Properties

Label 370.2.r.e.193.1
Level 370370
Weight 22
Character 370.193
Analytic conductor 2.9542.954
Analytic rank 00
Dimension 1616
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [370,2,Mod(23,370)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(370, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([9, 5]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("370.23");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 370=2537 370 = 2 \cdot 5 \cdot 37
Weight: k k == 2 2
Character orbit: [χ][\chi] == 370.r (of order 1212, degree 44, minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: 2.954464874792.95446487479
Analytic rank: 00
Dimension: 1616
Relative dimension: 44 over Q(ζ12)\Q(\zeta_{12})
Coefficient field: Q[x]/(x16)\mathbb{Q}[x]/(x^{16} - \cdots)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: x164x15+12x1448x13+67x1224x11+118x10176x9+351x8++4 x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 Copy content Toggle raw display
Coefficient ring: Z[a1,,a7]\Z[a_1, \ldots, a_{7}]
Coefficient ring index: 1 1
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 193.1
Root 0.1176300.893490i0.117630 - 0.893490i of defining polynomial
Character χ\chi == 370.193
Dual form 370.2.r.e.347.1

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(0.866025+0.500000i)q2+(0.3927941.46593i)q3+(0.5000000.866025i)q4+(1.19306+1.89119i)q5+(1.07313+1.07313i)q6+(0.5520372.06023i)q7+1.00000iq8+(0.6034250.348387i)q9+(0.08762652.23435i)q10+1.24199iq11+(1.465930.392794i)q12+(3.608722.08350i)q13+(1.50819+1.50819i)q14+(3.24097+1.00609i)q15+(0.5000000.866025i)q16+(2.828104.89842i)q17+(0.348387+0.603425i)q18+(0.6470492.41482i)q19+(1.04129+1.97882i)q20+(2.80331+1.61849i)q21+(0.6209951.07560i)q22+7.58025iq23+(1.465930.392794i)q24+(2.153214.51262i)q25+4.16699q26+(3.967133.96713i)q27+(2.060230.552037i)q28+(7.297977.29797i)q29+(3.30981+0.749185i)q30+(6.72707+6.72707i)q31+(0.866025+0.500000i)q32+(1.820670.487846i)q33+(4.89842+2.82810i)q34+(4.55490+1.41398i)q350.696775iq36+(0.5869886.05437i)q37+(1.76777+1.76777i)q38+(1.63677+6.10850i)q39+(1.891191.19306i)q40+(4.66912+2.69572i)q41+(1.618492.80331i)q426.61187iq43+(1.07560+0.620995i)q44+(0.0610560+1.55684i)q45+(3.790126.56469i)q46+(3.36364+3.36364i)q47+(1.07313+1.07313i)q48+(2.122371.22535i)q49+(4.12104+2.83144i)q50+(6.06986+6.06986i)q51+(3.60872+2.08350i)q52+(1.865516.96219i)q53+(5.41920+1.45207i)q54+(2.348841.48177i)q55+(2.060230.552037i)q56+(3.28579+1.89705i)q57+(9.96921+2.67124i)q58+(11.7504+3.14851i)q59+(2.491792.30372i)q60+(0.279654+1.04368i)q61+(2.462289.18935i)q62+(1.050871.05087i)q631.00000q64+(8.245714.33904i)q65+(1.33282+1.33282i)q66+(9.479792.54010i)q675.65620q68+(11.11212.97747i)q69+(4.65165+1.05291i)q70+(4.906818.49885i)q71+(0.348387+0.603425i)q72+(10.7498+10.7498i)q73+(3.53553+4.94975i)q74+(5.76939+4.92897i)q75+(2.414820.647049i)q76+(2.558790.685625i)q77+(1.636776.10850i)q78+(0.454017+1.69441i)q79+(2.23435+0.0876265i)q80+(3.21209+5.56350i)q815.39144q82+(0.0295859+0.110416i)q83+3.23698iq84+(12.6379+0.495634i)q85+(3.30593+5.72604i)q86+(7.83168+13.5649i)q871.24199q88+(1.84256+6.87653i)q89+(0.7255431.37879i)q90+(2.30033+8.58496i)q91+(6.56469+3.79012i)q92+(12.5037+7.21903i)q93+(1.231184.59481i)q94+(5.33885+1.65734i)q95+(0.3927941.46593i)q96+0.402849q97+(1.22535+2.12237i)q98+(0.432694+0.749448i)q99+O(q100)q+(-0.866025 + 0.500000i) q^{2} +(-0.392794 - 1.46593i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.19306 + 1.89119i) q^{5} +(1.07313 + 1.07313i) q^{6} +(-0.552037 - 2.06023i) q^{7} +1.00000i q^{8} +(0.603425 - 0.348387i) q^{9} +(0.0876265 - 2.23435i) q^{10} +1.24199i q^{11} +(-1.46593 - 0.392794i) q^{12} +(-3.60872 - 2.08350i) q^{13} +(1.50819 + 1.50819i) q^{14} +(3.24097 + 1.00609i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.82810 - 4.89842i) q^{17} +(-0.348387 + 0.603425i) q^{18} +(-0.647049 - 2.41482i) q^{19} +(1.04129 + 1.97882i) q^{20} +(-2.80331 + 1.61849i) q^{21} +(-0.620995 - 1.07560i) q^{22} +7.58025i q^{23} +(1.46593 - 0.392794i) q^{24} +(-2.15321 - 4.51262i) q^{25} +4.16699 q^{26} +(-3.96713 - 3.96713i) q^{27} +(-2.06023 - 0.552037i) q^{28} +(-7.29797 - 7.29797i) q^{29} +(-3.30981 + 0.749185i) q^{30} +(-6.72707 + 6.72707i) q^{31} +(0.866025 + 0.500000i) q^{32} +(1.82067 - 0.487846i) q^{33} +(4.89842 + 2.82810i) q^{34} +(4.55490 + 1.41398i) q^{35} -0.696775i q^{36} +(-0.586988 - 6.05437i) q^{37} +(1.76777 + 1.76777i) q^{38} +(-1.63677 + 6.10850i) q^{39} +(-1.89119 - 1.19306i) q^{40} +(4.66912 + 2.69572i) q^{41} +(1.61849 - 2.80331i) q^{42} -6.61187i q^{43} +(1.07560 + 0.620995i) q^{44} +(-0.0610560 + 1.55684i) q^{45} +(-3.79012 - 6.56469i) q^{46} +(-3.36364 + 3.36364i) q^{47} +(-1.07313 + 1.07313i) q^{48} +(2.12237 - 1.22535i) q^{49} +(4.12104 + 2.83144i) q^{50} +(-6.06986 + 6.06986i) q^{51} +(-3.60872 + 2.08350i) q^{52} +(1.86551 - 6.96219i) q^{53} +(5.41920 + 1.45207i) q^{54} +(-2.34884 - 1.48177i) q^{55} +(2.06023 - 0.552037i) q^{56} +(-3.28579 + 1.89705i) q^{57} +(9.96921 + 2.67124i) q^{58} +(11.7504 + 3.14851i) q^{59} +(2.49179 - 2.30372i) q^{60} +(0.279654 + 1.04368i) q^{61} +(2.46228 - 9.18935i) q^{62} +(-1.05087 - 1.05087i) q^{63} -1.00000 q^{64} +(8.24571 - 4.33904i) q^{65} +(-1.33282 + 1.33282i) q^{66} +(9.47979 - 2.54010i) q^{67} -5.65620 q^{68} +(11.1121 - 2.97747i) q^{69} +(-4.65165 + 1.05291i) q^{70} +(4.90681 - 8.49885i) q^{71} +(0.348387 + 0.603425i) q^{72} +(-10.7498 + 10.7498i) q^{73} +(3.53553 + 4.94975i) q^{74} +(-5.76939 + 4.92897i) q^{75} +(-2.41482 - 0.647049i) q^{76} +(2.55879 - 0.685625i) q^{77} +(-1.63677 - 6.10850i) q^{78} +(0.454017 + 1.69441i) q^{79} +(2.23435 + 0.0876265i) q^{80} +(-3.21209 + 5.56350i) q^{81} -5.39144 q^{82} +(-0.0295859 + 0.110416i) q^{83} +3.23698i q^{84} +(12.6379 + 0.495634i) q^{85} +(3.30593 + 5.72604i) q^{86} +(-7.83168 + 13.5649i) q^{87} -1.24199 q^{88} +(-1.84256 + 6.87653i) q^{89} +(-0.725543 - 1.37879i) q^{90} +(-2.30033 + 8.58496i) q^{91} +(6.56469 + 3.79012i) q^{92} +(12.5037 + 7.21903i) q^{93} +(1.23118 - 4.59481i) q^{94} +(5.33885 + 1.65734i) q^{95} +(0.392794 - 1.46593i) q^{96} +0.402849 q^{97} +(-1.22535 + 2.12237i) q^{98} +(0.432694 + 0.749448i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 16q16q3+8q48q6+24q94q108q12+12q138q1616q17+24q19+12q2012q21+8q22+8q24+16q25+8q2616q2716q29+8q99+O(q100) 16 q - 16 q^{3} + 8 q^{4} - 8 q^{6} + 24 q^{9} - 4 q^{10} - 8 q^{12} + 12 q^{13} - 8 q^{16} - 16 q^{17} + 24 q^{19} + 12 q^{20} - 12 q^{21} + 8 q^{22} + 8 q^{24} + 16 q^{25} + 8 q^{26} - 16 q^{27} - 16 q^{29}+ \cdots - 8 q^{99}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/370Z)×\left(\mathbb{Z}/370\mathbb{Z}\right)^\times.

nn 261261 297297
χ(n)\chi(n) e(112)e\left(\frac{1}{12}\right) e(34)e\left(\frac{3}{4}\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 −0.866025 + 0.500000i −0.612372 + 0.353553i
33 −0.392794 1.46593i −0.226780 0.846353i −0.981684 0.190518i 0.938983π-0.938983\pi
0.754904 0.655835i 0.227683π-0.227683\pi
44 0.500000 0.866025i 0.250000 0.433013i
55 −1.19306 + 1.89119i −0.533554 + 0.845766i
66 1.07313 + 1.07313i 0.438104 + 0.438104i
77 −0.552037 2.06023i −0.208650 0.778694i −0.988306 0.152485i 0.951272π-0.951272\pi
0.779655 0.626209i 0.215394π-0.215394\pi
88 1.00000i 0.353553i
99 0.603425 0.348387i 0.201142 0.116129i
1010 0.0876265 2.23435i 0.0277099 0.706564i
1111 1.24199i 0.374474i 0.982315 + 0.187237i 0.0599533π0.0599533\pi
−0.982315 + 0.187237i 0.940047π0.940047\pi
1212 −1.46593 0.392794i −0.423176 0.113390i
1313 −3.60872 2.08350i −1.00088 0.577858i −0.0923705 0.995725i 0.529444π-0.529444\pi
−0.908508 + 0.417867i 0.862778π0.862778\pi
1414 1.50819 + 1.50819i 0.403082 + 0.403082i
1515 3.24097 + 1.00609i 0.836816 + 0.259772i
1616 −0.500000 0.866025i −0.125000 0.216506i
1717 −2.82810 4.89842i −0.685916 1.18804i −0.973148 0.230180i 0.926069π-0.926069\pi
0.287233 0.957861i 0.407265π-0.407265\pi
1818 −0.348387 + 0.603425i −0.0821157 + 0.142229i
1919 −0.647049 2.41482i −0.148443 0.553997i −0.999578 0.0290502i 0.990752π-0.990752\pi
0.851135 0.524947i 0.175915π-0.175915\pi
2020 1.04129 + 1.97882i 0.232839 + 0.442477i
2121 −2.80331 + 1.61849i −0.611732 + 0.353184i
2222 −0.620995 1.07560i −0.132397 0.229318i
2323 7.58025i 1.58059i 0.612726 + 0.790296i 0.290073π0.290073\pi
−0.612726 + 0.790296i 0.709927π0.709927\pi
2424 1.46593 0.392794i 0.299231 0.0801787i
2525 −2.15321 4.51262i −0.430641 0.902523i
2626 4.16699 0.817214
2727 −3.96713 3.96713i −0.763474 0.763474i
2828 −2.06023 0.552037i −0.389347 0.104325i
2929 −7.29797 7.29797i −1.35520 1.35520i −0.879736 0.475462i 0.842281π-0.842281\pi
−0.475462 0.879736i 0.657719π-0.657719\pi
3030 −3.30981 + 0.749185i −0.604286 + 0.136782i
3131 −6.72707 + 6.72707i −1.20822 + 1.20822i −0.236613 + 0.971604i 0.576037π0.576037\pi
−0.971604 + 0.236613i 0.923963π0.923963\pi
3232 0.866025 + 0.500000i 0.153093 + 0.0883883i
3333 1.82067 0.487846i 0.316937 0.0849231i
3434 4.89842 + 2.82810i 0.840072 + 0.485016i
3535 4.55490 + 1.41398i 0.769919 + 0.239005i
3636 0.696775i 0.116129i
3737 −0.586988 6.05437i −0.0965003 0.995333i
3838 1.76777 + 1.76777i 0.286770 + 0.286770i
3939 −1.63677 + 6.10850i −0.262093 + 0.978143i
4040 −1.89119 1.19306i −0.299024 0.188640i
4141 4.66912 + 2.69572i 0.729195 + 0.421001i 0.818128 0.575037i 0.195012π-0.195012\pi
−0.0889327 + 0.996038i 0.528346π0.528346\pi
4242 1.61849 2.80331i 0.249739 0.432560i
4343 6.61187i 1.00830i −0.863616 0.504150i 0.831806π-0.831806\pi
0.863616 0.504150i 0.168194π-0.168194\pi
4444 1.07560 + 0.620995i 0.162152 + 0.0936186i
4545 −0.0610560 + 1.55684i −0.00910168 + 0.232080i
4646 −3.79012 6.56469i −0.558823 0.967911i
4747 −3.36364 + 3.36364i −0.490637 + 0.490637i −0.908507 0.417870i 0.862777π-0.862777\pi
0.417870 + 0.908507i 0.362777π0.362777\pi
4848 −1.07313 + 1.07313i −0.154893 + 0.154893i
4949 2.12237 1.22535i 0.303196 0.175050i
5050 4.12104 + 2.83144i 0.582803 + 0.400426i
5151 −6.06986 + 6.06986i −0.849950 + 0.849950i
5252 −3.60872 + 2.08350i −0.500439 + 0.288929i
5353 1.86551 6.96219i 0.256248 0.956330i −0.711144 0.703046i 0.751823π-0.751823\pi
0.967392 0.253284i 0.0815107π-0.0815107\pi
5454 5.41920 + 1.45207i 0.737459 + 0.197602i
5555 −2.34884 1.48177i −0.316718 0.199802i
5656 2.06023 0.552037i 0.275310 0.0737691i
5757 −3.28579 + 1.89705i −0.435213 + 0.251271i
5858 9.96921 + 2.67124i 1.30902 + 0.350751i
5959 11.7504 + 3.14851i 1.52977 + 0.409900i 0.922944 0.384935i 0.125776π-0.125776\pi
0.606826 + 0.794835i 0.292443π0.292443\pi
6060 2.49179 2.30372i 0.321688 0.297409i
6161 0.279654 + 1.04368i 0.0358061 + 0.133630i 0.981515 0.191384i 0.0612976π-0.0612976\pi
−0.945709 + 0.325014i 0.894631π0.894631\pi
6262 2.46228 9.18935i 0.312710 1.16705i
6363 −1.05087 1.05087i −0.132397 0.132397i
6464 −1.00000 −0.125000
6565 8.24571 4.33904i 1.02275 0.538191i
6666 −1.33282 + 1.33282i −0.164059 + 0.164059i
6767 9.47979 2.54010i 1.15814 0.310323i 0.371918 0.928266i 0.378700π-0.378700\pi
0.786223 + 0.617943i 0.212034π0.212034\pi
6868 −5.65620 −0.685916
6969 11.1121 2.97747i 1.33774 0.358446i
7070 −4.65165 + 1.05291i −0.555979 + 0.125847i
7171 4.90681 8.49885i 0.582332 1.00863i −0.412871 0.910790i 0.635474π-0.635474\pi
0.995202 0.0978382i 0.0311928π-0.0311928\pi
7272 0.348387 + 0.603425i 0.0410578 + 0.0711143i
7373 −10.7498 + 10.7498i −1.25816 + 1.25816i −0.306196 + 0.951969i 0.599056π0.599056\pi
−0.951969 + 0.306196i 0.900944π0.900944\pi
7474 3.53553 + 4.94975i 0.410997 + 0.575396i
7575 −5.76939 + 4.92897i −0.666192 + 0.569148i
7676 −2.41482 0.647049i −0.276999 0.0742216i
7777 2.55879 0.685625i 0.291601 0.0781342i
7878 −1.63677 6.10850i −0.185327 0.691651i
7979 0.454017 + 1.69441i 0.0510809 + 0.190637i 0.986752 0.162238i 0.0518711π-0.0518711\pi
−0.935671 + 0.352874i 0.885204π0.885204\pi
8080 2.23435 + 0.0876265i 0.249808 + 0.00979695i
8181 −3.21209 + 5.56350i −0.356899 + 0.618167i
8282 −5.39144 −0.595385
8383 −0.0295859 + 0.110416i −0.00324747 + 0.0121197i −0.967531 0.252754i 0.918664π-0.918664\pi
0.964283 + 0.264874i 0.0853303π0.0853303\pi
8484 3.23698i 0.353184i
8585 12.6379 + 0.495634i 1.37078 + 0.0537590i
8686 3.30593 + 5.72604i 0.356488 + 0.617455i
8787 −7.83168 + 13.5649i −0.839645 + 1.45431i
8888 −1.24199 −0.132397
8989 −1.84256 + 6.87653i −0.195311 + 0.728910i 0.796875 + 0.604144i 0.206485π0.206485\pi
−0.992186 + 0.124766i 0.960182π0.960182\pi
9090 −0.725543 1.37879i −0.0764790 0.145337i
9191 −2.30033 + 8.58496i −0.241140 + 0.899948i
9292 6.56469 + 3.79012i 0.684416 + 0.395148i
9393 12.5037 + 7.21903i 1.29658 + 0.748579i
9494 1.23118 4.59481i 0.126986 0.473919i
9595 5.33885 + 1.65734i 0.547755 + 0.170039i
9696 0.392794 1.46593i 0.0400893 0.149615i
9797 0.402849 0.0409031 0.0204516 0.999791i 0.493490π-0.493490\pi
0.0204516 + 0.999791i 0.493490π0.493490\pi
9898 −1.22535 + 2.12237i −0.123779 + 0.214392i
9999 0.432694 + 0.749448i 0.0434874 + 0.0753223i
100100 −4.98464 0.391577i −0.498464 0.0391577i
101101 10.2921i 1.02410i 0.858956 + 0.512049i 0.171114π0.171114\pi
−0.858956 + 0.512049i 0.828886π0.828886\pi
102102 2.22172 8.29158i 0.219983 0.820988i
103103 7.89579 0.777995 0.388997 0.921239i 0.372821π-0.372821\pi
0.388997 + 0.921239i 0.372821π0.372821\pi
104104 2.08350 3.60872i 0.204303 0.353864i
105105 0.283646 7.23255i 0.0276810 0.705825i
106106 1.86551 + 6.96219i 0.181195 + 0.676228i
107107 0.879327 + 3.28169i 0.0850078 + 0.317253i 0.995316 0.0966784i 0.0308218π-0.0308218\pi
−0.910308 + 0.413932i 0.864155π0.864155\pi
108108 −5.41920 + 1.45207i −0.521463 + 0.139725i
109109 −3.45589 0.926002i −0.331014 0.0886949i 0.0894844 0.995988i 0.471478π-0.471478\pi
−0.420498 + 0.907293i 0.638145π0.638145\pi
110110 2.77504 + 0.108831i 0.264590 + 0.0103767i
111111 −8.64470 + 3.23860i −0.820518 + 0.307394i
112112 −1.50819 + 1.50819i −0.142511 + 0.142511i
113113 −1.99492 3.45530i −0.187666 0.325048i 0.756805 0.653640i 0.226759π-0.226759\pi
−0.944472 + 0.328593i 0.893426π0.893426\pi
114114 1.89705 3.28579i 0.177675 0.307742i
115115 −14.3357 9.04371i −1.33681 0.843330i
116116 −9.96921 + 2.67124i −0.925618 + 0.248019i
117117 −2.90345 −0.268424
118118 −11.7504 + 3.14851i −1.08171 + 0.289843i
119119 −8.53065 + 8.53065i −0.782003 + 0.782003i
120120 −1.00609 + 3.24097i −0.0918433 + 0.295859i
121121 9.45746 0.859769
122122 −0.764030 0.764030i −0.0691720 0.0691720i
123123 2.11772 7.90345i 0.190949 0.712630i
124124 2.46228 + 9.18935i 0.221119 + 0.825228i
125125 11.1031 + 1.31171i 0.993094 + 0.117323i
126126 1.43552 + 0.384645i 0.127886 + 0.0342669i
127127 6.97904 + 1.87003i 0.619290 + 0.165938i 0.554805 0.831980i 0.312793π-0.312793\pi
0.0644850 + 0.997919i 0.479460π0.479460\pi
128128 0.866025 0.500000i 0.0765466 0.0441942i
129129 −9.69251 + 2.59710i −0.853378 + 0.228662i
130130 −4.97148 + 7.88057i −0.436027 + 0.691172i
131131 −3.93914 1.05549i −0.344164 0.0922184i 0.0825968 0.996583i 0.473679π-0.473679\pi
−0.426761 + 0.904365i 0.640345π0.640345\pi
132132 0.487846 1.82067i 0.0424616 0.158469i
133133 −4.61789 + 2.66614i −0.400422 + 0.231184i
134134 −6.93969 + 6.93969i −0.599498 + 0.599498i
135135 12.2356 2.76957i 1.05307 0.238366i
136136 4.89842 2.82810i 0.420036 0.242508i
137137 7.39158 7.39158i 0.631505 0.631505i −0.316940 0.948446i 0.602655π-0.602655\pi
0.948446 + 0.316940i 0.102655π0.102655\pi
138138 −8.13461 + 8.13461i −0.692464 + 0.692464i
139139 −10.5923 18.3463i −0.898424 1.55612i −0.829509 0.558494i 0.811380π-0.811380\pi
−0.0689152 0.997623i 0.521954π-0.521954\pi
140140 3.50199 3.23767i 0.295972 0.273633i
141141 6.25206 + 3.60963i 0.526518 + 0.303985i
142142 9.81363i 0.823541i
143143 2.58768 4.48200i 0.216393 0.374803i
144144 −0.603425 0.348387i −0.0502854 0.0290323i
145145 22.5088 5.09492i 1.86925 0.423110i
146146 3.93469 14.6844i 0.325637 1.21529i
147147 −2.62993 2.62993i −0.216913 0.216913i
148148 −5.53674 2.51884i −0.455117 0.207047i
149149 17.9119i 1.46740i −0.679473 0.733700i 0.737792π-0.737792\pi
0.679473 0.733700i 0.262208π-0.262208\pi
150150 2.53196 7.15331i 0.206734 0.584065i
151151 −4.95829 2.86267i −0.403500 0.232961i 0.284493 0.958678i 0.408175π-0.408175\pi
−0.687993 + 0.725717i 0.741508π0.741508\pi
152152 2.41482 0.647049i 0.195868 0.0524826i
153153 −3.41309 1.97055i −0.275932 0.159310i
154154 −1.87316 + 1.87316i −0.150944 + 0.150944i
155155 −4.69636 20.7480i −0.377221 1.66652i
156156 4.47173 + 4.47173i 0.358025 + 0.358025i
157157 −7.02982 1.88363i −0.561040 0.150330i −0.0328561 0.999460i 0.510460π-0.510460\pi
−0.528184 + 0.849130i 0.677127π0.677127\pi
158158 −1.24040 1.24040i −0.0986807 0.0986807i
159159 −10.9388 −0.867505
160160 −1.97882 + 1.04129i −0.156439 + 0.0823211i
161161 15.6171 4.18458i 1.23080 0.329791i
162162 6.42418i 0.504731i
163163 8.87349 + 15.3693i 0.695025 + 1.20382i 0.970172 + 0.242417i 0.0779401π0.0779401\pi
−0.275147 + 0.961402i 0.588727π0.588727\pi
164164 4.66912 2.69572i 0.364597 0.210500i
165165 −1.24956 + 4.02526i −0.0972780 + 0.313366i
166166 −0.0295859 0.110416i −0.00229631 0.00856995i
167167 −5.00522 + 8.66929i −0.387315 + 0.670850i −0.992087 0.125549i 0.959931π-0.959931\pi
0.604772 + 0.796398i 0.293264π0.293264\pi
168168 −1.61849 2.80331i −0.124869 0.216280i
169169 2.18190 + 3.77917i 0.167839 + 0.290705i
170170 −11.1926 + 5.88974i −0.858433 + 0.451722i
171171 −1.23174 1.23174i −0.0941933 0.0941933i
172172 −5.72604 3.30593i −0.436607 0.252075i
173173 2.46568 + 0.660678i 0.187463 + 0.0502304i 0.351329 0.936252i 0.385730π-0.385730\pi
−0.163866 + 0.986483i 0.552397π0.552397\pi
174174 15.6634i 1.18744i
175175 −8.10838 + 6.92723i −0.612936 + 0.523650i
176176 1.07560 0.620995i 0.0810761 0.0468093i
177177 18.4619i 1.38768i
178178 −1.84256 6.87653i −0.138106 0.515417i
179179 −3.90524 3.90524i −0.291892 0.291892i 0.545936 0.837827i 0.316174π-0.316174\pi
−0.837827 + 0.545936i 0.816174π0.816174\pi
180180 1.31773 + 0.831295i 0.0982181 + 0.0619611i
181181 10.4223 18.0520i 0.774685 1.34179i −0.160287 0.987071i 0.551242π-0.551242\pi
0.934971 0.354723i 0.115425π-0.115425\pi
182182 −2.30033 8.58496i −0.170512 0.636360i
183183 1.42012 0.819905i 0.104978 0.0606091i
184184 −7.58025 −0.558823
185185 12.1503 + 6.11314i 0.893307 + 0.449447i
186186 −14.4381 −1.05865
187187 6.08379 3.51248i 0.444891 0.256858i
188188 1.23118 + 4.59481i 0.0897928 + 0.335111i
189189 −5.98320 + 10.3632i −0.435214 + 0.753812i
190190 −5.45225 + 1.23413i −0.395548 + 0.0895333i
191191 −1.86603 1.86603i −0.135021 0.135021i 0.636366 0.771387i 0.280437π-0.280437\pi
−0.771387 + 0.636366i 0.780437π0.780437\pi
192192 0.392794 + 1.46593i 0.0283474 + 0.105794i
193193 19.7620i 1.42250i −0.702938 0.711251i 0.748129π-0.748129\pi
0.702938 0.711251i 0.251871π-0.251871\pi
194194 −0.348877 + 0.201424i −0.0250479 + 0.0144614i
195195 −9.59957 10.3833i −0.687440 0.743560i
196196 2.45070i 0.175050i
197197 −11.6260 3.11519i −0.828321 0.221948i −0.180340 0.983604i 0.557720π-0.557720\pi
−0.647981 + 0.761656i 0.724386π0.724386\pi
198198 −0.749448 0.432694i −0.0532609 0.0307502i
199199 1.28100 + 1.28100i 0.0908079 + 0.0908079i 0.751052 0.660244i 0.229547π-0.229547\pi
−0.660244 + 0.751052i 0.729547π0.729547\pi
200200 4.51262 2.15321i 0.319090 0.152255i
201201 −7.44720 12.8989i −0.525285 0.909821i
202202 −5.14603 8.91319i −0.362074 0.627130i
203203 −11.0067 + 19.0642i −0.772522 + 1.33805i
204204 2.22172 + 8.29158i 0.155552 + 0.580526i
205205 −10.6687 + 5.61404i −0.745133 + 0.392102i
206206 −6.83795 + 3.94789i −0.476423 + 0.275063i
207207 2.64086 + 4.57411i 0.183553 + 0.317923i
208208 4.16699i 0.288929i
209209 2.99918 0.803629i 0.207458 0.0555882i
210210 3.37063 + 6.40540i 0.232596 + 0.442014i
211211 −2.01843 −0.138955 −0.0694773 0.997584i 0.522133π-0.522133\pi
−0.0694773 + 0.997584i 0.522133π0.522133\pi
212212 −5.09668 5.09668i −0.350041 0.350041i
213213 −14.3860 3.85473i −0.985716 0.264122i
214214 −2.40237 2.40237i −0.164222 0.164222i
215215 12.5043 + 7.88837i 0.852786 + 0.537982i
216216 3.96713 3.96713i 0.269929 0.269929i
217217 17.5729 + 10.1457i 1.19293 + 0.688736i
218218 3.45589 0.926002i 0.234062 0.0627168i
219219 19.9808 + 11.5359i 1.35018 + 0.779525i
220220 −2.45767 + 1.29327i −0.165696 + 0.0871923i
221221 23.5693i 1.58545i
222222 5.86723 7.12706i 0.393783 0.478337i
223223 9.90448 + 9.90448i 0.663253 + 0.663253i 0.956145 0.292892i 0.0946177π-0.0946177\pi
−0.292892 + 0.956145i 0.594618π0.594618\pi
224224 0.552037 2.06023i 0.0368845 0.137655i
225225 −2.87144 1.97287i −0.191429 0.131525i
226226 3.45530 + 1.99492i 0.229843 + 0.132700i
227227 −9.89342 + 17.1359i −0.656649 + 1.13735i 0.324829 + 0.945773i 0.394693π0.394693\pi
−0.981478 + 0.191577i 0.938640π0.938640\pi
228228 3.79410i 0.251271i
229229 −6.54334 3.77780i −0.432396 0.249644i 0.267971 0.963427i 0.413647π-0.413647\pi
−0.700367 + 0.713783i 0.746980π0.746980\pi
230230 16.9369 + 0.664231i 1.11679 + 0.0437981i
231231 −2.01015 3.48168i −0.132258 0.229078i
232232 7.29797 7.29797i 0.479135 0.479135i
233233 −9.92585 + 9.92585i −0.650264 + 0.650264i −0.953056 0.302793i 0.902081π-0.902081\pi
0.302793 + 0.953056i 0.402081π0.402081\pi
234234 2.51446 1.45173i 0.164376 0.0949023i
235235 −2.34825 10.3743i −0.153183 0.676745i
236236 8.60188 8.60188i 0.559934 0.559934i
237237 2.30555 1.33111i 0.149762 0.0864649i
238238 3.12243 11.6531i 0.202397 0.755357i
239239 −8.58662 2.30078i −0.555423 0.148825i −0.0298200 0.999555i 0.509493π-0.509493\pi
−0.525603 + 0.850730i 0.676160π0.676160\pi
240240 −0.749185 3.30981i −0.0483597 0.213647i
241241 −8.80585 + 2.35952i −0.567234 + 0.151990i −0.531028 0.847354i 0.678194π-0.678194\pi
−0.0362065 + 0.999344i 0.511527π0.511527\pi
242242 −8.19040 + 4.72873i −0.526499 + 0.303974i
243243 −6.84022 1.83283i −0.438800 0.117576i
244244 1.04368 + 0.279654i 0.0668150 + 0.0179030i
245245 −0.214747 + 5.47573i −0.0137197 + 0.349832i
246246 2.11772 + 7.90345i 0.135021 + 0.503906i
247247 −2.69625 + 10.0625i −0.171558 + 0.640263i
248248 −6.72707 6.72707i −0.427169 0.427169i
249249 0.173483 0.0109940
250250 −10.2714 + 4.41559i −0.649623 + 0.279267i
251251 0.286913 0.286913i 0.0181098 0.0181098i −0.697994 0.716104i 0.745924π-0.745924\pi
0.716104 + 0.697994i 0.245924π0.245924\pi
252252 −1.43552 + 0.384645i −0.0904290 + 0.0242304i
253253 −9.41460 −0.591891
254254 −6.97904 + 1.87003i −0.437904 + 0.117336i
255255 −4.23754 18.7210i −0.265365 1.17235i
256256 −0.500000 + 0.866025i −0.0312500 + 0.0541266i
257257 7.54430 + 13.0671i 0.470600 + 0.815103i 0.999435 0.0336216i 0.0107041π-0.0107041\pi
−0.528834 + 0.848725i 0.677371π0.677371\pi
258258 7.09541 7.09541i 0.441741 0.441741i
259259 −12.1494 + 4.55157i −0.754925 + 0.282821i
260260 0.365139 9.31052i 0.0226450 0.577414i
261261 −6.94629 1.86125i −0.429965 0.115209i
262262 3.93914 1.05549i 0.243361 0.0652083i
263263 5.31582 + 19.8389i 0.327787 + 1.22332i 0.911480 + 0.411344i 0.134941π0.134941\pi
−0.583693 + 0.811974i 0.698393π0.698393\pi
264264 0.487846 + 1.82067i 0.0300249 + 0.112054i
265265 10.9412 + 11.8344i 0.672110 + 0.726979i
266266 2.66614 4.61789i 0.163471 0.283141i
267267 10.8042 0.661208
268268 2.54010 9.47979i 0.155161 0.579070i
269269 6.60785i 0.402888i −0.979500 0.201444i 0.935437π-0.935437\pi
0.979500 0.201444i 0.0645634π-0.0645634\pi
270270 −9.21158 + 8.51633i −0.560599 + 0.518287i
271271 −6.90495 11.9597i −0.419446 0.726501i 0.576438 0.817141i 0.304442π-0.304442\pi
−0.995884 + 0.0906397i 0.971109π0.971109\pi
272272 −2.82810 + 4.89842i −0.171479 + 0.297010i
273273 13.4885 0.816359
274274 −2.70551 + 10.0971i −0.163446 + 0.609987i
275275 5.60463 2.67426i 0.337972 0.161264i
276276 2.97747 11.1121i 0.179223 0.668869i
277277 0.200429 + 0.115718i 0.0120426 + 0.00695279i 0.506009 0.862528i 0.331120π-0.331120\pi
−0.493967 + 0.869481i 0.664454π0.664454\pi
278278 18.3463 + 10.5923i 1.10034 + 0.635282i
279279 −1.71565 + 6.40290i −0.102713 + 0.383332i
280280 −1.41398 + 4.55490i −0.0845012 + 0.272208i
281281 4.01948 15.0009i 0.239782 0.894879i −0.736153 0.676816i 0.763359π-0.763359\pi
0.975935 0.218063i 0.0699739π-0.0699739\pi
282282 −7.21925 −0.429900
283283 15.3798 26.6386i 0.914235 1.58350i 0.106217 0.994343i 0.466126π-0.466126\pi
0.808018 0.589158i 0.200541π-0.200541\pi
284284 −4.90681 8.49885i −0.291166 0.504314i
285285 0.332464 8.47735i 0.0196935 0.502155i
286286 5.17536i 0.306026i
287287 2.97628 11.1076i 0.175684 0.655662i
288288 0.696775 0.0410578
289289 −7.49632 + 12.9840i −0.440960 + 0.763766i
290290 −16.9457 + 15.6667i −0.995086 + 0.919981i
291291 −0.158236 0.590547i −0.00927599 0.0346185i
292292 3.93469 + 14.6844i 0.230260 + 0.859342i
293293 6.11166 1.63761i 0.357047 0.0956704i −0.0758367 0.997120i 0.524163π-0.524163\pi
0.432884 + 0.901450i 0.357496π0.357496\pi
294294 3.59255 + 0.962621i 0.209522 + 0.0561412i
295295 −19.9734 + 18.4659i −1.16289 + 1.07512i
296296 6.05437 0.586988i 0.351903 0.0341180i
297297 4.92714 4.92714i 0.285901 0.285901i
298298 8.95595 + 15.5122i 0.518804 + 0.898595i
299299 15.7934 27.3550i 0.913357 1.58198i
300300 1.38391 + 7.46093i 0.0799003 + 0.430757i
301301 −13.6220 + 3.65000i −0.785157 + 0.210382i
302302 5.72534 0.329456
303303 15.0874 4.04266i 0.866749 0.232245i
304304 −1.76777 + 1.76777i −0.101389 + 0.101389i
305305 −2.30745 0.716300i −0.132124 0.0410152i
306306 3.94110 0.225298
307307 13.1849 + 13.1849i 0.752500 + 0.752500i 0.974945 0.222445i 0.0714039π-0.0714039\pi
−0.222445 + 0.974945i 0.571404π0.571404\pi
308308 0.685625 2.55879i 0.0390671 0.145800i
309309 −3.10141 11.5746i −0.176433 0.658458i
310310 14.4412 + 15.6201i 0.820203 + 0.887162i
311311 1.39722 + 0.374385i 0.0792292 + 0.0212294i 0.298216 0.954498i 0.403608π-0.403608\pi
−0.218987 + 0.975728i 0.570275π0.570275\pi
312312 −6.10850 1.63677i −0.345826 0.0926637i
313313 −5.24388 + 3.02756i −0.296402 + 0.171128i −0.640825 0.767687i 0.721408π-0.721408\pi
0.344424 + 0.938814i 0.388074π0.388074\pi
314314 7.02982 1.88363i 0.396715 0.106300i
315315 3.24115 0.733643i 0.182618 0.0413361i
316316 1.69441 + 0.454017i 0.0953183 + 0.0255405i
317317 −4.63520 + 17.2988i −0.260339 + 0.971598i 0.704703 + 0.709502i 0.251080π0.251080\pi
−0.965042 + 0.262095i 0.915586π0.915586\pi
318318 9.47329 5.46941i 0.531236 0.306709i
319319 9.06401 9.06401i 0.507487 0.507487i
320320 1.19306 1.89119i 0.0666942 0.105721i
321321 4.46533 2.57806i 0.249230 0.143893i
322322 −11.4325 + 11.4325i −0.637107 + 0.637107i
323323 −9.99887 + 9.99887i −0.556352 + 0.556352i
324324 3.21209 + 5.56350i 0.178449 + 0.309084i
325325 −1.63170 + 20.7710i −0.0905102 + 1.15217i
326326 −15.3693 8.87349i −0.851229 0.491457i
327327 5.42980i 0.300269i
328328 −2.69572 + 4.66912i −0.148846 + 0.257809i
329329 8.78672 + 5.07301i 0.484427 + 0.279684i
330330 −0.930480 4.11076i −0.0512213 0.226290i
331331 1.42272 5.30966i 0.0781997 0.291845i −0.915740 0.401771i 0.868395π-0.868395\pi
0.993940 + 0.109926i 0.0350614π0.0350614\pi
332332 0.0808302 + 0.0808302i 0.00443613 + 0.00443613i
333333 −2.46347 3.44886i −0.134997 0.188996i
334334 10.0104i 0.547746i
335335 −6.50616 + 20.9586i −0.355469 + 1.14509i
336336 2.80331 + 1.61849i 0.152933 + 0.0882959i
337337 −7.29082 + 1.95357i −0.397156 + 0.106418i −0.451869 0.892084i 0.649242π-0.649242\pi
0.0547125 + 0.998502i 0.482576π0.482576\pi
338338 −3.77917 2.18190i −0.205560 0.118680i
339339 −4.28163 + 4.28163i −0.232546 + 0.232546i
340340 6.74820 10.6970i 0.365973 0.580124i
341341 −8.35496 8.35496i −0.452446 0.452446i
342342 1.68258 + 0.450847i 0.0909837 + 0.0243790i
343343 −14.2535 14.2535i −0.769616 0.769616i
344344 6.61187 0.356488
345345 −7.62643 + 24.5674i −0.410593 + 1.32266i
346346 −2.46568 + 0.660678i −0.132556 + 0.0355183i
347347 13.7347i 0.737316i −0.929565 0.368658i 0.879817π-0.879817\pi
0.929565 0.368658i 0.120183π-0.120183\pi
348348 7.83168 + 13.5649i 0.419822 + 0.727154i
349349 −5.31791 + 3.07030i −0.284661 + 0.164349i −0.635532 0.772075i 0.719219π-0.719219\pi
0.350871 + 0.936424i 0.385886π0.385886\pi
350350 3.55845 10.0533i 0.190207 0.537374i
351351 6.05076 + 22.5817i 0.322966 + 1.20532i
352352 −0.620995 + 1.07560i −0.0330992 + 0.0573294i
353353 −15.3041 26.5075i −0.814556 1.41085i −0.909647 0.415383i 0.863648π-0.863648\pi
0.0950909 0.995469i 0.469686π-0.469686\pi
354354 9.23095 + 15.9885i 0.490619 + 0.849778i
355355 10.2188 + 19.4194i 0.542358 + 1.03067i
356356 5.03397 + 5.03397i 0.266800 + 0.266800i
357357 15.8561 + 9.15452i 0.839193 + 0.484508i
358358 5.33466 + 1.42942i 0.281946 + 0.0755471i
359359 10.8846i 0.574467i 0.957861 + 0.287234i 0.0927356π0.0927356\pi
−0.957861 + 0.287234i 0.907264π0.907264\pi
360360 −1.55684 0.0610560i −0.0820526 0.00321793i
361361 11.0418 6.37499i 0.581148 0.335526i
362362 20.8446i 1.09557i
363363 −3.71483 13.8639i −0.194978 0.727668i
364364 6.28463 + 6.28463i 0.329404 + 0.329404i
365365 −7.50472 33.1550i −0.392815 1.73541i
366366 −0.819905 + 1.42012i −0.0428571 + 0.0742307i
367367 −3.29675 12.3036i −0.172089 0.642244i −0.997029 0.0770245i 0.975458π-0.975458\pi
0.824940 0.565220i 0.191209π-0.191209\pi
368368 6.56469 3.79012i 0.342208 0.197574i
369369 3.75662 0.195562
370370 −13.5790 + 0.781014i −0.705940 + 0.0406030i
371371 −15.3736 −0.798155
372372 12.5037 7.21903i 0.648288 0.374289i
373373 4.47900 + 16.7159i 0.231914 + 0.865514i 0.979516 + 0.201367i 0.0645384π0.0645384\pi
−0.747602 + 0.664147i 0.768795π0.768795\pi
374374 −3.51248 + 6.08379i −0.181626 + 0.314585i
375375 −2.43837 16.7916i −0.125917 0.867114i
376376 −3.36364 3.36364i −0.173466 0.173466i
377377 11.1310 + 41.5416i 0.573278 + 2.13950i
378378 11.9664i 0.615485i
379379 23.2093 13.3999i 1.19218 0.688308i 0.233382 0.972385i 0.425021π-0.425021\pi
0.958801 + 0.284077i 0.0916873π0.0916873\pi
380380 4.10472 3.79491i 0.210568 0.194675i
381381 10.9653i 0.561769i
382382 2.54904 + 0.683014i 0.130420 + 0.0349460i
383383 1.80031 + 1.03941i 0.0919915 + 0.0531113i 0.545290 0.838247i 0.316420π-0.316420\pi
−0.453299 + 0.891359i 0.649753π0.649753\pi
384384 −1.07313 1.07313i −0.0547630 0.0547630i
385385 −1.75614 + 5.65715i −0.0895014 + 0.288315i
386386 9.88101 + 17.1144i 0.502930 + 0.871101i
387387 −2.30349 3.98976i −0.117093 0.202811i
388388 0.201424 0.348877i 0.0102258 0.0177116i
389389 6.45889 + 24.1049i 0.327479 + 1.22217i 0.911797 + 0.410642i 0.134695π0.134695\pi
−0.584318 + 0.811525i 0.698638π0.698638\pi
390390 13.5051 + 4.19238i 0.683857 + 0.212289i
391391 37.1312 21.4377i 1.87781 1.08415i
392392 1.22535 + 2.12237i 0.0618896 + 0.107196i
393393 6.18907i 0.312197i
394394 11.6260 3.11519i 0.585712 0.156941i
395395 −3.74613 1.16291i −0.188488 0.0585123i
396396 0.865388 0.0434874
397397 −6.29578 6.29578i −0.315976 0.315976i 0.531243 0.847219i 0.321725π-0.321725\pi
−0.847219 + 0.531243i 0.821725π0.821725\pi
398398 −1.74988 0.468880i −0.0877137 0.0235028i
399399 5.72224 + 5.72224i 0.286470 + 0.286470i
400400 −2.83144 + 4.12104i −0.141572 + 0.206052i
401401 15.3810 15.3810i 0.768091 0.768091i −0.209680 0.977770i 0.567242π-0.567242\pi
0.977770 + 0.209680i 0.0672421π0.0672421\pi
402402 12.8989 + 7.44720i 0.643340 + 0.371433i
403403 38.2919 10.2603i 1.90746 0.511101i
404404 8.91319 + 5.14603i 0.443448 + 0.256025i
405405 −6.68943 12.7123i −0.332400 0.631678i
406406 22.0135i 1.09251i
407407 7.51948 0.729034i 0.372727 0.0361369i
408408 −6.06986 6.06986i −0.300503 0.300503i
409409 8.95667 33.4267i 0.442879 1.65285i −0.278598 0.960408i 0.589870π-0.589870\pi
0.721477 0.692438i 0.243464π-0.243464\pi
410410 6.43232 10.1962i 0.317670 0.503557i
411411 −13.7389 7.93214i −0.677689 0.391264i
412412 3.94789 6.83795i 0.194499 0.336882i
413413 25.9466i 1.27675i
414414 −4.57411 2.64086i −0.224805 0.129791i
415415 −0.173520 0.187686i −0.00851776 0.00921313i
416416 −2.08350 3.60872i −0.102152 0.176932i
417417 −22.7338 + 22.7338i −1.11328 + 1.11328i
418418 −2.19555 + 2.19555i −0.107388 + 0.107388i
419419 −33.4282 + 19.2998i −1.63307 + 0.942855i −0.649935 + 0.759990i 0.725204π0.725204\pi
−0.983138 + 0.182865i 0.941463π0.941463\pi
420420 −6.12175 3.86192i −0.298711 0.188442i
421421 −10.7713 + 10.7713i −0.524962 + 0.524962i −0.919066 0.394104i 0.871055π-0.871055\pi
0.394104 + 0.919066i 0.371055π0.371055\pi
422422 1.74801 1.00922i 0.0850920 0.0491279i
423423 −0.857852 + 3.20155i −0.0417102 + 0.155665i
424424 6.96219 + 1.86551i 0.338114 + 0.0905973i
425425 −16.0152 + 23.3094i −0.776851 + 1.13067i
426426 14.3860 3.85473i 0.697006 0.186762i
427427 1.99585 1.15230i 0.0965860 0.0557639i
428428 3.28169 + 0.879327i 0.158627 + 0.0425039i
429429 −7.58670 2.03285i −0.366289 0.0981469i
430430 −14.7732 0.579375i −0.712428 0.0279399i
431431 2.95967 + 11.0456i 0.142562 + 0.532050i 0.999852 + 0.0172153i 0.00548006π0.00548006\pi
−0.857289 + 0.514835i 0.827853π0.827853\pi
432432 −1.45207 + 5.41920i −0.0698627 + 0.260731i
433433 22.3552 + 22.3552i 1.07432 + 1.07432i 0.997007 + 0.0773168i 0.0246353π0.0246353\pi
0.0773168 + 0.997007i 0.475365π0.475365\pi
434434 −20.2914 −0.974020
435435 −16.3101 30.9949i −0.782009 1.48609i
436436 −2.52989 + 2.52989i −0.121160 + 0.121160i
437437 18.3049 4.90479i 0.875643 0.234628i
438438 −23.0718 −1.10241
439439 10.0097 2.68209i 0.477737 0.128009i −0.0119114 0.999929i 0.503792π-0.503792\pi
0.489649 + 0.871920i 0.337125π0.337125\pi
440440 1.48177 2.34884i 0.0706407 0.111977i
441441 0.853794 1.47882i 0.0406569 0.0704198i
442442 −11.7847 20.4117i −0.560540 0.970883i
443443 −10.5760 + 10.5760i −0.502480 + 0.502480i −0.912208 0.409728i 0.865624π-0.865624\pi
0.409728 + 0.912208i 0.365624π0.365624\pi
444444 −1.51764 + 9.10583i −0.0720239 + 0.432143i
445445 −10.8065 11.6888i −0.512279 0.554100i
446446 −13.5298 3.62529i −0.640653 0.171663i
447447 −26.2575 + 7.03568i −1.24194 + 0.332776i
448448 0.552037 + 2.06023i 0.0260813 + 0.0973368i
449449 −9.97134 37.2136i −0.470577 1.75622i −0.637705 0.770281i 0.720116π-0.720116\pi
0.167128 0.985935i 0.446551π-0.446551\pi
450450 3.47317 + 0.272841i 0.163727 + 0.0128618i
451451 −3.34806 + 5.79901i −0.157654 + 0.273065i
452452 −3.98984 −0.187666
453453 −2.24888 + 8.39293i −0.105662 + 0.394334i
454454 19.7868i 0.928642i
455455 −13.4914 14.5928i −0.632485 0.684119i
456456 −1.89705 3.28579i −0.0888375 0.153871i
457457 16.2870 28.2100i 0.761875 1.31961i −0.180008 0.983665i 0.557612π-0.557612\pi
0.941883 0.335941i 0.109054π-0.109054\pi
458458 7.55560 0.353050
459459 −8.21320 + 30.6521i −0.383359 + 1.43072i
460460 −14.9999 + 7.89323i −0.699375 + 0.368024i
461461 2.39516 8.93886i 0.111554 0.416324i −0.887452 0.460900i 0.847527π-0.847527\pi
0.999006 + 0.0445754i 0.0141935π0.0141935\pi
462462 3.48168 + 2.01015i 0.161983 + 0.0935207i
463463 18.2579 + 10.5412i 0.848518 + 0.489892i 0.860150 0.510040i 0.170370π-0.170370\pi
−0.0116328 + 0.999932i 0.503703π0.503703\pi
464464 −2.67124 + 9.96921i −0.124009 + 0.462809i
465465 −28.5703 + 15.0342i −1.32492 + 0.697194i
466466 3.63311 13.5590i 0.168301 0.628107i
467467 −25.5763 −1.18353 −0.591764 0.806111i 0.701568π-0.701568\pi
−0.591764 + 0.806111i 0.701568π0.701568\pi
468468 −1.45173 + 2.51446i −0.0671061 + 0.116231i
469469 −10.4664 18.1283i −0.483293 0.837088i
470470 7.22080 + 7.81028i 0.333071 + 0.360262i
471471 11.0451i 0.508930i
472472 −3.14851 + 11.7504i −0.144922 + 0.540855i
473473 8.21188 0.377583
474474 −1.33111 + 2.30555i −0.0611399 + 0.105897i
475475 −9.50392 + 8.11948i −0.436070 + 0.372548i
476476 3.12243 + 11.6531i 0.143117 + 0.534118i
477477 −1.29984 4.85108i −0.0595157 0.222116i
478478 8.58662 2.30078i 0.392743 0.105235i
479479 7.17989 + 1.92385i 0.328058 + 0.0879027i 0.419089 0.907945i 0.362350π-0.362350\pi
−0.0910312 + 0.995848i 0.529016π0.529016\pi
480480 2.30372 + 2.49179i 0.105150 + 0.113734i
481481 −10.4960 + 23.0715i −0.478576 + 1.05197i
482482 6.44633 6.44633i 0.293622 0.293622i
483483 −12.2686 21.2498i −0.558239 0.966898i
484484 4.72873 8.19040i 0.214942 0.372291i
485485 −0.480624 + 0.761864i −0.0218240 + 0.0345945i
486486 6.84022 1.83283i 0.310279 0.0831389i
487487 −8.24270 −0.373512 −0.186756 0.982406i 0.559797π-0.559797\pi
−0.186756 + 0.982406i 0.559797π0.559797\pi
488488 −1.04368 + 0.279654i −0.0472454 + 0.0126594i
489489 19.0449 19.0449i 0.861238 0.861238i
490490 −2.55189 4.84950i −0.115283 0.219078i
491491 −16.2420 −0.732990 −0.366495 0.930420i 0.619442π-0.619442\pi
−0.366495 + 0.930420i 0.619442π0.619442\pi
492492 −5.78573 5.78573i −0.260841 0.260841i
493493 −15.1091 + 56.3879i −0.680479 + 2.53958i
494494 −2.69625 10.0625i −0.121310 0.452734i
495495 −1.93358 0.0758309i −0.0869079 0.00340835i
496496 9.18935 + 2.46228i 0.412614 + 0.110560i
497497 −20.2183 5.41749i −0.906916 0.243007i
498498 −0.150241 + 0.0867414i −0.00673244 + 0.00388698i
499499 15.4708 4.14540i 0.692570 0.185574i 0.104670 0.994507i 0.466621π-0.466621\pi
0.587900 + 0.808934i 0.299955π0.299955\pi
500500 6.68753 8.95974i 0.299076 0.400692i
501501 14.6745 + 3.93203i 0.655611 + 0.175670i
502502 −0.105017 + 0.391930i −0.00468716 + 0.0174927i
503503 25.4176 14.6748i 1.13331 0.654318i 0.188547 0.982064i 0.439622π-0.439622\pi
0.944766 + 0.327746i 0.106289π0.106289\pi
504504 1.05087 1.05087i 0.0468095 0.0468095i
505505 −19.4643 12.2791i −0.866148 0.546412i
506506 8.15328 4.70730i 0.362458 0.209265i
507507 4.68294 4.68294i 0.207977 0.207977i
508508 5.10901 5.10901i 0.226676 0.226676i
509509 −3.64938 6.32090i −0.161756 0.280169i 0.773743 0.633500i 0.218382π-0.218382\pi
−0.935498 + 0.353331i 0.885049π0.885049\pi
510510 13.0303 + 14.0941i 0.576991 + 0.624096i
511511 28.0813 + 16.2127i 1.24224 + 0.717208i
512512 1.00000i 0.0441942i
513513 −7.01297 + 12.1468i −0.309630 + 0.536295i
514514 −13.0671 7.54430i −0.576365 0.332765i
515515 −9.42016 + 14.9324i −0.415102 + 0.658002i
516516 −2.59710 + 9.69251i −0.114331 + 0.426689i
517517 −4.17761 4.17761i −0.183731 0.183731i
518518 8.24588 10.0165i 0.362303 0.440098i
519519 3.87402i 0.170051i
520520 4.33904 + 8.24571i 0.190279 + 0.361598i
521521 −17.5971 10.1597i −0.770942 0.445104i 0.0622684 0.998059i 0.480167π-0.480167\pi
−0.833211 + 0.552956i 0.813500π0.813500\pi
522522 6.94629 1.86125i 0.304031 0.0814648i
523523 −6.63703 3.83189i −0.290217 0.167557i 0.347823 0.937560i 0.386921π-0.386921\pi
−0.638040 + 0.770003i 0.720254π0.720254\pi
524524 −2.88365 + 2.88365i −0.125973 + 0.125973i
525525 13.3397 + 9.16531i 0.582194 + 0.400007i
526526 −14.5231 14.5231i −0.633236 0.633236i
527527 51.9768 + 13.9271i 2.26415 + 0.606676i
528528 −1.33282 1.33282i −0.0580036 0.0580036i
529529 −34.4602 −1.49827
530530 −15.3925 4.77828i −0.668608 0.207555i
531531 8.18737 2.19380i 0.355302 0.0952028i
532532 5.33228i 0.231184i
533533 −11.2330 19.4562i −0.486557 0.842741i
534534 −9.35673 + 5.40211i −0.404905 + 0.233772i
535535 −7.25540 2.25229i −0.313678 0.0973750i
536536 2.54010 + 9.47979i 0.109716 + 0.409465i
537537 −4.19084 + 7.25875i −0.180848 + 0.313238i
538538 3.30393 + 5.72257i 0.142442 + 0.246717i
539539 1.52188 + 2.63597i 0.0655519 + 0.113539i
540540 3.71930 11.9811i 0.160053 0.515586i
541541 29.5324 + 29.5324i 1.26970 + 1.26970i 0.946245 + 0.323450i 0.104843π0.104843\pi
0.323450 + 0.946245i 0.395157π0.395157\pi
542542 11.9597 + 6.90495i 0.513714 + 0.296593i
543543 −30.5567 8.18764i −1.31131 0.351365i
544544 5.65620i 0.242508i
545545 5.87434 5.43097i 0.251629 0.232637i
546546 −11.6814 + 6.74424i −0.499916 + 0.288627i
547547 6.72856i 0.287693i −0.989600 0.143846i 0.954053π-0.954053\pi
0.989600 0.143846i 0.0459471π-0.0459471\pi
548548 −2.70551 10.0971i −0.115573 0.431326i
549549 0.532357 + 0.532357i 0.0227204 + 0.0227204i
550550 −3.51662 + 5.11829i −0.149949 + 0.218245i
551551 −12.9011 + 22.3454i −0.549606 + 0.951946i
552552 2.97747 + 11.1121i 0.126730 + 0.472962i
553553 3.24025 1.87076i 0.137789 0.0795528i
554554 −0.231435 −0.00983274
555555 4.18885 20.2126i 0.177807 0.857978i
556556 −21.1845 −0.898424
557557 0.851828 0.491803i 0.0360931 0.0208384i −0.481845 0.876257i 0.660033π-0.660033\pi
0.517938 + 0.855418i 0.326700π0.326700\pi
558558 −1.71565 6.40290i −0.0726294 0.271057i
559559 −13.7758 + 23.8604i −0.582654 + 1.00919i
560560 −1.05291 4.65165i −0.0444937 0.196568i
561561 −7.53870 7.53870i −0.318284 0.318284i
562562 4.01948 + 15.0009i 0.169552 + 0.632775i
563563 31.0003i 1.30651i −0.757139 0.653254i 0.773403π-0.773403\pi
0.757139 0.653254i 0.226597π-0.226597\pi
564564 6.25206 3.60963i 0.263259 0.151993i
565565 8.91470 + 0.349616i 0.375044 + 0.0147085i
566566 30.7596i 1.29292i
567567 13.2353 + 3.54639i 0.555830 + 0.148934i
568568 8.49885 + 4.90681i 0.356604 + 0.205885i
569569 5.62158 + 5.62158i 0.235669 + 0.235669i 0.815054 0.579385i 0.196707π-0.196707\pi
−0.579385 + 0.815054i 0.696707π0.696707\pi
570570 3.95075 + 7.50783i 0.165479 + 0.314469i
571571 −7.18338 12.4420i −0.300615 0.520680i 0.675660 0.737213i 0.263859π-0.263859\pi
−0.976275 + 0.216533i 0.930525π0.930525\pi
572572 −2.58768 4.48200i −0.108196 0.187402i
573573 −2.00249 + 3.46842i −0.0836554 + 0.144895i
574574 2.97628 + 11.1076i 0.124227 + 0.463623i
575575 34.2068 16.3218i 1.42652 0.680668i
576576 −0.603425 + 0.348387i −0.0251427 + 0.0145161i
577577 −0.183869 0.318471i −0.00765458 0.0132581i 0.862173 0.506614i 0.169103π-0.169103\pi
−0.869827 + 0.493356i 0.835770π0.835770\pi
578578 14.9926i 0.623612i
579579 −28.9697 + 7.76240i −1.20394 + 0.322594i
580580 6.84206 22.0406i 0.284101 0.915187i
581581 0.243815 0.0101152
582582 0.432310 + 0.432310i 0.0179198 + 0.0179198i
583583 8.64698 + 2.31695i 0.358121 + 0.0959583i
584584 −10.7498 10.7498i −0.444828 0.444828i
585585 3.46400 5.49098i 0.143219 0.227024i
586586 −4.47404 + 4.47404i −0.184821 + 0.184821i
587587 −2.89163 1.66948i −0.119350 0.0689068i 0.439136 0.898420i 0.355284π-0.355284\pi
−0.558487 + 0.829514i 0.688618π0.688618\pi
588588 −3.59255 + 0.962621i −0.148154 + 0.0396978i
589589 20.5974 + 11.8919i 0.848701 + 0.489998i
590590 8.06451 25.9786i 0.332011 1.06952i
591591 18.2665i 0.751385i
592592 −4.94975 + 3.53553i −0.203433 + 0.145310i
593593 −30.9214 30.9214i −1.26979 1.26979i −0.946196 0.323595i 0.895108π-0.895108\pi
−0.323595 0.946196i 0.604892π-0.604892\pi
594594 −1.80346 + 6.73059i −0.0739967 + 0.276160i
595595 −5.95549 26.3107i −0.244151 1.07863i
596596 −15.5122 8.95595i −0.635403 0.366850i
597597 1.37469 2.38103i 0.0562622 0.0974489i
598598 31.5868i 1.29168i
599599 −10.3730 5.98884i −0.423828 0.244697i 0.272886 0.962047i 0.412022π-0.412022\pi
−0.696714 + 0.717349i 0.745355π0.745355\pi
600600 −4.92897 5.76939i −0.201224 0.235535i
601601 −2.65131 4.59220i −0.108149 0.187320i 0.806871 0.590727i 0.201159π-0.201159\pi
−0.915020 + 0.403407i 0.867826π0.867826\pi
602602 9.97197 9.97197i 0.406427 0.406427i
603603 4.83540 4.83540i 0.196913 0.196913i
604604 −4.95829 + 2.86267i −0.201750 + 0.116480i
605605 −11.2833 + 17.8859i −0.458733 + 0.727164i
606606 −11.0447 + 11.0447i −0.448662 + 0.448662i
607607 20.5512 11.8652i 0.834148 0.481595i −0.0211229 0.999777i 0.506724π-0.506724\pi
0.855271 + 0.518181i 0.173391π0.173391\pi
608608 0.647049 2.41482i 0.0262413 0.0979338i
609609 32.2701 + 8.64676i 1.30765 + 0.350384i
610610 2.35646 0.533391i 0.0954103 0.0215964i
611611 19.1465 5.13030i 0.774586 0.207550i
612612 −3.41309 + 1.97055i −0.137966 + 0.0796548i
613613 31.6675 + 8.48528i 1.27904 + 0.342717i 0.833487 0.552539i 0.186341π-0.186341\pi
0.445551 + 0.895256i 0.353008π0.353008\pi
614614 −18.0109 4.82599i −0.726859 0.194761i
615615 12.4204 + 13.4343i 0.500837 + 0.541724i
616616 0.685625 + 2.55879i 0.0276246 + 0.103096i
617617 −10.9431 + 40.8403i −0.440553 + 1.64417i 0.286863 + 0.957972i 0.407387π0.407387\pi
−0.727417 + 0.686196i 0.759279π0.759279\pi
618618 8.47322 + 8.47322i 0.340843 + 0.340843i
619619 −26.3358 −1.05853 −0.529263 0.848458i 0.677532π-0.677532\pi
−0.529263 + 0.848458i 0.677532π0.677532\pi
620620 −20.3165 6.30682i −0.815929 0.253288i
621621 30.0718 30.0718i 1.20674 1.20674i
622622 −1.39722 + 0.374385i −0.0560235 + 0.0150115i
623623 15.1844 0.608350
624624 6.10850 1.63677i 0.244536 0.0655231i
625625 −15.7274 + 19.4332i −0.629096 + 0.777327i
626626 3.02756 5.24388i 0.121006 0.209588i
627627 −2.35612 4.08092i −0.0940944 0.162976i
628628 −5.14618 + 5.14618i −0.205355 + 0.205355i
629629 −27.9968 + 19.9977i −1.11630 + 0.797361i
630630 −2.44010 + 2.25593i −0.0972158 + 0.0898784i
631631 −25.9691 6.95841i −1.03381 0.277010i −0.298267 0.954483i 0.596409π-0.596409\pi
−0.735548 + 0.677473i 0.763075π0.763075\pi
632632 −1.69441 + 0.454017i −0.0674002 + 0.0180598i
633633 0.792828 + 2.95887i 0.0315121 + 0.117605i
634634 −4.63520 17.2988i −0.184087 0.687023i
635635 −11.8630 + 10.9676i −0.470769 + 0.435238i
636636 −5.46941 + 9.47329i −0.216876 + 0.375641i
637637 −10.2121 −0.404617
638638 −3.31766 + 12.3817i −0.131347 + 0.490195i
639639 6.83789i 0.270503i
640640 −0.0876265 + 2.23435i −0.00346374 + 0.0883205i
641641 −7.65325 13.2558i −0.302285 0.523573i 0.674368 0.738395i 0.264416π-0.264416\pi
−0.976653 + 0.214822i 0.931083π0.931083\pi
642642 −2.57806 + 4.46533i −0.101748 + 0.176232i
643643 36.8625 1.45372 0.726858 0.686788i 0.240980π-0.240980\pi
0.726858 + 0.686788i 0.240980π0.240980\pi
644644 4.18458 15.6171i 0.164896 0.615398i
645645 6.65215 21.4289i 0.261928 0.843761i
646646 3.65984 13.6587i 0.143994 0.537395i
647647 −31.6509 18.2737i −1.24433 0.718413i −0.274355 0.961629i 0.588464π-0.588464\pi
−0.969972 + 0.243216i 0.921798π0.921798\pi
648648 −5.56350 3.21209i −0.218555 0.126183i
649649 −3.91041 + 14.5939i −0.153497 + 0.572859i
650650 −8.97239 18.8040i −0.351926 0.737555i
651651 7.97035 29.7457i 0.312383 1.16583i
652652 17.7470 0.695025
653653 1.49778 2.59423i 0.0586126 0.101520i −0.835230 0.549900i 0.814666π-0.814666\pi
0.893843 + 0.448380i 0.147999π0.147999\pi
654654 −2.71490 4.70235i −0.106161 0.183876i
655655 6.69576 6.19039i 0.261625 0.241879i
656656 5.39144i 0.210500i
657657 −2.74159 + 10.2317i −0.106960 + 0.399179i
658658 −10.1460 −0.395533
659659 −8.79071 + 15.2259i −0.342437 + 0.593119i −0.984885 0.173211i 0.944586π-0.944586\pi
0.642447 + 0.766330i 0.277919π0.277919\pi
660660 2.86120 + 3.09478i 0.111372 + 0.120464i
661661 −6.22906 23.2472i −0.242282 0.904210i −0.974730 0.223386i 0.928289π-0.928289\pi
0.732448 0.680823i 0.238378π-0.238378\pi
662662 1.42272 + 5.30966i 0.0552955 + 0.206366i
663663 34.5509 9.25789i 1.34185 0.359547i
664664 −0.110416 0.0295859i −0.00428497 0.00114816i
665665 0.467249 11.9142i 0.0181191 0.462012i
666666 3.85786 + 1.75506i 0.149489 + 0.0680073i
667667 55.3204 55.3204i 2.14201 2.14201i
668668 5.00522 + 8.66929i 0.193658 + 0.335425i
669669 10.6288 18.4097i 0.410934 0.711758i
670670 −4.84480 21.4038i −0.187171 0.826899i
671671 −1.29625 + 0.347328i −0.0500410 + 0.0134085i
672672 −3.23698 −0.124869
673673 13.0415 3.49445i 0.502712 0.134701i 0.00145339 0.999999i 0.499537π-0.499537\pi
0.501258 + 0.865298i 0.332871π0.332871\pi
674674 5.33725 5.33725i 0.205583 0.205583i
675675 −9.36008 + 26.4442i −0.360270 + 1.01784i
676676 4.36381 0.167839
677677 −22.4520 22.4520i −0.862902 0.862902i 0.128772 0.991674i 0.458896π-0.458896\pi
−0.991674 + 0.128772i 0.958896π0.958896\pi
678678 1.56718 5.84881i 0.0601873 0.224622i
679679 −0.222388 0.829962i −0.00853445 0.0318510i
680680 −0.495634 + 12.6379i −0.0190067 + 0.484643i
681681 29.0060 + 7.77214i 1.11151 + 0.297829i
682682 11.4131 + 3.05813i 0.437030 + 0.117102i
683683 −17.9138 + 10.3425i −0.685453 + 0.395747i −0.801906 0.597450i 0.796181π-0.796181\pi
0.116453 + 0.993196i 0.462847π0.462847\pi
684684 −1.68258 + 0.450847i −0.0643352 + 0.0172386i
685685 5.16028 + 22.7975i 0.197164 + 0.871048i
686686 19.4706 + 5.21714i 0.743392 + 0.199191i
687687 −2.96779 + 11.0759i −0.113228 + 0.422574i
688688 −5.72604 + 3.30593i −0.218303 + 0.126038i
689689 −21.2378 + 21.2378i −0.809096 + 0.809096i
690690 −5.67901 25.0892i −0.216196 0.955129i
691691 −29.7824 + 17.1949i −1.13297 + 0.654123i −0.944681 0.327990i 0.893629π-0.893629\pi
−0.188293 + 0.982113i 0.560295π0.560295\pi
692692 1.80501 1.80501i 0.0686160 0.0686160i
693693 1.30517 1.30517i 0.0495794 0.0495794i
694694 6.86734 + 11.8946i 0.260681 + 0.451512i
695695 47.3337 + 1.85633i 1.79547 + 0.0704145i
696696 −13.5649 7.83168i −0.514175 0.296859i
697697 30.4951i 1.15508i
698698 3.07030 5.31791i 0.116212 0.201286i
699699 18.4494 + 10.6517i 0.697819 + 0.402886i
700700 1.94497 + 10.4857i 0.0735129 + 0.396321i
701701 −6.71711 + 25.0686i −0.253702 + 0.946827i 0.715107 + 0.699015i 0.246378π0.246378\pi
−0.968808 + 0.247812i 0.920289π0.920289\pi
702702 −16.5310 16.5310i −0.623922 0.623922i
703703 −14.2404 + 5.33495i −0.537087 + 0.201211i
704704 1.24199i 0.0468093i
705705 −14.2856 + 7.51732i −0.538026 + 0.283119i
706706 26.5075 + 15.3041i 0.997623 + 0.575978i
707707 21.2040 5.68160i 0.797460 0.213679i
708708 −15.9885 9.23095i −0.600884 0.346920i
709709 −7.52915 + 7.52915i −0.282763 + 0.282763i −0.834210 0.551447i 0.814076π-0.814076\pi
0.551447 + 0.834210i 0.314076π0.314076\pi
710710 −18.5594 11.7083i −0.696523 0.439403i
711711 0.864278 + 0.864278i 0.0324129 + 0.0324129i
712712 −6.87653 1.84256i −0.257709 0.0690528i
713713 −50.9929 50.9929i −1.90970 1.90970i
714714 −18.3090 −0.685198
715715 5.38905 + 10.2411i 0.201539 + 0.382995i
716716 −5.33466 + 1.42942i −0.199366 + 0.0534199i
717717 13.4911i 0.503834i
718718 −5.44230 9.42634i −0.203105 0.351788i
719719 44.8295 25.8823i 1.67186 0.965248i 0.705262 0.708947i 0.250829π-0.250829\pi
0.966597 0.256301i 0.0825039π-0.0825039\pi
720720 1.37879 0.725543i 0.0513845 0.0270394i
721721 −4.35877 16.2671i −0.162329 0.605820i
722722 −6.37499 + 11.0418i −0.237253 + 0.410933i
723723 6.91776 + 11.9819i 0.257274 + 0.445612i
724724 −10.4223 18.0520i −0.387342 0.670897i
725725 −17.2189 + 48.6470i −0.639494 + 1.80670i
726726 10.1491 + 10.1491i 0.376669 + 0.376669i
727727 −22.8390 13.1861i −0.847052 0.489046i 0.0126028 0.999921i 0.495988π-0.495988\pi
−0.859655 + 0.510875i 0.829322π0.829322\pi
728728 −8.58496 2.30033i −0.318180 0.0852560i
729729 30.0197i 1.11184i
730730 23.0768 + 24.9607i 0.854109 + 0.923837i
731731 −32.3877 + 18.6990i −1.19790 + 0.691609i
732732 1.63981i 0.0606091i
733733 −9.72011 36.2759i −0.359020 1.33988i −0.875349 0.483492i 0.839368π-0.839368\pi
0.516329 0.856391i 0.327298π-0.327298\pi
734734 9.00688 + 9.00688i 0.332450 + 0.332450i
735735 8.11137 1.83603i 0.299192 0.0677230i
736736 −3.79012 + 6.56469i −0.139706 + 0.241978i
737737 3.15478 + 11.7738i 0.116208 + 0.433694i
738738 −3.25333 + 1.87831i −0.119757 + 0.0691415i
739739 39.7737 1.46310 0.731549 0.681788i 0.238798π-0.238798\pi
0.731549 + 0.681788i 0.238798π0.238798\pi
740740 11.3693 7.46589i 0.417943 0.274452i
741741 15.8100 0.580794
742742 13.3139 7.68678i 0.488768 0.282190i
743743 10.1080 + 37.7236i 0.370827 + 1.38395i 0.859347 + 0.511393i 0.170870π0.170870\pi
−0.488520 + 0.872553i 0.662463π0.662463\pi
744744 −7.21903 + 12.5037i −0.264663 + 0.458409i
745745 33.8748 + 21.3700i 1.24108 + 0.782937i
746746 −12.2369 12.2369i −0.448023 0.448023i
747747 0.0206147 + 0.0769351i 0.000754252 + 0.00281491i
748748 7.02495i 0.256858i
749749 6.27563 3.62323i 0.229306 0.132390i
750750 10.5075 + 13.3228i 0.383679 + 0.486478i
751751 21.9626i 0.801428i −0.916203 0.400714i 0.868762π-0.868762\pi
0.916203 0.400714i 0.131238π-0.131238\pi
752752 4.59481 + 1.23118i 0.167556 + 0.0448964i
753753 −0.533290 0.307895i −0.0194342 0.0112203i
754754 −30.4106 30.4106i −1.10749 1.10749i
755755 11.3294 5.96173i 0.412319 0.216970i
756756 5.98320 + 10.3632i 0.217607 + 0.376906i
757757 0.0633581 + 0.109739i 0.00230279 + 0.00398855i 0.867175 0.498004i 0.165934π-0.165934\pi
−0.864872 + 0.501993i 0.832600π0.832600\pi
758758 −13.3999 + 23.2093i −0.486707 + 0.843001i
759759 3.69800 + 13.8011i 0.134229 + 0.500948i
760760 −1.65734 + 5.33885i −0.0601179 + 0.193661i
761761 9.07376 5.23874i 0.328923 0.189904i −0.326440 0.945218i 0.605849π-0.605849\pi
0.655363 + 0.755314i 0.272516π0.272516\pi
762762 5.48265 + 9.49623i 0.198615 + 0.344012i
763763 7.63111i 0.276265i
764764 −2.54904 + 0.683014i −0.0922211 + 0.0247106i
765765 7.79872 4.10382i 0.281963 0.148374i
766766 −2.07882 −0.0751107
767767 −35.8439 35.8439i −1.29425 1.29425i
768768 1.46593 + 0.392794i 0.0528970 + 0.0141737i
769769 25.1503 + 25.1503i 0.906945 + 0.906945i 0.996024 0.0890797i 0.0283926π-0.0283926\pi
−0.0890797 + 0.996024i 0.528393π0.528393\pi
770770 −1.30771 5.77731i −0.0471266 0.208200i
771771 16.1921 16.1921i 0.583142 0.583142i
772772 −17.1144 9.88101i −0.615961 0.355625i
773773 43.6165 11.6870i 1.56878 0.420352i 0.633348 0.773867i 0.281680π-0.281680\pi
0.935429 + 0.353515i 0.115014π0.115014\pi
774774 3.98976 + 2.30349i 0.143409 + 0.0827972i
775775 44.8414 + 15.8719i 1.61075 + 0.570136i
776776 0.402849i 0.0144614i
777777 11.4445 + 16.0222i 0.410568 + 0.574795i
778778 −17.6460 17.6460i −0.632640 0.632640i
779779 3.48852 13.0194i 0.124989 0.466467i
780780 −13.7919 + 3.12184i −0.493831 + 0.111780i
781781 10.5555 + 6.09422i 0.377705 + 0.218068i
782782 −21.4377 + 37.1312i −0.766611 + 1.32781i
783783 57.9039i 2.06932i
784784 −2.12237 1.22535i −0.0757990 0.0437626i
785785 11.9493 11.0474i 0.426489 0.394300i
786786 −3.09453 5.35989i −0.110378 0.191181i
787787 4.28839 4.28839i 0.152865 0.152865i −0.626532 0.779396i 0.715526π-0.715526\pi
0.779396 + 0.626532i 0.215526π0.215526\pi
788788 −8.51085 + 8.51085i −0.303187 + 0.303187i
789789 26.9943 15.5852i 0.961024 0.554847i
790790 3.82570 0.865957i 0.136112 0.0308094i
791791 −6.01745 + 6.01745i −0.213956 + 0.213956i
792792 −0.749448 + 0.432694i −0.0266305 + 0.0153751i
793793 1.16532 4.34902i 0.0413816 0.154438i
794794 8.60020 + 2.30442i 0.305210 + 0.0817807i
795795 13.0507 20.6874i 0.462860 0.733706i
796796 1.74988 0.468880i 0.0620230 0.0166190i
797797 −46.5814 + 26.8938i −1.65000 + 0.952628i −0.672930 + 0.739706i 0.734965π0.734965\pi
−0.977069 + 0.212922i 0.931702π0.931702\pi
798798 −7.81672 2.09449i −0.276709 0.0741440i
799799 25.9892 + 6.96378i 0.919432 + 0.246361i
800800 0.391577 4.98464i 0.0138443 0.176234i
801801 1.28385 + 4.79139i 0.0453626 + 0.169295i
802802 −5.62984 + 21.0108i −0.198796 + 0.741918i
803803 −13.3511 13.3511i −0.471150 0.471150i
804804 −14.8944 −0.525285
805805 −10.7183 + 34.5273i −0.377770 + 1.21693i
806806 −28.0316 + 28.0316i −0.987372 + 0.987372i
807807 −9.68662 + 2.59552i −0.340985 + 0.0913667i
808808 −10.2921 −0.362074
809809 −4.87488 + 1.30622i −0.171392 + 0.0459243i −0.343494 0.939155i 0.611611π-0.611611\pi
0.172103 + 0.985079i 0.444944π0.444944\pi
810810 12.1494 + 7.66445i 0.426885 + 0.269301i
811811 −0.576314 + 0.998205i −0.0202371 + 0.0350517i −0.875967 0.482372i 0.839775π-0.839775\pi
0.855729 + 0.517423i 0.173109π0.173109\pi
812812 11.0067 + 19.0642i 0.386261 + 0.669024i
813813 −14.8198 + 14.8198i −0.519754 + 0.519754i
814814 −6.14754 + 4.39110i −0.215471 + 0.153908i
815815 −39.6530 1.55511i −1.38898 0.0544730i
816816 8.29158 + 2.22172i 0.290263 + 0.0777758i
817817 −15.9665 + 4.27820i −0.558596 + 0.149675i
818818 8.95667 + 33.4267i 0.313163 + 1.16874i
819819 1.60281 + 5.98178i 0.0560069 + 0.209020i
820820 −0.472433 + 12.0464i −0.0164981 + 0.420677i
821821 26.8808 46.5589i 0.938145 1.62492i 0.169218 0.985579i 0.445876π-0.445876\pi
0.768927 0.639337i 0.220791π-0.220791\pi
822822 15.8643 0.553330
823823 −12.3170 + 45.9677i −0.429344 + 1.60233i 0.324907 + 0.945746i 0.394667π0.394667\pi
−0.754251 + 0.656587i 0.772000π0.772000\pi
824824 7.89579i 0.275063i
825825 −6.12173 7.16554i −0.213131 0.249472i
826826 12.9733 + 22.4704i 0.451399 + 0.781845i
827827 −1.56275 + 2.70676i −0.0543422 + 0.0941234i −0.891917 0.452199i 0.850640π-0.850640\pi
0.837575 + 0.546323i 0.183973π0.183973\pi
828828 5.28173 0.183553
829829 1.17247 4.37573i 0.0407217 0.151975i −0.942571 0.334005i 0.891600π-0.891600\pi
0.983293 + 0.182029i 0.0582666π0.0582666\pi
830830 0.244116 + 0.0757806i 0.00847338 + 0.00263038i
831831 0.0909062 0.339267i 0.00315350 0.0117690i
832832 3.60872 + 2.08350i 0.125110 + 0.0722322i
833833 −12.0046 6.93084i −0.415934 0.240139i
834834 8.32115 31.0549i 0.288138 1.07534i
835835 −10.4237 19.8088i −0.360729 0.685512i
836836 0.803629 2.99918i 0.0277941 0.103729i
837837 53.3743 1.84489
838838 19.2998 33.4282i 0.666699 1.15476i
839839 −1.29920 2.25028i −0.0448534 0.0776884i 0.842727 0.538341i 0.180949π-0.180949\pi
−0.887581 + 0.460653i 0.847615π0.847615\pi
840840 7.23255 + 0.283646i 0.249547 + 0.00978670i
841841 77.5206i 2.67313i
842842 3.94257 14.7139i 0.135870 0.507074i
843843 −23.5690 −0.811761
844844 −1.00922 + 1.74801i −0.0347387 + 0.0601691i
845845 −9.75027 0.382385i −0.335420 0.0131545i
846846 −0.857852 3.20155i −0.0294936 0.110072i
847847 −5.22087 19.4845i −0.179391 0.669497i
848848 −6.96219 + 1.86551i −0.239083 + 0.0640620i
849849 −45.0913 12.0822i −1.54753 0.414659i
850850 2.21484 28.1942i 0.0759683 0.967052i
851851 45.8937 4.44952i 1.57321 0.152528i
852852 −10.5313 + 10.5313i −0.360797 + 0.360797i
853853 2.72407 + 4.71823i 0.0932704 + 0.161549i 0.908885 0.417046i 0.136935π-0.136935\pi
−0.815615 + 0.578595i 0.803601π0.803601\pi
854854 −1.15230 + 1.99585i −0.0394311 + 0.0682966i
855855 3.79899 0.859911i 0.129923 0.0294083i
856856 −3.28169 + 0.879327i −0.112166 + 0.0300548i
857857 18.8571 0.644145 0.322072 0.946715i 0.395621π-0.395621\pi
0.322072 + 0.946715i 0.395621π0.395621\pi
858858 7.58670 2.03285i 0.259006 0.0694004i
859859 −7.44096 + 7.44096i −0.253882 + 0.253882i −0.822560 0.568678i 0.807455π-0.807455\pi
0.568678 + 0.822560i 0.307455π0.307455\pi
860860 13.0837 6.88486i 0.446150 0.234772i
861861 −17.4520 −0.594762
862862 −8.08597 8.08597i −0.275409 0.275409i
863863 5.09357 19.0095i 0.173387 0.647090i −0.823433 0.567413i 0.807944π-0.807944\pi
0.996821 0.0796772i 0.0253889π-0.0253889\pi
864864 −1.45207 5.41920i −0.0494004 0.184365i
865865 −4.19118 + 3.87485i −0.142504 + 0.131749i
866866 −30.5378 8.18258i −1.03772 0.278055i
867867 21.9781 + 5.88902i 0.746416 + 0.200002i
868868 17.5729 10.1457i 0.596463 0.344368i
869869 −2.10445 + 0.563885i −0.0713885 + 0.0191285i
870870 29.6224 + 18.6874i 1.00429 + 0.633561i
871871 −39.5022 10.5846i −1.33848 0.358645i
872872 0.926002 3.45589i 0.0313584 0.117031i
873873 0.243089 0.140347i 0.00822731 0.00475004i
874874 −13.4001 + 13.4001i −0.453266 + 0.453266i
875875 −3.42692 23.5991i −0.115851 0.797796i
876876 19.9808 11.5359i 0.675088 0.389762i
877877 −10.4044 + 10.4044i −0.351331 + 0.351331i −0.860605 0.509274i 0.829914π-0.829914\pi
0.509274 + 0.860605i 0.329914π0.329914\pi
878878 −7.32762 + 7.32762i −0.247295 + 0.247295i
879879 −4.80124 8.31599i −0.161942 0.280491i
880880 −0.108831 + 2.77504i −0.00366870 + 0.0935467i
881881 24.3451 + 14.0557i 0.820209 + 0.473548i 0.850488 0.525994i 0.176306π-0.176306\pi
−0.0302797 + 0.999541i 0.509640π0.509640\pi
882882 1.70759i 0.0574975i
883883 2.79091 4.83400i 0.0939216 0.162677i −0.815236 0.579128i 0.803393π-0.803393\pi
0.909158 + 0.416451i 0.136726π0.136726\pi
884884 20.4117 + 11.7847i 0.686518 + 0.396361i
885885 34.9150 + 22.0262i 1.17365 + 0.740402i
886886 3.87108 14.4471i 0.130051 0.485359i
887887 −12.3904 12.3904i −0.416030 0.416030i 0.467803 0.883833i 0.345046π-0.345046\pi
−0.883833 + 0.467803i 0.845046π0.845046\pi
888888 −3.23860 8.64470i −0.108680 0.290097i
889889 15.4108i 0.516860i
890890 15.2031 + 4.71949i 0.509609 + 0.158198i
891891 −6.90982 3.98939i −0.231488 0.133650i
892892 13.5298 3.62529i 0.453010 0.121384i
893893 10.2990 + 5.94613i 0.344643 + 0.198980i
894894 19.2218 19.2218i 0.642874 0.642874i
895895 12.0448 2.72636i 0.402612 0.0911323i
896896 −1.50819 1.50819i −0.0503852 0.0503852i
897897 −46.3039 12.4071i −1.54604 0.414261i
898898 27.2422 + 27.2422i 0.909084 + 0.909084i
899899 98.1878 3.27475
900900 −3.14428 + 1.50030i −0.104809 + 0.0500100i
901901 −39.3796 + 10.5517i −1.31192 + 0.351529i
902902 6.69612i 0.222956i
903903 10.7012 + 18.5351i 0.356115 + 0.616810i
904904 3.45530 1.99492i 0.114922 0.0663501i
905905 21.7053 + 41.2477i 0.721508 + 1.37112i
906906 −2.24888 8.39293i −0.0747140 0.278836i
907907 −0.331736 + 0.574584i −0.0110151 + 0.0190788i −0.871480 0.490430i 0.836840π-0.836840\pi
0.860465 + 0.509509i 0.170173π0.170173\pi
908908 9.89342 + 17.1359i 0.328325 + 0.568675i
909909 3.58563 + 6.21049i 0.118928 + 0.205989i
910910 18.9802 + 5.89202i 0.629189 + 0.195319i
911911 −27.6384 27.6384i −0.915702 0.915702i 0.0810110 0.996713i 0.474185π-0.474185\pi
−0.996713 + 0.0810110i 0.974185π0.974185\pi
912912 3.28579 + 1.89705i 0.108803 + 0.0628176i
913913 −0.137136 0.0367454i −0.00453853 0.00121610i
914914 32.5741i 1.07745i
915915 −0.143691 + 3.66391i −0.00475027 + 0.121125i
916916 −6.54334 + 3.77780i −0.216198 + 0.124822i
917917 8.69820i 0.287240i
918918 −8.21320 30.6521i −0.271076 1.01167i
919919 −16.7230 16.7230i −0.551641 0.551641i 0.375273 0.926914i 0.377549π-0.377549\pi
−0.926914 + 0.375273i 0.877549π0.877549\pi
920920 9.04371 14.3357i 0.298162 0.472634i
921921 14.1491 24.5070i 0.466229 0.807532i
922922 2.39516 + 8.93886i 0.0788804 + 0.294386i
923923 −35.4146 + 20.4466i −1.16569 + 0.673009i
924924 −4.02030 −0.132258
925925 −26.0572 + 15.6852i −0.856754 + 0.515725i
926926 −21.0824 −0.692812
927927 4.76451 2.75079i 0.156487 0.0903479i
928928 −2.67124 9.96921i −0.0876878 0.327255i
929929 −8.45362 + 14.6421i −0.277354 + 0.480392i −0.970726 0.240188i 0.922791π-0.922791\pi
0.693372 + 0.720580i 0.256124π0.256124\pi
930930 17.2255 27.3051i 0.564847 0.895371i
931931 −4.33228 4.33228i −0.141985 0.141985i
932932 3.63311 + 13.5590i 0.119007 + 0.444139i
933933 2.19528i 0.0718702i
934934 22.1497 12.7881i 0.724760 0.418440i
935935 −0.615573 + 15.6962i −0.0201314 + 0.513321i
936936 2.90345i 0.0949023i
937937 8.78346 + 2.35352i 0.286943 + 0.0768862i 0.399420 0.916768i 0.369212π-0.369212\pi
−0.112477 + 0.993654i 0.535878π0.535878\pi
938938 18.1283 + 10.4664i 0.591911 + 0.341740i
939939 6.49794 + 6.49794i 0.212052 + 0.212052i
940940 −10.1585 3.15351i −0.331335 0.102856i
941941 −0.722576 1.25154i −0.0235553 0.0407990i 0.854007 0.520261i 0.174165π-0.174165\pi
−0.877563 + 0.479462i 0.840832π0.840832\pi
942942 −5.52253 9.56531i −0.179934 0.311655i
943943 −20.4342 + 35.3931i −0.665430 + 1.15256i
944944 −3.14851 11.7504i −0.102475 0.382442i
945945 −12.4605 23.6793i −0.405339 0.770288i
946946 −7.11169 + 4.10594i −0.231221 + 0.133496i
947947 −25.4993 44.1661i −0.828616 1.43520i −0.899124 0.437693i 0.855796π-0.855796\pi
0.0705085 0.997511i 0.477538π-0.477538\pi
948948 2.66222i 0.0864649i
949949 61.1899 16.3958i 1.98631 0.532230i
950950 4.17089 11.7836i 0.135322 0.382312i
951951 27.1794 0.881354
952952 −8.53065 8.53065i −0.276480 0.276480i
953953 −34.3639 9.20777i −1.11315 0.298269i −0.345044 0.938586i 0.612136π-0.612136\pi
−0.768110 + 0.640317i 0.778803π0.778803\pi
954954 3.55124 + 3.55124i 0.114975 + 0.114975i
955955 5.75530 1.30273i 0.186237 0.0421553i
956956 −6.28584 + 6.28584i −0.203299 + 0.203299i
957957 −16.8474 9.72688i −0.544601 0.314425i
958958 −7.17989 + 1.92385i −0.231972 + 0.0621566i
959959 −19.3088 11.1479i −0.623513 0.359986i
960960 −3.24097 1.00609i −0.104602 0.0324715i
961961 59.5069i 1.91958i
962962 −2.44598 25.2285i −0.0788614 0.813400i
963963 1.67391 + 1.67391i 0.0539410 + 0.0539410i
964964 −2.35952 + 8.80585i −0.0759950 + 0.283617i
965965 37.3738 + 23.5773i 1.20310 + 0.758981i
966966 21.2498 + 12.2686i 0.683700 + 0.394735i
967967 23.7442 41.1262i 0.763563 1.32253i −0.177439 0.984132i 0.556781π-0.556781\pi
0.941003 0.338399i 0.109885π-0.109885\pi
968968 9.45746i 0.303974i
969969 18.5851 + 10.7301i 0.597039 + 0.344701i
970970 0.0353003 0.900105i 0.00113342 0.0289006i
971971 30.3430 + 52.5556i 0.973753 + 1.68659i 0.683989 + 0.729492i 0.260244π0.260244\pi
0.289764 + 0.957098i 0.406423π0.406423\pi
972972 −5.00739 + 5.00739i −0.160612 + 0.160612i
973973 −31.9504 + 31.9504i −1.02428 + 1.02428i
974974 7.13839 4.12135i 0.228729 0.132057i
975975 31.0896 5.76675i 0.995664 0.184684i
976976 0.764030 0.764030i 0.0244560 0.0244560i
977977 −13.7786 + 7.95510i −0.440818 + 0.254506i −0.703944 0.710255i 0.748580π-0.748580\pi
0.263127 + 0.964761i 0.415246π0.415246\pi
978978 −6.97090 + 26.0158i −0.222905 + 0.831892i
979979 −8.54058 2.28844i −0.272958 0.0731389i
980980 4.63475 + 2.92384i 0.148052 + 0.0933987i
981981 −2.40797 + 0.645215i −0.0768807 + 0.0206001i
982982 14.0660 8.12099i 0.448863 0.259151i
983983 3.74405 + 1.00321i 0.119417 + 0.0319976i 0.318032 0.948080i 0.396978π-0.396978\pi
−0.198616 + 0.980077i 0.563645π0.563645\pi
984984 7.90345 + 2.11772i 0.251953 + 0.0675106i
985985 19.7620 18.2705i 0.629670 0.582145i
986986 −15.1091 56.3879i −0.481171 1.79576i
987987 3.98530 14.8733i 0.126853 0.473423i
988988 7.36628 + 7.36628i 0.234353 + 0.234353i
989989 50.1196 1.59371
990990 1.71244 0.901118i 0.0544251 0.0286394i
991991 −37.7253 + 37.7253i −1.19838 + 1.19838i −0.223732 + 0.974651i 0.571824π0.571824\pi
−0.974651 + 0.223732i 0.928176π0.928176\pi
992992 −9.18935 + 2.46228i −0.291762 + 0.0781774i
993993 −8.34240 −0.264738
994994 20.2183 5.41749i 0.641287 0.171832i
995995 −3.95094 + 0.894306i −0.125253 + 0.0283514i
996996 0.0867414 0.150241i 0.00274851 0.00476056i
997997 −7.17533 12.4280i −0.227245 0.393600i 0.729746 0.683719i 0.239639π-0.239639\pi
−0.956991 + 0.290119i 0.906305π0.906305\pi
998998 −11.3254 + 11.3254i −0.358501 + 0.358501i
999999 −21.6898 + 26.3471i −0.686235 + 0.833586i
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 370.2.r.e.193.1 yes 16
5.2 odd 4 370.2.q.e.267.1 16
37.14 odd 12 370.2.q.e.273.1 yes 16
185.162 even 12 inner 370.2.r.e.347.1 yes 16
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
370.2.q.e.267.1 16 5.2 odd 4
370.2.q.e.273.1 yes 16 37.14 odd 12
370.2.r.e.193.1 yes 16 1.1 even 1 trivial
370.2.r.e.347.1 yes 16 185.162 even 12 inner