Properties

Label 352.2.n.a.45.7
Level 352352
Weight 22
Character 352.45
Analytic conductor 2.8112.811
Analytic rank 00
Dimension 160160
Inner twists 22

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [352,2,Mod(45,352)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(352, base_ring=CyclotomicField(8))
 
chi = DirichletCharacter(H, H._module([0, 7, 0]))
 
N = Newforms(chi, 2, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("352.45");
 
S:= CuspForms(chi, 2);
 
N := Newforms(S);
 
Level: N N == 352=2511 352 = 2^{5} \cdot 11
Weight: k k == 2 2
Character orbit: [χ][\chi] == 352.n (of order 88, 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: 2.810734151152.81073415115
Analytic rank: 00
Dimension: 160160
Relative dimension: 4040 over Q(ζ8)\Q(\zeta_{8})
Twist minimal: yes
Sato-Tate group: SU(2)[C8]\mathrm{SU}(2)[C_{8}]

Embedding invariants

Embedding label 45.7
Character χ\chi == 352.45
Dual form 352.2.n.a.133.7

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+(1.21532+0.723188i)q2+(0.4435241.07076i)q3+(0.9539991.75781i)q4+(2.952831.22310i)q5+(0.235339+1.62207i)q6+(0.544294+0.544294i)q7+(0.111813+2.82622i)q8+(1.17150+1.17150i)q9+(2.70410+3.62191i)q10+(0.382683+0.923880i)q11+(1.459071.80114i)q12+(2.32285+0.962156i)q13+(0.2678641.05512i)q143.70425iq15+(2.179773.35389i)q163.46265iq17+(2.270960.576532i)q18+(1.896210.785436i)q19+(0.6670186.35734i)q20+(0.341402+0.824218i)q21+(1.133220.846056i)q22+(0.6695340.669534i)q23+(3.07580+1.13377i)q24+(3.687693.68769i)q25+(3.51882+0.510531i)q26+(4.986282.06538i)q27+(0.437509+1.47602i)q28+(0.762793+1.84154i)q29+(2.67887+4.50185i)q304.05527q31+(5.07461+2.49966i)q32+1.15898q33+(2.50415+4.20822i)q34+(0.941481+2.27294i)q35+(3.176890.941664i)q36+(5.373712.22586i)q37+(2.872520.416761i)q38+(2.060482.06048i)q39+(3.78692+8.20858i)q40+(3.077873.07787i)q41+(1.010980.754789i)q42+(3.30436+7.97743i)q43+(1.98908+0.208696i)q44+(4.89211+2.02638i)q45+(1.29790+0.329498i)q466.97739iq47+(4.55800+0.846487i)q48+6.40749iq49+(1.81483+7.14862i)q50+(3.707671.53577i)q51+(3.907283.16523i)q52+(4.9056011.8432i)q53+(4.56625+6.11611i)q54+(2.26000+2.26000i)q55+(1.599151.47743i)q56+(1.68203+1.68203i)q57+(0.4047462.78971i)q58+(10.1996+4.22479i)q59+(6.511373.53385i)q60+(2.45277+5.92151i)q61+(4.928442.93272i)q621.27528q63+(7.97500+0.632013i)q64+8.03580q65+(1.40854+0.838164i)q66+(3.06636+7.40285i)q67+(6.086673.30336i)q68+(1.01387+0.419957i)q69+(0.4995613.44321i)q70+(5.631815.63181i)q71+(3.17993+3.44191i)q72+(1.23542+1.23542i)q73+(4.92105+6.59133i)q74+(2.313065.58422i)q75+(3.18963+2.58387i)q76+(0.7111550.294570i)q77+(1.01403+3.99426i)q785.32846iq79+(10.53877.23739i)q801.28490iq81+(5.96647+1.51471i)q82+(4.831092.00110i)q83+(1.77451+0.186183i)q84+(4.2351810.2246i)q85+(9.785037.30545i)q86+(1.63354+1.63354i)q87+(2.56829+1.18485i)q88+(4.28348+4.28348i)q89+(7.41093+1.07522i)q90+(1.78801+0.740618i)q91+(1.81565+0.538177i)q92+(1.79861+4.34223i)q93+(5.04596+8.47975i)q946.55985q95+(4.927264.32504i)q96+13.1781q97+(4.633827.78714i)q98+(0.634012+1.53064i)q99+O(q100)q+(-1.21532 + 0.723188i) q^{2} +(0.443524 - 1.07076i) q^{3} +(0.953999 - 1.75781i) q^{4} +(2.95283 - 1.22310i) q^{5} +(0.235339 + 1.62207i) q^{6} +(-0.544294 + 0.544294i) q^{7} +(0.111813 + 2.82622i) q^{8} +(1.17150 + 1.17150i) q^{9} +(-2.70410 + 3.62191i) q^{10} +(0.382683 + 0.923880i) q^{11} +(-1.45907 - 1.80114i) q^{12} +(2.32285 + 0.962156i) q^{13} +(0.267864 - 1.05512i) q^{14} -3.70425i q^{15} +(-2.17977 - 3.35389i) q^{16} -3.46265i q^{17} +(-2.27096 - 0.576532i) q^{18} +(-1.89621 - 0.785436i) q^{19} +(0.667018 - 6.35734i) q^{20} +(0.341402 + 0.824218i) q^{21} +(-1.13322 - 0.846056i) q^{22} +(-0.669534 - 0.669534i) q^{23} +(3.07580 + 1.13377i) q^{24} +(3.68769 - 3.68769i) q^{25} +(-3.51882 + 0.510531i) q^{26} +(4.98628 - 2.06538i) q^{27} +(0.437509 + 1.47602i) q^{28} +(-0.762793 + 1.84154i) q^{29} +(2.67887 + 4.50185i) q^{30} -4.05527 q^{31} +(5.07461 + 2.49966i) q^{32} +1.15898 q^{33} +(2.50415 + 4.20822i) q^{34} +(-0.941481 + 2.27294i) q^{35} +(3.17689 - 0.941664i) q^{36} +(5.37371 - 2.22586i) q^{37} +(2.87252 - 0.416761i) q^{38} +(2.06048 - 2.06048i) q^{39} +(3.78692 + 8.20858i) q^{40} +(-3.07787 - 3.07787i) q^{41} +(-1.01098 - 0.754789i) q^{42} +(3.30436 + 7.97743i) q^{43} +(1.98908 + 0.208696i) q^{44} +(4.89211 + 2.02638i) q^{45} +(1.29790 + 0.329498i) q^{46} -6.97739i q^{47} +(-4.55800 + 0.846487i) q^{48} +6.40749i q^{49} +(-1.81483 + 7.14862i) q^{50} +(-3.70767 - 1.53577i) q^{51} +(3.90728 - 3.16523i) q^{52} +(-4.90560 - 11.8432i) q^{53} +(-4.56625 + 6.11611i) q^{54} +(2.26000 + 2.26000i) q^{55} +(-1.59915 - 1.47743i) q^{56} +(-1.68203 + 1.68203i) q^{57} +(-0.404746 - 2.78971i) q^{58} +(-10.1996 + 4.22479i) q^{59} +(-6.51137 - 3.53385i) q^{60} +(-2.45277 + 5.92151i) q^{61} +(4.92844 - 2.93272i) q^{62} -1.27528 q^{63} +(-7.97500 + 0.632013i) q^{64} +8.03580 q^{65} +(-1.40854 + 0.838164i) q^{66} +(-3.06636 + 7.40285i) q^{67} +(-6.08667 - 3.30336i) q^{68} +(-1.01387 + 0.419957i) q^{69} +(-0.499561 - 3.44321i) q^{70} +(5.63181 - 5.63181i) q^{71} +(-3.17993 + 3.44191i) q^{72} +(1.23542 + 1.23542i) q^{73} +(-4.92105 + 6.59133i) q^{74} +(-2.31306 - 5.58422i) q^{75} +(-3.18963 + 2.58387i) q^{76} +(-0.711155 - 0.294570i) q^{77} +(-1.01403 + 3.99426i) q^{78} -5.32846i q^{79} +(-10.5387 - 7.23739i) q^{80} -1.28490i q^{81} +(5.96647 + 1.51471i) q^{82} +(-4.83109 - 2.00110i) q^{83} +(1.77451 + 0.186183i) q^{84} +(-4.23518 - 10.2246i) q^{85} +(-9.78503 - 7.30545i) q^{86} +(1.63354 + 1.63354i) q^{87} +(-2.56829 + 1.18485i) q^{88} +(-4.28348 + 4.28348i) q^{89} +(-7.41093 + 1.07522i) q^{90} +(-1.78801 + 0.740618i) q^{91} +(-1.81565 + 0.538177i) q^{92} +(-1.79861 + 4.34223i) q^{93} +(5.04596 + 8.47975i) q^{94} -6.55985 q^{95} +(4.92726 - 4.32504i) q^{96} +13.1781 q^{97} +(-4.63382 - 7.78714i) q^{98} +(-0.634012 + 1.53064i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 160q16q1016q1416q20+24q2448q27+40q28+80q3048q3148q35+56q3616q3848q3964q40104q4880q50+32q51+64q54++56q98+O(q100) 160 q - 16 q^{10} - 16 q^{14} - 16 q^{20} + 24 q^{24} - 48 q^{27} + 40 q^{28} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 56 q^{36} - 16 q^{38} - 48 q^{39} - 64 q^{40} - 104 q^{48} - 80 q^{50} + 32 q^{51} + 64 q^{54}+ \cdots + 56 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/352Z)×\left(\mathbb{Z}/352\mathbb{Z}\right)^\times.

nn 133133 287287 321321
χ(n)\chi(n) e(78)e\left(\frac{7}{8}\right) 11 11

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 −1.21532 + 0.723188i −0.859360 + 0.511371i
33 0.443524 1.07076i 0.256069 0.618205i −0.742603 0.669732i 0.766409π-0.766409\pi
0.998672 + 0.0515273i 0.0164089π0.0164089\pi
44 0.953999 1.75781i 0.476999 0.878904i
55 2.95283 1.22310i 1.32055 0.546988i 0.392602 0.919708i 0.371575π-0.371575\pi
0.927944 + 0.372720i 0.121575π0.121575\pi
66 0.235339 + 1.62207i 0.0960767 + 0.662207i
77 −0.544294 + 0.544294i −0.205724 + 0.205724i −0.802447 0.596723i 0.796469π-0.796469\pi
0.596723 + 0.802447i 0.296469π0.296469\pi
88 0.111813 + 2.82622i 0.0395317 + 0.999218i
99 1.17150 + 1.17150i 0.390501 + 0.390501i
1010 −2.70410 + 3.62191i −0.855110 + 1.14535i
1111 0.382683 + 0.923880i 0.115383 + 0.278560i
1212 −1.45907 1.80114i −0.421198 0.519943i
1313 2.32285 + 0.962156i 0.644243 + 0.266854i 0.680791 0.732478i 0.261636π-0.261636\pi
−0.0365481 + 0.999332i 0.511636π0.511636\pi
1414 0.267864 1.05512i 0.0715897 0.281992i
1515 3.70425i 0.956434i
1616 −2.17977 3.35389i −0.544943 0.838473i
1717 3.46265i 0.839816i −0.907567 0.419908i 0.862062π-0.862062\pi
0.907567 0.419908i 0.137938π-0.137938\pi
1818 −2.27096 0.576532i −0.535272 0.135890i
1919 −1.89621 0.785436i −0.435020 0.180191i 0.154416 0.988006i 0.450650π-0.450650\pi
−0.589437 + 0.807815i 0.700650π0.700650\pi
2020 0.667018 6.35734i 0.149150 1.42155i
2121 0.341402 + 0.824218i 0.0745000 + 0.179859i
2222 −1.13322 0.846056i −0.241603 0.180380i
2323 −0.669534 0.669534i −0.139607 0.139607i 0.633849 0.773457i 0.281474π-0.281474\pi
−0.773457 + 0.633849i 0.781474π0.781474\pi
2424 3.07580 + 1.13377i 0.627844 + 0.231430i
2525 3.68769 3.68769i 0.737539 0.737539i
2626 −3.51882 + 0.510531i −0.690098 + 0.100123i
2727 4.98628 2.06538i 0.959609 0.397483i
2828 0.437509 + 1.47602i 0.0826813 + 0.278942i
2929 −0.762793 + 1.84154i −0.141647 + 0.341966i −0.978743 0.205090i 0.934251π-0.934251\pi
0.837096 + 0.547056i 0.184251π0.184251\pi
3030 2.67887 + 4.50185i 0.489093 + 0.821922i
3131 −4.05527 −0.728347 −0.364174 0.931331i 0.618649π-0.618649\pi
−0.364174 + 0.931331i 0.618649π0.618649\pi
3232 5.07461 + 2.49966i 0.897073 + 0.441882i
3333 1.15898 0.201753
3434 2.50415 + 4.20822i 0.429458 + 0.721704i
3535 −0.941481 + 2.27294i −0.159139 + 0.384196i
3636 3.17689 0.941664i 0.529481 0.156944i
3737 5.37371 2.22586i 0.883432 0.365930i 0.105605 0.994408i 0.466322π-0.466322\pi
0.777827 + 0.628478i 0.216322π0.216322\pi
3838 2.87252 0.416761i 0.465984 0.0676076i
3939 2.06048 2.06048i 0.329941 0.329941i
4040 3.78692 + 8.20858i 0.598764 + 1.29789i
4141 −3.07787 3.07787i −0.480683 0.480683i 0.424667 0.905350i 0.360391π-0.360391\pi
−0.905350 + 0.424667i 0.860391π0.860391\pi
4242 −1.01098 0.754789i −0.155997 0.116466i
4343 3.30436 + 7.97743i 0.503910 + 1.21655i 0.947338 + 0.320236i 0.103762π0.103762\pi
−0.443428 + 0.896310i 0.646238π0.646238\pi
4444 1.98908 + 0.208696i 0.299865 + 0.0314621i
4545 4.89211 + 2.02638i 0.729273 + 0.302075i
4646 1.29790 + 0.329498i 0.191364 + 0.0485819i
4747 6.97739i 1.01776i −0.860839 0.508878i 0.830060π-0.830060\pi
0.860839 0.508878i 0.169940π-0.169940\pi
4848 −4.55800 + 0.846487i −0.657891 + 0.122180i
4949 6.40749i 0.915355i
5050 −1.81483 + 7.14862i −0.256655 + 1.01097i
5151 −3.70767 1.53577i −0.519178 0.215051i
5252 3.90728 3.16523i 0.541842 0.438938i
5353 −4.90560 11.8432i −0.673836 1.62678i −0.775035 0.631919i 0.782268π-0.782268\pi
0.101198 0.994866i 0.467732π-0.467732\pi
5454 −4.56625 + 6.11611i −0.621389 + 0.832298i
5555 2.26000 + 2.26000i 0.304738 + 0.304738i
5656 −1.59915 1.47743i −0.213696 0.197430i
5757 −1.68203 + 1.68203i −0.222790 + 0.222790i
5858 −0.404746 2.78971i −0.0531458 0.366306i
5959 −10.1996 + 4.22479i −1.32787 + 0.550021i −0.930047 0.367441i 0.880234π-0.880234\pi
−0.397822 + 0.917462i 0.630234π0.630234\pi
6060 −6.51137 3.53385i −0.840614 0.456219i
6161 −2.45277 + 5.92151i −0.314045 + 0.758172i 0.685502 + 0.728071i 0.259583π0.259583\pi
−0.999547 + 0.0301010i 0.990417π0.990417\pi
6262 4.92844 2.93272i 0.625912 0.372456i
6363 −1.27528 −0.160671
6464 −7.97500 + 0.632013i −0.996874 + 0.0790017i
6565 8.03580 0.996718
6666 −1.40854 + 0.838164i −0.173379 + 0.103171i
6767 −3.06636 + 7.40285i −0.374615 + 0.904402i 0.618340 + 0.785911i 0.287806π0.287806\pi
−0.992955 + 0.118491i 0.962194π0.962194\pi
6868 −6.08667 3.30336i −0.738117 0.400592i
6969 −1.01387 + 0.419957i −0.122055 + 0.0505569i
7070 −0.499561 3.44321i −0.0597089 0.411542i
7171 5.63181 5.63181i 0.668373 0.668373i −0.288966 0.957339i 0.593312π-0.593312\pi
0.957339 + 0.288966i 0.0933116π0.0933116\pi
7272 −3.17993 + 3.44191i −0.374758 + 0.405633i
7373 1.23542 + 1.23542i 0.144595 + 0.144595i 0.775699 0.631103i 0.217398π-0.217398\pi
−0.631103 + 0.775699i 0.717398π0.717398\pi
7474 −4.92105 + 6.59133i −0.572061 + 0.766227i
7575 −2.31306 5.58422i −0.267089 0.644811i
7676 −3.18963 + 2.58387i −0.365875 + 0.296390i
7777 −0.711155 0.294570i −0.0810436 0.0335694i
7878 −1.01403 + 3.99426i −0.114816 + 0.452260i
7979 5.32846i 0.599499i −0.954018 0.299749i 0.903097π-0.903097\pi
0.954018 0.299749i 0.0969031π-0.0969031\pi
8080 −10.5387 7.23739i −1.17826 0.809164i
8181 1.28490i 0.142767i
8282 5.96647 + 1.51471i 0.658887 + 0.167272i
8383 −4.83109 2.00110i −0.530281 0.219650i 0.101445 0.994841i 0.467653π-0.467653\pi
−0.631726 + 0.775192i 0.717653π0.717653\pi
8484 1.77451 + 0.186183i 0.193615 + 0.0203143i
8585 −4.23518 10.2246i −0.459369 1.10902i
8686 −9.78503 7.30545i −1.05515 0.787767i
8787 1.63354 + 1.63354i 0.175134 + 0.175134i
8888 −2.56829 + 1.18485i −0.273781 + 0.126305i
8989 −4.28348 + 4.28348i −0.454048 + 0.454048i −0.896696 0.442648i 0.854039π-0.854039\pi
0.442648 + 0.896696i 0.354039π0.354039\pi
9090 −7.41093 + 1.07522i −0.781181 + 0.113338i
9191 −1.78801 + 0.740618i −0.187434 + 0.0776379i
9292 −1.81565 + 0.538177i −0.189294 + 0.0561089i
9393 −1.79861 + 4.34223i −0.186507 + 0.450268i
9494 5.04596 + 8.47975i 0.520451 + 0.874619i
9595 −6.55985 −0.673027
9696 4.92726 4.32504i 0.502886 0.441423i
9797 13.1781 1.33804 0.669018 0.743246i 0.266715π-0.266715\pi
0.669018 + 0.743246i 0.266715π0.266715\pi
9898 −4.63382 7.78714i −0.468086 0.786620i
9999 −0.634012 + 1.53064i −0.0637207 + 0.153835i
100100 −2.96420 10.0003i −0.296420 1.00003i
101101 −9.78129 + 4.05154i −0.973275 + 0.403144i −0.811930 0.583755i 0.801583π-0.801583\pi
−0.161344 + 0.986898i 0.551583π0.551583\pi
102102 5.61666 0.814897i 0.556132 0.0806868i
103103 −6.75733 + 6.75733i −0.665819 + 0.665819i −0.956745 0.290926i 0.906037π-0.906037\pi
0.290926 + 0.956745i 0.406037π0.406037\pi
104104 −2.45954 + 6.67246i −0.241178 + 0.654288i
105105 2.01620 + 2.01620i 0.196761 + 0.196761i
106106 14.5267 + 10.8456i 1.41096 + 1.05341i
107107 −6.37055 15.3799i −0.615864 1.48683i −0.856466 0.516204i 0.827345π-0.827345\pi
0.240601 0.970624i 0.422655π-0.422655\pi
108108 1.12636 10.7353i 0.108384 1.03300i
109109 −1.19440 0.494736i −0.114403 0.0473871i 0.324748 0.945801i 0.394721π-0.394721\pi
−0.439151 + 0.898413i 0.644721π0.644721\pi
110110 −4.38102 1.11221i −0.417714 0.106046i
111111 6.74119i 0.639845i
112112 3.01194 + 0.639066i 0.284602 + 0.0603861i
113113 19.3552i 1.82079i 0.413744 + 0.910393i 0.364221π0.364221\pi
−0.413744 + 0.910393i 0.635779π0.635779\pi
114114 0.827779 3.26063i 0.0775286 0.305386i
115115 −2.79593 1.15811i −0.260722 0.107994i
116116 2.50938 + 3.09767i 0.232990 + 0.287612i
117117 1.59406 + 3.84839i 0.147371 + 0.355784i
118118 9.34039 12.5107i 0.859853 1.15170i
119119 1.88470 + 1.88470i 0.172770 + 0.172770i
120120 10.4690 0.414182i 0.955687 0.0378095i
121121 −0.707107 + 0.707107i −0.0642824 + 0.0642824i
122122 −1.30147 8.97034i −0.117829 0.812136i
123123 −4.66078 + 1.93056i −0.420248 + 0.174072i
124124 −3.86872 + 7.12838i −0.347421 + 0.640147i
125125 0.263194 0.635405i 0.0235407 0.0568324i
126126 1.54988 0.922270i 0.138074 0.0821623i
127127 −1.19298 −0.105860 −0.0529298 0.998598i 0.516856π-0.516856\pi
−0.0529298 + 0.998598i 0.516856π0.516856\pi
128128 9.23510 6.53552i 0.816275 0.577664i
129129 10.0075 0.881111
130130 −9.76606 + 5.81139i −0.856540 + 0.509693i
131131 −7.77233 + 18.7641i −0.679071 + 1.63942i 0.0866409 + 0.996240i 0.472387π0.472387\pi
−0.765712 + 0.643183i 0.777613π0.777613\pi
132132 1.10567 2.03727i 0.0962362 0.177322i
133133 1.45960 0.604588i 0.126564 0.0524244i
134134 −1.62705 11.2144i −0.140555 0.968774i
135135 12.1975 12.1975i 1.04979 1.04979i
136136 9.78620 0.387168i 0.839160 0.0331994i
137137 11.2859 + 11.2859i 0.964218 + 0.964218i 0.999382 0.0351637i 0.0111953π-0.0111953\pi
−0.0351637 + 0.999382i 0.511195π0.511195\pi
138138 0.928463 1.24360i 0.0790360 0.105862i
139139 5.49063 + 13.2556i 0.465709 + 1.12432i 0.966018 + 0.258475i 0.0832198π0.0832198\pi
−0.500309 + 0.865847i 0.666780π0.666780\pi
140140 3.09721 + 3.82332i 0.261762 + 0.323130i
141141 −7.47112 3.09464i −0.629182 0.260616i
142142 −2.77159 + 10.9173i −0.232586 + 0.916159i
143143 2.51424i 0.210251i
144144 1.37548 6.48270i 0.114624 0.540225i
145145 6.37074i 0.529061i
146146 −2.39488 0.607990i −0.198201 0.0503176i
147147 6.86090 + 2.84188i 0.565877 + 0.234394i
148148 1.21387 11.5694i 0.0997797 0.951000i
149149 −3.77221 9.10692i −0.309031 0.746068i −0.999737 0.0229316i 0.992700π-0.992700\pi
0.690706 0.723136i 0.257300π-0.257300\pi
150150 6.84955 + 5.11383i 0.559263 + 0.417543i
151151 −5.85800 5.85800i −0.476717 0.476717i 0.427363 0.904080i 0.359443π-0.359443\pi
−0.904080 + 0.427363i 0.859443π0.859443\pi
152152 2.00779 5.44692i 0.162853 0.441804i
153153 4.05650 4.05650i 0.327949 0.327949i
154154 1.07731 0.156302i 0.0868120 0.0125952i
155155 −11.9745 + 4.96000i −0.961816 + 0.398397i
156156 −1.65623 5.58763i −0.132605 0.447368i
157157 −6.12539 + 14.7880i −0.488860 + 1.18021i 0.466435 + 0.884556i 0.345538π0.345538\pi
−0.955294 + 0.295656i 0.904462π0.904462\pi
158158 3.85348 + 6.47578i 0.306566 + 0.515185i
159159 −14.8570 −1.17823
160160 18.0418 + 1.17431i 1.42633 + 0.0928370i
161161 0.728847 0.0574412
162162 0.929225 + 1.56156i 0.0730068 + 0.122688i
163163 −2.27774 + 5.49896i −0.178407 + 0.430711i −0.987633 0.156786i 0.949887π-0.949887\pi
0.809226 + 0.587497i 0.199887π0.199887\pi
164164 −8.34659 + 2.47402i −0.651759 + 0.193188i
165165 3.42228 1.41756i 0.266425 0.110357i
166166 7.31849 1.06181i 0.568025 0.0824123i
167167 14.6563 14.6563i 1.13414 1.13414i 0.144658 0.989482i 0.453792π-0.453792\pi
0.989482 0.144658i 0.0462082π-0.0462082\pi
168168 −2.29124 + 1.05703i −0.176773 + 0.0815519i
169169 −4.72250 4.72250i −0.363269 0.363269i
170170 12.5414 + 9.36334i 0.961882 + 0.718135i
171171 −1.30127 3.14155i −0.0995109 0.240241i
172172 17.1751 + 1.80203i 1.30959 + 0.137403i
173173 −16.8952 6.99823i −1.28452 0.532066i −0.367172 0.930153i 0.619674π-0.619674\pi
−0.917348 + 0.398087i 0.869674π0.869674\pi
174174 −3.16663 0.803915i −0.240061 0.0609446i
175175 4.01438i 0.303459i
176176 2.26443 3.29733i 0.170688 0.248545i
177177 12.7951i 0.961739i
178178 2.10803 8.30355i 0.158004 0.622377i
179179 10.7599 + 4.45688i 0.804230 + 0.333123i 0.746649 0.665218i 0.231661π-0.231661\pi
0.0575808 + 0.998341i 0.481661π0.481661\pi
180180 8.22906 6.66623i 0.613358 0.496872i
181181 2.71805 + 6.56194i 0.202031 + 0.487745i 0.992127 0.125238i 0.0399694π-0.0399694\pi
−0.790096 + 0.612983i 0.789969π0.789969\pi
182182 1.63740 2.19315i 0.121372 0.162567i
183183 5.25267 + 5.25267i 0.388288 + 0.388288i
184184 1.81739 1.96711i 0.133979 0.145017i
185185 13.1452 13.1452i 0.966454 0.966454i
186186 −0.954362 6.57792i −0.0699772 0.482316i
187187 3.19907 1.32510i 0.233939 0.0969008i
188188 −12.2649 6.65642i −0.894510 0.485469i
189189 −1.58983 + 3.83818i −0.115643 + 0.279186i
190190 7.97231 4.74401i 0.578372 0.344166i
191191 0.926541 0.0670422 0.0335211 0.999438i 0.489328π-0.489328\pi
0.0335211 + 0.999438i 0.489328π0.489328\pi
192192 −2.86037 + 8.81964i −0.206429 + 0.636503i
193193 −4.31258 −0.310426 −0.155213 0.987881i 0.549606π-0.549606\pi
−0.155213 + 0.987881i 0.549606π0.549606\pi
194194 −16.0156 + 9.53026i −1.14985 + 0.684233i
195195 3.56407 8.60443i 0.255228 0.616176i
196196 11.2631 + 6.11273i 0.804509 + 0.436624i
197197 24.1259 9.99329i 1.71890 0.711992i 0.719047 0.694962i 0.244579π-0.244579\pi
0.999855 0.0170305i 0.00542123π-0.00542123\pi
198198 −0.336414 2.31873i −0.0239079 0.164785i
199199 5.51477 5.51477i 0.390932 0.390932i −0.484088 0.875019i 0.660848π-0.660848\pi
0.875019 + 0.484088i 0.160848π0.160848\pi
200200 10.8345 + 10.0099i 0.766118 + 0.707806i
201201 6.56668 + 6.56668i 0.463178 + 0.463178i
202202 8.95736 11.9976i 0.630237 0.844150i
203203 −0.587158 1.41753i −0.0412104 0.0994908i
204204 −6.23670 + 5.05226i −0.436657 + 0.353729i
205205 −12.8530 5.32388i −0.897691 0.371836i
206206 3.32549 13.0991i 0.231698 0.912659i
207207 1.56872i 0.109034i
208208 −1.83632 9.88787i −0.127326 0.685601i
209209 2.05244i 0.141970i
210210 −3.90843 0.992236i −0.269707 0.0684708i
211211 6.47376 + 2.68152i 0.445672 + 0.184603i 0.594221 0.804302i 0.297460π-0.297460\pi
−0.148549 + 0.988905i 0.547460π0.547460\pi
212212 −25.4980 2.67527i −1.75121 0.183738i
213213 −3.53248 8.52817i −0.242042 0.584341i
214214 18.8648 + 14.0843i 1.28957 + 0.962786i
215215 19.5144 + 19.5144i 1.33087 + 1.33087i
216216 6.39475 + 13.8614i 0.435108 + 0.943146i
217217 2.20726 2.20726i 0.149838 0.149838i
218218 1.80936 0.262513i 0.122545 0.0177796i
219219 1.87078 0.774904i 0.126416 0.0523632i
220220 6.12868 1.81661i 0.413195 0.122476i
221221 3.33161 8.04322i 0.224108 0.541045i
222222 4.87515 + 8.19269i 0.327198 + 0.549858i
223223 3.43663 0.230133 0.115067 0.993358i 0.463292π-0.463292\pi
0.115067 + 0.993358i 0.463292π0.463292\pi
224224 −4.12263 + 1.40153i −0.275455 + 0.0936438i
225225 8.64028 0.576019
226226 −13.9975 23.5228i −0.931098 1.56471i
227227 −6.05107 + 14.6086i −0.401623 + 0.969605i 0.585649 + 0.810565i 0.300840π0.300840\pi
−0.987272 + 0.159040i 0.949160π0.949160\pi
228228 1.35203 + 4.56134i 0.0895404 + 0.302082i
229229 −22.0262 + 9.12353i −1.45553 + 0.602900i −0.963507 0.267683i 0.913742π-0.913742\pi
−0.492022 + 0.870583i 0.663742π0.663742\pi
230230 4.23548 0.614507i 0.279279 0.0405194i
231231 −0.630829 + 0.630829i −0.0415055 + 0.0415055i
232232 −5.28989 1.94991i −0.347298 0.128018i
233233 −19.5904 19.5904i −1.28341 1.28341i −0.938715 0.344693i 0.887983π-0.887983\pi
−0.344693 0.938715i 0.612017π-0.612017\pi
234234 −4.72040 3.52422i −0.308582 0.230386i
235235 −8.53406 20.6030i −0.556701 1.34399i
236236 −2.30399 + 21.9593i −0.149977 + 1.42943i
237237 −5.70552 2.36330i −0.370613 0.153513i
238238 −3.65350 0.927519i −0.236822 0.0601221i
239239 24.5821i 1.59008i 0.606556 + 0.795041i 0.292551π0.292551\pi
−0.606556 + 0.795041i 0.707449π0.707449\pi
240240 −12.4237 + 8.07443i −0.801944 + 0.521203i
241241 10.7978i 0.695547i −0.937579 0.347774i 0.886938π-0.886938\pi
0.937579 0.347774i 0.113062π-0.113062\pi
242242 0.347989 1.37073i 0.0223696 0.0881139i
243243 13.5830 + 5.62627i 0.871350 + 0.360925i
244244 8.06894 + 9.96061i 0.516561 + 0.637663i
245245 7.83701 + 18.9202i 0.500688 + 1.20877i
246246 4.26817 5.71686i 0.272129 0.364494i
247247 −3.64890 3.64890i −0.232174 0.232174i
248248 −0.453430 11.4611i −0.0287928 0.727778i
249249 −4.28541 + 4.28541i −0.271577 + 0.271577i
250250 0.139653 + 0.962558i 0.00883246 + 0.0608775i
251251 15.4615 6.40436i 0.975920 0.404239i 0.163008 0.986625i 0.447881π-0.447881\pi
0.812913 + 0.582385i 0.197881π0.197881\pi
252252 −1.21662 + 2.24170i −0.0766398 + 0.141214i
253253 0.362349 0.874788i 0.0227807 0.0549975i
254254 1.44985 0.862747i 0.0909715 0.0541335i
255255 −12.8265 −0.803229
256256 −6.49718 + 14.6214i −0.406074 + 0.913840i
257257 −20.7719 −1.29572 −0.647858 0.761761i 0.724335π-0.724335\pi
−0.647858 + 0.761761i 0.724335π0.724335\pi
258258 −12.1623 + 7.23730i −0.757191 + 0.450575i
259259 −1.71335 + 4.13640i −0.106463 + 0.257024i
260260 7.66614 14.1254i 0.475434 0.876019i
261261 −3.05099 + 1.26376i −0.188851 + 0.0782248i
262262 −4.12408 28.4252i −0.254787 1.75611i
263263 14.3138 14.3138i 0.882624 0.882624i −0.111176 0.993801i 0.535462π-0.535462\pi
0.993801 + 0.111176i 0.0354619π0.0354619\pi
264264 0.129589 + 3.27554i 0.00797566 + 0.201596i
265265 −28.9708 28.9708i −1.77966 1.77966i
266266 −1.33665 + 1.79034i −0.0819555 + 0.109773i
267267 2.68676 + 6.48641i 0.164427 + 0.396962i
268268 10.0875 + 12.4524i 0.616191 + 0.760650i
269269 −18.8459 7.80622i −1.14905 0.475953i −0.274837 0.961491i 0.588624π-0.588624\pi
−0.874216 + 0.485537i 0.838624π0.838624\pi
270270 −6.00274 + 23.6448i −0.365315 + 1.43898i
271271 1.27900i 0.0776939i 0.999245 + 0.0388469i 0.0123685π0.0123685\pi
−0.999245 + 0.0388469i 0.987632π0.987632\pi
272272 −11.6134 + 7.54779i −0.704163 + 0.457652i
273273 2.24302i 0.135754i
274274 −21.8778 5.55413i −1.32168 0.335537i
275275 4.81820 + 1.99576i 0.290549 + 0.120349i
276276 −0.229023 + 2.18282i −0.0137856 + 0.131390i
277277 −8.25944 19.9400i −0.496261 1.19808i −0.951483 0.307703i 0.900440π-0.900440\pi
0.455221 0.890378i 0.349560π-0.349560\pi
278278 −16.2591 12.1390i −0.975157 0.728047i
279279 −4.75075 4.75075i −0.284420 0.284420i
280280 −6.52908 2.40669i −0.390187 0.143827i
281281 3.33569 3.33569i 0.198990 0.198990i −0.600577 0.799567i 0.705062π-0.705062\pi
0.799567 + 0.600577i 0.205062π0.205062\pi
282282 11.3178 1.64205i 0.673965 0.0977827i
283283 0.585643 0.242581i 0.0348128 0.0144199i −0.365209 0.930926i 0.619003π-0.619003\pi
0.400022 + 0.916506i 0.369003π0.369003\pi
284284 −4.52690 15.2724i −0.268622 0.906249i
285285 −2.90945 + 7.02404i −0.172341 + 0.416068i
286286 −1.81826 3.05560i −0.107516 0.180681i
287287 3.35053 0.197776
288288 3.01656 + 8.87328i 0.177753 + 0.522863i
289289 5.01005 0.294709
290290 −4.60724 7.74248i −0.270547 0.454654i
291291 5.84482 14.1106i 0.342629 0.827180i
292292 3.35023 0.993044i 0.196057 0.0581135i
293293 8.66842 3.59058i 0.506415 0.209764i −0.114823 0.993386i 0.536630π-0.536630\pi
0.621238 + 0.783622i 0.286630π0.286630\pi
294294 −10.3934 + 1.50793i −0.606154 + 0.0879444i
295295 −24.9502 + 24.9502i −1.45266 + 1.45266i
296296 6.89162 + 14.9384i 0.400567 + 0.868276i
297297 3.81633 + 3.81633i 0.221446 + 0.221446i
298298 11.1704 + 8.33979i 0.647087 + 0.483111i
299299 −0.911031 2.19942i −0.0526863 0.127196i
300300 −12.0226 1.26143i −0.694128 0.0728285i
301301 −6.14061 2.54353i −0.353939 0.146606i
302302 11.3558 + 2.88290i 0.653451 + 0.165892i
303303 12.2704i 0.704916i
304304 1.49904 + 8.07175i 0.0859759 + 0.462947i
305305 20.4852i 1.17298i
306306 −1.99633 + 7.86356i −0.114123 + 0.449530i
307307 5.10875 + 2.11611i 0.291572 + 0.120773i 0.523675 0.851918i 0.324561π-0.324561\pi
−0.232103 + 0.972691i 0.574561π0.574561\pi
308308 −1.19624 + 0.969054i −0.0681620 + 0.0552170i
309309 4.23845 + 10.2325i 0.241117 + 0.582108i
310310 10.9658 14.6878i 0.622817 0.834211i
311311 7.05432 + 7.05432i 0.400014 + 0.400014i 0.878238 0.478224i 0.158719π-0.158719\pi
−0.478224 + 0.878238i 0.658719π0.658719\pi
312312 6.05375 + 5.59298i 0.342726 + 0.316640i
313313 −10.7947 + 10.7947i −0.610154 + 0.610154i −0.942986 0.332832i 0.891996π-0.891996\pi
0.332832 + 0.942986i 0.391996π0.391996\pi
314314 −3.25020 22.4020i −0.183420 1.26422i
315315 −3.76570 + 1.55980i −0.212173 + 0.0878849i
316316 −9.36641 5.08335i −0.526902 0.285961i
317317 9.61563 23.2142i 0.540068 1.30384i −0.384607 0.923081i 0.625663π-0.625663\pi
0.924675 0.380758i 0.124337π-0.124337\pi
318318 18.0560 10.7444i 1.01253 0.602515i
319319 −1.99327 −0.111602
320320 −22.7758 + 11.6205i −1.27321 + 0.649604i
321321 −19.2937 −1.07687
322322 −0.885781 + 0.527093i −0.0493627 + 0.0293738i
323323 −2.71969 + 6.56591i −0.151328 + 0.365337i
324324 −2.25861 1.22579i −0.125478 0.0680997i
325325 12.1141 5.01782i 0.671969 0.278339i
326326 −1.20860 8.33022i −0.0669379 0.461368i
327327 −1.05949 + 1.05949i −0.0585899 + 0.0585899i
328328 8.35458 9.04287i 0.461305 0.499309i
329329 3.79775 + 3.79775i 0.209377 + 0.209377i
330330 −3.13401 + 4.19774i −0.172521 + 0.231078i
331331 −9.54415 23.0416i −0.524594 1.26648i −0.935022 0.354589i 0.884621π-0.884621\pi
0.410428 0.911893i 0.365379π-0.365379\pi
332332 −8.12641 + 6.58308i −0.445995 + 0.361293i
333333 8.90292 + 3.68771i 0.487877 + 0.202085i
334334 −7.21282 + 28.4114i −0.394668 + 1.55460i
335335 25.6098i 1.39921i
336336 2.02016 2.94163i 0.110209 0.160479i
337337 25.2384i 1.37482i −0.726269 0.687410i 0.758747π-0.758747\pi
0.726269 0.687410i 0.241253π-0.241253\pi
338338 9.15459 + 2.32409i 0.497944 + 0.126414i
339339 20.7249 + 8.58451i 1.12562 + 0.466247i
340340 −22.0133 2.30965i −1.19384 0.125258i
341341 −1.55188 3.74658i −0.0840392 0.202889i
342342 3.85340 + 2.87692i 0.208368 + 0.155566i
343343 −7.29762 7.29762i −0.394034 0.394034i
344344 −22.1765 + 10.2308i −1.19568 + 0.551608i
345345 −2.48012 + 2.48012i −0.133525 + 0.133525i
346346 25.5941 3.71334i 1.37595 0.199630i
347347 14.3160 5.92989i 0.768524 0.318333i 0.0362498 0.999343i 0.488459π-0.488459\pi
0.732275 + 0.681010i 0.238459π0.238459\pi
348348 4.42984 1.31305i 0.237464 0.0703870i
349349 −11.3291 + 27.3509i −0.606433 + 1.46406i 0.260419 + 0.965496i 0.416139π0.416139\pi
−0.866853 + 0.498564i 0.833861π0.833861\pi
350350 −2.90315 4.87875i −0.155180 0.260780i
351351 13.5696 0.724292
352352 −0.367416 + 5.64491i −0.0195833 + 0.300875i
353353 6.76267 0.359941 0.179970 0.983672i 0.442400π-0.442400\pi
0.179970 + 0.983672i 0.442400π0.442400\pi
354354 −9.25326 15.5501i −0.491805 0.826480i
355355 9.74150 23.5181i 0.517025 1.24821i
356356 3.44310 + 11.6160i 0.182484 + 0.615645i
357357 2.85398 1.18216i 0.151048 0.0625663i
358358 −16.2998 + 2.36487i −0.861473 + 0.124987i
359359 17.8241 17.8241i 0.940720 0.940720i −0.0576185 0.998339i 0.518351π-0.518351\pi
0.998339 + 0.0576185i 0.0183507π0.0183507\pi
360360 −5.17999 + 14.0527i −0.273009 + 0.740645i
361361 −10.4563 10.4563i −0.550333 0.550333i
362362 −8.04881 6.00919i −0.423036 0.315836i
363363 0.443524 + 1.07076i 0.0232790 + 0.0562004i
364364 −0.403896 + 3.84953i −0.0211699 + 0.201770i
365365 5.15904 + 2.13695i 0.270037 + 0.111853i
366366 −10.1823 2.58500i −0.532239 0.135120i
367367 20.7924i 1.08536i −0.839941 0.542678i 0.817411π-0.817411\pi
0.839941 0.542678i 0.182589π-0.182589\pi
368368 −0.786112 + 3.70498i −0.0409789 + 0.193135i
369369 7.21146i 0.375414i
370370 −6.46915 + 25.4820i −0.336315 + 1.32475i
371371 9.11626 + 3.77608i 0.473293 + 0.196044i
372372 5.91693 + 7.30408i 0.306778 + 0.378699i
373373 10.1172 + 24.4251i 0.523850 + 1.26468i 0.935495 + 0.353341i 0.114954π0.114954\pi
−0.411645 + 0.911344i 0.635046π0.635046\pi
374374 −2.92960 + 3.92395i −0.151486 + 0.202902i
375375 −0.563635 0.563635i −0.0291060 0.0291060i
376376 19.7196 0.780160i 1.01696 0.0402337i
377377 −3.54371 + 3.54371i −0.182510 + 0.182510i
378378 −0.843580 5.81435i −0.0433891 0.299058i
379379 11.0476 4.57605i 0.567475 0.235056i −0.0804519 0.996758i 0.525636π-0.525636\pi
0.647927 + 0.761703i 0.275636π0.275636\pi
380380 −6.25809 + 11.5310i −0.321033 + 0.591526i
381381 −0.529114 + 1.27740i −0.0271074 + 0.0654429i
382382 −1.12604 + 0.670063i −0.0576134 + 0.0342834i
383383 18.3152 0.935864 0.467932 0.883764i 0.344999π-0.344999\pi
0.467932 + 0.883764i 0.344999π0.344999\pi
384384 −2.90200 12.7873i −0.148092 0.652547i
385385 −2.46021 −0.125384
386386 5.24116 3.11881i 0.266768 0.158743i
387387 −5.47451 + 13.2166i −0.278285 + 0.671840i
388388 12.5719 23.1646i 0.638242 1.17600i
389389 −13.5344 + 5.60611i −0.686219 + 0.284241i −0.698424 0.715684i 0.746115π-0.746115\pi
0.0122048 + 0.999926i 0.496115π0.496115\pi
390390 1.89114 + 13.0346i 0.0957614 + 0.660034i
391391 −2.31836 + 2.31836i −0.117245 + 0.117245i
392392 −18.1089 + 0.716438i −0.914640 + 0.0361856i
393393 16.6446 + 16.6446i 0.839610 + 0.839610i
394394 −22.0937 + 29.5926i −1.11306 + 1.49085i
395395 −6.51726 15.7340i −0.327919 0.791666i
396396 2.08573 + 2.57470i 0.104812 + 0.129384i
397397 31.9998 + 13.2548i 1.60602 + 0.665237i 0.992251 0.124246i 0.0396511π-0.0396511\pi
0.613773 + 0.789483i 0.289651π0.289651\pi
398398 −2.71399 + 10.6904i −0.136040 + 0.535862i
399399 1.83104i 0.0916666i
400400 −20.4065 4.32979i −1.02032 0.216489i
401401 13.0539i 0.651879i −0.945391 0.325939i 0.894319π-0.894319\pi
0.945391 0.325939i 0.105681π-0.105681\pi
402402 −12.7296 3.23167i −0.634893 0.161181i
403403 −9.41978 3.90180i −0.469232 0.194362i
404404 −2.20951 + 21.0588i −0.109927 + 1.04771i
405405 −1.57157 3.79410i −0.0780917 0.188530i
406406 1.73872 + 1.29812i 0.0862913 + 0.0644246i
407407 4.11286 + 4.11286i 0.203867 + 0.203867i
408408 3.92585 10.6504i 0.194359 0.527274i
409409 13.9131 13.9131i 0.687958 0.687958i −0.273822 0.961780i 0.588288π-0.588288\pi
0.961780 + 0.273822i 0.0882880π0.0882880\pi
410410 19.4706 2.82491i 0.961586 0.139512i
411411 17.0901 7.07893i 0.842990 0.349178i
412412 5.43160 + 18.3246i 0.267596 + 0.902786i
413413 3.25203 7.85109i 0.160022 0.386327i
414414 1.13448 + 1.90650i 0.0557567 + 0.0936992i
415415 −16.7129 −0.820406
416416 9.38250 + 10.6889i 0.460015 + 0.524067i
417417 16.6288 0.814315
418418 1.48430 + 2.49437i 0.0725996 + 0.122004i
419419 −12.0802 + 29.1643i −0.590158 + 1.42477i 0.293191 + 0.956054i 0.405283π0.405283\pi
−0.883350 + 0.468715i 0.844717π0.844717\pi
420420 5.46756 1.62064i 0.266789 0.0790793i
421421 18.8663 7.81469i 0.919489 0.380865i 0.127808 0.991799i 0.459206π-0.459206\pi
0.791681 + 0.610934i 0.209206π0.209206\pi
422422 −9.80693 + 1.42285i −0.477394 + 0.0692630i
423423 8.17402 8.17402i 0.397435 0.397435i
424424 32.9229 15.1885i 1.59888 0.737619i
425425 −12.7692 12.7692i −0.619397 0.619397i
426426 10.4606 + 7.80980i 0.506816 + 0.378386i
427427 −1.88802 4.55808i −0.0913675 0.220581i
428428 −33.1123 3.47417i −1.60055 0.167931i
429429 2.69215 + 1.11512i 0.129978 + 0.0538387i
430430 −37.8288 9.60365i −1.82427 0.463129i
431431 36.5150i 1.75887i −0.476022 0.879433i 0.657922π-0.657922\pi
0.476022 0.879433i 0.342078π-0.342078\pi
432432 −17.7960 12.2214i −0.856212 0.588001i
433433 15.4998i 0.744871i 0.928058 + 0.372436i 0.121477π0.121477\pi
−0.928058 + 0.372436i 0.878523π0.878523\pi
434434 −1.08626 + 4.27878i −0.0521421 + 0.205388i
435435 6.82155 + 2.82558i 0.327068 + 0.135476i
436436 −2.00910 + 1.62754i −0.0962187 + 0.0779453i
437437 0.743701 + 1.79545i 0.0355760 + 0.0858882i
438438 −1.71320 + 2.29468i −0.0818597 + 0.109644i
439439 −2.92729 2.92729i −0.139712 0.139712i 0.633792 0.773504i 0.281498π-0.281498\pi
−0.773504 + 0.633792i 0.781498π0.781498\pi
440440 −6.13455 + 6.63994i −0.292453 + 0.316547i
441441 −7.50639 + 7.50639i −0.357447 + 0.357447i
442442 1.76779 + 12.1845i 0.0840852 + 0.579555i
443443 27.6395 11.4487i 1.31319 0.543943i 0.387379 0.921921i 0.373381π-0.373381\pi
0.925815 + 0.377978i 0.123381π0.123381\pi
444444 −11.8497 6.43109i −0.562362 0.305206i
445445 −7.40925 + 17.8875i −0.351232 + 0.847950i
446446 −4.17660 + 2.48533i −0.197768 + 0.117684i
447447 −11.4244 −0.540356
448448 3.99674 4.68475i 0.188828 0.221333i
449449 15.2099 0.717800 0.358900 0.933376i 0.383152π-0.383152\pi
0.358900 + 0.933376i 0.383152π0.383152\pi
450450 −10.5007 + 6.24855i −0.495007 + 0.294559i
451451 1.66573 4.02143i 0.0784362 0.189362i
452452 34.0228 + 18.4649i 1.60030 + 0.868514i
453453 −8.87069 + 3.67436i −0.416781 + 0.172636i
454454 −3.21076 22.1301i −0.150689 1.03862i
455455 −4.37384 + 4.37384i −0.205049 + 0.205049i
456456 −4.94185 4.56571i −0.231423 0.213809i
457457 −18.5887 18.5887i −0.869542 0.869542i 0.122880 0.992422i 0.460787π-0.460787\pi
−0.992422 + 0.122880i 0.960787π0.960787\pi
458458 20.1708 27.0170i 0.942518 1.26242i
459459 −7.15170 17.2657i −0.333813 0.805895i
460460 −4.70305 + 3.80987i −0.219281 + 0.177636i
461461 −11.2192 4.64714i −0.522530 0.216439i 0.105798 0.994388i 0.466260π-0.466260\pi
−0.628328 + 0.777949i 0.716260π0.716260\pi
462462 0.310450 1.22287i 0.0144435 0.0568929i
463463 18.8259i 0.874915i −0.899239 0.437458i 0.855879π-0.855879\pi
0.899239 0.437458i 0.144121π-0.144121\pi
464464 7.83905 1.45582i 0.363919 0.0675850i
465465 15.0217i 0.696616i
466466 37.9761 + 9.64103i 1.75921 + 0.446612i
467467 −35.1913 14.5767i −1.62846 0.674531i −0.633403 0.773822i 0.718342π-0.718342\pi
−0.995058 + 0.0992914i 0.968342π0.968342\pi
468468 8.28546 + 0.869317i 0.382996 + 0.0401842i
469469 −2.36033 5.69833i −0.108990 0.263124i
470470 25.2715 + 18.8675i 1.16569 + 0.870294i
471471 13.1177 + 13.1177i 0.604431 + 0.604431i
472472 −13.0806 28.3538i −0.602084 1.30509i
473473 −6.10566 + 6.10566i −0.280739 + 0.280739i
474474 8.64313 1.25400i 0.396992 0.0575979i
475475 −9.88909 + 4.09619i −0.453742 + 0.187946i
476476 5.11094 1.51494i 0.234260 0.0694371i
477477 8.12738 19.6212i 0.372127 0.898394i
478478 −17.7775 29.8751i −0.813122 1.36645i
479479 2.83141 0.129371 0.0646853 0.997906i 0.479396π-0.479396\pi
0.0646853 + 0.997906i 0.479396π0.479396\pi
480480 9.25938 18.7977i 0.422631 0.857992i
481481 14.6240 0.666795
482482 7.80883 + 13.1228i 0.355683 + 0.597725i
483483 0.323261 0.780422i 0.0147089 0.0355104i
484484 0.568379 + 1.91754i 0.0258354 + 0.0871607i
485485 38.9128 16.1182i 1.76694 0.731889i
486486 −20.5765 + 2.98536i −0.933370 + 0.135419i
487487 −0.948636 + 0.948636i −0.0429868 + 0.0429868i −0.728273 0.685287i 0.759677π-0.759677\pi
0.685287 + 0.728273i 0.259677π0.259677\pi
488488 −17.0097 6.26996i −0.769994 0.283828i
489489 4.87784 + 4.87784i 0.220584 + 0.220584i
490490 −23.2073 17.3265i −1.04840 0.782730i
491491 14.3747 + 34.7036i 0.648721 + 1.56615i 0.814612 + 0.580007i 0.196950π0.196950\pi
−0.165891 + 0.986144i 0.553050π0.553050\pi
492492 −1.05283 + 10.0345i −0.0474651 + 0.452390i
493493 6.37662 + 2.64128i 0.287189 + 0.118957i
494494 7.07342 + 1.79574i 0.318248 + 0.0807940i
495495 5.29519i 0.238001i
496496 8.83956 + 13.6009i 0.396908 + 0.610699i
497497 6.13072i 0.275001i
498498 2.10898 8.30730i 0.0945058 0.372259i
499499 −26.9875 11.1786i −1.20813 0.500422i −0.314510 0.949254i 0.601840π-0.601840\pi
−0.893616 + 0.448832i 0.851840π0.851840\pi
500500 −0.865834 1.06882i −0.0387213 0.0477991i
501501 −9.19300 22.1939i −0.410713 0.991548i
502502 −14.1591 + 18.9649i −0.631951 + 0.846445i
503503 11.9194 + 11.9194i 0.531459 + 0.531459i 0.921006 0.389548i 0.127369π-0.127369\pi
−0.389548 + 0.921006i 0.627369π0.627369\pi
504504 −0.142593 3.60423i −0.00635159 0.160545i
505505 −23.9270 + 23.9270i −1.06474 + 1.06474i
506506 0.192267 + 1.32519i 0.00854729 + 0.0589120i
507507 −7.15121 + 2.96213i −0.317597 + 0.131553i
508508 −1.13810 + 2.09702i −0.0504950 + 0.0930404i
509509 0.380641 0.918948i 0.0168716 0.0407316i −0.915219 0.402956i 0.867983π-0.867983\pi
0.932091 + 0.362225i 0.117983π0.117983\pi
510510 15.5883 9.27600i 0.690263 0.410748i
511511 −1.34487 −0.0594934
512512 −2.67791 22.4684i −0.118348 0.992972i
513513 −11.0773 −0.489073
514514 25.2445 15.0220i 1.11349 0.662592i
515515 −11.6883 + 28.2181i −0.515050 + 1.24344i
516516 9.54714 17.5912i 0.420289 0.774411i
517517 6.44626 2.67013i 0.283506 0.117432i
518518 −0.909125 6.26613i −0.0399447 0.275318i
519519 −14.9869 + 14.9869i −0.657851 + 0.657851i
520520 0.898504 + 22.7109i 0.0394020 + 0.995939i
521521 −9.33168 9.33168i −0.408828 0.408828i 0.472502 0.881330i 0.343351π-0.343351\pi
−0.881330 + 0.472502i 0.843351π0.843351\pi
522522 2.79398 3.74231i 0.122289 0.163796i
523523 11.0568 + 26.6934i 0.483480 + 1.16722i 0.957946 + 0.286949i 0.0926411π0.0926411\pi
−0.474466 + 0.880274i 0.657359π0.657359\pi
524524 25.5688 + 31.5631i 1.11698 + 1.37884i
525525 4.29845 + 1.78048i 0.187600 + 0.0777063i
526526 −7.04424 + 27.7473i −0.307144 + 1.20984i
527527 14.0420i 0.611678i
528528 −2.52632 3.88711i −0.109944 0.169165i
529529 22.1034i 0.961020i
530530 56.1601 + 14.2574i 2.43944 + 0.619303i
531531 −16.8982 6.99945i −0.733318 0.303750i
532532 0.329712 3.14248i 0.0142948 0.136244i
533533 −4.18804 10.1108i −0.181404 0.437948i
534534 −7.95617 5.94003i −0.344297 0.257050i
535535 −37.6223 37.6223i −1.62655 1.62655i
536536 −21.2649 7.83846i −0.918504 0.338570i
537537 9.54452 9.54452i 0.411877 0.411877i
538538 28.5491 4.14207i 1.23084 0.178577i
539539 −5.91975 + 2.45204i −0.254982 + 0.105617i
540540 −9.80442 33.0771i −0.421915 1.42341i
541541 −6.48221 + 15.6494i −0.278692 + 0.672822i −0.999800 0.0200006i 0.993633π-0.993633\pi
0.721108 + 0.692823i 0.243633π0.243633\pi
542542 −0.924959 1.55440i −0.0397304 0.0667670i
543543 8.23180 0.353260
544544 8.65545 17.5716i 0.371099 0.753376i
545545 −4.13197 −0.176994
546546 −1.62212 2.72598i −0.0694204 0.116661i
547547 8.37376 20.2160i 0.358036 0.864376i −0.637540 0.770417i 0.720048π-0.720048\pi
0.995576 0.0939585i 0.0299521π-0.0299521\pi
548548 30.6051 9.07169i 1.30739 0.387523i
549549 −9.81049 + 4.06364i −0.418702 + 0.173432i
550550 −7.29896 + 1.05898i −0.311229 + 0.0451549i
551551 2.89283 2.89283i 0.123239 0.123239i
552552 −1.30025 2.81845i −0.0553424 0.119961i
553553 2.90025 + 2.90025i 0.123331 + 0.123331i
554554 24.4582 + 18.2604i 1.03913 + 0.775809i
555555 −8.24516 19.9056i −0.349988 0.844945i
556556 28.5388 + 2.99431i 1.21031 + 0.126987i
557557 −22.4053 9.28058i −0.949344 0.393231i −0.146360 0.989231i 0.546756π-0.546756\pi
−0.802984 + 0.596000i 0.796756π0.796756\pi
558558 9.20937 + 2.33799i 0.389864 + 0.0989751i
559559 21.7097i 0.918222i
560560 9.67540 1.79686i 0.408860 0.0759312i
561561 4.01316i 0.169436i
562562 −1.64159 + 6.46625i −0.0692464 + 0.272762i
563563 15.2112 + 6.30068i 0.641075 + 0.265542i 0.679450 0.733722i 0.262218π-0.262218\pi
−0.0383755 + 0.999263i 0.512218π0.512218\pi
564564 −12.5672 + 10.1805i −0.529175 + 0.428677i
565565 23.6734 + 57.1527i 0.995949 + 2.40443i
566566 −0.536311 + 0.718343i −0.0225428 + 0.0301942i
567567 0.699364 + 0.699364i 0.0293705 + 0.0293705i
568568 16.5464 + 15.2870i 0.694272 + 0.641428i
569569 −17.8883 + 17.8883i −0.749915 + 0.749915i −0.974463 0.224548i 0.927910π-0.927910\pi
0.224548 + 0.974463i 0.427910π0.427910\pi
570570 −1.54379 10.6405i −0.0646622 0.445683i
571571 19.2874 7.98909i 0.807151 0.334333i 0.0593344 0.998238i 0.481102π-0.481102\pi
0.747817 + 0.663905i 0.231102π0.231102\pi
572572 4.41954 + 2.39858i 0.184790 + 0.100290i
573573 0.410943 0.992105i 0.0171674 0.0414458i
574574 −4.07197 + 2.42307i −0.169961 + 0.101137i
575575 −4.93807 −0.205932
576576 −10.0831 8.60232i −0.420130 0.358430i
577577 19.2320 0.800638 0.400319 0.916376i 0.368899π-0.368899\pi
0.400319 + 0.916376i 0.368899π0.368899\pi
578578 −6.08881 + 3.62321i −0.253261 + 0.150706i
579579 −1.91273 + 4.61775i −0.0794905 + 0.191907i
580580 11.1985 + 6.07768i 0.464994 + 0.252362i
581581 3.71872 1.54035i 0.154279 0.0639043i
582582 3.10133 + 21.3758i 0.128554 + 0.886056i
583583 9.06437 9.06437i 0.375408 0.375408i
584584 −3.35344 + 3.62971i −0.138766 + 0.150198i
585585 9.41396 + 9.41396i 0.389219 + 0.389219i
586586 −7.93823 + 10.6326i −0.327925 + 0.439228i
587587 −9.27341 22.3880i −0.382755 0.924051i −0.991431 0.130633i 0.958299π-0.958299\pi
0.608676 0.793419i 0.291701π-0.291701\pi
588588 11.5408 9.34899i 0.475933 0.385546i
589589 7.68963 + 3.18515i 0.316846 + 0.131242i
590590 12.2788 48.3661i 0.505509 1.99120i
591591 30.2654i 1.24495i
592592 −19.1788 13.1710i −0.788243 0.541323i
593593 16.9693i 0.696847i −0.937337 0.348423i 0.886717π-0.886717\pi
0.937337 0.348423i 0.113283π-0.113283\pi
594594 −7.39798 1.87813i −0.303543 0.0770608i
595595 7.87038 + 3.26002i 0.322654 + 0.133648i
596596 −19.6069 2.05717i −0.803129 0.0842650i
597597 −3.45907 8.35094i −0.141570 0.341781i
598598 2.69779 + 2.01415i 0.110321 + 0.0823649i
599599 10.9763 + 10.9763i 0.448480 + 0.448480i 0.894849 0.446369i 0.147283π-0.147283\pi
−0.446369 + 0.894849i 0.647283π0.647283\pi
600600 15.5236 7.16160i 0.633748 0.292371i
601601 −24.1575 + 24.1575i −0.985407 + 0.985407i −0.999895 0.0144882i 0.995388π-0.995388\pi
0.0144882 + 0.999895i 0.495388π0.495388\pi
602602 9.30225 1.34962i 0.379131 0.0550065i
603603 −12.2647 + 5.08021i −0.499457 + 0.206882i
604604 −15.8858 + 4.70871i −0.646382 + 0.191595i
605605 −1.22310 + 2.95283i −0.0497262 + 0.120050i
606606 −8.87380 14.9124i −0.360473 0.605776i
607607 −11.5860 −0.470261 −0.235131 0.971964i 0.575552π-0.575552\pi
−0.235131 + 0.971964i 0.575552π0.575552\pi
608608 −7.65921 8.72567i −0.310622 0.353872i
609609 −1.77825 −0.0720584
610610 −14.8147 24.8961i −0.599828 1.00801i
611611 6.71334 16.2074i 0.271593 0.655682i
612612 −3.26065 11.0004i −0.131804 0.444667i
613613 −6.31913 + 2.61747i −0.255227 + 0.105719i −0.506629 0.862164i 0.669109π-0.669109\pi
0.251402 + 0.967883i 0.419109π0.419109\pi
614614 −7.73911 + 1.12283i −0.312325 + 0.0453139i
615615 −11.4012 + 11.4012i −0.459741 + 0.459741i
616616 0.753002 2.04281i 0.0303393 0.0823073i
617617 −14.5350 14.5350i −0.585158 0.585158i 0.351158 0.936316i 0.385788π-0.385788\pi
−0.936316 + 0.351158i 0.885788π0.885788\pi
618618 −12.5511 9.37059i −0.504880 0.376940i
619619 6.68173 + 16.1311i 0.268561 + 0.648364i 0.999416 0.0341686i 0.0108783π-0.0108783\pi
−0.730855 + 0.682533i 0.760878π0.760878\pi
620620 −2.70493 + 25.7807i −0.108633 + 1.03538i
621621 −4.72133 1.95564i −0.189460 0.0784770i
622622 −13.6748 3.47165i −0.548311 0.139200i
623623 4.66295i 0.186817i
624624 −11.4020 2.41925i −0.456446 0.0968475i
625625 23.8778i 0.955111i
626626 5.31242 20.9257i 0.212327 0.836357i
627627 −2.19768 0.910308i −0.0877668 0.0363542i
628628 20.1509 + 24.8750i 0.804107 + 0.992621i
629629 −7.70739 18.6073i −0.307314 0.741921i
630630 3.44849 4.61896i 0.137391 0.184024i
631631 7.73226 + 7.73226i 0.307817 + 0.307817i 0.844062 0.536245i 0.180158π-0.180158\pi
−0.536245 + 0.844062i 0.680158π0.680158\pi
632632 15.0594 0.595789i 0.599030 0.0236992i
633633 5.74254 5.74254i 0.228246 0.228246i
634634 5.10216 + 35.1666i 0.202633 + 1.39664i
635635 −3.52266 + 1.45913i −0.139792 + 0.0579039i
636636 −14.1735 + 26.1157i −0.562017 + 1.03555i
637637 −6.16500 + 14.8836i −0.244266 + 0.589711i
638638 2.42246 1.44151i 0.0959062 0.0570700i
639639 13.1954 0.522000
640640 19.2761 30.5937i 0.761953 1.20932i
641641 −25.2046 −0.995522 −0.497761 0.867314i 0.665844π-0.665844\pi
−0.497761 + 0.867314i 0.665844π0.665844\pi
642642 23.4480 13.9530i 0.925417 0.550679i
643643 −1.80757 + 4.36386i −0.0712837 + 0.172094i −0.955506 0.294973i 0.904689π-0.904689\pi
0.884222 + 0.467067i 0.154689π0.154689\pi
644644 0.695319 1.28117i 0.0273994 0.0504853i
645645 29.5504 12.2402i 1.16355 0.481957i
646646 −1.44310 9.94652i −0.0567779 0.391341i
647647 −29.4720 + 29.4720i −1.15866 + 1.15866i −0.173902 + 0.984763i 0.555638π0.555638\pi
−0.984763 + 0.173902i 0.944362π0.944362\pi
648648 3.63141 0.143668i 0.142655 0.00564382i
649649 −7.80640 7.80640i −0.306428 0.306428i
650650 −11.0937 + 14.8590i −0.435129 + 0.582819i
651651 −1.38448 3.34242i −0.0542619 0.131000i
652652 7.49314 + 9.24983i 0.293454 + 0.362251i
653653 33.9870 + 14.0779i 1.33002 + 0.550910i 0.930660 0.365886i 0.119234π-0.119234\pi
0.399355 + 0.916796i 0.369234π0.369234\pi
654654 0.521407 2.05383i 0.0203886 0.0803110i
655655 64.9134i 2.53638i
656656 −3.61378 + 17.0319i −0.141095 + 0.664984i
657657 2.89460i 0.112929i
658658 −7.36197 1.86899i −0.286999 0.0728608i
659659 1.06355 + 0.440539i 0.0414302 + 0.0171610i 0.403302 0.915067i 0.367862π-0.367862\pi
−0.361872 + 0.932228i 0.617862π0.617862\pi
660660 0.773063 7.36806i 0.0300915 0.286802i
661661 −5.03257 12.1497i −0.195744 0.472569i 0.795281 0.606241i 0.207323π-0.207323\pi
−0.991026 + 0.133672i 0.957323π0.957323\pi
662662 28.2626 + 21.1007i 1.09846 + 0.820102i
663663 −7.13473 7.13473i −0.277090 0.277090i
664664 5.11537 13.8775i 0.198515 0.538550i
665665 3.57049 3.57049i 0.138458 0.138458i
666666 −13.4868 + 1.95674i −0.522602 + 0.0758221i
667667 1.74369 0.722261i 0.0675160 0.0279660i
668668 −11.7809 39.7451i −0.455816 1.53778i
669669 1.52423 3.67981i 0.0589300 0.142270i
670670 −18.5207 31.1241i −0.715518 1.20243i
671671 −6.40940 −0.247432
672672 −0.327781 + 5.03597i −0.0126444 + 0.194267i
673673 16.3757 0.631237 0.315618 0.948886i 0.397788π-0.397788\pi
0.315618 + 0.948886i 0.397788π0.397788\pi
674674 18.2521 + 30.6726i 0.703044 + 1.18147i
675675 10.7714 26.0044i 0.414590 1.00091i
676676 −12.8065 + 3.79598i −0.492558 + 0.145999i
677677 −7.18701 + 2.97696i −0.276219 + 0.114414i −0.516493 0.856291i 0.672763π-0.672763\pi
0.240274 + 0.970705i 0.422763π0.422763\pi
678678 −31.3955 + 4.55504i −1.20574 + 0.174935i
679679 −7.17278 + 7.17278i −0.275266 + 0.275266i
680680 28.4234 13.1128i 1.08999 0.502851i
681681 12.9585 + 12.9585i 0.496571 + 0.496571i
682682 4.59551 + 3.43098i 0.175971 + 0.131379i
683683 8.98311 + 21.6872i 0.343729 + 0.829836i 0.997332 + 0.0729982i 0.0232567π0.0232567\pi
−0.653603 + 0.756838i 0.726743π0.726743\pi
684684 −6.76366 0.709649i −0.258615 0.0271341i
685685 47.1291 + 19.5215i 1.80071 + 0.745878i
686686 14.1465 + 3.59138i 0.540115 + 0.137120i
687687 27.6313i 1.05420i
688688 19.5527 28.4715i 0.745439 1.08546i
689689 32.2299i 1.22786i
690690 1.22055 4.80774i 0.0464654 0.183027i
691691 22.5022 + 9.32071i 0.856023 + 0.354577i 0.767151 0.641467i 0.221674π-0.221674\pi
0.0888724 + 0.996043i 0.471674π0.471674\pi
692692 −28.4196 + 23.0222i −1.08035 + 0.875174i
693693 −0.488030 1.17821i −0.0185387 0.0447565i
694694 −13.1101 + 17.5599i −0.497653 + 0.666564i
695695 32.4258 + 32.4258i 1.22998 + 1.22998i
696696 −4.43408 + 4.79938i −0.168074 + 0.181920i
697697 −10.6576 + 10.6576i −0.403685 + 0.403685i
698698 −6.01136 41.4331i −0.227533 1.56827i
699699 −29.6654 + 12.2878i −1.12205 + 0.464768i
700700 7.05651 + 3.82971i 0.266711 + 0.144750i
701701 −7.18195 + 17.3388i −0.271259 + 0.654876i −0.999538 0.0304044i 0.990320π-0.990320\pi
0.728279 + 0.685281i 0.240320π0.240320\pi
702702 −16.4914 + 9.81337i −0.622427 + 0.370382i
703703 −11.9380 −0.450248
704704 −3.63580 7.12607i −0.137029 0.268574i
705705 −25.8460 −0.973417
706706 −8.21880 + 4.89068i −0.309319 + 0.184063i
707707 3.11867 7.52913i 0.117290 0.283162i
708708 22.4913 + 12.2065i 0.845276 + 0.458749i
709709 −4.87997 + 2.02135i −0.183271 + 0.0759134i −0.472432 0.881367i 0.656624π-0.656624\pi
0.289161 + 0.957281i 0.406624π0.406624\pi
710710 5.16895 + 35.6269i 0.193987 + 1.33705i
711711 6.24231 6.24231i 0.234105 0.234105i
712712 −12.5850 11.6271i −0.471642 0.435744i
713713 2.71514 + 2.71514i 0.101683 + 0.101683i
714714 −2.61357 + 3.50066i −0.0978104 + 0.131009i
715715 3.07517 + 7.42411i 0.115005 + 0.277646i
716716 18.0992 14.6619i 0.676400 0.547941i
717717 26.3216 + 10.9027i 0.982997 + 0.407171i
718718 −8.77179 + 34.5521i −0.327360 + 1.28947i
719719 12.6660i 0.472363i −0.971709 0.236182i 0.924104π-0.924104\pi
0.971709 0.236182i 0.0758960π-0.0758960\pi
720720 −3.86744 20.8247i −0.144131 0.776090i
721721 7.35595i 0.273950i
722722 20.2697 + 5.14588i 0.754358 + 0.191510i
723723 −11.5619 4.78908i −0.429991 0.178108i
724724 14.1276 + 1.48228i 0.525050 + 0.0550886i
725725 3.97810 + 9.60399i 0.147743 + 0.356683i
726726 −1.31339 0.980566i −0.0487443 0.0363922i
727727 −29.3015 29.3015i −1.08673 1.08673i −0.995863 0.0908704i 0.971035π-0.971035\pi
−0.0908704 0.995863i 0.528965π-0.528965\pi
728728 −2.29307 4.97049i −0.0849868 0.184219i
729729 14.7745 14.7745i 0.547203 0.547203i
730730 −7.81529 + 1.13389i −0.289257 + 0.0419671i
731731 27.6230 11.4418i 1.02168 0.423192i
732732 14.2442 4.22214i 0.526481 0.156055i
733733 7.21333 17.4145i 0.266430 0.643220i −0.732880 0.680358i 0.761824π-0.761824\pi
0.999310 + 0.0371385i 0.0118243π0.0118243\pi
734734 15.0368 + 25.2694i 0.555019 + 0.932711i
735735 23.7350 0.875477
736736 −1.72402 5.07123i −0.0635481 0.186928i
737737 −8.01278 −0.295155
738738 5.21524 + 8.76423i 0.191976 + 0.322616i
739739 5.51588 13.3165i 0.202905 0.489855i −0.789370 0.613918i 0.789592π-0.789592\pi
0.992274 + 0.124063i 0.0395924π0.0395924\pi
740740 −10.5662 35.6472i −0.388422 1.31042i
741741 −5.52548 + 2.28873i −0.202984 + 0.0840786i
742742 −13.8100 + 2.00363i −0.506980 + 0.0735556i
743743 −35.4362 + 35.4362i −1.30003 + 1.30003i −0.371657 + 0.928370i 0.621210π0.621210\pi
−0.928370 + 0.371657i 0.878790π0.878790\pi
744744 −12.4732 4.59774i −0.457289 0.168561i
745745 −22.2774 22.2774i −0.816180 0.816180i
746746 −29.9596 22.3677i −1.09690 0.818938i
747747 −3.31534 8.00393i −0.121302 0.292848i
748748 0.722641 6.88749i 0.0264224 0.251832i
749749 11.8386 + 4.90372i 0.432574 + 0.179178i
750750 1.09261 + 0.277382i 0.0398965 + 0.0101286i
751751 36.4981i 1.33184i −0.746025 0.665918i 0.768040π-0.768040\pi
0.746025 0.665918i 0.231960π-0.231960\pi
752752 −23.4014 + 15.2091i −0.853361 + 0.554620i
753753 19.3961i 0.706832i
754754 1.74397 6.86950i 0.0635115 0.250172i
755755 −24.4626 10.1327i −0.890286 0.368768i
756756 5.23009 + 6.45622i 0.190216 + 0.234811i
757757 11.4221 + 27.5754i 0.415144 + 1.00225i 0.983735 + 0.179626i 0.0574888π0.0574888\pi
−0.568591 + 0.822620i 0.692511π0.692511\pi
758758 −10.1170 + 13.5508i −0.367464 + 0.492188i
759759 −0.775980 0.775980i −0.0281663 0.0281663i
760760 −0.733474 18.5396i −0.0266059 0.672501i
761761 25.9070 25.9070i 0.939128 0.939128i −0.0591223 0.998251i 0.518830π-0.518830\pi
0.998251 + 0.0591223i 0.0188302π0.0188302\pi
762762 −0.280754 1.93509i −0.0101706 0.0701010i
763763 0.919386 0.380822i 0.0332840 0.0137867i
764764 0.883919 1.62868i 0.0319791 0.0589236i
765765 7.01665 16.9397i 0.253687 0.612455i
766766 −22.2588 + 13.2454i −0.804244 + 0.478574i
767767 −27.7570 −1.00225
768768 12.7744 + 13.4419i 0.460958 + 0.485043i
769769 11.7538 0.423855 0.211927 0.977285i 0.432026π-0.432026\pi
0.211927 + 0.977285i 0.432026π0.432026\pi
770770 2.98994 1.77919i 0.107750 0.0641177i
771771 −9.21285 + 22.2418i −0.331793 + 0.801018i
772772 −4.11420 + 7.58069i −0.148073 + 0.272835i
773773 −17.1842 + 7.11792i −0.618072 + 0.256014i −0.669676 0.742654i 0.733567π-0.733567\pi
0.0516034 + 0.998668i 0.483567π0.483567\pi
774774 −2.90484 20.0215i −0.104412 0.719659i
775775 −14.9546 + 14.9546i −0.537184 + 0.537184i
776776 1.47348 + 37.2442i 0.0528949 + 1.33699i
777777 3.66919 + 3.66919i 0.131632 + 0.131632i
778778 12.3943 16.6011i 0.444357 0.595178i
779779 3.41882 + 8.25376i 0.122492 + 0.295722i
780780 −11.7248 14.4736i −0.419816 0.518237i
781781 7.35831 + 3.04791i 0.263301 + 0.109063i
782782 1.14094 4.49416i 0.0407998 0.160711i
783783 10.7579i 0.384456i
784784 21.4900 13.9669i 0.767501 0.498817i
785785 51.1585i 1.82592i
786786 −32.2657 8.19133i −1.15088 0.292175i
787787 −23.7898 9.85404i −0.848013 0.351259i −0.0840052 0.996465i 0.526771π-0.526771\pi
−0.764008 + 0.645207i 0.776771π0.776771\pi
788788 5.44983 51.9423i 0.194142 1.85037i
789789 −8.97813 21.6751i −0.319630 0.771655i
790790 19.2992 + 14.4087i 0.686635 + 0.512638i
791791 −10.5349 10.5349i −0.374579 0.374579i
792792 −4.39681 1.62071i −0.156234 0.0575895i
793793 −11.3948 + 11.3948i −0.404643 + 0.404643i
794794 −48.4756 + 7.03312i −1.72034 + 0.249596i
795795 −43.8701 + 18.1716i −1.55591 + 0.644480i
796796 −4.43282 14.9550i −0.157117 0.530065i
797797 5.34885 12.9133i 0.189466 0.457411i −0.800391 0.599478i 0.795375π-0.795375\pi
0.989857 + 0.142067i 0.0453749π0.0453749\pi
798798 1.32419 + 2.22530i 0.0468756 + 0.0787746i
799799 −24.1602 −0.854728
800800 27.9316 9.49563i 0.987531 0.335721i
801801 −10.0362 −0.354612
802802 9.44039 + 15.8646i 0.333352 + 0.560198i
803803 −0.668606 + 1.61416i −0.0235946 + 0.0569624i
804804 17.8076 5.27836i 0.628025 0.186153i
805805 2.15216 0.891455i 0.0758537 0.0314196i
806806 14.2698 2.07034i 0.502631 0.0729246i
807807 −16.7172 + 16.7172i −0.588473 + 0.588473i
808808 −12.5442 27.1910i −0.441304 0.956577i
809809 2.78835 + 2.78835i 0.0980333 + 0.0980333i 0.754422 0.656389i 0.227917π-0.227917\pi
−0.656389 + 0.754422i 0.727917π0.727917\pi
810810 4.65380 + 3.47450i 0.163518 + 0.122081i
811811 −21.3595 51.5664i −0.750034 1.81074i −0.559019 0.829155i 0.688822π-0.688822\pi
−0.191015 0.981587i 0.561178π-0.561178\pi
812812 −3.05189 0.320206i −0.107100 0.0112370i
813813 1.36951 + 0.567268i 0.0480307 + 0.0198950i
814814 −7.97280 2.02406i −0.279447 0.0709434i
815815 19.0234i 0.666360i
816816 2.93109 + 15.7828i 0.102609 + 0.552507i
817817 17.7222i 0.620023i
818818 −6.84706 + 26.9706i −0.239402 + 0.943005i
819819 −2.96229 1.22702i −0.103511 0.0428756i
820820 −21.6201 + 17.5141i −0.755006 + 0.611618i
821821 12.3726 + 29.8701i 0.431806 + 1.04247i 0.978705 + 0.205273i 0.0658083π0.0658083\pi
−0.546899 + 0.837199i 0.684192π0.684192\pi
822822 −15.6505 + 20.9625i −0.545873 + 0.731150i
823823 −6.06607 6.06607i −0.211450 0.211450i 0.593433 0.804883i 0.297772π-0.297772\pi
−0.804883 + 0.593433i 0.797772π0.797772\pi
824824 −19.8532 18.3421i −0.691620 0.638978i
825825 4.27398 4.27398i 0.148801 0.148801i
826826 1.72556 + 11.8934i 0.0600400 + 0.413825i
827827 −28.5678 + 11.8332i −0.993399 + 0.411479i −0.819372 0.573262i 0.805678π-0.805678\pi
−0.174027 + 0.984741i 0.555678π0.555678\pi
828828 −2.75751 1.49656i −0.0958301 0.0520090i
829829 −7.99577 + 19.3035i −0.277704 + 0.670438i −0.999771 0.0213854i 0.993192π-0.993192\pi
0.722067 + 0.691823i 0.243192π0.243192\pi
830830 20.3115 12.0866i 0.705024 0.419532i
831831 −25.0143 −0.867737
832832 −19.1328 6.20512i −0.663311 0.215124i
833833 22.1869 0.768730
834834 −20.2093 + 12.0257i −0.699790 + 0.416417i
835835 25.3514 61.2038i 0.877323 2.11804i
836836 −3.60780 1.95803i −0.124778 0.0677198i
837837 −20.2207 + 8.37568i −0.698929 + 0.289506i
838838 −6.40991 44.1802i −0.221427 1.52618i
839839 −0.981871 + 0.981871i −0.0338980 + 0.0338980i −0.723853 0.689955i 0.757630π-0.757630\pi
0.689955 + 0.723853i 0.257630π0.257630\pi
840840 −5.47279 + 5.92367i −0.188829 + 0.204386i
841841 17.6967 + 17.6967i 0.610230 + 0.610230i
842842 −17.2771 + 23.1412i −0.595409 + 0.797500i
843843 −2.09227 5.05118i −0.0720616 0.173972i
844844 10.8896 8.82146i 0.374834 0.303647i
845845 −19.7208 8.16864i −0.678417 0.281010i
846846 −4.02269 + 15.8454i −0.138303 + 0.544776i
847847 0.769748i 0.0264489i
848848 −29.0276 + 42.2683i −0.996812 + 1.45150i
849849 0.734674i 0.0252140i
850850 24.7532 + 6.28411i 0.849026 + 0.215543i
851851 −5.08817 2.10759i −0.174420 0.0722472i
852852 −18.3609 1.92644i −0.629033 0.0659987i
853853 −2.73939 6.61346i −0.0937948 0.226441i 0.870018 0.493019i 0.164107π-0.164107\pi
−0.963813 + 0.266579i 0.914107π0.914107\pi
854854 5.59089 + 4.17412i 0.191316 + 0.142836i
855855 −7.68488 7.68488i −0.262817 0.262817i
856856 42.7545 19.7242i 1.46132 0.674160i
857857 10.5144 10.5144i 0.359165 0.359165i −0.504340 0.863505i 0.668264π-0.668264\pi
0.863505 + 0.504340i 0.168264π0.168264\pi
858858 −4.07826 + 0.591698i −0.139230 + 0.0202002i
859859 19.3962 8.03415i 0.661789 0.274122i −0.0264024 0.999651i 0.508405π-0.508405\pi
0.688191 + 0.725530i 0.258405π0.258405\pi
860860 52.9193 15.6859i 1.80453 0.534884i
861861 1.48604 3.58763i 0.0506442 0.122266i
862862 26.4072 + 44.3774i 0.899433 + 1.51150i
863863 −24.2050 −0.823948 −0.411974 0.911196i 0.635161π-0.635161\pi
−0.411974 + 0.911196i 0.635161π0.635161\pi
864864 30.4662 + 1.98298i 1.03648 + 0.0674624i
865865 −58.4483 −1.98730
866866 −11.2092 18.8372i −0.380906 0.640113i
867867 2.22208 5.36458i 0.0754658 0.182191i
868868 −1.77421 5.98566i −0.0602207 0.203166i
869869 4.92286 2.03911i 0.166997 0.0691722i
870870 −10.3338 + 1.49928i −0.350348 + 0.0508305i
871871 −14.2454 + 14.2454i −0.482687 + 0.482687i
872872 1.26468 3.43095i 0.0428275 0.116186i
873873 15.4382 + 15.4382i 0.522504 + 0.522504i
874874 −2.20228 1.64421i −0.0744933 0.0556163i
875875 0.202593 + 0.489102i 0.00684889 + 0.0165347i
876876 0.422593 4.02774i 0.0142781 0.136085i
877877 22.9668 + 9.51317i 0.775534 + 0.321237i 0.735112 0.677946i 0.237130π-0.237130\pi
0.0404224 + 0.999183i 0.487130π0.487130\pi
878878 5.67458 + 1.44061i 0.191508 + 0.0486183i
879879 10.8743i 0.366782i
880880 2.65351 12.5061i 0.0894497 0.421580i
881881 8.10838i 0.273178i 0.990628 + 0.136589i 0.0436140π0.0436140\pi
−0.990628 + 0.136589i 0.956386π0.956386\pi
882882 3.69412 14.5512i 0.124388 0.489964i
883883 −15.8996 6.58581i −0.535063 0.221630i 0.0987563 0.995112i 0.468514π-0.468514\pi
−0.633819 + 0.773481i 0.718514π0.718514\pi
884884 −10.9601 13.5295i −0.368627 0.455048i
885885 15.6497 + 37.7818i 0.526059 + 1.27002i
886886 −25.3113 + 33.9023i −0.850349 + 1.13897i
887887 7.11744 + 7.11744i 0.238980 + 0.238980i 0.816428 0.577448i 0.195951π-0.195951\pi
−0.577448 + 0.816428i 0.695951π0.695951\pi
888888 19.0521 0.753750i 0.639345 0.0252942i
889889 0.649331 0.649331i 0.0217779 0.0217779i
890890 −3.93143 27.0973i −0.131782 0.908304i
891891 1.18709 0.491710i 0.0397691 0.0164729i
892892 3.27854 6.04093i 0.109774 0.202265i
893893 −5.48029 + 13.2306i −0.183391 + 0.442745i
894894 13.8843 8.26199i 0.464360 0.276322i
895895 37.2233 1.24424
896896 −1.46937 + 8.58386i −0.0490881 + 0.286767i
897897 −2.75912 −0.0921245
898898 −18.4849 + 10.9996i −0.616848 + 0.367062i
899899 3.09333 7.46795i 0.103168 0.249070i
900900 8.24282 15.1879i 0.274761 0.506265i
901901 −41.0088 + 16.9864i −1.36620 + 0.565899i
902902 0.883856 + 6.09196i 0.0294292 + 0.202840i
903903 −5.44702 + 5.44702i −0.181266 + 0.181266i
904904 −54.7021 + 2.16416i −1.81936 + 0.0719789i
905905 16.0519 + 16.0519i 0.533582 + 0.533582i
906906 8.12346 10.8807i 0.269884 0.361487i
907907 −0.0171283 0.0413514i −0.000568736 0.00137305i 0.923595 0.383370i 0.125237π-0.125237\pi
−0.924164 + 0.381997i 0.875237π0.875237\pi
908908 19.9063 + 24.5732i 0.660615 + 0.815489i
909909 −16.2052 6.71241i −0.537492 0.222637i
910910 2.15250 8.47872i 0.0713547 0.281067i
911911 16.2134i 0.537173i −0.963256 0.268586i 0.913443π-0.913443\pi
0.963256 0.268586i 0.0865565π-0.0865565\pi
912912 9.30779 + 1.97490i 0.308212 + 0.0653956i
913913 5.22913i 0.173059i
914914 36.0343 + 9.14806i 1.19191 + 0.302591i
915915 21.9348 + 9.08569i 0.725142 + 0.300364i
916916 −4.97551 + 47.4216i −0.164395 + 1.56685i
917917 −5.98274 14.4436i −0.197567 0.476970i
918918 21.1780 + 15.8113i 0.698977 + 0.521852i
919919 30.4938 + 30.4938i 1.00590 + 1.00590i 0.999983 + 0.00591395i 0.00188248π0.00188248\pi
0.00591395 + 0.999983i 0.498118π0.498118\pi
920920 2.96045 8.03139i 0.0976033 0.264787i
921921 4.53171 4.53171i 0.149325 0.149325i
922922 16.9957 2.46583i 0.559722 0.0812077i
923923 18.5005 7.66317i 0.608952 0.252236i
924924 0.507066 + 1.71069i 0.0166812 + 0.0562774i
925925 11.6083 28.0249i 0.381678 0.921453i
926926 13.6147 + 22.8795i 0.447406 + 0.751867i
927927 −15.8324 −0.520006
928928 −8.47411 + 7.43840i −0.278176 + 0.244177i
929929 16.0909 0.527926 0.263963 0.964533i 0.414970π-0.414970\pi
0.263963 + 0.964533i 0.414970π0.414970\pi
930930 −10.8635 18.2562i −0.356229 0.598644i
931931 5.03267 12.1499i 0.164939 0.398198i
932932 −53.1253 + 15.7469i −1.74018 + 0.515807i
933933 10.6823 4.42474i 0.349721 0.144859i
934934 53.3104 7.73458i 1.74437 0.253083i
935935 7.82558 7.82558i 0.255924 0.255924i
936936 −10.6982 + 4.93545i −0.349680 + 0.161320i
937937 18.5678 + 18.5678i 0.606584 + 0.606584i 0.942052 0.335468i 0.108894π-0.108894\pi
−0.335468 + 0.942052i 0.608894π0.608894\pi
938938 6.98951 + 5.21833i 0.228216 + 0.170384i
939939 6.77086 + 16.3463i 0.220959 + 0.533442i
940940 −44.3576 4.65404i −1.44679 0.151798i
941941 −46.9249 19.4369i −1.52971 0.633626i −0.550201 0.835033i 0.685449π-0.685449\pi
−0.979508 + 0.201407i 0.935449π0.935449\pi
942942 −25.4287 6.45561i −0.828512 0.210335i
943943 4.12148i 0.134214i
944944 36.4022 + 24.9991i 1.18479 + 0.813652i
945945 13.2780i 0.431934i
946946 3.00478 11.8359i 0.0976939 0.384817i
947947 30.9941 + 12.8382i 1.00717 + 0.417185i 0.824423 0.565975i 0.191500π-0.191500\pi
0.182750 + 0.983159i 0.441500π0.441500\pi
948948 −9.59729 + 7.77461i −0.311705 + 0.252508i
949949 1.68103 + 4.05837i 0.0545686 + 0.131740i
950950 9.05607 12.1298i 0.293818 0.393544i
951951 −20.5921 20.5921i −0.667745 0.667745i
952952 −5.11584 + 5.53731i −0.165805 + 0.179465i
953953 21.3166 21.3166i 0.690513 0.690513i −0.271832 0.962345i 0.587629π-0.587629\pi
0.962345 + 0.271832i 0.0876294π0.0876294\pi
954954 4.31248 + 29.7237i 0.139622 + 0.962339i
955955 2.73592 1.13325i 0.0885322 0.0366713i
956956 43.2106 + 23.4513i 1.39753 + 0.758468i
957957 −0.884065 + 2.13432i −0.0285778 + 0.0689928i
958958 −3.44107 + 2.04764i −0.111176 + 0.0661564i
959959 −12.2857 −0.396725
960960 2.34114 + 29.5414i 0.0755599 + 0.953445i
961961 −14.5548 −0.469510
962962 −17.7728 + 10.5759i −0.573017 + 0.340980i
963963 10.5544 25.4807i 0.340112 0.821103i
964964 −18.9804 10.3011i −0.611319 0.331775i
965965 −12.7343 + 5.27473i −0.409932 + 0.169799i
966966 0.171526 + 1.18224i 0.00551876 + 0.0380380i
967967 2.35492 2.35492i 0.0757292 0.0757292i −0.668228 0.743957i 0.732947π-0.732947\pi
0.743957 + 0.668228i 0.232947π0.232947\pi
968968 −2.07750 1.91937i −0.0667734 0.0616910i
969969 5.82428 + 5.82428i 0.187103 + 0.187103i
970970 −35.6349 + 47.7300i −1.14417 + 1.53252i
971971 2.59167 + 6.25684i 0.0831706 + 0.200792i 0.959994 0.280021i 0.0903416π-0.0903416\pi
−0.876823 + 0.480813i 0.840342π0.840342\pi
972972 22.8481 18.5089i 0.732852 0.593672i
973973 −10.2034 4.22640i −0.327107 0.135492i
974974 0.466853 1.83894i 0.0149589 0.0589234i
975975 15.1968i 0.486688i
976976 25.2066 4.68123i 0.806843 0.149842i
977977 31.7772i 1.01664i −0.861167 0.508322i 0.830266π-0.830266\pi
0.861167 0.508322i 0.169734π-0.169734\pi
978978 −9.45572 2.40054i −0.302361 0.0767606i
979979 −5.59663 2.31820i −0.178869 0.0740901i
980980 40.7346 + 4.27391i 1.30122 + 0.136525i
981981 −0.819656 1.97882i −0.0261696 0.0631790i
982982 −42.5670 31.7803i −1.35837 1.01415i
983983 −11.1801 11.1801i −0.356589 0.356589i 0.505965 0.862554i 0.331137π-0.331137\pi
−0.862554 + 0.505965i 0.831137π0.831137\pi
984984 −5.97731 12.9565i −0.190550 0.413038i
985985 59.0170 59.0170i 1.88044 1.88044i
986986 −9.65977 + 1.40149i −0.307630 + 0.0446327i
987987 5.75088 2.38209i 0.183053 0.0758229i
988988 −9.89511 + 2.93302i −0.314805 + 0.0933117i
989989 3.12878 7.55354i 0.0994894 0.240189i
990990 −3.82941 6.43534i −0.121707 0.204528i
991991 41.8311 1.32881 0.664404 0.747374i 0.268686π-0.268686\pi
0.664404 + 0.747374i 0.268686π0.268686\pi
992992 −20.5789 10.1368i −0.653381 0.321843i
993993 −28.9052 −0.917278
994994 −4.43366 7.45078i −0.140627 0.236324i
995995 9.53905 23.0293i 0.302408 0.730078i
996996 3.44465 + 11.6212i 0.109148 + 0.368232i
997997 45.5709 18.8761i 1.44324 0.597811i 0.482662 0.875807i 0.339670π-0.339670\pi
0.960582 + 0.277996i 0.0896701π0.0896701\pi
998998 40.8826 5.93148i 1.29412 0.187758i
999999 22.1975 22.1975i 0.702299 0.702299i
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 352.2.n.a.45.7 160
32.5 even 8 inner 352.2.n.a.133.7 yes 160
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
352.2.n.a.45.7 160 1.1 even 1 trivial
352.2.n.a.133.7 yes 160 32.5 even 8 inner