LMFDB - Embedded newform 153.2.s.a.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [153,2,Mod(5,153)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(153, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([40, 15]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("153.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 153 = 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	153.s (of order $48$, degree $16$, 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:	$1.22171115093$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$16$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	153.11
Dual form			153.2.s.a.14.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53625 - 2.00208i) q^{2} +(-1.72157 + 0.190287i) q^{3} +(-1.13062 + 4.21953i) q^{4} +(3.62526 + 0.237612i) q^{5} +(3.02572 + 3.15438i) q^{6} +(0.115282 + 1.75887i) q^{7} +(5.52180 - 2.28721i) q^{8} +(2.92758 - 0.655185i) q^{9} +O(q^{10})$	\(q+(-1.53625 - 2.00208i) q^{2} +(-1.72157 + 0.190287i) q^{3} +(-1.13062 + 4.21953i) q^{4} +(3.62526 + 0.237612i) q^{5} +(3.02572 + 3.15438i) q^{6} +(0.115282 + 1.75887i) q^{7} +(5.52180 - 2.28721i) q^{8} +(2.92758 - 0.655185i) q^{9} +(-5.09359 - 7.62309i) q^{10} +(0.00330703 + 0.00290019i) q^{11} +(1.14351 - 7.47934i) q^{12} +(-2.63273 - 0.705439i) q^{13} +(3.34429 - 2.93287i) q^{14} +(-6.28634 + 0.280777i) q^{15} +(-5.49578 - 3.17299i) q^{16} +(4.10519 - 0.383985i) q^{17} +(-5.80923 - 4.85472i) q^{18} +(6.69553 + 2.77338i) q^{19} +(-5.10140 + 15.0283i) q^{20} +(-0.533157 - 3.00607i) q^{21} +(0.000725982 - 0.0110763i) q^{22} +(-1.62305 - 4.78136i) q^{23} +(-9.07092 + 4.98831i) q^{24} +(8.12884 + 1.07018i) q^{25} +(2.63219 + 6.35467i) q^{26} +(-4.91535 + 1.68503i) q^{27} +(-7.55194 - 1.50217i) q^{28} +(4.06670 - 2.00547i) q^{29} +(10.2195 + 12.1544i) q^{30} +(-0.219566 - 0.250367i) q^{31} +(0.530062 + 4.02622i) q^{32} +(-0.00624514 - 0.00436358i) q^{33} +(-7.07536 - 7.62901i) q^{34} +6.40375i q^{35} +(-0.545408 + 13.0938i) q^{36} +(0.151512 + 0.761704i) q^{37} +(-4.73348 - 17.6656i) q^{38} +(4.66666 + 0.713483i) q^{39} +(20.5615 - 6.97967i) q^{40} +(-3.04838 + 6.18150i) q^{41} +(-5.19933 + 5.68550i) q^{42} +(-1.30212 + 9.89055i) q^{43} +(-0.0159764 + 0.0106751i) q^{44} +(10.7689 - 1.67959i) q^{45} +(-7.07925 + 10.5948i) q^{46} +(-4.72986 + 1.26736i) q^{47} +(10.0651 + 4.41673i) q^{48} +(3.85978 - 0.508150i) q^{49} +(-10.3453 - 17.9186i) q^{50} +(-6.99428 + 1.44222i) q^{51} +(5.95324 - 10.3113i) q^{52} +(1.83285 - 4.42488i) q^{53} +(10.9248 + 7.25230i) q^{54} +(0.0112997 + 0.0112997i) q^{55} +(4.65946 + 9.44845i) q^{56} +(-12.0545 - 3.50048i) q^{57} +(-10.2626 - 5.06094i) q^{58} +(-7.04508 - 5.40588i) q^{59} +(5.92272 - 26.8429i) q^{60} +(-8.03867 + 0.526882i) q^{61} +(-0.163946 + 0.824214i) q^{62} +(1.48988 + 5.07370i) q^{63} +(-1.72806 + 1.72806i) q^{64} +(-9.37672 - 3.18297i) q^{65} +(0.000857863 + 0.0192068i) q^{66} +(6.84774 - 3.95355i) q^{67} +(-3.02117 + 17.7561i) q^{68} +(3.70403 + 7.92258i) q^{69} +(12.8208 - 9.83776i) q^{70} +(-7.33915 + 1.45985i) q^{71} +(14.6670 - 10.3138i) q^{72} +(-4.87788 - 3.25929i) q^{73} +(1.29223 - 1.47351i) q^{74} +(-14.1980 - 0.295573i) q^{75} +(-19.2725 + 25.1164i) q^{76} +(-0.00471981 + 0.00615097i) q^{77} +(-5.74070 - 10.4391i) q^{78} +(3.25903 - 3.71621i) q^{79} +(-19.1697 - 12.8088i) q^{80} +(8.14147 - 3.83621i) q^{81} +(17.0589 - 3.39323i) q^{82} +(6.51878 - 5.00204i) q^{83} +(13.2870 + 1.14905i) q^{84} +(14.9736 - 0.416603i) q^{85} +(21.8020 - 12.5874i) q^{86} +(-6.61948 + 4.22640i) q^{87} +(0.0248941 + 0.00845040i) q^{88} +(-1.47920 + 1.47920i) q^{89} +(-19.9064 - 18.9800i) q^{90} +(0.937266 - 4.71196i) q^{91} +(22.0102 - 1.44262i) q^{92} +(0.425639 + 0.389243i) q^{93} +(9.80361 + 7.52257i) q^{94} +(23.6141 + 11.6452i) q^{95} +(-1.67868 - 6.83054i) q^{96} +(-0.138880 - 0.281621i) q^{97} +(-6.94694 - 6.94694i) q^{98} +(0.0115818 + 0.00632382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	$ 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) $ 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/153\mathbb{Z}\right)^\times$.

$n$	$37$	$137$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.53625	−	2.00208i	−1.08629	−	1.41568i	−0.901433	−	0.432918i	$-0.857484\pi$
$2$	−1.53625	−	2.00208i	−1.08629	−	1.41568i	−0.184859	−	0.982765i	$-0.559183\pi$
$3$	−1.72157	+	0.190287i	−0.993947	+	0.109863i
$3$	−1.72157	+	0.190287i	−0.993947	+	0.109863i
$4$	−1.13062	+	4.21953i	−0.565310	+	2.10976i
$5$	3.62526	+	0.237612i	1.62127	+	0.106263i	0.848772	−	0.528759i	$-0.177342\pi$
$5$	3.62526	+	0.237612i	1.62127	+	0.106263i	0.772494	+	0.635022i	$0.219009\pi$
$6$	3.02572	+	3.15438i	1.23525	+	1.28777i
$7$	0.115282	+	1.75887i	0.0435726	+	0.664790i	0.962656	+	0.270727i	$0.0872641\pi$
$7$	0.115282	+	1.75887i	0.0435726	+	0.664790i	−0.919083	+	0.394063i	$0.871069\pi$
$8$	5.52180	−	2.28721i	1.95225	−	0.808649i
$9$	2.92758	−	0.655185i	0.975860	−	0.218395i
$10$	−5.09359	−	7.62309i	−1.61073	−	2.41063i
$11$	0.00330703	+	0.00290019i	0.000997107	+	0.000874439i	0.659844	−	0.751402i	$-0.270622\pi$
$11$	0.00330703	+	0.00290019i	0.000997107	+	0.000874439i	−0.658847	+	0.752277i	$0.728956\pi$
$12$	1.14351	−	7.47934i	0.330104	−	2.15910i
$13$	−2.63273	−	0.705439i	−0.730189	−	0.195653i	−0.125475	−	0.992097i	$-0.540046\pi$
$13$	−2.63273	−	0.705439i	−0.730189	−	0.195653i	−0.604713	+	0.796443i	$0.706712\pi$
$14$	3.34429	−	2.93287i	0.893800	−	0.783841i
$15$	−6.28634	+	0.280777i	−1.62313	+	0.0724962i
$16$	−5.49578	−	3.17299i	−1.37394	−	0.793247i
$17$	4.10519	−	0.383985i	0.995654	−	0.0931300i
$17$	4.10519	−	0.383985i	0.995654	−	0.0931300i
$18$	−5.80923	−	4.85472i	−1.36925	−	1.14427i
$19$	6.69553	+	2.77338i	1.53606	+	0.636257i	0.980729	−	0.195372i	$-0.0625914\pi$
$19$	6.69553	+	2.77338i	1.53606	+	0.636257i	0.555331	+	0.831629i	$0.312591\pi$
$20$	−5.10140	+	15.0283i	−1.14071	+	3.36042i
$21$	−0.533157	−	3.00607i	−0.116344	−	0.655979i
$22$	0.000725982	−	0.0110763i	0.000154780	−	0.00236148i
$23$	−1.62305	−	4.78136i	−0.338430	−	0.996983i	−0.974313	−	0.225197i	$-0.927697\pi$
$23$	−1.62305	−	4.78136i	−0.338430	−	0.996983i	0.635883	−	0.771785i	$-0.280636\pi$
$24$	−9.07092	+	4.98831i	−1.85159	+	1.01823i
$25$	8.12884	+	1.07018i	1.62577	+	0.214036i
$26$	2.63219	+	6.35467i	0.516215	+	1.24625i
$27$	−4.91535	+	1.68503i	−0.945960	+	0.324283i
$28$	−7.55194	−	1.50217i	−1.42718	−	0.283884i
$29$	4.06670	−	2.00547i	0.755167	−	0.372407i	−0.0235990	−	0.999722i	$-0.507512\pi$
$29$	4.06670	−	2.00547i	0.755167	−	0.372407i	0.778766	+	0.627314i	$0.215846\pi$
$30$	10.2195	+	12.1544i	1.86582	+	2.21908i
$31$	−0.219566	−	0.250367i	−0.0394352	−	0.0449673i	0.731786	−	0.681535i	$-0.238687\pi$
$31$	−0.219566	−	0.250367i	−0.0394352	−	0.0449673i	−0.771221	+	0.636567i	$0.780354\pi$
$32$	0.530062	+	4.02622i	0.0937026	+	0.711742i
$33$	−0.00624514	−	0.00436358i	−0.00108714	−	0.000759601i
$34$	−7.07536	−	7.62901i	−1.21341	−	1.30836i
$35$			6.40375i			1.08243i
$36$	−0.545408	+	13.0938i	−0.0909014	+	2.18230i
$37$	0.151512	+	0.761704i	0.0249085	+	0.125223i	0.991239	−	0.132081i	$-0.0421658\pi$
$37$	0.151512	+	0.761704i	0.0249085	+	0.125223i	−0.966330	+	0.257304i	$0.917166\pi$
$38$	−4.73348	−	17.6656i	−0.767872	−	2.86574i
$39$	4.66666	+	0.713483i	0.747264	+	0.114249i
$40$	20.5615	−	6.97967i	3.25105	−	1.10358i
$41$	−3.04838	+	6.18150i	−0.476077	+	0.965389i	0.517863	+	0.855464i	$0.326728\pi$
$41$	−3.04838	+	6.18150i	−0.476077	+	0.965389i	−0.993940	+	0.109925i	$0.964939\pi$
$42$	−5.19933	+	5.68550i	−0.802274	+	0.877291i
$43$	−1.30212	+	9.89055i	−0.198571	+	1.50829i	0.544318	+	0.838879i	$0.316789\pi$
$43$	−1.30212	+	9.89055i	−0.198571	+	1.50829i	−0.742888	+	0.669415i	$0.766545\pi$
$44$	−0.0159764	+	0.0106751i	−0.00240854	+	0.00160933i
$45$	10.7689	−	1.67959i	1.60534	−	0.250378i
$46$	−7.07925	+	10.5948i	−1.04378	+	1.56212i
$47$	−4.72986	+	1.26736i	−0.689922	+	0.184864i	−0.586712	−	0.809796i	$-0.699578\pi$
$47$	−4.72986	+	1.26736i	−0.689922	+	0.184864i	−0.103210	+	0.994660i	$0.532911\pi$
$48$	10.0651	+	4.41673i	1.45278	+	0.637500i
$49$	3.85978	−	0.508150i	0.551398	−	0.0725929i
$50$	−10.3453	−	17.9186i	−1.46305	−	2.53408i
$51$	−6.99428	+	1.44222i	−0.979396	+	0.201951i
$52$	5.95324	−	10.3113i	0.825566	−	1.42992i
$53$	1.83285	−	4.42488i	0.251761	−	0.607804i	−0.746586	−	0.665289i	$-0.768308\pi$
$53$	1.83285	−	4.42488i	0.251761	−	0.607804i	0.998346	+	0.0574852i	$0.0183082\pi$
$54$	10.9248	+	7.25230i	1.48667	+	0.986913i
$55$	0.0112997	+	0.0112997i	0.00152365	+	0.00152365i
$56$	4.65946	+	9.44845i	0.622647	+	1.26260i
$57$	−12.0545	−	3.50048i	−1.59666	−	0.463650i
$58$	−10.2626	−	5.06094i	−1.34754	−	0.664535i
$59$	−7.04508	−	5.40588i	−0.917192	−	0.703786i	0.0381554	−	0.999272i	$-0.487852\pi$
$59$	−7.04508	−	5.40588i	−0.917192	−	0.703786i	−0.955347	+	0.295486i	$0.904518\pi$
$60$	5.92272	−	26.8429i	0.764620	−	3.46540i
$61$	−8.03867	+	0.526882i	−1.02925	+	0.0674604i	−0.570657	−	0.821188i	$-0.693312\pi$
$61$	−8.03867	+	0.526882i	−1.02925	+	0.0674604i	−0.458589	+	0.888649i	$0.651645\pi$
$62$	−0.163946	+	0.824214i	−0.0208212	+	0.104675i
$63$	1.48988	+	5.07370i	0.187708	+	0.639226i
$64$	−1.72806	+	1.72806i	−0.216007	+	0.216007i
$65$	−9.37672	−	3.18297i	−1.16304	−	0.394799i
$66$	0.000857863		0.0192068i	0.000105596		0.00236419i
$67$	6.84774	−	3.95355i	0.836585	−	0.483003i	−0.0195168	−	0.999810i	$-0.506213\pi$
$67$	6.84774	−	3.95355i	0.836585	−	0.483003i	0.856102	+	0.516807i	$0.172879\pi$
$68$	−3.02117	+	17.7561i	−0.366371	+	2.15324i
$69$	3.70403	+	7.92258i	0.445913	+	0.953767i
$70$	12.8208	−	9.83776i	1.53238	−	1.17584i
$71$	−7.33915	+	1.45985i	−0.870997	+	0.173252i	−0.610302	−	0.792169i	$-0.708952\pi$
$71$	−7.33915	+	1.45985i	−0.870997	+	0.173252i	−0.260695	+	0.965421i	$0.583952\pi$
$72$	14.6670	−	10.3138i	1.72852	−	1.21549i
$73$	−4.87788	−	3.25929i	−0.570912	−	0.381472i	0.236347	−	0.971669i	$-0.424050\pi$
$73$	−4.87788	−	3.25929i	−0.570912	−	0.381472i	−0.807259	+	0.590197i	$0.799050\pi$
$74$	1.29223	−	1.47351i	0.150219	−	0.171292i
$75$	−14.1980	−	0.295573i	−1.63944	−	0.0341298i
$76$	−19.2725	+	25.1164i	−2.21070	+	2.88104i
$77$	−0.00471981	+	0.00615097i	−0.000537872	+	0.000700968i
$78$	−5.74070	−	10.4391i	−0.650006	−	1.18200i
$79$	3.25903	−	3.71621i	0.366669	−	0.418106i	−0.538857	−	0.842398i	$-0.681144\pi$
$79$	3.25903	−	3.71621i	0.366669	−	0.418106i	0.905526	+	0.424292i	$0.139477\pi$
$80$	−19.1697	−	12.8088i	−2.14324	−	1.43206i
$81$	8.14147	−	3.83621i	0.904607	−	0.426246i
$82$	17.0589	−	3.39323i	1.88384	−	0.374720i
$83$	6.51878	−	5.00204i	0.715529	−	0.549045i	−0.185584	−	0.982628i	$-0.559418\pi$
$83$	6.51878	−	5.00204i	0.715529	−	0.549045i	0.901113	+	0.433583i	$0.142751\pi$
$84$	13.2870	+	1.14905i	1.44973	+	0.125372i
$85$	14.9736	−	0.416603i	1.62412	−	0.0451869i
$86$	21.8020	−	12.5874i	2.35097	−	1.35734i
$87$	−6.61948	+	4.22640i	−0.709682	+	0.453118i
$88$	0.0248941	+	0.00845040i	0.00265372	+	0.000900816i
$89$	−1.47920	+	1.47920i	−0.156795	+	0.156795i	−0.781145	−	0.624350i	$-0.785364\pi$
$89$	−1.47920	+	1.47920i	−0.156795	+	0.156795i	0.624350	+	0.781145i	$0.285364\pi$
$90$	−19.9064	−	18.9800i	−2.09832	−	2.00067i
$91$	0.937266	−	4.71196i	0.0982522	−	0.493947i
$92$	22.0102	−	1.44262i	2.29472	−	0.150404i
$93$	0.425639	+	0.389243i	0.0441367	+	0.0403626i
$94$	9.80361	+	7.52257i	1.01116	+	0.775894i
$95$	23.6141	+	11.6452i	2.42275	+	1.19477i
$96$	−1.67868	−	6.83054i	−0.171329	−	0.697139i
$97$	−0.138880	−	0.281621i	−0.0141012	−	0.0285943i	0.889708	−	0.456530i	$-0.150908\pi$
$97$	−0.138880	−	0.281621i	−0.0141012	−	0.0285943i	−0.903809	+	0.427935i	$0.859241\pi$
$98$	−6.94694	−	6.94694i	−0.701747	−	0.701747i
$99$	0.0115818	+	0.00632382i	0.00116401	+	0.000635567i
$100$	−13.7063	+	33.0899i	−1.37063	+	3.30899i
$101$	−4.16613	+	7.21595i	−0.414546	+	0.718014i	−0.995381	−	0.0960071i	$-0.969393\pi$
$101$	−4.16613	+	7.21595i	−0.414546	+	0.718014i	0.580835	+	0.814021i	$0.302726\pi$
$102$	13.6324	+	11.7875i	1.34981	+	1.16714i
$103$	−3.71221	−	6.42974i	−0.365775	−	0.633541i	0.623125	−	0.782122i	$-0.285863\pi$
$103$	−3.71221	−	6.42974i	−0.365775	−	0.633541i	−0.988900	+	0.148581i	$0.952529\pi$
$104$	−16.1509	+	2.12631i	−1.58373	+	0.208502i
$105$	−1.21855	−	11.0245i	−0.118919	−	1.07588i
$106$	−11.6747	+	3.12822i	−1.13394	+	0.303839i
$107$	−3.29877	+	4.93696i	−0.318904	+	0.477274i	−0.955941	−	0.293560i	$-0.905160\pi$
$107$	−3.29877	+	4.93696i	−0.318904	+	0.477274i	0.637037	+	0.770834i	$0.280160\pi$
$108$	−1.55263	−	22.6456i	−0.149402	−	2.17907i
$109$	−8.24059	+	5.50619i	−0.789306	+	0.527397i	−0.883653	−	0.468142i	$-0.844924\pi$
$109$	−8.24059	+	5.50619i	−0.789306	+	0.527397i	0.0943474	+	0.995539i	$0.469924\pi$
$110$	0.00526375	−	0.0399821i	0.000501879	−	0.00381215i
$111$	−0.405781	−	1.28249i	−0.0385151	−	0.121729i
$112$	4.94730	−	10.0321i	0.467476	−	0.947948i
$113$	−10.2547	+	3.48101i	−0.964683	+	0.327466i	−0.758955	−	0.651144i	$-0.774290\pi$
$113$	−10.2547	+	3.48101i	−0.964683	+	0.327466i	−0.205728	+	0.978609i	$0.565956\pi$
$114$	11.5105	+	29.5118i	1.07806	+	2.76403i
$115$	−4.74788	−	17.7193i	−0.442742	−	1.65234i
$116$	3.86427	+	19.4270i	0.358788	+	1.80375i
$117$	−8.16973	−	0.340302i	−0.755292	−	0.0314609i
$118$			22.4096i			2.06297i
$119$	1.14863	+	7.17622i	0.105295	+	0.657843i
$120$	−34.0698	+	15.9286i	−3.11013	+	1.45407i
$121$	−1.43579	−	10.9059i	−0.130526	−	0.991443i
$122$	13.4043	+	15.2846i	1.21356	+	1.38380i
$123$	4.07173	−	11.2219i	0.367135	−	1.01185i
$124$	1.30468	−	0.643395i	0.117163	−	0.0577786i
$125$	11.3987	+	2.26735i	1.01953	+	0.202798i
$126$	7.86912	−	10.7773i	0.701037	−	0.960121i
$127$	−2.78236	−	6.71720i	−0.246894	−	0.596055i	0.751043	−	0.660253i	$-0.229551\pi$
$127$	−2.78236	−	6.71720i	−0.246894	−	0.596055i	−0.997937	+	0.0641981i	$0.979551\pi$
$128$	14.1669	+	1.86511i	1.25219	+	0.164854i
$129$	0.359631	−	17.2750i	0.0316637	−	1.52098i
$130$	8.03243	+	23.6628i	0.704491	+	2.07536i
$131$	0.00303181	−	0.0462565i	0.000264890	−	0.00404145i	−0.997724	−	0.0674237i	$-0.978522\pi$
$131$	0.00303181	−	0.0462565i	0.000264890	−	0.00404145i	0.997989	+	0.0633823i	$0.0201887\pi$
$132$	0.0254731	−	0.0214180i	0.00221715	−	0.00186420i
$133$	−4.10614	+	12.0963i	−0.356047	+	1.04888i
$134$	−18.4352	−	7.63609i	−1.59255	−	0.659658i
$135$	−18.2198	+	4.94071i	−1.56811	+	0.425229i
$136$	21.7898	−	11.5097i	1.86846	−	0.986948i
$137$	−12.0960	−	6.98362i	−1.03343	−	0.596651i	−0.115464	−	0.993312i	$-0.536836\pi$
$137$	−12.0960	−	6.98362i	−1.03343	−	0.596651i	−0.917965	+	0.396661i	$0.870169\pi$
$138$	10.1713	−	19.5868i	0.865841	−	1.66734i
$139$	−4.01436	+	3.52050i	−0.340493	+	0.298605i	−0.812466	−	0.583009i	$-0.801875\pi$
$139$	−4.01436	+	3.52050i	−0.340493	+	0.298605i	0.471973	+	0.881613i	$0.343542\pi$
$140$	−27.0208	−	7.24021i	−2.28368	−	0.611909i
$141$	7.90161	−	3.08188i	0.665436	−	0.259541i
$142$	14.1975	+	12.4509i	1.19143	+	1.04485i
$143$	−0.00666062	−	0.00996832i	−0.000556989	−	0.000833593i
$144$	−18.1682	−	5.68843i	−1.51402	−	0.474036i
$145$	15.2194	−	6.30407i	1.26390	−	0.523525i
$146$	0.968272	+	14.7730i	0.0801348	+	1.22262i
$147$	−6.54818	+	1.60928i	−0.540085	+	0.132731i
$148$	−3.38534	−	0.221887i	−0.278273	−	0.0182390i
$149$	0.916778	−	3.42146i	0.0751054	−	0.280297i	−0.918152	−	0.396229i	$-0.870319\pi$
$149$	0.916778	−	3.42146i	0.0751054	−	0.280297i	0.993257	+	0.115932i	$0.0369854\pi$
$150$	21.2199	+	28.8795i	1.73260	+	2.35800i
$151$	−1.29682	−	1.69004i	−0.105533	−	0.137534i	0.737601	−	0.675237i	$-0.235959\pi$
$151$	−1.29682	−	1.69004i	−0.105533	−	0.137534i	−0.843134	+	0.537703i	$0.819292\pi$
$152$	43.3147			3.51329
$153$	11.7667	−	3.81380i	0.951280	−	0.308328i
$154$	0.0195655			0.00157663
$155$	−0.736494	−	0.959818i	−0.0591566	−	0.0770944i
$156$	−8.28678	+	18.8844i	−0.663473	+	1.51196i
$157$	−3.10106	+	11.5733i	−0.247492	+	0.923651i	0.724623	+	0.689145i	$0.242014\pi$
$157$	−3.10106	+	11.5733i	−0.247492	+	0.923651i	−0.972115	+	0.234506i	$0.924653\pi$
$158$	−12.4468	−	0.815807i	−0.990215	−	0.0649021i
$159$	−2.31337	+	7.96649i	−0.183462	+	0.631784i
$160$	0.964935	+	14.7221i	0.0762848	+	1.16388i
$161$	8.22268	−	3.40595i	0.648038	−	0.268426i
$162$	−20.1877	−	10.4065i	−1.58610	−	0.817610i
$163$	4.55777	+	6.82118i	0.356992	+	0.534276i	0.965883	−	0.258977i	$-0.0833855\pi$
$163$	4.55777	+	6.82118i	0.356992	+	0.534276i	−0.608891	+	0.793254i	$0.708385\pi$
$164$	−22.6365	−	19.8517i	−1.76761	−	1.55015i
$165$	−0.0216034	−	0.0173030i	−0.00168182	−	0.00134704i
$166$	−20.0289	−	5.36674i	−1.55455	−	0.416540i
$167$	13.5258	−	11.8618i	1.04666	−	0.917896i	0.0499338	−	0.998753i	$-0.484099\pi$
$167$	13.5258	−	11.8618i	1.04666	−	0.917896i	0.996726	+	0.0808567i	$0.0257656\pi$
$168$	−9.81950	−	15.3795i	−0.757591	−	1.18655i
$169$	−4.82469	−	2.78554i	−0.371130	−	0.214272i
$170$	−23.8373	−	29.3383i	−1.82824	−	2.25015i
$171$	21.4188	+	3.73248i	1.63794	+	0.285430i
$172$	−40.2613	−	16.6768i	−3.06989	−	1.27159i
$173$	−3.71478	+	10.9434i	−0.282429	+	0.832010i	0.709442	+	0.704764i	$0.248947\pi$
$173$	−3.71478	+	10.9434i	−0.282429	+	0.832010i	−0.991871	+	0.127246i	$0.959386\pi$
$174$	18.6307	+	6.75991i	1.41239	+	0.512468i
$175$	−0.945198	+	14.4209i	−0.0714503	+	1.09012i
$176$	−0.00897243	−	0.0264319i	−0.000676323	−	0.00199238i
$177$	13.1572	+	7.96599i	0.988959	+	0.598761i
$178$	5.23390	+	0.689056i	0.392297	+	0.0516469i
$179$	−2.50923	−	6.05782i	−0.187549	−	0.452783i	0.801938	−	0.597407i	$-0.203802\pi$
$179$	−2.50923	−	6.05782i	−0.187549	−	0.452783i	−0.989487	+	0.144625i	$0.953802\pi$
$180$	−5.08849	+	47.3388i	−0.379274	+	3.52843i
$181$	10.0902	+	2.00706i	0.749998	+	0.149184i	0.555266	−	0.831673i	$-0.312616\pi$
$181$	10.0902	+	2.00706i	0.749998	+	0.149184i	0.194732	+	0.980857i	$0.437616\pi$
$182$	−10.8736	+	5.36226i	−0.806003	+	0.397477i
$183$	13.7388	−	2.43672i	1.01560	−	0.180128i
$184$	−19.8981	−	22.6895i	−1.46691	−	1.67269i
$185$	0.368282	+	2.79738i	0.0270766	+	0.205667i
$186$	0.125407	−	1.45014i	0.00919529	−	0.106329i
$187$	0.0146896	+	0.0106360i	0.00107421	+	0.000777778i
$188$		−	21.3907i		−	1.56008i
$189$	−3.53039	−	8.45121i	−0.256798	−	0.614735i
$190$	−12.9625	−	65.1671i	−0.940402	−	4.72772i
$191$	−5.98137	−	22.3228i	−0.432797	−	1.61522i	−0.746284	−	0.665627i	$-0.768164\pi$
$191$	−5.98137	−	22.3228i	−0.432797	−	1.61522i	0.313487	−	0.949592i	$-0.398503\pi$
$192$	2.64614	−	3.30380i	0.190969	−	0.238431i
$193$	−12.6221	+	4.28463i	−0.908560	+	0.308415i	−0.736314	−	0.676639i	$-0.763436\pi$
$193$	−12.6221	+	4.28463i	−0.908560	+	0.308415i	−0.172246	+	0.985054i	$0.555102\pi$
$194$	−0.350473	+	0.710689i	−0.0251625	+	0.0510245i
$195$	16.7483	+	3.69542i	1.19937	+	0.264634i
$196$	−2.21979	+	16.8610i	−0.158557	+	1.20436i
$197$	−3.47171	+	2.31973i	−0.247349	+	0.165274i	−0.673065	−	0.739584i	$-0.735022\pi$
$197$	−3.47171	+	2.31973i	−0.247349	+	0.165274i	0.425715	+	0.904857i	$0.360022\pi$
$198$	−0.00513168	−	0.0329025i	−0.000364693	−	0.00233828i
$199$	8.55412	−	12.8021i	0.606386	−	0.907520i	−0.393545	−	0.919305i	$-0.628751\pi$
$199$	8.55412	−	12.8021i	0.606386	−	0.907520i	0.999931	+	0.0117852i	$0.00375145\pi$
$200$	47.3336	−	12.6830i	3.34699	−	0.896823i
$201$	−11.0365	+	8.10933i	−0.778457	+	0.571988i
$202$	20.8471	−	2.74458i	1.46680	−	0.193108i
$203$	3.99619	+	6.92160i	0.280477	+	0.485801i
$204$	1.82238	−	31.1432i	0.127592	−	2.18046i
$205$	−12.5200	+	21.6852i	−0.874433	+	1.51456i
$206$	−7.16996	+	17.3098i	−0.499555	+	1.20603i
$207$	−7.88430	−	12.9344i	−0.547997	−	0.899005i
$208$	12.2306	+	12.2306i	0.848037	+	0.848037i
$209$	0.0140990	+	0.0285899i	0.000975248	+	0.00197761i
$210$	−20.1999	+	19.3760i	−1.39392	+	1.33707i
$211$	−13.7470	−	6.77928i	−0.946384	−	0.466705i	−0.0974715	−	0.995238i	$-0.531075\pi$
$211$	−13.7470	−	6.77928i	−0.946384	−	0.466705i	−0.848913	+	0.528533i	$0.822742\pi$
$212$	16.5987	+	12.7366i	1.14000	+	0.874753i
$213$	12.3570	−	3.90977i	0.846691	−	0.267893i
$214$	14.9519	−	0.980000i	1.02209	−	0.0669914i
$215$	−7.07063	+	35.5464i	−0.482213	+	2.42425i
$216$	−23.2876	+	20.5468i	−1.58452	+	1.39803i
$217$	0.415051	−	0.415051i	0.0281755	−	0.0281755i
$218$	23.6834	+	8.03944i	1.60404	+	0.544500i
$219$	9.01779	+	4.68289i	0.609366	+	0.316441i
$220$	−0.0604552	+	0.0349038i	−0.00407589	+	0.00235322i
$221$	−11.0787	−	1.88503i	−0.745236	−	0.126801i
$222$	−1.94427	+	2.78263i	−0.130491	+	0.186758i
$223$	11.2460	−	8.62937i	0.753089	−	0.577865i	−0.159281	−	0.987233i	$-0.550917\pi$
$223$	11.2460	−	8.62937i	0.753089	−	0.577865i	0.912369	+	0.409368i	$0.134251\pi$
$224$	−7.02049	+	1.39646i	−0.469076	+	0.0933051i
$225$	24.4990	−	2.19285i	1.63327	−	0.146190i
$226$	22.7230	+	15.1831i	1.51151	+	1.00996i
$227$	−14.7424	+	16.8105i	−0.978487	+	1.11575i	0.0147781	+	0.999891i	$0.495296\pi$
$227$	−14.7424	+	16.8105i	−0.978487	+	1.11575i	−0.993266	+	0.115860i	$0.963038\pi$
$228$	28.3995	−	46.9068i	1.88080	−	3.10648i
$229$	16.8576	−	21.9693i	1.11398	−	1.45177i	0.236838	−	0.971549i	$-0.423889\pi$
$229$	16.8576	−	21.9693i	1.11398	−	1.45177i	0.877146	−	0.480223i	$-0.159444\pi$
$230$	−28.1816	+	36.7270i	−1.85824	+	2.42170i
$231$	0.00695501	−	0.0114874i	0.000457606	−	0.000755817i
$232$	17.8686	−	20.3752i	1.17313	−	1.33770i
$233$	0.548308	+	0.366368i	0.0359209	+	0.0240016i	0.573401	−	0.819275i	$-0.305624\pi$
$233$	0.548308	+	0.366368i	0.0359209	+	0.0240016i	−0.537480	+	0.843276i	$0.680624\pi$
$234$	11.8694	+	16.8792i	0.775929	+	1.10343i
$235$	−17.4481	+	3.47065i	−1.13819	+	0.226400i
$236$	30.7756	−	23.6149i	2.00332	−	1.53720i
$237$	−4.90348	+	7.01785i	−0.318515	+	0.455858i
$238$	12.6028	−	13.3241i	0.816916	−	0.863674i
$239$	5.08597	−	2.93638i	0.328984	−	0.189939i	−0.326406	−	0.945230i	$-0.605838\pi$
$239$	5.08597	−	2.93638i	0.328984	−	0.189939i	0.655390	+	0.755291i	$0.272504\pi$
$240$	35.4392	+	18.4034i	2.28759	+	1.18793i
$241$	14.1739	+	4.81140i	0.913024	+	0.309930i	0.738131	−	0.674658i	$-0.235709\pi$
$241$	14.1739	+	4.81140i	0.913024	+	0.309930i	0.174893	+	0.984587i	$0.444042\pi$
$242$	−19.6287	+	19.6287i	−1.26178	+	1.26178i
$243$	−13.2861	+	8.15352i	−0.852303	+	0.523048i
$244$	6.86548	−	34.5151i	0.439517	−	2.20960i
$245$	14.1135	−	0.925046i	0.901676	−	0.0590990i
$246$	−28.7224	+	9.08777i	−1.83127	+	0.579415i
$247$	−15.6711	−	12.0249i	−0.997128	−	0.765123i
$248$	−1.78504	−	0.880285i	−0.113350	−	0.0558981i
$249$	−10.2707	+	9.85178i	−0.650879	+	0.624331i
$250$	−12.9719	−	26.3043i	−0.820413	−	1.66363i
$251$	13.1783	+	13.1783i	0.831810	+	0.831810i	0.987764	−	0.155955i	$-0.0498454\pi$
$251$	13.1783	+	13.1783i	0.831810	+	0.831810i	−0.155955	+	0.987764i	$0.549845\pi$
$252$	−23.0931	+	0.550181i	−1.45473	+	0.0346581i
$253$	0.00849936	−	0.0205193i	0.000534350	−	0.00129003i
$254$	−9.17397	+	15.8898i	−0.575626	+	0.997014i
$255$	−25.6988	+	3.56650i	−1.60932	+	0.223343i
$256$	−15.5859	−	26.9956i	−0.974120	−	1.68723i
$257$	6.33402	−	0.833890i	0.395105	−	0.0520166i	0.0696439	−	0.997572i	$-0.477814\pi$
$257$	6.33402	−	0.833890i	0.395105	−	0.0520166i	0.325461	+	0.945555i	$0.394480\pi$
$258$	−35.1384	+	25.8187i	−2.18762	+	1.60740i
$259$	−1.32227	+	0.354301i	−0.0821619	+	0.0220152i
$260$	24.0321	−	35.9666i	1.49041	−	2.23056i
$261$	10.5916	−	8.53563i	0.655606	−	0.528342i
$262$	−0.0972667	+	0.0649915i	−0.00600916	+	0.00401519i
$263$	−0.116008	+	0.881165i	−0.00715334	+	0.0543350i	−0.994649	−	0.103310i	$-0.967057\pi$
$263$	−0.116008	+	0.881165i	−0.00715334	+	0.0543350i	0.987496	+	0.157645i	$0.0503901\pi$
$264$	−0.0444648	−	0.00981090i	−0.00273662	−	0.000603819i
$265$	7.69595	−	15.6058i	0.472758	−	0.958659i
$266$	30.5258	−	10.3621i	1.87165	−	0.635341i
$267$	2.26507	−	2.82802i	0.138620	−	0.173072i
$268$	8.93992	+	33.3642i	0.546092	+	2.03804i
$269$	−5.76044	−	28.9597i	−0.351220	−	1.76570i	−0.602825	−	0.797873i	$-0.705958\pi$
$269$	−5.76044	−	28.9597i	−0.351220	−	1.76570i	0.251605	−	0.967830i	$-0.419042\pi$
$270$	37.8819	+	28.8873i	2.30542	+	1.75803i
$271$			2.49143i			0.151344i	0.997133	+	0.0756718i	$0.0241101\pi$
$271$			2.49143i			0.151344i	−0.997133	+	0.0756718i	$0.975890\pi$
$272$	−23.7796	−	10.9154i	−1.44185	−	0.661844i
$273$	−0.716940	+	8.29030i	−0.0433912	+	0.501752i
$274$	4.60069	+	34.9457i	0.277938	+	2.11115i
$275$	0.0237786	+	0.0271143i	0.00143390	+	0.00163505i
$276$	−37.6174	+	6.67183i	−2.26430	+	0.401597i
$277$	−18.0526	+	8.90254i	−1.08467	+	0.534902i	−0.894600	−	0.446868i	$-0.852539\pi$
$277$	−18.0526	+	8.90254i	−1.08467	+	0.534902i	−0.190074	+	0.981770i	$0.560873\pi$
$278$	13.2154	+	2.62870i	0.792605	+	0.157659i
$279$	−0.806834	−	0.589114i	−0.0483039	−	0.0352693i
$280$	14.6467	+	35.3603i	0.875308	+	2.11318i
$281$	−24.4133	−	3.21407i	−1.45637	−	0.191735i	−0.639606	−	0.768703i	$-0.720902\pi$
$281$	−24.4133	−	3.21407i	−1.45637	−	0.191735i	−0.816767	+	0.576968i	$0.804236\pi$
$282$	−18.3090	−	11.0851i	−1.09029	−	0.660108i
$283$	5.53437	+	16.3037i	0.328984	+	0.969156i	0.978040	+	0.208416i	$0.0668307\pi$
$283$	5.53437	+	16.3037i	0.328984	+	0.969156i	−0.649056	+	0.760741i	$0.724836\pi$
$284$	2.13792	−	32.6183i	0.126862	−	1.93554i
$285$	−42.8691	−	15.5545i	−2.53935	−	0.921367i
$286$	−0.00972499	+	0.0286489i	−0.000575051	+	0.00169405i
$287$	−11.2239	−	4.64908i	−0.662525	−	0.274427i
$288$	4.18972	+	11.4398i	0.246882	+	0.674097i
$289$	16.7051	−	3.15266i	0.982654	−	0.185450i
$290$	−36.0020	−	20.7858i	−2.11411	−	1.22058i
$291$	0.292681	+	0.458402i	0.0171572	+	0.0268720i
$292$	19.2677	−	16.8973i	1.12756	−	0.988841i
$293$	27.8015	+	7.44939i	1.62418	+	0.435198i	0.952226	−	0.305395i	$-0.0987884\pi$
$293$	27.8015	+	7.44939i	1.62418	+	0.435198i	0.671954	+	0.740593i	$0.265455\pi$
$294$	13.2815	+	10.6377i	0.774595	+	0.620404i
$295$	−24.2558	−	21.2717i	−1.41223	−	1.23849i
$296$	2.57880	+	3.85944i	0.149889	+	0.224325i
$297$	−0.0211421	−	0.00868301i	−0.00122679	−	0.000503839i
$298$	−8.25843	+	3.42076i	−0.478398	+	0.198159i
$299$	0.900109	+	13.7330i	0.0520547	+	0.794201i
$300$	17.2997	−	59.5746i	0.998798	−	3.43954i
$301$	−17.5463	−	1.15004i	−1.01135	−	0.0662875i
$302$	−1.39137	+	5.19265i	−0.0800642	+	0.298804i
$303$	5.79917	−	13.2155i	0.333154	−	0.759211i
$304$	−27.9972	−	36.4867i	−1.60575	−	2.09266i
$305$	−29.2675			−1.67585
$306$	−25.7121	−	17.6989i	−1.46986	−	1.01178i
$307$	−3.58071			−0.204362			−0.102181	−	0.994766i	$-0.532582\pi$
$307$	−3.58071			−0.204362			−0.102181	+	0.994766i	$0.532582\pi$
$308$	−0.0206179	−	0.0268698i	−0.00117481	−	0.00153105i
$309$	7.61432	+	10.3628i	0.433163	+	0.589521i
$310$	−0.790192	+	2.94904i	−0.0448799	+	0.167494i
$311$	−12.5694	−	0.823843i	−0.712746	−	0.0467159i	−0.295283	−	0.955410i	$-0.595414\pi$
$311$	−12.5694	−	0.823843i	−0.712746	−	0.0467159i	−0.417463	+	0.908694i	$0.637081\pi$
$312$	27.4003	−	6.73390i	1.55123	−	0.381232i
$313$	−0.313224	−	4.77888i	−0.0177045	−	0.270118i	−0.997529	−	0.0702577i	$-0.977618\pi$
$313$	−0.313224	−	4.77888i	−0.0177045	−	0.270118i	0.979824	−	0.199860i	$-0.0640488\pi$
$314$	27.9347	−	11.5709i	1.57645	−	0.652985i
$315$	4.19564	+	18.7475i	0.236398	+	1.05630i
$316$	11.9959	+	17.9532i	0.674824	+	1.00994i
$317$	1.35316	+	1.18669i	0.0760011	+	0.0666512i	0.696504	−	0.717553i	$-0.254738\pi$
$317$	1.35316	+	1.18669i	0.0760011	+	0.0666512i	−0.620503	+	0.784204i	$0.713071\pi$
$318$	19.5034	−	7.60698i	1.09370	−	0.426578i
$319$	0.0192649	+	0.00516203i	0.00107863	+	0.000289018i
$320$	−6.67527	+	5.85406i	−0.373159	+	0.327252i
$321$	4.73961	−	9.12702i	0.264539	−	0.509420i
$322$	−19.4511	−	11.2301i	−1.08396	−	0.625827i
$323$	28.5513	+	8.81426i	1.58864	+	0.490439i
$324$	6.98212	+	38.6905i	0.387896	+	2.14947i
$325$	−20.6461	−	8.55190i	−1.14524	−	0.474374i
$326$	6.65468	−	19.6040i	0.368568	−	1.08577i
$327$	13.1390	−	11.0474i	0.726587	−	0.610920i
$328$	−2.69418	+	41.1053i	−0.148761	+	2.26966i
$329$	−2.77440	−	8.17311i	−0.152957	−	0.450598i
$330$	−0.00145379	+	0.0698335i	−8.00286e−5	+	0.00384421i
$331$	4.65723	+	0.613136i	0.255985	+	0.0337010i	0.257426	−	0.966298i	$-0.417126\pi$
$331$	4.65723	+	0.613136i	0.255985	+	0.0337010i	−0.00144169	+	0.999999i	$0.500459\pi$
$332$	13.7360	+	33.1616i	0.753860	+	1.81998i
$333$	0.942622	+	2.13068i	0.0516554	+	0.116761i
$334$	−44.5273	−	8.85704i	−2.43643	−	0.484636i
$335$	25.7643	−	12.7055i	1.40765	−	0.694178i
$336$	−6.60812	+	18.2124i	−0.360503	+	0.993568i
$337$	18.1356	+	20.6796i	0.987907	+	1.12649i	0.991967	+	0.126500i	$0.0403744\pi$
$337$	18.1356	+	20.6796i	0.987907	+	1.12649i	−0.00405984	+	0.999992i	$0.501292\pi$
$338$	1.83506	+	13.9387i	0.0998143	+	0.758165i
$339$	16.9918	−	7.94413i	0.922867	−	0.431466i
$340$	−15.1716	+	63.6526i	−0.822795	+	3.45205i
$341$		−	0.00146475i		−	7.93209e-5i
$342$	−25.4319	−	48.6161i	−1.37520	−	2.62886i
$343$	3.74586	+	18.8317i	0.202257	+	1.01682i
$344$	15.4317	+	57.5919i	0.832021	+	3.10515i
$345$	11.5456	+	29.6016i	0.621592	+	1.59369i
$346$	27.6163	−	9.37448i	1.48466	−	0.503975i
$347$	6.08648	−	12.3422i	0.326740	−	0.662562i	−0.670077	−	0.742292i	$-0.733739\pi$
$347$	6.08648	−	12.3422i	0.326740	−	0.662562i	0.996817	+	0.0797294i	$0.0254056\pi$
$348$	−10.3493	−	32.7095i	−0.554781	−	1.75341i
$349$	−2.20353	+	16.7375i	−0.117953	+	0.895938i	0.825493	+	0.564412i	$0.190897\pi$
$349$	−2.20353	+	16.7375i	−0.117953	+	0.895938i	−0.943446	+	0.331526i	$0.892436\pi$
$350$	30.3239	−	20.2618i	1.62088	−	1.08304i
$351$	14.1295	−	0.968745i	0.754176	−	0.0517078i
$352$	−0.00992386	+	0.0148521i	−0.000528944	+	0.000791620i
$353$	−0.849678	+	0.227671i	−0.0452238	+	0.0121177i	−0.281360	−	0.959602i	$-0.590786\pi$
$353$	−0.849678	+	0.227671i	−0.0452238	+	0.0121177i	0.236136	+	0.971720i	$0.424119\pi$
$354$	−4.26426	−	38.5796i	−0.226643	−	2.05048i
$355$	−26.9532	+	3.54846i	−1.43053	+	0.188333i
$356$	−4.56912	−	7.91395i	−0.242163	−	0.419438i
$357$	−3.34300	−	12.1358i	−0.176930	−	0.642293i
$358$	−8.27343	+	14.3300i	−0.437264	+	0.757364i
$359$	−1.54156	+	3.72165i	−0.0813603	+	0.196421i	−0.959325	−	0.282305i	$-0.908901\pi$
$359$	−1.54156	+	3.72165i	−0.0813603	+	0.196421i	0.877965	+	0.478726i	$0.158901\pi$
$360$	55.6223	−	33.9051i	2.93155	−	1.78696i
$361$	23.7035	+	23.7035i	1.24755	+	1.24755i
$362$	−11.4827	−	23.2847i	−0.603519	−	1.22382i
$363$	4.54705	+	18.5020i	0.238658	+	0.971102i
$364$	18.8225	+	9.28225i	0.986570	+	0.486522i
$365$	−16.9091	−	12.9748i	−0.885065	−	0.679134i
$366$	−25.9848	−	23.7628i	−1.35825	−	1.24210i
$367$	−1.56010	+	0.102254i	−0.0814365	+	0.00533763i	−0.106067	−	0.994359i	$-0.533826\pi$
$367$	−1.56010	+	0.102254i	−0.0814365	+	0.00533763i	0.0246304	+	0.999697i	$0.492159\pi$
$368$	−6.25126	+	31.4272i	−0.325870	+	1.63826i
$369$	−4.87435	+	20.0941i	−0.253749	+	1.04606i
$370$	5.03480	−	5.03480i	0.261747	−	0.261747i
$371$	7.99408	+	2.71362i	0.415032	+	0.140884i
$372$	−2.12366	+	1.35591i	−0.110107	+	0.0703007i
$373$	6.57672	−	3.79707i	0.340529	−	0.196605i	−0.319977	−	0.947425i	$-0.603675\pi$
$373$	6.57672	−	3.79707i	0.340529	−	0.196605i	0.660506	+	0.750821i	$0.270342\pi$
$374$	−0.00127286	−	0.0457492i	−6.58178e−5	−	0.00236564i
$375$	−20.0551	−	1.73435i	−1.03564	−	0.0895616i
$376$	−23.2187	+	17.8163i	−1.19741	+	0.918806i
$377$	−12.1213	+	2.41107i	−0.624277	+	0.124176i
$378$	−11.4964	+	20.0513i	−0.591312	+	1.03133i
$379$	−1.23948	−	0.828191i	−0.0636676	−	0.0425413i	0.523329	−	0.852131i	$-0.324690\pi$
$379$	−1.23948	−	0.828191i	−0.0636676	−	0.0425413i	−0.586997	+	0.809589i	$0.699690\pi$
$380$	−75.8357	+	86.4740i	−3.89029	+	4.43602i
$381$	6.06821	+	11.0347i	0.310884	+	0.565323i
$382$	−35.5031	+	46.2685i	−1.81650	+	2.36730i
$383$	1.47314	−	1.91984i	0.0752740	−	0.0980990i	−0.754199	−	0.656646i	$-0.771974\pi$
$383$	1.47314	−	1.91984i	0.0752740	−	0.0980990i	0.829473	+	0.558547i	$0.188641\pi$
$384$	−24.7441	−	0.515123i	−1.26272	−	0.0262872i
$385$	−0.0185721	+	0.0211774i	−0.000946521	+	0.00107930i
$386$	27.9689	+	18.6882i	1.42358	+	0.951205i
$387$	2.66809	+	29.8085i	0.135627	+	1.51525i
$388$	1.34533	−	0.267603i	0.0682988	−	0.0135855i
$389$	−4.71163	+	3.61536i	−0.238889	+	0.183306i	−0.721267	−	0.692657i	$-0.756440\pi$
$389$	−4.71163	+	3.61536i	−0.238889	+	0.183306i	0.482378	+	0.875963i	$0.339773\pi$
$390$	−18.3311	−	39.2086i	−0.928231	−	1.98540i
$391$	−8.49891	−	19.0052i	−0.429808	−	0.961132i
$392$	20.1507	−	11.6340i	1.01777	−	0.587607i
$393$	0.00358256	+	0.0802105i	0.000180716	+	0.00404608i
$394$	9.97769	+	3.38697i	0.502669	+	0.170633i
$395$	12.6978	−	12.6978i	0.638898	−	0.638898i
$396$	−0.0397781	+	0.0417197i	−0.00199892	+	0.00209650i
$397$	−2.75034	+	13.8269i	−0.138036	+	0.693952i	0.848341	+	0.529450i	$0.177602\pi$
$397$	−2.75034	+	13.8269i	−0.138036	+	0.693952i	−0.986377	+	0.164502i	$0.947398\pi$
$398$	−38.7722	+	2.54126i	−1.94347	+	0.127382i
$399$	4.76721	−	21.6059i	0.238659	−	1.08165i
$400$	−41.2786	−	31.6742i	−2.06393	−	1.58371i
$401$	−33.0025	−	16.2750i	−1.64806	−	0.812736i	−0.998630	−	0.0523178i	$-0.983339\pi$
$401$	−33.0025	−	16.2750i	−1.64806	−	0.812736i	−0.649434	−	0.760418i	$-0.724994\pi$
$402$	33.1904	+	9.63806i	1.65539	+	0.480703i
$403$	0.401440	+	0.814040i	0.0199972	+	0.0405502i
$404$	−25.7376	−	25.7376i	−1.28049	−	1.28049i
$405$	30.4265	−	11.9728i	1.51190	−	0.594932i
$406$	7.71845	−	18.6340i	0.383060	−	0.924789i
$407$	−0.00170803	+	0.00295839i	−8.46638e−5	+	0.000146642i
$408$	−35.3224	+	23.9610i	−1.74872	+	1.18625i
$409$	6.77273	+	11.7307i	0.334890	+	0.580046i	0.983464	−	0.181106i	$-0.0579676\pi$
$409$	6.77273	+	11.7307i	0.334890	+	0.580046i	−0.648574	+	0.761152i	$0.724634\pi$
$410$	62.6493	−	8.24794i	3.09403	−	0.407337i
$411$	22.1529	+	9.72105i	1.09272	+	0.479504i
$412$	31.3276	−	8.39420i	1.54340	−	0.413552i
$413$	8.69607	−	13.0146i	0.427905	−	0.640406i
$414$	−13.7835	+	35.6555i	−0.677422	+	1.75237i
$415$	24.8208	−	16.5848i	1.21841	−	0.814114i
$416$	1.44474	−	10.9739i	0.0708342	−	0.538039i
$417$	6.24107	−	6.82465i	0.305627	−	0.334204i
$418$	0.0355797	−	0.0721486i	0.00174026	−	0.00352890i
$419$	−15.2597	+	5.17997i	−0.745486	+	0.253058i	−0.668232	−	0.743953i	$-0.732949\pi$
$419$	−15.2597	+	5.17997i	−0.745486	+	0.253058i	−0.0772539	+	0.997011i	$0.524615\pi$
$420$	47.8959	+	7.32278i	2.33708	+	0.357315i
$421$	8.64313	+	32.2566i	0.421241	+	1.57209i	0.771998	+	0.635625i	$0.219257\pi$
$421$	8.64313	+	32.2566i	0.421241	+	1.57209i	−0.350758	+	0.936466i	$0.614076\pi$
$422$	7.54619	+	37.9373i	0.367343	+	1.84676i
$423$	−13.0167	+	6.80924i	−0.632894	+	0.331077i
$424$		−	28.6254i		−	1.39017i
$425$	33.7813	+	1.27195i	1.63864	+	0.0616984i
$426$	−26.8112	−	18.7334i	−1.29901	−	0.907636i
$427$	−1.85343	−	14.0782i	−0.0896940	−	0.681293i
$428$	−17.1020	−	19.5011i	−0.826656	−	0.942620i
$429$	0.0133635	+	0.0158937i	0.000645198	+	0.000767355i
$430$	82.0290	−	40.4522i	3.95579	−	1.95078i
$431$	19.2088	+	3.82087i	0.925257	+	0.184045i	0.634652	−	0.772798i	$-0.281143\pi$
$431$	19.2088	+	3.82087i	0.925257	+	0.184045i	0.290605	+	0.956843i	$0.406143\pi$
$432$	32.3602	+	6.33582i	1.55693	+	0.304832i
$433$	3.66201	+	8.84087i	0.175985	+	0.424865i	0.987117	−	0.159997i	$-0.0511485\pi$
$433$	3.66201	+	8.84087i	0.175985	+	0.424865i	−0.811133	+	0.584862i	$0.801149\pi$
$434$	−1.46859	−	0.193343i	−0.0704944	−	0.00928076i
$435$	−25.0016	+	13.7489i	−1.19873	+	0.659211i
$436$	−13.9166	−	40.9968i	−0.666482	−	1.96339i
$437$	2.39333	−	36.5151i	0.114488	−	1.74675i
$438$	−4.47806	−	25.2484i	−0.213970	−	1.20642i
$439$	7.44163	−	21.9223i	0.355170	−	1.04630i	−0.611714	−	0.791079i	$-0.709520\pi$
$439$	7.44163	−	21.9223i	0.355170	−	1.04630i	0.966884	−	0.255217i	$-0.0821469\pi$
$440$	0.0882397	+	0.0365501i	0.00420666	+	0.00174246i
$441$	10.9669	−	4.01652i	0.522233	−	0.191263i
$442$	13.2457	+	25.0764i	0.630035	+	1.19276i
$443$	10.9059	+	6.29650i	0.518153	+	0.299156i	0.736179	−	0.676787i	$-0.236628\pi$
$443$	10.9059	+	6.29650i	0.518153	+	0.299156i	−0.218026	+	0.975943i	$0.569962\pi$
$444$	5.87030	−	0.262194i	0.278592	−	0.0124432i
$445$	−5.71397	+	5.01101i	−0.270868	+	0.237545i
$446$	−34.5533	−	9.25854i	−1.63615	−	0.438405i
$447$	−0.927233	+	6.06473i	−0.0438566	+	0.286852i
$448$	−3.23864	−	2.84021i	−0.153012	−	0.134188i
$449$	−8.28164	−	12.3944i	−0.390835	−	0.584926i	0.582919	−	0.812530i	$-0.301911\pi$
$449$	−8.28164	−	12.3944i	−0.390835	−	0.584926i	−0.973754	+	0.227605i	$0.926911\pi$
$450$	−42.0268	−	45.6802i	−1.98116	−	2.15338i
$451$	−0.0280086	+	0.0116015i	−0.00131887	+	0.000546295i
$452$	−3.09403	−	47.2058i	−0.145531	−	2.22037i
$453$	2.55415	+	2.66275i	0.120004	+	0.125107i
$454$	56.3039	+	3.69035i	2.64247	+	0.173197i
$455$	4.51745	−	16.8594i	0.211782	−	0.790379i
$456$	−74.5691	+	8.24225i	−3.49202	+	0.385979i
$457$	−18.0395	−	23.5096i	−0.843853	−	1.09973i	−0.993816	−	0.111040i	$-0.964582\pi$
$457$	−18.0395	−	23.5096i	−0.843853	−	1.09973i	0.149962	−	0.988692i	$-0.452085\pi$
$458$	−69.8818			−3.26536
$459$	−19.5314	+	8.80477i	−0.911648	+	0.410971i
$460$	80.1354			3.73633
$461$	9.15656	+	11.9331i	0.426463	+	0.555778i	0.956325	−	0.292306i	$-0.0944227\pi$
$461$	9.15656	+	11.9331i	0.426463	+	0.555778i	−0.529861	+	0.848084i	$0.677756\pi$
$462$	−0.0336834	+	0.00372307i	−0.00156709	+	0.000173213i
$463$	4.09817	−	15.2946i	0.190458	−	0.710799i	−0.802938	−	0.596062i	$-0.796731\pi$
$463$	4.09817	−	15.2946i	0.190458	−	0.710799i	0.993396	−	0.114736i	$-0.0366023\pi$
$464$	−28.7130	−	1.88195i	−1.33297	−	0.0873674i
$465$	1.45056	+	1.51224i	0.0672683	+	0.0701286i
$466$	−0.108841	−	1.66059i	−0.00504195	−	0.0769252i
$467$	17.0186	−	7.04935i	0.787528	−	0.326205i	0.0475789	−	0.998867i	$-0.484849\pi$
$467$	17.0186	−	7.04935i	0.787528	−	0.326205i	0.739949	+	0.672663i	$0.234849\pi$
$468$	10.6728	−	34.0877i	0.493349	−	1.57570i
$469$	7.74320	+	11.5885i	0.357548	+	0.535108i
$470$	33.7532	+	29.6008i	1.55692	+	1.36538i
$471$	3.13643	−	20.5143i	0.144519	−	0.945250i
$472$	−51.2659	−	13.7367i	−2.35971	−	0.632281i
$473$	−0.0329906	+	0.0289320i	−0.00151691	+	0.00133029i
$474$	21.5832	−	0.964006i	0.991351	−	0.0442783i
$475$	51.4589	+	29.7098i	2.36110	+	1.36318i
$476$	−31.5789	−	3.26688i	−1.44742	−	0.149737i
$477$	2.46669	−	14.1551i	0.112942	−	0.648115i
$478$	−13.6922	−	5.67149i	−0.626266	−	0.259408i
$479$	10.5611	−	31.1120i	0.482549	−	1.42154i	−0.384409	−	0.923163i	$-0.625595\pi$
$479$	10.5611	−	31.1120i	0.482549	−	1.42154i	0.866958	−	0.498381i	$-0.166072\pi$
$480$	−4.46262	−	25.1614i	−0.203690	−	1.14845i
$481$	0.138444	−	2.11225i	0.00631250	−	0.0963101i
$482$	−12.1419	−	35.7689i	−0.553048	−	1.62923i
$483$	−13.5078	+	7.42823i	−0.614625	+	0.337996i
$484$	47.6410	+	6.27206i	2.16550	+	0.285093i
$485$	−0.436561	−	1.05395i	−0.0198232	−	0.0478574i
$486$	36.7347	+	14.0740i	1.66632	+	0.638408i
$487$	−24.8334	−	4.93968i	−1.12531	−	0.223838i	−0.402860	−	0.915261i	$-0.631984\pi$
$487$	−24.8334	−	4.93968i	−1.12531	−	0.223838i	−0.722450	+	0.691423i	$0.756984\pi$
$488$	−43.1829	+	21.2954i	−1.95480	+	0.963999i
$489$	−9.14449	−	10.8758i	−0.413528	−	0.491822i
$490$	−23.5338	−	26.8352i	−1.06315	−	1.21229i
$491$	4.66341	+	35.4221i	0.210457	+	1.59858i	0.691829	+	0.722062i	$0.256805\pi$
$491$	4.66341	+	35.4221i	0.210457	+	1.59858i	−0.481372	+	0.876516i	$0.659861\pi$
$492$	42.7477	+	29.8685i	1.92722	+	1.34658i
$493$	15.9245	−	9.79440i	0.717203	−	0.441118i
$494$			49.8479i			2.24276i
$495$	0.0404843	+	0.0256775i	0.00181963	+	0.00115412i
$496$	0.412274	+	2.07264i	0.0185116	+	0.0930643i
$497$	−3.41376	−	12.7403i	−0.153128	−	0.571481i
$498$	35.5024	+	5.42794i	1.59090	+	0.243232i
$499$	−10.4485	+	3.54680i	−0.467741	+	0.158777i	−0.545352	−	0.838207i	$-0.683604\pi$
$499$	−10.4485	+	3.54680i	−0.467741	+	0.158777i	0.0776113	+	0.996984i	$0.475271\pi$
$500$	−22.4548	+	45.5337i	−1.00421	+	2.03633i
$501$	−21.0284	+	22.9947i	−0.939482	+	1.02733i
$502$	6.13886	−	46.6293i	0.273991	−	2.08117i
$503$	−37.0868	+	24.7806i	−1.65362	+	1.10491i	−0.768074	+	0.640361i	$0.778785\pi$
$503$	−37.0868	+	24.7806i	−1.65362	+	1.10491i	−0.885546	+	0.464552i	$0.846215\pi$
$504$	19.8314	+	24.6083i	0.883363	+	1.09614i
$505$	−16.8179	+	25.1698i	−0.748388	+	1.12004i
$506$	−0.0541383	+	0.0145063i	−0.00240674	+	0.000644884i
$507$	8.83608	+	3.87741i	0.392424	+	0.172202i
$508$	31.4892	−	4.14563i	1.39711	−	0.183933i
$509$	18.5162	+	32.0710i	0.820717	+	1.42152i	0.905149	+	0.425094i	$0.139759\pi$
$509$	18.5162	+	32.0710i	0.820717	+	1.42152i	−0.0844324	+	0.996429i	$0.526908\pi$
$510$	46.6202	+	45.9720i	2.06438	+	2.03567i
$511$	5.17034	−	8.95529i	0.228722	−	0.396159i
$512$	−19.1671	+	46.2734i	−0.847072	+	2.04501i
$513$	−37.5841	−	2.34999i	−1.65938	−	0.103755i
$514$	−11.4001	−	11.4001i	−0.502839	−	0.502839i
$515$	−11.9300	−	24.1916i	−0.525697	−	1.06601i
$516$	72.4858	+	21.0489i	3.19101	+	0.926628i
$517$	−0.0193174	−	0.00952628i	−0.000849578	−	0.000418965i
$518$	2.74068	+	2.10300i	0.120418	+	0.0924003i
$519$	4.31285	−	19.5466i	0.189313	−	0.858002i
$520$	−59.0565	+	3.87077i	−2.58980	+	0.169744i
$521$	5.72949	−	28.8041i	0.251014	−	1.26193i	−0.625375	−	0.780325i	$-0.715054\pi$
$521$	5.72949	−	28.8041i	0.251014	−	1.26193i	0.876388	−	0.481606i	$-0.159946\pi$
$522$	−33.3604	−	8.09244i	−1.46014	−	0.354196i
$523$	−2.09852	+	2.09852i	−0.0917620	+	0.0917620i	−0.751498	−	0.659736i	$-0.770668\pi$
$523$	−2.09852	+	2.09852i	−0.0917620	+	0.0917620i	0.659736	+	0.751498i	$0.270668\pi$
$524$	0.191753	+	0.0650913i	0.00837675	+	0.00284353i
$525$	−1.11690	−	25.0065i	−0.0487456	−	1.09137i
$526$	1.94238	−	1.12143i	0.0846917	−	0.0488968i
$527$	−0.997497	−	0.943493i	−0.0434516	−	0.0410992i
$528$	0.0204763	+	0.0437970i	0.000891117	+	0.00190602i
$529$	−1.97999	+	1.51930i	−0.0860865	+	0.0660565i
$530$	−43.0670	+	8.56656i	−1.87071	+	0.372108i
$531$	−24.1669	−	11.2103i	−1.04875	−	0.486487i
$532$	−46.3982	−	31.0023i	−2.01162	−	1.34412i
$533$	12.3862	−	14.1238i	0.536508	−	0.611770i
$534$	−9.14162	−	0.190310i	−0.395597	−	0.00823552i
$535$	−13.1320	+	17.1139i	−0.567745	+	0.739900i
$536$	28.7693	−	37.4929i	1.24265	−	1.61945i
$537$	5.47253	+	9.95146i	0.236157	+	0.429437i
$538$	−49.1301	+	56.0221i	−2.11815	+	2.41529i
$539$	0.0142381	+	0.00951363i	0.000613280	+	0.000409781i
$540$	−0.247805	−	82.4651i	−0.0106638	−	3.54873i
$541$	−36.8721	+	7.33432i	−1.58526	+	0.315327i	−0.907530	−	0.419988i	$-0.862034\pi$
$541$	−36.8721	+	7.33432i	−1.58526	+	0.315327i	−0.677726	+	0.735315i	$0.737034\pi$
$542$	4.98804	−	3.82745i	0.214254	−	0.164403i
$543$	−17.7528	−	1.53526i	−0.761847	−	0.0658841i
$544$	3.72201	+	16.3249i	0.159580	+	0.699922i
$545$	−31.1827	+	18.0033i	−1.33572	+	0.771177i
$546$	17.6992	−	11.3006i	0.757457	−	0.483620i
$547$	16.5721	+	5.62548i	0.708573	+	0.240528i	0.652380	−	0.757892i	$-0.273770\pi$
$547$	16.5721	+	5.62548i	0.708573	+	0.240528i	0.0561929	+	0.998420i	$0.482104\pi$
$548$	43.1435	−	43.1435i	1.84300	−	1.84300i
$549$	−23.1887	+	6.80931i	−0.989668	+	0.290614i
$550$	0.0177551	−	0.0892609i	0.000757080	−	0.00380610i
$551$	32.7907	−	2.14921i	1.39693	−	0.0915596i
$552$	38.5735	+	35.2751i	1.64180	+	1.50141i
$553$	6.91203	+	5.30379i	0.293929	+	0.225540i
$554$	45.5568	+	22.4661i	1.93552	+	0.954495i
$555$	−1.16633	−	4.74579i	−0.0495078	−	0.201448i
$556$	−10.3161	−	20.9190i	−0.437501	−	0.887165i
$557$	−19.6981	−	19.6981i	−0.834633	−	0.834633i	0.153513	−	0.988147i	$-0.450941\pi$
$557$	−19.6981	−	19.6981i	−0.834633	−	0.834633i	−0.988147	+	0.153513i	$0.950941\pi$
$558$	0.0600464	+	2.52037i	0.00254197	+	0.106696i
$559$	10.4053	−	25.1206i	0.440097	−	1.06249i
$560$	20.3190	−	35.1936i	0.858636	−	1.48720i
$561$	−0.0273130	−	0.0155153i	−0.00115316	−	0.000655055i
$562$	31.0700	+	53.8149i	1.31061	+	2.27004i
$563$	−19.5721	+	2.57671i	−0.824865	+	0.108596i	−0.531129	−	0.847291i	$-0.678232\pi$
$563$	−19.5721	+	2.57671i	−0.824865	+	0.108596i	−0.293736	+	0.955887i	$0.594899\pi$
$564$	4.07038	+	36.8255i	0.171394	+	1.55063i
$565$	−38.0032	+	10.1829i	−1.59881	+	0.428399i
$566$	24.1392	−	36.1268i	1.01465	−	1.51852i
$567$	7.68597	+	13.8775i	0.322780	+	0.582801i
$568$	−37.1864	+	24.8471i	−1.56031	+	1.04256i
$569$	−3.38873	+	25.7399i	−0.142063	+	1.07907i	0.760751	+	0.649043i	$0.224831\pi$
$569$	−3.38873	+	25.7399i	−0.142063	+	1.07907i	−0.902814	+	0.430031i	$0.858503\pi$
$570$	34.7164	+	109.723i	1.45411	+	4.59579i
$571$	16.8647	−	34.1983i	0.705766	−	1.43115i	−0.187794	−	0.982209i	$-0.560134\pi$
$571$	16.8647	−	34.1983i	0.705766	−	1.43115i	0.893560	−	0.448944i	$-0.148200\pi$
$572$	0.0495923	−	0.0168343i	0.00207356	−	0.000703878i
$573$	14.5451	+	37.2920i	0.607629	+	1.55789i
$574$	7.93484	+	29.6132i	0.331194	+	1.23603i
$575$	−8.07661	−	40.6039i	−0.336818	−	1.69330i
$576$	−3.92683	+	6.19123i	−0.163618	+	0.257968i
$577$			5.96756i			0.248433i	0.992255	+	0.124216i	$0.0396417\pi$
$577$			5.96756i			0.248433i	−0.992255	+	0.124216i	$0.960358\pi$
$578$	−31.9751	−	28.6017i	−1.32999	−	1.18967i
$579$	20.9145	−	9.77811i	0.869177	−	0.406364i
$580$	9.39290	+	71.3461i	0.390019	+	2.96249i
$581$	9.54943	+	10.8890i	0.396177	+	0.451753i
$582$	0.468128	−	1.29019i	0.0194045	−	0.0534801i
$583$	0.0188943	−	0.00931761i	0.000782520	−	0.000385896i
$584$	−34.3894	−	6.84047i	−1.42304	−	0.283061i
$585$	−29.5366	−	3.17491i	−1.22119	−	0.131266i
$586$	−27.7957	−	67.1049i	−1.14823	−	2.77208i
$587$	40.7446	+	5.36412i	1.68171	+	0.221401i	0.910009	−	0.414588i	$-0.136074\pi$
$587$	40.7446	+	5.36412i	1.68171	+	0.221401i	0.771698	+	0.635989i	$0.219408\pi$
$588$	0.613083	−	29.4497i	0.0252831	−	1.21449i
$589$	−0.775748	−	2.28528i	−0.0319642	−	0.0941634i
$590$	−5.32479	+	81.2406i	−0.219218	+	3.34462i
$591$	5.53537	−	4.65419i	0.227695	−	0.191448i
$592$	1.58420	−	4.66690i	0.0651102	−	0.191808i
$593$	22.8806	+	9.47747i	0.939595	+	0.389193i	0.799311	−	0.600918i	$-0.205198\pi$
$593$	22.8806	+	9.47747i	0.939595	+	0.389193i	0.140285	+	0.990111i	$0.455198\pi$
$594$	0.0150955	+	0.0556674i	0.000619375	+	0.00228406i
$595$	2.45894	+	26.2886i	0.100807	+	1.07773i
$596$	13.4004	+	7.73674i	0.548903	+	0.316909i
$597$	−12.2904	+	23.6675i	−0.503013	+	0.968646i
$598$	26.1118	−	22.8994i	1.06779	−	0.936427i
$599$	−9.12183	−	2.44419i	−0.372708	−	0.0998668i	0.0676027	−	0.997712i	$-0.478465\pi$
$599$	−9.12183	−	2.44419i	−0.372708	−	0.0998668i	−0.440311	+	0.897846i	$0.645132\pi$
$600$	−79.0745	+	30.8416i	−3.22820	+	1.25910i
$601$	−26.4113	−	23.1621i	−1.07734	−	0.944801i	−0.0786970	−	0.996899i	$-0.525076\pi$
$601$	−26.4113	−	23.1621i	−1.07734	−	0.944801i	−0.998642	+	0.0520977i	$0.983409\pi$
$602$	24.6530	+	36.8958i	1.00478	+	1.50376i
$603$	17.4570	−	16.0609i	0.710905	−	0.654049i
$604$	8.59739	−	3.56116i	0.349823	−	0.144901i
$605$	−2.61373	−	39.8778i	−0.106263	−	1.62126i
$606$	−35.3674	+	8.69192i	−1.43670	+	0.353085i
$607$	22.0895	+	1.44782i	0.896585	+	0.0587653i	0.506724	−	0.862109i	$-0.330856\pi$
$607$	22.0895	+	1.44782i	0.896585	+	0.0587653i	0.389861	+	0.920874i	$0.372523\pi$
$608$	−7.61720	+	28.4278i	−0.308918	+	1.15290i
$609$	−8.19679	−	11.1556i	−0.332151	−	0.452046i
$610$	44.9621	+	58.5958i	1.82046	+	2.37247i
$611$	13.3465			0.539942
$612$	2.78881	+	53.9618i	0.112731	+	2.18128i
$613$	29.7531			1.20172			0.600859	−	0.799355i	$-0.294825\pi$
$613$	29.7531			1.20172			0.600859	+	0.799355i	$0.294825\pi$
$614$	5.50087	+	7.16887i	0.221997	+	0.289312i
$615$	17.4275	−	39.7150i	0.702746	−	1.60146i
$616$	−0.0119933	+	0.0447596i	−0.000483224	+	0.00180342i
$617$	−3.85486	−	0.252661i	−0.155191	−	0.0101717i	−0.0123904	−	0.999923i	$-0.503944\pi$
$617$	−3.85486	−	0.252661i	−0.155191	−	0.0101717i	−0.142801	+	0.989751i	$0.545611\pi$
$618$	9.04972	−	31.1644i	0.364033	−	1.25361i
$619$	1.54458	+	23.5657i	0.0620819	+	0.947187i	0.909353	+	0.416026i	$0.136577\pi$
$619$	1.54458	+	23.5657i	0.0620819	+	0.947187i	−0.847271	+	0.531161i	$0.821756\pi$
$620$	4.88267	−	2.02247i	0.196093	−	0.0812243i
$621$	16.0346	+	20.7672i	0.643446	+	0.833359i
$622$	17.6604	+	26.4306i	0.708116	+	1.05977i
$623$	−2.77225	−	2.43119i	−0.111068	−	0.0974038i
$624$	−23.3830	−	18.7284i	−0.936071	−	0.749736i
$625$	1.18655	+	0.317936i	0.0474621	+	0.0127174i
$626$	−9.08650	+	7.96864i	−0.363169	+	0.318491i
$627$	−0.0297127	−	0.0465366i	−0.00118661	−	0.00185849i
$628$	−45.3278	−	26.1700i	−1.80878	−	1.04430i
$629$	0.914469	+	3.06876i	0.0364623	+	0.122359i
$630$	31.0884	−	37.2008i	1.23859	−	1.48212i
$631$	−4.15324	−	1.72033i	−0.165338	−	0.0684852i	0.298479	−	0.954416i	$-0.403521\pi$
$631$	−4.15324	−	1.72033i	−0.165338	−	0.0684852i	−0.463817	+	0.885931i	$0.653521\pi$
$632$	9.49597	−	27.9742i	0.377729	−	1.11275i
$633$	24.9564	+	9.05510i	0.991929	+	0.359908i
$634$	0.297055	−	4.53219i	0.0117976	−	0.179996i
$635$	−8.49068	−	25.0127i	−0.336942	−	0.992600i
$636$	−30.9993	−	18.7684i	−1.22920	−	0.744215i
$637$	−10.5202	−	1.38502i	−0.416827	−	0.0548764i
$638$	−0.0192610	−	0.0465001i	−0.000762549	−	0.00184096i
$639$	−20.5295	+	9.08233i	−0.812134	+	0.359291i
$640$	50.9155	+	10.1277i	2.01261	+	0.400333i
$641$	−23.6058	+	11.6411i	−0.932371	+	0.459795i	−0.844030	−	0.536296i	$-0.819823\pi$
$641$	−23.6058	+	11.6411i	−0.932371	+	0.459795i	−0.0883412	+	0.996090i	$0.528157\pi$
$642$	−25.5542	+	4.53230i	−1.00854	+	0.178875i
$643$	27.4422	+	31.2918i	1.08221	+	1.23403i	0.970708	+	0.240264i	$0.0772340\pi$
$643$	27.4422	+	31.2918i	1.08221	+	1.23403i	0.111506	+	0.993764i	$0.464433\pi$
$644$	5.07477	+	38.5467i	0.199974	+	1.51895i
$645$	5.40851	−	62.5410i	0.212960	−	2.46255i
$646$	−26.2151	−	70.7029i	−1.03142	−	2.78177i
$647$		−	46.9564i		−	1.84605i	−0.384744	−	0.923023i	$-0.625710\pi$
$647$		−	46.9564i		−	1.84605i	0.384744	−	0.923023i	$-0.374290\pi$
$648$	36.1814	−	39.8040i	1.42134	−	1.56365i
$649$	−0.00762023	−	0.0383095i	−0.000299120	−	0.00150378i
$650$	14.5960	+	54.4730i	0.572502	+	2.13661i
$651$	−0.635559	+	0.793516i	−0.0249095	+	0.0311004i
$652$	−33.9353	+	11.5195i	−1.32901	+	0.451138i
$653$	−10.7884	+	21.8768i	−0.422184	+	0.856104i	0.577040	+	0.816716i	$0.304208\pi$
$653$	−10.7884	+	21.8768i	−0.422184	+	0.856104i	−0.999224	+	0.0393881i	$0.987459\pi$
$654$	−42.3024	−	9.33377i	−1.65415	−	0.364979i
$655$	0.0219822	−	0.166971i	0.000858916	−	0.00652411i
$656$	36.3670	−	24.2997i	1.41989	−	0.948743i
$657$	−16.4158	−	6.34594i	−0.640442	−	0.247579i
$658$	−12.1010	+	18.1105i	−0.471748	+	0.706020i
$659$	9.42245	−	2.52474i	0.367046	−	0.0983498i	−0.0705814	−	0.997506i	$-0.522485\pi$
$659$	9.42245	−	2.52474i	0.367046	−	0.0983498i	0.437628	+	0.899156i	$0.355819\pi$
$660$	0.0974359	−	0.0715931i	0.00379269	−	0.00278676i
$661$	−31.3123	+	4.12234i	−1.21791	+	0.160340i	−0.711957	−	0.702223i	$-0.752191\pi$
$661$	−31.3123	+	4.12234i	−1.21791	+	0.160340i	−0.505949	+	0.862563i	$0.668858\pi$
$662$	−5.92712	−	10.2661i	−0.230364	−	0.399002i
$663$	19.4315	+	1.13706i	0.754656	+	0.0441596i
$664$	24.5547	−	42.5301i	0.952909	−	1.65049i
$665$	−17.7600	+	42.8765i	−0.688705	+	1.66268i
$666$	2.81769	−	5.16046i	0.109183	−	0.199964i
$667$	−16.1894	−	16.1894i	−0.626855	−	0.626855i
$668$	34.7588	+	70.4838i	1.34486	+	2.72710i
$669$	−17.7187	+	16.9960i	−0.685044	+	0.657103i
$670$	−65.0178	−	32.0632i	−2.51186	−	1.23871i
$671$	−0.0281122	−	0.0215712i	−0.00108526	−	0.000832748i
$672$	11.8205	−	3.74001i	0.455986	−	0.144274i
$673$	32.0005	−	2.09743i	1.23353	−	0.0808499i	0.565351	−	0.824850i	$-0.308741\pi$
$673$	32.0005	−	2.09743i	1.23353	−	0.0808499i	0.668179	+	0.744000i	$0.267074\pi$
$674$	13.5415	−	68.0779i	0.521600	−	2.62226i
$675$	−41.7594	+	8.43699i	−1.60732	+	0.324740i
$676$	17.2086	−	17.2086i	0.661867	−	0.661867i
$677$	−13.6412	−	4.63058i	−0.524275	−	0.177967i	0.0467397	−	0.998907i	$-0.485117\pi$
$677$	−13.6412	−	4.63058i	−0.524275	−	0.177967i	−0.571015	+	0.820940i	$0.693450\pi$
$678$	−42.0084	−	21.8147i	−1.61332	−	0.837789i
$679$	0.479324	−	0.276738i	0.0183948	−	0.0106202i
$680$	81.7285	−	36.5481i	3.13414	−	1.40156i
$681$	22.1812	−	31.7457i	0.849985	−	1.21650i
$682$	−0.00293255	+	0.00225023i	−0.000112293	+	8.61656e-5i
$683$	−9.33116	+	1.85608i	−0.357047	+	0.0710210i	−0.370355	−	0.928890i	$-0.620764\pi$
$683$	−9.33116	+	1.85608i	−0.357047	+	0.0710210i	0.0133078	+	0.999911i	$0.495764\pi$
$684$	−39.9658	+	86.1572i	−1.52813	+	3.29430i
$685$	−42.1917	−	28.1916i	−1.61206	−	1.07715i
$686$	31.9480	−	36.4297i	1.21978	−	1.39089i
$687$	−24.8411	+	41.0294i	−0.947746	+	1.56537i
$688$	38.5387	−	50.2246i	1.46928	−	1.91480i
$689$	−7.94687	+	10.3566i	−0.302752	+	0.394554i
$690$	41.5278	−	68.5905i	1.58094	−	2.61120i
$691$	−1.29536	+	1.47708i	−0.0492780	+	0.0561908i	−0.775954	−	0.630790i	$-0.782731\pi$
$691$	−1.29536	+	1.47708i	−0.0492780	+	0.0561908i	0.726676	+	0.686981i	$0.241064\pi$
$692$	−41.9759	−	28.0474i	−1.59568	−	1.06620i
$693$	−0.00978759	+	0.0210998i	−0.000371800	+	0.000801516i
$694$	−34.0603	+	6.77502i	−1.29291	+	0.257176i
$695$	−15.3896	+	11.8089i	−0.583761	+	0.447936i
$696$	−26.8848	+	38.4775i	−1.01907	+	1.45848i
$697$	−10.1406	+	26.5468i	−0.384101	+	1.00553i
$698$	36.8950	−	21.3013i	1.39650	−	0.806267i
$699$	−1.01366	−	0.526390i	−0.0383403	−	0.0199099i
$700$	−59.7809	−	20.2929i	−2.25951	−	0.766999i
$701$	−5.35432	+	5.35432i	−0.202230	+	0.202230i	−0.800955	−	0.598725i	$-0.795674\pi$
$701$	−5.35432	+	5.35432i	−0.202230	+	0.202230i	0.598725	+	0.800955i	$0.295674\pi$
$702$	−23.6459	−	26.8001i	−0.892458	−	1.01151i
$703$	−1.09804	+	5.52022i	−0.0414133	+	0.208199i
$704$	−0.0107264		0.000703048i	−0.000404268		2.64971e-5i
$705$	29.3777	−	9.29512i	1.10643	−	0.350074i
$706$	1.76113	+	1.35136i	0.0662810	+	0.0508592i
$707$	−13.1722	−	6.49581i	−0.495392	−	0.244300i
$708$	−48.4886	+	46.5109i	−1.82231	+	1.74799i
$709$	−11.9262	−	24.1840i	−0.447898	−	0.908248i	−0.997352	−	0.0727240i	$-0.976831\pi$
$709$	−11.9262	−	24.1840i	−0.447898	−	0.908248i	0.549454	−	0.835524i	$-0.314836\pi$
$710$	48.5112	+	48.5112i	1.82059	+	1.82059i
$711$	7.10626	−	13.0148i	0.266506	−	0.488092i
$712$	−4.78462	+	11.5511i	−0.179311	+	0.432895i
$713$	−0.840728	+	1.45618i	−0.0314855	+	0.0545345i
$714$	−19.1611	+	25.3365i	−0.717086	+	0.948195i
$715$	−0.0217779	−	0.0377204i	−0.000814447	−	0.00141066i
$716$	28.3981	−	3.73869i	1.06129	−	0.139721i
$717$	−8.19707	+	6.02297i	−0.306125	+	0.224932i
$718$	9.81925	−	2.63106i	0.366451	−	0.0981903i
$719$	−6.86730	+	10.2776i	−0.256107	+	0.383291i	−0.937136	−	0.348966i	$-0.886533\pi$
$719$	−6.86730	+	10.2776i	−0.256107	+	0.383291i	0.681028	+	0.732257i	$0.261533\pi$
$720$	−64.5129	−	24.9390i	−2.40425	−	0.929423i
$721$	10.8811	−	7.27053i	0.405234	−	0.270769i
$722$	11.0418	−	83.8707i	0.410933	−	3.12134i
$723$	−25.3169	−	5.58603i	−0.941547	−	0.207747i
$724$	−19.8770	+	40.3066i	−0.738724	+	1.49798i
$725$	35.2038	−	11.9501i	1.30744	−	0.443815i
$726$	30.0570	−	37.5272i	1.11552	−	1.39276i
$727$	0.773799	+	2.88786i	0.0286986	+	0.107105i	0.978789	−	0.204869i	$-0.0656767\pi$
$727$	0.773799	+	2.88786i	0.0286986	+	0.107105i	−0.950091	+	0.311973i	$0.899010\pi$
$728$	−5.60181	−	28.1622i	−0.207617	−	1.04376i
$729$	21.3214	−	16.5650i	0.789680	−	0.613518i
$730$			53.7860i			1.99071i
$731$	−1.54761	+	41.1025i	−0.0572403	+	1.52023i
$732$	−5.25159	+	60.7265i	−0.194104	+	2.24451i
$733$	−5.50281	−	41.7980i	−0.203251	−	1.54384i	−0.723799	−	0.690011i	$-0.757606\pi$
$733$	−5.50281	−	41.7980i	−0.203251	−	1.54384i	0.520548	−	0.853832i	$-0.325728\pi$
$734$	2.60142	+	2.96635i	0.0960203	+	0.109490i
$735$	−24.1212	+	4.27814i	−0.889726	+	0.157802i
$736$	18.3905	−	9.06919i	0.677883	−	0.334295i
$737$	0.0341117	+	0.00678524i	0.00125652	+	0.000249938i
$738$	47.7182	−	21.1107i	1.75653	−	0.777096i
$739$	−1.99645	−	4.81986i	−0.0734407	−	0.177301i	0.882896	−	0.469568i	$-0.155590\pi$
$739$	−1.99645	−	4.81986i	−0.0734407	−	0.177301i	−0.956337	+	0.292267i	$0.905590\pi$
$740$	−12.2200	−	1.60879i	−0.449216	−	0.0591405i
$741$	29.2670	+	17.7196i	1.07515	+	0.650945i
$742$	−6.84801	−	20.1736i	−0.251398	−	0.740595i
$743$	−0.548811	+	8.37324i	−0.0201339	+	0.307185i	0.975901	+	0.218216i	$0.0700237\pi$
$743$	−0.548811	+	8.37324i	−0.0201339	+	0.307185i	−0.996034	+	0.0889685i	$0.971643\pi$
$744$	3.24057	+	1.17580i	0.118805	+	0.0431068i
$745$	4.13654	−	12.1859i	0.151551	−	0.446455i
$746$	−17.7055	−	7.33386i	−0.648245	−	0.268512i
$747$	15.8070	−	18.9149i	0.578348	−	0.692059i
$748$	−0.0614871	+	0.0499580i	−0.00224819	+	0.00182664i
$749$	−9.06376	−	5.23296i	−0.331182	−	0.191208i
$750$	27.3373	+	42.8163i	0.998218	+	1.56343i
$751$	−21.9263	+	19.2289i	−0.800103	+	0.701671i	−0.958309	−	0.285735i	$-0.907762\pi$
$751$	−21.9263	+	19.2289i	−0.800103	+	0.701671i	0.158206	+	0.987406i	$0.449429\pi$
$752$	30.0156	+	8.04265i	1.09456	+	0.293285i
$753$	−25.1951	−	20.1797i	−0.918159	−	0.735390i
$754$	23.4484	+	20.5637i	0.853942	+	0.748887i
$755$	−4.29972	−	6.43499i	−0.156483	−	0.234193i
$756$	39.6517	−	5.34150i	1.44212	−	0.194269i
$757$	−12.1124	+	5.01713i	−0.440234	+	0.182351i	−0.591780	−	0.806099i	$-0.701575\pi$
$757$	−12.1124	+	5.01713i	−0.440234	+	0.182351i	0.151546	+	0.988450i	$0.451575\pi$
$758$	0.246039	+	3.75383i	0.00893655	+	0.136345i
$759$	−0.0107276	+	0.0369426i	−0.000389389	+	0.00134093i
$760$	157.027	+	10.2921i	5.69597	+	0.373334i
$761$	−12.0145	+	44.8386i	−0.435524	+	1.62540i	0.304284	+	0.952581i	$0.401583\pi$
$761$	−12.0145	+	44.8386i	−0.435524	+	1.62540i	−0.739809	+	0.672817i	$0.765084\pi$
$762$	12.7700	−	29.1010i	0.462607	−	1.05422i
$763$	−10.6347	−	13.8594i	−0.385001	−	0.501743i
$764$	100.954			3.65240
$765$	43.5635	−	11.0301i	1.57504	−	0.398795i
$766$	−6.10677			−0.220647
$767$	14.7343	+	19.2021i	0.532025	+	0.693348i
$768$	31.9691	+	43.5089i	1.15359	+	1.56999i
$769$	10.1533	−	37.8926i	0.366137	−	1.36644i	−0.499736	−	0.866178i	$-0.666570\pi$
$769$	10.1533	−	37.8926i	0.366137	−	1.36644i	0.865873	−	0.500264i	$-0.166764\pi$
$770$	0.0709302	+	0.00464901i	0.00255615	+	0.000167539i
$771$	−10.7458	+	2.64088i	−0.386999	+	0.0951090i
$772$	−3.80832	−	58.1037i	−0.137064	−	2.09120i
$773$	14.3033	−	5.92460i	0.514452	−	0.213093i	−0.110326	−	0.993895i	$-0.535189\pi$
$773$	14.3033	−	5.92460i	0.514452	−	0.213093i	0.624778	+	0.780802i	$0.285189\pi$
$774$	55.5801	−	51.1350i	1.99779	−	1.83801i
$775$	−1.51688	−	2.27017i	−0.0544879	−	0.0815469i
$776$	−1.41099	−	1.23741i	−0.0506518	−	0.0444204i
$777$	2.20896	−	0.861565i	0.0792459	−	0.0309085i
$778$	14.4765	+	3.87896i	0.519006	+	0.139067i
$779$	−37.5542	+	32.9341i	−1.34552	+	1.17999i
$780$	−34.5289	+	66.4920i	−1.23633	+	2.38079i
$781$	−0.0285046	−	0.0164572i	−0.00101998	−	0.000588883i
$782$	−24.9934	+	46.2121i	−0.893761	+	1.65254i
$783$	−16.6100	+	16.7101i	−0.593592	+	0.597171i
$784$	−22.8249	−	9.45436i	−0.815173	−	0.337656i
$785$	−13.9921	+	41.2195i	−0.499400	+	1.47119i
$786$	0.155084	−	0.130396i	0.00553166	−	0.00465107i
$787$	−3.47120	+	52.9602i	−0.123735	+	1.88783i	0.261783	+	0.965127i	$0.415690\pi$
$787$	−3.47120	+	52.9602i	−0.123735	+	1.88783i	−0.385517	+	0.922701i	$0.625977\pi$
$788$	−5.86296	−	17.2717i	−0.208859	−	0.615280i
$789$	0.0320401	−	1.53906i	0.00114066	−	0.0547920i
$790$	−44.9291	−	5.91503i	−1.59851	−	0.210447i
$791$	−7.30482	−	17.6354i	−0.259730	−	0.627043i
$792$	0.0784160	+	0.00842901i	0.00278639	+	0.000299512i
$793$	21.5353	+	4.28365i	0.764743	+	0.152117i
$794$	31.9077	−	15.7352i	1.13236	−	0.558420i
$795$	−10.2795	+	28.3309i	−0.364576	+	1.00479i
$796$	44.3476	+	50.5687i	1.57186	+	1.79236i
$797$	−2.33764	−	17.7561i	−0.0828033	−	0.628954i	−0.981650	−	0.190691i	$-0.938927\pi$
$797$	−2.33764	−	17.7561i	−0.0828033	−	0.628954i	0.898847	−	0.438263i	$-0.144406\pi$
$798$	−50.5804	+	23.6477i	−1.79053	+	0.837120i
$799$	−18.9303	+	7.01896i	−0.669707	+	0.248313i
$800$			33.2958i			1.17718i
$801$	−3.36133	+	5.29963i	−0.118767	+	0.187253i
$802$	18.1161	+	91.0760i	0.639703	+	3.21601i
$803$	−0.00667872	−	0.0249253i	−0.000235687	−	0.000879596i
$804$	−21.7395	−	55.7376i	−0.766691	−	1.96571i
$805$	30.6187	−	10.3936i	1.07917	−	0.366328i
$806$	1.01306	−	2.05428i	0.0356835	−	0.0723590i
$807$	15.4276	+	48.7599i	0.543079	+	1.71643i
$808$	−6.50019	+	49.3739i	−0.228676	+	1.73697i
$809$	−2.58244	+	1.72553i	−0.0907936	+	0.0606664i	−0.600138	−	0.799896i	$-0.704888\pi$
$809$	−2.58244	+	1.72553i	−0.0907936	+	0.0606664i	0.509345	+	0.860563i	$0.329888\pi$
$810$	−70.7131	−	42.5230i	−2.48460	−	1.49411i
$811$	21.2994	−	31.8767i	0.747922	−	1.11934i	−0.240945	−	0.970539i	$-0.577457\pi$
$811$	21.2994	−	31.8767i	0.747922	−	1.11934i	0.988867	−	0.148805i	$-0.0475427\pi$
$812$	−33.7241	+	9.03633i	−1.18348	+	0.317113i
$813$	−0.474088	−	4.28916i	−0.0166270	−	0.150427i
$814$	0.00854689	−	0.00112522i	0.000299568	−	3.94389e-5i
$815$	14.9023	+	25.8116i	0.522005	+	0.904139i
$816$	43.0152	+	14.2667i	1.50583	+	0.499433i
$817$	−36.1486	+	62.6112i	−1.26468	+	2.19049i
$818$	13.0812	−	31.5808i	0.457374	−	1.10420i
$819$	−0.343280	−	14.4087i	−0.0119952	−	0.503481i
$820$	−77.3462	−	77.3462i	−2.70105	−	2.70105i
$821$	1.20995	+	2.45354i	0.0422276	+	0.0856291i	0.916964	−	0.398970i	$-0.130632\pi$
$821$	1.20995	+	2.45354i	0.0422276	+	0.0856291i	−0.874736	+	0.484599i	$0.838966\pi$
$822$	−14.5701	−	59.2858i	−0.508191	−	2.06783i
$823$	25.7989	+	12.7226i	0.899292	+	0.443482i	0.832334	−	0.554274i	$-0.187004\pi$
$823$	25.7989	+	12.7226i	0.899292	+	0.443482i	0.0669580	+	0.997756i	$0.478671\pi$
$824$	−35.2042	−	27.0132i	−1.22640	−	0.941048i
$825$	−0.0460959	−	0.0421543i	−0.00160485	−	0.00146762i
$826$	−39.4155	+	2.58343i	−1.37144	+	0.0898891i
$827$	2.28342	−	11.4795i	0.0794021	−	0.399181i	−0.920561	−	0.390599i	$-0.872268\pi$
$827$	2.28342	−	11.4795i	0.0794021	−	0.399181i	0.999963	−	0.00858271i	$-0.00273199\pi$
$828$	63.4913	−	18.6441i	2.20648	−	0.647928i
$829$	31.7097	−	31.7097i	1.10133	−	1.10133i	0.107074	−	0.994251i	$-0.465852\pi$
$829$	31.7097	−	31.7097i	1.10133	−	1.10133i	0.994251	−	0.107074i	$-0.0341482\pi$
$830$	−71.3350	−	24.2150i	−2.47607	−	0.840513i
$831$	29.3847	−	18.7615i	1.01934	−	0.650829i
$832$	5.76856	−	3.33048i	0.199989	−	0.115464i
$833$	15.6500	−	3.56815i	0.542241	−	0.123629i
$834$	−23.2513	−	2.01076i	−0.805128	−	0.0696270i
$835$	51.8532	−	39.7883i	1.79445	−	1.37693i
$836$	−0.136577	+	0.0271668i	−0.00472360	+	0.000939583i
$837$	1.50112	+	0.860668i	0.0518863	+	0.0297490i
$838$	33.8134	+	22.5934i	1.16807	+	0.780476i
$839$	22.0242	−	25.1138i	0.760361	−	0.867026i	−0.234091	−	0.972215i	$-0.575211\pi$
$839$	22.0242	−	25.1138i	0.760361	−	0.867026i	0.994452	+	0.105189i	$0.0335446\pi$
$840$	−31.9439	−	58.0880i	−1.10217	−	2.00423i
$841$	−5.13796	+	6.69592i	−0.177171	+	0.230894i
$842$	51.3023	−	66.8584i	1.76799	−	2.30409i
$843$	42.6406	+	0.887691i	1.46862	+	0.0305737i
$844$	44.1480	−	50.3412i	1.51964	−	1.73281i
$845$	−16.8289	−	11.2447i	−0.578932	−	0.386830i
$846$	33.6295	+	15.5998i	1.15621	+	0.536331i
$847$	19.0165	−	3.78261i	0.653414	−	0.129972i
$848$	−24.1130	+	18.5026i	−0.828044	+	0.635380i
$849$	−12.6302	−	27.0148i	−0.433467	−	0.927147i
$850$	−49.3500	−	69.5869i	−1.69269	−	2.38681i
$851$	3.39607	−	1.96072i	0.116416	−	0.0672127i
$852$	2.52629	+	56.5614i	0.0865492	+	1.93776i
$853$	−17.4464	−	5.92225i	−0.597353	−	0.202774i	0.00635482	−	0.999980i	$-0.497977\pi$
$853$	−17.4464	−	5.92225i	−0.597353	−	0.202774i	−0.603708	+	0.797206i	$0.706311\pi$
$854$	−25.3384	+	25.3384i	−0.867062	+	0.867062i
$855$	76.7619	+	18.6206i	2.62520	+	0.636811i
$856$	−6.92332	+	34.8059i	−0.236634	+	1.18964i
$857$	35.9232	−	2.35453i	1.22711	−	0.0804293i	0.561979	−	0.827152i	$-0.310040\pi$
$857$	35.9232	−	2.35453i	1.22711	−	0.0804293i	0.665136	+	0.746722i	$0.268374\pi$
$858$	0.0112907	−	0.0511715i	0.000385458	−	0.00174697i
$859$	−17.8982	−	13.7337i	−0.610677	−	0.468589i	0.256530	−	0.966536i	$-0.417421\pi$
$859$	−17.8982	−	13.7337i	−0.610677	−	0.468589i	−0.867207	+	0.497947i	$0.834087\pi$
$860$	−141.995	−	70.0242i	−4.84199	−	2.38781i
$861$	20.2073	+	5.86794i	0.688664	+	0.199979i
$862$	−21.8599	−	44.3274i	−0.744550	−	1.50980i
$863$	−5.14585	−	5.14585i	−0.175167	−	0.175167i	0.614078	−	0.789245i	$-0.289528\pi$
$863$	−5.14585	−	5.14585i	−0.175167	−	0.175167i	−0.789245	+	0.614078i	$0.789528\pi$
$864$	−9.38973	−	18.8971i	−0.319445	−	0.642893i
$865$	−16.0673	+	38.7899i	−0.546305	+	1.31890i
$866$	12.0744	−	20.9134i	0.410304	−	0.710667i
$867$	−28.1590	+	8.60628i	−0.956331	+	0.292285i
$868$	1.28205	+	2.22058i	0.0435158	+	0.0753715i
$869$	0.0215554	−	0.00283782i	0.000731216	−	9.62665e-5i
$870$	65.9351	+	28.9333i	2.23541	+	0.980932i
$871$	−20.8173	+	5.57797i	−0.705366	+	0.189002i
$872$	−32.9092	+	49.2520i	−1.11444	+	1.66788i
$873$	−0.591097	−	0.733477i	−0.0200056	−	0.0248244i
$874$	−76.7829	+	51.3047i	−2.59722	+	1.73541i
$875$	−2.67389	+	20.3102i	−0.0903941	+	0.686612i
$876$	−29.9553	+	32.7563i	−1.01210	+	1.10673i
$877$	5.22060	−	10.5863i	0.176287	−	0.357475i	−0.790738	−	0.612154i	$-0.790303\pi$
$877$	5.22060	−	10.5863i	0.176287	−	0.357475i	0.967026	+	0.254679i	$0.0819698\pi$
$878$	−55.3224	+	18.7794i	−1.86704	+	0.633775i
$879$	−49.2796	−	7.53434i	−1.66216	−	0.254127i
$880$	−0.0262469	−	0.0979546i	−0.000884782	−	0.00330205i
$881$	8.34107	+	41.9334i	0.281018	+	1.41277i	0.820920	+	0.571043i	$0.193461\pi$
$881$	8.34107	+	41.9334i	0.281018	+	1.41277i	−0.539902	+	0.841728i	$0.681539\pi$
$882$	−24.8893	−	15.7862i	−0.838066	−	0.531549i
$883$		−	57.5230i		−	1.93580i	−0.251328	−	0.967902i	$-0.580867\pi$
$883$		−	57.5230i		−	1.93580i	0.251328	−	0.967902i	$-0.419133\pi$
$884$	20.4798	−	44.6158i	0.688809	−	1.50059i
$885$	45.8057	+	32.0051i	1.53974	+	1.07584i
$886$	−4.14802	−	31.5074i	−0.139356	−	1.05851i
$887$	4.06056	+	4.63018i	0.136340	+	0.155466i	0.815981	−	0.578079i	$-0.196198\pi$
$887$	4.06056	+	4.63018i	0.136340	+	0.155466i	−0.679641	+	0.733545i	$0.737864\pi$
$888$	−5.17397	−	6.15357i	−0.173627	−	0.206500i
$889$	11.4939	−	5.66817i	0.385494	−	0.190104i
$890$	18.8105	+	3.74164i	0.630530	+	0.125420i
$891$	0.0380498	+	0.0109253i	0.00127472	+	0.000366011i
$892$	23.6969	+	57.2094i	0.793431	+	1.91551i
$893$	−35.1838	−	4.63204i	−1.17738	−	0.155005i
$894$	13.5665	−	7.46053i	0.453732	−	0.249518i
$895$	−7.65721	−	22.5574i	−0.255952	−	0.754011i
$896$	−1.64728	+	25.1327i	−0.0550319	+	0.839625i
$897$	−4.16282	−	23.4710i	−0.138992	−	0.783674i
$898$	−12.0918	+	35.6213i	−0.403509	+	1.18870i
$899$	−1.39501	−	0.577834i	−0.0465263	−	0.0192718i
$900$	−18.4463	+	105.854i	−0.614876	+	3.52845i
$901$	5.82509	−	18.8687i	0.194062	−	0.628609i
$902$	0.0662554	+	0.0382526i	0.00220606	+	0.00127367i
$903$	30.4259	−	1.35896i	1.01251	−	0.0452234i
$904$	−48.6627	+	42.6761i	−1.61850	+	1.41939i
$905$	36.1027	+	9.67368i	1.20009	+	0.321564i
$906$	1.40723	−	9.20426i	0.0467522	−	0.305791i
$907$	13.1654	+	11.5458i	0.437151	+	0.383371i	0.849443	−	0.527681i	$-0.176938\pi$
$907$	13.1654	+	11.5458i	0.437151	+	0.383371i	−0.412292	+	0.911052i	$0.635272\pi$
$908$	−54.2643	−	81.2123i	−1.80082	−	2.69512i
$909$	−7.46891	+	23.8549i	−0.247728	+	0.791216i
$910$	−40.6937	+	16.8559i	−1.34898	+	0.558767i
$911$	3.71015	+	56.6059i	0.122923	+	1.87544i	0.402645	+	0.915356i	$0.368091\pi$
$911$	3.71015	+	56.6059i	0.122923	+	1.87544i	−0.279722	+	0.960081i	$0.590242\pi$
$912$	55.1421	+	57.4868i	1.82594	+	1.90358i
$913$	0.0360646	+	0.00236380i	0.00119357	+	7.82304e-5i
$914$	−19.3548	+	72.2331i	−0.640200	+	2.38926i
$915$	50.3859	−	5.56923i	1.66571	−	0.184113i
$916$	73.6406	+	95.9702i	2.43315	+	3.17095i
$917$	0.0817086			0.00269825
$918$	47.6329	+	25.5771i	1.57212	+	0.844170i
$919$	−13.0297			−0.429812			−0.214906	−	0.976635i	$-0.568944\pi$
$919$	−13.0297			−0.429812			−0.214906	+	0.976635i	$0.568944\pi$
$920$	−66.7447	−	86.9833i	−2.20051	−	2.86776i
$921$	6.16444	−	0.681365i	0.203125	−	0.0224517i
$922$	9.82417	−	36.6643i	0.323542	−	1.20747i
$923$	20.3519	+	1.33393i	0.669890	+	0.0439069i
$924$	0.0406081	+	0.0423348i	0.00133591	+	0.00139271i
$925$	0.416458	+	6.35392i	0.0136930	+	0.208915i
$926$	−36.9167	+	15.2914i	−1.21316	+	0.502507i
$927$	−15.0805	−	16.3914i	−0.495308	−	0.538364i
$928$	10.2301	+	15.3104i	0.335819	+	0.502589i
$929$	11.4897	+	10.0762i	0.376966	+	0.330590i	0.826773	−	0.562535i	$-0.190174\pi$
$929$	11.4897	+	10.0762i	0.376966	+	0.330590i	−0.449807	+	0.893126i	$0.648507\pi$
$930$	0.799203	−	5.22733i	0.0262069	−	0.171411i
$931$	27.2526	+	7.30231i	0.893168	+	0.239324i
$932$	−2.16583	+	1.89938i	−0.0709440	+	0.0622163i
$933$	21.7959	−	0.973502i	0.713564	−	0.0318710i
$934$	−40.2582	−	23.2431i	−1.31729	−	0.760537i
$935$	0.0507264	+	0.0420486i	0.00165893	+	0.00137513i
$936$	−45.8900	+	16.8068i	−1.49996	+	0.549347i
$937$	46.5720	+	19.2907i	1.52144	+	0.630201i	0.977880	−	0.209169i	$-0.0670758\pi$
$937$	46.5720	+	19.2907i	1.52144	+	0.630201i	0.543561	+	0.839370i	$0.317076\pi$
$938$	11.3056	−	33.3053i	0.369142	−	1.08746i
$939$	1.44860	+	8.16755i	0.0472732	+	0.266538i
$940$	5.08269	−	77.5469i	0.165779	−	2.52930i
$941$	10.5351	+	31.0355i	0.343436	+	1.01173i	0.972204	+	0.234137i	$0.0752263\pi$
$941$	10.5351	+	31.0355i	0.343436	+	1.01173i	−0.628768	+	0.777593i	$0.716440\pi$
$942$	−45.8896	+	25.2357i	−1.49516	+	0.822225i
$943$	34.5037	+	4.54250i	1.12359	+	0.147924i
$944$	21.5654	+	52.0635i	0.701894	+	1.69452i
$945$	−10.7905	−	31.4767i	−0.351015	−	1.02394i
$946$	0.108606	+	0.0216030i	0.00353108	+	0.000702375i
$947$	−16.2307	+	8.00408i	−0.527426	+	0.260098i	−0.686450	−	0.727177i	$-0.740832\pi$
$947$	−16.2307	+	8.00408i	−0.527426	+	0.260098i	0.159024	+	0.987275i	$0.449165\pi$
$948$	−24.0680	−	28.6249i	−0.781694	−	0.929694i
$949$	10.5429	+	12.0219i	0.342238	+	0.390247i
$950$	−19.5723	−	148.666i	−0.635009	−	4.82337i
$951$	−2.55537	−	1.78548i	−0.0828635	−	0.0578981i
$952$	22.7560	+	36.9985i	0.737527	+	1.19913i
$953$			21.1366i			0.684683i	0.939576	+	0.342341i	$0.111220\pi$
$953$			21.1366i			0.684683i	−0.939576	+	0.342341i	$0.888780\pi$
$954$	−32.1290	+	16.8072i	−1.04021	+	0.544152i
$955$	−16.3799	−	82.3472i	−0.530040	−	2.66469i
$956$	6.63986	+	24.7803i	0.214749	+	0.801453i
$957$	−0.0341482	−	0.00522089i	−0.00110385	−	0.000168768i
$958$	−78.5132	+	26.6516i	−2.53665	+	0.861075i
$959$	10.8888	−	22.0803i	0.351618	−	0.713011i
$960$	10.3780	−	11.3484i	0.334948	−	0.366267i
$961$	4.03184	−	30.6248i	0.130059	−	0.987898i
$962$	−4.44157	+	2.96776i	−0.143202	+	0.0956844i
$963$	−6.42280	+	16.6147i	−0.206972	+	0.535400i
$964$	−36.3272	+	54.3675i	−1.17002	+	1.75106i
$965$	−46.7766	+	12.5337i	−1.50579	+	0.403475i
$966$	35.6232	+	15.6320i	1.14616	+	0.502952i
$967$	8.63349	−	1.13662i	0.277634	−	0.0365512i	0.00957666	−	0.999954i	$-0.496952\pi$
$967$	8.63349	−	1.13662i	0.277634	−	0.0365512i	0.268058	+	0.963403i	$0.413618\pi$
$968$	−32.8721	−	56.9362i	−1.05655	−	1.83000i
$969$	−50.8303	−	9.74137i	−1.63290	−	0.312938i
$970$	−1.43943	+	2.49316i	−0.0462172	+	0.0800505i
$971$	−7.16045	+	17.2869i	−0.229790	+	0.554762i	−0.996152	−	0.0876476i	$-0.972065\pi$
$971$	−7.16045	+	17.2869i	−0.229790	+	0.554762i	0.766362	+	0.642409i	$0.222065\pi$
$972$	−19.3825	−	65.2796i	−0.621694	−	2.09384i
$973$	−6.65488	−	6.65488i	−0.213346	−	0.213346i
$974$	28.2607	+	57.3070i	0.905531	+	1.83624i
$975$	37.1710	+	10.7940i	1.19042	+	0.345684i
$976$	45.8505	+	22.6110i	1.46764	+	0.723760i
$977$	27.3827	+	21.0115i	0.876051	+	0.672217i	0.945590	−	0.325362i	$-0.105486\pi$
$977$	27.3827	+	21.0115i	0.876051	+	0.672217i	−0.0695388	+	0.997579i	$0.522153\pi$
$978$	−7.72606	+	35.0160i	−0.247052	+	1.11969i
$979$	−0.00918172		0.000601802i	−0.000293449		1.92337e-5i
$980$	−12.0537	+	60.5981i	−0.385042	+	1.93573i
$981$	−20.5174	+	21.5189i	−0.655071	+	0.687047i
$982$	63.7537	−	63.7537i	2.03446	−	2.03446i
$983$	−30.2560	−	10.2705i	−0.965016	−	0.327579i	−0.205928	−	0.978567i	$-0.566021\pi$
$983$	−30.2560	−	10.2705i	−0.965016	−	0.327579i	−0.759088	+	0.650989i	$0.774355\pi$
$984$	−3.18361	−	71.2782i	−0.101490	−	2.27227i
$985$	−13.1371	+	7.58469i	−0.418582	+	0.241668i
$986$	−44.0731	−	16.8354i	−1.40357	−	0.536150i
$987$	6.33155	+	13.5426i	0.201535	+	0.431066i
$988$	68.4573	−	52.5291i	2.17792	−	1.67117i
$989$	49.4037	−	9.82701i	1.57095	−	0.312481i
$990$	−0.0107856	−	0.120500i	−0.000342790	−	0.00382973i
$991$	12.2108	+	8.15901i	0.387889	+	0.259179i	0.734190	−	0.678944i	$-0.237562\pi$
$991$	12.2108	+	8.15901i	0.387889	+	0.259179i	−0.346300	+	0.938124i	$0.612562\pi$
$992$	0.891650	−	1.01673i	0.0283099	−	0.0322813i
$993$	−8.13440	−	0.169342i	−0.258137	−	0.00537390i
$994$	−20.2627	+	26.4069i	−0.642695	+	0.837576i
$995$	34.0529	−	44.3786i	1.07955	−	1.40690i
$996$	−29.9576	−	54.4761i	−0.949244	−	1.72614i
$997$	32.3728	−	36.9141i	1.02526	−	1.16908i	0.0397894	−	0.999208i	$-0.487331\pi$
$997$	32.3728	−	36.9141i	1.02526	−	1.16908i	0.985466	−	0.169872i	$-0.0543354\pi$
$998$	23.1525	+	15.4700i	0.732880	+	0.489695i
$999$	−2.02823	−	3.48874i	−0.0641703	−	0.110379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	153.2.s.a.11.2	✓	256
3.2	odd	2		459.2.y.a.62.15		256
9.4	even	3		459.2.y.a.368.15		256
9.5	odd	6	inner	153.2.s.a.113.2	yes	256
17.14	odd	16	inner	153.2.s.a.65.2	yes	256
51.14	even	16		459.2.y.a.116.15		256
153.14	even	48	inner	153.2.s.a.14.2	yes	256
153.31	odd	48		459.2.y.a.422.15		256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
153.2.s.a.11.2	✓	256	1.1	even	1	trivial
153.2.s.a.14.2	yes	256	153.14	even	48	inner
153.2.s.a.65.2	yes	256	17.14	odd	16	inner
153.2.s.a.113.2	yes	256	9.5	odd	6	inner
459.2.y.a.62.15		256	3.2	odd	2
459.2.y.a.116.15		256	51.14	even	16
459.2.y.a.368.15		256	9.4	even	3
459.2.y.a.422.15		256	153.31	odd	48

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 153 = 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	153.s (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53625 - 2.00208i) q^{2} +(-1.72157 + 0.190287i) q^{3} +(-1.13062 + 4.21953i) q^{4} +(3.62526 + 0.237612i) q^{5} +(3.02572 + 3.15438i) q^{6} +(0.115282 + 1.75887i) q^{7} +(5.52180 - 2.28721i) q^{8} +(2.92758 - 0.655185i) q^{9} +O(q^{10})\)	\(q+(-1.53625 - 2.00208i) q^{2} +(-1.72157 + 0.190287i) q^{3} +(-1.13062 + 4.21953i) q^{4} +(3.62526 + 0.237612i) q^{5} +(3.02572 + 3.15438i) q^{6} +(0.115282 + 1.75887i) q^{7} +(5.52180 - 2.28721i) q^{8} +(2.92758 - 0.655185i) q^{9} +(-5.09359 - 7.62309i) q^{10} +(0.00330703 + 0.00290019i) q^{11} +(1.14351 - 7.47934i) q^{12} +(-2.63273 - 0.705439i) q^{13} +(3.34429 - 2.93287i) q^{14} +(-6.28634 + 0.280777i) q^{15} +(-5.49578 - 3.17299i) q^{16} +(4.10519 - 0.383985i) q^{17} +(-5.80923 - 4.85472i) q^{18} +(6.69553 + 2.77338i) q^{19} +(-5.10140 + 15.0283i) q^{20} +(-0.533157 - 3.00607i) q^{21} +(0.000725982 - 0.0110763i) q^{22} +(-1.62305 - 4.78136i) q^{23} +(-9.07092 + 4.98831i) q^{24} +(8.12884 + 1.07018i) q^{25} +(2.63219 + 6.35467i) q^{26} +(-4.91535 + 1.68503i) q^{27} +(-7.55194 - 1.50217i) q^{28} +(4.06670 - 2.00547i) q^{29} +(10.2195 + 12.1544i) q^{30} +(-0.219566 - 0.250367i) q^{31} +(0.530062 + 4.02622i) q^{32} +(-0.00624514 - 0.00436358i) q^{33} +(-7.07536 - 7.62901i) q^{34} +6.40375i q^{35} +(-0.545408 + 13.0938i) q^{36} +(0.151512 + 0.761704i) q^{37} +(-4.73348 - 17.6656i) q^{38} +(4.66666 + 0.713483i) q^{39} +(20.5615 - 6.97967i) q^{40} +(-3.04838 + 6.18150i) q^{41} +(-5.19933 + 5.68550i) q^{42} +(-1.30212 + 9.89055i) q^{43} +(-0.0159764 + 0.0106751i) q^{44} +(10.7689 - 1.67959i) q^{45} +(-7.07925 + 10.5948i) q^{46} +(-4.72986 + 1.26736i) q^{47} +(10.0651 + 4.41673i) q^{48} +(3.85978 - 0.508150i) q^{49} +(-10.3453 - 17.9186i) q^{50} +(-6.99428 + 1.44222i) q^{51} +(5.95324 - 10.3113i) q^{52} +(1.83285 - 4.42488i) q^{53} +(10.9248 + 7.25230i) q^{54} +(0.0112997 + 0.0112997i) q^{55} +(4.65946 + 9.44845i) q^{56} +(-12.0545 - 3.50048i) q^{57} +(-10.2626 - 5.06094i) q^{58} +(-7.04508 - 5.40588i) q^{59} +(5.92272 - 26.8429i) q^{60} +(-8.03867 + 0.526882i) q^{61} +(-0.163946 + 0.824214i) q^{62} +(1.48988 + 5.07370i) q^{63} +(-1.72806 + 1.72806i) q^{64} +(-9.37672 - 3.18297i) q^{65} +(0.000857863 + 0.0192068i) q^{66} +(6.84774 - 3.95355i) q^{67} +(-3.02117 + 17.7561i) q^{68} +(3.70403 + 7.92258i) q^{69} +(12.8208 - 9.83776i) q^{70} +(-7.33915 + 1.45985i) q^{71} +(14.6670 - 10.3138i) q^{72} +(-4.87788 - 3.25929i) q^{73} +(1.29223 - 1.47351i) q^{74} +(-14.1980 - 0.295573i) q^{75} +(-19.2725 + 25.1164i) q^{76} +(-0.00471981 + 0.00615097i) q^{77} +(-5.74070 - 10.4391i) q^{78} +(3.25903 - 3.71621i) q^{79} +(-19.1697 - 12.8088i) q^{80} +(8.14147 - 3.83621i) q^{81} +(17.0589 - 3.39323i) q^{82} +(6.51878 - 5.00204i) q^{83} +(13.2870 + 1.14905i) q^{84} +(14.9736 - 0.416603i) q^{85} +(21.8020 - 12.5874i) q^{86} +(-6.61948 + 4.22640i) q^{87} +(0.0248941 + 0.00845040i) q^{88} +(-1.47920 + 1.47920i) q^{89} +(-19.9064 - 18.9800i) q^{90} +(0.937266 - 4.71196i) q^{91} +(22.0102 - 1.44262i) q^{92} +(0.425639 + 0.389243i) q^{93} +(9.80361 + 7.52257i) q^{94} +(23.6141 + 11.6452i) q^{95} +(-1.67868 - 6.83054i) q^{96} +(-0.138880 - 0.281621i) q^{97} +(-6.94694 - 6.94694i) q^{98} +(0.0115818 + 0.00632382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9	\( 256 q - 24 q^{2} - 16 q^{3} - 8 q^{4} - 24 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{9} - 32 q^{10} - 24 q^{11} + 32 q^{12} - 8 q^{13} - 24 q^{14} - 40 q^{15} - 64 q^{18} - 32 q^{19} - 24 q^{20} + 32 q^{21} - 8 q^{22} - 24 q^{23} - 40 q^{24} - 8 q^{25} - 16 q^{27} - 32 q^{28} - 24 q^{29} - 16 q^{30} - 8 q^{31} - 24 q^{32} - 56 q^{34} - 32 q^{36} - 32 q^{37} - 8 q^{40} - 24 q^{41} + 32 q^{42} + 16 q^{43} + 16 q^{45} - 32 q^{46} + 96 q^{47} + 40 q^{48} - 8 q^{49} + 16 q^{51} - 16 q^{52} - 32 q^{55} + 216 q^{56} - 32 q^{57} - 8 q^{58} - 24 q^{59} + 256 q^{60} - 8 q^{61} - 88 q^{63} - 96 q^{64} + 24 q^{65} - 96 q^{66} - 24 q^{68} + 160 q^{69} + 8 q^{70} - 88 q^{72} - 32 q^{73} - 24 q^{74} - 112 q^{75} - 8 q^{76} - 24 q^{77} + 192 q^{78} - 8 q^{79} - 72 q^{81} + 160 q^{82} - 24 q^{83} - 8 q^{85} + 192 q^{86} + 32 q^{87} - 8 q^{88} + 64 q^{90} - 128 q^{91} - 24 q^{92} + 48 q^{93} - 8 q^{94} + 216 q^{95} + 88 q^{96} - 8 q^{97} + 88 q^{99}+O(q^{100}) \) 256 * q - 24 * q^2 - 16 * q^3 - 8 * q^4 - 24 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^9 - 32 * q^10 - 24 * q^11 + 32 * q^12 - 8 * q^13 - 24 * q^14 - 40 * q^15 - 64 * q^18 - 32 * q^19 - 24 * q^20 + 32 * q^21 - 8 * q^22 - 24 * q^23 - 40 * q^24 - 8 * q^25 - 16 * q^27 - 32 * q^28 - 24 * q^29 - 16 * q^30 - 8 * q^31 - 24 * q^32 - 56 * q^34 - 32 * q^36 - 32 * q^37 - 8 * q^40 - 24 * q^41 + 32 * q^42 + 16 * q^43 + 16 * q^45 - 32 * q^46 + 96 * q^47 + 40 * q^48 - 8 * q^49 + 16 * q^51 - 16 * q^52 - 32 * q^55 + 216 * q^56 - 32 * q^57 - 8 * q^58 - 24 * q^59 + 256 * q^60 - 8 * q^61 - 88 * q^63 - 96 * q^64 + 24 * q^65 - 96 * q^66 - 24 * q^68 + 160 * q^69 + 8 * q^70 - 88 * q^72 - 32 * q^73 - 24 * q^74 - 112 * q^75 - 8 * q^76 - 24 * q^77 + 192 * q^78 - 8 * q^79 - 72 * q^81 + 160 * q^82 - 24 * q^83 - 8 * q^85 + 192 * q^86 + 32 * q^87 - 8 * q^88 + 64 * q^90 - 128 * q^91 - 24 * q^92 + 48 * q^93 - 8 * q^94 + 216 * q^95 + 88 * q^96 - 8 * q^97 + 88 * q^99

Introduction

L-functions

Modular forms

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