Properties

Label 637.2.g.l.263.3
Level 637637
Weight 22
Character 637.263
Analytic conductor 5.0865.086
Analytic rank 00
Dimension 1212
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [637,2,Mod(263,637)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(637, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4, 2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("637.263");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 637=7213 637 = 7^{2} \cdot 13
Weight: k k == 2 2
Character orbit: [χ][\chi] == 637.g (of order 33, degree 22, not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 5.086470608765.08647060876
Analytic rank: 00
Dimension: 1212
Relative dimension: 66 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: Q[x]/(x12)\mathbb{Q}[x]/(x^{12} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12x11+7x102x9+33x811x7+55x6+17x5+47x4+x3+8x2+x+1 x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 Copy content Toggle raw display
Coefficient ring: Z[a1,,a4]\Z[a_1, \ldots, a_{4}]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 91)
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 263.3
Root 0.4374420.757672i-0.437442 - 0.757672i of defining polynomial
Character χ\chi == 637.263
Dual form 637.2.g.l.373.3

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.1340630.232203i)q2+1.14301q3+(0.964054+1.66979i)q4+(1.280882.21854i)q5+(0.1532350.265410i)q6+1.05323q81.69353q90.686871q10+3.94600q11+(1.10192+1.90859i)q12+(3.15374+1.74755i)q13+(1.464052.53582i)q15+(1.78691+3.09502i)q16+(0.392550+0.679916i)q17+(0.227039+0.393243i)q18+7.49527q19+(2.469674.27760i)q20+(0.5290110.916274i)q22+(3.977596.88938i)q23+1.20385q24+(0.781294+1.35324i)q25+(0.8285850.498028i)q265.36475q27+(1.175862.03666i)q290.785100q30+(1.27718+2.21215i)q31+(1.53234+2.65409i)q32+4.51032q33+0.210505q34+(1.632662.82784i)q36+(3.37858+5.85187i)q37+(1.004841.74043i)q38+(3.60475+1.99746i)q39+(1.349052.33663i)q40+(1.218742.11091i)q41+(1.124731.94809i)q43+(3.80416+6.58900i)q44+(2.16920+3.75717i)q45+(1.066491.84722i)q46+(0.658276+1.14017i)q47+(2.04246+3.53764i)q48+(0.209485+0.362838i)q50+(0.448688+0.777151i)q51+(0.122340+6.95082i)q52+(4.63977+8.03632i)q53+(0.719212+1.24571i)q54+(5.054348.75438i)q55+8.56716q570.630558q58+(4.483357.76540i)q59+(2.822864.88933i)q609.44547q61+(0.342445+0.593132i)q626.32592q64+(0.1625469.23511i)q65+(0.6046651.04731i)q661.35256q67+(0.756879+1.31095i)q68+(4.546427.87463i)q69+(6.15808+10.6661i)q711.78367q72+(0.3842950.665619i)q73+(0.905882+1.56903i)q74+(0.893026+1.54677i)q75+(7.22585+12.5155i)q76+(0.9470800.569251i)q78+(3.096425.36316i)q79+9.15525q801.05136q810.653548q82+1.07292q83+(1.005621.74178i)q85+(0.3015680.522332i)q86+(1.344022.32792i)q87+4.15603q88+(3.831496.63634i)q89+1.16324q90+15.3384q92+(1.45983+2.52850i)q93+0.353001q94+(9.6005216.6286i)q95+(1.75148+3.03365i)q96+(1.18601+2.05423i)q976.68267q99+O(q100)q+(0.134063 - 0.232203i) q^{2} +1.14301 q^{3} +(0.964054 + 1.66979i) q^{4} +(-1.28088 - 2.21854i) q^{5} +(0.153235 - 0.265410i) q^{6} +1.05323 q^{8} -1.69353 q^{9} -0.686871 q^{10} +3.94600 q^{11} +(1.10192 + 1.90859i) q^{12} +(3.15374 + 1.74755i) q^{13} +(-1.46405 - 2.53582i) q^{15} +(-1.78691 + 3.09502i) q^{16} +(0.392550 + 0.679916i) q^{17} +(-0.227039 + 0.393243i) q^{18} +7.49527 q^{19} +(2.46967 - 4.27760i) q^{20} +(0.529011 - 0.916274i) q^{22} +(3.97759 - 6.88938i) q^{23} +1.20385 q^{24} +(-0.781294 + 1.35324i) q^{25} +(0.828585 - 0.498028i) q^{26} -5.36475 q^{27} +(-1.17586 - 2.03666i) q^{29} -0.785100 q^{30} +(-1.27718 + 2.21215i) q^{31} +(1.53234 + 2.65409i) q^{32} +4.51032 q^{33} +0.210505 q^{34} +(-1.63266 - 2.82784i) q^{36} +(-3.37858 + 5.85187i) q^{37} +(1.00484 - 1.74043i) q^{38} +(3.60475 + 1.99746i) q^{39} +(-1.34905 - 2.33663i) q^{40} +(-1.21874 - 2.11091i) q^{41} +(1.12473 - 1.94809i) q^{43} +(3.80416 + 6.58900i) q^{44} +(2.16920 + 3.75717i) q^{45} +(-1.06649 - 1.84722i) q^{46} +(0.658276 + 1.14017i) q^{47} +(-2.04246 + 3.53764i) q^{48} +(0.209485 + 0.362838i) q^{50} +(0.448688 + 0.777151i) q^{51} +(0.122340 + 6.95082i) q^{52} +(-4.63977 + 8.03632i) q^{53} +(-0.719212 + 1.24571i) q^{54} +(-5.05434 - 8.75438i) q^{55} +8.56716 q^{57} -0.630558 q^{58} +(-4.48335 - 7.76540i) q^{59} +(2.82286 - 4.88933i) q^{60} -9.44547 q^{61} +(0.342445 + 0.593132i) q^{62} -6.32592 q^{64} +(-0.162546 - 9.23511i) q^{65} +(0.604665 - 1.04731i) q^{66} -1.35256 q^{67} +(-0.756879 + 1.31095i) q^{68} +(4.54642 - 7.87463i) q^{69} +(-6.15808 + 10.6661i) q^{71} -1.78367 q^{72} +(0.384295 - 0.665619i) q^{73} +(0.905882 + 1.56903i) q^{74} +(-0.893026 + 1.54677i) q^{75} +(7.22585 + 12.5155i) q^{76} +(0.947080 - 0.569251i) q^{78} +(-3.09642 - 5.36316i) q^{79} +9.15525 q^{80} -1.05136 q^{81} -0.653548 q^{82} +1.07292 q^{83} +(1.00562 - 1.74178i) q^{85} +(-0.301568 - 0.522332i) q^{86} +(-1.34402 - 2.32792i) q^{87} +4.15603 q^{88} +(3.83149 - 6.63634i) q^{89} +1.16324 q^{90} +15.3384 q^{92} +(-1.45983 + 2.52850i) q^{93} +0.353001 q^{94} +(-9.60052 - 16.6286i) q^{95} +(1.75148 + 3.03365i) q^{96} +(-1.18601 + 2.05423i) q^{97} -6.68267 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+2q2+2q34q4q5+9q66q86q9+8q108q115q12+2q132q15+8q165q17+3q182q19+q205q22q23+20q99+O(q100) 12 q + 2 q^{2} + 2 q^{3} - 4 q^{4} - q^{5} + 9 q^{6} - 6 q^{8} - 6 q^{9} + 8 q^{10} - 8 q^{11} - 5 q^{12} + 2 q^{13} - 2 q^{15} + 8 q^{16} - 5 q^{17} + 3 q^{18} - 2 q^{19} + q^{20} - 5 q^{22} - q^{23}+ \cdots - 20 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/637Z)×\left(\mathbb{Z}/637\mathbb{Z}\right)^\times.

nn 197197 248248
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\right) e(23)e\left(\frac{2}{3}\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 0.134063 0.232203i 0.0947966 0.164193i −0.814727 0.579845i 0.803113π-0.803113\pi
0.909524 + 0.415652i 0.136447π0.136447\pi
33 1.14301 0.659917 0.329958 0.943996i 0.392965π-0.392965\pi
0.329958 + 0.943996i 0.392965π0.392965\pi
44 0.964054 + 1.66979i 0.482027 + 0.834896i
55 −1.28088 2.21854i −0.572826 0.992163i −0.996274 0.0862431i 0.972514π-0.972514\pi
0.423448 0.905920i 0.360820π-0.360820\pi
66 0.153235 0.265410i 0.0625578 0.108353i
77 0 0
88 1.05323 0.372371
99 −1.69353 −0.564510
1010 −0.686871 −0.217208
1111 3.94600 1.18976 0.594882 0.803813i 0.297199π-0.297199\pi
0.594882 + 0.803813i 0.297199π0.297199\pi
1212 1.10192 + 1.90859i 0.318098 + 0.550961i
1313 3.15374 + 1.74755i 0.874690 + 0.484682i
1414 0 0
1515 −1.46405 2.53582i −0.378017 0.654745i
1616 −1.78691 + 3.09502i −0.446728 + 0.773755i
1717 0.392550 + 0.679916i 0.0952073 + 0.164904i 0.909695 0.415277i 0.136315π-0.136315\pi
−0.814488 + 0.580181i 0.802982π0.802982\pi
1818 −0.227039 + 0.393243i −0.0535136 + 0.0926883i
1919 7.49527 1.71953 0.859767 0.510687i 0.170609π-0.170609\pi
0.859767 + 0.510687i 0.170609π0.170609\pi
2020 2.46967 4.27760i 0.552235 0.956500i
2121 0 0
2222 0.529011 0.916274i 0.112786 0.195350i
2323 3.97759 6.88938i 0.829384 1.43654i −0.0691375 0.997607i 0.522025π-0.522025\pi
0.898522 0.438929i 0.144642π-0.144642\pi
2424 1.20385 0.245734
2525 −0.781294 + 1.35324i −0.156259 + 0.270648i
2626 0.828585 0.498028i 0.162499 0.0976714i
2727 −5.36475 −1.03245
2828 0 0
2929 −1.17586 2.03666i −0.218353 0.378198i 0.735952 0.677034i 0.236735π-0.236735\pi
−0.954304 + 0.298836i 0.903402π0.903402\pi
3030 −0.785100 −0.143339
3131 −1.27718 + 2.21215i −0.229389 + 0.397313i −0.957627 0.288011i 0.907006π-0.907006\pi
0.728238 + 0.685324i 0.240339π0.240339\pi
3232 1.53234 + 2.65409i 0.270882 + 0.469182i
3333 4.51032 0.785145
3434 0.210505 0.0361013
3535 0 0
3636 −1.63266 2.82784i −0.272109 0.471307i
3737 −3.37858 + 5.85187i −0.555435 + 0.962041i 0.442435 + 0.896801i 0.354115π0.354115\pi
−0.997870 + 0.0652406i 0.979219π0.979219\pi
3838 1.00484 1.74043i 0.163006 0.282334i
3939 3.60475 + 1.99746i 0.577223 + 0.319850i
4040 −1.34905 2.33663i −0.213304 0.369453i
4141 −1.21874 2.11091i −0.190335 0.329669i 0.755027 0.655694i 0.227624π-0.227624\pi
−0.945361 + 0.326025i 0.894291π0.894291\pi
4242 0 0
4343 1.12473 1.94809i 0.171520 0.297081i −0.767432 0.641131i 0.778466π-0.778466\pi
0.938951 + 0.344050i 0.111799π0.111799\pi
4444 3.80416 + 6.58900i 0.573499 + 0.993329i
4545 2.16920 + 3.75717i 0.323366 + 0.560086i
4646 −1.06649 1.84722i −0.157246 0.272357i
4747 0.658276 + 1.14017i 0.0960195 + 0.166311i 0.910034 0.414534i 0.136056π-0.136056\pi
−0.814014 + 0.580845i 0.802722π0.802722\pi
4848 −2.04246 + 3.53764i −0.294803 + 0.510614i
4949 0 0
5050 0.209485 + 0.362838i 0.0296256 + 0.0513130i
5151 0.448688 + 0.777151i 0.0628289 + 0.108823i
5252 0.122340 + 6.95082i 0.0169655 + 0.963905i
5353 −4.63977 + 8.03632i −0.637321 + 1.10387i 0.348697 + 0.937236i 0.386624π0.386624\pi
−0.986018 + 0.166637i 0.946709π0.946709\pi
5454 −0.719212 + 1.24571i −0.0978724 + 0.169520i
5555 −5.05434 8.75438i −0.681528 1.18044i
5656 0 0
5757 8.56716 1.13475
5858 −0.630558 −0.0827963
5959 −4.48335 7.76540i −0.583683 1.01097i −0.995038 0.0994935i 0.968278π-0.968278\pi
0.411355 0.911475i 0.365056π-0.365056\pi
6060 2.82286 4.88933i 0.364429 0.631210i
6161 −9.44547 −1.20937 −0.604684 0.796465i 0.706701π-0.706701\pi
−0.604684 + 0.796465i 0.706701π0.706701\pi
6262 0.342445 + 0.593132i 0.0434906 + 0.0753279i
6363 0 0
6464 −6.32592 −0.790741
6565 −0.162546 9.23511i −0.0201613 1.14547i
6666 0.604665 1.04731i 0.0744291 0.128915i
6767 −1.35256 −0.165242 −0.0826209 0.996581i 0.526329π-0.526329\pi
−0.0826209 + 0.996581i 0.526329π0.526329\pi
6868 −0.756879 + 1.31095i −0.0917851 + 0.158976i
6969 4.54642 7.87463i 0.547324 0.947994i
7070 0 0
7171 −6.15808 + 10.6661i −0.730829 + 1.26583i 0.225700 + 0.974197i 0.427533π0.427533\pi
−0.956529 + 0.291637i 0.905800π0.905800\pi
7272 −1.78367 −0.210207
7373 0.384295 0.665619i 0.0449783 0.0779048i −0.842660 0.538446i 0.819011π-0.819011\pi
0.887638 + 0.460542i 0.152345π0.152345\pi
7474 0.905882 + 1.56903i 0.105307 + 0.182396i
7575 −0.893026 + 1.54677i −0.103118 + 0.178605i
7676 7.22585 + 12.5155i 0.828862 + 1.43563i
7777 0 0
7878 0.947080 0.569251i 0.107236 0.0644550i
7979 −3.09642 5.36316i −0.348375 0.603402i 0.637586 0.770379i 0.279933π-0.279933\pi
−0.985961 + 0.166976i 0.946600π0.946600\pi
8080 9.15525 1.02359
8181 −1.05136 −0.116818
8282 −0.653548 −0.0721723
8383 1.07292 0.117768 0.0588841 0.998265i 0.481246π-0.481246\pi
0.0588841 + 0.998265i 0.481246π0.481246\pi
8484 0 0
8585 1.00562 1.74178i 0.109074 0.188922i
8686 −0.301568 0.522332i −0.0325190 0.0563245i
8787 −1.34402 2.32792i −0.144094 0.249579i
8888 4.15603 0.443034
8989 3.83149 6.63634i 0.406138 0.703451i −0.588316 0.808631i 0.700209π-0.700209\pi
0.994453 + 0.105180i 0.0335420π0.0335420\pi
9090 1.16324 0.122616
9191 0 0
9292 15.3384 1.59914
9393 −1.45983 + 2.52850i −0.151378 + 0.262194i
9494 0.353001 0.0364093
9595 −9.60052 16.6286i −0.984993 1.70606i
9696 1.75148 + 3.03365i 0.178760 + 0.309621i
9797 −1.18601 + 2.05423i −0.120421 + 0.208575i −0.919934 0.392074i 0.871758π-0.871758\pi
0.799513 + 0.600649i 0.205091π0.205091\pi
9898 0 0
9999 −6.68267 −0.671634
100100 −3.01284 −0.301284
101101 0.797330 0.0793373 0.0396686 0.999213i 0.487370π-0.487370\pi
0.0396686 + 0.999213i 0.487370π0.487370\pi
102102 0.240609 0.0238239
103103 1.08309 + 1.87597i 0.106720 + 0.184844i 0.914440 0.404722i 0.132632π-0.132632\pi
−0.807720 + 0.589567i 0.799299π0.799299\pi
104104 3.32160 + 1.84056i 0.325710 + 0.180482i
105105 0 0
106106 1.24404 + 2.15474i 0.120832 + 0.209287i
107107 5.76311 9.98201i 0.557141 0.964997i −0.440592 0.897707i 0.645232π-0.645232\pi
0.997733 0.0672896i 0.0214351π-0.0214351\pi
108108 −5.17191 8.95801i −0.497667 0.861985i
109109 −4.03912 + 6.99595i −0.386877 + 0.670091i −0.992028 0.126020i 0.959780π-0.959780\pi
0.605151 + 0.796111i 0.293113π0.293113\pi
110110 −2.71039 −0.258426
111111 −3.86174 + 6.68874i −0.366541 + 0.634867i
112112 0 0
113113 −4.02067 + 6.96401i −0.378233 + 0.655119i −0.990805 0.135296i 0.956802π-0.956802\pi
0.612572 + 0.790415i 0.290135π0.290135\pi
114114 1.14854 1.98932i 0.107570 0.186317i
115115 −20.3792 −1.90037
116116 2.26719 3.92690i 0.210504 0.364603i
117117 −5.34096 2.95952i −0.493772 0.273608i
118118 −2.40420 −0.221325
119119 0 0
120120 −1.54198 2.67079i −0.140763 0.243808i
121121 4.57093 0.415539
122122 −1.26628 + 2.19327i −0.114644 + 0.198569i
123123 −1.39303 2.41279i −0.125605 0.217554i
124124 −4.92510 −0.442287
125125 −8.80581 −0.787615
126126 0 0
127127 −0.894023 1.54849i −0.0793317 0.137406i 0.823630 0.567127i 0.191945π-0.191945\pi
−0.902962 + 0.429721i 0.858612π0.858612\pi
128128 −3.91275 + 6.77709i −0.345842 + 0.599015i
129129 1.28558 2.22668i 0.113189 0.196049i
130130 −2.16621 1.20034i −0.189989 0.105277i
131131 −3.19545 5.53469i −0.279188 0.483568i 0.691995 0.721902i 0.256732π-0.256732\pi
−0.971183 + 0.238334i 0.923399π0.923399\pi
132132 4.34819 + 7.53129i 0.378461 + 0.655514i
133133 0 0
134134 −0.181328 + 0.314069i −0.0156644 + 0.0271315i
135135 6.87158 + 11.9019i 0.591412 + 1.02436i
136136 0.413443 + 0.716105i 0.0354525 + 0.0614055i
137137 −5.01827 8.69190i −0.428740 0.742599i 0.568022 0.823014i 0.307709π-0.307709\pi
−0.996762 + 0.0804144i 0.974376π0.974376\pi
138138 −1.21901 2.11139i −0.103769 0.179733i
139139 −2.77278 + 4.80260i −0.235184 + 0.407351i −0.959326 0.282300i 0.908903π-0.908903\pi
0.724142 + 0.689651i 0.242236π0.242236\pi
140140 0 0
141141 0.752416 + 1.30322i 0.0633648 + 0.109751i
142142 1.65114 + 2.85985i 0.138560 + 0.239993i
143143 12.4447 + 6.89582i 1.04068 + 0.576658i
144144 3.02619 5.24151i 0.252182 0.436793i
145145 −3.01228 + 5.21742i −0.250156 + 0.433283i
146146 −0.103039 0.178469i −0.00852759 0.0147702i
147147 0 0
148148 −13.0285 −1.07094
149149 18.4651 1.51272 0.756359 0.654157i 0.226976π-0.226976\pi
0.756359 + 0.654157i 0.226976π0.226976\pi
150150 0.239443 + 0.414727i 0.0195504 + 0.0338623i
151151 −0.803678 + 1.39201i −0.0654024 + 0.113280i −0.896872 0.442289i 0.854166π-0.854166\pi
0.831470 + 0.555570i 0.187500π0.187500\pi
152152 7.89421 0.640305
153153 −0.664795 1.15146i −0.0537455 0.0930900i
154154 0 0
155155 6.54366 0.525600
156156 0.139836 + 7.94485i 0.0111958 + 0.636097i
157157 −0.822967 + 1.42542i −0.0656799 + 0.113761i −0.896995 0.442040i 0.854255π-0.854255\pi
0.831315 + 0.555801i 0.187588π0.187588\pi
158158 −1.66046 −0.132099
159159 −5.30330 + 9.18558i −0.420579 + 0.728464i
160160 3.92548 6.79913i 0.310337 0.537519i
161161 0 0
162162 −0.140949 + 0.244130i −0.0110740 + 0.0191807i
163163 −6.54819 −0.512894 −0.256447 0.966558i 0.582552π-0.582552\pi
−0.256447 + 0.966558i 0.582552π0.582552\pi
164164 2.34986 4.07007i 0.183493 0.317819i
165165 −5.77716 10.0063i −0.449751 0.778992i
166166 0.143838 0.249135i 0.0111640 0.0193367i
167167 4.77440 + 8.26950i 0.369454 + 0.639913i 0.989480 0.144668i 0.0462114π-0.0462114\pi
−0.620026 + 0.784581i 0.712878π0.712878\pi
168168 0 0
169169 6.89216 + 11.0226i 0.530166 + 0.847894i
170170 −0.269631 0.467015i −0.0206798 0.0358184i
171171 −12.6935 −0.970694
172172 4.33720 0.330709
173173 −11.1316 −0.846322 −0.423161 0.906054i 0.639080π-0.639080\pi
−0.423161 + 0.906054i 0.639080π0.639080\pi
174174 −0.720733 −0.0546386
175175 0 0
176176 −7.05115 + 12.2130i −0.531501 + 0.920586i
177177 −5.12451 8.87592i −0.385182 0.667155i
178178 −1.02732 1.77937i −0.0770009 0.133369i
179179 −12.6435 −0.945017 −0.472508 0.881326i 0.656651π-0.656651\pi
−0.472508 + 0.881326i 0.656651π0.656651\pi
180180 −4.18246 + 7.24424i −0.311742 + 0.539954i
181181 −14.9158 −1.10868 −0.554341 0.832289i 0.687030π-0.687030\pi
−0.554341 + 0.832289i 0.687030π0.687030\pi
182182 0 0
183183 −10.7963 −0.798082
184184 4.18930 7.25607i 0.308839 0.534925i
185185 17.3102 1.27267
186186 0.391418 + 0.677956i 0.0287001 + 0.0497101i
187187 1.54900 + 2.68295i 0.113274 + 0.196197i
188188 −1.26923 + 2.19837i −0.0925680 + 0.160332i
189189 0 0
190190 −5.14829 −0.373496
191191 −14.1306 −1.02245 −0.511226 0.859447i 0.670808π-0.670808\pi
−0.511226 + 0.859447i 0.670808π0.670808\pi
192192 −7.23059 −0.521823
193193 3.89454 0.280335 0.140167 0.990128i 0.455236π-0.455236\pi
0.140167 + 0.990128i 0.455236π0.455236\pi
194194 0.317999 + 0.550790i 0.0228310 + 0.0395444i
195195 −0.185791 10.5558i −0.0133048 0.755917i
196196 0 0
197197 5.85445 + 10.1402i 0.417112 + 0.722459i 0.995648 0.0931979i 0.0297089π-0.0297089\pi
−0.578536 + 0.815657i 0.696376π0.696376\pi
198198 −0.895897 + 1.55174i −0.0636686 + 0.110277i
199199 1.74842 + 3.02835i 0.123942 + 0.214674i 0.921319 0.388808i 0.127113π-0.127113\pi
−0.797377 + 0.603482i 0.793780π0.793780\pi
200200 −0.822878 + 1.42527i −0.0581863 + 0.100782i
201201 −1.54599 −0.109046
202202 0.106892 0.185143i 0.00752090 0.0130266i
203203 0 0
204204 −0.865120 + 1.49843i −0.0605705 + 0.104911i
205205 −3.12210 + 5.40764i −0.218057 + 0.377686i
206206 0.580807 0.0404667
207207 −6.73617 + 11.6674i −0.468196 + 0.810939i
208208 −11.0441 + 6.63818i −0.765774 + 0.460275i
209209 29.5764 2.04584
210210 0 0
211211 −9.50258 16.4589i −0.654184 1.13308i −0.982098 0.188373i 0.939679π-0.939679\pi
0.327913 0.944708i 0.393655π-0.393655\pi
212212 −17.8920 −1.22882
213213 −7.03874 + 12.1915i −0.482286 + 0.835345i
214214 −1.54524 2.67643i −0.105630 0.182957i
215215 −5.76256 −0.393004
216216 −5.65029 −0.384453
217217 0 0
218218 1.08299 + 1.87579i 0.0733492 + 0.127045i
219219 0.439253 0.760808i 0.0296820 0.0514106i
220220 9.74533 16.8794i 0.657030 1.13801i
221221 0.0498153 + 2.83028i 0.00335094 + 0.190385i
222222 1.03543 + 1.79342i 0.0694936 + 0.120366i
223223 −5.98311 10.3630i −0.400658 0.693961i 0.593147 0.805094i 0.297885π-0.297885\pi
−0.993805 + 0.111133i 0.964552π0.964552\pi
224224 0 0
225225 1.32315 2.29175i 0.0882097 0.152784i
226226 1.07804 + 1.86723i 0.0717104 + 0.124206i
227227 7.69209 + 13.3231i 0.510542 + 0.884284i 0.999925 + 0.0122157i 0.00388847π0.00388847\pi
−0.489384 + 0.872069i 0.662778π0.662778\pi
228228 8.25921 + 14.3054i 0.546980 + 0.947396i
229229 4.33084 + 7.50123i 0.286190 + 0.495695i 0.972897 0.231239i 0.0742779π-0.0742779\pi
−0.686707 + 0.726934i 0.740945π0.740945\pi
230230 −2.73209 + 4.73212i −0.180149 + 0.312027i
231231 0 0
232232 −1.23845 2.14506i −0.0813082 0.140830i
233233 −10.1253 17.5376i −0.663333 1.14893i −0.979734 0.200301i 0.935808π-0.935808\pi
0.316402 0.948625i 0.397525π-0.397525\pi
234234 −1.40323 + 0.843426i −0.0917322 + 0.0551365i
235235 1.68634 2.92083i 0.110005 0.190534i
236236 8.64440 14.9725i 0.562702 0.974629i
237237 −3.53924 6.13014i −0.229898 0.398195i
238238 0 0
239239 16.5526 1.07070 0.535350 0.844630i 0.320180π-0.320180\pi
0.535350 + 0.844630i 0.320180π0.320180\pi
240240 10.4645 0.675483
241241 −8.20038 14.2035i −0.528233 0.914926i −0.999458 0.0329132i 0.989522π-0.989522\pi
0.471225 0.882013i 0.343812π-0.343812\pi
242242 0.612791 1.06138i 0.0393917 0.0682284i
243243 14.8925 0.955356
244244 −9.10595 15.7720i −0.582949 1.00970i
245245 0 0
246246 −0.747011 −0.0476277
247247 23.6381 + 13.0983i 1.50406 + 0.833427i
248248 −1.34516 + 2.32989i −0.0854178 + 0.147948i
249249 1.22636 0.0777172
250250 −1.18053 + 2.04474i −0.0746632 + 0.129321i
251251 −10.2154 + 17.6935i −0.644788 + 1.11681i 0.339563 + 0.940583i 0.389721π0.389721\pi
−0.984350 + 0.176222i 0.943612π0.943612\pi
252252 0 0
253253 15.6956 27.1855i 0.986772 1.70914i
254254 −0.479420 −0.0300815
255255 1.14943 1.99087i 0.0719800 0.124673i
256256 −5.27682 9.13972i −0.329801 0.571232i
257257 6.88895 11.9320i 0.429721 0.744299i −0.567127 0.823630i 0.691945π-0.691945\pi
0.996848 + 0.0793315i 0.0252786π0.0252786\pi
258258 −0.344695 0.597030i −0.0214598 0.0371695i
259259 0 0
260260 15.2640 9.17456i 0.946633 0.568982i
261261 1.99136 + 3.44914i 0.123262 + 0.213496i
262262 −1.71356 −0.105864
263263 25.9173 1.59813 0.799065 0.601244i 0.205328π-0.205328\pi
0.799065 + 0.601244i 0.205328π0.205328\pi
264264 4.75038 0.292366
265265 23.7719 1.46030
266266 0 0
267267 4.37943 7.58540i 0.268017 0.464219i
268268 −1.30394 2.25850i −0.0796510 0.137960i
269269 −15.0333 26.0384i −0.916596 1.58759i −0.804547 0.593889i 0.797592π-0.797592\pi
−0.112050 0.993703i 0.535742π-0.535742\pi
270270 3.68489 0.224255
271271 7.22527 12.5145i 0.438904 0.760204i −0.558701 0.829369i 0.688700π-0.688700\pi
0.997605 + 0.0691651i 0.0220335π0.0220335\pi
272272 −2.80581 −0.170127
273273 0 0
274274 −2.69105 −0.162572
275275 −3.08299 + 5.33989i −0.185911 + 0.322008i
276276 17.5320 1.05530
277277 7.66274 + 13.2723i 0.460409 + 0.797452i 0.998981 0.0451272i 0.0143693π-0.0143693\pi
−0.538572 + 0.842580i 0.681036π0.681036\pi
278278 0.743453 + 1.28770i 0.0445894 + 0.0772310i
279279 2.16295 3.74634i 0.129492 0.224287i
280280 0 0
281281 5.29279 0.315741 0.157871 0.987460i 0.449537π-0.449537\pi
0.157871 + 0.987460i 0.449537π0.449537\pi
282282 0.403483 0.0240271
283283 30.7845 1.82995 0.914975 0.403511i 0.132210π-0.132210\pi
0.914975 + 0.403511i 0.132210π0.132210\pi
284284 −23.7469 −1.40912
285285 −10.9735 19.0066i −0.650013 1.12586i
286286 3.26960 1.96522i 0.193335 0.116206i
287287 0 0
288288 −2.59507 4.49479i −0.152916 0.264858i
289289 8.19181 14.1886i 0.481871 0.834625i
290290 0.807667 + 1.39892i 0.0474279 + 0.0821474i
291291 −1.35562 + 2.34800i −0.0794677 + 0.137642i
292292 1.48193 0.0867231
293293 −8.75864 + 15.1704i −0.511685 + 0.886265i 0.488223 + 0.872719i 0.337645π0.337645\pi
−0.999908 + 0.0135461i 0.995688π0.995688\pi
294294 0 0
295295 −11.4853 + 19.8930i −0.668697 + 1.15822i
296296 −3.55840 + 6.16333i −0.206828 + 0.358237i
297297 −21.1693 −1.22837
298298 2.47548 4.28765i 0.143400 0.248377i
299299 24.5838 14.7763i 1.42172 0.854536i
300300 −3.44370 −0.198822
301301 0 0
302302 0.215486 + 0.373233i 0.0123998 + 0.0214772i
303303 0.911355 0.0523560
304304 −13.3934 + 23.1980i −0.768163 + 1.33050i
305305 12.0985 + 20.9552i 0.692757 + 1.19989i
306306 −0.356497 −0.0203796
307307 8.63573 0.492867 0.246434 0.969160i 0.420741π-0.420741\pi
0.246434 + 0.969160i 0.420741π0.420741\pi
308308 0 0
309309 1.23798 + 2.14425i 0.0704262 + 0.121982i
310310 0.877260 1.51946i 0.0498250 0.0862995i
311311 −8.21130 + 14.2224i −0.465620 + 0.806478i −0.999229 0.0392535i 0.987502π-0.987502\pi
0.533609 + 0.845731i 0.320835π0.320835\pi
312312 3.79662 + 2.10378i 0.214941 + 0.119103i
313313 5.02308 + 8.70024i 0.283921 + 0.491766i 0.972347 0.233541i 0.0750312π-0.0750312\pi
−0.688426 + 0.725307i 0.741698π0.741698\pi
314314 0.220658 + 0.382191i 0.0124525 + 0.0215683i
315315 0 0
316316 5.97024 10.3408i 0.335852 0.581713i
317317 −5.07249 8.78581i −0.284899 0.493460i 0.687685 0.726009i 0.258627π-0.258627\pi
−0.972585 + 0.232549i 0.925294π0.925294\pi
318318 1.42195 + 2.46289i 0.0797389 + 0.138112i
319319 −4.63996 8.03665i −0.259788 0.449966i
320320 8.10273 + 14.0343i 0.452957 + 0.784544i
321321 6.58729 11.4095i 0.367667 0.636817i
322322 0 0
323323 2.94227 + 5.09616i 0.163712 + 0.283558i
324324 −1.01357 1.75556i −0.0563095 0.0975310i
325325 −4.82885 + 2.90242i −0.267856 + 0.160998i
326326 −0.877867 + 1.52051i −0.0486206 + 0.0842133i
327327 −4.61674 + 7.99644i −0.255307 + 0.442204i
328328 −1.28360 2.22327i −0.0708751 0.122759i
329329 0 0
330330 −3.09801 −0.170540
331331 2.31916 0.127473 0.0637363 0.997967i 0.479698π-0.479698\pi
0.0637363 + 0.997967i 0.479698π0.479698\pi
332332 1.03435 + 1.79155i 0.0567675 + 0.0983242i
333333 5.72172 9.91032i 0.313549 0.543082i
334334 2.56027 0.140092
335335 1.73247 + 3.00072i 0.0946547 + 0.163947i
336336 0 0
337337 −15.9998 −0.871565 −0.435783 0.900052i 0.643528π-0.643528\pi
−0.435783 + 0.900052i 0.643528π0.643528\pi
338338 3.48347 0.122662i 0.189476 0.00667193i
339339 −4.59567 + 7.95993i −0.249602 + 0.432324i
340340 3.87788 0.210307
341341 −5.03977 + 8.72913i −0.272919 + 0.472709i
342342 −1.70172 + 2.94747i −0.0920185 + 0.159381i
343343 0 0
344344 1.18459 2.05178i 0.0638690 0.110624i
345345 −23.2936 −1.25409
346346 −1.49234 + 2.58480i −0.0802285 + 0.138960i
347347 11.4104 + 19.7634i 0.612543 + 1.06096i 0.990810 + 0.135259i 0.0431867π0.0431867\pi
−0.378267 + 0.925696i 0.623480π0.623480\pi
348348 2.59142 4.48848i 0.138915 0.240608i
349349 −11.3511 19.6607i −0.607612 1.05241i −0.991633 0.129090i 0.958794π-0.958794\pi
0.384021 0.923324i 0.374539π-0.374539\pi
350350 0 0
351351 −16.9190 9.37515i −0.903071 0.500408i
352352 6.04662 + 10.4731i 0.322286 + 0.558216i
353353 27.2644 1.45114 0.725568 0.688150i 0.241577π-0.241577\pi
0.725568 + 0.688150i 0.241577π0.241577\pi
354354 −2.74802 −0.146056
355355 31.5510 1.67455
356356 14.7751 0.783077
357357 0 0
358358 −1.69502 + 2.93585i −0.0895844 + 0.155165i
359359 7.21309 + 12.4934i 0.380692 + 0.659378i 0.991161 0.132662i 0.0423524π-0.0423524\pi
−0.610469 + 0.792040i 0.709019π0.709019\pi
360360 2.28466 + 3.95715i 0.120412 + 0.208560i
361361 37.1791 1.95679
362362 −1.99965 + 3.46350i −0.105099 + 0.182037i
363363 5.22461 0.274221
364364 0 0
365365 −1.96894 −0.103059
366366 −1.44737 + 2.50693i −0.0756555 + 0.131039i
367367 11.3917 0.594643 0.297322 0.954777i 0.403907π-0.403907\pi
0.297322 + 0.954777i 0.403907π0.403907\pi
368368 14.2152 + 24.6214i 0.741018 + 1.28348i
369369 2.06397 + 3.57489i 0.107446 + 0.186102i
370370 2.32065 4.01948i 0.120645 0.208963i
371371 0 0
372372 −5.62943 −0.291872
373373 −30.9629 −1.60320 −0.801599 0.597862i 0.796017π-0.796017\pi
−0.801599 + 0.597862i 0.796017π0.796017\pi
374374 0.830653 0.0429521
375375 −10.0651 −0.519760
376376 0.693313 + 1.20085i 0.0357549 + 0.0619293i
377377 −0.149219 8.47796i −0.00768518 0.436637i
378378 0 0
379379 −5.29330 9.16826i −0.271898 0.470942i 0.697450 0.716634i 0.254318π-0.254318\pi
−0.969348 + 0.245692i 0.920985π0.920985\pi
380380 18.5109 32.0617i 0.949587 1.64473i
381381 −1.02188 1.76994i −0.0523523 0.0906768i
382382 −1.89438 + 3.28116i −0.0969249 + 0.167879i
383383 −30.7517 −1.57134 −0.785668 0.618648i 0.787681π-0.787681\pi
−0.785668 + 0.618648i 0.787681π0.787681\pi
384384 −4.47231 + 7.74627i −0.228227 + 0.395300i
385385 0 0
386386 0.522112 0.904324i 0.0265748 0.0460289i
387387 −1.90476 + 3.29915i −0.0968246 + 0.167705i
388388 −4.57351 −0.232185
389389 8.18978 14.1851i 0.415239 0.719214i −0.580215 0.814463i 0.697031π-0.697031\pi
0.995453 + 0.0952492i 0.0303648π0.0303648\pi
390390 −2.47600 1.37200i −0.125377 0.0694738i
391391 6.24561 0.315854
392392 0 0
393393 −3.65243 6.32620i −0.184241 0.319114i
394394 3.13945 0.158163
395395 −7.93227 + 13.7391i −0.399116 + 0.691289i
396396 −6.44246 11.1587i −0.323746 0.560744i
397397 15.8827 0.797127 0.398564 0.917141i 0.369509π-0.369509\pi
0.398564 + 0.917141i 0.369509π0.369509\pi
398398 0.937591 0.0469972
399399 0 0
400400 −2.79221 4.83624i −0.139610 0.241812i
401401 −3.31787 + 5.74671i −0.165686 + 0.286977i −0.936899 0.349601i 0.886317π-0.886317\pi
0.771212 + 0.636578i 0.219651π0.219651\pi
402402 −0.207259 + 0.358984i −0.0103372 + 0.0179045i
403403 −7.89373 + 4.74460i −0.393215 + 0.236345i
404404 0.768670 + 1.33137i 0.0382427 + 0.0662384i
405405 1.34667 + 2.33250i 0.0669164 + 0.115903i
406406 0 0
407407 −13.3319 + 23.0915i −0.660836 + 1.14460i
408408 0.472570 + 0.818515i 0.0233957 + 0.0405225i
409409 2.93617 + 5.08560i 0.145184 + 0.251467i 0.929442 0.368969i 0.120289π-0.120289\pi
−0.784257 + 0.620436i 0.786956π0.786956\pi
410410 0.837115 + 1.44992i 0.0413421 + 0.0716067i
411411 −5.73593 9.93492i −0.282933 0.490053i
412412 −2.08831 + 3.61707i −0.102884 + 0.178200i
413413 0 0
414414 1.80614 + 3.12832i 0.0887667 + 0.153749i
415415 −1.37428 2.38032i −0.0674607 0.116845i
416416 0.194457 + 11.0482i 0.00953403 + 0.541680i
417417 −3.16932 + 5.48942i −0.155202 + 0.268818i
418418 3.96508 6.86773i 0.193939 0.335911i
419419 −15.0712 26.1040i −0.736274 1.27526i −0.954162 0.299290i 0.903250π-0.903250\pi
0.217888 0.975974i 0.430083π-0.430083\pi
420420 0 0
421421 40.0580 1.95231 0.976153 0.217083i 0.0696543π-0.0696543\pi
0.976153 + 0.217083i 0.0696543π0.0696543\pi
422422 −5.09576 −0.248058
423423 −1.11481 1.93091i −0.0542040 0.0938840i
424424 −4.88672 + 8.46405i −0.237320 + 0.411051i
425425 −1.22679 −0.0595079
426426 1.88726 + 3.26884i 0.0914382 + 0.158376i
427427 0 0
428428 22.2238 1.07423
429429 14.2244 + 7.88199i 0.686759 + 0.380546i
430430 −0.772544 + 1.33809i −0.0372554 + 0.0645282i
431431 −3.91587 −0.188621 −0.0943104 0.995543i 0.530065π-0.530065\pi
−0.0943104 + 0.995543i 0.530065π0.530065\pi
432432 9.58632 16.6040i 0.461222 0.798860i
433433 −20.3963 + 35.3274i −0.980182 + 1.69772i −0.318532 + 0.947912i 0.603190π0.603190\pi
−0.661650 + 0.749813i 0.730144π0.730144\pi
434434 0 0
435435 −3.44306 + 5.96355i −0.165082 + 0.285930i
436436 −15.5757 −0.745941
437437 29.8131 51.6378i 1.42615 2.47017i
438438 −0.117775 0.203992i −0.00562750 0.00974711i
439439 −12.7811 + 22.1376i −0.610010 + 1.05657i 0.381228 + 0.924481i 0.375501π0.375501\pi
−0.991238 + 0.132087i 0.957832π0.957832\pi
440440 −5.32336 9.22033i −0.253781 0.439562i
441441 0 0
442442 0.663878 + 0.367867i 0.0315775 + 0.0174977i
443443 13.7282 + 23.7779i 0.652247 + 1.12972i 0.982576 + 0.185859i 0.0595067π0.0595067\pi
−0.330330 + 0.943866i 0.607160π0.607160\pi
444444 −14.8917 −0.706730
445445 −19.6307 −0.930584
446446 −3.20844 −0.151924
447447 21.1057 0.998267
448448 0 0
449449 7.40181 12.8203i 0.349313 0.605028i −0.636815 0.771017i 0.719748π-0.719748\pi
0.986128 + 0.165989i 0.0530816π0.0530816\pi
450450 −0.354769 0.614477i −0.0167240 0.0289667i
451451 −4.80913 8.32966i −0.226453 0.392229i
452452 −15.5046 −0.729275
453453 −0.918611 + 1.59108i −0.0431601 + 0.0747555i
454454 4.12489 0.193590
455455 0 0
456456 9.02315 0.422548
457457 0.325975 0.564606i 0.0152485 0.0264112i −0.858300 0.513147i 0.828479π-0.828479\pi
0.873549 + 0.486736i 0.161813π0.161813\pi
458458 2.32241 0.108519
459459 −2.10593 3.64758i −0.0982965 0.170254i
460460 −19.6467 34.0290i −0.916031 1.58661i
461461 6.24774 10.8214i 0.290986 0.504003i −0.683057 0.730365i 0.739350π-0.739350\pi
0.974043 + 0.226362i 0.0726833π0.0726833\pi
462462 0 0
463463 −0.309503 −0.0143838 −0.00719190 0.999974i 0.502289π-0.502289\pi
−0.00719190 + 0.999974i 0.502289π0.502289\pi
464464 8.40466 0.390176
465465 7.47946 0.346852
466466 −5.42972 −0.251527
467467 12.2387 + 21.1980i 0.566338 + 0.980926i 0.996924 + 0.0783762i 0.0249735π0.0249735\pi
−0.430586 + 0.902549i 0.641693π0.641693\pi
468468 −0.207187 11.7714i −0.00957722 0.544134i
469469 0 0
470470 −0.452151 0.783149i −0.0208562 0.0361240i
471471 −0.940659 + 1.62927i −0.0433433 + 0.0750727i
472472 −4.72198 8.17871i −0.217347 0.376456i
473473 4.43818 7.68716i 0.204068 0.353456i
474474 −1.89792 −0.0871742
475475 −5.85601 + 10.1429i −0.268692 + 0.465389i
476476 0 0
477477 7.85759 13.6097i 0.359774 0.623147i
478478 2.21909 3.84357i 0.101499 0.175801i
479479 −8.13850 −0.371858 −0.185929 0.982563i 0.559529π-0.559529\pi
−0.185929 + 0.982563i 0.559529π0.559529\pi
480480 4.48686 7.77147i 0.204796 0.354718i
481481 −20.8816 + 12.5511i −0.952118 + 0.572279i
482482 −4.39746 −0.200299
483483 0 0
484484 4.40662 + 7.63250i 0.200301 + 0.346932i
485485 6.07653 0.275921
486486 1.99653 3.45809i 0.0905645 0.156862i
487487 −2.30480 3.99203i −0.104440 0.180896i 0.809069 0.587714i 0.199972π-0.199972\pi
−0.913509 + 0.406817i 0.866638π0.866638\pi
488488 −9.94821 −0.450334
489489 −7.48464 −0.338467
490490 0 0
491491 −6.50947 11.2747i −0.293768 0.508822i 0.680929 0.732349i 0.261576π-0.261576\pi
−0.974698 + 0.223527i 0.928243π0.928243\pi
492492 2.68591 4.65213i 0.121090 0.209734i
493493 0.923171 1.59898i 0.0415775 0.0720144i
494494 6.21047 3.73286i 0.279422 0.167949i
495495 8.55969 + 14.8258i 0.384729 + 0.666371i
496496 −4.56443 7.90582i −0.204949 0.354982i
497497 0 0
498498 0.164409 0.284764i 0.00736733 0.0127606i
499499 16.1603 + 27.9905i 0.723436 + 1.25303i 0.959614 + 0.281319i 0.0907717π0.0907717\pi
−0.236178 + 0.971710i 0.575895π0.575895\pi
500500 −8.48928 14.7039i −0.379652 0.657577i
501501 5.45718 + 9.45211i 0.243809 + 0.422289i
502502 2.73900 + 4.74408i 0.122247 + 0.211739i
503503 −15.9126 + 27.5615i −0.709509 + 1.22891i 0.255531 + 0.966801i 0.417750π0.417750\pi
−0.965039 + 0.262105i 0.915583π0.915583\pi
504504 0 0
505505 −1.02128 1.76891i −0.0454465 0.0787156i
506506 −4.20838 7.28912i −0.187085 0.324041i
507507 7.87780 + 12.5990i 0.349866 + 0.559539i
508508 1.72377 2.98566i 0.0764801 0.132467i
509509 1.12788 1.95354i 0.0499922 0.0865891i −0.839946 0.542669i 0.817414π-0.817414\pi
0.889939 + 0.456080i 0.150747π0.150747\pi
510510 −0.308191 0.533802i −0.0136469 0.0236372i
511511 0 0
512512 −18.4807 −0.816739
513513 −40.2102 −1.77533
514514 −1.84710 3.19927i −0.0814722 0.141114i
515515 2.77461 4.80576i 0.122264 0.211767i
516516 4.95746 0.218240
517517 2.59756 + 4.49911i 0.114241 + 0.197870i
518518 0 0
519519 −12.7236 −0.558502
520520 −0.171197 9.72665i −0.00750749 0.426542i
521521 5.38562 9.32817i 0.235948 0.408675i −0.723600 0.690220i 0.757514π-0.757514\pi
0.959548 + 0.281546i 0.0908471π0.0908471\pi
522522 1.06787 0.0467393
523523 3.70397 6.41546i 0.161963 0.280528i −0.773610 0.633663i 0.781551π-0.781551\pi
0.935573 + 0.353134i 0.114884π0.114884\pi
524524 6.16118 10.6715i 0.269152 0.466186i
525525 0 0
526526 3.47454 6.01809i 0.151497 0.262401i
527527 −2.00543 −0.0873580
528528 −8.05953 + 13.9595i −0.350746 + 0.607510i
529529 −20.1424 34.8877i −0.875757 1.51686i
530530 3.18692 5.51991i 0.138431 0.239770i
531531 7.59270 + 13.1509i 0.329495 + 0.570702i
532532 0 0
533533 −0.154660 8.78707i −0.00669906 0.380610i
534534 −1.17424 2.03384i −0.0508142 0.0880127i
535535 −29.5274 −1.27658
536536 −1.42455 −0.0615313
537537 −14.4516 −0.623632
538538 −8.06161 −0.347561
539539 0 0
540540 −13.2492 + 22.9482i −0.570153 + 0.987534i
541541 −16.2741 28.1875i −0.699676 1.21188i −0.968579 0.248708i 0.919994π-0.919994\pi
0.268902 0.963168i 0.413339π-0.413339\pi
542542 −1.93728 3.35546i −0.0832132 0.144129i
543543 −17.0489 −0.731638
544544 −1.20304 + 2.08373i −0.0515799 + 0.0893391i
545545 20.6944 0.886453
546546 0 0
547547 −13.4997 −0.577206 −0.288603 0.957449i 0.593191π-0.593191\pi
−0.288603 + 0.957449i 0.593191π0.593191\pi
548548 9.67577 16.7589i 0.413329 0.715906i
549549 15.9962 0.682701
550550 0.826627 + 1.43176i 0.0352475 + 0.0610504i
551551 −8.81342 15.2653i −0.375464 0.650323i
552552 4.78840 8.29376i 0.203808 0.353006i
553553 0 0
554554 4.10915 0.174581
555555 19.7857 0.839856
556556 −10.6925 −0.453461
557557 −29.7703 −1.26141 −0.630703 0.776024i 0.717233π-0.717233\pi
−0.630703 + 0.776024i 0.717233π0.717233\pi
558558 −0.579941 1.00449i −0.0245509 0.0425233i
559559 6.95148 4.17825i 0.294016 0.176721i
560560 0 0
561561 1.77052 + 3.06664i 0.0747516 + 0.129474i
562562 0.709566 1.22900i 0.0299312 0.0518424i
563563 7.06629 + 12.2392i 0.297809 + 0.515819i 0.975634 0.219403i 0.0704110π-0.0704110\pi
−0.677826 + 0.735223i 0.737078π0.737078\pi
564564 −1.45074 + 2.51275i −0.0610872 + 0.105806i
565565 20.6000 0.866647
566566 4.12705 7.14826i 0.173473 0.300464i
567567 0 0
568568 −6.48584 + 11.2338i −0.272140 + 0.471360i
569569 12.1270 21.0046i 0.508391 0.880558i −0.491562 0.870842i 0.663574π-0.663574\pi
0.999953 0.00971585i 0.00309270π-0.00309270\pi
570570 −5.88454 −0.246476
571571 −0.604159 + 1.04643i −0.0252832 + 0.0437919i −0.878390 0.477944i 0.841382π-0.841382\pi
0.853107 + 0.521736i 0.174715π0.174715\pi
572572 0.482755 + 27.4279i 0.0201850 + 1.14682i
573573 −16.1514 −0.674732
574574 0 0
575575 6.21533 + 10.7653i 0.259197 + 0.448943i
576576 10.7131 0.446381
577577 −7.30518 + 12.6529i −0.304119 + 0.526749i −0.977065 0.212943i 0.931695π-0.931695\pi
0.672946 + 0.739692i 0.265029π0.265029\pi
578578 −2.19643 3.80433i −0.0913595 0.158239i
579579 4.45149 0.184998
580580 −11.6160 −0.482328
581581 0 0
582582 0.363475 + 0.629558i 0.0150665 + 0.0260960i
583583 −18.3085 + 31.7113i −0.758262 + 1.31335i
584584 0.404749 0.701046i 0.0167486 0.0290095i
585585 0.275276 + 15.6399i 0.0113813 + 0.646632i
586586 2.34841 + 4.06757i 0.0970120 + 0.168030i
587587 10.7548 + 18.6278i 0.443897 + 0.768852i 0.997975 0.0636132i 0.0202624π-0.0202624\pi
−0.554078 + 0.832465i 0.686929π0.686929\pi
588588 0 0
589589 −9.57284 + 16.5806i −0.394442 + 0.683193i
590590 3.07949 + 5.33383i 0.126780 + 0.219590i
591591 6.69168 + 11.5903i 0.275259 + 0.476763i
592592 −12.0744 20.9135i −0.496256 0.859541i
593593 −1.32429 2.29373i −0.0543820 0.0941923i 0.837553 0.546356i 0.183986π-0.183986\pi
−0.891935 + 0.452164i 0.850652π0.850652\pi
594594 −2.83801 + 4.91558i −0.116445 + 0.201689i
595595 0 0
596596 17.8013 + 30.8328i 0.729171 + 1.26296i
597597 1.99846 + 3.46143i 0.0817915 + 0.141667i
598598 −0.135340 7.68939i −0.00553445 0.314443i
599599 20.1250 34.8576i 0.822287 1.42424i −0.0816889 0.996658i 0.526031π-0.526031\pi
0.903975 0.427584i 0.140635π-0.140635\pi
600600 −0.940558 + 1.62909i −0.0383981 + 0.0665075i
601601 19.1725 + 33.2077i 0.782061 + 1.35457i 0.930739 + 0.365683i 0.119165π0.119165\pi
−0.148679 + 0.988886i 0.547502π0.547502\pi
602602 0 0
603603 2.29060 0.0932806
604604 −3.09916 −0.126103
605605 −5.85480 10.1408i −0.238031 0.412283i
606606 0.122179 0.211620i 0.00496317 0.00859646i
607607 −42.5547 −1.72724 −0.863620 0.504143i 0.831808π-0.831808\pi
−0.863620 + 0.504143i 0.831808π0.831808\pi
608608 11.4853 + 19.8931i 0.465791 + 0.806773i
609609 0 0
610610 6.48782 0.262684
611611 0.0835364 + 4.74616i 0.00337952 + 0.192009i
612612 1.28180 2.22014i 0.0518136 0.0897438i
613613 15.2652 0.616556 0.308278 0.951296i 0.400247π-0.400247\pi
0.308278 + 0.951296i 0.400247π0.400247\pi
614614 1.15773 2.00524i 0.0467221 0.0809251i
615615 −3.56859 + 6.18098i −0.143899 + 0.249241i
616616 0 0
617617 −6.99061 + 12.1081i −0.281431 + 0.487453i −0.971737 0.236064i 0.924142π-0.924142\pi
0.690306 + 0.723517i 0.257476π0.257476\pi
618618 0.663868 0.0267047
619619 −4.25792 + 7.37494i −0.171140 + 0.296424i −0.938819 0.344411i 0.888079π-0.888079\pi
0.767678 + 0.640835i 0.221412π0.221412\pi
620620 6.30845 + 10.9265i 0.253353 + 0.438821i
621621 −21.3388 + 36.9598i −0.856295 + 1.48315i
622622 2.20166 + 3.81338i 0.0882784 + 0.152903i
623623 0 0
624624 −12.6236 + 7.58750i −0.505347 + 0.303743i
625625 15.1856 + 26.3023i 0.607425 + 1.05209i
626626 2.69363 0.107659
627627 33.8060 1.35008
628628 −3.17354 −0.126638
629629 −5.30504 −0.211526
630630 0 0
631631 −18.4146 + 31.8950i −0.733074 + 1.26972i 0.222490 + 0.974935i 0.428582π0.428582\pi
−0.955563 + 0.294786i 0.904752π0.904752\pi
632632 −3.26123 5.64861i −0.129725 0.224690i
633633 −10.8615 18.8127i −0.431707 0.747739i
634634 −2.72013 −0.108030
635635 −2.29027 + 3.96686i −0.0908865 + 0.157420i
636636 −20.4507 −0.810922
637637 0 0
638638 −2.48818 −0.0985081
639639 10.4289 18.0634i 0.412561 0.714576i
640640 20.0470 0.792428
641641 −12.9374 22.4082i −0.510996 0.885070i −0.999919 0.0127435i 0.995944π-0.995944\pi
0.488923 0.872327i 0.337390π-0.337390\pi
642642 −1.76622 3.05918i −0.0697071 0.120736i
643643 20.2626 35.0958i 0.799078 1.38404i −0.121139 0.992636i 0.538655π-0.538655\pi
0.920217 0.391408i 0.128012π-0.128012\pi
644644 0 0
645645 −6.58666 −0.259350
646646 1.57779 0.0620774
647647 −1.78400 −0.0701364 −0.0350682 0.999385i 0.511165π-0.511165\pi
−0.0350682 + 0.999385i 0.511165π0.511165\pi
648648 −1.10732 −0.0434997
649649 −17.6913 30.6423i −0.694445 1.20281i
650650 0.0265840 + 1.51038i 0.00104271 + 0.0592420i
651651 0 0
652652 −6.31281 10.9341i −0.247229 0.428213i
653653 −6.20210 + 10.7424i −0.242707 + 0.420381i −0.961484 0.274860i 0.911369π-0.911369\pi
0.718778 + 0.695240i 0.244702π0.244702\pi
654654 1.23787 + 2.14405i 0.0484044 + 0.0838389i
655655 −8.18597 + 14.1785i −0.319852 + 0.554000i
656656 8.71109 0.340111
657657 −0.650815 + 1.12725i −0.0253907 + 0.0439780i
658658 0 0
659659 0.564336 0.977458i 0.0219834 0.0380764i −0.854824 0.518917i 0.826335π-0.826335\pi
0.876808 + 0.480841i 0.159669π0.159669\pi
660660 11.1390 19.2933i 0.433585 0.750991i
661661 28.9254 1.12507 0.562534 0.826774i 0.309826π-0.309826\pi
0.562534 + 0.826774i 0.309826π0.309826\pi
662662 0.310913 0.538517i 0.0120840 0.0209301i
663663 0.0569393 + 3.23503i 0.00221134 + 0.125638i
664664 1.13003 0.0438535
665665 0 0
666666 −1.53414 2.65721i −0.0594467 0.102965i
667667 −18.7084 −0.724393
668668 −9.20556 + 15.9445i −0.356174 + 0.616911i
669669 −6.83874 11.8451i −0.264401 0.457956i
670670 0.929036 0.0358918
671671 −37.2718 −1.43886
672672 0 0
673673 3.54980 + 6.14843i 0.136835 + 0.237005i 0.926297 0.376795i 0.122974π-0.122974\pi
−0.789462 + 0.613799i 0.789640π0.789640\pi
674674 −2.14498 + 3.71521i −0.0826214 + 0.143104i
675675 4.19145 7.25980i 0.161329 0.279430i
676676 −11.7610 + 22.1349i −0.452348 + 0.851341i
677677 −25.2010 43.6494i −0.968552 1.67758i −0.699752 0.714386i 0.746706π-0.746706\pi
−0.268800 0.963196i 0.586627π-0.586627\pi
678678 1.23221 + 2.13426i 0.0473229 + 0.0819657i
679679 0 0
680680 1.05914 1.83449i 0.0406162 0.0703493i
681681 8.79213 + 15.2284i 0.336915 + 0.583554i
682682 1.35129 + 2.34050i 0.0517435 + 0.0896224i
683683 −13.7641 23.8401i −0.526669 0.912217i −0.999517 0.0310735i 0.990107π-0.990107\pi
0.472848 0.881144i 0.343226π-0.343226\pi
684684 −12.2372 21.1954i −0.467901 0.810428i
685685 −12.8556 + 22.2665i −0.491186 + 0.850760i
686686 0 0
687687 4.95019 + 8.57398i 0.188861 + 0.327118i
688688 4.01958 + 6.96212i 0.153245 + 0.265428i
689689 −28.6765 + 17.2362i −1.09249 + 0.656649i
690690 −3.12280 + 5.40885i −0.118883 + 0.205912i
691691 −12.1669 + 21.0737i −0.462851 + 0.801682i −0.999102 0.0423772i 0.986507π-0.986507\pi
0.536251 + 0.844059i 0.319840π0.319840\pi
692692 −10.7315 18.5875i −0.407950 0.706591i
693693 0 0
694694 6.11884 0.232268
695695 14.2064 0.538879
696696 −1.41556 2.45182i −0.0536566 0.0929360i
697697 0.956829 1.65728i 0.0362425 0.0627738i
698698 −6.08704 −0.230398
699699 −11.5733 20.0456i −0.437744 0.758195i
700700 0 0
701701 −20.5588 −0.776495 −0.388248 0.921555i 0.626919π-0.626919\pi
−0.388248 + 0.921555i 0.626919π0.626919\pi
702702 −4.44515 + 2.67180i −0.167771 + 0.100840i
703703 −25.3234 + 43.8613i −0.955088 + 1.65426i
704704 −24.9621 −0.940795
705705 1.92751 3.33854i 0.0725940 0.125737i
706706 3.65513 6.33088i 0.137563 0.238266i
707707 0 0
708708 9.88062 17.1137i 0.371336 0.643174i
709709 40.9089 1.53637 0.768183 0.640230i 0.221161π-0.221161\pi
0.768183 + 0.640230i 0.221161π0.221161\pi
710710 4.22981 7.32624i 0.158742 0.274949i
711711 5.24388 + 9.08267i 0.196661 + 0.340627i
712712 4.03543 6.98956i 0.151234 0.261945i
713713 10.1602 + 17.5980i 0.380503 + 0.659051i
714714 0 0
715715 −0.641405 36.4418i −0.0239872 1.36284i
716716 −12.1890 21.1119i −0.455524 0.788990i
717717 18.9198 0.706572
718718 3.86802 0.144353
719719 1.19947 0.0447326 0.0223663 0.999750i 0.492880π-0.492880\pi
0.0223663 + 0.999750i 0.492880π0.492880\pi
720720 −15.5047 −0.577826
721721 0 0
722722 4.98433 8.63311i 0.185497 0.321291i
723723 −9.37311 16.2347i −0.348590 0.603775i
724724 −14.3796 24.9063i −0.534415 0.925634i
725725 3.67478 0.136478
726726 0.700425 1.21317i 0.0259952 0.0450250i
727727 2.06230 0.0764865 0.0382433 0.999268i 0.487824π-0.487824\pi
0.0382433 + 0.999268i 0.487824π0.487824\pi
728728 0 0
729729 20.1764 0.747273
730730 −0.263961 + 0.457194i −0.00976964 + 0.0169215i
731731 1.76605 0.0653197
732732 −10.4082 18.0275i −0.384697 0.666315i
733733 15.0310 + 26.0345i 0.555184 + 0.961606i 0.997889 + 0.0649392i 0.0206853π0.0206853\pi
−0.442706 + 0.896667i 0.645981π0.645981\pi
734734 1.52720 2.64520i 0.0563702 0.0976360i
735735 0 0
736736 24.3801 0.898662
737737 −5.33721 −0.196599
738738 1.10680 0.0407420
739739 44.2548 1.62794 0.813969 0.580908i 0.197303π-0.197303\pi
0.813969 + 0.580908i 0.197303π0.197303\pi
740740 16.6880 + 28.9044i 0.613461 + 1.06255i
741741 27.0186 + 14.9715i 0.992553 + 0.549992i
742742 0 0
743743 4.31326 + 7.47078i 0.158238 + 0.274076i 0.934233 0.356662i 0.116085π-0.116085\pi
−0.775995 + 0.630739i 0.782752π0.782752\pi
744744 −1.53753 + 2.66308i −0.0563686 + 0.0976334i
745745 −23.6515 40.9656i −0.866524 1.50086i
746746 −4.15097 + 7.18969i −0.151978 + 0.263233i
747747 −1.81702 −0.0664814
748748 −2.98665 + 5.17302i −0.109203 + 0.189144i
749749 0 0
750750 −1.34936 + 2.33715i −0.0492715 + 0.0853408i
751751 −2.86105 + 4.95549i −0.104401 + 0.180828i −0.913493 0.406853i 0.866626π-0.866626\pi
0.809092 + 0.587682i 0.199959π0.199959\pi
752752 −4.70512 −0.171578
753753 −11.6763 + 20.2239i −0.425506 + 0.736998i
754754 −1.98862 1.10193i −0.0724211 0.0401299i
755755 4.11765 0.149857
756756 0 0
757757 17.3611 + 30.0703i 0.631000 + 1.09292i 0.987348 + 0.158571i 0.0506887π0.0506887\pi
−0.356347 + 0.934354i 0.615978π0.615978\pi
758758 −2.83853 −0.103100
759759 17.9402 31.0733i 0.651187 1.12789i
760760 −10.1115 17.5137i −0.366783 0.635287i
761761 53.1735 1.92754 0.963768 0.266741i 0.0859467π-0.0859467\pi
0.963768 + 0.266741i 0.0859467π0.0859467\pi
762762 −0.547981 −0.0198513
763763 0 0
764764 −13.6226 23.5951i −0.492849 0.853640i
765765 −1.70304 + 2.94976i −0.0615736 + 0.106649i
766766 −4.12265 + 7.14063i −0.148957 + 0.258002i
767767 −0.568946 32.3249i −0.0205434 1.16719i
768768 −6.03145 10.4468i −0.217641 0.376966i
769769 2.45578 + 4.25354i 0.0885578 + 0.153387i 0.906902 0.421342i 0.138441π-0.138441\pi
−0.818344 + 0.574729i 0.805108π0.805108\pi
770770 0 0
771771 7.87414 13.6384i 0.283580 0.491175i
772772 3.75455 + 6.50306i 0.135129 + 0.234050i
773773 −11.4903 19.9018i −0.413279 0.715819i 0.581967 0.813212i 0.302283π-0.302283\pi
−0.995246 + 0.0973926i 0.968950π0.968950\pi
774774 0.510715 + 0.884585i 0.0183573 + 0.0317957i
775775 −1.99571 3.45667i −0.0716881 0.124167i
776776 −1.24913 + 2.16356i −0.0448413 + 0.0776674i
777777 0 0
778778 −2.19589 3.80339i −0.0787264 0.136358i
779779 −9.13476 15.8219i −0.327287 0.566877i
780780 17.4469 10.4866i 0.624699 0.375481i
781781 −24.2998 + 42.0885i −0.869515 + 1.50604i
782782 0.837302 1.45025i 0.0299419 0.0518608i
783783 6.30821 + 10.9261i 0.225437 + 0.390469i
784784 0 0
785785 4.21648 0.150493
786786 −1.95862 −0.0698616
787787 −1.59387 2.76067i −0.0568154 0.0984071i 0.836219 0.548396i 0.184761π-0.184761\pi
−0.893034 + 0.449989i 0.851428π0.851428\pi
788788 −11.2880 + 19.5514i −0.402119 + 0.696490i
789789 29.6237 1.05463
790790 2.12684 + 3.68380i 0.0756696 + 0.131064i
791791 0 0
792792 −7.03836 −0.250097
793793 −29.7886 16.5064i −1.05782 0.586159i
794794 2.12927 3.68800i 0.0755650 0.130882i
795795 27.1715 0.963674
796796 −3.37114 + 5.83899i −0.119487 + 0.206958i
797797 27.3255 47.3291i 0.967918 1.67648i 0.266355 0.963875i 0.414180π-0.414180\pi
0.701562 0.712608i 0.252486π-0.252486\pi
798798 0 0
799799 −0.516813 + 0.895146i −0.0182835 + 0.0316680i
800800 −4.78884 −0.169311
801801 −6.48875 + 11.2388i −0.229269 + 0.397105i
802802 0.889604 + 1.54084i 0.0314130 + 0.0544089i
803803 1.51643 2.62653i 0.0535136 0.0926883i
804804 −1.49042 2.58148i −0.0525630 0.0910418i
805805 0 0
806806 0.0434569 + 2.46902i 0.00153070 + 0.0869677i
807807 −17.1832 29.7622i −0.604877 1.04768i
808808 0.839768 0.0295429
809809 −20.2995 −0.713694 −0.356847 0.934163i 0.616148π-0.616148\pi
−0.356847 + 0.934163i 0.616148π0.616148\pi
810810 0.722151 0.0253738
811811 −2.43587 −0.0855350 −0.0427675 0.999085i 0.513617π-0.513617\pi
−0.0427675 + 0.999085i 0.513617π0.513617\pi
812812 0 0
813813 8.25855 14.3042i 0.289640 0.501671i
814814 3.57461 + 6.19141i 0.125290 + 0.217009i
815815 8.38742 + 14.5274i 0.293799 + 0.508874i
816816 −3.20706 −0.112270
817817 8.43015 14.6015i 0.294934 0.510840i
818818 1.57452 0.0550519
819819 0 0
820820 −12.0395 −0.420438
821821 −22.6762 + 39.2763i −0.791405 + 1.37075i 0.133692 + 0.991023i 0.457317π0.457317\pi
−0.925097 + 0.379731i 0.876017π0.876017\pi
822822 −3.07589 −0.107284
823823 1.37871 + 2.38800i 0.0480588 + 0.0832403i 0.889054 0.457802i 0.151363π-0.151363\pi
−0.840995 + 0.541042i 0.818030π0.818030\pi
824824 1.14074 + 1.97581i 0.0397394 + 0.0688307i
825825 −3.52388 + 6.10354i −0.122686 + 0.212498i
826826 0 0
827827 −8.64504 −0.300618 −0.150309 0.988639i 0.548027π-0.548027\pi
−0.150309 + 0.988639i 0.548027π0.548027\pi
828828 −25.9761 −0.902733
829829 29.5741 1.02715 0.513576 0.858044i 0.328320π-0.328320\pi
0.513576 + 0.858044i 0.328320π0.328320\pi
830830 −0.736958 −0.0255802
831831 8.75858 + 15.1703i 0.303832 + 0.526252i
832832 −19.9503 11.0548i −0.691653 0.383258i
833833 0 0
834834 0.849774 + 1.47185i 0.0294253 + 0.0509660i
835835 12.2308 21.1844i 0.423266 0.733117i
836836 28.5132 + 49.3863i 0.986150 + 1.70806i
837837 6.85177 11.8676i 0.236832 0.410204i
838838 −8.08191 −0.279185
839839 12.6236 21.8648i 0.435817 0.754857i −0.561545 0.827446i 0.689793π-0.689793\pi
0.997362 + 0.0725895i 0.0231263π0.0231263\pi
840840 0 0
841841 11.7347 20.3251i 0.404644 0.700865i
842842 5.37028 9.30159i 0.185072 0.320554i
843843 6.04971 0.208363
844844 18.3220 31.7346i 0.630669 1.09235i
845845 15.6262 29.4092i 0.537556 1.01171i
846846 −0.597818 −0.0205534
847847 0 0
848848 −16.5817 28.7204i −0.569418 0.986261i
849849 35.1870 1.20761
850850 −0.164466 + 0.284864i −0.00564115 + 0.00977076i
851851 26.8772 + 46.5526i 0.921338 + 1.59580i
852852 −27.1429 −0.929901
853853 35.1368 1.20306 0.601531 0.798850i 0.294558π-0.294558\pi
0.601531 + 0.798850i 0.294558π0.294558\pi
854854 0 0
855855 16.2588 + 28.1610i 0.556039 + 0.963087i
856856 6.06986 10.5133i 0.207463 0.359337i
857857 −0.671345 + 1.16280i −0.0229327 + 0.0397206i −0.877264 0.480008i 0.840634π-0.840634\pi
0.854331 + 0.519729i 0.173967π0.173967\pi
858858 3.73718 2.24626i 0.127585 0.0766862i
859859 2.38386 + 4.12897i 0.0813363 + 0.140879i 0.903824 0.427904i 0.140748π-0.140748\pi
−0.822488 + 0.568783i 0.807415π0.807415\pi
860860 −5.55542 9.62228i −0.189438 0.328117i
861861 0 0
862862 −0.524972 + 0.909278i −0.0178806 + 0.0309701i
863863 13.3052 + 23.0453i 0.452915 + 0.784472i 0.998566 0.0535407i 0.0170507π-0.0170507\pi
−0.545650 + 0.838013i 0.683717π0.683717\pi
864864 −8.22062 14.2385i −0.279671 0.484405i
865865 14.2583 + 24.6960i 0.484795 + 0.839690i
866866 5.46875 + 9.47216i 0.185836 + 0.321877i
867867 9.36331 16.2177i 0.317995 0.550783i
868868 0 0
869869 −12.2185 21.1630i −0.414484 0.717907i
870870 0.923171 + 1.59898i 0.0312984 + 0.0542105i
871871 −4.26563 2.36366i −0.144535 0.0800897i
872872 −4.25410 + 7.36831i −0.144062 + 0.249523i
873873 2.00854 3.47890i 0.0679788 0.117743i
874874 −7.99364 13.8454i −0.270389 0.468328i
875875 0 0
876876 1.69385 0.0572300
877877 8.03696 0.271389 0.135695 0.990751i 0.456673π-0.456673\pi
0.135695 + 0.990751i 0.456673π0.456673\pi
878878 3.42694 + 5.93564i 0.115654 + 0.200318i
879879 −10.0112 + 17.3399i −0.337670 + 0.584861i
880880 36.1266 1.21783
881881 −27.3349 47.3454i −0.920935 1.59511i −0.797971 0.602695i 0.794093π-0.794093\pi
−0.122964 0.992411i 0.539240π-0.539240\pi
882882 0 0
883883 −8.45085 −0.284394 −0.142197 0.989838i 0.545417π-0.545417\pi
−0.142197 + 0.989838i 0.545417π0.545417\pi
884884 −4.67795 + 2.81172i −0.157337 + 0.0945685i
885885 −13.1277 + 22.7379i −0.441284 + 0.764327i
886886 7.36176 0.247323
887887 −5.17784 + 8.96829i −0.173855 + 0.301126i −0.939764 0.341823i 0.888956π-0.888956\pi
0.765909 + 0.642948i 0.222289π0.222289\pi
888888 −4.06729 + 7.04475i −0.136489 + 0.236406i
889889 0 0
890890 −2.63174 + 4.55831i −0.0882162 + 0.152795i
891891 −4.14868 −0.138986
892892 11.5361 19.9811i 0.386256 0.669016i
893893 4.93396 + 8.54587i 0.165109 + 0.285977i
894894 2.82949 4.90082i 0.0946323 0.163908i
895895 16.1947 + 28.0501i 0.541330 + 0.937611i
896896 0 0
897897 28.0995 16.8895i 0.938215 0.563923i
898898 −1.98461 3.43745i −0.0662274 0.114709i
899899 6.00718 0.200351
900900 5.10234 0.170078
901901 −7.28536 −0.242711
902902 −2.57890 −0.0858680
903903 0 0
904904 −4.23468 + 7.33467i −0.140843 + 0.243948i
905905 19.1053 + 33.0914i 0.635082 + 1.09999i
906906 0.246303 + 0.426609i 0.00818287 + 0.0141731i
907907 18.4804 0.613631 0.306815 0.951769i 0.400737π-0.400737\pi
0.306815 + 0.951769i 0.400737π0.400737\pi
908908 −14.8312 + 25.6884i −0.492190 + 0.852498i
909909 −1.35030 −0.0447867
910910 0 0
911911 −26.6282 −0.882230 −0.441115 0.897451i 0.645417π-0.645417\pi
−0.441115 + 0.897451i 0.645417π0.645417\pi
912912 −15.3088 + 26.5155i −0.506924 + 0.878017i
913913 4.23374 0.140116
914914 −0.0874022 0.151385i −0.00289101 0.00500737i
915915 13.8287 + 23.9520i 0.457162 + 0.791828i
916916 −8.35033 + 14.4632i −0.275903 + 0.477877i
917917 0 0
918918 −1.12931 −0.0372727
919919 −11.1493 −0.367783 −0.183891 0.982947i 0.558869π-0.558869\pi
−0.183891 + 0.982947i 0.558869π0.558869\pi
920920 −21.4639 −0.707644
921921 9.87072 0.325251
922922 −1.67518 2.90149i −0.0551690 0.0955555i
923923 −38.0605 + 22.8766i −1.25278 + 0.752993i
924924 0 0
925925 −5.27933 9.14406i −0.173583 0.300655i
926926 −0.0414927 + 0.0718675i −0.00136354 + 0.00236171i
927927 −1.83424 3.17700i −0.0602445 0.104347i
928928 3.60365 6.24170i 0.118296 0.204894i
929929 −7.74510 −0.254108 −0.127054 0.991896i 0.540552π-0.540552\pi
−0.127054 + 0.991896i 0.540552π0.540552\pi
930930 1.00272 1.73676i 0.0328804 0.0569505i
931931 0 0
932932 19.5227 33.8144i 0.639489 1.10763i
933933 −9.38559 + 16.2563i −0.307270 + 0.532208i
934934 6.56299 0.214748
935935 3.96817 6.87306i 0.129773 0.224773i
936936 −5.62523 3.11704i −0.183866 0.101884i
937937 −36.4239 −1.18992 −0.594959 0.803756i 0.702832π-0.702832\pi
−0.594959 + 0.803756i 0.702832π0.702832\pi
938938 0 0
939939 5.74143 + 9.94445i 0.187364 + 0.324525i
940940 6.50291 0.212101
941941 −9.89466 + 17.1381i −0.322557 + 0.558685i −0.981015 0.193933i 0.937876π-0.937876\pi
0.658458 + 0.752617i 0.271209π0.271209\pi
942942 0.252214 + 0.436848i 0.00821759 + 0.0142333i
943943 −19.3905 −0.631442
944944 32.0454 1.04299
945945 0 0
946946 −1.18999 2.06112i −0.0386899 0.0670129i
947947 −4.97398 + 8.61519i −0.161633 + 0.279956i −0.935454 0.353448i 0.885009π-0.885009\pi
0.773822 + 0.633403i 0.218343π0.218343\pi
948948 6.82403 11.8196i 0.221634 0.383882i
949949 2.37517 1.42762i 0.0771012 0.0463424i
950950 1.57014 + 2.71957i 0.0509422 + 0.0882345i
951951 −5.79790 10.0423i −0.188010 0.325643i
952952 0 0
953953 −0.0105567 + 0.0182847i −0.000341965 + 0.000592300i −0.866196 0.499704i 0.833442π-0.833442\pi
0.865854 + 0.500296i 0.166776π0.166776\pi
954954 −2.10682 3.64912i −0.0682108 0.118144i
955955 18.0995 + 31.3493i 0.585686 + 1.01444i
956956 15.9576 + 27.6394i 0.516106 + 0.893922i
957957 −5.30352 9.18596i −0.171438 0.296940i
958958 −1.09107 + 1.88979i −0.0352508 + 0.0610562i
959959 0 0
960960 9.26150 + 16.0414i 0.298914 + 0.517733i
961961 12.2376 + 21.1962i 0.394761 + 0.683747i
962962 0.114958 + 6.53140i 0.00370640 + 0.210581i
963963 −9.76001 + 16.9048i −0.314512 + 0.544751i
964964 15.8112 27.3858i 0.509245 0.882039i
965965 −4.98842 8.64020i −0.160583 0.278138i
966966 0 0
967967 −19.8102 −0.637053 −0.318526 0.947914i 0.603188π-0.603188\pi
−0.318526 + 0.947914i 0.603188π0.603188\pi
968968 4.81422 0.154735
969969 3.36304 + 5.82495i 0.108036 + 0.187124i
970970 0.814635 1.41099i 0.0261563 0.0453041i
971971 3.61774 0.116099 0.0580493 0.998314i 0.481512π-0.481512\pi
0.0580493 + 0.998314i 0.481512π0.481512\pi
972972 14.3572 + 24.8674i 0.460508 + 0.797622i
973973 0 0
974974 −1.23595 −0.0396024
975975 −5.51942 + 3.31750i −0.176763 + 0.106245i
976976 16.8782 29.2339i 0.540258 0.935755i
977977 2.16169 0.0691586 0.0345793 0.999402i 0.488991π-0.488991\pi
0.0345793 + 0.999402i 0.488991π0.488991\pi
978978 −1.00341 + 1.73796i −0.0320855 + 0.0555737i
979979 15.1191 26.1870i 0.483208 0.836941i
980980 0 0
981981 6.84036 11.8479i 0.218396 0.378273i
982982 −3.49071 −0.111393
983983 −15.0545 + 26.0752i −0.480165 + 0.831671i −0.999741 0.0227535i 0.992757π-0.992757\pi
0.519576 + 0.854424i 0.326090π0.326090\pi
984984 −1.46717 2.54121i −0.0467717 0.0810109i
985985 14.9977 25.9767i 0.477865 0.827687i
986986 −0.247525 0.428727i −0.00788281 0.0136534i
987987 0 0
988988 0.916973 + 52.0983i 0.0291728 + 1.65747i
989989 −8.94742 15.4974i −0.284511 0.492788i
990990 4.59014 0.145884
991991 −27.1460 −0.862323 −0.431161 0.902275i 0.641896π-0.641896\pi
−0.431161 + 0.902275i 0.641896π0.641896\pi
992992 −7.82832 −0.248549
993993 2.65082 0.0841213
994994 0 0
995995 4.47902 7.75790i 0.141995 0.245942i
996996 1.18227 + 2.04776i 0.0374618 + 0.0648858i
997997 25.4005 + 43.9949i 0.804441 + 1.39333i 0.916668 + 0.399650i 0.130868π0.130868\pi
−0.112227 + 0.993683i 0.535798π0.535798\pi
998998 8.66599 0.274317
999999 18.1252 31.3938i 0.573456 0.993256i
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 637.2.g.l.263.3 12
7.2 even 3 637.2.h.l.471.4 12
7.3 odd 6 637.2.f.k.393.3 12
7.4 even 3 637.2.f.j.393.3 12
7.5 odd 6 91.2.h.b.16.4 yes 12
7.6 odd 2 91.2.g.b.81.3 yes 12
13.9 even 3 637.2.h.l.165.4 12
21.5 even 6 819.2.s.d.289.3 12
21.20 even 2 819.2.n.d.172.4 12
91.3 odd 6 8281.2.a.bz.1.4 6
91.9 even 3 inner 637.2.g.l.373.3 12
91.10 odd 6 8281.2.a.ce.1.3 6
91.48 odd 6 91.2.h.b.74.4 yes 12
91.55 odd 6 1183.2.e.h.508.3 12
91.61 odd 6 91.2.g.b.9.3 12
91.62 odd 6 1183.2.e.g.508.4 12
91.68 odd 6 1183.2.e.h.170.3 12
91.74 even 3 637.2.f.j.295.3 12
91.75 odd 6 1183.2.e.g.170.4 12
91.81 even 3 8281.2.a.ca.1.4 6
91.87 odd 6 637.2.f.k.295.3 12
91.88 even 6 8281.2.a.cf.1.3 6
273.152 even 6 819.2.n.d.100.4 12
273.230 even 6 819.2.s.d.802.3 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
91.2.g.b.9.3 12 91.61 odd 6
91.2.g.b.81.3 yes 12 7.6 odd 2
91.2.h.b.16.4 yes 12 7.5 odd 6
91.2.h.b.74.4 yes 12 91.48 odd 6
637.2.f.j.295.3 12 91.74 even 3
637.2.f.j.393.3 12 7.4 even 3
637.2.f.k.295.3 12 91.87 odd 6
637.2.f.k.393.3 12 7.3 odd 6
637.2.g.l.263.3 12 1.1 even 1 trivial
637.2.g.l.373.3 12 91.9 even 3 inner
637.2.h.l.165.4 12 13.9 even 3
637.2.h.l.471.4 12 7.2 even 3
819.2.n.d.100.4 12 273.152 even 6
819.2.n.d.172.4 12 21.20 even 2
819.2.s.d.289.3 12 21.5 even 6
819.2.s.d.802.3 12 273.230 even 6
1183.2.e.g.170.4 12 91.75 odd 6
1183.2.e.g.508.4 12 91.62 odd 6
1183.2.e.h.170.3 12 91.68 odd 6
1183.2.e.h.508.3 12 91.55 odd 6
8281.2.a.bz.1.4 6 91.3 odd 6
8281.2.a.ca.1.4 6 91.81 even 3
8281.2.a.ce.1.3 6 91.10 odd 6
8281.2.a.cf.1.3 6 91.88 even 6