Properties

Label 961.2.c.h.521.4
Level 961961
Weight 22
Character 961.521
Analytic conductor 7.6747.674
Analytic rank 00
Dimension 88
Inner twists 44

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [961,2,Mod(439,961)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(961, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([4]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("961.439");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 961=312 961 = 31^{2}
Weight: k k == 2 2
Character orbit: [χ][\chi] == 961.c (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: 7.673623634257.67362363425
Analytic rank: 00
Dimension: 88
Relative dimension: 44 over Q(ζ3)\Q(\zeta_{3})
Coefficient field: 8.0.207360000.1
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x8+6x6+32x4+24x2+16 x^{8} + 6x^{6} + 32x^{4} + 24x^{2} + 16 Copy content Toggle raw display
Coefficient ring: Z[a1,,a5]\Z[a_1, \ldots, a_{5}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C3]\mathrm{SU}(2)[C_{3}]

Embedding invariants

Embedding label 521.4
Root 0.4370160.756934i-0.437016 - 0.756934i of defining polynomial
Character χ\chi == 961.521
Dual form 961.2.c.h.439.4

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+2.61803q2+(0.437016+0.756934i)q3+4.85410q4+(1.11803+1.93649i)q5+(1.14412+1.98168i)q6+(0.500000+0.866025i)q7+7.47214q8+(1.118031.93649i)q9+(2.92705+5.06980i)q10+(2.12132+3.67423i)q11+(2.12132+3.67423i)q12+(1.311052.27080i)q13+(1.30902+2.26728i)q141.95440q15+9.85410q16+(1.851233.20642i)q17+(2.927055.06980i)q18+(0.5000000.866025i)q19+(5.42705+9.39993i)q20+(0.437016+0.756934i)q21+(5.55369+9.61927i)q222.62210q23+(3.26544+5.65591i)q24+(3.432375.94504i)q26+4.57649q27+(2.42705+4.20378i)q280.540182q295.11667q30+10.8541q323.70820q33+(4.846588.39453i)q342.23607q35+(5.427059.39993i)q36+(2.121323.67423i)q37+(1.309022.26728i)q38+2.29180q39+(8.35410+14.4697i)q40+(0.7360681.27491i)q41+(1.14412+1.98168i)q42+(4.84658+8.39453i)q43+(10.2971+17.8351i)q44+(2.50000+4.33013i)q456.86474q469.70820q47+(4.30640+7.45890i)q48+(3.000005.19615i)q49+(1.618032.80252i)q51+(6.3639611.0227i)q52+(6.8647411.8901i)q53+11.9814q54+(4.743428.21584i)q55+(3.73607+6.47106i)q56+(0.4370160.756934i)q571.41421q58+(5.9721410.3440i)q599.48683q60+13.9358q61+2.23607q63+8.70820q64+(2.93159+5.07767i)q659.70820q66+(3.00000+5.19615i)q67+(8.9860615.5643i)q68+(1.145901.98475i)q695.85410q70+(0.7360681.27491i)q71+(8.3541014.4697i)q72+(2.12132+3.67423i)q73+(5.553699.61927i)q74+(2.427054.20378i)q764.24264q77+6.00000q78+(0.810272+1.40343i)q79+(11.0172+19.0824i)q80+(1.354102.34537i)q81+(1.927053.33775i)q82+(1.581142.73861i)q83+(2.12132+3.67423i)q84+8.27895q85+(12.6885+21.9772i)q86+(0.2360680.408882i)q87+(15.8508+27.4544i)q8815.3500q89+(6.54508+11.3364i)q90+2.62210q9112.7279q9225.4164q94+2.23607q95+(4.74342+8.21584i)q967.00000q97+(7.8541013.6037i)q98+(4.74342+8.21584i)q99+O(q100)q+2.61803 q^{2} +(0.437016 + 0.756934i) q^{3} +4.85410 q^{4} +(-1.11803 + 1.93649i) q^{5} +(1.14412 + 1.98168i) q^{6} +(0.500000 + 0.866025i) q^{7} +7.47214 q^{8} +(1.11803 - 1.93649i) q^{9} +(-2.92705 + 5.06980i) q^{10} +(-2.12132 + 3.67423i) q^{11} +(2.12132 + 3.67423i) q^{12} +(1.31105 - 2.27080i) q^{13} +(1.30902 + 2.26728i) q^{14} -1.95440 q^{15} +9.85410 q^{16} +(-1.85123 - 3.20642i) q^{17} +(2.92705 - 5.06980i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-5.42705 + 9.39993i) q^{20} +(-0.437016 + 0.756934i) q^{21} +(-5.55369 + 9.61927i) q^{22} -2.62210 q^{23} +(3.26544 + 5.65591i) q^{24} +(3.43237 - 5.94504i) q^{26} +4.57649 q^{27} +(2.42705 + 4.20378i) q^{28} -0.540182 q^{29} -5.11667 q^{30} +10.8541 q^{32} -3.70820 q^{33} +(-4.84658 - 8.39453i) q^{34} -2.23607 q^{35} +(5.42705 - 9.39993i) q^{36} +(-2.12132 - 3.67423i) q^{37} +(-1.30902 - 2.26728i) q^{38} +2.29180 q^{39} +(-8.35410 + 14.4697i) q^{40} +(0.736068 - 1.27491i) q^{41} +(-1.14412 + 1.98168i) q^{42} +(4.84658 + 8.39453i) q^{43} +(-10.2971 + 17.8351i) q^{44} +(2.50000 + 4.33013i) q^{45} -6.86474 q^{46} -9.70820 q^{47} +(4.30640 + 7.45890i) q^{48} +(3.00000 - 5.19615i) q^{49} +(1.61803 - 2.80252i) q^{51} +(6.36396 - 11.0227i) q^{52} +(6.86474 - 11.8901i) q^{53} +11.9814 q^{54} +(-4.74342 - 8.21584i) q^{55} +(3.73607 + 6.47106i) q^{56} +(0.437016 - 0.756934i) q^{57} -1.41421 q^{58} +(-5.97214 - 10.3440i) q^{59} -9.48683 q^{60} +13.9358 q^{61} +2.23607 q^{63} +8.70820 q^{64} +(2.93159 + 5.07767i) q^{65} -9.70820 q^{66} +(-3.00000 + 5.19615i) q^{67} +(-8.98606 - 15.5643i) q^{68} +(-1.14590 - 1.98475i) q^{69} -5.85410 q^{70} +(0.736068 - 1.27491i) q^{71} +(8.35410 - 14.4697i) q^{72} +(-2.12132 + 3.67423i) q^{73} +(-5.55369 - 9.61927i) q^{74} +(-2.42705 - 4.20378i) q^{76} -4.24264 q^{77} +6.00000 q^{78} +(0.810272 + 1.40343i) q^{79} +(-11.0172 + 19.0824i) q^{80} +(-1.35410 - 2.34537i) q^{81} +(1.92705 - 3.33775i) q^{82} +(1.58114 - 2.73861i) q^{83} +(-2.12132 + 3.67423i) q^{84} +8.27895 q^{85} +(12.6885 + 21.9772i) q^{86} +(-0.236068 - 0.408882i) q^{87} +(-15.8508 + 27.4544i) q^{88} -15.3500 q^{89} +(6.54508 + 11.3364i) q^{90} +2.62210 q^{91} -12.7279 q^{92} -25.4164 q^{94} +2.23607 q^{95} +(4.74342 + 8.21584i) q^{96} -7.00000 q^{97} +(7.85410 - 13.6037i) q^{98} +(4.74342 + 8.21584i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 8q+12q2+12q4+4q7+24q810q10+6q14+52q16+10q184q1930q20+6q28+60q32+24q33+30q366q38+72q3940q4012q41++36q98+O(q100) 8 q + 12 q^{2} + 12 q^{4} + 4 q^{7} + 24 q^{8} - 10 q^{10} + 6 q^{14} + 52 q^{16} + 10 q^{18} - 4 q^{19} - 30 q^{20} + 6 q^{28} + 60 q^{32} + 24 q^{33} + 30 q^{36} - 6 q^{38} + 72 q^{39} - 40 q^{40} - 12 q^{41}+ \cdots + 36 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/961Z)×\left(\mathbb{Z}/961\mathbb{Z}\right)^\times.

nn 33
χ(n)\chi(n) e(13)e\left(\frac{1}{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 2.61803 1.85123 0.925615 0.378467i 0.123549π-0.123549\pi
0.925615 + 0.378467i 0.123549π0.123549\pi
33 0.437016 + 0.756934i 0.252311 + 0.437016i 0.964162 0.265315i 0.0854760π-0.0854760\pi
−0.711850 + 0.702331i 0.752143π0.752143\pi
44 4.85410 2.42705
55 −1.11803 + 1.93649i −0.500000 + 0.866025i 0.500000 + 0.866025i 0.333333π0.333333\pi
−1.00000 π\pi
66 1.14412 + 1.98168i 0.467086 + 0.809017i
77 0.500000 + 0.866025i 0.188982 + 0.327327i 0.944911 0.327327i 0.106148π-0.106148\pi
−0.755929 + 0.654654i 0.772814π0.772814\pi
88 7.47214 2.64180
99 1.11803 1.93649i 0.372678 0.645497i
1010 −2.92705 + 5.06980i −0.925615 + 1.60321i
1111 −2.12132 + 3.67423i −0.639602 + 1.10782i 0.345918 + 0.938265i 0.387568π0.387568\pi
−0.985520 + 0.169559i 0.945766π0.945766\pi
1212 2.12132 + 3.67423i 0.612372 + 1.06066i
1313 1.31105 2.27080i 0.363619 0.629807i −0.624934 0.780677i 0.714874π-0.714874\pi
0.988554 + 0.150870i 0.0482076π0.0482076\pi
1414 1.30902 + 2.26728i 0.349850 + 0.605957i
1515 −1.95440 −0.504623
1616 9.85410 2.46353
1717 −1.85123 3.20642i −0.448989 0.777672i 0.549331 0.835605i 0.314882π-0.314882\pi
−0.998320 + 0.0579326i 0.981549π0.981549\pi
1818 2.92705 5.06980i 0.689913 1.19496i
1919 −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i 0.203260π-0.203260\pi
−0.917663 + 0.397360i 0.869927π0.869927\pi
2020 −5.42705 + 9.39993i −1.21353 + 2.10189i
2121 −0.437016 + 0.756934i −0.0953647 + 0.165177i
2222 −5.55369 + 9.61927i −1.18405 + 2.05084i
2323 −2.62210 −0.546745 −0.273372 0.961908i 0.588139π-0.588139\pi
−0.273372 + 0.961908i 0.588139π0.588139\pi
2424 3.26544 + 5.65591i 0.666556 + 1.15451i
2525 0 0
2626 3.43237 5.94504i 0.673143 1.16592i
2727 4.57649 0.880746
2828 2.42705 + 4.20378i 0.458670 + 0.794439i
2929 −0.540182 −0.100309 −0.0501546 0.998741i 0.515971π-0.515971\pi
−0.0501546 + 0.998741i 0.515971π0.515971\pi
3030 −5.11667 −0.934172
3131 0 0
3232 10.8541 1.91875
3333 −3.70820 −0.645515
3434 −4.84658 8.39453i −0.831182 1.43965i
3535 −2.23607 −0.377964
3636 5.42705 9.39993i 0.904508 1.56665i
3737 −2.12132 3.67423i −0.348743 0.604040i 0.637284 0.770629i 0.280058π-0.280058\pi
−0.986026 + 0.166589i 0.946725π0.946725\pi
3838 −1.30902 2.26728i −0.212351 0.367802i
3939 2.29180 0.366981
4040 −8.35410 + 14.4697i −1.32090 + 2.28787i
4141 0.736068 1.27491i 0.114955 0.199107i −0.802807 0.596239i 0.796661π-0.796661\pi
0.917762 + 0.397132i 0.129994π0.129994\pi
4242 −1.14412 + 1.98168i −0.176542 + 0.305780i
4343 4.84658 + 8.39453i 0.739097 + 1.28015i 0.952902 + 0.303277i 0.0980808π0.0980808\pi
−0.213806 + 0.976876i 0.568586π0.568586\pi
4444 −10.2971 + 17.8351i −1.55235 + 2.68874i
4545 2.50000 + 4.33013i 0.372678 + 0.645497i
4646 −6.86474 −1.01215
4747 −9.70820 −1.41609 −0.708044 0.706169i 0.750422π-0.750422\pi
−0.708044 + 0.706169i 0.750422π0.750422\pi
4848 4.30640 + 7.45890i 0.621575 + 1.07660i
4949 3.00000 5.19615i 0.428571 0.742307i
5050 0 0
5151 1.61803 2.80252i 0.226570 0.392431i
5252 6.36396 11.0227i 0.882523 1.52857i
5353 6.86474 11.8901i 0.942944 1.63323i 0.183128 0.983089i 0.441378π-0.441378\pi
0.759816 0.650138i 0.225289π-0.225289\pi
5454 11.9814 1.63046
5555 −4.74342 8.21584i −0.639602 1.10782i
5656 3.73607 + 6.47106i 0.499253 + 0.864732i
5757 0.437016 0.756934i 0.0578842 0.100258i
5858 −1.41421 −0.185695
5959 −5.97214 10.3440i −0.777506 1.34668i −0.933375 0.358902i 0.883151π-0.883151\pi
0.155869 0.987778i 0.450182π-0.450182\pi
6060 −9.48683 −1.22474
6161 13.9358 1.78430 0.892148 0.451742i 0.149197π-0.149197\pi
0.892148 + 0.451742i 0.149197π0.149197\pi
6262 0 0
6363 2.23607 0.281718
6464 8.70820 1.08853
6565 2.93159 + 5.07767i 0.363619 + 0.629807i
6666 −9.70820 −1.19500
6767 −3.00000 + 5.19615i −0.366508 + 0.634811i −0.989017 0.147802i 0.952780π-0.952780\pi
0.622509 + 0.782613i 0.286114π0.286114\pi
6868 −8.98606 15.5643i −1.08972 1.88745i
6969 −1.14590 1.98475i −0.137950 0.238936i
7070 −5.85410 −0.699699
7171 0.736068 1.27491i 0.0873552 0.151304i −0.819037 0.573740i 0.805492π-0.805492\pi
0.906392 + 0.422437i 0.138825π0.138825\pi
7272 8.35410 14.4697i 0.984540 1.70527i
7373 −2.12132 + 3.67423i −0.248282 + 0.430037i −0.963049 0.269326i 0.913199π-0.913199\pi
0.714767 + 0.699362i 0.246533π0.246533\pi
7474 −5.55369 9.61927i −0.645603 1.11822i
7575 0 0
7676 −2.42705 4.20378i −0.278402 0.482206i
7777 −4.24264 −0.483494
7878 6.00000 0.679366
7979 0.810272 + 1.40343i 0.0911628 + 0.157899i 0.908001 0.418969i 0.137608π-0.137608\pi
−0.816838 + 0.576867i 0.804275π0.804275\pi
8080 −11.0172 + 19.0824i −1.23176 + 2.13348i
8181 −1.35410 2.34537i −0.150456 0.260597i
8282 1.92705 3.33775i 0.212807 0.368593i
8383 1.58114 2.73861i 0.173553 0.300602i −0.766107 0.642713i 0.777809π-0.777809\pi
0.939659 + 0.342111i 0.111142π0.111142\pi
8484 −2.12132 + 3.67423i −0.231455 + 0.400892i
8585 8.27895 0.897978
8686 12.6885 + 21.9772i 1.36824 + 2.36986i
8787 −0.236068 0.408882i −0.0253091 0.0438367i
8888 −15.8508 + 27.4544i −1.68970 + 2.92665i
8989 −15.3500 −1.62710 −0.813549 0.581496i 0.802468π-0.802468\pi
−0.813549 + 0.581496i 0.802468π0.802468\pi
9090 6.54508 + 11.3364i 0.689913 + 1.19496i
9191 2.62210 0.274870
9292 −12.7279 −1.32698
9393 0 0
9494 −25.4164 −2.62150
9595 2.23607 0.229416
9696 4.74342 + 8.21584i 0.484123 + 0.838525i
9797 −7.00000 −0.710742 −0.355371 0.934725i 0.615646π-0.615646\pi
−0.355371 + 0.934725i 0.615646π0.615646\pi
9898 7.85410 13.6037i 0.793384 1.37418i
9999 4.74342 + 8.21584i 0.476731 + 0.825723i
100100 0 0
101101 2.23607 0.222497 0.111249 0.993793i 0.464515π-0.464515\pi
0.111249 + 0.993793i 0.464515π0.464515\pi
102102 4.23607 7.33708i 0.419433 0.726480i
103103 −5.35410 + 9.27358i −0.527555 + 0.913753i 0.471929 + 0.881637i 0.343558π0.343558\pi
−0.999484 + 0.0321160i 0.989775π0.989775\pi
104104 9.79633 16.9677i 0.960609 1.66382i
105105 −0.977198 1.69256i −0.0953647 0.165177i
106106 17.9721 31.1286i 1.74561 3.02348i
107107 −0.736068 1.27491i −0.0711584 0.123250i 0.828251 0.560357i 0.189336π-0.189336\pi
−0.899409 + 0.437108i 0.856003π0.856003\pi
108108 22.2148 2.13762
109109 −1.29180 −0.123732 −0.0618658 0.998084i 0.519705π-0.519705\pi
−0.0618658 + 0.998084i 0.519705π0.519705\pi
110110 −12.4184 21.5093i −1.18405 2.05084i
111111 1.85410 3.21140i 0.175984 0.304812i
112112 4.92705 + 8.53390i 0.465563 + 0.806378i
113113 4.88197 8.45581i 0.459257 0.795456i −0.539665 0.841880i 0.681449π-0.681449\pi
0.998922 + 0.0464238i 0.0147825π0.0147825\pi
114114 1.14412 1.98168i 0.107157 0.185601i
115115 2.93159 5.07767i 0.273372 0.473495i
116116 −2.62210 −0.243456
117117 −2.93159 5.07767i −0.271026 0.469431i
118118 −15.6353 27.0811i −1.43934 2.49301i
119119 1.85123 3.20642i 0.169702 0.293932i
120120 −14.6035 −1.33311
121121 −3.50000 6.06218i −0.318182 0.551107i
122122 36.4844 3.30314
123123 1.28669 0.116017
124124 0 0
125125 −11.1803 −1.00000
126126 5.85410 0.521525
127127 4.74342 + 8.21584i 0.420910 + 0.729038i 0.996029 0.0890323i 0.0283774π-0.0283774\pi
−0.575119 + 0.818070i 0.695044π0.695044\pi
128128 1.09017 0.0963583
129129 −4.23607 + 7.33708i −0.372965 + 0.645994i
130130 7.67501 + 13.2935i 0.673143 + 1.16592i
131131 −3.70820 6.42280i −0.323987 0.561162i 0.657320 0.753612i 0.271690π-0.271690\pi
−0.981307 + 0.192450i 0.938357π0.938357\pi
132132 −18.0000 −1.56670
133133 0.500000 0.866025i 0.0433555 0.0750939i
134134 −7.85410 + 13.6037i −0.678491 + 1.17518i
135135 −5.11667 + 8.86234i −0.440373 + 0.762749i
136136 −13.8326 23.9588i −1.18614 2.05445i
137137 1.31105 2.27080i 0.112010 0.194008i −0.804570 0.593857i 0.797604π-0.797604\pi
0.916581 + 0.399850i 0.130938π0.130938\pi
138138 −3.00000 5.19615i −0.255377 0.442326i
139139 −17.9721 −1.52437 −0.762187 0.647356i 0.775875π-0.775875\pi
−0.762187 + 0.647356i 0.775875π0.775875\pi
140140 −10.8541 −0.917339
141141 −4.24264 7.34847i −0.357295 0.618853i
142142 1.92705 3.33775i 0.161715 0.280098i
143143 5.56231 + 9.63420i 0.465143 + 0.805652i
144144 11.0172 19.0824i 0.918102 1.59020i
145145 0.603941 1.04606i 0.0501546 0.0868703i
146146 −5.55369 + 9.61927i −0.459627 + 0.796097i
147147 5.24419 0.432534
148148 −10.2971 17.8351i −0.846417 1.46604i
149149 6.70820 + 11.6190i 0.549557 + 0.951861i 0.998305 + 0.0582028i 0.0185370π0.0185370\pi
−0.448747 + 0.893659i 0.648130π0.648130\pi
150150 0 0
151151 12.5216 1.01899 0.509496 0.860473i 0.329832π-0.329832\pi
0.509496 + 0.860473i 0.329832π0.329832\pi
152152 −3.73607 6.47106i −0.303035 0.524872i
153153 −8.27895 −0.669313
154154 −11.1074 −0.895058
155155 0 0
156156 11.1246 0.890682
157157 8.70820 0.694990 0.347495 0.937682i 0.387032π-0.387032\pi
0.347495 + 0.937682i 0.387032π0.387032\pi
158158 2.12132 + 3.67423i 0.168763 + 0.292306i
159159 12.0000 0.951662
160160 −12.1353 + 21.0189i −0.959376 + 1.66169i
161161 −1.31105 2.27080i −0.103325 0.178964i
162162 −3.54508 6.14027i −0.278528 0.482425i
163163 14.4164 1.12918 0.564590 0.825371i 0.309034π-0.309034\pi
0.564590 + 0.825371i 0.309034π0.309034\pi
164164 3.57295 6.18853i 0.279000 0.483243i
165165 4.14590 7.18091i 0.322758 0.559033i
166166 4.13948 7.16978i 0.321286 0.556483i
167167 0.540182 + 0.935622i 0.0418005 + 0.0724006i 0.886169 0.463363i 0.153357π-0.153357\pi
−0.844368 + 0.535763i 0.820024π0.820024\pi
168168 −3.26544 + 5.65591i −0.251934 + 0.436363i
169169 3.06231 + 5.30407i 0.235562 + 0.408005i
170170 21.6746 1.66236
171171 −2.23607 −0.170996
172172 23.5258 + 40.7479i 1.79383 + 3.10700i
173173 −9.00000 + 15.5885i −0.684257 + 1.18517i 0.289412 + 0.957205i 0.406540π0.406540\pi
−0.973670 + 0.227964i 0.926793π0.926793\pi
174174 −0.618034 1.07047i −0.0468530 0.0811518i
175175 0 0
176176 −20.9037 + 36.2063i −1.57568 + 2.72915i
177177 5.21984 9.04103i 0.392347 0.679565i
178178 −40.1869 −3.01213
179179 −6.63405 11.4905i −0.495852 0.858841i 0.504136 0.863624i 0.331811π-0.331811\pi
−0.999989 + 0.00478274i 0.998478π0.998478\pi
180180 12.1353 + 21.0189i 0.904508 + 1.56665i
181181 −4.34581 + 7.52716i −0.323021 + 0.559489i −0.981110 0.193451i 0.938032π-0.938032\pi
0.658089 + 0.752940i 0.271365π0.271365\pi
182182 6.86474 0.508848
183183 6.09017 + 10.5485i 0.450198 + 0.779766i
184184 −19.5927 −1.44439
185185 9.48683 0.697486
186186 0 0
187187 15.7082 1.14870
188188 −47.1246 −3.43692
189189 2.28825 + 3.96336i 0.166445 + 0.288292i
190190 5.85410 0.424701
191191 −4.88197 + 8.45581i −0.353247 + 0.611841i −0.986816 0.161845i 0.948256π-0.948256\pi
0.633570 + 0.773686i 0.281589π0.281589\pi
192192 3.80562 + 6.59154i 0.274647 + 0.475703i
193193 10.3541 + 17.9338i 0.745305 + 1.29091i 0.950052 + 0.312091i 0.101029π0.101029\pi
−0.204748 + 0.978815i 0.565637π0.565637\pi
194194 −18.3262 −1.31575
195195 −2.56231 + 4.43804i −0.183491 + 0.317815i
196196 14.5623 25.2227i 1.04016 1.80162i
197197 0.540182 0.935622i 0.0384863 0.0666603i −0.846141 0.532960i 0.821080π-0.821080\pi
0.884627 + 0.466299i 0.154413π0.154413\pi
198198 12.4184 + 21.5093i 0.882539 + 1.52860i
199199 −11.6082 + 20.1059i −0.822880 + 1.42527i 0.0806485 + 0.996743i 0.474301π0.474301\pi
−0.903529 + 0.428528i 0.859032π0.859032\pi
200200 0 0
201201 −5.24419 −0.369897
202202 5.85410 0.411893
203203 −0.270091 0.467811i −0.0189567 0.0328339i
204204 7.85410 13.6037i 0.549897 0.952450i
205205 1.64590 + 2.85078i 0.114955 + 0.199107i
206206 −14.0172 + 24.2785i −0.976626 + 1.69157i
207207 −2.93159 + 5.07767i −0.203760 + 0.352922i
208208 12.9192 22.3767i 0.895785 1.55155i
209209 4.24264 0.293470
210210 −2.55834 4.43117i −0.176542 0.305780i
211211 2.50000 + 4.33013i 0.172107 + 0.298098i 0.939156 0.343490i 0.111609π-0.111609\pi
−0.767049 + 0.641588i 0.778276π0.778276\pi
212212 33.3221 57.7156i 2.28857 3.96393i
213213 1.28669 0.0881628
214214 −1.92705 3.33775i −0.131730 0.228164i
215215 −21.6746 −1.47819
216216 34.1962 2.32675
217217 0 0
218218 −3.38197 −0.229056
219219 −3.70820 −0.250577
220220 −23.0250 39.8805i −1.55235 2.68874i
221221 −9.70820 −0.653044
222222 4.85410 8.40755i 0.325786 0.564278i
223223 −8.07262 13.9822i −0.540583 0.936316i −0.998871 0.0475128i 0.984871π-0.984871\pi
0.458288 0.888804i 0.348463π-0.348463\pi
224224 5.42705 + 9.39993i 0.362610 + 0.628059i
225225 0 0
226226 12.7812 22.1376i 0.850190 1.47257i
227227 −1.14590 + 1.98475i −0.0760559 + 0.131733i −0.901545 0.432685i 0.857566π-0.857566\pi
0.825489 + 0.564418i 0.190899π0.190899\pi
228228 2.12132 3.67423i 0.140488 0.243332i
229229 −2.12132 3.67423i −0.140181 0.242800i 0.787384 0.616463i 0.211435π-0.211435\pi
−0.927565 + 0.373663i 0.878102π0.878102\pi
230230 7.67501 13.2935i 0.506075 0.876548i
231231 −1.85410 3.21140i −0.121991 0.211295i
232232 −4.03631 −0.264997
233233 −13.4721 −0.882589 −0.441294 0.897362i 0.645481π-0.645481\pi
−0.441294 + 0.897362i 0.645481π0.645481\pi
234234 −7.67501 13.2935i −0.501731 0.869024i
235235 10.8541 18.7999i 0.708044 1.22637i
236236 −28.9894 50.2110i −1.88705 3.26846i
237237 −0.708204 + 1.22665i −0.0460028 + 0.0796792i
238238 4.84658 8.39453i 0.314157 0.544136i
239239 −6.05446 + 10.4866i −0.391631 + 0.678324i −0.992665 0.120899i 0.961422π-0.961422\pi
0.601034 + 0.799223i 0.294756π0.294756\pi
240240 −19.2588 −1.24315
241241 11.6082 + 20.1059i 0.747747 + 1.29514i 0.948900 + 0.315576i 0.102198π0.102198\pi
−0.201153 + 0.979560i 0.564469π0.564469\pi
242242 −9.16312 15.8710i −0.589028 1.02023i
243243 8.04827 13.9400i 0.516296 0.894252i
244244 67.6458 4.33058
245245 6.70820 + 11.6190i 0.428571 + 0.742307i
246246 3.36861 0.214775
247247 −2.62210 −0.166840
248248 0 0
249249 2.76393 0.175157
250250 −29.2705 −1.85123
251251 −5.51428 9.55102i −0.348058 0.602855i 0.637846 0.770164i 0.279826π-0.279826\pi
−0.985905 + 0.167309i 0.946492π0.946492\pi
252252 10.8541 0.683744
253253 5.56231 9.63420i 0.349699 0.605697i
254254 12.4184 + 21.5093i 0.779201 + 1.34962i
255255 3.61803 + 6.26662i 0.226570 + 0.392431i
256256 −14.5623 −0.910144
257257 −3.02786 + 5.24441i −0.188873 + 0.327138i −0.944875 0.327432i 0.893817π-0.893817\pi
0.756002 + 0.654570i 0.227150π0.227150\pi
258258 −11.0902 + 19.2087i −0.690444 + 1.19588i
259259 2.12132 3.67423i 0.131812 0.228306i
260260 14.2302 + 24.6475i 0.882523 + 1.52857i
261261 −0.603941 + 1.04606i −0.0373830 + 0.0647493i
262262 −9.70820 16.8151i −0.599775 1.03884i
263263 18.5123 1.14152 0.570759 0.821118i 0.306649π-0.306649\pi
0.570759 + 0.821118i 0.306649π0.306649\pi
264264 −27.7082 −1.70532
265265 15.3500 + 26.5870i 0.942944 + 1.63323i
266266 1.30902 2.26728i 0.0802610 0.139016i
267267 −6.70820 11.6190i −0.410535 0.711068i
268268 −14.5623 + 25.2227i −0.889534 + 1.54072i
269269 −1.08036 + 1.87124i −0.0658709 + 0.114092i −0.897080 0.441868i 0.854316π-0.854316\pi
0.831209 + 0.555960i 0.187649π0.187649\pi
270270 −13.3956 + 23.2019i −0.815232 + 1.41202i
271271 −18.5911 −1.12933 −0.564665 0.825320i 0.690994π-0.690994\pi
−0.564665 + 0.825320i 0.690994π0.690994\pi
272272 −18.2422 31.5964i −1.10610 1.91581i
273273 1.14590 + 1.98475i 0.0693529 + 0.120123i
274274 3.43237 5.94504i 0.207357 0.359153i
275275 0 0
276276 −5.56231 9.63420i −0.334811 0.579910i
277277 10.1058 0.607200 0.303600 0.952800i 0.401811π-0.401811\pi
0.303600 + 0.952800i 0.401811π0.401811\pi
278278 −47.0516 −2.82197
279279 0 0
280280 −16.7082 −0.998506
281281 13.3607 0.797031 0.398516 0.917162i 0.369525π-0.369525\pi
0.398516 + 0.917162i 0.369525π0.369525\pi
282282 −11.1074 19.2385i −0.661435 1.14564i
283283 24.0000 1.42665 0.713326 0.700832i 0.247188π-0.247188\pi
0.713326 + 0.700832i 0.247188π0.247188\pi
284284 3.57295 6.18853i 0.212016 0.367222i
285285 0.977198 + 1.69256i 0.0578842 + 0.100258i
286286 14.5623 + 25.2227i 0.861087 + 1.49145i
287287 1.47214 0.0868974
288288 12.1353 21.0189i 0.715077 1.23855i
289289 1.64590 2.85078i 0.0968175 0.167693i
290290 1.58114 2.73861i 0.0928477 0.160817i
291291 −3.05911 5.29854i −0.179328 0.310606i
292292 −10.2971 + 17.8351i −0.602593 + 1.04372i
293293 1.14590 + 1.98475i 0.0669441 + 0.115951i 0.897555 0.440903i 0.145342π-0.145342\pi
−0.830611 + 0.556854i 0.812008π0.812008\pi
294294 13.7295 0.800719
295295 26.7082 1.55501
296296 −15.8508 27.4544i −0.921309 1.59575i
297297 −9.70820 + 16.8151i −0.563327 + 0.975711i
298298 17.5623 + 30.4188i 1.01736 + 1.76211i
299299 −3.43769 + 5.95426i −0.198807 + 0.344344i
300300 0 0
301301 −4.84658 + 8.39453i −0.279352 + 0.483852i
302302 32.7820 1.88639
303303 0.977198 + 1.69256i 0.0561385 + 0.0972348i
304304 −4.92705 8.53390i −0.282586 0.489453i
305305 −15.5807 + 26.9866i −0.892148 + 1.54525i
306306 −21.6746 −1.23905
307307 −12.0623 20.8925i −0.688432 1.19240i −0.972345 0.233549i 0.924966π-0.924966\pi
0.283913 0.958850i 0.408367π-0.408367\pi
308308 −20.5942 −1.17346
309309 −9.35931 −0.532433
310310 0 0
311311 25.4721 1.44439 0.722196 0.691688i 0.243133π-0.243133\pi
0.722196 + 0.691688i 0.243133π0.243133\pi
312312 17.1246 0.969490
313313 5.76002 + 9.97665i 0.325576 + 0.563913i 0.981629 0.190801i 0.0611086π-0.0611086\pi
−0.656053 + 0.754715i 0.727775π0.727775\pi
314314 22.7984 1.28659
315315 −2.50000 + 4.33013i −0.140859 + 0.243975i
316316 3.93314 + 6.81241i 0.221257 + 0.383228i
317317 −13.1180 22.7211i −0.736782 1.27614i −0.953937 0.300007i 0.903011π-0.903011\pi
0.217155 0.976137i 0.430322π-0.430322\pi
318318 31.4164 1.76174
319319 1.14590 1.98475i 0.0641580 0.111125i
320320 −9.73607 + 16.8634i −0.544263 + 0.942691i
321321 0.643347 1.11431i 0.0359081 0.0621947i
322322 −3.43237 5.94504i −0.191278 0.331304i
323323 −1.85123 + 3.20642i −0.103005 + 0.178410i
324324 −6.57295 11.3847i −0.365164 0.632482i
325325 0 0
326326 37.7426 2.09037
327327 −0.564536 0.977804i −0.0312189 0.0540727i
328328 5.50000 9.52628i 0.303687 0.526001i
329329 −4.85410 8.40755i −0.267615 0.463523i
330330 10.8541 18.7999i 0.597499 1.03490i
331331 −15.6445 + 27.0970i −0.859897 + 1.48939i 0.0121285 + 0.999926i 0.496139π0.496139\pi
−0.872026 + 0.489460i 0.837194π0.837194\pi
332332 7.67501 13.2935i 0.421221 0.729576i
333333 −9.48683 −0.519875
334334 1.41421 + 2.44949i 0.0773823 + 0.134030i
335335 −6.70820 11.6190i −0.366508 0.634811i
336336 −4.30640 + 7.45890i −0.234933 + 0.406917i
337337 −15.3500 −0.836169 −0.418084 0.908408i 0.637298π-0.637298\pi
−0.418084 + 0.908408i 0.637298π0.637298\pi
338338 8.01722 + 13.8862i 0.436079 + 0.755312i
339339 8.53399 0.463503
340340 40.1869 2.17944
341341 0 0
342342 −5.85410 −0.316554
343343 13.0000 0.701934
344344 36.2143 + 62.7250i 1.95255 + 3.38191i
345345 5.12461 0.275900
346346 −23.5623 + 40.8111i −1.26672 + 2.19402i
347347 10.7979 + 18.7025i 0.579661 + 1.00400i 0.995518 + 0.0945718i 0.0301482π0.0301482\pi
−0.415857 + 0.909430i 0.636518π0.636518\pi
348348 −1.14590 1.98475i −0.0614266 0.106394i
349349 6.00000 0.321173 0.160586 0.987022i 0.448662π-0.448662\pi
0.160586 + 0.987022i 0.448662π0.448662\pi
350350 0 0
351351 6.00000 10.3923i 0.320256 0.554700i
352352 −23.0250 + 39.8805i −1.22724 + 2.12564i
353353 −4.78282 8.28409i −0.254564 0.440918i 0.710213 0.703987i 0.248599π-0.248599\pi
−0.964777 + 0.263069i 0.915265π0.915265\pi
354354 13.6657 23.6697i 0.726324 1.25803i
355355 1.64590 + 2.85078i 0.0873552 + 0.151304i
356356 −74.5106 −3.94905
357357 3.23607 0.171271
358358 −17.3682 30.0826i −0.917936 1.58991i
359359 −7.11803 + 12.3288i −0.375675 + 0.650689i −0.990428 0.138031i 0.955923π-0.955923\pi
0.614752 + 0.788720i 0.289256π0.289256\pi
360360 18.6803 + 32.3553i 0.984540 + 1.70527i
361361 9.00000 15.5885i 0.473684 0.820445i
362362 −11.3775 + 19.7064i −0.597986 + 1.03574i
363363 3.05911 5.29854i 0.160562 0.278101i
364364 12.7279 0.667124
365365 −4.74342 8.21584i −0.248282 0.430037i
366366 15.9443 + 27.6163i 0.833420 + 1.44353i
367367 −3.32920 + 5.76635i −0.173783 + 0.301001i −0.939739 0.341892i 0.888932π-0.888932\pi
0.765956 + 0.642892i 0.222266π0.222266\pi
368368 −25.8384 −1.34692
369369 −1.64590 2.85078i −0.0856820 0.148406i
370370 24.8369 1.29121
371371 13.7295 0.712799
372372 0 0
373373 −9.29180 −0.481111 −0.240555 0.970635i 0.577330π-0.577330\pi
−0.240555 + 0.970635i 0.577330π0.577330\pi
374374 41.1246 2.12650
375375 −4.88599 8.46278i −0.252311 0.437016i
376376 −72.5410 −3.74102
377377 −0.708204 + 1.22665i −0.0364744 + 0.0631754i
378378 5.99070 + 10.3762i 0.308129 + 0.533694i
379379 −3.70820 6.42280i −0.190478 0.329917i 0.754931 0.655804i 0.227670π-0.227670\pi
−0.945409 + 0.325887i 0.894337π0.894337\pi
380380 10.8541 0.556804
381381 −4.14590 + 7.18091i −0.212401 + 0.367889i
382382 −12.7812 + 22.1376i −0.653941 + 1.13266i
383383 3.20168 5.54548i 0.163598 0.283361i −0.772558 0.634944i 0.781023π-0.781023\pi
0.936157 + 0.351583i 0.114357π0.114357\pi
384384 0.476422 + 0.825187i 0.0243123 + 0.0421101i
385385 4.74342 8.21584i 0.241747 0.418718i
386386 27.1074 + 46.9514i 1.37973 + 2.38976i
387387 21.6746 1.10178
388388 −33.9787 −1.72501
389389 8.40647 + 14.5604i 0.426225 + 0.738243i 0.996534 0.0831870i 0.0265099π-0.0265099\pi
−0.570309 + 0.821430i 0.693177π0.693177\pi
390390 −6.70820 + 11.6190i −0.339683 + 0.588348i
391391 4.85410 + 8.40755i 0.245482 + 0.425188i
392392 22.4164 38.8264i 1.13220 1.96103i
393393 3.24109 5.61373i 0.163491 0.283175i
394394 1.41421 2.44949i 0.0712470 0.123404i
395395 −3.62365 −0.182326
396396 23.0250 + 39.8805i 1.15705 + 2.00407i
397397 −7.35410 12.7377i −0.369092 0.639286i 0.620332 0.784339i 0.286998π-0.286998\pi
−0.989424 + 0.145054i 0.953665π0.953665\pi
398398 −30.3905 + 52.6380i −1.52334 + 2.63850i
399399 0.874032 0.0437563
400400 0 0
401401 −0.540182 −0.0269754 −0.0134877 0.999909i 0.504293π-0.504293\pi
−0.0134877 + 0.999909i 0.504293π0.504293\pi
402402 −13.7295 −0.684764
403403 0 0
404404 10.8541 0.540012
405405 6.05573 0.300912
406406 −0.707107 1.22474i −0.0350931 0.0607831i
407407 18.0000 0.892227
408408 12.0902 20.9408i 0.598553 1.03672i
409409 −15.0405 26.0509i −0.743706 1.28814i −0.950797 0.309815i 0.899733π-0.899733\pi
0.207091 0.978322i 0.433600π-0.433600\pi
410410 4.30902 + 7.46344i 0.212807 + 0.368593i
411411 2.29180 0.113046
412412 −25.9894 + 45.0149i −1.28040 + 2.21772i
413413 5.97214 10.3440i 0.293870 0.508997i
414414 −7.67501 + 13.2935i −0.377206 + 0.653340i
415415 3.53553 + 6.12372i 0.173553 + 0.300602i
416416 14.2302 24.6475i 0.697695 1.20844i
417417 −7.85410 13.6037i −0.384617 0.666176i
418418 11.1074 0.543280
419419 30.5967 1.49475 0.747374 0.664403i 0.231314π-0.231314\pi
0.747374 + 0.664403i 0.231314π0.231314\pi
420420 −4.74342 8.21584i −0.231455 0.400892i
421421 −13.2082 + 22.8773i −0.643728 + 1.11497i 0.340865 + 0.940112i 0.389280π0.389280\pi
−0.984594 + 0.174858i 0.944053π0.944053\pi
422422 6.54508 + 11.3364i 0.318610 + 0.551848i
423423 −10.8541 + 18.7999i −0.527744 + 0.914080i
424424 51.2942 88.8442i 2.49107 4.31466i
425425 0 0
426426 3.36861 0.163210
427427 6.96790 + 12.0688i 0.337200 + 0.584048i
428428 −3.57295 6.18853i −0.172705 0.299134i
429429 −4.86163 + 8.42060i −0.234722 + 0.406550i
430430 −56.7448 −2.73648
431431 17.9443 + 31.0804i 0.864345 + 1.49709i 0.867696 + 0.497095i 0.165600π0.165600\pi
−0.00335076 + 0.999994i 0.501067π0.501067\pi
432432 45.0972 2.16974
433433 −25.8384 −1.24171 −0.620857 0.783924i 0.713215π-0.713215\pi
−0.620857 + 0.783924i 0.713215π0.713215\pi
434434 0 0
435435 1.05573 0.0506183
436436 −6.27051 −0.300303
437437 1.31105 + 2.27080i 0.0627159 + 0.108627i
438438 −9.70820 −0.463876
439439 12.5000 21.6506i 0.596592 1.03333i −0.396728 0.917936i 0.629854π-0.629854\pi
0.993320 0.115392i 0.0368124π-0.0368124\pi
440440 −35.4435 61.3899i −1.68970 2.92665i
441441 −6.70820 11.6190i −0.319438 0.553283i
442442 −25.4164 −1.20894
443443 −3.02786 + 5.24441i −0.143858 + 0.249170i −0.928946 0.370214i 0.879284π-0.879284\pi
0.785088 + 0.619384i 0.212618π0.212618\pi
444444 9.00000 15.5885i 0.427121 0.739795i
445445 17.1618 29.7252i 0.813549 1.40911i
446446 −21.1344 36.6058i −1.00074 1.73334i
447447 −5.86319 + 10.1553i −0.277319 + 0.480331i
448448 4.35410 + 7.54153i 0.205712 + 0.356304i
449449 33.7047 1.59062 0.795311 0.606201i 0.207307π-0.207307\pi
0.795311 + 0.606201i 0.207307π0.207307\pi
450450 0 0
451451 3.12287 + 5.40897i 0.147050 + 0.254699i
452452 23.6976 41.0454i 1.11464 1.93061i
453453 5.47214 + 9.47802i 0.257103 + 0.445316i
454454 −3.00000 + 5.19615i −0.140797 + 0.243868i
455455 −2.93159 + 5.07767i −0.137435 + 0.238045i
456456 3.26544 5.65591i 0.152918 0.264862i
457457 11.3137 0.529233 0.264616 0.964354i 0.414755π-0.414755\pi
0.264616 + 0.964354i 0.414755π0.414755\pi
458458 −5.55369 9.61927i −0.259507 0.449479i
459459 −8.47214 14.6742i −0.395445 0.684932i
460460 14.2302 24.6475i 0.663489 1.14920i
461461 5.16538 0.240576 0.120288 0.992739i 0.461618π-0.461618\pi
0.120288 + 0.992739i 0.461618π0.461618\pi
462462 −4.85410 8.40755i −0.225833 0.391155i
463463 −3.82998 −0.177994 −0.0889971 0.996032i 0.528366π-0.528366\pi
−0.0889971 + 0.996032i 0.528366π0.528366\pi
464464 −5.32300 −0.247114
465465 0 0
466466 −35.2705 −1.63387
467467 −15.6525 −0.724310 −0.362155 0.932118i 0.617959π-0.617959\pi
−0.362155 + 0.932118i 0.617959π0.617959\pi
468468 −14.2302 24.6475i −0.657794 1.13933i
469469 −6.00000 −0.277054
470470 28.4164 49.2187i 1.31075 2.27029i
471471 3.80562 + 6.59154i 0.175354 + 0.303722i
472472 −44.6246 77.2921i −2.05401 3.55766i
473473 −41.1246 −1.89091
474474 −1.85410 + 3.21140i −0.0851617 + 0.147504i
475475 0 0
476476 8.98606 15.5643i 0.411875 0.713389i
477477 −15.3500 26.5870i −0.702829 1.21734i
478478 −15.8508 + 27.4544i −0.724998 + 1.25573i
479479 −8.26393 14.3136i −0.377589 0.654003i 0.613122 0.789988i 0.289913π-0.289913\pi
−0.990711 + 0.135985i 0.956580π0.956580\pi
480480 −21.2132 −0.968246
481481 −11.1246 −0.507239
482482 30.3905 + 52.6380i 1.38425 + 2.39759i
483483 1.14590 1.98475i 0.0521402 0.0903094i
484484 −16.9894 29.4264i −0.772243 1.33756i
485485 7.82624 13.5554i 0.355371 0.615521i
486486 21.0706 36.4954i 0.955783 1.65547i
487487 −14.0390 + 24.3162i −0.636166 + 1.10187i 0.350100 + 0.936712i 0.386148π0.386148\pi
−0.986267 + 0.165160i 0.947186π0.947186\pi
488488 104.130 4.71375
489489 6.30020 + 10.9123i 0.284905 + 0.493470i
490490 17.5623 + 30.4188i 0.793384 + 1.37418i
491491 7.94510 13.7613i 0.358557 0.621040i −0.629163 0.777274i 0.716602π-0.716602\pi
0.987720 + 0.156234i 0.0499354π0.0499354\pi
492492 6.24574 0.281580
493493 1.00000 + 1.73205i 0.0450377 + 0.0780076i
494494 −6.86474 −0.308859
495495 −21.2132 −0.953463
496496 0 0
497497 1.47214 0.0660343
498498 7.23607 0.324256
499499 −9.19239 15.9217i −0.411508 0.712752i 0.583547 0.812079i 0.301664π-0.301664\pi
−0.995055 + 0.0993269i 0.968331π0.968331\pi
500500 −54.2705 −2.42705
501501 −0.472136 + 0.817763i −0.0210935 + 0.0365350i
502502 −14.4366 25.0049i −0.644336 1.11602i
503503 16.4443 + 28.4823i 0.733214 + 1.26996i 0.955503 + 0.294983i 0.0953139π0.0953139\pi
−0.222289 + 0.974981i 0.571353π0.571353\pi
504504 16.7082 0.744243
505505 −2.50000 + 4.33013i −0.111249 + 0.192688i
506506 14.5623 25.2227i 0.647373 1.12128i
507507 −2.67655 + 4.63593i −0.118870 + 0.205889i
508508 23.0250 + 39.8805i 1.02157 + 1.76941i
509509 3.97255 6.88066i 0.176080 0.304980i −0.764454 0.644678i 0.776992π-0.776992\pi
0.940535 + 0.339698i 0.110325π0.110325\pi
510510 9.47214 + 16.4062i 0.419433 + 0.726480i
511511 −4.24264 −0.187683
512512 −40.3050 −1.78124
513513 −2.28825 3.96336i −0.101029 0.174987i
514514 −7.92705 + 13.7301i −0.349647 + 0.605607i
515515 −11.9721 20.7363i −0.527555 0.913753i
516516 −20.5623 + 35.6150i −0.905205 + 1.56786i
517517 20.5942 35.6702i 0.905732 1.56877i
518518 5.55369 9.61927i 0.244015 0.422647i
519519 −15.7326 −0.690583
520520 21.9053 + 37.9410i 0.960609 + 1.66382i
521521 6.70820 + 11.6190i 0.293892 + 0.509035i 0.974726 0.223402i 0.0717161π-0.0717161\pi
−0.680835 + 0.732437i 0.738383π0.738383\pi
522522 −1.58114 + 2.73861i −0.0692046 + 0.119866i
523523 0.618993 0.0270667 0.0135333 0.999908i 0.495692π-0.495692\pi
0.0135333 + 0.999908i 0.495692π0.495692\pi
524524 −18.0000 31.1769i −0.786334 1.36197i
525525 0 0
526526 48.4658 2.11321
527527 0 0
528528 −36.5410 −1.59024
529529 −16.1246 −0.701070
530530 40.1869 + 69.6057i 1.74561 + 3.02348i
531531 −26.7082 −1.15904
532532 2.42705 4.20378i 0.105226 0.182257i
533533 −1.93004 3.34293i −0.0835994 0.144798i
534534 −17.5623 30.4188i −0.759995 1.31635i
535535 3.29180 0.142317
536536 −22.4164 + 38.8264i −0.968241 + 1.67704i
537537 5.79837 10.0431i 0.250218 0.433391i
538538 −2.82843 + 4.89898i −0.121942 + 0.211210i
539539 12.7279 + 22.0454i 0.548230 + 0.949563i
540540 −24.8369 + 43.0187i −1.06881 + 1.85123i
541541 −12.9164 22.3719i −0.555320 0.961842i −0.997879 0.0651025i 0.979263π-0.979263\pi
0.442559 0.896739i 0.354071π-0.354071\pi
542542 −48.6722 −2.09065
543543 −7.59675 −0.326008
544544 −20.0934 34.8028i −0.861499 1.49216i
545545 1.44427 2.50155i 0.0618658 0.107155i
546546 3.00000 + 5.19615i 0.128388 + 0.222375i
547547 −1.20820 + 2.09267i −0.0516591 + 0.0894761i −0.890699 0.454594i 0.849784π-0.849784\pi
0.839040 + 0.544070i 0.183118π0.183118\pi
548548 6.36396 11.0227i 0.271855 0.470867i
549549 15.5807 26.9866i 0.664968 1.15176i
550550 0 0
551551 0.270091 + 0.467811i 0.0115063 + 0.0199294i
552552 −8.56231 14.8303i −0.364436 0.631222i
553553 −0.810272 + 1.40343i −0.0344563 + 0.0596800i
554554 26.4574 1.12407
555555 4.14590 + 7.18091i 0.175984 + 0.304812i
556556 −87.2385 −3.69974
557557 −10.6460 −0.451086 −0.225543 0.974233i 0.572416π-0.572416\pi
−0.225543 + 0.974233i 0.572416π0.572416\pi
558558 0 0
559559 25.4164 1.07500
560560 −22.0344 −0.931125
561561 6.86474 + 11.8901i 0.289829 + 0.501999i
562562 34.9787 1.47549
563563 −4.88197 + 8.45581i −0.205750 + 0.356370i −0.950372 0.311117i 0.899297π-0.899297\pi
0.744621 + 0.667487i 0.232630π0.232630\pi
564564 −20.5942 35.6702i −0.867173 1.50199i
565565 10.9164 + 18.9078i 0.459257 + 0.795456i
566566 62.8328 2.64106
567567 1.35410 2.34537i 0.0568669 0.0984964i
568568 5.50000 9.52628i 0.230775 0.399714i
569569 5.86319 10.1553i 0.245798 0.425734i −0.716558 0.697527i 0.754284π-0.754284\pi
0.962356 + 0.271794i 0.0876168π0.0876168\pi
570570 2.55834 + 4.43117i 0.107157 + 0.185601i
571571 1.31105 2.27080i 0.0548657 0.0950301i −0.837288 0.546762i 0.815860π-0.815860\pi
0.892154 + 0.451732i 0.149194π0.149194\pi
572572 27.0000 + 46.7654i 1.12893 + 1.95536i
573573 −8.53399 −0.356513
574574 3.85410 0.160867
575575 0 0
576576 9.73607 16.8634i 0.405669 0.702640i
577577 15.0000 + 25.9808i 0.624458 + 1.08159i 0.988645 + 0.150268i 0.0480135π0.0480135\pi
−0.364187 + 0.931326i 0.618653π0.618653\pi
578578 4.30902 7.46344i 0.179231 0.310438i
579579 −9.04982 + 15.6747i −0.376098 + 0.651420i
580580 2.93159 5.07767i 0.121728 0.210839i
581581 3.16228 0.131193
582582 −8.00886 13.8718i −0.331978 0.575003i
583583 29.1246 + 50.4453i 1.20622 + 2.08923i
584584 −15.8508 + 27.4544i −0.655911 + 1.13607i
585585 13.1105 0.542052
586586 3.00000 + 5.19615i 0.123929 + 0.214651i
587587 −15.7326 −0.649353 −0.324676 0.945825i 0.605255π-0.605255\pi
−0.324676 + 0.945825i 0.605255π0.605255\pi
588588 25.4558 1.04978
589589 0 0
590590 69.9230 2.87868
591591 0.944272 0.0388422
592592 −20.9037 36.2063i −0.859137 1.48807i
593593 5.18034 0.212731 0.106366 0.994327i 0.466079π-0.466079\pi
0.106366 + 0.994327i 0.466079π0.466079\pi
594594 −25.4164 + 44.0225i −1.04285 + 1.80627i
595595 4.13948 + 7.16978i 0.169702 + 0.293932i
596596 32.5623 + 56.3996i 1.33380 + 2.31022i
597597 −20.2918 −0.830488
598598 −9.00000 + 15.5885i −0.368037 + 0.637459i
599599 −3.02786 + 5.24441i −0.123715 + 0.214281i −0.921230 0.389018i 0.872814π-0.872814\pi
0.797515 + 0.603299i 0.206148π0.206148\pi
600600 0 0
601601 −9.08922 15.7430i −0.370757 0.642170i 0.618925 0.785450i 0.287568π-0.287568\pi
−0.989682 + 0.143280i 0.954235π0.954235\pi
602602 −12.6885 + 21.9772i −0.517145 + 0.895722i
603603 6.70820 + 11.6190i 0.273179 + 0.473160i
604604 60.7811 2.47315
605605 15.6525 0.636364
606606 2.55834 + 4.43117i 0.103925 + 0.180004i
607607 −7.56231 + 13.0983i −0.306945 + 0.531644i −0.977692 0.210042i 0.932640π-0.932640\pi
0.670748 + 0.741685i 0.265973π0.265973\pi
608608 −5.42705 9.39993i −0.220096 0.381217i
609609 0.236068 0.408882i 0.00956596 0.0165687i
610610 −40.7908 + 70.6518i −1.65157 + 2.86061i
611611 −12.7279 + 22.0454i −0.514917 + 0.891862i
612612 −40.1869 −1.62446
613613 −0.294445 0.509993i −0.0118925 0.0205984i 0.860018 0.510264i 0.170452π-0.170452\pi
−0.871910 + 0.489665i 0.837119π0.837119\pi
614614 −31.5795 54.6973i −1.27445 2.20741i
615615 −1.43857 + 2.49167i −0.0580086 + 0.100474i
616616 −31.7016 −1.27729
617617 3.43769 + 5.95426i 0.138396 + 0.239710i 0.926890 0.375334i 0.122472π-0.122472\pi
−0.788493 + 0.615043i 0.789139π0.789139\pi
618618 −24.5030 −0.985655
619619 25.8384 1.03853 0.519267 0.854612i 0.326205π-0.326205\pi
0.519267 + 0.854612i 0.326205π0.326205\pi
620620 0 0
621621 −12.0000 −0.481543
622622 66.6869 2.67390
623623 −7.67501 13.2935i −0.307493 0.532593i
624624 22.5836 0.904067
625625 12.5000 21.6506i 0.500000 0.866025i
626626 15.0799 + 26.1192i 0.602715 + 1.04393i
627627 1.85410 + 3.21140i 0.0740457 + 0.128251i
628628 42.2705 1.68678
629629 −7.85410 + 13.6037i −0.313164 + 0.542415i
630630 −6.54508 + 11.3364i −0.260762 + 0.451654i
631631 11.8145 20.4633i 0.470327 0.814631i −0.529097 0.848561i 0.677469π-0.677469\pi
0.999424 + 0.0339308i 0.0108026π0.0108026\pi
632632 6.05446 + 10.4866i 0.240834 + 0.417136i
633633 −2.18508 + 3.78467i −0.0868491 + 0.150427i
634634 −34.3435 59.4846i −1.36395 2.36244i
635635 −21.2132 −0.841820
636636 58.2492 2.30973
637637 −7.86629 13.6248i −0.311674 0.539835i
638638 3.00000 5.19615i 0.118771 0.205718i
639639 −1.64590 2.85078i −0.0651107 0.112775i
640640 −1.21885 + 2.11111i −0.0481792 + 0.0834488i
641641 4.24264 7.34847i 0.167574 0.290247i −0.769992 0.638053i 0.779740π-0.779740\pi
0.937566 + 0.347806i 0.113073π0.113073\pi
642642 1.68430 2.91730i 0.0664742 0.115137i
643643 −4.65530 −0.183587 −0.0917936 0.995778i 0.529260π-0.529260\pi
−0.0917936 + 0.995778i 0.529260π0.529260\pi
644644 −6.36396 11.0227i −0.250775 0.434355i
645645 −9.47214 16.4062i −0.372965 0.645994i
646646 −4.84658 + 8.39453i −0.190686 + 0.330278i
647647 31.7804 1.24942 0.624708 0.780858i 0.285218π-0.285218\pi
0.624708 + 0.780858i 0.285218π0.285218\pi
648648 −10.1180 17.5249i −0.397474 0.688445i
649649 50.6753 1.98918
650650 0 0
651651 0 0
652652 69.9787 2.74058
653653 24.6525 0.964726 0.482363 0.875971i 0.339779π-0.339779\pi
0.482363 + 0.875971i 0.339779π0.339779\pi
654654 −1.47797 2.55992i −0.0577933 0.100101i
655655 16.5836 0.647975
656656 7.25329 12.5631i 0.283193 0.490505i
657657 4.74342 + 8.21584i 0.185058 + 0.320530i
658658 −12.7082 22.0113i −0.495417 0.858088i
659659 24.8197 0.966837 0.483418 0.875389i 0.339395π-0.339395\pi
0.483418 + 0.875389i 0.339395π0.339395\pi
660660 20.1246 34.8569i 0.783349 1.35680i
661661 −3.91641 + 6.78342i −0.152331 + 0.263844i −0.932084 0.362243i 0.882011π-0.882011\pi
0.779753 + 0.626087i 0.215345π0.215345\pi
662662 −40.9577 + 70.9409i −1.59187 + 2.75720i
663663 −4.24264 7.34847i −0.164771 0.285391i
664664 11.8145 20.4633i 0.458491 0.794130i
665665 1.11803 + 1.93649i 0.0433555 + 0.0750939i
666666 −24.8369 −0.962408
667667 1.41641 0.0548435
668668 2.62210 + 4.54160i 0.101452 + 0.175720i
669669 7.05573 12.2209i 0.272790 0.472487i
670670 −17.5623 30.4188i −0.678491 1.17518i
671671 −29.5623 + 51.2034i −1.14124 + 1.97669i
672672 −4.74342 + 8.21584i −0.182981 + 0.316933i
673673 −19.9903 + 34.6242i −0.770568 + 1.33466i 0.166684 + 0.986010i 0.446694π0.446694\pi
−0.937252 + 0.348653i 0.886639π0.886639\pi
674674 −40.1869 −1.54794
675675 0 0
676676 14.8647 + 25.7465i 0.571721 + 0.990250i
677677 10.6066 18.3712i 0.407645 0.706062i −0.586981 0.809601i 0.699683π-0.699683\pi
0.994625 + 0.103540i 0.0330168π0.0330168\pi
678678 22.3423 0.858050
679679 −3.50000 6.06218i −0.134318 0.232645i
680680 61.8614 2.37228
681681 −2.00310 −0.0767591
682682 0 0
683683 −41.1803 −1.57572 −0.787861 0.615853i 0.788811π-0.788811\pi
−0.787861 + 0.615853i 0.788811π0.788811\pi
684684 −10.8541 −0.415017
685685 2.93159 + 5.07767i 0.112010 + 0.194008i
686686 34.0344 1.29944
687687 1.85410 3.21140i 0.0707384 0.122523i
688688 47.7587 + 82.7205i 1.82078 + 3.15369i
689689 −18.0000 31.1769i −0.685745 1.18775i
690690 13.4164 0.510754
691691 24.2082 41.9298i 0.920923 1.59509i 0.122934 0.992415i 0.460770π-0.460770\pi
0.797989 0.602671i 0.205897π-0.205897\pi
692692 −43.6869 + 75.6680i −1.66073 + 2.87646i
693693 −4.74342 + 8.21584i −0.180187 + 0.312094i
694694 28.2692 + 48.9637i 1.07308 + 1.85864i
695695 20.0934 34.8028i 0.762187 1.32015i
696696 −1.76393 3.05522i −0.0668617 0.115808i
697697 −5.45052 −0.206453
698698 15.7082 0.594564
699699 −5.88754 10.1975i −0.222687 0.385706i
700700 0 0
701701 1.82624 + 3.16314i 0.0689761 + 0.119470i 0.898451 0.439074i 0.144693π-0.144693\pi
−0.829475 + 0.558544i 0.811360π0.811360\pi
702702 15.7082 27.2074i 0.592868 1.02688i
703703 −2.12132 + 3.67423i −0.0800071 + 0.138576i
704704 −18.4729 + 31.9960i −0.696223 + 1.20589i
705705 18.9737 0.714590
706706 −12.5216 21.6880i −0.471256 0.816240i
707707 1.11803 + 1.93649i 0.0420480 + 0.0728293i
708708 25.3376 43.8861i 0.952246 1.64934i
709709 −41.1884 −1.54686 −0.773432 0.633880i 0.781462π-0.781462\pi
−0.773432 + 0.633880i 0.781462π0.781462\pi
710710 4.30902 + 7.46344i 0.161715 + 0.280098i
711711 3.62365 0.135897
712712 −114.697 −4.29847
713713 0 0
714714 8.47214 0.317062
715715 −24.8754 −0.930287
716716 −32.2024 55.7761i −1.20346 2.08445i
717717 −10.5836 −0.395251
718718 −18.6353 + 32.2772i −0.695462 + 1.20457i
719719 18.7824 + 32.5320i 0.700465 + 1.21324i 0.968303 + 0.249777i 0.0803573π0.0803573\pi
−0.267839 + 0.963464i 0.586309π0.586309\pi
720720 24.6353 + 42.6695i 0.918102 + 1.59020i
721721 −10.7082 −0.398794
722722 23.5623 40.8111i 0.876898 1.51883i
723723 −10.1459 + 17.5732i −0.377330 + 0.653555i
724724 −21.0950 + 36.5376i −0.783989 + 1.35791i
725725 0 0
726726 8.00886 13.8718i 0.297237 0.514829i
727727 15.2082 + 26.3414i 0.564041 + 0.976948i 0.997138 + 0.0756005i 0.0240874π0.0240874\pi
−0.433097 + 0.901347i 0.642579π0.642579\pi
728728 19.5927 0.726152
729729 5.94427 0.220158
730730 −12.4184 21.5093i −0.459627 0.796097i
731731 17.9443 31.0804i 0.663693 1.14955i
732732 29.5623 + 51.2034i 1.09265 + 1.89253i
733733 7.20820 12.4850i 0.266241 0.461143i −0.701647 0.712525i 0.747552π-0.747552\pi
0.967888 + 0.251382i 0.0808849π0.0808849\pi
734734 −8.71597 + 15.0965i −0.321712 + 0.557222i
735735 −5.86319 + 10.1553i −0.216267 + 0.374585i
736736 −28.4605 −1.04907
737737 −12.7279 22.0454i −0.468839 0.812053i
738738 −4.30902 7.46344i −0.158617 0.274733i
739739 17.5745 30.4399i 0.646489 1.11975i −0.337467 0.941337i 0.609570π-0.609570\pi
0.983956 0.178414i 0.0570965π-0.0570965\pi
740740 46.0501 1.69283
741741 −1.14590 1.98475i −0.0420956 0.0729117i
742742 35.9442 1.31955
743743 −36.4844 −1.33848 −0.669242 0.743045i 0.733381π-0.733381\pi
−0.669242 + 0.743045i 0.733381π0.733381\pi
744744 0 0
745745 −30.0000 −1.09911
746746 −24.3262 −0.890647
747747 −3.53553 6.12372i −0.129358 0.224055i
748748 76.2492 2.78795
749749 0.736068 1.27491i 0.0268953 0.0465841i
750750 −12.7917 22.1558i −0.467086 0.809017i
751751 18.7705 + 32.5115i 0.684946 + 1.18636i 0.973454 + 0.228883i 0.0735074π0.0735074\pi
−0.288508 + 0.957477i 0.593159π0.593159\pi
752752 −95.6656 −3.48857
753753 4.81966 8.34790i 0.175638 0.304214i
754754 −1.85410 + 3.21140i −0.0675224 + 0.116952i
755755 −13.9996 + 24.2480i −0.509496 + 0.882474i
756756 11.1074 + 19.2385i 0.403971 + 0.699699i
757757 −4.64025 + 8.03715i −0.168653 + 0.292115i −0.937946 0.346780i 0.887275π-0.887275\pi
0.769294 + 0.638895i 0.220608π0.220608\pi
758758 −9.70820 16.8151i −0.352618 0.610752i
759759 9.72327 0.352932
760760 16.7082 0.606070
761761 −20.0934 34.8028i −0.728386 1.26160i −0.957565 0.288218i 0.906937π-0.906937\pi
0.229178 0.973384i 0.426396π-0.426396\pi
762762 −10.8541 + 18.7999i −0.393203 + 0.681047i
763763 −0.645898 1.11873i −0.0233831 0.0405007i
764764 −23.6976 + 41.0454i −0.857348 + 1.48497i
765765 9.25615 16.0321i 0.334657 0.579642i
766766 8.38212 14.5183i 0.302858 0.524566i
767767 −31.3190 −1.13086
768768 −6.36396 11.0227i −0.229640 0.397748i
769769 −27.0623 46.8733i −0.975892 1.69029i −0.676960 0.736019i 0.736703π-0.736703\pi
−0.298931 0.954275i 0.596630π-0.596630\pi
770770 12.4184 21.5093i 0.447529 0.775143i
771771 −5.29290 −0.190619
772772 50.2599 + 87.0526i 1.80889 + 3.13309i
773773 −11.1862 −0.402339 −0.201170 0.979556i 0.564474π-0.564474\pi
−0.201170 + 0.979556i 0.564474π0.564474\pi
774774 56.7448 2.03965
775775 0 0
776776 −52.3050 −1.87764
777777 3.70820 0.133031
778778 22.0084 + 38.1197i 0.789040 + 1.36666i
779779 −1.47214 −0.0527447
780780 −12.4377 + 21.5427i −0.445341 + 0.771353i
781781 3.12287 + 5.40897i 0.111745 + 0.193548i
782782 12.7082 + 22.0113i 0.454444 + 0.787121i
783783 −2.47214 −0.0883469
784784 29.5623 51.2034i 1.05580 1.82869i
785785 −9.73607 + 16.8634i −0.347495 + 0.601879i
786786 8.48528 14.6969i 0.302660 0.524222i
787787 18.7824 + 32.5320i 0.669520 + 1.15964i 0.978039 + 0.208424i 0.0668334π0.0668334\pi
−0.308519 + 0.951218i 0.599833π0.599833\pi
788788 2.62210 4.54160i 0.0934083 0.161788i
789789 8.09017 + 14.0126i 0.288018 + 0.498861i
790790 −9.48683 −0.337526
791791 9.76393 0.347165
792792 35.4435 + 61.3899i 1.25943 + 2.18139i
793793 18.2705 31.6455i 0.648805 1.12376i
794794 −19.2533 33.3477i −0.683274 1.18346i
795795 −13.4164 + 23.2379i −0.475831 + 0.824163i
796796 −56.3472 + 97.5961i −1.99717 + 3.45920i
797797 6.86474 11.8901i 0.243161 0.421168i −0.718452 0.695577i 0.755149π-0.755149\pi
0.961613 + 0.274409i 0.0884822π0.0884822\pi
798798 2.28825 0.0810030
799799 17.9721 + 31.1286i 0.635808 + 1.10125i
800800 0 0
801801 −17.1618 + 29.7252i −0.606384 + 1.05029i
802802 −1.41421 −0.0499376
803803 −9.00000 15.5885i −0.317603 0.550105i
804804 −25.4558 −0.897758
805805 5.86319 0.206650
806806 0 0
807807 −1.88854 −0.0664799
808808 16.7082 0.587793
809809 −23.7565 41.1474i −0.835234 1.44667i −0.893840 0.448386i 0.851999π-0.851999\pi
0.0586064 0.998281i 0.481334π-0.481334\pi
810810 15.8541 0.557056
811811 8.29180 14.3618i 0.291164 0.504311i −0.682921 0.730492i 0.739291π-0.739291\pi
0.974085 + 0.226181i 0.0726240π0.0726240\pi
812812 −1.31105 2.27080i −0.0460088 0.0796895i
813813 −8.12461 14.0722i −0.284943 0.493535i
814814 47.1246 1.65172
815815 −16.1180 + 27.9173i −0.564590 + 0.977899i
816816 15.9443 27.6163i 0.558161 0.966763i
817817 4.84658 8.39453i 0.169560 0.293687i
818818 −39.3766 68.2023i −1.37677 2.38464i
819819 2.93159 5.07767i 0.102438 0.177428i
820820 7.98936 + 13.8380i 0.279000 + 0.483243i
821821 23.8353 0.831858 0.415929 0.909397i 0.363457π-0.363457\pi
0.415929 + 0.909397i 0.363457π0.363457\pi
822822 6.00000 0.209274
823823 6.76157 + 11.7114i 0.235694 + 0.408233i 0.959474 0.281797i 0.0909305π-0.0909305\pi
−0.723780 + 0.690030i 0.757597π0.757597\pi
824824 −40.0066 + 69.2934i −1.39370 + 2.41395i
825825 0 0
826826 15.6353 27.0811i 0.544020 0.942270i
827827 9.17734 15.8956i 0.319127 0.552745i −0.661179 0.750228i 0.729944π-0.729944\pi
0.980306 + 0.197484i 0.0632769π0.0632769\pi
828828 −14.2302 + 24.6475i −0.494535 + 0.856560i
829829 51.0879 1.77436 0.887178 0.461427i 0.152662π-0.152662\pi
0.887178 + 0.461427i 0.152662π0.152662\pi
830830 9.25615 + 16.0321i 0.321286 + 0.556483i
831831 4.41641 + 7.64944i 0.153203 + 0.265356i
832832 11.4169 19.7746i 0.395809 0.685561i
833833 −22.2148 −0.769696
834834 −20.5623 35.6150i −0.712014 1.23325i
835835 −2.41577 −0.0836010
836836 20.5942 0.712266
837837 0 0
838838 80.1033 2.76712
839839 −19.4164 −0.670329 −0.335164 0.942160i 0.608792π-0.608792\pi
−0.335164 + 0.942160i 0.608792π0.608792\pi
840840 −7.30175 12.6470i −0.251934 0.436363i
841841 −28.7082 −0.989938
842842 −34.5795 + 59.8935i −1.19169 + 2.06407i
843843 5.83883 + 10.1132i 0.201100 + 0.348315i
844844 12.1353 + 21.0189i 0.417713 + 0.723500i
845845 −13.6950 −0.471124
846846 −28.4164 + 49.2187i −0.976976 + 1.69217i
847847 3.50000 6.06218i 0.120261 0.208299i
848848 67.6458 117.166i 2.32297 4.02350i
849849 10.4884 + 18.1664i 0.359960 + 0.623470i
850850 0 0
851851 5.56231 + 9.63420i 0.190673 + 0.330256i
852852 6.24574 0.213976
853853 −32.2918 −1.10565 −0.552825 0.833297i 0.686450π-0.686450\pi
−0.552825 + 0.833297i 0.686450π0.686450\pi
854854 18.2422 + 31.5964i 0.624235 + 1.08121i
855855 2.50000 4.33013i 0.0854982 0.148087i
856856 −5.50000 9.52628i −0.187986 0.325602i
857857 3.00000 5.19615i 0.102478 0.177497i −0.810227 0.586116i 0.800656π-0.800656\pi
0.912705 + 0.408619i 0.133990π0.133990\pi
858858 −12.7279 + 22.0454i −0.434524 + 0.752618i
859859 20.8005 36.0276i 0.709705 1.22925i −0.255261 0.966872i 0.582161π-0.582161\pi
0.964966 0.262374i 0.0845052π-0.0845052\pi
860860 −105.211 −3.58765
861861 0.643347 + 1.11431i 0.0219252 + 0.0379756i
862862 46.9787 + 81.3695i 1.60010 + 2.77146i
863863 15.5413 26.9183i 0.529032 0.916310i −0.470395 0.882456i 0.655889π-0.655889\pi
0.999427 0.0338541i 0.0107782π-0.0107782\pi
864864 49.6737 1.68993
865865 −20.1246 34.8569i −0.684257 1.18517i
866866 −67.6458 −2.29870
867867 2.87714 0.0977126
868868 0 0
869869 −6.87539 −0.233232
870870 2.76393 0.0937061
871871 7.86629 + 13.6248i 0.266539 + 0.461659i
872872 −9.65248 −0.326874
873873 −7.82624 + 13.5554i −0.264878 + 0.458782i
874874 3.43237 + 5.94504i 0.116102 + 0.201094i
875875 −5.59017 9.68246i −0.188982 0.327327i
876876 −18.0000 −0.608164
877877 14.3541 24.8620i 0.484704 0.839531i −0.515142 0.857105i 0.672261π-0.672261\pi
0.999846 + 0.0175736i 0.00559415π0.00559415\pi
878878 32.7254 56.6821i 1.10443 1.91293i
879879 −1.00155 + 1.73474i −0.0337815 + 0.0585113i
880880 −46.7421 80.9597i −1.57568 2.72915i
881881 −3.62365 + 6.27634i −0.122084 + 0.211455i −0.920589 0.390532i 0.872291π-0.872291\pi
0.798505 + 0.601988i 0.205624π0.205624\pi
882882 −17.5623 30.4188i −0.591354 1.02425i
883883 −33.9411 −1.14221 −0.571105 0.820877i 0.693485π-0.693485\pi
−0.571105 + 0.820877i 0.693485π0.693485\pi
884884 −47.1246 −1.58497
885885 11.6719 + 20.2163i 0.392347 + 0.679565i
886886 −7.92705 + 13.7301i −0.266314 + 0.461270i
887887 −12.6803 21.9630i −0.425764 0.737445i 0.570727 0.821140i 0.306661π-0.306661\pi
−0.996491 + 0.0836945i 0.973328π0.973328\pi
888888 13.8541 23.9960i 0.464913 0.805253i
889889 −4.74342 + 8.21584i −0.159089 + 0.275550i
890890 44.9303 77.8215i 1.50607 2.60858i
891891 11.4899 0.384927
892892 −39.1853 67.8710i −1.31202 2.27249i
893893 4.85410 + 8.40755i 0.162436 + 0.281348i
894894 −15.3500 + 26.5870i −0.513381 + 0.889203i
895895 29.6684 0.991705
896896 0.545085 + 0.944115i 0.0182100 + 0.0315407i
897897 −6.00931 −0.200645
898898 88.2400 2.94461
899899 0 0
900900 0 0
901901 −50.8328 −1.69349
902902 8.17578 + 14.1609i 0.272224 + 0.471506i
903903 −8.47214 −0.281935
904904 36.4787 63.1830i 1.21326 2.10143i
905905 −9.71752 16.8312i −0.323021 0.559489i
906906 14.3262 + 24.8138i 0.475957 + 0.824382i
907907 11.5410 0.383213 0.191607 0.981472i 0.438630π-0.438630\pi
0.191607 + 0.981472i 0.438630π0.438630\pi
908908 −5.56231 + 9.63420i −0.184592 + 0.319722i
909909 2.50000 4.33013i 0.0829198 0.143621i
910910 −7.67501 + 13.2935i −0.254424 + 0.440675i
911911 13.4594 + 23.3123i 0.445929 + 0.772372i 0.998116 0.0613480i 0.0195400π-0.0195400\pi
−0.552187 + 0.833720i 0.686207π0.686207\pi
912912 4.30640 7.45890i 0.142599 0.246989i
913913 6.70820 + 11.6190i 0.222009 + 0.384531i
914914 29.6197 0.979732
915915 −27.2361 −0.900397
916916 −10.2971 17.8351i −0.340226 0.589289i
917917 3.70820 6.42280i 0.122456 0.212099i
918918 −22.1803 38.4175i −0.732060 1.26797i
919919 21.2705 36.8416i 0.701649 1.21529i −0.266238 0.963907i 0.585781π-0.585781\pi
0.967887 0.251385i 0.0808860π-0.0808860\pi
920920 21.9053 37.9410i 0.722195 1.25088i
921921 10.5428 18.2607i 0.347398 0.601712i
922922 13.5231 0.445361
923923 −1.93004 3.34293i −0.0635281 0.110034i
924924 −9.00000 15.5885i −0.296078 0.512823i
925925 0 0
926926 −10.0270 −0.329508
927927 11.9721 + 20.7363i 0.393217 + 0.681071i
928928 −5.86319 −0.192468
929929 10.6460 0.349284 0.174642 0.984632i 0.444123π-0.444123\pi
0.174642 + 0.984632i 0.444123π0.444123\pi
930930 0 0
931931 −6.00000 −0.196642
932932 −65.3951 −2.14209
933933 11.1317 + 19.2807i 0.364437 + 0.631223i
934934 −40.9787 −1.34086
935935 −17.5623 + 30.4188i −0.574349 + 0.994801i
936936 −21.9053 37.9410i −0.715996 1.24014i
937937 −12.1246 21.0004i −0.396094 0.686055i 0.597146 0.802132i 0.296301π-0.296301\pi
−0.993240 + 0.116078i 0.962968π0.962968\pi
938938 −15.7082 −0.512891
939939 −5.03444 + 8.71991i −0.164293 + 0.284563i
940940 52.6869 91.2564i 1.71846 2.97646i
941941 −12.7673 + 22.1137i −0.416203 + 0.720885i −0.995554 0.0941935i 0.969973π-0.969973\pi
0.579351 + 0.815078i 0.303306π0.303306\pi
942942 9.96325 + 17.2569i 0.324620 + 0.562259i
943943 −1.93004 + 3.34293i −0.0628508 + 0.108861i
944944 −58.8500 101.931i −1.91541 3.31758i
945945 −10.2333 −0.332891
946946 −107.666 −3.50051
947947 −20.0934 34.8028i −0.652949 1.13094i −0.982404 0.186769i 0.940198π-0.940198\pi
0.329455 0.944171i 0.393135π-0.393135\pi
948948 −3.43769 + 5.95426i −0.111651 + 0.193385i
949949 5.56231 + 9.63420i 0.180560 + 0.312739i
950950 0 0
951951 11.4656 19.8590i 0.371797 0.643971i
952952 13.8326 23.9588i 0.448318 0.776510i
953953 18.6699 0.604778 0.302389 0.953185i 0.402216π-0.402216\pi
0.302389 + 0.953185i 0.402216π0.402216\pi
954954 −40.1869 69.6057i −1.30110 2.25357i
955955 −10.9164 18.9078i −0.353247 0.611841i
956956 −29.3890 + 50.9032i −0.950508 + 1.64633i
957957 2.00310 0.0647511
958958 −21.6353 37.4734i −0.699003 1.21071i
959959 2.62210 0.0846719
960960 −17.0193 −0.549295
961961 0 0
962962 −29.1246 −0.939015
963963 −3.29180 −0.106077
964964 56.3472 + 97.5961i 1.81482 + 3.14336i
965965 −46.3050 −1.49061
966966 3.00000 5.19615i 0.0965234 0.167183i
967967 −22.0084 38.1197i −0.707743 1.22585i −0.965692 0.259689i 0.916380π-0.916380\pi
0.257949 0.966158i 0.416953π-0.416953\pi
968968 −26.1525 45.2974i −0.840572 1.45591i
969969 −3.23607 −0.103957
970970 20.4894 35.4886i 0.657874 1.13947i
971971 −26.9443 + 46.6688i −0.864683 + 1.49767i 0.00267892 + 0.999996i 0.499147π0.499147\pi
−0.867362 + 0.497678i 0.834186π0.834186\pi
972972 39.0671 67.6662i 1.25308 2.17039i
973973 −8.98606 15.5643i −0.288080 0.498969i
974974 −36.7545 + 63.6607i −1.17769 + 2.03982i
975975 0 0
976976 137.325 4.39566
977977 −42.4853 −1.35922 −0.679612 0.733571i 0.737852π-0.737852\pi
−0.679612 + 0.733571i 0.737852π0.737852\pi
978978 16.4941 + 28.5687i 0.527424 + 0.913526i
979979 32.5623 56.3996i 1.04070 1.80254i
980980 32.5623 + 56.3996i 1.04016 + 1.80162i
981981 −1.44427 + 2.50155i −0.0461121 + 0.0798684i
982982 20.8005 36.0276i 0.663772 1.14969i
983983 −26.9582 + 46.6929i −0.859832 + 1.48927i 0.0122564 + 0.999925i 0.496099π0.496099\pi
−0.872089 + 0.489348i 0.837235π0.837235\pi
984984 9.61435 0.306494
985985 1.20788 + 2.09211i 0.0384863 + 0.0666603i
986986 2.61803 + 4.53457i 0.0833752 + 0.144410i
987987 4.24264 7.34847i 0.135045 0.233904i
988988 −12.7279 −0.404929
989989 −12.7082 22.0113i −0.404097 0.699917i
990990 −55.5369 −1.76508
991991 −13.9358 −0.442685 −0.221343 0.975196i 0.571044π-0.571044\pi
−0.221343 + 0.975196i 0.571044π0.571044\pi
992992 0 0
993993 −27.3475 −0.867847
994994 3.85410 0.122245
995995 −25.9566 44.9582i −0.822880 1.42527i
996996 13.4164 0.425115
997997 29.3328 50.8059i 0.928980 1.60904i 0.143947 0.989585i 0.454021π-0.454021\pi
0.785033 0.619454i 0.212646π-0.212646\pi
998998 −24.0660 41.6835i −0.761795 1.31947i
999999 −9.70820 16.8151i −0.307154 0.532006i
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 961.2.c.h.521.4 8
31.2 even 5 961.2.g.p.844.2 16
31.3 odd 30 961.2.d.j.628.2 8
31.4 even 5 961.2.g.i.338.2 16
31.5 even 3 inner 961.2.c.h.439.4 8
31.6 odd 6 961.2.a.h.1.4 yes 4
31.7 even 15 961.2.d.h.388.2 8
31.8 even 5 961.2.g.i.732.1 16
31.9 even 15 961.2.g.i.816.2 16
31.10 even 15 961.2.g.p.547.1 16
31.11 odd 30 961.2.g.i.235.2 16
31.12 odd 30 961.2.d.j.531.2 8
31.13 odd 30 961.2.g.p.846.1 16
31.14 even 15 961.2.d.h.374.2 8
31.15 odd 10 961.2.g.p.448.2 16
31.16 even 5 961.2.g.p.448.1 16
31.17 odd 30 961.2.d.h.374.1 8
31.18 even 15 961.2.g.p.846.2 16
31.19 even 15 961.2.d.j.531.1 8
31.20 even 15 961.2.g.i.235.1 16
31.21 odd 30 961.2.g.p.547.2 16
31.22 odd 30 961.2.g.i.816.1 16
31.23 odd 10 961.2.g.i.732.2 16
31.24 odd 30 961.2.d.h.388.1 8
31.25 even 3 961.2.a.h.1.3 4
31.26 odd 6 inner 961.2.c.h.439.3 8
31.27 odd 10 961.2.g.i.338.1 16
31.28 even 15 961.2.d.j.628.1 8
31.29 odd 10 961.2.g.p.844.1 16
31.30 odd 2 inner 961.2.c.h.521.3 8
93.56 odd 6 8649.2.a.r.1.1 4
93.68 even 6 8649.2.a.r.1.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
961.2.a.h.1.3 4 31.25 even 3
961.2.a.h.1.4 yes 4 31.6 odd 6
961.2.c.h.439.3 8 31.26 odd 6 inner
961.2.c.h.439.4 8 31.5 even 3 inner
961.2.c.h.521.3 8 31.30 odd 2 inner
961.2.c.h.521.4 8 1.1 even 1 trivial
961.2.d.h.374.1 8 31.17 odd 30
961.2.d.h.374.2 8 31.14 even 15
961.2.d.h.388.1 8 31.24 odd 30
961.2.d.h.388.2 8 31.7 even 15
961.2.d.j.531.1 8 31.19 even 15
961.2.d.j.531.2 8 31.12 odd 30
961.2.d.j.628.1 8 31.28 even 15
961.2.d.j.628.2 8 31.3 odd 30
961.2.g.i.235.1 16 31.20 even 15
961.2.g.i.235.2 16 31.11 odd 30
961.2.g.i.338.1 16 31.27 odd 10
961.2.g.i.338.2 16 31.4 even 5
961.2.g.i.732.1 16 31.8 even 5
961.2.g.i.732.2 16 31.23 odd 10
961.2.g.i.816.1 16 31.22 odd 30
961.2.g.i.816.2 16 31.9 even 15
961.2.g.p.448.1 16 31.16 even 5
961.2.g.p.448.2 16 31.15 odd 10
961.2.g.p.547.1 16 31.10 even 15
961.2.g.p.547.2 16 31.21 odd 30
961.2.g.p.844.1 16 31.29 odd 10
961.2.g.p.844.2 16 31.2 even 5
961.2.g.p.846.1 16 31.13 odd 30
961.2.g.p.846.2 16 31.18 even 15
8649.2.a.r.1.1 4 93.56 odd 6
8649.2.a.r.1.2 4 93.68 even 6