Properties

Label 350.4.a.h.1.1
Level 350350
Weight 44
Character 350.1
Self dual yes
Analytic conductor 20.65120.651
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] = [350,4,Mod(1,350)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(350, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("350.1");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 350=2527 350 = 2 \cdot 5^{2} \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 350.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: 20.650668502020.6506685020
Analytic rank: 11
Dimension: 11
Coefficient field: Q\mathbb{Q}
Coefficient ring: Z\mathbb{Z}
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Character χ\chi == 350.1

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) == q2.00000q2+4.00000q3+4.00000q48.00000q6+7.00000q78.00000q811.0000q9+5.00000q11+16.0000q1282.0000q1314.0000q14+16.0000q16+12.0000q17+22.0000q1842.0000q19+28.0000q2110.0000q22175.000q2332.0000q24+164.000q26152.000q27+28.0000q28+1.00000q29+226.000q3132.0000q32+20.0000q3324.0000q3444.0000q36+19.0000q37+84.0000q38328.000q39+16.0000q4156.0000q42281.000q43+20.0000q44+350.000q46334.000q47+64.0000q48+49.0000q49+48.0000q51328.000q52+398.000q53+304.000q5456.0000q56168.000q572.00000q58+106.000q59+48.0000q61452.000q6277.0000q63+64.0000q6440.0000q66483.000q67+48.0000q68700.000q6915.0000q71+88.0000q721044.00q7338.0000q74168.000q76+35.0000q77+656.000q781253.00q79311.000q8132.0000q82758.000q83+112.000q84+562.000q86+4.00000q8740.0000q88+86.0000q89574.000q91700.000q92+904.000q93+668.000q94128.000q96710.000q9798.0000q9855.0000q99+O(q100)q-2.00000 q^{2} +4.00000 q^{3} +4.00000 q^{4} -8.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} -11.0000 q^{9} +5.00000 q^{11} +16.0000 q^{12} -82.0000 q^{13} -14.0000 q^{14} +16.0000 q^{16} +12.0000 q^{17} +22.0000 q^{18} -42.0000 q^{19} +28.0000 q^{21} -10.0000 q^{22} -175.000 q^{23} -32.0000 q^{24} +164.000 q^{26} -152.000 q^{27} +28.0000 q^{28} +1.00000 q^{29} +226.000 q^{31} -32.0000 q^{32} +20.0000 q^{33} -24.0000 q^{34} -44.0000 q^{36} +19.0000 q^{37} +84.0000 q^{38} -328.000 q^{39} +16.0000 q^{41} -56.0000 q^{42} -281.000 q^{43} +20.0000 q^{44} +350.000 q^{46} -334.000 q^{47} +64.0000 q^{48} +49.0000 q^{49} +48.0000 q^{51} -328.000 q^{52} +398.000 q^{53} +304.000 q^{54} -56.0000 q^{56} -168.000 q^{57} -2.00000 q^{58} +106.000 q^{59} +48.0000 q^{61} -452.000 q^{62} -77.0000 q^{63} +64.0000 q^{64} -40.0000 q^{66} -483.000 q^{67} +48.0000 q^{68} -700.000 q^{69} -15.0000 q^{71} +88.0000 q^{72} -1044.00 q^{73} -38.0000 q^{74} -168.000 q^{76} +35.0000 q^{77} +656.000 q^{78} -1253.00 q^{79} -311.000 q^{81} -32.0000 q^{82} -758.000 q^{83} +112.000 q^{84} +562.000 q^{86} +4.00000 q^{87} -40.0000 q^{88} +86.0000 q^{89} -574.000 q^{91} -700.000 q^{92} +904.000 q^{93} +668.000 q^{94} -128.000 q^{96} -710.000 q^{97} -98.0000 q^{98} -55.0000 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 −2.00000 −0.707107
33 4.00000 0.769800 0.384900 0.922958i 0.374236π-0.374236\pi
0.384900 + 0.922958i 0.374236π0.374236\pi
44 4.00000 0.500000
55 0 0
66 −8.00000 −0.544331
77 7.00000 0.377964
88 −8.00000 −0.353553
99 −11.0000 −0.407407
1010 0 0
1111 5.00000 0.137051 0.0685253 0.997649i 0.478171π-0.478171\pi
0.0685253 + 0.997649i 0.478171π0.478171\pi
1212 16.0000 0.384900
1313 −82.0000 −1.74944 −0.874720 0.484629i 0.838954π-0.838954\pi
−0.874720 + 0.484629i 0.838954π0.838954\pi
1414 −14.0000 −0.267261
1515 0 0
1616 16.0000 0.250000
1717 12.0000 0.171202 0.0856008 0.996330i 0.472719π-0.472719\pi
0.0856008 + 0.996330i 0.472719π0.472719\pi
1818 22.0000 0.288081
1919 −42.0000 −0.507130 −0.253565 0.967318i 0.581603π-0.581603\pi
−0.253565 + 0.967318i 0.581603π0.581603\pi
2020 0 0
2121 28.0000 0.290957
2222 −10.0000 −0.0969094
2323 −175.000 −1.58652 −0.793261 0.608881i 0.791619π-0.791619\pi
−0.793261 + 0.608881i 0.791619π0.791619\pi
2424 −32.0000 −0.272166
2525 0 0
2626 164.000 1.23704
2727 −152.000 −1.08342
2828 28.0000 0.188982
2929 1.00000 0.00640329 0.00320164 0.999995i 0.498981π-0.498981\pi
0.00320164 + 0.999995i 0.498981π0.498981\pi
3030 0 0
3131 226.000 1.30938 0.654690 0.755897i 0.272799π-0.272799\pi
0.654690 + 0.755897i 0.272799π0.272799\pi
3232 −32.0000 −0.176777
3333 20.0000 0.105502
3434 −24.0000 −0.121058
3535 0 0
3636 −44.0000 −0.203704
3737 19.0000 0.0844211 0.0422106 0.999109i 0.486560π-0.486560\pi
0.0422106 + 0.999109i 0.486560π0.486560\pi
3838 84.0000 0.358595
3939 −328.000 −1.34672
4040 0 0
4141 16.0000 0.0609459 0.0304729 0.999536i 0.490299π-0.490299\pi
0.0304729 + 0.999536i 0.490299π0.490299\pi
4242 −56.0000 −0.205738
4343 −281.000 −0.996560 −0.498280 0.867016i 0.666035π-0.666035\pi
−0.498280 + 0.867016i 0.666035π0.666035\pi
4444 20.0000 0.0685253
4545 0 0
4646 350.000 1.12184
4747 −334.000 −1.03657 −0.518286 0.855207i 0.673430π-0.673430\pi
−0.518286 + 0.855207i 0.673430π0.673430\pi
4848 64.0000 0.192450
4949 49.0000 0.142857
5050 0 0
5151 48.0000 0.131791
5252 −328.000 −0.874720
5353 398.000 1.03150 0.515750 0.856739i 0.327513π-0.327513\pi
0.515750 + 0.856739i 0.327513π0.327513\pi
5454 304.000 0.766096
5555 0 0
5656 −56.0000 −0.133631
5757 −168.000 −0.390388
5858 −2.00000 −0.00452781
5959 106.000 0.233899 0.116949 0.993138i 0.462688π-0.462688\pi
0.116949 + 0.993138i 0.462688π0.462688\pi
6060 0 0
6161 48.0000 0.100750 0.0503752 0.998730i 0.483958π-0.483958\pi
0.0503752 + 0.998730i 0.483958π0.483958\pi
6262 −452.000 −0.925872
6363 −77.0000 −0.153986
6464 64.0000 0.125000
6565 0 0
6666 −40.0000 −0.0746009
6767 −483.000 −0.880714 −0.440357 0.897823i 0.645148π-0.645148\pi
−0.440357 + 0.897823i 0.645148π0.645148\pi
6868 48.0000 0.0856008
6969 −700.000 −1.22131
7070 0 0
7171 −15.0000 −0.0250729 −0.0125364 0.999921i 0.503991π-0.503991\pi
−0.0125364 + 0.999921i 0.503991π0.503991\pi
7272 88.0000 0.144040
7373 −1044.00 −1.67385 −0.836924 0.547319i 0.815649π-0.815649\pi
−0.836924 + 0.547319i 0.815649π0.815649\pi
7474 −38.0000 −0.0596947
7575 0 0
7676 −168.000 −0.253565
7777 35.0000 0.0518003
7878 656.000 0.952274
7979 −1253.00 −1.78447 −0.892237 0.451567i 0.850865π-0.850865\pi
−0.892237 + 0.451567i 0.850865π0.850865\pi
8080 0 0
8181 −311.000 −0.426612
8282 −32.0000 −0.0430952
8383 −758.000 −1.00243 −0.501213 0.865324i 0.667113π-0.667113\pi
−0.501213 + 0.865324i 0.667113π0.667113\pi
8484 112.000 0.145479
8585 0 0
8686 562.000 0.704675
8787 4.00000 0.00492925
8888 −40.0000 −0.0484547
8989 86.0000 0.102427 0.0512134 0.998688i 0.483691π-0.483691\pi
0.0512134 + 0.998688i 0.483691π0.483691\pi
9090 0 0
9191 −574.000 −0.661226
9292 −700.000 −0.793261
9393 904.000 1.00796
9494 668.000 0.732967
9595 0 0
9696 −128.000 −0.136083
9797 −710.000 −0.743192 −0.371596 0.928395i 0.621189π-0.621189\pi
−0.371596 + 0.928395i 0.621189π0.621189\pi
9898 −98.0000 −0.101015
9999 −55.0000 −0.0558354
100100 0 0
101101 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
102102 −96.0000 −0.0931904
103103 838.000 0.801656 0.400828 0.916153i 0.368722π-0.368722\pi
0.400828 + 0.916153i 0.368722π0.368722\pi
104104 656.000 0.618520
105105 0 0
106106 −796.000 −0.729381
107107 2164.00 1.95516 0.977578 0.210572i 0.0675326π-0.0675326\pi
0.977578 + 0.210572i 0.0675326π0.0675326\pi
108108 −608.000 −0.541711
109109 −1827.00 −1.60546 −0.802729 0.596344i 0.796619π-0.796619\pi
−0.802729 + 0.596344i 0.796619π0.796619\pi
110110 0 0
111111 76.0000 0.0649874
112112 112.000 0.0944911
113113 93.0000 0.0774222 0.0387111 0.999250i 0.487675π-0.487675\pi
0.0387111 + 0.999250i 0.487675π0.487675\pi
114114 336.000 0.276046
115115 0 0
116116 4.00000 0.00320164
117117 902.000 0.712734
118118 −212.000 −0.165391
119119 84.0000 0.0647081
120120 0 0
121121 −1306.00 −0.981217
122122 −96.0000 −0.0712412
123123 64.0000 0.0469161
124124 904.000 0.654690
125125 0 0
126126 154.000 0.108884
127127 1433.00 1.00125 0.500623 0.865666i 0.333104π-0.333104\pi
0.500623 + 0.865666i 0.333104π0.333104\pi
128128 −128.000 −0.0883883
129129 −1124.00 −0.767153
130130 0 0
131131 868.000 0.578912 0.289456 0.957191i 0.406526π-0.406526\pi
0.289456 + 0.957191i 0.406526π0.406526\pi
132132 80.0000 0.0527508
133133 −294.000 −0.191677
134134 966.000 0.622759
135135 0 0
136136 −96.0000 −0.0605289
137137 2646.00 1.65010 0.825048 0.565063i 0.191148π-0.191148\pi
0.825048 + 0.565063i 0.191148π0.191148\pi
138138 1400.00 0.863594
139139 896.000 0.546746 0.273373 0.961908i 0.411861π-0.411861\pi
0.273373 + 0.961908i 0.411861π0.411861\pi
140140 0 0
141141 −1336.00 −0.797954
142142 30.0000 0.0177292
143143 −410.000 −0.239762
144144 −176.000 −0.101852
145145 0 0
146146 2088.00 1.18359
147147 196.000 0.109971
148148 76.0000 0.0422106
149149 2523.00 1.38720 0.693598 0.720362i 0.256024π-0.256024\pi
0.693598 + 0.720362i 0.256024π0.256024\pi
150150 0 0
151151 2433.00 1.31122 0.655612 0.755098i 0.272411π-0.272411\pi
0.655612 + 0.755098i 0.272411π0.272411\pi
152152 336.000 0.179297
153153 −132.000 −0.0697488
154154 −70.0000 −0.0366283
155155 0 0
156156 −1312.00 −0.673359
157157 2572.00 1.30744 0.653720 0.756737i 0.273208π-0.273208\pi
0.653720 + 0.756737i 0.273208π0.273208\pi
158158 2506.00 1.26181
159159 1592.00 0.794049
160160 0 0
161161 −1225.00 −0.599649
162162 622.000 0.301660
163163 −2488.00 −1.19555 −0.597777 0.801663i 0.703949π-0.703949\pi
−0.597777 + 0.801663i 0.703949π0.703949\pi
164164 64.0000 0.0304729
165165 0 0
166166 1516.00 0.708822
167167 −3054.00 −1.41512 −0.707562 0.706652i 0.750205π-0.750205\pi
−0.707562 + 0.706652i 0.750205π0.750205\pi
168168 −224.000 −0.102869
169169 4527.00 2.06054
170170 0 0
171171 462.000 0.206608
172172 −1124.00 −0.498280
173173 3894.00 1.71130 0.855651 0.517553i 0.173157π-0.173157\pi
0.855651 + 0.517553i 0.173157π0.173157\pi
174174 −8.00000 −0.00348551
175175 0 0
176176 80.0000 0.0342627
177177 424.000 0.180055
178178 −172.000 −0.0724267
179179 −1108.00 −0.462658 −0.231329 0.972876i 0.574307π-0.574307\pi
−0.231329 + 0.972876i 0.574307π0.574307\pi
180180 0 0
181181 −1920.00 −0.788467 −0.394233 0.919010i 0.628990π-0.628990\pi
−0.394233 + 0.919010i 0.628990π0.628990\pi
182182 1148.00 0.467557
183183 192.000 0.0775576
184184 1400.00 0.560920
185185 0 0
186186 −1808.00 −0.712737
187187 60.0000 0.0234633
188188 −1336.00 −0.518286
189189 −1064.00 −0.409495
190190 0 0
191191 −936.000 −0.354589 −0.177295 0.984158i 0.556735π-0.556735\pi
−0.177295 + 0.984158i 0.556735π0.556735\pi
192192 256.000 0.0962250
193193 −3163.00 −1.17968 −0.589839 0.807521i 0.700809π-0.700809\pi
−0.589839 + 0.807521i 0.700809π0.700809\pi
194194 1420.00 0.525516
195195 0 0
196196 196.000 0.0714286
197197 349.000 0.126219 0.0631097 0.998007i 0.479898π-0.479898\pi
0.0631097 + 0.998007i 0.479898π0.479898\pi
198198 110.000 0.0394816
199199 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
200200 0 0
201201 −1932.00 −0.677974
202202 0 0
203203 7.00000 0.00242022
204204 192.000 0.0658955
205205 0 0
206206 −1676.00 −0.566857
207207 1925.00 0.646361
208208 −1312.00 −0.437360
209209 −210.000 −0.0695024
210210 0 0
211211 1676.00 0.546827 0.273414 0.961897i 0.411847π-0.411847\pi
0.273414 + 0.961897i 0.411847π0.411847\pi
212212 1592.00 0.515750
213213 −60.0000 −0.0193011
214214 −4328.00 −1.38250
215215 0 0
216216 1216.00 0.383048
217217 1582.00 0.494899
218218 3654.00 1.13523
219219 −4176.00 −1.28853
220220 0 0
221221 −984.000 −0.299507
222222 −152.000 −0.0459530
223223 −1176.00 −0.353143 −0.176571 0.984288i 0.556501π-0.556501\pi
−0.176571 + 0.984288i 0.556501π0.556501\pi
224224 −224.000 −0.0668153
225225 0 0
226226 −186.000 −0.0547457
227227 −2234.00 −0.653197 −0.326599 0.945163i 0.605903π-0.605903\pi
−0.326599 + 0.945163i 0.605903π0.605903\pi
228228 −672.000 −0.195194
229229 4274.00 1.23334 0.616668 0.787223i 0.288482π-0.288482\pi
0.616668 + 0.787223i 0.288482π0.288482\pi
230230 0 0
231231 140.000 0.0398759
232232 −8.00000 −0.00226390
233233 5427.00 1.52590 0.762950 0.646458i 0.223750π-0.223750\pi
0.762950 + 0.646458i 0.223750π0.223750\pi
234234 −1804.00 −0.503979
235235 0 0
236236 424.000 0.116949
237237 −5012.00 −1.37369
238238 −168.000 −0.0457556
239239 3516.00 0.951595 0.475797 0.879555i 0.342160π-0.342160\pi
0.475797 + 0.879555i 0.342160π0.342160\pi
240240 0 0
241241 −3890.00 −1.03974 −0.519869 0.854246i 0.674019π-0.674019\pi
−0.519869 + 0.854246i 0.674019π0.674019\pi
242242 2612.00 0.693825
243243 2860.00 0.755017
244244 192.000 0.0503752
245245 0 0
246246 −128.000 −0.0331747
247247 3444.00 0.887192
248248 −1808.00 −0.462936
249249 −3032.00 −0.771667
250250 0 0
251251 2512.00 0.631697 0.315849 0.948810i 0.397711π-0.397711\pi
0.315849 + 0.948810i 0.397711π0.397711\pi
252252 −308.000 −0.0769928
253253 −875.000 −0.217434
254254 −2866.00 −0.707988
255255 0 0
256256 256.000 0.0625000
257257 −6934.00 −1.68300 −0.841500 0.540257i 0.818327π-0.818327\pi
−0.841500 + 0.540257i 0.818327π0.818327\pi
258258 2248.00 0.542459
259259 133.000 0.0319082
260260 0 0
261261 −11.0000 −0.00260875
262262 −1736.00 −0.409353
263263 −5505.00 −1.29070 −0.645348 0.763889i 0.723287π-0.723287\pi
−0.645348 + 0.763889i 0.723287π0.723287\pi
264264 −160.000 −0.0373005
265265 0 0
266266 588.000 0.135536
267267 344.000 0.0788482
268268 −1932.00 −0.440357
269269 −8698.00 −1.97147 −0.985737 0.168294i 0.946174π-0.946174\pi
−0.985737 + 0.168294i 0.946174π0.946174\pi
270270 0 0
271271 2054.00 0.460412 0.230206 0.973142i 0.426060π-0.426060\pi
0.230206 + 0.973142i 0.426060π0.426060\pi
272272 192.000 0.0428004
273273 −2296.00 −0.509012
274274 −5292.00 −1.16679
275275 0 0
276276 −2800.00 −0.610653
277277 −8450.00 −1.83289 −0.916446 0.400158i 0.868955π-0.868955\pi
−0.916446 + 0.400158i 0.868955π0.868955\pi
278278 −1792.00 −0.386608
279279 −2486.00 −0.533451
280280 0 0
281281 4469.00 0.948748 0.474374 0.880323i 0.342674π-0.342674\pi
0.474374 + 0.880323i 0.342674π0.342674\pi
282282 2672.00 0.564239
283283 794.000 0.166779 0.0833894 0.996517i 0.473425π-0.473425\pi
0.0833894 + 0.996517i 0.473425π0.473425\pi
284284 −60.0000 −0.0125364
285285 0 0
286286 820.000 0.169537
287287 112.000 0.0230354
288288 352.000 0.0720201
289289 −4769.00 −0.970690
290290 0 0
291291 −2840.00 −0.572109
292292 −4176.00 −0.836924
293293 6462.00 1.28844 0.644222 0.764839i 0.277181π-0.277181\pi
0.644222 + 0.764839i 0.277181π0.277181\pi
294294 −392.000 −0.0777616
295295 0 0
296296 −152.000 −0.0298474
297297 −760.000 −0.148484
298298 −5046.00 −0.980896
299299 14350.0 2.77552
300300 0 0
301301 −1967.00 −0.376664
302302 −4866.00 −0.927175
303303 0 0
304304 −672.000 −0.126782
305305 0 0
306306 264.000 0.0493199
307307 −56.0000 −0.0104107 −0.00520536 0.999986i 0.501657π-0.501657\pi
−0.00520536 + 0.999986i 0.501657π0.501657\pi
308308 140.000 0.0259001
309309 3352.00 0.617115
310310 0 0
311311 10656.0 1.94291 0.971457 0.237215i 0.0762347π-0.0762347\pi
0.971457 + 0.237215i 0.0762347π0.0762347\pi
312312 2624.00 0.476137
313313 2010.00 0.362977 0.181489 0.983393i 0.441908π-0.441908\pi
0.181489 + 0.983393i 0.441908π0.441908\pi
314314 −5144.00 −0.924499
315315 0 0
316316 −5012.00 −0.892237
317317 −3903.00 −0.691528 −0.345764 0.938322i 0.612380π-0.612380\pi
−0.345764 + 0.938322i 0.612380π0.612380\pi
318318 −3184.00 −0.561478
319319 5.00000 0.000877574 0
320320 0 0
321321 8656.00 1.50508
322322 2450.00 0.424016
323323 −504.000 −0.0868214
324324 −1244.00 −0.213306
325325 0 0
326326 4976.00 0.845384
327327 −7308.00 −1.23588
328328 −128.000 −0.0215476
329329 −2338.00 −0.391788
330330 0 0
331331 −3277.00 −0.544170 −0.272085 0.962273i 0.587713π-0.587713\pi
−0.272085 + 0.962273i 0.587713π0.587713\pi
332332 −3032.00 −0.501213
333333 −209.000 −0.0343938
334334 6108.00 1.00064
335335 0 0
336336 448.000 0.0727393
337337 −6462.00 −1.04453 −0.522266 0.852782i 0.674913π-0.674913\pi
−0.522266 + 0.852782i 0.674913π0.674913\pi
338338 −9054.00 −1.45702
339339 372.000 0.0595996
340340 0 0
341341 1130.00 0.179451
342342 −924.000 −0.146094
343343 343.000 0.0539949
344344 2248.00 0.352337
345345 0 0
346346 −7788.00 −1.21007
347347 3787.00 0.585870 0.292935 0.956132i 0.405368π-0.405368\pi
0.292935 + 0.956132i 0.405368π0.405368\pi
348348 16.0000 0.00246463
349349 7398.00 1.13469 0.567344 0.823481i 0.307971π-0.307971\pi
0.567344 + 0.823481i 0.307971π0.307971\pi
350350 0 0
351351 12464.0 1.89538
352352 −160.000 −0.0242274
353353 9654.00 1.45561 0.727805 0.685784i 0.240540π-0.240540\pi
0.727805 + 0.685784i 0.240540π0.240540\pi
354354 −848.000 −0.127318
355355 0 0
356356 344.000 0.0512134
357357 336.000 0.0498123
358358 2216.00 0.327149
359359 −7691.00 −1.13068 −0.565342 0.824857i 0.691256π-0.691256\pi
−0.565342 + 0.824857i 0.691256π0.691256\pi
360360 0 0
361361 −5095.00 −0.742820
362362 3840.00 0.557530
363363 −5224.00 −0.755341
364364 −2296.00 −0.330613
365365 0 0
366366 −384.000 −0.0548415
367367 6836.00 0.972306 0.486153 0.873874i 0.338400π-0.338400\pi
0.486153 + 0.873874i 0.338400π0.338400\pi
368368 −2800.00 −0.396631
369369 −176.000 −0.0248298
370370 0 0
371371 2786.00 0.389870
372372 3616.00 0.503981
373373 −12123.0 −1.68286 −0.841428 0.540370i 0.818284π-0.818284\pi
−0.841428 + 0.540370i 0.818284π0.818284\pi
374374 −120.000 −0.0165910
375375 0 0
376376 2672.00 0.366484
377377 −82.0000 −0.0112022
378378 2128.00 0.289557
379379 10811.0 1.46523 0.732617 0.680641i 0.238299π-0.238299\pi
0.732617 + 0.680641i 0.238299π0.238299\pi
380380 0 0
381381 5732.00 0.770759
382382 1872.00 0.250733
383383 12778.0 1.70477 0.852383 0.522918i 0.175157π-0.175157\pi
0.852383 + 0.522918i 0.175157π0.175157\pi
384384 −512.000 −0.0680414
385385 0 0
386386 6326.00 0.834158
387387 3091.00 0.406006
388388 −2840.00 −0.371596
389389 −383.000 −0.0499200 −0.0249600 0.999688i 0.507946π-0.507946\pi
−0.0249600 + 0.999688i 0.507946π0.507946\pi
390390 0 0
391391 −2100.00 −0.271615
392392 −392.000 −0.0505076
393393 3472.00 0.445647
394394 −698.000 −0.0892506
395395 0 0
396396 −220.000 −0.0279177
397397 −12050.0 −1.52336 −0.761678 0.647956i 0.775624π-0.775624\pi
−0.761678 + 0.647956i 0.775624π0.775624\pi
398398 0 0
399399 −1176.00 −0.147553
400400 0 0
401401 −7523.00 −0.936860 −0.468430 0.883501i 0.655180π-0.655180\pi
−0.468430 + 0.883501i 0.655180π0.655180\pi
402402 3864.00 0.479400
403403 −18532.0 −2.29068
404404 0 0
405405 0 0
406406 −14.0000 −0.00171135
407407 95.0000 0.0115700
408408 −384.000 −0.0465952
409409 −4534.00 −0.548146 −0.274073 0.961709i 0.588371π-0.588371\pi
−0.274073 + 0.961709i 0.588371π0.588371\pi
410410 0 0
411411 10584.0 1.27024
412412 3352.00 0.400828
413413 742.000 0.0884054
414414 −3850.00 −0.457046
415415 0 0
416416 2624.00 0.309260
417417 3584.00 0.420885
418418 420.000 0.0491456
419419 8494.00 0.990356 0.495178 0.868792i 0.335103π-0.335103\pi
0.495178 + 0.868792i 0.335103π0.335103\pi
420420 0 0
421421 −8765.00 −1.01468 −0.507340 0.861746i 0.669371π-0.669371\pi
−0.507340 + 0.861746i 0.669371π0.669371\pi
422422 −3352.00 −0.386665
423423 3674.00 0.422307
424424 −3184.00 −0.364690
425425 0 0
426426 120.000 0.0136479
427427 336.000 0.0380800
428428 8656.00 0.977578
429429 −1640.00 −0.184569
430430 0 0
431431 −6696.00 −0.748341 −0.374170 0.927360i 0.622073π-0.622073\pi
−0.374170 + 0.927360i 0.622073π0.622073\pi
432432 −2432.00 −0.270856
433433 4148.00 0.460370 0.230185 0.973147i 0.426067π-0.426067\pi
0.230185 + 0.973147i 0.426067π0.426067\pi
434434 −3164.00 −0.349947
435435 0 0
436436 −7308.00 −0.802729
437437 7350.00 0.804572
438438 8352.00 0.911128
439439 6182.00 0.672097 0.336049 0.941845i 0.390909π-0.390909\pi
0.336049 + 0.941845i 0.390909π0.390909\pi
440440 0 0
441441 −539.000 −0.0582011
442442 1968.00 0.211783
443443 −616.000 −0.0660656 −0.0330328 0.999454i 0.510517π-0.510517\pi
−0.0330328 + 0.999454i 0.510517π0.510517\pi
444444 304.000 0.0324937
445445 0 0
446446 2352.00 0.249709
447447 10092.0 1.06786
448448 448.000 0.0472456
449449 −8653.00 −0.909488 −0.454744 0.890622i 0.650269π-0.650269\pi
−0.454744 + 0.890622i 0.650269π0.650269\pi
450450 0 0
451451 80.0000 0.00835267
452452 372.000 0.0387111
453453 9732.00 1.00938
454454 4468.00 0.461880
455455 0 0
456456 1344.00 0.138023
457457 7785.00 0.796864 0.398432 0.917198i 0.369554π-0.369554\pi
0.398432 + 0.917198i 0.369554π0.369554\pi
458458 −8548.00 −0.872100
459459 −1824.00 −0.185484
460460 0 0
461461 −14718.0 −1.48695 −0.743477 0.668762i 0.766825π-0.766825\pi
−0.743477 + 0.668762i 0.766825π0.766825\pi
462462 −280.000 −0.0281965
463463 −2864.00 −0.287476 −0.143738 0.989616i 0.545912π-0.545912\pi
−0.143738 + 0.989616i 0.545912π0.545912\pi
464464 16.0000 0.00160082
465465 0 0
466466 −10854.0 −1.07897
467467 1878.00 0.186089 0.0930444 0.995662i 0.470340π-0.470340\pi
0.0930444 + 0.995662i 0.470340π0.470340\pi
468468 3608.00 0.356367
469469 −3381.00 −0.332879
470470 0 0
471471 10288.0 1.00647
472472 −848.000 −0.0826957
473473 −1405.00 −0.136579
474474 10024.0 0.971345
475475 0 0
476476 336.000 0.0323541
477477 −4378.00 −0.420241
478478 −7032.00 −0.672879
479479 −9914.00 −0.945683 −0.472842 0.881147i 0.656772π-0.656772\pi
−0.472842 + 0.881147i 0.656772π0.656772\pi
480480 0 0
481481 −1558.00 −0.147690
482482 7780.00 0.735206
483483 −4900.00 −0.461610
484484 −5224.00 −0.490609
485485 0 0
486486 −5720.00 −0.533878
487487 12883.0 1.19874 0.599368 0.800474i 0.295419π-0.295419\pi
0.599368 + 0.800474i 0.295419π0.295419\pi
488488 −384.000 −0.0356206
489489 −9952.00 −0.920337
490490 0 0
491491 −16567.0 −1.52273 −0.761363 0.648326i 0.775469π-0.775469\pi
−0.761363 + 0.648326i 0.775469π0.775469\pi
492492 256.000 0.0234581
493493 12.0000 0.00109625
494494 −6888.00 −0.627340
495495 0 0
496496 3616.00 0.327345
497497 −105.000 −0.00947665
498498 6064.00 0.545651
499499 2044.00 0.183371 0.0916854 0.995788i 0.470775π-0.470775\pi
0.0916854 + 0.995788i 0.470775π0.470775\pi
500500 0 0
501501 −12216.0 −1.08936
502502 −5024.00 −0.446677
503503 14610.0 1.29508 0.647542 0.762029i 0.275797π-0.275797\pi
0.647542 + 0.762029i 0.275797π0.275797\pi
504504 616.000 0.0544421
505505 0 0
506506 1750.00 0.153749
507507 18108.0 1.58620
508508 5732.00 0.500623
509509 18074.0 1.57390 0.786951 0.617016i 0.211659π-0.211659\pi
0.786951 + 0.617016i 0.211659π0.211659\pi
510510 0 0
511511 −7308.00 −0.632655
512512 −512.000 −0.0441942
513513 6384.00 0.549436
514514 13868.0 1.19006
515515 0 0
516516 −4496.00 −0.383576
517517 −1670.00 −0.142063
518518 −266.000 −0.0225625
519519 15576.0 1.31736
520520 0 0
521521 −13554.0 −1.13975 −0.569877 0.821730i 0.693009π-0.693009\pi
−0.569877 + 0.821730i 0.693009π0.693009\pi
522522 22.0000 0.00184466
523523 −11984.0 −1.00196 −0.500979 0.865460i 0.667027π-0.667027\pi
−0.500979 + 0.865460i 0.667027π0.667027\pi
524524 3472.00 0.289456
525525 0 0
526526 11010.0 0.912659
527527 2712.00 0.224168
528528 320.000 0.0263754
529529 18458.0 1.51705
530530 0 0
531531 −1166.00 −0.0952921
532532 −1176.00 −0.0958385
533533 −1312.00 −0.106621
534534 −688.000 −0.0557541
535535 0 0
536536 3864.00 0.311379
537537 −4432.00 −0.356154
538538 17396.0 1.39404
539539 245.000 0.0195787
540540 0 0
541541 3863.00 0.306993 0.153497 0.988149i 0.450947π-0.450947\pi
0.153497 + 0.988149i 0.450947π0.450947\pi
542542 −4108.00 −0.325560
543543 −7680.00 −0.606962
544544 −384.000 −0.0302645
545545 0 0
546546 4592.00 0.359926
547547 −19579.0 −1.53042 −0.765208 0.643783i 0.777364π-0.777364\pi
−0.765208 + 0.643783i 0.777364π0.777364\pi
548548 10584.0 0.825048
549549 −528.000 −0.0410464
550550 0 0
551551 −42.0000 −0.00324730
552552 5600.00 0.431797
553553 −8771.00 −0.674468
554554 16900.0 1.29605
555555 0 0
556556 3584.00 0.273373
557557 7437.00 0.565738 0.282869 0.959159i 0.408714π-0.408714\pi
0.282869 + 0.959159i 0.408714π0.408714\pi
558558 4972.00 0.377207
559559 23042.0 1.74342
560560 0 0
561561 240.000 0.0180620
562562 −8938.00 −0.670866
563563 5690.00 0.425941 0.212971 0.977059i 0.431686π-0.431686\pi
0.212971 + 0.977059i 0.431686π0.431686\pi
564564 −5344.00 −0.398977
565565 0 0
566566 −1588.00 −0.117930
567567 −2177.00 −0.161244
568568 120.000 0.00886459
569569 −24771.0 −1.82505 −0.912526 0.409019i 0.865871π-0.865871\pi
−0.912526 + 0.409019i 0.865871π0.865871\pi
570570 0 0
571571 −8633.00 −0.632714 −0.316357 0.948640i 0.602460π-0.602460\pi
−0.316357 + 0.948640i 0.602460π0.602460\pi
572572 −1640.00 −0.119881
573573 −3744.00 −0.272963
574574 −224.000 −0.0162885
575575 0 0
576576 −704.000 −0.0509259
577577 −1666.00 −0.120202 −0.0601009 0.998192i 0.519142π-0.519142\pi
−0.0601009 + 0.998192i 0.519142π0.519142\pi
578578 9538.00 0.686381
579579 −12652.0 −0.908116
580580 0 0
581581 −5306.00 −0.378881
582582 5680.00 0.404542
583583 1990.00 0.141368
584584 8352.00 0.591795
585585 0 0
586586 −12924.0 −0.911067
587587 7536.00 0.529888 0.264944 0.964264i 0.414647π-0.414647\pi
0.264944 + 0.964264i 0.414647π0.414647\pi
588588 784.000 0.0549857
589589 −9492.00 −0.664026
590590 0 0
591591 1396.00 0.0971637
592592 304.000 0.0211053
593593 −3568.00 −0.247083 −0.123541 0.992339i 0.539425π-0.539425\pi
−0.123541 + 0.992339i 0.539425π0.539425\pi
594594 1520.00 0.104994
595595 0 0
596596 10092.0 0.693598
597597 0 0
598598 −28700.0 −1.96259
599599 −24901.0 −1.69854 −0.849272 0.527956i 0.822958π-0.822958\pi
−0.849272 + 0.527956i 0.822958π0.822958\pi
600600 0 0
601601 −23744.0 −1.61154 −0.805772 0.592226i 0.798249π-0.798249\pi
−0.805772 + 0.592226i 0.798249π0.798249\pi
602602 3934.00 0.266342
603603 5313.00 0.358809
604604 9732.00 0.655612
605605 0 0
606606 0 0
607607 22894.0 1.53087 0.765436 0.643513i 0.222524π-0.222524\pi
0.765436 + 0.643513i 0.222524π0.222524\pi
608608 1344.00 0.0896487
609609 28.0000 0.00186308
610610 0 0
611611 27388.0 1.81342
612612 −528.000 −0.0348744
613613 7811.00 0.514655 0.257327 0.966324i 0.417158π-0.417158\pi
0.257327 + 0.966324i 0.417158π0.417158\pi
614614 112.000 0.00736149
615615 0 0
616616 −280.000 −0.0183142
617617 −11833.0 −0.772089 −0.386044 0.922480i 0.626159π-0.626159\pi
−0.386044 + 0.922480i 0.626159π0.626159\pi
618618 −6704.00 −0.436366
619619 −4186.00 −0.271809 −0.135904 0.990722i 0.543394π-0.543394\pi
−0.135904 + 0.990722i 0.543394π0.543394\pi
620620 0 0
621621 26600.0 1.71887
622622 −21312.0 −1.37385
623623 602.000 0.0387137
624624 −5248.00 −0.336680
625625 0 0
626626 −4020.00 −0.256664
627627 −840.000 −0.0535030
628628 10288.0 0.653720
629629 228.000 0.0144530
630630 0 0
631631 12079.0 0.762056 0.381028 0.924563i 0.375570π-0.375570\pi
0.381028 + 0.924563i 0.375570π0.375570\pi
632632 10024.0 0.630907
633633 6704.00 0.420948
634634 7806.00 0.488984
635635 0 0
636636 6368.00 0.397025
637637 −4018.00 −0.249920
638638 −10.0000 −0.000620539 0
639639 165.000 0.0102149
640640 0 0
641641 4017.00 0.247523 0.123761 0.992312i 0.460504π-0.460504\pi
0.123761 + 0.992312i 0.460504π0.460504\pi
642642 −17312.0 −1.06425
643643 −13508.0 −0.828466 −0.414233 0.910171i 0.635950π-0.635950\pi
−0.414233 + 0.910171i 0.635950π0.635950\pi
644644 −4900.00 −0.299825
645645 0 0
646646 1008.00 0.0613920
647647 1346.00 0.0817878 0.0408939 0.999163i 0.486979π-0.486979\pi
0.0408939 + 0.999163i 0.486979π0.486979\pi
648648 2488.00 0.150830
649649 530.000 0.0320560
650650 0 0
651651 6328.00 0.380974
652652 −9952.00 −0.597777
653653 10274.0 0.615701 0.307850 0.951435i 0.400390π-0.400390\pi
0.307850 + 0.951435i 0.400390π0.400390\pi
654654 14616.0 0.873900
655655 0 0
656656 256.000 0.0152365
657657 11484.0 0.681938
658658 4676.00 0.277036
659659 −13116.0 −0.775306 −0.387653 0.921805i 0.626714π-0.626714\pi
−0.387653 + 0.921805i 0.626714π0.626714\pi
660660 0 0
661661 23070.0 1.35752 0.678759 0.734361i 0.262518π-0.262518\pi
0.678759 + 0.734361i 0.262518π0.262518\pi
662662 6554.00 0.384786
663663 −3936.00 −0.230560
664664 6064.00 0.354411
665665 0 0
666666 418.000 0.0243201
667667 −175.000 −0.0101590
668668 −12216.0 −0.707562
669669 −4704.00 −0.271849
670670 0 0
671671 240.000 0.0138079
672672 −896.000 −0.0514344
673673 −24922.0 −1.42745 −0.713724 0.700427i 0.752993π-0.752993\pi
−0.713724 + 0.700427i 0.752993π0.752993\pi
674674 12924.0 0.738596
675675 0 0
676676 18108.0 1.03027
677677 −14294.0 −0.811467 −0.405733 0.913991i 0.632984π-0.632984\pi
−0.405733 + 0.913991i 0.632984π0.632984\pi
678678 −744.000 −0.0421433
679679 −4970.00 −0.280900
680680 0 0
681681 −8936.00 −0.502832
682682 −2260.00 −0.126891
683683 4979.00 0.278940 0.139470 0.990226i 0.455460π-0.455460\pi
0.139470 + 0.990226i 0.455460π0.455460\pi
684684 1848.00 0.103304
685685 0 0
686686 −686.000 −0.0381802
687687 17096.0 0.949422
688688 −4496.00 −0.249140
689689 −32636.0 −1.80455
690690 0 0
691691 6744.00 0.371279 0.185640 0.982618i 0.440564π-0.440564\pi
0.185640 + 0.982618i 0.440564π0.440564\pi
692692 15576.0 0.855651
693693 −385.000 −0.0211038
694694 −7574.00 −0.414272
695695 0 0
696696 −32.0000 −0.00174275
697697 192.000 0.0104340
698698 −14796.0 −0.802345
699699 21708.0 1.17464
700700 0 0
701701 −17682.0 −0.952696 −0.476348 0.879257i 0.658040π-0.658040\pi
−0.476348 + 0.879257i 0.658040π0.658040\pi
702702 −24928.0 −1.34024
703703 −798.000 −0.0428124
704704 320.000 0.0171313
705705 0 0
706706 −19308.0 −1.02927
707707 0 0
708708 1696.00 0.0900277
709709 −3514.00 −0.186137 −0.0930684 0.995660i 0.529668π-0.529668\pi
−0.0930684 + 0.995660i 0.529668π0.529668\pi
710710 0 0
711711 13783.0 0.727008
712712 −688.000 −0.0362133
713713 −39550.0 −2.07736
714714 −672.000 −0.0352226
715715 0 0
716716 −4432.00 −0.231329
717717 14064.0 0.732538
718718 15382.0 0.799514
719719 −34132.0 −1.77039 −0.885194 0.465222i 0.845974π-0.845974\pi
−0.885194 + 0.465222i 0.845974π0.845974\pi
720720 0 0
721721 5866.00 0.302998
722722 10190.0 0.525253
723723 −15560.0 −0.800391
724724 −7680.00 −0.394233
725725 0 0
726726 10448.0 0.534107
727727 −22112.0 −1.12804 −0.564022 0.825759i 0.690747π-0.690747\pi
−0.564022 + 0.825759i 0.690747π0.690747\pi
728728 4592.00 0.233779
729729 19837.0 1.00782
730730 0 0
731731 −3372.00 −0.170613
732732 768.000 0.0387788
733733 22180.0 1.11765 0.558825 0.829286i 0.311252π-0.311252\pi
0.558825 + 0.829286i 0.311252π0.311252\pi
734734 −13672.0 −0.687524
735735 0 0
736736 5600.00 0.280460
737737 −2415.00 −0.120702
738738 352.000 0.0175573
739739 −16279.0 −0.810328 −0.405164 0.914244i 0.632786π-0.632786\pi
−0.405164 + 0.914244i 0.632786π0.632786\pi
740740 0 0
741741 13776.0 0.682961
742742 −5572.00 −0.275680
743743 −29068.0 −1.43526 −0.717632 0.696422i 0.754774π-0.754774\pi
−0.717632 + 0.696422i 0.754774π0.754774\pi
744744 −7232.00 −0.356368
745745 0 0
746746 24246.0 1.18996
747747 8338.00 0.408396
748748 240.000 0.0117316
749749 15148.0 0.738980
750750 0 0
751751 20.0000 0.000971785 0 0.000485892 1.00000i 0.499845π-0.499845\pi
0.000485892 1.00000i 0.499845π0.499845\pi
752752 −5344.00 −0.259143
753753 10048.0 0.486281
754754 164.000 0.00792112
755755 0 0
756756 −4256.00 −0.204748
757757 −22961.0 −1.10242 −0.551210 0.834367i 0.685834π-0.685834\pi
−0.551210 + 0.834367i 0.685834π0.685834\pi
758758 −21622.0 −1.03608
759759 −3500.00 −0.167381
760760 0 0
761761 2832.00 0.134901 0.0674507 0.997723i 0.478513π-0.478513\pi
0.0674507 + 0.997723i 0.478513π0.478513\pi
762762 −11464.0 −0.545009
763763 −12789.0 −0.606806
764764 −3744.00 −0.177295
765765 0 0
766766 −25556.0 −1.20545
767767 −8692.00 −0.409192
768768 1024.00 0.0481125
769769 −20204.0 −0.947432 −0.473716 0.880678i 0.657088π-0.657088\pi
−0.473716 + 0.880678i 0.657088π0.657088\pi
770770 0 0
771771 −27736.0 −1.29557
772772 −12652.0 −0.589839
773773 27882.0 1.29734 0.648671 0.761069i 0.275325π-0.275325\pi
0.648671 + 0.761069i 0.275325π0.275325\pi
774774 −6182.00 −0.287090
775775 0 0
776776 5680.00 0.262758
777777 532.000 0.0245629
778778 766.000 0.0352988
779779 −672.000 −0.0309074
780780 0 0
781781 −75.0000 −0.00343625
782782 4200.00 0.192061
783783 −152.000 −0.00693747
784784 784.000 0.0357143
785785 0 0
786786 −6944.00 −0.315120
787787 −36304.0 −1.64434 −0.822171 0.569240i 0.807238π-0.807238\pi
−0.822171 + 0.569240i 0.807238π0.807238\pi
788788 1396.00 0.0631097
789789 −22020.0 −0.993578
790790 0 0
791791 651.000 0.0292628
792792 440.000 0.0197408
793793 −3936.00 −0.176257
794794 24100.0 1.07718
795795 0 0
796796 0 0
797797 21096.0 0.937589 0.468795 0.883307i 0.344688π-0.344688\pi
0.468795 + 0.883307i 0.344688π0.344688\pi
798798 2352.00 0.104336
799799 −4008.00 −0.177463
800800 0 0
801801 −946.000 −0.0417294
802802 15046.0 0.662460
803803 −5220.00 −0.229402
804804 −7728.00 −0.338987
805805 0 0
806806 37064.0 1.61976
807807 −34792.0 −1.51764
808808 0 0
809809 15879.0 0.690081 0.345041 0.938588i 0.387865π-0.387865\pi
0.345041 + 0.938588i 0.387865π0.387865\pi
810810 0 0
811811 33402.0 1.44624 0.723121 0.690721i 0.242707π-0.242707\pi
0.723121 + 0.690721i 0.242707π0.242707\pi
812812 28.0000 0.00121011
813813 8216.00 0.354425
814814 −190.000 −0.00818120
815815 0 0
816816 768.000 0.0329478
817817 11802.0 0.505385
818818 9068.00 0.387598
819819 6314.00 0.269388
820820 0 0
821821 10506.0 0.446604 0.223302 0.974749i 0.428316π-0.428316\pi
0.223302 + 0.974749i 0.428316π0.428316\pi
822822 −21168.0 −0.898198
823823 −1035.00 −0.0438370 −0.0219185 0.999760i 0.506977π-0.506977\pi
−0.0219185 + 0.999760i 0.506977π0.506977\pi
824824 −6704.00 −0.283428
825825 0 0
826826 −1484.00 −0.0625121
827827 −30137.0 −1.26719 −0.633595 0.773665i 0.718421π-0.718421\pi
−0.633595 + 0.773665i 0.718421π0.718421\pi
828828 7700.00 0.323181
829829 35464.0 1.48578 0.742892 0.669411i 0.233453π-0.233453\pi
0.742892 + 0.669411i 0.233453π0.233453\pi
830830 0 0
831831 −33800.0 −1.41096
832832 −5248.00 −0.218680
833833 588.000 0.0244574
834834 −7168.00 −0.297611
835835 0 0
836836 −840.000 −0.0347512
837837 −34352.0 −1.41861
838838 −16988.0 −0.700287
839839 −1492.00 −0.0613940 −0.0306970 0.999529i 0.509773π-0.509773\pi
−0.0306970 + 0.999529i 0.509773π0.509773\pi
840840 0 0
841841 −24388.0 −0.999959
842842 17530.0 0.717487
843843 17876.0 0.730347
844844 6704.00 0.273414
845845 0 0
846846 −7348.00 −0.298616
847847 −9142.00 −0.370865
848848 6368.00 0.257875
849849 3176.00 0.128386
850850 0 0
851851 −3325.00 −0.133936
852852 −240.000 −0.00965055
853853 −19288.0 −0.774219 −0.387109 0.922034i 0.626526π-0.626526\pi
−0.387109 + 0.922034i 0.626526π0.626526\pi
854854 −672.000 −0.0269267
855855 0 0
856856 −17312.0 −0.691252
857857 −2656.00 −0.105866 −0.0529330 0.998598i 0.516857π-0.516857\pi
−0.0529330 + 0.998598i 0.516857π0.516857\pi
858858 3280.00 0.130510
859859 3786.00 0.150380 0.0751901 0.997169i 0.476044π-0.476044\pi
0.0751901 + 0.997169i 0.476044π0.476044\pi
860860 0 0
861861 448.000 0.0177326
862862 13392.0 0.529157
863863 45503.0 1.79483 0.897416 0.441185i 0.145442π-0.145442\pi
0.897416 + 0.441185i 0.145442π0.145442\pi
864864 4864.00 0.191524
865865 0 0
866866 −8296.00 −0.325531
867867 −19076.0 −0.747238
868868 6328.00 0.247450
869869 −6265.00 −0.244563
870870 0 0
871871 39606.0 1.54076
872872 14616.0 0.567615
873873 7810.00 0.302782
874874 −14700.0 −0.568919
875875 0 0
876876 −16704.0 −0.644265
877877 32626.0 1.25622 0.628108 0.778126i 0.283830π-0.283830\pi
0.628108 + 0.778126i 0.283830π0.283830\pi
878878 −12364.0 −0.475245
879879 25848.0 0.991845
880880 0 0
881881 −25754.0 −0.984874 −0.492437 0.870348i 0.663894π-0.663894\pi
−0.492437 + 0.870348i 0.663894π0.663894\pi
882882 1078.00 0.0411544
883883 9165.00 0.349294 0.174647 0.984631i 0.444122π-0.444122\pi
0.174647 + 0.984631i 0.444122π0.444122\pi
884884 −3936.00 −0.149753
885885 0 0
886886 1232.00 0.0467154
887887 −1472.00 −0.0557214 −0.0278607 0.999612i 0.508869π-0.508869\pi
−0.0278607 + 0.999612i 0.508869π0.508869\pi
888888 −608.000 −0.0229765
889889 10031.0 0.378435
890890 0 0
891891 −1555.00 −0.0584674
892892 −4704.00 −0.176571
893893 14028.0 0.525677
894894 −20184.0 −0.755094
895895 0 0
896896 −896.000 −0.0334077
897897 57400.0 2.13660
898898 17306.0 0.643105
899899 226.000 0.00838434
900900 0 0
901901 4776.00 0.176594
902902 −160.000 −0.00590623
903903 −7868.00 −0.289956
904904 −744.000 −0.0273729
905905 0 0
906906 −19464.0 −0.713740
907907 −22412.0 −0.820483 −0.410242 0.911977i 0.634556π-0.634556\pi
−0.410242 + 0.911977i 0.634556π0.634556\pi
908908 −8936.00 −0.326599
909909 0 0
910910 0 0
911911 15163.0 0.551452 0.275726 0.961236i 0.411082π-0.411082\pi
0.275726 + 0.961236i 0.411082π0.411082\pi
912912 −2688.00 −0.0975971
913913 −3790.00 −0.137383
914914 −15570.0 −0.563468
915915 0 0
916916 17096.0 0.616668
917917 6076.00 0.218808
918918 3648.00 0.131157
919919 −6501.00 −0.233350 −0.116675 0.993170i 0.537224π-0.537224\pi
−0.116675 + 0.993170i 0.537224π0.537224\pi
920920 0 0
921921 −224.000 −0.00801417
922922 29436.0 1.05143
923923 1230.00 0.0438634
924924 560.000 0.0199379
925925 0 0
926926 5728.00 0.203276
927927 −9218.00 −0.326601
928928 −32.0000 −0.00113195
929929 1464.00 0.0517032 0.0258516 0.999666i 0.491770π-0.491770\pi
0.0258516 + 0.999666i 0.491770π0.491770\pi
930930 0 0
931931 −2058.00 −0.0724471
932932 21708.0 0.762950
933933 42624.0 1.49566
934934 −3756.00 −0.131585
935935 0 0
936936 −7216.00 −0.251990
937937 14064.0 0.490342 0.245171 0.969480i 0.421156π-0.421156\pi
0.245171 + 0.969480i 0.421156π0.421156\pi
938938 6762.00 0.235381
939939 8040.00 0.279420
940940 0 0
941941 −39114.0 −1.35503 −0.677513 0.735511i 0.736942π-0.736942\pi
−0.677513 + 0.735511i 0.736942π0.736942\pi
942942 −20576.0 −0.711680
943943 −2800.00 −0.0966920
944944 1696.00 0.0584747
945945 0 0
946946 2810.00 0.0965761
947947 15068.0 0.517048 0.258524 0.966005i 0.416764π-0.416764\pi
0.258524 + 0.966005i 0.416764π0.416764\pi
948948 −20048.0 −0.686845
949949 85608.0 2.92830
950950 0 0
951951 −15612.0 −0.532338
952952 −672.000 −0.0228778
953953 −27847.0 −0.946540 −0.473270 0.880917i 0.656927π-0.656927\pi
−0.473270 + 0.880917i 0.656927π0.656927\pi
954954 8756.00 0.297155
955955 0 0
956956 14064.0 0.475797
957957 20.0000 0.000675557 0
958958 19828.0 0.668699
959959 18522.0 0.623677
960960 0 0
961961 21285.0 0.714478
962962 3116.00 0.104432
963963 −23804.0 −0.796545
964964 −15560.0 −0.519869
965965 0 0
966966 9800.00 0.326408
967967 33704.0 1.12084 0.560418 0.828210i 0.310641π-0.310641\pi
0.560418 + 0.828210i 0.310641π0.310641\pi
968968 10448.0 0.346913
969969 −2016.00 −0.0668351
970970 0 0
971971 −30006.0 −0.991698 −0.495849 0.868409i 0.665143π-0.665143\pi
−0.495849 + 0.868409i 0.665143π0.665143\pi
972972 11440.0 0.377508
973973 6272.00 0.206651
974974 −25766.0 −0.847634
975975 0 0
976976 768.000 0.0251876
977977 −14457.0 −0.473409 −0.236704 0.971582i 0.576067π-0.576067\pi
−0.236704 + 0.971582i 0.576067π0.576067\pi
978978 19904.0 0.650777
979979 430.000 0.0140377
980980 0 0
981981 20097.0 0.654075
982982 33134.0 1.07673
983983 43742.0 1.41928 0.709640 0.704564i 0.248857π-0.248857\pi
0.709640 + 0.704564i 0.248857π0.248857\pi
984984 −512.000 −0.0165874
985985 0 0
986986 −24.0000 −0.000775168 0
987987 −9352.00 −0.301598
988988 13776.0 0.443596
989989 49175.0 1.58107
990990 0 0
991991 −8201.00 −0.262879 −0.131440 0.991324i 0.541960π-0.541960\pi
−0.131440 + 0.991324i 0.541960π0.541960\pi
992992 −7232.00 −0.231468
993993 −13108.0 −0.418902
994994 210.000 0.00670100
995995 0 0
996996 −12128.0 −0.385834
997997 −4274.00 −0.135766 −0.0678831 0.997693i 0.521624π-0.521624\pi
−0.0678831 + 0.997693i 0.521624π0.521624\pi
998998 −4088.00 −0.129663
999999 −2888.00 −0.0914637
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 350.4.a.h.1.1 1
5.2 odd 4 350.4.c.c.99.1 2
5.3 odd 4 350.4.c.c.99.2 2
5.4 even 2 350.4.a.n.1.1 yes 1
7.6 odd 2 2450.4.a.e.1.1 1
35.34 odd 2 2450.4.a.bk.1.1 1
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
350.4.a.h.1.1 1 1.1 even 1 trivial
350.4.a.n.1.1 yes 1 5.4 even 2
350.4.c.c.99.1 2 5.2 odd 4
350.4.c.c.99.2 2 5.3 odd 4
2450.4.a.e.1.1 1 7.6 odd 2
2450.4.a.bk.1.1 1 35.34 odd 2