Properties

Label 1008.2.q.k.529.2
Level 10081008
Weight 22
Character 1008.529
Analytic conductor 8.0498.049
Analytic rank 00
Dimension 2222
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1008,2,Mod(529,1008)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1008.529");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1008=24327 1008 = 2^{4} \cdot 3^{2} \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1008.q (of order 33, degree 22, 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: 8.048920523758.04892052375
Analytic rank: 00
Dimension: 2222
Relative dimension: 1111 over Q(ζ3)\Q(\zeta_{3})
Twist minimal: no (minimal twist has level 504)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 529.2
Character χ\chi == 1008.529
Dual form 1008.2.q.k.625.2

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+(1.579010.711841i)q3+(1.92048+3.32636i)q5+(2.553360.693065i)q7+(1.98656+2.24801i)q9+(0.903316+1.56459i)q11+(0.6927131.19981i)q13+(5.400303.88530i)q15+(0.833405+1.44350i)q17+(0.0802084+0.138925i)q19+(4.525150.723229i)q21+(1.600192.77161i)q23+(4.876468.44627i)q25+(1.536584.96376i)q27+(3.78000+6.54716i)q293.22021q31+(0.3126093.11352i)q33+(2.59829+9.82442i)q35+(1.58395+2.74348i)q37+(0.239726+2.38762i)q39+(6.00329+10.3980i)q41+(3.45480+5.98389i)q43+(11.2929+2.29078i)q4511.4384q47+(6.039323.53929i)q49+(2.343501.68605i)q51+(1.374502.38071i)q536.93918q55+(0.02775760.276460i)q5715.0705q599.20285q61+(6.63044+4.36317i)q63+5.32136q65+12.3366q67+(4.49967+3.23733i)q69+6.93289q71+(6.22457+10.7813i)q73+(1.68759+16.8080i)q75+(3.39085+3.36891i)q7716.0743q79+(1.10712+8.93165i)q81+(1.452802.51633i)q83+(3.201075.54441i)q85+(10.62927.64729i)q87+(5.04034+8.73012i)q89+(2.600302.58347i)q91+(5.08476+2.29228i)q930.616153q95+(4.188307.25435i)q97+(1.72272+5.13882i)q99+O(q100)q+(-1.57901 - 0.711841i) q^{3} +(-1.92048 + 3.32636i) q^{5} +(2.55336 - 0.693065i) q^{7} +(1.98656 + 2.24801i) q^{9} +(0.903316 + 1.56459i) q^{11} +(-0.692713 - 1.19981i) q^{13} +(5.40030 - 3.88530i) q^{15} +(-0.833405 + 1.44350i) q^{17} +(0.0802084 + 0.138925i) q^{19} +(-4.52515 - 0.723229i) q^{21} +(1.60019 - 2.77161i) q^{23} +(-4.87646 - 8.44627i) q^{25} +(-1.53658 - 4.96376i) q^{27} +(-3.78000 + 6.54716i) q^{29} -3.22021 q^{31} +(-0.312609 - 3.11352i) q^{33} +(-2.59829 + 9.82442i) q^{35} +(1.58395 + 2.74348i) q^{37} +(0.239726 + 2.38762i) q^{39} +(6.00329 + 10.3980i) q^{41} +(-3.45480 + 5.98389i) q^{43} +(-11.2929 + 2.29078i) q^{45} -11.4384 q^{47} +(6.03932 - 3.53929i) q^{49} +(2.34350 - 1.68605i) q^{51} +(1.37450 - 2.38071i) q^{53} -6.93918 q^{55} +(-0.0277576 - 0.276460i) q^{57} -15.0705 q^{59} -9.20285 q^{61} +(6.63044 + 4.36317i) q^{63} +5.32136 q^{65} +12.3366 q^{67} +(-4.49967 + 3.23733i) q^{69} +6.93289 q^{71} +(-6.22457 + 10.7813i) q^{73} +(1.68759 + 16.8080i) q^{75} +(3.39085 + 3.36891i) q^{77} -16.0743 q^{79} +(-1.10712 + 8.93165i) q^{81} +(1.45280 - 2.51633i) q^{83} +(-3.20107 - 5.54441i) q^{85} +(10.6292 - 7.64729i) q^{87} +(5.04034 + 8.73012i) q^{89} +(-2.60030 - 2.58347i) q^{91} +(5.08476 + 2.29228i) q^{93} -0.616153 q^{95} +(4.18830 - 7.25435i) q^{97} +(-1.72272 + 5.13882i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 22q2q3+3q5+5q7+10q9+3q113q13+q15+7q17+q192q2310q25+4q27+9q298q31+29q3314q35+2q37+16q39++56q99+O(q100) 22 q - 2 q^{3} + 3 q^{5} + 5 q^{7} + 10 q^{9} + 3 q^{11} - 3 q^{13} + q^{15} + 7 q^{17} + q^{19} - 2 q^{23} - 10 q^{25} + 4 q^{27} + 9 q^{29} - 8 q^{31} + 29 q^{33} - 14 q^{35} + 2 q^{37} + 16 q^{39}+ \cdots + 56 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1008Z)×\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times.

nn 127127 577577 757757 785785
χ(n)\chi(n) 11 e(23)e\left(\frac{2}{3}\right) 11 e(23)e\left(\frac{2}{3}\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 −1.57901 0.711841i −0.911644 0.410982i
44 0 0
55 −1.92048 + 3.32636i −0.858863 + 1.48759i 0.0141515 + 0.999900i 0.495495π0.495495\pi
−0.873014 + 0.487694i 0.837838π0.837838\pi
66 0 0
77 2.55336 0.693065i 0.965080 0.261954i
88 0 0
99 1.98656 + 2.24801i 0.662188 + 0.749337i
1010 0 0
1111 0.903316 + 1.56459i 0.272360 + 0.471741i 0.969466 0.245227i 0.0788625π-0.0788625\pi
−0.697106 + 0.716968i 0.745529π0.745529\pi
1212 0 0
1313 −0.692713 1.19981i −0.192124 0.332769i 0.753830 0.657070i 0.228204π-0.228204\pi
−0.945954 + 0.324301i 0.894871π0.894871\pi
1414 0 0
1515 5.40030 3.88530i 1.39435 1.00318i
1616 0 0
1717 −0.833405 + 1.44350i −0.202130 + 0.350100i −0.949215 0.314629i 0.898120π-0.898120\pi
0.747084 + 0.664729i 0.231453π0.231453\pi
1818 0 0
1919 0.0802084 + 0.138925i 0.0184011 + 0.0318716i 0.875079 0.483980i 0.160809π-0.160809\pi
−0.856678 + 0.515851i 0.827476π0.827476\pi
2020 0 0
2121 −4.52515 0.723229i −0.987468 0.157822i
2222 0 0
2323 1.60019 2.77161i 0.333663 0.577921i −0.649564 0.760307i 0.725049π-0.725049\pi
0.983227 + 0.182386i 0.0583819π0.0583819\pi
2424 0 0
2525 −4.87646 8.44627i −0.975291 1.68925i
2626 0 0
2727 −1.53658 4.96376i −0.295716 0.955276i
2828 0 0
2929 −3.78000 + 6.54716i −0.701929 + 1.21578i 0.265859 + 0.964012i 0.414344π0.414344\pi
−0.967788 + 0.251765i 0.918989π0.918989\pi
3030 0 0
3131 −3.22021 −0.578367 −0.289184 0.957274i 0.593384π-0.593384\pi
−0.289184 + 0.957274i 0.593384π0.593384\pi
3232 0 0
3333 −0.312609 3.11352i −0.0544182 0.541995i
3434 0 0
3535 −2.59829 + 9.82442i −0.439190 + 1.66063i
3636 0 0
3737 1.58395 + 2.74348i 0.260399 + 0.451025i 0.966348 0.257238i 0.0828124π-0.0828124\pi
−0.705949 + 0.708263i 0.749479π0.749479\pi
3838 0 0
3939 0.239726 + 2.38762i 0.0383869 + 0.382326i
4040 0 0
4141 6.00329 + 10.3980i 0.937556 + 1.62389i 0.770011 + 0.638030i 0.220250π0.220250\pi
0.167545 + 0.985864i 0.446416π0.446416\pi
4242 0 0
4343 −3.45480 + 5.98389i −0.526852 + 0.912535i 0.472658 + 0.881246i 0.343295π0.343295\pi
−0.999510 + 0.0312891i 0.990039π0.990039\pi
4444 0 0
4545 −11.2929 + 2.29078i −1.68344 + 0.341489i
4646 0 0
4747 −11.4384 −1.66846 −0.834232 0.551414i 0.814089π-0.814089\pi
−0.834232 + 0.551414i 0.814089π0.814089\pi
4848 0 0
4949 6.03932 3.53929i 0.862760 0.505613i
5050 0 0
5151 2.34350 1.68605i 0.328156 0.236095i
5252 0 0
5353 1.37450 2.38071i 0.188802 0.327015i −0.756049 0.654515i 0.772873π-0.772873\pi
0.944851 + 0.327500i 0.106206π0.106206\pi
5454 0 0
5555 −6.93918 −0.935679
5656 0 0
5757 −0.0277576 0.276460i −0.00367658 0.0366180i
5858 0 0
5959 −15.0705 −1.96202 −0.981009 0.193964i 0.937866π-0.937866\pi
−0.981009 + 0.193964i 0.937866π0.937866\pi
6060 0 0
6161 −9.20285 −1.17830 −0.589152 0.808022i 0.700538π-0.700538\pi
−0.589152 + 0.808022i 0.700538π0.700538\pi
6262 0 0
6363 6.63044 + 4.36317i 0.835357 + 0.549708i
6464 0 0
6565 5.32136 0.660033
6666 0 0
6767 12.3366 1.50716 0.753578 0.657359i 0.228326π-0.228326\pi
0.753578 + 0.657359i 0.228326π0.228326\pi
6868 0 0
6969 −4.49967 + 3.23733i −0.541697 + 0.389729i
7070 0 0
7171 6.93289 0.822783 0.411391 0.911459i 0.365043π-0.365043\pi
0.411391 + 0.911459i 0.365043π0.365043\pi
7272 0 0
7373 −6.22457 + 10.7813i −0.728531 + 1.26185i 0.228973 + 0.973433i 0.426463π0.426463\pi
−0.957504 + 0.288420i 0.906870π0.906870\pi
7474 0 0
7575 1.68759 + 16.8080i 0.194866 + 1.94082i
7676 0 0
7777 3.39085 + 3.36891i 0.386424 + 0.383922i
7878 0 0
7979 −16.0743 −1.80850 −0.904251 0.427001i 0.859570π-0.859570\pi
−0.904251 + 0.427001i 0.859570π0.859570\pi
8080 0 0
8181 −1.10712 + 8.93165i −0.123013 + 0.992405i
8282 0 0
8383 1.45280 2.51633i 0.159466 0.276203i −0.775210 0.631703i 0.782356π-0.782356\pi
0.934676 + 0.355500i 0.115689π0.115689\pi
8484 0 0
8585 −3.20107 5.54441i −0.347205 0.601376i
8686 0 0
8787 10.6292 7.64729i 1.13957 0.819875i
8888 0 0
8989 5.04034 + 8.73012i 0.534275 + 0.925391i 0.999198 + 0.0400399i 0.0127485π0.0127485\pi
−0.464923 + 0.885351i 0.653918π0.653918\pi
9090 0 0
9191 −2.60030 2.58347i −0.272585 0.270821i
9292 0 0
9393 5.08476 + 2.29228i 0.527265 + 0.237698i
9494 0 0
9595 −0.616153 −0.0632160
9696 0 0
9797 4.18830 7.25435i 0.425257 0.736567i −0.571187 0.820820i 0.693517π-0.693517\pi
0.996444 + 0.0842527i 0.0268503π0.0268503\pi
9898 0 0
9999 −1.72272 + 5.13882i −0.173140 + 0.516471i
100100 0 0
101101 −4.05750 7.02780i −0.403736 0.699292i 0.590437 0.807084i 0.298955π-0.298955\pi
−0.994173 + 0.107792i 0.965622π0.965622\pi
102102 0 0
103103 −3.76891 + 6.52794i −0.371362 + 0.643217i −0.989775 0.142635i 0.954442π-0.954442\pi
0.618414 + 0.785853i 0.287776π0.287776\pi
104104 0 0
105105 11.0962 13.6633i 1.08287 1.33340i
106106 0 0
107107 2.95731 + 5.12221i 0.285894 + 0.495183i 0.972826 0.231539i 0.0743762π-0.0743762\pi
−0.686932 + 0.726722i 0.741043π0.741043\pi
108108 0 0
109109 −4.48409 + 7.76668i −0.429498 + 0.743913i −0.996829 0.0795776i 0.974643π-0.974643\pi
0.567331 + 0.823490i 0.307976π0.307976\pi
110110 0 0
111111 −0.548154 5.45951i −0.0520285 0.518193i
112112 0 0
113113 −7.98131 13.8240i −0.750819 1.30046i −0.947426 0.319974i 0.896326π-0.896326\pi
0.196608 0.980482i 0.437007π-0.437007\pi
114114 0 0
115115 6.14626 + 10.6456i 0.573142 + 0.992710i
116116 0 0
117117 1.32108 3.94074i 0.122134 0.364321i
118118 0 0
119119 −1.12755 + 4.26338i −0.103362 + 0.390824i
120120 0 0
121121 3.86804 6.69964i 0.351640 0.609059i
122122 0 0
123123 −2.07755 20.6920i −0.187326 1.86573i
124124 0 0
125125 18.2557 1.63284
126126 0 0
127127 −8.60913 −0.763937 −0.381968 0.924175i 0.624754π-0.624754\pi
−0.381968 + 0.924175i 0.624754π0.624754\pi
128128 0 0
129129 9.71476 6.98937i 0.855337 0.615380i
130130 0 0
131131 −0.964831 + 1.67114i −0.0842976 + 0.146008i −0.905092 0.425216i 0.860198π-0.860198\pi
0.820794 + 0.571224i 0.193531π0.193531\pi
132132 0 0
133133 0.301085 + 0.299136i 0.0261074 + 0.0259384i
134134 0 0
135135 19.4622 + 4.42154i 1.67504 + 0.380546i
136136 0 0
137137 1.85442 + 3.21195i 0.158434 + 0.274416i 0.934304 0.356477i 0.116022π-0.116022\pi
−0.775870 + 0.630893i 0.782689π0.782689\pi
138138 0 0
139139 −0.134568 0.233079i −0.0114139 0.0197695i 0.860262 0.509852i 0.170300π-0.170300\pi
−0.871676 + 0.490083i 0.836967π0.836967\pi
140140 0 0
141141 18.0614 + 8.14233i 1.52104 + 0.685708i
142142 0 0
143143 1.25148 2.16762i 0.104654 0.181266i
144144 0 0
145145 −14.5188 25.1473i −1.20572 2.08837i
146146 0 0
147147 −12.0556 + 1.28955i −0.994328 + 0.106361i
148148 0 0
149149 −4.15880 + 7.20325i −0.340702 + 0.590113i −0.984563 0.175029i 0.943998π-0.943998\pi
0.643861 + 0.765142i 0.277331π0.277331\pi
150150 0 0
151151 4.87069 + 8.43628i 0.396371 + 0.686535i 0.993275 0.115778i 0.0369360π-0.0369360\pi
−0.596904 + 0.802313i 0.703603π0.703603\pi
152152 0 0
153153 −4.90062 + 0.994101i −0.396192 + 0.0803683i
154154 0 0
155155 6.18434 10.7116i 0.496738 0.860376i
156156 0 0
157157 24.2580 1.93600 0.968001 0.250947i 0.0807420π-0.0807420\pi
0.968001 + 0.250947i 0.0807420π0.0807420\pi
158158 0 0
159159 −3.86504 + 2.78074i −0.306518 + 0.220527i
160160 0 0
161161 2.16496 8.18597i 0.170623 0.645145i
162162 0 0
163163 −3.91401 6.77927i −0.306569 0.530993i 0.671040 0.741421i 0.265848π-0.265848\pi
−0.977609 + 0.210428i 0.932514π0.932514\pi
164164 0 0
165165 10.9571 + 4.93960i 0.853006 + 0.384547i
166166 0 0
167167 2.15395 + 3.73076i 0.166678 + 0.288695i 0.937250 0.348658i 0.113363π-0.113363\pi
−0.770572 + 0.637353i 0.780029π0.780029\pi
168168 0 0
169169 5.54030 9.59608i 0.426177 0.738160i
170170 0 0
171171 −0.152966 + 0.456293i −0.0116976 + 0.0348936i
172172 0 0
173173 −17.3359 −1.31803 −0.659014 0.752131i 0.729026π-0.729026\pi
−0.659014 + 0.752131i 0.729026π0.729026\pi
174174 0 0
175175 −18.3052 18.1867i −1.38374 1.37478i
176176 0 0
177177 23.7966 + 10.7278i 1.78866 + 0.806353i
178178 0 0
179179 9.68644 16.7774i 0.723998 1.25400i −0.235387 0.971902i 0.575636π-0.575636\pi
0.959385 0.282100i 0.0910310π-0.0910310\pi
180180 0 0
181181 2.89036 0.214839 0.107420 0.994214i 0.465741π-0.465741\pi
0.107420 + 0.994214i 0.465741π0.465741\pi
182182 0 0
183183 14.5314 + 6.55097i 1.07419 + 0.484261i
184184 0 0
185185 −12.1677 −0.894590
186186 0 0
187187 −3.01131 −0.220209
188188 0 0
189189 −7.36367 11.6093i −0.535628 0.844454i
190190 0 0
191191 −3.70044 −0.267755 −0.133877 0.990998i 0.542743π-0.542743\pi
−0.133877 + 0.990998i 0.542743π0.542743\pi
192192 0 0
193193 −12.7670 −0.918991 −0.459495 0.888180i 0.651970π-0.651970\pi
−0.459495 + 0.888180i 0.651970π0.651970\pi
194194 0 0
195195 −8.40249 3.78796i −0.601715 0.271261i
196196 0 0
197197 2.44715 0.174352 0.0871762 0.996193i 0.472216π-0.472216\pi
0.0871762 + 0.996193i 0.472216π0.472216\pi
198198 0 0
199199 −2.24829 + 3.89415i −0.159377 + 0.276049i −0.934644 0.355584i 0.884282π-0.884282\pi
0.775267 + 0.631633i 0.217615π0.217615\pi
200200 0 0
201201 −19.4797 8.78170i −1.37399 0.619413i
202202 0 0
203203 −5.11411 + 19.3371i −0.358940 + 1.35720i
204204 0 0
205205 −46.1167 −3.22093
206206 0 0
207207 9.40950 1.90874i 0.654006 0.132666i
208208 0 0
209209 −0.144907 + 0.250986i −0.0100234 + 0.0173611i
210210 0 0
211211 −1.09087 1.88945i −0.0750987 0.130075i 0.826030 0.563625i 0.190594π-0.190594\pi
−0.901129 + 0.433551i 0.857261π0.857261\pi
212212 0 0
213213 −10.9471 4.93512i −0.750085 0.338149i
214214 0 0
215215 −13.2697 22.9838i −0.904988 1.56749i
216216 0 0
217217 −8.22237 + 2.23182i −0.558171 + 0.151506i
218218 0 0
219219 17.5032 12.5929i 1.18276 0.850947i
220220 0 0
221221 2.30924 0.155336
222222 0 0
223223 2.87967 4.98773i 0.192837 0.334003i −0.753352 0.657617i 0.771564π-0.771564\pi
0.946189 + 0.323614i 0.104898π0.104898\pi
224224 0 0
225225 9.29992 27.7414i 0.619995 1.84943i
226226 0 0
227227 8.29135 + 14.3610i 0.550316 + 0.953175i 0.998252 + 0.0591094i 0.0188261π0.0188261\pi
−0.447935 + 0.894066i 0.647841π0.647841\pi
228228 0 0
229229 7.29688 12.6386i 0.482191 0.835180i −0.517600 0.855623i 0.673174π-0.673174\pi
0.999791 + 0.0204432i 0.00650771π0.00650771\pi
230230 0 0
231231 −2.95608 7.73329i −0.194496 0.508813i
232232 0 0
233233 0.949438 + 1.64448i 0.0621998 + 0.107733i 0.895448 0.445165i 0.146855π-0.146855\pi
−0.833249 + 0.552898i 0.813522π0.813522\pi
234234 0 0
235235 21.9672 38.0483i 1.43298 2.48200i
236236 0 0
237237 25.3816 + 11.4424i 1.64871 + 0.743261i
238238 0 0
239239 4.46351 + 7.73103i 0.288721 + 0.500079i 0.973505 0.228667i 0.0734368π-0.0734368\pi
−0.684784 + 0.728746i 0.740103π0.740103\pi
240240 0 0
241241 12.1465 + 21.0383i 0.782423 + 1.35520i 0.930527 + 0.366224i 0.119350π0.119350\pi
−0.148104 + 0.988972i 0.547317π0.547317\pi
242242 0 0
243243 8.10607 13.3151i 0.520005 0.854164i
244244 0 0
245245 0.174600 + 26.8861i 0.0111548 + 1.71769i
246246 0 0
247247 0.111123 0.192470i 0.00707057 0.0122466i
248248 0 0
249249 −4.08522 + 2.93915i −0.258890 + 0.186261i
250250 0 0
251251 5.64873 0.356545 0.178272 0.983981i 0.442949π-0.442949\pi
0.178272 + 0.983981i 0.442949π0.442949\pi
252252 0 0
253253 5.78191 0.363506
254254 0 0
255255 1.10779 + 11.0334i 0.0693724 + 0.690935i
256256 0 0
257257 11.7856 20.4132i 0.735163 1.27334i −0.219489 0.975615i 0.570439π-0.570439\pi
0.954652 0.297724i 0.0962275π-0.0962275\pi
258258 0 0
259259 5.94580 + 5.90731i 0.369454 + 0.367063i
260260 0 0
261261 −22.2273 + 4.50886i −1.37584 + 0.279091i
262262 0 0
263263 12.8203 + 22.2053i 0.790531 + 1.36924i 0.925639 + 0.378409i 0.123529π0.123529\pi
−0.135108 + 0.990831i 0.543138π0.543138\pi
264264 0 0
265265 5.27940 + 9.14419i 0.324311 + 0.561723i
266266 0 0
267267 −1.74430 17.3729i −0.106749 1.06320i
268268 0 0
269269 −8.27239 + 14.3282i −0.504376 + 0.873606i 0.495611 + 0.868545i 0.334944π0.334944\pi
−0.999987 + 0.00506090i 0.998389π0.998389\pi
270270 0 0
271271 −8.90748 15.4282i −0.541091 0.937197i −0.998842 0.0481166i 0.984678π-0.984678\pi
0.457751 0.889081i 0.348655π-0.348655\pi
272272 0 0
273273 2.26689 + 5.93032i 0.137198 + 0.358920i
274274 0 0
275275 8.80996 15.2593i 0.531260 0.920170i
276276 0 0
277277 2.92191 + 5.06089i 0.175560 + 0.304080i 0.940355 0.340194i 0.110493π-0.110493\pi
−0.764795 + 0.644274i 0.777160π0.777160\pi
278278 0 0
279279 −6.39716 7.23908i −0.382988 0.433392i
280280 0 0
281281 −10.5591 + 18.2889i −0.629905 + 1.09103i 0.357666 + 0.933850i 0.383573π0.383573\pi
−0.987570 + 0.157177i 0.949761π0.949761\pi
282282 0 0
283283 12.7762 0.759468 0.379734 0.925096i 0.376016π-0.376016\pi
0.379734 + 0.925096i 0.376016π0.376016\pi
284284 0 0
285285 0.972914 + 0.438603i 0.0576304 + 0.0259806i
286286 0 0
287287 22.5351 + 22.3892i 1.33020 + 1.32159i
288288 0 0
289289 7.11087 + 12.3164i 0.418287 + 0.724494i
290290 0 0
291291 −11.7773 + 8.47330i −0.690399 + 0.496714i
292292 0 0
293293 5.93828 + 10.2854i 0.346918 + 0.600880i 0.985700 0.168508i 0.0538948π-0.0538948\pi
−0.638782 + 0.769388i 0.720561π0.720561\pi
294294 0 0
295295 28.9426 50.1301i 1.68510 2.91869i
296296 0 0
297297 6.37822 6.88796i 0.370102 0.399680i
298298 0 0
299299 −4.43389 −0.256419
300300 0 0
301301 −4.67413 + 17.6734i −0.269413 + 1.01868i
302302 0 0
303303 1.40417 + 13.9853i 0.0806676 + 0.803433i
304304 0 0
305305 17.6739 30.6120i 1.01200 1.75284i
306306 0 0
307307 3.93298 0.224467 0.112234 0.993682i 0.464200π-0.464200\pi
0.112234 + 0.993682i 0.464200π0.464200\pi
308308 0 0
309309 10.5980 7.62484i 0.602900 0.433762i
310310 0 0
311311 −1.98221 −0.112401 −0.0562005 0.998420i 0.517899π-0.517899\pi
−0.0562005 + 0.998420i 0.517899π0.517899\pi
312312 0 0
313313 20.4995 1.15870 0.579349 0.815080i 0.303307π-0.303307\pi
0.579349 + 0.815080i 0.303307π0.303307\pi
314314 0 0
315315 −27.2471 + 13.6759i −1.53520 + 0.770548i
316316 0 0
317317 9.51416 0.534369 0.267184 0.963645i 0.413907π-0.413907\pi
0.267184 + 0.963645i 0.413907π0.413907\pi
318318 0 0
319319 −13.6581 −0.764709
320320 0 0
321321 −1.02343 10.1932i −0.0571224 0.568927i
322322 0 0
323323 −0.267384 −0.0148777
324324 0 0
325325 −6.75597 + 11.7017i −0.374754 + 0.649093i
326326 0 0
327327 12.6091 9.07172i 0.697284 0.501667i
328328 0 0
329329 −29.2064 + 7.92756i −1.61020 + 0.437061i
330330 0 0
331331 −1.52986 −0.0840886 −0.0420443 0.999116i 0.513387π-0.513387\pi
−0.0420443 + 0.999116i 0.513387π0.513387\pi
332332 0 0
333333 −3.02076 + 9.01083i −0.165536 + 0.493790i
334334 0 0
335335 −23.6921 + 41.0360i −1.29444 + 2.24204i
336336 0 0
337337 10.6972 + 18.5281i 0.582714 + 1.00929i 0.995156 + 0.0983063i 0.0313425π0.0313425\pi
−0.412442 + 0.910984i 0.635324π0.635324\pi
338338 0 0
339339 2.76208 + 27.5098i 0.150016 + 1.49413i
340340 0 0
341341 −2.90887 5.03831i −0.157524 0.272840i
342342 0 0
343343 12.9676 13.2227i 0.700185 0.713961i
344344 0 0
345345 −2.12703 21.1848i −0.114515 1.14055i
346346 0 0
347347 −5.14381 −0.276134 −0.138067 0.990423i 0.544089π-0.544089\pi
−0.138067 + 0.990423i 0.544089π0.544089\pi
348348 0 0
349349 0.207526 0.359446i 0.0111086 0.0192407i −0.860418 0.509590i 0.829797π-0.829797\pi
0.871526 + 0.490349i 0.163131π0.163131\pi
350350 0 0
351351 −4.89118 + 5.28208i −0.261072 + 0.281936i
352352 0 0
353353 6.04122 + 10.4637i 0.321542 + 0.556926i 0.980806 0.194985i 0.0624657π-0.0624657\pi
−0.659265 + 0.751911i 0.729132π0.729132\pi
354354 0 0
355355 −13.3145 + 23.0613i −0.706658 + 1.22397i
356356 0 0
357357 4.81526 5.92930i 0.254851 0.313812i
358358 0 0
359359 8.14926 + 14.1149i 0.430102 + 0.744958i 0.996882 0.0789113i 0.0251444π-0.0251444\pi
−0.566780 + 0.823869i 0.691811π0.691811\pi
360360 0 0
361361 9.48713 16.4322i 0.499323 0.864852i
362362 0 0
363363 −10.8768 + 7.82540i −0.570882 + 0.410727i
364364 0 0
365365 −23.9083 41.4104i −1.25142 2.16752i
366366 0 0
367367 17.3500 + 30.0511i 0.905664 + 1.56866i 0.820024 + 0.572330i 0.193960π0.193960\pi
0.0856404 + 0.996326i 0.472706π0.472706\pi
368368 0 0
369369 −11.4489 + 34.1518i −0.596007 + 1.77787i
370370 0 0
371371 1.85962 7.03143i 0.0965465 0.365054i
372372 0 0
373373 7.75329 13.4291i 0.401450 0.695332i −0.592451 0.805606i 0.701840π-0.701840\pi
0.993901 + 0.110274i 0.0351730π0.0351730\pi
374374 0 0
375375 −28.8260 12.9952i −1.48857 0.671067i
376376 0 0
377377 10.4738 0.539430
378378 0 0
379379 16.1820 0.831214 0.415607 0.909544i 0.363569π-0.363569\pi
0.415607 + 0.909544i 0.363569π0.363569\pi
380380 0 0
381381 13.5939 + 6.12833i 0.696438 + 0.313964i
382382 0 0
383383 2.17027 3.75902i 0.110896 0.192077i −0.805236 0.592955i 0.797961π-0.797961\pi
0.916132 + 0.400877i 0.131295π0.131295\pi
384384 0 0
385385 −17.7183 + 4.80931i −0.903006 + 0.245105i
386386 0 0
387387 −20.3151 + 4.12095i −1.03267 + 0.209480i
388388 0 0
389389 −12.7731 22.1237i −0.647624 1.12172i −0.983689 0.179879i 0.942429π-0.942429\pi
0.336065 0.941839i 0.390904π-0.390904\pi
390390 0 0
391391 2.66722 + 4.61975i 0.134887 + 0.233631i
392392 0 0
393393 2.71306 1.95194i 0.136856 0.0984623i
394394 0 0
395395 30.8703 53.4690i 1.55326 2.69032i
396396 0 0
397397 2.28225 + 3.95297i 0.114543 + 0.198394i 0.917597 0.397512i 0.130126π-0.130126\pi
−0.803054 + 0.595906i 0.796793π0.796793\pi
398398 0 0
399399 −0.262480 0.686665i −0.0131404 0.0343762i
400400 0 0
401401 −0.668128 + 1.15723i −0.0333647 + 0.0577894i −0.882226 0.470827i 0.843956π-0.843956\pi
0.848861 + 0.528616i 0.177289π0.177289\pi
402402 0 0
403403 2.23068 + 3.86366i 0.111118 + 0.192463i
404404 0 0
405405 −27.5837 20.8357i −1.37064 1.03533i
406406 0 0
407407 −2.86161 + 4.95645i −0.141845 + 0.245682i
408408 0 0
409409 20.6664 1.02189 0.510944 0.859614i 0.329296π-0.329296\pi
0.510944 + 0.859614i 0.329296π0.329296\pi
410410 0 0
411411 −0.641757 6.39177i −0.0316555 0.315283i
412412 0 0
413413 −38.4806 + 10.4449i −1.89350 + 0.513958i
414414 0 0
415415 5.58015 + 9.66510i 0.273919 + 0.474441i
416416 0 0
417417 0.0465699 + 0.463826i 0.00228054 + 0.0227137i
418418 0 0
419419 −10.5227 18.2259i −0.514069 0.890394i −0.999867 0.0163228i 0.994804π-0.994804\pi
0.485797 0.874071i 0.338529π-0.338529\pi
420420 0 0
421421 −8.51630 + 14.7507i −0.415059 + 0.718903i −0.995435 0.0954456i 0.969572π-0.969572\pi
0.580376 + 0.814349i 0.302906π0.302906\pi
422422 0 0
423423 −22.7231 25.7137i −1.10484 1.25024i
424424 0 0
425425 16.2563 0.788544
426426 0 0
427427 −23.4982 + 6.37818i −1.13716 + 0.308662i
428428 0 0
429429 −3.51910 + 2.53185i −0.169904 + 0.122239i
430430 0 0
431431 −18.2925 + 31.6836i −0.881121 + 1.52615i −0.0310244 + 0.999519i 0.509877π0.509877\pi
−0.850096 + 0.526627i 0.823456π0.823456\pi
432432 0 0
433433 −23.6571 −1.13689 −0.568444 0.822722i 0.692454π-0.692454\pi
−0.568444 + 0.822722i 0.692454π0.692454\pi
434434 0 0
435435 5.02450 + 50.0430i 0.240906 + 2.39938i
436436 0 0
437437 0.513395 0.0245590
438438 0 0
439439 −20.7864 −0.992082 −0.496041 0.868299i 0.665213π-0.665213\pi
−0.496041 + 0.868299i 0.665213π0.665213\pi
440440 0 0
441441 19.9539 + 6.54543i 0.950185 + 0.311687i
442442 0 0
443443 −7.42807 −0.352918 −0.176459 0.984308i 0.556464π-0.556464\pi
−0.176459 + 0.984308i 0.556464π0.556464\pi
444444 0 0
445445 −38.7194 −1.83547
446446 0 0
447447 11.6944 8.41363i 0.553125 0.397951i
448448 0 0
449449 −8.15800 −0.385000 −0.192500 0.981297i 0.561660π-0.561660\pi
−0.192500 + 0.981297i 0.561660π0.561660\pi
450450 0 0
451451 −10.8457 + 18.7854i −0.510705 + 0.884568i
452452 0 0
453453 −1.68559 16.7882i −0.0791960 0.788776i
454454 0 0
455455 13.5873 3.68805i 0.636985 0.172898i
456456 0 0
457457 14.3058 0.669199 0.334600 0.942360i 0.391399π-0.391399\pi
0.334600 + 0.942360i 0.391399π0.391399\pi
458458 0 0
459459 8.44578 + 1.91876i 0.394215 + 0.0895602i
460460 0 0
461461 7.71961 13.3708i 0.359538 0.622738i −0.628346 0.777934i 0.716268π-0.716268\pi
0.987884 + 0.155196i 0.0496009π0.0496009\pi
462462 0 0
463463 −10.5531 18.2785i −0.490444 0.849474i 0.509496 0.860473i 0.329832π-0.329832\pi
−0.999940 + 0.0109995i 0.996499π0.996499\pi
464464 0 0
465465 −17.3901 + 12.5115i −0.806447 + 0.580206i
466466 0 0
467467 −3.49896 6.06037i −0.161912 0.280440i 0.773642 0.633623i 0.218433π-0.218433\pi
−0.935555 + 0.353182i 0.885100π0.885100\pi
468468 0 0
469469 31.4998 8.55007i 1.45453 0.394805i
470470 0 0
471471 −38.3037 17.2679i −1.76494 0.795661i
472472 0 0
473473 −12.4831 −0.573974
474474 0 0
475475 0.782265 1.35492i 0.0358928 0.0621681i
476476 0 0
477477 8.08240 1.63953i 0.370068 0.0750691i
478478 0 0
479479 1.54406 + 2.67440i 0.0705500 + 0.122196i 0.899142 0.437656i 0.144191π-0.144191\pi
−0.828592 + 0.559852i 0.810858π0.810858\pi
480480 0 0
481481 2.19444 3.80089i 0.100058 0.173305i
482482 0 0
483483 −9.24561 + 11.3846i −0.420690 + 0.518019i
484484 0 0
485485 16.0871 + 27.8636i 0.730475 + 1.26522i
486486 0 0
487487 −4.90011 + 8.48725i −0.222045 + 0.384594i −0.955429 0.295221i 0.904607π-0.904607\pi
0.733384 + 0.679815i 0.237940π0.237940\pi
488488 0 0
489489 1.35452 + 13.4907i 0.0612533 + 0.610071i
490490 0 0
491491 −9.98641 17.2970i −0.450680 0.780601i 0.547748 0.836643i 0.315485π-0.315485\pi
−0.998428 + 0.0560419i 0.982152π0.982152\pi
492492 0 0
493493 −6.30055 10.9129i −0.283762 0.491491i
494494 0 0
495495 −13.7851 15.5994i −0.619596 0.701140i
496496 0 0
497497 17.7022 4.80495i 0.794052 0.215531i
498498 0 0
499499 −10.1650 + 17.6062i −0.455046 + 0.788163i −0.998691 0.0511526i 0.983710π-0.983710\pi
0.543645 + 0.839315i 0.317044π0.317044\pi
500500 0 0
501501 −0.745415 7.42419i −0.0333027 0.331688i
502502 0 0
503503 23.9595 1.06830 0.534151 0.845389i 0.320631π-0.320631\pi
0.534151 + 0.845389i 0.320631π0.320631\pi
504504 0 0
505505 31.1693 1.38702
506506 0 0
507507 −15.5791 + 11.2085i −0.691891 + 0.497788i
508508 0 0
509509 −5.03046 + 8.71302i −0.222971 + 0.386198i −0.955709 0.294314i 0.904909π-0.904909\pi
0.732737 + 0.680511i 0.238242π0.238242\pi
510510 0 0
511511 −8.42146 + 31.8425i −0.372544 + 1.40863i
512512 0 0
513513 0.566343 0.611605i 0.0250047 0.0270030i
514514 0 0
515515 −14.4762 25.0735i −0.637898 1.10487i
516516 0 0
517517 −10.3325 17.8964i −0.454423 0.787083i
518518 0 0
519519 27.3737 + 12.3404i 1.20157 + 0.541685i
520520 0 0
521521 7.99821 13.8533i 0.350408 0.606924i −0.635913 0.771761i 0.719376π-0.719376\pi
0.986321 + 0.164836i 0.0527096π0.0527096\pi
522522 0 0
523523 18.7103 + 32.4072i 0.818146 + 1.41707i 0.907047 + 0.421029i 0.138331π0.138331\pi
−0.0889016 + 0.996040i 0.528336π0.528336\pi
524524 0 0
525525 15.9581 + 41.7474i 0.696468 + 1.82201i
526526 0 0
527527 2.68374 4.64838i 0.116906 0.202487i
528528 0 0
529529 6.37877 + 11.0484i 0.277338 + 0.480364i
530530 0 0
531531 −29.9386 33.8788i −1.29922 1.47021i
532532 0 0
533533 8.31711 14.4057i 0.360254 0.623978i
534534 0 0
535535 −22.7178 −0.982175
536536 0 0
537537 −27.2379 + 19.5965i −1.17540 + 0.845653i
538538 0 0
539539 10.9930 + 6.25195i 0.473500 + 0.269291i
540540 0 0
541541 0.229159 + 0.396916i 0.00985233 + 0.0170647i 0.870910 0.491443i 0.163531π-0.163531\pi
−0.861057 + 0.508508i 0.830197π0.830197\pi
542542 0 0
543543 −4.56392 2.05748i −0.195857 0.0882949i
544544 0 0
545545 −17.2232 29.8314i −0.737760 1.27784i
546546 0 0
547547 11.2013 19.4011i 0.478931 0.829533i −0.520777 0.853693i 0.674358π-0.674358\pi
0.999708 + 0.0241596i 0.00769098π0.00769098\pi
548548 0 0
549549 −18.2821 20.6881i −0.780259 0.882948i
550550 0 0
551551 −1.21275 −0.0516650
552552 0 0
553553 −41.0436 + 11.1405i −1.74535 + 0.473744i
554554 0 0
555555 19.2130 + 8.66149i 0.815547 + 0.367660i
556556 0 0
557557 10.4155 18.0401i 0.441317 0.764383i −0.556471 0.830867i 0.687845π-0.687845\pi
0.997787 + 0.0664841i 0.0211782π0.0211782\pi
558558 0 0
559559 9.57275 0.404884
560560 0 0
561561 4.75490 + 2.14357i 0.200752 + 0.0905018i
562562 0 0
563563 −8.80605 −0.371131 −0.185565 0.982632i 0.559412π-0.559412\pi
−0.185565 + 0.982632i 0.559412π0.559412\pi
564564 0 0
565565 61.3117 2.57940
566566 0 0
567567 3.36333 + 23.5730i 0.141247 + 0.989974i
568568 0 0
569569 18.9857 0.795923 0.397962 0.917402i 0.369718π-0.369718\pi
0.397962 + 0.917402i 0.369718π0.369718\pi
570570 0 0
571571 15.7597 0.659523 0.329762 0.944064i 0.393032π-0.393032\pi
0.329762 + 0.944064i 0.393032π0.393032\pi
572572 0 0
573573 5.84305 + 2.63413i 0.244097 + 0.110042i
574574 0 0
575575 −31.2131 −1.30167
576576 0 0
577577 −15.9306 + 27.5927i −0.663201 + 1.14870i 0.316569 + 0.948570i 0.397469π0.397469\pi
−0.979770 + 0.200128i 0.935864π0.935864\pi
578578 0 0
579579 20.1593 + 9.08809i 0.837792 + 0.377688i
580580 0 0
581581 1.96555 7.43199i 0.0815449 0.308331i
582582 0 0
583583 4.96644 0.205689
584584 0 0
585585 10.5712 + 11.9625i 0.437066 + 0.494587i
586586 0 0
587587 20.3597 35.2640i 0.840333 1.45550i −0.0492799 0.998785i 0.515693π-0.515693\pi
0.889613 0.456715i 0.150974π-0.150974\pi
588588 0 0
589589 −0.258288 0.447368i −0.0106426 0.0184335i
590590 0 0
591591 −3.86409 1.74198i −0.158947 0.0716557i
592592 0 0
593593 −14.0693 24.3688i −0.577759 1.00071i −0.995736 0.0922500i 0.970594π-0.970594\pi
0.417977 0.908458i 0.362739π-0.362739\pi
594594 0 0
595595 −12.0161 11.9383i −0.492613 0.489425i
596596 0 0
597597 6.32209 4.54849i 0.258746 0.186157i
598598 0 0
599599 −32.9926 −1.34804 −0.674020 0.738713i 0.735434π-0.735434\pi
−0.674020 + 0.738713i 0.735434π0.735434\pi
600600 0 0
601601 −1.98103 + 3.43124i −0.0808079 + 0.139963i −0.903597 0.428383i 0.859083π-0.859083\pi
0.822789 + 0.568347i 0.192417π0.192417\pi
602602 0 0
603603 24.5075 + 27.7328i 0.998021 + 1.12937i
604604 0 0
605605 14.8570 + 25.7330i 0.604021 + 1.04620i
606606 0 0
607607 17.0132 29.4676i 0.690543 1.19605i −0.281118 0.959673i 0.590705π-0.590705\pi
0.971660 0.236382i 0.0759615π-0.0759615\pi
608608 0 0
609609 21.8402 26.8930i 0.885008 1.08976i
610610 0 0
611611 7.92354 + 13.7240i 0.320552 + 0.555212i
612612 0 0
613613 −15.2967 + 26.4946i −0.617827 + 1.07011i 0.372054 + 0.928211i 0.378654π0.378654\pi
−0.989881 + 0.141897i 0.954680π0.954680\pi
614614 0 0
615615 72.8188 + 32.8277i 2.93634 + 1.32374i
616616 0 0
617617 18.7646 + 32.5013i 0.755435 + 1.30845i 0.945158 + 0.326614i 0.105908π0.105908\pi
−0.189723 + 0.981838i 0.560759π0.560759\pi
618618 0 0
619619 −2.92302 5.06282i −0.117486 0.203492i 0.801285 0.598283i 0.204150π-0.204150\pi
−0.918771 + 0.394791i 0.870817π0.870817\pi
620620 0 0
621621 −16.2164 3.68415i −0.650744 0.147840i
622622 0 0
623623 18.9203 + 18.7979i 0.758028 + 0.753121i
624624 0 0
625625 −10.6774 + 18.4937i −0.427095 + 0.739749i
626626 0 0
627627 0.407472 0.293160i 0.0162729 0.0117077i
628628 0 0
629629 −5.28028 −0.210539
630630 0 0
631631 −25.6347 −1.02050 −0.510251 0.860025i 0.670448π-0.670448\pi
−0.510251 + 0.860025i 0.670448π0.670448\pi
632632 0 0
633633 0.377516 + 3.75999i 0.0150049 + 0.149446i
634634 0 0
635635 16.5336 28.6371i 0.656117 1.13643i
636636 0 0
637637 −8.43001 4.79435i −0.334009 0.189959i
638638 0 0
639639 13.7726 + 15.5852i 0.544837 + 0.616542i
640640 0 0
641641 −12.9824 22.4861i −0.512772 0.888147i −0.999890 0.0148113i 0.995285π-0.995285\pi
0.487118 0.873336i 0.338048π-0.338048\pi
642642 0 0
643643 22.5634 + 39.0809i 0.889812 + 1.54120i 0.840097 + 0.542436i 0.182498π0.182498\pi
0.0497151 + 0.998763i 0.484169π0.484169\pi
644644 0 0
645645 4.59223 + 45.7377i 0.180819 + 1.80092i
646646 0 0
647647 −2.70324 + 4.68215i −0.106275 + 0.184074i −0.914259 0.405131i 0.867226π-0.867226\pi
0.807983 + 0.589206i 0.200559π0.200559\pi
648648 0 0
649649 −13.6135 23.5792i −0.534375 0.925564i
650650 0 0
651651 14.5719 + 2.32895i 0.571119 + 0.0912788i
652652 0 0
653653 15.9515 27.6288i 0.624231 1.08120i −0.364458 0.931220i 0.618746π-0.618746\pi
0.988689 0.149980i 0.0479211π-0.0479211\pi
654654 0 0
655655 −3.70587 6.41875i −0.144800 0.250801i
656656 0 0
657657 −36.6020 + 7.42479i −1.42798 + 0.289669i
658658 0 0
659659 −2.50215 + 4.33385i −0.0974699 + 0.168823i −0.910637 0.413208i 0.864408π-0.864408\pi
0.813167 + 0.582031i 0.197742π0.197742\pi
660660 0 0
661661 9.63406 0.374721 0.187361 0.982291i 0.440007π-0.440007\pi
0.187361 + 0.982291i 0.440007π0.440007\pi
662662 0 0
663663 −3.64632 1.64381i −0.141611 0.0638404i
664664 0 0
665665 −1.57326 + 0.427034i −0.0610085 + 0.0165597i
666666 0 0
667667 12.0975 + 20.9534i 0.468415 + 0.811319i
668668 0 0
669669 −8.09751 + 5.82583i −0.313068 + 0.225240i
670670 0 0
671671 −8.31308 14.3987i −0.320923 0.555855i
672672 0 0
673673 13.5885 23.5359i 0.523797 0.907243i −0.475819 0.879543i 0.657848π-0.657848\pi
0.999616 0.0276998i 0.00881825π-0.00881825\pi
674674 0 0
675675 −34.4322 + 37.1840i −1.32529 + 1.43121i
676676 0 0
677677 −38.0502 −1.46239 −0.731194 0.682169i 0.761037π-0.761037\pi
−0.731194 + 0.682169i 0.761037π0.761037\pi
678678 0 0
679679 5.66651 21.4257i 0.217461 0.822244i
680680 0 0
681681 −2.86937 28.5784i −0.109955 1.09513i
682682 0 0
683683 −15.0571 + 26.0797i −0.576146 + 0.997913i 0.419771 + 0.907630i 0.362111π0.362111\pi
−0.995916 + 0.0902831i 0.971223π0.971223\pi
684684 0 0
685685 −14.2455 −0.544293
686686 0 0
687687 −20.5185 + 14.7622i −0.782830 + 0.563215i
688688 0 0
689689 −3.80854 −0.145094
690690 0 0
691691 −14.3902 −0.547429 −0.273714 0.961811i 0.588252π-0.588252\pi
−0.273714 + 0.961811i 0.588252π0.588252\pi
692692 0 0
693693 −0.837189 + 14.3152i −0.0318022 + 0.543791i
694694 0 0
695695 1.03374 0.0392120
696696 0 0
697697 −20.0127 −0.758034
698698 0 0
699699 −0.328571 3.27250i −0.0124277 0.123777i
700700 0 0
701701 14.4170 0.544521 0.272261 0.962224i 0.412229π-0.412229\pi
0.272261 + 0.962224i 0.412229π0.412229\pi
702702 0 0
703703 −0.254092 + 0.440100i −0.00958325 + 0.0165987i
704704 0 0
705705 −61.7708 + 44.4416i −2.32642 + 1.67377i
706706 0 0
707707 −15.2310 15.1324i −0.572820 0.569113i
708708 0 0
709709 11.4882 0.431448 0.215724 0.976454i 0.430789π-0.430789\pi
0.215724 + 0.976454i 0.430789π0.430789\pi
710710 0 0
711711 −31.9327 36.1353i −1.19757 1.35518i
712712 0 0
713713 −5.15296 + 8.92519i −0.192980 + 0.334251i
714714 0 0
715715 4.80686 + 8.32573i 0.179766 + 0.311365i
716716 0 0
717717 −1.54468 15.3847i −0.0576871 0.574552i
718718 0 0
719719 −17.9451 31.0818i −0.669240 1.15916i −0.978117 0.208055i 0.933287π-0.933287\pi
0.308877 0.951102i 0.400047π-0.400047\pi
720720 0 0
721721 −5.09910 + 19.2803i −0.189901 + 0.718036i
722722 0 0
723723 −4.20351 41.8661i −0.156330 1.55702i
724724 0 0
725725 73.7321 2.73834
726726 0 0
727727 5.03060 8.71326i 0.186575 0.323157i −0.757531 0.652799i 0.773595π-0.773595\pi
0.944106 + 0.329642i 0.106928π0.106928\pi
728728 0 0
729729 −22.2778 + 15.2545i −0.825104 + 0.564980i
730730 0 0
731731 −5.75850 9.97401i −0.212986 0.368902i
732732 0 0
733733 −16.5690 + 28.6984i −0.611992 + 1.06000i 0.378913 + 0.925432i 0.376298π0.376298\pi
−0.990904 + 0.134568i 0.957035π0.957035\pi
734734 0 0
735735 18.8629 42.5778i 0.695770 1.57051i
736736 0 0
737737 11.1438 + 19.3017i 0.410489 + 0.710987i
738738 0 0
739739 −21.9237 + 37.9729i −0.806475 + 1.39686i 0.108816 + 0.994062i 0.465294π0.465294\pi
−0.915291 + 0.402793i 0.868039π0.868039\pi
740740 0 0
741741 −0.312473 + 0.224811i −0.0114790 + 0.00825865i
742742 0 0
743743 −4.50115 7.79622i −0.165131 0.286016i 0.771571 0.636144i 0.219471π-0.219471\pi
−0.936702 + 0.350128i 0.886138π0.886138\pi
744744 0 0
745745 −15.9738 27.6673i −0.585233 1.01365i
746746 0 0
747747 8.54283 1.73293i 0.312566 0.0634046i
748748 0 0
749749 11.1011 + 11.0293i 0.405626 + 0.403000i
750750 0 0
751751 5.59141 9.68460i 0.204033 0.353396i −0.745791 0.666180i 0.767928π-0.767928\pi
0.949824 + 0.312784i 0.101262π0.101262\pi
752752 0 0
753753 −8.91942 4.02100i −0.325042 0.146533i
754754 0 0
755755 −37.4162 −1.36171
756756 0 0
757757 42.1431 1.53172 0.765859 0.643009i 0.222314π-0.222314\pi
0.765859 + 0.643009i 0.222314π0.222314\pi
758758 0 0
759759 −9.12971 4.11580i −0.331388 0.149394i
760760 0 0
761761 −1.14155 + 1.97721i −0.0413810 + 0.0716740i −0.885974 0.463735i 0.846509π-0.846509\pi
0.844593 + 0.535409i 0.179842π0.179842\pi
762762 0 0
763763 −6.06670 + 22.9389i −0.219629 + 0.830444i
764764 0 0
765765 6.10478 18.2104i 0.220719 0.658398i
766766 0 0
767767 10.4396 + 18.0819i 0.376951 + 0.652898i
768768 0 0
769769 8.96676 + 15.5309i 0.323350 + 0.560058i 0.981177 0.193111i 0.0618577π-0.0618577\pi
−0.657827 + 0.753169i 0.728524π0.728524\pi
770770 0 0
771771 −33.1405 + 23.8432i −1.19353 + 0.858693i
772772 0 0
773773 17.4807 30.2775i 0.628737 1.08901i −0.359068 0.933311i 0.616905π-0.616905\pi
0.987805 0.155694i 0.0497613π-0.0497613\pi
774774 0 0
775775 15.7032 + 27.1988i 0.564077 + 0.977009i
776776 0 0
777777 −5.18343 13.5602i −0.185955 0.486469i
778778 0 0
779779 −0.963028 + 1.66801i −0.0345041 + 0.0597628i
780780 0 0
781781 6.26259 + 10.8471i 0.224093 + 0.388141i
782782 0 0
783783 38.3068 + 8.70277i 1.36897 + 0.311011i
784784 0 0
785785 −46.5870 + 80.6910i −1.66276 + 2.87998i
786786 0 0
787787 28.3564 1.01079 0.505397 0.862887i 0.331346π-0.331346\pi
0.505397 + 0.862887i 0.331346π0.331346\pi
788788 0 0
789789 −4.43668 44.1885i −0.157950 1.57315i
790790 0 0
791791 −29.9601 29.7662i −1.06526 1.05836i
792792 0 0
793793 6.37494 + 11.0417i 0.226381 + 0.392103i
794794 0 0
795795 −1.82703 18.1969i −0.0647982 0.645377i
796796 0 0
797797 −9.51922 16.4878i −0.337188 0.584027i 0.646715 0.762732i 0.276143π-0.276143\pi
−0.983903 + 0.178705i 0.942809π0.942809\pi
798798 0 0
799799 9.53283 16.5113i 0.337247 0.584129i
800800 0 0
801801 −9.61246 + 28.6737i −0.339640 + 1.01313i
802802 0 0
803803 −22.4910 −0.793691
804804 0 0
805805 23.0717 + 22.9224i 0.813172 + 0.807908i
806806 0 0
807807 23.2616 16.7358i 0.818847 0.589128i
808808 0 0
809809 −10.4529 + 18.1050i −0.367505 + 0.636538i −0.989175 0.146742i 0.953121π-0.953121\pi
0.621670 + 0.783280i 0.286455π0.286455\pi
810810 0 0
811811 −17.5392 −0.615884 −0.307942 0.951405i 0.599640π-0.599640\pi
−0.307942 + 0.951405i 0.599640π0.599640\pi
812812 0 0
813813 3.08260 + 30.7021i 0.108111 + 1.07677i
814814 0 0
815815 30.0671 1.05320
816816 0 0
817817 −1.10842 −0.0387786
818818 0 0
819819 0.642004 10.9777i 0.0224334 0.383593i
820820 0 0
821821 −34.9762 −1.22068 −0.610339 0.792140i 0.708967π-0.708967\pi
−0.610339 + 0.792140i 0.708967π0.708967\pi
822822 0 0
823823 30.4235 1.06050 0.530249 0.847842i 0.322099π-0.322099\pi
0.530249 + 0.847842i 0.322099π0.322099\pi
824824 0 0
825825 −24.7732 + 17.8233i −0.862493 + 0.620529i
826826 0 0
827827 25.6276 0.891158 0.445579 0.895243i 0.352998π-0.352998\pi
0.445579 + 0.895243i 0.352998π0.352998\pi
828828 0 0
829829 23.9403 41.4658i 0.831481 1.44017i −0.0653833 0.997860i 0.520827π-0.520827\pi
0.896864 0.442307i 0.145840π-0.145840\pi
830830 0 0
831831 −1.01118 10.0712i −0.0350775 0.349364i
832832 0 0
833833 0.0757689 + 11.6674i 0.00262524 + 0.404252i
834834 0 0
835835 −16.5465 −0.572614
836836 0 0
837837 4.94813 + 15.9844i 0.171032 + 0.552501i
838838 0 0
839839 21.8466 37.8394i 0.754227 1.30636i −0.191530 0.981487i 0.561345π-0.561345\pi
0.945758 0.324873i 0.105322π-0.105322\pi
840840 0 0
841841 −14.0769 24.3818i −0.485409 0.840753i
842842 0 0
843843 29.6918 21.3621i 1.02264 0.735749i
844844 0 0
845845 21.2800 + 36.8581i 0.732055 + 1.26796i
846846 0 0
847847 5.23322 19.7874i 0.179816 0.679904i
848848 0 0
849849 −20.1738 9.09464i −0.692364 0.312127i
850850 0 0
851851 10.1385 0.347543
852852 0 0
853853 8.33994 14.4452i 0.285554 0.494594i −0.687189 0.726478i 0.741156π-0.741156\pi
0.972743 + 0.231884i 0.0744890π0.0744890\pi
854854 0 0
855855 −1.22403 1.38512i −0.0418609 0.0473701i
856856 0 0
857857 −7.21452 12.4959i −0.246443 0.426852i 0.716093 0.698005i 0.245929π-0.245929\pi
−0.962536 + 0.271152i 0.912595π0.912595\pi
858858 0 0
859859 11.3867 19.7223i 0.388508 0.672915i −0.603741 0.797180i 0.706324π-0.706324\pi
0.992249 + 0.124265i 0.0396573π0.0396573\pi
860860 0 0
861861 −19.6456 51.3942i −0.669521 1.75151i
862862 0 0
863863 5.97266 + 10.3450i 0.203312 + 0.352146i 0.949594 0.313484i 0.101496π-0.101496\pi
−0.746282 + 0.665630i 0.768163π0.768163\pi
864864 0 0
865865 33.2933 57.6656i 1.13200 1.96069i
866866 0 0
867867 −2.46085 24.5096i −0.0835748 0.832388i
868868 0 0
869869 −14.5202 25.1497i −0.492563 0.853145i
870870 0 0
871871 −8.54572 14.8016i −0.289561 0.501534i
872872 0 0
873873 24.6282 4.99588i 0.833538 0.169085i
874874 0 0
875875 46.6134 12.6524i 1.57582 0.427729i
876876 0 0
877877 28.3099 49.0342i 0.955957 1.65577i 0.223794 0.974636i 0.428156π-0.428156\pi
0.732163 0.681130i 0.238511π-0.238511\pi
878878 0 0
879879 −2.05505 20.4679i −0.0693152 0.690365i
880880 0 0
881881 −6.41130 −0.216002 −0.108001 0.994151i 0.534445π-0.534445\pi
−0.108001 + 0.994151i 0.534445π0.534445\pi
882882 0 0
883883 25.7180 0.865481 0.432741 0.901518i 0.357547π-0.357547\pi
0.432741 + 0.901518i 0.357547π0.357547\pi
884884 0 0
885885 −81.3854 + 58.5535i −2.73574 + 1.96825i
886886 0 0
887887 9.99472 17.3114i 0.335590 0.581259i −0.648008 0.761633i 0.724398π-0.724398\pi
0.983598 + 0.180375i 0.0577311π0.0577311\pi
888888 0 0
889889 −21.9822 + 5.96669i −0.737261 + 0.200116i
890890 0 0
891891 −14.9744 + 6.33591i −0.501662 + 0.212261i
892892 0 0
893893 −0.917456 1.58908i −0.0307015 0.0531766i
894894 0 0
895895 37.2051 + 64.4412i 1.24363 + 2.15403i
896896 0 0
897897 7.00118 + 3.15623i 0.233762 + 0.105383i
898898 0 0
899899 12.1724 21.0832i 0.405973 0.703166i
900900 0 0
901901 2.29104 + 3.96819i 0.0763254 + 0.132200i
902902 0 0
903903 19.9612 24.5794i 0.664267 0.817950i
904904 0 0
905905 −5.55087 + 9.61439i −0.184517 + 0.319593i
906906 0 0
907907 12.1517 + 21.0474i 0.403491 + 0.698866i 0.994145 0.108059i 0.0344635π-0.0344635\pi
−0.590654 + 0.806925i 0.701130π0.701130\pi
908908 0 0
909909 7.73809 23.0825i 0.256656 0.765598i
910910 0 0
911911 −19.7871 + 34.2723i −0.655577 + 1.13549i 0.326171 + 0.945311i 0.394241π0.394241\pi
−0.981749 + 0.190183i 0.939092π0.939092\pi
912912 0 0
913913 5.24936 0.173728
914914 0 0
915915 −49.6981 + 35.7558i −1.64297 + 1.18205i
916916 0 0
917917 −1.30536 + 4.93571i −0.0431067 + 0.162991i
918918 0 0
919919 12.9220 + 22.3815i 0.426257 + 0.738298i 0.996537 0.0831519i 0.0264987π-0.0264987\pi
−0.570280 + 0.821450i 0.693165π0.693165\pi
920920 0 0
921921 −6.21023 2.79966i −0.204634 0.0922518i
922922 0 0
923923 −4.80251 8.31818i −0.158076 0.273796i
924924 0 0
925925 15.4481 26.7569i 0.507930 0.879761i
926926 0 0
927927 −22.1621 + 4.49563i −0.727898 + 0.147656i
928928 0 0
929929 50.8506 1.66836 0.834178 0.551496i 0.185943π-0.185943\pi
0.834178 + 0.551496i 0.185943π0.185943\pi
930930 0 0
931931 0.976100 + 0.555132i 0.0319904 + 0.0181937i
932932 0 0
933933 3.12994 + 1.41102i 0.102470 + 0.0461948i
934934 0 0
935935 5.78315 10.0167i 0.189129 0.327581i
936936 0 0
937937 32.7623 1.07030 0.535149 0.844758i 0.320256π-0.320256\pi
0.535149 + 0.844758i 0.320256π0.320256\pi
938938 0 0
939939 −32.3689 14.5923i −1.05632 0.476203i
940940 0 0
941941 50.6793 1.65210 0.826048 0.563599i 0.190584π-0.190584\pi
0.826048 + 0.563599i 0.190584π0.190584\pi
942942 0 0
943943 38.4256 1.25131
944944 0 0
945945 52.7586 2.19879i 1.71624 0.0715267i
946946 0 0
947947 11.5255 0.374530 0.187265 0.982309i 0.440038π-0.440038\pi
0.187265 + 0.982309i 0.440038π0.440038\pi
948948 0 0
949949 17.2474 0.559873
950950 0 0
951951 −15.0230 6.77257i −0.487154 0.219616i
952952 0 0
953953 −45.7747 −1.48279 −0.741395 0.671069i 0.765835π-0.765835\pi
−0.741395 + 0.671069i 0.765835π0.765835\pi
954954 0 0
955955 7.10661 12.3090i 0.229965 0.398310i
956956 0 0
957957 21.5664 + 9.72243i 0.697142 + 0.314281i
958958 0 0
959959 6.96111 + 6.91605i 0.224786 + 0.223331i
960960 0 0
961961 −20.6302 −0.665491
962962 0 0
963963 −5.63990 + 16.8237i −0.181743 + 0.542135i
964964 0 0
965965 24.5188 42.4678i 0.789287 1.36709i
966966 0 0
967967 4.07666 + 7.06098i 0.131097 + 0.227066i 0.924100 0.382152i 0.124817π-0.124817\pi
−0.793003 + 0.609218i 0.791484π0.791484\pi
968968 0 0
969969 0.422203 + 0.190335i 0.0135631 + 0.00611444i
970970 0 0
971971 −14.1137 24.4457i −0.452932 0.784501i 0.545635 0.838023i 0.316288π-0.316288\pi
−0.998567 + 0.0535223i 0.982955π0.982955\pi
972972 0 0
973973 −0.505141 0.501871i −0.0161941 0.0160893i
974974 0 0
975975 18.9975 13.6679i 0.608407 0.437724i
976976 0 0
977977 −15.6502 −0.500694 −0.250347 0.968156i 0.580545π-0.580545\pi
−0.250347 + 0.968156i 0.580545π0.580545\pi
978978 0 0
979979 −9.10603 + 15.7721i −0.291030 + 0.504079i
980980 0 0
981981 −26.3675 + 5.34871i −0.841850 + 0.170771i
982982 0 0
983983 1.47581 + 2.55617i 0.0470710 + 0.0815293i 0.888601 0.458681i 0.151678π-0.151678\pi
−0.841530 + 0.540210i 0.818345π0.818345\pi
984984 0 0
985985 −4.69970 + 8.14012i −0.149745 + 0.259366i
986986 0 0
987987 51.7605 + 8.27259i 1.64755 + 0.263319i
988988 0 0
989989 11.0567 + 19.1507i 0.351582 + 0.608958i
990990 0 0
991991 −15.8182 + 27.3979i −0.502482 + 0.870324i 0.497514 + 0.867456i 0.334246π0.334246\pi
−0.999996 + 0.00286819i 0.999087π0.999087\pi
992992 0 0
993993 2.41567 + 1.08902i 0.0766588 + 0.0345589i
994994 0 0
995995 −8.63557 14.9572i −0.273766 0.474176i
996996 0 0
997997 0.792608 + 1.37284i 0.0251021 + 0.0434782i 0.878304 0.478103i 0.158676π-0.158676\pi
−0.853201 + 0.521582i 0.825342π0.825342\pi
998998 0 0
999999 11.1841 12.0779i 0.353849 0.382129i
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 1008.2.q.k.529.2 22
3.2 odd 2 3024.2.q.k.2881.11 22
4.3 odd 2 504.2.q.d.25.10 22
7.2 even 3 1008.2.t.k.961.10 22
9.4 even 3 1008.2.t.k.193.10 22
9.5 odd 6 3024.2.t.l.1873.1 22
12.11 even 2 1512.2.q.c.1369.11 22
21.2 odd 6 3024.2.t.l.289.1 22
28.23 odd 6 504.2.t.d.457.2 yes 22
36.23 even 6 1512.2.t.d.361.1 22
36.31 odd 6 504.2.t.d.193.2 yes 22
63.23 odd 6 3024.2.q.k.2305.11 22
63.58 even 3 inner 1008.2.q.k.625.2 22
84.23 even 6 1512.2.t.d.289.1 22
252.23 even 6 1512.2.q.c.793.11 22
252.247 odd 6 504.2.q.d.121.10 yes 22
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
504.2.q.d.25.10 22 4.3 odd 2
504.2.q.d.121.10 yes 22 252.247 odd 6
504.2.t.d.193.2 yes 22 36.31 odd 6
504.2.t.d.457.2 yes 22 28.23 odd 6
1008.2.q.k.529.2 22 1.1 even 1 trivial
1008.2.q.k.625.2 22 63.58 even 3 inner
1008.2.t.k.193.10 22 9.4 even 3
1008.2.t.k.961.10 22 7.2 even 3
1512.2.q.c.793.11 22 252.23 even 6
1512.2.q.c.1369.11 22 12.11 even 2
1512.2.t.d.289.1 22 84.23 even 6
1512.2.t.d.361.1 22 36.23 even 6
3024.2.q.k.2305.11 22 63.23 odd 6
3024.2.q.k.2881.11 22 3.2 odd 2
3024.2.t.l.289.1 22 21.2 odd 6
3024.2.t.l.1873.1 22 9.5 odd 6