Properties

Label 1458.3.b.c.1457.16
Level 14581458
Weight 33
Character 1458.1457
Analytic conductor 39.72839.728
Analytic rank 00
Dimension 3636
Inner twists 22

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [1458,3,Mod(1457,1458)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1458, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 3, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1458.1457"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 1458=236 1458 = 2 \cdot 3^{6}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 1458.b (of order 22, degree 11, minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [36] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 39.727622543739.7276225437
Analytic rank: 00
Dimension: 3636
Twist minimal: no (minimal twist has level 54)
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 1457.16
Character χ\chi == 1458.1457
Dual form 1458.3.b.c.1457.21

qq-expansion

Copy content comment:q-expansion
 
Copy content sage:f.q_expansion() # note that sage often uses an isomorphic number field
 
Copy content gp:mfcoefs(f, 20)
 
f(q)f(q) == q1.41421iq22.00000q4+7.63957iq5+5.75438q7+2.82843iq8+10.8040q108.15026iq11+23.4613q138.13793iq14+4.00000q167.38231iq17+15.6026q1915.2791iq2011.5262q22+31.0764iq2333.3630q2533.1793iq2611.5088q2828.3184iq29+16.0044q315.65685iq3210.4402q34+43.9610iq3511.9809q3722.0654iq3821.6080q408.26339iq4145.0827q43+16.3005iq44+43.9486q4667.6105iq4715.8871q49+47.1824iq5046.9226q52+16.4115iq53+62.2645q55+16.2759iq5640.0482q58+58.2441iq59+71.3542q6122.6337iq628.00000q64+179.234iq65+50.1960q67+14.7646iq68+62.1703q7040.9183iq71+99.5384q73+16.9436iq7431.2052q7646.8997iq77+77.0529q79+30.5583iq8011.6862q82+105.482iq83+56.3976q85+63.7566iq86+23.0524q880.348951iq89+135.005q9162.1527iq9295.6157q94+119.197iq95+63.9662q97+22.4677iq98+O(q100)q-1.41421i q^{2} -2.00000 q^{4} +7.63957i q^{5} +5.75438 q^{7} +2.82843i q^{8} +10.8040 q^{10} -8.15026i q^{11} +23.4613 q^{13} -8.13793i q^{14} +4.00000 q^{16} -7.38231i q^{17} +15.6026 q^{19} -15.2791i q^{20} -11.5262 q^{22} +31.0764i q^{23} -33.3630 q^{25} -33.1793i q^{26} -11.5088 q^{28} -28.3184i q^{29} +16.0044 q^{31} -5.65685i q^{32} -10.4402 q^{34} +43.9610i q^{35} -11.9809 q^{37} -22.0654i q^{38} -21.6080 q^{40} -8.26339i q^{41} -45.0827 q^{43} +16.3005i q^{44} +43.9486 q^{46} -67.6105i q^{47} -15.8871 q^{49} +47.1824i q^{50} -46.9226 q^{52} +16.4115i q^{53} +62.2645 q^{55} +16.2759i q^{56} -40.0482 q^{58} +58.2441i q^{59} +71.3542 q^{61} -22.6337i q^{62} -8.00000 q^{64} +179.234i q^{65} +50.1960 q^{67} +14.7646i q^{68} +62.1703 q^{70} -40.9183i q^{71} +99.5384 q^{73} +16.9436i q^{74} -31.2052 q^{76} -46.8997i q^{77} +77.0529 q^{79} +30.5583i q^{80} -11.6862 q^{82} +105.482i q^{83} +56.3976 q^{85} +63.7566i q^{86} +23.0524 q^{88} -0.348951i q^{89} +135.005 q^{91} -62.1527i q^{92} -95.6157 q^{94} +119.197i q^{95} +63.9662 q^{97} +22.4677i q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 36q72q4+144q16180q25+252q4936q61288q64+180q67252q73+396q91+O(q100) 36 q - 72 q^{4} + 144 q^{16} - 180 q^{25} + 252 q^{49} - 36 q^{61} - 288 q^{64} + 180 q^{67} - 252 q^{73} + 396 q^{91}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1458Z)×\left(\mathbb{Z}/1458\mathbb{Z}\right)^\times.

nn 731731
χ(n)\chi(n) 1-1

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 − 1.41421i − 0.707107i
33 0 0
44 −2.00000 −0.500000
55 7.63957i 1.52791i 0.645268 + 0.763957i 0.276746π0.276746\pi
−0.645268 + 0.763957i 0.723254π0.723254\pi
66 0 0
77 5.75438 0.822055 0.411027 0.911623i 0.365170π-0.365170\pi
0.411027 + 0.911623i 0.365170π0.365170\pi
88 2.82843i 0.353553i
99 0 0
1010 10.8040 1.08040
1111 − 8.15026i − 0.740933i −0.928846 0.370466i 0.879198π-0.879198\pi
0.928846 0.370466i 0.120802π-0.120802\pi
1212 0 0
1313 23.4613 1.80471 0.902357 0.430990i 0.141836π-0.141836\pi
0.902357 + 0.430990i 0.141836π0.141836\pi
1414 − 8.13793i − 0.581281i
1515 0 0
1616 4.00000 0.250000
1717 − 7.38231i − 0.434253i −0.976143 0.217127i 0.930332π-0.930332\pi
0.976143 0.217127i 0.0696685π-0.0696685\pi
1818 0 0
1919 15.6026 0.821189 0.410595 0.911818i 0.365321π-0.365321\pi
0.410595 + 0.911818i 0.365321π0.365321\pi
2020 − 15.2791i − 0.763957i
2121 0 0
2222 −11.5262 −0.523919
2323 31.0764i 1.35115i 0.737293 + 0.675573i 0.236104π0.236104\pi
−0.737293 + 0.675573i 0.763896π0.763896\pi
2424 0 0
2525 −33.3630 −1.33452
2626 − 33.1793i − 1.27613i
2727 0 0
2828 −11.5088 −0.411027
2929 − 28.3184i − 0.976496i −0.872705 0.488248i 0.837636π-0.837636\pi
0.872705 0.488248i 0.162364π-0.162364\pi
3030 0 0
3131 16.0044 0.516272 0.258136 0.966109i 0.416892π-0.416892\pi
0.258136 + 0.966109i 0.416892π0.416892\pi
3232 − 5.65685i − 0.176777i
3333 0 0
3434 −10.4402 −0.307064
3535 43.9610i 1.25603i
3636 0 0
3737 −11.9809 −0.323809 −0.161904 0.986806i 0.551764π-0.551764\pi
−0.161904 + 0.986806i 0.551764π0.551764\pi
3838 − 22.0654i − 0.580669i
3939 0 0
4040 −21.6080 −0.540199
4141 − 8.26339i − 0.201546i −0.994909 0.100773i 0.967868π-0.967868\pi
0.994909 0.100773i 0.0321316π-0.0321316\pi
4242 0 0
4343 −45.0827 −1.04844 −0.524218 0.851584i 0.675642π-0.675642\pi
−0.524218 + 0.851584i 0.675642π0.675642\pi
4444 16.3005i 0.370466i
4545 0 0
4646 43.9486 0.955405
4747 − 67.6105i − 1.43852i −0.694740 0.719261i 0.744481π-0.744481\pi
0.694740 0.719261i 0.255519π-0.255519\pi
4848 0 0
4949 −15.8871 −0.324226
5050 47.1824i 0.943648i
5151 0 0
5252 −46.9226 −0.902357
5353 16.4115i 0.309652i 0.987942 + 0.154826i 0.0494816π0.0494816\pi
−0.987942 + 0.154826i 0.950518π0.950518\pi
5454 0 0
5555 62.2645 1.13208
5656 16.2759i 0.290640i
5757 0 0
5858 −40.0482 −0.690487
5959 58.2441i 0.987187i 0.869693 + 0.493594i 0.164317π0.164317\pi
−0.869693 + 0.493594i 0.835683π0.835683\pi
6060 0 0
6161 71.3542 1.16974 0.584870 0.811127i 0.301145π-0.301145\pi
0.584870 + 0.811127i 0.301145π0.301145\pi
6262 − 22.6337i − 0.365059i
6363 0 0
6464 −8.00000 −0.125000
6565 179.234i 2.75745i
6666 0 0
6767 50.1960 0.749193 0.374597 0.927188i 0.377781π-0.377781\pi
0.374597 + 0.927188i 0.377781π0.377781\pi
6868 14.7646i 0.217127i
6969 0 0
7070 62.1703 0.888146
7171 − 40.9183i − 0.576315i −0.957583 0.288157i 0.906957π-0.906957\pi
0.957583 0.288157i 0.0930426π-0.0930426\pi
7272 0 0
7373 99.5384 1.36354 0.681770 0.731567i 0.261211π-0.261211\pi
0.681770 + 0.731567i 0.261211π0.261211\pi
7474 16.9436i 0.228967i
7575 0 0
7676 −31.2052 −0.410595
7777 − 46.8997i − 0.609088i
7878 0 0
7979 77.0529 0.975354 0.487677 0.873024i 0.337844π-0.337844\pi
0.487677 + 0.873024i 0.337844π0.337844\pi
8080 30.5583i 0.381978i
8181 0 0
8282 −11.6862 −0.142515
8383 105.482i 1.27087i 0.772156 + 0.635433i 0.219178π0.219178\pi
−0.772156 + 0.635433i 0.780822π0.780822\pi
8484 0 0
8585 56.3976 0.663502
8686 63.7566i 0.741356i
8787 0 0
8888 23.0524 0.261959
8989 − 0.348951i − 0.00392080i −0.999998 0.00196040i 0.999376π-0.999376\pi
0.999998 0.00196040i 0.000624015π-0.000624015\pi
9090 0 0
9191 135.005 1.48357
9292 − 62.1527i − 0.675573i
9393 0 0
9494 −95.6157 −1.01719
9595 119.197i 1.25471i
9696 0 0
9797 63.9662 0.659445 0.329723 0.944078i 0.393045π-0.393045\pi
0.329723 + 0.944078i 0.393045π0.393045\pi
9898 22.4677i 0.229262i
9999 0 0
100100 66.7260 0.667260
101101 166.725i 1.65074i 0.564593 + 0.825370i 0.309033π0.309033\pi
−0.564593 + 0.825370i 0.690967π0.690967\pi
102102 0 0
103103 −100.610 −0.976800 −0.488400 0.872620i 0.662419π-0.662419\pi
−0.488400 + 0.872620i 0.662419π0.662419\pi
104104 66.3585i 0.638063i
105105 0 0
106106 23.2094 0.218957
107107 − 6.57806i − 0.0614772i −0.999527 0.0307386i 0.990214π-0.990214\pi
0.999527 0.0307386i 0.00978594π-0.00978594\pi
108108 0 0
109109 198.876 1.82455 0.912276 0.409576i 0.134323π-0.134323\pi
0.912276 + 0.409576i 0.134323π0.134323\pi
110110 − 88.0553i − 0.800502i
111111 0 0
112112 23.0175 0.205514
113113 − 5.24721i − 0.0464355i −0.999730 0.0232177i 0.992609π-0.992609\pi
0.999730 0.0232177i 0.00739110π-0.00739110\pi
114114 0 0
115115 −237.410 −2.06443
116116 56.6368i 0.488248i
117117 0 0
118118 82.3695 0.698047
119119 − 42.4806i − 0.356980i
120120 0 0
121121 54.5732 0.451018
122122 − 100.910i − 0.827132i
123123 0 0
124124 −32.0088 −0.258136
125125 − 63.8896i − 0.511117i
126126 0 0
127127 44.4382 0.349907 0.174954 0.984577i 0.444022π-0.444022\pi
0.174954 + 0.984577i 0.444022π0.444022\pi
128128 11.3137i 0.0883883i
129129 0 0
130130 253.475 1.94981
131131 − 40.1802i − 0.306719i −0.988170 0.153360i 0.950991π-0.950991\pi
0.988170 0.153360i 0.0490093π-0.0490093\pi
132132 0 0
133133 89.7834 0.675063
134134 − 70.9878i − 0.529760i
135135 0 0
136136 20.8803 0.153532
137137 51.5369i 0.376182i 0.982152 + 0.188091i 0.0602300π0.0602300\pi
−0.982152 + 0.188091i 0.939770π0.939770\pi
138138 0 0
139139 −107.649 −0.774455 −0.387228 0.921984i 0.626567π-0.626567\pi
−0.387228 + 0.921984i 0.626567π0.626567\pi
140140 − 87.9220i − 0.628014i
141141 0 0
142142 −57.8673 −0.407516
143143 − 191.216i − 1.33717i
144144 0 0
145145 216.340 1.49200
146146 − 140.769i − 0.964168i
147147 0 0
148148 23.9619 0.161904
149149 141.101i 0.946987i 0.880797 + 0.473493i 0.157007π0.157007\pi
−0.880797 + 0.473493i 0.842993π0.842993\pi
150150 0 0
151151 −131.182 −0.868755 −0.434378 0.900731i 0.643032π-0.643032\pi
−0.434378 + 0.900731i 0.643032π0.643032\pi
152152 44.1308i 0.290334i
153153 0 0
154154 −66.3263 −0.430690
155155 122.267i 0.788818i
156156 0 0
157157 192.772 1.22785 0.613924 0.789365i 0.289590π-0.289590\pi
0.613924 + 0.789365i 0.289590π0.289590\pi
158158 − 108.969i − 0.689679i
159159 0 0
160160 43.2159 0.270099
161161 178.825i 1.11072i
162162 0 0
163163 80.4819 0.493754 0.246877 0.969047i 0.420596π-0.420596\pi
0.246877 + 0.969047i 0.420596π0.420596\pi
164164 16.5268i 0.100773i
165165 0 0
166166 149.174 0.898638
167167 − 108.270i − 0.648321i −0.946002 0.324161i 0.894918π-0.894918\pi
0.946002 0.324161i 0.105082π-0.105082\pi
168168 0 0
169169 381.431 2.25699
170170 − 79.7583i − 0.469167i
171171 0 0
172172 90.1655 0.524218
173173 − 84.6632i − 0.489383i −0.969601 0.244691i 0.921313π-0.921313\pi
0.969601 0.244691i 0.0786866π-0.0786866\pi
174174 0 0
175175 −191.983 −1.09705
176176 − 32.6011i − 0.185233i
177177 0 0
178178 −0.493491 −0.00277242
179179 167.767i 0.937248i 0.883398 + 0.468624i 0.155250π0.155250\pi
−0.883398 + 0.468624i 0.844750π0.844750\pi
180180 0 0
181181 −289.465 −1.59925 −0.799627 0.600497i 0.794970π-0.794970\pi
−0.799627 + 0.600497i 0.794970π0.794970\pi
182182 − 190.926i − 1.04905i
183183 0 0
184184 −87.8972 −0.477702
185185 − 91.5291i − 0.494752i
186186 0 0
187187 −60.1678 −0.321753
188188 135.221i 0.719261i
189189 0 0
190190 168.570 0.887211
191191 − 40.3377i − 0.211192i −0.994409 0.105596i 0.966325π-0.966325\pi
0.994409 0.105596i 0.0336751π-0.0336751\pi
192192 0 0
193193 −242.523 −1.25660 −0.628299 0.777972i 0.716249π-0.716249\pi
−0.628299 + 0.777972i 0.716249π0.716249\pi
194194 − 90.4619i − 0.466298i
195195 0 0
196196 31.7741 0.162113
197197 − 5.45517i − 0.0276912i −0.999904 0.0138456i 0.995593π-0.995593\pi
0.999904 0.0138456i 0.00440733π-0.00440733\pi
198198 0 0
199199 −143.015 −0.718667 −0.359333 0.933209i 0.616996π-0.616996\pi
−0.359333 + 0.933209i 0.616996π0.616996\pi
200200 − 94.3648i − 0.471824i
201201 0 0
202202 235.784 1.16725
203203 − 162.955i − 0.802733i
204204 0 0
205205 63.1288 0.307945
206206 142.285i 0.690702i
207207 0 0
208208 93.8451 0.451178
209209 − 127.165i − 0.608446i
210210 0 0
211211 −8.63782 −0.0409375 −0.0204688 0.999790i 0.506516π-0.506516\pi
−0.0204688 + 0.999790i 0.506516π0.506516\pi
212212 − 32.8231i − 0.154826i
213213 0 0
214214 −9.30278 −0.0434709
215215 − 344.413i − 1.60192i
216216 0 0
217217 92.0956 0.424404
218218 − 281.253i − 1.29015i
219219 0 0
220220 −124.529 −0.566041
221221 − 173.198i − 0.783703i
222222 0 0
223223 −306.810 −1.37583 −0.687915 0.725791i 0.741474π-0.741474\pi
−0.687915 + 0.725791i 0.741474π0.741474\pi
224224 − 32.5517i − 0.145320i
225225 0 0
226226 −7.42068 −0.0328348
227227 − 11.8982i − 0.0524148i −0.999657 0.0262074i 0.991657π-0.991657\pi
0.999657 0.0262074i 0.00834303π-0.00834303\pi
228228 0 0
229229 −385.366 −1.68282 −0.841409 0.540398i 0.818274π-0.818274\pi
−0.841409 + 0.540398i 0.818274π0.818274\pi
230230 335.748i 1.45978i
231231 0 0
232232 80.0965 0.345243
233233 9.60654i 0.0412298i 0.999787 + 0.0206149i 0.00656239π0.00656239\pi
−0.999787 + 0.0206149i 0.993438π0.993438\pi
234234 0 0
235235 516.515 2.19794
236236 − 116.488i − 0.493594i
237237 0 0
238238 −60.0767 −0.252423
239239 102.957i 0.430782i 0.976528 + 0.215391i 0.0691025π0.0691025\pi
−0.976528 + 0.215391i 0.930897π0.930897\pi
240240 0 0
241241 106.473 0.441798 0.220899 0.975297i 0.429101π-0.429101\pi
0.220899 + 0.975297i 0.429101π0.429101\pi
242242 − 77.1782i − 0.318918i
243243 0 0
244244 −142.708 −0.584870
245245 − 121.370i − 0.495389i
246246 0 0
247247 366.057 1.48201
248248 45.2673i 0.182530i
249249 0 0
250250 −90.3535 −0.361414
251251 81.6007i 0.325102i 0.986700 + 0.162551i 0.0519723π0.0519723\pi
−0.986700 + 0.162551i 0.948028π0.948028\pi
252252 0 0
253253 253.281 1.00111
254254 − 62.8451i − 0.247422i
255255 0 0
256256 16.0000 0.0625000
257257 − 439.294i − 1.70931i −0.519193 0.854657i 0.673767π-0.673767\pi
0.519193 0.854657i 0.326233π-0.326233\pi
258258 0 0
259259 −68.9429 −0.266189
260260 − 358.468i − 1.37872i
261261 0 0
262262 −56.8234 −0.216883
263263 450.911i 1.71449i 0.514908 + 0.857245i 0.327826π0.327826\pi
−0.514908 + 0.857245i 0.672174π0.672174\pi
264264 0 0
265265 −125.377 −0.473121
266266 − 126.973i − 0.477342i
267267 0 0
268268 −100.392 −0.374597
269269 363.566i 1.35155i 0.737110 + 0.675773i 0.236190π0.236190\pi
−0.737110 + 0.675773i 0.763810π0.763810\pi
270270 0 0
271271 −70.6655 −0.260758 −0.130379 0.991464i 0.541619π-0.541619\pi
−0.130379 + 0.991464i 0.541619π0.541619\pi
272272 − 29.5292i − 0.108563i
273273 0 0
274274 72.8842 0.266001
275275 271.917i 0.988789i
276276 0 0
277277 −233.500 −0.842962 −0.421481 0.906837i 0.638490π-0.638490\pi
−0.421481 + 0.906837i 0.638490π0.638490\pi
278278 152.239i 0.547622i
279279 0 0
280280 −124.341 −0.444073
281281 289.317i 1.02960i 0.857311 + 0.514799i 0.172134π0.172134\pi
−0.857311 + 0.514799i 0.827866π0.827866\pi
282282 0 0
283283 153.403 0.542060 0.271030 0.962571i 0.412636π-0.412636\pi
0.271030 + 0.962571i 0.412636π0.412636\pi
284284 81.8367i 0.288157i
285285 0 0
286286 −270.420 −0.945523
287287 − 47.5508i − 0.165682i
288288 0 0
289289 234.502 0.811424
290290 − 305.951i − 1.05500i
291291 0 0
292292 −199.077 −0.681770
293293 − 163.328i − 0.557434i −0.960373 0.278717i 0.910091π-0.910091\pi
0.960373 0.278717i 0.0899091π-0.0899091\pi
294294 0 0
295295 −444.959 −1.50834
296296 − 33.8872i − 0.114484i
297297 0 0
298298 199.547 0.669621
299299 729.091i 2.43843i
300300 0 0
301301 −259.423 −0.861872
302302 185.519i 0.614303i
303303 0 0
304304 62.4104 0.205297
305305 545.115i 1.78726i
306306 0 0
307307 −326.648 −1.06400 −0.532000 0.846744i 0.678560π-0.678560\pi
−0.532000 + 0.846744i 0.678560π0.678560\pi
308308 93.7995i 0.304544i
309309 0 0
310310 172.911 0.557779
311311 − 465.553i − 1.49695i −0.663161 0.748477i 0.730786π-0.730786\pi
0.663161 0.748477i 0.269214π-0.269214\pi
312312 0 0
313313 219.310 0.700669 0.350335 0.936625i 0.386068π-0.386068\pi
0.350335 + 0.936625i 0.386068π0.386068\pi
314314 − 272.621i − 0.868220i
315315 0 0
316316 −154.106 −0.487677
317317 − 127.383i − 0.401838i −0.979608 0.200919i 0.935607π-0.935607\pi
0.979608 0.200919i 0.0643928π-0.0643928\pi
318318 0 0
319319 −230.802 −0.723518
320320 − 61.1165i − 0.190989i
321321 0 0
322322 252.897 0.785395
323323 − 115.183i − 0.356604i
324324 0 0
325325 −782.738 −2.40843
326326 − 113.819i − 0.349137i
327327 0 0
328328 23.3724 0.0712573
329329 − 389.057i − 1.18254i
330330 0 0
331331 271.665 0.820739 0.410370 0.911919i 0.365400π-0.365400\pi
0.410370 + 0.911919i 0.365400π0.365400\pi
332332 − 210.964i − 0.635433i
333333 0 0
334334 −153.116 −0.458432
335335 383.475i 1.14470i
336336 0 0
337337 513.337 1.52325 0.761627 0.648015i 0.224401π-0.224401\pi
0.761627 + 0.648015i 0.224401π0.224401\pi
338338 − 539.426i − 1.59593i
339339 0 0
340340 −112.795 −0.331751
341341 − 130.440i − 0.382523i
342342 0 0
343343 −373.385 −1.08859
344344 − 127.513i − 0.370678i
345345 0 0
346346 −119.732 −0.346046
347347 179.150i 0.516281i 0.966107 + 0.258141i 0.0831098π0.0831098\pi
−0.966107 + 0.258141i 0.916890π0.916890\pi
348348 0 0
349349 −345.505 −0.989985 −0.494992 0.868897i 0.664829π-0.664829\pi
−0.494992 + 0.868897i 0.664829π0.664829\pi
350350 271.506i 0.775730i
351351 0 0
352352 −46.1048 −0.130980
353353 245.720i 0.696091i 0.937478 + 0.348046i 0.113155π0.113155\pi
−0.937478 + 0.348046i 0.886845π0.886845\pi
354354 0 0
355355 312.598 0.880559
356356 0.697902i 0.00196040i
357357 0 0
358358 237.259 0.662735
359359 − 555.660i − 1.54780i −0.633309 0.773899i 0.718304π-0.718304\pi
0.633309 0.773899i 0.281696π-0.281696\pi
360360 0 0
361361 −117.559 −0.325648
362362 409.365i 1.13084i
363363 0 0
364364 −270.010 −0.741787
365365 760.430i 2.08337i
366366 0 0
367367 398.565 1.08601 0.543004 0.839730i 0.317287π-0.317287\pi
0.543004 + 0.839730i 0.317287π0.317287\pi
368368 124.305i 0.337787i
369369 0 0
370370 −129.442 −0.349842
371371 94.4383i 0.254551i
372372 0 0
373373 409.675 1.09832 0.549162 0.835716i 0.314947π-0.314947\pi
0.549162 + 0.835716i 0.314947π0.314947\pi
374374 85.0901i 0.227514i
375375 0 0
376376 191.231 0.508594
377377 − 664.385i − 1.76230i
378378 0 0
379379 −61.5139 −0.162306 −0.0811529 0.996702i 0.525860π-0.525860\pi
−0.0811529 + 0.996702i 0.525860π0.525860\pi
380380 − 238.394i − 0.627353i
381381 0 0
382382 −57.0462 −0.149335
383383 203.341i 0.530917i 0.964122 + 0.265458i 0.0855233π0.0855233\pi
−0.964122 + 0.265458i 0.914477π0.914477\pi
384384 0 0
385385 358.294 0.930633
386386 342.980i 0.888549i
387387 0 0
388388 −127.932 −0.329723
389389 255.004i 0.655538i 0.944758 + 0.327769i 0.106297π0.106297\pi
−0.944758 + 0.327769i 0.893703π0.893703\pi
390390 0 0
391391 229.415 0.586740
392392 − 44.9354i − 0.114631i
393393 0 0
394394 −7.71477 −0.0195806
395395 588.651i 1.49026i
396396 0 0
397397 −27.6278 −0.0695914 −0.0347957 0.999394i 0.511078π-0.511078\pi
−0.0347957 + 0.999394i 0.511078π0.511078\pi
398398 202.253i 0.508174i
399399 0 0
400400 −133.452 −0.333630
401401 374.465i 0.933829i 0.884303 + 0.466914i 0.154634π0.154634\pi
−0.884303 + 0.466914i 0.845366π0.845366\pi
402402 0 0
403403 375.484 0.931722
404404 − 333.449i − 0.825370i
405405 0 0
406406 −230.453 −0.567618
407407 97.6477i 0.239921i
408408 0 0
409409 204.938 0.501071 0.250536 0.968107i 0.419393π-0.419393\pi
0.250536 + 0.968107i 0.419393π0.419393\pi
410410 − 89.2775i − 0.217750i
411411 0 0
412412 201.221 0.488400
413413 335.159i 0.811522i
414414 0 0
415415 −805.835 −1.94177
416416 − 132.717i − 0.319031i
417417 0 0
418418 −179.839 −0.430237
419419 − 239.000i − 0.570405i −0.958467 0.285202i 0.907939π-0.907939\pi
0.958467 0.285202i 0.0920608π-0.0920608\pi
420420 0 0
421421 199.488 0.473844 0.236922 0.971529i 0.423861π-0.423861\pi
0.236922 + 0.971529i 0.423861π0.423861\pi
422422 12.2157i 0.0289472i
423423 0 0
424424 −46.4188 −0.109478
425425 246.296i 0.579520i
426426 0 0
427427 410.599 0.961591
428428 13.1561i 0.0307386i
429429 0 0
430430 −487.073 −1.13273
431431 − 235.094i − 0.545461i −0.962090 0.272731i 0.912073π-0.912073\pi
0.962090 0.272731i 0.0879267π-0.0879267\pi
432432 0 0
433433 −391.650 −0.904504 −0.452252 0.891890i 0.649379π-0.649379\pi
−0.452252 + 0.891890i 0.649379π0.649379\pi
434434 − 130.243i − 0.300099i
435435 0 0
436436 −397.752 −0.912276
437437 484.872i 1.10955i
438438 0 0
439439 81.2695 0.185124 0.0925621 0.995707i 0.470494π-0.470494\pi
0.0925621 + 0.995707i 0.470494π0.470494\pi
440440 176.111i 0.400251i
441441 0 0
442442 −244.940 −0.554162
443443 − 527.706i − 1.19121i −0.803277 0.595605i 0.796912π-0.796912\pi
0.803277 0.595605i 0.203088π-0.203088\pi
444444 0 0
445445 2.66583 0.00599064
446446 433.895i 0.972859i
447447 0 0
448448 −46.0351 −0.102757
449449 120.226i 0.267765i 0.990997 + 0.133882i 0.0427445π0.0427445\pi
−0.990997 + 0.133882i 0.957256π0.957256\pi
450450 0 0
451451 −67.3488 −0.149332
452452 10.4944i 0.0232177i
453453 0 0
454454 −16.8265 −0.0370629
455455 1031.38i 2.26677i
456456 0 0
457457 −143.140 −0.313216 −0.156608 0.987661i 0.550056π-0.550056\pi
−0.156608 + 0.987661i 0.550056π0.550056\pi
458458 544.989i 1.18993i
459459 0 0
460460 474.820 1.03222
461461 − 236.139i − 0.512232i −0.966646 0.256116i 0.917557π-0.917557\pi
0.966646 0.256116i 0.0824429π-0.0824429\pi
462462 0 0
463463 148.324 0.320353 0.160177 0.987088i 0.448794π-0.448794\pi
0.160177 + 0.987088i 0.448794π0.448794\pi
464464 − 113.274i − 0.244124i
465465 0 0
466466 13.5857 0.0291539
467467 − 90.2013i − 0.193150i −0.995326 0.0965752i 0.969211π-0.969211\pi
0.995326 0.0965752i 0.0307888π-0.0307888\pi
468468 0 0
469469 288.847 0.615878
470470 − 730.463i − 1.55418i
471471 0 0
472472 −164.739 −0.349023
473473 367.436i 0.776821i
474474 0 0
475475 −520.549 −1.09589
476476 84.9613i 0.178490i
477477 0 0
478478 145.603 0.304609
479479 − 258.118i − 0.538868i −0.963019 0.269434i 0.913163π-0.913163\pi
0.963019 0.269434i 0.0868366π-0.0868366\pi
480480 0 0
481481 −281.088 −0.584382
482482 − 150.576i − 0.312398i
483483 0 0
484484 −109.146 −0.225509
485485 488.674i 1.00758i
486486 0 0
487487 −103.107 −0.211718 −0.105859 0.994381i 0.533759π-0.533759\pi
−0.105859 + 0.994381i 0.533759π0.533759\pi
488488 201.820i 0.413566i
489489 0 0
490490 −171.643 −0.350293
491491 − 764.752i − 1.55754i −0.627310 0.778770i 0.715844π-0.715844\pi
0.627310 0.778770i 0.284156π-0.284156\pi
492492 0 0
493493 −209.055 −0.424047
494494 − 517.683i − 1.04794i
495495 0 0
496496 64.0177 0.129068
497497 − 235.460i − 0.473762i
498498 0 0
499499 −718.977 −1.44084 −0.720418 0.693540i 0.756050π-0.756050\pi
−0.720418 + 0.693540i 0.756050π0.756050\pi
500500 127.779i 0.255558i
501501 0 0
502502 115.401 0.229882
503503 − 585.028i − 1.16308i −0.813519 0.581538i 0.802451π-0.802451\pi
0.813519 0.581538i 0.197549π-0.197549\pi
504504 0 0
505505 −1273.70 −2.52219
506506 − 358.193i − 0.707891i
507507 0 0
508508 −88.8764 −0.174954
509509 − 883.436i − 1.73563i −0.496886 0.867816i 0.665523π-0.665523\pi
0.496886 0.867816i 0.334477π-0.334477\pi
510510 0 0
511511 572.782 1.12090
512512 − 22.6274i − 0.0441942i
513513 0 0
514514 −621.255 −1.20867
515515 − 768.620i − 1.49247i
516516 0 0
517517 −551.044 −1.06585
518518 97.5000i 0.188224i
519519 0 0
520520 −506.950 −0.974904
521521 26.0398i 0.0499804i 0.999688 + 0.0249902i 0.00795545π0.00795545\pi
−0.999688 + 0.0249902i 0.992045π0.992045\pi
522522 0 0
523523 578.821 1.10673 0.553366 0.832938i 0.313343π-0.313343\pi
0.553366 + 0.832938i 0.313343π0.313343\pi
524524 80.3605i 0.153360i
525525 0 0
526526 637.684 1.21233
527527 − 118.150i − 0.224193i
528528 0 0
529529 −436.741 −0.825597
530530 177.310i 0.334547i
531531 0 0
532532 −179.567 −0.337531
533533 − 193.870i − 0.363733i
534534 0 0
535535 50.2535 0.0939318
536536 141.976i 0.264880i
537537 0 0
538538 514.160 0.955688
539539 129.484i 0.240229i
540540 0 0
541541 −84.9565 −0.157036 −0.0785180 0.996913i 0.525019π-0.525019\pi
−0.0785180 + 0.996913i 0.525019π0.525019\pi
542542 99.9360i 0.184384i
543543 0 0
544544 −41.7606 −0.0767659
545545 1519.33i 2.78776i
546546 0 0
547547 −864.185 −1.57986 −0.789931 0.613195i 0.789884π-0.789884\pi
−0.789931 + 0.613195i 0.789884π0.789884\pi
548548 − 103.074i − 0.188091i
549549 0 0
550550 384.549 0.699180
551551 − 441.840i − 0.801888i
552552 0 0
553553 443.392 0.801794
554554 330.219i 0.596064i
555555 0 0
556556 215.299 0.387228
557557 261.397i 0.469294i 0.972081 + 0.234647i 0.0753934π0.0753934\pi
−0.972081 + 0.234647i 0.924607π0.924607\pi
558558 0 0
559559 −1057.70 −1.89213
560560 175.844i 0.314007i
561561 0 0
562562 409.156 0.728036
563563 − 787.033i − 1.39793i −0.715158 0.698963i 0.753645π-0.753645\pi
0.715158 0.698963i 0.246355π-0.246355\pi
564564 0 0
565565 40.0864 0.0709494
566566 − 216.944i − 0.383294i
567567 0 0
568568 115.735 0.203758
569569 264.418i 0.464707i 0.972631 + 0.232354i 0.0746427π0.0746427\pi
−0.972631 + 0.232354i 0.925357π0.925357\pi
570570 0 0
571571 −63.6987 −0.111556 −0.0557782 0.998443i 0.517764π-0.517764\pi
−0.0557782 + 0.998443i 0.517764π0.517764\pi
572572 382.431i 0.668586i
573573 0 0
574574 −67.2469 −0.117155
575575 − 1036.80i − 1.80313i
576576 0 0
577577 −970.722 −1.68236 −0.841180 0.540755i 0.818139π-0.818139\pi
−0.841180 + 0.540755i 0.818139π0.818139\pi
578578 − 331.635i − 0.573763i
579579 0 0
580580 −432.680 −0.746001
581581 606.983i 1.04472i
582582 0 0
583583 133.758 0.229431
584584 281.537i 0.482084i
585585 0 0
586586 −230.981 −0.394165
587587 101.662i 0.173190i 0.996244 + 0.0865948i 0.0275985π0.0275985\pi
−0.996244 + 0.0865948i 0.972401π0.972401\pi
588588 0 0
589589 249.711 0.423957
590590 629.268i 1.06656i
591591 0 0
592592 −47.9237 −0.0809522
593593 926.755i 1.56282i 0.624016 + 0.781412i 0.285500π0.285500\pi
−0.624016 + 0.781412i 0.714500π0.714500\pi
594594 0 0
595595 324.534 0.545435
596596 − 282.202i − 0.473493i
597597 0 0
598598 1031.09 1.72423
599599 − 562.278i − 0.938695i −0.883014 0.469347i 0.844489π-0.844489\pi
0.883014 0.469347i 0.155511π-0.155511\pi
600600 0 0
601601 380.292 0.632765 0.316382 0.948632i 0.397532π-0.397532\pi
0.316382 + 0.948632i 0.397532π0.397532\pi
602602 366.880i 0.609436i
603603 0 0
604604 262.364 0.434378
605605 416.916i 0.689117i
606606 0 0
607607 −1124.48 −1.85251 −0.926257 0.376893i 0.876992π-0.876992\pi
−0.926257 + 0.376893i 0.876992π0.876992\pi
608608 − 88.2616i − 0.145167i
609609 0 0
610610 770.909 1.26379
611611 − 1586.23i − 2.59612i
612612 0 0
613613 626.817 1.02254 0.511270 0.859420i 0.329175π-0.329175\pi
0.511270 + 0.859420i 0.329175π0.329175\pi
614614 461.950i 0.752362i
615615 0 0
616616 132.653 0.215345
617617 − 176.294i − 0.285727i −0.989742 0.142864i 0.954369π-0.954369\pi
0.989742 0.142864i 0.0456311π-0.0456311\pi
618618 0 0
619619 929.905 1.50227 0.751135 0.660149i 0.229507π-0.229507\pi
0.751135 + 0.660149i 0.229507π0.229507\pi
620620 − 244.534i − 0.394409i
621621 0 0
622622 −658.391 −1.05851
623623 − 2.00800i − 0.00322311i
624624 0 0
625625 −345.986 −0.553577
626626 − 310.151i − 0.495448i
627627 0 0
628628 −385.544 −0.613924
629629 88.4469i 0.140615i
630630 0 0
631631 −654.106 −1.03662 −0.518309 0.855193i 0.673438π-0.673438\pi
−0.518309 + 0.855193i 0.673438π0.673438\pi
632632 217.939i 0.344840i
633633 0 0
634634 −180.146 −0.284142
635635 339.489i 0.534628i
636636 0 0
637637 −372.731 −0.585134
638638 326.404i 0.511605i
639639 0 0
640640 −86.4318 −0.135050
641641 736.054i 1.14829i 0.818754 + 0.574145i 0.194665π0.194665\pi
−0.818754 + 0.574145i 0.805335π0.805335\pi
642642 0 0
643643 −712.261 −1.10771 −0.553857 0.832612i 0.686845π-0.686845\pi
−0.553857 + 0.832612i 0.686845π0.686845\pi
644644 − 357.651i − 0.555358i
645645 0 0
646646 −162.894 −0.252157
647647 291.136i 0.449978i 0.974361 + 0.224989i 0.0722346π0.0722346\pi
−0.974361 + 0.224989i 0.927765π0.927765\pi
648648 0 0
649649 474.704 0.731440
650650 1106.96i 1.70301i
651651 0 0
652652 −160.964 −0.246877
653653 − 1162.93i − 1.78090i −0.455081 0.890450i 0.650390π-0.650390\pi
0.455081 0.890450i 0.349610π-0.349610\pi
654654 0 0
655655 306.960 0.468641
656656 − 33.0536i − 0.0503866i
657657 0 0
658658 −550.210 −0.836185
659659 − 529.292i − 0.803174i −0.915821 0.401587i 0.868459π-0.868459\pi
0.915821 0.401587i 0.131541π-0.131541\pi
660660 0 0
661661 3.85043 0.00582516 0.00291258 0.999996i 0.499073π-0.499073\pi
0.00291258 + 0.999996i 0.499073π0.499073\pi
662662 − 384.192i − 0.580350i
663663 0 0
664664 −298.348 −0.449319
665665 685.906i 1.03144i
666666 0 0
667667 880.033 1.31939
668668 216.539i 0.324161i
669669 0 0
670670 542.316 0.809427
671671 − 581.555i − 0.866700i
672672 0 0
673673 −414.813 −0.616364 −0.308182 0.951327i 0.599721π-0.599721\pi
−0.308182 + 0.951327i 0.599721π0.599721\pi
674674 − 725.968i − 1.07710i
675675 0 0
676676 −762.863 −1.12850
677677 − 1187.49i − 1.75405i −0.480444 0.877025i 0.659524π-0.659524\pi
0.480444 0.877025i 0.340476π-0.340476\pi
678678 0 0
679679 368.086 0.542100
680680 159.517i 0.234583i
681681 0 0
682682 −184.470 −0.270484
683683 513.834i 0.752320i 0.926555 + 0.376160i 0.122756π0.122756\pi
−0.926555 + 0.376160i 0.877244π0.877244\pi
684684 0 0
685685 −393.720 −0.574774
686686 528.046i 0.769747i
687687 0 0
688688 −180.331 −0.262109
689689 385.036i 0.558833i
690690 0 0
691691 529.360 0.766079 0.383039 0.923732i 0.374877π-0.374877\pi
0.383039 + 0.923732i 0.374877π0.374877\pi
692692 169.326i 0.244691i
693693 0 0
694694 253.356 0.365066
695695 − 822.394i − 1.18330i
696696 0 0
697697 −61.0029 −0.0875221
698698 488.617i 0.700025i
699699 0 0
700700 383.967 0.548524
701701 13.0718i 0.0186474i 0.999957 + 0.00932369i 0.00296787π0.00296787\pi
−0.999957 + 0.00932369i 0.997032π0.997032\pi
702702 0 0
703703 −186.934 −0.265908
704704 65.2021i 0.0926166i
705705 0 0
706706 347.501 0.492211
707707 959.398i 1.35700i
708708 0 0
709709 −762.984 −1.07614 −0.538071 0.842900i 0.680847π-0.680847\pi
−0.538071 + 0.842900i 0.680847π0.680847\pi
710710 − 442.081i − 0.622649i
711711 0 0
712712 0.986982 0.00138621
713713 497.359i 0.697559i
714714 0 0
715715 1460.80 2.04308
716716 − 335.535i − 0.468624i
717717 0 0
718718 −785.821 −1.09446
719719 903.516i 1.25663i 0.777959 + 0.628315i 0.216255π0.216255\pi
−0.777959 + 0.628315i 0.783745π0.783745\pi
720720 0 0
721721 −578.951 −0.802983
722722 166.253i 0.230268i
723723 0 0
724724 578.930 0.799627
725725 944.786i 1.30315i
726726 0 0
727727 −964.599 −1.32682 −0.663411 0.748256i 0.730892π-0.730892\pi
−0.663411 + 0.748256i 0.730892π0.730892\pi
728728 381.852i 0.524523i
729729 0 0
730730 1075.41 1.47317
731731 332.815i 0.455287i
732732 0 0
733733 549.731 0.749974 0.374987 0.927030i 0.377647π-0.377647\pi
0.374987 + 0.927030i 0.377647π0.377647\pi
734734 − 563.656i − 0.767924i
735735 0 0
736736 175.794 0.238851
737737 − 409.110i − 0.555102i
738738 0 0
739739 522.615 0.707192 0.353596 0.935398i 0.384959π-0.384959\pi
0.353596 + 0.935398i 0.384959π0.384959\pi
740740 183.058i 0.247376i
741741 0 0
742742 133.556 0.179995
743743 498.311i 0.670674i 0.942098 + 0.335337i 0.108850π0.108850\pi
−0.942098 + 0.335337i 0.891150π0.891150\pi
744744 0 0
745745 −1077.95 −1.44691
746746 − 579.367i − 0.776632i
747747 0 0
748748 120.336 0.160876
749749 − 37.8527i − 0.0505376i
750750 0 0
751751 401.886 0.535135 0.267567 0.963539i 0.413780π-0.413780\pi
0.267567 + 0.963539i 0.413780π0.413780\pi
752752 − 270.442i − 0.359631i
753753 0 0
754754 −939.583 −1.24613
755755 − 1002.17i − 1.32738i
756756 0 0
757757 564.958 0.746312 0.373156 0.927769i 0.378276π-0.378276\pi
0.373156 + 0.927769i 0.378276π0.378276\pi
758758 86.9938i 0.114768i
759759 0 0
760760 −337.140 −0.443606
761761 − 359.307i − 0.472151i −0.971735 0.236076i 0.924139π-0.924139\pi
0.971735 0.236076i 0.0758613π-0.0758613\pi
762762 0 0
763763 1144.41 1.49988
764764 80.6754i 0.105596i
765765 0 0
766766 287.568 0.375415
767767 1366.48i 1.78159i
768768 0 0
769769 −600.467 −0.780841 −0.390420 0.920637i 0.627670π-0.627670\pi
−0.390420 + 0.920637i 0.627670π0.627670\pi
770770 − 506.704i − 0.658057i
771771 0 0
772772 485.047 0.628299
773773 229.599i 0.297023i 0.988911 + 0.148512i 0.0474482π0.0474482\pi
−0.988911 + 0.148512i 0.952552π0.952552\pi
774774 0 0
775775 −533.955 −0.688974
776776 180.924i 0.233149i
777777 0 0
778778 360.630 0.463535
779779 − 128.930i − 0.165508i
780780 0 0
781781 −333.495 −0.427010
782782 − 324.442i − 0.414888i
783783 0 0
784784 −63.5482 −0.0810564
785785 1472.70i 1.87605i
786786 0 0
787787 −1049.16 −1.33311 −0.666554 0.745456i 0.732232π-0.732232\pi
−0.666554 + 0.745456i 0.732232π0.732232\pi
788788 10.9103i 0.0138456i
789789 0 0
790790 832.478 1.05377
791791 − 30.1945i − 0.0381725i
792792 0 0
793793 1674.06 2.11105
794794 39.0716i 0.0492086i
795795 0 0
796796 286.029 0.359333
797797 − 1490.08i − 1.86961i −0.355162 0.934805i 0.615574π-0.615574\pi
0.355162 0.934805i 0.384426π-0.384426\pi
798798 0 0
799799 −499.122 −0.624683
800800 188.730i 0.235912i
801801 0 0
802802 529.574 0.660317
803803 − 811.264i − 1.01029i
804804 0 0
805805 −1366.15 −1.69708
806806 − 531.015i − 0.658827i
807807 0 0
808808 −471.569 −0.583625
809809 1326.92i 1.64020i 0.572222 + 0.820099i 0.306082π0.306082\pi
−0.572222 + 0.820099i 0.693918π0.693918\pi
810810 0 0
811811 412.746 0.508935 0.254467 0.967081i 0.418100π-0.418100\pi
0.254467 + 0.967081i 0.418100π0.418100\pi
812812 325.910i 0.401367i
813813 0 0
814814 138.095 0.169650
815815 614.847i 0.754413i
816816 0 0
817817 −703.408 −0.860965
818818 − 289.826i − 0.354311i
819819 0 0
820820 −126.258 −0.153973
821821 − 270.948i − 0.330022i −0.986292 0.165011i 0.947234π-0.947234\pi
0.986292 0.165011i 0.0527660π-0.0527660\pi
822822 0 0
823823 718.060 0.872491 0.436246 0.899828i 0.356308π-0.356308\pi
0.436246 + 0.899828i 0.356308π0.356308\pi
824824 − 284.569i − 0.345351i
825825 0 0
826826 473.986 0.573833
827827 − 1115.81i − 1.34923i −0.738171 0.674614i 0.764310π-0.764310\pi
0.738171 0.674614i 0.235690π-0.235690\pi
828828 0 0
829829 1123.75 1.35555 0.677774 0.735270i 0.262945π-0.262945\pi
0.677774 + 0.735270i 0.262945π0.262945\pi
830830 1139.62i 1.37304i
831831 0 0
832832 −187.690 −0.225589
833833 117.283i 0.140796i
834834 0 0
835835 827.133 0.990579
836836 254.331i 0.304223i
837837 0 0
838838 −337.996 −0.403337
839839 − 253.356i − 0.301973i −0.988536 0.150987i 0.951755π-0.951755\pi
0.988536 0.150987i 0.0482451π-0.0482451\pi
840840 0 0
841841 39.0691 0.0464556
842842 − 282.119i − 0.335058i
843843 0 0
844844 17.2756 0.0204688
845845 2913.97i 3.44849i
846846 0 0
847847 314.035 0.370762
848848 65.6462i 0.0774129i
849849 0 0
850850 348.315 0.409782
851851 − 372.324i − 0.437513i
852852 0 0
853853 797.504 0.934940 0.467470 0.884009i 0.345166π-0.345166\pi
0.467470 + 0.884009i 0.345166π0.345166\pi
854854 − 580.675i − 0.679948i
855855 0 0
856856 18.6056 0.0217355
857857 − 1117.98i − 1.30453i −0.757990 0.652266i 0.773818π-0.773818\pi
0.757990 0.652266i 0.226182π-0.226182\pi
858858 0 0
859859 −1024.40 −1.19255 −0.596276 0.802779i 0.703354π-0.703354\pi
−0.596276 + 0.802779i 0.703354π0.703354\pi
860860 688.825i 0.800960i
861861 0 0
862862 −332.473 −0.385699
863863 − 1691.86i − 1.96044i −0.197921 0.980218i 0.563419π-0.563419\pi
0.197921 0.980218i 0.436581π-0.436581\pi
864864 0 0
865865 646.790 0.747734
866866 553.877i 0.639581i
867867 0 0
868868 −184.191 −0.212202
869869 − 628.002i − 0.722672i
870870 0 0
871871 1177.66 1.35208
872872 562.507i 0.645076i
873873 0 0
874874 685.713 0.784568
875875 − 367.645i − 0.420166i
876876 0 0
877877 210.381 0.239887 0.119944 0.992781i 0.461729π-0.461729\pi
0.119944 + 0.992781i 0.461729π0.461729\pi
878878 − 114.932i − 0.130903i
879879 0 0
880880 249.058 0.283020
881881 756.115i 0.858247i 0.903246 + 0.429123i 0.141177π0.141177\pi
−0.903246 + 0.429123i 0.858823π0.858823\pi
882882 0 0
883883 1283.92 1.45404 0.727021 0.686615i 0.240904π-0.240904\pi
0.727021 + 0.686615i 0.240904π0.240904\pi
884884 346.397i 0.391852i
885885 0 0
886886 −746.289 −0.842313
887887 − 454.977i − 0.512939i −0.966552 0.256469i 0.917441π-0.917441\pi
0.966552 0.256469i 0.0825593π-0.0825593\pi
888888 0 0
889889 255.715 0.287643
890890 − 3.77006i − 0.00423602i
891891 0 0
892892 613.620 0.687915
893893 − 1054.90i − 1.18130i
894894 0 0
895895 −1281.67 −1.43203
896896 65.1034i 0.0726601i
897897 0 0
898898 170.026 0.189338
899899 − 453.219i − 0.504137i
900900 0 0
901901 121.155 0.134467
902902 95.2456i 0.105594i
903903 0 0
904904 14.8414 0.0164174
905905 − 2211.39i − 2.44352i
906906 0 0
907907 1565.38 1.72589 0.862946 0.505296i 0.168617π-0.168617\pi
0.862946 + 0.505296i 0.168617π0.168617\pi
908908 23.7963i 0.0262074i
909909 0 0
910910 1458.59 1.60285
911911 962.212i 1.05622i 0.849177 + 0.528108i 0.177098π0.177098\pi
−0.849177 + 0.528108i 0.822902π0.822902\pi
912912 0 0
913913 859.705 0.941626
914914 202.430i 0.221477i
915915 0 0
916916 770.731 0.841409
917917 − 231.213i − 0.252140i
918918 0 0
919919 −1645.52 −1.79055 −0.895277 0.445509i 0.853023π-0.853023\pi
−0.895277 + 0.445509i 0.853023π0.853023\pi
920920 − 671.497i − 0.729888i
921921 0 0
922922 −333.951 −0.362203
923923 − 959.996i − 1.04008i
924924 0 0
925925 399.720 0.432129
926926 − 209.761i − 0.226524i
927927 0 0
928928 −160.193 −0.172622
929929 − 1362.56i − 1.46670i −0.679853 0.733348i 0.737957π-0.737957\pi
0.679853 0.733348i 0.262043π-0.262043\pi
930930 0 0
931931 −247.879 −0.266251
932932 − 19.2131i − 0.0206149i
933933 0 0
934934 −127.564 −0.136578
935935 − 459.656i − 0.491610i
936936 0 0
937937 350.586 0.374157 0.187079 0.982345i 0.440098π-0.440098\pi
0.187079 + 0.982345i 0.440098π0.440098\pi
938938 − 408.491i − 0.435492i
939939 0 0
940940 −1033.03 −1.09897
941941 303.734i 0.322778i 0.986891 + 0.161389i 0.0515974π0.0515974\pi
−0.986891 + 0.161389i 0.948403π0.948403\pi
942942 0 0
943943 256.796 0.272318
944944 232.976i 0.246797i
945945 0 0
946946 519.633 0.549295
947947 − 1424.55i − 1.50428i −0.659005 0.752139i 0.729022π-0.729022\pi
0.659005 0.752139i 0.270978π-0.270978\pi
948948 0 0
949949 2335.30 2.46080
950950 736.168i 0.774914i
951951 0 0
952952 120.153 0.126212
953953 − 636.885i − 0.668294i −0.942521 0.334147i 0.891552π-0.891552\pi
0.942521 0.334147i 0.108448π-0.108448\pi
954954 0 0
955955 308.163 0.322683
956956 − 205.914i − 0.215391i
957957 0 0
958958 −365.034 −0.381037
959959 296.563i 0.309242i
960960 0 0
961961 −704.859 −0.733464
962962 397.518i 0.413221i
963963 0 0
964964 −212.946 −0.220899
965965 − 1852.77i − 1.91997i
966966 0 0
967967 −618.697 −0.639811 −0.319905 0.947450i 0.603651π-0.603651\pi
−0.319905 + 0.947450i 0.603651π0.603651\pi
968968 154.356i 0.159459i
969969 0 0
970970 691.090 0.712463
971971 − 1356.90i − 1.39743i −0.715402 0.698713i 0.753756π-0.753756\pi
0.715402 0.698713i 0.246244π-0.246244\pi
972972 0 0
973973 −619.455 −0.636645
974974 145.815i 0.149707i
975975 0 0
976976 285.417 0.292435
977977 − 182.369i − 0.186663i −0.995635 0.0933314i 0.970248π-0.970248\pi
0.995635 0.0933314i 0.0297516π-0.0297516\pi
978978 0 0
979979 −2.84404 −0.00290505
980980 242.740i 0.247694i
981981 0 0
982982 −1081.52 −1.10135
983983 − 1270.39i − 1.29236i −0.763187 0.646178i 0.776366π-0.776366\pi
0.763187 0.646178i 0.223634π-0.223634\pi
984984 0 0
985985 41.6751 0.0423098
986986 295.648i 0.299846i
987987 0 0
988988 −732.114 −0.741006
989989 − 1401.01i − 1.41659i
990990 0 0
991991 549.168 0.554155 0.277078 0.960848i 0.410634π-0.410634\pi
0.277078 + 0.960848i 0.410634π0.410634\pi
992992 − 90.5347i − 0.0912648i
993993 0 0
994994 −332.990 −0.335000
995995 − 1092.57i − 1.09806i
996996 0 0
997997 −1378.50 −1.38265 −0.691325 0.722544i 0.742973π-0.742973\pi
−0.691325 + 0.722544i 0.742973π0.742973\pi
998998 1016.79i 1.01883i
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 1458.3.b.c.1457.16 36
3.2 odd 2 inner 1458.3.b.c.1457.21 36
27.2 odd 18 162.3.f.a.17.4 36
27.13 even 9 162.3.f.a.143.4 36
27.14 odd 18 54.3.f.a.47.3 yes 36
27.25 even 9 54.3.f.a.23.3 36
108.79 odd 18 432.3.bc.c.401.3 36
108.95 even 18 432.3.bc.c.209.3 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
54.3.f.a.23.3 36 27.25 even 9
54.3.f.a.47.3 yes 36 27.14 odd 18
162.3.f.a.17.4 36 27.2 odd 18
162.3.f.a.143.4 36 27.13 even 9
432.3.bc.c.209.3 36 108.95 even 18
432.3.bc.c.401.3 36 108.79 odd 18
1458.3.b.c.1457.16 36 1.1 even 1 trivial
1458.3.b.c.1457.21 36 3.2 odd 2 inner