Properties

Label 315.4.a.o.1.3
Level 315315
Weight 44
Character 315.1
Self dual yes
Analytic conductor 18.58618.586
Analytic rank 00
Dimension 33
CM no
Inner twists 11

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [315,4,Mod(1,315)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(315, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 4, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("315.1"); S:= CuspForms(chi, 4); N := Newforms(S);
 
Level: N N == 315=3257 315 = 3^{2} \cdot 5 \cdot 7
Weight: k k == 4 4
Character orbit: [χ][\chi] == 315.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,2,0,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(4)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 18.585601651818.5856016518
Analytic rank: 00
Dimension: 33
Coefficient field: 3.3.22952.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x3x218x+14 x^{3} - x^{2} - 18x + 14 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 1.3
Root 4.15010-4.15010 of defining polynomial
Character χ\chi == 315.1

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q+5.15010q2+18.5235q4+5.00000q5+7.00000q7+54.1971q8+25.7505q1014.0073q1110.5931q13+36.0507q14+130.932q16+131.801q17+38.6871q19+92.6176q2072.1391q22102.481q23+25.0000q2554.5553q26+129.665q28232.376q29165.501q31+240.738q32+678.789q34+35.0000q35+280.004q37+199.242q38+270.986q40122.271q41431.844q43259.465q44527.787q46+295.692q47+49.0000q49+128.752q50196.221q52+243.639q5370.0366q55+379.380q561196.76q58+566.480q59188.012q61852.346q62+192.364q6452.9653q65871.647q67+2441.42q68+180.253q70176.800q71220.524q73+1442.05q74+716.621q7698.0513q77190.494q79+654.662q80629.710q82+518.241q83+659.006q852224.04q86759.157q88598.355q8974.1515q911898.31q92+1522.85q94+193.436q951882.24q97+252.355q98+O(q100)q+5.15010 q^{2} +18.5235 q^{4} +5.00000 q^{5} +7.00000 q^{7} +54.1971 q^{8} +25.7505 q^{10} -14.0073 q^{11} -10.5931 q^{13} +36.0507 q^{14} +130.932 q^{16} +131.801 q^{17} +38.6871 q^{19} +92.6176 q^{20} -72.1391 q^{22} -102.481 q^{23} +25.0000 q^{25} -54.5553 q^{26} +129.665 q^{28} -232.376 q^{29} -165.501 q^{31} +240.738 q^{32} +678.789 q^{34} +35.0000 q^{35} +280.004 q^{37} +199.242 q^{38} +270.986 q^{40} -122.271 q^{41} -431.844 q^{43} -259.465 q^{44} -527.787 q^{46} +295.692 q^{47} +49.0000 q^{49} +128.752 q^{50} -196.221 q^{52} +243.639 q^{53} -70.0366 q^{55} +379.380 q^{56} -1196.76 q^{58} +566.480 q^{59} -188.012 q^{61} -852.346 q^{62} +192.364 q^{64} -52.9653 q^{65} -871.647 q^{67} +2441.42 q^{68} +180.253 q^{70} -176.800 q^{71} -220.524 q^{73} +1442.05 q^{74} +716.621 q^{76} -98.0513 q^{77} -190.494 q^{79} +654.662 q^{80} -629.710 q^{82} +518.241 q^{83} +659.006 q^{85} -2224.04 q^{86} -759.157 q^{88} -598.355 q^{89} -74.1515 q^{91} -1898.31 q^{92} +1522.85 q^{94} +193.436 q^{95} -1882.24 q^{97} +252.355 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 3q+2q2+14q4+15q5+21q7+66q8+10q1020q11+14q14+114q16+234q1782q19+70q20236q22+30q23+75q25+76q26+98q28++98q98+O(q100) 3 q + 2 q^{2} + 14 q^{4} + 15 q^{5} + 21 q^{7} + 66 q^{8} + 10 q^{10} - 20 q^{11} + 14 q^{14} + 114 q^{16} + 234 q^{17} - 82 q^{19} + 70 q^{20} - 236 q^{22} + 30 q^{23} + 75 q^{25} + 76 q^{26} + 98 q^{28}+ \cdots + 98 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 5.15010 1.82083 0.910417 0.413691i 0.135761π-0.135761\pi
0.910417 + 0.413691i 0.135761π0.135761\pi
33 0 0
44 18.5235 2.31544
55 5.00000 0.447214
66 0 0
77 7.00000 0.377964
88 54.1971 2.39520
99 0 0
1010 25.7505 0.814302
1111 −14.0073 −0.383943 −0.191971 0.981401i 0.561488π-0.561488\pi
−0.191971 + 0.981401i 0.561488π0.561488\pi
1212 0 0
1313 −10.5931 −0.225999 −0.113000 0.993595i 0.536046π-0.536046\pi
−0.113000 + 0.993595i 0.536046π0.536046\pi
1414 36.0507 0.688211
1515 0 0
1616 130.932 2.04582
1717 131.801 1.88038 0.940191 0.340649i 0.110647π-0.110647\pi
0.940191 + 0.340649i 0.110647π0.110647\pi
1818 0 0
1919 38.6871 0.467128 0.233564 0.972341i 0.424961π-0.424961\pi
0.233564 + 0.972341i 0.424961π0.424961\pi
2020 92.6176 1.03550
2121 0 0
2222 −72.1391 −0.699096
2323 −102.481 −0.929076 −0.464538 0.885553i 0.653780π-0.653780\pi
−0.464538 + 0.885553i 0.653780π0.653780\pi
2424 0 0
2525 25.0000 0.200000
2626 −54.5553 −0.411507
2727 0 0
2828 129.665 0.875154
2929 −232.376 −1.48797 −0.743986 0.668195i 0.767067π-0.767067\pi
−0.743986 + 0.668195i 0.767067π0.767067\pi
3030 0 0
3131 −165.501 −0.958866 −0.479433 0.877578i 0.659158π-0.659158\pi
−0.479433 + 0.877578i 0.659158π0.659158\pi
3232 240.738 1.32990
3333 0 0
3434 678.789 3.42386
3535 35.0000 0.169031
3636 0 0
3737 280.004 1.24412 0.622059 0.782970i 0.286296π-0.286296\pi
0.622059 + 0.782970i 0.286296π0.286296\pi
3838 199.242 0.850563
3939 0 0
4040 270.986 1.07116
4141 −122.271 −0.465746 −0.232873 0.972507i 0.574813π-0.574813\pi
−0.232873 + 0.972507i 0.574813π0.574813\pi
4242 0 0
4343 −431.844 −1.53153 −0.765764 0.643122i 0.777639π-0.777639\pi
−0.765764 + 0.643122i 0.777639π0.777639\pi
4444 −259.465 −0.888996
4545 0 0
4646 −527.787 −1.69169
4747 295.692 0.917685 0.458842 0.888518i 0.348264π-0.348264\pi
0.458842 + 0.888518i 0.348264π0.348264\pi
4848 0 0
4949 49.0000 0.142857
5050 128.752 0.364167
5151 0 0
5252 −196.221 −0.523287
5353 243.639 0.631441 0.315721 0.948852i 0.397754π-0.397754\pi
0.315721 + 0.948852i 0.397754π0.397754\pi
5454 0 0
5555 −70.0366 −0.171704
5656 379.380 0.905299
5757 0 0
5858 −1196.76 −2.70935
5959 566.480 1.24999 0.624995 0.780628i 0.285101π-0.285101\pi
0.624995 + 0.780628i 0.285101π0.285101\pi
6060 0 0
6161 −188.012 −0.394630 −0.197315 0.980340i 0.563222π-0.563222\pi
−0.197315 + 0.980340i 0.563222π0.563222\pi
6262 −852.346 −1.74594
6363 0 0
6464 192.364 0.375711
6565 −52.9653 −0.101070
6666 0 0
6767 −871.647 −1.58938 −0.794692 0.607013i 0.792367π-0.792367\pi
−0.794692 + 0.607013i 0.792367π0.792367\pi
6868 2441.42 4.35391
6969 0 0
7070 180.253 0.307777
7171 −176.800 −0.295525 −0.147762 0.989023i 0.547207π-0.547207\pi
−0.147762 + 0.989023i 0.547207π0.547207\pi
7272 0 0
7373 −220.524 −0.353566 −0.176783 0.984250i 0.556569π-0.556569\pi
−0.176783 + 0.984250i 0.556569π0.556569\pi
7474 1442.05 2.26533
7575 0 0
7676 716.621 1.08161
7777 −98.0513 −0.145117
7878 0 0
7979 −190.494 −0.271294 −0.135647 0.990757i 0.543311π-0.543311\pi
−0.135647 + 0.990757i 0.543311π0.543311\pi
8080 654.662 0.914918
8181 0 0
8282 −629.710 −0.848047
8383 518.241 0.685353 0.342676 0.939453i 0.388667π-0.388667\pi
0.342676 + 0.939453i 0.388667π0.388667\pi
8484 0 0
8585 659.006 0.840932
8686 −2224.04 −2.78866
8787 0 0
8888 −759.157 −0.919618
8989 −598.355 −0.712646 −0.356323 0.934363i 0.615970π-0.615970\pi
−0.356323 + 0.934363i 0.615970π0.615970\pi
9090 0 0
9191 −74.1515 −0.0854196
9292 −1898.31 −2.15122
9393 0 0
9494 1522.85 1.67095
9595 193.436 0.208906
9696 0 0
9797 −1882.24 −1.97023 −0.985116 0.171889i 0.945013π-0.945013\pi
−0.985116 + 0.171889i 0.945013π0.945013\pi
9898 252.355 0.260119
9999 0 0
100100 463.088 0.463088
101101 190.791 0.187964 0.0939821 0.995574i 0.470040π-0.470040\pi
0.0939821 + 0.995574i 0.470040π0.470040\pi
102102 0 0
103103 −1496.53 −1.43163 −0.715813 0.698292i 0.753944π-0.753944\pi
−0.715813 + 0.698292i 0.753944π0.753944\pi
104104 −574.114 −0.541312
105105 0 0
106106 1254.76 1.14975
107107 −1965.85 −1.77613 −0.888066 0.459716i 0.847951π-0.847951\pi
−0.888066 + 0.459716i 0.847951π0.847951\pi
108108 0 0
109109 −870.482 −0.764927 −0.382464 0.923971i 0.624924π-0.624924\pi
−0.382464 + 0.923971i 0.624924π0.624924\pi
110110 −360.696 −0.312645
111111 0 0
112112 916.527 0.773247
113113 2051.20 1.70762 0.853809 0.520587i 0.174287π-0.174287\pi
0.853809 + 0.520587i 0.174287π0.174287\pi
114114 0 0
115115 −512.405 −0.415496
116116 −4304.42 −3.44531
117117 0 0
118118 2917.43 2.27603
119119 922.608 0.710717
120120 0 0
121121 −1134.79 −0.852588
122122 −968.279 −0.718556
123123 0 0
124124 −3065.66 −2.22020
125125 125.000 0.0894427
126126 0 0
127127 2501.15 1.74757 0.873785 0.486313i 0.161659π-0.161659\pi
0.873785 + 0.486313i 0.161659π0.161659\pi
128128 −935.209 −0.645793
129129 0 0
130130 −272.777 −0.184032
131131 534.190 0.356278 0.178139 0.984005i 0.442992π-0.442992\pi
0.178139 + 0.984005i 0.442992π0.442992\pi
132132 0 0
133133 270.810 0.176558
134134 −4489.07 −2.89400
135135 0 0
136136 7143.24 4.50388
137137 503.159 0.313779 0.156890 0.987616i 0.449853π-0.449853\pi
0.156890 + 0.987616i 0.449853π0.449853\pi
138138 0 0
139139 1424.87 0.869466 0.434733 0.900559i 0.356843π-0.356843\pi
0.434733 + 0.900559i 0.356843π0.356843\pi
140140 648.323 0.391381
141141 0 0
142142 −910.536 −0.538102
143143 148.381 0.0867707
144144 0 0
145145 −1161.88 −0.665441
146146 −1135.72 −0.643786
147147 0 0
148148 5186.66 2.88068
149149 1482.49 0.815105 0.407552 0.913182i 0.366382π-0.366382\pi
0.407552 + 0.913182i 0.366382π0.366382\pi
150150 0 0
151151 −1267.34 −0.683008 −0.341504 0.939880i 0.610936π-0.610936\pi
−0.341504 + 0.939880i 0.610936π0.610936\pi
152152 2096.73 1.11886
153153 0 0
154154 −504.974 −0.264233
155155 −827.505 −0.428818
156156 0 0
157157 3234.00 1.64396 0.821979 0.569517i 0.192870π-0.192870\pi
0.821979 + 0.569517i 0.192870π0.192870\pi
158158 −981.063 −0.493982
159159 0 0
160160 1203.69 0.594750
161161 −717.367 −0.351158
162162 0 0
163163 1758.52 0.845017 0.422508 0.906359i 0.361150π-0.361150\pi
0.422508 + 0.906359i 0.361150π0.361150\pi
164164 −2264.90 −1.07841
165165 0 0
166166 2668.99 1.24791
167167 1682.57 0.779646 0.389823 0.920890i 0.372536π-0.372536\pi
0.389823 + 0.920890i 0.372536π0.372536\pi
168168 0 0
169169 −2084.79 −0.948924
170170 3393.95 1.53120
171171 0 0
172172 −7999.28 −3.54616
173173 3211.53 1.41138 0.705688 0.708523i 0.250638π-0.250638\pi
0.705688 + 0.708523i 0.250638π0.250638\pi
174174 0 0
175175 175.000 0.0755929
176176 −1834.01 −0.785477
177177 0 0
178178 −3081.59 −1.29761
179179 3311.97 1.38295 0.691476 0.722399i 0.256961π-0.256961\pi
0.691476 + 0.722399i 0.256961π0.256961\pi
180180 0 0
181181 2062.42 0.846954 0.423477 0.905907i 0.360809π-0.360809\pi
0.423477 + 0.905907i 0.360809π0.360809\pi
182182 −381.887 −0.155535
183183 0 0
184184 −5554.17 −2.22532
185185 1400.02 0.556386
186186 0 0
187187 −1846.18 −0.721958
188188 5477.26 2.12484
189189 0 0
190190 996.212 0.380383
191191 2783.01 1.05430 0.527150 0.849772i 0.323261π-0.323261\pi
0.527150 + 0.849772i 0.323261π0.323261\pi
192192 0 0
193193 300.293 0.111998 0.0559988 0.998431i 0.482166π-0.482166\pi
0.0559988 + 0.998431i 0.482166π0.482166\pi
194194 −9693.72 −3.58747
195195 0 0
196196 907.652 0.330777
197197 −1485.64 −0.537295 −0.268648 0.963239i 0.586577π-0.586577\pi
−0.268648 + 0.963239i 0.586577π0.586577\pi
198198 0 0
199199 −3040.55 −1.08311 −0.541555 0.840665i 0.682164π-0.682164\pi
−0.541555 + 0.840665i 0.682164π0.682164\pi
200200 1354.93 0.479039
201201 0 0
202202 982.591 0.342252
203203 −1626.63 −0.562400
204204 0 0
205205 −611.357 −0.208288
206206 −7707.28 −2.60676
207207 0 0
208208 −1386.98 −0.462353
209209 −541.903 −0.179350
210210 0 0
211211 −2886.74 −0.941855 −0.470928 0.882172i 0.656081π-0.656081\pi
−0.470928 + 0.882172i 0.656081π0.656081\pi
212212 4513.05 1.46206
213213 0 0
214214 −10124.3 −3.23404
215215 −2159.22 −0.684920
216216 0 0
217217 −1158.51 −0.362417
218218 −4483.07 −1.39281
219219 0 0
220220 −1297.32 −0.397571
221221 −1396.18 −0.424964
222222 0 0
223223 4591.34 1.37874 0.689369 0.724410i 0.257888π-0.257888\pi
0.689369 + 0.724410i 0.257888π0.257888\pi
224224 1685.16 0.502655
225225 0 0
226226 10563.9 3.10929
227227 −2547.05 −0.744729 −0.372364 0.928087i 0.621453π-0.621453\pi
−0.372364 + 0.928087i 0.621453π0.621453\pi
228228 0 0
229229 2007.40 0.579269 0.289635 0.957137i 0.406466π-0.406466\pi
0.289635 + 0.957137i 0.406466π0.406466\pi
230230 −2638.94 −0.756549
231231 0 0
232232 −12594.1 −3.56399
233233 2810.65 0.790266 0.395133 0.918624i 0.370699π-0.370699\pi
0.395133 + 0.918624i 0.370699π0.370699\pi
234234 0 0
235235 1478.46 0.410401
236236 10493.2 2.89428
237237 0 0
238238 4751.52 1.29410
239239 1848.68 0.500339 0.250170 0.968202i 0.419514π-0.419514\pi
0.250170 + 0.968202i 0.419514π0.419514\pi
240240 0 0
241241 5722.64 1.52958 0.764788 0.644283i 0.222844π-0.222844\pi
0.764788 + 0.644283i 0.222844π0.222844\pi
242242 −5844.30 −1.55242
243243 0 0
244244 −3482.64 −0.913742
245245 245.000 0.0638877
246246 0 0
247247 −409.815 −0.105571
248248 −8969.68 −2.29667
249249 0 0
250250 643.762 0.162860
251251 1723.38 0.433381 0.216691 0.976240i 0.430474π-0.430474\pi
0.216691 + 0.976240i 0.430474π0.430474\pi
252252 0 0
253253 1435.48 0.356712
254254 12881.2 3.18203
255255 0 0
256256 −6355.33 −1.55159
257257 −5754.01 −1.39660 −0.698298 0.715807i 0.746059π-0.746059\pi
−0.698298 + 0.715807i 0.746059π0.746059\pi
258258 0 0
259259 1960.03 0.470232
260260 −981.104 −0.234021
261261 0 0
262262 2751.13 0.648723
263263 −6680.33 −1.56626 −0.783130 0.621857i 0.786378π-0.786378\pi
−0.783130 + 0.621857i 0.786378π0.786378\pi
264264 0 0
265265 1218.19 0.282389
266266 1394.70 0.321483
267267 0 0
268268 −16146.0 −3.68012
269269 7468.96 1.69290 0.846451 0.532466i 0.178735π-0.178735\pi
0.846451 + 0.532466i 0.178735π0.178735\pi
270270 0 0
271271 −757.673 −0.169835 −0.0849176 0.996388i 0.527063π-0.527063\pi
−0.0849176 + 0.996388i 0.527063π0.527063\pi
272272 17257.0 3.84692
273273 0 0
274274 2591.32 0.571340
275275 −350.183 −0.0767885
276276 0 0
277277 1169.29 0.253632 0.126816 0.991926i 0.459524π-0.459524\pi
0.126816 + 0.991926i 0.459524π0.459524\pi
278278 7338.22 1.58315
279279 0 0
280280 1896.90 0.404862
281281 5735.20 1.21756 0.608778 0.793341i 0.291660π-0.291660\pi
0.608778 + 0.793341i 0.291660π0.291660\pi
282282 0 0
283283 −9010.69 −1.89269 −0.946343 0.323164i 0.895253π-0.895253\pi
−0.946343 + 0.323164i 0.895253π0.895253\pi
284284 −3274.95 −0.684270
285285 0 0
286286 764.174 0.157995
287287 −855.900 −0.176035
288288 0 0
289289 12458.6 2.53583
290290 −5983.80 −1.21166
291291 0 0
292292 −4084.87 −0.818662
293293 5303.84 1.05752 0.528760 0.848771i 0.322657π-0.322657\pi
0.528760 + 0.848771i 0.322657π0.322657\pi
294294 0 0
295295 2832.40 0.559013
296296 15175.4 2.97991
297297 0 0
298298 7634.99 1.48417
299299 1085.59 0.209970
300300 0 0
301301 −3022.91 −0.578863
302302 −6526.90 −1.24365
303303 0 0
304304 5065.40 0.955659
305305 −940.059 −0.176484
306306 0 0
307307 8783.81 1.63296 0.816480 0.577374i 0.195922π-0.195922\pi
0.816480 + 0.577374i 0.195922π0.195922\pi
308308 −1816.25 −0.336009
309309 0 0
310310 −4261.73 −0.780807
311311 −2357.25 −0.429799 −0.214899 0.976636i 0.568942π-0.568942\pi
−0.214899 + 0.976636i 0.568942π0.568942\pi
312312 0 0
313313 −2633.84 −0.475635 −0.237817 0.971310i 0.576432π-0.576432\pi
−0.237817 + 0.971310i 0.576432π0.576432\pi
314314 16655.4 2.99338
315315 0 0
316316 −3528.62 −0.628166
317317 −842.572 −0.149286 −0.0746428 0.997210i 0.523782π-0.523782\pi
−0.0746428 + 0.997210i 0.523782π0.523782\pi
318318 0 0
319319 3254.97 0.571296
320320 961.820 0.168023
321321 0 0
322322 −3694.51 −0.639401
323323 5099.01 0.878379
324324 0 0
325325 −264.827 −0.0451998
326326 9056.54 1.53864
327327 0 0
328328 −6626.76 −1.11555
329329 2069.85 0.346852
330330 0 0
331331 11058.8 1.83639 0.918197 0.396125i 0.129645π-0.129645\pi
0.918197 + 0.396125i 0.129645π0.129645\pi
332332 9599.64 1.58689
333333 0 0
334334 8665.38 1.41961
335335 −4358.24 −0.710794
336336 0 0
337337 −1197.28 −0.193531 −0.0967657 0.995307i 0.530850π-0.530850\pi
−0.0967657 + 0.995307i 0.530850π0.530850\pi
338338 −10736.9 −1.72783
339339 0 0
340340 12207.1 1.94713
341341 2318.23 0.368150
342342 0 0
343343 343.000 0.0539949
344344 −23404.7 −3.66831
345345 0 0
346346 16539.7 2.56988
347347 −518.087 −0.0801509 −0.0400755 0.999197i 0.512760π-0.512760\pi
−0.0400755 + 0.999197i 0.512760π0.512760\pi
348348 0 0
349349 −1776.08 −0.272412 −0.136206 0.990681i 0.543491π-0.543491\pi
−0.136206 + 0.990681i 0.543491π0.543491\pi
350350 901.267 0.137642
351351 0 0
352352 −3372.09 −0.510606
353353 −7507.35 −1.13194 −0.565972 0.824425i 0.691499π-0.691499\pi
−0.565972 + 0.824425i 0.691499π0.691499\pi
354354 0 0
355355 −883.999 −0.132163
356356 −11083.6 −1.65009
357357 0 0
358358 17057.0 2.51813
359359 −4915.58 −0.722658 −0.361329 0.932438i 0.617677π-0.617677\pi
−0.361329 + 0.932438i 0.617677π0.617677\pi
360360 0 0
361361 −5362.31 −0.781791
362362 10621.7 1.54216
363363 0 0
364364 −1373.55 −0.197784
365365 −1102.62 −0.158120
366366 0 0
367367 −3628.98 −0.516161 −0.258080 0.966123i 0.583090π-0.583090\pi
−0.258080 + 0.966123i 0.583090π0.583090\pi
368368 −13418.1 −1.90072
369369 0 0
370370 7210.24 1.01309
371371 1705.47 0.238662
372372 0 0
373373 −2836.97 −0.393814 −0.196907 0.980422i 0.563090π-0.563090\pi
−0.196907 + 0.980422i 0.563090π0.563090\pi
374374 −9508.02 −1.31457
375375 0 0
376376 16025.7 2.19804
377377 2461.58 0.336280
378378 0 0
379379 9703.96 1.31519 0.657597 0.753370i 0.271573π-0.271573\pi
0.657597 + 0.753370i 0.271573π0.271573\pi
380380 3583.11 0.483709
381381 0 0
382382 14332.8 1.91971
383383 −3855.90 −0.514431 −0.257216 0.966354i 0.582805π-0.582805\pi
−0.257216 + 0.966354i 0.582805π0.582805\pi
384384 0 0
385385 −490.256 −0.0648981
386386 1546.54 0.203929
387387 0 0
388388 −34865.7 −4.56195
389389 7106.46 0.926251 0.463125 0.886293i 0.346728π-0.346728\pi
0.463125 + 0.886293i 0.346728π0.346728\pi
390390 0 0
391391 −13507.1 −1.74702
392392 2655.66 0.342171
393393 0 0
394394 −7651.17 −0.978326
395395 −952.470 −0.121327
396396 0 0
397397 −6775.82 −0.856596 −0.428298 0.903637i 0.640887π-0.640887\pi
−0.428298 + 0.903637i 0.640887π0.640887\pi
398398 −15659.1 −1.97217
399399 0 0
400400 3273.31 0.409164
401401 6444.62 0.802566 0.401283 0.915954i 0.368564π-0.368564\pi
0.401283 + 0.915954i 0.368564π0.368564\pi
402402 0 0
403403 1753.16 0.216703
404404 3534.11 0.435220
405405 0 0
406406 −8377.32 −1.02404
407407 −3922.11 −0.477670
408408 0 0
409409 4807.99 0.581270 0.290635 0.956834i 0.406133π-0.406133\pi
0.290635 + 0.956834i 0.406133π0.406133\pi
410410 −3148.55 −0.379258
411411 0 0
412412 −27721.0 −3.31484
413413 3965.36 0.472452
414414 0 0
415415 2591.20 0.306499
416416 −2550.15 −0.300556
417417 0 0
418418 −2790.85 −0.326567
419419 −4521.51 −0.527184 −0.263592 0.964634i 0.584907π-0.584907\pi
−0.263592 + 0.964634i 0.584907π0.584907\pi
420420 0 0
421421 −5821.82 −0.673962 −0.336981 0.941511i 0.609406π-0.609406\pi
−0.336981 + 0.941511i 0.609406π0.609406\pi
422422 −14867.0 −1.71496
423423 0 0
424424 13204.5 1.51243
425425 3295.03 0.376076
426426 0 0
427427 −1316.08 −0.149156
428428 −36414.5 −4.11252
429429 0 0
430430 −11120.2 −1.24713
431431 −8382.59 −0.936833 −0.468417 0.883508i 0.655175π-0.655175\pi
−0.468417 + 0.883508i 0.655175π0.655175\pi
432432 0 0
433433 2628.05 0.291677 0.145838 0.989308i 0.453412π-0.453412\pi
0.145838 + 0.989308i 0.453412π0.453412\pi
434434 −5966.42 −0.659902
435435 0 0
436436 −16124.4 −1.77114
437437 −3964.69 −0.433998
438438 0 0
439439 −4122.97 −0.448243 −0.224121 0.974561i 0.571951π-0.571951\pi
−0.224121 + 0.974561i 0.571951π0.571951\pi
440440 −3795.78 −0.411266
441441 0 0
442442 −7190.46 −0.773790
443443 −210.327 −0.0225574 −0.0112787 0.999936i 0.503590π-0.503590\pi
−0.0112787 + 0.999936i 0.503590π0.503590\pi
444444 0 0
445445 −2991.77 −0.318705
446446 23645.8 2.51045
447447 0 0
448448 1346.55 0.142005
449449 4414.35 0.463978 0.231989 0.972718i 0.425477π-0.425477\pi
0.231989 + 0.972718i 0.425477π0.425477\pi
450450 0 0
451451 1712.70 0.178820
452452 37995.4 3.95388
453453 0 0
454454 −13117.5 −1.35603
455455 −370.757 −0.0382008
456456 0 0
457457 14355.4 1.46941 0.734704 0.678388i 0.237321π-0.237321\pi
0.734704 + 0.678388i 0.237321π0.237321\pi
458458 10338.3 1.05475
459459 0 0
460460 −9491.54 −0.962055
461461 −14366.9 −1.45149 −0.725744 0.687965i 0.758504π-0.758504\pi
−0.725744 + 0.687965i 0.758504π0.758504\pi
462462 0 0
463463 11634.1 1.16778 0.583892 0.811832i 0.301529π-0.301529\pi
0.583892 + 0.811832i 0.301529π0.301529\pi
464464 −30425.6 −3.04412
465465 0 0
466466 14475.1 1.43894
467467 −12112.2 −1.20019 −0.600094 0.799929i 0.704870π-0.704870\pi
−0.600094 + 0.799929i 0.704870π0.704870\pi
468468 0 0
469469 −6101.53 −0.600730
470470 7614.23 0.747273
471471 0 0
472472 30701.6 2.99397
473473 6048.99 0.588018
474474 0 0
475475 967.178 0.0934256
476476 17089.9 1.64562
477477 0 0
478478 9520.88 0.911035
479479 11380.8 1.08560 0.542801 0.839861i 0.317364π-0.317364\pi
0.542801 + 0.839861i 0.317364π0.317364\pi
480480 0 0
481481 −2966.10 −0.281170
482482 29472.2 2.78510
483483 0 0
484484 −21020.4 −1.97412
485485 −9411.20 −0.881115
486486 0 0
487487 −11615.5 −1.08080 −0.540401 0.841408i 0.681727π-0.681727\pi
−0.540401 + 0.841408i 0.681727π0.681727\pi
488488 −10189.7 −0.945217
489489 0 0
490490 1261.77 0.116329
491491 −6045.64 −0.555674 −0.277837 0.960628i 0.589617π-0.589617\pi
−0.277837 + 0.960628i 0.589617π0.589617\pi
492492 0 0
493493 −30627.5 −2.79795
494494 −2110.59 −0.192226
495495 0 0
496496 −21669.4 −1.96167
497497 −1237.60 −0.111698
498498 0 0
499499 860.279 0.0771771 0.0385886 0.999255i 0.487714π-0.487714\pi
0.0385886 + 0.999255i 0.487714π0.487714\pi
500500 2315.44 0.207099
501501 0 0
502502 8875.57 0.789115
503503 3341.49 0.296202 0.148101 0.988972i 0.452684π-0.452684\pi
0.148101 + 0.988972i 0.452684π0.452684\pi
504504 0 0
505505 953.953 0.0840601
506506 7392.89 0.649514
507507 0 0
508508 46330.1 4.04639
509509 19754.5 1.72024 0.860122 0.510088i 0.170387π-0.170387\pi
0.860122 + 0.510088i 0.170387π0.170387\pi
510510 0 0
511511 −1543.67 −0.133636
512512 −25248.9 −2.17940
513513 0 0
514514 −29633.7 −2.54297
515515 −7482.65 −0.640243
516516 0 0
517517 −4141.86 −0.352338
518518 10094.3 0.856215
519519 0 0
520520 −2870.57 −0.242082
521521 20754.2 1.74522 0.872609 0.488420i 0.162427π-0.162427\pi
0.872609 + 0.488420i 0.162427π0.162427\pi
522522 0 0
523523 −9495.26 −0.793879 −0.396940 0.917845i 0.629928π-0.629928\pi
−0.396940 + 0.917845i 0.629928π0.629928\pi
524524 9895.07 0.824939
525525 0 0
526526 −34404.3 −2.85190
527527 −21813.2 −1.80303
528528 0 0
529529 −1664.65 −0.136817
530530 6273.82 0.514184
531531 0 0
532532 5016.35 0.408809
533533 1295.23 0.105258
534534 0 0
535535 −9829.26 −0.794310
536536 −47240.8 −3.80689
537537 0 0
538538 38465.9 3.08250
539539 −686.359 −0.0548489
540540 0 0
541541 15585.9 1.23862 0.619308 0.785148i 0.287413π-0.287413\pi
0.619308 + 0.785148i 0.287413π0.287413\pi
542542 −3902.09 −0.309242
543543 0 0
544544 31729.5 2.50072
545545 −4352.41 −0.342086
546546 0 0
547547 −23104.6 −1.80600 −0.902998 0.429644i 0.858639π-0.858639\pi
−0.902998 + 0.429644i 0.858639π0.858639\pi
548548 9320.27 0.726537
549549 0 0
550550 −1803.48 −0.139819
551551 −8989.96 −0.695073
552552 0 0
553553 −1333.46 −0.102540
554554 6021.98 0.461822
555555 0 0
556556 26393.6 2.01320
557557 −21731.2 −1.65311 −0.826553 0.562859i 0.809701π-0.809701\pi
−0.826553 + 0.562859i 0.809701π0.809701\pi
558558 0 0
559559 4574.56 0.346124
560560 4582.63 0.345807
561561 0 0
562562 29536.8 2.21697
563563 13595.1 1.01770 0.508850 0.860855i 0.330071π-0.330071\pi
0.508850 + 0.860855i 0.330071π0.330071\pi
564564 0 0
565565 10256.0 0.763670
566566 −46405.9 −3.44627
567567 0 0
568568 −9582.04 −0.707840
569569 −10018.2 −0.738107 −0.369054 0.929408i 0.620318π-0.620318\pi
−0.369054 + 0.929408i 0.620318π0.620318\pi
570570 0 0
571571 −6658.73 −0.488020 −0.244010 0.969773i 0.578463π-0.578463\pi
−0.244010 + 0.969773i 0.578463π0.578463\pi
572572 2748.53 0.200912
573573 0 0
574574 −4407.97 −0.320531
575575 −2562.02 −0.185815
576576 0 0
577577 −12676.0 −0.914570 −0.457285 0.889320i 0.651178π-0.651178\pi
−0.457285 + 0.889320i 0.651178π0.651178\pi
578578 64162.8 4.61733
579579 0 0
580580 −21522.1 −1.54079
581581 3627.68 0.259039
582582 0 0
583583 −3412.73 −0.242437
584584 −11951.8 −0.846861
585585 0 0
586586 27315.3 1.92557
587587 −18625.6 −1.30965 −0.654823 0.755782i 0.727257π-0.727257\pi
−0.654823 + 0.755782i 0.727257π0.727257\pi
588588 0 0
589589 −6402.76 −0.447913
590590 14587.1 1.01787
591591 0 0
592592 36661.6 2.54524
593593 −19417.3 −1.34465 −0.672323 0.740258i 0.734703π-0.734703\pi
−0.672323 + 0.740258i 0.734703π0.734703\pi
594594 0 0
595595 4613.04 0.317842
596596 27461.0 1.88733
597597 0 0
598598 5590.88 0.382321
599599 −13376.9 −0.912461 −0.456231 0.889862i 0.650801π-0.650801\pi
−0.456231 + 0.889862i 0.650801π0.650801\pi
600600 0 0
601601 14963.9 1.01562 0.507812 0.861468i 0.330454π-0.330454\pi
0.507812 + 0.861468i 0.330454π0.330454\pi
602602 −15568.3 −1.05401
603603 0 0
604604 −23475.5 −1.58146
605605 −5673.97 −0.381289
606606 0 0
607607 20270.8 1.35546 0.677731 0.735310i 0.262963π-0.262963\pi
0.677731 + 0.735310i 0.262963π0.262963\pi
608608 9313.45 0.621234
609609 0 0
610610 −4841.40 −0.321348
611611 −3132.29 −0.207396
612612 0 0
613613 13005.1 0.856888 0.428444 0.903568i 0.359062π-0.359062\pi
0.428444 + 0.903568i 0.359062π0.359062\pi
614614 45237.5 2.97335
615615 0 0
616616 −5314.10 −0.347583
617617 −11107.4 −0.724745 −0.362372 0.932033i 0.618033π-0.618033\pi
−0.362372 + 0.932033i 0.618033π0.618033\pi
618618 0 0
619619 348.077 0.0226016 0.0113008 0.999936i 0.496403π-0.496403\pi
0.0113008 + 0.999936i 0.496403π0.496403\pi
620620 −15328.3 −0.992902
621621 0 0
622622 −12140.1 −0.782593
623623 −4188.48 −0.269355
624624 0 0
625625 625.000 0.0400000
626626 −13564.6 −0.866052
627627 0 0
628628 59905.1 3.80649
629629 36904.8 2.33942
630630 0 0
631631 7548.88 0.476254 0.238127 0.971234i 0.423467π-0.423467\pi
0.238127 + 0.971234i 0.423467π0.423467\pi
632632 −10324.2 −0.649804
633633 0 0
634634 −4339.33 −0.271825
635635 12505.8 0.781537
636636 0 0
637637 −519.060 −0.0322856
638638 16763.4 1.04023
639639 0 0
640640 −4676.04 −0.288808
641641 8720.39 0.537340 0.268670 0.963232i 0.413416π-0.413416\pi
0.268670 + 0.963232i 0.413416π0.413416\pi
642642 0 0
643643 −10517.6 −0.645061 −0.322530 0.946559i 0.604533π-0.604533\pi
−0.322530 + 0.946559i 0.604533π0.604533\pi
644644 −13288.2 −0.813085
645645 0 0
646646 26260.4 1.59938
647647 −6194.54 −0.376402 −0.188201 0.982130i 0.560266π-0.560266\pi
−0.188201 + 0.982130i 0.560266π0.560266\pi
648648 0 0
649649 −7934.87 −0.479925
650650 −1363.88 −0.0823014
651651 0 0
652652 32573.9 1.95658
653653 16726.9 1.00241 0.501205 0.865329i 0.332890π-0.332890\pi
0.501205 + 0.865329i 0.332890π0.332890\pi
654654 0 0
655655 2670.95 0.159332
656656 −16009.3 −0.952832
657657 0 0
658658 10659.9 0.631561
659659 −9874.87 −0.583718 −0.291859 0.956461i 0.594274π-0.594274\pi
−0.291859 + 0.956461i 0.594274π0.594274\pi
660660 0 0
661661 −26873.6 −1.58134 −0.790668 0.612245i 0.790267π-0.790267\pi
−0.790668 + 0.612245i 0.790267π0.790267\pi
662662 56953.9 3.34377
663663 0 0
664664 28087.1 1.64156
665665 1354.05 0.0789591
666666 0 0
667667 23814.1 1.38244
668668 31167.0 1.80522
669669 0 0
670670 −22445.3 −1.29424
671671 2633.54 0.151515
672672 0 0
673673 270.279 0.0154807 0.00774034 0.999970i 0.497536π-0.497536\pi
0.00774034 + 0.999970i 0.497536π0.497536\pi
674674 −6166.12 −0.352389
675675 0 0
676676 −38617.6 −2.19718
677677 −5216.49 −0.296139 −0.148070 0.988977i 0.547306π-0.547306\pi
−0.148070 + 0.988977i 0.547306π0.547306\pi
678678 0 0
679679 −13175.7 −0.744678
680680 35716.2 2.01420
681681 0 0
682682 11939.1 0.670339
683683 597.154 0.0334546 0.0167273 0.999860i 0.494675π-0.494675\pi
0.0167273 + 0.999860i 0.494675π0.494675\pi
684684 0 0
685685 2515.79 0.140326
686686 1766.48 0.0983158
687687 0 0
688688 −56542.4 −3.13323
689689 −2580.88 −0.142705
690690 0 0
691691 −32491.9 −1.78878 −0.894392 0.447283i 0.852392π-0.852392\pi
−0.894392 + 0.447283i 0.852392π0.852392\pi
692692 59488.8 3.26795
693693 0 0
694694 −2668.20 −0.145942
695695 7124.35 0.388837
696696 0 0
697697 −16115.5 −0.875780
698698 −9147.01 −0.496016
699699 0 0
700700 3241.61 0.175031
701701 25288.3 1.36252 0.681260 0.732041i 0.261432π-0.261432\pi
0.681260 + 0.732041i 0.261432π0.261432\pi
702702 0 0
703703 10832.5 0.581162
704704 −2694.51 −0.144251
705705 0 0
706706 −38663.6 −2.06108
707707 1335.53 0.0710438
708708 0 0
709709 20110.2 1.06524 0.532618 0.846355i 0.321208π-0.321208\pi
0.532618 + 0.846355i 0.321208π0.321208\pi
710710 −4552.68 −0.240647
711711 0 0
712712 −32429.1 −1.70693
713713 16960.7 0.890860
714714 0 0
715715 741.903 0.0388050
716716 61349.4 3.20214
717717 0 0
718718 −25315.7 −1.31584
719719 −5650.46 −0.293083 −0.146542 0.989205i 0.546814π-0.546814\pi
−0.146542 + 0.989205i 0.546814π0.546814\pi
720720 0 0
721721 −10475.7 −0.541104
722722 −27616.4 −1.42351
723723 0 0
724724 38203.3 1.96107
725725 −5809.40 −0.297594
726726 0 0
727727 6571.94 0.335268 0.167634 0.985849i 0.446387π-0.446387\pi
0.167634 + 0.985849i 0.446387π0.446387\pi
728728 −4018.80 −0.204597
729729 0 0
730730 −5678.59 −0.287910
731731 −56917.6 −2.87985
732732 0 0
733733 −31444.0 −1.58446 −0.792231 0.610222i 0.791080π-0.791080\pi
−0.792231 + 0.610222i 0.791080π0.791080\pi
734734 −18689.6 −0.939843
735735 0 0
736736 −24671.0 −1.23558
737737 12209.4 0.610232
738738 0 0
739739 8157.80 0.406075 0.203038 0.979171i 0.434919π-0.434919\pi
0.203038 + 0.979171i 0.434919π0.434919\pi
740740 25933.3 1.28828
741741 0 0
742742 8783.35 0.434565
743743 −5705.69 −0.281725 −0.140862 0.990029i 0.544987π-0.544987\pi
−0.140862 + 0.990029i 0.544987π0.544987\pi
744744 0 0
745745 7412.47 0.364526
746746 −14610.7 −0.717070
747747 0 0
748748 −34197.8 −1.67165
749749 −13761.0 −0.671315
750750 0 0
751751 −7296.31 −0.354522 −0.177261 0.984164i 0.556724π-0.556724\pi
−0.177261 + 0.984164i 0.556724π0.556724\pi
752752 38715.7 1.87742
753753 0 0
754754 12677.4 0.612311
755755 −6336.68 −0.305451
756756 0 0
757757 8240.48 0.395648 0.197824 0.980238i 0.436613π-0.436613\pi
0.197824 + 0.980238i 0.436613π0.436613\pi
758758 49976.3 2.39475
759759 0 0
760760 10483.7 0.500371
761761 −30887.8 −1.47133 −0.735665 0.677345i 0.763130π-0.763130\pi
−0.735665 + 0.677345i 0.763130π0.763130\pi
762762 0 0
763763 −6093.37 −0.289115
764764 51551.1 2.44117
765765 0 0
766766 −19858.2 −0.936694
767767 −6000.76 −0.282497
768768 0 0
769769 30953.0 1.45149 0.725743 0.687966i 0.241496π-0.241496\pi
0.725743 + 0.687966i 0.241496π0.241496\pi
770770 −2524.87 −0.118169
771771 0 0
772772 5562.48 0.259324
773773 −6620.92 −0.308070 −0.154035 0.988065i 0.549227π-0.549227\pi
−0.154035 + 0.988065i 0.549227π0.549227\pi
774774 0 0
775775 −4137.52 −0.191773
776776 −102012. −4.71910
777777 0 0
778778 36598.9 1.68655
779779 −4730.33 −0.217563
780780 0 0
781781 2476.49 0.113465
782782 −69563.0 −3.18103
783783 0 0
784784 6415.69 0.292260
785785 16170.0 0.735201
786786 0 0
787787 −10068.6 −0.456044 −0.228022 0.973656i 0.573226π-0.573226\pi
−0.228022 + 0.973656i 0.573226π0.573226\pi
788788 −27519.2 −1.24407
789789 0 0
790790 −4905.32 −0.220916
791791 14358.4 0.645419
792792 0 0
793793 1991.62 0.0891861
794794 −34896.1 −1.55972
795795 0 0
796796 −56321.7 −2.50788
797797 42016.5 1.86738 0.933690 0.358084i 0.116570π-0.116570\pi
0.933690 + 0.358084i 0.116570π0.116570\pi
798798 0 0
799799 38972.6 1.72560
800800 6018.45 0.265980
801801 0 0
802802 33190.4 1.46134
803803 3088.95 0.135749
804804 0 0
805805 −3586.83 −0.157043
806806 9028.96 0.394580
807807 0 0
808808 10340.3 0.450211
809809 −32805.5 −1.42568 −0.712842 0.701324i 0.752593π-0.752593\pi
−0.712842 + 0.701324i 0.752593π0.752593\pi
810810 0 0
811811 15395.7 0.666606 0.333303 0.942820i 0.391837π-0.391837\pi
0.333303 + 0.942820i 0.391837π0.391837\pi
812812 −30131.0 −1.30220
813813 0 0
814814 −20199.2 −0.869758
815815 8792.59 0.377903
816816 0 0
817817 −16706.8 −0.715419
818818 24761.6 1.05840
819819 0 0
820820 −11324.5 −0.482278
821821 10626.7 0.451734 0.225867 0.974158i 0.427479π-0.427479\pi
0.225867 + 0.974158i 0.427479π0.427479\pi
822822 0 0
823823 −42578.1 −1.80338 −0.901689 0.432384i 0.857672π-0.857672\pi
−0.901689 + 0.432384i 0.857672π0.857672\pi
824824 −81107.7 −3.42903
825825 0 0
826826 20422.0 0.860257
827827 733.624 0.0308472 0.0154236 0.999881i 0.495090π-0.495090\pi
0.0154236 + 0.999881i 0.495090π0.495090\pi
828828 0 0
829829 15778.0 0.661028 0.330514 0.943801i 0.392778π-0.392778\pi
0.330514 + 0.943801i 0.392778π0.392778\pi
830830 13344.9 0.558084
831831 0 0
832832 −2037.73 −0.0849104
833833 6458.26 0.268626
834834 0 0
835835 8412.83 0.348668
836836 −10037.9 −0.415275
837837 0 0
838838 −23286.2 −0.959916
839839 16776.8 0.690343 0.345172 0.938540i 0.387821π-0.387821\pi
0.345172 + 0.938540i 0.387821π0.387821\pi
840840 0 0
841841 29609.7 1.21406
842842 −29983.0 −1.22717
843843 0 0
844844 −53472.6 −2.18081
845845 −10423.9 −0.424372
846846 0 0
847847 −7943.56 −0.322248
848848 31900.2 1.29181
849849 0 0
850850 16969.7 0.684773
851851 −28695.1 −1.15588
852852 0 0
853853 7646.57 0.306933 0.153466 0.988154i 0.450956π-0.450956\pi
0.153466 + 0.988154i 0.450956π0.450956\pi
854854 −6777.95 −0.271589
855855 0 0
856856 −106544. −4.25419
857857 26980.3 1.07541 0.537707 0.843132i 0.319291π-0.319291\pi
0.537707 + 0.843132i 0.319291π0.319291\pi
858858 0 0
859859 3034.02 0.120511 0.0602557 0.998183i 0.480808π-0.480808\pi
0.0602557 + 0.998183i 0.480808π0.480808\pi
860860 −39996.4 −1.58589
861861 0 0
862862 −43171.2 −1.70582
863863 −25954.5 −1.02376 −0.511879 0.859058i 0.671050π-0.671050\pi
−0.511879 + 0.859058i 0.671050π0.671050\pi
864864 0 0
865865 16057.6 0.631186
866866 13534.7 0.531095
867867 0 0
868868 −21459.6 −0.839155
869869 2668.31 0.104161
870870 0 0
871871 9233.42 0.359199
872872 −47177.6 −1.83215
873873 0 0
874874 −20418.6 −0.790238
875875 875.000 0.0338062
876876 0 0
877877 −11235.7 −0.432616 −0.216308 0.976325i 0.569402π-0.569402\pi
−0.216308 + 0.976325i 0.569402π0.569402\pi
878878 −21233.7 −0.816176
879879 0 0
880880 −9170.07 −0.351276
881881 −4594.31 −0.175694 −0.0878468 0.996134i 0.527999π-0.527999\pi
−0.0878468 + 0.996134i 0.527999π0.527999\pi
882882 0 0
883883 −14162.1 −0.539741 −0.269871 0.962897i 0.586981π-0.586981\pi
−0.269871 + 0.962897i 0.586981π0.586981\pi
884884 −25862.1 −0.983979
885885 0 0
886886 −1083.20 −0.0410733
887887 −31024.2 −1.17440 −0.587199 0.809442i 0.699770π-0.699770\pi
−0.587199 + 0.809442i 0.699770π0.699770\pi
888888 0 0
889889 17508.1 0.660519
890890 −15407.9 −0.580309
891891 0 0
892892 85047.7 3.19238
893893 11439.5 0.428676
894894 0 0
895895 16559.9 0.618475
896896 −6546.46 −0.244087
897897 0 0
898898 22734.4 0.844828
899899 38458.5 1.42677
900900 0 0
901901 32111.9 1.18735
902902 8820.55 0.325601
903903 0 0
904904 111169. 4.09008
905905 10312.1 0.378770
906906 0 0
907907 −10594.5 −0.387855 −0.193928 0.981016i 0.562123π-0.562123\pi
−0.193928 + 0.981016i 0.562123π0.562123\pi
908908 −47180.2 −1.72437
909909 0 0
910910 −1909.44 −0.0695574
911911 1469.37 0.0534384 0.0267192 0.999643i 0.491494π-0.491494\pi
0.0267192 + 0.999643i 0.491494π0.491494\pi
912912 0 0
913913 −7259.17 −0.263136
914914 73931.9 2.67555
915915 0 0
916916 37184.1 1.34126
917917 3739.33 0.134660
918918 0 0
919919 41834.6 1.50163 0.750813 0.660515i 0.229662π-0.229662\pi
0.750813 + 0.660515i 0.229662π0.229662\pi
920920 −27770.9 −0.995194
921921 0 0
922922 −73991.2 −2.64292
923923 1872.85 0.0667884
924924 0 0
925925 7000.10 0.248824
926926 59916.9 2.12634
927927 0 0
928928 −55941.7 −1.97885
929929 8570.23 0.302670 0.151335 0.988483i 0.451643π-0.451643\pi
0.151335 + 0.988483i 0.451643π0.451643\pi
930930 0 0
931931 1895.67 0.0667326
932932 52063.1 1.82981
933933 0 0
934934 −62379.3 −2.18534
935935 −9230.91 −0.322870
936936 0 0
937937 41260.3 1.43854 0.719271 0.694730i 0.244476π-0.244476\pi
0.719271 + 0.694730i 0.244476π0.244476\pi
938938 −31423.5 −1.09383
939939 0 0
940940 27386.3 0.950259
941941 47969.6 1.66181 0.830905 0.556414i 0.187823π-0.187823\pi
0.830905 + 0.556414i 0.187823π0.187823\pi
942942 0 0
943943 12530.5 0.432714
944944 74170.6 2.55725
945945 0 0
946946 31152.9 1.07068
947947 −15666.3 −0.537577 −0.268789 0.963199i 0.586623π-0.586623\pi
−0.268789 + 0.963199i 0.586623π0.586623\pi
948948 0 0
949949 2336.02 0.0799057
950950 4981.06 0.170113
951951 0 0
952952 50002.7 1.70231
953953 27495.7 0.934600 0.467300 0.884099i 0.345227π-0.345227\pi
0.467300 + 0.884099i 0.345227π0.345227\pi
954954 0 0
955955 13915.0 0.471497
956956 34244.0 1.15851
957957 0 0
958958 58612.4 1.97670
959959 3522.11 0.118597
960960 0 0
961961 −2400.42 −0.0805755
962962 −15275.7 −0.511963
963963 0 0
964964 106003. 3.54164
965965 1501.46 0.0500869
966966 0 0
967967 51246.2 1.70421 0.852103 0.523374i 0.175327π-0.175327\pi
0.852103 + 0.523374i 0.175327π0.175327\pi
968968 −61502.6 −2.04212
969969 0 0
970970 −48468.6 −1.60436
971971 40446.0 1.33674 0.668370 0.743829i 0.266992π-0.266992\pi
0.668370 + 0.743829i 0.266992π0.266992\pi
972972 0 0
973973 9974.08 0.328627
974974 −59821.2 −1.96796
975975 0 0
976976 −24616.8 −0.807342
977977 21457.8 0.702656 0.351328 0.936253i 0.385730π-0.385730\pi
0.351328 + 0.936253i 0.385730π0.385730\pi
978978 0 0
979979 8381.35 0.273615
980980 4538.26 0.147928
981981 0 0
982982 −31135.6 −1.01179
983983 −8746.68 −0.283801 −0.141900 0.989881i 0.545321π-0.545321\pi
−0.141900 + 0.989881i 0.545321π0.545321\pi
984984 0 0
985985 −7428.18 −0.240286
986986 −157734. −5.09461
987987 0 0
988988 −7591.22 −0.244442
989989 44255.8 1.42291
990990 0 0
991991 −29046.2 −0.931061 −0.465531 0.885032i 0.654137π-0.654137\pi
−0.465531 + 0.885032i 0.654137π0.654137\pi
992992 −39842.3 −1.27520
993993 0 0
994994 −6373.75 −0.203383
995995 −15202.8 −0.484382
996996 0 0
997997 −4656.30 −0.147910 −0.0739552 0.997262i 0.523562π-0.523562\pi
−0.0739552 + 0.997262i 0.523562π0.523562\pi
998998 4430.52 0.140527
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 315.4.a.o.1.3 yes 3
3.2 odd 2 315.4.a.n.1.1 3
5.4 even 2 1575.4.a.bb.1.1 3
7.6 odd 2 2205.4.a.bl.1.3 3
15.14 odd 2 1575.4.a.be.1.3 3
21.20 even 2 2205.4.a.bk.1.1 3
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
315.4.a.n.1.1 3 3.2 odd 2
315.4.a.o.1.3 yes 3 1.1 even 1 trivial
1575.4.a.bb.1.1 3 5.4 even 2
1575.4.a.be.1.3 3 15.14 odd 2
2205.4.a.bk.1.1 3 21.20 even 2
2205.4.a.bl.1.3 3 7.6 odd 2