Properties

Label 99.4.f.e.91.4
Level 9999
Weight 44
Character 99.91
Analytic conductor 5.8415.841
Analytic rank 00
Dimension 2424
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [99,4,Mod(37,99)]
 
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([0, 2]))
 
N = Newforms(chi, 4, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("99.37");
 
S:= CuspForms(chi, 4);
 
N := Newforms(S);
 
Level: N N == 99=3211 99 = 3^{2} \cdot 11
Weight: k k == 4 4
Character orbit: [χ][\chi] == 99.f (of order 55, 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: 5.841189090575.84118909057
Analytic rank: 00
Dimension: 2424
Relative dimension: 66 over Q(ζ5)\Q(\zeta_{5})
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 91.4
Character χ\chi == 99.91
Dual form 99.4.f.e.37.4

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+(1.399171.01656i)q2+(1.54785+4.76378i)q4+(3.78707+2.75147i)q5+(2.91496+8.97133i)q7+(6.95243+21.3974i)q8+8.09578q10+(20.8997+29.9032i)q11+(4.36138+3.16873i)q13+(5.04133+15.5156i)q14+(0.9392520.682406i)q16+(68.6535+49.8797i)q17+(15.731648.4167i)q19+(18.9692+13.7819i)q20+(59.6405+20.5940i)q22+52.9969q23+(31.855898.0420i)q25+(2.88112+8.86717i)q26+(38.225627.7725i)q28+(35.2655108.536i)q29+(67.7468+49.2209i)q31181.996q32+146.763q34+(35.7235+25.9547i)q35+(47.0244+144.726i)q37+(71.229451.7512i)q38+(32.5449+100.163i)q40+(56.9163175.170i)q4146.4843q43+(174.802+53.2758i)q44+(74.151753.8744i)q46+(120.309370.274i)q47+(205.505+149.308i)q49+(144.237104.794i)q50+(8.3443825.6814i)q52+(462.541336.055i)q53+(3.12935+170.751i)q55212.229q56+(60.9906187.710i)q58+(24.4445+75.2324i)q59+(584.546424.697i)q61+(44.7534+137.737i)q62+(247.130+179.550i)q6425.2355q65+608.961q67+(343.881+249.844i)q68+(23.5989+72.6299i)q70+(740.521+538.020i)q71+(186.265573.266i)q73+(81.3272+250.299i)q74+254.997q76+(329.194+100.331i)q77+(298.418216.813i)q79+(1.679395.16865i)q80+(257.706187.234i)q82+(797.245+579.233i)q83+(122.753+377.796i)q85+(65.0394+47.2539i)q86+(494.548+655.099i)q88+1156.34q89+(15.714448.3641i)q91+(82.0312+252.466i)q92+(544.737395.775i)q94+(73.6406226.643i)q95+(478.658+347.765i)q97+439.317q98+O(q100)q+(1.39917 - 1.01656i) q^{2} +(-1.54785 + 4.76378i) q^{4} +(3.78707 + 2.75147i) q^{5} +(-2.91496 + 8.97133i) q^{7} +(6.95243 + 21.3974i) q^{8} +8.09578 q^{10} +(20.8997 + 29.9032i) q^{11} +(-4.36138 + 3.16873i) q^{13} +(5.04133 + 15.5156i) q^{14} +(-0.939252 - 0.682406i) q^{16} +(68.6535 + 49.8797i) q^{17} +(-15.7316 - 48.4167i) q^{19} +(-18.9692 + 13.7819i) q^{20} +(59.6405 + 20.5940i) q^{22} +52.9969 q^{23} +(-31.8558 - 98.0420i) q^{25} +(-2.88112 + 8.86717i) q^{26} +(-38.2256 - 27.7725i) q^{28} +(35.2655 - 108.536i) q^{29} +(-67.7468 + 49.2209i) q^{31} -181.996 q^{32} +146.763 q^{34} +(-35.7235 + 25.9547i) q^{35} +(-47.0244 + 144.726i) q^{37} +(-71.2294 - 51.7512i) q^{38} +(-32.5449 + 100.163i) q^{40} +(-56.9163 - 175.170i) q^{41} -46.4843 q^{43} +(-174.802 + 53.2758i) q^{44} +(74.1517 - 53.8744i) q^{46} +(-120.309 - 370.274i) q^{47} +(205.505 + 149.308i) q^{49} +(-144.237 - 104.794i) q^{50} +(-8.34438 - 25.6814i) q^{52} +(462.541 - 336.055i) q^{53} +(-3.12935 + 170.751i) q^{55} -212.229 q^{56} +(-60.9906 - 187.710i) q^{58} +(-24.4445 + 75.2324i) q^{59} +(-584.546 - 424.697i) q^{61} +(-44.7534 + 137.737i) q^{62} +(-247.130 + 179.550i) q^{64} -25.2355 q^{65} +608.961 q^{67} +(-343.881 + 249.844i) q^{68} +(-23.5989 + 72.6299i) q^{70} +(740.521 + 538.020i) q^{71} +(186.265 - 573.266i) q^{73} +(81.3272 + 250.299i) q^{74} +254.997 q^{76} +(-329.194 + 100.331i) q^{77} +(298.418 - 216.813i) q^{79} +(-1.67939 - 5.16865i) q^{80} +(-257.706 - 187.234i) q^{82} +(797.245 + 579.233i) q^{83} +(122.753 + 377.796i) q^{85} +(-65.0394 + 47.2539i) q^{86} +(-494.548 + 655.099i) q^{88} +1156.34 q^{89} +(-15.7144 - 48.3641i) q^{91} +(-82.0312 + 252.466i) q^{92} +(-544.737 - 395.775i) q^{94} +(73.6406 - 226.643i) q^{95} +(-478.658 + 347.765i) q^{97} +439.317 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 24q4q428q7+208q10+20q13224q1640q19586q22+362q25150q28+670q312520q34516q37+2002q40+4008q43+2174q46+342q49+1224q97+O(q100) 24 q - 4 q^{4} - 28 q^{7} + 208 q^{10} + 20 q^{13} - 224 q^{16} - 40 q^{19} - 586 q^{22} + 362 q^{25} - 150 q^{28} + 670 q^{31} - 2520 q^{34} - 516 q^{37} + 2002 q^{40} + 4008 q^{43} + 2174 q^{46} + 342 q^{49}+ \cdots - 1224 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(45)e\left(\frac{4}{5}\right) 11

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 1.39917 1.01656i 0.494681 0.359407i −0.312301 0.949983i 0.601100π-0.601100\pi
0.806982 + 0.590577i 0.201100π0.201100\pi
33 0 0
44 −1.54785 + 4.76378i −0.193481 + 0.595473i
55 3.78707 + 2.75147i 0.338726 + 0.246099i 0.744124 0.668041i 0.232867π-0.232867\pi
−0.405398 + 0.914140i 0.632867π0.632867\pi
66 0 0
77 −2.91496 + 8.97133i −0.157393 + 0.484406i −0.998396 0.0566252i 0.981966π-0.981966\pi
0.841002 + 0.541031i 0.181966π0.181966\pi
88 6.95243 + 21.3974i 0.307257 + 0.945640i
99 0 0
1010 8.09578 0.256011
1111 20.8997 + 29.9032i 0.572862 + 0.819652i
1212 0 0
1313 −4.36138 + 3.16873i −0.0930483 + 0.0676036i −0.633337 0.773876i 0.718315π-0.718315\pi
0.540288 + 0.841480i 0.318315π0.318315\pi
1414 5.04133 + 15.5156i 0.0962395 + 0.296195i
1515 0 0
1616 −0.939252 0.682406i −0.0146758 0.0106626i
1717 68.6535 + 49.8797i 0.979466 + 0.711623i 0.957589 0.288137i 0.0930359π-0.0930359\pi
0.0218765 + 0.999761i 0.493036π0.493036\pi
1818 0 0
1919 −15.7316 48.4167i −0.189951 0.584608i 0.810048 0.586364i 0.199441π-0.199441\pi
−0.999998 + 0.00175558i 0.999441π0.999441\pi
2020 −18.9692 + 13.7819i −0.212082 + 0.154087i
2121 0 0
2222 59.6405 + 20.5940i 0.577973 + 0.199576i
2323 52.9969 0.480462 0.240231 0.970716i 0.422777π-0.422777\pi
0.240231 + 0.970716i 0.422777π0.422777\pi
2424 0 0
2525 −31.8558 98.0420i −0.254846 0.784336i
2626 −2.88112 + 8.86717i −0.0217321 + 0.0668844i
2727 0 0
2828 −38.2256 27.7725i −0.257998 0.187447i
2929 35.2655 108.536i 0.225815 0.694988i −0.772393 0.635145i 0.780940π-0.780940\pi
0.998208 0.0598424i 0.0190598π-0.0190598\pi
3030 0 0
3131 −67.7468 + 49.2209i −0.392506 + 0.285172i −0.766482 0.642266i 0.777994π-0.777994\pi
0.373976 + 0.927439i 0.377994π0.377994\pi
3232 −181.996 −1.00540
3333 0 0
3434 146.763 0.740285
3535 −35.7235 + 25.9547i −0.172525 + 0.125347i
3636 0 0
3737 −47.0244 + 144.726i −0.208939 + 0.643049i 0.790589 + 0.612347i 0.209774π0.209774\pi
−0.999529 + 0.0307025i 0.990226π0.990226\pi
3838 −71.2294 51.7512i −0.304077 0.220925i
3939 0 0
4040 −32.5449 + 100.163i −0.128645 + 0.395929i
4141 −56.9163 175.170i −0.216801 0.667244i −0.999021 0.0442420i 0.985913π-0.985913\pi
0.782220 0.623002i 0.214087π-0.214087\pi
4242 0 0
4343 −46.4843 −0.164856 −0.0824278 0.996597i 0.526267π-0.526267\pi
−0.0824278 + 0.996597i 0.526267π0.526267\pi
4444 −174.802 + 53.2758i −0.598918 + 0.182537i
4545 0 0
4646 74.1517 53.8744i 0.237675 0.172681i
4747 −120.309 370.274i −0.373381 1.14915i −0.944564 0.328326i 0.893515π-0.893515\pi
0.571183 0.820823i 0.306485π-0.306485\pi
4848 0 0
4949 205.505 + 149.308i 0.599140 + 0.435301i
5050 −144.237 104.794i −0.407963 0.296403i
5151 0 0
5252 −8.34438 25.6814i −0.0222530 0.0684878i
5353 462.541 336.055i 1.19877 0.870958i 0.204607 0.978844i 0.434408π-0.434408\pi
0.994163 + 0.107887i 0.0344083π0.0344083\pi
5454 0 0
5555 −3.12935 + 170.751i −0.00767204 + 0.418618i
5656 −212.229 −0.506434
5757 0 0
5858 −60.9906 187.710i −0.138077 0.424957i
5959 −24.4445 + 75.2324i −0.0539390 + 0.166007i −0.974397 0.224834i 0.927816π-0.927816\pi
0.920458 + 0.390841i 0.127816π0.127816\pi
6060 0 0
6161 −584.546 424.697i −1.22694 0.891425i −0.230284 0.973123i 0.573966π-0.573966\pi
−0.996657 + 0.0816982i 0.973966π0.973966\pi
6262 −44.7534 + 137.737i −0.0916724 + 0.282139i
6363 0 0
6464 −247.130 + 179.550i −0.482675 + 0.350684i
6565 −25.2355 −0.0481551
6666 0 0
6767 608.961 1.11039 0.555197 0.831719i 0.312643π-0.312643\pi
0.555197 + 0.831719i 0.312643π0.312643\pi
6868 −343.881 + 249.844i −0.613260 + 0.445560i
6969 0 0
7070 −23.5989 + 72.6299i −0.0402944 + 0.124013i
7171 740.521 + 538.020i 1.23780 + 0.899313i 0.997450 0.0713741i 0.0227384π-0.0227384\pi
0.240348 + 0.970687i 0.422738π0.422738\pi
7272 0 0
7373 186.265 573.266i 0.298640 0.919119i −0.683335 0.730105i 0.739471π-0.739471\pi
0.981975 0.189013i 0.0605290π-0.0605290\pi
7474 81.3272 + 250.299i 0.127758 + 0.393199i
7575 0 0
7676 254.997 0.384870
7777 −329.194 + 100.331i −0.487209 + 0.148490i
7878 0 0
7979 298.418 216.813i 0.424996 0.308777i −0.354649 0.935000i 0.615400π-0.615400\pi
0.779645 + 0.626222i 0.215400π0.215400\pi
8080 −1.67939 5.16865i −0.00234703 0.00722340i
8181 0 0
8282 −257.706 187.234i −0.347059 0.252153i
8383 797.245 + 579.233i 1.05433 + 0.766012i 0.973030 0.230678i 0.0740943π-0.0740943\pi
0.0812954 + 0.996690i 0.474094π0.474094\pi
8484 0 0
8585 122.753 + 377.796i 0.156641 + 0.482091i
8686 −65.0394 + 47.2539i −0.0815510 + 0.0592502i
8787 0 0
8888 −494.548 + 655.099i −0.599080 + 0.793565i
8989 1156.34 1.37721 0.688605 0.725137i 0.258224π-0.258224\pi
0.688605 + 0.725137i 0.258224π0.258224\pi
9090 0 0
9191 −15.7144 48.3641i −0.0181024 0.0557135i
9292 −82.0312 + 252.466i −0.0929602 + 0.286102i
9393 0 0
9494 −544.737 395.775i −0.597717 0.434266i
9595 73.6406 226.643i 0.0795302 0.244769i
9696 0 0
9797 −478.658 + 347.765i −0.501035 + 0.364023i −0.809412 0.587241i 0.800214π-0.800214\pi
0.308377 + 0.951264i 0.400214π0.400214\pi
9898 439.317 0.452833
9999 0 0
100100 516.359 0.516359
101101 −662.096 + 481.041i −0.652287 + 0.473915i −0.864050 0.503407i 0.832080π-0.832080\pi
0.211762 + 0.977321i 0.432080π0.432080\pi
102102 0 0
103103 −463.889 + 1427.70i −0.443770 + 1.36578i 0.440057 + 0.897970i 0.354958π0.354958\pi
−0.883827 + 0.467814i 0.845042π0.845042\pi
104104 −98.1246 71.2917i −0.0925184 0.0672185i
105105 0 0
106106 305.553 940.397i 0.279981 0.861692i
107107 204.593 + 629.673i 0.184848 + 0.568904i 0.999946 0.0104195i 0.00331668π-0.00331668\pi
−0.815097 + 0.579324i 0.803317π0.803317\pi
108108 0 0
109109 1666.14 1.46411 0.732053 0.681247i 0.238562π-0.238562\pi
0.732053 + 0.681247i 0.238562π0.238562\pi
110110 169.199 + 242.090i 0.146659 + 0.209840i
111111 0 0
112112 8.85998 6.43715i 0.00747490 0.00543083i
113113 −440.511 1355.75i −0.366723 1.12866i −0.948895 0.315593i 0.897797π-0.897797\pi
0.582171 0.813066i 0.302203π-0.302203\pi
114114 0 0
115115 200.703 + 145.819i 0.162745 + 0.118241i
116116 462.457 + 335.995i 0.370156 + 0.268934i
117117 0 0
118118 42.2760 + 130.112i 0.0329815 + 0.101507i
119119 −647.609 + 470.516i −0.498876 + 0.362455i
120120 0 0
121121 −457.409 + 1249.94i −0.343658 + 0.939095i
122122 −1249.61 −0.927329
123123 0 0
124124 −129.616 398.918i −0.0938700 0.288902i
125125 329.936 1015.44i 0.236083 0.726589i
126126 0 0
127127 −1998.96 1452.33i −1.39668 1.01475i −0.995095 0.0989279i 0.968459π-0.968459\pi
−0.401587 0.915821i 0.631541π-0.631541\pi
128128 286.666 882.268i 0.197953 0.609236i
129129 0 0
130130 −35.3087 + 25.6533i −0.0238214 + 0.0173073i
131131 −1695.42 −1.13076 −0.565380 0.824831i 0.691270π-0.691270\pi
−0.565380 + 0.824831i 0.691270π0.691270\pi
132132 0 0
133133 480.219 0.313085
134134 852.040 619.043i 0.549291 0.399083i
135135 0 0
136136 −589.986 + 1815.79i −0.371992 + 1.14487i
137137 −1029.78 748.176i −0.642187 0.466576i 0.218414 0.975856i 0.429912π-0.429912\pi
−0.860601 + 0.509280i 0.829912π0.829912\pi
138138 0 0
139139 999.189 3075.19i 0.609713 1.87650i 0.149319 0.988789i 0.452292π-0.452292\pi
0.460394 0.887715i 0.347708π-0.347708\pi
140140 −68.3478 210.353i −0.0412603 0.126986i
141141 0 0
142142 1583.04 0.935534
143143 −185.906 64.1940i −0.108715 0.0375397i
144144 0 0
145145 432.187 314.002i 0.247525 0.179838i
146146 −322.140 991.445i −0.182606 0.562004i
147147 0 0
148148 −616.657 448.028i −0.342493 0.248836i
149149 −1327.84 964.731i −0.730072 0.530428i 0.159514 0.987196i 0.449007π-0.449007\pi
−0.889586 + 0.456767i 0.849007π0.849007\pi
150150 0 0
151151 −20.2191 62.2281i −0.0108967 0.0335367i 0.945460 0.325737i 0.105613π-0.105613\pi
−0.956357 + 0.292201i 0.905613π0.905613\pi
152152 926.619 673.228i 0.494465 0.359250i
153153 0 0
154154 −358.606 + 475.024i −0.187645 + 0.248562i
155155 −391.992 −0.203133
156156 0 0
157157 −429.420 1321.62i −0.218290 0.671826i −0.998904 0.0468130i 0.985094π-0.985094\pi
0.780614 0.625013i 0.214906π-0.214906\pi
158158 197.134 606.718i 0.0992606 0.305493i
159159 0 0
160160 −689.233 500.757i −0.340554 0.247427i
161161 −154.484 + 475.453i −0.0756214 + 0.232739i
162162 0 0
163163 −2018.89 + 1466.81i −0.970134 + 0.704844i −0.955482 0.295049i 0.904664π-0.904664\pi
−0.0146519 + 0.999893i 0.504664π0.504664\pi
164164 922.571 0.439273
165165 0 0
166166 1704.30 0.796865
167167 −893.670 + 649.289i −0.414097 + 0.300859i −0.775259 0.631644i 0.782380π-0.782380\pi
0.361161 + 0.932503i 0.382380π0.382380\pi
168168 0 0
169169 −669.930 + 2061.83i −0.304929 + 0.938476i
170170 555.804 + 403.815i 0.250754 + 0.182183i
171171 0 0
172172 71.9506 221.441i 0.0318964 0.0981671i
173173 −850.878 2618.73i −0.373937 1.15086i −0.944193 0.329393i 0.893156π-0.893156\pi
0.570256 0.821467i 0.306844π-0.306844\pi
174174 0 0
175175 972.426 0.420048
176176 0.776128 42.3487i 0.000332402 0.0181373i
177177 0 0
178178 1617.91 1175.48i 0.681279 0.494978i
179179 1317.84 + 4055.88i 0.550277 + 1.69358i 0.708100 + 0.706112i 0.249553π0.249553\pi
−0.157823 + 0.987467i 0.550447π0.550447\pi
180180 0 0
181181 983.685 + 714.689i 0.403960 + 0.293494i 0.771152 0.636651i 0.219681π-0.219681\pi
−0.367192 + 0.930145i 0.619681π0.619681\pi
182182 −71.1519 51.6949i −0.0289787 0.0210543i
183183 0 0
184184 368.458 + 1134.00i 0.147625 + 0.454344i
185185 −576.294 + 418.702i −0.229027 + 0.166398i
186186 0 0
187187 −56.7301 + 3095.43i −0.0221846 + 1.21048i
188188 1950.13 0.756529
189189 0 0
190190 −127.359 391.971i −0.0486295 0.149666i
191191 −1378.93 + 4243.91i −0.522387 + 1.60774i 0.247040 + 0.969005i 0.420542π0.420542\pi
−0.769427 + 0.638735i 0.779458π0.779458\pi
192192 0 0
193193 −3934.29 2858.43i −1.46734 1.06608i −0.981374 0.192105i 0.938469π-0.938469\pi
−0.485964 0.873979i 0.661531π-0.661531\pi
194194 −316.201 + 973.165i −0.117020 + 0.360151i
195195 0 0
196196 −1029.36 + 747.876i −0.375132 + 0.272549i
197197 1082.10 0.391353 0.195677 0.980668i 0.437310π-0.437310\pi
0.195677 + 0.980668i 0.437310π0.437310\pi
198198 0 0
199199 3503.59 1.24805 0.624027 0.781403i 0.285496π-0.285496\pi
0.624027 + 0.781403i 0.285496π0.285496\pi
200200 1876.37 1363.26i 0.663396 0.481986i
201201 0 0
202202 −437.379 + 1346.12i −0.152346 + 0.468873i
203203 870.915 + 632.757i 0.301115 + 0.218773i
204204 0 0
205205 266.430 819.986i 0.0907720 0.279367i
206206 802.281 + 2469.17i 0.271348 + 0.835122i
207207 0 0
208208 6.25879 0.00208639
209209 1119.03 1482.32i 0.370360 0.490594i
210210 0 0
211211 −1346.68 + 978.420i −0.439380 + 0.319229i −0.785389 0.619003i 0.787537π-0.787537\pi
0.346008 + 0.938231i 0.387537π0.387537\pi
212212 884.953 + 2723.61i 0.286693 + 0.882349i
213213 0 0
214214 926.358 + 673.038i 0.295909 + 0.214990i
215215 −176.040 127.900i −0.0558409 0.0405708i
216216 0 0
217217 −244.098 751.256i −0.0763615 0.235017i
218218 2331.22 1693.73i 0.724266 0.526210i
219219 0 0
220220 −808.575 279.203i −0.247791 0.0855631i
221221 −457.479 −0.139246
222222 0 0
223223 −299.904 923.008i −0.0900584 0.277171i 0.895876 0.444304i 0.146549π-0.146549\pi
−0.985934 + 0.167133i 0.946549π0.946549\pi
224224 530.512 1632.75i 0.158243 0.487021i
225225 0 0
226226 −1994.55 1449.12i −0.587059 0.426523i
227227 −926.181 + 2850.49i −0.270805 + 0.833452i 0.719494 + 0.694499i 0.244374π0.244374\pi
−0.990299 + 0.138954i 0.955626π0.955626\pi
228228 0 0
229229 65.2714 47.4224i 0.0188352 0.0136846i −0.578328 0.815804i 0.696295π-0.696295\pi
0.597163 + 0.802120i 0.296295π0.296295\pi
230230 429.052 0.123004
231231 0 0
232232 2567.57 0.726592
233233 1982.72 1440.53i 0.557477 0.405031i −0.273058 0.961998i 0.588035π-0.588035\pi
0.830535 + 0.556967i 0.188035π0.188035\pi
234234 0 0
235235 563.177 1733.28i 0.156330 0.481135i
236236 −320.555 232.897i −0.0884166 0.0642384i
237237 0 0
238238 −427.810 + 1316.66i −0.116516 + 0.358599i
239239 −28.2604 86.9764i −0.00764858 0.0235399i 0.947159 0.320763i 0.103939π-0.103939\pi
−0.954808 + 0.297223i 0.903939π0.903939\pi
240240 0 0
241241 189.338 0.0506073 0.0253036 0.999680i 0.491945π-0.491945\pi
0.0253036 + 0.999680i 0.491945π0.491945\pi
242242 630.637 + 2213.85i 0.167516 + 0.588065i
243243 0 0
244244 2927.95 2127.28i 0.768209 0.558137i
245245 367.446 + 1130.88i 0.0958174 + 0.294896i
246246 0 0
247247 222.031 + 161.315i 0.0571962 + 0.0415555i
248248 −1524.21 1107.40i −0.390271 0.283548i
249249 0 0
250250 −570.614 1756.17i −0.144355 0.444280i
251251 −4126.35 + 2997.97i −1.03766 + 0.753905i −0.969828 0.243792i 0.921609π-0.921609\pi
−0.0678331 + 0.997697i 0.521609π0.521609\pi
252252 0 0
253253 1107.62 + 1584.78i 0.275238 + 0.393811i
254254 −4273.25 −1.05562
255255 0 0
256256 −1250.94 3850.00i −0.305406 0.939941i
257257 791.745 2436.74i 0.192170 0.591439i −0.807828 0.589418i 0.799357π-0.799357\pi
0.999998 0.00202014i 0.000643032π-0.000643032\pi
258258 0 0
259259 −1161.31 843.742i −0.278612 0.202423i
260260 39.0607 120.216i 0.00931708 0.0286750i
261261 0 0
262262 −2372.18 + 1723.49i −0.559365 + 0.406403i
263263 2068.82 0.485052 0.242526 0.970145i 0.422024π-0.422024\pi
0.242526 + 0.970145i 0.422024π0.422024\pi
264264 0 0
265265 2676.32 0.620397
266266 671.908 488.170i 0.154877 0.112525i
267267 0 0
268268 −942.579 + 2900.96i −0.214840 + 0.661210i
269269 −5574.83 4050.35i −1.26358 0.918045i −0.264653 0.964344i 0.585257π-0.585257\pi
−0.998928 + 0.0462986i 0.985257π0.985257\pi
270270 0 0
271271 65.7913 202.485i 0.0147474 0.0453878i −0.943412 0.331623i 0.892404π-0.892404\pi
0.958159 + 0.286235i 0.0924038π0.0924038\pi
272272 −30.4447 93.6992i −0.00678670 0.0208873i
273273 0 0
274274 −2201.39 −0.485369
275275 2266.00 3001.64i 0.496891 0.658202i
276276 0 0
277277 −999.154 + 725.928i −0.216727 + 0.157461i −0.690852 0.722996i 0.742764π-0.742764\pi
0.474125 + 0.880457i 0.342764π0.342764\pi
278278 −1728.07 5318.44i −0.372815 1.14741i
279279 0 0
280280 −803.727 583.942i −0.171542 0.124633i
281281 −1117.78 812.117i −0.237300 0.172409i 0.462779 0.886473i 0.346852π-0.346852\pi
−0.700080 + 0.714065i 0.746852π0.746852\pi
282282 0 0
283283 540.993 + 1665.00i 0.113635 + 0.349732i 0.991660 0.128883i 0.0411390π-0.0411390\pi
−0.878025 + 0.478615i 0.841139π0.841139\pi
284284 −3709.22 + 2694.91i −0.775007 + 0.563075i
285285 0 0
286286 −325.371 + 99.1660i −0.0672714 + 0.0205028i
287287 1737.42 0.357340
288288 0 0
289289 707.119 + 2176.29i 0.143928 + 0.442965i
290290 285.502 878.684i 0.0578112 0.177925i
291291 0 0
292292 2442.60 + 1774.66i 0.489529 + 0.355664i
293293 2551.21 7851.82i 0.508680 1.56556i −0.285814 0.958285i 0.592264π-0.592264\pi
0.794495 0.607271i 0.207736π-0.207736\pi
294294 0 0
295295 −299.573 + 217.652i −0.0591247 + 0.0429566i
296296 −3423.70 −0.672291
297297 0 0
298298 −2838.57 −0.551792
299299 −231.140 + 167.933i −0.0447062 + 0.0324809i
300300 0 0
301301 135.500 417.026i 0.0259471 0.0798571i
302302 −91.5483 66.5137i −0.0174438 0.0126736i
303303 0 0
304304 −18.2640 + 56.2108i −0.00344576 + 0.0106050i
305305 −1045.18 3216.72i −0.196218 0.603898i
306306 0 0
307307 3649.18 0.678403 0.339201 0.940714i 0.389843π-0.389843\pi
0.339201 + 0.940714i 0.389843π0.389843\pi
308308 31.5867 1723.50i 0.00584358 0.318850i
309309 0 0
310310 −548.463 + 398.482i −0.100486 + 0.0730073i
311311 1416.80 + 4360.46i 0.258326 + 0.795045i 0.993156 + 0.116794i 0.0372617π0.0372617\pi
−0.734830 + 0.678251i 0.762738π0.762738\pi
312312 0 0
313313 2506.95 + 1821.41i 0.452720 + 0.328920i 0.790669 0.612244i 0.209733π-0.209733\pi
−0.337949 + 0.941165i 0.609733π0.609733\pi
314314 −1944.33 1412.64i −0.349443 0.253885i
315315 0 0
316316 570.947 + 1757.19i 0.101640 + 0.312816i
317317 −2004.46 + 1456.33i −0.355148 + 0.258030i −0.751025 0.660273i 0.770440π-0.770440\pi
0.395878 + 0.918303i 0.370440π0.370440\pi
318318 0 0
319319 3982.62 1213.81i 0.699009 0.213042i
320320 −1429.92 −0.249798
321321 0 0
322322 267.175 + 822.281i 0.0462394 + 0.142310i
323323 1334.99 4108.66i 0.229971 0.707777i
324324 0 0
325325 449.603 + 326.656i 0.0767369 + 0.0557527i
326326 −1333.68 + 4104.63i −0.226581 + 0.697346i
327327 0 0
328328 3352.48 2435.72i 0.564359 0.410031i
329329 3672.55 0.615423
330330 0 0
331331 −7320.24 −1.21558 −0.607790 0.794098i 0.707944π-0.707944\pi
−0.607790 + 0.794098i 0.707944π0.707944\pi
332332 −3993.35 + 2901.34i −0.660132 + 0.479614i
333333 0 0
334334 −590.357 + 1816.93i −0.0967153 + 0.297659i
335335 2306.18 + 1675.54i 0.376120 + 0.273267i
336336 0 0
337337 110.688 340.662i 0.0178918 0.0550654i −0.941712 0.336420i 0.890784π-0.890784\pi
0.959604 + 0.281355i 0.0907838π0.0907838\pi
338338 1158.62 + 3565.87i 0.186452 + 0.573840i
339339 0 0
340340 −1989.74 −0.317379
341341 −2887.75 997.149i −0.458594 0.158354i
342342 0 0
343343 −4556.13 + 3310.22i −0.717224 + 0.521093i
344344 −323.179 994.643i −0.0506531 0.155894i
345345 0 0
346346 −3852.61 2799.09i −0.598606 0.434913i
347347 4305.99 + 3128.49i 0.666161 + 0.483994i 0.868738 0.495272i 0.164932π-0.164932\pi
−0.202577 + 0.979266i 0.564932π0.564932\pi
348348 0 0
349349 −2741.98 8438.95i −0.420559 1.29435i −0.907184 0.420735i 0.861772π-0.861772\pi
0.486625 0.873611i 0.338228π-0.338228\pi
350350 1360.59 988.525i 0.207790 0.150968i
351351 0 0
352352 −3803.66 5442.28i −0.575954 0.824075i
353353 6975.14 1.05170 0.525849 0.850578i 0.323748π-0.323748\pi
0.525849 + 0.850578i 0.323748π0.323748\pi
354354 0 0
355355 1324.06 + 4075.04i 0.197955 + 0.609241i
356356 −1789.83 + 5508.55i −0.266464 + 0.820091i
357357 0 0
358358 5966.90 + 4335.21i 0.880896 + 0.640008i
359359 −1504.86 + 4631.50i −0.221236 + 0.680894i 0.777416 + 0.628987i 0.216530π0.216530\pi
−0.998652 + 0.0519074i 0.983470π0.983470\pi
360360 0 0
361361 3452.35 2508.28i 0.503331 0.365692i
362362 2102.86 0.305315
363363 0 0
364364 254.719 0.0366784
365365 2282.72 1658.50i 0.327351 0.237835i
366366 0 0
367367 2530.11 7786.88i 0.359866 1.10755i −0.593268 0.805005i 0.702163π-0.702163\pi
0.953134 0.302548i 0.0978373π-0.0978373\pi
368368 −49.7775 36.1654i −0.00705117 0.00512297i
369369 0 0
370370 −380.699 + 1171.67i −0.0534908 + 0.164628i
371371 1666.58 + 5129.19i 0.233219 + 0.717775i
372372 0 0
373373 −817.268 −0.113449 −0.0567246 0.998390i 0.518066π-0.518066\pi
−0.0567246 + 0.998390i 0.518066π0.518066\pi
374374 3067.30 + 4388.70i 0.424082 + 0.606776i
375375 0 0
376376 7086.45 5148.61i 0.971957 0.706168i
377377 190.115 + 585.113i 0.0259719 + 0.0799334i
378378 0 0
379379 −78.6699 57.1570i −0.0106623 0.00774660i 0.582441 0.812873i 0.302098π-0.302098\pi
−0.593104 + 0.805126i 0.702098π0.702098\pi
380380 965.692 + 701.616i 0.130366 + 0.0947162i
381381 0 0
382382 2384.82 + 7339.71i 0.319418 + 0.983068i
383383 9880.66 7178.72i 1.31822 0.957743i 0.318267 0.948001i 0.396899π-0.396899\pi
0.999953 0.00974165i 0.00310091π-0.00310091\pi
384384 0 0
385385 −1522.74 525.806i −0.201574 0.0696040i
386386 −8410.49 −1.10902
387387 0 0
388388 −915.790 2818.51i −0.119825 0.368784i
389389 −1344.09 + 4136.69i −0.175188 + 0.539174i −0.999642 0.0267554i 0.991482π-0.991482\pi
0.824454 + 0.565929i 0.191482π0.191482\pi
390390 0 0
391391 3638.42 + 2643.47i 0.470596 + 0.341908i
392392 −1766.05 + 5435.33i −0.227548 + 0.700320i
393393 0 0
394394 1514.04 1100.02i 0.193595 0.140655i
395395 1726.69 0.219947
396396 0 0
397397 −11423.8 −1.44420 −0.722098 0.691791i 0.756822π-0.756822\pi
−0.722098 + 0.691791i 0.756822π0.756822\pi
398398 4902.11 3561.59i 0.617388 0.448559i
399399 0 0
400400 −36.9839 + 113.825i −0.00462299 + 0.0142281i
401401 12585.5 + 9143.87i 1.56730 + 1.13871i 0.929684 + 0.368359i 0.120080π0.120080\pi
0.637618 + 0.770352i 0.279920π0.279920\pi
402402 0 0
403403 139.502 429.342i 0.0172434 0.0530696i
404404 −1266.75 3898.66i −0.155998 0.480113i
405405 0 0
406406 1861.79 0.227584
407407 −5310.57 + 1618.55i −0.646770 + 0.197121i
408408 0 0
409409 −9197.12 + 6682.10i −1.11190 + 0.807845i −0.982962 0.183808i 0.941158π-0.941158\pi
−0.128940 + 0.991652i 0.541158π0.541158\pi
410410 −460.782 1418.14i −0.0555034 0.170822i
411411 0 0
412412 −6083.24 4419.73i −0.727427 0.528506i
413413 −603.680 438.599i −0.0719253 0.0522568i
414414 0 0
415415 1425.48 + 4387.19i 0.168613 + 0.518937i
416416 793.754 576.696i 0.0935505 0.0679684i
417417 0 0
418418 58.8587 3211.57i 0.00688725 0.375797i
419419 3798.45 0.442880 0.221440 0.975174i 0.428924π-0.428924\pi
0.221440 + 0.975174i 0.428924π0.428924\pi
420420 0 0
421421 4277.70 + 13165.4i 0.495208 + 1.52409i 0.816633 + 0.577157i 0.195838π0.195838\pi
−0.321425 + 0.946935i 0.604162π0.604162\pi
422422 −889.614 + 2737.95i −0.102620 + 0.315833i
423423 0 0
424424 10406.5 + 7560.76i 1.19194 + 0.865997i
425425 2703.29 8319.88i 0.308539 0.949585i
426426 0 0
427427 5514.03 4006.18i 0.624924 0.454034i
428428 −3316.30 −0.374532
429429 0 0
430430 −376.327 −0.0422049
431431 −10280.2 + 7469.03i −1.14891 + 0.834735i −0.988336 0.152289i 0.951336π-0.951336\pi
−0.160578 + 0.987023i 0.551336π0.551336\pi
432432 0 0
433433 5000.41 15389.7i 0.554975 1.70804i −0.141034 0.990005i 0.545043π-0.545043\pi
0.696009 0.718033i 0.254957π-0.254957\pi
434434 −1105.23 802.995i −0.122241 0.0888134i
435435 0 0
436436 −2578.94 + 7937.15i −0.283277 + 0.871836i
437437 −833.724 2565.94i −0.0912641 0.280882i
438438 0 0
439439 −14356.7 −1.56084 −0.780419 0.625256i 0.784994π-0.784994\pi
−0.780419 + 0.625256i 0.784994π0.784994\pi
440440 −3675.37 + 1120.17i −0.398219 + 0.121368i
441441 0 0
442442 −640.090 + 465.053i −0.0688823 + 0.0500459i
443443 −1131.96 3483.80i −0.121401 0.373635i 0.871827 0.489814i 0.162935π-0.162935\pi
−0.993228 + 0.116179i 0.962935π0.962935\pi
444444 0 0
445445 4379.14 + 3181.63i 0.466497 + 0.338930i
446446 −1357.91 986.576i −0.144167 0.104744i
447447 0 0
448448 −890.430 2740.46i −0.0939037 0.289006i
449449 2659.66 1932.36i 0.279548 0.203104i −0.439172 0.898403i 0.644728π-0.644728\pi
0.718720 + 0.695299i 0.244728π0.244728\pi
450450 0 0
451451 4048.63 5362.98i 0.422711 0.559940i
452452 7140.35 0.743040
453453 0 0
454454 1601.80 + 4929.83i 0.165586 + 0.509622i
455455 73.5605 226.396i 0.00757928 0.0233266i
456456 0 0
457457 6050.71 + 4396.10i 0.619344 + 0.449980i 0.852692 0.522413i 0.174968π-0.174968\pi
−0.233348 + 0.972393i 0.574968π0.574968\pi
458458 43.1182 132.704i 0.00439908 0.0135390i
459459 0 0
460460 −1005.31 + 730.401i −0.101897 + 0.0740328i
461461 −16077.1 −1.62427 −0.812134 0.583471i 0.801694π-0.801694\pi
−0.812134 + 0.583471i 0.801694π0.801694\pi
462462 0 0
463463 −8332.21 −0.836352 −0.418176 0.908366i 0.637330π-0.637330\pi
−0.418176 + 0.908366i 0.637330π0.637330\pi
464464 −107.189 + 77.8773i −0.0107244 + 0.00779173i
465465 0 0
466466 1309.78 4031.08i 0.130202 0.400722i
467467 −14316.8 10401.7i −1.41863 1.03070i −0.991995 0.126274i 0.959698π-0.959698\pi
−0.426637 0.904423i 0.640302π-0.640302\pi
468468 0 0
469469 −1775.10 + 5463.19i −0.174769 + 0.537882i
470470 −973.997 2997.66i −0.0955897 0.294195i
471471 0 0
472472 −1779.73 −0.173556
473473 −971.506 1390.03i −0.0944395 0.135124i
474474 0 0
475475 −4245.73 + 3084.71i −0.410121 + 0.297971i
476476 −1239.03 3813.36i −0.119309 0.367195i
477477 0 0
478478 −127.957 92.9665i −0.0122440 0.00889579i
479479 6413.14 + 4659.42i 0.611741 + 0.444456i 0.850027 0.526739i 0.176586π-0.176586\pi
−0.238286 + 0.971195i 0.576586π0.576586\pi
480480 0 0
481481 −253.506 780.212i −0.0240310 0.0739597i
482482 264.916 192.473i 0.0250345 0.0181886i
483483 0 0
484484 −5246.42 4113.70i −0.492714 0.386336i
485485 −2769.58 −0.259299
486486 0 0
487487 −848.093 2610.16i −0.0789133 0.242870i 0.903815 0.427923i 0.140754π-0.140754\pi
−0.982729 + 0.185053i 0.940754π0.940754\pi
488488 5023.40 15460.4i 0.465981 1.43414i
489489 0 0
490490 1663.72 + 1208.77i 0.153386 + 0.111442i
491491 4252.16 13086.8i 0.390830 1.20285i −0.541332 0.840809i 0.682080π-0.682080\pi
0.932162 0.362042i 0.117920π-0.117920\pi
492492 0 0
493493 7834.85 5692.35i 0.715748 0.520021i
494494 474.644 0.0432292
495495 0 0
496496 97.2200 0.00880102
497497 −6985.34 + 5075.15i −0.630454 + 0.458051i
498498 0 0
499499 3285.52 10111.8i 0.294750 0.907147i −0.688555 0.725184i 0.741755π-0.741755\pi
0.983305 0.181963i 0.0582452π-0.0582452\pi
500500 4326.64 + 3143.49i 0.386987 + 0.281162i
501501 0 0
502502 −2725.86 + 8389.33i −0.242353 + 0.745885i
503503 −3896.04 11990.8i −0.345360 1.06291i −0.961391 0.275186i 0.911261π-0.911261\pi
0.616032 0.787721i 0.288739π-0.288739\pi
504504 0 0
505505 −3830.98 −0.337577
506506 3160.76 + 1091.42i 0.277694 + 0.0958885i
507507 0 0
508508 10012.6 7274.61i 0.874487 0.635352i
509509 −3953.17 12166.6i −0.344246 1.05948i −0.961986 0.273099i 0.911951π-0.911951\pi
0.617740 0.786383i 0.288049π-0.288049\pi
510510 0 0
511511 4600.00 + 3342.09i 0.398223 + 0.289326i
512512 339.995 + 247.021i 0.0293472 + 0.0213220i
513513 0 0
514514 −1369.30 4214.27i −0.117504 0.361641i
515515 −5685.06 + 4130.44i −0.486435 + 0.353415i
516516 0 0
517517 8557.97 11336.2i 0.728006 0.964346i
518518 −2482.58 −0.210576
519519 0 0
520520 −175.448 539.974i −0.0147960 0.0455374i
521521 −3241.09 + 9975.04i −0.272542 + 0.838799i 0.717317 + 0.696747i 0.245370π0.245370\pi
−0.989859 + 0.142052i 0.954630π0.954630\pi
522522 0 0
523523 5438.69 + 3951.44i 0.454718 + 0.330372i 0.791456 0.611227i 0.209324π-0.209324\pi
−0.336738 + 0.941598i 0.609324π0.609324\pi
524524 2624.25 8076.61i 0.218780 0.673337i
525525 0 0
526526 2894.63 2103.07i 0.239946 0.174331i
527527 −7106.18 −0.587382
528528 0 0
529529 −9358.32 −0.769156
530530 3744.63 2720.63i 0.306898 0.222975i
531531 0 0
532532 −743.306 + 2287.66i −0.0605760 + 0.186434i
533533 803.300 + 583.632i 0.0652810 + 0.0474294i
534534 0 0
535535 −957.717 + 2947.55i −0.0773938 + 0.238194i
536536 4233.76 + 13030.2i 0.341177 + 1.05003i
537537 0 0
538538 −11917.5 −0.955021
539539 −169.814 + 9265.76i −0.0135703 + 0.740454i
540540 0 0
541541 −10028.7 + 7286.29i −0.796984 + 0.579042i −0.910028 0.414547i 0.863940π-0.863940\pi
0.113044 + 0.993590i 0.463940π0.463940\pi
542542 −113.784 350.191i −0.00901742 0.0277528i
543543 0 0
544544 −12494.7 9077.92i −0.984752 0.715464i
545545 6309.81 + 4584.34i 0.495931 + 0.360315i
546546 0 0
547547 −1865.99 5742.92i −0.145857 0.448902i 0.851263 0.524739i 0.175837π-0.175837\pi
−0.997120 + 0.0758369i 0.975837π0.975837\pi
548548 5158.08 3747.57i 0.402085 0.292132i
549549 0 0
550550 119.187 6503.31i 0.00924024 0.504186i
551551 −5809.74 −0.449190
552552 0 0
553553 1075.23 + 3309.21i 0.0826823 + 0.254470i
554554 −660.039 + 2031.39i −0.0506180 + 0.155786i
555555 0 0
556556 13102.9 + 9519.84i 0.999439 + 0.726135i
557557 −4667.78 + 14365.9i −0.355081 + 1.09283i 0.600882 + 0.799338i 0.294816π0.294816\pi
−0.955963 + 0.293488i 0.905184π0.905184\pi
558558 0 0
559559 202.736 147.296i 0.0153395 0.0111448i
560560 51.2650 0.00386847
561561 0 0
562562 −2389.53 −0.179353
563563 1735.56 1260.96i 0.129920 0.0943927i −0.520927 0.853601i 0.674414π-0.674414\pi
0.650848 + 0.759208i 0.274414π0.274414\pi
564564 0 0
565565 2062.06 6346.38i 0.153543 0.472556i
566566 2449.51 + 1779.67i 0.181909 + 0.132165i
567567 0 0
568568 −6363.80 + 19585.8i −0.470104 + 1.44683i
569569 6431.23 + 19793.3i 0.473833 + 1.45831i 0.847525 + 0.530755i 0.178092π0.178092\pi
−0.373692 + 0.927553i 0.621908π0.621908\pi
570570 0 0
571571 −4825.78 −0.353683 −0.176841 0.984239i 0.556588π-0.556588\pi
−0.176841 + 0.984239i 0.556588π0.556588\pi
572572 593.561 786.256i 0.0433882 0.0574738i
573573 0 0
574574 2430.94 1766.18i 0.176769 0.128431i
575575 −1688.26 5195.93i −0.122444 0.376844i
576576 0 0
577577 16941.5 + 12308.7i 1.22233 + 0.888073i 0.996291 0.0860455i 0.0274230π-0.0274230\pi
0.226037 + 0.974119i 0.427423π0.427423\pi
578578 3201.70 + 2326.17i 0.230403 + 0.167398i
579579 0 0
580580 826.879 + 2544.87i 0.0591970 + 0.182190i
581581 −7520.42 + 5463.91i −0.537005 + 0.390157i
582582 0 0
583583 19716.1 + 6808.02i 1.40061 + 0.483635i
584584 13561.4 0.960915
585585 0 0
586586 −4412.24 13579.5i −0.311037 0.957274i
587587 1727.29 5316.06i 0.121453 0.373794i −0.871785 0.489889i 0.837037π-0.837037\pi
0.993238 + 0.116094i 0.0370375π0.0370375\pi
588588 0 0
589589 3448.88 + 2505.76i 0.241271 + 0.175294i
590590 −197.897 + 609.065i −0.0138090 + 0.0424997i
591591 0 0
592592 142.930 103.845i 0.00992293 0.00720943i
593593 21114.0 1.46214 0.731069 0.682303i 0.239022π-0.239022\pi
0.731069 + 0.682303i 0.239022π0.239022\pi
594594 0 0
595595 −3747.15 −0.258182
596596 6651.06 4832.28i 0.457111 0.332110i
597597 0 0
598598 −152.690 + 469.933i −0.0104414 + 0.0321354i
599599 6571.14 + 4774.21i 0.448229 + 0.325658i 0.788896 0.614526i 0.210653π-0.210653\pi
−0.340667 + 0.940184i 0.610653π0.610653\pi
600600 0 0
601601 489.767 1507.35i 0.0332413 0.102306i −0.933059 0.359723i 0.882871π-0.882871\pi
0.966301 + 0.257417i 0.0828713π0.0828713\pi
602602 −234.343 721.234i −0.0158656 0.0488294i
603603 0 0
604604 327.737 0.0220785
605605 −5171.40 + 3475.05i −0.347516 + 0.233522i
606606 0 0
607607 −13583.2 + 9868.80i −0.908281 + 0.659905i −0.940579 0.339574i 0.889717π-0.889717\pi
0.0322987 + 0.999478i 0.489717π0.489717\pi
608608 2863.08 + 8811.67i 0.190976 + 0.587764i
609609 0 0
610610 −4732.35 3438.26i −0.314111 0.228215i
611611 1698.01 + 1233.68i 0.112429 + 0.0816845i
612612 0 0
613613 −1429.28 4398.87i −0.0941731 0.289835i 0.892864 0.450326i 0.148692π-0.148692\pi
−0.987037 + 0.160491i 0.948692π0.948692\pi
614614 5105.82 3709.60i 0.335593 0.243823i
615615 0 0
616616 −4435.52 6346.34i −0.290117 0.415100i
617617 −581.103 −0.0379163 −0.0189581 0.999820i 0.506035π-0.506035\pi
−0.0189581 + 0.999820i 0.506035π0.506035\pi
618618 0 0
619619 5742.03 + 17672.2i 0.372846 + 1.14750i 0.944920 + 0.327301i 0.106139π0.106139\pi
−0.572074 + 0.820202i 0.693861π0.693861\pi
620620 606.744 1867.37i 0.0393023 0.120960i
621621 0 0
622622 6414.99 + 4660.76i 0.413533 + 0.300450i
623623 −3370.68 + 10373.9i −0.216763 + 0.667129i
624624 0 0
625625 −6381.50 + 4636.43i −0.408416 + 0.296732i
626626 5359.22 0.342168
627627 0 0
628628 6960.59 0.442289
629629 −10447.3 + 7590.39i −0.662258 + 0.481159i
630630 0 0
631631 3758.79 11568.4i 0.237139 0.729840i −0.759691 0.650284i 0.774650π-0.774650\pi
0.996830 0.0795558i 0.0253502π-0.0253502\pi
632632 6713.98 + 4877.99i 0.422575 + 0.307019i
633633 0 0
634634 −1324.15 + 4075.30i −0.0829472 + 0.255285i
635635 −3574.16 11000.1i −0.223364 0.687444i
636636 0 0
637637 −1369.40 −0.0851769
638638 4338.45 5746.89i 0.269218 0.356617i
639639 0 0
640640 3513.16 2552.46i 0.216984 0.157648i
641641 5677.31 + 17473.0i 0.349829 + 1.07666i 0.958948 + 0.283583i 0.0915232π0.0915232\pi
−0.609119 + 0.793079i 0.708477π0.708477\pi
642642 0 0
643643 −370.655 269.297i −0.0227328 0.0165164i 0.576361 0.817195i 0.304472π-0.304472\pi
−0.599094 + 0.800679i 0.704472π0.704472\pi
644644 −2025.84 1471.86i −0.123958 0.0900610i
645645 0 0
646646 −2308.82 7105.80i −0.140618 0.432777i
647647 6335.74 4603.19i 0.384983 0.279706i −0.378414 0.925637i 0.623530π-0.623530\pi
0.763396 + 0.645930i 0.223530π0.223530\pi
648648 0 0
649649 −2760.57 + 841.362i −0.166968 + 0.0508880i
650650 961.135 0.0579982
651651 0 0
652652 −3862.63 11888.0i −0.232013 0.714062i
653653 −4743.85 + 14600.1i −0.284289 + 0.874953i 0.702321 + 0.711860i 0.252147π0.252147\pi
−0.986611 + 0.163093i 0.947853π0.947853\pi
654654 0 0
655655 −6420.68 4664.89i −0.383018 0.278279i
656656 −66.0786 + 203.369i −0.00393283 + 0.0121040i
657657 0 0
658658 5138.51 3733.35i 0.304438 0.221187i
659659 −5177.35 −0.306041 −0.153020 0.988223i 0.548900π-0.548900\pi
−0.153020 + 0.988223i 0.548900π0.548900\pi
660660 0 0
661661 −11234.4 −0.661073 −0.330536 0.943793i 0.607230π-0.607230\pi
−0.330536 + 0.943793i 0.607230π0.607230\pi
662662 −10242.3 + 7441.43i −0.601324 + 0.436887i
663663 0 0
664664 −6851.27 + 21086.0i −0.400423 + 1.23238i
665665 1818.63 + 1321.31i 0.106050 + 0.0770499i
666666 0 0
667667 1868.96 5752.08i 0.108496 0.333915i
668668 −1709.81 5262.25i −0.0990337 0.304794i
669669 0 0
670670 4930.02 0.284273
671671 483.025 26355.9i 0.0277898 1.51633i
672672 0 0
673673 7158.27 5200.79i 0.410002 0.297884i −0.363601 0.931555i 0.618453π-0.618453\pi
0.773603 + 0.633671i 0.218453π0.218453\pi
674674 −191.431 589.165i −0.0109401 0.0336703i
675675 0 0
676676 −8785.17 6382.80i −0.499839 0.363154i
677677 −22816.5 16577.2i −1.29529 0.941082i −0.295391 0.955377i 0.595450π-0.595450\pi
−0.999898 + 0.0142945i 0.995450π0.995450\pi
678678 0 0
679679 −1724.65 5307.92i −0.0974756 0.299999i
680680 −7230.41 + 5253.20i −0.407755 + 0.296252i
681681 0 0
682682 −5054.11 + 1540.38i −0.283771 + 0.0864871i
683683 1139.02 0.0638117 0.0319058 0.999491i 0.489842π-0.489842\pi
0.0319058 + 0.999491i 0.489842π0.489842\pi
684684 0 0
685685 −1841.25 5666.79i −0.102702 0.316083i
686686 −3009.77 + 9263.11i −0.167512 + 0.515550i
687687 0 0
688688 43.6605 + 31.7212i 0.00241939 + 0.00175779i
689689 −952.446 + 2931.33i −0.0526637 + 0.162082i
690690 0 0
691691 15183.7 11031.6i 0.835909 0.607324i −0.0853155 0.996354i 0.527190π-0.527190\pi
0.921225 + 0.389030i 0.127190π0.127190\pi
692692 13792.1 0.757655
693693 0 0
694694 9205.09 0.503488
695695 12245.3 8896.72i 0.668331 0.485571i
696696 0 0
697697 4829.94 14865.0i 0.262478 0.807823i
698698 −12415.2 9020.15i −0.673239 0.489137i
699699 0 0
700700 −1505.17 + 4632.43i −0.0812714 + 0.250128i
701701 −1169.64 3599.79i −0.0630196 0.193955i 0.914589 0.404384i 0.132514π-0.132514\pi
−0.977609 + 0.210429i 0.932514π0.932514\pi
702702 0 0
703703 7746.93 0.415620
704704 −10534.1 3637.44i −0.563945 0.194732i
705705 0 0
706706 9759.41 7090.63i 0.520255 0.377988i
707707 −2385.59 7342.10i −0.126902 0.390563i
708708 0 0
709709 −1462.15 1062.32i −0.0774503 0.0562709i 0.548386 0.836225i 0.315242π-0.315242\pi
−0.625837 + 0.779954i 0.715242π0.715242\pi
710710 5995.09 + 4355.69i 0.316890 + 0.230234i
711711 0 0
712712 8039.37 + 24742.6i 0.423157 + 1.30234i
713713 −3590.37 + 2608.56i −0.188584 + 0.137014i
714714 0 0
715715 −527.413 754.624i −0.0275862 0.0394704i
716716 −21361.1 −1.11495
717717 0 0
718718 2602.62 + 8010.03i 0.135277 + 0.416339i
719719 10208.8 31419.5i 0.529520 1.62970i −0.225680 0.974202i 0.572460π-0.572460\pi
0.755200 0.655494i 0.227540π-0.227540\pi
720720 0 0
721721 −11456.2 8323.40i −0.591748 0.429930i
722722 2280.62 7019.01i 0.117556 0.361801i
723723 0 0
724724 −4927.22 + 3579.83i −0.252926 + 0.183762i
725725 −11764.5 −0.602652
726726 0 0
727727 1906.51 0.0972606 0.0486303 0.998817i 0.484514π-0.484514\pi
0.0486303 + 0.998817i 0.484514π0.484514\pi
728728 925.611 672.496i 0.0471228 0.0342367i
729729 0 0
730730 1507.96 4641.03i 0.0764551 0.235305i
731731 −3191.31 2318.62i −0.161470 0.117315i
732732 0 0
733733 2986.92 9192.78i 0.150511 0.463224i −0.847168 0.531325i 0.821694π-0.821694\pi
0.997678 + 0.0681014i 0.0216941π0.0216941\pi
734734 −4375.75 13467.2i −0.220043 0.677224i
735735 0 0
736736 −9645.24 −0.483055
737737 12727.1 + 18209.9i 0.636103 + 0.910137i
738738 0 0
739739 −20359.0 + 14791.7i −1.01342 + 0.736293i −0.964924 0.262531i 0.915443π-0.915443\pi
−0.0484964 + 0.998823i 0.515443π0.515443\pi
740740 −1102.59 3393.43i −0.0547731 0.168574i
741741 0 0
742742 7545.93 + 5482.44i 0.373342 + 0.271249i
743743 −25301.6 18382.7i −1.24930 0.907667i −0.251115 0.967957i 0.580797π-0.580797\pi
−0.998181 + 0.0602905i 0.980797π0.980797\pi
744744 0 0
745745 −2374.19 7307.01i −0.116757 0.359340i
746746 −1143.50 + 830.799i −0.0561212 + 0.0407744i
747747 0 0
748748 −14658.2 5061.50i −0.716518 0.247416i
749749 −6245.38 −0.304675
750750 0 0
751751 4771.36 + 14684.7i 0.231837 + 0.713520i 0.997525 + 0.0703084i 0.0223983π0.0223983\pi
−0.765689 + 0.643211i 0.777602π0.777602\pi
752752 −139.677 + 429.880i −0.00677325 + 0.0208459i
753753 0 0
754754 860.804 + 625.410i 0.0415764 + 0.0302070i
755755 94.6473 291.295i 0.00456234 0.0140414i
756756 0 0
757757 −23225.1 + 16874.0i −1.11510 + 0.810167i −0.983459 0.181130i 0.942024π-0.942024\pi
−0.131641 + 0.991298i 0.542024π0.542024\pi
758758 −168.176 −0.00805861
759759 0 0
760760 5361.54 0.255899
761761 31306.9 22745.8i 1.49129 1.08349i 0.517602 0.855622i 0.326825π-0.326825\pi
0.973692 0.227867i 0.0731751π-0.0731751\pi
762762 0 0
763763 −4856.74 + 14947.5i −0.230440 + 0.709222i
764764 −18082.7 13137.8i −0.856294 0.622134i
765765 0 0
766766 6527.15 20088.5i 0.307879 0.947554i
767767 −131.779 405.575i −0.00620374 0.0190932i
768768 0 0
769769 9520.91 0.446467 0.223233 0.974765i 0.428339π-0.428339\pi
0.223233 + 0.974765i 0.428339π0.428339\pi
770770 −2665.08 + 812.257i −0.124731 + 0.0380152i
771771 0 0
772772 19706.6 14317.7i 0.918726 0.667494i
773773 6442.57 + 19828.2i 0.299771 + 0.922601i 0.981577 + 0.191067i 0.0611949π0.0611949\pi
−0.681806 + 0.731533i 0.738805π0.738805\pi
774774 0 0
775775 6983.85 + 5074.06i 0.323700 + 0.235182i
776776 −10769.1 7824.22i −0.498181 0.361950i
777777 0 0
778778 2324.57 + 7154.28i 0.107120 + 0.329683i
779779 −7585.79 + 5511.40i −0.348895 + 0.253487i
780780 0 0
781781 −611.911 + 33388.4i −0.0280357 + 1.52975i
782782 7778.01 0.355679
783783 0 0
784784 −91.1322 280.476i −0.00415143 0.0127768i
785785 2010.15 6186.61i 0.0913954 0.281286i
786786 0 0
787787 −22007.2 15989.1i −0.996786 0.724207i −0.0353890 0.999374i 0.511267π-0.511267\pi
−0.961397 + 0.275166i 0.911267π0.911267\pi
788788 −1674.93 + 5154.90i −0.0757194 + 0.233040i
789789 0 0
790790 2415.93 1755.27i 0.108804 0.0790504i
791791 13447.0 0.604449
792792 0 0
793793 3895.17 0.174428
794794 −15983.9 + 11613.0i −0.714417 + 0.519054i
795795 0 0
796796 −5423.02 + 16690.3i −0.241474 + 0.743182i
797797 −10894.2 7915.11i −0.484182 0.351778i 0.318761 0.947835i 0.396733π-0.396733\pi
−0.802942 + 0.596057i 0.796733π0.796733\pi
798798 0 0
799799 10209.5 31421.6i 0.452047 1.39126i
800800 5797.63 + 17843.3i 0.256222 + 0.788569i
801801 0 0
802802 26904.5 1.18458
803803 21035.4 6411.12i 0.924437 0.281748i
804804 0 0
805805 −1893.24 + 1375.52i −0.0828917 + 0.0602244i
806806 −241.264 742.534i −0.0105436 0.0324499i
807807 0 0
808808 −14896.2 10822.7i −0.648572 0.471215i
809809 26245.3 + 19068.3i 1.14059 + 0.828686i 0.987201 0.159481i 0.0509819π-0.0509819\pi
0.153387 + 0.988166i 0.450982π0.450982\pi
810810 0 0
811811 8831.27 + 27179.8i 0.382377 + 1.17684i 0.938365 + 0.345645i 0.112340π0.112340\pi
−0.555988 + 0.831190i 0.687660π0.687660\pi
812812 −4362.36 + 3169.44i −0.188533 + 0.136977i
813813 0 0
814814 −5785.05 + 7663.12i −0.249098 + 0.329966i
815815 −11681.6 −0.502071
816816 0 0
817817 731.270 + 2250.62i 0.0313145 + 0.0963760i
818818 −6075.60 + 18698.8i −0.259692 + 0.799251i
819819 0 0
820820 3493.85 + 2538.43i 0.148793 + 0.108105i
821821 −2345.53 + 7218.81i −0.0997072 + 0.306867i −0.988452 0.151535i 0.951578π-0.951578\pi
0.888745 + 0.458403i 0.151578π0.151578\pi
822822 0 0
823823 −3277.29 + 2381.09i −0.138808 + 0.100850i −0.655022 0.755609i 0.727341π-0.727341\pi
0.516214 + 0.856460i 0.327341π0.327341\pi
824824 −33774.3 −1.42789
825825 0 0
826826 −1290.51 −0.0543615
827827 23949.1 17400.0i 1.00700 0.731630i 0.0434246 0.999057i 0.486173π-0.486173\pi
0.963578 + 0.267426i 0.0861732π0.0861732\pi
828828 0 0
829829 65.8920 202.795i 0.00276058 0.00849621i −0.949667 0.313262i 0.898578π-0.898578\pi
0.952427 + 0.304766i 0.0985782π0.0985782\pi
830830 6454.32 + 4689.34i 0.269919 + 0.196108i
831831 0 0
832832 508.880 1566.17i 0.0212046 0.0652611i
833833 6661.20 + 20501.1i 0.277067 + 0.852724i
834834 0 0
835835 −5170.89 −0.214307
836836 5329.35 + 7625.24i 0.220478 + 0.315460i
837837 0 0
838838 5314.68 3861.34i 0.219084 0.159174i
839839 3132.38 + 9640.46i 0.128893 + 0.396693i 0.994590 0.103875i 0.0331243π-0.0331243\pi
−0.865697 + 0.500569i 0.833124π0.833124\pi
840840 0 0
841841 9194.69 + 6680.33i 0.377001 + 0.273908i
842842 19368.6 + 14072.1i 0.792739 + 0.575959i
843843 0 0
844844 −2576.53 7929.74i −0.105080 0.323404i
845845 −8210.14 + 5965.01i −0.334245 + 0.242843i
846846 0 0
847847 −9880.25 7747.08i −0.400814 0.314277i
848848 −663.768 −0.0268796
849849 0 0
850850 −4675.26 14389.0i −0.188659 0.580633i
851851 −2492.15 + 7670.04i −0.100387 + 0.308961i
852852 0 0
853853 −23714.3 17229.4i −0.951888 0.691587i −0.000635352 1.00000i 0.500202π-0.500202\pi
−0.951253 + 0.308413i 0.900202π0.900202\pi
854854 3642.56 11210.6i 0.145955 0.449204i
855855 0 0
856856 −12050.9 + 8755.52i −0.481183 + 0.349600i
857857 22219.3 0.885642 0.442821 0.896610i 0.353978π-0.353978\pi
0.442821 + 0.896610i 0.353978π0.353978\pi
858858 0 0
859859 25401.2 1.00894 0.504468 0.863430i 0.331689π-0.331689\pi
0.504468 + 0.863430i 0.331689π0.331689\pi
860860 881.771 640.644i 0.0349630 0.0254021i
861861 0 0
862862 −6791.11 + 20900.9i −0.268337 + 0.825855i
863863 2925.53 + 2125.52i 0.115395 + 0.0838395i 0.643986 0.765037i 0.277279π-0.277279\pi
−0.528591 + 0.848877i 0.677279π0.677279\pi
864864 0 0
865865 3983.03 12258.5i 0.156563 0.481852i
866866 −8648.05 26616.0i −0.339345 1.04440i
867867 0 0
868868 3956.65 0.154721
869869 12720.3 + 4392.35i 0.496554 + 0.171462i
870870 0 0
871871 −2655.91 + 1929.63i −0.103320 + 0.0750666i
872872 11583.8 + 35651.1i 0.449857 + 1.38452i
873873 0 0
874874 −3774.94 2742.66i −0.146098 0.106146i
875875 8148.09 + 5919.93i 0.314806 + 0.228720i
876876 0 0
877877 −4644.26 14293.6i −0.178820 0.550352i 0.820967 0.570976i 0.193435π-0.193435\pi
−0.999787 + 0.0206233i 0.993435π0.993435\pi
878878 −20087.5 + 14594.4i −0.772117 + 0.560976i
879879 0 0
880880 119.461 158.242i 0.00457615 0.00606176i
881881 41424.1 1.58412 0.792062 0.610440i 0.209008π-0.209008\pi
0.792062 + 0.610440i 0.209008π0.209008\pi
882882 0 0
883883 −9718.72 29911.2i −0.370398 1.13997i −0.946532 0.322611i 0.895439π-0.895439\pi
0.576134 0.817355i 0.304561π-0.304561\pi
884884 708.107 2179.33i 0.0269414 0.0829172i
885885 0 0
886886 −5125.28 3723.73i −0.194342 0.141198i
887887 3774.50 11616.7i 0.142881 0.439742i −0.853851 0.520517i 0.825739π-0.825739\pi
0.996732 + 0.0807744i 0.0257393π0.0257393\pi
888888 0 0
889889 18856.2 13699.8i 0.711379 0.516847i
890890 9361.46 0.352581
891891 0 0
892892 4861.22 0.182473
893893 −16034.8 + 11650.0i −0.600878 + 0.436564i
894894 0 0
895895 −6168.89 + 18985.9i −0.230395 + 0.709082i
896896 7079.49 + 5143.55i 0.263961 + 0.191779i
897897 0 0
898898 1756.97 5407.39i 0.0652904 0.200943i
899899 2953.12 + 9088.78i 0.109557 + 0.337183i
900900 0 0
901901 48517.4 1.79395
902902 212.949 11619.4i 0.00786078 0.428917i
903903 0 0
904904 25946.9 18851.6i 0.954626 0.693577i
905905 1758.84 + 5413.16i 0.0646032 + 0.198828i
906906 0 0
907907 −9356.29 6797.74i −0.342525 0.248859i 0.403201 0.915111i 0.367897π-0.367897\pi
−0.745727 + 0.666252i 0.767897π0.767897\pi
908908 −12145.5 8824.25i −0.443903 0.322514i
909909 0 0
910910 −127.221 391.545i −0.00463442 0.0142633i
911911 22625.1 16438.1i 0.822836 0.597826i −0.0946871 0.995507i 0.530185π-0.530185\pi
0.917524 + 0.397681i 0.130185π0.130185\pi
912912 0 0
913913 −658.784 + 35946.0i −0.0238801 + 1.30300i
914914 12934.9 0.468104
915915 0 0
916916 124.880 + 384.342i 0.00450454 + 0.0138635i
917917 4942.08 15210.2i 0.177974 0.547747i
918918 0 0
919919 −36164.5 26275.1i −1.29810 0.943128i −0.298170 0.954513i 0.596376π-0.596376\pi
−0.999935 + 0.0113846i 0.996376π0.996376\pi
920920 −1724.78 + 5308.33i −0.0618090 + 0.190229i
921921 0 0
922922 −22494.6 + 16343.3i −0.803494 + 0.583773i
923923 −4934.53 −0.175972
924924 0 0
925925 15687.2 0.557614
926926 −11658.2 + 8470.16i −0.413727 + 0.300591i
927927 0 0
928928 −6418.19 + 19753.2i −0.227034 + 0.698739i
929929 −532.665 387.004i −0.0188118 0.0136676i 0.578340 0.815796i 0.303701π-0.303701\pi
−0.597151 + 0.802129i 0.703701π0.703701\pi
930930 0 0
931931 3996.10 12298.7i 0.140673 0.432948i
932932 3793.42 + 11674.9i 0.133324 + 0.410328i
933933 0 0
934934 −30605.6 −1.07221
935935 −8731.82 + 11566.5i −0.305413 + 0.404563i
936936 0 0
937937 −14039.2 + 10200.1i −0.489479 + 0.355627i −0.804984 0.593297i 0.797826π-0.797826\pi
0.315505 + 0.948924i 0.397826π0.397826\pi
938938 3069.98 + 9448.42i 0.106864 + 0.328893i
939939 0 0
940940 7385.27 + 5365.71i 0.256256 + 0.186181i
941941 −14197.6 10315.1i −0.491847 0.357348i 0.314047 0.949407i 0.398315π-0.398315\pi
−0.805894 + 0.592060i 0.798315π0.798315\pi
942942 0 0
943943 −3016.39 9283.49i −0.104165 0.320585i
944944 74.2986 53.9811i 0.00256167 0.00186116i
945945 0 0
946946 −2772.35 957.300i −0.0952820 0.0329012i
947947 −27129.0 −0.930912 −0.465456 0.885071i 0.654110π-0.654110\pi
−0.465456 + 0.885071i 0.654110π0.654110\pi
948948 0 0
949949 1004.15 + 3090.45i 0.0343478 + 0.105712i
950950 −2804.72 + 8632.05i −0.0957866 + 0.294801i
951951 0 0
952952 −14570.3 10585.9i −0.496035 0.360390i
953953 −11526.6 + 35475.1i −0.391797 + 1.20583i 0.539631 + 0.841901i 0.318564π0.318564\pi
−0.931428 + 0.363925i 0.881436π0.881436\pi
954954 0 0
955955 −16899.1 + 12277.9i −0.572609 + 0.416025i
956956 458.080 0.0154972
957957 0 0
958958 13709.6 0.462357
959959 9713.89 7057.55i 0.327088 0.237644i
960960 0 0
961961 −7039.00 + 21663.8i −0.236279 + 0.727193i
962962 −1147.83 833.946i −0.0384693 0.0279496i
963963 0 0
964964 −293.067 + 901.967i −0.00979154 + 0.0301353i
965965 −7034.56 21650.2i −0.234664 0.722221i
966966 0 0
967967 48055.1 1.59809 0.799043 0.601274i 0.205340π-0.205340\pi
0.799043 + 0.601274i 0.205340π0.205340\pi
968968 −29925.5 1097.26i −0.993637 0.0364331i
969969 0 0
970970 −3875.11 + 2815.43i −0.128270 + 0.0931939i
971971 −11666.7 35906.3i −0.385583 1.18670i −0.936056 0.351850i 0.885553π-0.885553\pi
0.550473 0.834853i 0.314447π-0.314447\pi
972972 0 0
973973 24675.9 + 17928.1i 0.813025 + 0.590698i
974974 −3840.00 2789.93i −0.126326 0.0917813i
975975 0 0
976976 259.220 + 797.796i 0.00850145 + 0.0261648i
977977 24275.8 17637.4i 0.794935 0.577554i −0.114489 0.993425i 0.536523π-0.536523\pi
0.909424 + 0.415870i 0.136523π0.136523\pi
978978 0 0
979979 24167.1 + 34578.3i 0.788951 + 1.12883i
980980 −5956.03 −0.194141
981981 0 0
982982 −7353.98 22633.2i −0.238977 0.735494i
983983 −11384.0 + 35036.3i −0.369372 + 1.13681i 0.577825 + 0.816161i 0.303902π0.303902\pi
−0.947198 + 0.320651i 0.896098π0.896098\pi
984984 0 0
985985 4098.00 + 2977.37i 0.132562 + 0.0963117i
986986 5175.68 15929.1i 0.167168 0.514489i
987987 0 0
988988 −1112.14 + 808.015i −0.0358115 + 0.0260186i
989989 −2463.53 −0.0792069
990990 0 0
991991 22406.6 0.718233 0.359117 0.933293i 0.383078π-0.383078\pi
0.359117 + 0.933293i 0.383078π0.383078\pi
992992 12329.7 8958.03i 0.394624 0.286711i
993993 0 0
994994 −4614.50 + 14202.0i −0.147247 + 0.453179i
995995 13268.3 + 9640.01i 0.422748 + 0.307145i
996996 0 0
997997 5913.47 18199.8i 0.187845 0.578127i −0.812141 0.583462i 0.801698π-0.801698\pi
0.999986 + 0.00533409i 0.00169790π0.00169790\pi
998998 −5682.21 17488.0i −0.180228 0.554684i
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 99.4.f.e.91.4 yes 24
3.2 odd 2 inner 99.4.f.e.91.3 yes 24
11.2 odd 10 1089.4.a.bl.1.8 12
11.4 even 5 inner 99.4.f.e.37.4 yes 24
11.9 even 5 1089.4.a.bm.1.5 12
33.2 even 10 1089.4.a.bl.1.5 12
33.20 odd 10 1089.4.a.bm.1.8 12
33.26 odd 10 inner 99.4.f.e.37.3 24
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
99.4.f.e.37.3 24 33.26 odd 10 inner
99.4.f.e.37.4 yes 24 11.4 even 5 inner
99.4.f.e.91.3 yes 24 3.2 odd 2 inner
99.4.f.e.91.4 yes 24 1.1 even 1 trivial
1089.4.a.bl.1.5 12 33.2 even 10
1089.4.a.bl.1.8 12 11.2 odd 10
1089.4.a.bm.1.5 12 11.9 even 5
1089.4.a.bm.1.8 12 33.20 odd 10