Properties

Label 850.2.a.p.1.3
Level 850850
Weight 22
Character 850.1
Self dual yes
Analytic conductor 6.7876.787
Analytic rank 00
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] = [850,2,Mod(1,850)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(850, 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("850.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 850=25217 850 = 2 \cdot 5^{2} \cdot 17
Weight: k k == 2 2
Character orbit: [χ][\chi] == 850.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: 6.787284171816.78728417181
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.568.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x26x2 x^{3} - x^{2} - 6x - 2 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 170)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.3
Root 1.76156-1.76156 of defining polynomial
Character χ\chi == 850.1

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) == q1.00000q2+2.62620q3+1.00000q42.62620q60.864641q71.00000q8+3.89692q9+2.00000q11+2.62620q12+2.62620q13+0.864641q14+1.00000q161.00000q173.89692q180.896916q192.27072q212.00000q22+3.13536q232.62620q242.62620q26+2.35548q270.864641q28+9.49084q29+9.01395q311.00000q32+5.25240q33+1.00000q34+3.89692q3610.1816q37+0.896916q38+6.89692q39+9.52311q41+2.27072q427.25240q43+2.00000q443.13536q46+10.4200q47+2.62620q486.25240q492.62620q51+2.62620q5211.4017q532.35548q54+0.864641q562.35548q579.49084q584.14931q59+3.28467q619.01395q623.36943q63+1.00000q645.25240q661.25240q671.00000q68+8.23407q6912.5371q713.89692q72+2.62620q73+10.1816q740.896916q761.72928q776.89692q787.91087q795.50479q819.52311q82+4.20617q832.27072q84+7.25240q86+24.9248q872.00000q88+4.14931q892.27072q91+3.13536q92+23.6724q9310.4200q942.62620q96+6.14931q97+6.25240q98+7.79383q99+O(q100)q-1.00000 q^{2} +2.62620 q^{3} +1.00000 q^{4} -2.62620 q^{6} -0.864641 q^{7} -1.00000 q^{8} +3.89692 q^{9} +2.00000 q^{11} +2.62620 q^{12} +2.62620 q^{13} +0.864641 q^{14} +1.00000 q^{16} -1.00000 q^{17} -3.89692 q^{18} -0.896916 q^{19} -2.27072 q^{21} -2.00000 q^{22} +3.13536 q^{23} -2.62620 q^{24} -2.62620 q^{26} +2.35548 q^{27} -0.864641 q^{28} +9.49084 q^{29} +9.01395 q^{31} -1.00000 q^{32} +5.25240 q^{33} +1.00000 q^{34} +3.89692 q^{36} -10.1816 q^{37} +0.896916 q^{38} +6.89692 q^{39} +9.52311 q^{41} +2.27072 q^{42} -7.25240 q^{43} +2.00000 q^{44} -3.13536 q^{46} +10.4200 q^{47} +2.62620 q^{48} -6.25240 q^{49} -2.62620 q^{51} +2.62620 q^{52} -11.4017 q^{53} -2.35548 q^{54} +0.864641 q^{56} -2.35548 q^{57} -9.49084 q^{58} -4.14931 q^{59} +3.28467 q^{61} -9.01395 q^{62} -3.36943 q^{63} +1.00000 q^{64} -5.25240 q^{66} -1.25240 q^{67} -1.00000 q^{68} +8.23407 q^{69} -12.5371 q^{71} -3.89692 q^{72} +2.62620 q^{73} +10.1816 q^{74} -0.896916 q^{76} -1.72928 q^{77} -6.89692 q^{78} -7.91087 q^{79} -5.50479 q^{81} -9.52311 q^{82} +4.20617 q^{83} -2.27072 q^{84} +7.25240 q^{86} +24.9248 q^{87} -2.00000 q^{88} +4.14931 q^{89} -2.27072 q^{91} +3.13536 q^{92} +23.6724 q^{93} -10.4200 q^{94} -2.62620 q^{96} +6.14931 q^{97} +6.25240 q^{98} +7.79383 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q3q2q3+3q4+q63q8+8q9+6q11q12q13+3q163q178q18+q1912q216q22+12q23+q24+q267q27++16q99+O(q100) 3 q - 3 q^{2} - q^{3} + 3 q^{4} + q^{6} - 3 q^{8} + 8 q^{9} + 6 q^{11} - q^{12} - q^{13} + 3 q^{16} - 3 q^{17} - 8 q^{18} + q^{19} - 12 q^{21} - 6 q^{22} + 12 q^{23} + q^{24} + q^{26} - 7 q^{27}+ \cdots + 16 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 −1.00000 −0.707107
33 2.62620 1.51624 0.758118 0.652117i 0.226119π-0.226119\pi
0.758118 + 0.652117i 0.226119π0.226119\pi
44 1.00000 0.500000
55 0 0
66 −2.62620 −1.07214
77 −0.864641 −0.326804 −0.163402 0.986560i 0.552247π-0.552247\pi
−0.163402 + 0.986560i 0.552247π0.552247\pi
88 −1.00000 −0.353553
99 3.89692 1.29897
1010 0 0
1111 2.00000 0.603023 0.301511 0.953463i 0.402509π-0.402509\pi
0.301511 + 0.953463i 0.402509π0.402509\pi
1212 2.62620 0.758118
1313 2.62620 0.728376 0.364188 0.931325i 0.381347π-0.381347\pi
0.364188 + 0.931325i 0.381347π0.381347\pi
1414 0.864641 0.231085
1515 0 0
1616 1.00000 0.250000
1717 −1.00000 −0.242536
1818 −3.89692 −0.918512
1919 −0.896916 −0.205767 −0.102883 0.994693i 0.532807π-0.532807\pi
−0.102883 + 0.994693i 0.532807π0.532807\pi
2020 0 0
2121 −2.27072 −0.495511
2222 −2.00000 −0.426401
2323 3.13536 0.653768 0.326884 0.945065i 0.394001π-0.394001\pi
0.326884 + 0.945065i 0.394001π0.394001\pi
2424 −2.62620 −0.536070
2525 0 0
2626 −2.62620 −0.515040
2727 2.35548 0.453312
2828 −0.864641 −0.163402
2929 9.49084 1.76240 0.881202 0.472739i 0.156735π-0.156735\pi
0.881202 + 0.472739i 0.156735π0.156735\pi
3030 0 0
3131 9.01395 1.61895 0.809477 0.587152i 0.199751π-0.199751\pi
0.809477 + 0.587152i 0.199751π0.199751\pi
3232 −1.00000 −0.176777
3333 5.25240 0.914325
3434 1.00000 0.171499
3535 0 0
3636 3.89692 0.649486
3737 −10.1816 −1.67384 −0.836921 0.547323i 0.815647π-0.815647\pi
−0.836921 + 0.547323i 0.815647π0.815647\pi
3838 0.896916 0.145499
3939 6.89692 1.10439
4040 0 0
4141 9.52311 1.48726 0.743630 0.668591i 0.233102π-0.233102\pi
0.743630 + 0.668591i 0.233102π0.233102\pi
4242 2.27072 0.350379
4343 −7.25240 −1.10598 −0.552990 0.833188i 0.686513π-0.686513\pi
−0.552990 + 0.833188i 0.686513π0.686513\pi
4444 2.00000 0.301511
4545 0 0
4646 −3.13536 −0.462283
4747 10.4200 1.51992 0.759959 0.649971i 0.225219π-0.225219\pi
0.759959 + 0.649971i 0.225219π0.225219\pi
4848 2.62620 0.379059
4949 −6.25240 −0.893199
5050 0 0
5151 −2.62620 −0.367741
5252 2.62620 0.364188
5353 −11.4017 −1.56615 −0.783073 0.621930i 0.786349π-0.786349\pi
−0.783073 + 0.621930i 0.786349π0.786349\pi
5454 −2.35548 −0.320540
5555 0 0
5656 0.864641 0.115542
5757 −2.35548 −0.311991
5858 −9.49084 −1.24621
5959 −4.14931 −0.540194 −0.270097 0.962833i 0.587056π-0.587056\pi
−0.270097 + 0.962833i 0.587056π0.587056\pi
6060 0 0
6161 3.28467 0.420559 0.210280 0.977641i 0.432563π-0.432563\pi
0.210280 + 0.977641i 0.432563π0.432563\pi
6262 −9.01395 −1.14477
6363 −3.36943 −0.424509
6464 1.00000 0.125000
6565 0 0
6666 −5.25240 −0.646525
6767 −1.25240 −0.153005 −0.0765023 0.997069i 0.524375π-0.524375\pi
−0.0765023 + 0.997069i 0.524375π0.524375\pi
6868 −1.00000 −0.121268
6969 8.23407 0.991266
7070 0 0
7171 −12.5371 −1.48788 −0.743938 0.668249i 0.767044π-0.767044\pi
−0.743938 + 0.668249i 0.767044π0.767044\pi
7272 −3.89692 −0.459256
7373 2.62620 0.307373 0.153687 0.988120i 0.450885π-0.450885\pi
0.153687 + 0.988120i 0.450885π0.450885\pi
7474 10.1816 1.18359
7575 0 0
7676 −0.896916 −0.102883
7777 −1.72928 −0.197070
7878 −6.89692 −0.780922
7979 −7.91087 −0.890042 −0.445021 0.895520i 0.646804π-0.646804\pi
−0.445021 + 0.895520i 0.646804π0.646804\pi
8080 0 0
8181 −5.50479 −0.611644
8282 −9.52311 −1.05165
8383 4.20617 0.461687 0.230843 0.972991i 0.425851π-0.425851\pi
0.230843 + 0.972991i 0.425851π0.425851\pi
8484 −2.27072 −0.247756
8585 0 0
8686 7.25240 0.782046
8787 24.9248 2.67222
8888 −2.00000 −0.213201
8989 4.14931 0.439826 0.219913 0.975519i 0.429423π-0.429423\pi
0.219913 + 0.975519i 0.429423π0.429423\pi
9090 0 0
9191 −2.27072 −0.238036
9292 3.13536 0.326884
9393 23.6724 2.45472
9494 −10.4200 −1.07474
9595 0 0
9696 −2.62620 −0.268035
9797 6.14931 0.624368 0.312184 0.950022i 0.398939π-0.398939\pi
0.312184 + 0.950022i 0.398939π0.398939\pi
9898 6.25240 0.631587
9999 7.79383 0.783310
100100 0 0
101101 0.206167 0.0205144 0.0102572 0.999947i 0.496735π-0.496735\pi
0.0102572 + 0.999947i 0.496735π0.496735\pi
102102 2.62620 0.260032
103103 −4.77551 −0.470545 −0.235273 0.971929i 0.575598π-0.575598\pi
−0.235273 + 0.971929i 0.575598π0.575598\pi
104104 −2.62620 −0.257520
105105 0 0
106106 11.4017 1.10743
107107 −6.29862 −0.608911 −0.304456 0.952527i 0.598474π-0.598474\pi
−0.304456 + 0.952527i 0.598474π0.598474\pi
108108 2.35548 0.226656
109109 5.55539 0.532110 0.266055 0.963958i 0.414280π-0.414280\pi
0.266055 + 0.963958i 0.414280π0.414280\pi
110110 0 0
111111 −26.7389 −2.53794
112112 −0.864641 −0.0817009
113113 −10.6262 −0.999629 −0.499814 0.866133i 0.666598π-0.666598\pi
−0.499814 + 0.866133i 0.666598π0.666598\pi
114114 2.35548 0.220611
115115 0 0
116116 9.49084 0.881202
117117 10.2341 0.946140
118118 4.14931 0.381975
119119 0.864641 0.0792615
120120 0 0
121121 −7.00000 −0.636364
122122 −3.28467 −0.297380
123123 25.0096 2.25504
124124 9.01395 0.809477
125125 0 0
126126 3.36943 0.300173
127127 14.3555 1.27384 0.636921 0.770929i 0.280208π-0.280208\pi
0.636921 + 0.770929i 0.280208π0.280208\pi
128128 −1.00000 −0.0883883
129129 −19.0462 −1.67693
130130 0 0
131131 17.0462 1.48934 0.744668 0.667435i 0.232608π-0.232608\pi
0.744668 + 0.667435i 0.232608π0.232608\pi
132132 5.25240 0.457162
133133 0.775511 0.0672453
134134 1.25240 0.108191
135135 0 0
136136 1.00000 0.0857493
137137 −14.5048 −1.23923 −0.619614 0.784907i 0.712711π-0.712711\pi
−0.619614 + 0.784907i 0.712711π0.712711\pi
138138 −8.23407 −0.700931
139139 −14.7110 −1.24777 −0.623884 0.781517i 0.714446π-0.714446\pi
−0.623884 + 0.781517i 0.714446π0.714446\pi
140140 0 0
141141 27.3651 2.30455
142142 12.5371 1.05209
143143 5.25240 0.439227
144144 3.89692 0.324743
145145 0 0
146146 −2.62620 −0.217346
147147 −16.4200 −1.35430
148148 −10.1816 −0.836921
149149 10.0000 0.819232 0.409616 0.912258i 0.365663π-0.365663\pi
0.409616 + 0.912258i 0.365663π0.365663\pi
150150 0 0
151151 −5.18785 −0.422181 −0.211090 0.977467i 0.567701π-0.567701\pi
−0.211090 + 0.977467i 0.567701π0.567701\pi
152152 0.896916 0.0727495
153153 −3.89692 −0.315047
154154 1.72928 0.139349
155155 0 0
156156 6.89692 0.552195
157157 −10.2341 −0.816768 −0.408384 0.912810i 0.633908π-0.633908\pi
−0.408384 + 0.912810i 0.633908π0.633908\pi
158158 7.91087 0.629355
159159 −29.9431 −2.37465
160160 0 0
161161 −2.71096 −0.213654
162162 5.50479 0.432497
163163 −6.47689 −0.507309 −0.253654 0.967295i 0.581633π-0.581633\pi
−0.253654 + 0.967295i 0.581633π0.581633\pi
164164 9.52311 0.743630
165165 0 0
166166 −4.20617 −0.326462
167167 3.84632 0.297637 0.148819 0.988865i 0.452453π-0.452453\pi
0.148819 + 0.988865i 0.452453π0.452453\pi
168168 2.27072 0.175190
169169 −6.10308 −0.469468
170170 0 0
171171 −3.49521 −0.267285
172172 −7.25240 −0.552990
173173 23.9109 1.81791 0.908955 0.416895i 0.136882π-0.136882\pi
0.908955 + 0.416895i 0.136882π0.136882\pi
174174 −24.9248 −1.88955
175175 0 0
176176 2.00000 0.150756
177177 −10.8969 −0.819062
178178 −4.14931 −0.311004
179179 −14.7110 −1.09955 −0.549774 0.835313i 0.685286π-0.685286\pi
−0.549774 + 0.835313i 0.685286π0.685286\pi
180180 0 0
181181 −23.4340 −1.74183 −0.870917 0.491430i 0.836474π-0.836474\pi
−0.870917 + 0.491430i 0.836474π0.836474\pi
182182 2.27072 0.168317
183183 8.62620 0.637667
184184 −3.13536 −0.231142
185185 0 0
186186 −23.6724 −1.73575
187187 −2.00000 −0.146254
188188 10.4200 0.759959
189189 −2.03664 −0.148144
190190 0 0
191191 18.5048 1.33896 0.669480 0.742830i 0.266517π-0.266517\pi
0.669480 + 0.742830i 0.266517π0.266517\pi
192192 2.62620 0.189530
193193 −5.45856 −0.392916 −0.196458 0.980512i 0.562944π-0.562944\pi
−0.196458 + 0.980512i 0.562944π0.562944\pi
194194 −6.14931 −0.441495
195195 0 0
196196 −6.25240 −0.446600
197197 13.9388 0.993097 0.496548 0.868009i 0.334601π-0.334601\pi
0.496548 + 0.868009i 0.334601π0.334601\pi
198198 −7.79383 −0.553884
199199 −11.2847 −0.799949 −0.399975 0.916526i 0.630981π-0.630981\pi
−0.399975 + 0.916526i 0.630981π0.630981\pi
200200 0 0
201201 −3.28904 −0.231991
202202 −0.206167 −0.0145059
203203 −8.20617 −0.575960
204204 −2.62620 −0.183871
205205 0 0
206206 4.77551 0.332726
207207 12.2182 0.849226
208208 2.62620 0.182094
209209 −1.79383 −0.124082
210210 0 0
211211 −14.8401 −1.02163 −0.510816 0.859690i 0.670657π-0.670657\pi
−0.510816 + 0.859690i 0.670657π0.670657\pi
212212 −11.4017 −0.783073
213213 −32.9248 −2.25597
214214 6.29862 0.430565
215215 0 0
216216 −2.35548 −0.160270
217217 −7.79383 −0.529080
218218 −5.55539 −0.376258
219219 6.89692 0.466050
220220 0 0
221221 −2.62620 −0.176657
222222 26.7389 1.79460
223223 3.30925 0.221604 0.110802 0.993843i 0.464658π-0.464658\pi
0.110802 + 0.993843i 0.464658π0.464658\pi
224224 0.864641 0.0577712
225225 0 0
226226 10.6262 0.706844
227227 −24.7187 −1.64063 −0.820317 0.571909i 0.806203π-0.806203\pi
−0.820317 + 0.571909i 0.806203π0.806203\pi
228228 −2.35548 −0.155995
229229 4.27072 0.282217 0.141109 0.989994i 0.454933π-0.454933\pi
0.141109 + 0.989994i 0.454933π0.454933\pi
230230 0 0
231231 −4.54144 −0.298805
232232 −9.49084 −0.623104
233233 0.832365 0.0545301 0.0272650 0.999628i 0.491320π-0.491320\pi
0.0272650 + 0.999628i 0.491320π0.491320\pi
234234 −10.2341 −0.669022
235235 0 0
236236 −4.14931 −0.270097
237237 −20.7755 −1.34951
238238 −0.864641 −0.0560463
239239 −4.71096 −0.304727 −0.152363 0.988325i 0.548688π-0.548688\pi
−0.152363 + 0.988325i 0.548688π0.548688\pi
240240 0 0
241241 −23.4865 −1.51290 −0.756448 0.654054i 0.773067π-0.773067\pi
−0.756448 + 0.654054i 0.773067π0.773067\pi
242242 7.00000 0.449977
243243 −21.5231 −1.38071
244244 3.28467 0.210280
245245 0 0
246246 −25.0096 −1.59455
247247 −2.35548 −0.149876
248248 −9.01395 −0.572387
249249 11.0462 0.700026
250250 0 0
251251 −6.29862 −0.397566 −0.198783 0.980044i 0.563699π-0.563699\pi
−0.198783 + 0.980044i 0.563699π0.563699\pi
252252 −3.36943 −0.212254
253253 6.27072 0.394237
254254 −14.3555 −0.900743
255255 0 0
256256 1.00000 0.0625000
257257 −1.49521 −0.0932685 −0.0466342 0.998912i 0.514850π-0.514850\pi
−0.0466342 + 0.998912i 0.514850π0.514850\pi
258258 19.0462 1.18577
259259 8.80342 0.547018
260260 0 0
261261 36.9850 2.28931
262262 −17.0462 −1.05312
263263 −9.94315 −0.613121 −0.306560 0.951851i 0.599178π-0.599178\pi
−0.306560 + 0.951851i 0.599178π0.599178\pi
264264 −5.25240 −0.323263
265265 0 0
266266 −0.775511 −0.0475496
267267 10.8969 0.666880
268268 −1.25240 −0.0765023
269269 1.96772 0.119974 0.0599871 0.998199i 0.480894π-0.480894\pi
0.0599871 + 0.998199i 0.480894π0.480894\pi
270270 0 0
271271 8.84006 0.536995 0.268498 0.963280i 0.413473π-0.413473\pi
0.268498 + 0.963280i 0.413473π0.413473\pi
272272 −1.00000 −0.0606339
273273 −5.96336 −0.360919
274274 14.5048 0.876267
275275 0 0
276276 8.23407 0.495633
277277 −19.8463 −1.19245 −0.596225 0.802817i 0.703333π-0.703333\pi
−0.596225 + 0.802817i 0.703333π0.703333\pi
278278 14.7110 0.882305
279279 35.1266 2.10298
280280 0 0
281281 −11.9065 −0.710282 −0.355141 0.934813i 0.615567π-0.615567\pi
−0.355141 + 0.934813i 0.615567π0.615567\pi
282282 −27.3651 −1.62957
283283 13.7370 0.816579 0.408289 0.912853i 0.366125π-0.366125\pi
0.408289 + 0.912853i 0.366125π0.366125\pi
284284 −12.5371 −0.743938
285285 0 0
286286 −5.25240 −0.310581
287287 −8.23407 −0.486042
288288 −3.89692 −0.229628
289289 1.00000 0.0588235
290290 0 0
291291 16.1493 0.946689
292292 2.62620 0.153687
293293 −12.1772 −0.711401 −0.355700 0.934600i 0.615758π-0.615758\pi
−0.355700 + 0.934600i 0.615758π0.615758\pi
294294 16.4200 0.957636
295295 0 0
296296 10.1816 0.591793
297297 4.71096 0.273358
298298 −10.0000 −0.579284
299299 8.23407 0.476189
300300 0 0
301301 6.27072 0.361438
302302 5.18785 0.298527
303303 0.541436 0.0311047
304304 −0.896916 −0.0514417
305305 0 0
306306 3.89692 0.222772
307307 23.7938 1.35799 0.678993 0.734145i 0.262417π-0.262417\pi
0.678993 + 0.734145i 0.262417π0.262417\pi
308308 −1.72928 −0.0985350
309309 −12.5414 −0.713457
310310 0 0
311311 32.9205 1.86675 0.933374 0.358906i 0.116850π-0.116850\pi
0.933374 + 0.358906i 0.116850π0.116850\pi
312312 −6.89692 −0.390461
313313 −29.0462 −1.64179 −0.820895 0.571079i 0.806525π-0.806525\pi
−0.820895 + 0.571079i 0.806525π0.806525\pi
314314 10.2341 0.577542
315315 0 0
316316 −7.91087 −0.445021
317317 20.6864 1.16186 0.580931 0.813953i 0.302688π-0.302688\pi
0.580931 + 0.813953i 0.302688π0.302688\pi
318318 29.9431 1.67913
319319 18.9817 1.06277
320320 0 0
321321 −16.5414 −0.923253
322322 2.71096 0.151076
323323 0.896916 0.0499058
324324 −5.50479 −0.305822
325325 0 0
326326 6.47689 0.358722
327327 14.5896 0.806804
328328 −9.52311 −0.525826
329329 −9.00958 −0.496714
330330 0 0
331331 4.02021 0.220971 0.110485 0.993878i 0.464759π-0.464759\pi
0.110485 + 0.993878i 0.464759π0.464759\pi
332332 4.20617 0.230843
333333 −39.6768 −2.17428
334334 −3.84632 −0.210461
335335 0 0
336336 −2.27072 −0.123878
337337 2.21386 0.120597 0.0602984 0.998180i 0.480795π-0.480795\pi
0.0602984 + 0.998180i 0.480795π0.480795\pi
338338 6.10308 0.331964
339339 −27.9065 −1.51567
340340 0 0
341341 18.0279 0.976266
342342 3.49521 0.188999
343343 11.4586 0.618704
344344 7.25240 0.391023
345345 0 0
346346 −23.9109 −1.28546
347347 −1.37380 −0.0737496 −0.0368748 0.999320i 0.511740π-0.511740\pi
−0.0368748 + 0.999320i 0.511740π0.511740\pi
348348 24.9248 1.33611
349349 −20.8680 −1.11704 −0.558518 0.829492i 0.688630π-0.688630\pi
−0.558518 + 0.829492i 0.688630π0.688630\pi
350350 0 0
351351 6.18596 0.330182
352352 −2.00000 −0.106600
353353 −13.7572 −0.732221 −0.366111 0.930571i 0.619311π-0.619311\pi
−0.366111 + 0.930571i 0.619311π0.619311\pi
354354 10.8969 0.579165
355355 0 0
356356 4.14931 0.219913
357357 2.27072 0.120179
358358 14.7110 0.777498
359359 9.31695 0.491730 0.245865 0.969304i 0.420928π-0.420928\pi
0.245865 + 0.969304i 0.420928π0.420928\pi
360360 0 0
361361 −18.1955 −0.957660
362362 23.4340 1.23166
363363 −18.3834 −0.964878
364364 −2.27072 −0.119018
365365 0 0
366366 −8.62620 −0.450899
367367 12.3878 0.646636 0.323318 0.946290i 0.395202π-0.395202\pi
0.323318 + 0.946290i 0.395202π0.395202\pi
368368 3.13536 0.163442
369369 37.1108 1.93191
370370 0 0
371371 9.85838 0.511822
372372 23.6724 1.22736
373373 −23.3169 −1.20731 −0.603653 0.797247i 0.706289π-0.706289\pi
−0.603653 + 0.797247i 0.706289π0.706289\pi
374374 2.00000 0.103418
375375 0 0
376376 −10.4200 −0.537372
377377 24.9248 1.28369
378378 2.03664 0.104754
379379 28.9817 1.48869 0.744344 0.667796i 0.232762π-0.232762\pi
0.744344 + 0.667796i 0.232762π0.232762\pi
380380 0 0
381381 37.7003 1.93145
382382 −18.5048 −0.946788
383383 14.9527 0.764049 0.382024 0.924152i 0.375227π-0.375227\pi
0.382024 + 0.924152i 0.375227π0.375227\pi
384384 −2.62620 −0.134018
385385 0 0
386386 5.45856 0.277834
387387 −28.2620 −1.43664
388388 6.14931 0.312184
389389 −19.3169 −0.979408 −0.489704 0.871889i 0.662895π-0.662895\pi
−0.489704 + 0.871889i 0.662895π0.662895\pi
390390 0 0
391391 −3.13536 −0.158562
392392 6.25240 0.315794
393393 44.7668 2.25818
394394 −13.9388 −0.702225
395395 0 0
396396 7.79383 0.391655
397397 9.57560 0.480586 0.240293 0.970700i 0.422757π-0.422757\pi
0.240293 + 0.970700i 0.422757π0.422757\pi
398398 11.2847 0.565649
399399 2.03664 0.101960
400400 0 0
401401 11.3169 0.565141 0.282571 0.959246i 0.408813π-0.408813\pi
0.282571 + 0.959246i 0.408813π0.408813\pi
402402 3.28904 0.164042
403403 23.6724 1.17921
404404 0.206167 0.0102572
405405 0 0
406406 8.20617 0.407265
407407 −20.3632 −1.00937
408408 2.62620 0.130016
409409 −9.10308 −0.450119 −0.225059 0.974345i 0.572258π-0.572258\pi
−0.225059 + 0.974345i 0.572258π0.572258\pi
410410 0 0
411411 −38.0925 −1.87896
412412 −4.77551 −0.235273
413413 3.58767 0.176537
414414 −12.2182 −0.600493
415415 0 0
416416 −2.62620 −0.128760
417417 −38.6339 −1.89191
418418 1.79383 0.0877392
419419 −4.02791 −0.196776 −0.0983881 0.995148i 0.531369π-0.531369\pi
−0.0983881 + 0.995148i 0.531369π0.531369\pi
420420 0 0
421421 15.2524 0.743356 0.371678 0.928362i 0.378782π-0.378782\pi
0.371678 + 0.928362i 0.378782π0.378782\pi
422422 14.8401 0.722403
423423 40.6060 1.97433
424424 11.4017 0.553716
425425 0 0
426426 32.9248 1.59521
427427 −2.84006 −0.137440
428428 −6.29862 −0.304456
429429 13.7938 0.665973
430430 0 0
431431 −4.45231 −0.214460 −0.107230 0.994234i 0.534198π-0.534198\pi
−0.107230 + 0.994234i 0.534198π0.534198\pi
432432 2.35548 0.113328
433433 10.7110 0.514736 0.257368 0.966313i 0.417145π-0.417145\pi
0.257368 + 0.966313i 0.417145π0.417145\pi
434434 7.79383 0.374116
435435 0 0
436436 5.55539 0.266055
437437 −2.81215 −0.134524
438438 −6.89692 −0.329547
439439 5.09871 0.243348 0.121674 0.992570i 0.461174π-0.461174\pi
0.121674 + 0.992570i 0.461174π0.461174\pi
440440 0 0
441441 −24.3651 −1.16024
442442 2.62620 0.124916
443443 10.8034 0.513286 0.256643 0.966506i 0.417384π-0.417384\pi
0.256643 + 0.966506i 0.417384π0.417384\pi
444444 −26.7389 −1.26897
445445 0 0
446446 −3.30925 −0.156698
447447 26.2620 1.24215
448448 −0.864641 −0.0408504
449449 −5.82174 −0.274745 −0.137372 0.990519i 0.543866π-0.543866\pi
−0.137372 + 0.990519i 0.543866π0.543866\pi
450450 0 0
451451 19.0462 0.896852
452452 −10.6262 −0.499814
453453 −13.6243 −0.640126
454454 24.7187 1.16010
455455 0 0
456456 2.35548 0.110305
457457 13.7014 0.640923 0.320462 0.947261i 0.396162π-0.396162\pi
0.320462 + 0.947261i 0.396162π0.396162\pi
458458 −4.27072 −0.199558
459459 −2.35548 −0.109944
460460 0 0
461461 −27.0741 −1.26097 −0.630484 0.776202i 0.717144π-0.717144\pi
−0.630484 + 0.776202i 0.717144π0.717144\pi
462462 4.54144 0.211287
463463 37.3372 1.73520 0.867602 0.497258i 0.165660π-0.165660\pi
0.867602 + 0.497258i 0.165660π0.165660\pi
464464 9.49084 0.440601
465465 0 0
466466 −0.832365 −0.0385586
467467 35.3449 1.63556 0.817782 0.575528i 0.195203π-0.195203\pi
0.817782 + 0.575528i 0.195203π0.195203\pi
468468 10.2341 0.473070
469469 1.08287 0.0500024
470470 0 0
471471 −26.8767 −1.23841
472472 4.14931 0.190988
473473 −14.5048 −0.666931
474474 20.7755 0.954251
475475 0 0
476476 0.864641 0.0396308
477477 −44.4315 −2.03438
478478 4.71096 0.215474
479479 31.0419 1.41834 0.709169 0.705038i 0.249070π-0.249070\pi
0.709169 + 0.705038i 0.249070π0.249070\pi
480480 0 0
481481 −26.7389 −1.21919
482482 23.4865 1.06978
483483 −7.11952 −0.323949
484484 −7.00000 −0.318182
485485 0 0
486486 21.5231 0.976308
487487 13.1633 0.596485 0.298242 0.954490i 0.403600π-0.403600\pi
0.298242 + 0.954490i 0.403600π0.403600\pi
488488 −3.28467 −0.148690
489489 −17.0096 −0.769200
490490 0 0
491491 24.3555 1.09915 0.549574 0.835445i 0.314790π-0.314790\pi
0.549574 + 0.835445i 0.314790π0.314790\pi
492492 25.0096 1.12752
493493 −9.49084 −0.427446
494494 2.35548 0.105978
495495 0 0
496496 9.01395 0.404738
497497 10.8401 0.486243
498498 −11.0462 −0.494993
499499 36.2620 1.62331 0.811655 0.584138i 0.198567π-0.198567\pi
0.811655 + 0.584138i 0.198567π0.198567\pi
500500 0 0
501501 10.1012 0.451288
502502 6.29862 0.281121
503503 −42.3511 −1.88834 −0.944171 0.329455i 0.893135π-0.893135\pi
−0.944171 + 0.329455i 0.893135π0.893135\pi
504504 3.36943 0.150086
505505 0 0
506506 −6.27072 −0.278767
507507 −16.0279 −0.711824
508508 14.3555 0.636921
509509 −1.70138 −0.0754121 −0.0377061 0.999289i 0.512005π-0.512005\pi
−0.0377061 + 0.999289i 0.512005π0.512005\pi
510510 0 0
511511 −2.27072 −0.100451
512512 −1.00000 −0.0441942
513513 −2.11267 −0.0932766
514514 1.49521 0.0659508
515515 0 0
516516 −19.0462 −0.838463
517517 20.8401 0.916545
518518 −8.80342 −0.386800
519519 62.7947 2.75638
520520 0 0
521521 3.01832 0.132235 0.0661175 0.997812i 0.478939π-0.478939\pi
0.0661175 + 0.997812i 0.478939π0.478939\pi
522522 −36.9850 −1.61879
523523 −5.79383 −0.253347 −0.126673 0.991944i 0.540430π-0.540430\pi
−0.126673 + 0.991944i 0.540430π0.540430\pi
524524 17.0462 0.744668
525525 0 0
526526 9.94315 0.433542
527527 −9.01395 −0.392654
528528 5.25240 0.228581
529529 −13.1695 −0.572588
530530 0 0
531531 −16.1695 −0.701698
532532 0.775511 0.0336226
533533 25.0096 1.08329
534534 −10.8969 −0.471556
535535 0 0
536536 1.25240 0.0540953
537537 −38.6339 −1.66718
538538 −1.96772 −0.0848346
539539 −12.5048 −0.538620
540540 0 0
541541 0.258654 0.0111204 0.00556019 0.999985i 0.498230π-0.498230\pi
0.00556019 + 0.999985i 0.498230π0.498230\pi
542542 −8.84006 −0.379713
543543 −61.5423 −2.64103
544544 1.00000 0.0428746
545545 0 0
546546 5.96336 0.255208
547547 32.4113 1.38581 0.692903 0.721030i 0.256331π-0.256331\pi
0.692903 + 0.721030i 0.256331π0.256331\pi
548548 −14.5048 −0.619614
549549 12.8001 0.546295
550550 0 0
551551 −8.51249 −0.362644
552552 −8.23407 −0.350465
553553 6.84006 0.290869
554554 19.8463 0.843189
555555 0 0
556556 −14.7110 −0.623884
557557 −22.9248 −0.971356 −0.485678 0.874138i 0.661427π-0.661427\pi
−0.485678 + 0.874138i 0.661427π0.661427\pi
558558 −35.1266 −1.48703
559559 −19.0462 −0.805570
560560 0 0
561561 −5.25240 −0.221756
562562 11.9065 0.502245
563563 17.8863 0.753817 0.376909 0.926250i 0.376987π-0.376987\pi
0.376909 + 0.926250i 0.376987π0.376987\pi
564564 27.3651 1.15228
565565 0 0
566566 −13.7370 −0.577408
567567 4.75967 0.199887
568568 12.5371 0.526044
569569 12.3555 0.517969 0.258984 0.965882i 0.416612π-0.416612\pi
0.258984 + 0.965882i 0.416612π0.416612\pi
570570 0 0
571571 −27.3169 −1.14318 −0.571589 0.820540i 0.693673π-0.693673\pi
−0.571589 + 0.820540i 0.693673π0.693673\pi
572572 5.25240 0.219614
573573 48.5972 2.03018
574574 8.23407 0.343684
575575 0 0
576576 3.89692 0.162372
577577 10.6339 0.442695 0.221347 0.975195i 0.428955π-0.428955\pi
0.221347 + 0.975195i 0.428955π0.428955\pi
578578 −1.00000 −0.0415945
579579 −14.3353 −0.595753
580580 0 0
581581 −3.63682 −0.150881
582582 −16.1493 −0.669411
583583 −22.8034 −0.944421
584584 −2.62620 −0.108673
585585 0 0
586586 12.1772 0.503036
587587 −22.3757 −0.923544 −0.461772 0.886999i 0.652786π-0.652786\pi
−0.461772 + 0.886999i 0.652786π0.652786\pi
588588 −16.4200 −0.677151
589589 −8.08476 −0.333127
590590 0 0
591591 36.6060 1.50577
592592 −10.1816 −0.418461
593593 12.1695 0.499742 0.249871 0.968279i 0.419612π-0.419612\pi
0.249871 + 0.968279i 0.419612π0.419612\pi
594594 −4.71096 −0.193293
595595 0 0
596596 10.0000 0.409616
597597 −29.6358 −1.21291
598598 −8.23407 −0.336716
599599 −25.1387 −1.02714 −0.513569 0.858048i 0.671677π-0.671677\pi
−0.513569 + 0.858048i 0.671677π0.671677\pi
600600 0 0
601601 −4.50479 −0.183754 −0.0918772 0.995770i 0.529287π-0.529287\pi
−0.0918772 + 0.995770i 0.529287π0.529287\pi
602602 −6.27072 −0.255575
603603 −4.88048 −0.198749
604604 −5.18785 −0.211090
605605 0 0
606606 −0.541436 −0.0219944
607607 7.00626 0.284375 0.142188 0.989840i 0.454586π-0.454586\pi
0.142188 + 0.989840i 0.454586π0.454586\pi
608608 0.896916 0.0363748
609609 −21.5510 −0.873291
610610 0 0
611611 27.3651 1.10707
612612 −3.89692 −0.157524
613613 −7.46626 −0.301559 −0.150780 0.988567i 0.548178π-0.548178\pi
−0.150780 + 0.988567i 0.548178π0.548178\pi
614614 −23.7938 −0.960241
615615 0 0
616616 1.72928 0.0696747
617617 −36.1772 −1.45644 −0.728220 0.685343i 0.759652π-0.759652\pi
−0.728220 + 0.685343i 0.759652π0.759652\pi
618618 12.5414 0.504491
619619 −4.27072 −0.171655 −0.0858273 0.996310i 0.527353π-0.527353\pi
−0.0858273 + 0.996310i 0.527353π0.527353\pi
620620 0 0
621621 7.38528 0.296361
622622 −32.9205 −1.31999
623623 −3.58767 −0.143737
624624 6.89692 0.276098
625625 0 0
626626 29.0462 1.16092
627627 −4.71096 −0.188138
628628 −10.2341 −0.408384
629629 10.1816 0.405966
630630 0 0
631631 26.0279 1.03615 0.518077 0.855334i 0.326648π-0.326648\pi
0.518077 + 0.855334i 0.326648π0.326648\pi
632632 7.91087 0.314677
633633 −38.9729 −1.54904
634634 −20.6864 −0.821561
635635 0 0
636636 −29.9431 −1.18732
637637 −16.4200 −0.650585
638638 −18.9817 −0.751492
639639 −48.8559 −1.93271
640640 0 0
641641 12.6831 0.500950 0.250475 0.968123i 0.419413π-0.419413\pi
0.250475 + 0.968123i 0.419413π0.419413\pi
642642 16.5414 0.652838
643643 −25.1108 −0.990272 −0.495136 0.868815i 0.664882π-0.664882\pi
−0.495136 + 0.868815i 0.664882π0.664882\pi
644644 −2.71096 −0.106827
645645 0 0
646646 −0.896916 −0.0352887
647647 −38.0635 −1.49643 −0.748215 0.663456i 0.769089π-0.769089\pi
−0.748215 + 0.663456i 0.769089π0.769089\pi
648648 5.50479 0.216249
649649 −8.29862 −0.325750
650650 0 0
651651 −20.4681 −0.802210
652652 −6.47689 −0.253654
653653 −45.2682 −1.77148 −0.885742 0.464179i 0.846350π-0.846350\pi
−0.885742 + 0.464179i 0.846350π0.846350\pi
654654 −14.5896 −0.570497
655655 0 0
656656 9.52311 0.371815
657657 10.2341 0.399269
658658 9.00958 0.351230
659659 40.7466 1.58726 0.793630 0.608400i 0.208188π-0.208188\pi
0.793630 + 0.608400i 0.208188π0.208188\pi
660660 0 0
661661 2.53270 0.0985106 0.0492553 0.998786i 0.484315π-0.484315\pi
0.0492553 + 0.998786i 0.484315π0.484315\pi
662662 −4.02021 −0.156250
663663 −6.89692 −0.267854
664664 −4.20617 −0.163231
665665 0 0
666666 39.6768 1.53744
667667 29.7572 1.15220
668668 3.84632 0.148819
669669 8.69075 0.336004
670670 0 0
671671 6.56934 0.253607
672672 2.27072 0.0875949
673673 37.0818 1.42940 0.714700 0.699431i 0.246563π-0.246563\pi
0.714700 + 0.699431i 0.246563π0.246563\pi
674674 −2.21386 −0.0852748
675675 0 0
676676 −6.10308 −0.234734
677677 44.3790 1.70562 0.852812 0.522218i 0.174895π-0.174895\pi
0.852812 + 0.522218i 0.174895π0.174895\pi
678678 27.9065 1.07174
679679 −5.31695 −0.204046
680680 0 0
681681 −64.9161 −2.48759
682682 −18.0279 −0.690324
683683 −7.46626 −0.285688 −0.142844 0.989745i 0.545625π-0.545625\pi
−0.142844 + 0.989745i 0.545625π0.545625\pi
684684 −3.49521 −0.133643
685685 0 0
686686 −11.4586 −0.437490
687687 11.2158 0.427908
688688 −7.25240 −0.276495
689689 −29.9431 −1.14074
690690 0 0
691691 26.8959 1.02317 0.511584 0.859233i 0.329059π-0.329059\pi
0.511584 + 0.859233i 0.329059π0.329059\pi
692692 23.9109 0.908955
693693 −6.73887 −0.255988
694694 1.37380 0.0521488
695695 0 0
696696 −24.9248 −0.944773
697697 −9.52311 −0.360714
698698 20.8680 0.789864
699699 2.18596 0.0826805
700700 0 0
701701 23.7938 0.898681 0.449340 0.893361i 0.351659π-0.351659\pi
0.449340 + 0.893361i 0.351659π0.351659\pi
702702 −6.18596 −0.233474
703703 9.13203 0.344421
704704 2.00000 0.0753778
705705 0 0
706706 13.7572 0.517759
707707 −0.178261 −0.00670419
708708 −10.8969 −0.409531
709709 −17.0140 −0.638972 −0.319486 0.947591i 0.603510π-0.603510\pi
−0.319486 + 0.947591i 0.603510π0.603510\pi
710710 0 0
711711 −30.8280 −1.15614
712712 −4.14931 −0.155502
713713 28.2620 1.05842
714714 −2.27072 −0.0849795
715715 0 0
716716 −14.7110 −0.549774
717717 −12.3719 −0.462038
718718 −9.31695 −0.347705
719719 −23.8665 −0.890071 −0.445036 0.895513i 0.646809π-0.646809\pi
−0.445036 + 0.895513i 0.646809π0.646809\pi
720720 0 0
721721 4.12910 0.153776
722722 18.1955 0.677168
723723 −61.6801 −2.29391
724724 −23.4340 −0.870917
725725 0 0
726726 18.3834 0.682271
727727 28.3834 1.05268 0.526341 0.850274i 0.323564π-0.323564\pi
0.526341 + 0.850274i 0.323564π0.323564\pi
728728 2.27072 0.0841584
729729 −40.0096 −1.48184
730730 0 0
731731 7.25240 0.268240
732732 8.62620 0.318833
733733 28.2216 1.04239 0.521194 0.853439i 0.325487π-0.325487\pi
0.521194 + 0.853439i 0.325487π0.325487\pi
734734 −12.3878 −0.457240
735735 0 0
736736 −3.13536 −0.115571
737737 −2.50479 −0.0922652
738738 −37.1108 −1.36607
739739 0.226378 0.00832746 0.00416373 0.999991i 0.498675π-0.498675\pi
0.00416373 + 0.999991i 0.498675π0.498675\pi
740740 0 0
741741 −6.18596 −0.227247
742742 −9.85838 −0.361913
743743 47.6035 1.74640 0.873202 0.487359i 0.162040π-0.162040\pi
0.873202 + 0.487359i 0.162040π0.162040\pi
744744 −23.6724 −0.867873
745745 0 0
746746 23.3169 0.853694
747747 16.3911 0.599718
748748 −2.00000 −0.0731272
749749 5.44605 0.198994
750750 0 0
751751 0.124733 0.00455157 0.00227578 0.999997i 0.499276π-0.499276\pi
0.00227578 + 0.999997i 0.499276π0.499276\pi
752752 10.4200 0.379979
753753 −16.5414 −0.602803
754754 −24.9248 −0.907709
755755 0 0
756756 −2.03664 −0.0740720
757757 33.7774 1.22766 0.613830 0.789438i 0.289628π-0.289628\pi
0.613830 + 0.789438i 0.289628π0.289628\pi
758758 −28.9817 −1.05266
759759 16.4681 0.597756
760760 0 0
761761 11.4219 0.414044 0.207022 0.978336i 0.433623π-0.433623\pi
0.207022 + 0.978336i 0.433623π0.433623\pi
762762 −37.7003 −1.36574
763763 −4.80342 −0.173895
764764 18.5048 0.669480
765765 0 0
766766 −14.9527 −0.540264
767767 −10.8969 −0.393465
768768 2.62620 0.0947648
769769 12.1127 0.436794 0.218397 0.975860i 0.429917π-0.429917\pi
0.218397 + 0.975860i 0.429917π0.429917\pi
770770 0 0
771771 −3.92671 −0.141417
772772 −5.45856 −0.196458
773773 37.4586 1.34729 0.673645 0.739055i 0.264728π-0.264728\pi
0.673645 + 0.739055i 0.264728π0.264728\pi
774774 28.2620 1.01586
775775 0 0
776776 −6.14931 −0.220747
777777 23.1195 0.829408
778778 19.3169 0.692546
779779 −8.54144 −0.306029
780780 0 0
781781 −25.0741 −0.897223
782782 3.13536 0.112120
783783 22.3555 0.798920
784784 −6.25240 −0.223300
785785 0 0
786786 −44.7668 −1.59678
787787 −25.0664 −0.893522 −0.446761 0.894653i 0.647423π-0.647423\pi
−0.446761 + 0.894653i 0.647423π0.647423\pi
788788 13.9388 0.496548
789789 −26.1127 −0.929636
790790 0 0
791791 9.18785 0.326682
792792 −7.79383 −0.276942
793793 8.62620 0.306325
794794 −9.57560 −0.339825
795795 0 0
796796 −11.2847 −0.399975
797797 −19.5510 −0.692533 −0.346266 0.938136i 0.612551π-0.612551\pi
−0.346266 + 0.938136i 0.612551π0.612551\pi
798798 −2.03664 −0.0720964
799799 −10.4200 −0.368634
800800 0 0
801801 16.1695 0.571322
802802 −11.3169 −0.399615
803803 5.25240 0.185353
804804 −3.28904 −0.115996
805805 0 0
806806 −23.6724 −0.833826
807807 5.16763 0.181909
808808 −0.206167 −0.00725294
809809 20.1974 0.710104 0.355052 0.934847i 0.384463π-0.384463\pi
0.355052 + 0.934847i 0.384463π0.384463\pi
810810 0 0
811811 28.1570 0.988726 0.494363 0.869255i 0.335401π-0.335401\pi
0.494363 + 0.869255i 0.335401π0.335401\pi
812812 −8.20617 −0.287980
813813 23.2158 0.814212
814814 20.3632 0.713729
815815 0 0
816816 −2.62620 −0.0919353
817817 6.50479 0.227574
818818 9.10308 0.318282
819819 −8.84880 −0.309202
820820 0 0
821821 −51.2759 −1.78954 −0.894771 0.446525i 0.852661π-0.852661\pi
−0.894771 + 0.446525i 0.852661π0.852661\pi
822822 38.0925 1.32863
823823 52.9850 1.84694 0.923471 0.383669i 0.125340π-0.125340\pi
0.923471 + 0.383669i 0.125340π0.125340\pi
824824 4.77551 0.166363
825825 0 0
826826 −3.58767 −0.124831
827827 39.7205 1.38122 0.690609 0.723228i 0.257342π-0.257342\pi
0.690609 + 0.723228i 0.257342π0.257342\pi
828828 12.2182 0.424613
829829 23.0096 0.799156 0.399578 0.916699i 0.369157π-0.369157\pi
0.399578 + 0.916699i 0.369157π0.369157\pi
830830 0 0
831831 −52.1204 −1.80804
832832 2.62620 0.0910470
833833 6.25240 0.216633
834834 38.6339 1.33778
835835 0 0
836836 −1.79383 −0.0620410
837837 21.2322 0.733892
838838 4.02791 0.139142
839839 2.39545 0.0827002 0.0413501 0.999145i 0.486834π-0.486834\pi
0.0413501 + 0.999145i 0.486834π0.486834\pi
840840 0 0
841841 61.0760 2.10607
842842 −15.2524 −0.525632
843843 −31.2688 −1.07696
844844 −14.8401 −0.510816
845845 0 0
846846 −40.6060 −1.39606
847847 6.05249 0.207966
848848 −11.4017 −0.391536
849849 36.0760 1.23813
850850 0 0
851851 −31.9229 −1.09430
852852 −32.9248 −1.12799
853853 −2.24614 −0.0769063 −0.0384532 0.999260i 0.512243π-0.512243\pi
−0.0384532 + 0.999260i 0.512243π0.512243\pi
854854 2.84006 0.0971849
855855 0 0
856856 6.29862 0.215283
857857 −18.3188 −0.625760 −0.312880 0.949793i 0.601294π-0.601294\pi
−0.312880 + 0.949793i 0.601294π0.601294\pi
858858 −13.7938 −0.470914
859859 −42.1127 −1.43687 −0.718433 0.695596i 0.755140π-0.755140\pi
−0.718433 + 0.695596i 0.755140π0.755140\pi
860860 0 0
861861 −21.6243 −0.736954
862862 4.45231 0.151646
863863 44.8313 1.52608 0.763038 0.646354i 0.223707π-0.223707\pi
0.763038 + 0.646354i 0.223707π0.223707\pi
864864 −2.35548 −0.0801351
865865 0 0
866866 −10.7110 −0.363973
867867 2.62620 0.0891904
868868 −7.79383 −0.264540
869869 −15.8217 −0.536716
870870 0 0
871871 −3.28904 −0.111445
872872 −5.55539 −0.188129
873873 23.9634 0.811037
874874 2.81215 0.0951226
875875 0 0
876876 6.89692 0.233025
877877 2.29530 0.0775067 0.0387533 0.999249i 0.487661π-0.487661\pi
0.0387533 + 0.999249i 0.487661π0.487661\pi
878878 −5.09871 −0.172073
879879 −31.9798 −1.07865
880880 0 0
881881 −20.9171 −0.704716 −0.352358 0.935865i 0.614620π-0.614620\pi
−0.352358 + 0.935865i 0.614620π0.614620\pi
882882 24.3651 0.820414
883883 −26.6743 −0.897662 −0.448831 0.893617i 0.648160π-0.648160\pi
−0.448831 + 0.893617i 0.648160π0.648160\pi
884884 −2.62620 −0.0883286
885885 0 0
886886 −10.8034 −0.362948
887887 −29.1633 −0.979207 −0.489603 0.871945i 0.662858π-0.662858\pi
−0.489603 + 0.871945i 0.662858π0.662858\pi
888888 26.7389 0.897298
889889 −12.4123 −0.416296
890890 0 0
891891 −11.0096 −0.368835
892892 3.30925 0.110802
893893 −9.34590 −0.312748
894894 −26.2620 −0.878332
895895 0 0
896896 0.864641 0.0288856
897897 21.6243 0.722015
898898 5.82174 0.194274
899899 85.5500 2.85325
900900 0 0
901901 11.4017 0.379846
902902 −19.0462 −0.634170
903903 16.4681 0.548026
904904 10.6262 0.353422
905905 0 0
906906 13.6243 0.452637
907907 23.2322 0.771412 0.385706 0.922622i 0.373958π-0.373958\pi
0.385706 + 0.922622i 0.373958π0.373958\pi
908908 −24.7187 −0.820317
909909 0.803417 0.0266477
910910 0 0
911911 −20.8646 −0.691276 −0.345638 0.938368i 0.612338π-0.612338\pi
−0.345638 + 0.938368i 0.612338π0.612338\pi
912912 −2.35548 −0.0779977
913913 8.41233 0.278408
914914 −13.7014 −0.453201
915915 0 0
916916 4.27072 0.141109
917917 −14.7389 −0.486720
918918 2.35548 0.0777424
919919 18.2062 0.600566 0.300283 0.953850i 0.402919π-0.402919\pi
0.300283 + 0.953850i 0.402919π0.402919\pi
920920 0 0
921921 62.4873 2.05903
922922 27.0741 0.891639
923923 −32.9248 −1.08373
924924 −4.54144 −0.149402
925925 0 0
926926 −37.3372 −1.22698
927927 −18.6098 −0.611225
928928 −9.49084 −0.311552
929929 17.2803 0.566948 0.283474 0.958980i 0.408513π-0.408513\pi
0.283474 + 0.958980i 0.408513π0.408513\pi
930930 0 0
931931 5.60788 0.183791
932932 0.832365 0.0272650
933933 86.4556 2.83043
934934 −35.3449 −1.15652
935935 0 0
936936 −10.2341 −0.334511
937937 50.2986 1.64318 0.821592 0.570076i 0.193086π-0.193086\pi
0.821592 + 0.570076i 0.193086π0.193086\pi
938938 −1.08287 −0.0353571
939939 −76.2811 −2.48934
940940 0 0
941941 20.7153 0.675300 0.337650 0.941272i 0.390368π-0.390368\pi
0.337650 + 0.941272i 0.390368π0.390368\pi
942942 26.8767 0.875690
943943 29.8584 0.972323
944944 −4.14931 −0.135049
945945 0 0
946946 14.5048 0.471591
947947 −8.89692 −0.289111 −0.144555 0.989497i 0.546175π-0.546175\pi
−0.144555 + 0.989497i 0.546175π0.546175\pi
948948 −20.7755 −0.674757
949949 6.89692 0.223883
950950 0 0
951951 54.3265 1.76166
952952 −0.864641 −0.0280232
953953 17.2158 0.557673 0.278836 0.960339i 0.410051π-0.410051\pi
0.278836 + 0.960339i 0.410051π0.410051\pi
954954 44.4315 1.43852
955955 0 0
956956 −4.71096 −0.152363
957957 49.8496 1.61141
958958 −31.0419 −1.00292
959959 12.5414 0.404984
960960 0 0
961961 50.2514 1.62101
962962 26.7389 0.862096
963963 −24.5452 −0.790958
964964 −23.4865 −0.756448
965965 0 0
966966 7.11952 0.229067
967967 1.90754 0.0613424 0.0306712 0.999530i 0.490236π-0.490236\pi
0.0306712 + 0.999530i 0.490236π0.490236\pi
968968 7.00000 0.224989
969969 2.35548 0.0756689
970970 0 0
971971 −4.97398 −0.159623 −0.0798113 0.996810i 0.525432π-0.525432\pi
−0.0798113 + 0.996810i 0.525432π0.525432\pi
972972 −21.5231 −0.690354
973973 12.7197 0.407775
974974 −13.1633 −0.421778
975975 0 0
976976 3.28467 0.105140
977977 51.2716 1.64032 0.820161 0.572132i 0.193884π-0.193884\pi
0.820161 + 0.572132i 0.193884π0.193884\pi
978978 17.0096 0.543907
979979 8.29862 0.265225
980980 0 0
981981 21.6489 0.691196
982982 −24.3555 −0.777215
983983 9.88296 0.315218 0.157609 0.987502i 0.449622π-0.449622\pi
0.157609 + 0.987502i 0.449622π0.449622\pi
984984 −25.0096 −0.797276
985985 0 0
986986 9.49084 0.302250
987987 −23.6610 −0.753136
988988 −2.35548 −0.0749378
989989 −22.7389 −0.723054
990990 0 0
991991 −37.7807 −1.20014 −0.600072 0.799946i 0.704861π-0.704861\pi
−0.600072 + 0.799946i 0.704861π0.704861\pi
992992 −9.01395 −0.286193
993993 10.5579 0.335044
994994 −10.8401 −0.343826
995995 0 0
996996 11.0462 0.350013
997997 −8.14494 −0.257953 −0.128976 0.991648i 0.541169π-0.541169\pi
−0.128976 + 0.991648i 0.541169π0.541169\pi
998998 −36.2620 −1.14785
999999 −23.9825 −0.758774
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 850.2.a.p.1.3 3
3.2 odd 2 7650.2.a.do.1.2 3
4.3 odd 2 6800.2.a.bp.1.1 3
5.2 odd 4 170.2.c.b.69.1 6
5.3 odd 4 170.2.c.b.69.6 yes 6
5.4 even 2 850.2.a.q.1.1 3
15.2 even 4 1530.2.d.g.919.6 6
15.8 even 4 1530.2.d.g.919.3 6
15.14 odd 2 7650.2.a.dj.1.2 3
20.3 even 4 1360.2.e.c.1089.2 6
20.7 even 4 1360.2.e.c.1089.5 6
20.19 odd 2 6800.2.a.bk.1.3 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
170.2.c.b.69.1 6 5.2 odd 4
170.2.c.b.69.6 yes 6 5.3 odd 4
850.2.a.p.1.3 3 1.1 even 1 trivial
850.2.a.q.1.1 3 5.4 even 2
1360.2.e.c.1089.2 6 20.3 even 4
1360.2.e.c.1089.5 6 20.7 even 4
1530.2.d.g.919.3 6 15.8 even 4
1530.2.d.g.919.6 6 15.2 even 4
6800.2.a.bk.1.3 3 20.19 odd 2
6800.2.a.bp.1.1 3 4.3 odd 2
7650.2.a.dj.1.2 3 15.14 odd 2
7650.2.a.do.1.2 3 3.2 odd 2