Properties

Label 1200.3.bg.k.1057.1
Level 12001200
Weight 33
Character 1200.1057
Analytic conductor 32.69832.698
Analytic rank 00
Dimension 44
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] = [1200,3,Mod(193,1200)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1200, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 0, 0, 3])) 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("1200.193"); S:= CuspForms(chi, 3); N := Newforms(S);
 
Level: N N == 1200=24352 1200 = 2^{4} \cdot 3 \cdot 5^{2}
Weight: k k == 3 3
Character orbit: [χ][\chi] == 1200.bg (of order 44, degree 22, not minimal)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [4,0,0,0,0,0,4,0,0,0,-16,0,32,0,0,0,40,0,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(21)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 32.697631723232.6976317232
Analytic rank: 00
Dimension: 44
Relative dimension: 22 over Q(i)\Q(i)
Coefficient field: Q(i,6)\Q(i, \sqrt{6})
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: x4+9 x^{4} + 9 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 15)
Sato-Tate group: SU(2)[C4]\mathrm{SU}(2)[C_{4}]

Embedding invariants

Embedding label 1057.1
Root 1.22474+1.22474i1.22474 + 1.22474i of defining polynomial
Character χ\chi == 1200.1057
Dual form 1200.3.bg.k.193.1

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+(1.22474+1.22474i)q3+(3.44949+3.44949i)q73.00000iq911.3485q11+(5.550515.55051i)q13+(17.3485+17.3485i)q178.69694iq198.44949q21+(11.550511.5505i)q23+(3.67423+3.67423i)q27+35.1464iq2910.6969q31+(13.899013.8990i)q33+(6.04541+6.04541i)q37+13.5959iq39+0.696938q41+(26.4949+26.4949i)q43+(44.2474+44.2474i)q4725.2020iq4942.4949q51+(0.6969380.696938i)q53+(10.6515+10.6515i)q57+39.9342iq59+5.90918q61+(10.348510.3485i)q63+(45.101045.1010i)q67+28.2929iq69+68.0000q71+(77.7878+77.7878i)q73+(39.146439.1464i)q77+24.4949iq799.00000q81+(13.146413.1464i)q83+(43.045443.0454i)q87+82.1816iq89+38.2929q91+(13.101013.1010i)q93+(24.5959+24.5959i)q97+34.0454iq99+O(q100)q+(-1.22474 + 1.22474i) q^{3} +(3.44949 + 3.44949i) q^{7} -3.00000i q^{9} -11.3485 q^{11} +(5.55051 - 5.55051i) q^{13} +(17.3485 + 17.3485i) q^{17} -8.69694i q^{19} -8.44949 q^{21} +(11.5505 - 11.5505i) q^{23} +(3.67423 + 3.67423i) q^{27} +35.1464i q^{29} -10.6969 q^{31} +(13.8990 - 13.8990i) q^{33} +(6.04541 + 6.04541i) q^{37} +13.5959i q^{39} +0.696938 q^{41} +(-26.4949 + 26.4949i) q^{43} +(44.2474 + 44.2474i) q^{47} -25.2020i q^{49} -42.4949 q^{51} +(0.696938 - 0.696938i) q^{53} +(10.6515 + 10.6515i) q^{57} +39.9342i q^{59} +5.90918 q^{61} +(10.3485 - 10.3485i) q^{63} +(-45.1010 - 45.1010i) q^{67} +28.2929i q^{69} +68.0000 q^{71} +(-77.7878 + 77.7878i) q^{73} +(-39.1464 - 39.1464i) q^{77} +24.4949i q^{79} -9.00000 q^{81} +(13.1464 - 13.1464i) q^{83} +(-43.0454 - 43.0454i) q^{87} +82.1816i q^{89} +38.2929 q^{91} +(13.1010 - 13.1010i) q^{93} +(24.5959 + 24.5959i) q^{97} +34.0454i q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 4q+4q716q11+32q13+40q1724q21+56q23+16q31+36q3364q3756q418q43+128q4772q5156q53+72q57+200q61+12q63++20q97+O(q100) 4 q + 4 q^{7} - 16 q^{11} + 32 q^{13} + 40 q^{17} - 24 q^{21} + 56 q^{23} + 16 q^{31} + 36 q^{33} - 64 q^{37} - 56 q^{41} - 8 q^{43} + 128 q^{47} - 72 q^{51} - 56 q^{53} + 72 q^{57} + 200 q^{61} + 12 q^{63}+ \cdots + 20 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1200Z)×\left(\mathbb{Z}/1200\mathbb{Z}\right)^\times.

nn 401401 577577 751751 901901
χ(n)\chi(n) 11 e(14)e\left(\frac{1}{4}\right) 11 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 −1.22474 + 1.22474i −0.408248 + 0.408248i
44 0 0
55 0 0
66 0 0
77 3.44949 + 3.44949i 0.492784 + 0.492784i 0.909182 0.416398i 0.136708π-0.136708\pi
−0.416398 + 0.909182i 0.636708π0.636708\pi
88 0 0
99 3.00000i 0.333333i
1010 0 0
1111 −11.3485 −1.03168 −0.515840 0.856685i 0.672520π-0.672520\pi
−0.515840 + 0.856685i 0.672520π0.672520\pi
1212 0 0
1313 5.55051 5.55051i 0.426962 0.426962i −0.460630 0.887592i 0.652376π-0.652376\pi
0.887592 + 0.460630i 0.152376π0.152376\pi
1414 0 0
1515 0 0
1616 0 0
1717 17.3485 + 17.3485i 1.02050 + 1.02050i 0.999785 + 0.0207127i 0.00659354π0.00659354\pi
0.0207127 + 0.999785i 0.493406π0.493406\pi
1818 0 0
1919 8.69694i 0.457734i −0.973458 0.228867i 0.926498π-0.926498\pi
0.973458 0.228867i 0.0735020π-0.0735020\pi
2020 0 0
2121 −8.44949 −0.402357
2222 0 0
2323 11.5505 11.5505i 0.502196 0.502196i −0.409924 0.912120i 0.634445π-0.634445\pi
0.912120 + 0.409924i 0.134445π0.134445\pi
2424 0 0
2525 0 0
2626 0 0
2727 3.67423 + 3.67423i 0.136083 + 0.136083i
2828 0 0
2929 35.1464i 1.21195i 0.795485 + 0.605973i 0.207216π0.207216\pi
−0.795485 + 0.605973i 0.792784π0.792784\pi
3030 0 0
3131 −10.6969 −0.345063 −0.172531 0.985004i 0.555195π-0.555195\pi
−0.172531 + 0.985004i 0.555195π0.555195\pi
3232 0 0
3333 13.8990 13.8990i 0.421181 0.421181i
3434 0 0
3535 0 0
3636 0 0
3737 6.04541 + 6.04541i 0.163389 + 0.163389i 0.784066 0.620677i 0.213142π-0.213142\pi
−0.620677 + 0.784066i 0.713142π0.713142\pi
3838 0 0
3939 13.5959i 0.348613i
4040 0 0
4141 0.696938 0.0169985 0.00849925 0.999964i 0.497295π-0.497295\pi
0.00849925 + 0.999964i 0.497295π0.497295\pi
4242 0 0
4343 −26.4949 + 26.4949i −0.616160 + 0.616160i −0.944544 0.328384i 0.893496π-0.893496\pi
0.328384 + 0.944544i 0.393496π0.393496\pi
4444 0 0
4545 0 0
4646 0 0
4747 44.2474 + 44.2474i 0.941435 + 0.941435i 0.998377 0.0569424i 0.0181351π-0.0181351\pi
−0.0569424 + 0.998377i 0.518135π0.518135\pi
4848 0 0
4949 25.2020i 0.514327i
5050 0 0
5151 −42.4949 −0.833233
5252 0 0
5353 0.696938 0.696938i 0.0131498 0.0131498i −0.700501 0.713651i 0.747040π-0.747040\pi
0.713651 + 0.700501i 0.247040π0.247040\pi
5454 0 0
5555 0 0
5656 0 0
5757 10.6515 + 10.6515i 0.186869 + 0.186869i
5858 0 0
5959 39.9342i 0.676851i 0.940993 + 0.338425i 0.109894π0.109894\pi
−0.940993 + 0.338425i 0.890106π0.890106\pi
6060 0 0
6161 5.90918 0.0968719 0.0484359 0.998826i 0.484576π-0.484576\pi
0.0484359 + 0.998826i 0.484576π0.484576\pi
6262 0 0
6363 10.3485 10.3485i 0.164261 0.164261i
6464 0 0
6565 0 0
6666 0 0
6767 −45.1010 45.1010i −0.673150 0.673150i 0.285291 0.958441i 0.407910π-0.407910\pi
−0.958441 + 0.285291i 0.907910π0.907910\pi
6868 0 0
6969 28.2929i 0.410041i
7070 0 0
7171 68.0000 0.957746 0.478873 0.877884i 0.341045π-0.341045\pi
0.478873 + 0.877884i 0.341045π0.341045\pi
7272 0 0
7373 −77.7878 + 77.7878i −1.06559 + 1.06559i −0.0678931 + 0.997693i 0.521628π0.521628\pi
−0.997693 + 0.0678931i 0.978372π0.978372\pi
7474 0 0
7575 0 0
7676 0 0
7777 −39.1464 39.1464i −0.508395 0.508395i
7878 0 0
7979 24.4949i 0.310062i 0.987910 + 0.155031i 0.0495477π0.0495477\pi
−0.987910 + 0.155031i 0.950452π0.950452\pi
8080 0 0
8181 −9.00000 −0.111111
8282 0 0
8383 13.1464 13.1464i 0.158391 0.158391i −0.623463 0.781853i 0.714275π-0.714275\pi
0.781853 + 0.623463i 0.214275π0.214275\pi
8484 0 0
8585 0 0
8686 0 0
8787 −43.0454 43.0454i −0.494775 0.494775i
8888 0 0
8989 82.1816i 0.923389i 0.887039 + 0.461695i 0.152758π0.152758\pi
−0.887039 + 0.461695i 0.847242π0.847242\pi
9090 0 0
9191 38.2929 0.420801
9292 0 0
9393 13.1010 13.1010i 0.140871 0.140871i
9494 0 0
9595 0 0
9696 0 0
9797 24.5959 + 24.5959i 0.253566 + 0.253566i 0.822431 0.568865i 0.192617π-0.192617\pi
−0.568865 + 0.822431i 0.692617π0.692617\pi
9898 0 0
9999 34.0454i 0.343893i
100100 0 0
101101 −105.621 −1.04575 −0.522876 0.852409i 0.675141π-0.675141\pi
−0.522876 + 0.852409i 0.675141π0.675141\pi
102102 0 0
103103 −89.2474 + 89.2474i −0.866480 + 0.866480i −0.992081 0.125601i 0.959914π-0.959914\pi
0.125601 + 0.992081i 0.459914π0.459914\pi
104104 0 0
105105 0 0
106106 0 0
107107 68.7423 + 68.7423i 0.642452 + 0.642452i 0.951158 0.308706i 0.0998958π-0.0998958\pi
−0.308706 + 0.951158i 0.599896π0.599896\pi
108108 0 0
109109 68.6969i 0.630247i 0.949051 + 0.315124i 0.102046π0.102046\pi
−0.949051 + 0.315124i 0.897954π0.897954\pi
110110 0 0
111111 −14.8082 −0.133407
112112 0 0
113113 −97.6413 + 97.6413i −0.864083 + 0.864083i −0.991809 0.127727i 0.959232π-0.959232\pi
0.127727 + 0.991809i 0.459232π0.459232\pi
114114 0 0
115115 0 0
116116 0 0
117117 −16.6515 16.6515i −0.142321 0.142321i
118118 0 0
119119 119.687i 1.00577i
120120 0 0
121121 7.78775 0.0643616
122122 0 0
123123 −0.853572 + 0.853572i −0.00693961 + 0.00693961i
124124 0 0
125125 0 0
126126 0 0
127127 164.621 + 164.621i 1.29623 + 1.29623i 0.930865 + 0.365362i 0.119055π0.119055\pi
0.365362 + 0.930865i 0.380945π0.380945\pi
128128 0 0
129129 64.8990i 0.503093i
130130 0 0
131131 −106.136 −0.810200 −0.405100 0.914272i 0.632763π-0.632763\pi
−0.405100 + 0.914272i 0.632763π0.632763\pi
132132 0 0
133133 30.0000 30.0000i 0.225564 0.225564i
134134 0 0
135135 0 0
136136 0 0
137137 166.631 + 166.631i 1.21629 + 1.21629i 0.968923 + 0.247363i 0.0795639π0.0795639\pi
0.247363 + 0.968923i 0.420436π0.420436\pi
138138 0 0
139139 191.171i 1.37533i 0.726026 + 0.687667i 0.241365π0.241365\pi
−0.726026 + 0.687667i 0.758635π0.758635\pi
140140 0 0
141141 −108.384 −0.768679
142142 0 0
143143 −62.9898 + 62.9898i −0.440488 + 0.440488i
144144 0 0
145145 0 0
146146 0 0
147147 30.8661 + 30.8661i 0.209973 + 0.209973i
148148 0 0
149149 84.8536i 0.569487i 0.958604 + 0.284744i 0.0919084π0.0919084\pi
−0.958604 + 0.284744i 0.908092π0.908092\pi
150150 0 0
151151 −148.969 −0.986552 −0.493276 0.869873i 0.664201π-0.664201\pi
−0.493276 + 0.869873i 0.664201π0.664201\pi
152152 0 0
153153 52.0454 52.0454i 0.340166 0.340166i
154154 0 0
155155 0 0
156156 0 0
157157 −16.8536 16.8536i −0.107348 0.107348i 0.651393 0.758741i 0.274185π-0.274185\pi
−0.758741 + 0.651393i 0.774185π0.774185\pi
158158 0 0
159159 1.70714i 0.0107368i
160160 0 0
161161 79.6867 0.494949
162162 0 0
163163 130.606 130.606i 0.801265 0.801265i −0.182029 0.983293i 0.558266π-0.558266\pi
0.983293 + 0.182029i 0.0582664π0.0582664\pi
164164 0 0
165165 0 0
166166 0 0
167167 −45.0352 45.0352i −0.269672 0.269672i 0.559296 0.828968i 0.311071π-0.311071\pi
−0.828968 + 0.559296i 0.811071π0.811071\pi
168168 0 0
169169 107.384i 0.635406i
170170 0 0
171171 −26.0908 −0.152578
172172 0 0
173173 −146.631 + 146.631i −0.847579 + 0.847579i −0.989831 0.142252i 0.954566π-0.954566\pi
0.142252 + 0.989831i 0.454566π0.454566\pi
174174 0 0
175175 0 0
176176 0 0
177177 −48.9092 48.9092i −0.276323 0.276323i
178178 0 0
179179 183.712i 1.02632i −0.858292 0.513161i 0.828474π-0.828474\pi
0.858292 0.513161i 0.171526π-0.171526\pi
180180 0 0
181181 −286.272 −1.58162 −0.790808 0.612064i 0.790339π-0.790339\pi
−0.790808 + 0.612064i 0.790339π0.790339\pi
182182 0 0
183183 −7.23724 + 7.23724i −0.0395478 + 0.0395478i
184184 0 0
185185 0 0
186186 0 0
187187 −196.879 196.879i −1.05283 1.05283i
188188 0 0
189189 25.3485i 0.134119i
190190 0 0
191191 −48.0908 −0.251784 −0.125892 0.992044i 0.540179π-0.540179\pi
−0.125892 + 0.992044i 0.540179π0.540179\pi
192192 0 0
193193 255.565 255.565i 1.32417 1.32417i 0.413809 0.910364i 0.364198π-0.364198\pi
0.910364 0.413809i 0.135802π-0.135802\pi
194194 0 0
195195 0 0
196196 0 0
197197 96.6969 + 96.6969i 0.490847 + 0.490847i 0.908573 0.417726i 0.137173π-0.137173\pi
−0.417726 + 0.908573i 0.637173π0.637173\pi
198198 0 0
199199 192.606i 0.967870i −0.875104 0.483935i 0.839207π-0.839207\pi
0.875104 0.483935i 0.160793π-0.160793\pi
200200 0 0
201201 110.474 0.549624
202202 0 0
203203 −121.237 + 121.237i −0.597228 + 0.597228i
204204 0 0
205205 0 0
206206 0 0
207207 −34.6515 34.6515i −0.167399 0.167399i
208208 0 0
209209 98.6969i 0.472234i
210210 0 0
211211 −147.212 −0.697688 −0.348844 0.937181i 0.613426π-0.613426\pi
−0.348844 + 0.937181i 0.613426π0.613426\pi
212212 0 0
213213 −83.2827 + 83.2827i −0.390998 + 0.390998i
214214 0 0
215215 0 0
216216 0 0
217217 −36.8990 36.8990i −0.170041 0.170041i
218218 0 0
219219 190.540i 0.870047i
220220 0 0
221221 192.586 0.871429
222222 0 0
223223 167.429 167.429i 0.750803 0.750803i −0.223826 0.974629i 0.571855π-0.571855\pi
0.974629 + 0.223826i 0.0718548π0.0718548\pi
224224 0 0
225225 0 0
226226 0 0
227227 253.171 + 253.171i 1.11529 + 1.11529i 0.992423 + 0.122870i 0.0392098π0.0392098\pi
0.122870 + 0.992423i 0.460790π0.460790\pi
228228 0 0
229229 224.202i 0.979048i −0.871990 0.489524i 0.837171π-0.837171\pi
0.871990 0.489524i 0.162829π-0.162829\pi
230230 0 0
231231 95.8888 0.415103
232232 0 0
233233 205.712 205.712i 0.882883 0.882883i −0.110944 0.993827i 0.535387π-0.535387\pi
0.993827 + 0.110944i 0.0353873π0.0353873\pi
234234 0 0
235235 0 0
236236 0 0
237237 −30.0000 30.0000i −0.126582 0.126582i
238238 0 0
239239 345.798i 1.44685i 0.690401 + 0.723427i 0.257434π0.257434\pi
−0.690401 + 0.723427i 0.742566π0.742566\pi
240240 0 0
241241 101.576 0.421475 0.210738 0.977543i 0.432413π-0.432413\pi
0.210738 + 0.977543i 0.432413π0.432413\pi
242242 0 0
243243 11.0227 11.0227i 0.0453609 0.0453609i
244244 0 0
245245 0 0
246246 0 0
247247 −48.2724 48.2724i −0.195435 0.195435i
248248 0 0
249249 32.2020i 0.129325i
250250 0 0
251251 331.258 1.31975 0.659876 0.751375i 0.270609π-0.270609\pi
0.659876 + 0.751375i 0.270609π0.270609\pi
252252 0 0
253253 −131.081 + 131.081i −0.518105 + 0.518105i
254254 0 0
255255 0 0
256256 0 0
257257 −33.2372 33.2372i −0.129328 0.129328i 0.639480 0.768808i 0.279150π-0.279150\pi
−0.768808 + 0.639480i 0.779150π0.779150\pi
258258 0 0
259259 41.7071i 0.161031i
260260 0 0
261261 105.439 0.403982
262262 0 0
263263 −278.157 + 278.157i −1.05763 + 1.05763i −0.0593952 + 0.998235i 0.518917π0.518917\pi
−0.998235 + 0.0593952i 0.981083π0.981083\pi
264264 0 0
265265 0 0
266266 0 0
267267 −100.652 100.652i −0.376972 0.376972i
268268 0 0
269269 488.499i 1.81598i −0.418988 0.907992i 0.637615π-0.637615\pi
0.418988 0.907992i 0.362385π-0.362385\pi
270270 0 0
271271 −131.576 −0.485518 −0.242759 0.970087i 0.578053π-0.578053\pi
−0.242759 + 0.970087i 0.578053π0.578053\pi
272272 0 0
273273 −46.8990 + 46.8990i −0.171791 + 0.171791i
274274 0 0
275275 0 0
276276 0 0
277277 −101.510 101.510i −0.366461 0.366461i 0.499724 0.866185i 0.333435π-0.333435\pi
−0.866185 + 0.499724i 0.833435π0.833435\pi
278278 0 0
279279 32.0908i 0.115021i
280280 0 0
281281 343.303 1.22172 0.610860 0.791739i 0.290824π-0.290824\pi
0.610860 + 0.791739i 0.290824π0.290824\pi
282282 0 0
283283 1.19184 1.19184i 0.00421143 0.00421143i −0.704998 0.709209i 0.749052π-0.749052\pi
0.709209 + 0.704998i 0.249052π0.249052\pi
284284 0 0
285285 0 0
286286 0 0
287287 2.40408 + 2.40408i 0.00837659 + 0.00837659i
288288 0 0
289289 312.939i 1.08283i
290290 0 0
291291 −60.2474 −0.207036
292292 0 0
293293 −96.5653 + 96.5653i −0.329574 + 0.329574i −0.852425 0.522850i 0.824869π-0.824869\pi
0.522850 + 0.852425i 0.324869π0.324869\pi
294294 0 0
295295 0 0
296296 0 0
297297 −41.6969 41.6969i −0.140394 0.140394i
298298 0 0
299299 128.222i 0.428838i
300300 0 0
301301 −182.788 −0.607268
302302 0 0
303303 129.359 129.359i 0.426926 0.426926i
304304 0 0
305305 0 0
306306 0 0
307307 −124.969 124.969i −0.407066 0.407066i 0.473648 0.880714i 0.342937π-0.342937\pi
−0.880714 + 0.473648i 0.842937π0.842937\pi
308308 0 0
309309 218.611i 0.707478i
310310 0 0
311311 586.302 1.88522 0.942608 0.333902i 0.108365π-0.108365\pi
0.942608 + 0.333902i 0.108365π0.108365\pi
312312 0 0
313313 102.373 102.373i 0.327072 0.327072i −0.524400 0.851472i 0.675710π-0.675710\pi
0.851472 + 0.524400i 0.175710π0.175710\pi
314314 0 0
315315 0 0
316316 0 0
317317 108.783 + 108.783i 0.343165 + 0.343165i 0.857556 0.514391i 0.171982π-0.171982\pi
−0.514391 + 0.857556i 0.671982π0.671982\pi
318318 0 0
319319 398.858i 1.25034i
320320 0 0
321321 −168.384 −0.524560
322322 0 0
323323 150.879 150.879i 0.467116 0.467116i
324324 0 0
325325 0 0
326326 0 0
327327 −84.1362 84.1362i −0.257297 0.257297i
328328 0 0
329329 305.262i 0.927849i
330330 0 0
331331 245.423 0.741461 0.370730 0.928741i 0.379107π-0.379107\pi
0.370730 + 0.928741i 0.379107π0.379107\pi
332332 0 0
333333 18.1362 18.1362i 0.0544631 0.0544631i
334334 0 0
335335 0 0
336336 0 0
337337 −213.808 213.808i −0.634446 0.634446i 0.314734 0.949180i 0.398085π-0.398085\pi
−0.949180 + 0.314734i 0.898085π0.898085\pi
338338 0 0
339339 239.171i 0.705520i
340340 0 0
341341 121.394 0.355994
342342 0 0
343343 255.959 255.959i 0.746237 0.746237i
344344 0 0
345345 0 0
346346 0 0
347347 −160.050 160.050i −0.461239 0.461239i 0.437822 0.899062i 0.355750π-0.355750\pi
−0.899062 + 0.437822i 0.855750π0.855750\pi
348348 0 0
349349 298.009i 0.853894i −0.904277 0.426947i 0.859589π-0.859589\pi
0.904277 0.426947i 0.140411π-0.140411\pi
350350 0 0
351351 40.7878 0.116204
352352 0 0
353353 22.5199 22.5199i 0.0637957 0.0637957i −0.674489 0.738285i 0.735636π-0.735636\pi
0.738285 + 0.674489i 0.235636π0.235636\pi
354354 0 0
355355 0 0
356356 0 0
357357 −146.586 146.586i −0.410604 0.410604i
358358 0 0
359359 48.2724i 0.134464i −0.997737 0.0672318i 0.978583π-0.978583\pi
0.997737 0.0672318i 0.0214167π-0.0214167\pi
360360 0 0
361361 285.363 0.790480
362362 0 0
363363 −9.53801 + 9.53801i −0.0262755 + 0.0262755i
364364 0 0
365365 0 0
366366 0 0
367367 146.510 + 146.510i 0.399209 + 0.399209i 0.877954 0.478745i 0.158908π-0.158908\pi
−0.478745 + 0.877954i 0.658908π0.658908\pi
368368 0 0
369369 2.09082i 0.00566617i
370370 0 0
371371 4.80816 0.0129600
372372 0 0
373373 −86.2066 + 86.2066i −0.231117 + 0.231117i −0.813159 0.582042i 0.802254π-0.802254\pi
0.582042 + 0.813159i 0.302254π0.302254\pi
374374 0 0
375375 0 0
376376 0 0
377377 195.081 + 195.081i 0.517455 + 0.517455i
378378 0 0
379379 210.000i 0.554090i 0.960857 + 0.277045i 0.0893551π0.0893551\pi
−0.960857 + 0.277045i 0.910645π0.910645\pi
380380 0 0
381381 −403.237 −1.05837
382382 0 0
383383 −10.6311 + 10.6311i −0.0277575 + 0.0277575i −0.720849 0.693092i 0.756248π-0.756248\pi
0.693092 + 0.720849i 0.256248π0.256248\pi
384384 0 0
385385 0 0
386386 0 0
387387 79.4847 + 79.4847i 0.205387 + 0.205387i
388388 0 0
389389 535.337i 1.37619i −0.725621 0.688094i 0.758448π-0.758448\pi
0.725621 0.688094i 0.241552π-0.241552\pi
390390 0 0
391391 400.767 1.02498
392392 0 0
393393 129.990 129.990i 0.330763 0.330763i
394394 0 0
395395 0 0
396396 0 0
397397 −118.742 118.742i −0.299099 0.299099i 0.541562 0.840661i 0.317833π-0.317833\pi
−0.840661 + 0.541562i 0.817833π0.817833\pi
398398 0 0
399399 73.4847i 0.184172i
400400 0 0
401401 420.302 1.04813 0.524067 0.851677i 0.324414π-0.324414\pi
0.524067 + 0.851677i 0.324414π0.324414\pi
402402 0 0
403403 −59.3735 + 59.3735i −0.147329 + 0.147329i
404404 0 0
405405 0 0
406406 0 0
407407 −68.6061 68.6061i −0.168565 0.168565i
408408 0 0
409409 515.110i 1.25944i −0.776823 0.629719i 0.783170π-0.783170\pi
0.776823 0.629719i 0.216830π-0.216830\pi
410410 0 0
411411 −408.161 −0.993093
412412 0 0
413413 −137.753 + 137.753i −0.333541 + 0.333541i
414414 0 0
415415 0 0
416416 0 0
417417 −234.136 234.136i −0.561478 0.561478i
418418 0 0
419419 88.6015i 0.211460i 0.994395 + 0.105730i 0.0337178π0.0337178\pi
−0.994395 + 0.105730i 0.966282π0.966282\pi
420420 0 0
421421 −257.151 −0.610810 −0.305405 0.952223i 0.598792π-0.598792\pi
−0.305405 + 0.952223i 0.598792π0.598792\pi
422422 0 0
423423 132.742 132.742i 0.313812 0.313812i
424424 0 0
425425 0 0
426426 0 0
427427 20.3837 + 20.3837i 0.0477369 + 0.0477369i
428428 0 0
429429 154.293i 0.359657i
430430 0 0
431431 −804.636 −1.86690 −0.933452 0.358702i 0.883219π-0.883219\pi
−0.933452 + 0.358702i 0.883219π0.883219\pi
432432 0 0
433433 344.848 344.848i 0.796416 0.796416i −0.186113 0.982528i 0.559589π-0.559589\pi
0.982528 + 0.186113i 0.0595890π0.0595890\pi
434434 0 0
435435 0 0
436436 0 0
437437 −100.454 100.454i −0.229872 0.229872i
438438 0 0
439439 432.929i 0.986170i −0.869981 0.493085i 0.835869π-0.835869\pi
0.869981 0.493085i 0.164131π-0.164131\pi
440440 0 0
441441 −75.6061 −0.171442
442442 0 0
443443 245.131 245.131i 0.553342 0.553342i −0.374062 0.927404i 0.622035π-0.622035\pi
0.927404 + 0.374062i 0.122035π0.122035\pi
444444 0 0
445445 0 0
446446 0 0
447447 −103.924 103.924i −0.232492 0.232492i
448448 0 0
449449 386.091i 0.859890i 0.902855 + 0.429945i 0.141467π0.141467\pi
−0.902855 + 0.429945i 0.858533π0.858533\pi
450450 0 0
451451 −7.90918 −0.0175370
452452 0 0
453453 182.449 182.449i 0.402758 0.402758i
454454 0 0
455455 0 0
456456 0 0
457457 223.747 + 223.747i 0.489599 + 0.489599i 0.908180 0.418580i 0.137472π-0.137472\pi
−0.418580 + 0.908180i 0.637472π0.637472\pi
458458 0 0
459459 127.485i 0.277744i
460460 0 0
461461 −722.620 −1.56751 −0.783753 0.621073i 0.786697π-0.786697\pi
−0.783753 + 0.621073i 0.786697π0.786697\pi
462462 0 0
463463 −129.702 + 129.702i −0.280133 + 0.280133i −0.833162 0.553029i 0.813472π-0.813472\pi
0.553029 + 0.833162i 0.313472π0.313472\pi
464464 0 0
465465 0 0
466466 0 0
467467 415.258 + 415.258i 0.889203 + 0.889203i 0.994446 0.105244i 0.0335623π-0.0335623\pi
−0.105244 + 0.994446i 0.533562π0.533562\pi
468468 0 0
469469 311.151i 0.663435i
470470 0 0
471471 41.2827 0.0876489
472472 0 0
473473 300.677 300.677i 0.635680 0.635680i
474474 0 0
475475 0 0
476476 0 0
477477 −2.09082 2.09082i −0.00438326 0.00438326i
478478 0 0
479479 304.949i 0.636637i −0.947984 0.318318i 0.896882π-0.896882\pi
0.947984 0.318318i 0.103118π-0.103118\pi
480480 0 0
481481 67.1102 0.139522
482482 0 0
483483 −97.5959 + 97.5959i −0.202062 + 0.202062i
484484 0 0
485485 0 0
486486 0 0
487487 −429.318 429.318i −0.881556 0.881556i 0.112137 0.993693i 0.464231π-0.464231\pi
−0.993693 + 0.112137i 0.964231π0.964231\pi
488488 0 0
489489 319.918i 0.654230i
490490 0 0
491491 414.318 0.843825 0.421912 0.906637i 0.361359π-0.361359\pi
0.421912 + 0.906637i 0.361359π0.361359\pi
492492 0 0
493493 −609.737 + 609.737i −1.23679 + 1.23679i
494494 0 0
495495 0 0
496496 0 0
497497 234.565 + 234.565i 0.471962 + 0.471962i
498498 0 0
499499 367.585i 0.736643i −0.929699 0.368321i 0.879933π-0.879933\pi
0.929699 0.368321i 0.120067π-0.120067\pi
500500 0 0
501501 110.313 0.220186
502502 0 0
503503 −9.59133 + 9.59133i −0.0190683 + 0.0190683i −0.716577 0.697508i 0.754292π-0.754292\pi
0.697508 + 0.716577i 0.254292π0.254292\pi
504504 0 0
505505 0 0
506506 0 0
507507 −131.518 131.518i −0.259404 0.259404i
508508 0 0
509509 777.489i 1.52748i 0.645522 + 0.763742i 0.276640π0.276640\pi
−0.645522 + 0.763742i 0.723360π0.723360\pi
510510 0 0
511511 −536.656 −1.05021
512512 0 0
513513 31.9546 31.9546i 0.0622897 0.0622897i
514514 0 0
515515 0 0
516516 0 0
517517 −502.141 502.141i −0.971259 0.971259i
518518 0 0
519519 359.171i 0.692045i
520520 0 0
521521 321.605 0.617284 0.308642 0.951178i 0.400125π-0.400125\pi
0.308642 + 0.951178i 0.400125π0.400125\pi
522522 0 0
523523 −582.454 + 582.454i −1.11368 + 1.11368i −0.121030 + 0.992649i 0.538620π0.538620\pi
−0.992649 + 0.121030i 0.961380π0.961380\pi
524524 0 0
525525 0 0
526526 0 0
527527 −185.576 185.576i −0.352136 0.352136i
528528 0 0
529529 262.171i 0.495598i
530530 0 0
531531 119.803 0.225617
532532 0 0
533533 3.86836 3.86836i 0.00725772 0.00725772i
534534 0 0
535535 0 0
536536 0 0
537537 225.000 + 225.000i 0.418994 + 0.418994i
538538 0 0
539539 286.005i 0.530621i
540540 0 0
541541 460.697 0.851566 0.425783 0.904825i 0.359999π-0.359999\pi
0.425783 + 0.904825i 0.359999π0.359999\pi
542542 0 0
543543 350.611 350.611i 0.645692 0.645692i
544544 0 0
545545 0 0
546546 0 0
547547 −661.778 661.778i −1.20983 1.20983i −0.971081 0.238750i 0.923262π-0.923262\pi
−0.238750 0.971081i 0.576738π-0.576738\pi
548548 0 0
549549 17.7276i 0.0322906i
550550 0 0
551551 305.666 0.554748
552552 0 0
553553 −84.4949 + 84.4949i −0.152794 + 0.152794i
554554 0 0
555555 0 0
556556 0 0
557557 −125.909 125.909i −0.226049 0.226049i 0.584991 0.811040i 0.301098π-0.301098\pi
−0.811040 + 0.584991i 0.801098π0.801098\pi
558558 0 0
559559 294.120i 0.526155i
560560 0 0
561561 482.252 0.859629
562562 0 0
563563 −200.009 + 200.009i −0.355256 + 0.355256i −0.862061 0.506805i 0.830826π-0.830826\pi
0.506805 + 0.862061i 0.330826π0.330826\pi
564564 0 0
565565 0 0
566566 0 0
567567 −31.0454 31.0454i −0.0547538 0.0547538i
568568 0 0
569569 599.839i 1.05420i −0.849804 0.527099i 0.823280π-0.823280\pi
0.849804 0.527099i 0.176720π-0.176720\pi
570570 0 0
571571 247.970 0.434274 0.217137 0.976141i 0.430328π-0.430328\pi
0.217137 + 0.976141i 0.430328π0.430328\pi
572572 0 0
573573 58.8990 58.8990i 0.102791 0.102791i
574574 0 0
575575 0 0
576576 0 0
577577 292.121 + 292.121i 0.506276 + 0.506276i 0.913381 0.407105i 0.133462π-0.133462\pi
−0.407105 + 0.913381i 0.633462π0.633462\pi
578578 0 0
579579 626.005i 1.08118i
580580 0 0
581581 90.6969 0.156105
582582 0 0
583583 −7.90918 + 7.90918i −0.0135664 + 0.0135664i
584584 0 0
585585 0 0
586586 0 0
587587 611.217 + 611.217i 1.04126 + 1.04126i 0.999112 + 0.0421437i 0.0134187π0.0134187\pi
0.0421437 + 0.999112i 0.486581π0.486581\pi
588588 0 0
589589 93.0306i 0.157947i
590590 0 0
591591 −236.858 −0.400775
592592 0 0
593593 −524.742 + 524.742i −0.884894 + 0.884894i −0.994027 0.109133i 0.965193π-0.965193\pi
0.109133 + 0.994027i 0.465193π0.465193\pi
594594 0 0
595595 0 0
596596 0 0
597597 235.893 + 235.893i 0.395131 + 0.395131i
598598 0 0
599599 368.858i 0.615790i 0.951420 + 0.307895i 0.0996245π0.0996245\pi
−0.951420 + 0.307895i 0.900375π0.900375\pi
600600 0 0
601601 932.484 1.55155 0.775777 0.631007i 0.217358π-0.217358\pi
0.775777 + 0.631007i 0.217358π0.217358\pi
602602 0 0
603603 −135.303 + 135.303i −0.224383 + 0.224383i
604604 0 0
605605 0 0
606606 0 0
607607 513.611 + 513.611i 0.846146 + 0.846146i 0.989650 0.143504i 0.0458369π-0.0458369\pi
−0.143504 + 0.989650i 0.545837π0.545837\pi
608608 0 0
609609 296.969i 0.487634i
610610 0 0
611611 491.192 0.803915
612612 0 0
613613 615.287 615.287i 1.00373 1.00373i 0.00373821 0.999993i 0.498810π-0.498810\pi
0.999993 0.00373821i 0.00118991π-0.00118991\pi
614614 0 0
615615 0 0
616616 0 0
617617 −546.752 546.752i −0.886145 0.886145i 0.108005 0.994150i 0.465554π-0.465554\pi
−0.994150 + 0.108005i 0.965554π0.965554\pi
618618 0 0
619619 152.869i 0.246962i −0.992347 0.123481i 0.960594π-0.960594\pi
0.992347 0.123481i 0.0394058π-0.0394058\pi
620620 0 0
621621 84.8786 0.136680
622622 0 0
623623 −283.485 + 283.485i −0.455032 + 0.455032i
624624 0 0
625625 0 0
626626 0 0
627627 −120.879 120.879i −0.192789 0.192789i
628628 0 0
629629 209.757i 0.333477i
630630 0 0
631631 41.4847 0.0657444 0.0328722 0.999460i 0.489535π-0.489535\pi
0.0328722 + 0.999460i 0.489535π0.489535\pi
632632 0 0
633633 180.297 180.297i 0.284830 0.284830i
634634 0 0
635635 0 0
636636 0 0
637637 −139.884 139.884i −0.219598 0.219598i
638638 0 0
639639 204.000i 0.319249i
640640 0 0
641641 47.2122 0.0736541 0.0368270 0.999322i 0.488275π-0.488275\pi
0.0368270 + 0.999322i 0.488275π0.488275\pi
642642 0 0
643643 460.372 460.372i 0.715976 0.715976i −0.251803 0.967779i 0.581023π-0.581023\pi
0.967779 + 0.251803i 0.0810234π0.0810234\pi
644644 0 0
645645 0 0
646646 0 0
647647 −281.287 281.287i −0.434756 0.434756i 0.455487 0.890243i 0.349465π-0.349465\pi
−0.890243 + 0.455487i 0.849465π0.849465\pi
648648 0 0
649649 453.192i 0.698293i
650650 0 0
651651 90.3837 0.138838
652652 0 0
653653 −89.8230 + 89.8230i −0.137554 + 0.137554i −0.772531 0.634977i 0.781010π-0.781010\pi
0.634977 + 0.772531i 0.281010π0.281010\pi
654654 0 0
655655 0 0
656656 0 0
657657 233.363 + 233.363i 0.355195 + 0.355195i
658658 0 0
659659 1081.24i 1.64072i −0.571844 0.820362i 0.693772π-0.693772\pi
0.571844 0.820362i 0.306228π-0.306228\pi
660660 0 0
661661 −632.393 −0.956721 −0.478361 0.878163i 0.658769π-0.658769\pi
−0.478361 + 0.878163i 0.658769π0.658769\pi
662662 0 0
663663 −235.868 + 235.868i −0.355759 + 0.355759i
664664 0 0
665665 0 0
666666 0 0
667667 405.959 + 405.959i 0.608634 + 0.608634i
668668 0 0
669669 410.116i 0.613028i
670670 0 0
671671 −67.0602 −0.0999407
672672 0 0
673673 −233.293 + 233.293i −0.346646 + 0.346646i −0.858859 0.512213i 0.828826π-0.828826\pi
0.512213 + 0.858859i 0.328826π0.328826\pi
674674 0 0
675675 0 0
676676 0 0
677677 48.3883 + 48.3883i 0.0714745 + 0.0714745i 0.741940 0.670466i 0.233906π-0.233906\pi
−0.670466 + 0.741940i 0.733906π0.733906\pi
678678 0 0
679679 169.687i 0.249907i
680680 0 0
681681 −620.141 −0.910633
682682 0 0
683683 213.410 213.410i 0.312459 0.312459i −0.533402 0.845862i 0.679087π-0.679087\pi
0.845862 + 0.533402i 0.179087π0.179087\pi
684684 0 0
685685 0 0
686686 0 0
687687 274.590 + 274.590i 0.399695 + 0.399695i
688688 0 0
689689 7.73673i 0.0112289i
690690 0 0
691691 −151.121 −0.218700 −0.109350 0.994003i 0.534877π-0.534877\pi
−0.109350 + 0.994003i 0.534877π0.534877\pi
692692 0 0
693693 −117.439 + 117.439i −0.169465 + 0.169465i
694694 0 0
695695 0 0
696696 0 0
697697 12.0908 + 12.0908i 0.0173469 + 0.0173469i
698698 0 0
699699 503.889i 0.720871i
700700 0 0
701701 −745.680 −1.06374 −0.531869 0.846827i 0.678510π-0.678510\pi
−0.531869 + 0.846827i 0.678510π0.678510\pi
702702 0 0
703703 52.5765 52.5765i 0.0747888 0.0747888i
704704 0 0
705705 0 0
706706 0 0
707707 −364.338 364.338i −0.515330 0.515330i
708708 0 0
709709 719.049i 1.01417i 0.861895 + 0.507087i 0.169278π0.169278\pi
−0.861895 + 0.507087i 0.830722π0.830722\pi
710710 0 0
711711 73.4847 0.103354
712712 0 0
713713 −123.555 + 123.555i −0.173289 + 0.173289i
714714 0 0
715715 0 0
716716 0 0
717717 −423.514 423.514i −0.590675 0.590675i
718718 0 0
719719 605.271i 0.841824i 0.907101 + 0.420912i 0.138290π0.138290\pi
−0.907101 + 0.420912i 0.861710π0.861710\pi
720720 0 0
721721 −615.716 −0.853975
722722 0 0
723723 −124.404 + 124.404i −0.172067 + 0.172067i
724724 0 0
725725 0 0
726726 0 0
727727 −246.126 246.126i −0.338550 0.338550i 0.517271 0.855821i 0.326948π-0.326948\pi
−0.855821 + 0.517271i 0.826948π0.826948\pi
728728 0 0
729729 27.0000i 0.0370370i
730730 0 0
731731 −919.292 −1.25758
732732 0 0
733733 270.763 270.763i 0.369390 0.369390i −0.497865 0.867255i 0.665882π-0.665882\pi
0.867255 + 0.497865i 0.165882π0.165882\pi
734734 0 0
735735 0 0
736736 0 0
737737 511.828 + 511.828i 0.694474 + 0.694474i
738738 0 0
739739 515.666i 0.697789i 0.937162 + 0.348895i 0.113443π0.113443\pi
−0.937162 + 0.348895i 0.886557π0.886557\pi
740740 0 0
741741 118.243 0.159572
742742 0 0
743743 420.702 420.702i 0.566220 0.566220i −0.364847 0.931067i 0.618879π-0.618879\pi
0.931067 + 0.364847i 0.118879π0.118879\pi
744744 0 0
745745 0 0
746746 0 0
747747 −39.4393 39.4393i −0.0527969 0.0527969i
748748 0 0
749749 474.252i 0.633180i
750750 0 0
751751 859.787 1.14486 0.572428 0.819955i 0.306002π-0.306002\pi
0.572428 + 0.819955i 0.306002π0.306002\pi
752752 0 0
753753 −405.706 + 405.706i −0.538786 + 0.538786i
754754 0 0
755755 0 0
756756 0 0
757757 956.075 + 956.075i 1.26298 + 1.26298i 0.949642 + 0.313337i 0.101447π0.101447\pi
0.313337 + 0.949642i 0.398553π0.398553\pi
758758 0 0
759759 321.081i 0.423031i
760760 0 0
761761 −322.758 −0.424124 −0.212062 0.977256i 0.568018π-0.568018\pi
−0.212062 + 0.977256i 0.568018π0.568018\pi
762762 0 0
763763 −236.969 + 236.969i −0.310576 + 0.310576i
764764 0 0
765765 0 0
766766 0 0
767767 221.655 + 221.655i 0.288990 + 0.288990i
768768 0 0
769769 692.402i 0.900393i 0.892930 + 0.450196i 0.148646π0.148646\pi
−0.892930 + 0.450196i 0.851354π0.851354\pi
770770 0 0
771771 81.4143 0.105596
772772 0 0
773773 −375.226 + 375.226i −0.485415 + 0.485415i −0.906856 0.421441i 0.861525π-0.861525\pi
0.421441 + 0.906856i 0.361525π0.361525\pi
774774 0 0
775775 0 0
776776 0 0
777777 −51.0806 51.0806i −0.0657408 0.0657408i
778778 0 0
779779 6.06123i 0.00778078i
780780 0 0
781781 −771.696 −0.988087
782782 0 0
783783 −129.136 + 129.136i −0.164925 + 0.164925i
784784 0 0
785785 0 0
786786 0 0
787787 910.990 + 910.990i 1.15755 + 1.15755i 0.985001 + 0.172546i 0.0551993π0.0551993\pi
0.172546 + 0.985001i 0.444801π0.444801\pi
788788 0 0
789789 681.342i 0.863551i
790790 0 0
791791 −673.626 −0.851613
792792 0 0
793793 32.7990 32.7990i 0.0413606 0.0413606i
794794 0 0
795795 0 0
796796 0 0
797797 7.21683 + 7.21683i 0.00905500 + 0.00905500i 0.711620 0.702565i 0.247962π-0.247962\pi
−0.702565 + 0.711620i 0.747962π0.747962\pi
798798 0 0
799799 1535.25i 1.92147i
800800 0 0
801801 246.545 0.307796
802802 0 0
803803 882.772 882.772i 1.09934 1.09934i
804804 0 0
805805 0 0
806806 0 0
807807 598.287 + 598.287i 0.741372 + 0.741372i
808808 0 0
809809 150.000i 0.185414i −0.995693 0.0927070i 0.970448π-0.970448\pi
0.995693 0.0927070i 0.0295520π-0.0295520\pi
810810 0 0
811811 −1336.85 −1.64839 −0.824197 0.566304i 0.808373π-0.808373\pi
−0.824197 + 0.566304i 0.808373π0.808373\pi
812812 0 0
813813 161.146 161.146i 0.198212 0.198212i
814814 0 0
815815 0 0
816816 0 0
817817 230.424 + 230.424i 0.282037 + 0.282037i
818818 0 0
819819 114.879i 0.140267i
820820 0 0
821821 −33.8934 −0.0412830 −0.0206415 0.999787i 0.506571π-0.506571\pi
−0.0206415 + 0.999787i 0.506571π0.506571\pi
822822 0 0
823823 481.631 481.631i 0.585214 0.585214i −0.351117 0.936331i 0.614198π-0.614198\pi
0.936331 + 0.351117i 0.114198π0.114198\pi
824824 0 0
825825 0 0
826826 0 0
827827 350.756 + 350.756i 0.424131 + 0.424131i 0.886623 0.462492i 0.153045π-0.153045\pi
−0.462492 + 0.886623i 0.653045π0.653045\pi
828828 0 0
829829 697.423i 0.841283i −0.907227 0.420641i 0.861805π-0.861805\pi
0.907227 0.420641i 0.138195π-0.138195\pi
830830 0 0
831831 248.647 0.299214
832832 0 0
833833 437.217 437.217i 0.524870 0.524870i
834834 0 0
835835 0 0
836836 0 0
837837 −39.3031 39.3031i −0.0469571 0.0469571i
838838 0 0
839839 72.3724i 0.0862604i −0.999069 0.0431302i 0.986267π-0.986267\pi
0.999069 0.0431302i 0.0137330π-0.0137330\pi
840840 0 0
841841 −394.271 −0.468813
842842 0 0
843843 −420.459 + 420.459i −0.498765 + 0.498765i
844844 0 0
845845 0 0
846846 0 0
847847 26.8638 + 26.8638i 0.0317164 + 0.0317164i
848848 0 0
849849 2.91939i 0.00343862i
850850 0 0
851851 139.655 0.164107
852852 0 0
853853 74.5699 74.5699i 0.0874207 0.0874207i −0.662044 0.749465i 0.730311π-0.730311\pi
0.749465 + 0.662044i 0.230311π0.230311\pi
854854 0 0
855855 0 0
856856 0 0
857857 293.176 + 293.176i 0.342096 + 0.342096i 0.857155 0.515059i 0.172230π-0.172230\pi
−0.515059 + 0.857155i 0.672230π0.672230\pi
858858 0 0
859859 786.867i 0.916027i 0.888945 + 0.458014i 0.151439π0.151439\pi
−0.888945 + 0.458014i 0.848561π0.848561\pi
860860 0 0
861861 −5.88877 −0.00683946
862862 0 0
863863 −1072.68 + 1072.68i −1.24297 + 1.24297i −0.284204 + 0.958764i 0.591729π0.591729\pi
−0.958764 + 0.284204i 0.908271π0.908271\pi
864864 0 0
865865 0 0
866866 0 0
867867 −383.270 383.270i −0.442065 0.442065i
868868 0 0
869869 277.980i 0.319884i
870870 0 0
871871 −500.667 −0.574819
872872 0 0
873873 73.7878 73.7878i 0.0845221 0.0845221i
874874 0 0
875875 0 0
876876 0 0
877877 −239.460 239.460i −0.273044 0.273044i 0.557280 0.830324i 0.311845π-0.311845\pi
−0.830324 + 0.557280i 0.811845π0.811845\pi
878878 0 0
879879 236.536i 0.269096i
880880 0 0
881881 62.8490 0.0713382 0.0356691 0.999364i 0.488644π-0.488644\pi
0.0356691 + 0.999364i 0.488644π0.488644\pi
882882 0 0
883883 −158.061 + 158.061i −0.179005 + 0.179005i −0.790922 0.611917i 0.790399π-0.790399\pi
0.611917 + 0.790922i 0.290399π0.290399\pi
884884 0 0
885885 0 0
886886 0 0
887887 30.2066 + 30.2066i 0.0340548 + 0.0340548i 0.723929 0.689874i 0.242334π-0.242334\pi
−0.689874 + 0.723929i 0.742334π0.742334\pi
888888 0 0
889889 1135.72i 1.27752i
890890 0 0
891891 102.136 0.114631
892892 0 0
893893 384.817 384.817i 0.430926 0.430926i
894894 0 0
895895 0 0
896896 0 0
897897 157.040 + 157.040i 0.175072 + 0.175072i
898898 0 0
899899 375.959i 0.418197i
900900 0 0
901901 24.1816 0.0268387
902902 0 0
903903 223.868 223.868i 0.247916 0.247916i
904904 0 0
905905 0 0
906906 0 0
907907 571.342 + 571.342i 0.629925 + 0.629925i 0.948049 0.318124i 0.103053π-0.103053\pi
−0.318124 + 0.948049i 0.603053π0.603053\pi
908908 0 0
909909 316.863i 0.348584i
910910 0 0
911911 −173.362 −0.190299 −0.0951494 0.995463i 0.530333π-0.530333\pi
−0.0951494 + 0.995463i 0.530333π0.530333\pi
912912 0 0
913913 −149.192 + 149.192i −0.163408 + 0.163408i
914914 0 0
915915 0 0
916916 0 0
917917 −366.116 366.116i −0.399254 0.399254i
918918 0 0
919919 1147.42i 1.24856i −0.781202 0.624278i 0.785393π-0.785393\pi
0.781202 0.624278i 0.214607π-0.214607\pi
920920 0 0
921921 306.111 0.332368
922922 0 0
923923 377.435 377.435i 0.408922 0.408922i
924924 0 0
925925 0 0
926926 0 0
927927 267.742 + 267.742i 0.288827 + 0.288827i
928928 0 0
929929 220.293i 0.237129i −0.992946 0.118565i 0.962171π-0.962171\pi
0.992946 0.118565i 0.0378292π-0.0378292\pi
930930 0 0
931931 −219.181 −0.235425
932932 0 0
933933 −718.070 + 718.070i −0.769636 + 0.769636i
934934 0 0
935935 0 0
936936 0 0
937937 396.090 + 396.090i 0.422721 + 0.422721i 0.886140 0.463418i 0.153377π-0.153377\pi
−0.463418 + 0.886140i 0.653377π0.653377\pi
938938 0 0
939939 250.763i 0.267053i
940940 0 0
941941 185.771 0.197419 0.0987093 0.995116i 0.468529π-0.468529\pi
0.0987093 + 0.995116i 0.468529π0.468529\pi
942942 0 0
943943 8.04999 8.04999i 0.00853658 0.00853658i
944944 0 0
945945 0 0
946946 0 0
947947 −845.190 845.190i −0.892492 0.892492i 0.102265 0.994757i 0.467391π-0.467391\pi
−0.994757 + 0.102265i 0.967391π0.967391\pi
948948 0 0
949949 863.523i 0.909930i
950950 0 0
951951 −266.463 −0.280193
952952 0 0
953953 630.499 630.499i 0.661594 0.661594i −0.294161 0.955756i 0.595040π-0.595040\pi
0.955756 + 0.294161i 0.0950403π0.0950403\pi
954954 0 0
955955 0 0
956956 0 0
957957 488.499 + 488.499i 0.510449 + 0.510449i
958958 0 0
959959 1149.58i 1.19873i
960960 0 0
961961 −846.576 −0.880932
962962 0 0
963963 206.227 206.227i 0.214151 0.214151i
964964 0 0
965965 0 0
966966 0 0
967967 −381.690 381.690i −0.394716 0.394716i 0.481649 0.876364i 0.340038π-0.340038\pi
−0.876364 + 0.481649i 0.840038π0.840038\pi
968968 0 0
969969 369.576i 0.381399i
970970 0 0
971971 1000.44 1.03032 0.515159 0.857095i 0.327733π-0.327733\pi
0.515159 + 0.857095i 0.327733π0.327733\pi
972972 0 0
973973 −659.444 + 659.444i −0.677743 + 0.677743i
974974 0 0
975975 0 0
976976 0 0
977977 −593.662 593.662i −0.607637 0.607637i 0.334691 0.942328i 0.391368π-0.391368\pi
−0.942328 + 0.334691i 0.891368π0.891368\pi
978978 0 0
979979 932.636i 0.952641i
980980 0 0
981981 206.091 0.210082
982982 0 0
983983 −1217.34 + 1217.34i −1.23839 + 1.23839i −0.277731 + 0.960659i 0.589582π0.589582\pi
−0.960659 + 0.277731i 0.910418π0.910418\pi
984984 0 0
985985 0 0
986986 0 0
987987 −373.868 373.868i −0.378793 0.378793i
988988 0 0
989989 612.059i 0.618867i
990990 0 0
991991 544.061 0.549002 0.274501 0.961587i 0.411487π-0.411487\pi
0.274501 + 0.961587i 0.411487π0.411487\pi
992992 0 0
993993 −300.581 + 300.581i −0.302700 + 0.302700i
994994 0 0
995995 0 0
996996 0 0
997997 316.733 + 316.733i 0.317686 + 0.317686i 0.847878 0.530192i 0.177880π-0.177880\pi
−0.530192 + 0.847878i 0.677880π0.677880\pi
998998 0 0
999999 44.4245i 0.0444690i
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 1200.3.bg.k.1057.1 4
4.3 odd 2 75.3.f.c.7.1 4
5.2 odd 4 240.3.bg.a.193.2 4
5.3 odd 4 inner 1200.3.bg.k.193.1 4
5.4 even 2 240.3.bg.a.97.2 4
12.11 even 2 225.3.g.a.82.2 4
15.2 even 4 720.3.bh.k.433.2 4
15.14 odd 2 720.3.bh.k.577.2 4
20.3 even 4 75.3.f.c.43.1 4
20.7 even 4 15.3.f.a.13.2 yes 4
20.19 odd 2 15.3.f.a.7.2 4
40.19 odd 2 960.3.bg.i.577.2 4
40.27 even 4 960.3.bg.i.193.2 4
40.29 even 2 960.3.bg.h.577.1 4
40.37 odd 4 960.3.bg.h.193.1 4
60.23 odd 4 225.3.g.a.118.2 4
60.47 odd 4 45.3.g.b.28.1 4
60.59 even 2 45.3.g.b.37.1 4
180.7 even 12 405.3.l.h.28.1 8
180.47 odd 12 405.3.l.f.28.2 8
180.59 even 6 405.3.l.f.217.2 8
180.67 even 12 405.3.l.h.298.2 8
180.79 odd 6 405.3.l.h.352.2 8
180.119 even 6 405.3.l.f.352.1 8
180.139 odd 6 405.3.l.h.217.1 8
180.167 odd 12 405.3.l.f.298.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
15.3.f.a.7.2 4 20.19 odd 2
15.3.f.a.13.2 yes 4 20.7 even 4
45.3.g.b.28.1 4 60.47 odd 4
45.3.g.b.37.1 4 60.59 even 2
75.3.f.c.7.1 4 4.3 odd 2
75.3.f.c.43.1 4 20.3 even 4
225.3.g.a.82.2 4 12.11 even 2
225.3.g.a.118.2 4 60.23 odd 4
240.3.bg.a.97.2 4 5.4 even 2
240.3.bg.a.193.2 4 5.2 odd 4
405.3.l.f.28.2 8 180.47 odd 12
405.3.l.f.217.2 8 180.59 even 6
405.3.l.f.298.1 8 180.167 odd 12
405.3.l.f.352.1 8 180.119 even 6
405.3.l.h.28.1 8 180.7 even 12
405.3.l.h.217.1 8 180.139 odd 6
405.3.l.h.298.2 8 180.67 even 12
405.3.l.h.352.2 8 180.79 odd 6
720.3.bh.k.433.2 4 15.2 even 4
720.3.bh.k.577.2 4 15.14 odd 2
960.3.bg.h.193.1 4 40.37 odd 4
960.3.bg.h.577.1 4 40.29 even 2
960.3.bg.i.193.2 4 40.27 even 4
960.3.bg.i.577.2 4 40.19 odd 2
1200.3.bg.k.193.1 4 5.3 odd 4 inner
1200.3.bg.k.1057.1 4 1.1 even 1 trivial