i
876876 0 0
877877 −17.2679 + 17.2679i −0.583097 + 0.583097i −0.935753 0.352656i 0.885279π-0.885279\pi
0.352656 + 0.935753i 0.385279π0.385279\pi
878878 −45.0518 + 45.0518i −1.52042 + 1.52042i
879879 0 0
880880 −13.6077 2.78461i −0.458715 0.0938692i
881881 30.0131i 1.01117i 0.862778 + 0.505583i 0.168722π0.168722\pi
−0.862778 + 0.505583i 0.831278π0.831278\pi
882882 0 0
883883 −24.6340 24.6340i −0.828999 0.828999i 0.158379 0.987378i 0.449373π-0.449373\pi
−0.987378 + 0.158379i 0.949373π0.949373\pi
884884 −13.3843 −0.450161
885885 0 0
886886 −63.4641 −2.13212
887887 16.2127 + 16.2127i 0.544369 + 0.544369i 0.924807 0.380438i 0.124227π-0.124227\pi
−0.380438 + 0.924807i 0.624227π0.624227\pi
888888 0 0
889889 6.00000i 0.201234i
890890 −32.7028 + 21.5921i −1.09620 + 0.723770i
891891 0 0
892892 9.85641 9.85641i 0.330017 0.330017i
893893 2.63896 2.63896i 0.0883094 0.0883094i
894894 0 0
895895 2.32051 11.3397i 0.0775660 0.379046i
896896 0 0
897897 0 0
898898 −9.07180 9.07180i −0.302730 0.302730i
899899 4.69591 0.156617
900900 0 0
901901 38.7846 1.29210
902902 6.21166 + 6.21166i 0.206826 + 0.206826i
903903 0 0
904904 0 0
905905 −8.24504 + 40.2915i −0.274075 + 1.33933i
906906 0 0
907907 −6.33975 + 6.33975i −0.210508 + 0.210508i −0.804483 0.593975i 0.797558π-0.797558\pi
0.593975 + 0.804483i 0.297558π0.297558\pi
908908 34.2929 34.2929i 1.13805 1.13805i
909909 0 0
910910 −12.9282 + 8.53590i −0.428566 + 0.282962i
911911 57.4007i 1.90177i −0.309542 0.950886i 0.600176π-0.600176\pi
0.309542 0.950886i 0.399824π-0.399824\pi
912912 0 0
913913 −1.17691 1.17691i −0.0389502 0.0389502i
914914 0.0743295 0.00245860
915915 0 0
916916 25.3205 0.836613
917917 −30.4428 30.4428i −1.00531 1.00531i
918918 0 0
919919 43.7128i 1.44195i 0.692960 + 0.720976i 0.256306π0.256306\pi
−0.692960 + 0.720976i 0.743694π0.743694\pi
920920 0 0
921921 0 0
922922 24.8756 24.8756i 0.819236 0.819236i
923923 0.554803 0.554803i 0.0182616 0.0182616i
924924 0 0
925925 −22.7321 + 9.12436i −0.747425 + 0.300007i
926926 28.2099i 0.927036i
927927 0 0
928928 −49.5692 49.5692i −1.62719 1.62719i
929929 −5.00052 −0.164062 −0.0820308 0.996630i 0.526141π-0.526141\pi
−0.0820308 + 0.996630i 0.526141π0.526141\pi
930930 0 0
931931 4.19615 0.137523
932932 −10.9348 10.9348i −0.358180 0.358180i
933933 0 0
934934 22.3923i 0.732699i
935935 −12.3676 18.7315i −0.404463 0.612586i
936936 0 0
937937 −13.7583 + 13.7583i −0.449465 + 0.449465i −0.895177 0.445712i 0.852951π-0.852951\pi
0.445712 + 0.895177i 0.352951π0.352951\pi
938938 63.3350 63.3350i 2.06796 2.06796i
939939 0 0
940940 9.19615 + 13.9282i 0.299945 + 0.454288i
941941 37.6018i 1.22578i −0.790167 0.612891i 0.790006π-0.790006\pi
0.790167 0.612891i 0.209994π-0.209994\pi
942942 0 0
943943 6.92820 + 6.92820i 0.225613 + 0.225613i
944944 53.5370 1.74248
945945 0 0
946946 13.6077 0.442424
947947 −31.6675 31.6675i −1.02906 1.02906i −0.999565 0.0294905i 0.990612π-0.990612\pi
−0.0294905 0.999565i 0.509388π-0.509388\pi
948948 0 0
949949 5.71281i 0.185446i
950950 9.28032 3.72500i 0.301093 0.120855i
951951 0 0
952952 0 0
953953 34.9764 34.9764i 1.13300 1.13300i 0.143320 0.989676i 0.454222π-0.454222\pi
0.989676 0.143320i 0.0457780π-0.0457780\pi
954954 0 0
955955 −5.66987 1.16025i −0.183473 0.0375449i
956956 16.2870i 0.526760i
957957 0 0
958958 −33.6077 33.6077i −1.08582 1.08582i
959959 −5.13922 −0.165954
960960 0 0
961961 −30.7128 −0.990736
962962 7.17260 + 7.17260i 0.231254 + 0.231254i
963963 0 0
964964 56.7846i 1.82891i
965965 30.2533 19.9749i 0.973888 0.643013i
966966 0 0
967967 −25.9808 + 25.9808i −0.835485 + 0.835485i −0.988261 0.152776i 0.951179π-0.951179\pi
0.152776 + 0.988261i 0.451179π0.451179\pi
968968 0 0
969969 0 0
970970 7.17691 35.0718i 0.230437 1.12609i
971971 26.0106i 0.834721i 0.908741 + 0.417361i 0.137045π0.137045\pi
−0.908741 + 0.417361i 0.862955π0.862955\pi
972972 0 0
973973 −23.0263 23.0263i −0.738189 0.738189i
974974 −76.1645 −2.44047
975975 0 0
976976 −51.4256 −1.64609
977977 2.24642 + 2.24642i 0.0718693 + 0.0718693i 0.742128 0.670258i 0.233817π-0.233817\pi
−0.670258 + 0.742128i 0.733817π0.733817\pi
978978 0 0
979979 13.6077i 0.434904i
980980 −3.76217 + 18.3848i −0.120178 + 0.587280i
981981 0 0
982982 −53.3205 + 53.3205i −1.70153 + 1.70153i
983983 −13.9391 + 13.9391i −0.444587 + 0.444587i −0.893550 0.448963i 0.851793π-0.851793\pi
0.448963 + 0.893550i 0.351793π0.351793\pi
984984 0 0
985985 25.8564 17.0718i 0.823854 0.543953i
986986 113.286i 3.60775i
987987 0 0
988988 −1.46410 1.46410i −0.0465793 0.0465793i
989989 15.1774 0.482614
990990 0 0
991991 26.1436 0.830479 0.415239 0.909712i 0.363698π-0.363698\pi
0.415239 + 0.909712i 0.363698π0.363698\pi
992992 −3.03150 3.03150i −0.0962502 0.0962502i
993993 0 0
994994 5.07180i 0.160868i
995995 21.3197 + 4.36276i 0.675881 + 0.138309i
996996 0 0
997997 −16.3660 + 16.3660i −0.518317 + 0.518317i −0.917062 0.398745i 0.869446π-0.869446\pi
0.398745 + 0.917062i 0.369446π0.369446\pi
998998 59.0180 59.0180i 1.86818 1.86818i
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 855.2.n.c.818.4 yes 8
3.2 odd 2 inner 855.2.n.c.818.1 yes 8
5.2 odd 4 inner 855.2.n.c.647.1 8
15.2 even 4 inner 855.2.n.c.647.4 yes 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
855.2.n.c.647.1 8 5.2 odd 4 inner
855.2.n.c.647.4 yes 8 15.2 even 4 inner
855.2.n.c.818.1 yes 8 3.2 odd 2 inner
855.2.n.c.818.4 yes 8 1.1 even 1 trivial