Properties

Label 176.3.n.c.129.2
Level 176176
Weight 33
Character 176.129
Analytic conductor 4.7964.796
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] = [176,3,Mod(17,176)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(176, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 0, 9]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("176.17");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 176=2411 176 = 2^{4} \cdot 11
Weight: k k == 3 3
Character orbit: [χ][\chi] == 176.n (of order 1010, degree 44, not 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: 4.795652652744.79565265274
Analytic rank: 00
Dimension: 88
Relative dimension: 22 over Q(ζ10)\Q(\zeta_{10})
Coefficient field: Q[x]/(x8)\mathbb{Q}[x]/(x^{8} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8x7+19x637x5+229x4+196x3+1496x2+2952x+26896 x^{8} - x^{7} + 19x^{6} - 37x^{5} + 229x^{4} + 196x^{3} + 1496x^{2} + 2952x + 26896 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 44)
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 129.2
Root 3.089412.24459i3.08941 - 2.24459i of defining polynomial
Character χ\chi == 176.129
Dual form 176.3.n.c.161.2

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+(1.37103+4.21961i)q3+(5.307793.85634i)q5+(10.95323.55892i)q7+(8.64421+6.28038i)q9+(9.32350+5.83715i)q11+(2.97320+4.09226i)q13+(8.9950727.6840i)q15+(5.03681+6.93258i)q17+(10.30453.34815i)q1951.0977iq2111.7519q23+(5.57590+17.1609i)q25+(6.047534.39379i)q27+(19.2505+6.25487i)q29+(29.4488+21.3958i)q31+(37.413331.3386i)q33+(44.4130+61.1293i)q35+(11.4023+35.0927i)q37+(13.1914+18.1564i)q39+(40.3205+13.1009i)q4172.4430iq43+70.1009q45+(3.37433+10.3851i)q47+(67.6654+49.1618i)q49+(36.158411.7486i)q51+(58.4943+42.4986i)q53+(71.9972+4.97215i)q55+(28.2557+38.8907i)q57+(1.38239+4.25455i)q59+(63.860687.8965i)q61+(117.03338.0264i)q6333.1866iq65+37.6104q67+(16.112349.5886i)q69+(43.387531.5228i)q71+(23.72597.70902i)q73+(64.7673+47.0562i)q75+(122.89630.7541i)q77+(41.8941+57.6623i)q79+(19.4674+59.9146i)q81+(6.78240+9.33518i)q83+(53.468717.3730i)q85+89.8052iq8775.6980q89+(18.002155.4048i)q91+(130.65794.9280i)q93+(67.605921.9665i)q95+(2.41589+1.75525i)q97+(43.9347109.013i)q99+O(q100)q+(1.37103 + 4.21961i) q^{3} +(-5.30779 - 3.85634i) q^{5} +(-10.9532 - 3.55892i) q^{7} +(-8.64421 + 6.28038i) q^{9} +(-9.32350 + 5.83715i) q^{11} +(2.97320 + 4.09226i) q^{13} +(8.99507 - 27.6840i) q^{15} +(-5.03681 + 6.93258i) q^{17} +(10.3045 - 3.34815i) q^{19} -51.0977i q^{21} -11.7519 q^{23} +(5.57590 + 17.1609i) q^{25} +(-6.04753 - 4.39379i) q^{27} +(19.2505 + 6.25487i) q^{29} +(-29.4488 + 21.3958i) q^{31} +(-37.4133 - 31.3386i) q^{33} +(44.4130 + 61.1293i) q^{35} +(-11.4023 + 35.0927i) q^{37} +(-13.1914 + 18.1564i) q^{39} +(-40.3205 + 13.1009i) q^{41} -72.4430i q^{43} +70.1009 q^{45} +(3.37433 + 10.3851i) q^{47} +(67.6654 + 49.1618i) q^{49} +(-36.1584 - 11.7486i) q^{51} +(-58.4943 + 42.4986i) q^{53} +(71.9972 + 4.97215i) q^{55} +(28.2557 + 38.8907i) q^{57} +(-1.38239 + 4.25455i) q^{59} +(63.8606 - 87.8965i) q^{61} +(117.033 - 38.0264i) q^{63} -33.1866i q^{65} +37.6104 q^{67} +(-16.1123 - 49.5886i) q^{69} +(-43.3875 - 31.5228i) q^{71} +(-23.7259 - 7.70902i) q^{73} +(-64.7673 + 47.0562i) q^{75} +(122.896 - 30.7541i) q^{77} +(41.8941 + 57.6623i) q^{79} +(-19.4674 + 59.9146i) q^{81} +(-6.78240 + 9.33518i) q^{83} +(53.4687 - 17.3730i) q^{85} +89.8052i q^{87} -75.6980 q^{89} +(-18.0021 - 55.4048i) q^{91} +(-130.657 - 94.9280i) q^{93} +(-67.6059 - 21.9665i) q^{95} +(-2.41589 + 1.75525i) q^{97} +(43.9347 - 109.013i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+5q3q515q7q917q1115q13+63q1575q17+30q19100q23+51q25100q27+125q2973q3120q33+155q3575q37++419q99+O(q100) 8 q + 5 q^{3} - q^{5} - 15 q^{7} - q^{9} - 17 q^{11} - 15 q^{13} + 63 q^{15} - 75 q^{17} + 30 q^{19} - 100 q^{23} + 51 q^{25} - 100 q^{27} + 125 q^{29} - 73 q^{31} - 20 q^{33} + 155 q^{35} - 75 q^{37}+ \cdots + 419 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/176Z)×\left(\mathbb{Z}/176\mathbb{Z}\right)^\times.

nn 111111 133133 145145
χ(n)\chi(n) 11 11 e(310)e\left(\frac{3}{10}\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 0
33 1.37103 + 4.21961i 0.457011 + 1.40654i 0.868758 + 0.495238i 0.164919π0.164919\pi
−0.411746 + 0.911298i 0.635081π0.635081\pi
44 0 0
55 −5.30779 3.85634i −1.06156 0.771267i −0.0871824 0.996192i 0.527786π-0.527786\pi
−0.974376 + 0.224925i 0.927786π0.927786\pi
66 0 0
77 −10.9532 3.55892i −1.56475 0.508417i −0.606676 0.794950i 0.707497π-0.707497\pi
−0.958070 + 0.286533i 0.907497π0.907497\pi
88 0 0
99 −8.64421 + 6.28038i −0.960467 + 0.697820i
1010 0 0
1111 −9.32350 + 5.83715i −0.847591 + 0.530650i
1212 0 0
1313 2.97320 + 4.09226i 0.228708 + 0.314789i 0.907913 0.419159i 0.137675π-0.137675\pi
−0.679205 + 0.733949i 0.737675π0.737675\pi
1414 0 0
1515 8.99507 27.6840i 0.599671 1.84560i
1616 0 0
1717 −5.03681 + 6.93258i −0.296283 + 0.407799i −0.931042 0.364911i 0.881099π-0.881099\pi
0.634759 + 0.772710i 0.281099π0.281099\pi
1818 0 0
1919 10.3045 3.34815i 0.542344 0.176218i −0.0250177 0.999687i 0.507964π-0.507964\pi
0.567362 + 0.823469i 0.307964π0.307964\pi
2020 0 0
2121 51.0977i 2.43322i
2222 0 0
2323 −11.7519 −0.510954 −0.255477 0.966815i 0.582232π-0.582232\pi
−0.255477 + 0.966815i 0.582232π0.582232\pi
2424 0 0
2525 5.57590 + 17.1609i 0.223036 + 0.686434i
2626 0 0
2727 −6.04753 4.39379i −0.223983 0.162733i
2828 0 0
2929 19.2505 + 6.25487i 0.663810 + 0.215685i 0.621494 0.783419i 0.286526π-0.286526\pi
0.0423166 + 0.999104i 0.486526π0.486526\pi
3030 0 0
3131 −29.4488 + 21.3958i −0.949961 + 0.690187i −0.950798 0.309813i 0.899734π-0.899734\pi
0.000836644 1.00000i 0.499734π0.499734\pi
3232 0 0
3333 −37.4133 31.3386i −1.13374 0.949654i
3434 0 0
3535 44.4130 + 61.1293i 1.26894 + 1.74655i
3636 0 0
3737 −11.4023 + 35.0927i −0.308170 + 0.948450i 0.670305 + 0.742086i 0.266163π0.266163\pi
−0.978475 + 0.206365i 0.933837π0.933837\pi
3838 0 0
3939 −13.1914 + 18.1564i −0.338241 + 0.465548i
4040 0 0
4141 −40.3205 + 13.1009i −0.983426 + 0.319534i −0.756224 0.654313i 0.772958π-0.772958\pi
−0.227202 + 0.973848i 0.572958π0.572958\pi
4242 0 0
4343 72.4430i 1.68472i −0.538915 0.842360i 0.681165π-0.681165\pi
0.538915 0.842360i 0.318835π-0.318835\pi
4444 0 0
4545 70.1009 1.55780
4646 0 0
4747 3.37433 + 10.3851i 0.0717943 + 0.220960i 0.980515 0.196445i 0.0629396π-0.0629396\pi
−0.908721 + 0.417405i 0.862940π0.862940\pi
4848 0 0
4949 67.6654 + 49.1618i 1.38093 + 1.00330i
5050 0 0
5151 −36.1584 11.7486i −0.708989 0.230364i
5252 0 0
5353 −58.4943 + 42.4986i −1.10367 + 0.801860i −0.981654 0.190668i 0.938934π-0.938934\pi
−0.122011 + 0.992529i 0.538934π0.538934\pi
5454 0 0
5555 71.9972 + 4.97215i 1.30904 + 0.0904028i
5656 0 0
5757 28.2557 + 38.8907i 0.495714 + 0.682292i
5858 0 0
5959 −1.38239 + 4.25455i −0.0234303 + 0.0721110i −0.962088 0.272739i 0.912070π-0.912070\pi
0.938658 + 0.344850i 0.112070π0.112070\pi
6060 0 0
6161 63.8606 87.8965i 1.04689 1.44093i 0.155424 0.987848i 0.450326π-0.450326\pi
0.891470 0.453079i 0.149674π-0.149674\pi
6262 0 0
6363 117.033 38.0264i 1.85767 0.603594i
6464 0 0
6565 33.1866i 0.510562i
6666 0 0
6767 37.6104 0.561349 0.280674 0.959803i 0.409442π-0.409442\pi
0.280674 + 0.959803i 0.409442π0.409442\pi
6868 0 0
6969 −16.1123 49.5886i −0.233512 0.718675i
7070 0 0
7171 −43.3875 31.5228i −0.611091 0.443984i 0.238707 0.971092i 0.423276π-0.423276\pi
−0.849798 + 0.527108i 0.823276π0.823276\pi
7272 0 0
7373 −23.7259 7.70902i −0.325013 0.105603i 0.141966 0.989872i 0.454658π-0.454658\pi
−0.466979 + 0.884269i 0.654658π0.654658\pi
7474 0 0
7575 −64.7673 + 47.0562i −0.863564 + 0.627416i
7676 0 0
7777 122.896 30.7541i 1.59606 0.399404i
7878 0 0
7979 41.8941 + 57.6623i 0.530305 + 0.729903i 0.987177 0.159630i 0.0510301π-0.0510301\pi
−0.456872 + 0.889533i 0.651030π0.651030\pi
8080 0 0
8181 −19.4674 + 59.9146i −0.240339 + 0.739686i
8282 0 0
8383 −6.78240 + 9.33518i −0.0817157 + 0.112472i −0.847918 0.530127i 0.822144π-0.822144\pi
0.766202 + 0.642600i 0.222144π0.222144\pi
8484 0 0
8585 53.4687 17.3730i 0.629044 0.204389i
8686 0 0
8787 89.8052i 1.03224i
8888 0 0
8989 −75.6980 −0.850540 −0.425270 0.905067i 0.639821π-0.639821\pi
−0.425270 + 0.905067i 0.639821π0.639821\pi
9090 0 0
9191 −18.0021 55.4048i −0.197826 0.608844i
9292 0 0
9393 −130.657 94.9280i −1.40492 1.02073i
9494 0 0
9595 −67.6059 21.9665i −0.711641 0.231226i
9696 0 0
9797 −2.41589 + 1.75525i −0.0249061 + 0.0180953i −0.600169 0.799873i 0.704900π-0.704900\pi
0.575263 + 0.817969i 0.304900π0.304900\pi
9898 0 0
9999 43.9347 109.013i 0.443785 1.10114i
100100 0 0
101101 26.1228 + 35.9549i 0.258641 + 0.355989i 0.918514 0.395388i 0.129390π-0.129390\pi
−0.659873 + 0.751377i 0.729390π0.729390\pi
102102 0 0
103103 −16.6882 + 51.3610i −0.162021 + 0.498650i −0.998804 0.0488842i 0.984433π-0.984433\pi
0.836783 + 0.547534i 0.184433π0.184433\pi
104104 0 0
105105 −197.050 + 271.216i −1.87667 + 2.58301i
106106 0 0
107107 −124.961 + 40.6022i −1.16786 + 0.379460i −0.827843 0.560960i 0.810432π-0.810432\pi
−0.340015 + 0.940420i 0.610432π0.610432\pi
108108 0 0
109109 6.96523i 0.0639012i −0.999489 0.0319506i 0.989828π-0.989828\pi
0.999489 0.0319506i 0.0101719π-0.0101719\pi
110110 0 0
111111 −163.710 −1.47487
112112 0 0
113113 16.8926 + 51.9900i 0.149492 + 0.460089i 0.997561 0.0697966i 0.0222350π-0.0222350\pi
−0.848069 + 0.529885i 0.822235π0.822235\pi
114114 0 0
115115 62.3768 + 45.3194i 0.542407 + 0.394082i
116116 0 0
117117 −51.4020 16.7015i −0.439333 0.142748i
118118 0 0
119119 79.8418 58.0085i 0.670940 0.487466i
120120 0 0
121121 52.8553 108.845i 0.436820 0.899549i
122122 0 0
123123 −110.561 152.175i −0.898874 1.23719i
124124 0 0
125125 −14.1026 + 43.4033i −0.112821 + 0.347226i
126126 0 0
127127 4.79238 6.59615i 0.0377353 0.0519382i −0.789732 0.613451i 0.789781π-0.789781\pi
0.827468 + 0.561513i 0.189781π0.189781\pi
128128 0 0
129129 305.681 99.3218i 2.36962 0.769936i
130130 0 0
131131 162.483i 1.24033i −0.784473 0.620163i 0.787066π-0.787066\pi
0.784473 0.620163i 0.212934π-0.212934\pi
132132 0 0
133133 −124.784 −0.938223
134134 0 0
135135 15.1551 + 46.6427i 0.112260 + 0.345501i
136136 0 0
137137 −190.008 138.049i −1.38692 1.00766i −0.996195 0.0871507i 0.972224π-0.972224\pi
−0.390726 0.920507i 0.627776π-0.627776\pi
138138 0 0
139139 225.896 + 73.3980i 1.62515 + 0.528043i 0.973149 0.230175i 0.0739299π-0.0739299\pi
0.652001 + 0.758218i 0.273930π0.273930\pi
140140 0 0
141141 −39.1949 + 28.4767i −0.277978 + 0.201963i
142142 0 0
143143 −51.6078 20.7992i −0.360894 0.145449i
144144 0 0
145145 −78.0568 107.436i −0.538323 0.740937i
146146 0 0
147147 −114.672 + 352.924i −0.780081 + 2.40084i
148148 0 0
149149 96.3895 132.669i 0.646909 0.890394i −0.352051 0.935981i 0.614516π-0.614516\pi
0.998960 + 0.0455865i 0.0145157π0.0145157\pi
150150 0 0
151151 41.8105 13.5851i 0.276891 0.0899673i −0.167280 0.985909i 0.553498π-0.553498\pi
0.444171 + 0.895942i 0.353498π0.353498\pi
152152 0 0
153153 91.5598i 0.598430i
154154 0 0
155155 238.817 1.54076
156156 0 0
157157 2.48642 + 7.65241i 0.0158371 + 0.0487414i 0.958663 0.284545i 0.0918425π-0.0918425\pi
−0.942826 + 0.333286i 0.891842π0.891842\pi
158158 0 0
159159 −259.525 188.556i −1.63223 1.18589i
160160 0 0
161161 128.722 + 41.8242i 0.799513 + 0.259777i
162162 0 0
163163 −102.128 + 74.2001i −0.626550 + 0.455216i −0.855203 0.518292i 0.826568π-0.826568\pi
0.228653 + 0.973508i 0.426568π0.426568\pi
164164 0 0
165165 77.7301 + 310.617i 0.471091 + 1.88253i
166166 0 0
167167 −124.601 171.498i −0.746112 1.02694i −0.998244 0.0592423i 0.981132π-0.981132\pi
0.252131 0.967693i 0.418868π-0.418868\pi
168168 0 0
169169 44.3172 136.394i 0.262232 0.807067i
170170 0 0
171171 −68.0469 + 93.6585i −0.397935 + 0.547710i
172172 0 0
173173 −239.490 + 77.8150i −1.38434 + 0.449798i −0.904092 0.427338i 0.859452π-0.859452\pi
−0.480243 + 0.877136i 0.659452π0.659452\pi
174174 0 0
175175 207.811i 1.18749i
176176 0 0
177177 −19.8478 −0.112135
178178 0 0
179179 68.5335 + 210.924i 0.382869 + 1.17835i 0.938015 + 0.346596i 0.112662π0.112662\pi
−0.555146 + 0.831753i 0.687338π0.687338\pi
180180 0 0
181181 1.59618 + 1.15970i 0.00881869 + 0.00640716i 0.592186 0.805801i 0.298265π-0.298265\pi
−0.583367 + 0.812209i 0.698265π0.698265\pi
182182 0 0
183183 458.444 + 148.957i 2.50516 + 0.813975i
184184 0 0
185185 195.850 142.293i 1.05865 0.769154i
186186 0 0
187187 6.49420 94.0366i 0.0347283 0.502869i
188188 0 0
189189 50.6029 + 69.6488i 0.267740 + 0.368512i
190190 0 0
191191 6.42642 19.7785i 0.0336462 0.103552i −0.932823 0.360335i 0.882662π-0.882662\pi
0.966469 + 0.256783i 0.0826624π0.0826624\pi
192192 0 0
193193 −109.830 + 151.168i −0.569068 + 0.783255i −0.992444 0.122699i 0.960845π-0.960845\pi
0.423376 + 0.905954i 0.360845π0.360845\pi
194194 0 0
195195 140.034 45.4999i 0.718124 0.233333i
196196 0 0
197197 325.621i 1.65290i 0.563011 + 0.826449i 0.309643π0.309643\pi
−0.563011 + 0.826449i 0.690357π0.690357\pi
198198 0 0
199199 76.6068 0.384959 0.192479 0.981301i 0.438347π-0.438347\pi
0.192479 + 0.981301i 0.438347π0.438347\pi
200200 0 0
201201 51.5651 + 158.701i 0.256543 + 0.789557i
202202 0 0
203203 −188.594 137.022i −0.929037 0.674985i
204204 0 0
205205 264.534 + 85.9524i 1.29041 + 0.419280i
206206 0 0
207207 101.586 73.8066i 0.490754 0.356554i
208208 0 0
209209 −76.5307 + 91.3656i −0.366175 + 0.437156i
210210 0 0
211211 134.868 + 185.630i 0.639186 + 0.879764i 0.998572 0.0534249i 0.0170138π-0.0170138\pi
−0.359386 + 0.933189i 0.617014π0.617014\pi
212212 0 0
213213 73.5284 226.297i 0.345204 1.06243i
214214 0 0
215215 −279.365 + 384.512i −1.29937 + 1.78843i
216216 0 0
217217 398.705 129.547i 1.83735 0.596991i
218218 0 0
219219 110.683i 0.505404i
220220 0 0
221221 −43.3454 −0.196133
222222 0 0
223223 −105.098 323.459i −0.471293 1.45049i −0.850893 0.525339i 0.823938π-0.823938\pi
0.379600 0.925151i 0.376062π-0.376062\pi
224224 0 0
225225 −155.976 113.323i −0.693227 0.503659i
226226 0 0
227227 176.746 + 57.4282i 0.778616 + 0.252988i 0.671249 0.741232i 0.265758π-0.265758\pi
0.107367 + 0.994219i 0.465758π0.465758\pi
228228 0 0
229229 −120.106 + 87.2618i −0.524479 + 0.381056i −0.818288 0.574808i 0.805077π-0.805077\pi
0.293810 + 0.955864i 0.405077π0.405077\pi
230230 0 0
231231 298.265 + 476.409i 1.29119 + 2.06238i
232232 0 0
233233 47.8872 + 65.9111i 0.205525 + 0.282880i 0.899319 0.437292i 0.144063π-0.144063\pi
−0.693795 + 0.720173i 0.744063π0.744063\pi
234234 0 0
235235 22.1383 68.1347i 0.0942056 0.289935i
236236 0 0
237237 −185.874 + 255.834i −0.784279 + 1.07947i
238238 0 0
239239 −191.525 + 62.2303i −0.801360 + 0.260378i −0.680934 0.732345i 0.738426π-0.738426\pi
−0.120426 + 0.992722i 0.538426π0.538426\pi
240240 0 0
241241 381.337i 1.58231i −0.611616 0.791155i 0.709480π-0.709480\pi
0.611616 0.791155i 0.290520π-0.290520\pi
242242 0 0
243243 −346.783 −1.42709
244244 0 0
245245 −169.569 521.881i −0.692120 2.13013i
246246 0 0
247247 44.3390 + 32.2141i 0.179510 + 0.130422i
248248 0 0
249249 −48.6897 15.8202i −0.195541 0.0635351i
250250 0 0
251251 84.0788 61.0868i 0.334975 0.243374i −0.407563 0.913177i 0.633621π-0.633621\pi
0.742539 + 0.669803i 0.233621π0.233621\pi
252252 0 0
253253 109.569 68.5978i 0.433080 0.271138i
254254 0 0
255255 146.615 + 201.798i 0.574960 + 0.791365i
256256 0 0
257257 −49.5999 + 152.653i −0.192996 + 0.593980i 0.806998 + 0.590554i 0.201091π0.201091\pi
−0.999994 + 0.00342612i 0.998909π0.998909\pi
258258 0 0
259259 249.784 343.798i 0.964416 1.32740i
260260 0 0
261261 −205.688 + 66.8321i −0.788077 + 0.256062i
262262 0 0
263263 203.520i 0.773840i 0.922113 + 0.386920i 0.126461π0.126461\pi
−0.922113 + 0.386920i 0.873539π0.873539\pi
264264 0 0
265265 474.364 1.79005
266266 0 0
267267 −103.785 319.416i −0.388706 1.19631i
268268 0 0
269269 −182.799 132.812i −0.679552 0.493723i 0.193657 0.981069i 0.437965π-0.437965\pi
−0.873209 + 0.487346i 0.837965π0.837965\pi
270270 0 0
271271 −276.556 89.8585i −1.02050 0.331581i −0.249474 0.968382i 0.580258π-0.580258\pi
−0.771029 + 0.636800i 0.780258π0.780258\pi
272272 0 0
273273 209.105 151.924i 0.765953 0.556498i
274274 0 0
275275 −152.157 127.452i −0.553300 0.463461i
276276 0 0
277277 112.068 + 154.248i 0.404577 + 0.556853i 0.961885 0.273453i 0.0881658π-0.0881658\pi
−0.557308 + 0.830306i 0.688166π0.688166\pi
278278 0 0
279279 120.188 369.899i 0.430780 1.32580i
280280 0 0
281281 12.7725 17.5799i 0.0454538 0.0625618i −0.785685 0.618627i 0.787689π-0.787689\pi
0.831139 + 0.556065i 0.187689π0.187689\pi
282282 0 0
283283 −52.2884 + 16.9895i −0.184765 + 0.0600337i −0.399938 0.916542i 0.630968π-0.630968\pi
0.215173 + 0.976576i 0.430968π0.430968\pi
284284 0 0
285285 315.387i 1.10662i
286286 0 0
287287 488.264 1.70127
288288 0 0
289289 66.6147 + 205.019i 0.230501 + 0.709409i
290290 0 0
291291 −10.7187 7.78761i −0.0368341 0.0267615i
292292 0 0
293293 417.197 + 135.556i 1.42388 + 0.462647i 0.916833 0.399271i 0.130737π-0.130737\pi
0.507048 + 0.861918i 0.330737π0.330737\pi
294294 0 0
295295 23.7444 17.2513i 0.0804895 0.0584790i
296296 0 0
297297 82.0314 + 5.66512i 0.276200 + 0.0190745i
298298 0 0
299299 −34.9409 48.0920i −0.116859 0.160843i
300300 0 0
301301 −257.819 + 793.484i −0.856540 + 2.63616i
302302 0 0
303303 −115.900 + 159.523i −0.382510 + 0.526480i
304304 0 0
305305 −677.917 + 220.269i −2.22268 + 0.722192i
306306 0 0
307307 232.888i 0.758594i 0.925275 + 0.379297i 0.123834π0.123834\pi
−0.925275 + 0.379297i 0.876166π0.876166\pi
308308 0 0
309309 −239.603 −0.775415
310310 0 0
311311 47.0093 + 144.680i 0.151155 + 0.465208i 0.997751 0.0670284i 0.0213518π-0.0213518\pi
−0.846596 + 0.532236i 0.821352π0.821352\pi
312312 0 0
313313 −81.4642 59.1872i −0.260269 0.189097i 0.449997 0.893030i 0.351425π-0.351425\pi
−0.710266 + 0.703934i 0.751425π0.751425\pi
314314 0 0
315315 −767.831 249.483i −2.43756 0.792011i
316316 0 0
317317 −270.287 + 196.375i −0.852639 + 0.619478i −0.925872 0.377836i 0.876668π-0.876668\pi
0.0732335 + 0.997315i 0.476668π0.476668\pi
318318 0 0
319319 −215.993 + 54.0509i −0.677093 + 0.169438i
320320 0 0
321321 −342.651 471.619i −1.06745 1.46922i
322322 0 0
323323 −28.6907 + 88.3010i −0.0888258 + 0.273378i
324324 0 0
325325 −53.6484 + 73.8408i −0.165072 + 0.227202i
326326 0 0
327327 29.3905 9.54956i 0.0898793 0.0292036i
328328 0 0
329329 125.760i 0.382248i
330330 0 0
331331 −168.614 −0.509409 −0.254705 0.967019i 0.581978π-0.581978\pi
−0.254705 + 0.967019i 0.581978π0.581978\pi
332332 0 0
333333 −121.832 374.959i −0.365860 1.12600i
334334 0 0
335335 −199.628 145.038i −0.595905 0.432950i
336336 0 0
337337 −497.959 161.797i −1.47762 0.480108i −0.544220 0.838942i 0.683174π-0.683174\pi
−0.933401 + 0.358834i 0.883174π0.883174\pi
338338 0 0
339339 −196.217 + 142.560i −0.578812 + 0.420531i
340340 0 0
341341 149.675 371.381i 0.438930 1.08909i
342342 0 0
343343 −234.487 322.744i −0.683636 0.940945i
344344 0 0
345345 −105.709 + 325.340i −0.306404 + 0.943015i
346346 0 0
347347 −281.084 + 386.879i −0.810040 + 1.11493i 0.181277 + 0.983432i 0.441977π0.441977\pi
−0.991317 + 0.131493i 0.958023π0.958023\pi
348348 0 0
349349 −9.13440 + 2.96795i −0.0261731 + 0.00850415i −0.322074 0.946714i 0.604380π-0.604380\pi
0.295901 + 0.955219i 0.404380π0.404380\pi
350350 0 0
351351 37.8117i 0.107726i
352352 0 0
353353 691.089 1.95776 0.978880 0.204436i 0.0655361π-0.0655361\pi
0.978880 + 0.204436i 0.0655361π0.0655361\pi
354354 0 0
355355 108.729 + 334.633i 0.306279 + 0.942629i
356356 0 0
357357 354.239 + 257.370i 0.992266 + 0.720923i
358358 0 0
359359 −43.9277 14.2730i −0.122361 0.0397576i 0.247196 0.968965i 0.420491π-0.420491\pi
−0.369558 + 0.929208i 0.620491π0.620491\pi
360360 0 0
361361 −197.082 + 143.188i −0.545933 + 0.396644i
362362 0 0
363363 531.751 + 73.7978i 1.46488 + 0.203300i
364364 0 0
365365 96.2037 + 132.413i 0.263572 + 0.362775i
366366 0 0
367367 −140.965 + 433.846i −0.384101 + 1.18214i 0.553030 + 0.833162i 0.313472π0.313472\pi
−0.937131 + 0.348979i 0.886528π0.886528\pi
368368 0 0
369369 266.260 366.475i 0.721571 0.993157i
370370 0 0
371371 791.950 257.320i 2.13464 0.693585i
372372 0 0
373373 99.8021i 0.267566i −0.991011 0.133783i 0.957288π-0.957288\pi
0.991011 0.133783i 0.0427125π-0.0427125\pi
374374 0 0
375375 −202.480 −0.539947
376376 0 0
377377 31.6391 + 97.3751i 0.0839233 + 0.258289i
378378 0 0
379379 313.281 + 227.612i 0.826600 + 0.600560i 0.918595 0.395199i 0.129324π-0.129324\pi
−0.0919953 + 0.995759i 0.529324π0.529324\pi
380380 0 0
381381 34.4037 + 11.1784i 0.0902984 + 0.0293397i
382382 0 0
383383 490.495 356.366i 1.28067 0.930458i 0.281093 0.959681i 0.409303π-0.409303\pi
0.999573 + 0.0292222i 0.00930304π0.00930304\pi
384384 0 0
385385 −770.906 310.693i −2.00235 0.806996i
386386 0 0
387387 454.970 + 626.212i 1.17563 + 1.61812i
388388 0 0
389389 179.028 550.992i 0.460226 1.41643i −0.404662 0.914466i 0.632611π-0.632611\pi
0.864888 0.501964i 0.167389π-0.167389\pi
390390 0 0
391391 59.1923 81.4712i 0.151387 0.208366i
392392 0 0
393393 685.614 222.769i 1.74456 0.566843i
394394 0 0
395395 467.617i 1.18384i
396396 0 0
397397 −163.072 −0.410761 −0.205381 0.978682i 0.565843π-0.565843\pi
−0.205381 + 0.978682i 0.565843π0.565843\pi
398398 0 0
399399 −171.083 526.538i −0.428778 1.31964i
400400 0 0
401401 604.368 + 439.099i 1.50715 + 1.09501i 0.967422 + 0.253171i 0.0814736π0.0814736\pi
0.539730 + 0.841838i 0.318526π0.318526\pi
402402 0 0
403403 −175.114 56.8981i −0.434527 0.141186i
404404 0 0
405405 334.380 242.941i 0.825629 0.599855i
406406 0 0
407407 −98.5319 393.743i −0.242093 0.967428i
408408 0 0
409409 −71.6699 98.6451i −0.175232 0.241186i 0.712363 0.701812i 0.247625π-0.247625\pi
−0.887595 + 0.460625i 0.847625π0.847625\pi
410410 0 0
411411 322.005 991.030i 0.783468 2.41127i
412412 0 0
413413 30.2832 41.6812i 0.0733249 0.100923i
414414 0 0
415415 71.9992 23.3940i 0.173492 0.0563710i
416416 0 0
417417 1053.82i 2.52715i
418418 0 0
419419 −330.708 −0.789279 −0.394640 0.918836i 0.629131π-0.629131\pi
−0.394640 + 0.918836i 0.629131π0.629131\pi
420420 0 0
421421 197.794 + 608.747i 0.469819 + 1.44595i 0.852819 + 0.522206i 0.174891π0.174891\pi
−0.383000 + 0.923748i 0.625109π0.625109\pi
422422 0 0
423423 −94.3910 68.5791i −0.223147 0.162126i
424424 0 0
425425 −147.054 47.7807i −0.346009 0.112425i
426426 0 0
427427 −1012.30 + 735.476i −2.37072 + 1.72243i
428428 0 0
429429 17.0083 246.281i 0.0396463 0.574082i
430430 0 0
431431 85.8703 + 118.190i 0.199235 + 0.274223i 0.896931 0.442170i 0.145791π-0.145791\pi
−0.697696 + 0.716394i 0.745791π0.745791\pi
432432 0 0
433433 28.3924 87.3827i 0.0655713 0.201808i −0.912903 0.408177i 0.866165π-0.866165\pi
0.978474 + 0.206369i 0.0661647π0.0661647\pi
434434 0 0
435435 346.319 476.667i 0.796136 1.09579i
436436 0 0
437437 −121.098 + 39.3472i −0.277112 + 0.0900393i
438438 0 0
439439 358.371i 0.816335i 0.912907 + 0.408168i 0.133832π0.133832\pi
−0.912907 + 0.408168i 0.866168π0.866168\pi
440440 0 0
441441 −893.668 −2.02646
442442 0 0
443443 253.799 + 781.114i 0.572910 + 1.76324i 0.643186 + 0.765710i 0.277612π0.277612\pi
−0.0702760 + 0.997528i 0.522388π0.522388\pi
444444 0 0
445445 401.790 + 291.917i 0.902898 + 0.655994i
446446 0 0
447447 691.963 + 224.833i 1.54802 + 0.502981i
448448 0 0
449449 −131.173 + 95.3029i −0.292145 + 0.212256i −0.724197 0.689593i 0.757790π-0.757790\pi
0.432052 + 0.901849i 0.357790π0.357790\pi
450450 0 0
451451 299.456 357.503i 0.663982 0.792690i
452452 0 0
453453 114.647 + 157.798i 0.253084 + 0.348341i
454454 0 0
455455 −118.108 + 363.500i −0.259578 + 0.798900i
456456 0 0
457457 213.638 294.048i 0.467479 0.643430i −0.508559 0.861027i 0.669822π-0.669822\pi
0.976039 + 0.217597i 0.0698217π0.0698217\pi
458458 0 0
459459 60.9206 19.7943i 0.132725 0.0431249i
460460 0 0
461461 487.885i 1.05832i −0.848523 0.529159i 0.822507π-0.822507\pi
0.848523 0.529159i 0.177493π-0.177493\pi
462462 0 0
463463 −367.635 −0.794028 −0.397014 0.917812i 0.629954π-0.629954\pi
−0.397014 + 0.917812i 0.629954π0.629954\pi
464464 0 0
465465 327.427 + 1007.72i 0.704144 + 2.16713i
466466 0 0
467467 333.686 + 242.437i 0.714531 + 0.519137i 0.884632 0.466289i 0.154409π-0.154409\pi
−0.170101 + 0.985427i 0.554409π0.554409\pi
468468 0 0
469469 −411.955 133.852i −0.878368 0.285399i
470470 0 0
471471 −28.8812 + 20.9834i −0.0613189 + 0.0445508i
472472 0 0
473473 422.861 + 675.422i 0.893998 + 1.42795i
474474 0 0
475475 114.914 + 158.166i 0.241924 + 0.332980i
476476 0 0
477477 238.729 734.733i 0.500481 1.54032i
478478 0 0
479479 312.503 430.123i 0.652407 0.897961i −0.346794 0.937941i 0.612730π-0.612730\pi
0.999200 + 0.0399806i 0.0127296π0.0127296\pi
480480 0 0
481481 −177.510 + 57.6764i −0.369043 + 0.119909i
482482 0 0
483483 600.497i 1.24326i
484484 0 0
485485 19.5919 0.0403956
486486 0 0
487487 198.833 + 611.946i 0.408282 + 1.25656i 0.918124 + 0.396294i 0.129704π0.129704\pi
−0.509842 + 0.860268i 0.670296π0.670296\pi
488488 0 0
489489 −453.116 329.208i −0.926618 0.673227i
490490 0 0
491491 −713.624 231.871i −1.45341 0.472241i −0.527360 0.849642i 0.676818π-0.676818\pi
−0.926050 + 0.377401i 0.876818π0.876818\pi
492492 0 0
493493 −140.324 + 101.951i −0.284632 + 0.206797i
494494 0 0
495495 −653.586 + 409.190i −1.32038 + 0.826646i
496496 0 0
497497 363.045 + 499.689i 0.730474 + 1.00541i
498498 0 0
499499 −56.8823 + 175.066i −0.113993 + 0.350833i −0.991736 0.128298i 0.959048π-0.959048\pi
0.877743 + 0.479132i 0.159048π0.159048\pi
500500 0 0
501501 552.823 760.896i 1.10344 1.51875i
502502 0 0
503503 −422.195 + 137.180i −0.839355 + 0.272723i −0.696981 0.717090i 0.745474π-0.745474\pi
−0.142374 + 0.989813i 0.545474π0.545474\pi
504504 0 0
505505 291.580i 0.577385i
506506 0 0
507507 636.291 1.25501
508508 0 0
509509 −154.181 474.520i −0.302909 0.932259i −0.980449 0.196773i 0.936954π-0.936954\pi
0.677540 0.735486i 0.263046π-0.263046\pi
510510 0 0
511511 232.440 + 168.877i 0.454872 + 0.330484i
512512 0 0
513513 −77.0281 25.0279i −0.150152 0.0487874i
514514 0 0
515515 286.643 208.258i 0.556588 0.404385i
516516 0 0
517517 −92.0802 77.1293i −0.178105 0.149186i
518518 0 0
519519 −656.698 903.867i −1.26531 1.74155i
520520 0 0
521521 −79.1535 + 243.610i −0.151926 + 0.467581i −0.997836 0.0657445i 0.979058π-0.979058\pi
0.845910 + 0.533325i 0.179058π0.179058\pi
522522 0 0
523523 429.405 591.025i 0.821041 1.13007i −0.168484 0.985704i 0.553887π-0.553887\pi
0.989525 0.144362i 0.0461129π-0.0461129\pi
524524 0 0
525525 876.880 284.916i 1.67025 0.542697i
526526 0 0
527527 311.923i 0.591884i
528528 0 0
529529 −390.892 −0.738926
530530 0 0
531531 −14.7706 45.4591i −0.0278165 0.0856104i
532532 0 0
533533 −173.493 126.050i −0.325503 0.236492i
534534 0 0
535535 819.842 + 266.383i 1.53242 + 0.497912i
536536 0 0
537537 −796.057 + 578.369i −1.48241 + 1.07704i
538538 0 0
539539 −917.843 63.3865i −1.70286 0.117600i
540540 0 0
541541 −207.051 284.981i −0.382718 0.526766i 0.573584 0.819147i 0.305553π-0.305553\pi
−0.956302 + 0.292380i 0.905553π0.905553\pi
542542 0 0
543543 −2.70504 + 8.32525i −0.00498165 + 0.0153320i
544544 0 0
545545 −26.8603 + 36.9700i −0.0492849 + 0.0678348i
546546 0 0
547547 −794.486 + 258.144i −1.45244 + 0.471927i −0.925752 0.378131i 0.876567π-0.876567\pi
−0.526690 + 0.850058i 0.676567π0.676567\pi
548548 0 0
549549 1160.86i 2.11451i
550550 0 0
551551 219.310 0.398021
552552 0 0
553553 −253.660 780.686i −0.458698 1.41173i
554554 0 0
555555 868.940 + 631.322i 1.56566 + 1.13752i
556556 0 0
557557 373.525 + 121.366i 0.670601 + 0.217891i 0.624476 0.781044i 0.285313π-0.285313\pi
0.0461252 + 0.998936i 0.485313π0.485313\pi
558558 0 0
559559 296.456 215.388i 0.530332 0.385309i
560560 0 0
561561 405.701 101.524i 0.723175 0.180970i
562562 0 0
563563 −228.481 314.478i −0.405828 0.558575i 0.556366 0.830937i 0.312195π-0.312195\pi
−0.962195 + 0.272362i 0.912195π0.912195\pi
564564 0 0
565565 110.829 341.096i 0.196157 0.603709i
566566 0 0
567567 426.462 586.975i 0.752138 1.03523i
568568 0 0
569569 −626.840 + 203.673i −1.10165 + 0.357948i −0.802738 0.596332i 0.796624π-0.796624\pi
−0.298914 + 0.954280i 0.596624π0.596624\pi
570570 0 0
571571 893.667i 1.56509i −0.622593 0.782546i 0.713921π-0.713921\pi
0.622593 0.782546i 0.286079π-0.286079\pi
572572 0 0
573573 92.2683 0.161027
574574 0 0
575575 −65.5276 201.673i −0.113961 0.350736i
576576 0 0
577577 14.3594 + 10.4327i 0.0248864 + 0.0180810i 0.600159 0.799881i 0.295104π-0.295104\pi
−0.575273 + 0.817962i 0.695104π0.695104\pi
578578 0 0
579579 −788.452 256.183i −1.36175 0.442459i
580580 0 0
581581 107.512 78.1123i 0.185047 0.134445i
582582 0 0
583583 297.301 737.676i 0.509950 1.26531i
584584 0 0
585585 208.424 + 286.871i 0.356281 + 0.490378i
586586 0 0
587587 50.3870 155.075i 0.0858382 0.264183i −0.898920 0.438113i 0.855647π-0.855647\pi
0.984758 + 0.173931i 0.0556468π0.0556468\pi
588588 0 0
589589 −231.820 + 319.073i −0.393582 + 0.541719i
590590 0 0
591591 −1373.99 + 446.438i −2.32486 + 0.755393i
592592 0 0
593593 513.367i 0.865711i −0.901463 0.432855i 0.857506π-0.857506\pi
0.901463 0.432855i 0.142494π-0.142494\pi
594594 0 0
595595 −647.484 −1.08821
596596 0 0
597597 105.031 + 323.251i 0.175931 + 0.541458i
598598 0 0
599599 749.454 + 544.510i 1.25118 + 0.909032i 0.998290 0.0584638i 0.0186202π-0.0186202\pi
0.252886 + 0.967496i 0.418620π0.418620\pi
600600 0 0
601601 152.709 + 49.6182i 0.254092 + 0.0825594i 0.433293 0.901253i 0.357351π-0.357351\pi
−0.179202 + 0.983812i 0.557351π0.557351\pi
602602 0 0
603603 −325.112 + 236.208i −0.539157 + 0.391721i
604604 0 0
605605 −700.289 + 373.901i −1.15750 + 0.618018i
606606 0 0
607607 −309.898 426.539i −0.510541 0.702700i 0.473469 0.880810i 0.343001π-0.343001\pi
−0.984010 + 0.178111i 0.943001π0.943001\pi
608608 0 0
609609 319.609 983.656i 0.524810 1.61520i
610610 0 0
611611 −32.4661 + 44.6858i −0.0531360 + 0.0731355i
612612 0 0
613613 −630.712 + 204.931i −1.02889 + 0.334308i −0.774353 0.632754i 0.781924π-0.781924\pi
−0.254541 + 0.967062i 0.581924π0.581924\pi
614614 0 0
615615 1234.07i 2.00662i
616616 0 0
617617 −260.782 −0.422661 −0.211331 0.977415i 0.567780π-0.567780\pi
−0.211331 + 0.977415i 0.567780π0.567780\pi
618618 0 0
619619 −328.398 1010.70i −0.530529 1.63280i −0.753115 0.657889i 0.771450π-0.771450\pi
0.222586 0.974913i 0.428550π-0.428550\pi
620620 0 0
621621 71.0702 + 51.6355i 0.114445 + 0.0831490i
622622 0 0
623623 829.138 + 269.403i 1.33088 + 0.432429i
624624 0 0
625625 607.179 441.141i 0.971486 0.705826i
626626 0 0
627627 −490.453 197.664i −0.782222 0.315254i
628628 0 0
629629 −185.851 255.803i −0.295471 0.406681i
630630 0 0
631631 −161.533 + 497.148i −0.255996 + 0.787874i 0.737636 + 0.675199i 0.235942π0.235942\pi
−0.993632 + 0.112675i 0.964058π0.964058\pi
632632 0 0
633633 −598.378 + 823.597i −0.945305 + 1.30110i
634634 0 0
635635 −50.8740 + 16.5300i −0.0801165 + 0.0260314i
636636 0 0
637637 423.072i 0.664164i
638638 0 0
639639 573.026 0.896754
640640 0 0
641641 −343.291 1056.54i −0.535556 1.64827i −0.742445 0.669907i 0.766334π-0.766334\pi
0.206889 0.978364i 0.433666π-0.433666\pi
642642 0 0
643643 −716.585 520.630i −1.11444 0.809689i −0.131084 0.991371i 0.541846π-0.541846\pi
−0.983357 + 0.181683i 0.941846π0.941846\pi
644644 0 0
645645 −2005.51 651.630i −3.10932 1.01028i
646646 0 0
647647 −92.5424 + 67.2360i −0.143033 + 0.103920i −0.657001 0.753890i 0.728175π-0.728175\pi
0.513968 + 0.857810i 0.328175π0.328175\pi
648648 0 0
649649 −11.9458 47.7365i −0.0184064 0.0735539i
650650 0 0
651651 1093.28 + 1504.77i 1.67938 + 2.31147i
652652 0 0
653653 −50.6565 + 155.905i −0.0775750 + 0.238751i −0.982322 0.187197i 0.940060π-0.940060\pi
0.904747 + 0.425949i 0.140060π0.140060\pi
654654 0 0
655655 −626.588 + 862.425i −0.956623 + 1.31668i
656656 0 0
657657 253.507 82.3695i 0.385856 0.125372i
658658 0 0
659659 116.651i 0.177012i 0.996076 + 0.0885062i 0.0282093π0.0282093\pi
−0.996076 + 0.0885062i 0.971791π0.971791\pi
660660 0 0
661661 205.962 0.311591 0.155796 0.987789i 0.450206π-0.450206\pi
0.155796 + 0.987789i 0.450206π0.450206\pi
662662 0 0
663663 −59.4280 182.901i −0.0896350 0.275868i
664664 0 0
665665 662.325 + 481.208i 0.995978 + 0.723620i
666666 0 0
667667 −226.231 73.5068i −0.339176 0.110205i
668668 0 0
669669 1220.78 886.947i 1.82478 1.32578i
670670 0 0
671671 −82.3384 + 1192.27i −0.122710 + 1.77685i
672672 0 0
673673 16.4238 + 22.6055i 0.0244039 + 0.0335891i 0.821045 0.570864i 0.193392π-0.193392\pi
−0.796641 + 0.604453i 0.793392π0.793392\pi
674674 0 0
675675 41.6808 128.280i 0.0617493 0.190045i
676676 0 0
677677 317.546 437.064i 0.469049 0.645590i −0.507306 0.861766i 0.669359π-0.669359\pi
0.976354 + 0.216176i 0.0693585π0.0693585\pi
678678 0 0
679679 32.7086 10.6277i 0.0481717 0.0156519i
680680 0 0
681681 824.534i 1.21077i
682682 0 0
683683 1117.89 1.63674 0.818369 0.574694i 0.194879π-0.194879\pi
0.818369 + 0.574694i 0.194879π0.194879\pi
684684 0 0
685685 476.161 + 1465.47i 0.695125 + 2.13937i
686686 0 0
687687 −532.880 387.160i −0.775662 0.563551i
688688 0 0
689689 −347.831 113.017i −0.504834 0.164031i
690690 0 0
691691 404.704 294.035i 0.585679 0.425521i −0.255088 0.966918i 0.582104π-0.582104\pi
0.840767 + 0.541397i 0.182104π0.182104\pi
692692 0 0
693693 −869.194 + 1037.68i −1.25425 + 1.49737i
694694 0 0
695695 −915.961 1260.71i −1.31793 1.81397i
696696 0 0
697697 112.264 345.512i 0.161067 0.495713i
698698 0 0
699699 −212.464 + 292.432i −0.303954 + 0.418357i
700700 0 0
701701 615.162 199.878i 0.877549 0.285133i 0.164610 0.986359i 0.447364π-0.447364\pi
0.712939 + 0.701226i 0.247364π0.247364\pi
702702 0 0
703703 399.790i 0.568691i
704704 0 0
705705 317.854 0.450857
706706 0 0
707707 −158.168 486.791i −0.223717 0.688531i
708708 0 0
709709 638.569 + 463.948i 0.900662 + 0.654369i 0.938636 0.344910i 0.112090π-0.112090\pi
−0.0379740 + 0.999279i 0.512090π0.512090\pi
710710 0 0
711711 −724.283 235.334i −1.01868 0.330990i
712712 0 0
713713 346.080 251.442i 0.485386 0.352654i
714714 0 0
715715 193.715 + 309.415i 0.270930 + 0.432748i
716716 0 0
717717 −525.175 722.841i −0.732461 1.00815i
718718 0 0
719719 76.5507 235.599i 0.106468 0.327676i −0.883604 0.468235i 0.844890π-0.844890\pi
0.990072 + 0.140559i 0.0448900π0.0448900\pi
720720 0 0
721721 365.579 503.176i 0.507044 0.697887i
722722 0 0
723723 1609.09 522.825i 2.22558 0.723133i
724724 0 0
725725 365.231i 0.503768i
726726 0 0
727727 133.030 0.182986 0.0914928 0.995806i 0.470836π-0.470836\pi
0.0914928 + 0.995806i 0.470836π0.470836\pi
728728 0 0
729729 −300.244 924.057i −0.411858 1.26757i
730730 0 0
731731 502.217 + 364.882i 0.687027 + 0.499154i
732732 0 0
733733 −392.639 127.576i −0.535661 0.174047i 0.0286800 0.999589i 0.490870π-0.490870\pi
−0.564341 + 0.825542i 0.690870π0.690870\pi
734734 0 0
735735 1969.65 1431.03i 2.67979 1.94698i
736736 0 0
737737 −350.660 + 219.538i −0.475794 + 0.297880i
738738 0 0
739739 −46.5395 64.0561i −0.0629763 0.0866794i 0.776367 0.630281i 0.217060π-0.217060\pi
−0.839343 + 0.543602i 0.817060π0.817060\pi
740740 0 0
741741 −75.1408 + 231.260i −0.101405 + 0.312091i
742742 0 0
743743 −302.034 + 415.714i −0.406506 + 0.559507i −0.962362 0.271771i 0.912391π-0.912391\pi
0.555856 + 0.831279i 0.312391π0.312391\pi
744744 0 0
745745 −1023.23 + 332.468i −1.37346 + 0.446266i
746746 0 0
747747 123.291i 0.165049i
748748 0 0
749749 1513.22 2.02033
750750 0 0
751751 15.0351 + 46.2733i 0.0200201 + 0.0616156i 0.960567 0.278047i 0.0896871π-0.0896871\pi
−0.940547 + 0.339663i 0.889687π0.889687\pi
752752 0 0
753753 373.037 + 271.027i 0.495401 + 0.359930i
754754 0 0
755755 −274.310 89.1288i −0.363325 0.118051i
756756 0 0
757757 165.372 120.149i 0.218456 0.158718i −0.473175 0.880968i 0.656892π-0.656892\pi
0.691632 + 0.722250i 0.256892π0.256892\pi
758758 0 0
759759 439.679 + 368.289i 0.579287 + 0.485229i
760760 0 0
761761 218.796 + 301.147i 0.287512 + 0.395726i 0.928204 0.372072i 0.121353π-0.121353\pi
−0.640692 + 0.767798i 0.721353π0.721353\pi
762762 0 0
763763 −24.7887 + 76.2917i −0.0324884 + 0.0999891i
764764 0 0
765765 −353.085 + 485.980i −0.461549 + 0.635268i
766766 0 0
767767 −21.5208 + 6.99255i −0.0280585 + 0.00911675i
768768 0 0
769769 1491.70i 1.93979i 0.243531 + 0.969893i 0.421694π0.421694\pi
−0.243531 + 0.969893i 0.578306π0.578306\pi
770770 0 0
771771 −712.138 −0.923655
772772 0 0
773773 −209.903 646.014i −0.271543 0.835723i −0.990113 0.140269i 0.955203π-0.955203\pi
0.718570 0.695454i 0.244797π-0.244797\pi
774774 0 0
775775 −531.374 386.066i −0.685644 0.498149i
776776 0 0
777777 1793.15 + 582.631i 2.30779 + 0.749847i
778778 0 0
779779 −371.620 + 269.998i −0.477047 + 0.346595i
780780 0 0
781781 588.527 + 40.6439i 0.753555 + 0.0520408i
782782 0 0
783783 −88.9355 122.409i −0.113583 0.156334i
784784 0 0
785785 16.3129 50.2058i 0.0207807 0.0639565i
786786 0 0
787787 311.831 429.199i 0.396228 0.545361i −0.563564 0.826072i 0.690570π-0.690570\pi
0.959792 + 0.280711i 0.0905703π0.0905703\pi
788788 0 0
789789 −858.774 + 279.033i −1.08843 + 0.353654i
790790 0 0
791791 629.577i 0.795926i
792792 0 0
793793 549.566 0.693022
794794 0 0
795795 650.370 + 2001.63i 0.818075 + 2.51778i
796796 0 0
797797 −723.680 525.784i −0.908005 0.659704i 0.0325047 0.999472i 0.489652π-0.489652\pi
−0.940509 + 0.339768i 0.889652π0.889652\pi
798798 0 0
799799 −88.9917 28.9151i −0.111379 0.0361892i
800800 0 0
801801 654.349 475.413i 0.816916 0.593524i
802802 0 0
803803 266.207 66.6168i 0.331516 0.0829599i
804804 0 0
805805 −521.939 718.388i −0.648372 0.892407i
806806 0 0
807807 309.789 953.431i 0.383877 1.18145i
808808 0 0
809809 634.298 873.036i 0.784052 1.07915i −0.210772 0.977535i 0.567598π-0.567598\pi
0.994823 0.101619i 0.0324023π-0.0324023\pi
810810 0 0
811811 −1130.95 + 367.469i −1.39452 + 0.453106i −0.907414 0.420237i 0.861947π-0.861947\pi
−0.487104 + 0.873344i 0.661947π0.661947\pi
812812 0 0
813813 1290.16i 1.58691i
814814 0 0
815815 828.213 1.01621
816816 0 0
817817 −242.550 746.491i −0.296878 0.913698i
818818 0 0
819819 503.578 + 365.871i 0.614869 + 0.446728i
820820 0 0
821821 1011.88 + 328.781i 1.23250 + 0.400464i 0.851620 0.524159i 0.175620π-0.175620\pi
0.380882 + 0.924623i 0.375620π0.375620\pi
822822 0 0
823823 832.874 605.118i 1.01200 0.735259i 0.0473700 0.998877i 0.484916π-0.484916\pi
0.964627 + 0.263619i 0.0849160π0.0849160\pi
824824 0 0
825825 329.184 816.786i 0.399011 0.990043i
826826 0 0
827827 654.331 + 900.610i 0.791211 + 1.08901i 0.993956 + 0.109776i 0.0350135π0.0350135\pi
−0.202746 + 0.979231i 0.564986π0.564986\pi
828828 0 0
829829 −399.558 + 1229.71i −0.481976 + 1.48337i 0.354338 + 0.935117i 0.384706π0.384706\pi
−0.836314 + 0.548251i 0.815294π0.815294\pi
830830 0 0
831831 −497.218 + 684.362i −0.598337 + 0.823540i
832832 0 0
833833 −681.636 + 221.477i −0.818290 + 0.265879i
834834 0 0
835835 1390.78i 1.66560i
836836 0 0
837837 272.101 0.325091
838838 0 0
839839 −380.239 1170.26i −0.453205 1.39482i −0.873229 0.487309i 0.837978π-0.837978\pi
0.420024 0.907513i 0.362022π-0.362022\pi
840840 0 0
841841 −348.925 253.509i −0.414893 0.301437i
842842 0 0
843843 91.6917 + 29.7924i 0.108768 + 0.0353410i
844844 0 0
845845 −761.209 + 553.051i −0.900839 + 0.654498i
846846 0 0
847847 −966.307 + 1004.10i −1.14086 + 1.18548i
848848 0 0
849849 −143.378 197.343i −0.168879 0.232442i
850850 0 0
851851 133.999 412.407i 0.157461 0.484614i
852852 0 0
853853 −509.204 + 700.859i −0.596956 + 0.821640i −0.995425 0.0955420i 0.969542π-0.969542\pi
0.398469 + 0.917182i 0.369542π0.369542\pi
854854 0 0
855855 722.357 234.708i 0.844862 0.274512i
856856 0 0
857857 1219.98i 1.42354i −0.702411 0.711772i 0.747893π-0.747893\pi
0.702411 0.711772i 0.252107π-0.252107\pi
858858 0 0
859859 469.893 0.547023 0.273512 0.961869i 0.411815π-0.411815\pi
0.273512 + 0.961869i 0.411815π0.411815\pi
860860 0 0
861861 669.427 + 2060.28i 0.777499 + 2.39290i
862862 0 0
863863 3.42992 + 2.49198i 0.00397442 + 0.00288758i 0.589771 0.807571i 0.299218π-0.299218\pi
−0.585796 + 0.810458i 0.699218π0.699218\pi
864864 0 0
865865 1571.24 + 510.528i 1.81647 + 0.590206i
866866 0 0
867867 −773.769 + 562.176i −0.892467 + 0.648415i
868868 0 0
869869 −727.184 293.072i −0.836805 0.337252i
870870 0 0
871871 111.823 + 153.912i 0.128385 + 0.176707i
872872 0 0
873873 9.85983 30.3454i 0.0112942 0.0347599i
874874 0 0
875875 308.938 425.216i 0.353071 0.485961i
876876 0 0
877877 404.726 131.503i 0.461489 0.149947i −0.0690394 0.997614i 0.521993π-0.521993\pi
0.530529 + 0.847667i 0.321993π0.321993\pi
878878 0 0
879879 1946.26i 2.21417i
880880 0 0
881881 −1669.31 −1.89479 −0.947396 0.320064i 0.896296π-0.896296\pi
−0.947396 + 0.320064i 0.896296π0.896296\pi
882882 0 0
883883 65.8838 + 202.770i 0.0746136 + 0.229637i 0.981407 0.191938i 0.0614773π-0.0614773\pi
−0.906793 + 0.421575i 0.861477π0.861477\pi
884884 0 0
885885 105.348 + 76.5399i 0.119037 + 0.0864857i
886886 0 0
887887 498.213 + 161.879i 0.561683 + 0.182502i 0.576078 0.817394i 0.304582π-0.304582\pi
−0.0143952 + 0.999896i 0.504582π0.504582\pi
888888 0 0
889889 −75.9672 + 55.1934i −0.0854524 + 0.0620848i
890890 0 0
891891 −168.226 672.248i −0.188806 0.754487i
892892 0 0
893893 69.5419 + 95.7162i 0.0778744 + 0.107185i
894894 0 0
895895 449.634 1383.83i 0.502384 1.54618i
896896 0 0
897897 155.024 213.373i 0.172825 0.237874i
898898 0 0
899899 −700.732 + 227.682i −0.779457 + 0.253261i
900900 0 0
901901 619.574i 0.687651i
902902 0 0
903903 −3701.67 −4.09930
904904 0 0
905905 −4.00004 12.3108i −0.00441993 0.0136031i
906906 0 0
907907 705.473 + 512.556i 0.777810 + 0.565112i 0.904321 0.426853i 0.140378π-0.140378\pi
−0.126511 + 0.991965i 0.540378π0.540378\pi
908908 0 0
909909 −451.621 146.741i −0.496833 0.161431i
910910 0 0
911911 −733.848 + 533.172i −0.805541 + 0.585260i −0.912534 0.409000i 0.865878π-0.865878\pi
0.106993 + 0.994260i 0.465878π0.465878\pi
912912 0 0
913913 8.74487 126.626i 0.00957817 0.138693i
914914 0 0
915915 −1858.89 2558.55i −2.03158 2.79623i
916916 0 0
917917 −578.263 + 1779.71i −0.630603 + 1.94080i
918918 0 0
919919 708.097 974.612i 0.770508 1.06051i −0.225758 0.974183i 0.572486π-0.572486\pi
0.996267 0.0863305i 0.0275141π-0.0275141\pi
920920 0 0
921921 −982.698 + 319.298i −1.06699 + 0.346686i
922922 0 0
923923 271.277i 0.293908i
924924 0 0
925925 −665.798 −0.719782
926926 0 0
927927 −178.310 548.783i −0.192352 0.591999i
928928 0 0
929929 1387.31 + 1007.94i 1.49334 + 1.08497i 0.972942 + 0.231050i 0.0742160π0.0742160\pi
0.520397 + 0.853924i 0.325784π0.325784\pi
930930 0 0
931931 861.860 + 280.035i 0.925736 + 0.300790i
932932 0 0
933933 −546.040 + 396.721i −0.585252 + 0.425210i
934934 0 0
935935 −397.107 + 474.083i −0.424713 + 0.507040i
936936 0 0
937937 −525.277 722.982i −0.560595 0.771593i 0.430807 0.902444i 0.358229π-0.358229\pi
−0.991402 + 0.130851i 0.958229π0.958229\pi
938938 0 0
939939 138.057 424.895i 0.147025 0.452497i
940940 0 0
941941 −856.109 + 1178.33i −0.909786 + 1.25221i 0.0574535 + 0.998348i 0.481702π0.481702\pi
−0.967240 + 0.253865i 0.918298π0.918298\pi
942942 0 0
943943 473.843 153.961i 0.502485 0.163267i
944944 0 0
945945 564.823i 0.597697i
946946 0 0
947947 −1026.37 −1.08381 −0.541906 0.840439i 0.682297π-0.682297\pi
−0.541906 + 0.840439i 0.682297π0.682297\pi
948948 0 0
949949 −38.9946 120.013i −0.0410902 0.126463i
950950 0 0
951951 −1199.20 871.267i −1.26098 0.916159i
952952 0 0
953953 73.2826 + 23.8110i 0.0768968 + 0.0249853i 0.347213 0.937786i 0.387128π-0.387128\pi
−0.270316 + 0.962772i 0.587128π0.587128\pi
954954 0 0
955955 −110.383 + 80.1977i −0.115584 + 0.0839766i
956956 0 0
957957 −524.207 837.299i −0.547760 0.874920i
958958 0 0
959959 1589.90 + 2188.31i 1.65787 + 2.28186i
960960 0 0
961961 112.486 346.196i 0.117051 0.360245i
962962 0 0
963963 825.190 1135.78i 0.856895 1.17941i
964964 0 0
965965 1165.91 378.828i 1.20820 0.392567i
966966 0 0
967967 637.935i 0.659705i 0.944032 + 0.329853i 0.106999π0.106999\pi
−0.944032 + 0.329853i 0.893001π0.893001\pi
968968 0 0
969969 −411.931 −0.425110
970970 0 0
971971 −415.360 1278.35i −0.427766 1.31653i −0.900321 0.435226i 0.856668π-0.856668\pi
0.472556 0.881301i 0.343332π-0.343332\pi
972972 0 0
973973 −2213.07 1607.89i −2.27448 1.65251i
974974 0 0
975975 −385.133 125.137i −0.395008 0.128346i
976976 0 0
977977 −620.481 + 450.806i −0.635088 + 0.461418i −0.858159 0.513384i 0.828392π-0.828392\pi
0.223071 + 0.974802i 0.428392π0.428392\pi
978978 0 0
979979 705.771 441.861i 0.720910 0.451339i
980980 0 0
981981 43.7443 + 60.2089i 0.0445915 + 0.0613750i
982982 0 0
983983 −198.170 + 609.906i −0.201598 + 0.620454i 0.798238 + 0.602342i 0.205765π0.205765\pi
−0.999836 + 0.0181119i 0.994235π0.994235\pi
984984 0 0
985985 1255.70 1728.33i 1.27483 1.75465i
986986 0 0
987987 530.656 172.421i 0.537646 0.174692i
988988 0 0
989989 851.345i 0.860814i
990990 0 0
991991 1547.49 1.56154 0.780770 0.624818i 0.214827π-0.214827\pi
0.780770 + 0.624818i 0.214827π0.214827\pi
992992 0 0
993993 −231.176 711.487i −0.232806 0.716502i
994994 0 0
995995 −406.613 295.422i −0.408656 0.296906i
996996 0 0
997997 1848.46 + 600.601i 1.85402 + 0.602408i 0.996059 + 0.0886972i 0.0282703π0.0282703\pi
0.857963 + 0.513711i 0.171730π0.171730\pi
998998 0 0
999999 223.146 162.125i 0.223369 0.162287i
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 176.3.n.c.129.2 8
4.3 odd 2 44.3.f.a.41.1 yes 8
11.7 odd 10 inner 176.3.n.c.161.2 8
12.11 even 2 396.3.t.a.217.2 8
44.3 odd 10 484.3.f.d.457.2 8
44.7 even 10 44.3.f.a.29.1 8
44.15 odd 10 484.3.f.a.161.1 8
44.19 even 10 484.3.f.e.457.2 8
44.27 odd 10 484.3.f.e.233.2 8
44.31 odd 10 484.3.d.c.241.2 8
44.35 even 10 484.3.d.c.241.1 8
44.39 even 10 484.3.f.d.233.2 8
44.43 even 2 484.3.f.a.481.1 8
132.35 odd 10 4356.3.f.g.1693.1 8
132.95 odd 10 396.3.t.a.73.2 8
132.119 even 10 4356.3.f.g.1693.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
44.3.f.a.29.1 8 44.7 even 10
44.3.f.a.41.1 yes 8 4.3 odd 2
176.3.n.c.129.2 8 1.1 even 1 trivial
176.3.n.c.161.2 8 11.7 odd 10 inner
396.3.t.a.73.2 8 132.95 odd 10
396.3.t.a.217.2 8 12.11 even 2
484.3.d.c.241.1 8 44.35 even 10
484.3.d.c.241.2 8 44.31 odd 10
484.3.f.a.161.1 8 44.15 odd 10
484.3.f.a.481.1 8 44.43 even 2
484.3.f.d.233.2 8 44.39 even 10
484.3.f.d.457.2 8 44.3 odd 10
484.3.f.e.233.2 8 44.27 odd 10
484.3.f.e.457.2 8 44.19 even 10
4356.3.f.g.1693.1 8 132.35 odd 10
4356.3.f.g.1693.2 8 132.119 even 10