Properties

Label 841.2.d.j.645.2
Level 841841
Weight 22
Character 841.645
Analytic conductor 6.7156.715
Analytic rank 00
Dimension 1212
Inner twists 66

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [841,2,Mod(190,841)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(841, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([2]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("841.190");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 841=292 841 = 29^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 841.d (of order 77, degree 66, 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: 6.715418809996.71541880999
Analytic rank: 00
Dimension: 1212
Relative dimension: 22 over Q(ζ7)\Q(\zeta_{7})
Coefficient field: 12.0.74049191673856.2
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x12+2x10+4x8+8x6+16x4+32x2+64 x^{12} + 2x^{10} + 4x^{8} + 8x^{6} + 16x^{4} + 32x^{2} + 64 Copy content Toggle raw display
Coefficient ring: Z[a1,a2,a3]\Z[a_1, a_2, a_3]
Coefficient ring index: 1 1
Twist minimal: no (minimal twist has level 29)
Sato-Tate group: SU(2)[C7]\mathrm{SU}(2)[C_{7}]

Embedding invariants

Embedding label 645.2
Root 0.881748+1.10568i-0.881748 + 1.10568i of defining polynomial
Character χ\chi == 841.645
Dual form 841.2.d.j.605.2

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+(0.537213+2.35368i)q2+(2.175131.04749i)q3+(3.44929+1.66109i)q4+(0.222521+0.974928i)q5+(1.296955.68230i)q6+(2.54832+1.22721i)q7+(2.752223.45117i)q8+(1.76350+2.21135i)q9+(2.17513+1.04749i)q10+(0.258258+0.323845i)q11+9.24264q12+(2.38699+2.99318i)q13+(1.51947+6.65722i)q14+(0.5372132.35368i)q15+(1.870472.34549i)q16+0.828427q17+(4.25745+5.33868i)q18+(5.40581+2.60330i)q19+(2.386992.99318i)q20+(4.257455.33868i)q21+(0.9009690.433884i)q22+(0.813727+3.56517i)q23+(2.37137+10.3897i)q24+(3.603881.73553i)q25+(8.327334.01023i)q26+(0.0921712+0.403828i)q2710.8284q28+5.82843q30+(2.241029.81857i)q31+(1.428740.688047i)q32+(0.9009690.433884i)q33+(0.445042+1.94986i)q34+(0.629384+2.75751i)q35+(9.756084.69828i)q36+(2.493963.12733i)q37+(9.0314311.3250i)q38+(8.327334.01023i)q39+(2.752223.45117i)q404.48528q41+(10.278412.8887i)q42+(0.797913+3.49588i)q43+(0.3528711.54603i)q44+(1.76350+2.21135i)q458.82843q46+(2.02175+2.53520i)q47+(6.52539+3.14246i)q48+(0.623490+0.781831i)q49+(6.02095+7.55003i)q50+(1.801940.867767i)q51+(3.2614614.2894i)q52+(2.110679.24747i)q53+(0.900969+0.433884i)q54+(0.3731940.179721i)q55+(2.7782412.1722i)q56+14.4853q573.65685q59+(2.05668+9.01091i)q60+(4.35026+2.09498i)q61+(21.905910.5493i)q62+(1.78017+7.79942i)q63+(2.187039.58201i)q64+(3.449291.66109i)q65+(1.50524+1.88751i)q66+(3.52699+4.42271i)q67+(2.85749+1.37609i)q68+(5.504436.90234i)q696.82843q70+(5.50443+6.90234i)q71+(2.7782412.1722i)q72+(0.890084+3.89971i)q73+(6.020957.55003i)q749.65685q75+(14.321917.9591i)q76+(1.05555+0.508326i)q77+(13.9124+17.4456i)q78+(1.505241.88751i)q79+(2.70291+1.30165i)q80+(2.110679.24747i)q81+(2.4095510.5569i)q82+(6.89859+3.32218i)q83+(23.5533+11.3426i)q84+(0.184342+0.807657i)q858.65685q86+1.82843q88+(2.77824+12.1722i)q89+(6.152202.96274i)q90+(9.75608+4.69828i)q91+(3.1152913.6490i)q92+(5.41031+23.7041i)q93+(7.053173.39663i)q94+(3.740944.69099i)q95+(2.38699+2.99318i)q96+(4.04110+1.94609i)q97+(1.50524+1.88751i)q981.17157q99+O(q100)q+(0.537213 + 2.35368i) q^{2} +(-2.17513 - 1.04749i) q^{3} +(-3.44929 + 1.66109i) q^{4} +(0.222521 + 0.974928i) q^{5} +(1.29695 - 5.68230i) q^{6} +(2.54832 + 1.22721i) q^{7} +(-2.75222 - 3.45117i) q^{8} +(1.76350 + 2.21135i) q^{9} +(-2.17513 + 1.04749i) q^{10} +(-0.258258 + 0.323845i) q^{11} +9.24264 q^{12} +(-2.38699 + 2.99318i) q^{13} +(-1.51947 + 6.65722i) q^{14} +(0.537213 - 2.35368i) q^{15} +(1.87047 - 2.34549i) q^{16} +0.828427 q^{17} +(-4.25745 + 5.33868i) q^{18} +(-5.40581 + 2.60330i) q^{19} +(-2.38699 - 2.99318i) q^{20} +(-4.25745 - 5.33868i) q^{21} +(-0.900969 - 0.433884i) q^{22} +(-0.813727 + 3.56517i) q^{23} +(2.37137 + 10.3897i) q^{24} +(3.60388 - 1.73553i) q^{25} +(-8.32733 - 4.01023i) q^{26} +(0.0921712 + 0.403828i) q^{27} -10.8284 q^{28} +5.82843 q^{30} +(-2.24102 - 9.81857i) q^{31} +(-1.42874 - 0.688047i) q^{32} +(0.900969 - 0.433884i) q^{33} +(0.445042 + 1.94986i) q^{34} +(-0.629384 + 2.75751i) q^{35} +(-9.75608 - 4.69828i) q^{36} +(-2.49396 - 3.12733i) q^{37} +(-9.03143 - 11.3250i) q^{38} +(8.32733 - 4.01023i) q^{39} +(2.75222 - 3.45117i) q^{40} -4.48528 q^{41} +(10.2784 - 12.8887i) q^{42} +(-0.797913 + 3.49588i) q^{43} +(0.352871 - 1.54603i) q^{44} +(-1.76350 + 2.21135i) q^{45} -8.82843 q^{46} +(-2.02175 + 2.53520i) q^{47} +(-6.52539 + 3.14246i) q^{48} +(0.623490 + 0.781831i) q^{49} +(6.02095 + 7.55003i) q^{50} +(-1.80194 - 0.867767i) q^{51} +(3.26146 - 14.2894i) q^{52} +(-2.11067 - 9.24747i) q^{53} +(-0.900969 + 0.433884i) q^{54} +(-0.373194 - 0.179721i) q^{55} +(-2.77824 - 12.1722i) q^{56} +14.4853 q^{57} -3.65685 q^{59} +(2.05668 + 9.01091i) q^{60} +(4.35026 + 2.09498i) q^{61} +(21.9059 - 10.5493i) q^{62} +(1.78017 + 7.79942i) q^{63} +(2.18703 - 9.58201i) q^{64} +(-3.44929 - 1.66109i) q^{65} +(1.50524 + 1.88751i) q^{66} +(3.52699 + 4.42271i) q^{67} +(-2.85749 + 1.37609i) q^{68} +(5.50443 - 6.90234i) q^{69} -6.82843 q^{70} +(-5.50443 + 6.90234i) q^{71} +(2.77824 - 12.1722i) q^{72} +(-0.890084 + 3.89971i) q^{73} +(6.02095 - 7.55003i) q^{74} -9.65685 q^{75} +(14.3219 - 17.9591i) q^{76} +(-1.05555 + 0.508326i) q^{77} +(13.9124 + 17.4456i) q^{78} +(-1.50524 - 1.88751i) q^{79} +(2.70291 + 1.30165i) q^{80} +(2.11067 - 9.24747i) q^{81} +(-2.40955 - 10.5569i) q^{82} +(-6.89859 + 3.32218i) q^{83} +(23.5533 + 11.3426i) q^{84} +(0.184342 + 0.807657i) q^{85} -8.65685 q^{86} +1.82843 q^{88} +(2.77824 + 12.1722i) q^{89} +(-6.15220 - 2.96274i) q^{90} +(-9.75608 + 4.69828i) q^{91} +(-3.11529 - 13.6490i) q^{92} +(-5.41031 + 23.7041i) q^{93} +(-7.05317 - 3.39663i) q^{94} +(-3.74094 - 4.69099i) q^{95} +(2.38699 + 2.99318i) q^{96} +(-4.04110 + 1.94609i) q^{97} +(-1.50524 + 1.88751i) q^{98} -1.17157 q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 12q+2q22q32q4+2q5+6q6+6q82q102q11+60q12+2q138q14+2q156q1624q17+8q1812q19+2q20+8q212q22+48q99+O(q100) 12 q + 2 q^{2} - 2 q^{3} - 2 q^{4} + 2 q^{5} + 6 q^{6} + 6 q^{8} - 2 q^{10} - 2 q^{11} + 60 q^{12} + 2 q^{13} - 8 q^{14} + 2 q^{15} - 6 q^{16} - 24 q^{17} + 8 q^{18} - 12 q^{19} + 2 q^{20} + 8 q^{21} - 2 q^{22}+ \cdots - 48 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/841Z)×\left(\mathbb{Z}/841\mathbb{Z}\right)^\times.

nn 22
χ(n)\chi(n) e(37)e\left(\frac{3}{7}\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 0.537213 + 2.35368i 0.379867 + 1.66431i 0.697876 + 0.716218i 0.254129π0.254129\pi
−0.318009 + 0.948088i 0.603014π0.603014\pi
33 −2.17513 1.04749i −1.25581 0.604767i −0.316749 0.948510i 0.602591π-0.602591\pi
−0.939064 + 0.343742i 0.888305π0.888305\pi
44 −3.44929 + 1.66109i −1.72465 + 0.830546i
55 0.222521 + 0.974928i 0.0995144 + 0.436001i 0.999999 + 0.00111393i 0.000354575π0.000354575\pi
−0.900485 + 0.434887i 0.856788π0.856788\pi
66 1.29695 5.68230i 0.529476 2.31979i
77 2.54832 + 1.22721i 0.963176 + 0.463841i 0.848287 0.529537i 0.177634π-0.177634\pi
0.114889 + 0.993378i 0.463349π0.463349\pi
88 −2.75222 3.45117i −0.973056 1.22017i
99 1.76350 + 2.21135i 0.587832 + 0.737118i
1010 −2.17513 + 1.04749i −0.687837 + 0.331245i
1111 −0.258258 + 0.323845i −0.0778677 + 0.0976430i −0.819240 0.573452i 0.805604π-0.805604\pi
0.741372 + 0.671095i 0.234176π0.234176\pi
1212 9.24264 2.66812
1313 −2.38699 + 2.99318i −0.662031 + 0.830160i −0.993563 0.113284i 0.963863π-0.963863\pi
0.331532 + 0.943444i 0.392434π0.392434\pi
1414 −1.51947 + 6.65722i −0.406095 + 1.77922i
1515 0.537213 2.35368i 0.138708 0.607719i
1616 1.87047 2.34549i 0.467617 0.586374i
1717 0.828427 0.200923 0.100462 0.994941i 0.467968π-0.467968\pi
0.100462 + 0.994941i 0.467968π0.467968\pi
1818 −4.25745 + 5.33868i −1.00349 + 1.25834i
1919 −5.40581 + 2.60330i −1.24018 + 0.597239i −0.934862 0.355012i 0.884477π-0.884477\pi
−0.305317 + 0.952251i 0.598762π0.598762\pi
2020 −2.38699 2.99318i −0.533746 0.669296i
2121 −4.25745 5.33868i −0.929053 1.16500i
2222 −0.900969 0.433884i −0.192087 0.0925043i
2323 −0.813727 + 3.56517i −0.169674 + 0.743389i 0.816455 + 0.577409i 0.195936π0.195936\pi
−0.986129 + 0.165981i 0.946921π0.946921\pi
2424 2.37137 + 10.3897i 0.484055 + 2.12078i
2525 3.60388 1.73553i 0.720775 0.347107i
2626 −8.32733 4.01023i −1.63312 0.786471i
2727 0.0921712 + 0.403828i 0.0177384 + 0.0777168i
2828 −10.8284 −2.04638
2929 0 0
3030 5.82843 1.06412
3131 −2.24102 9.81857i −0.402500 1.76347i −0.617220 0.786791i 0.711741π-0.711741\pi
0.214720 0.976676i 0.431116π-0.431116\pi
3232 −1.42874 0.688047i −0.252569 0.121631i
3333 0.900969 0.433884i 0.156839 0.0755295i
3434 0.445042 + 1.94986i 0.0763241 + 0.334398i
3535 −0.629384 + 2.75751i −0.106385 + 0.466105i
3636 −9.75608 4.69828i −1.62601 0.783046i
3737 −2.49396 3.12733i −0.410004 0.514129i 0.533360 0.845889i 0.320929π-0.320929\pi
−0.943364 + 0.331759i 0.892358π0.892358\pi
3838 −9.03143 11.3250i −1.46509 1.83717i
3939 8.32733 4.01023i 1.33344 0.642151i
4040 2.75222 3.45117i 0.435164 0.545678i
4141 −4.48528 −0.700483 −0.350242 0.936659i 0.613901π-0.613901\pi
−0.350242 + 0.936659i 0.613901π0.613901\pi
4242 10.2784 12.8887i 1.58599 1.98877i
4343 −0.797913 + 3.49588i −0.121681 + 0.533117i 0.876940 + 0.480601i 0.159581π0.159581\pi
−0.998620 + 0.0525165i 0.983276π0.983276\pi
4444 0.352871 1.54603i 0.0531973 0.233072i
4545 −1.76350 + 2.21135i −0.262886 + 0.329649i
4646 −8.82843 −1.30168
4747 −2.02175 + 2.53520i −0.294903 + 0.369797i −0.907105 0.420905i 0.861713π-0.861713\pi
0.612202 + 0.790702i 0.290284π0.290284\pi
4848 −6.52539 + 3.14246i −0.941859 + 0.453576i
4949 0.623490 + 0.781831i 0.0890700 + 0.111690i
5050 6.02095 + 7.55003i 0.851491 + 1.06774i
5151 −1.80194 0.867767i −0.252322 0.121512i
5252 3.26146 14.2894i 0.452283 1.98158i
5353 −2.11067 9.24747i −0.289923 1.27024i −0.884630 0.466294i 0.845589π-0.845589\pi
0.594706 0.803943i 0.297268π-0.297268\pi
5454 −0.900969 + 0.433884i −0.122606 + 0.0590441i
5555 −0.373194 0.179721i −0.0503214 0.0242335i
5656 −2.77824 12.1722i −0.371257 1.62659i
5757 14.4853 1.91862
5858 0 0
5959 −3.65685 −0.476082 −0.238041 0.971255i 0.576505π-0.576505\pi
−0.238041 + 0.971255i 0.576505π0.576505\pi
6060 2.05668 + 9.01091i 0.265516 + 1.16330i
6161 4.35026 + 2.09498i 0.556994 + 0.268234i 0.691132 0.722728i 0.257112π-0.257112\pi
−0.134138 + 0.990963i 0.542827π0.542827\pi
6262 21.9059 10.5493i 2.78205 1.33977i
6363 1.78017 + 7.79942i 0.224280 + 0.982635i
6464 2.18703 9.58201i 0.273379 1.19775i
6565 −3.44929 1.66109i −0.427832 0.206033i
6666 1.50524 + 1.88751i 0.185282 + 0.232336i
6767 3.52699 + 4.42271i 0.430891 + 0.540320i 0.949117 0.314924i 0.101979π-0.101979\pi
−0.518226 + 0.855243i 0.673408π0.673408\pi
6868 −2.85749 + 1.37609i −0.346521 + 0.166876i
6969 5.50443 6.90234i 0.662656 0.830944i
7070 −6.82843 −0.816153
7171 −5.50443 + 6.90234i −0.653256 + 0.819157i −0.992590 0.121509i 0.961227π-0.961227\pi
0.339334 + 0.940666i 0.389798π0.389798\pi
7272 2.77824 12.1722i 0.327418 1.43451i
7373 −0.890084 + 3.89971i −0.104176 + 0.456427i 0.895753 + 0.444552i 0.146637π0.146637\pi
−0.999929 + 0.0118748i 0.996220π0.996220\pi
7474 6.02095 7.55003i 0.699921 0.877673i
7575 −9.65685 −1.11508
7676 14.3219 17.9591i 1.64284 2.06005i
7777 −1.05555 + 0.508326i −0.120291 + 0.0579292i
7878 13.9124 + 17.4456i 1.57527 + 1.97532i
7979 −1.50524 1.88751i −0.169352 0.212361i 0.689911 0.723894i 0.257649π-0.257649\pi
−0.859264 + 0.511532i 0.829078π0.829078\pi
8080 2.70291 + 1.30165i 0.302194 + 0.145529i
8181 2.11067 9.24747i 0.234519 1.02750i
8282 −2.40955 10.5569i −0.266090 1.16582i
8383 −6.89859 + 3.32218i −0.757218 + 0.364657i −0.772324 0.635229i 0.780906π-0.780906\pi
0.0151057 + 0.999886i 0.495192π0.495192\pi
8484 23.5533 + 11.3426i 2.56987 + 1.23758i
8585 0.184342 + 0.807657i 0.0199947 + 0.0876027i
8686 −8.65685 −0.933493
8787 0 0
8888 1.82843 0.194911
8989 2.77824 + 12.1722i 0.294492 + 1.29026i 0.878201 + 0.478292i 0.158744π0.158744\pi
−0.583708 + 0.811964i 0.698399π0.698399\pi
9090 −6.15220 2.96274i −0.648499 0.312301i
9191 −9.75608 + 4.69828i −1.02271 + 0.492513i
9292 −3.11529 13.6490i −0.324792 1.42301i
9393 −5.41031 + 23.7041i −0.561023 + 2.45800i
9494 −7.05317 3.39663i −0.727479 0.350335i
9595 −3.74094 4.69099i −0.383812 0.481285i
9696 2.38699 + 2.99318i 0.243621 + 0.305491i
9797 −4.04110 + 1.94609i −0.410311 + 0.197596i −0.627641 0.778503i 0.715980π-0.715980\pi
0.217330 + 0.976098i 0.430265π0.430265\pi
9898 −1.50524 + 1.88751i −0.152052 + 0.190667i
9999 −1.17157 −0.117748
100100 −9.54794 + 11.9727i −0.954794 + 1.19727i
101101 0.521399 2.28440i 0.0518811 0.227306i −0.942340 0.334657i 0.891380π-0.891380\pi
0.994221 + 0.107351i 0.0342368π0.0342368\pi
102102 1.07443 4.70737i 0.106384 0.466099i
103103 −3.01048 + 3.77502i −0.296631 + 0.371963i −0.907704 0.419611i 0.862167π-0.862167\pi
0.611073 + 0.791574i 0.290738π0.290738\pi
104104 16.8995 1.65713
105105 4.25745 5.33868i 0.415485 0.521002i
106106 20.6317 9.93572i 2.00393 0.965042i
107107 −9.24537 11.5933i −0.893784 1.12077i −0.992079 0.125612i 0.959910π-0.959910\pi
0.0982954 0.995157i 0.468661π-0.468661\pi
108108 −0.988722 1.23982i −0.0951398 0.119302i
109109 −11.4034 5.49160i −1.09225 0.526000i −0.201037 0.979584i 0.564431π-0.564431\pi
−0.891214 + 0.453583i 0.850145π0.850145\pi
110110 0.222521 0.974928i 0.0212165 0.0929557i
111111 2.14885 + 9.41474i 0.203960 + 0.893607i
112112 7.64497 3.68163i 0.722382 0.347881i
113113 11.9952 + 5.77660i 1.12842 + 0.543417i 0.902483 0.430726i 0.141742π-0.141742\pi
0.225934 + 0.974143i 0.427457π0.427457\pi
114114 7.78168 + 34.0938i 0.728821 + 3.19317i
115115 −3.65685 −0.341003
116116 0 0
117117 −10.8284 −1.00109
118118 −1.96451 8.60708i −0.180848 0.792346i
119119 2.11110 + 1.01665i 0.193524 + 0.0931964i
120120 −9.60149 + 4.62384i −0.876492 + 0.422097i
121121 2.40955 + 10.5569i 0.219050 + 0.959721i
122122 −2.59389 + 11.3646i −0.234840 + 1.02890i
123123 9.75608 + 4.69828i 0.879676 + 0.423630i
124124 24.0395 + 30.1446i 2.15881 + 2.70706i
125125 5.61141 + 7.03648i 0.501900 + 0.629362i
126126 −17.4011 + 8.37990i −1.55021 + 0.746541i
127127 −2.70791 + 3.39561i −0.240288 + 0.301311i −0.887323 0.461149i 0.847437π-0.847437\pi
0.647035 + 0.762460i 0.276009π0.276009\pi
128128 20.5563 1.81694
129129 5.39746 6.76820i 0.475220 0.595907i
130130 2.05668 9.01091i 0.180383 0.790309i
131131 −4.74275 + 20.7793i −0.414376 + 1.81550i 0.148447 + 0.988920i 0.452573π0.452573\pi
−0.562822 + 0.826578i 0.690284π0.690284\pi
132132 −2.38699 + 2.99318i −0.207760 + 0.260523i
133133 −16.9706 −1.47153
134134 −8.51491 + 10.6774i −0.735576 + 0.922383i
135135 −0.373194 + 0.179721i −0.0321194 + 0.0154679i
136136 −2.28001 2.85904i −0.195509 0.245161i
137137 7.48188 + 9.38198i 0.639220 + 0.801556i 0.990905 0.134562i 0.0429627π-0.0429627\pi
−0.351685 + 0.936118i 0.614391π0.614391\pi
138138 19.2030 + 9.24767i 1.63467 + 0.787214i
139139 −3.11529 + 13.6490i −0.264236 + 1.15769i 0.652370 + 0.757900i 0.273775π0.273775\pi
−0.916606 + 0.399792i 0.869082π0.869082\pi
140140 −2.40955 10.5569i −0.203644 0.892224i
141141 7.05317 3.39663i 0.593984 0.286048i
142142 −19.2030 9.24767i −1.61148 0.776047i
143143 −0.352871 1.54603i −0.0295085 0.129285i
144144 8.48528 0.707107
145145 0 0
146146 −9.65685 −0.799207
147147 −0.537213 2.35368i −0.0443086 0.194129i
148148 13.7972 + 6.64437i 1.13412 + 0.546164i
149149 7.05317 3.39663i 0.577818 0.278263i −0.122062 0.992522i 0.538951π-0.538951\pi
0.699881 + 0.714260i 0.253237π0.253237\pi
150150 −5.18779 22.7292i −0.423581 1.85583i
151151 3.14692 13.7876i 0.256093 1.12202i −0.669296 0.742996i 0.733404π-0.733404\pi
0.925389 0.379020i 0.123739π-0.123739\pi
152152 23.8624 + 11.4915i 1.93550 + 0.932086i
153153 1.46093 + 1.83195i 0.118109 + 0.148104i
154154 −1.76350 2.21135i −0.142107 0.178196i
155155 9.07372 4.36967i 0.728819 0.350981i
156156 −22.0620 + 27.6649i −1.76638 + 2.21497i
157157 8.48528 0.677199 0.338600 0.940931i 0.390047π-0.390047\pi
0.338600 + 0.940931i 0.390047π0.390047\pi
158158 3.63396 4.55685i 0.289103 0.362523i
159159 −5.09562 + 22.3254i −0.404109 + 1.77052i
160160 0.352871 1.54603i 0.0278969 0.122224i
161161 −6.44885 + 8.08660i −0.508240 + 0.637313i
162162 22.8995 1.79915
163163 2.44965 3.07176i 0.191871 0.240599i −0.676585 0.736364i 0.736541π-0.736541\pi
0.868457 + 0.495765i 0.165112π0.165112\pi
164164 15.4711 7.45047i 1.20809 0.581784i
165165 0.623490 + 0.781831i 0.0485386 + 0.0608655i
166166 −11.5254 14.4524i −0.894543 1.12172i
167167 2.85749 + 1.37609i 0.221119 + 0.106485i 0.541164 0.840917i 0.317984π-0.317984\pi
−0.320045 + 0.947402i 0.603698π0.603698\pi
168168 −6.70726 + 29.3864i −0.517476 + 2.26721i
169169 −0.368685 1.61531i −0.0283604 0.124255i
170170 −1.80194 + 0.867767i −0.138202 + 0.0665547i
171171 −15.2899 7.36325i −1.16925 0.563082i
172172 −3.05475 13.3837i −0.232923 1.02050i
173173 12.3431 0.938432 0.469216 0.883083i 0.344537π-0.344537\pi
0.469216 + 0.883083i 0.344537π0.344537\pi
174174 0 0
175175 11.3137 0.855236
176176 0.276514 + 1.21149i 0.0208430 + 0.0913191i
177177 7.95414 + 3.83051i 0.597870 + 0.287919i
178178 −27.1571 + 13.0782i −2.03551 + 0.980251i
179179 1.44311 + 6.32268i 0.107863 + 0.472579i 0.999792 + 0.0204033i 0.00649502π0.00649502\pi
−0.891929 + 0.452176i 0.850648π0.850648\pi
180180 2.40955 10.5569i 0.179597 0.786868i
181181 −7.49039 3.60718i −0.556756 0.268120i 0.134275 0.990944i 0.457129π-0.457129\pi
−0.691032 + 0.722824i 0.742844π0.742844\pi
182182 −16.2994 20.4387i −1.20819 1.51502i
183183 −7.26793 9.11370i −0.537261 0.673704i
184184 14.5436 7.00381i 1.07217 0.516328i
185185 2.49396 3.12733i 0.183360 0.229926i
186186 −58.6985 −4.30398
187187 −0.213948 + 0.268282i −0.0156454 + 0.0196187i
188188 2.76242 12.1030i 0.201470 0.882699i
189189 −0.260699 + 1.14220i −0.0189631 + 0.0830828i
190190 9.03143 11.3250i 0.655208 0.821605i
191191 25.3137 1.83164 0.915818 0.401594i 0.131544π-0.131544\pi
0.915818 + 0.401594i 0.131544π0.131544\pi
192192 −14.7941 + 18.5512i −1.06767 + 1.33882i
193193 4.65943 2.24386i 0.335393 0.161517i −0.258605 0.965983i 0.583263π-0.583263\pi
0.593998 + 0.804466i 0.297549π0.297549\pi
194194 −6.75141 8.46601i −0.484723 0.607824i
195195 5.76269 + 7.22619i 0.412675 + 0.517478i
196196 −3.44929 1.66109i −0.246378 0.118649i
197197 −0.445042 + 1.94986i −0.0317079 + 0.138921i −0.988304 0.152495i 0.951269π-0.951269\pi
0.956596 + 0.291416i 0.0941264π0.0941264\pi
198198 −0.629384 2.75751i −0.0447284 0.195968i
199199 0.437223 0.210556i 0.0309939 0.0149259i −0.418323 0.908299i 0.637382π-0.637382\pi
0.449317 + 0.893373i 0.351668π0.351668\pi
200200 −15.9083 7.66102i −1.12488 0.541716i
201201 −3.03894 13.3144i −0.214350 0.939129i
202202 5.65685 0.398015
203203 0 0
204204 7.65685 0.536087
205205 −0.998069 4.37283i −0.0697082 0.305411i
206206 −10.5025 5.05772i −0.731741 0.352388i
207207 −9.31885 + 4.48772i −0.647705 + 0.311918i
208208 2.55572 + 11.1973i 0.177207 + 0.776395i
209209 0.553027 2.42297i 0.0382537 0.167600i
210210 14.8527 + 7.15270i 1.02494 + 0.493583i
211211 −12.0862 15.1556i −0.832049 1.04336i −0.998358 0.0572828i 0.981756π-0.981756\pi
0.166309 0.986074i 0.446815π-0.446815\pi
212212 22.6412 + 28.3912i 1.55501 + 1.94992i
213213 19.2030 9.24767i 1.31577 0.633640i
214214 22.3203 27.9888i 1.52578 1.91327i
215215 −3.58579 −0.244549
216216 1.14001 1.42952i 0.0775676 0.0972666i
217217 6.33857 27.7711i 0.430290 1.88522i
218218 6.79943 29.7902i 0.460515 2.01765i
219219 6.02095 7.55003i 0.406858 0.510184i
220220 1.58579 0.106914
221221 −1.97744 + 2.47964i −0.133017 + 0.166798i
222222 −21.0049 + 10.1154i −1.40976 + 0.678904i
223223 −1.97744 2.47964i −0.132419 0.166049i 0.711201 0.702989i 0.248152π-0.248152\pi
−0.843620 + 0.536940i 0.819580π0.819580\pi
224224 −2.79653 3.50673i −0.186851 0.234304i
225225 10.1933 + 4.90883i 0.679553 + 0.327256i
226226 −7.15230 + 31.3363i −0.475764 + 2.08446i
227227 1.81180 + 7.93800i 0.120253 + 0.526863i 0.998790 + 0.0491879i 0.0156633π0.0156633\pi
−0.878536 + 0.477675i 0.841480π0.841480\pi
228228 −49.9640 + 24.0614i −3.30895 + 1.59350i
229229 3.16665 + 1.52498i 0.209258 + 0.100773i 0.535577 0.844486i 0.320094π-0.320094\pi
−0.326319 + 0.945260i 0.605808π0.605808\pi
230230 −1.96451 8.60708i −0.129536 0.567534i
231231 2.82843 0.186097
232232 0 0
233233 18.3137 1.19977 0.599885 0.800086i 0.295213π-0.295213\pi
0.599885 + 0.800086i 0.295213π0.295213\pi
234234 −5.81717 25.4867i −0.380280 1.66612i
235235 −2.92152 1.40693i −0.190579 0.0917779i
236236 12.6136 6.07437i 0.821073 0.395408i
237237 1.29695 + 5.68230i 0.0842458 + 0.369105i
238238 −1.25877 + 5.51503i −0.0815938 + 0.357486i
239239 17.7102 + 8.52879i 1.14558 + 0.551682i 0.907703 0.419614i 0.137835π-0.137835\pi
0.237876 + 0.971296i 0.423549π0.423549\pi
240240 −4.51571 5.66252i −0.291488 0.365514i
241241 −11.4184 14.3182i −0.735524 0.922319i 0.263580 0.964638i 0.415097π-0.415097\pi
−0.999104 + 0.0423191i 0.986525π0.986525\pi
242242 −23.5533 + 11.3426i −1.51406 + 0.729133i
243243 −13.5028 + 16.9320i −0.866207 + 1.08619i
244244 −18.4853 −1.18340
245245 −0.623490 + 0.781831i −0.0398333 + 0.0499494i
246246 −5.81717 + 25.4867i −0.370889 + 1.62497i
247247 5.11143 22.3946i 0.325233 1.42494i
248248 −27.7178 + 34.7570i −1.76008 + 2.20707i
249249 18.4853 1.17146
250250 −13.5471 + 16.9876i −0.856796 + 1.07439i
251251 −18.0834 + 8.70851i −1.14141 + 0.549676i −0.906444 0.422326i 0.861214π-0.861214\pi
−0.234971 + 0.972002i 0.575499π0.575499\pi
252252 −19.0959 23.9455i −1.20293 1.50842i
253253 −0.944412 1.18425i −0.0593746 0.0744535i
254254 −9.44691 4.54939i −0.592752 0.285454i
255255 0.445042 1.94986i 0.0278696 0.122105i
256256 6.66908 + 29.2191i 0.416817 + 1.82620i
257257 16.3720 7.88435i 1.02126 0.491812i 0.153159 0.988202i 0.451055π-0.451055\pi
0.868100 + 0.496389i 0.165341π0.165341\pi
258258 18.8298 + 9.06795i 1.17229 + 0.564546i
259259 −2.51754 11.0301i −0.156432 0.685374i
260260 14.6569 0.908980
261261 0 0
262262 −51.4558 −3.17895
263263 −0.613570 2.68823i −0.0378344 0.165763i 0.952481 0.304597i 0.0985218π-0.0985218\pi
−0.990316 + 0.138834i 0.955665π0.955665\pi
264264 −3.97707 1.91526i −0.244772 0.117876i
265265 8.54594 4.11551i 0.524973 0.252814i
266266 −9.11681 39.9433i −0.558987 2.44908i
267267 6.70726 29.3864i 0.410477 1.79842i
268268 −19.5122 9.39656i −1.19189 0.573986i
269269 19.6124 + 24.5932i 1.19579 + 1.49947i 0.819607 + 0.572926i 0.194192π0.194192\pi
0.376182 + 0.926546i 0.377237π0.377237\pi
270270 −0.623490 0.781831i −0.0379444 0.0475807i
271271 −14.9168 + 7.18353i −0.906128 + 0.436368i −0.828099 0.560583i 0.810577π-0.810577\pi
−0.0780298 + 0.996951i 0.524863π0.524863\pi
272272 1.54955 1.94307i 0.0939551 0.117816i
273273 26.1421 1.58219
274274 −18.0629 + 22.6501i −1.09122 + 1.36834i
275275 −0.368685 + 1.61531i −0.0222325 + 0.0974071i
276276 −7.52098 + 32.9516i −0.452710 + 1.98345i
277277 −10.7949 + 13.5364i −0.648604 + 0.813324i −0.992049 0.125849i 0.959835π-0.959835\pi
0.343445 + 0.939173i 0.388406π0.388406\pi
278278 −33.7990 −2.02713
279279 17.7603 22.2707i 1.06328 1.33331i
280280 11.2488 5.41716i 0.672247 0.323737i
281281 19.9333 + 24.9956i 1.18912 + 1.49111i 0.829947 + 0.557842i 0.188370π0.188370\pi
0.359175 + 0.933270i 0.383058π0.383058\pi
282282 11.7836 + 14.7762i 0.701706 + 0.879911i
283283 −10.5025 5.05772i −0.624307 0.300650i 0.0948571 0.995491i 0.469761π-0.469761\pi
−0.719164 + 0.694841i 0.755475π0.755475\pi
284284 7.52098 32.9516i 0.446288 1.95532i
285285 3.22328 + 14.1221i 0.190931 + 0.836521i
286286 3.44929 1.66109i 0.203961 0.0982224i
287287 −11.4300 5.50438i −0.674689 0.324913i
288288 −0.998069 4.37283i −0.0588118 0.257671i
289289 −16.3137 −0.959630
290290 0 0
291291 10.8284 0.634774
292292 −3.40762 14.9298i −0.199416 0.873698i
293293 −6.89859 3.32218i −0.403020 0.194084i 0.221382 0.975187i 0.428943π-0.428943\pi
−0.624402 + 0.781103i 0.714657π0.714657\pi
294294 5.25123 2.52886i 0.306258 0.147486i
295295 −0.813727 3.56517i −0.0473770 0.207572i
296296 −3.92902 + 17.2142i −0.228370 + 1.00055i
297297 −0.154582 0.0744427i −0.00896975 0.00431960i
298298 11.7836 + 14.7762i 0.682608 + 0.855963i
299299 −8.72886 10.9456i −0.504803 0.633003i
300300 33.3093 16.0409i 1.92311 0.926123i
301301 −6.32352 + 7.92944i −0.364482 + 0.457045i
302302 34.1421 1.96466
303303 −3.52699 + 4.42271i −0.202620 + 0.254078i
304304 −4.00538 + 17.5487i −0.229724 + 1.00649i
305305 −1.07443 + 4.70737i −0.0615215 + 0.269543i
306306 −3.52699 + 4.42271i −0.201625 + 0.252829i
307307 2.89949 0.165483 0.0827415 0.996571i 0.473632π-0.473632\pi
0.0827415 + 0.996571i 0.473632π0.473632\pi
308308 2.79653 3.50673i 0.159347 0.199815i
309309 10.5025 5.05772i 0.597464 0.287724i
310310 15.1593 + 19.0092i 0.860993 + 1.07965i
311311 1.67488 + 2.10023i 0.0949735 + 0.119093i 0.827047 0.562132i 0.190019π-0.190019\pi
−0.732074 + 0.681225i 0.761447π0.761447\pi
312312 −36.7586 17.7020i −2.08105 1.00218i
313313 −2.18703 + 9.58201i −0.123618 + 0.541607i 0.874754 + 0.484568i 0.161023π0.161023\pi
−0.998372 + 0.0570392i 0.981834π0.981834\pi
314314 4.55840 + 19.9717i 0.257246 + 1.12707i
315315 −7.20775 + 3.47107i −0.406111 + 0.195573i
316316 8.32733 + 4.01023i 0.468449 + 0.225593i
317317 6.99958 + 30.6672i 0.393136 + 1.72244i 0.653497 + 0.756929i 0.273301π0.273301\pi
−0.260361 + 0.965511i 0.583842π0.583842\pi
318318 −55.2843 −3.10019
319319 0 0
320320 9.82843 0.549426
321321 7.96602 + 34.9014i 0.444620 + 1.94801i
322322 −22.4977 10.8343i −1.25375 0.603773i
323323 −4.47832 + 2.15665i −0.249181 + 0.119999i
324324 8.08056 + 35.4032i 0.448920 + 1.96685i
325325 −3.40762 + 14.9298i −0.189021 + 0.828154i
326326 8.54594 + 4.11551i 0.473316 + 0.227937i
327327 19.0516 + 23.8899i 1.05355 + 1.32112i
328328 12.3445 + 15.4795i 0.681609 + 0.854711i
329329 −8.26330 + 3.97940i −0.455571 + 0.219391i
330330 −1.50524 + 1.88751i −0.0828606 + 0.103904i
331331 −2.41421 −0.132697 −0.0663486 0.997797i 0.521135π-0.521135\pi
−0.0663486 + 0.997797i 0.521135π0.521135\pi
332332 18.2768 22.9184i 1.00307 1.25781i
333333 2.51754 11.0301i 0.137960 0.604443i
334334 −1.70381 + 7.46488i −0.0932284 + 0.408460i
335335 −3.52699 + 4.42271i −0.192700 + 0.241638i
336336 −20.4853 −1.11756
337337 13.5914 17.0431i 0.740373 0.928399i −0.258923 0.965898i 0.583368π-0.583368\pi
0.999297 + 0.0374991i 0.0119391π0.0119391\pi
338338 3.60388 1.73553i 0.196025 0.0944007i
339339 −20.0403 25.1297i −1.08844 1.36486i
340340 −1.97744 2.47964i −0.107242 0.134477i
341341 3.75846 + 1.80998i 0.203532 + 0.0980158i
342342 9.11681 39.9433i 0.492981 2.15989i
343343 −3.77631 16.5451i −0.203901 0.893350i
344344 14.2609 6.86770i 0.768897 0.370281i
345345 7.95414 + 3.83051i 0.428236 + 0.206228i
346346 6.63090 + 29.0519i 0.356479 + 1.56184i
347347 2.48528 0.133417 0.0667084 0.997773i 0.478750π-0.478750\pi
0.0667084 + 0.997773i 0.478750π0.478750\pi
348348 0 0
349349 −5.14214 −0.275252 −0.137626 0.990484i 0.543947π-0.543947\pi
−0.137626 + 0.990484i 0.543947π0.543947\pi
350350 6.07787 + 26.6289i 0.324876 + 1.42337i
351351 −1.42874 0.688047i −0.0762607 0.0367252i
352352 0.591805 0.284998i 0.0315433 0.0151905i
353353 −6.00151 26.2944i −0.319428 1.39951i −0.838558 0.544812i 0.816601π-0.816601\pi
0.519130 0.854695i 0.326256π-0.326256\pi
354354 −4.74275 + 20.7793i −0.252074 + 1.10441i
355355 −7.95414 3.83051i −0.422162 0.203302i
356356 −29.8022 37.3708i −1.57951 1.98065i
357357 −3.52699 4.42271i −0.186668 0.234074i
358358 −14.1063 + 6.79325i −0.745543 + 0.359035i
359359 2.44965 3.07176i 0.129288 0.162121i −0.712974 0.701190i 0.752652π-0.752652\pi
0.842262 + 0.539069i 0.181224π0.181224\pi
360360 12.4853 0.658032
361361 10.5993 13.2911i 0.557859 0.699533i
362362 4.46623 19.5678i 0.234740 1.02846i
363363 5.81717 25.4867i 0.305322 1.33770i
364364 25.8473 32.4115i 1.35477 1.69882i
365365 −4.00000 −0.209370
366366 17.5463 22.0024i 0.917162 1.15008i
367367 −16.2174 + 7.80991i −0.846543 + 0.407674i −0.806293 0.591516i 0.798530π-0.798530\pi
−0.0402500 + 0.999190i 0.512815π0.512815\pi
368368 6.84003 + 8.57713i 0.356561 + 0.447114i
369369 −7.90977 9.91854i −0.411766 0.516339i
370370 8.70053 + 4.18995i 0.452319 + 0.217825i
371371 5.96989 26.1558i 0.309941 1.35794i
372372 −20.7130 90.7495i −1.07392 4.70514i
373373 23.7078 11.4171i 1.22755 0.591155i 0.296142 0.955144i 0.404300π-0.404300\pi
0.931403 + 0.363989i 0.118586π0.118586\pi
374374 −0.746387 0.359441i −0.0385948 0.0185863i
375375 −4.83492 21.1832i −0.249674 1.09389i
376376 14.3137 0.738173
377377 0 0
378378 −2.82843 −0.145479
379379 1.55110 + 6.79580i 0.0796745 + 0.349077i 0.999014 0.0443876i 0.0141337π-0.0141337\pi
−0.919340 + 0.393464i 0.871277π0.871277\pi
380380 20.6958 + 9.96655i 1.06167 + 0.511273i
381381 9.44691 4.54939i 0.483980 0.233072i
382382 13.5989 + 59.5805i 0.695778 + 3.04840i
383383 0.782098 3.42660i 0.0399634 0.175091i −0.951008 0.309167i 0.899950π-0.899950\pi
0.990971 + 0.134077i 0.0428068π0.0428068\pi
384384 −44.7128 21.5325i −2.28174 1.09883i
385385 −0.730464 0.915973i −0.0372279 0.0466823i
386386 7.78445 + 9.76139i 0.396218 + 0.496841i
387387 −9.13775 + 4.40051i −0.464498 + 0.223690i
388388 10.7063 13.4253i 0.543530 0.681565i
389389 3.02944 0.153599 0.0767993 0.997047i 0.475530π-0.475530\pi
0.0767993 + 0.997047i 0.475530π0.475530\pi
390390 −13.9124 + 17.4456i −0.704480 + 0.883390i
391391 −0.674113 + 2.95348i −0.0340914 + 0.149364i
392392 0.982255 4.30354i 0.0496114 0.217362i
393393 32.0822 40.2298i 1.61833 2.02932i
394394 −4.82843 −0.243253
395395 1.50524 1.88751i 0.0757367 0.0949708i
396396 4.04110 1.94609i 0.203073 0.0977947i
397397 12.0603 + 15.1231i 0.605287 + 0.759006i 0.986192 0.165609i 0.0529589π-0.0529589\pi
−0.380905 + 0.924614i 0.624387π0.624387\pi
398398 0.730464 + 0.915973i 0.0366148 + 0.0459136i
399399 36.9132 + 17.7765i 1.84797 + 0.889936i
400400 2.67025 11.6991i 0.133513 0.584957i
401401 4.15154 + 18.1891i 0.207318 + 0.908320i 0.966343 + 0.257258i 0.0828190π0.0828190\pi
−0.759025 + 0.651062i 0.774324π0.774324\pi
402402 29.7055 14.3054i 1.48157 0.713488i
403403 34.7381 + 16.7290i 1.73043 + 0.833329i
404404 1.99614 + 8.74565i 0.0993116 + 0.435112i
405405 9.48528 0.471327
406406 0 0
407407 1.65685 0.0821272
408408 1.96451 + 8.60708i 0.0972577 + 0.426114i
409409 17.0919 + 8.23102i 0.845139 + 0.406998i 0.805771 0.592227i 0.201751π-0.201751\pi
0.0393683 + 0.999225i 0.487465π0.487465\pi
410410 9.75608 4.69828i 0.481818 0.232031i
411411 −6.44656 28.2442i −0.317985 1.39318i
412412 4.11336 18.0218i 0.202651 0.887871i
413413 −9.31885 4.48772i −0.458551 0.220826i
414414 −15.5689 19.5228i −0.765169 0.959492i
415415 −4.77397 5.98637i −0.234345 0.293859i
416416 5.46984 2.63414i 0.268181 0.129149i
417417 21.0733 26.4251i 1.03197 1.29404i
418418 6.00000 0.293470
419419 −5.93233 + 7.43891i −0.289813 + 0.363414i −0.905330 0.424710i 0.860376π-0.860376\pi
0.615516 + 0.788124i 0.288948π0.288948\pi
420420 −5.81717 + 25.4867i −0.283849 + 1.24362i
421421 −8.25835 + 36.1822i −0.402487 + 1.76341i 0.214783 + 0.976662i 0.431096π0.431096\pi
−0.617270 + 0.786751i 0.711762π0.711762\pi
422422 29.1787 36.5889i 1.42040 1.78112i
423423 −9.17157 −0.445937
424424 −26.1056 + 32.7353i −1.26780 + 1.58977i
425425 2.98555 1.43776i 0.144820 0.0697418i
426426 32.0822 + 40.2298i 1.55439 + 1.94914i
427427 8.51491 + 10.6774i 0.412065 + 0.516714i
428428 51.1476 + 24.6314i 2.47231 + 1.19060i
429429 −0.851905 + 3.73244i −0.0411304 + 0.180204i
430430 −1.92633 8.43981i −0.0928959 0.407004i
431431 −17.7102 + 8.52879i −0.853071 + 0.410817i −0.808717 0.588199i 0.799837π-0.799837\pi
−0.0443544 + 0.999016i 0.514123π0.514123\pi
432432 1.11958 + 0.539162i 0.0538658 + 0.0259404i
433433 −6.81524 29.8595i −0.327520 1.43496i −0.823842 0.566819i 0.808174π-0.808174\pi
0.496323 0.868138i 0.334683π-0.334683\pi
434434 68.7696 3.30104
435435 0 0
436436 48.4558 2.32061
437437 −4.88236 21.3910i −0.233555 1.02327i
438438 21.0049 + 10.1154i 1.00365 + 0.483334i
439439 0.309164 0.148885i 0.0147556 0.00710591i −0.426491 0.904492i 0.640251π-0.640251\pi
0.441247 + 0.897386i 0.354536π0.354536\pi
440440 0.406863 + 1.78258i 0.0193964 + 0.0849814i
441441 −0.629384 + 2.75751i −0.0299707 + 0.131310i
442442 −6.89859 3.32218i −0.328132 0.158020i
443443 −15.1777 19.0322i −0.721114 0.904249i 0.277286 0.960787i 0.410565π-0.410565\pi
−0.998400 + 0.0565385i 0.981994π0.981994\pi
444444 −23.0508 28.9047i −1.09394 1.37176i
445445 −11.2488 + 5.41716i −0.533247 + 0.256798i
446446 4.77397 5.98637i 0.226054 0.283463i
447447 −18.8995 −0.893915
448448 17.3324 21.7341i 0.818878 1.02684i
449449 7.78168 34.0938i 0.367240 1.60898i −0.367085 0.930187i 0.619644π-0.619644\pi
0.734325 0.678798i 0.237499π-0.237499\pi
450450 −6.07787 + 26.6289i −0.286514 + 1.25530i
451451 1.15836 1.45254i 0.0545450 0.0683973i
452452 −50.9706 −2.39745
453453 −21.2873 + 26.6934i −1.00016 + 1.25417i
454454 −17.7102 + 8.52879i −0.831182 + 0.400276i
455455 −6.75141 8.46601i −0.316511 0.396892i
456456 −39.8666 49.9912i −1.86693 2.34105i
457457 −0.927491 0.446656i −0.0433862 0.0208937i 0.412065 0.911155i 0.364808π-0.364808\pi
−0.455451 + 0.890261i 0.650522π0.650522\pi
458458 −1.88815 + 8.27254i −0.0882276 + 0.386550i
459459 0.0763571 + 0.334542i 0.00356404 + 0.0156151i
460460 12.6136 6.07437i 0.588110 0.283219i
461461 −12.6136 6.07437i −0.587472 0.282912i 0.116441 0.993198i 0.462851π-0.462851\pi
−0.703913 + 0.710286i 0.748566π0.748566\pi
462462 1.51947 + 6.65722i 0.0706920 + 0.309722i
463463 −26.0000 −1.20832 −0.604161 0.796862i 0.706492π-0.706492\pi
−0.604161 + 0.796862i 0.706492π0.706492\pi
464464 0 0
465465 −24.3137 −1.12752
466466 9.83836 + 43.1047i 0.455753 + 1.99679i
467467 34.5570 + 16.6418i 1.59911 + 0.770089i 0.999543 0.0302389i 0.00962679π-0.00962679\pi
0.599563 + 0.800328i 0.295341π0.295341\pi
468468 37.3504 17.9870i 1.72652 0.831450i
469469 3.56033 + 15.5988i 0.164401 + 0.720288i
470470 1.74199 7.63215i 0.0803520 0.352045i
471471 −18.4566 8.88823i −0.850435 0.409548i
472472 10.0645 + 12.6204i 0.463254 + 0.580902i
473473 −0.926058 1.16124i −0.0425802 0.0533939i
474474 −12.6776 + 6.10521i −0.582301 + 0.280421i
475475 −14.9638 + 18.7640i −0.686584 + 0.860949i
476476 −8.97056 −0.411165
477477 16.7273 20.9753i 0.765888 0.960393i
478478 −10.5599 + 46.2660i −0.482999 + 2.11616i
479479 −1.53528 + 6.72651i −0.0701488 + 0.307342i −0.997815 0.0660682i 0.978954π-0.978954\pi
0.927666 + 0.373410i 0.121812π0.121812\pi
480480 −2.38699 + 2.99318i −0.108950 + 0.136620i
481481 15.3137 0.698245
482482 27.5665 34.5673i 1.25562 1.57450i
483483 22.4977 10.8343i 1.02368 0.492979i
484484 −25.8473 32.4115i −1.17488 1.47325i
485485 −2.79653 3.50673i −0.126984 0.159233i
486486 −47.1065 22.6853i −2.13679 1.02903i
487487 2.56227 11.2260i 0.116107 0.508700i −0.883111 0.469164i 0.844555π-0.844555\pi
0.999218 0.0395351i 0.0125877π-0.0125877\pi
488488 −4.74275 20.7793i −0.214694 0.940636i
489489 −8.54594 + 4.11551i −0.386461 + 0.186110i
490490 −2.17513 1.04749i −0.0982624 0.0473207i
491491 4.72693 + 20.7100i 0.213323 + 0.934631i 0.962290 + 0.272024i 0.0876930π0.0876930\pi
−0.748967 + 0.662607i 0.769450π0.769450\pi
492492 −41.4558 −1.86897
493493 0 0
494494 55.4558 2.49508
495495 −0.260699 1.14220i −0.0117176 0.0513380i
496496 −27.2212 13.1090i −1.22227 0.588612i
497497 −22.4977 + 10.8343i −1.00916 + 0.485986i
498498 9.93053 + 43.5085i 0.444998 + 1.94966i
499499 −4.22135 + 18.4949i −0.188973 + 0.827947i 0.788186 + 0.615438i 0.211021π0.211021\pi
−0.977159 + 0.212509i 0.931836π0.931836\pi
500500 −31.0436 14.9498i −1.38831 0.668577i
501501 −4.77397 5.98637i −0.213285 0.267451i
502502 −30.2117 37.8843i −1.34842 1.69086i
503503 −0.245134 + 0.118050i −0.0109300 + 0.00526360i −0.439341 0.898320i 0.644788π-0.644788\pi
0.428411 + 0.903584i 0.359074π0.359074\pi
504504 22.0177 27.6094i 0.980748 1.22982i
505505 2.34315 0.104269
506506 2.28001 2.85904i 0.101359 0.127100i
507507 −0.890084 + 3.89971i −0.0395300 + 0.173192i
508508 3.69995 16.2105i 0.164159 0.719226i
509509 −6.55582 + 8.22074i −0.290582 + 0.364378i −0.905598 0.424136i 0.860578π-0.860578\pi
0.615017 + 0.788514i 0.289149π0.289149\pi
510510 4.82843 0.213806
511511 −7.05398 + 8.84541i −0.312050 + 0.391298i
512512 −28.1486 + 13.5557i −1.24401 + 0.599082i
513513 −1.54955 1.94307i −0.0684142 0.0857887i
514514 27.3525 + 34.2990i 1.20647 + 1.51286i
515515 −4.35026 2.09498i −0.191695 0.0923157i
516516 −7.37482 + 32.3112i −0.324658 + 1.42242i
517517 −0.298878 1.30947i −0.0131446 0.0575904i
518518 24.6088 11.8510i 1.08125 0.520702i
519519 −26.8480 12.9293i −1.17849 0.567533i
520520 3.76049 + 16.4758i 0.164908 + 0.722511i
521521 −29.1421 −1.27674 −0.638370 0.769730i 0.720391π-0.720391\pi
−0.638370 + 0.769730i 0.720391π0.720391\pi
522522 0 0
523523 4.68629 0.204917 0.102459 0.994737i 0.467329π-0.467329\pi
0.102459 + 0.994737i 0.467329π0.467329\pi
524524 −18.1573 79.5521i −0.793204 3.47525i
525525 −24.6088 11.8510i −1.07402 0.517219i
526526 5.99762 2.88830i 0.261509 0.125936i
527527 −1.85652 8.13397i −0.0808715 0.354321i
528528 0.667563 2.92478i 0.0290519 0.127285i
529529 8.67400 + 4.17718i 0.377131 + 0.181617i
530530 14.2776 + 17.9035i 0.620179 + 0.777680i
531531 −6.44885 8.08660i −0.279856 0.350928i
532532 58.5365 28.1897i 2.53788 1.22218i
533533 10.7063 13.4253i 0.463741 0.581513i
534534 72.7696 3.14905
535535 9.24537 11.5933i 0.399712 0.501223i
536536 5.55647 24.3445i 0.240003 1.05152i
537537 3.48398 15.2643i 0.150345 0.658703i
538538 −47.3485 + 59.3732i −2.04134 + 2.55976i
539539 −0.414214 −0.0178414
540540 0.988722 1.23982i 0.0425478 0.0533533i
541541 9.31885 4.48772i 0.400649 0.192942i −0.222699 0.974887i 0.571487π-0.571487\pi
0.623347 + 0.781945i 0.285772π0.285772\pi
542542 −24.9212 31.2502i −1.07046 1.34231i
543543 12.5141 + 15.6922i 0.537032 + 0.673416i
544544 −1.18361 0.569997i −0.0507469 0.0244384i
545545 2.81642 12.3395i 0.120642 0.528567i
546546 14.0439 + 61.5303i 0.601023 + 2.63326i
547547 −32.2538 + 15.5326i −1.37907 + 0.664126i −0.968802 0.247838i 0.920280π-0.920280\pi
−0.410270 + 0.911964i 0.634566π0.634566\pi
548548 −41.3915 19.9331i −1.76816 0.851500i
549549 3.03894 + 13.3144i 0.129699 + 0.568247i
550550 −4.00000 −0.170561
551551 0 0
552552 −38.9706 −1.65870
553553 −1.51947 6.65722i −0.0646144 0.283094i
554554 −37.6596 18.1359i −1.60000 0.770521i
555555 −8.70053 + 4.18995i −0.369317 + 0.177854i
556556 −11.9267 52.2542i −0.505804 2.21607i
557557 3.85266 16.8796i 0.163243 0.715212i −0.825353 0.564617i 0.809024π-0.809024\pi
0.988596 0.150595i 0.0481190π-0.0481190\pi
558558 61.9592 + 29.8380i 2.62294 + 1.26314i
559559 −8.55922 10.7329i −0.362016 0.453954i
560560 5.29049 + 6.63406i 0.223564 + 0.280340i
561561 0.746387 0.359441i 0.0315125 0.0151756i
562562 −48.1233 + 60.3447i −2.02996 + 2.54549i
563563 −0.757359 −0.0319189 −0.0159594 0.999873i 0.505080π-0.505080\pi
−0.0159594 + 0.999873i 0.505080π0.505080\pi
564564 −18.6863 + 23.4319i −0.786837 + 0.986662i
565565 −2.96258 + 12.9799i −0.124637 + 0.546069i
566566 6.26221 27.4366i 0.263221 1.15324i
567567 16.7273 20.9753i 0.702479 0.880880i
568568 38.9706 1.63517
569569 −24.7256 + 31.0050i −1.03655 + 1.29980i −0.0836584 + 0.996494i 0.526660π0.526660\pi
−0.952895 + 0.303302i 0.901911π0.901911\pi
570570 −31.5074 + 15.1732i −1.31970 + 0.635534i
571571 9.12005 + 11.4362i 0.381662 + 0.478589i 0.935142 0.354274i 0.115272π-0.115272\pi
−0.553480 + 0.832863i 0.686700π0.686700\pi
572572 3.78525 + 4.74655i 0.158269 + 0.198463i
573573 −55.0606 26.5158i −2.30019 1.10771i
574574 6.81524 29.8595i 0.284463 1.24631i
575575 3.25491 + 14.2607i 0.135739 + 0.594711i
576576 25.0460 12.0615i 1.04358 0.502564i
577577 26.8480 + 12.9293i 1.11770 + 0.538254i 0.899180 0.437580i 0.144164π-0.144164\pi
0.218516 + 0.975833i 0.429879π0.429879\pi
578578 −8.76394 38.3973i −0.364532 1.59712i
579579 −12.4853 −0.518871
580580 0 0
581581 −21.6569 −0.898478
582582 5.81717 + 25.4867i 0.241130 + 1.05646i
583583 3.53985 + 1.70470i 0.146605 + 0.0706015i
584584 15.9083 7.66102i 0.658289 0.317015i
585585 −2.40955 10.5569i −0.0996227 0.436476i
586586 4.11336 18.0218i 0.169921 0.744474i
587587 −6.89859 3.32218i −0.284735 0.137121i 0.286065 0.958210i 0.407653π-0.407653\pi
−0.570800 + 0.821089i 0.693367π0.693367\pi
588588 5.76269 + 7.22619i 0.237649 + 0.298003i
589589 37.6752 + 47.2433i 1.55238 + 1.94662i
590590 7.95414 3.83051i 0.327467 0.157700i
591591 3.01048 3.77502i 0.123834 0.155283i
592592 −12.0000 −0.493197
593593 −12.1489 + 15.2342i −0.498894 + 0.625594i −0.965980 0.258619i 0.916733π-0.916733\pi
0.467085 + 0.884212i 0.345304π0.345304\pi
594594 0.0921712 0.403828i 0.00378183 0.0165693i
595595 −0.521399 + 2.28440i −0.0213753 + 0.0936512i
596596 −18.6863 + 23.4319i −0.765422 + 0.959809i
597597 −1.17157 −0.0479493
598598 21.0733 26.4251i 0.861752 1.08060i
599599 −8.89261 + 4.28246i −0.363342 + 0.174976i −0.606643 0.794974i 0.707484π-0.707484\pi
0.243300 + 0.969951i 0.421770π0.421770\pi
600600 26.5778 + 33.3275i 1.08503 + 1.36059i
601601 −10.7063 13.4253i −0.436719 0.547628i 0.513956 0.857816i 0.328179π-0.328179\pi
−0.950675 + 0.310188i 0.899608π0.899608\pi
602602 −22.0605 10.6238i −0.899118 0.432992i
603603 −3.56033 + 15.5988i −0.144988 + 0.635234i
604604 12.0478 + 52.7847i 0.490216 + 2.14778i
605605 −9.75608 + 4.69828i −0.396641 + 0.191012i
606606 −12.3044 5.92549i −0.499832 0.240706i
607607 1.71962 + 7.53417i 0.0697974 + 0.305802i 0.997762 0.0668661i 0.0213000π-0.0213000\pi
−0.927965 + 0.372668i 0.878443π0.878443\pi
608608 9.51472 0.385873
609609 0 0
610610 −11.6569 −0.471972
611611 −2.76242 12.1030i −0.111756 0.489633i
612612 −8.08220 3.89218i −0.326703 0.157332i
613613 8.10872 3.90495i 0.327508 0.157720i −0.262903 0.964822i 0.584680π-0.584680\pi
0.590411 + 0.807103i 0.298966π0.298966\pi
614614 1.55765 + 6.82450i 0.0628615 + 0.275414i
615615 −2.40955 + 10.5569i −0.0971625 + 0.425697i
616616 4.65943 + 2.24386i 0.187734 + 0.0904078i
617617 0.427896 + 0.536564i 0.0172264 + 0.0216013i 0.790370 0.612630i 0.209888π-0.209888\pi
−0.773144 + 0.634231i 0.781317π0.781317\pi
618618 17.5463 + 22.0024i 0.705817 + 0.885067i
619619 −30.2597 + 14.5723i −1.21624 + 0.585711i −0.928263 0.371925i 0.878698π-0.878698\pi
−0.287979 + 0.957637i 0.592983π0.592983\pi
620620 −24.0395 + 30.1446i −0.965449 + 1.21063i
621621 −1.51472 −0.0607836
622622 −4.04351 + 5.07040i −0.162130 + 0.203304i
623623 −7.85804 + 34.4283i −0.314826 + 1.37934i
624624 6.17004 27.0327i 0.246999 1.08218i
625625 6.85839 8.60015i 0.274336 0.344006i
626626 −23.7279 −0.948358
627627 −3.74094 + 4.69099i −0.149399 + 0.187340i
628628 −29.2682 + 14.0948i −1.16793 + 0.562445i
629629 −2.06606 2.59076i −0.0823793 0.103300i
630630 −12.0419 15.1001i −0.479761 0.601601i
631631 33.1813 + 15.9793i 1.32093 + 0.636124i 0.955576 0.294746i 0.0952351π-0.0952351\pi
0.365350 + 0.930870i 0.380949π0.380949\pi
632632 −2.37137 + 10.3897i −0.0943282 + 0.413279i
633633 10.4138 + 45.6256i 0.413910 + 1.81346i
634634 −68.4206 + 32.9496i −2.71733 + 1.30860i
635635 −3.91304 1.88442i −0.155284 0.0747809i
636636 −19.5082 85.4710i −0.773550 3.38915i
637637 −3.82843 −0.151688
638638 0 0
639639 −24.9706 −0.987820
640640 4.57422 + 20.0410i 0.180812 + 0.792188i
641641 −16.0363 7.72269i −0.633397 0.305028i 0.0894967 0.995987i 0.471474π-0.471474\pi
−0.722894 + 0.690959i 0.757188π0.757188\pi
642642 −77.8675 + 37.4990i −3.07319 + 1.47997i
643643 −7.22866 31.6708i −0.285070 1.24897i −0.891201 0.453609i 0.850136π-0.850136\pi
0.606130 0.795365i 0.292721π-0.292721\pi
644644 8.81138 38.6052i 0.347217 1.52126i
645645 7.79956 + 3.75607i 0.307107 + 0.147895i
646646 −7.48188 9.38198i −0.294371 0.369129i
647647 24.7256 + 31.0050i 0.972065 + 1.21893i 0.975739 + 0.218938i 0.0702593π0.0702593\pi
−0.00367336 + 0.999993i 0.501169π0.501169\pi
648648 −37.7236 + 18.1667i −1.48192 + 0.713657i
649649 0.944412 1.18425i 0.0370714 0.0464861i
650650 −36.9706 −1.45010
651651 −42.8771 + 53.7662i −1.68049 + 2.10726i
652652 −3.34708 + 14.6645i −0.131082 + 0.574306i
653653 6.70726 29.3864i 0.262475 1.14998i −0.656082 0.754690i 0.727787π-0.727787\pi
0.918557 0.395289i 0.129356π-0.129356\pi
654654 −45.9946 + 57.6754i −1.79853 + 2.25528i
655655 −21.3137 −0.832796
656656 −8.38958 + 10.5202i −0.327558 + 0.410745i
657657 −10.1933 + 4.90883i −0.397678 + 0.191512i
658658 −13.8054 17.3114i −0.538190 0.674869i
659659 8.98712 + 11.2695i 0.350088 + 0.438997i 0.925431 0.378915i 0.123703π-0.123703\pi
−0.575343 + 0.817912i 0.695131π0.695131\pi
660660 −3.44929 1.66109i −0.134264 0.0646579i
661661 −7.41300 + 32.4785i −0.288332 + 1.26327i 0.598481 + 0.801137i 0.295771π0.295771\pi
−0.886813 + 0.462129i 0.847086π0.847086\pi
662662 −1.29695 5.68230i −0.0504073 0.220849i
663663 6.89859 3.32218i 0.267919 0.129023i
664664 30.4518 + 14.6648i 1.18176 + 0.569106i
665665 −3.77631 16.5451i −0.146439 0.641591i
666666 27.3137 1.05838
667667 0 0
668668 −12.1421 −0.469793
669669 1.70381 + 7.46488i 0.0658731 + 0.288609i
670670 −12.3044 5.92549i −0.475360 0.228922i
671671 −1.80194 + 0.867767i −0.0695630 + 0.0334998i
672672 2.40955 + 10.5569i 0.0929505 + 0.407243i
673673 4.81255 21.0852i 0.185510 0.812774i −0.793436 0.608654i 0.791710π-0.791710\pi
0.978946 0.204120i 0.0654331π-0.0654331\pi
674674 47.4157 + 22.8342i 1.82638 + 0.879540i
675675 1.03303 + 1.29538i 0.0397614 + 0.0498592i
676676 3.95489 + 4.95927i 0.152111 + 0.190741i
677677 19.8213 9.54544i 0.761795 0.366861i −0.0123051 0.999924i 0.503917π-0.503917\pi
0.774100 + 0.633063i 0.218203π0.218203\pi
678678 48.3815 60.6685i 1.85808 2.32996i
679679 −12.6863 −0.486855
680680 2.28001 2.85904i 0.0874344 0.109639i
681681 4.37406 19.1640i 0.167614 0.734367i
682682 −2.24102 + 9.81857i −0.0858132 + 0.375972i
683683 13.0749 16.3954i 0.500298 0.627354i −0.465998 0.884786i 0.654305π-0.654305\pi
0.966297 + 0.257431i 0.0828761π0.0828761\pi
684684 64.9706 2.48421
685685 −7.48188 + 9.38198i −0.285868 + 0.358467i
686686 36.9132 17.7765i 1.40935 0.678708i
687687 −5.29049 6.63406i −0.201845 0.253105i
688688 6.70710 + 8.41044i 0.255706 + 0.320645i
689689 32.7175 + 15.7559i 1.24644 + 0.600253i
690690 −4.74275 + 20.7793i −0.180553 + 0.791056i
691691 −10.6810 46.7965i −0.406325 1.78022i −0.600887 0.799334i 0.705186π-0.705186\pi
0.194562 0.980890i 0.437671π-0.437671\pi
692692 −42.5751 + 20.5031i −1.61846 + 0.779411i
693693 −2.98555 1.43776i −0.113412 0.0546161i
694694 1.33513 + 5.84957i 0.0506807 + 0.222047i
695695 −14.0000 −0.531050
696696 0 0
697697 −3.71573 −0.140743
698698 −2.76242 12.1030i −0.104559 0.458104i
699699 −39.8347 19.1834i −1.50669 0.725582i
700700 −39.0243 + 18.7931i −1.47498 + 0.710313i
701701 8.92592 + 39.1070i 0.337127 + 1.47705i 0.805011 + 0.593260i 0.202160π0.202160\pi
−0.467883 + 0.883790i 0.654983π0.654983\pi
702702 0.851905 3.73244i 0.0321531 0.140872i
703703 21.6233 + 10.4132i 0.815536 + 0.392742i
704704 2.53827 + 3.18289i 0.0956646 + 0.119960i
705705 4.88094 + 6.12051i 0.183827 + 0.230512i
706706 58.6645 28.2513i 2.20787 1.06325i
707707 4.13213 5.18152i 0.155405 0.194871i
708708 −33.7990 −1.27024
709709 18.1698 22.7842i 0.682382 0.855680i −0.313189 0.949691i 0.601397π-0.601397\pi
0.995571 + 0.0940107i 0.0299688π0.0299688\pi
710710 4.74275 20.7793i 0.177992 0.779834i
711711 1.51947 6.65722i 0.0569845 0.249665i
712712 34.3622 43.0888i 1.28778 1.61482i
713713 36.8284 1.37924
714714 8.51491 10.6774i 0.318662 0.399590i
715715 1.42874 0.688047i 0.0534320 0.0257315i
716716 −15.4803 19.4116i −0.578525 0.725447i
717717 −29.5882 37.1025i −1.10499 1.38562i
718718 8.54594 + 4.11551i 0.318932 + 0.153589i
719719 4.48205 19.6371i 0.167152 0.732341i −0.819974 0.572400i 0.806012π-0.806012\pi
0.987127 0.159941i 0.0511305π-0.0511305\pi
720720 1.88815 + 8.27254i 0.0703673 + 0.308299i
721721 −12.3044 + 5.92549i −0.458240 + 0.220677i
722722 36.9772 + 17.8073i 1.37615 + 0.662719i
723723 9.83836 + 43.1047i 0.365893 + 1.60308i
724724 31.8284 1.18289
725725 0 0
726726 63.1127 2.34233
727727 −0.292328 1.28077i −0.0108418 0.0475012i 0.969218 0.246205i 0.0791838π-0.0791838\pi
−0.980059 + 0.198704i 0.936327π0.936327\pi
728728 43.0654 + 20.7392i 1.59611 + 0.768646i
729729 21.4687 10.3388i 0.795136 0.382917i
730730 −2.14885 9.41474i −0.0795326 0.348455i
731731 −0.661012 + 2.89608i −0.0244484 + 0.107116i
732732 40.2079 + 19.3631i 1.48613 + 0.715681i
733733 −25.7220 32.2543i −0.950063 1.19134i −0.981428 0.191833i 0.938557π-0.938557\pi
0.0313650 0.999508i 0.490015π-0.490015\pi
734734 −27.0943 33.9751i −1.00007 1.25405i
735735 2.17513 1.04749i 0.0802309 0.0386372i
736736 3.61561 4.53383i 0.133273 0.167119i
737737 −2.34315 −0.0863109
738738 19.0959 23.9455i 0.702929 0.881445i
739739 −0.905898 + 3.96900i −0.0333240 + 0.146002i −0.988853 0.148895i 0.952428π-0.952428\pi
0.955529 + 0.294897i 0.0952854π0.0952854\pi
740740 −3.40762 + 14.9298i −0.125267 + 0.548829i
741741 −34.5762 + 43.3571i −1.27019 + 1.59276i
742742 64.7696 2.37777
743743 14.7498 18.4957i 0.541118 0.678540i −0.433825 0.900997i 0.642836π-0.642836\pi
0.974943 + 0.222457i 0.0714077π0.0714077\pi
744744 96.6973 46.5670i 3.54509 1.70723i
745745 4.88094 + 6.12051i 0.178824 + 0.224238i
746746 39.6084 + 49.6673i 1.45017 + 1.81845i
747747 −19.5122 9.39656i −0.713912 0.343802i
748748 0.292328 1.28077i 0.0106886 0.0468296i
749749 −9.33278 40.8896i −0.341012 1.49407i
750750 47.2611 22.7597i 1.72573 0.831068i
751751 −22.8069 10.9832i −0.832234 0.400783i −0.0312816 0.999511i 0.509959π-0.509959\pi
−0.800953 + 0.598728i 0.795673π0.795673\pi
752752 2.16467 + 9.48402i 0.0789373 + 0.345847i
753753 48.4558 1.76583
754754 0 0
755755 14.1421 0.514685
756756 −0.998069 4.37283i −0.0362994 0.159038i
757757 −22.9880 11.0704i −0.835512 0.402361i −0.0333324 0.999444i 0.510612π-0.510612\pi
−0.802179 + 0.597083i 0.796326π0.796326\pi
758758 −15.1619 + 7.30158i −0.550705 + 0.265205i
759759 0.813727 + 3.56517i 0.0295364 + 0.129407i
760760 −5.89353 + 25.8212i −0.213781 + 0.936635i
761761 −41.0824 19.7842i −1.48923 0.717177i −0.500344 0.865826i 0.666793π-0.666793\pi
−0.988890 + 0.148649i 0.952508π0.952508\pi
762762 15.7828 + 19.7911i 0.571752 + 0.716954i
763763 −22.3203 27.9888i −0.808049 1.01326i
764764 −87.3144 + 42.0484i −3.15892 + 1.52126i
765765 −1.46093 + 1.83195i −0.0528199 + 0.0662341i
766766 8.48528 0.306586
767767 8.72886 10.9456i 0.315181 0.395224i
768768 16.1006 70.5412i 0.580980 2.54544i
769769 10.9286 47.8813i 0.394096 1.72665i −0.255896 0.966704i 0.582371π-0.582371\pi
0.649992 0.759941i 0.274772π-0.274772\pi
770770 1.76350 2.21135i 0.0635520 0.0796916i
771771 −43.8701 −1.57994
772772 −12.3445 + 15.4795i −0.444287 + 0.557118i
773773 17.5822 8.46712i 0.632386 0.304541i −0.0900935 0.995933i 0.528717π-0.528717\pi
0.722480 + 0.691392i 0.243002π0.243002\pi
774774 −15.2663 19.1434i −0.548737 0.688094i
775775 −25.1168 31.4955i −0.902223 1.13135i
776776 17.8383 + 8.59046i 0.640357 + 0.308380i
777777 −6.07787 + 26.6289i −0.218042 + 0.955306i
778778 1.62745 + 7.13034i 0.0583470 + 0.255635i
779779 24.2466 11.6765i 0.868724 0.418356i
780780 −31.8806 15.3529i −1.14151 0.549721i
781781 −0.813727 3.56517i −0.0291174 0.127572i
782782 −7.31371 −0.261538
783783 0 0
784784 3.00000 0.107143
785785 1.88815 + 8.27254i 0.0673911 + 0.295260i
786786 111.923 + 53.8994i 3.99217 + 1.92253i
787787 48.7273 23.4658i 1.73694 0.836467i 0.752990 0.658032i 0.228611π-0.228611\pi
0.983952 0.178435i 0.0571036π-0.0571036\pi
788788 −1.70381 7.46488i −0.0606957 0.265925i
789789 −1.48129 + 6.48995i −0.0527353 + 0.231048i
790790 5.25123 + 2.52886i 0.186830 + 0.0899728i
791791 23.4787 + 29.4413i 0.834805 + 1.04681i
792792 3.22442 + 4.04330i 0.114575 + 0.143672i
793793 −16.6547 + 8.02046i −0.591424 + 0.284815i
794794 −29.1160 + 36.5103i −1.03329 + 1.29570i
795795 −22.8995 −0.812161
796796 −1.15836 + 1.45254i −0.0410570 + 0.0514838i
797797 −11.5133 + 50.4429i −0.407821 + 1.78678i 0.186397 + 0.982474i 0.440319π0.440319\pi
−0.594218 + 0.804304i 0.702538π0.702538\pi
798798 −22.0099 + 96.4318i −0.779143 + 3.41365i
799799 −1.67488 + 2.10023i −0.0592528 + 0.0743007i
800800 −6.34315 −0.224264
801801 −22.0177 + 27.6094i −0.777958 + 0.975529i
802802 −40.5811 + 19.5428i −1.43297 + 0.690081i
803803 −1.03303 1.29538i −0.0364549 0.0457130i
804804 32.5987 + 40.8775i 1.14967 + 1.44164i
805805 −9.31885 4.48772i −0.328446 0.158171i
806806 −20.7130 + 90.7495i −0.729583 + 3.19651i
807807 −16.8985 74.0371i −0.594855 2.60623i
808808 −9.31885 + 4.48772i −0.327836 + 0.157878i
809809 −32.6910 15.7432i −1.14935 0.553500i −0.240515 0.970646i 0.577316π-0.577316\pi
−0.908840 + 0.417146i 0.863030π0.863030\pi
810810 5.09562 + 22.3254i 0.179042 + 0.784433i
811811 10.8284 0.380238 0.190119 0.981761i 0.439113π-0.439113\pi
0.190119 + 0.981761i 0.439113π0.439113\pi
812812 0 0
813813 39.9706 1.40183
814814 0.890084 + 3.89971i 0.0311974 + 0.136685i
815815 3.53985 + 1.70470i 0.123995 + 0.0597130i
816816 −5.40581 + 2.60330i −0.189241 + 0.0911338i
817817 −4.78748 20.9753i −0.167493 0.733833i
818818 −10.1912 + 44.6507i −0.356328 + 1.56118i
819819 −27.5943 13.2887i −0.964225 0.464346i
820820 10.7063 + 13.4253i 0.373880 + 0.468831i
821821 −0.926058 1.16124i −0.0323196 0.0405275i 0.765409 0.643544i 0.222537π-0.222537\pi
−0.797729 + 0.603017i 0.793965π0.793965\pi
822822 63.0148 30.3463i 2.19789 1.05845i
823823 −33.8457 + 42.4412i −1.17979 + 1.47941i −0.336713 + 0.941607i 0.609315π0.609315\pi
−0.843074 + 0.537798i 0.819256π0.819256\pi
824824 21.3137 0.742498
825825 2.49396 3.12733i 0.0868285 0.108880i
826826 5.55647 24.3445i 0.193334 0.847053i
827827 −7.32083 + 32.0746i −0.254570 + 1.11534i 0.672394 + 0.740194i 0.265266π0.265266\pi
−0.926964 + 0.375151i 0.877591π0.877591\pi
828828 24.6889 30.9589i 0.858000 1.07590i
829829 −29.7990 −1.03496 −0.517481 0.855695i 0.673130π-0.673130\pi
−0.517481 + 0.855695i 0.673130π0.673130\pi
830830 11.5254 14.4524i 0.400052 0.501649i
831831 37.6596 18.1359i 1.30640 0.629127i
832832 23.4603 + 29.4183i 0.813340 + 1.01990i
833833 0.516516 + 0.647690i 0.0178962 + 0.0224411i
834834 73.5172 + 35.4040i 2.54569 + 1.22594i
835835 −0.705741 + 3.09205i −0.0244232 + 0.107005i
836836 2.11722 + 9.27616i 0.0732257 + 0.320823i
837837 3.75846 1.80998i 0.129911 0.0625620i
838838 −20.6958 9.96655i −0.714923 0.344289i
839839 1.76435 + 7.73014i 0.0609122 + 0.266874i 0.996209 0.0869898i 0.0277248π-0.0277248\pi
−0.935297 + 0.353864i 0.884868π0.884868\pi
840840 −30.1421 −1.04000
841841 0 0
842842 −89.5980 −3.08775
843843 −17.1750 75.2486i −0.591539 2.59170i
844844 66.8638 + 32.1999i 2.30155 + 1.10837i
845845 1.49277 0.718882i 0.0513530 0.0247303i
846846 −4.92709 21.5870i −0.169397 0.742176i
847847 −6.81524 + 29.8595i −0.234174 + 1.02599i
848848 −25.6378 12.3465i −0.880407 0.423982i
849849 17.5463 + 22.0024i 0.602189 + 0.755121i
850850 4.98792 + 6.25465i 0.171084 + 0.214533i
851851 13.1788 6.34660i 0.451765 0.217559i
852852 −50.8755 + 63.7959i −1.74297 + 2.18561i
853853 −22.9706 −0.786497 −0.393249 0.919432i 0.628649π-0.628649\pi
−0.393249 + 0.919432i 0.628649π0.628649\pi
854854 −20.5568 + 25.7774i −0.703440 + 0.882085i
855855 3.77631 16.5451i 0.129147 0.565830i
856856 −14.5653 + 63.8147i −0.497832 + 2.18114i
857857 −3.84791 + 4.82513i −0.131442 + 0.164823i −0.843197 0.537605i 0.819329π-0.819329\pi
0.711755 + 0.702428i 0.247901π0.247901\pi
858858 −9.24264 −0.315539
859859 12.3002 15.4239i 0.419676 0.526257i −0.526385 0.850247i 0.676453π-0.676453\pi
0.946061 + 0.323989i 0.105024π0.105024\pi
860860 12.3684 5.95632i 0.421760 0.203109i
861861 19.0959 + 23.9455i 0.650786 + 0.816060i
862862 −29.5882 37.1025i −1.00778 1.26372i
863863 −15.4180 7.42492i −0.524835 0.252747i 0.152654 0.988280i 0.451218π-0.451218\pi
−0.677490 + 0.735532i 0.736932π0.736932\pi
864864 0.146164 0.640386i 0.00497259 0.0217864i
865865 2.74661 + 12.0337i 0.0933875 + 0.409157i
866866 66.6187 32.0819i 2.26379 1.09019i
867867 35.4845 + 17.0884i 1.20512 + 0.580353i
868868 24.2668 + 106.320i 0.823667 + 3.60872i
869869 1.00000 0.0339227
870870 0 0
871871 −21.6569 −0.733815
872872 12.4323 + 54.4693i 0.421009 + 1.84456i
873873 −11.4300 5.50438i −0.386845 0.186295i
874874 47.7248 22.9831i 1.61432 0.777414i
875875 5.66446 + 24.8176i 0.191494 + 0.838988i
876876 −8.22672 + 36.0436i −0.277955 + 1.21780i
877877 33.4639 + 16.1154i 1.13000 + 0.544177i 0.902967 0.429711i 0.141384π-0.141384\pi
0.227029 + 0.973888i 0.427099π0.427099\pi
878878 0.516516 + 0.647690i 0.0174316 + 0.0218585i
879879 11.5254 + 14.4524i 0.388742 + 0.487467i
880880 −1.11958 + 0.539162i −0.0377411 + 0.0181751i
881881 8.72886 10.9456i 0.294083 0.368768i −0.612737 0.790287i 0.709931π-0.709931\pi
0.906820 + 0.421519i 0.138503π0.138503\pi
882882 −6.82843 −0.229925
883883 23.9585 30.0430i 0.806267 1.01103i −0.193287 0.981142i 0.561915π-0.561915\pi
0.999553 0.0298842i 0.00951387π-0.00951387\pi
884884 2.70188 11.8377i 0.0908740 0.398145i
885885 −1.96451 + 8.60708i −0.0660363 + 0.289324i
886886 36.6422 45.9479i 1.23102 1.54365i
887887 17.1005 0.574179 0.287089 0.957904i 0.407312π-0.407312\pi
0.287089 + 0.957904i 0.407312π0.407312\pi
888888 26.5778 33.3275i 0.891891 1.11840i
889889 −11.0677 + 5.32995i −0.371200 + 0.178761i
890890 −18.7933 23.5661i −0.629953 0.789936i
891891 2.44965 + 3.07176i 0.0820663 + 0.102908i
892892 10.9397 + 5.26828i 0.366288 + 0.176395i
893893 4.32933 18.9680i 0.144876 0.634741i
894894 −10.1531 44.4834i −0.339569 1.48775i
895895 −5.84304 + 2.81386i −0.195311 + 0.0940569i
896896 52.3843 + 25.2269i 1.75004 + 0.842772i
897897 7.52098 + 32.9516i 0.251118 + 1.10022i
898898 84.4264 2.81735
899899 0 0
900900 −43.3137 −1.44379
901901 −1.74854 7.66085i −0.0582523 0.255220i
902902 4.04110 + 1.94609i 0.134554 + 0.0647977i
903903 22.0605 10.6238i 0.734127 0.353537i
904904 −13.0775 57.2961i −0.434950 1.90564i
905905 1.84997 8.10527i 0.0614952 0.269428i
906906 −74.2636 35.7635i −2.46724 1.18816i
907907 13.8940 + 17.4225i 0.461343 + 0.578506i 0.957028 0.289997i 0.0936542π-0.0936542\pi
−0.495684 + 0.868503i 0.665083π0.665083\pi
908908 −19.4352 24.3709i −0.644978 0.808777i
909909 5.97110 2.87553i 0.198049 0.0953753i
910910 16.2994 20.4387i 0.540318 0.677538i
911911 −15.4437 −0.511671 −0.255835 0.966720i 0.582351π-0.582351\pi
−0.255835 + 0.966720i 0.582351π0.582351\pi
912912 27.0943 33.9751i 0.897181 1.12503i
913913 0.705741 3.09205i 0.0233566 0.102332i
914914 0.553027 2.42297i 0.0182925 0.0801447i
915915 7.26793 9.11370i 0.240270 0.301289i
916916 −13.4558 −0.444594
917917 −37.5866 + 47.1321i −1.24122 + 1.55644i
918918 −0.746387 + 0.359441i −0.0246344 + 0.0118633i
919919 5.07654 + 6.36578i 0.167460 + 0.209988i 0.858479 0.512848i 0.171410π-0.171410\pi
−0.691020 + 0.722836i 0.742838π0.742838\pi
920920 10.0645 + 12.6204i 0.331815 + 0.416083i
921921 −6.30678 3.03719i −0.207816 0.100079i
922922 7.52098 32.9516i 0.247690 1.08520i
923923 −7.52098 32.9516i −0.247556 1.08461i
924924 −9.75608 + 4.69828i −0.320951 + 0.154562i
925925 −14.4155 6.94214i −0.473979 0.228256i
926926 −13.9675 61.1958i −0.459002 2.01102i
927927 −13.6569 −0.448550
928928 0 0
929929 18.6863 0.613077 0.306539 0.951858i 0.400829π-0.400829\pi
0.306539 + 0.951858i 0.400829π0.400829\pi
930930 −13.0616 57.2268i −0.428308 1.87654i
931931 −5.40581 2.60330i −0.177168 0.0853198i
932932 −63.1694 + 30.4208i −2.06918 + 0.996465i
933933 −1.44311 6.32268i −0.0472453 0.206995i
934934 −20.6050 + 90.2764i −0.674216 + 2.95393i
935935 −0.309164 0.148885i −0.0101107 0.00486907i
936936 29.8022 + 37.3708i 0.974115 + 1.22150i
937937 −10.3670 12.9998i −0.338676 0.424686i 0.583105 0.812397i 0.301837π-0.301837\pi
−0.921781 + 0.387710i 0.873266π0.873266\pi
938938 −34.8021 + 16.7598i −1.13633 + 0.547227i
939939 14.7941 18.5512i 0.482788 0.605397i
940940 12.4142 0.404907
941941 −35.2883 + 44.2501i −1.15036 + 1.44251i −0.273436 + 0.961890i 0.588160π0.588160\pi
−0.876928 + 0.480621i 0.840411π0.840411\pi
942942 11.0050 48.2159i 0.358561 1.57096i
943943 3.64979 15.9908i 0.118854 0.520732i
944944 −6.84003 + 8.57713i −0.222624 + 0.279162i
945945 −1.17157 −0.0381113
946946 2.23570 2.80348i 0.0726889 0.0911490i
947947 −2.35624 + 1.13470i −0.0765674 + 0.0368729i −0.471776 0.881719i 0.656387π-0.656387\pi
0.395208 + 0.918592i 0.370672π0.370672\pi
948948 −13.9124 17.4456i −0.451853 0.566605i
949949 −9.54794 11.9727i −0.309939 0.388652i
950950 −52.2032 25.1397i −1.69369 0.815640i
951951 16.8985 74.0371i 0.547971 2.40082i
952952 −2.30157 10.0838i −0.0745942 0.326819i
953953 32.0992 15.4582i 1.03979 0.500739i 0.165538 0.986203i 0.447064π-0.447064\pi
0.874256 + 0.485465i 0.161350π0.161350\pi
954954 58.3554 + 28.1025i 1.88932 + 0.909851i
955955 5.63283 + 24.6790i 0.182274 + 0.798595i
956956 −75.2548 −2.43392
957957 0 0
958958 −16.6569 −0.538159
959959 7.55261 + 33.0902i 0.243887 + 1.06854i
960960 −21.3781 10.2952i −0.689976 0.332275i
961961 −63.4520 + 30.5569i −2.04684 + 0.985706i
962962 8.22672 + 36.0436i 0.265240 + 1.16209i
963963 9.33278 40.8896i 0.300745 1.31765i
964964 63.1694 + 30.4208i 2.03455 + 0.979787i
965965 3.22442 + 4.04330i 0.103798 + 0.130158i
966966 37.5866 + 47.1321i 1.20933 + 1.51645i
967967 31.7525 15.2912i 1.02109 0.491732i 0.153048 0.988219i 0.451091π-0.451091\pi
0.868044 + 0.496487i 0.165377π0.165377\pi
968968 29.8022 37.3708i 0.957878 1.20114i
969969 12.0000 0.385496
970970 6.75141 8.46601i 0.216775 0.271827i
971971 3.48398 15.2643i 0.111806 0.489855i −0.887757 0.460312i 0.847738π-0.847738\pi
0.999564 0.0295431i 0.00940522π-0.00940522\pi
972972 18.4496 80.8329i 0.591771 2.59272i
973973 −24.6889 + 30.9589i −0.791491 + 0.992498i
974974 27.7990 0.890737
975975 23.0508 28.9047i 0.738215 0.925693i
976976 13.0508 6.28493i 0.417746 0.201176i
977977 22.5526 + 28.2801i 0.721522 + 0.904760i 0.998423 0.0561387i 0.0178789π-0.0178789\pi
−0.276901 + 0.960898i 0.589307π0.589307\pi
978978 −14.2776 17.9035i −0.456547 0.572492i
979979 −4.65943 2.24386i −0.148916 0.0717141i
980980 0.851905 3.73244i 0.0272131 0.119228i
981981 −7.96602 34.9014i −0.254336 1.11432i
982982 −46.2055 + 22.2514i −1.47448 + 0.710071i
983983 19.7042 + 9.48906i 0.628468 + 0.302654i 0.720873 0.693067i 0.243741π-0.243741\pi
−0.0924051 + 0.995721i 0.529455π0.529455\pi
984984 −10.6363 46.6006i −0.339072 1.48557i
985985 −2.00000 −0.0637253
986986 0 0
987987 22.1421 0.704792
988988 19.5687 + 85.7363i 0.622565 + 2.72763i
989989 −11.8141 5.68939i −0.375668 0.180912i
990990 2.54832 1.22721i 0.0809911 0.0390032i
991991 2.85459 + 12.5068i 0.0906792 + 0.397291i 0.999816 0.0192072i 0.00611423π-0.00611423\pi
−0.909136 + 0.416499i 0.863257π0.863257\pi
992992 −3.55378 + 15.5701i −0.112833 + 0.494353i
993993 5.25123 + 2.52886i 0.166643 + 0.0802509i
994994 −37.5866 47.1321i −1.19218 1.49494i
995995 0.302568 + 0.379408i 0.00959205 + 0.0120281i
996996 −63.7612 + 30.7058i −2.02035 + 0.972949i
997997 17.6350 22.1135i 0.558505 0.700343i −0.419776 0.907628i 0.637891π-0.637891\pi
0.978281 + 0.207285i 0.0664628π0.0664628\pi
998998 −45.7990 −1.44974
999999 1.03303 1.29538i 0.0326837 0.0409840i
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 841.2.d.j.645.2 12
29.2 odd 28 841.2.b.a.840.4 4
29.3 odd 28 841.2.e.k.63.1 24
29.4 even 14 841.2.d.f.605.1 12
29.5 even 14 841.2.a.d.1.2 2
29.6 even 14 841.2.d.f.571.1 12
29.7 even 7 inner 841.2.d.j.778.1 12
29.8 odd 28 841.2.e.k.651.1 24
29.9 even 14 841.2.d.f.190.1 12
29.10 odd 28 841.2.e.k.236.4 24
29.11 odd 28 841.2.e.k.267.4 24
29.12 odd 4 841.2.e.k.196.1 24
29.13 even 14 841.2.d.f.574.2 12
29.14 odd 28 841.2.e.k.270.1 24
29.15 odd 28 841.2.e.k.270.4 24
29.16 even 7 inner 841.2.d.j.574.1 12
29.17 odd 4 841.2.e.k.196.4 24
29.18 odd 28 841.2.e.k.267.1 24
29.19 odd 28 841.2.e.k.236.1 24
29.20 even 7 inner 841.2.d.j.190.2 12
29.21 odd 28 841.2.e.k.651.4 24
29.22 even 14 841.2.d.f.778.2 12
29.23 even 7 inner 841.2.d.j.571.2 12
29.24 even 7 29.2.a.a.1.1 2
29.25 even 7 inner 841.2.d.j.605.2 12
29.26 odd 28 841.2.e.k.63.4 24
29.27 odd 28 841.2.b.a.840.1 4
29.28 even 2 841.2.d.f.645.1 12
87.5 odd 14 7569.2.a.c.1.1 2
87.53 odd 14 261.2.a.d.1.2 2
116.111 odd 14 464.2.a.h.1.1 2
145.24 even 14 725.2.a.b.1.2 2
145.53 odd 28 725.2.b.b.349.4 4
145.82 odd 28 725.2.b.b.349.1 4
203.111 odd 14 1421.2.a.j.1.1 2
232.53 even 14 1856.2.a.r.1.1 2
232.227 odd 14 1856.2.a.w.1.2 2
319.285 odd 14 3509.2.a.j.1.2 2
348.227 even 14 4176.2.a.bq.1.2 2
377.285 even 14 4901.2.a.g.1.2 2
435.314 odd 14 6525.2.a.o.1.1 2
493.169 even 14 8381.2.a.e.1.1 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
29.2.a.a.1.1 2 29.24 even 7
261.2.a.d.1.2 2 87.53 odd 14
464.2.a.h.1.1 2 116.111 odd 14
725.2.a.b.1.2 2 145.24 even 14
725.2.b.b.349.1 4 145.82 odd 28
725.2.b.b.349.4 4 145.53 odd 28
841.2.a.d.1.2 2 29.5 even 14
841.2.b.a.840.1 4 29.27 odd 28
841.2.b.a.840.4 4 29.2 odd 28
841.2.d.f.190.1 12 29.9 even 14
841.2.d.f.571.1 12 29.6 even 14
841.2.d.f.574.2 12 29.13 even 14
841.2.d.f.605.1 12 29.4 even 14
841.2.d.f.645.1 12 29.28 even 2
841.2.d.f.778.2 12 29.22 even 14
841.2.d.j.190.2 12 29.20 even 7 inner
841.2.d.j.571.2 12 29.23 even 7 inner
841.2.d.j.574.1 12 29.16 even 7 inner
841.2.d.j.605.2 12 29.25 even 7 inner
841.2.d.j.645.2 12 1.1 even 1 trivial
841.2.d.j.778.1 12 29.7 even 7 inner
841.2.e.k.63.1 24 29.3 odd 28
841.2.e.k.63.4 24 29.26 odd 28
841.2.e.k.196.1 24 29.12 odd 4
841.2.e.k.196.4 24 29.17 odd 4
841.2.e.k.236.1 24 29.19 odd 28
841.2.e.k.236.4 24 29.10 odd 28
841.2.e.k.267.1 24 29.18 odd 28
841.2.e.k.267.4 24 29.11 odd 28
841.2.e.k.270.1 24 29.14 odd 28
841.2.e.k.270.4 24 29.15 odd 28
841.2.e.k.651.1 24 29.8 odd 28
841.2.e.k.651.4 24 29.21 odd 28
1421.2.a.j.1.1 2 203.111 odd 14
1856.2.a.r.1.1 2 232.53 even 14
1856.2.a.w.1.2 2 232.227 odd 14
3509.2.a.j.1.2 2 319.285 odd 14
4176.2.a.bq.1.2 2 348.227 even 14
4901.2.a.g.1.2 2 377.285 even 14
6525.2.a.o.1.1 2 435.314 odd 14
7569.2.a.c.1.1 2 87.5 odd 14
8381.2.a.e.1.1 2 493.169 even 14