Properties

Label 45.3.k.a.13.2
Level 4545
Weight 33
Character 45.13
Analytic conductor 1.2261.226
Analytic rank 00
Dimension 4040
Inner twists 44

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [45,3,Mod(7,45)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(45, base_ring=CyclotomicField(12))
 
chi = DirichletCharacter(H, H._module([8, 3]))
 
N = Newforms(chi, 3, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("45.7");
 
S:= CuspForms(chi, 3);
 
N := Newforms(S);
 
Level: N N == 45=325 45 = 3^{2} \cdot 5
Weight: k k == 3 3
Character orbit: [χ][\chi] == 45.k (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: 1.226161189621.22616118962
Analytic rank: 00
Dimension: 4040
Relative dimension: 1010 over Q(ζ12)\Q(\zeta_{12})
Twist minimal: yes
Sato-Tate group: SU(2)[C12]\mathrm{SU}(2)[C_{12}]

Embedding invariants

Embedding label 13.2
Character χ\chi == 45.13
Dual form 45.3.k.a.7.2

qq-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
f(q)f(q) == q+(3.224230.863931i)q2+(1.086212.79645i)q3+(6.18520+3.57103i)q4+(4.889991.04305i)q5+(5.91814+8.07800i)q6+(8.799702.35787i)q7+(7.416207.41620i)q8+(6.640286.07508i)q9+(14.8654+7.58766i)q10+(1.02371+1.77311i)q11+(16.704613.4177i)q12+(4.182691.12075i)q13+(26.3352+15.2047i)q14+(8.22842+12.5417i)q15+(3.22036+5.57783i)q16+(17.158517.1585i)q17+(16.1614+25.3242i)q1818.6363iq19+(26.520823.9138i)q20+(16.1520+22.0468i)q21+(1.768826.60133i)q22+(11.5078+3.08350i)q23+(28.7946+12.6835i)q24+(22.8241+10.2010i)q2514.4542q26+(24.2014+11.9704i)q27+(46.007946.0079i)q28+(19.491811.2536i)q29+(37.365533.3284i)q30+(11.936820.6752i)q31+(5.29373+19.7565i)q32+(6.070380.936770i)q33+(70.1467+40.4992i)q34+(40.5711+20.7085i)q35+(19.377261.2882i)q36+(33.2840+33.2840i)q37+(16.1005+60.0877i)q38+(1.4091712.9141i)q39+(28.5297+44.0007i)q40+(2.157563.73700i)q41+(71.124757.1297i)q42+(8.1505130.4181i)q43+14.6227iq44+(26.1343+36.6333i)q45+39.7677q46+(0.8389900.224807i)q47+(19.09612.94688i)q48+(29.4398+16.9971i)q49+(64.777252.6090i)q50+(29.345166.6207i)q51+(29.8730+8.00445i)q52+(3.333163.33316i)q53+(88.372717.6870i)q54+(3.156479.73828i)q55+(47.7739+82.7467i)q56+(52.115520.2430i)q57+(72.5684+19.4446i)q58+(66.325438.2930i)q59+(95.6810+48.1888i)q60+(35.3623+61.2493i)q61+(56.3490+56.3490i)q62+(44.1082+69.1158i)q6394.0358iq64+(21.6223+1.11769i)q65+(20.38162.22403i)q66+(5.59919+20.8965i)q67+(167.40244.8553i)q68+(3.87703+35.5302i)q69+(112.920101.820i)q7028.6105q71+(4.19166+94.2997i)q72+(48.1316+48.1316i)q73+(136.07178.5604i)q74+(53.318552.7460i)q75+(66.5507115.269i)q76+(4.8275318.0166i)q77+(15.7004+40.4205i)q78+(0.201686+0.116444i)q79+(9.9295930.6346i)q80+(7.18677+80.6805i)q81+(10.1850+10.1850i)q82+(41.1240153.477i)q83+(178.633+78.6845i)q84+(101.802+66.0077i)q85+(52.5583+91.0337i)q86+(10.297966.7316i)q87+(5.5577420.7418i)q88+103.385iq89+(52.6145140.692i)q9039.4490q91+(82.189122.0225i)q92+(44.851255.8384i)q93+(2.51088+1.44966i)q94+(19.4386+91.1313i)q95+(60.9981+6.65606i)q96+(69.7287+18.6837i)q97+(80.236680.2366i)q98+(3.9740917.9931i)q99+O(q100)q+(-3.22423 - 0.863931i) q^{2} +(1.08621 - 2.79645i) q^{3} +(6.18520 + 3.57103i) q^{4} +(-4.88999 - 1.04305i) q^{5} +(-5.91814 + 8.07800i) q^{6} +(-8.79970 - 2.35787i) q^{7} +(-7.41620 - 7.41620i) q^{8} +(-6.64028 - 6.07508i) q^{9} +(14.8654 + 7.58766i) q^{10} +(1.02371 + 1.77311i) q^{11} +(16.7046 - 13.4177i) q^{12} +(4.18269 - 1.12075i) q^{13} +(26.3352 + 15.2047i) q^{14} +(-8.22842 + 12.5417i) q^{15} +(3.22036 + 5.57783i) q^{16} +(17.1585 - 17.1585i) q^{17} +(16.1614 + 25.3242i) q^{18} -18.6363i q^{19} +(-26.5208 - 23.9138i) q^{20} +(-16.1520 + 22.0468i) q^{21} +(-1.76882 - 6.60133i) q^{22} +(-11.5078 + 3.08350i) q^{23} +(-28.7946 + 12.6835i) q^{24} +(22.8241 + 10.2010i) q^{25} -14.4542 q^{26} +(-24.2014 + 11.9704i) q^{27} +(-46.0079 - 46.0079i) q^{28} +(19.4918 - 11.2536i) q^{29} +(37.3655 - 33.3284i) q^{30} +(11.9368 - 20.6752i) q^{31} +(5.29373 + 19.7565i) q^{32} +(6.07038 - 0.936770i) q^{33} +(-70.1467 + 40.4992i) q^{34} +(40.5711 + 20.7085i) q^{35} +(-19.3772 - 61.2882i) q^{36} +(-33.2840 + 33.2840i) q^{37} +(-16.1005 + 60.0877i) q^{38} +(1.40917 - 12.9141i) q^{39} +(28.5297 + 44.0007i) q^{40} +(2.15756 - 3.73700i) q^{41} +(71.1247 - 57.1297i) q^{42} +(8.15051 - 30.4181i) q^{43} +14.6227i q^{44} +(26.1343 + 36.6333i) q^{45} +39.7677 q^{46} +(-0.838990 - 0.224807i) q^{47} +(19.0961 - 2.94688i) q^{48} +(29.4398 + 16.9971i) q^{49} +(-64.7772 - 52.6090i) q^{50} +(-29.3451 - 66.6207i) q^{51} +(29.8730 + 8.00445i) q^{52} +(-3.33316 - 3.33316i) q^{53} +(88.3727 - 17.6870i) q^{54} +(-3.15647 - 9.73828i) q^{55} +(47.7739 + 82.7467i) q^{56} +(-52.1155 - 20.2430i) q^{57} +(-72.5684 + 19.4446i) q^{58} +(-66.3254 - 38.2930i) q^{59} +(-95.6810 + 48.1888i) q^{60} +(35.3623 + 61.2493i) q^{61} +(-56.3490 + 56.3490i) q^{62} +(44.1082 + 69.1158i) q^{63} -94.0358i q^{64} +(-21.6223 + 1.11769i) q^{65} +(-20.3816 - 2.22403i) q^{66} +(5.59919 + 20.8965i) q^{67} +(167.402 - 44.8553i) q^{68} +(-3.87703 + 35.5302i) q^{69} +(-112.920 - 101.820i) q^{70} -28.6105 q^{71} +(4.19166 + 94.2997i) q^{72} +(48.1316 + 48.1316i) q^{73} +(136.071 - 78.5604i) q^{74} +(53.3185 - 52.7460i) q^{75} +(66.5507 - 115.269i) q^{76} +(-4.82753 - 18.0166i) q^{77} +(-15.7004 + 40.4205i) q^{78} +(-0.201686 + 0.116444i) q^{79} +(-9.92959 - 30.6346i) q^{80} +(7.18677 + 80.6805i) q^{81} +(-10.1850 + 10.1850i) q^{82} +(41.1240 - 153.477i) q^{83} +(-178.633 + 78.6845i) q^{84} +(-101.802 + 66.0077i) q^{85} +(-52.5583 + 91.0337i) q^{86} +(-10.2979 - 66.7316i) q^{87} +(5.55774 - 20.7418i) q^{88} +103.385i q^{89} +(-52.6145 - 140.692i) q^{90} -39.4490 q^{91} +(-82.1891 - 22.0225i) q^{92} +(-44.8512 - 55.8384i) q^{93} +(2.51088 + 1.44966i) q^{94} +(-19.4386 + 91.1313i) q^{95} +(60.9981 + 6.65606i) q^{96} +(69.7287 + 18.6837i) q^{97} +(-80.2366 - 80.2366i) q^{98} +(3.97409 - 17.9931i) q^{99} +O(q^{100})
Tr(f)(q)\operatorname{Tr}(f)(q) == 40q2q26q32q524q62q724q88q10+8q1130q122q1330q15+28q16+28q17+48q18114q20+12q21+14q22+82q23+1876q98+O(q100) 40 q - 2 q^{2} - 6 q^{3} - 2 q^{5} - 24 q^{6} - 2 q^{7} - 24 q^{8} - 8 q^{10} + 8 q^{11} - 30 q^{12} - 2 q^{13} - 30 q^{15} + 28 q^{16} + 28 q^{17} + 48 q^{18} - 114 q^{20} + 12 q^{21} + 14 q^{22} + 82 q^{23}+ \cdots - 1876 q^{98}+O(q^{100}) Copy content Toggle raw display

Character values

We give the values of χ\chi on generators for (Z/45Z)×\left(\mathbb{Z}/45\mathbb{Z}\right)^\times.

nn 1111 3737
χ(n)\chi(n) e(13)e\left(\frac{1}{3}\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 −3.22423 0.863931i −1.61212 0.431965i −0.663444 0.748226i 0.730906π-0.730906\pi
−0.948672 + 0.316261i 0.897573π0.897573\pi
33 1.08621 2.79645i 0.362071 0.932151i
44 6.18520 + 3.57103i 1.54630 + 0.892757i
55 −4.88999 1.04305i −0.977999 0.208610i
66 −5.91814 + 8.07800i −0.986357 + 1.34633i
77 −8.79970 2.35787i −1.25710 0.336839i −0.432024 0.901862i 0.642201π-0.642201\pi
−0.825075 + 0.565023i 0.808867π0.808867\pi
88 −7.41620 7.41620i −0.927025 0.927025i
99 −6.64028 6.07508i −0.737809 0.675009i
1010 14.8654 + 7.58766i 1.48654 + 0.758766i
1111 1.02371 + 1.77311i 0.0930642 + 0.161192i 0.908799 0.417234i 0.137000π-0.137000\pi
−0.815735 + 0.578426i 0.803667π0.803667\pi
1212 16.7046 13.4177i 1.39205 1.11814i
1313 4.18269 1.12075i 0.321746 0.0862115i −0.0943314 0.995541i 0.530071π-0.530071\pi
0.416077 + 0.909329i 0.363405π0.363405\pi
1414 26.3352 + 15.2047i 1.88109 + 1.08605i
1515 −8.22842 + 12.5417i −0.548561 + 0.836110i
1616 3.22036 + 5.57783i 0.201273 + 0.348615i
1717 17.1585 17.1585i 1.00932 1.00932i 0.00936716 0.999956i 0.497018π-0.497018\pi
0.999956 0.00936716i 0.00298170π-0.00298170\pi
1818 16.1614 + 25.3242i 0.897854 + 1.40690i
1919 18.6363i 0.980857i −0.871481 0.490428i 0.836840π-0.836840\pi
0.871481 0.490428i 0.163160π-0.163160\pi
2020 −26.5208 23.9138i −1.32604 1.19569i
2121 −16.1520 + 22.0468i −0.769143 + 1.04985i
2222 −1.76882 6.60133i −0.0804010 0.300061i
2323 −11.5078 + 3.08350i −0.500338 + 0.134065i −0.500157 0.865935i 0.666724π-0.666724\pi
−0.000180980 1.00000i 0.500058π0.500058\pi
2424 −28.7946 + 12.6835i −1.19978 + 0.528478i
2525 22.8241 + 10.2010i 0.912963 + 0.408042i
2626 −14.4542 −0.555932
2727 −24.2014 + 11.9704i −0.896349 + 0.443348i
2828 −46.0079 46.0079i −1.64314 1.64314i
2929 19.4918 11.2536i 0.672131 0.388055i −0.124753 0.992188i 0.539814π-0.539814\pi
0.796883 + 0.604133i 0.206480π0.206480\pi
3030 37.3655 33.3284i 1.24552 1.11095i
3131 11.9368 20.6752i 0.385059 0.666941i −0.606719 0.794917i 0.707514π-0.707514\pi
0.991777 + 0.127975i 0.0408478π0.0408478\pi
3232 5.29373 + 19.7565i 0.165429 + 0.617389i
3333 6.07038 0.936770i 0.183951 0.0283870i
3434 −70.1467 + 40.4992i −2.06314 + 1.19115i
3535 40.5711 + 20.7085i 1.15917 + 0.591672i
3636 −19.3772 61.2882i −0.538256 1.70245i
3737 −33.2840 + 33.2840i −0.899568 + 0.899568i −0.995398 0.0958294i 0.969450π-0.969450\pi
0.0958294 + 0.995398i 0.469450π0.469450\pi
3838 −16.1005 + 60.0877i −0.423696 + 1.58126i
3939 1.40917 12.9141i 0.0361326 0.331130i
4040 28.5297 + 44.0007i 0.713242 + 1.10002i
4141 2.15756 3.73700i 0.0526234 0.0911464i −0.838514 0.544880i 0.816575π-0.816575\pi
0.891137 + 0.453734i 0.149908π0.149908\pi
4242 71.1247 57.1297i 1.69345 1.36023i
4343 8.15051 30.4181i 0.189547 0.707398i −0.804065 0.594542i 0.797333π-0.797333\pi
0.993611 0.112856i 0.0360000π-0.0360000\pi
4444 14.6227i 0.332335i
4545 26.1343 + 36.6333i 0.580763 + 0.814073i
4646 39.7677 0.864514
4747 −0.838990 0.224807i −0.0178509 0.00478312i 0.249883 0.968276i 0.419608π-0.419608\pi
−0.267733 + 0.963493i 0.586275π0.586275\pi
4848 19.0961 2.94688i 0.397836 0.0613933i
4949 29.4398 + 16.9971i 0.600813 + 0.346880i
5050 −64.7772 52.6090i −1.29554 1.05218i
5151 −29.3451 66.6207i −0.575395 1.30629i
5252 29.8730 + 8.00445i 0.574481 + 0.153932i
5353 −3.33316 3.33316i −0.0628899 0.0628899i 0.674962 0.737852i 0.264160π-0.264160\pi
−0.737852 + 0.674962i 0.764160π0.764160\pi
5454 88.3727 17.6870i 1.63653 0.327537i
5555 −3.15647 9.73828i −0.0573904 0.177060i
5656 47.7739 + 82.7467i 0.853105 + 1.47762i
5757 −52.1155 20.2430i −0.914306 0.355140i
5858 −72.5684 + 19.4446i −1.25118 + 0.335252i
5959 −66.3254 38.2930i −1.12416 0.649033i −0.181699 0.983354i 0.558160π-0.558160\pi
−0.942459 + 0.334321i 0.891493π0.891493\pi
6060 −95.6810 + 48.1888i −1.59468 + 0.803146i
6161 35.3623 + 61.2493i 0.579710 + 1.00409i 0.995512 + 0.0946322i 0.0301675π0.0301675\pi
−0.415802 + 0.909455i 0.636499π0.636499\pi
6262 −56.3490 + 56.3490i −0.908855 + 0.908855i
6363 44.1082 + 69.1158i 0.700131 + 1.09708i
6464 94.0358i 1.46931i
6565 −21.6223 + 1.11769i −0.332651 + 0.0171952i
6666 −20.3816 2.22403i −0.308813 0.0336974i
6767 5.59919 + 20.8965i 0.0835700 + 0.311888i 0.995040 0.0994800i 0.0317179π-0.0317179\pi
−0.911470 + 0.411368i 0.865051π0.865051\pi
6868 167.402 44.8553i 2.46180 0.659637i
6969 −3.87703 + 35.5302i −0.0561888 + 0.514931i
7070 −112.920 101.820i −1.61314 1.45457i
7171 −28.6105 −0.402965 −0.201483 0.979492i 0.564576π-0.564576\pi
−0.201483 + 0.979492i 0.564576π0.564576\pi
7272 4.19166 + 94.2997i 0.0582175 + 1.30972i
7373 48.1316 + 48.1316i 0.659336 + 0.659336i 0.955223 0.295887i 0.0956151π-0.0956151\pi
−0.295887 + 0.955223i 0.595615π0.595615\pi
7474 136.071 78.5604i 1.83879 1.06163i
7575 53.3185 52.7460i 0.710914 0.703279i
7676 66.5507 115.269i 0.875667 1.51670i
7777 −4.82753 18.0166i −0.0626953 0.233982i
7878 −15.7004 + 40.4205i −0.201287 + 0.518212i
7979 −0.201686 + 0.116444i −0.00255299 + 0.00147397i −0.501276 0.865287i 0.667136π-0.667136\pi
0.498723 + 0.866761i 0.333803π0.333803\pi
8080 −9.92959 30.6346i −0.124120 0.382932i
8181 7.18677 + 80.6805i 0.0887255 + 0.996056i
8282 −10.1850 + 10.1850i −0.124207 + 0.124207i
8383 41.1240 153.477i 0.495470 1.84912i −0.0319094 0.999491i 0.510159π-0.510159\pi
0.527380 0.849630i 0.323175π-0.323175\pi
8484 −178.633 + 78.6845i −2.12658 + 0.936720i
8585 −101.802 + 66.0077i −1.19767 + 0.776562i
8686 −52.5583 + 91.0337i −0.611143 + 1.05853i
8787 −10.2979 66.7316i −0.118367 0.767030i
8888 5.55774 20.7418i 0.0631561 0.235702i
8989 103.385i 1.16163i 0.814035 + 0.580816i 0.197266π0.197266\pi
−0.814035 + 0.580816i 0.802734π0.802734\pi
9090 −52.6145 140.692i −0.584606 1.56325i
9191 −39.4490 −0.433506
9292 −82.1891 22.0225i −0.893360 0.239375i
9393 −44.8512 55.8384i −0.482271 0.600413i
9494 2.51088 + 1.44966i 0.0267115 + 0.0154219i
9595 −19.4386 + 91.1313i −0.204617 + 0.959277i
9696 60.9981 + 6.65606i 0.635397 + 0.0693340i
9797 69.7287 + 18.6837i 0.718852 + 0.192616i 0.599660 0.800255i 0.295303π-0.295303\pi
0.119193 + 0.992871i 0.461969π0.461969\pi
9898 −80.2366 80.2366i −0.818741 0.818741i
9999 3.97409 17.9931i 0.0401424 0.181748i
100100 104.743 + 144.601i 1.04743 + 1.44601i
101101 −31.0086 53.7085i −0.307016 0.531767i 0.670692 0.741736i 0.265997π-0.265997\pi
−0.977708 + 0.209969i 0.932664π0.932664\pi
102102 37.0599 + 240.153i 0.363332 + 2.35444i
103103 51.0537 13.6798i 0.495667 0.132813i −0.00232157 0.999997i 0.500739π-0.500739\pi
0.497988 + 0.867184i 0.334072π0.334072\pi
104104 −39.3314 22.7080i −0.378186 0.218346i
105105 101.979 90.9612i 0.971230 0.866297i
106106 7.86727 + 13.6265i 0.0742195 + 0.128552i
107107 84.3909 84.3909i 0.788700 0.788700i −0.192581 0.981281i 0.561686π-0.561686\pi
0.981281 + 0.192581i 0.0616859π0.0616859\pi
108108 −192.437 12.3846i −1.78183 0.114672i
109109 102.481i 0.940190i −0.882616 0.470095i 0.844220π-0.844220\pi
0.882616 0.470095i 0.155780π-0.155780\pi
110110 1.76399 + 34.1255i 0.0160363 + 0.310231i
111111 56.9237 + 129.231i 0.512826 + 1.16424i
112112 −15.1864 56.6764i −0.135593 0.506040i
113113 39.2529 10.5178i 0.347371 0.0930777i −0.0809152 0.996721i 0.525784π-0.525784\pi
0.428286 + 0.903643i 0.359118π0.359118\pi
114114 150.544 + 110.292i 1.32056 + 0.967475i
115115 59.4892 3.07508i 0.517297 0.0267398i
116116 160.747 1.38575
117117 −34.5829 17.9681i −0.295580 0.153574i
118118 180.766 + 180.766i 1.53192 + 1.53192i
119119 −191.447 + 110.532i −1.60880 + 0.928840i
120120 154.035 31.9878i 1.28363 0.266565i
121121 58.4041 101.159i 0.482678 0.836023i
122122 −61.1012 228.033i −0.500829 1.86912i
123123 −8.10678 10.0927i −0.0659088 0.0820544i
124124 147.663 85.2534i 1.19083 0.687528i
125125 −100.969 73.6897i −0.807755 0.589518i
126126 −82.5039 260.952i −0.654793 2.07105i
127127 −81.3527 + 81.3527i −0.640572 + 0.640572i −0.950696 0.310124i 0.899630π-0.899630\pi
0.310124 + 0.950696i 0.399630π0.399630\pi
128128 −60.0655 + 224.167i −0.469261 + 1.75131i
129129 −76.2096 55.8331i −0.590772 0.432814i
130130 70.6811 + 15.0765i 0.543701 + 0.115973i
131131 −41.3420 + 71.6064i −0.315588 + 0.546614i −0.979562 0.201141i 0.935535π-0.935535\pi
0.663975 + 0.747755i 0.268868π0.268868\pi
132132 40.8918 + 15.8834i 0.309786 + 0.120329i
133133 −43.9420 + 163.994i −0.330391 + 1.23303i
134134 72.2124i 0.538899i
135135 130.831 33.2919i 0.969116 0.246606i
136136 −254.502 −1.87134
137137 150.637 + 40.3630i 1.09954 + 0.294621i 0.762577 0.646898i 0.223934π-0.223934\pi
0.336962 + 0.941518i 0.390601π0.390601\pi
138138 43.1961 111.208i 0.313015 0.805857i
139139 1.35272 + 0.780993i 0.00973180 + 0.00561866i 0.504858 0.863202i 0.331545π-0.331545\pi
−0.495126 + 0.868821i 0.664878π0.664878\pi
140140 176.990 + 272.967i 1.26421 + 1.94976i
141141 −1.53998 + 2.10201i −0.0109219 + 0.0149079i
142142 92.2470 + 24.7175i 0.649627 + 0.174067i
143143 6.26906 + 6.26906i 0.0438396 + 0.0438396i
144144 12.5017 56.6024i 0.0868171 0.393072i
145145 −107.053 + 34.6990i −0.738295 + 0.239304i
146146 −113.605 196.770i −0.778117 1.34774i
147147 79.5095 63.8646i 0.540881 0.434453i
148148 −324.727 + 87.0102i −2.19410 + 0.587907i
149149 87.4092 + 50.4657i 0.586639 + 0.338696i 0.763767 0.645492i 0.223347π-0.223347\pi
−0.177128 + 0.984188i 0.556681π0.556681\pi
150150 −217.480 + 124.002i −1.44987 + 0.826678i
151151 −109.094 188.956i −0.722477 1.25137i −0.960004 0.279986i 0.909670π-0.909670\pi
0.237527 0.971381i 0.423663π-0.423663\pi
152152 −138.210 + 138.210i −0.909279 + 0.909279i
153153 −218.177 + 9.69804i −1.42599 + 0.0633859i
154154 62.2604i 0.404288i
155155 −79.9363 + 88.6508i −0.515718 + 0.571941i
156156 54.8325 74.8439i 0.351490 0.479769i
157157 −68.7136 256.443i −0.437666 1.63339i −0.734604 0.678496i 0.762632π-0.762632\pi
0.296937 0.954897i 0.404035π-0.404035\pi
158158 0.750883 0.201198i 0.00475242 0.00127341i
159159 −12.9416 + 5.70051i −0.0813934 + 0.0358522i
160160 −5.27928 102.131i −0.0329955 0.638316i
161161 108.535 0.674133
162162 46.5306 266.342i 0.287226 1.64408i
163163 −161.076 161.076i −0.988199 0.988199i 0.0117324 0.999931i 0.496265π-0.496265\pi
−0.999931 + 0.0117324i 0.996265π0.996265\pi
164164 26.6899 15.4094i 0.162743 0.0939598i
165165 −30.6612 1.75093i −0.185826 0.0106117i
166166 −265.187 + 459.317i −1.59751 + 2.76697i
167167 15.4399 + 57.6223i 0.0924542 + 0.345044i 0.996621 0.0821354i 0.0261740π-0.0261740\pi
−0.904167 + 0.427179i 0.859507π0.859507\pi
168168 283.290 43.7167i 1.68625 0.260219i
169169 −130.119 + 75.1245i −0.769938 + 0.444524i
170170 385.260 124.874i 2.26624 0.734555i
171171 −113.217 + 123.750i −0.662087 + 0.723685i
172172 159.037 159.037i 0.924631 0.924631i
173173 25.0902 93.6378i 0.145030 0.541259i −0.854724 0.519083i 0.826274π-0.826274\pi
0.999754 0.0221766i 0.00705962π-0.00705962\pi
174174 −24.4487 + 224.055i −0.140510 + 1.28767i
175175 −176.792 143.582i −1.01024 0.820470i
176176 −6.59341 + 11.4201i −0.0374626 + 0.0648871i
177177 −179.128 + 143.881i −1.01202 + 0.812889i
178178 89.3176 333.338i 0.501784 1.87269i
179179 89.4315i 0.499617i 0.968295 + 0.249809i 0.0803677π0.0803677\pi
−0.968295 + 0.249809i 0.919632π0.919632\pi
180180 30.8276 + 319.911i 0.171265 + 1.77728i
181181 307.336 1.69799 0.848995 0.528401i 0.177208π-0.177208\pi
0.848995 + 0.528401i 0.177208π0.177208\pi
182182 127.193 + 34.0812i 0.698861 + 0.187259i
183183 209.692 32.3592i 1.14586 0.176826i
184184 108.212 + 62.4761i 0.588107 + 0.339544i
185185 197.476 128.042i 1.06744 0.692117i
186186 96.3703 + 218.784i 0.518120 + 1.17626i
187187 47.9892 + 12.8587i 0.256627 + 0.0687629i
188188 −4.38653 4.38653i −0.0233326 0.0233326i
189189 241.190 48.2721i 1.27614 0.255408i
190190 141.406 277.035i 0.744241 1.45808i
191191 81.7990 + 141.680i 0.428267 + 0.741780i 0.996719 0.0809360i 0.0257910π-0.0257910\pi
−0.568452 + 0.822716i 0.692458π0.692458\pi
192192 −262.966 102.143i −1.36962 0.531994i
193193 245.520 65.7869i 1.27212 0.340865i 0.441280 0.897369i 0.354524π-0.354524\pi
0.830845 + 0.556504i 0.187858π0.187858\pi
194194 −208.680 120.481i −1.07567 0.621039i
195195 −20.3609 + 61.6799i −0.104415 + 0.316307i
196196 121.394 + 210.261i 0.619358 + 1.07276i
197197 −83.9878 + 83.9878i −0.426334 + 0.426334i −0.887377 0.461044i 0.847475π-0.847475\pi
0.461044 + 0.887377i 0.347475π0.347475\pi
198198 −28.3582 + 54.5805i −0.143223 + 0.275659i
199199 165.065i 0.829471i 0.909942 + 0.414736i 0.136126π0.136126\pi
−0.909942 + 0.414736i 0.863874π0.863874\pi
200200 −93.6150 244.921i −0.468075 1.22460i
201201 64.5179 + 7.04014i 0.320985 + 0.0350256i
202202 53.5786 + 199.958i 0.265240 + 0.989891i
203203 −198.056 + 53.0690i −0.975647 + 0.261424i
204204 56.3987 516.855i 0.276464 2.53360i
205205 −14.4483 + 16.0235i −0.0704797 + 0.0781633i
206206 −176.427 −0.856443
207207 95.1473 + 49.4353i 0.459649 + 0.238818i
208208 19.7211 + 19.7211i 0.0948132 + 0.0948132i
209209 33.0442 19.0781i 0.158106 0.0912827i
210210 −407.389 + 205.177i −1.93995 + 0.977034i
211211 5.87275 10.1719i 0.0278329 0.0482081i −0.851773 0.523910i 0.824473π-0.824473\pi
0.879606 + 0.475702i 0.157806π0.157806\pi
212212 −8.71347 32.5191i −0.0411013 0.153392i
213213 −31.0771 + 80.0080i −0.145902 + 0.375624i
214214 −345.004 + 199.188i −1.61217 + 0.930785i
215215 −71.5837 + 140.243i −0.332947 + 0.652293i
216216 268.258 + 90.7077i 1.24193 + 0.419943i
217217 −153.790 + 153.790i −0.708709 + 0.708709i
218218 −88.5362 + 330.422i −0.406129 + 1.51570i
219219 186.879 82.3165i 0.853327 0.375874i
220220 15.2523 71.5051i 0.0693285 0.325023i
221221 52.5383 90.9991i 0.237730 0.411761i
222222 −71.8888 465.848i −0.323823 2.09841i
223223 −3.31460 + 12.3702i −0.0148637 + 0.0554720i −0.972959 0.230976i 0.925808π-0.925808\pi
0.958096 + 0.286448i 0.0924747π0.0924747\pi
224224 186.333i 0.831843i
225225 −89.5863 206.396i −0.398161 0.917315i
226226 −135.647 −0.600208
227227 427.557 + 114.563i 1.88351 + 0.504685i 0.999293 + 0.0376093i 0.0119742π0.0119742\pi
0.884217 + 0.467076i 0.154692π0.154692\pi
228228 −250.056 311.313i −1.09674 1.36541i
229229 164.262 + 94.8369i 0.717303 + 0.414135i 0.813759 0.581202i 0.197417π-0.197417\pi
−0.0964562 + 0.995337i 0.530751π0.530751\pi
230230 −194.464 41.4797i −0.845494 0.180347i
231231 −55.6263 6.06989i −0.240806 0.0262766i
232232 −228.014 61.0961i −0.982818 0.263345i
233233 −62.7917 62.7917i −0.269492 0.269492i 0.559403 0.828896i 0.311030π-0.311030\pi
−0.828896 + 0.559403i 0.811030π0.811030\pi
234234 95.9802 + 87.8106i 0.410172 + 0.375259i
235235 3.86817 + 1.97441i 0.0164603 + 0.00840176i
236236 −273.491 473.699i −1.15886 2.00720i
237237 0.106555 + 0.690489i 0.000449599 + 0.00291345i
238238 712.762 190.984i 2.99480 0.802454i
239239 57.9140 + 33.4367i 0.242318 + 0.139902i 0.616242 0.787557i 0.288654π-0.288654\pi
−0.373924 + 0.927460i 0.621988π0.621988\pi
240240 −96.4538 5.50805i −0.401891 0.0229502i
241241 29.6700 + 51.3900i 0.123112 + 0.213236i 0.920993 0.389578i 0.127379π-0.127379\pi
−0.797881 + 0.602815i 0.794046π0.794046\pi
242242 −275.702 + 275.702i −1.13927 + 1.13927i
243243 233.426 + 67.5388i 0.960599 + 0.277937i
244244 505.119i 2.07016i
245245 −126.232 113.823i −0.515232 0.464584i
246246 17.4188 + 39.5449i 0.0708080 + 0.160751i
247247 −20.8866 77.9498i −0.0845611 0.315586i
248248 −241.857 + 64.8054i −0.975230 + 0.261312i
249249 −384.522 281.710i −1.54426 1.13137i
250250 261.886 + 324.823i 1.04754 + 1.29929i
251251 −88.5781 −0.352901 −0.176450 0.984310i 0.556461π-0.556461\pi
−0.176450 + 0.984310i 0.556461π0.556461\pi
252252 26.0038 + 585.007i 0.103190 + 2.32146i
253253 −17.2480 17.2480i −0.0681737 0.0681737i
254254 332.583 192.017i 1.30938 0.755972i
255255 74.0087 + 356.383i 0.290230 + 1.39758i
256256 199.259 345.126i 0.778354 1.34815i
257257 −40.6797 151.819i −0.158287 0.590734i −0.998801 0.0489452i 0.984414π-0.984414\pi
0.840515 0.541789i 0.182253π-0.182253\pi
258258 197.482 + 245.859i 0.765433 + 0.952940i
259259 371.369 214.410i 1.43386 0.827837i
260260 −137.730 70.3008i −0.529730 0.270388i
261261 −197.797 43.6872i −0.757845 0.167384i
262262 195.159 195.159i 0.744882 0.744882i
263263 −90.8401 + 339.020i −0.345400 + 1.28905i 0.546745 + 0.837299i 0.315867π0.315867\pi
−0.892145 + 0.451750i 0.850800π0.850800\pi
264264 −51.9664 38.0719i −0.196843 0.144212i
265265 12.8225 + 19.7758i 0.0483867 + 0.0746257i
266266 283.358 490.791i 1.06526 1.84508i
267267 289.112 + 112.298i 1.08282 + 0.420593i
268268 −39.9897 + 149.244i −0.149215 + 0.556880i
269269 81.1798i 0.301784i 0.988550 + 0.150892i 0.0482145π0.0482145\pi
−0.988550 + 0.150892i 0.951785π0.951785\pi
270270 −450.590 5.68787i −1.66885 0.0210662i
271271 −96.4105 −0.355758 −0.177879 0.984052i 0.556924π-0.556924\pi
−0.177879 + 0.984052i 0.556924π0.556924\pi
272272 150.964 + 40.4506i 0.555014 + 0.148716i
273273 −42.8500 + 110.317i −0.156960 + 0.404092i
274274 −450.817 260.280i −1.64532 0.949925i
275275 5.27758 + 50.9125i 0.0191912 + 0.185136i
276276 −150.860 + 205.917i −0.546593 + 0.746075i
277277 −423.206 113.398i −1.52782 0.409378i −0.605512 0.795836i 0.707032π-0.707032\pi
−0.922307 + 0.386458i 0.873698π0.873698\pi
278278 −3.68676 3.68676i −0.0132617 0.0132617i
279279 −204.867 + 64.7719i −0.734292 + 0.232157i
280280 −147.305 454.462i −0.526088 1.62308i
281281 −95.5531 165.503i −0.340047 0.588978i 0.644394 0.764693i 0.277110π-0.277110\pi
−0.984441 + 0.175715i 0.943776π0.943776\pi
282282 6.78125 5.44693i 0.0240470 0.0193153i
283283 −334.424 + 89.6088i −1.18171 + 0.316639i −0.795605 0.605815i 0.792847π-0.792847\pi
−0.386107 + 0.922454i 0.626180π0.626180\pi
284284 −176.962 102.169i −0.623105 0.359750i
285285 233.730 + 153.347i 0.820105 + 0.538060i
286286 −14.7969 25.6289i −0.0517373 0.0896117i
287287 −27.7972 + 27.7972i −0.0968545 + 0.0968545i
288288 84.8702 163.348i 0.294688 0.567182i
289289 299.828i 1.03747i
290290 375.141 19.3916i 1.29359 0.0668674i
291291 127.988 174.698i 0.439822 0.600338i
292292 125.824 + 469.582i 0.430905 + 1.60816i
293293 289.453 77.5588i 0.987895 0.264706i 0.271529 0.962430i 0.412471π-0.412471\pi
0.716366 + 0.697725i 0.245804π0.245804\pi
294294 −311.532 + 137.224i −1.05963 + 0.466748i
295295 284.389 + 256.433i 0.964031 + 0.869265i
296296 493.682 1.66784
297297 −46.0000 30.6576i −0.154882 0.103224i
298298 −238.229 238.229i −0.799426 0.799426i
299299 −44.6776 + 25.7946i −0.149423 + 0.0862697i
300300 518.143 135.842i 1.72714 0.452808i
301301 −143.444 + 248.452i −0.476558 + 0.825423i
302302 188.499 + 703.489i 0.624170 + 2.32944i
303303 −183.875 + 28.3753i −0.606849 + 0.0936477i
304304 103.950 60.0156i 0.341941 0.197420i
305305 −109.035 336.394i −0.357493 1.10293i
306306 711.831 + 157.221i 2.32624 + 0.513793i
307307 138.397 138.397i 0.450805 0.450805i −0.444817 0.895622i 0.646731π-0.646731\pi
0.895622 + 0.444817i 0.146731π0.146731\pi
308308 34.4785 128.676i 0.111943 0.417778i
309309 17.2003 157.628i 0.0556643 0.510124i
310310 334.321 216.771i 1.07846 0.699263i
311311 53.6367 92.9015i 0.172465 0.298719i −0.766816 0.641867i 0.778160π-0.778160\pi
0.939281 + 0.343148i 0.111493π0.111493\pi
312312 −106.224 + 85.3226i −0.340462 + 0.273470i
313313 −141.559 + 528.306i −0.452266 + 1.68788i 0.243738 + 0.969841i 0.421626π0.421626\pi
−0.696004 + 0.718038i 0.745040π0.745040\pi
314314 886.195i 2.82228i
315315 −143.598 383.983i −0.455865 1.21899i
316316 −1.66329 −0.00526359
317317 −421.463 112.931i −1.32954 0.356248i −0.476994 0.878906i 0.658274π-0.658274\pi
−0.852542 + 0.522658i 0.824941π0.824941\pi
318318 46.6514 7.19916i 0.146703 0.0226389i
319319 39.9077 + 23.0407i 0.125103 + 0.0722280i
320320 −98.0842 + 459.834i −0.306513 + 1.43698i
321321 −144.329 327.661i −0.449622 1.02075i
322322 −349.943 93.7670i −1.08678 0.291202i
323323 −319.771 319.771i −0.990002 0.990002i
324324 −243.661 + 524.690i −0.752040 + 1.61941i
325325 106.899 + 17.0877i 0.328920 + 0.0525777i
326326 380.189 + 658.507i 1.16622 + 2.01996i
327327 −286.582 111.316i −0.876398 0.340415i
328328 −43.7152 + 11.7135i −0.133278 + 0.0357118i
329329 6.85279 + 3.95646i 0.0208292 + 0.0120257i
330330 97.3463 + 32.1346i 0.294989 + 0.0973775i
331331 −293.152 507.754i −0.885655 1.53400i −0.844961 0.534827i 0.820377π-0.820377\pi
−0.0406933 0.999172i 0.512957π-0.512957\pi
332332 802.431 802.431i 2.41696 2.41696i
333333 423.219 18.8122i 1.27093 0.0564932i
334334 199.127i 0.596188i
335335 −5.58391 108.024i −0.0166684 0.322459i
336336 −174.989 19.0946i −0.520799 0.0568292i
337337 123.174 + 459.691i 0.365501 + 1.36407i 0.866740 + 0.498760i 0.166211π0.166211\pi
−0.501239 + 0.865309i 0.667122π0.667122\pi
338338 484.438 129.805i 1.43325 0.384038i
339339 13.2245 121.193i 0.0390104 0.357502i
340340 −865.382 + 44.7328i −2.54524 + 0.131567i
341341 48.8792 0.143341
342342 471.949 301.188i 1.37997 0.880667i
343343 96.6647 + 96.6647i 0.281821 + 0.281821i
344344 −286.033 + 165.141i −0.831490 + 0.480061i
345345 56.0186 169.699i 0.162373 0.491880i
346346 −161.793 + 280.234i −0.467610 + 0.809925i
347347 −45.4544 169.638i −0.130992 0.488870i 0.868990 0.494830i 0.164770π-0.164770\pi
−0.999982 + 0.00595969i 0.998103π0.998103\pi
348348 174.606 449.523i 0.501741 1.29173i
349349 298.148 172.136i 0.854292 0.493226i −0.00780468 0.999970i 0.502484π-0.502484\pi
0.862097 + 0.506744i 0.169151π0.169151\pi
350350 445.974 + 615.679i 1.27421 + 1.75908i
351351 −87.8113 + 77.1923i −0.250175 + 0.219921i
352352 −29.6112 + 29.6112i −0.0841227 + 0.0841227i
353353 −69.7848 + 260.440i −0.197691 + 0.737792i 0.793863 + 0.608096i 0.208067π0.208067\pi
−0.991554 + 0.129695i 0.958600π0.958600\pi
354354 701.854 309.153i 1.98264 0.873314i
355355 139.905 + 29.8423i 0.394100 + 0.0840628i
356356 −369.191 + 639.458i −1.03705 + 1.79623i
357357 101.145 + 655.434i 0.283320 + 1.83595i
358358 77.2626 288.348i 0.215817 0.805441i
359359 411.438i 1.14607i −0.819532 0.573033i 0.805767π-0.805767\pi
0.819532 0.573033i 0.194233π-0.194233\pi
360360 77.8623 465.497i 0.216284 1.29305i
361361 13.6890 0.0379198
362362 −990.923 265.517i −2.73736 0.733473i
363363 −219.446 273.204i −0.604536 0.752628i
364364 −244.000 140.873i −0.670330 0.387015i
365365 −185.159 285.567i −0.507286 0.782375i
366366 −704.051 76.8255i −1.92364 0.209906i
367367 626.938 + 167.988i 1.70828 + 0.457732i 0.975001 0.222199i 0.0713234π-0.0713234\pi
0.733277 + 0.679930i 0.237990π0.237990\pi
368368 −54.2584 54.2584i −0.147441 0.147441i
369369 −37.0294 + 11.7074i −0.100351 + 0.0317274i
370370 −747.327 + 242.231i −2.01980 + 0.654679i
371371 21.4716 + 37.1900i 0.0578751 + 0.100243i
372372 −78.0134 505.537i −0.209714 1.35897i
373373 −107.220 + 28.7295i −0.287453 + 0.0770229i −0.399664 0.916662i 0.630873π-0.630873\pi
0.112211 + 0.993684i 0.464207π0.464207\pi
374374 −143.619 82.9186i −0.384009 0.221708i
375375 −315.744 + 202.313i −0.841984 + 0.539502i
376376 4.55491 + 7.88933i 0.0121141 + 0.0209823i
377377 68.9157 68.9157i 0.182800 0.182800i
378378 −819.356 52.7309i −2.16761 0.139500i
379379 317.077i 0.836614i 0.908306 + 0.418307i 0.137376π0.137376\pi
−0.908306 + 0.418307i 0.862624π0.862624\pi
380380 −445.664 + 494.250i −1.17280 + 1.30066i
381381 139.133 + 315.865i 0.365177 + 0.829043i
382382 −141.337 527.478i −0.369993 1.38083i
383383 −86.0774 + 23.0644i −0.224745 + 0.0602203i −0.369434 0.929257i 0.620448π-0.620448\pi
0.144689 + 0.989477i 0.453782π0.453782\pi
384384 561.629 + 411.464i 1.46258 + 1.07152i
385385 4.81436 + 93.1365i 0.0125048 + 0.241913i
386386 −848.449 −2.19806
387387 −238.914 + 152.470i −0.617350 + 0.393979i
388388 364.566 + 364.566i 0.939602 + 0.939602i
389389 −64.0677 + 36.9895i −0.164698 + 0.0950887i −0.580084 0.814557i 0.696980π-0.696980\pi
0.415385 + 0.909646i 0.363647π0.363647\pi
390390 118.935 181.280i 0.304963 0.464820i
391391 −144.548 + 250.364i −0.369687 + 0.640318i
392392 −92.2778 344.386i −0.235403 0.878535i
393393 155.338 + 193.391i 0.395261 + 0.492088i
394394 343.356 198.237i 0.871461 0.503138i
395395 1.10770 0.359039i 0.00280431 0.000908961i
396396 88.8343 97.0991i 0.224329 0.245200i
397397 331.663 331.663i 0.835422 0.835422i −0.152830 0.988252i 0.548839π-0.548839\pi
0.988252 + 0.152830i 0.0488387π0.0488387\pi
398398 142.605 532.207i 0.358303 1.33720i
399399 410.870 + 301.013i 1.02975 + 0.754420i
400400 16.6022 + 160.160i 0.0415054 + 0.400400i
401401 −324.360 + 561.808i −0.808877 + 1.40102i 0.104765 + 0.994497i 0.466591π0.466591\pi
−0.913642 + 0.406520i 0.866742π0.866742\pi
402402 −201.939 78.4380i −0.502335 0.195119i
403403 26.7564 99.8561i 0.0663930 0.247782i
404404 442.930i 1.09636i
405405 49.0108 402.024i 0.121014 0.992651i
406406 684.428 1.68578
407407 −93.0893 24.9432i −0.228721 0.0612855i
408408 −276.443 + 711.702i −0.677556 + 1.74437i
409409 545.487 + 314.937i 1.33371 + 0.770017i 0.985866 0.167536i 0.0535812π-0.0535812\pi
0.347842 + 0.937553i 0.386914π0.386914\pi
410410 60.4280 39.1810i 0.147385 0.0955635i
411411 276.497 377.406i 0.672742 0.918262i
412412 364.628 + 97.7018i 0.885019 + 0.237140i
413413 493.353 + 493.353i 1.19456 + 1.19456i
414414 −264.069 241.592i −0.637847 0.583555i
415415 −361.181 + 707.607i −0.870315 + 1.70508i
416416 44.2841 + 76.7023i 0.106452 + 0.184380i
417417 3.65335 2.93449i 0.00876103 0.00703715i
418418 −123.024 + 32.9643i −0.294317 + 0.0788619i
419419 153.113 + 88.3997i 0.365424 + 0.210978i 0.671457 0.741043i 0.265669π-0.265669\pi
−0.306033 + 0.952021i 0.599002π0.599002\pi
420420 955.587 198.443i 2.27521 0.472483i
421421 44.6779 + 77.3843i 0.106123 + 0.183811i 0.914197 0.405271i 0.132823π-0.132823\pi
−0.808073 + 0.589082i 0.799490π0.799490\pi
422422 −27.7229 + 27.7229i −0.0656941 + 0.0656941i
423423 4.20542 + 6.58972i 0.00994188 + 0.0155785i
424424 49.4388i 0.116601i
425425 566.661 216.592i 1.33332 0.509629i
426426 169.321 231.116i 0.397468 0.542526i
427427 −166.760 622.355i −0.390538 1.45751i
428428 823.337 220.612i 1.92368 0.515449i
429429 24.3407 10.7216i 0.0567381 0.0249921i
430430 351.963 390.333i 0.818518 0.907751i
431431 648.364 1.50433 0.752163 0.658977i 0.229011π-0.229011\pi
0.752163 + 0.658977i 0.229011π0.229011\pi
432432 −144.706 96.4425i −0.334968 0.223247i
433433 −481.270 481.270i −1.11148 1.11148i −0.992951 0.118526i 0.962183π-0.962183\pi
−0.118526 0.992951i 0.537817π-0.537817\pi
434434 628.718 362.991i 1.44866 0.836384i
435435 −19.2479 + 337.059i −0.0442481 + 0.774847i
436436 365.961 633.864i 0.839361 1.45382i
437437 57.4649 + 214.462i 0.131499 + 0.490760i
438438 −673.656 + 103.957i −1.53803 + 0.237345i
439439 −543.519 + 313.801i −1.23808 + 0.714809i −0.968702 0.248225i 0.920153π-0.920153\pi
−0.269382 + 0.963033i 0.586820π0.586820\pi
440440 −48.8120 + 95.6301i −0.110936 + 0.217341i
441441 −92.2302 291.715i −0.209139 0.661485i
442442 −248.013 + 248.013i −0.561115 + 0.561115i
443443 139.184 519.441i 0.314185 1.17255i −0.610562 0.791969i 0.709056π-0.709056\pi
0.924746 0.380584i 0.124277π-0.124277\pi
444444 −109.402 + 1002.59i −0.246401 + 2.25809i
445445 107.836 505.553i 0.242328 1.13607i
446446 21.3741 37.0210i 0.0479239 0.0830067i
447447 236.070 189.619i 0.528121 0.424204i
448448 −221.724 + 827.486i −0.494920 + 1.84707i
449449 252.073i 0.561410i −0.959794 0.280705i 0.909432π-0.909432\pi
0.959794 0.280705i 0.0905683π-0.0905683\pi
450450 110.535 + 742.865i 0.245634 + 1.65081i
451451 8.83482 0.0195894
452452 280.346 + 75.1186i 0.620235 + 0.166191i
453453 −646.907 + 99.8294i −1.42805 + 0.220374i
454454 −1279.57 738.759i −2.81843 1.62722i
455455 192.905 + 41.1474i 0.423968 + 0.0904338i
456456 236.373 + 536.624i 0.518361 + 1.17681i
457457 −285.126 76.3993i −0.623908 0.167176i −0.0670042 0.997753i 0.521344π-0.521344\pi
−0.556904 + 0.830577i 0.688011π0.688011\pi
458458 −447.688 447.688i −0.977484 0.977484i
459459 −209.866 + 620.654i −0.457224 + 1.35219i
460460 378.934 + 193.417i 0.823769 + 0.420473i
461461 254.881 + 441.467i 0.552887 + 0.957629i 0.998065 + 0.0621865i 0.0198074π0.0198074\pi
−0.445177 + 0.895443i 0.646859π0.646859\pi
462462 174.108 + 67.6280i 0.376858 + 0.146381i
463463 285.192 76.4168i 0.615964 0.165047i 0.0626719 0.998034i 0.480038π-0.480038\pi
0.553293 + 0.832987i 0.313371π0.313371\pi
464464 125.541 + 72.4813i 0.270563 + 0.156210i
465465 161.080 + 319.832i 0.346408 + 0.687810i
466466 148.208 + 256.703i 0.318042 + 0.550865i
467467 −375.745 + 375.745i −0.804593 + 0.804593i −0.983810 0.179217i 0.942644π-0.942644\pi
0.179217 + 0.983810i 0.442644π0.442644\pi
468468 −149.738 234.633i −0.319952 0.501352i
469469 197.085i 0.420223i
470470 −10.7661 9.70781i −0.0229067 0.0206549i
471471 −791.767 86.3970i −1.68103 0.183433i
472472 207.894 + 775.871i 0.440453 + 1.64379i
473473 62.2784 16.6875i 0.131667 0.0352800i
474474 0.252977 2.31835i 0.000533706 0.00489104i
475475 190.109 425.356i 0.400230 0.895486i
476476 −1578.85 −3.31691
477477 1.88391 + 42.3824i 0.00394951 + 0.0888520i
478478 −157.841 157.841i −0.330212 0.330212i
479479 −375.237 + 216.643i −0.783376 + 0.452282i −0.837625 0.546245i 0.816057π-0.816057\pi
0.0542492 + 0.998527i 0.482723π0.482723\pi
480480 −291.338 96.1723i −0.606954 0.200359i
481481 −101.914 + 176.520i −0.211879 + 0.366985i
482482 −51.2656 191.326i −0.106360 0.396942i
483483 117.892 303.514i 0.244084 0.628393i
484484 722.482 417.125i 1.49273 0.861828i
485485 −321.485 164.094i −0.662855 0.338338i
486486 −694.270 419.424i −1.42854 0.863013i
487487 417.712 417.712i 0.857725 0.857725i −0.133345 0.991070i 0.542572π-0.542572\pi
0.991070 + 0.133345i 0.0425719π0.0425719\pi
488488 191.983 716.491i 0.393408 1.46822i
489489 −625.406 + 275.479i −1.27895 + 0.563352i
490490 308.665 + 476.047i 0.629930 + 0.971525i
491491 385.003 666.845i 0.784121 1.35814i −0.145402 0.989373i 0.546447π-0.546447\pi
0.929523 0.368765i 0.120219π-0.120219\pi
492492 −14.1008 91.3748i −0.0286601 0.185721i
493493 141.355 527.544i 0.286724 1.07007i
494494 269.373i 0.545289i
495495 −38.2010 + 83.8408i −0.0771737 + 0.169375i
496496 153.764 0.310007
497497 251.764 + 67.4600i 0.506567 + 0.135734i
498498 996.409 + 1240.50i 2.00082 + 2.49096i
499499 84.7687 + 48.9412i 0.169877 + 0.0980786i 0.582528 0.812811i 0.302064π-0.302064\pi
−0.412651 + 0.910889i 0.635397π0.635397\pi
500500 −361.368 816.350i −0.722736 1.63270i
501501 177.909 + 19.4133i 0.355108 + 0.0387491i
502502 285.596 + 76.5253i 0.568917 + 0.152441i
503503 350.849 + 350.849i 0.697512 + 0.697512i 0.963873 0.266361i 0.0858213π-0.0858213\pi
−0.266361 + 0.963873i 0.585821π0.585821\pi
504504 185.461 839.692i 0.367979 1.66606i
505505 95.6112 + 294.978i 0.189329 + 0.584114i
506506 40.7104 + 70.5125i 0.0804553 + 0.139353i
507507 68.7447 + 445.474i 0.135591 + 0.878647i
508508 −793.696 + 212.670i −1.56239 + 0.418642i
509509 −389.842 225.075i −0.765897 0.442191i 0.0655119 0.997852i 0.479132π-0.479132\pi
−0.831409 + 0.555661i 0.812465π0.812465\pi
510510 69.2692 1213.00i 0.135822 2.37843i
511511 −310.055 537.031i −0.606761 1.05094i
512512 −284.213 + 284.213i −0.555104 + 0.555104i
513513 223.084 + 451.025i 0.434861 + 0.879190i
514514 524.643i 1.02071i
515515 −263.921 + 13.6424i −0.512468 + 0.0264902i
516516 −271.991 617.485i −0.527113 1.19668i
517517 −0.460272 1.71776i −0.000890275 0.00332255i
518518 −1382.61 + 370.470i −2.66914 + 0.715194i
519519 −234.600 171.874i −0.452024 0.331164i
520520 168.645 + 152.067i 0.324317 + 0.292436i
521521 749.947 1.43944 0.719718 0.694266i 0.244271π-0.244271\pi
0.719718 + 0.694266i 0.244271π0.244271\pi
522522 600.002 + 311.741i 1.14943 + 0.597205i
523523 377.284 + 377.284i 0.721385 + 0.721385i 0.968887 0.247502i 0.0796098π-0.0796098\pi
−0.247502 + 0.968887i 0.579610π0.579610\pi
524524 −511.417 + 295.267i −0.975986 + 0.563486i
525525 −593.555 + 338.430i −1.13058 + 0.644629i
526526 585.779 1014.60i 1.11365 1.92890i
527527 −149.937 559.573i −0.284511 1.06181i
528528 24.7740 + 30.8428i 0.0469204 + 0.0584145i
529529 −335.207 + 193.532i −0.633661 + 0.365844i
530530 −24.2577 74.8395i −0.0457693 0.141207i
531531 207.786 + 657.208i 0.391312 + 1.23768i
532532 −857.415 + 857.415i −1.61168 + 1.61168i
533533 4.83616 18.0488i 0.00907348 0.0338627i
534534 −835.146 611.848i −1.56394 1.14578i
535535 −500.695 + 324.647i −0.935878 + 0.606816i
536536 113.448 196.497i 0.211656 0.366599i
537537 250.091 + 97.1416i 0.465719 + 0.180897i
538538 70.1337 261.743i 0.130360 0.486510i
539539 69.6001i 0.129128i
540540 928.100 + 261.283i 1.71870 + 0.483857i
541541 861.919 1.59320 0.796598 0.604509i 0.206631π-0.206631\pi
0.796598 + 0.604509i 0.206631π0.206631\pi
542542 310.850 + 83.2920i 0.573524 + 0.153675i
543543 333.832 859.451i 0.614793 1.58278i
544544 429.824 + 248.159i 0.790117 + 0.456174i
545545 −106.893 + 501.130i −0.196133 + 0.919504i
546546 233.465 318.669i 0.427591 0.583643i
547547 −385.325 103.247i −0.704433 0.188752i −0.111218 0.993796i 0.535475π-0.535475\pi
−0.593215 + 0.805044i 0.702142π0.702142\pi
548548 787.582 + 787.582i 1.43719 + 1.43719i
549549 137.279 621.542i 0.250052 1.13213i
550550 26.9687 168.713i 0.0490340 0.306751i
551551 −209.725 363.254i −0.380626 0.659264i
552552 292.252 234.747i 0.529442 0.425266i
553553 2.04934 0.549118i 0.00370585 0.000992981i
554554 1266.55 + 731.241i 2.28619 + 1.31993i
555555 −143.562 691.312i −0.258670 1.24561i
556556 5.57790 + 9.66120i 0.0100322 + 0.0173763i
557557 −262.321 + 262.321i −0.470954 + 0.470954i −0.902223 0.431269i 0.858066π-0.858066\pi
0.431269 + 0.902223i 0.358066π0.358066\pi
558558 716.499 31.8487i 1.28405 0.0570765i
559559 136.364i 0.243943i
560560 15.1450 + 292.988i 0.0270446 + 0.523192i
561561 88.0851 120.232i 0.157014 0.214318i
562562 165.102 + 616.171i 0.293777 + 1.09639i
563563 −877.872 + 235.225i −1.55928 + 0.417806i −0.932434 0.361341i 0.882319π-0.882319\pi
−0.626841 + 0.779147i 0.715653π0.715653\pi
564564 −17.0314 + 7.50202i −0.0301976 + 0.0133015i
565565 −202.917 + 10.4891i −0.359145 + 0.0185647i
566566 1155.68 2.04183
567567 126.993 726.910i 0.223973 1.28203i
568568 212.181 + 212.181i 0.373559 + 0.373559i
569569 632.780 365.336i 1.11209 0.642066i 0.172721 0.984971i 0.444744π-0.444744\pi
0.939370 + 0.342905i 0.111411π0.111411\pi
570570 −621.118 696.353i −1.08968 1.22167i
571571 −348.293 + 603.262i −0.609971 + 1.05650i 0.381273 + 0.924462i 0.375486π0.375486\pi
−0.991245 + 0.132039i 0.957848π0.957848\pi
572572 16.3884 + 61.1624i 0.0286511 + 0.106927i
573573 485.052 74.8523i 0.846514 0.130632i
574574 113.640 65.6099i 0.197978 0.114303i
575575 −294.109 47.0132i −0.511494 0.0817621i
576576 −571.275 + 624.424i −0.991797 + 1.08407i
577577 −524.179 + 524.179i −0.908455 + 0.908455i −0.996148 0.0876926i 0.972051π-0.972051\pi
0.0876926 + 0.996148i 0.472051π0.472051\pi
578578 −259.031 + 966.715i −0.448150 + 1.67252i
579579 82.7171 758.044i 0.142862 1.30923i
580580 −786.054 167.668i −1.35527 0.289083i
581581 −723.758 + 1253.59i −1.24571 + 2.15763i
582582 −563.591 + 452.695i −0.968370 + 0.777827i
583583 2.49789 9.32225i 0.00428454 0.0159901i
584584 713.907i 1.22244i
585585 150.369 + 123.936i 0.257040 + 0.211856i
586586 −1000.27 −1.70695
587587 527.677 + 141.391i 0.898938 + 0.240870i 0.678560 0.734545i 0.262604π-0.262604\pi
0.220378 + 0.975415i 0.429271π0.429271\pi
588588 719.845 111.085i 1.22423 0.188920i
589589 −385.309 222.458i −0.654174 0.377688i
590590 −695.396 1072.49i −1.17864 1.81778i
591591 143.639 + 326.096i 0.243044 + 0.551770i
592592 −292.839 78.4661i −0.494661 0.132544i
593593 −61.2676 61.2676i −0.103318 0.103318i 0.653558 0.756876i 0.273275π-0.273275\pi
−0.756876 + 0.653558i 0.773275π0.773275\pi
594594 121.829 + 138.588i 0.205099 + 0.233314i
595595 1051.47 340.812i 1.76717 0.572793i
596596 360.429 + 624.282i 0.604747 + 1.04745i
597597 461.596 + 179.295i 0.773192 + 0.300327i
598598 166.336 44.5696i 0.278154 0.0745310i
599599 572.037 + 330.266i 0.954987 + 0.551362i 0.894626 0.446815i 0.147442π-0.147442\pi
0.0603602 + 0.998177i 0.480775π0.480775\pi
600600 −786.595 4.24624i −1.31099 0.00707706i
601601 65.1748 + 112.886i 0.108444 + 0.187830i 0.915140 0.403136i 0.132080π-0.132080\pi
−0.806696 + 0.590966i 0.798747π0.798747\pi
602602 677.143 677.143i 1.12482 1.12482i
603603 89.7675 172.774i 0.148868 0.286524i
604604 1558.31i 2.57999i
605605 −391.109 + 433.747i −0.646462 + 0.716938i
606606 617.371 + 67.3669i 1.01876 + 0.111167i
607607 −84.0689 313.749i −0.138499 0.516885i −0.999959 0.00905986i 0.997116π-0.997116\pi
0.861460 0.507826i 0.169551π-0.169551\pi
608608 368.187 98.6554i 0.605571 0.162262i
609609 −66.7263 + 611.499i −0.109567 + 1.00410i
610610 60.9344 + 1178.81i 0.0998924 + 1.93248i
611611 −3.76119 −0.00615580
612612 −1384.10 719.130i −2.26160 1.17505i
613613 −778.916 778.916i −1.27066 1.27066i −0.945741 0.324921i 0.894662π-0.894662\pi
−0.324921 0.945741i 0.605338π-0.605338\pi
614614 −565.790 + 326.659i −0.921482 + 0.532018i
615615 29.1149 + 57.8090i 0.0473413 + 0.0939983i
616616 −97.8128 + 169.417i −0.158787 + 0.275027i
617617 −88.7130 331.081i −0.143781 0.536599i −0.999807 0.0196651i 0.993740π-0.993740\pi
0.856025 0.516934i 0.172927π-0.172927\pi
618618 −191.637 + 493.370i −0.310093 + 0.798334i
619619 −448.805 + 259.118i −0.725049 + 0.418607i −0.816608 0.577192i 0.804148π-0.804148\pi
0.0915591 + 0.995800i 0.470815π0.470815\pi
620620 −810.996 + 262.868i −1.30806 + 0.423981i
621621 241.594 212.378i 0.389040 0.341993i
622622 −253.198 + 253.198i −0.407070 + 0.407070i
623623 243.769 909.758i 0.391282 1.46029i
624624 76.5706 33.7279i 0.122709 0.0540511i
625625 416.878 + 465.659i 0.667004 + 0.745054i
626626 912.840 1581.09i 1.45821 2.52569i
627627 −17.4579 113.129i −0.0278435 0.180430i
628628 490.756 1831.53i 0.781459 2.91645i
629629 1142.21i 1.81591i
630630 131.257 + 1362.11i 0.208345 + 2.16208i
631631 −48.4016 −0.0767062 −0.0383531 0.999264i 0.512211π-0.512211\pi
−0.0383531 + 0.999264i 0.512211π0.512211\pi
632632 2.35932 + 0.632177i 0.00373309 + 0.00100028i
633633 −22.0662 27.4717i −0.0348597 0.0433992i
634634 1261.33 + 728.230i 1.98948 + 1.14863i
635635 482.669 312.959i 0.760109 0.492849i
636636 −100.403 10.9559i −0.157866 0.0172262i
637637 142.187 + 38.0990i 0.223214 + 0.0598100i
638638 −108.766 108.766i −0.170480 0.170480i
639639 189.982 + 173.811i 0.297312 + 0.272005i
640640 527.538 1033.53i 0.824278 1.61488i
641641 −313.217 542.507i −0.488637 0.846345i 0.511277 0.859416i 0.329173π-0.329173\pi
−0.999915 + 0.0130711i 0.995839π0.995839\pi
642642 182.272 + 1181.15i 0.283913 + 1.83979i
643643 −467.479 + 125.261i −0.727028 + 0.194807i −0.603305 0.797510i 0.706150π-0.706150\pi
−0.123723 + 0.992317i 0.539483π0.539483\pi
644644 671.313 + 387.583i 1.04241 + 0.601836i
645645 314.428 + 352.514i 0.487485 + 0.546533i
646646 754.755 + 1307.27i 1.16835 + 2.02364i
647647 −388.357 + 388.357i −0.600242 + 0.600242i −0.940377 0.340135i 0.889527π-0.889527\pi
0.340135 + 0.940377i 0.389527π0.389527\pi
648648 545.045 651.642i 0.841118 1.00562i
649649 156.803i 0.241607i
650650 −329.904 147.448i −0.507545 0.226843i
651651 263.017 + 597.114i 0.404021 + 0.917226i
652652 −421.082 1571.50i −0.645831 2.41027i
653653 −191.192 + 51.2298i −0.292791 + 0.0784530i −0.402225 0.915541i 0.631763π-0.631763\pi
0.109434 + 0.993994i 0.465096π0.465096\pi
654654 827.839 + 606.495i 1.26581 + 0.927363i
655655 276.851 307.033i 0.422674 0.468753i
656656 27.7925 0.0423666
657657 −27.2041 612.010i −0.0414066 0.931523i
658658 −18.6769 18.6769i −0.0283843 0.0283843i
659659 97.2838 56.1668i 0.147623 0.0852304i −0.424369 0.905489i 0.639504π-0.639504\pi
0.571992 + 0.820259i 0.306171π0.306171\pi
660660 −183.393 120.322i −0.277869 0.182306i
661661 55.4873 96.1067i 0.0839444 0.145396i −0.820997 0.570933i 0.806582π-0.806582\pi
0.904941 + 0.425537i 0.139915π0.139915\pi
662662 506.525 + 1890.38i 0.765144 + 2.85556i
663663 −197.407 245.765i −0.297748 0.370687i
664664 −1443.20 + 833.232i −2.17349 + 1.25487i
665665 385.930 756.094i 0.580346 1.13698i
666666 −1380.81 304.976i −2.07329 0.457923i
667667 −189.607 + 189.607i −0.284268 + 0.284268i
668668 −110.272 + 411.542i −0.165078 + 0.616081i
669669 30.9924 + 22.7058i 0.0463265 + 0.0339400i
670670 −75.3213 + 353.118i −0.112420 + 0.527042i
671671 −72.4012 + 125.403i −0.107900 + 0.186889i
672672 −521.071 202.397i −0.775403 0.301186i
673673 54.3747 202.929i 0.0807945 0.301529i −0.913690 0.406412i 0.866780π-0.866780\pi
0.994485 + 0.104882i 0.0334466π0.0334466\pi
674674 1588.56i 2.35692i
675675 −674.486 + 26.3338i −0.999239 + 0.0390131i
676676 −1073.09 −1.58741
677677 −723.857 193.957i −1.06921 0.286495i −0.319043 0.947740i 0.603361π-0.603361\pi
−0.750169 + 0.661246i 0.770028π0.770028\pi
678678 −147.342 + 379.331i −0.217318 + 0.559485i
679679 −569.537 328.822i −0.838788 0.484275i
680680 1244.51 + 265.459i 1.83016 + 0.390380i
681681 784.789 1071.20i 1.15241 1.57298i
682682 −157.598 42.2282i −0.231082 0.0619182i
683683 441.268 + 441.268i 0.646074 + 0.646074i 0.952042 0.305968i 0.0989800π-0.0989800\pi
−0.305968 + 0.952042i 0.598980π0.598980\pi
684684 −1142.18 + 361.119i −1.66986 + 0.527952i
685685 −694.513 354.497i −1.01389 0.517514i
686686 −228.158 395.181i −0.332592 0.576066i
687687 443.631 356.339i 0.645751 0.518688i
688688 195.915 52.4952i 0.284760 0.0763012i
689689 −17.6772 10.2060i −0.0256564 0.0148127i
690690 −327.225 + 498.752i −0.474239 + 0.722829i
691691 396.083 + 686.036i 0.573202 + 0.992816i 0.996234 + 0.0867010i 0.0276325π0.0276325\pi
−0.423032 + 0.906115i 0.639034π0.639034\pi
692692 489.571 489.571i 0.707473 0.707473i
693693 −77.3961 + 148.963i −0.111683 + 0.214954i
694694 586.222i 0.844700i
695695 −5.80018 5.23001i −0.00834558 0.00752519i
696696 −418.524 + 571.266i −0.601327 + 0.820785i
697697 −27.1009 101.142i −0.0388822 0.145110i
698698 −1110.01 + 297.427i −1.59027 + 0.426113i
699699 −243.799 + 107.389i −0.348783 + 0.153632i
700700 −580.759 1519.42i −0.829656 2.17059i
701701 −1185.25 −1.69080 −0.845401 0.534133i 0.820638π-0.820638\pi
−0.845401 + 0.534133i 0.820638π0.820638\pi
702702 349.813 173.023i 0.498309 0.246471i
703703 620.290 + 620.290i 0.882348 + 0.882348i
704704 166.736 96.2650i 0.236841 0.136740i
705705 9.72301 8.67252i 0.0137915 0.0123015i
706706 450.005 779.431i 0.637401 1.10401i
707707 146.229 + 545.733i 0.206830 + 0.771899i
708708 −1621.75 + 250.265i −2.29060 + 0.353481i
709709 −237.674 + 137.221i −0.335224 + 0.193542i −0.658158 0.752880i 0.728664π-0.728664\pi
0.322934 + 0.946421i 0.395331π0.395331\pi
710710 −425.306 217.087i −0.599022 0.305756i
711711 2.04666 + 0.452042i 0.00287856 + 0.000635783i
712712 766.725 766.725i 1.07686 1.07686i
713713 −73.6143 + 274.732i −0.103246 + 0.385319i
714714 240.133 2200.65i 0.336321 3.08215i
715715 −24.1167 37.1946i −0.0337297 0.0520205i
716716 −319.362 + 553.152i −0.446037 + 0.772558i
717717 156.411 125.634i 0.218146 0.175222i
718718 −355.454 + 1326.57i −0.495061 + 1.84759i
719719 1409.12i 1.95983i −0.199416 0.979915i 0.563904π-0.563904\pi
0.199416 0.979915i 0.436096π-0.436096\pi
720720 −120.172 + 263.745i −0.166906 + 0.366313i
721721 −481.512 −0.667839
722722 −44.1367 11.8264i −0.0611311 0.0163800i
723723 175.937 27.1503i 0.243344 0.0375523i
724724 1900.94 + 1097.51i 2.62560 + 1.51589i
725725 559.680 58.0164i 0.771973 0.0800226i
726726 471.517 + 1070.46i 0.649473 + 1.47446i
727727 688.962 + 184.607i 0.947678 + 0.253930i 0.699377 0.714753i 0.253461π-0.253461\pi
0.248302 + 0.968683i 0.420128π0.420128\pi
728728 292.562 + 292.562i 0.401870 + 0.401870i
729729 442.419 579.402i 0.606884 0.794790i
730730 350.287 + 1080.70i 0.479845 + 1.48041i
731731 −382.079 661.780i −0.522680 0.905308i
732732 1412.54 + 548.667i 1.92970 + 0.749545i
733733 858.390 230.005i 1.17106 0.313786i 0.379688 0.925115i 0.376031π-0.376031\pi
0.791377 + 0.611329i 0.209365π0.209365\pi
734734 −1876.26 1083.26i −2.55622 1.47583i
735735 −455.415 + 229.365i −0.619612 + 0.312061i
736736 −121.838 211.030i −0.165541 0.286725i
737737 −31.3198 + 31.3198i −0.0424964 + 0.0424964i
738738 129.506 5.75659i 0.175482 0.00780025i
739739 719.160i 0.973153i 0.873638 + 0.486577i 0.161755π0.161755\pi
−0.873638 + 0.486577i 0.838245π0.838245\pi
740740 1678.67 86.7727i 2.26847 0.117260i
741741 −240.670 26.2617i −0.324791 0.0354409i
742742 −37.1000 138.459i −0.0500000 0.186603i
743743 160.887 43.1096i 0.216537 0.0580210i −0.148919 0.988849i 0.547579π-0.547579\pi
0.365457 + 0.930828i 0.380913π0.380913\pi
744744 −81.4830 + 746.734i −0.109520 + 1.00368i
745745 −374.792 337.950i −0.503077 0.453624i
746746 370.523 0.496679
747747 −1205.46 + 769.299i −1.61374 + 1.02985i
748748 250.904 + 250.904i 0.335433 + 0.335433i
749749 −941.597 + 543.631i −1.25714 + 0.725809i
750750 1192.82 379.525i 1.59042 0.506033i
751751 241.781 418.776i 0.321945 0.557625i −0.658945 0.752192i 0.728997π-0.728997\pi
0.980889 + 0.194567i 0.0623301π0.0623301\pi
752752 −1.44792 5.40371i −0.00192542 0.00718578i
753753 −96.2146 + 247.704i −0.127775 + 0.328957i
754754 −281.739 + 162.662i −0.373659 + 0.215732i
755755 336.378 + 1037.79i 0.445534 + 1.37455i
756756 1664.19 + 562.723i 2.20131 + 0.744343i
757757 144.792 144.792i 0.191270 0.191270i −0.604974 0.796245i 0.706817π-0.706817\pi
0.796245 + 0.604974i 0.206817π0.206817\pi
758758 273.932 1022.33i 0.361388 1.34872i
759759 −66.9680 + 29.4981i −0.0882319 + 0.0388645i
760760 820.009 531.687i 1.07896 0.699589i
761761 149.929 259.685i 0.197016 0.341241i −0.750544 0.660821i 0.770208π-0.770208\pi
0.947559 + 0.319580i 0.103542π0.103542\pi
762762 −175.710 1138.62i −0.230591 1.49426i
763763 −241.636 + 901.799i −0.316692 + 1.18191i
764764 1168.43i 1.52935i
765765 1077.00 + 180.146i 1.40784 + 0.235485i
766766 297.459 0.388328
767767 −320.335 85.8336i −0.417647 0.111908i
768768 −748.691 932.097i −0.974858 1.21367i
769769 96.6554 + 55.8040i 0.125690 + 0.0725670i 0.561527 0.827459i 0.310214π-0.310214\pi
−0.435837 + 0.900026i 0.643548π0.643548\pi
770770 64.9408 304.453i 0.0843388 0.395393i
771771 −468.740 51.1485i −0.607964 0.0663405i
772772 1753.52 + 469.854i 2.27140 + 0.608619i
773773 −43.6287 43.6287i −0.0564408 0.0564408i 0.678323 0.734764i 0.262707π-0.262707\pi
−0.734764 + 0.678323i 0.762707π0.762707\pi
774774 902.039 285.193i 1.16543 0.368467i
775775 483.355 350.124i 0.623684 0.451773i
776776 −378.559 655.684i −0.487834 0.844954i
777777 −196.201 1271.41i −0.252512 1.63631i
778778 238.526 63.9127i 0.306588 0.0821500i
779779 −69.6438 40.2089i −0.0894015 0.0516160i
780780 −346.197 + 308.793i −0.443842 + 0.395889i
781781 −29.2888 50.7297i −0.0375016 0.0649547i
782782 682.353 682.353i 0.872574 0.872574i
783783 −337.019 + 505.678i −0.430420 + 0.645821i
784784 218.947i 0.279270i
785785 68.5260 + 1325.68i 0.0872943 + 1.68876i
786786 −333.769 757.737i −0.424642 0.964042i
787787 319.011 + 1190.57i 0.405351 + 1.51279i 0.803407 + 0.595430i 0.203018π0.203018\pi
−0.398056 + 0.917361i 0.630315π0.630315\pi
788788 −819.404 + 219.559i −1.03985 + 0.278628i
789789 849.381 + 622.277i 1.07653 + 0.788691i
790790 −3.88167 + 0.200649i −0.00491351 + 0.000253986i
791791 −370.213 −0.468032
792792 −162.913 + 103.967i −0.205698 + 0.131272i
793793 216.555 + 216.555i 0.273083 + 0.273083i
794794 −1355.89 + 782.824i −1.70767 + 0.985925i
795795 69.2300 14.3767i 0.0870818 0.0180839i
796796 −589.451 + 1020.96i −0.740516 + 1.28261i
797797 −197.069 735.470i −0.247263 0.922799i −0.972232 0.234017i 0.924813π-0.924813\pi
0.724969 0.688781i 0.241854π-0.241854\pi
798798 −1064.69 1325.50i −1.33419 1.66103i
799799 −18.2532 + 10.5385i −0.0228450 + 0.0131896i
800800 −80.7119 + 504.925i −0.100890 + 0.631156i
801801 628.073 686.507i 0.784112 0.857063i
802802 1531.17 1531.17i 1.90920 1.90920i
803803 −36.0700 + 134.615i −0.0449191 + 0.167640i
804804 373.916 + 273.940i 0.465069 + 0.340721i
805805 −530.737 113.208i −0.659301 0.140631i
806806 −172.538 + 298.844i −0.214066 + 0.370774i
807807 227.015 + 88.1785i 0.281308 + 0.109267i
808808 −168.347 + 628.279i −0.208350 + 0.777573i
809809 225.758i 0.279058i −0.990218 0.139529i 0.955441π-0.955441\pi
0.990218 0.139529i 0.0445589π-0.0445589\pi
810810 −505.343 + 1253.88i −0.623880 + 1.54799i
811811 −149.469 −0.184303 −0.0921513 0.995745i 0.529374π-0.529374\pi
−0.0921513 + 0.995745i 0.529374π0.529374\pi
812812 −1414.53 379.022i −1.74203 0.466776i
813813 −104.722 + 269.607i −0.128810 + 0.331620i
814814 278.593 + 160.845i 0.342251 + 0.197599i
815815 619.652 + 955.674i 0.760309 + 1.17261i
816816 277.097 378.225i 0.339580 0.463511i
817817 −566.881 151.895i −0.693856 0.185918i
818818 −1486.69 1486.69i −1.81747 1.81747i
819819 261.953 + 239.656i 0.319844 + 0.292620i
820820 −146.586 + 47.5130i −0.178764 + 0.0579426i
821821 2.78890 + 4.83052i 0.00339696 + 0.00588370i 0.867719 0.497055i 0.165585π-0.165585\pi
−0.864322 + 0.502939i 0.832252π0.832252\pi
822822 −1217.54 + 977.970i −1.48120 + 1.18974i
823823 625.506 167.604i 0.760032 0.203650i 0.142069 0.989857i 0.454625π-0.454625\pi
0.617963 + 0.786207i 0.287958π0.287958\pi
824824 −480.076 277.172i −0.582617 0.336374i
825825 148.107 + 40.5433i 0.179524 + 0.0491434i
826826 −1164.46 2016.91i −1.40976 2.44178i
827827 230.120 230.120i 0.278258 0.278258i −0.554155 0.832413i 0.686959π-0.686959\pi
0.832413 + 0.554155i 0.186959π0.186959\pi
828828 411.971 + 645.541i 0.497549 + 0.779639i
829829 1504.68i 1.81505i −0.419994 0.907527i 0.637968π-0.637968\pi
0.419994 0.907527i 0.362032π-0.362032\pi
830830 1775.85 1969.45i 2.13958 2.37284i
831831 −776.803 + 1060.30i −0.934781 + 1.27593i
832832 −105.390 393.323i −0.126671 0.472744i
833833 796.788 213.499i 0.956528 0.256301i
834834 −14.3145 + 6.30524i −0.0171636 + 0.00756024i
835835 −15.3977 297.877i −0.0184404 0.356739i
836836 272.513 0.325973
837837 −41.3979 + 643.258i −0.0494598 + 0.768528i
838838 −417.300 417.300i −0.497971 0.497971i
839839 915.370 528.489i 1.09103 0.629904i 0.157176 0.987571i 0.449761π-0.449761\pi
0.933849 + 0.357667i 0.116428π0.116428\pi
840840 −1430.88 81.7115i −1.70343 0.0972756i
841841 −167.214 + 289.622i −0.198827 + 0.344378i
842842 −77.1972 288.104i −0.0916831 0.342166i
843843 −566.612 + 87.4384i −0.672137 + 0.103723i
844844 72.6483 41.9435i 0.0860762 0.0496961i
845845 714.642 231.637i 0.845730 0.274127i
846846 −7.86618 24.8800i −0.00929809 0.0294089i
847847 −752.457 + 752.457i −0.888379 + 0.888379i
848848 7.85783 29.3258i 0.00926631 0.0345823i
849849 −112.669 + 1032.54i −0.132708 + 1.21618i
850850 −2014.17 + 208.788i −2.36961 + 0.245633i
851851 280.394 485.656i 0.329487 0.570689i
852852 −477.929 + 383.888i −0.560949 + 0.450573i
853853 191.675 715.340i 0.224707 0.838617i −0.757815 0.652469i 0.773733π-0.773733\pi
0.982522 0.186148i 0.0596003π-0.0596003\pi
854854 2150.69i 2.51837i
855855 682.708 487.047i 0.798489 0.569645i
856856 −1251.72 −1.46229
857857 1218.31 + 326.446i 1.42160 + 0.380918i 0.886052 0.463585i 0.153437π-0.153437\pi
0.535551 + 0.844503i 0.320104π0.320104\pi
858858 −87.7427 + 13.5403i −0.102264 + 0.0157812i
859859 −37.7603 21.8009i −0.0439584 0.0253794i 0.477860 0.878436i 0.341413π-0.341413\pi
−0.521818 + 0.853057i 0.674746π0.674746\pi
860860 −943.571 + 611.804i −1.09718 + 0.711400i
861861 47.5399 + 107.927i 0.0552148 + 0.125351i
862862 −2090.48 560.142i −2.42515 0.649817i
863863 −274.423 274.423i −0.317988 0.317988i 0.530006 0.847994i 0.322190π-0.322190\pi
−0.847994 + 0.530006i 0.822190π0.822190\pi
864864 −364.609 414.767i −0.422001 0.480054i
865865 −220.360 + 431.718i −0.254751 + 0.499096i
866866 1135.94 + 1967.51i 1.31171 + 2.27195i
867867 −838.454 325.677i −0.967075 0.375637i
868868 −1500.41 + 402.033i −1.72858 + 0.463172i
869869 −0.412935 0.238408i −0.000475184 0.000274348i
870870 353.255 1070.13i 0.406040 1.23003i
871871 46.8394 + 81.1282i 0.0537766 + 0.0931438i
872872 −760.017 + 760.017i −0.871579 + 0.871579i
873873 −349.513 547.673i −0.400359 0.627346i
874874 741.121i 0.847965i
875875 714.749 + 886.520i 0.816856 + 1.01317i
876876 1449.84 + 158.205i 1.65506 + 0.180599i
877877 −46.0094 171.710i −0.0524623 0.195792i 0.934721 0.355382i 0.115649π-0.115649\pi
−0.987183 + 0.159590i 0.948983π0.948983\pi
878878 2023.53 542.205i 2.30471 0.617545i
879879 97.5184 893.687i 0.110942 1.01671i
880880 44.1535 48.9671i 0.0501745 0.0556444i
881881 −1000.82 −1.13600 −0.568000 0.823029i 0.692282π-0.692282\pi
−0.568000 + 0.823029i 0.692282π0.692282\pi
882882 45.3500 + 1020.24i 0.0514172 + 1.15673i
883883 766.494 + 766.494i 0.868057 + 0.868057i 0.992257 0.124201i 0.0396366π-0.0396366\pi
−0.124201 + 0.992257i 0.539637π0.539637\pi
884884 649.920 375.232i 0.735204 0.424470i
885885 1026.01 516.739i 1.15933 0.583886i
886886 −897.522 + 1554.55i −1.01300 + 1.75457i
887887 166.511 + 621.429i 0.187724 + 0.700596i 0.994031 + 0.109099i 0.0347964π0.0347964\pi
−0.806307 + 0.591498i 0.798537π0.798537\pi
888888 536.244 1380.56i 0.603878 1.55468i
889889 907.698 524.060i 1.02103 0.589494i
890890 −784.452 + 1536.86i −0.881406 + 1.72681i
891891 −135.698 + 95.3361i −0.152299 + 0.106999i
892892 −64.6759 + 64.6759i −0.0725067 + 0.0725067i
893893 −4.18956 + 15.6357i −0.00469156 + 0.0175091i
894894 −924.963 + 407.428i −1.03463 + 0.455736i
895895 93.2817 437.319i 0.104225 0.488625i
896896 1057.12 1830.98i 1.17982 2.04350i
897897 23.6041 + 152.957i 0.0263145 + 0.170521i
898898 −217.774 + 812.743i −0.242510 + 0.905058i
899899 537.328i 0.597696i
900900 182.937 1596.52i 0.203263 1.77391i
901901 −114.384 −0.126952
902902 −28.4855 7.63268i −0.0315804 0.00846195i
903903 538.974 + 671.006i 0.596871 + 0.743086i
904904 −369.109 213.105i −0.408307 0.235736i
905905 −1502.87 320.568i −1.66063 0.354218i
906906 2172.02 + 237.009i 2.39738 + 0.261600i
907907 638.156 + 170.993i 0.703589 + 0.188526i 0.592838 0.805322i 0.298008π-0.298008\pi
0.110752 + 0.993848i 0.464674π0.464674\pi
908908 2235.42 + 2235.42i 2.46191 + 2.46191i
909909 −120.377 + 545.019i −0.132428 + 0.599581i
910910 −586.423 299.326i −0.644421 0.328929i
911911 536.476 + 929.204i 0.588887 + 1.01998i 0.994379 + 0.105884i 0.0337671π0.0337671\pi
−0.405491 + 0.914099i 0.632900π0.632900\pi
912912 −54.9189 355.881i −0.0602181 0.390221i
913913 314.231 84.1979i 0.344174 0.0922211i
914914 853.309 + 492.658i 0.933598 + 0.539013i
915915 −1059.14 60.4830i −1.15753 0.0661017i
916916 677.331 + 1173.17i 0.739444 + 1.28075i
917917 532.635 532.635i 0.580846 0.580846i
918918 1212.86 1819.82i 1.32120 1.98238i
919919 728.665i 0.792889i −0.918059 0.396444i 0.870244π-0.870244\pi
0.918059 0.396444i 0.129756π-0.129756\pi
920920 −463.989 418.378i −0.504336 0.454759i
921921 −236.692 537.349i −0.256995 0.583441i
922922 −440.399 1643.59i −0.477656 1.78264i
923923 −119.669 + 32.0652i −0.129652 + 0.0347402i
924924 −322.384 236.187i −0.348901 0.255613i
925925 −1099.21 + 420.146i −1.18833 + 0.454212i
926926 −985.543 −1.06430
927927 −422.117 219.317i −0.455358 0.236588i
928928 325.515 + 325.515i 0.350771 + 0.350771i
929929 844.876 487.790i 0.909447 0.525070i 0.0291940 0.999574i 0.490706π-0.490706\pi
0.880253 + 0.474504i 0.157373π0.157373\pi
930930 −243.047 1170.37i −0.261341 1.25847i
931931 316.763 548.649i 0.340239 0.589312i
932932 −164.149 612.611i −0.176125 0.657308i
933933 −201.534 250.903i −0.216006 0.268921i
934934 1536.11 886.871i 1.64465 0.949541i
935935 −221.255 112.934i −0.236636 0.120785i
936936 123.219 + 389.729i 0.131644 + 0.416377i
937937 −141.251 + 141.251i −0.150749 + 0.150749i −0.778452 0.627704i 0.783995π-0.783995\pi
0.627704 + 0.778452i 0.283995π0.283995\pi
938938 −170.268 + 635.447i −0.181522 + 0.677449i
939939 1323.62 + 969.716i 1.40961 + 1.03271i
940940 16.8747 + 26.0255i 0.0179518 + 0.0276867i
941941 557.909 966.326i 0.592889 1.02691i −0.400952 0.916099i 0.631321π-0.631321\pi
0.993841 0.110815i 0.0353461π-0.0353461\pi
942942 2478.20 + 962.596i 2.63079 + 1.02186i
943943 −13.3057 + 49.6574i −0.0141099 + 0.0526589i
944944 493.269i 0.522531i
945945 −1229.77 15.5235i −1.30134 0.0164270i
946946 −215.217 −0.227502
947947 −766.094 205.274i −0.808969 0.216763i −0.169451 0.985539i 0.554199π-0.554199\pi
−0.639518 + 0.768776i 0.720866π0.720866\pi
948948 −1.80669 + 4.65132i −0.00190579 + 0.00490646i
949949 255.263 + 147.376i 0.268981 + 0.155296i
950950 −980.435 + 1207.21i −1.03204 + 1.27074i
951951 −773.604 + 1055.93i −0.813464 + 1.11034i
952952 2239.54 + 600.082i 2.35245 + 0.630338i
953953 −80.4623 80.4623i −0.0844305 0.0844305i 0.663630 0.748061i 0.269015π-0.269015\pi
−0.748061 + 0.663630i 0.769015π0.769015\pi
954954 30.5413 138.278i 0.0320139 0.144946i
955955 −252.217 778.135i −0.264102 0.814801i
956956 238.807 + 413.625i 0.249798 + 0.432662i
957957 107.781 86.5729i 0.112623 0.0904628i
958958 1397.02 374.330i 1.45826 0.390741i
959959 −1230.39 710.365i −1.28299 0.740735i
960960 1179.36 + 773.765i 1.22850 + 0.806006i
961961 195.525 + 338.658i 0.203459 + 0.352402i
962962 481.095 481.095i 0.500099 0.500099i
963963 −1073.06 + 47.6980i −1.11429 + 0.0495306i
964964 423.810i 0.439636i
965965 −1269.21 + 65.6073i −1.31524 + 0.0679869i
966966 −642.328 + 876.748i −0.664935 + 0.907607i
967967 87.9314 + 328.164i 0.0909322 + 0.339363i 0.996371 0.0851126i 0.0271250π-0.0271250\pi
−0.905439 + 0.424476i 0.860458π0.860458\pi
968968 −1183.35 + 317.078i −1.22247 + 0.327560i
969969 −1241.56 + 546.884i −1.28128 + 0.564380i
970970 894.776 + 806.818i 0.922449 + 0.831771i
971971 1786.19 1.83954 0.919769 0.392460i 0.128376π-0.128376\pi
0.919769 + 0.392460i 0.128376π0.128376\pi
972972 1202.60 + 1251.31i 1.23724 + 1.28736i
973973 −10.0620 10.0620i −0.0103413 0.0103413i
974974 −1707.67 + 985.926i −1.75326 + 1.01224i
975975 163.900 280.377i 0.168103 0.287566i
976976 −227.759 + 394.490i −0.233360 + 0.404191i
977977 −199.197 743.412i −0.203886 0.760913i −0.989786 0.142560i 0.954467π-0.954467\pi
0.785900 0.618353i 0.212200π-0.212200\pi
978978 2254.45 347.902i 2.30516 0.355728i
979979 −183.313 + 105.836i −0.187246 + 0.108106i
980980 −374.304 1154.80i −0.381943 1.17836i
981981 −622.578 + 680.501i −0.634637 + 0.693681i
982982 −1817.45 + 1817.45i −1.85076 + 1.85076i
983983 −21.2470 + 79.2948i −0.0216144 + 0.0806661i −0.975891 0.218260i 0.929962π-0.929962\pi
0.954276 + 0.298926i 0.0966285π0.0966285\pi
984984 −14.7279 + 134.971i −0.0149674 + 0.137166i
985985 498.303 323.096i 0.505892 0.328016i
986986 −911.523 + 1578.80i −0.924466 + 1.60122i
987987 18.5076 14.8660i 0.0187514 0.0150618i
988988 149.173 556.722i 0.150985 0.563484i
989989 375.177i 0.379350i
990990 195.602 237.319i 0.197577 0.239716i
991991 −515.156 −0.519835 −0.259917 0.965631i 0.583695π-0.583695\pi
−0.259917 + 0.965631i 0.583695π0.583695\pi
992992 471.659 + 126.381i 0.475462 + 0.127400i
993993 −1738.33 + 268.256i −1.75059 + 0.270147i
994994 −753.465 435.013i −0.758013 0.437639i
995995 172.171 807.166i 0.173036 0.811222i
996996 −1372.35 3115.57i −1.37786 3.12808i
997997 358.637 + 96.0965i 0.359716 + 0.0963856i 0.434151 0.900840i 0.357049π-0.357049\pi
−0.0744346 + 0.997226i 0.523715π0.523715\pi
998998 −231.032 231.032i −0.231495 0.231495i
999999 407.098 1203.94i 0.407505 1.20515i
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 45.3.k.a.13.2 yes 40
3.2 odd 2 135.3.l.a.118.9 40
5.2 odd 4 inner 45.3.k.a.22.9 yes 40
5.3 odd 4 225.3.o.b.157.2 40
5.4 even 2 225.3.o.b.193.9 40
9.2 odd 6 135.3.l.a.73.2 40
9.4 even 3 405.3.g.h.163.9 20
9.5 odd 6 405.3.g.g.163.2 20
9.7 even 3 inner 45.3.k.a.43.9 yes 40
15.2 even 4 135.3.l.a.37.2 40
45.2 even 12 135.3.l.a.127.9 40
45.7 odd 12 inner 45.3.k.a.7.2 40
45.22 odd 12 405.3.g.h.82.9 20
45.32 even 12 405.3.g.g.82.2 20
45.34 even 6 225.3.o.b.43.2 40
45.43 odd 12 225.3.o.b.7.9 40
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
45.3.k.a.7.2 40 45.7 odd 12 inner
45.3.k.a.13.2 yes 40 1.1 even 1 trivial
45.3.k.a.22.9 yes 40 5.2 odd 4 inner
45.3.k.a.43.9 yes 40 9.7 even 3 inner
135.3.l.a.37.2 40 15.2 even 4
135.3.l.a.73.2 40 9.2 odd 6
135.3.l.a.118.9 40 3.2 odd 2
135.3.l.a.127.9 40 45.2 even 12
225.3.o.b.7.9 40 45.43 odd 12
225.3.o.b.43.2 40 45.34 even 6
225.3.o.b.157.2 40 5.3 odd 4
225.3.o.b.193.9 40 5.4 even 2
405.3.g.g.82.2 20 45.32 even 12
405.3.g.g.163.2 20 9.5 odd 6
405.3.g.h.82.9 20 45.22 odd 12
405.3.g.h.163.9 20 9.4 even 3