LMFDB - Embedded newform 507.2.q.a.55.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, degree $24$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$360$
Relative dimension:	$15$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			55.4
Character	$\chi$	$=$	507.55
Dual form			507.2.q.a.295.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.18444 + 1.45068i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.301514 - 1.47691i) q^{4} +(0.266003 + 2.19074i) q^{5} +(-1.29733 + 1.35067i) q^{6} +(-0.690655 + 0.436744i) q^{7} +(-0.816908 - 0.428746i) q^{8} +(0.987050 + 0.160411i) q^{9} +(-3.49312 - 2.20892i) q^{10} +(-4.18193 + 0.679630i) q^{11} +(-0.181694 - 1.49639i) q^{12} +(-2.97288 - 2.04009i) q^{13} +(0.184466 - 1.51922i) q^{14} +(0.0888599 + 2.20504i) q^{15} +(4.36307 - 1.85893i) q^{16} +(-2.90665 + 1.83806i) q^{17} +(-1.40181 + 1.24190i) q^{18} +(-0.845977 + 1.46528i) q^{19} +(3.15532 - 1.05340i) q^{20} +(-0.723559 + 0.379753i) q^{21} +(3.96734 - 6.87163i) q^{22} +(2.34548 + 4.06249i) q^{23} +(-0.779759 - 0.493090i) q^{24} +(0.126145 - 0.0310920i) q^{25} +(6.48073 - 1.89632i) q^{26} +(0.970942 + 0.239316i) q^{27} +(0.853275 + 0.888354i) q^{28} +(-2.19327 + 2.68627i) q^{29} +(-3.30405 - 2.48283i) q^{30} +(-6.36143 - 1.56795i) q^{31} +(-1.95774 + 6.75889i) q^{32} +(-4.22306 + 0.340921i) q^{33} +(0.776335 - 6.39370i) q^{34} +(-1.14051 - 1.39687i) q^{35} +(-0.0606959 - 1.50615i) q^{36} +(0.854022 + 2.94843i) q^{37} +(-1.12363 - 2.96278i) q^{38} +(-2.79908 - 2.27270i) q^{39} +(0.721970 - 1.90368i) q^{40} +(1.63292 + 0.131823i) q^{41} +(0.306115 - 1.49945i) q^{42} +(1.06821 - 3.68789i) q^{43} +(2.26467 + 5.97144i) q^{44} +(-0.0888599 + 2.20504i) q^{45} +(-8.67147 - 1.40925i) q^{46} +(1.18546 + 1.05023i) q^{47} +(4.49850 - 1.50182i) q^{48} +(-2.71459 + 5.72087i) q^{49} +(-0.104307 + 0.219823i) q^{50} +(-3.04513 + 1.59821i) q^{51} +(-2.11668 + 5.00580i) q^{52} +(5.63816 + 2.95913i) q^{53} +(-1.49720 + 1.12507i) q^{54} +(-2.60130 - 8.98073i) q^{55} +(0.751454 - 0.0606637i) q^{56} +(-0.961140 + 1.39245i) q^{57} +(-1.29911 - 6.36347i) q^{58} +(-3.58605 - 1.52788i) q^{59} +(3.22985 - 0.796088i) q^{60} +(0.619958 - 15.3841i) q^{61} +(9.80934 - 7.37124i) q^{62} +(-0.751770 + 0.320299i) q^{63} +(-2.09798 - 3.03945i) q^{64} +(3.67851 - 7.05547i) q^{65} +(4.50741 - 6.53011i) q^{66} +(-2.06099 + 10.0954i) q^{67} +(3.59105 + 3.73868i) q^{68} +(2.01098 + 4.23805i) q^{69} +3.37727 q^{70} +(1.14280 + 2.40840i) q^{71} +(-0.737554 - 0.554236i) q^{72} +(-0.217535 + 0.573593i) q^{73} +(-5.28876 - 2.25333i) q^{74} +(0.128238 - 0.0208407i) q^{75} +(2.41916 + 0.807634i) q^{76} +(2.59145 - 2.29582i) q^{77} +(6.61231 - 1.36869i) q^{78} +(4.69846 + 4.16248i) q^{79} +(5.23301 + 9.06384i) q^{80} +(0.948536 + 0.316668i) q^{81} +(-2.12533 + 2.21271i) q^{82} +(-4.14530 - 6.00551i) q^{83} +(0.779026 + 0.954133i) q^{84} +(-4.79988 - 5.87878i) q^{85} +(4.08472 + 5.91773i) q^{86} +(-2.40232 + 2.50108i) q^{87} +(3.70764 + 1.23779i) q^{88} +(-1.11585 - 1.93272i) q^{89} +(-3.09355 - 2.74065i) q^{90} +(2.94423 + 0.110613i) q^{91} +(5.29276 - 4.68897i) q^{92} +(-6.21463 - 2.07475i) q^{93} +(-2.92766 + 0.475791i) q^{94} +(-3.43506 - 1.46354i) q^{95} +(-2.49525 + 6.57944i) q^{96} +(8.76267 + 6.58472i) q^{97} +(-5.08388 - 10.7140i) q^{98} -4.23680 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21}+ \cdots + 30 q^{99}+O(q^{100}) $ 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{28}{39}\right)$

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 $

$2$	−1.18444	+	1.45068i	−0.837528	+	1.02579i	0.161713	+	0.986838i	$0.448298\pi$
$2$	−1.18444	+	1.45068i	−0.837528	+	1.02579i	−0.999241	+	0.0389476i	$0.987599\pi$
$3$	0.996757	+	0.0804666i	0.575478	+	0.0464574i
$3$	0.996757	+	0.0804666i	0.575478	+	0.0464574i
$4$	−0.301514	−	1.47691i	−0.150757	−	0.738457i
$5$	0.266003	+	2.19074i	0.118960	+	0.979727i	0.922906	+	0.385024i	$0.125807\pi$
$5$	0.266003	+	2.19074i	0.118960	+	0.979727i	−0.803946	+	0.594702i	$0.797270\pi$
$6$	−1.29733	+	1.35067i	−0.529634	+	0.551408i
$7$	−0.690655	+	0.436744i	−0.261043	+	0.165074i	−0.658576	−	0.752514i	$-0.728841\pi$
$7$	−0.690655	+	0.436744i	−0.261043	+	0.165074i	0.397533	+	0.917588i	$0.369867\pi$
$8$	−0.816908	−	0.428746i	−0.288821	−	0.151585i
$9$	0.987050	+	0.160411i	0.329017	+	0.0534704i
$10$	−3.49312	−	2.20892i	−1.10462	−	0.698521i
$11$	−4.18193	+	0.679630i	−1.26090	+	0.204916i	−0.753877	−	0.657016i	$-0.771818\pi$
$11$	−4.18193	+	0.679630i	−1.26090	+	0.204916i	−0.507024	+	0.861932i	$0.669254\pi$
$12$	−0.181694	−	1.49639i	−0.0524506	−	0.431969i
$13$	−2.97288	−	2.04009i	−0.824529	−	0.565820i
$13$	−2.97288	−	2.04009i	−0.824529	−	0.565820i
$14$	0.184466	−	1.51922i	0.0493007	−	0.406028i
$15$	0.0888599	+	2.20504i	0.0229435	+	0.569338i
$16$	4.36307	−	1.85893i	1.09077	−	0.464732i
$17$	−2.90665	+	1.83806i	−0.704967	+	0.445794i	−0.838252	−	0.545284i	$-0.816422\pi$
$17$	−2.90665	+	1.83806i	−0.704967	+	0.445794i	0.133284	+	0.991078i	$0.457448\pi$
$18$	−1.40181	+	1.24190i	−0.330410	+	0.292718i
$19$	−0.845977	+	1.46528i	−0.194080	+	0.336157i	−0.946599	−	0.322414i	$-0.895506\pi$
$19$	−0.845977	+	1.46528i	−0.194080	+	0.336157i	0.752518	+	0.658571i	$0.228839\pi$
$20$	3.15532	−	1.05340i	0.705552	−	0.235548i
$21$	−0.723559	+	0.379753i	−0.157894	+	0.0828689i
$22$	3.96734	−	6.87163i	0.845839	−	1.46504i
$23$	2.34548	+	4.06249i	0.489067	+	0.847088i	0.999921	−	0.0125789i	$-0.00400410\pi$
$23$	2.34548	+	4.06249i	0.489067	+	0.847088i	−0.510854	+	0.859667i	$0.670671\pi$
$24$	−0.779759	−	0.493090i	−0.159168	−	0.100652i
$25$	0.126145	−	0.0310920i	0.0252290	−	0.00621840i
$26$	6.48073	−	1.89632i	1.27098	−	0.371900i
$27$	0.970942	+	0.239316i	0.186858	+	0.0460563i
$28$	0.853275	+	0.888354i	0.161254	+	0.167883i
$29$	−2.19327	+	2.68627i	−0.407281	+	0.498828i	−0.936993	−	0.349349i	$-0.886403\pi$
$29$	−2.19327	+	2.68627i	−0.407281	+	0.498828i	0.529712	+	0.848178i	$0.322300\pi$
$30$	−3.30405	−	2.48283i	−0.603234	−	0.453301i
$31$	−6.36143	−	1.56795i	−1.14255	−	0.281612i	−0.377764	−	0.925902i	$-0.623307\pi$
$31$	−6.36143	−	1.56795i	−1.14255	−	0.281612i	−0.764782	+	0.644290i	$0.777153\pi$
$32$	−1.95774	+	6.75889i	−0.346082	+	1.19481i
$33$	−4.22306	+	0.340921i	−0.735141	+	0.0593467i
$34$	0.776335	−	6.39370i	0.133140	−	1.09651i
$35$	−1.14051	−	1.39687i	−0.192781	−	0.236114i
$36$	−0.0606959	−	1.50615i	−0.0101160	−	0.251026i
$37$	0.854022	+	2.94843i	0.140400	+	0.484718i	0.999639	−	0.0268562i	$-0.00854961\pi$
$37$	0.854022	+	2.94843i	0.140400	+	0.484718i	−0.859239	+	0.511574i	$0.829062\pi$
$38$	−1.12363	−	2.96278i	−0.182277	−	0.480626i
$39$	−2.79908	−	2.27270i	−0.448212	−	0.363922i
$40$	0.721970	−	1.90368i	0.114153	−	0.300998i
$41$	1.63292	+	0.131823i	0.255019	+	0.0205873i	0.207315	−	0.978274i	$-0.433527\pi$
$41$	1.63292	+	0.131823i	0.255019	+	0.0205873i	0.0477041	+	0.998862i	$0.484810\pi$
$42$	0.306115	−	1.49945i	0.0472345	−	0.231370i
$43$	1.06821	−	3.68789i	0.162901	−	0.562398i	−0.836984	−	0.547227i	$-0.815683\pi$
$43$	1.06821	−	3.68789i	0.162901	−	0.562398i	0.999885	−	0.0151714i	$-0.00482939\pi$
$44$	2.26467	+	5.97144i	0.341411	+	0.900228i
$45$	−0.0888599	+	2.20504i	−0.0132465	+	0.328707i
$46$	−8.67147	−	1.40925i	−1.27854	−	0.207783i
$47$	1.18546	+	1.05023i	0.172917	+	0.153192i	0.745143	−	0.666905i	$-0.232381\pi$
$47$	1.18546	+	1.05023i	0.172917	+	0.153192i	−0.572225	+	0.820096i	$0.693920\pi$
$48$	4.49850	−	1.50182i	0.649302	−	0.216769i
$49$	−2.71459	+	5.72087i	−0.387798	+	0.817268i
$50$	−0.104307	+	0.219823i	−0.0147513	+	0.0310876i
$51$	−3.04513	+	1.59821i	−0.426404	+	0.223794i
$52$	−2.11668	+	5.00580i	−0.293530	+	0.694180i
$53$	5.63816	+	2.95913i	0.774461	+	0.406468i	0.805158	−	0.593060i	$-0.202080\pi$
$53$	5.63816	+	2.95913i	0.774461	+	0.406468i	−0.0306971	+	0.999529i	$0.509773\pi$
$54$	−1.49720	+	1.12507i	−0.203743	+	0.153103i
$55$	−2.60130	−	8.98073i	−0.350759	−	1.21096i
$56$	0.751454	−	0.0606637i	0.100417	−	0.00810652i
$57$	−0.961140	+	1.39245i	−0.127306	+	0.184435i
$58$	−1.29911	−	6.36347i	−0.170582	−	0.835565i
$59$	−3.58605	−	1.52788i	−0.466865	−	0.198912i	0.145707	−	0.989328i	$-0.453454\pi$
$59$	−3.58605	−	1.52788i	−0.466865	−	0.198912i	−0.612571	+	0.790415i	$0.709865\pi$
$60$	3.22985	−	0.796088i	0.416972	−	0.102774i
$61$	0.619958	−	15.3841i	0.0793774	−	1.96973i	−0.128890	−	0.991659i	$-0.541141\pi$
$61$	0.619958	−	15.3841i	0.0793774	−	1.96973i	0.208268	−	0.978072i	$-0.433218\pi$
$62$	9.80934	−	7.37124i	1.24579	−	0.936149i
$63$	−0.751770	+	0.320299i	−0.0947141	+	0.0403539i
$64$	−2.09798	−	3.03945i	−0.262248	−	0.379931i
$65$	3.67851	−	7.05547i	0.456263	−	0.875123i
$66$	4.50741	−	6.53011i	0.554824	−	0.803801i
$67$	−2.06099	+	10.0954i	−0.251790	+	1.23335i	0.635488	+	0.772111i	$0.280799\pi$
$67$	−2.06099	+	10.0954i	−0.251790	+	1.23335i	−0.887277	+	0.461236i	$0.847406\pi$
$68$	3.59105	+	3.73868i	0.435479	+	0.453381i
$69$	2.01098	+	4.23805i	0.242094	+	0.510202i
$70$	3.37727			0.403661
$71$	1.14280	+	2.40840i	0.135625	+	0.285825i	0.959888	−	0.280383i	$-0.0904614\pi$
$71$	1.14280	+	2.40840i	0.135625	+	0.285825i	−0.824263	+	0.566207i	$0.808410\pi$
$72$	−0.737554	−	0.554236i	−0.0869215	−	0.0653173i
$73$	−0.217535	+	0.573593i	−0.0254606	+	0.0671340i	−0.947144	−	0.320809i	$-0.896045\pi$
$73$	−0.217535	+	0.573593i	−0.0254606	+	0.0671340i	0.921683	+	0.387943i	$0.126814\pi$
$74$	−5.28876	−	2.25333i	−0.614806	−	0.261944i
$75$	0.128238	−	0.0208407i	0.0148076	−	0.00240648i
$76$	2.41916	+	0.807634i	0.277497	+	0.0926420i
$77$	2.59145	−	2.29582i	0.295323	−	0.261634i
$78$	6.61231	−	1.36869i	0.748696	−	0.154974i
$79$	4.69846	+	4.16248i	0.528619	+	0.468315i	0.884714	−	0.466134i	$-0.154354\pi$
$79$	4.69846	+	4.16248i	0.528619	+	0.468315i	−0.356095	+	0.934450i	$0.615892\pi$
$80$	5.23301	+	9.06384i	0.585068	+	1.01337i
$81$	0.948536	+	0.316668i	0.105393	+	0.0351853i
$82$	−2.12533	+	2.21271i	−0.234704	+	0.244352i
$83$	−4.14530	−	6.00551i	−0.455006	−	0.659190i	0.526599	−	0.850114i	$-0.323467\pi$
$83$	−4.14530	−	6.00551i	−0.455006	−	0.659190i	−0.981605	+	0.190924i	$0.938852\pi$
$84$	0.779026	+	0.954133i	0.0849987	+	0.104104i
$85$	−4.79988	−	5.87878i	−0.520620	−	0.637643i
$86$	4.08472	+	5.91773i	0.440466	+	0.638125i
$87$	−2.40232	+	2.50108i	−0.257555	+	0.268144i
$88$	3.70764	+	1.23779i	0.395236	+	0.131949i
$89$	−1.11585	−	1.93272i	−0.118280	−	0.204867i	0.800806	−	0.598924i	$-0.204405\pi$
$89$	−1.11585	−	1.93272i	−0.118280	−	0.204867i	−0.919086	+	0.394056i	$0.871071\pi$
$90$	−3.09355	−	2.74065i	−0.326089	−	0.288890i
$91$	2.94423	+	0.110613i	0.308640	+	0.0115954i
$92$	5.29276	−	4.68897i	0.551808	−	0.488859i
$93$	−6.21463	−	2.07475i	−0.644427	−	0.215141i
$94$	−2.92766	+	0.475791i	−0.301965	+	0.0490741i
$95$	−3.43506	−	1.46354i	−0.352430	−	0.150156i
$96$	−2.49525	+	6.57944i	−0.254671	+	0.671511i
$97$	8.76267	+	6.58472i	0.889714	+	0.668577i	0.943999	−	0.329948i	$-0.107031\pi$
$97$	8.76267	+	6.58472i	0.889714	+	0.668577i	−0.0542845	+	0.998526i	$0.517288\pi$
$98$	−5.08388	−	10.7140i	−0.513549	−	1.08228i
$99$	−4.23680			−0.425814
$100$	−0.0839547	−	0.176931i	−0.00839547	−	0.0176931i
$101$	3.02852	+	3.15302i	0.301349	+	0.313737i	0.854610	−	0.519271i	$-0.173796\pi$
$101$	3.02852	+	3.15302i	0.301349	+	0.313737i	−0.553261	+	0.833008i	$0.686617\pi$
$102$	1.28830	−	6.31050i	0.127560	−	0.624832i
$103$	−7.87250	+	11.4053i	−0.775700	+	1.12380i	0.213459	+	0.976952i	$0.431527\pi$
$103$	−7.87250	+	11.4053i	−0.775700	+	1.12380i	−0.989160	+	0.146844i	$0.953088\pi$
$104$	1.55389	+	2.94118i	0.152371	+	0.288406i
$105$	−1.02441	−	1.48411i	−0.0999720	−	0.144834i
$106$	−10.9708	+	4.67424i	−1.06558	+	0.454002i
$107$	−4.30910	+	3.23808i	−0.416577	+	0.313037i	−0.788283	−	0.615313i	$-0.789029\pi$
$107$	−4.30910	+	3.23808i	−0.416577	+	0.313037i	0.371706	+	0.928351i	$0.378773\pi$
$108$	0.0606959	−	1.50615i	0.00584047	−	0.144930i
$109$	14.1474	−	3.48701i	1.35507	−	0.333995i	0.506118	−	0.862464i	$-0.331080\pi$
$109$	14.1474	−	3.48701i	1.35507	−	0.333995i	0.848953	+	0.528469i	$0.177234\pi$
$110$	16.1092	+	6.86351i	1.53596	+	0.654410i
$111$	0.614003	+	3.00759i	0.0582786	+	0.285467i
$112$	−2.20150	+	3.18942i	−0.208022	+	0.301372i
$113$	−2.33641	+	0.188615i	−0.219791	+	0.0177434i	−0.189872	−	0.981809i	$-0.560807\pi$
$113$	−2.33641	+	0.188615i	−0.219791	+	0.0177434i	−0.0299196	+	0.999552i	$0.509525\pi$
$114$	−0.881585	−	3.04358i	−0.0825680	−	0.285058i
$115$	−8.27594	+	6.21897i	−0.771736	+	0.579922i
$116$	4.62870	+	2.42933i	0.429764	+	0.225557i
$117$	−2.60713	−	2.49056i	−0.241029	−	0.230252i
$118$	6.46394	−	3.39253i	0.595053	−	0.312308i
$119$	1.20474	−	2.53893i	0.110438	−	0.232743i
$120$	0.872811	−	1.83941i	0.0796764	−	0.167914i
$121$	6.59277	−	2.20099i	0.599343	−	0.200090i
$122$	21.5831	+	19.1209i	1.95404	+	1.73113i
$123$	1.61702	+	0.262791i	0.145802	+	0.0236951i
$124$	−0.397668	+	9.86804i	−0.0357117	+	0.886176i
$125$	4.01443	+	10.5852i	0.359061	+	0.946766i
$126$	0.425777	−	1.46995i	0.0379313	−	0.130954i
$127$	−4.10401	+	20.1028i	−0.364172	+	1.78383i	0.223471	+	0.974711i	$0.428261\pi$
$127$	−4.10401	+	20.1028i	−0.364172	+	1.78383i	−0.587643	+	0.809121i	$0.699944\pi$
$128$	−7.13358	−	0.575882i	−0.630525	−	0.0509013i
$129$	1.36150	−	3.58998i	0.119873	−	0.316080i
$130$	5.87824	+	13.6931i	0.515556	+	1.20097i
$131$	3.82581	+	10.0878i	0.334263	+	0.881378i	0.991782	+	0.127940i	$0.0408366\pi$
$131$	3.82581	+	10.0878i	0.334263	+	0.881378i	−0.657519	+	0.753438i	$0.728394\pi$
$132$	1.77682	+	6.13430i	0.154653	+	0.533923i
$133$	−0.0556716	−	1.38148i	−0.00482734	−	0.119789i
$134$	−12.2040	−	14.9472i	−1.05427	−	1.29124i
$135$	−0.266003	+	2.19074i	−0.0228939	+	0.188548i
$136$	3.16253	−	0.255306i	0.271185	−	0.0218923i
$137$	−5.82400	+	20.1068i	−0.497578	+	1.71784i	0.181157	+	0.983454i	$0.442016\pi$
$137$	−5.82400	+	20.1068i	−0.497578	+	1.71784i	−0.678735	+	0.734384i	$0.737471\pi$
$138$	−8.52995	−	2.10244i	−0.726118	−	0.178972i
$139$	7.02175	+	5.27650i	0.595577	+	0.447547i	0.855298	−	0.518137i	$-0.173374\pi$
$139$	7.02175	+	5.27650i	0.595577	+	0.447547i	−0.259721	+	0.965684i	$0.583631\pi$
$140$	−1.71917	+	2.10561i	−0.145297	+	0.177956i
$141$	1.09711	+	1.14221i	0.0923933	+	0.0961917i
$142$	−4.84740	−	1.19478i	−0.406785	−	0.100263i
$143$	13.8189	+	6.51107i	1.15559	+	0.544483i
$144$	4.60476	−	1.13497i	0.383730	−	0.0945809i
$145$	−6.46833	−	4.09032i	−0.537166	−	0.339683i
$146$	−0.574442	−	0.994963i	−0.0475412	−	0.0823437i
$147$	−3.16612	+	5.48389i	−0.261138	+	0.452304i
$148$	4.09707	−	2.15031i	0.336777	−	0.176754i
$149$	1.83184	−	0.611559i	0.150070	−	0.0501008i	−0.240640	−	0.970614i	$-0.577357\pi$
$149$	1.83184	−	0.611559i	0.150070	−	0.0501008i	0.390711	+	0.920513i	$0.372229\pi$
$150$	−0.121657	+	0.210717i	−0.00993328	+	0.0172050i
$151$	8.51367	−	7.54245i	0.692832	−	0.613796i	−0.241415	−	0.970422i	$-0.577611\pi$
$151$	8.51367	−	7.54245i	0.692832	−	0.613796i	0.934247	+	0.356626i	$0.116073\pi$
$152$	1.31932	−	0.834286i	0.107011	−	0.0676695i
$153$	−3.16386	+	1.34799i	−0.255783	+	0.108979i
$154$	0.261080	+	6.47864i	0.0210384	+	0.522064i
$155$	1.74280	−	14.3533i	0.139985	−	1.15288i
$156$	−2.51261	+	4.81925i	−0.201170	+	0.385849i
$157$	2.23878	+	18.4380i	0.178674	+	1.47151i	0.755770	+	0.654837i	$0.227263\pi$
$157$	2.23878	+	18.4380i	0.178674	+	1.47151i	−0.577096	+	0.816676i	$0.695814\pi$
$158$	−11.6035	+	1.88575i	−0.923124	+	0.150022i
$159$	5.38177	+	3.40322i	0.426802	+	0.269893i
$160$	−15.3277	−	2.49099i	−1.21176	−	0.196930i
$161$	−3.39419	−	1.78141i	−0.267500	−	0.140395i
$162$	−1.58287	+	1.00095i	−0.124362	+	0.0786418i
$163$	−0.0434380	+	0.0452237i	−0.00340233	+	0.00354220i	−0.722901	−	0.690951i	$-0.757192\pi$
$163$	−0.0434380	+	0.0452237i	−0.00340233	+	0.00354220i	0.719499	+	0.694493i	$0.244371\pi$
$164$	−0.297657	−	2.45143i	−0.0232431	−	0.191424i
$165$	−1.87022	−	9.16092i	−0.145596	−	0.713177i
$166$	13.6219	+	1.09968i	1.05727	+	0.0853515i
$167$	4.25966	−	5.21714i	0.329623	−	0.403715i	−0.583030	−	0.812451i	$-0.698133\pi$
$167$	4.25966	−	5.21714i	0.329623	−	0.403715i	0.912653	+	0.408736i	$0.134030\pi$
$168$	0.753899			0.0581646
$169$	4.67604	+	12.1299i	0.359696	+	0.933070i
$170$	14.2134			1.09012
$171$	−1.07007	+	1.31060i	−0.0818302	+	0.100224i
$172$	−5.76878	−	0.465704i	−0.439865	−	0.0355096i
$173$	−4.18086	−	20.4792i	−0.317865	−	1.55701i	−0.753846	−	0.657051i	$-0.771804\pi$
$173$	−4.18086	−	20.4792i	−0.317865	−	1.55701i	0.435981	−	0.899956i	$-0.356401\pi$
$174$	−0.782853	−	6.44737i	−0.0593479	−	0.488774i
$175$	−0.0735436	+	0.0765670i	−0.00555937	+	0.00578792i
$176$	−16.9827	+	10.7392i	−1.28012	+	0.809497i
$177$	−3.45148	−	1.81148i	−0.259429	−	0.136159i
$178$	4.12542	+	0.670445i	0.309213	+	0.0502520i
$179$	−9.69243	−	6.12912i	−0.724446	−	0.458112i	0.120671	−	0.992692i	$-0.461495\pi$
$179$	−9.69243	−	6.12912i	−0.724446	−	0.458112i	−0.845118	+	0.534581i	$0.820470\pi$
$180$	3.28344	−	0.533611i	0.244733	−	0.0397730i
$181$	−2.38591	−	19.6497i	−0.177343	−	1.46055i	−0.761106	−	0.648627i	$-0.775343\pi$
$181$	−2.38591	−	19.6497i	−0.177343	−	1.46055i	0.583763	−	0.811924i	$-0.301580\pi$
$182$	−3.64774	+	4.14013i	−0.270389	+	0.306887i
$183$	1.85585	−	15.2843i	0.137189	−	1.12985i
$184$	−0.174263	−	4.32430i	−0.0128469	−	0.318792i
$185$	−6.23205	+	2.65523i	−0.458189	+	0.195216i
$186$	10.3707	−	6.55802i	0.760415	−	0.480857i
$187$	10.9062	−	9.66208i	0.797543	−	0.706561i
$188$	1.19366	−	2.06748i	0.0870568	−	0.150787i
$189$	−0.775106	+	0.258768i	−0.0563807	+	0.0188226i
$190$	6.19177	−	3.24969i	0.449198	−	0.235757i
$191$	2.77471	−	4.80593i	0.200771	−	0.347745i	−0.748006	−	0.663692i	$-0.768989\pi$
$191$	2.77471	−	4.80593i	0.200771	−	0.347745i	0.948777	+	0.315947i	$0.102322\pi$
$192$	−1.84660	−	3.19841i	−0.133267	−	0.230825i
$193$	17.8738	+	11.3027i	1.28659	+	0.813588i	0.989952	−	0.141403i	$-0.0451614\pi$
$193$	17.8738	+	11.3027i	1.28659	+	0.813588i	0.296634	+	0.954991i	$0.404136\pi$
$194$	−19.9312	+	4.91260i	−1.43098	+	0.352704i
$195$	4.23431	−	6.73659i	0.303225	−	0.482417i
$196$	9.26772	+	2.28429i	0.661980	+	0.163163i
$197$	2.51219	+	2.61547i	0.178986	+	0.186345i	0.804652	−	0.593747i	$-0.202352\pi$
$197$	2.51219	+	2.61547i	0.178986	+	0.186345i	−0.625665	+	0.780091i	$0.715172\pi$
$198$	5.01825	−	6.14624i	0.356631	−	0.436794i
$199$	−15.3772	−	11.5552i	−1.09006	−	0.819126i	−0.105541	−	0.994415i	$-0.533657\pi$
$199$	−15.3772	−	11.5552i	−1.09006	−	0.819126i	−0.984517	+	0.175289i	$0.943914\pi$
$200$	−0.116380	−	0.0286850i	−0.00822928	−	0.00202833i
$201$	−2.86664	+	9.89680i	−0.202197	+	0.698067i
$202$	−8.16113	+	0.658834i	−0.574215	+	0.0463554i
$203$	0.341583	−	2.81319i	0.0239744	−	0.197447i
$204$	3.27856	+	4.01551i	0.229545	+	0.281142i
$205$	0.145573	+	3.61236i	0.0101673	+	0.252298i
$206$	−7.22088	−	24.9294i	−0.503103	−	1.73691i
$207$	1.66344	+	4.38613i	0.115617	+	0.304857i
$208$	−16.7633	−	3.37469i	−1.16232	−	0.233992i
$209$	2.54197	−	6.70264i	0.175832	−	0.463631i
$210$	3.36632	+	0.271758i	0.232298	+	0.0187531i
$211$	0.0385552	−	0.188856i	0.00265425	−	0.0130014i	−0.978442	−	0.206522i	$-0.933786\pi$
$211$	0.0385552	−	0.188856i	0.00265425	−	0.0130014i	0.981096	+	0.193521i	$0.0619906\pi$
$212$	2.67040	−	9.21930i	0.183404	−	0.633184i
$213$	0.945299	+	2.49255i	0.0647708	+	0.170787i
$214$	0.406470	−	10.0865i	0.0277857	−	0.689496i
$215$	8.36335	+	1.35918i	0.570375	+	0.0926950i
$216$	−0.690564	−	0.611787i	−0.0469870	−	0.0416268i
$217$	5.07835	−	1.69540i	0.344741	−	0.115091i
$218$	−11.6982	+	24.6534i	−0.792303	+	1.66974i
$219$	−0.262985	+	0.554229i	−0.0177709	+	0.0374513i
$220$	−12.4794	+	6.54971i	−0.841363	+	0.441581i
$221$	12.3909	+	0.465521i	0.833505	+	0.0313143i
$222$	−5.09029	−	2.67159i	−0.341638	−	0.179306i
$223$	8.31954	−	6.25173i	0.557118	−	0.418647i	−0.284535	−	0.958666i	$-0.591839\pi$
$223$	8.31954	−	6.25173i	0.557118	−	0.418647i	0.841653	+	0.540019i	$0.181583\pi$
$224$	−1.59978	−	5.52309i	−0.106890	−	0.369027i
$225$	0.129499	−	0.0104542i	0.00863327	−	0.000696950i
$226$	2.49373	−	3.61279i	0.165880	−	0.240319i
$227$	−0.934399	−	4.57699i	−0.0620183	−	0.303785i	0.936936	−	0.349500i	$-0.113649\pi$
$227$	−0.934399	−	4.57699i	−0.0620183	−	0.303785i	−0.998955	+	0.0457147i	$0.985443\pi$
$228$	2.34633	+	0.999677i	0.155389	+	0.0662052i
$229$	17.3690	−	4.28109i	1.14778	−	0.282902i	0.380852	−	0.924636i	$-0.375631\pi$
$229$	17.3690	−	4.28109i	1.14778	−	0.282902i	0.766927	+	0.641734i	$0.221785\pi$
$230$	0.780655	−	19.3718i	0.0514749	−	1.27734i
$231$	2.76778	−	2.07985i	0.182107	−	0.136844i
$232$	2.94343	−	1.25408i	0.193246	−	0.0823344i
$233$	−12.5624	−	18.1998i	−0.822993	−	1.19231i	−0.978860	−	0.204533i	$-0.934432\pi$
$233$	−12.5624	−	18.1998i	−0.822993	−	1.19231i	0.155867	−	0.987778i	$-0.450183\pi$
$234$	6.70100	−	0.832184i	0.438058	−	0.0544016i
$235$	−1.98543	+	2.87640i	−0.129515	+	0.187636i
$236$	−1.17529	+	5.75697i	−0.0765051	+	0.374747i
$237$	4.34829	+	4.52705i	0.282452	+	0.294063i
$238$	2.25623	+	4.75490i	0.146250	+	0.308214i
$239$	−29.2952			−1.89495			−0.947475	−	0.319831i	$-0.896374\pi$
$239$	−29.2952			−1.89495			−0.947475	+	0.319831i	$0.896374\pi$
$240$	4.48671	+	9.45553i	0.289616	+	0.610352i
$241$	5.12816	+	3.85356i	0.330334	+	0.248230i	0.752948	−	0.658080i	$-0.228631\pi$
$241$	5.12816	+	3.85356i	0.330334	+	0.248230i	−0.422614	+	0.906310i	$0.638888\pi$
$242$	−4.61583	+	12.1709i	−0.296717	+	0.782378i
$243$	0.919979	+	0.391967i	0.0590167	+	0.0251447i
$244$	−22.9079	+	3.72290i	−1.46653	+	0.238334i
$245$	−13.2550	−	4.42517i	−0.846832	−	0.282714i
$246$	−2.29649	+	2.03451i	−0.146419	+	0.129716i
$247$	5.50429	−	2.63022i	0.350229	−	0.167357i
$248$	4.52445	+	4.00831i	0.287303	+	0.254528i
$249$	−3.64862	−	6.31959i	−0.231222	−	0.400488i
$250$	−20.1105	−	6.71389i	−1.27190	−	0.424624i
$251$	18.1128	−	18.8574i	1.14327	−	1.19027i	0.164266	−	0.986416i	$-0.447474\pi$
$251$	18.1128	−	18.8574i	1.14327	−	1.19027i	0.979002	−	0.203852i	$-0.0653461\pi$
$252$	0.699724	+	1.01372i	0.0440785	+	0.0638587i
$253$	−12.5696	−	15.3950i	−0.790247	−	0.967877i
$254$	−24.3017	−	29.7642i	−1.52482	−	1.86757i
$255$	−4.31127	−	6.24595i	−0.269982	−	0.391136i
$256$	14.4015	−	14.9935i	0.900093	−	0.937096i
$257$	9.08736	+	3.03381i	0.566854	+	0.189244i	0.585628	−	0.810580i	$-0.300848\pi$
$257$	9.08736	+	3.03381i	0.566854	+	0.189244i	−0.0187739	+	0.999824i	$0.505976\pi$
$258$	3.59529	+	6.22723i	0.223833	+	0.387690i
$259$	−1.87754	−	1.66336i	−0.116665	−	0.103356i
$260$	−11.5294	−	3.30551i	−0.715025	−	0.204999i
$261$	−2.59578	+	2.29966i	−0.160675	+	0.142345i
$262$	−19.1657	−	6.39844i	−1.18406	−	0.395297i
$263$	3.84599	−	0.625034i	0.237154	−	0.0385413i	−0.0406726	−	0.999173i	$-0.512950\pi$
$263$	3.84599	−	0.625034i	0.237154	−	0.0385413i	0.277827	+	0.960631i	$0.410386\pi$
$264$	3.59602	+	1.53212i	0.221320	+	0.0942955i
$265$	−4.98291	+	13.1389i	−0.306098	+	0.807114i
$266$	2.07002	+	1.55552i	0.126921	+	0.0953749i
$267$	−0.956717	−	2.01624i	−0.0585501	−	0.123392i
$268$	15.5314			0.948733
$269$	−3.42137	−	7.21038i	−0.208604	−	0.439625i	0.772000	−	0.635623i	$-0.219257\pi$
$269$	−3.42137	−	7.21038i	−0.208604	−	0.439625i	−0.980604	+	0.195998i	$0.937205\pi$
$270$	−2.86299	−	2.98069i	−0.174236	−	0.181399i
$271$	−5.00498	+	24.5160i	−0.304031	+	1.48924i	0.484797	+	0.874627i	$0.338893\pi$
$271$	−5.00498	+	24.5160i	−0.304031	+	1.48924i	−0.788828	+	0.614614i	$0.789312\pi$
$272$	−9.26511	+	13.4228i	−0.561780	+	0.813878i
$273$	2.92579	+	0.347167i	0.177077	+	0.0210115i
$274$	−22.2703	−	32.2641i	−1.34540	−	1.94914i
$275$	−0.506400	+	0.215757i	−0.0305370	+	0.0130106i
$276$	5.65290	−	4.24788i	0.340265	−	0.255692i
$277$	0.444450	−	11.0289i	0.0267044	−	0.662664i	−0.929303	−	0.369319i	$-0.879591\pi$
$277$	0.444450	−	11.0289i	0.0267044	−	0.662664i	0.956007	−	0.293344i	$-0.0947682\pi$
$278$	−15.9714	+	3.93659i	−0.957899	+	0.236101i
$279$	−6.02753	−	2.56809i	−0.360859	−	0.153748i
$280$	0.332787	+	1.63010i	0.0198879	+	0.0974172i
$281$	8.84755	−	12.8179i	0.527801	−	0.764651i	−0.464886	−	0.885371i	$-0.653905\pi$
$281$	8.84755	−	12.8179i	0.527801	−	0.764651i	0.992687	+	0.120719i	$0.0385201\pi$
$282$	−2.95645	+	0.238669i	−0.176054	+	0.0142125i
$283$	8.58027	+	29.6225i	0.510044	+	1.76088i	0.638979	+	0.769224i	$0.279357\pi$
$283$	8.58027	+	29.6225i	0.510044	+	1.76088i	−0.128935	+	0.991653i	$0.541156\pi$
$284$	3.21243	−	2.41398i	0.190623	−	0.143244i
$285$	−3.30616	−	1.73521i	−0.195840	−	0.102785i
$286$	−25.8132	+	12.3348i	−1.52637	+	0.729372i
$287$	−1.18536	+	0.622123i	−0.0699694	+	0.0367228i
$288$	−3.01659	+	6.35732i	−0.177754	+	0.374609i
$289$	−2.21759	+	4.67347i	−0.130446	+	0.274910i
$290$	13.5951	−	4.53872i	0.798333	−	0.266523i
$291$	8.20441	+	7.26847i	0.480951	+	0.426085i
$292$	0.912738	+	0.148334i	0.0534139	+	0.00868061i
$293$	−0.940690	+	23.3430i	−0.0549557	+	1.36371i	0.702900	+	0.711289i	$0.251888\pi$
$293$	−0.940690	+	23.3430i	−0.0549557	+	1.36371i	−0.757856	+	0.652422i	$0.773753\pi$
$294$	−4.20527	−	11.0884i	−0.245256	−	0.646688i
$295$	2.39327	−	8.26252i	0.139341	−	0.481062i
$296$	0.566470	−	2.77475i	0.0329254	−	0.161279i
$297$	−4.22306	−	0.340921i	−0.245047	−	0.0197822i
$298$	−1.28254	+	3.38177i	−0.0742954	+	0.195901i
$299$	1.31503	−	16.8623i	0.0760499	−	0.975173i
$300$	−0.0694455	−	0.183113i	−0.00400943	−	0.0105720i
$301$	0.872899	+	3.01360i	0.0503131	+	0.173701i
$302$	0.857724	+	21.2842i	0.0493565	+	1.22477i
$303$	2.76498	+	3.38649i	0.158844	+	0.194549i
$304$	−0.967212	+	7.96570i	−0.0554734	+	0.456865i
$305$	33.8674	−	2.73406i	1.93924	−	0.156552i
$306$	1.79190	−	6.18637i	0.102436	−	0.353651i
$307$	−19.7545	−	4.86904i	−1.12745	−	0.277891i	−0.368875	−	0.929479i	$-0.620257\pi$
$307$	−19.7545	−	4.86904i	−1.12745	−	0.277891i	−0.758573	+	0.651588i	$0.774103\pi$
$308$	−4.17209	−	3.13512i	−0.237727	−	0.178640i
$309$	−8.76471	+	10.7348i	−0.498607	+	0.610683i
$310$	18.7578	+	19.5289i	1.06537	+	1.10917i
$311$	−17.0748	−	4.20857i	−0.968225	−	0.238646i	−0.276666	−	0.960966i	$-0.589230\pi$
$311$	−17.0748	−	4.20857i	−0.968225	−	0.238646i	−0.691559	+	0.722320i	$0.743076\pi$
$312$	1.31218	+	3.05668i	0.0742877	+	0.173050i
$313$	−19.2914	+	4.75489i	−1.09041	+	0.268762i	−0.743230	−	0.669036i	$-0.766707\pi$
$313$	−19.2914	+	4.75489i	−1.09041	+	0.268762i	−0.347181	+	0.937798i	$0.612861\pi$
$314$	−29.3993	−	18.5910i	−1.65910	−	1.04915i
$315$	−0.901665	−	1.56173i	−0.0508030	−	0.0879935i
$316$	4.73096	−	8.19427i	0.266138	−	0.460964i
$317$	12.7355	−	6.68409i	0.715295	−	0.375416i	−0.0674798	−	0.997721i	$-0.521496\pi$
$317$	12.7355	−	6.68409i	0.715295	−	0.375416i	0.782775	+	0.622305i	$0.213804\pi$
$318$	−11.3114	+	3.77629i	−0.634311	+	0.211764i
$319$	7.34645	−	12.7244i	0.411322	−	0.712431i
$320$	6.10056	−	5.40462i	0.341032	−	0.302128i
$321$	−4.55569	+	2.88084i	−0.254274	+	0.160793i
$322$	6.60448	−	2.81390i	0.368053	−	0.156813i
$323$	−0.234296	−	5.81400i	−0.0130366	−	0.323500i
$324$	0.181694	−	1.49639i	0.0100941	−	0.0831326i
$325$	−0.438445	−	0.164915i	−0.0243206	−	0.00914784i
$326$	−0.0141553	−	0.116580i	−0.000783991	−	0.00645674i
$327$	14.3821	−	2.33731i	0.795330	−	0.129254i
$328$	−1.27743	−	0.807796i	−0.0705341	−	0.0446030i
$329$	−1.27743	−	0.207602i	−0.0704268	−	0.0114455i
$330$	15.5047	+	8.13751i	0.853507	+	0.447955i
$331$	6.65403	−	4.20775i	0.365738	−	0.231279i	−0.338937	−	0.940809i	$-0.610067\pi$
$331$	6.65403	−	4.20775i	0.365738	−	0.231279i	0.704675	+	0.709530i	$0.251093\pi$
$332$	−7.61975	+	7.93300i	−0.418188	+	0.435380i
$333$	0.370002	+	3.04724i	0.0202760	+	0.166988i
$334$	2.52307	+	12.3588i	0.138056	+	0.676244i
$335$	−22.6645	−	1.82967i	−1.23830	−	0.0999656i
$336$	−2.45100	+	3.00193i	−0.133713	+	0.163769i
$337$	−20.0837			−1.09403			−0.547014	−	0.837124i	$-0.684235\pi$
$337$	−20.0837			−1.09403			−0.547014	+	0.837124i	$0.684235\pi$
$338$	−23.1351	−	7.58375i	−1.25838	−	0.412501i
$339$	−2.34401			−0.127309
$340$	−7.23522	+	8.86154i	−0.392385	+	0.480584i
$341$	27.6687	+	2.23365i	1.49834	+	0.120959i
$342$	−0.633820	−	3.10465i	−0.0342730	−	0.167880i
$343$	−1.31320	−	10.8151i	−0.0709059	−	0.583963i
$344$	−2.45380	+	2.55468i	−0.132300	+	0.137739i
$345$	−8.74953	+	5.53286i	−0.471059	+	0.297879i
$346$	34.6608	+	18.1914i	1.86338	+	0.977975i
$347$	−3.24833	−	0.527905i	−0.174379	−	0.0283394i	0.0725946	−	0.997362i	$-0.476872\pi$
$347$	−3.24833	−	0.527905i	−0.174379	−	0.0283394i	−0.246974	+	0.969022i	$0.579436\pi$
$348$	4.41821	+	2.79390i	0.236841	+	0.149769i
$349$	17.2923	−	2.81027i	0.925634	−	0.150430i	0.321133	−	0.947034i	$-0.395936\pi$
$349$	17.2923	−	2.81027i	0.925634	−	0.150430i	0.604501	+	0.796604i	$0.293372\pi$
$350$	−0.0239660	−	0.197377i	−0.00128103	−	0.0105503i
$351$	−2.39827	−	2.69227i	−0.128010	−	0.143703i
$352$	3.59358	−	29.5958i	0.191538	−	1.57746i
$353$	0.653153	+	16.2078i	0.0347638	+	0.862656i	0.918678	+	0.395007i	$0.129258\pi$
$353$	0.653153	+	16.2078i	0.0347638	+	0.862656i	−0.883914	+	0.467649i	$0.845101\pi$
$354$	6.71596	−	2.86140i	0.356949	−	0.152082i
$355$	−4.97218	+	3.14422i	−0.263896	+	0.166878i
$356$	−2.51801	+	2.23076i	−0.133454	+	0.118230i
$357$	1.40513	−	2.43375i	0.0743673	−	0.128808i
$358$	20.3715	−	6.80101i	1.07667	−	0.359445i
$359$	−22.2283	+	11.6663i	−1.17316	+	0.615723i	−0.934703	−	0.355429i	$-0.884335\pi$
$359$	−22.2283	+	11.6663i	−1.17316	+	0.615723i	−0.238460	+	0.971152i	$0.576642\pi$
$360$	1.01799	−	1.76321i	0.0536529	−	0.0929295i
$361$	8.06865	+	13.9753i	0.424666	+	0.735542i
$362$	31.3314	+	19.8128i	1.64674	+	1.04134i
$363$	6.74850	−	1.66336i	0.354204	−	0.0873035i
$364$	−0.724362	−	4.38173i	−0.0379669	−	0.229665i
$365$	−1.31446	−	0.323984i	−0.0688018	−	0.0169581i
$366$	19.9745	+	20.7957i	1.04408	+	1.08701i
$367$	5.74803	−	7.04005i	0.300045	−	0.367488i	−0.602474	−	0.798138i	$-0.705818\pi$
$367$	5.74803	−	7.04005i	0.300045	−	0.367488i	0.902519	+	0.430650i	$0.141716\pi$
$368$	17.7854	+	13.3648i	0.927127	+	0.696691i
$369$	1.59063	+	0.392054i	0.0828048	+	0.0204095i
$370$	3.52962	−	12.1857i	0.183496	−	0.633503i
$371$	−5.18641	+	0.418690i	−0.269265	+	0.0217373i
$372$	−1.19043	+	9.80404i	−0.0617207	+	0.508316i
$373$	16.0513	+	19.6593i	0.831104	+	1.01792i	0.999482	+	0.0321948i	$0.0102497\pi$
$373$	16.0513	+	19.6593i	0.831104	+	1.01792i	−0.168378	+	0.985723i	$0.553853\pi$
$374$	1.09877	+	27.2656i	0.0568159	+	1.40987i
$375$	3.14966	+	10.8739i	0.162648	+	0.561524i
$376$	−0.518132	−	1.36620i	−0.0267206	−	0.0704565i
$377$	12.0006	−	3.51149i	0.618062	−	0.180851i
$378$	0.542679	−	1.43093i	0.0279124	−	0.0735989i
$379$	−16.9635	−	1.36944i	−0.871358	−	0.0703433i	−0.363306	−	0.931670i	$-0.618352\pi$
$379$	−16.9635	−	1.36944i	−0.871358	−	0.0703433i	−0.508052	+	0.861327i	$0.669634\pi$
$380$	−1.12581	+	5.51457i	−0.0577527	+	0.282892i
$381$	−5.70830	+	19.7073i	−0.292445	+	1.00964i
$382$	3.68538	+	9.71756i	0.188561	+	0.497194i
$383$	1.32691	−	32.9270i	0.0678021	−	1.68249i	−0.505249	−	0.862973i	$-0.668599\pi$
$383$	1.32691	−	32.9270i	0.0678021	−	1.68249i	0.573051	−	0.819519i	$-0.305760\pi$
$384$	−7.06411	−	1.14803i	−0.360489	−	0.0585851i
$385$	5.71888	+	5.06648i	0.291461	+	0.258212i
$386$	−37.5672	+	12.5418i	−1.91212	+	0.638359i
$387$	1.64596	−	3.46878i	0.0836687	−	0.176328i
$388$	7.08299	−	14.9271i	0.359585	−	0.757808i
$389$	21.9974	−	11.5451i	1.11531	−	0.585361i	0.196677	−	0.980468i	$-0.436985\pi$
$389$	21.9974	−	11.5451i	1.11531	−	0.585361i	0.918635	+	0.395108i	$0.129293\pi$
$390$	4.75734	+	14.1217i	0.240897	+	0.715082i
$391$	−14.2846	−	7.49714i	−0.722403	−	0.379146i
$392$	4.67037	−	3.50956i	0.235889	−	0.177259i
$393$	3.00167	+	10.3630i	0.151414	+	0.522743i
$394$	−6.76976	+	0.546512i	−0.341056	+	0.0275329i
$395$	−7.86908	+	11.4003i	−0.395936	+	0.573613i
$396$	1.27745	+	6.25739i	0.0641945	+	0.314445i
$397$	27.3916	+	11.6705i	1.37474	+	0.585724i	0.947890	−	0.318597i	$-0.103212\pi$
$397$	27.3916	+	11.6705i	1.37474	+	0.585724i	0.426854	+	0.904321i	$0.359622\pi$
$398$	34.9762	−	8.62087i	1.75320	−	0.432125i
$399$	0.0556716	−	1.38148i	0.00278706	−	0.0691603i
$400$	0.492582	−	0.370151i	0.0246291	−	0.0185076i
$401$	9.25882	−	3.94482i	0.462364	−	0.196995i	−0.148207	−	0.988956i	$-0.547350\pi$
$401$	9.25882	−	3.94482i	0.462364	−	0.196995i	0.610571	+	0.791962i	$0.290940\pi$
$402$	−10.9617	−	15.8808i	−0.546721	−	0.792062i
$403$	15.7130	+	17.6392i	0.782720	+	0.878673i
$404$	3.74360	−	5.42354i	0.186251	−	0.269831i
$405$	−0.441422	+	2.16223i	−0.0219344	+	0.107442i
$406$	3.67645	+	3.82759i	0.182459	+	0.189960i
$407$	−5.57530	−	11.7497i	−0.276358	−	0.582411i
$408$	3.17282			0.157078
$409$	−8.20480	−	17.2912i	−0.405701	−	0.854997i	−0.998757	−	0.0498361i	$-0.984130\pi$
$409$	−8.20480	−	17.2912i	−0.405701	−	0.854997i	0.593056	−	0.805161i	$-0.297921\pi$
$410$	−5.41280	−	4.06745i	−0.267319	−	0.200877i
$411$	−7.42304	+	19.5729i	−0.366151	+	0.965462i
$412$	19.2183	+	8.18815i	0.946817	+	0.403401i
$413$	3.14402	−	0.510953i	0.154707	−	0.0251423i
$414$	−8.33311	−	2.78200i	−0.409550	−	0.136728i
$415$	12.0538	−	10.6787i	0.591699	−	0.524199i
$416$	19.6089	−	16.0994i	0.961404	−	0.789338i
$417$	6.57440	+	5.82441i	0.321950	+	0.285222i
$418$	6.71255	+	11.6265i	0.328322	+	0.568670i
$419$	1.74857	+	0.583757i	0.0854230	+	0.0285184i	0.359058	−	0.933315i	$-0.383098\pi$
$419$	1.74857	+	0.583757i	0.0854230	+	0.0285184i	−0.273635	+	0.961834i	$0.588226\pi$
$420$	−1.88303	+	1.96044i	−0.0918825	+	0.0956598i
$421$	−15.3502	−	22.2386i	−0.748122	−	1.08384i	−0.993435	−	0.114397i	$-0.963506\pi$
$421$	−15.3502	−	22.2386i	−0.748122	−	1.08384i	0.245314	−	0.969444i	$-0.421109\pi$
$422$	0.228303	+	0.279621i	0.0111136	+	0.0136117i
$423$	1.00164	+	1.22679i	0.0487015	+	0.0596485i
$424$	−3.33714	−	4.83468i	−0.162066	−	0.234793i
$425$	−0.309511	+	0.322236i	−0.0150135	+	0.0156307i
$426$	−4.73554	−	1.58096i	−0.229438	−	0.0765976i
$427$	6.29073	+	10.8959i	0.304430	+	0.527288i
$428$	6.08162	+	5.38785i	0.293966	+	0.260431i
$429$	13.2502	+	7.60192i	0.639724	+	0.367024i
$430$	−11.8776	+	10.5227i	−0.572791	+	0.507448i
$431$	−6.00898	−	2.00609i	−0.289442	−	0.0966300i	0.168239	−	0.985746i	$-0.446192\pi$
$431$	−6.00898	−	2.00609i	−0.289442	−	0.0966300i	−0.457682	+	0.889116i	$0.651320\pi$
$432$	4.68115	−	0.760762i	0.225222	−	0.0366022i
$433$	−28.0408	−	11.9471i	−1.34755	−	0.574139i	−0.406890	−	0.913477i	$-0.633387\pi$
$433$	−28.0408	−	11.9471i	−1.34755	−	0.574139i	−0.940665	+	0.339338i	$0.889797\pi$
$434$	−3.55553	+	9.37516i	−0.170671	+	0.450022i
$435$	−6.11822	−	4.59755i	−0.293346	−	0.220435i
$436$	−9.41564	−	19.8430i	−0.450927	−	0.950309i
$437$	−7.93690			−0.379673
$438$	−0.492518	−	1.03796i	−0.0235334	−	0.0495956i
$439$	−8.47723	−	8.82574i	−0.404596	−	0.421229i	0.487466	−	0.873142i	$-0.337921\pi$
$439$	−8.47723	−	8.82574i	−0.404596	−	0.421229i	−0.892062	+	0.451913i	$0.850742\pi$
$440$	−1.72543	+	8.45173i	−0.0822568	+	0.402920i
$441$	−3.59713	+	5.21134i	−0.171292	+	0.248159i
$442$	−15.3517	+	17.4239i	−0.730205	+	0.828771i
$443$	−8.14436	−	11.7991i	−0.386950	−	0.560594i	0.580305	−	0.814399i	$-0.302933\pi$
$443$	−8.14436	−	11.7991i	−0.386950	−	0.560594i	−0.967255	+	0.253805i	$0.918318\pi$
$444$	4.25681	−	1.81366i	0.202019	−	0.0860724i
$445$	3.93725	−	2.95865i	0.186643	−	0.140253i
$446$	−0.784768	+	19.4738i	−0.0371598	+	0.922112i
$447$	1.87511	−	0.462174i	0.0886897	−	0.0218601i
$448$	2.77644	+	1.18293i	0.131175	+	0.0558883i
$449$	0.422189	+	2.06802i	0.0199243	+	0.0975958i	0.988537	−	0.150980i	$-0.0482428\pi$
$449$	0.422189	+	2.06802i	0.0199243	+	0.0975958i	−0.968613	+	0.248575i	$0.920038\pi$
$450$	−0.138219	+	0.200244i	−0.00651569	+	0.00943960i
$451$	−6.91835	+	0.558507i	−0.325772	+	0.0262991i
$452$	0.983028	+	3.39381i	0.0462378	+	0.159631i
$453$	9.09298	−	6.83293i	0.427225	−	0.321039i
$454$	7.74649	+	4.06567i	0.363561	+	0.190811i
$455$	0.540852	+	6.47946i	0.0253555	+	0.303762i
$456$	1.38217	−	0.725419i	0.0647261	−	0.0339709i
$457$	−1.76153	+	3.71235i	−0.0824009	+	0.173656i	−0.940469	−	0.339880i	$-0.889614\pi$
$457$	−1.76153	+	3.71235i	−0.0824009	+	0.173656i	0.858068	+	0.513536i	$0.171665\pi$
$458$	−14.3622	+	30.2676i	−0.671100	+	1.41431i
$459$	−3.26207	+	1.08904i	−0.152260	+	0.0508320i
$460$	11.6802	+	10.3477i	0.544592	+	0.482466i
$461$	15.1901	+	2.46863i	0.707472	+	0.114975i	0.503492	−	0.864000i	$-0.332048\pi$
$461$	15.1901	+	2.46863i	0.707472	+	0.114975i	0.203980	+	0.978975i	$0.434612\pi$
$462$	−0.261080	+	6.47864i	−0.0121465	+	0.301414i
$463$	−8.95043	−	23.6003i	−0.415962	−	1.09680i	−0.965287	−	0.261192i	$-0.915884\pi$
$463$	−8.95043	−	23.6003i	−0.415962	−	1.09680i	0.549325	−	0.835609i	$-0.314885\pi$
$464$	−4.57581	+	15.7975i	−0.212427	+	0.733382i
$465$	2.89211	−	14.1665i	0.134118	−	0.656956i
$466$	41.2816	+	3.33260i	1.91234	+	0.154380i
$467$	−7.57797	+	19.9815i	−0.350666	+	0.924631i	0.637390	+	0.770541i	$0.280014\pi$
$467$	−7.57797	+	19.9815i	−0.350666	+	0.924631i	−0.988057	+	0.154090i	$0.950755\pi$
$468$	−2.89225	+	4.60144i	−0.133694	+	0.212702i
$469$	−2.98567	−	7.87255i	−0.137865	−	0.363521i
$470$	−1.82110	−	6.28716i	−0.0840010	−	0.290005i
$471$	0.747876	+	18.5584i	0.0344603	+	0.855124i
$472$	2.27441	+	2.78564i	0.104688	+	0.128220i
$473$	−1.96078	+	16.1485i	−0.0901570	+	0.742509i
$474$	−11.7176	+	0.945942i	−0.538207	+	0.0434486i
$475$	−0.0611576	+	0.211140i	−0.00280610	+	0.00968779i
$476$	−4.11302	−	1.01377i	−0.188520	−	0.0464660i
$477$	5.09047	+	3.82524i	0.233077	+	0.175146i
$478$	34.6985	−	42.4980i	1.58707	−	1.94381i
$479$	−21.4563	−	22.3384i	−0.980366	−	1.02067i	−0.999782	−	0.0208572i	$-0.993360\pi$
$479$	−21.4563	−	22.3384i	−0.980366	−	1.02067i	0.0194169	−	0.999811i	$-0.493819\pi$
$480$	−15.0776	−	3.71628i	−0.688193	−	0.169624i
$481$	3.47616	−	10.5076i	0.158499	−	0.479106i
$482$	−11.6643	+	2.87499i	−0.531294	+	0.130952i
$483$	−3.23984	−	2.04875i	−0.147418	−	0.0932214i
$484$	−5.23849	−	9.07333i	−0.238113	−	0.412424i
$485$	−12.0945	+	20.9483i	−0.549182	+	0.951211i
$486$	−1.65828	+	0.870333i	−0.0752212	+	0.0394791i
$487$	11.9052	−	3.97455i	0.539478	−	0.180104i	−0.0338550	−	0.999427i	$-0.510778\pi$
$487$	11.9052	−	3.97455i	0.539478	−	0.180104i	0.573333	+	0.819323i	$0.305650\pi$
$488$	−7.10232	+	12.3016i	−0.321507	+	0.556866i
$489$	−0.0469361	+	0.0415818i	−0.00212253	+	0.00188039i
$490$	22.1193	−	13.9874i	0.999249	−	0.631887i
$491$	−27.6987	+	11.8013i	−1.25003	+	0.532586i	−0.912634	−	0.408778i	$-0.865955\pi$
$491$	−27.6987	+	11.8013i	−1.25003	+	0.532586i	−0.337392	+	0.941364i	$0.609545\pi$
$492$	−0.0994340	−	2.46743i	−0.00448283	−	0.111240i
$493$	1.43757	−	11.8394i	0.0647447	−	0.533221i
$494$	−2.70391	+	11.1003i	−0.121655	+	0.499426i
$495$	−1.12700	−	9.28171i	−0.0506550	−	0.417182i
$496$	−30.6700	+	4.98437i	−1.37713	+	0.223805i
$497$	−1.84114	−	1.16426i	−0.0825862	−	0.0522244i
$498$	13.4893	+	2.19222i	0.604469	+	0.0982358i
$499$	−12.9612	−	6.80255i	−0.580222	−	0.304524i	0.148961	−	0.988843i	$-0.452407\pi$
$499$	−12.9612	−	6.80255i	−0.580222	−	0.304524i	−0.729183	+	0.684319i	$0.760099\pi$
$500$	14.4230	−	9.12054i	0.645015	−	0.407883i
$501$	4.66566	−	4.85746i	0.208446	−	0.217015i
$502$	5.90248	+	48.6113i	0.263441	+	2.16963i
$503$	4.53766	+	22.2269i	0.202324	+	0.991049i	0.946411	+	0.322966i	$0.104680\pi$
$503$	4.53766	+	22.2269i	0.202324	+	0.991049i	−0.744086	+	0.668083i	$0.767115\pi$
$504$	0.751454	+	0.0606637i	0.0334724	+	0.00270217i
$505$	−6.10184	+	7.47339i	−0.271528	+	0.332562i
$506$	37.2213			1.65469
$507$	3.68483	+	12.4668i	0.163649	+	0.553672i
$508$	30.9274			1.37218
$509$	9.76890	−	11.9647i	0.432999	−	0.530327i	−0.511306	−	0.859399i	$-0.670838\pi$
$509$	9.76890	−	11.9647i	0.432999	−	0.530327i	0.944305	+	0.329071i	$0.106736\pi$
$510$	14.1673	+	1.14370i	0.627339	+	0.0506441i
$511$	−0.100272	−	0.491163i	−0.00443575	−	0.0217278i
$512$	2.96776	+	24.4417i	0.131158	+	1.08018i
$513$	−1.17206	+	1.22024i	−0.0517476	+	0.0538750i
$514$	−15.1645	+	9.58947i	−0.668879	+	0.422974i
$515$	−27.0801	−	14.2127i	−1.19329	−	0.626287i
$516$	−5.71260	−	0.928388i	−0.251483	−	0.0408700i
$517$	−5.67129	−	3.58631i	−0.249423	−	0.157726i
$518$	4.63684	−	0.753560i	0.203731	−	0.0331095i
$519$	−2.51941	−	20.7492i	−0.110590	−	0.910790i
$520$	−6.03001	+	4.18652i	−0.264433	+	0.183591i
$521$	−1.35404	+	11.1515i	−0.0593216	+	0.488558i	0.932524	+	0.361109i	$0.117602\pi$
$521$	−1.35404	+	11.1515i	−0.0593216	+	0.488558i	−0.991845	+	0.127448i	$0.959321\pi$
$522$	−0.261516	−	6.48946i	−0.0114463	−	0.284036i
$523$	30.1327	−	12.8383i	1.31761	−	0.561381i	0.385217	−	0.922826i	$-0.374127\pi$
$523$	30.1327	−	12.8383i	1.31761	−	0.561381i	0.932393	+	0.361445i	$0.117717\pi$
$524$	13.7453	−	8.69201i	0.600467	−	0.379712i
$525$	−0.0794662	+	0.0704009i	−0.00346819	+	0.00307255i
$526$	−3.64863	+	6.31962i	−0.159088	+	0.275548i
$527$	21.3724	−	7.13517i	0.930999	−	0.310813i
$528$	−17.7917	+	9.33783i	−0.774286	+	0.406377i
$529$	0.497430	−	0.861574i	0.0216274	−	0.0374597i
$530$	−13.1583	−	22.7908i	−0.571560	−	0.989971i
$531$	−3.29453	−	2.08333i	−0.142970	−	0.0904090i
$532$	−2.02353	+	0.498756i	−0.0877313	+	0.0216238i
$533$	−4.58554	−	3.72320i	−0.198622	−	0.161270i
$534$	4.05809	+	1.00023i	0.175611	+	0.0432842i
$535$	−8.24002	−	8.57877i	−0.356247	−	0.370892i
$536$	6.01200	−	7.36336i	0.259679	−	0.318049i
$537$	−9.16781	−	6.88916i	−0.395620	−	0.297289i
$538$	14.5124	+	3.57698i	0.625672	+	0.154214i
$539$	7.46415	−	25.7692i	0.321504	−	1.10996i
$540$	3.31573	−	0.267673i	0.142686	−	0.0115188i
$541$	0.206212	−	1.69831i	0.00886576	−	0.0730161i	−0.987604	−	0.156963i	$-0.949830\pi$
$541$	0.206212	−	1.69831i	0.00886576	−	0.0730161i	0.996470	+	0.0839471i	$0.0267527\pi$
$542$	−29.6367	−	36.2984i	−1.27301	−	1.55915i
$543$	−0.797025	−	19.7780i	−0.0342036	−	0.848754i
$544$	−6.73276	−	23.2442i	−0.288665	−	0.996586i
$545$	11.4024	+	30.0656i	0.488424	+	1.28787i
$546$	−3.96906	+	3.83318i	−0.169860	+	0.164045i
$547$	−11.8038	+	31.1241i	−0.504695	+	1.33077i	0.404552	+	0.914515i	$0.367428\pi$
$547$	−11.8038	+	31.1241i	−0.504695	+	1.33077i	−0.909247	+	0.416257i	$0.863342\pi$
$548$	31.4520	+	2.53907i	1.34356	+	0.108464i
$549$	3.07971	−	15.0854i	0.131439	−	0.643830i
$550$	0.286808	−	0.990175i	0.0122295	−	0.0422212i
$551$	−2.08067	−	5.48628i	−0.0886395	−	0.233723i
$552$	0.174263	−	4.32430i	0.00741714	−	0.184054i
$553$	−5.06296	−	0.822810i	−0.215299	−	0.0349895i
$554$	15.4730	+	13.7079i	0.657385	+	0.582392i
$555$	−6.42550	+	2.14515i	−0.272747	+	0.0910564i
$556$	5.67578	−	11.9615i	0.240707	−	0.507279i
$557$	17.9625	−	37.8553i	0.761098	−	1.60398i	−0.0354266	−	0.999372i	$-0.511279\pi$
$557$	17.9625	−	37.8553i	0.761098	−	1.60398i	0.796524	−	0.604607i	$-0.206670\pi$
$558$	10.8647	−	5.70226i	0.459941	−	0.241396i
$559$	−10.6993	+	8.78442i	−0.452533	+	0.371541i
$560$	−7.57279	−	3.97450i	−0.320009	−	0.167953i
$561$	11.6483	−	8.75316i	0.491794	−	0.369559i
$562$	8.11523	+	28.0170i	0.342320	+	1.18183i
$563$	−14.5820	+	1.17718i	−0.614558	+	0.0496123i	−0.383827	−	0.923405i	$-0.625394\pi$
$563$	−14.5820	+	1.17718i	−0.614558	+	0.0496123i	−0.230732	+	0.973017i	$0.574112\pi$
$564$	1.35616	−	1.96473i	0.0571044	−	0.0827301i
$565$	−1.03470	−	5.06829i	−0.0435301	−	0.213224i
$566$	−53.1356	−	22.6390i	−2.23346	−	0.951588i
$567$	−0.793415	+	0.195559i	−0.0333203	+	0.00821271i
$568$	0.0990304	−	2.45741i	0.00415522	−	0.103111i
$569$	10.8893	−	8.18281i	0.456505	−	0.343041i	−0.347483	−	0.937686i	$-0.612964\pi$
$569$	10.8893	−	8.18281i	0.456505	−	0.343041i	0.803989	+	0.594645i	$0.202707\pi$
$570$	6.43318	−	2.74092i	0.269456	−	0.114805i
$571$	3.63815	+	5.27076i	0.152252	+	0.220575i	0.891686	−	0.452654i	$-0.149523\pi$
$571$	3.63815	+	5.27076i	0.152252	+	0.220575i	−0.739435	+	0.673228i	$0.764907\pi$
$572$	5.44970	−	22.3725i	0.227863	−	0.935441i
$573$	3.15242	−	4.56708i	0.131694	−	0.190792i
$574$	0.501487	−	2.45644i	0.0209316	−	0.102530i
$575$	0.422182	+	0.439538i	0.0176062	+	0.0183300i
$576$	−1.58325	−	3.33663i	−0.0659688	−	0.139026i
$577$	3.77065			0.156974			0.0784871	−	0.996915i	$-0.474991\pi$
$577$	3.77065			0.156974			0.0784871	+	0.996915i	$0.474991\pi$
$578$	−4.15310	−	8.75247i	−0.172746	−	0.364055i
$579$	16.9064	+	12.7043i	0.702605	+	0.527973i
$580$	−4.09076	+	10.7865i	−0.169860	+	0.447883i
$581$	5.48585	+	2.33730i	0.227591	+	0.0969676i
$582$	−20.2619	+	3.29287i	−0.839882	+	0.136494i
$583$	−25.5895	−	8.54304i	−1.05981	−	0.353817i
$584$	0.423632	−	0.375306i	0.0175300	−	0.0155303i
$585$	4.76265	−	6.37403i	0.196911	−	0.263534i
$586$	−32.7490	−	29.0131i	−1.35285	−	1.19852i
$587$	−0.523639	−	0.906969i	−0.0216129	−	0.0374346i	0.855017	−	0.518601i	$-0.173547\pi$
$587$	−0.523639	−	0.906969i	−0.0216129	−	0.0374346i	−0.876630	+	0.481166i	$0.840213\pi$
$588$	9.05386	+	3.02262i	0.373375	+	0.124651i
$589$	7.67910	−	7.99479i	0.316412	−	0.329420i
$590$	9.15158	+	13.2583i	0.376764	+	0.545837i
$591$	2.29359	+	2.80914i	0.0943457	+	0.115552i
$592$	9.20707	+	11.2766i	0.378408	+	0.463466i
$593$	15.8162	+	22.9137i	0.649493	+	0.940953i	0.999990	+	0.00438901i	$0.00139707\pi$
$593$	15.8162	+	22.9137i	0.649493	+	0.940953i	−0.350498	+	0.936564i	$0.613988\pi$
$594$	5.49654	−	5.72251i	0.225526	−	0.234797i
$595$	5.88258	+	1.96389i	0.241162	+	0.0805118i
$596$	−1.45555	−	2.52108i	−0.0596215	−	0.103267i
$597$	−14.3975	−	12.7551i	−0.589250	−	0.522030i
$598$	22.9042	+	21.8801i	0.936624	+	0.894745i
$599$	6.85406	−	6.07216i	0.280049	−	0.248102i	−0.511392	−	0.859348i	$-0.670870\pi$
$599$	6.85406	−	6.07216i	0.280049	−	0.248102i	0.791441	+	0.611246i	$0.209331\pi$
$600$	−0.113694	−	0.0379566i	−0.00464154	−	0.00154957i
$601$	−20.9104	+	3.39828i	−0.852954	+	0.138619i	−0.571142	−	0.820851i	$-0.693500\pi$
$601$	−20.9104	+	3.39828i	−0.852954	+	0.138619i	−0.281812	+	0.959470i	$0.590935\pi$
$602$	−5.40566	−	2.30314i	−0.220318	−	0.0938689i
$603$	−3.65371	+	9.63404i	−0.148791	+	0.392329i
$604$	−13.7065	−	10.2998i	−0.557711	−	0.419093i
$605$	6.57549	+	13.8575i	0.267332	+	0.563390i
$606$	−8.18768			−0.332602
$607$	6.50209	+	13.7029i	0.263912	+	0.556183i	0.991542	−	0.129787i	$-0.0414295\pi$
$607$	6.50209	+	13.7029i	0.263912	+	0.556183i	−0.727630	+	0.685970i	$0.759378\pi$
$608$	−8.24743	−	8.58649i	−0.334478	−	0.348228i
$609$	0.566843	−	2.77658i	0.0229696	−	0.112513i
$610$	−36.1477	+	52.3691i	−1.46358	+	2.12036i
$611$	−1.38168	−	5.54066i	−0.0558966	−	0.224151i
$612$	2.94482	+	4.26631i	0.119037	+	0.172455i
$613$	−15.5119	+	6.60900i	−0.626519	+	0.266935i	−0.681803	−	0.731536i	$-0.738804\pi$
$613$	−15.5119	+	6.60900i	−0.626519	+	0.266935i	0.0552839	+	0.998471i	$0.482394\pi$
$614$	30.4615	−	22.8903i	1.22932	−	0.923778i
$615$	−0.145573	+	3.61236i	−0.00587007	+	0.145664i
$616$	−3.10130	+	0.764403i	−0.124955	+	0.0307987i
$617$	1.08053	+	0.460369i	0.0435003	+	0.0185338i	0.413607	−	0.910455i	$-0.364269\pi$
$617$	1.08053	+	0.460369i	0.0435003	+	0.0185338i	−0.370107	+	0.928989i	$0.620679\pi$
$618$	−5.19149	−	25.4296i	−0.208832	−	1.02293i
$619$	−5.39105	+	7.81029i	−0.216685	+	0.313922i	−0.916220	−	0.400676i	$-0.868775\pi$
$619$	−5.39105	+	7.81029i	−0.216685	+	0.313922i	0.699535	+	0.714598i	$0.253391\pi$
$620$	−21.7240	+	1.75375i	−0.872458	+	0.0704321i
$621$	1.30511	+	4.50576i	0.0523722	+	0.180810i
$622$	26.3295	−	19.7853i	1.05572	−	0.793319i
$623$	1.61477	+	0.847498i	0.0646945	+	0.0339543i
$624$	−16.4374	−	4.71263i	−0.658021	−	0.188656i
$625$	−21.5463	+	11.3084i	−0.861850	+	0.452334i
$626$	15.9517	−	33.6175i	0.637558	−	1.34362i
$627$	3.07307	−	6.47636i	0.122727	−	0.258641i
$628$	26.5563	−	8.86580i	1.05971	−	0.353784i
$629$	−7.90172	−	7.00031i	−0.315062	−	0.279121i
$630$	3.33354	+	0.541753i	0.132811	+	0.0215839i
$631$	1.74411	−	43.2796i	0.0694319	−	1.72293i	−0.471498	−	0.881867i	$-0.656287\pi$
$631$	1.74411	−	43.2796i	0.0694319	−	1.72293i	0.540930	−	0.841068i	$-0.318072\pi$
$632$	−2.05357	−	5.41481i	−0.0816865	−	0.215390i
$633$	0.0536268	−	0.185141i	0.00213147	−	0.00735870i
$634$	−5.38797	+	26.3920i	−0.213984	+	1.04816i
$635$	−45.1315	−	3.64339i	−1.79099	−	0.144584i
$636$	3.40359	−	8.97452i	0.134961	−	0.355863i
$637$	19.7413	−	11.4695i	0.782177	−	0.454437i
$638$	9.75761	+	25.7287i	0.386308	+	1.01861i
$639$	0.741667	+	2.56053i	0.0293399	+	0.101293i
$640$	−0.635951	−	15.7810i	−0.0251382	−	0.623798i
$641$	25.3737	+	31.0772i	1.00220	+	1.22747i	0.973689	+	0.227881i	$0.0731798\pi$
$641$	25.3737	+	31.0772i	1.00220	+	1.22747i	0.0285132	+	0.999593i	$0.490923\pi$
$642$	1.21677	−	10.0210i	0.0480222	−	0.395499i
$643$	41.2152	−	3.32724i	1.62537	−	0.131213i	0.766094	−	0.642728i	$-0.222197\pi$
$643$	41.2152	−	3.32724i	1.62537	−	0.131213i	0.859274	+	0.511515i	$0.170915\pi$
$644$	−1.60759	+	5.55004i	−0.0633479	+	0.218702i
$645$	8.22686	+	2.02774i	0.323932	+	0.0798421i
$646$	8.71177	+	6.54647i	0.342760	+	0.257567i
$647$	30.4437	−	37.2868i	1.19687	−	1.46589i	0.347832	−	0.937557i	$-0.386918\pi$
$647$	30.4437	−	37.2868i	1.19687	−	1.46589i	0.849034	−	0.528338i	$-0.177185\pi$
$648$	−0.639097	−	0.665370i	−0.0251061	−	0.0261382i
$649$	16.0350	+	3.95228i	0.629430	+	0.155141i
$650$	0.758552	−	0.440711i	0.0297529	−	0.0172861i
$651$	5.19830	−	1.28127i	0.203738	−	0.0502168i
$652$	0.0798887	+	0.0505186i	0.00312868	+	0.00197846i
$653$	20.6107	+	35.6988i	0.806559	+	1.39700i	0.915233	+	0.402924i	$0.132006\pi$
$653$	20.6107	+	35.6988i	0.806559	+	1.39700i	−0.108674	+	0.994077i	$0.534661\pi$
$654$	−13.6441	+	23.6322i	−0.533525	+	0.924092i
$655$	−21.0821	+	11.0647i	−0.823745	+	0.432335i
$656$	7.36958	−	2.46033i	0.287734	−	0.0960597i
$657$	−0.306729	+	0.531270i	−0.0119666	+	0.0207268i
$658$	1.81420	−	1.60724i	0.0707250	−	0.0626569i
$659$	12.9166	−	8.16798i	0.503160	−	0.318179i	−0.258659	−	0.965969i	$-0.583281\pi$
$659$	12.9166	−	8.16798i	0.503160	−	0.318179i	0.761820	+	0.647789i	$0.224306\pi$
$660$	−12.9660	+	5.52429i	−0.504701	+	0.215033i
$661$	0.448181	+	11.1215i	0.0174322	+	0.432576i	0.984215	+	0.176977i	$0.0566318\pi$
$661$	0.448181	+	11.1215i	0.0174322	+	0.432576i	−0.966783	+	0.255599i	$0.917727\pi$
$662$	−1.77722	+	14.6367i	−0.0690735	+	0.568872i
$663$	12.3133	+	1.46107i	0.478209	+	0.0567432i
$664$	0.811491	+	6.68323i	0.0314920	+	0.259360i
$665$	3.01164	−	0.489439i	0.116786	−	0.0189796i
$666$	−4.85881	−	3.07253i	−0.188275	−	0.119058i
$667$	−16.0572	−	2.60956i	−0.621739	−	0.101042i
$668$	−8.98962	−	4.71811i	−0.347819	−	0.182549i
$669$	8.79562	−	5.56201i	0.340058	−	0.215040i
$670$	29.4991	−	30.7118i	1.13965	−	1.18650i
$671$	7.86287	+	64.7566i	0.303543	+	2.49990i
$672$	−1.15017	−	5.63391i	−0.0443688	−	0.217333i
$673$	−17.7141	−	1.43003i	−0.682827	−	0.0551235i	−0.265815	−	0.964024i	$-0.585641\pi$
$673$	−17.7141	−	1.43003i	−0.682827	−	0.0551235i	−0.417013	+	0.908901i	$0.636923\pi$
$674$	23.7880	−	29.1350i	0.916278	−	1.12224i
$675$	0.129920			0.00500064
$676$	16.5049	−	10.5634i	0.634805	−	0.406286i
$677$	32.5442			1.25078			0.625388	−	0.780314i	$-0.284941\pi$
$677$	32.5442			1.25078			0.625388	+	0.780314i	$0.284941\pi$
$678$	2.77635	−	3.40041i	0.106625	−	0.130592i
$679$	−8.92782	−	0.720728i	−0.342618	−	0.0276590i
$680$	1.40055	+	6.86035i	0.0537087	+	0.263083i
$681$	−0.563075	−	4.63734i	−0.0215771	−	0.177703i
$682$	−36.0123	+	37.4928i	−1.37898	+	1.43567i
$683$	0.237038	−	0.149894i	0.00907000	−	0.00573552i	−0.529923	−	0.848046i	$-0.677779\pi$
$683$	0.237038	−	0.149894i	0.00907000	−	0.00573552i	0.538993	+	0.842310i	$0.318805\pi$
$684$	2.25828	+	1.18524i	0.0863474	+	0.0453186i
$685$	−45.5978	−	7.41037i	−1.74220	−	0.283136i
$686$	17.2447	+	10.9049i	0.658406	+	0.416351i
$687$	17.6572	−	2.86958i	0.673665	−	0.109481i
$688$	−2.19485	−	18.0762i	−0.0836780	−	0.689151i
$689$	−10.7247	−	20.2995i	−0.408577	−	0.773350i
$690$	2.33690	−	19.2461i	0.0889643	−	0.732687i
$691$	1.16090	+	28.8074i	0.0441627	+	1.09588i	0.857628	+	0.514271i	$0.171937\pi$
$691$	1.16090	+	28.8074i	0.0441627	+	1.09588i	−0.813465	+	0.581614i	$0.802421\pi$
$692$	−28.9855	+	12.3495i	−1.10186	+	0.469459i
$693$	2.92617	−	1.85040i	0.111156	−	0.0702908i
$694$	4.61328	−	4.08701i	0.175118	−	0.155141i
$695$	−9.69161	+	16.7864i	−0.367624	+	0.636743i
$696$	3.03480	−	1.01316i	0.115034	−	0.0384039i
$697$	−4.98863	+	2.61823i	−0.188958	+	0.0991727i
$698$	−16.4049	+	28.4141i	−0.620935	+	1.07549i
$699$	−11.0572	−	19.1517i	−0.418223	−	0.724383i
$700$	0.135257	+	0.0855315i	0.00511224	+	0.00323279i
$701$	38.9619	−	9.60324i	1.47157	−	0.362709i	0.579636	−	0.814876i	$-0.303195\pi$
$701$	38.9619	−	9.60324i	1.47157	−	0.362709i	0.891934	+	0.452166i	$0.149349\pi$
$702$	6.74623	−	0.290280i	0.254620	−	0.0109559i
$703$	−5.04274	−	1.24292i	−0.190191	−	0.0468778i
$704$	10.8393	+	11.2849i	0.408522	+	0.425317i
$705$	−2.21045	+	2.70731i	−0.0832504	+	0.101963i
$706$	−24.2860	−	18.2497i	−0.914015	−	0.686838i
$707$	−3.46872	−	0.854963i	−0.130455	−	0.0321542i
$708$	−1.63473	+	5.64373i	−0.0614368	+	0.212104i
$709$	11.7194	−	0.946087i	0.440131	−	0.0355310i	0.141585	−	0.989926i	$-0.454780\pi$
$709$	11.7194	−	0.946087i	0.440131	−	0.0355310i	0.298546	+	0.954395i	$0.403498\pi$
$710$	1.32801	−	10.9372i	0.0498395	−	0.410465i
$711$	3.96991	+	4.86226i	0.148883	+	0.182349i
$712$	0.0829051	+	2.05727i	0.00310700	+	0.0770994i
$713$	−8.55082	−	29.5209i	−0.320231	−	1.10556i
$714$	1.86630	+	4.92103i	0.0698446	+	0.184165i
$715$	−10.5882	+	32.0055i	−0.395975	+	1.19694i
$716$	−6.12978	+	16.1629i	−0.229081	+	0.604036i
$717$	−29.2002	−	2.35728i	−1.09050	−	0.0880344i
$718$	9.40406	−	46.0641i	0.350957	−	1.71910i
$719$	−9.92419	+	34.2623i	−0.370110	+	1.27777i	0.532178	+	0.846633i	$0.321374\pi$
$719$	−9.92419	+	34.2623i	−0.370110	+	1.27777i	−0.902288	+	0.431135i	$0.858113\pi$
$720$	3.71130	+	9.78590i	0.138312	+	0.364699i
$721$	0.455994	−	11.3154i	0.0169821	−	0.421407i
$722$	−29.8305	−	4.84793i	−1.11018	−	0.180421i
$723$	4.80145	+	4.25371i	0.178568	+	0.158197i
$724$	−28.3015	+	9.44844i	−1.05182	+	0.351149i
$725$	−0.193149	+	0.407053i	−0.00717338	+	0.0151176i
$726$	−5.58022	+	11.7601i	−0.207101	+	0.436457i
$727$	8.05108	−	4.22553i	0.298598	−	0.156716i	−0.308770	−	0.951137i	$-0.599917\pi$
$727$	8.05108	−	4.22553i	0.298598	−	0.156716i	0.607368	+	0.794420i	$0.292225\pi$
$728$	−2.35774	−	1.35269i	−0.0873838	−	0.0501341i
$729$	0.885456	+	0.464723i	0.0327947	+	0.0172120i
$730$	2.02690	−	1.52311i	0.0750188	−	0.0563730i
$731$	3.67364	+	12.6829i	0.135874	+	0.469093i
$732$	−23.1332	+	1.86750i	−0.855027	+	0.0690249i
$733$	−21.8994	+	31.7268i	−0.808873	+	1.17185i	0.173484	+	0.984837i	$0.444498\pi$
$733$	−21.8994	+	31.7268i	−0.808873	+	1.17185i	−0.982357	+	0.187018i	$0.940118\pi$
$734$	3.40465	+	16.6771i	0.125668	+	0.615563i
$735$	−12.8560	−	5.47741i	−0.474199	−	0.202037i
$736$	−32.0498	+	7.89956i	−1.18137	+	0.291182i
$737$	1.75778	−	43.6189i	0.0647488	−	1.60672i
$738$	−2.45275	+	1.84312i	−0.0902871	+	0.0678464i
$739$	−2.61024	+	1.11212i	−0.0960191	+	0.0409099i	−0.439442	−	0.898271i	$-0.644824\pi$
$739$	−2.61024	+	1.11212i	−0.0960191	+	0.0409099i	0.343423	+	0.939181i	$0.388414\pi$
$740$	5.80059	+	8.40361i	0.213234	+	0.308923i
$741$	5.69808	−	2.17878i	0.209324	−	0.0800394i
$742$	5.53562	−	8.01973i	0.203219	−	0.294414i
$743$	1.81288	−	8.88009i	0.0665082	−	0.325779i	−0.932902	−	0.360132i	$-0.882732\pi$
$743$	1.81288	−	8.88009i	0.0665082	−	0.325779i	0.999410	+	0.0343526i	$0.0109369\pi$
$744$	4.18724	+	4.35938i	0.153512	+	0.159823i
$745$	1.82704	+	3.85040i	0.0669375	+	0.141068i
$746$	−47.5311			−1.74024
$747$	−3.12827	−	6.59269i	−0.114457	−	0.241214i
$748$	−17.5584	−	13.1943i	−0.642000	−	0.482432i
$749$	1.56189	−	4.11837i	0.0570703	−	0.150482i
$750$	−19.5051	−	8.31034i	−0.712225	−	0.303451i
$751$	−33.7242	+	5.48071i	−1.23061	+	0.199994i	−0.740735	−	0.671797i	$-0.765523\pi$
$751$	−33.7242	+	5.48071i	−1.23061	+	0.199994i	−0.489878	+	0.871791i	$0.662959\pi$
$752$	7.12455	+	2.37852i	0.259806	+	0.0867359i
$753$	19.5714	−	17.3388i	0.713222	−	0.631860i
$754$	−9.11997	+	21.5682i	−0.332130	+	0.785466i
$755$	18.7882	+	16.6449i	0.683772	+	0.605769i
$756$	0.615884	+	1.06674i	0.0223995	+	0.0387970i
$757$	8.78201	+	2.93187i	0.319188	+	0.106560i	0.471747	−	0.881734i	$-0.343623\pi$
$757$	8.78201	+	2.93187i	0.319188	+	0.106560i	−0.152560	+	0.988294i	$0.548752\pi$
$758$	22.0790	−	22.9866i	0.801944	−	0.834912i
$759$	−11.2901	−	16.3565i	−0.409805	−	0.593705i
$760$	2.17864	+	2.66835i	0.0790277	+	0.0967913i
$761$	18.5268	+	22.6912i	0.671597	+	0.822557i	0.992200	−	0.124657i	$-0.0397830\pi$
$761$	18.5268	+	22.6912i	0.671597	+	0.822557i	−0.320603	+	0.947214i	$0.603886\pi$
$762$	−21.8279	−	31.6231i	−0.790740	−	1.14559i
$763$	−8.24802	+	8.58710i	−0.298598	+	0.310874i
$764$	−7.93456	−	2.64894i	−0.287062	−	0.0958354i
$765$	−3.79470	−	6.57261i	−0.137198	−	0.237633i
$766$	46.1949	+	40.9251i	1.66909	+	1.47869i
$767$	7.54391	+	11.8581i	0.272395	+	0.428170i
$768$	15.5613	−	13.7861i	0.561519	−	0.497462i
$769$	−1.85389	−	0.618918i	−0.0668529	−	0.0223188i	0.283045	−	0.959107i	$-0.408655\pi$
$769$	−1.85389	−	0.618918i	−0.0668529	−	0.0223188i	−0.349898	+	0.936788i	$0.613784\pi$
$770$	−14.1235	+	2.29530i	−0.508977	+	0.0827168i
$771$	8.81377	+	3.75520i	0.317420	+	0.135240i
$772$	11.3039	−	29.8060i	0.406838	−	1.07274i
$773$	−41.0172	−	30.8224i	−1.47529	−	1.10861i	−0.969245	−	0.246096i	$-0.920852\pi$
$773$	−41.0172	−	30.8224i	−1.47529	−	1.10861i	−0.506041	−	0.862509i	$-0.668892\pi$
$774$	3.08255	+	6.49633i	0.110800	+	0.233506i
$775$	−0.851214			−0.0305765
$776$	−4.33512	−	9.13607i	−0.155622	−	0.327966i
$777$	−1.73761	−	1.80904i	−0.0623364	−	0.0648991i
$778$	−9.30639	+	45.5857i	−0.333650	+	1.63433i
$779$	−1.57457	+	2.28116i	−0.0564148	+	0.0817310i
$780$	−11.2261	−	4.22253i	−0.401958	−	0.151191i
$781$	−6.41594	−	9.29509i	−0.229580	−	0.332604i
$782$	27.7952	−	11.8424i	0.993956	−	0.423485i
$783$	−2.77241	+	2.08333i	−0.0990778	+	0.0744521i
$784$	−1.20923	+	30.0068i	−0.0431868	+	1.07167i
$785$	−39.7973	+	9.80915i	−1.42043	+	0.350103i
$786$	−18.5887	−	7.91989i	−0.663035	−	0.282493i
$787$	1.90263	+	9.31970i	0.0678215	+	0.332211i	0.999519	−	0.0310245i	$-0.00987700\pi$
$787$	1.90263	+	9.31970i	0.0678215	+	0.332211i	−0.931697	+	0.363236i	$0.881672\pi$
$788$	3.10536	−	4.49889i	0.110624	−	0.160266i
$789$	3.88381	−	0.313534i	0.138267	−	0.0111621i
$790$	−7.21775	−	24.9185i	−0.256796	−	0.886562i
$791$	1.53128	−	1.15068i	0.0544460	−	0.0409135i
$792$	3.46108	+	1.81651i	0.122984	+	0.0645470i
$793$	−33.2280	+	44.4703i	−1.17996	+	1.57919i
$794$	−49.3739	+	25.9134i	−1.75221	+	0.919632i
$795$	−6.02399	+	12.6953i	−0.213649	+	0.450256i
$796$	−12.4296	+	26.1948i	−0.440555	+	0.928450i
$797$	44.7148	−	14.9280i	1.58388	−	0.528776i	0.617647	−	0.786455i	$-0.288086\pi$
$797$	44.7148	−	14.9280i	1.58388	−	0.528776i	0.966231	+	0.257679i	$0.0829577\pi$
$798$	1.93814	+	1.71704i	0.0686094	+	0.0607826i
$799$	−5.37611	−	0.873703i	−0.190193	−	0.0309094i
$800$	−0.0368116	+	0.913471i	−0.00130149	+	0.0322961i
$801$	−0.791375	−	2.08668i	−0.0279618	−	0.0737293i
$802$	−5.24389	+	18.1040i	−0.185168	+	0.639274i
$803$	0.519887	−	2.54657i	0.0183464	−	0.0898666i
$804$	15.4811	+	1.24976i	0.545975	+	0.0440756i
$805$	2.99973	−	7.90963i	0.105726	−	0.278778i
$806$	−44.2000	+	1.90186i	−1.55688	+	0.0669901i
$807$	−2.83008	−	7.46230i	−0.0996235	−	0.262686i
$808$	−1.12217	−	3.87419i	−0.0394779	−	0.136294i
$809$	0.411688	+	10.2159i	0.0144742	+	0.359173i	0.990155	+	0.139976i	$0.0447026\pi$
$809$	0.411688	+	10.2159i	0.0144742	+	0.359173i	−0.975681	+	0.219197i	$0.929656\pi$
$810$	−2.61386	−	3.20140i	−0.0918417	−	0.112486i
$811$	5.09422	−	41.9547i	0.178882	−	1.47323i	−0.576045	−	0.817418i	$-0.695405\pi$
$811$	5.09422	−	41.9547i	0.178882	−	1.47323i	0.754927	−	0.655809i	$-0.227672\pi$
$812$	−4.25783	+	0.343727i	−0.149420	+	0.0120625i
$813$	−6.96147	+	24.0338i	−0.244149	+	0.842901i
$814$	23.6487	+	5.82888i	0.828886	+	0.204302i
$815$	−0.110628	−	0.0831315i	−0.00387513	−	0.00291197i
$816$	−10.3152	+	12.6338i	−0.361103	+	0.442270i
$817$	4.50010	+	4.68510i	0.157438	+	0.163911i
$818$	34.8022	+	8.57797i	1.21683	+	0.299922i
$819$	2.88836	+	0.581469i	0.100928	+	0.0203182i
$820$	5.29125	−	1.30418i	0.184778	−	0.0455438i
$821$	−28.7799	−	18.1993i	−1.00442	−	0.635160i	−0.0723326	−	0.997381i	$-0.523044\pi$
$821$	−28.7799	−	18.1993i	−1.00442	−	0.635160i	−0.932092	+	0.362221i	$0.882019\pi$
$822$	−19.6019	−	33.9515i	−0.683695	−	1.18419i
$823$	−24.1567	+	41.8406i	−0.842049	+	1.45847i	0.0461110	+	0.998936i	$0.485317\pi$
$823$	−24.1567	+	41.8406i	−0.842049	+	1.45847i	−0.888160	+	0.459535i	$0.848016\pi$
$824$	11.3211	−	5.94176i	0.394389	−	0.206991i
$825$	−0.522119	+	0.174309i	−0.0181778	+	0.00606865i
$826$	−2.98268	+	5.16616i	−0.103781	+	0.179754i
$827$	5.73052	−	5.07680i	0.199270	−	0.176538i	−0.557587	−	0.830119i	$-0.688273\pi$
$827$	5.73052	−	5.07680i	0.199270	−	0.176538i	0.756856	+	0.653581i	$0.226734\pi$
$828$	5.97638	−	3.77923i	0.207694	−	0.131337i
$829$	5.19706	−	2.21426i	0.180501	−	0.0769045i	−0.299825	−	0.953994i	$-0.596928\pi$
$829$	5.19706	−	2.21426i	0.180501	−	0.0769045i	0.480327	+	0.877090i	$0.340518\pi$
$830$	1.21438	+	30.1346i	0.0421518	+	1.04599i
$831$	1.33047	−	10.9574i	0.0461534	−	0.380108i
$832$	0.0362870	+	13.3160i	0.00125802	+	0.461649i
$833$	−2.62492	−	21.6182i	−0.0909481	−	0.749025i
$834$	−16.2363	+	2.63866i	−0.562219	+	0.0913694i
$835$	12.5625	+	7.94402i	0.434742	+	0.274914i
$836$	−10.6657	−	1.73334i	−0.368879	−	0.0599487i
$837$	−5.80134	−	3.04478i	−0.200524	−	0.105243i
$838$	−2.91792	+	1.84518i	−0.100798	+	0.0637407i
$839$	−5.44293	+	5.66669i	−0.187911	+	0.195636i	−0.808493	−	0.588505i	$-0.799717\pi$
$839$	−5.44293	+	5.66669i	−0.187911	+	0.195636i	0.620583	+	0.784141i	$0.286896\pi$
$840$	0.200540	+	1.65159i	0.00691928	+	0.0569854i
$841$	3.39513	+	16.6305i	0.117074	+	0.573464i
$842$	50.4424	+	4.07213i	1.73836	+	0.140335i
$843$	9.85028	−	12.0644i	0.339261	−	0.415520i
$844$	−0.290549			−0.0100011
$845$	−25.3296	+	13.4706i	−0.871364	+	0.463402i
$846$	−2.96607			−0.101975
$847$	−3.59206	+	4.39948i	−0.123425	+	0.151168i
$848$	30.1005	+	2.42996i	1.03365	+	0.0834453i
$849$	6.16883	+	30.2169i	0.211714	+	1.03704i
$850$	−0.100862	−	0.830672i	−0.00345953	−	0.0284918i
$851$	−9.97487	+	10.3849i	−0.341934	+	0.355991i
$852$	3.39626	−	2.14766i	0.116354	−	0.0735777i
$853$	−23.3665	−	12.2637i	−0.800055	−	0.419901i	0.0145667	−	0.999894i	$-0.495363\pi$
$853$	−23.3665	−	12.2637i	−0.800055	−	0.419901i	−0.814622	+	0.579993i	$0.803055\pi$
$854$	−23.2574	−	3.77970i	−0.795853	−	0.129339i
$855$	−3.15581	−	1.99561i	−0.107926	−	0.0682486i
$856$	4.90846	−	0.797702i	0.167768	−	0.0272649i
$857$	−5.50174	−	45.3109i	−0.187936	−	1.54779i	−0.715705	−	0.698402i	$-0.753895\pi$
$857$	−5.50174	−	45.3109i	−0.187936	−	1.54779i	0.527769	−	0.849388i	$-0.323028\pi$
$858$	−26.7220	+	10.2177i	−0.912275	+	0.348827i
$859$	−0.233752	+	1.92512i	−0.00797551	+	0.0656842i	−0.996153	−	0.0876286i	$-0.972071\pi$
$859$	−0.233752	+	1.92512i	−0.00797551	+	0.0656842i	0.988178	+	0.153313i	$0.0489942\pi$
$860$	−0.514281	−	12.7618i	−0.0175368	−	0.435172i
$861$	−1.23157	+	0.524725i	−0.0419719	+	0.0178826i
$862$	10.0275	−	6.34100i	0.341538	−	0.215975i
$863$	4.09457	−	3.62747i	0.139381	−	0.123480i	−0.590552	−	0.807000i	$-0.701090\pi$
$863$	4.09457	−	3.62747i	0.139381	−	0.123480i	0.729933	+	0.683519i	$0.239551\pi$
$864$	−3.51835	+	6.09397i	−0.119697	+	0.207321i
$865$	43.7524	−	14.6067i	1.48763	−	0.496643i
$866$	50.5441	−	26.5276i	1.71756	−	0.901444i
$867$	−2.58646	+	4.47987i	−0.0878406	+	0.152144i
$868$	−4.03515	−	6.98909i	−0.136962	−	0.237225i
$869$	−22.4776	−	14.2140i	−0.762501	−	0.482176i
$870$	13.9163	−	3.43005i	0.471805	−	0.116290i
$871$	26.7226	−	25.8078i	0.905460	−	0.874463i
$872$	−13.0521	−	3.21706i	−0.442001	−	0.108943i
$873$	7.59293	+	7.90508i	0.256982	+	0.267546i
$874$	9.40080	−	11.5139i	0.317987	−	0.389463i
$875$	−7.39559	−	5.55743i	−0.250017	−	0.187875i
$876$	0.897842	+	0.221298i	0.0303353	+	0.00747697i
$877$	9.59304	−	33.1190i	0.323934	−	1.11835i	−0.619006	−	0.785387i	$-0.712464\pi$
$877$	9.59304	−	33.1190i	0.323934	−	1.11835i	0.942940	−	0.332964i	$-0.108049\pi$
$878$	22.8441	−	1.84417i	0.770952	−	0.0622377i
$879$	−2.81597	+	23.1916i	−0.0949803	+	0.782233i
$880$	−28.0442	−	34.3479i	−0.945369	−	1.15787i
$881$	1.46631	+	36.3860i	0.0494011	+	1.22588i	0.813805	+	0.581138i	$0.197392\pi$
$881$	1.46631	+	36.3860i	0.0494011	+	1.22588i	−0.764404	+	0.644738i	$0.776966\pi$
$882$	−3.29939	−	11.3908i	−0.111096	−	0.383549i
$883$	−2.17699	−	5.74026i	−0.0732616	−	0.193175i	0.893383	−	0.449295i	$-0.148325\pi$
$883$	−2.17699	−	5.74026i	−0.0732616	−	0.193175i	−0.966645	+	0.256120i	$0.917556\pi$
$884$	−3.04851	−	18.4407i	−0.102532	−	0.620228i
$885$	3.05036	−	8.04315i	0.102537	−	0.270367i
$886$	26.7633	+	2.16056i	0.899131	+	0.0725854i
$887$	8.44960	−	41.3889i	0.283710	−	1.38970i	−0.548921	−	0.835874i	$-0.684961\pi$
$887$	8.44960	−	41.3889i	0.283710	−	1.38970i	0.832631	−	0.553829i	$-0.186834\pi$
$888$	0.787908	−	2.72017i	0.0264404	−	0.0912830i
$889$	−5.94530	−	15.6765i	−0.199399	−	0.525772i
$890$	−0.371394	+	9.21604i	−0.0124491	+	0.308922i
$891$	−4.18193	−	0.679630i	−0.140100	−	0.0227685i
$892$	−11.7417	−	10.4023i	−0.393142	−	0.348293i
$893$	−2.54175	+	0.848560i	−0.0850563	+	0.0283960i
$894$	−1.55050	+	3.26760i	−0.0518564	+	0.109285i
$895$	10.8491	−	22.8639i	0.362644	−	0.764256i
$896$	5.17836	−	2.71781i	0.172997	−	0.0907957i
$897$	2.66761	−	16.7018i	0.0890691	−	0.557657i
$898$	−3.50009	−	1.83699i	−0.116800	−	0.0613011i
$899$	18.1643	−	13.6496i	0.605813	−	0.455239i
$900$	−0.0544858	−	0.188107i	−0.00181619	−	0.00627023i
$901$	−21.8272	+	1.76208i	−0.727171	+	0.0587033i
$902$	7.38418	−	10.6978i	0.245866	−	0.356199i
$903$	0.627575	+	3.07406i	0.0208844	+	0.102298i
$904$	1.98950	+	0.847647i	0.0661698	+	0.0281923i
$905$	42.4127	−	10.4538i	1.40984	−	0.347495i
$906$	−0.857724	+	21.2842i	−0.0284960	+	0.707120i
$907$	18.3158	−	13.7634i	0.608166	−	0.457007i	−0.251504	−	0.967856i	$-0.580925\pi$
$907$	18.3158	−	13.7634i	0.608166	−	0.457007i	0.859670	+	0.510849i	$0.170669\pi$
$908$	−6.47808	+	2.76005i	−0.214983	+	0.0915956i
$909$	2.48352	+	3.59800i	0.0823731	+	0.119338i
$910$	−10.0402	−	6.88995i	−0.332830	−	0.228400i
$911$	−11.5523	+	16.7363i	−0.382743	+	0.554499i	−0.966249	−	0.257610i	$-0.917065\pi$
$911$	−11.5523	+	16.7363i	−0.382743	+	0.554499i	0.583506	+	0.812109i	$0.301681\pi$
$912$	−1.60505	+	7.86205i	−0.0531485	+	0.260338i
$913$	21.4169	+	22.2974i	0.708796	+	0.737935i
$914$	−3.29899	−	6.95248i	−0.109121	−	0.229968i
$915$	33.9776			1.12326
$916$	−11.5598	−	24.3618i	−0.381947	−	0.804936i
$917$	−7.04812	−	5.29632i	−0.232749	−	0.174900i
$918$	2.28389	−	6.02212i	0.0753795	−	0.198760i
$919$	39.4800	+	16.8209i	1.30233	+	0.554869i	0.928052	−	0.372449i	$-0.121482\pi$
$919$	39.4800	+	16.8209i	1.30233	+	0.554869i	0.374273	+	0.927319i	$0.377892\pi$
$920$	9.42704	−	1.53204i	0.310800	−	0.0505100i
$921$	−19.2986	−	6.44283i	−0.635911	−	0.212298i
$922$	−21.5730	+	19.1120i	−0.710467	+	0.629419i
$923$	1.51595	−	9.49131i	0.0498982	−	0.312410i
$924$	−3.90629	−	3.46067i	−0.128508	−	0.113848i
$925$	0.199403	+	0.345376i	0.00655634	+	0.0113559i
$926$	44.8378	+	14.9691i	1.47346	+	0.491914i
$927$	−9.60009	+	9.99475i	−0.315308	+	0.328271i
$928$	−13.8624	−	20.0831i	−0.455054	−	0.659260i
$929$	18.2458	+	22.3471i	0.598627	+	0.733185i	0.981679	−	0.190542i	$-0.0610245\pi$
$929$	18.2458	+	22.3471i	0.598627	+	0.733185i	−0.383052	+	0.923727i	$0.625127\pi$
$930$	17.1255	+	20.9749i	0.561568	+	0.687796i
$931$	−6.08618	−	8.81735i	−0.199466	−	0.288977i
$932$	−23.0918	+	24.0412i	−0.756398	+	0.787494i
$933$	−16.6808	−	5.56888i	−0.546106	−	0.182317i
$934$	−20.0110	−	34.6601i	−0.654780	−	1.13411i
$935$	24.0682	+	21.3225i	0.787113	+	0.697321i
$936$	1.06197	+	3.15235i	0.0347115	+	0.103038i
$937$	22.8529	−	20.2459i	0.746571	−	0.661404i	−0.201491	−	0.979490i	$-0.564579\pi$
$937$	22.8529	−	20.2459i	0.746571	−	0.661404i	0.948062	+	0.318086i	$0.103040\pi$
$938$	14.9569	+	4.99335i	0.488360	+	0.163039i
$939$	−19.6114	+	3.18716i	−0.639994	+	0.104009i
$940$	4.84683	+	2.06504i	0.158086	+	0.0673542i
$941$	6.52499	−	17.2050i	0.212709	−	0.560867i	−0.785617	−	0.618713i	$-0.787654\pi$
$941$	6.52499	−	17.2050i	0.212709	−	0.560867i	0.998325	+	0.0578466i	$0.0184234\pi$
$942$	−27.8081	−	20.8964i	−0.906035	−	0.680841i
$943$	3.29445	+	6.94291i	0.107282	+	0.226092i
$944$	−18.4864			−0.601681
$945$	−0.773074	−	1.62922i	−0.0251481	−	0.0529985i
$946$	−21.1039	−	21.9715i	−0.686146	−	0.714354i
$947$	−9.60596	+	47.0531i	−0.312152	+	1.52902i	0.456716	+	0.889612i	$0.349025\pi$
$947$	−9.60596	+	47.0531i	−0.312152	+	1.52902i	−0.768868	+	0.639408i	$0.779180\pi$
$948$	5.37499	−	7.78702i	0.174572	−	0.252911i
$949$	1.81689	−	1.26143i	0.0589788	−	0.0409478i
$950$	−0.233859	−	0.338804i	−0.00758740	−	0.0109923i
$951$	13.2320	−	5.63764i	0.429078	−	0.182813i
$952$	−2.07271	+	1.55754i	−0.0671771	+	0.0504803i
$953$	−2.19246	+	54.4054i	−0.0710208	+	1.76236i	0.435550	+	0.900164i	$0.356554\pi$
$953$	−2.19246	+	54.4054i	−0.0710208	+	1.76236i	−0.506571	+	0.862198i	$0.669087\pi$
$954$	−11.5786	+	2.85386i	−0.374870	+	0.0923972i
$955$	11.2666	+	4.80025i	0.364579	+	0.155332i
$956$	8.83292	+	43.2665i	0.285677	+	1.39934i
$957$	8.34652	−	12.0920i	0.269805	−	0.390880i
$958$	57.8197	−	4.66769i	1.86807	−	0.150806i
$959$	−4.75914	−	16.4304i	−0.153681	−	0.530567i
$960$	6.51567	−	4.89621i	0.210292	−	0.158024i
$961$	10.5601	+	5.54239i	0.340650	+	0.178787i
$962$	11.1259	+	17.4885i	0.358712	+	0.563850i
$963$	−4.77273	+	2.50492i	−0.153799	+	0.0807199i
$964$	4.14516	−	8.73575i	0.133507	−	0.281359i
$965$	−20.0068	+	42.1634i	−0.644041	+	1.35729i
$966$	6.80948	−	2.27334i	0.219092	−	0.0731435i
$967$	−28.4219	−	25.1796i	−0.913988	−	0.809723i	0.0681906	−	0.997672i	$-0.478277\pi$
$967$	−28.4219	−	25.1796i	−0.913988	−	0.809723i	−0.982179	+	0.187950i	$0.939816\pi$
$968$	−6.32936	−	1.02862i	−0.203433	−	0.0330611i
$969$	0.234296	−	5.81400i	0.00752668	−	0.186773i
$970$	−16.0640	−	42.3572i	−0.515783	−	1.36001i
$971$	10.0187	−	34.5885i	0.321514	−	1.11000i	−0.623189	−	0.782071i	$-0.714163\pi$
$971$	10.0187	−	34.5885i	0.321514	−	1.11000i	0.944704	−	0.327925i	$-0.106349\pi$
$972$	0.301514	−	1.47691i	0.00967107	−	0.0473720i
$973$	−7.15409	−	0.577538i	−0.229350	−	0.0185150i
$974$	−8.33528	+	21.9783i	−0.267079	+	0.704231i
$975$	−0.423753	−	0.199660i	−0.0135710	−	0.00639425i
$976$	−25.8930	−	68.2743i	−0.828815	−	2.18541i
$977$	1.56736	+	5.41116i	0.0501443	+	0.173118i	0.981682	−	0.190526i	$-0.0610194\pi$
$977$	1.56736	+	5.41116i	0.0501443	+	0.173118i	−0.931538	+	0.363645i	$0.881532\pi$
$978$	−0.00472866	−	0.117341i	−0.000151206	−	0.00375214i
$979$	5.97996	+	7.32412i	0.191120	+	0.234080i
$980$	−2.53903	+	20.9108i	−0.0811062	+	0.667970i
$981$	14.5235	−	1.17246i	0.463700	−	0.0374337i
$982$	15.6876	−	54.1600i	0.500612	−	1.72831i
$983$	27.4134	+	6.75680i	0.874353	+	0.215509i	0.650861	−	0.759197i	$-0.274408\pi$
$983$	27.4134	+	6.75680i	0.874353	+	0.215509i	0.223492	+	0.974706i	$0.428254\pi$
$984$	−1.20828	−	0.907966i	−0.0385187	−	0.0289449i
$985$	−5.06155	+	6.19928i	−0.161274	+	0.197525i
$986$	15.4725	+	16.1086i	0.492745	+	0.513002i
$987$	−1.25658	−	0.309719i	−0.0399974	−	0.00985846i
$988$	−5.54422	−	7.33631i	−0.176385	−	0.233399i
$989$	17.4875	−	4.31028i	0.556071	−	0.137059i
$990$	14.7997	+	9.35873i	0.470364	+	0.297440i
$991$	9.96018	+	17.2515i	0.316395	+	0.548013i	0.979733	−	0.200307i	$-0.0641940\pi$
$991$	9.96018	+	17.2515i	0.316395	+	0.548013i	−0.663338	+	0.748320i	$0.730861\pi$
$992$	23.0516	−	39.9265i	0.731889	−	1.26767i
$993$	6.97103	−	3.65868i	0.221219	−	0.116105i
$994$	3.86969	−	1.29189i	0.122739	−	0.0409764i
$995$	21.2240	−	36.7610i	0.672845	−	1.16540i
$996$	−8.23338	+	7.29414i	−0.260885	+	0.231124i
$997$	−52.5571	+	33.2351i	−1.66450	+	1.05257i	−0.739084	+	0.673613i	$0.764741\pi$
$997$	−52.5571	+	33.2351i	−1.66450	+	1.05257i	−0.925416	+	0.378953i	$0.876284\pi$
$998$	25.2201	−	10.7453i	0.798328	−	0.340136i
$999$	0.123601	+	3.06713i	0.00391057	+	0.0970397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.a.55.4	✓	360
169.126	even	39	inner	507.2.q.a.295.4	yes	360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.a.55.4	✓	360	1.1	even	1	trivial
507.2.q.a.295.4	yes	360	169.126	even	39	inner

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18444 + 1.45068i) q^{2} +(0.996757 + 0.0804666i) q^{3} +(-0.301514 - 1.47691i) q^{4} +(0.266003 + 2.19074i) q^{5} +(-1.29733 + 1.35067i) q^{6} +(-0.690655 + 0.436744i) q^{7} +(-0.816908 - 0.428746i) q^{8} +(0.987050 + 0.160411i) q^{9} +(-3.49312 - 2.20892i) q^{10} +(-4.18193 + 0.679630i) q^{11} +(-0.181694 - 1.49639i) q^{12} +(-2.97288 - 2.04009i) q^{13} +(0.184466 - 1.51922i) q^{14} +(0.0888599 + 2.20504i) q^{15} +(4.36307 - 1.85893i) q^{16} +(-2.90665 + 1.83806i) q^{17} +(-1.40181 + 1.24190i) q^{18} +(-0.845977 + 1.46528i) q^{19} +(3.15532 - 1.05340i) q^{20} +(-0.723559 + 0.379753i) q^{21} +(3.96734 - 6.87163i) q^{22} +(2.34548 + 4.06249i) q^{23} +(-0.779759 - 0.493090i) q^{24} +(0.126145 - 0.0310920i) q^{25} +(6.48073 - 1.89632i) q^{26} +(0.970942 + 0.239316i) q^{27} +(0.853275 + 0.888354i) q^{28} +(-2.19327 + 2.68627i) q^{29} +(-3.30405 - 2.48283i) q^{30} +(-6.36143 - 1.56795i) q^{31} +(-1.95774 + 6.75889i) q^{32} +(-4.22306 + 0.340921i) q^{33} +(0.776335 - 6.39370i) q^{34} +(-1.14051 - 1.39687i) q^{35} +(-0.0606959 - 1.50615i) q^{36} +(0.854022 + 2.94843i) q^{37} +(-1.12363 - 2.96278i) q^{38} +(-2.79908 - 2.27270i) q^{39} +(0.721970 - 1.90368i) q^{40} +(1.63292 + 0.131823i) q^{41} +(0.306115 - 1.49945i) q^{42} +(1.06821 - 3.68789i) q^{43} +(2.26467 + 5.97144i) q^{44} +(-0.0888599 + 2.20504i) q^{45} +(-8.67147 - 1.40925i) q^{46} +(1.18546 + 1.05023i) q^{47} +(4.49850 - 1.50182i) q^{48} +(-2.71459 + 5.72087i) q^{49} +(-0.104307 + 0.219823i) q^{50} +(-3.04513 + 1.59821i) q^{51} +(-2.11668 + 5.00580i) q^{52} +(5.63816 + 2.95913i) q^{53} +(-1.49720 + 1.12507i) q^{54} +(-2.60130 - 8.98073i) q^{55} +(0.751454 - 0.0606637i) q^{56} +(-0.961140 + 1.39245i) q^{57} +(-1.29911 - 6.36347i) q^{58} +(-3.58605 - 1.52788i) q^{59} +(3.22985 - 0.796088i) q^{60} +(0.619958 - 15.3841i) q^{61} +(9.80934 - 7.37124i) q^{62} +(-0.751770 + 0.320299i) q^{63} +(-2.09798 - 3.03945i) q^{64} +(3.67851 - 7.05547i) q^{65} +(4.50741 - 6.53011i) q^{66} +(-2.06099 + 10.0954i) q^{67} +(3.59105 + 3.73868i) q^{68} +(2.01098 + 4.23805i) q^{69} +3.37727 q^{70} +(1.14280 + 2.40840i) q^{71} +(-0.737554 - 0.554236i) q^{72} +(-0.217535 + 0.573593i) q^{73} +(-5.28876 - 2.25333i) q^{74} +(0.128238 - 0.0208407i) q^{75} +(2.41916 + 0.807634i) q^{76} +(2.59145 - 2.29582i) q^{77} +(6.61231 - 1.36869i) q^{78} +(4.69846 + 4.16248i) q^{79} +(5.23301 + 9.06384i) q^{80} +(0.948536 + 0.316668i) q^{81} +(-2.12533 + 2.21271i) q^{82} +(-4.14530 - 6.00551i) q^{83} +(0.779026 + 0.954133i) q^{84} +(-4.79988 - 5.87878i) q^{85} +(4.08472 + 5.91773i) q^{86} +(-2.40232 + 2.50108i) q^{87} +(3.70764 + 1.23779i) q^{88} +(-1.11585 - 1.93272i) q^{89} +(-3.09355 - 2.74065i) q^{90} +(2.94423 + 0.110613i) q^{91} +(5.29276 - 4.68897i) q^{92} +(-6.21463 - 2.07475i) q^{93} +(-2.92766 + 0.475791i) q^{94} +(-3.43506 - 1.46354i) q^{95} +(-2.49525 + 6.57944i) q^{96} +(8.76267 + 6.58472i) q^{97} +(-5.08388 - 10.7140i) q^{98} -4.23680 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 360 q + q^{2} - 15 q^{3} + 15 q^{4} + 2 q^{5} - q^{6} + 2 q^{7} + 6 q^{8} + 15 q^{9} - q^{10} - 2 q^{11} + 30 q^{12} - 19 q^{13} + q^{15} + 15 q^{16} - 7 q^{17} - 2 q^{18} - 6 q^{19} + q^{20} + 4 q^{21}+ \cdots + 30 q^{99}+O(q^{100}) \) 360 * q + q^2 - 15 * q^3 + 15 * q^4 + 2 * q^5 - q^6 + 2 * q^7 + 6 * q^8 + 15 * q^9 - q^10 - 2 * q^11 + 30 * q^12 - 19 * q^13 + q^15 + 15 * q^16 - 7 * q^17 - 2 * q^18 - 6 * q^19 + q^20 + 4 * q^21 + 22 * q^22 + 46 * q^23 + 3 * q^24 + 28 * q^25 + 34 * q^26 + 30 * q^27 - 2 * q^28 + 36 * q^29 + q^30 - 34 * q^31 - 190 * q^32 + 15 * q^33 - 51 * q^34 - 80 * q^35 + 15 * q^36 + q^37 - 53 * q^38 + 5 * q^39 - 45 * q^40 + 9 * q^41 + 130 * q^42 + 78 * q^43 + 35 * q^44 - q^45 - 318 * q^46 - 12 * q^47 - 15 * q^48 - 71 * q^49 + 48 * q^50 - 14 * q^51 - 63 * q^52 - 26 * q^53 - q^54 - 61 * q^55 - 4 * q^56 - 38 * q^57 - 27 * q^58 + 208 * q^59 - 180 * q^60 - 3 * q^61 - 61 * q^62 + 2 * q^63 + 140 * q^64 + 45 * q^65 - 60 * q^66 - 80 * q^67 - 140 * q^68 + 6 * q^69 - 100 * q^70 + 84 * q^71 - 3 * q^72 + 134 * q^73 - 151 * q^74 - 12 * q^75 + 32 * q^76 + 82 * q^77 - 63 * q^78 + 4 * q^79 - 155 * q^80 + 15 * q^81 - 56 * q^82 + 106 * q^83 + 2 * q^84 - 19 * q^85 + q^86 - 49 * q^87 + 8 * q^88 - 14 * q^89 + 2 * q^90 - 368 * q^91 + 36 * q^92 - 4 * q^93 - 59 * q^94 + 104 * q^95 + 75 * q^96 - 28 * q^97 + 101 * q^98 + 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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