Properties

Label 975.6.a.u.1.7
Level 975975
Weight 66
Character 975.1
Self dual yes
Analytic conductor 156.374156.374
Analytic rank 11
Dimension 1111
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] = [975,6,Mod(1,975)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(975, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 0]))
 
N = Newforms(chi, 6, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("975.1");
 
S:= CuspForms(chi, 6);
 
N := Newforms(S);
 
Level: N N == 975=35213 975 = 3 \cdot 5^{2} \cdot 13
Weight: k k == 6 6
Character orbit: [χ][\chi] == 975.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: 156.374224318156.374224318
Analytic rank: 11
Dimension: 1111
Coefficient field: Q[x]/(x11)\mathbb{Q}[x]/(x^{11} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x112x10286x9+442x8+28715x729138x61208172x5+509768x4++55036800 x^{11} - 2 x^{10} - 286 x^{9} + 442 x^{8} + 28715 x^{7} - 29138 x^{6} - 1208172 x^{5} + 509768 x^{4} + \cdots + 55036800 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 2535311 2^{5}\cdot 3\cdot 5^{3}\cdot 11
Twist minimal: yes
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.7
Root 2.299892.29989 of defining polynomial
Character χ\chi == 975.1

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+2.29989q29.00000q326.7105q420.6990q6228.917q7135.028q8+81.0000q9+59.1539q11+240.395q12+169.000q13526.484q14+544.187q162342.37q17+186.291q18+2145.80q19+2060.25q21+136.047q221152.00q23+1215.25q24+388.681q26729.000q27+6114.49q28+5872.31q29+4568.68q31+5572.46q32532.385q335387.20q342163.55q36+9110.68q37+4935.11q381521.00q398258.68q41+4738.36q42+498.716q431580.03q442649.47q4618526.7q474897.69q48+35596.0q49+21081.4q514514.08q5210763.3q531676.62q54+30910.2q5619312.2q57+13505.7q58+3060.98q59+40411.1q61+10507.5q6218542.3q634597.96q641224.43q66+69675.2q67+62566.0q68+10368.0q6972896.6q7110937.2q72+5906.20q73+20953.6q7457315.5q7613541.3q773498.13q78+93605.5q79+6561.00q8118994.1q82+28221.8q8355030.4q84+1146.99q8652850.8q877987.41q88+34970.9q8938687.0q91+30770.5q9241118.1q9342609.3q9450152.1q96+67239.7q97+81867.0q98+4791.46q99+O(q100)q+2.29989 q^{2} -9.00000 q^{3} -26.7105 q^{4} -20.6990 q^{6} -228.917 q^{7} -135.028 q^{8} +81.0000 q^{9} +59.1539 q^{11} +240.395 q^{12} +169.000 q^{13} -526.484 q^{14} +544.187 q^{16} -2342.37 q^{17} +186.291 q^{18} +2145.80 q^{19} +2060.25 q^{21} +136.047 q^{22} -1152.00 q^{23} +1215.25 q^{24} +388.681 q^{26} -729.000 q^{27} +6114.49 q^{28} +5872.31 q^{29} +4568.68 q^{31} +5572.46 q^{32} -532.385 q^{33} -5387.20 q^{34} -2163.55 q^{36} +9110.68 q^{37} +4935.11 q^{38} -1521.00 q^{39} -8258.68 q^{41} +4738.36 q^{42} +498.716 q^{43} -1580.03 q^{44} -2649.47 q^{46} -18526.7 q^{47} -4897.69 q^{48} +35596.0 q^{49} +21081.4 q^{51} -4514.08 q^{52} -10763.3 q^{53} -1676.62 q^{54} +30910.2 q^{56} -19312.2 q^{57} +13505.7 q^{58} +3060.98 q^{59} +40411.1 q^{61} +10507.5 q^{62} -18542.3 q^{63} -4597.96 q^{64} -1224.43 q^{66} +69675.2 q^{67} +62566.0 q^{68} +10368.0 q^{69} -72896.6 q^{71} -10937.2 q^{72} +5906.20 q^{73} +20953.6 q^{74} -57315.5 q^{76} -13541.3 q^{77} -3498.13 q^{78} +93605.5 q^{79} +6561.00 q^{81} -18994.1 q^{82} +28221.8 q^{83} -55030.4 q^{84} +1146.99 q^{86} -52850.8 q^{87} -7987.41 q^{88} +34970.9 q^{89} -38687.0 q^{91} +30770.5 q^{92} -41118.1 q^{93} -42609.3 q^{94} -50152.1 q^{96} +67239.7 q^{97} +81867.0 q^{98} +4791.46 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 11q+2q299q3+224q418q655q7+270q8+891q9125q112016q12+1859q131311q14+5756q164507q17+162q18+142q19+495q21+10125q99+O(q100) 11 q + 2 q^{2} - 99 q^{3} + 224 q^{4} - 18 q^{6} - 55 q^{7} + 270 q^{8} + 891 q^{9} - 125 q^{11} - 2016 q^{12} + 1859 q^{13} - 1311 q^{14} + 5756 q^{16} - 4507 q^{17} + 162 q^{18} + 142 q^{19} + 495 q^{21}+ \cdots - 10125 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 2.29989 0.406567 0.203283 0.979120i 0.434839π-0.434839\pi
0.203283 + 0.979120i 0.434839π0.434839\pi
33 −9.00000 −0.577350
44 −26.7105 −0.834703
55 0 0
66 −20.6990 −0.234732
77 −228.917 −1.76577 −0.882883 0.469593i 0.844401π-0.844401\pi
−0.882883 + 0.469593i 0.844401π0.844401\pi
88 −135.028 −0.745930
99 81.0000 0.333333
1010 0 0
1111 59.1539 0.147401 0.0737007 0.997280i 0.476519π-0.476519\pi
0.0737007 + 0.997280i 0.476519π0.476519\pi
1212 240.395 0.481916
1313 169.000 0.277350
1414 −526.484 −0.717902
1515 0 0
1616 544.187 0.531433
1717 −2342.37 −1.96577 −0.982887 0.184208i 0.941028π-0.941028\pi
−0.982887 + 0.184208i 0.941028π0.941028\pi
1818 186.291 0.135522
1919 2145.80 1.36366 0.681830 0.731511i 0.261184π-0.261184\pi
0.681830 + 0.731511i 0.261184π0.261184\pi
2020 0 0
2121 2060.25 1.01947
2222 136.047 0.0599285
2323 −1152.00 −0.454080 −0.227040 0.973885i 0.572905π-0.572905\pi
−0.227040 + 0.973885i 0.572905π0.572905\pi
2424 1215.25 0.430663
2525 0 0
2626 388.681 0.112761
2727 −729.000 −0.192450
2828 6114.49 1.47389
2929 5872.31 1.29662 0.648312 0.761374i 0.275475π-0.275475\pi
0.648312 + 0.761374i 0.275475π0.275475\pi
3030 0 0
3131 4568.68 0.853859 0.426930 0.904285i 0.359595π-0.359595\pi
0.426930 + 0.904285i 0.359595π0.359595\pi
3232 5572.46 0.961993
3333 −532.385 −0.0851022
3434 −5387.20 −0.799219
3535 0 0
3636 −2163.55 −0.278234
3737 9110.68 1.09407 0.547037 0.837109i 0.315756π-0.315756\pi
0.547037 + 0.837109i 0.315756π0.315756\pi
3838 4935.11 0.554419
3939 −1521.00 −0.160128
4040 0 0
4141 −8258.68 −0.767275 −0.383638 0.923484i 0.625329π-0.625329\pi
−0.383638 + 0.923484i 0.625329π0.625329\pi
4242 4738.36 0.414481
4343 498.716 0.0411322 0.0205661 0.999788i 0.493453π-0.493453\pi
0.0205661 + 0.999788i 0.493453π0.493453\pi
4444 −1580.03 −0.123036
4545 0 0
4646 −2649.47 −0.184614
4747 −18526.7 −1.22336 −0.611678 0.791107i 0.709505π-0.709505\pi
−0.611678 + 0.791107i 0.709505π0.709505\pi
4848 −4897.69 −0.306823
4949 35596.0 2.11793
5050 0 0
5151 21081.4 1.13494
5252 −4514.08 −0.231505
5353 −10763.3 −0.526327 −0.263164 0.964751i 0.584766π-0.584766\pi
−0.263164 + 0.964751i 0.584766π0.584766\pi
5454 −1676.62 −0.0782438
5555 0 0
5656 30910.2 1.31714
5757 −19312.2 −0.787309
5858 13505.7 0.527165
5959 3060.98 0.114480 0.0572401 0.998360i 0.481770π-0.481770\pi
0.0572401 + 0.998360i 0.481770π0.481770\pi
6060 0 0
6161 40411.1 1.39052 0.695258 0.718760i 0.255290π-0.255290\pi
0.695258 + 0.718760i 0.255290π0.255290\pi
6262 10507.5 0.347151
6363 −18542.3 −0.588589
6464 −4597.96 −0.140318
6565 0 0
6666 −1224.43 −0.0345997
6767 69675.2 1.89623 0.948115 0.317926i 0.102986π-0.102986\pi
0.948115 + 0.317926i 0.102986π0.102986\pi
6868 62566.0 1.64084
6969 10368.0 0.262163
7070 0 0
7171 −72896.6 −1.71618 −0.858088 0.513503i 0.828347π-0.828347\pi
−0.858088 + 0.513503i 0.828347π0.828347\pi
7272 −10937.2 −0.248643
7373 5906.20 0.129718 0.0648591 0.997894i 0.479340π-0.479340\pi
0.0648591 + 0.997894i 0.479340π0.479340\pi
7474 20953.6 0.444814
7575 0 0
7676 −57315.5 −1.13825
7777 −13541.3 −0.260276
7878 −3498.13 −0.0651028
7979 93605.5 1.68746 0.843731 0.536767i 0.180355π-0.180355\pi
0.843731 + 0.536767i 0.180355π0.180355\pi
8080 0 0
8181 6561.00 0.111111
8282 −18994.1 −0.311949
8383 28221.8 0.449665 0.224833 0.974397i 0.427816π-0.427816\pi
0.224833 + 0.974397i 0.427816π0.427816\pi
8484 −55030.4 −0.850951
8585 0 0
8686 1146.99 0.0167230
8787 −52850.8 −0.748607
8888 −7987.41 −0.109951
8989 34970.9 0.467985 0.233992 0.972238i 0.424821π-0.424821\pi
0.233992 + 0.972238i 0.424821π0.424821\pi
9090 0 0
9191 −38687.0 −0.489735
9292 30770.5 0.379022
9393 −41118.1 −0.492976
9494 −42609.3 −0.497376
9595 0 0
9696 −50152.1 −0.555407
9797 67239.7 0.725599 0.362799 0.931867i 0.381821π-0.381821\pi
0.362799 + 0.931867i 0.381821π0.381821\pi
9898 81867.0 0.861080
9999 4791.46 0.0491338
100100 0 0
101101 −162082. −1.58100 −0.790498 0.612465i 0.790178π-0.790178\pi
−0.790498 + 0.612465i 0.790178π0.790178\pi
102102 48484.8 0.461429
103103 −105332. −0.978289 −0.489145 0.872203i 0.662691π-0.662691\pi
−0.489145 + 0.872203i 0.662691π0.662691\pi
104104 −22819.7 −0.206884
105105 0 0
106106 −24754.4 −0.213987
107107 234277. 1.97820 0.989100 0.147244i 0.0470403π-0.0470403\pi
0.989100 + 0.147244i 0.0470403π0.0470403\pi
108108 19472.0 0.160639
109109 −205781. −1.65897 −0.829487 0.558525i 0.811367π-0.811367\pi
−0.829487 + 0.558525i 0.811367π0.811367\pi
110110 0 0
111111 −81996.1 −0.631663
112112 −124574. −0.938386
113113 −161817. −1.19214 −0.596070 0.802933i 0.703272π-0.703272\pi
−0.596070 + 0.802933i 0.703272π0.703272\pi
114114 −44416.0 −0.320094
115115 0 0
116116 −156853. −1.08230
117117 13689.0 0.0924500
118118 7039.91 0.0465438
119119 536209. 3.47110
120120 0 0
121121 −157552. −0.978273
122122 92941.1 0.565338
123123 74328.1 0.442986
124124 −122032. −0.712719
125125 0 0
126126 −42645.2 −0.239301
127127 −2226.71 −0.0122505 −0.00612527 0.999981i 0.501950π-0.501950\pi
−0.00612527 + 0.999981i 0.501950π0.501950\pi
128128 −188893. −1.01904
129129 −4488.44 −0.0237477
130130 0 0
131131 −180748. −0.920228 −0.460114 0.887860i 0.652191π-0.652191\pi
−0.460114 + 0.887860i 0.652191π0.652191\pi
132132 14220.3 0.0710351
133133 −491211. −2.40790
134134 160245. 0.770945
135135 0 0
136136 316285. 1.46633
137137 105032. 0.478100 0.239050 0.971007i 0.423164π-0.423164\pi
0.239050 + 0.971007i 0.423164π0.423164\pi
138138 23845.2 0.106587
139139 −356298. −1.56414 −0.782072 0.623188i 0.785837π-0.785837\pi
−0.782072 + 0.623188i 0.785837π0.785837\pi
140140 0 0
141141 166740. 0.706305
142142 −167654. −0.697740
143143 9997.00 0.0408818
144144 44079.2 0.177144
145145 0 0
146146 13583.6 0.0527391
147147 −320364. −1.22279
148148 −243351. −0.913226
149149 295683. 1.09109 0.545545 0.838082i 0.316323π-0.316323\pi
0.545545 + 0.838082i 0.316323π0.316323\pi
150150 0 0
151151 122209. 0.436174 0.218087 0.975929i 0.430018π-0.430018\pi
0.218087 + 0.975929i 0.430018π0.430018\pi
152152 −289743. −1.01719
153153 −189732. −0.655258
154154 −31143.6 −0.105820
155155 0 0
156156 40626.7 0.133660
157157 −67878.4 −0.219777 −0.109889 0.993944i 0.535049π-0.535049\pi
−0.109889 + 0.993944i 0.535049π0.535049\pi
158158 215282. 0.686066
159159 96869.8 0.303875
160160 0 0
161161 263712. 0.801799
162162 15089.6 0.0451741
163163 157781. 0.465142 0.232571 0.972579i 0.425286π-0.425286\pi
0.232571 + 0.972579i 0.425286π0.425286\pi
164164 220594. 0.640447
165165 0 0
166166 64907.0 0.182819
167167 −548705. −1.52247 −0.761233 0.648478i 0.775406π-0.775406\pi
−0.761233 + 0.648478i 0.775406π0.775406\pi
168168 −278191. −0.760450
169169 28561.0 0.0769231
170170 0 0
171171 173810. 0.454553
172172 −13321.0 −0.0343332
173173 471036. 1.19657 0.598285 0.801283i 0.295849π-0.295849\pi
0.598285 + 0.801283i 0.295849π0.295849\pi
174174 −121551. −0.304359
175175 0 0
176176 32190.8 0.0783339
177177 −27548.8 −0.0660951
178178 80429.2 0.190267
179179 −371293. −0.866133 −0.433066 0.901362i 0.642568π-0.642568\pi
−0.433066 + 0.901362i 0.642568π0.642568\pi
180180 0 0
181181 510409. 1.15804 0.579018 0.815315i 0.303436π-0.303436\pi
0.579018 + 0.815315i 0.303436π0.303436\pi
182182 −88975.8 −0.199110
183183 −363700. −0.802815
184184 155552. 0.338712
185185 0 0
186186 −94567.1 −0.200428
187187 −138560. −0.289758
188188 494857. 1.02114
189189 166881. 0.339822
190190 0 0
191191 60794.2 0.120581 0.0602905 0.998181i 0.480797π-0.480797\pi
0.0602905 + 0.998181i 0.480797π0.480797\pi
192192 41381.6 0.0810129
193193 473665. 0.915331 0.457666 0.889124i 0.348686π-0.348686\pi
0.457666 + 0.889124i 0.348686π0.348686\pi
194194 154644. 0.295004
195195 0 0
196196 −950788. −1.76784
197197 471821. 0.866186 0.433093 0.901349i 0.357422π-0.357422\pi
0.433093 + 0.901349i 0.357422π0.357422\pi
198198 11019.8 0.0199762
199199 874843. 1.56602 0.783010 0.622009i 0.213683π-0.213683\pi
0.783010 + 0.622009i 0.213683π0.213683\pi
200200 0 0
201201 −627077. −1.09479
202202 −372770. −0.642780
203203 −1.34427e6 −2.28954
204204 −563094. −0.947339
205205 0 0
206206 −242252. −0.397740
207207 −93311.9 −0.151360
208208 91967.7 0.147393
209209 126933. 0.201005
210210 0 0
211211 −37674.0 −0.0582554 −0.0291277 0.999576i 0.509273π-0.509273\pi
−0.0291277 + 0.999576i 0.509273π0.509273\pi
212212 287493. 0.439327
213213 656070. 0.990834
214214 538811. 0.804271
215215 0 0
216216 98435.2 0.143554
217217 −1.04585e6 −1.50772
218218 −473274. −0.674484
219219 −53155.8 −0.0748928
220220 0 0
221221 −395861. −0.545208
222222 −188582. −0.256813
223223 −1.13356e6 −1.52645 −0.763225 0.646133i 0.776385π-0.776385\pi
−0.763225 + 0.646133i 0.776385π0.776385\pi
224224 −1.27563e6 −1.69865
225225 0 0
226226 −372160. −0.484685
227227 329692. 0.424663 0.212331 0.977198i 0.431894π-0.431894\pi
0.212331 + 0.977198i 0.431894π0.431894\pi
228228 515839. 0.657170
229229 −66202.8 −0.0834233 −0.0417117 0.999130i 0.513281π-0.513281\pi
−0.0417117 + 0.999130i 0.513281π0.513281\pi
230230 0 0
231231 121872. 0.150271
232232 −792925. −0.967191
233233 −847118. −1.02224 −0.511121 0.859509i 0.670770π-0.670770\pi
−0.511121 + 0.859509i 0.670770π0.670770\pi
234234 31483.2 0.0375871
235235 0 0
236236 −81760.3 −0.0955569
237237 −842450. −0.974256
238238 1.23322e6 1.41123
239239 646882. 0.732538 0.366269 0.930509i 0.380635π-0.380635\pi
0.366269 + 0.930509i 0.380635π0.380635\pi
240240 0 0
241241 −1.51311e6 −1.67814 −0.839068 0.544027i 0.816899π-0.816899\pi
−0.839068 + 0.544027i 0.816899π0.816899\pi
242242 −362352. −0.397733
243243 −59049.0 −0.0641500
244244 −1.07940e6 −1.16067
245245 0 0
246246 170947. 0.180104
247247 362641. 0.378211
248248 −616898. −0.636919
249249 −253996. −0.259614
250250 0 0
251251 −404872. −0.405633 −0.202816 0.979217i 0.565009π-0.565009\pi
−0.202816 + 0.979217i 0.565009π0.565009\pi
252252 495274. 0.491297
253253 −68145.1 −0.0669320
254254 −5121.19 −0.00498066
255255 0 0
256256 −287300. −0.273990
257257 −1.76267e6 −1.66471 −0.832353 0.554245i 0.813007π-0.813007\pi
−0.832353 + 0.554245i 0.813007π0.813007\pi
258258 −10322.9 −0.00965503
259259 −2.08559e6 −1.93188
260260 0 0
261261 475658. 0.432208
262262 −415701. −0.374134
263263 567933. 0.506300 0.253150 0.967427i 0.418533π-0.418533\pi
0.253150 + 0.967427i 0.418533π0.418533\pi
264264 71886.7 0.0634802
265265 0 0
266266 −1.12973e6 −0.978974
267267 −314738. −0.270191
268268 −1.86106e6 −1.58279
269269 −242686. −0.204486 −0.102243 0.994759i 0.532602π-0.532602\pi
−0.102243 + 0.994759i 0.532602π0.532602\pi
270270 0 0
271271 389530. 0.322194 0.161097 0.986939i 0.448497π-0.448497\pi
0.161097 + 0.986939i 0.448497π0.448497\pi
272272 −1.27469e6 −1.04468
273273 348183. 0.282749
274274 241561. 0.194380
275275 0 0
276276 −276934. −0.218828
277277 −1.13298e6 −0.887206 −0.443603 0.896223i 0.646300π-0.646300\pi
−0.443603 + 0.896223i 0.646300π0.646300\pi
278278 −819447. −0.635929
279279 370063. 0.284620
280280 0 0
281281 886440. 0.669705 0.334852 0.942271i 0.391314π-0.391314\pi
0.334852 + 0.942271i 0.391314π0.391314\pi
282282 383484. 0.287160
283283 1.37650e6 1.02167 0.510836 0.859678i 0.329336π-0.329336\pi
0.510836 + 0.859678i 0.329336π0.329336\pi
284284 1.94711e6 1.43250
285285 0 0
286286 22992.0 0.0166212
287287 1.89055e6 1.35483
288288 451369. 0.320664
289289 4.06685e6 2.86427
290290 0 0
291291 −605157. −0.418925
292292 −157757. −0.108276
293293 −239467. −0.162958 −0.0814790 0.996675i 0.525964π-0.525964\pi
−0.0814790 + 0.996675i 0.525964π0.525964\pi
294294 −736803. −0.497145
295295 0 0
296296 −1.23019e6 −0.816102
297297 −43123.2 −0.0283674
298298 680038. 0.443601
299299 −194688. −0.125939
300300 0 0
301301 −114165. −0.0726299
302302 281067. 0.177334
303303 1.45874e6 0.912788
304304 1.16772e6 0.724694
305305 0 0
306306 −436363. −0.266406
307307 −1.67234e6 −1.01269 −0.506347 0.862330i 0.669004π-0.669004\pi
−0.506347 + 0.862330i 0.669004π0.669004\pi
308308 361696. 0.217253
309309 947988. 0.564816
310310 0 0
311311 −1.00067e6 −0.586664 −0.293332 0.956011i 0.594764π-0.594764\pi
−0.293332 + 0.956011i 0.594764π0.594764\pi
312312 205377. 0.119444
313313 612773. 0.353540 0.176770 0.984252i 0.443435π-0.443435\pi
0.176770 + 0.984252i 0.443435π0.443435\pi
314314 −156113. −0.0893541
315315 0 0
316316 −2.50025e6 −1.40853
317317 −1.52019e6 −0.849670 −0.424835 0.905271i 0.639668π-0.639668\pi
−0.424835 + 0.905271i 0.639668π0.639668\pi
318318 222790. 0.123546
319319 347370. 0.191124
320320 0 0
321321 −2.10849e6 −1.14211
322322 606509. 0.325985
323323 −5.02627e6 −2.68065
324324 −175248. −0.0927448
325325 0 0
326326 362879. 0.189111
327327 1.85203e6 0.957810
328328 1.11515e6 0.572333
329329 4.24108e6 2.16016
330330 0 0
331331 −1.70279e6 −0.854260 −0.427130 0.904190i 0.640475π-0.640475\pi
−0.427130 + 0.904190i 0.640475π0.640475\pi
332332 −753819. −0.375337
333333 737965. 0.364691
334334 −1.26196e6 −0.618985
335335 0 0
336336 1.12116e6 0.541778
337337 −2.16136e6 −1.03670 −0.518350 0.855168i 0.673454π-0.673454\pi
−0.518350 + 0.855168i 0.673454π0.673454\pi
338338 65687.2 0.0312744
339339 1.45635e6 0.688282
340340 0 0
341341 270255. 0.125860
342342 399744. 0.184806
343343 −4.30113e6 −1.97400
344344 −67340.5 −0.0306817
345345 0 0
346346 1.08333e6 0.486486
347347 −1.30185e6 −0.580413 −0.290207 0.956964i 0.593724π-0.593724\pi
−0.290207 + 0.956964i 0.593724π0.593724\pi
348348 1.41167e6 0.624865
349349 −806129. −0.354275 −0.177138 0.984186i 0.556684π-0.556684\pi
−0.177138 + 0.984186i 0.556684π0.556684\pi
350350 0 0
351351 −123201. −0.0533761
352352 329632. 0.141799
353353 1.21170e6 0.517555 0.258778 0.965937i 0.416680π-0.416680\pi
0.258778 + 0.965937i 0.416680π0.416680\pi
354354 −63359.2 −0.0268721
355355 0 0
356356 −934091. −0.390629
357357 −4.82588e6 −2.00404
358358 −853933. −0.352141
359359 40339.1 0.0165193 0.00825963 0.999966i 0.497371π-0.497371\pi
0.00825963 + 0.999966i 0.497371π0.497371\pi
360360 0 0
361361 2.12837e6 0.859567
362362 1.17388e6 0.470819
363363 1.41797e6 0.564806
364364 1.03335e6 0.408784
365365 0 0
366366 −836470. −0.326398
367367 −3.28931e6 −1.27479 −0.637396 0.770537i 0.719988π-0.719988\pi
−0.637396 + 0.770537i 0.719988π0.719988\pi
368368 −626903. −0.241313
369369 −668953. −0.255758
370370 0 0
371371 2.46390e6 0.929371
372372 1.09829e6 0.411489
373373 1.73305e6 0.644970 0.322485 0.946575i 0.395482π-0.395482\pi
0.322485 + 0.946575i 0.395482π0.395482\pi
374374 −318674. −0.117806
375375 0 0
376376 2.50162e6 0.912538
377377 992421. 0.359619
378378 383807. 0.138160
379379 425983. 0.152333 0.0761665 0.997095i 0.475732π-0.475732\pi
0.0761665 + 0.997095i 0.475732π0.475732\pi
380380 0 0
381381 20040.4 0.00707285
382382 139820. 0.0490242
383383 4.18083e6 1.45635 0.728175 0.685391i 0.240369π-0.240369\pi
0.728175 + 0.685391i 0.240369π0.240369\pi
384384 1.70004e6 0.588344
385385 0 0
386386 1.08938e6 0.372143
387387 40396.0 0.0137107
388388 −1.79601e6 −0.605660
389389 −1.92802e6 −0.646008 −0.323004 0.946398i 0.604693π-0.604693\pi
−0.323004 + 0.946398i 0.604693π0.604693\pi
390390 0 0
391391 2.69841e6 0.892619
392392 −4.80645e6 −1.57983
393393 1.62673e6 0.531294
394394 1.08514e6 0.352163
395395 0 0
396396 −127982. −0.0410121
397397 1.51118e6 0.481216 0.240608 0.970622i 0.422653π-0.422653\pi
0.240608 + 0.970622i 0.422653π0.422653\pi
398398 2.01204e6 0.636692
399399 4.42090e6 1.39020
400400 0 0
401401 −201369. −0.0625362 −0.0312681 0.999511i 0.509955π-0.509955\pi
−0.0312681 + 0.999511i 0.509955π0.509955\pi
402402 −1.44221e6 −0.445105
403403 772107. 0.236818
404404 4.32928e6 1.31966
405405 0 0
406406 −3.09168e6 −0.930850
407407 538932. 0.161268
408408 −2.84657e6 −0.846586
409409 3.36373e6 0.994291 0.497145 0.867667i 0.334382π-0.334382\pi
0.497145 + 0.867667i 0.334382π0.334382\pi
410410 0 0
411411 −945286. −0.276031
412412 2.81347e6 0.816581
413413 −700710. −0.202145
414414 −214607. −0.0615379
415415 0 0
416416 941745. 0.266809
417417 3.20668e6 0.903059
418418 291931. 0.0817221
419419 −1.76055e6 −0.489906 −0.244953 0.969535i 0.578772π-0.578772\pi
−0.244953 + 0.969535i 0.578772π0.578772\pi
420420 0 0
421421 2.40677e6 0.661803 0.330901 0.943665i 0.392647π-0.392647\pi
0.330901 + 0.943665i 0.392647π0.392647\pi
422422 −86646.1 −0.0236847
423423 −1.50066e6 −0.407786
424424 1.45334e6 0.392603
425425 0 0
426426 1.50889e6 0.402840
427427 −9.25079e6 −2.45533
428428 −6.25766e6 −1.65121
429429 −89973.0 −0.0236031
430430 0 0
431431 3.02707e6 0.784927 0.392463 0.919768i 0.371623π-0.371623\pi
0.392463 + 0.919768i 0.371623π0.371623\pi
432432 −396713. −0.102274
433433 −998142. −0.255842 −0.127921 0.991784i 0.540830π-0.540830\pi
−0.127921 + 0.991784i 0.540830π0.540830\pi
434434 −2.40534e6 −0.612987
435435 0 0
436436 5.49652e6 1.38475
437437 −2.47196e6 −0.619210
438438 −122252. −0.0304489
439439 2.45313e6 0.607519 0.303759 0.952749i 0.401758π-0.401758\pi
0.303759 + 0.952749i 0.401758π0.401758\pi
440440 0 0
441441 2.88328e6 0.705977
442442 −910437. −0.221663
443443 2.53464e6 0.613631 0.306815 0.951769i 0.400737π-0.400737\pi
0.306815 + 0.951769i 0.400737π0.400737\pi
444444 2.19016e6 0.527252
445445 0 0
446446 −2.60706e6 −0.620604
447447 −2.66114e6 −0.629941
448448 1.05255e6 0.247770
449449 −1.70620e6 −0.399405 −0.199703 0.979857i 0.563998π-0.563998\pi
−0.199703 + 0.979857i 0.563998π0.563998\pi
450450 0 0
451451 −488533. −0.113097
452452 4.32220e6 0.995083
453453 −1.09988e6 −0.251825
454454 758256. 0.172654
455455 0 0
456456 2.60769e6 0.587277
457457 −382585. −0.0856915 −0.0428458 0.999082i 0.513642π-0.513642\pi
−0.0428458 + 0.999082i 0.513642π0.513642\pi
458458 −152259. −0.0339172
459459 1.70759e6 0.378313
460460 0 0
461461 −7.16362e6 −1.56993 −0.784964 0.619541i 0.787319π-0.787319\pi
−0.784964 + 0.619541i 0.787319π0.787319\pi
462462 280292. 0.0610950
463463 3.22317e6 0.698764 0.349382 0.936980i 0.386392π-0.386392\pi
0.349382 + 0.936980i 0.386392π0.386392\pi
464464 3.19564e6 0.689069
465465 0 0
466466 −1.94828e6 −0.415610
467467 −5.46265e6 −1.15907 −0.579537 0.814946i 0.696767π-0.696767\pi
−0.579537 + 0.814946i 0.696767π0.696767\pi
468468 −365640. −0.0771683
469469 −1.59498e7 −3.34830
470470 0 0
471471 610906. 0.126888
472472 −413317. −0.0853941
473473 29501.0 0.00606294
474474 −1.93754e6 −0.396100
475475 0 0
476476 −1.43224e7 −2.89734
477477 −871828. −0.175442
478478 1.48776e6 0.297826
479479 −5.39101e6 −1.07357 −0.536786 0.843718i 0.680362π-0.680362\pi
−0.536786 + 0.843718i 0.680362π0.680362\pi
480480 0 0
481481 1.53970e6 0.303441
482482 −3.47998e6 −0.682275
483483 −2.37341e6 −0.462919
484484 4.20829e6 0.816568
485485 0 0
486486 −135806. −0.0260813
487487 7.84939e6 1.49973 0.749866 0.661590i 0.230118π-0.230118\pi
0.749866 + 0.661590i 0.230118π0.230118\pi
488488 −5.45662e6 −1.03723
489489 −1.42003e6 −0.268550
490490 0 0
491491 1.12840e6 0.211231 0.105616 0.994407i 0.466319π-0.466319\pi
0.105616 + 0.994407i 0.466319π0.466319\pi
492492 −1.98534e6 −0.369762
493493 −1.37552e7 −2.54887
494494 834034. 0.153768
495495 0 0
496496 2.48622e6 0.453769
497497 1.66873e7 3.03036
498498 −584163. −0.105551
499499 9.57003e6 1.72053 0.860265 0.509848i 0.170298π-0.170298\pi
0.860265 + 0.509848i 0.170298π0.170298\pi
500500 0 0
501501 4.93835e6 0.878997
502502 −931160. −0.164917
503503 8.58409e6 1.51278 0.756388 0.654123i 0.226962π-0.226962\pi
0.756388 + 0.654123i 0.226962π0.226962\pi
504504 2.50372e6 0.439046
505505 0 0
506506 −156726. −0.0272123
507507 −257049. −0.0444116
508508 59476.6 0.0102256
509509 −7.23162e6 −1.23720 −0.618602 0.785705i 0.712300π-0.712300\pi
−0.618602 + 0.785705i 0.712300π0.712300\pi
510510 0 0
511511 −1.35203e6 −0.229052
512512 5.38383e6 0.907646
513513 −1.56429e6 −0.262436
514514 −4.05394e6 −0.676815
515515 0 0
516516 119889. 0.0198223
517517 −1.09592e6 −0.180324
518518 −4.79663e6 −0.785437
519519 −4.23932e6 −0.690841
520520 0 0
521521 −1.15289e7 −1.86078 −0.930389 0.366573i 0.880531π-0.880531\pi
−0.930389 + 0.366573i 0.880531π0.880531\pi
522522 1.09396e6 0.175722
523523 9.32605e6 1.49088 0.745442 0.666571i 0.232239π-0.232239\pi
0.745442 + 0.666571i 0.232239π0.232239\pi
524524 4.82787e6 0.768117
525525 0 0
526526 1.30618e6 0.205845
527527 −1.07015e7 −1.67850
528528 −289717. −0.0452261
529529 −5.10924e6 −0.793812
530530 0 0
531531 247939. 0.0381600
532532 1.31205e7 2.00989
533533 −1.39572e6 −0.212804
534534 −723863. −0.109851
535535 0 0
536536 −9.40808e6 −1.41445
537537 3.34164e6 0.500062
538538 −558151. −0.0831373
539539 2.10564e6 0.312186
540540 0 0
541541 −3.26784e6 −0.480029 −0.240014 0.970769i 0.577152π-0.577152\pi
−0.240014 + 0.970769i 0.577152π0.577152\pi
542542 895876. 0.130994
543543 −4.59368e6 −0.668592
544544 −1.30528e7 −1.89106
545545 0 0
546546 800782. 0.114956
547547 −5.16606e6 −0.738229 −0.369114 0.929384i 0.620339π-0.620339\pi
−0.369114 + 0.929384i 0.620339π0.620339\pi
548548 −2.80545e6 −0.399072
549549 3.27330e6 0.463505
550550 0 0
551551 1.26008e7 1.76815
552552 −1.39997e6 −0.195555
553553 −2.14279e7 −2.97966
554554 −2.60574e6 −0.360709
555555 0 0
556556 9.51691e6 1.30560
557557 7.71027e6 1.05301 0.526504 0.850173i 0.323503π-0.323503\pi
0.526504 + 0.850173i 0.323503π0.323503\pi
558558 851104. 0.115717
559559 84283.0 0.0114080
560560 0 0
561561 1.24704e6 0.167292
562562 2.03871e6 0.272280
563563 −8.33451e6 −1.10818 −0.554088 0.832458i 0.686933π-0.686933\pi
−0.554088 + 0.832458i 0.686933π0.686933\pi
564564 −4.45371e6 −0.589555
565565 0 0
566566 3.16581e6 0.415378
567567 −1.50193e6 −0.196196
568568 9.84306e6 1.28015
569569 −1.88775e6 −0.244435 −0.122218 0.992503i 0.539001π-0.539001\pi
−0.122218 + 0.992503i 0.539001π0.539001\pi
570570 0 0
571571 7.84065e6 1.00638 0.503190 0.864176i 0.332160π-0.332160\pi
0.503190 + 0.864176i 0.332160π0.332160\pi
572572 −267025. −0.0341241
573573 −547148. −0.0696174
574574 4.34806e6 0.550828
575575 0 0
576576 −372434. −0.0467728
577577 −4.39327e6 −0.549349 −0.274674 0.961537i 0.588570π-0.588570\pi
−0.274674 + 0.961537i 0.588570π0.588570\pi
578578 9.35331e6 1.16452
579579 −4.26299e6 −0.528467
580580 0 0
581581 −6.46045e6 −0.794004
582582 −1.39180e6 −0.170321
583583 −636691. −0.0775814
584584 −797500. −0.0967606
585585 0 0
586586 −550747. −0.0662534
587587 1.21559e7 1.45610 0.728049 0.685525i 0.240427π-0.240427\pi
0.728049 + 0.685525i 0.240427π0.240427\pi
588588 8.55709e6 1.02066
589589 9.80349e6 1.16437
590590 0 0
591591 −4.24639e6 −0.500093
592592 4.95792e6 0.581427
593593 1.27303e7 1.48663 0.743315 0.668941i 0.233252π-0.233252\pi
0.743315 + 0.668941i 0.233252π0.233252\pi
594594 −99178.5 −0.0115332
595595 0 0
596596 −7.89784e6 −0.910736
597597 −7.87359e6 −0.904142
598598 −447760. −0.0512027
599599 4.00848e6 0.456470 0.228235 0.973606i 0.426705π-0.426705\pi
0.228235 + 0.973606i 0.426705π0.426705\pi
600600 0 0
601601 2.62995e6 0.297003 0.148502 0.988912i 0.452555π-0.452555\pi
0.148502 + 0.988912i 0.452555π0.452555\pi
602602 −262566. −0.0295289
603603 5.64369e6 0.632077
604604 −3.26426e6 −0.364076
605605 0 0
606606 3.35493e6 0.371109
607607 −6.42797e6 −0.708112 −0.354056 0.935224i 0.615198π-0.615198\pi
−0.354056 + 0.935224i 0.615198π0.615198\pi
608608 1.19574e7 1.31183
609609 1.20985e7 1.32186
610610 0 0
611611 −3.13101e6 −0.339298
612612 5.06784e6 0.546946
613613 −1.20038e7 −1.29023 −0.645116 0.764084i 0.723191π-0.723191\pi
−0.645116 + 0.764084i 0.723191π0.723191\pi
614614 −3.84619e6 −0.411728
615615 0 0
616616 1.82845e6 0.194148
617617 8.45943e6 0.894599 0.447300 0.894384i 0.352386π-0.352386\pi
0.447300 + 0.894384i 0.352386π0.352386\pi
618618 2.18027e6 0.229635
619619 1.08577e7 1.13897 0.569483 0.822003i 0.307144π-0.307144\pi
0.569483 + 0.822003i 0.307144π0.307144\pi
620620 0 0
621621 839807. 0.0873877
622622 −2.30143e6 −0.238518
623623 −8.00544e6 −0.826352
624624 −827709. −0.0850974
625625 0 0
626626 1.40931e6 0.143738
627627 −1.14239e6 −0.116050
628628 1.81307e6 0.183449
629629 −2.13406e7 −2.15070
630630 0 0
631631 1.62647e7 1.62620 0.813099 0.582126i 0.197779π-0.197779\pi
0.813099 + 0.582126i 0.197779π0.197779\pi
632632 −1.26393e7 −1.25873
633633 339066. 0.0336337
634634 −3.49627e6 −0.345448
635635 0 0
636636 −2.58744e6 −0.253646
637637 6.01573e6 0.587408
638638 798913. 0.0777048
639639 −5.90463e6 −0.572058
640640 0 0
641641 −1.24335e7 −1.19523 −0.597613 0.801785i 0.703884π-0.703884\pi
−0.597613 + 0.801785i 0.703884π0.703884\pi
642642 −4.84930e6 −0.464346
643643 5.47279e6 0.522013 0.261006 0.965337i 0.415946π-0.415946\pi
0.261006 + 0.965337i 0.415946π0.415946\pi
644644 −7.04388e6 −0.669264
645645 0 0
646646 −1.15599e7 −1.08986
647647 1.77694e7 1.66883 0.834414 0.551138i 0.185806π-0.185806\pi
0.834414 + 0.551138i 0.185806π0.185806\pi
648648 −885917. −0.0828811
649649 181069. 0.0168745
650650 0 0
651651 9.41264e6 0.870480
652652 −4.21441e6 −0.388256
653653 2.12465e7 1.94987 0.974933 0.222498i 0.0714210π-0.0714210\pi
0.974933 + 0.222498i 0.0714210π0.0714210\pi
654654 4.25947e6 0.389414
655655 0 0
656656 −4.49427e6 −0.407755
657657 478402. 0.0432394
658658 9.75401e6 0.878250
659659 2.08310e7 1.86852 0.934258 0.356597i 0.116063π-0.116063\pi
0.934258 + 0.356597i 0.116063π0.116063\pi
660660 0 0
661661 1.36207e7 1.21254 0.606272 0.795258i 0.292664π-0.292664\pi
0.606272 + 0.795258i 0.292664π0.292664\pi
662662 −3.91622e6 −0.347314
663663 3.56275e6 0.314776
664664 −3.81073e6 −0.335419
665665 0 0
666666 1.69724e6 0.148271
667667 −6.76490e6 −0.588771
668668 1.46562e7 1.27081
669669 1.02020e7 0.881296
670670 0 0
671671 2.39047e6 0.204964
672672 1.14807e7 0.980718
673673 −6.82294e6 −0.580676 −0.290338 0.956924i 0.593768π-0.593768\pi
−0.290338 + 0.956924i 0.593768π0.593768\pi
674674 −4.97090e6 −0.421488
675675 0 0
676676 −762879. −0.0642079
677677 7.93083e6 0.665038 0.332519 0.943096i 0.392101π-0.392101\pi
0.332519 + 0.943096i 0.392101π0.392101\pi
678678 3.34944e6 0.279833
679679 −1.53923e7 −1.28124
680680 0 0
681681 −2.96723e6 −0.245179
682682 621557. 0.0511705
683683 −1.34275e7 −1.10140 −0.550698 0.834705i 0.685638π-0.685638\pi
−0.550698 + 0.834705i 0.685638π0.685638\pi
684684 −4.64256e6 −0.379417
685685 0 0
686686 −9.89213e6 −0.802564
687687 595825. 0.0481645
688688 271395. 0.0218590
689689 −1.81900e6 −0.145977
690690 0 0
691691 −6.45401e6 −0.514203 −0.257101 0.966384i 0.582767π-0.582767\pi
−0.257101 + 0.966384i 0.582767π0.582767\pi
692692 −1.25816e7 −0.998782
693693 −1.09685e6 −0.0867587
694694 −2.99411e6 −0.235977
695695 0 0
696696 7.13633e6 0.558408
697697 1.93449e7 1.50829
698698 −1.85401e6 −0.144037
699699 7.62406e6 0.590192
700700 0 0
701701 −1.35502e7 −1.04148 −0.520740 0.853715i 0.674344π-0.674344\pi
−0.520740 + 0.853715i 0.674344π0.674344\pi
702702 −283349. −0.0217009
703703 1.95497e7 1.49194
704704 −271987. −0.0206831
705705 0 0
706706 2.78677e6 0.210421
707707 3.71033e7 2.79167
708708 735842. 0.0551698
709709 1.41562e6 0.105762 0.0528812 0.998601i 0.483160π-0.483160\pi
0.0528812 + 0.998601i 0.483160π0.483160\pi
710710 0 0
711711 7.58205e6 0.562487
712712 −4.72204e6 −0.349084
713713 −5.26311e6 −0.387720
714714 −1.10990e7 −0.814776
715715 0 0
716716 9.91743e6 0.722964
717717 −5.82194e6 −0.422931
718718 92775.6 0.00671619
719719 6.11475e6 0.441120 0.220560 0.975373i 0.429212π-0.429212\pi
0.220560 + 0.975373i 0.429212π0.429212\pi
720720 0 0
721721 2.41123e7 1.72743
722722 4.89502e6 0.349472
723723 1.36180e7 0.968872
724724 −1.36333e7 −0.966616
725725 0 0
726726 3.26117e6 0.229631
727727 −1.44079e7 −1.01103 −0.505515 0.862818i 0.668697π-0.668697\pi
−0.505515 + 0.862818i 0.668697π0.668697\pi
728728 5.22382e6 0.365308
729729 531441. 0.0370370
730730 0 0
731731 −1.16818e6 −0.0808567
732732 9.71461e6 0.670112
733733 −9.95927e6 −0.684649 −0.342324 0.939582i 0.611214π-0.611214\pi
−0.342324 + 0.939582i 0.611214π0.611214\pi
734734 −7.56504e6 −0.518288
735735 0 0
736736 −6.41946e6 −0.436822
737737 4.12156e6 0.279507
738738 −1.53852e6 −0.103983
739739 −5.09810e6 −0.343398 −0.171699 0.985149i 0.554926π-0.554926\pi
−0.171699 + 0.985149i 0.554926π0.554926\pi
740740 0 0
741741 −3.26377e6 −0.218360
742742 5.66671e6 0.377852
743743 −1.43927e7 −0.956465 −0.478232 0.878233i 0.658722π-0.658722\pi
−0.478232 + 0.878233i 0.658722π0.658722\pi
744744 5.55208e6 0.367725
745745 0 0
746746 3.98583e6 0.262224
747747 2.28597e6 0.149888
748748 3.70102e6 0.241862
749749 −5.36300e7 −3.49304
750750 0 0
751751 −5.64574e6 −0.365276 −0.182638 0.983180i 0.558464π-0.558464\pi
−0.182638 + 0.983180i 0.558464π0.558464\pi
752752 −1.00820e7 −0.650132
753753 3.64384e6 0.234192
754754 2.28246e6 0.146209
755755 0 0
756756 −4.45746e6 −0.283650
757757 8.05893e6 0.511137 0.255569 0.966791i 0.417737π-0.417737\pi
0.255569 + 0.966791i 0.417737π0.417737\pi
758758 979714. 0.0619336
759759 613306. 0.0386432
760760 0 0
761761 1.08877e7 0.681513 0.340757 0.940152i 0.389317π-0.389317\pi
0.340757 + 0.940152i 0.389317π0.389317\pi
762762 46090.8 0.00287559
763763 4.71069e7 2.92936
764764 −1.62384e6 −0.100649
765765 0 0
766766 9.61546e6 0.592104
767767 517305. 0.0317511
768768 2.58570e6 0.158188
769769 −1.39723e7 −0.852024 −0.426012 0.904718i 0.640082π-0.640082\pi
−0.426012 + 0.904718i 0.640082π0.640082\pi
770770 0 0
771771 1.58640e7 0.961119
772772 −1.26518e7 −0.764030
773773 −1.39598e7 −0.840291 −0.420145 0.907457i 0.638021π-0.638021\pi
−0.420145 + 0.907457i 0.638021π0.638021\pi
774774 92906.3 0.00557433
775775 0 0
776776 −9.07922e6 −0.541246
777777 1.87703e7 1.11537
778778 −4.43424e6 −0.262645
779779 −1.77215e7 −1.04630
780780 0 0
781781 −4.31212e6 −0.252966
782782 6.20604e6 0.362909
783783 −4.28092e6 −0.249536
784784 1.93709e7 1.12554
785785 0 0
786786 3.74131e6 0.216007
787787 1.67531e7 0.964182 0.482091 0.876121i 0.339877π-0.339877\pi
0.482091 + 0.876121i 0.339877π0.339877\pi
788788 −1.26026e7 −0.723009
789789 −5.11140e6 −0.292313
790790 0 0
791791 3.70426e7 2.10504
792792 −646980. −0.0366503
793793 6.82948e6 0.385660
794794 3.47555e6 0.195646
795795 0 0
796796 −2.33675e7 −1.30716
797797 −3.77172e6 −0.210326 −0.105163 0.994455i 0.533536π-0.533536\pi
−0.105163 + 0.994455i 0.533536π0.533536\pi
798798 1.01676e7 0.565211
799799 4.33964e7 2.40484
800800 0 0
801801 2.83264e6 0.155995
802802 −463126. −0.0254251
803803 349374. 0.0191206
804804 1.67495e7 0.913824
805805 0 0
806806 1.77576e6 0.0962824
807807 2.18417e6 0.118060
808808 2.18855e7 1.17931
809809 −1.66028e7 −0.891889 −0.445944 0.895061i 0.647132π-0.647132\pi
−0.445944 + 0.895061i 0.647132π0.647132\pi
810810 0 0
811811 −1.33967e7 −0.715229 −0.357614 0.933869i 0.616410π-0.616410\pi
−0.357614 + 0.933869i 0.616410π0.616410\pi
812812 3.59062e7 1.91108
813813 −3.50577e6 −0.186019
814814 1.23948e6 0.0655662
815815 0 0
816816 1.14722e7 0.603145
817817 1.07015e6 0.0560903
818818 7.73622e6 0.404246
819819 −3.13365e6 −0.163245
820820 0 0
821821 −3.43509e7 −1.77861 −0.889303 0.457319i 0.848810π-0.848810\pi
−0.889303 + 0.457319i 0.848810π0.848810\pi
822822 −2.17405e6 −0.112225
823823 2.61045e7 1.34343 0.671716 0.740809i 0.265558π-0.265558\pi
0.671716 + 0.740809i 0.265558π0.265558\pi
824824 1.42227e7 0.729735
825825 0 0
826826 −1.61156e6 −0.0821855
827827 −1.80085e7 −0.915619 −0.457809 0.889050i 0.651366π-0.651366\pi
−0.457809 + 0.889050i 0.651366π0.651366\pi
828828 2.49241e6 0.126341
829829 603123. 0.0304803 0.0152402 0.999884i 0.495149π-0.495149\pi
0.0152402 + 0.999884i 0.495149π0.495149\pi
830830 0 0
831831 1.01969e7 0.512229
832832 −777054. −0.0389173
833833 −8.33792e7 −4.16337
834834 7.37502e6 0.367154
835835 0 0
836836 −3.39043e6 −0.167780
837837 −3.33057e6 −0.164325
838838 −4.04906e6 −0.199179
839839 −1.88617e7 −0.925075 −0.462537 0.886600i 0.653061π-0.653061\pi
−0.462537 + 0.886600i 0.653061π0.653061\pi
840840 0 0
841841 1.39729e7 0.681236
842842 5.53530e6 0.269067
843843 −7.97796e6 −0.386654
844844 1.00629e6 0.0486259
845845 0 0
846846 −3.45136e6 −0.165792
847847 3.60663e7 1.72740
848848 −5.85725e6 −0.279708
849849 −1.23885e7 −0.589862
850850 0 0
851851 −1.04955e7 −0.496797
852852 −1.75240e7 −0.827053
853853 −3.84677e7 −1.81019 −0.905095 0.425209i 0.860200π-0.860200\pi
−0.905095 + 0.425209i 0.860200π0.860200\pi
854854 −2.12758e7 −0.998255
855855 0 0
856856 −3.16339e7 −1.47560
857857 1.67613e7 0.779571 0.389785 0.920906i 0.372549π-0.372549\pi
0.389785 + 0.920906i 0.372549π0.372549\pi
858858 −206928. −0.00959624
859859 −4.29704e6 −0.198695 −0.0993474 0.995053i 0.531676π-0.531676\pi
−0.0993474 + 0.995053i 0.531676π0.531676\pi
860860 0 0
861861 −1.70150e7 −0.782210
862862 6.96193e6 0.319125
863863 −3.78429e7 −1.72965 −0.864824 0.502076i 0.832570π-0.832570\pi
−0.864824 + 0.502076i 0.832570π0.832570\pi
864864 −4.06232e6 −0.185136
865865 0 0
866866 −2.29562e6 −0.104017
867867 −3.66017e7 −1.65369
868868 2.79351e7 1.25850
869869 5.53713e6 0.248734
870870 0 0
871871 1.17751e7 0.525920
872872 2.77862e7 1.23748
873873 5.44642e6 0.241866
874874 −5.68524e6 −0.251750
875875 0 0
876876 1.41982e6 0.0625133
877877 636892. 0.0279619 0.0139809 0.999902i 0.495550π-0.495550\pi
0.0139809 + 0.999902i 0.495550π0.495550\pi
878878 5.64193e6 0.246997
879879 2.15520e6 0.0940839
880880 0 0
881881 −1.61380e7 −0.700501 −0.350251 0.936656i 0.613904π-0.613904\pi
−0.350251 + 0.936656i 0.613904π0.613904\pi
882882 6.63123e6 0.287027
883883 −4.30661e7 −1.85880 −0.929401 0.369070i 0.879676π-0.879676\pi
−0.929401 + 0.369070i 0.879676π0.879676\pi
884884 1.05736e7 0.455087
885885 0 0
886886 5.82939e6 0.249482
887887 1.14749e7 0.489710 0.244855 0.969560i 0.421260π-0.421260\pi
0.244855 + 0.969560i 0.421260π0.421260\pi
888888 1.10717e7 0.471177
889889 509733. 0.0216316
890890 0 0
891891 388108. 0.0163779
892892 3.02780e7 1.27413
893893 −3.97546e7 −1.66824
894894 −6.12034e6 −0.256113
895895 0 0
896896 4.32409e7 1.79939
897897 1.75219e6 0.0727110
898898 −3.92407e6 −0.162385
899899 2.68287e7 1.10714
900900 0 0
901901 2.52117e7 1.03464
902902 −1.12357e6 −0.0459816
903903 1.02748e6 0.0419329
904904 2.18497e7 0.889252
905905 0 0
906906 −2.52960e6 −0.102384
907907 −2.78914e7 −1.12578 −0.562888 0.826533i 0.690310π-0.690310\pi
−0.562888 + 0.826533i 0.690310π0.690310\pi
908908 −8.80624e6 −0.354467
909909 −1.31286e7 −0.526998
910910 0 0
911911 3.28566e7 1.31168 0.655838 0.754901i 0.272315π-0.272315\pi
0.655838 + 0.754901i 0.272315π0.272315\pi
912912 −1.05095e7 −0.418402
913913 1.66943e6 0.0662813
914914 −879904. −0.0348393
915915 0 0
916916 1.76831e6 0.0696337
917917 4.13763e7 1.62491
918918 3.92727e6 0.153810
919919 −4.82181e7 −1.88331 −0.941655 0.336580i 0.890730π-0.890730\pi
−0.941655 + 0.336580i 0.890730π0.890730\pi
920920 0 0
921921 1.50510e7 0.584679
922922 −1.64755e7 −0.638281
923923 −1.23195e7 −0.475981
924924 −3.25526e6 −0.125431
925925 0 0
926926 7.41293e6 0.284094
927927 −8.53189e6 −0.326096
928928 3.27232e7 1.24734
929929 3.03481e7 1.15370 0.576850 0.816850i 0.304282π-0.304282\pi
0.576850 + 0.816850i 0.304282π0.304282\pi
930930 0 0
931931 7.63821e7 2.88813
932932 2.26269e7 0.853269
933933 9.00601e6 0.338710
934934 −1.25635e7 −0.471241
935935 0 0
936936 −1.84839e6 −0.0689612
937937 1.60933e7 0.598820 0.299410 0.954125i 0.403210π-0.403210\pi
0.299410 + 0.954125i 0.403210π0.403210\pi
938938 −3.66829e7 −1.36131
939939 −5.51496e6 −0.204116
940940 0 0
941941 −1.68509e6 −0.0620366 −0.0310183 0.999519i 0.509875π-0.509875\pi
−0.0310183 + 0.999519i 0.509875π0.509875\pi
942942 1.40502e6 0.0515886
943943 9.51399e6 0.348404
944944 1.66575e6 0.0608385
945945 0 0
946946 67849.0 0.00246499
947947 8.47809e6 0.307201 0.153601 0.988133i 0.450913π-0.450913\pi
0.153601 + 0.988133i 0.450913π0.450913\pi
948948 2.25023e7 0.813215
949949 998147. 0.0359773
950950 0 0
951951 1.36817e7 0.490557
952952 −7.24031e7 −2.58920
953953 2.42401e7 0.864573 0.432286 0.901736i 0.357707π-0.357707\pi
0.432286 + 0.901736i 0.357707π0.357707\pi
954954 −2.00511e6 −0.0713291
955955 0 0
956956 −1.72785e7 −0.611452
957957 −3.12633e6 −0.110346
958958 −1.23987e7 −0.436479
959959 −2.40436e7 −0.844213
960960 0 0
961961 −7.75633e6 −0.270924
962962 3.54115e6 0.123369
963963 1.89764e7 0.659400
964964 4.04159e7 1.40075
965965 0 0
966966 −5.45858e6 −0.188207
967967 2.22310e7 0.764528 0.382264 0.924053i 0.375144π-0.375144\pi
0.382264 + 0.924053i 0.375144π0.375144\pi
968968 2.12739e7 0.729723
969969 4.52364e7 1.54767
970970 0 0
971971 −2.48740e7 −0.846636 −0.423318 0.905981i 0.639135π-0.639135\pi
−0.423318 + 0.905981i 0.639135π0.639135\pi
972972 1.57723e6 0.0535462
973973 8.15628e7 2.76191
974974 1.80527e7 0.609741
975975 0 0
976976 2.19912e7 0.738966
977977 −3.30020e7 −1.10613 −0.553063 0.833140i 0.686541π-0.686541\pi
−0.553063 + 0.833140i 0.686541π0.686541\pi
978978 −3.26591e6 −0.109184
979979 2.06866e6 0.0689816
980980 0 0
981981 −1.66683e7 −0.552992
982982 2.59519e6 0.0858797
983983 6.32809e6 0.208876 0.104438 0.994531i 0.466696π-0.466696\pi
0.104438 + 0.994531i 0.466696π0.466696\pi
984984 −1.00364e7 −0.330437
985985 0 0
986986 −3.16353e7 −1.03629
987987 −3.81697e7 −1.24717
988988 −9.68632e6 −0.315694
989989 −574520. −0.0186773
990990 0 0
991991 1.37930e7 0.446145 0.223072 0.974802i 0.428391π-0.428391\pi
0.223072 + 0.974802i 0.428391π0.428391\pi
992992 2.54588e7 0.821407
993993 1.53251e7 0.493207
994994 3.83789e7 1.23205
995995 0 0
996996 6.78437e6 0.216701
997997 −4.62221e7 −1.47269 −0.736346 0.676605i 0.763450π-0.763450\pi
−0.736346 + 0.676605i 0.763450π0.763450\pi
998998 2.20100e7 0.699510
999999 −6.64168e6 −0.210554
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 975.6.a.u.1.7 yes 11
5.4 even 2 975.6.a.r.1.5 11
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
975.6.a.r.1.5 11 5.4 even 2
975.6.a.u.1.7 yes 11 1.1 even 1 trivial