Properties

Label 4925.2.a.r.1.17
Level 49254925
Weight 22
Character 4925.1
Self dual yes
Analytic conductor 39.32639.326
Analytic rank 11
Dimension 4949
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] = [4925,2,Mod(1,4925)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(4925, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("4925.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 4925=52197 4925 = 5^{2} \cdot 197
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4925.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [49,-5,-22] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 39.326322995539.3263229955
Analytic rank: 11
Dimension: 4949
Twist minimal: no (minimal twist has level 985)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.17
Character χ\chi == 4925.1

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) == q1.27373q23.21433q30.377621q4+4.09418q6+0.234977q7+3.02844q8+7.33194q90.577101q11+1.21380q12+3.89397q130.299296q143.10216q163.49246q179.33888q18+7.16189q190.755293q21+0.735069q224.85751q239.73441q244.95986q2613.9243q270.0887321q28+8.44483q295.57555q312.10557q32+1.85499q33+4.44844q342.76869q365.18286q379.12229q3812.5165q39+4.90259q41+0.962037q423.12584q43+0.217925q44+6.18714q466.99306q47+9.97138q486.94479q49+11.2259q511.47045q52+12.1609q53+17.7357q54+0.711612q5623.0207q5710.7564q5814.3710q597.71724q61+7.10173q62+1.72283q63+8.88625q642.36276q662.57664q67+1.31883q68+15.6136q69+7.82253q71+22.2043q728.14734q73+6.60155q742.70448q760.135605q77+15.9426q780.388882q79+22.7615q816.24456q82+5.26069q83+0.285214q84+3.98147q8627.1445q871.74771q88+8.36693q89+0.914993q91+1.83430q92+17.9217q93+8.90725q94+6.76801q96+8.83287q97+8.84576q984.23127q99+O(q100)q-1.27373 q^{2} -3.21433 q^{3} -0.377621 q^{4} +4.09418 q^{6} +0.234977 q^{7} +3.02844 q^{8} +7.33194 q^{9} -0.577101 q^{11} +1.21380 q^{12} +3.89397 q^{13} -0.299296 q^{14} -3.10216 q^{16} -3.49246 q^{17} -9.33888 q^{18} +7.16189 q^{19} -0.755293 q^{21} +0.735069 q^{22} -4.85751 q^{23} -9.73441 q^{24} -4.95986 q^{26} -13.9243 q^{27} -0.0887321 q^{28} +8.44483 q^{29} -5.57555 q^{31} -2.10557 q^{32} +1.85499 q^{33} +4.44844 q^{34} -2.76869 q^{36} -5.18286 q^{37} -9.12229 q^{38} -12.5165 q^{39} +4.90259 q^{41} +0.962037 q^{42} -3.12584 q^{43} +0.217925 q^{44} +6.18714 q^{46} -6.99306 q^{47} +9.97138 q^{48} -6.94479 q^{49} +11.2259 q^{51} -1.47045 q^{52} +12.1609 q^{53} +17.7357 q^{54} +0.711612 q^{56} -23.0207 q^{57} -10.7564 q^{58} -14.3710 q^{59} -7.71724 q^{61} +7.10173 q^{62} +1.72283 q^{63} +8.88625 q^{64} -2.36276 q^{66} -2.57664 q^{67} +1.31883 q^{68} +15.6136 q^{69} +7.82253 q^{71} +22.2043 q^{72} -8.14734 q^{73} +6.60155 q^{74} -2.70448 q^{76} -0.135605 q^{77} +15.9426 q^{78} -0.388882 q^{79} +22.7615 q^{81} -6.24456 q^{82} +5.26069 q^{83} +0.285214 q^{84} +3.98147 q^{86} -27.1445 q^{87} -1.74771 q^{88} +8.36693 q^{89} +0.914993 q^{91} +1.83430 q^{92} +17.9217 q^{93} +8.90725 q^{94} +6.76801 q^{96} +8.83287 q^{97} +8.84576 q^{98} -4.23127 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 49q5q222q3+49q4+2q632q715q8+51q92q1144q1232q138q14+49q1614q1725q18+4q19+10q2138q2224q23++22q99+O(q100) 49 q - 5 q^{2} - 22 q^{3} + 49 q^{4} + 2 q^{6} - 32 q^{7} - 15 q^{8} + 51 q^{9} - 2 q^{11} - 44 q^{12} - 32 q^{13} - 8 q^{14} + 49 q^{16} - 14 q^{17} - 25 q^{18} + 4 q^{19} + 10 q^{21} - 38 q^{22} - 24 q^{23}+ \cdots + 22 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 −1.27373 −0.900661 −0.450330 0.892862i 0.648694π-0.648694\pi
−0.450330 + 0.892862i 0.648694π0.648694\pi
33 −3.21433 −1.85580 −0.927898 0.372834i 0.878386π-0.878386\pi
−0.927898 + 0.372834i 0.878386π0.878386\pi
44 −0.377621 −0.188810
55 0 0
66 4.09418 1.67144
77 0.234977 0.0888128 0.0444064 0.999014i 0.485860π-0.485860\pi
0.0444064 + 0.999014i 0.485860π0.485860\pi
88 3.02844 1.07071
99 7.33194 2.44398
1010 0 0
1111 −0.577101 −0.174002 −0.0870012 0.996208i 0.527728π-0.527728\pi
−0.0870012 + 0.996208i 0.527728π0.527728\pi
1212 1.21380 0.350394
1313 3.89397 1.07999 0.539997 0.841667i 0.318425π-0.318425\pi
0.539997 + 0.841667i 0.318425π0.318425\pi
1414 −0.299296 −0.0799902
1515 0 0
1616 −3.10216 −0.775540
1717 −3.49246 −0.847047 −0.423523 0.905885i 0.639207π-0.639207\pi
−0.423523 + 0.905885i 0.639207π0.639207\pi
1818 −9.33888 −2.20120
1919 7.16189 1.64305 0.821525 0.570173i 0.193124π-0.193124\pi
0.821525 + 0.570173i 0.193124π0.193124\pi
2020 0 0
2121 −0.755293 −0.164818
2222 0.735069 0.156717
2323 −4.85751 −1.01286 −0.506430 0.862281i 0.669035π-0.669035\pi
−0.506430 + 0.862281i 0.669035π0.669035\pi
2424 −9.73441 −1.98703
2525 0 0
2626 −4.95986 −0.972708
2727 −13.9243 −2.67973
2828 −0.0887321 −0.0167688
2929 8.44483 1.56817 0.784083 0.620656i 0.213134π-0.213134\pi
0.784083 + 0.620656i 0.213134π0.213134\pi
3030 0 0
3131 −5.57555 −1.00140 −0.500699 0.865621i 0.666924π-0.666924\pi
−0.500699 + 0.865621i 0.666924π0.666924\pi
3232 −2.10557 −0.372216
3333 1.85499 0.322913
3434 4.44844 0.762901
3535 0 0
3636 −2.76869 −0.461449
3737 −5.18286 −0.852057 −0.426028 0.904710i 0.640088π-0.640088\pi
−0.426028 + 0.904710i 0.640088π0.640088\pi
3838 −9.12229 −1.47983
3939 −12.5165 −2.00425
4040 0 0
4141 4.90259 0.765656 0.382828 0.923820i 0.374950π-0.374950\pi
0.382828 + 0.923820i 0.374950π0.374950\pi
4242 0.962037 0.148446
4343 −3.12584 −0.476686 −0.238343 0.971181i 0.576604π-0.576604\pi
−0.238343 + 0.971181i 0.576604π0.576604\pi
4444 0.217925 0.0328535
4545 0 0
4646 6.18714 0.912243
4747 −6.99306 −1.02004 −0.510021 0.860162i 0.670363π-0.670363\pi
−0.510021 + 0.860162i 0.670363π0.670363\pi
4848 9.97138 1.43924
4949 −6.94479 −0.992112
5050 0 0
5151 11.2259 1.57195
5252 −1.47045 −0.203914
5353 12.1609 1.67042 0.835212 0.549929i 0.185345π-0.185345\pi
0.835212 + 0.549929i 0.185345π0.185345\pi
5454 17.7357 2.41353
5555 0 0
5656 0.711612 0.0950932
5757 −23.0207 −3.04917
5858 −10.7564 −1.41239
5959 −14.3710 −1.87095 −0.935475 0.353393i 0.885028π-0.885028\pi
−0.935475 + 0.353393i 0.885028π0.885028\pi
6060 0 0
6161 −7.71724 −0.988092 −0.494046 0.869436i 0.664482π-0.664482\pi
−0.494046 + 0.869436i 0.664482π0.664482\pi
6262 7.10173 0.901920
6363 1.72283 0.217057
6464 8.88625 1.11078
6565 0 0
6666 −2.36276 −0.290835
6767 −2.57664 −0.314787 −0.157393 0.987536i 0.550309π-0.550309\pi
−0.157393 + 0.987536i 0.550309π0.550309\pi
6868 1.31883 0.159931
6969 15.6136 1.87966
7070 0 0
7171 7.82253 0.928363 0.464182 0.885740i 0.346348π-0.346348\pi
0.464182 + 0.885740i 0.346348π0.346348\pi
7272 22.2043 2.61680
7373 −8.14734 −0.953574 −0.476787 0.879019i 0.658199π-0.658199\pi
−0.476787 + 0.879019i 0.658199π0.658199\pi
7474 6.60155 0.767414
7575 0 0
7676 −2.70448 −0.310225
7777 −0.135605 −0.0154537
7878 15.9426 1.80515
7979 −0.388882 −0.0437526 −0.0218763 0.999761i 0.506964π-0.506964\pi
−0.0218763 + 0.999761i 0.506964π0.506964\pi
8080 0 0
8181 22.7615 2.52906
8282 −6.24456 −0.689597
8383 5.26069 0.577436 0.288718 0.957414i 0.406771π-0.406771\pi
0.288718 + 0.957414i 0.406771π0.406771\pi
8484 0.285214 0.0311195
8585 0 0
8686 3.98147 0.429333
8787 −27.1445 −2.91020
8888 −1.74771 −0.186307
8989 8.36693 0.886893 0.443446 0.896301i 0.353756π-0.353756\pi
0.443446 + 0.896301i 0.353756π0.353756\pi
9090 0 0
9191 0.914993 0.0959173
9292 1.83430 0.191239
9393 17.9217 1.85839
9494 8.90725 0.918712
9595 0 0
9696 6.76801 0.690757
9797 8.83287 0.896842 0.448421 0.893822i 0.351987π-0.351987\pi
0.448421 + 0.893822i 0.351987π0.351987\pi
9898 8.84576 0.893556
9999 −4.23127 −0.425258
100100 0 0
101101 1.70238 0.169393 0.0846967 0.996407i 0.473008π-0.473008\pi
0.0846967 + 0.996407i 0.473008π0.473008\pi
102102 −14.2988 −1.41579
103103 −2.80970 −0.276848 −0.138424 0.990373i 0.544204π-0.544204\pi
−0.138424 + 0.990373i 0.544204π0.544204\pi
104104 11.7927 1.15637
105105 0 0
106106 −15.4896 −1.50448
107107 −6.50076 −0.628452 −0.314226 0.949348i 0.601745π-0.601745\pi
−0.314226 + 0.949348i 0.601745π0.601745\pi
108108 5.25810 0.505961
109109 11.9904 1.14847 0.574236 0.818690i 0.305299π-0.305299\pi
0.574236 + 0.818690i 0.305299π0.305299\pi
110110 0 0
111111 16.6594 1.58124
112112 −0.728935 −0.0688779
113113 −9.74277 −0.916522 −0.458261 0.888818i 0.651528π-0.651528\pi
−0.458261 + 0.888818i 0.651528π0.651528\pi
114114 29.3221 2.74626
115115 0 0
116116 −3.18895 −0.296086
117117 28.5504 2.63948
118118 18.3048 1.68509
119119 −0.820647 −0.0752286
120120 0 0
121121 −10.6670 −0.969723
122122 9.82965 0.889935
123123 −15.7586 −1.42090
124124 2.10544 0.189075
125125 0 0
126126 −2.19442 −0.195494
127127 10.3084 0.914723 0.457361 0.889281i 0.348795π-0.348795\pi
0.457361 + 0.889281i 0.348795π0.348795\pi
128128 −7.10750 −0.628220
129129 10.0475 0.884633
130130 0 0
131131 19.5189 1.70537 0.852686 0.522423i 0.174972π-0.174972\pi
0.852686 + 0.522423i 0.174972π0.174972\pi
132132 −0.700485 −0.0609694
133133 1.68288 0.145924
134134 3.28193 0.283516
135135 0 0
136136 −10.5767 −0.906945
137137 3.03314 0.259139 0.129569 0.991570i 0.458641π-0.458641\pi
0.129569 + 0.991570i 0.458641π0.458641\pi
138138 −19.8875 −1.69294
139139 2.29531 0.194686 0.0973428 0.995251i 0.468966π-0.468966\pi
0.0973428 + 0.995251i 0.468966π0.468966\pi
140140 0 0
141141 22.4780 1.89299
142142 −9.96376 −0.836140
143143 −2.24722 −0.187922
144144 −22.7448 −1.89540
145145 0 0
146146 10.3775 0.858847
147147 22.3229 1.84116
148148 1.95716 0.160877
149149 12.8336 1.05137 0.525685 0.850679i 0.323809π-0.323809\pi
0.525685 + 0.850679i 0.323809π0.323809\pi
150150 0 0
151151 −4.69271 −0.381887 −0.190944 0.981601i 0.561155π-0.561155\pi
−0.190944 + 0.981601i 0.561155π0.561155\pi
152152 21.6893 1.75924
153153 −25.6065 −2.07016
154154 0.172724 0.0139185
155155 0 0
156156 4.72650 0.378423
157157 3.54513 0.282933 0.141466 0.989943i 0.454818π-0.454818\pi
0.141466 + 0.989943i 0.454818π0.454818\pi
158158 0.495329 0.0394063
159159 −39.0891 −3.09997
160160 0 0
161161 −1.14140 −0.0899550
162162 −28.9919 −2.27782
163163 2.45347 0.192171 0.0960853 0.995373i 0.469368π-0.469368\pi
0.0960853 + 0.995373i 0.469368π0.469368\pi
164164 −1.85132 −0.144564
165165 0 0
166166 −6.70068 −0.520074
167167 −6.34224 −0.490777 −0.245389 0.969425i 0.578916π-0.578916\pi
−0.245389 + 0.969425i 0.578916π0.578916\pi
168168 −2.28736 −0.176474
169169 2.16303 0.166387
170170 0 0
171171 52.5105 4.01558
172172 1.18038 0.0900034
173173 −7.16447 −0.544705 −0.272352 0.962198i 0.587802π-0.587802\pi
−0.272352 + 0.962198i 0.587802π0.587802\pi
174174 34.5747 2.62110
175175 0 0
176176 1.79026 0.134946
177177 46.1933 3.47210
178178 −10.6572 −0.798790
179179 −7.39749 −0.552914 −0.276457 0.961026i 0.589160π-0.589160\pi
−0.276457 + 0.961026i 0.589160π0.589160\pi
180180 0 0
181181 −20.1924 −1.50089 −0.750445 0.660933i 0.770161π-0.770161\pi
−0.750445 + 0.660933i 0.770161π0.770161\pi
182182 −1.16545 −0.0863889
183183 24.8058 1.83370
184184 −14.7107 −1.08448
185185 0 0
186186 −22.8273 −1.67378
187187 2.01550 0.147388
188188 2.64073 0.192595
189189 −3.27188 −0.237994
190190 0 0
191191 −20.5634 −1.48791 −0.743957 0.668227i 0.767053π-0.767053\pi
−0.743957 + 0.668227i 0.767053π0.767053\pi
192192 −28.5634 −2.06138
193193 −2.68844 −0.193518 −0.0967591 0.995308i 0.530848π-0.530848\pi
−0.0967591 + 0.995308i 0.530848π0.530848\pi
194194 −11.2507 −0.807750
195195 0 0
196196 2.62250 0.187321
197197 1.00000 0.0712470
198198 5.38948 0.383014
199199 −5.33760 −0.378373 −0.189186 0.981941i 0.560585π-0.560585\pi
−0.189186 + 0.981941i 0.560585π0.560585\pi
200200 0 0
201201 8.28218 0.584180
202202 −2.16837 −0.152566
203203 1.98434 0.139273
204204 −4.23915 −0.296800
205205 0 0
206206 3.57878 0.249346
207207 −35.6149 −2.47541
208208 −12.0797 −0.837579
209209 −4.13313 −0.285895
210210 0 0
211211 −27.4653 −1.89079 −0.945395 0.325927i 0.894324π-0.894324\pi
−0.945395 + 0.325927i 0.894324π0.894324\pi
212212 −4.59220 −0.315393
213213 −25.1442 −1.72285
214214 8.28019 0.566022
215215 0 0
216216 −42.1689 −2.86923
217217 −1.31012 −0.0889370
218218 −15.2725 −1.03438
219219 26.1883 1.76964
220220 0 0
221221 −13.5996 −0.914805
222222 −21.2196 −1.42416
223223 24.1738 1.61880 0.809399 0.587260i 0.199793π-0.199793\pi
0.809399 + 0.587260i 0.199793π0.199793\pi
224224 −0.494760 −0.0330576
225225 0 0
226226 12.4096 0.825476
227227 17.8340 1.18368 0.591842 0.806054i 0.298401π-0.298401\pi
0.591842 + 0.806054i 0.298401π0.298401\pi
228228 8.69309 0.575714
229229 −26.4544 −1.74816 −0.874079 0.485784i 0.838534π-0.838534\pi
−0.874079 + 0.485784i 0.838534π0.838534\pi
230230 0 0
231231 0.435880 0.0286788
232232 25.5747 1.67906
233233 30.1629 1.97604 0.988019 0.154335i 0.0493235π-0.0493235\pi
0.988019 + 0.154335i 0.0493235π0.0493235\pi
234234 −36.3654 −2.37728
235235 0 0
236236 5.42680 0.353255
237237 1.25000 0.0811959
238238 1.04528 0.0677554
239239 4.58904 0.296840 0.148420 0.988924i 0.452581π-0.452581\pi
0.148420 + 0.988924i 0.452581π0.452581\pi
240240 0 0
241241 23.5615 1.51773 0.758864 0.651249i 0.225755π-0.225755\pi
0.758864 + 0.651249i 0.225755π0.225755\pi
242242 13.5868 0.873391
243243 −31.3902 −2.01368
244244 2.91419 0.186562
245245 0 0
246246 20.0721 1.27975
247247 27.8882 1.77448
248248 −16.8852 −1.07221
249249 −16.9096 −1.07160
250250 0 0
251251 12.0057 0.757794 0.378897 0.925439i 0.376304π-0.376304\pi
0.378897 + 0.925439i 0.376304π0.376304\pi
252252 −0.650578 −0.0409826
253253 2.80327 0.176240
254254 −13.1301 −0.823855
255255 0 0
256256 −8.71948 −0.544967
257257 −14.1205 −0.880812 −0.440406 0.897799i 0.645165π-0.645165\pi
−0.440406 + 0.897799i 0.645165π0.645165\pi
258258 −12.7978 −0.796754
259259 −1.21785 −0.0756736
260260 0 0
261261 61.9170 3.83257
262262 −24.8617 −1.53596
263263 10.3347 0.637268 0.318634 0.947878i 0.396776π-0.396776\pi
0.318634 + 0.947878i 0.396776π0.396776\pi
264264 5.61774 0.345748
265265 0 0
266266 −2.14352 −0.131428
267267 −26.8941 −1.64589
268268 0.972993 0.0594350
269269 −15.0254 −0.916112 −0.458056 0.888923i 0.651454π-0.651454\pi
−0.458056 + 0.888923i 0.651454π0.651454\pi
270270 0 0
271271 −3.06893 −0.186424 −0.0932120 0.995646i 0.529713π-0.529713\pi
−0.0932120 + 0.995646i 0.529713π0.529713\pi
272272 10.8342 0.656919
273273 −2.94109 −0.178003
274274 −3.86339 −0.233396
275275 0 0
276276 −5.89604 −0.354900
277277 −32.3023 −1.94086 −0.970429 0.241385i 0.922398π-0.922398\pi
−0.970429 + 0.241385i 0.922398π0.922398\pi
278278 −2.92360 −0.175346
279279 −40.8796 −2.44740
280280 0 0
281281 −29.3552 −1.75118 −0.875592 0.483052i 0.839528π-0.839528\pi
−0.875592 + 0.483052i 0.839528π0.839528\pi
282282 −28.6309 −1.70494
283283 −15.3472 −0.912298 −0.456149 0.889903i 0.650772π-0.650772\pi
−0.456149 + 0.889903i 0.650772π0.650772\pi
284284 −2.95395 −0.175285
285285 0 0
286286 2.86234 0.169254
287287 1.15200 0.0680001
288288 −15.4379 −0.909689
289289 −4.80271 −0.282512
290290 0 0
291291 −28.3918 −1.66436
292292 3.07661 0.180045
293293 25.7169 1.50240 0.751199 0.660075i 0.229476π-0.229476\pi
0.751199 + 0.660075i 0.229476π0.229476\pi
294294 −28.4332 −1.65826
295295 0 0
296296 −15.6960 −0.912310
297297 8.03572 0.466280
298298 −16.3465 −0.946928
299299 −18.9150 −1.09388
300300 0 0
301301 −0.734500 −0.0423359
302302 5.97723 0.343951
303303 −5.47202 −0.314360
304304 −22.2173 −1.27425
305305 0 0
306306 32.6157 1.86452
307307 2.60692 0.148785 0.0743924 0.997229i 0.476298π-0.476298\pi
0.0743924 + 0.997229i 0.476298π0.476298\pi
308308 0.0512074 0.00291781
309309 9.03130 0.513773
310310 0 0
311311 −19.8431 −1.12520 −0.562599 0.826730i 0.690199π-0.690199\pi
−0.562599 + 0.826730i 0.690199π0.690199\pi
312312 −37.9055 −2.14598
313313 −18.1393 −1.02529 −0.512647 0.858599i 0.671335π-0.671335\pi
−0.512647 + 0.858599i 0.671335π0.671335\pi
314314 −4.51553 −0.254826
315315 0 0
316316 0.146850 0.00826095
317317 5.29542 0.297420 0.148710 0.988881i 0.452488π-0.452488\pi
0.148710 + 0.988881i 0.452488π0.452488\pi
318318 49.7888 2.79202
319319 −4.87352 −0.272865
320320 0 0
321321 20.8956 1.16628
322322 1.45383 0.0810189
323323 −25.0126 −1.39174
324324 −8.59522 −0.477512
325325 0 0
326326 −3.12505 −0.173081
327327 −38.5412 −2.13133
328328 14.8472 0.819800
329329 −1.64321 −0.0905929
330330 0 0
331331 29.2462 1.60752 0.803760 0.594954i 0.202830π-0.202830\pi
0.803760 + 0.594954i 0.202830π0.202830\pi
332332 −1.98655 −0.109026
333333 −38.0004 −2.08241
334334 8.07828 0.442024
335335 0 0
336336 2.34304 0.127823
337337 23.6870 1.29031 0.645156 0.764051i 0.276793π-0.276793\pi
0.645156 + 0.764051i 0.276793π0.276793\pi
338338 −2.75511 −0.149858
339339 31.3165 1.70088
340340 0 0
341341 3.21766 0.174246
342342 −66.8840 −3.61667
343343 −3.27670 −0.176925
344344 −9.46642 −0.510395
345345 0 0
346346 9.12558 0.490594
347347 −7.92141 −0.425244 −0.212622 0.977135i 0.568200π-0.568200\pi
−0.212622 + 0.977135i 0.568200π0.568200\pi
348348 10.2503 0.549475
349349 −25.6673 −1.37394 −0.686969 0.726687i 0.741059π-0.741059\pi
−0.686969 + 0.726687i 0.741059π0.741059\pi
350350 0 0
351351 −54.2208 −2.89409
352352 1.21513 0.0647665
353353 −13.2644 −0.705995 −0.352997 0.935624i 0.614838π-0.614838\pi
−0.352997 + 0.935624i 0.614838π0.614838\pi
354354 −58.8376 −3.12718
355355 0 0
356356 −3.15953 −0.167455
357357 2.63783 0.139609
358358 9.42238 0.497988
359359 −5.67509 −0.299520 −0.149760 0.988722i 0.547850π-0.547850\pi
−0.149760 + 0.988722i 0.547850π0.547850\pi
360360 0 0
361361 32.2926 1.69961
362362 25.7196 1.35179
363363 34.2871 1.79961
364364 −0.345520 −0.0181102
365365 0 0
366366 −31.5958 −1.65154
367367 −18.8576 −0.984361 −0.492180 0.870493i 0.663800π-0.663800\pi
−0.492180 + 0.870493i 0.663800π0.663800\pi
368368 15.0688 0.785514
369369 35.9455 1.87125
370370 0 0
371371 2.85752 0.148355
372372 −6.76760 −0.350884
373373 22.6052 1.17045 0.585226 0.810870i 0.301006π-0.301006\pi
0.585226 + 0.810870i 0.301006π0.301006\pi
374374 −2.56720 −0.132747
375375 0 0
376376 −21.1781 −1.09217
377377 32.8840 1.69361
378378 4.16748 0.214352
379379 −13.2151 −0.678815 −0.339408 0.940639i 0.610227π-0.610227\pi
−0.339408 + 0.940639i 0.610227π0.610227\pi
380380 0 0
381381 −33.1346 −1.69754
382382 26.1921 1.34011
383383 −9.06658 −0.463281 −0.231640 0.972801i 0.574409π-0.574409\pi
−0.231640 + 0.972801i 0.574409π0.574409\pi
384384 22.8459 1.16585
385385 0 0
386386 3.42434 0.174294
387387 −22.9185 −1.16501
388388 −3.33548 −0.169333
389389 24.1714 1.22554 0.612768 0.790263i 0.290056π-0.290056\pi
0.612768 + 0.790263i 0.290056π0.290056\pi
390390 0 0
391391 16.9647 0.857940
392392 −21.0319 −1.06227
393393 −62.7402 −3.16482
394394 −1.27373 −0.0641694
395395 0 0
396396 1.59782 0.0802932
397397 −10.7768 −0.540870 −0.270435 0.962738i 0.587167π-0.587167\pi
−0.270435 + 0.962738i 0.587167π0.587167\pi
398398 6.79865 0.340785
399399 −5.40933 −0.270805
400400 0 0
401401 0.512588 0.0255974 0.0127987 0.999918i 0.495926π-0.495926\pi
0.0127987 + 0.999918i 0.495926π0.495926\pi
402402 −10.5492 −0.526148
403403 −21.7111 −1.08150
404404 −0.642855 −0.0319832
405405 0 0
406406 −2.52750 −0.125438
407407 2.99103 0.148260
408408 33.9971 1.68311
409409 29.1701 1.44237 0.721183 0.692744i 0.243598π-0.243598\pi
0.721183 + 0.692744i 0.243598π0.243598\pi
410410 0 0
411411 −9.74953 −0.480909
412412 1.06100 0.0522717
413413 −3.37686 −0.166164
414414 45.3637 2.22950
415415 0 0
416416 −8.19905 −0.401991
417417 −7.37789 −0.361297
418418 5.26448 0.257494
419419 −7.18784 −0.351149 −0.175574 0.984466i 0.556178π-0.556178\pi
−0.175574 + 0.984466i 0.556178π0.556178\pi
420420 0 0
421421 16.3859 0.798598 0.399299 0.916821i 0.369254π-0.369254\pi
0.399299 + 0.916821i 0.369254π0.369254\pi
422422 34.9833 1.70296
423423 −51.2727 −2.49296
424424 36.8284 1.78855
425425 0 0
426426 32.0268 1.55171
427427 −1.81337 −0.0877552
428428 2.45482 0.118658
429429 7.22330 0.348744
430430 0 0
431431 −24.6531 −1.18750 −0.593750 0.804650i 0.702353π-0.702353\pi
−0.593750 + 0.804650i 0.702353π0.702353\pi
432432 43.1954 2.07824
433433 16.5810 0.796831 0.398415 0.917205i 0.369560π-0.369560\pi
0.398415 + 0.917205i 0.369560π0.369560\pi
434434 1.66874 0.0801021
435435 0 0
436436 −4.52783 −0.216844
437437 −34.7889 −1.66418
438438 −33.3567 −1.59384
439439 14.3127 0.683110 0.341555 0.939862i 0.389046π-0.389046\pi
0.341555 + 0.939862i 0.389046π0.389046\pi
440440 0 0
441441 −50.9187 −2.42470
442442 17.3221 0.823929
443443 −1.91828 −0.0911403 −0.0455702 0.998961i 0.514510π-0.514510\pi
−0.0455702 + 0.998961i 0.514510π0.514510\pi
444444 −6.29095 −0.298555
445445 0 0
446446 −30.7908 −1.45799
447447 −41.2515 −1.95113
448448 2.08806 0.0986516
449449 21.6287 1.02072 0.510360 0.859961i 0.329512π-0.329512\pi
0.510360 + 0.859961i 0.329512π0.329512\pi
450450 0 0
451451 −2.82929 −0.133226
452452 3.67907 0.173049
453453 15.0839 0.708705
454454 −22.7157 −1.06610
455455 0 0
456456 −69.7168 −3.26479
457457 −19.6638 −0.919835 −0.459917 0.887962i 0.652121π-0.652121\pi
−0.459917 + 0.887962i 0.652121π0.652121\pi
458458 33.6957 1.57450
459459 48.6301 2.26986
460460 0 0
461461 10.3420 0.481676 0.240838 0.970565i 0.422578π-0.422578\pi
0.240838 + 0.970565i 0.422578π0.422578\pi
462462 −0.555192 −0.0258299
463463 10.9518 0.508973 0.254486 0.967076i 0.418094π-0.418094\pi
0.254486 + 0.967076i 0.418094π0.418094\pi
464464 −26.1972 −1.21618
465465 0 0
466466 −38.4193 −1.77974
467467 −20.9307 −0.968556 −0.484278 0.874914i 0.660918π-0.660918\pi
−0.484278 + 0.874914i 0.660918π0.660918\pi
468468 −10.7812 −0.498362
469469 −0.605450 −0.0279571
470470 0 0
471471 −11.3952 −0.525065
472472 −43.5218 −2.00325
473473 1.80393 0.0829446
474474 −1.59215 −0.0731300
475475 0 0
476476 0.309893 0.0142039
477477 89.1627 4.08248
478478 −5.84518 −0.267352
479479 −20.8556 −0.952916 −0.476458 0.879197i 0.658080π-0.658080\pi
−0.476458 + 0.879197i 0.658080π0.658080\pi
480480 0 0
481481 −20.1819 −0.920216
482482 −30.0109 −1.36696
483483 3.66884 0.166938
484484 4.02806 0.183094
485485 0 0
486486 39.9825 1.81364
487487 27.2853 1.23642 0.618208 0.786015i 0.287859π-0.287859\pi
0.618208 + 0.786015i 0.287859π0.287859\pi
488488 −23.3712 −1.05796
489489 −7.88627 −0.356630
490490 0 0
491491 15.6305 0.705395 0.352697 0.935737i 0.385265π-0.385265\pi
0.352697 + 0.935737i 0.385265π0.385265\pi
492492 5.95076 0.268281
493493 −29.4933 −1.32831
494494 −35.5219 −1.59821
495495 0 0
496496 17.2963 0.776625
497497 1.83811 0.0824506
498498 21.5382 0.965150
499499 −22.7946 −1.02042 −0.510212 0.860048i 0.670433π-0.670433\pi
−0.510212 + 0.860048i 0.670433π0.670433\pi
500500 0 0
501501 20.3861 0.910783
502502 −15.2920 −0.682515
503503 21.7516 0.969858 0.484929 0.874554i 0.338845π-0.338845\pi
0.484929 + 0.874554i 0.338845π0.338845\pi
504504 5.21750 0.232406
505505 0 0
506506 −3.57060 −0.158733
507507 −6.95270 −0.308780
508508 −3.89267 −0.172709
509509 −36.9506 −1.63781 −0.818904 0.573930i 0.805418π-0.805418\pi
−0.818904 + 0.573930i 0.805418π0.805418\pi
510510 0 0
511511 −1.91444 −0.0846896
512512 25.3212 1.11905
513513 −99.7242 −4.40293
514514 17.9856 0.793312
515515 0 0
516516 −3.79414 −0.167028
517517 4.03570 0.177490
518518 1.55121 0.0681562
519519 23.0290 1.01086
520520 0 0
521521 0.0246447 0.00107970 0.000539852 1.00000i 0.499828π-0.499828\pi
0.000539852 1.00000i 0.499828π0.499828\pi
522522 −78.8653 −3.45184
523523 21.2265 0.928168 0.464084 0.885791i 0.346384π-0.346384\pi
0.464084 + 0.885791i 0.346384π0.346384\pi
524524 −7.37074 −0.321992
525525 0 0
526526 −13.1636 −0.573962
527527 19.4724 0.848231
528528 −5.75449 −0.250432
529529 0.595377 0.0258860
530530 0 0
531531 −105.368 −4.57256
532532 −0.635489 −0.0275520
533533 19.0906 0.826904
534534 34.2557 1.48239
535535 0 0
536536 −7.80319 −0.337047
537537 23.7780 1.02610
538538 19.1382 0.825106
539539 4.00784 0.172630
540540 0 0
541541 −25.2530 −1.08571 −0.542855 0.839827i 0.682657π-0.682657\pi
−0.542855 + 0.839827i 0.682657π0.682657\pi
542542 3.90897 0.167905
543543 64.9051 2.78535
544544 7.35363 0.315284
545545 0 0
546546 3.74615 0.160320
547547 12.9296 0.552830 0.276415 0.961038i 0.410854π-0.410854\pi
0.276415 + 0.961038i 0.410854π0.410854\pi
548548 −1.14538 −0.0489281
549549 −56.5823 −2.41488
550550 0 0
551551 60.4809 2.57657
552552 47.2850 2.01258
553553 −0.0913781 −0.00388579
554554 41.1443 1.74806
555555 0 0
556556 −0.866757 −0.0367587
557557 9.53791 0.404134 0.202067 0.979372i 0.435234π-0.435234\pi
0.202067 + 0.979372i 0.435234π0.435234\pi
558558 52.0694 2.20427
559559 −12.1719 −0.514818
560560 0 0
561561 −6.47850 −0.273522
562562 37.3905 1.57722
563563 −16.4517 −0.693356 −0.346678 0.937984i 0.612690π-0.612690\pi
−0.346678 + 0.937984i 0.612690π0.612690\pi
564564 −8.48817 −0.357417
565565 0 0
566566 19.5482 0.821671
567567 5.34842 0.224613
568568 23.6900 0.994012
569569 33.1531 1.38985 0.694926 0.719082i 0.255437π-0.255437\pi
0.694926 + 0.719082i 0.255437π0.255437\pi
570570 0 0
571571 −21.2096 −0.887595 −0.443798 0.896127i 0.646369π-0.646369\pi
−0.443798 + 0.896127i 0.646369π0.646369\pi
572572 0.848596 0.0354816
573573 66.0976 2.76127
574574 −1.46733 −0.0612450
575575 0 0
576576 65.1534 2.71472
577577 −3.39956 −0.141526 −0.0707628 0.997493i 0.522543π-0.522543\pi
−0.0707628 + 0.997493i 0.522543π0.522543\pi
578578 6.11733 0.254448
579579 8.64155 0.359130
580580 0 0
581581 1.23614 0.0512837
582582 36.1634 1.49902
583583 −7.01805 −0.290658
584584 −24.6737 −1.02101
585585 0 0
586586 −32.7563 −1.35315
587587 −37.5978 −1.55183 −0.775914 0.630839i 0.782711π-0.782711\pi
−0.775914 + 0.630839i 0.782711π0.782711\pi
588588 −8.42958 −0.347630
589589 −39.9315 −1.64535
590590 0 0
591591 −3.21433 −0.132220
592592 16.0781 0.660804
593593 17.6880 0.726360 0.363180 0.931719i 0.381691π-0.381691\pi
0.363180 + 0.931719i 0.381691π0.381691\pi
594594 −10.2353 −0.419960
595595 0 0
596596 −4.84624 −0.198510
597597 17.1568 0.702183
598598 24.0925 0.985217
599599 2.70489 0.110519 0.0552595 0.998472i 0.482401π-0.482401\pi
0.0552595 + 0.998472i 0.482401π0.482401\pi
600600 0 0
601601 −26.9989 −1.10131 −0.550654 0.834733i 0.685622π-0.685622\pi
−0.550654 + 0.834733i 0.685622π0.685622\pi
602602 0.935552 0.0381302
603603 −18.8918 −0.769332
604604 1.77206 0.0721043
605605 0 0
606606 6.96986 0.283131
607607 −6.45409 −0.261964 −0.130982 0.991385i 0.541813π-0.541813\pi
−0.130982 + 0.991385i 0.541813π0.541813\pi
608608 −15.0799 −0.611570
609609 −6.37833 −0.258463
610610 0 0
611611 −27.2308 −1.10164
612612 9.66956 0.390869
613613 9.63640 0.389211 0.194605 0.980882i 0.437657π-0.437657\pi
0.194605 + 0.980882i 0.437657π0.437657\pi
614614 −3.32050 −0.134005
615615 0 0
616616 −0.410672 −0.0165465
617617 8.69198 0.349926 0.174963 0.984575i 0.444019π-0.444019\pi
0.174963 + 0.984575i 0.444019π0.444019\pi
618618 −11.5034 −0.462735
619619 −22.1646 −0.890870 −0.445435 0.895314i 0.646951π-0.646951\pi
−0.445435 + 0.895314i 0.646951π0.646951\pi
620620 0 0
621621 67.6373 2.71419
622622 25.2747 1.01342
623623 1.96603 0.0787675
624624 38.8283 1.55438
625625 0 0
626626 23.1045 0.923443
627627 13.2853 0.530562
628628 −1.33872 −0.0534206
629629 18.1009 0.721732
630630 0 0
631631 −2.65768 −0.105800 −0.0529002 0.998600i 0.516847π-0.516847\pi
−0.0529002 + 0.998600i 0.516847π0.516847\pi
632632 −1.17770 −0.0468466
633633 88.2827 3.50892
634634 −6.74492 −0.267875
635635 0 0
636636 14.7608 0.585306
637637 −27.0428 −1.07148
638638 6.20753 0.245759
639639 57.3543 2.26890
640640 0 0
641641 27.4000 1.08224 0.541118 0.840946i 0.318001π-0.318001\pi
0.541118 + 0.840946i 0.318001π0.318001\pi
642642 −26.6153 −1.05042
643643 −26.5633 −1.04755 −0.523777 0.851856i 0.675477π-0.675477\pi
−0.523777 + 0.851856i 0.675477π0.675477\pi
644644 0.431017 0.0169844
645645 0 0
646646 31.8592 1.25349
647647 −25.6395 −1.00799 −0.503996 0.863706i 0.668137π-0.668137\pi
−0.503996 + 0.863706i 0.668137π0.668137\pi
648648 68.9318 2.70790
649649 8.29354 0.325550
650650 0 0
651651 4.21118 0.165049
652652 −0.926482 −0.0362838
653653 17.4067 0.681179 0.340589 0.940212i 0.389373π-0.389373\pi
0.340589 + 0.940212i 0.389373π0.389373\pi
654654 49.0909 1.91961
655655 0 0
656656 −15.2086 −0.593797
657657 −59.7358 −2.33052
658658 2.09299 0.0815934
659659 18.2733 0.711827 0.355913 0.934519i 0.384170π-0.384170\pi
0.355913 + 0.934519i 0.384170π0.384170\pi
660660 0 0
661661 13.4912 0.524748 0.262374 0.964966i 0.415495π-0.415495\pi
0.262374 + 0.964966i 0.415495π0.415495\pi
662662 −37.2517 −1.44783
663663 43.7135 1.69769
664664 15.9317 0.618269
665665 0 0
666666 48.4021 1.87554
667667 −41.0208 −1.58833
668668 2.39496 0.0926639
669669 −77.7026 −3.00416
670670 0 0
671671 4.45363 0.171930
672672 1.59033 0.0613481
673673 −24.5543 −0.946497 −0.473249 0.880929i 0.656919π-0.656919\pi
−0.473249 + 0.880929i 0.656919π0.656919\pi
674674 −30.1707 −1.16213
675675 0 0
676676 −0.816805 −0.0314156
677677 21.6592 0.832429 0.416215 0.909266i 0.363356π-0.363356\pi
0.416215 + 0.909266i 0.363356π0.363356\pi
678678 −39.8887 −1.53191
679679 2.07552 0.0796511
680680 0 0
681681 −57.3245 −2.19668
682682 −4.09841 −0.156936
683683 21.0697 0.806209 0.403105 0.915154i 0.367931π-0.367931\pi
0.403105 + 0.915154i 0.367931π0.367931\pi
684684 −19.8291 −0.758183
685685 0 0
686686 4.17362 0.159349
687687 85.0334 3.24423
688688 9.69686 0.369689
689689 47.3541 1.80405
690690 0 0
691691 22.7420 0.865146 0.432573 0.901599i 0.357606π-0.357606\pi
0.432573 + 0.901599i 0.357606π0.357606\pi
692692 2.70545 0.102846
693693 −0.994249 −0.0377684
694694 10.0897 0.383000
695695 0 0
696696 −82.2055 −3.11599
697697 −17.1221 −0.648547
698698 32.6931 1.23745
699699 −96.9536 −3.66712
700700 0 0
701701 −35.8276 −1.35319 −0.676596 0.736355i 0.736545π-0.736545\pi
−0.676596 + 0.736355i 0.736545π0.736545\pi
702702 69.0625 2.60660
703703 −37.1191 −1.39997
704704 −5.12826 −0.193279
705705 0 0
706706 16.8953 0.635862
707707 0.400020 0.0150443
708708 −17.4436 −0.655569
709709 −18.4033 −0.691152 −0.345576 0.938391i 0.612316π-0.612316\pi
−0.345576 + 0.938391i 0.612316π0.612316\pi
710710 0 0
711711 −2.85126 −0.106930
712712 25.3387 0.949609
713713 27.0833 1.01428
714714 −3.35988 −0.125740
715715 0 0
716716 2.79345 0.104396
717717 −14.7507 −0.550875
718718 7.22852 0.269766
719719 22.9617 0.856326 0.428163 0.903702i 0.359161π-0.359161\pi
0.428163 + 0.903702i 0.359161π0.359161\pi
720720 0 0
721721 −0.660213 −0.0245876
722722 −41.1320 −1.53077
723723 −75.7345 −2.81659
724724 7.62507 0.283384
725725 0 0
726726 −43.6724 −1.62084
727727 19.2162 0.712691 0.356345 0.934354i 0.384023π-0.384023\pi
0.356345 + 0.934354i 0.384023π0.384023\pi
728728 2.77100 0.102700
729729 32.6140 1.20792
730730 0 0
731731 10.9169 0.403776
732732 −9.36718 −0.346221
733733 0.407800 0.0150624 0.00753122 0.999972i 0.497603π-0.497603\pi
0.00753122 + 0.999972i 0.497603π0.497603\pi
734734 24.0195 0.886575
735735 0 0
736736 10.2278 0.377003
737737 1.48698 0.0547736
738738 −45.7847 −1.68536
739739 −23.3824 −0.860135 −0.430068 0.902797i 0.641510π-0.641510\pi
−0.430068 + 0.902797i 0.641510π0.641510\pi
740740 0 0
741741 −89.6420 −3.29308
742742 −3.63970 −0.133618
743743 −49.3094 −1.80899 −0.904493 0.426488i 0.859751π-0.859751\pi
−0.904493 + 0.426488i 0.859751π0.859751\pi
744744 54.2747 1.98981
745745 0 0
746746 −28.7928 −1.05418
747747 38.5710 1.41124
748748 −0.761096 −0.0278284
749749 −1.52753 −0.0558146
750750 0 0
751751 0.947118 0.0345608 0.0172804 0.999851i 0.494499π-0.494499\pi
0.0172804 + 0.999851i 0.494499π0.494499\pi
752752 21.6936 0.791084
753753 −38.5903 −1.40631
754754 −41.8852 −1.52537
755755 0 0
756756 1.23553 0.0449358
757757 −42.8580 −1.55770 −0.778850 0.627210i 0.784197π-0.784197\pi
−0.778850 + 0.627210i 0.784197π0.784197\pi
758758 16.8325 0.611382
759759 −9.01065 −0.327066
760760 0 0
761761 −14.6514 −0.531113 −0.265556 0.964095i 0.585556π-0.585556\pi
−0.265556 + 0.964095i 0.585556π0.585556\pi
762762 42.2045 1.52891
763763 2.81747 0.101999
764764 7.76517 0.280934
765765 0 0
766766 11.5483 0.417259
767767 −55.9604 −2.02061
768768 28.0273 1.01135
769769 −0.134376 −0.00484571 −0.00242285 0.999997i 0.500771π-0.500771\pi
−0.00242285 + 0.999997i 0.500771π0.500771\pi
770770 0 0
771771 45.3879 1.63461
772772 1.01521 0.0365383
773773 −15.4519 −0.555767 −0.277884 0.960615i 0.589633π-0.589633\pi
−0.277884 + 0.960615i 0.589633π0.589633\pi
774774 29.1919 1.04928
775775 0 0
776776 26.7498 0.960262
777777 3.91458 0.140435
778778 −30.7877 −1.10379
779779 35.1118 1.25801
780780 0 0
781781 −4.51439 −0.161538
782782 −21.6083 −0.772713
783783 −117.588 −4.20226
784784 21.5438 0.769423
785785 0 0
786786 79.9139 2.85043
787787 −42.6277 −1.51951 −0.759757 0.650207i 0.774682π-0.774682\pi
−0.759757 + 0.650207i 0.774682π0.774682\pi
788788 −0.377621 −0.0134522
789789 −33.2193 −1.18264
790790 0 0
791791 −2.28932 −0.0813989
792792 −12.8141 −0.455330
793793 −30.0507 −1.06713
794794 13.7266 0.487140
795795 0 0
796796 2.01559 0.0714407
797797 11.6332 0.412069 0.206035 0.978545i 0.433944π-0.433944\pi
0.206035 + 0.978545i 0.433944π0.433944\pi
798798 6.89000 0.243903
799799 24.4230 0.864024
800800 0 0
801801 61.3458 2.16755
802802 −0.652897 −0.0230546
803803 4.70184 0.165924
804804 −3.12752 −0.110299
805805 0 0
806806 27.6539 0.974069
807807 48.2965 1.70012
808808 5.15556 0.181372
809809 −37.3413 −1.31285 −0.656425 0.754391i 0.727932π-0.727932\pi
−0.656425 + 0.754391i 0.727932π0.727932\pi
810810 0 0
811811 −9.00258 −0.316123 −0.158062 0.987429i 0.550524π-0.550524\pi
−0.158062 + 0.987429i 0.550524π0.550524\pi
812812 −0.749328 −0.0262962
813813 9.86455 0.345965
814814 −3.80976 −0.133532
815815 0 0
816816 −34.8247 −1.21911
817817 −22.3869 −0.783219
818818 −37.1547 −1.29908
819819 6.70867 0.234420
820820 0 0
821821 8.55499 0.298571 0.149286 0.988794i 0.452303π-0.452303\pi
0.149286 + 0.988794i 0.452303π0.452303\pi
822822 12.4182 0.433136
823823 27.1990 0.948097 0.474049 0.880499i 0.342792π-0.342792\pi
0.474049 + 0.880499i 0.342792π0.342792\pi
824824 −8.50899 −0.296425
825825 0 0
826826 4.30119 0.149658
827827 −8.38311 −0.291509 −0.145755 0.989321i 0.546561π-0.546561\pi
−0.145755 + 0.989321i 0.546561π0.546561\pi
828828 13.4489 0.467383
829829 37.2591 1.29406 0.647030 0.762464i 0.276011π-0.276011\pi
0.647030 + 0.762464i 0.276011π0.276011\pi
830830 0 0
831831 103.830 3.60184
832832 34.6028 1.19964
833833 24.2544 0.840365
834834 9.39741 0.325406
835835 0 0
836836 1.56076 0.0539799
837837 77.6356 2.68348
838838 9.15534 0.316266
839839 −12.5348 −0.432750 −0.216375 0.976310i 0.569423π-0.569423\pi
−0.216375 + 0.976310i 0.569423π0.569423\pi
840840 0 0
841841 42.3152 1.45914
842842 −20.8711 −0.719265
843843 94.3573 3.24984
844844 10.3715 0.357001
845845 0 0
846846 65.3074 2.24531
847847 −2.50649 −0.0861239
848848 −37.7250 −1.29548
849849 49.3311 1.69304
850850 0 0
851851 25.1758 0.863015
852852 9.49498 0.325293
853853 20.8885 0.715210 0.357605 0.933873i 0.383593π-0.383593\pi
0.357605 + 0.933873i 0.383593π0.383593\pi
854854 2.30974 0.0790377
855855 0 0
856856 −19.6872 −0.672893
857857 −30.0053 −1.02496 −0.512481 0.858699i 0.671273π-0.671273\pi
−0.512481 + 0.858699i 0.671273π0.671273\pi
858858 −9.20051 −0.314100
859859 44.8428 1.53002 0.765008 0.644020i 0.222735π-0.222735\pi
0.765008 + 0.644020i 0.222735π0.222735\pi
860860 0 0
861861 −3.70290 −0.126194
862862 31.4013 1.06953
863863 −10.1816 −0.346586 −0.173293 0.984870i 0.555441π-0.555441\pi
−0.173293 + 0.984870i 0.555441π0.555441\pi
864864 29.3186 0.997439
865865 0 0
866866 −21.1196 −0.717674
867867 15.4375 0.524285
868868 0.494730 0.0167922
869869 0.224424 0.00761306
870870 0 0
871871 −10.0334 −0.339968
872872 36.3122 1.22969
873873 64.7620 2.19186
874874 44.3116 1.49886
875875 0 0
876876 −9.88924 −0.334126
877877 −35.3951 −1.19521 −0.597604 0.801792i 0.703880π-0.703880\pi
−0.597604 + 0.801792i 0.703880π0.703880\pi
878878 −18.2305 −0.615250
879879 −82.6628 −2.78815
880880 0 0
881881 46.3047 1.56005 0.780023 0.625750i 0.215207π-0.215207\pi
0.780023 + 0.625750i 0.215207π0.215207\pi
882882 64.8565 2.18383
883883 −36.2361 −1.21944 −0.609722 0.792616i 0.708719π-0.708719\pi
−0.609722 + 0.792616i 0.708719π0.708719\pi
884884 5.13548 0.172725
885885 0 0
886886 2.44337 0.0820865
887887 26.9498 0.904887 0.452443 0.891793i 0.350552π-0.350552\pi
0.452443 + 0.891793i 0.350552π0.350552\pi
888888 50.4521 1.69306
889889 2.42223 0.0812391
890890 0 0
891891 −13.1357 −0.440062
892892 −9.12853 −0.305646
893893 −50.0835 −1.67598
894894 52.5431 1.75731
895895 0 0
896896 −1.67010 −0.0557940
897897 60.7991 2.03002
898898 −27.5490 −0.919322
899899 −47.0846 −1.57036
900900 0 0
901901 −42.4714 −1.41493
902902 3.60374 0.119992
903903 2.36093 0.0785667
904904 −29.5054 −0.981334
905905 0 0
906906 −19.2128 −0.638303
907907 −5.26836 −0.174933 −0.0874664 0.996167i 0.527877π-0.527877\pi
−0.0874664 + 0.996167i 0.527877π0.527877\pi
908908 −6.73449 −0.223492
909909 12.4818 0.413994
910910 0 0
911911 20.8539 0.690919 0.345459 0.938434i 0.387723π-0.387723\pi
0.345459 + 0.938434i 0.387723π0.387723\pi
912912 71.4139 2.36475
913913 −3.03595 −0.100475
914914 25.0463 0.828459
915915 0 0
916916 9.98975 0.330070
917917 4.58648 0.151459
918918 −61.9414 −2.04437
919919 −9.82871 −0.324219 −0.162110 0.986773i 0.551830π-0.551830\pi
−0.162110 + 0.986773i 0.551830π0.551830\pi
920920 0 0
921921 −8.37951 −0.276114
922922 −13.1729 −0.433827
923923 30.4607 1.00263
924924 −0.164598 −0.00541486
925925 0 0
926926 −13.9496 −0.458412
927927 −20.6005 −0.676610
928928 −17.7812 −0.583697
929929 14.8642 0.487677 0.243839 0.969816i 0.421593π-0.421593\pi
0.243839 + 0.969816i 0.421593π0.421593\pi
930930 0 0
931931 −49.7378 −1.63009
932932 −11.3901 −0.373096
933933 63.7823 2.08814
934934 26.6599 0.872340
935935 0 0
936936 86.4630 2.82613
937937 −56.7633 −1.85438 −0.927189 0.374594i 0.877782π-0.877782\pi
−0.927189 + 0.374594i 0.877782π0.877782\pi
938938 0.771178 0.0251798
939939 58.3058 1.90274
940940 0 0
941941 −10.6242 −0.346341 −0.173170 0.984892i 0.555401π-0.555401\pi
−0.173170 + 0.984892i 0.555401π0.555401\pi
942942 14.5144 0.472905
943943 −23.8144 −0.775503
944944 44.5813 1.45100
945945 0 0
946946 −2.29771 −0.0747049
947947 −35.9492 −1.16819 −0.584095 0.811685i 0.698551π-0.698551\pi
−0.584095 + 0.811685i 0.698551π0.698551\pi
948948 −0.472024 −0.0153306
949949 −31.7255 −1.02985
950950 0 0
951951 −17.0212 −0.551952
952952 −2.48528 −0.0805484
953953 54.1752 1.75491 0.877454 0.479661i 0.159240π-0.159240\pi
0.877454 + 0.479661i 0.159240π0.159240\pi
954954 −113.569 −3.67693
955955 0 0
956956 −1.73292 −0.0560466
957957 15.6651 0.506381
958958 26.5643 0.858254
959959 0.712717 0.0230148
960960 0 0
961961 0.0867807 0.00279938
962962 25.7062 0.828803
963963 −47.6632 −1.53592
964964 −8.89731 −0.286563
965965 0 0
966966 −4.67310 −0.150355
967967 5.91237 0.190129 0.0950645 0.995471i 0.469694π-0.469694\pi
0.0950645 + 0.995471i 0.469694π0.469694\pi
968968 −32.3042 −1.03830
969969 80.3989 2.58279
970970 0 0
971971 −25.0906 −0.805195 −0.402597 0.915377i 0.631893π-0.631893\pi
−0.402597 + 0.915377i 0.631893π0.631893\pi
972972 11.8536 0.380204
973973 0.539344 0.0172906
974974 −34.7540 −1.11359
975975 0 0
976976 23.9401 0.766305
977977 49.9680 1.59862 0.799309 0.600920i 0.205199π-0.205199\pi
0.799309 + 0.600920i 0.205199π0.205199\pi
978978 10.0450 0.321202
979979 −4.82856 −0.154322
980980 0 0
981981 87.9129 2.80684
982982 −19.9090 −0.635321
983983 −43.1014 −1.37472 −0.687361 0.726316i 0.741231π-0.741231\pi
−0.687361 + 0.726316i 0.741231π0.741231\pi
984984 −47.7239 −1.52138
985985 0 0
986986 37.5663 1.19636
987987 5.28181 0.168122
988988 −10.5312 −0.335041
989989 15.1838 0.482817
990990 0 0
991991 −39.3870 −1.25117 −0.625585 0.780156i 0.715140π-0.715140\pi
−0.625585 + 0.780156i 0.715140π0.715140\pi
992992 11.7397 0.372737
993993 −94.0072 −2.98323
994994 −2.34125 −0.0742600
995995 0 0
996996 6.38542 0.202330
997997 53.8563 1.70565 0.852823 0.522200i 0.174888π-0.174888\pi
0.852823 + 0.522200i 0.174888π0.174888\pi
998998 29.0340 0.919056
999999 72.1676 2.28328
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 4925.2.a.r.1.17 49
5.2 odd 4 985.2.b.a.789.31 98
5.3 odd 4 985.2.b.a.789.68 yes 98
5.4 even 2 4925.2.a.s.1.33 49
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
985.2.b.a.789.31 98 5.2 odd 4
985.2.b.a.789.68 yes 98 5.3 odd 4
4925.2.a.r.1.17 49 1.1 even 1 trivial
4925.2.a.s.1.33 49 5.4 even 2