Properties

Label 891.2.a.l.1.2
Level 891891
Weight 22
Character 891.1
Self dual yes
Analytic conductor 7.1157.115
Analytic rank 11
Dimension 33
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] = [891,2,Mod(1,891)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(891, 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("891.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 891=3411 891 = 3^{4} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 891.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: 7.114670820107.11467082010
Analytic rank: 11
Dimension: 33
Coefficient field: Q(ζ18)+\Q(\zeta_{18})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x33x1 x^{3} - 3x - 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 99)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 0.347296-0.347296 of defining polynomial
Character χ\chi == 891.1

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+0.347296q21.87939q4+0.652704q5+0.532089q71.34730q8+0.226682q101.00000q112.30541q13+0.184793q14+3.29086q164.41147q174.18479q191.22668q200.347296q22+1.41147q234.57398q250.800660q261.00000q28+6.35504q292.16250q31+3.83750q321.53209q34+0.347296q353.16250q371.45336q380.879385q409.31315q4112.2986q43+1.87939q44+0.490200q463.86484q476.71688q491.58853q50+4.33275q52+12.6236q530.652704q550.716881q56+2.20708q583.23442q598.53209q610.751030q625.24897q641.50475q65+4.96316q67+8.29086q68+0.120615q70+9.98545q717.49525q731.09833q74+7.86484q760.532089q774.87939q79+2.14796q803.23442q824.59627q832.87939q854.27126q86+1.34730q8816.9513q891.22668q912.65270q921.34224q942.73143q95+12.6459q972.33275q98+O(q100)q+0.347296 q^{2} -1.87939 q^{4} +0.652704 q^{5} +0.532089 q^{7} -1.34730 q^{8} +0.226682 q^{10} -1.00000 q^{11} -2.30541 q^{13} +0.184793 q^{14} +3.29086 q^{16} -4.41147 q^{17} -4.18479 q^{19} -1.22668 q^{20} -0.347296 q^{22} +1.41147 q^{23} -4.57398 q^{25} -0.800660 q^{26} -1.00000 q^{28} +6.35504 q^{29} -2.16250 q^{31} +3.83750 q^{32} -1.53209 q^{34} +0.347296 q^{35} -3.16250 q^{37} -1.45336 q^{38} -0.879385 q^{40} -9.31315 q^{41} -12.2986 q^{43} +1.87939 q^{44} +0.490200 q^{46} -3.86484 q^{47} -6.71688 q^{49} -1.58853 q^{50} +4.33275 q^{52} +12.6236 q^{53} -0.652704 q^{55} -0.716881 q^{56} +2.20708 q^{58} -3.23442 q^{59} -8.53209 q^{61} -0.751030 q^{62} -5.24897 q^{64} -1.50475 q^{65} +4.96316 q^{67} +8.29086 q^{68} +0.120615 q^{70} +9.98545 q^{71} -7.49525 q^{73} -1.09833 q^{74} +7.86484 q^{76} -0.532089 q^{77} -4.87939 q^{79} +2.14796 q^{80} -3.23442 q^{82} -4.59627 q^{83} -2.87939 q^{85} -4.27126 q^{86} +1.34730 q^{88} -16.9513 q^{89} -1.22668 q^{91} -2.65270 q^{92} -1.34224 q^{94} -2.73143 q^{95} +12.6459 q^{97} -2.33275 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+3q53q73q86q103q119q133q146q163q179q19+3q206q236q25+12q263q286q299q31+9q3212q37++12q98+O(q100) 3 q + 3 q^{5} - 3 q^{7} - 3 q^{8} - 6 q^{10} - 3 q^{11} - 9 q^{13} - 3 q^{14} - 6 q^{16} - 3 q^{17} - 9 q^{19} + 3 q^{20} - 6 q^{23} - 6 q^{25} + 12 q^{26} - 3 q^{28} - 6 q^{29} - 9 q^{31} + 9 q^{32} - 12 q^{37}+ \cdots + 12 q^{98}+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 0.347296 0.245576 0.122788 0.992433i 0.460817π-0.460817\pi
0.122788 + 0.992433i 0.460817π0.460817\pi
33 0 0
44 −1.87939 −0.939693
55 0.652704 0.291898 0.145949 0.989292i 0.453376π-0.453376\pi
0.145949 + 0.989292i 0.453376π0.453376\pi
66 0 0
77 0.532089 0.201111 0.100555 0.994931i 0.467938π-0.467938\pi
0.100555 + 0.994931i 0.467938π0.467938\pi
88 −1.34730 −0.476341
99 0 0
1010 0.226682 0.0716830
1111 −1.00000 −0.301511
1212 0 0
1313 −2.30541 −0.639405 −0.319702 0.947518i 0.603583π-0.603583\pi
−0.319702 + 0.947518i 0.603583π0.603583\pi
1414 0.184793 0.0493879
1515 0 0
1616 3.29086 0.822715
1717 −4.41147 −1.06994 −0.534970 0.844871i 0.679677π-0.679677\pi
−0.534970 + 0.844871i 0.679677π0.679677\pi
1818 0 0
1919 −4.18479 −0.960057 −0.480029 0.877253i 0.659374π-0.659374\pi
−0.480029 + 0.877253i 0.659374π0.659374\pi
2020 −1.22668 −0.274294
2121 0 0
2222 −0.347296 −0.0740438
2323 1.41147 0.294313 0.147156 0.989113i 0.452988π-0.452988\pi
0.147156 + 0.989113i 0.452988π0.452988\pi
2424 0 0
2525 −4.57398 −0.914796
2626 −0.800660 −0.157022
2727 0 0
2828 −1.00000 −0.188982
2929 6.35504 1.18010 0.590050 0.807366i 0.299108π-0.299108\pi
0.590050 + 0.807366i 0.299108π0.299108\pi
3030 0 0
3131 −2.16250 −0.388397 −0.194199 0.980962i 0.562211π-0.562211\pi
−0.194199 + 0.980962i 0.562211π0.562211\pi
3232 3.83750 0.678380
3333 0 0
3434 −1.53209 −0.262751
3535 0.347296 0.0587038
3636 0 0
3737 −3.16250 −0.519912 −0.259956 0.965620i 0.583708π-0.583708\pi
−0.259956 + 0.965620i 0.583708π0.583708\pi
3838 −1.45336 −0.235767
3939 0 0
4040 −0.879385 −0.139043
4141 −9.31315 −1.45447 −0.727235 0.686389i 0.759195π-0.759195\pi
−0.727235 + 0.686389i 0.759195π0.759195\pi
4242 0 0
4343 −12.2986 −1.87552 −0.937759 0.347285i 0.887104π-0.887104\pi
−0.937759 + 0.347285i 0.887104π0.887104\pi
4444 1.87939 0.283328
4545 0 0
4646 0.490200 0.0722760
4747 −3.86484 −0.563744 −0.281872 0.959452i 0.590955π-0.590955\pi
−0.281872 + 0.959452i 0.590955π0.590955\pi
4848 0 0
4949 −6.71688 −0.959554
5050 −1.58853 −0.224651
5151 0 0
5252 4.33275 0.600844
5353 12.6236 1.73399 0.866993 0.498320i 0.166050π-0.166050\pi
0.866993 + 0.498320i 0.166050π0.166050\pi
5454 0 0
5555 −0.652704 −0.0880105
5656 −0.716881 −0.0957973
5757 0 0
5858 2.20708 0.289804
5959 −3.23442 −0.421086 −0.210543 0.977585i 0.567523π-0.567523\pi
−0.210543 + 0.977585i 0.567523π0.567523\pi
6060 0 0
6161 −8.53209 −1.09242 −0.546211 0.837648i 0.683930π-0.683930\pi
−0.546211 + 0.837648i 0.683930π0.683930\pi
6262 −0.751030 −0.0953809
6363 0 0
6464 −5.24897 −0.656121
6565 −1.50475 −0.186641
6666 0 0
6767 4.96316 0.606347 0.303173 0.952935i 0.401954π-0.401954\pi
0.303173 + 0.952935i 0.401954π0.401954\pi
6868 8.29086 1.00541
6969 0 0
7070 0.120615 0.0144162
7171 9.98545 1.18506 0.592528 0.805550i 0.298130π-0.298130\pi
0.592528 + 0.805550i 0.298130π0.298130\pi
7272 0 0
7373 −7.49525 −0.877253 −0.438626 0.898669i 0.644535π-0.644535\pi
−0.438626 + 0.898669i 0.644535π0.644535\pi
7474 −1.09833 −0.127678
7575 0 0
7676 7.86484 0.902159
7777 −0.532089 −0.0606372
7878 0 0
7979 −4.87939 −0.548974 −0.274487 0.961591i 0.588508π-0.588508\pi
−0.274487 + 0.961591i 0.588508π0.588508\pi
8080 2.14796 0.240149
8181 0 0
8282 −3.23442 −0.357182
8383 −4.59627 −0.504506 −0.252253 0.967661i 0.581171π-0.581171\pi
−0.252253 + 0.967661i 0.581171π0.581171\pi
8484 0 0
8585 −2.87939 −0.312313
8686 −4.27126 −0.460582
8787 0 0
8888 1.34730 0.143622
8989 −16.9513 −1.79683 −0.898417 0.439143i 0.855282π-0.855282\pi
−0.898417 + 0.439143i 0.855282π0.855282\pi
9090 0 0
9191 −1.22668 −0.128591
9292 −2.65270 −0.276563
9393 0 0
9494 −1.34224 −0.138442
9595 −2.73143 −0.280239
9696 0 0
9797 12.6459 1.28400 0.641998 0.766706i 0.278106π-0.278106\pi
0.641998 + 0.766706i 0.278106π0.278106\pi
9898 −2.33275 −0.235643
9999 0 0
100100 8.59627 0.859627
101101 17.0915 1.70067 0.850335 0.526242i 0.176399π-0.176399\pi
0.850335 + 0.526242i 0.176399π0.176399\pi
102102 0 0
103103 2.85978 0.281783 0.140891 0.990025i 0.455003π-0.455003\pi
0.140891 + 0.990025i 0.455003π0.455003\pi
104104 3.10607 0.304575
105105 0 0
106106 4.38413 0.425825
107107 9.92902 0.959874 0.479937 0.877303i 0.340659π-0.340659\pi
0.479937 + 0.877303i 0.340659π0.340659\pi
108108 0 0
109109 13.8161 1.32335 0.661673 0.749792i 0.269847π-0.269847\pi
0.661673 + 0.749792i 0.269847π0.269847\pi
110110 −0.226682 −0.0216132
111111 0 0
112112 1.75103 0.165457
113113 1.75877 0.165451 0.0827256 0.996572i 0.473637π-0.473637\pi
0.0827256 + 0.996572i 0.473637π0.473637\pi
114114 0 0
115115 0.921274 0.0859093
116116 −11.9436 −1.10893
117117 0 0
118118 −1.12330 −0.103408
119119 −2.34730 −0.215176
120120 0 0
121121 1.00000 0.0909091
122122 −2.96316 −0.268272
123123 0 0
124124 4.06418 0.364974
125125 −6.24897 −0.558925
126126 0 0
127127 6.90167 0.612425 0.306212 0.951963i 0.400938π-0.400938\pi
0.306212 + 0.951963i 0.400938π0.400938\pi
128128 −9.49794 −0.839507
129129 0 0
130130 −0.522593 −0.0458345
131131 10.3405 0.903453 0.451726 0.892157i 0.350808π-0.350808\pi
0.451726 + 0.892157i 0.350808π0.350808\pi
132132 0 0
133133 −2.22668 −0.193078
134134 1.72369 0.148904
135135 0 0
136136 5.94356 0.509656
137137 14.1848 1.21189 0.605944 0.795507i 0.292795π-0.292795\pi
0.605944 + 0.795507i 0.292795π0.292795\pi
138138 0 0
139139 0.101014 0.00856793 0.00428396 0.999991i 0.498636π-0.498636\pi
0.00428396 + 0.999991i 0.498636π0.498636\pi
140140 −0.652704 −0.0551635
141141 0 0
142142 3.46791 0.291021
143143 2.30541 0.192788
144144 0 0
145145 4.14796 0.344469
146146 −2.60307 −0.215432
147147 0 0
148148 5.94356 0.488558
149149 −3.06149 −0.250807 −0.125403 0.992106i 0.540023π-0.540023\pi
−0.125403 + 0.992106i 0.540023π0.540023\pi
150150 0 0
151151 19.4020 1.57891 0.789455 0.613808i 0.210363π-0.210363\pi
0.789455 + 0.613808i 0.210363π0.210363\pi
152152 5.63816 0.457315
153153 0 0
154154 −0.184793 −0.0148910
155155 −1.41147 −0.113372
156156 0 0
157157 −12.7246 −1.01554 −0.507768 0.861494i 0.669529π-0.669529\pi
−0.507768 + 0.861494i 0.669529π0.669529\pi
158158 −1.69459 −0.134815
159159 0 0
160160 2.50475 0.198018
161161 0.751030 0.0591894
162162 0 0
163163 −12.7888 −1.00170 −0.500848 0.865535i 0.666978π-0.666978\pi
−0.500848 + 0.865535i 0.666978π0.666978\pi
164164 17.5030 1.36675
165165 0 0
166166 −1.59627 −0.123894
167167 20.7246 1.60372 0.801860 0.597512i 0.203844π-0.203844\pi
0.801860 + 0.597512i 0.203844π0.203844\pi
168168 0 0
169169 −7.68510 −0.591161
170170 −1.00000 −0.0766965
171171 0 0
172172 23.1138 1.76241
173173 −22.5030 −1.71087 −0.855435 0.517909i 0.826710π-0.826710\pi
−0.855435 + 0.517909i 0.826710π0.826710\pi
174174 0 0
175175 −2.43376 −0.183975
176176 −3.29086 −0.248058
177177 0 0
178178 −5.88713 −0.441259
179179 −10.7219 −0.801395 −0.400697 0.916210i 0.631232π-0.631232\pi
−0.400697 + 0.916210i 0.631232π0.631232\pi
180180 0 0
181181 −4.15745 −0.309021 −0.154510 0.987991i 0.549380π-0.549380\pi
−0.154510 + 0.987991i 0.549380π0.549380\pi
182182 −0.426022 −0.0315789
183183 0 0
184184 −1.90167 −0.140193
185185 −2.06418 −0.151761
186186 0 0
187187 4.41147 0.322599
188188 7.26352 0.529747
189189 0 0
190190 −0.948615 −0.0688198
191191 2.40373 0.173928 0.0869640 0.996211i 0.472283π-0.472283\pi
0.0869640 + 0.996211i 0.472283π0.472283\pi
192192 0 0
193193 −0.453363 −0.0326338 −0.0163169 0.999867i 0.505194π-0.505194\pi
−0.0163169 + 0.999867i 0.505194π0.505194\pi
194194 4.39187 0.315318
195195 0 0
196196 12.6236 0.901686
197197 −19.6236 −1.39812 −0.699062 0.715061i 0.746399π-0.746399\pi
−0.699062 + 0.715061i 0.746399π0.746399\pi
198198 0 0
199199 3.63041 0.257353 0.128677 0.991687i 0.458927π-0.458927\pi
0.128677 + 0.991687i 0.458927π0.458927\pi
200200 6.16250 0.435755
201201 0 0
202202 5.93582 0.417643
203203 3.38144 0.237331
204204 0 0
205205 −6.07873 −0.424557
206206 0.993193 0.0691990
207207 0 0
208208 −7.58677 −0.526048
209209 4.18479 0.289468
210210 0 0
211211 21.6732 1.49205 0.746024 0.665919i 0.231961π-0.231961\pi
0.746024 + 0.665919i 0.231961π0.231961\pi
212212 −23.7246 −1.62941
213213 0 0
214214 3.44831 0.235722
215215 −8.02734 −0.547460
216216 0 0
217217 −1.15064 −0.0781108
218218 4.79830 0.324982
219219 0 0
220220 1.22668 0.0827029
221221 10.1702 0.684125
222222 0 0
223223 19.1361 1.28145 0.640724 0.767771i 0.278634π-0.278634\pi
0.640724 + 0.767771i 0.278634π0.278634\pi
224224 2.04189 0.136429
225225 0 0
226226 0.610815 0.0406308
227227 −15.5936 −1.03498 −0.517491 0.855689i 0.673134π-0.673134\pi
−0.517491 + 0.855689i 0.673134π0.673134\pi
228228 0 0
229229 −15.4115 −1.01842 −0.509209 0.860643i 0.670062π-0.670062\pi
−0.509209 + 0.860643i 0.670062π0.670062\pi
230230 0.319955 0.0210972
231231 0 0
232232 −8.56212 −0.562131
233233 4.29086 0.281104 0.140552 0.990073i 0.455112π-0.455112\pi
0.140552 + 0.990073i 0.455112π0.455112\pi
234234 0 0
235235 −2.52259 −0.164556
236236 6.07873 0.395691
237237 0 0
238238 −0.815207 −0.0528421
239239 −20.1334 −1.30232 −0.651161 0.758940i 0.725718π-0.725718\pi
−0.651161 + 0.758940i 0.725718π0.725718\pi
240240 0 0
241241 −7.44562 −0.479615 −0.239807 0.970820i 0.577084π-0.577084\pi
−0.239807 + 0.970820i 0.577084π0.577084\pi
242242 0.347296 0.0223251
243243 0 0
244244 16.0351 1.02654
245245 −4.38413 −0.280092
246246 0 0
247247 9.64765 0.613865
248248 2.91353 0.185010
249249 0 0
250250 −2.17024 −0.137258
251251 12.5202 0.790270 0.395135 0.918623i 0.370698π-0.370698\pi
0.395135 + 0.918623i 0.370698π0.370698\pi
252252 0 0
253253 −1.41147 −0.0887386
254254 2.39693 0.150397
255255 0 0
256256 7.19934 0.449959
257257 6.48339 0.404423 0.202211 0.979342i 0.435187π-0.435187\pi
0.202211 + 0.979342i 0.435187π0.435187\pi
258258 0 0
259259 −1.68273 −0.104560
260260 2.82800 0.175385
261261 0 0
262262 3.59121 0.221866
263263 2.09833 0.129388 0.0646942 0.997905i 0.479393π-0.479393\pi
0.0646942 + 0.997905i 0.479393π0.479393\pi
264264 0 0
265265 8.23947 0.506147
266266 −0.773318 −0.0474152
267267 0 0
268268 −9.32770 −0.569780
269269 29.2490 1.78334 0.891671 0.452685i 0.149534π-0.149534\pi
0.891671 + 0.452685i 0.149534π0.149534\pi
270270 0 0
271271 −21.7246 −1.31968 −0.659838 0.751408i 0.729375π-0.729375\pi
−0.659838 + 0.751408i 0.729375π0.729375\pi
272272 −14.5175 −0.880255
273273 0 0
274274 4.92633 0.297610
275275 4.57398 0.275821
276276 0 0
277277 −4.45605 −0.267738 −0.133869 0.990999i 0.542740π-0.542740\pi
−0.133869 + 0.990999i 0.542740π0.542740\pi
278278 0.0350819 0.00210407
279279 0 0
280280 −0.467911 −0.0279630
281281 −20.4953 −1.22264 −0.611322 0.791382i 0.709362π-0.709362\pi
−0.611322 + 0.791382i 0.709362π0.709362\pi
282282 0 0
283283 6.88713 0.409397 0.204699 0.978825i 0.434379π-0.434379\pi
0.204699 + 0.978825i 0.434379π0.434379\pi
284284 −18.7665 −1.11359
285285 0 0
286286 0.800660 0.0473440
287287 −4.95542 −0.292509
288288 0 0
289289 2.46110 0.144771
290290 1.44057 0.0845932
291291 0 0
292292 14.0865 0.824348
293293 −13.8084 −0.806695 −0.403348 0.915047i 0.632153π-0.632153\pi
−0.403348 + 0.915047i 0.632153π0.632153\pi
294294 0 0
295295 −2.11112 −0.122914
296296 4.26083 0.247656
297297 0 0
298298 −1.06324 −0.0615921
299299 −3.25402 −0.188185
300300 0 0
301301 −6.54395 −0.377187
302302 6.73824 0.387742
303303 0 0
304304 −13.7716 −0.789853
305305 −5.56893 −0.318876
306306 0 0
307307 −0.601319 −0.0343191 −0.0171595 0.999853i 0.505462π-0.505462\pi
−0.0171595 + 0.999853i 0.505462π0.505462\pi
308308 1.00000 0.0569803
309309 0 0
310310 −0.490200 −0.0278415
311311 1.94087 0.110057 0.0550285 0.998485i 0.482475π-0.482475\pi
0.0550285 + 0.998485i 0.482475π0.482475\pi
312312 0 0
313313 2.01960 0.114155 0.0570773 0.998370i 0.481822π-0.481822\pi
0.0570773 + 0.998370i 0.481822π0.481822\pi
314314 −4.41921 −0.249391
315315 0 0
316316 9.17024 0.515867
317317 5.84936 0.328533 0.164266 0.986416i 0.447474π-0.447474\pi
0.164266 + 0.986416i 0.447474π0.447474\pi
318318 0 0
319319 −6.35504 −0.355814
320320 −3.42602 −0.191520
321321 0 0
322322 0.260830 0.0145355
323323 18.4611 1.02720
324324 0 0
325325 10.5449 0.584925
326326 −4.44150 −0.245992
327327 0 0
328328 12.5476 0.692824
329329 −2.05644 −0.113375
330330 0 0
331331 11.7219 0.644296 0.322148 0.946689i 0.395595π-0.395595\pi
0.322148 + 0.946689i 0.395595π0.395595\pi
332332 8.63816 0.474080
333333 0 0
334334 7.19759 0.393834
335335 3.23947 0.176991
336336 0 0
337337 12.5963 0.686162 0.343081 0.939306i 0.388529π-0.388529\pi
0.343081 + 0.939306i 0.388529π0.388529\pi
338338 −2.66901 −0.145175
339339 0 0
340340 5.41147 0.293478
341341 2.16250 0.117106
342342 0 0
343343 −7.29860 −0.394087
344344 16.5699 0.893387
345345 0 0
346346 −7.81521 −0.420148
347347 −23.8452 −1.28008 −0.640040 0.768342i 0.721082π-0.721082\pi
−0.640040 + 0.768342i 0.721082π0.721082\pi
348348 0 0
349349 −8.48246 −0.454056 −0.227028 0.973888i 0.572901π-0.572901\pi
−0.227028 + 0.973888i 0.572901π0.572901\pi
350350 −0.845237 −0.0451798
351351 0 0
352352 −3.83750 −0.204539
353353 7.44656 0.396340 0.198170 0.980168i 0.436500π-0.436500\pi
0.198170 + 0.980168i 0.436500π0.436500\pi
354354 0 0
355355 6.51754 0.345915
356356 31.8580 1.68847
357357 0 0
358358 −3.72369 −0.196803
359359 −22.9290 −1.21015 −0.605074 0.796170i 0.706856π-0.706856\pi
−0.605074 + 0.796170i 0.706856π0.706856\pi
360360 0 0
361361 −1.48751 −0.0782901
362362 −1.44387 −0.0758880
363363 0 0
364364 2.30541 0.120836
365365 −4.89218 −0.256068
366366 0 0
367367 15.3063 0.798984 0.399492 0.916737i 0.369186π-0.369186\pi
0.399492 + 0.916737i 0.369186π0.369186\pi
368368 4.64496 0.242135
369369 0 0
370370 −0.716881 −0.0372689
371371 6.71688 0.348723
372372 0 0
373373 −27.3901 −1.41821 −0.709103 0.705105i 0.750900π-0.750900\pi
−0.709103 + 0.705105i 0.750900π0.750900\pi
374374 1.53209 0.0792224
375375 0 0
376376 5.20708 0.268535
377377 −14.6509 −0.754562
378378 0 0
379379 11.2713 0.578966 0.289483 0.957183i 0.406517π-0.406517\pi
0.289483 + 0.957183i 0.406517π0.406517\pi
380380 5.13341 0.263338
381381 0 0
382382 0.834808 0.0427125
383383 33.3628 1.70476 0.852379 0.522924i 0.175159π-0.175159\pi
0.852379 + 0.522924i 0.175159π0.175159\pi
384384 0 0
385385 −0.347296 −0.0176999
386386 −0.157451 −0.00801406
387387 0 0
388388 −23.7665 −1.20656
389389 12.2490 0.621047 0.310524 0.950566i 0.399496π-0.399496\pi
0.310524 + 0.950566i 0.399496π0.399496\pi
390390 0 0
391391 −6.22668 −0.314897
392392 9.04963 0.457075
393393 0 0
394394 −6.81521 −0.343345
395395 −3.18479 −0.160244
396396 0 0
397397 −11.4287 −0.573591 −0.286795 0.957992i 0.592590π-0.592590\pi
−0.286795 + 0.957992i 0.592590π0.592590\pi
398398 1.26083 0.0631997
399399 0 0
400400 −15.0523 −0.752616
401401 21.6946 1.08338 0.541688 0.840580i 0.317785π-0.317785\pi
0.541688 + 0.840580i 0.317785π0.317785\pi
402402 0 0
403403 4.98545 0.248343
404404 −32.1215 −1.59811
405405 0 0
406406 1.17436 0.0582827
407407 3.16250 0.156759
408408 0 0
409409 −28.5895 −1.41366 −0.706829 0.707385i 0.749875π-0.749875\pi
−0.706829 + 0.707385i 0.749875π0.749875\pi
410410 −2.11112 −0.104261
411411 0 0
412412 −5.37464 −0.264789
413413 −1.72100 −0.0846849
414414 0 0
415415 −3.00000 −0.147264
416416 −8.84699 −0.433759
417417 0 0
418418 1.45336 0.0710863
419419 −8.61081 −0.420666 −0.210333 0.977630i 0.567455π-0.567455\pi
−0.210333 + 0.977630i 0.567455π0.567455\pi
420420 0 0
421421 −34.4320 −1.67811 −0.839057 0.544044i 0.816892π-0.816892\pi
−0.839057 + 0.544044i 0.816892π0.816892\pi
422422 7.52704 0.366410
423423 0 0
424424 −17.0077 −0.825969
425425 20.1780 0.978776
426426 0 0
427427 −4.53983 −0.219698
428428 −18.6604 −0.901987
429429 0 0
430430 −2.78787 −0.134443
431431 14.2463 0.686219 0.343110 0.939295i 0.388520π-0.388520\pi
0.343110 + 0.939295i 0.388520π0.388520\pi
432432 0 0
433433 −24.6023 −1.18231 −0.591154 0.806558i 0.701328π-0.701328\pi
−0.591154 + 0.806558i 0.701328π0.701328\pi
434434 −0.399615 −0.0191821
435435 0 0
436436 −25.9659 −1.24354
437437 −5.90673 −0.282557
438438 0 0
439439 4.17293 0.199163 0.0995816 0.995029i 0.468250π-0.468250\pi
0.0995816 + 0.995029i 0.468250π0.468250\pi
440440 0.879385 0.0419230
441441 0 0
442442 3.53209 0.168004
443443 −29.2645 −1.39040 −0.695198 0.718818i 0.744683π-0.744683\pi
−0.695198 + 0.718818i 0.744683π0.744683\pi
444444 0 0
445445 −11.0642 −0.524492
446446 6.64590 0.314692
447447 0 0
448448 −2.79292 −0.131953
449449 −15.7956 −0.745441 −0.372720 0.927944i 0.621575π-0.621575\pi
−0.372720 + 0.927944i 0.621575π0.621575\pi
450450 0 0
451451 9.31315 0.438539
452452 −3.30541 −0.155473
453453 0 0
454454 −5.41559 −0.254166
455455 −0.800660 −0.0375355
456456 0 0
457457 9.48515 0.443696 0.221848 0.975081i 0.428791π-0.428791\pi
0.221848 + 0.975081i 0.428791π0.428791\pi
458458 −5.35235 −0.250099
459459 0 0
460460 −1.73143 −0.0807283
461461 −28.9445 −1.34808 −0.674040 0.738695i 0.735442π-0.735442\pi
−0.674040 + 0.738695i 0.735442π0.735442\pi
462462 0 0
463463 −22.8803 −1.06334 −0.531669 0.846952i 0.678435π-0.678435\pi
−0.531669 + 0.846952i 0.678435π0.678435\pi
464464 20.9135 0.970886
465465 0 0
466466 1.49020 0.0690322
467467 10.2412 0.473908 0.236954 0.971521i 0.423851π-0.423851\pi
0.236954 + 0.971521i 0.423851π0.423851\pi
468468 0 0
469469 2.64084 0.121943
470470 −0.876087 −0.0404109
471471 0 0
472472 4.35773 0.200581
473473 12.2986 0.565490
474474 0 0
475475 19.1411 0.878256
476476 4.41147 0.202200
477477 0 0
478478 −6.99226 −0.319818
479479 19.3310 0.883256 0.441628 0.897198i 0.354401π-0.354401\pi
0.441628 + 0.897198i 0.354401π0.354401\pi
480480 0 0
481481 7.29086 0.332435
482482 −2.58584 −0.117782
483483 0 0
484484 −1.87939 −0.0854266
485485 8.25402 0.374796
486486 0 0
487487 27.2104 1.23302 0.616510 0.787347i 0.288546π-0.288546\pi
0.616510 + 0.787347i 0.288546π0.288546\pi
488488 11.4953 0.520366
489489 0 0
490490 −1.52259 −0.0687838
491491 −36.0378 −1.62636 −0.813181 0.582011i 0.802266π-0.802266\pi
−0.813181 + 0.582011i 0.802266π0.802266\pi
492492 0 0
493493 −28.0351 −1.26264
494494 3.35059 0.150750
495495 0 0
496496 −7.11650 −0.319540
497497 5.31315 0.238327
498498 0 0
499499 −7.89218 −0.353302 −0.176651 0.984274i 0.556526π-0.556526\pi
−0.176651 + 0.984274i 0.556526π0.556526\pi
500500 11.7442 0.525218
501501 0 0
502502 4.34823 0.194071
503503 −37.2550 −1.66112 −0.830558 0.556932i 0.811978π-0.811978\pi
−0.830558 + 0.556932i 0.811978π0.811978\pi
504504 0 0
505505 11.1557 0.496422
506506 −0.490200 −0.0217920
507507 0 0
508508 −12.9709 −0.575491
509509 4.08915 0.181249 0.0906243 0.995885i 0.471114π-0.471114\pi
0.0906243 + 0.995885i 0.471114π0.471114\pi
510510 0 0
511511 −3.98814 −0.176425
512512 21.4962 0.950006
513513 0 0
514514 2.25166 0.0993164
515515 1.86659 0.0822519
516516 0 0
517517 3.86484 0.169975
518518 −0.584407 −0.0256774
519519 0 0
520520 2.02734 0.0889048
521521 7.29322 0.319522 0.159761 0.987156i 0.448928π-0.448928\pi
0.159761 + 0.987156i 0.448928π0.448928\pi
522522 0 0
523523 −14.3105 −0.625753 −0.312876 0.949794i 0.601293π-0.601293\pi
−0.312876 + 0.949794i 0.601293π0.601293\pi
524524 −19.4338 −0.848968
525525 0 0
526526 0.728741 0.0317746
527527 9.53983 0.415562
528528 0 0
529529 −21.0077 −0.913380
530530 2.86154 0.124297
531531 0 0
532532 4.18479 0.181434
533533 21.4706 0.929995
534534 0 0
535535 6.48070 0.280185
536536 −6.68685 −0.288828
537537 0 0
538538 10.1581 0.437945
539539 6.71688 0.289317
540540 0 0
541541 −36.1411 −1.55383 −0.776915 0.629606i 0.783216π-0.783216\pi
−0.776915 + 0.629606i 0.783216π0.783216\pi
542542 −7.54488 −0.324080
543543 0 0
544544 −16.9290 −0.725826
545545 9.01785 0.386282
546546 0 0
547547 −18.7870 −0.803276 −0.401638 0.915799i 0.631559π-0.631559\pi
−0.401638 + 0.915799i 0.631559π0.631559\pi
548548 −26.6587 −1.13880
549549 0 0
550550 1.58853 0.0677350
551551 −26.5945 −1.13296
552552 0 0
553553 −2.59627 −0.110404
554554 −1.54757 −0.0657500
555555 0 0
556556 −0.189845 −0.00805122
557557 −3.99319 −0.169197 −0.0845985 0.996415i 0.526961π-0.526961\pi
−0.0845985 + 0.996415i 0.526961π0.526961\pi
558558 0 0
559559 28.3533 1.19922
560560 1.14290 0.0482965
561561 0 0
562562 −7.11793 −0.300252
563563 −22.6905 −0.956289 −0.478145 0.878281i 0.658691π-0.658691\pi
−0.478145 + 0.878281i 0.658691π0.658691\pi
564564 0 0
565565 1.14796 0.0482949
566566 2.39187 0.100538
567567 0 0
568568 −13.4534 −0.564491
569569 25.3209 1.06151 0.530753 0.847526i 0.321909π-0.321909\pi
0.530753 + 0.847526i 0.321909π0.321909\pi
570570 0 0
571571 33.3141 1.39415 0.697075 0.716998i 0.254484π-0.254484\pi
0.697075 + 0.716998i 0.254484π0.254484\pi
572572 −4.33275 −0.181161
573573 0 0
574574 −1.72100 −0.0718332
575575 −6.45605 −0.269236
576576 0 0
577577 −1.18479 −0.0493236 −0.0246618 0.999696i 0.507851π-0.507851\pi
−0.0246618 + 0.999696i 0.507851π0.507851\pi
578578 0.854732 0.0355522
579579 0 0
580580 −7.79561 −0.323695
581581 −2.44562 −0.101462
582582 0 0
583583 −12.6236 −0.522816
584584 10.0983 0.417872
585585 0 0
586586 −4.79561 −0.198105
587587 31.8043 1.31270 0.656352 0.754455i 0.272099π-0.272099\pi
0.656352 + 0.754455i 0.272099π0.272099\pi
588588 0 0
589589 9.04963 0.372884
590590 −0.733184 −0.0301847
591591 0 0
592592 −10.4074 −0.427740
593593 26.3381 1.08158 0.540789 0.841159i 0.318126π-0.318126\pi
0.540789 + 0.841159i 0.318126π0.318126\pi
594594 0 0
595595 −1.53209 −0.0628095
596596 5.75372 0.235681
597597 0 0
598598 −1.13011 −0.0462136
599599 15.2645 0.623689 0.311844 0.950133i 0.399053π-0.399053\pi
0.311844 + 0.950133i 0.399053π0.399053\pi
600600 0 0
601601 8.50711 0.347012 0.173506 0.984833i 0.444490π-0.444490\pi
0.173506 + 0.984833i 0.444490π0.444490\pi
602602 −2.27269 −0.0926279
603603 0 0
604604 −36.4638 −1.48369
605605 0.652704 0.0265362
606606 0 0
607607 12.5202 0.508180 0.254090 0.967181i 0.418224π-0.418224\pi
0.254090 + 0.967181i 0.418224π0.418224\pi
608608 −16.0591 −0.651284
609609 0 0
610610 −1.93407 −0.0783081
611611 8.91002 0.360461
612612 0 0
613613 −8.52259 −0.344224 −0.172112 0.985077i 0.555059π-0.555059\pi
−0.172112 + 0.985077i 0.555059π0.555059\pi
614614 −0.208836 −0.00842793
615615 0 0
616616 0.716881 0.0288840
617617 −20.4884 −0.824834 −0.412417 0.910995i 0.635315π-0.635315\pi
−0.412417 + 0.910995i 0.635315π0.635315\pi
618618 0 0
619619 −26.8016 −1.07725 −0.538623 0.842547i 0.681055π-0.681055\pi
−0.538623 + 0.842547i 0.681055π0.681055\pi
620620 2.65270 0.106535
621621 0 0
622622 0.674059 0.0270273
623623 −9.01960 −0.361363
624624 0 0
625625 18.7912 0.751647
626626 0.701400 0.0280336
627627 0 0
628628 23.9145 0.954291
629629 13.9513 0.556275
630630 0 0
631631 18.9736 0.755327 0.377663 0.925943i 0.376728π-0.376728\pi
0.377663 + 0.925943i 0.376728π0.376728\pi
632632 6.57398 0.261499
633633 0 0
634634 2.03146 0.0806796
635635 4.50475 0.178765
636636 0 0
637637 15.4851 0.613544
638638 −2.20708 −0.0873792
639639 0 0
640640 −6.19934 −0.245050
641641 −29.6313 −1.17037 −0.585184 0.810901i 0.698978π-0.698978\pi
−0.585184 + 0.810901i 0.698978π0.698978\pi
642642 0 0
643643 43.5773 1.71852 0.859260 0.511539i 0.170924π-0.170924\pi
0.859260 + 0.511539i 0.170924π0.170924\pi
644644 −1.41147 −0.0556199
645645 0 0
646646 6.41147 0.252256
647647 −21.0583 −0.827887 −0.413944 0.910302i 0.635849π-0.635849\pi
−0.413944 + 0.910302i 0.635849π0.635849\pi
648648 0 0
649649 3.23442 0.126962
650650 3.66220 0.143643
651651 0 0
652652 24.0351 0.941286
653653 1.33956 0.0524209 0.0262104 0.999656i 0.491656π-0.491656\pi
0.0262104 + 0.999656i 0.491656π0.491656\pi
654654 0 0
655655 6.74928 0.263716
656656 −30.6483 −1.19661
657657 0 0
658658 −0.714193 −0.0278421
659659 −18.9459 −0.738029 −0.369014 0.929424i 0.620305π-0.620305\pi
−0.369014 + 0.929424i 0.620305π0.620305\pi
660660 0 0
661661 27.6117 1.07397 0.536986 0.843591i 0.319563π-0.319563\pi
0.536986 + 0.843591i 0.319563π0.319563\pi
662662 4.07098 0.158223
663663 0 0
664664 6.19253 0.240317
665665 −1.45336 −0.0563590
666666 0 0
667667 8.96997 0.347319
668668 −38.9495 −1.50700
669669 0 0
670670 1.12506 0.0434648
671671 8.53209 0.329378
672672 0 0
673673 20.7425 0.799563 0.399782 0.916610i 0.369086π-0.369086\pi
0.399782 + 0.916610i 0.369086π0.369086\pi
674674 4.37464 0.168505
675675 0 0
676676 14.4433 0.555510
677677 −27.6064 −1.06100 −0.530500 0.847685i 0.677996π-0.677996\pi
−0.530500 + 0.847685i 0.677996π0.677996\pi
678678 0 0
679679 6.72874 0.258225
680680 3.87939 0.148768
681681 0 0
682682 0.751030 0.0287584
683683 31.4843 1.20471 0.602357 0.798227i 0.294228π-0.294228\pi
0.602357 + 0.798227i 0.294228π0.294228\pi
684684 0 0
685685 9.25847 0.353748
686686 −2.53478 −0.0967782
687687 0 0
688688 −40.4730 −1.54302
689689 −29.1026 −1.10872
690690 0 0
691691 −23.8881 −0.908745 −0.454372 0.890812i 0.650136π-0.650136\pi
−0.454372 + 0.890812i 0.650136π0.650136\pi
692692 42.2918 1.60769
693693 0 0
694694 −8.28136 −0.314356
695695 0.0659325 0.00250096
696696 0 0
697697 41.0847 1.55619
698698 −2.94593 −0.111505
699699 0 0
700700 4.57398 0.172880
701701 7.03684 0.265778 0.132889 0.991131i 0.457575π-0.457575\pi
0.132889 + 0.991131i 0.457575π0.457575\pi
702702 0 0
703703 13.2344 0.499146
704704 5.24897 0.197828
705705 0 0
706706 2.58616 0.0973315
707707 9.09421 0.342023
708708 0 0
709709 −12.9007 −0.484497 −0.242249 0.970214i 0.577885π-0.577885\pi
−0.242249 + 0.970214i 0.577885π0.577885\pi
710710 2.26352 0.0849483
711711 0 0
712712 22.8384 0.855906
713713 −3.05232 −0.114310
714714 0 0
715715 1.50475 0.0562744
716716 20.1506 0.753065
717717 0 0
718718 −7.96316 −0.297183
719719 17.2671 0.643956 0.321978 0.946747i 0.395652π-0.395652\pi
0.321978 + 0.946747i 0.395652π0.395652\pi
720720 0 0
721721 1.52166 0.0566696
722722 −0.516607 −0.0192261
723723 0 0
724724 7.81345 0.290385
725725 −29.0678 −1.07955
726726 0 0
727727 40.6067 1.50602 0.753009 0.658010i 0.228601π-0.228601\pi
0.753009 + 0.658010i 0.228601π0.228601\pi
728728 1.65270 0.0612533
729729 0 0
730730 −1.69904 −0.0628841
731731 54.2550 2.00669
732732 0 0
733733 −15.7493 −0.581713 −0.290856 0.956767i 0.593940π-0.593940\pi
−0.290856 + 0.956767i 0.593940π0.593940\pi
734734 5.31584 0.196211
735735 0 0
736736 5.41653 0.199656
737737 −4.96316 −0.182820
738738 0 0
739739 2.27538 0.0837011 0.0418506 0.999124i 0.486675π-0.486675\pi
0.0418506 + 0.999124i 0.486675π0.486675\pi
740740 3.87939 0.142609
741741 0 0
742742 2.33275 0.0856379
743743 −35.1735 −1.29039 −0.645196 0.764017i 0.723224π-0.723224\pi
−0.645196 + 0.764017i 0.723224π0.723224\pi
744744 0 0
745745 −1.99825 −0.0732100
746746 −9.51249 −0.348277
747747 0 0
748748 −8.29086 −0.303144
749749 5.28312 0.193041
750750 0 0
751751 −33.5066 −1.22267 −0.611337 0.791370i 0.709368π-0.709368\pi
−0.611337 + 0.791370i 0.709368π0.709368\pi
752752 −12.7186 −0.463801
753753 0 0
754754 −5.08822 −0.185302
755755 12.6637 0.460881
756756 0 0
757757 45.4570 1.65216 0.826081 0.563551i 0.190565π-0.190565\pi
0.826081 + 0.563551i 0.190565π0.190565\pi
758758 3.91447 0.142180
759759 0 0
760760 3.68004 0.133489
761761 −29.2739 −1.06118 −0.530590 0.847629i 0.678030π-0.678030\pi
−0.530590 + 0.847629i 0.678030π0.678030\pi
762762 0 0
763763 7.35142 0.266139
764764 −4.51754 −0.163439
765765 0 0
766766 11.5868 0.418647
767767 7.45666 0.269244
768768 0 0
769769 −44.3661 −1.59988 −0.799941 0.600079i 0.795136π-0.795136\pi
−0.799941 + 0.600079i 0.795136π0.795136\pi
770770 −0.120615 −0.00434665
771771 0 0
772772 0.852044 0.0306657
773773 −21.6372 −0.778237 −0.389118 0.921188i 0.627220π-0.627220\pi
−0.389118 + 0.921188i 0.627220π0.627220\pi
774774 0 0
775775 9.89124 0.355304
776776 −17.0378 −0.611620
777777 0 0
778778 4.25402 0.152514
779779 38.9736 1.39637
780780 0 0
781781 −9.98545 −0.357308
782782 −2.16250 −0.0773310
783783 0 0
784784 −22.1043 −0.789440
785785 −8.30541 −0.296433
786786 0 0
787787 18.7834 0.669557 0.334778 0.942297i 0.391339π-0.391339\pi
0.334778 + 0.942297i 0.391339π0.391339\pi
788788 36.8803 1.31381
789789 0 0
790790 −1.10607 −0.0393521
791791 0.935822 0.0332740
792792 0 0
793793 19.6699 0.698500
794794 −3.96915 −0.140860
795795 0 0
796796 −6.82295 −0.241833
797797 27.7202 0.981899 0.490950 0.871188i 0.336650π-0.336650\pi
0.490950 + 0.871188i 0.336650π0.336650\pi
798798 0 0
799799 17.0496 0.603173
800800 −17.5526 −0.620579
801801 0 0
802802 7.53445 0.266051
803803 7.49525 0.264502
804804 0 0
805805 0.490200 0.0172773
806806 1.73143 0.0609870
807807 0 0
808808 −23.0273 −0.810099
809809 −5.05737 −0.177808 −0.0889038 0.996040i 0.528336π-0.528336\pi
−0.0889038 + 0.996040i 0.528336π0.528336\pi
810810 0 0
811811 25.6709 0.901426 0.450713 0.892669i 0.351170π-0.351170\pi
0.450713 + 0.892669i 0.351170π0.351170\pi
812812 −6.35504 −0.223018
813813 0 0
814814 1.09833 0.0384963
815815 −8.34730 −0.292393
816816 0 0
817817 51.4671 1.80061
818818 −9.92902 −0.347160
819819 0 0
820820 11.4243 0.398953
821821 3.86484 0.134884 0.0674419 0.997723i 0.478516π-0.478516\pi
0.0674419 + 0.997723i 0.478516π0.478516\pi
822822 0 0
823823 27.8357 0.970293 0.485146 0.874433i 0.338766π-0.338766\pi
0.485146 + 0.874433i 0.338766π0.338766\pi
824824 −3.85298 −0.134225
825825 0 0
826826 −0.597697 −0.0207965
827827 −1.24392 −0.0432553 −0.0216276 0.999766i 0.506885π-0.506885\pi
−0.0216276 + 0.999766i 0.506885π0.506885\pi
828828 0 0
829829 −31.5794 −1.09680 −0.548398 0.836217i 0.684762π-0.684762\pi
−0.548398 + 0.836217i 0.684762π0.684762\pi
830830 −1.04189 −0.0361645
831831 0 0
832832 12.1010 0.419527
833833 29.6313 1.02667
834834 0 0
835835 13.5270 0.468122
836836 −7.86484 −0.272011
837837 0 0
838838 −2.99050 −0.103305
839839 9.86720 0.340654 0.170327 0.985388i 0.445518π-0.445518\pi
0.170327 + 0.985388i 0.445518π0.445518\pi
840840 0 0
841841 11.3865 0.392638
842842 −11.9581 −0.412104
843843 0 0
844844 −40.7324 −1.40207
845845 −5.01609 −0.172559
846846 0 0
847847 0.532089 0.0182828
848848 41.5425 1.42658
849849 0 0
850850 7.00774 0.240364
851851 −4.46379 −0.153017
852852 0 0
853853 57.5366 1.97002 0.985009 0.172505i 0.0551862π-0.0551862\pi
0.985009 + 0.172505i 0.0551862π0.0551862\pi
854854 −1.57667 −0.0539524
855855 0 0
856856 −13.3773 −0.457228
857857 −15.4037 −0.526182 −0.263091 0.964771i 0.584742π-0.584742\pi
−0.263091 + 0.964771i 0.584742π0.584742\pi
858858 0 0
859859 −42.5732 −1.45258 −0.726289 0.687390i 0.758756π-0.758756\pi
−0.726289 + 0.687390i 0.758756π0.758756\pi
860860 15.0865 0.514444
861861 0 0
862862 4.94768 0.168519
863863 −38.3536 −1.30557 −0.652786 0.757542i 0.726400π-0.726400\pi
−0.652786 + 0.757542i 0.726400π0.726400\pi
864864 0 0
865865 −14.6878 −0.499400
866866 −8.54427 −0.290346
867867 0 0
868868 2.16250 0.0734002
869869 4.87939 0.165522
870870 0 0
871871 −11.4421 −0.387701
872872 −18.6144 −0.630364
873873 0 0
874874 −2.05138 −0.0693891
875875 −3.32501 −0.112406
876876 0 0
877877 −12.4703 −0.421091 −0.210546 0.977584i 0.567524π-0.567524\pi
−0.210546 + 0.977584i 0.567524π0.567524\pi
878878 1.44924 0.0489096
879879 0 0
880880 −2.14796 −0.0724076
881881 −22.9172 −0.772099 −0.386049 0.922478i 0.626161π-0.626161\pi
−0.386049 + 0.922478i 0.626161π0.626161\pi
882882 0 0
883883 44.2300 1.48846 0.744229 0.667925i 0.232817π-0.232817\pi
0.744229 + 0.667925i 0.232817π0.232817\pi
884884 −19.1138 −0.642867
885885 0 0
886886 −10.1634 −0.341447
887887 24.7743 0.831838 0.415919 0.909402i 0.363460π-0.363460\pi
0.415919 + 0.909402i 0.363460π0.363460\pi
888888 0 0
889889 3.67230 0.123165
890890 −3.84255 −0.128803
891891 0 0
892892 −35.9641 −1.20417
893893 16.1735 0.541227
894894 0 0
895895 −6.99825 −0.233926
896896 −5.05375 −0.168834
897897 0 0
898898 −5.48576 −0.183062
899899 −13.7428 −0.458348
900900 0 0
901901 −55.6887 −1.85526
902902 3.23442 0.107694
903903 0 0
904904 −2.36959 −0.0788112
905905 −2.71358 −0.0902026
906906 0 0
907907 30.4979 1.01267 0.506334 0.862338i 0.331000π-0.331000\pi
0.506334 + 0.862338i 0.331000π0.331000\pi
908908 29.3063 0.972565
909909 0 0
910910 −0.278066 −0.00921780
911911 53.8827 1.78521 0.892606 0.450837i 0.148874π-0.148874\pi
0.892606 + 0.450837i 0.148874π0.148874\pi
912912 0 0
913913 4.59627 0.152114
914914 3.29416 0.108961
915915 0 0
916916 28.9641 0.957001
917917 5.50206 0.181694
918918 0 0
919919 5.19841 0.171480 0.0857398 0.996318i 0.472675π-0.472675\pi
0.0857398 + 0.996318i 0.472675π0.472675\pi
920920 −1.24123 −0.0409221
921921 0 0
922922 −10.0523 −0.331055
923923 −23.0205 −0.757730
924924 0 0
925925 14.4652 0.475614
926926 −7.94625 −0.261130
927927 0 0
928928 24.3874 0.800557
929929 −23.8735 −0.783265 −0.391632 0.920122i 0.628089π-0.628089\pi
−0.391632 + 0.920122i 0.628089π0.628089\pi
930930 0 0
931931 28.1088 0.921227
932932 −8.06418 −0.264151
933933 0 0
934934 3.55674 0.116380
935935 2.87939 0.0941660
936936 0 0
937937 18.7219 0.611619 0.305809 0.952093i 0.401073π-0.401073\pi
0.305809 + 0.952093i 0.401073π0.401073\pi
938938 0.917156 0.0299462
939939 0 0
940940 4.74092 0.154632
941941 33.5627 1.09411 0.547057 0.837095i 0.315748π-0.315748\pi
0.547057 + 0.837095i 0.315748π0.315748\pi
942942 0 0
943943 −13.1453 −0.428069
944944 −10.6440 −0.346434
945945 0 0
946946 4.27126 0.138871
947947 −43.6759 −1.41928 −0.709638 0.704566i 0.751142π-0.751142\pi
−0.709638 + 0.704566i 0.751142π0.751142\pi
948948 0 0
949949 17.2796 0.560920
950950 6.64765 0.215678
951951 0 0
952952 3.16250 0.102497
953953 39.4397 1.27758 0.638789 0.769382i 0.279436π-0.279436\pi
0.638789 + 0.769382i 0.279436π0.279436\pi
954954 0 0
955955 1.56893 0.0507692
956956 37.8384 1.22378
957957 0 0
958958 6.71358 0.216906
959959 7.54757 0.243724
960960 0 0
961961 −26.3236 −0.849148
962962 2.53209 0.0816378
963963 0 0
964964 13.9932 0.450690
965965 −0.295912 −0.00952574
966966 0 0
967967 6.58853 0.211873 0.105936 0.994373i 0.466216π-0.466216\pi
0.105936 + 0.994373i 0.466216π0.466216\pi
968968 −1.34730 −0.0433037
969969 0 0
970970 2.86659 0.0920407
971971 17.0327 0.546606 0.273303 0.961928i 0.411884π-0.411884\pi
0.273303 + 0.961928i 0.411884π0.411884\pi
972972 0 0
973973 0.0537486 0.00172310
974974 9.45007 0.302800
975975 0 0
976976 −28.0779 −0.898752
977977 7.54900 0.241514 0.120757 0.992682i 0.461468π-0.461468\pi
0.120757 + 0.992682i 0.461468π0.461468\pi
978978 0 0
979979 16.9513 0.541766
980980 8.23947 0.263200
981981 0 0
982982 −12.5158 −0.399395
983983 −3.84699 −0.122700 −0.0613500 0.998116i 0.519541π-0.519541\pi
−0.0613500 + 0.998116i 0.519541π0.519541\pi
984984 0 0
985985 −12.8084 −0.408110
986986 −9.73648 −0.310073
987987 0 0
988988 −18.1317 −0.576845
989989 −17.3592 −0.551989
990990 0 0
991991 40.1121 1.27420 0.637101 0.770781i 0.280134π-0.280134\pi
0.637101 + 0.770781i 0.280134π0.280134\pi
992992 −8.29860 −0.263481
993993 0 0
994994 1.84524 0.0585274
995995 2.36959 0.0751209
996996 0 0
997997 −16.5648 −0.524613 −0.262306 0.964985i 0.584483π-0.584483\pi
−0.262306 + 0.964985i 0.584483π0.584483\pi
998998 −2.74092 −0.0867625
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 891.2.a.l.1.2 3
3.2 odd 2 891.2.a.k.1.2 3
9.2 odd 6 297.2.e.d.199.2 6
9.4 even 3 99.2.e.d.34.2 6
9.5 odd 6 297.2.e.d.100.2 6
9.7 even 3 99.2.e.d.67.2 yes 6
11.10 odd 2 9801.2.a.be.1.2 3
33.32 even 2 9801.2.a.bd.1.2 3
99.43 odd 6 1089.2.e.h.364.2 6
99.76 odd 6 1089.2.e.h.727.2 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.e.d.34.2 6 9.4 even 3
99.2.e.d.67.2 yes 6 9.7 even 3
297.2.e.d.100.2 6 9.5 odd 6
297.2.e.d.199.2 6 9.2 odd 6
891.2.a.k.1.2 3 3.2 odd 2
891.2.a.l.1.2 3 1.1 even 1 trivial
1089.2.e.h.364.2 6 99.43 odd 6
1089.2.e.h.727.2 6 99.76 odd 6
9801.2.a.bd.1.2 3 33.32 even 2
9801.2.a.be.1.2 3 11.10 odd 2