Properties

Label 832.2.i.k.705.1
Level 832832
Weight 22
Character 832.705
Analytic conductor 6.6446.644
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [832,2,Mod(321,832)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(832, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("832.321");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 832=2613 832 = 2^{6} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 832.i (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: 6.643553448176.64355344817
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q(2,3)\Q(\sqrt{2}, \sqrt{-3})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4+2x2+4 x^{4} + 2x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 416)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 705.1
Root 0.7071071.22474i-0.707107 - 1.22474i of defining polynomial
Character χ\chi == 832.705
Dual form 832.2.i.k.321.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(1.207112.09077i)q32.82843q5+(2.20711+3.82282i)q7+(1.41421+2.44949i)q9+(1.62132+2.80821i)q11+(1.000003.46410i)q13+(3.41421+5.91359i)q15+(2.914215.04757i)q17+(0.621320+1.07616i)q19+10.6569q21+(0.6213201.07616i)q23+3.00000q250.414214q27+(4.32843+7.49706i)q29+5.65685q31+(3.914216.77962i)q33+(6.2426410.8126i)q35+(3.742646.48244i)q37+(8.44975+2.09077i)q39+(2.91421+5.04757i)q41+(2.035533.52565i)q43+(4.000006.92820i)q45+6.00000q47+(6.2426410.8126i)q4914.0711q51+2.82843q53+(4.585797.94282i)q55+3.00000q57+(0.621320+1.07616i)q59+(3.500006.06218i)q61+(6.2426410.8126i)q63+(2.82843+9.79796i)q65+(6.62132+11.4685i)q67+(1.50000+2.59808i)q69+(3.621326.27231i)q71+12.4853q73+(3.621326.27231i)q7514.3137q776.00000q79+(4.74264+8.21449i)q814.00000q83+(8.24264+14.2767i)q85+(10.449718.0995i)q87+(1.67157+2.89525i)q89+(11.0355+11.4685i)q91+(6.8284311.8272i)q93+(1.757363.04384i)q95+(4.500007.79423i)q979.17157q99+O(q100)q+(-1.20711 - 2.09077i) q^{3} -2.82843 q^{5} +(-2.20711 + 3.82282i) q^{7} +(-1.41421 + 2.44949i) q^{9} +(1.62132 + 2.80821i) q^{11} +(1.00000 - 3.46410i) q^{13} +(3.41421 + 5.91359i) q^{15} +(2.91421 - 5.04757i) q^{17} +(-0.621320 + 1.07616i) q^{19} +10.6569 q^{21} +(-0.621320 - 1.07616i) q^{23} +3.00000 q^{25} -0.414214 q^{27} +(4.32843 + 7.49706i) q^{29} +5.65685 q^{31} +(3.91421 - 6.77962i) q^{33} +(6.24264 - 10.8126i) q^{35} +(-3.74264 - 6.48244i) q^{37} +(-8.44975 + 2.09077i) q^{39} +(2.91421 + 5.04757i) q^{41} +(2.03553 - 3.52565i) q^{43} +(4.00000 - 6.92820i) q^{45} +6.00000 q^{47} +(-6.24264 - 10.8126i) q^{49} -14.0711 q^{51} +2.82843 q^{53} +(-4.58579 - 7.94282i) q^{55} +3.00000 q^{57} +(-0.621320 + 1.07616i) q^{59} +(3.50000 - 6.06218i) q^{61} +(-6.24264 - 10.8126i) q^{63} +(-2.82843 + 9.79796i) q^{65} +(6.62132 + 11.4685i) q^{67} +(-1.50000 + 2.59808i) q^{69} +(3.62132 - 6.27231i) q^{71} +12.4853 q^{73} +(-3.62132 - 6.27231i) q^{75} -14.3137 q^{77} -6.00000 q^{79} +(4.74264 + 8.21449i) q^{81} -4.00000 q^{83} +(-8.24264 + 14.2767i) q^{85} +(10.4497 - 18.0995i) q^{87} +(1.67157 + 2.89525i) q^{89} +(11.0355 + 11.4685i) q^{91} +(-6.82843 - 11.8272i) q^{93} +(1.75736 - 3.04384i) q^{95} +(4.50000 - 7.79423i) q^{97} -9.17157 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q2q36q72q11+4q13+8q15+6q17+6q19+20q21+6q23+12q25+4q27+6q29+10q33+8q35+2q3714q39+6q416q43+48q99+O(q100) 4 q - 2 q^{3} - 6 q^{7} - 2 q^{11} + 4 q^{13} + 8 q^{15} + 6 q^{17} + 6 q^{19} + 20 q^{21} + 6 q^{23} + 12 q^{25} + 4 q^{27} + 6 q^{29} + 10 q^{33} + 8 q^{35} + 2 q^{37} - 14 q^{39} + 6 q^{41} - 6 q^{43}+ \cdots - 48 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/832Z)×\left(\mathbb{Z}/832\mathbb{Z}\right)^\times.

nn 261261 703703 769769
χ(n)\chi(n) 11 11 e(13)e\left(\frac{1}{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 −1.20711 2.09077i −0.696923 1.20711i −0.969528 0.244981i 0.921218π-0.921218\pi
0.272605 0.962126i 0.412115π-0.412115\pi
44 0 0
55 −2.82843 −1.26491 −0.632456 0.774597i 0.717953π-0.717953\pi
−0.632456 + 0.774597i 0.717953π0.717953\pi
66 0 0
77 −2.20711 + 3.82282i −0.834208 + 1.44489i 0.0604657 + 0.998170i 0.480741π0.480741\pi
−0.894674 + 0.446720i 0.852592π0.852592\pi
88 0 0
99 −1.41421 + 2.44949i −0.471405 + 0.816497i
1010 0 0
1111 1.62132 + 2.80821i 0.488846 + 0.846707i 0.999918 0.0128314i 0.00408449π-0.00408449\pi
−0.511071 + 0.859538i 0.670751π0.670751\pi
1212 0 0
1313 1.00000 3.46410i 0.277350 0.960769i
1414 0 0
1515 3.41421 + 5.91359i 0.881546 + 1.52688i
1616 0 0
1717 2.91421 5.04757i 0.706801 1.22421i −0.259237 0.965814i 0.583471π-0.583471\pi
0.966038 0.258401i 0.0831955π-0.0831955\pi
1818 0 0
1919 −0.621320 + 1.07616i −0.142541 + 0.246888i −0.928453 0.371451i 0.878861π-0.878861\pi
0.785912 + 0.618338i 0.212194π0.212194\pi
2020 0 0
2121 10.6569 2.32552
2222 0 0
2323 −0.621320 1.07616i −0.129554 0.224395i 0.793950 0.607983i 0.208021π-0.208021\pi
−0.923504 + 0.383589i 0.874688π0.874688\pi
2424 0 0
2525 3.00000 0.600000
2626 0 0
2727 −0.414214 −0.0797154
2828 0 0
2929 4.32843 + 7.49706i 0.803769 + 1.39217i 0.917119 + 0.398613i 0.130508π0.130508\pi
−0.113350 + 0.993555i 0.536158π0.536158\pi
3030 0 0
3131 5.65685 1.01600 0.508001 0.861357i 0.330385π-0.330385\pi
0.508001 + 0.861357i 0.330385π0.330385\pi
3232 0 0
3333 3.91421 6.77962i 0.681377 1.18018i
3434 0 0
3535 6.24264 10.8126i 1.05520 1.82766i
3636 0 0
3737 −3.74264 6.48244i −0.615286 1.06571i −0.990334 0.138702i 0.955707π-0.955707\pi
0.375048 0.927005i 0.377626π-0.377626\pi
3838 0 0
3939 −8.44975 + 2.09077i −1.35304 + 0.334791i
4040 0 0
4141 2.91421 + 5.04757i 0.455124 + 0.788297i 0.998695 0.0510654i 0.0162617π-0.0162617\pi
−0.543572 + 0.839363i 0.682928π0.682928\pi
4242 0 0
4343 2.03553 3.52565i 0.310416 0.537656i −0.668036 0.744129i 0.732865π-0.732865\pi
0.978452 + 0.206472i 0.0661983π0.0661983\pi
4444 0 0
4545 4.00000 6.92820i 0.596285 1.03280i
4646 0 0
4747 6.00000 0.875190 0.437595 0.899172i 0.355830π-0.355830\pi
0.437595 + 0.899172i 0.355830π0.355830\pi
4848 0 0
4949 −6.24264 10.8126i −0.891806 1.54465i
5050 0 0
5151 −14.0711 −1.97034
5252 0 0
5353 2.82843 0.388514 0.194257 0.980951i 0.437770π-0.437770\pi
0.194257 + 0.980951i 0.437770π0.437770\pi
5454 0 0
5555 −4.58579 7.94282i −0.618347 1.07101i
5656 0 0
5757 3.00000 0.397360
5858 0 0
5959 −0.621320 + 1.07616i −0.0808890 + 0.140104i −0.903632 0.428310i 0.859109π-0.859109\pi
0.822743 + 0.568414i 0.192443π0.192443\pi
6060 0 0
6161 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i 0.685424π-0.685424\pi
0.998264 + 0.0588933i 0.0187572π0.0187572\pi
6262 0 0
6363 −6.24264 10.8126i −0.786499 1.36226i
6464 0 0
6565 −2.82843 + 9.79796i −0.350823 + 1.21529i
6666 0 0
6767 6.62132 + 11.4685i 0.808923 + 1.40110i 0.913610 + 0.406591i 0.133282π0.133282\pi
−0.104687 + 0.994505i 0.533384π0.533384\pi
6868 0 0
6969 −1.50000 + 2.59808i −0.180579 + 0.312772i
7070 0 0
7171 3.62132 6.27231i 0.429772 0.744386i −0.567081 0.823662i 0.691927π-0.691927\pi
0.996853 + 0.0792756i 0.0252607π0.0252607\pi
7272 0 0
7373 12.4853 1.46129 0.730646 0.682757i 0.239219π-0.239219\pi
0.730646 + 0.682757i 0.239219π0.239219\pi
7474 0 0
7575 −3.62132 6.27231i −0.418154 0.724264i
7676 0 0
7777 −14.3137 −1.63120
7878 0 0
7979 −6.00000 −0.675053 −0.337526 0.941316i 0.609590π-0.609590\pi
−0.337526 + 0.941316i 0.609590π0.609590\pi
8080 0 0
8181 4.74264 + 8.21449i 0.526960 + 0.912722i
8282 0 0
8383 −4.00000 −0.439057 −0.219529 0.975606i 0.570452π-0.570452\pi
−0.219529 + 0.975606i 0.570452π0.570452\pi
8484 0 0
8585 −8.24264 + 14.2767i −0.894040 + 1.54852i
8686 0 0
8787 10.4497 18.0995i 1.12033 1.94047i
8888 0 0
8989 1.67157 + 2.89525i 0.177186 + 0.306896i 0.940916 0.338641i 0.109967π-0.109967\pi
−0.763729 + 0.645537i 0.776634π0.776634\pi
9090 0 0
9191 11.0355 + 11.4685i 1.15684 + 1.20222i
9292 0 0
9393 −6.82843 11.8272i −0.708075 1.22642i
9494 0 0
9595 1.75736 3.04384i 0.180301 0.312291i
9696 0 0
9797 4.50000 7.79423i 0.456906 0.791384i −0.541890 0.840450i 0.682291π-0.682291\pi
0.998796 + 0.0490655i 0.0156243π0.0156243\pi
9898 0 0
9999 −9.17157 −0.921778
100100 0 0
101101 5.91421 + 10.2437i 0.588486 + 1.01929i 0.994431 + 0.105390i 0.0336092π0.0336092\pi
−0.405945 + 0.913898i 0.633057π0.633057\pi
102102 0 0
103103 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
104104 0 0
105105 −30.1421 −2.94157
106106 0 0
107107 9.62132 + 16.6646i 0.930128 + 1.61103i 0.783099 + 0.621897i 0.213638π0.213638\pi
0.147029 + 0.989132i 0.453029π0.453029\pi
108108 0 0
109109 8.48528 0.812743 0.406371 0.913708i 0.366794π-0.366794\pi
0.406371 + 0.913708i 0.366794π0.366794\pi
110110 0 0
111111 −9.03553 + 15.6500i −0.857615 + 1.48543i
112112 0 0
113113 0.0857864 0.148586i 0.00807011 0.0139778i −0.861962 0.506973i 0.830765π-0.830765\pi
0.870032 + 0.492995i 0.164098π0.164098\pi
114114 0 0
115115 1.75736 + 3.04384i 0.163875 + 0.283839i
116116 0 0
117117 7.07107 + 7.34847i 0.653720 + 0.679366i
118118 0 0
119119 12.8640 + 22.2810i 1.17924 + 2.04250i
120120 0 0
121121 0.242641 0.420266i 0.0220582 0.0382060i
122122 0 0
123123 7.03553 12.1859i 0.634373 1.09877i
124124 0 0
125125 5.65685 0.505964
126126 0 0
127127 −0.792893 1.37333i −0.0703579 0.121863i 0.828700 0.559693i 0.189081π-0.189081\pi
−0.899058 + 0.437829i 0.855747π0.855747\pi
128128 0 0
129129 −9.82843 −0.865345
130130 0 0
131131 4.00000 0.349482 0.174741 0.984614i 0.444091π-0.444091\pi
0.174741 + 0.984614i 0.444091π0.444091\pi
132132 0 0
133133 −2.74264 4.75039i −0.237817 0.411911i
134134 0 0
135135 1.17157 0.100833
136136 0 0
137137 −4.67157 + 8.09140i −0.399119 + 0.691295i −0.993617 0.112802i 0.964017π-0.964017\pi
0.594498 + 0.804097i 0.297351π0.297351\pi
138138 0 0
139139 −0.621320 + 1.07616i −0.0526997 + 0.0912786i −0.891172 0.453666i 0.850116π-0.850116\pi
0.838472 + 0.544944i 0.183449π0.183449\pi
140140 0 0
141141 −7.24264 12.5446i −0.609940 1.05645i
142142 0 0
143143 11.3492 2.80821i 0.949071 0.234834i
144144 0 0
145145 −12.2426 21.2049i −1.01670 1.76097i
146146 0 0
147147 −15.0711 + 26.1039i −1.24304 + 2.15301i
148148 0 0
149149 −1.67157 + 2.89525i −0.136941 + 0.237188i −0.926337 0.376696i 0.877060π-0.877060\pi
0.789397 + 0.613884i 0.210394π0.210394\pi
150150 0 0
151151 −16.9706 −1.38104 −0.690522 0.723311i 0.742619π-0.742619\pi
−0.690522 + 0.723311i 0.742619π0.742619\pi
152152 0 0
153153 8.24264 + 14.2767i 0.666378 + 1.15420i
154154 0 0
155155 −16.0000 −1.28515
156156 0 0
157157 0.485281 0.0387297 0.0193648 0.999812i 0.493836π-0.493836\pi
0.0193648 + 0.999812i 0.493836π0.493836\pi
158158 0 0
159159 −3.41421 5.91359i −0.270765 0.468978i
160160 0 0
161161 5.48528 0.432301
162162 0 0
163163 8.37868 14.5123i 0.656269 1.13669i −0.325305 0.945609i 0.605467π-0.605467\pi
0.981574 0.191082i 0.0611996π-0.0611996\pi
164164 0 0
165165 −11.0711 + 19.1757i −0.861881 + 1.49282i
166166 0 0
167167 7.86396 + 13.6208i 0.608532 + 1.05401i 0.991483 + 0.130239i 0.0415745π0.0415745\pi
−0.382951 + 0.923769i 0.625092π0.625092\pi
168168 0 0
169169 −11.0000 6.92820i −0.846154 0.532939i
170170 0 0
171171 −1.75736 3.04384i −0.134389 0.232768i
172172 0 0
173173 −4.50000 + 7.79423i −0.342129 + 0.592584i −0.984828 0.173534i 0.944481π-0.944481\pi
0.642699 + 0.766119i 0.277815π0.277815\pi
174174 0 0
175175 −6.62132 + 11.4685i −0.500525 + 0.866934i
176176 0 0
177177 3.00000 0.225494
178178 0 0
179179 −6.37868 11.0482i −0.476765 0.825781i 0.522881 0.852406i 0.324857π-0.324857\pi
−0.999645 + 0.0266249i 0.991524π0.991524\pi
180180 0 0
181181 0.485281 0.0360707 0.0180353 0.999837i 0.494259π-0.494259\pi
0.0180353 + 0.999837i 0.494259π0.494259\pi
182182 0 0
183183 −16.8995 −1.24925
184184 0 0
185185 10.5858 + 18.3351i 0.778282 + 1.34802i
186186 0 0
187187 18.8995 1.38207
188188 0 0
189189 0.914214 1.58346i 0.0664993 0.115180i
190190 0 0
191191 −3.37868 + 5.85204i −0.244473 + 0.423439i −0.961983 0.273109i 0.911948π-0.911948\pi
0.717511 + 0.696548i 0.245282π0.245282\pi
192192 0 0
193193 9.74264 + 16.8747i 0.701291 + 1.21467i 0.968014 + 0.250898i 0.0807258π0.0807258\pi
−0.266723 + 0.963773i 0.585941π0.585941\pi
194194 0 0
195195 23.8995 5.91359i 1.71148 0.423481i
196196 0 0
197197 1.50000 + 2.59808i 0.106871 + 0.185105i 0.914501 0.404584i 0.132584π-0.132584\pi
−0.807630 + 0.589689i 0.799250π0.799250\pi
198198 0 0
199199 12.1066 20.9692i 0.858214 1.48647i −0.0154165 0.999881i 0.504907π-0.504907\pi
0.873631 0.486590i 0.161759π-0.161759\pi
200200 0 0
201201 15.9853 27.6873i 1.12751 1.95291i
202202 0 0
203203 −38.2132 −2.68204
204204 0 0
205205 −8.24264 14.2767i −0.575691 0.997126i
206206 0 0
207207 3.51472 0.244290
208208 0 0
209209 −4.02944 −0.278722
210210 0 0
211211 6.79289 + 11.7656i 0.467642 + 0.809980i 0.999316 0.0369691i 0.0117703π-0.0117703\pi
−0.531674 + 0.846949i 0.678437π0.678437\pi
212212 0 0
213213 −17.4853 −1.19807
214214 0 0
215215 −5.75736 + 9.97204i −0.392649 + 0.680087i
216216 0 0
217217 −12.4853 + 21.6251i −0.847556 + 1.46801i
218218 0 0
219219 −15.0711 26.1039i −1.01841 1.76394i
220220 0 0
221221 −14.5711 15.1427i −0.980156 1.01861i
222222 0 0
223223 −3.44975 5.97514i −0.231012 0.400125i 0.727094 0.686538i 0.240870π-0.240870\pi
−0.958106 + 0.286413i 0.907537π0.907537\pi
224224 0 0
225225 −4.24264 + 7.34847i −0.282843 + 0.489898i
226226 0 0
227227 7.86396 13.6208i 0.521949 0.904043i −0.477725 0.878510i 0.658538π-0.658538\pi
0.999674 0.0255332i 0.00812837π-0.00812837\pi
228228 0 0
229229 −8.48528 −0.560723 −0.280362 0.959894i 0.590454π-0.590454\pi
−0.280362 + 0.959894i 0.590454π0.590454\pi
230230 0 0
231231 17.2782 + 29.9267i 1.13682 + 1.96903i
232232 0 0
233233 −20.4853 −1.34204 −0.671018 0.741441i 0.734143π-0.734143\pi
−0.671018 + 0.741441i 0.734143π0.734143\pi
234234 0 0
235235 −16.9706 −1.10704
236236 0 0
237237 7.24264 + 12.5446i 0.470460 + 0.814861i
238238 0 0
239239 −8.97056 −0.580257 −0.290129 0.956988i 0.593698π-0.593698\pi
−0.290129 + 0.956988i 0.593698π0.593698\pi
240240 0 0
241241 −15.2279 + 26.3755i −0.980917 + 1.69900i −0.322078 + 0.946713i 0.604381π0.604381\pi
−0.658838 + 0.752285i 0.728952π0.728952\pi
242242 0 0
243243 10.8284 18.7554i 0.694644 1.20316i
244244 0 0
245245 17.6569 + 30.5826i 1.12806 + 1.95385i
246246 0 0
247247 3.10660 + 3.22848i 0.197668 + 0.205423i
248248 0 0
249249 4.82843 + 8.36308i 0.305989 + 0.529989i
250250 0 0
251251 8.86396 15.3528i 0.559488 0.969062i −0.438051 0.898950i 0.644331π-0.644331\pi
0.997539 0.0701119i 0.0223356π-0.0223356\pi
252252 0 0
253253 2.01472 3.48960i 0.126664 0.219389i
254254 0 0
255255 39.7990 2.49231
256256 0 0
257257 −8.39949 14.5484i −0.523946 0.907501i −0.999611 0.0278749i 0.991126π-0.991126\pi
0.475665 0.879626i 0.342207π-0.342207\pi
258258 0 0
259259 33.0416 2.05311
260260 0 0
261261 −24.4853 −1.51560
262262 0 0
263263 −4.62132 8.00436i −0.284963 0.493570i 0.687637 0.726054i 0.258648π-0.258648\pi
−0.972600 + 0.232484i 0.925315π0.925315\pi
264264 0 0
265265 −8.00000 −0.491436
266266 0 0
267267 4.03553 6.98975i 0.246971 0.427766i
268268 0 0
269269 2.74264 4.75039i 0.167222 0.289637i −0.770220 0.637778i 0.779854π-0.779854\pi
0.937442 + 0.348141i 0.113187π0.113187\pi
270270 0 0
271271 −12.6213 21.8608i −0.766691 1.32795i −0.939348 0.342965i 0.888569π-0.888569\pi
0.172658 0.984982i 0.444765π-0.444765\pi
272272 0 0
273273 10.6569 36.9164i 0.644982 2.23428i
274274 0 0
275275 4.86396 + 8.42463i 0.293308 + 0.508024i
276276 0 0
277277 6.74264 11.6786i 0.405126 0.701699i −0.589210 0.807980i 0.700561π-0.700561\pi
0.994336 + 0.106281i 0.0338943π0.0338943\pi
278278 0 0
279279 −8.00000 + 13.8564i −0.478947 + 0.829561i
280280 0 0
281281 −2.14214 −0.127789 −0.0638945 0.997957i 0.520352π-0.520352\pi
−0.0638945 + 0.997957i 0.520352π0.520352\pi
282282 0 0
283283 −5.20711 9.01897i −0.309530 0.536122i 0.668729 0.743506i 0.266839π-0.266839\pi
−0.978260 + 0.207384i 0.933505π0.933505\pi
284284 0 0
285285 −8.48528 −0.502625
286286 0 0
287287 −25.7279 −1.51867
288288 0 0
289289 −8.48528 14.6969i −0.499134 0.864526i
290290 0 0
291291 −21.7279 −1.27371
292292 0 0
293293 1.15685 2.00373i 0.0675841 0.117059i −0.830253 0.557386i 0.811804π-0.811804\pi
0.897837 + 0.440327i 0.145138π0.145138\pi
294294 0 0
295295 1.75736 3.04384i 0.102317 0.177219i
296296 0 0
297297 −0.671573 1.16320i −0.0389686 0.0674956i
298298 0 0
299299 −4.34924 + 1.07616i −0.251523 + 0.0622358i
300300 0 0
301301 8.98528 + 15.5630i 0.517903 + 0.897034i
302302 0 0
303303 14.2782 24.7305i 0.820260 1.42073i
304304 0 0
305305 −9.89949 + 17.1464i −0.566843 + 0.981802i
306306 0 0
307307 −12.0000 −0.684876 −0.342438 0.939540i 0.611253π-0.611253\pi
−0.342438 + 0.939540i 0.611253π0.611253\pi
308308 0 0
309309 0 0
310310 0 0
311311 24.0000 1.36092 0.680458 0.732787i 0.261781π-0.261781\pi
0.680458 + 0.732787i 0.261781π0.261781\pi
312312 0 0
313313 20.4853 1.15790 0.578948 0.815364i 0.303463π-0.303463\pi
0.578948 + 0.815364i 0.303463π0.303463\pi
314314 0 0
315315 17.6569 + 30.5826i 0.994851 + 1.72313i
316316 0 0
317317 17.3137 0.972435 0.486217 0.873838i 0.338376π-0.338376\pi
0.486217 + 0.873838i 0.338376π0.338376\pi
318318 0 0
319319 −14.0355 + 24.3103i −0.785839 + 1.36111i
320320 0 0
321321 23.2279 40.2319i 1.29646 2.24553i
322322 0 0
323323 3.62132 + 6.27231i 0.201496 + 0.349001i
324324 0 0
325325 3.00000 10.3923i 0.166410 0.576461i
326326 0 0
327327 −10.2426 17.7408i −0.566419 0.981067i
328328 0 0
329329 −13.2426 + 22.9369i −0.730090 + 1.26455i
330330 0 0
331331 −3.62132 + 6.27231i −0.199046 + 0.344757i −0.948219 0.317616i 0.897118π-0.897118\pi
0.749174 + 0.662374i 0.230451π0.230451\pi
332332 0 0
333333 21.1716 1.16020
334334 0 0
335335 −18.7279 32.4377i −1.02322 1.77226i
336336 0 0
337337 4.48528 0.244329 0.122164 0.992510i 0.461016π-0.461016\pi
0.122164 + 0.992510i 0.461016π0.461016\pi
338338 0 0
339339 −0.414214 −0.0224970
340340 0 0
341341 9.17157 + 15.8856i 0.496669 + 0.860255i
342342 0 0
343343 24.2132 1.30739
344344 0 0
345345 4.24264 7.34847i 0.228416 0.395628i
346346 0 0
347347 −15.6213 + 27.0569i −0.838596 + 1.45249i 0.0524719 + 0.998622i 0.483290π0.483290\pi
−0.891068 + 0.453869i 0.850043π0.850043\pi
348348 0 0
349349 17.2279 + 29.8396i 0.922190 + 1.59728i 0.796020 + 0.605270i 0.206935π0.206935\pi
0.126170 + 0.992009i 0.459732π0.459732\pi
350350 0 0
351351 −0.414214 + 1.43488i −0.0221091 + 0.0765881i
352352 0 0
353353 7.32843 + 12.6932i 0.390053 + 0.675591i 0.992456 0.122601i 0.0391234π-0.0391234\pi
−0.602403 + 0.798192i 0.705790π0.705790\pi
354354 0 0
355355 −10.2426 + 17.7408i −0.543623 + 0.941583i
356356 0 0
357357 31.0563 53.7912i 1.64368 2.84693i
358358 0 0
359359 −8.00000 −0.422224 −0.211112 0.977462i 0.567708π-0.567708\pi
−0.211112 + 0.977462i 0.567708π0.567708\pi
360360 0 0
361361 8.72792 + 15.1172i 0.459364 + 0.795642i
362362 0 0
363363 −1.17157 −0.0614916
364364 0 0
365365 −35.3137 −1.84840
366366 0 0
367367 −4.13604 7.16383i −0.215899 0.373949i 0.737651 0.675182i 0.235935π-0.235935\pi
−0.953550 + 0.301233i 0.902602π0.902602\pi
368368 0 0
369369 −16.4853 −0.858189
370370 0 0
371371 −6.24264 + 10.8126i −0.324102 + 0.561361i
372372 0 0
373373 18.7426 32.4632i 0.970457 1.68088i 0.276280 0.961077i 0.410898π-0.410898\pi
0.694178 0.719804i 0.255768π-0.255768\pi
374374 0 0
375375 −6.82843 11.8272i −0.352618 0.610753i
376376 0 0
377377 30.2990 7.49706i 1.56048 0.386118i
378378 0 0
379379 −13.6924 23.7159i −0.703331 1.21820i −0.967291 0.253671i 0.918362π-0.918362\pi
0.263960 0.964534i 0.414971π-0.414971\pi
380380 0 0
381381 −1.91421 + 3.31552i −0.0980681 + 0.169859i
382382 0 0
383383 −7.86396 + 13.6208i −0.401830 + 0.695989i −0.993947 0.109863i 0.964959π-0.964959\pi
0.592117 + 0.805852i 0.298292π0.298292\pi
384384 0 0
385385 40.4853 2.06332
386386 0 0
387387 5.75736 + 9.97204i 0.292663 + 0.506907i
388388 0 0
389389 16.6274 0.843044 0.421522 0.906818i 0.361496π-0.361496\pi
0.421522 + 0.906818i 0.361496π0.361496\pi
390390 0 0
391391 −7.24264 −0.366276
392392 0 0
393393 −4.82843 8.36308i −0.243562 0.421862i
394394 0 0
395395 16.9706 0.853882
396396 0 0
397397 −5.74264 + 9.94655i −0.288215 + 0.499203i −0.973384 0.229181i 0.926395π-0.926395\pi
0.685169 + 0.728384i 0.259728π0.259728\pi
398398 0 0
399399 −6.62132 + 11.4685i −0.331481 + 0.574141i
400400 0 0
401401 −5.57107 9.64937i −0.278206 0.481867i 0.692733 0.721194i 0.256406π-0.256406\pi
−0.970939 + 0.239327i 0.923073π0.923073\pi
402402 0 0
403403 5.65685 19.5959i 0.281788 0.976142i
404404 0 0
405405 −13.4142 23.2341i −0.666558 1.15451i
406406 0 0
407407 12.1360 21.0202i 0.601561 1.04193i
408408 0 0
409409 5.25736 9.10601i 0.259960 0.450263i −0.706271 0.707941i 0.749624π-0.749624\pi
0.966231 + 0.257678i 0.0829574π0.0829574\pi
410410 0 0
411411 22.5563 1.11262
412412 0 0
413413 −2.74264 4.75039i −0.134957 0.233752i
414414 0 0
415415 11.3137 0.555368
416416 0 0
417417 3.00000 0.146911
418418 0 0
419419 −5.86396 10.1567i −0.286473 0.496186i 0.686492 0.727137i 0.259150π-0.259150\pi
−0.972965 + 0.230951i 0.925816π0.925816\pi
420420 0 0
421421 −0.485281 −0.0236512 −0.0118256 0.999930i 0.503764π-0.503764\pi
−0.0118256 + 0.999930i 0.503764π0.503764\pi
422422 0 0
423423 −8.48528 + 14.6969i −0.412568 + 0.714590i
424424 0 0
425425 8.74264 15.1427i 0.424080 0.734529i
426426 0 0
427427 15.4497 + 26.7597i 0.747666 + 1.29499i
428428 0 0
429429 −19.5711 20.3389i −0.944900 0.981969i
430430 0 0
431431 17.3492 + 30.0498i 0.835684 + 1.44745i 0.893473 + 0.449118i 0.148262π0.148262\pi
−0.0577890 + 0.998329i 0.518405π0.518405\pi
432432 0 0
433433 1.25736 2.17781i 0.0604248 0.104659i −0.834231 0.551416i 0.814088π-0.814088\pi
0.894655 + 0.446757i 0.147421π0.147421\pi
434434 0 0
435435 −29.5563 + 51.1931i −1.41712 + 2.45452i
436436 0 0
437437 1.54416 0.0738670
438438 0 0
439439 14.0355 + 24.3103i 0.669879 + 1.16027i 0.977937 + 0.208898i 0.0669876π0.0669876\pi
−0.308058 + 0.951368i 0.599679π0.599679\pi
440440 0 0
441441 35.3137 1.68161
442442 0 0
443443 28.9706 1.37643 0.688216 0.725505i 0.258394π-0.258394\pi
0.688216 + 0.725505i 0.258394π0.258394\pi
444444 0 0
445445 −4.72792 8.18900i −0.224125 0.388196i
446446 0 0
447447 8.07107 0.381748
448448 0 0
449449 −6.25736 + 10.8381i −0.295303 + 0.511480i −0.975055 0.221962i 0.928754π-0.928754\pi
0.679752 + 0.733442i 0.262087π0.262087\pi
450450 0 0
451451 −9.44975 + 16.3674i −0.444971 + 0.770713i
452452 0 0
453453 20.4853 + 35.4815i 0.962482 + 1.66707i
454454 0 0
455455 −31.2132 32.4377i −1.46330 1.52070i
456456 0 0
457457 −15.5000 26.8468i −0.725059 1.25584i −0.958950 0.283577i 0.908479π-0.908479\pi
0.233890 0.972263i 0.424854π-0.424854\pi
458458 0 0
459459 −1.20711 + 2.09077i −0.0563429 + 0.0975888i
460460 0 0
461461 0.600505 1.04011i 0.0279683 0.0484425i −0.851702 0.524026i 0.824430π-0.824430\pi
0.879671 + 0.475583i 0.157763π0.157763\pi
462462 0 0
463463 18.3431 0.852478 0.426239 0.904611i 0.359838π-0.359838\pi
0.426239 + 0.904611i 0.359838π0.359838\pi
464464 0 0
465465 19.3137 + 33.4523i 0.895652 + 1.55131i
466466 0 0
467467 −6.97056 −0.322559 −0.161280 0.986909i 0.551562π-0.551562\pi
−0.161280 + 0.986909i 0.551562π0.551562\pi
468468 0 0
469469 −58.4558 −2.69924
470470 0 0
471471 −0.585786 1.01461i −0.0269916 0.0467508i
472472 0 0
473473 13.2010 0.606983
474474 0 0
475475 −1.86396 + 3.22848i −0.0855244 + 0.148133i
476476 0 0
477477 −4.00000 + 6.92820i −0.183147 + 0.317221i
478478 0 0
479479 4.37868 + 7.58410i 0.200067 + 0.346526i 0.948550 0.316628i 0.102551π-0.102551\pi
−0.748483 + 0.663154i 0.769217π0.769217\pi
480480 0 0
481481 −26.1985 + 6.48244i −1.19455 + 0.295574i
482482 0 0
483483 −6.62132 11.4685i −0.301281 0.521833i
484484 0 0
485485 −12.7279 + 22.0454i −0.577945 + 1.00103i
486486 0 0
487487 6.44975 11.1713i 0.292266 0.506219i −0.682079 0.731278i 0.738924π-0.738924\pi
0.974345 + 0.225059i 0.0722574π0.0722574\pi
488488 0 0
489489 −40.4558 −1.82948
490490 0 0
491491 11.1066 + 19.2372i 0.501234 + 0.868163i 0.999999 + 0.00142539i 0.000453717π0.000453717\pi
−0.498765 + 0.866737i 0.666213π0.666213\pi
492492 0 0
493493 50.4558 2.27242
494494 0 0
495495 25.9411 1.16597
496496 0 0
497497 15.9853 + 27.6873i 0.717038 + 1.24195i
498498 0 0
499499 17.6569 0.790429 0.395215 0.918589i 0.370670π-0.370670\pi
0.395215 + 0.918589i 0.370670π0.370670\pi
500500 0 0
501501 18.9853 32.8835i 0.848200 1.46913i
502502 0 0
503503 −7.37868 + 12.7802i −0.328999 + 0.569843i −0.982314 0.187244i 0.940045π-0.940045\pi
0.653314 + 0.757087i 0.273378π0.273378\pi
504504 0 0
505505 −16.7279 28.9736i −0.744383 1.28931i
506506 0 0
507507 −1.20711 + 31.3616i −0.0536095 + 1.39282i
508508 0 0
509509 −2.57107 4.45322i −0.113961 0.197386i 0.803403 0.595435i 0.203020π-0.203020\pi
−0.917364 + 0.398050i 0.869687π0.869687\pi
510510 0 0
511511 −27.5563 + 47.7290i −1.21902 + 2.11141i
512512 0 0
513513 0.257359 0.445759i 0.0113627 0.0196808i
514514 0 0
515515 0 0
516516 0 0
517517 9.72792 + 16.8493i 0.427834 + 0.741029i
518518 0 0
519519 21.7279 0.953750
520520 0 0
521521 −9.17157 −0.401814 −0.200907 0.979610i 0.564389π-0.564389\pi
−0.200907 + 0.979610i 0.564389π0.564389\pi
522522 0 0
523523 −8.20711 14.2151i −0.358872 0.621584i 0.628901 0.777485i 0.283505π-0.283505\pi
−0.987773 + 0.155901i 0.950172π0.950172\pi
524524 0 0
525525 31.9706 1.39531
526526 0 0
527527 16.4853 28.5533i 0.718110 1.24380i
528528 0 0
529529 10.7279 18.5813i 0.466431 0.807883i
530530 0 0
531531 −1.75736 3.04384i −0.0762629 0.132091i
532532 0 0
533533 20.3995 5.04757i 0.883600 0.218634i
534534 0 0
535535 −27.2132 47.1347i −1.17653 2.03781i
536536 0 0
537537 −15.3995 + 26.6727i −0.664537 + 1.15101i
538538 0 0
539539 20.2426 35.0613i 0.871912 1.51020i
540540 0 0
541541 2.00000 0.0859867 0.0429934 0.999075i 0.486311π-0.486311\pi
0.0429934 + 0.999075i 0.486311π0.486311\pi
542542 0 0
543543 −0.585786 1.01461i −0.0251385 0.0435412i
544544 0 0
545545 −24.0000 −1.02805
546546 0 0
547547 −36.0000 −1.53925 −0.769624 0.638497i 0.779557π-0.779557\pi
−0.769624 + 0.638497i 0.779557π0.779557\pi
548548 0 0
549549 9.89949 + 17.1464i 0.422500 + 0.731792i
550550 0 0
551551 −10.7574 −0.458279
552552 0 0
553553 13.2426 22.9369i 0.563134 0.975377i
554554 0 0
555555 25.5563 44.2649i 1.08481 1.87894i
556556 0 0
557557 4.32843 + 7.49706i 0.183401 + 0.317660i 0.943037 0.332689i 0.107956π-0.107956\pi
−0.759635 + 0.650349i 0.774623π0.774623\pi
558558 0 0
559559 −10.1777 10.5769i −0.430470 0.447357i
560560 0 0
561561 −22.8137 39.5145i −0.963196 1.66830i
562562 0 0
563563 16.3492 28.3177i 0.689038 1.19345i −0.283111 0.959087i 0.591366π-0.591366\pi
0.972149 0.234362i 0.0753002π-0.0753002\pi
564564 0 0
565565 −0.242641 + 0.420266i −0.0102080 + 0.0176807i
566566 0 0
567567 −41.8701 −1.75838
568568 0 0
569569 12.9853 + 22.4912i 0.544371 + 0.942879i 0.998646 + 0.0520172i 0.0165651π0.0165651\pi
−0.454275 + 0.890862i 0.650102π0.650102\pi
570570 0 0
571571 −40.2843 −1.68584 −0.842922 0.538036i 0.819167π-0.819167\pi
−0.842922 + 0.538036i 0.819167π0.819167\pi
572572 0 0
573573 16.3137 0.681515
574574 0 0
575575 −1.86396 3.22848i −0.0777325 0.134637i
576576 0 0
577577 4.48528 0.186725 0.0933624 0.995632i 0.470238π-0.470238\pi
0.0933624 + 0.995632i 0.470238π0.470238\pi
578578 0 0
579579 23.5208 40.7392i 0.977492 1.69307i
580580 0 0
581581 8.82843 15.2913i 0.366265 0.634389i
582582 0 0
583583 4.58579 + 7.94282i 0.189924 + 0.328958i
584584 0 0
585585 −20.0000 20.7846i −0.826898 0.859338i
586586 0 0
587587 −10.3492 17.9254i −0.427159 0.739861i 0.569460 0.822019i 0.307152π-0.307152\pi
−0.996619 + 0.0821578i 0.973819π0.973819\pi
588588 0 0
589589 −3.51472 + 6.08767i −0.144821 + 0.250838i
590590 0 0
591591 3.62132 6.27231i 0.148961 0.258008i
592592 0 0
593593 14.8284 0.608931 0.304465 0.952523i 0.401522π-0.401522\pi
0.304465 + 0.952523i 0.401522π0.401522\pi
594594 0 0
595595 −36.3848 63.0203i −1.49163 2.58358i
596596 0 0
597597 −58.4558 −2.39244
598598 0 0
599599 47.9411 1.95882 0.979411 0.201878i 0.0647045π-0.0647045\pi
0.979411 + 0.201878i 0.0647045π0.0647045\pi
600600 0 0
601601 5.25736 + 9.10601i 0.214452 + 0.371442i 0.953103 0.302646i 0.0978701π-0.0978701\pi
−0.738651 + 0.674088i 0.764537π0.764537\pi
602602 0 0
603603 −37.4558 −1.52532
604604 0 0
605605 −0.686292 + 1.18869i −0.0279017 + 0.0483272i
606606 0 0
607607 0.792893 1.37333i 0.0321825 0.0557418i −0.849486 0.527612i 0.823088π-0.823088\pi
0.881668 + 0.471870i 0.156421π0.156421\pi
608608 0 0
609609 46.1274 + 79.8950i 1.86918 + 3.23751i
610610 0 0
611611 6.00000 20.7846i 0.242734 0.840855i
612612 0 0
613613 −7.25736 12.5701i −0.293122 0.507702i 0.681424 0.731889i 0.261361π-0.261361\pi
−0.974546 + 0.224186i 0.928028π0.928028\pi
614614 0 0
615615 −19.8995 + 34.4669i −0.802425 + 1.38984i
616616 0 0
617617 22.1569 38.3768i 0.892001 1.54499i 0.0545289 0.998512i 0.482634π-0.482634\pi
0.837472 0.546479i 0.184032π-0.184032\pi
618618 0 0
619619 4.97056 0.199784 0.0998919 0.994998i 0.468150π-0.468150\pi
0.0998919 + 0.994998i 0.468150π0.468150\pi
620620 0 0
621621 0.257359 + 0.445759i 0.0103275 + 0.0178877i
622622 0 0
623623 −14.7574 −0.591241
624624 0 0
625625 −31.0000 −1.24000
626626 0 0
627627 4.86396 + 8.42463i 0.194248 + 0.336447i
628628 0 0
629629 −43.6274 −1.73954
630630 0 0
631631 3.62132 6.27231i 0.144162 0.249697i −0.784898 0.619625i 0.787285π-0.787285\pi
0.929060 + 0.369929i 0.120618π0.120618\pi
632632 0 0
633633 16.3995 28.4048i 0.651821 1.12899i
634634 0 0
635635 2.24264 + 3.88437i 0.0889965 + 0.154146i
636636 0 0
637637 −43.6985 + 10.8126i −1.73140 + 0.428410i
638638 0 0
639639 10.2426 + 17.7408i 0.405193 + 0.701814i
640640 0 0
641641 11.3995 19.7445i 0.450253 0.779861i −0.548148 0.836381i 0.684667π-0.684667\pi
0.998401 + 0.0565200i 0.0180005π0.0180005\pi
642642 0 0
643643 −0.106602 + 0.184640i −0.00420396 + 0.00728147i −0.868120 0.496355i 0.834671π-0.834671\pi
0.863916 + 0.503636i 0.168005π0.168005\pi
644644 0 0
645645 27.7990 1.09458
646646 0 0
647647 −11.6213 20.1287i −0.456881 0.791342i 0.541913 0.840435i 0.317700π-0.317700\pi
−0.998794 + 0.0490931i 0.984367π0.984367\pi
648648 0 0
649649 −4.02944 −0.158169
650650 0 0
651651 60.2843 2.36273
652652 0 0
653653 11.5711 + 20.0417i 0.452811 + 0.784291i 0.998559 0.0536576i 0.0170879π-0.0170879\pi
−0.545749 + 0.837949i 0.683755π0.683755\pi
654654 0 0
655655 −11.3137 −0.442063
656656 0 0
657657 −17.6569 + 30.5826i −0.688859 + 1.19314i
658658 0 0
659659 −12.1066 + 20.9692i −0.471606 + 0.816846i −0.999472 0.0324816i 0.989659π-0.989659\pi
0.527866 + 0.849328i 0.322992π0.322992\pi
660660 0 0
661661 −12.2279 21.1794i −0.475611 0.823782i 0.523999 0.851719i 0.324440π-0.324440\pi
−0.999610 + 0.0279366i 0.991106π0.991106\pi
662662 0 0
663663 −14.0711 + 48.7436i −0.546475 + 1.89304i
664664 0 0
665665 7.75736 + 13.4361i 0.300817 + 0.521031i
666666 0 0
667667 5.37868 9.31615i 0.208263 0.360723i
668668 0 0
669669 −8.32843 + 14.4253i −0.321996 + 0.557713i
670670 0 0
671671 22.6985 0.876265
672672 0 0
673673 4.01472 + 6.95370i 0.154756 + 0.268045i 0.932970 0.359954i 0.117208π-0.117208\pi
−0.778214 + 0.627999i 0.783874π0.783874\pi
674674 0 0
675675 −1.24264 −0.0478293
676676 0 0
677677 25.4558 0.978348 0.489174 0.872186i 0.337298π-0.337298\pi
0.489174 + 0.872186i 0.337298π0.337298\pi
678678 0 0
679679 19.8640 + 34.4054i 0.762309 + 1.32036i
680680 0 0
681681 −37.9706 −1.45504
682682 0 0
683683 −4.62132 + 8.00436i −0.176830 + 0.306278i −0.940793 0.338982i 0.889918π-0.889918\pi
0.763963 + 0.645260i 0.223251π0.223251\pi
684684 0 0
685685 13.2132 22.8859i 0.504851 0.874427i
686686 0 0
687687 10.2426 + 17.7408i 0.390781 + 0.676853i
688688 0 0
689689 2.82843 9.79796i 0.107754 0.373273i
690690 0 0
691691 −8.03553 13.9180i −0.305686 0.529464i 0.671728 0.740798i 0.265552π-0.265552\pi
−0.977414 + 0.211334i 0.932219π0.932219\pi
692692 0 0
693693 20.2426 35.0613i 0.768954 1.33187i
694694 0 0
695695 1.75736 3.04384i 0.0666604 0.115459i
696696 0 0
697697 33.9706 1.28673
698698 0 0
699699 24.7279 + 42.8300i 0.935296 + 1.61998i
700700 0 0
701701 8.48528 0.320485 0.160242 0.987078i 0.448772π-0.448772\pi
0.160242 + 0.987078i 0.448772π0.448772\pi
702702 0 0
703703 9.30152 0.350813
704704 0 0
705705 20.4853 + 35.4815i 0.771520 + 1.33631i
706706 0 0
707707 −52.2132 −1.96368
708708 0 0
709709 −9.74264 + 16.8747i −0.365893 + 0.633744i −0.988919 0.148456i 0.952570π-0.952570\pi
0.623026 + 0.782201i 0.285903π0.285903\pi
710710 0 0
711711 8.48528 14.6969i 0.318223 0.551178i
712712 0 0
713713 −3.51472 6.08767i −0.131627 0.227985i
714714 0 0
715715 −32.1005 + 7.94282i −1.20049 + 0.297044i
716716 0 0
717717 10.8284 + 18.7554i 0.404395 + 0.700433i
718718 0 0
719719 −11.3787 + 19.7085i −0.424353 + 0.735001i −0.996360 0.0852478i 0.972832π-0.972832\pi
0.572007 + 0.820249i 0.306165π0.306165\pi
720720 0 0
721721 0 0
722722 0 0
723723 73.5269 2.73450
724724 0 0
725725 12.9853 + 22.4912i 0.482261 + 0.835301i
726726 0 0
727727 −35.3137 −1.30971 −0.654856 0.755753i 0.727271π-0.727271\pi
−0.654856 + 0.755753i 0.727271π0.727271\pi
728728 0 0
729729 −23.8284 −0.882534
730730 0 0
731731 −11.8640 20.5490i −0.438804 0.760032i
732732 0 0
733733 −43.9411 −1.62300 −0.811501 0.584351i 0.801349π-0.801349\pi
−0.811501 + 0.584351i 0.801349π0.801349\pi
734734 0 0
735735 42.6274 73.8329i 1.57234 2.72337i
736736 0 0
737737 −21.4706 + 37.1881i −0.790878 + 1.36984i
738738 0 0
739739 15.1066 + 26.1654i 0.555705 + 0.962510i 0.997848 + 0.0655653i 0.0208851π0.0208851\pi
−0.442143 + 0.896945i 0.645782π0.645782\pi
740740 0 0
741741 3.00000 10.3923i 0.110208 0.381771i
742742 0 0
743743 −3.62132 6.27231i −0.132853 0.230109i 0.791922 0.610622i 0.209081π-0.209081\pi
−0.924775 + 0.380513i 0.875747π0.875747\pi
744744 0 0
745745 4.72792 8.18900i 0.173218 0.300022i
746746 0 0
747747 5.65685 9.79796i 0.206973 0.358489i
748748 0 0
749749 −84.9411 −3.10368
750750 0 0
751751 8.55025 + 14.8095i 0.312003 + 0.540405i 0.978796 0.204838i 0.0656667π-0.0656667\pi
−0.666793 + 0.745243i 0.732333π0.732333\pi
752752 0 0
753753 −42.7990 −1.55968
754754 0 0
755755 48.0000 1.74690
756756 0 0
757757 −11.7426 20.3389i −0.426794 0.739228i 0.569793 0.821789i 0.307024π-0.307024\pi
−0.996586 + 0.0825605i 0.973690π0.973690\pi
758758 0 0
759759 −9.72792 −0.353101
760760 0 0
761761 −14.7426 + 25.5350i −0.534420 + 0.925643i 0.464771 + 0.885431i 0.346137π0.346137\pi
−0.999191 + 0.0402121i 0.987197π0.987197\pi
762762 0 0
763763 −18.7279 + 32.4377i −0.677996 + 1.17432i
764764 0 0
765765 −23.3137 40.3805i −0.842909 1.45996i
766766 0 0
767767 3.10660 + 3.22848i 0.112173 + 0.116573i
768768 0 0
769769 22.7132 + 39.3404i 0.819059 + 1.41865i 0.906376 + 0.422471i 0.138837π0.138837\pi
−0.0873172 + 0.996181i 0.527829π0.527829\pi
770770 0 0
771771 −20.2782 + 35.1228i −0.730301 + 1.26492i
772772 0 0
773773 −5.74264 + 9.94655i −0.206548 + 0.357752i −0.950625 0.310342i 0.899556π-0.899556\pi
0.744077 + 0.668094i 0.232890π0.232890\pi
774774 0 0
775775 16.9706 0.609601
776776 0 0
777777 −39.8848 69.0825i −1.43086 2.47832i
778778 0 0
779779 −7.24264 −0.259495
780780 0 0
781781 23.4853 0.840369
782782 0 0
783783 −1.79289 3.10538i −0.0640728 0.110977i
784784 0 0
785785 −1.37258 −0.0489896
786786 0 0
787787 19.0061 32.9195i 0.677494 1.17345i −0.298239 0.954491i 0.596399π-0.596399\pi
0.975733 0.218963i 0.0702674π-0.0702674\pi
788788 0 0
789789 −11.1569 + 19.3242i −0.397195 + 0.687961i
790790 0 0
791791 0.378680 + 0.655892i 0.0134643 + 0.0233208i
792792 0 0
793793 −17.5000 18.1865i −0.621443 0.645823i
794794 0 0
795795 9.65685 + 16.7262i 0.342493 + 0.593216i
796796 0 0
797797 −16.5000 + 28.5788i −0.584460 + 1.01231i 0.410483 + 0.911868i 0.365360π0.365360\pi
−0.994943 + 0.100446i 0.967973π0.967973\pi
798798 0 0
799799 17.4853 30.2854i 0.618585 1.07142i
800800 0 0
801801 −9.45584 −0.334106
802802 0 0
803803 20.2426 + 35.0613i 0.714347 + 1.23729i
804804 0 0
805805 −15.5147 −0.546822
806806 0 0
807807 −13.2426 −0.466163
808808 0 0
809809 2.91421 + 5.04757i 0.102458 + 0.177463i 0.912697 0.408637i 0.133996π-0.133996\pi
−0.810239 + 0.586100i 0.800663π0.800663\pi
810810 0 0
811811 12.3431 0.433426 0.216713 0.976235i 0.430466π-0.430466\pi
0.216713 + 0.976235i 0.430466π0.430466\pi
812812 0 0
813813 −30.4706 + 52.7766i −1.06865 + 1.85095i
814814 0 0
815815 −23.6985 + 41.0470i −0.830122 + 1.43781i
816816 0 0
817817 2.52944 + 4.38111i 0.0884938 + 0.153276i
818818 0 0
819819 −43.6985 + 10.8126i −1.52695 + 0.377822i
820820 0 0
821821 9.98528 + 17.2950i 0.348489 + 0.603600i 0.985981 0.166856i 0.0533616π-0.0533616\pi
−0.637492 + 0.770457i 0.720028π0.720028\pi
822822 0 0
823823 0.106602 0.184640i 0.00371590 0.00643613i −0.864161 0.503215i 0.832151π-0.832151\pi
0.867877 + 0.496778i 0.165484π0.165484\pi
824824 0 0
825825 11.7426 20.3389i 0.408826 0.708108i
826826 0 0
827827 −21.9411 −0.762968 −0.381484 0.924376i 0.624587π-0.624587\pi
−0.381484 + 0.924376i 0.624587π0.624587\pi
828828 0 0
829829 17.9853 + 31.1514i 0.624655 + 1.08193i 0.988608 + 0.150516i 0.0480936π0.0480936\pi
−0.363953 + 0.931417i 0.618573π0.618573\pi
830830 0 0
831831 −32.5563 −1.12937
832832 0 0
833833 −72.7696 −2.52132
834834 0 0
835835 −22.2426 38.5254i −0.769738 1.33323i
836836 0 0
837837 −2.34315 −0.0809910
838838 0 0
839839 −5.34924 + 9.26516i −0.184676 + 0.319869i −0.943467 0.331465i 0.892457π-0.892457\pi
0.758791 + 0.651334i 0.225790π0.225790\pi
840840 0 0
841841 −22.9706 + 39.7862i −0.792088 + 1.37194i
842842 0 0
843843 2.58579 + 4.47871i 0.0890592 + 0.154255i
844844 0 0
845845 31.1127 + 19.5959i 1.07031 + 0.674120i
846846 0 0
847847 1.07107 + 1.85514i 0.0368023 + 0.0637435i
848848 0 0
849849 −12.5711 + 21.7737i −0.431438 + 0.747272i
850850 0 0
851851 −4.65076 + 8.05535i −0.159426 + 0.276134i
852852 0 0
853853 41.4558 1.41942 0.709711 0.704493i 0.248826π-0.248826\pi
0.709711 + 0.704493i 0.248826π0.248826\pi
854854 0 0
855855 4.97056 + 8.60927i 0.169990 + 0.294431i
856856 0 0
857857 33.1716 1.13312 0.566560 0.824021i 0.308274π-0.308274\pi
0.566560 + 0.824021i 0.308274π0.308274\pi
858858 0 0
859859 −36.0000 −1.22830 −0.614152 0.789188i 0.710502π-0.710502\pi
−0.614152 + 0.789188i 0.710502π0.710502\pi
860860 0 0
861861 31.0563 + 53.7912i 1.05840 + 1.83320i
862862 0 0
863863 −32.0000 −1.08929 −0.544646 0.838666i 0.683336π-0.683336\pi
−0.544646 + 0.838666i 0.683336π0.683336\pi
864864 0 0
865865 12.7279 22.0454i 0.432762 0.749566i
866866 0 0
867867 −20.4853 + 35.4815i −0.695717 + 1.20502i
868868 0 0
869869 −9.72792 16.8493i −0.329997 0.571572i
870870 0 0
871871 46.3492 11.4685i 1.57048 0.388594i
872872 0 0
873873 12.7279 + 22.0454i 0.430775 + 0.746124i
874874 0 0
875875 −12.4853 + 21.6251i −0.422080 + 0.731063i
876876 0 0
877877 11.9853 20.7591i 0.404714 0.700986i −0.589574 0.807714i 0.700704π-0.700704\pi
0.994288 + 0.106729i 0.0340377π0.0340377\pi
878878 0 0
879879 −5.58579 −0.188404
880880 0 0
881881 −9.08579 15.7370i −0.306108 0.530194i 0.671399 0.741096i 0.265694π-0.265694\pi
−0.977507 + 0.210901i 0.932360π0.932360\pi
882882 0 0
883883 27.5980 0.928746 0.464373 0.885640i 0.346280π-0.346280\pi
0.464373 + 0.885640i 0.346280π0.346280\pi
884884 0 0
885885 −8.48528 −0.285230
886886 0 0
887887 −12.1066 20.9692i −0.406500 0.704078i 0.587995 0.808865i 0.299918π-0.299918\pi
−0.994495 + 0.104786i 0.966584π0.966584\pi
888888 0 0
889889 7.00000 0.234772
890890 0 0
891891 −15.3787 + 26.6367i −0.515205 + 0.892362i
892892 0 0
893893 −3.72792 + 6.45695i −0.124750 + 0.216074i
894894 0 0
895895 18.0416 + 31.2490i 0.603065 + 1.04454i
896896 0 0
897897 7.50000 + 7.79423i 0.250418 + 0.260242i
898898 0 0
899899 24.4853 + 42.4098i 0.816630 + 1.41444i
900900 0 0
901901 8.24264 14.2767i 0.274602 0.475625i
902902 0 0
903903 21.6924 37.5723i 0.721877 1.25033i
904904 0 0
905905 −1.37258 −0.0456262
906906 0 0
907907 18.1066 + 31.3616i 0.601220 + 1.04134i 0.992637 + 0.121130i 0.0386517π0.0386517\pi
−0.391417 + 0.920213i 0.628015π0.628015\pi
908908 0 0
909909 −33.4558 −1.10966
910910 0 0
911911 24.0000 0.795155 0.397578 0.917568i 0.369851π-0.369851\pi
0.397578 + 0.917568i 0.369851π0.369851\pi
912912 0 0
913913 −6.48528 11.2328i −0.214631 0.371753i
914914 0 0
915915 47.7990 1.58019
916916 0 0
917917 −8.82843 + 15.2913i −0.291540 + 0.504963i
918918 0 0
919919 −19.1777 + 33.2167i −0.632613 + 1.09572i 0.354403 + 0.935093i 0.384684π0.384684\pi
−0.987016 + 0.160625i 0.948649π0.948649\pi
920920 0 0
921921 14.4853 + 25.0892i 0.477306 + 0.826719i
922922 0 0
923923 −18.1066 18.8169i −0.595986 0.619367i
924924 0 0
925925 −11.2279 19.4473i −0.369172 0.639424i
926926 0 0
927927 0 0
928928 0 0
929929 5.05635 8.75785i 0.165893 0.287336i −0.771079 0.636740i 0.780283π-0.780283\pi
0.936972 + 0.349404i 0.113616π0.113616\pi
930930 0 0
931931 15.5147 0.508474
932932 0 0
933933 −28.9706 50.1785i −0.948454 1.64277i
934934 0 0
935935 −53.4558 −1.74819
936936 0 0
937937 −45.4558 −1.48498 −0.742489 0.669858i 0.766355π-0.766355\pi
−0.742489 + 0.669858i 0.766355π0.766355\pi
938938 0 0
939939 −24.7279 42.8300i −0.806965 1.39770i
940940 0 0
941941 18.0000 0.586783 0.293392 0.955992i 0.405216π-0.405216\pi
0.293392 + 0.955992i 0.405216π0.405216\pi
942942 0 0
943943 3.62132 6.27231i 0.117926 0.204255i
944944 0 0
945945 −2.58579 + 4.47871i −0.0841156 + 0.145693i
946946 0 0
947947 1.62132 + 2.80821i 0.0526858 + 0.0912545i 0.891166 0.453678i 0.149888π-0.149888\pi
−0.838480 + 0.544933i 0.816555π0.816555\pi
948948 0 0
949949 12.4853 43.2503i 0.405289 1.40396i
950950 0 0
951951 −20.8995 36.1990i −0.677713 1.17383i
952952 0 0
953953 1.67157 2.89525i 0.0541476 0.0937863i −0.837681 0.546160i 0.816089π-0.816089\pi
0.891829 + 0.452373i 0.149423π0.149423\pi
954954 0 0
955955 9.55635 16.5521i 0.309236 0.535613i
956956 0 0
957957 67.7696 2.19068
958958 0 0
959959 −20.6213 35.7172i −0.665897 1.15337i
960960 0 0
961961 1.00000 0.0322581
962962 0 0
963963 −54.4264 −1.75387
964964 0 0
965965 −27.5563 47.7290i −0.887070 1.53645i
966966 0 0
967967 7.02944 0.226051 0.113026 0.993592i 0.463946π-0.463946\pi
0.113026 + 0.993592i 0.463946π0.463946\pi
968968 0 0
969969 8.74264 15.1427i 0.280854 0.486454i
970970 0 0
971971 16.3787 28.3687i 0.525617 0.910395i −0.473938 0.880558i 0.657168π-0.657168\pi
0.999555 0.0298368i 0.00949877π-0.00949877\pi
972972 0 0
973973 −2.74264 4.75039i −0.0879250 0.152291i
974974 0 0
975975 −25.3492 + 6.27231i −0.811825 + 0.200875i
976976 0 0
977977 −21.6421 37.4853i −0.692393 1.19926i −0.971052 0.238870i 0.923223π-0.923223\pi
0.278658 0.960390i 0.410110π-0.410110\pi
978978 0 0
979979 −5.42031 + 9.38825i −0.173234 + 0.300050i
980980 0 0
981981 −12.0000 + 20.7846i −0.383131 + 0.663602i
982982 0 0
983983 0.970563 0.0309561 0.0154781 0.999880i 0.495073π-0.495073\pi
0.0154781 + 0.999880i 0.495073π0.495073\pi
984984 0 0
985985 −4.24264 7.34847i −0.135182 0.234142i
986986 0 0
987987 63.9411 2.03527
988988 0 0
989989 −5.05887 −0.160863
990990 0 0
991991 −29.0772 50.3631i −0.923667 1.59984i −0.793692 0.608320i 0.791844π-0.791844\pi
−0.129975 0.991517i 0.541490π-0.541490\pi
992992 0 0
993993 17.4853 0.554879
994994 0 0
995995 −34.2426 + 59.3100i −1.08556 + 1.88025i
996996 0 0
997997 −17.4706 + 30.2599i −0.553298 + 0.958341i 0.444735 + 0.895662i 0.353298π0.353298\pi
−0.998034 + 0.0626788i 0.980036π0.980036\pi
998998 0 0
999999 1.55025 + 2.68512i 0.0490478 + 0.0849533i
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 832.2.i.k.705.1 4
4.3 odd 2 832.2.i.p.705.2 4
8.3 odd 2 416.2.i.c.289.1 4
8.5 even 2 416.2.i.f.289.2 yes 4
13.9 even 3 inner 832.2.i.k.321.1 4
52.35 odd 6 832.2.i.p.321.2 4
104.3 odd 6 5408.2.a.be.1.2 2
104.29 even 6 5408.2.a.o.1.1 2
104.35 odd 6 416.2.i.c.321.1 yes 4
104.61 even 6 416.2.i.f.321.2 yes 4
104.75 odd 6 5408.2.a.bf.1.2 2
104.101 even 6 5408.2.a.n.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
416.2.i.c.289.1 4 8.3 odd 2
416.2.i.c.321.1 yes 4 104.35 odd 6
416.2.i.f.289.2 yes 4 8.5 even 2
416.2.i.f.321.2 yes 4 104.61 even 6
832.2.i.k.321.1 4 13.9 even 3 inner
832.2.i.k.705.1 4 1.1 even 1 trivial
832.2.i.p.321.2 4 52.35 odd 6
832.2.i.p.705.2 4 4.3 odd 2
5408.2.a.n.1.1 2 104.101 even 6
5408.2.a.o.1.1 2 104.29 even 6
5408.2.a.be.1.2 2 104.3 odd 6
5408.2.a.bf.1.2 2 104.75 odd 6