Properties

Label 135.3.l.a.37.10
Level 135135
Weight 33
Character 135.37
Analytic conductor 3.6783.678
Analytic rank 00
Dimension 4040
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [135,3,Mod(37,135)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(135, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([4, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("135.37");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 135=335 135 = 3^{3} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 135.l (of order 1212, degree 44, not 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: 3.678483568863.67848356886
Analytic rank: 00
Dimension: 4040
Relative dimension: 1010 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: no (minimal twist has level 45)
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 37.10
Character χ\chi == 135.37
Dual form 135.3.l.a.73.10

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+(0.9304973.47266i)q2+(7.729474.46261i)q4+(4.99913+0.0933744i)q5+(1.283234.78910i)q7+(12.5207+12.5207i)q8+(4.32742+17.4472i)q10+(1.377642.38615i)q11+(2.45318+9.15539i)q13+(15.43698.91249i)q14+(13.9793+24.2129i)q16+(9.175049.17504i)q1732.1912iq19+(39.0573+21.5874i)q20+(9.56819+2.56379i)q22+(0.1794120.669573i)q23+(24.98260.933581i)q25+34.0763q26+(31.2906+31.2906i)q28+(30.134917.3984i)q29+(12.848222.2537i)q31+(28.67657.68384i)q32+(40.3992+23.3245i)q34+(5.96788+24.0611i)q35+(13.033113.0331i)q37+(111.78929.9538i)q38+(61.423663.7618i)q40+(20.2139+35.0116i)q41+(3.68527+0.987466i)q43+24.5915iq442.49214q46+(0.993231+3.70679i)q47+(21.1465+12.2089i)q49+(20.004287.6247i)q50+(21.895281.7139i)q52+(31.224031.2240i)q53+(7.10982+11.8000i)q55+(43.8959+76.0300i)q56+(32.3783120.837i)q58+(36.8611+21.2818i)q59+(6.5699411.3795i)q61+(65.324365.3243i)q62+5.10100iq64+(13.118645.5399i)q65+(44.9977+12.0571i)q67+(29.9735+111.863i)q68+(78.0031+43.1133i)q70+114.062q71+(18.7982+18.7982i)q73+(57.3867+33.1322i)q74+(143.657+248.821i)q76+(13.1953+3.53568i)q77+(18.3057+10.5688i)q79+(72.1453119.738i)q80+(102.774+102.774i)q82+(14.7688+3.95730i)q83+(46.7239+45.0105i)q85+(6.8582811.8789i)q86+(47.1254+12.6272i)q88+92.4405iq89+46.9941q91+(1.60129+5.97609i)q92+(11.9482+6.89832i)q94+(3.00583+160.928i)q95+(40.7091+151.928i)q97+(62.074262.0742i)q98+O(q100)q+(0.930497 - 3.47266i) q^{2} +(-7.72947 - 4.46261i) q^{4} +(-4.99913 + 0.0933744i) q^{5} +(1.28323 - 4.78910i) q^{7} +(-12.5207 + 12.5207i) q^{8} +(-4.32742 + 17.4472i) q^{10} +(-1.37764 - 2.38615i) q^{11} +(2.45318 + 9.15539i) q^{13} +(-15.4369 - 8.91249i) q^{14} +(13.9793 + 24.2129i) q^{16} +(-9.17504 - 9.17504i) q^{17} -32.1912i q^{19} +(39.0573 + 21.5874i) q^{20} +(-9.56819 + 2.56379i) q^{22} +(-0.179412 - 0.669573i) q^{23} +(24.9826 - 0.933581i) q^{25} +34.0763 q^{26} +(-31.2906 + 31.2906i) q^{28} +(30.1349 - 17.3984i) q^{29} +(12.8482 - 22.2537i) q^{31} +(28.6765 - 7.68384i) q^{32} +(-40.3992 + 23.3245i) q^{34} +(-5.96788 + 24.0611i) q^{35} +(-13.0331 - 13.0331i) q^{37} +(-111.789 - 29.9538i) q^{38} +(61.4236 - 63.7618i) q^{40} +(-20.2139 + 35.0116i) q^{41} +(3.68527 + 0.987466i) q^{43} +24.5915i q^{44} -2.49214 q^{46} +(-0.993231 + 3.70679i) q^{47} +(21.1465 + 12.2089i) q^{49} +(20.0042 - 87.6247i) q^{50} +(21.8952 - 81.7139i) q^{52} +(31.2240 - 31.2240i) q^{53} +(7.10982 + 11.8000i) q^{55} +(43.8959 + 76.0300i) q^{56} +(-32.3783 - 120.837i) q^{58} +(36.8611 + 21.2818i) q^{59} +(-6.56994 - 11.3795i) q^{61} +(-65.3243 - 65.3243i) q^{62} +5.10100i q^{64} +(-13.1186 - 45.5399i) q^{65} +(-44.9977 + 12.0571i) q^{67} +(29.9735 + 111.863i) q^{68} +(78.0031 + 43.1133i) q^{70} +114.062 q^{71} +(-18.7982 + 18.7982i) q^{73} +(-57.3867 + 33.1322i) q^{74} +(-143.657 + 248.821i) q^{76} +(-13.1953 + 3.53568i) q^{77} +(-18.3057 + 10.5688i) q^{79} +(-72.1453 - 119.738i) q^{80} +(102.774 + 102.774i) q^{82} +(14.7688 + 3.95730i) q^{83} +(46.7239 + 45.0105i) q^{85} +(6.85828 - 11.8789i) q^{86} +(47.1254 + 12.6272i) q^{88} +92.4405i q^{89} +46.9941 q^{91} +(-1.60129 + 5.97609i) q^{92} +(11.9482 + 6.89832i) q^{94} +(3.00583 + 160.928i) q^{95} +(-40.7091 + 151.928i) q^{97} +(62.0742 - 62.0742i) q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q+2q2+2q52q7+24q88q108q112q13+28q1628q17+114q20+14q2282q238q25+112q2688q284q31+14q32352q35++1876q98+O(q100) 40 q + 2 q^{2} + 2 q^{5} - 2 q^{7} + 24 q^{8} - 8 q^{10} - 8 q^{11} - 2 q^{13} + 28 q^{16} - 28 q^{17} + 114 q^{20} + 14 q^{22} - 82 q^{23} - 8 q^{25} + 112 q^{26} - 88 q^{28} - 4 q^{31} + 14 q^{32} - 352 q^{35}+ \cdots + 1876 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/135Z)×\left(\mathbb{Z}/135\mathbb{Z}\right)^\times.

nn 5656 8282
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) e(14)e\left(\frac{1}{4}\right)

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 0.930497 3.47266i 0.465249 1.73633i −0.190815 0.981626i 0.561113π-0.561113\pi
0.656063 0.754706i 0.272220π-0.272220\pi
33 0 0
44 −7.72947 4.46261i −1.93237 1.11565i
55 −4.99913 + 0.0933744i −0.999826 + 0.0186749i
66 0 0
77 1.28323 4.78910i 0.183319 0.684157i −0.811665 0.584123i 0.801438π-0.801438\pi
0.994984 0.100033i 0.0318950π-0.0318950\pi
88 −12.5207 + 12.5207i −1.56509 + 1.56509i
99 0 0
1010 −4.32742 + 17.4472i −0.432742 + 1.74472i
1111 −1.37764 2.38615i −0.125240 0.216923i 0.796587 0.604525i 0.206637π-0.206637\pi
−0.921827 + 0.387602i 0.873304π0.873304\pi
1212 0 0
1313 2.45318 + 9.15539i 0.188706 + 0.704261i 0.993807 + 0.111123i 0.0354446π0.0354446\pi
−0.805101 + 0.593138i 0.797889π0.797889\pi
1414 −15.4369 8.91249i −1.10263 0.636606i
1515 0 0
1616 13.9793 + 24.2129i 0.873708 + 1.51331i
1717 −9.17504 9.17504i −0.539708 0.539708i 0.383735 0.923443i 0.374638π-0.374638\pi
−0.923443 + 0.383735i 0.874638π0.874638\pi
1818 0 0
1919 32.1912i 1.69427i −0.531375 0.847137i 0.678324π-0.678324\pi
0.531375 0.847137i 0.321676π-0.321676\pi
2020 39.0573 + 21.5874i 1.95286 + 1.07937i
2121 0 0
2222 −9.56819 + 2.56379i −0.434918 + 0.116536i
2323 −0.179412 0.669573i −0.00780050 0.0291119i 0.961916 0.273346i 0.0881303π-0.0881303\pi
−0.969716 + 0.244234i 0.921464π0.921464\pi
2424 0 0
2525 24.9826 0.933581i 0.999302 0.0373432i
2626 34.0763 1.31063
2727 0 0
2828 −31.2906 + 31.2906i −1.11752 + 1.11752i
2929 30.1349 17.3984i 1.03913 0.599944i 0.119546 0.992829i 0.461856π-0.461856\pi
0.919588 + 0.392884i 0.128523π0.128523\pi
3030 0 0
3131 12.8482 22.2537i 0.414457 0.717860i −0.580914 0.813965i 0.697305π-0.697305\pi
0.995371 + 0.0961042i 0.0306382π0.0306382\pi
3232 28.6765 7.68384i 0.896140 0.240120i
3333 0 0
3434 −40.3992 + 23.3245i −1.18821 + 0.686014i
3535 −5.96788 + 24.0611i −0.170511 + 0.687461i
3636 0 0
3737 −13.0331 13.0331i −0.352245 0.352245i 0.508699 0.860944i 0.330127π-0.330127\pi
−0.860944 + 0.508699i 0.830127π0.830127\pi
3838 −111.789 29.9538i −2.94182 0.788259i
3939 0 0
4040 61.4236 63.7618i 1.53559 1.59405i
4141 −20.2139 + 35.0116i −0.493023 + 0.853941i −0.999968 0.00803768i 0.997442π-0.997442\pi
0.506945 + 0.861979i 0.330775π0.330775\pi
4242 0 0
4343 3.68527 + 0.987466i 0.0857040 + 0.0229643i 0.301416 0.953493i 0.402541π-0.402541\pi
−0.215712 + 0.976457i 0.569207π0.569207\pi
4444 24.5915i 0.558899i
4545 0 0
4646 −2.49214 −0.0541770
4747 −0.993231 + 3.70679i −0.0211326 + 0.0788679i −0.975687 0.219169i 0.929665π-0.929665\pi
0.954554 + 0.298037i 0.0963320π0.0963320\pi
4848 0 0
4949 21.1465 + 12.2089i 0.431561 + 0.249162i
5050 20.0042 87.6247i 0.400084 1.75249i
5151 0 0
5252 21.8952 81.7139i 0.421061 1.57142i
5353 31.2240 31.2240i 0.589132 0.589132i −0.348265 0.937396i 0.613229π-0.613229\pi
0.937396 + 0.348265i 0.113229π0.113229\pi
5454 0 0
5555 7.10982 + 11.8000i 0.129269 + 0.214546i
5656 43.8959 + 76.0300i 0.783856 + 1.35768i
5757 0 0
5858 −32.3783 120.837i −0.558247 2.08340i
5959 36.8611 + 21.2818i 0.624765 + 0.360708i 0.778722 0.627369i 0.215868π-0.215868\pi
−0.153957 + 0.988078i 0.549202π0.549202\pi
6060 0 0
6161 −6.56994 11.3795i −0.107704 0.186549i 0.807136 0.590366i 0.201017π-0.201017\pi
−0.914840 + 0.403817i 0.867683π0.867683\pi
6262 −65.3243 65.3243i −1.05362 1.05362i
6363 0 0
6464 5.10100i 0.0797032i
6565 −13.1186 45.5399i −0.201825 0.700614i
6666 0 0
6767 −44.9977 + 12.0571i −0.671607 + 0.179957i −0.578479 0.815697i 0.696353π-0.696353\pi
−0.0931285 + 0.995654i 0.529687π0.529687\pi
6868 29.9735 + 111.863i 0.440787 + 1.64504i
6969 0 0
7070 78.0031 + 43.1133i 1.11433 + 0.615904i
7171 114.062 1.60651 0.803254 0.595637i 0.203100π-0.203100\pi
0.803254 + 0.595637i 0.203100π0.203100\pi
7272 0 0
7373 −18.7982 + 18.7982i −0.257510 + 0.257510i −0.824041 0.566531i 0.808285π-0.808285\pi
0.566531 + 0.824041i 0.308285π0.308285\pi
7474 −57.3867 + 33.1322i −0.775496 + 0.447733i
7575 0 0
7676 −143.657 + 248.821i −1.89022 + 3.27396i
7777 −13.1953 + 3.53568i −0.171368 + 0.0459179i
7878 0 0
7979 −18.3057 + 10.5688i −0.231717 + 0.133782i −0.611364 0.791350i 0.709379π-0.709379\pi
0.379647 + 0.925132i 0.376046π0.376046\pi
8080 −72.1453 119.738i −0.901816 1.49673i
8181 0 0
8282 102.774 + 102.774i 1.25335 + 1.25335i
8383 14.7688 + 3.95730i 0.177938 + 0.0476783i 0.346688 0.937981i 0.387306π-0.387306\pi
−0.168750 + 0.985659i 0.553973π0.553973\pi
8484 0 0
8585 46.7239 + 45.0105i 0.549693 + 0.529535i
8686 6.85828 11.8789i 0.0797474 0.138127i
8787 0 0
8888 47.1254 + 12.6272i 0.535516 + 0.143491i
8989 92.4405i 1.03866i 0.854575 + 0.519329i 0.173818π0.173818\pi
−0.854575 + 0.519329i 0.826182π0.826182\pi
9090 0 0
9191 46.9941 0.516418
9292 −1.60129 + 5.97609i −0.0174053 + 0.0649574i
9393 0 0
9494 11.9482 + 6.89832i 0.127109 + 0.0733864i
9595 3.00583 + 160.928i 0.0316404 + 1.69398i
9696 0 0
9797 −40.7091 + 151.928i −0.419681 + 1.56627i 0.355590 + 0.934642i 0.384280π0.384280\pi
−0.775271 + 0.631629i 0.782387π0.782387\pi
9898 62.0742 62.0742i 0.633411 0.633411i
9999 0 0
100100 −197.268 104.271i −1.97268 1.04271i
101101 −41.2983 71.5307i −0.408894 0.708225i 0.585872 0.810404i 0.300752π-0.300752\pi
−0.994766 + 0.102178i 0.967419π0.967419\pi
102102 0 0
103103 −12.9609 48.3706i −0.125834 0.469617i 0.874034 0.485864i 0.161495π-0.161495\pi
−0.999868 + 0.0162466i 0.994828π0.994828\pi
104104 −145.348 83.9166i −1.39757 0.806890i
105105 0 0
106106 −79.3765 137.484i −0.748835 1.29702i
107107 57.4669 + 57.4669i 0.537074 + 0.537074i 0.922668 0.385595i 0.126004π-0.126004\pi
−0.385595 + 0.922668i 0.626004π0.626004\pi
108108 0 0
109109 145.852i 1.33809i −0.743220 0.669047i 0.766702π-0.766702\pi
0.743220 0.669047i 0.233298π-0.233298\pi
110110 47.5932 13.7101i 0.432665 0.124638i
111111 0 0
112112 133.897 35.8775i 1.19551 0.320335i
113113 −14.0319 52.3679i −0.124176 0.463432i 0.875633 0.482978i 0.160445π-0.160445\pi
−0.999809 + 0.0195453i 0.993778π0.993778\pi
114114 0 0
115115 0.959422 + 3.33053i 0.00834280 + 0.0289611i
116116 −310.569 −2.67732
117117 0 0
118118 108.204 108.204i 0.916980 0.916980i
119119 −55.7139 + 32.1664i −0.468184 + 0.270306i
120120 0 0
121121 56.7042 98.2145i 0.468630 0.811690i
122122 −45.6304 + 12.2266i −0.374019 + 0.100218i
123123 0 0
124124 −198.619 + 114.673i −1.60177 + 0.924780i
125125 −124.804 + 6.99982i −0.998431 + 0.0559986i
126126 0 0
127127 50.4054 + 50.4054i 0.396893 + 0.396893i 0.877136 0.480243i 0.159451π-0.159451\pi
−0.480243 + 0.877136i 0.659451π0.659451\pi
128128 132.420 + 35.4818i 1.03453 + 0.277202i
129129 0 0
130130 −170.352 + 3.18185i −1.31040 + 0.0244758i
131131 89.6936 155.354i 0.684684 1.18591i −0.288852 0.957374i 0.593274π-0.593274\pi
0.973536 0.228534i 0.0733931π-0.0733931\pi
132132 0 0
133133 −154.167 41.3089i −1.15915 0.310593i
134134 167.481i 1.24986i
135135 0 0
136136 229.756 1.68938
137137 36.5154 136.277i 0.266536 0.994725i −0.694768 0.719234i 0.744493π-0.744493\pi
0.961304 0.275491i 0.0888404π-0.0888404\pi
138138 0 0
139139 236.063 + 136.291i 1.69829 + 0.980510i 0.947381 + 0.320108i 0.103719π0.103719\pi
0.750912 + 0.660402i 0.229614π0.229614\pi
140140 153.504 159.347i 1.09646 1.13820i
141141 0 0
142142 106.134 396.099i 0.747426 2.78943i
143143 18.4665 18.4665i 0.129137 0.129137i
144144 0 0
145145 −149.024 + 89.7906i −1.02775 + 0.619245i
146146 47.7882 + 82.7716i 0.327317 + 0.566929i
147147 0 0
148148 42.5772 + 158.900i 0.287684 + 1.07365i
149149 −174.004 100.461i −1.16781 0.674235i −0.214646 0.976692i 0.568860π-0.568860\pi
−0.953163 + 0.302457i 0.902193π0.902193\pi
150150 0 0
151151 58.6560 + 101.595i 0.388450 + 0.672816i 0.992241 0.124327i 0.0396771π-0.0396771\pi
−0.603791 + 0.797143i 0.706344π0.706344\pi
152152 403.057 + 403.057i 2.65169 + 2.65169i
153153 0 0
154154 49.1129i 0.318915i
155155 −62.1517 + 112.449i −0.400979 + 0.725475i
156156 0 0
157157 −205.058 + 54.9450i −1.30610 + 0.349968i −0.843753 0.536731i 0.819659π-0.819659\pi
−0.462346 + 0.886700i 0.652992π0.652992\pi
158158 19.6684 + 73.4036i 0.124484 + 0.464580i
159159 0 0
160160 −142.640 + 41.0902i −0.891500 + 0.256814i
161161 −3.43688 −0.0213471
162162 0 0
163163 61.1545 61.1545i 0.375181 0.375181i −0.494179 0.869360i 0.664531π-0.664531\pi
0.869360 + 0.494179i 0.164531π0.164531\pi
164164 312.486 180.414i 1.90540 1.10008i
165165 0 0
166166 27.4847 47.6049i 0.165571 0.286777i
167167 −234.945 + 62.9533i −1.40686 + 0.376966i −0.880802 0.473486i 0.842996π-0.842996\pi
−0.526054 + 0.850451i 0.676329π0.676329\pi
168168 0 0
169169 68.5552 39.5803i 0.405652 0.234203i
170170 199.783 120.374i 1.17519 0.708084i
171171 0 0
172172 −24.0785 24.0785i −0.139991 0.139991i
173173 16.3284 + 4.37517i 0.0943835 + 0.0252900i 0.305702 0.952127i 0.401109π-0.401109\pi
−0.211318 + 0.977417i 0.567776π0.567776\pi
174174 0 0
175175 27.5875 120.842i 0.157643 0.690525i
176176 38.5171 66.7135i 0.218847 0.379054i
177177 0 0
178178 321.015 + 86.0157i 1.80345 + 0.483234i
179179 274.512i 1.53359i −0.641895 0.766793i 0.721851π-0.721851\pi
0.641895 0.766793i 0.278149π-0.278149\pi
180180 0 0
181181 −261.649 −1.44557 −0.722787 0.691070i 0.757139π-0.757139\pi
−0.722787 + 0.691070i 0.757139π0.757139\pi
182182 43.7279 163.195i 0.240263 0.896674i
183183 0 0
184184 10.6299 + 6.13718i 0.0577712 + 0.0333542i
185185 66.3709 + 63.9370i 0.358762 + 0.345606i
186186 0 0
187187 −9.25307 + 34.5329i −0.0494817 + 0.184668i
188188 24.2191 24.2191i 0.128825 0.128825i
189189 0 0
190190 561.646 + 139.305i 2.95603 + 0.733183i
191191 89.7939 + 155.528i 0.470125 + 0.814280i 0.999416 0.0341597i 0.0108755π-0.0108755\pi
−0.529291 + 0.848440i 0.677542π0.677542\pi
192192 0 0
193193 6.95596 + 25.9600i 0.0360412 + 0.134508i 0.981602 0.190937i 0.0611526π-0.0611526\pi
−0.945561 + 0.325445i 0.894486π0.894486\pi
194194 489.716 + 282.738i 2.52431 + 1.45741i
195195 0 0
196196 −108.967 188.737i −0.555956 0.962944i
197197 −118.588 118.588i −0.601967 0.601967i 0.338867 0.940834i 0.389956π-0.389956\pi
−0.940834 + 0.338867i 0.889956π0.889956\pi
198198 0 0
199199 23.9129i 0.120166i −0.998193 0.0600828i 0.980864π-0.980864\pi
0.998193 0.0600828i 0.0191365π-0.0191365\pi
200200 −301.111 + 324.489i −1.50555 + 1.62244i
201201 0 0
202202 −286.830 + 76.8559i −1.41995 + 0.380475i
203203 −44.6524 166.645i −0.219963 0.820912i
204204 0 0
205205 97.7829 176.915i 0.476990 0.862999i
206206 −180.035 −0.873956
207207 0 0
208208 −187.385 + 187.385i −0.900889 + 0.900889i
209209 −76.8130 + 44.3480i −0.367526 + 0.212191i
210210 0 0
211211 68.1081 117.967i 0.322787 0.559084i −0.658275 0.752778i 0.728713π-0.728713\pi
0.981062 + 0.193694i 0.0620468π0.0620468\pi
212212 −380.685 + 102.004i −1.79568 + 0.481152i
213213 0 0
214214 253.036 146.090i 1.18241 0.682665i
215215 −18.5154 4.59236i −0.0861180 0.0213598i
216216 0 0
217217 −90.0878 90.0878i −0.415151 0.415151i
218218 −506.496 135.715i −2.32338 0.622547i
219219 0 0
220220 −2.29622 122.936i −0.0104374 0.558801i
221221 61.4931 106.509i 0.278249 0.481942i
222222 0 0
223223 −387.566 103.848i −1.73796 0.465686i −0.755970 0.654606i 0.772834π-0.772834\pi
−0.981992 + 0.188921i 0.939501π0.939501\pi
224224 147.195i 0.657119i
225225 0 0
226226 −194.913 −0.862445
227227 −48.9929 + 182.844i −0.215828 + 0.805480i 0.770046 + 0.637988i 0.220233π0.220233\pi
−0.985874 + 0.167491i 0.946433π0.946433\pi
228228 0 0
229229 −128.197 74.0143i −0.559810 0.323207i 0.193259 0.981148i 0.438094π-0.438094\pi
−0.753069 + 0.657941i 0.771428π0.771428\pi
230230 12.4585 0.232702i 0.0541676 0.00101175i
231231 0 0
232232 −159.470 + 595.151i −0.687372 + 2.56531i
233233 −191.869 + 191.869i −0.823473 + 0.823473i −0.986604 0.163131i 0.947841π-0.947841\pi
0.163131 + 0.986604i 0.447841π0.447841\pi
234234 0 0
235235 4.61917 18.6235i 0.0196561 0.0792488i
236236 −189.945 328.994i −0.804850 1.39404i
237237 0 0
238238 59.8616 + 223.406i 0.251519 + 0.938682i
239239 113.709 + 65.6499i 0.475770 + 0.274686i 0.718652 0.695370i 0.244760π-0.244760\pi
−0.242882 + 0.970056i 0.578093π0.578093\pi
240240 0 0
241241 106.787 + 184.961i 0.443101 + 0.767473i 0.997918 0.0644993i 0.0205450π-0.0205450\pi
−0.554817 + 0.831972i 0.687212π0.687212\pi
242242 −288.303 288.303i −1.19133 1.19133i
243243 0 0
244244 117.276i 0.480640i
245245 −106.854 59.0594i −0.436139 0.241059i
246246 0 0
247247 294.723 78.9708i 1.19321 0.319720i
248248 117.764 + 439.501i 0.474854 + 1.77218i
249249 0 0
250250 −91.8216 + 439.915i −0.367287 + 1.75966i
251251 −48.4611 −0.193072 −0.0965360 0.995329i 0.530776π-0.530776\pi
−0.0965360 + 0.995329i 0.530776π0.530776\pi
252252 0 0
253253 −1.35054 + 1.35054i −0.00533809 + 0.00533809i
254254 221.943 128.139i 0.873792 0.504484i
255255 0 0
256256 236.231 409.164i 0.922777 1.59830i
257257 450.204 120.632i 1.75177 0.469385i 0.766766 0.641927i 0.221865π-0.221865\pi
0.985002 + 0.172542i 0.0551979π0.0551979\pi
258258 0 0
259259 −79.1411 + 45.6921i −0.305564 + 0.176418i
260260 −101.827 + 410.543i −0.391641 + 1.57901i
261261 0 0
262262 −456.032 456.032i −1.74058 1.74058i
263263 104.698 + 28.0536i 0.398090 + 0.106668i 0.452309 0.891861i 0.350600π-0.350600\pi
−0.0542194 + 0.998529i 0.517267π0.517267\pi
264264 0 0
265265 −153.177 + 159.008i −0.578027 + 0.600031i
266266 −286.904 + 496.932i −1.07859 + 1.86816i
267267 0 0
268268 401.614 + 107.612i 1.49856 + 0.401538i
269269 271.965i 1.01102i −0.862821 0.505510i 0.831304π-0.831304\pi
0.862821 0.505510i 0.168696π-0.168696\pi
270270 0 0
271271 283.330 1.04550 0.522749 0.852487i 0.324907π-0.324907\pi
0.522749 + 0.852487i 0.324907π0.324907\pi
272272 93.8935 350.415i 0.345197 1.28829i
273273 0 0
274274 −439.268 253.611i −1.60317 0.925589i
275275 −36.6447 58.3260i −0.133254 0.212094i
276276 0 0
277277 −38.5154 + 143.741i −0.139045 + 0.518922i 0.860904 + 0.508768i 0.169899π0.169899\pi
−0.999948 + 0.0101539i 0.996768π0.996768\pi
278278 692.948 692.948i 2.49262 2.49262i
279279 0 0
280280 −226.541 375.985i −0.809074 1.34280i
281281 126.241 + 218.657i 0.449258 + 0.778137i 0.998338 0.0576326i 0.0183552π-0.0183552\pi
−0.549080 + 0.835770i 0.685022π0.685022\pi
282282 0 0
283283 124.137 + 463.286i 0.438647 + 1.63705i 0.732184 + 0.681107i 0.238501π0.238501\pi
−0.293537 + 0.955948i 0.594832π0.594832\pi
284284 −881.639 509.015i −3.10436 1.79230i
285285 0 0
286286 −46.9450 81.3111i −0.164143 0.284304i
287287 141.735 + 141.735i 0.493849 + 0.493849i
288288 0 0
289289 120.637i 0.417430i
290290 173.146 + 601.059i 0.597056 + 2.07262i
291291 0 0
292292 229.189 61.4111i 0.784895 0.210312i
293293 52.5299 + 196.044i 0.179283 + 0.669093i 0.995782 + 0.0917468i 0.0292450π0.0292450\pi
−0.816499 + 0.577346i 0.804088π0.804088\pi
294294 0 0
295295 −186.261 102.948i −0.631392 0.348978i
296296 326.367 1.10259
297297 0 0
298298 −510.777 + 510.777i −1.71402 + 1.71402i
299299 5.69008 3.28517i 0.0190304 0.0109872i
300300 0 0
301301 9.45814 16.3820i 0.0314224 0.0544252i
302302 407.385 109.159i 1.34896 0.361452i
303303 0 0
304304 779.443 450.011i 2.56396 1.48030i
305305 33.9065 + 56.2739i 0.111169 + 0.184505i
306306 0 0
307307 364.680 + 364.680i 1.18788 + 1.18788i 0.977652 + 0.210232i 0.0674220π0.0674220\pi
0.210232 + 0.977652i 0.432578π0.432578\pi
308308 117.771 + 31.5567i 0.382374 + 0.102457i
309309 0 0
310310 332.664 + 320.465i 1.07311 + 1.03376i
311311 102.480 177.501i 0.329518 0.570743i −0.652898 0.757446i 0.726447π-0.726447\pi
0.982416 + 0.186703i 0.0597803π0.0597803\pi
312312 0 0
313313 343.429 + 92.0214i 1.09722 + 0.293998i 0.761631 0.648011i 0.224399π-0.224399\pi
0.335586 + 0.942010i 0.391066π0.391066\pi
314314 763.222i 2.43064i
315315 0 0
316316 188.657 0.597017
317317 6.68768 24.9588i 0.0210968 0.0787343i −0.954575 0.297971i 0.903690π-0.903690\pi
0.975672 + 0.219237i 0.0703567π0.0703567\pi
318318 0 0
319319 −83.0303 47.9375i −0.260283 0.150274i
320320 −0.476303 25.5006i −0.00148845 0.0796893i
321321 0 0
322322 −3.19801 + 11.9351i −0.00993169 + 0.0370656i
323323 −295.356 + 295.356i −0.914414 + 0.914414i
324324 0 0
325325 69.8340 + 226.435i 0.214874 + 0.696723i
326326 −155.465 269.273i −0.476886 0.825992i
327327 0 0
328328 −185.277 691.464i −0.564869 2.10812i
329329 16.4776 + 9.51337i 0.0500840 + 0.0289160i
330330 0 0
331331 96.8582 + 167.763i 0.292623 + 0.506838i 0.974429 0.224695i 0.0721386π-0.0721386\pi
−0.681806 + 0.731533i 0.738805π0.738805\pi
332332 −96.4953 96.4953i −0.290649 0.290649i
333333 0 0
334334 874.462i 2.61815i
335335 223.823 64.4766i 0.668129 0.192467i
336336 0 0
337337 88.6729 23.7598i 0.263124 0.0705039i −0.124845 0.992176i 0.539843π-0.539843\pi
0.387969 + 0.921672i 0.373177π0.373177\pi
338338 −73.6588 274.898i −0.217925 0.813309i
339339 0 0
340340 −160.287 556.418i −0.471431 1.63652i
341341 −70.8008 −0.207627
342342 0 0
343343 257.393 257.393i 0.750417 0.750417i
344344 −58.5061 + 33.7785i −0.170076 + 0.0981933i
345345 0 0
346346 30.3870 52.6318i 0.0878236 0.152115i
347347 −5.84253 + 1.56550i −0.0168372 + 0.00451153i −0.267228 0.963633i 0.586108π-0.586108\pi
0.250391 + 0.968145i 0.419441π0.419441\pi
348348 0 0
349349 67.8704 39.1850i 0.194471 0.112278i −0.399603 0.916688i 0.630852π-0.630852\pi
0.594074 + 0.804410i 0.297519π0.297519\pi
350350 −393.973 208.245i −1.12564 0.594986i
351351 0 0
352352 −57.8408 57.8408i −0.164320 0.164320i
353353 −38.2322 10.2443i −0.108307 0.0290207i 0.204259 0.978917i 0.434522π-0.434522\pi
−0.312565 + 0.949896i 0.601188π0.601188\pi
354354 0 0
355355 −570.211 + 10.6505i −1.60623 + 0.0300013i
356356 412.526 714.516i 1.15878 2.00707i
357357 0 0
358358 −953.287 255.433i −2.66281 0.713499i
359359 116.601i 0.324795i 0.986725 + 0.162398i 0.0519227π0.0519227\pi
−0.986725 + 0.162398i 0.948077π0.948077\pi
360360 0 0
361361 −675.274 −1.87056
362362 −243.464 + 908.619i −0.672552 + 2.51000i
363363 0 0
364364 −363.239 209.716i −0.997910 0.576144i
365365 92.2195 95.7300i 0.252656 0.262274i
366366 0 0
367367 112.479 419.779i 0.306483 1.14381i −0.625177 0.780483i 0.714973π-0.714973\pi
0.931661 0.363329i 0.118360π-0.118360\pi
368368 13.7043 13.7043i 0.0372398 0.0372398i
369369 0 0
370370 283.790 170.991i 0.766999 0.462137i
371371 −109.467 189.602i −0.295059 0.511058i
372372 0 0
373373 −167.428 624.849i −0.448868 1.67520i −0.705516 0.708694i 0.749285π-0.749285\pi
0.256647 0.966505i 0.417382π-0.417382\pi
374374 111.311 + 64.2656i 0.297624 + 0.171833i
375375 0 0
376376 −33.9757 58.8477i −0.0903610 0.156510i
377377 233.215 + 233.215i 0.618608 + 0.618608i
378378 0 0
379379 297.836i 0.785846i −0.919571 0.392923i 0.871464π-0.871464\pi
0.919571 0.392923i 0.128536π-0.128536\pi
380380 694.925 1257.30i 1.82875 3.30869i
381381 0 0
382382 623.648 167.106i 1.63259 0.437450i
383383 111.047 + 414.434i 0.289941 + 1.08207i 0.945153 + 0.326629i 0.105913π0.105913\pi
−0.655212 + 0.755445i 0.727421π0.727421\pi
384384 0 0
385385 65.6351 18.9074i 0.170481 0.0491102i
386386 96.6228 0.250318
387387 0 0
388388 992.656 992.656i 2.55839 2.55839i
389389 197.682 114.132i 0.508181 0.293398i −0.223905 0.974611i 0.571880π-0.571880\pi
0.732086 + 0.681213i 0.238547π0.238547\pi
390390 0 0
391391 −4.49725 + 7.78947i −0.0115019 + 0.0199219i
392392 −417.634 + 111.905i −1.06539 + 0.285471i
393393 0 0
394394 −522.160 + 301.469i −1.32528 + 0.765151i
395395 90.5255 54.5440i 0.229178 0.138086i
396396 0 0
397397 120.533 + 120.533i 0.303609 + 0.303609i 0.842424 0.538815i 0.181128π-0.181128\pi
−0.538815 + 0.842424i 0.681128π0.681128\pi
398398 −83.0416 22.2509i −0.208647 0.0559069i
399399 0 0
400400 371.844 + 591.850i 0.929610 + 1.47962i
401401 −226.669 + 392.602i −0.565259 + 0.979057i 0.431766 + 0.901985i 0.357890π0.357890\pi
−0.997026 + 0.0770720i 0.975443π0.975443\pi
402402 0 0
403403 235.260 + 63.0377i 0.583772 + 0.156421i
404404 737.193i 1.82473i
405405 0 0
406406 −620.251 −1.52771
407407 −13.1439 + 49.0538i −0.0322946 + 0.120525i
408408 0 0
409409 427.158 + 246.620i 1.04440 + 0.602982i 0.921075 0.389385i 0.127312π-0.127312\pi
0.123320 + 0.992367i 0.460646π0.460646\pi
410410 −523.379 504.186i −1.27653 1.22972i
411411 0 0
412412 −115.679 + 431.718i −0.280773 + 1.04786i
413413 149.222 149.222i 0.361312 0.361312i
414414 0 0
415415 −74.2008 18.4040i −0.178797 0.0443470i
416416 140.697 + 243.695i 0.338214 + 0.585805i
417417 0 0
418418 82.5314 + 308.011i 0.197444 + 0.736870i
419419 22.7963 + 13.1615i 0.0544066 + 0.0314116i 0.526957 0.849892i 0.323333π-0.323333\pi
−0.472550 + 0.881304i 0.656666π0.656666\pi
420420 0 0
421421 243.419 + 421.613i 0.578192 + 1.00146i 0.995687 + 0.0927780i 0.0295747π0.0295747\pi
−0.417495 + 0.908679i 0.637092π0.637092\pi
422422 −346.284 346.284i −0.820579 0.820579i
423423 0 0
424424 781.894i 1.84409i
425425 −237.782 220.650i −0.559486 0.519177i
426426 0 0
427427 −62.9281 + 16.8615i −0.147373 + 0.0394884i
428428 −187.736 700.641i −0.438636 1.63701i
429429 0 0
430430 −33.1762 + 60.0244i −0.0771540 + 0.139592i
431431 −73.2818 −0.170027 −0.0850137 0.996380i 0.527093π-0.527093\pi
−0.0850137 + 0.996380i 0.527093π0.527093\pi
432432 0 0
433433 79.7731 79.7731i 0.184234 0.184234i −0.608964 0.793198i 0.708415π-0.708415\pi
0.793198 + 0.608964i 0.208415π0.208415\pi
434434 −396.671 + 229.018i −0.913989 + 0.527692i
435435 0 0
436436 −650.882 + 1127.36i −1.49285 + 2.58569i
437437 −21.5544 + 5.77547i −0.0493235 + 0.0132162i
438438 0 0
439439 −97.4363 + 56.2549i −0.221951 + 0.128143i −0.606853 0.794814i 0.707568π-0.707568\pi
0.384903 + 0.922957i 0.374235π0.374235\pi
440440 −236.765 58.7248i −0.538102 0.133465i
441441 0 0
442442 −312.651 312.651i −0.707356 0.707356i
443443 154.045 + 41.2762i 0.347731 + 0.0931742i 0.428457 0.903562i 0.359057π-0.359057\pi
−0.0807263 + 0.996736i 0.525724π0.525724\pi
444444 0 0
445445 −8.63158 462.122i −0.0193968 1.03848i
446446 −721.258 + 1249.25i −1.61717 + 2.80102i
447447 0 0
448448 24.4292 + 6.54578i 0.0545295 + 0.0146111i
449449 291.806i 0.649901i −0.945731 0.324951i 0.894652π-0.894652\pi
0.945731 0.324951i 0.105348π-0.105348\pi
450450 0 0
451451 111.390 0.246985
452452 −125.238 + 467.395i −0.277075 + 1.03406i
453453 0 0
454454 589.367 + 340.271i 1.29817 + 0.749497i
455455 −234.929 + 4.38804i −0.516328 + 0.00964405i
456456 0 0
457457 121.316 452.757i 0.265462 0.990716i −0.696506 0.717551i 0.745263π-0.745263\pi
0.961967 0.273165i 0.0880705π-0.0880705\pi
458458 −376.313 + 376.313i −0.821645 + 0.821645i
459459 0 0
460460 7.44703 30.0247i 0.0161892 0.0652712i
461461 248.770 + 430.882i 0.539631 + 0.934668i 0.998924 + 0.0463832i 0.0147695π0.0147695\pi
−0.459293 + 0.888285i 0.651897π0.651897\pi
462462 0 0
463463 235.850 + 880.204i 0.509395 + 1.90109i 0.426391 + 0.904539i 0.359785π0.359785\pi
0.0830044 + 0.996549i 0.473548π0.473548\pi
464464 842.531 + 486.435i 1.81580 + 1.04835i
465465 0 0
466466 487.764 + 844.831i 1.04670 + 1.81294i
467467 204.884 + 204.884i 0.438724 + 0.438724i 0.891582 0.452859i 0.149596π-0.149596\pi
−0.452859 + 0.891582i 0.649596π0.649596\pi
468468 0 0
469469 230.970i 0.492474i
470470 −60.3749 33.3699i −0.128457 0.0709998i
471471 0 0
472472 −727.991 + 195.065i −1.54235 + 0.413273i
473473 −2.72075 10.1540i −0.00575212 0.0214672i
474474 0 0
475475 −30.0531 804.219i −0.0632697 1.69309i
476476 574.185 1.20627
477477 0 0
478478 333.786 333.786i 0.698297 0.698297i
479479 177.082 102.238i 0.369691 0.213441i −0.303632 0.952789i 0.598199π-0.598199\pi
0.673324 + 0.739348i 0.264866π0.264866\pi
480480 0 0
481481 87.3504 151.295i 0.181602 0.314543i
482482 741.673 198.731i 1.53874 0.412304i
483483 0 0
484484 −876.586 + 506.097i −1.81113 + 1.04566i
485485 189.324 763.310i 0.390358 1.57384i
486486 0 0
487487 −506.650 506.650i −1.04035 1.04035i −0.999151 0.0411985i 0.986882π-0.986882\pi
−0.0411985 0.999151i 0.513118π-0.513118\pi
488488 224.740 + 60.2188i 0.460532 + 0.123399i
489489 0 0
490490 −304.521 + 316.113i −0.621471 + 0.645129i
491491 104.633 181.229i 0.213101 0.369102i −0.739582 0.673066i 0.764977π-0.764977\pi
0.952684 + 0.303964i 0.0983102π0.0983102\pi
492492 0 0
493493 −436.120 116.858i −0.884624 0.237034i
494494 1096.96i 2.22056i
495495 0 0
496496 718.435 1.44846
497497 146.368 546.254i 0.294504 1.09910i
498498 0 0
499499 −287.007 165.704i −0.575165 0.332072i 0.184044 0.982918i 0.441081π-0.441081\pi
−0.759210 + 0.650846i 0.774414π0.774414\pi
500500 995.905 + 502.846i 1.99181 + 1.00569i
501501 0 0
502502 −45.0929 + 168.289i −0.0898265 + 0.335237i
503503 278.209 278.209i 0.553100 0.553100i −0.374234 0.927334i 0.622094π-0.622094\pi
0.927334 + 0.374234i 0.122094π0.122094\pi
504504 0 0
505505 213.135 + 353.735i 0.422049 + 0.700466i
506506 3.43329 + 5.94663i 0.00678515 + 0.0117522i
507507 0 0
508508 −164.667 614.546i −0.324148 1.20974i
509509 −679.279 392.182i −1.33454 0.770495i −0.348546 0.937292i 0.613324π-0.613324\pi
−0.985991 + 0.166797i 0.946658π0.946658\pi
510510 0 0
511511 65.9040 + 114.149i 0.128971 + 0.223384i
512512 −813.324 813.324i −1.58852 1.58852i
513513 0 0
514514 1675.66i 3.26003i
515515 69.3096 + 240.601i 0.134582 + 0.467186i
516516 0 0
517517 10.2133 2.73664i 0.0197549 0.00529330i
518518 85.0329 + 317.347i 0.164156 + 0.612639i
519519 0 0
520520 734.448 + 405.938i 1.41240 + 0.780650i
521521 −763.749 −1.46593 −0.732964 0.680267i 0.761864π-0.761864\pi
−0.732964 + 0.680267i 0.761864π0.761864\pi
522522 0 0
523523 −284.699 + 284.699i −0.544358 + 0.544358i −0.924803 0.380445i 0.875771π-0.875771\pi
0.380445 + 0.924803i 0.375771π0.375771\pi
524524 −1386.57 + 800.535i −2.64612 + 1.52774i
525525 0 0
526526 194.842 337.476i 0.370421 0.641589i
527527 −322.061 + 86.2959i −0.611121 + 0.163749i
528528 0 0
529529 457.711 264.260i 0.865239 0.499546i
530530 409.651 + 679.889i 0.772926 + 1.28281i
531531 0 0
532532 1007.28 + 1007.28i 1.89339 + 1.89339i
533533 −370.133 99.1769i −0.694434 0.186073i
534534 0 0
535535 −292.650 281.918i −0.547010 0.526950i
536536 412.440 714.367i 0.769478 1.33277i
537537 0 0
538538 −944.442 253.062i −1.75547 0.470376i
539539 67.2782i 0.124820i
540540 0 0
541541 120.576 0.222876 0.111438 0.993771i 0.464454π-0.464454\pi
0.111438 + 0.993771i 0.464454π0.464454\pi
542542 263.638 983.909i 0.486416 1.81533i
543543 0 0
544544 −333.608 192.608i −0.613249 0.354060i
545545 13.6189 + 729.134i 0.0249887 + 1.33786i
546546 0 0
547547 59.6213 222.510i 0.108997 0.406782i −0.889771 0.456407i 0.849136π-0.849136\pi
0.998768 + 0.0496252i 0.0158027π0.0158027\pi
548548 −890.397 + 890.397i −1.62481 + 1.62481i
549549 0 0
550550 −236.644 + 72.9827i −0.430262 + 0.132696i
551551 −560.075 970.078i −1.01647 1.76058i
552552 0 0
553553 27.1244 + 101.230i 0.0490496 + 0.183056i
554554 463.327 + 267.502i 0.836330 + 0.482855i
555555 0 0
556556 −1216.43 2106.91i −2.18782 3.78941i
557557 664.417 + 664.417i 1.19285 + 1.19285i 0.976264 + 0.216586i 0.0694922π0.0694922\pi
0.216586 + 0.976264i 0.430508π0.430508\pi
558558 0 0
559559 36.1626i 0.0646915i
560560 −666.017 + 191.859i −1.18932 + 0.342605i
561561 0 0
562562 876.788 234.935i 1.56012 0.418033i
563563 −71.6752 267.496i −0.127309 0.475125i 0.872602 0.488432i 0.162431π-0.162431\pi
−0.999911 + 0.0133066i 0.995764π0.995764\pi
564564 0 0
565565 75.0372 + 260.483i 0.132809 + 0.461033i
566566 1724.35 3.04655
567567 0 0
568568 −1428.14 + 1428.14i −2.51433 + 2.51433i
569569 −830.591 + 479.542i −1.45974 + 0.842780i −0.998998 0.0447548i 0.985749π-0.985749\pi
−0.460740 + 0.887535i 0.652416π0.652416\pi
570570 0 0
571571 −222.371 + 385.158i −0.389442 + 0.674533i −0.992375 0.123259i 0.960665π-0.960665\pi
0.602933 + 0.797792i 0.293999π0.293999\pi
572572 −225.145 + 60.3275i −0.393611 + 0.105468i
573573 0 0
574574 624.080 360.313i 1.08725 0.627723i
575575 −5.10726 16.5602i −0.00888219 0.0288003i
576576 0 0
577577 670.378 + 670.378i 1.16183 + 1.16183i 0.984074 + 0.177761i 0.0568852π0.0568852\pi
0.177761 + 0.984074i 0.443115π0.443115\pi
578578 −418.933 112.253i −0.724797 0.194209i
579579 0 0
580580 1552.57 28.9992i 2.67685 0.0499986i
581581 37.9038 65.6513i 0.0652388 0.112997i
582582 0 0
583583 −117.521 31.4895i −0.201579 0.0540129i
584584 470.735i 0.806053i
585585 0 0
586586 729.675 1.24518
587587 116.613 435.207i 0.198660 0.741410i −0.792629 0.609704i 0.791288π-0.791288\pi
0.991289 0.131705i 0.0420452π-0.0420452\pi
588588 0 0
589589 −716.373 413.598i −1.21625 0.702204i
590590 −530.820 + 551.027i −0.899696 + 0.933945i
591591 0 0
592592 133.375 497.762i 0.225295 0.840814i
593593 −292.884 + 292.884i −0.493902 + 0.493902i −0.909533 0.415631i 0.863561π-0.863561\pi
0.415631 + 0.909533i 0.363561π0.363561\pi
594594 0 0
595595 275.517 166.006i 0.463054 0.279002i
596596 896.636 + 1553.02i 1.50442 + 2.60574i
597597 0 0
598598 −6.11368 22.8166i −0.0102235 0.0381548i
599599 434.899 + 251.089i 0.726042 + 0.419180i 0.816972 0.576677i 0.195651π-0.195651\pi
−0.0909308 + 0.995857i 0.528984π0.528984\pi
600600 0 0
601601 −99.8075 172.872i −0.166069 0.287640i 0.770965 0.636877i 0.219774π-0.219774\pi
−0.937034 + 0.349237i 0.886441π0.886441\pi
602602 −48.0883 48.0883i −0.0798810 0.0798810i
603603 0 0
604604 1047.04i 1.73350i
605605 −274.301 + 496.282i −0.453390 + 0.820301i
606606 0 0
607607 −837.927 + 224.522i −1.38044 + 0.369888i −0.871281 0.490785i 0.836710π-0.836710\pi
−0.509159 + 0.860672i 0.670043π0.670043\pi
608608 −247.352 923.131i −0.406829 1.51831i
609609 0 0
610610 226.970 65.3831i 0.372083 0.107185i
611611 −36.3737 −0.0595314
612612 0 0
613613 −31.6781 + 31.6781i −0.0516771 + 0.0516771i −0.732473 0.680796i 0.761634π-0.761634\pi
0.680796 + 0.732473i 0.261634π0.261634\pi
614614 1605.75 927.078i 2.61522 1.50990i
615615 0 0
616616 120.946 209.485i 0.196341 0.340072i
617617 −253.302 + 67.8722i −0.410539 + 0.110004i −0.458177 0.888861i 0.651497π-0.651497\pi
0.0476380 + 0.998865i 0.484831π0.484831\pi
618618 0 0
619619 −422.528 + 243.947i −0.682598 + 0.394098i −0.800833 0.598887i 0.795610π-0.795610\pi
0.118235 + 0.992986i 0.462276π0.462276\pi
620620 982.214 591.809i 1.58422 0.954531i
621621 0 0
622622 −521.044 521.044i −0.837691 0.837691i
623623 442.707 + 118.623i 0.710605 + 0.190406i
624624 0 0
625625 623.257 46.6465i 0.997211 0.0746344i
626626 639.119 1106.99i 1.02096 1.76835i
627627 0 0
628628 1830.18 + 490.396i 2.91431 + 0.780886i
629629 239.158i 0.380219i
630630 0 0
631631 263.490 0.417576 0.208788 0.977961i 0.433048π-0.433048\pi
0.208788 + 0.977961i 0.433048π0.433048\pi
632632 96.8714 361.529i 0.153277 0.572039i
633633 0 0
634634 −80.4505 46.4481i −0.126894 0.0732620i
635635 −256.690 247.276i −0.404236 0.389412i
636636 0 0
637637 −59.9014 + 223.555i −0.0940367 + 0.350950i
638638 −243.730 + 243.730i −0.382023 + 0.382023i
639639 0 0
640640 −665.298 165.014i −1.03953 0.257834i
641641 459.262 + 795.464i 0.716477 + 1.24097i 0.962387 + 0.271682i 0.0875797π0.0875797\pi
−0.245911 + 0.969293i 0.579087π0.579087\pi
642642 0 0
643643 10.9456 + 40.8497i 0.0170228 + 0.0635298i 0.973915 0.226914i 0.0728637π-0.0728637\pi
−0.956892 + 0.290444i 0.906197π0.906197\pi
644644 26.5652 + 15.3374i 0.0412504 + 0.0238159i
645645 0 0
646646 750.843 + 1300.50i 1.16230 + 2.01316i
647647 12.5734 + 12.5734i 0.0194334 + 0.0194334i 0.716757 0.697323i 0.245626π-0.245626\pi
−0.697323 + 0.716757i 0.745626π0.745626\pi
648648 0 0
649649 117.275i 0.180701i
650650 851.313 31.8130i 1.30971 0.0489430i
651651 0 0
652652 −745.601 + 199.783i −1.14356 + 0.306416i
653653 −137.591 513.495i −0.210705 0.786363i −0.987634 0.156775i 0.949890π-0.949890\pi
0.776929 0.629588i 0.216776π-0.216776\pi
654654 0 0
655655 −433.884 + 785.009i −0.662418 + 1.19849i
656656 −1130.31 −1.72303
657657 0 0
658658 48.3691 48.3691i 0.0735093 0.0735093i
659659 64.8393 37.4350i 0.0983905 0.0568058i −0.449997 0.893030i 0.648575π-0.648575\pi
0.548388 + 0.836224i 0.315242π0.315242\pi
660660 0 0
661661 11.3687 19.6912i 0.0171993 0.0297900i −0.857298 0.514821i 0.827858π-0.827858\pi
0.874497 + 0.485031i 0.161192π0.161192\pi
662662 672.712 180.253i 1.01618 0.272285i
663663 0 0
664664 −234.465 + 135.368i −0.353110 + 0.203868i
665665 774.557 + 192.113i 1.16475 + 0.288892i
666666 0 0
667667 −17.0560 17.0560i −0.0255713 0.0255713i
668668 2096.93 + 561.872i 3.13912 + 0.841125i
669669 0 0
670670 −15.6384 837.259i −0.0233409 1.24964i
671671 −18.1021 + 31.3537i −0.0269777 + 0.0467268i
672672 0 0
673673 619.582 + 166.017i 0.920628 + 0.246681i 0.687854 0.725849i 0.258553π-0.258553\pi
0.232774 + 0.972531i 0.425220π0.425220\pi
674674 330.040i 0.489673i
675675 0 0
676676 −706.526 −1.04516
677677 150.613 562.095i 0.222471 0.830273i −0.760931 0.648833i 0.775258π-0.775258\pi
0.983402 0.181440i 0.0580758π-0.0580758\pi
678678 0 0
679679 675.360 + 389.919i 0.994639 + 0.574255i
680680 −1148.58 + 21.4534i −1.68909 + 0.0315490i
681681 0 0
682682 −65.8799 + 245.867i −0.0965982 + 0.360509i
683683 −599.384 + 599.384i −0.877576 + 0.877576i −0.993283 0.115708i 0.963086π-0.963086\pi
0.115708 + 0.993283i 0.463086π0.463086\pi
684684 0 0
685685 −169.820 + 684.677i −0.247913 + 0.999529i
686686 −654.336 1133.34i −0.953842 1.65210i
687687 0 0
688688 27.6082 + 103.035i 0.0401282 + 0.149761i
689689 362.466 + 209.270i 0.526075 + 0.303730i
690690 0 0
691691 −348.543 603.695i −0.504404 0.873654i −0.999987 0.00509303i 0.998379π-0.998379\pi
0.495583 0.868561i 0.334955π-0.334955\pi
692692 −106.685 106.685i −0.154169 0.154169i
693693 0 0
694694 21.7458i 0.0313340i
695695 −1192.83 659.293i −1.71631 0.948624i
696696 0 0
697697 506.696 135.769i 0.726967 0.194790i
698698 −72.9231 272.153i −0.104474 0.389904i
699699 0 0
700700 −752.507 + 810.932i −1.07501 + 1.15847i
701701 643.602 0.918119 0.459060 0.888405i 0.348186π-0.348186\pi
0.459060 + 0.888405i 0.348186π0.348186\pi
702702 0 0
703703 −419.550 + 419.550i −0.596800 + 0.596800i
704704 12.1718 7.02736i 0.0172894 0.00998205i
705705 0 0
706706 −71.1500 + 123.235i −0.100779 + 0.174554i
707707 −395.563 + 105.991i −0.559495 + 0.149916i
708708 0 0
709709 −1069.69 + 617.583i −1.50872 + 0.871062i −0.508775 + 0.860899i 0.669902π0.669902\pi
−0.999948 + 0.0101629i 0.996765π0.996765\pi
710710 −493.594 + 1990.06i −0.695203 + 2.80290i
711711 0 0
712712 −1157.42 1157.42i −1.62559 1.62559i
713713 −17.2056 4.61022i −0.0241312 0.00646594i
714714 0 0
715715 −90.5922 + 94.0408i −0.126702 + 0.131526i
716716 −1225.04 + 2121.83i −1.71095 + 2.96345i
717717 0 0
718718 404.918 + 108.497i 0.563952 + 0.151110i
719719 219.618i 0.305449i 0.988269 + 0.152724i 0.0488047π0.0488047\pi
−0.988269 + 0.152724i 0.951195π0.951195\pi
720720 0 0
721721 −248.283 −0.344360
722722 −628.340 + 2345.00i −0.870278 + 3.24792i
723723 0 0
724724 2022.41 + 1167.64i 2.79338 + 1.61276i
725725 736.604 462.789i 1.01601 0.638330i
726726 0 0
727727 73.8261 275.523i 0.101549 0.378986i −0.896382 0.443283i 0.853814π-0.853814\pi
0.997931 + 0.0642969i 0.0204805π0.0204805\pi
728728 −588.400 + 588.400i −0.808242 + 0.808242i
729729 0 0
730730 −246.628 409.324i −0.337847 0.560718i
731731 −24.7525 42.8726i −0.0338611 0.0586492i
732732 0 0
733733 −181.709 678.149i −0.247898 0.925169i −0.971905 0.235375i 0.924368π-0.924368\pi
0.724006 0.689793i 0.242299π-0.242299\pi
734734 −1353.09 781.206i −1.84345 1.06431i
735735 0 0
736736 −10.2898 17.8224i −0.0139807 0.0242153i
737737 90.7608 + 90.7608i 0.123149 + 0.123149i
738738 0 0
739739 1147.21i 1.55238i 0.630497 + 0.776192i 0.282851π0.282851\pi
−0.630497 + 0.776192i 0.717149π0.717149\pi
740740 −227.686 790.387i −0.307684 1.06809i
741741 0 0
742742 −760.284 + 203.717i −1.02464 + 0.274552i
743743 −226.953 847.001i −0.305455 1.13997i −0.932553 0.361034i 0.882424π-0.882424\pi
0.627098 0.778941i 0.284243π-0.284243\pi
744744 0 0
745745 879.246 + 485.970i 1.18020 + 0.652308i
746746 −2325.68 −3.11754
747747 0 0
748748 225.628 225.628i 0.301642 0.301642i
749749 348.958 201.471i 0.465899 0.268987i
750750 0 0
751751 147.537 255.542i 0.196455 0.340269i −0.750922 0.660391i 0.770391π-0.770391\pi
0.947376 + 0.320122i 0.103724π0.103724\pi
752752 −103.637 + 27.7694i −0.137815 + 0.0369274i
753753 0 0
754754 1026.88 592.872i 1.36192 0.786303i
755755 −302.715 502.410i −0.400947 0.665444i
756756 0 0
757757 89.6510 + 89.6510i 0.118429 + 0.118429i 0.763838 0.645408i 0.223313π-0.223313\pi
−0.645408 + 0.763838i 0.723313π0.723313\pi
758758 −1034.28 277.135i −1.36449 0.365614i
759759 0 0
760760 −2052.57 1977.30i −2.70075 2.60171i
761761 −80.6635 + 139.713i −0.105997 + 0.183592i −0.914145 0.405387i 0.867137π-0.867137\pi
0.808148 + 0.588979i 0.200470π0.200470\pi
762762 0 0
763763 −698.501 187.163i −0.915466 0.245298i
764764 1602.86i 2.09798i
765765 0 0
766766 1542.52 2.01373
767767 −104.416 + 389.686i −0.136136 + 0.508065i
768768 0 0
769769 −129.486 74.7588i −0.168382 0.0972156i 0.413440 0.910531i 0.364327π-0.364327\pi
−0.581823 + 0.813316i 0.697660π0.697660\pi
770770 −4.58589 245.522i −0.00595570 0.318859i
771771 0 0
772772 62.0835 231.699i 0.0804190 0.300128i
773773 994.453 994.453i 1.28649 1.28649i 0.349578 0.936907i 0.386325π-0.386325\pi
0.936907 0.349578i 0.113675π-0.113675\pi
774774 0 0
775775 300.204 567.949i 0.387361 0.732837i
776776 −1392.55 2411.96i −1.79452 3.10819i
777777 0 0
778778 −212.399 792.684i −0.273006 1.01887i
779779 1127.06 + 650.711i 1.44681 + 0.835316i
780780 0 0
781781 −157.137 272.169i −0.201200 0.348488i
782782 22.8655 + 22.8655i 0.0292398 + 0.0292398i
783783 0 0
784784 682.690i 0.870778i
785785 1019.98 293.824i 1.29934 0.374298i
786786 0 0
787787 −887.757 + 237.874i −1.12803 + 0.302254i −0.774128 0.633030i 0.781811π-0.781811\pi
−0.353899 + 0.935284i 0.615144π0.615144\pi
788788 387.409 + 1445.83i 0.491635 + 1.83481i
789789 0 0
790790 −105.179 365.118i −0.133138 0.462174i
791791 −268.801 −0.339824
792792 0 0
793793 88.0662 88.0662i 0.111055 0.111055i
794794 530.725 306.414i 0.668420 0.385912i
795795 0 0
796796 −106.714 + 184.834i −0.134063 + 0.232204i
797797 −860.450 + 230.557i −1.07961 + 0.289281i −0.754437 0.656373i 0.772090π-0.772090\pi
−0.325175 + 0.945654i 0.605423π0.605423\pi
798798 0 0
799799 43.1229 24.8970i 0.0539711 0.0311602i
800800 709.239 218.734i 0.886549 0.273417i
801801 0 0
802802 1152.46 + 1152.46i 1.43698 + 1.43698i
803803 70.7526 + 18.9581i 0.0881104 + 0.0236091i
804804 0 0
805805 17.1814 0.320916i 0.0213433 0.000398654i
806806 437.818 758.323i 0.543198 0.940847i
807807 0 0
808808 1412.70 + 378.532i 1.74839 + 0.468480i
809809 1398.60i 1.72880i 0.502802 + 0.864402i 0.332302π0.332302\pi
−0.502802 + 0.864402i 0.667698π0.667698\pi
810810 0 0
811811 −347.451 −0.428423 −0.214211 0.976787i 0.568718π-0.568718\pi
−0.214211 + 0.976787i 0.568718π0.568718\pi
812812 −398.533 + 1487.34i −0.490804 + 1.83170i
813813 0 0
814814 158.117 + 91.2888i 0.194247 + 0.112148i
815815 −300.009 + 311.430i −0.368109 + 0.382122i
816816 0 0
817817 31.7877 118.633i 0.0389079 0.145206i
818818 1253.90 1253.90i 1.53288 1.53288i
819819 0 0
820820 −1545.31 + 931.090i −1.88453 + 1.13548i
821821 493.294 + 854.410i 0.600845 + 1.04069i 0.992693 + 0.120665i 0.0385026π0.0385026\pi
−0.391848 + 0.920030i 0.628164π0.628164\pi
822822 0 0
823823 65.3381 + 243.845i 0.0793902 + 0.296288i 0.994193 0.107613i 0.0343207π-0.0343207\pi
−0.914803 + 0.403901i 0.867654π0.867654\pi
824824 767.914 + 443.356i 0.931935 + 0.538053i
825825 0 0
826826 −379.347 657.049i −0.459258 0.795458i
827827 −1054.44 1054.44i −1.27502 1.27502i −0.943419 0.331604i 0.892410π-0.892410\pi
−0.331604 0.943419i 0.607590π-0.607590\pi
828828 0 0
829829 819.644i 0.988714i −0.869259 0.494357i 0.835404π-0.835404\pi
0.869259 0.494357i 0.164596π-0.164596\pi
830830 −132.955 + 240.550i −0.160186 + 0.289819i
831831 0 0
832832 −46.7017 + 12.5137i −0.0561318 + 0.0150405i
833833 −82.0024 306.037i −0.0984423 0.367392i
834834 0 0
835835 1168.64 336.649i 1.39957 0.403173i
836836 791.631 0.946928
837837 0 0
838838 66.9173 66.9173i 0.0798536 0.0798536i
839839 −425.345 + 245.573i −0.506966 + 0.292697i −0.731586 0.681749i 0.761219π-0.761219\pi
0.224619 + 0.974447i 0.427886π0.427886\pi
840840 0 0
841841 184.907 320.269i 0.219866 0.380819i
842842 1690.62 453.001i 2.00786 0.538006i
843843 0 0
844844 −1052.88 + 607.880i −1.24749 + 0.720237i
845845 −339.020 + 204.268i −0.401207 + 0.241738i
846846 0 0
847847 −397.594 397.594i −0.469415 0.469415i
848848 1192.51 + 319.533i 1.40627 + 0.376808i
849849 0 0
850850 −987.500 + 620.421i −1.16176 + 0.729907i
851851 −6.38831 + 11.0649i −0.00750682 + 0.0130022i
852852 0 0
853853 336.484 + 90.1607i 0.394472 + 0.105698i 0.450602 0.892725i 0.351209π-0.351209\pi
−0.0561301 + 0.998423i 0.517876π0.517876\pi
854854 234.218i 0.274260i
855855 0 0
856856 −1439.05 −1.68114
857857 −210.885 + 787.034i −0.246074 + 0.918359i 0.726767 + 0.686884i 0.241022π0.241022\pi
−0.972841 + 0.231475i 0.925645π0.925645\pi
858858 0 0
859859 101.706 + 58.7201i 0.118401 + 0.0683587i 0.558031 0.829820i 0.311557π-0.311557\pi
−0.439630 + 0.898179i 0.644890π0.644890\pi
860860 122.620 + 118.123i 0.142581 + 0.137353i
861861 0 0
862862 −68.1886 + 254.483i −0.0791051 + 0.295224i
863863 148.570 148.570i 0.172155 0.172155i −0.615770 0.787926i 0.711155π-0.711155\pi
0.787926 + 0.615770i 0.211155π0.211155\pi
864864 0 0
865865 −82.0360 20.3474i −0.0948394 0.0235230i
866866 −202.797 351.254i −0.234176 0.405605i
867867 0 0
868868 294.304 + 1098.36i 0.339060 + 1.26539i
869869 50.4374 + 29.1200i 0.0580407 + 0.0335098i
870870 0 0
871871 −220.775 382.393i −0.253473 0.439028i
872872 1826.18 + 1826.18i 2.09424 + 2.09424i
873873 0 0
874874 80.2251i 0.0917907i
875875 −126.630 + 606.680i −0.144720 + 0.693349i
876876 0 0
877877 480.790 128.827i 0.548221 0.146895i 0.0259318 0.999664i 0.491745π-0.491745\pi
0.522289 + 0.852768i 0.325078π0.325078\pi
878878 104.690 + 390.709i 0.119237 + 0.444998i
879879 0 0
880880 −186.322 + 337.106i −0.211730 + 0.383075i
881881 −306.447 −0.347840 −0.173920 0.984760i 0.555643π-0.555643\pi
−0.173920 + 0.984760i 0.555643π0.555643\pi
882882 0 0
883883 930.058 930.058i 1.05329 1.05329i 0.0547963 0.998498i 0.482549π-0.482549\pi
0.998498 0.0547963i 0.0174509π-0.0174509\pi
884884 −950.617 + 548.839i −1.07536 + 0.620859i
885885 0 0
886886 286.676 496.538i 0.323563 0.560427i
887887 130.986 35.0975i 0.147673 0.0395688i −0.184225 0.982884i 0.558978π-0.558978\pi
0.331898 + 0.943315i 0.392311π0.392311\pi
888888 0 0
889889 306.078 176.714i 0.344295 0.198779i
890890 −1612.83 400.029i −1.81216 0.449471i
891891 0 0
892892 2532.24 + 2532.24i 2.83884 + 2.83884i
893893 119.326 + 31.9733i 0.133624 + 0.0358044i
894894 0 0
895895 25.6324 + 1372.32i 0.0286395 + 1.53332i
896896 339.852 588.641i 0.379299 0.656965i
897897 0 0
898898 −1013.34 271.524i −1.12844 0.302366i
899899 894.149i 0.994604i
900900 0 0
901901 −572.962 −0.635918
902902 103.649 386.822i 0.114910 0.428849i
903903 0 0
904904 831.374 + 479.994i 0.919661 + 0.530967i
905905 1308.02 24.4313i 1.44532 0.0269959i
906906 0 0
907907 35.1572 131.208i 0.0387621 0.144662i −0.943833 0.330423i 0.892808π-0.892808\pi
0.982595 + 0.185761i 0.0594751π0.0594751\pi
908908 1194.65 1194.65i 1.31569 1.31569i
909909 0 0
910910 −203.363 + 819.914i −0.223476 + 0.901004i
911911 −545.263 944.423i −0.598532 1.03669i −0.993038 0.117795i 0.962417π-0.962417\pi
0.394506 0.918894i 0.370916π-0.370916\pi
912912 0 0
913913 −10.9035 40.6924i −0.0119425 0.0445700i
914914 −1459.39 842.579i −1.59671 0.921859i
915915 0 0
916916 660.594 + 1144.18i 0.721173 + 1.24911i
917917 −628.907 628.907i −0.685831 0.685831i
918918 0 0
919919 367.996i 0.400431i −0.979752 0.200215i 0.935836π-0.935836\pi
0.979752 0.200215i 0.0641642π-0.0641642\pi
920920 −53.7133 29.6880i −0.0583840 0.0322695i
921921 0 0
922922 1727.79 462.959i 1.87396 0.502125i
923923 279.815 + 1044.28i 0.303158 + 1.13140i
924924 0 0
925925 −337.767 313.432i −0.365153 0.338845i
926926 3276.11 3.53792
927927 0 0
928928 730.476 730.476i 0.787151 0.787151i
929929 −62.7337 + 36.2193i −0.0675282 + 0.0389874i −0.533384 0.845873i 0.679080π-0.679080\pi
0.465856 + 0.884861i 0.345747π0.345747\pi
930930 0 0
931931 393.020 680.731i 0.422148 0.731182i
932932 2339.28 626.810i 2.50996 0.672542i
933933 0 0
934934 902.137 520.849i 0.965886 0.557655i
935935 43.0328 173.499i 0.0460244 0.185560i
936936 0 0
937937 −887.903 887.903i −0.947602 0.947602i 0.0510921 0.998694i 0.483730π-0.483730\pi
−0.998694 + 0.0510921i 0.983730π0.983730\pi
938938 802.082 + 214.917i 0.855099 + 0.229123i
939939 0 0
940940 −118.813 + 123.336i −0.126397 + 0.131208i
941941 −190.349 + 329.694i −0.202284 + 0.350366i −0.949264 0.314480i 0.898170π-0.898170\pi
0.746980 + 0.664846i 0.231503π0.231503\pi
942942 0 0
943943 27.0694 + 7.25323i 0.0287056 + 0.00769165i
944944 1190.02i 1.26061i
945945 0 0
946946 −37.7930 −0.0399504
947947 139.605 521.012i 0.147418 0.550172i −0.852218 0.523187i 0.824743π-0.824743\pi
0.999636 0.0269844i 0.00859046π-0.00859046\pi
948948 0 0
949949 −218.221 125.990i −0.229948 0.132761i
950950 −2820.75 643.959i −2.96921 0.677852i
951951 0 0
952952 294.831 1100.33i 0.309697 1.15580i
953953 52.0743 52.0743i 0.0546425 0.0546425i −0.679258 0.733900i 0.737698π-0.737698\pi
0.733900 + 0.679258i 0.237698π0.237698\pi
954954 0 0
955955 −463.413 769.118i −0.485250 0.805359i
956956 −585.940 1014.88i −0.612908 1.06159i
957957 0 0
958958 −190.265 710.080i −0.198607 0.741210i
959959 −605.788 349.752i −0.631687 0.364705i
960960 0 0
961961 150.349 + 260.413i 0.156451 + 0.270981i
962962 −444.118 444.118i −0.461662 0.461662i
963963 0 0
964964 1906.20i 1.97739i
965965 −37.1977 129.128i −0.0385469 0.133811i
966966 0 0
967967 278.265 74.5608i 0.287761 0.0771053i −0.112051 0.993702i 0.535742π-0.535742\pi
0.399812 + 0.916597i 0.369075π0.369075\pi
968968 519.740 + 1939.70i 0.536921 + 2.00382i
969969 0 0
970970 −2474.55 1367.72i −2.55109 1.41002i
971971 227.938 0.234745 0.117373 0.993088i 0.462553π-0.462553\pi
0.117373 + 0.993088i 0.462553π0.462553\pi
972972 0 0
973973 955.634 955.634i 0.982152 0.982152i
974974 −2230.86 + 1287.99i −2.29041 + 1.32237i
975975 0 0
976976 183.687 318.155i 0.188203 0.325978i
977977 −613.083 + 164.275i −0.627516 + 0.168142i −0.558542 0.829476i 0.688639π-0.688639\pi
−0.0689735 + 0.997618i 0.521972π0.521972\pi
978978 0 0
979979 220.577 127.350i 0.225308 0.130082i
980980 562.365 + 933.345i 0.573842 + 0.952393i
981981 0 0
982982 −531.988 531.988i −0.541739 0.541739i
983983 1316.59 + 352.779i 1.33936 + 0.358880i 0.856196 0.516651i 0.172821π-0.172821\pi
0.483163 + 0.875531i 0.339488π0.339488\pi
984984 0 0
985985 603.908 + 581.761i 0.613104 + 0.590621i
986986 −811.616 + 1405.76i −0.823140 + 1.42572i
987987 0 0
988988 −2630.47 704.832i −2.66242 0.713393i
989989 2.64472i 0.00267414i
990990 0 0
991991 1111.32 1.12141 0.560705 0.828016i 0.310530π-0.310530\pi
0.560705 + 0.828016i 0.310530π0.310530\pi
992992 197.447 736.881i 0.199039 0.742823i
993993 0 0
994994 −1760.76 1016.58i −1.77139 1.02271i
995995 2.23286 + 119.544i 0.00224408 + 0.120145i
996996 0 0
997997 −164.802 + 615.048i −0.165297 + 0.616898i 0.832705 + 0.553717i 0.186791π0.186791\pi
−0.998002 + 0.0631810i 0.979875π0.979875\pi
998998 −842.493 + 842.493i −0.844182 + 0.844182i
999999 0 0
Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 135.3.l.a.37.10 40
3.2 odd 2 45.3.k.a.22.1 yes 40
5.3 odd 4 inner 135.3.l.a.118.1 40
9.2 odd 6 45.3.k.a.7.10 40
9.4 even 3 405.3.g.g.82.10 20
9.5 odd 6 405.3.g.h.82.1 20
9.7 even 3 inner 135.3.l.a.127.1 40
15.2 even 4 225.3.o.b.193.1 40
15.8 even 4 45.3.k.a.13.10 yes 40
15.14 odd 2 225.3.o.b.157.10 40
45.2 even 12 225.3.o.b.43.10 40
45.13 odd 12 405.3.g.g.163.10 20
45.23 even 12 405.3.g.h.163.1 20
45.29 odd 6 225.3.o.b.7.1 40
45.38 even 12 45.3.k.a.43.1 yes 40
45.43 odd 12 inner 135.3.l.a.73.10 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.3.k.a.7.10 40 9.2 odd 6
45.3.k.a.13.10 yes 40 15.8 even 4
45.3.k.a.22.1 yes 40 3.2 odd 2
45.3.k.a.43.1 yes 40 45.38 even 12
135.3.l.a.37.10 40 1.1 even 1 trivial
135.3.l.a.73.10 40 45.43 odd 12 inner
135.3.l.a.118.1 40 5.3 odd 4 inner
135.3.l.a.127.1 40 9.7 even 3 inner
225.3.o.b.7.1 40 45.29 odd 6
225.3.o.b.43.10 40 45.2 even 12
225.3.o.b.157.10 40 15.14 odd 2
225.3.o.b.193.1 40 15.2 even 4
405.3.g.g.82.10 20 9.4 even 3
405.3.g.g.163.10 20 45.13 odd 12
405.3.g.h.82.1 20 9.5 odd 6
405.3.g.h.163.1 20 45.23 even 12