Properties

Label 7942.2.a.w.1.2
Level 79427942
Weight 22
Character 7942.1
Self dual yes
Analytic conductor 63.41763.417
Analytic rank 11
Dimension 22
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] = [7942,2,Mod(1,7942)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7942, 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("7942.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7942=211192 7942 = 2 \cdot 11 \cdot 19^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7942.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: 63.417189285363.4171892853
Analytic rank: 11
Dimension: 22
Coefficient field: Q(21)\Q(\sqrt{21})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x2x5 x^{2} - x - 5 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: no (minimal twist has level 418)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.2
Root 2.791292.79129 of defining polynomial
Character χ\chi == 7942.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q1.00000q2+2.79129q3+1.00000q40.791288q52.79129q60.208712q71.00000q8+4.79129q9+0.791288q10+1.00000q11+2.79129q125.79129q13+0.208712q142.20871q15+1.00000q16+1.58258q174.79129q180.791288q200.582576q211.00000q22+7.58258q232.79129q244.37386q25+5.79129q26+5.00000q270.208712q286.79129q29+2.20871q30+6.20871q311.00000q32+2.79129q331.58258q34+0.165151q35+4.79129q368.00000q3716.1652q39+0.791288q403.79129q41+0.582576q426.37386q43+1.00000q443.79129q457.58258q469.16515q47+2.79129q486.95644q49+4.37386q50+4.41742q515.79129q527.58258q535.00000q540.791288q55+0.208712q56+6.79129q582.20871q60+2.00000q616.20871q621.00000q63+1.00000q64+4.58258q652.79129q66+0.208712q67+1.58258q68+21.1652q690.165151q702.37386q714.79129q72+0.417424q73+8.00000q7412.2087q750.208712q77+16.1652q783.58258q790.791288q800.417424q81+3.79129q82+0.791288q830.582576q841.25227q85+6.37386q8618.9564q871.00000q88+13.5826q89+3.79129q90+1.20871q91+7.58258q92+17.3303q93+9.16515q942.79129q968.00000q97+6.95644q98+4.79129q99+O(q100)q-1.00000 q^{2} +2.79129 q^{3} +1.00000 q^{4} -0.791288 q^{5} -2.79129 q^{6} -0.208712 q^{7} -1.00000 q^{8} +4.79129 q^{9} +0.791288 q^{10} +1.00000 q^{11} +2.79129 q^{12} -5.79129 q^{13} +0.208712 q^{14} -2.20871 q^{15} +1.00000 q^{16} +1.58258 q^{17} -4.79129 q^{18} -0.791288 q^{20} -0.582576 q^{21} -1.00000 q^{22} +7.58258 q^{23} -2.79129 q^{24} -4.37386 q^{25} +5.79129 q^{26} +5.00000 q^{27} -0.208712 q^{28} -6.79129 q^{29} +2.20871 q^{30} +6.20871 q^{31} -1.00000 q^{32} +2.79129 q^{33} -1.58258 q^{34} +0.165151 q^{35} +4.79129 q^{36} -8.00000 q^{37} -16.1652 q^{39} +0.791288 q^{40} -3.79129 q^{41} +0.582576 q^{42} -6.37386 q^{43} +1.00000 q^{44} -3.79129 q^{45} -7.58258 q^{46} -9.16515 q^{47} +2.79129 q^{48} -6.95644 q^{49} +4.37386 q^{50} +4.41742 q^{51} -5.79129 q^{52} -7.58258 q^{53} -5.00000 q^{54} -0.791288 q^{55} +0.208712 q^{56} +6.79129 q^{58} -2.20871 q^{60} +2.00000 q^{61} -6.20871 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.58258 q^{65} -2.79129 q^{66} +0.208712 q^{67} +1.58258 q^{68} +21.1652 q^{69} -0.165151 q^{70} -2.37386 q^{71} -4.79129 q^{72} +0.417424 q^{73} +8.00000 q^{74} -12.2087 q^{75} -0.208712 q^{77} +16.1652 q^{78} -3.58258 q^{79} -0.791288 q^{80} -0.417424 q^{81} +3.79129 q^{82} +0.791288 q^{83} -0.582576 q^{84} -1.25227 q^{85} +6.37386 q^{86} -18.9564 q^{87} -1.00000 q^{88} +13.5826 q^{89} +3.79129 q^{90} +1.20871 q^{91} +7.58258 q^{92} +17.3303 q^{93} +9.16515 q^{94} -2.79129 q^{96} -8.00000 q^{97} +6.95644 q^{98} +4.79129 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q2q2+q3+2q4+3q5q65q72q8+5q93q10+2q11+q127q13+5q149q15+2q166q175q18+3q20+8q21++5q99+O(q100) 2 q - 2 q^{2} + q^{3} + 2 q^{4} + 3 q^{5} - q^{6} - 5 q^{7} - 2 q^{8} + 5 q^{9} - 3 q^{10} + 2 q^{11} + q^{12} - 7 q^{13} + 5 q^{14} - 9 q^{15} + 2 q^{16} - 6 q^{17} - 5 q^{18} + 3 q^{20} + 8 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −1.00000 −0.707107
33 2.79129 1.61155 0.805775 0.592221i 0.201749π-0.201749\pi
0.805775 + 0.592221i 0.201749π0.201749\pi
44 1.00000 0.500000
55 −0.791288 −0.353875 −0.176937 0.984222i 0.556619π-0.556619\pi
−0.176937 + 0.984222i 0.556619π0.556619\pi
66 −2.79129 −1.13954
77 −0.208712 −0.0788858 −0.0394429 0.999222i 0.512558π-0.512558\pi
−0.0394429 + 0.999222i 0.512558π0.512558\pi
88 −1.00000 −0.353553
99 4.79129 1.59710
1010 0.791288 0.250227
1111 1.00000 0.301511
1212 2.79129 0.805775
1313 −5.79129 −1.60621 −0.803107 0.595835i 0.796821π-0.796821\pi
−0.803107 + 0.595835i 0.796821π0.796821\pi
1414 0.208712 0.0557807
1515 −2.20871 −0.570287
1616 1.00000 0.250000
1717 1.58258 0.383831 0.191915 0.981411i 0.438530π-0.438530\pi
0.191915 + 0.981411i 0.438530π0.438530\pi
1818 −4.79129 −1.12932
1919 0 0
2020 −0.791288 −0.176937
2121 −0.582576 −0.127128
2222 −1.00000 −0.213201
2323 7.58258 1.58108 0.790538 0.612413i 0.209801π-0.209801\pi
0.790538 + 0.612413i 0.209801π0.209801\pi
2424 −2.79129 −0.569769
2525 −4.37386 −0.874773
2626 5.79129 1.13576
2727 5.00000 0.962250
2828 −0.208712 −0.0394429
2929 −6.79129 −1.26111 −0.630555 0.776144i 0.717173π-0.717173\pi
−0.630555 + 0.776144i 0.717173π0.717173\pi
3030 2.20871 0.403254
3131 6.20871 1.11512 0.557559 0.830137i 0.311738π-0.311738\pi
0.557559 + 0.830137i 0.311738π0.311738\pi
3232 −1.00000 −0.176777
3333 2.79129 0.485901
3434 −1.58258 −0.271409
3535 0.165151 0.0279157
3636 4.79129 0.798548
3737 −8.00000 −1.31519 −0.657596 0.753371i 0.728427π-0.728427\pi
−0.657596 + 0.753371i 0.728427π0.728427\pi
3838 0 0
3939 −16.1652 −2.58850
4040 0.791288 0.125114
4141 −3.79129 −0.592100 −0.296050 0.955172i 0.595669π-0.595669\pi
−0.296050 + 0.955172i 0.595669π0.595669\pi
4242 0.582576 0.0898934
4343 −6.37386 −0.972005 −0.486003 0.873957i 0.661545π-0.661545\pi
−0.486003 + 0.873957i 0.661545π0.661545\pi
4444 1.00000 0.150756
4545 −3.79129 −0.565172
4646 −7.58258 −1.11799
4747 −9.16515 −1.33687 −0.668437 0.743768i 0.733037π-0.733037\pi
−0.668437 + 0.743768i 0.733037π0.733037\pi
4848 2.79129 0.402888
4949 −6.95644 −0.993777
5050 4.37386 0.618558
5151 4.41742 0.618563
5252 −5.79129 −0.803107
5353 −7.58258 −1.04155 −0.520773 0.853695i 0.674356π-0.674356\pi
−0.520773 + 0.853695i 0.674356π0.674356\pi
5454 −5.00000 −0.680414
5555 −0.791288 −0.106697
5656 0.208712 0.0278903
5757 0 0
5858 6.79129 0.891740
5959 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
6060 −2.20871 −0.285144
6161 2.00000 0.256074 0.128037 0.991769i 0.459132π-0.459132\pi
0.128037 + 0.991769i 0.459132π0.459132\pi
6262 −6.20871 −0.788507
6363 −1.00000 −0.125988
6464 1.00000 0.125000
6565 4.58258 0.568399
6666 −2.79129 −0.343584
6767 0.208712 0.0254982 0.0127491 0.999919i 0.495942π-0.495942\pi
0.0127491 + 0.999919i 0.495942π0.495942\pi
6868 1.58258 0.191915
6969 21.1652 2.54798
7070 −0.165151 −0.0197394
7171 −2.37386 −0.281726 −0.140863 0.990029i 0.544988π-0.544988\pi
−0.140863 + 0.990029i 0.544988π0.544988\pi
7272 −4.79129 −0.564659
7373 0.417424 0.0488558 0.0244279 0.999702i 0.492224π-0.492224\pi
0.0244279 + 0.999702i 0.492224π0.492224\pi
7474 8.00000 0.929981
7575 −12.2087 −1.40974
7676 0 0
7777 −0.208712 −0.0237850
7878 16.1652 1.83034
7979 −3.58258 −0.403071 −0.201536 0.979481i 0.564593π-0.564593\pi
−0.201536 + 0.979481i 0.564593π0.564593\pi
8080 −0.791288 −0.0884687
8181 −0.417424 −0.0463805
8282 3.79129 0.418678
8383 0.791288 0.0868551 0.0434276 0.999057i 0.486172π-0.486172\pi
0.0434276 + 0.999057i 0.486172π0.486172\pi
8484 −0.582576 −0.0635642
8585 −1.25227 −0.135828
8686 6.37386 0.687311
8787 −18.9564 −2.03234
8888 −1.00000 −0.106600
8989 13.5826 1.43975 0.719875 0.694104i 0.244199π-0.244199\pi
0.719875 + 0.694104i 0.244199π0.244199\pi
9090 3.79129 0.399637
9191 1.20871 0.126707
9292 7.58258 0.790538
9393 17.3303 1.79707
9494 9.16515 0.945313
9595 0 0
9696 −2.79129 −0.284885
9797 −8.00000 −0.812277 −0.406138 0.913812i 0.633125π-0.633125\pi
−0.406138 + 0.913812i 0.633125π0.633125\pi
9898 6.95644 0.702706
9999 4.79129 0.481543
100100 −4.37386 −0.437386
101101 −4.41742 −0.439550 −0.219775 0.975551i 0.570532π-0.570532\pi
−0.219775 + 0.975551i 0.570532π0.570532\pi
102102 −4.41742 −0.437390
103103 19.9564 1.96637 0.983183 0.182622i 0.0584585π-0.0584585\pi
0.983183 + 0.182622i 0.0584585π0.0584585\pi
104104 5.79129 0.567882
105105 0.460985 0.0449875
106106 7.58258 0.736485
107107 −18.0000 −1.74013 −0.870063 0.492941i 0.835922π-0.835922\pi
−0.870063 + 0.492941i 0.835922π0.835922\pi
108108 5.00000 0.481125
109109 10.0000 0.957826 0.478913 0.877862i 0.341031π-0.341031\pi
0.478913 + 0.877862i 0.341031π0.341031\pi
110110 0.791288 0.0754463
111111 −22.3303 −2.11950
112112 −0.208712 −0.0197214
113113 3.16515 0.297752 0.148876 0.988856i 0.452434π-0.452434\pi
0.148876 + 0.988856i 0.452434π0.452434\pi
114114 0 0
115115 −6.00000 −0.559503
116116 −6.79129 −0.630555
117117 −27.7477 −2.56528
118118 0 0
119119 −0.330303 −0.0302788
120120 2.20871 0.201627
121121 1.00000 0.0909091
122122 −2.00000 −0.181071
123123 −10.5826 −0.954199
124124 6.20871 0.557559
125125 7.41742 0.663435
126126 1.00000 0.0890871
127127 −18.7477 −1.66359 −0.831796 0.555082i 0.812687π-0.812687\pi
−0.831796 + 0.555082i 0.812687π0.812687\pi
128128 −1.00000 −0.0883883
129129 −17.7913 −1.56644
130130 −4.58258 −0.401918
131131 17.3739 1.51796 0.758981 0.651113i 0.225698π-0.225698\pi
0.758981 + 0.651113i 0.225698π0.225698\pi
132132 2.79129 0.242950
133133 0 0
134134 −0.208712 −0.0180300
135135 −3.95644 −0.340516
136136 −1.58258 −0.135705
137137 9.79129 0.836526 0.418263 0.908326i 0.362639π-0.362639\pi
0.418263 + 0.908326i 0.362639π0.362639\pi
138138 −21.1652 −1.80170
139139 −16.7913 −1.42422 −0.712109 0.702069i 0.752260π-0.752260\pi
−0.712109 + 0.702069i 0.752260π0.752260\pi
140140 0.165151 0.0139578
141141 −25.5826 −2.15444
142142 2.37386 0.199210
143143 −5.79129 −0.484292
144144 4.79129 0.399274
145145 5.37386 0.446275
146146 −0.417424 −0.0345463
147147 −19.4174 −1.60152
148148 −8.00000 −0.657596
149149 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
150150 12.2087 0.996837
151151 −2.00000 −0.162758 −0.0813788 0.996683i 0.525932π-0.525932\pi
−0.0813788 + 0.996683i 0.525932π0.525932\pi
152152 0 0
153153 7.58258 0.613015
154154 0.208712 0.0168185
155155 −4.91288 −0.394612
156156 −16.1652 −1.29425
157157 11.9564 0.954228 0.477114 0.878841i 0.341683π-0.341683\pi
0.477114 + 0.878841i 0.341683π0.341683\pi
158158 3.58258 0.285014
159159 −21.1652 −1.67851
160160 0.791288 0.0625568
161161 −1.58258 −0.124724
162162 0.417424 0.0327960
163163 −2.41742 −0.189347 −0.0946736 0.995508i 0.530181π-0.530181\pi
−0.0946736 + 0.995508i 0.530181π0.530181\pi
164164 −3.79129 −0.296050
165165 −2.20871 −0.171948
166166 −0.791288 −0.0614158
167167 −18.0000 −1.39288 −0.696441 0.717614i 0.745234π-0.745234\pi
−0.696441 + 0.717614i 0.745234π0.745234\pi
168168 0.582576 0.0449467
169169 20.5390 1.57992
170170 1.25227 0.0960449
171171 0 0
172172 −6.37386 −0.486003
173173 9.95644 0.756974 0.378487 0.925607i 0.376444π-0.376444\pi
0.378487 + 0.925607i 0.376444π0.376444\pi
174174 18.9564 1.43708
175175 0.912878 0.0690071
176176 1.00000 0.0753778
177177 0 0
178178 −13.5826 −1.01806
179179 18.9564 1.41687 0.708435 0.705776i 0.249401π-0.249401\pi
0.708435 + 0.705776i 0.249401π0.249401\pi
180180 −3.79129 −0.282586
181181 8.74773 0.650213 0.325107 0.945677i 0.394600π-0.394600\pi
0.325107 + 0.945677i 0.394600π0.394600\pi
182182 −1.20871 −0.0895957
183183 5.58258 0.412676
184184 −7.58258 −0.558995
185185 6.33030 0.465413
186186 −17.3303 −1.27072
187187 1.58258 0.115729
188188 −9.16515 −0.668437
189189 −1.04356 −0.0759079
190190 0 0
191191 −18.0000 −1.30243 −0.651217 0.758891i 0.725741π-0.725741\pi
−0.651217 + 0.758891i 0.725741π0.725741\pi
192192 2.79129 0.201444
193193 6.37386 0.458801 0.229400 0.973332i 0.426323π-0.426323\pi
0.229400 + 0.973332i 0.426323π0.426323\pi
194194 8.00000 0.574367
195195 12.7913 0.916003
196196 −6.95644 −0.496889
197197 −9.16515 −0.652990 −0.326495 0.945199i 0.605868π-0.605868\pi
−0.326495 + 0.945199i 0.605868π0.605868\pi
198198 −4.79129 −0.340502
199199 −20.7477 −1.47077 −0.735384 0.677651i 0.762998π-0.762998\pi
−0.735384 + 0.677651i 0.762998π0.762998\pi
200200 4.37386 0.309279
201201 0.582576 0.0410917
202202 4.41742 0.310809
203203 1.41742 0.0994837
204204 4.41742 0.309282
205205 3.00000 0.209529
206206 −19.9564 −1.39043
207207 36.3303 2.52513
208208 −5.79129 −0.401554
209209 0 0
210210 −0.460985 −0.0318110
211211 8.74773 0.602218 0.301109 0.953590i 0.402643π-0.402643\pi
0.301109 + 0.953590i 0.402643π0.402643\pi
212212 −7.58258 −0.520773
213213 −6.62614 −0.454015
214214 18.0000 1.23045
215215 5.04356 0.343968
216216 −5.00000 −0.340207
217217 −1.29583 −0.0879669
218218 −10.0000 −0.677285
219219 1.16515 0.0787336
220220 −0.791288 −0.0533486
221221 −9.16515 −0.616515
222222 22.3303 1.49871
223223 −11.1652 −0.747674 −0.373837 0.927494i 0.621958π-0.621958\pi
−0.373837 + 0.927494i 0.621958π0.621958\pi
224224 0.208712 0.0139452
225225 −20.9564 −1.39710
226226 −3.16515 −0.210543
227227 −1.58258 −0.105039 −0.0525196 0.998620i 0.516725π-0.516725\pi
−0.0525196 + 0.998620i 0.516725π0.516725\pi
228228 0 0
229229 −4.62614 −0.305704 −0.152852 0.988249i 0.548846π-0.548846\pi
−0.152852 + 0.988249i 0.548846π0.548846\pi
230230 6.00000 0.395628
231231 −0.582576 −0.0383307
232232 6.79129 0.445870
233233 −3.16515 −0.207356 −0.103678 0.994611i 0.533061π-0.533061\pi
−0.103678 + 0.994611i 0.533061π0.533061\pi
234234 27.7477 1.81393
235235 7.25227 0.473086
236236 0 0
237237 −10.0000 −0.649570
238238 0.330303 0.0214103
239239 −6.79129 −0.439292 −0.219646 0.975580i 0.570490π-0.570490\pi
−0.219646 + 0.975580i 0.570490π0.570490\pi
240240 −2.20871 −0.142572
241241 4.79129 0.308634 0.154317 0.988021i 0.450682π-0.450682\pi
0.154317 + 0.988021i 0.450682π0.450682\pi
242242 −1.00000 −0.0642824
243243 −16.1652 −1.03699
244244 2.00000 0.128037
245245 5.50455 0.351673
246246 10.5826 0.674720
247247 0 0
248248 −6.20871 −0.394254
249249 2.20871 0.139971
250250 −7.41742 −0.469119
251251 12.0000 0.757433 0.378717 0.925513i 0.376365π-0.376365\pi
0.378717 + 0.925513i 0.376365π0.376365\pi
252252 −1.00000 −0.0629941
253253 7.58258 0.476712
254254 18.7477 1.17634
255255 −3.49545 −0.218894
256256 1.00000 0.0625000
257257 −1.58258 −0.0987184 −0.0493592 0.998781i 0.515718π-0.515718\pi
−0.0493592 + 0.998781i 0.515718π0.515718\pi
258258 17.7913 1.10764
259259 1.66970 0.103750
260260 4.58258 0.284199
261261 −32.5390 −2.01411
262262 −17.3739 −1.07336
263263 −9.95644 −0.613940 −0.306970 0.951719i 0.599315π-0.599315\pi
−0.306970 + 0.951719i 0.599315π0.599315\pi
264264 −2.79129 −0.171792
265265 6.00000 0.368577
266266 0 0
267267 37.9129 2.32023
268268 0.208712 0.0127491
269269 −10.7477 −0.655300 −0.327650 0.944799i 0.606257π-0.606257\pi
−0.327650 + 0.944799i 0.606257π0.606257\pi
270270 3.95644 0.240781
271271 7.37386 0.447930 0.223965 0.974597i 0.428100π-0.428100\pi
0.223965 + 0.974597i 0.428100π0.428100\pi
272272 1.58258 0.0959577
273273 3.37386 0.204196
274274 −9.79129 −0.591513
275275 −4.37386 −0.263754
276276 21.1652 1.27399
277277 −22.0000 −1.32185 −0.660926 0.750451i 0.729836π-0.729836\pi
−0.660926 + 0.750451i 0.729836π0.729836\pi
278278 16.7913 1.00707
279279 29.7477 1.78095
280280 −0.165151 −0.00986968
281281 19.1216 1.14070 0.570349 0.821402i 0.306808π-0.306808\pi
0.570349 + 0.821402i 0.306808π0.306808\pi
282282 25.5826 1.52342
283283 −32.1216 −1.90943 −0.954715 0.297521i 0.903840π-0.903840\pi
−0.954715 + 0.297521i 0.903840π0.903840\pi
284284 −2.37386 −0.140863
285285 0 0
286286 5.79129 0.342446
287287 0.791288 0.0467082
288288 −4.79129 −0.282329
289289 −14.4955 −0.852674
290290 −5.37386 −0.315564
291291 −22.3303 −1.30903
292292 0.417424 0.0244279
293293 −2.20871 −0.129034 −0.0645172 0.997917i 0.520551π-0.520551\pi
−0.0645172 + 0.997917i 0.520551π0.520551\pi
294294 19.4174 1.13245
295295 0 0
296296 8.00000 0.464991
297297 5.00000 0.290129
298298 0 0
299299 −43.9129 −2.53955
300300 −12.2087 −0.704870
301301 1.33030 0.0766774
302302 2.00000 0.115087
303303 −12.3303 −0.708357
304304 0 0
305305 −1.58258 −0.0906180
306306 −7.58258 −0.433467
307307 32.7477 1.86901 0.934506 0.355948i 0.115842π-0.115842\pi
0.934506 + 0.355948i 0.115842π0.115842\pi
308308 −0.208712 −0.0118925
309309 55.7042 3.16890
310310 4.91288 0.279033
311311 19.9129 1.12916 0.564578 0.825380i 0.309039π-0.309039\pi
0.564578 + 0.825380i 0.309039π0.309039\pi
312312 16.1652 0.915171
313313 4.37386 0.247225 0.123613 0.992331i 0.460552π-0.460552\pi
0.123613 + 0.992331i 0.460552π0.460552\pi
314314 −11.9564 −0.674741
315315 0.791288 0.0445840
316316 −3.58258 −0.201536
317317 −28.7477 −1.61463 −0.807317 0.590119i 0.799081π-0.799081\pi
−0.807317 + 0.590119i 0.799081π0.799081\pi
318318 21.1652 1.18688
319319 −6.79129 −0.380239
320320 −0.791288 −0.0442343
321321 −50.2432 −2.80430
322322 1.58258 0.0881935
323323 0 0
324324 −0.417424 −0.0231902
325325 25.3303 1.40507
326326 2.41742 0.133889
327327 27.9129 1.54359
328328 3.79129 0.209339
329329 1.91288 0.105460
330330 2.20871 0.121586
331331 −25.2087 −1.38560 −0.692798 0.721132i 0.743622π-0.743622\pi
−0.692798 + 0.721132i 0.743622π0.743622\pi
332332 0.791288 0.0434276
333333 −38.3303 −2.10049
334334 18.0000 0.984916
335335 −0.165151 −0.00902318
336336 −0.582576 −0.0317821
337337 27.3739 1.49115 0.745575 0.666422i 0.232175π-0.232175\pi
0.745575 + 0.666422i 0.232175π0.232175\pi
338338 −20.5390 −1.11718
339339 8.83485 0.479843
340340 −1.25227 −0.0679140
341341 6.20871 0.336221
342342 0 0
343343 2.91288 0.157281
344344 6.37386 0.343656
345345 −16.7477 −0.901667
346346 −9.95644 −0.535261
347347 15.1652 0.814108 0.407054 0.913404i 0.366556π-0.366556\pi
0.407054 + 0.913404i 0.366556π0.366556\pi
348348 −18.9564 −1.01617
349349 −31.4955 −1.68591 −0.842957 0.537982i 0.819187π-0.819187\pi
−0.842957 + 0.537982i 0.819187π0.819187\pi
350350 −0.912878 −0.0487954
351351 −28.9564 −1.54558
352352 −1.00000 −0.0533002
353353 −33.1652 −1.76520 −0.882601 0.470122i 0.844210π-0.844210\pi
−0.882601 + 0.470122i 0.844210π0.844210\pi
354354 0 0
355355 1.87841 0.0996956
356356 13.5826 0.719875
357357 −0.921970 −0.0487958
358358 −18.9564 −1.00188
359359 −29.7042 −1.56773 −0.783863 0.620934i 0.786754π-0.786754\pi
−0.783863 + 0.620934i 0.786754π0.786754\pi
360360 3.79129 0.199818
361361 0 0
362362 −8.74773 −0.459770
363363 2.79129 0.146505
364364 1.20871 0.0633537
365365 −0.330303 −0.0172888
366366 −5.58258 −0.291806
367367 −16.3303 −0.852435 −0.426217 0.904621i 0.640154π-0.640154\pi
−0.426217 + 0.904621i 0.640154π0.640154\pi
368368 7.58258 0.395269
369369 −18.1652 −0.945640
370370 −6.33030 −0.329097
371371 1.58258 0.0821632
372372 17.3303 0.898534
373373 −4.37386 −0.226470 −0.113235 0.993568i 0.536121π-0.536121\pi
−0.113235 + 0.993568i 0.536121π0.536121\pi
374374 −1.58258 −0.0818330
375375 20.7042 1.06916
376376 9.16515 0.472657
377377 39.3303 2.02561
378378 1.04356 0.0536750
379379 −28.2087 −1.44898 −0.724492 0.689283i 0.757926π-0.757926\pi
−0.724492 + 0.689283i 0.757926π0.757926\pi
380380 0 0
381381 −52.3303 −2.68096
382382 18.0000 0.920960
383383 −12.9564 −0.662043 −0.331022 0.943623i 0.607393π-0.607393\pi
−0.331022 + 0.943623i 0.607393π0.607393\pi
384384 −2.79129 −0.142442
385385 0.165151 0.00841689
386386 −6.37386 −0.324421
387387 −30.5390 −1.55239
388388 −8.00000 −0.406138
389389 −31.1216 −1.57793 −0.788964 0.614440i 0.789382π-0.789382\pi
−0.788964 + 0.614440i 0.789382π0.789382\pi
390390 −12.7913 −0.647712
391391 12.0000 0.606866
392392 6.95644 0.351353
393393 48.4955 2.44627
394394 9.16515 0.461734
395395 2.83485 0.142637
396396 4.79129 0.240771
397397 26.9564 1.35290 0.676452 0.736486i 0.263516π-0.263516\pi
0.676452 + 0.736486i 0.263516π0.263516\pi
398398 20.7477 1.03999
399399 0 0
400400 −4.37386 −0.218693
401401 4.41742 0.220596 0.110298 0.993899i 0.464820π-0.464820\pi
0.110298 + 0.993899i 0.464820π0.464820\pi
402402 −0.582576 −0.0290562
403403 −35.9564 −1.79112
404404 −4.41742 −0.219775
405405 0.330303 0.0164129
406406 −1.41742 −0.0703456
407407 −8.00000 −0.396545
408408 −4.41742 −0.218695
409409 −10.3739 −0.512955 −0.256477 0.966550i 0.582562π-0.582562\pi
−0.256477 + 0.966550i 0.582562π0.582562\pi
410410 −3.00000 −0.148159
411411 27.3303 1.34810
412412 19.9564 0.983183
413413 0 0
414414 −36.3303 −1.78554
415415 −0.626136 −0.0307358
416416 5.79129 0.283941
417417 −46.8693 −2.29520
418418 0 0
419419 −24.3303 −1.18861 −0.594307 0.804239i 0.702573π-0.702573\pi
−0.594307 + 0.804239i 0.702573π0.702573\pi
420420 0.460985 0.0224938
421421 38.7477 1.88845 0.944224 0.329303i 0.106814π-0.106814\pi
0.944224 + 0.329303i 0.106814π0.106814\pi
422422 −8.74773 −0.425833
423423 −43.9129 −2.13512
424424 7.58258 0.368242
425425 −6.92197 −0.335765
426426 6.62614 0.321037
427427 −0.417424 −0.0202006
428428 −18.0000 −0.870063
429429 −16.1652 −0.780461
430430 −5.04356 −0.243222
431431 −33.4955 −1.61342 −0.806710 0.590948i 0.798754π-0.798754\pi
−0.806710 + 0.590948i 0.798754π0.798754\pi
432432 5.00000 0.240563
433433 2.41742 0.116174 0.0580870 0.998312i 0.481500π-0.481500\pi
0.0580870 + 0.998312i 0.481500π0.481500\pi
434434 1.29583 0.0622020
435435 15.0000 0.719195
436436 10.0000 0.478913
437437 0 0
438438 −1.16515 −0.0556731
439439 12.8348 0.612574 0.306287 0.951939i 0.400913π-0.400913\pi
0.306287 + 0.951939i 0.400913π0.400913\pi
440440 0.791288 0.0377232
441441 −33.3303 −1.58716
442442 9.16515 0.435942
443443 18.3303 0.870899 0.435449 0.900213i 0.356589π-0.356589\pi
0.435449 + 0.900213i 0.356589π0.356589\pi
444444 −22.3303 −1.05975
445445 −10.7477 −0.509491
446446 11.1652 0.528685
447447 0 0
448448 −0.208712 −0.00986072
449449 10.7477 0.507217 0.253608 0.967307i 0.418383π-0.418383\pi
0.253608 + 0.967307i 0.418383π0.418383\pi
450450 20.9564 0.987896
451451 −3.79129 −0.178525
452452 3.16515 0.148876
453453 −5.58258 −0.262292
454454 1.58258 0.0742740
455455 −0.956439 −0.0448386
456456 0 0
457457 −32.7477 −1.53187 −0.765937 0.642916i 0.777725π-0.777725\pi
−0.765937 + 0.642916i 0.777725π0.777725\pi
458458 4.62614 0.216165
459459 7.91288 0.369342
460460 −6.00000 −0.279751
461461 6.33030 0.294832 0.147416 0.989075i 0.452904π-0.452904\pi
0.147416 + 0.989075i 0.452904π0.452904\pi
462462 0.582576 0.0271039
463463 32.6606 1.51787 0.758934 0.651168i 0.225721π-0.225721\pi
0.758934 + 0.651168i 0.225721π0.225721\pi
464464 −6.79129 −0.315278
465465 −13.7133 −0.635937
466466 3.16515 0.146623
467467 4.41742 0.204414 0.102207 0.994763i 0.467410π-0.467410\pi
0.102207 + 0.994763i 0.467410π0.467410\pi
468468 −27.7477 −1.28264
469469 −0.0435608 −0.00201145
470470 −7.25227 −0.334522
471471 33.3739 1.53779
472472 0 0
473473 −6.37386 −0.293071
474474 10.0000 0.459315
475475 0 0
476476 −0.330303 −0.0151394
477477 −36.3303 −1.66345
478478 6.79129 0.310626
479479 −8.20871 −0.375066 −0.187533 0.982258i 0.560049π-0.560049\pi
−0.187533 + 0.982258i 0.560049π0.560049\pi
480480 2.20871 0.100813
481481 46.3303 2.11248
482482 −4.79129 −0.218237
483483 −4.41742 −0.201000
484484 1.00000 0.0454545
485485 6.33030 0.287444
486486 16.1652 0.733266
487487 23.1216 1.04774 0.523870 0.851798i 0.324488π-0.324488\pi
0.523870 + 0.851798i 0.324488π0.324488\pi
488488 −2.00000 −0.0905357
489489 −6.74773 −0.305143
490490 −5.50455 −0.248670
491491 38.8693 1.75415 0.877074 0.480356i 0.159492π-0.159492\pi
0.877074 + 0.480356i 0.159492π0.159492\pi
492492 −10.5826 −0.477099
493493 −10.7477 −0.484053
494494 0 0
495495 −3.79129 −0.170406
496496 6.20871 0.278779
497497 0.495454 0.0222242
498498 −2.20871 −0.0989748
499499 17.1652 0.768418 0.384209 0.923246i 0.374474π-0.374474\pi
0.384209 + 0.923246i 0.374474π0.374474\pi
500500 7.41742 0.331717
501501 −50.2432 −2.24470
502502 −12.0000 −0.535586
503503 −9.95644 −0.443936 −0.221968 0.975054i 0.571248π-0.571248\pi
−0.221968 + 0.975054i 0.571248π0.571248\pi
504504 1.00000 0.0445435
505505 3.49545 0.155546
506506 −7.58258 −0.337087
507507 57.3303 2.54613
508508 −18.7477 −0.831796
509509 27.1652 1.20407 0.602037 0.798468i 0.294356π-0.294356\pi
0.602037 + 0.798468i 0.294356π0.294356\pi
510510 3.49545 0.154781
511511 −0.0871215 −0.00385403
512512 −1.00000 −0.0441942
513513 0 0
514514 1.58258 0.0698044
515515 −15.7913 −0.695847
516516 −17.7913 −0.783218
517517 −9.16515 −0.403083
518518 −1.66970 −0.0733623
519519 27.7913 1.21990
520520 −4.58258 −0.200959
521521 −14.8348 −0.649927 −0.324963 0.945727i 0.605352π-0.605352\pi
−0.324963 + 0.945727i 0.605352π0.605352\pi
522522 32.5390 1.42419
523523 −24.7477 −1.08214 −0.541071 0.840977i 0.681981π-0.681981\pi
−0.541071 + 0.840977i 0.681981π0.681981\pi
524524 17.3739 0.758981
525525 2.54811 0.111208
526526 9.95644 0.434121
527527 9.82576 0.428017
528528 2.79129 0.121475
529529 34.4955 1.49980
530530 −6.00000 −0.260623
531531 0 0
532532 0 0
533533 21.9564 0.951039
534534 −37.9129 −1.64065
535535 14.2432 0.615786
536536 −0.208712 −0.00901499
537537 52.9129 2.28336
538538 10.7477 0.463367
539539 −6.95644 −0.299635
540540 −3.95644 −0.170258
541541 9.91288 0.426188 0.213094 0.977032i 0.431646π-0.431646\pi
0.213094 + 0.977032i 0.431646π0.431646\pi
542542 −7.37386 −0.316735
543543 24.4174 1.04785
544544 −1.58258 −0.0678524
545545 −7.91288 −0.338950
546546 −3.37386 −0.144388
547547 24.8348 1.06186 0.530931 0.847415i 0.321842π-0.321842\pi
0.530931 + 0.847415i 0.321842π0.321842\pi
548548 9.79129 0.418263
549549 9.58258 0.408974
550550 4.37386 0.186502
551551 0 0
552552 −21.1652 −0.900849
553553 0.747727 0.0317966
554554 22.0000 0.934690
555555 17.6697 0.750037
556556 −16.7913 −0.712109
557557 −39.1652 −1.65948 −0.829740 0.558150i 0.811512π-0.811512\pi
−0.829740 + 0.558150i 0.811512π0.811512\pi
558558 −29.7477 −1.25932
559559 36.9129 1.56125
560560 0.165151 0.00697892
561561 4.41742 0.186504
562562 −19.1216 −0.806596
563563 −42.6606 −1.79793 −0.898965 0.438020i 0.855680π-0.855680\pi
−0.898965 + 0.438020i 0.855680π0.855680\pi
564564 −25.5826 −1.07722
565565 −2.50455 −0.105367
566566 32.1216 1.35017
567567 0.0871215 0.00365876
568568 2.37386 0.0996051
569569 −18.9564 −0.794695 −0.397348 0.917668i 0.630069π-0.630069\pi
−0.397348 + 0.917668i 0.630069π0.630069\pi
570570 0 0
571571 10.2087 0.427221 0.213611 0.976919i 0.431478π-0.431478\pi
0.213611 + 0.976919i 0.431478π0.431478\pi
572572 −5.79129 −0.242146
573573 −50.2432 −2.09894
574574 −0.791288 −0.0330277
575575 −33.1652 −1.38308
576576 4.79129 0.199637
577577 34.8693 1.45163 0.725814 0.687891i 0.241463π-0.241463\pi
0.725814 + 0.687891i 0.241463π0.241463\pi
578578 14.4955 0.602931
579579 17.7913 0.739381
580580 5.37386 0.223138
581581 −0.165151 −0.00685163
582582 22.3303 0.925621
583583 −7.58258 −0.314038
584584 −0.417424 −0.0172731
585585 21.9564 0.907787
586586 2.20871 0.0912411
587587 15.1652 0.625933 0.312966 0.949764i 0.398677π-0.398677\pi
0.312966 + 0.949764i 0.398677π0.398677\pi
588588 −19.4174 −0.800761
589589 0 0
590590 0 0
591591 −25.5826 −1.05233
592592 −8.00000 −0.328798
593593 21.1652 0.869149 0.434574 0.900636i 0.356899π-0.356899\pi
0.434574 + 0.900636i 0.356899π0.356899\pi
594594 −5.00000 −0.205152
595595 0.261365 0.0107149
596596 0 0
597597 −57.9129 −2.37022
598598 43.9129 1.79573
599599 −3.95644 −0.161656 −0.0808279 0.996728i 0.525756π-0.525756\pi
−0.0808279 + 0.996728i 0.525756π0.525756\pi
600600 12.2087 0.498419
601601 19.7913 0.807303 0.403652 0.914913i 0.367741π-0.367741\pi
0.403652 + 0.914913i 0.367741π0.367741\pi
602602 −1.33030 −0.0542191
603603 1.00000 0.0407231
604604 −2.00000 −0.0813788
605605 −0.791288 −0.0321704
606606 12.3303 0.500884
607607 29.9129 1.21413 0.607063 0.794654i 0.292347π-0.292347\pi
0.607063 + 0.794654i 0.292347π0.292347\pi
608608 0 0
609609 3.95644 0.160323
610610 1.58258 0.0640766
611611 53.0780 2.14731
612612 7.58258 0.306507
613613 14.0000 0.565455 0.282727 0.959200i 0.408761π-0.408761\pi
0.282727 + 0.959200i 0.408761π0.408761\pi
614614 −32.7477 −1.32159
615615 8.37386 0.337667
616616 0.208712 0.00840925
617617 9.79129 0.394182 0.197091 0.980385i 0.436850π-0.436850\pi
0.197091 + 0.980385i 0.436850π0.436850\pi
618618 −55.7042 −2.24075
619619 17.1652 0.689926 0.344963 0.938616i 0.387892π-0.387892\pi
0.344963 + 0.938616i 0.387892π0.387892\pi
620620 −4.91288 −0.197306
621621 37.9129 1.52139
622622 −19.9129 −0.798434
623623 −2.83485 −0.113576
624624 −16.1652 −0.647124
625625 16.0000 0.640000
626626 −4.37386 −0.174815
627627 0 0
628628 11.9564 0.477114
629629 −12.6606 −0.504811
630630 −0.791288 −0.0315257
631631 9.91288 0.394625 0.197313 0.980341i 0.436779π-0.436779\pi
0.197313 + 0.980341i 0.436779π0.436779\pi
632632 3.58258 0.142507
633633 24.4174 0.970505
634634 28.7477 1.14172
635635 14.8348 0.588703
636636 −21.1652 −0.839253
637637 40.2867 1.59622
638638 6.79129 0.268870
639639 −11.3739 −0.449943
640640 0.791288 0.0312784
641641 −25.5826 −1.01045 −0.505225 0.862987i 0.668591π-0.668591\pi
−0.505225 + 0.862987i 0.668591π0.668591\pi
642642 50.2432 1.98294
643643 −10.3303 −0.407387 −0.203694 0.979035i 0.565295π-0.565295\pi
−0.203694 + 0.979035i 0.565295π0.565295\pi
644644 −1.58258 −0.0623622
645645 14.0780 0.554322
646646 0 0
647647 −19.9129 −0.782856 −0.391428 0.920209i 0.628019π-0.628019\pi
−0.391428 + 0.920209i 0.628019π0.628019\pi
648648 0.417424 0.0163980
649649 0 0
650650 −25.3303 −0.993536
651651 −3.61704 −0.141763
652652 −2.41742 −0.0946736
653653 −49.2867 −1.92874 −0.964370 0.264559i 0.914774π-0.914774\pi
−0.964370 + 0.264559i 0.914774π0.914774\pi
654654 −27.9129 −1.09148
655655 −13.7477 −0.537168
656656 −3.79129 −0.148025
657657 2.00000 0.0780274
658658 −1.91288 −0.0745718
659659 37.9129 1.47688 0.738438 0.674321i 0.235564π-0.235564\pi
0.738438 + 0.674321i 0.235564π0.235564\pi
660660 −2.20871 −0.0859740
661661 −32.0000 −1.24466 −0.622328 0.782757i 0.713813π-0.713813\pi
−0.622328 + 0.782757i 0.713813π0.713813\pi
662662 25.2087 0.979764
663663 −25.5826 −0.993545
664664 −0.791288 −0.0307079
665665 0 0
666666 38.3303 1.48527
667667 −51.4955 −1.99391
668668 −18.0000 −0.696441
669669 −31.1652 −1.20491
670670 0.165151 0.00638035
671671 2.00000 0.0772091
672672 0.582576 0.0224733
673673 34.9564 1.34747 0.673736 0.738972i 0.264689π-0.264689\pi
0.673736 + 0.738972i 0.264689π0.264689\pi
674674 −27.3739 −1.05440
675675 −21.8693 −0.841750
676676 20.5390 0.789962
677677 −0.460985 −0.0177171 −0.00885855 0.999961i 0.502820π-0.502820\pi
−0.00885855 + 0.999961i 0.502820π0.502820\pi
678678 −8.83485 −0.339300
679679 1.66970 0.0640771
680680 1.25227 0.0480225
681681 −4.41742 −0.169276
682682 −6.20871 −0.237744
683683 24.6606 0.943612 0.471806 0.881702i 0.343602π-0.343602\pi
0.471806 + 0.881702i 0.343602π0.343602\pi
684684 0 0
685685 −7.74773 −0.296025
686686 −2.91288 −0.111214
687687 −12.9129 −0.492657
688688 −6.37386 −0.243001
689689 43.9129 1.67295
690690 16.7477 0.637575
691691 23.4955 0.893809 0.446905 0.894582i 0.352526π-0.352526\pi
0.446905 + 0.894582i 0.352526π0.352526\pi
692692 9.95644 0.378487
693693 −1.00000 −0.0379869
694694 −15.1652 −0.575661
695695 13.2867 0.503995
696696 18.9564 0.718542
697697 −6.00000 −0.227266
698698 31.4955 1.19212
699699 −8.83485 −0.334165
700700 0.912878 0.0345036
701701 −42.3303 −1.59879 −0.799397 0.600804i 0.794847π-0.794847\pi
−0.799397 + 0.600804i 0.794847π0.794847\pi
702702 28.9564 1.09289
703703 0 0
704704 1.00000 0.0376889
705705 20.2432 0.762402
706706 33.1652 1.24819
707707 0.921970 0.0346743
708708 0 0
709709 28.2087 1.05940 0.529700 0.848185i 0.322304π-0.322304\pi
0.529700 + 0.848185i 0.322304π0.322304\pi
710710 −1.87841 −0.0704954
711711 −17.1652 −0.643743
712712 −13.5826 −0.509029
713713 47.0780 1.76309
714714 0.921970 0.0345039
715715 4.58258 0.171379
716716 18.9564 0.708435
717717 −18.9564 −0.707941
718718 29.7042 1.10855
719719 35.0780 1.30819 0.654095 0.756413i 0.273050π-0.273050\pi
0.654095 + 0.756413i 0.273050π0.273050\pi
720720 −3.79129 −0.141293
721721 −4.16515 −0.155118
722722 0 0
723723 13.3739 0.497379
724724 8.74773 0.325107
725725 29.7042 1.10319
726726 −2.79129 −0.103594
727727 29.4955 1.09393 0.546963 0.837157i 0.315784π-0.315784\pi
0.546963 + 0.837157i 0.315784π0.315784\pi
728728 −1.20871 −0.0447979
729729 −43.8693 −1.62479
730730 0.330303 0.0122251
731731 −10.0871 −0.373086
732732 5.58258 0.206338
733733 35.4955 1.31105 0.655527 0.755172i 0.272446π-0.272446\pi
0.655527 + 0.755172i 0.272446π0.272446\pi
734734 16.3303 0.602762
735735 15.3648 0.566738
736736 −7.58258 −0.279497
737737 0.208712 0.00768801
738738 18.1652 0.668668
739739 16.0436 0.590172 0.295086 0.955471i 0.404652π-0.404652\pi
0.295086 + 0.955471i 0.404652π0.404652\pi
740740 6.33030 0.232707
741741 0 0
742742 −1.58258 −0.0580982
743743 −26.8348 −0.984475 −0.492238 0.870461i 0.663821π-0.663821\pi
−0.492238 + 0.870461i 0.663821π0.663821\pi
744744 −17.3303 −0.635360
745745 0 0
746746 4.37386 0.160139
747747 3.79129 0.138716
748748 1.58258 0.0578647
749749 3.75682 0.137271
750750 −20.7042 −0.756009
751751 −26.3303 −0.960806 −0.480403 0.877048i 0.659510π-0.659510\pi
−0.480403 + 0.877048i 0.659510π0.659510\pi
752752 −9.16515 −0.334219
753753 33.4955 1.22064
754754 −39.3303 −1.43233
755755 1.58258 0.0575958
756756 −1.04356 −0.0379539
757757 −28.7913 −1.04644 −0.523219 0.852199i 0.675269π-0.675269\pi
−0.523219 + 0.852199i 0.675269π0.675269\pi
758758 28.2087 1.02459
759759 21.1652 0.768246
760760 0 0
761761 4.08712 0.148158 0.0740790 0.997252i 0.476398π-0.476398\pi
0.0740790 + 0.997252i 0.476398π0.476398\pi
762762 52.3303 1.89573
763763 −2.08712 −0.0755589
764764 −18.0000 −0.651217
765765 −6.00000 −0.216930
766766 12.9564 0.468135
767767 0 0
768768 2.79129 0.100722
769769 44.3303 1.59859 0.799296 0.600938i 0.205206π-0.205206\pi
0.799296 + 0.600938i 0.205206π0.205206\pi
770770 −0.165151 −0.00595164
771771 −4.41742 −0.159090
772772 6.37386 0.229400
773773 −15.4955 −0.557333 −0.278666 0.960388i 0.589892π-0.589892\pi
−0.278666 + 0.960388i 0.589892π0.589892\pi
774774 30.5390 1.09770
775775 −27.1561 −0.975474
776776 8.00000 0.287183
777777 4.66061 0.167198
778778 31.1216 1.11576
779779 0 0
780780 12.7913 0.458002
781781 −2.37386 −0.0849435
782782 −12.0000 −0.429119
783783 −33.9564 −1.21350
784784 −6.95644 −0.248444
785785 −9.46099 −0.337677
786786 −48.4955 −1.72978
787787 5.58258 0.198997 0.0994987 0.995038i 0.468276π-0.468276\pi
0.0994987 + 0.995038i 0.468276π0.468276\pi
788788 −9.16515 −0.326495
789789 −27.7913 −0.989396
790790 −2.83485 −0.100859
791791 −0.660606 −0.0234884
792792 −4.79129 −0.170251
793793 −11.5826 −0.411309
794794 −26.9564 −0.956648
795795 16.7477 0.593981
796796 −20.7477 −0.735384
797797 −50.2432 −1.77970 −0.889852 0.456249i 0.849193π-0.849193\pi
−0.889852 + 0.456249i 0.849193π0.849193\pi
798798 0 0
799799 −14.5045 −0.513134
800800 4.37386 0.154639
801801 65.0780 2.29942
802802 −4.41742 −0.155985
803803 0.417424 0.0147306
804804 0.582576 0.0205459
805805 1.25227 0.0441368
806806 35.9564 1.26651
807807 −30.0000 −1.05605
808808 4.41742 0.155404
809809 −5.66970 −0.199336 −0.0996680 0.995021i 0.531778π-0.531778\pi
−0.0996680 + 0.995021i 0.531778π0.531778\pi
810810 −0.330303 −0.0116057
811811 −23.4955 −0.825037 −0.412518 0.910949i 0.635351π-0.635351\pi
−0.412518 + 0.910949i 0.635351π0.635351\pi
812812 1.41742 0.0497418
813813 20.5826 0.721862
814814 8.00000 0.280400
815815 1.91288 0.0670052
816816 4.41742 0.154641
817817 0 0
818818 10.3739 0.362714
819819 5.79129 0.202364
820820 3.00000 0.104765
821821 17.0780 0.596027 0.298014 0.954562i 0.403676π-0.403676\pi
0.298014 + 0.954562i 0.403676π0.403676\pi
822822 −27.3303 −0.953254
823823 −37.4955 −1.30701 −0.653505 0.756922i 0.726702π-0.726702\pi
−0.653505 + 0.756922i 0.726702π0.726702\pi
824824 −19.9564 −0.695216
825825 −12.2087 −0.425053
826826 0 0
827827 −48.0000 −1.66912 −0.834562 0.550914i 0.814279π-0.814279\pi
−0.834562 + 0.550914i 0.814279π0.814279\pi
828828 36.3303 1.26257
829829 10.0000 0.347314 0.173657 0.984806i 0.444442π-0.444442\pi
0.173657 + 0.984806i 0.444442π0.444442\pi
830830 0.626136 0.0217335
831831 −61.4083 −2.13023
832832 −5.79129 −0.200777
833833 −11.0091 −0.381442
834834 46.8693 1.62295
835835 14.2432 0.492906
836836 0 0
837837 31.0436 1.07302
838838 24.3303 0.840476
839839 3.95644 0.136591 0.0682957 0.997665i 0.478244π-0.478244\pi
0.0682957 + 0.997665i 0.478244π0.478244\pi
840840 −0.460985 −0.0159055
841841 17.1216 0.590400
842842 −38.7477 −1.33533
843843 53.3739 1.83829
844844 8.74773 0.301109
845845 −16.2523 −0.559095
846846 43.9129 1.50976
847847 −0.208712 −0.00717143
848848 −7.58258 −0.260387
849849 −89.6606 −3.07714
850850 6.92197 0.237422
851851 −60.6606 −2.07942
852852 −6.62614 −0.227008
853853 11.1652 0.382288 0.191144 0.981562i 0.438780π-0.438780\pi
0.191144 + 0.981562i 0.438780π0.438780\pi
854854 0.417424 0.0142840
855855 0 0
856856 18.0000 0.615227
857857 25.2867 0.863779 0.431889 0.901927i 0.357847π-0.357847\pi
0.431889 + 0.901927i 0.357847π0.357847\pi
858858 16.1652 0.551869
859859 41.4955 1.41581 0.707903 0.706309i 0.249641π-0.249641\pi
0.707903 + 0.706309i 0.249641π0.249641\pi
860860 5.04356 0.171984
861861 2.20871 0.0752727
862862 33.4955 1.14086
863863 8.53901 0.290671 0.145336 0.989382i 0.453574π-0.453574\pi
0.145336 + 0.989382i 0.453574π0.453574\pi
864864 −5.00000 −0.170103
865865 −7.87841 −0.267874
866866 −2.41742 −0.0821474
867867 −40.4610 −1.37413
868868 −1.29583 −0.0439835
869869 −3.58258 −0.121531
870870 −15.0000 −0.508548
871871 −1.20871 −0.0409556
872872 −10.0000 −0.338643
873873 −38.3303 −1.29728
874874 0 0
875875 −1.54811 −0.0523356
876876 1.16515 0.0393668
877877 53.1216 1.79379 0.896894 0.442245i 0.145818π-0.145818\pi
0.896894 + 0.442245i 0.145818π0.145818\pi
878878 −12.8348 −0.433155
879879 −6.16515 −0.207945
880880 −0.791288 −0.0266743
881881 28.1216 0.947440 0.473720 0.880675i 0.342911π-0.342911\pi
0.473720 + 0.880675i 0.342911π0.342911\pi
882882 33.3303 1.12229
883883 −23.9129 −0.804732 −0.402366 0.915479i 0.631812π-0.631812\pi
−0.402366 + 0.915479i 0.631812π0.631812\pi
884884 −9.16515 −0.308257
885885 0 0
886886 −18.3303 −0.615819
887887 33.4955 1.12467 0.562334 0.826910i 0.309904π-0.309904\pi
0.562334 + 0.826910i 0.309904π0.309904\pi
888888 22.3303 0.749356
889889 3.91288 0.131234
890890 10.7477 0.360265
891891 −0.417424 −0.0139842
892892 −11.1652 −0.373837
893893 0 0
894894 0 0
895895 −15.0000 −0.501395
896896 0.208712 0.00697258
897897 −122.573 −4.09261
898898 −10.7477 −0.358656
899899 −42.1652 −1.40629
900900 −20.9564 −0.698548
901901 −12.0000 −0.399778
902902 3.79129 0.126236
903903 3.71326 0.123569
904904 −3.16515 −0.105271
905905 −6.92197 −0.230094
906906 5.58258 0.185469
907907 −8.00000 −0.265636 −0.132818 0.991140i 0.542403π-0.542403\pi
−0.132818 + 0.991140i 0.542403π0.542403\pi
908908 −1.58258 −0.0525196
909909 −21.1652 −0.702004
910910 0.956439 0.0317057
911911 20.8348 0.690289 0.345145 0.938549i 0.387830π-0.387830\pi
0.345145 + 0.938549i 0.387830π0.387830\pi
912912 0 0
913913 0.791288 0.0261878
914914 32.7477 1.08320
915915 −4.41742 −0.146036
916916 −4.62614 −0.152852
917917 −3.62614 −0.119746
918918 −7.91288 −0.261164
919919 −8.28674 −0.273354 −0.136677 0.990616i 0.543642π-0.543642\pi
−0.136677 + 0.990616i 0.543642π0.543642\pi
920920 6.00000 0.197814
921921 91.4083 3.01201
922922 −6.33030 −0.208477
923923 13.7477 0.452512
924924 −0.582576 −0.0191653
925925 34.9909 1.15049
926926 −32.6606 −1.07329
927927 95.6170 3.14048
928928 6.79129 0.222935
929929 −21.7913 −0.714949 −0.357474 0.933923i 0.616362π-0.616362\pi
−0.357474 + 0.933923i 0.616362π0.616362\pi
930930 13.7133 0.449675
931931 0 0
932932 −3.16515 −0.103678
933933 55.5826 1.81969
934934 −4.41742 −0.144543
935935 −1.25227 −0.0409537
936936 27.7477 0.906963
937937 53.8258 1.75841 0.879205 0.476443i 0.158074π-0.158074\pi
0.879205 + 0.476443i 0.158074π0.158074\pi
938938 0.0435608 0.00142231
939939 12.2087 0.398416
940940 7.25227 0.236543
941941 45.1652 1.47234 0.736171 0.676796i 0.236632π-0.236632\pi
0.736171 + 0.676796i 0.236632π0.236632\pi
942942 −33.3739 −1.08738
943943 −28.7477 −0.936155
944944 0 0
945945 0.825757 0.0268619
946946 6.37386 0.207232
947947 −47.0780 −1.52983 −0.764915 0.644131i 0.777219π-0.777219\pi
−0.764915 + 0.644131i 0.777219π0.777219\pi
948948 −10.0000 −0.324785
949949 −2.41742 −0.0784729
950950 0 0
951951 −80.2432 −2.60206
952952 0.330303 0.0107052
953953 33.1652 1.07432 0.537162 0.843479i 0.319496π-0.319496\pi
0.537162 + 0.843479i 0.319496π0.319496\pi
954954 36.3303 1.17624
955955 14.2432 0.460899
956956 −6.79129 −0.219646
957957 −18.9564 −0.612775
958958 8.20871 0.265211
959959 −2.04356 −0.0659900
960960 −2.20871 −0.0712859
961961 7.54811 0.243487
962962 −46.3303 −1.49375
963963 −86.2432 −2.77915
964964 4.79129 0.154317
965965 −5.04356 −0.162358
966966 4.41742 0.142128
967967 −13.4955 −0.433985 −0.216992 0.976173i 0.569625π-0.569625\pi
−0.216992 + 0.976173i 0.569625π0.569625\pi
968968 −1.00000 −0.0321412
969969 0 0
970970 −6.33030 −0.203254
971971 −40.2867 −1.29286 −0.646432 0.762972i 0.723739π-0.723739\pi
−0.646432 + 0.762972i 0.723739π0.723739\pi
972972 −16.1652 −0.518497
973973 3.50455 0.112351
974974 −23.1216 −0.740864
975975 70.7042 2.26435
976976 2.00000 0.0640184
977977 39.1652 1.25300 0.626502 0.779420i 0.284486π-0.284486\pi
0.626502 + 0.779420i 0.284486π0.284486\pi
978978 6.74773 0.215769
979979 13.5826 0.434101
980980 5.50455 0.175836
981981 47.9129 1.52974
982982 −38.8693 −1.24037
983983 −2.20871 −0.0704470 −0.0352235 0.999379i 0.511214π-0.511214\pi
−0.0352235 + 0.999379i 0.511214π0.511214\pi
984984 10.5826 0.337360
985985 7.25227 0.231077
986986 10.7477 0.342277
987987 5.33939 0.169955
988988 0 0
989989 −48.3303 −1.53681
990990 3.79129 0.120495
991991 16.9564 0.538639 0.269320 0.963051i 0.413201π-0.413201\pi
0.269320 + 0.963051i 0.413201π0.413201\pi
992992 −6.20871 −0.197127
993993 −70.3648 −2.23296
994994 −0.495454 −0.0157149
995995 16.4174 0.520467
996996 2.20871 0.0699857
997997 −14.0871 −0.446144 −0.223072 0.974802i 0.571608π-0.571608\pi
−0.223072 + 0.974802i 0.571608π0.571608\pi
998998 −17.1652 −0.543353
999999 −40.0000 −1.26554
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 7942.2.a.w.1.2 2
19.18 odd 2 418.2.a.f.1.1 2
57.56 even 2 3762.2.a.s.1.2 2
76.75 even 2 3344.2.a.l.1.2 2
209.208 even 2 4598.2.a.y.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
418.2.a.f.1.1 2 19.18 odd 2
3344.2.a.l.1.2 2 76.75 even 2
3762.2.a.s.1.2 2 57.56 even 2
4598.2.a.y.1.1 2 209.208 even 2
7942.2.a.w.1.2 2 1.1 even 1 trivial