Properties

Label 7744.2.a.dv.1.1
Level 77447744
Weight 22
Character 7744.1
Self dual yes
Analytic conductor 61.83661.836
Analytic rank 11
Dimension 66
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] = [7744,2,Mod(1,7744)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(7744, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 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("7744.1");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 7744=26112 7744 = 2^{6} \cdot 11^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 7744.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: 61.836151325361.8361513253
Analytic rank: 11
Dimension: 66
Coefficient field: 6.6.19898000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x6x510x4+7x3+24x215x5 x^{6} - x^{5} - 10x^{4} + 7x^{3} + 24x^{2} - 15x - 5 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 352)
Fricke sign: +1+1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 2.865642.86564 of defining polynomial
Character χ\chi == 7744.1

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) == q1.86564q3+2.22111q50.973509q7+0.480595q95.76323q134.14378q153.97580q17+2.81392q19+1.81621q21+1.20615q230.0666695q25+4.70029q272.08367q29+6.84856q312.16227q35+9.41004q37+10.7521q39+4.40102q41+8.84372q43+1.06745q45+1.44564q476.05228q49+7.41739q51+10.2399q535.24976q573.52945q594.13538q610.467864q6312.8008q65+12.2596q672.25024q699.44515q716.62134q73+0.124381q75+7.76432q7910.2108q8117.2597q838.83068q85+3.88737q870.470432q89+5.61056q9112.7769q93+6.25003q959.06025q97+O(q100)q-1.86564 q^{3} +2.22111 q^{5} -0.973509 q^{7} +0.480595 q^{9} -5.76323 q^{13} -4.14378 q^{15} -3.97580 q^{17} +2.81392 q^{19} +1.81621 q^{21} +1.20615 q^{23} -0.0666695 q^{25} +4.70029 q^{27} -2.08367 q^{29} +6.84856 q^{31} -2.16227 q^{35} +9.41004 q^{37} +10.7521 q^{39} +4.40102 q^{41} +8.84372 q^{43} +1.06745 q^{45} +1.44564 q^{47} -6.05228 q^{49} +7.41739 q^{51} +10.2399 q^{53} -5.24976 q^{57} -3.52945 q^{59} -4.13538 q^{61} -0.467864 q^{63} -12.8008 q^{65} +12.2596 q^{67} -2.25024 q^{69} -9.44515 q^{71} -6.62134 q^{73} +0.124381 q^{75} +7.76432 q^{79} -10.2108 q^{81} -17.2597 q^{83} -8.83068 q^{85} +3.88737 q^{87} -0.470432 q^{89} +5.61056 q^{91} -12.7769 q^{93} +6.25003 q^{95} -9.06025 q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 6q+5q32q7+7q94q138q159q17+5q1912q216q23+4q25+26q2710q2912q3126q35+12q372q3917q41+11q43+21q97+O(q100) 6 q + 5 q^{3} - 2 q^{7} + 7 q^{9} - 4 q^{13} - 8 q^{15} - 9 q^{17} + 5 q^{19} - 12 q^{21} - 6 q^{23} + 4 q^{25} + 26 q^{27} - 10 q^{29} - 12 q^{31} - 26 q^{35} + 12 q^{37} - 2 q^{39} - 17 q^{41} + 11 q^{43}+ \cdots - 21 q^{97}+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 0
33 −1.86564 −1.07713 −0.538563 0.842586i 0.681032π-0.681032\pi
−0.538563 + 0.842586i 0.681032π0.681032\pi
44 0 0
55 2.22111 0.993311 0.496655 0.867948i 0.334561π-0.334561\pi
0.496655 + 0.867948i 0.334561π0.334561\pi
66 0 0
77 −0.973509 −0.367952 −0.183976 0.982931i 0.558897π-0.558897\pi
−0.183976 + 0.982931i 0.558897π0.558897\pi
88 0 0
99 0.480595 0.160198
1010 0 0
1111 0 0
1212 0 0
1313 −5.76323 −1.59843 −0.799216 0.601044i 0.794752π-0.794752\pi
−0.799216 + 0.601044i 0.794752π0.794752\pi
1414 0 0
1515 −4.14378 −1.06992
1616 0 0
1717 −3.97580 −0.964273 −0.482136 0.876096i 0.660139π-0.660139\pi
−0.482136 + 0.876096i 0.660139π0.660139\pi
1818 0 0
1919 2.81392 0.645558 0.322779 0.946474i 0.395383π-0.395383\pi
0.322779 + 0.946474i 0.395383π0.395383\pi
2020 0 0
2121 1.81621 0.396330
2222 0 0
2323 1.20615 0.251500 0.125750 0.992062i 0.459866π-0.459866\pi
0.125750 + 0.992062i 0.459866π0.459866\pi
2424 0 0
2525 −0.0666695 −0.0133339
2626 0 0
2727 4.70029 0.904571
2828 0 0
2929 −2.08367 −0.386928 −0.193464 0.981107i 0.561972π-0.561972\pi
−0.193464 + 0.981107i 0.561972π0.561972\pi
3030 0 0
3131 6.84856 1.23004 0.615019 0.788512i 0.289148π-0.289148\pi
0.615019 + 0.788512i 0.289148π0.289148\pi
3232 0 0
3333 0 0
3434 0 0
3535 −2.16227 −0.365490
3636 0 0
3737 9.41004 1.54700 0.773501 0.633795i 0.218504π-0.218504\pi
0.773501 + 0.633795i 0.218504π0.218504\pi
3838 0 0
3939 10.7521 1.72171
4040 0 0
4141 4.40102 0.687323 0.343662 0.939094i 0.388333π-0.388333\pi
0.343662 + 0.939094i 0.388333π0.388333\pi
4242 0 0
4343 8.84372 1.34865 0.674327 0.738432i 0.264434π-0.264434\pi
0.674327 + 0.738432i 0.264434π0.264434\pi
4444 0 0
4545 1.06745 0.159127
4646 0 0
4747 1.44564 0.210869 0.105434 0.994426i 0.466377π-0.466377\pi
0.105434 + 0.994426i 0.466377π0.466377\pi
4848 0 0
4949 −6.05228 −0.864611
5050 0 0
5151 7.41739 1.03864
5252 0 0
5353 10.2399 1.40656 0.703282 0.710911i 0.251717π-0.251717\pi
0.703282 + 0.710911i 0.251717π0.251717\pi
5454 0 0
5555 0 0
5656 0 0
5757 −5.24976 −0.695347
5858 0 0
5959 −3.52945 −0.459495 −0.229748 0.973250i 0.573790π-0.573790\pi
−0.229748 + 0.973250i 0.573790π0.573790\pi
6060 0 0
6161 −4.13538 −0.529482 −0.264741 0.964320i 0.585286π-0.585286\pi
−0.264741 + 0.964320i 0.585286π0.585286\pi
6262 0 0
6363 −0.467864 −0.0589453
6464 0 0
6565 −12.8008 −1.58774
6666 0 0
6767 12.2596 1.49774 0.748872 0.662714i 0.230596π-0.230596\pi
0.748872 + 0.662714i 0.230596π0.230596\pi
6868 0 0
6969 −2.25024 −0.270897
7070 0 0
7171 −9.44515 −1.12093 −0.560467 0.828177i 0.689378π-0.689378\pi
−0.560467 + 0.828177i 0.689378π0.689378\pi
7272 0 0
7373 −6.62134 −0.774969 −0.387485 0.921876i 0.626656π-0.626656\pi
−0.387485 + 0.921876i 0.626656π0.626656\pi
7474 0 0
7575 0.124381 0.0143623
7676 0 0
7777 0 0
7878 0 0
7979 7.76432 0.873554 0.436777 0.899570i 0.356120π-0.356120\pi
0.436777 + 0.899570i 0.356120π0.356120\pi
8080 0 0
8181 −10.2108 −1.13453
8282 0 0
8383 −17.2597 −1.89450 −0.947251 0.320492i 0.896152π-0.896152\pi
−0.947251 + 0.320492i 0.896152π0.896152\pi
8484 0 0
8585 −8.83068 −0.957822
8686 0 0
8787 3.88737 0.416770
8888 0 0
8989 −0.470432 −0.0498657 −0.0249328 0.999689i 0.507937π-0.507937\pi
−0.0249328 + 0.999689i 0.507937π0.507937\pi
9090 0 0
9191 5.61056 0.588146
9292 0 0
9393 −12.7769 −1.32490
9494 0 0
9595 6.25003 0.641240
9696 0 0
9797 −9.06025 −0.919929 −0.459965 0.887937i 0.652138π-0.652138\pi
−0.459965 + 0.887937i 0.652138π0.652138\pi
9898 0 0
9999 0 0
100100 0 0
101101 −13.2414 −1.31757 −0.658786 0.752331i 0.728930π-0.728930\pi
−0.658786 + 0.752331i 0.728930π0.728930\pi
102102 0 0
103103 −15.2000 −1.49770 −0.748849 0.662740i 0.769393π-0.769393\pi
−0.748849 + 0.662740i 0.769393π0.769393\pi
104104 0 0
105105 4.03401 0.393679
106106 0 0
107107 20.5113 1.98290 0.991449 0.130493i 0.0416559π-0.0416559\pi
0.991449 + 0.130493i 0.0416559π0.0416559\pi
108108 0 0
109109 −4.79668 −0.459438 −0.229719 0.973257i 0.573781π-0.573781\pi
−0.229719 + 0.973257i 0.573781π0.573781\pi
110110 0 0
111111 −17.5557 −1.66631
112112 0 0
113113 6.52271 0.613605 0.306803 0.951773i 0.400741π-0.400741\pi
0.306803 + 0.951773i 0.400741π0.400741\pi
114114 0 0
115115 2.67900 0.249818
116116 0 0
117117 −2.76978 −0.256066
118118 0 0
119119 3.87047 0.354806
120120 0 0
121121 0 0
122122 0 0
123123 −8.21069 −0.740333
124124 0 0
125125 −11.2536 −1.00656
126126 0 0
127127 −13.5342 −1.20096 −0.600482 0.799638i 0.705025π-0.705025\pi
−0.600482 + 0.799638i 0.705025π0.705025\pi
128128 0 0
129129 −16.4992 −1.45267
130130 0 0
131131 −11.8240 −1.03306 −0.516532 0.856268i 0.672777π-0.672777\pi
−0.516532 + 0.856268i 0.672777π0.672777\pi
132132 0 0
133133 −2.73938 −0.237534
134134 0 0
135135 10.4399 0.898520
136136 0 0
137137 −16.7357 −1.42983 −0.714914 0.699212i 0.753534π-0.753534\pi
−0.714914 + 0.699212i 0.753534π0.753534\pi
138138 0 0
139139 11.5502 0.979676 0.489838 0.871814i 0.337056π-0.337056\pi
0.489838 + 0.871814i 0.337056π0.337056\pi
140140 0 0
141141 −2.69705 −0.227132
142142 0 0
143143 0 0
144144 0 0
145145 −4.62806 −0.384340
146146 0 0
147147 11.2913 0.931295
148148 0 0
149149 15.5034 1.27009 0.635043 0.772476i 0.280982π-0.280982\pi
0.635043 + 0.772476i 0.280982π0.280982\pi
150150 0 0
151151 −9.59246 −0.780623 −0.390312 0.920683i 0.627633π-0.627633\pi
−0.390312 + 0.920683i 0.627633π0.627633\pi
152152 0 0
153153 −1.91075 −0.154475
154154 0 0
155155 15.2114 1.22181
156156 0 0
157157 3.20127 0.255489 0.127744 0.991807i 0.459226π-0.459226\pi
0.127744 + 0.991807i 0.459226π0.459226\pi
158158 0 0
159159 −19.1040 −1.51505
160160 0 0
161161 −1.17420 −0.0925399
162162 0 0
163163 23.6441 1.85195 0.925974 0.377587i 0.123246π-0.123246\pi
0.925974 + 0.377587i 0.123246π0.123246\pi
164164 0 0
165165 0 0
166166 0 0
167167 −7.84707 −0.607225 −0.303612 0.952796i 0.598193π-0.598193\pi
−0.303612 + 0.952796i 0.598193π0.598193\pi
168168 0 0
169169 20.2148 1.55499
170170 0 0
171171 1.35236 0.103417
172172 0 0
173173 −1.88641 −0.143421 −0.0717107 0.997425i 0.522846π-0.522846\pi
−0.0717107 + 0.997425i 0.522846π0.522846\pi
174174 0 0
175175 0.0649034 0.00490623
176176 0 0
177177 6.58467 0.494934
178178 0 0
179179 −3.06573 −0.229144 −0.114572 0.993415i 0.536550π-0.536550\pi
−0.114572 + 0.993415i 0.536550π0.536550\pi
180180 0 0
181181 −6.72316 −0.499729 −0.249864 0.968281i 0.580386π-0.580386\pi
−0.249864 + 0.968281i 0.580386π0.580386\pi
182182 0 0
183183 7.71512 0.570318
184184 0 0
185185 20.9007 1.53665
186186 0 0
187187 0 0
188188 0 0
189189 −4.57577 −0.332839
190190 0 0
191191 −1.80547 −0.130639 −0.0653197 0.997864i 0.520807π-0.520807\pi
−0.0653197 + 0.997864i 0.520807π0.520807\pi
192192 0 0
193193 −0.810851 −0.0583663 −0.0291832 0.999574i 0.509291π-0.509291\pi
−0.0291832 + 0.999574i 0.509291π0.509291\pi
194194 0 0
195195 23.8816 1.71019
196196 0 0
197197 −18.6154 −1.32629 −0.663147 0.748489i 0.730780π-0.730780\pi
−0.663147 + 0.748489i 0.730780π0.730780\pi
198198 0 0
199199 −16.8109 −1.19170 −0.595848 0.803097i 0.703184π-0.703184\pi
−0.595848 + 0.803097i 0.703184π0.703184\pi
200200 0 0
201201 −22.8719 −1.61326
202202 0 0
203203 2.02847 0.142371
204204 0 0
205205 9.77514 0.682726
206206 0 0
207207 0.579671 0.0402899
208208 0 0
209209 0 0
210210 0 0
211211 −0.384111 −0.0264433 −0.0132216 0.999913i 0.504209π-0.504209\pi
−0.0132216 + 0.999913i 0.504209π0.504209\pi
212212 0 0
213213 17.6212 1.20739
214214 0 0
215215 19.6429 1.33963
216216 0 0
217217 −6.66713 −0.452595
218218 0 0
219219 12.3530 0.834739
220220 0 0
221221 22.9134 1.54132
222222 0 0
223223 −23.3143 −1.56124 −0.780622 0.625004i 0.785098π-0.785098\pi
−0.780622 + 0.625004i 0.785098π0.785098\pi
224224 0 0
225225 −0.0320410 −0.00213607
226226 0 0
227227 2.72537 0.180889 0.0904445 0.995901i 0.471171π-0.471171\pi
0.0904445 + 0.995901i 0.471171π0.471171\pi
228228 0 0
229229 −24.9517 −1.64885 −0.824426 0.565969i 0.808502π-0.808502\pi
−0.824426 + 0.565969i 0.808502π0.808502\pi
230230 0 0
231231 0 0
232232 0 0
233233 −21.1389 −1.38486 −0.692428 0.721487i 0.743459π-0.743459\pi
−0.692428 + 0.721487i 0.743459π0.743459\pi
234234 0 0
235235 3.21094 0.209458
236236 0 0
237237 −14.4854 −0.940927
238238 0 0
239239 0.208006 0.0134548 0.00672741 0.999977i 0.497859π-0.497859\pi
0.00672741 + 0.999977i 0.497859π0.497859\pi
240240 0 0
241241 1.25123 0.0805990 0.0402995 0.999188i 0.487169π-0.487169\pi
0.0402995 + 0.999188i 0.487169π0.487169\pi
242242 0 0
243243 4.94878 0.317465
244244 0 0
245245 −13.4428 −0.858828
246246 0 0
247247 −16.2173 −1.03188
248248 0 0
249249 32.2004 2.04062
250250 0 0
251251 −22.3385 −1.40999 −0.704996 0.709211i 0.749051π-0.749051\pi
−0.704996 + 0.709211i 0.749051π0.749051\pi
252252 0 0
253253 0 0
254254 0 0
255255 16.4748 1.03169
256256 0 0
257257 21.6595 1.35108 0.675542 0.737321i 0.263909π-0.263909\pi
0.675542 + 0.737321i 0.263909π0.263909\pi
258258 0 0
259259 −9.16076 −0.569222
260260 0 0
261261 −1.00140 −0.0619852
262262 0 0
263263 11.3447 0.699545 0.349773 0.936835i 0.386259π-0.386259\pi
0.349773 + 0.936835i 0.386259π0.386259\pi
264264 0 0
265265 22.7440 1.39716
266266 0 0
267267 0.877654 0.0537116
268268 0 0
269269 −14.3791 −0.876708 −0.438354 0.898802i 0.644438π-0.644438\pi
−0.438354 + 0.898802i 0.644438π0.644438\pi
270270 0 0
271271 −11.0116 −0.668908 −0.334454 0.942412i 0.608552π-0.608552\pi
−0.334454 + 0.942412i 0.608552π0.608552\pi
272272 0 0
273273 −10.4673 −0.633507
274274 0 0
275275 0 0
276276 0 0
277277 5.90241 0.354641 0.177321 0.984153i 0.443257π-0.443257\pi
0.177321 + 0.984153i 0.443257π0.443257\pi
278278 0 0
279279 3.29139 0.197050
280280 0 0
281281 13.1988 0.787376 0.393688 0.919244i 0.371199π-0.371199\pi
0.393688 + 0.919244i 0.371199π0.371199\pi
282282 0 0
283283 −8.74336 −0.519739 −0.259869 0.965644i 0.583680π-0.583680\pi
−0.259869 + 0.965644i 0.583680π0.583680\pi
284284 0 0
285285 −11.6603 −0.690696
286286 0 0
287287 −4.28443 −0.252902
288288 0 0
289289 −1.19303 −0.0701783
290290 0 0
291291 16.9031 0.990879
292292 0 0
293293 1.51630 0.0885830 0.0442915 0.999019i 0.485897π-0.485897\pi
0.0442915 + 0.999019i 0.485897π0.485897\pi
294294 0 0
295295 −7.83930 −0.456422
296296 0 0
297297 0 0
298298 0 0
299299 −6.95133 −0.402006
300300 0 0
301301 −8.60944 −0.496240
302302 0 0
303303 24.7037 1.41919
304304 0 0
305305 −9.18514 −0.525940
306306 0 0
307307 −5.53572 −0.315940 −0.157970 0.987444i 0.550495π-0.550495\pi
−0.157970 + 0.987444i 0.550495π0.550495\pi
308308 0 0
309309 28.3576 1.61321
310310 0 0
311311 9.16048 0.519443 0.259722 0.965684i 0.416369π-0.416369\pi
0.259722 + 0.965684i 0.416369π0.416369\pi
312312 0 0
313313 16.2744 0.919882 0.459941 0.887949i 0.347871π-0.347871\pi
0.459941 + 0.887949i 0.347871π0.347871\pi
314314 0 0
315315 −1.03918 −0.0585510
316316 0 0
317317 3.54644 0.199188 0.0995938 0.995028i 0.468246π-0.468246\pi
0.0995938 + 0.995028i 0.468246π0.468246\pi
318318 0 0
319319 0 0
320320 0 0
321321 −38.2665 −2.13583
322322 0 0
323323 −11.1876 −0.622494
324324 0 0
325325 0.384232 0.0213133
326326 0 0
327327 8.94885 0.494873
328328 0 0
329329 −1.40735 −0.0775896
330330 0 0
331331 16.2332 0.892257 0.446128 0.894969i 0.352802π-0.352802\pi
0.446128 + 0.894969i 0.352802π0.352802\pi
332332 0 0
333333 4.52242 0.247827
334334 0 0
335335 27.2299 1.48773
336336 0 0
337337 −8.46084 −0.460892 −0.230446 0.973085i 0.574018π-0.574018\pi
−0.230446 + 0.973085i 0.574018π0.574018\pi
338338 0 0
339339 −12.1690 −0.660929
340340 0 0
341341 0 0
342342 0 0
343343 12.7065 0.686087
344344 0 0
345345 −4.99803 −0.269085
346346 0 0
347347 −5.39095 −0.289401 −0.144701 0.989475i 0.546222π-0.546222\pi
−0.144701 + 0.989475i 0.546222π0.546222\pi
348348 0 0
349349 −12.9250 −0.691859 −0.345929 0.938261i 0.612436π-0.612436\pi
−0.345929 + 0.938261i 0.612436π0.612436\pi
350350 0 0
351351 −27.0889 −1.44590
352352 0 0
353353 34.5770 1.84035 0.920173 0.391511i 0.128047π-0.128047\pi
0.920173 + 0.391511i 0.128047π0.128047\pi
354354 0 0
355355 −20.9787 −1.11343
356356 0 0
357357 −7.22089 −0.382170
358358 0 0
359359 −23.1986 −1.22437 −0.612187 0.790713i 0.709710π-0.709710\pi
−0.612187 + 0.790713i 0.709710π0.709710\pi
360360 0 0
361361 −11.0818 −0.583254
362362 0 0
363363 0 0
364364 0 0
365365 −14.7067 −0.769785
366366 0 0
367367 −15.4707 −0.807566 −0.403783 0.914855i 0.632305π-0.632305\pi
−0.403783 + 0.914855i 0.632305π0.632305\pi
368368 0 0
369369 2.11511 0.110108
370370 0 0
371371 −9.96868 −0.517548
372372 0 0
373373 −30.5787 −1.58331 −0.791653 0.610970i 0.790779π-0.790779\pi
−0.791653 + 0.610970i 0.790779π0.790779\pi
374374 0 0
375375 20.9952 1.08419
376376 0 0
377377 12.0087 0.618478
378378 0 0
379379 −2.71862 −0.139646 −0.0698230 0.997559i 0.522243π-0.522243\pi
−0.0698230 + 0.997559i 0.522243π0.522243\pi
380380 0 0
381381 25.2498 1.29359
382382 0 0
383383 18.4024 0.940319 0.470159 0.882582i 0.344196π-0.344196\pi
0.470159 + 0.882582i 0.344196π0.344196\pi
384384 0 0
385385 0 0
386386 0 0
387387 4.25025 0.216052
388388 0 0
389389 −0.636434 −0.0322685 −0.0161342 0.999870i 0.505136π-0.505136\pi
−0.0161342 + 0.999870i 0.505136π0.505136\pi
390390 0 0
391391 −4.79542 −0.242515
392392 0 0
393393 22.0592 1.11274
394394 0 0
395395 17.2454 0.867711
396396 0 0
397397 19.6411 0.985760 0.492880 0.870097i 0.335944π-0.335944\pi
0.492880 + 0.870097i 0.335944π0.335944\pi
398398 0 0
399399 5.11068 0.255854
400400 0 0
401401 −5.75683 −0.287482 −0.143741 0.989615i 0.545913π-0.545913\pi
−0.143741 + 0.989615i 0.545913π0.545913\pi
402402 0 0
403403 −39.4698 −1.96613
404404 0 0
405405 −22.6793 −1.12695
406406 0 0
407407 0 0
408408 0 0
409409 23.1324 1.14382 0.571912 0.820315i 0.306202π-0.306202\pi
0.571912 + 0.820315i 0.306202π0.306202\pi
410410 0 0
411411 31.2227 1.54010
412412 0 0
413413 3.43595 0.169072
414414 0 0
415415 −38.3358 −1.88183
416416 0 0
417417 −21.5485 −1.05523
418418 0 0
419419 −20.6359 −1.00813 −0.504065 0.863666i 0.668163π-0.668163\pi
−0.504065 + 0.863666i 0.668163π0.668163\pi
420420 0 0
421421 −30.1427 −1.46906 −0.734532 0.678574i 0.762598π-0.762598\pi
−0.734532 + 0.678574i 0.762598π0.762598\pi
422422 0 0
423423 0.694770 0.0337809
424424 0 0
425425 0.265065 0.0128575
426426 0 0
427427 4.02583 0.194824
428428 0 0
429429 0 0
430430 0 0
431431 −32.6765 −1.57397 −0.786985 0.616972i 0.788359π-0.788359\pi
−0.786985 + 0.616972i 0.788359π0.788359\pi
432432 0 0
433433 28.0266 1.34687 0.673436 0.739245i 0.264818π-0.264818\pi
0.673436 + 0.739245i 0.264818π0.264818\pi
434434 0 0
435435 8.63428 0.413982
436436 0 0
437437 3.39402 0.162358
438438 0 0
439439 19.4940 0.930399 0.465200 0.885206i 0.345983π-0.345983\pi
0.465200 + 0.885206i 0.345983π0.345983\pi
440440 0 0
441441 −2.90870 −0.138509
442442 0 0
443443 8.91652 0.423637 0.211818 0.977309i 0.432061π-0.432061\pi
0.211818 + 0.977309i 0.432061π0.432061\pi
444444 0 0
445445 −1.04488 −0.0495321
446446 0 0
447447 −28.9237 −1.36804
448448 0 0
449449 0.730919 0.0344942 0.0172471 0.999851i 0.494510π-0.494510\pi
0.0172471 + 0.999851i 0.494510π0.494510\pi
450450 0 0
451451 0 0
452452 0 0
453453 17.8960 0.840829
454454 0 0
455455 12.4617 0.584212
456456 0 0
457457 1.63396 0.0764332 0.0382166 0.999269i 0.487832π-0.487832\pi
0.0382166 + 0.999269i 0.487832π0.487832\pi
458458 0 0
459459 −18.6874 −0.872253
460460 0 0
461461 2.38755 0.111199 0.0555996 0.998453i 0.482293π-0.482293\pi
0.0555996 + 0.998453i 0.482293π0.482293\pi
462462 0 0
463463 16.3739 0.760961 0.380480 0.924789i 0.375759π-0.375759\pi
0.380480 + 0.924789i 0.375759π0.375759\pi
464464 0 0
465465 −28.3789 −1.31604
466466 0 0
467467 22.0348 1.01965 0.509825 0.860278i 0.329710π-0.329710\pi
0.509825 + 0.860278i 0.329710π0.329710\pi
468468 0 0
469469 −11.9348 −0.551098
470470 0 0
471471 −5.97240 −0.275194
472472 0 0
473473 0 0
474474 0 0
475475 −0.187603 −0.00860781
476476 0 0
477477 4.92127 0.225329
478478 0 0
479479 −24.6894 −1.12809 −0.564044 0.825745i 0.690755π-0.690755\pi
−0.564044 + 0.825745i 0.690755π0.690755\pi
480480 0 0
481481 −54.2323 −2.47278
482482 0 0
483483 2.19063 0.0996771
484484 0 0
485485 −20.1238 −0.913776
486486 0 0
487487 19.5180 0.884446 0.442223 0.896905i 0.354190π-0.354190\pi
0.442223 + 0.896905i 0.354190π0.354190\pi
488488 0 0
489489 −44.1113 −1.99478
490490 0 0
491491 14.7670 0.666425 0.333213 0.942852i 0.391867π-0.391867\pi
0.333213 + 0.942852i 0.391867π0.391867\pi
492492 0 0
493493 8.28426 0.373104
494494 0 0
495495 0 0
496496 0 0
497497 9.19494 0.412449
498498 0 0
499499 −17.7602 −0.795054 −0.397527 0.917590i 0.630131π-0.630131\pi
−0.397527 + 0.917590i 0.630131π0.630131\pi
500500 0 0
501501 14.6398 0.654057
502502 0 0
503503 −16.4173 −0.732013 −0.366007 0.930612i 0.619275π-0.619275\pi
−0.366007 + 0.930612i 0.619275π0.619275\pi
504504 0 0
505505 −29.4107 −1.30876
506506 0 0
507507 −37.7135 −1.67491
508508 0 0
509509 13.4609 0.596645 0.298322 0.954465i 0.403573π-0.403573\pi
0.298322 + 0.954465i 0.403573π0.403573\pi
510510 0 0
511511 6.44593 0.285151
512512 0 0
513513 13.2263 0.583954
514514 0 0
515515 −33.7608 −1.48768
516516 0 0
517517 0 0
518518 0 0
519519 3.51936 0.154483
520520 0 0
521521 −36.4464 −1.59675 −0.798373 0.602163i 0.794306π-0.794306\pi
−0.798373 + 0.602163i 0.794306π0.794306\pi
522522 0 0
523523 11.3383 0.495788 0.247894 0.968787i 0.420261π-0.420261\pi
0.247894 + 0.968787i 0.420261π0.420261\pi
524524 0 0
525525 −0.121086 −0.00528463
526526 0 0
527527 −27.2285 −1.18609
528528 0 0
529529 −21.5452 −0.936748
530530 0 0
531531 −1.69624 −0.0736104
532532 0 0
533533 −25.3641 −1.09864
534534 0 0
535535 45.5578 1.96963
536536 0 0
537537 5.71954 0.246816
538538 0 0
539539 0 0
540540 0 0
541541 −40.8576 −1.75660 −0.878302 0.478106i 0.841323π-0.841323\pi
−0.878302 + 0.478106i 0.841323π0.841323\pi
542542 0 0
543543 12.5430 0.538270
544544 0 0
545545 −10.6539 −0.456365
546546 0 0
547547 −32.7961 −1.40226 −0.701129 0.713034i 0.747320π-0.747320\pi
−0.701129 + 0.713034i 0.747320π0.747320\pi
548548 0 0
549549 −1.98744 −0.0848221
550550 0 0
551551 −5.86329 −0.249785
552552 0 0
553553 −7.55864 −0.321426
554554 0 0
555555 −38.9932 −1.65517
556556 0 0
557557 7.50056 0.317809 0.158904 0.987294i 0.449204π-0.449204\pi
0.158904 + 0.987294i 0.449204π0.449204\pi
558558 0 0
559559 −50.9684 −2.15573
560560 0 0
561561 0 0
562562 0 0
563563 11.7203 0.493951 0.246976 0.969022i 0.420563π-0.420563\pi
0.246976 + 0.969022i 0.420563π0.420563\pi
564564 0 0
565565 14.4877 0.609501
566566 0 0
567567 9.94032 0.417454
568568 0 0
569569 7.42622 0.311323 0.155662 0.987810i 0.450249π-0.450249\pi
0.155662 + 0.987810i 0.450249π0.450249\pi
570570 0 0
571571 −37.7892 −1.58143 −0.790714 0.612185i 0.790291π-0.790291\pi
−0.790714 + 0.612185i 0.790291π0.790291\pi
572572 0 0
573573 3.36835 0.140715
574574 0 0
575575 −0.0804136 −0.00335348
576576 0 0
577577 −21.4699 −0.893802 −0.446901 0.894583i 0.647472π-0.647472\pi
−0.446901 + 0.894583i 0.647472π0.647472\pi
578578 0 0
579579 1.51275 0.0628678
580580 0 0
581581 16.8025 0.697086
582582 0 0
583583 0 0
584584 0 0
585585 −6.15199 −0.254353
586586 0 0
587587 1.97188 0.0813883 0.0406941 0.999172i 0.487043π-0.487043\pi
0.0406941 + 0.999172i 0.487043π0.487043\pi
588588 0 0
589589 19.2713 0.794061
590590 0 0
591591 34.7296 1.42858
592592 0 0
593593 7.57118 0.310911 0.155456 0.987843i 0.450315π-0.450315\pi
0.155456 + 0.987843i 0.450315π0.450315\pi
594594 0 0
595595 8.59675 0.352432
596596 0 0
597597 31.3631 1.28361
598598 0 0
599599 10.2478 0.418714 0.209357 0.977839i 0.432863π-0.432863\pi
0.209357 + 0.977839i 0.432863π0.432863\pi
600600 0 0
601601 3.45161 0.140794 0.0703970 0.997519i 0.477573π-0.477573\pi
0.0703970 + 0.997519i 0.477573π0.477573\pi
602602 0 0
603603 5.89189 0.239936
604604 0 0
605605 0 0
606606 0 0
607607 −3.14665 −0.127719 −0.0638593 0.997959i 0.520341π-0.520341\pi
−0.0638593 + 0.997959i 0.520341π0.520341\pi
608608 0 0
609609 −3.78439 −0.153351
610610 0 0
611611 −8.33158 −0.337060
612612 0 0
613613 −45.8250 −1.85086 −0.925428 0.378923i 0.876294π-0.876294\pi
−0.925428 + 0.378923i 0.876294π0.876294\pi
614614 0 0
615615 −18.2369 −0.735381
616616 0 0
617617 6.41440 0.258234 0.129117 0.991629i 0.458786π-0.458786\pi
0.129117 + 0.991629i 0.458786π0.458786\pi
618618 0 0
619619 29.7618 1.19623 0.598115 0.801411i 0.295917π-0.295917\pi
0.598115 + 0.801411i 0.295917π0.295917\pi
620620 0 0
621621 5.66927 0.227500
622622 0 0
623623 0.457969 0.0183482
624624 0 0
625625 −24.6622 −0.986488
626626 0 0
627627 0 0
628628 0 0
629629 −37.4124 −1.49173
630630 0 0
631631 48.7020 1.93879 0.969397 0.245498i 0.0789514π-0.0789514\pi
0.969397 + 0.245498i 0.0789514π0.0789514\pi
632632 0 0
633633 0.716611 0.0284827
634634 0 0
635635 −30.0609 −1.19293
636636 0 0
637637 34.8807 1.38202
638638 0 0
639639 −4.53929 −0.179572
640640 0 0
641641 16.8534 0.665669 0.332835 0.942985i 0.391995π-0.391995\pi
0.332835 + 0.942985i 0.391995π0.391995\pi
642642 0 0
643643 6.56513 0.258903 0.129452 0.991586i 0.458678π-0.458678\pi
0.129452 + 0.991586i 0.458678π0.458678\pi
644644 0 0
645645 −36.6465 −1.44295
646646 0 0
647647 3.53053 0.138800 0.0693998 0.997589i 0.477892π-0.477892\pi
0.0693998 + 0.997589i 0.477892π0.477892\pi
648648 0 0
649649 0 0
650650 0 0
651651 12.4384 0.487501
652652 0 0
653653 6.13537 0.240096 0.120048 0.992768i 0.461695π-0.461695\pi
0.120048 + 0.992768i 0.461695π0.461695\pi
654654 0 0
655655 −26.2623 −1.02615
656656 0 0
657657 −3.18218 −0.124149
658658 0 0
659659 −27.9511 −1.08882 −0.544410 0.838819i 0.683246π-0.683246\pi
−0.544410 + 0.838819i 0.683246π0.683246\pi
660660 0 0
661661 −11.5665 −0.449886 −0.224943 0.974372i 0.572220π-0.572220\pi
−0.224943 + 0.974372i 0.572220π0.572220\pi
662662 0 0
663663 −42.7481 −1.66020
664664 0 0
665665 −6.08446 −0.235945
666666 0 0
667667 −2.51323 −0.0973125
668668 0 0
669669 43.4961 1.68165
670670 0 0
671671 0 0
672672 0 0
673673 −14.1644 −0.545999 −0.273000 0.962014i 0.588016π-0.588016\pi
−0.273000 + 0.962014i 0.588016π0.588016\pi
674674 0 0
675675 −0.313366 −0.0120615
676676 0 0
677677 −25.3891 −0.975784 −0.487892 0.872904i 0.662234π-0.662234\pi
−0.487892 + 0.872904i 0.662234π0.662234\pi
678678 0 0
679679 8.82024 0.338490
680680 0 0
681681 −5.08454 −0.194840
682682 0 0
683683 −14.6841 −0.561870 −0.280935 0.959727i 0.590645π-0.590645\pi
−0.280935 + 0.959727i 0.590645π0.590645\pi
684684 0 0
685685 −37.1719 −1.42026
686686 0 0
687687 46.5507 1.77602
688688 0 0
689689 −59.0152 −2.24830
690690 0 0
691691 31.8808 1.21280 0.606401 0.795159i 0.292613π-0.292613\pi
0.606401 + 0.795159i 0.292613π0.292613\pi
692692 0 0
693693 0 0
694694 0 0
695695 25.6543 0.973122
696696 0 0
697697 −17.4976 −0.662767
698698 0 0
699699 39.4375 1.49166
700700 0 0
701701 16.7002 0.630759 0.315380 0.948966i 0.397868π-0.397868\pi
0.315380 + 0.948966i 0.397868π0.397868\pi
702702 0 0
703703 26.4791 0.998680
704704 0 0
705705 −5.99044 −0.225613
706706 0 0
707707 12.8907 0.484803
708708 0 0
709709 26.6741 1.00177 0.500884 0.865514i 0.333008π-0.333008\pi
0.500884 + 0.865514i 0.333008π0.333008\pi
710710 0 0
711711 3.73149 0.139942
712712 0 0
713713 8.26041 0.309355
714714 0 0
715715 0 0
716716 0 0
717717 −0.388064 −0.0144925
718718 0 0
719719 19.6224 0.731791 0.365896 0.930656i 0.380763π-0.380763\pi
0.365896 + 0.930656i 0.380763π0.380763\pi
720720 0 0
721721 14.7973 0.551081
722722 0 0
723723 −2.33434 −0.0868152
724724 0 0
725725 0.138917 0.00515926
726726 0 0
727727 −23.9815 −0.889424 −0.444712 0.895674i 0.646694π-0.646694\pi
−0.444712 + 0.895674i 0.646694π0.646694\pi
728728 0 0
729729 21.3998 0.792586
730730 0 0
731731 −35.1609 −1.30047
732732 0 0
733733 15.3420 0.566669 0.283334 0.959021i 0.408559π-0.408559\pi
0.283334 + 0.959021i 0.408559π0.408559\pi
734734 0 0
735735 25.0793 0.925065
736736 0 0
737737 0 0
738738 0 0
739739 −3.19534 −0.117542 −0.0587712 0.998271i 0.518718π-0.518718\pi
−0.0587712 + 0.998271i 0.518718π0.518718\pi
740740 0 0
741741 30.2555 1.11147
742742 0 0
743743 −30.9590 −1.13578 −0.567888 0.823106i 0.692239π-0.692239\pi
−0.567888 + 0.823106i 0.692239π0.692239\pi
744744 0 0
745745 34.4347 1.26159
746746 0 0
747747 −8.29495 −0.303496
748748 0 0
749749 −19.9679 −0.729611
750750 0 0
751751 −17.9709 −0.655769 −0.327884 0.944718i 0.606336π-0.606336\pi
−0.327884 + 0.944718i 0.606336π0.606336\pi
752752 0 0
753753 41.6755 1.51874
754754 0 0
755755 −21.3059 −0.775402
756756 0 0
757757 −14.6884 −0.533858 −0.266929 0.963716i 0.586009π-0.586009\pi
−0.266929 + 0.963716i 0.586009π0.586009\pi
758758 0 0
759759 0 0
760760 0 0
761761 −13.2646 −0.480841 −0.240420 0.970669i 0.577285π-0.577285\pi
−0.240420 + 0.970669i 0.577285π0.577285\pi
762762 0 0
763763 4.66961 0.169051
764764 0 0
765765 −4.24398 −0.153442
766766 0 0
767767 20.3410 0.734472
768768 0 0
769769 −30.0680 −1.08428 −0.542139 0.840289i 0.682385π-0.682385\pi
−0.542139 + 0.840289i 0.682385π0.682385\pi
770770 0 0
771771 −40.4088 −1.45529
772772 0 0
773773 −10.5402 −0.379104 −0.189552 0.981871i 0.560703π-0.560703\pi
−0.189552 + 0.981871i 0.560703π0.560703\pi
774774 0 0
775775 −0.456590 −0.0164012
776776 0 0
777777 17.0906 0.613123
778778 0 0
779779 12.3841 0.443707
780780 0 0
781781 0 0
782782 0 0
783783 −9.79386 −0.350004
784784 0 0
785785 7.11037 0.253780
786786 0 0
787787 37.5551 1.33870 0.669348 0.742949i 0.266573π-0.266573\pi
0.669348 + 0.742949i 0.266573π0.266573\pi
788788 0 0
789789 −21.1651 −0.753498
790790 0 0
791791 −6.34992 −0.225777
792792 0 0
793793 23.8332 0.846340
794794 0 0
795795 −42.4321 −1.50491
796796 0 0
797797 −15.7550 −0.558072 −0.279036 0.960281i 0.590015π-0.590015\pi
−0.279036 + 0.960281i 0.590015π0.590015\pi
798798 0 0
799799 −5.74759 −0.203335
800800 0 0
801801 −0.226087 −0.00798840
802802 0 0
803803 0 0
804804 0 0
805805 −2.60803 −0.0919209
806806 0 0
807807 26.8261 0.944325
808808 0 0
809809 −35.5605 −1.25024 −0.625120 0.780529i 0.714950π-0.714950\pi
−0.625120 + 0.780529i 0.714950π0.714950\pi
810810 0 0
811811 7.79005 0.273546 0.136773 0.990602i 0.456327π-0.456327\pi
0.136773 + 0.990602i 0.456327π0.456327\pi
812812 0 0
813813 20.5436 0.720497
814814 0 0
815815 52.5161 1.83956
816816 0 0
817817 24.8856 0.870635
818818 0 0
819819 2.69641 0.0942200
820820 0 0
821821 6.03130 0.210494 0.105247 0.994446i 0.466437π-0.466437\pi
0.105247 + 0.994446i 0.466437π0.466437\pi
822822 0 0
823823 −50.0562 −1.74485 −0.872425 0.488749i 0.837454π-0.837454\pi
−0.872425 + 0.488749i 0.837454π0.837454\pi
824824 0 0
825825 0 0
826826 0 0
827827 28.3258 0.984985 0.492492 0.870317i 0.336086π-0.336086\pi
0.492492 + 0.870317i 0.336086π0.336086\pi
828828 0 0
829829 5.42617 0.188459 0.0942293 0.995551i 0.469961π-0.469961\pi
0.0942293 + 0.995551i 0.469961π0.469961\pi
830830 0 0
831831 −11.0117 −0.381993
832832 0 0
833833 24.0626 0.833721
834834 0 0
835835 −17.4292 −0.603163
836836 0 0
837837 32.1902 1.11266
838838 0 0
839839 40.4123 1.39519 0.697594 0.716493i 0.254254π-0.254254\pi
0.697594 + 0.716493i 0.254254π0.254254\pi
840840 0 0
841841 −24.6583 −0.850287
842842 0 0
843843 −24.6242 −0.848102
844844 0 0
845845 44.8993 1.54458
846846 0 0
847847 0 0
848848 0 0
849849 16.3119 0.559824
850850 0 0
851851 11.3499 0.389071
852852 0 0
853853 24.0406 0.823133 0.411566 0.911380i 0.364982π-0.364982\pi
0.411566 + 0.911380i 0.364982π0.364982\pi
854854 0 0
855855 3.00374 0.102726
856856 0 0
857857 42.9442 1.46695 0.733474 0.679718i 0.237898π-0.237898\pi
0.733474 + 0.679718i 0.237898π0.237898\pi
858858 0 0
859859 −12.9486 −0.441800 −0.220900 0.975296i 0.570899π-0.570899\pi
−0.220900 + 0.975296i 0.570899π0.570899\pi
860860 0 0
861861 7.99318 0.272407
862862 0 0
863863 11.7658 0.400513 0.200256 0.979744i 0.435822π-0.435822\pi
0.200256 + 0.979744i 0.435822π0.435822\pi
864864 0 0
865865 −4.18993 −0.142462
866866 0 0
867867 2.22576 0.0755909
868868 0 0
869869 0 0
870870 0 0
871871 −70.6547 −2.39404
872872 0 0
873873 −4.35431 −0.147371
874874 0 0
875875 10.9555 0.370364
876876 0 0
877877 41.4239 1.39879 0.699393 0.714738i 0.253454π-0.253454\pi
0.699393 + 0.714738i 0.253454π0.253454\pi
878878 0 0
879879 −2.82886 −0.0954150
880880 0 0
881881 −44.7091 −1.50629 −0.753143 0.657857i 0.771463π-0.771463\pi
−0.753143 + 0.657857i 0.771463π0.771463\pi
882882 0 0
883883 21.9335 0.738119 0.369060 0.929406i 0.379680π-0.379680\pi
0.369060 + 0.929406i 0.379680π0.379680\pi
884884 0 0
885885 14.6253 0.491623
886886 0 0
887887 17.4780 0.586855 0.293427 0.955981i 0.405204π-0.405204\pi
0.293427 + 0.955981i 0.405204π0.405204\pi
888888 0 0
889889 13.1756 0.441897
890890 0 0
891891 0 0
892892 0 0
893893 4.06793 0.136128
894894 0 0
895895 −6.80933 −0.227611
896896 0 0
897897 12.9687 0.433011
898898 0 0
899899 −14.2702 −0.475936
900900 0 0
901901 −40.7119 −1.35631
902902 0 0
903903 16.0621 0.534513
904904 0 0
905905 −14.9329 −0.496386
906906 0 0
907907 −16.4521 −0.546282 −0.273141 0.961974i 0.588063π-0.588063\pi
−0.273141 + 0.961974i 0.588063π0.588063\pi
908908 0 0
909909 −6.36377 −0.211073
910910 0 0
911911 −15.1884 −0.503214 −0.251607 0.967829i 0.580959π-0.580959\pi
−0.251607 + 0.967829i 0.580959π0.580959\pi
912912 0 0
913913 0 0
914914 0 0
915915 17.1361 0.566503
916916 0 0
917917 11.5107 0.380118
918918 0 0
919919 −41.8476 −1.38042 −0.690212 0.723607i 0.742483π-0.742483\pi
−0.690212 + 0.723607i 0.742483π0.742483\pi
920920 0 0
921921 10.3276 0.340307
922922 0 0
923923 54.4346 1.79174
924924 0 0
925925 −0.627363 −0.0206276
926926 0 0
927927 −7.30504 −0.239929
928928 0 0
929929 0.313961 0.0103007 0.00515037 0.999987i 0.498361π-0.498361\pi
0.00515037 + 0.999987i 0.498361π0.498361\pi
930930 0 0
931931 −17.0307 −0.558157
932932 0 0
933933 −17.0901 −0.559505
934934 0 0
935935 0 0
936936 0 0
937937 −10.5890 −0.345927 −0.172963 0.984928i 0.555334π-0.555334\pi
−0.172963 + 0.984928i 0.555334π0.555334\pi
938938 0 0
939939 −30.3620 −0.990828
940940 0 0
941941 −58.8538 −1.91858 −0.959290 0.282422i 0.908862π-0.908862\pi
−0.959290 + 0.282422i 0.908862π0.908862\pi
942942 0 0
943943 5.30830 0.172862
944944 0 0
945945 −10.1633 −0.330612
946946 0 0
947947 −15.0139 −0.487887 −0.243943 0.969789i 0.578441π-0.578441\pi
−0.243943 + 0.969789i 0.578441π0.578441\pi
948948 0 0
949949 38.1603 1.23874
950950 0 0
951951 −6.61635 −0.214550
952952 0 0
953953 10.7187 0.347213 0.173607 0.984815i 0.444458π-0.444458\pi
0.173607 + 0.984815i 0.444458π0.444458\pi
954954 0 0
955955 −4.01015 −0.129765
956956 0 0
957957 0 0
958958 0 0
959959 16.2924 0.526108
960960 0 0
961961 15.9028 0.512993
962962 0 0
963963 9.85761 0.317657
964964 0 0
965965 −1.80099 −0.0579759
966966 0 0
967967 43.1296 1.38695 0.693477 0.720479i 0.256078π-0.256078\pi
0.693477 + 0.720479i 0.256078π0.256078\pi
968968 0 0
969969 20.8720 0.670504
970970 0 0
971971 16.5561 0.531310 0.265655 0.964068i 0.414412π-0.414412\pi
0.265655 + 0.964068i 0.414412π0.414412\pi
972972 0 0
973973 −11.2442 −0.360473
974974 0 0
975975 −0.716836 −0.0229571
976976 0 0
977977 1.56159 0.0499597 0.0249799 0.999688i 0.492048π-0.492048\pi
0.0249799 + 0.999688i 0.492048π0.492048\pi
978978 0 0
979979 0 0
980980 0 0
981981 −2.30526 −0.0736013
982982 0 0
983983 −48.6006 −1.55012 −0.775059 0.631889i 0.782280π-0.782280\pi
−0.775059 + 0.631889i 0.782280π0.782280\pi
984984 0 0
985985 −41.3469 −1.31742
986986 0 0
987987 2.62560 0.0835737
988988 0 0
989989 10.6669 0.339187
990990 0 0
991991 13.0806 0.415518 0.207759 0.978180i 0.433383π-0.433383\pi
0.207759 + 0.978180i 0.433383π0.433383\pi
992992 0 0
993993 −30.2852 −0.961072
994994 0 0
995995 −37.3389 −1.18372
996996 0 0
997997 −30.5715 −0.968211 −0.484105 0.875010i 0.660855π-0.660855\pi
−0.484105 + 0.875010i 0.660855π0.660855\pi
998998 0 0
999999 44.2299 1.39937
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 7744.2.a.dv.1.1 6
4.3 odd 2 7744.2.a.du.1.6 6
8.3 odd 2 3872.2.a.bq.1.1 6
8.5 even 2 3872.2.a.bn.1.6 6
11.3 even 5 704.2.m.n.449.3 12
11.4 even 5 704.2.m.n.577.3 12
11.10 odd 2 7744.2.a.dw.1.1 6
44.3 odd 10 704.2.m.m.449.1 12
44.15 odd 10 704.2.m.m.577.1 12
44.43 even 2 7744.2.a.dt.1.6 6
88.3 odd 10 352.2.m.e.97.3 12
88.21 odd 2 3872.2.a.bo.1.6 6
88.37 even 10 352.2.m.f.225.1 yes 12
88.43 even 2 3872.2.a.bp.1.1 6
88.59 odd 10 352.2.m.e.225.3 yes 12
88.69 even 10 352.2.m.f.97.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
352.2.m.e.97.3 12 88.3 odd 10
352.2.m.e.225.3 yes 12 88.59 odd 10
352.2.m.f.97.1 yes 12 88.69 even 10
352.2.m.f.225.1 yes 12 88.37 even 10
704.2.m.m.449.1 12 44.3 odd 10
704.2.m.m.577.1 12 44.15 odd 10
704.2.m.n.449.3 12 11.3 even 5
704.2.m.n.577.3 12 11.4 even 5
3872.2.a.bn.1.6 6 8.5 even 2
3872.2.a.bo.1.6 6 88.21 odd 2
3872.2.a.bp.1.1 6 88.43 even 2
3872.2.a.bq.1.1 6 8.3 odd 2
7744.2.a.dt.1.6 6 44.43 even 2
7744.2.a.du.1.6 6 4.3 odd 2
7744.2.a.dv.1.1 6 1.1 even 1 trivial
7744.2.a.dw.1.1 6 11.10 odd 2