Properties

Label 900.2.k.n.307.2
Level 900900
Weight 22
Character 900.307
Analytic conductor 7.1877.187
Analytic rank 00
Dimension 1212
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [900,2,Mod(307,900)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(900, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("900.307");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 900=223252 900 = 2^{2} \cdot 3^{2} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 900.k (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: 7.186536181927.18653618192
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(i)\Q(i)
Coefficient field: 12.0.426337261060096.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x124x93x8+4x7+8x6+8x512x432x3+64 x^{12} - 4x^{9} - 3x^{8} + 4x^{7} + 8x^{6} + 8x^{5} - 12x^{4} - 32x^{3} + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,,a13]\Z[a_1, \ldots, a_{13}]
Coefficient ring index: 26 2^{6}
Twist minimal: no (minimal twist has level 60)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 307.2
Root 0.7601981.19252i-0.760198 - 1.19252i of defining polynomial
Character χ\chi == 900.307
Dual form 900.2.k.n.343.2

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+(1.19252+0.760198i)q2+(0.8441991.81310i)q4+(0.6113930.611393i)q7+(0.371591+2.80391i)q8+5.12822iq11+(1.76156+1.76156i)q13+(0.264318+1.19388i)q14+(2.574663.06123i)q16+(3.761563.76156i)q17+1.22279q19+(3.898466.11549i)q22+(1.07700+1.07700i)q23+(0.7615573.43982i)q26+(0.5923791.62465i)q28+0.864641iq29+7.81086iq31+(5.39747+1.69333i)q32+(7.34525+1.62620i)q34+(1.76156+1.76156i)q37+(1.45820+0.929560i)q385.52311q41+(6.20522+6.20522i)q43+(9.29797+4.32924i)q44+(2.103080.465611i)q46+(2.29979+2.29979i)q47+6.25240iq49+(1.70677+4.68098i)q52+(2.62620+2.62620i)q53+(1.94148+1.48710i)q56+(0.6572981.03110i)q580.528636q59+4.98168q61+(5.937809.31460i)q62+(7.72384+2.08382i)q64+(6.20522+6.20522i)q67+(9.99558+3.64457i)q688.10243iq71+(2.252402.25240i)q73+(3.439820.761557i)q74+(1.032282.21703i)q76+(3.13536+3.13536i)q7715.9133q79+(6.586414.19866i)q82+(7.95665+7.95665i)q83+(12.11702.68264i)q86+(14.3791+1.90560i)q88+7.25240iq89+2.15401iq91+(2.861921.04351i)q92+(0.9942474.49084i)q94+(0.7938330.793833i)q97+(4.753067.45610i)q98+O(q100)q+(-1.19252 + 0.760198i) q^{2} +(0.844199 - 1.81310i) q^{4} +(0.611393 - 0.611393i) q^{7} +(0.371591 + 2.80391i) q^{8} +5.12822i q^{11} +(-1.76156 + 1.76156i) q^{13} +(-0.264318 + 1.19388i) q^{14} +(-2.57466 - 3.06123i) q^{16} +(-3.76156 - 3.76156i) q^{17} +1.22279 q^{19} +(-3.89846 - 6.11549i) q^{22} +(1.07700 + 1.07700i) q^{23} +(0.761557 - 3.43982i) q^{26} +(-0.592379 - 1.62465i) q^{28} +0.864641i q^{29} +7.81086i q^{31} +(5.39747 + 1.69333i) q^{32} +(7.34525 + 1.62620i) q^{34} +(1.76156 + 1.76156i) q^{37} +(-1.45820 + 0.929560i) q^{38} -5.52311 q^{41} +(6.20522 + 6.20522i) q^{43} +(9.29797 + 4.32924i) q^{44} +(-2.10308 - 0.465611i) q^{46} +(-2.29979 + 2.29979i) q^{47} +6.25240i q^{49} +(1.70677 + 4.68098i) q^{52} +(-2.62620 + 2.62620i) q^{53} +(1.94148 + 1.48710i) q^{56} +(-0.657298 - 1.03110i) q^{58} -0.528636 q^{59} +4.98168 q^{61} +(-5.93780 - 9.31460i) q^{62} +(-7.72384 + 2.08382i) q^{64} +(-6.20522 + 6.20522i) q^{67} +(-9.99558 + 3.64457i) q^{68} -8.10243i q^{71} +(2.25240 - 2.25240i) q^{73} +(-3.43982 - 0.761557i) q^{74} +(1.03228 - 2.21703i) q^{76} +(3.13536 + 3.13536i) q^{77} -15.9133 q^{79} +(6.58641 - 4.19866i) q^{82} +(7.95665 + 7.95665i) q^{83} +(-12.1170 - 2.68264i) q^{86} +(-14.3791 + 1.90560i) q^{88} +7.25240i q^{89} +2.15401i q^{91} +(2.86192 - 1.04351i) q^{92} +(0.994247 - 4.49084i) q^{94} +(-0.793833 - 0.793833i) q^{97} +(-4.75306 - 7.45610i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q12q8+4q13+12q1620q1712q2216q26+4q28+20q324q37+16q3816q4140q46+8q52+4q53+64q56+20q5832q61++24q98+O(q100) 12 q - 12 q^{8} + 4 q^{13} + 12 q^{16} - 20 q^{17} - 12 q^{22} - 16 q^{26} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 16 q^{38} - 16 q^{41} - 40 q^{46} + 8 q^{52} + 4 q^{53} + 64 q^{56} + 20 q^{58} - 32 q^{61}+ \cdots + 24 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/900Z)×\left(\mathbb{Z}/900\mathbb{Z}\right)^\times.

nn 101101 451451 577577
χ(n)\chi(n) 11 1-1 e(14)e\left(\frac{1}{4}\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 −1.19252 + 0.760198i −0.843238 + 0.537541i
33 0 0
44 0.844199 1.81310i 0.422099 0.906550i
55 0 0
66 0 0
77 0.611393 0.611393i 0.231085 0.231085i −0.582060 0.813145i 0.697753π-0.697753\pi
0.813145 + 0.582060i 0.197753π0.197753\pi
88 0.371591 + 2.80391i 0.131377 + 0.991332i
99 0 0
1010 0 0
1111 5.12822i 1.54622i 0.634274 + 0.773108i 0.281299π0.281299\pi
−0.634274 + 0.773108i 0.718701π0.718701\pi
1212 0 0
1313 −1.76156 + 1.76156i −0.488568 + 0.488568i −0.907854 0.419286i 0.862280π-0.862280\pi
0.419286 + 0.907854i 0.362280π0.362280\pi
1414 −0.264318 + 1.19388i −0.0706419 + 0.319077i
1515 0 0
1616 −2.57466 3.06123i −0.643664 0.765308i
1717 −3.76156 3.76156i −0.912312 0.912312i 0.0841421 0.996454i 0.473185π-0.473185\pi
−0.996454 + 0.0841421i 0.973185π0.973185\pi
1818 0 0
1919 1.22279 0.280527 0.140263 0.990114i 0.455205π-0.455205\pi
0.140263 + 0.990114i 0.455205π0.455205\pi
2020 0 0
2121 0 0
2222 −3.89846 6.11549i −0.831154 1.30383i
2323 1.07700 + 1.07700i 0.224571 + 0.224571i 0.810420 0.585849i 0.199239π-0.199239\pi
−0.585849 + 0.810420i 0.699239π0.699239\pi
2424 0 0
2525 0 0
2626 0.761557 3.43982i 0.149354 0.674604i
2727 0 0
2828 −0.592379 1.62465i −0.111949 0.307031i
2929 0.864641i 0.160560i 0.996772 + 0.0802799i 0.0255814π0.0255814\pi
−0.996772 + 0.0802799i 0.974419π0.974419\pi
3030 0 0
3131 7.81086i 1.40287i 0.712732 + 0.701436i 0.247457π0.247457\pi
−0.712732 + 0.701436i 0.752543π0.752543\pi
3232 5.39747 + 1.69333i 0.954146 + 0.299341i
3333 0 0
3434 7.34525 + 1.62620i 1.25970 + 0.278891i
3535 0 0
3636 0 0
3737 1.76156 + 1.76156i 0.289598 + 0.289598i 0.836921 0.547323i 0.184353π-0.184353\pi
−0.547323 + 0.836921i 0.684353π0.684353\pi
3838 −1.45820 + 0.929560i −0.236551 + 0.150795i
3939 0 0
4040 0 0
4141 −5.52311 −0.862566 −0.431283 0.902217i 0.641939π-0.641939\pi
−0.431283 + 0.902217i 0.641939π0.641939\pi
4242 0 0
4343 6.20522 + 6.20522i 0.946288 + 0.946288i 0.998629 0.0523416i 0.0166685π-0.0166685\pi
−0.0523416 + 0.998629i 0.516668π0.516668\pi
4444 9.29797 + 4.32924i 1.40172 + 0.652657i
4545 0 0
4646 −2.10308 0.465611i −0.310083 0.0686506i
4747 −2.29979 + 2.29979i −0.335459 + 0.335459i −0.854655 0.519196i 0.826231π-0.826231\pi
0.519196 + 0.854655i 0.326231π0.326231\pi
4848 0 0
4949 6.25240i 0.893199i
5050 0 0
5151 0 0
5252 1.70677 + 4.68098i 0.236687 + 0.649135i
5353 −2.62620 + 2.62620i −0.360736 + 0.360736i −0.864084 0.503348i 0.832101π-0.832101\pi
0.503348 + 0.864084i 0.332101π0.332101\pi
5454 0 0
5555 0 0
5656 1.94148 + 1.48710i 0.259441 + 0.198723i
5757 0 0
5858 −0.657298 1.03110i −0.0863075 0.135390i
5959 −0.528636 −0.0688225 −0.0344113 0.999408i 0.510956π-0.510956\pi
−0.0344113 + 0.999408i 0.510956π0.510956\pi
6060 0 0
6161 4.98168 0.637838 0.318919 0.947782i 0.396680π-0.396680\pi
0.318919 + 0.947782i 0.396680π0.396680\pi
6262 −5.93780 9.31460i −0.754101 1.18295i
6363 0 0
6464 −7.72384 + 2.08382i −0.965480 + 0.260477i
6565 0 0
6666 0 0
6767 −6.20522 + 6.20522i −0.758089 + 0.758089i −0.975974 0.217886i 0.930084π-0.930084\pi
0.217886 + 0.975974i 0.430084π0.430084\pi
6868 −9.99558 + 3.64457i −1.21214 + 0.441969i
6969 0 0
7070 0 0
7171 8.10243i 0.961581i −0.876835 0.480791i 0.840350π-0.840350\pi
0.876835 0.480791i 0.159650π-0.159650\pi
7272 0 0
7373 2.25240 2.25240i 0.263623 0.263623i −0.562901 0.826524i 0.690315π-0.690315\pi
0.826524 + 0.562901i 0.190315π0.190315\pi
7474 −3.43982 0.761557i −0.399871 0.0885292i
7575 0 0
7676 1.03228 2.21703i 0.118410 0.254311i
7777 3.13536 + 3.13536i 0.357307 + 0.357307i
7878 0 0
7979 −15.9133 −1.79039 −0.895193 0.445680i 0.852962π-0.852962\pi
−0.895193 + 0.445680i 0.852962π0.852962\pi
8080 0 0
8181 0 0
8282 6.58641 4.19866i 0.727348 0.463664i
8383 7.95665 + 7.95665i 0.873355 + 0.873355i 0.992836 0.119481i 0.0381231π-0.0381231\pi
−0.119481 + 0.992836i 0.538123π0.538123\pi
8484 0 0
8585 0 0
8686 −12.1170 2.68264i −1.30661 0.289277i
8787 0 0
8888 −14.3791 + 1.90560i −1.53281 + 0.203138i
8989 7.25240i 0.768752i 0.923177 + 0.384376i 0.125583π0.125583\pi
−0.923177 + 0.384376i 0.874417π0.874417\pi
9090 0 0
9191 2.15401i 0.225801i
9292 2.86192 1.04351i 0.298376 0.108793i
9393 0 0
9494 0.994247 4.49084i 0.102549 0.463195i
9595 0 0
9696 0 0
9797 −0.793833 0.793833i −0.0806015 0.0806015i 0.665657 0.746258i 0.268152π-0.268152\pi
−0.746258 + 0.665657i 0.768152π0.768152\pi
9898 −4.75306 7.45610i −0.480131 0.753179i
9999 0 0
100100 0 0
101101 10.1170 1.00668 0.503341 0.864088i 0.332104π-0.332104\pi
0.503341 + 0.864088i 0.332104π0.332104\pi
102102 0 0
103103 3.82267 + 3.82267i 0.376659 + 0.376659i 0.869895 0.493236i 0.164186π-0.164186\pi
−0.493236 + 0.869895i 0.664186π0.664186\pi
104104 −5.59383 4.28467i −0.548520 0.420147i
105105 0 0
106106 1.13536 5.12822i 0.110276 0.498097i
107107 −5.51107 + 5.51107i −0.532775 + 0.532775i −0.921397 0.388622i 0.872951π-0.872951\pi
0.388622 + 0.921397i 0.372951π0.372951\pi
108108 0 0
109109 7.31695i 0.700836i −0.936593 0.350418i 0.886039π-0.886039\pi
0.936593 0.350418i 0.113961π-0.113961\pi
110110 0 0
111111 0 0
112112 −3.44575 0.297490i −0.325592 0.0281101i
113113 −0.509161 + 0.509161i −0.0478978 + 0.0478978i −0.730650 0.682752i 0.760783π-0.760783\pi
0.682752 + 0.730650i 0.260783π0.260783\pi
114114 0 0
115115 0 0
116116 1.56768 + 0.729929i 0.145555 + 0.0677722i
117117 0 0
118118 0.630408 0.401868i 0.0580337 0.0369949i
119119 −4.59958 −0.421643
120120 0 0
121121 −15.2986 −1.39078
122122 −5.94074 + 3.78706i −0.537849 + 0.342864i
123123 0 0
124124 14.1619 + 6.59392i 1.27177 + 0.592152i
125125 0 0
126126 0 0
127127 −7.49103 + 7.49103i −0.664722 + 0.664722i −0.956489 0.291767i 0.905757π-0.905757\pi
0.291767 + 0.956489i 0.405757π0.405757\pi
128128 7.62671 8.35664i 0.674112 0.738629i
129129 0 0
130130 0 0
131131 13.9964i 1.22287i 0.791296 + 0.611434i 0.209407π0.209407\pi
−0.791296 + 0.611434i 0.790593π0.790593\pi
132132 0 0
133133 0.747604 0.747604i 0.0648255 0.0648255i
134134 2.68264 12.1170i 0.231745 1.04675i
135135 0 0
136136 9.14931 11.9448i 0.784547 1.02426i
137137 7.01395 + 7.01395i 0.599242 + 0.599242i 0.940111 0.340869i 0.110721π-0.110721\pi
−0.340869 + 0.940111i 0.610721π0.610721\pi
138138 0 0
139139 2.28006 0.193392 0.0966960 0.995314i 0.469173π-0.469173\pi
0.0966960 + 0.995314i 0.469173π0.469173\pi
140140 0 0
141141 0 0
142142 6.15945 + 9.66229i 0.516889 + 0.810842i
143143 −9.03365 9.03365i −0.755432 0.755432i
144144 0 0
145145 0 0
146146 −0.973757 + 4.39829i −0.0805887 + 0.364005i
147147 0 0
148148 4.68098 1.70677i 0.384774 0.140296i
149149 10.1170i 0.828820i −0.910090 0.414410i 0.863988π-0.863988\pi
0.910090 0.414410i 0.136012π-0.136012\pi
150150 0 0
151151 7.93691i 0.645897i 0.946417 + 0.322948i 0.104674π0.104674\pi
−0.946417 + 0.322948i 0.895326π0.895326\pi
152152 0.454377 + 3.42859i 0.0368548 + 0.278095i
153153 0 0
154154 −6.12247 1.35548i −0.493362 0.109228i
155155 0 0
156156 0 0
157157 −9.01395 9.01395i −0.719392 0.719392i 0.249089 0.968481i 0.419869π-0.419869\pi
−0.968481 + 0.249089i 0.919869π0.919869\pi
158158 18.9769 12.0972i 1.50972 0.962405i
159159 0 0
160160 0 0
161161 1.31695 0.103790
162162 0 0
163163 −13.0849 13.0849i −1.02489 1.02489i −0.999682 0.0252033i 0.991977π-0.991977\pi
−0.0252033 0.999682i 0.508023π-0.508023\pi
164164 −4.66261 + 10.0140i −0.364088 + 0.781958i
165165 0 0
166166 −15.5371 3.43982i −1.20591 0.266982i
167167 11.3334 11.3334i 0.877008 0.877008i −0.116216 0.993224i 0.537076π-0.537076\pi
0.993224 + 0.116216i 0.0370765π0.0370765\pi
168168 0 0
169169 6.79383i 0.522603i
170170 0 0
171171 0 0
172172 16.4891 6.01224i 1.25728 0.458429i
173173 7.96772 7.96772i 0.605775 0.605775i −0.336064 0.941839i 0.609096π-0.609096\pi
0.941839 + 0.336064i 0.109096π0.109096\pi
174174 0 0
175175 0 0
176176 15.6987 13.2034i 1.18333 0.995244i
177177 0 0
178178 −5.51325 8.64861i −0.413236 0.648241i
179179 −12.6475 −0.945320 −0.472660 0.881245i 0.656706π-0.656706\pi
−0.472660 + 0.881245i 0.656706π0.656706\pi
180180 0 0
181181 7.72928 0.574513 0.287256 0.957854i 0.407257π-0.407257\pi
0.287256 + 0.957854i 0.407257π0.407257\pi
182182 −1.63747 2.56869i −0.121378 0.190404i
183183 0 0
184184 −2.61962 + 3.42003i −0.193121 + 0.252128i
185185 0 0
186186 0 0
187187 19.2901 19.2901i 1.41063 1.41063i
188188 2.22827 + 6.11123i 0.162513 + 0.445707i
189189 0 0
190190 0 0
191191 7.04516i 0.509770i 0.966971 + 0.254885i 0.0820376π0.0820376\pi
−0.966971 + 0.254885i 0.917962π0.917962\pi
192192 0 0
193193 11.5048 11.5048i 0.828133 0.828133i −0.159125 0.987258i 0.550867π-0.550867\pi
0.987258 + 0.159125i 0.0508674π0.0508674\pi
194194 1.55013 + 0.343190i 0.111293 + 0.0246396i
195195 0 0
196196 11.3362 + 5.27827i 0.809730 + 0.377019i
197197 7.87859 + 7.87859i 0.561327 + 0.561327i 0.929684 0.368358i 0.120080π-0.120080\pi
−0.368358 + 0.929684i 0.620080π0.620080\pi
198198 0 0
199199 11.4792 0.813741 0.406870 0.913486i 0.366620π-0.366620\pi
0.406870 + 0.913486i 0.366620π0.366620\pi
200200 0 0
201201 0 0
202202 −12.0648 + 7.69095i −0.848873 + 0.541133i
203203 0.528636 + 0.528636i 0.0371030 + 0.0371030i
204204 0 0
205205 0 0
206206 −7.46460 1.65262i −0.520083 0.115143i
207207 0 0
208208 9.92794 + 0.857132i 0.688379 + 0.0594314i
209209 6.27072i 0.433755i
210210 0 0
211211 5.49134i 0.378039i −0.981973 0.189020i 0.939469π-0.939469\pi
0.981973 0.189020i 0.0605310π-0.0605310\pi
212212 2.54452 + 6.97859i 0.174759 + 0.479292i
213213 0 0
214214 2.38255 10.7616i 0.162868 0.735645i
215215 0 0
216216 0 0
217217 4.77551 + 4.77551i 0.324183 + 0.324183i
218218 5.56233 + 8.72559i 0.376728 + 0.590972i
219219 0 0
220220 0 0
221221 13.2524 0.891453
222222 0 0
223223 10.8678 + 10.8678i 0.727764 + 0.727764i 0.970174 0.242410i 0.0779380π-0.0779380\pi
−0.242410 + 0.970174i 0.577938π0.577938\pi
224224 4.33526 2.26469i 0.289662 0.151316i
225225 0 0
226226 0.220121 0.994247i 0.0146422 0.0661363i
227227 4.98244 4.98244i 0.330696 0.330696i −0.522155 0.852851i 0.674872π-0.674872\pi
0.852851 + 0.522155i 0.174872π0.174872\pi
228228 0 0
229229 25.7572i 1.70208i −0.525098 0.851041i 0.675972π-0.675972\pi
0.525098 0.851041i 0.324028π-0.324028\pi
230230 0 0
231231 0 0
232232 −2.42438 + 0.321293i −0.159168 + 0.0210939i
233233 −0.715328 + 0.715328i −0.0468627 + 0.0468627i −0.730150 0.683287i 0.760550π-0.760550\pi
0.683287 + 0.730150i 0.260550π0.260550\pi
234234 0 0
235235 0 0
236236 −0.446274 + 0.958469i −0.0290499 + 0.0623910i
237237 0 0
238238 5.48509 3.49659i 0.355545 0.226650i
239239 26.9354 1.74231 0.871154 0.491009i 0.163372π-0.163372\pi
0.871154 + 0.491009i 0.163372π0.163372\pi
240240 0 0
241241 14.0925 0.907775 0.453887 0.891059i 0.350037π-0.350037\pi
0.453887 + 0.891059i 0.350037π0.350037\pi
242242 18.2439 11.6300i 1.17276 0.747603i
243243 0 0
244244 4.20553 9.03228i 0.269231 0.578232i
245245 0 0
246246 0 0
247247 −2.15401 + 2.15401i −0.137056 + 0.137056i
248248 −21.9010 + 2.90245i −1.39071 + 0.184306i
249249 0 0
250250 0 0
251251 17.2471i 1.08863i −0.838882 0.544314i 0.816790π-0.816790\pi
0.838882 0.544314i 0.183210π-0.183210\pi
252252 0 0
253253 −5.52311 + 5.52311i −0.347235 + 0.347235i
254254 3.23853 14.6279i 0.203203 0.917834i
255255 0 0
256256 −2.74229 + 15.7632i −0.171393 + 0.985203i
257257 −15.0140 15.0140i −0.936545 0.936545i 0.0615588 0.998103i 0.480393π-0.480393\pi
−0.998103 + 0.0615588i 0.980393π0.980393\pi
258258 0 0
259259 2.15401 0.133844
260260 0 0
261261 0 0
262262 −10.6400 16.6909i −0.657341 1.03117i
263263 −6.73386 6.73386i −0.415228 0.415228i 0.468327 0.883555i 0.344857π-0.344857\pi
−0.883555 + 0.468327i 0.844857π0.844857\pi
264264 0 0
265265 0 0
266266 −0.323204 + 1.45986i −0.0198169 + 0.0895096i
267267 0 0
268268 6.01224 + 16.4891i 0.367256 + 1.00723i
269269 25.7047i 1.56724i −0.621238 0.783622i 0.713370π-0.713370\pi
0.621238 0.783622i 0.286630π-0.286630\pi
270270 0 0
271271 0.931222i 0.0565677i −0.999600 0.0282839i 0.990996π-0.990996\pi
0.999600 0.0282839i 0.00900423π-0.00900423\pi
272272 −1.83029 + 21.1997i −0.110977 + 1.28542i
273273 0 0
274274 −13.6963 3.03228i −0.827421 0.183186i
275275 0 0
276276 0 0
277277 22.0602 + 22.0602i 1.32547 + 1.32547i 0.909277 + 0.416190i 0.136635π0.136635\pi
0.416190 + 0.909277i 0.363365π0.363365\pi
278278 −2.71901 + 1.73330i −0.163075 + 0.103956i
279279 0 0
280280 0 0
281281 −8.56934 −0.511204 −0.255602 0.966782i 0.582274π-0.582274\pi
−0.255602 + 0.966782i 0.582274π0.582274\pi
282282 0 0
283283 −11.5705 11.5705i −0.687796 0.687796i 0.273949 0.961744i 0.411670π-0.411670\pi
−0.961744 + 0.273949i 0.911670π0.911670\pi
284284 −14.6905 6.84006i −0.871721 0.405883i
285285 0 0
286286 17.6402 + 3.90543i 1.04308 + 0.230933i
287287 −3.37680 + 3.37680i −0.199326 + 0.199326i
288288 0 0
289289 11.2986i 0.664625i
290290 0 0
291291 0 0
292292 −2.18235 5.98529i −0.127712 0.350262i
293293 12.8969 12.8969i 0.753446 0.753446i −0.221675 0.975121i 0.571152π-0.571152\pi
0.975121 + 0.221675i 0.0711523π0.0711523\pi
294294 0 0
295295 0 0
296296 −4.28467 + 5.59383i −0.249041 + 0.325135i
297297 0 0
298298 7.69095 + 12.0648i 0.445525 + 0.698892i
299299 −3.79441 −0.219436
300300 0 0
301301 7.58767 0.437346
302302 −6.03362 9.46491i −0.347196 0.544644i
303303 0 0
304304 −3.14826 3.74324i −0.180565 0.214689i
305305 0 0
306306 0 0
307307 −1.60564 + 1.60564i −0.0916387 + 0.0916387i −0.751440 0.659801i 0.770640π-0.770640\pi
0.659801 + 0.751440i 0.270640π0.270640\pi
308308 8.33158 3.03785i 0.474736 0.173098i
309309 0 0
310310 0 0
311311 19.4161i 1.10099i −0.834839 0.550494i 0.814439π-0.814439\pi
0.834839 0.550494i 0.185561π-0.185561\pi
312312 0 0
313313 −17.7110 + 17.7110i −1.00108 + 1.00108i −0.00108322 + 0.999999i 0.500345π0.500345\pi
−0.999999 + 0.00108322i 0.999655π0.999655\pi
314314 17.6017 + 3.89692i 0.993321 + 0.219916i
315315 0 0
316316 −13.4340 + 28.8524i −0.755721 + 1.62307i
317317 −7.78946 7.78946i −0.437500 0.437500i 0.453670 0.891170i 0.350115π-0.350115\pi
−0.891170 + 0.453670i 0.850115π0.850115\pi
318318 0 0
319319 −4.43407 −0.248260
320320 0 0
321321 0 0
322322 −1.57048 + 1.00114i −0.0875196 + 0.0557914i
323323 −4.59958 4.59958i −0.255928 0.255928i
324324 0 0
325325 0 0
326326 25.5510 + 5.65685i 1.41514 + 0.313304i
327327 0 0
328328 −2.05234 15.4863i −0.113322 0.855089i
329329 2.81215i 0.155039i
330330 0 0
331331 31.7005i 1.74242i −0.490912 0.871209i 0.663336π-0.663336\pi
0.490912 0.871209i 0.336664π-0.336664\pi
332332 21.1432 7.70919i 1.16038 0.423097i
333333 0 0
334334 −4.89968 + 22.1310i −0.268098 + 1.21095i
335335 0 0
336336 0 0
337337 −18.9634 18.9634i −1.03300 1.03300i −0.999437 0.0335632i 0.989314π-0.989314\pi
−0.0335632 0.999437i 0.510686π-0.510686\pi
338338 −5.16466 8.10177i −0.280920 0.440678i
339339 0 0
340340 0 0
341341 −40.0558 −2.16914
342342 0 0
343343 8.10243 + 8.10243i 0.437490 + 0.437490i
344344 −15.0931 + 19.7047i −0.813765 + 1.06241i
345345 0 0
346346 −3.44461 + 15.5587i −0.185183 + 0.836441i
347347 −7.71957 + 7.71957i −0.414408 + 0.414408i −0.883271 0.468863i 0.844664π-0.844664\pi
0.468863 + 0.883271i 0.344664π0.344664\pi
348348 0 0
349349 27.0741i 1.44925i 0.689146 + 0.724623i 0.257986π0.257986\pi
−0.689146 + 0.724623i 0.742014π0.742014\pi
350350 0 0
351351 0 0
352352 −8.68375 + 27.6794i −0.462846 + 1.47532i
353353 −9.96772 + 9.96772i −0.530528 + 0.530528i −0.920730 0.390201i 0.872405π-0.872405\pi
0.390201 + 0.920730i 0.372405π0.372405\pi
354354 0 0
355355 0 0
356356 13.1493 + 6.12247i 0.696912 + 0.324490i
357357 0 0
358358 15.0824 9.61461i 0.797129 0.508148i
359359 −14.2334 −0.751211 −0.375606 0.926780i 0.622565π-0.622565\pi
−0.375606 + 0.926780i 0.622565π0.622565\pi
360360 0 0
361361 −17.5048 −0.921305
362362 −9.21731 + 5.87578i −0.484451 + 0.308824i
363363 0 0
364364 3.90543 + 1.81841i 0.204700 + 0.0953107i
365365 0 0
366366 0 0
367367 −2.89145 + 2.89145i −0.150933 + 0.150933i −0.778534 0.627602i 0.784037π-0.784037\pi
0.627602 + 0.778534i 0.284037π0.284037\pi
368368 0.524045 6.06988i 0.0273177 0.316414i
369369 0 0
370370 0 0
371371 3.21128i 0.166721i
372372 0 0
373373 11.2847 11.2847i 0.584298 0.584298i −0.351783 0.936081i 0.614425π-0.614425\pi
0.936081 + 0.351783i 0.114425π0.114425\pi
374374 −8.33950 + 37.6681i −0.431225 + 1.94777i
375375 0 0
376376 −7.30299 5.59383i −0.376623 0.288480i
377377 −1.52311 1.52311i −0.0784444 0.0784444i
378378 0 0
379379 15.4562 0.793932 0.396966 0.917833i 0.370063π-0.370063\pi
0.396966 + 0.917833i 0.370063π0.370063\pi
380380 0 0
381381 0 0
382382 −5.35571 8.40148i −0.274022 0.429857i
383383 12.5562 + 12.5562i 0.641593 + 0.641593i 0.950947 0.309354i 0.100113π-0.100113\pi
−0.309354 + 0.950947i 0.600113π0.600113\pi
384384 0 0
385385 0 0
386386 −4.97376 + 22.4656i −0.253158 + 1.14347i
387387 0 0
388388 −2.10945 + 0.769144i −0.107091 + 0.0390474i
389389 5.16327i 0.261788i 0.991396 + 0.130894i 0.0417848π0.0417848\pi
−0.991396 + 0.130894i 0.958215π0.958215\pi
390390 0 0
391391 8.10243i 0.409757i
392392 −17.5312 + 2.32333i −0.885458 + 0.117346i
393393 0 0
394394 −15.3847 3.40608i −0.775068 0.171596i
395395 0 0
396396 0 0
397397 3.46293 + 3.46293i 0.173800 + 0.173800i 0.788646 0.614847i 0.210782π-0.210782\pi
−0.614847 + 0.788646i 0.710782π0.710782\pi
398398 −13.6892 + 8.72648i −0.686177 + 0.437419i
399399 0 0
400400 0 0
401401 −3.49521 −0.174542 −0.0872712 0.996185i 0.527815π-0.527815\pi
−0.0872712 + 0.996185i 0.527815π0.527815\pi
402402 0 0
403403 −13.7593 13.7593i −0.685399 0.685399i
404404 8.54079 18.3432i 0.424920 0.912608i
405405 0 0
406406 −1.03228 0.228540i −0.0512310 0.0113423i
407407 −9.03365 + 9.03365i −0.447781 + 0.447781i
408408 0 0
409409 14.8034i 0.731982i −0.930618 0.365991i 0.880730π-0.880730\pi
0.930618 0.365991i 0.119270π-0.119270\pi
410410 0 0
411411 0 0
412412 10.1580 3.70379i 0.500448 0.182473i
413413 −0.323204 + 0.323204i −0.0159039 + 0.0159039i
414414 0 0
415415 0 0
416416 −12.4908 + 6.52505i −0.612414 + 0.319917i
417417 0 0
418418 −4.76699 7.47795i −0.233161 0.365758i
419419 19.0701 0.931634 0.465817 0.884881i 0.345760π-0.345760\pi
0.465817 + 0.884881i 0.345760π0.345760\pi
420420 0 0
421421 −20.8034 −1.01390 −0.506948 0.861976i 0.669226π-0.669226\pi
−0.506948 + 0.861976i 0.669226π0.669226\pi
422422 4.17450 + 6.54852i 0.203212 + 0.318777i
423423 0 0
424424 −8.33950 6.38776i −0.405002 0.310217i
425425 0 0
426426 0 0
427427 3.04577 3.04577i 0.147395 0.147395i
428428 5.33968 + 14.6446i 0.258103 + 0.707872i
429429 0 0
430430 0 0
431431 15.3302i 0.738428i −0.929344 0.369214i 0.879627π-0.879627\pi
0.929344 0.369214i 0.120373π-0.120373\pi
432432 0 0
433433 −16.2803 + 16.2803i −0.782381 + 0.782381i −0.980232 0.197851i 0.936604π-0.936604\pi
0.197851 + 0.980232i 0.436604π0.436604\pi
434434 −9.32521 2.06455i −0.447625 0.0991016i
435435 0 0
436436 −13.2663 6.17696i −0.635343 0.295823i
437437 1.31695 + 1.31695i 0.0629981 + 0.0629981i
438438 0 0
439439 24.6554 1.17674 0.588368 0.808593i 0.299770π-0.299770\pi
0.588368 + 0.808593i 0.299770π0.299770\pi
440440 0 0
441441 0 0
442442 −15.8037 + 10.0744i −0.751706 + 0.479192i
443443 1.77116 + 1.77116i 0.0841501 + 0.0841501i 0.747929 0.663779i 0.231048π-0.231048\pi
−0.663779 + 0.747929i 0.731048π0.731048\pi
444444 0 0
445445 0 0
446446 −21.2218 4.69839i −1.00488 0.222475i
447447 0 0
448448 −3.44827 + 5.99634i −0.162916 + 0.283300i
449449 33.1512i 1.56450i 0.622963 + 0.782251i 0.285929π0.285929\pi
−0.622963 + 0.782251i 0.714071π0.714071\pi
450450 0 0
451451 28.3237i 1.33371i
452452 0.493326 + 1.35299i 0.0232041 + 0.0636394i
453453 0 0
454454 −2.15401 + 9.72928i −0.101093 + 0.456618i
455455 0 0
456456 0 0
457457 7.50479 + 7.50479i 0.351059 + 0.351059i 0.860504 0.509444i 0.170149π-0.170149\pi
−0.509444 + 0.860504i 0.670149π0.670149\pi
458458 19.5806 + 30.7159i 0.914939 + 1.43526i
459459 0 0
460460 0 0
461461 27.0216 1.25852 0.629262 0.777193i 0.283357π-0.283357\pi
0.629262 + 0.777193i 0.283357π0.283357\pi
462462 0 0
463463 −27.7123 27.7123i −1.28790 1.28790i −0.936059 0.351843i 0.885555π-0.885555\pi
−0.351843 0.936059i 0.614445π-0.614445\pi
464464 2.64687 2.22615i 0.122878 0.103347i
465465 0 0
466466 0.309251 1.39683i 0.0143258 0.0647070i
467467 −2.00823 + 2.00823i −0.0929296 + 0.0929296i −0.752043 0.659114i 0.770932π-0.770932\pi
0.659114 + 0.752043i 0.270932π0.270932\pi
468468 0 0
469469 7.58767i 0.350366i
470470 0 0
471471 0 0
472472 −0.196436 1.48225i −0.00904172 0.0682260i
473473 −31.8217 + 31.8217i −1.46317 + 1.46317i
474474 0 0
475475 0 0
476476 −3.88296 + 8.33950i −0.177975 + 0.382240i
477477 0 0
478478 −32.1210 + 20.4763i −1.46918 + 0.936562i
479479 13.7593 0.628678 0.314339 0.949311i 0.398217π-0.398217\pi
0.314339 + 0.949311i 0.398217π0.398217\pi
480480 0 0
481481 −6.20617 −0.282977
482482 −16.8055 + 10.7131i −0.765470 + 0.487966i
483483 0 0
484484 −12.9151 + 27.7379i −0.587049 + 1.26081i
485485 0 0
486486 0 0
487487 24.3355 24.3355i 1.10275 1.10275i 0.108671 0.994078i 0.465340π-0.465340\pi
0.994078 0.108671i 0.0346596π-0.0346596\pi
488488 1.85115 + 13.9682i 0.0837975 + 0.632310i
489489 0 0
490490 0 0
491491 28.8918i 1.30387i 0.758275 + 0.651935i 0.226043π0.226043\pi
−0.758275 + 0.651935i 0.773957π0.773957\pi
492492 0 0
493493 3.25240 3.25240i 0.146481 0.146481i
494494 0.931222 4.20617i 0.0418977 0.189244i
495495 0 0
496496 23.9109 20.1103i 1.07363 0.902979i
497497 −4.95377 4.95377i −0.222207 0.222207i
498498 0 0
499499 −12.5365 −0.561211 −0.280605 0.959823i 0.590535π-0.590535\pi
−0.280605 + 0.959823i 0.590535π0.590535\pi
500500 0 0
501501 0 0
502502 13.1112 + 20.5675i 0.585182 + 0.917972i
503503 −9.01392 9.01392i −0.401911 0.401911i 0.476995 0.878906i 0.341726π-0.341726\pi
−0.878906 + 0.476995i 0.841726π0.841726\pi
504504 0 0
505505 0 0
506506 2.38776 10.7851i 0.106149 0.479455i
507507 0 0
508508 7.25806 + 19.9059i 0.322025 + 0.883182i
509509 22.5448i 0.999279i 0.866233 + 0.499640i 0.166534π0.166534\pi
−0.866233 + 0.499640i 0.833466π0.833466\pi
510510 0 0
511511 2.75420i 0.121839i
512512 −8.71295 20.8826i −0.385062 0.922891i
513513 0 0
514514 29.3180 + 6.49084i 1.29316 + 0.286299i
515515 0 0
516516 0 0
517517 −11.7938 11.7938i −0.518692 0.518692i
518518 −2.56869 + 1.63747i −0.112862 + 0.0719464i
519519 0 0
520520 0 0
521521 18.9046 0.828226 0.414113 0.910225i 0.364092π-0.364092\pi
0.414113 + 0.910225i 0.364092π0.364092\pi
522522 0 0
523523 21.8269 + 21.8269i 0.954426 + 0.954426i 0.999006 0.0445800i 0.0141949π-0.0141949\pi
−0.0445800 + 0.999006i 0.514195π0.514195\pi
524524 25.3768 + 11.8157i 1.10859 + 0.516172i
525525 0 0
526526 13.1493 + 2.91118i 0.573337 + 0.126934i
527527 29.3810 29.3810i 1.27986 1.27986i
528528 0 0
529529 20.6801i 0.899136i
530530 0 0
531531 0 0
532532 −0.724353 1.98661i −0.0314047 0.0861303i
533533 9.72928 9.72928i 0.421422 0.421422i
534534 0 0
535535 0 0
536536 −19.7047 15.0931i −0.851114 0.651922i
537537 0 0
538538 19.5407 + 30.6533i 0.842457 + 1.32156i
539539 −32.0637 −1.38108
540540 0 0
541541 7.85838 0.337858 0.168929 0.985628i 0.445969π-0.445969\pi
0.168929 + 0.985628i 0.445969π0.445969\pi
542542 0.707913 + 1.11050i 0.0304075 + 0.0477000i
543543 0 0
544544 −13.9333 26.6724i −0.597387 1.14357i
545545 0 0
546546 0 0
547547 −17.8105 + 17.8105i −0.761522 + 0.761522i −0.976597 0.215076i 0.931000π-0.931000\pi
0.215076 + 0.976597i 0.431000π0.431000\pi
548548 18.6382 6.79582i 0.796183 0.290303i
549549 0 0
550550 0 0
551551 1.05727i 0.0450413i
552552 0 0
553553 −9.72928 + 9.72928i −0.413731 + 0.413731i
554554 −43.0773 9.53707i −1.83018 0.405191i
555555 0 0
556556 1.92482 4.13397i 0.0816307 0.175319i
557557 23.3372 + 23.3372i 0.988827 + 0.988827i 0.999938 0.0111112i 0.00353686π-0.00353686\pi
−0.0111112 + 0.999938i 0.503537π0.503537\pi
558558 0 0
559559 −21.8617 −0.924652
560560 0 0
561561 0 0
562562 10.2191 6.51439i 0.431067 0.274793i
563563 −5.27400 5.27400i −0.222273 0.222273i 0.587182 0.809455i 0.300237π-0.300237\pi
−0.809455 + 0.587182i 0.800237π0.800237\pi
564564 0 0
565565 0 0
566566 22.5939 + 5.00217i 0.949693 + 0.210257i
567567 0 0
568568 22.7185 3.01079i 0.953247 0.126330i
569569 28.5606i 1.19732i −0.801002 0.598661i 0.795699π-0.795699\pi
0.801002 0.598661i 0.204301π-0.204301\pi
570570 0 0
571571 32.2837i 1.35103i 0.737347 + 0.675515i 0.236078π0.236078\pi
−0.737347 + 0.675515i 0.763922π0.763922\pi
572572 −24.0051 + 8.75270i −1.00370 + 0.365969i
573573 0 0
574574 1.45986 6.59392i 0.0609333 0.275225i
575575 0 0
576576 0 0
577577 −27.0279 27.0279i −1.12519 1.12519i −0.990949 0.134237i 0.957142π-0.957142\pi
−0.134237 0.990949i 0.542858π-0.542858\pi
578578 −8.58919 13.4738i −0.357263 0.560437i
579579 0 0
580580 0 0
581581 9.72928 0.403639
582582 0 0
583583 −13.4677 13.4677i −0.557776 0.557776i
584584 7.15249 + 5.47855i 0.295972 + 0.226704i
585585 0 0
586586 −5.57560 + 25.1840i −0.230326 + 1.04034i
587587 17.1558 17.1558i 0.708096 0.708096i −0.258039 0.966135i 0.583076π-0.583076\pi
0.966135 + 0.258039i 0.0830761π0.0830761\pi
588588 0 0
589589 9.55102i 0.393543i
590590 0 0
591591 0 0
592592 0.857132 9.92794i 0.0352279 0.408036i
593593 −21.5833 + 21.5833i −0.886320 + 0.886320i −0.994167 0.107848i 0.965604π-0.965604\pi
0.107848 + 0.994167i 0.465604π0.465604\pi
594594 0 0
595595 0 0
596596 −18.3432 8.54079i −0.751366 0.349844i
597597 0 0
598598 4.52490 2.88450i 0.185037 0.117956i
599599 23.7636 0.970955 0.485478 0.874249i 0.338646π-0.338646\pi
0.485478 + 0.874249i 0.338646π0.338646\pi
600600 0 0
601601 22.1695 0.904314 0.452157 0.891938i 0.350655π-0.350655\pi
0.452157 + 0.891938i 0.350655π0.350655\pi
602602 −9.04843 + 5.76813i −0.368786 + 0.235091i
603603 0 0
604604 14.3904 + 6.70033i 0.585537 + 0.272633i
605605 0 0
606606 0 0
607607 −9.35348 + 9.35348i −0.379646 + 0.379646i −0.870974 0.491328i 0.836511π-0.836511\pi
0.491328 + 0.870974i 0.336511π0.336511\pi
608608 6.59995 + 2.07058i 0.267663 + 0.0839731i
609609 0 0
610610 0 0
611611 8.10243i 0.327789i
612612 0 0
613613 24.1247 24.1247i 0.974389 0.974389i −0.0252913 0.999680i 0.508051π-0.508051\pi
0.999680 + 0.0252913i 0.00805134π0.00805134\pi
614614 0.694151 3.13536i 0.0280137 0.126533i
615615 0 0
616616 −7.62620 + 9.95634i −0.307268 + 0.401152i
617617 3.82611 + 3.82611i 0.154033 + 0.154033i 0.779917 0.625883i 0.215261π-0.215261\pi
−0.625883 + 0.779917i 0.715261π0.715261\pi
618618 0 0
619619 30.1297 1.21101 0.605507 0.795840i 0.292971π-0.292971\pi
0.605507 + 0.795840i 0.292971π0.292971\pi
620620 0 0
621621 0 0
622622 14.7601 + 23.1541i 0.591826 + 0.928395i
623623 4.43407 + 4.43407i 0.177647 + 0.177647i
624624 0 0
625625 0 0
626626 7.65681 34.5845i 0.306028 1.38227i
627627 0 0
628628 −23.9528 + 8.73362i −0.955819 + 0.348509i
629629 13.2524i 0.528408i
630630 0 0
631631 21.5701i 0.858694i 0.903140 + 0.429347i 0.141256π0.141256\pi
−0.903140 + 0.429347i 0.858744π0.858744\pi
632632 −5.91324 44.6195i −0.235216 1.77487i
633633 0 0
634634 15.2106 + 3.36754i 0.604090 + 0.133742i
635635 0 0
636636 0 0
637637 −11.0140 11.0140i −0.436389 0.436389i
638638 5.28771 3.37077i 0.209342 0.133450i
639639 0 0
640640 0 0
641641 −48.3911 −1.91133 −0.955666 0.294452i 0.904863π-0.904863\pi
−0.955666 + 0.294452i 0.904863π0.904863\pi
642642 0 0
643643 23.3413 + 23.3413i 0.920491 + 0.920491i 0.997064 0.0765729i 0.0243978π-0.0243978\pi
−0.0765729 + 0.997064i 0.524398π0.524398\pi
644644 1.11177 2.38776i 0.0438097 0.0940907i
645645 0 0
646646 8.98168 + 1.98849i 0.353379 + 0.0782362i
647647 −32.4465 + 32.4465i −1.27560 + 1.27560i −0.332501 + 0.943103i 0.607892π0.607892\pi
−0.943103 + 0.332501i 0.892108π0.892108\pi
648648 0 0
649649 2.71096i 0.106414i
650650 0 0
651651 0 0
652652 −34.7704 + 12.6779i −1.36171 + 0.496506i
653653 18.4725 18.4725i 0.722885 0.722885i −0.246307 0.969192i 0.579217π-0.579217\pi
0.969192 + 0.246307i 0.0792170π0.0792170\pi
654654 0 0
655655 0 0
656656 14.2201 + 16.9075i 0.555202 + 0.660128i
657657 0 0
658658 −2.13779 3.35355i −0.0833399 0.130735i
659659 47.5028 1.85045 0.925223 0.379423i 0.123878π-0.123878\pi
0.925223 + 0.379423i 0.123878π0.123878\pi
660660 0 0
661661 −46.1204 −1.79387 −0.896937 0.442158i 0.854213π-0.854213\pi
−0.896937 + 0.442158i 0.854213π0.854213\pi
662662 24.0987 + 37.8035i 0.936621 + 1.46927i
663663 0 0
664664 −19.3531 + 25.2663i −0.751046 + 0.980525i
665665 0 0
666666 0 0
667667 −0.931222 + 0.931222i −0.0360571 + 0.0360571i
668668 −10.9810 30.1163i −0.424867 1.16524i
669669 0 0
670670 0 0
671671 25.5471i 0.986236i
672672 0 0
673673 −3.60599 + 3.60599i −0.139001 + 0.139001i −0.773183 0.634183i 0.781337π-0.781337\pi
0.634183 + 0.773183i 0.281337π0.281337\pi
674674 37.0300 + 8.19825i 1.42634 + 0.315785i
675675 0 0
676676 12.3179 + 5.73535i 0.473765 + 0.220590i
677677 −8.26635 8.26635i −0.317702 0.317702i 0.530182 0.847884i 0.322124π-0.322124\pi
−0.847884 + 0.530182i 0.822124π0.822124\pi
678678 0 0
679679 −0.970688 −0.0372516
680680 0 0
681681 0 0
682682 47.7673 30.4503i 1.82910 1.16600i
683683 −8.43079 8.43079i −0.322595 0.322595i 0.527167 0.849762i 0.323254π-0.323254\pi
−0.849762 + 0.527167i 0.823254π0.823254\pi
684684 0 0
685685 0 0
686686 −15.8217 3.50285i −0.604077 0.133739i
687687 0 0
688688 3.01932 34.9719i 0.115110 1.33329i
689689 9.25240i 0.352488i
690690 0 0
691691 21.9182i 0.833809i 0.908950 + 0.416905i 0.136885π0.136885\pi
−0.908950 + 0.416905i 0.863115π0.863115\pi
692692 −7.71993 21.1726i −0.293468 0.804862i
693693 0 0
694694 3.33733 15.0741i 0.126683 0.572206i
695695 0 0
696696 0 0
697697 20.7755 + 20.7755i 0.786929 + 0.786929i
698698 −20.5817 32.2864i −0.779029 1.22206i
699699 0 0
700700 0 0
701701 21.8184 0.824070 0.412035 0.911168i 0.364818π-0.364818\pi
0.412035 + 0.911168i 0.364818π0.364818\pi
702702 0 0
703703 2.15401 + 2.15401i 0.0812400 + 0.0812400i
704704 −10.6863 39.6095i −0.402754 1.49284i
705705 0 0
706706 4.30925 19.4641i 0.162181 0.732542i
707707 6.18549 6.18549i 0.232629 0.232629i
708708 0 0
709709 31.7938i 1.19404i −0.802225 0.597021i 0.796351π-0.796351\pi
0.802225 0.597021i 0.203649π-0.203649\pi
710710 0 0
711711 0 0
712712 −20.3351 + 2.69493i −0.762089 + 0.100997i
713713 −8.41233 + 8.41233i −0.315044 + 0.315044i
714714 0 0
715715 0 0
716716 −10.6770 + 22.9312i −0.399019 + 0.856979i
717717 0 0
718718 16.9736 10.8202i 0.633450 0.403807i
719719 −52.0874 −1.94253 −0.971265 0.237999i 0.923508π-0.923508\pi
−0.971265 + 0.237999i 0.923508π0.923508\pi
720720 0 0
721721 4.67432 0.174081
722722 20.8748 13.3071i 0.776879 0.495239i
723723 0 0
724724 6.52505 14.0140i 0.242502 0.520824i
725725 0 0
726726 0 0
727727 8.13069 8.13069i 0.301551 0.301551i −0.540070 0.841620i 0.681602π-0.681602\pi
0.841620 + 0.540070i 0.181602π0.181602\pi
728728 −6.03965 + 0.800411i −0.223844 + 0.0296652i
729729 0 0
730730 0 0
731731 46.6826i 1.72662i
732732 0 0
733733 29.9956 29.9956i 1.10791 1.10791i 0.114489 0.993424i 0.463477π-0.463477\pi
0.993424 0.114489i 0.0365232π-0.0365232\pi
734734 1.25003 5.64618i 0.0461396 0.208404i
735735 0 0
736736 3.98937 + 7.63682i 0.147050 + 0.281497i
737737 −31.8217 31.8217i −1.17217 1.17217i
738738 0 0
739739 −39.4719 −1.45200 −0.725999 0.687696i 0.758622π-0.758622\pi
−0.725999 + 0.687696i 0.758622π0.758622\pi
740740 0 0
741741 0 0
742742 −2.44121 3.82951i −0.0896196 0.140586i
743743 12.2252 + 12.2252i 0.448499 + 0.448499i 0.894855 0.446356i 0.147279π-0.147279\pi
−0.446356 + 0.894855i 0.647279π0.647279\pi
744744 0 0
745745 0 0
746746 −4.87859 + 22.0358i −0.178618 + 0.806786i
747747 0 0
748748 −18.6902 51.2595i −0.683380 1.87423i
749749 6.73887i 0.246233i
750750 0 0
751751 28.9069i 1.05483i −0.849609 0.527413i 0.823162π-0.823162\pi
0.849609 0.527413i 0.176838π-0.176838\pi
752752 12.9614 + 1.11902i 0.472652 + 0.0408066i
753753 0 0
754754 2.97421 + 0.658473i 0.108314 + 0.0239802i
755755 0 0
756756 0 0
757757 16.2018 + 16.2018i 0.588864 + 0.588864i 0.937324 0.348459i 0.113295π-0.113295\pi
−0.348459 + 0.937324i 0.613295π0.613295\pi
758758 −18.4318 + 11.7498i −0.669474 + 0.426771i
759759 0 0
760760 0 0
761761 6.64641 0.240932 0.120466 0.992717i 0.461561π-0.461561\pi
0.120466 + 0.992717i 0.461561π0.461561\pi
762762 0 0
763763 −4.47353 4.47353i −0.161953 0.161953i
764764 12.7736 + 5.94751i 0.462131 + 0.215173i
765765 0 0
766766 −24.5187 5.42831i −0.885898 0.196133i
767767 0.931222 0.931222i 0.0336245 0.0336245i
768768 0 0
769769 29.3449i 1.05820i 0.848559 + 0.529101i 0.177471π0.177471\pi
−0.848559 + 0.529101i 0.822529π0.822529\pi
770770 0 0
771771 0 0
772772 −11.1470 30.5717i −0.401189 1.10030i
773773 37.5833 37.5833i 1.35178 1.35178i 0.468104 0.883674i 0.344937π-0.344937\pi
0.883674 0.468104i 0.155063π-0.155063\pi
774774 0 0
775775 0 0
776776 1.93086 2.52082i 0.0693137 0.0904921i
777777 0 0
778778 −3.92510 6.15729i −0.140722 0.220749i
779779 −6.75359 −0.241973
780780 0 0
781781 41.5510 1.48681
782782 6.15945 + 9.66229i 0.220261 + 0.345523i
783783 0 0
784784 19.1400 16.0978i 0.683573 0.574920i
785785 0 0
786786 0 0
787787 7.59353 7.59353i 0.270680 0.270680i −0.558694 0.829374i 0.688697π-0.688697\pi
0.829374 + 0.558694i 0.188697π0.188697\pi
788788 20.9358 7.63357i 0.745806 0.271935i
789789 0 0
790790 0 0
791791 0.622595i 0.0221369i
792792 0 0
793793 −8.77551 + 8.77551i −0.311628 + 0.311628i
794794 −6.76212 1.49710i −0.239979 0.0531300i
795795 0 0
796796 9.69075 20.8130i 0.343479 0.737696i
797797 27.4908 + 27.4908i 0.973775 + 0.973775i 0.999665 0.0258893i 0.00824175π-0.00824175\pi
−0.0258893 + 0.999665i 0.508242π0.508242\pi
798798 0 0
799799 17.3016 0.612086
800800 0 0
801801 0 0
802802 4.16810 2.65705i 0.147181 0.0938237i
803803 11.5508 + 11.5508i 0.407618 + 0.407618i
804804 0 0
805805 0 0
806806 26.8680 + 5.94842i 0.946384 + 0.209524i
807807 0 0
808808 3.75940 + 28.3673i 0.132255 + 0.997957i
809809 47.7205i 1.67776i 0.544313 + 0.838882i 0.316791π0.316791\pi
−0.544313 + 0.838882i 0.683209π0.683209\pi
810810 0 0
811811 37.3179i 1.31041i 0.755451 + 0.655205i 0.227418π0.227418\pi
−0.755451 + 0.655205i 0.772582π0.772582\pi
812812 1.40474 0.512195i 0.0492968 0.0179745i
813813 0 0
814814 3.90543 17.6402i 0.136885 0.618287i
815815 0 0
816816 0 0
817817 7.58767 + 7.58767i 0.265459 + 0.265459i
818818 11.2535 + 17.6533i 0.393470 + 0.617235i
819819 0 0
820820 0 0
821821 0.686380 0.0239548 0.0119774 0.999928i 0.496187π-0.496187\pi
0.0119774 + 0.999928i 0.496187π0.496187\pi
822822 0 0
823823 27.2553 + 27.2553i 0.950059 + 0.950059i 0.998811 0.0487521i 0.0155244π-0.0155244\pi
−0.0487521 + 0.998811i 0.515524π0.515524\pi
824824 −9.29797 + 12.1389i −0.323910 + 0.422879i
825825 0 0
826826 0.139728 0.631126i 0.00486175 0.0219597i
827827 −31.4437 + 31.4437i −1.09341 + 1.09341i −0.0982432 + 0.995162i 0.531322π0.531322\pi
−0.995162 + 0.0982432i 0.968678π0.968678\pi
828828 0 0
829829 0.270718i 0.00940243i −0.999989 0.00470122i 0.998504π-0.998504\pi
0.999989 0.00470122i 0.00149645π-0.00149645\pi
830830 0 0
831831 0 0
832832 9.93522 17.2767i 0.344442 0.598964i
833833 23.5187 23.5187i 0.814876 0.814876i
834834 0 0
835835 0 0
836836 11.3694 + 5.29373i 0.393220 + 0.183088i
837837 0 0
838838 −22.7414 + 14.4970i −0.785589 + 0.500792i
839839 −31.0214 −1.07098 −0.535489 0.844542i 0.679873π-0.679873\pi
−0.535489 + 0.844542i 0.679873π0.679873\pi
840840 0 0
841841 28.2524 0.974221
842842 24.8085 15.8147i 0.854956 0.545011i
843843 0 0
844844 −9.95634 4.63578i −0.342711 0.159570i
845845 0 0
846846 0 0
847847 −9.35348 + 9.35348i −0.321389 + 0.321389i
848848 14.8010 + 1.27785i 0.508267 + 0.0438814i
849849 0 0
850850 0 0
851851 3.79441i 0.130071i
852852 0 0
853853 −3.82611 + 3.82611i −0.131003 + 0.131003i −0.769568 0.638565i 0.779528π-0.779528\pi
0.638565 + 0.769568i 0.279528π0.279528\pi
854854 −1.31675 + 5.94751i −0.0450581 + 0.203520i
855855 0 0
856856 −17.5004 13.4047i −0.598152 0.458163i
857857 20.7711 + 20.7711i 0.709529 + 0.709529i 0.966436 0.256907i 0.0827035π-0.0827035\pi
−0.256907 + 0.966436i 0.582704π0.582704\pi
858858 0 0
859859 1.69693 0.0578985 0.0289492 0.999581i 0.490784π-0.490784\pi
0.0289492 + 0.999581i 0.490784π0.490784\pi
860860 0 0
861861 0 0
862862 11.6540 + 18.2815i 0.396935 + 0.622670i
863863 5.92869 + 5.92869i 0.201815 + 0.201815i 0.800777 0.598962i 0.204420π-0.204420\pi
−0.598962 + 0.800777i 0.704420π0.704420\pi
864864 0 0
865865 0 0
866866 7.03831 31.7908i 0.239171 1.08030i
867867 0 0
868868 12.6900 4.62699i 0.430725 0.157050i
869869 81.6068i 2.76832i
870870 0 0
871871 21.8617i 0.740756i
872872 20.5161 2.71891i 0.694762 0.0920740i
873873 0 0
874874 −2.57162 0.569343i −0.0869865 0.0192583i
875875 0 0
876876 0 0
877877 10.0323 + 10.0323i 0.338766 + 0.338766i 0.855903 0.517137i 0.173002π-0.173002\pi
−0.517137 + 0.855903i 0.673002π0.673002\pi
878878 −29.4020 + 18.7430i −0.992269 + 0.632544i
879879 0 0
880880 0 0
881881 29.8130 1.00443 0.502213 0.864744i 0.332519π-0.332519\pi
0.502213 + 0.864744i 0.332519π0.332519\pi
882882 0 0
883883 5.56557 + 5.56557i 0.187296 + 0.187296i 0.794526 0.607230i 0.207719π-0.207719\pi
−0.607230 + 0.794526i 0.707719π0.707719\pi
884884 11.1877 24.0279i 0.376282 0.808146i
885885 0 0
886886 −3.45856 0.765707i −0.116193 0.0257244i
887887 8.59630 8.59630i 0.288636 0.288636i −0.547905 0.836541i 0.684574π-0.684574\pi
0.836541 + 0.547905i 0.184574π0.184574\pi
888888 0 0
889889 9.15994i 0.307214i
890890 0 0
891891 0 0
892892 28.8791 10.5298i 0.966943 0.352565i
893893 −2.81215 + 2.81215i −0.0941052 + 0.0941052i
894894 0 0
895895 0 0
896896 −0.446274 9.77211i −0.0149090 0.326463i
897897 0 0
898898 −25.2015 39.5334i −0.840984 1.31925i
899899 −6.75359 −0.225245
900900 0 0
901901 19.7572 0.658207
902902 21.5316 + 33.7766i 0.716925 + 1.12464i
903903 0 0
904904 −1.61684 1.23844i −0.0537754 0.0411900i
905905 0 0
906906 0 0
907907 −31.6263 + 31.6263i −1.05013 + 1.05013i −0.0514592 + 0.998675i 0.516387π0.516387\pi
−0.998675 + 0.0514592i 0.983613π0.983613\pi
908908 −4.82748 13.2398i −0.160206 0.439379i
909909 0 0
910910 0 0
911911 42.2656i 1.40032i 0.713985 + 0.700161i 0.246888π0.246888\pi
−0.713985 + 0.700161i 0.753112π0.753112\pi
912912 0 0
913913 −40.8034 + 40.8034i −1.35040 + 1.35040i
914914 −14.6547 3.24448i −0.484735 0.107318i
915915 0 0
916916 −46.7003 21.7442i −1.54302 0.718448i
917917 8.55728 + 8.55728i 0.282586 + 0.282586i
918918 0 0
919919 −31.2829 −1.03193 −0.515964 0.856610i 0.672566π-0.672566\pi
−0.515964 + 0.856610i 0.672566π0.672566\pi
920920 0 0
921921 0 0
922922 −32.2238 + 20.5418i −1.06123 + 0.676508i
923923 14.2729 + 14.2729i 0.469798 + 0.469798i
924924 0 0
925925 0 0
926926 54.1143 + 11.9806i 1.77831 + 0.393707i
927927 0 0
928928 −1.46412 + 4.66687i −0.0480621 + 0.153198i
929929 22.1050i 0.725241i −0.931937 0.362620i 0.881882π-0.881882\pi
0.931937 0.362620i 0.118118π-0.118118\pi
930930 0 0
931931 7.64535i 0.250566i
932932 0.693082 + 1.90084i 0.0227026 + 0.0622641i
933933 0 0
934934 0.868197 3.92150i 0.0284083 0.128315i
935935 0 0
936936 0 0
937937 15.2986 + 15.2986i 0.499784 + 0.499784i 0.911371 0.411586i 0.135025π-0.135025\pi
−0.411586 + 0.911371i 0.635025π0.635025\pi
938938 −5.76813 9.04843i −0.188336 0.295442i
939939 0 0
940940 0 0
941941 −25.5264 −0.832138 −0.416069 0.909333i 0.636593π-0.636593\pi
−0.416069 + 0.909333i 0.636593π0.636593\pi
942942 0 0
943943 −5.94842 5.94842i −0.193707 0.193707i
944944 1.36106 + 1.61828i 0.0442986 + 0.0526704i
945945 0 0
946946 13.7572 62.1388i 0.447285 2.02031i
947947 11.9881 11.9881i 0.389562 0.389562i −0.484969 0.874531i 0.661169π-0.661169\pi
0.874531 + 0.484969i 0.161169π0.161169\pi
948948 0 0
949949 7.93545i 0.257596i
950950 0 0
951951 0 0
952952 −1.70916 12.8968i −0.0553943 0.417988i
953953 5.99563 5.99563i 0.194218 0.194218i −0.603298 0.797516i 0.706147π-0.706147\pi
0.797516 + 0.603298i 0.206147π0.206147\pi
954954 0 0
955955 0 0
956956 22.7389 48.8366i 0.735427 1.57949i
957957 0 0
958958 −16.4082 + 10.4598i −0.530125 + 0.337940i
959959 8.57657 0.276952
960960 0 0
961961 −30.0096 −0.968051
962962 7.40097 4.71791i 0.238617 0.152112i
963963 0 0
964964 11.8968 25.5510i 0.383171 0.822943i
965965 0 0
966966 0 0
967967 1.66866 1.66866i 0.0536606 0.0536606i −0.679767 0.733428i 0.737919π-0.737919\pi
0.733428 + 0.679767i 0.237919π0.237919\pi
968968 −5.68483 42.8960i −0.182717 1.37873i
969969 0 0
970970 0 0
971971 4.79719i 0.153949i −0.997033 0.0769745i 0.975474π-0.975474\pi
0.997033 0.0769745i 0.0245260π-0.0245260\pi
972972 0 0
973973 1.39401 1.39401i 0.0446900 0.0446900i
974974 −10.5208 + 47.5204i −0.337107 + 1.52265i
975975 0 0
976976 −12.8261 15.2501i −0.410554 0.488143i
977977 −25.0140 25.0140i −0.800267 0.800267i 0.182870 0.983137i 0.441461π-0.441461\pi
−0.983137 + 0.182870i 0.941461π0.941461\pi
978978 0 0
979979 −37.1919 −1.18866
980980 0 0
981981 0 0
982982 −21.9635 34.4540i −0.700884 1.09947i
983983 −30.9151 30.9151i −0.986038 0.986038i 0.0138655 0.999904i 0.495586π-0.495586\pi
−0.999904 + 0.0138655i 0.995586π0.995586\pi
984984 0 0
985985 0 0
986986 −1.40608 + 6.35101i −0.0447786 + 0.202257i
987987 0 0
988988 2.08702 + 5.72384i 0.0663969 + 0.182100i
989989 13.3661i 0.425017i
990990 0 0
991991 26.5873i 0.844575i −0.906462 0.422287i 0.861227π-0.861227\pi
0.906462 0.422287i 0.138773π-0.138773\pi
992992 −13.2264 + 42.1589i −0.419937 + 1.33855i
993993 0 0
994994 9.67331 + 2.14162i 0.306819 + 0.0679280i
995995 0 0
996996 0 0
997997 2.47252 + 2.47252i 0.0783054 + 0.0783054i 0.745175 0.666869i 0.232366π-0.232366\pi
−0.666869 + 0.745175i 0.732366π0.732366\pi
998998 14.9500 9.53021i 0.473234 0.301674i
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 900.2.k.n.307.2 12
3.2 odd 2 300.2.j.d.7.5 12
4.3 odd 2 inner 900.2.k.n.307.5 12
5.2 odd 4 180.2.k.e.163.2 12
5.3 odd 4 inner 900.2.k.n.343.5 12
5.4 even 2 180.2.k.e.127.5 12
12.11 even 2 300.2.j.d.7.2 12
15.2 even 4 60.2.j.a.43.5 yes 12
15.8 even 4 300.2.j.d.43.2 12
15.14 odd 2 60.2.j.a.7.2 12
20.3 even 4 inner 900.2.k.n.343.2 12
20.7 even 4 180.2.k.e.163.5 12
20.19 odd 2 180.2.k.e.127.2 12
60.23 odd 4 300.2.j.d.43.5 12
60.47 odd 4 60.2.j.a.43.2 yes 12
60.59 even 2 60.2.j.a.7.5 yes 12
120.29 odd 2 960.2.w.g.127.2 12
120.59 even 2 960.2.w.g.127.5 12
120.77 even 4 960.2.w.g.703.5 12
120.107 odd 4 960.2.w.g.703.2 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
60.2.j.a.7.2 12 15.14 odd 2
60.2.j.a.7.5 yes 12 60.59 even 2
60.2.j.a.43.2 yes 12 60.47 odd 4
60.2.j.a.43.5 yes 12 15.2 even 4
180.2.k.e.127.2 12 20.19 odd 2
180.2.k.e.127.5 12 5.4 even 2
180.2.k.e.163.2 12 5.2 odd 4
180.2.k.e.163.5 12 20.7 even 4
300.2.j.d.7.2 12 12.11 even 2
300.2.j.d.7.5 12 3.2 odd 2
300.2.j.d.43.2 12 15.8 even 4
300.2.j.d.43.5 12 60.23 odd 4
900.2.k.n.307.2 12 1.1 even 1 trivial
900.2.k.n.307.5 12 4.3 odd 2 inner
900.2.k.n.343.2 12 20.3 even 4 inner
900.2.k.n.343.5 12 5.3 odd 4 inner
960.2.w.g.127.2 12 120.29 odd 2
960.2.w.g.127.5 12 120.59 even 2
960.2.w.g.703.2 12 120.107 odd 4
960.2.w.g.703.5 12 120.77 even 4