Properties

Label 960.2.w.f.127.1
Level 960960
Weight 22
Character 960.127
Analytic conductor 7.6667.666
Analytic rank 00
Dimension 88
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [960,2,Mod(127,960)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(960, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([2, 0, 0, 1]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("960.127");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 960=2635 960 = 2^{6} \cdot 3 \cdot 5
Weight: k k == 2 2
Character orbit: [χ][\chi] == 960.w (of order 44, degree 22, not minimal)

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: no
Analytic conductor: 7.665638594047.66563859404
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(i)\Q(i)
Coefficient field: 8.0.1698758656.6
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+18x6+97x4+176x2+64 x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 480)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 127.1
Root 3.16053i-3.16053i of defining polynomial
Character χ\chi == 960.127
Dual form 960.2.w.f.703.1

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+(0.7071070.707107i)q3+(2.23483+0.0743018i)q5+(3.160533.16053i)q7+1.00000iq9+4.46967iq11+(2.519292.51929i)q13+(1.63280+1.52773i)q15+(2.309132.30913i)q17+2.61827q194.46967q21+(1.641241.64124i)q23+(4.988960.332104i)q25+(0.7071070.707107i)q278.17246iq29+4.00000iq31+(3.160533.16053i)q33+(6.82843+7.29809i)q35+(5.801775.80177i)q373.56282q392.61827q41+(5.149495.14949i)q43+(0.07430182.23483i)q45+(0.679824+0.679824i)q4712.9779iq49+3.26561iq51+(7.817397.81739i)q53+(0.3321049.98896i)q55+(1.851401.85140i)q57+4.88998q5912.2751q61+(3.16053+3.16053i)q63+(5.44301+5.81739i)q65+(9.446709.44670i)q67+2.32106iq695.65685iq71+(5.61827+5.61827i)q73+(3.762563.29289i)q75+(14.1265+14.1265i)q77+3.57969q791.00000q81+(1.34403+1.34403i)q83+(5.33210+4.98896i)q85+(5.77880+5.77880i)q8717.6348iq8915.9246iq91+(2.828432.82843i)q93+(5.85140+0.194542i)q95+(1.321061.32106i)q974.46967q99+O(q100)q+(-0.707107 - 0.707107i) q^{3} +(-2.23483 + 0.0743018i) q^{5} +(3.16053 - 3.16053i) q^{7} +1.00000i q^{9} +4.46967i q^{11} +(2.51929 - 2.51929i) q^{13} +(1.63280 + 1.52773i) q^{15} +(-2.30913 - 2.30913i) q^{17} +2.61827 q^{19} -4.46967 q^{21} +(-1.64124 - 1.64124i) q^{23} +(4.98896 - 0.332104i) q^{25} +(0.707107 - 0.707107i) q^{27} -8.17246i q^{29} +4.00000i q^{31} +(3.16053 - 3.16053i) q^{33} +(-6.82843 + 7.29809i) q^{35} +(-5.80177 - 5.80177i) q^{37} -3.56282 q^{39} -2.61827 q^{41} +(-5.14949 - 5.14949i) q^{43} +(-0.0743018 - 2.23483i) q^{45} +(-0.679824 + 0.679824i) q^{47} -12.9779i q^{49} +3.26561i q^{51} +(7.81739 - 7.81739i) q^{53} +(-0.332104 - 9.98896i) q^{55} +(-1.85140 - 1.85140i) q^{57} +4.88998 q^{59} -12.2751 q^{61} +(3.16053 + 3.16053i) q^{63} +(-5.44301 + 5.81739i) q^{65} +(9.44670 - 9.44670i) q^{67} +2.32106i q^{69} -5.65685i q^{71} +(-5.61827 + 5.61827i) q^{73} +(-3.76256 - 3.29289i) q^{75} +(14.1265 + 14.1265i) q^{77} +3.57969 q^{79} -1.00000 q^{81} +(1.34403 + 1.34403i) q^{83} +(5.33210 + 4.98896i) q^{85} +(-5.77880 + 5.77880i) q^{87} -17.6348i q^{89} -15.9246i q^{91} +(2.82843 - 2.82843i) q^{93} +(-5.85140 + 0.194542i) q^{95} +(-1.32106 - 1.32106i) q^{97} -4.46967 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+4q7+12q13+4q154q178q194q25+4q3332q3512q3724q39+8q41+24q434q45+24q474q534q558q57+16q59++32q97+O(q100) 8 q + 4 q^{7} + 12 q^{13} + 4 q^{15} - 4 q^{17} - 8 q^{19} - 4 q^{25} + 4 q^{33} - 32 q^{35} - 12 q^{37} - 24 q^{39} + 8 q^{41} + 24 q^{43} - 4 q^{45} + 24 q^{47} - 4 q^{53} - 4 q^{55} - 8 q^{57} + 16 q^{59}+ \cdots + 32 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/960Z)×\left(\mathbb{Z}/960\mathbb{Z}\right)^\times.

nn 511511 577577 641641 901901
χ(n)\chi(n) 1-1 e(14)e\left(\frac{1}{4}\right) 11 11

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 0 0
33 −0.707107 0.707107i −0.408248 0.408248i
44 0 0
55 −2.23483 + 0.0743018i −0.999448 + 0.0332288i
66 0 0
77 3.16053 3.16053i 1.19457 1.19457i 0.218799 0.975770i 0.429786π-0.429786\pi
0.975770 0.218799i 0.0702137π-0.0702137\pi
88 0 0
99 1.00000i 0.333333i
1010 0 0
1111 4.46967i 1.34766i 0.738889 + 0.673828i 0.235351π0.235351\pi
−0.738889 + 0.673828i 0.764649π0.764649\pi
1212 0 0
1313 2.51929 2.51929i 0.698726 0.698726i −0.265410 0.964136i 0.585507π-0.585507\pi
0.964136 + 0.265410i 0.0855072π0.0855072\pi
1414 0 0
1515 1.63280 + 1.52773i 0.421588 + 0.394457i
1616 0 0
1717 −2.30913 2.30913i −0.560047 0.560047i 0.369273 0.929321i 0.379607π-0.379607\pi
−0.929321 + 0.369273i 0.879607π0.879607\pi
1818 0 0
1919 2.61827 0.600672 0.300336 0.953833i 0.402901π-0.402901\pi
0.300336 + 0.953833i 0.402901π0.402901\pi
2020 0 0
2121 −4.46967 −0.975361
2222 0 0
2323 −1.64124 1.64124i −0.342222 0.342222i 0.514980 0.857202i 0.327799π-0.327799\pi
−0.857202 + 0.514980i 0.827799π0.827799\pi
2424 0 0
2525 4.98896 0.332104i 0.997792 0.0664208i
2626 0 0
2727 0.707107 0.707107i 0.136083 0.136083i
2828 0 0
2929 8.17246i 1.51759i −0.651331 0.758794i 0.725789π-0.725789\pi
0.651331 0.758794i 0.274211π-0.274211\pi
3030 0 0
3131 4.00000i 0.718421i 0.933257 + 0.359211i 0.116954π0.116954\pi
−0.933257 + 0.359211i 0.883046π0.883046\pi
3232 0 0
3333 3.16053 3.16053i 0.550178 0.550178i
3434 0 0
3535 −6.82843 + 7.29809i −1.15421 + 1.23360i
3636 0 0
3737 −5.80177 5.80177i −0.953805 0.953805i 0.0451739 0.998979i 0.485616π-0.485616\pi
−0.998979 + 0.0451739i 0.985616π0.985616\pi
3838 0 0
3939 −3.56282 −0.570507
4040 0 0
4141 −2.61827 −0.408905 −0.204453 0.978876i 0.565541π-0.565541\pi
−0.204453 + 0.978876i 0.565541π0.565541\pi
4242 0 0
4343 −5.14949 5.14949i −0.785290 0.785290i 0.195428 0.980718i 0.437390π-0.437390\pi
−0.980718 + 0.195428i 0.937390π0.937390\pi
4444 0 0
4545 −0.0743018 2.23483i −0.0110763 0.333149i
4646 0 0
4747 −0.679824 + 0.679824i −0.0991625 + 0.0991625i −0.754948 0.655785i 0.772338π-0.772338\pi
0.655785 + 0.754948i 0.272338π0.272338\pi
4848 0 0
4949 12.9779i 1.85399i
5050 0 0
5151 3.26561i 0.457277i
5252 0 0
5353 7.81739 7.81739i 1.07380 1.07380i 0.0767501 0.997050i 0.475546π-0.475546\pi
0.997050 0.0767501i 0.0244544π-0.0244544\pi
5454 0 0
5555 −0.332104 9.98896i −0.0447809 1.34691i
5656 0 0
5757 −1.85140 1.85140i −0.245223 0.245223i
5858 0 0
5959 4.88998 0.636621 0.318311 0.947986i 0.396885π-0.396885\pi
0.318311 + 0.947986i 0.396885π0.396885\pi
6060 0 0
6161 −12.2751 −1.57167 −0.785834 0.618437i 0.787766π-0.787766\pi
−0.785834 + 0.618437i 0.787766π0.787766\pi
6262 0 0
6363 3.16053 + 3.16053i 0.398190 + 0.398190i
6464 0 0
6565 −5.44301 + 5.81739i −0.675122 + 0.721558i
6666 0 0
6767 9.44670 9.44670i 1.15410 1.15410i 0.168375 0.985723i 0.446148π-0.446148\pi
0.985723 0.168375i 0.0538518π-0.0538518\pi
6868 0 0
6969 2.32106i 0.279423i
7070 0 0
7171 5.65685i 0.671345i −0.941979 0.335673i 0.891036π-0.891036\pi
0.941979 0.335673i 0.108964π-0.108964\pi
7272 0 0
7373 −5.61827 + 5.61827i −0.657569 + 0.657569i −0.954804 0.297235i 0.903935π-0.903935\pi
0.297235 + 0.954804i 0.403935π0.403935\pi
7474 0 0
7575 −3.76256 3.29289i −0.434463 0.380231i
7676 0 0
7777 14.1265 + 14.1265i 1.60987 + 1.60987i
7878 0 0
7979 3.57969 0.402746 0.201373 0.979515i 0.435460π-0.435460\pi
0.201373 + 0.979515i 0.435460π0.435460\pi
8080 0 0
8181 −1.00000 −0.111111
8282 0 0
8383 1.34403 + 1.34403i 0.147527 + 0.147527i 0.777012 0.629486i 0.216734π-0.216734\pi
−0.629486 + 0.777012i 0.716734π0.716734\pi
8484 0 0
8585 5.33210 + 4.98896i 0.578348 + 0.541129i
8686 0 0
8787 −5.77880 + 5.77880i −0.619553 + 0.619553i
8888 0 0
8989 17.6348i 1.86928i −0.355593 0.934641i 0.615721π-0.615721\pi
0.355593 0.934641i 0.384279π-0.384279\pi
9090 0 0
9191 15.9246i 1.66935i
9292 0 0
9393 2.82843 2.82843i 0.293294 0.293294i
9494 0 0
9595 −5.85140 + 0.194542i −0.600341 + 0.0199596i
9696 0 0
9797 −1.32106 1.32106i −0.134134 0.134134i 0.636852 0.770986i 0.280236π-0.280236\pi
−0.770986 + 0.636852i 0.780236π0.780236\pi
9898 0 0
9999 −4.46967 −0.449218
100100 0 0
101101 1.47702 0.146969 0.0734845 0.997296i 0.476588π-0.476588\pi
0.0734845 + 0.997296i 0.476588π0.476588\pi
102102 0 0
103103 9.11459 + 9.11459i 0.898088 + 0.898088i 0.995267 0.0971794i 0.0309821π-0.0309821\pi
−0.0971794 + 0.995267i 0.530982π0.530982\pi
104104 0 0
105105 9.98896 0.332104i 0.974823 0.0324101i
106106 0 0
107107 2.06155 2.06155i 0.199298 0.199298i −0.600401 0.799699i 0.704992π-0.704992\pi
0.799699 + 0.600401i 0.204992π0.204992\pi
108108 0 0
109109 9.70279i 0.929359i 0.885479 + 0.464679i 0.153830π0.153830\pi
−0.885479 + 0.464679i 0.846170π0.846170\pi
110110 0 0
111111 8.20494i 0.778779i
112112 0 0
113113 −4.63020 + 4.63020i −0.435572 + 0.435572i −0.890519 0.454946i 0.849658π-0.849658\pi
0.454946 + 0.890519i 0.349658π0.349658\pi
114114 0 0
115115 3.78984 + 3.54595i 0.353405 + 0.330661i
116116 0 0
117117 2.51929 + 2.51929i 0.232909 + 0.232909i
118118 0 0
119119 −14.5962 −1.33803
120120 0 0
121121 −8.97792 −0.816174
122122 0 0
123123 1.85140 + 1.85140i 0.166935 + 0.166935i
124124 0 0
125125 −11.1248 + 1.11289i −0.995034 + 0.0995396i
126126 0 0
127127 −10.1991 + 10.1991i −0.905025 + 0.905025i −0.995865 0.0908403i 0.971045π-0.971045\pi
0.0908403 + 0.995865i 0.471045π0.471045\pi
128128 0 0
129129 7.28248i 0.641186i
130130 0 0
131131 12.4697i 1.08948i 0.838605 + 0.544740i 0.183372π0.183372\pi
−0.838605 + 0.544740i 0.816628π0.816628\pi
132132 0 0
133133 8.27512 8.27512i 0.717544 0.717544i
134134 0 0
135135 −1.52773 + 1.63280i −0.131486 + 0.140529i
136136 0 0
137137 4.63020 + 4.63020i 0.395584 + 0.395584i 0.876672 0.481088i 0.159758π-0.159758\pi
−0.481088 + 0.876672i 0.659758π0.659758\pi
138138 0 0
139139 −3.00735 −0.255080 −0.127540 0.991833i 0.540708π-0.540708\pi
−0.127540 + 0.991833i 0.540708π0.540708\pi
140140 0 0
141141 0.961416 0.0809658
142142 0 0
143143 11.2604 + 11.2604i 0.941642 + 0.941642i
144144 0 0
145145 0.607228 + 18.2641i 0.0504276 + 1.51675i
146146 0 0
147147 −9.17677 + 9.17677i −0.756887 + 0.756887i
148148 0 0
149149 0.148604i 0.0121741i −0.999981 0.00608704i 0.998062π-0.998062\pi
0.999981 0.00608704i 0.00193758π-0.00193758\pi
150150 0 0
151151 20.6200i 1.67804i −0.544104 0.839018i 0.683130π-0.683130\pi
0.544104 0.839018i 0.316870π-0.316870\pi
152152 0 0
153153 2.30913 2.30913i 0.186682 0.186682i
154154 0 0
155155 −0.297207 8.93933i −0.0238723 0.718024i
156156 0 0
157157 9.77969 + 9.77969i 0.780504 + 0.780504i 0.979916 0.199412i 0.0639031π-0.0639031\pi
−0.199412 + 0.979916i 0.563903π0.563903\pi
158158 0 0
159159 −11.0555 −0.876754
160160 0 0
161161 −10.3744 −0.817615
162162 0 0
163163 10.4081 + 10.4081i 0.815226 + 0.815226i 0.985412 0.170186i 0.0544368π-0.0544368\pi
−0.170186 + 0.985412i 0.554437π0.554437\pi
164164 0 0
165165 −6.82843 + 7.29809i −0.531592 + 0.568156i
166166 0 0
167167 6.06155 6.06155i 0.469057 0.469057i −0.432552 0.901609i 0.642387π-0.642387\pi
0.901609 + 0.432552i 0.142387π0.142387\pi
168168 0 0
169169 0.306334i 0.0235641i
170170 0 0
171171 2.61827i 0.200224i
172172 0 0
173173 −0.355074 + 0.355074i −0.0269957 + 0.0269957i −0.720476 0.693480i 0.756077π-0.756077\pi
0.693480 + 0.720476i 0.256077π0.256077\pi
174174 0 0
175175 14.7181 16.8174i 1.11259 1.27127i
176176 0 0
177177 −3.45774 3.45774i −0.259900 0.259900i
178178 0 0
179179 15.7521 1.17737 0.588685 0.808362i 0.299646π-0.299646\pi
0.588685 + 0.808362i 0.299646π0.299646\pi
180180 0 0
181181 −7.77996 −0.578280 −0.289140 0.957287i 0.593369π-0.593369\pi
−0.289140 + 0.957287i 0.593369π0.593369\pi
182182 0 0
183183 8.67982 + 8.67982i 0.641631 + 0.641631i
184184 0 0
185185 13.3971 + 12.5349i 0.984972 + 0.921585i
186186 0 0
187187 10.3211 10.3211i 0.754751 0.754751i
188188 0 0
189189 4.46967i 0.325120i
190190 0 0
191191 9.35965i 0.677240i 0.940923 + 0.338620i 0.109960π0.109960\pi
−0.940923 + 0.338620i 0.890040π0.890040\pi
192192 0 0
193193 17.1759 17.1759i 1.23635 1.23635i 0.274863 0.961483i 0.411368π-0.411368\pi
0.961483 0.274863i 0.0886325π-0.0886325\pi
194194 0 0
195195 7.96230 0.264724i 0.570192 0.0189573i
196196 0 0
197197 −1.83947 1.83947i −0.131057 0.131057i 0.638536 0.769592i 0.279541π-0.279541\pi
−0.769592 + 0.638536i 0.779541π0.779541\pi
198198 0 0
199199 0.442397 0.0313607 0.0156804 0.999877i 0.495009π-0.495009\pi
0.0156804 + 0.999877i 0.495009π0.495009\pi
200200 0 0
201201 −13.3596 −0.942317
202202 0 0
203203 −25.8293 25.8293i −1.81286 1.81286i
204204 0 0
205205 5.85140 0.194542i 0.408679 0.0135874i
206206 0 0
207207 1.64124 1.64124i 0.114074 0.114074i
208208 0 0
209209 11.7028i 0.809499i
210210 0 0
211211 5.30633i 0.365303i 0.983178 + 0.182652i 0.0584680π0.0584680\pi
−0.983178 + 0.182652i 0.941532π0.941532\pi
212212 0 0
213213 −4.00000 + 4.00000i −0.274075 + 0.274075i
214214 0 0
215215 11.8909 + 11.1256i 0.810950 + 0.758762i
216216 0 0
217217 12.6421 + 12.6421i 0.858203 + 0.858203i
218218 0 0
219219 7.94543 0.536903
220220 0 0
221221 −11.6348 −0.782639
222222 0 0
223223 −5.48159 5.48159i −0.367075 0.367075i 0.499335 0.866409i 0.333578π-0.333578\pi
−0.866409 + 0.499335i 0.833578π0.833578\pi
224224 0 0
225225 0.332104 + 4.98896i 0.0221403 + 0.332597i
226226 0 0
227227 −9.51649 + 9.51649i −0.631632 + 0.631632i −0.948477 0.316845i 0.897376π-0.897376\pi
0.316845 + 0.948477i 0.397376π0.397376\pi
228228 0 0
229229 5.25862i 0.347500i 0.984790 + 0.173750i 0.0555884π0.0555884\pi
−0.984790 + 0.173750i 0.944412π0.944412\pi
230230 0 0
231231 19.9779i 1.31445i
232232 0 0
233233 2.92740 2.92740i 0.191781 0.191781i −0.604684 0.796465i 0.706701π-0.706701\pi
0.796465 + 0.604684i 0.206701π0.206701\pi
234234 0 0
235235 1.46878 1.56980i 0.0958126 0.102403i
236236 0 0
237237 −2.53122 2.53122i −0.164420 0.164420i
238238 0 0
239239 12.6421 0.817751 0.408876 0.912590i 0.365921π-0.365921\pi
0.408876 + 0.912590i 0.365921π0.365921\pi
240240 0 0
241241 14.5650 0.938211 0.469106 0.883142i 0.344576π-0.344576\pi
0.469106 + 0.883142i 0.344576π0.344576\pi
242242 0 0
243243 0.707107 + 0.707107i 0.0453609 + 0.0453609i
244244 0 0
245245 0.964283 + 29.0035i 0.0616058 + 1.85296i
246246 0 0
247247 6.59619 6.59619i 0.419705 0.419705i
248248 0 0
249249 1.90075i 0.120455i
250250 0 0
251251 18.5468i 1.17067i 0.810793 + 0.585333i 0.199036π0.199036\pi
−0.810793 + 0.585333i 0.800964π0.800964\pi
252252 0 0
253253 7.33579 7.33579i 0.461197 0.461197i
254254 0 0
255255 −0.242641 7.29809i −0.0151947 0.457024i
256256 0 0
257257 13.2485 + 13.2485i 0.826417 + 0.826417i 0.987019 0.160602i 0.0513437π-0.0513437\pi
−0.160602 + 0.987019i 0.551344π0.551344\pi
258258 0 0
259259 −36.6734 −2.27877
260260 0 0
261261 8.17246 0.505863
262262 0 0
263263 −22.5806 22.5806i −1.39238 1.39238i −0.819967 0.572411i 0.806008π-0.806008\pi
−0.572411 0.819967i 0.693992π-0.693992\pi
264264 0 0
265265 −16.8897 + 18.0514i −1.03753 + 1.10889i
266266 0 0
267267 −12.4697 + 12.4697i −0.763131 + 0.763131i
268268 0 0
269269 6.82019i 0.415834i −0.978146 0.207917i 0.933332π-0.933332\pi
0.978146 0.207917i 0.0666684π-0.0666684\pi
270270 0 0
271271 2.74138i 0.166527i 0.996528 + 0.0832634i 0.0265343π0.0265343\pi
−0.996528 + 0.0832634i 0.973466π0.973466\pi
272272 0 0
273273 −11.2604 + 11.2604i −0.681510 + 0.681510i
274274 0 0
275275 1.48440 + 22.2990i 0.0895124 + 1.34468i
276276 0 0
277277 7.75583 + 7.75583i 0.466003 + 0.466003i 0.900617 0.434614i 0.143115π-0.143115\pi
−0.434614 + 0.900617i 0.643115π0.643115\pi
278278 0 0
279279 −4.00000 −0.239474
280280 0 0
281281 4.54110 0.270899 0.135450 0.990784i 0.456752π-0.456752\pi
0.135450 + 0.990784i 0.456752π0.456752\pi
282282 0 0
283283 7.91295 + 7.91295i 0.470376 + 0.470376i 0.902036 0.431660i 0.142072π-0.142072\pi
−0.431660 + 0.902036i 0.642072π0.642072\pi
284284 0 0
285285 4.27512 + 4.00000i 0.253236 + 0.236940i
286286 0 0
287287 −8.27512 + 8.27512i −0.488465 + 0.488465i
288288 0 0
289289 6.33579i 0.372694i
290290 0 0
291291 1.86826i 0.109520i
292292 0 0
293293 −15.0999 + 15.0999i −0.882143 + 0.882143i −0.993752 0.111609i 0.964400π-0.964400\pi
0.111609 + 0.993752i 0.464400π0.464400\pi
294294 0 0
295295 −10.9283 + 0.363334i −0.636270 + 0.0211541i
296296 0 0
297297 3.16053 + 3.16053i 0.183393 + 0.183393i
298298 0 0
299299 −8.26952 −0.478239
300300 0 0
301301 −32.5502 −1.87617
302302 0 0
303303 −1.04441 1.04441i −0.0599999 0.0599999i
304304 0 0
305305 27.4329 0.912064i 1.57080 0.0522246i
306306 0 0
307307 4.43197 4.43197i 0.252946 0.252946i −0.569232 0.822177i 0.692759π-0.692759\pi
0.822177 + 0.569232i 0.192759π0.192759\pi
308308 0 0
309309 12.8900i 0.733285i
310310 0 0
311311 23.5355i 1.33458i 0.744799 + 0.667288i 0.232545π0.232545\pi
−0.744799 + 0.667288i 0.767455π0.767455\pi
312312 0 0
313313 −18.6035 + 18.6035i −1.05153 + 1.05153i −0.0529364 + 0.998598i 0.516858π0.516858\pi
−0.998598 + 0.0529364i 0.983142π0.983142\pi
314314 0 0
315315 −7.29809 6.82843i −0.411201 0.384738i
316316 0 0
317317 −7.56953 7.56953i −0.425147 0.425147i 0.461824 0.886971i 0.347195π-0.347195\pi
−0.886971 + 0.461824i 0.847195π0.847195\pi
318318 0 0
319319 36.5282 2.04518
320320 0 0
321321 −2.91548 −0.162726
322322 0 0
323323 −6.04594 6.04594i −0.336405 0.336405i
324324 0 0
325325 11.7320 13.4053i 0.650773 0.743593i
326326 0 0
327327 6.86091 6.86091i 0.379409 0.379409i
328328 0 0
329329 4.29721i 0.236913i
330330 0 0
331331 13.8020i 0.758629i −0.925268 0.379314i 0.876160π-0.876160\pi
0.925268 0.379314i 0.123840π-0.123840\pi
332332 0 0
333333 5.80177 5.80177i 0.317935 0.317935i
334334 0 0
335335 −20.4099 + 21.8137i −1.11511 + 1.19181i
336336 0 0
337337 10.9541 + 10.9541i 0.596706 + 0.596706i 0.939434 0.342729i 0.111351π-0.111351\pi
−0.342729 + 0.939434i 0.611351π0.611351\pi
338338 0 0
339339 6.54809 0.355643
340340 0 0
341341 −17.8787 −0.968184
342342 0 0
343343 −18.8934 18.8934i −1.02015 1.02015i
344344 0 0
345345 −0.172459 5.18719i −0.00928489 0.279269i
346346 0 0
347347 13.3934 13.3934i 0.718995 0.718995i −0.249405 0.968399i 0.580235π-0.580235\pi
0.968399 + 0.249405i 0.0802350π0.0802350\pi
348348 0 0
349349 21.6035i 1.15641i 0.815891 + 0.578206i 0.196247π0.196247\pi
−0.815891 + 0.578206i 0.803753π0.803753\pi
350350 0 0
351351 3.56282i 0.190169i
352352 0 0
353353 25.9678 25.9678i 1.38212 1.38212i 0.541286 0.840839i 0.317938π-0.317938\pi
0.840839 0.541286i 0.182062π-0.182062\pi
354354 0 0
355355 0.420314 + 12.6421i 0.0223080 + 0.670974i
356356 0 0
357357 10.3211 + 10.3211i 0.546249 + 0.546249i
358358 0 0
359359 8.93933 0.471800 0.235900 0.971777i 0.424196π-0.424196\pi
0.235900 + 0.971777i 0.424196π0.424196\pi
360360 0 0
361361 −12.1447 −0.639193
362362 0 0
363363 6.34835 + 6.34835i 0.333202 + 0.333202i
364364 0 0
365365 12.1384 12.9733i 0.635355 0.679056i
366366 0 0
367367 −13.7788 + 13.7788i −0.719248 + 0.719248i −0.968451 0.249204i 0.919831π-0.919831\pi
0.249204 + 0.968451i 0.419831π0.419831\pi
368368 0 0
369369 2.61827i 0.136302i
370370 0 0
371371 49.4142i 2.56546i
372372 0 0
373373 12.4439 12.4439i 0.644321 0.644321i −0.307294 0.951615i 0.599424π-0.599424\pi
0.951615 + 0.307294i 0.0994235π0.0994235\pi
374374 0 0
375375 8.65336 + 7.07950i 0.446858 + 0.365584i
376376 0 0
377377 −20.5888 20.5888i −1.06038 1.06038i
378378 0 0
379379 34.9190 1.79367 0.896835 0.442366i 0.145861π-0.145861\pi
0.896835 + 0.442366i 0.145861π0.145861\pi
380380 0 0
381381 14.4237 0.738950
382382 0 0
383383 −5.69455 5.69455i −0.290978 0.290978i 0.546489 0.837467i 0.315964π-0.315964\pi
−0.837467 + 0.546489i 0.815964π0.815964\pi
384384 0 0
385385 −32.6200 30.5208i −1.66247 1.55548i
386386 0 0
387387 5.14949 5.14949i 0.261763 0.261763i
388388 0 0
389389 8.44581i 0.428220i −0.976810 0.214110i 0.931315π-0.931315\pi
0.976810 0.214110i 0.0686850π-0.0686850\pi
390390 0 0
391391 7.57969i 0.383321i
392392 0 0
393393 8.81739 8.81739i 0.444778 0.444778i
394394 0 0
395395 −8.00000 + 0.265977i −0.402524 + 0.0133828i
396396 0 0
397397 −18.0769 18.0769i −0.907253 0.907253i 0.0887965 0.996050i 0.471698π-0.471698\pi
−0.996050 + 0.0887965i 0.971698π0.971698\pi
398398 0 0
399399 −11.7028 −0.585872
400400 0 0
401401 −31.8787 −1.59194 −0.795972 0.605333i 0.793040π-0.793040\pi
−0.795972 + 0.605333i 0.793040π0.793040\pi
402402 0 0
403403 10.0772 + 10.0772i 0.501980 + 0.501980i
404404 0 0
405405 2.23483 0.0743018i 0.111050 0.00369209i
406406 0 0
407407 25.9320 25.9320i 1.28540 1.28540i
408408 0 0
409409 27.3063i 1.35021i −0.737721 0.675106i 0.764098π-0.764098\pi
0.737721 0.675106i 0.235902π-0.235902\pi
410410 0 0
411411 6.54809i 0.322993i
412412 0 0
413413 15.4549 15.4549i 0.760488 0.760488i
414414 0 0
415415 −3.10355 2.90382i −0.152347 0.142543i
416416 0 0
417417 2.12652 + 2.12652i 0.104136 + 0.104136i
418418 0 0
419419 16.1412 0.788551 0.394275 0.918992i 0.370996π-0.370996\pi
0.394275 + 0.918992i 0.370996π0.370996\pi
420420 0 0
421421 20.6200 1.00496 0.502480 0.864589i 0.332421π-0.332421\pi
0.502480 + 0.864589i 0.332421π0.332421\pi
422422 0 0
423423 −0.679824 0.679824i −0.0330542 0.0330542i
424424 0 0
425425 −12.2871 10.7533i −0.596010 0.521612i
426426 0 0
427427 −38.7959 + 38.7959i −1.87747 + 1.87747i
428428 0 0
429429 15.9246i 0.768847i
430430 0 0
431431 2.54848i 0.122756i 0.998115 + 0.0613779i 0.0195495π0.0195495\pi
−0.998115 + 0.0613779i 0.980451π0.980451\pi
432432 0 0
433433 6.77996 6.77996i 0.325824 0.325824i −0.525172 0.850996i 0.675999π-0.675999\pi
0.850996 + 0.525172i 0.175999π0.175999\pi
434434 0 0
435435 12.4853 13.3440i 0.598623 0.639797i
436436 0 0
437437 −4.29721 4.29721i −0.205563 0.205563i
438438 0 0
439439 −15.0698 −0.719243 −0.359622 0.933098i 0.617094π-0.617094\pi
−0.359622 + 0.933098i 0.617094π0.617094\pi
440440 0 0
441441 12.9779 0.617996
442442 0 0
443443 −9.69059 9.69059i −0.460414 0.460414i 0.438377 0.898791i 0.355553π-0.355553\pi
−0.898791 + 0.438377i 0.855553π0.855553\pi
444444 0 0
445445 1.31030 + 39.4108i 0.0621139 + 1.86825i
446446 0 0
447447 −0.105079 + 0.105079i −0.00497005 + 0.00497005i
448448 0 0
449449 20.1759i 0.952158i 0.879402 + 0.476079i 0.157942π0.157942\pi
−0.879402 + 0.476079i 0.842058π0.842058\pi
450450 0 0
451451 11.7028i 0.551063i
452452 0 0
453453 −14.5806 + 14.5806i −0.685055 + 0.685055i
454454 0 0
455455 1.18323 + 35.5888i 0.0554705 + 1.66843i
456456 0 0
457457 −0.579686 0.579686i −0.0271165 0.0271165i 0.693419 0.720535i 0.256104π-0.256104\pi
−0.720535 + 0.693419i 0.756104π0.756104\pi
458458 0 0
459459 −3.26561 −0.152426
460460 0 0
461461 4.40164 0.205005 0.102503 0.994733i 0.467315π-0.467315\pi
0.102503 + 0.994733i 0.467315π0.467315\pi
462462 0 0
463463 0.786155 + 0.786155i 0.0365357 + 0.0365357i 0.725139 0.688603i 0.241776π-0.241776\pi
−0.688603 + 0.725139i 0.741776π0.741776\pi
464464 0 0
465465 −6.11091 + 6.53122i −0.283386 + 0.302878i
466466 0 0
467467 19.6430 19.6430i 0.908970 0.908970i −0.0872190 0.996189i 0.527798π-0.527798\pi
0.996189 + 0.0872190i 0.0277980π0.0277980\pi
468468 0 0
469469 59.7132i 2.75730i
470470 0 0
471471 13.8306i 0.637279i
472472 0 0
473473 23.0165 23.0165i 1.05830 1.05830i
474474 0 0
475475 13.0624 0.869539i 0.599346 0.0398972i
476476 0 0
477477 7.81739 + 7.81739i 0.357933 + 0.357933i
478478 0 0
479479 30.6274 1.39940 0.699701 0.714436i 0.253316π-0.253316\pi
0.699701 + 0.714436i 0.253316π0.253316\pi
480480 0 0
481481 −29.2327 −1.33290
482482 0 0
483483 7.33579 + 7.33579i 0.333790 + 0.333790i
484484 0 0
485485 3.05051 + 2.85420i 0.138517 + 0.129602i
486486 0 0
487487 −24.7641 + 24.7641i −1.12217 + 1.12217i −0.130752 + 0.991415i 0.541739π0.541739\pi
−0.991415 + 0.130752i 0.958261π0.958261\pi
488488 0 0
489489 14.7193i 0.665629i
490490 0 0
491491 23.3318i 1.05295i 0.850190 + 0.526475i 0.176487π0.176487\pi
−0.850190 + 0.526475i 0.823513π0.823513\pi
492492 0 0
493493 −18.8713 + 18.8713i −0.849921 + 0.849921i
494494 0 0
495495 9.98896 0.332104i 0.448970 0.0149270i
496496 0 0
497497 −17.8787 17.8787i −0.801968 0.801968i
498498 0 0
499499 −40.4051 −1.80878 −0.904389 0.426708i 0.859673π-0.859673\pi
−0.904389 + 0.426708i 0.859673π0.859673\pi
500500 0 0
501501 −8.57233 −0.382984
502502 0 0
503503 −0.160805 0.160805i −0.00716996 0.00716996i 0.703513 0.710683i 0.251614π-0.251614\pi
−0.710683 + 0.703513i 0.751614π0.751614\pi
504504 0 0
505505 −3.30089 + 0.109745i −0.146888 + 0.00488360i
506506 0 0
507507 0.216611 0.216611i 0.00962002 0.00962002i
508508 0 0
509509 11.4862i 0.509115i −0.967058 0.254558i 0.918070π-0.918070\pi
0.967058 0.254558i 0.0819299π-0.0819299\pi
510510 0 0
511511 35.5134i 1.57102i
512512 0 0
513513 1.85140 1.85140i 0.0817411 0.0817411i
514514 0 0
515515 −21.0468 19.6924i −0.927434 0.867749i
516516 0 0
517517 −3.03858 3.03858i −0.133637 0.133637i
518518 0 0
519519 0.502150 0.0220419
520520 0 0
521521 16.3744 0.717374 0.358687 0.933458i 0.383224π-0.383224\pi
0.358687 + 0.933458i 0.383224π0.383224\pi
522522 0 0
523523 5.02638 + 5.02638i 0.219788 + 0.219788i 0.808409 0.588621i 0.200329π-0.200329\pi
−0.588621 + 0.808409i 0.700329π0.700329\pi
524524 0 0
525525 −22.2990 + 1.48440i −0.973207 + 0.0647843i
526526 0 0
527527 9.23654 9.23654i 0.402350 0.402350i
528528 0 0
529529 17.6127i 0.765768i
530530 0 0
531531 4.88998i 0.212207i
532532 0 0
533533 −6.59619 + 6.59619i −0.285713 + 0.285713i
534534 0 0
535535 −4.45405 + 4.76041i −0.192565 + 0.205810i
536536 0 0
537537 −11.1384 11.1384i −0.480660 0.480660i
538538 0 0
539539 58.0070 2.49854
540540 0 0
541541 32.3302 1.38998 0.694992 0.719017i 0.255408π-0.255408\pi
0.694992 + 0.719017i 0.255408π0.255408\pi
542542 0 0
543543 5.50126 + 5.50126i 0.236082 + 0.236082i
544544 0 0
545545 −0.720935 21.6841i −0.0308815 0.928846i
546546 0 0
547547 −8.01165 + 8.01165i −0.342554 + 0.342554i −0.857327 0.514773i 0.827876π-0.827876\pi
0.514773 + 0.857327i 0.327876π0.327876\pi
548548 0 0
549549 12.2751i 0.523890i
550550 0 0
551551 21.3977i 0.911573i
552552 0 0
553553 11.3137 11.3137i 0.481108 0.481108i
554554 0 0
555555 −0.609642 18.3367i −0.0258779 0.778349i
556556 0 0
557557 −0.138448 0.138448i −0.00586624 0.00586624i 0.704168 0.710034i 0.251320π-0.251320\pi
−0.710034 + 0.704168i 0.751320π0.751320\pi
558558 0 0
559559 −25.9461 −1.09740
560560 0 0
561561 −14.5962 −0.616251
562562 0 0
563563 14.7843 + 14.7843i 0.623082 + 0.623082i 0.946318 0.323236i 0.104771π-0.104771\pi
−0.323236 + 0.946318i 0.604771π0.604771\pi
564564 0 0
565565 10.0037 10.6918i 0.420858 0.449805i
566566 0 0
567567 −3.16053 + 3.16053i −0.132730 + 0.132730i
568568 0 0
569569 29.9558i 1.25581i 0.778288 + 0.627907i 0.216088π0.216088\pi
−0.778288 + 0.627907i 0.783912π0.783912\pi
570570 0 0
571571 8.52134i 0.356607i 0.983976 + 0.178303i 0.0570609π0.0570609\pi
−0.983976 + 0.178303i 0.942939π0.942939\pi
572572 0 0
573573 6.61827 6.61827i 0.276482 0.276482i
574574 0 0
575575 −8.73314 7.64301i −0.364197 0.318736i
576576 0 0
577577 10.9779 + 10.9779i 0.457017 + 0.457017i 0.897675 0.440658i 0.145255π-0.145255\pi
−0.440658 + 0.897675i 0.645255π0.645255\pi
578578 0 0
579579 −24.2904 −1.00947
580580 0 0
581581 8.49571 0.352461
582582 0 0
583583 34.9411 + 34.9411i 1.44711 + 1.44711i
584584 0 0
585585 −5.81739 5.44301i −0.240519 0.225041i
586586 0 0
587587 −18.0174 + 18.0174i −0.743657 + 0.743657i −0.973280 0.229623i 0.926251π-0.926251\pi
0.229623 + 0.973280i 0.426251π0.426251\pi
588588 0 0
589589 10.4731i 0.431536i
590590 0 0
591591 2.60140i 0.107007i
592592 0 0
593593 −25.8906 + 25.8906i −1.06320 + 1.06320i −0.0653359 + 0.997863i 0.520812π0.520812\pi
−0.997863 + 0.0653359i 0.979188π0.979188\pi
594594 0 0
595595 32.6200 1.08452i 1.33729 0.0444611i
596596 0 0
597597 −0.312822 0.312822i −0.0128030 0.0128030i
598598 0 0
599599 −8.89517 −0.363447 −0.181723 0.983350i 0.558168π-0.558168\pi
−0.181723 + 0.983350i 0.558168π0.558168\pi
600600 0 0
601601 35.3393 1.44152 0.720761 0.693184i 0.243793π-0.243793\pi
0.720761 + 0.693184i 0.243793π0.243793\pi
602602 0 0
603603 9.44670 + 9.44670i 0.384699 + 0.384699i
604604 0 0
605605 20.0641 0.667075i 0.815724 0.0271205i
606606 0 0
607607 4.90926 4.90926i 0.199261 0.199261i −0.600422 0.799683i 0.705001π-0.705001\pi
0.799683 + 0.600422i 0.205001π0.205001\pi
608608 0 0
609609 36.5282i 1.48020i
610610 0 0
611611 3.42535i 0.138575i
612612 0 0
613613 −1.87894 + 1.87894i −0.0758896 + 0.0758896i −0.744033 0.668143i 0.767089π-0.767089\pi
0.668143 + 0.744033i 0.267089π0.267089\pi
614614 0 0
615615 −4.27512 4.00000i −0.172390 0.161296i
616616 0 0
617617 −5.07260 5.07260i −0.204215 0.204215i 0.597588 0.801803i 0.296126π-0.296126\pi
−0.801803 + 0.597588i 0.796126π0.796126\pi
618618 0 0
619619 −46.2769 −1.86003 −0.930013 0.367527i 0.880204π-0.880204\pi
−0.930013 + 0.367527i 0.880204π0.880204\pi
620620 0 0
621621 −2.32106 −0.0931410
622622 0 0
623623 −55.7352 55.7352i −2.23299 2.23299i
624624 0 0
625625 24.7794 3.31371i 0.991177 0.132548i
626626 0 0
627627 8.27512 8.27512i 0.330477 0.330477i
628628 0 0
629629 26.7941i 1.06835i
630630 0 0
631631 36.6457i 1.45884i 0.684066 + 0.729421i 0.260210π0.260210\pi
−0.684066 + 0.729421i 0.739790π0.739790\pi
632632 0 0
633633 3.75214 3.75214i 0.149134 0.149134i
634634 0 0
635635 22.0355 23.5511i 0.874453 0.934598i
636636 0 0
637637 −32.6952 32.6952i −1.29543 1.29543i
638638 0 0
639639 5.65685 0.223782
640640 0 0
641641 −12.1520 −0.479976 −0.239988 0.970776i 0.577143π-0.577143\pi
−0.239988 + 0.970776i 0.577143π0.577143\pi
642642 0 0
643643 6.53122 + 6.53122i 0.257566 + 0.257566i 0.824064 0.566497i 0.191702π-0.191702\pi
−0.566497 + 0.824064i 0.691702π0.691702\pi
644644 0 0
645645 −0.541101 16.2751i −0.0213058 0.640832i
646646 0 0
647647 17.6192 17.6192i 0.692681 0.692681i −0.270140 0.962821i 0.587070π-0.587070\pi
0.962821 + 0.270140i 0.0870701π0.0870701\pi
648648 0 0
649649 21.8566i 0.857946i
650650 0 0
651651 17.8787i 0.700720i
652652 0 0
653653 −0.727677 + 0.727677i −0.0284762 + 0.0284762i −0.721202 0.692725i 0.756410π-0.756410\pi
0.692725 + 0.721202i 0.256410π0.256410\pi
654654 0 0
655655 −0.926519 27.8676i −0.0362021 1.08888i
656656 0 0
657657 −5.61827 5.61827i −0.219190 0.219190i
658658 0 0
659659 −44.9004 −1.74907 −0.874535 0.484963i 0.838833π-0.838833\pi
−0.874535 + 0.484963i 0.838833π0.838833\pi
660660 0 0
661661 −14.9320 −0.580786 −0.290393 0.956907i 0.593786π-0.593786\pi
−0.290393 + 0.956907i 0.593786π0.593786\pi
662662 0 0
663663 8.22703 + 8.22703i 0.319511 + 0.319511i
664664 0 0
665665 −17.8787 + 19.1084i −0.693305 + 0.740991i
666666 0 0
667667 −13.4130 + 13.4130i −0.519352 + 0.519352i
668668 0 0
669669 7.75214i 0.299715i
670670 0 0
671671 54.8657i 2.11807i
672672 0 0
673673 2.55583 2.55583i 0.0985200 0.0985200i −0.656129 0.754649i 0.727807π-0.727807\pi
0.754649 + 0.656129i 0.227807π0.227807\pi
674674 0 0
675675 3.29289 3.76256i 0.126744 0.144821i
676676 0 0
677677 −17.7147 17.7147i −0.680832 0.680832i 0.279356 0.960188i 0.409879π-0.409879\pi
−0.960188 + 0.279356i 0.909879π0.909879\pi
678678 0 0
679679 −8.35052 −0.320464
680680 0 0
681681 13.4584 0.515725
682682 0 0
683683 11.3968 + 11.3968i 0.436086 + 0.436086i 0.890693 0.454606i 0.150220π-0.150220\pi
−0.454606 + 0.890693i 0.650220π0.650220\pi
684684 0 0
685685 −10.6918 10.0037i −0.408511 0.382221i
686686 0 0
687687 3.71841 3.71841i 0.141866 0.141866i
688688 0 0
689689 39.3886i 1.50058i
690690 0 0
691691 6.94671i 0.264265i −0.991232 0.132133i 0.957818π-0.957818\pi
0.991232 0.132133i 0.0421825π-0.0421825\pi
692692 0 0
693693 −14.1265 + 14.1265i −0.536622 + 0.536622i
694694 0 0
695695 6.72093 0.223452i 0.254940 0.00847601i
696696 0 0
697697 6.04594 + 6.04594i 0.229006 + 0.229006i
698698 0 0
699699 −4.13998 −0.156588
700700 0 0
701701 9.70621 0.366598 0.183299 0.983057i 0.441322π-0.441322\pi
0.183299 + 0.983057i 0.441322π0.441322\pi
702702 0 0
703703 −15.1906 15.1906i −0.572924 0.572924i
704704 0 0
705705 −2.14860 + 0.0714349i −0.0809211 + 0.00269039i
706706 0 0
707707 4.66817 4.66817i 0.175565 0.175565i
708708 0 0
709709 10.7414i 0.403401i 0.979447 + 0.201700i 0.0646467π0.0646467\pi
−0.979447 + 0.201700i 0.935353π0.935353\pi
710710 0 0
711711 3.57969i 0.134249i
712712 0 0
713713 6.56496 6.56496i 0.245860 0.245860i
714714 0 0
715715 −26.0018 24.3284i −0.972411 0.909832i
716716 0 0
717717 −8.93933 8.93933i −0.333845 0.333845i
718718 0 0
719719 43.8640 1.63585 0.817925 0.575325i 0.195124π-0.195124\pi
0.817925 + 0.575325i 0.195124π0.195124\pi
720720 0 0
721721 57.6139 2.14565
722722 0 0
723723 −10.2990 10.2990i −0.383023 0.383023i
724724 0 0
725725 −2.71411 40.7721i −0.100799 1.51424i
726726 0 0
727727 9.95522 9.95522i 0.369219 0.369219i −0.497974 0.867192i 0.665922π-0.665922\pi
0.867192 + 0.497974i 0.165922π0.165922\pi
728728 0 0
729729 1.00000i 0.0370370i
730730 0 0
731731 23.7817i 0.879599i
732732 0 0
733733 −16.9924 + 16.9924i −0.627628 + 0.627628i −0.947471 0.319843i 0.896370π-0.896370\pi
0.319843 + 0.947471i 0.396370π0.396370\pi
734734 0 0
735735 19.8267 21.1904i 0.731319 0.781620i
736736 0 0
737737 42.2236 + 42.2236i 1.55533 + 1.55533i
738738 0 0
739739 −27.9025 −1.02641 −0.513205 0.858266i 0.671542π-0.671542\pi
−0.513205 + 0.858266i 0.671542π0.671542\pi
740740 0 0
741741 −9.32842 −0.342688
742742 0 0
743743 20.2907 + 20.2907i 0.744395 + 0.744395i 0.973420 0.229025i 0.0735539π-0.0735539\pi
−0.229025 + 0.973420i 0.573554π0.573554\pi
744744 0 0
745745 0.0110415 + 0.332104i 0.000404530 + 0.0121674i
746746 0 0
747747 −1.34403 + 1.34403i −0.0491756 + 0.0491756i
748748 0 0
749749 13.0312i 0.476150i
750750 0 0
751751 1.97054i 0.0719061i −0.999353 0.0359531i 0.988553π-0.988553\pi
0.999353 0.0359531i 0.0114467π-0.0114467\pi
752752 0 0
753753 13.1146 13.1146i 0.477922 0.477922i
754754 0 0
755755 1.53211 + 46.0824i 0.0557591 + 1.67711i
756756 0 0
757757 −9.13933 9.13933i −0.332175 0.332175i 0.521237 0.853412i 0.325471π-0.325471\pi
−0.853412 + 0.521237i 0.825471π0.825471\pi
758758 0 0
759759 −10.3744 −0.376566
760760 0 0
761761 −23.7800 −0.862023 −0.431011 0.902346i 0.641843π-0.641843\pi
−0.431011 + 0.902346i 0.641843π0.641843\pi
762762 0 0
763763 30.6660 + 30.6660i 1.11018 + 1.11018i
764764 0 0
765765 −4.98896 + 5.33210i −0.180376 + 0.192783i
766766 0 0
767767 12.3193 12.3193i 0.444824 0.444824i
768768 0 0
769769 17.7022i 0.638359i −0.947694 0.319180i 0.896593π-0.896593\pi
0.947694 0.319180i 0.103407π-0.103407\pi
770770 0 0
771771 18.7362i 0.674766i
772772 0 0
773773 −9.30178 + 9.30178i −0.334562 + 0.334562i −0.854316 0.519754i 0.826024π-0.826024\pi
0.519754 + 0.854316i 0.326024π0.326024\pi
774774 0 0
775775 1.32842 + 19.9558i 0.0477181 + 0.716835i
776776 0 0
777777 25.9320 + 25.9320i 0.930305 + 0.930305i
778778 0 0
779779 −6.85534 −0.245618
780780 0 0
781781 25.2843 0.904742
782782 0 0
783783 −5.77880 5.77880i −0.206518 0.206518i
784784 0 0
785785 −22.5826 21.1293i −0.806008 0.754138i
786786 0 0
787787 18.1642 18.1642i 0.647484 0.647484i −0.304900 0.952384i 0.598623π-0.598623\pi
0.952384 + 0.304900i 0.0986230π0.0986230\pi
788788 0 0
789789 31.9338i 1.13687i
790790 0 0
791791 29.2678i 1.04064i
792792 0 0
793793 −30.9246 + 30.9246i −1.09817 + 1.09817i
794794 0 0
795795 24.7071 0.821440i 0.876270 0.0291335i
796796 0 0
797797 4.75098 + 4.75098i 0.168289 + 0.168289i 0.786227 0.617938i 0.212032π-0.212032\pi
−0.617938 + 0.786227i 0.712032π0.712032\pi
798798 0 0
799799 3.13961 0.111071
800800 0 0
801801 17.6348 0.623094
802802 0 0
803803 −25.1118 25.1118i −0.886176 0.886176i
804804 0 0
805805 23.1850 0.770835i 0.817164 0.0271684i
806806 0 0
807807 −4.82260 + 4.82260i −0.169764 + 0.169764i
808808 0 0
809809 37.7891i 1.32859i 0.747469 + 0.664297i 0.231269π0.231269\pi
−0.747469 + 0.664297i 0.768731π0.768731\pi
810810 0 0
811811 44.4215i 1.55985i 0.625872 + 0.779926i 0.284743π0.284743\pi
−0.625872 + 0.779926i 0.715257π0.715257\pi
812812 0 0
813813 1.93845 1.93845i 0.0679843 0.0679843i
814814 0 0
815815 −24.0337 22.4871i −0.841865 0.787687i
816816 0 0
817817 −13.4828 13.4828i −0.471702 0.471702i
818818 0 0
819819 15.9246 0.556451
820820 0 0
821821 29.3648 1.02484 0.512420 0.858735i 0.328749π-0.328749\pi
0.512420 + 0.858735i 0.328749π0.328749\pi
822822 0 0
823823 22.7402 + 22.7402i 0.792674 + 0.792674i 0.981928 0.189254i 0.0606070π-0.0606070\pi
−0.189254 + 0.981928i 0.560607π0.560607\pi
824824 0 0
825825 14.7181 16.8174i 0.512420 0.585506i
826826 0 0
827827 −1.50001 + 1.50001i −0.0521605 + 0.0521605i −0.732706 0.680545i 0.761743π-0.761743\pi
0.680545 + 0.732706i 0.261743π0.261743\pi
828828 0 0
829829 29.0642i 1.00944i 0.863283 + 0.504721i 0.168405π0.168405\pi
−0.863283 + 0.504721i 0.831595π0.831595\pi
830830 0 0
831831 10.9684i 0.380490i
832832 0 0
833833 −29.9678 + 29.9678i −1.03832 + 1.03832i
834834 0 0
835835 −13.0962 + 13.9969i −0.453212 + 0.484384i
836836 0 0
837837 2.82843 + 2.82843i 0.0977647 + 0.0977647i
838838 0 0
839839 −38.3779 −1.32495 −0.662476 0.749083i 0.730495π-0.730495\pi
−0.662476 + 0.749083i 0.730495π0.730495\pi
840840 0 0
841841 −37.7891 −1.30307
842842 0 0
843843 −3.21104 3.21104i −0.110594 0.110594i
844844 0 0
845845 −0.0227612 0.684605i −0.000783008 0.0235511i
846846 0 0
847847 −28.3750 + 28.3750i −0.974976 + 0.974976i
848848 0 0
849849 11.1906i 0.384060i
850850 0 0
851851 19.0442i 0.652826i
852852 0 0
853853 −28.1467 + 28.1467i −0.963724 + 0.963724i −0.999365 0.0356404i 0.988653π-0.988653\pi
0.0356404 + 0.999365i 0.488653π0.488653\pi
854854 0 0
855855 −0.194542 5.85140i −0.00665320 0.200114i
856856 0 0
857857 −13.5990 13.5990i −0.464533 0.464533i 0.435605 0.900138i 0.356534π-0.356534\pi
−0.900138 + 0.435605i 0.856534π0.856534\pi
858858 0 0
859859 −14.9155 −0.508910 −0.254455 0.967085i 0.581896π-0.581896\pi
−0.254455 + 0.967085i 0.581896π0.581896\pi
860860 0 0
861861 11.7028 0.398830
862862 0 0
863863 8.95495 + 8.95495i 0.304830 + 0.304830i 0.842900 0.538070i 0.180846π-0.180846\pi
−0.538070 + 0.842900i 0.680846π0.680846\pi
864864 0 0
865865 0.767147 0.819913i 0.0260838 0.0278779i
866866 0 0
867867 −4.48008 + 4.48008i −0.152152 + 0.152152i
868868 0 0
869869 16.0000i 0.542763i
870870 0 0
871871 47.5980i 1.61280i
872872 0 0
873873 1.32106 1.32106i 0.0447112 0.0447112i
874874 0 0
875875 −31.6430 + 38.6776i −1.06973 + 1.30754i
876876 0 0
877877 37.8274 + 37.8274i 1.27734 + 1.27734i 0.942151 + 0.335190i 0.108800π0.108800\pi
0.335190 + 0.942151i 0.391200π0.391200\pi
878878 0 0
879879 21.3544 0.720267
880880 0 0
881881 23.7119 0.798876 0.399438 0.916760i 0.369205π-0.369205\pi
0.399438 + 0.916760i 0.369205π0.369205\pi
882882 0 0
883883 −9.39338 9.39338i −0.316113 0.316113i 0.531159 0.847272i 0.321757π-0.321757\pi
−0.847272 + 0.531159i 0.821757π0.821757\pi
884884 0 0
885885 7.98438 + 7.47055i 0.268392 + 0.251120i
886886 0 0
887887 −0.825014 + 0.825014i −0.0277013 + 0.0277013i −0.720822 0.693120i 0.756235π-0.756235\pi
0.693120 + 0.720822i 0.256235π0.256235\pi
888888 0 0
889889 64.4693i 2.16223i
890890 0 0
891891 4.46967i 0.149739i
892892 0 0
893893 −1.77996 + 1.77996i −0.0595641 + 0.0595641i
894894 0 0
895895 −35.2034 + 1.17041i −1.17672 + 0.0391226i
896896 0 0
897897 5.84744 + 5.84744i 0.195240 + 0.195240i
898898 0 0
899899 32.6898 1.09027
900900 0 0
901901 −36.1028 −1.20276
902902 0 0
903903 23.0165 + 23.0165i 0.765941 + 0.765941i
904904 0 0
905905 17.3869 0.578065i 0.577961 0.0192155i
906906 0 0
907907 −1.59189 + 1.59189i −0.0528578 + 0.0528578i −0.733042 0.680184i 0.761900π-0.761900\pi
0.680184 + 0.733042i 0.261900π0.261900\pi
908908 0 0
909909 1.47702i 0.0489897i
910910 0 0
911911 55.3926i 1.83524i 0.397458 + 0.917620i 0.369892π0.369892\pi
−0.397458 + 0.917620i 0.630108π0.630108\pi
912912 0 0
913913 −6.00737 + 6.00737i −0.198815 + 0.198815i
914914 0 0
915915 −20.0429 18.7530i −0.662597 0.619956i
916916 0 0
917917 39.4108 + 39.4108i 1.30146 + 1.30146i
918918 0 0
919919 4.31369 0.142295 0.0711477 0.997466i 0.477334π-0.477334\pi
0.0711477 + 0.997466i 0.477334π0.477334\pi
920920 0 0
921921 −6.26775 −0.206529
922922 0 0
923923 −14.2513 14.2513i −0.469086 0.469086i
924924 0 0
925925 −30.8716 27.0180i −1.01505 0.888346i
926926 0 0
927927 −9.11459 + 9.11459i −0.299363 + 0.299363i
928928 0 0
929929 19.9774i 0.655436i 0.944776 + 0.327718i 0.106280π0.106280\pi
−0.944776 + 0.327718i 0.893720π0.893720\pi
930930 0 0
931931 33.9797i 1.11364i
932932 0 0
933933 16.6421 16.6421i 0.544839 0.544839i
934934 0 0
935935 −22.2990 + 23.8327i −0.729255 + 0.779414i
936936 0 0
937937 −8.97792 8.97792i −0.293296 0.293296i 0.545085 0.838381i 0.316497π-0.316497\pi
−0.838381 + 0.545085i 0.816497π0.816497\pi
938938 0 0
939939 26.3094 0.858574
940940 0 0
941941 37.9831 1.23821 0.619107 0.785307i 0.287495π-0.287495\pi
0.619107 + 0.785307i 0.287495π0.287495\pi
942942 0 0
943943 4.29721 + 4.29721i 0.139936 + 0.139936i
944944 0 0
945945 0.332104 + 9.98896i 0.0108034 + 0.324941i
946946 0 0
947947 39.0815 39.0815i 1.26998 1.26998i 0.323878 0.946099i 0.395013π-0.395013\pi
0.946099 0.323878i 0.104987π-0.104987\pi
948948 0 0
949949 28.3081i 0.918921i
950950 0 0
951951 10.7049i 0.347131i
952952 0 0
953953 −1.27232 + 1.27232i −0.0412146 + 0.0412146i −0.727414 0.686199i 0.759278π-0.759278\pi
0.686199 + 0.727414i 0.259278π0.259278\pi
954954 0 0
955955 −0.695439 20.9172i −0.0225039 0.676866i
956956 0 0
957957 −25.8293 25.8293i −0.834943 0.834943i
958958 0 0
959959 29.2678 0.945106
960960 0 0
961961 15.0000 0.483871
962962 0 0
963963 2.06155 + 2.06155i 0.0664326 + 0.0664326i
964964 0 0
965965 −37.1090 + 39.6614i −1.19458 + 1.27675i
966966 0 0
967967 1.67778 1.67778i 0.0539537 0.0539537i −0.679615 0.733569i 0.737853π-0.737853\pi
0.733569 + 0.679615i 0.237853π0.237853\pi
968968 0 0
969969 8.55025i 0.274674i
970970 0 0
971971 15.9887i 0.513102i 0.966531 + 0.256551i 0.0825862π0.0825862\pi
−0.966531 + 0.256551i 0.917414π0.917414\pi
972972 0 0
973973 −9.50484 + 9.50484i −0.304711 + 0.304711i
974974 0 0
975975 −17.7747 + 1.18323i −0.569247 + 0.0378936i
976976 0 0
977977 16.7754 + 16.7754i 0.536692 + 0.536692i 0.922556 0.385864i 0.126096π-0.126096\pi
−0.385864 + 0.922556i 0.626096π0.626096\pi
978978 0 0
979979 78.8215 2.51915
980980 0 0
981981 −9.70279 −0.309786
982982 0 0
983983 −34.3367 34.3367i −1.09517 1.09517i −0.994967 0.100203i 0.968051π-0.968051\pi
−0.100203 0.994967i 0.531949π-0.531949\pi
984984 0 0
985985 4.24758 + 3.97423i 0.135339 + 0.126629i
986986 0 0
987987 3.03858 3.03858i 0.0967192 0.0967192i
988988 0 0
989989 16.9031i 0.537487i
990990 0 0
991991 26.7414i 0.849468i −0.905318 0.424734i 0.860368π-0.860368\pi
0.905318 0.424734i 0.139632π-0.139632\pi
992992 0 0
993993 −9.75952 + 9.75952i −0.309709 + 0.309709i
994994 0 0
995995 −0.988685 + 0.0328709i −0.0313434 + 0.00104208i
996996 0 0
997997 9.80177 + 9.80177i 0.310425 + 0.310425i 0.845074 0.534649i 0.179556π-0.179556\pi
−0.534649 + 0.845074i 0.679556π0.679556\pi
998998 0 0
999999 −8.20494 −0.259593
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 960.2.w.f.127.1 8
4.3 odd 2 960.2.w.e.127.3 8
5.3 odd 4 960.2.w.e.703.3 8
8.3 odd 2 480.2.w.c.127.2 8
8.5 even 2 480.2.w.d.127.4 yes 8
20.3 even 4 inner 960.2.w.f.703.1 8
24.5 odd 2 1440.2.x.r.127.1 8
24.11 even 2 1440.2.x.q.127.1 8
40.3 even 4 480.2.w.d.223.4 yes 8
40.13 odd 4 480.2.w.c.223.2 yes 8
40.19 odd 2 2400.2.w.j.607.4 8
40.27 even 4 2400.2.w.i.2143.1 8
40.29 even 2 2400.2.w.i.607.1 8
40.37 odd 4 2400.2.w.j.2143.4 8
120.53 even 4 1440.2.x.q.703.1 8
120.83 odd 4 1440.2.x.r.703.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
480.2.w.c.127.2 8 8.3 odd 2
480.2.w.c.223.2 yes 8 40.13 odd 4
480.2.w.d.127.4 yes 8 8.5 even 2
480.2.w.d.223.4 yes 8 40.3 even 4
960.2.w.e.127.3 8 4.3 odd 2
960.2.w.e.703.3 8 5.3 odd 4
960.2.w.f.127.1 8 1.1 even 1 trivial
960.2.w.f.703.1 8 20.3 even 4 inner
1440.2.x.q.127.1 8 24.11 even 2
1440.2.x.q.703.1 8 120.53 even 4
1440.2.x.r.127.1 8 24.5 odd 2
1440.2.x.r.703.1 8 120.83 odd 4
2400.2.w.i.607.1 8 40.29 even 2
2400.2.w.i.2143.1 8 40.27 even 4
2400.2.w.j.607.4 8 40.19 odd 2
2400.2.w.j.2143.4 8 40.37 odd 4