LMFDB - Embedded newform 80.2.l.a.61.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [80,2,Mod(21,80)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("80.21"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(80, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.l (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			61.1
Root			$1.26868 + 0.624862i$ of defining polynomial
Character	$\chi$	$=$	80.61
Dual form			80.2.l.a.21.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37735 - 0.320793i) q^{2} +(-0.720673 - 0.720673i) q^{3} +(1.79418 + 0.883688i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.761432 + 1.22381i) q^{6} -4.02840i q^{7} +(-2.18774 - 1.79271i) q^{8} -1.96126i q^{9} +(-1.20077 + 0.747098i) q^{10} +(-0.646837 + 0.646837i) q^{11} +(-0.656170 - 1.92987i) q^{12} +(4.91492 + 4.91492i) q^{13} +(-1.29228 + 5.54851i) q^{14} -1.01919 q^{15} +(2.43819 + 3.17100i) q^{16} -2.70862 q^{17} +(-0.629159 + 2.70134i) q^{18} +(-0.438397 - 0.438397i) q^{19} +(1.89354 - 0.643818i) q^{20} +(-2.90316 + 2.90316i) q^{21} +(1.09842 - 0.683420i) q^{22} +3.60080i q^{23} +(0.284686 + 2.86860i) q^{24} -1.00000i q^{25} +(-5.19289 - 8.34623i) q^{26} +(-3.57545 + 3.57545i) q^{27} +(3.55985 - 7.22769i) q^{28} +(2.00921 + 2.00921i) q^{29} +(1.40377 + 0.326948i) q^{30} +4.30994 q^{31} +(-2.34101 - 5.14973i) q^{32} +0.932316 q^{33} +(3.73072 + 0.868908i) q^{34} +(-2.84851 - 2.84851i) q^{35} +(1.73314 - 3.51886i) q^{36} +(-0.743961 + 0.743961i) q^{37} +(0.463191 + 0.744461i) q^{38} -7.08410i q^{39} +(-2.81460 + 0.279327i) q^{40} -0.603979i q^{41} +(4.92998 - 3.06735i) q^{42} +(-5.03010 + 5.03010i) q^{43} +(-1.73215 + 0.588942i) q^{44} +(-1.38682 - 1.38682i) q^{45} +(1.15511 - 4.95956i) q^{46} +10.8177 q^{47} +(0.528115 - 4.04239i) q^{48} -9.22800 q^{49} +(-0.320793 + 1.37735i) q^{50} +(1.95203 + 1.95203i) q^{51} +(4.47501 + 13.1615i) q^{52} +(4.07420 - 4.07420i) q^{53} +(6.07162 - 3.77766i) q^{54} +0.914766i q^{55} +(-7.22175 + 8.81308i) q^{56} +0.631882i q^{57} +(-2.12285 - 3.41193i) q^{58} +(1.22845 - 1.22845i) q^{59} +(-1.82861 - 0.900642i) q^{60} +(-6.98912 - 6.98912i) q^{61} +(-5.93629 - 1.38260i) q^{62} -7.90074 q^{63} +(1.57239 + 7.84395i) q^{64} +6.95074 q^{65} +(-1.28413 - 0.299081i) q^{66} +(5.24219 + 5.24219i) q^{67} +(-4.85977 - 2.39358i) q^{68} +(2.59500 - 2.59500i) q^{69} +(3.00961 + 4.83717i) q^{70} +13.7940i q^{71} +(-3.51597 + 4.29072i) q^{72} -1.30876i q^{73} +(1.26335 - 0.786036i) q^{74} +(-0.720673 + 0.720673i) q^{75} +(-0.399159 - 1.17397i) q^{76} +(2.60572 + 2.60572i) q^{77} +(-2.27253 + 9.75728i) q^{78} +0.611127 q^{79} +(3.96630 + 0.518173i) q^{80} -0.730326 q^{81} +(-0.193752 + 0.831890i) q^{82} +(1.29471 + 1.29471i) q^{83} +(-7.77429 + 2.64331i) q^{84} +(-1.91529 + 1.91529i) q^{85} +(8.54182 - 5.31458i) q^{86} -2.89597i q^{87} +(2.57470 - 0.255519i) q^{88} -10.9236i q^{89} +(1.46525 + 2.35502i) q^{90} +(19.7993 - 19.7993i) q^{91} +(-3.18199 + 6.46050i) q^{92} +(-3.10606 - 3.10606i) q^{93} +(-14.8998 - 3.47025i) q^{94} -0.619987 q^{95} +(-2.02417 + 5.39837i) q^{96} -12.7571 q^{97} +(12.7102 + 2.96028i) q^{98} +(1.26862 + 1.26862i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36}+ \cdots - 8 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−1.37735	−	0.320793i	−0.973933	−	0.226835i
$2$	−1.37735	−	0.320793i	−0.973933	−	0.226835i
$3$	−0.720673	−	0.720673i	−0.416081	−	0.416081i	0.467770	−	0.883850i	$-0.345058\pi$
$3$	−0.720673	−	0.720673i	−0.416081	−	0.416081i	−0.883850	+	0.467770i	$0.845058\pi$
$4$	1.79418	+	0.883688i	0.897092	+	0.441844i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$	0.761432	+	1.22381i	0.310853	+	0.499617i
$7$		−	4.02840i		−	1.52259i	−0.648405	−	0.761296i	$-0.724563\pi$
$7$		−	4.02840i		−	1.52259i	0.648405	−	0.761296i	$-0.275437\pi$
$8$	−2.18774	−	1.79271i	−0.773482	−	0.633818i
$9$		−	1.96126i		−	0.653754i
$10$	−1.20077	+	0.747098i	−0.379716	+	0.236253i
$11$	−0.646837	+	0.646837i	−0.195029	+	0.195029i	−0.797865	−	0.602836i	$-0.794037\pi$
$11$	−0.646837	+	0.646837i	−0.195029	+	0.195029i	0.602836	+	0.797865i	$0.294037\pi$
$12$	−0.656170	−	1.92987i	−0.189420	−	0.557106i
$13$	4.91492	+	4.91492i	1.36315	+	1.36315i	0.869867	+	0.493286i	$0.164204\pi$
$13$	4.91492	+	4.91492i	1.36315	+	1.36315i	0.493286	+	0.869867i	$0.335796\pi$
$14$	−1.29228	+	5.54851i	−0.345377	+	1.48290i
$15$	−1.01919			−0.263153
$16$	2.43819	+	3.17100i	0.609548	+	0.792749i
$17$	−2.70862			−0.656938			−0.328469	−	0.944515i	$-0.606533\pi$
$17$	−2.70862			−0.656938			−0.328469	+	0.944515i	$0.606533\pi$
$18$	−0.629159	+	2.70134i	−0.148294	+	0.636712i
$19$	−0.438397	−	0.438397i	−0.100575	−	0.100575i	0.655029	−	0.755604i	$-0.272656\pi$
$19$	−0.438397	−	0.438397i	−0.100575	−	0.100575i	−0.755604	+	0.655029i	$0.772656\pi$
$20$	1.89354	−	0.643818i	0.423409	−	0.143962i
$21$	−2.90316	+	2.90316i	−0.633521	+	0.633521i
$22$	1.09842	−	0.683420i	0.234184	−	0.145706i
$23$			3.60080i			0.750819i	0.926859	+	0.375410i	$0.122498\pi$
$23$			3.60080i			0.750819i	−0.926859	+	0.375410i	$0.877502\pi$
$24$	0.284686	+	2.86860i	0.0581113	+	0.585551i
$25$		−	1.00000i		−	0.200000i
$26$	−5.19289	−	8.34623i	−1.01841	−	1.63683i
$27$	−3.57545	+	3.57545i	−0.688095	+	0.688095i
$28$	3.55985	−	7.22769i	0.672748	−	1.36590i
$29$	2.00921	+	2.00921i	0.373102	+	0.373102i	0.868606	−	0.495504i	$-0.165017\pi$
$29$	2.00921	+	2.00921i	0.373102	+	0.373102i	−0.495504	+	0.868606i	$0.665017\pi$
$30$	1.40377	+	0.326948i	0.256293	+	0.0596922i
$31$	4.30994			0.774087			0.387044	−	0.922061i	$-0.373496\pi$
$31$	4.30994			0.774087			0.387044	+	0.922061i	$0.373496\pi$
$32$	−2.34101	−	5.14973i	−0.413835	−	0.910352i
$33$	0.932316			0.162295
$34$	3.73072	+	0.868908i	0.639814	+	0.149016i
$35$	−2.84851	−	2.84851i	−0.481486	−	0.481486i
$36$	1.73314	−	3.51886i	0.288857	−	0.586477i
$37$	−0.743961	+	0.743961i	−0.122306	+	0.122306i	−0.765611	−	0.643304i	$-0.777563\pi$
$37$	−0.743961	+	0.743961i	−0.122306	+	0.122306i	0.643304	+	0.765611i	$0.277563\pi$
$38$	0.463191	+	0.744461i	0.0751395	+	0.120767i
$39$		−	7.08410i		−	1.13436i
$40$	−2.81460	+	0.279327i	−0.445027	+	0.0441655i
$41$		−	0.603979i		−	0.0943256i	−0.998887	−	0.0471628i	$-0.984982\pi$
$41$		−	0.603979i		−	0.0943256i	0.998887	−	0.0471628i	$-0.0150180\pi$
$42$	4.92998	−	3.06735i	0.760712	−	0.473303i
$43$	−5.03010	+	5.03010i	−0.767083	+	0.767083i	−0.977592	−	0.210509i	$-0.932488\pi$
$43$	−5.03010	+	5.03010i	−0.767083	+	0.767083i	0.210509	+	0.977592i	$0.432488\pi$
$44$	−1.73215	+	0.588942i	−0.261131	+	0.0887864i
$45$	−1.38682	−	1.38682i	−0.206735	−	0.206735i
$46$	1.15511	−	4.95956i	0.170312	−	0.731248i
$47$	10.8177			1.57793			0.788963	−	0.614440i	$-0.210618\pi$
$47$	10.8177			1.57793			0.788963	+	0.614440i	$0.210618\pi$
$48$	0.528115	−	4.04239i	0.0762268	−	0.583469i
$49$	−9.22800			−1.31829
$50$	−0.320793	+	1.37735i	−0.0453670	+	0.194787i
$51$	1.95203	+	1.95203i	0.273339	+	0.273339i
$52$	4.47501	+	13.1615i	0.620572	+	1.82517i
$53$	4.07420	−	4.07420i	0.559634	−	0.559634i	−0.369569	−	0.929203i	$-0.620495\pi$
$53$	4.07420	−	4.07420i	0.559634	−	0.559634i	0.929203	+	0.369569i	$0.120495\pi$
$54$	6.07162	−	3.77766i	0.826243	−	0.514075i
$55$			0.914766i			0.123347i
$56$	−7.22175	+	8.81308i	−0.965047	+	1.17770i
$57$			0.631882i			0.0836948i
$58$	−2.12285	−	3.41193i	−0.278744	−	0.448009i
$59$	1.22845	−	1.22845i	0.159931	−	0.159931i	−0.622605	−	0.782536i	$-0.713926\pi$
$59$	1.22845	−	1.22845i	0.159931	−	0.159931i	0.782536	+	0.622605i	$0.213926\pi$
$60$	−1.82861	−	0.900642i	−0.236072	−	0.116272i
$61$	−6.98912	−	6.98912i	−0.894865	−	0.894865i	0.100112	−	0.994976i	$-0.468080\pi$
$61$	−6.98912	−	6.98912i	−0.894865	−	0.894865i	−0.994976	+	0.100112i	$0.968080\pi$
$62$	−5.93629	−	1.38260i	−0.753909	−	0.175590i
$63$	−7.90074			−0.995400
$64$	1.57239	+	7.84395i	0.196548	+	0.980494i
$65$	6.95074			0.862134
$66$	−1.28413	−	0.299081i	−0.158065	−	0.0368143i
$67$	5.24219	+	5.24219i	0.640435	+	0.640435i	0.950662	−	0.310227i	$-0.100405\pi$
$67$	5.24219	+	5.24219i	0.640435	+	0.640435i	−0.310227	+	0.950662i	$0.600405\pi$
$68$	−4.85977	−	2.39358i	−0.589334	−	0.290264i
$69$	2.59500	−	2.59500i	0.312401	−	0.312401i
$70$	3.00961	+	4.83717i	0.359717	+	0.578153i
$71$			13.7940i			1.63704i	0.574475	+	0.818522i	$0.305206\pi$
$71$			13.7940i			1.63704i	−0.574475	+	0.818522i	$0.694794\pi$
$72$	−3.51597	+	4.29072i	−0.414361	+	0.505667i
$73$		−	1.30876i		−	0.153179i	−0.997063	−	0.0765895i	$-0.975597\pi$
$73$		−	1.30876i		−	0.153179i	0.997063	−	0.0765895i	$-0.0244031\pi$
$74$	1.26335	−	0.786036i	0.146862	−	0.0913749i
$75$	−0.720673	+	0.720673i	−0.0832162	+	0.0832162i
$76$	−0.399159	−	1.17397i	−0.0457866	−	0.134664i
$77$	2.60572	+	2.60572i	0.296949	+	0.296949i
$78$	−2.27253	+	9.75728i	−0.257313	+	1.10479i
$79$	0.611127			0.0687571			0.0343786	−	0.999409i	$-0.489055\pi$
$79$	0.611127			0.0687571			0.0343786	+	0.999409i	$0.489055\pi$
$80$	3.96630	+	0.518173i	0.443445	+	0.0579335i
$81$	−0.730326			−0.0811473
$82$	−0.193752	+	0.831890i	−0.0213963	+	0.0918669i
$83$	1.29471	+	1.29471i	0.142113	+	0.142113i	0.774584	−	0.632471i	$-0.217959\pi$
$83$	1.29471	+	1.29471i	0.142113	+	0.142113i	−0.632471	+	0.774584i	$0.717959\pi$
$84$	−7.77429	+	2.64331i	−0.848244	+	0.288409i
$85$	−1.91529	+	1.91529i	−0.207742	+	0.207742i
$86$	8.54182	−	5.31458i	0.921089	−	0.573086i
$87$		−	2.89597i		−	0.310481i
$88$	2.57470	−	0.255519i	0.274464	−	0.0272384i
$89$		−	10.9236i		−	1.15790i	−0.815363	−	0.578950i	$-0.803463\pi$
$89$		−	10.9236i		−	1.15790i	0.815363	−	0.578950i	$-0.196537\pi$
$90$	1.46525	+	2.35502i	0.154451	+	0.248241i
$91$	19.7993	−	19.7993i	2.07553	−	2.07553i
$92$	−3.18199	+	6.46050i	−0.331745	+	0.673554i
$93$	−3.10606	−	3.10606i	−0.322083	−	0.322083i
$94$	−14.8998	−	3.47025i	−1.53680	−	0.357929i
$95$	−0.619987			−0.0636093
$96$	−2.02417	+	5.39837i	−0.206591	+	0.550969i
$97$	−12.7571			−1.29528			−0.647642	−	0.761945i	$-0.724245\pi$
$97$	−12.7571			−1.29528			−0.647642	+	0.761945i	$0.724245\pi$
$98$	12.7102	+	2.96028i	1.28392	+	0.299033i
$99$	1.26862	+	1.26862i	0.127501	+	0.127501i
$100$	0.883688	−	1.79418i	0.0883688	−	0.179418i
$101$	−8.59804	+	8.59804i	−0.855537	+	0.855537i	−0.990809	−	0.135272i	$-0.956809\pi$
$101$	−8.59804	+	8.59804i	−0.855537	+	0.855537i	0.135272	+	0.990809i	$0.456809\pi$
$102$	−2.06243	−	3.31483i	−0.204211	−	0.328217i
$103$		−	12.0328i		−	1.18563i	−0.805338	−	0.592815i	$-0.798016\pi$
$103$		−	12.0328i		−	1.18563i	0.805338	−	0.592815i	$-0.201984\pi$
$104$	−1.94153	−	19.5636i	−0.190383	−	1.91837i
$105$			4.10569i			0.400674i
$106$	−6.91857	+	4.30462i	−0.671991	+	0.418102i
$107$	−2.37309	+	2.37309i	−0.229415	+	0.229415i	−0.812448	−	0.583033i	$-0.801866\pi$
$107$	−2.37309	+	2.37309i	−0.229415	+	0.229415i	0.583033	+	0.812448i	$0.301866\pi$
$108$	−9.57459	+	3.25543i	−0.921315	+	0.313254i
$109$	−3.24479	−	3.24479i	−0.310794	−	0.310794i	0.534423	−	0.845217i	$-0.320529\pi$
$109$	−3.24479	−	3.24479i	−0.310794	−	0.310794i	−0.845217	+	0.534423i	$0.820529\pi$
$110$	0.293450	−	1.25995i	0.0279794	−	0.120132i
$111$	1.07230			0.101779
$112$	12.7740	−	9.82200i	1.20703	−	0.928092i
$113$	17.3173			1.62907			0.814536	−	0.580114i	$-0.196992\pi$
$113$	17.3173			1.62907			0.814536	+	0.580114i	$0.196992\pi$
$114$	0.202703	−	0.870322i	0.0189849	−	0.0815131i
$115$	2.54615	+	2.54615i	0.237430	+	0.237430i
$116$	1.82938	+	5.38042i	0.169854	+	0.499559i
$117$	9.63944	−	9.63944i	0.891166	−	0.891166i
$118$	−2.08609	+	1.29793i	−0.192040	+	0.119484i
$119$			10.9114i			1.00025i
$120$	2.22971	+	1.82710i	0.203544	+	0.166791i
$121$			10.1632i			0.923928i
$122$	7.38440	+	11.8685i	0.668552	+	1.07452i
$123$	−0.435271	+	0.435271i	−0.0392471	+	0.0392471i
$124$	7.73282	+	3.80864i	0.694428	+	0.342026i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$	10.8821	+	2.53450i	0.969453	+	0.225791i
$127$	−15.5438			−1.37929			−0.689645	−	0.724147i	$-0.742234\pi$
$127$	−15.5438			−1.37929			−0.689645	+	0.724147i	$0.742234\pi$
$128$	0.350558	−	11.3083i	0.0309852	−	0.999520i
$129$	7.25011			0.638337
$130$	−9.57360	−	2.22975i	−0.839661	−	0.195562i
$131$	−11.2770	−	11.2770i	−0.985280	−	0.985280i	0.0146129	−	0.999893i	$-0.495348\pi$
$131$	−11.2770	−	11.2770i	−0.985280	−	0.985280i	−0.999893	+	0.0146129i	$0.995348\pi$
$132$	1.67275	+	0.823877i	0.145594	+	0.0717093i
$133$	−1.76604	+	1.76604i	−0.153135	+	0.153135i
$134$	−5.53867	−	8.90198i	−0.478468	−	0.769014i
$135$			5.05645i			0.435190i
$136$	5.92576	+	4.85578i	0.508130	+	0.416379i
$137$			3.67273i			0.313782i	0.987616	+	0.156891i	$0.0501472\pi$
$137$			3.67273i			0.313782i	−0.987616	+	0.156891i	$0.949853\pi$
$138$	−4.40668	+	2.74176i	−0.375122	+	0.233395i
$139$	−5.23552	+	5.23552i	−0.444071	+	0.444071i	−0.893378	−	0.449307i	$-0.851671\pi$
$139$	−5.23552	+	5.23552i	−0.444071	+	0.444071i	0.449307	+	0.893378i	$0.351671\pi$
$140$	−2.59355	−	7.62794i	−0.219195	−	0.644679i
$141$	−7.79604	−	7.79604i	−0.656545	−	0.656545i
$142$	4.42501	−	18.9991i	0.371339	−	1.59437i
$143$	−6.35830			−0.531708
$144$	6.21915	−	4.78193i	0.518263	−	0.398494i
$145$	2.84146			0.235970
$146$	−0.419842	+	1.80262i	−0.0347464	+	0.149186i
$147$	6.65037	+	6.65037i	0.548514	+	0.548514i
$148$	−1.99223	+	0.677373i	−0.163760	+	0.0556797i
$149$	−3.29391	+	3.29391i	−0.269848	+	0.269848i	−0.829039	−	0.559191i	$-0.811112\pi$
$149$	−3.29391	+	3.29391i	−0.269848	+	0.269848i	0.559191	+	0.829039i	$0.311112\pi$
$150$	1.22381	−	0.761432i	0.0999233	−	0.0621706i
$151$			6.93206i			0.564123i	0.959396	+	0.282061i	$0.0910182\pi$
$151$			6.93206i			0.564123i	−0.959396	+	0.282061i	$0.908982\pi$
$152$	0.173179	+	1.74502i	0.0140467	+	0.141539i
$153$			5.31232i			0.429475i
$154$	−2.75309	−	4.42488i	−0.221850	−	0.356567i
$155$	3.04759	−	3.04759i	0.244788	−	0.244788i
$156$	6.26013	−	12.7102i	0.501212	−	1.01763i
$157$	5.65633	+	5.65633i	0.451425	+	0.451425i	0.895827	−	0.444403i	$-0.146584\pi$
$157$	5.65633	+	5.65633i	0.451425	+	0.451425i	−0.444403	+	0.895827i	$0.646584\pi$
$158$	−0.841735	−	0.196045i	−0.0669649	−	0.0155965i
$159$	−5.87233			−0.465706
$160$	−5.29675	−	1.98607i	−0.418745	−	0.157012i
$161$	14.5055			1.14319
$162$	1.00591	+	0.234283i	0.0790321	+	0.0184070i
$163$	−10.9746	−	10.9746i	−0.859593	−	0.859593i	0.131697	−	0.991290i	$-0.457957\pi$
$163$	−10.9746	−	10.9746i	−0.859593	−	0.859593i	−0.991290	+	0.131697i	$0.957957\pi$
$164$	0.533729	−	1.08365i	0.0416772	−	0.0846188i
$165$	0.659247	−	0.659247i	0.0513223	−	0.0513223i
$166$	−1.36793	−	2.19860i	−0.106172	−	0.170645i
$167$		−	11.7686i		−	0.910685i	−0.890316	−	0.455343i	$-0.849517\pi$
$167$		−	11.7686i		−	0.910685i	0.890316	−	0.455343i	$-0.150483\pi$
$168$	11.5559	−	1.14683i	0.891555	−	0.0884798i
$169$			35.3128i			2.71637i
$170$	3.25243	−	2.02361i	0.249450	−	0.155204i
$171$	−0.859811	+	0.859811i	−0.0657514	+	0.0657514i
$172$	−13.4700	+	4.57988i	−1.02707	+	0.349213i
$173$	−1.40225	−	1.40225i	−0.106611	−	0.106611i	0.651789	−	0.758400i	$-0.274019\pi$
$173$	−1.40225	−	1.40225i	−0.106611	−	0.106611i	−0.758400	+	0.651789i	$0.774019\pi$
$174$	−0.929008	+	3.98877i	−0.0704279	+	0.302388i
$175$	−4.02840			−0.304518
$176$	−3.62823	−	0.474007i	−0.273488	−	0.0357296i
$177$	−1.77063			−0.133088
$178$	−3.50421	+	15.0456i	−0.262652	+	1.12772i
$179$	9.66131	+	9.66131i	0.722120	+	0.722120i	0.969037	−	0.246917i	$-0.0794174\pi$
$179$	9.66131	+	9.66131i	0.722120	+	0.722120i	−0.246917	+	0.969037i	$0.579417\pi$
$180$	−1.26269	−	3.71373i	−0.0941157	−	0.276805i
$181$	0.294844	−	0.294844i	0.0219156	−	0.0219156i	−0.696064	−	0.717980i	$-0.745067\pi$
$181$	0.294844	−	0.294844i	0.0219156	−	0.0219156i	0.717980	+	0.696064i	$0.245067\pi$
$182$	−33.6220	+	20.9190i	−2.49223	+	1.55062i
$183$			10.0737i			0.744672i
$184$	6.45519	−	7.87761i	0.475883	−	0.580745i
$185$			1.05212i			0.0773533i
$186$	3.28172	+	5.27452i	0.240628	+	0.386747i
$187$	1.75204	−	1.75204i	0.128122	−	0.128122i
$188$	19.4090	+	9.55949i	1.41555	+	0.697198i
$189$	14.4033	+	14.4033i	1.04769	+	1.04769i
$190$	0.853939	+	0.198888i	0.0619512	+	0.0144288i
$191$	−16.9352			−1.22539			−0.612694	−	0.790320i	$-0.709914\pi$
$191$	−16.9352			−1.22539			−0.612694	+	0.790320i	$0.709914\pi$
$192$	4.51975	−	6.78610i	0.326185	−	0.489745i
$193$	−16.5927			−1.19437			−0.597185	−	0.802103i	$-0.703714\pi$
$193$	−16.5927			−1.19437			−0.597185	+	0.802103i	$0.703714\pi$
$194$	17.5709	+	4.09238i	1.26152	+	0.293816i
$195$	−5.00921	−	5.00921i	−0.358717	−	0.358717i
$196$	−16.5567	−	8.15468i	−1.18262	−	0.582477i
$197$	−2.38392	+	2.38392i	−0.169847	+	0.169847i	−0.786912	−	0.617065i	$-0.788322\pi$
$197$	−2.38392	+	2.38392i	−0.169847	+	0.169847i	0.617065	+	0.786912i	$0.288322\pi$
$198$	−1.34036	−	2.15429i	−0.0952556	−	0.153099i
$199$		−	10.1411i		−	0.718883i	−0.933168	−	0.359442i	$-0.882967\pi$
$199$		−	10.1411i		−	0.718883i	0.933168	−	0.359442i	$-0.117033\pi$
$200$	−1.79271	+	2.18774i	−0.126764	+	0.154696i
$201$		−	7.55581i		−	0.532946i
$202$	14.6007	−	9.08431i	1.02730	−	0.639170i
$203$	8.09392	−	8.09392i	0.568082	−	0.568082i
$204$	1.77732	+	5.22729i	0.124437	+	0.365984i
$205$	−0.427078	−	0.427078i	−0.0298284	−	0.0298284i
$206$	−3.86005	+	16.5734i	−0.268942	+	1.15473i
$207$	7.06211			0.490851
$208$	−3.60169	+	27.5687i	−0.249732	+	1.91155i
$209$	0.567143			0.0392301
$210$	1.31708	−	5.65497i	0.0908869	−	0.390230i
$211$	−2.81171	−	2.81171i	−0.193566	−	0.193566i	0.603669	−	0.797235i	$-0.293705\pi$
$211$	−2.81171	−	2.81171i	−0.193566	−	0.193566i	−0.797235	+	0.603669i	$0.793705\pi$
$212$	10.9102	−	3.70954i	0.749314	−	0.254772i
$213$	9.94095	−	9.94095i	0.681143	−	0.681143i
$214$	4.02984	−	2.50730i	0.275474	−	0.171396i
$215$			7.11363i			0.485146i
$216$	14.2319	−	1.41240i	0.968356	−	0.0961018i
$217$		−	17.3621i		−	1.17862i
$218$	3.42830	+	5.51011i	0.232194	+	0.373192i
$219$	−0.943190	+	0.943190i	−0.0637349	+	0.0637349i
$220$	−0.808368	+	1.64126i	−0.0545001	+	0.110654i
$221$	−13.3127	−	13.3127i	−0.895507	−	0.895507i
$222$	−1.47694	−	0.343988i	−0.0991256	−	0.0230869i
$223$	14.0502			0.940871			0.470436	−	0.882434i	$-0.344097\pi$
$223$	14.0502			0.940871			0.470436	+	0.882434i	$0.344097\pi$
$224$	−20.7452	+	9.43051i	−1.38609	+	0.630102i
$225$	−1.96126			−0.130751
$226$	−23.8519	−	5.55526i	−1.58661	−	0.369530i
$227$	−13.3495	−	13.3495i	−0.886037	−	0.886037i	0.108103	−	0.994140i	$-0.465522\pi$
$227$	−13.3495	−	13.3495i	−0.886037	−	0.886037i	−0.994140	+	0.108103i	$0.965522\pi$
$228$	−0.558387	+	1.13371i	−0.0369801	+	0.0750819i
$229$	8.78589	−	8.78589i	0.580588	−	0.580588i	−0.354477	−	0.935065i	$-0.615341\pi$
$229$	8.78589	−	8.78589i	0.580588	−	0.580588i	0.935065	+	0.354477i	$0.115341\pi$
$230$	−2.69015	−	4.32373i	−0.177383	−	0.285098i
$231$		−	3.75574i		−	0.247110i
$232$	−0.793696	−	7.99757i	−0.0521087	−	0.525066i
$233$		−	15.1472i		−	0.992329i	−0.868229	−	0.496165i	$-0.834741\pi$
$233$		−	15.1472i		−	0.992329i	0.868229	−	0.496165i	$-0.165259\pi$
$234$	−16.3691	+	10.1846i	−1.07008	+	0.665789i
$235$	7.64928	−	7.64928i	0.498984	−	0.498984i
$236$	3.28964	−	1.11850i	0.214137	−	0.0728082i
$237$	−0.440423	−	0.440423i	−0.0286085	−	0.0286085i
$238$	3.50031	−	15.0288i	0.226891	−	0.974175i
$239$	17.9151			1.15883			0.579414	−	0.815033i	$-0.303281\pi$
$239$	17.9151			1.15883			0.579414	+	0.815033i	$0.303281\pi$
$240$	−2.48497	−	3.23184i	−0.160404	−	0.208614i
$241$	25.6594			1.65287			0.826433	−	0.563035i	$-0.190366\pi$
$241$	25.6594			1.65287			0.826433	+	0.563035i	$0.190366\pi$
$242$	3.26028	−	13.9983i	0.209579	−	0.899844i
$243$	11.2527	+	11.2527i	0.721859	+	0.721859i
$244$	−6.36356	−	18.7160i	−0.407385	−	1.19817i
$245$	−6.52518	+	6.52518i	−0.416879	+	0.416879i
$246$	0.739153	−	0.459889i	0.0471266	−	0.0293214i
$247$		−	4.30937i		−	0.274199i
$248$	−9.42901	−	7.72646i	−0.598743	−	0.490631i
$249$		−	1.86613i		−	0.118261i
$250$	0.747098	+	1.20077i	0.0472506	+	0.0759432i
$251$	−5.95195	+	5.95195i	−0.375684	+	0.375684i	−0.869542	−	0.493858i	$-0.835586\pi$
$251$	−5.95195	+	5.95195i	−0.375684	+	0.375684i	0.493858	+	0.869542i	$0.335586\pi$
$252$	−14.1754	−	6.98179i	−0.892965	−	0.439812i
$253$	−2.32913	−	2.32913i	−0.146431	−	0.146431i
$254$	21.4093	+	4.98635i	1.34334	+	0.312871i
$255$	2.76059			0.172875
$256$	−4.11046	+	15.4630i	−0.256904	+	0.966437i
$257$	−4.17369			−0.260348			−0.130174	−	0.991491i	$-0.541554\pi$
$257$	−4.17369			−0.260348			−0.130174	+	0.991491i	$0.541554\pi$
$258$	−9.98594	−	2.32579i	−0.621697	−	0.144797i
$259$	2.99697	+	2.99697i	0.186223	+	0.186223i
$260$	12.4709	+	6.14229i	0.773413	+	0.380929i
$261$	3.94059	−	3.94059i	0.243917	−	0.243917i
$262$	11.9148	+	19.1500i	0.736101	+	1.18309i
$263$		−	9.14469i		−	0.563885i	−0.959431	−	0.281943i	$-0.909021\pi$
$263$		−	9.14469i		−	0.563885i	0.959431	−	0.281943i	$-0.0909788\pi$
$264$	−2.03966	−	1.67137i	−0.125533	−	0.102866i
$265$		−	5.76178i		−	0.353944i
$266$	2.99899	−	1.86592i	0.183880	−	0.114407i
$267$	−7.87234	+	7.87234i	−0.481780	+	0.481780i
$268$	4.77299	+	14.0379i	0.291557	+	0.857502i
$269$	−8.40029	−	8.40029i	−0.512175	−	0.512175i	0.403017	−	0.915192i	$-0.367961\pi$
$269$	−8.40029	−	8.40029i	−0.512175	−	0.512175i	−0.915192	+	0.403017i	$0.867961\pi$
$270$	1.62207	−	6.96449i	0.0987162	−	0.423846i
$271$	18.7794			1.14077			0.570383	−	0.821379i	$-0.306795\pi$
$271$	18.7794			1.14077			0.570383	+	0.821379i	$0.306795\pi$
$272$	−6.60414	−	8.58904i	−0.400435	−	0.520787i
$273$	−28.5376			−1.72717
$274$	1.17819	−	5.05863i	0.0711768	−	0.305603i
$275$	0.646837	+	0.646837i	0.0390057	+	0.0390057i
$276$	6.94908	−	2.36274i	0.418285	−	0.142220i
$277$	−3.54167	+	3.54167i	−0.212798	+	0.212798i	−0.805455	−	0.592657i	$-0.798079\pi$
$277$	−3.54167	+	3.54167i	−0.212798	+	0.212798i	0.592657	+	0.805455i	$0.298079\pi$
$278$	8.89066	−	5.53162i	0.533226	−	0.331765i
$279$		−	8.45291i		−	0.506062i
$280$	1.12524	+	11.3383i	0.0672460	+	0.677595i
$281$			2.31811i			0.138287i	0.997607	+	0.0691433i	$0.0220266\pi$
$281$			2.31811i			0.138287i	−0.997607	+	0.0691433i	$0.977973\pi$
$282$	8.23696	+	13.2388i	0.490504	+	0.788358i
$283$	−1.63197	+	1.63197i	−0.0970108	+	0.0970108i	−0.753947	−	0.656936i	$-0.771852\pi$
$283$	−1.63197	+	1.63197i	−0.0970108	+	0.0970108i	0.656936	+	0.753947i	$0.271852\pi$
$284$	−12.1896	+	24.7489i	−0.723318	+	1.46858i
$285$	0.446808	+	0.446808i	0.0264666	+	0.0264666i
$286$	8.75761	+	2.03970i	0.517848	+	0.120610i
$287$	−2.43307			−0.143619
$288$	−10.1000	+	4.59132i	−0.595146	+	0.270546i
$289$	−9.66335			−0.568433
$290$	−3.91368	−	0.911520i	−0.229819	−	0.0535263i
$291$	9.19367	+	9.19367i	0.538943	+	0.538943i
$292$	1.15654	−	2.34816i	0.0676813	−	0.137416i
$293$	−11.5789	+	11.5789i	−0.676444	+	0.676444i	−0.959194	−	0.282750i	$-0.908753\pi$
$293$	−11.5789	+	11.5789i	−0.676444	+	0.676444i	0.282750	+	0.959194i	$0.408753\pi$
$294$	−7.02650	−	11.2933i	−0.409794	−	0.658638i
$295$		−	1.73729i		−	0.101149i
$296$	2.96129	−	0.293885i	0.172122	−	0.0170817i
$297$		−	4.62546i		−	0.268397i
$298$	5.59353	−	3.48020i	0.324024	−	0.201603i
$299$	−17.6976	+	17.6976i	−1.02348	+	1.02348i
$300$	−1.92987	+	0.656170i	−0.111421	+	0.0378840i
$301$	20.2632	+	20.2632i	1.16795	+	1.16795i
$302$	2.22376	−	9.54787i	0.127963	−	0.549418i
$303$	12.3927			0.711945
$304$	0.321261	−	2.45905i	0.0184256	−	0.141036i
$305$	−9.88410			−0.565962
$306$	1.70415	−	7.31692i	0.0974200	−	0.418280i
$307$	11.7116	+	11.7116i	0.668415	+	0.668415i	0.957349	−	0.288934i	$-0.0933008\pi$
$307$	11.7116	+	11.7116i	0.668415	+	0.668415i	−0.288934	+	0.957349i	$0.593301\pi$
$308$	2.37249	+	6.97778i	0.135185	+	0.397596i
$309$	−8.67174	+	8.67174i	−0.493318	+	0.493318i
$310$	−5.17523	+	3.21995i	−0.293934	+	0.182881i
$311$			11.2068i			0.635477i	0.948178	+	0.317739i	$0.102923\pi$
$311$			11.2068i			0.635477i	−0.948178	+	0.317739i	$0.897077\pi$
$312$	−12.6997	+	15.4981i	−0.718981	+	0.877410i
$313$			7.50635i			0.424284i	0.977239	+	0.212142i	$0.0680439\pi$
$313$			7.50635i			0.424284i	−0.977239	+	0.212142i	$0.931956\pi$
$314$	−5.97624	−	9.60526i	−0.337259	−	0.542056i
$315$	−5.58667	+	5.58667i	−0.314773	+	0.314773i
$316$	1.09647	+	0.540046i	0.0616815	+	0.0303799i
$317$	16.2854	+	16.2854i	0.914680	+	0.914680i	0.996636	−	0.0819564i	$-0.0261168\pi$
$317$	16.2854	+	16.2854i	0.914680	+	0.914680i	−0.0819564	+	0.996636i	$0.526117\pi$
$318$	8.08825	+	1.88380i	0.453566	+	0.105638i
$319$	−2.59927			−0.145531
$320$	6.65836	+	4.43467i	0.372214	+	0.247905i
$321$	3.42044			0.190910
$322$	−19.9791	−	4.65325i	−1.11339	−	0.259316i
$323$	1.18745	+	1.18745i	0.0660716	+	0.0660716i
$324$	−1.31034	−	0.645380i	−0.0727966	−	0.0358545i
$325$	4.91492	−	4.91492i	0.272631	−	0.272631i
$326$	11.5952	+	18.6364i	0.642201	+	1.03217i
$327$			4.67686i			0.258631i
$328$	−1.08276	+	1.32135i	−0.0597853	+	0.0729592i
$329$		−	43.5781i		−	2.40254i
$330$	−1.11950	+	0.696532i	−0.0616262	+	0.0383428i
$331$	−19.3846	+	19.3846i	−1.06547	+	1.06547i	−0.0677707	+	0.997701i	$0.521589\pi$
$331$	−19.3846	+	19.3846i	−1.06547	+	1.06547i	−0.997701	+	0.0677707i	$0.978411\pi$
$332$	1.17883	+	3.46707i	0.0646966	+	0.190280i
$333$	1.45910	+	1.45910i	0.0799582	+	0.0799582i
$334$	−3.77530	+	16.2095i	−0.206575	+	0.886946i
$335$	7.41357			0.405047
$336$	−16.2844	−	2.12746i	−0.888385	−	0.116062i
$337$	−7.82991			−0.426522			−0.213261	−	0.976995i	$-0.568408\pi$
$337$	−7.82991			−0.426522			−0.213261	+	0.976995i	$0.568408\pi$
$338$	11.3281	−	48.6381i	0.616168	−	2.64557i
$339$	−12.4801	−	12.4801i	−0.677825	−	0.677825i
$340$	−5.12889	+	1.74386i	−0.278153	+	0.0945741i
$341$	−2.78783	+	2.78783i	−0.150969	+	0.150969i
$342$	1.46008	−	0.908439i	0.0789522	−	0.0491227i
$343$			8.97529i			0.484620i
$344$	20.0220	−	1.98703i	1.07952	−	0.107133i
$345$		−	3.66988i		−	0.197580i
$346$	1.48156	+	2.38123i	0.0796491	+	0.128015i
$347$	8.91753	−	8.91753i	0.478718	−	0.478718i	−0.426004	−	0.904721i	$-0.640079\pi$
$347$	8.91753	−	8.91753i	0.478718	−	0.478718i	0.904721	+	0.426004i	$0.140079\pi$
$348$	2.55914	−	5.19591i	0.137184	−	0.278530i
$349$	−6.69072	−	6.69072i	−0.358146	−	0.358146i	0.504983	−	0.863129i	$-0.331499\pi$
$349$	−6.69072	−	6.69072i	−0.358146	−	0.358146i	−0.863129	+	0.504983i	$0.831499\pi$
$350$	5.54851	+	1.29228i	0.296581	+	0.0690754i
$351$	−35.1461			−1.87596
$352$	4.84528	+	1.81678i	0.258255	+	0.0968350i
$353$	−2.05215			−0.109225			−0.0546126	−	0.998508i	$-0.517392\pi$
$353$	−2.05215			−0.109225			−0.0546126	+	0.998508i	$0.517392\pi$
$354$	2.43877	+	0.568004i	0.129619	+	0.0301891i
$355$	9.75382	+	9.75382i	0.517679	+	0.517679i
$356$	9.65305	−	19.5989i	0.511611	−	1.03874i
$357$	7.86357	−	7.86357i	0.416184	−	0.416184i
$358$	−10.2077	−	16.4063i	−0.539495	−	0.867099i
$359$			9.52634i			0.502781i	0.967886	+	0.251391i	$0.0808879\pi$
$359$			9.52634i			0.502781i	−0.967886	+	0.251391i	$0.919112\pi$
$360$	0.547833	+	5.52017i	0.0288733	+	0.290938i
$361$		−	18.6156i		−	0.979769i
$362$	−0.500688	+	0.311520i	−0.0263156	+	0.0163731i
$363$	7.32435	−	7.32435i	0.384429	−	0.384429i
$364$	53.0199	−	18.0271i	2.77900	−	0.944879i
$365$	−0.925435	−	0.925435i	−0.0484395	−	0.0484395i
$366$	3.23158	−	13.8751i	0.168918	−	0.725261i
$367$	−3.39736			−0.177341			−0.0886703	−	0.996061i	$-0.528262\pi$
$367$	−3.39736			−0.177341			−0.0886703	+	0.996061i	$0.528262\pi$
$368$	−11.4181	+	8.77944i	−0.595211	+	0.457660i
$369$	−1.18456			−0.0616657
$370$	0.337512	−	1.44914i	0.0175464	−	0.0753370i
$371$	−16.4125	−	16.4125i	−0.852094	−	0.852094i
$372$	−2.82805	−	8.31762i	−0.146628	−	0.431248i
$373$	−22.4895	+	22.4895i	−1.16446	+	1.16446i	−0.180971	+	0.983488i	$0.557924\pi$
$373$	−22.4895	+	22.4895i	−1.16446	+	1.16446i	−0.983488	+	0.180971i	$0.942076\pi$
$374$	−2.97521	+	1.85113i	−0.153845	+	0.0957196i
$375$			1.01919i			0.0526305i
$376$	−23.6663	−	19.3930i	−1.22050	−	1.00012i
$377$			19.7502i			1.01719i
$378$	−15.2179	−	24.4589i	−0.782726	−	1.25803i
$379$	14.9819	−	14.9819i	0.769567	−	0.769567i	−0.208463	−	0.978030i	$-0.566846\pi$
$379$	14.9819	−	14.9819i	0.769567	−	0.769567i	0.978030	+	0.208463i	$0.0668462\pi$
$380$	−1.11237	−	0.547875i	−0.0570634	−	0.0281054i
$381$	11.2020	+	11.2020i	0.573896	+	0.573896i
$382$	23.3257	+	5.43269i	1.19345	+	0.277961i
$383$	26.1197			1.33466			0.667328	−	0.744764i	$-0.267438\pi$
$383$	26.1197			1.33466			0.667328	+	0.744764i	$0.267438\pi$
$384$	−8.40221	+	7.89693i	−0.428773	+	0.402989i
$385$	3.68504			0.187807
$386$	22.8540	+	5.32283i	1.16324	+	0.270925i
$387$	9.86534	+	9.86534i	0.501483	+	0.501483i
$388$	−22.8885	−	11.2733i	−1.16199	−	0.572313i
$389$	−2.08395	+	2.08395i	−0.105660	+	0.105660i	−0.757961	−	0.652300i	$-0.773804\pi$
$389$	−2.08395	+	2.08395i	−0.105660	+	0.105660i	0.652300	+	0.757961i	$0.273804\pi$
$390$	5.29252	+	8.50636i	0.267997	+	0.430736i
$391$		−	9.75322i		−	0.493241i
$392$	20.1884	+	16.5431i	1.01967	+	0.835554i
$393$			16.2541i			0.819912i
$394$	4.04823	−	2.51874i	0.203947	−	0.126892i
$395$	0.432132	−	0.432132i	0.0217429	−	0.0217429i
$396$	1.15507	+	3.39719i	0.0580444	+	0.170715i
$397$	1.43282	+	1.43282i	0.0719114	+	0.0719114i	0.742148	−	0.670236i	$-0.233807\pi$
$397$	1.43282	+	1.43282i	0.0719114	+	0.0719114i	−0.670236	+	0.742148i	$0.733807\pi$
$398$	−3.25319	+	13.9678i	−0.163068	+	0.700144i
$399$	2.54547			0.127433
$400$	3.17100	−	2.43819i	0.158550	−	0.121910i
$401$	−29.9853			−1.49739			−0.748697	−	0.662912i	$-0.769320\pi$
$401$	−29.9853			−1.49739			−0.748697	+	0.662912i	$0.769320\pi$
$402$	−2.42385	+	10.4070i	−0.120891	+	0.519053i
$403$	21.1830	+	21.1830i	1.05520	+	1.05520i
$404$	−23.0244	+	7.82847i	−1.14551	+	0.389481i
$405$	−0.516418	+	0.516418i	−0.0256610	+	0.0256610i
$406$	−13.7446	+	8.55168i	−0.682134	+	0.424413i
$407$		−	0.962443i		−	0.0477065i
$408$	−0.771107	−	7.76996i	−0.0381755	−	0.384670i
$409$		−	4.17833i		−	0.206605i	−0.994650	−	0.103302i	$-0.967059\pi$
$409$		−	4.17833i		−	0.206605i	0.994650	−	0.103302i	$-0.0329410\pi$
$410$	0.451232	+	0.725238i	0.0222847	+	0.0358170i
$411$	2.64684	−	2.64684i	0.130559	−	0.130559i
$412$	10.6333	−	21.5891i	0.523864	−	1.06362i
$413$	−4.94870	−	4.94870i	−0.243510	−	0.243510i
$414$	−9.72699	−	2.26548i	−0.478056	−	0.111342i
$415$	1.83100			0.0898801
$416$	13.8046	−	36.8163i	0.676828	−	1.80507i
$417$	7.54620			0.369539
$418$	−0.781154	−	0.181935i	−0.0382075	−	0.00889876i
$419$	−24.4667	−	24.4667i	−1.19528	−	1.19528i	−0.975565	−	0.219712i	$-0.929488\pi$
$419$	−24.4667	−	24.4667i	−1.19528	−	1.19528i	−0.219712	−	0.975565i	$-0.570512\pi$
$420$	−3.62815	+	7.36636i	−0.177035	+	0.359441i
$421$	25.6017	−	25.6017i	1.24775	−	1.24775i	0.291039	−	0.956711i	$-0.405999\pi$
$421$	25.6017	−	25.6017i	1.24775	−	1.24775i	0.956711	−	0.291039i	$-0.0940008\pi$
$422$	2.97073	+	4.77468i	0.144613	+	0.232428i
$423$		−	21.2164i		−	1.03158i
$424$	−16.2171	+	1.60942i	−0.787573	+	0.0781604i
$425$			2.70862i			0.131388i
$426$	−16.8811	+	10.5032i	−0.817894	+	0.508881i
$427$	−28.1550	+	28.1550i	−1.36251	+	1.36251i
$428$	−6.35482	+	2.16069i	−0.307172	+	0.104441i
$429$	4.58226	+	4.58226i	0.221233	+	0.221233i
$430$	2.28200	−	9.79796i	0.110048	−	0.472500i
$431$	17.6126			0.848367			0.424184	−	0.905576i	$-0.360561\pi$
$431$	17.6126			0.848367			0.424184	+	0.905576i	$0.360561\pi$
$432$	−20.0554	−	2.62012i	−0.964914	−	0.126060i
$433$	27.0568			1.30027			0.650133	−	0.759820i	$-0.274713\pi$
$433$	27.0568			1.30027			0.650133	+	0.759820i	$0.274713\pi$
$434$	−5.56966	+	23.9137i	−0.267352	+	1.14790i
$435$	−2.04776	−	2.04776i	−0.0981827	−	0.0981827i
$436$	−2.95436	−	8.68912i	−0.141488	−	0.416134i
$437$	1.57858	−	1.57858i	0.0755138	−	0.0755138i
$438$	1.60167	−	0.996533i	0.0765308	−	0.0476162i
$439$		−	22.9965i		−	1.09756i	−0.835967	−	0.548780i	$-0.815092\pi$
$439$		−	22.9965i		−	1.09756i	0.835967	−	0.548780i	$-0.184908\pi$
$440$	1.63991	−	2.00127i	0.0781796	−	0.0954067i
$441$			18.0985i			0.861834i
$442$	14.0656	+	22.6068i	0.669032	+	1.07530i
$443$	−13.7715	+	13.7715i	−0.654303	+	0.654303i	−0.954026	−	0.299723i	$-0.903106\pi$
$443$	−13.7715	+	13.7715i	−0.654303	+	0.654303i	0.299723	+	0.954026i	$0.403106\pi$
$444$	1.92391	+	0.947583i	0.0913048	+	0.0449703i
$445$	−7.72415	−	7.72415i	−0.366160	−	0.366160i
$446$	−19.3520	−	4.50721i	−0.916346	−	0.213422i
$447$	4.74766			0.224557
$448$	31.5986	−	6.33421i	1.49289	−	0.299263i
$449$	6.88838			0.325083			0.162541	−	0.986702i	$-0.448031\pi$
$449$	6.88838			0.325083			0.162541	+	0.986702i	$0.448031\pi$
$450$	2.70134	+	0.629159i	0.127342	+	0.0296588i
$451$	0.390676	+	0.390676i	0.0183962	+	0.0183962i
$452$	31.0704	+	15.3031i	1.46143	+	0.719796i
$453$	4.99575	−	4.99575i	0.234721	−	0.234721i
$454$	14.1045	+	22.6693i	0.661957	+	1.06392i
$455$		−	28.0004i		−	1.31268i
$456$	1.13278	−	1.38239i	0.0530473	−	0.0647364i
$457$			2.52622i			0.118171i	0.998253	+	0.0590857i	$0.0188185\pi$
$457$			2.52622i			0.118171i	−0.998253	+	0.0590857i	$0.981181\pi$
$458$	−14.9197	+	9.28279i	−0.697152	+	0.433756i
$459$	9.68454	−	9.68454i	0.452036	−	0.452036i
$460$	2.31826	+	6.81827i	0.108089	+	0.317903i
$461$	9.23502	+	9.23502i	0.430118	+	0.430118i	0.888668	−	0.458550i	$-0.151631\pi$
$461$	9.23502	+	9.23502i	0.430118	+	0.430118i	−0.458550	+	0.888668i	$0.651631\pi$
$462$	−1.20482	+	5.17297i	−0.0560531	+	0.240668i
$463$	−11.2676			−0.523652			−0.261826	−	0.965115i	$-0.584325\pi$
$463$	−11.2676			−0.523652			−0.261826	+	0.965115i	$0.584325\pi$
$464$	−1.47237	+	11.2701i	−0.0683530	+	0.523199i
$465$	−4.39263			−0.203703
$466$	−4.85913	+	20.8631i	−0.225095	+	0.966462i
$467$	−25.8291	−	25.8291i	−1.19523	−	1.19523i	−0.975579	−	0.219650i	$-0.929508\pi$
$467$	−25.8291	−	25.8291i	−1.19523	−	1.19523i	−0.219650	−	0.975579i	$-0.570492\pi$
$468$	25.8132	−	8.77666i	1.19321	−	0.405701i
$469$	21.1176	−	21.1176i	0.975122	−	0.975122i
$470$	−12.9896	+	8.08190i	−0.599164	+	0.372790i
$471$		−	8.15273i		−	0.375658i
$472$	−4.88979	+	0.485273i	−0.225071	+	0.0223365i
$473$		−	6.50731i		−	0.299206i
$474$	0.465331	+	0.747901i	0.0213734	+	0.0343522i
$475$	−0.438397	+	0.438397i	−0.0201150	+	0.0201150i
$476$	−9.64229	+	19.5771i	−0.441954	+	0.897315i
$477$	−7.99056	−	7.99056i	−0.365863	−	0.365863i
$478$	−24.6753	−	5.74703i	−1.12862	−	0.262863i
$479$	−15.7261			−0.718545			−0.359273	−	0.933233i	$-0.616975\pi$
$479$	−15.7261			−0.718545			−0.359273	+	0.933233i	$0.616975\pi$
$480$	2.38592	+	5.24853i	0.108902	+	0.239561i
$481$	−7.31301			−0.333445
$482$	−35.3419	−	8.23135i	−1.60978	−	0.374928i
$483$	−10.4537	−	10.4537i	−0.475660	−	0.475660i
$484$	−8.98110	+	18.2347i	−0.408232	+	0.828848i
$485$	−9.02061	+	9.02061i	−0.409605	+	0.409605i
$486$	−11.8891	−	19.1086i	−0.539300	−	0.866785i
$487$			35.3717i			1.60284i	0.598100	+	0.801422i	$0.295923\pi$
$487$			35.3717i			1.60284i	−0.598100	+	0.801422i	$0.704077\pi$
$488$	2.76090	+	27.8198i	0.124980	+	1.25934i
$489$			15.8181i			0.715320i
$490$	11.0807	−	6.89423i	0.500575	−	0.311449i
$491$	7.95703	−	7.95703i	0.359096	−	0.359096i	−0.504384	−	0.863480i	$-0.668280\pi$
$491$	7.95703	−	7.95703i	0.359096	−	0.359096i	0.863480	+	0.504384i	$0.168280\pi$
$492$	−1.16560	+	0.396312i	−0.0525493	+	0.0178671i
$493$	−5.44221	−	5.44221i	−0.245105	−	0.245105i
$494$	−1.38242	+	5.93551i	−0.0621978	+	0.267051i
$495$	1.79409			0.0806385
$496$	10.5084	+	13.6668i	0.471843	+	0.613657i
$497$	55.5677			2.49255
$498$	−0.598640	+	2.57031i	−0.0268257	+	0.115178i
$499$	11.5864	+	11.5864i	0.518677	+	0.518677i	0.917171	−	0.398494i	$-0.130467\pi$
$499$	11.5864	+	11.5864i	0.518677	+	0.518677i	−0.398494	+	0.917171i	$0.630467\pi$
$500$	−0.643818	−	1.89354i	−0.0287924	−	0.0846817i
$501$	−8.48135	+	8.48135i	−0.378919	+	0.378919i
$502$	10.1073	−	6.28857i	0.451109	−	0.280673i
$503$			23.5051i			1.04804i	0.851706	+	0.524020i	$0.175568\pi$
$503$			23.5051i			1.04804i	−0.851706	+	0.524020i	$0.824432\pi$
$504$	17.2847	+	14.1637i	0.769924	+	0.630903i
$505$			12.1595i			0.541089i
$506$	2.46086	+	3.95520i	0.109399	+	0.175830i
$507$	25.4490	−	25.4490i	1.13023	−	1.13023i
$508$	−27.8885	−	13.7359i	−1.23735	−	0.609431i
$509$	−3.08381	−	3.08381i	−0.136687	−	0.136687i	0.635452	−	0.772140i	$-0.280814\pi$
$509$	−3.08381	−	3.08381i	−0.136687	−	0.136687i	−0.772140	+	0.635452i	$0.780814\pi$
$510$	−3.80230	−	0.885578i	−0.168369	−	0.0392141i
$511$	−5.27222			−0.233229
$512$	10.6220	−	19.9793i	0.469429	−	0.882970i
$513$	3.13493			0.138411
$514$	5.74863	+	1.33889i	0.253561	+	0.0590559i
$515$	−8.50850	−	8.50850i	−0.374929	−	0.374929i
$516$	13.0080	+	6.40684i	0.572647	+	0.282045i
$517$	−6.99730	+	6.99730i	−0.307741	+	0.307741i
$518$	−3.16647	−	5.08928i	−0.139127	−	0.223610i
$519$			2.02113i			0.0887178i
$520$	−15.2064	−	12.4607i	−0.666845	−	0.546436i
$521$			11.5762i			0.507161i	0.967314	+	0.253580i	$0.0816083\pi$
$521$			11.5762i			0.507161i	−0.967314	+	0.253580i	$0.918392\pi$
$522$	−6.69169	+	4.16346i	−0.292887	+	0.182230i
$523$	3.97900	−	3.97900i	0.173990	−	0.173990i	−0.614740	−	0.788730i	$-0.710739\pi$
$523$	3.97900	−	3.97900i	0.173990	−	0.173990i	0.788730	+	0.614740i	$0.210739\pi$
$524$	−10.2677	−	30.1985i	−0.448547	−	1.31923i
$525$	2.90316	+	2.90316i	0.126704	+	0.126704i
$526$	−2.93355	+	12.5954i	−0.127909	+	0.549187i
$527$	−11.6740			−0.508527
$528$	2.27316	+	2.95637i	0.0989268	+	0.128660i
$529$	10.0342			0.436271
$530$	−1.84834	+	7.93599i	−0.0802868	+	0.344717i
$531$	−2.40932	−	2.40932i	−0.104555	−	0.104555i
$532$	−4.72923	+	1.60797i	−0.205038	+	0.0697143i
$533$	2.96851	−	2.96851i	0.128580	−	0.128580i
$534$	13.3684	−	8.31758i	0.578506	−	0.359937i
$535$			3.35605i			0.145095i
$536$	−2.07081	−	20.8663i	−0.0894454	−	0.901285i
$537$		−	13.9253i		−	0.600921i
$538$	8.87539	+	14.2649i	0.382645	+	0.615003i
$539$	5.96902	−	5.96902i	0.257104	−	0.257104i
$540$	−4.46832	+	9.07219i	−0.192286	+	0.390405i
$541$	17.2148	+	17.2148i	0.740123	+	0.740123i	0.972602	−	0.232478i	$-0.0746835\pi$
$541$	17.2148	+	17.2148i	0.740123	+	0.740123i	−0.232478	+	0.972602i	$0.574684\pi$
$542$	−25.8658	−	6.02429i	−1.11103	−	0.258765i
$543$	−0.424973			−0.0182373
$544$	6.34091	+	13.9487i	0.271864	+	0.598045i
$545$	−4.58882			−0.196564
$546$	39.3062	+	9.15466i	1.68215	+	0.391783i
$547$	−20.3610	−	20.3610i	−0.870573	−	0.870573i	0.121962	−	0.992535i	$-0.461081\pi$
$547$	−20.3610	−	20.3610i	−0.870573	−	0.870573i	−0.992535	+	0.121962i	$0.961081\pi$
$548$	−3.24555	+	6.58955i	−0.138643	+	0.281492i
$549$	−13.7075	+	13.7075i	−0.585021	+	0.585021i
$550$	−0.683420	−	1.09842i	−0.0291411	−	0.0468369i
$551$		−	1.76167i		−	0.0750495i
$552$	−10.3293	+	1.02510i	−0.439643	+	0.0436311i
$553$		−	2.46186i		−	0.104689i
$554$	6.01426	−	3.74197i	0.255521	−	0.158981i
$555$	0.758234	−	0.758234i	0.0321852	−	0.0321852i
$556$	−14.0201	+	4.76692i	−0.594583	+	0.202162i
$557$	−22.7029	−	22.7029i	−0.961954	−	0.961954i	0.0373478	−	0.999302i	$-0.488109\pi$
$557$	−22.7029	−	22.7029i	−0.961954	−	0.961954i	−0.999302	+	0.0373478i	$0.988109\pi$
$558$	−2.71163	+	11.6426i	−0.114793	+	0.492871i
$559$	−49.4451			−2.09130
$560$	2.08741	−	15.9778i	0.0882091	−	0.675186i
$561$	−2.52529			−0.106618
$562$	0.743632	−	3.19284i	0.0313682	−	0.134682i
$563$	15.4153	+	15.4153i	0.649676	+	0.649676i	0.952915	−	0.303238i	$-0.0980678\pi$
$563$	15.4153	+	15.4153i	0.649676	+	0.649676i	−0.303238	+	0.952915i	$0.598068\pi$
$564$	−7.09826	−	20.8768i	−0.298891	−	0.879072i
$565$	12.2452	−	12.2452i	0.515158	−	0.515158i
$566$	2.77133	−	1.72427i	0.116488	−	0.0724766i
$567$			2.94204i			0.123554i
$568$	24.7286	−	30.1776i	1.03759	−	1.26622i
$569$			22.6529i			0.949660i	0.880078	+	0.474830i	$0.157490\pi$
$569$			22.6529i			0.949660i	−0.880078	+	0.474830i	$0.842510\pi$
$570$	−0.472078	−	0.758744i	−0.0197732	−	0.0317803i
$571$	−13.4941	+	13.4941i	−0.564710	+	0.564710i	−0.930642	−	0.365931i	$-0.880750\pi$
$571$	−13.4941	+	13.4941i	−0.564710	+	0.564710i	0.365931	+	0.930642i	$0.380750\pi$
$572$	−11.4080	−	5.61876i	−0.476991	−	0.234932i
$573$	12.2047	+	12.2047i	0.509860	+	0.509860i
$574$	3.35119	+	0.780511i	0.139876	+	0.0325779i
$575$	3.60080			0.150164
$576$	15.3840	−	3.08386i	0.641002	−	0.128494i
$577$	6.08684			0.253398			0.126699	−	0.991941i	$-0.459562\pi$
$577$	6.08684			0.253398			0.126699	+	0.991941i	$0.459562\pi$
$578$	13.3098	+	3.09994i	0.553615	+	0.128940i
$579$	11.9579	+	11.9579i	0.496955	+	0.496955i
$580$	5.09810	+	2.51096i	0.211687	+	0.104262i
$581$	5.21561	−	5.21561i	0.216380	−	0.216380i
$582$	−9.71363	−	15.6122i	−0.402643	−	0.647145i
$583$			5.27068i			0.218289i
$584$	−2.34623	+	2.86323i	−0.0970877	+	0.118481i
$585$		−	13.6322i		−	0.563623i
$586$	19.6625	−	12.2337i	0.812252	−	0.505370i
$587$	21.4418	−	21.4418i	0.884999	−	0.884999i	−0.109039	−	0.994038i	$-0.534777\pi$
$587$	21.4418	−	21.4418i	0.884999	−	0.884999i	0.994038	+	0.109039i	$0.0347772\pi$
$588$	6.05514	+	17.8088i	0.249710	+	0.734425i
$589$	−1.88946	−	1.88946i	−0.0778540	−	0.0778540i
$590$	−0.557312	+	2.39286i	−0.0229442	+	0.0985126i
$591$	3.43605			0.141340
$592$	−4.17301	−	0.545180i	−0.171510	−	0.0224068i
$593$	−28.2005			−1.15806			−0.579028	−	0.815308i	$-0.696568\pi$
$593$	−28.2005			−1.15806			−0.579028	+	0.815308i	$0.696568\pi$
$594$	−1.48382	+	6.37088i	−0.0608817	+	0.261400i
$595$	7.71554	+	7.71554i	0.316306	+	0.316306i
$596$	−8.82067	+	2.99909i	−0.361309	+	0.122848i
$597$	−7.30841	+	7.30841i	−0.299113	+	0.299113i
$598$	30.0531	−	18.6986i	1.22896	−	0.764641i
$599$			38.0516i			1.55475i	0.629039	+	0.777374i	$0.283449\pi$
$599$			38.0516i			1.55475i	−0.629039	+	0.777374i	$0.716551\pi$
$600$	2.86860	−	0.284686i	0.117110	−	0.0116223i
$601$		−	19.0716i		−	0.777947i	−0.921249	−	0.388974i	$-0.872830\pi$
$601$		−	19.0716i		−	0.777947i	0.921249	−	0.388974i	$-0.127170\pi$
$602$	−21.4093	−	34.4099i	−0.872577	−	1.40244i
$603$	10.2813	−	10.2813i	0.418687	−	0.418687i
$604$	−6.12578	+	12.4374i	−0.249254	+	0.506070i
$605$	7.18647	+	7.18647i	0.292172	+	0.292172i
$606$	−17.0691	−	3.97551i	−0.693386	−	0.161494i
$607$	5.73433			0.232749			0.116375	−	0.993205i	$-0.462873\pi$
$607$	5.73433			0.232749			0.116375	+	0.993205i	$0.462873\pi$
$608$	−1.23133	+	3.28392i	−0.0499372	+	0.133180i
$609$	−11.6661			−0.472736
$610$	13.6139	+	3.17075i	0.551209	+	0.128380i
$611$	53.1682	+	53.1682i	2.15096	+	2.15096i
$612$	−4.69443	+	9.53127i	−0.189761	+	0.385279i
$613$	5.36917	−	5.36917i	0.216859	−	0.216859i	−0.590315	−	0.807173i	$-0.700996\pi$
$613$	5.36917	−	5.36917i	0.216859	−	0.216859i	0.807173	+	0.590315i	$0.200996\pi$
$614$	−12.3739	−	19.8879i	−0.499372	−	0.802611i
$615$			0.615566i			0.0248220i
$616$	−1.02933	−	10.3719i	−0.0414730	−	0.417897i
$617$			28.2915i			1.13897i	0.822000	+	0.569487i	$0.192858\pi$
$617$			28.2915i			1.13897i	−0.822000	+	0.569487i	$0.807142\pi$
$618$	14.7259	−	9.16219i	0.592361	−	0.368557i
$619$	18.9669	−	18.9669i	0.762345	−	0.762345i	−0.214401	−	0.976746i	$-0.568780\pi$
$619$	18.9669	−	18.9669i	0.762345	−	0.762345i	0.976746	+	0.214401i	$0.0687799\pi$
$620$	8.16104	−	2.77481i	0.327755	−	0.111439i
$621$	−12.8745	−	12.8745i	−0.516635	−	0.516635i
$622$	3.59505	−	15.4356i	0.144148	−	0.618912i
$623$	−44.0046			−1.76301
$624$	22.4637	−	17.2724i	0.899266	−	0.691449i
$625$	−1.00000			−0.0400000
$626$	2.40798	−	10.3389i	0.0962424	−	0.413224i
$627$	−0.408725	−	0.408725i	−0.0163229	−	0.0163229i
$628$	5.15007	+	15.1469i	0.205510	+	0.604429i
$629$	2.01511	−	2.01511i	0.0803477	−	0.0803477i
$630$	9.48696	−	5.90263i	0.377970	−	0.235166i
$631$		−	41.7662i		−	1.66269i	−0.555758	−	0.831344i	$-0.687572\pi$
$631$		−	41.7662i		−	1.66269i	0.555758	−	0.831344i	$-0.312428\pi$
$632$	−1.33699	−	1.09557i	−0.0531824	−	0.0435795i
$633$			4.05265i			0.161078i
$634$	−17.2065	−	27.6549i	−0.683356	−	1.09832i
$635$	−10.9911	+	10.9911i	−0.436170	+	0.436170i
$636$	−10.5360	−	5.18931i	−0.417781	−	0.205769i
$637$	−45.3549	−	45.3549i	−1.79703	−	1.79703i
$638$	3.58010	+	0.833827i	0.141738	+	0.0330115i
$639$	27.0536			1.07022
$640$	−7.74828	−	8.24404i	−0.306278	−	0.325874i
$641$	−2.85195			−0.112645			−0.0563227	−	0.998413i	$-0.517938\pi$
$641$	−2.85195			−0.112645			−0.0563227	+	0.998413i	$0.517938\pi$
$642$	−4.71114	−	1.09725i	−0.185934	−	0.0433051i
$643$	−31.8921	−	31.8921i	−1.25770	−	1.25770i	−0.952187	−	0.305516i	$-0.901171\pi$
$643$	−31.8921	−	31.8921i	−1.25770	−	1.25770i	−0.305516	−	0.952187i	$-0.598829\pi$
$644$	26.0255	+	12.8183i	1.02555	+	0.505112i
$645$	5.12660	−	5.12660i	0.201860	−	0.201860i
$646$	−1.25461	−	2.01646i	−0.0493620	−	0.0793367i
$647$		−	7.83402i		−	0.307987i	−0.988072	−	0.153994i	$-0.950786\pi$
$647$		−	7.83402i		−	0.307987i	0.988072	−	0.153994i	$-0.0492135\pi$
$648$	1.59776	+	1.30926i	0.0627660	+	0.0514327i
$649$			1.58922i			0.0623823i
$650$	−8.34623	+	5.19289i	−0.327366	+	0.203682i
$651$	−12.5124	+	12.5124i	−0.490401	+	0.490401i
$652$	−9.99228	−	29.3884i	−0.391328	−	1.15094i
$653$	−12.6822	−	12.6822i	−0.496292	−	0.496292i	0.413989	−	0.910282i	$-0.364135\pi$
$653$	−12.6822	−	12.6822i	−0.496292	−	0.496292i	−0.910282	+	0.413989i	$0.864135\pi$
$654$	1.50030	−	6.44167i	0.0586665	−	0.251889i
$655$	−15.9482			−0.623146
$656$	1.91522	−	1.47262i	0.0747766	−	0.0574960i
$657$	−2.56682			−0.100141
$658$	−13.9795	+	60.0223i	−0.544980	+	2.33991i
$659$	12.9694	+	12.9694i	0.505217	+	0.505217i	0.913055	−	0.407837i	$-0.133717\pi$
$659$	12.9694	+	12.9694i	0.505217	+	0.505217i	−0.407837	+	0.913055i	$0.633717\pi$
$660$	1.76538	−	0.600241i	0.0687173	−	0.0233644i
$661$	−6.85796	+	6.85796i	−0.266744	+	0.266744i	−0.827787	−	0.561043i	$-0.810400\pi$
$661$	−6.85796	+	6.85796i	−0.266744	+	0.266744i	0.561043	+	0.827787i	$0.310400\pi$
$662$	32.9177	−	20.4809i	1.27938	−	0.796012i
$663$			19.1882i			0.745206i
$664$	−0.511447	−	5.15352i	−0.0198480	−	0.199996i
$665$			2.49756i			0.0968511i
$666$	−1.54162	−	2.47776i	−0.0597366	−	0.0960113i
$667$	−7.23478	+	7.23478i	−0.280132	+	0.280132i
$668$	10.3998	−	21.1151i	0.402381	−	0.816968i
$669$	−10.1256	−	10.1256i	−0.391478	−	0.391478i
$670$	−10.2111	−	2.37822i	−0.394489	−	0.0918788i
$671$	9.04164			0.349049
$672$	21.7468	+	8.15416i	0.838901	+	0.314554i
$673$	23.1277			0.891508			0.445754	−	0.895155i	$-0.352936\pi$
$673$	23.1277			0.891508			0.445754	+	0.895155i	$0.352936\pi$
$674$	10.7845	+	2.51178i	0.415404	+	0.0967501i
$675$	3.57545	+	3.57545i	0.137619	+	0.137619i
$676$	−31.2055	+	63.3577i	−1.20021	+	2.43684i
$677$	−20.2521	+	20.2521i	−0.778352	+	0.778352i	−0.979550	−	0.201199i	$-0.935516\pi$
$677$	−20.2521	+	20.2521i	−0.778352	+	0.778352i	0.201199	+	0.979550i	$0.435516\pi$
$678$	13.1859	+	21.1930i	0.506402	+	0.813911i
$679$			51.3905i			1.97219i
$680$	7.62370	−	0.756592i	0.292355	−	0.0290140i
$681$			19.2412i			0.737326i
$682$	4.73413	−	2.94550i	0.181279	−	0.112789i
$683$	26.2957	−	26.2957i	1.00618	−	1.00618i	0.00619708	−	0.999981i	$-0.498027\pi$
$683$	26.2957	−	26.2957i	1.00618	−	1.00618i	0.999981	−	0.00619708i	$-0.00197260\pi$
$684$	−2.30246	+	0.782854i	−0.0880369	+	0.0299332i
$685$	2.59701	+	2.59701i	0.0992267	+	0.0992267i
$686$	2.87921	−	12.3621i	0.109929	−	0.471988i
$687$	−12.6635			−0.483143
$688$	−28.2148	−	3.68610i	−1.07568	−	0.140531i
$689$	40.0487			1.52573
$690$	−1.17727	+	5.05471i	−0.0448180	+	0.192430i
$691$	−4.91230	−	4.91230i	−0.186873	−	0.186873i	0.607470	−	0.794343i	$-0.292185\pi$
$691$	−4.91230	−	4.91230i	−0.186873	−	0.186873i	−0.794343	+	0.607470i	$0.792185\pi$
$692$	−1.27674	−	3.75505i	−0.0485346	−	0.142746i
$693$	5.11049	−	5.11049i	0.194132	−	0.194132i
$694$	−15.1432	+	9.42187i	−0.574829	+	0.357649i
$695$			7.40414i			0.280855i
$696$	−5.19164	+	6.33563i	−0.196789	+	0.240151i
$697$			1.63595i			0.0619661i
$698$	7.06912	+	11.3618i	0.267570	+	0.430050i
$699$	−10.9162	+	10.9162i	−0.412889	+	0.412889i
$700$	−7.22769	−	3.55985i	−0.273181	−	0.134550i
$701$	−12.3598	−	12.3598i	−0.466824	−	0.466824i	0.434060	−	0.900884i	$-0.357081\pi$
$701$	−12.3598	−	12.3598i	−0.466824	−	0.466824i	−0.900884	+	0.434060i	$0.857081\pi$
$702$	48.4084	+	11.2746i	1.82706	+	0.425533i
$703$	0.652300			0.0246020
$704$	−6.09084	−	4.05668i	−0.229557	−	0.152892i
$705$	−11.0253			−0.415235
$706$	2.82653	+	0.658317i	0.106378	+	0.0247761i
$707$	34.6363	+	34.6363i	1.30263	+	1.30263i
$708$	−3.17683	−	1.56468i	−0.119393	−	0.0588043i
$709$	−26.6076	+	26.6076i	−0.999270	+	0.999270i	−1.00000		0.000729493i	$-0.999768\pi$
$709$	−26.6076	+	26.6076i	−0.999270	+	0.999270i	0.000729493		1.00000i	$0.499768\pi$
$710$	−10.3055	−	16.5634i	−0.386757	−	0.621612i
$711$		−	1.19858i		−	0.0449502i
$712$	−19.5828	+	23.8980i	−0.733898	+	0.895614i
$713$			15.5192i			0.581200i
$714$	−13.3535	+	8.30830i	−0.499741	+	0.310930i
$715$	−4.49600	+	4.49600i	−0.168141	+	0.168141i
$716$	8.79658	+	25.8717i	0.328744	+	0.966872i
$717$	−12.9109	−	12.9109i	−0.482166	−	0.482166i
$718$	3.05598	−	13.1211i	0.114048	−	0.489675i
$719$	50.9765			1.90110			0.950551	−	0.310570i	$-0.100520\pi$
$719$	50.9765			1.90110			0.950551	+	0.310570i	$0.100520\pi$
$720$	1.01627	−	7.77894i	0.0378743	−	0.289904i
$721$	−48.4731			−1.80523
$722$	−5.97176	+	25.6402i	−0.222246	+	0.954230i
$723$	−18.4920	−	18.4920i	−0.687726	−	0.687726i
$724$	0.789555	−	0.268454i	0.0293436	−	0.00997703i
$725$	2.00921	−	2.00921i	0.0746203	−	0.0746203i
$726$	−12.4378	+	7.73859i	−0.461610	+	0.287206i
$727$			13.2824i			0.492616i	0.969192	+	0.246308i	$0.0792175\pi$
$727$			13.2824i			0.492616i	−0.969192	+	0.246308i	$0.920782\pi$
$728$	−78.8099	+	7.82126i	−2.92089	+	0.289875i
$729$		−	14.0280i		−	0.519556i
$730$	0.977774	+	1.57152i	0.0361890	+	0.0581646i
$731$	13.6246	−	13.6246i	0.503926	−	0.503926i
$732$	−8.90204	+	18.0741i	−0.329029	+	0.668039i
$733$	21.3075	+	21.3075i	0.787012	+	0.787012i	0.981003	−	0.193991i	$-0.0621434\pi$
$733$	21.3075	+	21.3075i	0.787012	+	0.787012i	−0.193991	+	0.981003i	$0.562143\pi$
$734$	4.67935	+	1.08985i	0.172718	+	0.0402270i
$735$	9.40505			0.346910
$736$	18.5431	−	8.42950i	0.683509	−	0.310715i
$737$	−6.78168			−0.249807
$738$	1.63155	+	0.379999i	0.0600583	+	0.0139879i
$739$	5.83841	+	5.83841i	0.214769	+	0.214769i	0.806290	−	0.591521i	$-0.201472\pi$
$739$	5.83841	+	5.83841i	0.214769	+	0.214769i	−0.591521	+	0.806290i	$0.701472\pi$
$740$	−0.929745	+	1.88769i	−0.0341781	+	0.0693930i
$741$	−3.10565	+	3.10565i	−0.114089	+	0.114089i
$742$	17.3407	+	27.8708i	0.636598	+	1.02317i
$743$		−	3.25778i		−	0.119516i	−0.998213	−	0.0597582i	$-0.980967\pi$
$743$		−	3.25778i		−	0.119516i	0.998213	−	0.0597582i	$-0.0190330\pi$
$744$	1.22698	+	12.3635i	0.0449832	+	0.453267i
$745$			4.65829i			0.170667i
$746$	38.1903	−	23.7614i	1.39825	−	0.869966i
$747$	2.53926	−	2.53926i	0.0929068	−	0.0929068i
$748$	4.69174	−	1.59522i	0.171547	−	0.0583271i
$749$	9.55975	+	9.55975i	0.349306	+	0.349306i
$750$	0.326948	−	1.40377i	0.0119384	−	0.0512586i
$751$	20.7322			0.756530			0.378265	−	0.925697i	$-0.376521\pi$
$751$	20.7322			0.756530			0.378265	+	0.925697i	$0.376521\pi$
$752$	26.3757	+	34.3030i	0.961821	+	1.25090i
$753$	8.57882			0.312630
$754$	6.33574	−	27.2030i	0.230734	−	0.990675i
$755$	4.90171	+	4.90171i	0.178391	+	0.178391i
$756$	13.1142	+	38.5703i	0.476958	+	1.40279i
$757$	23.3278	−	23.3278i	0.847862	−	0.847862i	−0.142004	−	0.989866i	$-0.545355\pi$
$757$	23.3278	−	23.3278i	0.847862	−	0.847862i	0.989866	+	0.142004i	$0.0453547\pi$
$758$	−25.4414	+	15.8292i	−0.924072	+	0.574942i
$759$			3.35709i			0.121854i
$760$	1.35637	+	1.11146i	0.0492007	+	0.0403168i
$761$		−	24.0242i		−	0.870878i	−0.900218	−	0.435439i	$-0.856593\pi$
$761$		−	24.0242i		−	0.870878i	0.900218	−	0.435439i	$-0.143407\pi$
$762$	−11.8356	−	19.0226i	−0.428757	−	0.689116i
$763$	−13.0713	+	13.0713i	−0.473213	+	0.473213i
$764$	−30.3849	−	14.9654i	−1.09929	−	0.541430i
$765$	3.75638	+	3.75638i	0.135812	+	0.135812i
$766$	−35.9760	−	8.37903i	−1.29987	−	0.302747i
$767$	12.0755			0.436021
$768$	14.1061	−	8.18147i	0.509009	−	0.295223i
$769$	−2.70862			−0.0976754			−0.0488377	−	0.998807i	$-0.515552\pi$
$769$	−2.70862			−0.0976754			−0.0488377	+	0.998807i	$0.515552\pi$
$770$	−5.07559	−	1.18214i	−0.182912	−	0.0426012i
$771$	3.00787	+	3.00787i	0.108326	+	0.108326i
$772$	−29.7704	−	14.6628i	−1.07146	−	0.527726i
$773$	22.9473	−	22.9473i	0.825358	−	0.825358i	−0.161513	−	0.986871i	$-0.551637\pi$
$773$	22.9473	−	22.9473i	0.825358	−	0.825358i	0.986871	+	0.161513i	$0.0516373\pi$
$774$	−10.4233	−	16.7527i	−0.374657	−	0.602165i
$775$		−	4.30994i		−	0.154817i
$776$	27.9091	+	22.8697i	1.00188	+	0.820974i
$777$		−	4.31967i		−	0.154967i
$778$	3.53884	−	2.20181i	0.126873	−	0.0789386i
$779$	−0.264783	+	0.264783i	−0.00948682	+	0.00948682i
$780$	−4.56087	−	13.4140i	−0.163305	−	0.480299i
$781$	−8.92246	−	8.92246i	−0.319271	−	0.319271i
$782$	−3.12876	+	13.4336i	−0.111884	+	0.480384i
$783$	−14.3677			−0.513459
$784$	−22.4996	−	29.2620i	−0.803558	−	1.04507i
$785$	7.99926			0.285506
$786$	5.21421	−	22.3876i	0.185985	−	0.798540i
$787$	−14.0592	−	14.0592i	−0.501157	−	0.501157i	0.410641	−	0.911797i	$-0.365305\pi$
$787$	−14.0592	−	14.0592i	−0.501157	−	0.501157i	−0.911797	+	0.410641i	$0.865305\pi$
$788$	−6.38383	+	2.17055i	−0.227414	+	0.0773225i
$789$	−6.59033	+	6.59033i	−0.234622	+	0.234622i
$790$	−0.733822	+	0.456572i	−0.0261082	+	0.0162441i
$791$		−	69.7609i		−	2.48041i
$792$	−0.501139	−	5.04966i	−0.0178072	−	0.179432i
$793$		−	68.7019i		−	2.43967i
$794$	−1.51386	−	2.43314i	−0.0537249	−	0.0863489i
$795$	−4.15236	+	4.15236i	−0.147269	+	0.147269i
$796$	8.96157	−	18.1950i	0.317634	−	0.644904i
$797$	35.4258	+	35.4258i	1.25485	+	1.25485i	0.953521	+	0.301326i	$0.0974293\pi$
$797$	35.4258	+	35.4258i	1.25485	+	1.25485i	0.301326	+	0.953521i	$0.402571\pi$
$798$	−3.50601	−	0.816570i	−0.124111	−	0.0289063i
$799$	−29.3011			−1.03660
$800$	−5.14973	+	2.34101i	−0.182070	+	0.0827671i
$801$	−21.4240			−0.756981
$802$	41.3003	+	9.61908i	1.45836	+	0.339661i
$803$	0.846556	+	0.846556i	0.0298743	+	0.0298743i
$804$	6.67698	−	13.5565i	0.235479	−	0.478101i
$805$	10.2569	−	10.2569i	0.361509	−	0.361509i
$806$	−22.3810	−	35.9717i	−0.788338	−	1.26705i
$807$			12.1077i			0.426212i
$808$	34.2240	−	3.39646i	1.20400	−	0.119487i
$809$		−	16.9217i		−	0.594935i	−0.954732	−	0.297467i	$-0.903858\pi$
$809$		−	16.9217i		−	0.594935i	0.954732	−	0.297467i	$-0.0961420\pi$
$810$	0.876952	−	0.545625i	0.0308130	−	0.0191713i
$811$	−20.4270	+	20.4270i	−0.717288	+	0.717288i	−0.968049	−	0.250761i	$-0.919319\pi$
$811$	−20.4270	+	20.4270i	−0.717288	+	0.717288i	0.250761	+	0.968049i	$0.419319\pi$
$812$	21.6745	−	7.36948i	0.760625	−	0.258618i
$813$	−13.5338	−	13.5338i	−0.474651	−	0.474651i
$814$	−0.308745	+	1.32562i	−0.0108215	+	0.0464630i
$815$	−15.5204			−0.543655
$816$	−1.43046	+	10.9493i	−0.0500763	+	0.383303i
$817$	4.41036			0.154299
$818$	−1.34038	+	5.75502i	−0.0468652	+	0.201219i
$819$	−38.8315	−	38.8315i	−1.35688	−	1.35688i
$820$	−0.388852	−	1.14366i	−0.0135793	−	0.0399383i
$821$	32.4563	−	32.4563i	1.13273	−	1.13273i	0.143013	−	0.989721i	$-0.454321\pi$
$821$	32.4563	−	32.4563i	1.13273	−	1.13273i	0.989721	−	0.143013i	$-0.0456792\pi$
$822$	−4.49471	+	2.79653i	−0.156771	+	0.0975403i
$823$		−	6.50705i		−	0.226821i	−0.993548	−	0.113411i	$-0.963822\pi$
$823$		−	6.50705i		−	0.226821i	0.993548	−	0.113411i	$-0.0361776\pi$
$824$	−21.5714	+	26.3247i	−0.751475	+	0.917064i
$825$		−	0.932316i		−	0.0324591i
$826$	5.22858	+	8.40360i	0.181926	+	0.292399i
$827$	27.0528	−	27.0528i	0.940718	−	0.940718i	−0.0576204	−	0.998339i	$-0.518351\pi$
$827$	27.0528	−	27.0528i	0.940718	−	0.940718i	0.998339	+	0.0576204i	$0.0183513\pi$
$828$	12.6707	+	6.24070i	0.440338	+	0.216879i
$829$	−8.54216	−	8.54216i	−0.296682	−	0.296682i	0.543031	−	0.839713i	$-0.317277\pi$
$829$	−8.54216	−	8.54216i	−0.296682	−	0.296682i	−0.839713	+	0.543031i	$0.817277\pi$
$830$	−2.52192	−	0.587371i	−0.0875372	−	0.0203879i
$831$	5.10477			0.177083
$832$	−30.8242	+	46.2805i	−1.06864	+	1.60449i
$833$	24.9952			0.866032
$834$	−10.3938	−	2.42077i	−0.359906	−	0.0838243i
$835$	−8.32169	−	8.32169i	−0.287984	−	0.287984i
$836$	1.01756	+	0.501178i	0.0351930	+	0.0173336i
$837$	−15.4099	+	15.4099i	−0.532646	+	0.532646i
$838$	25.8505	+	41.5480i	0.892990	+	1.43525i
$839$		−	24.4138i		−	0.842860i	−0.906861	−	0.421430i	$-0.861528\pi$
$839$		−	24.4138i		−	0.842860i	0.906861	−	0.421430i	$-0.138472\pi$
$840$	7.36030	−	8.98216i	0.253955	−	0.309914i
$841$		−	20.9261i		−	0.721590i
$842$	−43.4753	+	27.0496i	−1.49826	+	0.932192i
$843$	1.67060	−	1.67060i	0.0575384	−	0.0575384i
$844$	−2.56005	−	7.52940i	−0.0881205	−	0.259173i
$845$	24.9700	+	24.9700i	0.858993	+	0.858993i
$846$	−6.80606	+	29.2224i	−0.233997	+	1.00469i
$847$	40.9414			1.40676
$848$	22.8529	+	2.98560i	0.784773	+	0.102526i
$849$	2.35224			0.0807287
$850$	0.868908	−	3.73072i	0.0298033	−	0.127963i
$851$	−2.67885	−	2.67885i	−0.0918299	−	0.0918299i
$852$	26.6206	−	9.05119i	0.912006	−	0.310089i
$853$	8.23270	−	8.23270i	0.281882	−	0.281882i	−0.551977	−	0.833859i	$-0.686126\pi$
$853$	8.23270	−	8.23270i	0.281882	−	0.281882i	0.833859	+	0.551977i	$0.186126\pi$
$854$	47.8111	−	29.7473i	1.63606	−	1.01793i
$855$			1.21596i			0.0415848i
$856$	9.44595	−	0.937436i	0.322856	−	0.0320409i
$857$			4.73909i			0.161884i	0.996719	+	0.0809421i	$0.0257929\pi$
$857$			4.73909i			0.161884i	−0.996719	+	0.0809421i	$0.974207\pi$
$858$	−4.84141	−	7.78133i	−0.165283	−	0.265650i
$859$	−9.65120	+	9.65120i	−0.329295	+	0.329295i	−0.852318	−	0.523024i	$-0.824804\pi$
$859$	−9.65120	+	9.65120i	−0.329295	+	0.329295i	0.523024	+	0.852318i	$0.324804\pi$
$860$	−6.28623	+	12.7632i	−0.214359	+	0.435220i
$861$	1.75345	+	1.75345i	0.0597573	+	0.0597573i
$862$	−24.2586	−	5.64999i	−0.826253	−	0.192439i
$863$	−3.80368			−0.129479			−0.0647393	−	0.997902i	$-0.520622\pi$
$863$	−3.80368			−0.129479			−0.0647393	+	0.997902i	$0.520622\pi$
$864$	26.7827	+	10.0424i	0.911167	+	0.341650i
$865$	−1.98309			−0.0674269
$866$	−37.2667	−	8.67963i	−1.26637	−	0.294946i
$867$	6.96412	+	6.96412i	0.236514	+	0.236514i
$868$	15.3427	−	31.1509i	0.520766	−	1.05733i
$869$	−0.395300	+	0.395300i	−0.0134096	+	0.0134096i
$870$	2.16358	+	3.47739i	0.0733521	+	0.117895i
$871$			51.5299i			1.74602i
$872$	1.28178	+	12.9157i	0.0434066	+	0.437381i
$873$			25.0199i			0.846796i
$874$	−2.68066	+	1.66786i	−0.0906745	+	0.0564162i
$875$	−2.84851	+	2.84851i	−0.0962972	+	0.0962972i
$876$	−2.52574	+	0.858770i	−0.0853369	+	0.0290152i
$877$	2.38917	+	2.38917i	0.0806765	+	0.0806765i	0.746294	−	0.665617i	$-0.231832\pi$
$877$	2.38917	+	2.38917i	0.0806765	+	0.0806765i	−0.665617	+	0.746294i	$0.731832\pi$
$878$	−7.37710	+	31.6742i	−0.248965	+	1.06895i
$879$	16.6891			0.562911
$880$	−2.90072	+	2.23037i	−0.0977833	+	0.0751859i
$881$	−23.6195			−0.795762			−0.397881	−	0.917437i	$-0.630254\pi$
$881$	−23.6195			−0.795762			−0.397881	+	0.917437i	$0.630254\pi$
$882$	5.80588	−	24.9280i	0.195494	−	0.839369i
$883$	−9.64752	−	9.64752i	−0.324665	−	0.324665i	0.525889	−	0.850553i	$-0.323733\pi$
$883$	−9.64752	−	9.64752i	−0.324665	−	0.324665i	−0.850553	+	0.525889i	$0.823733\pi$
$884$	−12.1211	−	35.6496i	−0.407677	−	1.19903i
$885$	−1.25202	+	1.25202i	−0.0420862	+	0.0420862i
$886$	23.3860	−	14.5504i	0.785667	−	0.488829i
$887$		−	8.91140i		−	0.299215i	−0.988745	−	0.149608i	$-0.952199\pi$
$887$		−	8.91140i		−	0.299215i	0.988745	−	0.149608i	$-0.0478011\pi$
$888$	−2.34592	−	1.92233i	−0.0787239	−	0.0645092i
$889$			62.6167i			2.10010i
$890$	8.16100	+	13.1167i	0.273557	+	0.439673i
$891$	0.472402	−	0.472402i	0.0158261	−	0.0158261i
$892$	25.2087	+	12.4160i	0.844048	+	0.415718i
$893$	−4.74246	−	4.74246i	−0.158700	−	0.158700i
$894$	−6.53919	−	1.52302i	−0.218703	−	0.0509373i
$895$	13.6632			0.456709
$896$	−45.5543	−	1.41219i	−1.52186	−	0.0471779i
$897$	25.5084			0.851702
$898$	−9.48771	−	2.20974i	−0.316609	−	0.0737401i
$899$	8.65959	+	8.65959i	0.288813	+	0.288813i
$900$	−3.51886	−	1.73314i	−0.117295	−	0.0577714i
$901$	−11.0355	+	11.0355i	−0.367645	+	0.367645i
$902$	−0.412771	−	0.663423i	−0.0137438	−	0.0220896i
$903$		−	29.2064i		−	0.971927i
$904$	−37.8856	−	31.0448i	−1.26006	−	1.03254i
$905$		−	0.416973i		−	0.0138606i
$906$	−8.48349	+	5.27829i	−0.281845	+	0.175359i
$907$	23.4874	−	23.4874i	0.779886	−	0.779886i	−0.199925	−	0.979811i	$-0.564070\pi$
$907$	23.4874	−	23.4874i	0.779886	−	0.779886i	0.979811	+	0.199925i	$0.0640699\pi$
$908$	−12.1547	−	35.7482i	−0.403366	−	1.18635i
$909$	16.8630	+	16.8630i	0.559310	+	0.559310i
$910$	−8.98233	+	38.5663i	−0.297761	+	1.27846i
$911$	−1.77171			−0.0586993			−0.0293497	−	0.999569i	$-0.509344\pi$
$911$	−1.77171			−0.0586993			−0.0293497	+	0.999569i	$0.509344\pi$
$912$	−2.00370	+	1.54065i	−0.0663490	+	0.0510160i
$913$	−1.67493			−0.0554322
$914$	0.810392	−	3.47948i	0.0268054	−	0.115091i
$915$	7.12321	+	7.12321i	0.235486	+	0.235486i
$916$	23.5275	−	7.99951i	0.777370	−	0.264311i
$917$	−45.4285	+	45.4285i	−1.50018	+	1.50018i
$918$	−16.4457	+	10.2323i	−0.542790	+	0.337715i
$919$		−	46.2001i		−	1.52400i	−0.647576	−	0.762001i	$-0.724217\pi$
$919$		−	46.2001i		−	1.52400i	0.647576	−	0.762001i	$-0.275783\pi$
$920$	−1.00580	−	10.1348i	−0.0331603	−	0.334135i
$921$		−	16.8804i		−	0.556229i
$922$	−9.75733	−	15.6824i	−0.321340	−	0.516472i
$923$	−67.7963	+	67.7963i	−2.23154	+	2.23154i
$924$	3.31891	−	6.73849i	0.109184	−	0.221680i
$925$	0.743961	+	0.743961i	0.0244613	+	0.0244613i
$926$	15.5195	+	3.61458i	0.510002	+	0.118782i
$927$	−23.5995			−0.775110
$928$	5.64332	−	15.0505i	0.185251	−	0.494056i
$929$	−35.5011			−1.16475			−0.582376	−	0.812920i	$-0.697877\pi$
$929$	−35.5011			−1.16475			−0.582376	+	0.812920i	$0.697877\pi$
$930$	6.05018	+	1.40912i	0.198393	+	0.0462070i
$931$	4.04553	+	4.04553i	0.132587	+	0.132587i
$932$	13.3854	−	27.1769i	0.438455	−	0.890210i
$933$	8.07641	−	8.07641i	0.264410	−	0.264410i
$934$	27.2899	+	43.8615i	0.892953	+	1.43519i
$935$		−	2.47776i		−	0.0810313i
$936$	−38.3693	+	3.80785i	−1.25414	+	0.124463i
$937$			10.0385i			0.327945i	0.986465	+	0.163972i	$0.0524308\pi$
$937$			10.0385i			0.327945i	−0.986465	+	0.163972i	$0.947569\pi$
$938$	−35.8608	+	22.3120i	−1.17089	+	0.728512i
$939$	5.40962	−	5.40962i	0.176536	−	0.176536i
$940$	20.4838	−	6.96464i	0.668108	−	0.227161i
$941$	42.3367	+	42.3367i	1.38014	+	1.38014i	0.844359	+	0.535777i	$0.179981\pi$
$941$	42.3367	+	42.3367i	1.38014	+	1.38014i	0.535777	+	0.844359i	$0.320019\pi$
$942$	−2.61534	+	11.2292i	−0.0852124	+	0.365866i
$943$	2.17481			0.0708215
$944$	6.89062	+	0.900220i	0.224271	+	0.0292997i
$945$	20.3694			0.662616
$946$	−2.08750	+	8.96284i	−0.0678705	+	0.291407i
$947$	−36.3384	−	36.3384i	−1.18084	−	1.18084i	−0.979527	−	0.201313i	$-0.935479\pi$
$947$	−36.3384	−	36.3384i	−1.18084	−	1.18084i	−0.201313	−	0.979527i	$-0.564521\pi$
$948$	−0.401003	−	1.17940i	−0.0130240	−	0.0383050i
$949$	6.43246	−	6.43246i	0.208807	−	0.208807i
$950$	0.744461	−	0.463191i	0.0241535	−	0.0150279i
$951$		−	23.4729i		−	0.761161i
$952$	19.5610	−	23.8713i	0.633976	−	0.773674i
$953$			32.7338i			1.06035i	0.847888	+	0.530176i	$0.177874\pi$
$953$			32.7338i			1.06035i	−0.847888	+	0.530176i	$0.822126\pi$
$954$	8.44248	+	13.5691i	0.273335	+	0.439316i
$955$	−11.9750	+	11.9750i	−0.387502	+	0.387502i
$956$	32.1429	+	15.8313i	1.03958	+	0.512022i
$957$	1.87322	+	1.87322i	0.0605527	+	0.0605527i
$958$	21.6604	+	5.04483i	0.699815	+	0.162991i
$959$	14.7952			0.477762
$960$	−1.60255	−	7.99444i	−0.0517222	−	0.258020i
$961$	−12.4244			−0.400789
$962$	10.0726	+	2.34596i	0.324753	+	0.0756369i
$963$	4.65424	+	4.65424i	0.149981	+	0.149981i
$964$	46.0377	+	22.6749i	1.48277	+	0.730309i
$965$	−11.7328	+	11.7328i	−0.377693	+	0.377693i
$966$	11.0449	+	17.7519i	0.355365	+	0.571157i
$967$			49.7169i			1.59879i	0.600807	+	0.799394i	$0.294846\pi$
$967$			49.7169i			1.59879i	−0.600807	+	0.799394i	$0.705154\pi$
$968$	18.2197	−	22.2344i	0.585602	−	0.714641i
$969$		−	1.71153i		−	0.0549823i
$970$	15.3183	−	9.53078i	0.491840	−	0.306015i
$971$	−24.7937	+	24.7937i	−0.795667	+	0.795667i	−0.982409	−	0.186742i	$-0.940207\pi$
$971$	−24.7937	+	24.7937i	−0.795667	+	0.795667i	0.186742	+	0.982409i	$0.440207\pi$
$972$	10.2455	+	30.1332i	0.328625	+	0.966523i
$973$	21.0908	+	21.0908i	0.676139	+	0.676139i
$974$	11.3470	−	48.7192i	0.363581	−	1.56106i
$975$	−7.08410			−0.226873
$976$	5.12168	−	39.2033i	0.163941	−	1.25487i
$977$	−49.4546			−1.58219			−0.791096	−	0.611692i	$-0.790489\pi$
$977$	−49.4546			−1.58219			−0.791096	+	0.611692i	$0.790489\pi$
$978$	5.07434	−	21.7871i	0.162260	−	0.696674i
$979$	7.06579	+	7.06579i	0.225824	+	0.225824i
$980$	−17.4736	+	5.94115i	−0.558174	+	0.189783i
$981$	−6.36387	+	6.36387i	−0.203183	+	0.203183i
$982$	−13.5122	+	8.40706i	−0.431191	+	0.268280i
$983$		−	23.9656i		−	0.764383i	−0.924083	−	0.382191i	$-0.875170\pi$
$983$		−	23.9656i		−	0.764383i	0.924083	−	0.382191i	$-0.124830\pi$
$984$	1.73257	−	0.171944i	0.0552324	−	0.00548138i
$985$			3.37137i			0.107421i
$986$	5.75000	+	9.24164i	0.183117	+	0.294314i
$987$	−31.4056	+	31.4056i	−0.999650	+	0.999650i
$988$	3.80814	−	7.73180i	0.121153	−	0.245981i
$989$	−18.1124	−	18.1124i	−0.575940	−	0.575940i
$990$	−2.47110	−	0.575533i	−0.0785366	−	0.0182916i
$991$	28.8345			0.915957			0.457978	−	0.888963i	$-0.348574\pi$
$991$	28.8345			0.915957			0.457978	+	0.888963i	$0.348574\pi$
$992$	−10.0896	−	22.1950i	−0.320345	−	0.704692i
$993$	27.9399			0.886645
$994$	−76.5361	−	17.8257i	−2.42758	−	0.565397i
$995$	−7.17084	−	7.17084i	−0.227331	−	0.227331i
$996$	1.64907	−	3.34817i	0.0522529	−	0.106091i
$997$	6.03212	−	6.03212i	0.191039	−	0.191039i	−0.605106	−	0.796145i	$-0.706869\pi$
$997$	6.03212	−	6.03212i	0.191039	−	0.191039i	0.796145	+	0.605106i	$0.206869\pi$
$998$	−12.2416	−	19.6753i	−0.387503	−	0.622811i
$999$		−	5.31998i		−	0.168317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.l.a.61.1	yes	16
3.2	odd	2		720.2.t.c.541.8		16
4.3	odd	2		320.2.l.a.81.6		16
5.2	odd	4		400.2.q.h.349.4		16
5.3	odd	4		400.2.q.g.349.5		16
5.4	even	2		400.2.l.h.301.8		16
8.3	odd	2		640.2.l.a.161.3		16
8.5	even	2		640.2.l.b.161.6		16
12.11	even	2		2880.2.t.c.721.4		16
16.3	odd	4		640.2.l.a.481.3		16
16.5	even	4	inner	80.2.l.a.21.1	✓	16
16.11	odd	4		320.2.l.a.241.6		16
16.13	even	4		640.2.l.b.481.6		16
20.3	even	4		1600.2.q.h.849.3		16
20.7	even	4		1600.2.q.g.849.6		16
20.19	odd	2		1600.2.l.i.401.3		16
32.5	even	8		5120.2.a.v.1.5		8
32.11	odd	8		5120.2.a.u.1.5		8
32.21	even	8		5120.2.a.s.1.4		8
32.27	odd	8		5120.2.a.t.1.4		8
48.5	odd	4		720.2.t.c.181.8		16
48.11	even	4		2880.2.t.c.2161.1		16
80.27	even	4		1600.2.q.h.49.3		16
80.37	odd	4		400.2.q.g.149.5		16
80.43	even	4		1600.2.q.g.49.6		16
80.53	odd	4		400.2.q.h.149.4		16
80.59	odd	4		1600.2.l.i.1201.3		16
80.69	even	4		400.2.l.h.101.8		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.1	✓	16	16.5	even	4	inner
80.2.l.a.61.1	yes	16	1.1	even	1	trivial
320.2.l.a.81.6		16	4.3	odd	2
320.2.l.a.241.6		16	16.11	odd	4
400.2.l.h.101.8		16	80.69	even	4
400.2.l.h.301.8		16	5.4	even	2
400.2.q.g.149.5		16	80.37	odd	4
400.2.q.g.349.5		16	5.3	odd	4
400.2.q.h.149.4		16	80.53	odd	4
400.2.q.h.349.4		16	5.2	odd	4
640.2.l.a.161.3		16	8.3	odd	2
640.2.l.a.481.3		16	16.3	odd	4
640.2.l.b.161.6		16	8.5	even	2
640.2.l.b.481.6		16	16.13	even	4
720.2.t.c.181.8		16	48.5	odd	4
720.2.t.c.541.8		16	3.2	odd	2
1600.2.l.i.401.3		16	20.19	odd	2
1600.2.l.i.1201.3		16	80.59	odd	4
1600.2.q.g.49.6		16	80.43	even	4
1600.2.q.g.849.6		16	20.7	even	4
1600.2.q.h.49.3		16	80.27	even	4
1600.2.q.h.849.3		16	20.3	even	4
2880.2.t.c.721.4		16	12.11	even	2
2880.2.t.c.2161.1		16	48.11	even	4
5120.2.a.s.1.4		8	32.21	even	8
5120.2.a.t.1.4		8	32.27	odd	8
5120.2.a.u.1.5		8	32.11	odd	8
5120.2.a.v.1.5		8	32.5	even	8

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.37735 - 0.320793i) q^{2} +(-0.720673 - 0.720673i) q^{3} +(1.79418 + 0.883688i) q^{4} +(0.707107 - 0.707107i) q^{5} +(0.761432 + 1.22381i) q^{6} -4.02840i q^{7} +(-2.18774 - 1.79271i) q^{8} -1.96126i q^{9} +(-1.20077 + 0.747098i) q^{10} +(-0.646837 + 0.646837i) q^{11} +(-0.656170 - 1.92987i) q^{12} +(4.91492 + 4.91492i) q^{13} +(-1.29228 + 5.54851i) q^{14} -1.01919 q^{15} +(2.43819 + 3.17100i) q^{16} -2.70862 q^{17} +(-0.629159 + 2.70134i) q^{18} +(-0.438397 - 0.438397i) q^{19} +(1.89354 - 0.643818i) q^{20} +(-2.90316 + 2.90316i) q^{21} +(1.09842 - 0.683420i) q^{22} +3.60080i q^{23} +(0.284686 + 2.86860i) q^{24} -1.00000i q^{25} +(-5.19289 - 8.34623i) q^{26} +(-3.57545 + 3.57545i) q^{27} +(3.55985 - 7.22769i) q^{28} +(2.00921 + 2.00921i) q^{29} +(1.40377 + 0.326948i) q^{30} +4.30994 q^{31} +(-2.34101 - 5.14973i) q^{32} +0.932316 q^{33} +(3.73072 + 0.868908i) q^{34} +(-2.84851 - 2.84851i) q^{35} +(1.73314 - 3.51886i) q^{36} +(-0.743961 + 0.743961i) q^{37} +(0.463191 + 0.744461i) q^{38} -7.08410i q^{39} +(-2.81460 + 0.279327i) q^{40} -0.603979i q^{41} +(4.92998 - 3.06735i) q^{42} +(-5.03010 + 5.03010i) q^{43} +(-1.73215 + 0.588942i) q^{44} +(-1.38682 - 1.38682i) q^{45} +(1.15511 - 4.95956i) q^{46} +10.8177 q^{47} +(0.528115 - 4.04239i) q^{48} -9.22800 q^{49} +(-0.320793 + 1.37735i) q^{50} +(1.95203 + 1.95203i) q^{51} +(4.47501 + 13.1615i) q^{52} +(4.07420 - 4.07420i) q^{53} +(6.07162 - 3.77766i) q^{54} +0.914766i q^{55} +(-7.22175 + 8.81308i) q^{56} +0.631882i q^{57} +(-2.12285 - 3.41193i) q^{58} +(1.22845 - 1.22845i) q^{59} +(-1.82861 - 0.900642i) q^{60} +(-6.98912 - 6.98912i) q^{61} +(-5.93629 - 1.38260i) q^{62} -7.90074 q^{63} +(1.57239 + 7.84395i) q^{64} +6.95074 q^{65} +(-1.28413 - 0.299081i) q^{66} +(5.24219 + 5.24219i) q^{67} +(-4.85977 - 2.39358i) q^{68} +(2.59500 - 2.59500i) q^{69} +(3.00961 + 4.83717i) q^{70} +13.7940i q^{71} +(-3.51597 + 4.29072i) q^{72} -1.30876i q^{73} +(1.26335 - 0.786036i) q^{74} +(-0.720673 + 0.720673i) q^{75} +(-0.399159 - 1.17397i) q^{76} +(2.60572 + 2.60572i) q^{77} +(-2.27253 + 9.75728i) q^{78} +0.611127 q^{79} +(3.96630 + 0.518173i) q^{80} -0.730326 q^{81} +(-0.193752 + 0.831890i) q^{82} +(1.29471 + 1.29471i) q^{83} +(-7.77429 + 2.64331i) q^{84} +(-1.91529 + 1.91529i) q^{85} +(8.54182 - 5.31458i) q^{86} -2.89597i q^{87} +(2.57470 - 0.255519i) q^{88} -10.9236i q^{89} +(1.46525 + 2.35502i) q^{90} +(19.7993 - 19.7993i) q^{91} +(-3.18199 + 6.46050i) q^{92} +(-3.10606 - 3.10606i) q^{93} +(-14.8998 - 3.47025i) q^{94} -0.619987 q^{95} +(-2.02417 + 5.39837i) q^{96} -12.7571 q^{97} +(12.7102 + 2.96028i) q^{98} +(1.26862 + 1.26862i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} - 12 q^{6} + 4 q^{10} - 8 q^{11} - 12 q^{12} + 4 q^{14} - 8 q^{15} + 16 q^{16} - 8 q^{19} + 8 q^{20} - 20 q^{22} + 8 q^{24} - 16 q^{26} + 24 q^{27} - 4 q^{28} - 16 q^{29} + 16 q^{34} - 4 q^{36}+ \cdots - 8 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 - 12 * q^6 + 4 * q^10 - 8 * q^11 - 12 * q^12 + 4 * q^14 - 8 * q^15 + 16 * q^16 - 8 * q^19 + 8 * q^20 - 20 * q^22 + 8 * q^24 - 16 * q^26 + 24 * q^27 - 4 * q^28 - 16 * q^29 + 16 * q^34 - 4 * q^36 - 16 * q^37 + 20 * q^38 + 60 * q^42 + 8 * q^43 + 40 * q^44 - 4 * q^46 - 40 * q^47 - 40 * q^48 - 16 * q^49 - 4 * q^50 - 32 * q^51 + 56 * q^52 + 16 * q^53 + 32 * q^54 + 16 * q^56 - 12 * q^58 - 8 * q^59 - 28 * q^60 + 16 * q^61 - 8 * q^62 + 40 * q^63 - 16 * q^64 + 40 * q^67 - 48 * q^68 + 16 * q^69 - 8 * q^70 - 40 * q^72 - 72 * q^74 + 16 * q^77 - 16 * q^78 + 16 * q^79 + 16 * q^80 - 16 * q^81 - 76 * q^82 + 40 * q^83 - 64 * q^84 - 16 * q^85 + 28 * q^86 + 36 * q^90 + 32 * q^91 - 52 * q^92 - 48 * q^93 - 36 * q^94 + 32 * q^95 + 8 * q^96 + 60 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more