Properties

Label 315.10.a.b.1.1
Level 315315
Weight 1010
Character 315.1
Self dual yes
Analytic conductor 162.236162.236
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] = [315,10,Mod(1,315)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(315, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 10, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("315.1");
 
S:= CuspForms(chi, 10);
 
N := Newforms(S);
 
Level: N N == 315=3257 315 = 3^{2} \cdot 5 \cdot 7
Weight: k k == 10 10
Character orbit: [χ][\chi] == 315.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: 162.236288392162.236288392
Analytic rank: 11
Dimension: 22
Coefficient field: Q(ζ8)+\Q(\zeta_{8})^+
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x22 x^{2} - 2 Copy content Toggle raw display
Coefficient ring: Z[a1,a2]\Z[a_1, a_2]
Coefficient ring index: 2 2
Twist minimal: no (minimal twist has level 35)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.41421-1.41421 of defining polynomial
Character χ\chi == 315.1

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+9.17157q2427.882q4625.000q5+2401.00q78620.20q85732.23q1035089.6q1177401.4q13+22020.9q14+140015.q16+229907.q17+16433.6q19+267426.q20321827.q22+2.57284e6q23+390625.q25709892.q261.02735e6q28+6.62817e6q298.17416e6q31+5.69770e6q32+2.10861e6q341.50062e6q35+9.70272e6q37+150722.q38+5.38762e6q402.98108e7q411.95343e7q43+1.50142e7q44+2.35970e7q465.93794e6q47+5.76480e6q49+3.58265e6q50+3.31187e7q52+2.74263e7q53+2.19310e7q552.06971e7q56+6.07908e7q585.24915e7q59+2.23282e7q617.49699e7q621.94308e7q64+4.83759e7q65+2.74351e8q679.83733e7q681.37631e7q70+3.63673e8q71+2.09245e7q73+8.89892e7q747.03163e6q768.42501e7q772.65896e8q798.75093e7q802.73412e8q82+9.43764e6q831.43692e8q851.79160e8q86+3.02479e8q88+6.64876e8q891.85841e8q911.10087e9q925.44603e7q941.02710e7q951.20731e9q97+5.28723e7q98+O(q100)q+9.17157 q^{2} -427.882 q^{4} -625.000 q^{5} +2401.00 q^{7} -8620.20 q^{8} -5732.23 q^{10} -35089.6 q^{11} -77401.4 q^{13} +22020.9 q^{14} +140015. q^{16} +229907. q^{17} +16433.6 q^{19} +267426. q^{20} -321827. q^{22} +2.57284e6 q^{23} +390625. q^{25} -709892. q^{26} -1.02735e6 q^{28} +6.62817e6 q^{29} -8.17416e6 q^{31} +5.69770e6 q^{32} +2.10861e6 q^{34} -1.50062e6 q^{35} +9.70272e6 q^{37} +150722. q^{38} +5.38762e6 q^{40} -2.98108e7 q^{41} -1.95343e7 q^{43} +1.50142e7 q^{44} +2.35970e7 q^{46} -5.93794e6 q^{47} +5.76480e6 q^{49} +3.58265e6 q^{50} +3.31187e7 q^{52} +2.74263e7 q^{53} +2.19310e7 q^{55} -2.06971e7 q^{56} +6.07908e7 q^{58} -5.24915e7 q^{59} +2.23282e7 q^{61} -7.49699e7 q^{62} -1.94308e7 q^{64} +4.83759e7 q^{65} +2.74351e8 q^{67} -9.83733e7 q^{68} -1.37631e7 q^{70} +3.63673e8 q^{71} +2.09245e7 q^{73} +8.89892e7 q^{74} -7.03163e6 q^{76} -8.42501e7 q^{77} -2.65896e8 q^{79} -8.75093e7 q^{80} -2.73412e8 q^{82} +9.43764e6 q^{83} -1.43692e8 q^{85} -1.79160e8 q^{86} +3.02479e8 q^{88} +6.64876e8 q^{89} -1.85841e8 q^{91} -1.10087e9 q^{92} -5.44603e7 q^{94} -1.02710e7 q^{95} -1.20731e9 q^{97} +5.28723e7 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+24q2720q41250q5+4802q720544q815000q1018566q1151090q13+57624q14+112768q16+373910q17143276q19+450000q2076808q22++138355224q98+O(q100) 2 q + 24 q^{2} - 720 q^{4} - 1250 q^{5} + 4802 q^{7} - 20544 q^{8} - 15000 q^{10} - 18566 q^{11} - 51090 q^{13} + 57624 q^{14} + 112768 q^{16} + 373910 q^{17} - 143276 q^{19} + 450000 q^{20} - 76808 q^{22}+ \cdots + 138355224 q^{98}+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 9.17157 0.405330 0.202665 0.979248i 0.435040π-0.435040\pi
0.202665 + 0.979248i 0.435040π0.435040\pi
33 0 0
44 −427.882 −0.835708
55 −625.000 −0.447214
66 0 0
77 2401.00 0.377964
88 −8620.20 −0.744067
99 0 0
1010 −5732.23 −0.181269
1111 −35089.6 −0.722622 −0.361311 0.932445i 0.617671π-0.617671\pi
−0.361311 + 0.932445i 0.617671π0.617671\pi
1212 0 0
1313 −77401.4 −0.751629 −0.375815 0.926695i 0.622637π-0.622637\pi
−0.375815 + 0.926695i 0.622637π0.622637\pi
1414 22020.9 0.153200
1515 0 0
1616 140015. 0.534115
1717 229907. 0.667626 0.333813 0.942639i 0.391665π-0.391665\pi
0.333813 + 0.942639i 0.391665π0.391665\pi
1818 0 0
1919 16433.6 0.0289295 0.0144647 0.999895i 0.495396π-0.495396\pi
0.0144647 + 0.999895i 0.495396π0.495396\pi
2020 267426. 0.373740
2121 0 0
2222 −321827. −0.292900
2323 2.57284e6 1.91707 0.958535 0.284975i 0.0919852π-0.0919852\pi
0.958535 + 0.284975i 0.0919852π0.0919852\pi
2424 0 0
2525 390625. 0.200000
2626 −709892. −0.304658
2727 0 0
2828 −1.02735e6 −0.315868
2929 6.62817e6 1.74022 0.870108 0.492862i 0.164049π-0.164049\pi
0.870108 + 0.492862i 0.164049π0.164049\pi
3030 0 0
3131 −8.17416e6 −1.58970 −0.794851 0.606805i 0.792451π-0.792451\pi
−0.794851 + 0.606805i 0.792451π0.792451\pi
3232 5.69770e6 0.960560
3333 0 0
3434 2.10861e6 0.270609
3535 −1.50062e6 −0.169031
3636 0 0
3737 9.70272e6 0.851110 0.425555 0.904933i 0.360079π-0.360079\pi
0.425555 + 0.904933i 0.360079π0.360079\pi
3838 150722. 0.0117260
3939 0 0
4040 5.38762e6 0.332757
4141 −2.98108e7 −1.64758 −0.823789 0.566896i 0.808144π-0.808144\pi
−0.823789 + 0.566896i 0.808144π0.808144\pi
4242 0 0
4343 −1.95343e7 −0.871343 −0.435672 0.900106i 0.643489π-0.643489\pi
−0.435672 + 0.900106i 0.643489π0.643489\pi
4444 1.50142e7 0.603900
4545 0 0
4646 2.35970e7 0.777046
4747 −5.93794e6 −0.177499 −0.0887494 0.996054i 0.528287π-0.528287\pi
−0.0887494 + 0.996054i 0.528287π0.528287\pi
4848 0 0
4949 5.76480e6 0.142857
5050 3.58265e6 0.0810660
5151 0 0
5252 3.31187e7 0.628142
5353 2.74263e7 0.477448 0.238724 0.971088i 0.423271π-0.423271\pi
0.238724 + 0.971088i 0.423271π0.423271\pi
5454 0 0
5555 2.19310e7 0.323166
5656 −2.06971e7 −0.281231
5757 0 0
5858 6.07908e7 0.705362
5959 −5.24915e7 −0.563969 −0.281984 0.959419i 0.590993π-0.590993\pi
−0.281984 + 0.959419i 0.590993π0.590993\pi
6060 0 0
6161 2.23282e7 0.206476 0.103238 0.994657i 0.467080π-0.467080\pi
0.103238 + 0.994657i 0.467080π0.467080\pi
6262 −7.49699e7 −0.644354
6363 0 0
6464 −1.94308e7 −0.144771
6565 4.83759e7 0.336139
6666 0 0
6767 2.74351e8 1.66330 0.831649 0.555302i 0.187397π-0.187397\pi
0.831649 + 0.555302i 0.187397π0.187397\pi
6868 −9.83733e7 −0.557940
6969 0 0
7070 −1.37631e7 −0.0685133
7171 3.63673e8 1.69843 0.849216 0.528046i 0.177075π-0.177075\pi
0.849216 + 0.528046i 0.177075π0.177075\pi
7272 0 0
7373 2.09245e7 0.0862387 0.0431193 0.999070i 0.486270π-0.486270\pi
0.0431193 + 0.999070i 0.486270π0.486270\pi
7474 8.89892e7 0.344980
7575 0 0
7676 −7.03163e6 −0.0241766
7777 −8.42501e7 −0.273125
7878 0 0
7979 −2.65896e8 −0.768051 −0.384025 0.923323i 0.625462π-0.625462\pi
−0.384025 + 0.923323i 0.625462π0.625462\pi
8080 −8.75093e7 −0.238863
8181 0 0
8282 −2.73412e8 −0.667813
8383 9.43764e6 0.0218279 0.0109140 0.999940i 0.496526π-0.496526\pi
0.0109140 + 0.999940i 0.496526π0.496526\pi
8484 0 0
8585 −1.43692e8 −0.298571
8686 −1.79160e8 −0.353182
8787 0 0
8888 3.02479e8 0.537679
8989 6.64876e8 1.12327 0.561637 0.827384i 0.310172π-0.310172\pi
0.561637 + 0.827384i 0.310172π0.310172\pi
9090 0 0
9191 −1.85841e8 −0.284089
9292 −1.10087e9 −1.60211
9393 0 0
9494 −5.44603e7 −0.0719456
9595 −1.02710e7 −0.0129377
9696 0 0
9797 −1.20731e9 −1.38467 −0.692336 0.721575i 0.743418π-0.743418\pi
−0.692336 + 0.721575i 0.743418π0.743418\pi
9898 5.28723e7 0.0579043
9999 0 0
100100 −1.67142e8 −0.167142
101101 −1.18204e9 −1.13028 −0.565139 0.824996i 0.691177π-0.691177\pi
−0.565139 + 0.824996i 0.691177π0.691177\pi
102102 0 0
103103 1.97811e9 1.73174 0.865870 0.500268i 0.166765π-0.166765\pi
0.865870 + 0.500268i 0.166765π0.166765\pi
104104 6.67215e8 0.559263
105105 0 0
106106 2.51542e8 0.193524
107107 −1.67828e8 −0.123776 −0.0618881 0.998083i 0.519712π-0.519712\pi
−0.0618881 + 0.998083i 0.519712π0.519712\pi
108108 0 0
109109 −1.02540e9 −0.695784 −0.347892 0.937535i 0.613102π-0.613102\pi
−0.347892 + 0.937535i 0.613102π0.613102\pi
110110 2.01142e8 0.130989
111111 0 0
112112 3.36176e8 0.201876
113113 −1.27533e9 −0.735814 −0.367907 0.929863i 0.619926π-0.619926\pi
−0.367907 + 0.929863i 0.619926π0.619926\pi
114114 0 0
115115 −1.60803e9 −0.857340
116116 −2.83608e9 −1.45431
117117 0 0
118118 −4.81430e8 −0.228594
119119 5.52008e8 0.252339
120120 0 0
121121 −1.12667e9 −0.477818
122122 2.04785e8 0.0836909
123123 0 0
124124 3.49758e9 1.32853
125125 −2.44141e8 −0.0894427
126126 0 0
127127 −2.90339e9 −0.990349 −0.495174 0.868794i 0.664896π-0.664896\pi
−0.495174 + 0.868794i 0.664896π0.664896\pi
128128 −3.09543e9 −1.01924
129129 0 0
130130 4.43683e8 0.136247
131131 −2.05173e9 −0.608694 −0.304347 0.952561i 0.598438π-0.598438\pi
−0.304347 + 0.952561i 0.598438π0.598438\pi
132132 0 0
133133 3.94570e7 0.0109343
134134 2.51623e9 0.674185
135135 0 0
136136 −1.98185e9 −0.496759
137137 −3.25539e9 −0.789514 −0.394757 0.918786i 0.629171π-0.629171\pi
−0.394757 + 0.918786i 0.629171π0.629171\pi
138138 0 0
139139 −8.26776e9 −1.87854 −0.939272 0.343173i 0.888498π-0.888498\pi
−0.939272 + 0.343173i 0.888498π0.888498\pi
140140 6.42091e8 0.141260
141141 0 0
142142 3.33545e9 0.688425
143143 2.71598e9 0.543143
144144 0 0
145145 −4.14261e9 −0.778248
146146 1.91910e8 0.0349551
147147 0 0
148148 −4.15162e9 −0.711279
149149 −1.07127e9 −0.178058 −0.0890289 0.996029i 0.528376π-0.528376\pi
−0.0890289 + 0.996029i 0.528376π0.528376\pi
150150 0 0
151151 1.97304e9 0.308844 0.154422 0.988005i 0.450649π-0.450649\pi
0.154422 + 0.988005i 0.450649π0.450649\pi
152152 −1.41661e8 −0.0215255
153153 0 0
154154 −7.72706e8 −0.110706
155155 5.10885e9 0.710936
156156 0 0
157157 −4.61623e9 −0.606372 −0.303186 0.952931i 0.598050π-0.598050\pi
−0.303186 + 0.952931i 0.598050π0.598050\pi
158158 −2.43868e9 −0.311314
159159 0 0
160160 −3.56106e9 −0.429576
161161 6.17740e9 0.724584
162162 0 0
163163 6.26525e9 0.695175 0.347588 0.937648i 0.387001π-0.387001\pi
0.347588 + 0.937648i 0.387001π0.387001\pi
164164 1.27555e10 1.37689
165165 0 0
166166 8.65580e7 0.00884751
167167 6.21672e9 0.618496 0.309248 0.950981i 0.399923π-0.399923\pi
0.309248 + 0.950981i 0.399923π0.399923\pi
168168 0 0
169169 −4.61353e9 −0.435054
170170 −1.31788e9 −0.121020
171171 0 0
172172 8.35837e9 0.728188
173173 −8.97209e9 −0.761528 −0.380764 0.924672i 0.624339π-0.624339\pi
−0.380764 + 0.924672i 0.624339π0.624339\pi
174174 0 0
175175 9.37891e8 0.0755929
176176 −4.91306e9 −0.385963
177177 0 0
178178 6.09796e9 0.455297
179179 −1.76242e10 −1.28313 −0.641565 0.767069i 0.721714π-0.721714\pi
−0.641565 + 0.767069i 0.721714π0.721714\pi
180180 0 0
181181 1.62250e9 0.112365 0.0561824 0.998421i 0.482107π-0.482107\pi
0.0561824 + 0.998421i 0.482107π0.482107\pi
182182 −1.70445e9 −0.115150
183183 0 0
184184 −2.21784e10 −1.42643
185185 −6.06420e9 −0.380628
186186 0 0
187187 −8.06735e9 −0.482441
188188 2.54074e9 0.148337
189189 0 0
190190 −9.42010e7 −0.00524402
191191 −1.66601e10 −0.905788 −0.452894 0.891564i 0.649608π-0.649608\pi
−0.452894 + 0.891564i 0.649608π0.649608\pi
192192 0 0
193193 2.41341e10 1.25206 0.626028 0.779801i 0.284680π-0.284680\pi
0.626028 + 0.779801i 0.284680π0.284680\pi
194194 −1.10730e10 −0.561249
195195 0 0
196196 −2.46666e9 −0.119387
197197 3.89843e9 0.184413 0.0922066 0.995740i 0.470608π-0.470608\pi
0.0922066 + 0.995740i 0.470608π0.470608\pi
198198 0 0
199199 −1.87489e10 −0.847493 −0.423747 0.905781i 0.639285π-0.639285\pi
−0.423747 + 0.905781i 0.639285π0.639285\pi
200200 −3.36727e9 −0.148813
201201 0 0
202202 −1.08411e10 −0.458135
203203 1.59142e10 0.657740
204204 0 0
205205 1.86317e10 0.736820
206206 1.81424e10 0.701927
207207 0 0
208208 −1.08373e10 −0.401456
209209 −5.76647e8 −0.0209051
210210 0 0
211211 −2.20489e9 −0.0765801 −0.0382900 0.999267i 0.512191π-0.512191\pi
−0.0382900 + 0.999267i 0.512191π0.512191\pi
212212 −1.17352e10 −0.399007
213213 0 0
214214 −1.53925e9 −0.0501702
215215 1.22089e10 0.389677
216216 0 0
217217 −1.96262e10 −0.600851
218218 −9.40454e9 −0.282022
219219 0 0
220220 −9.38388e9 −0.270072
221221 −1.77952e10 −0.501807
222222 0 0
223223 −2.65324e10 −0.718463 −0.359231 0.933249i 0.616961π-0.616961\pi
−0.359231 + 0.933249i 0.616961π0.616961\pi
224224 1.36802e10 0.363058
225225 0 0
226226 −1.16967e10 −0.298248
227227 −7.78091e10 −1.94498 −0.972488 0.232955i 0.925161π-0.925161\pi
−0.972488 + 0.232955i 0.925161π0.925161\pi
228228 0 0
229229 4.84637e10 1.16455 0.582274 0.812993i 0.302163π-0.302163\pi
0.582274 + 0.812993i 0.302163π0.302163\pi
230230 −1.47481e10 −0.347506
231231 0 0
232232 −5.71362e10 −1.29484
233233 2.38429e10 0.529978 0.264989 0.964251i 0.414632π-0.414632\pi
0.264989 + 0.964251i 0.414632π0.414632\pi
234234 0 0
235235 3.71121e9 0.0793799
236236 2.24602e10 0.471313
237237 0 0
238238 5.06278e9 0.102280
239239 −6.25895e10 −1.24083 −0.620413 0.784275i 0.713035π-0.713035\pi
−0.620413 + 0.784275i 0.713035π0.713035\pi
240240 0 0
241241 −7.96605e10 −1.52113 −0.760565 0.649262i 0.775078π-0.775078\pi
−0.760565 + 0.649262i 0.775078π0.775078\pi
242242 −1.03333e10 −0.193674
243243 0 0
244244 −9.55384e9 −0.172554
245245 −3.60300e9 −0.0638877
246246 0 0
247247 −1.27198e9 −0.0217442
248248 7.04629e10 1.18285
249249 0 0
250250 −2.23915e9 −0.0362538
251251 5.44549e10 0.865975 0.432988 0.901400i 0.357459π-0.357459\pi
0.432988 + 0.901400i 0.357459π0.357459\pi
252252 0 0
253253 −9.02799e10 −1.38532
254254 −2.66286e10 −0.401418
255255 0 0
256256 −1.84414e10 −0.268358
257257 5.35278e10 0.765385 0.382693 0.923876i 0.374997π-0.374997\pi
0.382693 + 0.923876i 0.374997π0.374997\pi
258258 0 0
259259 2.32962e10 0.321689
260260 −2.06992e10 −0.280914
261261 0 0
262262 −1.88176e10 −0.246722
263263 5.81425e10 0.749364 0.374682 0.927153i 0.377752π-0.377752\pi
0.374682 + 0.927153i 0.377752π0.377752\pi
264264 0 0
265265 −1.71414e10 −0.213521
266266 3.61883e8 0.00443201
267267 0 0
268268 −1.17390e11 −1.39003
269269 −4.67380e10 −0.544233 −0.272116 0.962264i 0.587724π-0.587724\pi
−0.272116 + 0.962264i 0.587724π0.587724\pi
270270 0 0
271271 2.68147e10 0.302003 0.151001 0.988534i 0.451750π-0.451750\pi
0.151001 + 0.988534i 0.451750π0.451750\pi
272272 3.21905e10 0.356589
273273 0 0
274274 −2.98570e10 −0.320014
275275 −1.37069e10 −0.144524
276276 0 0
277277 1.12549e11 1.14863 0.574316 0.818633i 0.305268π-0.305268\pi
0.574316 + 0.818633i 0.305268π0.305268\pi
278278 −7.58284e10 −0.761431
279279 0 0
280280 1.29357e10 0.125770
281281 4.60761e10 0.440857 0.220428 0.975403i 0.429254π-0.429254\pi
0.220428 + 0.975403i 0.429254π0.429254\pi
282282 0 0
283283 7.94071e10 0.735902 0.367951 0.929845i 0.380059π-0.380059\pi
0.367951 + 0.929845i 0.380059π0.380059\pi
284284 −1.55609e11 −1.41939
285285 0 0
286286 2.49098e10 0.220152
287287 −7.15757e10 −0.622726
288288 0 0
289289 −6.57304e10 −0.554276
290290 −3.79942e10 −0.315447
291291 0 0
292292 −8.95322e9 −0.0720703
293293 1.41265e11 1.11977 0.559887 0.828569i 0.310844π-0.310844\pi
0.559887 + 0.828569i 0.310844π0.310844\pi
294294 0 0
295295 3.28072e10 0.252215
296296 −8.36393e10 −0.633283
297297 0 0
298298 −9.82523e9 −0.0721721
299299 −1.99142e11 −1.44093
300300 0 0
301301 −4.69018e10 −0.329337
302302 1.80958e10 0.125184
303303 0 0
304304 2.30094e9 0.0154517
305305 −1.39551e10 −0.0923389
306306 0 0
307307 −5.58349e10 −0.358742 −0.179371 0.983781i 0.557406π-0.557406\pi
−0.179371 + 0.983781i 0.557406π0.557406\pi
308308 3.60491e10 0.228253
309309 0 0
310310 4.68562e10 0.288164
311311 −5.26501e10 −0.319137 −0.159569 0.987187i 0.551010π-0.551010\pi
−0.159569 + 0.987187i 0.551010π0.551010\pi
312312 0 0
313313 −2.51256e11 −1.47968 −0.739838 0.672785i 0.765098π-0.765098\pi
−0.739838 + 0.672785i 0.765098π0.765098\pi
314314 −4.23381e10 −0.245781
315315 0 0
316316 1.13772e11 0.641866
317317 1.16999e11 0.650749 0.325375 0.945585i 0.394510π-0.394510\pi
0.325375 + 0.945585i 0.394510π0.394510\pi
318318 0 0
319319 −2.32580e11 −1.25752
320320 1.21442e10 0.0647434
321321 0 0
322322 5.66564e10 0.293696
323323 3.77820e9 0.0193141
324324 0 0
325325 −3.02349e10 −0.150326
326326 5.74622e10 0.281775
327327 0 0
328328 2.56975e11 1.22591
329329 −1.42570e10 −0.0670883
330330 0 0
331331 −2.51419e11 −1.15126 −0.575629 0.817711i 0.695243π-0.695243\pi
−0.575629 + 0.817711i 0.695243π0.695243\pi
332332 −4.03820e9 −0.0182417
333333 0 0
334334 5.70171e10 0.250695
335335 −1.71469e11 −0.743849
336336 0 0
337337 6.11427e10 0.258232 0.129116 0.991630i 0.458786π-0.458786\pi
0.129116 + 0.991630i 0.458786π0.458786\pi
338338 −4.23133e10 −0.176340
339339 0 0
340340 6.14833e10 0.249518
341341 2.86828e11 1.14875
342342 0 0
343343 1.38413e10 0.0539949
344344 1.68389e11 0.648338
345345 0 0
346346 −8.22882e10 −0.308670
347347 1.68668e11 0.624524 0.312262 0.949996i 0.398913π-0.398913\pi
0.312262 + 0.949996i 0.398913π0.398913\pi
348348 0 0
349349 −3.31182e11 −1.19496 −0.597479 0.801885i 0.703831π-0.703831\pi
−0.597479 + 0.801885i 0.703831π0.703831\pi
350350 8.60193e9 0.0306401
351351 0 0
352352 −1.99930e11 −0.694122
353353 −3.78560e11 −1.29762 −0.648811 0.760949i 0.724734π-0.724734\pi
−0.648811 + 0.760949i 0.724734π0.724734\pi
354354 0 0
355355 −2.27295e11 −0.759562
356356 −2.84489e11 −0.938728
357357 0 0
358358 −1.61641e11 −0.520091
359359 1.60137e11 0.508822 0.254411 0.967096i 0.418118π-0.418118\pi
0.254411 + 0.967096i 0.418118π0.418118\pi
360360 0 0
361361 −3.22418e11 −0.999163
362362 1.48809e10 0.0455449
363363 0 0
364364 7.95179e10 0.237415
365365 −1.30778e10 −0.0385671
366366 0 0
367367 5.13837e11 1.47852 0.739261 0.673419i 0.235175π-0.235175\pi
0.739261 + 0.673419i 0.235175π0.235175\pi
368368 3.60236e11 1.02394
369369 0 0
370370 −5.56182e10 −0.154280
371371 6.58505e10 0.180458
372372 0 0
373373 −6.70900e10 −0.179460 −0.0897301 0.995966i 0.528600π-0.528600\pi
−0.0897301 + 0.995966i 0.528600π0.528600\pi
374374 −7.39903e10 −0.195548
375375 0 0
376376 5.11862e10 0.132071
377377 −5.13030e11 −1.30800
378378 0 0
379379 4.15471e11 1.03434 0.517171 0.855882i 0.326985π-0.326985\pi
0.517171 + 0.855882i 0.326985π0.326985\pi
380380 4.39477e9 0.0108121
381381 0 0
382382 −1.52799e11 −0.367143
383383 3.51976e11 0.835831 0.417915 0.908486i 0.362761π-0.362761\pi
0.417915 + 0.908486i 0.362761π0.362761\pi
384384 0 0
385385 5.26563e10 0.122145
386386 2.21348e11 0.507496
387387 0 0
388388 5.16588e11 1.15718
389389 2.60061e11 0.575840 0.287920 0.957654i 0.407036π-0.407036\pi
0.287920 + 0.957654i 0.407036π0.407036\pi
390390 0 0
391391 5.91516e11 1.27989
392392 −4.96937e10 −0.106295
393393 0 0
394394 3.57548e10 0.0747482
395395 1.66185e11 0.343483
396396 0 0
397397 7.34338e11 1.48367 0.741837 0.670580i 0.233955π-0.233955\pi
0.741837 + 0.670580i 0.233955π0.233955\pi
398398 −1.71957e11 −0.343514
399399 0 0
400400 5.46933e10 0.106823
401401 −8.08296e11 −1.56106 −0.780532 0.625116i 0.785052π-0.785052\pi
−0.780532 + 0.625116i 0.785052π0.785052\pi
402402 0 0
403403 6.32691e11 1.19487
404404 5.05773e11 0.944581
405405 0 0
406406 1.45959e11 0.266602
407407 −3.40464e11 −0.615030
408408 0 0
409409 −9.11153e11 −1.61004 −0.805020 0.593248i 0.797845π-0.797845\pi
−0.805020 + 0.593248i 0.797845π0.797845\pi
410410 1.70882e11 0.298655
411411 0 0
412412 −8.46398e11 −1.44723
413413 −1.26032e11 −0.213160
414414 0 0
415415 −5.89853e9 −0.00976174
416416 −4.41010e11 −0.721985
417417 0 0
418418 −5.28876e9 −0.00847345
419419 −4.94109e11 −0.783177 −0.391589 0.920140i 0.628074π-0.628074\pi
−0.391589 + 0.920140i 0.628074π0.628074\pi
420420 0 0
421421 −1.15145e10 −0.0178639 −0.00893197 0.999960i 0.502843π-0.502843\pi
−0.00893197 + 0.999960i 0.502843π0.502843\pi
422422 −2.02223e10 −0.0310402
423423 0 0
424424 −2.36420e11 −0.355253
425425 8.98076e10 0.133525
426426 0 0
427427 5.36100e10 0.0780406
428428 7.18106e10 0.103441
429429 0 0
430430 1.11975e11 0.157948
431431 9.42534e11 1.31568 0.657839 0.753159i 0.271471π-0.271471\pi
0.657839 + 0.753159i 0.271471π0.271471\pi
432432 0 0
433433 1.01849e12 1.39239 0.696196 0.717852i 0.254875π-0.254875\pi
0.696196 + 0.717852i 0.254875π0.254875\pi
434434 −1.80003e11 −0.243543
435435 0 0
436436 4.38751e11 0.581472
437437 4.22810e10 0.0554598
438438 0 0
439439 −7.89357e11 −1.01434 −0.507169 0.861847i 0.669308π-0.669308\pi
−0.507169 + 0.861847i 0.669308π0.669308\pi
440440 −1.89049e11 −0.240457
441441 0 0
442442 −1.63210e11 −0.203397
443443 −1.06770e12 −1.31714 −0.658572 0.752518i 0.728839π-0.728839\pi
−0.658572 + 0.752518i 0.728839π0.728839\pi
444444 0 0
445445 −4.15547e11 −0.502343
446446 −2.43344e11 −0.291215
447447 0 0
448448 −4.66533e10 −0.0547182
449449 3.31695e9 0.00385150 0.00192575 0.999998i 0.499387π-0.499387\pi
0.00192575 + 0.999998i 0.499387π0.499387\pi
450450 0 0
451451 1.04605e12 1.19058
452452 5.45689e11 0.614926
453453 0 0
454454 −7.13632e11 −0.788357
455455 1.16150e11 0.127049
456456 0 0
457457 −7.03146e11 −0.754089 −0.377045 0.926195i 0.623060π-0.623060\pi
−0.377045 + 0.926195i 0.623060π0.623060\pi
458458 4.44489e11 0.472026
459459 0 0
460460 6.88046e11 0.716485
461461 1.86192e12 1.92003 0.960015 0.279950i 0.0903178π-0.0903178\pi
0.960015 + 0.279950i 0.0903178π0.0903178\pi
462462 0 0
463463 −1.06950e11 −0.108160 −0.0540799 0.998537i 0.517223π-0.517223\pi
−0.0540799 + 0.998537i 0.517223π0.517223\pi
464464 9.28043e11 0.929474
465465 0 0
466466 2.18677e11 0.214816
467467 −4.13997e11 −0.402783 −0.201392 0.979511i 0.564546π-0.564546\pi
−0.201392 + 0.979511i 0.564546π0.564546\pi
468468 0 0
469469 6.58717e11 0.628667
470470 3.40377e10 0.0321751
471471 0 0
472472 4.52487e11 0.419631
473473 6.85450e11 0.629652
474474 0 0
475475 6.41936e9 0.00578589
476476 −2.36194e11 −0.210881
477477 0 0
478478 −5.74044e11 −0.502944
479479 8.54131e10 0.0741336 0.0370668 0.999313i 0.488199π-0.488199\pi
0.0370668 + 0.999313i 0.488199π0.488199\pi
480480 0 0
481481 −7.51004e11 −0.639719
482482 −7.30612e11 −0.616560
483483 0 0
484484 4.82082e11 0.399316
485485 7.54571e11 0.619244
486486 0 0
487487 4.94789e11 0.398602 0.199301 0.979938i 0.436133π-0.436133\pi
0.199301 + 0.979938i 0.436133π0.436133\pi
488488 −1.92474e11 −0.153632
489489 0 0
490490 −3.30452e10 −0.0258956
491491 −1.11163e12 −0.863168 −0.431584 0.902073i 0.642045π-0.642045\pi
−0.431584 + 0.902073i 0.642045π0.642045\pi
492492 0 0
493493 1.52387e12 1.16181
494494 −1.16661e10 −0.00881359
495495 0 0
496496 −1.14450e12 −0.849083
497497 8.73178e11 0.641947
498498 0 0
499499 8.18377e11 0.590882 0.295441 0.955361i 0.404533π-0.404533\pi
0.295441 + 0.955361i 0.404533π0.404533\pi
500500 1.04463e11 0.0747480
501501 0 0
502502 4.99437e11 0.351006
503503 −3.13384e11 −0.218284 −0.109142 0.994026i 0.534810π-0.534810\pi
−0.109142 + 0.994026i 0.534810π0.534810\pi
504504 0 0
505505 7.38773e11 0.505475
506506 −8.28009e11 −0.561510
507507 0 0
508508 1.24231e12 0.827642
509509 1.02554e12 0.677211 0.338606 0.940928i 0.390045π-0.390045\pi
0.338606 + 0.940928i 0.390045π0.390045\pi
510510 0 0
511511 5.02397e10 0.0325951
512512 1.41572e12 0.910467
513513 0 0
514514 4.90934e11 0.310234
515515 −1.23632e12 −0.774458
516516 0 0
517517 2.08360e11 0.128265
518518 2.13663e11 0.130390
519519 0 0
520520 −4.17010e11 −0.250110
521521 3.18952e12 1.89651 0.948255 0.317510i 0.102847π-0.102847\pi
0.948255 + 0.317510i 0.102847π0.102847\pi
522522 0 0
523523 9.43708e11 0.551544 0.275772 0.961223i 0.411067π-0.411067\pi
0.275772 + 0.961223i 0.411067π0.411067\pi
524524 8.77898e11 0.508690
525525 0 0
526526 5.33258e11 0.303740
527527 −1.87930e12 −1.06133
528528 0 0
529529 4.81837e12 2.67516
530530 −1.57214e11 −0.0865465
531531 0 0
532532 −1.68829e10 −0.00913789
533533 2.30740e12 1.23837
534534 0 0
535535 1.04892e11 0.0553544
536536 −2.36496e12 −1.23761
537537 0 0
538538 −4.28661e11 −0.220594
539539 −2.02284e11 −0.103232
540540 0 0
541541 −8.78618e11 −0.440973 −0.220487 0.975390i 0.570765π-0.570765\pi
−0.220487 + 0.975390i 0.570765π0.570765\pi
542542 2.45933e11 0.122411
543543 0 0
544544 1.30994e12 0.641295
545545 6.40875e11 0.311164
546546 0 0
547547 4.56216e11 0.217885 0.108943 0.994048i 0.465254π-0.465254\pi
0.108943 + 0.994048i 0.465254π0.465254\pi
548548 1.39292e12 0.659803
549549 0 0
550550 −1.25713e11 −0.0585801
551551 1.08925e11 0.0503435
552552 0 0
553553 −6.38416e11 −0.290296
554554 1.03225e12 0.465575
555555 0 0
556556 3.53763e12 1.56991
557557 −1.63980e12 −0.721842 −0.360921 0.932596i 0.617538π-0.617538\pi
−0.360921 + 0.932596i 0.617538π0.617538\pi
558558 0 0
559559 1.51198e12 0.654927
560560 −2.10110e11 −0.0902818
561561 0 0
562562 4.22590e11 0.178692
563563 −4.36151e11 −0.182957 −0.0914786 0.995807i 0.529159π-0.529159\pi
−0.0914786 + 0.995807i 0.529159π0.529159\pi
564564 0 0
565565 7.97079e11 0.329066
566566 7.28288e11 0.298283
567567 0 0
568568 −3.13493e12 −1.26375
569569 −1.76284e12 −0.705029 −0.352514 0.935806i 0.614673π-0.614673\pi
−0.352514 + 0.935806i 0.614673π0.614673\pi
570570 0 0
571571 2.37232e11 0.0933922 0.0466961 0.998909i 0.485131π-0.485131\pi
0.0466961 + 0.998909i 0.485131π0.485131\pi
572572 −1.16212e12 −0.453909
573573 0 0
574574 −6.56462e11 −0.252410
575575 1.00502e12 0.383414
576576 0 0
577577 −3.72080e12 −1.39748 −0.698739 0.715377i 0.746255π-0.746255\pi
−0.698739 + 0.715377i 0.746255π0.746255\pi
578578 −6.02851e11 −0.224665
579579 0 0
580580 1.77255e12 0.650388
581581 2.26598e10 0.00825017
582582 0 0
583583 −9.62377e11 −0.345014
584584 −1.80373e11 −0.0641674
585585 0 0
586586 1.29562e12 0.453878
587587 6.46176e11 0.224636 0.112318 0.993672i 0.464172π-0.464172\pi
0.112318 + 0.993672i 0.464172π0.464172\pi
588588 0 0
589589 −1.34331e11 −0.0459892
590590 3.00894e11 0.102230
591591 0 0
592592 1.35853e12 0.454590
593593 5.05774e12 1.67962 0.839808 0.542883i 0.182667π-0.182667\pi
0.839808 + 0.542883i 0.182667π0.182667\pi
594594 0 0
595595 −3.45005e11 −0.112849
596596 4.58377e11 0.148804
597597 0 0
598598 −1.82644e12 −0.584051
599599 4.61588e11 0.146499 0.0732494 0.997314i 0.476663π-0.476663\pi
0.0732494 + 0.997314i 0.476663π0.476663\pi
600600 0 0
601601 −6.31800e12 −1.97535 −0.987677 0.156509i 0.949976π-0.949976\pi
−0.987677 + 0.156509i 0.949976π0.949976\pi
602602 −4.30163e11 −0.133490
603603 0 0
604604 −8.44227e11 −0.258103
605605 7.04169e11 0.213687
606606 0 0
607607 −1.45276e12 −0.434356 −0.217178 0.976132i 0.569685π-0.569685\pi
−0.217178 + 0.976132i 0.569685π0.569685\pi
608608 9.36335e10 0.0277885
609609 0 0
610610 −1.27990e11 −0.0374277
611611 4.59605e11 0.133413
612612 0 0
613613 1.20124e12 0.343603 0.171802 0.985132i 0.445041π-0.445041\pi
0.171802 + 0.985132i 0.445041π0.445041\pi
614614 −5.12094e11 −0.145409
615615 0 0
616616 7.26252e11 0.203224
617617 −3.13545e12 −0.870997 −0.435498 0.900189i 0.643428π-0.643428\pi
−0.435498 + 0.900189i 0.643428π0.643428\pi
618618 0 0
619619 −5.17127e12 −1.41576 −0.707880 0.706333i 0.750348π-0.750348\pi
−0.707880 + 0.706333i 0.750348π0.750348\pi
620620 −2.18599e12 −0.594135
621621 0 0
622622 −4.82884e11 −0.129356
623623 1.59637e12 0.424557
624624 0 0
625625 1.52588e11 0.0400000
626626 −2.30441e12 −0.599757
627627 0 0
628628 1.97520e12 0.506749
629629 2.23073e12 0.568223
630630 0 0
631631 −6.37331e12 −1.60042 −0.800208 0.599723i 0.795278π-0.795278\pi
−0.800208 + 0.599723i 0.795278π0.795278\pi
632632 2.29208e12 0.571481
633633 0 0
634634 1.07306e12 0.263768
635635 1.81462e12 0.442897
636636 0 0
637637 −4.46204e11 −0.107376
638638 −2.13312e12 −0.509710
639639 0 0
640640 1.93465e12 0.455818
641641 5.74174e12 1.34333 0.671665 0.740855i 0.265579π-0.265579\pi
0.671665 + 0.740855i 0.265579π0.265579\pi
642642 0 0
643643 −5.85135e11 −0.134992 −0.0674958 0.997720i 0.521501π-0.521501\pi
−0.0674958 + 0.997720i 0.521501π0.521501\pi
644644 −2.64320e12 −0.605541
645645 0 0
646646 3.46520e10 0.00782857
647647 1.80915e12 0.405887 0.202943 0.979190i 0.434949π-0.434949\pi
0.202943 + 0.979190i 0.434949π0.434949\pi
648648 0 0
649649 1.84191e12 0.407536
650650 −2.77302e11 −0.0609316
651651 0 0
652652 −2.68079e12 −0.580963
653653 −2.43900e12 −0.524932 −0.262466 0.964941i 0.584536π-0.584536\pi
−0.262466 + 0.964941i 0.584536π0.584536\pi
654654 0 0
655655 1.28233e12 0.272216
656656 −4.17396e12 −0.879996
657657 0 0
658658 −1.30759e11 −0.0271929
659659 −7.42836e12 −1.53429 −0.767147 0.641471i 0.778324π-0.778324\pi
−0.767147 + 0.641471i 0.778324π0.778324\pi
660660 0 0
661661 −6.34861e12 −1.29352 −0.646759 0.762695i 0.723876π-0.723876\pi
−0.646759 + 0.762695i 0.723876π0.723876\pi
662662 −2.30591e12 −0.466640
663663 0 0
664664 −8.13544e10 −0.0162414
665665 −2.46606e10 −0.00488997
666666 0 0
667667 1.70533e13 3.33611
668668 −2.66002e12 −0.516882
669669 0 0
670670 −1.57264e12 −0.301505
671671 −7.83487e11 −0.149204
672672 0 0
673673 3.17186e12 0.596000 0.298000 0.954566i 0.403680π-0.403680\pi
0.298000 + 0.954566i 0.403680π0.403680\pi
674674 5.60774e11 0.104669
675675 0 0
676676 1.97405e12 0.363578
677677 2.32240e12 0.424901 0.212450 0.977172i 0.431856π-0.431856\pi
0.212450 + 0.977172i 0.431856π0.431856\pi
678678 0 0
679679 −2.89876e12 −0.523357
680680 1.23866e12 0.222157
681681 0 0
682682 2.63066e12 0.465624
683683 −3.78639e12 −0.665782 −0.332891 0.942965i 0.608024π-0.608024\pi
−0.332891 + 0.942965i 0.608024π0.608024\pi
684684 0 0
685685 2.03462e12 0.353081
686686 1.26946e11 0.0218858
687687 0 0
688688 −2.73509e12 −0.465397
689689 −2.12283e12 −0.358864
690690 0 0
691691 −5.70532e12 −0.951982 −0.475991 0.879450i 0.657911π-0.657911\pi
−0.475991 + 0.879450i 0.657911π0.657911\pi
692692 3.83900e12 0.636415
693693 0 0
694694 1.54695e12 0.253138
695695 5.16735e12 0.840111
696696 0 0
697697 −6.85372e12 −1.09997
698698 −3.03746e12 −0.484352
699699 0 0
700700 −4.01307e11 −0.0631736
701701 −6.25160e12 −0.977823 −0.488912 0.872333i 0.662606π-0.662606\pi
−0.488912 + 0.872333i 0.662606π0.662606\pi
702702 0 0
703703 1.59450e11 0.0246222
704704 6.81818e11 0.104614
705705 0 0
706706 −3.47199e12 −0.525965
707707 −2.83807e12 −0.427205
708708 0 0
709709 −8.01996e12 −1.19197 −0.595983 0.802997i 0.703238π-0.703238\pi
−0.595983 + 0.802997i 0.703238π0.703238\pi
710710 −2.08466e12 −0.307873
711711 0 0
712712 −5.73136e12 −0.835791
713713 −2.10308e13 −3.04757
714714 0 0
715715 −1.69749e12 −0.242901
716716 7.54107e12 1.07232
717717 0 0
718718 1.46871e12 0.206241
719719 −1.35002e12 −0.188391 −0.0941953 0.995554i 0.530028π-0.530028\pi
−0.0941953 + 0.995554i 0.530028π0.530028\pi
720720 0 0
721721 4.74944e12 0.654537
722722 −2.95708e12 −0.404991
723723 0 0
724724 −6.94238e11 −0.0939042
725725 2.58913e12 0.348043
726726 0 0
727727 −1.47778e13 −1.96203 −0.981013 0.193941i 0.937873π-0.937873\pi
−0.981013 + 0.193941i 0.937873π0.937873\pi
728728 1.60198e12 0.211381
729729 0 0
730730 −1.19944e11 −0.0156324
731731 −4.49108e12 −0.581731
732732 0 0
733733 −6.70116e12 −0.857398 −0.428699 0.903447i 0.641028π-0.641028\pi
−0.428699 + 0.903447i 0.641028π0.641028\pi
734734 4.71269e12 0.599290
735735 0 0
736736 1.46593e13 1.84146
737737 −9.62686e12 −1.20193
738738 0 0
739739 −1.39054e13 −1.71508 −0.857540 0.514417i 0.828008π-0.828008\pi
−0.857540 + 0.514417i 0.828008π0.828008\pi
740740 2.59476e12 0.318094
741741 0 0
742742 6.03953e11 0.0731452
743743 3.43953e12 0.414047 0.207024 0.978336i 0.433622π-0.433622\pi
0.207024 + 0.978336i 0.433622π0.433622\pi
744744 0 0
745745 6.69544e11 0.0796298
746746 −6.15321e11 −0.0727407
747747 0 0
748748 3.45188e12 0.403179
749749 −4.02955e11 −0.0467830
750750 0 0
751751 1.00823e13 1.15660 0.578298 0.815826i 0.303717π-0.303717\pi
0.578298 + 0.815826i 0.303717π0.303717\pi
752752 −8.31401e11 −0.0948047
753753 0 0
754754 −4.70529e12 −0.530170
755755 −1.23315e12 −0.138119
756756 0 0
757757 −1.02703e13 −1.13672 −0.568360 0.822780i 0.692422π-0.692422\pi
−0.568360 + 0.822780i 0.692422π0.692422\pi
758758 3.81052e12 0.419250
759759 0 0
760760 8.85379e10 0.00962649
761761 3.20840e12 0.346783 0.173391 0.984853i 0.444527π-0.444527\pi
0.173391 + 0.984853i 0.444527π0.444527\pi
762762 0 0
763763 −2.46199e12 −0.262982
764764 7.12855e12 0.756974
765765 0 0
766766 3.22817e12 0.338787
767767 4.06292e12 0.423896
768768 0 0
769769 1.52349e13 1.57098 0.785491 0.618872i 0.212410π-0.212410\pi
0.785491 + 0.618872i 0.212410π0.212410\pi
770770 4.82941e11 0.0495092
771771 0 0
772772 −1.03266e13 −1.04635
773773 8.54195e11 0.0860497 0.0430249 0.999074i 0.486301π-0.486301\pi
0.0430249 + 0.999074i 0.486301π0.486301\pi
774774 0 0
775775 −3.19303e12 −0.317940
776776 1.04073e13 1.03029
777777 0 0
778778 2.38517e12 0.233405
779779 −4.89898e11 −0.0476636
780780 0 0
781781 −1.27611e13 −1.22732
782782 5.42513e12 0.518776
783783 0 0
784784 8.07158e11 0.0763021
785785 2.88514e12 0.271178
786786 0 0
787787 4.25016e12 0.394929 0.197465 0.980310i 0.436729π-0.436729\pi
0.197465 + 0.980310i 0.436729π0.436729\pi
788788 −1.66807e12 −0.154116
789789 0 0
790790 1.52418e12 0.139224
791791 −3.06206e12 −0.278112
792792 0 0
793793 −1.72823e12 −0.155193
794794 6.73503e12 0.601378
795795 0 0
796796 8.02231e12 0.708256
797797 −2.02157e13 −1.77470 −0.887352 0.461093i 0.847458π-0.847458\pi
−0.887352 + 0.461093i 0.847458π0.847458\pi
798798 0 0
799799 −1.36518e12 −0.118503
800800 2.22566e12 0.192112
801801 0 0
802802 −7.41334e12 −0.632746
803803 −7.34231e11 −0.0623179
804804 0 0
805805 −3.86087e12 −0.324044
806806 5.80278e12 0.484315
807807 0 0
808808 1.01894e13 0.841002
809809 6.65781e12 0.546466 0.273233 0.961948i 0.411907π-0.411907\pi
0.273233 + 0.961948i 0.411907π0.411907\pi
810810 0 0
811811 −9.35525e12 −0.759384 −0.379692 0.925113i 0.623970π-0.623970\pi
−0.379692 + 0.925113i 0.623970π0.623970\pi
812812 −6.80942e12 −0.549678
813813 0 0
814814 −3.12259e12 −0.249290
815815 −3.91578e12 −0.310892
816816 0 0
817817 −3.21018e11 −0.0252075
818818 −8.35671e12 −0.652597
819819 0 0
820820 −7.97219e12 −0.615766
821821 −1.61631e13 −1.24160 −0.620798 0.783971i 0.713191π-0.713191\pi
−0.620798 + 0.783971i 0.713191π0.713191\pi
822822 0 0
823823 5.97042e12 0.453634 0.226817 0.973937i 0.427168π-0.427168\pi
0.226817 + 0.973937i 0.427168π0.427168\pi
824824 −1.70517e13 −1.28853
825825 0 0
826826 −1.15591e12 −0.0864003
827827 −7.76424e12 −0.577197 −0.288599 0.957450i 0.593189π-0.593189\pi
−0.288599 + 0.957450i 0.593189π0.593189\pi
828828 0 0
829829 −4.09585e12 −0.301195 −0.150598 0.988595i 0.548120π-0.548120\pi
−0.150598 + 0.988595i 0.548120π0.548120\pi
830830 −5.40988e10 −0.00395673
831831 0 0
832832 1.50397e12 0.108814
833833 1.32537e12 0.0953751
834834 0 0
835835 −3.88545e12 −0.276600
836836 2.46737e11 0.0174705
837837 0 0
838838 −4.53176e12 −0.317445
839839 −4.46741e11 −0.0311263 −0.0155631 0.999879i 0.504954π-0.504954\pi
−0.0155631 + 0.999879i 0.504954π0.504954\pi
840840 0 0
841841 2.94256e13 2.02835
842842 −1.05606e11 −0.00724079
843843 0 0
844844 9.43433e11 0.0639985
845845 2.88345e12 0.194562
846846 0 0
847847 −2.70513e12 −0.180598
848848 3.84009e12 0.255012
849849 0 0
850850 8.23677e11 0.0541217
851851 2.49636e13 1.63164
852852 0 0
853853 2.72968e13 1.76539 0.882696 0.469945i 0.155726π-0.155726\pi
0.882696 + 0.469945i 0.155726π0.155726\pi
854854 4.91688e11 0.0316322
855855 0 0
856856 1.44671e12 0.0920979
857857 −7.67571e12 −0.486077 −0.243038 0.970017i 0.578144π-0.578144\pi
−0.243038 + 0.970017i 0.578144π0.578144\pi
858858 0 0
859859 −1.67172e13 −1.04759 −0.523797 0.851843i 0.675485π-0.675485\pi
−0.523797 + 0.851843i 0.675485π0.675485\pi
860860 −5.22398e12 −0.325656
861861 0 0
862862 8.64452e12 0.533284
863863 2.85615e13 1.75280 0.876401 0.481582i 0.159938π-0.159938\pi
0.876401 + 0.481582i 0.159938π0.159938\pi
864864 0 0
865865 5.60756e12 0.340566
866866 9.34116e12 0.564378
867867 0 0
868868 8.39769e12 0.502135
869869 9.33018e12 0.555010
870870 0 0
871871 −2.12351e13 −1.25018
872872 8.83916e12 0.517710
873873 0 0
874874 3.87783e11 0.0224795
875875 −5.86182e11 −0.0338062
876876 0 0
877877 −8.40714e12 −0.479899 −0.239950 0.970785i 0.577131π-0.577131\pi
−0.239950 + 0.970785i 0.577131π0.577131\pi
878878 −7.23964e12 −0.411142
879879 0 0
880880 3.07066e12 0.172608
881881 1.99694e13 1.11680 0.558398 0.829573i 0.311416π-0.311416\pi
0.558398 + 0.829573i 0.311416π0.311416\pi
882882 0 0
883883 −2.36498e13 −1.30919 −0.654597 0.755978i 0.727162π-0.727162\pi
−0.654597 + 0.755978i 0.727162π0.727162\pi
884884 7.61423e12 0.419364
885885 0 0
886886 −9.79250e12 −0.533878
887887 3.83859e12 0.208217 0.104108 0.994566i 0.466801π-0.466801\pi
0.104108 + 0.994566i 0.466801π0.466801\pi
888888 0 0
889889 −6.97103e12 −0.374317
890890 −3.81122e12 −0.203615
891891 0 0
892892 1.13527e13 0.600425
893893 −9.75816e10 −0.00513495
894894 0 0
895895 1.10151e13 0.573833
896896 −7.43213e12 −0.385237
897897 0 0
898898 3.04216e10 0.00156113
899899 −5.41798e13 −2.76642
900900 0 0
901901 6.30551e12 0.318756
902902 9.59390e12 0.482576
903903 0 0
904904 1.09936e13 0.547495
905905 −1.01406e12 −0.0502511
906906 0 0
907907 −2.31944e13 −1.13802 −0.569009 0.822331i 0.692673π-0.692673\pi
−0.569009 + 0.822331i 0.692673π0.692673\pi
908908 3.32931e13 1.62543
909909 0 0
910910 1.06528e12 0.0514966
911911 −1.70743e13 −0.821317 −0.410659 0.911789i 0.634701π-0.634701\pi
−0.410659 + 0.911789i 0.634701π0.634701\pi
912912 0 0
913913 −3.31163e11 −0.0157733
914914 −6.44896e12 −0.305655
915915 0 0
916916 −2.07368e13 −0.973221
917917 −4.92620e12 −0.230065
918918 0 0
919919 1.49265e13 0.690301 0.345151 0.938547i 0.387828π-0.387828\pi
0.345151 + 0.938547i 0.387828π0.387828\pi
920920 1.38615e13 0.637919
921921 0 0
922922 1.70768e13 0.778246
923923 −2.81488e13 −1.27659
924924 0 0
925925 3.79012e12 0.170222
926926 −9.80898e11 −0.0438404
927927 0 0
928928 3.77653e13 1.67158
929929 −2.92103e12 −0.128666 −0.0643332 0.997928i 0.520492π-0.520492\pi
−0.0643332 + 0.997928i 0.520492π0.520492\pi
930930 0 0
931931 9.47362e10 0.00413278
932932 −1.02020e13 −0.442906
933933 0 0
934934 −3.79701e12 −0.163260
935935 5.04210e12 0.215754
936936 0 0
937937 −3.53996e13 −1.50027 −0.750135 0.661284i 0.770012π-0.770012\pi
−0.750135 + 0.661284i 0.770012π0.770012\pi
938938 6.04147e12 0.254818
939939 0 0
940940 −1.58796e12 −0.0663384
941941 4.67286e13 1.94280 0.971402 0.237439i 0.0763080π-0.0763080\pi
0.971402 + 0.237439i 0.0763080π0.0763080\pi
942942 0 0
943943 −7.66985e13 −3.15852
944944 −7.34960e12 −0.301224
945945 0 0
946946 6.28665e12 0.255217
947947 5.22799e12 0.211232 0.105616 0.994407i 0.466319π-0.466319\pi
0.105616 + 0.994407i 0.466319π0.466319\pi
948948 0 0
949949 −1.61958e12 −0.0648195
950950 5.88756e10 0.00234520
951951 0 0
952952 −4.75842e12 −0.187757
953953 2.46017e13 0.966156 0.483078 0.875577i 0.339519π-0.339519\pi
0.483078 + 0.875577i 0.339519π0.339519\pi
954954 0 0
955955 1.04125e13 0.405081
956956 2.67809e13 1.03697
957957 0 0
958958 7.83373e11 0.0300486
959959 −7.81618e12 −0.298408
960960 0 0
961961 4.03773e13 1.52715
962962 −6.88788e12 −0.259297
963963 0 0
964964 3.40853e13 1.27122
965965 −1.50838e13 −0.559936
966966 0 0
967967 1.24062e13 0.456267 0.228134 0.973630i 0.426738π-0.426738\pi
0.228134 + 0.973630i 0.426738π0.426738\pi
968968 9.71212e12 0.355529
969969 0 0
970970 6.92060e12 0.250998
971971 −5.30324e12 −0.191450 −0.0957248 0.995408i 0.530517π-0.530517\pi
−0.0957248 + 0.995408i 0.530517π0.530517\pi
972972 0 0
973973 −1.98509e13 −0.710023
974974 4.53799e12 0.161565
975975 0 0
976976 3.12628e12 0.110282
977977 1.45131e13 0.509606 0.254803 0.966993i 0.417989π-0.417989\pi
0.254803 + 0.966993i 0.417989π0.417989\pi
978978 0 0
979979 −2.33302e13 −0.811702
980980 1.54166e12 0.0533914
981981 0 0
982982 −1.01954e13 −0.349868
983983 3.61534e13 1.23498 0.617488 0.786580i 0.288150π-0.288150\pi
0.617488 + 0.786580i 0.288150π0.288150\pi
984984 0 0
985985 −2.43652e12 −0.0824721
986986 1.39763e13 0.470917
987987 0 0
988988 5.44258e11 0.0181718
989989 −5.02586e13 −1.67043
990990 0 0
991991 4.94162e13 1.62756 0.813782 0.581170i 0.197405π-0.197405\pi
0.813782 + 0.581170i 0.197405π0.197405\pi
992992 −4.65739e13 −1.52700
993993 0 0
994994 8.00841e12 0.260200
995995 1.17180e13 0.379010
996996 0 0
997997 −3.03522e13 −0.972886 −0.486443 0.873712i 0.661706π-0.661706\pi
−0.486443 + 0.873712i 0.661706π0.661706\pi
998998 7.50580e12 0.239502
999999 0 0
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 315.10.a.b.1.1 2
3.2 odd 2 35.10.a.b.1.2 2
15.2 even 4 175.10.b.c.99.2 4
15.8 even 4 175.10.b.c.99.3 4
15.14 odd 2 175.10.a.c.1.1 2
21.20 even 2 245.10.a.c.1.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
35.10.a.b.1.2 2 3.2 odd 2
175.10.a.c.1.1 2 15.14 odd 2
175.10.b.c.99.2 4 15.2 even 4
175.10.b.c.99.3 4 15.8 even 4
245.10.a.c.1.2 2 21.20 even 2
315.10.a.b.1.1 2 1.1 even 1 trivial