Properties

Label 1850.2.a.bb.1.2
Level 18501850
Weight 22
Character 1850.1
Self dual yes
Analytic conductor 14.77214.772
Analytic rank 11
Dimension 33
CM no
Inner twists 11

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1850,2,Mod(1,1850)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1850.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1850=25237 1850 = 2 \cdot 5^{2} \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1850.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: 14.772324373914.7723243739
Analytic rank: 11
Dimension: 33
Coefficient field: 3.3.148.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x3x23x+1 x^{3} - x^{2} - 3x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 2.170092.17009 of defining polynomial
Character χ\chi == 1850.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+1.00000q21.53919q3+1.00000q41.53919q6+2.87936q7+1.00000q80.630898q91.09171q111.53919q124.53919q13+2.87936q14+1.00000q162.80098q170.630898q185.04945q194.43188q211.09171q227.41855q231.53919q244.53919q26+5.58864q27+2.87936q28+6.68035q29+3.51026q31+1.00000q32+1.68035q332.80098q340.630898q361.00000q375.04945q38+6.98667q398.07838q414.43188q4210.2329q431.09171q447.41855q468.68035q471.53919q48+1.29072q49+4.31124q514.53919q52+10.0989q53+5.58864q54+2.87936q56+7.77205q57+6.68035q58+10.2329q59+6.29791q61+3.51026q621.81658q63+1.00000q64+1.68035q6613.2979q672.80098q68+11.4186q69+6.29791q710.630898q7212.7093q731.00000q745.04945q763.14342q77+6.98667q78+2.58145q796.70928q818.07838q828.48360q834.43188q8410.2329q8610.2823q871.09171q886.51026q8913.0700q917.41855q925.40295q938.68035q941.53919q963.07838q97+1.29072q98+0.688756q99+O(q100)q+1.00000 q^{2} -1.53919 q^{3} +1.00000 q^{4} -1.53919 q^{6} +2.87936 q^{7} +1.00000 q^{8} -0.630898 q^{9} -1.09171 q^{11} -1.53919 q^{12} -4.53919 q^{13} +2.87936 q^{14} +1.00000 q^{16} -2.80098 q^{17} -0.630898 q^{18} -5.04945 q^{19} -4.43188 q^{21} -1.09171 q^{22} -7.41855 q^{23} -1.53919 q^{24} -4.53919 q^{26} +5.58864 q^{27} +2.87936 q^{28} +6.68035 q^{29} +3.51026 q^{31} +1.00000 q^{32} +1.68035 q^{33} -2.80098 q^{34} -0.630898 q^{36} -1.00000 q^{37} -5.04945 q^{38} +6.98667 q^{39} -8.07838 q^{41} -4.43188 q^{42} -10.2329 q^{43} -1.09171 q^{44} -7.41855 q^{46} -8.68035 q^{47} -1.53919 q^{48} +1.29072 q^{49} +4.31124 q^{51} -4.53919 q^{52} +10.0989 q^{53} +5.58864 q^{54} +2.87936 q^{56} +7.77205 q^{57} +6.68035 q^{58} +10.2329 q^{59} +6.29791 q^{61} +3.51026 q^{62} -1.81658 q^{63} +1.00000 q^{64} +1.68035 q^{66} -13.2979 q^{67} -2.80098 q^{68} +11.4186 q^{69} +6.29791 q^{71} -0.630898 q^{72} -12.7093 q^{73} -1.00000 q^{74} -5.04945 q^{76} -3.14342 q^{77} +6.98667 q^{78} +2.58145 q^{79} -6.70928 q^{81} -8.07838 q^{82} -8.48360 q^{83} -4.43188 q^{84} -10.2329 q^{86} -10.2823 q^{87} -1.09171 q^{88} -6.51026 q^{89} -13.0700 q^{91} -7.41855 q^{92} -5.40295 q^{93} -8.68035 q^{94} -1.53919 q^{96} -3.07838 q^{97} +1.29072 q^{98} +0.688756 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+3q23q3+3q43q64q7+3q8+2q9q113q1212q134q14+3q16+q17+2q18+3q19q228q233q2412q26++28q99+O(q100) 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{6} - 4 q^{7} + 3 q^{8} + 2 q^{9} - q^{11} - 3 q^{12} - 12 q^{13} - 4 q^{14} + 3 q^{16} + q^{17} + 2 q^{18} + 3 q^{19} - q^{22} - 8 q^{23} - 3 q^{24} - 12 q^{26}+ \cdots + 28 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 1.00000 0.707107
33 −1.53919 −0.888651 −0.444326 0.895865i 0.646557π-0.646557\pi
−0.444326 + 0.895865i 0.646557π0.646557\pi
44 1.00000 0.500000
55 0 0
66 −1.53919 −0.628371
77 2.87936 1.08830 0.544148 0.838989i 0.316853π-0.316853\pi
0.544148 + 0.838989i 0.316853π0.316853\pi
88 1.00000 0.353553
99 −0.630898 −0.210299
1010 0 0
1111 −1.09171 −0.329163 −0.164581 0.986364i 0.552627π-0.552627\pi
−0.164581 + 0.986364i 0.552627π0.552627\pi
1212 −1.53919 −0.444326
1313 −4.53919 −1.25894 −0.629472 0.777023i 0.716729π-0.716729\pi
−0.629472 + 0.777023i 0.716729π0.716729\pi
1414 2.87936 0.769542
1515 0 0
1616 1.00000 0.250000
1717 −2.80098 −0.679338 −0.339669 0.940545i 0.610315π-0.610315\pi
−0.339669 + 0.940545i 0.610315π0.610315\pi
1818 −0.630898 −0.148704
1919 −5.04945 −1.15842 −0.579211 0.815177i 0.696639π-0.696639\pi
−0.579211 + 0.815177i 0.696639π0.696639\pi
2020 0 0
2121 −4.43188 −0.967116
2222 −1.09171 −0.232753
2323 −7.41855 −1.54687 −0.773437 0.633873i 0.781464π-0.781464\pi
−0.773437 + 0.633873i 0.781464π0.781464\pi
2424 −1.53919 −0.314186
2525 0 0
2626 −4.53919 −0.890208
2727 5.58864 1.07553
2828 2.87936 0.544148
2929 6.68035 1.24051 0.620255 0.784401i 0.287029π-0.287029\pi
0.620255 + 0.784401i 0.287029π0.287029\pi
3030 0 0
3131 3.51026 0.630461 0.315231 0.949015i 0.397918π-0.397918\pi
0.315231 + 0.949015i 0.397918π0.397918\pi
3232 1.00000 0.176777
3333 1.68035 0.292511
3434 −2.80098 −0.480365
3535 0 0
3636 −0.630898 −0.105150
3737 −1.00000 −0.164399
3838 −5.04945 −0.819129
3939 6.98667 1.11876
4040 0 0
4141 −8.07838 −1.26163 −0.630815 0.775933i 0.717279π-0.717279\pi
−0.630815 + 0.775933i 0.717279π0.717279\pi
4242 −4.43188 −0.683854
4343 −10.2329 −1.56050 −0.780249 0.625469i 0.784908π-0.784908\pi
−0.780249 + 0.625469i 0.784908π0.784908\pi
4444 −1.09171 −0.164581
4545 0 0
4646 −7.41855 −1.09381
4747 −8.68035 −1.26616 −0.633079 0.774087i 0.718209π-0.718209\pi
−0.633079 + 0.774087i 0.718209π0.718209\pi
4848 −1.53919 −0.222163
4949 1.29072 0.184389
5050 0 0
5151 4.31124 0.603695
5252 −4.53919 −0.629472
5353 10.0989 1.38719 0.693595 0.720365i 0.256026π-0.256026\pi
0.693595 + 0.720365i 0.256026π0.256026\pi
5454 5.58864 0.760517
5555 0 0
5656 2.87936 0.384771
5757 7.77205 1.02943
5858 6.68035 0.877172
5959 10.2329 1.33221 0.666103 0.745860i 0.267961π-0.267961\pi
0.666103 + 0.745860i 0.267961π0.267961\pi
6060 0 0
6161 6.29791 0.806365 0.403183 0.915120i 0.367904π-0.367904\pi
0.403183 + 0.915120i 0.367904π0.367904\pi
6262 3.51026 0.445803
6363 −1.81658 −0.228868
6464 1.00000 0.125000
6565 0 0
6666 1.68035 0.206836
6767 −13.2979 −1.62460 −0.812299 0.583241i 0.801784π-0.801784\pi
−0.812299 + 0.583241i 0.801784π0.801784\pi
6868 −2.80098 −0.339669
6969 11.4186 1.37463
7070 0 0
7171 6.29791 0.747425 0.373712 0.927545i 0.378085π-0.378085\pi
0.373712 + 0.927545i 0.378085π0.378085\pi
7272 −0.630898 −0.0743520
7373 −12.7093 −1.48751 −0.743754 0.668453i 0.766957π-0.766957\pi
−0.743754 + 0.668453i 0.766957π0.766957\pi
7474 −1.00000 −0.116248
7575 0 0
7676 −5.04945 −0.579211
7777 −3.14342 −0.358226
7878 6.98667 0.791084
7979 2.58145 0.290436 0.145218 0.989400i 0.453612π-0.453612\pi
0.145218 + 0.989400i 0.453612π0.453612\pi
8080 0 0
8181 −6.70928 −0.745475
8282 −8.07838 −0.892108
8383 −8.48360 −0.931196 −0.465598 0.884996i 0.654161π-0.654161\pi
−0.465598 + 0.884996i 0.654161π0.654161\pi
8484 −4.43188 −0.483558
8585 0 0
8686 −10.2329 −1.10344
8787 −10.2823 −1.10238
8888 −1.09171 −0.116377
8989 −6.51026 −0.690086 −0.345043 0.938587i 0.612136π-0.612136\pi
−0.345043 + 0.938587i 0.612136π0.612136\pi
9090 0 0
9191 −13.0700 −1.37010
9292 −7.41855 −0.773437
9393 −5.40295 −0.560260
9494 −8.68035 −0.895309
9595 0 0
9696 −1.53919 −0.157093
9797 −3.07838 −0.312562 −0.156281 0.987713i 0.549951π-0.549951\pi
−0.156281 + 0.987713i 0.549951π0.549951\pi
9898 1.29072 0.130383
9999 0.688756 0.0692226
100100 0 0
101101 −15.9155 −1.58365 −0.791825 0.610748i 0.790869π-0.790869\pi
−0.791825 + 0.610748i 0.790869π0.790869\pi
102102 4.31124 0.426877
103103 10.5886 1.04333 0.521665 0.853151i 0.325311π-0.325311\pi
0.521665 + 0.853151i 0.325311π0.325311\pi
104104 −4.53919 −0.445104
105105 0 0
106106 10.0989 0.980892
107107 4.03612 0.390186 0.195093 0.980785i 0.437499π-0.437499\pi
0.195093 + 0.980785i 0.437499π0.437499\pi
108108 5.58864 0.537767
109109 −4.49693 −0.430728 −0.215364 0.976534i 0.569094π-0.569094\pi
−0.215364 + 0.976534i 0.569094π0.569094\pi
110110 0 0
111111 1.53919 0.146093
112112 2.87936 0.272074
113113 −3.58864 −0.337591 −0.168795 0.985651i 0.553988π-0.553988\pi
−0.168795 + 0.985651i 0.553988π0.553988\pi
114114 7.77205 0.727920
115115 0 0
116116 6.68035 0.620255
117117 2.86376 0.264755
118118 10.2329 0.942012
119119 −8.06505 −0.739322
120120 0 0
121121 −9.80817 −0.891652
122122 6.29791 0.570186
123123 12.4341 1.12115
124124 3.51026 0.315231
125125 0 0
126126 −1.81658 −0.161834
127127 −8.14116 −0.722411 −0.361205 0.932486i 0.617635π-0.617635\pi
−0.361205 + 0.932486i 0.617635π0.617635\pi
128128 1.00000 0.0883883
129129 15.7503 1.38674
130130 0 0
131131 −1.46800 −0.128260 −0.0641298 0.997942i 0.520427π-0.520427\pi
−0.0641298 + 0.997942i 0.520427π0.520427\pi
132132 1.68035 0.146255
133133 −14.5392 −1.26071
134134 −13.2979 −1.14876
135135 0 0
136136 −2.80098 −0.240182
137137 6.17727 0.527760 0.263880 0.964555i 0.414998π-0.414998\pi
0.263880 + 0.964555i 0.414998π0.414998\pi
138138 11.4186 0.972012
139139 13.0338 1.10552 0.552758 0.833342i 0.313575π-0.313575\pi
0.552758 + 0.833342i 0.313575π0.313575\pi
140140 0 0
141141 13.3607 1.12517
142142 6.29791 0.528509
143143 4.95547 0.414397
144144 −0.630898 −0.0525748
145145 0 0
146146 −12.7093 −1.05183
147147 −1.98667 −0.163858
148148 −1.00000 −0.0821995
149149 −4.40522 −0.360890 −0.180445 0.983585i 0.557754π-0.557754\pi
−0.180445 + 0.983585i 0.557754π0.557754\pi
150150 0 0
151151 2.92162 0.237758 0.118879 0.992909i 0.462070π-0.462070\pi
0.118879 + 0.992909i 0.462070π0.462070\pi
152152 −5.04945 −0.409564
153153 1.76713 0.142864
154154 −3.14342 −0.253304
155155 0 0
156156 6.98667 0.559381
157157 −22.1906 −1.77100 −0.885502 0.464636i 0.846185π-0.846185\pi
−0.885502 + 0.464636i 0.846185π0.846185\pi
158158 2.58145 0.205369
159159 −15.5441 −1.23273
160160 0 0
161161 −21.3607 −1.68346
162162 −6.70928 −0.527130
163163 14.6248 1.14550 0.572750 0.819730i 0.305877π-0.305877\pi
0.572750 + 0.819730i 0.305877π0.305877\pi
164164 −8.07838 −0.630815
165165 0 0
166166 −8.48360 −0.658455
167167 6.34736 0.491174 0.245587 0.969375i 0.421019π-0.421019\pi
0.245587 + 0.969375i 0.421019π0.421019\pi
168168 −4.43188 −0.341927
169169 7.60424 0.584941
170170 0 0
171171 3.18568 0.243615
172172 −10.2329 −0.780249
173173 1.23513 0.0939054 0.0469527 0.998897i 0.485049π-0.485049\pi
0.0469527 + 0.998897i 0.485049π0.485049\pi
174174 −10.2823 −0.779500
175175 0 0
176176 −1.09171 −0.0822906
177177 −15.7503 −1.18387
178178 −6.51026 −0.487965
179179 1.76487 0.131912 0.0659562 0.997823i 0.478990π-0.478990\pi
0.0659562 + 0.997823i 0.478990π0.478990\pi
180180 0 0
181181 6.49693 0.482913 0.241456 0.970412i 0.422375π-0.422375\pi
0.241456 + 0.970412i 0.422375π0.422375\pi
182182 −13.0700 −0.968810
183183 −9.69368 −0.716577
184184 −7.41855 −0.546903
185185 0 0
186186 −5.40295 −0.396164
187187 3.05786 0.223613
188188 −8.68035 −0.633079
189189 16.0917 1.17050
190190 0 0
191191 21.2039 1.53426 0.767131 0.641490i 0.221683π-0.221683\pi
0.767131 + 0.641490i 0.221683π0.221683\pi
192192 −1.53919 −0.111081
193193 −8.14342 −0.586177 −0.293088 0.956085i 0.594683π-0.594683\pi
−0.293088 + 0.956085i 0.594683π0.594683\pi
194194 −3.07838 −0.221015
195195 0 0
196196 1.29072 0.0921946
197197 24.8443 1.77008 0.885041 0.465513i 0.154130π-0.154130\pi
0.885041 + 0.465513i 0.154130π0.154130\pi
198198 0.688756 0.0489478
199199 −8.47027 −0.600441 −0.300221 0.953870i 0.597060π-0.597060\pi
−0.300221 + 0.953870i 0.597060π0.597060\pi
200200 0 0
201201 20.4680 1.44370
202202 −15.9155 −1.11981
203203 19.2351 1.35004
204204 4.31124 0.301847
205205 0 0
206206 10.5886 0.737745
207207 4.68035 0.325307
208208 −4.53919 −0.314736
209209 5.51253 0.381309
210210 0 0
211211 21.7370 1.49644 0.748218 0.663453i 0.230910π-0.230910\pi
0.748218 + 0.663453i 0.230910π0.230910\pi
212212 10.0989 0.693595
213213 −9.69368 −0.664200
214214 4.03612 0.275903
215215 0 0
216216 5.58864 0.380259
217217 10.1073 0.686129
218218 −4.49693 −0.304570
219219 19.5620 1.32188
220220 0 0
221221 12.7142 0.855249
222222 1.53919 0.103304
223223 −16.6537 −1.11521 −0.557607 0.830105i 0.688280π-0.688280\pi
−0.557607 + 0.830105i 0.688280π0.688280\pi
224224 2.87936 0.192385
225225 0 0
226226 −3.58864 −0.238713
227227 11.2123 0.744190 0.372095 0.928195i 0.378640π-0.378640\pi
0.372095 + 0.928195i 0.378640π0.378640\pi
228228 7.77205 0.514717
229229 −7.62863 −0.504114 −0.252057 0.967712i 0.581107π-0.581107\pi
−0.252057 + 0.967712i 0.581107π0.581107\pi
230230 0 0
231231 4.83832 0.318338
232232 6.68035 0.438586
233233 0.0494483 0.00323947 0.00161973 0.999999i 0.499484π-0.499484\pi
0.00161973 + 0.999999i 0.499484π0.499484\pi
234234 2.86376 0.187210
235235 0 0
236236 10.2329 0.666103
237237 −3.97334 −0.258096
238238 −8.06505 −0.522779
239239 −14.7070 −0.951317 −0.475659 0.879630i 0.657790π-0.657790\pi
−0.475659 + 0.879630i 0.657790π0.657790\pi
240240 0 0
241241 −14.8999 −0.959786 −0.479893 0.877327i 0.659324π-0.659324\pi
−0.479893 + 0.877327i 0.659324π0.659324\pi
242242 −9.80817 −0.630493
243243 −6.43907 −0.413067
244244 6.29791 0.403183
245245 0 0
246246 12.4341 0.792772
247247 22.9204 1.45839
248248 3.51026 0.222902
249249 13.0579 0.827508
250250 0 0
251251 6.23513 0.393558 0.196779 0.980448i 0.436952π-0.436952\pi
0.196779 + 0.980448i 0.436952π0.436952\pi
252252 −1.81658 −0.114434
253253 8.09890 0.509173
254254 −8.14116 −0.510822
255255 0 0
256256 1.00000 0.0625000
257257 −16.1568 −1.00783 −0.503915 0.863753i 0.668108π-0.668108\pi
−0.503915 + 0.863753i 0.668108π0.668108\pi
258258 15.7503 0.980572
259259 −2.87936 −0.178915
260260 0 0
261261 −4.21461 −0.260878
262262 −1.46800 −0.0906933
263263 18.6537 1.15024 0.575118 0.818071i 0.304956π-0.304956\pi
0.575118 + 0.818071i 0.304956π0.304956\pi
264264 1.68035 0.103418
265265 0 0
266266 −14.5392 −0.891455
267267 10.0205 0.613246
268268 −13.2979 −0.812299
269269 21.8310 1.33106 0.665529 0.746372i 0.268206π-0.268206\pi
0.665529 + 0.746372i 0.268206π0.268206\pi
270270 0 0
271271 24.9783 1.51732 0.758661 0.651486i 0.225854π-0.225854\pi
0.758661 + 0.651486i 0.225854π0.225854\pi
272272 −2.80098 −0.169835
273273 20.1171 1.21755
274274 6.17727 0.373183
275275 0 0
276276 11.4186 0.687316
277277 0.822726 0.0494328 0.0247164 0.999695i 0.492132π-0.492132\pi
0.0247164 + 0.999695i 0.492132π0.492132\pi
278278 13.0338 0.781718
279279 −2.21461 −0.132585
280280 0 0
281281 −1.65142 −0.0985153 −0.0492576 0.998786i 0.515686π-0.515686\pi
−0.0492576 + 0.998786i 0.515686π0.515686\pi
282282 13.3607 0.795618
283283 −15.1340 −0.899621 −0.449811 0.893124i 0.648508π-0.648508\pi
−0.449811 + 0.893124i 0.648508π0.648508\pi
284284 6.29791 0.373712
285285 0 0
286286 4.95547 0.293023
287287 −23.2606 −1.37303
288288 −0.630898 −0.0371760
289289 −9.15449 −0.538499
290290 0 0
291291 4.73820 0.277758
292292 −12.7093 −0.743754
293293 25.4524 1.48695 0.743473 0.668766i 0.233177π-0.233177\pi
0.743473 + 0.668766i 0.233177π0.233177\pi
294294 −1.98667 −0.115865
295295 0 0
296296 −1.00000 −0.0581238
297297 −6.10116 −0.354025
298298 −4.40522 −0.255188
299299 33.6742 1.94743
300300 0 0
301301 −29.4641 −1.69828
302302 2.92162 0.168120
303303 24.4969 1.40731
304304 −5.04945 −0.289606
305305 0 0
306306 1.76713 0.101020
307307 27.8176 1.58764 0.793818 0.608155i 0.208090π-0.208090\pi
0.793818 + 0.608155i 0.208090π0.208090\pi
308308 −3.14342 −0.179113
309309 −16.2979 −0.927156
310310 0 0
311311 0.0650468 0.00368846 0.00184423 0.999998i 0.499413π-0.499413\pi
0.00184423 + 0.999998i 0.499413π0.499413\pi
312312 6.98667 0.395542
313313 −22.5464 −1.27440 −0.637198 0.770700i 0.719907π-0.719907\pi
−0.637198 + 0.770700i 0.719907π0.719907\pi
314314 −22.1906 −1.25229
315315 0 0
316316 2.58145 0.145218
317317 24.4775 1.37479 0.687395 0.726283i 0.258754π-0.258754\pi
0.687395 + 0.726283i 0.258754π0.258754\pi
318318 −15.5441 −0.871670
319319 −7.29299 −0.408329
320320 0 0
321321 −6.21235 −0.346739
322322 −21.3607 −1.19038
323323 14.1434 0.786961
324324 −6.70928 −0.372738
325325 0 0
326326 14.6248 0.809990
327327 6.92162 0.382767
328328 −8.07838 −0.446054
329329 −24.9939 −1.37796
330330 0 0
331331 −1.91321 −0.105160 −0.0525798 0.998617i 0.516744π-0.516744\pi
−0.0525798 + 0.998617i 0.516744π0.516744\pi
332332 −8.48360 −0.465598
333333 0.630898 0.0345730
334334 6.34736 0.347312
335335 0 0
336336 −4.43188 −0.241779
337337 12.6286 0.687925 0.343963 0.938983i 0.388231π-0.388231\pi
0.343963 + 0.938983i 0.388231π0.388231\pi
338338 7.60424 0.413616
339339 5.52359 0.300000
340340 0 0
341341 −3.83218 −0.207524
342342 3.18568 0.172262
343343 −16.4391 −0.887626
344344 −10.2329 −0.551719
345345 0 0
346346 1.23513 0.0664012
347347 8.33403 0.447394 0.223697 0.974659i 0.428187π-0.428187\pi
0.223697 + 0.974659i 0.428187π0.428187\pi
348348 −10.2823 −0.551190
349349 2.11837 0.113394 0.0566969 0.998391i 0.481943π-0.481943\pi
0.0566969 + 0.998391i 0.481943π0.481943\pi
350350 0 0
351351 −25.3679 −1.35404
352352 −1.09171 −0.0581883
353353 −28.4534 −1.51442 −0.757212 0.653169i 0.773439π-0.773439\pi
−0.757212 + 0.653169i 0.773439π0.773439\pi
354354 −15.7503 −0.837120
355355 0 0
356356 −6.51026 −0.345043
357357 12.4136 0.656999
358358 1.76487 0.0932761
359359 2.65368 0.140056 0.0700280 0.997545i 0.477691π-0.477691\pi
0.0700280 + 0.997545i 0.477691π0.477691\pi
360360 0 0
361361 6.49693 0.341944
362362 6.49693 0.341471
363363 15.0966 0.792368
364364 −13.0700 −0.685052
365365 0 0
366366 −9.69368 −0.506697
367367 31.7575 1.65773 0.828864 0.559450i 0.188988π-0.188988\pi
0.828864 + 0.559450i 0.188988π0.188988\pi
368368 −7.41855 −0.386719
369369 5.09663 0.265320
370370 0 0
371371 29.0784 1.50967
372372 −5.40295 −0.280130
373373 −25.1122 −1.30026 −0.650131 0.759822i 0.725286π-0.725286\pi
−0.650131 + 0.759822i 0.725286π0.725286\pi
374374 3.05786 0.158118
375375 0 0
376376 −8.68035 −0.447655
377377 −30.3234 −1.56173
378378 16.0917 0.827668
379379 22.5330 1.15744 0.578722 0.815525i 0.303551π-0.303551\pi
0.578722 + 0.815525i 0.303551π0.303551\pi
380380 0 0
381381 12.5308 0.641971
382382 21.2039 1.08489
383383 12.5886 0.643249 0.321625 0.946867i 0.395771π-0.395771\pi
0.321625 + 0.946867i 0.395771π0.395771\pi
384384 −1.53919 −0.0785464
385385 0 0
386386 −8.14342 −0.414489
387387 6.45589 0.328171
388388 −3.07838 −0.156281
389389 −0.879362 −0.0445854 −0.0222927 0.999751i 0.507097π-0.507097\pi
−0.0222927 + 0.999751i 0.507097π0.507097\pi
390390 0 0
391391 20.7792 1.05085
392392 1.29072 0.0651914
393393 2.25953 0.113978
394394 24.8443 1.25164
395395 0 0
396396 0.688756 0.0346113
397397 29.6814 1.48967 0.744833 0.667251i 0.232529π-0.232529\pi
0.744833 + 0.667251i 0.232529π0.232529\pi
398398 −8.47027 −0.424576
399399 22.3786 1.12033
400400 0 0
401401 −13.9867 −0.698461 −0.349230 0.937037i 0.613557π-0.613557\pi
−0.349230 + 0.937037i 0.613557π0.613557\pi
402402 20.4680 1.02085
403403 −15.9337 −0.793716
404404 −15.9155 −0.791825
405405 0 0
406406 19.2351 0.954624
407407 1.09171 0.0541140
408408 4.31124 0.213438
409409 −21.9060 −1.08318 −0.541592 0.840642i 0.682178π-0.682178\pi
−0.541592 + 0.840642i 0.682178π0.682178\pi
410410 0 0
411411 −9.50799 −0.468995
412412 10.5886 0.521665
413413 29.4641 1.44983
414414 4.68035 0.230026
415415 0 0
416416 −4.53919 −0.222552
417417 −20.0616 −0.982419
418418 5.51253 0.269627
419419 −34.8648 −1.70326 −0.851629 0.524146i 0.824385π-0.824385\pi
−0.851629 + 0.524146i 0.824385π0.824385\pi
420420 0 0
421421 −4.76487 −0.232225 −0.116113 0.993236i 0.537043π-0.537043\pi
−0.116113 + 0.993236i 0.537043π0.537043\pi
422422 21.7370 1.05814
423423 5.47641 0.266272
424424 10.0989 0.490446
425425 0 0
426426 −9.69368 −0.469660
427427 18.1340 0.877564
428428 4.03612 0.195093
429429 −7.62741 −0.368255
430430 0 0
431431 2.66597 0.128415 0.0642076 0.997937i 0.479548π-0.479548\pi
0.0642076 + 0.997937i 0.479548π0.479548\pi
432432 5.58864 0.268883
433433 −32.3074 −1.55259 −0.776297 0.630368i 0.782904π-0.782904\pi
−0.776297 + 0.630368i 0.782904π0.782904\pi
434434 10.1073 0.485166
435435 0 0
436436 −4.49693 −0.215364
437437 37.4596 1.79194
438438 19.5620 0.934707
439439 −22.1568 −1.05748 −0.528742 0.848783i 0.677336π-0.677336\pi
−0.528742 + 0.848783i 0.677336π0.677336\pi
440440 0 0
441441 −0.814315 −0.0387769
442442 12.7142 0.604753
443443 −39.1061 −1.85799 −0.928993 0.370097i 0.879324π-0.879324\pi
−0.928993 + 0.370097i 0.879324π0.879324\pi
444444 1.53919 0.0730467
445445 0 0
446446 −16.6537 −0.788575
447447 6.78047 0.320705
448448 2.87936 0.136037
449449 30.8915 1.45786 0.728929 0.684589i 0.240018π-0.240018\pi
0.728929 + 0.684589i 0.240018π0.240018\pi
450450 0 0
451451 8.81924 0.415282
452452 −3.58864 −0.168795
453453 −4.49693 −0.211284
454454 11.2123 0.526222
455455 0 0
456456 7.77205 0.363960
457457 0.438025 0.0204899 0.0102450 0.999948i 0.496739π-0.496739\pi
0.0102450 + 0.999948i 0.496739π0.496739\pi
458458 −7.62863 −0.356462
459459 −15.6537 −0.730651
460460 0 0
461461 0.523590 0.0243860 0.0121930 0.999926i 0.496119π-0.496119\pi
0.0121930 + 0.999926i 0.496119π0.496119\pi
462462 4.83832 0.225099
463463 29.1845 1.35632 0.678158 0.734916i 0.262778π-0.262778\pi
0.678158 + 0.734916i 0.262778π0.262778\pi
464464 6.68035 0.310127
465465 0 0
466466 0.0494483 0.00229065
467467 −9.49079 −0.439181 −0.219591 0.975592i 0.570472π-0.570472\pi
−0.219591 + 0.975592i 0.570472π0.570472\pi
468468 2.86376 0.132378
469469 −38.2895 −1.76804
470470 0 0
471471 34.1555 1.57380
472472 10.2329 0.471006
473473 11.1713 0.513657
474474 −3.97334 −0.182501
475475 0 0
476476 −8.06505 −0.369661
477477 −6.37137 −0.291725
478478 −14.7070 −0.672683
479479 −6.12291 −0.279763 −0.139881 0.990168i 0.544672π-0.544672\pi
−0.139881 + 0.990168i 0.544672π0.544672\pi
480480 0 0
481481 4.53919 0.206969
482482 −14.8999 −0.678671
483483 32.8781 1.49601
484484 −9.80817 −0.445826
485485 0 0
486486 −6.43907 −0.292082
487487 −10.3018 −0.466819 −0.233409 0.972379i 0.574988π-0.574988\pi
−0.233409 + 0.972379i 0.574988π0.574988\pi
488488 6.29791 0.285093
489489 −22.5103 −1.01795
490490 0 0
491491 −10.5380 −0.475572 −0.237786 0.971318i 0.576422π-0.576422\pi
−0.237786 + 0.971318i 0.576422π0.576422\pi
492492 12.4341 0.560575
493493 −18.7115 −0.842726
494494 22.9204 1.03124
495495 0 0
496496 3.51026 0.157615
497497 18.1340 0.813420
498498 13.0579 0.585137
499499 −31.2123 −1.39726 −0.698628 0.715485i 0.746206π-0.746206\pi
−0.698628 + 0.715485i 0.746206π0.746206\pi
500500 0 0
501501 −9.76979 −0.436482
502502 6.23513 0.278288
503503 36.1978 1.61398 0.806990 0.590565i 0.201095π-0.201095\pi
0.806990 + 0.590565i 0.201095π0.201095\pi
504504 −1.81658 −0.0809170
505505 0 0
506506 8.09890 0.360040
507507 −11.7044 −0.519809
508508 −8.14116 −0.361205
509509 −33.6092 −1.48970 −0.744850 0.667232i 0.767479π-0.767479\pi
−0.744850 + 0.667232i 0.767479π0.767479\pi
510510 0 0
511511 −36.5946 −1.61885
512512 1.00000 0.0441942
513513 −28.2195 −1.24592
514514 −16.1568 −0.712644
515515 0 0
516516 15.7503 0.693369
517517 9.47641 0.416772
518518 −2.87936 −0.126512
519519 −1.90110 −0.0834492
520520 0 0
521521 5.42082 0.237490 0.118745 0.992925i 0.462113π-0.462113\pi
0.118745 + 0.992925i 0.462113π0.462113\pi
522522 −4.21461 −0.184469
523523 31.3545 1.37104 0.685519 0.728054i 0.259575π-0.259575\pi
0.685519 + 0.728054i 0.259575π0.259575\pi
524524 −1.46800 −0.0641298
525525 0 0
526526 18.6537 0.813339
527527 −9.83218 −0.428297
528528 1.68035 0.0731277
529529 32.0349 1.39282
530530 0 0
531531 −6.45589 −0.280162
532532 −14.5392 −0.630354
533533 36.6693 1.58832
534534 10.0205 0.433630
535535 0 0
536536 −13.2979 −0.574382
537537 −2.71646 −0.117224
538538 21.8310 0.941199
539539 −1.40910 −0.0606940
540540 0 0
541541 −9.98440 −0.429263 −0.214631 0.976695i 0.568855π-0.568855\pi
−0.214631 + 0.976695i 0.568855π0.568855\pi
542542 24.9783 1.07291
543543 −10.0000 −0.429141
544544 −2.80098 −0.120091
545545 0 0
546546 20.1171 0.860934
547547 −32.9649 −1.40948 −0.704739 0.709466i 0.748936π-0.748936\pi
−0.704739 + 0.709466i 0.748936π0.748936\pi
548548 6.17727 0.263880
549549 −3.97334 −0.169578
550550 0 0
551551 −33.7321 −1.43703
552552 11.4186 0.486006
553553 7.43293 0.316080
554554 0.822726 0.0349543
555555 0 0
556556 13.0338 0.552758
557557 21.7009 0.919495 0.459748 0.888050i 0.347940π-0.347940\pi
0.459748 + 0.888050i 0.347940π0.347940\pi
558558 −2.21461 −0.0937521
559559 46.4489 1.96458
560560 0 0
561561 −4.70662 −0.198714
562562 −1.65142 −0.0696608
563563 1.05559 0.0444879 0.0222439 0.999753i 0.492919π-0.492919\pi
0.0222439 + 0.999753i 0.492919π0.492919\pi
564564 13.3607 0.562587
565565 0 0
566566 −15.1340 −0.636128
567567 −19.3184 −0.811298
568568 6.29791 0.264255
569569 −41.4196 −1.73640 −0.868200 0.496215i 0.834723π-0.834723\pi
−0.868200 + 0.496215i 0.834723π0.834723\pi
570570 0 0
571571 21.4452 0.897454 0.448727 0.893669i 0.351878π-0.351878\pi
0.448727 + 0.893669i 0.351878π0.351878\pi
572572 4.95547 0.207199
573573 −32.6369 −1.36342
574574 −23.2606 −0.970878
575575 0 0
576576 −0.630898 −0.0262874
577577 −17.2667 −0.718823 −0.359411 0.933179i 0.617023π-0.617023\pi
−0.359411 + 0.933179i 0.617023π0.617023\pi
578578 −9.15449 −0.380777
579579 12.5343 0.520906
580580 0 0
581581 −24.4273 −1.01342
582582 4.73820 0.196405
583583 −11.0251 −0.456611
584584 −12.7093 −0.525914
585585 0 0
586586 25.4524 1.05143
587587 9.63090 0.397510 0.198755 0.980049i 0.436310π-0.436310\pi
0.198755 + 0.980049i 0.436310π0.436310\pi
588588 −1.98667 −0.0819288
589589 −17.7249 −0.730341
590590 0 0
591591 −38.2401 −1.57299
592592 −1.00000 −0.0410997
593593 −2.78992 −0.114568 −0.0572842 0.998358i 0.518244π-0.518244\pi
−0.0572842 + 0.998358i 0.518244π0.518244\pi
594594 −6.10116 −0.250334
595595 0 0
596596 −4.40522 −0.180445
597597 13.0373 0.533583
598598 33.6742 1.37704
599599 25.2606 1.03212 0.516060 0.856553i 0.327398π-0.327398\pi
0.516060 + 0.856553i 0.327398π0.327398\pi
600600 0 0
601601 35.4040 1.44416 0.722080 0.691810i 0.243186π-0.243186\pi
0.722080 + 0.691810i 0.243186π0.243186\pi
602602 −29.4641 −1.20087
603603 8.38962 0.341652
604604 2.92162 0.118879
605605 0 0
606606 24.4969 0.995120
607607 −38.2485 −1.55246 −0.776229 0.630452i 0.782870π-0.782870\pi
−0.776229 + 0.630452i 0.782870π0.782870\pi
608608 −5.04945 −0.204782
609609 −29.6065 −1.19972
610610 0 0
611611 39.4017 1.59402
612612 1.76713 0.0714322
613613 46.3279 1.87117 0.935583 0.353107i 0.114875π-0.114875\pi
0.935583 + 0.353107i 0.114875π0.114875\pi
614614 27.8176 1.12263
615615 0 0
616616 −3.14342 −0.126652
617617 −23.7503 −0.956152 −0.478076 0.878319i 0.658666π-0.658666\pi
−0.478076 + 0.878319i 0.658666π0.658666\pi
618618 −16.2979 −0.655598
619619 −6.53797 −0.262783 −0.131392 0.991331i 0.541945π-0.541945\pi
−0.131392 + 0.991331i 0.541945π0.541945\pi
620620 0 0
621621 −41.4596 −1.66372
622622 0.0650468 0.00260814
623623 −18.7454 −0.751018
624624 6.98667 0.279691
625625 0 0
626626 −22.5464 −0.901134
627627 −8.48482 −0.338851
628628 −22.1906 −0.885502
629629 2.80098 0.111683
630630 0 0
631631 27.1506 1.08085 0.540424 0.841393i 0.318264π-0.318264\pi
0.540424 + 0.841393i 0.318264π0.318264\pi
632632 2.58145 0.102685
633633 −33.4573 −1.32981
634634 24.4775 0.972124
635635 0 0
636636 −15.5441 −0.616364
637637 −5.85884 −0.232136
638638 −7.29299 −0.288732
639639 −3.97334 −0.157183
640640 0 0
641641 31.9877 1.26344 0.631719 0.775197i 0.282350π-0.282350\pi
0.631719 + 0.775197i 0.282350π0.282350\pi
642642 −6.21235 −0.245182
643643 −26.2784 −1.03632 −0.518160 0.855284i 0.673383π-0.673383\pi
−0.518160 + 0.855284i 0.673383π0.673383\pi
644644 −21.3607 −0.841729
645645 0 0
646646 14.1434 0.556466
647647 −31.3679 −1.23320 −0.616599 0.787277i 0.711490π-0.711490\pi
−0.616599 + 0.787277i 0.711490π0.711490\pi
648648 −6.70928 −0.263565
649649 −11.1713 −0.438512
650650 0 0
651651 −15.5571 −0.609729
652652 14.6248 0.572750
653653 25.3184 0.990787 0.495393 0.868669i 0.335024π-0.335024\pi
0.495393 + 0.868669i 0.335024π0.335024\pi
654654 6.92162 0.270657
655655 0 0
656656 −8.07838 −0.315408
657657 8.01825 0.312822
658658 −24.9939 −0.974362
659659 −38.2072 −1.48834 −0.744172 0.667989i 0.767156π-0.767156\pi
−0.744172 + 0.667989i 0.767156π0.767156\pi
660660 0 0
661661 13.7899 0.536366 0.268183 0.963368i 0.413577π-0.413577\pi
0.268183 + 0.963368i 0.413577π0.413577\pi
662662 −1.91321 −0.0743591
663663 −19.5695 −0.760018
664664 −8.48360 −0.329227
665665 0 0
666666 0.630898 0.0244468
667667 −49.5585 −1.91891
668668 6.34736 0.245587
669669 25.6332 0.991035
670670 0 0
671671 −6.87549 −0.265425
672672 −4.43188 −0.170964
673673 −4.41628 −0.170235 −0.0851176 0.996371i 0.527127π-0.527127\pi
−0.0851176 + 0.996371i 0.527127π0.527127\pi
674674 12.6286 0.486437
675675 0 0
676676 7.60424 0.292471
677677 38.1399 1.46584 0.732918 0.680317i 0.238158π-0.238158\pi
0.732918 + 0.680317i 0.238158π0.238158\pi
678678 5.52359 0.212132
679679 −8.86376 −0.340160
680680 0 0
681681 −17.2579 −0.661325
682682 −3.83218 −0.146742
683683 22.6514 0.866732 0.433366 0.901218i 0.357326π-0.357326\pi
0.433366 + 0.901218i 0.357326π0.357326\pi
684684 3.18568 0.121808
685685 0 0
686686 −16.4391 −0.627647
687687 11.7419 0.447982
688688 −10.2329 −0.390124
689689 −45.8408 −1.74640
690690 0 0
691691 −15.8443 −0.602745 −0.301373 0.953506i 0.597445π-0.597445\pi
−0.301373 + 0.953506i 0.597445π0.597445\pi
692692 1.23513 0.0469527
693693 1.98318 0.0753347
694694 8.33403 0.316355
695695 0 0
696696 −10.2823 −0.389750
697697 22.6274 0.857074
698698 2.11837 0.0801815
699699 −0.0761103 −0.00287876
700700 0 0
701701 −2.92284 −0.110394 −0.0551972 0.998475i 0.517579π-0.517579\pi
−0.0551972 + 0.998475i 0.517579π0.517579\pi
702702 −25.3679 −0.957449
703703 5.04945 0.190444
704704 −1.09171 −0.0411453
705705 0 0
706706 −28.4534 −1.07086
707707 −45.8264 −1.72348
708708 −15.7503 −0.591933
709709 −8.45136 −0.317397 −0.158699 0.987327i 0.550730π-0.550730\pi
−0.158699 + 0.987327i 0.550730π0.550730\pi
710710 0 0
711711 −1.62863 −0.0610784
712712 −6.51026 −0.243982
713713 −26.0410 −0.975245
714714 12.4136 0.464568
715715 0 0
716716 1.76487 0.0659562
717717 22.6369 0.845389
718718 2.65368 0.0990346
719719 −15.3763 −0.573439 −0.286719 0.958015i 0.592565π-0.592565\pi
−0.286719 + 0.958015i 0.592565π0.592565\pi
720720 0 0
721721 30.4885 1.13545
722722 6.49693 0.241791
723723 22.9337 0.852915
724724 6.49693 0.241456
725725 0 0
726726 15.0966 0.560288
727727 15.7275 0.583302 0.291651 0.956525i 0.405795π-0.405795\pi
0.291651 + 0.956525i 0.405795π0.405795\pi
728728 −13.0700 −0.484405
729729 30.0388 1.11255
730730 0 0
731731 28.6621 1.06011
732732 −9.69368 −0.358289
733733 −15.7275 −0.580909 −0.290455 0.956889i 0.593807π-0.593807\pi
−0.290455 + 0.956889i 0.593807π0.593807\pi
734734 31.7575 1.17219
735735 0 0
736736 −7.41855 −0.273451
737737 14.5174 0.534757
738738 5.09663 0.187610
739739 45.0472 1.65709 0.828544 0.559924i 0.189170π-0.189170\pi
0.828544 + 0.559924i 0.189170π0.189170\pi
740740 0 0
741741 −35.2788 −1.29600
742742 29.0784 1.06750
743743 9.31965 0.341905 0.170952 0.985279i 0.445316π-0.445316\pi
0.170952 + 0.985279i 0.445316π0.445316\pi
744744 −5.40295 −0.198082
745745 0 0
746746 −25.1122 −0.919424
747747 5.35228 0.195830
748748 3.05786 0.111806
749749 11.6214 0.424638
750750 0 0
751751 11.6020 0.423362 0.211681 0.977339i 0.432106π-0.432106\pi
0.211681 + 0.977339i 0.432106π0.432106\pi
752752 −8.68035 −0.316540
753753 −9.59705 −0.349736
754754 −30.3234 −1.10431
755755 0 0
756756 16.0917 0.585250
757757 −38.3545 −1.39402 −0.697010 0.717062i 0.745487π-0.745487\pi
−0.697010 + 0.717062i 0.745487π0.745487\pi
758758 22.5330 0.818437
759759 −12.4657 −0.452477
760760 0 0
761761 −45.3318 −1.64328 −0.821638 0.570010i 0.806939π-0.806939\pi
−0.821638 + 0.570010i 0.806939π0.806939\pi
762762 12.5308 0.453942
763763 −12.9483 −0.468759
764764 21.2039 0.767131
765765 0 0
766766 12.5886 0.454846
767767 −46.4489 −1.67717
768768 −1.53919 −0.0555407
769769 −31.7454 −1.14477 −0.572384 0.819986i 0.693981π-0.693981\pi
−0.572384 + 0.819986i 0.693981π0.693981\pi
770770 0 0
771771 24.8683 0.895610
772772 −8.14342 −0.293088
773773 38.0482 1.36850 0.684250 0.729248i 0.260130π-0.260130\pi
0.684250 + 0.729248i 0.260130π0.260130\pi
774774 6.45589 0.232052
775775 0 0
776776 −3.07838 −0.110507
777777 4.43188 0.158993
778778 −0.879362 −0.0315266
779779 40.7914 1.46150
780780 0 0
781781 −6.87549 −0.246024
782782 20.7792 0.743064
783783 37.3340 1.33421
784784 1.29072 0.0460973
785785 0 0
786786 2.25953 0.0805947
787787 15.1506 0.540061 0.270031 0.962852i 0.412966π-0.412966\pi
0.270031 + 0.962852i 0.412966π0.412966\pi
788788 24.8443 0.885041
789789 −28.7115 −1.02216
790790 0 0
791791 −10.3330 −0.367399
792792 0.688756 0.0244739
793793 −28.5874 −1.01517
794794 29.6814 1.05335
795795 0 0
796796 −8.47027 −0.300221
797797 −43.1350 −1.52792 −0.763960 0.645263i 0.776748π-0.776748\pi
−0.763960 + 0.645263i 0.776748π0.776748\pi
798798 22.3786 0.792192
799799 24.3135 0.860150
800800 0 0
801801 4.10731 0.145125
802802 −13.9867 −0.493886
803803 13.8748 0.489632
804804 20.4680 0.721851
805805 0 0
806806 −15.9337 −0.561242
807807 −33.6020 −1.18285
808808 −15.9155 −0.559905
809809 33.3874 1.17384 0.586918 0.809646i 0.300341π-0.300341\pi
0.586918 + 0.809646i 0.300341π0.300341\pi
810810 0 0
811811 10.9216 0.383510 0.191755 0.981443i 0.438582π-0.438582\pi
0.191755 + 0.981443i 0.438582π0.438582\pi
812812 19.2351 0.675021
813813 −38.4463 −1.34837
814814 1.09171 0.0382644
815815 0 0
816816 4.31124 0.150924
817817 51.6703 1.80772
818818 −21.9060 −0.765926
819819 8.24581 0.288132
820820 0 0
821821 −32.7910 −1.14441 −0.572206 0.820110i 0.693912π-0.693912\pi
−0.572206 + 0.820110i 0.693912π0.693912\pi
822822 −9.50799 −0.331629
823823 −9.83218 −0.342728 −0.171364 0.985208i 0.554817π-0.554817\pi
−0.171364 + 0.985208i 0.554817π0.554817\pi
824824 10.5886 0.368873
825825 0 0
826826 29.4641 1.02519
827827 −17.0228 −0.591940 −0.295970 0.955197i 0.595643π-0.595643\pi
−0.295970 + 0.955197i 0.595643π0.595643\pi
828828 4.68035 0.162653
829829 12.8260 0.445467 0.222733 0.974879i 0.428502π-0.428502\pi
0.222733 + 0.974879i 0.428502π0.428502\pi
830830 0 0
831831 −1.26633 −0.0439285
832832 −4.53919 −0.157368
833833 −3.61530 −0.125263
834834 −20.0616 −0.694675
835835 0 0
836836 5.51253 0.190655
837837 19.6176 0.678082
838838 −34.8648 −1.20438
839839 −11.5018 −0.397088 −0.198544 0.980092i 0.563621π-0.563621\pi
−0.198544 + 0.980092i 0.563621π0.563621\pi
840840 0 0
841841 15.6270 0.538863
842842 −4.76487 −0.164208
843843 2.54184 0.0875457
844844 21.7370 0.748218
845845 0 0
846846 5.47641 0.188283
847847 −28.2413 −0.970382
848848 10.0989 0.346798
849849 23.2940 0.799449
850850 0 0
851851 7.41855 0.254305
852852 −9.69368 −0.332100
853853 −40.5946 −1.38993 −0.694966 0.719042i 0.744581π-0.744581\pi
−0.694966 + 0.719042i 0.744581π0.744581\pi
854854 18.1340 0.620532
855855 0 0
856856 4.03612 0.137952
857857 −38.0361 −1.29929 −0.649645 0.760238i 0.725082π-0.725082\pi
−0.649645 + 0.760238i 0.725082π0.725082\pi
858858 −7.62741 −0.260395
859859 −40.9506 −1.39721 −0.698607 0.715505i 0.746197π-0.746197\pi
−0.698607 + 0.715505i 0.746197π0.746197\pi
860860 0 0
861861 35.8024 1.22014
862862 2.66597 0.0908033
863863 −33.0817 −1.12611 −0.563057 0.826418i 0.690375π-0.690375\pi
−0.563057 + 0.826418i 0.690375π0.690375\pi
864864 5.58864 0.190129
865865 0 0
866866 −32.3074 −1.09785
867867 14.0905 0.478538
868868 10.1073 0.343064
869869 −2.81819 −0.0956006
870870 0 0
871871 60.3617 2.04528
872872 −4.49693 −0.152285
873873 1.94214 0.0657315
874874 37.4596 1.26709
875875 0 0
876876 19.5620 0.660938
877877 −25.5057 −0.861267 −0.430634 0.902527i 0.641710π-0.641710\pi
−0.430634 + 0.902527i 0.641710π0.641710\pi
878878 −22.1568 −0.747754
879879 −39.1761 −1.32138
880880 0 0
881881 15.6514 0.527310 0.263655 0.964617i 0.415072π-0.415072\pi
0.263655 + 0.964617i 0.415072π0.415072\pi
882882 −0.814315 −0.0274194
883883 −56.1071 −1.88816 −0.944078 0.329723i 0.893045π-0.893045\pi
−0.944078 + 0.329723i 0.893045π0.893045\pi
884884 12.7142 0.427625
885885 0 0
886886 −39.1061 −1.31379
887887 47.5052 1.59507 0.797534 0.603275i 0.206138π-0.206138\pi
0.797534 + 0.603275i 0.206138π0.206138\pi
888888 1.53919 0.0516518
889889 −23.4413 −0.786197
890890 0 0
891891 7.32457 0.245382
892892 −16.6537 −0.557607
893893 43.8310 1.46675
894894 6.78047 0.226773
895895 0 0
896896 2.87936 0.0961927
897897 −51.8310 −1.73059
898898 30.8915 1.03086
899899 23.4497 0.782093
900900 0 0
901901 −28.2868 −0.942372
902902 8.81924 0.293648
903903 45.3509 1.50918
904904 −3.58864 −0.119356
905905 0 0
906906 −4.49693 −0.149400
907907 −15.8394 −0.525938 −0.262969 0.964804i 0.584702π-0.584702\pi
−0.262969 + 0.964804i 0.584702π0.584702\pi
908908 11.2123 0.372095
909909 10.0410 0.333040
910910 0 0
911911 11.9539 0.396049 0.198025 0.980197i 0.436547π-0.436547\pi
0.198025 + 0.980197i 0.436547π0.436547\pi
912912 7.77205 0.257358
913913 9.26162 0.306515
914914 0.438025 0.0144886
915915 0 0
916916 −7.62863 −0.252057
917917 −4.22690 −0.139585
918918 −15.6537 −0.516649
919919 −34.8781 −1.15052 −0.575262 0.817969i 0.695100π-0.695100\pi
−0.575262 + 0.817969i 0.695100π0.695100\pi
920920 0 0
921921 −42.8166 −1.41085
922922 0.523590 0.0172435
923923 −28.5874 −0.940966
924924 4.83832 0.159169
925925 0 0
926926 29.1845 0.959061
927927 −6.68035 −0.219411
928928 6.68035 0.219293
929929 −52.5439 −1.72391 −0.861955 0.506984i 0.830760π-0.830760\pi
−0.861955 + 0.506984i 0.830760π0.830760\pi
930930 0 0
931931 −6.51745 −0.213601
932932 0.0494483 0.00161973
933933 −0.100119 −0.00327776
934934 −9.49079 −0.310548
935935 0 0
936936 2.86376 0.0936050
937937 13.3318 0.435530 0.217765 0.976001i 0.430123π-0.430123\pi
0.217765 + 0.976001i 0.430123π0.430123\pi
938938 −38.2895 −1.25020
939939 34.7031 1.13249
940940 0 0
941941 14.5281 0.473603 0.236802 0.971558i 0.423901π-0.423901\pi
0.236802 + 0.971558i 0.423901π0.423901\pi
942942 34.1555 1.11285
943943 59.9299 1.95158
944944 10.2329 0.333051
945945 0 0
946946 11.1713 0.363211
947947 24.6803 0.802003 0.401002 0.916077i 0.368662π-0.368662\pi
0.401002 + 0.916077i 0.368662π0.368662\pi
948948 −3.97334 −0.129048
949949 57.6898 1.87269
950950 0 0
951951 −37.6754 −1.22171
952952 −8.06505 −0.261390
953953 40.5936 1.31495 0.657477 0.753474i 0.271624π-0.271624\pi
0.657477 + 0.753474i 0.271624π0.271624\pi
954954 −6.37137 −0.206281
955955 0 0
956956 −14.7070 −0.475659
957957 11.2253 0.362862
958958 −6.12291 −0.197822
959959 17.7866 0.574360
960960 0 0
961961 −18.6781 −0.602519
962962 4.53919 0.146349
963963 −2.54638 −0.0820558
964964 −14.8999 −0.479893
965965 0 0
966966 32.8781 1.05784
967967 1.06400 0.0342160 0.0171080 0.999854i 0.494554π-0.494554\pi
0.0171080 + 0.999854i 0.494554π0.494554\pi
968968 −9.80817 −0.315247
969969 −21.7694 −0.699334
970970 0 0
971971 11.9333 0.382959 0.191480 0.981497i 0.438671π-0.438671\pi
0.191480 + 0.981497i 0.438671π0.438671\pi
972972 −6.43907 −0.206533
973973 37.5292 1.20313
974974 −10.3018 −0.330091
975975 0 0
976976 6.29791 0.201591
977977 19.1867 0.613838 0.306919 0.951736i 0.400702π-0.400702\pi
0.306919 + 0.951736i 0.400702π0.400702\pi
978978 −22.5103 −0.719799
979979 7.10731 0.227151
980980 0 0
981981 2.83710 0.0905817
982982 −10.5380 −0.336280
983983 22.9171 0.730942 0.365471 0.930823i 0.380908π-0.380908\pi
0.365471 + 0.930823i 0.380908π0.380908\pi
984984 12.4341 0.396386
985985 0 0
986986 −18.7115 −0.595897
987987 38.4703 1.22452
988988 22.9204 0.729195
989989 75.9130 2.41389
990990 0 0
991991 −52.2772 −1.66064 −0.830320 0.557287i 0.811842π-0.811842\pi
−0.830320 + 0.557287i 0.811842π0.811842\pi
992992 3.51026 0.111451
993993 2.94479 0.0934502
994994 18.1340 0.575175
995995 0 0
996996 13.0579 0.413754
997997 −48.8892 −1.54834 −0.774168 0.632980i 0.781832π-0.781832\pi
−0.774168 + 0.632980i 0.781832π0.781832\pi
998998 −31.2123 −0.988010
999999 −5.58864 −0.176817
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 1850.2.a.bb.1.2 yes 3
5.2 odd 4 1850.2.b.n.149.5 6
5.3 odd 4 1850.2.b.n.149.2 6
5.4 even 2 1850.2.a.ba.1.2 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1850.2.a.ba.1.2 3 5.4 even 2
1850.2.a.bb.1.2 yes 3 1.1 even 1 trivial
1850.2.b.n.149.2 6 5.3 odd 4
1850.2.b.n.149.5 6 5.2 odd 4