Properties

Label 435.2.a.f.1.2
Level 435435
Weight 22
Character 435.1
Self dual yes
Analytic conductor 3.4733.473
Analytic rank 00
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] = [435,2,Mod(1,435)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(435, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("435.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 435=3529 435 = 3 \cdot 5 \cdot 29
Weight: k k == 2 2
Character orbit: [χ][\chi] == 435.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: 3.473492487933.47349248793
Analytic rank: 00
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]\Z[a_1, a_2]
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 1.79129-1.79129 of defining polynomial
Character χ\chi == 435.1

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+1.79129q2+1.00000q3+1.20871q4+1.00000q5+1.79129q6+1.00000q71.41742q8+1.00000q9+1.79129q10+5.00000q11+1.20871q124.58258q13+1.79129q14+1.00000q154.95644q163.00000q17+1.79129q18+3.58258q19+1.20871q20+1.00000q21+8.95644q224.00000q231.41742q24+1.00000q258.20871q26+1.00000q27+1.20871q28+1.00000q29+1.79129q30+4.00000q316.04356q32+5.00000q335.37386q34+1.00000q35+1.20871q364.00000q37+6.41742q384.58258q391.41742q409.16515q41+1.79129q429.58258q43+6.04356q44+1.00000q457.16515q46+10.5826q474.95644q486.00000q49+1.79129q503.00000q515.53901q52+0.417424q53+1.79129q54+5.00000q551.41742q56+3.58258q57+1.79129q587.58258q59+1.20871q60+12.7477q61+7.16515q62+1.00000q630.912878q644.58258q65+8.95644q664.16515q673.62614q684.00000q69+1.79129q709.58258q711.41742q72+4.00000q737.16515q74+1.00000q75+4.33030q76+5.00000q778.20871q78+7.58258q794.95644q80+1.00000q8116.4174q8211.5826q83+1.20871q843.00000q8517.1652q86+1.00000q877.08712q88+1.41742q89+1.79129q904.58258q914.83485q92+4.00000q93+18.9564q94+3.58258q956.04356q96+11.5826q9710.7477q98+5.00000q99+O(q100)q+1.79129 q^{2} +1.00000 q^{3} +1.20871 q^{4} +1.00000 q^{5} +1.79129 q^{6} +1.00000 q^{7} -1.41742 q^{8} +1.00000 q^{9} +1.79129 q^{10} +5.00000 q^{11} +1.20871 q^{12} -4.58258 q^{13} +1.79129 q^{14} +1.00000 q^{15} -4.95644 q^{16} -3.00000 q^{17} +1.79129 q^{18} +3.58258 q^{19} +1.20871 q^{20} +1.00000 q^{21} +8.95644 q^{22} -4.00000 q^{23} -1.41742 q^{24} +1.00000 q^{25} -8.20871 q^{26} +1.00000 q^{27} +1.20871 q^{28} +1.00000 q^{29} +1.79129 q^{30} +4.00000 q^{31} -6.04356 q^{32} +5.00000 q^{33} -5.37386 q^{34} +1.00000 q^{35} +1.20871 q^{36} -4.00000 q^{37} +6.41742 q^{38} -4.58258 q^{39} -1.41742 q^{40} -9.16515 q^{41} +1.79129 q^{42} -9.58258 q^{43} +6.04356 q^{44} +1.00000 q^{45} -7.16515 q^{46} +10.5826 q^{47} -4.95644 q^{48} -6.00000 q^{49} +1.79129 q^{50} -3.00000 q^{51} -5.53901 q^{52} +0.417424 q^{53} +1.79129 q^{54} +5.00000 q^{55} -1.41742 q^{56} +3.58258 q^{57} +1.79129 q^{58} -7.58258 q^{59} +1.20871 q^{60} +12.7477 q^{61} +7.16515 q^{62} +1.00000 q^{63} -0.912878 q^{64} -4.58258 q^{65} +8.95644 q^{66} -4.16515 q^{67} -3.62614 q^{68} -4.00000 q^{69} +1.79129 q^{70} -9.58258 q^{71} -1.41742 q^{72} +4.00000 q^{73} -7.16515 q^{74} +1.00000 q^{75} +4.33030 q^{76} +5.00000 q^{77} -8.20871 q^{78} +7.58258 q^{79} -4.95644 q^{80} +1.00000 q^{81} -16.4174 q^{82} -11.5826 q^{83} +1.20871 q^{84} -3.00000 q^{85} -17.1652 q^{86} +1.00000 q^{87} -7.08712 q^{88} +1.41742 q^{89} +1.79129 q^{90} -4.58258 q^{91} -4.83485 q^{92} +4.00000 q^{93} +18.9564 q^{94} +3.58258 q^{95} -6.04356 q^{96} +11.5826 q^{97} -10.7477 q^{98} +5.00000 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2qq2+2q3+7q4+2q5q6+2q712q8+2q9q10+10q11+7q12q14+2q15+13q166q17q182q19+7q20+2q21++10q99+O(q100) 2 q - q^{2} + 2 q^{3} + 7 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} - 12 q^{8} + 2 q^{9} - q^{10} + 10 q^{11} + 7 q^{12} - q^{14} + 2 q^{15} + 13 q^{16} - 6 q^{17} - q^{18} - 2 q^{19} + 7 q^{20} + 2 q^{21}+ \cdots + 10 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 1.79129 1.26663 0.633316 0.773893i 0.281693π-0.281693\pi
0.633316 + 0.773893i 0.281693π0.281693\pi
33 1.00000 0.577350
44 1.20871 0.604356
55 1.00000 0.447214
66 1.79129 0.731290
77 1.00000 0.377964 0.188982 0.981981i 0.439481π-0.439481\pi
0.188982 + 0.981981i 0.439481π0.439481\pi
88 −1.41742 −0.501135
99 1.00000 0.333333
1010 1.79129 0.566455
1111 5.00000 1.50756 0.753778 0.657129i 0.228229π-0.228229\pi
0.753778 + 0.657129i 0.228229π0.228229\pi
1212 1.20871 0.348925
1313 −4.58258 −1.27098 −0.635489 0.772110i 0.719201π-0.719201\pi
−0.635489 + 0.772110i 0.719201π0.719201\pi
1414 1.79129 0.478742
1515 1.00000 0.258199
1616 −4.95644 −1.23911
1717 −3.00000 −0.727607 −0.363803 0.931476i 0.618522π-0.618522\pi
−0.363803 + 0.931476i 0.618522π0.618522\pi
1818 1.79129 0.422211
1919 3.58258 0.821899 0.410950 0.911658i 0.365197π-0.365197\pi
0.410950 + 0.911658i 0.365197π0.365197\pi
2020 1.20871 0.270276
2121 1.00000 0.218218
2222 8.95644 1.90952
2323 −4.00000 −0.834058 −0.417029 0.908893i 0.636929π-0.636929\pi
−0.417029 + 0.908893i 0.636929π0.636929\pi
2424 −1.41742 −0.289331
2525 1.00000 0.200000
2626 −8.20871 −1.60986
2727 1.00000 0.192450
2828 1.20871 0.228425
2929 1.00000 0.185695
3030 1.79129 0.327043
3131 4.00000 0.718421 0.359211 0.933257i 0.383046π-0.383046\pi
0.359211 + 0.933257i 0.383046π0.383046\pi
3232 −6.04356 −1.06836
3333 5.00000 0.870388
3434 −5.37386 −0.921610
3535 1.00000 0.169031
3636 1.20871 0.201452
3737 −4.00000 −0.657596 −0.328798 0.944400i 0.606644π-0.606644\pi
−0.328798 + 0.944400i 0.606644π0.606644\pi
3838 6.41742 1.04104
3939 −4.58258 −0.733799
4040 −1.41742 −0.224114
4141 −9.16515 −1.43136 −0.715678 0.698430i 0.753882π-0.753882\pi
−0.715678 + 0.698430i 0.753882π0.753882\pi
4242 1.79129 0.276402
4343 −9.58258 −1.46133 −0.730665 0.682737i 0.760790π-0.760790\pi
−0.730665 + 0.682737i 0.760790π0.760790\pi
4444 6.04356 0.911101
4545 1.00000 0.149071
4646 −7.16515 −1.05644
4747 10.5826 1.54363 0.771814 0.635849i 0.219350π-0.219350\pi
0.771814 + 0.635849i 0.219350π0.219350\pi
4848 −4.95644 −0.715400
4949 −6.00000 −0.857143
5050 1.79129 0.253326
5151 −3.00000 −0.420084
5252 −5.53901 −0.768123
5353 0.417424 0.0573376 0.0286688 0.999589i 0.490873π-0.490873\pi
0.0286688 + 0.999589i 0.490873π0.490873\pi
5454 1.79129 0.243763
5555 5.00000 0.674200
5656 −1.41742 −0.189411
5757 3.58258 0.474524
5858 1.79129 0.235208
5959 −7.58258 −0.987167 −0.493584 0.869698i 0.664313π-0.664313\pi
−0.493584 + 0.869698i 0.664313π0.664313\pi
6060 1.20871 0.156044
6161 12.7477 1.63218 0.816090 0.577925i 0.196138π-0.196138\pi
0.816090 + 0.577925i 0.196138π0.196138\pi
6262 7.16515 0.909975
6363 1.00000 0.125988
6464 −0.912878 −0.114110
6565 −4.58258 −0.568399
6666 8.95644 1.10246
6767 −4.16515 −0.508854 −0.254427 0.967092i 0.581887π-0.581887\pi
−0.254427 + 0.967092i 0.581887π0.581887\pi
6868 −3.62614 −0.439734
6969 −4.00000 −0.481543
7070 1.79129 0.214100
7171 −9.58258 −1.13724 −0.568621 0.822599i 0.692523π-0.692523\pi
−0.568621 + 0.822599i 0.692523π0.692523\pi
7272 −1.41742 −0.167045
7373 4.00000 0.468165 0.234082 0.972217i 0.424791π-0.424791\pi
0.234082 + 0.972217i 0.424791π0.424791\pi
7474 −7.16515 −0.832932
7575 1.00000 0.115470
7676 4.33030 0.496720
7777 5.00000 0.569803
7878 −8.20871 −0.929454
7979 7.58258 0.853106 0.426553 0.904462i 0.359728π-0.359728\pi
0.426553 + 0.904462i 0.359728π0.359728\pi
8080 −4.95644 −0.554147
8181 1.00000 0.111111
8282 −16.4174 −1.81300
8383 −11.5826 −1.27135 −0.635676 0.771956i 0.719279π-0.719279\pi
−0.635676 + 0.771956i 0.719279π0.719279\pi
8484 1.20871 0.131881
8585 −3.00000 −0.325396
8686 −17.1652 −1.85097
8787 1.00000 0.107211
8888 −7.08712 −0.755490
8989 1.41742 0.150247 0.0751233 0.997174i 0.476065π-0.476065\pi
0.0751233 + 0.997174i 0.476065π0.476065\pi
9090 1.79129 0.188818
9191 −4.58258 −0.480384
9292 −4.83485 −0.504068
9393 4.00000 0.414781
9494 18.9564 1.95521
9595 3.58258 0.367565
9696 −6.04356 −0.616818
9797 11.5826 1.17603 0.588016 0.808849i 0.299909π-0.299909\pi
0.588016 + 0.808849i 0.299909π0.299909\pi
9898 −10.7477 −1.08568
9999 5.00000 0.502519
100100 1.20871 0.120871
101101 −0.582576 −0.0579684 −0.0289842 0.999580i 0.509227π-0.509227\pi
−0.0289842 + 0.999580i 0.509227π0.509227\pi
102102 −5.37386 −0.532092
103103 15.1652 1.49427 0.747133 0.664674i 0.231430π-0.231430\pi
0.747133 + 0.664674i 0.231430π0.231430\pi
104104 6.49545 0.636932
105105 1.00000 0.0975900
106106 0.747727 0.0726257
107107 5.16515 0.499334 0.249667 0.968332i 0.419679π-0.419679\pi
0.249667 + 0.968332i 0.419679π0.419679\pi
108108 1.20871 0.116308
109109 14.1652 1.35678 0.678388 0.734704i 0.262679π-0.262679\pi
0.678388 + 0.734704i 0.262679π0.262679\pi
110110 8.95644 0.853963
111111 −4.00000 −0.379663
112112 −4.95644 −0.468339
113113 −14.1652 −1.33255 −0.666273 0.745708i 0.732111π-0.732111\pi
−0.666273 + 0.745708i 0.732111π0.732111\pi
114114 6.41742 0.601047
115115 −4.00000 −0.373002
116116 1.20871 0.112226
117117 −4.58258 −0.423659
118118 −13.5826 −1.25038
119119 −3.00000 −0.275010
120120 −1.41742 −0.129393
121121 14.0000 1.27273
122122 22.8348 2.06737
123123 −9.16515 −0.826394
124124 4.83485 0.434182
125125 1.00000 0.0894427
126126 1.79129 0.159581
127127 2.00000 0.177471 0.0887357 0.996055i 0.471717π-0.471717\pi
0.0887357 + 0.996055i 0.471717π0.471717\pi
128128 10.4519 0.923826
129129 −9.58258 −0.843699
130130 −8.20871 −0.719952
131131 −15.0000 −1.31056 −0.655278 0.755388i 0.727449π-0.727449\pi
−0.655278 + 0.755388i 0.727449π0.727449\pi
132132 6.04356 0.526024
133133 3.58258 0.310649
134134 −7.46099 −0.644531
135135 1.00000 0.0860663
136136 4.25227 0.364629
137137 16.3303 1.39519 0.697596 0.716491i 0.254253π-0.254253\pi
0.697596 + 0.716491i 0.254253π0.254253\pi
138138 −7.16515 −0.609938
139139 −9.41742 −0.798776 −0.399388 0.916782i 0.630777π-0.630777\pi
−0.399388 + 0.916782i 0.630777π0.630777\pi
140140 1.20871 0.102155
141141 10.5826 0.891214
142142 −17.1652 −1.44047
143143 −22.9129 −1.91607
144144 −4.95644 −0.413037
145145 1.00000 0.0830455
146146 7.16515 0.592992
147147 −6.00000 −0.494872
148148 −4.83485 −0.397422
149149 16.7477 1.37203 0.686014 0.727589i 0.259359π-0.259359\pi
0.686014 + 0.727589i 0.259359π0.259359\pi
150150 1.79129 0.146258
151151 7.16515 0.583092 0.291546 0.956557i 0.405830π-0.405830\pi
0.291546 + 0.956557i 0.405830π0.405830\pi
152152 −5.07803 −0.411883
153153 −3.00000 −0.242536
154154 8.95644 0.721730
155155 4.00000 0.321288
156156 −5.53901 −0.443476
157157 10.7477 0.857762 0.428881 0.903361i 0.358908π-0.358908\pi
0.428881 + 0.903361i 0.358908π0.358908\pi
158158 13.5826 1.08057
159159 0.417424 0.0331039
160160 −6.04356 −0.477785
161161 −4.00000 −0.315244
162162 1.79129 0.140737
163163 7.58258 0.593913 0.296957 0.954891i 0.404028π-0.404028\pi
0.296957 + 0.954891i 0.404028π0.404028\pi
164164 −11.0780 −0.865049
165165 5.00000 0.389249
166166 −20.7477 −1.61034
167167 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
168168 −1.41742 −0.109357
169169 8.00000 0.615385
170170 −5.37386 −0.412157
171171 3.58258 0.273966
172172 −11.5826 −0.883163
173173 −3.16515 −0.240642 −0.120321 0.992735i 0.538392π-0.538392\pi
−0.120321 + 0.992735i 0.538392π0.538392\pi
174174 1.79129 0.135797
175175 1.00000 0.0755929
176176 −24.7822 −1.86803
177177 −7.58258 −0.569941
178178 2.53901 0.190307
179179 4.74773 0.354862 0.177431 0.984133i 0.443221π-0.443221\pi
0.177431 + 0.984133i 0.443221π0.443221\pi
180180 1.20871 0.0900921
181181 16.1652 1.20155 0.600773 0.799420i 0.294860π-0.294860\pi
0.600773 + 0.799420i 0.294860π0.294860\pi
182182 −8.20871 −0.608470
183183 12.7477 0.942339
184184 5.66970 0.417976
185185 −4.00000 −0.294086
186186 7.16515 0.525374
187187 −15.0000 −1.09691
188188 12.7913 0.932901
189189 1.00000 0.0727393
190190 6.41742 0.465569
191191 −4.00000 −0.289430 −0.144715 0.989473i 0.546227π-0.546227\pi
−0.144715 + 0.989473i 0.546227π0.546227\pi
192192 −0.912878 −0.0658813
193193 −20.3303 −1.46341 −0.731704 0.681623i 0.761274π-0.761274\pi
−0.731704 + 0.681623i 0.761274π0.761274\pi
194194 20.7477 1.48960
195195 −4.58258 −0.328165
196196 −7.25227 −0.518019
197197 −16.3303 −1.16349 −0.581743 0.813373i 0.697629π-0.697629\pi
−0.581743 + 0.813373i 0.697629π0.697629\pi
198198 8.95644 0.636506
199199 13.4174 0.951136 0.475568 0.879679i 0.342243π-0.342243\pi
0.475568 + 0.879679i 0.342243π0.342243\pi
200200 −1.41742 −0.100227
201201 −4.16515 −0.293787
202202 −1.04356 −0.0734247
203203 1.00000 0.0701862
204204 −3.62614 −0.253880
205205 −9.16515 −0.640122
206206 27.1652 1.89269
207207 −4.00000 −0.278019
208208 22.7133 1.57488
209209 17.9129 1.23906
210210 1.79129 0.123611
211211 20.3303 1.39960 0.699798 0.714341i 0.253273π-0.253273\pi
0.699798 + 0.714341i 0.253273π0.253273\pi
212212 0.504546 0.0346523
213213 −9.58258 −0.656587
214214 9.25227 0.632472
215215 −9.58258 −0.653526
216216 −1.41742 −0.0964435
217217 4.00000 0.271538
218218 25.3739 1.71853
219219 4.00000 0.270295
220220 6.04356 0.407457
221221 13.7477 0.924772
222222 −7.16515 −0.480893
223223 7.00000 0.468755 0.234377 0.972146i 0.424695π-0.424695\pi
0.234377 + 0.972146i 0.424695π0.424695\pi
224224 −6.04356 −0.403802
225225 1.00000 0.0666667
226226 −25.3739 −1.68784
227227 −7.58258 −0.503273 −0.251637 0.967822i 0.580969π-0.580969\pi
−0.251637 + 0.967822i 0.580969π0.580969\pi
228228 4.33030 0.286781
229229 −17.1652 −1.13431 −0.567153 0.823613i 0.691955π-0.691955\pi
−0.567153 + 0.823613i 0.691955π0.691955\pi
230230 −7.16515 −0.472456
231231 5.00000 0.328976
232232 −1.41742 −0.0930585
233233 −13.1652 −0.862478 −0.431239 0.902238i 0.641923π-0.641923\pi
−0.431239 + 0.902238i 0.641923π0.641923\pi
234234 −8.20871 −0.536620
235235 10.5826 0.690331
236236 −9.16515 −0.596601
237237 7.58258 0.492541
238238 −5.37386 −0.348336
239239 −26.0000 −1.68180 −0.840900 0.541190i 0.817974π-0.817974\pi
−0.840900 + 0.541190i 0.817974π0.817974\pi
240240 −4.95644 −0.319937
241241 29.3303 1.88933 0.944665 0.328035i 0.106387π-0.106387\pi
0.944665 + 0.328035i 0.106387π0.106387\pi
242242 25.0780 1.61208
243243 1.00000 0.0641500
244244 15.4083 0.986417
245245 −6.00000 −0.383326
246246 −16.4174 −1.04674
247247 −16.4174 −1.04462
248248 −5.66970 −0.360026
249249 −11.5826 −0.734016
250250 1.79129 0.113291
251251 16.1652 1.02034 0.510168 0.860075i 0.329583π-0.329583\pi
0.510168 + 0.860075i 0.329583π0.329583\pi
252252 1.20871 0.0761417
253253 −20.0000 −1.25739
254254 3.58258 0.224791
255255 −3.00000 −0.187867
256256 20.5481 1.28426
257257 12.7477 0.795181 0.397591 0.917563i 0.369846π-0.369846\pi
0.397591 + 0.917563i 0.369846π0.369846\pi
258258 −17.1652 −1.06866
259259 −4.00000 −0.248548
260260 −5.53901 −0.343515
261261 1.00000 0.0618984
262262 −26.8693 −1.65999
263263 30.3303 1.87025 0.935123 0.354322i 0.115288π-0.115288\pi
0.935123 + 0.354322i 0.115288π0.115288\pi
264264 −7.08712 −0.436182
265265 0.417424 0.0256422
266266 6.41742 0.393478
267267 1.41742 0.0867450
268268 −5.03447 −0.307529
269269 22.5826 1.37688 0.688442 0.725291i 0.258295π-0.258295\pi
0.688442 + 0.725291i 0.258295π0.258295\pi
270270 1.79129 0.109014
271271 1.16515 0.0707779 0.0353890 0.999374i 0.488733π-0.488733\pi
0.0353890 + 0.999374i 0.488733π0.488733\pi
272272 14.8693 0.901585
273273 −4.58258 −0.277350
274274 29.2523 1.76719
275275 5.00000 0.301511
276276 −4.83485 −0.291024
277277 −24.9129 −1.49687 −0.748435 0.663208i 0.769194π-0.769194\pi
−0.748435 + 0.663208i 0.769194π0.769194\pi
278278 −16.8693 −1.01175
279279 4.00000 0.239474
280280 −1.41742 −0.0847073
281281 −0.417424 −0.0249014 −0.0124507 0.999922i 0.503963π-0.503963\pi
−0.0124507 + 0.999922i 0.503963π0.503963\pi
282282 18.9564 1.12884
283283 −0.834849 −0.0496266 −0.0248133 0.999692i 0.507899π-0.507899\pi
−0.0248133 + 0.999692i 0.507899π0.507899\pi
284284 −11.5826 −0.687299
285285 3.58258 0.212213
286286 −41.0436 −2.42696
287287 −9.16515 −0.541002
288288 −6.04356 −0.356120
289289 −8.00000 −0.470588
290290 1.79129 0.105188
291291 11.5826 0.678983
292292 4.83485 0.282938
293293 30.1652 1.76227 0.881133 0.472868i 0.156781π-0.156781\pi
0.881133 + 0.472868i 0.156781π0.156781\pi
294294 −10.7477 −0.626820
295295 −7.58258 −0.441475
296296 5.66970 0.329544
297297 5.00000 0.290129
298298 30.0000 1.73785
299299 18.3303 1.06007
300300 1.20871 0.0697850
301301 −9.58258 −0.552330
302302 12.8348 0.738563
303303 −0.582576 −0.0334681
304304 −17.7568 −1.01842
305305 12.7477 0.729933
306306 −5.37386 −0.307203
307307 0 0 1.00000i 0.5π-0.5\pi
1.00000i 0.5π0.5\pi
308308 6.04356 0.344364
309309 15.1652 0.862715
310310 7.16515 0.406953
311311 −3.00000 −0.170114 −0.0850572 0.996376i 0.527107π-0.527107\pi
−0.0850572 + 0.996376i 0.527107π0.527107\pi
312312 6.49545 0.367733
313313 10.5826 0.598163 0.299081 0.954228i 0.403320π-0.403320\pi
0.299081 + 0.954228i 0.403320π0.403320\pi
314314 19.2523 1.08647
315315 1.00000 0.0563436
316316 9.16515 0.515580
317317 −25.0000 −1.40414 −0.702070 0.712108i 0.747741π-0.747741\pi
−0.702070 + 0.712108i 0.747741π0.747741\pi
318318 0.747727 0.0419305
319319 5.00000 0.279946
320320 −0.912878 −0.0510315
321321 5.16515 0.288291
322322 −7.16515 −0.399298
323323 −10.7477 −0.598020
324324 1.20871 0.0671507
325325 −4.58258 −0.254196
326326 13.5826 0.752269
327327 14.1652 0.783335
328328 12.9909 0.717303
329329 10.5826 0.583436
330330 8.95644 0.493036
331331 −8.33030 −0.457875 −0.228937 0.973441i 0.573525π-0.573525\pi
−0.228937 + 0.973441i 0.573525π0.573525\pi
332332 −14.0000 −0.768350
333333 −4.00000 −0.219199
334334 0 0
335335 −4.16515 −0.227567
336336 −4.95644 −0.270396
337337 −21.1652 −1.15294 −0.576470 0.817119i 0.695570π-0.695570\pi
−0.576470 + 0.817119i 0.695570π0.695570\pi
338338 14.3303 0.779466
339339 −14.1652 −0.769345
340340 −3.62614 −0.196655
341341 20.0000 1.08306
342342 6.41742 0.347015
343343 −13.0000 −0.701934
344344 13.5826 0.732323
345345 −4.00000 −0.215353
346346 −5.66970 −0.304805
347347 7.16515 0.384645 0.192323 0.981332i 0.438398π-0.438398\pi
0.192323 + 0.981332i 0.438398π0.438398\pi
348348 1.20871 0.0647938
349349 −4.33030 −0.231796 −0.115898 0.993261i 0.536975π-0.536975\pi
−0.115898 + 0.993261i 0.536975π0.536975\pi
350350 1.79129 0.0957484
351351 −4.58258 −0.244600
352352 −30.2178 −1.61061
353353 −14.8348 −0.789579 −0.394790 0.918772i 0.629183π-0.629183\pi
−0.394790 + 0.918772i 0.629183π0.629183\pi
354354 −13.5826 −0.721906
355355 −9.58258 −0.508590
356356 1.71326 0.0908025
357357 −3.00000 −0.158777
358358 8.50455 0.449479
359359 −27.1652 −1.43372 −0.716861 0.697216i 0.754422π-0.754422\pi
−0.716861 + 0.697216i 0.754422π0.754422\pi
360360 −1.41742 −0.0747048
361361 −6.16515 −0.324482
362362 28.9564 1.52192
363363 14.0000 0.734809
364364 −5.53901 −0.290323
365365 4.00000 0.209370
366366 22.8348 1.19360
367367 −37.4955 −1.95725 −0.978623 0.205661i 0.934066π-0.934066\pi
−0.978623 + 0.205661i 0.934066π0.934066\pi
368368 19.8258 1.03349
369369 −9.16515 −0.477119
370370 −7.16515 −0.372498
371371 0.417424 0.0216716
372372 4.83485 0.250675
373373 28.3303 1.46689 0.733444 0.679750i 0.237912π-0.237912\pi
0.733444 + 0.679750i 0.237912π0.237912\pi
374374 −26.8693 −1.38938
375375 1.00000 0.0516398
376376 −15.0000 −0.773566
377377 −4.58258 −0.236015
378378 1.79129 0.0921339
379379 −26.0000 −1.33553 −0.667765 0.744372i 0.732749π-0.732749\pi
−0.667765 + 0.744372i 0.732749π0.732749\pi
380380 4.33030 0.222140
381381 2.00000 0.102463
382382 −7.16515 −0.366601
383383 3.58258 0.183061 0.0915305 0.995802i 0.470824π-0.470824\pi
0.0915305 + 0.995802i 0.470824π0.470824\pi
384384 10.4519 0.533371
385385 5.00000 0.254824
386386 −36.4174 −1.85360
387387 −9.58258 −0.487110
388388 14.0000 0.710742
389389 −6.58258 −0.333750 −0.166875 0.985978i 0.553368π-0.553368\pi
−0.166875 + 0.985978i 0.553368π0.553368\pi
390390 −8.20871 −0.415664
391391 12.0000 0.606866
392392 8.50455 0.429544
393393 −15.0000 −0.756650
394394 −29.2523 −1.47371
395395 7.58258 0.381521
396396 6.04356 0.303700
397397 10.8348 0.543785 0.271893 0.962328i 0.412350π-0.412350\pi
0.271893 + 0.962328i 0.412350π0.412350\pi
398398 24.0345 1.20474
399399 3.58258 0.179353
400400 −4.95644 −0.247822
401401 12.4174 0.620097 0.310048 0.950721i 0.399655π-0.399655\pi
0.310048 + 0.950721i 0.399655π0.399655\pi
402402 −7.46099 −0.372120
403403 −18.3303 −0.913097
404404 −0.704166 −0.0350336
405405 1.00000 0.0496904
406406 1.79129 0.0889001
407407 −20.0000 −0.991363
408408 4.25227 0.210519
409409 −2.74773 −0.135866 −0.0679332 0.997690i 0.521640π-0.521640\pi
−0.0679332 + 0.997690i 0.521640π0.521640\pi
410410 −16.4174 −0.810799
411411 16.3303 0.805514
412412 18.3303 0.903069
413413 −7.58258 −0.373114
414414 −7.16515 −0.352148
415415 −11.5826 −0.568566
416416 27.6951 1.35786
417417 −9.41742 −0.461173
418418 32.0871 1.56943
419419 −37.1652 −1.81564 −0.907818 0.419364i 0.862253π-0.862253\pi
−0.907818 + 0.419364i 0.862253π0.862253\pi
420420 1.20871 0.0589791
421421 4.41742 0.215292 0.107646 0.994189i 0.465669π-0.465669\pi
0.107646 + 0.994189i 0.465669π0.465669\pi
422422 36.4174 1.77277
423423 10.5826 0.514542
424424 −0.591667 −0.0287339
425425 −3.00000 −0.145521
426426 −17.1652 −0.831654
427427 12.7477 0.616906
428428 6.24318 0.301776
429429 −22.9129 −1.10624
430430 −17.1652 −0.827777
431431 −39.1652 −1.88652 −0.943259 0.332057i 0.892258π-0.892258\pi
−0.943259 + 0.332057i 0.892258π0.892258\pi
432432 −4.95644 −0.238467
433433 25.0780 1.20517 0.602587 0.798053i 0.294137π-0.294137\pi
0.602587 + 0.798053i 0.294137π0.294137\pi
434434 7.16515 0.343938
435435 1.00000 0.0479463
436436 17.1216 0.819975
437437 −14.3303 −0.685511
438438 7.16515 0.342364
439439 −16.9129 −0.807208 −0.403604 0.914934i 0.632243π-0.632243\pi
−0.403604 + 0.914934i 0.632243π0.632243\pi
440440 −7.08712 −0.337865
441441 −6.00000 −0.285714
442442 24.6261 1.17135
443443 0.582576 0.0276790 0.0138395 0.999904i 0.495595π-0.495595\pi
0.0138395 + 0.999904i 0.495595π0.495595\pi
444444 −4.83485 −0.229452
445445 1.41742 0.0671924
446446 12.5390 0.593740
447447 16.7477 0.792140
448448 −0.912878 −0.0431295
449449 −30.0780 −1.41947 −0.709735 0.704469i 0.751185π-0.751185\pi
−0.709735 + 0.704469i 0.751185π0.751185\pi
450450 1.79129 0.0844421
451451 −45.8258 −2.15785
452452 −17.1216 −0.805332
453453 7.16515 0.336648
454454 −13.5826 −0.637462
455455 −4.58258 −0.214834
456456 −5.07803 −0.237801
457457 −3.74773 −0.175311 −0.0876556 0.996151i 0.527938π-0.527938\pi
−0.0876556 + 0.996151i 0.527938π0.527938\pi
458458 −30.7477 −1.43675
459459 −3.00000 −0.140028
460460 −4.83485 −0.225426
461461 −9.16515 −0.426864 −0.213432 0.976958i 0.568464π-0.568464\pi
−0.213432 + 0.976958i 0.568464π0.568464\pi
462462 8.95644 0.416691
463463 −0.165151 −0.00767524 −0.00383762 0.999993i 0.501222π-0.501222\pi
−0.00383762 + 0.999993i 0.501222π0.501222\pi
464464 −4.95644 −0.230097
465465 4.00000 0.185496
466466 −23.5826 −1.09244
467467 −8.00000 −0.370196 −0.185098 0.982720i 0.559260π-0.559260\pi
−0.185098 + 0.982720i 0.559260π0.559260\pi
468468 −5.53901 −0.256041
469469 −4.16515 −0.192329
470470 18.9564 0.874395
471471 10.7477 0.495229
472472 10.7477 0.494704
473473 −47.9129 −2.20304
474474 13.5826 0.623868
475475 3.58258 0.164380
476476 −3.62614 −0.166204
477477 0.417424 0.0191125
478478 −46.5735 −2.13022
479479 −19.1652 −0.875678 −0.437839 0.899053i 0.644256π-0.644256\pi
−0.437839 + 0.899053i 0.644256π0.644256\pi
480480 −6.04356 −0.275850
481481 18.3303 0.835790
482482 52.5390 2.39309
483483 −4.00000 −0.182006
484484 16.9220 0.769180
485485 11.5826 0.525938
486486 1.79129 0.0812545
487487 2.33030 0.105596 0.0527980 0.998605i 0.483186π-0.483186\pi
0.0527980 + 0.998605i 0.483186π0.483186\pi
488488 −18.0689 −0.817942
489489 7.58258 0.342896
490490 −10.7477 −0.485533
491491 16.0000 0.722070 0.361035 0.932552i 0.382424π-0.382424\pi
0.361035 + 0.932552i 0.382424π0.382424\pi
492492 −11.0780 −0.499436
493493 −3.00000 −0.135113
494494 −29.4083 −1.32314
495495 5.00000 0.224733
496496 −19.8258 −0.890203
497497 −9.58258 −0.429837
498498 −20.7477 −0.929728
499499 −13.4174 −0.600646 −0.300323 0.953837i 0.597095π-0.597095\pi
−0.300323 + 0.953837i 0.597095π0.597095\pi
500500 1.20871 0.0540553
501501 0 0
502502 28.9564 1.29239
503503 −22.9129 −1.02163 −0.510817 0.859689i 0.670657π-0.670657\pi
−0.510817 + 0.859689i 0.670657π0.670657\pi
504504 −1.41742 −0.0631371
505505 −0.582576 −0.0259243
506506 −35.8258 −1.59265
507507 8.00000 0.355292
508508 2.41742 0.107256
509509 26.7477 1.18557 0.592786 0.805360i 0.298028π-0.298028\pi
0.592786 + 0.805360i 0.298028π0.298028\pi
510510 −5.37386 −0.237959
511511 4.00000 0.176950
512512 15.9038 0.702855
513513 3.58258 0.158175
514514 22.8348 1.00720
515515 15.1652 0.668256
516516 −11.5826 −0.509894
517517 52.9129 2.32711
518518 −7.16515 −0.314819
519519 −3.16515 −0.138935
520520 6.49545 0.284845
521521 43.0780 1.88728 0.943641 0.330970i 0.107376π-0.107376\pi
0.943641 + 0.330970i 0.107376π0.107376\pi
522522 1.79129 0.0784025
523523 −33.3303 −1.45743 −0.728716 0.684816i 0.759883π-0.759883\pi
−0.728716 + 0.684816i 0.759883π0.759883\pi
524524 −18.1307 −0.792043
525525 1.00000 0.0436436
526526 54.3303 2.36891
527527 −12.0000 −0.522728
528528 −24.7822 −1.07851
529529 −7.00000 −0.304348
530530 0.747727 0.0324792
531531 −7.58258 −0.329056
532532 4.33030 0.187742
533533 42.0000 1.81922
534534 2.53901 0.109874
535535 5.16515 0.223309
536536 5.90379 0.255005
537537 4.74773 0.204880
538538 40.4519 1.74400
539539 −30.0000 −1.29219
540540 1.20871 0.0520147
541541 −31.4955 −1.35410 −0.677048 0.735939i 0.736741π-0.736741\pi
−0.677048 + 0.735939i 0.736741π0.736741\pi
542542 2.08712 0.0896495
543543 16.1652 0.693713
544544 18.1307 0.777347
545545 14.1652 0.606768
546546 −8.20871 −0.351300
547547 4.16515 0.178089 0.0890445 0.996028i 0.471619π-0.471619\pi
0.0890445 + 0.996028i 0.471619π0.471619\pi
548548 19.7386 0.843193
549549 12.7477 0.544060
550550 8.95644 0.381904
551551 3.58258 0.152623
552552 5.66970 0.241318
553553 7.58258 0.322444
554554 −44.6261 −1.89598
555555 −4.00000 −0.169791
556556 −11.3830 −0.482745
557557 −22.7477 −0.963852 −0.481926 0.876212i 0.660063π-0.660063\pi
−0.481926 + 0.876212i 0.660063π0.660063\pi
558558 7.16515 0.303325
559559 43.9129 1.85732
560560 −4.95644 −0.209448
561561 −15.0000 −0.633300
562562 −0.747727 −0.0315410
563563 −14.5826 −0.614582 −0.307291 0.951616i 0.599423π-0.599423\pi
−0.307291 + 0.951616i 0.599423π0.599423\pi
564564 12.7913 0.538610
565565 −14.1652 −0.595932
566566 −1.49545 −0.0628586
567567 1.00000 0.0419961
568568 13.5826 0.569912
569569 28.5826 1.19824 0.599122 0.800658i 0.295516π-0.295516\pi
0.599122 + 0.800658i 0.295516π0.295516\pi
570570 6.41742 0.268796
571571 12.0000 0.502184 0.251092 0.967963i 0.419210π-0.419210\pi
0.251092 + 0.967963i 0.419210π0.419210\pi
572572 −27.6951 −1.15799
573573 −4.00000 −0.167102
574574 −16.4174 −0.685250
575575 −4.00000 −0.166812
576576 −0.912878 −0.0380366
577577 −19.1652 −0.797856 −0.398928 0.916982i 0.630618π-0.630618\pi
−0.398928 + 0.916982i 0.630618π0.630618\pi
578578 −14.3303 −0.596062
579579 −20.3303 −0.844899
580580 1.20871 0.0501890
581581 −11.5826 −0.480526
582582 20.7477 0.860021
583583 2.08712 0.0864397
584584 −5.66970 −0.234614
585585 −4.58258 −0.189466
586586 54.0345 2.23214
587587 −11.5826 −0.478064 −0.239032 0.971012i 0.576830π-0.576830\pi
−0.239032 + 0.971012i 0.576830π0.576830\pi
588588 −7.25227 −0.299079
589589 14.3303 0.590470
590590 −13.5826 −0.559186
591591 −16.3303 −0.671739
592592 19.8258 0.814834
593593 8.41742 0.345662 0.172831 0.984951i 0.444709π-0.444709\pi
0.172831 + 0.984951i 0.444709π0.444709\pi
594594 8.95644 0.367487
595595 −3.00000 −0.122988
596596 20.2432 0.829193
597597 13.4174 0.549139
598598 32.8348 1.34272
599599 0.165151 0.00674790 0.00337395 0.999994i 0.498926π-0.498926\pi
0.00337395 + 0.999994i 0.498926π0.498926\pi
600600 −1.41742 −0.0578661
601601 −32.3303 −1.31878 −0.659390 0.751801i 0.729185π-0.729185\pi
−0.659390 + 0.751801i 0.729185π0.729185\pi
602602 −17.1652 −0.699599
603603 −4.16515 −0.169618
604604 8.66061 0.352395
605605 14.0000 0.569181
606606 −1.04356 −0.0423918
607607 3.58258 0.145412 0.0727061 0.997353i 0.476836π-0.476836\pi
0.0727061 + 0.997353i 0.476836π0.476836\pi
608608 −21.6515 −0.878085
609609 1.00000 0.0405220
610610 22.8348 0.924556
611611 −48.4955 −1.96192
612612 −3.62614 −0.146578
613613 −43.7477 −1.76695 −0.883477 0.468474i 0.844804π-0.844804\pi
−0.883477 + 0.468474i 0.844804π0.844804\pi
614614 0 0
615615 −9.16515 −0.369575
616616 −7.08712 −0.285548
617617 15.4955 0.623823 0.311912 0.950111i 0.399031π-0.399031\pi
0.311912 + 0.950111i 0.399031π0.399031\pi
618618 27.1652 1.09274
619619 13.1652 0.529152 0.264576 0.964365i 0.414768π-0.414768\pi
0.264576 + 0.964365i 0.414768π0.414768\pi
620620 4.83485 0.194172
621621 −4.00000 −0.160514
622622 −5.37386 −0.215472
623623 1.41742 0.0567879
624624 22.7133 0.909258
625625 1.00000 0.0400000
626626 18.9564 0.757652
627627 17.9129 0.715371
628628 12.9909 0.518394
629629 12.0000 0.478471
630630 1.79129 0.0713666
631631 10.9129 0.434435 0.217217 0.976123i 0.430302π-0.430302\pi
0.217217 + 0.976123i 0.430302π0.430302\pi
632632 −10.7477 −0.427522
633633 20.3303 0.808057
634634 −44.7822 −1.77853
635635 2.00000 0.0793676
636636 0.504546 0.0200065
637637 27.4955 1.08941
638638 8.95644 0.354589
639639 −9.58258 −0.379081
640640 10.4519 0.413147
641641 −6.58258 −0.259996 −0.129998 0.991514i 0.541497π-0.541497\pi
−0.129998 + 0.991514i 0.541497π0.541497\pi
642642 9.25227 0.365158
643643 43.6606 1.72181 0.860903 0.508769i 0.169899π-0.169899\pi
0.860903 + 0.508769i 0.169899π0.169899\pi
644644 −4.83485 −0.190520
645645 −9.58258 −0.377314
646646 −19.2523 −0.757471
647647 24.7477 0.972934 0.486467 0.873699i 0.338285π-0.338285\pi
0.486467 + 0.873699i 0.338285π0.338285\pi
648648 −1.41742 −0.0556817
649649 −37.9129 −1.48821
650650 −8.20871 −0.321972
651651 4.00000 0.156772
652652 9.16515 0.358935
653653 26.1652 1.02392 0.511961 0.859009i 0.328919π-0.328919\pi
0.511961 + 0.859009i 0.328919π0.328919\pi
654654 25.3739 0.992197
655655 −15.0000 −0.586098
656656 45.4265 1.77361
657657 4.00000 0.156055
658658 18.9564 0.738999
659659 18.1652 0.707614 0.353807 0.935318i 0.384887π-0.384887\pi
0.353807 + 0.935318i 0.384887π0.384887\pi
660660 6.04356 0.235245
661661 25.0000 0.972387 0.486194 0.873851i 0.338385π-0.338385\pi
0.486194 + 0.873851i 0.338385π0.338385\pi
662662 −14.9220 −0.579959
663663 13.7477 0.533917
664664 16.4174 0.637120
665665 3.58258 0.138926
666666 −7.16515 −0.277644
667667 −4.00000 −0.154881
668668 0 0
669669 7.00000 0.270636
670670 −7.46099 −0.288243
671671 63.7386 2.46060
672672 −6.04356 −0.233135
673673 1.74773 0.0673699 0.0336850 0.999433i 0.489276π-0.489276\pi
0.0336850 + 0.999433i 0.489276π0.489276\pi
674674 −37.9129 −1.46035
675675 1.00000 0.0384900
676676 9.66970 0.371911
677677 44.8258 1.72279 0.861397 0.507932i 0.169590π-0.169590\pi
0.861397 + 0.507932i 0.169590π0.169590\pi
678678 −25.3739 −0.974477
679679 11.5826 0.444498
680680 4.25227 0.163067
681681 −7.58258 −0.290565
682682 35.8258 1.37184
683683 7.16515 0.274167 0.137083 0.990560i 0.456227π-0.456227\pi
0.137083 + 0.990560i 0.456227π0.456227\pi
684684 4.33030 0.165573
685685 16.3303 0.623949
686686 −23.2867 −0.889092
687687 −17.1652 −0.654891
688688 47.4955 1.81075
689689 −1.91288 −0.0728749
690690 −7.16515 −0.272773
691691 42.9129 1.63248 0.816241 0.577711i 0.196054π-0.196054\pi
0.816241 + 0.577711i 0.196054π0.196054\pi
692692 −3.82576 −0.145433
693693 5.00000 0.189934
694694 12.8348 0.487204
695695 −9.41742 −0.357223
696696 −1.41742 −0.0537273
697697 27.4955 1.04146
698698 −7.75682 −0.293600
699699 −13.1652 −0.497952
700700 1.20871 0.0456850
701701 −23.0780 −0.871645 −0.435823 0.900033i 0.643542π-0.643542\pi
−0.435823 + 0.900033i 0.643542π0.643542\pi
702702 −8.20871 −0.309818
703703 −14.3303 −0.540478
704704 −4.56439 −0.172027
705705 10.5826 0.398563
706706 −26.5735 −1.00011
707707 −0.582576 −0.0219100
708708 −9.16515 −0.344447
709709 10.0000 0.375558 0.187779 0.982211i 0.439871π-0.439871\pi
0.187779 + 0.982211i 0.439871π0.439871\pi
710710 −17.1652 −0.644197
711711 7.58258 0.284369
712712 −2.00909 −0.0752939
713713 −16.0000 −0.599205
714714 −5.37386 −0.201112
715715 −22.9129 −0.856893
716716 5.73864 0.214463
717717 −26.0000 −0.970988
718718 −48.6606 −1.81600
719719 7.91288 0.295101 0.147550 0.989055i 0.452861π-0.452861\pi
0.147550 + 0.989055i 0.452861π0.452861\pi
720720 −4.95644 −0.184716
721721 15.1652 0.564780
722722 −11.0436 −0.410999
723723 29.3303 1.09081
724724 19.5390 0.726162
725725 1.00000 0.0371391
726726 25.0780 0.930733
727727 9.66970 0.358629 0.179315 0.983792i 0.442612π-0.442612\pi
0.179315 + 0.983792i 0.442612π0.442612\pi
728728 6.49545 0.240738
729729 1.00000 0.0370370
730730 7.16515 0.265194
731731 28.7477 1.06327
732732 15.4083 0.569508
733733 −38.4174 −1.41898 −0.709490 0.704716i 0.751075π-0.751075\pi
−0.709490 + 0.704716i 0.751075π0.751075\pi
734734 −67.1652 −2.47911
735735 −6.00000 −0.221313
736736 24.1742 0.891074
737737 −20.8258 −0.767127
738738 −16.4174 −0.604334
739739 19.2523 0.708206 0.354103 0.935206i 0.384786π-0.384786\pi
0.354103 + 0.935206i 0.384786π0.384786\pi
740740 −4.83485 −0.177733
741741 −16.4174 −0.603109
742742 0.747727 0.0274499
743743 29.7477 1.09134 0.545669 0.838001i 0.316276π-0.316276\pi
0.545669 + 0.838001i 0.316276π0.316276\pi
744744 −5.66970 −0.207861
745745 16.7477 0.613589
746746 50.7477 1.85801
747747 −11.5826 −0.423784
748748 −18.1307 −0.662923
749749 5.16515 0.188731
750750 1.79129 0.0654086
751751 −17.4955 −0.638418 −0.319209 0.947684i 0.603417π-0.603417\pi
−0.319209 + 0.947684i 0.603417π0.603417\pi
752752 −52.4519 −1.91272
753753 16.1652 0.589091
754754 −8.20871 −0.298944
755755 7.16515 0.260767
756756 1.20871 0.0439604
757757 −2.33030 −0.0846963 −0.0423481 0.999103i 0.513484π-0.513484\pi
−0.0423481 + 0.999103i 0.513484π0.513484\pi
758758 −46.5735 −1.69163
759759 −20.0000 −0.725954
760760 −5.07803 −0.184200
761761 36.4174 1.32013 0.660065 0.751208i 0.270529π-0.270529\pi
0.660065 + 0.751208i 0.270529π0.270529\pi
762762 3.58258 0.129783
763763 14.1652 0.512813
764764 −4.83485 −0.174919
765765 −3.00000 −0.108465
766766 6.41742 0.231871
767767 34.7477 1.25467
768768 20.5481 0.741466
769769 25.5826 0.922531 0.461266 0.887262i 0.347396π-0.347396\pi
0.461266 + 0.887262i 0.347396π0.347396\pi
770770 8.95644 0.322768
771771 12.7477 0.459098
772772 −24.5735 −0.884419
773773 −5.16515 −0.185778 −0.0928888 0.995676i 0.529610π-0.529610\pi
−0.0928888 + 0.995676i 0.529610π0.529610\pi
774774 −17.1652 −0.616989
775775 4.00000 0.143684
776776 −16.4174 −0.589351
777777 −4.00000 −0.143499
778778 −11.7913 −0.422738
779779 −32.8348 −1.17643
780780 −5.53901 −0.198329
781781 −47.9129 −1.71446
782782 21.4955 0.768676
783783 1.00000 0.0357371
784784 29.7386 1.06209
785785 10.7477 0.383603
786786 −26.8693 −0.958397
787787 −24.0000 −0.855508 −0.427754 0.903895i 0.640695π-0.640695\pi
−0.427754 + 0.903895i 0.640695π0.640695\pi
788788 −19.7386 −0.703160
789789 30.3303 1.07979
790790 13.5826 0.483246
791791 −14.1652 −0.503655
792792 −7.08712 −0.251830
793793 −58.4174 −2.07446
794794 19.4083 0.688776
795795 0.417424 0.0148045
796796 16.2178 0.574825
797797 32.3303 1.14520 0.572599 0.819836i 0.305935π-0.305935\pi
0.572599 + 0.819836i 0.305935π0.305935\pi
798798 6.41742 0.227174
799799 −31.7477 −1.12315
800800 −6.04356 −0.213672
801801 1.41742 0.0500822
802802 22.2432 0.785434
803803 20.0000 0.705785
804804 −5.03447 −0.177552
805805 −4.00000 −0.140981
806806 −32.8348 −1.15656
807807 22.5826 0.794944
808808 0.825757 0.0290500
809809 44.0780 1.54970 0.774851 0.632145i 0.217825π-0.217825\pi
0.774851 + 0.632145i 0.217825π0.217825\pi
810810 1.79129 0.0629394
811811 32.5826 1.14413 0.572064 0.820209i 0.306143π-0.306143\pi
0.572064 + 0.820209i 0.306143π0.306143\pi
812812 1.20871 0.0424175
813813 1.16515 0.0408636
814814 −35.8258 −1.25569
815815 7.58258 0.265606
816816 14.8693 0.520530
817817 −34.3303 −1.20107
818818 −4.92197 −0.172093
819819 −4.58258 −0.160128
820820 −11.0780 −0.386862
821821 −31.4955 −1.09920 −0.549599 0.835428i 0.685220π-0.685220\pi
−0.549599 + 0.835428i 0.685220π0.685220\pi
822822 29.2523 1.02029
823823 51.0780 1.78047 0.890234 0.455503i 0.150541π-0.150541\pi
0.890234 + 0.455503i 0.150541π0.150541\pi
824824 −21.4955 −0.748830
825825 5.00000 0.174078
826826 −13.5826 −0.472598
827827 −43.8258 −1.52397 −0.761985 0.647594i 0.775775π-0.775775\pi
−0.761985 + 0.647594i 0.775775π0.775775\pi
828828 −4.83485 −0.168023
829829 4.00000 0.138926 0.0694629 0.997585i 0.477871π-0.477871\pi
0.0694629 + 0.997585i 0.477871π0.477871\pi
830830 −20.7477 −0.720164
831831 −24.9129 −0.864218
832832 4.18333 0.145031
833833 18.0000 0.623663
834834 −16.8693 −0.584137
835835 0 0
836836 21.6515 0.748833
837837 4.00000 0.138260
838838 −66.5735 −2.29974
839839 −48.4955 −1.67425 −0.837125 0.547012i 0.815765π-0.815765\pi
−0.837125 + 0.547012i 0.815765π0.815765\pi
840840 −1.41742 −0.0489058
841841 1.00000 0.0344828
842842 7.91288 0.272696
843843 −0.417424 −0.0143769
844844 24.5735 0.845854
845845 8.00000 0.275208
846846 18.9564 0.651736
847847 14.0000 0.481046
848848 −2.06894 −0.0710476
849849 −0.834849 −0.0286519
850850 −5.37386 −0.184322
851851 16.0000 0.548473
852852 −11.5826 −0.396813
853853 20.7477 0.710389 0.355194 0.934792i 0.384415π-0.384415\pi
0.355194 + 0.934792i 0.384415π0.384415\pi
854854 22.8348 0.781392
855855 3.58258 0.122522
856856 −7.32121 −0.250234
857857 −46.6606 −1.59390 −0.796948 0.604048i 0.793554π-0.793554\pi
−0.796948 + 0.604048i 0.793554π0.793554\pi
858858 −41.0436 −1.40120
859859 −47.5826 −1.62350 −0.811748 0.584007i 0.801484π-0.801484\pi
−0.811748 + 0.584007i 0.801484π0.801484\pi
860860 −11.5826 −0.394963
861861 −9.16515 −0.312348
862862 −70.1561 −2.38952
863863 −6.41742 −0.218452 −0.109226 0.994017i 0.534837π-0.534837\pi
−0.109226 + 0.994017i 0.534837π0.534837\pi
864864 −6.04356 −0.205606
865865 −3.16515 −0.107618
866866 44.9220 1.52651
867867 −8.00000 −0.271694
868868 4.83485 0.164105
869869 37.9129 1.28611
870870 1.79129 0.0607303
871871 19.0871 0.646742
872872 −20.0780 −0.679928
873873 11.5826 0.392011
874874 −25.6697 −0.868290
875875 1.00000 0.0338062
876876 4.83485 0.163354
877877 19.6697 0.664198 0.332099 0.943244i 0.392243π-0.392243\pi
0.332099 + 0.943244i 0.392243π0.392243\pi
878878 −30.2958 −1.02243
879879 30.1652 1.01745
880880 −24.7822 −0.835408
881881 −32.0780 −1.08074 −0.540368 0.841429i 0.681715π-0.681715\pi
−0.540368 + 0.841429i 0.681715π0.681715\pi
882882 −10.7477 −0.361895
883883 16.0000 0.538443 0.269221 0.963078i 0.413234π-0.413234\pi
0.269221 + 0.963078i 0.413234π0.413234\pi
884884 16.6170 0.558892
885885 −7.58258 −0.254885
886886 1.04356 0.0350591
887887 −44.9129 −1.50803 −0.754013 0.656859i 0.771885π-0.771885\pi
−0.754013 + 0.656859i 0.771885π0.771885\pi
888888 5.66970 0.190263
889889 2.00000 0.0670778
890890 2.53901 0.0851080
891891 5.00000 0.167506
892892 8.46099 0.283295
893893 37.9129 1.26871
894894 30.0000 1.00335
895895 4.74773 0.158699
896896 10.4519 0.349173
897897 18.3303 0.612031
898898 −53.8784 −1.79795
899899 4.00000 0.133407
900900 1.20871 0.0402904
901901 −1.25227 −0.0417193
902902 −82.0871 −2.73320
903903 −9.58258 −0.318888
904904 20.0780 0.667785
905905 16.1652 0.537348
906906 12.8348 0.426409
907907 23.5826 0.783047 0.391523 0.920168i 0.371948π-0.371948\pi
0.391523 + 0.920168i 0.371948π0.371948\pi
908908 −9.16515 −0.304156
909909 −0.582576 −0.0193228
910910 −8.20871 −0.272116
911911 −50.8258 −1.68393 −0.841966 0.539530i 0.818602π-0.818602\pi
−0.841966 + 0.539530i 0.818602π0.818602\pi
912912 −17.7568 −0.587987
913913 −57.9129 −1.91664
914914 −6.71326 −0.222055
915915 12.7477 0.421427
916916 −20.7477 −0.685524
917917 −15.0000 −0.495344
918918 −5.37386 −0.177364
919919 18.9129 0.623878 0.311939 0.950102i 0.399021π-0.399021\pi
0.311939 + 0.950102i 0.399021π0.399021\pi
920920 5.66970 0.186924
921921 0 0
922922 −16.4174 −0.540679
923923 43.9129 1.44541
924924 6.04356 0.198819
925925 −4.00000 −0.131519
926926 −0.295834 −0.00972170
927927 15.1652 0.498089
928928 −6.04356 −0.198390
929929 15.6697 0.514106 0.257053 0.966397i 0.417248π-0.417248\pi
0.257053 + 0.966397i 0.417248π0.417248\pi
930930 7.16515 0.234955
931931 −21.4955 −0.704485
932932 −15.9129 −0.521244
933933 −3.00000 −0.0982156
934934 −14.3303 −0.468902
935935 −15.0000 −0.490552
936936 6.49545 0.212311
937937 −18.5826 −0.607066 −0.303533 0.952821i 0.598166π-0.598166\pi
−0.303533 + 0.952821i 0.598166π0.598166\pi
938938 −7.46099 −0.243610
939939 10.5826 0.345349
940940 12.7913 0.417206
941941 19.9129 0.649141 0.324571 0.945861i 0.394780π-0.394780\pi
0.324571 + 0.945861i 0.394780π0.394780\pi
942942 19.2523 0.627273
943943 36.6606 1.19383
944944 37.5826 1.22321
945945 1.00000 0.0325300
946946 −85.8258 −2.79044
947947 −54.9129 −1.78443 −0.892214 0.451612i 0.850849π-0.850849\pi
−0.892214 + 0.451612i 0.850849π0.850849\pi
948948 9.16515 0.297670
949949 −18.3303 −0.595027
950950 6.41742 0.208209
951951 −25.0000 −0.810681
952952 4.25227 0.137817
953953 −37.5826 −1.21742 −0.608710 0.793393i 0.708313π-0.708313\pi
−0.608710 + 0.793393i 0.708313π0.708313\pi
954954 0.747727 0.0242086
955955 −4.00000 −0.129437
956956 −31.4265 −1.01641
957957 5.00000 0.161627
958958 −34.3303 −1.10916
959959 16.3303 0.527333
960960 −0.912878 −0.0294630
961961 −15.0000 −0.483871
962962 32.8348 1.05864
963963 5.16515 0.166445
964964 35.4519 1.14183
965965 −20.3303 −0.654456
966966 −7.16515 −0.230535
967967 9.25227 0.297533 0.148767 0.988872i 0.452470π-0.452470\pi
0.148767 + 0.988872i 0.452470π0.452470\pi
968968 −19.8439 −0.637808
969969 −10.7477 −0.345267
970970 20.7477 0.666169
971971 20.0000 0.641831 0.320915 0.947108i 0.396010π-0.396010\pi
0.320915 + 0.947108i 0.396010π0.396010\pi
972972 1.20871 0.0387695
973973 −9.41742 −0.301909
974974 4.17424 0.133751
975975 −4.58258 −0.146760
976976 −63.1833 −2.02245
977977 −2.50455 −0.0801275 −0.0400638 0.999197i 0.512756π-0.512756\pi
−0.0400638 + 0.999197i 0.512756π0.512756\pi
978978 13.5826 0.434323
979979 7.08712 0.226505
980980 −7.25227 −0.231665
981981 14.1652 0.452258
982982 28.6606 0.914597
983983 55.1652 1.75950 0.879748 0.475441i 0.157712π-0.157712\pi
0.879748 + 0.475441i 0.157712π0.157712\pi
984984 12.9909 0.414135
985985 −16.3303 −0.520327
986986 −5.37386 −0.171139
987987 10.5826 0.336847
988988 −19.8439 −0.631320
989989 38.3303 1.21883
990990 8.95644 0.284654
991991 16.0780 0.510735 0.255368 0.966844i 0.417803π-0.417803\pi
0.255368 + 0.966844i 0.417803π0.417803\pi
992992 −24.1742 −0.767533
993993 −8.33030 −0.264354
994994 −17.1652 −0.544446
995995 13.4174 0.425361
996996 −14.0000 −0.443607
997997 −0.834849 −0.0264399 −0.0132200 0.999913i 0.504208π-0.504208\pi
−0.0132200 + 0.999913i 0.504208π0.504208\pi
998998 −24.0345 −0.760798
999999 −4.00000 −0.126554
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 435.2.a.f.1.2 2
3.2 odd 2 1305.2.a.m.1.1 2
4.3 odd 2 6960.2.a.bw.1.1 2
5.2 odd 4 2175.2.c.f.349.3 4
5.3 odd 4 2175.2.c.f.349.2 4
5.4 even 2 2175.2.a.r.1.1 2
15.14 odd 2 6525.2.a.t.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
435.2.a.f.1.2 2 1.1 even 1 trivial
1305.2.a.m.1.1 2 3.2 odd 2
2175.2.a.r.1.1 2 5.4 even 2
2175.2.c.f.349.2 4 5.3 odd 4
2175.2.c.f.349.3 4 5.2 odd 4
6525.2.a.t.1.2 2 15.14 odd 2
6960.2.a.bw.1.1 2 4.3 odd 2