Properties

Label 2320.4.a.o.1.1
Level 23202320
Weight 44
Character 2320.1
Self dual yes
Analytic conductor 136.884136.884
Analytic rank 11
Dimension 66
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [2320,4,Mod(1,2320)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2320, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2320.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 2320=24529 2320 = 2^{4} \cdot 5 \cdot 29
Weight: k k == 4 4
Character orbit: [χ][\chi] == 2320.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [6,0,5,0,-30,0,-9] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 136.884431213136.884431213
Analytic rank: 11
Dimension: 66
Coefficient field: Q[x]/(x6)\mathbb{Q}[x]/(x^{6} - \cdots)
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x6x591x4+90x3+1784x21456x3720 x^{6} - x^{5} - 91x^{4} + 90x^{3} + 1784x^{2} - 1456x - 3720 Copy content Toggle raw display
Coefficient ring: Z[a1,,a17]\Z[a_1, \ldots, a_{17}]
Coefficient ring index: 25 2^{5}
Twist minimal: no (minimal twist has level 580)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.14528-1.14528 of defining polynomial
Character χ\chi == 2320.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q7.69185q35.00000q5+16.0448q7+32.1646q9+31.0846q11+15.0566q13+38.4593q1583.1924q1711.6142q19123.414q2122.9471q23+25.0000q2539.7251q2729.0000q29+117.340q31239.098q3380.2241q35126.486q37115.813q39500.344q41+5.84778q43160.823q45+301.232q4785.5639q49+639.903q51+31.2007q53155.423q55+89.3350q5731.3542q59+80.8436q61+516.074q6375.2828q65+191.752q67+176.506q69269.462q71+600.914q73192.296q75+498.746q77389.072q79562.884q81+271.037q83+415.962q85+223.064q87165.976q89+241.580q91902.559q93+58.0712q95+1209.58q97+999.822q99+O(q100)q-7.69185 q^{3} -5.00000 q^{5} +16.0448 q^{7} +32.1646 q^{9} +31.0846 q^{11} +15.0566 q^{13} +38.4593 q^{15} -83.1924 q^{17} -11.6142 q^{19} -123.414 q^{21} -22.9471 q^{23} +25.0000 q^{25} -39.7251 q^{27} -29.0000 q^{29} +117.340 q^{31} -239.098 q^{33} -80.2241 q^{35} -126.486 q^{37} -115.813 q^{39} -500.344 q^{41} +5.84778 q^{43} -160.823 q^{45} +301.232 q^{47} -85.5639 q^{49} +639.903 q^{51} +31.2007 q^{53} -155.423 q^{55} +89.3350 q^{57} -31.3542 q^{59} +80.8436 q^{61} +516.074 q^{63} -75.2828 q^{65} +191.752 q^{67} +176.506 q^{69} -269.462 q^{71} +600.914 q^{73} -192.296 q^{75} +498.746 q^{77} -389.072 q^{79} -562.884 q^{81} +271.037 q^{83} +415.962 q^{85} +223.064 q^{87} -165.976 q^{89} +241.580 q^{91} -902.559 q^{93} +58.0712 q^{95} +1209.58 q^{97} +999.822 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+5q330q59q7+45q9+10q11+13q1325q1523q1710q1952q2175q23+150q25+116q27174q29+127q3172q33+45q35++2976q99+O(q100) 6 q + 5 q^{3} - 30 q^{5} - 9 q^{7} + 45 q^{9} + 10 q^{11} + 13 q^{13} - 25 q^{15} - 23 q^{17} - 10 q^{19} - 52 q^{21} - 75 q^{23} + 150 q^{25} + 116 q^{27} - 174 q^{29} + 127 q^{31} - 72 q^{33} + 45 q^{35}+ \cdots + 2976 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −7.69185 −1.48030 −0.740149 0.672443i 0.765245π-0.765245\pi
−0.740149 + 0.672443i 0.765245π0.765245\pi
44 0 0
55 −5.00000 −0.447214
66 0 0
77 16.0448 0.866339 0.433169 0.901313i 0.357395π-0.357395\pi
0.433169 + 0.901313i 0.357395π0.357395\pi
88 0 0
99 32.1646 1.19128
1010 0 0
1111 31.0846 0.852032 0.426016 0.904716i 0.359917π-0.359917\pi
0.426016 + 0.904716i 0.359917π0.359917\pi
1212 0 0
1313 15.0566 0.321226 0.160613 0.987017i 0.448653π-0.448653\pi
0.160613 + 0.987017i 0.448653π0.448653\pi
1414 0 0
1515 38.4593 0.662009
1616 0 0
1717 −83.1924 −1.18689 −0.593444 0.804875i 0.702232π-0.702232\pi
−0.593444 + 0.804875i 0.702232π0.702232\pi
1818 0 0
1919 −11.6142 −0.140236 −0.0701181 0.997539i 0.522338π-0.522338\pi
−0.0701181 + 0.997539i 0.522338π0.522338\pi
2020 0 0
2121 −123.414 −1.28244
2222 0 0
2323 −22.9471 −0.208035 −0.104018 0.994575i 0.533170π-0.533170\pi
−0.104018 + 0.994575i 0.533170π0.533170\pi
2424 0 0
2525 25.0000 0.200000
2626 0 0
2727 −39.7251 −0.283152
2828 0 0
2929 −29.0000 −0.185695
3030 0 0
3131 117.340 0.679833 0.339917 0.940456i 0.389601π-0.389601\pi
0.339917 + 0.940456i 0.389601π0.389601\pi
3232 0 0
3333 −239.098 −1.26126
3434 0 0
3535 −80.2241 −0.387438
3636 0 0
3737 −126.486 −0.562003 −0.281001 0.959707i 0.590667π-0.590667\pi
−0.281001 + 0.959707i 0.590667π0.590667\pi
3838 0 0
3939 −115.813 −0.475510
4040 0 0
4141 −500.344 −1.90587 −0.952935 0.303175i 0.901953π-0.901953\pi
−0.952935 + 0.303175i 0.901953π0.901953\pi
4242 0 0
4343 5.84778 0.0207390 0.0103695 0.999946i 0.496699π-0.496699\pi
0.0103695 + 0.999946i 0.496699π0.496699\pi
4444 0 0
4545 −160.823 −0.532757
4646 0 0
4747 301.232 0.934876 0.467438 0.884026i 0.345177π-0.345177\pi
0.467438 + 0.884026i 0.345177π0.345177\pi
4848 0 0
4949 −85.5639 −0.249458
5050 0 0
5151 639.903 1.75695
5252 0 0
5353 31.2007 0.0808632 0.0404316 0.999182i 0.487127π-0.487127\pi
0.0404316 + 0.999182i 0.487127π0.487127\pi
5454 0 0
5555 −155.423 −0.381040
5656 0 0
5757 89.3350 0.207591
5858 0 0
5959 −31.3542 −0.0691859 −0.0345930 0.999401i 0.511013π-0.511013\pi
−0.0345930 + 0.999401i 0.511013π0.511013\pi
6060 0 0
6161 80.8436 0.169688 0.0848440 0.996394i 0.472961π-0.472961\pi
0.0848440 + 0.996394i 0.472961π0.472961\pi
6262 0 0
6363 516.074 1.03205
6464 0 0
6565 −75.2828 −0.143657
6666 0 0
6767 191.752 0.349645 0.174822 0.984600i 0.444065π-0.444065\pi
0.174822 + 0.984600i 0.444065π0.444065\pi
6868 0 0
6969 176.506 0.307954
7070 0 0
7171 −269.462 −0.450412 −0.225206 0.974311i 0.572306π-0.572306\pi
−0.225206 + 0.974311i 0.572306π0.572306\pi
7272 0 0
7373 600.914 0.963447 0.481724 0.876323i 0.340011π-0.340011\pi
0.481724 + 0.876323i 0.340011π0.340011\pi
7474 0 0
7575 −192.296 −0.296059
7676 0 0
7777 498.746 0.738148
7878 0 0
7979 −389.072 −0.554101 −0.277050 0.960855i 0.589357π-0.589357\pi
−0.277050 + 0.960855i 0.589357π0.589357\pi
8080 0 0
8181 −562.884 −0.772132
8282 0 0
8383 271.037 0.358435 0.179218 0.983809i 0.442643π-0.442643\pi
0.179218 + 0.983809i 0.442643π0.442643\pi
8484 0 0
8585 415.962 0.530793
8686 0 0
8787 223.064 0.274884
8888 0 0
8989 −165.976 −0.197679 −0.0988397 0.995103i 0.531513π-0.531513\pi
−0.0988397 + 0.995103i 0.531513π0.531513\pi
9090 0 0
9191 241.580 0.278290
9292 0 0
9393 −902.559 −1.00636
9494 0 0
9595 58.0712 0.0627156
9696 0 0
9797 1209.58 1.26612 0.633061 0.774102i 0.281798π-0.281798\pi
0.633061 + 0.774102i 0.281798π0.281798\pi
9898 0 0
9999 999.822 1.01501
100100 0 0
101101 1545.49 1.52259 0.761295 0.648405i 0.224564π-0.224564\pi
0.761295 + 0.648405i 0.224564π0.224564\pi
102102 0 0
103103 378.011 0.361617 0.180808 0.983518i 0.442129π-0.442129\pi
0.180808 + 0.983518i 0.442129π0.442129\pi
104104 0 0
105105 617.072 0.573524
106106 0 0
107107 262.102 0.236807 0.118403 0.992966i 0.462222π-0.462222\pi
0.118403 + 0.992966i 0.462222π0.462222\pi
108108 0 0
109109 1337.54 1.17535 0.587676 0.809096i 0.300043π-0.300043\pi
0.587676 + 0.809096i 0.300043π0.300043\pi
110110 0 0
111111 972.908 0.831931
112112 0 0
113113 −501.976 −0.417893 −0.208947 0.977927i 0.567004π-0.567004\pi
−0.208947 + 0.977927i 0.567004π0.567004\pi
114114 0 0
115115 114.736 0.0930362
116116 0 0
117117 484.288 0.382670
118118 0 0
119119 −1334.81 −1.02825
120120 0 0
121121 −364.750 −0.274042
122122 0 0
123123 3848.57 2.82125
124124 0 0
125125 −125.000 −0.0894427
126126 0 0
127127 1572.60 1.09878 0.549392 0.835565i 0.314859π-0.314859\pi
0.549392 + 0.835565i 0.314859π0.314859\pi
128128 0 0
129129 −44.9802 −0.0306999
130130 0 0
131131 487.458 0.325110 0.162555 0.986700i 0.448027π-0.448027\pi
0.162555 + 0.986700i 0.448027π0.448027\pi
132132 0 0
133133 −186.348 −0.121492
134134 0 0
135135 198.625 0.126629
136136 0 0
137137 561.363 0.350076 0.175038 0.984562i 0.443995π-0.443995\pi
0.175038 + 0.984562i 0.443995π0.443995\pi
138138 0 0
139139 −527.373 −0.321807 −0.160904 0.986970i 0.551441π-0.551441\pi
−0.160904 + 0.986970i 0.551441π0.551441\pi
140140 0 0
141141 −2317.03 −1.38389
142142 0 0
143143 468.027 0.273695
144144 0 0
145145 145.000 0.0830455
146146 0 0
147147 658.145 0.369271
148148 0 0
149149 190.524 0.104754 0.0523768 0.998627i 0.483320π-0.483320\pi
0.0523768 + 0.998627i 0.483320π0.483320\pi
150150 0 0
151151 1056.81 0.569550 0.284775 0.958594i 0.408081π-0.408081\pi
0.284775 + 0.958594i 0.408081π0.408081\pi
152152 0 0
153153 −2675.85 −1.41392
154154 0 0
155155 −586.698 −0.304031
156156 0 0
157157 −708.890 −0.360354 −0.180177 0.983634i 0.557667π-0.557667\pi
−0.180177 + 0.983634i 0.557667π0.557667\pi
158158 0 0
159159 −239.991 −0.119702
160160 0 0
161161 −368.183 −0.180229
162162 0 0
163163 443.505 0.213116 0.106558 0.994306i 0.466017π-0.466017\pi
0.106558 + 0.994306i 0.466017π0.466017\pi
164164 0 0
165165 1195.49 0.564053
166166 0 0
167167 −3330.52 −1.54325 −0.771627 0.636075i 0.780557π-0.780557\pi
−0.771627 + 0.636075i 0.780557π0.780557\pi
168168 0 0
169169 −1970.30 −0.896814
170170 0 0
171171 −373.567 −0.167061
172172 0 0
173173 −2160.18 −0.949339 −0.474670 0.880164i 0.657432π-0.657432\pi
−0.474670 + 0.880164i 0.657432π0.657432\pi
174174 0 0
175175 401.120 0.173268
176176 0 0
177177 241.172 0.102416
178178 0 0
179179 108.508 0.0453087 0.0226544 0.999743i 0.492788π-0.492788\pi
0.0226544 + 0.999743i 0.492788π0.492788\pi
180180 0 0
181181 687.869 0.282480 0.141240 0.989975i 0.454891π-0.454891\pi
0.141240 + 0.989975i 0.454891π0.454891\pi
182182 0 0
183183 −621.837 −0.251189
184184 0 0
185185 632.428 0.251335
186186 0 0
187187 −2586.00 −1.01127
188188 0 0
189189 −637.381 −0.245305
190190 0 0
191191 −3943.02 −1.49375 −0.746877 0.664963i 0.768447π-0.768447\pi
−0.746877 + 0.664963i 0.768447π0.768447\pi
192192 0 0
193193 −3124.06 −1.16516 −0.582578 0.812775i 0.697956π-0.697956\pi
−0.582578 + 0.812775i 0.697956π0.697956\pi
194194 0 0
195195 579.064 0.212655
196196 0 0
197197 −2176.53 −0.787164 −0.393582 0.919290i 0.628764π-0.628764\pi
−0.393582 + 0.919290i 0.628764π0.628764\pi
198198 0 0
199199 1250.92 0.445604 0.222802 0.974864i 0.428480π-0.428480\pi
0.222802 + 0.974864i 0.428480π0.428480\pi
200200 0 0
201201 −1474.93 −0.517578
202202 0 0
203203 −465.300 −0.160875
204204 0 0
205205 2501.72 0.852331
206206 0 0
207207 −738.085 −0.247828
208208 0 0
209209 −361.024 −0.119486
210210 0 0
211211 −3838.31 −1.25232 −0.626162 0.779693i 0.715375π-0.715375\pi
−0.626162 + 0.779693i 0.715375π0.715375\pi
212212 0 0
213213 2072.66 0.666744
214214 0 0
215215 −29.2389 −0.00927477
216216 0 0
217217 1882.69 0.588966
218218 0 0
219219 −4622.14 −1.42619
220220 0 0
221221 −1252.59 −0.381260
222222 0 0
223223 −1723.40 −0.517521 −0.258761 0.965942i 0.583314π-0.583314\pi
−0.258761 + 0.965942i 0.583314π0.583314\pi
224224 0 0
225225 804.114 0.238256
226226 0 0
227227 3406.40 0.995995 0.497997 0.867179i 0.334069π-0.334069\pi
0.497997 + 0.867179i 0.334069π0.334069\pi
228228 0 0
229229 4538.85 1.30976 0.654881 0.755732i 0.272719π-0.272719\pi
0.654881 + 0.755732i 0.272719π0.272719\pi
230230 0 0
231231 −3836.28 −1.09268
232232 0 0
233233 414.870 0.116648 0.0583242 0.998298i 0.481424π-0.481424\pi
0.0583242 + 0.998298i 0.481424π0.481424\pi
234234 0 0
235235 −1506.16 −0.418089
236236 0 0
237237 2992.68 0.820234
238238 0 0
239239 1307.91 0.353982 0.176991 0.984212i 0.443364π-0.443364\pi
0.176991 + 0.984212i 0.443364π0.443364\pi
240240 0 0
241241 −3942.50 −1.05377 −0.526886 0.849936i 0.676641π-0.676641\pi
−0.526886 + 0.849936i 0.676641π0.676641\pi
242242 0 0
243243 5402.20 1.42614
244244 0 0
245245 427.820 0.111561
246246 0 0
247247 −174.870 −0.0450475
248248 0 0
249249 −2084.77 −0.530591
250250 0 0
251251 −921.189 −0.231653 −0.115827 0.993269i 0.536952π-0.536952\pi
−0.115827 + 0.993269i 0.536952π0.536952\pi
252252 0 0
253253 −713.302 −0.177253
254254 0 0
255255 −3199.52 −0.785731
256256 0 0
257257 −679.151 −0.164841 −0.0824207 0.996598i 0.526265π-0.526265\pi
−0.0824207 + 0.996598i 0.526265π0.526265\pi
258258 0 0
259259 −2029.44 −0.486885
260260 0 0
261261 −932.772 −0.221215
262262 0 0
263263 −5846.60 −1.37079 −0.685393 0.728173i 0.740370π-0.740370\pi
−0.685393 + 0.728173i 0.740370π0.740370\pi
264264 0 0
265265 −156.004 −0.0361631
266266 0 0
267267 1276.67 0.292624
268268 0 0
269269 −921.923 −0.208961 −0.104481 0.994527i 0.533318π-0.533318\pi
−0.104481 + 0.994527i 0.533318π0.533318\pi
270270 0 0
271271 −6533.88 −1.46459 −0.732297 0.680985i 0.761552π-0.761552\pi
−0.732297 + 0.680985i 0.761552π0.761552\pi
272272 0 0
273273 −1858.19 −0.411953
274274 0 0
275275 777.114 0.170406
276276 0 0
277277 6758.46 1.46598 0.732990 0.680239i 0.238124π-0.238124\pi
0.732990 + 0.680239i 0.238124π0.238124\pi
278278 0 0
279279 3774.18 0.809872
280280 0 0
281281 −9049.56 −1.92118 −0.960590 0.277970i 0.910338π-0.910338\pi
−0.960590 + 0.277970i 0.910338π0.910338\pi
282282 0 0
283283 −7660.93 −1.60917 −0.804585 0.593837i 0.797612π-0.797612\pi
−0.804585 + 0.593837i 0.797612π0.797612\pi
284284 0 0
285285 −446.675 −0.0928377
286286 0 0
287287 −8027.93 −1.65113
288288 0 0
289289 2007.97 0.408705
290290 0 0
291291 −9303.88 −1.87424
292292 0 0
293293 4977.90 0.992533 0.496267 0.868170i 0.334704π-0.334704\pi
0.496267 + 0.868170i 0.334704π0.334704\pi
294294 0 0
295295 156.771 0.0309409
296296 0 0
297297 −1234.84 −0.241254
298298 0 0
299299 −345.505 −0.0668263
300300 0 0
301301 93.8265 0.0179670
302302 0 0
303303 −11887.7 −2.25389
304304 0 0
305305 −404.218 −0.0758868
306306 0 0
307307 171.110 0.0318103 0.0159052 0.999874i 0.494937π-0.494937\pi
0.0159052 + 0.999874i 0.494937π0.494937\pi
308308 0 0
309309 −2907.60 −0.535300
310310 0 0
311311 3881.41 0.707700 0.353850 0.935302i 0.384872π-0.384872\pi
0.353850 + 0.935302i 0.384872π0.384872\pi
312312 0 0
313313 3578.45 0.646217 0.323108 0.946362i 0.395272π-0.395272\pi
0.323108 + 0.946362i 0.395272π0.395272\pi
314314 0 0
315315 −2580.37 −0.461548
316316 0 0
317317 4025.99 0.713319 0.356660 0.934234i 0.383916π-0.383916\pi
0.356660 + 0.934234i 0.383916π0.383916\pi
318318 0 0
319319 −901.452 −0.158218
320320 0 0
321321 −2016.05 −0.350544
322322 0 0
323323 966.216 0.166445
324324 0 0
325325 376.414 0.0642452
326326 0 0
327327 −10288.2 −1.73987
328328 0 0
329329 4833.21 0.809919
330330 0 0
331331 446.811 0.0741962 0.0370981 0.999312i 0.488189π-0.488189\pi
0.0370981 + 0.999312i 0.488189π0.488189\pi
332332 0 0
333333 −4068.35 −0.669503
334334 0 0
335335 −958.758 −0.156366
336336 0 0
337337 3235.03 0.522918 0.261459 0.965215i 0.415796π-0.415796\pi
0.261459 + 0.965215i 0.415796π0.415796\pi
338338 0 0
339339 3861.13 0.618607
340340 0 0
341341 3647.45 0.579240
342342 0 0
343343 −6876.23 −1.08245
344344 0 0
345345 −882.530 −0.137721
346346 0 0
347347 −3281.37 −0.507646 −0.253823 0.967251i 0.581688π-0.581688\pi
−0.253823 + 0.967251i 0.581688π0.581688\pi
348348 0 0
349349 −8576.39 −1.31543 −0.657713 0.753269i 0.728476π-0.728476\pi
−0.657713 + 0.753269i 0.728476π0.728476\pi
350350 0 0
351351 −598.123 −0.0909556
352352 0 0
353353 −12116.6 −1.82692 −0.913459 0.406931i 0.866599π-0.866599\pi
−0.913459 + 0.406931i 0.866599π0.866599\pi
354354 0 0
355355 1347.31 0.201431
356356 0 0
357357 10267.1 1.52211
358358 0 0
359359 8234.49 1.21058 0.605292 0.796004i 0.293056π-0.293056\pi
0.605292 + 0.796004i 0.293056π0.293056\pi
360360 0 0
361361 −6724.11 −0.980334
362362 0 0
363363 2805.60 0.405663
364364 0 0
365365 −3004.57 −0.430867
366366 0 0
367367 −6135.07 −0.872611 −0.436306 0.899799i 0.643713π-0.643713\pi
−0.436306 + 0.899799i 0.643713π0.643713\pi
368368 0 0
369369 −16093.4 −2.27042
370370 0 0
371371 500.610 0.0700549
372372 0 0
373373 5421.05 0.752524 0.376262 0.926513i 0.377209π-0.377209\pi
0.376262 + 0.926513i 0.377209π0.377209\pi
374374 0 0
375375 961.481 0.132402
376376 0 0
377377 −436.640 −0.0596502
378378 0 0
379379 13190.8 1.78777 0.893884 0.448298i 0.147969π-0.147969\pi
0.893884 + 0.448298i 0.147969π0.147969\pi
380380 0 0
381381 −12096.2 −1.62653
382382 0 0
383383 8801.65 1.17426 0.587132 0.809491i 0.300257π-0.300257\pi
0.587132 + 0.809491i 0.300257π0.300257\pi
384384 0 0
385385 −2493.73 −0.330110
386386 0 0
387387 188.091 0.0247060
388388 0 0
389389 −7098.28 −0.925185 −0.462593 0.886571i 0.653081π-0.653081\pi
−0.462593 + 0.886571i 0.653081π0.653081\pi
390390 0 0
391391 1909.03 0.246915
392392 0 0
393393 −3749.45 −0.481259
394394 0 0
395395 1945.36 0.247801
396396 0 0
397397 −983.121 −0.124286 −0.0621428 0.998067i 0.519793π-0.519793\pi
−0.0621428 + 0.998067i 0.519793π0.519793\pi
398398 0 0
399399 1433.36 0.179844
400400 0 0
401401 −11566.4 −1.44039 −0.720196 0.693771i 0.755948π-0.755948\pi
−0.720196 + 0.693771i 0.755948π0.755948\pi
402402 0 0
403403 1766.73 0.218380
404404 0 0
405405 2814.42 0.345308
406406 0 0
407407 −3931.75 −0.478844
408408 0 0
409409 −5076.95 −0.613787 −0.306893 0.951744i 0.599290π-0.599290\pi
−0.306893 + 0.951744i 0.599290π0.599290\pi
410410 0 0
411411 −4317.92 −0.518217
412412 0 0
413413 −503.072 −0.0599384
414414 0 0
415415 −1355.18 −0.160297
416416 0 0
417417 4056.48 0.476370
418418 0 0
419419 7054.26 0.822490 0.411245 0.911525i 0.365094π-0.365094\pi
0.411245 + 0.911525i 0.365094π0.365094\pi
420420 0 0
421421 −47.7238 −0.00552474 −0.00276237 0.999996i 0.500879π-0.500879\pi
−0.00276237 + 0.999996i 0.500879π0.500879\pi
422422 0 0
423423 9688.99 1.11370
424424 0 0
425425 −2079.81 −0.237378
426426 0 0
427427 1297.12 0.147007
428428 0 0
429429 −3599.99 −0.405150
430430 0 0
431431 −11596.3 −1.29600 −0.647999 0.761641i 0.724394π-0.724394\pi
−0.647999 + 0.761641i 0.724394π0.724394\pi
432432 0 0
433433 3017.20 0.334867 0.167434 0.985883i 0.446452π-0.446452\pi
0.167434 + 0.985883i 0.446452π0.446452\pi
434434 0 0
435435 −1115.32 −0.122932
436436 0 0
437437 266.514 0.0291741
438438 0 0
439439 2030.54 0.220757 0.110379 0.993890i 0.464794π-0.464794\pi
0.110379 + 0.993890i 0.464794π0.464794\pi
440440 0 0
441441 −2752.13 −0.297174
442442 0 0
443443 2622.89 0.281303 0.140652 0.990059i 0.455080π-0.455080\pi
0.140652 + 0.990059i 0.455080π0.455080\pi
444444 0 0
445445 829.882 0.0884049
446446 0 0
447447 −1465.48 −0.155067
448448 0 0
449449 −8289.68 −0.871301 −0.435651 0.900116i 0.643482π-0.643482\pi
−0.435651 + 0.900116i 0.643482π0.643482\pi
450450 0 0
451451 −15553.0 −1.62386
452452 0 0
453453 −8128.83 −0.843103
454454 0 0
455455 −1207.90 −0.124455
456456 0 0
457457 11291.3 1.15577 0.577885 0.816118i 0.303878π-0.303878\pi
0.577885 + 0.816118i 0.303878π0.303878\pi
458458 0 0
459459 3304.82 0.336069
460460 0 0
461461 −4292.63 −0.433683 −0.216841 0.976207i 0.569575π-0.569575\pi
−0.216841 + 0.976207i 0.569575π0.569575\pi
462462 0 0
463463 −4006.35 −0.402140 −0.201070 0.979577i 0.564442π-0.564442\pi
−0.201070 + 0.979577i 0.564442π0.564442\pi
464464 0 0
465465 4512.80 0.450056
466466 0 0
467467 −7220.10 −0.715432 −0.357716 0.933831i 0.616444π-0.616444\pi
−0.357716 + 0.933831i 0.616444π0.616444\pi
468468 0 0
469469 3076.62 0.302911
470470 0 0
471471 5452.67 0.533431
472472 0 0
473473 181.776 0.0176703
474474 0 0
475475 −290.356 −0.0280472
476476 0 0
477477 1003.56 0.0963307
478478 0 0
479479 16656.9 1.58888 0.794438 0.607346i 0.207766π-0.207766\pi
0.794438 + 0.607346i 0.207766π0.207766\pi
480480 0 0
481481 −1904.44 −0.180530
482482 0 0
483483 2832.01 0.266792
484484 0 0
485485 −6047.88 −0.566227
486486 0 0
487487 10289.5 0.957412 0.478706 0.877975i 0.341106π-0.341106\pi
0.478706 + 0.877975i 0.341106π0.341106\pi
488488 0 0
489489 −3411.37 −0.315475
490490 0 0
491491 −14263.3 −1.31099 −0.655493 0.755201i 0.727539π-0.727539\pi
−0.655493 + 0.755201i 0.727539π0.727539\pi
492492 0 0
493493 2412.58 0.220400
494494 0 0
495495 −4999.11 −0.453926
496496 0 0
497497 −4323.47 −0.390210
498498 0 0
499499 −1843.00 −0.165339 −0.0826693 0.996577i 0.526345π-0.526345\pi
−0.0826693 + 0.996577i 0.526345π0.526345\pi
500500 0 0
501501 25617.9 2.28448
502502 0 0
503503 4350.87 0.385678 0.192839 0.981230i 0.438231π-0.438231\pi
0.192839 + 0.981230i 0.438231π0.438231\pi
504504 0 0
505505 −7727.43 −0.680923
506506 0 0
507507 15155.3 1.32755
508508 0 0
509509 16783.1 1.46148 0.730742 0.682653i 0.239174π-0.239174\pi
0.730742 + 0.682653i 0.239174π0.239174\pi
510510 0 0
511511 9641.55 0.834671
512512 0 0
513513 461.376 0.0397081
514514 0 0
515515 −1890.06 −0.161720
516516 0 0
517517 9363.66 0.796544
518518 0 0
519519 16615.8 1.40530
520520 0 0
521521 −4014.47 −0.337576 −0.168788 0.985652i 0.553985π-0.553985\pi
−0.168788 + 0.985652i 0.553985π0.553985\pi
522522 0 0
523523 −15944.4 −1.33308 −0.666538 0.745471i 0.732225π-0.732225\pi
−0.666538 + 0.745471i 0.732225π0.732225\pi
524524 0 0
525525 −3085.36 −0.256488
526526 0 0
527527 −9761.76 −0.806886
528528 0 0
529529 −11640.4 −0.956721
530530 0 0
531531 −1008.49 −0.0824198
532532 0 0
533533 −7533.46 −0.612215
534534 0 0
535535 −1310.51 −0.105903
536536 0 0
537537 −834.627 −0.0670704
538538 0 0
539539 −2659.72 −0.212546
540540 0 0
541541 −20434.2 −1.62391 −0.811954 0.583721i 0.801596π-0.801596\pi
−0.811954 + 0.583721i 0.801596π0.801596\pi
542542 0 0
543543 −5290.99 −0.418155
544544 0 0
545545 −6687.72 −0.525634
546546 0 0
547547 −6626.20 −0.517945 −0.258973 0.965885i 0.583384π-0.583384\pi
−0.258973 + 0.965885i 0.583384π0.583384\pi
548548 0 0
549549 2600.30 0.202146
550550 0 0
551551 336.813 0.0260412
552552 0 0
553553 −6242.58 −0.480039
554554 0 0
555555 −4864.54 −0.372051
556556 0 0
557557 −10434.1 −0.793727 −0.396864 0.917878i 0.629901π-0.629901\pi
−0.396864 + 0.917878i 0.629901π0.629901\pi
558558 0 0
559559 88.0474 0.00666191
560560 0 0
561561 19891.1 1.49698
562562 0 0
563563 7846.64 0.587383 0.293691 0.955900i 0.405116π-0.405116\pi
0.293691 + 0.955900i 0.405116π0.405116\pi
564564 0 0
565565 2509.88 0.186888
566566 0 0
567567 −9031.37 −0.668927
568568 0 0
569569 −25122.3 −1.85093 −0.925465 0.378832i 0.876326π-0.876326\pi
−0.925465 + 0.378832i 0.876326π0.876326\pi
570570 0 0
571571 −11500.3 −0.842862 −0.421431 0.906861i 0.638472π-0.638472\pi
−0.421431 + 0.906861i 0.638472π0.638472\pi
572572 0 0
573573 30329.1 2.21120
574574 0 0
575575 −573.679 −0.0416071
576576 0 0
577577 −9164.70 −0.661233 −0.330617 0.943765i 0.607257π-0.607257\pi
−0.330617 + 0.943765i 0.607257π0.607257\pi
578578 0 0
579579 24029.8 1.72478
580580 0 0
581581 4348.73 0.310526
582582 0 0
583583 969.861 0.0688980
584584 0 0
585585 −2421.44 −0.171135
586586 0 0
587587 4624.15 0.325143 0.162572 0.986697i 0.448021π-0.448021\pi
0.162572 + 0.986697i 0.448021π0.448021\pi
588588 0 0
589589 −1362.81 −0.0953373
590590 0 0
591591 16741.5 1.16524
592592 0 0
593593 −17603.7 −1.21905 −0.609526 0.792766i 0.708640π-0.708640\pi
−0.609526 + 0.792766i 0.708640π0.708640\pi
594594 0 0
595595 6674.03 0.459846
596596 0 0
597597 −9621.86 −0.659626
598598 0 0
599599 −16865.8 −1.15044 −0.575222 0.817997i 0.695084π-0.695084\pi
−0.575222 + 0.817997i 0.695084π0.695084\pi
600600 0 0
601601 13746.3 0.932987 0.466494 0.884525i 0.345517π-0.345517\pi
0.466494 + 0.884525i 0.345517π0.345517\pi
602602 0 0
603603 6167.61 0.416525
604604 0 0
605605 1823.75 0.122555
606606 0 0
607607 9415.05 0.629564 0.314782 0.949164i 0.398069π-0.398069\pi
0.314782 + 0.949164i 0.398069π0.398069\pi
608608 0 0
609609 3579.02 0.238143
610610 0 0
611611 4535.52 0.300307
612612 0 0
613613 −11753.3 −0.774409 −0.387205 0.921994i 0.626559π-0.626559\pi
−0.387205 + 0.921994i 0.626559π0.626559\pi
614614 0 0
615615 −19242.9 −1.26170
616616 0 0
617617 11464.2 0.748027 0.374014 0.927423i 0.377981π-0.377981\pi
0.374014 + 0.927423i 0.377981π0.377981\pi
618618 0 0
619619 7416.72 0.481588 0.240794 0.970576i 0.422592π-0.422592\pi
0.240794 + 0.970576i 0.422592π0.422592\pi
620620 0 0
621621 911.577 0.0589055
622622 0 0
623623 −2663.06 −0.171257
624624 0 0
625625 625.000 0.0400000
626626 0 0
627627 2776.94 0.176874
628628 0 0
629629 10522.6 0.667035
630630 0 0
631631 13552.5 0.855020 0.427510 0.904011i 0.359391π-0.359391\pi
0.427510 + 0.904011i 0.359391π0.359391\pi
632632 0 0
633633 29523.7 1.85381
634634 0 0
635635 −7862.99 −0.491391
636636 0 0
637637 −1288.30 −0.0801322
638638 0 0
639639 −8667.13 −0.536567
640640 0 0
641641 −21456.3 −1.32211 −0.661055 0.750337i 0.729891π-0.729891\pi
−0.661055 + 0.750337i 0.729891π0.729891\pi
642642 0 0
643643 5794.95 0.355413 0.177706 0.984084i 0.443132π-0.443132\pi
0.177706 + 0.984084i 0.443132π0.443132\pi
644644 0 0
645645 224.901 0.0137294
646646 0 0
647647 13848.5 0.841486 0.420743 0.907180i 0.361769π-0.361769\pi
0.420743 + 0.907180i 0.361769π0.361769\pi
648648 0 0
649649 −974.632 −0.0589486
650650 0 0
651651 −14481.4 −0.871844
652652 0 0
653653 −7835.40 −0.469561 −0.234780 0.972048i 0.575437π-0.575437\pi
−0.234780 + 0.972048i 0.575437π0.575437\pi
654654 0 0
655655 −2437.29 −0.145394
656656 0 0
657657 19328.1 1.14774
658658 0 0
659659 −21053.2 −1.24449 −0.622243 0.782824i 0.713779π-0.713779\pi
−0.622243 + 0.782824i 0.713779π0.713779\pi
660660 0 0
661661 2587.65 0.152266 0.0761330 0.997098i 0.475743π-0.475743\pi
0.0761330 + 0.997098i 0.475743π0.475743\pi
662662 0 0
663663 9634.74 0.564377
664664 0 0
665665 931.741 0.0543329
666666 0 0
667667 665.467 0.0386312
668668 0 0
669669 13256.1 0.766085
670670 0 0
671671 2512.99 0.144580
672672 0 0
673673 20359.3 1.16611 0.583057 0.812431i 0.301856π-0.301856\pi
0.583057 + 0.812431i 0.301856π0.301856\pi
674674 0 0
675675 −993.127 −0.0566303
676676 0 0
677677 16020.3 0.909471 0.454736 0.890627i 0.349734π-0.349734\pi
0.454736 + 0.890627i 0.349734π0.349734\pi
678678 0 0
679679 19407.4 1.09689
680680 0 0
681681 −26201.5 −1.47437
682682 0 0
683683 11079.7 0.620722 0.310361 0.950619i 0.399550π-0.399550\pi
0.310361 + 0.950619i 0.399550π0.399550\pi
684684 0 0
685685 −2806.81 −0.156559
686686 0 0
687687 −34912.2 −1.93884
688688 0 0
689689 469.775 0.0259753
690690 0 0
691691 1573.50 0.0866265 0.0433133 0.999062i 0.486209π-0.486209\pi
0.0433133 + 0.999062i 0.486209π0.486209\pi
692692 0 0
693693 16042.0 0.879341
694694 0 0
695695 2636.87 0.143917
696696 0 0
697697 41624.8 2.26206
698698 0 0
699699 −3191.12 −0.172674
700700 0 0
701701 −28271.6 −1.52326 −0.761630 0.648012i 0.775600π-0.775600\pi
−0.761630 + 0.648012i 0.775600π0.775600\pi
702702 0 0
703703 1469.03 0.0788132
704704 0 0
705705 11585.2 0.618897
706706 0 0
707707 24797.0 1.31908
708708 0 0
709709 −14638.5 −0.775401 −0.387700 0.921785i 0.626730π-0.626730\pi
−0.387700 + 0.921785i 0.626730π0.626730\pi
710710 0 0
711711 −12514.3 −0.660089
712712 0 0
713713 −2692.61 −0.141429
714714 0 0
715715 −2340.13 −0.122400
716716 0 0
717717 −10060.3 −0.523999
718718 0 0
719719 2609.41 0.135347 0.0676735 0.997708i 0.478442π-0.478442\pi
0.0676735 + 0.997708i 0.478442π0.478442\pi
720720 0 0
721721 6065.12 0.313283
722722 0 0
723723 30325.2 1.55990
724724 0 0
725725 −725.000 −0.0371391
726726 0 0
727727 −8386.64 −0.427845 −0.213923 0.976851i 0.568624π-0.568624\pi
−0.213923 + 0.976851i 0.568624π0.568624\pi
728728 0 0
729729 −26355.0 −1.33897
730730 0 0
731731 −486.490 −0.0246149
732732 0 0
733733 29969.0 1.51014 0.755068 0.655646i 0.227604π-0.227604\pi
0.755068 + 0.655646i 0.227604π0.227604\pi
734734 0 0
735735 −3290.73 −0.165143
736736 0 0
737737 5960.52 0.297908
738738 0 0
739739 −908.616 −0.0452286 −0.0226143 0.999744i 0.507199π-0.507199\pi
−0.0226143 + 0.999744i 0.507199π0.507199\pi
740740 0 0
741741 1345.08 0.0666837
742742 0 0
743743 32141.4 1.58702 0.793508 0.608560i 0.208253π-0.208253\pi
0.793508 + 0.608560i 0.208253π0.208253\pi
744744 0 0
745745 −952.618 −0.0468473
746746 0 0
747747 8717.77 0.426997
748748 0 0
749749 4205.37 0.205155
750750 0 0
751751 −9075.10 −0.440952 −0.220476 0.975392i 0.570761π-0.570761\pi
−0.220476 + 0.975392i 0.570761π0.570761\pi
752752 0 0
753753 7085.65 0.342915
754754 0 0
755755 −5284.05 −0.254711
756756 0 0
757757 −28009.3 −1.34480 −0.672402 0.740187i 0.734737π-0.734737\pi
−0.672402 + 0.740187i 0.734737π0.734737\pi
758758 0 0
759759 5486.61 0.262387
760760 0 0
761761 −18706.3 −0.891066 −0.445533 0.895265i 0.646986π-0.646986\pi
−0.445533 + 0.895265i 0.646986π0.646986\pi
762762 0 0
763763 21460.6 1.01825
764764 0 0
765765 13379.2 0.632323
766766 0 0
767767 −472.086 −0.0222243
768768 0 0
769769 7774.27 0.364561 0.182280 0.983247i 0.441652π-0.441652\pi
0.182280 + 0.983247i 0.441652π0.441652\pi
770770 0 0
771771 5223.92 0.244014
772772 0 0
773773 −24000.1 −1.11672 −0.558359 0.829600i 0.688569π-0.688569\pi
−0.558359 + 0.829600i 0.688569π0.688569\pi
774774 0 0
775775 2933.49 0.135967
776776 0 0
777777 15610.1 0.720734
778778 0 0
779779 5811.12 0.267272
780780 0 0
781781 −8376.12 −0.383766
782782 0 0
783783 1152.03 0.0525799
784784 0 0
785785 3544.45 0.161155
786786 0 0
787787 −20749.3 −0.939814 −0.469907 0.882716i 0.655713π-0.655713\pi
−0.469907 + 0.882716i 0.655713π0.655713\pi
788788 0 0
789789 44971.2 2.02917
790790 0 0
791791 −8054.12 −0.362037
792792 0 0
793793 1217.23 0.0545082
794794 0 0
795795 1199.96 0.0535321
796796 0 0
797797 1546.40 0.0687282 0.0343641 0.999409i 0.489059π-0.489059\pi
0.0343641 + 0.999409i 0.489059π0.489059\pi
798798 0 0
799799 −25060.2 −1.10959
800800 0 0
801801 −5338.56 −0.235491
802802 0 0
803803 18679.1 0.820888
804804 0 0
805805 1840.91 0.0806008
806806 0 0
807807 7091.29 0.309325
808808 0 0
809809 14261.2 0.619773 0.309886 0.950774i 0.399709π-0.399709\pi
0.309886 + 0.950774i 0.399709π0.399709\pi
810810 0 0
811811 8098.05 0.350630 0.175315 0.984512i 0.443906π-0.443906\pi
0.175315 + 0.984512i 0.443906π0.443906\pi
812812 0 0
813813 50257.7 2.16804
814814 0 0
815815 −2217.52 −0.0953085
816816 0 0
817817 −67.9175 −0.00290836
818818 0 0
819819 7770.31 0.331522
820820 0 0
821821 −31734.9 −1.34903 −0.674517 0.738259i 0.735648π-0.735648\pi
−0.674517 + 0.738259i 0.735648π0.735648\pi
822822 0 0
823823 −9300.47 −0.393918 −0.196959 0.980412i 0.563107π-0.563107\pi
−0.196959 + 0.980412i 0.563107π0.563107\pi
824824 0 0
825825 −5977.45 −0.252252
826826 0 0
827827 19533.5 0.821338 0.410669 0.911784i 0.365295π-0.365295\pi
0.410669 + 0.911784i 0.365295π0.365295\pi
828828 0 0
829829 1108.39 0.0464366 0.0232183 0.999730i 0.492609π-0.492609\pi
0.0232183 + 0.999730i 0.492609π0.492609\pi
830830 0 0
831831 −51985.1 −2.17009
832832 0 0
833833 7118.27 0.296078
834834 0 0
835835 16652.6 0.690164
836836 0 0
837837 −4661.33 −0.192496
838838 0 0
839839 −40285.1 −1.65768 −0.828841 0.559484i 0.810999π-0.810999\pi
−0.828841 + 0.559484i 0.810999π0.810999\pi
840840 0 0
841841 841.000 0.0344828
842842 0 0
843843 69607.9 2.84392
844844 0 0
845845 9851.50 0.401067
846846 0 0
847847 −5852.34 −0.237413
848848 0 0
849849 58926.8 2.38205
850850 0 0
851851 2902.48 0.116916
852852 0 0
853853 −4959.80 −0.199086 −0.0995430 0.995033i 0.531738π-0.531738\pi
−0.0995430 + 0.995033i 0.531738π0.531738\pi
854854 0 0
855855 1867.83 0.0747118
856856 0 0
857857 2961.63 0.118048 0.0590241 0.998257i 0.481201π-0.481201\pi
0.0590241 + 0.998257i 0.481201π0.481201\pi
858858 0 0
859859 10657.4 0.423312 0.211656 0.977344i 0.432114π-0.432114\pi
0.211656 + 0.977344i 0.432114π0.432114\pi
860860 0 0
861861 61749.7 2.44416
862862 0 0
863863 −10244.1 −0.404072 −0.202036 0.979378i 0.564756π-0.564756\pi
−0.202036 + 0.979378i 0.564756π0.564756\pi
864864 0 0
865865 10800.9 0.424557
866866 0 0
867867 −15445.0 −0.605005
868868 0 0
869869 −12094.1 −0.472112
870870 0 0
871871 2887.12 0.112315
872872 0 0
873873 38905.5 1.50831
874874 0 0
875875 −2005.60 −0.0774877
876876 0 0
877877 −43671.7 −1.68151 −0.840757 0.541413i 0.817889π-0.817889\pi
−0.840757 + 0.541413i 0.817889π0.817889\pi
878878 0 0
879879 −38289.3 −1.46924
880880 0 0
881881 −37652.8 −1.43990 −0.719952 0.694024i 0.755836π-0.755836\pi
−0.719952 + 0.694024i 0.755836π0.755836\pi
882882 0 0
883883 26609.6 1.01414 0.507070 0.861905i 0.330728π-0.330728\pi
0.507070 + 0.861905i 0.330728π0.330728\pi
884884 0 0
885885 −1205.86 −0.0458017
886886 0 0
887887 49149.8 1.86053 0.930265 0.366889i 0.119577π-0.119577\pi
0.930265 + 0.366889i 0.119577π0.119577\pi
888888 0 0
889889 25232.1 0.951919
890890 0 0
891891 −17497.0 −0.657881
892892 0 0
893893 −3498.58 −0.131104
894894 0 0
895895 −542.540 −0.0202627
896896 0 0
897897 2657.57 0.0989228
898898 0 0
899899 −3402.85 −0.126242
900900 0 0
901901 −2595.66 −0.0959756
902902 0 0
903903 −721.700 −0.0265965
904904 0 0
905905 −3439.35 −0.126329
906906 0 0
907907 −36813.3 −1.34770 −0.673852 0.738867i 0.735361π-0.735361\pi
−0.673852 + 0.738867i 0.735361π0.735361\pi
908908 0 0
909909 49709.9 1.81383
910910 0 0
911911 −17126.7 −0.622868 −0.311434 0.950268i 0.600809π-0.600809\pi
−0.311434 + 0.950268i 0.600809π0.600809\pi
912912 0 0
913913 8425.05 0.305398
914914 0 0
915915 3109.18 0.112335
916916 0 0
917917 7821.17 0.281655
918918 0 0
919919 −30450.8 −1.09301 −0.546507 0.837455i 0.684043π-0.684043\pi
−0.546507 + 0.837455i 0.684043π0.684043\pi
920920 0 0
921921 −1316.15 −0.0470888
922922 0 0
923923 −4057.17 −0.144684
924924 0 0
925925 −3162.14 −0.112401
926926 0 0
927927 12158.6 0.430787
928928 0 0
929929 −19086.8 −0.674077 −0.337038 0.941491i 0.609425π-0.609425\pi
−0.337038 + 0.941491i 0.609425π0.609425\pi
930930 0 0
931931 993.760 0.0349830
932932 0 0
933933 −29855.3 −1.04761
934934 0 0
935935 12930.0 0.452252
936936 0 0
937937 17125.4 0.597079 0.298540 0.954397i 0.403500π-0.403500\pi
0.298540 + 0.954397i 0.403500π0.403500\pi
938938 0 0
939939 −27524.9 −0.956593
940940 0 0
941941 −34308.1 −1.18854 −0.594269 0.804267i 0.702558π-0.702558\pi
−0.594269 + 0.804267i 0.702558π0.702558\pi
942942 0 0
943943 11481.5 0.396488
944944 0 0
945945 3186.91 0.109704
946946 0 0
947947 4103.52 0.140809 0.0704046 0.997519i 0.477571π-0.477571\pi
0.0704046 + 0.997519i 0.477571π0.477571\pi
948948 0 0
949949 9047.69 0.309484
950950 0 0
951951 −30967.3 −1.05592
952952 0 0
953953 24975.5 0.848936 0.424468 0.905443i 0.360461π-0.360461\pi
0.424468 + 0.905443i 0.360461π0.360461\pi
954954 0 0
955955 19715.1 0.668027
956956 0 0
957957 6933.84 0.234210
958958 0 0
959959 9006.96 0.303285
960960 0 0
961961 −16022.4 −0.537827
962962 0 0
963963 8430.38 0.282103
964964 0 0
965965 15620.3 0.521073
966966 0 0
967967 −16482.8 −0.548140 −0.274070 0.961710i 0.588370π-0.588370\pi
−0.274070 + 0.961710i 0.588370π0.588370\pi
968968 0 0
969969 −7431.99 −0.246388
970970 0 0
971971 40016.5 1.32254 0.661272 0.750146i 0.270017π-0.270017\pi
0.661272 + 0.750146i 0.270017π0.270017\pi
972972 0 0
973973 −8461.60 −0.278794
974974 0 0
975975 −2895.32 −0.0951020
976976 0 0
977977 43518.5 1.42506 0.712529 0.701643i 0.247550π-0.247550\pi
0.712529 + 0.701643i 0.247550π0.247550\pi
978978 0 0
979979 −5159.30 −0.168429
980980 0 0
981981 43021.5 1.40017
982982 0 0
983983 −31243.2 −1.01374 −0.506869 0.862023i 0.669197π-0.669197\pi
−0.506869 + 0.862023i 0.669197π0.669197\pi
984984 0 0
985985 10882.6 0.352030
986986 0 0
987987 −37176.3 −1.19892
988988 0 0
989989 −134.190 −0.00431445
990990 0 0
991991 −20703.7 −0.663648 −0.331824 0.943341i 0.607664π-0.607664\pi
−0.331824 + 0.943341i 0.607664π0.607664\pi
992992 0 0
993993 −3436.80 −0.109832
994994 0 0
995995 −6254.58 −0.199280
996996 0 0
997997 57742.0 1.83421 0.917104 0.398647i 0.130520π-0.130520\pi
0.917104 + 0.398647i 0.130520π0.130520\pi
998998 0 0
999999 5024.65 0.159132
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 2320.4.a.o.1.1 6
4.3 odd 2 580.4.a.a.1.6 6
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.4.a.a.1.6 6 4.3 odd 2
2320.4.a.o.1.1 6 1.1 even 1 trivial