Properties

Label 297.2.f.b.163.1
Level 297297
Weight 22
Character 297.163
Analytic conductor 2.3722.372
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] = [297,2,Mod(82,297)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(297, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("297.82");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 297=3311 297 = 3^{3} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 297.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: 2.371556940032.37155694003
Analytic rank: 00
Dimension: 1616
Relative dimension: 44 over Q(ζ5)\Q(\zeta_{5})
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: x169x14+51x12249x10+1476x82875x6+2335x4+125x2+25 x^{16} - 9x^{14} + 51x^{12} - 249x^{10} + 1476x^{8} - 2875x^{6} + 2335x^{4} + 125x^{2} + 25 Copy content Toggle raw display
Coefficient ring: Z[a1,,a11]\Z[a_1, \ldots, a_{11}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C5]\mathrm{SU}(2)[C_{5}]

Embedding invariants

Embedding label 163.1
Root 1.18970+0.386556i-1.18970 + 0.386556i of defining polynomial
Character χ\chi == 297.163
Dual form 297.2.f.b.82.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.760284+2.33991i)q2+(3.279132.38243i)q4+(0.3058600.941339i)q5+(3.496722.54052i)q7+(4.086842.96926i)q8+2.43519q10+(2.79120+1.79142i)q11+(1.118033.44095i)q13+(8.603106.25052i)q14+(1.33563+4.11065i)q16+(0.8162082.51203i)q17+(3.096292.24958i)q19+(1.23972+3.81546i)q20+(6.31388+5.16917i)q223.45011q23+(3.252522.36309i)q25+(7.20151+5.23221i)q26+(5.41361+16.6614i)q28+(8.431686.12597i)q29+(0.521582+1.60526i)q310.530785q32+6.49848q34+(1.32198+4.06865i)q35+(2.618031.90211i)q37+(2.90977+8.95537i)q38+(4.045082.93893i)q40+(9.63335+6.99904i)q412.12307q43+(4.8847712.5241i)q44+(2.623078.07297i)q46+(3.478612.52736i)q47+(3.60973+11.1096i)q49+(3.05659+9.40723i)q50+(11.8640+8.61970i)q52+(2.930219.01826i)q53+(0.8326233.17539i)q5521.8340q56+(20.744715.0719i)q58+(5.23607+3.80423i)q59+(1.486564.57516i)q61+(3.359632.44091i)q62+(2.26771+6.97930i)q643.58107q65+0.854102q67+(3.30828+10.1818i)q68+(8.515206.18665i)q70+(1.16751+3.59324i)q71+(9.229526.70564i)q73+(6.441234.67983i)q7415.5126q76+(5.2089113.3552i)q77+(1.898415.84272i)q79+(3.461002.51456i)q80+(9.0530627.8625i)q82+(1.038313.19558i)q83+(2.11503+1.53666i)q85+(1.614134.96779i)q86+(16.72640.966542i)q88+13.2605q89+(12.6513+9.19169i)q91+(11.3134+8.21964i)q92+(3.26907+10.0612i)q94+(3.064652.22660i)q95+(0.114759+0.353191i)q9728.7399q98+O(q100)q+(-0.760284 + 2.33991i) q^{2} +(-3.27913 - 2.38243i) q^{4} +(-0.305860 - 0.941339i) q^{5} +(-3.49672 - 2.54052i) q^{7} +(4.08684 - 2.96926i) q^{8} +2.43519 q^{10} +(2.79120 + 1.79142i) q^{11} +(1.11803 - 3.44095i) q^{13} +(8.60310 - 6.25052i) q^{14} +(1.33563 + 4.11065i) q^{16} +(-0.816208 - 2.51203i) q^{17} +(3.09629 - 2.24958i) q^{19} +(-1.23972 + 3.81546i) q^{20} +(-6.31388 + 5.16917i) q^{22} -3.45011 q^{23} +(3.25252 - 2.36309i) q^{25} +(7.20151 + 5.23221i) q^{26} +(5.41361 + 16.6614i) q^{28} +(-8.43168 - 6.12597i) q^{29} +(-0.521582 + 1.60526i) q^{31} -0.530785 q^{32} +6.49848 q^{34} +(-1.32198 + 4.06865i) q^{35} +(-2.61803 - 1.90211i) q^{37} +(2.90977 + 8.95537i) q^{38} +(-4.04508 - 2.93893i) q^{40} +(-9.63335 + 6.99904i) q^{41} -2.12307 q^{43} +(-4.88477 - 12.5241i) q^{44} +(2.62307 - 8.07297i) q^{46} +(3.47861 - 2.52736i) q^{47} +(3.60973 + 11.1096i) q^{49} +(3.05659 + 9.40723i) q^{50} +(-11.8640 + 8.61970i) q^{52} +(2.93021 - 9.01826i) q^{53} +(0.832623 - 3.17539i) q^{55} -21.8340 q^{56} +(20.7447 - 15.0719i) q^{58} +(5.23607 + 3.80423i) q^{59} +(-1.48656 - 4.57516i) q^{61} +(-3.35963 - 2.44091i) q^{62} +(-2.26771 + 6.97930i) q^{64} -3.58107 q^{65} +0.854102 q^{67} +(-3.30828 + 10.1818i) q^{68} +(-8.51520 - 6.18665i) q^{70} +(1.16751 + 3.59324i) q^{71} +(-9.22952 - 6.70564i) q^{73} +(6.44123 - 4.67983i) q^{74} -15.5126 q^{76} +(-5.20891 - 13.3552i) q^{77} +(1.89841 - 5.84272i) q^{79} +(3.46100 - 2.51456i) q^{80} +(-9.05306 - 27.8625i) q^{82} +(-1.03831 - 3.19558i) q^{83} +(-2.11503 + 1.53666i) q^{85} +(1.61413 - 4.96779i) q^{86} +(16.7264 - 0.966542i) q^{88} +13.2605 q^{89} +(-12.6513 + 9.19169i) q^{91} +(11.3134 + 8.21964i) q^{92} +(3.26907 + 10.0612i) q^{94} +(-3.06465 - 2.22660i) q^{95} +(-0.114759 + 0.353191i) q^{97} -28.7399 q^{98} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q10q4+12q1010q162q1936q22+32q25+42q2826q3148q3424q3720q40+24q4316q46+24q4940q5216q55+106q58++72q97+O(q100) 16 q - 10 q^{4} + 12 q^{10} - 10 q^{16} - 2 q^{19} - 36 q^{22} + 32 q^{25} + 42 q^{28} - 26 q^{31} - 48 q^{34} - 24 q^{37} - 20 q^{40} + 24 q^{43} - 16 q^{46} + 24 q^{49} - 40 q^{52} - 16 q^{55} + 106 q^{58}+ \cdots + 72 q^{97}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/297Z)×\left(\mathbb{Z}/297\mathbb{Z}\right)^\times.

nn 5656 244244
χ(n)\chi(n) 11 e(35)e\left(\frac{3}{5}\right)

Coefficient data

For each nn we display the coefficients of the qq-expansion ana_n, the Satake parameters αp\alpha_p, and the Satake angles θp=Arg(αp)\theta_p = \textrm{Arg}(\alpha_p).



Display apa_p with pp up to: 50 250 1000 (See ana_n instead) (See ana_n instead) (See ana_n instead) Display ana_n with nn up to: 50 250 1000 (See only apa_p) (See only apa_p) (See only apa_p)
Significant digits:
nn ana_n an/n(k1)/2a_n / n^{(k-1)/2} αn \alpha_n θn \theta_n
pp apa_p ap/p(k1)/2a_p / p^{(k-1)/2} αp \alpha_p θp \theta_p
22 −0.760284 + 2.33991i −0.537602 + 1.65457i 0.200357 + 0.979723i 0.435790π0.435790\pi
−0.737959 + 0.674846i 0.764210π0.764210\pi
33 0 0
44 −3.27913 2.38243i −1.63956 1.19121i
55 −0.305860 0.941339i −0.136785 0.420980i 0.859079 0.511843i 0.171037π-0.171037\pi
−0.995863 + 0.0908638i 0.971037π0.971037\pi
66 0 0
77 −3.49672 2.54052i −1.32164 0.960226i −0.999910 0.0133937i 0.995737π-0.995737\pi
−0.321727 0.946832i 0.604263π-0.604263\pi
88 4.08684 2.96926i 1.44492 1.04979i
99 0 0
1010 2.43519 0.770075
1111 2.79120 + 1.79142i 0.841578 + 0.540135i
1212 0 0
1313 1.11803 3.44095i 0.310087 0.954349i −0.667643 0.744482i 0.732697π-0.732697\pi
0.977730 0.209868i 0.0673033π-0.0673033\pi
1414 8.60310 6.25052i 2.29927 1.67052i
1515 0 0
1616 1.33563 + 4.11065i 0.333908 + 1.02766i
1717 −0.816208 2.51203i −0.197959 0.609257i −0.999929 0.0118921i 0.996215π-0.996215\pi
0.801970 0.597365i 0.203785π-0.203785\pi
1818 0 0
1919 3.09629 2.24958i 0.710337 0.516090i −0.172945 0.984931i 0.555328π-0.555328\pi
0.883282 + 0.468841i 0.155328π0.155328\pi
2020 −1.23972 + 3.81546i −0.277209 + 0.853163i
2121 0 0
2222 −6.31388 + 5.16917i −1.34612 + 1.10207i
2323 −3.45011 −0.719398 −0.359699 0.933068i 0.617121π-0.617121\pi
−0.359699 + 0.933068i 0.617121π0.617121\pi
2424 0 0
2525 3.25252 2.36309i 0.650503 0.472618i
2626 7.20151 + 5.23221i 1.41233 + 1.02612i
2727 0 0
2828 5.41361 + 16.6614i 1.02308 + 3.14870i
2929 −8.43168 6.12597i −1.56572 1.13756i −0.931112 0.364733i 0.881160π-0.881160\pi
−0.634611 0.772832i 0.718840π-0.718840\pi
3030 0 0
3131 −0.521582 + 1.60526i −0.0936788 + 0.288314i −0.986907 0.161290i 0.948435π-0.948435\pi
0.893228 + 0.449603i 0.148435π0.148435\pi
3232 −0.530785 −0.0938305
3333 0 0
3434 6.49848 1.11448
3535 −1.32198 + 4.06865i −0.223456 + 0.687727i
3636 0 0
3737 −2.61803 1.90211i −0.430402 0.312705i 0.351408 0.936223i 0.385703π-0.385703\pi
−0.781810 + 0.623517i 0.785703π0.785703\pi
3838 2.90977 + 8.95537i 0.472028 + 1.45275i
3939 0 0
4040 −4.04508 2.93893i −0.639584 0.464685i
4141 −9.63335 + 6.99904i −1.50448 + 1.09307i −0.535921 + 0.844268i 0.680035π0.680035\pi
−0.968555 + 0.248798i 0.919965π0.919965\pi
4242 0 0
4343 −2.12307 −0.323764 −0.161882 0.986810i 0.551756π-0.551756\pi
−0.161882 + 0.986810i 0.551756π0.551756\pi
4444 −4.88477 12.5241i −0.736406 1.88809i
4545 0 0
4646 2.62307 8.07297i 0.386750 1.19029i
4747 3.47861 2.52736i 0.507407 0.368653i −0.304432 0.952534i 0.598467π-0.598467\pi
0.811839 + 0.583881i 0.198467π0.198467\pi
4848 0 0
4949 3.60973 + 11.1096i 0.515675 + 1.58709i
5050 3.05659 + 9.40723i 0.432267 + 1.33038i
5151 0 0
5252 −11.8640 + 8.61970i −1.64524 + 1.19534i
5353 2.93021 9.01826i 0.402496 1.23875i −0.520473 0.853878i 0.674244π-0.674244\pi
0.922968 0.384876i 0.125756π-0.125756\pi
5454 0 0
5555 0.832623 3.17539i 0.112271 0.428170i
5656 −21.8340 −2.91770
5757 0 0
5858 20.7447 15.0719i 2.72391 1.97904i
5959 5.23607 + 3.80423i 0.681679 + 0.495269i 0.873914 0.486080i 0.161574π-0.161574\pi
−0.192235 + 0.981349i 0.561574π0.561574\pi
6060 0 0
6161 −1.48656 4.57516i −0.190334 0.585789i 0.809665 0.586892i 0.199649π-0.199649\pi
−0.999999 + 0.00110319i 0.999649π0.999649\pi
6262 −3.35963 2.44091i −0.426673 0.309996i
6363 0 0
6464 −2.26771 + 6.97930i −0.283464 + 0.872413i
6565 −3.58107 −0.444177
6666 0 0
6767 0.854102 0.104345 0.0521726 0.998638i 0.483385π-0.483385\pi
0.0521726 + 0.998638i 0.483385π0.483385\pi
6868 −3.30828 + 10.1818i −0.401187 + 1.23473i
6969 0 0
7070 −8.51520 6.18665i −1.01776 0.739446i
7171 1.16751 + 3.59324i 0.138558 + 0.426439i 0.996127 0.0879314i 0.0280256π-0.0280256\pi
−0.857568 + 0.514371i 0.828026π0.828026\pi
7272 0 0
7373 −9.22952 6.70564i −1.08023 0.784835i −0.102510 0.994732i 0.532687π-0.532687\pi
−0.977724 + 0.209897i 0.932687π0.932687\pi
7474 6.44123 4.67983i 0.748778 0.544019i
7575 0 0
7676 −15.5126 −1.77942
7777 −5.20891 13.3552i −0.593610 1.52197i
7878 0 0
7979 1.89841 5.84272i 0.213588 0.657357i −0.785663 0.618655i 0.787678π-0.787678\pi
0.999251 0.0387017i 0.0123222π-0.0123222\pi
8080 3.46100 2.51456i 0.386951 0.281137i
8181 0 0
8282 −9.05306 27.8625i −0.999743 3.07689i
8383 −1.03831 3.19558i −0.113969 0.350761i 0.877762 0.479098i 0.159036π-0.159036\pi
−0.991731 + 0.128337i 0.959036π0.959036\pi
8484 0 0
8585 −2.11503 + 1.53666i −0.229407 + 0.166674i
8686 1.61413 4.96779i 0.174056 0.535690i
8787 0 0
8888 16.7264 0.966542i 1.78304 0.103034i
8989 13.2605 1.40561 0.702806 0.711381i 0.251930π-0.251930\pi
0.702806 + 0.711381i 0.251930π0.251930\pi
9090 0 0
9191 −12.6513 + 9.19169i −1.32621 + 0.963550i
9292 11.3134 + 8.21964i 1.17950 + 0.856957i
9393 0 0
9494 3.26907 + 10.0612i 0.337178 + 1.03773i
9595 −3.06465 2.22660i −0.314427 0.228444i
9696 0 0
9797 −0.114759 + 0.353191i −0.0116520 + 0.0358612i −0.956713 0.291031i 0.906002π-0.906002\pi
0.945061 + 0.326893i 0.106002π0.106002\pi
9898 −28.7399 −2.90317
9999 0 0
100100 −16.2953 −1.62953
101101 −4.01546 + 12.3583i −0.399553 + 1.22970i 0.525805 + 0.850605i 0.323764π0.323764\pi
−0.925358 + 0.379094i 0.876236π0.876236\pi
102102 0 0
103103 9.54968 + 6.93825i 0.940958 + 0.683646i 0.948651 0.316324i 0.102449π-0.102449\pi
−0.00769290 + 0.999970i 0.502449π0.502449\pi
104104 −5.64788 17.3824i −0.553820 1.70448i
105105 0 0
106106 18.8742 + 13.7129i 1.83322 + 1.33191i
107107 −3.82493 + 2.77898i −0.369770 + 0.268654i −0.757116 0.653281i 0.773392π-0.773392\pi
0.387345 + 0.921935i 0.373392π0.373392\pi
108108 0 0
109109 16.1864 1.55037 0.775186 0.631733i 0.217656π-0.217656\pi
0.775186 + 0.631733i 0.217656π0.217656\pi
110110 6.79711 + 4.36246i 0.648079 + 0.415945i
111111 0 0
112112 5.77285 17.7670i 0.545483 1.67882i
113113 0.687408 0.499431i 0.0646659 0.0469825i −0.554983 0.831862i 0.687275π-0.687275\pi
0.619649 + 0.784879i 0.287275π0.287275\pi
114114 0 0
115115 1.05525 + 3.24773i 0.0984026 + 0.302852i
116116 13.0539 + 40.1757i 1.21202 + 3.73022i
117117 0 0
118118 −12.8825 + 9.35966i −1.18593 + 0.861627i
119119 −3.52781 + 10.8575i −0.323393 + 0.995302i
120120 0 0
121121 4.58160 + 10.0004i 0.416509 + 0.909132i
122122 11.8357 1.07155
123123 0 0
124124 5.53475 4.02123i 0.497036 0.361117i
125125 −7.22304 5.24784i −0.646048 0.469381i
126126 0 0
127127 3.60148 + 11.0842i 0.319580 + 0.983566i 0.973828 + 0.227286i 0.0729853π0.0729853\pi
−0.654248 + 0.756280i 0.727015π0.727015\pi
128128 −15.4657 11.2365i −1.36699 0.993174i
129129 0 0
130130 2.72263 8.37939i 0.238790 0.734921i
131131 0.242802 0.0212137 0.0106068 0.999944i 0.496624π-0.496624\pi
0.0106068 + 0.999944i 0.496624π0.496624\pi
132132 0 0
133133 −16.5420 −1.43437
134134 −0.649360 + 1.99852i −0.0560962 + 0.172646i
135135 0 0
136136 −10.7946 7.84273i −0.925629 0.672509i
137137 −0.140507 0.432435i −0.0120043 0.0369454i 0.944875 0.327431i 0.106183π-0.106183\pi
−0.956879 + 0.290486i 0.906183π0.906183\pi
138138 0 0
139139 14.4337 + 10.4867i 1.22425 + 0.889468i 0.996446 0.0842390i 0.0268459π-0.0268459\pi
0.227803 + 0.973707i 0.426846π0.426846\pi
140140 14.0282 10.1921i 1.18560 0.861389i
141141 0 0
142142 −9.29551 −0.780062
143143 9.28487 7.60152i 0.776440 0.635671i
144144 0 0
145145 −3.18771 + 9.81076i −0.264725 + 0.814739i
146146 22.7077 16.4981i 1.87930 1.36539i
147147 0 0
148148 4.05323 + 12.4745i 0.333173 + 1.02540i
149149 −4.92523 15.1583i −0.403491 1.24182i −0.922149 0.386835i 0.873568π-0.873568\pi
0.518658 0.854982i 0.326432π-0.326432\pi
150150 0 0
151151 −4.89743 + 3.55819i −0.398547 + 0.289562i −0.768949 0.639310i 0.779220π-0.779220\pi
0.370402 + 0.928872i 0.379220π0.379220\pi
152152 5.97443 18.3874i 0.484590 1.49141i
153153 0 0
154154 35.2103 2.03464i 2.83733 0.163956i
155155 1.67063 0.134188
156156 0 0
157157 −6.05296 + 4.39773i −0.483079 + 0.350977i −0.802516 0.596630i 0.796506π-0.796506\pi
0.319438 + 0.947607i 0.396506π0.396506\pi
158158 12.2281 + 8.88425i 0.972817 + 0.706793i
159159 0 0
160160 0.162346 + 0.499649i 0.0128346 + 0.0395007i
161161 12.0641 + 8.76508i 0.950784 + 0.690785i
162162 0 0
163163 4.31902 13.2926i 0.338292 1.04115i −0.626786 0.779191i 0.715630π-0.715630\pi
0.965078 0.261963i 0.0843699π-0.0843699\pi
164164 48.2637 3.76876
165165 0 0
166166 8.26679 0.641628
167167 −1.97499 + 6.07840i −0.152829 + 0.470361i −0.997935 0.0642395i 0.979538π-0.979538\pi
0.845105 + 0.534600i 0.179538π0.179538\pi
168168 0 0
169169 −0.0729490 0.0530006i −0.00561146 0.00407697i
170170 −1.98762 6.11727i −0.152444 0.469174i
171171 0 0
172172 6.96181 + 5.05805i 0.530833 + 0.385673i
173173 6.34726 4.61155i 0.482573 0.350610i −0.319748 0.947503i 0.603598π-0.603598\pi
0.802321 + 0.596893i 0.203598π0.203598\pi
174174 0 0
175175 −17.3766 −1.31355
176176 −3.63590 + 13.8663i −0.274066 + 1.04521i
177177 0 0
178178 −10.0818 + 31.0285i −0.755660 + 2.32568i
179179 −3.94392 + 2.86542i −0.294782 + 0.214172i −0.725339 0.688392i 0.758317π-0.758317\pi
0.430557 + 0.902563i 0.358317π0.358317\pi
180180 0 0
181181 2.79558 + 8.60390i 0.207794 + 0.639523i 0.999587 + 0.0287340i 0.00914758π0.00914758\pi
−0.791794 + 0.610789i 0.790852π0.790852\pi
182182 −11.8892 36.5912i −0.881285 2.71232i
183183 0 0
184184 −14.1001 + 10.2443i −1.03947 + 0.755220i
185185 −0.989783 + 3.04624i −0.0727703 + 0.223964i
186186 0 0
187187 2.22191 8.47375i 0.162482 0.619662i
188188 −17.4280 −1.27107
189189 0 0
190190 7.54005 5.47817i 0.547013 0.397428i
191191 −15.1833 11.0313i −1.09863 0.798200i −0.117793 0.993038i 0.537582π-0.537582\pi
−0.980835 + 0.194838i 0.937582π0.937582\pi
192192 0 0
193193 −5.34678 16.4557i −0.384870 1.18451i −0.936575 0.350468i 0.886023π-0.886023\pi
0.551705 0.834039i 0.313977π-0.313977\pi
194194 −0.739188 0.537051i −0.0530706 0.0385580i
195195 0 0
196196 14.6310 45.0297i 1.04507 3.21641i
197197 6.06800 0.432327 0.216164 0.976357i 0.430646π-0.430646\pi
0.216164 + 0.976357i 0.430646π0.430646\pi
198198 0 0
199199 −10.1108 −0.716738 −0.358369 0.933580i 0.616667π-0.616667\pi
−0.358369 + 0.933580i 0.616667π0.616667\pi
200200 6.27588 19.3152i 0.443771 1.36579i
201201 0 0
202202 −25.8645 18.7917i −1.81982 1.32218i
203203 13.9201 + 42.8417i 0.977000 + 3.00690i
204204 0 0
205205 9.53492 + 6.92752i 0.665948 + 0.483839i
206206 −23.4954 + 17.0704i −1.63700 + 1.18935i
207207 0 0
208208 15.6378 1.08429
209209 12.6723 0.732275i 0.876562 0.0506525i
210210 0 0
211211 4.55535 14.0199i 0.313603 0.965172i −0.662722 0.748865i 0.730599π-0.730599\pi
0.976325 0.216307i 0.0694011π-0.0694011\pi
212212 −31.0939 + 22.5910i −2.13554 + 1.55156i
213213 0 0
214214 −3.59453 11.0628i −0.245717 0.756239i
215215 0.649360 + 1.99852i 0.0442860 + 0.136298i
216216 0 0
217217 5.90203 4.28807i 0.400656 0.291093i
218218 −12.3062 + 37.8747i −0.833483 + 2.56520i
219219 0 0
220220 −10.2954 + 8.42885i −0.694116 + 0.568273i
221221 −9.55633 −0.642828
222222 0 0
223223 −0.496725 + 0.360892i −0.0332632 + 0.0241671i −0.604293 0.796762i 0.706544π-0.706544\pi
0.571029 + 0.820930i 0.306544π0.306544\pi
224224 1.85601 + 1.34847i 0.124010 + 0.0900985i
225225 0 0
226226 0.646000 + 1.98818i 0.0429713 + 0.132252i
227227 9.39297 + 6.82439i 0.623433 + 0.452951i 0.854119 0.520078i 0.174097π-0.174097\pi
−0.230686 + 0.973028i 0.574097π0.574097\pi
228228 0 0
229229 0.251367 0.773628i 0.0166108 0.0511228i −0.942408 0.334467i 0.891444π-0.891444\pi
0.959018 + 0.283344i 0.0914438π0.0914438\pi
230230 −8.40169 −0.553991
231231 0 0
232232 −52.6486 −3.45655
233233 5.33097 16.4070i 0.349243 1.07486i −0.610029 0.792379i 0.708842π-0.708842\pi
0.959273 0.282482i 0.0911577π-0.0911577\pi
234234 0 0
235235 −3.44307 2.50153i −0.224601 0.163182i
236236 −8.10646 24.9491i −0.527686 1.62405i
237237 0 0
238238 −22.7234 16.5095i −1.47294 1.07015i
239239 −0.161603 + 0.117411i −0.0104532 + 0.00759470i −0.593000 0.805203i 0.702056π-0.702056\pi
0.582546 + 0.812797i 0.302056π0.302056\pi
240240 0 0
241241 14.8309 0.955345 0.477672 0.878538i 0.341481π-0.341481\pi
0.477672 + 0.878538i 0.341481π0.341481\pi
242242 −26.8835 + 3.11736i −1.72814 + 0.200391i
243243 0 0
244244 −6.02536 + 18.5442i −0.385734 + 1.18717i
245245 9.35383 6.79596i 0.597594 0.434178i
246246 0 0
247247 −4.27896 13.1693i −0.272264 0.837942i
248248 2.63483 + 8.10917i 0.167312 + 0.514933i
249249 0 0
250250 17.7711 12.9114i 1.12394 0.816591i
251251 −2.63483 + 8.10917i −0.166309 + 0.511846i −0.999130 0.0416955i 0.986724π-0.986724\pi
0.832821 + 0.553542i 0.186724π0.186724\pi
252252 0 0
253253 −9.62996 6.18062i −0.605430 0.388572i
254254 −28.6743 −1.79918
255255 0 0
256256 26.1768 19.0186i 1.63605 1.18866i
257257 −10.5161 7.64039i −0.655976 0.476595i 0.209325 0.977846i 0.432873π-0.432873\pi
−0.865302 + 0.501251i 0.832873π0.832873\pi
258258 0 0
259259 4.32219 + 13.3023i 0.268568 + 0.826567i
260260 11.7428 + 8.53163i 0.728256 + 0.529109i
261261 0 0
262262 −0.184598 + 0.568135i −0.0114045 + 0.0350995i
263263 14.8529 0.915868 0.457934 0.888986i 0.348590π-0.348590\pi
0.457934 + 0.888986i 0.348590π0.348590\pi
264264 0 0
265265 −9.38548 −0.576545
266266 12.5766 38.7068i 0.771121 2.37327i
267267 0 0
268268 −2.80071 2.03484i −0.171081 0.124297i
269269 1.17789 + 3.62517i 0.0718172 + 0.221031i 0.980522 0.196408i 0.0629278π-0.0629278\pi
−0.908705 + 0.417439i 0.862928π0.862928\pi
270270 0 0
271271 11.1948 + 8.13347i 0.680033 + 0.494073i 0.873369 0.487060i 0.161931π-0.161931\pi
−0.193335 + 0.981133i 0.561931π0.561931\pi
272272 9.23591 6.71028i 0.560010 0.406871i
273273 0 0
274274 1.11869 0.0675823
275275 13.3117 0.769223i 0.802727 0.0463859i
276276 0 0
277277 0.759571 2.33772i 0.0456382 0.140460i −0.925641 0.378403i 0.876473π-0.876473\pi
0.971279 + 0.237943i 0.0764732π0.0764732\pi
278278 −35.5116 + 25.8007i −2.12984 + 1.54742i
279279 0 0
280280 6.67815 + 20.5532i 0.399096 + 1.22829i
281281 −6.15581 18.9456i −0.367225 1.13020i −0.948576 0.316549i 0.897476π-0.897476\pi
0.581352 0.813652i 0.302524π-0.302524\pi
282282 0 0
283283 −5.81564 + 4.22531i −0.345704 + 0.251169i −0.747065 0.664752i 0.768537π-0.768537\pi
0.401361 + 0.915920i 0.368537π0.368537\pi
284284 4.73220 14.5642i 0.280804 0.864227i
285285 0 0
286286 10.7278 + 27.5051i 0.634346 + 1.62641i
287287 51.4664 3.03796
288288 0 0
289289 8.10919 5.89167i 0.477011 0.346569i
290290 −20.5328 14.9179i −1.20572 0.876010i
291291 0 0
292292 14.2891 + 43.9773i 0.836206 + 2.57358i
293293 −13.8033 10.0287i −0.806396 0.585881i 0.106387 0.994325i 0.466072π-0.466072\pi
−0.912784 + 0.408444i 0.866072π0.866072\pi
294294 0 0
295295 1.97957 6.09248i 0.115255 0.354718i
296296 −16.3474 −0.950172
297297 0 0
298298 39.2137 2.27159
299299 −3.85734 + 11.8717i −0.223076 + 0.686557i
300300 0 0
301301 7.42378 + 5.39369i 0.427899 + 0.310887i
302302 −4.60242 14.1648i −0.264840 0.815093i
303303 0 0
304304 13.3827 + 9.72313i 0.767553 + 0.557660i
305305 −3.85210 + 2.79871i −0.220571 + 0.160254i
306306 0 0
307307 7.48842 0.427387 0.213693 0.976901i 0.431451π-0.431451\pi
0.213693 + 0.976901i 0.431451π0.431451\pi
308308 −14.7371 + 56.2033i −0.839726 + 3.20248i
309309 0 0
310310 −1.27015 + 3.90912i −0.0721397 + 0.222023i
311311 8.51155 6.18400i 0.482645 0.350662i −0.319704 0.947518i 0.603583π-0.603583\pi
0.802349 + 0.596855i 0.203583π0.203583\pi
312312 0 0
313313 −3.22449 9.92395i −0.182259 0.560935i 0.817632 0.575742i 0.195287π-0.195287\pi
−0.999890 + 0.0148070i 0.995287π0.995287\pi
314314 −5.68834 17.5069i −0.321012 0.987973i
315315 0 0
316316 −20.1450 + 14.6362i −1.13324 + 0.823350i
317317 −3.95173 + 12.1622i −0.221951 + 0.683096i 0.776635 + 0.629950i 0.216925π0.216925\pi
−0.998587 + 0.0531456i 0.983075π0.983075\pi
318318 0 0
319319 −12.5603 32.2035i −0.703241 1.80305i
320320 7.26349 0.406042
321321 0 0
322322 −29.6817 + 21.5650i −1.65409 + 1.20177i
323323 −8.17824 5.94184i −0.455049 0.330613i
324324 0 0
325325 −4.49487 13.8338i −0.249330 0.767360i
326326 27.8198 + 20.2122i 1.54079 + 1.11945i
327327 0 0
328328 −18.5880 + 57.2079i −1.02635 + 3.15878i
329329 −18.5845 −1.02460
330330 0 0
331331 16.3849 0.900598 0.450299 0.892878i 0.351317π-0.351317\pi
0.450299 + 0.892878i 0.351317π0.351317\pi
332332 −4.20849 + 12.9524i −0.230971 + 0.710856i
333333 0 0
334334 −12.7214 9.24262i −0.696083 0.505734i
335335 −0.261235 0.804000i −0.0142728 0.0439272i
336336 0 0
337337 −23.5160 17.0854i −1.28100 0.930698i −0.281414 0.959586i 0.590803π-0.590803\pi
−0.999583 + 0.0288881i 0.990803π0.990803\pi
338338 0.179479 0.130399i 0.00976235 0.00709277i
339339 0 0
340340 10.5964 0.574671
341341 −4.33155 + 3.54624i −0.234566 + 0.192039i
342342 0 0
343343 6.25252 19.2433i 0.337604 1.03904i
344344 −8.67663 + 6.30394i −0.467813 + 0.339886i
345345 0 0
346346 5.96491 + 18.3581i 0.320676 + 0.986939i
347347 6.66940 + 20.5263i 0.358032 + 1.10191i 0.954231 + 0.299072i 0.0966771π0.0966771\pi
−0.596199 + 0.802837i 0.703323π0.703323\pi
348348 0 0
349349 −19.5785 + 14.2246i −1.04801 + 0.761426i −0.971833 0.235669i 0.924272π-0.924272\pi
−0.0761789 + 0.997094i 0.524272π0.524272\pi
350350 13.2112 40.6598i 0.706167 2.17336i
351351 0 0
352352 −1.48153 0.950862i −0.0789657 0.0506811i
353353 20.9800 1.11666 0.558328 0.829621i 0.311443π-0.311443\pi
0.558328 + 0.829621i 0.311443π0.311443\pi
354354 0 0
355355 3.02536 2.19805i 0.160570 0.116661i
356356 −43.4830 31.5922i −2.30459 1.67438i
357357 0 0
358358 −3.70635 11.4070i −0.195886 0.602876i
359359 12.6882 + 9.21850i 0.669657 + 0.486534i 0.869910 0.493210i 0.164177π-0.164177\pi
−0.200254 + 0.979744i 0.564177π0.564177\pi
360360 0 0
361361 −1.34496 + 4.13936i −0.0707873 + 0.217861i
362362 −22.2578 −1.16984
363363 0 0
364364 63.3837 3.32221
365365 −3.48934 + 10.7391i −0.182640 + 0.562110i
366366 0 0
367367 6.62952 + 4.81663i 0.346058 + 0.251426i 0.747214 0.664584i 0.231391π-0.231391\pi
−0.401155 + 0.916010i 0.631391π0.631391\pi
368368 −4.60807 14.1822i −0.240212 0.739298i
369369 0 0
370370 −6.37542 4.63201i −0.331442 0.240807i
371371 −33.1572 + 24.0901i −1.72144 + 1.25070i
372372 0 0
373373 30.8172 1.59565 0.797826 0.602888i 0.205983π-0.205983\pi
0.797826 + 0.602888i 0.205983π0.205983\pi
374374 18.1386 + 11.6415i 0.937923 + 0.601970i
375375 0 0
376376 6.71213 20.6578i 0.346152 1.06535i
377377 −30.5061 + 22.1640i −1.57114 + 1.14150i
378378 0 0
379379 6.12378 + 18.8470i 0.314557 + 0.968108i 0.975936 + 0.218056i 0.0699715π0.0699715\pi
−0.661379 + 0.750052i 0.730029π0.730029\pi
380380 4.74468 + 14.6026i 0.243397 + 0.749098i
381381 0 0
382382 37.3560 27.1407i 1.91130 1.38864i
383383 7.31619 22.5169i 0.373840 1.15056i −0.570418 0.821354i 0.693219π-0.693219\pi
0.944258 0.329206i 0.106781π-0.106781\pi
384384 0 0
385385 −10.9786 + 8.98817i −0.559521 + 0.458080i
386386 42.5700 2.16675
387387 0 0
388388 1.21776 0.884756i 0.0618225 0.0449167i
389389 6.89001 + 5.00589i 0.349338 + 0.253809i 0.748591 0.663032i 0.230731π-0.230731\pi
−0.399254 + 0.916841i 0.630731π0.630731\pi
390390 0 0
391391 2.81601 + 8.66679i 0.142412 + 0.438298i
392392 47.7397 + 34.6849i 2.41122 + 1.75185i
393393 0 0
394394 −4.61341 + 14.1986i −0.232420 + 0.715315i
395395 −6.08063 −0.305949
396396 0 0
397397 −3.78373 −0.189900 −0.0949499 0.995482i 0.530269π-0.530269\pi
−0.0949499 + 0.995482i 0.530269π0.530269\pi
398398 7.68710 23.6585i 0.385320 1.18589i
399399 0 0
400400 14.0580 + 10.2137i 0.702899 + 0.510686i
401401 −5.42428 16.6942i −0.270876 0.833670i −0.990281 0.139079i 0.955586π-0.955586\pi
0.719405 0.694590i 0.244414π-0.244414\pi
402402 0 0
403403 4.94049 + 3.58948i 0.246103 + 0.178805i
404404 42.6100 30.9580i 2.11993 1.54022i
405405 0 0
406406 −110.829 −5.50035
407407 −3.89996 9.99919i −0.193314 0.495641i
408408 0 0
409409 8.74225 26.9059i 0.432276 1.33041i −0.463576 0.886057i 0.653434π-0.653434\pi
0.895852 0.444352i 0.146566π-0.146566\pi
410410 −23.4591 + 17.0440i −1.15856 + 0.841743i
411411 0 0
412412 −14.7848 45.5028i −0.728393 2.24176i
413413 −8.64439 26.6047i −0.425363 1.30913i
414414 0 0
415415 −2.69055 + 1.95480i −0.132074 + 0.0959573i
416416 −0.593436 + 1.82641i −0.0290956 + 0.0895470i
417417 0 0
418418 −7.92110 + 30.2089i −0.387434 + 1.47756i
419419 32.2357 1.57482 0.787409 0.616430i 0.211422π-0.211422\pi
0.787409 + 0.616430i 0.211422π0.211422\pi
420420 0 0
421421 23.0100 16.7177i 1.12144 0.814772i 0.137011 0.990570i 0.456250π-0.456250\pi
0.984426 + 0.175798i 0.0562504π0.0562504\pi
422422 29.3421 + 21.3183i 1.42835 + 1.03776i
423423 0 0
424424 −14.8023 45.5568i −0.718863 2.21243i
425425 −8.59088 6.24164i −0.416719 0.302764i
426426 0 0
427427 −6.42519 + 19.7747i −0.310937 + 0.956965i
428428 19.1632 0.926286
429429 0 0
430430 −5.17007 −0.249323
431431 8.27921 25.4808i 0.398796 1.22737i −0.527170 0.849760i 0.676747π-0.676747\pi
0.925966 0.377607i 0.123253π-0.123253\pi
432432 0 0
433433 7.60672 + 5.52661i 0.365556 + 0.265592i 0.755366 0.655304i 0.227459π-0.227459\pi
−0.389810 + 0.920895i 0.627459π0.627459\pi
434434 5.54651 + 17.0704i 0.266241 + 0.819405i
435435 0 0
436436 −53.0771 38.5628i −2.54193 1.84682i
437437 −10.6825 + 7.76132i −0.511015 + 0.371274i
438438 0 0
439439 −17.8962 −0.854139 −0.427069 0.904219i 0.640454π-0.640454\pi
−0.427069 + 0.904219i 0.640454π0.640454\pi
440440 −6.02578 15.4496i −0.287268 0.736531i
441441 0 0
442442 7.26552 22.3610i 0.345586 1.06360i
443443 −14.8708 + 10.8042i −0.706531 + 0.513325i −0.882053 0.471151i 0.843839π-0.843839\pi
0.175522 + 0.984476i 0.443839π0.443839\pi
444444 0 0
445445 −4.05586 12.4826i −0.192266 0.591734i
446446 −0.466803 1.43667i −0.0221038 0.0680285i
447447 0 0
448448 25.6606 18.6435i 1.21235 0.880824i
449449 −1.85302 + 5.70301i −0.0874494 + 0.269142i −0.985212 0.171337i 0.945191π-0.945191\pi
0.897763 + 0.440479i 0.145191π0.145191\pi
450450 0 0
451451 −39.4268 + 2.27830i −1.85654 + 0.107281i
452452 −3.44396 −0.161990
453453 0 0
454454 −23.1098 + 16.7903i −1.08460 + 0.788006i
455455 12.5220 + 9.09777i 0.587041 + 0.426510i
456456 0 0
457457 7.89068 + 24.2850i 0.369110 + 1.13600i 0.947367 + 0.320150i 0.103733π0.103733\pi
−0.578257 + 0.815855i 0.696267π0.696267\pi
458458 1.61911 + 1.17635i 0.0756562 + 0.0549674i
459459 0 0
460460 4.27717 13.1638i 0.199424 0.613764i
461461 31.5683 1.47028 0.735142 0.677913i 0.237115π-0.237115\pi
0.735142 + 0.677913i 0.237115π0.237115\pi
462462 0 0
463463 3.76414 0.174934 0.0874671 0.996167i 0.472123π-0.472123\pi
0.0874671 + 0.996167i 0.472123π0.472123\pi
464464 13.9201 42.8417i 0.646225 1.98888i
465465 0 0
466466 34.3380 + 24.9480i 1.59068 + 1.15569i
467467 −1.80825 5.56521i −0.0836756 0.257527i 0.900462 0.434935i 0.143229π-0.143229\pi
−0.984137 + 0.177408i 0.943229π0.943229\pi
468468 0 0
469469 −2.98656 2.16986i −0.137907 0.100195i
470470 8.47108 6.15460i 0.390742 0.283890i
471471 0 0
472472 32.6948 1.50490
473473 −5.92590 3.80331i −0.272473 0.174876i
474474 0 0
475475 4.75475 14.6336i 0.218163 0.671436i
476476 37.4352 27.1983i 1.71584 1.24663i
477477 0 0
478478 −0.151868 0.467402i −0.00694629 0.0213785i
479479 −7.93853 24.4323i −0.362721 1.11634i −0.951396 0.307970i 0.900350π-0.900350\pi
0.588675 0.808370i 0.299650π-0.299650\pi
480480 0 0
481481 −9.47214 + 6.88191i −0.431892 + 0.313788i
482482 −11.2757 + 34.7031i −0.513595 + 1.58068i
483483 0 0
484484 8.80169 43.7081i 0.400077 1.98673i
485485 0.367573 0.0166906
486486 0 0
487487 4.29919 3.12355i 0.194815 0.141541i −0.486102 0.873902i 0.661582π-0.661582\pi
0.680917 + 0.732361i 0.261582π0.261582\pi
488488 −19.6602 14.2840i −0.889975 0.646605i
489489 0 0
490490 8.79038 + 27.0540i 0.397109 + 1.22218i
491491 −1.99393 1.44868i −0.0899850 0.0653779i 0.541883 0.840454i 0.317712π-0.317712\pi
−0.631868 + 0.775076i 0.717712π0.717712\pi
492492 0 0
493493 −8.50662 + 26.1807i −0.383119 + 1.17912i
494494 34.0682 1.53280
495495 0 0
496496 −7.29531 −0.327569
497497 5.04622 15.5307i 0.226354 0.696646i
498498 0 0
499499 −18.0431 13.1091i −0.807722 0.586844i 0.105448 0.994425i 0.466372π-0.466372\pi
−0.913169 + 0.407581i 0.866372π0.866372\pi
500500 11.1827 + 34.4167i 0.500104 + 1.53916i
501501 0 0
502502 −16.9715 12.3305i −0.757477 0.550339i
503503 −21.0129 + 15.2667i −0.936917 + 0.680710i −0.947677 0.319232i 0.896575π-0.896575\pi
0.0107594 + 0.999942i 0.496575π0.496575\pi
504504 0 0
505505 12.8615 0.572331
506506 21.7836 17.8342i 0.968400 0.792829i
507507 0 0
508508 14.5976 44.9269i 0.647665 1.99331i
509509 22.5506 16.3840i 0.999538 0.726207i 0.0375492 0.999295i 0.488045π-0.488045\pi
0.961989 + 0.273088i 0.0880449π0.0880449\pi
510510 0 0
511511 15.2373 + 46.8955i 0.674058 + 2.07454i
512512 12.7852 + 39.3489i 0.565033 + 1.73899i
513513 0 0
514514 25.8731 18.7979i 1.14121 0.829139i
515515 3.61038 11.1116i 0.159093 0.489637i
516516 0 0
517517 14.2371 0.822694i 0.626145 0.0361820i
518518 −34.4124 −1.51199
519519 0 0
520520 −14.6353 + 10.6331i −0.641798 + 0.466294i
521521 −20.9287 15.2056i −0.916902 0.666168i 0.0258491 0.999666i 0.491771π-0.491771\pi
−0.942751 + 0.333498i 0.891771π0.891771\pi
522522 0 0
523523 −8.42503 25.9296i −0.368401 1.13382i −0.947824 0.318794i 0.896722π-0.896722\pi
0.579423 0.815027i 0.303278π-0.303278\pi
524524 −0.796178 0.578457i −0.0347812 0.0252700i
525525 0 0
526526 −11.2924 + 34.7544i −0.492372 + 1.51537i
527527 4.45819 0.194202
528528 0 0
529529 −11.0967 −0.482466
530530 7.13563 21.9612i 0.309952 0.953934i
531531 0 0
532532 54.2433 + 39.4100i 2.35174 + 1.70864i
533533 13.3130 + 40.9731i 0.576648 + 1.77474i
534534 0 0
535535 3.78585 + 2.75058i 0.163677 + 0.118918i
536536 3.49058 2.53605i 0.150770 0.109541i
537537 0 0
538538 −9.37812 −0.404320
539539 −9.82654 + 37.4757i −0.423259 + 1.61419i
540540 0 0
541541 −7.22580 + 22.2387i −0.310661 + 0.956118i 0.666842 + 0.745199i 0.267646π0.267646\pi
−0.977504 + 0.210919i 0.932354π0.932354\pi
542542 −27.5428 + 20.0110i −1.18307 + 0.859547i
543543 0 0
544544 0.433231 + 1.33335i 0.0185746 + 0.0571668i
545545 −4.95075 15.2368i −0.212067 0.652675i
546546 0 0
547547 −12.3642 + 8.98309i −0.528654 + 0.384089i −0.819854 0.572573i 0.805945π-0.805945\pi
0.291200 + 0.956662i 0.405945π0.405945\pi
548548 −0.569506 + 1.75276i −0.0243281 + 0.0748741i
549549 0 0
550550 −8.32077 + 31.7331i −0.354799 + 1.35310i
551551 −39.8878 −1.69928
552552 0 0
553553 −21.4818 + 15.6074i −0.913498 + 0.663695i
554554 4.89257 + 3.55466i 0.207866 + 0.151023i
555555 0 0
556556 −22.3461 68.7743i −0.947687 2.91668i
557557 −5.85761 4.25580i −0.248195 0.180324i 0.456732 0.889605i 0.349020π-0.349020\pi
−0.704926 + 0.709280i 0.749020π0.749020\pi
558558 0 0
559559 −2.37366 + 7.30537i −0.100395 + 0.308984i
560560 −18.4904 −0.781364
561561 0 0
562562 49.0113 2.06742
563563 −9.74643 + 29.9964i −0.410763 + 1.26420i 0.505223 + 0.862989i 0.331410π0.331410\pi
−0.915986 + 0.401210i 0.868590π0.868590\pi
564564 0 0
565565 −0.680384 0.494328i −0.0286240 0.0207965i
566566 −5.46532 16.8205i −0.229725 0.707019i
567567 0 0
568568 15.4407 + 11.2183i 0.647879 + 0.470711i
569569 9.04664 6.57277i 0.379255 0.275545i −0.381783 0.924252i 0.624690π-0.624690\pi
0.761038 + 0.648707i 0.224690π0.224690\pi
570570 0 0
571571 11.5906 0.485052 0.242526 0.970145i 0.422024π-0.422024\pi
0.242526 + 0.970145i 0.422024π0.422024\pi
572572 −48.5563 + 2.80585i −2.03024 + 0.117318i
573573 0 0
574574 −39.1290 + 120.427i −1.63321 + 5.02652i
575575 −11.2215 + 8.15293i −0.467971 + 0.340001i
576576 0 0
577577 5.23344 + 16.1069i 0.217871 + 0.670537i 0.998937 + 0.0460895i 0.0146760π0.0146760\pi
−0.781067 + 0.624448i 0.785324π0.785324\pi
578578 7.62072 + 23.4541i 0.316980 + 0.975564i
579579 0 0
580580 33.8263 24.5763i 1.40456 1.02047i
581581 −4.48776 + 13.8119i −0.186184 + 0.573015i
582582 0 0
583583 24.3343 19.9225i 1.00783 0.825107i
584584 −57.6304 −2.38476
585585 0 0
586586 33.9606 24.6738i 1.40290 1.01927i
587587 7.31900 + 5.31756i 0.302087 + 0.219479i 0.728494 0.685052i 0.240221π-0.240221\pi
−0.426406 + 0.904532i 0.640221π0.640221\pi
588588 0 0
589589 1.99621 + 6.14370i 0.0822523 + 0.253147i
590590 12.7508 + 9.26403i 0.524944 + 0.381394i
591591 0 0
592592 4.32219 13.3023i 0.177641 0.546722i
593593 20.4127 0.838248 0.419124 0.907929i 0.362337π-0.362337\pi
0.419124 + 0.907929i 0.362337π0.362337\pi
594594 0 0
595595 11.2996 0.463237
596596 −19.9631 + 61.4401i −0.817720 + 2.51668i
597597 0 0
598598 −24.8460 18.0517i −1.01603 0.738189i
599599 −12.9855 39.9652i −0.530573 1.63293i −0.753026 0.657991i 0.771406π-0.771406\pi
0.222453 0.974943i 0.428594π-0.428594\pi
600600 0 0
601601 8.65252 + 6.28642i 0.352944 + 0.256429i 0.750103 0.661321i 0.230004π-0.230004\pi
−0.397159 + 0.917750i 0.630004π0.630004\pi
602602 −18.2649 + 13.2703i −0.744423 + 0.540855i
603603 0 0
604604 24.5364 0.998373
605605 8.01249 7.37157i 0.325754 0.299697i
606606 0 0
607607 −14.0910 + 43.3676i −0.571936 + 1.76024i 0.0744490 + 0.997225i 0.476280π0.476280\pi
−0.646385 + 0.763012i 0.723720π0.723720\pi
608608 −1.64346 + 1.19405i −0.0666513 + 0.0484250i
609609 0 0
610610 −3.62006 11.1414i −0.146572 0.451102i
611611 −4.80732 14.7954i −0.194483 0.598558i
612612 0 0
613613 −21.9790 + 15.9687i −0.887725 + 0.644970i −0.935284 0.353899i 0.884856π-0.884856\pi
0.0475592 + 0.998868i 0.484856π0.484856\pi
614614 −5.69332 + 17.5222i −0.229764 + 0.707140i
615615 0 0
616616 −60.9432 39.1140i −2.45547 1.57595i
617617 7.83117 0.315271 0.157636 0.987497i 0.449613π-0.449613\pi
0.157636 + 0.987497i 0.449613π0.449613\pi
618618 0 0
619619 −30.6835 + 22.2929i −1.23327 + 0.896027i −0.997131 0.0756915i 0.975884π-0.975884\pi
−0.236144 + 0.971718i 0.575884π0.575884\pi
620620 −5.47820 3.98015i −0.220010 0.159847i
621621 0 0
622622 7.99883 + 24.6179i 0.320724 + 0.987087i
623623 −46.3684 33.6886i −1.85771 1.34971i
624624 0 0
625625 3.48099 10.7134i 0.139239 0.428535i
626626 25.6727 1.02609
627627 0 0
628628 30.3257 1.21013
629629 −2.64130 + 8.12910i −0.105316 + 0.324128i
630630 0 0
631631 22.3432 + 16.2333i 0.889468 + 0.646237i 0.935739 0.352692i 0.114734π-0.114734\pi
−0.0462710 + 0.998929i 0.514734π0.514734\pi
632632 −9.59006 29.5152i −0.381472 1.17405i
633633 0 0
634634 −25.4540 18.4934i −1.01091 0.734467i
635635 9.33247 6.78044i 0.370348 0.269073i
636636 0 0
637637 42.2634 1.67454
638638 84.9029 4.90614i 3.36134 0.194236i
639639 0 0
640640 −5.84701 + 17.9952i −0.231123 + 0.711324i
641641 −3.61805 + 2.62867i −0.142904 + 0.103826i −0.656940 0.753942i 0.728150π-0.728150\pi
0.514036 + 0.857769i 0.328150π0.328150\pi
642642 0 0
643643 −2.30885 7.10591i −0.0910522 0.280230i 0.895153 0.445760i 0.147067π-0.147067\pi
−0.986205 + 0.165530i 0.947067π0.947067\pi
644644 −18.6776 57.4836i −0.735999 2.26517i
645645 0 0
646646 20.1212 14.6189i 0.791657 0.575172i
647647 3.55862 10.9523i 0.139904 0.430579i −0.856417 0.516285i 0.827314π-0.827314\pi
0.996320 + 0.0857057i 0.0273145π0.0273145\pi
648648 0 0
649649 7.79994 + 19.9984i 0.306174 + 0.785006i
650650 35.7872 1.40369
651651 0 0
652652 −45.8312 + 33.2983i −1.79489 + 1.30406i
653653 17.1013 + 12.4248i 0.669226 + 0.486221i 0.869766 0.493464i 0.164270π-0.164270\pi
−0.200540 + 0.979686i 0.564270π0.564270\pi
654654 0 0
655655 −0.0742632 0.228559i −0.00290170 0.00893053i
656656 −41.6372 30.2512i −1.62566 1.18111i
657657 0 0
658658 14.1295 43.4862i 0.550826 1.69527i
659659 −27.0354 −1.05315 −0.526575 0.850129i 0.676524π-0.676524\pi
−0.526575 + 0.850129i 0.676524π0.676524\pi
660660 0 0
661661 −26.7618 −1.04091 −0.520456 0.853888i 0.674238π-0.674238\pi
−0.520456 + 0.853888i 0.674238π0.674238\pi
662662 −12.4572 + 38.3393i −0.484163 + 1.49010i
663663 0 0
664664 −13.7319 9.97683i −0.532902 0.387176i
665665 5.05952 + 15.5716i 0.196200 + 0.603841i
666666 0 0
667667 29.0902 + 21.1353i 1.12638 + 0.818362i
668668 20.9576 15.2266i 0.810874 0.589134i
669669 0 0
670670 2.07990 0.0803536
671671 4.04677 15.4332i 0.156224 0.595794i
672672 0 0
673673 15.1845 46.7332i 0.585321 1.80143i −0.0126574 0.999920i 0.504029π-0.504029\pi
0.597978 0.801512i 0.295971π-0.295971\pi
674674 57.8571 42.0356i 2.22857 1.61915i
675675 0 0
676676 0.112939 + 0.347591i 0.00434382 + 0.0133689i
677677 14.1181 + 43.4511i 0.542603 + 1.66996i 0.726622 + 0.687038i 0.241089π0.241089\pi
−0.184019 + 0.982923i 0.558911π0.558911\pi
678678 0 0
679679 1.29857 0.943466i 0.0498345 0.0362069i
680680 −4.08104 + 12.5601i −0.156501 + 0.481660i
681681 0 0
682682 −5.00468 12.8316i −0.191639 0.491347i
683683 −47.1991 −1.80602 −0.903012 0.429615i 0.858649π-0.858649\pi
−0.903012 + 0.429615i 0.858649π0.858649\pi
684684 0 0
685685 −0.364093 + 0.264529i −0.0139113 + 0.0101071i
686686 40.2739 + 29.2607i 1.53766 + 1.11718i
687687 0 0
688688 −2.83563 8.72717i −0.108107 0.332720i
689689 −27.7554 20.1655i −1.05740 0.768243i
690690 0 0
691691 9.20361 28.3258i 0.350122 1.07756i −0.608662 0.793429i 0.708294π-0.708294\pi
0.958784 0.284135i 0.0917065π-0.0917065\pi
692692 −31.8002 −1.20886
693693 0 0
694694 −53.1004 −2.01566
695695 5.45684 16.7944i 0.206990 0.637049i
696696 0 0
697697 25.4446 + 18.4866i 0.963783 + 0.700229i
698698 −18.3991 56.6267i −0.696417 2.14335i
699699 0 0
700700 56.9802 + 41.3985i 2.15365 + 1.56472i
701701 −0.479434 + 0.348329i −0.0181080 + 0.0131562i −0.596802 0.802388i 0.703562π-0.703562\pi
0.578694 + 0.815544i 0.303562π0.303562\pi
702702 0 0
703703 −12.3851 −0.467115
704704 −18.8325 + 15.4182i −0.709778 + 0.581095i
705705 0 0
706706 −15.9508 + 49.0915i −0.600316 + 1.84758i
707707 45.4375 33.0123i 1.70885 1.24155i
708708 0 0
709709 −10.4557 32.1793i −0.392672 1.20852i −0.930760 0.365631i 0.880853π-0.880853\pi
0.538088 0.842888i 0.319147π-0.319147\pi
710710 2.84312 + 8.75023i 0.106700 + 0.328390i
711711 0 0
712712 54.1937 39.3740i 2.03099 1.47560i
713713 1.79952 5.53834i 0.0673924 0.207412i
714714 0 0
715715 −9.99547 6.41521i −0.373810 0.239915i
716716 19.7593 0.738439
717717 0 0
718718 −31.2171 + 22.6806i −1.16501 + 0.846431i
719719 −39.3929 28.6206i −1.46911 1.06737i −0.980871 0.194657i 0.937641π-0.937641\pi
−0.488236 0.872712i 0.662359π-0.662359\pi
720720 0 0
721721 −15.7659 48.5223i −0.587151 1.80707i
722722 −8.66319 6.29417i −0.322410 0.234245i
723723 0 0
724724 11.3311 34.8736i 0.421117 1.29607i
725725 −41.9004 −1.55614
726726 0 0
727727 −38.4706 −1.42680 −0.713399 0.700758i 0.752845π-0.752845\pi
−0.713399 + 0.700758i 0.752845π0.752845\pi
728728 −24.4112 + 75.1299i −0.904739 + 2.78450i
729729 0 0
730730 −22.4756 16.3295i −0.831861 0.604382i
731731 1.73286 + 5.33320i 0.0640922 + 0.197256i
732732 0 0
733733 −7.72793 5.61467i −0.285437 0.207382i 0.435848 0.900020i 0.356448π-0.356448\pi
−0.721286 + 0.692638i 0.756448π0.756448\pi
734734 −16.3108 + 11.8505i −0.602043 + 0.437410i
735735 0 0
736736 1.83127 0.0675015
737737 2.38397 + 1.53006i 0.0878146 + 0.0563605i
738738 0 0
739739 5.87978 18.0961i 0.216291 0.665675i −0.782768 0.622313i 0.786193π-0.786193\pi
0.999059 0.0433623i 0.0138070π-0.0138070\pi
740740 10.5031 7.63092i 0.386100 0.280518i
741741 0 0
742742 −31.1599 95.9004i −1.14392 3.52061i
743743 3.92913 + 12.0926i 0.144146 + 0.443635i 0.996900 0.0786769i 0.0250695π-0.0250695\pi
−0.852754 + 0.522312i 0.825070π0.825070\pi
744744 0 0
745745 −12.7627 + 9.27263i −0.467588 + 0.339723i
746746 −23.4298 + 72.1095i −0.857826 + 2.64012i
747747 0 0
748748 −27.4740 + 22.4930i −1.00455 + 0.822425i
749749 20.4348 0.746671
750750 0 0
751751 30.8657 22.4252i 1.12630 0.818308i 0.141151 0.989988i 0.454920π-0.454920\pi
0.985153 + 0.171680i 0.0549196π0.0549196\pi
752752 15.0352 + 10.9237i 0.548277 + 0.398347i
753753 0 0
754754 −28.6685 88.2325i −1.04404 3.21324i
755755 4.84739 + 3.52184i 0.176415 + 0.128173i
756756 0 0
757757 2.01311 6.19571i 0.0731677 0.225187i −0.907784 0.419437i 0.862227π-0.862227\pi
0.980952 + 0.194250i 0.0622274π0.0622274\pi
758758 −48.7563 −1.77091
759759 0 0
760760 −19.1361 −0.694140
761761 −13.8835 + 42.7291i −0.503278 + 1.54893i 0.300369 + 0.953823i 0.402890π0.402890\pi
−0.803646 + 0.595107i 0.797110π0.797110\pi
762762 0 0
763763 −56.5992 41.1217i −2.04903 1.48871i
764764 23.5068 + 72.3464i 0.850445 + 2.61740i
765765 0 0
766766 47.1252 + 34.2385i 1.70270 + 1.23709i
767767 18.9443 13.7638i 0.684039 0.496983i
768768 0 0
769769 −0.0822779 −0.00296702 −0.00148351 0.999999i 0.500472π-0.500472\pi
−0.00148351 + 0.999999i 0.500472π0.500472\pi
770770 −12.6847 32.5225i −0.457125 1.17203i
771771 0 0
772772 −21.6717 + 66.6986i −0.779982 + 2.40054i
773773 −15.3850 + 11.1779i −0.553361 + 0.402040i −0.829023 0.559215i 0.811103π-0.811103\pi
0.275662 + 0.961255i 0.411103π0.411103\pi
774774 0 0
775775 2.09693 + 6.45369i 0.0753240 + 0.231823i
776776 0.579717 + 1.78419i 0.0208106 + 0.0640486i
777777 0 0
778778 −16.9517 + 12.3161i −0.607748 + 0.441555i
779779 −14.0827 + 43.3421i −0.504565 + 1.55289i
780780 0 0
781781 −3.17825 + 12.1210i −0.113727 + 0.433722i
782782 −22.4205 −0.801755
783783 0 0
784784 −40.8464 + 29.6766i −1.45880 + 1.05988i
785785 5.99111 + 4.35280i 0.213832 + 0.155358i
786786 0 0
787787 2.66677 + 8.20747i 0.0950601 + 0.292565i 0.987269 0.159057i 0.0508455π-0.0508455\pi
−0.892209 + 0.451622i 0.850845π0.850845\pi
788788 −19.8978 14.4566i −0.708829 0.514994i
789789 0 0
790790 4.62300 14.2281i 0.164479 0.506214i
791791 −3.67249 −0.130579
792792 0 0
793793 −17.4049 −0.618068
794794 2.87671 8.85359i 0.102091 0.314202i
795795 0 0
796796 33.1547 + 24.0883i 1.17514 + 0.853788i
797797 5.12156 + 15.7626i 0.181415 + 0.558338i 0.999868 0.0162351i 0.00516802π-0.00516802\pi
−0.818453 + 0.574573i 0.805168π0.805168\pi
798798 0 0
799799 −9.18806 6.67552i −0.325050 0.236163i
800800 −1.72639 + 1.25429i −0.0610370 + 0.0443460i
801801 0 0
802802 43.1870 1.52499
803803 −13.7488 35.2508i −0.485184 1.24397i
804804 0 0
805805 4.56099 14.0373i 0.160754 0.494749i
806806 −12.1552 + 8.83130i −0.428150 + 0.311069i
807807 0 0
808808 20.2846 + 62.4295i 0.713608 + 2.19626i
809809 6.99703 + 21.5347i 0.246003 + 0.757118i 0.995470 + 0.0950768i 0.0303097π0.0303097\pi
−0.749467 + 0.662041i 0.769690π0.769690\pi
810810 0 0
811811 45.7773 33.2592i 1.60746 1.16789i 0.736635 0.676290i 0.236413π-0.236413\pi
0.870823 0.491597i 0.163587π-0.163587\pi
812812 56.4213 173.647i 1.98000 6.09382i
813813 0 0
814814 26.3623 1.52336i 0.923999 0.0533936i
815815 −13.8338 −0.484578
816816 0 0
817817 −6.57362 + 4.77601i −0.229982 + 0.167092i
818818 56.3108 + 40.9122i 1.96886 + 1.43046i
819819 0 0
820820 −14.7619 45.4325i −0.515508 1.58657i
821821 38.3065 + 27.8313i 1.33690 + 0.971318i 0.999552 + 0.0299397i 0.00953152π0.00953152\pi
0.337353 + 0.941378i 0.390468π0.390468\pi
822822 0 0
823823 −2.15721 + 6.63922i −0.0751957 + 0.231429i −0.981589 0.191007i 0.938825π-0.938825\pi
0.906393 + 0.422435i 0.138825π0.138825\pi
824824 59.6296 2.07729
825825 0 0
826826 68.8249 2.39472
827827 12.3062 37.8747i 0.427929 1.31703i −0.472232 0.881474i 0.656551π-0.656551\pi
0.900161 0.435557i 0.143449π-0.143449\pi
828828 0 0
829829 26.7634 + 19.4447i 0.929530 + 0.675343i 0.945878 0.324524i 0.105204π-0.105204\pi
−0.0163480 + 0.999866i 0.505204π0.505204\pi
830830 −2.52848 7.78186i −0.0877648 0.270112i
831831 0 0
832832 21.4801 + 15.6062i 0.744688 + 0.541047i
833833 24.9614 18.1355i 0.864860 0.628357i
834834 0 0
835835 6.32591 0.218917
836836 −43.2987 27.7896i −1.49752 0.961125i
837837 0 0
838838 −24.5083 + 75.4288i −0.846626 + 2.60565i
839839 27.6635 20.0987i 0.955052 0.693886i 0.00305543 0.999995i 0.499027π-0.499027\pi
0.951996 + 0.306110i 0.0990274π0.0990274\pi
840840 0 0
841841 24.6042 + 75.7238i 0.848419 + 2.61117i
842842 21.6239 + 66.5515i 0.745209 + 2.29352i
843843 0 0
844844 −48.3390 + 35.1204i −1.66390 + 1.20889i
845845 −0.0275793 + 0.0848805i −0.000948758 + 0.00291998i
846846 0 0
847847 9.38576 46.6085i 0.322498 1.60149i
848848 40.9846 1.40742
849849 0 0
850850 21.1364 15.3565i 0.724973 0.526724i
851851 9.03251 + 6.56250i 0.309631 + 0.224960i
852852 0 0
853853 −2.36127 7.26723i −0.0808482 0.248825i 0.902460 0.430774i 0.141759π-0.141759\pi
−0.983308 + 0.181949i 0.941759π0.941759\pi
854854 −41.3861 30.0688i −1.41620 1.02893i
855855 0 0
856856 −7.38038 + 22.7145i −0.252256 + 0.776365i
857857 −27.6052 −0.942976 −0.471488 0.881873i 0.656283π-0.656283\pi
−0.471488 + 0.881873i 0.656283π0.656283\pi
858858 0 0
859859 −17.0244 −0.580864 −0.290432 0.956896i 0.593799π-0.593799\pi
−0.290432 + 0.956896i 0.593799π0.593799\pi
860860 2.63200 8.10047i 0.0897506 0.276224i
861861 0 0
862862 53.3283 + 38.7453i 1.81637 + 1.31967i
863863 −3.17117 9.75984i −0.107948 0.332229i 0.882463 0.470381i 0.155884π-0.155884\pi
−0.990411 + 0.138152i 0.955884π0.955884\pi
864864 0 0
865865 −6.28240 4.56443i −0.213608 0.155195i
866866 −18.7150 + 13.5973i −0.635963 + 0.462054i
867867 0 0
868868 −29.5695 −1.00366
869869 15.7656 12.9073i 0.534813 0.437851i
870870 0 0
871871 0.954915 2.93893i 0.0323561 0.0995817i
872872 66.1511 48.0616i 2.24016 1.62757i
873873 0 0
874874 −10.0391 30.8970i −0.339576 1.04511i
875875 11.9247 + 36.7005i 0.403129 + 1.24070i
876876 0 0
877877 18.0108 13.0856i 0.608181 0.441869i −0.240592 0.970626i 0.577342π-0.577342\pi
0.848773 + 0.528757i 0.177342π0.177342\pi
878878 13.6062 41.8755i 0.459187 1.41323i
879879 0 0
880880 14.1650 0.818529i 0.477501 0.0275926i
881881 3.58540 0.120795 0.0603976 0.998174i 0.480763π-0.480763\pi
0.0603976 + 0.998174i 0.480763π0.480763\pi
882882 0 0
883883 −36.3972 + 26.4441i −1.22486 + 0.889916i −0.996495 0.0836583i 0.973340π-0.973340\pi
−0.228370 + 0.973574i 0.573340π0.573340\pi
884884 31.3364 + 22.7673i 1.05396 + 0.765745i
885885 0 0
886886 −13.9750 43.0106i −0.469499 1.44497i
887887 11.9764 + 8.70139i 0.402129 + 0.292164i 0.770408 0.637551i 0.220053π-0.220053\pi
−0.368278 + 0.929716i 0.620053π0.620053\pi
888888 0 0
889889 15.5663 47.9081i 0.522077 1.60679i
890890 32.2919 1.08243
891891 0 0
892892 2.48862 0.0833253
893893 5.08527 15.6508i 0.170172 0.523735i
894894 0 0
895895 3.90362 + 2.83615i 0.130484 + 0.0948019i
896896 25.5328 + 78.5817i 0.852989 + 2.62523i
897897 0 0
898898 −11.9357 8.67181i −0.398300 0.289382i
899899 14.2316 10.3399i 0.474651 0.344854i
900900 0 0
901901 −25.0458 −0.834397
902902 24.6446 93.9876i 0.820575 3.12944i
903903 0 0
904904 1.32638 4.08219i 0.0441149 0.135772i
905905 7.24413 5.26317i 0.240803 0.174954i
906906 0 0
907907 7.40837 + 22.8006i 0.245991 + 0.757083i 0.995472 + 0.0950565i 0.0303032π0.0303032\pi
−0.749481 + 0.662026i 0.769697π0.769697\pi
908908 −14.5421 44.7561i −0.482598 1.48528i
909909 0 0
910910 −30.8083 + 22.3835i −1.02128 + 0.742006i
911911 6.93704 21.3500i 0.229835 0.707358i −0.767930 0.640534i 0.778713π-0.778713\pi
0.997765 0.0668244i 0.0212867π-0.0212867\pi
912912 0 0
913913 2.82652 10.7796i 0.0935442 0.356751i
914914 −62.8240 −2.07803
915915 0 0
916916 −2.66738 + 1.93796i −0.0881326 + 0.0640321i
917917 −0.849011 0.616842i −0.0280368 0.0203699i
918918 0 0
919919 5.84951 + 18.0029i 0.192958 + 0.593862i 0.999994 + 0.00336124i 0.00106992π0.00106992\pi
−0.807037 + 0.590501i 0.798930π0.798930\pi
920920 13.9560 + 10.1396i 0.460116 + 0.334294i
921921 0 0
922922 −24.0009 + 73.8672i −0.790428 + 2.43269i
923923 13.6695 0.449937
924924 0 0
925925 −13.0101 −0.427768
926926 −2.86181 + 8.80775i −0.0940450 + 0.289441i
927927 0 0
928928 4.47541 + 3.25158i 0.146913 + 0.106738i
929929 −6.82412 21.0025i −0.223892 0.689069i −0.998402 0.0565076i 0.982003π-0.982003\pi
0.774510 0.632562i 0.217997π-0.217997\pi
930930 0 0
931931 36.1687 + 26.2781i 1.18538 + 0.861231i
932932 −56.5695 + 41.1001i −1.85300 + 1.34628i
933933 0 0
934934 14.3969 0.471080
935935 −8.65627 + 0.500206i −0.283090 + 0.0163585i
936936 0 0
937937 3.73772 11.5035i 0.122106 0.375804i −0.871257 0.490828i 0.836694π-0.836694\pi
0.993363 + 0.115024i 0.0366945π0.0366945\pi
938938 7.34792 5.33858i 0.239918 0.174311i
939939 0 0
940940 5.33054 + 16.4057i 0.173863 + 0.535095i
941941 6.37683 + 19.6259i 0.207879 + 0.639785i 0.999583 + 0.0288803i 0.00919417π0.00919417\pi
−0.791704 + 0.610905i 0.790806π0.790806\pi
942942 0 0
943943 33.2361 24.1475i 1.08232 0.786350i
944944 −8.64439 + 26.6047i −0.281351 + 0.865909i
945945 0 0
946946 13.4048 10.9745i 0.435827 0.356812i
947947 5.27445 0.171397 0.0856983 0.996321i 0.472688π-0.472688\pi
0.0856983 + 0.996321i 0.472688π0.472688\pi
948948 0 0
949949 −33.3927 + 24.2612i −1.08397 + 0.787553i
950950 30.6264 + 22.2514i 0.993653 + 0.721931i
951951 0 0
952952 17.8211 + 54.8477i 0.577586 + 1.77763i
953953 43.2076 + 31.3922i 1.39963 + 1.01689i 0.994730 + 0.102532i 0.0326945π0.0326945\pi
0.404902 + 0.914360i 0.367306π0.367306\pi
954954 0 0
955955 −5.74026 + 17.6667i −0.185751 + 0.571681i
956956 0.809640 0.0261856
957957 0 0
958958 63.2050 2.04206
959959 −0.607297 + 1.86907i −0.0196106 + 0.0603553i
960960 0 0
961961 22.7747 + 16.5468i 0.734668 + 0.533767i
962962 −8.90156 27.3962i −0.286998 0.883288i
963963 0 0
964964 −48.6326 35.3336i −1.56635 1.13802i
965965 −13.8550 + 10.0663i −0.446009 + 0.324044i
966966 0 0
967967 44.5529 1.43273 0.716363 0.697728i 0.245806π-0.245806\pi
0.716363 + 0.697728i 0.245806π0.245806\pi
968968 48.4182 + 27.2663i 1.55622 + 0.876372i
969969 0 0
970970 −0.279460 + 0.860089i −0.00897291 + 0.0276158i
971971 −32.0517 + 23.2869i −1.02859 + 0.747313i −0.968026 0.250852i 0.919289π-0.919289\pi
−0.0605623 + 0.998164i 0.519289π0.519289\pi
972972 0 0
973973 −23.8290 73.3381i −0.763922 2.35111i
974974 4.04022 + 12.4345i 0.129457 + 0.398428i
975975 0 0
976976 16.8214 12.2214i 0.538439 0.391199i
977977 17.5677 54.0679i 0.562041 1.72979i −0.114541 0.993418i 0.536540π-0.536540\pi
0.676583 0.736367i 0.263460π-0.263460\pi
978978 0 0
979979 37.0128 + 23.7552i 1.18293 + 0.759220i
980980 −46.8633 −1.49699
981981 0 0
982982 4.90574 3.56423i 0.156548 0.113739i
983983 9.04164 + 6.56913i 0.288383 + 0.209523i 0.722566 0.691302i 0.242963π-0.242963\pi
−0.434182 + 0.900825i 0.642963π0.642963\pi
984984 0 0
985985 −1.85596 5.71205i −0.0591357 0.182001i
986986 −54.7931 39.8095i −1.74497 1.26779i
987987 0 0
988988 −17.3436 + 53.3781i −0.551774 + 1.69818i
989989 7.32482 0.232916
990990 0 0
991991 −37.0475 −1.17685 −0.588426 0.808551i 0.700252π-0.700252\pi
−0.588426 + 0.808551i 0.700252π0.700252\pi
992992 0.276848 0.852050i 0.00878993 0.0270526i
993993 0 0
994994 32.5039 + 23.6154i 1.03096 + 0.749036i
995995 3.09250 + 9.51772i 0.0980387 + 0.301732i
996996 0 0
997997 −34.8630 25.3294i −1.10412 0.802191i −0.122394 0.992482i 0.539057π-0.539057\pi
−0.981728 + 0.190290i 0.939057π0.939057\pi
998998 44.3921 32.2527i 1.40521 1.02094i
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 297.2.f.b.163.1 yes 16
3.2 odd 2 inner 297.2.f.b.163.4 yes 16
9.2 odd 6 891.2.n.h.757.1 32
9.4 even 3 891.2.n.h.460.1 32
9.5 odd 6 891.2.n.h.460.4 32
9.7 even 3 891.2.n.h.757.4 32
11.4 even 5 3267.2.a.bj.1.1 8
11.5 even 5 inner 297.2.f.b.82.1 16
11.7 odd 10 3267.2.a.bi.1.8 8
33.5 odd 10 inner 297.2.f.b.82.4 yes 16
33.26 odd 10 3267.2.a.bj.1.8 8
33.29 even 10 3267.2.a.bi.1.1 8
99.5 odd 30 891.2.n.h.379.1 32
99.16 even 15 891.2.n.h.676.1 32
99.38 odd 30 891.2.n.h.676.4 32
99.49 even 15 891.2.n.h.379.4 32
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
297.2.f.b.82.1 16 11.5 even 5 inner
297.2.f.b.82.4 yes 16 33.5 odd 10 inner
297.2.f.b.163.1 yes 16 1.1 even 1 trivial
297.2.f.b.163.4 yes 16 3.2 odd 2 inner
891.2.n.h.379.1 32 99.5 odd 30
891.2.n.h.379.4 32 99.49 even 15
891.2.n.h.460.1 32 9.4 even 3
891.2.n.h.460.4 32 9.5 odd 6
891.2.n.h.676.1 32 99.16 even 15
891.2.n.h.676.4 32 99.38 odd 30
891.2.n.h.757.1 32 9.2 odd 6
891.2.n.h.757.4 32 9.7 even 3
3267.2.a.bi.1.1 8 33.29 even 10
3267.2.a.bi.1.8 8 11.7 odd 10
3267.2.a.bj.1.1 8 11.4 even 5
3267.2.a.bj.1.8 8 33.26 odd 10