Properties

Label 252.5.z.b.145.2
Level 252252
Weight 55
Character 252.145
Analytic conductor 26.04926.049
Analytic rank 00
Dimension 44
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [252,5,Mod(73,252)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(252, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 0, 1]))
 
N = Newforms(chi, 5, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("252.73");
 
S:= CuspForms(chi, 5);
 
N := Newforms(S);
 
Level: N N == 252=22327 252 = 2^{2} \cdot 3^{2} \cdot 7
Weight: k k == 5 5
Character orbit: [χ][\chi] == 252.z (of order 66, degree 22, minimal)

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: no
Analytic conductor: 26.049230697126.0492306971
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(ζ6)\Q(\zeta_{6})
Coefficient field: Q(3,19)\Q(\sqrt{-3}, \sqrt{-19})
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x4x34x25x+25 x^{4} - x^{3} - 4x^{2} - 5x + 25 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 32 3^{2}
Twist minimal: no (minimal twist has level 84)
Sato-Tate group: SU(2)[C6]\mathrm{SU}(2)[C_{6}]

Embedding invariants

Embedding label 145.2
Root 2.13746+0.656712i2.13746 + 0.656712i of defining polynomial
Character χ\chi == 252.145
Dual form 252.5.z.b.73.2

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+(7.23713+4.17836i)q5+(17.500045.7684i)q7+(38.8866+67.3536i)q1194.1795iq13+(93.5257+53.9971i)q17+(253.304146.245i)q19+(126.598+219.274i)q23+(277.583480.787i)q25548.310q29+(354.232204.516i)q31+(64.5872404.353i)q35+(135.232+234.229i)q373063.45iq41+553.062q43+(2037.621176.42i)q47+(1788.50+1601.90i)q49+(2511.814350.58i)q53+649.929iq55+(2913.62+1682.18i)q59+(2871.611657.92i)q61+(393.516681.589i)q65+(299.491518.734i)q675363.24q71+(1241.26+716.640i)q73+(2402.152958.47i)q77+(5586.989676.93i)q79+1326.79iq83902.477q85+(10705.2+6180.67i)q89+(4310.45+1648.14i)q91+(1222.132116.79i)q955319.78iq97+O(q100)q+(7.23713 + 4.17836i) q^{5} +(-17.5000 - 45.7684i) q^{7} +(38.8866 + 67.3536i) q^{11} -94.1795i q^{13} +(-93.5257 + 53.9971i) q^{17} +(-253.304 - 146.245i) q^{19} +(-126.598 + 219.274i) q^{23} +(-277.583 - 480.787i) q^{25} -548.310 q^{29} +(354.232 - 204.516i) q^{31} +(64.5872 - 404.353i) q^{35} +(-135.232 + 234.229i) q^{37} -3063.45i q^{41} +553.062 q^{43} +(-2037.62 - 1176.42i) q^{47} +(-1788.50 + 1601.90i) q^{49} +(-2511.81 - 4350.58i) q^{53} +649.929i q^{55} +(-2913.62 + 1682.18i) q^{59} +(-2871.61 - 1657.92i) q^{61} +(393.516 - 681.589i) q^{65} +(-299.491 - 518.734i) q^{67} -5363.24 q^{71} +(-1241.26 + 716.640i) q^{73} +(2402.15 - 2958.47i) q^{77} +(5586.98 - 9676.93i) q^{79} +1326.79i q^{83} -902.477 q^{85} +(10705.2 + 6180.67i) q^{89} +(-4310.45 + 1648.14i) q^{91} +(-1222.13 - 2116.79i) q^{95} -5319.78i q^{97} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q39q570q73q11510q17+459q19144q23227q25+570q29+2640q31+2478q35+433q3798q43+1770q477154q49+213q53+4857q59+19656q95+O(q100) 4 q - 39 q^{5} - 70 q^{7} - 3 q^{11} - 510 q^{17} + 459 q^{19} - 144 q^{23} - 227 q^{25} + 570 q^{29} + 2640 q^{31} + 2478 q^{35} + 433 q^{37} - 98 q^{43} + 1770 q^{47} - 7154 q^{49} + 213 q^{53} + 4857 q^{59}+ \cdots - 19656 q^{95}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/252Z)×\left(\mathbb{Z}/252\mathbb{Z}\right)^\times.

nn 2929 7373 127127
χ(n)\chi(n) 11 e(56)e\left(\frac{5}{6}\right) 11

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 0 0
44 0 0
55 7.23713 + 4.17836i 0.289485 + 0.167134i 0.637710 0.770277i 0.279882π-0.279882\pi
−0.348225 + 0.937411i 0.613215π0.613215\pi
66 0 0
77 −17.5000 45.7684i −0.357143 0.934050i
88 0 0
99 0 0
1010 0 0
1111 38.8866 + 67.3536i 0.321377 + 0.556641i 0.980772 0.195155i 0.0625210π-0.0625210\pi
−0.659395 + 0.751796i 0.729188π0.729188\pi
1212 0 0
1313 94.1795i 0.557275i −0.960396 0.278638i 0.910117π-0.910117\pi
0.960396 0.278638i 0.0898829π-0.0898829\pi
1414 0 0
1515 0 0
1616 0 0
1717 −93.5257 + 53.9971i −0.323618 + 0.186841i −0.653004 0.757354i 0.726492π-0.726492\pi
0.329386 + 0.944195i 0.393158π0.393158\pi
1818 0 0
1919 −253.304 146.245i −0.701674 0.405112i 0.106296 0.994334i 0.466101π-0.466101\pi
−0.807971 + 0.589223i 0.799434π0.799434\pi
2020 0 0
2121 0 0
2222 0 0
2323 −126.598 + 219.274i −0.239316 + 0.414507i −0.960518 0.278217i 0.910256π-0.910256\pi
0.721202 + 0.692724i 0.243590π0.243590\pi
2424 0 0
2525 −277.583 480.787i −0.444132 0.769260i
2626 0 0
2727 0 0
2828 0 0
2929 −548.310 −0.651974 −0.325987 0.945374i 0.605697π-0.605697\pi
−0.325987 + 0.945374i 0.605697π0.605697\pi
3030 0 0
3131 354.232 204.516i 0.368607 0.212816i −0.304242 0.952595i 0.598403π-0.598403\pi
0.672850 + 0.739779i 0.265070π0.265070\pi
3232 0 0
3333 0 0
3434 0 0
3535 64.5872 404.353i 0.0527242 0.330084i
3636 0 0
3737 −135.232 + 234.229i −0.0987817 + 0.171095i −0.911181 0.412007i 0.864828π-0.864828\pi
0.812399 + 0.583102i 0.198161π0.198161\pi
3838 0 0
3939 0 0
4040 0 0
4141 3063.45i 1.82239i −0.411970 0.911197i 0.635159π-0.635159\pi
0.411970 0.911197i 0.364841π-0.364841\pi
4242 0 0
4343 553.062 0.299114 0.149557 0.988753i 0.452215π-0.452215\pi
0.149557 + 0.988753i 0.452215π0.452215\pi
4444 0 0
4545 0 0
4646 0 0
4747 −2037.62 1176.42i −0.922418 0.532558i −0.0380121 0.999277i 0.512103π-0.512103\pi
−0.884406 + 0.466719i 0.845436π0.845436\pi
4848 0 0
4949 −1788.50 + 1601.90i −0.744898 + 0.667178i
5050 0 0
5151 0 0
5252 0 0
5353 −2511.81 4350.58i −0.894199 1.54880i −0.834792 0.550565i 0.814412π-0.814412\pi
−0.0594072 0.998234i 0.518921π-0.518921\pi
5454 0 0
5555 649.929i 0.214853i
5656 0 0
5757 0 0
5858 0 0
5959 −2913.62 + 1682.18i −0.837007 + 0.483246i −0.856246 0.516569i 0.827209π-0.827209\pi
0.0192386 + 0.999815i 0.493876π0.493876\pi
6060 0 0
6161 −2871.61 1657.92i −0.771730 0.445559i 0.0617613 0.998091i 0.480328π-0.480328\pi
−0.833491 + 0.552532i 0.813662π0.813662\pi
6262 0 0
6363 0 0
6464 0 0
6565 393.516 681.589i 0.0931398 0.161323i
6666 0 0
6767 −299.491 518.734i −0.0667167 0.115557i 0.830737 0.556664i 0.187919π-0.187919\pi
−0.897454 + 0.441108i 0.854586π0.854586\pi
6868 0 0
6969 0 0
7070 0 0
7171 −5363.24 −1.06392 −0.531962 0.846768i 0.678545π-0.678545\pi
−0.531962 + 0.846768i 0.678545π0.678545\pi
7272 0 0
7373 −1241.26 + 716.640i −0.232925 + 0.134479i −0.611921 0.790919i 0.709603π-0.709603\pi
0.378996 + 0.925398i 0.376269π0.376269\pi
7474 0 0
7575 0 0
7676 0 0
7777 2402.15 2958.47i 0.405153 0.498983i
7878 0 0
7979 5586.98 9676.93i 0.895205 1.55054i 0.0616549 0.998098i 0.480362π-0.480362\pi
0.833550 0.552443i 0.186304π-0.186304\pi
8080 0 0
8181 0 0
8282 0 0
8383 1326.79i 0.192595i 0.995353 + 0.0962977i 0.0307001π0.0307001\pi
−0.995353 + 0.0962977i 0.969300π0.969300\pi
8484 0 0
8585 −902.477 −0.124910
8686 0 0
8787 0 0
8888 0 0
8989 10705.2 + 6180.67i 1.35150 + 0.780289i 0.988460 0.151484i 0.0484051π-0.0484051\pi
0.363041 + 0.931773i 0.381738π0.381738\pi
9090 0 0
9191 −4310.45 + 1648.14i −0.520523 + 0.199027i
9292 0 0
9393 0 0
9494 0 0
9595 −1222.13 2116.79i −0.135416 0.234548i
9696 0 0
9797 5319.78i 0.565393i −0.959209 0.282696i 0.908771π-0.908771\pi
0.959209 0.282696i 0.0912289π-0.0912289\pi
9898 0 0
9999 0 0
100100 0 0
101101 3965.54 2289.51i 0.388740 0.224439i −0.292874 0.956151i 0.594612π-0.594612\pi
0.681614 + 0.731712i 0.261278π0.261278\pi
102102 0 0
103103 −6332.08 3655.83i −0.596859 0.344597i 0.170946 0.985280i 0.445318π-0.445318\pi
−0.767805 + 0.640684i 0.778651π0.778651\pi
104104 0 0
105105 0 0
106106 0 0
107107 −9698.96 + 16799.1i −0.847145 + 1.46730i 0.0366010 + 0.999330i 0.488347π0.488347\pi
−0.883746 + 0.467968i 0.844986π0.844986\pi
108108 0 0
109109 6465.30 + 11198.2i 0.544172 + 0.942533i 0.998659 + 0.0517795i 0.0164893π0.0164893\pi
−0.454487 + 0.890753i 0.650177π0.650177\pi
110110 0 0
111111 0 0
112112 0 0
113113 −5153.13 −0.403566 −0.201783 0.979430i 0.564674π-0.564674\pi
−0.201783 + 0.979430i 0.564674π0.564674\pi
114114 0 0
115115 −1832.41 + 1057.94i −0.138557 + 0.0799957i
116116 0 0
117117 0 0
118118 0 0
119119 4108.06 + 3335.58i 0.290097 + 0.235547i
120120 0 0
121121 4296.16 7441.17i 0.293434 0.508242i
122122 0 0
123123 0 0
124124 0 0
125125 9862.31i 0.631188i
126126 0 0
127127 10320.4 0.639865 0.319932 0.947440i 0.396340π-0.396340\pi
0.319932 + 0.947440i 0.396340π0.396340\pi
128128 0 0
129129 0 0
130130 0 0
131131 27221.9 + 15716.6i 1.58627 + 0.915832i 0.993915 + 0.110154i 0.0351345π0.0351345\pi
0.592354 + 0.805678i 0.298199π0.298199\pi
132132 0 0
133133 −2260.60 + 14152.6i −0.127797 + 0.800082i
134134 0 0
135135 0 0
136136 0 0
137137 −6927.98 11999.6i −0.369118 0.639332i 0.620310 0.784357i 0.287007π-0.287007\pi
−0.989428 + 0.145025i 0.953674π0.953674\pi
138138 0 0
139139 24750.2i 1.28100i 0.767959 + 0.640499i 0.221273π0.221273\pi
−0.767959 + 0.640499i 0.778727π0.778727\pi
140140 0 0
141141 0 0
142142 0 0
143143 6343.33 3662.33i 0.310203 0.179096i
144144 0 0
145145 −3968.19 2291.03i −0.188737 0.108967i
146146 0 0
147147 0 0
148148 0 0
149149 85.4878 148.069i 0.00385063 0.00666949i −0.864094 0.503331i 0.832108π-0.832108\pi
0.867944 + 0.496662i 0.165441π0.165441\pi
150150 0 0
151151 18574.4 + 32171.7i 0.814629 + 1.41098i 0.909594 + 0.415498i 0.136393π0.136393\pi
−0.0949648 + 0.995481i 0.530274π0.530274\pi
152152 0 0
153153 0 0
154154 0 0
155155 3418.16 0.142275
156156 0 0
157157 13150.6 7592.49i 0.533514 0.308024i −0.208932 0.977930i 0.566999π-0.566999\pi
0.742446 + 0.669906i 0.233665π0.233665\pi
158158 0 0
159159 0 0
160160 0 0
161161 12251.3 + 1956.90i 0.472640 + 0.0754946i
162162 0 0
163163 1890.00 3273.58i 0.0711357 0.123211i −0.828264 0.560339i 0.810671π-0.810671\pi
0.899399 + 0.437128i 0.144004π0.144004\pi
164164 0 0
165165 0 0
166166 0 0
167167 10590.5i 0.379739i −0.981809 0.189869i 0.939194π-0.939194\pi
0.981809 0.189869i 0.0608064π-0.0608064\pi
168168 0 0
169169 19691.2 0.689444
170170 0 0
171171 0 0
172172 0 0
173173 34763.8 + 20070.9i 1.16154 + 0.670616i 0.951673 0.307114i 0.0993632π-0.0993632\pi
0.209868 + 0.977730i 0.432697π0.432697\pi
174174 0 0
175175 −17147.2 + 21118.3i −0.559908 + 0.689577i
176176 0 0
177177 0 0
178178 0 0
179179 18788.4 + 32542.4i 0.586385 + 1.01565i 0.994701 + 0.102808i 0.0327826π0.0327826\pi
−0.408317 + 0.912840i 0.633884π0.633884\pi
180180 0 0
181181 39852.1i 1.21645i −0.793765 0.608224i 0.791882π-0.791882\pi
0.793765 0.608224i 0.208118π-0.208118\pi
182182 0 0
183183 0 0
184184 0 0
185185 −1957.38 + 1130.10i −0.0571917 + 0.0330196i
186186 0 0
187187 −7273.80 4199.53i −0.208007 0.120093i
188188 0 0
189189 0 0
190190 0 0
191191 −22747.5 + 39399.8i −0.623544 + 1.08001i 0.365277 + 0.930899i 0.380974π0.380974\pi
−0.988821 + 0.149111i 0.952359π0.952359\pi
192192 0 0
193193 −6045.20 10470.6i −0.162292 0.281097i 0.773399 0.633920i 0.218555π-0.218555\pi
−0.935690 + 0.352823i 0.885222π0.885222\pi
194194 0 0
195195 0 0
196196 0 0
197197 −43371.5 −1.11756 −0.558782 0.829315i 0.688731π-0.688731\pi
−0.558782 + 0.829315i 0.688731π0.688731\pi
198198 0 0
199199 19667.6 11355.1i 0.496645 0.286738i −0.230682 0.973029i 0.574096π-0.574096\pi
0.727327 + 0.686291i 0.240762π0.240762\pi
200200 0 0
201201 0 0
202202 0 0
203203 9595.42 + 25095.3i 0.232848 + 0.608976i
204204 0 0
205205 12800.2 22170.5i 0.304585 0.527556i
206206 0 0
207207 0 0
208208 0 0
209209 22748.0i 0.520775i
210210 0 0
211211 −75885.9 −1.70450 −0.852249 0.523137i 0.824762π-0.824762\pi
−0.852249 + 0.523137i 0.824762π0.824762\pi
212212 0 0
213213 0 0
214214 0 0
215215 4002.58 + 2310.89i 0.0865891 + 0.0499923i
216216 0 0
217217 −15559.4 12633.6i −0.330426 0.268292i
218218 0 0
219219 0 0
220220 0 0
221221 5085.42 + 8808.21i 0.104122 + 0.180345i
222222 0 0
223223 18276.7i 0.367526i 0.982971 + 0.183763i 0.0588279π0.0588279\pi
−0.982971 + 0.183763i 0.941172π0.941172\pi
224224 0 0
225225 0 0
226226 0 0
227227 10304.8 5949.48i 0.199981 0.115459i −0.396666 0.917963i 0.629833π-0.629833\pi
0.596646 + 0.802504i 0.296500π0.296500\pi
228228 0 0
229229 −254.071 146.688i −0.00484488 0.00279720i 0.497576 0.867421i 0.334224π-0.334224\pi
−0.502420 + 0.864623i 0.667557π0.667557\pi
230230 0 0
231231 0 0
232232 0 0
233233 35754.6 61928.8i 0.658598 1.14073i −0.322381 0.946610i 0.604483π-0.604483\pi
0.980979 0.194115i 0.0621835π-0.0621835\pi
234234 0 0
235235 −9831.01 17027.8i −0.178017 0.308335i
236236 0 0
237237 0 0
238238 0 0
239239 −62869.3 −1.10063 −0.550316 0.834956i 0.685493π-0.685493\pi
−0.550316 + 0.834956i 0.685493π0.685493\pi
240240 0 0
241241 52680.1 30414.9i 0.907011 0.523663i 0.0275425 0.999621i 0.491232π-0.491232\pi
0.879468 + 0.475958i 0.157899π0.157899\pi
242242 0 0
243243 0 0
244244 0 0
245245 −19636.9 + 4120.13i −0.327145 + 0.0686402i
246246 0 0
247247 −13773.3 + 23856.1i −0.225759 + 0.391026i
248248 0 0
249249 0 0
250250 0 0
251251 71630.1i 1.13697i −0.822695 0.568484i 0.807530π-0.807530\pi
0.822695 0.568484i 0.192470π-0.192470\pi
252252 0 0
253253 −19691.9 −0.307642
254254 0 0
255255 0 0
256256 0 0
257257 −50347.3 29068.0i −0.762271 0.440098i 0.0678393 0.997696i 0.478389π-0.478389\pi
−0.830111 + 0.557599i 0.811723π0.811723\pi
258258 0 0
259259 13086.9 + 2090.36i 0.195090 + 0.0311617i
260260 0 0
261261 0 0
262262 0 0
263263 −15899.6 27539.0i −0.229866 0.398140i 0.727902 0.685681i 0.240496π-0.240496\pi
−0.957768 + 0.287541i 0.907162π0.907162\pi
264264 0 0
265265 41980.9i 0.597806i
266266 0 0
267267 0 0
268268 0 0
269269 47568.2 27463.5i 0.657374 0.379535i −0.133902 0.990995i 0.542751π-0.542751\pi
0.791276 + 0.611460i 0.209417π0.209417\pi
270270 0 0
271271 79439.7 + 45864.6i 1.08168 + 0.624509i 0.931349 0.364127i 0.118633π-0.118633\pi
0.150332 + 0.988636i 0.451966π0.451966\pi
272272 0 0
273273 0 0
274274 0 0
275275 21588.5 37392.4i 0.285468 0.494445i
276276 0 0
277277 −3667.78 6352.78i −0.0478018 0.0827951i 0.841135 0.540826i 0.181888π-0.181888\pi
−0.888936 + 0.458031i 0.848555π0.848555\pi
278278 0 0
279279 0 0
280280 0 0
281281 −133185. −1.68671 −0.843356 0.537355i 0.819424π-0.819424\pi
−0.843356 + 0.537355i 0.819424π0.819424\pi
282282 0 0
283283 −108302. + 62528.0i −1.35227 + 0.780731i −0.988567 0.150785i 0.951820π-0.951820\pi
−0.363700 + 0.931516i 0.618487π0.618487\pi
284284 0 0
285285 0 0
286286 0 0
287287 −140209. + 53610.3i −1.70221 + 0.650855i
288288 0 0
289289 −35929.1 + 62231.1i −0.430181 + 0.745095i
290290 0 0
291291 0 0
292292 0 0
293293 137393.i 1.60040i −0.599730 0.800202i 0.704725π-0.704725\pi
0.599730 0.800202i 0.295275π-0.295275\pi
294294 0 0
295295 −28115.0 −0.323068
296296 0 0
297297 0 0
298298 0 0
299299 20651.1 + 11922.9i 0.230995 + 0.133365i
300300 0 0
301301 −9678.59 25312.8i −0.106827 0.279388i
302302 0 0
303303 0 0
304304 0 0
305305 −13854.8 23997.2i −0.148936 0.257965i
306306 0 0
307307 59400.1i 0.630247i −0.949051 0.315123i 0.897954π-0.897954\pi
0.949051 0.315123i 0.102046π-0.102046\pi
308308 0 0
309309 0 0
310310 0 0
311311 −39127.7 + 22590.4i −0.404542 + 0.233562i −0.688442 0.725291i 0.741705π-0.741705\pi
0.283900 + 0.958854i 0.408372π0.408372\pi
312312 0 0
313313 92305.3 + 53292.5i 0.942189 + 0.543973i 0.890646 0.454698i 0.150253π-0.150253\pi
0.0515431 + 0.998671i 0.483586π0.483586\pi
314314 0 0
315315 0 0
316316 0 0
317317 76611.8 132696.i 0.762390 1.32050i −0.179225 0.983808i 0.557359π-0.557359\pi
0.941615 0.336691i 0.109308π-0.109308\pi
318318 0 0
319319 −21321.9 36930.7i −0.209529 0.362916i
320320 0 0
321321 0 0
322322 0 0
323323 31587.3 0.302766
324324 0 0
325325 −45280.3 + 26142.6i −0.428689 + 0.247504i
326326 0 0
327327 0 0
328328 0 0
329329 −18184.6 + 113846.i −0.168001 + 1.05178i
330330 0 0
331331 56180.6 97307.7i 0.512779 0.888160i −0.487111 0.873340i 0.661949π-0.661949\pi
0.999890 0.0148198i 0.00471745π-0.00471745\pi
332332 0 0
333333 0 0
334334 0 0
335335 5005.53i 0.0446026i
336336 0 0
337337 −141074. −1.24219 −0.621093 0.783737i 0.713311π-0.713311\pi
−0.621093 + 0.783737i 0.713311π0.713311\pi
338338 0 0
339339 0 0
340340 0 0
341341 27549.8 + 15905.9i 0.236924 + 0.136788i
342342 0 0
343343 104615. + 53823.7i 0.889213 + 0.457494i
344344 0 0
345345 0 0
346346 0 0
347347 100247. + 173633.i 0.832557 + 1.44203i 0.896004 + 0.444046i 0.146457π0.146457\pi
−0.0634473 + 0.997985i 0.520209π0.520209\pi
348348 0 0
349349 209647.i 1.72122i −0.509263 0.860611i 0.670082π-0.670082\pi
0.509263 0.860611i 0.329918π-0.329918\pi
350350 0 0
351351 0 0
352352 0 0
353353 138290. 79841.9i 1.10979 0.640739i 0.171017 0.985268i 0.445295π-0.445295\pi
0.938776 + 0.344529i 0.111961π0.111961\pi
354354 0 0
355355 −38814.4 22409.5i −0.307990 0.177818i
356356 0 0
357357 0 0
358358 0 0
359359 −35094.0 + 60784.5i −0.272297 + 0.471633i −0.969450 0.245290i 0.921117π-0.921117\pi
0.697152 + 0.716923i 0.254450π0.254450\pi
360360 0 0
361361 −22385.1 38772.1i −0.171769 0.297512i
362362 0 0
363363 0 0
364364 0 0
365365 −11977.5 −0.0899044
366366 0 0
367367 205812. 118826.i 1.52806 0.882223i 0.528613 0.848863i 0.322712π-0.322712\pi
0.999443 0.0333603i 0.0106209π-0.0106209\pi
368368 0 0
369369 0 0
370370 0 0
371371 −155162. + 191097.i −1.12730 + 1.38837i
372372 0 0
373373 −122554. + 212269.i −0.880863 + 1.52570i −0.0304807 + 0.999535i 0.509704π0.509704\pi
−0.850383 + 0.526165i 0.823630π0.823630\pi
374374 0 0
375375 0 0
376376 0 0
377377 51639.6i 0.363329i
378378 0 0
379379 −95402.6 −0.664174 −0.332087 0.943249i 0.607753π-0.607753\pi
−0.332087 + 0.943249i 0.607753π0.607753\pi
380380 0 0
381381 0 0
382382 0 0
383383 57753.3 + 33343.9i 0.393712 + 0.227310i 0.683767 0.729700i 0.260340π-0.260340\pi
−0.290055 + 0.957010i 0.593674π0.593674\pi
384384 0 0
385385 29746.2 11373.8i 0.200683 0.0767331i
386386 0 0
387387 0 0
388388 0 0
389389 77439.5 + 134129.i 0.511757 + 0.886389i 0.999907 + 0.0136291i 0.00433840π0.00433840\pi
−0.488150 + 0.872760i 0.662328π0.662328\pi
390390 0 0
391391 27343.7i 0.178856i
392392 0 0
393393 0 0
394394 0 0
395395 80867.3 46688.8i 0.518297 0.299239i
396396 0 0
397397 174546. + 100774.i 1.10746 + 0.639392i 0.938170 0.346174i 0.112519π-0.112519\pi
0.169290 + 0.985566i 0.445853π0.445853\pi
398398 0 0
399399 0 0
400400 0 0
401401 16945.5 29350.5i 0.105382 0.182527i −0.808512 0.588479i 0.799727π-0.799727\pi
0.913894 + 0.405952i 0.133060π0.133060\pi
402402 0 0
403403 −19261.2 33361.4i −0.118597 0.205416i
404404 0 0
405405 0 0
406406 0 0
407407 −21034.9 −0.126985
408408 0 0
409409 −201013. + 116055.i −1.20165 + 0.693771i −0.960921 0.276822i 0.910719π-0.910719\pi
−0.240725 + 0.970593i 0.577385π0.577385\pi
410410 0 0
411411 0 0
412412 0 0
413413 127979. + 103914.i 0.750307 + 0.609218i
414414 0 0
415415 −5543.80 + 9602.15i −0.0321893 + 0.0557535i
416416 0 0
417417 0 0
418418 0 0
419419 162717.i 0.926838i −0.886139 0.463419i 0.846622π-0.846622\pi
0.886139 0.463419i 0.153378π-0.153378\pi
420420 0 0
421421 244086. 1.37714 0.688570 0.725170i 0.258239π-0.258239\pi
0.688570 + 0.725170i 0.258239π0.258239\pi
422422 0 0
423423 0 0
424424 0 0
425425 51922.2 + 29977.3i 0.287459 + 0.165964i
426426 0 0
427427 −25627.4 + 160443.i −0.140556 + 0.879962i
428428 0 0
429429 0 0
430430 0 0
431431 57761.7 + 100046.i 0.310946 + 0.538575i 0.978567 0.205926i 0.0660208π-0.0660208\pi
−0.667621 + 0.744501i 0.732687π0.732687\pi
432432 0 0
433433 54296.2i 0.289597i 0.989461 + 0.144798i 0.0462534π0.0462534\pi
−0.989461 + 0.144798i 0.953747π0.953747\pi
434434 0 0
435435 0 0
436436 0 0
437437 64135.7 37028.7i 0.335843 0.193899i
438438 0 0
439439 279367. + 161293.i 1.44959 + 0.836923i 0.998457 0.0555326i 0.0176857π-0.0176857\pi
0.451136 + 0.892455i 0.351019π0.351019\pi
440440 0 0
441441 0 0
442442 0 0
443443 105739. 183146.i 0.538802 0.933232i −0.460167 0.887832i 0.652211π-0.652211\pi
0.998969 0.0453997i 0.0144562π-0.0144562\pi
444444 0 0
445445 51650.1 + 89460.6i 0.260826 + 0.451764i
446446 0 0
447447 0 0
448448 0 0
449449 −223169. −1.10699 −0.553493 0.832854i 0.686705π-0.686705\pi
−0.553493 + 0.832854i 0.686705π0.686705\pi
450450 0 0
451451 206334. 119127.i 1.01442 0.585676i
452452 0 0
453453 0 0
454454 0 0
455455 −38081.8 6082.79i −0.183948 0.0293819i
456456 0 0
457457 93.6414 162.192i 0.000448369 0.000776598i −0.865801 0.500388i 0.833191π-0.833191\pi
0.866250 + 0.499612i 0.166524π0.166524\pi
458458 0 0
459459 0 0
460460 0 0
461461 8842.64i 0.0416083i 0.999784 + 0.0208042i 0.00662265π0.00662265\pi
−0.999784 + 0.0208042i 0.993377π0.993377\pi
462462 0 0
463463 −363326. −1.69486 −0.847431 0.530906i 0.821852π-0.821852\pi
−0.847431 + 0.530906i 0.821852π0.821852\pi
464464 0 0
465465 0 0
466466 0 0
467467 211698. + 122224.i 0.970698 + 0.560433i 0.899449 0.437026i 0.143968π-0.143968\pi
0.0712488 + 0.997459i 0.477302π0.477302\pi
468468 0 0
469469 −18500.6 + 22785.1i −0.0841084 + 0.103587i
470470 0 0
471471 0 0
472472 0 0
473473 21506.7 + 37250.8i 0.0961285 + 0.166499i
474474 0 0
475475 162381.i 0.719693i
476476 0 0
477477 0 0
478478 0 0
479479 30752.3 17754.8i 0.134031 0.0773829i −0.431485 0.902120i 0.642010π-0.642010\pi
0.565516 + 0.824737i 0.308677π0.308677\pi
480480 0 0
481481 22059.6 + 12736.1i 0.0953470 + 0.0550486i
482482 0 0
483483 0 0
484484 0 0
485485 22227.9 38499.9i 0.0944965 0.163673i
486486 0 0
487487 −27074.8 46894.9i −0.114158 0.197728i 0.803285 0.595595i 0.203084π-0.203084\pi
−0.917443 + 0.397867i 0.869750π0.869750\pi
488488 0 0
489489 0 0
490490 0 0
491491 −92603.2 −0.384117 −0.192058 0.981384i 0.561516π-0.561516\pi
−0.192058 + 0.981384i 0.561516π0.561516\pi
492492 0 0
493493 51281.1 29607.1i 0.210991 0.121816i
494494 0 0
495495 0 0
496496 0 0
497497 93856.7 + 245467.i 0.379973 + 0.993757i
498498 0 0
499499 −3480.87 + 6029.05i −0.0139794 + 0.0242130i −0.872930 0.487845i 0.837783π-0.837783\pi
0.858951 + 0.512058i 0.171117π0.171117\pi
500500 0 0
501501 0 0
502502 0 0
503503 466372.i 1.84330i −0.388021 0.921650i 0.626841π-0.626841\pi
0.388021 0.921650i 0.373159π-0.373159\pi
504504 0 0
505505 38265.5 0.150046
506506 0 0
507507 0 0
508508 0 0
509509 174228. + 100590.i 0.672483 + 0.388259i 0.797017 0.603957i 0.206410π-0.206410\pi
−0.124533 + 0.992215i 0.539743π0.539743\pi
510510 0 0
511511 54521.5 + 44269.2i 0.208798 + 0.169535i
512512 0 0
513513 0 0
514514 0 0
515515 −30550.7 52915.4i −0.115188 0.199511i
516516 0 0
517517 182988.i 0.684608i
518518 0 0
519519 0 0
520520 0 0
521521 −300077. + 173249.i −1.10549 + 0.638258i −0.937659 0.347557i 0.887011π-0.887011\pi
−0.167836 + 0.985815i 0.553678π0.553678\pi
522522 0 0
523523 −252492. 145776.i −0.923090 0.532946i −0.0384707 0.999260i 0.512249π-0.512249\pi
−0.884620 + 0.466313i 0.845582π0.845582\pi
524524 0 0
525525 0 0
526526 0 0
527527 −22086.5 + 38255.0i −0.0795254 + 0.137742i
528528 0 0
529529 107866. + 186830.i 0.385456 + 0.667629i
530530 0 0
531531 0 0
532532 0 0
533533 −288514. −1.01558
534534 0 0
535535 −140385. + 81051.4i −0.490471 + 0.283174i
536536 0 0
537537 0 0
538538 0 0
539539 −177442. 58169.6i −0.610772 0.200225i
540540 0 0
541541 193007. 334298.i 0.659445 1.14219i −0.321314 0.946973i 0.604125π-0.604125\pi
0.980759 0.195220i 0.0625422π-0.0625422\pi
542542 0 0
543543 0 0
544544 0 0
545545 108057.i 0.363799i
546546 0 0
547547 122247. 0.408566 0.204283 0.978912i 0.434514π-0.434514\pi
0.204283 + 0.978912i 0.434514π0.434514\pi
548548 0 0
549549 0 0
550550 0 0
551551 138889. + 80187.8i 0.457473 + 0.264122i
552552 0 0
553553 −540670. 86361.0i −1.76800 0.282402i
554554 0 0
555555 0 0
556556 0 0
557557 53061.4 + 91905.1i 0.171029 + 0.296230i 0.938780 0.344518i 0.111958π-0.111958\pi
−0.767751 + 0.640748i 0.778624π0.778624\pi
558558 0 0
559559 52087.2i 0.166689i
560560 0 0
561561 0 0
562562 0 0
563563 254823. 147122.i 0.803935 0.464152i −0.0409102 0.999163i 0.513026π-0.513026\pi
0.844845 + 0.535011i 0.179692π0.179692\pi
564564 0 0
565565 −37293.9 21531.6i −0.116826 0.0674497i
566566 0 0
567567 0 0
568568 0 0
569569 −237514. + 411386.i −0.733609 + 1.27065i 0.221722 + 0.975110i 0.428832π0.428832\pi
−0.955331 + 0.295538i 0.904501π0.904501\pi
570570 0 0
571571 −92589.2 160369.i −0.283980 0.491868i 0.688381 0.725349i 0.258322π-0.258322\pi
−0.972361 + 0.233481i 0.924988π0.924988\pi
572572 0 0
573573 0 0
574574 0 0
575575 140566. 0.425151
576576 0 0
577577 139857. 80746.6i 0.420081 0.242534i −0.275031 0.961435i 0.588688π-0.588688\pi
0.695112 + 0.718901i 0.255355π0.255355\pi
578578 0 0
579579 0 0
580580 0 0
581581 60725.1 23218.8i 0.179894 0.0687841i
582582 0 0
583583 195351. 338358.i 0.574750 0.995497i
584584 0 0
585585 0 0
586586 0 0
587587 333168.i 0.966911i −0.875369 0.483456i 0.839381π-0.839381\pi
0.875369 0.483456i 0.160619π-0.160619\pi
588588 0 0
589589 −119638. −0.344856
590590 0 0
591591 0 0
592592 0 0
593593 −97432.1 56252.5i −0.277072 0.159968i 0.355025 0.934857i 0.384472π-0.384472\pi
−0.632097 + 0.774889i 0.717806π0.717806\pi
594594 0 0
595595 15793.3 + 41305.0i 0.0446108 + 0.116672i
596596 0 0
597597 0 0
598598 0 0
599599 −202632. 350970.i −0.564749 0.978174i −0.997073 0.0764554i 0.975640π-0.975640\pi
0.432324 0.901718i 0.357694π-0.357694\pi
600600 0 0
601601 372831.i 1.03220i −0.856529 0.516098i 0.827384π-0.827384\pi
0.856529 0.516098i 0.172616π-0.172616\pi
602602 0 0
603603 0 0
604604 0 0
605605 62183.7 35901.8i 0.169889 0.0980856i
606606 0 0
607607 −472368. 272722.i −1.28204 0.740188i −0.304822 0.952409i 0.598597π-0.598597\pi
−0.977222 + 0.212221i 0.931930π0.931930\pi
608608 0 0
609609 0 0
610610 0 0
611611 −110795. + 191902.i −0.296782 + 0.514041i
612612 0 0
613613 219300. + 379838.i 0.583602 + 1.01083i 0.995048 + 0.0993946i 0.0316906π0.0316906\pi
−0.411446 + 0.911434i 0.634976π0.634976\pi
614614 0 0
615615 0 0
616616 0 0
617617 −663957. −1.74409 −0.872046 0.489423i 0.837207π-0.837207\pi
−0.872046 + 0.489423i 0.837207π0.837207\pi
618618 0 0
619619 237343. 137030.i 0.619434 0.357630i −0.157215 0.987564i 0.550251π-0.550251\pi
0.776649 + 0.629934i 0.216918π0.216918\pi
620620 0 0
621621 0 0
622622 0 0
623623 95538.1 598124.i 0.246150 1.54104i
624624 0 0
625625 −132281. + 229117.i −0.338639 + 0.586540i
626626 0 0
627627 0 0
628628 0 0
629629 29208.6i 0.0738260i
630630 0 0
631631 −217088. −0.545227 −0.272614 0.962124i 0.587888π-0.587888\pi
−0.272614 + 0.962124i 0.587888π0.587888\pi
632632 0 0
633633 0 0
634634 0 0
635635 74689.9 + 43122.2i 0.185231 + 0.106943i
636636 0 0
637637 150866. + 168440.i 0.371802 + 0.415113i
638638 0 0
639639 0 0
640640 0 0
641641 −261433. 452815.i −0.636274 1.10206i −0.986244 0.165298i 0.947141π-0.947141\pi
0.349969 0.936761i 0.386192π-0.386192\pi
642642 0 0
643643 447328.i 1.08194i 0.841041 + 0.540971i 0.181943π0.181943\pi
−0.841041 + 0.540971i 0.818057π0.818057\pi
644644 0 0
645645 0 0
646646 0 0
647647 168608. 97346.0i 0.402782 0.232546i −0.284901 0.958557i 0.591961π-0.591961\pi
0.687684 + 0.726010i 0.258628π0.258628\pi
648648 0 0
649649 −226602. 130829.i −0.537990 0.310609i
650650 0 0
651651 0 0
652652 0 0
653653 92320.8 159904.i 0.216508 0.375002i −0.737230 0.675642i 0.763867π-0.763867\pi
0.953738 + 0.300639i 0.0972001π0.0972001\pi
654654 0 0
655655 131339. + 227486.i 0.306134 + 0.530240i
656656 0 0
657657 0 0
658658 0 0
659659 −269400. −0.620336 −0.310168 0.950682i 0.600385π-0.600385\pi
−0.310168 + 0.950682i 0.600385π0.600385\pi
660660 0 0
661661 −273711. + 158027.i −0.626453 + 0.361683i −0.779377 0.626555i 0.784464π-0.784464\pi
0.152924 + 0.988238i 0.451131π0.451131\pi
662662 0 0
663663 0 0
664664 0 0
665665 −75495.0 + 92978.9i −0.170716 + 0.210252i
666666 0 0
667667 69414.9 120230.i 0.156028 0.270248i
668668 0 0
669669 0 0
670670 0 0
671671 257884.i 0.572769i
672672 0 0
673673 85940.2 0.189743 0.0948716 0.995490i 0.469756π-0.469756\pi
0.0948716 + 0.995490i 0.469756π0.469756\pi
674674 0 0
675675 0 0
676676 0 0
677677 43495.9 + 25112.3i 0.0949010 + 0.0547911i 0.546699 0.837329i 0.315884π-0.315884\pi
−0.451798 + 0.892120i 0.649217π0.649217\pi
678678 0 0
679679 −243478. + 93096.1i −0.528105 + 0.201926i
680680 0 0
681681 0 0
682682 0 0
683683 −373719. 647301.i −0.801132 1.38760i −0.918871 0.394557i 0.870898π-0.870898\pi
0.117739 0.993045i 0.462435π-0.462435\pi
684684 0 0
685685 115790.i 0.246769i
686686 0 0
687687 0 0
688688 0 0
689689 −409735. + 236561.i −0.863108 + 0.498315i
690690 0 0
691691 151644. + 87551.7i 0.317592 + 0.183362i 0.650319 0.759662i 0.274635π-0.274635\pi
−0.332727 + 0.943023i 0.607969π0.607969\pi
692692 0 0
693693 0 0
694694 0 0
695695 −103415. + 179120.i −0.214099 + 0.370830i
696696 0 0
697697 165417. + 286511.i 0.340498 + 0.589761i
698698 0 0
699699 0 0
700700 0 0
701701 91696.3 0.186602 0.0933009 0.995638i 0.470258π-0.470258\pi
0.0933009 + 0.995638i 0.470258π0.470258\pi
702702 0 0
703703 68509.8 39554.2i 0.138625 0.0800353i
704704 0 0
705705 0 0
706706 0 0
707707 −174184. 141430.i −0.348473 0.282946i
708708 0 0
709709 45597.2 78976.7i 0.0907081 0.157111i −0.817101 0.576494i 0.804420π-0.804420\pi
0.907809 + 0.419383i 0.137754π0.137754\pi
710710 0 0
711711 0 0
712712 0 0
713713 103565.i 0.203720i
714714 0 0
715715 61210.0 0.119732
716716 0 0
717717 0 0
718718 0 0
719719 143600. + 82907.7i 0.277778 + 0.160375i 0.632417 0.774628i 0.282063π-0.282063\pi
−0.354639 + 0.935003i 0.615396π0.615396\pi
720720 0 0
721721 −56510.1 + 353786.i −0.108707 + 0.680566i
722722 0 0
723723 0 0
724724 0 0
725725 152201. + 263620.i 0.289563 + 0.501537i
726726 0 0
727727 90288.3i 0.170829i −0.996345 0.0854147i 0.972778π-0.972778\pi
0.996345 0.0854147i 0.0272215π-0.0272215\pi
728728 0 0
729729 0 0
730730 0 0
731731 −51725.6 + 29863.8i −0.0967989 + 0.0558869i
732732 0 0
733733 −272185. 157146.i −0.506590 0.292480i 0.224841 0.974395i 0.427814π-0.427814\pi
−0.731431 + 0.681916i 0.761147π0.761147\pi
734734 0 0
735735 0 0
736736 0 0
737737 23292.4 40343.7i 0.0428825 0.0742746i
738738 0 0
739739 −56214.0 97365.4i −0.102933 0.178285i 0.809959 0.586487i 0.199489π-0.199489\pi
−0.912892 + 0.408201i 0.866156π0.866156\pi
740740 0 0
741741 0 0
742742 0 0
743743 805662. 1.45940 0.729702 0.683765i 0.239659π-0.239659\pi
0.729702 + 0.683765i 0.239659π0.239659\pi
744744 0 0
745745 1237.37 714.397i 0.00222940 0.00128714i
746746 0 0
747747 0 0
748748 0 0
749749 938600. + 149922.i 1.67308 + 0.267240i
750750 0 0
751751 184929. 320306.i 0.327887 0.567917i −0.654205 0.756317i 0.726997π-0.726997\pi
0.982092 + 0.188400i 0.0603300π0.0603300\pi
752752 0 0
753753 0 0
754754 0 0
755755 310441.i 0.544610i
756756 0 0
757757 736616. 1.28543 0.642716 0.766104i 0.277807π-0.277807\pi
0.642716 + 0.766104i 0.277807π0.277807\pi
758758 0 0
759759 0 0
760760 0 0
761761 111743. + 64515.1i 0.192954 + 0.111402i 0.593365 0.804934i 0.297799π-0.297799\pi
−0.400411 + 0.916336i 0.631133π0.631133\pi
762762 0 0
763763 399383. 491876.i 0.686026 0.844902i
764764 0 0
765765 0 0
766766 0 0
767767 158427. + 274404.i 0.269301 + 0.466444i
768768 0 0
769769 485806.i 0.821506i 0.911747 + 0.410753i 0.134734π0.134734\pi
−0.911747 + 0.410753i 0.865266π0.865266\pi
770770 0 0
771771 0 0
772772 0 0
773773 239185. 138094.i 0.400290 0.231108i −0.286319 0.958134i 0.592432π-0.592432\pi
0.686609 + 0.727027i 0.259098π0.259098\pi
774774 0 0
775775 −196657. 113540.i −0.327421 0.189037i
776776 0 0
777777 0 0
778778 0 0
779779 −448015. + 775984.i −0.738274 + 1.27873i
780780 0 0
781781 −208558. 361233.i −0.341921 0.592224i
782782 0 0
783783 0 0
784784 0 0
785785 126897. 0.205926
786786 0 0
787787 83633.8 48286.0i 0.135031 0.0779600i −0.430963 0.902370i 0.641826π-0.641826\pi
0.565994 + 0.824410i 0.308493π0.308493\pi
788788 0 0
789789 0 0
790790 0 0
791791 90179.8 + 235851.i 0.144131 + 0.376951i
792792 0 0
793793 −156142. + 270447.i −0.248299 + 0.430066i
794794 0 0
795795 0 0
796796 0 0
797797 540869.i 0.851481i 0.904845 + 0.425741i 0.139986π0.139986\pi
−0.904845 + 0.425741i 0.860014π0.860014\pi
798798 0 0
799799 254093. 0.398015
800800 0 0
801801 0 0
802802 0 0
803803 −96536.6 55735.4i −0.149713 0.0864371i
804804 0 0
805805 80487.6 + 65352.6i 0.124205 + 0.100849i
806806 0 0
807807 0 0
808808 0 0
809809 477611. + 827246.i 0.729755 + 1.26397i 0.956987 + 0.290132i 0.0936992π0.0936992\pi
−0.227232 + 0.973841i 0.572967π0.572967\pi
810810 0 0
811811 352574.i 0.536055i 0.963411 + 0.268027i 0.0863718π0.0863718\pi
−0.963411 + 0.268027i 0.913628π0.913628\pi
812812 0 0
813813 0 0
814814 0 0
815815 27356.4 15794.2i 0.0411854 0.0237784i
816816 0 0
817817 −140093. 80882.8i −0.209881 0.121175i
818818 0 0
819819 0 0
820820 0 0
821821 393020. 680731.i 0.583080 1.00992i −0.412031 0.911170i 0.635181π-0.635181\pi
0.995112 0.0987551i 0.0314860π-0.0314860\pi
822822 0 0
823823 −366023. 633971.i −0.540392 0.935987i −0.998881 0.0472866i 0.984943π-0.984943\pi
0.458489 0.888700i 0.348391π-0.348391\pi
824824 0 0
825825 0 0
826826 0 0
827827 279220. 0.408258 0.204129 0.978944i 0.434564π-0.434564\pi
0.204129 + 0.978944i 0.434564π0.434564\pi
828828 0 0
829829 −176164. + 101708.i −0.256335 + 0.147995i −0.622662 0.782491i 0.713949π-0.713949\pi
0.366327 + 0.930486i 0.380615π0.380615\pi
830830 0 0
831831 0 0
832832 0 0
833833 80773.1 246392.i 0.116406 0.355089i
834834 0 0
835835 44251.0 76645.0i 0.0634674 0.109929i
836836 0 0
837837 0 0
838838 0 0
839839 1.36972e6i 1.94584i 0.231134 + 0.972922i 0.425756π0.425756\pi
−0.231134 + 0.972922i 0.574244π0.574244\pi
840840 0 0
841841 −406637. −0.574930
842842 0 0
843843 0 0
844844 0 0
845845 142508. + 82276.9i 0.199584 + 0.115230i
846846 0 0
847847 −415753. 66408.1i −0.579521 0.0925666i
848848 0 0
849849 0 0
850850 0 0
851851 −34240.2 59305.8i −0.0472800 0.0818914i
852852 0 0
853853 110844.i 0.152340i 0.997095 + 0.0761702i 0.0242692π0.0242692\pi
−0.997095 + 0.0761702i 0.975731π0.975731\pi
854854 0 0
855855 0 0
856856 0 0
857857 −917323. + 529617.i −1.24899 + 0.721107i −0.970909 0.239449i 0.923033π-0.923033\pi
−0.278086 + 0.960556i 0.589700π0.589700\pi
858858 0 0
859859 1.00197e6 + 578485.i 1.35790 + 0.783982i 0.989340 0.145624i 0.0465188π-0.0465188\pi
0.368556 + 0.929605i 0.379852π0.379852\pi
860860 0 0
861861 0 0
862862 0 0
863863 −39295.5 + 68061.8i −0.0527620 + 0.0913864i −0.891200 0.453610i 0.850136π-0.850136\pi
0.838438 + 0.544997i 0.183469π0.183469\pi
864864 0 0
865865 167726. + 290511.i 0.224166 + 0.388267i
866866 0 0
867867 0 0
868868 0 0
869869 869035. 1.15079
870870 0 0
871871 −48854.2 + 28206.0i −0.0643970 + 0.0371796i
872872 0 0
873873 0 0
874874 0 0
875875 −451382. + 172590.i −0.589561 + 0.225424i
876876 0 0
877877 −32541.5 + 56363.6i −0.0423096 + 0.0732824i −0.886405 0.462911i 0.846805π-0.846805\pi
0.844095 + 0.536193i 0.180138π0.180138\pi
878878 0 0
879879 0 0
880880 0 0
881881 510450.i 0.657661i −0.944389 0.328830i 0.893346π-0.893346\pi
0.944389 0.328830i 0.106654π-0.106654\pi
882882 0 0
883883 684144. 0.877458 0.438729 0.898620i 0.355429π-0.355429\pi
0.438729 + 0.898620i 0.355429π0.355429\pi
884884 0 0
885885 0 0
886886 0 0
887887 −251921. 145447.i −0.320198 0.184866i 0.331283 0.943531i 0.392518π-0.392518\pi
−0.651481 + 0.758665i 0.725852π0.725852\pi
888888 0 0
889889 −180607. 472348.i −0.228523 0.597665i
890890 0 0
891891 0 0
892892 0 0
893893 344092. + 595985.i 0.431491 + 0.747365i
894894 0 0
895895 314018.i 0.392020i
896896 0 0
897897 0 0
898898 0 0
899899 −194229. + 112138.i −0.240322 + 0.138750i
900900 0 0
901901 469837. + 271261.i 0.578759 + 0.334147i
902902 0 0
903903 0 0
904904 0 0
905905 166516. 288414.i 0.203310 0.352144i
906906 0 0
907907 19708.0 + 34135.2i 0.0239567 + 0.0414942i 0.877755 0.479109i 0.159040π-0.159040\pi
−0.853798 + 0.520604i 0.825707π0.825707\pi
908908 0 0
909909 0 0
910910 0 0
911911 1.07089e6 1.29035 0.645173 0.764036i 0.276785π-0.276785\pi
0.645173 + 0.764036i 0.276785π0.276785\pi
912912 0 0
913913 −89364.1 + 51594.4i −0.107207 + 0.0618958i
914914 0 0
915915 0 0
916916 0 0
917917 242940. 1.52095e6i 0.288909 1.80874i
918918 0 0
919919 −607876. + 1.05287e6i −0.719754 + 1.24665i 0.241343 + 0.970440i 0.422412π0.422412\pi
−0.961097 + 0.276211i 0.910921π0.910921\pi
920920 0 0
921921 0 0
922922 0 0
923923 505107.i 0.592898i
924924 0 0
925925 150152. 0.175489
926926 0 0
927927 0 0
928928 0 0
929929 −1.29549e6 747949.i −1.50107 0.866644i −0.999999 0.00123791i 0.999606π-0.999606\pi
−0.501072 0.865406i 0.667061π-0.667061\pi
930930 0 0
931931 687305. 144207.i 0.792958 0.166375i
932932 0 0
933933 0 0
934934 0 0
935935 −35094.3 60785.1i −0.0401433 0.0695303i
936936 0 0
937937 254082.i 0.289398i −0.989476 0.144699i 0.953779π-0.953779\pi
0.989476 0.144699i 0.0462213π-0.0462213\pi
938938 0 0
939939 0 0
940940 0 0
941941 642429. 370907.i 0.725514 0.418876i −0.0912645 0.995827i 0.529091π-0.529091\pi
0.816779 + 0.576951i 0.195758π0.195758\pi
942942 0 0
943943 671735. + 387826.i 0.755395 + 0.436128i
944944 0 0
945945 0 0
946946 0 0
947947 477051. 826277.i 0.531943 0.921352i −0.467362 0.884066i 0.654795π-0.654795\pi
0.999305 0.0372859i 0.0118712π-0.0118712\pi
948948 0 0
949949 67492.8 + 116901.i 0.0749420 + 0.129803i
950950 0 0
951951 0 0
952952 0 0
953953 792911. 0.873049 0.436525 0.899692i 0.356209π-0.356209\pi
0.436525 + 0.899692i 0.356209π0.356209\pi
954954 0 0
955955 −329253. + 190094.i −0.361013 + 0.208431i
956956 0 0
957957 0 0
958958 0 0
959959 −427964. + 527076.i −0.465340 + 0.573108i
960960 0 0
961961 −378107. + 654901.i −0.409419 + 0.709135i
962962 0 0
963963 0 0
964964 0 0
965965 101036.i 0.108498i
966966 0 0
967967 −23877.3 −0.0255348 −0.0127674 0.999918i 0.504064π-0.504064\pi
−0.0127674 + 0.999918i 0.504064π0.504064\pi
968968 0 0
969969 0 0
970970 0 0
971971 −969512. 559748.i −1.02829 0.593682i −0.111794 0.993731i 0.535660π-0.535660\pi
−0.916494 + 0.400049i 0.868993π0.868993\pi
972972 0 0
973973 1.13278e6 433128.i 1.19652 0.457500i
974974 0 0
975975 0 0
976976 0 0
977977 −522163. 904413.i −0.547037 0.947497i −0.998476 0.0551943i 0.982422π-0.982422\pi
0.451438 0.892302i 0.350911π-0.350911\pi
978978 0 0
979979 961382.i 1.00307i
980980 0 0
981981 0 0
982982 0 0
983983 187897. 108482.i 0.194452 0.112267i −0.399613 0.916684i 0.630855π-0.630855\pi
0.594065 + 0.804417i 0.297522π0.297522\pi
984984 0 0
985985 −313885. 181222.i −0.323518 0.186783i
986986 0 0
987987 0 0
988988 0 0
989989 −70016.6 + 121272.i −0.0715828 + 0.123985i
990990 0 0
991991 −496994. 860819.i −0.506062 0.876525i −0.999975 0.00701423i 0.997767π-0.997767\pi
0.493913 0.869511i 0.335566π-0.335566\pi
992992 0 0
993993 0 0
994994 0 0
995995 189783. 0.191695
996996 0 0
997997 −674463. + 389402.i −0.678528 + 0.391748i −0.799300 0.600932i 0.794796π-0.794796\pi
0.120772 + 0.992680i 0.461463π0.461463\pi
998998 0 0
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 252.5.z.b.145.2 4
3.2 odd 2 84.5.m.a.61.1 4
7.3 odd 6 inner 252.5.z.b.73.2 4
12.11 even 2 336.5.bh.c.145.1 4
21.2 odd 6 588.5.d.a.97.4 4
21.5 even 6 588.5.d.a.97.1 4
21.11 odd 6 588.5.m.a.325.2 4
21.17 even 6 84.5.m.a.73.1 yes 4
21.20 even 2 588.5.m.a.313.2 4
84.59 odd 6 336.5.bh.c.241.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
84.5.m.a.61.1 4 3.2 odd 2
84.5.m.a.73.1 yes 4 21.17 even 6
252.5.z.b.73.2 4 7.3 odd 6 inner
252.5.z.b.145.2 4 1.1 even 1 trivial
336.5.bh.c.145.1 4 12.11 even 2
336.5.bh.c.241.1 4 84.59 odd 6
588.5.d.a.97.1 4 21.5 even 6
588.5.d.a.97.4 4 21.2 odd 6
588.5.m.a.313.2 4 21.20 even 2
588.5.m.a.325.2 4 21.11 odd 6