Properties

Label 1120.2.g.b.449.2
Level 11201120
Weight 22
Character 1120.449
Analytic conductor 8.9438.943
Analytic rank 00
Dimension 1010
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1120,2,Mod(449,1120)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1120, base_ring=CyclotomicField(2))
 
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("1120.449");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 1120=2557 1120 = 2^{5} \cdot 5 \cdot 7
Weight: k k == 2 2
Character orbit: [χ][\chi] == 1120.g (of order 22, degree 11, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 8.943245026388.94324502638
Analytic rank: 00
Dimension: 1010
Coefficient field: 10.0.65174749855744.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x10+13x8+56x6+97x4+61x2+4 x^{10} + 13x^{8} + 56x^{6} + 97x^{4} + 61x^{2} + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 23 2^{3}
Twist minimal: yes
Sato-Tate group: SU(2)[C2]\mathrm{SU}(2)[C_{2}]

Embedding invariants

Embedding label 449.2
Root 0.271831i-0.271831i of defining polynomial
Character χ\chi == 1120.449
Dual form 1120.2.g.b.449.9

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q2.19794iq3+(1.645141.51444i)q5+1.00000iq71.83094q91.37460q11+2.74160iq13+(3.328643.61591i)q156.94455iq171.29028q19+2.19794q218.31915iq23+(0.4129614.98292i)q252.56953iq27+8.40089q299.49323q31+3.02128iq33+(1.51444+1.64514i)q351.73860iq37+6.02587q395.30855q41+7.83136iq43+(3.01214+2.77284i)q453.48822iq471.00000q4915.2637q51+6.13448iq53+(2.26140+2.08174i)q55+2.83595iq576.26070q59+6.59883q611.83094iq63+(4.15198+4.51031i)q651.66187iq6718.2850q69+16.0236q71+2.13448iq73+(10.95210.907662i)q751.37460iq77+5.45132q7911.1405q81+2.54624iq83+(10.517111.4248i)q8518.4646iq871.43548q892.74160q91+20.8655iq93+(2.12268+1.95404i)q95+9.69375iq97+2.51680q99+O(q100)q-2.19794i q^{3} +(1.64514 - 1.51444i) q^{5} +1.00000i q^{7} -1.83094 q^{9} -1.37460 q^{11} +2.74160i q^{13} +(-3.32864 - 3.61591i) q^{15} -6.94455i q^{17} -1.29028 q^{19} +2.19794 q^{21} -8.31915i q^{23} +(0.412961 - 4.98292i) q^{25} -2.56953i q^{27} +8.40089 q^{29} -9.49323 q^{31} +3.02128i q^{33} +(1.51444 + 1.64514i) q^{35} -1.73860i q^{37} +6.02587 q^{39} -5.30855 q^{41} +7.83136i q^{43} +(-3.01214 + 2.77284i) q^{45} -3.48822i q^{47} -1.00000 q^{49} -15.2637 q^{51} +6.13448i q^{53} +(-2.26140 + 2.08174i) q^{55} +2.83595i q^{57} -6.26070 q^{59} +6.59883 q^{61} -1.83094i q^{63} +(4.15198 + 4.51031i) q^{65} -1.66187i q^{67} -18.2850 q^{69} +16.0236 q^{71} +2.13448i q^{73} +(-10.9521 - 0.907662i) q^{75} -1.37460i q^{77} +5.45132 q^{79} -11.1405 q^{81} +2.54624i q^{83} +(-10.5171 - 11.4248i) q^{85} -18.4646i q^{87} -1.43548 q^{89} -2.74160 q^{91} +20.8655i q^{93} +(-2.12268 + 1.95404i) q^{95} +9.69375i q^{97} +2.51680 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 10q2q514q98q114q15+24q194q21+6q25+24q2924q31+64q394q41+10q4510q4924q5116q55+32q5920q618q65++80q99+O(q100) 10 q - 2 q^{5} - 14 q^{9} - 8 q^{11} - 4 q^{15} + 24 q^{19} - 4 q^{21} + 6 q^{25} + 24 q^{29} - 24 q^{31} + 64 q^{39} - 4 q^{41} + 10 q^{45} - 10 q^{49} - 24 q^{51} - 16 q^{55} + 32 q^{59} - 20 q^{61} - 8 q^{65}+ \cdots + 80 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/1120Z)×\left(\mathbb{Z}/1120\mathbb{Z}\right)^\times.

nn 351351 421421 801801 897897
χ(n)\chi(n) 11 11 11 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 0 0
33 2.19794i 1.26898i −0.772931 0.634490i 0.781210π-0.781210\pi
0.772931 0.634490i 0.218790π-0.218790\pi
44 0 0
55 1.64514 1.51444i 0.735728 0.677277i
66 0 0
77 1.00000i 0.377964i
88 0 0
99 −1.83094 −0.610312
1010 0 0
1111 −1.37460 −0.414457 −0.207228 0.978293i 0.566444π-0.566444\pi
−0.207228 + 0.978293i 0.566444π0.566444\pi
1212 0 0
1313 2.74160i 0.760383i 0.924908 + 0.380192i 0.124142π0.124142\pi
−0.924908 + 0.380192i 0.875858π0.875858\pi
1414 0 0
1515 −3.32864 3.61591i −0.859451 0.933625i
1616 0 0
1717 6.94455i 1.68430i −0.539242 0.842151i 0.681289π-0.681289\pi
0.539242 0.842151i 0.318711π-0.318711\pi
1818 0 0
1919 −1.29028 −0.296010 −0.148005 0.988987i 0.547285π-0.547285\pi
−0.148005 + 0.988987i 0.547285π0.547285\pi
2020 0 0
2121 2.19794 0.479630
2222 0 0
2323 8.31915i 1.73466i −0.497731 0.867331i 0.665833π-0.665833\pi
0.497731 0.867331i 0.334167π-0.334167\pi
2424 0 0
2525 0.412961 4.98292i 0.0825921 0.996583i
2626 0 0
2727 2.56953i 0.494507i
2828 0 0
2929 8.40089 1.56001 0.780003 0.625775i 0.215217π-0.215217\pi
0.780003 + 0.625775i 0.215217π0.215217\pi
3030 0 0
3131 −9.49323 −1.70503 −0.852517 0.522699i 0.824925π-0.824925\pi
−0.852517 + 0.522699i 0.824925π0.824925\pi
3232 0 0
3333 3.02128i 0.525937i
3434 0 0
3535 1.51444 + 1.64514i 0.255987 + 0.278079i
3636 0 0
3737 1.73860i 0.285824i −0.989735 0.142912i 0.954353π-0.954353\pi
0.989735 0.142912i 0.0456465π-0.0456465\pi
3838 0 0
3939 6.02587 0.964912
4040 0 0
4141 −5.30855 −0.829057 −0.414528 0.910036i 0.636053π-0.636053\pi
−0.414528 + 0.910036i 0.636053π0.636053\pi
4242 0 0
4343 7.83136i 1.19427i 0.802140 + 0.597136i 0.203695π0.203695\pi
−0.802140 + 0.597136i 0.796305π0.796305\pi
4444 0 0
4545 −3.01214 + 2.77284i −0.449024 + 0.413350i
4646 0 0
4747 3.48822i 0.508809i −0.967098 0.254404i 0.918121π-0.918121\pi
0.967098 0.254404i 0.0818794π-0.0818794\pi
4848 0 0
4949 −1.00000 −0.142857
5050 0 0
5151 −15.2637 −2.13735
5252 0 0
5353 6.13448i 0.842635i 0.906913 + 0.421317i 0.138432π0.138432\pi
−0.906913 + 0.421317i 0.861568π0.861568\pi
5454 0 0
5555 −2.26140 + 2.08174i −0.304927 + 0.280702i
5656 0 0
5757 2.83595i 0.375631i
5858 0 0
5959 −6.26070 −0.815074 −0.407537 0.913189i 0.633612π-0.633612\pi
−0.407537 + 0.913189i 0.633612π0.633612\pi
6060 0 0
6161 6.59883 0.844894 0.422447 0.906388i 0.361171π-0.361171\pi
0.422447 + 0.906388i 0.361171π0.361171\pi
6262 0 0
6363 1.83094i 0.230676i
6464 0 0
6565 4.15198 + 4.51031i 0.514990 + 0.559435i
6666 0 0
6767 1.66187i 0.203030i −0.994834 0.101515i 0.967631π-0.967631\pi
0.994834 0.101515i 0.0323690π-0.0323690\pi
6868 0 0
6969 −18.2850 −2.20125
7070 0 0
7171 16.0236 1.90165 0.950825 0.309730i 0.100239π-0.100239\pi
0.950825 + 0.309730i 0.100239π0.100239\pi
7272 0 0
7373 2.13448i 0.249821i 0.992168 + 0.124911i 0.0398644π0.0398644\pi
−0.992168 + 0.124911i 0.960136π0.960136\pi
7474 0 0
7575 −10.9521 0.907662i −1.26465 0.104808i
7676 0 0
7777 1.37460i 0.156650i
7878 0 0
7979 5.45132 0.613322 0.306661 0.951819i 0.400788π-0.400788\pi
0.306661 + 0.951819i 0.400788π0.400788\pi
8080 0 0
8181 −11.1405 −1.23783
8282 0 0
8383 2.54624i 0.279486i 0.990188 + 0.139743i 0.0446277π0.0446277\pi
−0.990188 + 0.139743i 0.955372π0.955372\pi
8484 0 0
8585 −10.5171 11.4248i −1.14074 1.23919i
8686 0 0
8787 18.4646i 1.97962i
8888 0 0
8989 −1.43548 −0.152161 −0.0760804 0.997102i 0.524241π-0.524241\pi
−0.0760804 + 0.997102i 0.524241π0.524241\pi
9090 0 0
9191 −2.74160 −0.287398
9292 0 0
9393 20.8655i 2.16366i
9494 0 0
9595 −2.12268 + 1.95404i −0.217783 + 0.200481i
9696 0 0
9797 9.69375i 0.984251i 0.870524 + 0.492125i 0.163780π0.163780\pi
−0.870524 + 0.492125i 0.836220π0.836220\pi
9898 0 0
9999 2.51680 0.252948
100100 0 0
101101 8.25067 0.820973 0.410486 0.911867i 0.365359π-0.365359\pi
0.410486 + 0.911867i 0.365359π0.365359\pi
102102 0 0
103103 13.1501i 1.29572i −0.761761 0.647858i 0.775665π-0.775665\pi
0.761761 0.647858i 0.224335π-0.224335\pi
104104 0 0
105105 3.61591 3.32864i 0.352877 0.324842i
106106 0 0
107107 0.153454i 0.0148349i −0.999972 0.00741746i 0.997639π-0.997639\pi
0.999972 0.00741746i 0.00236107π-0.00236107\pi
108108 0 0
109109 8.23741 0.789001 0.394500 0.918896i 0.370918π-0.370918\pi
0.394500 + 0.918896i 0.370918π0.370918\pi
110110 0 0
111111 −3.82133 −0.362705
112112 0 0
113113 11.0532i 1.03979i 0.854229 + 0.519897i 0.174030π0.174030\pi
−0.854229 + 0.519897i 0.825970π0.825970\pi
114114 0 0
115115 −12.5988 13.6862i −1.17485 1.27624i
116116 0 0
117117 5.01969i 0.464071i
118118 0 0
119119 6.94455 0.636606
120120 0 0
121121 −9.11048 −0.828226
122122 0 0
123123 11.6679i 1.05206i
124124 0 0
125125 −6.86694 8.82299i −0.614198 0.789152i
126126 0 0
127127 7.74460i 0.687222i 0.939112 + 0.343611i 0.111650π0.111650\pi
−0.939112 + 0.343611i 0.888350π0.888350\pi
128128 0 0
129129 17.2128 1.51551
130130 0 0
131131 −4.75228 −0.415209 −0.207605 0.978213i 0.566567π-0.566567\pi
−0.207605 + 0.978213i 0.566567π0.566567\pi
132132 0 0
133133 1.29028i 0.111881i
134134 0 0
135135 −3.89140 4.22724i −0.334918 0.363823i
136136 0 0
137137 18.3002i 1.56349i −0.623599 0.781745i 0.714330π-0.714330\pi
0.623599 0.781745i 0.285670π-0.285670\pi
138138 0 0
139139 18.9370 1.60621 0.803106 0.595836i 0.203179π-0.203179\pi
0.803106 + 0.595836i 0.203179π0.203179\pi
140140 0 0
141141 −7.66688 −0.645668
142142 0 0
143143 3.76860i 0.315146i
144144 0 0
145145 13.8206 12.7226i 1.14774 1.05656i
146146 0 0
147147 2.19794i 0.181283i
148148 0 0
149149 −10.1155 −0.828694 −0.414347 0.910119i 0.635990π-0.635990\pi
−0.414347 + 0.910119i 0.635990π0.635990\pi
150150 0 0
151151 −0.567654 −0.0461951 −0.0230975 0.999733i 0.507353π-0.507353\pi
−0.0230975 + 0.999733i 0.507353π0.507353\pi
152152 0 0
153153 12.7150i 1.02795i
154154 0 0
155155 −15.6177 + 14.3769i −1.25444 + 1.15478i
156156 0 0
157157 2.87542i 0.229484i −0.993395 0.114742i 0.963396π-0.963396\pi
0.993395 0.114742i 0.0366041π-0.0366041\pi
158158 0 0
159159 13.4832 1.06929
160160 0 0
161161 8.31915 0.655641
162162 0 0
163163 10.2212i 0.800589i 0.916387 + 0.400294i 0.131092π0.131092\pi
−0.916387 + 0.400294i 0.868908π0.868908\pi
164164 0 0
165165 4.57554 + 4.97042i 0.356205 + 0.386947i
166166 0 0
167167 19.7672i 1.52963i 0.644249 + 0.764816i 0.277170π0.277170\pi
−0.644249 + 0.764816i 0.722830π0.722830\pi
168168 0 0
169169 5.48363 0.421817
170170 0 0
171171 2.36241 0.180658
172172 0 0
173173 21.7281i 1.65195i −0.563704 0.825977i 0.690624π-0.690624\pi
0.563704 0.825977i 0.309376π-0.309376\pi
174174 0 0
175175 4.98292 + 0.412961i 0.376673 + 0.0312169i
176176 0 0
177177 13.7606i 1.03431i
178178 0 0
179179 21.1611 1.58166 0.790828 0.612039i 0.209650π-0.209650\pi
0.790828 + 0.612039i 0.209650π0.209650\pi
180180 0 0
181181 11.8396 0.880031 0.440016 0.897990i 0.354973π-0.354973\pi
0.440016 + 0.897990i 0.354973π0.354973\pi
182182 0 0
183183 14.5038i 1.07215i
184184 0 0
185185 −2.63300 2.86023i −0.193582 0.210289i
186186 0 0
187187 9.54596i 0.698070i
188188 0 0
189189 2.56953 0.186906
190190 0 0
191191 1.82068 0.131739 0.0658697 0.997828i 0.479018π-0.479018\pi
0.0658697 + 0.997828i 0.479018π0.479018\pi
192192 0 0
193193 3.62770i 0.261128i −0.991440 0.130564i 0.958321π-0.958321\pi
0.991440 0.130564i 0.0416788π-0.0416788\pi
194194 0 0
195195 9.91339 9.12580i 0.709913 0.653512i
196196 0 0
197197 6.49380i 0.462664i 0.972875 + 0.231332i 0.0743084π0.0743084\pi
−0.972875 + 0.231332i 0.925692π0.925692\pi
198198 0 0
199199 4.69145 0.332568 0.166284 0.986078i 0.446823π-0.446823\pi
0.166284 + 0.986078i 0.446823π0.446823\pi
200200 0 0
201201 −3.65269 −0.257641
202202 0 0
203203 8.40089i 0.589627i
204204 0 0
205205 −8.73331 + 8.03947i −0.609961 + 0.561501i
206206 0 0
207207 15.2318i 1.05869i
208208 0 0
209209 1.77361 0.122683
210210 0 0
211211 17.0159 1.17142 0.585710 0.810521i 0.300816π-0.300816\pi
0.585710 + 0.810521i 0.300816π0.300816\pi
212212 0 0
213213 35.2189i 2.41316i
214214 0 0
215215 11.8601 + 12.8837i 0.808852 + 0.878659i
216216 0 0
217217 9.49323i 0.644442i
218218 0 0
219219 4.69145 0.317019
220220 0 0
221221 19.0392 1.28071
222222 0 0
223223 9.39251i 0.628969i 0.949263 + 0.314485i 0.101832π0.101832\pi
−0.949263 + 0.314485i 0.898168π0.898168\pi
224224 0 0
225225 −0.756104 + 9.12340i −0.0504069 + 0.608227i
226226 0 0
227227 14.3134i 0.950016i 0.879981 + 0.475008i 0.157555π0.157555\pi
−0.879981 + 0.475008i 0.842445π0.842445\pi
228228 0 0
229229 8.78351 0.580430 0.290215 0.956961i 0.406273π-0.406273\pi
0.290215 + 0.956961i 0.406273π0.406273\pi
230230 0 0
231231 −3.02128 −0.198786
232232 0 0
233233 14.7706i 0.967652i −0.875164 0.483826i 0.839247π-0.839247\pi
0.875164 0.483826i 0.160753π-0.160753\pi
234234 0 0
235235 −5.28268 5.73860i −0.344604 0.374345i
236236 0 0
237237 11.9817i 0.778294i
238238 0 0
239239 25.0525 1.62051 0.810256 0.586076i 0.199328π-0.199328\pi
0.810256 + 0.586076i 0.199328π0.199328\pi
240240 0 0
241241 3.32975 0.214488 0.107244 0.994233i 0.465797π-0.465797\pi
0.107244 + 0.994233i 0.465797π0.465797\pi
242242 0 0
243243 16.7775i 1.07628i
244244 0 0
245245 −1.64514 + 1.51444i −0.105104 + 0.0967538i
246246 0 0
247247 3.53742i 0.225081i
248248 0 0
249249 5.59648 0.354663
250250 0 0
251251 −9.89135 −0.624336 −0.312168 0.950027i 0.601055π-0.601055\pi
−0.312168 + 0.950027i 0.601055π0.601055\pi
252252 0 0
253253 11.4355i 0.718943i
254254 0 0
255255 −25.1109 + 23.1159i −1.57251 + 1.44758i
256256 0 0
257257 13.6117i 0.849073i 0.905411 + 0.424536i 0.139563π0.139563\pi
−0.905411 + 0.424536i 0.860437π0.860437\pi
258258 0 0
259259 1.73860 0.108031
260260 0 0
261261 −15.3815 −0.952090
262262 0 0
263263 4.11550i 0.253772i 0.991917 + 0.126886i 0.0404983π0.0404983\pi
−0.991917 + 0.126886i 0.959502π0.959502\pi
264264 0 0
265265 9.29028 + 10.0921i 0.570697 + 0.619950i
266266 0 0
267267 3.15510i 0.193089i
268268 0 0
269269 −10.7409 −0.654887 −0.327443 0.944871i 0.606187π-0.606187\pi
−0.327443 + 0.944871i 0.606187π0.606187\pi
270270 0 0
271271 −32.7438 −1.98904 −0.994521 0.104535i 0.966665π-0.966665\pi
−0.994521 + 0.104535i 0.966665π0.966665\pi
272272 0 0
273273 6.02587i 0.364702i
274274 0 0
275275 −0.567654 + 6.84950i −0.0342309 + 0.413041i
276276 0 0
277277 6.92623i 0.416157i 0.978112 + 0.208078i 0.0667209π0.0667209\pi
−0.978112 + 0.208078i 0.933279π0.933279\pi
278278 0 0
279279 17.3815 1.04060
280280 0 0
281281 −2.61209 −0.155824 −0.0779122 0.996960i 0.524825π-0.524825\pi
−0.0779122 + 0.996960i 0.524825π0.524825\pi
282282 0 0
283283 6.99972i 0.416090i −0.978119 0.208045i 0.933290π-0.933290\pi
0.978119 0.208045i 0.0667101π-0.0667101\pi
284284 0 0
285285 4.29487 + 4.66553i 0.254406 + 0.276362i
286286 0 0
287287 5.30855i 0.313354i
288288 0 0
289289 −31.2268 −1.83687
290290 0 0
291291 21.3063 1.24900
292292 0 0
293293 14.7099i 0.859362i 0.902981 + 0.429681i 0.141374π0.141374\pi
−0.902981 + 0.429681i 0.858626π0.858626\pi
294294 0 0
295295 −10.2997 + 9.48144i −0.599673 + 0.552031i
296296 0 0
297297 3.53207i 0.204952i
298298 0 0
299299 22.8078 1.31901
300300 0 0
301301 −7.83136 −0.451392
302302 0 0
303303 18.1345i 1.04180i
304304 0 0
305305 10.8560 9.99351i 0.621612 0.572227i
306306 0 0
307307 32.5567i 1.85811i −0.369942 0.929055i 0.620623π-0.620623\pi
0.369942 0.929055i 0.379377π-0.379377\pi
308308 0 0
309309 −28.9031 −1.64424
310310 0 0
311311 32.4065 1.83760 0.918802 0.394719i 0.129158π-0.129158\pi
0.918802 + 0.394719i 0.129158π0.129158\pi
312312 0 0
313313 21.2347i 1.20026i −0.799904 0.600128i 0.795116π-0.795116\pi
0.799904 0.600128i 0.204884π-0.204884\pi
314314 0 0
315315 −2.77284 3.01214i −0.156232 0.169715i
316316 0 0
317317 33.1847i 1.86384i 0.362667 + 0.931919i 0.381866π0.381866\pi
−0.362667 + 0.931919i 0.618134π0.618134\pi
318318 0 0
319319 −11.5478 −0.646555
320320 0 0
321321 −0.337282 −0.0188252
322322 0 0
323323 8.96040i 0.498570i
324324 0 0
325325 13.6612 + 1.13217i 0.757785 + 0.0628017i
326326 0 0
327327 18.1053i 1.00123i
328328 0 0
329329 3.48822 0.192312
330330 0 0
331331 −8.38585 −0.460928 −0.230464 0.973081i 0.574024π-0.574024\pi
−0.230464 + 0.973081i 0.574024π0.574024\pi
332332 0 0
333333 3.18326i 0.174442i
334334 0 0
335335 −2.51680 2.73401i −0.137507 0.149375i
336336 0 0
337337 8.59953i 0.468446i −0.972183 0.234223i 0.924745π-0.924745\pi
0.972183 0.234223i 0.0752546π-0.0752546\pi
338338 0 0
339339 24.2942 1.31948
340340 0 0
341341 13.0494 0.706663
342342 0 0
343343 1.00000i 0.0539949i
344344 0 0
345345 −30.0813 + 27.6915i −1.61952 + 1.49086i
346346 0 0
347347 5.37773i 0.288692i −0.989527 0.144346i 0.953892π-0.953892\pi
0.989527 0.144346i 0.0461078π-0.0461078\pi
348348 0 0
349349 11.1582 0.597284 0.298642 0.954365i 0.403466π-0.403466\pi
0.298642 + 0.954365i 0.403466π0.403466\pi
350350 0 0
351351 7.04463 0.376015
352352 0 0
353353 25.1040i 1.33615i −0.744093 0.668076i 0.767118π-0.767118\pi
0.744093 0.668076i 0.232882π-0.232882\pi
354354 0 0
355355 26.3610 24.2667i 1.39910 1.28794i
356356 0 0
357357 15.2637i 0.807841i
358358 0 0
359359 24.4545 1.29066 0.645329 0.763905i 0.276720π-0.276720\pi
0.645329 + 0.763905i 0.276720π0.276720\pi
360360 0 0
361361 −17.3352 −0.912378
362362 0 0
363363 20.0243i 1.05100i
364364 0 0
365365 3.23253 + 3.51151i 0.169198 + 0.183801i
366366 0 0
367367 22.6016i 1.17979i 0.807478 + 0.589897i 0.200832π0.200832\pi
−0.807478 + 0.589897i 0.799168π0.799168\pi
368368 0 0
369369 9.71962 0.505983
370370 0 0
371371 −6.13448 −0.318486
372372 0 0
373373 11.4377i 0.592221i 0.955154 + 0.296111i 0.0956897π0.0956897\pi
−0.955154 + 0.296111i 0.904310π0.904310\pi
374374 0 0
375375 −19.3924 + 15.0931i −1.00142 + 0.779405i
376376 0 0
377377 23.0319i 1.18620i
378378 0 0
379379 −22.5122 −1.15638 −0.578188 0.815904i 0.696240π-0.696240\pi
−0.578188 + 0.815904i 0.696240π0.696240\pi
380380 0 0
381381 17.0222 0.872072
382382 0 0
383383 20.0106i 1.02249i 0.859434 + 0.511247i 0.170816π0.170816\pi
−0.859434 + 0.511247i 0.829184π0.829184\pi
384384 0 0
385385 −2.08174 2.26140i −0.106095 0.115252i
386386 0 0
387387 14.3387i 0.728878i
388388 0 0
389389 22.5476 1.14321 0.571605 0.820529i 0.306321π-0.306321\pi
0.571605 + 0.820529i 0.306321π0.306321\pi
390390 0 0
391391 −57.7728 −2.92170
392392 0 0
393393 10.4452i 0.526892i
394394 0 0
395395 8.96818 8.25569i 0.451238 0.415389i
396396 0 0
397397 9.35871i 0.469700i 0.972032 + 0.234850i 0.0754599π0.0754599\pi
−0.972032 + 0.234850i 0.924540π0.924540\pi
398398 0 0
399399 −2.83595 −0.141975
400400 0 0
401401 −31.2475 −1.56042 −0.780212 0.625516i 0.784889π-0.784889\pi
−0.780212 + 0.625516i 0.784889π0.784889\pi
402402 0 0
403403 26.0266i 1.29648i
404404 0 0
405405 −18.3276 + 16.8716i −0.910707 + 0.838355i
406406 0 0
407407 2.38987i 0.118462i
408408 0 0
409409 28.0098 1.38499 0.692497 0.721421i 0.256511π-0.256511\pi
0.692497 + 0.721421i 0.256511π0.256511\pi
410410 0 0
411411 −40.2227 −1.98404
412412 0 0
413413 6.26070i 0.308069i
414414 0 0
415415 3.85612 + 4.18892i 0.189290 + 0.205626i
416416 0 0
417417 41.6223i 2.03825i
418418 0 0
419419 16.8212 0.821769 0.410885 0.911687i 0.365220π-0.365220\pi
0.410885 + 0.911687i 0.365220π0.365220\pi
420420 0 0
421421 −0.354309 −0.0172680 −0.00863398 0.999963i 0.502748π-0.502748\pi
−0.00863398 + 0.999963i 0.502748π0.502748\pi
422422 0 0
423423 6.38670i 0.310532i
424424 0 0
425425 −34.6041 2.86783i −1.67855 0.139110i
426426 0 0
427427 6.59883i 0.319340i
428428 0 0
429429 −8.28315 −0.399914
430430 0 0
431431 14.8578 0.715675 0.357837 0.933784i 0.383514π-0.383514\pi
0.357837 + 0.933784i 0.383514π0.383514\pi
432432 0 0
433433 13.6602i 0.656469i −0.944596 0.328235i 0.893546π-0.893546\pi
0.944596 0.328235i 0.106454π-0.106454\pi
434434 0 0
435435 −27.9635 30.3769i −1.34075 1.45646i
436436 0 0
437437 10.7340i 0.513477i
438438 0 0
439439 25.3663 1.21067 0.605334 0.795972i 0.293040π-0.293040\pi
0.605334 + 0.795972i 0.293040π0.293040\pi
440440 0 0
441441 1.83094 0.0871874
442442 0 0
443443 32.8555i 1.56101i 0.625148 + 0.780506i 0.285039π0.285039\pi
−0.625148 + 0.780506i 0.714961π0.714961\pi
444444 0 0
445445 −2.36157 + 2.17395i −0.111949 + 0.103055i
446446 0 0
447447 22.2332i 1.05160i
448448 0 0
449449 −34.2268 −1.61526 −0.807632 0.589687i 0.799251π-0.799251\pi
−0.807632 + 0.589687i 0.799251π0.799251\pi
450450 0 0
451451 7.29712 0.343608
452452 0 0
453453 1.24767i 0.0586206i
454454 0 0
455455 −4.51031 + 4.15198i −0.211447 + 0.194648i
456456 0 0
457457 21.8661i 1.02285i 0.859327 + 0.511427i 0.170883π0.170883\pi
−0.859327 + 0.511427i 0.829117π0.829117\pi
458458 0 0
459459 −17.8443 −0.832899
460460 0 0
461461 −32.8358 −1.52932 −0.764659 0.644436i 0.777092π-0.777092\pi
−0.764659 + 0.644436i 0.777092π0.777092\pi
462462 0 0
463463 20.9970i 0.975811i −0.872896 0.487906i 0.837761π-0.837761\pi
0.872896 0.487906i 0.162239π-0.162239\pi
464464 0 0
465465 31.5995 + 34.3267i 1.46539 + 1.59186i
466466 0 0
467467 9.88718i 0.457524i 0.973482 + 0.228762i 0.0734678π0.0734678\pi
−0.973482 + 0.228762i 0.926532π0.926532\pi
468468 0 0
469469 1.66187 0.0767381
470470 0 0
471471 −6.32000 −0.291210
472472 0 0
473473 10.7650i 0.494974i
474474 0 0
475475 −0.532833 + 6.42934i −0.0244481 + 0.294998i
476476 0 0
477477 11.2318i 0.514270i
478478 0 0
479479 −18.1115 −0.827534 −0.413767 0.910383i 0.635787π-0.635787\pi
−0.413767 + 0.910383i 0.635787π0.635787\pi
480480 0 0
481481 4.76654 0.217336
482482 0 0
483483 18.2850i 0.831996i
484484 0 0
485485 14.6806 + 15.9476i 0.666610 + 0.724141i
486486 0 0
487487 23.4907i 1.06447i −0.846597 0.532234i 0.821353π-0.821353\pi
0.846597 0.532234i 0.178647π-0.178647\pi
488488 0 0
489489 22.4656 1.01593
490490 0 0
491491 25.1693 1.13588 0.567938 0.823072i 0.307742π-0.307742\pi
0.567938 + 0.823072i 0.307742π0.307742\pi
492492 0 0
493493 58.3404i 2.62752i
494494 0 0
495495 4.14048 3.81153i 0.186101 0.171316i
496496 0 0
497497 16.0236i 0.718756i
498498 0 0
499499 17.5266 0.784601 0.392300 0.919837i 0.371679π-0.371679\pi
0.392300 + 0.919837i 0.371679π0.371679\pi
500500 0 0
501501 43.4471 1.94107
502502 0 0
503503 33.0352i 1.47297i −0.676456 0.736483i 0.736485π-0.736485\pi
0.676456 0.736483i 0.263515π-0.263515\pi
504504 0 0
505505 13.5735 12.4951i 0.604013 0.556026i
506506 0 0
507507 12.0527i 0.535278i
508508 0 0
509509 21.4535 0.950909 0.475455 0.879740i 0.342284π-0.342284\pi
0.475455 + 0.879740i 0.342284π0.342284\pi
510510 0 0
511511 −2.13448 −0.0944236
512512 0 0
513513 3.31541i 0.146379i
514514 0 0
515515 −19.9150 21.6337i −0.877559 0.953295i
516516 0 0
517517 4.79489i 0.210879i
518518 0 0
519519 −47.7569 −2.09630
520520 0 0
521521 23.4249 1.02626 0.513132 0.858310i 0.328485π-0.328485\pi
0.513132 + 0.858310i 0.328485π0.328485\pi
522522 0 0
523523 15.4736i 0.676611i −0.941036 0.338306i 0.890146π-0.890146\pi
0.941036 0.338306i 0.109854π-0.109854\pi
524524 0 0
525525 0.907662 10.9521i 0.0396136 0.477991i
526526 0 0
527527 65.9262i 2.87179i
528528 0 0
529529 −46.2083 −2.00906
530530 0 0
531531 11.4629 0.497449
532532 0 0
533533 14.5539i 0.630401i
534534 0 0
535535 −0.232396 0.252452i −0.0100473 0.0109145i
536536 0 0
537537 46.5108i 2.00709i
538538 0 0
539539 1.37460 0.0592081
540540 0 0
541541 −6.24274 −0.268396 −0.134198 0.990955i 0.542846π-0.542846\pi
−0.134198 + 0.990955i 0.542846π0.542846\pi
542542 0 0
543543 26.0227i 1.11674i
544544 0 0
545545 13.5517 12.4750i 0.580490 0.534372i
546546 0 0
547547 33.8997i 1.44945i −0.689040 0.724724i 0.741967π-0.741967\pi
0.689040 0.724724i 0.258033π-0.258033\pi
548548 0 0
549549 −12.0820 −0.515649
550550 0 0
551551 −10.8395 −0.461777
552552 0 0
553553 5.45132i 0.231814i
554554 0 0
555555 −6.28662 + 5.78717i −0.266852 + 0.245651i
556556 0 0
557557 0.161941i 0.00686165i −0.999994 0.00343083i 0.998908π-0.998908\pi
0.999994 0.00343083i 0.00109207π-0.00109207\pi
558558 0 0
559559 −21.4705 −0.908104
560560 0 0
561561 20.9814 0.885837
562562 0 0
563563 38.6514i 1.62896i 0.580189 + 0.814482i 0.302979π0.302979\pi
−0.580189 + 0.814482i 0.697021π0.697021\pi
564564 0 0
565565 16.7393 + 18.1840i 0.704228 + 0.765006i
566566 0 0
567567 11.1405i 0.467856i
568568 0 0
569569 26.9523 1.12990 0.564949 0.825126i 0.308896π-0.308896\pi
0.564949 + 0.825126i 0.308896π0.308896\pi
570570 0 0
571571 −24.2525 −1.01493 −0.507467 0.861671i 0.669418π-0.669418\pi
−0.507467 + 0.861671i 0.669418π0.669418\pi
572572 0 0
573573 4.00173i 0.167175i
574574 0 0
575575 −41.4536 3.43548i −1.72874 0.143269i
576576 0 0
577577 14.2848i 0.594684i 0.954771 + 0.297342i 0.0961001π0.0961001\pi
−0.954771 + 0.297342i 0.903900π0.903900\pi
578578 0 0
579579 −7.97347 −0.331366
580580 0 0
581581 −2.54624 −0.105636
582582 0 0
583583 8.43243i 0.349236i
584584 0 0
585585 −7.60201 8.25809i −0.314304 0.341430i
586586 0 0
587587 30.6314i 1.26429i −0.774849 0.632146i 0.782174π-0.782174\pi
0.774849 0.632146i 0.217826π-0.217826\pi
588588 0 0
589589 12.2489 0.504707
590590 0 0
591591 14.2730 0.587112
592592 0 0
593593 37.4568i 1.53817i −0.639149 0.769083i 0.720713π-0.720713\pi
0.639149 0.769083i 0.279287π-0.279287\pi
594594 0 0
595595 11.4248 10.5171i 0.468369 0.431159i
596596 0 0
597597 10.3115i 0.422022i
598598 0 0
599599 −18.9394 −0.773843 −0.386921 0.922113i 0.626462π-0.626462\pi
−0.386921 + 0.922113i 0.626462π0.626462\pi
600600 0 0
601601 −8.49158 −0.346379 −0.173189 0.984889i 0.555407π-0.555407\pi
−0.173189 + 0.984889i 0.555407π0.555407\pi
602602 0 0
603603 3.04278i 0.123911i
604604 0 0
605605 −14.9880 + 13.7973i −0.609349 + 0.560938i
606606 0 0
607607 23.4717i 0.952688i 0.879259 + 0.476344i 0.158038π0.158038\pi
−0.879259 + 0.476344i 0.841962π0.841962\pi
608608 0 0
609609 18.4646 0.748225
610610 0 0
611611 9.56329 0.386889
612612 0 0
613613 33.9078i 1.36952i 0.728767 + 0.684762i 0.240094π0.240094\pi
−0.728767 + 0.684762i 0.759906π0.759906\pi
614614 0 0
615615 17.6703 + 19.1953i 0.712534 + 0.774028i
616616 0 0
617617 23.7015i 0.954186i 0.878853 + 0.477093i 0.158310π0.158310\pi
−0.878853 + 0.477093i 0.841690π0.841690\pi
618618 0 0
619619 17.5275 0.704491 0.352246 0.935908i 0.385418π-0.385418\pi
0.352246 + 0.935908i 0.385418π0.385418\pi
620620 0 0
621621 −21.3763 −0.857803
622622 0 0
623623 1.43548i 0.0575113i
624624 0 0
625625 −24.6589 4.11550i −0.986357 0.164620i
626626 0 0
627627 3.89829i 0.155683i
628628 0 0
629629 −12.0738 −0.481413
630630 0 0
631631 13.9892 0.556902 0.278451 0.960450i 0.410179π-0.410179\pi
0.278451 + 0.960450i 0.410179π0.410179\pi
632632 0 0
633633 37.3998i 1.48651i
634634 0 0
635635 11.7287 + 12.7409i 0.465440 + 0.505609i
636636 0 0
637637 2.74160i 0.108626i
638638 0 0
639639 −29.3381 −1.16060
640640 0 0
641641 38.7939 1.53227 0.766133 0.642682i 0.222178π-0.222178\pi
0.766133 + 0.642682i 0.222178π0.222178\pi
642642 0 0
643643 40.9729i 1.61581i −0.589310 0.807907i 0.700600π-0.700600\pi
0.589310 0.807907i 0.299400π-0.299400\pi
644644 0 0
645645 28.3175 26.0678i 1.11500 1.02642i
646646 0 0
647647 7.17647i 0.282136i −0.990000 0.141068i 0.954946π-0.954946\pi
0.990000 0.141068i 0.0450536π-0.0450536\pi
648648 0 0
649649 8.60594 0.337813
650650 0 0
651651 −20.8655 −0.817785
652652 0 0
653653 21.6869i 0.848672i −0.905505 0.424336i 0.860508π-0.860508\pi
0.905505 0.424336i 0.139492π-0.139492\pi
654654 0 0
655655 −7.81817 + 7.19704i −0.305481 + 0.281211i
656656 0 0
657657 3.90809i 0.152469i
658658 0 0
659659 5.56012 0.216592 0.108296 0.994119i 0.465461π-0.465461\pi
0.108296 + 0.994119i 0.465461π0.465461\pi
660660 0 0
661661 −35.4543 −1.37901 −0.689507 0.724279i 0.742173π-0.742173\pi
−0.689507 + 0.724279i 0.742173π0.742173\pi
662662 0 0
663663 41.8470i 1.62520i
664664 0 0
665665 −1.95404 2.12268i −0.0757745 0.0823141i
666666 0 0
667667 69.8883i 2.70609i
668668 0 0
669669 20.6442 0.798149
670670 0 0
671671 −9.07073 −0.350172
672672 0 0
673673 28.8018i 1.11023i 0.831775 + 0.555114i 0.187325π0.187325\pi
−0.831775 + 0.555114i 0.812675π0.812675\pi
674674 0 0
675675 −12.8038 1.06112i −0.492817 0.0408424i
676676 0 0
677677 4.41481i 0.169675i 0.996395 + 0.0848375i 0.0270371π0.0270371\pi
−0.996395 + 0.0848375i 0.972963π0.972963\pi
678678 0 0
679679 −9.69375 −0.372012
680680 0 0
681681 31.4601 1.20555
682682 0 0
683683 29.9092i 1.14444i 0.820099 + 0.572221i 0.193918π0.193918\pi
−0.820099 + 0.572221i 0.806082π0.806082\pi
684684 0 0
685685 −27.7145 30.1063i −1.05892 1.15030i
686686 0 0
687687 19.3056i 0.736555i
688688 0 0
689689 −16.8183 −0.640726
690690 0 0
691691 2.79869 0.106467 0.0532337 0.998582i 0.483047π-0.483047\pi
0.0532337 + 0.998582i 0.483047π0.483047\pi
692692 0 0
693693 2.51680i 0.0956053i
694694 0 0
695695 31.1539 28.6788i 1.18174 1.08785i
696696 0 0
697697 36.8655i 1.39638i
698698 0 0
699699 −32.4648 −1.22793
700700 0 0
701701 −45.3081 −1.71126 −0.855632 0.517584i 0.826832π-0.826832\pi
−0.855632 + 0.517584i 0.826832π0.826832\pi
702702 0 0
703703 2.24327i 0.0846066i
704704 0 0
705705 −12.6131 + 11.6110i −0.475036 + 0.437296i
706706 0 0
707707 8.25067i 0.310298i
708708 0 0
709709 −11.2038 −0.420768 −0.210384 0.977619i 0.567471π-0.567471\pi
−0.210384 + 0.977619i 0.567471π0.567471\pi
710710 0 0
711711 −9.98102 −0.374318
712712 0 0
713713 78.9756i 2.95766i
714714 0 0
715715 −5.70730 6.19986i −0.213441 0.231862i
716716 0 0
717717 55.0639i 2.05640i
718718 0 0
719719 −22.1695 −0.826782 −0.413391 0.910554i 0.635656π-0.635656\pi
−0.413391 + 0.910554i 0.635656π0.635656\pi
720720 0 0
721721 13.1501 0.489735
722722 0 0
723723 7.31858i 0.272181i
724724 0 0
725725 3.46924 41.8609i 0.128844 1.55468i
726726 0 0
727727 17.4515i 0.647241i −0.946187 0.323620i 0.895100π-0.895100\pi
0.946187 0.323620i 0.104900π-0.104900\pi
728728 0 0
729729 3.45447 0.127943
730730 0 0
731731 54.3853 2.01151
732732 0 0
733733 26.0171i 0.960962i 0.877005 + 0.480481i 0.159538π0.159538\pi
−0.877005 + 0.480481i 0.840462π0.840462\pi
734734 0 0
735735 3.32864 + 3.61591i 0.122779 + 0.133375i
736736 0 0
737737 2.28440i 0.0841471i
738738 0 0
739739 −2.81093 −0.103402 −0.0517008 0.998663i 0.516464π-0.516464\pi
−0.0517008 + 0.998663i 0.516464π0.516464\pi
740740 0 0
741741 −7.77504 −0.285623
742742 0 0
743743 22.8466i 0.838159i 0.907950 + 0.419080i 0.137647π0.137647\pi
−0.907950 + 0.419080i 0.862353π0.862353\pi
744744 0 0
745745 −16.6414 + 15.3193i −0.609693 + 0.561255i
746746 0 0
747747 4.66200i 0.170574i
748748 0 0
749749 0.153454 0.00560707
750750 0 0
751751 −51.7651 −1.88893 −0.944467 0.328607i 0.893421π-0.893421\pi
−0.944467 + 0.328607i 0.893421π0.893421\pi
752752 0 0
753753 21.7406i 0.792271i
754754 0 0
755755 −0.933870 + 0.859677i −0.0339870 + 0.0312868i
756756 0 0
757757 8.13016i 0.295496i 0.989025 + 0.147748i 0.0472024π0.0472024\pi
−0.989025 + 0.147748i 0.952798π0.952798\pi
758758 0 0
759759 25.1345 0.912324
760760 0 0
761761 31.2494 1.13279 0.566395 0.824134i 0.308338π-0.308338\pi
0.566395 + 0.824134i 0.308338π0.308338\pi
762762 0 0
763763 8.23741i 0.298214i
764764 0 0
765765 19.2561 + 20.9180i 0.696206 + 0.756291i
766766 0 0
767767 17.1643i 0.619769i
768768 0 0
769769 −28.7711 −1.03751 −0.518757 0.854922i 0.673605π-0.673605\pi
−0.518757 + 0.854922i 0.673605π0.673605\pi
770770 0 0
771771 29.9176 1.07746
772772 0 0
773773 15.7175i 0.565318i 0.959220 + 0.282659i 0.0912165π0.0912165\pi
−0.959220 + 0.282659i 0.908783π0.908783\pi
774774 0 0
775775 −3.92033 + 47.3040i −0.140822 + 1.69921i
776776 0 0
777777 3.82133i 0.137089i
778778 0 0
779779 6.84950 0.245409
780780 0 0
781781 −22.0260 −0.788151
782782 0 0
783783 21.5864i 0.771434i
784784 0 0
785785 −4.35464 4.73046i −0.155424 0.168838i
786786 0 0
787787 28.8516i 1.02845i 0.857656 + 0.514224i 0.171920π0.171920\pi
−0.857656 + 0.514224i 0.828080π0.828080\pi
788788 0 0
789789 9.04561 0.322032
790790 0 0
791791 −11.0532 −0.393005
792792 0 0
793793 18.0914i 0.642443i
794794 0 0
795795 22.1817 20.4195i 0.786705 0.724204i
796796 0 0
797797 5.81776i 0.206076i −0.994677 0.103038i 0.967144π-0.967144\pi
0.994677 0.103038i 0.0328563π-0.0328563\pi
798798 0 0
799799 −24.2241 −0.856987
800800 0 0
801801 2.62827 0.0928655
802802 0 0
803803 2.93404i 0.103540i
804804 0 0
805805 13.6862 12.5988i 0.482374 0.444050i
806806 0 0
807807 23.6079i 0.831039i
808808 0 0
809809 −26.5157 −0.932242 −0.466121 0.884721i 0.654349π-0.654349\pi
−0.466121 + 0.884721i 0.654349π0.654349\pi
810810 0 0
811811 −55.5069 −1.94911 −0.974556 0.224144i 0.928041π-0.928041\pi
−0.974556 + 0.224144i 0.928041π0.928041\pi
812812 0 0
813813 71.9688i 2.52406i
814814 0 0
815815 15.4794 + 16.8153i 0.542220 + 0.589016i
816816 0 0
817817 10.1046i 0.353516i
818818 0 0
819819 5.01969 0.175402
820820 0 0
821821 −44.1325 −1.54024 −0.770118 0.637902i 0.779803π-0.779803\pi
−0.770118 + 0.637902i 0.779803π0.779803\pi
822822 0 0
823823 19.1816i 0.668629i 0.942461 + 0.334315i 0.108505π0.108505\pi
−0.942461 + 0.334315i 0.891495π0.891495\pi
824824 0 0
825825 15.0548 + 1.24767i 0.524141 + 0.0434383i
826826 0 0
827827 1.36085i 0.0473214i −0.999720 0.0236607i 0.992468π-0.992468\pi
0.999720 0.0236607i 0.00753214π-0.00753214\pi
828828 0 0
829829 −7.04654 −0.244737 −0.122368 0.992485i 0.539049π-0.539049\pi
−0.122368 + 0.992485i 0.539049π0.539049\pi
830830 0 0
831831 15.2234 0.528095
832832 0 0
833833 6.94455i 0.240615i
834834 0 0
835835 29.9362 + 32.5198i 1.03598 + 1.12539i
836836 0 0
837837 24.3932i 0.843151i
838838 0 0
839839 14.4808 0.499934 0.249967 0.968254i 0.419580π-0.419580\pi
0.249967 + 0.968254i 0.419580π0.419580\pi
840840 0 0
841841 41.5750 1.43362
842842 0 0
843843 5.74122i 0.197738i
844844 0 0
845845 9.02132 8.30461i 0.310343 0.285687i
846846 0 0
847847 9.11048i 0.313040i
848848 0 0
849849 −15.3850 −0.528011
850850 0 0
851851 −14.4637 −0.495808
852852 0 0
853853 13.3025i 0.455470i −0.973723 0.227735i 0.926868π-0.926868\pi
0.973723 0.227735i 0.0731319π-0.0731319\pi
854854 0 0
855855 3.88650 3.57773i 0.132915 0.122356i
856856 0 0
857857 36.0508i 1.23147i 0.787953 + 0.615736i 0.211141π0.211141\pi
−0.787953 + 0.615736i 0.788859π0.788859\pi
858858 0 0
859859 6.42934 0.219366 0.109683 0.993967i 0.465016π-0.465016\pi
0.109683 + 0.993967i 0.465016π0.465016\pi
860860 0 0
861861 −11.6679 −0.397640
862862 0 0
863863 2.28639i 0.0778295i −0.999243 0.0389148i 0.987610π-0.987610\pi
0.999243 0.0389148i 0.0123901π-0.0123901\pi
864864 0 0
865865 −32.9058 35.7457i −1.11883 1.21539i
866866 0 0
867867 68.6347i 2.33096i
868868 0 0
869869 −7.49337 −0.254195
870870 0 0
871871 4.55619 0.154380
872872 0 0
873873 17.7486i 0.600700i
874874 0 0
875875 8.82299 6.86694i 0.298272 0.232145i
876876 0 0
877877 28.7188i 0.969764i 0.874579 + 0.484882i 0.161138π0.161138\pi
−0.874579 + 0.484882i 0.838862π0.838862\pi
878878 0 0
879879 32.3315 1.09051
880880 0 0
881881 −36.4536 −1.22815 −0.614077 0.789246i 0.710472π-0.710472\pi
−0.614077 + 0.789246i 0.710472π0.710472\pi
882882 0 0
883883 22.6608i 0.762597i 0.924452 + 0.381298i 0.124523π0.124523\pi
−0.924452 + 0.381298i 0.875477π0.875477\pi
884884 0 0
885885 20.8396 + 22.6382i 0.700516 + 0.760973i
886886 0 0
887887 13.7308i 0.461035i −0.973068 0.230517i 0.925958π-0.925958\pi
0.973068 0.230517i 0.0740418π-0.0740418\pi
888888 0 0
889889 −7.74460 −0.259746
890890 0 0
891891 15.3137 0.513027
892892 0 0
893893 4.50076i 0.150612i
894894 0 0
895895 34.8129 32.0472i 1.16367 1.07122i
896896 0 0
897897 50.1301i 1.67380i
898898 0 0
899899 −79.7516 −2.65986
900900 0 0
901901 42.6012 1.41925
902902 0 0
903903 17.2128i 0.572808i
904904 0 0
905905 19.4778 17.9303i 0.647464 0.596025i
906906 0 0
907907 48.7472i 1.61863i 0.587378 + 0.809313i 0.300160π0.300160\pi
−0.587378 + 0.809313i 0.699840π0.699840\pi
908908 0 0
909909 −15.1064 −0.501049
910910 0 0
911911 54.1839 1.79519 0.897596 0.440820i 0.145312π-0.145312\pi
0.897596 + 0.440820i 0.145312π0.145312\pi
912912 0 0
913913 3.50006i 0.115835i
914914 0 0
915915 −21.9651 23.8608i −0.726145 0.788814i
916916 0 0
917917 4.75228i 0.156934i
918918 0 0
919919 29.3450 0.968003 0.484002 0.875067i 0.339183π-0.339183\pi
0.484002 + 0.875067i 0.339183π0.339183\pi
920920 0 0
921921 −71.5577 −2.35790
922922 0 0
923923 43.9303i 1.44598i
924924 0 0
925925 −8.66329 0.717972i −0.284847 0.0236068i
926926 0 0
927927 24.0770i 0.790791i
928928 0 0
929929 −36.9346 −1.21179 −0.605893 0.795546i 0.707184π-0.707184\pi
−0.605893 + 0.795546i 0.707184π0.707184\pi
930930 0 0
931931 1.29028 0.0422871
932932 0 0
933933 71.2275i 2.33188i
934934 0 0
935935 14.4568 + 15.7044i 0.472787 + 0.513590i
936936 0 0
937937 19.3625i 0.632544i −0.948668 0.316272i 0.897569π-0.897569\pi
0.948668 0.316272i 0.102431π-0.102431\pi
938938 0 0
939939 −46.6726 −1.52310
940940 0 0
941941 −13.6807 −0.445979 −0.222990 0.974821i 0.571582π-0.571582\pi
−0.222990 + 0.974821i 0.571582π0.571582\pi
942942 0 0
943943 44.1627i 1.43813i
944944 0 0
945945 4.22724 3.89140i 0.137512 0.126587i
946946 0 0
947947 12.0479i 0.391504i −0.980653 0.195752i 0.937285π-0.937285\pi
0.980653 0.195752i 0.0627147π-0.0627147\pi
948948 0 0
949949 −5.85188 −0.189960
950950 0 0
951951 72.9379 2.36517
952952 0 0
953953 34.6708i 1.12310i 0.827443 + 0.561549i 0.189794π0.189794\pi
−0.827443 + 0.561549i 0.810206π0.810206\pi
954954 0 0
955955 2.99526 2.75730i 0.0969244 0.0892241i
956956 0 0
957957 25.3815i 0.820466i
958958 0 0
959959 18.3002 0.590943
960960 0 0
961961 59.1214 1.90714
962962 0 0
963963 0.280964i 0.00905393i
964964 0 0
965965 −5.49393 5.96808i −0.176856 0.192119i
966966 0 0
967967 27.6483i 0.889111i 0.895751 + 0.444555i 0.146638π0.146638\pi
−0.895751 + 0.444555i 0.853362π0.853362\pi
968968 0 0
969969 19.6944 0.632675
970970 0 0
971971 50.6217 1.62453 0.812264 0.583290i 0.198235π-0.198235\pi
0.812264 + 0.583290i 0.198235π0.198235\pi
972972 0 0
973973 18.9370i 0.607091i
974974 0 0
975975 2.48845 30.0264i 0.0796941 0.961615i
976976 0 0
977977 27.3458i 0.874869i −0.899250 0.437435i 0.855887π-0.855887\pi
0.899250 0.437435i 0.144113π-0.144113\pi
978978 0 0
979979 1.97321 0.0630640
980980 0 0
981981 −15.0822 −0.481536
982982 0 0
983983 32.6694i 1.04199i −0.853559 0.520996i 0.825561π-0.825561\pi
0.853559 0.520996i 0.174439π-0.174439\pi
984984 0 0
985985 9.83445 + 10.6832i 0.313352 + 0.340395i
986986 0 0
987987 7.66688i 0.244040i
988988 0 0
989989 65.1503 2.07166
990990 0 0
991991 4.85330 0.154170 0.0770850 0.997025i 0.475439π-0.475439\pi
0.0770850 + 0.997025i 0.475439π0.475439\pi
992992 0 0
993993 18.4316i 0.584909i
994994 0 0
995995 7.71808 7.10490i 0.244680 0.225240i
996996 0 0
997997 41.2053i 1.30498i 0.757796 + 0.652492i 0.226276π0.226276\pi
−0.757796 + 0.652492i 0.773724π0.773724\pi
998998 0 0
999999 −4.46738 −0.141342
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 1120.2.g.b.449.2 10
4.3 odd 2 1120.2.g.c.449.9 yes 10
5.2 odd 4 5600.2.a.bw.1.1 5
5.3 odd 4 5600.2.a.bu.1.5 5
5.4 even 2 inner 1120.2.g.b.449.9 yes 10
8.3 odd 2 2240.2.g.n.449.2 10
8.5 even 2 2240.2.g.o.449.9 10
20.3 even 4 5600.2.a.bx.1.1 5
20.7 even 4 5600.2.a.bv.1.5 5
20.19 odd 2 1120.2.g.c.449.2 yes 10
40.19 odd 2 2240.2.g.n.449.9 10
40.29 even 2 2240.2.g.o.449.2 10
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1120.2.g.b.449.2 10 1.1 even 1 trivial
1120.2.g.b.449.9 yes 10 5.4 even 2 inner
1120.2.g.c.449.2 yes 10 20.19 odd 2
1120.2.g.c.449.9 yes 10 4.3 odd 2
2240.2.g.n.449.2 10 8.3 odd 2
2240.2.g.n.449.9 10 40.19 odd 2
2240.2.g.o.449.2 10 40.29 even 2
2240.2.g.o.449.9 10 8.5 even 2
5600.2.a.bu.1.5 5 5.3 odd 4
5600.2.a.bv.1.5 5 20.7 even 4
5600.2.a.bw.1.1 5 5.2 odd 4
5600.2.a.bx.1.1 5 20.3 even 4