Properties

Label 400.2.bi.b.303.2
Level 400400
Weight 22
Character 400.303
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 303.2
Root 0.500000+1.94194i0.500000 + 1.94194i of defining polynomial
Character χ\chi == 400.303
Dual form 400.2.bi.b.367.2

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+(2.014110.319003i)q3+(1.705821.44575i)q5+(3.137043.13704i)q7+(1.101690.357960i)q9+(3.22428+1.04763i)q11+(1.735143.40540i)q13+(3.896902.36772i)q15+(1.221237.71055i)q17+(0.375011+0.272461i)q19+(7.319065.31761i)q21+(2.52419+4.95399i)q23+(0.819639+4.93236i)q25+(3.34613+1.70494i)q27+(0.7192030.989898i)q29+(4.50368+6.19878i)q31+(6.82823+1.08149i)q33+(0.815862+9.88660i)q35+(1.21113+0.617102i)q37+(2.408427.41234i)q39+(0.4573001.40742i)q41+(5.57270+5.57270i)q43+(2.396800.982146i)q45+(0.1971551.24479i)q47+12.6821iq4915.9194iq51+(0.141520+0.893520i)q53+(3.985436.44855i)q55+(0.668395+0.668395i)q57+(3.246969.99313i)q59+(0.6495361.99907i)q61+(4.578982.33311i)q63+(7.88316+3.30042i)q65+(11.3499+1.79765i)q67+(6.66432+9.17264i)q69+(1.00694+1.38593i)q71+(5.494312.79949i)q73+(3.22428+9.67283i)q75+(6.8282313.4012i)q77+(13.5517+9.84590i)q79+(9.00703+6.54399i)q81+(1.122947.08995i)q83+(13.2307+11.3872i)q85+(1.132772.22319i)q87+(7.35916+2.39114i)q89+(16.1261+5.23968i)q91+(11.0483+11.0483i)q93+(1.03361+0.0774005i)q95+(10.89141.72503i)q97+3.92716q99+O(q100)q+(2.01411 - 0.319003i) q^{3} +(-1.70582 - 1.44575i) q^{5} +(-3.13704 - 3.13704i) q^{7} +(1.10169 - 0.357960i) q^{9} +(3.22428 + 1.04763i) q^{11} +(1.73514 - 3.40540i) q^{13} +(-3.89690 - 2.36772i) q^{15} +(1.22123 - 7.71055i) q^{17} +(-0.375011 + 0.272461i) q^{19} +(-7.31906 - 5.31761i) q^{21} +(2.52419 + 4.95399i) q^{23} +(0.819639 + 4.93236i) q^{25} +(-3.34613 + 1.70494i) q^{27} +(0.719203 - 0.989898i) q^{29} +(4.50368 + 6.19878i) q^{31} +(6.82823 + 1.08149i) q^{33} +(0.815862 + 9.88660i) q^{35} +(1.21113 + 0.617102i) q^{37} +(2.40842 - 7.41234i) q^{39} +(-0.457300 - 1.40742i) q^{41} +(-5.57270 + 5.57270i) q^{43} +(-2.39680 - 0.982146i) q^{45} +(-0.197155 - 1.24479i) q^{47} +12.6821i q^{49} -15.9194i q^{51} +(0.141520 + 0.893520i) q^{53} +(-3.98543 - 6.44855i) q^{55} +(-0.668395 + 0.668395i) q^{57} +(-3.24696 - 9.99313i) q^{59} +(0.649536 - 1.99907i) q^{61} +(-4.57898 - 2.33311i) q^{63} +(-7.88316 + 3.30042i) q^{65} +(11.3499 + 1.79765i) q^{67} +(6.66432 + 9.17264i) q^{69} +(-1.00694 + 1.38593i) q^{71} +(5.49431 - 2.79949i) q^{73} +(3.22428 + 9.67283i) q^{75} +(-6.82823 - 13.4012i) q^{77} +(13.5517 + 9.84590i) q^{79} +(-9.00703 + 6.54399i) q^{81} +(1.12294 - 7.08995i) q^{83} +(-13.2307 + 11.3872i) q^{85} +(1.13277 - 2.22319i) q^{87} +(7.35916 + 2.39114i) q^{89} +(-16.1261 + 5.23968i) q^{91} +(11.0483 + 11.0483i) q^{93} +(1.03361 + 0.0774005i) q^{95} +(10.8914 - 1.72503i) q^{97} +3.92716 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(720)e\left(\frac{7}{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 2.01411 0.319003i 1.16284 0.184176i 0.454965 0.890509i 0.349652π-0.349652\pi
0.707880 + 0.706333i 0.249652π0.249652\pi
44 0 0
55 −1.70582 1.44575i −0.762866 0.646557i
66 0 0
77 −3.13704 3.13704i −1.18569 1.18569i −0.978247 0.207444i 0.933486π-0.933486\pi
−0.207444 0.978247i 0.566514π-0.566514\pi
88 0 0
99 1.10169 0.357960i 0.367230 0.119320i
1010 0 0
1111 3.22428 + 1.04763i 0.972156 + 0.315873i 0.751686 0.659521i 0.229241π-0.229241\pi
0.220470 + 0.975394i 0.429241π0.429241\pi
1212 0 0
1313 1.73514 3.40540i 0.481240 0.944487i −0.514945 0.857223i 0.672188π-0.672188\pi
0.996185 0.0872636i 0.0278123π-0.0278123\pi
1414 0 0
1515 −3.89690 2.36772i −1.00617 0.611343i
1616 0 0
1717 1.22123 7.71055i 0.296192 1.87008i −0.170062 0.985433i 0.554397π-0.554397\pi
0.466254 0.884651i 0.345603π-0.345603\pi
1818 0 0
1919 −0.375011 + 0.272461i −0.0860333 + 0.0625069i −0.629970 0.776619i 0.716933π-0.716933\pi
0.543937 + 0.839126i 0.316933π0.316933\pi
2020 0 0
2121 −7.31906 5.31761i −1.59715 1.16040i
2222 0 0
2323 2.52419 + 4.95399i 0.526329 + 1.03298i 0.989203 + 0.146555i 0.0468185π0.0468185\pi
−0.462873 + 0.886424i 0.653182π0.653182\pi
2424 0 0
2525 0.819639 + 4.93236i 0.163928 + 0.986472i
2626 0 0
2727 −3.34613 + 1.70494i −0.643962 + 0.328115i
2828 0 0
2929 0.719203 0.989898i 0.133553 0.183819i −0.737003 0.675890i 0.763760π-0.763760\pi
0.870556 + 0.492070i 0.163760π0.163760\pi
3030 0 0
3131 4.50368 + 6.19878i 0.808884 + 1.11333i 0.991495 + 0.130148i 0.0415454π0.0415454\pi
−0.182610 + 0.983185i 0.558455π0.558455\pi
3232 0 0
3333 6.82823 + 1.08149i 1.18864 + 0.188262i
3434 0 0
3535 0.815862 + 9.88660i 0.137906 + 1.67114i
3636 0 0
3737 1.21113 + 0.617102i 0.199109 + 0.101451i 0.550702 0.834702i 0.314360π-0.314360\pi
−0.351593 + 0.936153i 0.614360π0.614360\pi
3838 0 0
3939 2.40842 7.41234i 0.385655 1.18692i
4040 0 0
4141 −0.457300 1.40742i −0.0714182 0.219803i 0.908976 0.416848i 0.136865π-0.136865\pi
−0.980394 + 0.197046i 0.936865π0.936865\pi
4242 0 0
4343 −5.57270 + 5.57270i −0.849829 + 0.849829i −0.990112 0.140283i 0.955199π-0.955199\pi
0.140283 + 0.990112i 0.455199π0.455199\pi
4444 0 0
4545 −2.39680 0.982146i −0.357294 0.146410i
4646 0 0
4747 −0.197155 1.24479i −0.0287580 0.181571i 0.969128 0.246558i 0.0792994π-0.0792994\pi
−0.997886 + 0.0649869i 0.979299π0.979299\pi
4848 0 0
4949 12.6821i 1.81173i
5050 0 0
5151 15.9194i 2.22917i
5252 0 0
5353 0.141520 + 0.893520i 0.0194392 + 0.122734i 0.995500 0.0947650i 0.0302100π-0.0302100\pi
−0.976060 + 0.217499i 0.930210π0.930210\pi
5454 0 0
5555 −3.98543 6.44855i −0.537395 0.869523i
5656 0 0
5757 −0.668395 + 0.668395i −0.0885311 + 0.0885311i
5858 0 0
5959 −3.24696 9.99313i −0.422719 1.30099i −0.905162 0.425067i 0.860250π-0.860250\pi
0.482443 0.875927i 0.339750π-0.339750\pi
6060 0 0
6161 0.649536 1.99907i 0.0831646 0.255954i −0.900824 0.434184i 0.857037π-0.857037\pi
0.983989 + 0.178229i 0.0570369π0.0570369\pi
6262 0 0
6363 −4.57898 2.33311i −0.576898 0.293944i
6464 0 0
6565 −7.88316 + 3.30042i −0.977786 + 0.409367i
6666 0 0
6767 11.3499 + 1.79765i 1.38661 + 0.219618i 0.804724 0.593649i 0.202313π-0.202313\pi
0.581890 + 0.813267i 0.302313π0.302313\pi
6868 0 0
6969 6.66432 + 9.17264i 0.802289 + 1.10426i
7070 0 0
7171 −1.00694 + 1.38593i −0.119502 + 0.164480i −0.864577 0.502500i 0.832414π-0.832414\pi
0.745075 + 0.666980i 0.232414π0.232414\pi
7272 0 0
7373 5.49431 2.79949i 0.643061 0.327656i −0.101870 0.994798i 0.532483π-0.532483\pi
0.744931 + 0.667142i 0.232483π0.232483\pi
7474 0 0
7575 3.22428 + 9.67283i 0.372307 + 1.11692i
7676 0 0
7777 −6.82823 13.4012i −0.778149 1.52720i
7878 0 0
7979 13.5517 + 9.84590i 1.52469 + 1.10775i 0.959102 + 0.283061i 0.0913501π0.0913501\pi
0.565586 + 0.824689i 0.308650π0.308650\pi
8080 0 0
8181 −9.00703 + 6.54399i −1.00078 + 0.727110i
8282 0 0
8383 1.12294 7.08995i 0.123258 0.778223i −0.846182 0.532895i 0.821104π-0.821104\pi
0.969440 0.245328i 0.0788958π-0.0788958\pi
8484 0 0
8585 −13.2307 + 11.3872i −1.43507 + 1.23512i
8686 0 0
8787 1.13277 2.22319i 0.121446 0.238351i
8888 0 0
8989 7.35916 + 2.39114i 0.780069 + 0.253460i 0.671870 0.740669i 0.265491π-0.265491\pi
0.108199 + 0.994129i 0.465491π0.465491\pi
9090 0 0
9191 −16.1261 + 5.23968i −1.69047 + 0.549267i
9292 0 0
9393 11.0483 + 11.0483i 1.14566 + 1.14566i
9494 0 0
9595 1.03361 + 0.0774005i 0.106046 + 0.00794112i
9696 0 0
9797 10.8914 1.72503i 1.10586 0.175151i 0.423305 0.905987i 0.360870π-0.360870\pi
0.682553 + 0.730837i 0.260870π0.260870\pi
9898 0 0
9999 3.92716 0.394695
100100 0 0
101101 −14.0912 −1.40213 −0.701064 0.713098i 0.747291π-0.747291\pi
−0.701064 + 0.713098i 0.747291π0.747291\pi
102102 0 0
103103 5.29439 0.838549i 0.521672 0.0826247i 0.109955 0.993937i 0.464929π-0.464929\pi
0.411717 + 0.911312i 0.364929π0.364929\pi
104104 0 0
105105 4.79709 + 19.6524i 0.468148 + 1.91788i
106106 0 0
107107 −2.89920 2.89920i −0.280276 0.280276i 0.552943 0.833219i 0.313505π-0.313505\pi
−0.833219 + 0.552943i 0.813505π0.813505\pi
108108 0 0
109109 −1.50151 + 0.487870i −0.143818 + 0.0467294i −0.380042 0.924969i 0.624090π-0.624090\pi
0.236223 + 0.971699i 0.424090π0.424090\pi
110110 0 0
111111 2.63620 + 0.856554i 0.250217 + 0.0813005i
112112 0 0
113113 0.368226 0.722684i 0.0346398 0.0679844i −0.873038 0.487652i 0.837853π-0.837853\pi
0.907678 + 0.419668i 0.137853π0.137853\pi
114114 0 0
115115 2.85641 12.0999i 0.266362 1.12833i
116116 0 0
117117 0.692583 4.37280i 0.0640293 0.404265i
118118 0 0
119119 −28.0194 + 20.3573i −2.56853 + 1.86615i
120120 0 0
121121 0.399243 + 0.290067i 0.0362948 + 0.0263698i
122122 0 0
123123 −1.37002 2.68882i −0.123531 0.242443i
124124 0 0
125125 5.73279 9.59871i 0.512756 0.858534i
126126 0 0
127127 −4.49175 + 2.28866i −0.398578 + 0.203086i −0.641778 0.766890i 0.721803π-0.721803\pi
0.243200 + 0.969976i 0.421803π0.421803\pi
128128 0 0
129129 −9.44630 + 13.0017i −0.831700 + 1.14474i
130130 0 0
131131 −0.911267 1.25425i −0.0796178 0.109584i 0.767351 0.641228i 0.221575π-0.221575\pi
−0.846968 + 0.531643i 0.821575π0.821575\pi
132132 0 0
133133 2.03115 + 0.321702i 0.176123 + 0.0278951i
134134 0 0
135135 8.17279 + 1.92933i 0.703402 + 0.166051i
136136 0 0
137137 11.2034 + 5.70842i 0.957172 + 0.487704i 0.861527 0.507712i 0.169509π-0.169509\pi
0.0956453 + 0.995415i 0.469509π0.469509\pi
138138 0 0
139139 −1.60657 + 4.94453i −0.136268 + 0.419389i −0.995785 0.0917174i 0.970764π-0.970764\pi
0.859517 + 0.511107i 0.170764π0.170764\pi
140140 0 0
141141 −0.794181 2.44424i −0.0668821 0.205842i
142142 0 0
143143 9.16216 9.16216i 0.766178 0.766178i
144144 0 0
145145 −2.65797 + 0.648803i −0.220733 + 0.0538801i
146146 0 0
147147 4.04562 + 25.5430i 0.333677 + 2.10675i
148148 0 0
149149 8.06154i 0.660427i −0.943906 0.330213i 0.892879π-0.892879\pi
0.943906 0.330213i 0.107121π-0.107121\pi
150150 0 0
151151 15.8238i 1.28772i 0.765143 + 0.643860i 0.222668π0.222668\pi
−0.765143 + 0.643860i 0.777332π0.777332\pi
152152 0 0
153153 −1.41466 8.93179i −0.114368 0.722092i
154154 0 0
155155 1.27940 17.0852i 0.102764 1.37231i
156156 0 0
157157 −7.45048 + 7.45048i −0.594613 + 0.594613i −0.938874 0.344261i 0.888130π-0.888130\pi
0.344261 + 0.938874i 0.388130π0.388130\pi
158158 0 0
159159 0.570071 + 1.75450i 0.0452096 + 0.139141i
160160 0 0
161161 7.62241 23.4594i 0.600730 1.84886i
162162 0 0
163163 −6.06500 3.09027i −0.475048 0.242049i 0.200038 0.979788i 0.435893π-0.435893\pi
−0.675086 + 0.737739i 0.735893π0.735893\pi
164164 0 0
165165 −10.0842 11.7167i −0.785052 0.912144i
166166 0 0
167167 −5.25160 0.831772i −0.406381 0.0643645i −0.0501023 0.998744i 0.515955π-0.515955\pi
−0.356279 + 0.934380i 0.615955π0.615955\pi
168168 0 0
169169 −0.944813 1.30042i −0.0726779 0.100033i
170170 0 0
171171 −0.315615 + 0.434406i −0.0241357 + 0.0332199i
172172 0 0
173173 17.9448 9.14333i 1.36432 0.695154i 0.390101 0.920772i 0.372440π-0.372440\pi
0.974216 + 0.225618i 0.0724400π0.0724400\pi
174174 0 0
175175 12.9018 18.0443i 0.975284 1.36402i
176176 0 0
177177 −9.72757 19.0914i −0.731169 1.43500i
178178 0 0
179179 8.37543 + 6.08510i 0.626009 + 0.454822i 0.855015 0.518603i 0.173548π-0.173548\pi
−0.229006 + 0.973425i 0.573548π0.573548\pi
180180 0 0
181181 −11.8861 + 8.63577i −0.883489 + 0.641892i −0.934172 0.356823i 0.883860π-0.883860\pi
0.0506835 + 0.998715i 0.483860π0.483860\pi
182182 0 0
183183 0.670526 4.23354i 0.0495667 0.312952i
184184 0 0
185185 −1.17380 2.80365i −0.0862993 0.206128i
186186 0 0
187187 12.0154 23.5816i 0.878653 1.72445i
188188 0 0
189189 15.8454 + 5.14848i 1.15258 + 0.374497i
190190 0 0
191191 9.35722 3.04034i 0.677064 0.219992i 0.0497547 0.998761i 0.484156π-0.484156\pi
0.627310 + 0.778770i 0.284156π0.284156\pi
192192 0 0
193193 −10.2775 10.2775i −0.739792 0.739792i 0.232746 0.972538i 0.425229π-0.425229\pi
−0.972538 + 0.232746i 0.925229π0.925229\pi
194194 0 0
195195 −14.8247 + 9.16216i −1.06162 + 0.656116i
196196 0 0
197197 −14.0391 + 2.22358i −1.00025 + 0.158424i −0.635021 0.772495i 0.719008π-0.719008\pi
−0.365227 + 0.930919i 0.619008π0.619008\pi
198198 0 0
199199 −15.1694 −1.07533 −0.537666 0.843158i 0.680694π-0.680694\pi
−0.537666 + 0.843158i 0.680694π0.680694\pi
200200 0 0
201201 23.4334 1.65287
202202 0 0
203203 −5.36152 + 0.849182i −0.376305 + 0.0596009i
204204 0 0
205205 −1.25471 + 3.06195i −0.0876325 + 0.213856i
206206 0 0
207207 4.55420 + 4.55420i 0.316539 + 0.316539i
208208 0 0
209209 −1.49458 + 0.485617i −0.103382 + 0.0335909i
210210 0 0
211211 −6.62163 2.15150i −0.455852 0.148115i 0.0720858 0.997398i 0.477034π-0.477034\pi
−0.527937 + 0.849283i 0.677034π0.677034\pi
212212 0 0
213213 −1.58597 + 3.11263i −0.108669 + 0.213274i
214214 0 0
215215 17.5627 1.44931i 1.19777 0.0988423i
216216 0 0
217217 5.31761 33.5741i 0.360983 2.27916i
218218 0 0
219219 10.1731 7.39117i 0.687433 0.499449i
220220 0 0
221221 −24.1385 17.5376i −1.62373 1.17971i
222222 0 0
223223 −5.44537 10.6871i −0.364649 0.715664i 0.633671 0.773603i 0.281547π-0.281547\pi
−0.998320 + 0.0579386i 0.981547π0.981547\pi
224224 0 0
225225 2.66858 + 5.14053i 0.177905 + 0.342702i
226226 0 0
227227 −6.46387 + 3.29351i −0.429022 + 0.218598i −0.655148 0.755500i 0.727394π-0.727394\pi
0.226126 + 0.974098i 0.427394π0.427394\pi
228228 0 0
229229 9.02359 12.4199i 0.596296 0.820731i −0.399067 0.916922i 0.630666π-0.630666\pi
0.995363 + 0.0961910i 0.0306659π0.0306659\pi
230230 0 0
231231 −18.0278 24.8131i −1.18614 1.63258i
232232 0 0
233233 −2.99885 0.474971i −0.196461 0.0311164i 0.0574284 0.998350i 0.481710π-0.481710\pi
−0.253889 + 0.967233i 0.581710π0.581710\pi
234234 0 0
235235 −1.46333 + 2.40842i −0.0954573 + 0.157108i
236236 0 0
237237 30.4355 + 15.5076i 1.97700 + 1.00733i
238238 0 0
239239 6.57625 20.2396i 0.425382 1.30919i −0.477245 0.878770i 0.658365π-0.658365\pi
0.902628 0.430422i 0.141635π-0.141635\pi
240240 0 0
241241 7.98714 + 24.5819i 0.514497 + 1.58346i 0.784196 + 0.620513i 0.213076π0.213076\pi
−0.269699 + 0.962945i 0.586924π0.586924\pi
242242 0 0
243243 −8.08705 + 8.08705i −0.518785 + 0.518785i
244244 0 0
245245 18.3351 21.6333i 1.17138 1.38210i
246246 0 0
247247 0.277144 + 1.74982i 0.0176342 + 0.111338i
248248 0 0
249249 14.6381i 0.927653i
250250 0 0
251251 14.8326i 0.936228i 0.883668 + 0.468114i 0.155066π0.155066\pi
−0.883668 + 0.468114i 0.844934π0.844934\pi
252252 0 0
253253 2.94872 + 18.6175i 0.185384 + 1.17047i
254254 0 0
255255 −23.0155 + 27.1557i −1.44128 + 1.70056i
256256 0 0
257257 −12.6464 + 12.6464i −0.788861 + 0.788861i −0.981307 0.192447i 0.938358π-0.938358\pi
0.192447 + 0.981307i 0.438358π0.438358\pi
258258 0 0
259259 −1.86349 5.73524i −0.115792 0.356371i
260260 0 0
261261 0.437994 1.34801i 0.0271111 0.0834395i
262262 0 0
263263 24.4275 + 12.4464i 1.50626 + 0.767479i 0.995724 0.0923755i 0.0294460π-0.0294460\pi
0.510539 + 0.859855i 0.329446π0.329446\pi
264264 0 0
265265 1.05040 1.72879i 0.0645253 0.106198i
266266 0 0
267267 15.5849 + 2.46841i 0.953780 + 0.151064i
268268 0 0
269269 −3.38943 4.66515i −0.206657 0.284439i 0.693090 0.720851i 0.256249π-0.256249\pi
−0.899747 + 0.436412i 0.856249π0.856249\pi
270270 0 0
271271 5.76191 7.93059i 0.350011 0.481749i −0.597321 0.802002i 0.703768π-0.703768\pi
0.947332 + 0.320253i 0.103768π0.103768\pi
272272 0 0
273273 −30.8081 + 15.6975i −1.86459 + 0.950057i
274274 0 0
275275 −2.52455 + 16.7620i −0.152236 + 1.01079i
276276 0 0
277277 4.24456 + 8.33042i 0.255031 + 0.500526i 0.982653 0.185451i 0.0593747π-0.0593747\pi
−0.727623 + 0.685978i 0.759375π0.759375\pi
278278 0 0
279279 7.18057 + 5.21699i 0.429889 + 0.312333i
280280 0 0
281281 3.63235 2.63906i 0.216688 0.157433i −0.474147 0.880446i 0.657243π-0.657243\pi
0.690834 + 0.723013i 0.257243π0.257243\pi
282282 0 0
283283 −3.98074 + 25.1334i −0.236631 + 1.49403i 0.527827 + 0.849352i 0.323007π0.323007\pi
−0.764457 + 0.644675i 0.776993π0.776993\pi
284284 0 0
285285 2.10649 0.173832i 0.124778 0.0102969i
286286 0 0
287287 −2.98058 + 5.84972i −0.175938 + 0.345298i
288288 0 0
289289 −41.7933 13.5795i −2.45843 0.798792i
290290 0 0
291291 21.3862 6.94880i 1.25368 0.407346i
292292 0 0
293293 −8.29104 8.29104i −0.484368 0.484368i 0.422156 0.906523i 0.361274π-0.361274\pi
−0.906523 + 0.422156i 0.861274π0.861274\pi
294294 0 0
295295 −8.90879 + 21.7408i −0.518690 + 1.26580i
296296 0 0
297297 −12.5750 + 1.99168i −0.729674 + 0.115569i
298298 0 0
299299 21.2501 1.22893
300300 0 0
301301 34.9636 2.01527
302302 0 0
303303 −28.3812 + 4.49514i −1.63046 + 0.258239i
304304 0 0
305305 −3.99814 + 2.47098i −0.228933 + 0.141488i
306306 0 0
307307 −15.0113 15.0113i −0.856740 0.856740i 0.134212 0.990953i 0.457150π-0.457150\pi
−0.990953 + 0.134212i 0.957150π0.957150\pi
308308 0 0
309309 10.3960 3.37785i 0.591406 0.192159i
310310 0 0
311311 −17.8463 5.79862i −1.01197 0.328810i −0.244332 0.969692i 0.578569π-0.578569\pi
−0.767639 + 0.640882i 0.778569π0.778569\pi
312312 0 0
313313 6.73195 13.2122i 0.380513 0.746798i −0.618734 0.785600i 0.712354π-0.712354\pi
0.999247 + 0.0388023i 0.0123543π0.0123543\pi
314314 0 0
315315 4.43784 + 10.5999i 0.250044 + 0.597237i
316316 0 0
317317 −2.47741 + 15.6418i −0.139145 + 0.878529i 0.815060 + 0.579377i 0.196704π0.196704\pi
−0.954205 + 0.299152i 0.903296π0.903296\pi
318318 0 0
319319 3.35596 2.43825i 0.187898 0.136516i
320320 0 0
321321 −6.76414 4.91444i −0.377538 0.274297i
322322 0 0
323323 1.64285 + 3.22428i 0.0914107 + 0.179404i
324324 0 0
325325 18.2188 + 5.76712i 1.01060 + 0.319902i
326326 0 0
327327 −2.86857 + 1.46161i −0.158632 + 0.0808271i
328328 0 0
329329 −3.28646 + 4.52343i −0.181189 + 0.249385i
330330 0 0
331331 11.1337 + 15.3242i 0.611964 + 0.842296i 0.996737 0.0807153i 0.0257205π-0.0257205\pi
−0.384774 + 0.923011i 0.625720π0.625720\pi
332332 0 0
333333 1.55519 + 0.246317i 0.0852237 + 0.0134981i
334334 0 0
335335 −16.7620 19.4756i −0.915805 1.06406i
336336 0 0
337337 24.3115 + 12.3873i 1.32433 + 0.674780i 0.965934 0.258790i 0.0833237π-0.0833237\pi
0.358396 + 0.933570i 0.383324π0.383324\pi
338338 0 0
339339 0.511107 1.57303i 0.0277595 0.0854351i
340340 0 0
341341 8.02707 + 24.7048i 0.434690 + 1.33784i
342342 0 0
343343 17.8249 17.8249i 0.962456 0.962456i
344344 0 0
345345 1.89319 25.2818i 0.101926 1.36113i
346346 0 0
347347 −3.77107 23.8096i −0.202441 1.27816i −0.854282 0.519809i 0.826003π-0.826003\pi
0.651841 0.758356i 0.273997π-0.273997\pi
348348 0 0
349349 17.6117i 0.942731i 0.881938 + 0.471366i 0.156239π0.156239\pi
−0.881938 + 0.471366i 0.843761π0.843761\pi
350350 0 0
351351 14.3532i 0.766116i
352352 0 0
353353 −1.73275 10.9402i −0.0922250 0.582286i −0.989915 0.141659i 0.954756π-0.954756\pi
0.897690 0.440627i 0.145244π-0.145244\pi
354354 0 0
355355 3.72136 0.908373i 0.197509 0.0482114i
356356 0 0
357357 −49.9400 + 49.9400i −2.64310 + 2.64310i
358358 0 0
359359 −8.01444 24.6659i −0.422986 1.30182i −0.904910 0.425603i 0.860062π-0.860062\pi
0.481924 0.876213i 0.339938π-0.339938\pi
360360 0 0
361361 −5.80493 + 17.8657i −0.305522 + 0.940301i
362362 0 0
363363 0.896651 + 0.456866i 0.0470620 + 0.0239793i
364364 0 0
365365 −13.4197 3.16795i −0.702417 0.165818i
366366 0 0
367367 −17.9407 2.84153i −0.936497 0.148327i −0.330511 0.943802i 0.607221π-0.607221\pi
−0.605986 + 0.795476i 0.707221π0.707221\pi
368368 0 0
369369 −1.00760 1.38685i −0.0524538 0.0721964i
370370 0 0
371371 2.35906 3.24696i 0.122476 0.168574i
372372 0 0
373373 −2.07223 + 1.05585i −0.107296 + 0.0546701i −0.506815 0.862055i 0.669177π-0.669177\pi
0.399519 + 0.916725i 0.369177π0.369177\pi
374374 0 0
375375 8.48442 21.1616i 0.438134 1.09278i
376376 0 0
377377 −2.12308 4.16678i −0.109344 0.214600i
378378 0 0
379379 −22.5526 16.3854i −1.15845 0.841664i −0.168870 0.985638i 0.554012π-0.554012\pi
−0.989581 + 0.143975i 0.954012π0.954012\pi
380380 0 0
381381 −8.31677 + 6.04249i −0.426081 + 0.309566i
382382 0 0
383383 −5.09982 + 32.1990i −0.260589 + 1.64529i 0.416314 + 0.909221i 0.363322π0.363322\pi
−0.676903 + 0.736072i 0.736678π0.736678\pi
384384 0 0
385385 −7.72694 + 32.7318i −0.393801 + 1.66817i
386386 0 0
387387 −4.14458 + 8.13419i −0.210681 + 0.413484i
388388 0 0
389389 7.24292 + 2.35337i 0.367231 + 0.119321i 0.486819 0.873503i 0.338157π-0.338157\pi
−0.119588 + 0.992824i 0.538157π0.538157\pi
390390 0 0
391391 41.2807 13.4129i 2.08765 0.678319i
392392 0 0
393393 −2.23550 2.23550i −0.112766 0.112766i
394394 0 0
395395 −8.88212 36.3877i −0.446908 1.83086i
396396 0 0
397397 30.3958 4.81421i 1.52552 0.241619i 0.663377 0.748285i 0.269122π-0.269122\pi
0.862142 + 0.506667i 0.169122π0.169122\pi
398398 0 0
399399 4.19357 0.209941
400400 0 0
401401 20.2946 1.01346 0.506732 0.862104i 0.330853π-0.330853\pi
0.506732 + 0.862104i 0.330853π0.330853\pi
402402 0 0
403403 28.9238 4.58108i 1.44080 0.228200i
404404 0 0
405405 24.8253 + 1.85901i 1.23358 + 0.0923750i
406406 0 0
407407 3.25852 + 3.25852i 0.161519 + 0.161519i
408408 0 0
409409 −16.9278 + 5.50016i −0.837024 + 0.271966i −0.696001 0.718041i 0.745039π-0.745039\pi
−0.141023 + 0.990006i 0.545039π0.545039\pi
410410 0 0
411411 24.3859 + 7.92345i 1.20287 + 0.390835i
412412 0 0
413413 −21.1630 + 41.5347i −1.04136 + 2.04379i
414414 0 0
415415 −12.1658 + 10.4707i −0.597195 + 0.513986i
416416 0 0
417417 −1.65849 + 10.4713i −0.0812167 + 0.512782i
418418 0 0
419419 −13.9634 + 10.1450i −0.682159 + 0.495617i −0.874073 0.485794i 0.838530π-0.838530\pi
0.191914 + 0.981412i 0.438530π0.438530\pi
420420 0 0
421421 22.6049 + 16.4235i 1.10170 + 0.800430i 0.981336 0.192300i 0.0615946π-0.0615946\pi
0.120362 + 0.992730i 0.461595π0.461595\pi
422422 0 0
423423 −0.662787 1.30079i −0.0322258 0.0632467i
424424 0 0
425425 39.0322 0.296310i 1.89334 0.0143732i
426426 0 0
427427 −8.30878 + 4.23354i −0.402090 + 0.204875i
428428 0 0
429429 15.5308 21.3763i 0.749834 1.03206i
430430 0 0
431431 7.16187 + 9.85746i 0.344975 + 0.474817i 0.945886 0.324498i 0.105196π-0.105196\pi
−0.600911 + 0.799316i 0.705196π0.705196\pi
432432 0 0
433433 −34.4645 5.45864i −1.65626 0.262326i −0.742877 0.669428i 0.766539π-0.766539\pi
−0.913383 + 0.407102i 0.866539π0.866539\pi
434434 0 0
435435 −5.14647 + 2.15466i −0.246754 + 0.103308i
436436 0 0
437437 −2.29637 1.17006i −0.109850 0.0559714i
438438 0 0
439439 −1.07430 + 3.30636i −0.0512736 + 0.157804i −0.973415 0.229050i 0.926438π-0.926438\pi
0.922141 + 0.386854i 0.126438π0.126438\pi
440440 0 0
441441 4.53968 + 13.9717i 0.216175 + 0.665319i
442442 0 0
443443 2.50489 2.50489i 0.119011 0.119011i −0.645093 0.764104i 0.723181π-0.723181\pi
0.764104 + 0.645093i 0.223181π0.223181\pi
444444 0 0
445445 −9.09642 14.7183i −0.431212 0.697715i
446446 0 0
447447 −2.57165 16.2368i −0.121635 0.767974i
448448 0 0
449449 20.1589i 0.951358i −0.879619 0.475679i 0.842202π-0.842202\pi
0.879619 0.475679i 0.157798π-0.157798\pi
450450 0 0
451451 5.01701i 0.236242i
452452 0 0
453453 5.04783 + 31.8708i 0.237168 + 1.49742i
454454 0 0
455455 35.0834 + 14.3763i 1.64473 + 0.673969i
456456 0 0
457457 −12.1697 + 12.1697i −0.569275 + 0.569275i −0.931925 0.362650i 0.881872π-0.881872\pi
0.362650 + 0.931925i 0.381872π0.381872\pi
458458 0 0
459459 9.05961 + 27.8826i 0.422866 + 1.30145i
460460 0 0
461461 5.73768 17.6588i 0.267231 0.822451i −0.723941 0.689862i 0.757671π-0.757671\pi
0.991171 0.132589i 0.0423290π-0.0423290\pi
462462 0 0
463463 11.7335 + 5.97851i 0.545301 + 0.277845i 0.704863 0.709343i 0.251008π-0.251008\pi
−0.159562 + 0.987188i 0.551008π0.551008\pi
464464 0 0
465465 −2.87337 34.8195i −0.133249 1.61471i
466466 0 0
467467 −25.2095 3.99280i −1.16656 0.184765i −0.457036 0.889448i 0.651089π-0.651089\pi
−0.709522 + 0.704684i 0.751089π0.751089\pi
468468 0 0
469469 −29.9659 41.2445i −1.38370 1.90450i
470470 0 0
471471 −12.6293 + 17.3828i −0.581929 + 0.800956i
472472 0 0
473473 −23.8061 + 12.1298i −1.09460 + 0.557729i
474474 0 0
475475 −1.65125 1.62637i −0.0757645 0.0746229i
476476 0 0
477477 0.475756 + 0.933723i 0.0217833 + 0.0427522i
478478 0 0
479479 10.4934 + 7.62388i 0.479455 + 0.348344i 0.801114 0.598511i 0.204241π-0.204241\pi
−0.321660 + 0.946855i 0.604241π0.604241\pi
480480 0 0
481481 4.20295 3.05362i 0.191638 0.139233i
482482 0 0
483483 7.86873 49.6812i 0.358040 2.26057i
484484 0 0
485485 −21.0728 12.8036i −0.956866 0.581384i
486486 0 0
487487 −12.8000 + 25.1215i −0.580025 + 1.13836i 0.395498 + 0.918467i 0.370572π0.370572\pi
−0.975523 + 0.219897i 0.929428π0.929428\pi
488488 0 0
489489 −13.2014 4.28938i −0.596986 0.193973i
490490 0 0
491491 −29.4078 + 9.55517i −1.32716 + 0.431219i −0.884946 0.465693i 0.845805π-0.845805\pi
−0.442209 + 0.896912i 0.645805π0.645805\pi
492492 0 0
493493 −6.75435 6.75435i −0.304201 0.304201i
494494 0 0
495495 −6.69903 5.67768i −0.301099 0.255193i
496496 0 0
497497 7.50654 1.18892i 0.336714 0.0533303i
498498 0 0
499499 −29.4300 −1.31747 −0.658733 0.752377i 0.728907π-0.728907\pi
−0.658733 + 0.752377i 0.728907π0.728907\pi
500500 0 0
501501 −10.8426 −0.484413
502502 0 0
503503 −17.2261 + 2.72834i −0.768073 + 0.121651i −0.528162 0.849144i 0.677118π-0.677118\pi
−0.239912 + 0.970795i 0.577118π0.577118\pi
504504 0 0
505505 24.0371 + 20.3723i 1.06963 + 0.906556i
506506 0 0
507507 −2.31779 2.31779i −0.102937 0.102937i
508508 0 0
509509 19.0616 6.19349i 0.844891 0.274522i 0.145586 0.989346i 0.453493π-0.453493\pi
0.699304 + 0.714824i 0.253493π0.253493\pi
510510 0 0
511511 −26.0180 8.45377i −1.15097 0.373973i
512512 0 0
513513 0.790303 1.55106i 0.0348927 0.0684809i
514514 0 0
515515 −10.2436 6.22393i −0.451387 0.274259i
516516 0 0
517517 0.668395 4.22008i 0.0293960 0.185599i
518518 0 0
519519 33.2260 24.1401i 1.45846 1.05963i
520520 0 0
521521 17.0280 + 12.3716i 0.746011 + 0.542009i 0.894588 0.446892i 0.147469π-0.147469\pi
−0.148577 + 0.988901i 0.547469π0.547469\pi
522522 0 0
523523 5.05993 + 9.93068i 0.221255 + 0.434238i 0.974776 0.223186i 0.0716459π-0.0716459\pi
−0.753520 + 0.657425i 0.771646π0.771646\pi
524524 0 0
525525 20.2294 40.4588i 0.882883 1.76577i
526526 0 0
527527 53.2961 27.1557i 2.32161 1.18292i
528528 0 0
529529 −4.65148 + 6.40221i −0.202238 + 0.278357i
530530 0 0
531531 −7.15429 9.84703i −0.310470 0.427325i
532532 0 0
533533 −5.58631 0.884785i −0.241970 0.0383243i
534534 0 0
535535 0.754004 + 9.13701i 0.0325984 + 0.395027i
536536 0 0
537537 18.8102 + 9.58425i 0.811718 + 0.413591i
538538 0 0
539539 −13.2861 + 40.8905i −0.572275 + 1.76128i
540540 0 0
541541 1.88970 + 5.81589i 0.0812444 + 0.250045i 0.983425 0.181313i 0.0580347π-0.0580347\pi
−0.902181 + 0.431358i 0.858035π0.858035\pi
542542 0 0
543543 −21.1851 + 21.1851i −0.909138 + 0.909138i
544544 0 0
545545 3.26664 + 1.33858i 0.139927 + 0.0573386i
546546 0 0
547547 1.65747 + 10.4648i 0.0708682 + 0.447444i 0.997451 + 0.0713535i 0.0227319π0.0227319\pi
−0.926583 + 0.376091i 0.877268π0.877268\pi
548548 0 0
549549 2.43486i 0.103917i
550550 0 0
551551 0.567177i 0.0241626i
552552 0 0
553553 −11.6253 73.3994i −0.494359 3.12126i
554554 0 0
555555 −3.25852 5.27240i −0.138317 0.223801i
556556 0 0
557557 −23.5420 + 23.5420i −0.997506 + 0.997506i −0.999997 0.00249078i 0.999207π-0.999207\pi
0.00249078 + 0.999997i 0.499207π0.499207\pi
558558 0 0
559559 9.30786 + 28.6466i 0.393680 + 1.21162i
560560 0 0
561561 16.6777 51.3287i 0.704133 2.16710i
562562 0 0
563563 −16.5402 8.42768i −0.697088 0.355184i 0.0692697 0.997598i 0.477933π-0.477933\pi
−0.766358 + 0.642414i 0.777933π0.777933\pi
564564 0 0
565565 −1.67294 + 0.700407i −0.0703813 + 0.0294664i
566566 0 0
567567 48.7842 + 7.72666i 2.04874 + 0.324489i
568568 0 0
569569 17.9240 + 24.6702i 0.751412 + 1.03423i 0.997880 + 0.0650792i 0.0207300π0.0207300\pi
−0.246468 + 0.969151i 0.579270π0.579270\pi
570570 0 0
571571 0.613924 0.844994i 0.0256919 0.0353619i −0.795978 0.605326i 0.793043π-0.793043\pi
0.821670 + 0.569964i 0.193043π0.193043\pi
572572 0 0
573573 17.8765 9.10855i 0.746803 0.380515i
574574 0 0
575575 −22.3660 + 16.5107i −0.932725 + 0.688543i
576576 0 0
577577 −14.6237 28.7007i −0.608794 1.19483i −0.965449 0.260590i 0.916083π-0.916083\pi
0.356655 0.934236i 0.383917π-0.383917\pi
578578 0 0
579579 −23.9786 17.4214i −0.996515 0.724010i
580580 0 0
581581 −25.7642 + 18.7188i −1.06888 + 0.776585i
582582 0 0
583583 −0.479781 + 3.02922i −0.0198705 + 0.125457i
584584 0 0
585585 −7.50337 + 6.45790i −0.310226 + 0.267001i
586586 0 0
587587 −12.5595 + 24.6494i −0.518386 + 1.01739i 0.472327 + 0.881423i 0.343414π0.343414\pi
−0.990713 + 0.135967i 0.956586π0.956586\pi
588588 0 0
589589 −3.37785 1.09753i −0.139182 0.0452230i
590590 0 0
591591 −27.5670 + 8.95706i −1.13395 + 0.368444i
592592 0 0
593593 25.4162 + 25.4162i 1.04372 + 1.04372i 0.999000 + 0.0447166i 0.0142385π0.0142385\pi
0.0447166 + 0.999000i 0.485762π0.485762\pi
594594 0 0
595595 77.2275 + 5.78308i 3.16602 + 0.237083i
596596 0 0
597597 −30.5528 + 4.83909i −1.25044 + 0.198051i
598598 0 0
599599 17.7420 0.724918 0.362459 0.932000i 0.381937π-0.381937\pi
0.362459 + 0.932000i 0.381937π0.381937\pi
600600 0 0
601601 32.5333 1.32706 0.663531 0.748148i 0.269057π-0.269057\pi
0.663531 + 0.748148i 0.269057π0.269057\pi
602602 0 0
603603 13.1476 2.08237i 0.535411 0.0848008i
604604 0 0
605605 −0.261673 1.07201i −0.0106385 0.0435833i
606606 0 0
607607 18.9437 + 18.9437i 0.768903 + 0.768903i 0.977913 0.209011i 0.0670244π-0.0670244\pi
−0.209011 + 0.977913i 0.567024π0.567024\pi
608608 0 0
609609 −10.5278 + 3.42069i −0.426607 + 0.138613i
610610 0 0
611611 −4.58108 1.48848i −0.185331 0.0602176i
612612 0 0
613613 19.1250 37.5349i 0.772452 1.51602i −0.0820818 0.996626i 0.526157π-0.526157\pi
0.854534 0.519396i 0.173843π-0.173843\pi
614614 0 0
615615 −1.55034 + 6.56735i −0.0625157 + 0.264821i
616616 0 0
617617 2.30094 14.5276i 0.0926325 0.584859i −0.897089 0.441850i 0.854322π-0.854322\pi
0.989721 0.143009i 0.0456777π-0.0456777\pi
618618 0 0
619619 28.6010 20.7799i 1.14957 0.835213i 0.161148 0.986930i 0.448480π-0.448480\pi
0.988424 + 0.151717i 0.0484802π0.0484802\pi
620620 0 0
621621 −16.8925 12.2731i −0.677872 0.492503i
622622 0 0
623623 −15.5849 30.5871i −0.624396 1.22545i
624624 0 0
625625 −23.6564 + 8.08551i −0.946255 + 0.323420i
626626 0 0
627627 −2.85532 + 1.45486i −0.114031 + 0.0581015i
628628 0 0
629629 6.23727 8.58486i 0.248696 0.342301i
630630 0 0
631631 −15.8748 21.8497i −0.631965 0.869825i 0.366190 0.930540i 0.380662π-0.380662\pi
−0.998155 + 0.0607152i 0.980662π0.980662\pi
632632 0 0
633633 −14.0230 2.22102i −0.557364 0.0882777i
634634 0 0
635635 10.9709 + 2.58989i 0.435368 + 0.102777i
636636 0 0
637637 43.1875 + 22.0051i 1.71115 + 0.871875i
638638 0 0
639639 −0.613225 + 1.88731i −0.0242588 + 0.0746609i
640640 0 0
641641 4.77172 + 14.6859i 0.188472 + 0.580057i 0.999991 0.00426935i 0.00135898π-0.00135898\pi
−0.811519 + 0.584326i 0.801359π0.801359\pi
642642 0 0
643643 6.76567 6.76567i 0.266812 0.266812i −0.561002 0.827814i 0.689584π-0.689584\pi
0.827814 + 0.561002i 0.189584π0.189584\pi
644644 0 0
645645 34.9109 8.52163i 1.37461 0.335539i
646646 0 0
647647 −0.544922 3.44050i −0.0214231 0.135260i 0.974659 0.223697i 0.0718127π-0.0718127\pi
−0.996082 + 0.0884372i 0.971813π0.971813\pi
648648 0 0
649649 35.6222i 1.39829i
650650 0 0
651651 69.3181i 2.71679i
652652 0 0
653653 2.45959 + 15.5293i 0.0962513 + 0.607707i 0.987914 + 0.155006i 0.0495396π0.0495396\pi
−0.891662 + 0.452701i 0.850460π0.850460\pi
654654 0 0
655655 −0.258872 + 3.45699i −0.0101150 + 0.135076i
656656 0 0
657657 5.05092 5.05092i 0.197055 0.197055i
658658 0 0
659659 1.70198 + 5.23816i 0.0662997 + 0.204050i 0.978718 0.205209i 0.0657874π-0.0657874\pi
−0.912418 + 0.409259i 0.865787π0.865787\pi
660660 0 0
661661 7.59689 23.3808i 0.295485 0.909409i −0.687573 0.726115i 0.741324π-0.741324\pi
0.983058 0.183294i 0.0586760π-0.0586760\pi
662662 0 0
663663 −54.2120 27.6224i −2.10542 1.07277i
664664 0 0
665665 −2.99967 3.48529i −0.116322 0.135154i
666666 0 0
667667 6.71935 + 1.06424i 0.260174 + 0.0412076i
668668 0 0
669669 −14.3768 19.7879i −0.555838 0.765046i
670670 0 0
671671 4.18857 5.76507i 0.161698 0.222558i
672672 0 0
673673 −2.82484 + 1.43933i −0.108890 + 0.0554821i −0.507587 0.861601i 0.669462π-0.669462\pi
0.398697 + 0.917083i 0.369462π0.369462\pi
674674 0 0
675675 −11.1520 15.1069i −0.429240 0.581464i
676676 0 0
677677 −0.808560 1.58689i −0.0310755 0.0609890i 0.874947 0.484219i 0.160896π-0.160896\pi
−0.906022 + 0.423230i 0.860896π0.860896\pi
678678 0 0
679679 −39.5784 28.7554i −1.51888 1.10353i
680680 0 0
681681 −11.9683 + 8.69546i −0.458625 + 0.333211i
682682 0 0
683683 5.36210 33.8550i 0.205175 1.29542i −0.643065 0.765812i 0.722337π-0.722337\pi
0.848240 0.529612i 0.177663π-0.177663\pi
684684 0 0
685685 −10.8581 25.9348i −0.414865 0.990919i
686686 0 0
687687 14.2125 27.8936i 0.542240 1.06421i
688688 0 0
689689 3.28834 + 1.06845i 0.125276 + 0.0407046i
690690 0 0
691691 −40.0444 + 13.0112i −1.52336 + 0.494970i −0.946728 0.322033i 0.895634π-0.895634\pi
−0.576633 + 0.817003i 0.695634π0.695634\pi
692692 0 0
693693 −12.3197 12.3197i −0.467986 0.467986i
694694 0 0
695695 9.88906 6.11177i 0.375113 0.231833i
696696 0 0
697697 −11.4105 + 1.80724i −0.432203 + 0.0684542i
698698 0 0
699699 −6.19151 −0.234185
700700 0 0
701701 −0.177945 −0.00672090 −0.00336045 0.999994i 0.501070π-0.501070\pi
−0.00336045 + 0.999994i 0.501070π0.501070\pi
702702 0 0
703703 −0.622323 + 0.0985662i −0.0234713 + 0.00371750i
704704 0 0
705705 −2.17902 + 5.31761i −0.0820665 + 0.200273i
706706 0 0
707707 44.2047 + 44.2047i 1.66249 + 1.66249i
708708 0 0
709709 −31.1456 + 10.1198i −1.16970 + 0.380057i −0.828529 0.559945i 0.810822π-0.810822\pi
−0.341167 + 0.940003i 0.610822π0.610822\pi
710710 0 0
711711 18.4542 + 5.99614i 0.692088 + 0.224873i
712712 0 0
713713 −19.3406 + 37.9581i −0.724311 + 1.42154i
714714 0 0
715715 −28.8751 + 2.38283i −1.07987 + 0.0891129i
716716 0 0
717717 6.78877 42.8626i 0.253531 1.60073i
718718 0 0
719719 6.46726 4.69874i 0.241188 0.175233i −0.460624 0.887595i 0.652374π-0.652374\pi
0.701812 + 0.712362i 0.252374π0.252374\pi
720720 0 0
721721 −19.2393 13.9782i −0.716509 0.520574i
722722 0 0
723723 23.9286 + 46.9626i 0.889915 + 1.74656i
724724 0 0
725725 5.47202 + 2.73601i 0.203226 + 0.101613i
726726 0 0
727727 −23.4758 + 11.9615i −0.870670 + 0.443629i −0.831448 0.555602i 0.812488π-0.812488\pi
−0.0392218 + 0.999231i 0.512488π0.512488\pi
728728 0 0
729729 5.92358 8.15311i 0.219392 0.301967i
730730 0 0
731731 36.1631 + 49.7742i 1.33754 + 1.84096i
732732 0 0
733733 0.729982 + 0.115618i 0.0269625 + 0.00427044i 0.169901 0.985461i 0.445655π-0.445655\pi
−0.142939 + 0.989732i 0.545655π0.545655\pi
734734 0 0
735735 30.0277 49.4208i 1.10759 1.82291i
736736 0 0
737737 34.7120 + 17.6867i 1.27863 + 0.651497i
738738 0 0
739739 −3.59062 + 11.0508i −0.132083 + 0.406510i −0.995125 0.0986224i 0.968556π-0.968556\pi
0.863042 + 0.505133i 0.168556π0.168556\pi
740740 0 0
741741 1.11639 + 3.43590i 0.0410117 + 0.126221i
742742 0 0
743743 −17.6779 + 17.6779i −0.648540 + 0.648540i −0.952640 0.304100i 0.901644π-0.901644\pi
0.304100 + 0.952640i 0.401644π0.401644\pi
744744 0 0
745745 −11.6549 + 13.7515i −0.427004 + 0.503817i
746746 0 0
747747 −1.30079 8.21289i −0.0475935 0.300494i
748748 0 0
749749 18.1898i 0.664641i
750750 0 0
751751 8.62520i 0.314738i −0.987540 0.157369i 0.949699π-0.949699\pi
0.987540 0.157369i 0.0503012π-0.0503012\pi
752752 0 0
753753 4.73166 + 29.8745i 0.172431 + 1.08869i
754754 0 0
755755 22.8772 26.9925i 0.832585 0.982358i
756756 0 0
757757 20.2477 20.2477i 0.735915 0.735915i −0.235870 0.971785i 0.575794π-0.575794\pi
0.971785 + 0.235870i 0.0757938π0.0757938\pi
758758 0 0
759759 11.8781 + 36.5569i 0.431146 + 1.32693i
760760 0 0
761761 −10.9950 + 33.8391i −0.398568 + 1.22667i 0.527580 + 0.849506i 0.323100π0.323100\pi
−0.926148 + 0.377161i 0.876900π0.876900\pi
762762 0 0
763763 6.24077 + 3.17983i 0.225931 + 0.115118i
764764 0 0
765765 −10.4999 + 17.2812i −0.379626 + 0.624805i
766766 0 0
767767 −39.6645 6.28224i −1.43220 0.226838i
768768 0 0
769769 5.38162 + 7.40717i 0.194066 + 0.267109i 0.894950 0.446166i 0.147211π-0.147211\pi
−0.700884 + 0.713275i 0.747211π0.747211\pi
770770 0 0
771771 −21.4369 + 29.5054i −0.772033 + 1.06261i
772772 0 0
773773 −4.35369 + 2.21832i −0.156591 + 0.0797873i −0.530530 0.847666i 0.678007π-0.678007\pi
0.373939 + 0.927453i 0.378007π0.378007\pi
774774 0 0
775775 −26.8832 + 27.2945i −0.965674 + 0.980448i
776776 0 0
777777 −5.58283 10.9569i −0.200283 0.393077i
778778 0 0
779779 0.554960 + 0.403202i 0.0198835 + 0.0144462i
780780 0 0
781781 −4.69860 + 3.41373i −0.168129 + 0.122153i
782782 0 0
783783 −0.718831 + 4.53852i −0.0256889 + 0.162193i
784784 0 0
785785 23.4807 1.93767i 0.838061 0.0691585i
786786 0 0
787787 −2.38805 + 4.68681i −0.0851248 + 0.167067i −0.929645 0.368458i 0.879886π-0.879886\pi
0.844520 + 0.535524i 0.179886π0.179886\pi
788788 0 0
789789 53.1700 + 17.2760i 1.89290 + 0.615041i
790790 0 0
791791 −3.42223 + 1.11195i −0.121681 + 0.0395364i
792792 0 0
793793 −5.68058 5.68058i −0.201723 0.201723i
794794 0 0
795795 1.56412 3.81704i 0.0554736 0.135376i
796796 0 0
797797 −29.1549 + 4.61769i −1.03272 + 0.163567i −0.649714 0.760179i 0.725111π-0.725111\pi
−0.383007 + 0.923746i 0.625111π0.625111\pi
798798 0 0
799799 −9.83876 −0.348070
800800 0 0
801801 8.96344 0.316707
802802 0 0
803803 20.6480 3.27032i 0.728653 0.115407i
804804 0 0
805805 −46.9187 + 28.9974i −1.65367 + 1.02202i
806806 0 0
807807 −8.31486 8.31486i −0.292697 0.292697i
808808 0 0
809809 29.7303 9.65994i 1.04526 0.339626i 0.264453 0.964398i 0.414808π-0.414808\pi
0.780807 + 0.624773i 0.214808π0.214808\pi
810810 0 0
811811 41.3581 + 13.4380i 1.45228 + 0.471874i 0.925702 0.378254i 0.123476π-0.123476\pi
0.526576 + 0.850128i 0.323476π0.323476\pi
812812 0 0
813813 9.07522 17.8111i 0.318282 0.624663i
814814 0 0
815815 5.87805 + 14.0399i 0.205899 + 0.491796i
816816 0 0
817817 0.571477 3.60817i 0.0199935 0.126234i
818818 0 0
819819 −15.8903 + 11.5450i −0.555253 + 0.403415i
820820 0 0
821821 −40.1380 29.1620i −1.40083 1.01776i −0.994578 0.103997i 0.966837π-0.966837\pi
−0.406249 0.913763i 0.633163π-0.633163\pi
822822 0 0
823823 −6.19436 12.1571i −0.215922 0.423771i 0.757485 0.652852i 0.226428π-0.226428\pi
−0.973407 + 0.229082i 0.926428π0.926428\pi
824824 0 0
825825 0.262404 + 34.5657i 0.00913572 + 1.20342i
826826 0 0
827827 23.8274 12.1406i 0.828558 0.422171i 0.0123460 0.999924i 0.496070π-0.496070\pi
0.816212 + 0.577752i 0.196070π0.196070\pi
828828 0 0
829829 −26.5793 + 36.5832i −0.923136 + 1.27059i 0.0393407 + 0.999226i 0.487474π0.487474\pi
−0.962477 + 0.271363i 0.912526π0.912526\pi
830830 0 0
831831 11.2064 + 15.4243i 0.388746 + 0.535064i
832832 0 0
833833 97.7858 + 15.4878i 3.38808 + 0.536619i
834834 0 0
835835 7.75576 + 9.01134i 0.268399 + 0.311850i
836836 0 0
837837 −25.6384 13.0634i −0.886192 0.451538i
838838 0 0
839839 −11.1825 + 34.4161i −0.386062 + 1.18818i 0.549645 + 0.835398i 0.314763π0.314763\pi
−0.935707 + 0.352778i 0.885237π0.885237\pi
840840 0 0
841841 8.49885 + 26.1568i 0.293064 + 0.901957i
842842 0 0
843843 6.47407 6.47407i 0.222979 0.222979i
844844 0 0
845845 −0.268402 + 3.58425i −0.00923330 + 0.123302i
846846 0 0
847847 −0.342490 2.16240i −0.0117681 0.0743008i
848848 0 0
849849 51.8912i 1.78090i
850850 0 0
851851 7.55761i 0.259072i
852852 0 0
853853 1.36501 + 8.61833i 0.0467371 + 0.295086i 0.999975 0.00713613i 0.00227152π-0.00227152\pi
−0.953237 + 0.302222i 0.902272π0.902272\pi
854854 0 0
855855 1.16642 0.284720i 0.0398908 0.00973722i
856856 0 0
857857 −33.2545 + 33.2545i −1.13595 + 1.13595i −0.146781 + 0.989169i 0.546891π0.546891\pi
−0.989169 + 0.146781i 0.953109π0.953109\pi
858858 0 0
859859 5.11046 + 15.7284i 0.174367 + 0.536645i 0.999604 0.0281409i 0.00895872π-0.00895872\pi
−0.825237 + 0.564786i 0.808959π0.808959\pi
860860 0 0
861861 −4.13713 + 12.7328i −0.140993 + 0.433931i
862862 0 0
863863 33.5995 + 17.1198i 1.14374 + 0.582764i 0.920013 0.391888i 0.128178π-0.128178\pi
0.223726 + 0.974652i 0.428178π0.428178\pi
864864 0 0
865865 −43.8295 10.3467i −1.49025 0.351800i
866866 0 0
867867 −88.5080 14.0183i −3.00589 0.476086i
868868 0 0
869869 33.3796 + 45.9431i 1.13233 + 1.55851i
870870 0 0
871871 25.8154 35.5318i 0.874721 1.20395i
872872 0 0
873873 11.3815 5.79915i 0.385205 0.196272i
874874 0 0
875875 −48.0956 + 12.1276i −1.62593 + 0.409986i
876876 0 0
877877 −9.78063 19.1956i −0.330269 0.648188i 0.664839 0.746987i 0.268500π-0.268500\pi
−0.995107 + 0.0987983i 0.968500π0.968500\pi
878878 0 0
879879 −19.3439 14.0542i −0.652454 0.474035i
880880 0 0
881881 8.59034 6.24125i 0.289416 0.210273i −0.433598 0.901106i 0.642756π-0.642756\pi
0.723014 + 0.690833i 0.242756π0.242756\pi
882882 0 0
883883 −2.52020 + 15.9119i −0.0848116 + 0.535479i 0.908301 + 0.418317i 0.137380π0.137380\pi
−0.993113 + 0.117162i 0.962620π0.962620\pi
884884 0 0
885885 −11.0079 + 46.6301i −0.370026 + 1.56745i
886886 0 0
887887 −3.23809 + 6.35512i −0.108725 + 0.213384i −0.938958 0.344032i 0.888207π-0.888207\pi
0.830233 + 0.557416i 0.188207π0.188207\pi
888888 0 0
889889 21.2704 + 6.91118i 0.713388 + 0.231794i
890890 0 0
891891 −35.8968 + 11.6636i −1.20259 + 0.390745i
892892 0 0
893893 0.413091 + 0.413091i 0.0138236 + 0.0138236i
894894 0 0
895895 −5.48945 22.4888i −0.183492 0.751718i
896896 0 0
897897 42.8000 6.77885i 1.42905 0.226339i
898898 0 0
899899 9.37522 0.312681
900900 0 0
901901 7.06236 0.235281
902902 0 0
903903 70.4204 11.1535i 2.34344 0.371165i
904904 0 0
905905 32.7607 + 2.45324i 1.08900 + 0.0815485i
906906 0 0
907907 −19.7382 19.7382i −0.655396 0.655396i 0.298891 0.954287i 0.403383π-0.403383\pi
−0.954287 + 0.298891i 0.903383π0.903383\pi
908908 0 0
909909 −15.5241 + 5.04410i −0.514903 + 0.167302i
910910 0 0
911911 7.60272 + 2.47027i 0.251889 + 0.0818438i 0.432240 0.901759i 0.357723π-0.357723\pi
−0.180351 + 0.983602i 0.557723π0.557723\pi
912912 0 0
913913 11.0483 21.6835i 0.365646 0.717620i
914914 0 0
915915 −7.26442 + 6.25224i −0.240154 + 0.206693i
916916 0 0
917917 −1.07596 + 6.79332i −0.0355312 + 0.224335i
918918 0 0
919919 45.7747 33.2573i 1.50997 1.09706i 0.543778 0.839229i 0.316993π-0.316993\pi
0.966191 0.257827i 0.0830066π-0.0830066\pi
920920 0 0
921921 −35.0230 25.4457i −1.15405 0.838464i
922922 0 0
923923 2.97247 + 5.83381i 0.0978402 + 0.192022i
924924 0 0
925925 −2.05108 + 6.47953i −0.0674391 + 0.213046i
926926 0 0
927927 5.53260 2.81900i 0.181715 0.0925882i
928928 0 0
929929 −35.5268 + 48.8984i −1.16560 + 1.60431i −0.477635 + 0.878558i 0.658506π0.658506\pi
−0.687961 + 0.725748i 0.741494π0.741494\pi
930930 0 0
931931 −3.45537 4.75591i −0.113245 0.155869i
932932 0 0
933933 −37.7941 5.98600i −1.23732 0.195973i
934934 0 0
935935 −54.5890 + 22.8547i −1.78525 + 0.747427i
936936 0 0
937937 −16.3594 8.33555i −0.534440 0.272311i 0.165873 0.986147i 0.446956π-0.446956\pi
−0.700312 + 0.713837i 0.746956π0.746956\pi
938938 0 0
939939 9.34413 28.7583i 0.304934 0.938491i
940940 0 0
941941 −17.3832 53.5000i −0.566676 1.74405i −0.662918 0.748692i 0.730682π-0.730682\pi
0.0962423 0.995358i 0.469318π-0.469318\pi
942942 0 0
943943 5.81806 5.81806i 0.189462 0.189462i
944944 0 0
945945 −19.5860 31.6908i −0.637132 1.03090i
946946 0 0
947947 −8.31394 52.4921i −0.270167 1.70576i −0.633200 0.773989i 0.718259π-0.718259\pi
0.363033 0.931776i 0.381741π-0.381741\pi
948948 0 0
949949 23.5678i 0.765043i
950950 0 0
951951 32.2945i 1.04722i
952952 0 0
953953 0.0979909 + 0.618690i 0.00317424 + 0.0200413i 0.989225 0.146406i 0.0467705π-0.0467705\pi
−0.986050 + 0.166447i 0.946771π0.946771\pi
954954 0 0
955955 −20.3573 8.34188i −0.658746 0.269937i
956956 0 0
957957 5.98145 5.98145i 0.193353 0.193353i
958958 0 0
959959 −17.2380 53.0532i −0.556645 1.71318i
960960 0 0
961961 −8.56224 + 26.3519i −0.276201 + 0.850060i
962962 0 0
963963 −4.23181 2.15622i −0.136368 0.0694831i
964964 0 0
965965 2.67291 + 32.3903i 0.0860440 + 1.04268i
966966 0 0
967967 −14.8068 2.34516i −0.476154 0.0754153i −0.0862550 0.996273i 0.527490π-0.527490\pi
−0.389899 + 0.920858i 0.627490π0.627490\pi
968968 0 0
969969 4.33743 + 5.96996i 0.139338 + 0.191783i
970970 0 0
971971 33.6414 46.3034i 1.07960 1.48595i 0.219647 0.975579i 0.429509π-0.429509\pi
0.859956 0.510368i 0.170491π-0.170491\pi
972972 0 0
973973 20.5511 10.4713i 0.658838 0.335695i
974974 0 0
975975 38.5344 + 5.80374i 1.23409 + 0.185868i
976976 0 0
977977 6.58360 + 12.9210i 0.210628 + 0.413381i 0.972016 0.234916i 0.0754816π-0.0754816\pi
−0.761388 + 0.648297i 0.775482π0.775482\pi
978978 0 0
979979 21.2229 + 15.4194i 0.678288 + 0.492805i
980980 0 0
981981 −1.47956 + 1.07496i −0.0472386 + 0.0343209i
982982 0 0
983983 2.85036 17.9964i 0.0909122 0.573997i −0.899615 0.436683i 0.856153π-0.856153\pi
0.990528 0.137314i 0.0438469π-0.0438469\pi
984984 0 0
985985 27.1630 + 16.5040i 0.865484 + 0.525861i
986986 0 0
987987 −5.17630 + 10.1591i −0.164763 + 0.323366i
988988 0 0
989989 −41.6737 13.5406i −1.32515 0.430566i
990990 0 0
991991 19.9240 6.47370i 0.632907 0.205644i 0.0250446 0.999686i 0.492027π-0.492027\pi
0.607862 + 0.794042i 0.292027π0.292027\pi
992992 0 0
993993 27.3129 + 27.3129i 0.866750 + 0.866750i
994994 0 0
995995 25.8763 + 21.9311i 0.820334 + 0.695264i
996996 0 0
997997 47.9547 7.59528i 1.51874 0.240545i 0.659339 0.751846i 0.270836π-0.270836\pi
0.859402 + 0.511301i 0.170836π0.170836\pi
998998 0 0
999999 −5.10471 −0.161506
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.303.2 yes 16
4.3 odd 2 inner 400.2.bi.b.303.1 16
25.17 odd 20 inner 400.2.bi.b.367.1 yes 16
100.67 even 20 inner 400.2.bi.b.367.2 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
400.2.bi.b.303.1 16 4.3 odd 2 inner
400.2.bi.b.303.2 yes 16 1.1 even 1 trivial
400.2.bi.b.367.1 yes 16 25.17 odd 20 inner
400.2.bi.b.367.2 yes 16 100.67 even 20 inner