Properties

Label 3042.2.a.y.1.1
Level 30423042
Weight 22
Character 3042.1
Self dual yes
Analytic conductor 24.29024.290
Analytic rank 00
Dimension 22
CM no
Inner twists 11

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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] = [3042,2,Mod(1,3042)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3042, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("3042.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Level: N N == 3042=232132 3042 = 2 \cdot 3^{2} \cdot 13^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 3042.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [2,2,0,2,4,0,2,2,0,4,6,0,0,2,0,2,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: 24.290492294924.2904922949
Analytic rank: 00
Dimension: 22
Coefficient field: Q(ζ12)+\Q(\zeta_{12})^+
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x23 x^{2} - 3 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 78)
Fricke sign: 1-1
Sato-Tate group: SU(2)\mathrm{SU}(2)

Embedding invariants

Embedding label 1.1
Root 1.73205-1.73205 of defining polynomial
Character χ\chi == 3042.1

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) == q+1.00000q2+1.00000q4+0.267949q50.732051q7+1.00000q8+0.267949q10+4.73205q110.732051q14+1.00000q16+2.26795q171.26795q19+0.267949q20+4.73205q22+6.19615q234.92820q250.732051q282.46410q29+5.46410q31+1.00000q32+2.26795q340.196152q3510.4641q371.26795q38+0.267949q40+11.3923q41+7.66025q43+4.73205q44+6.19615q468.19615q476.46410q494.92820q500.464102q53+1.26795q550.732051q562.46410q58+8.00000q59+1.19615q61+5.46410q62+1.00000q64+11.1244q67+2.26795q680.196152q70+1.26795q71+9.73205q7310.4641q741.26795q763.46410q779.46410q79+0.267949q80+11.3923q82+10.1962q83+0.607695q85+7.66025q86+4.73205q882.53590q89+6.19615q928.19615q940.339746q95+6.00000q976.46410q98+O(q100)q+1.00000 q^{2} +1.00000 q^{4} +0.267949 q^{5} -0.732051 q^{7} +1.00000 q^{8} +0.267949 q^{10} +4.73205 q^{11} -0.732051 q^{14} +1.00000 q^{16} +2.26795 q^{17} -1.26795 q^{19} +0.267949 q^{20} +4.73205 q^{22} +6.19615 q^{23} -4.92820 q^{25} -0.732051 q^{28} -2.46410 q^{29} +5.46410 q^{31} +1.00000 q^{32} +2.26795 q^{34} -0.196152 q^{35} -10.4641 q^{37} -1.26795 q^{38} +0.267949 q^{40} +11.3923 q^{41} +7.66025 q^{43} +4.73205 q^{44} +6.19615 q^{46} -8.19615 q^{47} -6.46410 q^{49} -4.92820 q^{50} -0.464102 q^{53} +1.26795 q^{55} -0.732051 q^{56} -2.46410 q^{58} +8.00000 q^{59} +1.19615 q^{61} +5.46410 q^{62} +1.00000 q^{64} +11.1244 q^{67} +2.26795 q^{68} -0.196152 q^{70} +1.26795 q^{71} +9.73205 q^{73} -10.4641 q^{74} -1.26795 q^{76} -3.46410 q^{77} -9.46410 q^{79} +0.267949 q^{80} +11.3923 q^{82} +10.1962 q^{83} +0.607695 q^{85} +7.66025 q^{86} +4.73205 q^{88} -2.53590 q^{89} +6.19615 q^{92} -8.19615 q^{94} -0.339746 q^{95} +6.00000 q^{97} -6.46410 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 2q+2q2+2q4+4q5+2q7+2q8+4q10+6q11+2q14+2q16+8q176q19+4q20+6q22+2q23+4q25+2q28+2q29+4q31+2q32+6q98+O(q100) 2 q + 2 q^{2} + 2 q^{4} + 4 q^{5} + 2 q^{7} + 2 q^{8} + 4 q^{10} + 6 q^{11} + 2 q^{14} + 2 q^{16} + 8 q^{17} - 6 q^{19} + 4 q^{20} + 6 q^{22} + 2 q^{23} + 4 q^{25} + 2 q^{28} + 2 q^{29} + 4 q^{31} + 2 q^{32}+ \cdots - 6 q^{98}+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 1.00000 0.707107
33 0 0
44 1.00000 0.500000
55 0.267949 0.119831 0.0599153 0.998203i 0.480917π-0.480917\pi
0.0599153 + 0.998203i 0.480917π0.480917\pi
66 0 0
77 −0.732051 −0.276689 −0.138345 0.990384i 0.544178π-0.544178\pi
−0.138345 + 0.990384i 0.544178π0.544178\pi
88 1.00000 0.353553
99 0 0
1010 0.267949 0.0847330
1111 4.73205 1.42677 0.713384 0.700774i 0.247162π-0.247162\pi
0.713384 + 0.700774i 0.247162π0.247162\pi
1212 0 0
1313 0 0
1414 −0.732051 −0.195649
1515 0 0
1616 1.00000 0.250000
1717 2.26795 0.550058 0.275029 0.961436i 0.411312π-0.411312\pi
0.275029 + 0.961436i 0.411312π0.411312\pi
1818 0 0
1919 −1.26795 −0.290887 −0.145444 0.989367i 0.546461π-0.546461\pi
−0.145444 + 0.989367i 0.546461π0.546461\pi
2020 0.267949 0.0599153
2121 0 0
2222 4.73205 1.00888
2323 6.19615 1.29199 0.645994 0.763343i 0.276443π-0.276443\pi
0.645994 + 0.763343i 0.276443π0.276443\pi
2424 0 0
2525 −4.92820 −0.985641
2626 0 0
2727 0 0
2828 −0.732051 −0.138345
2929 −2.46410 −0.457572 −0.228786 0.973477i 0.573476π-0.573476\pi
−0.228786 + 0.973477i 0.573476π0.573476\pi
3030 0 0
3131 5.46410 0.981382 0.490691 0.871334i 0.336744π-0.336744\pi
0.490691 + 0.871334i 0.336744π0.336744\pi
3232 1.00000 0.176777
3333 0 0
3434 2.26795 0.388950
3535 −0.196152 −0.0331558
3636 0 0
3737 −10.4641 −1.72029 −0.860144 0.510052i 0.829626π-0.829626\pi
−0.860144 + 0.510052i 0.829626π0.829626\pi
3838 −1.26795 −0.205689
3939 0 0
4040 0.267949 0.0423665
4141 11.3923 1.77918 0.889590 0.456761i 0.150990π-0.150990\pi
0.889590 + 0.456761i 0.150990π0.150990\pi
4242 0 0
4343 7.66025 1.16818 0.584089 0.811690i 0.301452π-0.301452\pi
0.584089 + 0.811690i 0.301452π0.301452\pi
4444 4.73205 0.713384
4545 0 0
4646 6.19615 0.913573
4747 −8.19615 −1.19553 −0.597766 0.801671i 0.703945π-0.703945\pi
−0.597766 + 0.801671i 0.703945π0.703945\pi
4848 0 0
4949 −6.46410 −0.923443
5050 −4.92820 −0.696953
5151 0 0
5252 0 0
5353 −0.464102 −0.0637493 −0.0318746 0.999492i 0.510148π-0.510148\pi
−0.0318746 + 0.999492i 0.510148π0.510148\pi
5454 0 0
5555 1.26795 0.170970
5656 −0.732051 −0.0978244
5757 0 0
5858 −2.46410 −0.323552
5959 8.00000 1.04151 0.520756 0.853706i 0.325650π-0.325650\pi
0.520756 + 0.853706i 0.325650π0.325650\pi
6060 0 0
6161 1.19615 0.153152 0.0765758 0.997064i 0.475601π-0.475601\pi
0.0765758 + 0.997064i 0.475601π0.475601\pi
6262 5.46410 0.693942
6363 0 0
6464 1.00000 0.125000
6565 0 0
6666 0 0
6767 11.1244 1.35906 0.679528 0.733649i 0.262185π-0.262185\pi
0.679528 + 0.733649i 0.262185π0.262185\pi
6868 2.26795 0.275029
6969 0 0
7070 −0.196152 −0.0234447
7171 1.26795 0.150478 0.0752389 0.997166i 0.476028π-0.476028\pi
0.0752389 + 0.997166i 0.476028π0.476028\pi
7272 0 0
7373 9.73205 1.13905 0.569525 0.821974i 0.307127π-0.307127\pi
0.569525 + 0.821974i 0.307127π0.307127\pi
7474 −10.4641 −1.21643
7575 0 0
7676 −1.26795 −0.145444
7777 −3.46410 −0.394771
7878 0 0
7979 −9.46410 −1.06479 −0.532397 0.846495i 0.678709π-0.678709\pi
−0.532397 + 0.846495i 0.678709π0.678709\pi
8080 0.267949 0.0299576
8181 0 0
8282 11.3923 1.25807
8383 10.1962 1.11917 0.559587 0.828772i 0.310960π-0.310960\pi
0.559587 + 0.828772i 0.310960π0.310960\pi
8484 0 0
8585 0.607695 0.0659138
8686 7.66025 0.826026
8787 0 0
8888 4.73205 0.504438
8989 −2.53590 −0.268805 −0.134402 0.990927i 0.542911π-0.542911\pi
−0.134402 + 0.990927i 0.542911π0.542911\pi
9090 0 0
9191 0 0
9292 6.19615 0.645994
9393 0 0
9494 −8.19615 −0.845369
9595 −0.339746 −0.0348572
9696 0 0
9797 6.00000 0.609208 0.304604 0.952479i 0.401476π-0.401476\pi
0.304604 + 0.952479i 0.401476π0.401476\pi
9898 −6.46410 −0.652973
9999 0 0
100100 −4.92820 −0.492820
101101 11.9282 1.18690 0.593450 0.804871i 0.297765π-0.297765\pi
0.593450 + 0.804871i 0.297765π0.297765\pi
102102 0 0
103103 −18.7321 −1.84572 −0.922862 0.385131i 0.874156π-0.874156\pi
−0.922862 + 0.385131i 0.874156π0.874156\pi
104104 0 0
105105 0 0
106106 −0.464102 −0.0450775
107107 0.196152 0.0189628 0.00948139 0.999955i 0.496982π-0.496982\pi
0.00948139 + 0.999955i 0.496982π0.496982\pi
108108 0 0
109109 5.46410 0.523366 0.261683 0.965154i 0.415723π-0.415723\pi
0.261683 + 0.965154i 0.415723π0.415723\pi
110110 1.26795 0.120894
111111 0 0
112112 −0.732051 −0.0691723
113113 18.6603 1.75541 0.877705 0.479202i 0.159074π-0.159074\pi
0.877705 + 0.479202i 0.159074π0.159074\pi
114114 0 0
115115 1.66025 0.154819
116116 −2.46410 −0.228786
117117 0 0
118118 8.00000 0.736460
119119 −1.66025 −0.152195
120120 0 0
121121 11.3923 1.03566
122122 1.19615 0.108295
123123 0 0
124124 5.46410 0.490691
125125 −2.66025 −0.237940
126126 0 0
127127 17.8564 1.58450 0.792250 0.610197i 0.208910π-0.208910\pi
0.792250 + 0.610197i 0.208910π0.208910\pi
128128 1.00000 0.0883883
129129 0 0
130130 0 0
131131 −13.4641 −1.17636 −0.588182 0.808729i 0.700156π-0.700156\pi
−0.588182 + 0.808729i 0.700156π0.700156\pi
132132 0 0
133133 0.928203 0.0804854
134134 11.1244 0.960998
135135 0 0
136136 2.26795 0.194475
137137 −1.92820 −0.164738 −0.0823688 0.996602i 0.526249π-0.526249\pi
−0.0823688 + 0.996602i 0.526249π0.526249\pi
138138 0 0
139139 −9.85641 −0.836009 −0.418005 0.908445i 0.637270π-0.637270\pi
−0.418005 + 0.908445i 0.637270π0.637270\pi
140140 −0.196152 −0.0165779
141141 0 0
142142 1.26795 0.106404
143143 0 0
144144 0 0
145145 −0.660254 −0.0548311
146146 9.73205 0.805430
147147 0 0
148148 −10.4641 −0.860144
149149 2.80385 0.229700 0.114850 0.993383i 0.463361π-0.463361\pi
0.114850 + 0.993383i 0.463361π0.463361\pi
150150 0 0
151151 −3.26795 −0.265942 −0.132971 0.991120i 0.542452π-0.542452\pi
−0.132971 + 0.991120i 0.542452π0.542452\pi
152152 −1.26795 −0.102844
153153 0 0
154154 −3.46410 −0.279145
155155 1.46410 0.117599
156156 0 0
157157 −23.5885 −1.88256 −0.941282 0.337622i 0.890378π-0.890378\pi
−0.941282 + 0.337622i 0.890378π0.890378\pi
158158 −9.46410 −0.752923
159159 0 0
160160 0.267949 0.0211832
161161 −4.53590 −0.357479
162162 0 0
163163 6.53590 0.511931 0.255966 0.966686i 0.417607π-0.417607\pi
0.255966 + 0.966686i 0.417607π0.417607\pi
164164 11.3923 0.889590
165165 0 0
166166 10.1962 0.791375
167167 −2.53590 −0.196234 −0.0981169 0.995175i 0.531282π-0.531282\pi
−0.0981169 + 0.995175i 0.531282π0.531282\pi
168168 0 0
169169 0 0
170170 0.607695 0.0466081
171171 0 0
172172 7.66025 0.584089
173173 16.3923 1.24628 0.623142 0.782109i 0.285856π-0.285856\pi
0.623142 + 0.782109i 0.285856π0.285856\pi
174174 0 0
175175 3.60770 0.272716
176176 4.73205 0.356692
177177 0 0
178178 −2.53590 −0.190074
179179 −22.0526 −1.64829 −0.824143 0.566382i 0.808343π-0.808343\pi
−0.824143 + 0.566382i 0.808343π0.808343\pi
180180 0 0
181181 8.80385 0.654385 0.327192 0.944958i 0.393897π-0.393897\pi
0.327192 + 0.944958i 0.393897π0.393897\pi
182182 0 0
183183 0 0
184184 6.19615 0.456786
185185 −2.80385 −0.206143
186186 0 0
187187 10.7321 0.784805
188188 −8.19615 −0.597766
189189 0 0
190190 −0.339746 −0.0246478
191191 −6.92820 −0.501307 −0.250654 0.968077i 0.580646π-0.580646\pi
−0.250654 + 0.968077i 0.580646π0.580646\pi
192192 0 0
193193 8.26795 0.595140 0.297570 0.954700i 0.403824π-0.403824\pi
0.297570 + 0.954700i 0.403824π0.403824\pi
194194 6.00000 0.430775
195195 0 0
196196 −6.46410 −0.461722
197197 9.85641 0.702240 0.351120 0.936330i 0.385801π-0.385801\pi
0.351120 + 0.936330i 0.385801π0.385801\pi
198198 0 0
199199 −3.80385 −0.269648 −0.134824 0.990870i 0.543047π-0.543047\pi
−0.134824 + 0.990870i 0.543047π0.543047\pi
200200 −4.92820 −0.348477
201201 0 0
202202 11.9282 0.839265
203203 1.80385 0.126605
204204 0 0
205205 3.05256 0.213200
206206 −18.7321 −1.30512
207207 0 0
208208 0 0
209209 −6.00000 −0.415029
210210 0 0
211211 −4.39230 −0.302379 −0.151189 0.988505i 0.548310π-0.548310\pi
−0.151189 + 0.988505i 0.548310π0.548310\pi
212212 −0.464102 −0.0318746
213213 0 0
214214 0.196152 0.0134087
215215 2.05256 0.139983
216216 0 0
217217 −4.00000 −0.271538
218218 5.46410 0.370076
219219 0 0
220220 1.26795 0.0854851
221221 0 0
222222 0 0
223223 13.0718 0.875352 0.437676 0.899133i 0.355802π-0.355802\pi
0.437676 + 0.899133i 0.355802π0.355802\pi
224224 −0.732051 −0.0489122
225225 0 0
226226 18.6603 1.24126
227227 −1.80385 −0.119726 −0.0598628 0.998207i 0.519066π-0.519066\pi
−0.0598628 + 0.998207i 0.519066π0.519066\pi
228228 0 0
229229 −15.8564 −1.04782 −0.523910 0.851773i 0.675527π-0.675527\pi
−0.523910 + 0.851773i 0.675527π0.675527\pi
230230 1.66025 0.109474
231231 0 0
232232 −2.46410 −0.161776
233233 −19.8564 −1.30084 −0.650418 0.759576i 0.725406π-0.725406\pi
−0.650418 + 0.759576i 0.725406π0.725406\pi
234234 0 0
235235 −2.19615 −0.143261
236236 8.00000 0.520756
237237 0 0
238238 −1.66025 −0.107618
239239 −9.66025 −0.624870 −0.312435 0.949939i 0.601145π-0.601145\pi
−0.312435 + 0.949939i 0.601145π0.601145\pi
240240 0 0
241241 17.5885 1.13297 0.566486 0.824071i 0.308302π-0.308302\pi
0.566486 + 0.824071i 0.308302π0.308302\pi
242242 11.3923 0.732325
243243 0 0
244244 1.19615 0.0765758
245245 −1.73205 −0.110657
246246 0 0
247247 0 0
248248 5.46410 0.346971
249249 0 0
250250 −2.66025 −0.168249
251251 −6.53590 −0.412542 −0.206271 0.978495i 0.566133π-0.566133\pi
−0.206271 + 0.978495i 0.566133π0.566133\pi
252252 0 0
253253 29.3205 1.84336
254254 17.8564 1.12041
255255 0 0
256256 1.00000 0.0625000
257257 −26.6603 −1.66302 −0.831510 0.555509i 0.812523π-0.812523\pi
−0.831510 + 0.555509i 0.812523π0.812523\pi
258258 0 0
259259 7.66025 0.475985
260260 0 0
261261 0 0
262262 −13.4641 −0.831815
263263 −28.0526 −1.72979 −0.864897 0.501949i 0.832617π-0.832617\pi
−0.864897 + 0.501949i 0.832617π0.832617\pi
264264 0 0
265265 −0.124356 −0.00763911
266266 0.928203 0.0569118
267267 0 0
268268 11.1244 0.679528
269269 1.46410 0.0892679 0.0446339 0.999003i 0.485788π-0.485788\pi
0.0446339 + 0.999003i 0.485788π0.485788\pi
270270 0 0
271271 −5.85641 −0.355751 −0.177876 0.984053i 0.556922π-0.556922\pi
−0.177876 + 0.984053i 0.556922π0.556922\pi
272272 2.26795 0.137515
273273 0 0
274274 −1.92820 −0.116487
275275 −23.3205 −1.40628
276276 0 0
277277 −2.26795 −0.136268 −0.0681339 0.997676i 0.521705π-0.521705\pi
−0.0681339 + 0.997676i 0.521705π0.521705\pi
278278 −9.85641 −0.591148
279279 0 0
280280 −0.196152 −0.0117223
281281 −22.3205 −1.33153 −0.665765 0.746162i 0.731895π-0.731895\pi
−0.665765 + 0.746162i 0.731895π0.731895\pi
282282 0 0
283283 8.33975 0.495746 0.247873 0.968792i 0.420268π-0.420268\pi
0.247873 + 0.968792i 0.420268π0.420268\pi
284284 1.26795 0.0752389
285285 0 0
286286 0 0
287287 −8.33975 −0.492280
288288 0 0
289289 −11.8564 −0.697436
290290 −0.660254 −0.0387715
291291 0 0
292292 9.73205 0.569525
293293 −14.5167 −0.848072 −0.424036 0.905645i 0.639387π-0.639387\pi
−0.424036 + 0.905645i 0.639387π0.639387\pi
294294 0 0
295295 2.14359 0.124805
296296 −10.4641 −0.608214
297297 0 0
298298 2.80385 0.162423
299299 0 0
300300 0 0
301301 −5.60770 −0.323222
302302 −3.26795 −0.188049
303303 0 0
304304 −1.26795 −0.0727219
305305 0.320508 0.0183522
306306 0 0
307307 −8.58846 −0.490169 −0.245085 0.969502i 0.578816π-0.578816\pi
−0.245085 + 0.969502i 0.578816π0.578816\pi
308308 −3.46410 −0.197386
309309 0 0
310310 1.46410 0.0831554
311311 −15.6603 −0.888012 −0.444006 0.896024i 0.646443π-0.646443\pi
−0.444006 + 0.896024i 0.646443π0.646443\pi
312312 0 0
313313 13.4641 0.761036 0.380518 0.924774i 0.375746π-0.375746\pi
0.380518 + 0.924774i 0.375746π0.375746\pi
314314 −23.5885 −1.33117
315315 0 0
316316 −9.46410 −0.532397
317317 3.33975 0.187579 0.0937894 0.995592i 0.470102π-0.470102\pi
0.0937894 + 0.995592i 0.470102π0.470102\pi
318318 0 0
319319 −11.6603 −0.652849
320320 0.267949 0.0149788
321321 0 0
322322 −4.53590 −0.252776
323323 −2.87564 −0.160005
324324 0 0
325325 0 0
326326 6.53590 0.361990
327327 0 0
328328 11.3923 0.629035
329329 6.00000 0.330791
330330 0 0
331331 −20.0000 −1.09930 −0.549650 0.835395i 0.685239π-0.685239\pi
−0.549650 + 0.835395i 0.685239π0.685239\pi
332332 10.1962 0.559587
333333 0 0
334334 −2.53590 −0.138758
335335 2.98076 0.162856
336336 0 0
337337 6.85641 0.373492 0.186746 0.982408i 0.440206π-0.440206\pi
0.186746 + 0.982408i 0.440206π0.440206\pi
338338 0 0
339339 0 0
340340 0.607695 0.0329569
341341 25.8564 1.40020
342342 0 0
343343 9.85641 0.532196
344344 7.66025 0.413013
345345 0 0
346346 16.3923 0.881256
347347 −8.87564 −0.476470 −0.238235 0.971208i 0.576569π-0.576569\pi
−0.238235 + 0.971208i 0.576569π0.576569\pi
348348 0 0
349349 19.3205 1.03420 0.517102 0.855924i 0.327011π-0.327011\pi
0.517102 + 0.855924i 0.327011π0.327011\pi
350350 3.60770 0.192839
351351 0 0
352352 4.73205 0.252219
353353 19.7846 1.05303 0.526514 0.850166i 0.323499π-0.323499\pi
0.526514 + 0.850166i 0.323499π0.323499\pi
354354 0 0
355355 0.339746 0.0180318
356356 −2.53590 −0.134402
357357 0 0
358358 −22.0526 −1.16551
359359 23.1244 1.22046 0.610228 0.792226i 0.291078π-0.291078\pi
0.610228 + 0.792226i 0.291078π0.291078\pi
360360 0 0
361361 −17.3923 −0.915384
362362 8.80385 0.462720
363363 0 0
364364 0 0
365365 2.60770 0.136493
366366 0 0
367367 −14.7321 −0.769007 −0.384503 0.923124i 0.625627π-0.625627\pi
−0.384503 + 0.923124i 0.625627π0.625627\pi
368368 6.19615 0.322997
369369 0 0
370370 −2.80385 −0.145765
371371 0.339746 0.0176387
372372 0 0
373373 −10.2679 −0.531654 −0.265827 0.964021i 0.585645π-0.585645\pi
−0.265827 + 0.964021i 0.585645π0.585645\pi
374374 10.7321 0.554941
375375 0 0
376376 −8.19615 −0.422684
377377 0 0
378378 0 0
379379 −1.46410 −0.0752058 −0.0376029 0.999293i 0.511972π-0.511972\pi
−0.0376029 + 0.999293i 0.511972π0.511972\pi
380380 −0.339746 −0.0174286
381381 0 0
382382 −6.92820 −0.354478
383383 5.46410 0.279203 0.139601 0.990208i 0.455418π-0.455418\pi
0.139601 + 0.990208i 0.455418π0.455418\pi
384384 0 0
385385 −0.928203 −0.0473056
386386 8.26795 0.420828
387387 0 0
388388 6.00000 0.304604
389389 29.7846 1.51014 0.755070 0.655644i 0.227603π-0.227603\pi
0.755070 + 0.655644i 0.227603π0.227603\pi
390390 0 0
391391 14.0526 0.710668
392392 −6.46410 −0.326486
393393 0 0
394394 9.85641 0.496559
395395 −2.53590 −0.127595
396396 0 0
397397 0.392305 0.0196892 0.00984461 0.999952i 0.496866π-0.496866\pi
0.00984461 + 0.999952i 0.496866π0.496866\pi
398398 −3.80385 −0.190670
399399 0 0
400400 −4.92820 −0.246410
401401 21.9282 1.09504 0.547521 0.836792i 0.315572π-0.315572\pi
0.547521 + 0.836792i 0.315572π0.315572\pi
402402 0 0
403403 0 0
404404 11.9282 0.593450
405405 0 0
406406 1.80385 0.0895235
407407 −49.5167 −2.45445
408408 0 0
409409 −14.2679 −0.705505 −0.352752 0.935717i 0.614754π-0.614754\pi
−0.352752 + 0.935717i 0.614754π0.614754\pi
410410 3.05256 0.150755
411411 0 0
412412 −18.7321 −0.922862
413413 −5.85641 −0.288175
414414 0 0
415415 2.73205 0.134111
416416 0 0
417417 0 0
418418 −6.00000 −0.293470
419419 10.5359 0.514712 0.257356 0.966317i 0.417149π-0.417149\pi
0.257356 + 0.966317i 0.417149π0.417149\pi
420420 0 0
421421 −32.7128 −1.59432 −0.797162 0.603765i 0.793667π-0.793667\pi
−0.797162 + 0.603765i 0.793667π0.793667\pi
422422 −4.39230 −0.213814
423423 0 0
424424 −0.464102 −0.0225388
425425 −11.1769 −0.542160
426426 0 0
427427 −0.875644 −0.0423754
428428 0.196152 0.00948139
429429 0 0
430430 2.05256 0.0989832
431431 −11.1244 −0.535841 −0.267921 0.963441i 0.586337π-0.586337\pi
−0.267921 + 0.963441i 0.586337π0.586337\pi
432432 0 0
433433 −14.8564 −0.713953 −0.356977 0.934113i 0.616192π-0.616192\pi
−0.356977 + 0.934113i 0.616192π0.616192\pi
434434 −4.00000 −0.192006
435435 0 0
436436 5.46410 0.261683
437437 −7.85641 −0.375823
438438 0 0
439439 −17.6603 −0.842878 −0.421439 0.906857i 0.638475π-0.638475\pi
−0.421439 + 0.906857i 0.638475π0.638475\pi
440440 1.26795 0.0604471
441441 0 0
442442 0 0
443443 −36.3923 −1.72905 −0.864525 0.502589i 0.832381π-0.832381\pi
−0.864525 + 0.502589i 0.832381π0.832381\pi
444444 0 0
445445 −0.679492 −0.0322110
446446 13.0718 0.618968
447447 0 0
448448 −0.732051 −0.0345861
449449 −23.3205 −1.10056 −0.550281 0.834979i 0.685480π-0.685480\pi
−0.550281 + 0.834979i 0.685480π0.685480\pi
450450 0 0
451451 53.9090 2.53847
452452 18.6603 0.877705
453453 0 0
454454 −1.80385 −0.0846588
455455 0 0
456456 0 0
457457 −18.6603 −0.872890 −0.436445 0.899731i 0.643763π-0.643763\pi
−0.436445 + 0.899731i 0.643763π0.643763\pi
458458 −15.8564 −0.740921
459459 0 0
460460 1.66025 0.0774097
461461 25.7321 1.19846 0.599231 0.800577i 0.295473π-0.295473\pi
0.599231 + 0.800577i 0.295473π0.295473\pi
462462 0 0
463463 28.0526 1.30371 0.651856 0.758342i 0.273990π-0.273990\pi
0.651856 + 0.758342i 0.273990π0.273990\pi
464464 −2.46410 −0.114393
465465 0 0
466466 −19.8564 −0.919830
467467 12.5885 0.582524 0.291262 0.956643i 0.405925π-0.405925\pi
0.291262 + 0.956643i 0.405925π0.405925\pi
468468 0 0
469469 −8.14359 −0.376036
470470 −2.19615 −0.101301
471471 0 0
472472 8.00000 0.368230
473473 36.2487 1.66672
474474 0 0
475475 6.24871 0.286711
476476 −1.66025 −0.0760976
477477 0 0
478478 −9.66025 −0.441850
479479 26.5359 1.21246 0.606228 0.795291i 0.292682π-0.292682\pi
0.606228 + 0.795291i 0.292682π0.292682\pi
480480 0 0
481481 0 0
482482 17.5885 0.801132
483483 0 0
484484 11.3923 0.517832
485485 1.60770 0.0730017
486486 0 0
487487 −21.1244 −0.957236 −0.478618 0.878023i 0.658862π-0.658862\pi
−0.478618 + 0.878023i 0.658862π0.658862\pi
488488 1.19615 0.0541473
489489 0 0
490490 −1.73205 −0.0782461
491491 −5.26795 −0.237739 −0.118870 0.992910i 0.537927π-0.537927\pi
−0.118870 + 0.992910i 0.537927π0.537927\pi
492492 0 0
493493 −5.58846 −0.251691
494494 0 0
495495 0 0
496496 5.46410 0.245345
497497 −0.928203 −0.0416356
498498 0 0
499499 −32.0000 −1.43252 −0.716258 0.697835i 0.754147π-0.754147\pi
−0.716258 + 0.697835i 0.754147π0.754147\pi
500500 −2.66025 −0.118970
501501 0 0
502502 −6.53590 −0.291711
503503 10.9808 0.489608 0.244804 0.969573i 0.421276π-0.421276\pi
0.244804 + 0.969573i 0.421276π0.421276\pi
504504 0 0
505505 3.19615 0.142227
506506 29.3205 1.30346
507507 0 0
508508 17.8564 0.792250
509509 10.2679 0.455119 0.227559 0.973764i 0.426925π-0.426925\pi
0.227559 + 0.973764i 0.426925π0.426925\pi
510510 0 0
511511 −7.12436 −0.315163
512512 1.00000 0.0441942
513513 0 0
514514 −26.6603 −1.17593
515515 −5.01924 −0.221174
516516 0 0
517517 −38.7846 −1.70575
518518 7.66025 0.336572
519519 0 0
520520 0 0
521521 17.4449 0.764273 0.382137 0.924106i 0.375188π-0.375188\pi
0.382137 + 0.924106i 0.375188π0.375188\pi
522522 0 0
523523 36.4449 1.59362 0.796811 0.604228i 0.206518π-0.206518\pi
0.796811 + 0.604228i 0.206518π0.206518\pi
524524 −13.4641 −0.588182
525525 0 0
526526 −28.0526 −1.22315
527527 12.3923 0.539817
528528 0 0
529529 15.3923 0.669231
530530 −0.124356 −0.00540166
531531 0 0
532532 0.928203 0.0402427
533533 0 0
534534 0 0
535535 0.0525589 0.00227232
536536 11.1244 0.480499
537537 0 0
538538 1.46410 0.0631219
539539 −30.5885 −1.31754
540540 0 0
541541 −40.3205 −1.73351 −0.866757 0.498731i 0.833800π-0.833800\pi
−0.866757 + 0.498731i 0.833800π0.833800\pi
542542 −5.85641 −0.251554
543543 0 0
544544 2.26795 0.0972375
545545 1.46410 0.0627152
546546 0 0
547547 6.19615 0.264928 0.132464 0.991188i 0.457711π-0.457711\pi
0.132464 + 0.991188i 0.457711π0.457711\pi
548548 −1.92820 −0.0823688
549549 0 0
550550 −23.3205 −0.994390
551551 3.12436 0.133102
552552 0 0
553553 6.92820 0.294617
554554 −2.26795 −0.0963559
555555 0 0
556556 −9.85641 −0.418005
557557 −30.3731 −1.28695 −0.643474 0.765468i 0.722508π-0.722508\pi
−0.643474 + 0.765468i 0.722508π0.722508\pi
558558 0 0
559559 0 0
560560 −0.196152 −0.00828895
561561 0 0
562562 −22.3205 −0.941534
563563 −21.0718 −0.888070 −0.444035 0.896009i 0.646453π-0.646453\pi
−0.444035 + 0.896009i 0.646453π0.646453\pi
564564 0 0
565565 5.00000 0.210352
566566 8.33975 0.350546
567567 0 0
568568 1.26795 0.0532020
569569 38.6410 1.61992 0.809958 0.586488i 0.199490π-0.199490\pi
0.809958 + 0.586488i 0.199490π0.199490\pi
570570 0 0
571571 −24.0526 −1.00657 −0.503284 0.864121i 0.667875π-0.667875\pi
−0.503284 + 0.864121i 0.667875π0.667875\pi
572572 0 0
573573 0 0
574574 −8.33975 −0.348094
575575 −30.5359 −1.27343
576576 0 0
577577 −0.267949 −0.0111549 −0.00557744 0.999984i 0.501775π-0.501775\pi
−0.00557744 + 0.999984i 0.501775π0.501775\pi
578578 −11.8564 −0.493161
579579 0 0
580580 −0.660254 −0.0274156
581581 −7.46410 −0.309663
582582 0 0
583583 −2.19615 −0.0909553
584584 9.73205 0.402715
585585 0 0
586586 −14.5167 −0.599678
587587 16.0000 0.660391 0.330195 0.943913i 0.392885π-0.392885\pi
0.330195 + 0.943913i 0.392885π0.392885\pi
588588 0 0
589589 −6.92820 −0.285472
590590 2.14359 0.0882503
591591 0 0
592592 −10.4641 −0.430072
593593 −36.8564 −1.51351 −0.756756 0.653698i 0.773217π-0.773217\pi
−0.756756 + 0.653698i 0.773217π0.773217\pi
594594 0 0
595595 −0.444864 −0.0182376
596596 2.80385 0.114850
597597 0 0
598598 0 0
599599 9.46410 0.386693 0.193346 0.981131i 0.438066π-0.438066\pi
0.193346 + 0.981131i 0.438066π0.438066\pi
600600 0 0
601601 −5.92820 −0.241816 −0.120908 0.992664i 0.538581π-0.538581\pi
−0.120908 + 0.992664i 0.538581π0.538581\pi
602602 −5.60770 −0.228553
603603 0 0
604604 −3.26795 −0.132971
605605 3.05256 0.124104
606606 0 0
607607 0.784610 0.0318463 0.0159232 0.999873i 0.494931π-0.494931\pi
0.0159232 + 0.999873i 0.494931π0.494931\pi
608608 −1.26795 −0.0514221
609609 0 0
610610 0.320508 0.0129770
611611 0 0
612612 0 0
613613 −11.3923 −0.460131 −0.230065 0.973175i 0.573894π-0.573894\pi
−0.230065 + 0.973175i 0.573894π0.573894\pi
614614 −8.58846 −0.346602
615615 0 0
616616 −3.46410 −0.139573
617617 35.2487 1.41906 0.709530 0.704675i 0.248907π-0.248907\pi
0.709530 + 0.704675i 0.248907π0.248907\pi
618618 0 0
619619 −10.5359 −0.423474 −0.211737 0.977327i 0.567912π-0.567912\pi
−0.211737 + 0.977327i 0.567912π0.567912\pi
620620 1.46410 0.0587997
621621 0 0
622622 −15.6603 −0.627919
623623 1.85641 0.0743754
624624 0 0
625625 23.9282 0.957128
626626 13.4641 0.538134
627627 0 0
628628 −23.5885 −0.941282
629629 −23.7321 −0.946259
630630 0 0
631631 −47.7128 −1.89942 −0.949709 0.313135i 0.898621π-0.898621\pi
−0.949709 + 0.313135i 0.898621π0.898621\pi
632632 −9.46410 −0.376462
633633 0 0
634634 3.33975 0.132638
635635 4.78461 0.189871
636636 0 0
637637 0 0
638638 −11.6603 −0.461634
639639 0 0
640640 0.267949 0.0105916
641641 −25.9808 −1.02618 −0.513089 0.858335i 0.671499π-0.671499\pi
−0.513089 + 0.858335i 0.671499π0.671499\pi
642642 0 0
643643 −13.8564 −0.546443 −0.273222 0.961951i 0.588089π-0.588089\pi
−0.273222 + 0.961951i 0.588089π0.588089\pi
644644 −4.53590 −0.178739
645645 0 0
646646 −2.87564 −0.113141
647647 −26.2487 −1.03194 −0.515972 0.856606i 0.672569π-0.672569\pi
−0.515972 + 0.856606i 0.672569π0.672569\pi
648648 0 0
649649 37.8564 1.48599
650650 0 0
651651 0 0
652652 6.53590 0.255966
653653 10.5359 0.412302 0.206151 0.978520i 0.433906π-0.433906\pi
0.206151 + 0.978520i 0.433906π0.433906\pi
654654 0 0
655655 −3.60770 −0.140964
656656 11.3923 0.444795
657657 0 0
658658 6.00000 0.233904
659659 −38.2487 −1.48996 −0.744979 0.667088i 0.767541π-0.767541\pi
−0.744979 + 0.667088i 0.767541π0.767541\pi
660660 0 0
661661 9.39230 0.365318 0.182659 0.983176i 0.441530π-0.441530\pi
0.182659 + 0.983176i 0.441530π0.441530\pi
662662 −20.0000 −0.777322
663663 0 0
664664 10.1962 0.395687
665665 0.248711 0.00964461
666666 0 0
667667 −15.2679 −0.591177
668668 −2.53590 −0.0981169
669669 0 0
670670 2.98076 0.115157
671671 5.66025 0.218512
672672 0 0
673673 14.0718 0.542428 0.271214 0.962519i 0.412575π-0.412575\pi
0.271214 + 0.962519i 0.412575π0.412575\pi
674674 6.85641 0.264099
675675 0 0
676676 0 0
677677 38.5359 1.48105 0.740527 0.672026i 0.234576π-0.234576\pi
0.740527 + 0.672026i 0.234576π0.234576\pi
678678 0 0
679679 −4.39230 −0.168561
680680 0.607695 0.0233040
681681 0 0
682682 25.8564 0.990093
683683 −37.8564 −1.44854 −0.724268 0.689519i 0.757822π-0.757822\pi
−0.724268 + 0.689519i 0.757822π0.757822\pi
684684 0 0
685685 −0.516660 −0.0197406
686686 9.85641 0.376319
687687 0 0
688688 7.66025 0.292044
689689 0 0
690690 0 0
691691 −26.3397 −1.00201 −0.501006 0.865444i 0.667036π-0.667036\pi
−0.501006 + 0.865444i 0.667036π0.667036\pi
692692 16.3923 0.623142
693693 0 0
694694 −8.87564 −0.336915
695695 −2.64102 −0.100179
696696 0 0
697697 25.8372 0.978653
698698 19.3205 0.731292
699699 0 0
700700 3.60770 0.136358
701701 −31.3205 −1.18296 −0.591480 0.806320i 0.701456π-0.701456\pi
−0.591480 + 0.806320i 0.701456π0.701456\pi
702702 0 0
703703 13.2679 0.500410
704704 4.73205 0.178346
705705 0 0
706706 19.7846 0.744604
707707 −8.73205 −0.328403
708708 0 0
709709 −40.8564 −1.53439 −0.767197 0.641411i 0.778349π-0.778349\pi
−0.767197 + 0.641411i 0.778349π0.778349\pi
710710 0.339746 0.0127504
711711 0 0
712712 −2.53590 −0.0950368
713713 33.8564 1.26793
714714 0 0
715715 0 0
716716 −22.0526 −0.824143
717717 0 0
718718 23.1244 0.862993
719719 22.5359 0.840447 0.420224 0.907421i 0.361952π-0.361952\pi
0.420224 + 0.907421i 0.361952π0.361952\pi
720720 0 0
721721 13.7128 0.510692
722722 −17.3923 −0.647275
723723 0 0
724724 8.80385 0.327192
725725 12.1436 0.451002
726726 0 0
727727 20.9808 0.778133 0.389067 0.921210i 0.372798π-0.372798\pi
0.389067 + 0.921210i 0.372798π0.372798\pi
728728 0 0
729729 0 0
730730 2.60770 0.0965151
731731 17.3731 0.642566
732732 0 0
733733 −19.0000 −0.701781 −0.350891 0.936416i 0.614121π-0.614121\pi
−0.350891 + 0.936416i 0.614121π0.614121\pi
734734 −14.7321 −0.543770
735735 0 0
736736 6.19615 0.228393
737737 52.6410 1.93906
738738 0 0
739739 10.9282 0.402000 0.201000 0.979591i 0.435581π-0.435581\pi
0.201000 + 0.979591i 0.435581π0.435581\pi
740740 −2.80385 −0.103071
741741 0 0
742742 0.339746 0.0124725
743743 −27.6077 −1.01283 −0.506414 0.862290i 0.669029π-0.669029\pi
−0.506414 + 0.862290i 0.669029π0.669029\pi
744744 0 0
745745 0.751289 0.0275251
746746 −10.2679 −0.375936
747747 0 0
748748 10.7321 0.392403
749749 −0.143594 −0.00524679
750750 0 0
751751 15.9090 0.580526 0.290263 0.956947i 0.406257π-0.406257\pi
0.290263 + 0.956947i 0.406257π0.406257\pi
752752 −8.19615 −0.298883
753753 0 0
754754 0 0
755755 −0.875644 −0.0318680
756756 0 0
757757 7.07180 0.257029 0.128514 0.991708i 0.458979π-0.458979\pi
0.128514 + 0.991708i 0.458979π0.458979\pi
758758 −1.46410 −0.0531786
759759 0 0
760760 −0.339746 −0.0123239
761761 −23.3205 −0.845368 −0.422684 0.906277i 0.638912π-0.638912\pi
−0.422684 + 0.906277i 0.638912π0.638912\pi
762762 0 0
763763 −4.00000 −0.144810
764764 −6.92820 −0.250654
765765 0 0
766766 5.46410 0.197426
767767 0 0
768768 0 0
769769 16.1436 0.582153 0.291076 0.956700i 0.405987π-0.405987\pi
0.291076 + 0.956700i 0.405987π0.405987\pi
770770 −0.928203 −0.0334501
771771 0 0
772772 8.26795 0.297570
773773 −35.0718 −1.26144 −0.630722 0.776009i 0.717241π-0.717241\pi
−0.630722 + 0.776009i 0.717241π0.717241\pi
774774 0 0
775775 −26.9282 −0.967290
776776 6.00000 0.215387
777777 0 0
778778 29.7846 1.06783
779779 −14.4449 −0.517541
780780 0 0
781781 6.00000 0.214697
782782 14.0526 0.502518
783783 0 0
784784 −6.46410 −0.230861
785785 −6.32051 −0.225589
786786 0 0
787787 −39.3205 −1.40162 −0.700812 0.713346i 0.747179π-0.747179\pi
−0.700812 + 0.713346i 0.747179π0.747179\pi
788788 9.85641 0.351120
789789 0 0
790790 −2.53590 −0.0902232
791791 −13.6603 −0.485703
792792 0 0
793793 0 0
794794 0.392305 0.0139224
795795 0 0
796796 −3.80385 −0.134824
797797 34.0000 1.20434 0.602171 0.798367i 0.294303π-0.294303\pi
0.602171 + 0.798367i 0.294303π0.294303\pi
798798 0 0
799799 −18.5885 −0.657612
800800 −4.92820 −0.174238
801801 0 0
802802 21.9282 0.774312
803803 46.0526 1.62516
804804 0 0
805805 −1.21539 −0.0428369
806806 0 0
807807 0 0
808808 11.9282 0.419633
809809 22.4115 0.787948 0.393974 0.919122i 0.371100π-0.371100\pi
0.393974 + 0.919122i 0.371100π0.371100\pi
810810 0 0
811811 45.1769 1.58638 0.793188 0.608977i 0.208420π-0.208420\pi
0.793188 + 0.608977i 0.208420π0.208420\pi
812812 1.80385 0.0633026
813813 0 0
814814 −49.5167 −1.73556
815815 1.75129 0.0613450
816816 0 0
817817 −9.71281 −0.339808
818818 −14.2679 −0.498867
819819 0 0
820820 3.05256 0.106600
821821 12.9282 0.451197 0.225599 0.974220i 0.427566π-0.427566\pi
0.225599 + 0.974220i 0.427566π0.427566\pi
822822 0 0
823823 −41.5692 −1.44901 −0.724506 0.689269i 0.757932π-0.757932\pi
−0.724506 + 0.689269i 0.757932π0.757932\pi
824824 −18.7321 −0.652562
825825 0 0
826826 −5.85641 −0.203770
827827 33.4641 1.16366 0.581830 0.813310i 0.302337π-0.302337\pi
0.581830 + 0.813310i 0.302337π0.302337\pi
828828 0 0
829829 12.1244 0.421096 0.210548 0.977583i 0.432475π-0.432475\pi
0.210548 + 0.977583i 0.432475π0.432475\pi
830830 2.73205 0.0948309
831831 0 0
832832 0 0
833833 −14.6603 −0.507948
834834 0 0
835835 −0.679492 −0.0235148
836836 −6.00000 −0.207514
837837 0 0
838838 10.5359 0.363957
839839 14.1436 0.488291 0.244146 0.969739i 0.421493π-0.421493\pi
0.244146 + 0.969739i 0.421493π0.421493\pi
840840 0 0
841841 −22.9282 −0.790628
842842 −32.7128 −1.12736
843843 0 0
844844 −4.39230 −0.151189
845845 0 0
846846 0 0
847847 −8.33975 −0.286557
848848 −0.464102 −0.0159373
849849 0 0
850850 −11.1769 −0.383365
851851 −64.8372 −2.22259
852852 0 0
853853 −8.17691 −0.279972 −0.139986 0.990153i 0.544706π-0.544706\pi
−0.139986 + 0.990153i 0.544706π0.544706\pi
854854 −0.875644 −0.0299639
855855 0 0
856856 0.196152 0.00670435
857857 19.4449 0.664224 0.332112 0.943240i 0.392239π-0.392239\pi
0.332112 + 0.943240i 0.392239π0.392239\pi
858858 0 0
859859 −22.8756 −0.780507 −0.390253 0.920707i 0.627613π-0.627613\pi
−0.390253 + 0.920707i 0.627613π0.627613\pi
860860 2.05256 0.0699917
861861 0 0
862862 −11.1244 −0.378897
863863 7.12436 0.242516 0.121258 0.992621i 0.461307π-0.461307\pi
0.121258 + 0.992621i 0.461307π0.461307\pi
864864 0 0
865865 4.39230 0.149343
866866 −14.8564 −0.504841
867867 0 0
868868 −4.00000 −0.135769
869869 −44.7846 −1.51921
870870 0 0
871871 0 0
872872 5.46410 0.185038
873873 0 0
874874 −7.85641 −0.265747
875875 1.94744 0.0658355
876876 0 0
877877 −10.0718 −0.340100 −0.170050 0.985435i 0.554393π-0.554393\pi
−0.170050 + 0.985435i 0.554393π0.554393\pi
878878 −17.6603 −0.596005
879879 0 0
880880 1.26795 0.0427426
881881 −51.8372 −1.74644 −0.873219 0.487327i 0.837972π-0.837972\pi
−0.873219 + 0.487327i 0.837972π0.837972\pi
882882 0 0
883883 29.0718 0.978344 0.489172 0.872187i 0.337299π-0.337299\pi
0.489172 + 0.872187i 0.337299π0.337299\pi
884884 0 0
885885 0 0
886886 −36.3923 −1.22262
887887 −10.1436 −0.340589 −0.170294 0.985393i 0.554472π-0.554472\pi
−0.170294 + 0.985393i 0.554472π0.554472\pi
888888 0 0
889889 −13.0718 −0.438414
890890 −0.679492 −0.0227766
891891 0 0
892892 13.0718 0.437676
893893 10.3923 0.347765
894894 0 0
895895 −5.90897 −0.197515
896896 −0.732051 −0.0244561
897897 0 0
898898 −23.3205 −0.778215
899899 −13.4641 −0.449053
900900 0 0
901901 −1.05256 −0.0350658
902902 53.9090 1.79497
903903 0 0
904904 18.6603 0.620631
905905 2.35898 0.0784153
906906 0 0
907907 15.6077 0.518245 0.259123 0.965844i 0.416567π-0.416567\pi
0.259123 + 0.965844i 0.416567π0.416567\pi
908908 −1.80385 −0.0598628
909909 0 0
910910 0 0
911911 9.46410 0.313560 0.156780 0.987634i 0.449889π-0.449889\pi
0.156780 + 0.987634i 0.449889π0.449889\pi
912912 0 0
913913 48.2487 1.59680
914914 −18.6603 −0.617226
915915 0 0
916916 −15.8564 −0.523910
917917 9.85641 0.325487
918918 0 0
919919 −57.9615 −1.91197 −0.955987 0.293409i 0.905210π-0.905210\pi
−0.955987 + 0.293409i 0.905210π0.905210\pi
920920 1.66025 0.0547370
921921 0 0
922922 25.7321 0.847440
923923 0 0
924924 0 0
925925 51.5692 1.69559
926926 28.0526 0.921864
927927 0 0
928928 −2.46410 −0.0808881
929929 9.24871 0.303440 0.151720 0.988423i 0.451519π-0.451519\pi
0.151720 + 0.988423i 0.451519π0.451519\pi
930930 0 0
931931 8.19615 0.268618
932932 −19.8564 −0.650418
933933 0 0
934934 12.5885 0.411907
935935 2.87564 0.0940436
936936 0 0
937937 43.2487 1.41287 0.706437 0.707776i 0.250301π-0.250301\pi
0.706437 + 0.707776i 0.250301π0.250301\pi
938938 −8.14359 −0.265898
939939 0 0
940940 −2.19615 −0.0716306
941941 −56.6410 −1.84644 −0.923222 0.384267i 0.874454π-0.874454\pi
−0.923222 + 0.384267i 0.874454π0.874454\pi
942942 0 0
943943 70.5885 2.29868
944944 8.00000 0.260378
945945 0 0
946946 36.2487 1.17855
947947 34.9282 1.13501 0.567507 0.823369i 0.307908π-0.307908\pi
0.567507 + 0.823369i 0.307908π0.307908\pi
948948 0 0
949949 0 0
950950 6.24871 0.202735
951951 0 0
952952 −1.66025 −0.0538091
953953 41.5692 1.34656 0.673280 0.739388i 0.264885π-0.264885\pi
0.673280 + 0.739388i 0.264885π0.264885\pi
954954 0 0
955955 −1.85641 −0.0600719
956956 −9.66025 −0.312435
957957 0 0
958958 26.5359 0.857336
959959 1.41154 0.0455811
960960 0 0
961961 −1.14359 −0.0368901
962962 0 0
963963 0 0
964964 17.5885 0.566486
965965 2.21539 0.0713159
966966 0 0
967967 18.8756 0.607000 0.303500 0.952831i 0.401845π-0.401845\pi
0.303500 + 0.952831i 0.401845π0.401845\pi
968968 11.3923 0.366163
969969 0 0
970970 1.60770 0.0516200
971971 18.2487 0.585629 0.292815 0.956169i 0.405408π-0.405408\pi
0.292815 + 0.956169i 0.405408π0.405408\pi
972972 0 0
973973 7.21539 0.231315
974974 −21.1244 −0.676868
975975 0 0
976976 1.19615 0.0382879
977977 32.0718 1.02607 0.513034 0.858368i 0.328522π-0.328522\pi
0.513034 + 0.858368i 0.328522π0.328522\pi
978978 0 0
979979 −12.0000 −0.383522
980980 −1.73205 −0.0553283
981981 0 0
982982 −5.26795 −0.168107
983983 −20.7846 −0.662926 −0.331463 0.943468i 0.607542π-0.607542\pi
−0.331463 + 0.943468i 0.607542π0.607542\pi
984984 0 0
985985 2.64102 0.0841498
986986 −5.58846 −0.177973
987987 0 0
988988 0 0
989989 47.4641 1.50927
990990 0 0
991991 −8.58846 −0.272821 −0.136411 0.990652i 0.543557π-0.543557\pi
−0.136411 + 0.990652i 0.543557π0.543557\pi
992992 5.46410 0.173485
993993 0 0
994994 −0.928203 −0.0294408
995995 −1.01924 −0.0323120
996996 0 0
997997 38.6603 1.22438 0.612191 0.790710i 0.290288π-0.290288\pi
0.612191 + 0.790710i 0.290288π0.290288\pi
998998 −32.0000 −1.01294
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 3042.2.a.y.1.1 2
3.2 odd 2 1014.2.a.i.1.2 2
12.11 even 2 8112.2.a.bj.1.2 2
13.5 odd 4 3042.2.b.i.1351.2 4
13.6 odd 12 234.2.l.c.127.1 4
13.8 odd 4 3042.2.b.i.1351.3 4
13.11 odd 12 234.2.l.c.199.1 4
13.12 even 2 3042.2.a.p.1.2 2
39.2 even 12 1014.2.i.a.823.1 4
39.5 even 4 1014.2.b.e.337.3 4
39.8 even 4 1014.2.b.e.337.2 4
39.11 even 12 78.2.i.a.43.2 4
39.17 odd 6 1014.2.e.g.991.1 4
39.20 even 12 1014.2.i.a.361.1 4
39.23 odd 6 1014.2.e.g.529.1 4
39.29 odd 6 1014.2.e.i.529.2 4
39.32 even 12 78.2.i.a.49.2 yes 4
39.35 odd 6 1014.2.e.i.991.2 4
39.38 odd 2 1014.2.a.k.1.1 2
52.11 even 12 1872.2.by.h.433.2 4
52.19 even 12 1872.2.by.h.1297.1 4
156.11 odd 12 624.2.bv.e.433.1 4
156.71 odd 12 624.2.bv.e.49.2 4
156.155 even 2 8112.2.a.bp.1.1 2
195.32 odd 12 1950.2.y.g.49.1 4
195.89 even 12 1950.2.bc.d.901.1 4
195.128 odd 12 1950.2.y.g.199.1 4
195.149 even 12 1950.2.bc.d.751.1 4
195.167 odd 12 1950.2.y.b.199.2 4
195.188 odd 12 1950.2.y.b.49.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
78.2.i.a.43.2 4 39.11 even 12
78.2.i.a.49.2 yes 4 39.32 even 12
234.2.l.c.127.1 4 13.6 odd 12
234.2.l.c.199.1 4 13.11 odd 12
624.2.bv.e.49.2 4 156.71 odd 12
624.2.bv.e.433.1 4 156.11 odd 12
1014.2.a.i.1.2 2 3.2 odd 2
1014.2.a.k.1.1 2 39.38 odd 2
1014.2.b.e.337.2 4 39.8 even 4
1014.2.b.e.337.3 4 39.5 even 4
1014.2.e.g.529.1 4 39.23 odd 6
1014.2.e.g.991.1 4 39.17 odd 6
1014.2.e.i.529.2 4 39.29 odd 6
1014.2.e.i.991.2 4 39.35 odd 6
1014.2.i.a.361.1 4 39.20 even 12
1014.2.i.a.823.1 4 39.2 even 12
1872.2.by.h.433.2 4 52.11 even 12
1872.2.by.h.1297.1 4 52.19 even 12
1950.2.y.b.49.2 4 195.188 odd 12
1950.2.y.b.199.2 4 195.167 odd 12
1950.2.y.g.49.1 4 195.32 odd 12
1950.2.y.g.199.1 4 195.128 odd 12
1950.2.bc.d.751.1 4 195.149 even 12
1950.2.bc.d.901.1 4 195.89 even 12
3042.2.a.p.1.2 2 13.12 even 2
3042.2.a.y.1.1 2 1.1 even 1 trivial
3042.2.b.i.1351.2 4 13.5 odd 4
3042.2.b.i.1351.3 4 13.8 odd 4
8112.2.a.bj.1.2 2 12.11 even 2
8112.2.a.bp.1.1 2 156.155 even 2