Properties

Label 99.2.j.a.8.3
Level 9999
Weight 22
Character 99.8
Analytic conductor 0.7910.791
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] = [99,2,Mod(8,99)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(99, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([5, 3]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.8");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 99=3211 99 = 3^{2} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 99.j (of order 1010, degree 44, 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: 0.7905189800110.790518980011
Analytic rank: 00
Dimension: 1616
Relative dimension: 44 over Q(ζ10)\Q(\zeta_{10})
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: x16+2x1416x1272x10+26x8+360x6+725x4+1000x2+625 x^{16} + 2x^{14} - 16x^{12} - 72x^{10} + 26x^{8} + 360x^{6} + 725x^{4} + 1000x^{2} + 625 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C10]\mathrm{SU}(2)[C_{10}]

Embedding invariants

Embedding label 8.3
Root 0.7528640.902863i0.752864 - 0.902863i of defining polynomial
Character χ\chi == 99.8
Dual form 99.2.j.a.62.3

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+(0.2052280.149107i)q2+(0.598148+1.84091i)q4+(1.717352.36373i)q5+(2.58586+0.840196i)q7+(0.308515+0.949513i)q80.741170iq10+(2.71994+1.89788i)q11+(1.678692.31052i)q13+(0.6559690.213137i)q14+(2.927052.12663i)q16+(3.609982.62280i)q17+(1.81761+0.590579i)q19+(3.32418+4.57534i)q20+(0.275220+0.795058i)q220.816370iq23+(1.092833.36340i)q25+(0.6890290.223879i)q26+(3.09345+4.25777i)q28+(2.95006+9.07936i)q29+(4.842813.51851i)q312.91456q321.13195q34+(6.426814.66935i)q35+(1.837505.65524i)q37+(0.284966+0.392222i)q38+(2.77422+0.901398i)q40+(2.606048.02058i)q41+11.8763iq43+(1.866906.14238i)q44+(0.1217260.167542i)q46+(7.340412.38504i)q47+(0.317615+0.230761i)q49+(0.7257850.527314i)q50+(5.257581.70829i)q52+(6.14564+8.45874i)q53+(0.185009+9.68851i)q55+2.71452iq56+(0.748358+2.30321i)q58+(0.08873320.0288312i)q59+(1.260241.73457i)q61+(0.4692461.44419i)q62+(5.255953.81867i)q648.34434q651.40778q67+(6.987665.07683i)q68+(0.6227281.91656i)q70+(2.121412.91987i)q71+(1.673380.543714i)q73+(0.4661291.43460i)q743.69932iq76+(8.62796+2.62237i)q77+(4.192605.77063i)q79+(10.0535+3.26659i)q80+(1.730751.25747i)q82+(6.33808+4.60488i)q83+(12.3992+4.02874i)q85+(1.77084+2.43735i)q86+(2.641201.99709i)q88+2.06830iq89+(2.399577.38512i)q91+(1.50286+0.488310i)q92+(1.150831.58398i)q94+(1.72551+5.31057i)q95+(1.35141+0.981858i)q97+0.0995913q98+O(q100)q+(0.205228 - 0.149107i) q^{2} +(-0.598148 + 1.84091i) q^{4} +(1.71735 - 2.36373i) q^{5} +(2.58586 + 0.840196i) q^{7} +(0.308515 + 0.949513i) q^{8} -0.741170i q^{10} +(-2.71994 + 1.89788i) q^{11} +(-1.67869 - 2.31052i) q^{13} +(0.655969 - 0.213137i) q^{14} +(-2.92705 - 2.12663i) q^{16} +(-3.60998 - 2.62280i) q^{17} +(-1.81761 + 0.590579i) q^{19} +(3.32418 + 4.57534i) q^{20} +(-0.275220 + 0.795058i) q^{22} -0.816370i q^{23} +(-1.09283 - 3.36340i) q^{25} +(-0.689029 - 0.223879i) q^{26} +(-3.09345 + 4.25777i) q^{28} +(-2.95006 + 9.07936i) q^{29} +(4.84281 - 3.51851i) q^{31} -2.91456 q^{32} -1.13195 q^{34} +(6.42681 - 4.66935i) q^{35} +(1.83750 - 5.65524i) q^{37} +(-0.284966 + 0.392222i) q^{38} +(2.77422 + 0.901398i) q^{40} +(-2.60604 - 8.02058i) q^{41} +11.8763i q^{43} +(-1.86690 - 6.14238i) q^{44} +(-0.121726 - 0.167542i) q^{46} +(7.34041 - 2.38504i) q^{47} +(0.317615 + 0.230761i) q^{49} +(-0.725785 - 0.527314i) q^{50} +(5.25758 - 1.70829i) q^{52} +(6.14564 + 8.45874i) q^{53} +(-0.185009 + 9.68851i) q^{55} +2.71452i q^{56} +(0.748358 + 2.30321i) q^{58} +(-0.0887332 - 0.0288312i) q^{59} +(1.26024 - 1.73457i) q^{61} +(0.469246 - 1.44419i) q^{62} +(5.25595 - 3.81867i) q^{64} -8.34434 q^{65} -1.40778 q^{67} +(6.98766 - 5.07683i) q^{68} +(0.622728 - 1.91656i) q^{70} +(2.12141 - 2.91987i) q^{71} +(-1.67338 - 0.543714i) q^{73} +(-0.466129 - 1.43460i) q^{74} -3.69932i q^{76} +(-8.62796 + 2.62237i) q^{77} +(-4.19260 - 5.77063i) q^{79} +(-10.0535 + 3.26659i) q^{80} +(-1.73075 - 1.25747i) q^{82} +(6.33808 + 4.60488i) q^{83} +(-12.3992 + 4.02874i) q^{85} +(1.77084 + 2.43735i) q^{86} +(-2.64120 - 1.99709i) q^{88} +2.06830i q^{89} +(-2.39957 - 7.38512i) q^{91} +(1.50286 + 0.488310i) q^{92} +(1.15083 - 1.58398i) q^{94} +(-1.72551 + 5.31057i) q^{95} +(-1.35141 + 0.981858i) q^{97} +0.0995913 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q4q420q1648q2232q25+40q28+16q31+40q3412q37+60q4040q4624q4940q52+16q55+12q58+36q64+96q67+76q70++60q97+O(q100) 16 q - 4 q^{4} - 20 q^{16} - 48 q^{22} - 32 q^{25} + 40 q^{28} + 16 q^{31} + 40 q^{34} - 12 q^{37} + 60 q^{40} - 40 q^{46} - 24 q^{49} - 40 q^{52} + 16 q^{55} + 12 q^{58} + 36 q^{64} + 96 q^{67} + 76 q^{70}+ \cdots + 60 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/99Z)×\left(\mathbb{Z}/99\mathbb{Z}\right)^\times.

nn 4646 5656
χ(n)\chi(n) e(310)e\left(\frac{3}{10}\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 0.205228 0.149107i 0.145118 0.105434i −0.512857 0.858474i 0.671413π-0.671413\pi
0.657975 + 0.753039i 0.271413π0.271413\pi
33 0 0
44 −0.598148 + 1.84091i −0.299074 + 0.920456i
55 1.71735 2.36373i 0.768021 1.05709i −0.228483 0.973548i 0.573376π-0.573376\pi
0.996504 0.0835427i 0.0266235π-0.0266235\pi
66 0 0
77 2.58586 + 0.840196i 0.977363 + 0.317564i 0.753785 0.657122i 0.228226π-0.228226\pi
0.223578 + 0.974686i 0.428226π0.428226\pi
88 0.308515 + 0.949513i 0.109077 + 0.335704i
99 0 0
1010 0.741170i 0.234379i
1111 −2.71994 + 1.89788i −0.820092 + 0.572232i
1212 0 0
1313 −1.67869 2.31052i −0.465586 0.640824i 0.510070 0.860133i 0.329620π-0.329620\pi
−0.975655 + 0.219309i 0.929620π0.929620\pi
1414 0.655969 0.213137i 0.175315 0.0569633i
1515 0 0
1616 −2.92705 2.12663i −0.731763 0.531657i
1717 −3.60998 2.62280i −0.875549 0.636124i 0.0565211 0.998401i 0.481999π-0.481999\pi
−0.932070 + 0.362278i 0.881999π0.881999\pi
1818 0 0
1919 −1.81761 + 0.590579i −0.416989 + 0.135488i −0.509995 0.860178i 0.670353π-0.670353\pi
0.0930053 + 0.995666i 0.470353π0.470353\pi
2020 3.32418 + 4.57534i 0.743310 + 1.02308i
2121 0 0
2222 −0.275220 + 0.795058i −0.0586771 + 0.169507i
2323 0.816370i 0.170225i −0.996371 0.0851124i 0.972875π-0.972875\pi
0.996371 0.0851124i 0.0271249π-0.0271249\pi
2424 0 0
2525 −1.09283 3.36340i −0.218567 0.672680i
2626 −0.689029 0.223879i −0.135130 0.0439063i
2727 0 0
2828 −3.09345 + 4.25777i −0.584608 + 0.804644i
2929 −2.95006 + 9.07936i −0.547813 + 1.68599i 0.166394 + 0.986059i 0.446788π0.446788\pi
−0.714207 + 0.699935i 0.753212π0.753212\pi
3030 0 0
3131 4.84281 3.51851i 0.869795 0.631943i −0.0607369 0.998154i 0.519345π-0.519345\pi
0.930532 + 0.366211i 0.119345π0.119345\pi
3232 −2.91456 −0.515226
3333 0 0
3434 −1.13195 −0.194127
3535 6.42681 4.66935i 1.08633 0.789265i
3636 0 0
3737 1.83750 5.65524i 0.302083 0.929717i −0.678666 0.734447i 0.737442π-0.737442\pi
0.980750 0.195270i 0.0625583π-0.0625583\pi
3838 −0.284966 + 0.392222i −0.0462275 + 0.0636267i
3939 0 0
4040 2.77422 + 0.901398i 0.438642 + 0.142524i
4141 −2.60604 8.02058i −0.406996 1.25260i −0.919217 0.393751i 0.871177π-0.871177\pi
0.512221 0.858853i 0.328823π-0.328823\pi
4242 0 0
4343 11.8763i 1.81112i 0.424214 + 0.905562i 0.360550π0.360550\pi
−0.424214 + 0.905562i 0.639450π0.639450\pi
4444 −1.86690 6.14238i −0.281446 0.925998i
4545 0 0
4646 −0.121726 0.167542i −0.0179475 0.0247027i
4747 7.34041 2.38504i 1.07071 0.347894i 0.279945 0.960016i 0.409684π-0.409684\pi
0.790764 + 0.612122i 0.209684π0.209684\pi
4848 0 0
4949 0.317615 + 0.230761i 0.0453735 + 0.0329658i
5050 −0.725785 0.527314i −0.102641 0.0745734i
5151 0 0
5252 5.25758 1.70829i 0.729094 0.236897i
5353 6.14564 + 8.45874i 0.844168 + 1.16190i 0.985118 + 0.171881i 0.0549845π0.0549845\pi
−0.140950 + 0.990017i 0.545016π0.545016\pi
5454 0 0
5555 −0.185009 + 9.68851i −0.0249466 + 1.30640i
5656 2.71452i 0.362743i
5757 0 0
5858 0.748358 + 2.30321i 0.0982642 + 0.302426i
5959 −0.0887332 0.0288312i −0.0115521 0.00375350i 0.303235 0.952916i 0.401933π-0.401933\pi
−0.314787 + 0.949162i 0.601933π0.601933\pi
6060 0 0
6161 1.26024 1.73457i 0.161357 0.222089i −0.720681 0.693267i 0.756171π-0.756171\pi
0.882038 + 0.471177i 0.156171π0.156171\pi
6262 0.469246 1.44419i 0.0595943 0.183412i
6363 0 0
6464 5.25595 3.81867i 0.656994 0.477334i
6565 −8.34434 −1.03499
6666 0 0
6767 −1.40778 −0.171988 −0.0859941 0.996296i 0.527407π-0.527407\pi
−0.0859941 + 0.996296i 0.527407π0.527407\pi
6868 6.98766 5.07683i 0.847378 0.615656i
6969 0 0
7070 0.622728 1.91656i 0.0744303 0.229073i
7171 2.12141 2.91987i 0.251765 0.346525i −0.664363 0.747410i 0.731297π-0.731297\pi
0.916128 + 0.400885i 0.131297π0.131297\pi
7272 0 0
7373 −1.67338 0.543714i −0.195854 0.0636369i 0.209447 0.977820i 0.432833π-0.432833\pi
−0.405302 + 0.914183i 0.632833π0.632833\pi
7474 −0.466129 1.43460i −0.0541863 0.166768i
7575 0 0
7676 3.69932i 0.424341i
7777 −8.62796 + 2.62237i −0.983247 + 0.298846i
7878 0 0
7979 −4.19260 5.77063i −0.471705 0.649246i 0.505180 0.863014i 0.331426π-0.331426\pi
−0.976884 + 0.213768i 0.931426π0.931426\pi
8080 −10.0535 + 3.26659i −1.12402 + 0.365216i
8181 0 0
8282 −1.73075 1.25747i −0.191130 0.138864i
8383 6.33808 + 4.60488i 0.695695 + 0.505452i 0.878527 0.477692i 0.158527π-0.158527\pi
−0.182833 + 0.983144i 0.558527π0.558527\pi
8484 0 0
8585 −12.3992 + 4.02874i −1.34488 + 0.436978i
8686 1.77084 + 2.43735i 0.190955 + 0.262826i
8787 0 0
8888 −2.64120 1.99709i −0.281553 0.212890i
8989 2.06830i 0.219240i 0.993974 + 0.109620i 0.0349633π0.0349633\pi
−0.993974 + 0.109620i 0.965037π0.965037\pi
9090 0 0
9191 −2.39957 7.38512i −0.251543 0.774171i
9292 1.50286 + 0.488310i 0.156684 + 0.0509099i
9393 0 0
9494 1.15083 1.58398i 0.118699 0.163375i
9595 −1.72551 + 5.31057i −0.177034 + 0.544853i
9696 0 0
9797 −1.35141 + 0.981858i −0.137215 + 0.0996926i −0.654275 0.756256i 0.727026π-0.727026\pi
0.517060 + 0.855949i 0.327026π0.327026\pi
9898 0.0995913 0.0100602
9999 0 0
100100 6.84540 0.684540
101101 −7.31972 + 5.31809i −0.728339 + 0.529170i −0.889038 0.457834i 0.848625π-0.848625\pi
0.160698 + 0.987004i 0.448625π0.448625\pi
102102 0 0
103103 −5.12132 + 15.7618i −0.504618 + 1.55306i 0.296793 + 0.954942i 0.404083π0.404083\pi
−0.801411 + 0.598114i 0.795917π0.795917\pi
104104 1.67597 2.30677i 0.164342 0.226198i
105105 0 0
106106 2.52251 + 0.819613i 0.245008 + 0.0796079i
107107 2.19803 + 6.76484i 0.212492 + 0.653982i 0.999322 + 0.0368130i 0.0117206π0.0117206\pi
−0.786830 + 0.617169i 0.788279π0.788279\pi
108108 0 0
109109 8.62045i 0.825690i −0.910801 0.412845i 0.864535π-0.864535\pi
0.910801 0.412845i 0.135465π-0.135465\pi
110110 1.40665 + 2.01594i 0.134119 + 0.192212i
111111 0 0
112112 −5.78216 7.95845i −0.546362 0.752003i
113113 10.8495 3.52523i 1.02064 0.331626i 0.249556 0.968360i 0.419715π-0.419715\pi
0.771083 + 0.636735i 0.219715π0.219715\pi
114114 0 0
115115 −1.92967 1.40199i −0.179943 0.130736i
116116 −14.9497 10.8616i −1.38805 1.00847i
117117 0 0
118118 −0.0225094 + 0.00731376i −0.00207216 + 0.000673286i
119119 −7.13123 9.81529i −0.653719 0.899767i
120120 0 0
121121 3.79611 10.3242i 0.345101 0.938566i
122122 0.543892i 0.0492417i
123123 0 0
124124 3.58054 + 11.0198i 0.321542 + 0.989606i
125125 4.06670 + 1.32135i 0.363737 + 0.118185i
126126 0 0
127127 −1.69463 + 2.33246i −0.150374 + 0.206973i −0.877558 0.479470i 0.840829π-0.840829\pi
0.727184 + 0.686443i 0.240829π0.240829\pi
128128 2.31057 7.11122i 0.204228 0.628549i
129129 0 0
130130 −1.71249 + 1.24420i −0.150195 + 0.109123i
131131 2.10155 0.183613 0.0918067 0.995777i 0.470736π-0.470736\pi
0.0918067 + 0.995777i 0.470736π0.470736\pi
132132 0 0
133133 −5.19630 −0.450576
134134 −0.288916 + 0.209910i −0.0249586 + 0.0181335i
135135 0 0
136136 1.37665 4.23690i 0.118047 0.363311i
137137 2.98245 4.10498i 0.254808 0.350712i −0.662380 0.749168i 0.730454π-0.730454\pi
0.917188 + 0.398455i 0.130454π0.130454\pi
138138 0 0
139139 16.6282 + 5.40283i 1.41039 + 0.458262i 0.912535 0.409000i 0.134122π-0.134122\pi
0.497852 + 0.867262i 0.334122π0.334122\pi
140140 4.75168 + 14.6242i 0.401590 + 1.23597i
141141 0 0
142142 0.915555i 0.0768317i
143143 8.95103 + 3.09852i 0.748523 + 0.259111i
144144 0 0
145145 16.3948 + 22.5656i 1.36152 + 1.87397i
146146 −0.424495 + 0.137927i −0.0351315 + 0.0114149i
147147 0 0
148148 9.31171 + 6.76535i 0.765418 + 0.556108i
149149 4.57623 + 3.32483i 0.374900 + 0.272381i 0.759240 0.650811i 0.225571π-0.225571\pi
−0.384340 + 0.923192i 0.625571π0.625571\pi
150150 0 0
151151 8.72640 2.83538i 0.710145 0.230740i 0.0683995 0.997658i 0.478211π-0.478211\pi
0.641745 + 0.766918i 0.278211π0.278211\pi
152152 −1.12152 1.54365i −0.0909677 0.125206i
153153 0 0
154154 −1.37968 + 1.82467i −0.111178 + 0.147036i
155155 17.4896i 1.40480i
156156 0 0
157157 −0.943653 2.90426i −0.0753117 0.231785i 0.906313 0.422607i 0.138885π-0.138885\pi
−0.981625 + 0.190821i 0.938885π0.938885\pi
158158 −1.72088 0.559147i −0.136906 0.0444833i
159159 0 0
160160 −5.00531 + 6.88922i −0.395705 + 0.544641i
161161 0.685911 2.11102i 0.0540573 0.166371i
162162 0 0
163163 −6.39488 + 4.64615i −0.500885 + 0.363914i −0.809355 0.587320i 0.800183π-0.800183\pi
0.308470 + 0.951234i 0.400183π0.400183\pi
164164 16.3240 1.27469
165165 0 0
166166 1.98737 0.154250
167167 −13.3065 + 9.66777i −1.02969 + 0.748115i −0.968247 0.249996i 0.919571π-0.919571\pi
−0.0614446 + 0.998110i 0.519571π0.519571\pi
168168 0 0
169169 1.49672 4.60642i 0.115132 0.354340i
170170 −1.94394 + 2.67561i −0.149094 + 0.205210i
171171 0 0
172172 −21.8633 7.10381i −1.66706 0.541660i
173173 −4.79669 14.7627i −0.364686 1.12239i −0.950178 0.311709i 0.899099π-0.899099\pi
0.585492 0.810678i 0.300901π-0.300901\pi
174174 0 0
175175 9.61547i 0.726861i
176176 11.9975 + 0.229100i 0.904344 + 0.0172691i
177177 0 0
178178 0.308398 + 0.424473i 0.0231154 + 0.0318156i
179179 −4.93538 + 1.60360i −0.368888 + 0.119859i −0.487594 0.873071i 0.662125π-0.662125\pi
0.118706 + 0.992929i 0.462125π0.462125\pi
180180 0 0
181181 −4.29773 3.12248i −0.319448 0.232092i 0.416492 0.909139i 0.363259π-0.363259\pi
−0.735940 + 0.677047i 0.763259π0.763259\pi
182182 −1.59363 1.15784i −0.118128 0.0858247i
183183 0 0
184184 0.775154 0.251863i 0.0571451 0.0185676i
185185 −10.2118 14.0554i −0.750788 1.03337i
186186 0 0
187187 14.7967 + 0.282553i 1.08204 + 0.0206624i
188188 14.9396i 1.08959i
189189 0 0
190190 0.437719 + 1.34716i 0.0317555 + 0.0977334i
191191 −10.3662 3.36817i −0.750069 0.243712i −0.0910582 0.995846i 0.529025π-0.529025\pi
−0.659011 + 0.752133i 0.729025π0.729025\pi
192192 0 0
193193 9.03216 12.4317i 0.650149 0.894853i −0.348956 0.937139i 0.613464π-0.613464\pi
0.999106 + 0.0422855i 0.0134639π0.0134639\pi
194194 −0.130946 + 0.403009i −0.00940134 + 0.0289344i
195195 0 0
196196 −0.614791 + 0.446672i −0.0439136 + 0.0319051i
197197 7.24149 0.515935 0.257967 0.966154i 0.416947π-0.416947\pi
0.257967 + 0.966154i 0.416947π0.416947\pi
198198 0 0
199199 −11.3726 −0.806181 −0.403090 0.915160i 0.632064π-0.632064\pi
−0.403090 + 0.915160i 0.632064π0.632064\pi
200200 2.85643 2.07532i 0.201980 0.146747i
201201 0 0
202202 −0.709247 + 2.18284i −0.0499024 + 0.153584i
203203 −15.2569 + 20.9993i −1.07082 + 1.47386i
204204 0 0
205205 −23.4339 7.61415i −1.63670 0.531795i
206206 1.29915 + 3.99838i 0.0905162 + 0.278580i
207207 0 0
208208 10.3330i 0.716463i
209209 3.82295 5.05595i 0.264439 0.349727i
210210 0 0
211211 −2.17376 2.99193i −0.149648 0.205973i 0.727611 0.685990i 0.240631π-0.240631\pi
−0.877259 + 0.480017i 0.840631π0.840631\pi
212212 −19.2478 + 6.25399i −1.32194 + 0.429526i
213213 0 0
214214 1.45978 + 1.06059i 0.0997885 + 0.0725006i
215215 28.0724 + 20.3958i 1.91452 + 1.39098i
216216 0 0
217217 15.4791 5.02946i 1.05079 0.341422i
218218 −1.28537 1.76916i −0.0870560 0.119822i
219219 0 0
220220 −17.7250 6.13575i −1.19502 0.413672i
221221 12.7438i 0.857243i
222222 0 0
223223 −0.0875209 0.269362i −0.00586083 0.0180378i 0.948083 0.318022i 0.103019π-0.103019\pi
−0.953944 + 0.299984i 0.903019π0.903019\pi
224224 −7.53664 2.44880i −0.503563 0.163618i
225225 0 0
226226 1.70099 2.34121i 0.113148 0.155735i
227227 5.64140 17.3625i 0.374433 1.15239i −0.569427 0.822042i 0.692835π-0.692835\pi
0.943860 0.330345i 0.107165π-0.107165\pi
228228 0 0
229229 −21.3385 + 15.5033i −1.41009 + 1.02449i −0.416777 + 0.909009i 0.636840π0.636840\pi
−0.993310 + 0.115479i 0.963160π0.963160\pi
230230 −0.605069 −0.0398971
231231 0 0
232232 −9.53111 −0.625748
233233 −8.73916 + 6.34937i −0.572521 + 0.415961i −0.836020 0.548699i 0.815123π-0.815123\pi
0.263499 + 0.964660i 0.415123π0.415123\pi
234234 0 0
235235 6.96844 21.4467i 0.454571 1.39903i
236236 0.106151 0.146105i 0.00690986 0.00951060i
237237 0 0
238238 −2.92705 0.951057i −0.189733 0.0616478i
239239 −2.29393 7.06000i −0.148382 0.456673i 0.849048 0.528315i 0.177176π-0.177176\pi
−0.997430 + 0.0716420i 0.977176π0.977176\pi
240240 0 0
241241 2.66873i 0.171908i −0.996299 0.0859539i 0.972606π-0.972606\pi
0.996299 0.0859539i 0.0273938π-0.0273938\pi
242242 −0.760344 2.68484i −0.0488767 0.172588i
243243 0 0
244244 2.43938 + 3.35752i 0.156165 + 0.214943i
245245 1.09091 0.354458i 0.0696957 0.0226455i
246246 0 0
247247 4.41576 + 3.20824i 0.280968 + 0.204135i
248248 4.83495 + 3.51280i 0.307020 + 0.223063i
249249 0 0
250250 1.03162 0.335194i 0.0652455 0.0211996i
251251 −14.2630 19.6313i −0.900271 1.23912i −0.970382 0.241577i 0.922335π-0.922335\pi
0.0701107 0.997539i 0.477665π-0.477665\pi
252252 0 0
253253 1.54937 + 2.22047i 0.0974081 + 0.139600i
254254 0.731367i 0.0458901i
255255 0 0
256256 3.42906 + 10.5535i 0.214316 + 0.659597i
257257 15.9360 + 5.17791i 0.994059 + 0.322989i 0.760489 0.649351i 0.224959π-0.224959\pi
0.233570 + 0.972340i 0.424959π0.424959\pi
258258 0 0
259259 9.50303 13.0798i 0.590490 0.812739i
260260 4.99116 15.3612i 0.309538 0.952661i
261261 0 0
262262 0.431296 0.313355i 0.0266456 0.0193591i
263263 −10.9146 −0.673021 −0.336511 0.941680i 0.609247π-0.609247\pi
−0.336511 + 0.941680i 0.609247π0.609247\pi
264264 0 0
265265 30.5484 1.87657
266266 −1.06642 + 0.774802i −0.0653866 + 0.0475062i
267267 0 0
268268 0.842064 2.59161i 0.0514373 0.158308i
269269 −9.22041 + 12.6908i −0.562178 + 0.773772i −0.991601 0.129331i 0.958717π-0.958717\pi
0.429423 + 0.903103i 0.358717π0.358717\pi
270270 0 0
271271 −2.76289 0.897717i −0.167834 0.0545324i 0.223895 0.974613i 0.428123π-0.428123\pi
−0.391728 + 0.920081i 0.628123π0.628123\pi
272272 4.98887 + 15.3542i 0.302495 + 0.930983i
273273 0 0
274274 1.28716i 0.0777601i
275275 9.35577 + 7.07416i 0.564174 + 0.426588i
276276 0 0
277277 12.4111 + 17.0824i 0.745709 + 1.02638i 0.998270 + 0.0587992i 0.0187272π0.0187272\pi
−0.252561 + 0.967581i 0.581273π0.581273\pi
278278 4.21817 1.37057i 0.252989 0.0822011i
279279 0 0
280280 6.41638 + 4.66177i 0.383452 + 0.278594i
281281 2.50015 + 1.81647i 0.149147 + 0.108361i 0.659856 0.751392i 0.270617π-0.270617\pi
−0.510709 + 0.859753i 0.670617π0.670617\pi
282282 0 0
283283 −21.3272 + 6.92961i −1.26777 + 0.411923i −0.864256 0.503052i 0.832211π-0.832211\pi
−0.403512 + 0.914975i 0.632211π0.632211\pi
284284 4.10631 + 5.65185i 0.243664 + 0.335375i
285285 0 0
286286 2.29901 0.698757i 0.135943 0.0413183i
287287 22.9297i 1.35350i
288288 0 0
289289 0.899570 + 2.76859i 0.0529159 + 0.162858i
290290 6.72935 + 2.18650i 0.395161 + 0.128396i
291291 0 0
292292 2.00186 2.75532i 0.117150 0.161243i
293293 6.40930 19.7258i 0.374435 1.15239i −0.569423 0.822044i 0.692833π-0.692833\pi
0.943859 0.330349i 0.107167π-0.107167\pi
294294 0 0
295295 −0.220535 + 0.160228i −0.0128400 + 0.00932883i
296296 5.93663 0.345059
297297 0 0
298298 1.43492 0.0831229
299299 −1.88624 + 1.37043i −0.109084 + 0.0792543i
300300 0 0
301301 −9.97845 + 30.7105i −0.575148 + 1.77012i
302302 1.36813 1.88306i 0.0787268 0.108358i
303303 0 0
304304 6.57619 + 2.13673i 0.377170 + 0.122550i
305305 −1.93578 5.95772i −0.110843 0.341138i
306306 0 0
307307 15.0077i 0.856533i 0.903652 + 0.428267i 0.140876π0.140876\pi
−0.903652 + 0.428267i 0.859124π0.859124\pi
308308 0.333256 17.4519i 0.0189890 0.994413i
309309 0 0
310310 −2.60781 3.58935i −0.148114 0.203861i
311311 −1.95824 + 0.636270i −0.111042 + 0.0360796i −0.364011 0.931395i 0.618593π-0.618593\pi
0.252969 + 0.967474i 0.418593π0.418593\pi
312312 0 0
313313 20.1223 + 14.6197i 1.13738 + 0.826355i 0.986752 0.162236i 0.0518705π-0.0518705\pi
0.150628 + 0.988591i 0.451870π0.451870\pi
314314 −0.626709 0.455330i −0.0353672 0.0256958i
315315 0 0
316316 13.1310 4.26652i 0.738677 0.240011i
317317 0.254351 + 0.350085i 0.0142858 + 0.0196627i 0.816100 0.577910i 0.196132π-0.196132\pi
−0.801814 + 0.597573i 0.796132π0.796132\pi
318318 0 0
319319 −9.20754 30.2941i −0.515523 1.69615i
320320 18.9816i 1.06111i
321321 0 0
322322 −0.173999 0.535513i −0.00969657 0.0298430i
323323 8.11053 + 2.63527i 0.451282 + 0.146630i
324324 0 0
325325 −5.93668 + 8.17113i −0.329308 + 0.453253i
326326 −0.619634 + 1.90704i −0.0343183 + 0.105621i
327327 0 0
328328 6.81164 4.94895i 0.376110 0.273260i
329329 20.9852 1.15695
330330 0 0
331331 −17.3090 −0.951391 −0.475696 0.879610i 0.657804π-0.657804\pi
−0.475696 + 0.879610i 0.657804π0.657804\pi
332332 −12.2683 + 8.91344i −0.673310 + 0.489189i
333333 0 0
334334 −1.28934 + 3.96819i −0.0705497 + 0.217130i
335335 −2.41766 + 3.32762i −0.132091 + 0.181807i
336336 0 0
337337 23.8381 + 7.74548i 1.29855 + 0.421923i 0.875076 0.483986i 0.160812π-0.160812\pi
0.423471 + 0.905910i 0.360812π0.360812\pi
338338 −0.379680 1.16853i −0.0206519 0.0635599i
339339 0 0
340340 25.2356i 1.36859i
341341 −6.49444 + 18.7612i −0.351694 + 1.01598i
342342 0 0
343343 −10.5596 14.5341i −0.570166 0.784766i
344344 −11.2767 + 3.66403i −0.608001 + 0.197551i
345345 0 0
346346 −3.18563 2.31449i −0.171260 0.124428i
347347 −16.8866 12.2688i −0.906519 0.658625i 0.0336127 0.999435i 0.489299π-0.489299\pi
−0.940132 + 0.340810i 0.889299π0.889299\pi
348348 0 0
349349 −17.1385 + 5.56865i −0.917405 + 0.298083i −0.729402 0.684085i 0.760202π-0.760202\pi
−0.188003 + 0.982168i 0.560202π0.560202\pi
350350 −1.43373 1.97336i −0.0766361 0.105481i
351351 0 0
352352 7.92742 5.53148i 0.422533 0.294829i
353353 16.2953i 0.867313i 0.901078 + 0.433656i 0.142777π0.142777\pi
−0.901078 + 0.433656i 0.857223π0.857223\pi
354354 0 0
355355 −3.25858 10.0289i −0.172947 0.532277i
356356 −3.80756 1.23715i −0.201800 0.0655689i
357357 0 0
358358 −0.773769 + 1.06500i −0.0408949 + 0.0562871i
359359 −7.65875 + 23.5712i −0.404213 + 1.24404i 0.517337 + 0.855782i 0.326923π0.326923\pi
−0.921550 + 0.388259i 0.873077π0.873077\pi
360360 0 0
361361 −12.4164 + 9.02103i −0.653494 + 0.474791i
362362 −1.34760 −0.0708281
363363 0 0
364364 15.0306 0.787820
365365 −4.15897 + 3.02167i −0.217690 + 0.158161i
366366 0 0
367367 2.76683 8.51544i 0.144428 0.444502i −0.852509 0.522712i 0.824920π-0.824920\pi
0.996937 + 0.0782097i 0.0249204π0.0249204\pi
368368 −1.73611 + 2.38956i −0.0905012 + 0.124564i
369369 0 0
370370 −4.19150 1.36190i −0.217906 0.0708018i
371371 8.78474 + 27.0367i 0.456081 + 1.40367i
372372 0 0
373373 16.9007i 0.875088i −0.899197 0.437544i 0.855848π-0.855848\pi
0.899197 0.437544i 0.144152π-0.144152\pi
374374 3.07882 2.14830i 0.159202 0.111086i
375375 0 0
376376 4.52926 + 6.23399i 0.233579 + 0.321493i
377377 25.9303 8.42527i 1.33548 0.433923i
378378 0 0
379379 −15.9625 11.5975i −0.819940 0.595722i 0.0967550 0.995308i 0.469154π-0.469154\pi
−0.916695 + 0.399587i 0.869154π0.869154\pi
380380 −8.74419 6.35302i −0.448567 0.325903i
381381 0 0
382382 −2.62964 + 0.854422i −0.134544 + 0.0437160i
383383 2.93889 + 4.04503i 0.150170 + 0.206691i 0.877474 0.479624i 0.159227π-0.159227\pi
−0.727304 + 0.686315i 0.759227π0.759227\pi
384384 0 0
385385 −8.61865 + 24.8977i −0.439247 + 1.26890i
386386 3.89808i 0.198407i
387387 0 0
388388 −0.999169 3.07513i −0.0507251 0.156116i
389389 −9.37115 3.04487i −0.475136 0.154381i 0.0616527 0.998098i 0.480363π-0.480363\pi
−0.536789 + 0.843716i 0.680363π0.680363\pi
390390 0 0
391391 −2.14118 + 2.94708i −0.108284 + 0.149040i
392392 −0.121121 + 0.372773i −0.00611754 + 0.0188279i
393393 0 0
394394 1.48615 1.07975i 0.0748714 0.0543972i
395395 −20.8403 −1.04859
396396 0 0
397397 −19.0245 −0.954812 −0.477406 0.878683i 0.658423π-0.658423\pi
−0.477406 + 0.878683i 0.658423π0.658423\pi
398398 −2.33397 + 1.69573i −0.116991 + 0.0849991i
399399 0 0
400400 −3.95391 + 12.1689i −0.197696 + 0.608445i
401401 18.0482 24.8413i 0.901286 1.24051i −0.0687699 0.997633i 0.521907π-0.521907\pi
0.970056 0.242881i 0.0780926π-0.0780926\pi
402402 0 0
403403 −16.2592 5.28293i −0.809928 0.263162i
404404 −5.41185 16.6560i −0.269250 0.828665i
405405 0 0
406406 6.58454i 0.326785i
407407 5.73509 + 18.8693i 0.284278 + 0.935315i
408408 0 0
409409 −6.97905 9.60583i −0.345092 0.474978i 0.600828 0.799378i 0.294838π-0.294838\pi
−0.945920 + 0.324400i 0.894838π0.894838\pi
410410 −5.94461 + 1.93152i −0.293584 + 0.0953911i
411411 0 0
412412 −25.9528 18.8558i −1.27860 0.928958i
413413 −0.205228 0.149107i −0.0100986 0.00733706i
414414 0 0
415415 21.7694 7.07330i 1.06862 0.347215i
416416 4.89265 + 6.73416i 0.239882 + 0.330169i
417417 0 0
418418 0.0306992 1.60765i 0.00150155 0.0786326i
419419 10.0629i 0.491606i 0.969320 + 0.245803i 0.0790516π0.0790516\pi
−0.969320 + 0.245803i 0.920948π0.920948\pi
420420 0 0
421421 −1.93337 5.95029i −0.0942265 0.289999i 0.892825 0.450404i 0.148720π-0.148720\pi
−0.987051 + 0.160405i 0.948720π0.948720\pi
422422 −0.892232 0.289904i −0.0434332 0.0141123i
423423 0 0
424424 −6.13566 + 8.44502i −0.297974 + 0.410126i
425425 −4.87643 + 15.0081i −0.236541 + 0.728000i
426426 0 0
427427 4.71618 3.42651i 0.228232 0.165820i
428428 −13.7682 −0.665512
429429 0 0
430430 8.80238 0.424489
431431 15.8885 11.5436i 0.765321 0.556038i −0.135217 0.990816i 0.543173π-0.543173\pi
0.900538 + 0.434778i 0.143173π0.143173\pi
432432 0 0
433433 9.66882 29.7576i 0.464654 1.43006i −0.394764 0.918783i 0.629174π-0.629174\pi
0.859418 0.511274i 0.170826π-0.170826\pi
434434 2.42681 3.34022i 0.116491 0.160335i
435435 0 0
436436 15.8695 + 5.15631i 0.760011 + 0.246942i
437437 0.482131 + 1.48385i 0.0230634 + 0.0709820i
438438 0 0
439439 20.1935i 0.963782i 0.876231 + 0.481891i 0.160050π0.160050\pi
−0.876231 + 0.481891i 0.839950π0.839950\pi
440440 −9.25644 + 2.81339i −0.441283 + 0.134123i
441441 0 0
442442 1.90019 + 2.61539i 0.0903828 + 0.124401i
443443 −23.1752 + 7.53009i −1.10109 + 0.357765i −0.802521 0.596624i 0.796509π-0.796509\pi
−0.298567 + 0.954389i 0.596509π0.596509\pi
444444 0 0
445445 4.88890 + 3.55199i 0.231756 + 0.168381i
446446 −0.0581253 0.0422305i −0.00275231 0.00199967i
447447 0 0
448448 16.7996 5.45852i 0.793706 0.257891i
449449 −1.94082 2.67131i −0.0915930 0.126067i 0.760761 0.649032i 0.224826π-0.224826\pi
−0.852354 + 0.522965i 0.824826π0.824826\pi
450450 0 0
451451 22.3104 + 16.8695i 1.05055 + 0.794354i
452452 22.0817i 1.03863i
453453 0 0
454454 −1.43109 4.40443i −0.0671642 0.206710i
455455 −21.5773 7.01089i −1.01156 0.328675i
456456 0 0
457457 −9.17968 + 12.6347i −0.429407 + 0.591028i −0.967817 0.251655i 0.919025π-0.919025\pi
0.538410 + 0.842683i 0.319025π0.319025\pi
458458 −2.06760 + 6.36342i −0.0966126 + 0.297343i
459459 0 0
460460 3.73517 2.71376i 0.174153 0.126530i
461461 36.5685 1.70316 0.851582 0.524221i 0.175644π-0.175644\pi
0.851582 + 0.524221i 0.175644π0.175644\pi
462462 0 0
463463 4.45531 0.207056 0.103528 0.994627i 0.466987π-0.466987\pi
0.103528 + 0.994627i 0.466987π0.466987\pi
464464 27.9434 20.3021i 1.29724 0.942499i
465465 0 0
466466 −0.846784 + 2.60613i −0.0392265 + 0.120727i
467467 24.4676 33.6768i 1.13223 1.55838i 0.348458 0.937325i 0.386706π-0.386706\pi
0.783769 0.621052i 0.213294π-0.213294\pi
468468 0 0
469469 −3.64033 1.18282i −0.168095 0.0546173i
470470 −1.76772 5.44049i −0.0815390 0.250951i
471471 0 0
472472 0.0931482i 0.00428749i
473473 −22.5398 32.3029i −1.03638 1.48529i
474474 0 0
475475 3.97270 + 5.46796i 0.182280 + 0.250887i
476476 22.3346 7.25696i 1.02371 0.332622i
477477 0 0
478478 −1.52347 1.10687i −0.0696819 0.0506269i
479479 −2.84896 2.06989i −0.130172 0.0945756i 0.520794 0.853682i 0.325636π-0.325636\pi
−0.650966 + 0.759107i 0.725636π0.725636\pi
480480 0 0
481481 −16.1512 + 5.24783i −0.736430 + 0.239281i
482482 −0.397925 0.547696i −0.0181250 0.0249469i
483483 0 0
484484 16.7353 + 13.1637i 0.760697 + 0.598351i
485485 4.88056i 0.221615i
486486 0 0
487487 9.85775 + 30.3390i 0.446697 + 1.37479i 0.880611 + 0.473839i 0.157132π0.157132\pi
−0.433914 + 0.900954i 0.642868π0.642868\pi
488488 2.03580 + 0.661472i 0.0921564 + 0.0299434i
489489 0 0
490490 0.171033 0.235407i 0.00772648 0.0106346i
491491 −7.54595 + 23.2241i −0.340544 + 1.04809i 0.623382 + 0.781917i 0.285758π0.285758\pi
−0.963926 + 0.266170i 0.914242π0.914242\pi
492492 0 0
493493 34.4630 25.0389i 1.55214 1.12769i
494494 1.38461 0.0622964
495495 0 0
496496 −21.6577 −0.972460
497497 7.93893 5.76797i 0.356110 0.258729i
498498 0 0
499499 −7.19057 + 22.1303i −0.321894 + 0.990689i 0.650929 + 0.759139i 0.274380π0.274380\pi
−0.972823 + 0.231550i 0.925620π0.925620\pi
500500 −4.86498 + 6.69608i −0.217569 + 0.299458i
501501 0 0
502502 −5.85431 1.90218i −0.261291 0.0848985i
503503 −11.2856 34.7334i −0.503199 1.54869i −0.803778 0.594930i 0.797180π-0.797180\pi
0.300579 0.953757i 0.402820π-0.402820\pi
504504 0 0
505505 26.4348i 1.17633i
506506 0.649061 + 0.224681i 0.0288543 + 0.00998829i
507507 0 0
508508 −3.28022 4.51483i −0.145536 0.200313i
509509 23.6347 7.67938i 1.04759 0.340383i 0.265868 0.964009i 0.414341π-0.414341\pi
0.781722 + 0.623627i 0.214341π0.214341\pi
510510 0 0
511511 −3.87030 2.81193i −0.171212 0.124393i
512512 14.3757 + 10.4445i 0.635321 + 0.461588i
513513 0 0
514514 4.04257 1.31351i 0.178310 0.0579364i
515515 28.4615 + 39.1739i 1.25416 + 1.72621i
516516 0 0
517517 −15.4389 + 20.4184i −0.679003 + 0.897999i
518518 4.10130i 0.180201i
519519 0 0
520520 −2.57436 7.92306i −0.112893 0.347449i
521521 −9.26334 3.00984i −0.405834 0.131864i 0.0989844 0.995089i 0.468441π-0.468441\pi
−0.504819 + 0.863225i 0.668441π0.668441\pi
522522 0 0
523523 19.5526 26.9118i 0.854975 1.17677i −0.127769 0.991804i 0.540782π-0.540782\pi
0.982744 0.184968i 0.0592182π-0.0592182\pi
524524 −1.25704 + 3.86877i −0.0549140 + 0.169008i
525525 0 0
526526 −2.23997 + 1.62743i −0.0976674 + 0.0709595i
527527 −26.7108 −1.16354
528528 0 0
529529 22.3335 0.971023
530530 6.26937 4.55496i 0.272324 0.197855i
531531 0 0
532532 3.10816 9.56592i 0.134756 0.414735i
533533 −14.1570 + 19.4854i −0.613207 + 0.844007i
534534 0 0
535535 19.7650 + 6.42205i 0.854517 + 0.277649i
536536 −0.434323 1.33671i −0.0187599 0.0577371i
537537 0 0
538538 3.97933i 0.171561i
539539 −1.30185 0.0248597i −0.0560746 0.00107078i
540540 0 0
541541 −6.85075 9.42925i −0.294537 0.405395i 0.635944 0.771735i 0.280611π-0.280611\pi
−0.930481 + 0.366340i 0.880611π0.880611\pi
542542 −0.700877 + 0.227729i −0.0301052 + 0.00978178i
543543 0 0
544544 10.5215 + 7.64432i 0.451106 + 0.327748i
545545 −20.3764 14.8043i −0.872829 0.634147i
546546 0 0
547547 0.773004 0.251164i 0.0330513 0.0107390i −0.292445 0.956282i 0.594469π-0.594469\pi
0.325496 + 0.945543i 0.394469π0.394469\pi
548548 5.77297 + 7.94581i 0.246609 + 0.339428i
549549 0 0
550550 2.97487 + 0.0568072i 0.126849 + 0.00242227i
551551 18.2450i 0.777264i
552552 0 0
553553 −5.99302 18.4446i −0.254849 0.784345i
554554 5.09419 + 1.65520i 0.216431 + 0.0703228i
555555 0 0
556556 −19.8923 + 27.3794i −0.843620 + 1.16114i
557557 −2.14843 + 6.61219i −0.0910320 + 0.280168i −0.986199 0.165563i 0.947056π-0.947056\pi
0.895167 + 0.445730i 0.147056π0.147056\pi
558558 0 0
559559 27.4405 19.9367i 1.16061 0.843233i
560560 −28.7416 −1.21455
561561 0 0
562562 0.783948 0.0330689
563563 23.2654 16.9033i 0.980519 0.712388i 0.0226941 0.999742i 0.492776π-0.492776\pi
0.957824 + 0.287354i 0.0927756π0.0927756\pi
564564 0 0
565565 10.2998 31.6994i 0.433314 1.33360i
566566 −3.34367 + 4.60217i −0.140545 + 0.193444i
567567 0 0
568568 3.42694 + 1.11348i 0.143791 + 0.0467207i
569569 3.22890 + 9.93752i 0.135362 + 0.416602i 0.995646 0.0932129i 0.0297137π-0.0297137\pi
−0.860284 + 0.509815i 0.829714π0.829714\pi
570570 0 0
571571 21.2530i 0.889409i −0.895677 0.444704i 0.853309π-0.853309\pi
0.895677 0.444704i 0.146691π-0.146691\pi
572572 −11.0581 + 14.6247i −0.462364 + 0.611489i
573573 0 0
574574 −3.41897 4.70580i −0.142705 0.196416i
575575 −2.74578 + 0.892157i −0.114507 + 0.0372055i
576576 0 0
577577 −12.6856 9.21665i −0.528110 0.383694i 0.291541 0.956558i 0.405832π-0.405832\pi
−0.819650 + 0.572864i 0.805832π0.805832\pi
578578 0.597432 + 0.434060i 0.0248499 + 0.0180545i
579579 0 0
580580 −51.3477 + 16.6839i −2.13210 + 0.692761i
581581 12.5204 + 17.2328i 0.519432 + 0.714937i
582582 0 0
583583 −32.7694 11.3436i −1.35717 0.469803i
584584 1.75664i 0.0726903i
585585 0 0
586586 −1.62588 5.00395i −0.0671646 0.206711i
587587 19.1691 + 6.22843i 0.791195 + 0.257075i 0.676613 0.736339i 0.263447π-0.263447\pi
0.114582 + 0.993414i 0.463447π0.463447\pi
588588 0 0
589589 −6.72441 + 9.25536i −0.277075 + 0.381360i
590590 −0.0213688 + 0.0657664i −0.000879739 + 0.00270756i
591591 0 0
592592 −17.4051 + 12.6455i −0.715343 + 0.519727i
593593 −40.5694 −1.66599 −0.832993 0.553284i 0.813374π-0.813374\pi
−0.832993 + 0.553284i 0.813374π0.813374\pi
594594 0 0
595595 −35.4475 −1.45320
596596 −8.85798 + 6.43570i −0.362837 + 0.263617i
597597 0 0
598598 −0.182768 + 0.562502i −0.00747394 + 0.0230024i
599599 6.42889 8.84861i 0.262678 0.361545i −0.657223 0.753696i 0.728269π-0.728269\pi
0.919901 + 0.392151i 0.128269π0.128269\pi
600600 0 0
601601 15.5556 + 5.05433i 0.634527 + 0.206170i 0.608580 0.793493i 0.291740π-0.291740\pi
0.0259478 + 0.999663i 0.491740π0.491740\pi
602602 2.53129 + 7.79050i 0.103168 + 0.317517i
603603 0 0
604604 17.7605i 0.722665i
605605 −17.8844 26.7032i −0.727104 1.08564i
606606 0 0
607607 −14.0272 19.3068i −0.569348 0.783641i 0.423129 0.906069i 0.360932π-0.360932\pi
−0.992477 + 0.122429i 0.960932π0.960932\pi
608608 5.29755 1.72128i 0.214844 0.0698070i
609609 0 0
610610 −1.28561 0.934052i −0.0520529 0.0378187i
611611 −17.8330 12.9564i −0.721445 0.524161i
612612 0 0
613613 0.0461533 0.0149961i 0.00186411 0.000605687i −0.308085 0.951359i 0.599688π-0.599688\pi
0.309949 + 0.950753i 0.399688π0.399688\pi
614614 2.23774 + 3.07999i 0.0903080 + 0.124298i
615615 0 0
616616 −5.15183 7.38332i −0.207573 0.297482i
617617 8.24561i 0.331956i 0.986129 + 0.165978i 0.0530780π0.0530780\pi
−0.986129 + 0.165978i 0.946922π0.946922\pi
618618 0 0
619619 −0.537464 1.65414i −0.0216025 0.0664857i 0.939674 0.342071i 0.111128π-0.111128\pi
−0.961277 + 0.275585i 0.911128π0.911128\pi
620620 32.1968 + 10.4614i 1.29305 + 0.420139i
621621 0 0
622622 −0.307013 + 0.422567i −0.0123101 + 0.0169434i
623623 −1.73778 + 5.34834i −0.0696227 + 0.214277i
624624 0 0
625625 24.4126 17.7368i 0.976506 0.709473i
626626 6.30955 0.252180
627627 0 0
628628 5.91094 0.235872
629629 −21.4659 + 15.5959i −0.855903 + 0.621850i
630630 0 0
631631 −8.14182 + 25.0580i −0.324121 + 0.997541i 0.647715 + 0.761883i 0.275725π0.275725\pi
−0.971836 + 0.235659i 0.924275π0.924275\pi
632632 4.18580 5.76126i 0.166502 0.229171i
633633 0 0
634634 0.104400 + 0.0339216i 0.00414625 + 0.00134720i
635635 2.60303 + 8.01130i 0.103298 + 0.317919i
636636 0 0
637637 1.12123i 0.0444249i
638638 −6.40670 4.84429i −0.253644 0.191787i
639639 0 0
640640 −12.8409 17.6740i −0.507582 0.698626i
641641 8.27017 2.68714i 0.326652 0.106136i −0.141100 0.989995i 0.545064π-0.545064\pi
0.467752 + 0.883860i 0.345064π0.345064\pi
642642 0 0
643643 17.4877 + 12.7055i 0.689646 + 0.501057i 0.876544 0.481322i 0.159843π-0.159843\pi
−0.186897 + 0.982379i 0.559843π0.559843\pi
644644 3.47592 + 2.52540i 0.136970 + 0.0995148i
645645 0 0
646646 2.05744 0.668503i 0.0809489 0.0263019i
647647 17.2616 + 23.7586i 0.678625 + 0.934048i 0.999916 0.0129330i 0.00411681π-0.00411681\pi
−0.321291 + 0.946980i 0.604117π0.604117\pi
648648 0 0
649649 0.296067 0.0899860i 0.0116216 0.00353226i
650650 2.56214i 0.100495i
651651 0 0
652652 −4.72806 14.5515i −0.185165 0.569880i
653653 22.5339 + 7.32170i 0.881818 + 0.286520i 0.714712 0.699419i 0.246558π-0.246558\pi
0.167106 + 0.985939i 0.446558π0.446558\pi
654654 0 0
655655 3.60909 4.96749i 0.141019 0.194096i
656656 −9.42876 + 29.0187i −0.368131 + 1.13299i
657657 0 0
658658 4.30674 3.12903i 0.167894 0.121982i
659659 −34.5941 −1.34759 −0.673797 0.738916i 0.735338π-0.735338\pi
−0.673797 + 0.738916i 0.735338π0.735338\pi
660660 0 0
661661 35.4913 1.38045 0.690225 0.723595i 0.257512π-0.257512\pi
0.690225 + 0.723595i 0.257512π0.257512\pi
662662 −3.55229 + 2.58089i −0.138064 + 0.100309i
663663 0 0
664664 −2.41700 + 7.43877i −0.0937979 + 0.288680i
665665 −8.92385 + 12.2826i −0.346052 + 0.476300i
666666 0 0
667667 7.41211 + 2.40834i 0.286998 + 0.0932513i
668668 −9.83822 30.2789i −0.380652 1.17153i
669669 0 0
670670 1.04341i 0.0403104i
671671 −0.135765 + 7.10971i −0.00524115 + 0.274467i
672672 0 0
673673 −12.2854 16.9095i −0.473569 0.651812i 0.503684 0.863888i 0.331978π-0.331978\pi
−0.977253 + 0.212076i 0.931978π0.931978\pi
674674 6.04715 1.96484i 0.232928 0.0756827i
675675 0 0
676676 7.58475 + 5.51064i 0.291721 + 0.211948i
677677 −19.6090 14.2468i −0.753634 0.547547i 0.143317 0.989677i 0.454223π-0.454223\pi
−0.896951 + 0.442130i 0.854223π0.854223\pi
678678 0 0
679679 −4.31951 + 1.40350i −0.165768 + 0.0538612i
680680 −7.65068 10.5303i −0.293390 0.403817i
681681 0 0
682682 1.46458 + 4.81868i 0.0560817 + 0.184517i
683683 17.6311i 0.674636i −0.941391 0.337318i 0.890480π-0.890480\pi
0.941391 0.337318i 0.109520π-0.109520\pi
684684 0 0
685685 −4.58116 14.0994i −0.175037 0.538709i
686686 −4.33425 1.40828i −0.165482 0.0537685i
687687 0 0
688688 25.2565 34.7626i 0.962896 1.32531i
689689 9.22748 28.3993i 0.351539 1.08193i
690690 0 0
691691 −23.5718 + 17.1259i −0.896713 + 0.651500i −0.937620 0.347663i 0.886976π-0.886976\pi
0.0409063 + 0.999163i 0.486976π0.486976\pi
692692 30.0459 1.14218
693693 0 0
694694 −5.29496 −0.200994
695695 41.3272 30.0260i 1.56763 1.13895i
696696 0 0
697697 −11.6286 + 35.7893i −0.440466 + 1.35562i
698698 −2.68698 + 3.69831i −0.101704 + 0.139983i
699699 0 0
700700 17.7012 + 5.75148i 0.669044 + 0.217385i
701701 4.54301 + 13.9820i 0.171587 + 0.528091i 0.999461 0.0328229i 0.0104497π-0.0104497\pi
−0.827874 + 0.560914i 0.810450π0.810450\pi
702702 0 0
703703 11.3642i 0.428611i
704704 −7.04848 + 20.3617i −0.265649 + 0.767411i
705705 0 0
706706 2.42974 + 3.34425i 0.0914445 + 0.125863i
707707 −23.3960 + 7.60182i −0.879897 + 0.285896i
708708 0 0
709709 −8.72312 6.33772i −0.327604 0.238018i 0.411810 0.911270i 0.364897π-0.364897\pi
−0.739413 + 0.673252i 0.764897π0.764897\pi
710710 −2.16412 1.57233i −0.0812180 0.0590083i
711711 0 0
712712 −1.96388 + 0.638103i −0.0735995 + 0.0239139i
713713 −2.87241 3.95353i −0.107572 0.148061i
714714 0 0
715715 22.6961 15.8366i 0.848785 0.592254i
716716 10.0448i 0.375391i
717717 0 0
718718 1.94284 + 5.97944i 0.0725060 + 0.223151i
719719 −30.1960 9.81128i −1.12612 0.365899i −0.314020 0.949416i 0.601676π-0.601676\pi
−0.812101 + 0.583517i 0.801676π0.801676\pi
720720 0 0
721721 −26.4860 + 36.4549i −0.986390 + 1.35765i
722722 −1.20309 + 3.70273i −0.0447744 + 0.137801i
723723 0 0
724724 8.31889 6.04403i 0.309169 0.224625i
725725 33.7614 1.25387
726726 0 0
727727 23.6418 0.876828 0.438414 0.898773i 0.355540π-0.355540\pi
0.438414 + 0.898773i 0.355540π0.355540\pi
728728 6.27196 4.55685i 0.232454 0.168888i
729729 0 0
730730 −0.402984 + 1.24026i −0.0149151 + 0.0459040i
731731 31.1493 42.8733i 1.15210 1.58573i
732732 0 0
733733 15.6206 + 5.07543i 0.576959 + 0.187465i 0.582938 0.812517i 0.301903π-0.301903\pi
−0.00597872 + 0.999982i 0.501903π0.501903\pi
734734 −0.701877 2.16016i −0.0259068 0.0797328i
735735 0 0
736736 2.37936i 0.0877043i
737737 3.82908 2.67181i 0.141046 0.0984172i
738738 0 0
739739 20.4813 + 28.1901i 0.753417 + 1.03699i 0.997733 + 0.0672942i 0.0214366π0.0214366\pi
−0.244316 + 0.969696i 0.578563π0.578563\pi
740740 31.9829 10.3919i 1.17571 0.382013i
741741 0 0
742742 5.83422 + 4.23881i 0.214181 + 0.155611i
743743 42.7101 + 31.0307i 1.56688 + 1.13841i 0.930068 + 0.367387i 0.119748π0.119748\pi
0.636813 + 0.771019i 0.280252π0.280252\pi
744744 0 0
745745 15.7180 5.10708i 0.575862 0.187109i
746746 −2.52001 3.46850i −0.0922643 0.126991i
747747 0 0
748748 −9.37077 + 27.0704i −0.342629 + 0.989791i
749749 19.3397i 0.706657i
750750 0 0
751751 15.8766 + 48.8631i 0.579345 + 1.78304i 0.620883 + 0.783903i 0.286774π0.286774\pi
−0.0415382 + 0.999137i 0.513226π0.513226\pi
752752 −26.5578 8.62917i −0.968465 0.314673i
753753 0 0
754754 4.06535 5.59548i 0.148051 0.203775i
755755 8.28421 25.4962i 0.301493 0.927900i
756756 0 0
757757 5.71877 4.15493i 0.207852 0.151013i −0.478989 0.877821i 0.658997π-0.658997\pi
0.686841 + 0.726807i 0.258997π0.258997\pi
758758 −5.00521 −0.181797
759759 0 0
760760 −5.57481 −0.202219
761761 −23.5688 + 17.1238i −0.854370 + 0.620736i −0.926347 0.376670i 0.877069π-0.877069\pi
0.0719775 + 0.997406i 0.477069π0.477069\pi
762762 0 0
763763 7.24287 22.2913i 0.262210 0.806998i
764764 12.4010 17.0685i 0.448653 0.617517i
765765 0 0
766766 1.20628 + 0.391945i 0.0435847 + 0.0141615i
767767 0.0823407 + 0.253419i 0.00297315 + 0.00915042i
768768 0 0
769769 44.2408i 1.59536i −0.603079 0.797682i 0.706060π-0.706060\pi
0.603079 0.797682i 0.293940π-0.293940\pi
770770 1.94362 + 6.39479i 0.0700432 + 0.230452i
771771 0 0
772772 17.4831 + 24.0634i 0.629230 + 0.866061i
773773 −38.0786 + 12.3725i −1.36959 + 0.445007i −0.899234 0.437468i 0.855875π-0.855875\pi
−0.470358 + 0.882476i 0.655875π0.655875\pi
774774 0 0
775775 −17.1266 12.4432i −0.615204 0.446972i
776776 −1.34922 0.980265i −0.0484341 0.0351895i
777777 0 0
778778 −2.37723 + 0.772409i −0.0852279 + 0.0276922i
779779 9.47357 + 13.0393i 0.339426 + 0.467180i
780780 0 0
781781 −0.228538 + 11.9680i −0.00817775 + 0.428250i
782782 0.924086i 0.0330453i
783783 0 0
784784 −0.438933 1.35090i −0.0156762 0.0482463i
785785 −8.48547 2.75709i −0.302859 0.0984049i
786786 0 0
787787 −16.6720 + 22.9470i −0.594292 + 0.817973i −0.995171 0.0981579i 0.968705π-0.968705\pi
0.400878 + 0.916131i 0.368705π0.368705\pi
788788 −4.33149 + 13.3309i −0.154303 + 0.474895i
789789 0 0
790790 −4.27701 + 3.10743i −0.152169 + 0.110558i
791791 31.0173 1.10285
792792 0 0
793793 −6.12332 −0.217446
794794 −3.90435 + 2.83668i −0.138560 + 0.100670i
795795 0 0
796796 6.80249 20.9359i 0.241108 0.742054i
797797 −8.78371 + 12.0897i −0.311135 + 0.428241i −0.935735 0.352704i 0.885262π-0.885262\pi
0.624600 + 0.780945i 0.285262π0.285262\pi
798798 0 0
799799 −32.7542 10.6425i −1.15876 0.376504i
800800 3.18513 + 9.80283i 0.112611 + 0.346582i
801801 0 0
802802 7.78923i 0.275047i
803803 5.58339 1.69700i 0.197034 0.0598860i
804804 0 0
805805 −3.81192 5.24666i −0.134352 0.184920i
806806 −4.12456 + 1.34015i −0.145281 + 0.0472048i
807807 0 0
808808 −7.30784 5.30946i −0.257089 0.186786i
809809 −24.0892 17.5019i −0.846933 0.615333i 0.0773660 0.997003i 0.475349π-0.475349\pi
−0.924299 + 0.381670i 0.875349π0.875349\pi
810810 0 0
811811 41.9856 13.6420i 1.47432 0.479034i 0.541906 0.840439i 0.317703π-0.317703\pi
0.932409 + 0.361405i 0.117703π0.117703\pi
812812 −29.5320 40.6473i −1.03637 1.42644i
813813 0 0
814814 3.99053 + 3.01735i 0.139868 + 0.105758i
815815 23.0948i 0.808975i
816816 0 0
817817 −7.01391 21.5866i −0.245386 0.755220i
818818 −2.86459 0.930761i −0.100158 0.0325433i
819819 0 0
820820 28.0340 38.5854i 0.978988 1.34746i
821821 1.23760 3.80893i 0.0431924 0.132933i −0.927135 0.374728i 0.877736π-0.877736\pi
0.970327 + 0.241795i 0.0777362π0.0777362\pi
822822 0 0
823823 −34.1262 + 24.7941i −1.18956 + 0.864268i −0.993218 0.116266i 0.962907π-0.962907\pi
−0.196345 + 0.980535i 0.562907π0.562907\pi
824824 −16.5460 −0.576409
825825 0 0
826826 −0.0643512 −0.00223906
827827 21.5183 15.6340i 0.748266 0.543647i −0.147023 0.989133i 0.546969π-0.546969\pi
0.895289 + 0.445486i 0.146969π0.146969\pi
828828 0 0
829829 3.77976 11.6329i 0.131276 0.404027i −0.863716 0.503979i 0.831869π-0.831869\pi
0.994992 + 0.0999518i 0.0318689π0.0318689\pi
830830 3.41300 4.69759i 0.118467 0.163056i
831831 0 0
832832 −17.6463 5.73362i −0.611774 0.198777i
833833 −0.541343 1.66608i −0.0187564 0.0577264i
834834 0 0
835835 48.0560i 1.66305i
836836 7.02087 + 10.0619i 0.242822 + 0.347999i
837837 0 0
838838 1.50045 + 2.06519i 0.0518321 + 0.0713408i
839839 9.17434 2.98092i 0.316733 0.102913i −0.146336 0.989235i 0.546748π-0.546748\pi
0.463069 + 0.886322i 0.346748π0.346748\pi
840840 0 0
841841 −50.2704 36.5236i −1.73346 1.25943i
842842 −1.28401 0.932887i −0.0442498 0.0321494i
843843 0 0
844844 6.80810 2.21209i 0.234345 0.0761432i
845845 −8.31793 11.4486i −0.286146 0.393846i
846846 0 0
847847 18.4906 23.5075i 0.635344 0.807727i
848848 37.8287i 1.29904i
849849 0 0
850850 1.23703 + 3.80718i 0.0424298 + 0.130585i
851851 −4.61677 1.50008i −0.158261 0.0514221i
852852 0 0
853853 −6.89976 + 9.49670i −0.236243 + 0.325161i −0.910634 0.413214i 0.864406π-0.864406\pi
0.674391 + 0.738374i 0.264406π0.264406\pi
854854 0.456976 1.40643i 0.0156374 0.0481270i
855855 0 0
856856 −5.74518 + 4.17412i −0.196366 + 0.142668i
857857 48.7738 1.66608 0.833041 0.553212i 0.186598π-0.186598\pi
0.833041 + 0.553212i 0.186598π0.186598\pi
858858 0 0
859859 −31.0880 −1.06071 −0.530355 0.847776i 0.677941π-0.677941\pi
−0.530355 + 0.847776i 0.677941π0.677941\pi
860860 −54.3383 + 39.4791i −1.85292 + 1.34623i
861861 0 0
862862 1.53952 4.73815i 0.0524362 0.161382i
863863 −30.6459 + 42.1805i −1.04320 + 1.43584i −0.148641 + 0.988891i 0.547490π0.547490\pi
−0.894559 + 0.446950i 0.852510π0.852510\pi
864864 0 0
865865 −43.1325 14.0146i −1.46655 0.476511i
866866 −2.45274 7.54876i −0.0833475 0.256517i
867867 0 0
868868 31.5040i 1.06931i
869869 22.3556 + 7.73868i 0.758361 + 0.262517i
870870 0 0
871871 2.36324 + 3.25272i 0.0800753 + 0.110214i
872872 8.18523 2.65954i 0.277187 0.0900635i
873873 0 0
874874 0.320198 + 0.232637i 0.0108309 + 0.00786907i
875875 9.40572 + 6.83366i 0.317971 + 0.231020i
876876 0 0
877877 16.1564 5.24952i 0.545561 0.177264i −0.0232530 0.999730i 0.507402π-0.507402\pi
0.568814 + 0.822466i 0.307402π0.307402\pi
878878 3.01098 + 4.14426i 0.101616 + 0.139862i
879879 0 0
880880 21.1454 27.9653i 0.712810 0.942710i
881881 50.3115i 1.69504i 0.530765 + 0.847519i 0.321905π0.321905\pi
−0.530765 + 0.847519i 0.678095π0.678095\pi
882882 0 0
883883 4.44037 + 13.6660i 0.149430 + 0.459899i 0.997554 0.0698990i 0.0222677π-0.0222677\pi
−0.848124 + 0.529798i 0.822268π0.822268\pi
884884 −23.4603 7.62270i −0.789054 0.256379i
885885 0 0
886886 −3.63341 + 5.00096i −0.122067 + 0.168011i
887887 −12.7625 + 39.2790i −0.428523 + 1.31886i 0.471057 + 0.882103i 0.343873π0.343873\pi
−0.899580 + 0.436756i 0.856127π0.856127\pi
888888 0 0
889889 −6.34181 + 4.60760i −0.212698 + 0.154534i
890890 1.53296 0.0513851
891891 0 0
892892 0.548221 0.0183558
893893 −11.9335 + 8.67018i −0.399339 + 0.290136i
894894 0 0
895895 −4.68529 + 14.4198i −0.156612 + 0.482002i
896896 11.9496 16.4473i 0.399209 0.549465i
897897 0 0
898898 −0.796620 0.258838i −0.0265836 0.00863752i
899899 17.6592 + 54.3495i 0.588968 + 1.81266i
900900 0 0
901901 46.6547i 1.55429i
902902 7.09406 + 0.135466i 0.236206 + 0.00451053i
903903 0 0
904904 6.69450 + 9.21419i 0.222656 + 0.306460i
905905 −14.7614 + 4.79627i −0.490685 + 0.159433i
906906 0 0
907907 21.1288 + 15.3510i 0.701571 + 0.509721i 0.880444 0.474151i 0.157245π-0.157245\pi
−0.178872 + 0.983872i 0.557245π0.557245\pi
908908 28.5883 + 20.7706i 0.948738 + 0.689298i
909909 0 0
910910 −5.47363 + 1.77849i −0.181449 + 0.0589563i
911911 −26.6929 36.7397i −0.884377 1.21724i −0.975189 0.221372i 0.928946π-0.928946\pi
0.0908128 0.995868i 0.471054π-0.471054\pi
912912 0 0
913913 −25.9787 0.496082i −0.859769 0.0164179i
914914 3.96175i 0.131043i
915915 0 0
916916 −15.7767 48.5555i −0.521275 1.60432i
917917 5.43431 + 1.76572i 0.179457 + 0.0583091i
918918 0 0
919919 −16.3737 + 22.5365i −0.540119 + 0.743410i −0.988630 0.150367i 0.951954π-0.951954\pi
0.448511 + 0.893777i 0.351954π0.351954\pi
920920 0.735874 2.26479i 0.0242610 0.0746678i
921921 0 0
922922 7.50486 5.45260i 0.247160 0.179572i
923923 −10.3076 −0.339280
924924 0 0
925925 −21.0289 −0.691427
926926 0.914353 0.664317i 0.0300475 0.0218308i
927927 0 0
928928 8.59813 26.4623i 0.282248 0.868669i
929929 −29.2450 + 40.2523i −0.959497 + 1.32063i −0.0123191 + 0.999924i 0.503921π0.503921\pi
−0.947178 + 0.320710i 0.896079π0.896079\pi
930930 0 0
931931 −0.713584 0.231857i −0.0233868 0.00759882i
932932 −6.46131 19.8859i −0.211647 0.651384i
933933 0 0
934934 10.5597i 0.345524i
935935 26.0789 34.4901i 0.852872 1.12795i
936936 0 0
937937 11.9943 + 16.5087i 0.391837 + 0.539317i 0.958672 0.284514i 0.0918323π-0.0918323\pi
−0.566835 + 0.823831i 0.691832π0.691832\pi
938938 −0.923462 + 0.300051i −0.0301521 + 0.00979702i
939939 0 0
940940 35.3132 + 25.6566i 1.15179 + 0.836825i
941941 −14.1929 10.3117i −0.462675 0.336153i 0.331904 0.943313i 0.392309π-0.392309\pi
−0.794580 + 0.607160i 0.792309π0.792309\pi
942942 0 0
943943 −6.54776 + 2.12750i −0.213224 + 0.0692808i
944944 0.198413 + 0.273093i 0.00645781 + 0.00888841i
945945 0 0
946946 −9.44237 3.26860i −0.306998 0.106271i
947947 47.0672i 1.52948i −0.644340 0.764739i 0.722868π-0.722868\pi
0.644340 0.764739i 0.277132π-0.277132\pi
948948 0 0
949949 1.55283 + 4.77911i 0.0504069 + 0.155136i
950950 1.63062 + 0.529820i 0.0529042 + 0.0171896i
951951 0 0
952952 7.11966 9.79937i 0.230749 0.317599i
953953 15.9545 49.1029i 0.516817 1.59060i −0.263136 0.964759i 0.584757π-0.584757\pi
0.779952 0.625839i 0.215243π-0.215243\pi
954954 0 0
955955 −25.7637 + 18.7185i −0.833695 + 0.605715i
956956 14.3689 0.464725
957957 0 0
958958 −0.893318 −0.0288618
959959 11.1612 8.10907i 0.360413 0.261855i
960960 0 0
961961 1.49341 4.59623i 0.0481744 0.148266i
962962 −2.53218 + 3.48525i −0.0816408 + 0.112369i
963963 0 0
964964 4.91289 + 1.59629i 0.158233 + 0.0514132i
965965 −13.8738 42.6991i −0.446613 1.37453i
966966 0 0
967967 33.6964i 1.08360i −0.840506 0.541802i 0.817742π-0.817742\pi
0.840506 0.541802i 0.182258π-0.182258\pi
968968 10.9741 + 0.419271i 0.352722 + 0.0134759i
969969 0 0
970970 0.727724 + 1.00163i 0.0233658 + 0.0321603i
971971 −53.1467 + 17.2684i −1.70556 + 0.554170i −0.989584 0.143955i 0.954018π-0.954018\pi
−0.715976 + 0.698125i 0.754018π0.754018\pi
972972 0 0
973973 38.4588 + 27.9419i 1.23293 + 0.895777i
974974 6.54684 + 4.75656i 0.209774 + 0.152410i
975975 0 0
976976 −7.37757 + 2.39712i −0.236150 + 0.0767299i
977977 −12.1432 16.7137i −0.388496 0.534719i 0.569314 0.822120i 0.307209π-0.307209\pi
−0.957810 + 0.287401i 0.907209π0.907209\pi
978978 0 0
979979 −3.92539 5.62565i −0.125456 0.179797i
980980 2.22029i 0.0709245i
981981 0 0
982982 1.91422 + 5.89137i 0.0610853 + 0.188001i
983983 47.6740 + 15.4902i 1.52056 + 0.494061i 0.945936 0.324354i 0.105147π-0.105147\pi
0.574628 + 0.818415i 0.305147π0.305147\pi
984984 0 0
985985 12.4362 17.1169i 0.396249 0.545390i
986986 3.33931 10.2773i 0.106345 0.327297i
987987 0 0
988988 −8.54737 + 6.21003i −0.271928 + 0.197567i
989989 9.69548 0.308298
990990 0 0
991991 45.3068 1.43922 0.719609 0.694379i 0.244321π-0.244321\pi
0.719609 + 0.694379i 0.244321π0.244321\pi
992992 −14.1147 + 10.2549i −0.448141 + 0.325594i
993993 0 0
994994 0.769246 2.36750i 0.0243990 0.0750924i
995995 −19.5307 + 26.8817i −0.619164 + 0.852206i
996996 0 0
997997 9.77676 + 3.17666i 0.309633 + 0.100606i 0.459712 0.888068i 0.347953π-0.347953\pi
−0.150079 + 0.988674i 0.547953π0.547953\pi
998998 1.82407 + 5.61392i 0.0577400 + 0.177705i
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 99.2.j.a.8.3 yes 16
3.2 odd 2 inner 99.2.j.a.8.2 16
4.3 odd 2 1584.2.cd.c.305.3 16
9.2 odd 6 891.2.u.c.701.3 32
9.4 even 3 891.2.u.c.107.3 32
9.5 odd 6 891.2.u.c.107.2 32
9.7 even 3 891.2.u.c.701.2 32
11.2 odd 10 1089.2.d.g.1088.10 16
11.7 odd 10 inner 99.2.j.a.62.2 yes 16
11.9 even 5 1089.2.d.g.1088.8 16
12.11 even 2 1584.2.cd.c.305.2 16
33.2 even 10 1089.2.d.g.1088.7 16
33.20 odd 10 1089.2.d.g.1088.9 16
33.29 even 10 inner 99.2.j.a.62.3 yes 16
44.7 even 10 1584.2.cd.c.161.2 16
99.7 odd 30 891.2.u.c.458.2 32
99.29 even 30 891.2.u.c.458.3 32
99.40 odd 30 891.2.u.c.755.3 32
99.95 even 30 891.2.u.c.755.2 32
132.95 odd 10 1584.2.cd.c.161.3 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.2.j.a.8.2 16 3.2 odd 2 inner
99.2.j.a.8.3 yes 16 1.1 even 1 trivial
99.2.j.a.62.2 yes 16 11.7 odd 10 inner
99.2.j.a.62.3 yes 16 33.29 even 10 inner
891.2.u.c.107.2 32 9.5 odd 6
891.2.u.c.107.3 32 9.4 even 3
891.2.u.c.458.2 32 99.7 odd 30
891.2.u.c.458.3 32 99.29 even 30
891.2.u.c.701.2 32 9.7 even 3
891.2.u.c.701.3 32 9.2 odd 6
891.2.u.c.755.2 32 99.95 even 30
891.2.u.c.755.3 32 99.40 odd 30
1089.2.d.g.1088.7 16 33.2 even 10
1089.2.d.g.1088.8 16 11.9 even 5
1089.2.d.g.1088.9 16 33.20 odd 10
1089.2.d.g.1088.10 16 11.2 odd 10
1584.2.cd.c.161.2 16 44.7 even 10
1584.2.cd.c.161.3 16 132.95 odd 10
1584.2.cd.c.305.2 16 12.11 even 2
1584.2.cd.c.305.3 16 4.3 odd 2