Properties

Label 400.2.bi.b.223.1
Level 400400
Weight 22
Character 400.223
Analytic conductor 3.1943.194
Analytic rank 00
Dimension 1616
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [400,2,Mod(47,400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(400, base_ring=CyclotomicField(20))
 
chi = DirichletCharacter(H, H._module([10, 0, 17]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("400.47");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 400=2452 400 = 2^{4} \cdot 5^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 400.bi (of order 2020, degree 88, 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: 3.194016080853.19401608085
Analytic rank: 00
Dimension: 1616
Relative dimension: 22 over Q(ζ20)\Q(\zeta_{20})
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x168x15+52x14224x13+806x122288x11+5530x1011062x9++521 x^{16} - 8 x^{15} + 52 x^{14} - 224 x^{13} + 806 x^{12} - 2288 x^{11} + 5530 x^{10} - 11062 x^{9} + \cdots + 521 Copy content Toggle raw display
Coefficient ring: Z[a1,,a9]\Z[a_1, \ldots, a_{9}]
Coefficient ring index: 24 2^{4}
Twist minimal: yes
Sato-Tate group: SU(2)[C20]\mathrm{SU}(2)[C_{20}]

Embedding invariants

Embedding label 223.1
Root 0.5000000.509304i0.500000 - 0.509304i of defining polynomial
Character χ\chi == 400.223
Dual form 400.2.bi.b.287.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.6480131.27180i)q3+(0.1669772.22982i)q5+(2.92911+2.92911i)q7+(0.5658080.778768i)q9+(2.25687+3.10632i)q11+(0.6453224.07440i)q13+(2.94409+1.23259i)q15+(0.2600740.132514i)q17+(2.419107.44523i)q19+(1.827145.62334i)q21+(0.2406361.51932i)q23+(4.944240.744661i)q25+(5.586480.884812i)q27+(5.30751+1.72451i)q29+(1.449000.470809i)q31+(2.488124.88322i)q33+(7.020516.04232i)q35+(2.98459+0.472712i)q37+(4.76364+3.46098i)q39+(5.49614+3.99318i)q41+(7.55900+7.55900i)q43+(1.642041.39169i)q45+(2.057811.04851i)q47+10.1594iq49+0.416632iq51+(7.080973.60793i)q53+(7.303394.51375i)q55+(7.90122+7.90122i)q57+(10.1729+7.39105i)q59+(5.630434.09075i)q61+(3.938420.623784i)q63+(9.19296+0.758621i)q65+(4.04794+7.94452i)q67+(2.08820+0.678497i)q69+(6.637362.15661i)q71+(14.83332.34937i)q73+(2.25687+6.77062i)q75+(2.48812+15.7094i)q77+(0.8159632.51127i)q79+(1.60242+4.93175i)q81+(2.281101.16228i)q83+(0.338910+0.557791i)q85+(1.246107.86758i)q87+(6.85369+9.43329i)q89+(10.044213.8246i)q91+(1.537751.53775i)q93+(17.0055+4.15099i)q95+(1.71702+3.36984i)q97+3.69606q99+O(q100)q+(-0.648013 - 1.27180i) q^{3} +(0.166977 - 2.22982i) q^{5} +(2.92911 + 2.92911i) q^{7} +(0.565808 - 0.778768i) q^{9} +(2.25687 + 3.10632i) q^{11} +(-0.645322 - 4.07440i) q^{13} +(-2.94409 + 1.23259i) q^{15} +(-0.260074 - 0.132514i) q^{17} +(-2.41910 - 7.44523i) q^{19} +(1.82714 - 5.62334i) q^{21} +(0.240636 - 1.51932i) q^{23} +(-4.94424 - 0.744661i) q^{25} +(-5.58648 - 0.884812i) q^{27} +(5.30751 + 1.72451i) q^{29} +(1.44900 - 0.470809i) q^{31} +(2.48812 - 4.88322i) q^{33} +(7.02051 - 6.04232i) q^{35} +(-2.98459 + 0.472712i) q^{37} +(-4.76364 + 3.46098i) q^{39} +(5.49614 + 3.99318i) q^{41} +(-7.55900 + 7.55900i) q^{43} +(-1.64204 - 1.39169i) q^{45} +(2.05781 - 1.04851i) q^{47} +10.1594i q^{49} +0.416632i q^{51} +(7.08097 - 3.60793i) q^{53} +(7.30339 - 4.51375i) q^{55} +(-7.90122 + 7.90122i) q^{57} +(10.1729 + 7.39105i) q^{59} +(5.63043 - 4.09075i) q^{61} +(3.93842 - 0.623784i) q^{63} +(-9.19296 + 0.758621i) q^{65} +(-4.04794 + 7.94452i) q^{67} +(-2.08820 + 0.678497i) q^{69} +(-6.63736 - 2.15661i) q^{71} +(-14.8333 - 2.34937i) q^{73} +(2.25687 + 6.77062i) q^{75} +(-2.48812 + 15.7094i) q^{77} +(0.815963 - 2.51127i) q^{79} +(1.60242 + 4.93175i) q^{81} +(-2.28110 - 1.16228i) q^{83} +(-0.338910 + 0.557791i) q^{85} +(-1.24610 - 7.86758i) q^{87} +(6.85369 + 9.43329i) q^{89} +(10.0442 - 13.8246i) q^{91} +(-1.53775 - 1.53775i) q^{93} +(-17.0055 + 4.15099i) q^{95} +(1.71702 + 3.36984i) q^{97} +3.69606 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q20q9+20q1720q2120q25+20q29+60q3320q37+28q4120q45+60q5320q5712q6120q6580q6940q7360q77+56q81++40q97+O(q100) 16 q - 20 q^{9} + 20 q^{17} - 20 q^{21} - 20 q^{25} + 20 q^{29} + 60 q^{33} - 20 q^{37} + 28 q^{41} - 20 q^{45} + 60 q^{53} - 20 q^{57} - 12 q^{61} - 20 q^{65} - 80 q^{69} - 40 q^{73} - 60 q^{77} + 56 q^{81}+ \cdots + 40 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/400Z)×\left(\mathbb{Z}/400\mathbb{Z}\right)^\times.

nn 101101 177177 351351
χ(n)\chi(n) 11 e(1120)e\left(\frac{11}{20}\right) 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 −0.648013 1.27180i −0.374131 0.734273i 0.624787 0.780795i 0.285186π-0.285186\pi
−0.998917 + 0.0465230i 0.985186π0.985186\pi
44 0 0
55 0.166977 2.22982i 0.0746746 0.997208i
66 0 0
77 2.92911 + 2.92911i 1.10710 + 1.10710i 0.993530 + 0.113571i 0.0362291π0.0362291\pi
0.113571 + 0.993530i 0.463771π0.463771\pi
88 0 0
99 0.565808 0.778768i 0.188603 0.259589i
1010 0 0
1111 2.25687 + 3.10632i 0.680473 + 0.936590i 0.999939 0.0110072i 0.00350377π-0.00350377\pi
−0.319467 + 0.947597i 0.603504π0.603504\pi
1212 0 0
1313 −0.645322 4.07440i −0.178980 1.13004i −0.899603 0.436708i 0.856144π-0.856144\pi
0.720623 0.693327i 0.243856π-0.243856\pi
1414 0 0
1515 −2.94409 + 1.23259i −0.760160 + 0.318254i
1616 0 0
1717 −0.260074 0.132514i −0.0630771 0.0321394i 0.422167 0.906518i 0.361269π-0.361269\pi
−0.485245 + 0.874378i 0.661269π0.661269\pi
1818 0 0
1919 −2.41910 7.44523i −0.554980 1.70805i −0.695996 0.718046i 0.745037π-0.745037\pi
0.141016 0.990007i 0.454963π-0.454963\pi
2020 0 0
2121 1.82714 5.62334i 0.398714 1.22711i
2222 0 0
2323 0.240636 1.51932i 0.0501761 0.316799i −0.949816 0.312809i 0.898730π-0.898730\pi
0.999992 0.00399005i 0.00127008π-0.00127008\pi
2424 0 0
2525 −4.94424 0.744661i −0.988847 0.148932i
2626 0 0
2727 −5.58648 0.884812i −1.07512 0.170282i
2828 0 0
2929 5.30751 + 1.72451i 0.985580 + 0.320234i 0.757089 0.653312i 0.226621π-0.226621\pi
0.228491 + 0.973546i 0.426621π0.426621\pi
3030 0 0
3131 1.44900 0.470809i 0.260248 0.0845598i −0.175987 0.984393i 0.556312π-0.556312\pi
0.436235 + 0.899833i 0.356312π0.356312\pi
3232 0 0
3333 2.48812 4.88322i 0.433127 0.850059i
3434 0 0
3535 7.02051 6.04232i 1.18668 1.02134i
3636 0 0
3737 −2.98459 + 0.472712i −0.490663 + 0.0777134i −0.396863 0.917878i 0.629901π-0.629901\pi
−0.0937997 + 0.995591i 0.529901π0.529901\pi
3838 0 0
3939 −4.76364 + 3.46098i −0.762792 + 0.554201i
4040 0 0
4141 5.49614 + 3.99318i 0.858353 + 0.623630i 0.927436 0.373981i 0.122007π-0.122007\pi
−0.0690833 + 0.997611i 0.522007π0.522007\pi
4242 0 0
4343 −7.55900 + 7.55900i −1.15274 + 1.15274i −0.166736 + 0.986002i 0.553323π0.553323\pi
−0.986002 + 0.166736i 0.946677π0.946677\pi
4444 0 0
4545 −1.64204 1.39169i −0.244781 0.207461i
4646 0 0
4747 2.05781 1.04851i 0.300163 0.152941i −0.297423 0.954746i 0.596127π-0.596127\pi
0.597585 + 0.801805i 0.296127π0.296127\pi
4848 0 0
4949 10.1594i 1.45135i
5050 0 0
5151 0.416632i 0.0583401i
5252 0 0
5353 7.08097 3.60793i 0.972645 0.495588i 0.105921 0.994375i 0.466221π-0.466221\pi
0.866725 + 0.498787i 0.166221π0.166221\pi
5454 0 0
5555 7.30339 4.51375i 0.984789 0.608633i
5656 0 0
5757 −7.90122 + 7.90122i −1.04654 + 1.04654i
5858 0 0
5959 10.1729 + 7.39105i 1.32440 + 0.962233i 0.999866 + 0.0163593i 0.00520757π0.00520757\pi
0.324534 + 0.945874i 0.394792π0.394792\pi
6060 0 0
6161 5.63043 4.09075i 0.720903 0.523766i −0.165770 0.986164i 0.553011π-0.553011\pi
0.886672 + 0.462398i 0.153011π0.153011\pi
6262 0 0
6363 3.93842 0.623784i 0.496194 0.0785894i
6464 0 0
6565 −9.19296 + 0.758621i −1.14025 + 0.0940954i
6666 0 0
6767 −4.04794 + 7.94452i −0.494534 + 0.970578i 0.499986 + 0.866033i 0.333338π0.333338\pi
−0.994520 + 0.104545i 0.966662π0.966662\pi
6868 0 0
6969 −2.08820 + 0.678497i −0.251389 + 0.0816814i
7070 0 0
7171 −6.63736 2.15661i −0.787710 0.255942i −0.112581 0.993643i 0.535912π-0.535912\pi
−0.675129 + 0.737700i 0.735912π0.735912\pi
7272 0 0
7373 −14.8333 2.34937i −1.73611 0.274973i −0.793427 0.608665i 0.791705π-0.791705\pi
−0.942682 + 0.333693i 0.891705π0.891705\pi
7474 0 0
7575 2.25687 + 6.77062i 0.260601 + 0.781804i
7676 0 0
7777 −2.48812 + 15.7094i −0.283548 + 1.79025i
7878 0 0
7979 0.815963 2.51127i 0.0918030 0.282540i −0.894604 0.446859i 0.852543π-0.852543\pi
0.986407 + 0.164319i 0.0525425π0.0525425\pi
8080 0 0
8181 1.60242 + 4.93175i 0.178047 + 0.547972i
8282 0 0
8383 −2.28110 1.16228i −0.250383 0.127577i 0.324295 0.945956i 0.394873π-0.394873\pi
−0.574679 + 0.818379i 0.694873π0.694873\pi
8484 0 0
8585 −0.338910 + 0.557791i −0.0367599 + 0.0605010i
8686 0 0
8787 −1.24610 7.86758i −0.133596 0.843493i
8888 0 0
8989 6.85369 + 9.43329i 0.726490 + 0.999927i 0.999283 + 0.0378546i 0.0120524π0.0120524\pi
−0.272794 + 0.962073i 0.587948π0.587948\pi
9090 0 0
9191 10.0442 13.8246i 1.05291 1.44921i
9292 0 0
9393 −1.53775 1.53775i −0.159457 0.159457i
9494 0 0
9595 −17.0055 + 4.15099i −1.74473 + 0.425882i
9696 0 0
9797 1.71702 + 3.36984i 0.174337 + 0.342155i 0.961597 0.274466i 0.0885011π-0.0885011\pi
−0.787260 + 0.616621i 0.788501π0.788501\pi
9898 0 0
9999 3.69606 0.371468
100100 0 0
101101 11.8096 1.17510 0.587551 0.809187i 0.300092π-0.300092\pi
0.587551 + 0.809187i 0.300092π0.300092\pi
102102 0 0
103103 2.75616 + 5.40928i 0.271573 + 0.532992i 0.986006 0.166712i 0.0533151π-0.0533151\pi
−0.714433 + 0.699704i 0.753315π0.753315\pi
104104 0 0
105105 −12.2340 5.01316i −1.19391 0.489235i
106106 0 0
107107 −2.65974 2.65974i −0.257127 0.257127i 0.566758 0.823884i 0.308198π-0.308198\pi
−0.823884 + 0.566758i 0.808198π0.808198\pi
108108 0 0
109109 −2.79215 + 3.84307i −0.267440 + 0.368099i −0.921523 0.388323i 0.873054π-0.873054\pi
0.654084 + 0.756422i 0.273054π0.273054\pi
110110 0 0
111111 2.53525 + 3.48947i 0.240635 + 0.331206i
112112 0 0
113113 1.61719 + 10.2106i 0.152133 + 0.960528i 0.939128 + 0.343569i 0.111636π0.111636\pi
−0.786995 + 0.616960i 0.788364π0.788364\pi
114114 0 0
115115 −3.34763 0.790268i −0.312168 0.0736929i
116116 0 0
117117 −3.53814 1.80277i −0.327101 0.166666i
118118 0 0
119119 −0.373636 1.14993i −0.0342512 0.105414i
120120 0 0
121121 −1.15655 + 3.55951i −0.105141 + 0.323592i
122122 0 0
123123 1.51694 9.57761i 0.136778 0.863584i
124124 0 0
125125 −2.48604 + 10.9004i −0.222358 + 0.974965i
126126 0 0
127127 9.12441 + 1.44516i 0.809660 + 0.128238i 0.547520 0.836792i 0.315572π-0.315572\pi
0.262140 + 0.965030i 0.415572π0.415572\pi
128128 0 0
129129 14.5119 + 4.71519i 1.27770 + 0.415149i
130130 0 0
131131 −20.0702 + 6.52122i −1.75355 + 0.569761i −0.996499 0.0836006i 0.973358π-0.973358\pi
−0.757046 + 0.653362i 0.773358π0.773358\pi
132132 0 0
133133 14.7221 28.8938i 1.27657 2.50541i
134134 0 0
135135 −2.90579 + 12.3091i −0.250091 + 1.05940i
136136 0 0
137137 −7.25033 + 1.14834i −0.619437 + 0.0981092i −0.458263 0.888817i 0.651528π-0.651528\pi
−0.161174 + 0.986926i 0.551528π0.551528\pi
138138 0 0
139139 −8.32767 + 6.05041i −0.706344 + 0.513189i −0.881992 0.471264i 0.843798π-0.843798\pi
0.175648 + 0.984453i 0.443798π0.443798\pi
140140 0 0
141141 −2.66698 1.93767i −0.224600 0.163181i
142142 0 0
143143 11.2000 11.2000i 0.936589 0.936589i
144144 0 0
145145 4.73160 11.5469i 0.392938 0.958914i
146146 0 0
147147 12.9207 6.58344i 1.06568 0.542993i
148148 0 0
149149 11.8576i 0.971416i 0.874121 + 0.485708i 0.161438π0.161438\pi
−0.874121 + 0.485708i 0.838562π0.838562\pi
150150 0 0
151151 13.0162i 1.05925i 0.848233 + 0.529624i 0.177667π0.177667\pi
−0.848233 + 0.529624i 0.822333π0.822333\pi
152152 0 0
153153 −0.250349 + 0.127559i −0.0202396 + 0.0103126i
154154 0 0
155155 −0.807871 3.30963i −0.0648898 0.265836i
156156 0 0
157157 −2.52932 + 2.52932i −0.201861 + 0.201861i −0.800797 0.598936i 0.795590π-0.795590\pi
0.598936 + 0.800797i 0.295590π0.295590\pi
158158 0 0
159159 −9.17712 6.66757i −0.727793 0.528772i
160160 0 0
161161 5.15510 3.74540i 0.406279 0.295179i
162162 0 0
163163 14.3738 2.27659i 1.12584 0.178316i 0.434382 0.900729i 0.356967π-0.356967\pi
0.691463 + 0.722412i 0.256967π0.256967\pi
164164 0 0
165165 −10.4733 6.36347i −0.815342 0.495395i
166166 0 0
167167 3.25120 6.38084i 0.251586 0.493765i −0.730327 0.683097i 0.760632π-0.760632\pi
0.981913 + 0.189333i 0.0606325π0.0606325\pi
168168 0 0
169169 −3.82057 + 1.24138i −0.293890 + 0.0954907i
170170 0 0
171171 −7.16686 2.32865i −0.548063 0.178077i
172172 0 0
173173 −7.30401 1.15684i −0.555313 0.0879530i −0.127531 0.991835i 0.540705π-0.540705\pi
−0.427783 + 0.903882i 0.640705π0.640705\pi
174174 0 0
175175 −12.3010 16.6634i −0.929871 1.25964i
176176 0 0
177177 2.80774 17.7274i 0.211043 1.33247i
178178 0 0
179179 −1.32026 + 4.06333i −0.0986805 + 0.303707i −0.988195 0.153199i 0.951042π-0.951042\pi
0.889515 + 0.456906i 0.151042π0.151042\pi
180180 0 0
181181 −5.03463 15.4950i −0.374221 1.15173i −0.944003 0.329938i 0.892972π-0.892972\pi
0.569782 0.821796i 0.307028π-0.307028\pi
182182 0 0
183183 −8.85119 4.50991i −0.654299 0.333382i
184184 0 0
185185 0.555707 + 6.73404i 0.0408564 + 0.495096i
186186 0 0
187187 −0.175322 1.10694i −0.0128208 0.0809474i
188188 0 0
189189 −13.7717 18.9552i −1.00175 1.37878i
190190 0 0
191191 −0.396240 + 0.545378i −0.0286709 + 0.0394622i −0.823112 0.567879i 0.807764π-0.807764\pi
0.794441 + 0.607341i 0.207764π0.207764\pi
192192 0 0
193193 −1.94252 1.94252i −0.139826 0.139826i 0.633729 0.773555i 0.281523π-0.281523\pi
−0.773555 + 0.633729i 0.781523π0.781523\pi
194194 0 0
195195 6.92197 + 11.2000i 0.495692 + 0.802047i
196196 0 0
197197 3.35301 + 6.58064i 0.238892 + 0.468852i 0.979060 0.203570i 0.0652544π-0.0652544\pi
−0.740169 + 0.672421i 0.765254π0.765254\pi
198198 0 0
199199 5.25484 0.372505 0.186253 0.982502i 0.440366π-0.440366\pi
0.186253 + 0.982502i 0.440366π0.440366\pi
200200 0 0
201201 12.7269 0.897689
202202 0 0
203203 10.4950 + 20.5976i 0.736605 + 1.44567i
204204 0 0
205205 9.82182 11.5887i 0.685986 0.809387i
206206 0 0
207207 −1.04704 1.04704i −0.0727744 0.0727744i
208208 0 0
209209 17.6677 24.3174i 1.22210 1.68207i
210210 0 0
211211 4.76815 + 6.56279i 0.328253 + 0.451801i 0.940964 0.338505i 0.109921π-0.109921\pi
−0.612712 + 0.790307i 0.709921π0.709921\pi
212212 0 0
213213 1.55833 + 9.83889i 0.106775 + 0.674149i
214214 0 0
215215 15.5931 + 18.1174i 1.06344 + 1.23560i
216216 0 0
217217 5.62334 + 2.86524i 0.381738 + 0.194505i
218218 0 0
219219 6.62427 + 20.3874i 0.447627 + 1.37765i
220220 0 0
221221 −0.372084 + 1.14516i −0.0250291 + 0.0770317i
222222 0 0
223223 −0.586047 + 3.70015i −0.0392446 + 0.247781i −0.999510 0.0313086i 0.990033π-0.990033\pi
0.960265 + 0.279089i 0.0900325π0.0900325\pi
224224 0 0
225225 −3.37741 + 3.42908i −0.225161 + 0.228605i
226226 0 0
227227 −9.19209 1.45588i −0.610101 0.0966304i −0.156264 0.987715i 0.549945π-0.549945\pi
−0.453837 + 0.891085i 0.649945π0.649945\pi
228228 0 0
229229 5.57028 + 1.80989i 0.368094 + 0.119601i 0.487223 0.873278i 0.338010π-0.338010\pi
−0.119128 + 0.992879i 0.538010π0.538010\pi
230230 0 0
231231 21.5915 7.01551i 1.42062 0.461587i
232232 0 0
233233 3.76580 7.39079i 0.246706 0.484187i −0.734134 0.679005i 0.762412π-0.762412\pi
0.980839 + 0.194818i 0.0624116π0.0624116\pi
234234 0 0
235235 −1.99438 4.76364i −0.130099 0.310745i
236236 0 0
237237 −3.72259 + 0.589600i −0.241808 + 0.0382986i
238238 0 0
239239 20.0914 14.5973i 1.29961 0.944219i 0.299654 0.954048i 0.403129π-0.403129\pi
0.999952 + 0.00982862i 0.00312860π0.00312860\pi
240240 0 0
241241 −5.83422 4.23881i −0.375815 0.273046i 0.383803 0.923415i 0.374614π-0.374614\pi
−0.759618 + 0.650369i 0.774614π0.774614\pi
242242 0 0
243243 −6.76464 + 6.76464i −0.433952 + 0.433952i
244244 0 0
245245 22.6537 + 1.69639i 1.44729 + 0.108379i
246246 0 0
247247 −28.7738 + 14.6610i −1.83083 + 0.932855i
248248 0 0
249249 3.65427i 0.231580i
250250 0 0
251251 29.3481i 1.85244i −0.376988 0.926218i 0.623040π-0.623040\pi
0.376988 0.926218i 0.376960π-0.376960\pi
252252 0 0
253253 5.26257 2.68141i 0.330855 0.168579i
254254 0 0
255255 0.929016 + 0.0695681i 0.0581772 + 0.00435652i
256256 0 0
257257 16.1302 16.1302i 1.00617 1.00617i 0.00619398 0.999981i 0.498028π-0.498028\pi
0.999981 0.00619398i 0.00197162π-0.00197162\pi
258258 0 0
259259 −10.1268 7.35757i −0.629250 0.457177i
260260 0 0
261261 4.34603 3.15757i 0.269012 0.195449i
262262 0 0
263263 −21.4105 + 3.39109i −1.32023 + 0.209103i −0.776478 0.630145i 0.782995π-0.782995\pi
−0.543749 + 0.839248i 0.682995π0.682995\pi
264264 0 0
265265 −6.86269 16.3918i −0.421572 1.00694i
266266 0 0
267267 7.55596 14.8294i 0.462417 0.907545i
268268 0 0
269269 −28.4092 + 9.23070i −1.73214 + 0.562806i −0.993756 0.111577i 0.964410π-0.964410\pi
−0.738382 + 0.674382i 0.764410π0.764410\pi
270270 0 0
271271 −16.2853 5.29141i −0.989261 0.321430i −0.230694 0.973026i 0.574100π-0.574100\pi
−0.758566 + 0.651596i 0.774100π0.774100\pi
272272 0 0
273273 −24.0909 3.81562i −1.45804 0.230932i
274274 0 0
275275 −8.84536 17.0390i −0.533395 1.02749i
276276 0 0
277277 −1.85546 + 11.7149i −0.111484 + 0.703882i 0.867115 + 0.498107i 0.165971π0.165971\pi
−0.978599 + 0.205775i 0.934029π0.934029\pi
278278 0 0
279279 0.453206 1.39482i 0.0271327 0.0835059i
280280 0 0
281281 5.76571 + 17.7450i 0.343953 + 1.05858i 0.962142 + 0.272549i 0.0878668π0.0878668\pi
−0.618189 + 0.786030i 0.712133π0.712133\pi
282282 0 0
283283 −14.0251 7.14616i −0.833708 0.424795i −0.0156126 0.999878i 0.504970π-0.504970\pi
−0.818095 + 0.575083i 0.804970π0.804970\pi
284284 0 0
285285 16.2990 + 18.9377i 0.965469 + 1.12177i
286286 0 0
287287 4.40234 + 27.7953i 0.259862 + 1.64071i
288288 0 0
289289 −9.94227 13.6844i −0.584839 0.804962i
290290 0 0
291291 3.17310 4.36740i 0.186010 0.256021i
292292 0 0
293293 23.5937 + 23.5937i 1.37836 + 1.37836i 0.847398 + 0.530959i 0.178168π0.178168\pi
0.530959 + 0.847398i 0.321832π0.321832\pi
294294 0 0
295295 18.1794 21.4497i 1.05845 1.24885i
296296 0 0
297297 −9.85947 19.3503i −0.572104 1.12282i
298298 0 0
299299 −6.34559 −0.366975
300300 0 0
301301 −44.2824 −2.55239
302302 0 0
303303 −7.65280 15.0195i −0.439642 0.862846i
304304 0 0
305305 −8.18149 13.2379i −0.468471 0.758002i
306306 0 0
307307 −0.100680 0.100680i −0.00574611 0.00574611i 0.704228 0.709974i 0.251293π-0.251293\pi
−0.709974 + 0.704228i 0.751293π0.751293\pi
308308 0 0
309309 5.09347 7.01057i 0.289758 0.398817i
310310 0 0
311311 6.25063 + 8.60326i 0.354441 + 0.487846i 0.948589 0.316509i 0.102511π-0.102511\pi
−0.594149 + 0.804355i 0.702511π0.702511\pi
312312 0 0
313313 3.65646 + 23.0860i 0.206676 + 1.30490i 0.844849 + 0.535005i 0.179690π0.179690\pi
−0.638173 + 0.769893i 0.720310π0.720310\pi
314314 0 0
315315 −0.733302 8.88614i −0.0413169 0.500677i
316316 0 0
317317 −8.59220 4.37794i −0.482586 0.245890i 0.195733 0.980657i 0.437291π-0.437291\pi
−0.678319 + 0.734767i 0.737291π0.737291\pi
318318 0 0
319319 6.62148 + 20.3788i 0.370732 + 1.14099i
320320 0 0
321321 −1.65910 + 5.10619i −0.0926021 + 0.285000i
322322 0 0
323323 −0.357453 + 2.25687i −0.0198892 + 0.125576i
324324 0 0
325325 0.156576 + 20.6254i 0.00868527 + 1.14409i
326326 0 0
327327 6.69695 + 1.06069i 0.370342 + 0.0586565i
328328 0 0
329329 9.09876 + 2.95637i 0.501631 + 0.162990i
330330 0 0
331331 −9.37813 + 3.04714i −0.515469 + 0.167486i −0.555188 0.831725i 0.687354π-0.687354\pi
0.0397191 + 0.999211i 0.487354π0.487354\pi
332332 0 0
333333 −1.32057 + 2.59177i −0.0723668 + 0.142028i
334334 0 0
335335 17.0390 + 10.3527i 0.930939 + 0.565631i
336336 0 0
337337 32.0835 5.08152i 1.74770 0.276808i 0.800937 0.598748i 0.204335π-0.204335\pi
0.946760 + 0.321940i 0.104335π0.104335\pi
338338 0 0
339339 11.9378 8.67331i 0.648372 0.471070i
340340 0 0
341341 4.73269 + 3.43850i 0.256290 + 0.186205i
342342 0 0
343343 −9.25432 + 9.25432i −0.499686 + 0.499686i
344344 0 0
345345 1.16425 + 4.76961i 0.0626809 + 0.256787i
346346 0 0
347347 −10.8276 + 5.51691i −0.581253 + 0.296163i −0.719788 0.694194i 0.755761π-0.755761\pi
0.138534 + 0.990358i 0.455761π0.455761\pi
348348 0 0
349349 13.9855i 0.748629i 0.927302 + 0.374314i 0.122122π0.122122\pi
−0.927302 + 0.374314i 0.877878π0.877878\pi
350350 0 0
351351 23.3326i 1.24540i
352352 0 0
353353 −10.8959 + 5.55174i −0.579930 + 0.295489i −0.719242 0.694759i 0.755511π-0.755511\pi
0.139312 + 0.990249i 0.455511π0.455511\pi
354354 0 0
355355 −5.91715 + 14.4400i −0.314050 + 0.766398i
356356 0 0
357357 −1.22036 + 1.22036i −0.0645884 + 0.0645884i
358358 0 0
359359 −16.3725 11.8953i −0.864105 0.627809i 0.0648934 0.997892i 0.479329π-0.479329\pi
−0.928999 + 0.370083i 0.879329π0.879329\pi
360360 0 0
361361 −34.2081 + 24.8536i −1.80043 + 1.30809i
362362 0 0
363363 5.27644 0.835705i 0.276941 0.0438632i
364364 0 0
365365 −7.71551 + 32.6834i −0.403848 + 1.71073i
366366 0 0
367367 4.25004 8.34118i 0.221850 0.435406i −0.753076 0.657934i 0.771431π-0.771431\pi
0.974926 + 0.222528i 0.0714307π0.0714307\pi
368368 0 0
369369 6.21952 2.02085i 0.323776 0.105201i
370370 0 0
371371 31.3090 + 10.1729i 1.62548 + 0.528151i
372372 0 0
373373 −32.0548 5.07698i −1.65974 0.262876i −0.745040 0.667020i 0.767570π-0.767570\pi
−0.914696 + 0.404143i 0.867570π0.867570\pi
374374 0 0
375375 15.4741 3.90189i 0.799081 0.201493i
376376 0 0
377377 3.60131 22.7378i 0.185477 1.17106i
378378 0 0
379379 3.21609 9.89812i 0.165200 0.508432i −0.833851 0.551989i 0.813869π-0.813869\pi
0.999051 + 0.0435569i 0.0138690π0.0138690\pi
380380 0 0
381381 −4.07478 12.5409i −0.208757 0.642489i
382382 0 0
383383 26.0530 + 13.2746i 1.33124 + 0.678303i 0.967423 0.253166i 0.0814719π-0.0814719\pi
0.363821 + 0.931469i 0.381472π0.381472\pi
384384 0 0
385385 34.6138 + 8.17120i 1.76408 + 0.416443i
386386 0 0
387387 1.60977 + 10.1637i 0.0818290 + 0.516648i
388388 0 0
389389 −15.6435 21.5314i −0.793155 1.09168i −0.993708 0.112002i 0.964274π-0.964274\pi
0.200553 0.979683i 0.435726π-0.435726\pi
390390 0 0
391391 −0.263914 + 0.363246i −0.0133467 + 0.0183702i
392392 0 0
393393 21.2994 + 21.2994i 1.07441 + 1.07441i
394394 0 0
395395 −5.46345 2.23878i −0.274896 0.112645i
396396 0 0
397397 10.2475 + 20.1119i 0.514308 + 1.00939i 0.991441 + 0.130556i 0.0416761π0.0416761\pi
−0.477133 + 0.878831i 0.658324π0.658324\pi
398398 0 0
399399 −46.2871 −2.31725
400400 0 0
401401 −6.67802 −0.333484 −0.166742 0.986001i 0.553325π-0.553325\pi
−0.166742 + 0.986001i 0.553325π0.553325\pi
402402 0 0
403403 −2.85334 5.59999i −0.142135 0.278955i
404404 0 0
405405 11.2645 2.74963i 0.559738 0.136630i
406406 0 0
407407 −8.20423 8.20423i −0.406669 0.406669i
408408 0 0
409409 −2.62566 + 3.61391i −0.129831 + 0.178696i −0.868983 0.494841i 0.835226π-0.835226\pi
0.739153 + 0.673538i 0.235226π0.235226\pi
410410 0 0
411411 6.15876 + 8.47681i 0.303789 + 0.418130i
412412 0 0
413413 8.14838 + 51.4469i 0.400956 + 2.53154i
414414 0 0
415415 −2.97257 + 4.89238i −0.145918 + 0.240158i
416416 0 0
417417 13.0913 + 6.67037i 0.641085 + 0.326649i
418418 0 0
419419 −10.9171 33.5994i −0.533335 1.64144i −0.747219 0.664577i 0.768612π-0.768612\pi
0.213885 0.976859i 0.431388π-0.431388\pi
420420 0 0
421421 −2.30880 + 7.10575i −0.112524 + 0.346313i −0.991423 0.130696i 0.958279π-0.958279\pi
0.878899 + 0.477009i 0.158279π0.158279\pi
422422 0 0
423423 0.347782 2.19581i 0.0169098 0.106764i
424424 0 0
425425 1.18719 + 0.848848i 0.0575870 + 0.0411752i
426426 0 0
427427 28.4744 + 4.50991i 1.37797 + 0.218250i
428428 0 0
429429 −21.5018 6.98637i −1.03812 0.337305i
430430 0 0
431431 1.66992 0.542590i 0.0804372 0.0261356i −0.268522 0.963274i 0.586535π-0.586535\pi
0.348959 + 0.937138i 0.386535π0.386535\pi
432432 0 0
433433 1.36660 2.68210i 0.0656745 0.128894i −0.855835 0.517248i 0.826956π-0.826956\pi
0.921510 + 0.388355i 0.126956π0.126956\pi
434434 0 0
435435 −17.7514 + 1.46488i −0.851115 + 0.0702357i
436436 0 0
437437 −11.8938 + 1.88379i −0.568957 + 0.0901139i
438438 0 0
439439 20.5365 14.9207i 0.980156 0.712125i 0.0224121 0.999749i 0.492865π-0.492865\pi
0.957743 + 0.287624i 0.0928654π0.0928654\pi
440440 0 0
441441 7.91184 + 5.74829i 0.376754 + 0.273728i
442442 0 0
443443 6.77536 6.77536i 0.321907 0.321907i −0.527591 0.849498i 0.676905π-0.676905\pi
0.849498 + 0.527591i 0.176905π0.176905\pi
444444 0 0
445445 22.1790 13.7074i 1.05139 0.649792i
446446 0 0
447447 15.0805 7.68391i 0.713284 0.363437i
448448 0 0
449449 20.3687i 0.961260i −0.876924 0.480630i 0.840408π-0.840408\pi
0.876924 0.480630i 0.159592π-0.159592\pi
450450 0 0
451451 26.0849i 1.22829i
452452 0 0
453453 16.5540 8.43470i 0.777776 0.396297i
454454 0 0
455455 −29.1493 24.7051i −1.36654 1.15819i
456456 0 0
457457 5.54512 5.54512i 0.259390 0.259390i −0.565416 0.824806i 0.691284π-0.691284\pi
0.824806 + 0.565416i 0.191284π0.191284\pi
458458 0 0
459459 1.33565 + 0.970403i 0.0623426 + 0.0452946i
460460 0 0
461461 −10.0726 + 7.31820i −0.469130 + 0.340843i −0.797102 0.603845i 0.793635π-0.793635\pi
0.327972 + 0.944687i 0.393635π0.393635\pi
462462 0 0
463463 14.8396 2.35037i 0.689656 0.109231i 0.198237 0.980154i 0.436478π-0.436478\pi
0.491419 + 0.870923i 0.336478π0.336478\pi
464464 0 0
465465 −3.68567 + 3.17213i −0.170919 + 0.147104i
466466 0 0
467467 −12.4383 + 24.4115i −0.575576 + 1.12963i 0.401325 + 0.915936i 0.368550π0.368550\pi
−0.976900 + 0.213695i 0.931450π0.931450\pi
468468 0 0
469469 −35.1273 + 11.4135i −1.62203 + 0.527029i
470470 0 0
471471 4.85581 + 1.57775i 0.223744 + 0.0726988i
472472 0 0
473473 −40.5404 6.42097i −1.86405 0.295236i
474474 0 0
475475 6.41644 + 38.6124i 0.294407 + 1.77166i
476476 0 0
477477 1.19673 7.55583i 0.0547943 0.345958i
478478 0 0
479479 −7.53740 + 23.1977i −0.344393 + 1.05993i 0.617515 + 0.786559i 0.288139π0.288139\pi
−0.961908 + 0.273373i 0.911861π0.911861\pi
480480 0 0
481481 3.85204 + 11.8554i 0.175638 + 0.540558i
482482 0 0
483483 −8.10396 4.12918i −0.368743 0.187884i
484484 0 0
485485 7.80085 3.26596i 0.354218 0.148300i
486486 0 0
487487 −2.80650 17.7196i −0.127175 0.802950i −0.965999 0.258547i 0.916756π-0.916756\pi
0.838824 0.544403i 0.183244π-0.183244\pi
488488 0 0
489489 −12.2098 16.8053i −0.552146 0.759963i
490490 0 0
491491 −16.3602 + 22.5178i −0.738324 + 1.01622i 0.260390 + 0.965504i 0.416149π0.416149\pi
−0.998713 + 0.0507117i 0.983851π0.983851\pi
492492 0 0
493493 −1.15182 1.15182i −0.0518754 0.0518754i
494494 0 0
495495 0.617159 8.24156i 0.0277392 0.370431i
496496 0 0
497497 −13.1246 25.7585i −0.588720 1.15543i
498498 0 0
499499 27.2018 1.21772 0.608860 0.793278i 0.291627π-0.291627\pi
0.608860 + 0.793278i 0.291627π0.291627\pi
500500 0 0
501501 −10.2220 −0.456684
502502 0 0
503503 −14.0273 27.5300i −0.625444 1.22750i −0.958633 0.284643i 0.908125π-0.908125\pi
0.333189 0.942860i 0.391875π-0.391875\pi
504504 0 0
505505 1.97194 26.3334i 0.0877503 1.17182i
506506 0 0
507507 4.05456 + 4.05456i 0.180069 + 0.180069i
508508 0 0
509509 19.5761 26.9441i 0.867693 1.19428i −0.111987 0.993710i 0.535721π-0.535721\pi
0.979680 0.200568i 0.0642786π-0.0642786\pi
510510 0 0
511511 −36.5669 50.3301i −1.61763 2.22647i
512512 0 0
513513 6.92664 + 43.7331i 0.305819 + 1.93086i
514514 0 0
515515 12.5220 5.24254i 0.551783 0.231014i
516516 0 0
517517 7.90122 + 4.02587i 0.347495 + 0.177058i
518518 0 0
519519 3.26182 + 10.0389i 0.143178 + 0.440657i
520520 0 0
521521 5.65254 17.3967i 0.247642 0.762164i −0.747548 0.664207i 0.768769π-0.768769\pi
0.995191 0.0979570i 0.0312308π-0.0312308\pi
522522 0 0
523523 2.44996 15.4684i 0.107129 0.676387i −0.874419 0.485172i 0.838757π-0.838757\pi
0.981548 0.191215i 0.0612428π-0.0612428\pi
524524 0 0
525525 −13.2213 + 26.4426i −0.577024 + 1.15405i
526526 0 0
527527 −0.439236 0.0695681i −0.0191334 0.00303043i
528528 0 0
529529 19.6239 + 6.37619i 0.853212 + 0.277225i
530530 0 0
531531 11.5118 3.74042i 0.499571 0.162321i
532532 0 0
533533 12.7230 24.9704i 0.551096 1.08159i
534534 0 0
535535 −6.37487 + 5.48663i −0.275610 + 0.237208i
536536 0 0
537537 6.02327 0.953993i 0.259923 0.0411678i
538538 0 0
539539 −31.5584 + 22.9285i −1.35932 + 0.987602i
540540 0 0
541541 −27.1227 19.7058i −1.16610 0.847220i −0.175561 0.984468i 0.556174π-0.556174\pi
−0.990537 + 0.137249i 0.956174π0.956174\pi
542542 0 0
543543 −16.4440 + 16.4440i −0.705679 + 0.705679i
544544 0 0
545545 8.10314 + 6.86772i 0.347100 + 0.294181i
546546 0 0
547547 14.4364 7.35569i 0.617254 0.314507i −0.117259 0.993101i 0.537411π-0.537411\pi
0.734513 + 0.678595i 0.237411π0.237411\pi
548548 0 0
549549 6.69938i 0.285922i
550550 0 0
551551 43.6874i 1.86115i
552552 0 0
553553 9.74586 4.96576i 0.414436 0.211166i
554554 0 0
555555 8.20423 5.07049i 0.348250 0.215230i
556556 0 0
557557 23.4966 23.4966i 0.995583 0.995583i −0.00440744 0.999990i 0.501403π-0.501403\pi
0.999990 + 0.00440744i 0.00140294π0.00140294\pi
558558 0 0
559559 35.6764 + 25.9204i 1.50895 + 1.09632i
560560 0 0
561561 −1.29419 + 0.940285i −0.0546408 + 0.0396988i
562562 0 0
563563 −18.2001 + 2.88261i −0.767043 + 0.121488i −0.527681 0.849443i 0.676938π-0.676938\pi
−0.239362 + 0.970930i 0.576938π0.576938\pi
564564 0 0
565565 23.0378 1.90112i 0.969207 0.0799809i
566566 0 0
567567 −9.75198 + 19.1393i −0.409545 + 0.803777i
568568 0 0
569569 1.24601 0.404854i 0.0522355 0.0169724i −0.282783 0.959184i 0.591258π-0.591258\pi
0.335018 + 0.942212i 0.391258π0.391258\pi
570570 0 0
571571 −4.68049 1.52078i −0.195872 0.0636428i 0.209438 0.977822i 0.432837π-0.432837\pi
−0.405310 + 0.914179i 0.632837π0.632837\pi
572572 0 0
573573 0.950379 + 0.150525i 0.0397027 + 0.00628828i
574574 0 0
575575 −2.32114 + 7.33267i −0.0967981 + 0.305793i
576576 0 0
577577 3.10016 19.5737i 0.129062 0.814862i −0.835207 0.549936i 0.814652π-0.814652\pi
0.964269 0.264927i 0.0853478π-0.0853478\pi
578578 0 0
579579 −1.21171 + 3.72927i −0.0503571 + 0.154983i
580580 0 0
581581 −3.27716 10.0861i −0.135959 0.418440i
582582 0 0
583583 27.1882 + 13.8531i 1.12602 + 0.573736i
584584 0 0
585585 −4.61066 + 7.58842i −0.190627 + 0.313742i
586586 0 0
587587 −4.17496 26.3597i −0.172319 1.08798i −0.910540 0.413421i 0.864334π-0.864334\pi
0.738221 0.674559i 0.235666π-0.235666\pi
588588 0 0
589589 −7.01057 9.64922i −0.288865 0.397589i
590590 0 0
591591 6.19645 8.52869i 0.254888 0.350823i
592592 0 0
593593 7.10899 + 7.10899i 0.291931 + 0.291931i 0.837843 0.545911i 0.183817π-0.183817\pi
−0.545911 + 0.837843i 0.683817π0.683817\pi
594594 0 0
595595 −2.62654 + 0.641130i −0.107678 + 0.0262838i
596596 0 0
597597 −3.40520 6.68309i −0.139366 0.273521i
598598 0 0
599599 39.7238 1.62307 0.811536 0.584302i 0.198632π-0.198632\pi
0.811536 + 0.584302i 0.198632π0.198632\pi
600600 0 0
601601 7.44239 0.303582 0.151791 0.988413i 0.451496π-0.451496\pi
0.151791 + 0.988413i 0.451496π0.451496\pi
602602 0 0
603603 3.89659 + 7.64748i 0.158681 + 0.311430i
604604 0 0
605605 7.74396 + 3.17327i 0.314837 + 0.129012i
606606 0 0
607607 −22.8498 22.8498i −0.927445 0.927445i 0.0700955 0.997540i 0.477670π-0.477670\pi
−0.997540 + 0.0700955i 0.977670π0.977670\pi
608608 0 0
609609 19.3951 26.6950i 0.785928 1.08174i
610610 0 0
611611 −5.59999 7.70772i −0.226551 0.311821i
612612 0 0
613613 −4.46309 28.1788i −0.180262 1.13813i −0.897406 0.441207i 0.854551π-0.854551\pi
0.717143 0.696926i 0.245449π-0.245449\pi
614614 0 0
615615 −21.1031 4.98177i −0.850959 0.200884i
616616 0 0
617617 −7.60111 3.87296i −0.306009 0.155920i 0.294242 0.955731i 0.404933π-0.404933\pi
−0.600251 + 0.799811i 0.704933π0.704933\pi
618618 0 0
619619 −6.83480 21.0353i −0.274714 0.845482i −0.989295 0.145929i 0.953383π-0.953383\pi
0.714581 0.699552i 0.246617π-0.246617\pi
620620 0 0
621621 −2.68862 + 8.27471i −0.107891 + 0.332053i
622622 0 0
623623 −7.55596 + 47.7064i −0.302723 + 1.91132i
624624 0 0
625625 23.8910 + 7.36356i 0.955638 + 0.294542i
626626 0 0
627627 −42.3757 6.71166i −1.69232 0.268038i
628628 0 0
629629 0.838853 + 0.272560i 0.0334473 + 0.0108677i
630630 0 0
631631 −14.3275 + 4.65528i −0.570368 + 0.185324i −0.579981 0.814630i 0.696940π-0.696940\pi
0.00961299 + 0.999954i 0.496940π0.496940\pi
632632 0 0
633633 5.25672 10.3169i 0.208936 0.410060i
634634 0 0
635635 4.74603 20.1045i 0.188341 0.797823i
636636 0 0
637637 41.3936 6.55610i 1.64007 0.259762i
638638 0 0
639639 −5.43497 + 3.94874i −0.215004 + 0.156210i
640640 0 0
641641 −26.9426 19.5749i −1.06417 0.773163i −0.0893123 0.996004i 0.528467π-0.528467\pi
−0.974855 + 0.222841i 0.928467π0.928467\pi
642642 0 0
643643 26.5370 26.5370i 1.04652 1.04652i 0.0476541 0.998864i 0.484825π-0.484825\pi
0.998864 0.0476541i 0.0151745π-0.0151745\pi
644644 0 0
645645 12.9372 31.5716i 0.509402 1.24313i
646646 0 0
647647 14.8905 7.58707i 0.585404 0.298278i −0.136092 0.990696i 0.543454π-0.543454\pi
0.721497 + 0.692418i 0.243454π0.243454\pi
648648 0 0
649649 48.2810i 1.89519i
650650 0 0
651651 9.00847i 0.353070i
652652 0 0
653653 −8.39806 + 4.27902i −0.328641 + 0.167451i −0.610524 0.791998i 0.709041π-0.709041\pi
0.281883 + 0.959449i 0.409041π0.409041\pi
654654 0 0
655655 11.1899 + 45.8420i 0.437225 + 1.79120i
656656 0 0
657657 −10.2224 + 10.2224i −0.398815 + 0.398815i
658658 0 0
659659 21.3774 + 15.5316i 0.832745 + 0.605025i 0.920335 0.391132i 0.127916π-0.127916\pi
−0.0875893 + 0.996157i 0.527916π0.527916\pi
660660 0 0
661661 17.7042 12.8628i 0.688612 0.500306i −0.187591 0.982247i 0.560068π-0.560068\pi
0.876204 + 0.481941i 0.160068π0.160068\pi
662662 0 0
663663 1.69752 0.268861i 0.0659264 0.0104417i
664664 0 0
665665 −61.9698 37.6523i −2.40308 1.46009i
666666 0 0
667667 3.89726 7.64880i 0.150903 0.296163i
668668 0 0
669669 5.08561 1.65242i 0.196621 0.0638861i
670670 0 0
671671 25.4143 + 8.25761i 0.981109 + 0.318782i
672672 0 0
673673 −7.36687 1.16680i −0.283972 0.0449768i 0.0128235 0.999918i 0.495918π-0.495918\pi
−0.296796 + 0.954941i 0.595918π0.595918\pi
674674 0 0
675675 26.9620 + 8.53475i 1.03777 + 0.328503i
676676 0 0
677677 −2.11287 + 13.3401i −0.0812042 + 0.512703i 0.913239 + 0.407425i 0.133573π0.133573\pi
−0.994443 + 0.105278i 0.966427π0.966427\pi
678678 0 0
679679 −4.84130 + 14.9000i −0.185792 + 0.571809i
680680 0 0
681681 4.10501 + 12.6339i 0.157304 + 0.484132i
682682 0 0
683683 28.3996 + 14.4703i 1.08668 + 0.553692i 0.903151 0.429323i 0.141248π-0.141248\pi
0.183530 + 0.983014i 0.441248π0.441248\pi
684684 0 0
685685 1.34995 + 16.3587i 0.0515791 + 0.625034i
686686 0 0
687687 −1.30780 8.25710i −0.0498955 0.315028i
688688 0 0
689689 −19.2697 26.5224i −0.734116 1.01042i
690690 0 0
691691 −15.1560 + 20.8605i −0.576563 + 0.793571i −0.993313 0.115450i 0.963169π-0.963169\pi
0.416750 + 0.909021i 0.363169π0.363169\pi
692692 0 0
693693 10.8262 + 10.8262i 0.411253 + 0.411253i
694694 0 0
695695 12.1008 + 19.5795i 0.459010 + 0.742694i
696696 0 0
697697 −0.900248 1.76684i −0.0340993 0.0669237i
698698 0 0
699699 −11.8399 −0.447825
700700 0 0
701701 20.3302 0.767860 0.383930 0.923362i 0.374570π-0.374570\pi
0.383930 + 0.923362i 0.374570π0.374570\pi
702702 0 0
703703 10.7395 + 21.0774i 0.405047 + 0.794949i
704704 0 0
705705 −4.76600 + 5.62334i −0.179498 + 0.211787i
706706 0 0
707707 34.5918 + 34.5918i 1.30096 + 1.30096i
708708 0 0
709709 −7.51229 + 10.3398i −0.282130 + 0.388319i −0.926438 0.376447i 0.877146π-0.877146\pi
0.644308 + 0.764766i 0.277146π0.277146\pi
710710 0 0
711711 −1.49402 2.05635i −0.0560302 0.0771190i
712712 0 0
713713 −0.366626 2.31479i −0.0137302 0.0866894i
714714 0 0
715715 −23.1038 26.8441i −0.864035 1.00391i
716716 0 0
717717 −31.5843 16.0930i −1.17954 0.601004i
718718 0 0
719719 3.29703 + 10.1472i 0.122959 + 0.378427i 0.993524 0.113626i 0.0362465π-0.0362465\pi
−0.870565 + 0.492053i 0.836247π0.836247\pi
720720 0 0
721721 −7.77127 + 23.9175i −0.289417 + 0.890735i
722722 0 0
723723 −1.61025 + 10.1667i −0.0598860 + 0.378105i
724724 0 0
725725 −24.9574 12.4787i −0.926895 0.463447i
726726 0 0
727727 −27.4276 4.34410i −1.01723 0.161114i −0.374518 0.927220i 0.622192π-0.622192\pi
−0.642714 + 0.766106i 0.722192π0.722192\pi
728728 0 0
729729 27.7821 + 9.02694i 1.02897 + 0.334331i
730730 0 0
731731 2.96757 0.964222i 0.109760 0.0356630i
732732 0 0
733733 14.4667 28.3925i 0.534339 1.04870i −0.453212 0.891403i 0.649722π-0.649722\pi
0.987551 0.157297i 0.0502779π-0.0502779\pi
734734 0 0
735735 −12.5224 29.9102i −0.461897 1.10326i
736736 0 0
737737 −33.8139 + 5.35560i −1.24555 + 0.197276i
738738 0 0
739739 −37.2176 + 27.0402i −1.36907 + 0.994688i −0.371262 + 0.928528i 0.621075π0.621075\pi
−0.997809 + 0.0661598i 0.978925π0.978925\pi
740740 0 0
741741 37.2915 + 27.0939i 1.36994 + 0.995319i
742742 0 0
743743 18.2973 18.2973i 0.671262 0.671262i −0.286745 0.958007i 0.592573π-0.592573\pi
0.958007 + 0.286745i 0.0925733π0.0925733\pi
744744 0 0
745745 26.4405 + 1.97996i 0.968704 + 0.0725401i
746746 0 0
747747 −2.19581 + 1.11882i −0.0803406 + 0.0409356i
748748 0 0
749749 15.5814i 0.569330i
750750 0 0
751751 3.66430i 0.133712i −0.997763 0.0668561i 0.978703π-0.978703\pi
0.997763 0.0668561i 0.0212968π-0.0212968\pi
752752 0 0
753753 −37.3248 + 19.0180i −1.36019 + 0.693053i
754754 0 0
755755 29.0240 + 2.17342i 1.05629 + 0.0790989i
756756 0 0
757757 −16.0349 + 16.0349i −0.582797 + 0.582797i −0.935671 0.352874i 0.885204π-0.885204\pi
0.352874 + 0.935671i 0.385204π0.385204\pi
758758 0 0
759759 −6.82042 4.95533i −0.247566 0.179867i
760760 0 0
761761 2.89867 2.10600i 0.105077 0.0763426i −0.534006 0.845481i 0.679314π-0.679314\pi
0.639083 + 0.769138i 0.279314π0.279314\pi
762762 0 0
763763 −19.4353 + 3.07825i −0.703606 + 0.111440i
764764 0 0
765765 0.242632 + 0.579535i 0.00877240 + 0.0209531i
766766 0 0
767767 23.5493 46.2181i 0.850317 1.66884i
768768 0 0
769769 −32.4148 + 10.5322i −1.16891 + 0.379802i −0.828236 0.560380i 0.810655π-0.810655\pi
−0.340674 + 0.940182i 0.610655π0.610655\pi
770770 0 0
771771 −30.9669 10.0618i −1.11525 0.362366i
772772 0 0
773773 7.62309 + 1.20738i 0.274183 + 0.0434264i 0.292012 0.956415i 0.405675π-0.405675\pi
−0.0178285 + 0.999841i 0.505675π0.505675\pi
774774 0 0
775775 −7.51480 + 1.24878i −0.269940 + 0.0448574i
776776 0 0
777777 −2.79502 + 17.6471i −0.100271 + 0.633085i
778778 0 0
779779 16.4344 50.5800i 0.588824 1.81222i
780780 0 0
781781 −8.28056 25.4849i −0.296302 0.911923i
782782 0 0
783783 −28.1244 14.3301i −1.00508 0.512116i
784784 0 0
785785 5.21759 + 6.06227i 0.186224 + 0.216372i
786786 0 0
787787 −3.28182 20.7206i −0.116984 0.738611i −0.974539 0.224218i 0.928017π-0.928017\pi
0.857555 0.514393i 0.171983π-0.171983\pi
788788 0 0
789789 18.1870 + 25.0323i 0.647476 + 0.891174i
790790 0 0
791791 −25.1709 + 34.6448i −0.894976 + 1.23183i
792792 0 0
793793 −20.3008 20.3008i −0.720902 0.720902i
794794 0 0
795795 −16.3999 + 19.3500i −0.581644 + 0.686275i
796796 0 0
797797 8.94048 + 17.5467i 0.316688 + 0.621535i 0.993399 0.114714i 0.0365951π-0.0365951\pi
−0.676711 + 0.736249i 0.736595π0.736595\pi
798798 0 0
799799 −0.674124 −0.0238488
800800 0 0
801801 11.2242 0.396588
802802 0 0
803803 −26.1790 51.3792i −0.923838 1.81313i
804804 0 0
805805 −7.49080 12.1204i −0.264016 0.427187i
806806 0 0
807807 30.1491 + 30.1491i 1.06130 + 1.06130i
808808 0 0
809809 −10.5652 + 14.5418i −0.371454 + 0.511263i −0.953295 0.302040i 0.902333π-0.902333\pi
0.581841 + 0.813302i 0.302333π0.302333\pi
810810 0 0
811811 3.88707 + 5.35010i 0.136494 + 0.187867i 0.871792 0.489876i 0.162958π-0.162958\pi
−0.735298 + 0.677743i 0.762958π0.762958\pi
812812 0 0
813813 3.82348 + 24.1405i 0.134095 + 0.846644i
814814 0 0
815815 −2.67629 32.4313i −0.0937464 1.13602i
816816 0 0
817817 74.5645 + 37.9925i 2.60868 + 1.32919i
818818 0 0
819819 −5.08309 15.6442i −0.177618 0.546651i
820820 0 0
821821 −0.360464 + 1.10939i −0.0125803 + 0.0387181i −0.957150 0.289594i 0.906480π-0.906480\pi
0.944569 + 0.328312i 0.106480π0.106480\pi
822822 0 0
823823 5.62489 35.5142i 0.196071 1.23795i −0.671640 0.740878i 0.734410π-0.734410\pi
0.867711 0.497068i 0.165590π-0.165590\pi
824824 0 0
825825 −15.9382 + 22.2910i −0.554898 + 0.776073i
826826 0 0
827827 17.3046 + 2.74077i 0.601739 + 0.0953060i 0.449869 0.893095i 0.351471π-0.351471\pi
0.151870 + 0.988401i 0.451471π0.451471\pi
828828 0 0
829829 15.2346 + 4.95002i 0.529120 + 0.171921i 0.561380 0.827558i 0.310271π-0.310271\pi
−0.0322604 + 0.999479i 0.510271π0.510271\pi
830830 0 0
831831 16.1014 5.23166i 0.558551 0.181484i
832832 0 0
833833 1.34627 2.64220i 0.0466454 0.0915467i
834834 0 0
835835 −13.6853 8.31507i −0.473599 0.287755i
836836 0 0
837837 −8.51140 + 1.34807i −0.294197 + 0.0465962i
838838 0 0
839839 −31.4048 + 22.8169i −1.08421 + 0.787727i −0.978413 0.206661i 0.933740π-0.933740\pi
−0.105800 + 0.994387i 0.533740π0.533740\pi
840840 0 0
841841 1.73420 + 1.25997i 0.0598001 + 0.0434473i
842842 0 0
843843 18.8318 18.8318i 0.648602 0.648602i
844844 0 0
845845 2.13011 + 8.72649i 0.0732779 + 0.300200i
846846 0 0
847847 −13.8139 + 7.03853i −0.474651 + 0.241847i
848848 0 0
849849 22.4679i 0.771098i
850850 0 0
851851 4.64828i 0.159341i
852852 0 0
853853 19.3009 9.83431i 0.660851 0.336720i −0.0911931 0.995833i 0.529068π-0.529068\pi
0.752044 + 0.659113i 0.229068π0.229068\pi
854854 0 0
855855 −6.38919 + 15.5920i −0.218506 + 0.533235i
856856 0 0
857857 −30.7036 + 30.7036i −1.04881 + 1.04881i −0.0500684 + 0.998746i 0.515944π0.515944\pi
−0.998746 + 0.0500684i 0.984056π0.984056\pi
858858 0 0
859859 −0.0460861 0.0334835i −0.00157244 0.00114244i 0.586999 0.809588i 0.300309π-0.300309\pi
−0.588571 + 0.808445i 0.700309π0.700309\pi
860860 0 0
861861 32.4972 23.6106i 1.10750 0.804648i
862862 0 0
863863 −9.17549 + 1.45326i −0.312337 + 0.0494694i −0.310635 0.950529i 0.600542π-0.600542\pi
−0.00170208 + 0.999999i 0.500542π0.500542\pi
864864 0 0
865865 −3.79916 + 16.0935i −0.129175 + 0.547195i
866866 0 0
867867 −10.9610 + 21.5122i −0.372256 + 0.730593i
868868 0 0
869869 9.64234 3.13299i 0.327094 0.106279i
870870 0 0
871871 34.9814 + 11.3661i 1.18530 + 0.385127i
872872 0 0
873873 3.59582 + 0.569523i 0.121700 + 0.0192754i
874874 0 0
875875 −39.2105 + 24.6467i −1.32556 + 0.833212i
876876 0 0
877877 −7.07858 + 44.6924i −0.239027 + 1.50916i 0.517779 + 0.855515i 0.326759π0.326759\pi
−0.756805 + 0.653640i 0.773241π0.773241\pi
878878 0 0
879879 14.7174 45.2954i 0.496404 1.52777i
880880 0 0
881881 5.21481 + 16.0495i 0.175691 + 0.540723i 0.999664 0.0259066i 0.00824725π-0.00824725\pi
−0.823973 + 0.566629i 0.808247π0.808247\pi
882882 0 0
883883 −11.4537 5.83596i −0.385448 0.196396i 0.250519 0.968112i 0.419399π-0.419399\pi
−0.635967 + 0.771716i 0.719399π0.719399\pi
884884 0 0
885885 −39.0601 9.22085i −1.31299 0.309955i
886886 0 0
887887 7.92120 + 50.0125i 0.265968 + 1.67926i 0.653132 + 0.757244i 0.273455π0.273455\pi
−0.387164 + 0.922011i 0.626545π0.626545\pi
888888 0 0
889889 22.4934 + 30.9595i 0.754404 + 1.03835i
890890 0 0
891891 −11.7031 + 16.1080i −0.392069 + 0.539637i
892892 0 0
893893 −12.7844 12.7844i −0.427815 0.427815i
894894 0 0
895895 8.84006 + 3.62242i 0.295490 + 0.121084i
896896 0 0
897897 4.11203 + 8.07031i 0.137297 + 0.269460i
898898 0 0
899899 8.50250 0.283574
900900 0 0
901901 −2.31967 −0.0772795
902902 0 0
903903 28.6956 + 56.3182i 0.954928 + 1.87415i
904904 0 0
905905 −35.3918 + 8.63902i −1.17646 + 0.287171i
906906 0 0
907907 18.8330 + 18.8330i 0.625339 + 0.625339i 0.946892 0.321553i 0.104205π-0.104205\pi
−0.321553 + 0.946892i 0.604205π0.604205\pi
908908 0 0
909909 6.68199 9.19697i 0.221628 0.305044i
910910 0 0
911911 6.27133 + 8.63174i 0.207778 + 0.285982i 0.900169 0.435540i 0.143443π-0.143443\pi
−0.692391 + 0.721523i 0.743443π0.743443\pi
912912 0 0
913913 −1.53775 9.70894i −0.0508920 0.321319i
914914 0 0
915915 −11.5343 + 18.9836i −0.381311 + 0.627577i
916916 0 0
917917 −77.8894 39.6866i −2.57214 1.31057i
918918 0 0
919919 −13.7726 42.3878i −0.454318 1.39825i −0.871934 0.489623i 0.837135π-0.837135\pi
0.417617 0.908623i 0.362865π-0.362865\pi
920920 0 0
921921 −0.0628025 + 0.193286i −0.00206941 + 0.00636900i
922922 0 0
923923 −4.50366 + 28.4350i −0.148240 + 0.935949i
924924 0 0
925925 15.1085 0.114695i 0.496765 0.00377116i
926926 0 0
927927 5.77203 + 0.914200i 0.189578 + 0.0300263i
928928 0 0
929929 3.04696 + 0.990017i 0.0999675 + 0.0324814i 0.358574 0.933501i 0.383263π-0.383263\pi
−0.258606 + 0.965983i 0.583263π0.583263\pi
930930 0 0
931931 75.6393 24.5767i 2.47898 0.805468i
932932 0 0
933933 6.89111 13.5246i 0.225605 0.442774i
934934 0 0
935935 −2.49755 + 0.206103i −0.0816787 + 0.00674029i
936936 0 0
937937 −45.1439 + 7.15010i −1.47479 + 0.233583i −0.841468 0.540307i 0.818308π-0.818308\pi
−0.633320 + 0.773890i 0.718308π0.718308\pi
938938 0 0
939939 26.9913 19.6103i 0.880827 0.639958i
940940 0 0
941941 −1.31101 0.952505i −0.0427377 0.0310508i 0.566211 0.824260i 0.308409π-0.308409\pi
−0.608949 + 0.793209i 0.708409π0.708409\pi
942942 0 0
943943 7.38947 7.38947i 0.240634 0.240634i
944944 0 0
945945 −44.5663 + 27.5435i −1.44974 + 0.895989i
946946 0 0
947947 6.11091 3.11366i 0.198578 0.101180i −0.351874 0.936047i 0.614455π-0.614455\pi
0.550452 + 0.834867i 0.314455π0.314455\pi
948948 0 0
949949 61.9530i 2.01108i
950950 0 0
951951 13.7645i 0.446345i
952952 0 0
953953 45.7444 23.3080i 1.48181 0.755019i 0.488725 0.872438i 0.337462π-0.337462\pi
0.993082 + 0.117419i 0.0374621π0.0374621\pi
954954 0 0
955955 1.14993 + 0.974612i 0.0372110 + 0.0315377i
956956 0 0
957957 21.6269 21.6269i 0.699099 0.699099i
958958 0 0
959959 −24.6007 17.8734i −0.794397 0.577163i
960960 0 0
961961 −23.2016 + 16.8569i −0.748438 + 0.543772i
962962 0 0
963963 −3.57622 + 0.566418i −0.115242 + 0.0182526i
964964 0 0
965965 −4.65584 + 4.00712i −0.149877 + 0.128994i
966966 0 0
967967 −19.2666 + 37.8129i −0.619573 + 1.21598i 0.341551 + 0.939863i 0.389048π0.389048\pi
−0.961124 + 0.276117i 0.910952π0.910952\pi
968968 0 0
969969 3.10192 1.00787i 0.0996480 0.0323776i
970970 0 0
971971 28.6325 + 9.30326i 0.918861 + 0.298556i 0.729999 0.683448i 0.239520π-0.239520\pi
0.188861 + 0.982004i 0.439520π0.439520\pi
972972 0 0
973973 −42.1150 6.67037i −1.35015 0.213842i
974974 0 0
975975 26.1298 13.5646i 0.836823 0.434416i
976976 0 0
977977 3.59037 22.6687i 0.114866 0.725235i −0.861282 0.508128i 0.830338π-0.830338\pi
0.976148 0.217107i 0.0696622π-0.0696622\pi
978978 0 0
979979 −13.8349 + 42.5795i −0.442166 + 1.36085i
980980 0 0
981981 1.41304 + 4.34888i 0.0451148 + 0.138849i
982982 0 0
983983 −45.8856 23.3799i −1.46352 0.745702i −0.472745 0.881199i 0.656737π-0.656737\pi
−0.990778 + 0.135497i 0.956737π0.956737\pi
984984 0 0
985985 15.2336 6.37780i 0.485382 0.203213i
986986 0 0
987987 −2.13622 13.4875i −0.0679966 0.429313i
988988 0 0
989989 9.66555 + 13.3035i 0.307347 + 0.423026i
990990 0 0
991991 7.43042 10.2271i 0.236035 0.324874i −0.674524 0.738253i 0.735651π-0.735651\pi
0.910559 + 0.413378i 0.135651π0.135651\pi
992992 0 0
993993 9.95250 + 9.95250i 0.315833 + 0.315833i
994994 0 0
995995 0.877439 11.7174i 0.0278167 0.371465i
996996 0 0
997997 10.5746 + 20.7537i 0.334900 + 0.657277i 0.995634 0.0933423i 0.0297551π-0.0297551\pi
−0.660735 + 0.750620i 0.729755π0.729755\pi
998998 0 0
999999 17.0916 0.540754
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 400.2.bi.b.223.1 16
4.3 odd 2 inner 400.2.bi.b.223.2 yes 16
25.12 odd 20 inner 400.2.bi.b.287.2 yes 16
100.87 even 20 inner 400.2.bi.b.287.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
400.2.bi.b.223.1 16 1.1 even 1 trivial
400.2.bi.b.223.2 yes 16 4.3 odd 2 inner
400.2.bi.b.287.1 yes 16 100.87 even 20 inner
400.2.bi.b.287.2 yes 16 25.12 odd 20 inner