Properties

Label 7350.2.a.ch.1.1
Level 73507350
Weight 22
Character 7350.1
Self dual yes
Analytic conductor 58.69058.690
Analytic rank 11
Dimension 11
CM no
Inner twists 11

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [7350,2,Mod(1,7350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7350, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("7350.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7350=235272 7350 = 2 \cdot 3 \cdot 5^{2} \cdot 7^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7350.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: 58.690045485658.6900454856
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 210)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 7350.1

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+1.00000q2+1.00000q3+1.00000q4+1.00000q6+1.00000q8+1.00000q95.00000q11+1.00000q12+1.00000q13+1.00000q162.00000q17+1.00000q187.00000q195.00000q223.00000q23+1.00000q24+1.00000q26+1.00000q27+6.00000q31+1.00000q325.00000q332.00000q34+1.00000q36+5.00000q377.00000q38+1.00000q39+9.00000q4110.0000q435.00000q443.00000q4613.0000q47+1.00000q482.00000q51+1.00000q52+1.00000q53+1.00000q547.00000q574.00000q59+2.00000q61+6.00000q62+1.00000q645.00000q666.00000q672.00000q683.00000q692.00000q71+1.00000q72+4.00000q73+5.00000q747.00000q76+1.00000q7814.0000q79+1.00000q81+9.00000q8210.0000q8310.0000q865.00000q8810.0000q893.00000q92+6.00000q9313.0000q94+1.00000q96+8.00000q975.00000q99+O(q100)q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{6} +1.00000 q^{8} +1.00000 q^{9} -5.00000 q^{11} +1.00000 q^{12} +1.00000 q^{13} +1.00000 q^{16} -2.00000 q^{17} +1.00000 q^{18} -7.00000 q^{19} -5.00000 q^{22} -3.00000 q^{23} +1.00000 q^{24} +1.00000 q^{26} +1.00000 q^{27} +6.00000 q^{31} +1.00000 q^{32} -5.00000 q^{33} -2.00000 q^{34} +1.00000 q^{36} +5.00000 q^{37} -7.00000 q^{38} +1.00000 q^{39} +9.00000 q^{41} -10.0000 q^{43} -5.00000 q^{44} -3.00000 q^{46} -13.0000 q^{47} +1.00000 q^{48} -2.00000 q^{51} +1.00000 q^{52} +1.00000 q^{53} +1.00000 q^{54} -7.00000 q^{57} -4.00000 q^{59} +2.00000 q^{61} +6.00000 q^{62} +1.00000 q^{64} -5.00000 q^{66} -6.00000 q^{67} -2.00000 q^{68} -3.00000 q^{69} -2.00000 q^{71} +1.00000 q^{72} +4.00000 q^{73} +5.00000 q^{74} -7.00000 q^{76} +1.00000 q^{78} -14.0000 q^{79} +1.00000 q^{81} +9.00000 q^{82} -10.0000 q^{83} -10.0000 q^{86} -5.00000 q^{88} -10.0000 q^{89} -3.00000 q^{92} +6.00000 q^{93} -13.0000 q^{94} +1.00000 q^{96} +8.00000 q^{97} -5.00000 q^{99} +O(q^{100})

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.00000 0.707107
33 1.00000 0.577350
44 1.00000 0.500000
55 0 0
66 1.00000 0.408248
77 0 0
88 1.00000 0.353553
99 1.00000 0.333333
1010 0 0
1111 −5.00000 −1.50756 −0.753778 0.657129i 0.771771π-0.771771\pi
−0.753778 + 0.657129i 0.771771π0.771771\pi
1212 1.00000 0.288675
1313 1.00000 0.277350 0.138675 0.990338i 0.455716π-0.455716\pi
0.138675 + 0.990338i 0.455716π0.455716\pi
1414 0 0
1515 0 0
1616 1.00000 0.250000
1717 −2.00000 −0.485071 −0.242536 0.970143i 0.577979π-0.577979\pi
−0.242536 + 0.970143i 0.577979π0.577979\pi
1818 1.00000 0.235702
1919 −7.00000 −1.60591 −0.802955 0.596040i 0.796740π-0.796740\pi
−0.802955 + 0.596040i 0.796740π0.796740\pi
2020 0 0
2121 0 0
2222 −5.00000 −1.06600
2323 −3.00000 −0.625543 −0.312772 0.949828i 0.601257π-0.601257\pi
−0.312772 + 0.949828i 0.601257π0.601257\pi
2424 1.00000 0.204124
2525 0 0
2626 1.00000 0.196116
2727 1.00000 0.192450
2828 0 0
2929 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
3030 0 0
3131 6.00000 1.07763 0.538816 0.842424i 0.318872π-0.318872\pi
0.538816 + 0.842424i 0.318872π0.318872\pi
3232 1.00000 0.176777
3333 −5.00000 −0.870388
3434 −2.00000 −0.342997
3535 0 0
3636 1.00000 0.166667
3737 5.00000 0.821995 0.410997 0.911636i 0.365181π-0.365181\pi
0.410997 + 0.911636i 0.365181π0.365181\pi
3838 −7.00000 −1.13555
3939 1.00000 0.160128
4040 0 0
4141 9.00000 1.40556 0.702782 0.711405i 0.251941π-0.251941\pi
0.702782 + 0.711405i 0.251941π0.251941\pi
4242 0 0
4343 −10.0000 −1.52499 −0.762493 0.646997i 0.776025π-0.776025\pi
−0.762493 + 0.646997i 0.776025π0.776025\pi
4444 −5.00000 −0.753778
4545 0 0
4646 −3.00000 −0.442326
4747 −13.0000 −1.89624 −0.948122 0.317905i 0.897021π-0.897021\pi
−0.948122 + 0.317905i 0.897021π0.897021\pi
4848 1.00000 0.144338
4949 0 0
5050 0 0
5151 −2.00000 −0.280056
5252 1.00000 0.138675
5353 1.00000 0.137361 0.0686803 0.997639i 0.478121π-0.478121\pi
0.0686803 + 0.997639i 0.478121π0.478121\pi
5454 1.00000 0.136083
5555 0 0
5656 0 0
5757 −7.00000 −0.927173
5858 0 0
5959 −4.00000 −0.520756 −0.260378 0.965507i 0.583847π-0.583847\pi
−0.260378 + 0.965507i 0.583847π0.583847\pi
6060 0 0
6161 2.00000 0.256074 0.128037 0.991769i 0.459132π-0.459132\pi
0.128037 + 0.991769i 0.459132π0.459132\pi
6262 6.00000 0.762001
6363 0 0
6464 1.00000 0.125000
6565 0 0
6666 −5.00000 −0.615457
6767 −6.00000 −0.733017 −0.366508 0.930415i 0.619447π-0.619447\pi
−0.366508 + 0.930415i 0.619447π0.619447\pi
6868 −2.00000 −0.242536
6969 −3.00000 −0.361158
7070 0 0
7171 −2.00000 −0.237356 −0.118678 0.992933i 0.537866π-0.537866\pi
−0.118678 + 0.992933i 0.537866π0.537866\pi
7272 1.00000 0.117851
7373 4.00000 0.468165 0.234082 0.972217i 0.424791π-0.424791\pi
0.234082 + 0.972217i 0.424791π0.424791\pi
7474 5.00000 0.581238
7575 0 0
7676 −7.00000 −0.802955
7777 0 0
7878 1.00000 0.113228
7979 −14.0000 −1.57512 −0.787562 0.616236i 0.788657π-0.788657\pi
−0.787562 + 0.616236i 0.788657π0.788657\pi
8080 0 0
8181 1.00000 0.111111
8282 9.00000 0.993884
8383 −10.0000 −1.09764 −0.548821 0.835940i 0.684923π-0.684923\pi
−0.548821 + 0.835940i 0.684923π0.684923\pi
8484 0 0
8585 0 0
8686 −10.0000 −1.07833
8787 0 0
8888 −5.00000 −0.533002
8989 −10.0000 −1.06000 −0.529999 0.847998i 0.677808π-0.677808\pi
−0.529999 + 0.847998i 0.677808π0.677808\pi
9090 0 0
9191 0 0
9292 −3.00000 −0.312772
9393 6.00000 0.622171
9494 −13.0000 −1.34085
9595 0 0
9696 1.00000 0.102062
9797 8.00000 0.812277 0.406138 0.913812i 0.366875π-0.366875\pi
0.406138 + 0.913812i 0.366875π0.366875\pi
9898 0 0
9999 −5.00000 −0.502519
100100 0 0
101101 −8.00000 −0.796030 −0.398015 0.917379i 0.630301π-0.630301\pi
−0.398015 + 0.917379i 0.630301π0.630301\pi
102102 −2.00000 −0.198030
103103 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
104104 1.00000 0.0980581
105105 0 0
106106 1.00000 0.0971286
107107 −12.0000 −1.16008 −0.580042 0.814587i 0.696964π-0.696964\pi
−0.580042 + 0.814587i 0.696964π0.696964\pi
108108 1.00000 0.0962250
109109 −18.0000 −1.72409 −0.862044 0.506834i 0.830816π-0.830816\pi
−0.862044 + 0.506834i 0.830816π0.830816\pi
110110 0 0
111111 5.00000 0.474579
112112 0 0
113113 −6.00000 −0.564433 −0.282216 0.959351i 0.591070π-0.591070\pi
−0.282216 + 0.959351i 0.591070π0.591070\pi
114114 −7.00000 −0.655610
115115 0 0
116116 0 0
117117 1.00000 0.0924500
118118 −4.00000 −0.368230
119119 0 0
120120 0 0
121121 14.0000 1.27273
122122 2.00000 0.181071
123123 9.00000 0.811503
124124 6.00000 0.538816
125125 0 0
126126 0 0
127127 −9.00000 −0.798621 −0.399310 0.916816i 0.630750π-0.630750\pi
−0.399310 + 0.916816i 0.630750π0.630750\pi
128128 1.00000 0.0883883
129129 −10.0000 −0.880451
130130 0 0
131131 17.0000 1.48530 0.742648 0.669681i 0.233569π-0.233569\pi
0.742648 + 0.669681i 0.233569π0.233569\pi
132132 −5.00000 −0.435194
133133 0 0
134134 −6.00000 −0.518321
135135 0 0
136136 −2.00000 −0.171499
137137 4.00000 0.341743 0.170872 0.985293i 0.445342π-0.445342\pi
0.170872 + 0.985293i 0.445342π0.445342\pi
138138 −3.00000 −0.255377
139139 8.00000 0.678551 0.339276 0.940687i 0.389818π-0.389818\pi
0.339276 + 0.940687i 0.389818π0.389818\pi
140140 0 0
141141 −13.0000 −1.09480
142142 −2.00000 −0.167836
143143 −5.00000 −0.418121
144144 1.00000 0.0833333
145145 0 0
146146 4.00000 0.331042
147147 0 0
148148 5.00000 0.410997
149149 −6.00000 −0.491539 −0.245770 0.969328i 0.579041π-0.579041\pi
−0.245770 + 0.969328i 0.579041π0.579041\pi
150150 0 0
151151 −22.0000 −1.79033 −0.895167 0.445730i 0.852944π-0.852944\pi
−0.895167 + 0.445730i 0.852944π0.852944\pi
152152 −7.00000 −0.567775
153153 −2.00000 −0.161690
154154 0 0
155155 0 0
156156 1.00000 0.0800641
157157 13.0000 1.03751 0.518756 0.854922i 0.326395π-0.326395\pi
0.518756 + 0.854922i 0.326395π0.326395\pi
158158 −14.0000 −1.11378
159159 1.00000 0.0793052
160160 0 0
161161 0 0
162162 1.00000 0.0785674
163163 12.0000 0.939913 0.469956 0.882690i 0.344270π-0.344270\pi
0.469956 + 0.882690i 0.344270π0.344270\pi
164164 9.00000 0.702782
165165 0 0
166166 −10.0000 −0.776151
167167 −19.0000 −1.47026 −0.735132 0.677924i 0.762880π-0.762880\pi
−0.735132 + 0.677924i 0.762880π0.762880\pi
168168 0 0
169169 −12.0000 −0.923077
170170 0 0
171171 −7.00000 −0.535303
172172 −10.0000 −0.762493
173173 7.00000 0.532200 0.266100 0.963945i 0.414265π-0.414265\pi
0.266100 + 0.963945i 0.414265π0.414265\pi
174174 0 0
175175 0 0
176176 −5.00000 −0.376889
177177 −4.00000 −0.300658
178178 −10.0000 −0.749532
179179 −11.0000 −0.822179 −0.411089 0.911595i 0.634852π-0.634852\pi
−0.411089 + 0.911595i 0.634852π0.634852\pi
180180 0 0
181181 2.00000 0.148659 0.0743294 0.997234i 0.476318π-0.476318\pi
0.0743294 + 0.997234i 0.476318π0.476318\pi
182182 0 0
183183 2.00000 0.147844
184184 −3.00000 −0.221163
185185 0 0
186186 6.00000 0.439941
187187 10.0000 0.731272
188188 −13.0000 −0.948122
189189 0 0
190190 0 0
191191 −16.0000 −1.15772 −0.578860 0.815427i 0.696502π-0.696502\pi
−0.578860 + 0.815427i 0.696502π0.696502\pi
192192 1.00000 0.0721688
193193 18.0000 1.29567 0.647834 0.761781i 0.275675π-0.275675\pi
0.647834 + 0.761781i 0.275675π0.275675\pi
194194 8.00000 0.574367
195195 0 0
196196 0 0
197197 27.0000 1.92367 0.961835 0.273629i 0.0882242π-0.0882242\pi
0.961835 + 0.273629i 0.0882242π0.0882242\pi
198198 −5.00000 −0.355335
199199 14.0000 0.992434 0.496217 0.868199i 0.334722π-0.334722\pi
0.496217 + 0.868199i 0.334722π0.334722\pi
200200 0 0
201201 −6.00000 −0.423207
202202 −8.00000 −0.562878
203203 0 0
204204 −2.00000 −0.140028
205205 0 0
206206 0 0
207207 −3.00000 −0.208514
208208 1.00000 0.0693375
209209 35.0000 2.42100
210210 0 0
211211 19.0000 1.30801 0.654007 0.756489i 0.273087π-0.273087\pi
0.654007 + 0.756489i 0.273087π0.273087\pi
212212 1.00000 0.0686803
213213 −2.00000 −0.137038
214214 −12.0000 −0.820303
215215 0 0
216216 1.00000 0.0680414
217217 0 0
218218 −18.0000 −1.21911
219219 4.00000 0.270295
220220 0 0
221221 −2.00000 −0.134535
222222 5.00000 0.335578
223223 16.0000 1.07144 0.535720 0.844396i 0.320040π-0.320040\pi
0.535720 + 0.844396i 0.320040π0.320040\pi
224224 0 0
225225 0 0
226226 −6.00000 −0.399114
227227 14.0000 0.929213 0.464606 0.885517i 0.346196π-0.346196\pi
0.464606 + 0.885517i 0.346196π0.346196\pi
228228 −7.00000 −0.463586
229229 4.00000 0.264327 0.132164 0.991228i 0.457808π-0.457808\pi
0.132164 + 0.991228i 0.457808π0.457808\pi
230230 0 0
231231 0 0
232232 0 0
233233 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
234234 1.00000 0.0653720
235235 0 0
236236 −4.00000 −0.260378
237237 −14.0000 −0.909398
238238 0 0
239239 20.0000 1.29369 0.646846 0.762620i 0.276088π-0.276088\pi
0.646846 + 0.762620i 0.276088π0.276088\pi
240240 0 0
241241 1.00000 0.0644157 0.0322078 0.999481i 0.489746π-0.489746\pi
0.0322078 + 0.999481i 0.489746π0.489746\pi
242242 14.0000 0.899954
243243 1.00000 0.0641500
244244 2.00000 0.128037
245245 0 0
246246 9.00000 0.573819
247247 −7.00000 −0.445399
248248 6.00000 0.381000
249249 −10.0000 −0.633724
250250 0 0
251251 3.00000 0.189358 0.0946792 0.995508i 0.469817π-0.469817\pi
0.0946792 + 0.995508i 0.469817π0.469817\pi
252252 0 0
253253 15.0000 0.943042
254254 −9.00000 −0.564710
255255 0 0
256256 1.00000 0.0625000
257257 −10.0000 −0.623783 −0.311891 0.950118i 0.600963π-0.600963\pi
−0.311891 + 0.950118i 0.600963π0.600963\pi
258258 −10.0000 −0.622573
259259 0 0
260260 0 0
261261 0 0
262262 17.0000 1.05026
263263 −24.0000 −1.47990 −0.739952 0.672660i 0.765152π-0.765152\pi
−0.739952 + 0.672660i 0.765152π0.765152\pi
264264 −5.00000 −0.307729
265265 0 0
266266 0 0
267267 −10.0000 −0.611990
268268 −6.00000 −0.366508
269269 −14.0000 −0.853595 −0.426798 0.904347i 0.640358π-0.640358\pi
−0.426798 + 0.904347i 0.640358π0.640358\pi
270270 0 0
271271 −8.00000 −0.485965 −0.242983 0.970031i 0.578126π-0.578126\pi
−0.242983 + 0.970031i 0.578126π0.578126\pi
272272 −2.00000 −0.121268
273273 0 0
274274 4.00000 0.241649
275275 0 0
276276 −3.00000 −0.180579
277277 −2.00000 −0.120168 −0.0600842 0.998193i 0.519137π-0.519137\pi
−0.0600842 + 0.998193i 0.519137π0.519137\pi
278278 8.00000 0.479808
279279 6.00000 0.359211
280280 0 0
281281 −11.0000 −0.656205 −0.328102 0.944642i 0.606409π-0.606409\pi
−0.328102 + 0.944642i 0.606409π0.606409\pi
282282 −13.0000 −0.774139
283283 26.0000 1.54554 0.772770 0.634686i 0.218871π-0.218871\pi
0.772770 + 0.634686i 0.218871π0.218871\pi
284284 −2.00000 −0.118678
285285 0 0
286286 −5.00000 −0.295656
287287 0 0
288288 1.00000 0.0589256
289289 −13.0000 −0.764706
290290 0 0
291291 8.00000 0.468968
292292 4.00000 0.234082
293293 1.00000 0.0584206 0.0292103 0.999573i 0.490701π-0.490701\pi
0.0292103 + 0.999573i 0.490701π0.490701\pi
294294 0 0
295295 0 0
296296 5.00000 0.290619
297297 −5.00000 −0.290129
298298 −6.00000 −0.347571
299299 −3.00000 −0.173494
300300 0 0
301301 0 0
302302 −22.0000 −1.26596
303303 −8.00000 −0.459588
304304 −7.00000 −0.401478
305305 0 0
306306 −2.00000 −0.114332
307307 2.00000 0.114146 0.0570730 0.998370i 0.481823π-0.481823\pi
0.0570730 + 0.998370i 0.481823π0.481823\pi
308308 0 0
309309 0 0
310310 0 0
311311 26.0000 1.47432 0.737162 0.675716i 0.236165π-0.236165\pi
0.737162 + 0.675716i 0.236165π0.236165\pi
312312 1.00000 0.0566139
313313 −10.0000 −0.565233 −0.282617 0.959233i 0.591202π-0.591202\pi
−0.282617 + 0.959233i 0.591202π0.591202\pi
314314 13.0000 0.733632
315315 0 0
316316 −14.0000 −0.787562
317317 −2.00000 −0.112331 −0.0561656 0.998421i 0.517887π-0.517887\pi
−0.0561656 + 0.998421i 0.517887π0.517887\pi
318318 1.00000 0.0560772
319319 0 0
320320 0 0
321321 −12.0000 −0.669775
322322 0 0
323323 14.0000 0.778981
324324 1.00000 0.0555556
325325 0 0
326326 12.0000 0.664619
327327 −18.0000 −0.995402
328328 9.00000 0.496942
329329 0 0
330330 0 0
331331 −15.0000 −0.824475 −0.412237 0.911077i 0.635253π-0.635253\pi
−0.412237 + 0.911077i 0.635253π0.635253\pi
332332 −10.0000 −0.548821
333333 5.00000 0.273998
334334 −19.0000 −1.03963
335335 0 0
336336 0 0
337337 14.0000 0.762629 0.381314 0.924445i 0.375472π-0.375472\pi
0.381314 + 0.924445i 0.375472π0.375472\pi
338338 −12.0000 −0.652714
339339 −6.00000 −0.325875
340340 0 0
341341 −30.0000 −1.62459
342342 −7.00000 −0.378517
343343 0 0
344344 −10.0000 −0.539164
345345 0 0
346346 7.00000 0.376322
347347 16.0000 0.858925 0.429463 0.903085i 0.358703π-0.358703\pi
0.429463 + 0.903085i 0.358703π0.358703\pi
348348 0 0
349349 24.0000 1.28469 0.642345 0.766415i 0.277962π-0.277962\pi
0.642345 + 0.766415i 0.277962π0.277962\pi
350350 0 0
351351 1.00000 0.0533761
352352 −5.00000 −0.266501
353353 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
354354 −4.00000 −0.212598
355355 0 0
356356 −10.0000 −0.529999
357357 0 0
358358 −11.0000 −0.581368
359359 −28.0000 −1.47778 −0.738892 0.673824i 0.764651π-0.764651\pi
−0.738892 + 0.673824i 0.764651π0.764651\pi
360360 0 0
361361 30.0000 1.57895
362362 2.00000 0.105118
363363 14.0000 0.734809
364364 0 0
365365 0 0
366366 2.00000 0.104542
367367 −37.0000 −1.93138 −0.965692 0.259690i 0.916380π-0.916380\pi
−0.965692 + 0.259690i 0.916380π0.916380\pi
368368 −3.00000 −0.156386
369369 9.00000 0.468521
370370 0 0
371371 0 0
372372 6.00000 0.311086
373373 −6.00000 −0.310668 −0.155334 0.987862i 0.549645π-0.549645\pi
−0.155334 + 0.987862i 0.549645π0.549645\pi
374374 10.0000 0.517088
375375 0 0
376376 −13.0000 −0.670424
377377 0 0
378378 0 0
379379 −1.00000 −0.0513665 −0.0256833 0.999670i 0.508176π-0.508176\pi
−0.0256833 + 0.999670i 0.508176π0.508176\pi
380380 0 0
381381 −9.00000 −0.461084
382382 −16.0000 −0.818631
383383 −9.00000 −0.459879 −0.229939 0.973205i 0.573853π-0.573853\pi
−0.229939 + 0.973205i 0.573853π0.573853\pi
384384 1.00000 0.0510310
385385 0 0
386386 18.0000 0.916176
387387 −10.0000 −0.508329
388388 8.00000 0.406138
389389 6.00000 0.304212 0.152106 0.988364i 0.451394π-0.451394\pi
0.152106 + 0.988364i 0.451394π0.451394\pi
390390 0 0
391391 6.00000 0.303433
392392 0 0
393393 17.0000 0.857537
394394 27.0000 1.36024
395395 0 0
396396 −5.00000 −0.251259
397397 −2.00000 −0.100377 −0.0501886 0.998740i 0.515982π-0.515982\pi
−0.0501886 + 0.998740i 0.515982π0.515982\pi
398398 14.0000 0.701757
399399 0 0
400400 0 0
401401 −27.0000 −1.34832 −0.674158 0.738587i 0.735493π-0.735493\pi
−0.674158 + 0.738587i 0.735493π0.735493\pi
402402 −6.00000 −0.299253
403403 6.00000 0.298881
404404 −8.00000 −0.398015
405405 0 0
406406 0 0
407407 −25.0000 −1.23920
408408 −2.00000 −0.0990148
409409 −10.0000 −0.494468 −0.247234 0.968956i 0.579522π-0.579522\pi
−0.247234 + 0.968956i 0.579522π0.579522\pi
410410 0 0
411411 4.00000 0.197305
412412 0 0
413413 0 0
414414 −3.00000 −0.147442
415415 0 0
416416 1.00000 0.0490290
417417 8.00000 0.391762
418418 35.0000 1.71191
419419 −3.00000 −0.146560 −0.0732798 0.997311i 0.523347π-0.523347\pi
−0.0732798 + 0.997311i 0.523347π0.523347\pi
420420 0 0
421421 −20.0000 −0.974740 −0.487370 0.873195i 0.662044π-0.662044\pi
−0.487370 + 0.873195i 0.662044π0.662044\pi
422422 19.0000 0.924906
423423 −13.0000 −0.632082
424424 1.00000 0.0485643
425425 0 0
426426 −2.00000 −0.0969003
427427 0 0
428428 −12.0000 −0.580042
429429 −5.00000 −0.241402
430430 0 0
431431 18.0000 0.867029 0.433515 0.901146i 0.357273π-0.357273\pi
0.433515 + 0.901146i 0.357273π0.357273\pi
432432 1.00000 0.0481125
433433 4.00000 0.192228 0.0961139 0.995370i 0.469359π-0.469359\pi
0.0961139 + 0.995370i 0.469359π0.469359\pi
434434 0 0
435435 0 0
436436 −18.0000 −0.862044
437437 21.0000 1.00457
438438 4.00000 0.191127
439439 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
440440 0 0
441441 0 0
442442 −2.00000 −0.0951303
443443 6.00000 0.285069 0.142534 0.989790i 0.454475π-0.454475\pi
0.142534 + 0.989790i 0.454475π0.454475\pi
444444 5.00000 0.237289
445445 0 0
446446 16.0000 0.757622
447447 −6.00000 −0.283790
448448 0 0
449449 9.00000 0.424736 0.212368 0.977190i 0.431882π-0.431882\pi
0.212368 + 0.977190i 0.431882π0.431882\pi
450450 0 0
451451 −45.0000 −2.11897
452452 −6.00000 −0.282216
453453 −22.0000 −1.03365
454454 14.0000 0.657053
455455 0 0
456456 −7.00000 −0.327805
457457 38.0000 1.77757 0.888783 0.458329i 0.151552π-0.151552\pi
0.888783 + 0.458329i 0.151552π0.151552\pi
458458 4.00000 0.186908
459459 −2.00000 −0.0933520
460460 0 0
461461 12.0000 0.558896 0.279448 0.960161i 0.409849π-0.409849\pi
0.279448 + 0.960161i 0.409849π0.409849\pi
462462 0 0
463463 15.0000 0.697109 0.348555 0.937288i 0.386673π-0.386673\pi
0.348555 + 0.937288i 0.386673π0.386673\pi
464464 0 0
465465 0 0
466466 0 0
467467 2.00000 0.0925490 0.0462745 0.998929i 0.485265π-0.485265\pi
0.0462745 + 0.998929i 0.485265π0.485265\pi
468468 1.00000 0.0462250
469469 0 0
470470 0 0
471471 13.0000 0.599008
472472 −4.00000 −0.184115
473473 50.0000 2.29900
474474 −14.0000 −0.643041
475475 0 0
476476 0 0
477477 1.00000 0.0457869
478478 20.0000 0.914779
479479 −8.00000 −0.365529 −0.182765 0.983157i 0.558505π-0.558505\pi
−0.182765 + 0.983157i 0.558505π0.558505\pi
480480 0 0
481481 5.00000 0.227980
482482 1.00000 0.0455488
483483 0 0
484484 14.0000 0.636364
485485 0 0
486486 1.00000 0.0453609
487487 −24.0000 −1.08754 −0.543772 0.839233i 0.683004π-0.683004\pi
−0.543772 + 0.839233i 0.683004π0.683004\pi
488488 2.00000 0.0905357
489489 12.0000 0.542659
490490 0 0
491491 24.0000 1.08310 0.541552 0.840667i 0.317837π-0.317837\pi
0.541552 + 0.840667i 0.317837π0.317837\pi
492492 9.00000 0.405751
493493 0 0
494494 −7.00000 −0.314945
495495 0 0
496496 6.00000 0.269408
497497 0 0
498498 −10.0000 −0.448111
499499 −28.0000 −1.25345 −0.626726 0.779240i 0.715605π-0.715605\pi
−0.626726 + 0.779240i 0.715605π0.715605\pi
500500 0 0
501501 −19.0000 −0.848857
502502 3.00000 0.133897
503503 24.0000 1.07011 0.535054 0.844818i 0.320291π-0.320291\pi
0.535054 + 0.844818i 0.320291π0.320291\pi
504504 0 0
505505 0 0
506506 15.0000 0.666831
507507 −12.0000 −0.532939
508508 −9.00000 −0.399310
509509 −14.0000 −0.620539 −0.310270 0.950649i 0.600419π-0.600419\pi
−0.310270 + 0.950649i 0.600419π0.600419\pi
510510 0 0
511511 0 0
512512 1.00000 0.0441942
513513 −7.00000 −0.309058
514514 −10.0000 −0.441081
515515 0 0
516516 −10.0000 −0.440225
517517 65.0000 2.85870
518518 0 0
519519 7.00000 0.307266
520520 0 0
521521 15.0000 0.657162 0.328581 0.944476i 0.393430π-0.393430\pi
0.328581 + 0.944476i 0.393430π0.393430\pi
522522 0 0
523523 12.0000 0.524723 0.262362 0.964970i 0.415499π-0.415499\pi
0.262362 + 0.964970i 0.415499π0.415499\pi
524524 17.0000 0.742648
525525 0 0
526526 −24.0000 −1.04645
527527 −12.0000 −0.522728
528528 −5.00000 −0.217597
529529 −14.0000 −0.608696
530530 0 0
531531 −4.00000 −0.173585
532532 0 0
533533 9.00000 0.389833
534534 −10.0000 −0.432742
535535 0 0
536536 −6.00000 −0.259161
537537 −11.0000 −0.474685
538538 −14.0000 −0.603583
539539 0 0
540540 0 0
541541 4.00000 0.171973 0.0859867 0.996296i 0.472596π-0.472596\pi
0.0859867 + 0.996296i 0.472596π0.472596\pi
542542 −8.00000 −0.343629
543543 2.00000 0.0858282
544544 −2.00000 −0.0857493
545545 0 0
546546 0 0
547547 14.0000 0.598597 0.299298 0.954160i 0.403247π-0.403247\pi
0.299298 + 0.954160i 0.403247π0.403247\pi
548548 4.00000 0.170872
549549 2.00000 0.0853579
550550 0 0
551551 0 0
552552 −3.00000 −0.127688
553553 0 0
554554 −2.00000 −0.0849719
555555 0 0
556556 8.00000 0.339276
557557 39.0000 1.65248 0.826242 0.563316i 0.190475π-0.190475\pi
0.826242 + 0.563316i 0.190475π0.190475\pi
558558 6.00000 0.254000
559559 −10.0000 −0.422955
560560 0 0
561561 10.0000 0.422200
562562 −11.0000 −0.464007
563563 30.0000 1.26435 0.632175 0.774826i 0.282163π-0.282163\pi
0.632175 + 0.774826i 0.282163π0.282163\pi
564564 −13.0000 −0.547399
565565 0 0
566566 26.0000 1.09286
567567 0 0
568568 −2.00000 −0.0839181
569569 −3.00000 −0.125767 −0.0628833 0.998021i 0.520030π-0.520030\pi
−0.0628833 + 0.998021i 0.520030π0.520030\pi
570570 0 0
571571 −8.00000 −0.334790 −0.167395 0.985890i 0.553535π-0.553535\pi
−0.167395 + 0.985890i 0.553535π0.553535\pi
572572 −5.00000 −0.209061
573573 −16.0000 −0.668410
574574 0 0
575575 0 0
576576 1.00000 0.0416667
577577 24.0000 0.999133 0.499567 0.866276i 0.333493π-0.333493\pi
0.499567 + 0.866276i 0.333493π0.333493\pi
578578 −13.0000 −0.540729
579579 18.0000 0.748054
580580 0 0
581581 0 0
582582 8.00000 0.331611
583583 −5.00000 −0.207079
584584 4.00000 0.165521
585585 0 0
586586 1.00000 0.0413096
587587 2.00000 0.0825488 0.0412744 0.999148i 0.486858π-0.486858\pi
0.0412744 + 0.999148i 0.486858π0.486858\pi
588588 0 0
589589 −42.0000 −1.73058
590590 0 0
591591 27.0000 1.11063
592592 5.00000 0.205499
593593 −34.0000 −1.39621 −0.698106 0.715994i 0.745974π-0.745974\pi
−0.698106 + 0.715994i 0.745974π0.745974\pi
594594 −5.00000 −0.205152
595595 0 0
596596 −6.00000 −0.245770
597597 14.0000 0.572982
598598 −3.00000 −0.122679
599599 −28.0000 −1.14405 −0.572024 0.820237i 0.693842π-0.693842\pi
−0.572024 + 0.820237i 0.693842π0.693842\pi
600600 0 0
601601 30.0000 1.22373 0.611863 0.790964i 0.290420π-0.290420\pi
0.611863 + 0.790964i 0.290420π0.290420\pi
602602 0 0
603603 −6.00000 −0.244339
604604 −22.0000 −0.895167
605605 0 0
606606 −8.00000 −0.324978
607607 13.0000 0.527654 0.263827 0.964570i 0.415015π-0.415015\pi
0.263827 + 0.964570i 0.415015π0.415015\pi
608608 −7.00000 −0.283887
609609 0 0
610610 0 0
611611 −13.0000 −0.525924
612612 −2.00000 −0.0808452
613613 −19.0000 −0.767403 −0.383701 0.923457i 0.625351π-0.625351\pi
−0.383701 + 0.923457i 0.625351π0.625351\pi
614614 2.00000 0.0807134
615615 0 0
616616 0 0
617617 −30.0000 −1.20775 −0.603877 0.797077i 0.706378π-0.706378\pi
−0.603877 + 0.797077i 0.706378π0.706378\pi
618618 0 0
619619 −15.0000 −0.602901 −0.301450 0.953482i 0.597471π-0.597471\pi
−0.301450 + 0.953482i 0.597471π0.597471\pi
620620 0 0
621621 −3.00000 −0.120386
622622 26.0000 1.04251
623623 0 0
624624 1.00000 0.0400320
625625 0 0
626626 −10.0000 −0.399680
627627 35.0000 1.39777
628628 13.0000 0.518756
629629 −10.0000 −0.398726
630630 0 0
631631 18.0000 0.716569 0.358284 0.933613i 0.383362π-0.383362\pi
0.358284 + 0.933613i 0.383362π0.383362\pi
632632 −14.0000 −0.556890
633633 19.0000 0.755182
634634 −2.00000 −0.0794301
635635 0 0
636636 1.00000 0.0396526
637637 0 0
638638 0 0
639639 −2.00000 −0.0791188
640640 0 0
641641 −33.0000 −1.30342 −0.651711 0.758468i 0.725948π-0.725948\pi
−0.651711 + 0.758468i 0.725948π0.725948\pi
642642 −12.0000 −0.473602
643643 38.0000 1.49857 0.749287 0.662246i 0.230396π-0.230396\pi
0.749287 + 0.662246i 0.230396π0.230396\pi
644644 0 0
645645 0 0
646646 14.0000 0.550823
647647 −1.00000 −0.0393141 −0.0196570 0.999807i 0.506257π-0.506257\pi
−0.0196570 + 0.999807i 0.506257π0.506257\pi
648648 1.00000 0.0392837
649649 20.0000 0.785069
650650 0 0
651651 0 0
652652 12.0000 0.469956
653653 −5.00000 −0.195665 −0.0978326 0.995203i 0.531191π-0.531191\pi
−0.0978326 + 0.995203i 0.531191π0.531191\pi
654654 −18.0000 −0.703856
655655 0 0
656656 9.00000 0.351391
657657 4.00000 0.156055
658658 0 0
659659 −36.0000 −1.40236 −0.701180 0.712984i 0.747343π-0.747343\pi
−0.701180 + 0.712984i 0.747343π0.747343\pi
660660 0 0
661661 −40.0000 −1.55582 −0.777910 0.628376i 0.783720π-0.783720\pi
−0.777910 + 0.628376i 0.783720π0.783720\pi
662662 −15.0000 −0.582992
663663 −2.00000 −0.0776736
664664 −10.0000 −0.388075
665665 0 0
666666 5.00000 0.193746
667667 0 0
668668 −19.0000 −0.735132
669669 16.0000 0.618596
670670 0 0
671671 −10.0000 −0.386046
672672 0 0
673673 −36.0000 −1.38770 −0.693849 0.720121i 0.744086π-0.744086\pi
−0.693849 + 0.720121i 0.744086π0.744086\pi
674674 14.0000 0.539260
675675 0 0
676676 −12.0000 −0.461538
677677 33.0000 1.26829 0.634147 0.773213i 0.281352π-0.281352\pi
0.634147 + 0.773213i 0.281352π0.281352\pi
678678 −6.00000 −0.230429
679679 0 0
680680 0 0
681681 14.0000 0.536481
682682 −30.0000 −1.14876
683683 4.00000 0.153056 0.0765279 0.997067i 0.475617π-0.475617\pi
0.0765279 + 0.997067i 0.475617π0.475617\pi
684684 −7.00000 −0.267652
685685 0 0
686686 0 0
687687 4.00000 0.152610
688688 −10.0000 −0.381246
689689 1.00000 0.0380970
690690 0 0
691691 20.0000 0.760836 0.380418 0.924815i 0.375780π-0.375780\pi
0.380418 + 0.924815i 0.375780π0.375780\pi
692692 7.00000 0.266100
693693 0 0
694694 16.0000 0.607352
695695 0 0
696696 0 0
697697 −18.0000 −0.681799
698698 24.0000 0.908413
699699 0 0
700700 0 0
701701 18.0000 0.679851 0.339925 0.940452i 0.389598π-0.389598\pi
0.339925 + 0.940452i 0.389598π0.389598\pi
702702 1.00000 0.0377426
703703 −35.0000 −1.32005
704704 −5.00000 −0.188445
705705 0 0
706706 0 0
707707 0 0
708708 −4.00000 −0.150329
709709 16.0000 0.600893 0.300446 0.953799i 0.402864π-0.402864\pi
0.300446 + 0.953799i 0.402864π0.402864\pi
710710 0 0
711711 −14.0000 −0.525041
712712 −10.0000 −0.374766
713713 −18.0000 −0.674105
714714 0 0
715715 0 0
716716 −11.0000 −0.411089
717717 20.0000 0.746914
718718 −28.0000 −1.04495
719719 2.00000 0.0745874 0.0372937 0.999304i 0.488126π-0.488126\pi
0.0372937 + 0.999304i 0.488126π0.488126\pi
720720 0 0
721721 0 0
722722 30.0000 1.11648
723723 1.00000 0.0371904
724724 2.00000 0.0743294
725725 0 0
726726 14.0000 0.519589
727727 53.0000 1.96566 0.982831 0.184510i 0.0590699π-0.0590699\pi
0.982831 + 0.184510i 0.0590699π0.0590699\pi
728728 0 0
729729 1.00000 0.0370370
730730 0 0
731731 20.0000 0.739727
732732 2.00000 0.0739221
733733 −21.0000 −0.775653 −0.387826 0.921732i 0.626774π-0.626774\pi
−0.387826 + 0.921732i 0.626774π0.626774\pi
734734 −37.0000 −1.36569
735735 0 0
736736 −3.00000 −0.110581
737737 30.0000 1.10506
738738 9.00000 0.331295
739739 47.0000 1.72892 0.864461 0.502699i 0.167660π-0.167660\pi
0.864461 + 0.502699i 0.167660π0.167660\pi
740740 0 0
741741 −7.00000 −0.257151
742742 0 0
743743 31.0000 1.13728 0.568640 0.822587i 0.307470π-0.307470\pi
0.568640 + 0.822587i 0.307470π0.307470\pi
744744 6.00000 0.219971
745745 0 0
746746 −6.00000 −0.219676
747747 −10.0000 −0.365881
748748 10.0000 0.365636
749749 0 0
750750 0 0
751751 4.00000 0.145962 0.0729810 0.997333i 0.476749π-0.476749\pi
0.0729810 + 0.997333i 0.476749π0.476749\pi
752752 −13.0000 −0.474061
753753 3.00000 0.109326
754754 0 0
755755 0 0
756756 0 0
757757 26.0000 0.944986 0.472493 0.881334i 0.343354π-0.343354\pi
0.472493 + 0.881334i 0.343354π0.343354\pi
758758 −1.00000 −0.0363216
759759 15.0000 0.544466
760760 0 0
761761 3.00000 0.108750 0.0543750 0.998521i 0.482683π-0.482683\pi
0.0543750 + 0.998521i 0.482683π0.482683\pi
762762 −9.00000 −0.326036
763763 0 0
764764 −16.0000 −0.578860
765765 0 0
766766 −9.00000 −0.325183
767767 −4.00000 −0.144432
768768 1.00000 0.0360844
769769 −51.0000 −1.83911 −0.919554 0.392965i 0.871449π-0.871449\pi
−0.919554 + 0.392965i 0.871449π0.871449\pi
770770 0 0
771771 −10.0000 −0.360141
772772 18.0000 0.647834
773773 −37.0000 −1.33080 −0.665399 0.746488i 0.731738π-0.731738\pi
−0.665399 + 0.746488i 0.731738π0.731738\pi
774774 −10.0000 −0.359443
775775 0 0
776776 8.00000 0.287183
777777 0 0
778778 6.00000 0.215110
779779 −63.0000 −2.25721
780780 0 0
781781 10.0000 0.357828
782782 6.00000 0.214560
783783 0 0
784784 0 0
785785 0 0
786786 17.0000 0.606370
787787 38.0000 1.35455 0.677277 0.735728i 0.263160π-0.263160\pi
0.677277 + 0.735728i 0.263160π0.263160\pi
788788 27.0000 0.961835
789789 −24.0000 −0.854423
790790 0 0
791791 0 0
792792 −5.00000 −0.177667
793793 2.00000 0.0710221
794794 −2.00000 −0.0709773
795795 0 0
796796 14.0000 0.496217
797797 −30.0000 −1.06265 −0.531327 0.847167i 0.678307π-0.678307\pi
−0.531327 + 0.847167i 0.678307π0.678307\pi
798798 0 0
799799 26.0000 0.919814
800800 0 0
801801 −10.0000 −0.353333
802802 −27.0000 −0.953403
803803 −20.0000 −0.705785
804804 −6.00000 −0.211604
805805 0 0
806806 6.00000 0.211341
807807 −14.0000 −0.492823
808808 −8.00000 −0.281439
809809 −9.00000 −0.316423 −0.158212 0.987405i 0.550573π-0.550573\pi
−0.158212 + 0.987405i 0.550573π0.550573\pi
810810 0 0
811811 −11.0000 −0.386262 −0.193131 0.981173i 0.561864π-0.561864\pi
−0.193131 + 0.981173i 0.561864π0.561864\pi
812812 0 0
813813 −8.00000 −0.280572
814814 −25.0000 −0.876250
815815 0 0
816816 −2.00000 −0.0700140
817817 70.0000 2.44899
818818 −10.0000 −0.349642
819819 0 0
820820 0 0
821821 6.00000 0.209401 0.104701 0.994504i 0.466612π-0.466612\pi
0.104701 + 0.994504i 0.466612π0.466612\pi
822822 4.00000 0.139516
823823 8.00000 0.278862 0.139431 0.990232i 0.455473π-0.455473\pi
0.139431 + 0.990232i 0.455473π0.455473\pi
824824 0 0
825825 0 0
826826 0 0
827827 42.0000 1.46048 0.730242 0.683189i 0.239408π-0.239408\pi
0.730242 + 0.683189i 0.239408π0.239408\pi
828828 −3.00000 −0.104257
829829 −2.00000 −0.0694629 −0.0347314 0.999397i 0.511058π-0.511058\pi
−0.0347314 + 0.999397i 0.511058π0.511058\pi
830830 0 0
831831 −2.00000 −0.0693792
832832 1.00000 0.0346688
833833 0 0
834834 8.00000 0.277017
835835 0 0
836836 35.0000 1.21050
837837 6.00000 0.207390
838838 −3.00000 −0.103633
839839 −2.00000 −0.0690477 −0.0345238 0.999404i 0.510991π-0.510991\pi
−0.0345238 + 0.999404i 0.510991π0.510991\pi
840840 0 0
841841 −29.0000 −1.00000
842842 −20.0000 −0.689246
843843 −11.0000 −0.378860
844844 19.0000 0.654007
845845 0 0
846846 −13.0000 −0.446949
847847 0 0
848848 1.00000 0.0343401
849849 26.0000 0.892318
850850 0 0
851851 −15.0000 −0.514193
852852 −2.00000 −0.0685189
853853 −49.0000 −1.67773 −0.838864 0.544341i 0.816780π-0.816780\pi
−0.838864 + 0.544341i 0.816780π0.816780\pi
854854 0 0
855855 0 0
856856 −12.0000 −0.410152
857857 −56.0000 −1.91292 −0.956462 0.291858i 0.905727π-0.905727\pi
−0.956462 + 0.291858i 0.905727π0.905727\pi
858858 −5.00000 −0.170697
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 0 0
862862 18.0000 0.613082
863863 −15.0000 −0.510606 −0.255303 0.966861i 0.582175π-0.582175\pi
−0.255303 + 0.966861i 0.582175π0.582175\pi
864864 1.00000 0.0340207
865865 0 0
866866 4.00000 0.135926
867867 −13.0000 −0.441503
868868 0 0
869869 70.0000 2.37459
870870 0 0
871871 −6.00000 −0.203302
872872 −18.0000 −0.609557
873873 8.00000 0.270759
874874 21.0000 0.710336
875875 0 0
876876 4.00000 0.135147
877877 27.0000 0.911725 0.455863 0.890050i 0.349331π-0.349331\pi
0.455863 + 0.890050i 0.349331π0.349331\pi
878878 0 0
879879 1.00000 0.0337292
880880 0 0
881881 3.00000 0.101073 0.0505363 0.998722i 0.483907π-0.483907\pi
0.0505363 + 0.998722i 0.483907π0.483907\pi
882882 0 0
883883 52.0000 1.74994 0.874970 0.484178i 0.160881π-0.160881\pi
0.874970 + 0.484178i 0.160881π0.160881\pi
884884 −2.00000 −0.0672673
885885 0 0
886886 6.00000 0.201574
887887 −12.0000 −0.402921 −0.201460 0.979497i 0.564569π-0.564569\pi
−0.201460 + 0.979497i 0.564569π0.564569\pi
888888 5.00000 0.167789
889889 0 0
890890 0 0
891891 −5.00000 −0.167506
892892 16.0000 0.535720
893893 91.0000 3.04520
894894 −6.00000 −0.200670
895895 0 0
896896 0 0
897897 −3.00000 −0.100167
898898 9.00000 0.300334
899899 0 0
900900 0 0
901901 −2.00000 −0.0666297
902902 −45.0000 −1.49834
903903 0 0
904904 −6.00000 −0.199557
905905 0 0
906906 −22.0000 −0.730901
907907 16.0000 0.531271 0.265636 0.964073i 0.414418π-0.414418\pi
0.265636 + 0.964073i 0.414418π0.414418\pi
908908 14.0000 0.464606
909909 −8.00000 −0.265343
910910 0 0
911911 −6.00000 −0.198789 −0.0993944 0.995048i 0.531691π-0.531691\pi
−0.0993944 + 0.995048i 0.531691π0.531691\pi
912912 −7.00000 −0.231793
913913 50.0000 1.65476
914914 38.0000 1.25693
915915 0 0
916916 4.00000 0.132164
917917 0 0
918918 −2.00000 −0.0660098
919919 56.0000 1.84727 0.923635 0.383274i 0.125203π-0.125203\pi
0.923635 + 0.383274i 0.125203π0.125203\pi
920920 0 0
921921 2.00000 0.0659022
922922 12.0000 0.395199
923923 −2.00000 −0.0658308
924924 0 0
925925 0 0
926926 15.0000 0.492931
927927 0 0
928928 0 0
929929 −33.0000 −1.08269 −0.541347 0.840799i 0.682086π-0.682086\pi
−0.541347 + 0.840799i 0.682086π0.682086\pi
930930 0 0
931931 0 0
932932 0 0
933933 26.0000 0.851202
934934 2.00000 0.0654420
935935 0 0
936936 1.00000 0.0326860
937937 −34.0000 −1.11073 −0.555366 0.831606i 0.687422π-0.687422\pi
−0.555366 + 0.831606i 0.687422π0.687422\pi
938938 0 0
939939 −10.0000 −0.326338
940940 0 0
941941 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
942942 13.0000 0.423563
943943 −27.0000 −0.879241
944944 −4.00000 −0.130189
945945 0 0
946946 50.0000 1.62564
947947 −12.0000 −0.389948 −0.194974 0.980808i 0.562462π-0.562462\pi
−0.194974 + 0.980808i 0.562462π0.562462\pi
948948 −14.0000 −0.454699
949949 4.00000 0.129845
950950 0 0
951951 −2.00000 −0.0648544
952952 0 0
953953 24.0000 0.777436 0.388718 0.921357i 0.372918π-0.372918\pi
0.388718 + 0.921357i 0.372918π0.372918\pi
954954 1.00000 0.0323762
955955 0 0
956956 20.0000 0.646846
957957 0 0
958958 −8.00000 −0.258468
959959 0 0
960960 0 0
961961 5.00000 0.161290
962962 5.00000 0.161206
963963 −12.0000 −0.386695
964964 1.00000 0.0322078
965965 0 0
966966 0 0
967967 24.0000 0.771788 0.385894 0.922543i 0.373893π-0.373893\pi
0.385894 + 0.922543i 0.373893π0.373893\pi
968968 14.0000 0.449977
969969 14.0000 0.449745
970970 0 0
971971 −39.0000 −1.25157 −0.625785 0.779996i 0.715221π-0.715221\pi
−0.625785 + 0.779996i 0.715221π0.715221\pi
972972 1.00000 0.0320750
973973 0 0
974974 −24.0000 −0.769010
975975 0 0
976976 2.00000 0.0640184
977977 −42.0000 −1.34370 −0.671850 0.740688i 0.734500π-0.734500\pi
−0.671850 + 0.740688i 0.734500π0.734500\pi
978978 12.0000 0.383718
979979 50.0000 1.59801
980980 0 0
981981 −18.0000 −0.574696
982982 24.0000 0.765871
983983 33.0000 1.05254 0.526268 0.850319i 0.323591π-0.323591\pi
0.526268 + 0.850319i 0.323591π0.323591\pi
984984 9.00000 0.286910
985985 0 0
986986 0 0
987987 0 0
988988 −7.00000 −0.222700
989989 30.0000 0.953945
990990 0 0
991991 −36.0000 −1.14358 −0.571789 0.820401i 0.693750π-0.693750\pi
−0.571789 + 0.820401i 0.693750π0.693750\pi
992992 6.00000 0.190500
993993 −15.0000 −0.476011
994994 0 0
995995 0 0
996996 −10.0000 −0.316862
997997 −10.0000 −0.316703 −0.158352 0.987383i 0.550618π-0.550618\pi
−0.158352 + 0.987383i 0.550618π0.550618\pi
998998 −28.0000 −0.886325
999999 5.00000 0.158193
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 7350.2.a.ch.1.1 1
5.2 odd 4 1470.2.g.a.589.2 2
5.3 odd 4 1470.2.g.a.589.1 2
5.4 even 2 7350.2.a.b.1.1 1
7.3 odd 6 1050.2.i.f.751.1 2
7.5 odd 6 1050.2.i.f.151.1 2
7.6 odd 2 7350.2.a.bn.1.1 1
35.2 odd 12 1470.2.n.i.949.2 4
35.3 even 12 210.2.n.a.79.2 yes 4
35.12 even 12 210.2.n.a.109.2 yes 4
35.13 even 4 1470.2.g.f.589.1 2
35.17 even 12 210.2.n.a.79.1 4
35.18 odd 12 1470.2.n.i.79.2 4
35.19 odd 6 1050.2.i.o.151.1 2
35.23 odd 12 1470.2.n.i.949.1 4
35.24 odd 6 1050.2.i.o.751.1 2
35.27 even 4 1470.2.g.f.589.2 2
35.32 odd 12 1470.2.n.i.79.1 4
35.33 even 12 210.2.n.a.109.1 yes 4
35.34 odd 2 7350.2.a.t.1.1 1
105.17 odd 12 630.2.u.c.289.2 4
105.38 odd 12 630.2.u.c.289.1 4
105.47 odd 12 630.2.u.c.109.1 4
105.68 odd 12 630.2.u.c.109.2 4
140.3 odd 12 1680.2.di.a.289.2 4
140.47 odd 12 1680.2.di.a.529.2 4
140.87 odd 12 1680.2.di.a.289.1 4
140.103 odd 12 1680.2.di.a.529.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
210.2.n.a.79.1 4 35.17 even 12
210.2.n.a.79.2 yes 4 35.3 even 12
210.2.n.a.109.1 yes 4 35.33 even 12
210.2.n.a.109.2 yes 4 35.12 even 12
630.2.u.c.109.1 4 105.47 odd 12
630.2.u.c.109.2 4 105.68 odd 12
630.2.u.c.289.1 4 105.38 odd 12
630.2.u.c.289.2 4 105.17 odd 12
1050.2.i.f.151.1 2 7.5 odd 6
1050.2.i.f.751.1 2 7.3 odd 6
1050.2.i.o.151.1 2 35.19 odd 6
1050.2.i.o.751.1 2 35.24 odd 6
1470.2.g.a.589.1 2 5.3 odd 4
1470.2.g.a.589.2 2 5.2 odd 4
1470.2.g.f.589.1 2 35.13 even 4
1470.2.g.f.589.2 2 35.27 even 4
1470.2.n.i.79.1 4 35.32 odd 12
1470.2.n.i.79.2 4 35.18 odd 12
1470.2.n.i.949.1 4 35.23 odd 12
1470.2.n.i.949.2 4 35.2 odd 12
1680.2.di.a.289.1 4 140.87 odd 12
1680.2.di.a.289.2 4 140.3 odd 12
1680.2.di.a.529.1 4 140.103 odd 12
1680.2.di.a.529.2 4 140.47 odd 12
7350.2.a.b.1.1 1 5.4 even 2
7350.2.a.t.1.1 1 35.34 odd 2
7350.2.a.bn.1.1 1 7.6 odd 2
7350.2.a.ch.1.1 1 1.1 even 1 trivial