Properties

Label 4925.2.a.k.1.5
Level 49254925
Weight 22
Character 4925.1
Self dual yes
Analytic conductor 39.32639.326
Analytic rank 00
Dimension 1414
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] = [4925,2,Mod(1,4925)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(4925, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("4925.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 4925=52197 4925 = 5^{2} \cdot 197
Weight: k k == 2 2
Character orbit: [χ][\chi] == 4925.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: 39.326322995539.3263229955
Analytic rank: 00
Dimension: 1414
Coefficient field: Q[x]/(x14)\mathbb{Q}[x]/(x^{14} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x146x13x12+66x1183x10218x9+446x8+178x7782x6+1 x^{14} - 6 x^{13} - x^{12} + 66 x^{11} - 83 x^{10} - 218 x^{9} + 446 x^{8} + 178 x^{7} - 782 x^{6} + \cdots - 1 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 985)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.5
Root 0.236045-0.236045 of defining polynomial
Character χ\chi == 4925.1

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) == q0.236045q2+2.87112q31.94428q40.677712q61.02221q7+0.931027q8+5.24331q9+0.916844q115.58226q124.99719q13+0.241286q14+3.66880q160.345734q171.23766q185.30778q192.93487q210.216416q22+7.21308q23+2.67309q24+1.17956q26+6.44081q27+1.98746q28+4.17022q29+9.99162q312.72806q32+2.63237q33+0.0816088q3410.1945q362.64110q37+1.25287q3814.3475q399.80072q41+0.692761q42+12.7545q431.78260q441.70261q46+8.43174q47+10.5336q485.95510q490.992644q51+9.71595q52+3.66822q531.52032q540.951701q5615.2393q570.984359q58+4.19018q59+2.70353q612.35847q625.35974q636.69366q640.621356q669.72899q67+0.672205q68+20.7096q69+0.435154q71+4.88167q72+6.14822q73+0.623419q74+10.3198q760.937203q77+3.38665q784.36466q79+2.76239q81+2.31341q82+9.26666q83+5.70622q843.01064q86+11.9732q87+0.853607q88+14.2366q89+5.10815q9114.0243q92+28.6871q931.99027q947.83257q96+11.0151q97+1.40567q98+4.80730q99+O(q100)q-0.236045 q^{2} +2.87112 q^{3} -1.94428 q^{4} -0.677712 q^{6} -1.02221 q^{7} +0.931027 q^{8} +5.24331 q^{9} +0.916844 q^{11} -5.58226 q^{12} -4.99719 q^{13} +0.241286 q^{14} +3.66880 q^{16} -0.345734 q^{17} -1.23766 q^{18} -5.30778 q^{19} -2.93487 q^{21} -0.216416 q^{22} +7.21308 q^{23} +2.67309 q^{24} +1.17956 q^{26} +6.44081 q^{27} +1.98746 q^{28} +4.17022 q^{29} +9.99162 q^{31} -2.72806 q^{32} +2.63237 q^{33} +0.0816088 q^{34} -10.1945 q^{36} -2.64110 q^{37} +1.25287 q^{38} -14.3475 q^{39} -9.80072 q^{41} +0.692761 q^{42} +12.7545 q^{43} -1.78260 q^{44} -1.70261 q^{46} +8.43174 q^{47} +10.5336 q^{48} -5.95510 q^{49} -0.992644 q^{51} +9.71595 q^{52} +3.66822 q^{53} -1.52032 q^{54} -0.951701 q^{56} -15.2393 q^{57} -0.984359 q^{58} +4.19018 q^{59} +2.70353 q^{61} -2.35847 q^{62} -5.35974 q^{63} -6.69366 q^{64} -0.621356 q^{66} -9.72899 q^{67} +0.672205 q^{68} +20.7096 q^{69} +0.435154 q^{71} +4.88167 q^{72} +6.14822 q^{73} +0.623419 q^{74} +10.3198 q^{76} -0.937203 q^{77} +3.38665 q^{78} -4.36466 q^{79} +2.76239 q^{81} +2.31341 q^{82} +9.26666 q^{83} +5.70622 q^{84} -3.01064 q^{86} +11.9732 q^{87} +0.853607 q^{88} +14.2366 q^{89} +5.10815 q^{91} -14.0243 q^{92} +28.6871 q^{93} -1.99027 q^{94} -7.83257 q^{96} +11.0151 q^{97} +1.40567 q^{98} +4.80730 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 14q+6q2+7q3+10q4+5q6+4q7+12q8+13q95q11+10q12+15q1315q14+18q16+18q17+29q18+20q195q2112q22+42q23++32q99+O(q100) 14 q + 6 q^{2} + 7 q^{3} + 10 q^{4} + 5 q^{6} + 4 q^{7} + 12 q^{8} + 13 q^{9} - 5 q^{11} + 10 q^{12} + 15 q^{13} - 15 q^{14} + 18 q^{16} + 18 q^{17} + 29 q^{18} + 20 q^{19} - 5 q^{21} - 12 q^{22} + 42 q^{23}+ \cdots + 32 q^{99}+O(q^{100}) Copy content Toggle raw display

Coefficient data

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



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.236045 −0.166909 −0.0834544 0.996512i 0.526595π-0.526595\pi
−0.0834544 + 0.996512i 0.526595π0.526595\pi
33 2.87112 1.65764 0.828820 0.559515i 0.189013π-0.189013\pi
0.828820 + 0.559515i 0.189013π0.189013\pi
44 −1.94428 −0.972141
55 0 0
66 −0.677712 −0.276675
77 −1.02221 −0.386357 −0.193179 0.981164i 0.561880π-0.561880\pi
−0.193179 + 0.981164i 0.561880π0.561880\pi
88 0.931027 0.329168
99 5.24331 1.74777
1010 0 0
1111 0.916844 0.276439 0.138219 0.990402i 0.455862π-0.455862\pi
0.138219 + 0.990402i 0.455862π0.455862\pi
1212 −5.58226 −1.61146
1313 −4.99719 −1.38597 −0.692985 0.720952i 0.743705π-0.743705\pi
−0.692985 + 0.720952i 0.743705π0.743705\pi
1414 0.241286 0.0644864
1515 0 0
1616 3.66880 0.917200
1717 −0.345734 −0.0838529 −0.0419264 0.999121i 0.513350π-0.513350\pi
−0.0419264 + 0.999121i 0.513350π0.513350\pi
1818 −1.23766 −0.291718
1919 −5.30778 −1.21769 −0.608845 0.793290i 0.708367π-0.708367\pi
−0.608845 + 0.793290i 0.708367π0.708367\pi
2020 0 0
2121 −2.93487 −0.640441
2222 −0.216416 −0.0461401
2323 7.21308 1.50403 0.752015 0.659146i 0.229082π-0.229082\pi
0.752015 + 0.659146i 0.229082π0.229082\pi
2424 2.67309 0.545642
2525 0 0
2626 1.17956 0.231331
2727 6.44081 1.23953
2828 1.98746 0.375594
2929 4.17022 0.774391 0.387195 0.921998i 0.373444π-0.373444\pi
0.387195 + 0.921998i 0.373444π0.373444\pi
3030 0 0
3131 9.99162 1.79455 0.897274 0.441474i 0.145544π-0.145544\pi
0.897274 + 0.441474i 0.145544π0.145544\pi
3232 −2.72806 −0.482257
3333 2.63237 0.458236
3434 0.0816088 0.0139958
3535 0 0
3636 −10.1945 −1.69908
3737 −2.64110 −0.434195 −0.217097 0.976150i 0.569659π-0.569659\pi
−0.217097 + 0.976150i 0.569659π0.569659\pi
3838 1.25287 0.203243
3939 −14.3475 −2.29744
4040 0 0
4141 −9.80072 −1.53061 −0.765307 0.643665i 0.777413π-0.777413\pi
−0.765307 + 0.643665i 0.777413π0.777413\pi
4242 0.692761 0.106895
4343 12.7545 1.94505 0.972524 0.232804i 0.0747899π-0.0747899\pi
0.972524 + 0.232804i 0.0747899π0.0747899\pi
4444 −1.78260 −0.268738
4545 0 0
4646 −1.70261 −0.251036
4747 8.43174 1.22990 0.614948 0.788568i 0.289177π-0.289177\pi
0.614948 + 0.788568i 0.289177π0.289177\pi
4848 10.5336 1.52039
4949 −5.95510 −0.850728
5050 0 0
5151 −0.992644 −0.138998
5252 9.71595 1.34736
5353 3.66822 0.503869 0.251935 0.967744i 0.418933π-0.418933\pi
0.251935 + 0.967744i 0.418933π0.418933\pi
5454 −1.52032 −0.206889
5555 0 0
5656 −0.951701 −0.127176
5757 −15.2393 −2.01849
5858 −0.984359 −0.129253
5959 4.19018 0.545515 0.272757 0.962083i 0.412064π-0.412064\pi
0.272757 + 0.962083i 0.412064π0.412064\pi
6060 0 0
6161 2.70353 0.346152 0.173076 0.984908i 0.444629π-0.444629\pi
0.173076 + 0.984908i 0.444629π0.444629\pi
6262 −2.35847 −0.299526
6363 −5.35974 −0.675264
6464 −6.69366 −0.836708
6565 0 0
6666 −0.621356 −0.0764837
6767 −9.72899 −1.18859 −0.594293 0.804249i 0.702568π-0.702568\pi
−0.594293 + 0.804249i 0.702568π0.702568\pi
6868 0.672205 0.0815169
6969 20.7096 2.49314
7070 0 0
7171 0.435154 0.0516432 0.0258216 0.999667i 0.491780π-0.491780\pi
0.0258216 + 0.999667i 0.491780π0.491780\pi
7272 4.88167 0.575310
7373 6.14822 0.719595 0.359797 0.933030i 0.382846π-0.382846\pi
0.359797 + 0.933030i 0.382846π0.382846\pi
7474 0.623419 0.0724709
7575 0 0
7676 10.3198 1.18377
7777 −0.937203 −0.106804
7878 3.38665 0.383463
7979 −4.36466 −0.491063 −0.245531 0.969389i 0.578962π-0.578962\pi
−0.245531 + 0.969389i 0.578962π0.578962\pi
8080 0 0
8181 2.76239 0.306932
8282 2.31341 0.255473
8383 9.26666 1.01715 0.508574 0.861018i 0.330173π-0.330173\pi
0.508574 + 0.861018i 0.330173π0.330173\pi
8484 5.70622 0.622600
8585 0 0
8686 −3.01064 −0.324646
8787 11.9732 1.28366
8888 0.853607 0.0909948
8989 14.2366 1.50908 0.754538 0.656256i 0.227861π-0.227861\pi
0.754538 + 0.656256i 0.227861π0.227861\pi
9090 0 0
9191 5.10815 0.535480
9292 −14.0243 −1.46213
9393 28.6871 2.97471
9494 −1.99027 −0.205281
9595 0 0
9696 −7.83257 −0.799408
9797 11.0151 1.11842 0.559209 0.829027i 0.311105π-0.311105\pi
0.559209 + 0.829027i 0.311105π0.311105\pi
9898 1.40567 0.141994
9999 4.80730 0.483152
100100 0 0
101101 11.5252 1.14680 0.573400 0.819276i 0.305624π-0.305624\pi
0.573400 + 0.819276i 0.305624π0.305624\pi
102102 0.234308 0.0232000
103103 −4.12363 −0.406313 −0.203157 0.979146i 0.565120π-0.565120\pi
−0.203157 + 0.979146i 0.565120π0.565120\pi
104104 −4.65252 −0.456217
105105 0 0
106106 −0.865864 −0.0841002
107107 10.2697 0.992805 0.496402 0.868092i 0.334654π-0.334654\pi
0.496402 + 0.868092i 0.334654π0.334654\pi
108108 −12.5228 −1.20500
109109 19.6212 1.87937 0.939685 0.342041i 0.111118π-0.111118\pi
0.939685 + 0.342041i 0.111118π0.111118\pi
110110 0 0
111111 −7.58292 −0.719739
112112 −3.75027 −0.354367
113113 14.9685 1.40812 0.704058 0.710142i 0.251369π-0.251369\pi
0.704058 + 0.710142i 0.251369π0.251369\pi
114114 3.59715 0.336904
115115 0 0
116116 −8.10809 −0.752817
117117 −26.2018 −2.42236
118118 −0.989070 −0.0910512
119119 0.353411 0.0323972
120120 0 0
121121 −10.1594 −0.923582
122122 −0.638154 −0.0577758
123123 −28.1390 −2.53721
124124 −19.4265 −1.74455
125125 0 0
126126 1.26514 0.112708
127127 −5.21953 −0.463159 −0.231579 0.972816i 0.574389π-0.574389\pi
−0.231579 + 0.972816i 0.574389π0.574389\pi
128128 7.03611 0.621910
129129 36.6197 3.22419
130130 0 0
131131 −1.76360 −0.154087 −0.0770433 0.997028i 0.524548π-0.524548\pi
−0.0770433 + 0.997028i 0.524548π0.524548\pi
132132 −5.11807 −0.445470
133133 5.42564 0.470463
134134 2.29648 0.198385
135135 0 0
136136 −0.321888 −0.0276017
137137 14.9252 1.27514 0.637571 0.770392i 0.279939π-0.279939\pi
0.637571 + 0.770392i 0.279939π0.279939\pi
138138 −4.88839 −0.416127
139139 −10.6367 −0.902195 −0.451097 0.892475i 0.648967π-0.648967\pi
−0.451097 + 0.892475i 0.648967π0.648967\pi
140140 0 0
141141 24.2085 2.03873
142142 −0.102716 −0.00861971
143143 −4.58164 −0.383136
144144 19.2367 1.60306
145145 0 0
146146 −1.45125 −0.120107
147147 −17.0978 −1.41020
148148 5.13505 0.422099
149149 −7.93007 −0.649656 −0.324828 0.945773i 0.605306π-0.605306\pi
−0.324828 + 0.945773i 0.605306π0.605306\pi
150150 0 0
151151 −23.5423 −1.91584 −0.957921 0.287033i 0.907331π-0.907331\pi
−0.957921 + 0.287033i 0.907331π0.907331\pi
152152 −4.94169 −0.400824
153153 −1.81279 −0.146556
154154 0.221222 0.0178266
155155 0 0
156156 27.8956 2.23344
157157 −6.13158 −0.489353 −0.244677 0.969605i 0.578682π-0.578682\pi
−0.244677 + 0.969605i 0.578682π0.578682\pi
158158 1.03025 0.0819627
159159 10.5319 0.835234
160160 0 0
161161 −7.37325 −0.581093
162162 −0.652047 −0.0512297
163163 7.33018 0.574144 0.287072 0.957909i 0.407318π-0.407318\pi
0.287072 + 0.957909i 0.407318π0.407318\pi
164164 19.0554 1.48797
165165 0 0
166166 −2.18735 −0.169771
167167 10.1434 0.784921 0.392461 0.919769i 0.371624π-0.371624\pi
0.392461 + 0.919769i 0.371624π0.371624\pi
168168 −2.73244 −0.210813
169169 11.9719 0.920915
170170 0 0
171171 −27.8304 −2.12824
172172 −24.7984 −1.89086
173173 −2.03837 −0.154975 −0.0774873 0.996993i 0.524690π-0.524690\pi
−0.0774873 + 0.996993i 0.524690π0.524690\pi
174174 −2.82621 −0.214254
175175 0 0
176176 3.36372 0.253550
177177 12.0305 0.904267
178178 −3.36047 −0.251878
179179 0.681587 0.0509442 0.0254721 0.999676i 0.491891π-0.491891\pi
0.0254721 + 0.999676i 0.491891π0.491891\pi
180180 0 0
181181 3.58428 0.266417 0.133209 0.991088i 0.457472π-0.457472\pi
0.133209 + 0.991088i 0.457472π0.457472\pi
182182 −1.20575 −0.0893763
183183 7.76216 0.573795
184184 6.71557 0.495078
185185 0 0
186186 −6.77144 −0.496506
187187 −0.316985 −0.0231802
188188 −16.3937 −1.19563
189189 −6.58383 −0.478903
190190 0 0
191191 15.4485 1.11782 0.558908 0.829229i 0.311220π-0.311220\pi
0.558908 + 0.829229i 0.311220π0.311220\pi
192192 −19.2183 −1.38696
193193 4.87672 0.351034 0.175517 0.984476i 0.443840π-0.443840\pi
0.175517 + 0.984476i 0.443840π0.443840\pi
194194 −2.60006 −0.186674
195195 0 0
196196 11.5784 0.827028
197197 1.00000 0.0712470
198198 −1.13474 −0.0806423
199199 −20.0659 −1.42244 −0.711218 0.702971i 0.751856π-0.751856\pi
−0.711218 + 0.702971i 0.751856π0.751856\pi
200200 0 0
201201 −27.9331 −1.97025
202202 −2.72046 −0.191411
203203 −4.26282 −0.299192
204204 1.92998 0.135126
205205 0 0
206206 0.973361 0.0678173
207207 37.8204 2.62870
208208 −18.3337 −1.27121
209209 −4.86641 −0.336617
210210 0 0
211211 −4.29538 −0.295706 −0.147853 0.989009i 0.547236π-0.547236\pi
−0.147853 + 0.989009i 0.547236π0.547236\pi
212212 −7.13206 −0.489832
213213 1.24938 0.0856059
214214 −2.42410 −0.165708
215215 0 0
216216 5.99657 0.408015
217217 −10.2135 −0.693337
218218 −4.63148 −0.313683
219219 17.6523 1.19283
220220 0 0
221221 1.72770 0.116218
222222 1.78991 0.120131
223223 −13.6428 −0.913589 −0.456795 0.889572i 0.651003π-0.651003\pi
−0.456795 + 0.889572i 0.651003π0.651003\pi
224224 2.78863 0.186323
225225 0 0
226226 −3.53323 −0.235027
227227 8.32757 0.552720 0.276360 0.961054i 0.410872π-0.410872\pi
0.276360 + 0.961054i 0.410872π0.410872\pi
228228 29.6294 1.96226
229229 −27.7853 −1.83611 −0.918053 0.396458i 0.870239π-0.870239\pi
−0.918053 + 0.396458i 0.870239π0.870239\pi
230230 0 0
231231 −2.69082 −0.177043
232232 3.88259 0.254904
233233 15.7592 1.03242 0.516211 0.856462i 0.327342π-0.327342\pi
0.516211 + 0.856462i 0.327342π0.327342\pi
234234 6.18480 0.404313
235235 0 0
236236 −8.14689 −0.530318
237237 −12.5314 −0.814005
238238 −0.0834209 −0.00540737
239239 −26.6777 −1.72564 −0.862818 0.505515i 0.831303π-0.831303\pi
−0.862818 + 0.505515i 0.831303π0.831303\pi
240240 0 0
241241 7.59582 0.489290 0.244645 0.969613i 0.421329π-0.421329\pi
0.244645 + 0.969613i 0.421329π0.421329\pi
242242 2.39807 0.154154
243243 −11.3913 −0.730752
244244 −5.25643 −0.336509
245245 0 0
246246 6.64206 0.423482
247247 26.5240 1.68768
248248 9.30247 0.590707
249249 26.6057 1.68607
250250 0 0
251251 −10.2993 −0.650088 −0.325044 0.945699i 0.605379π-0.605379\pi
−0.325044 + 0.945699i 0.605379π0.605379\pi
252252 10.4209 0.656452
253253 6.61327 0.415773
254254 1.23204 0.0773053
255255 0 0
256256 11.7265 0.732905
257257 16.8749 1.05263 0.526315 0.850290i 0.323573π-0.323573\pi
0.526315 + 0.850290i 0.323573π0.323573\pi
258258 −8.64390 −0.538146
259259 2.69975 0.167754
260260 0 0
261261 21.8658 1.35346
262262 0.416289 0.0257184
263263 −8.57005 −0.528452 −0.264226 0.964461i 0.585116π-0.585116\pi
−0.264226 + 0.964461i 0.585116π0.585116\pi
264264 2.45080 0.150837
265265 0 0
266266 −1.28069 −0.0785244
267267 40.8749 2.50151
268268 18.9159 1.15547
269269 26.3927 1.60919 0.804596 0.593822i 0.202382π-0.202382\pi
0.804596 + 0.593822i 0.202382π0.202382\pi
270270 0 0
271271 27.5722 1.67489 0.837447 0.546518i 0.184047π-0.184047\pi
0.837447 + 0.546518i 0.184047π0.184047\pi
272272 −1.26843 −0.0769099
273273 14.6661 0.887633
274274 −3.52300 −0.212832
275275 0 0
276276 −40.2653 −2.42369
277277 −9.89475 −0.594518 −0.297259 0.954797i 0.596072π-0.596072\pi
−0.297259 + 0.954797i 0.596072π0.596072\pi
278278 2.51074 0.150584
279279 52.3892 3.13646
280280 0 0
281281 27.3790 1.63330 0.816648 0.577135i 0.195830π-0.195830\pi
0.816648 + 0.577135i 0.195830π0.195830\pi
282282 −5.71429 −0.340281
283283 7.11007 0.422650 0.211325 0.977416i 0.432222π-0.432222\pi
0.211325 + 0.977416i 0.432222π0.432222\pi
284284 −0.846062 −0.0502045
285285 0 0
286286 1.08147 0.0639488
287287 10.0183 0.591364
288288 −14.3040 −0.842874
289289 −16.8805 −0.992969
290290 0 0
291291 31.6257 1.85393
292292 −11.9539 −0.699548
293293 −15.7053 −0.917512 −0.458756 0.888562i 0.651705π-0.651705\pi
−0.458756 + 0.888562i 0.651705π0.651705\pi
294294 4.03584 0.235375
295295 0 0
296296 −2.45894 −0.142923
297297 5.90522 0.342656
298298 1.87185 0.108433
299299 −36.0451 −2.08454
300300 0 0
301301 −13.0377 −0.751483
302302 5.55702 0.319771
303303 33.0902 1.90098
304304 −19.4732 −1.11686
305305 0 0
306306 0.427900 0.0244614
307307 8.97401 0.512174 0.256087 0.966654i 0.417567π-0.417567\pi
0.256087 + 0.966654i 0.417567π0.417567\pi
308308 1.82219 0.103829
309309 −11.8394 −0.673521
310310 0 0
311311 −9.76960 −0.553983 −0.276992 0.960872i 0.589337π-0.589337\pi
−0.276992 + 0.960872i 0.589337π0.589337\pi
312312 −13.3579 −0.756243
313313 0.449986 0.0254347 0.0127174 0.999919i 0.495952π-0.495952\pi
0.0127174 + 0.999919i 0.495952π0.495952\pi
314314 1.44733 0.0816773
315315 0 0
316316 8.48613 0.477382
317317 27.2882 1.53266 0.766330 0.642447i 0.222081π-0.222081\pi
0.766330 + 0.642447i 0.222081π0.222081\pi
318318 −2.48600 −0.139408
319319 3.82344 0.214072
320320 0 0
321321 29.4854 1.64571
322322 1.74042 0.0969896
323323 1.83508 0.102107
324324 −5.37087 −0.298381
325325 0 0
326326 −1.73025 −0.0958297
327327 56.3348 3.11532
328328 −9.12473 −0.503829
329329 −8.61897 −0.475179
330330 0 0
331331 4.69448 0.258032 0.129016 0.991643i 0.458818π-0.458818\pi
0.129016 + 0.991643i 0.458818π0.458818\pi
332332 −18.0170 −0.988812
333333 −13.8481 −0.758873
334334 −2.39430 −0.131010
335335 0 0
336336 −10.7675 −0.587413
337337 1.18729 0.0646760 0.0323380 0.999477i 0.489705π-0.489705\pi
0.0323380 + 0.999477i 0.489705π0.489705\pi
338338 −2.82590 −0.153709
339339 42.9763 2.33415
340340 0 0
341341 9.16076 0.496083
342342 6.56921 0.355222
343343 13.2428 0.715042
344344 11.8748 0.640247
345345 0 0
346346 0.481147 0.0258666
347347 −2.21480 −0.118896 −0.0594482 0.998231i 0.518934π-0.518934\pi
−0.0594482 + 0.998231i 0.518934π0.518934\pi
348348 −23.2793 −1.24790
349349 22.6828 1.21418 0.607092 0.794632i 0.292336π-0.292336\pi
0.607092 + 0.794632i 0.292336π0.292336\pi
350350 0 0
351351 −32.1860 −1.71796
352352 −2.50120 −0.133315
353353 12.2691 0.653016 0.326508 0.945194i 0.394128π-0.394128\pi
0.326508 + 0.945194i 0.394128π0.394128\pi
354354 −2.83973 −0.150930
355355 0 0
356356 −27.6800 −1.46704
357357 1.01469 0.0537029
358358 −0.160885 −0.00850304
359359 −18.9950 −1.00252 −0.501258 0.865298i 0.667129π-0.667129\pi
−0.501258 + 0.865298i 0.667129π0.667129\pi
360360 0 0
361361 9.17256 0.482767
362362 −0.846050 −0.0444674
363363 −29.1688 −1.53097
364364 −9.93169 −0.520562
365365 0 0
366366 −1.83222 −0.0957715
367367 −35.4991 −1.85304 −0.926519 0.376249i 0.877214π-0.877214\pi
−0.926519 + 0.376249i 0.877214π0.877214\pi
368368 26.4633 1.37950
369369 −51.3882 −2.67516
370370 0 0
371371 −3.74968 −0.194673
372372 −55.7759 −2.89184
373373 −22.1497 −1.14687 −0.573434 0.819252i 0.694389π-0.694389\pi
−0.573434 + 0.819252i 0.694389π0.694389\pi
374374 0.0748225 0.00386898
375375 0 0
376376 7.85018 0.404842
377377 −20.8394 −1.07328
378378 1.55408 0.0799332
379379 −0.0471576 −0.00242232 −0.00121116 0.999999i 0.500386π-0.500386\pi
−0.00121116 + 0.999999i 0.500386π0.500386\pi
380380 0 0
381381 −14.9859 −0.767750
382382 −3.64654 −0.186573
383383 27.8084 1.42094 0.710470 0.703727i 0.248482π-0.248482\pi
0.710470 + 0.703727i 0.248482π0.248482\pi
384384 20.2015 1.03090
385385 0 0
386386 −1.15112 −0.0585907
387387 66.8760 3.39950
388388 −21.4165 −1.08726
389389 −5.91034 −0.299666 −0.149833 0.988711i 0.547874π-0.547874\pi
−0.149833 + 0.988711i 0.547874π0.547874\pi
390390 0 0
391391 −2.49381 −0.126117
392392 −5.54436 −0.280032
393393 −5.06351 −0.255420
394394 −0.236045 −0.0118918
395395 0 0
396396 −9.34675 −0.469692
397397 10.7928 0.541673 0.270836 0.962625i 0.412700π-0.412700\pi
0.270836 + 0.962625i 0.412700π0.412700\pi
398398 4.73646 0.237417
399399 15.5777 0.779858
400400 0 0
401401 −25.3129 −1.26407 −0.632034 0.774941i 0.717780π-0.717780\pi
−0.632034 + 0.774941i 0.717780π0.717780\pi
402402 6.59345 0.328851
403403 −49.9300 −2.48719
404404 −22.4082 −1.11485
405405 0 0
406406 1.00622 0.0499377
407407 −2.42148 −0.120028
408408 −0.924178 −0.0457536
409409 11.0910 0.548415 0.274207 0.961671i 0.411585π-0.411585\pi
0.274207 + 0.961671i 0.411585π0.411585\pi
410410 0 0
411411 42.8519 2.11373
412412 8.01750 0.394994
413413 −4.28322 −0.210764
414414 −8.92731 −0.438753
415415 0 0
416416 13.6326 0.668394
417417 −30.5393 −1.49551
418418 1.14869 0.0561843
419419 −29.8386 −1.45771 −0.728856 0.684667i 0.759947π-0.759947\pi
−0.728856 + 0.684667i 0.759947π0.759947\pi
420420 0 0
421421 −31.3685 −1.52881 −0.764403 0.644739i 0.776966π-0.776966\pi
−0.764403 + 0.644739i 0.776966π0.776966\pi
422422 1.01390 0.0493560
423423 44.2103 2.14958
424424 3.41521 0.165857
425425 0 0
426426 −0.294909 −0.0142884
427427 −2.76356 −0.133738
428428 −19.9671 −0.965147
429429 −13.1544 −0.635102
430430 0 0
431431 −28.4126 −1.36859 −0.684293 0.729207i 0.739889π-0.739889\pi
−0.684293 + 0.729207i 0.739889π0.739889\pi
432432 23.6301 1.13690
433433 −29.6797 −1.42631 −0.713157 0.701005i 0.752735π-0.752735\pi
−0.713157 + 0.701005i 0.752735π0.752735\pi
434434 2.41084 0.115724
435435 0 0
436436 −38.1492 −1.82701
437437 −38.2855 −1.83144
438438 −4.16672 −0.199094
439439 19.0177 0.907664 0.453832 0.891087i 0.350057π-0.350057\pi
0.453832 + 0.891087i 0.350057π0.350057\pi
440440 0 0
441441 −31.2244 −1.48688
442442 −0.407814 −0.0193977
443443 12.5365 0.595628 0.297814 0.954624i 0.403742π-0.403742\pi
0.297814 + 0.954624i 0.403742π0.403742\pi
444444 14.7433 0.699688
445445 0 0
446446 3.22031 0.152486
447447 −22.7681 −1.07690
448448 6.84230 0.323268
449449 17.9879 0.848900 0.424450 0.905451i 0.360467π-0.360467\pi
0.424450 + 0.905451i 0.360467π0.360467\pi
450450 0 0
451451 −8.98573 −0.423122
452452 −29.1030 −1.36889
453453 −67.5926 −3.17578
454454 −1.96568 −0.0922539
455455 0 0
456456 −14.1882 −0.664422
457457 27.3085 1.27744 0.638718 0.769441i 0.279465π-0.279465\pi
0.638718 + 0.769441i 0.279465π0.279465\pi
458458 6.55858 0.306462
459459 −2.22681 −0.103939
460460 0 0
461461 −8.85519 −0.412427 −0.206214 0.978507i 0.566114π-0.566114\pi
−0.206214 + 0.978507i 0.566114π0.566114\pi
462462 0.635154 0.0295500
463463 17.7027 0.822714 0.411357 0.911474i 0.365055π-0.365055\pi
0.411357 + 0.911474i 0.365055π0.365055\pi
464464 15.2997 0.710271
465465 0 0
466466 −3.71988 −0.172320
467467 12.5779 0.582035 0.291018 0.956718i 0.406006π-0.406006\pi
0.291018 + 0.956718i 0.406006π0.406006\pi
468468 50.9437 2.35488
469469 9.94502 0.459219
470470 0 0
471471 −17.6045 −0.811171
472472 3.90117 0.179566
473473 11.6939 0.537687
474474 2.95798 0.135865
475475 0 0
476476 −0.687132 −0.0314946
477477 19.2336 0.880648
478478 6.29713 0.288024
479479 21.5408 0.984224 0.492112 0.870532i 0.336225π-0.336225\pi
0.492112 + 0.870532i 0.336225π0.336225\pi
480480 0 0
481481 13.1981 0.601781
482482 −1.79295 −0.0816668
483483 −21.1695 −0.963243
484484 19.7527 0.897852
485485 0 0
486486 2.68886 0.121969
487487 −4.30185 −0.194935 −0.0974677 0.995239i 0.531074π-0.531074\pi
−0.0974677 + 0.995239i 0.531074π0.531074\pi
488488 2.51706 0.113942
489489 21.0458 0.951724
490490 0 0
491491 −7.55139 −0.340789 −0.170395 0.985376i 0.554504π-0.554504\pi
−0.170395 + 0.985376i 0.554504π0.554504\pi
492492 54.7102 2.46653
493493 −1.44179 −0.0649349
494494 −6.26085 −0.281689
495495 0 0
496496 36.6573 1.64596
497497 −0.444816 −0.0199527
498498 −6.28013 −0.281419
499499 37.8523 1.69450 0.847250 0.531194i 0.178256π-0.178256\pi
0.847250 + 0.531194i 0.178256π0.178256\pi
500500 0 0
501501 29.1229 1.30112
502502 2.43110 0.108505
503503 −20.1705 −0.899360 −0.449680 0.893190i 0.648462π-0.648462\pi
−0.449680 + 0.893190i 0.648462π0.648462\pi
504504 −4.99007 −0.222275
505505 0 0
506506 −1.56103 −0.0693961
507507 34.3727 1.52654
508508 10.1483 0.450256
509509 19.5293 0.865623 0.432811 0.901484i 0.357522π-0.357522\pi
0.432811 + 0.901484i 0.357522π0.357522\pi
510510 0 0
511511 −6.28474 −0.278021
512512 −16.8402 −0.744239
513513 −34.1864 −1.50937
514514 −3.98324 −0.175693
515515 0 0
516516 −71.1991 −3.13437
517517 7.73060 0.339991
518518 −0.637262 −0.0279997
519519 −5.85241 −0.256892
520520 0 0
521521 19.9256 0.872958 0.436479 0.899714i 0.356225π-0.356225\pi
0.436479 + 0.899714i 0.356225π0.356225\pi
522522 −5.16130 −0.225904
523523 −0.645222 −0.0282136 −0.0141068 0.999900i 0.504490π-0.504490\pi
−0.0141068 + 0.999900i 0.504490π0.504490\pi
524524 3.42894 0.149794
525525 0 0
526526 2.02291 0.0882033
527527 −3.45445 −0.150478
528528 9.65763 0.420295
529529 29.0285 1.26211
530530 0 0
531531 21.9704 0.953435
532532 −10.5490 −0.457357
533533 48.9760 2.12139
534534 −9.64831 −0.417523
535535 0 0
536536 −9.05795 −0.391244
537537 1.95692 0.0844472
538538 −6.22986 −0.268588
539539 −5.45990 −0.235174
540540 0 0
541541 0.776828 0.0333984 0.0166992 0.999861i 0.494684π-0.494684\pi
0.0166992 + 0.999861i 0.494684π0.494684\pi
542542 −6.50828 −0.279555
543543 10.2909 0.441624
544544 0.943182 0.0404386
545545 0 0
546546 −3.46186 −0.148154
547547 −8.27780 −0.353933 −0.176967 0.984217i 0.556628π-0.556628\pi
−0.176967 + 0.984217i 0.556628π0.556628\pi
548548 −29.0187 −1.23962
549549 14.1755 0.604994
550550 0 0
551551 −22.1346 −0.942967
552552 19.2812 0.820662
553553 4.46158 0.189726
554554 2.33560 0.0992303
555555 0 0
556556 20.6808 0.877061
557557 11.5911 0.491130 0.245565 0.969380i 0.421026π-0.421026\pi
0.245565 + 0.969380i 0.421026π0.421026\pi
558558 −12.3662 −0.523503
559559 −63.7368 −2.69578
560560 0 0
561561 −0.910100 −0.0384244
562562 −6.46268 −0.272612
563563 −13.9955 −0.589840 −0.294920 0.955522i 0.595293π-0.595293\pi
−0.294920 + 0.955522i 0.595293π0.595293\pi
564564 −47.0682 −1.98193
565565 0 0
566566 −1.67829 −0.0705440
567567 −2.82373 −0.118585
568568 0.405140 0.0169993
569569 −40.7482 −1.70825 −0.854127 0.520065i 0.825908π-0.825908\pi
−0.854127 + 0.520065i 0.825908π0.825908\pi
570570 0 0
571571 −17.0553 −0.713742 −0.356871 0.934154i 0.616156π-0.616156\pi
−0.356871 + 0.934154i 0.616156π0.616156\pi
572572 8.90801 0.372463
573573 44.3545 1.85294
574574 −2.36478 −0.0987039
575575 0 0
576576 −35.0970 −1.46237
577577 −23.5705 −0.981255 −0.490627 0.871369i 0.663232π-0.663232\pi
−0.490627 + 0.871369i 0.663232π0.663232\pi
578578 3.98455 0.165735
579579 14.0016 0.581888
580580 0 0
581581 −9.47243 −0.392983
582582 −7.46509 −0.309438
583583 3.36319 0.139289
584584 5.72416 0.236867
585585 0 0
586586 3.70715 0.153141
587587 −0.0140745 −0.000580917 0 −0.000290459 1.00000i 0.500092π-0.500092\pi
−0.000290459 1.00000i 0.500092π0.500092\pi
588588 33.2429 1.37091
589589 −53.0334 −2.18520
590590 0 0
591591 2.87112 0.118102
592592 −9.68969 −0.398244
593593 7.67621 0.315224 0.157612 0.987501i 0.449620π-0.449620\pi
0.157612 + 0.987501i 0.449620π0.449620\pi
594594 −1.39390 −0.0571923
595595 0 0
596596 15.4183 0.631558
597597 −57.6117 −2.35789
598598 8.50826 0.347928
599599 −9.42711 −0.385181 −0.192591 0.981279i 0.561689π-0.561689\pi
−0.192591 + 0.981279i 0.561689π0.561689\pi
600600 0 0
601601 3.49753 0.142667 0.0713337 0.997453i 0.477274π-0.477274\pi
0.0713337 + 0.997453i 0.477274π0.477274\pi
602602 3.07749 0.125429
603603 −51.0121 −2.07737
604604 45.7728 1.86247
605605 0 0
606606 −7.81076 −0.317290
607607 −11.1635 −0.453112 −0.226556 0.973998i 0.572747π-0.572747\pi
−0.226556 + 0.973998i 0.572747π0.572747\pi
608608 14.4799 0.587239
609609 −12.2391 −0.495952
610610 0 0
611611 −42.1350 −1.70460
612612 3.52458 0.142473
613613 −44.5755 −1.80039 −0.900193 0.435490i 0.856575π-0.856575\pi
−0.900193 + 0.435490i 0.856575π0.856575\pi
614614 −2.11827 −0.0854864
615615 0 0
616616 −0.872561 −0.0351565
617617 −25.3603 −1.02097 −0.510484 0.859887i 0.670534π-0.670534\pi
−0.510484 + 0.859887i 0.670534π0.670534\pi
618618 2.79463 0.112417
619619 17.2831 0.694667 0.347333 0.937742i 0.387087π-0.387087\pi
0.347333 + 0.937742i 0.387087π0.387087\pi
620620 0 0
621621 46.4581 1.86430
622622 2.30606 0.0924647
623623 −14.5527 −0.583043
624624 −52.6382 −2.10721
625625 0 0
626626 −0.106217 −0.00424528
627627 −13.9720 −0.557989
628628 11.9215 0.475720
629629 0.913120 0.0364085
630630 0 0
631631 13.6827 0.544700 0.272350 0.962198i 0.412199π-0.412199\pi
0.272350 + 0.962198i 0.412199π0.412199\pi
632632 −4.06362 −0.161642
633633 −12.3325 −0.490175
634634 −6.44124 −0.255814
635635 0 0
636636 −20.4770 −0.811965
637637 29.7587 1.17908
638638 −0.902504 −0.0357305
639639 2.28165 0.0902606
640640 0 0
641641 4.80495 0.189784 0.0948921 0.995488i 0.469749π-0.469749\pi
0.0948921 + 0.995488i 0.469749π0.469749\pi
642642 −6.95987 −0.274684
643643 11.5218 0.454376 0.227188 0.973851i 0.427047π-0.427047\pi
0.227188 + 0.973851i 0.427047π0.427047\pi
644644 14.3357 0.564905
645645 0 0
646646 −0.433162 −0.0170425
647647 19.8337 0.779742 0.389871 0.920870i 0.372520π-0.372520\pi
0.389871 + 0.920870i 0.372520π0.372520\pi
648648 2.57186 0.101032
649649 3.84174 0.150802
650650 0 0
651651 −29.3241 −1.14930
652652 −14.2519 −0.558149
653653 −37.8833 −1.48249 −0.741244 0.671235i 0.765764π-0.765764\pi
−0.741244 + 0.671235i 0.765764π0.765764\pi
654654 −13.2975 −0.519974
655655 0 0
656656 −35.9569 −1.40388
657657 32.2370 1.25769
658658 2.03446 0.0793116
659659 −18.2539 −0.711072 −0.355536 0.934663i 0.615702π-0.615702\pi
−0.355536 + 0.934663i 0.615702π0.615702\pi
660660 0 0
661661 39.5364 1.53779 0.768895 0.639375i 0.220807π-0.220807\pi
0.768895 + 0.639375i 0.220807π0.220807\pi
662662 −1.10811 −0.0430678
663663 4.96043 0.192647
664664 8.62751 0.334813
665665 0 0
666666 3.26878 0.126663
667667 30.0801 1.16471
668668 −19.7217 −0.763055
669669 −39.1701 −1.51440
670670 0 0
671671 2.47872 0.0956898
672672 8.00649 0.308857
673673 −14.7965 −0.570364 −0.285182 0.958473i 0.592054π-0.592054\pi
−0.285182 + 0.958473i 0.592054π0.592054\pi
674674 −0.280254 −0.0107950
675675 0 0
676676 −23.2767 −0.895259
677677 −37.1563 −1.42803 −0.714017 0.700128i 0.753126π-0.753126\pi
−0.714017 + 0.700128i 0.753126π0.753126\pi
678678 −10.1443 −0.389590
679679 −11.2597 −0.432109
680680 0 0
681681 23.9094 0.916212
682682 −2.16235 −0.0828006
683683 29.5420 1.13039 0.565196 0.824957i 0.308801π-0.308801\pi
0.565196 + 0.824957i 0.308801π0.308801\pi
684684 54.1101 2.06895
685685 0 0
686686 −3.12589 −0.119347
687687 −79.7749 −3.04360
688688 46.7938 1.78400
689689 −18.3308 −0.698348
690690 0 0
691691 24.4783 0.931198 0.465599 0.884996i 0.345839π-0.345839\pi
0.465599 + 0.884996i 0.345839π0.345839\pi
692692 3.96317 0.150657
693693 −4.91405 −0.186669
694694 0.522791 0.0198449
695695 0 0
696696 11.1474 0.422540
697697 3.38844 0.128346
698698 −5.35416 −0.202658
699699 45.2466 1.71138
700700 0 0
701701 21.2361 0.802077 0.401039 0.916061i 0.368649π-0.368649\pi
0.401039 + 0.916061i 0.368649π0.368649\pi
702702 7.59732 0.286742
703703 14.0184 0.528714
704704 −6.13704 −0.231299
705705 0 0
706706 −2.89605 −0.108994
707707 −11.7811 −0.443074
708708 −23.3907 −0.879076
709709 −10.4005 −0.390599 −0.195300 0.980744i 0.562568π-0.562568\pi
−0.195300 + 0.980744i 0.562568π0.562568\pi
710710 0 0
711711 −22.8853 −0.858265
712712 13.2547 0.496739
713713 72.0703 2.69905
714714 −0.239511 −0.00896348
715715 0 0
716716 −1.32520 −0.0495250
717717 −76.5948 −2.86048
718718 4.48366 0.167329
719719 −35.5394 −1.32540 −0.662698 0.748887i 0.730589π-0.730589\pi
−0.662698 + 0.748887i 0.730589π0.730589\pi
720720 0 0
721721 4.21520 0.156982
722722 −2.16514 −0.0805780
723723 21.8085 0.811067
724724 −6.96885 −0.258995
725725 0 0
726726 6.88514 0.255532
727727 20.0589 0.743944 0.371972 0.928244i 0.378682π-0.378682\pi
0.371972 + 0.928244i 0.378682π0.378682\pi
728728 4.75583 0.176263
729729 −40.9929 −1.51826
730730 0 0
731731 −4.40968 −0.163098
732732 −15.0918 −0.557810
733733 7.54137 0.278547 0.139273 0.990254i 0.455523π-0.455523\pi
0.139273 + 0.990254i 0.455523π0.455523\pi
734734 8.37937 0.309288
735735 0 0
736736 −19.6777 −0.725329
737737 −8.91997 −0.328571
738738 12.1299 0.446508
739739 −2.97975 −0.109612 −0.0548059 0.998497i 0.517454π-0.517454\pi
−0.0548059 + 0.998497i 0.517454π0.517454\pi
740740 0 0
741741 76.1535 2.79757
742742 0.885091 0.0324927
743743 −50.0156 −1.83490 −0.917448 0.397856i 0.869754π-0.869754\pi
−0.917448 + 0.397856i 0.869754π0.869754\pi
744744 26.7085 0.979180
745745 0 0
746746 5.22832 0.191422
747747 48.5880 1.77774
748748 0.616308 0.0225344
749749 −10.4977 −0.383577
750750 0 0
751751 25.8694 0.943989 0.471995 0.881601i 0.343534π-0.343534\pi
0.471995 + 0.881601i 0.343534π0.343534\pi
752752 30.9344 1.12806
753753 −29.5706 −1.07761
754754 4.91903 0.179140
755755 0 0
756756 12.8008 0.465562
757757 52.5795 1.91103 0.955517 0.294936i 0.0952983π-0.0952983\pi
0.955517 + 0.294936i 0.0952983π0.0952983\pi
758758 0.0111313 0.000404307 0
759759 18.9875 0.689201
760760 0 0
761761 −47.2393 −1.71242 −0.856211 0.516626i 0.827188π-0.827188\pi
−0.856211 + 0.516626i 0.827188π0.827188\pi
762762 3.53734 0.128144
763763 −20.0569 −0.726109
764764 −30.0363 −1.08668
765765 0 0
766766 −6.56402 −0.237168
767767 −20.9391 −0.756068
768768 33.6681 1.21489
769769 19.1183 0.689425 0.344712 0.938708i 0.387976π-0.387976\pi
0.344712 + 0.938708i 0.387976π0.387976\pi
770770 0 0
771771 48.4499 1.74488
772772 −9.48172 −0.341255
773773 35.0337 1.26007 0.630037 0.776565i 0.283040π-0.283040\pi
0.630037 + 0.776565i 0.283040π0.283040\pi
774774 −15.7857 −0.567406
775775 0 0
776776 10.2554 0.368147
777777 7.75130 0.278076
778778 1.39510 0.0500169
779779 52.0201 1.86381
780780 0 0
781781 0.398968 0.0142762
782782 0.588650 0.0210501
783783 26.8596 0.959884
784784 −21.8481 −0.780288
785785 0 0
786786 1.19521 0.0426319
787787 −31.2968 −1.11561 −0.557806 0.829971i 0.688357π-0.688357\pi
−0.557806 + 0.829971i 0.688357π0.688357\pi
788788 −1.94428 −0.0692622
789789 −24.6056 −0.875983
790790 0 0
791791 −15.3009 −0.544036
792792 4.47573 0.159038
793793 −13.5101 −0.479756
794794 −2.54757 −0.0904099
795795 0 0
796796 39.0139 1.38281
797797 −31.3216 −1.10947 −0.554734 0.832027i 0.687180π-0.687180\pi
−0.554734 + 0.832027i 0.687180π0.687180\pi
798798 −3.67702 −0.130165
799799 −2.91514 −0.103130
800800 0 0
801801 74.6469 2.63752
802802 5.97498 0.210984
803803 5.63696 0.198924
804804 54.3098 1.91536
805805 0 0
806806 11.7857 0.415134
807807 75.7766 2.66746
808808 10.7303 0.377489
809809 4.76429 0.167504 0.0837518 0.996487i 0.473310π-0.473310\pi
0.0837518 + 0.996487i 0.473310π0.473310\pi
810810 0 0
811811 −0.713408 −0.0250511 −0.0125256 0.999922i 0.503987π-0.503987\pi
−0.0125256 + 0.999922i 0.503987π0.503987\pi
812812 8.28813 0.290856
813813 79.1631 2.77637
814814 0.571578 0.0200338
815815 0 0
816816 −3.64181 −0.127489
817817 −67.6983 −2.36846
818818 −2.61797 −0.0915352
819819 26.7836 0.935896
820820 0 0
821821 1.05247 0.0367315 0.0183658 0.999831i 0.494154π-0.494154\pi
0.0183658 + 0.999831i 0.494154π0.494154\pi
822822 −10.1150 −0.352800
823823 −36.9290 −1.28726 −0.643631 0.765336i 0.722573π-0.722573\pi
−0.643631 + 0.765336i 0.722573π0.722573\pi
824824 −3.83921 −0.133745
825825 0 0
826826 1.01103 0.0351783
827827 10.4375 0.362948 0.181474 0.983396i 0.441913π-0.441913\pi
0.181474 + 0.983396i 0.441913π0.441913\pi
828828 −73.5336 −2.55547
829829 −17.5141 −0.608291 −0.304145 0.952626i 0.598371π-0.598371\pi
−0.304145 + 0.952626i 0.598371π0.598371\pi
830830 0 0
831831 −28.4090 −0.985497
832832 33.4495 1.15965
833833 2.05888 0.0713360
834834 7.20863 0.249614
835835 0 0
836836 9.46168 0.327239
837837 64.3541 2.22440
838838 7.04325 0.243305
839839 23.0283 0.795026 0.397513 0.917597i 0.369873π-0.369873\pi
0.397513 + 0.917597i 0.369873π0.369873\pi
840840 0 0
841841 −11.6093 −0.400319
842842 7.40436 0.255171
843843 78.6084 2.70742
844844 8.35144 0.287468
845845 0 0
846846 −10.4356 −0.358783
847847 10.3850 0.356832
848848 13.4580 0.462149
849849 20.4138 0.700601
850850 0 0
851851 −19.0505 −0.653042
852852 −2.42914 −0.0832211
853853 −41.3312 −1.41515 −0.707577 0.706637i 0.750212π-0.750212\pi
−0.707577 + 0.706637i 0.750212π0.750212\pi
854854 0.652325 0.0223221
855855 0 0
856856 9.56133 0.326799
857857 14.1899 0.484718 0.242359 0.970187i 0.422079π-0.422079\pi
0.242359 + 0.970187i 0.422079π0.422079\pi
858858 3.10503 0.106004
859859 −15.4345 −0.526618 −0.263309 0.964712i 0.584814π-0.584814\pi
−0.263309 + 0.964712i 0.584814π0.584814\pi
860860 0 0
861861 28.7638 0.980269
862862 6.70664 0.228429
863863 3.73755 0.127228 0.0636138 0.997975i 0.479737π-0.479737\pi
0.0636138 + 0.997975i 0.479737π0.479737\pi
864864 −17.5709 −0.597774
865865 0 0
866866 7.00573 0.238064
867867 −48.4658 −1.64598
868868 19.8579 0.674021
869869 −4.00171 −0.135749
870870 0 0
871871 48.6176 1.64734
872872 18.2679 0.618628
873873 57.7558 1.95474
874874 9.03708 0.305684
875875 0 0
876876 −34.3210 −1.15960
877877 37.4630 1.26504 0.632518 0.774546i 0.282022π-0.282022\pi
0.632518 + 0.774546i 0.282022π0.282022\pi
878878 −4.48902 −0.151497
879879 −45.0917 −1.52091
880880 0 0
881881 −21.1306 −0.711907 −0.355953 0.934504i 0.615844π-0.615844\pi
−0.355953 + 0.934504i 0.615844π0.615844\pi
882882 7.37036 0.248173
883883 21.3153 0.717317 0.358658 0.933469i 0.383234π-0.383234\pi
0.358658 + 0.933469i 0.383234π0.383234\pi
884884 −3.35914 −0.112980
885885 0 0
886886 −2.95918 −0.0994156
887887 −28.5267 −0.957834 −0.478917 0.877860i 0.658971π-0.658971\pi
−0.478917 + 0.877860i 0.658971π0.658971\pi
888888 −7.05990 −0.236915
889889 5.33544 0.178945
890890 0 0
891891 2.53268 0.0848480
892892 26.5255 0.888138
893893 −44.7539 −1.49763
894894 5.37430 0.179743
895895 0 0
896896 −7.19235 −0.240280
897897 −103.490 −3.45542
898898 −4.24594 −0.141689
899899 41.6673 1.38968
900900 0 0
901901 −1.26823 −0.0422509
902902 2.12103 0.0706227
903903 −37.4329 −1.24569
904904 13.9361 0.463507
905905 0 0
906906 15.9549 0.530065
907907 7.24122 0.240441 0.120220 0.992747i 0.461640π-0.461640\pi
0.120220 + 0.992747i 0.461640π0.461640\pi
908908 −16.1912 −0.537322
909909 60.4302 2.00434
910910 0 0
911911 −30.4699 −1.00951 −0.504756 0.863262i 0.668418π-0.668418\pi
−0.504756 + 0.863262i 0.668418π0.668418\pi
912912 −55.9098 −1.85136
913913 8.49609 0.281179
914914 −6.44602 −0.213215
915915 0 0
916916 54.0225 1.78495
917917 1.80276 0.0595325
918918 0.525627 0.0173483
919919 −56.0316 −1.84831 −0.924157 0.382013i 0.875231π-0.875231\pi
−0.924157 + 0.382013i 0.875231π0.875231\pi
920920 0 0
921921 25.7654 0.849000
922922 2.09022 0.0688378
923923 −2.17454 −0.0715760
924924 5.23171 0.172111
925925 0 0
926926 −4.17863 −0.137318
927927 −21.6215 −0.710142
928928 −11.3766 −0.373455
929929 −17.8294 −0.584963 −0.292481 0.956271i 0.594481π-0.594481\pi
−0.292481 + 0.956271i 0.594481π0.594481\pi
930930 0 0
931931 31.6084 1.03592
932932 −30.6404 −1.00366
933933 −28.0497 −0.918305
934934 −2.96894 −0.0971468
935935 0 0
936936 −24.3946 −0.797363
937937 −10.3366 −0.337681 −0.168841 0.985643i 0.554002π-0.554002\pi
−0.168841 + 0.985643i 0.554002π0.554002\pi
938938 −2.34747 −0.0766476
939939 1.29196 0.0421616
940940 0 0
941941 4.39565 0.143294 0.0716470 0.997430i 0.477174π-0.477174\pi
0.0716470 + 0.997430i 0.477174π0.477174\pi
942942 4.15544 0.135392
943943 −70.6933 −2.30209
944944 15.3729 0.500347
945945 0 0
946946 −2.76029 −0.0897447
947947 13.1530 0.427415 0.213708 0.976898i 0.431446π-0.431446\pi
0.213708 + 0.976898i 0.431446π0.431446\pi
948948 24.3647 0.791328
949949 −30.7238 −0.997337
950950 0 0
951951 78.3477 2.54060
952952 0.329036 0.0106641
953953 −52.7707 −1.70941 −0.854706 0.519113i 0.826262π-0.826262\pi
−0.854706 + 0.519113i 0.826262π0.826262\pi
954954 −4.54000 −0.146988
955955 0 0
956956 51.8690 1.67756
957957 10.9776 0.354854
958958 −5.08459 −0.164276
959959 −15.2566 −0.492661
960960 0 0
961961 68.8325 2.22040
962962 −3.11534 −0.100443
963963 53.8470 1.73520
964964 −14.7684 −0.475659
965965 0 0
966966 4.99694 0.160774
967967 −40.7983 −1.31198 −0.655992 0.754768i 0.727750π-0.727750\pi
−0.655992 + 0.754768i 0.727750π0.727750\pi
968968 −9.45867 −0.304013
969969 5.26874 0.169256
970970 0 0
971971 59.3602 1.90496 0.952479 0.304603i 0.0985239π-0.0985239\pi
0.952479 + 0.304603i 0.0985239π0.0985239\pi
972972 22.1479 0.710394
973973 10.8729 0.348569
974974 1.01543 0.0325364
975975 0 0
976976 9.91872 0.317491
977977 21.8738 0.699806 0.349903 0.936786i 0.386215π-0.386215\pi
0.349903 + 0.936786i 0.386215π0.386215\pi
978978 −4.96775 −0.158851
979979 13.0527 0.417167
980980 0 0
981981 102.880 3.28471
982982 1.78247 0.0568808
983983 32.5706 1.03884 0.519421 0.854519i 0.326148π-0.326148\pi
0.519421 + 0.854519i 0.326148π0.326148\pi
984984 −26.1982 −0.835167
985985 0 0
986986 0.340327 0.0108382
987987 −24.7461 −0.787677
988988 −51.5701 −1.64066
989989 91.9994 2.92541
990990 0 0
991991 −0.493203 −0.0156671 −0.00783356 0.999969i 0.502494π-0.502494\pi
−0.00783356 + 0.999969i 0.502494π0.502494\pi
992992 −27.2577 −0.865433
993993 13.4784 0.427724
994994 0.104997 0.00333029
995995 0 0
996996 −51.7290 −1.63909
997997 −19.0675 −0.603872 −0.301936 0.953328i 0.597633π-0.597633\pi
−0.301936 + 0.953328i 0.597633π0.597633\pi
998998 −8.93483 −0.282827
999999 −17.0109 −0.538200
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 4925.2.a.k.1.5 14
5.4 even 2 985.2.a.f.1.10 14
15.14 odd 2 8865.2.a.v.1.5 14
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
985.2.a.f.1.10 14 5.4 even 2
4925.2.a.k.1.5 14 1.1 even 1 trivial
8865.2.a.v.1.5 14 15.14 odd 2