Properties

Label 7225.2.a.bq.1.5
Level 72257225
Weight 22
Character 7225.1
Self dual yes
Analytic conductor 57.69257.692
Analytic rank 00
Dimension 1212
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7225,2,Mod(1,7225)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7225, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("7225.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7225=52172 7225 = 5^{2} \cdot 17^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7225.a (trivial)

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: yes
Analytic conductor: 57.691915460457.6919154604
Analytic rank: 00
Dimension: 1212
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x124x1110x10+52x9+21x8232x7+44x6+424x5137x4++17 x^{12} - 4 x^{11} - 10 x^{10} + 52 x^{9} + 21 x^{8} - 232 x^{7} + 44 x^{6} + 424 x^{5} - 137 x^{4} + \cdots + 17 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 85)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 0.360254-0.360254 of defining polynomial
Character χ\chi == 7225.1

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) == q0.360254q2+0.0542373q31.87022q40.0195392q6+0.298718q7+1.39426q82.99706q92.76730q110.101435q12+1.97956q130.107615q14+3.23814q16+1.07970q18+2.81896q19+0.0162017q21+0.996933q226.73975q23+0.0756210q240.713144q260.325264q270.558668q28+4.72608q29+3.02620q313.95508q320.150091q33+5.60515q369.42129q371.01554q38+0.107366q393.10972q410.00583672q42+8.18506q43+5.17546q44+2.42803q461.08341q47+0.175628q486.91077q493.70220q522.68500q53+0.117178q54+0.416492q56+0.152893q571.70259q589.15435q59+11.1939q611.09020q620.895276q635.05145q64+0.0540709q6612.5585q670.365546q69+5.88778q714.17869q720.216666q73+3.39406q745.27208q760.826644q770.0386790q7810.6556q79+8.97353q81+1.12029q82+15.5747q830.0303006q842.94870q86+0.256329q873.85835q88+1.55264q89+0.591330q91+12.6048q92+0.164133q93+0.390304q940.214513q968.97035q97+2.48963q98+8.29377q99+O(q100)q-0.360254 q^{2} +0.0542373 q^{3} -1.87022 q^{4} -0.0195392 q^{6} +0.298718 q^{7} +1.39426 q^{8} -2.99706 q^{9} -2.76730 q^{11} -0.101435 q^{12} +1.97956 q^{13} -0.107615 q^{14} +3.23814 q^{16} +1.07970 q^{18} +2.81896 q^{19} +0.0162017 q^{21} +0.996933 q^{22} -6.73975 q^{23} +0.0756210 q^{24} -0.713144 q^{26} -0.325264 q^{27} -0.558668 q^{28} +4.72608 q^{29} +3.02620 q^{31} -3.95508 q^{32} -0.150091 q^{33} +5.60515 q^{36} -9.42129 q^{37} -1.01554 q^{38} +0.107366 q^{39} -3.10972 q^{41} -0.00583672 q^{42} +8.18506 q^{43} +5.17546 q^{44} +2.42803 q^{46} -1.08341 q^{47} +0.175628 q^{48} -6.91077 q^{49} -3.70220 q^{52} -2.68500 q^{53} +0.117178 q^{54} +0.416492 q^{56} +0.152893 q^{57} -1.70259 q^{58} -9.15435 q^{59} +11.1939 q^{61} -1.09020 q^{62} -0.895276 q^{63} -5.05145 q^{64} +0.0540709 q^{66} -12.5585 q^{67} -0.365546 q^{69} +5.88778 q^{71} -4.17869 q^{72} -0.216666 q^{73} +3.39406 q^{74} -5.27208 q^{76} -0.826644 q^{77} -0.0386790 q^{78} -10.6556 q^{79} +8.97353 q^{81} +1.12029 q^{82} +15.5747 q^{83} -0.0303006 q^{84} -2.94870 q^{86} +0.256329 q^{87} -3.85835 q^{88} +1.55264 q^{89} +0.591330 q^{91} +12.6048 q^{92} +0.164133 q^{93} +0.390304 q^{94} -0.214513 q^{96} -8.97035 q^{97} +2.48963 q^{98} +8.29377 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+4q28q3+12q4+8q616q7+12q8+12q9+16q1116q12+8q1316q14+12q164q18+16q2116q2216q23+16q2632q27++56q99+O(q100) 12 q + 4 q^{2} - 8 q^{3} + 12 q^{4} + 8 q^{6} - 16 q^{7} + 12 q^{8} + 12 q^{9} + 16 q^{11} - 16 q^{12} + 8 q^{13} - 16 q^{14} + 12 q^{16} - 4 q^{18} + 16 q^{21} - 16 q^{22} - 16 q^{23} + 16 q^{26} - 32 q^{27}+ \cdots + 56 q^{99}+O(q^{100}) Copy content Toggle raw display

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 −0.360254 −0.254738 −0.127369 0.991855i 0.540653π-0.540653\pi
−0.127369 + 0.991855i 0.540653π0.540653\pi
33 0.0542373 0.0313139 0.0156569 0.999877i 0.495016π-0.495016\pi
0.0156569 + 0.999877i 0.495016π0.495016\pi
44 −1.87022 −0.935108
55 0 0
66 −0.0195392 −0.00797685
77 0.298718 0.112905 0.0564524 0.998405i 0.482021π-0.482021\pi
0.0564524 + 0.998405i 0.482021π0.482021\pi
88 1.39426 0.492946
99 −2.99706 −0.999019
1010 0 0
1111 −2.76730 −0.834373 −0.417187 0.908821i 0.636984π-0.636984\pi
−0.417187 + 0.908821i 0.636984π0.636984\pi
1212 −0.101435 −0.0292819
1313 1.97956 0.549030 0.274515 0.961583i 0.411483π-0.411483\pi
0.274515 + 0.961583i 0.411483π0.411483\pi
1414 −0.107615 −0.0287612
1515 0 0
1616 3.23814 0.809536
1717 0 0
1818 1.07970 0.254489
1919 2.81896 0.646715 0.323357 0.946277i 0.395188π-0.395188\pi
0.323357 + 0.946277i 0.395188π0.395188\pi
2020 0 0
2121 0.0162017 0.00353549
2222 0.996933 0.212547
2323 −6.73975 −1.40534 −0.702668 0.711518i 0.748008π-0.748008\pi
−0.702668 + 0.711518i 0.748008π0.748008\pi
2424 0.0756210 0.0154361
2525 0 0
2626 −0.713144 −0.139859
2727 −0.325264 −0.0625971
2828 −0.558668 −0.105578
2929 4.72608 0.877610 0.438805 0.898582i 0.355402π-0.355402\pi
0.438805 + 0.898582i 0.355402π0.355402\pi
3030 0 0
3131 3.02620 0.543521 0.271761 0.962365i 0.412394π-0.412394\pi
0.271761 + 0.962365i 0.412394π0.412394\pi
3232 −3.95508 −0.699166
3333 −0.150091 −0.0261275
3434 0 0
3535 0 0
3636 5.60515 0.934191
3737 −9.42129 −1.54885 −0.774425 0.632665i 0.781961π-0.781961\pi
−0.774425 + 0.632665i 0.781961π0.781961\pi
3838 −1.01554 −0.164743
3939 0.107366 0.0171923
4040 0 0
4141 −3.10972 −0.485657 −0.242828 0.970069i 0.578075π-0.578075\pi
−0.242828 + 0.970069i 0.578075π0.578075\pi
4242 −0.00583672 −0.000900625 0
4343 8.18506 1.24821 0.624105 0.781341i 0.285464π-0.285464\pi
0.624105 + 0.781341i 0.285464π0.285464\pi
4444 5.17546 0.780229
4545 0 0
4646 2.42803 0.357993
4747 −1.08341 −0.158032 −0.0790159 0.996873i 0.525178π-0.525178\pi
−0.0790159 + 0.996873i 0.525178π0.525178\pi
4848 0.175628 0.0253497
4949 −6.91077 −0.987252
5050 0 0
5151 0 0
5252 −3.70220 −0.513403
5353 −2.68500 −0.368813 −0.184406 0.982850i 0.559036π-0.559036\pi
−0.184406 + 0.982850i 0.559036π0.559036\pi
5454 0.117178 0.0159459
5555 0 0
5656 0.416492 0.0556560
5757 0.152893 0.0202512
5858 −1.70259 −0.223561
5959 −9.15435 −1.19179 −0.595897 0.803061i 0.703203π-0.703203\pi
−0.595897 + 0.803061i 0.703203π0.703203\pi
6060 0 0
6161 11.1939 1.43323 0.716616 0.697468i 0.245690π-0.245690\pi
0.716616 + 0.697468i 0.245690π0.245690\pi
6262 −1.09020 −0.138456
6363 −0.895276 −0.112794
6464 −5.05145 −0.631432
6565 0 0
6666 0.0540709 0.00665567
6767 −12.5585 −1.53427 −0.767133 0.641488i 0.778317π-0.778317\pi
−0.767133 + 0.641488i 0.778317π0.778317\pi
6868 0 0
6969 −0.365546 −0.0440066
7070 0 0
7171 5.88778 0.698750 0.349375 0.936983i 0.386394π-0.386394\pi
0.349375 + 0.936983i 0.386394π0.386394\pi
7272 −4.17869 −0.492463
7373 −0.216666 −0.0253588 −0.0126794 0.999920i 0.504036π-0.504036\pi
−0.0126794 + 0.999920i 0.504036π0.504036\pi
7474 3.39406 0.394552
7575 0 0
7676 −5.27208 −0.604749
7777 −0.826644 −0.0942048
7878 −0.0386790 −0.00437953
7979 −10.6556 −1.19885 −0.599423 0.800432i 0.704603π-0.704603\pi
−0.599423 + 0.800432i 0.704603π0.704603\pi
8080 0 0
8181 8.97353 0.997059
8282 1.12029 0.123715
8383 15.5747 1.70954 0.854770 0.519007i 0.173698π-0.173698\pi
0.854770 + 0.519007i 0.173698π0.173698\pi
8484 −0.0303006 −0.00330607
8585 0 0
8686 −2.94870 −0.317967
8787 0.256329 0.0274814
8888 −3.85835 −0.411301
8989 1.55264 0.164579 0.0822897 0.996608i 0.473777π-0.473777\pi
0.0822897 + 0.996608i 0.473777π0.473777\pi
9090 0 0
9191 0.591330 0.0619882
9292 12.6048 1.31414
9393 0.164133 0.0170198
9494 0.390304 0.0402568
9595 0 0
9696 −0.214513 −0.0218936
9797 −8.97035 −0.910801 −0.455401 0.890287i 0.650504π-0.650504\pi
−0.455401 + 0.890287i 0.650504π0.650504\pi
9898 2.48963 0.251491
9999 8.29377 0.833555
100100 0 0
101101 6.92132 0.688697 0.344349 0.938842i 0.388100π-0.388100\pi
0.344349 + 0.938842i 0.388100π0.388100\pi
102102 0 0
103103 −12.9642 −1.27740 −0.638699 0.769457i 0.720527π-0.720527\pi
−0.638699 + 0.769457i 0.720527π0.720527\pi
104104 2.76002 0.270643
105105 0 0
106106 0.967283 0.0939508
107107 −3.62363 −0.350309 −0.175155 0.984541i 0.556043π-0.556043\pi
−0.175155 + 0.984541i 0.556043π0.556043\pi
108108 0.608314 0.0585351
109109 5.15037 0.493316 0.246658 0.969103i 0.420668π-0.420668\pi
0.246658 + 0.969103i 0.420668π0.420668\pi
110110 0 0
111111 −0.510985 −0.0485005
112112 0.967293 0.0914006
113113 −11.0065 −1.03541 −0.517704 0.855560i 0.673213π-0.673213\pi
−0.517704 + 0.855560i 0.673213π0.673213\pi
114114 −0.0550804 −0.00515875
115115 0 0
116116 −8.83879 −0.820661
117117 −5.93285 −0.548492
118118 3.29789 0.303596
119119 0 0
120120 0 0
121121 −3.34204 −0.303822
122122 −4.03265 −0.365099
123123 −0.168663 −0.0152078
124124 −5.65965 −0.508251
125125 0 0
126126 0.322527 0.0287330
127127 −7.33231 −0.650637 −0.325319 0.945604i 0.605472π-0.605472\pi
−0.325319 + 0.945604i 0.605472π0.605472\pi
128128 9.72997 0.860016
129129 0.443935 0.0390863
130130 0 0
131131 17.3220 1.51343 0.756716 0.653744i 0.226802π-0.226802\pi
0.756716 + 0.653744i 0.226802π0.226802\pi
132132 0.280703 0.0244320
133133 0.842076 0.0730173
134134 4.52426 0.390836
135135 0 0
136136 0 0
137137 13.9745 1.19392 0.596959 0.802272i 0.296375π-0.296375\pi
0.596959 + 0.802272i 0.296375π0.296375\pi
138138 0.131690 0.0112102
139139 3.62061 0.307096 0.153548 0.988141i 0.450930π-0.450930\pi
0.153548 + 0.988141i 0.450930π0.450930\pi
140140 0 0
141141 −0.0587613 −0.00494859
142142 −2.12110 −0.177999
143143 −5.47803 −0.458096
144144 −9.70491 −0.808742
145145 0 0
146146 0.0780548 0.00645986
147147 −0.374821 −0.0309147
148148 17.6199 1.44834
149149 12.8580 1.05336 0.526682 0.850062i 0.323436π-0.323436\pi
0.526682 + 0.850062i 0.323436π0.323436\pi
150150 0 0
151151 19.1642 1.55956 0.779779 0.626055i 0.215331π-0.215331\pi
0.779779 + 0.626055i 0.215331π0.215331\pi
152152 3.93038 0.318796
153153 0 0
154154 0.297802 0.0239976
155155 0 0
156156 −0.200797 −0.0160766
157157 2.70222 0.215661 0.107830 0.994169i 0.465610π-0.465610\pi
0.107830 + 0.994169i 0.465610π0.465610\pi
158158 3.83872 0.305392
159159 −0.145627 −0.0115490
160160 0 0
161161 −2.01329 −0.158669
162162 −3.23276 −0.253989
163163 17.1057 1.33983 0.669913 0.742440i 0.266332π-0.266332\pi
0.669913 + 0.742440i 0.266332π0.266332\pi
164164 5.81585 0.454142
165165 0 0
166166 −5.61084 −0.435486
167167 −8.85257 −0.685032 −0.342516 0.939512i 0.611279π-0.611279\pi
−0.342516 + 0.939512i 0.611279π0.611279\pi
168168 0.0225894 0.00174281
169169 −9.08135 −0.698566
170170 0 0
171171 −8.44860 −0.646081
172172 −15.3078 −1.16721
173173 19.1849 1.45860 0.729301 0.684193i 0.239845π-0.239845\pi
0.729301 + 0.684193i 0.239845π0.239845\pi
174174 −0.0923438 −0.00700057
175175 0 0
176176 −8.96092 −0.675455
177177 −0.496507 −0.0373197
178178 −0.559345 −0.0419247
179179 4.33533 0.324038 0.162019 0.986788i 0.448199π-0.448199\pi
0.162019 + 0.986788i 0.448199π0.448199\pi
180180 0 0
181181 −23.7783 −1.76743 −0.883715 0.468025i 0.844966π-0.844966\pi
−0.883715 + 0.468025i 0.844966π0.844966\pi
182182 −0.213029 −0.0157908
183183 0.607127 0.0448801
184184 −9.39699 −0.692755
185185 0 0
186186 −0.0591296 −0.00433559
187187 0 0
188188 2.02621 0.147777
189189 −0.0971623 −0.00706752
190190 0 0
191191 −7.27055 −0.526079 −0.263039 0.964785i 0.584725π-0.584725\pi
−0.263039 + 0.964785i 0.584725π0.584725\pi
192192 −0.273977 −0.0197726
193193 −22.1992 −1.59794 −0.798968 0.601373i 0.794620π-0.794620\pi
−0.798968 + 0.601373i 0.794620π0.794620\pi
194194 3.23161 0.232016
195195 0 0
196196 12.9246 0.923188
197197 −4.48140 −0.319286 −0.159643 0.987175i 0.551034π-0.551034\pi
−0.159643 + 0.987175i 0.551034π0.551034\pi
198198 −2.98787 −0.212338
199199 −0.399388 −0.0283119 −0.0141559 0.999900i 0.504506π-0.504506\pi
−0.0141559 + 0.999900i 0.504506π0.504506\pi
200200 0 0
201201 −0.681139 −0.0480438
202202 −2.49344 −0.175438
203203 1.41176 0.0990865
204204 0 0
205205 0 0
206206 4.67040 0.325402
207207 20.1994 1.40396
208208 6.41009 0.444460
209209 −7.80093 −0.539602
210210 0 0
211211 1.95016 0.134255 0.0671273 0.997744i 0.478617π-0.478617\pi
0.0671273 + 0.997744i 0.478617π0.478617\pi
212212 5.02153 0.344880
213213 0.319337 0.0218806
214214 1.30543 0.0892372
215215 0 0
216216 −0.453504 −0.0308570
217217 0.903981 0.0613662
218218 −1.85544 −0.125666
219219 −0.0117514 −0.000794083 0
220220 0 0
221221 0 0
222222 0.184085 0.0123550
223223 23.7306 1.58912 0.794558 0.607188i 0.207703π-0.207703\pi
0.794558 + 0.607188i 0.207703π0.207703\pi
224224 −1.18145 −0.0789393
225225 0 0
226226 3.96516 0.263758
227227 20.5598 1.36460 0.682301 0.731071i 0.260979π-0.260979\pi
0.682301 + 0.731071i 0.260979π0.260979\pi
228228 −0.285943 −0.0189370
229229 26.5965 1.75755 0.878773 0.477239i 0.158362π-0.158362\pi
0.878773 + 0.477239i 0.158362π0.158362\pi
230230 0 0
231231 −0.0448349 −0.00294992
232232 6.58939 0.432615
233233 23.4992 1.53948 0.769741 0.638356i 0.220385π-0.220385\pi
0.769741 + 0.638356i 0.220385π0.220385\pi
234234 2.13734 0.139722
235235 0 0
236236 17.1206 1.11446
237237 −0.577929 −0.0375405
238238 0 0
239239 5.25737 0.340071 0.170036 0.985438i 0.445612π-0.445612\pi
0.170036 + 0.985438i 0.445612π0.445612\pi
240240 0 0
241241 −5.43912 −0.350364 −0.175182 0.984536i 0.556051π-0.556051\pi
−0.175182 + 0.984536i 0.556051π0.556051\pi
242242 1.20398 0.0773950
243243 1.46249 0.0938189
244244 −20.9350 −1.34023
245245 0 0
246246 0.0607615 0.00387401
247247 5.58030 0.355066
248248 4.21932 0.267927
249249 0.844727 0.0535324
250250 0 0
251251 26.3864 1.66550 0.832748 0.553652i 0.186766π-0.186766\pi
0.832748 + 0.553652i 0.186766π0.186766\pi
252252 1.67436 0.105475
253253 18.6509 1.17257
254254 2.64150 0.165742
255255 0 0
256256 6.59764 0.412352
257257 18.7509 1.16965 0.584823 0.811161i 0.301164π-0.301164\pi
0.584823 + 0.811161i 0.301164π0.301164\pi
258258 −0.159930 −0.00995678
259259 −2.81431 −0.174873
260260 0 0
261261 −14.1643 −0.876750
262262 −6.24034 −0.385529
263263 −16.0011 −0.986668 −0.493334 0.869840i 0.664222π-0.664222\pi
−0.493334 + 0.869840i 0.664222π0.664222\pi
264264 −0.209266 −0.0128794
265265 0 0
266266 −0.303362 −0.0186003
267267 0.0842109 0.00515362
268268 23.4871 1.43470
269269 1.19638 0.0729447 0.0364724 0.999335i 0.488388π-0.488388\pi
0.0364724 + 0.999335i 0.488388π0.488388\pi
270270 0 0
271271 0.888590 0.0539780 0.0269890 0.999636i 0.491408π-0.491408\pi
0.0269890 + 0.999636i 0.491408π0.491408\pi
272272 0 0
273273 0.0320721 0.00194109
274274 −5.03436 −0.304137
275275 0 0
276276 0.683650 0.0411509
277277 −6.17873 −0.371244 −0.185622 0.982621i 0.559430π-0.559430\pi
−0.185622 + 0.982621i 0.559430π0.559430\pi
278278 −1.30434 −0.0782292
279279 −9.06970 −0.542989
280280 0 0
281281 27.8954 1.66410 0.832051 0.554700i 0.187167π-0.187167\pi
0.832051 + 0.554700i 0.187167π0.187167\pi
282282 0.0211690 0.00126060
283283 −29.7120 −1.76619 −0.883097 0.469190i 0.844546π-0.844546\pi
−0.883097 + 0.469190i 0.844546π0.844546\pi
284284 −11.0114 −0.653407
285285 0 0
286286 1.97349 0.116695
287287 −0.928930 −0.0548330
288288 11.8536 0.698481
289289 0 0
290290 0 0
291291 −0.486527 −0.0285207
292292 0.405212 0.0237132
293293 −22.4626 −1.31228 −0.656140 0.754639i 0.727812π-0.727812\pi
−0.656140 + 0.754639i 0.727812π0.727812\pi
294294 0.135031 0.00787517
295295 0 0
296296 −13.1358 −0.763500
297297 0.900104 0.0522293
298298 −4.63214 −0.268332
299299 −13.3417 −0.771572
300300 0 0
301301 2.44503 0.140929
302302 −6.90398 −0.397279
303303 0.375394 0.0215658
304304 9.12821 0.523539
305305 0 0
306306 0 0
307307 −5.53854 −0.316101 −0.158050 0.987431i 0.550521π-0.550521\pi
−0.158050 + 0.987431i 0.550521π0.550521\pi
308308 1.54600 0.0880917
309309 −0.703141 −0.0400003
310310 0 0
311311 22.5689 1.27977 0.639883 0.768473i 0.278983π-0.278983\pi
0.639883 + 0.768473i 0.278983π0.278983\pi
312312 0.149696 0.00847487
313313 −12.1857 −0.688775 −0.344387 0.938828i 0.611913π-0.611913\pi
−0.344387 + 0.938828i 0.611913π0.611913\pi
314314 −0.973486 −0.0549370
315315 0 0
316316 19.9282 1.12105
317317 21.9772 1.23436 0.617181 0.786821i 0.288275π-0.288275\pi
0.617181 + 0.786821i 0.288275π0.288275\pi
318318 0.0524628 0.00294197
319319 −13.0785 −0.732254
320320 0 0
321321 −0.196536 −0.0109695
322322 0.725296 0.0404192
323323 0 0
324324 −16.7825 −0.932358
325325 0 0
326326 −6.16242 −0.341305
327327 0.279342 0.0154476
328328 −4.33577 −0.239403
329329 −0.323635 −0.0178426
330330 0 0
331331 14.4620 0.794905 0.397452 0.917623i 0.369894π-0.369894\pi
0.397452 + 0.917623i 0.369894π0.369894\pi
332332 −29.1280 −1.59861
333333 28.2362 1.54733
334334 3.18918 0.174504
335335 0 0
336336 0.0524633 0.00286211
337337 24.2460 1.32076 0.660381 0.750931i 0.270395π-0.270395\pi
0.660381 + 0.750931i 0.270395π0.270395\pi
338338 3.27160 0.177951
339339 −0.596965 −0.0324227
340340 0 0
341341 −8.37441 −0.453500
342342 3.04365 0.164582
343343 −4.15540 −0.224370
344344 11.4121 0.615300
345345 0 0
346346 −6.91145 −0.371562
347347 −21.4962 −1.15398 −0.576989 0.816752i 0.695772π-0.695772\pi
−0.576989 + 0.816752i 0.695772π0.695772\pi
348348 −0.479392 −0.0256981
349349 24.1362 1.29198 0.645991 0.763345i 0.276444π-0.276444\pi
0.645991 + 0.763345i 0.276444π0.276444\pi
350350 0 0
351351 −0.643879 −0.0343677
352352 10.9449 0.583366
353353 7.24444 0.385583 0.192791 0.981240i 0.438246π-0.438246\pi
0.192791 + 0.981240i 0.438246π0.438246\pi
354354 0.178869 0.00950677
355355 0 0
356356 −2.90377 −0.153900
357357 0 0
358358 −1.56182 −0.0825449
359359 −17.2646 −0.911189 −0.455595 0.890187i 0.650573π-0.650573\pi
−0.455595 + 0.890187i 0.650573π0.650573\pi
360360 0 0
361361 −11.0534 −0.581760
362362 8.56626 0.450232
363363 −0.181263 −0.00951384
364364 −1.10591 −0.0579657
365365 0 0
366366 −0.218720 −0.0114327
367367 −37.4432 −1.95452 −0.977261 0.212042i 0.931989π-0.931989\pi
−0.977261 + 0.212042i 0.931989π0.931989\pi
368368 −21.8243 −1.13767
369369 9.32001 0.485180
370370 0 0
371371 −0.802058 −0.0416408
372372 −0.306964 −0.0159153
373373 29.8887 1.54758 0.773789 0.633443i 0.218359π-0.218359\pi
0.773789 + 0.633443i 0.218359π0.218359\pi
374374 0 0
375375 0 0
376376 −1.51056 −0.0779012
377377 9.35554 0.481835
378378 0.0350031 0.00180037
379379 30.0204 1.54205 0.771023 0.636807i 0.219745π-0.219745\pi
0.771023 + 0.636807i 0.219745π0.219745\pi
380380 0 0
381381 −0.397684 −0.0203740
382382 2.61925 0.134012
383383 19.7234 1.00782 0.503908 0.863757i 0.331895π-0.331895\pi
0.503908 + 0.863757i 0.331895π0.331895\pi
384384 0.527727 0.0269305
385385 0 0
386386 7.99738 0.407056
387387 −24.5311 −1.24699
388388 16.7765 0.851698
389389 3.71513 0.188364 0.0941822 0.995555i 0.469976π-0.469976\pi
0.0941822 + 0.995555i 0.469976π0.469976\pi
390390 0 0
391391 0 0
392392 −9.63543 −0.486663
393393 0.939499 0.0473915
394394 1.61444 0.0813345
395395 0 0
396396 −15.5111 −0.779464
397397 −5.17180 −0.259565 −0.129783 0.991542i 0.541428π-0.541428\pi
−0.129783 + 0.991542i 0.541428π0.541428\pi
398398 0.143881 0.00721212
399399 0.0456719 0.00228646
400400 0 0
401401 0.394746 0.0197127 0.00985635 0.999951i 0.496863π-0.496863\pi
0.00985635 + 0.999951i 0.496863π0.496863\pi
402402 0.245383 0.0122386
403403 5.99054 0.298410
404404 −12.9444 −0.644007
405405 0 0
406406 −0.508595 −0.0252411
407407 26.0716 1.29232
408408 0 0
409409 0.521080 0.0257657 0.0128829 0.999917i 0.495899π-0.495899\pi
0.0128829 + 0.999917i 0.495899π0.495899\pi
410410 0 0
411411 0.757936 0.0373862
412412 24.2458 1.19451
413413 −2.73457 −0.134559
414414 −7.27694 −0.357642
415415 0 0
416416 −7.82931 −0.383864
417417 0.196372 0.00961638
418418 2.81032 0.137457
419419 4.57224 0.223368 0.111684 0.993744i 0.464376π-0.464376\pi
0.111684 + 0.993744i 0.464376π0.464376\pi
420420 0 0
421421 7.55233 0.368078 0.184039 0.982919i 0.441083π-0.441083\pi
0.184039 + 0.982919i 0.441083π0.441083\pi
422422 −0.702554 −0.0341998
423423 3.24705 0.157877
424424 −3.74359 −0.181805
425425 0 0
426426 −0.115043 −0.00557383
427427 3.34382 0.161819
428428 6.77697 0.327577
429429 −0.297114 −0.0143448
430430 0 0
431431 −20.8886 −1.00617 −0.503083 0.864238i 0.667801π-0.667801\pi
−0.503083 + 0.864238i 0.667801π0.667801\pi
432432 −1.05325 −0.0506746
433433 −32.8510 −1.57872 −0.789359 0.613932i 0.789587π-0.789587\pi
−0.789359 + 0.613932i 0.789587π0.789587\pi
434434 −0.325663 −0.0156323
435435 0 0
436436 −9.63230 −0.461304
437437 −18.9991 −0.908852
438438 0.00423348 0.000202284 0
439439 24.0164 1.14624 0.573121 0.819471i 0.305733π-0.305733\pi
0.573121 + 0.819471i 0.305733π0.305733\pi
440440 0 0
441441 20.7120 0.986284
442442 0 0
443443 −8.36893 −0.397620 −0.198810 0.980038i 0.563708π-0.563708\pi
−0.198810 + 0.980038i 0.563708π0.563708\pi
444444 0.955653 0.0453533
445445 0 0
446446 −8.54904 −0.404809
447447 0.697380 0.0329850
448448 −1.50896 −0.0712917
449449 −24.5964 −1.16078 −0.580389 0.814339i 0.697099π-0.697099\pi
−0.580389 + 0.814339i 0.697099π0.697099\pi
450450 0 0
451451 8.60554 0.405219
452452 20.5846 0.968219
453453 1.03941 0.0488359
454454 −7.40676 −0.347617
455455 0 0
456456 0.213173 0.00998274
457457 −7.61053 −0.356005 −0.178003 0.984030i 0.556964π-0.556964\pi
−0.178003 + 0.984030i 0.556964π0.556964\pi
458458 −9.58151 −0.447715
459459 0 0
460460 0 0
461461 −7.22066 −0.336299 −0.168150 0.985761i 0.553779π-0.553779\pi
−0.168150 + 0.985761i 0.553779π0.553779\pi
462462 0.0161520 0.000751458 0
463463 23.0362 1.07058 0.535292 0.844667i 0.320202π-0.320202\pi
0.535292 + 0.844667i 0.320202π0.320202\pi
464464 15.3037 0.710457
465465 0 0
466466 −8.46569 −0.392165
467467 29.9045 1.38382 0.691908 0.721985i 0.256770π-0.256770\pi
0.691908 + 0.721985i 0.256770π0.256770\pi
468468 11.0957 0.512900
469469 −3.75145 −0.173226
470470 0 0
471471 0.146561 0.00675317
472472 −12.7636 −0.587491
473473 −22.6505 −1.04147
474474 0.208202 0.00956302
475475 0 0
476476 0 0
477477 8.04710 0.368451
478478 −1.89399 −0.0866292
479479 −9.65729 −0.441253 −0.220627 0.975358i 0.570810π-0.570810\pi
−0.220627 + 0.975358i 0.570810π0.570810\pi
480480 0 0
481481 −18.6500 −0.850366
482482 1.95947 0.0892512
483483 −0.109195 −0.00496855
484484 6.25033 0.284106
485485 0 0
486486 −0.526869 −0.0238993
487487 4.83011 0.218873 0.109436 0.993994i 0.465095π-0.465095\pi
0.109436 + 0.993994i 0.465095π0.465095\pi
488488 15.6072 0.706507
489489 0.927769 0.0419552
490490 0 0
491491 21.4747 0.969142 0.484571 0.874752i 0.338976π-0.338976\pi
0.484571 + 0.874752i 0.338976π0.338976\pi
492492 0.315436 0.0142209
493493 0 0
494494 −2.01033 −0.0904490
495495 0 0
496496 9.79927 0.440000
497497 1.75879 0.0788923
498498 −0.304317 −0.0136368
499499 18.6381 0.834357 0.417178 0.908825i 0.363019π-0.363019\pi
0.417178 + 0.908825i 0.363019π0.363019\pi
500500 0 0
501501 −0.480139 −0.0214510
502502 −9.50583 −0.424266
503503 18.5788 0.828389 0.414195 0.910188i 0.364063π-0.364063\pi
0.414195 + 0.910188i 0.364063π0.364063\pi
504504 −1.24825 −0.0556015
505505 0 0
506506 −6.71908 −0.298700
507507 −0.492548 −0.0218748
508508 13.7130 0.608416
509509 28.4343 1.26033 0.630163 0.776463i 0.282988π-0.282988\pi
0.630163 + 0.776463i 0.282988π0.282988\pi
510510 0 0
511511 −0.0647220 −0.00286313
512512 −21.8368 −0.965058
513513 −0.916908 −0.0404825
514514 −6.75508 −0.297954
515515 0 0
516516 −0.830255 −0.0365499
517517 2.99813 0.131857
518518 1.01387 0.0445468
519519 1.04054 0.0456745
520520 0 0
521521 −18.9733 −0.831236 −0.415618 0.909539i 0.636435π-0.636435\pi
−0.415618 + 0.909539i 0.636435π0.636435\pi
522522 5.10276 0.223342
523523 24.4504 1.06914 0.534571 0.845124i 0.320473π-0.320473\pi
0.534571 + 0.845124i 0.320473π0.320473\pi
524524 −32.3959 −1.41522
525525 0 0
526526 5.76445 0.251342
527527 0 0
528528 −0.486016 −0.0211511
529529 22.4243 0.974969
530530 0 0
531531 27.4361 1.19063
532532 −1.57486 −0.0682791
533533 −6.15587 −0.266640
534534 −0.0303374 −0.00131283
535535 0 0
536536 −17.5099 −0.756311
537537 0.235136 0.0101469
538538 −0.431002 −0.0185818
539539 19.1242 0.823737
540540 0 0
541541 −10.8105 −0.464780 −0.232390 0.972623i 0.574655π-0.574655\pi
−0.232390 + 0.972623i 0.574655π0.574655\pi
542542 −0.320119 −0.0137503
543543 −1.28967 −0.0553451
544544 0 0
545545 0 0
546546 −0.0115541 −0.000494471 0
547547 −7.27247 −0.310948 −0.155474 0.987840i 0.549691π-0.549691\pi
−0.155474 + 0.987840i 0.549691π0.549691\pi
548548 −26.1353 −1.11644
549549 −33.5488 −1.43183
550550 0 0
551551 13.3226 0.567564
552552 −0.509667 −0.0216929
553553 −3.18301 −0.135356
554554 2.22592 0.0945701
555555 0 0
556556 −6.77133 −0.287168
557557 18.3930 0.779335 0.389667 0.920956i 0.372590π-0.372590\pi
0.389667 + 0.920956i 0.372590π0.372590\pi
558558 3.26740 0.138320
559559 16.2028 0.685305
560560 0 0
561561 0 0
562562 −10.0495 −0.423911
563563 0.449134 0.0189288 0.00946438 0.999955i 0.496987π-0.496987\pi
0.00946438 + 0.999955i 0.496987π0.496987\pi
564564 0.109896 0.00462747
565565 0 0
566566 10.7039 0.449918
567567 2.68056 0.112573
568568 8.20911 0.344447
569569 14.3259 0.600573 0.300287 0.953849i 0.402918π-0.402918\pi
0.300287 + 0.953849i 0.402918π0.402918\pi
570570 0 0
571571 27.9925 1.17145 0.585724 0.810510i 0.300810π-0.300810\pi
0.585724 + 0.810510i 0.300810π0.300810\pi
572572 10.2451 0.428370
573573 −0.394335 −0.0164736
574574 0.334651 0.0139681
575575 0 0
576576 15.1395 0.630812
577577 −6.76924 −0.281807 −0.140904 0.990023i 0.545001π-0.545001\pi
−0.140904 + 0.990023i 0.545001π0.545001\pi
578578 0 0
579579 −1.20403 −0.0500376
580580 0 0
581581 4.65243 0.193015
582582 0.175274 0.00726533
583583 7.43020 0.307728
584584 −0.302089 −0.0125005
585585 0 0
586586 8.09226 0.334288
587587 24.7081 1.01981 0.509907 0.860230i 0.329680π-0.329680\pi
0.509907 + 0.860230i 0.329680π0.329680\pi
588588 0.700997 0.0289086
589589 8.53075 0.351503
590590 0 0
591591 −0.243059 −0.00999810
592592 −30.5075 −1.25385
593593 22.4505 0.921932 0.460966 0.887418i 0.347503π-0.347503\pi
0.460966 + 0.887418i 0.347503π0.347503\pi
594594 −0.324266 −0.0133048
595595 0 0
596596 −24.0472 −0.985010
597597 −0.0216617 −0.000886555 0
598598 4.80642 0.196549
599599 −19.1639 −0.783018 −0.391509 0.920174i 0.628047π-0.628047\pi
−0.391509 + 0.920174i 0.628047π0.628047\pi
600600 0 0
601601 23.2032 0.946477 0.473239 0.880934i 0.343085π-0.343085\pi
0.473239 + 0.880934i 0.343085π0.343085\pi
602602 −0.880832 −0.0359000
603603 37.6386 1.53276
604604 −35.8412 −1.45836
605605 0 0
606606 −0.135237 −0.00549364
607607 −1.86436 −0.0756720 −0.0378360 0.999284i 0.512046π-0.512046\pi
−0.0378360 + 0.999284i 0.512046π0.512046\pi
608608 −11.1492 −0.452161
609609 0.0765703 0.00310278
610610 0 0
611611 −2.14468 −0.0867643
612612 0 0
613613 0.383092 0.0154729 0.00773647 0.999970i 0.497537π-0.497537\pi
0.00773647 + 0.999970i 0.497537π0.497537\pi
614614 1.99528 0.0805230
615615 0 0
616616 −1.15256 −0.0464379
617617 11.6676 0.469719 0.234860 0.972029i 0.424537π-0.424537\pi
0.234860 + 0.972029i 0.424537π0.424537\pi
618618 0.253310 0.0101896
619619 13.4856 0.542030 0.271015 0.962575i 0.412641π-0.412641\pi
0.271015 + 0.962575i 0.412641π0.412641\pi
620620 0 0
621621 2.19220 0.0879699
622622 −8.13055 −0.326005
623623 0.463802 0.0185818
624624 0.347666 0.0139178
625625 0 0
626626 4.38994 0.175457
627627 −0.423101 −0.0168970
628628 −5.05373 −0.201666
629629 0 0
630630 0 0
631631 46.9395 1.86863 0.934316 0.356445i 0.116011π-0.116011\pi
0.934316 + 0.356445i 0.116011π0.116011\pi
632632 −14.8567 −0.590967
633633 0.105771 0.00420403
634634 −7.91738 −0.314439
635635 0 0
636636 0.272354 0.0107995
637637 −13.6803 −0.542032
638638 4.71158 0.186533
639639 −17.6460 −0.698065
640640 0 0
641641 39.5785 1.56326 0.781628 0.623745i 0.214390π-0.214390\pi
0.781628 + 0.623745i 0.214390π0.214390\pi
642642 0.0708028 0.00279436
643643 −17.7172 −0.698700 −0.349350 0.936992i 0.613598π-0.613598\pi
−0.349350 + 0.936992i 0.613598π0.613598\pi
644644 3.76528 0.148373
645645 0 0
646646 0 0
647647 14.8304 0.583045 0.291522 0.956564i 0.405838π-0.405838\pi
0.291522 + 0.956564i 0.405838π0.405838\pi
648648 12.5115 0.491497
649649 25.3328 0.994401
650650 0 0
651651 0.0490294 0.00192162
652652 −31.9915 −1.25288
653653 10.1986 0.399102 0.199551 0.979887i 0.436052π-0.436052\pi
0.199551 + 0.979887i 0.436052π0.436052\pi
654654 −0.100634 −0.00393511
655655 0 0
656656 −10.0697 −0.393157
657657 0.649360 0.0253340
658658 0.116591 0.00454518
659659 45.4453 1.77030 0.885148 0.465309i 0.154057π-0.154057\pi
0.885148 + 0.465309i 0.154057π0.154057\pi
660660 0 0
661661 −7.95091 −0.309254 −0.154627 0.987973i 0.549418π-0.549418\pi
−0.154627 + 0.987973i 0.549418π0.549418\pi
662662 −5.21001 −0.202493
663663 0 0
664664 21.7152 0.842712
665665 0 0
666666 −10.1722 −0.394165
667667 −31.8526 −1.23334
668668 16.5562 0.640580
669669 1.28708 0.0497614
670670 0 0
671671 −30.9769 −1.19585
672672 −0.0640789 −0.00247190
673673 −21.9876 −0.847558 −0.423779 0.905766i 0.639297π-0.639297\pi
−0.423779 + 0.905766i 0.639297π0.639297\pi
674674 −8.73472 −0.336449
675675 0 0
676676 16.9841 0.653234
677677 18.2370 0.700904 0.350452 0.936581i 0.386028π-0.386028\pi
0.350452 + 0.936581i 0.386028π0.386028\pi
678678 0.215059 0.00825930
679679 −2.67961 −0.102834
680680 0 0
681681 1.11511 0.0427310
682682 3.01692 0.115524
683683 −18.2031 −0.696523 −0.348262 0.937397i 0.613228π-0.613228\pi
−0.348262 + 0.937397i 0.613228π0.613228\pi
684684 15.8007 0.604156
685685 0 0
686686 1.49700 0.0571558
687687 1.44252 0.0550356
688688 26.5044 1.01047
689689 −5.31511 −0.202490
690690 0 0
691691 15.5626 0.592031 0.296015 0.955183i 0.404342π-0.404342\pi
0.296015 + 0.955183i 0.404342π0.404342\pi
692692 −35.8800 −1.36395
693693 2.47750 0.0941124
694694 7.74411 0.293962
695695 0 0
696696 0.357391 0.0135469
697697 0 0
698698 −8.69519 −0.329118
699699 1.27453 0.0482072
700700 0 0
701701 8.07561 0.305011 0.152506 0.988303i 0.451266π-0.451266\pi
0.152506 + 0.988303i 0.451266π0.451266\pi
702702 0.231960 0.00875477
703703 −26.5583 −1.00166
704704 13.9789 0.526849
705705 0 0
706706 −2.60984 −0.0982227
707707 2.06753 0.0777573
708708 0.928575 0.0348980
709709 −5.29018 −0.198677 −0.0993385 0.995054i 0.531673π-0.531673\pi
−0.0993385 + 0.995054i 0.531673π0.531673\pi
710710 0 0
711711 31.9354 1.19767
712712 2.16479 0.0811289
713713 −20.3958 −0.763830
714714 0 0
715715 0 0
716716 −8.10801 −0.303010
717717 0.285146 0.0106490
718718 6.21964 0.232115
719719 8.95929 0.334125 0.167063 0.985946i 0.446572π-0.446572\pi
0.167063 + 0.985946i 0.446572π0.446572\pi
720720 0 0
721721 −3.87263 −0.144224
722722 3.98205 0.148197
723723 −0.295003 −0.0109713
724724 44.4707 1.65274
725725 0 0
726726 0.0653008 0.00242354
727727 29.9868 1.11215 0.556074 0.831133i 0.312307π-0.312307\pi
0.556074 + 0.831133i 0.312307π0.312307\pi
728728 0.824469 0.0305569
729729 −26.8413 −0.994121
730730 0 0
731731 0 0
732732 −1.13546 −0.0419678
733733 −26.9685 −0.996104 −0.498052 0.867147i 0.665951π-0.665951\pi
−0.498052 + 0.867147i 0.665951π0.665951\pi
734734 13.4891 0.497892
735735 0 0
736736 26.6563 0.982564
737737 34.7532 1.28015
738738 −3.35758 −0.123594
739739 −34.8463 −1.28184 −0.640922 0.767606i 0.721448π-0.721448\pi
−0.640922 + 0.767606i 0.721448π0.721448\pi
740740 0 0
741741 0.302660 0.0111185
742742 0.288945 0.0106075
743743 17.0929 0.627077 0.313539 0.949575i 0.398486π-0.398486\pi
0.313539 + 0.949575i 0.398486π0.398486\pi
744744 0.228844 0.00838984
745745 0 0
746746 −10.7675 −0.394228
747747 −46.6781 −1.70786
748748 0 0
749749 −1.08244 −0.0395516
750750 0 0
751751 32.8813 1.19985 0.599927 0.800054i 0.295196π-0.295196\pi
0.599927 + 0.800054i 0.295196π0.295196\pi
752752 −3.50824 −0.127932
753753 1.43113 0.0521532
754754 −3.37037 −0.122742
755755 0 0
756756 0.181715 0.00660889
757757 17.4978 0.635968 0.317984 0.948096i 0.396994π-0.396994\pi
0.317984 + 0.948096i 0.396994π0.396994\pi
758758 −10.8150 −0.392818
759759 1.01158 0.0367179
760760 0 0
761761 −10.8439 −0.393092 −0.196546 0.980495i 0.562972π-0.562972\pi
−0.196546 + 0.980495i 0.562972π0.562972\pi
762762 0.143268 0.00519004
763763 1.53851 0.0556978
764764 13.5975 0.491941
765765 0 0
766766 −7.10543 −0.256730
767767 −18.1216 −0.654331
768768 0.357838 0.0129124
769769 14.8775 0.536497 0.268248 0.963350i 0.413555π-0.413555\pi
0.268248 + 0.963350i 0.413555π0.413555\pi
770770 0 0
771771 1.01699 0.0366262
772772 41.5174 1.49424
773773 −7.71506 −0.277491 −0.138746 0.990328i 0.544307π-0.544307\pi
−0.138746 + 0.990328i 0.544307π0.544307\pi
774774 8.83744 0.317655
775775 0 0
776776 −12.5070 −0.448976
777777 −0.152641 −0.00547595
778778 −1.33839 −0.0479836
779779 −8.76619 −0.314081
780780 0 0
781781 −16.2933 −0.583019
782782 0 0
783783 −1.53722 −0.0549358
784784 −22.3781 −0.799216
785785 0 0
786786 −0.338459 −0.0120724
787787 −38.2522 −1.36354 −0.681772 0.731565i 0.738790π-0.738790\pi
−0.681772 + 0.731565i 0.738790π0.738790\pi
788788 8.38119 0.298567
789789 −0.867854 −0.0308964
790790 0 0
791791 −3.28786 −0.116903
792792 11.5637 0.410898
793793 22.1590 0.786888
794794 1.86317 0.0661213
795795 0 0
796796 0.746943 0.0264747
797797 26.6162 0.942796 0.471398 0.881921i 0.343750π-0.343750\pi
0.471398 + 0.881921i 0.343750π0.343750\pi
798798 −0.0164535 −0.000582448 0
799799 0 0
800800 0 0
801801 −4.65335 −0.164418
802802 −0.142209 −0.00502158
803803 0.599580 0.0211587
804804 1.27388 0.0449262
805805 0 0
806806 −2.15812 −0.0760164
807807 0.0648885 0.00228418
808808 9.65014 0.339491
809809 16.4368 0.577887 0.288943 0.957346i 0.406696π-0.406696\pi
0.288943 + 0.957346i 0.406696π0.406696\pi
810810 0 0
811811 −3.64147 −0.127869 −0.0639347 0.997954i 0.520365π-0.520365\pi
−0.0639347 + 0.997954i 0.520365π0.520365\pi
812812 −2.64031 −0.0926566
813813 0.0481947 0.00169026
814814 −9.39240 −0.329203
815815 0 0
816816 0 0
817817 23.0734 0.807236
818818 −0.187721 −0.00656352
819819 −1.77225 −0.0619274
820820 0 0
821821 −35.5272 −1.23991 −0.619953 0.784639i 0.712848π-0.712848\pi
−0.619953 + 0.784639i 0.712848π0.712848\pi
822822 −0.273050 −0.00952371
823823 5.01622 0.174854 0.0874271 0.996171i 0.472136π-0.472136\pi
0.0874271 + 0.996171i 0.472136π0.472136\pi
824824 −18.0755 −0.629689
825825 0 0
826826 0.985141 0.0342774
827827 −39.0885 −1.35924 −0.679621 0.733564i 0.737856π-0.737856\pi
−0.679621 + 0.733564i 0.737856π0.737856\pi
828828 −37.7773 −1.31285
829829 −16.3998 −0.569587 −0.284794 0.958589i 0.591925π-0.591925\pi
−0.284794 + 0.958589i 0.591925π0.591925\pi
830830 0 0
831831 −0.335118 −0.0116251
832832 −9.99964 −0.346675
833833 0 0
834834 −0.0707439 −0.00244966
835835 0 0
836836 14.5894 0.504586
837837 −0.984314 −0.0340229
838838 −1.64717 −0.0569005
839839 29.9127 1.03270 0.516350 0.856378i 0.327290π-0.327290\pi
0.516350 + 0.856378i 0.327290π0.327290\pi
840840 0 0
841841 −6.66421 −0.229800
842842 −2.72076 −0.0937636
843843 1.51297 0.0521095
844844 −3.64722 −0.125543
845845 0 0
846846 −1.16976 −0.0402173
847847 −0.998327 −0.0343029
848848 −8.69441 −0.298567
849849 −1.61150 −0.0553064
850850 0 0
851851 63.4972 2.17666
852852 −0.597229 −0.0204607
853853 −35.9121 −1.22961 −0.614803 0.788680i 0.710765π-0.710765\pi
−0.614803 + 0.788680i 0.710765π0.710765\pi
854854 −1.20463 −0.0412215
855855 0 0
856856 −5.05229 −0.172684
857857 21.0716 0.719791 0.359896 0.932993i 0.382812π-0.382812\pi
0.359896 + 0.932993i 0.382812π0.382812\pi
858858 0.107036 0.00365417
859859 15.8539 0.540928 0.270464 0.962730i 0.412823π-0.412823\pi
0.270464 + 0.962730i 0.412823π0.412823\pi
860860 0 0
861861 −0.0503826 −0.00171704
862862 7.52520 0.256309
863863 −23.8125 −0.810587 −0.405294 0.914187i 0.632831π-0.632831\pi
−0.405294 + 0.914187i 0.632831π0.632831\pi
864864 1.28645 0.0437658
865865 0 0
866866 11.8347 0.402160
867867 0 0
868868 −1.69064 −0.0573841
869869 29.4872 1.00028
870870 0 0
871871 −24.8603 −0.842359
872872 7.18097 0.243178
873873 26.8847 0.909908
874874 6.84452 0.231519
875875 0 0
876876 0.0219776 0.000742554 0
877877 −17.9197 −0.605107 −0.302553 0.953132i 0.597839π-0.597839\pi
−0.302553 + 0.953132i 0.597839π0.597839\pi
878878 −8.65203 −0.291992
879879 −1.21831 −0.0410926
880880 0 0
881881 −33.7879 −1.13834 −0.569171 0.822219i 0.692736π-0.692736\pi
−0.569171 + 0.822219i 0.692736π0.692736\pi
882882 −7.46158 −0.251245
883883 26.0211 0.875680 0.437840 0.899053i 0.355744π-0.355744\pi
0.437840 + 0.899053i 0.355744π0.355744\pi
884884 0 0
885885 0 0
886886 3.01495 0.101289
887887 −29.6531 −0.995652 −0.497826 0.867277i 0.665868π-0.665868\pi
−0.497826 + 0.867277i 0.665868π0.665868\pi
888888 −0.712447 −0.0239082
889889 −2.19029 −0.0734601
890890 0 0
891891 −24.8325 −0.831919
892892 −44.3813 −1.48600
893893 −3.05410 −0.102202
894894 −0.251234 −0.00840254
895895 0 0
896896 2.90652 0.0971000
897897 −0.723619 −0.0241609
898898 8.86098 0.295695
899899 14.3020 0.477000
900900 0 0
901901 0 0
902902 −3.10018 −0.103225
903903 0.132612 0.00441303
904904 −15.3460 −0.510401
905905 0 0
906906 −0.374453 −0.0124404
907907 −6.01268 −0.199648 −0.0998238 0.995005i 0.531828π-0.531828\pi
−0.0998238 + 0.995005i 0.531828π0.531828\pi
908908 −38.4513 −1.27605
909909 −20.7436 −0.688022
910910 0 0
911911 −36.3470 −1.20423 −0.602115 0.798409i 0.705675π-0.705675\pi
−0.602115 + 0.798409i 0.705675π0.705675\pi
912912 0.495089 0.0163940
913913 −43.0998 −1.42639
914914 2.74173 0.0906883
915915 0 0
916916 −49.7412 −1.64350
917917 5.17440 0.170874
918918 0 0
919919 31.4827 1.03852 0.519259 0.854617i 0.326208π-0.326208\pi
0.519259 + 0.854617i 0.326208π0.326208\pi
920920 0 0
921921 −0.300395 −0.00989835
922922 2.60127 0.0856684
923923 11.6552 0.383635
924924 0.0838510 0.00275849
925925 0 0
926926 −8.29890 −0.272719
927927 38.8544 1.27615
928928 −18.6920 −0.613595
929929 −43.2005 −1.41736 −0.708682 0.705528i 0.750710π-0.750710\pi
−0.708682 + 0.705528i 0.750710π0.750710\pi
930930 0 0
931931 −19.4812 −0.638471
932932 −43.9486 −1.43958
933933 1.22408 0.0400744
934934 −10.7732 −0.352511
935935 0 0
936936 −8.27195 −0.270377
937937 11.5364 0.376877 0.188439 0.982085i 0.439657π-0.439657\pi
0.188439 + 0.982085i 0.439657π0.439657\pi
938938 1.35148 0.0441273
939939 −0.660917 −0.0215682
940940 0 0
941941 27.2725 0.889057 0.444528 0.895765i 0.353371π-0.353371\pi
0.444528 + 0.895765i 0.353371π0.353371\pi
942942 −0.0527992 −0.00172029
943943 20.9588 0.682511
944944 −29.6431 −0.964800
945945 0 0
946946 8.15996 0.265303
947947 22.7925 0.740657 0.370328 0.928901i 0.379245π-0.379245\pi
0.370328 + 0.928901i 0.379245π0.379245\pi
948948 1.08085 0.0351045
949949 −0.428902 −0.0139228
950950 0 0
951951 1.19198 0.0386527
952952 0 0
953953 28.9548 0.937938 0.468969 0.883215i 0.344626π-0.344626\pi
0.468969 + 0.883215i 0.344626π0.344626\pi
954954 −2.89900 −0.0938587
955955 0 0
956956 −9.83243 −0.318003
957957 −0.709341 −0.0229297
958958 3.47908 0.112404
959959 4.17443 0.134799
960960 0 0
961961 −21.8421 −0.704584
962962 6.71874 0.216621
963963 10.8602 0.349966
964964 10.1723 0.327629
965965 0 0
966966 0.0393381 0.00126568
967967 −50.6105 −1.62752 −0.813762 0.581198i 0.802584π-0.802584\pi
−0.813762 + 0.581198i 0.802584π0.802584\pi
968968 −4.65968 −0.149768
969969 0 0
970970 0 0
971971 −32.8412 −1.05392 −0.526962 0.849889i 0.676669π-0.676669\pi
−0.526962 + 0.849889i 0.676669π0.676669\pi
972972 −2.73518 −0.0877308
973973 1.08154 0.0346727
974974 −1.74007 −0.0557553
975975 0 0
976976 36.2475 1.16025
977977 21.6326 0.692089 0.346044 0.938218i 0.387525π-0.387525\pi
0.346044 + 0.938218i 0.387525π0.387525\pi
978978 −0.334233 −0.0106876
979979 −4.29662 −0.137321
980980 0 0
981981 −15.4360 −0.492832
982982 −7.73637 −0.246878
983983 −5.11049 −0.162999 −0.0814996 0.996673i 0.525971π-0.525971\pi
−0.0814996 + 0.996673i 0.525971π0.525971\pi
984984 −0.235160 −0.00749663
985985 0 0
986986 0 0
987987 −0.0175531 −0.000558720 0
988988 −10.4364 −0.332025
989989 −55.1653 −1.75415
990990 0 0
991991 −2.51317 −0.0798336 −0.0399168 0.999203i 0.512709π-0.512709\pi
−0.0399168 + 0.999203i 0.512709π0.512709\pi
992992 −11.9689 −0.380012
993993 0.784381 0.0248916
994994 −0.633611 −0.0200969
995995 0 0
996996 −1.57982 −0.0500586
997997 −36.0472 −1.14163 −0.570813 0.821080i 0.693372π-0.693372\pi
−0.570813 + 0.821080i 0.693372π0.693372\pi
998998 −6.71447 −0.212543
999999 3.06441 0.0969535
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 7225.2.a.bq.1.5 12
5.4 even 2 1445.2.a.q.1.8 12
17.5 odd 16 425.2.m.b.76.4 24
17.7 odd 16 425.2.m.b.151.4 24
17.16 even 2 7225.2.a.bs.1.5 12
85.4 even 4 1445.2.d.j.866.10 24
85.7 even 16 425.2.n.f.49.3 24
85.22 even 16 425.2.n.c.399.4 24
85.24 odd 16 85.2.l.a.66.3 24
85.39 odd 16 85.2.l.a.76.3 yes 24
85.58 even 16 425.2.n.c.49.4 24
85.64 even 4 1445.2.d.j.866.9 24
85.73 even 16 425.2.n.f.399.3 24
85.84 even 2 1445.2.a.p.1.8 12
255.194 even 16 765.2.be.b.406.4 24
255.209 even 16 765.2.be.b.586.4 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
85.2.l.a.66.3 24 85.24 odd 16
85.2.l.a.76.3 yes 24 85.39 odd 16
425.2.m.b.76.4 24 17.5 odd 16
425.2.m.b.151.4 24 17.7 odd 16
425.2.n.c.49.4 24 85.58 even 16
425.2.n.c.399.4 24 85.22 even 16
425.2.n.f.49.3 24 85.7 even 16
425.2.n.f.399.3 24 85.73 even 16
765.2.be.b.406.4 24 255.194 even 16
765.2.be.b.586.4 24 255.209 even 16
1445.2.a.p.1.8 12 85.84 even 2
1445.2.a.q.1.8 12 5.4 even 2
1445.2.d.j.866.9 24 85.64 even 4
1445.2.d.j.866.10 24 85.4 even 4
7225.2.a.bq.1.5 12 1.1 even 1 trivial
7225.2.a.bs.1.5 12 17.16 even 2