LMFDB - Embedded newform 224.2.bd.a.109.26

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [224,2,Mod(37,224)] 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("224.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(224, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([0, 3, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.bd (of order $24$, degree $8$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{24})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			109.26
Character	$\chi$	$=$	224.109
Dual form			224.2.bd.a.37.26

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.28627 + 0.587810i) q^{2} +(0.485121 + 0.632222i) q^{3} +(1.30896 + 1.51216i) q^{4} +(-0.749996 - 0.575492i) q^{5} +(0.252368 + 1.09836i) q^{6} +(-1.13756 + 2.38872i) q^{7} +(0.794808 + 2.71446i) q^{8} +(0.612095 - 2.28437i) q^{9} +(-0.626414 - 1.18109i) q^{10} +(2.53563 + 0.333822i) q^{11} +(-0.321016 + 1.56113i) q^{12} +(-0.319285 - 0.132252i) q^{13} +(-2.86731 + 2.40386i) q^{14} -0.753347i q^{15} +(-0.573250 + 3.95871i) q^{16} +(-2.51905 - 1.45438i) q^{17} +(2.13009 - 2.57851i) q^{18} +(-0.559620 - 4.25074i) q^{19} +(-0.111479 - 1.88741i) q^{20} +(-2.06205 + 0.439629i) q^{21} +(3.06527 + 1.91985i) q^{22} +(1.37917 - 5.14712i) q^{23} +(-1.33056 + 1.81934i) q^{24} +(-1.06279 - 3.96640i) q^{25} +(-0.332946 - 0.357790i) q^{26} +(3.94988 - 1.63609i) q^{27} +(-5.10113 + 1.40657i) q^{28} +(-1.28920 + 3.11239i) q^{29} +(0.442825 - 0.969004i) q^{30} +(-3.12364 + 5.41030i) q^{31} +(-3.06432 + 4.75499i) q^{32} +(1.01904 + 1.76503i) q^{33} +(-2.38528 - 3.35144i) q^{34} +(2.22785 - 1.13687i) q^{35} +(4.25554 - 2.06456i) q^{36} +(-0.385287 - 0.295641i) q^{37} +(1.77880 - 5.79653i) q^{38} +(-0.0712791 - 0.266017i) q^{39} +(0.966046 - 2.49324i) q^{40} +(-5.69568 - 5.69568i) q^{41} +(-2.91076 - 0.646614i) q^{42} +(2.80501 + 6.77189i) q^{43} +(2.81425 + 4.27124i) q^{44} +(-1.77370 + 1.36101i) q^{45} +(4.79950 - 5.80987i) q^{46} +(6.43663 - 3.71619i) q^{47} +(-2.78088 + 1.55803i) q^{48} +(-4.41194 - 5.43460i) q^{49} +(0.964452 - 5.72656i) q^{50} +(-0.302557 - 2.29815i) q^{51} +(-0.217945 - 0.655923i) q^{52} +(8.42902 + 1.10970i) q^{53} +(6.04231 + 0.217326i) q^{54} +(-1.70960 - 1.70960i) q^{55} +(-7.38821 - 1.18927i) q^{56} +(2.41593 - 2.41593i) q^{57} +(-3.48774 + 3.24556i) q^{58} +(-0.466000 + 3.53962i) q^{59} +(1.13918 - 0.986101i) q^{60} +(-12.8622 + 1.69334i) q^{61} +(-7.19805 + 5.12298i) q^{62} +(4.76042 + 4.06072i) q^{63} +(-6.73656 + 4.31495i) q^{64} +(0.163352 + 0.282935i) q^{65} +(0.273255 + 2.86929i) q^{66} +(-0.130990 - 0.170710i) q^{67} +(-1.09809 - 5.71293i) q^{68} +(3.92318 - 1.62503i) q^{69} +(3.53387 - 0.152770i) q^{70} +(-3.16194 + 3.16194i) q^{71} +(6.68732 - 0.154130i) q^{72} +(-3.47703 + 0.931668i) q^{73} +(-0.321800 - 0.606748i) q^{74} +(1.99206 - 2.59610i) q^{75} +(5.69527 - 6.41028i) q^{76} +(-3.68183 + 5.67716i) q^{77} +(0.0646837 - 0.384068i) q^{78} +(-3.13466 + 1.80979i) q^{79} +(2.70814 - 2.63911i) q^{80} +(-3.19378 - 1.84393i) q^{81} +(-3.97818 - 10.6741i) q^{82} +(13.8948 + 5.75543i) q^{83} +(-3.36393 - 2.54269i) q^{84} +(1.05230 + 2.54047i) q^{85} +(-0.372596 + 10.3593i) q^{86} +(-2.59314 + 0.694829i) q^{87} +(1.10919 + 7.14819i) q^{88} +(4.31608 + 1.15649i) q^{89} +(-3.08147 + 0.708022i) q^{90} +(0.679118 - 0.612238i) q^{91} +(9.58853 - 4.65185i) q^{92} +(-4.93585 + 0.649817i) q^{93} +(10.4636 - 0.996495i) q^{94} +(-2.02655 + 3.51009i) q^{95} +(-4.49278 + 0.369416i) q^{96} +11.3290 q^{97} +(-2.48041 - 9.58371i) q^{98} +(2.31462 - 5.58799i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) $ 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{8}\right)$

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 $

$2$	1.28627	+	0.587810i	0.909527	+	0.415644i
$2$	1.28627	+	0.587810i	0.909527	+	0.415644i
$3$	0.485121	+	0.632222i	0.280085	+	0.365013i	0.912118	−	0.409928i	$-0.134446\pi$
$3$	0.485121	+	0.632222i	0.280085	+	0.365013i	−0.632033	+	0.774941i	$0.717779\pi$
$4$	1.30896	+	1.51216i	0.654480	+	0.756080i
$5$	−0.749996	−	0.575492i	−0.335408	−	0.257368i	0.427301	−	0.904110i	$-0.359465\pi$
$5$	−0.749996	−	0.575492i	−0.335408	−	0.257368i	−0.762709	+	0.646742i	$0.776131\pi$
$6$	0.252368	+	1.09836i	0.103029	+	0.448405i
$7$	−1.13756	+	2.38872i	−0.429956	+	0.902850i
$7$	−1.13756	+	2.38872i	−0.429956	+	0.902850i
$8$	0.794808	+	2.71446i	0.281007	+	0.959706i
$9$	0.612095	−	2.28437i	0.204032	−	0.761456i
$10$	−0.626414	−	1.18109i	−0.198090	−	0.373494i
$11$	2.53563	+	0.333822i	0.764522	+	0.100651i	0.502695	−	0.864464i	$-0.332342\pi$
$11$	2.53563	+	0.333822i	0.764522	+	0.100651i	0.261827	+	0.965115i	$0.415675\pi$
$12$	−0.321016	+	1.56113i	−0.0926694	+	0.450660i
$13$	−0.319285	−	0.132252i	−0.0885538	−	0.0366802i	0.337967	−	0.941158i	$-0.390261\pi$
$13$	−0.319285	−	0.132252i	−0.0885538	−	0.0366802i	−0.426521	+	0.904478i	$0.640261\pi$
$14$	−2.86731	+	2.40386i	−0.766321	+	0.642458i
$15$		−	0.753347i		−	0.194513i
$16$	−0.573250	+	3.95871i	−0.143312	+	0.989677i
$17$	−2.51905	−	1.45438i	−0.610960	−	0.352738i	0.162381	−	0.986728i	$-0.448083\pi$
$17$	−2.51905	−	1.45438i	−0.610960	−	0.352738i	−0.773341	+	0.633990i	$0.781416\pi$
$18$	2.13009	−	2.57851i	0.502067	−	0.607761i
$19$	−0.559620	−	4.25074i	−0.128386	−	0.975186i	−0.927452	−	0.373943i	$-0.878006\pi$
$19$	−0.559620	−	4.25074i	−0.128386	−	0.975186i	0.799066	−	0.601243i	$-0.205328\pi$
$20$	−0.111479	−	1.88741i	−0.0249274	−	0.422037i
$21$	−2.06205	+	0.439629i	−0.449976	+	0.0959349i
$22$	3.06527	+	1.91985i	0.653518	+	0.409314i
$23$	1.37917	−	5.14712i	0.287576	−	1.07325i	−0.659361	−	0.751827i	$-0.729173\pi$
$23$	1.37917	−	5.14712i	0.287576	−	1.07325i	0.946936	−	0.321421i	$-0.104160\pi$
$24$	−1.33056	+	1.81934i	−0.271600	+	0.371370i
$25$	−1.06279	−	3.96640i	−0.212559	−	0.793279i
$26$	−0.332946	−	0.357790i	−0.0652962	−	0.0701685i
$27$	3.94988	−	1.63609i	0.760155	−	0.314867i
$28$	−5.10113	+	1.40657i	−0.964024	+	0.265817i
$29$	−1.28920	+	3.11239i	−0.239398	+	0.577957i	−0.997221	−	0.0745031i	$-0.976263\pi$
$29$	−1.28920	+	3.11239i	−0.239398	+	0.577957i	0.757823	+	0.652460i	$0.226263\pi$
$30$	0.442825	−	0.969004i	0.0808483	−	0.176915i
$31$	−3.12364	+	5.41030i	−0.561022	+	0.971718i	0.436386	+	0.899760i	$0.356258\pi$
$31$	−3.12364	+	5.41030i	−0.561022	+	0.971718i	−0.997408	+	0.0719586i	$0.977075\pi$
$32$	−3.06432	+	4.75499i	−0.541700	+	0.840572i
$33$	1.01904	+	1.76503i	0.177392	+	0.307252i
$34$	−2.38528	−	3.35144i	−0.409072	−	0.574767i
$35$	2.22785	−	1.13687i	0.376575	−	0.192167i
$36$	4.25554	−	2.06456i	0.709256	−	0.344094i
$37$	−0.385287	−	0.295641i	−0.0633407	−	0.0486031i	0.576606	−	0.817022i	$-0.304377\pi$
$37$	−0.385287	−	0.295641i	−0.0633407	−	0.0486031i	−0.639947	+	0.768419i	$0.721044\pi$
$38$	1.77880	−	5.79653i	0.288560	−	0.940321i
$39$	−0.0712791	−	0.266017i	−0.0114138	−	0.0425969i
$40$	0.966046	−	2.49324i	0.152745	−	0.394215i
$41$	−5.69568	−	5.69568i	−0.889516	−	0.889516i	0.104960	−	0.994476i	$-0.466528\pi$
$41$	−5.69568	−	5.69568i	−0.889516	−	0.889516i	−0.994476	+	0.104960i	$0.966528\pi$
$42$	−2.91076	−	0.646614i	−0.449141	−	0.0997747i
$43$	2.80501	+	6.77189i	0.427760	+	1.03270i	0.979996	+	0.199016i	$0.0637745\pi$
$43$	2.80501	+	6.77189i	0.427760	+	1.03270i	−0.552237	+	0.833687i	$0.686225\pi$
$44$	2.81425	+	4.27124i	0.424264	+	0.643913i
$45$	−1.77370	+	1.36101i	−0.264408	+	0.202888i
$46$	4.79950	−	5.80987i	0.707647	−	0.856619i
$47$	6.43663	−	3.71619i	0.938879	−	0.542062i	0.0492703	−	0.998785i	$-0.484310\pi$
$47$	6.43663	−	3.71619i	0.938879	−	0.542062i	0.889609	+	0.456723i	$0.150977\pi$
$48$	−2.78088	+	1.55803i	−0.401385	+	0.224883i
$49$	−4.41194	−	5.43460i	−0.630277	−	0.776371i
$50$	0.964452	−	5.72656i	0.136394	−	0.809858i
$51$	−0.302557	−	2.29815i	−0.0423665	−	0.321805i
$52$	−0.217945	−	0.655923i	−0.0302235	−	0.0909601i
$53$	8.42902	+	1.10970i	1.15782	+	0.152429i	0.684872	−	0.728663i	$-0.259858\pi$
$53$	8.42902	+	1.10970i	1.15782	+	0.152429i	0.472944	+	0.881093i	$0.343191\pi$
$54$	6.04231	+	0.217326i	0.822254	+	0.0295744i
$55$	−1.70960	−	1.70960i	−0.230523	−	0.230523i
$56$	−7.38821	−	1.18927i	−0.987291	−	0.158923i
$57$	2.41593	−	2.41593i	0.319997	−	0.319997i
$58$	−3.48774	+	3.24556i	−0.457963	+	0.426163i
$59$	−0.466000	+	3.53962i	−0.0606680	+	0.460819i	0.933966	+	0.357362i	$0.116324\pi$
$59$	−0.466000	+	3.53962i	−0.0606680	+	0.460819i	−0.994634	+	0.103457i	$0.967010\pi$
$60$	1.13918	−	0.986101i	0.147068	−	0.127305i
$61$	−12.8622	+	1.69334i	−1.64684	+	0.216810i	−0.896119	−	0.443813i	$-0.853625\pi$
$61$	−12.8622	+	1.69334i	−1.64684	+	0.216810i	−0.750717	+	0.660623i	$0.770292\pi$
$62$	−7.19805	+	5.12298i	−0.914154	+	0.650619i
$63$	4.76042	+	4.06072i	0.599756	+	0.511602i
$64$	−6.73656	+	4.31495i	−0.842070	+	0.539368i
$65$	0.163352	+	0.282935i	0.0202614	+	0.0350937i
$66$	0.273255	+	2.86929i	0.0336353	+	0.353186i
$67$	−0.130990	−	0.170710i	−0.0160030	−	0.0208555i	0.785283	−	0.619137i	$-0.212517\pi$
$67$	−0.130990	−	0.170710i	−0.0160030	−	0.0208555i	−0.801286	+	0.598281i	$0.795851\pi$
$68$	−1.09809	−	5.71293i	−0.133163	−	0.692795i
$69$	3.92318	−	1.62503i	0.472295	−	0.195631i
$70$	3.53387	−	0.152770i	0.422378	−	0.0182595i
$71$	−3.16194	+	3.16194i	−0.375253	+	0.375253i	−0.869386	−	0.494133i	$-0.835485\pi$
$71$	−3.16194	+	3.16194i	−0.375253	+	0.375253i	0.494133	+	0.869386i	$0.335485\pi$
$72$	6.68732	−	0.154130i	0.788108	−	0.0181644i
$73$	−3.47703	+	0.931668i	−0.406956	+	0.109043i	−0.456489	−	0.889729i	$-0.650893\pi$
$73$	−3.47703	+	0.931668i	−0.406956	+	0.109043i	0.0495334	+	0.998772i	$0.484227\pi$
$74$	−0.321800	−	0.606748i	−0.0374085	−	0.0705330i
$75$	1.99206	−	2.59610i	0.230023	−	0.299772i
$76$	5.69527	−	6.41028i	0.653292	−	0.735309i
$77$	−3.68183	+	5.67716i	−0.419583	+	0.646973i
$78$	0.0646837	−	0.384068i	0.00732398	−	0.0434871i
$79$	−3.13466	+	1.80979i	−0.352676	+	0.203618i	−0.665863	−	0.746074i	$-0.731937\pi$
$79$	−3.13466	+	1.80979i	−0.352676	+	0.203618i	0.313187	+	0.949691i	$0.398603\pi$
$80$	2.70814	−	2.63911i	0.302779	−	0.295062i
$81$	−3.19378	−	1.84393i	−0.354865	−	0.204881i
$82$	−3.97818	−	10.6741i	−0.439317	−	1.17876i
$83$	13.8948	+	5.75543i	1.52516	+	0.631741i	0.978617	−	0.205691i	$-0.0659443\pi$
$83$	13.8948	+	5.75543i	1.52516	+	0.631741i	0.546541	+	0.837432i	$0.315944\pi$
$84$	−3.36393	−	2.54269i	−0.367035	−	0.277430i
$85$	1.05230	+	2.54047i	0.114138	+	0.275553i
$86$	−0.372596	+	10.3593i	−0.0401780	+	1.11707i
$87$	−2.59314	+	0.694829i	−0.278014	+	0.0744935i
$88$	1.10919	+	7.14819i	0.118241	+	0.762000i
$89$	4.31608	+	1.15649i	0.457504	+	0.122588i	0.480208	−	0.877154i	$-0.340561\pi$
$89$	4.31608	+	1.15649i	0.457504	+	0.122588i	−0.0227046	+	0.999742i	$0.507228\pi$
$90$	−3.08147	+	0.708022i	−0.324816	+	0.0746320i
$91$	0.679118	−	0.612238i	0.0711909	−	0.0641799i
$92$	9.58853	−	4.65185i	0.999673	−	0.484989i
$93$	−4.93585	+	0.649817i	−0.511824	+	0.0673829i
$94$	10.4636	−	0.996495i	1.07924	−	0.102781i
$95$	−2.02655	+	3.51009i	−0.207920	+	0.360128i
$96$	−4.49278	+	0.369416i	−0.458542	+	0.0377033i
$97$	11.3290			1.15028			0.575141	−	0.818054i	$-0.304947\pi$
$97$	11.3290			1.15028			0.575141	+	0.818054i	$0.304947\pi$
$98$	−2.48041	−	9.58371i	−0.250560	−	0.968101i
$99$	2.31462	−	5.58799i	0.232628	−	0.561614i
$100$	4.60667	−	6.79896i	0.460667	−	0.679896i
$101$	−1.80254	+	13.6916i	−0.179359	+	1.36237i	0.630704	+	0.776024i	$0.282766\pi$
$101$	−1.80254	+	13.6916i	−0.179359	+	1.36237i	−0.810063	+	0.586343i	$0.800567\pi$
$102$	0.961706	−	3.13388i	0.0952231	−	0.310300i
$103$	−14.9796	−	4.01376i	−1.47598	−	0.395488i	−0.571003	−	0.820948i	$-0.693445\pi$
$103$	−14.9796	−	4.01376i	−1.47598	−	0.395488i	−0.904977	+	0.425461i	$0.860112\pi$
$104$	0.105223	−	0.971801i	0.0103179	−	0.0952929i
$105$	1.79953	+	0.856974i	0.175616	+	0.0836321i
$106$	10.1897	+	6.38203i	0.989709	+	0.619878i
$107$	−11.2889	+	14.7119i	−1.09133	+	1.42226i	−0.193947	+	0.981012i	$0.562129\pi$
$107$	−11.2889	+	14.7119i	−1.09133	+	1.42226i	−0.897388	+	0.441243i	$0.854538\pi$
$108$	7.64427	+	3.83127i	0.735570	+	0.368664i
$109$	5.90918	−	4.53427i	0.565996	−	0.434304i	−0.285716	−	0.958314i	$-0.592231\pi$
$109$	5.90918	−	4.53427i	0.565996	−	0.434304i	0.851712	+	0.524010i	$0.175565\pi$
$110$	−1.19408	−	3.20392i	−0.113851	−	0.305482i
$111$		−	0.387008i		−	0.0367332i
$112$	−8.80413	−	5.87258i	−0.831912	−	0.554907i
$113$			9.78669i			0.920654i	0.887749	+	0.460327i	$0.152268\pi$
$113$			9.78669i			0.920654i	−0.887749	+	0.460327i	$0.847732\pi$
$114$	4.52763	−	1.68742i	0.424051	−	0.158041i
$115$	−3.99649	+	3.06662i	−0.372675	+	0.285963i
$116$	−6.39394	+	2.12453i	−0.593662	+	0.197257i
$117$	−0.497546	+	0.648414i	−0.0459981	+	0.0599459i
$118$	−2.68002	+	4.27897i	−0.246716	+	0.393911i
$119$	6.33966	−	4.36287i	0.581155	−	0.399944i
$120$	2.04493	−	0.598766i	0.186676	−	0.0546596i
$121$	−4.30719	−	1.15411i	−0.391563	−	0.104919i
$122$	−17.5396	−	5.38244i	−1.58796	−	0.487303i
$123$	0.837840	−	6.36403i	0.0755455	−	0.573825i
$124$	−12.2699	+	2.35843i	−1.10187	+	0.211793i
$125$	−3.29439	+	7.95335i	−0.294659	+	0.711369i
$126$	3.73624	+	8.02138i	0.332850	+	0.714602i
$127$	−4.97732			−0.441666			−0.220833	−	0.975312i	$-0.570877\pi$
$127$	−4.97732			−0.441666			−0.220833	+	0.975312i	$0.570877\pi$
$128$	−11.2014	+	1.59035i	−0.990071	+	0.140569i
$129$	−2.92057	+	5.05857i	−0.257142	+	0.445382i
$130$	0.0438029	+	0.459949i	0.00384177	+	0.0403402i
$131$	14.4877	−	1.90734i	1.26579	−	0.166645i	0.532425	−	0.846477i	$-0.321281\pi$
$131$	14.4877	−	1.90734i	1.26579	−	0.166645i	0.733367	+	0.679833i	$0.237948\pi$
$132$	−1.33512	+	3.85130i	−0.116207	+	0.335212i
$133$	10.7904	+	3.49867i	0.935647	+	0.303374i
$134$	−0.0681434	−	0.296576i	−0.00588670	−	0.0256202i
$135$	−3.90395	−	1.04606i	−0.335999	−	0.0900306i
$136$	1.94568	−	7.99382i	0.166841	−	0.685464i
$137$	11.3598	−	3.04384i	0.970529	−	0.260052i	0.261478	−	0.965209i	$-0.415790\pi$
$137$	11.3598	−	3.04384i	0.970529	−	0.260052i	0.709051	+	0.705157i	$0.249124\pi$
$138$	6.00146	+	0.215857i	0.510879	+	0.0183750i
$139$	5.04163	+	12.1716i	0.427626	+	1.03238i	0.980038	+	0.198809i	$0.0637074\pi$
$139$	5.04163	+	12.1716i	0.427626	+	1.03238i	−0.552412	+	0.833571i	$0.686293\pi$
$140$	4.63530	+	1.88074i	0.391754	+	0.158952i
$141$	5.47200	+	2.26658i	0.460826	+	0.190880i
$142$	−5.92571	+	2.20847i	−0.497274	+	0.185331i
$143$	−0.765441	−	0.441927i	−0.0640094	−	0.0369558i
$144$	8.69227	+	3.73262i	0.724356	+	0.311052i
$145$	2.75805	−	1.59236i	0.229043	−	0.132238i
$146$	−5.02003	−	0.845460i	−0.415461	−	0.0699708i
$147$	1.29555	−	5.42576i	0.106855	−	0.447509i
$148$	−0.0572687	−	0.969597i	−0.00470746	−	0.0797003i
$149$	13.1747	−	17.1696i	1.07931	−	1.40659i	0.172521	−	0.985006i	$-0.444809\pi$
$149$	13.1747	−	17.1696i	1.07931	−	1.40659i	0.906791	−	0.421581i	$-0.138525\pi$
$150$	4.08833	−	2.16833i	0.333811	−	0.177043i
$151$	−17.9132	+	4.79982i	−1.45775	+	0.390604i	−0.898713	−	0.438537i	$-0.855497\pi$
$151$	−17.9132	+	4.79982i	−1.45775	+	0.390604i	−0.559040	+	0.829141i	$0.688830\pi$
$152$	11.0937	−	4.89759i	0.899814	−	0.397247i
$153$	−4.86423	+	4.86423i	−0.393250	+	0.393250i
$154$	−8.07290	+	5.13813i	−0.650533	+	0.414042i
$155$	5.45630	−	2.26007i	0.438260	−	0.181533i
$156$	0.308959	−	0.455991i	0.0247365	−	0.0365085i
$157$	5.31561	+	6.92743i	0.424231	+	0.552869i	0.955751	−	0.294177i	$-0.0950455\pi$
$157$	5.31561	+	6.92743i	0.424231	+	0.552869i	−0.531520	+	0.847046i	$0.678379\pi$
$158$	−5.09582	+	0.485296i	−0.405401	+	0.0386081i
$159$	3.38752	+	5.86735i	0.268648	+	0.465311i
$160$	5.03469	−	1.80273i	0.398027	−	0.142518i
$161$	10.7261	+	9.14956i	0.845337	+	0.721087i
$162$	−3.02417	−	4.24912i	−0.237602	−	0.333843i
$163$	−0.644519	+	0.0848526i	−0.0504826	+	0.00664617i	−0.155725	−	0.987800i	$-0.549771\pi$
$163$	−0.644519	+	0.0848526i	−0.0504826	+	0.00664617i	0.105243	+	0.994447i	$0.466438\pi$
$164$	1.15736	−	16.0682i	0.0903746	−	1.25471i
$165$	0.251484	−	1.91021i	0.0195780	−	0.148710i
$166$	14.4894	+	15.5705i	1.12459	+	1.20851i
$167$	−3.02336	+	3.02336i	−0.233954	+	0.233954i	−0.814341	−	0.580387i	$-0.802901\pi$
$167$	−3.02336	+	3.02336i	−0.233954	+	0.233954i	0.580387	+	0.814341i	$0.302901\pi$
$168$	−2.83229	−	5.24793i	−0.218516	−	0.404887i
$169$	−9.10794	−	9.10794i	−0.700610	−	0.700610i
$170$	−0.139779	+	3.88627i	−0.0107206	+	0.298064i
$171$	−10.0528	−	1.32348i	−0.768756	−	0.101209i
$172$	−6.56853	+	13.1057i	−0.500846	+	0.999304i
$173$	−1.70912	−	12.9820i	−0.129942	−	0.987005i	−0.924865	−	0.380295i	$-0.875822\pi$
$173$	−1.70912	−	12.9820i	−0.129942	−	0.987005i	0.794924	−	0.606710i	$-0.207511\pi$
$174$	−3.74389	−	0.630537i	−0.283824	−	0.0478009i
$175$	10.6836	+	1.97328i	0.807603	+	0.149166i
$176$	−2.77506	+	9.84647i	−0.209178	+	0.742205i
$177$	−2.46389	+	1.42253i	−0.185197	+	0.106924i
$178$	4.87183	+	4.02459i	0.365159	+	0.301656i
$179$	2.02704	−	1.55540i	0.151508	−	0.116256i	−0.530226	−	0.847857i	$-0.677893\pi$
$179$	2.02704	−	1.55540i	0.151508	−	0.116256i	0.681734	+	0.731600i	$0.261226\pi$
$180$	−4.37977	−	0.900615i	−0.326449	−	0.0671279i
$181$	−4.29280	−	10.3637i	−0.319081	−	0.770331i	−0.999303	−	0.0373244i	$-0.988117\pi$
$181$	−4.29280	−	10.3637i	−0.319081	−	0.770331i	0.680222	−	0.733006i	$-0.261883\pi$
$182$	1.23341	−	0.388308i	0.0914261	−	0.0287833i
$183$	−7.31029	−	7.31029i	−0.540392	−	0.540392i
$184$	15.0678	−	0.347284i	1.11081	−	0.0256021i
$185$	0.118824	+	0.443459i	0.00873614	+	0.0326037i
$186$	−6.73078	−	2.06550i	−0.493525	−	0.151450i
$187$	−5.90189	−	4.52868i	−0.431589	−	0.331170i
$188$	14.0448	+	4.86887i	1.02432	+	0.355099i
$189$	−0.585043	+	11.2963i	−0.0425556	+	0.821685i
$190$	−4.66995	+	3.32368i	−0.338794	+	0.241125i
$191$	−2.04423	−	3.54071i	−0.147915	−	0.256197i	0.782541	−	0.622599i	$-0.213923\pi$
$191$	−2.04423	−	3.54071i	−0.147915	−	0.256197i	−0.930457	+	0.366402i	$0.880590\pi$
$192$	−5.99605	−	2.16573i	−0.432728	−	0.156298i
$193$	2.56126	−	4.43623i	0.184363	−	0.319327i	−0.758998	−	0.651092i	$-0.774311\pi$
$193$	2.56126	−	4.43623i	0.184363	−	0.319327i	0.943362	+	0.331766i	$0.107644\pi$
$194$	14.5721	+	6.65928i	1.04621	+	0.478108i
$195$	−0.0996318	+	0.240532i	−0.00713478	+	0.0172249i
$196$	2.44293	−	13.7852i	0.174495	−	0.984658i
$197$	3.35482	−	1.38961i	0.239021	−	0.0990057i	−0.259958	−	0.965620i	$-0.583709\pi$
$197$	3.35482	−	1.38961i	0.239021	−	0.0990057i	0.498979	+	0.866614i	$0.333709\pi$
$198$	6.26189	−	5.82708i	0.445013	−	0.414113i
$199$	−0.620584	−	2.31605i	−0.0439920	−	0.164181i	0.940435	−	0.339973i	$-0.110418\pi$
$199$	−0.620584	−	2.31605i	−0.0439920	−	0.164181i	−0.984427	+	0.175792i	$0.943751\pi$
$200$	9.92190	−	6.03743i	0.701584	−	0.426911i
$201$	0.0443804	−	0.165630i	0.00313035	−	0.0116826i
$202$	−10.3666	+	16.5515i	−0.729392	+	1.16456i
$203$	−5.96809	−	6.62004i	−0.418878	−	0.464636i
$204$	3.07913	−	3.46570i	0.215582	−	0.242648i
$205$	0.993918	+	7.54956i	0.0694182	+	0.527284i
$206$	−16.9084	−	13.9679i	−1.17806	−	0.973189i
$207$	−10.9137	−	6.30105i	−0.758557	−	0.437953i
$208$	0.706578	−	1.18814i	0.0489924	−	0.0823829i
$209$		−	10.9651i		−	0.758473i
$210$	1.81094	+	2.16008i	0.124967	+	0.149060i
$211$	−20.0854	−	8.31962i	−1.38273	−	0.572747i	−0.437522	−	0.899208i	$-0.644144\pi$
$211$	−20.0854	−	8.31962i	−1.38273	−	0.572747i	−0.945211	+	0.326461i	$0.894144\pi$
$212$	9.35521	+	14.1986i	0.642518	+	0.975163i
$213$	−3.53297	−	0.465124i	−0.242075	−	0.0318698i
$214$	−23.1683	+	12.2877i	−1.58375	+	0.839973i
$215$	1.79342	−	6.69315i	0.122310	−	0.456469i
$216$	7.58051	+	9.42141i	0.515788	+	0.641045i
$217$	−9.37036	−	13.6160i	−0.636101	−	0.924314i
$218$	10.2661	−	2.35881i	0.695305	−	0.159759i
$219$	−2.27580	−	1.74628i	−0.153784	−	0.118003i
$220$	0.347390	−	4.82299i	0.0234210	−	0.325166i
$221$	0.611952	+	0.797511i	0.0411644	+	0.0536464i
$222$	0.227487	−	0.497795i	0.0152679	−	0.0334098i
$223$	22.6623			1.51758			0.758789	−	0.651337i	$-0.225791\pi$
$223$	22.6623			1.51758			0.758789	+	0.651337i	$0.225791\pi$
$224$	−7.87249	−	12.7289i	−0.526003	−	0.850483i
$225$	−9.71124			−0.647416
$226$	−5.75271	+	12.5883i	−0.382665	+	0.837360i
$227$	−8.56788	−	11.1659i	−0.568670	−	0.741106i	0.417163	−	0.908832i	$-0.363024\pi$
$227$	−8.56788	−	11.1659i	−0.568670	−	0.741106i	−0.985834	+	0.167726i	$0.946358\pi$
$228$	6.81561	+	0.490915i	0.451375	+	0.0325116i
$229$	−2.59408	−	1.99051i	−0.171422	−	0.131537i	0.519487	−	0.854478i	$-0.326123\pi$
$229$	−2.59408	−	1.99051i	−0.171422	−	0.131537i	−0.690909	+	0.722941i	$0.742790\pi$
$230$	−6.94314	+	1.59531i	−0.457817	+	0.105191i
$231$	−5.37536	+	0.426379i	−0.353673	+	0.0280537i
$232$	−9.47312	−	1.02571i	−0.621941	−	0.0673412i
$233$	7.78269	−	29.0454i	0.509861	−	1.90283i	0.0881193	−	0.996110i	$-0.471914\pi$
$233$	7.78269	−	29.0454i	0.509861	−	1.90283i	0.421741	−	0.906716i	$-0.361419\pi$
$234$	−1.02112	+	0.541571i	−0.0667527	+	0.0354036i
$235$	−6.96608	−	0.917102i	−0.454417	−	0.0598251i
$236$	−5.96244	+	3.92855i	−0.388122	+	0.255727i
$237$	−2.66488	−	1.10383i	−0.173103	−	0.0717014i
$238$	10.7190	−	1.88530i	0.694811	−	0.122206i
$239$		−	17.3767i		−	1.12400i	−0.827136	−	0.562002i	$-0.810031\pi$
$239$		−	17.3767i		−	1.12400i	0.827136	−	0.562002i	$-0.189969\pi$
$240$	2.98228	+	0.431856i	0.192505	+	0.0278762i
$241$	12.8104	+	7.39608i	0.825190	+	0.476424i	0.852203	−	0.523211i	$-0.175266\pi$
$241$	12.8104	+	7.39608i	0.825190	+	0.476424i	−0.0270130	+	0.999635i	$0.508600\pi$
$242$	−4.86180	−	4.01630i	−0.312528	−	0.258178i
$243$	−2.05772	−	15.6299i	−0.132003	−	1.00266i
$244$	−19.3967	−	17.2332i	−1.24175	−	1.10324i
$245$	0.181367	+	6.61496i	0.0115871	+	0.422614i
$246$	4.81852	−	7.69334i	0.307218	−	0.490510i
$247$	−0.383491	+	1.43121i	−0.0244010	+	0.0910656i
$248$	−17.1687	−	4.17883i	−1.09021	−	0.265356i
$249$	3.10197	+	11.5767i	0.196579	+	0.733644i
$250$	−8.91251	+	8.29365i	−0.563677	+	0.524537i
$251$	−3.40857	+	1.41188i	−0.215147	+	0.0891168i	−0.487654	−	0.873037i	$-0.662147\pi$
$251$	−3.40857	+	1.41188i	−0.215147	+	0.0891168i	0.272507	+	0.962154i	$0.412147\pi$
$252$	0.0907451	+	12.5138i	0.00571640	+	0.788297i
$253$	5.21528	−	12.5908i	0.327882	−	0.791576i
$254$	−6.40215	−	2.92572i	−0.401707	−	0.183576i
$255$	−1.09565	+	1.89772i	−0.0686123	+	0.118840i
$256$	−15.3428	−	4.53866i	−0.958923	−	0.283666i
$257$	14.0152	+	24.2750i	0.874242	+	1.51423i	0.857568	+	0.514370i	$0.171974\pi$
$257$	14.0152	+	24.2750i	0.874242	+	1.51423i	0.0166732	+	0.999861i	$0.494692\pi$
$258$	−6.73010	+	4.78993i	−0.418998	+	0.298208i
$259$	1.14449	−	0.584033i	0.0711150	−	0.0362900i
$260$	−0.214021	+	0.617365i	−0.0132730	+	0.0382873i
$261$	6.32074	+	4.85008i	0.391244	+	0.300212i
$262$	19.7561	+	6.06264i	1.22054	+	0.374551i
$263$	−1.96383	−	7.32911i	−0.121095	−	0.451932i	0.878576	−	0.477603i	$-0.158494\pi$
$263$	−1.96383	−	7.32911i	−0.121095	−	0.451932i	−0.999670	+	0.0256710i	$0.991828\pi$
$264$	−3.98115	+	4.16899i	−0.245023	+	0.256584i
$265$	−5.68311	−	5.68311i	−0.349111	−	0.349111i
$266$	11.8228	+	10.8429i	0.724901	+	0.664823i
$267$	1.36266	+	3.28976i	0.0833936	+	0.201330i
$268$	0.0866795	−	0.421531i	0.00529479	−	0.0257491i
$269$	15.4543	−	11.8585i	0.942264	−	0.723025i	−0.0186629	−	0.999826i	$-0.505941\pi$
$269$	15.4543	−	11.8585i	0.942264	−	0.723025i	0.960927	+	0.276801i	$0.0892742\pi$
$270$	−4.40664	−	3.64030i	−0.268179	−	0.221541i
$271$	−9.84145	+	5.68196i	−0.597826	+	0.345155i	−0.768186	−	0.640227i	$-0.778840\pi$
$271$	−9.84145	+	5.68196i	−0.597826	+	0.345155i	0.170360	+	0.985382i	$0.445507\pi$
$272$	7.20150	−	9.13848i	0.436655	−	0.554102i
$273$	0.716524	+	0.132344i	0.0433660	+	0.00800981i
$274$	16.4009	+	2.76219i	0.990812	+	0.166870i
$275$	−1.37078	−	10.4121i	−0.0826611	−	0.627874i
$276$	7.59260	+	3.80537i	0.457021	+	0.229056i
$277$	−0.0846056	−	0.0111385i	−0.00508346	−	0.000669250i	0.127984	−	0.991776i	$-0.459149\pi$
$277$	−0.0846056	−	0.0111385i	−0.00508346	−	0.000669250i	−0.133067	+	0.991107i	$0.542483\pi$
$278$	−0.669692	+	18.6194i	−0.0401654	+	1.11672i
$279$	10.4472	+	10.4472i	0.625455	+	0.625455i
$280$	4.85671	+	5.14381i	0.290244	+	0.307401i
$281$	−14.0521	+	14.0521i	−0.838277	+	0.838277i	−0.988632	−	0.150355i	$-0.951958\pi$
$281$	−14.0521	+	14.0521i	−0.838277	+	0.838277i	0.150355	+	0.988632i	$0.451958\pi$
$282$	5.70613	+	6.13192i	0.339795	+	0.365150i
$283$	−2.46926	+	18.7559i	−0.146782	+	1.11492i	0.746486	+	0.665401i	$0.231739\pi$
$283$	−2.46926	+	18.7559i	−0.146782	+	1.11492i	−0.893269	+	0.449523i	$0.851594\pi$
$284$	−8.92020	−	0.642504i	−0.529316	−	0.0381256i
$285$	−3.20228	+	0.421588i	−0.189687	+	0.0249727i
$286$	−0.724791	−	1.01837i	−0.0428578	−	0.0602175i
$287$	20.0845	−	7.12622i	1.18555	−	0.420647i
$288$	8.98650	+	9.91054i	0.529535	+	0.583984i
$289$	−4.26958	−	7.39512i	−0.251152	−	0.435007i
$290$	4.48359	−	0.426991i	0.263285	−	0.0250738i
$291$	5.49592	+	7.16242i	0.322176	+	0.419868i
$292$	−5.96012	−	4.03831i	−0.348790	−	0.236324i
$293$	−4.82835	+	1.99997i	−0.282075	+	0.116839i	−0.519236	−	0.854631i	$-0.673783\pi$
$293$	−4.82835	+	1.99997i	−0.282075	+	0.116839i	0.237160	+	0.971470i	$0.423783\pi$
$294$	4.85573	−	6.21743i	0.283192	−	0.362608i
$295$	2.38652	−	2.38652i	0.138949	−	0.138949i
$296$	0.496276	−	1.28082i	0.0288454	−	0.0744463i
$297$	10.5616	−	2.82998i	0.612847	−	0.164212i
$298$	27.0386	−	14.3404i	1.56630	−	0.830719i
$299$	−1.12106	+	1.46100i	−0.0648328	+	0.0844918i
$300$	6.53325	−	0.385882i	0.377197	−	0.0222789i
$301$	−19.3670	−	1.00303i	−1.11629	−	0.0578136i
$302$	−25.8625	−	4.35569i	−1.48822	−	0.250642i
$303$	−9.53059	+	5.50249i	−0.547518	+	0.316110i
$304$	17.1482	+	0.221360i	0.983519	+	0.0126959i
$305$	10.6211	+	6.13210i	0.608163	+	0.351123i
$306$	−9.11594	+	3.39745i	−0.521124	+	0.194220i
$307$	2.00124	+	0.828939i	0.114217	+	0.0473100i	0.439060	−	0.898458i	$-0.355312\pi$
$307$	2.00124	+	0.828939i	0.114217	+	0.0473100i	−0.324843	+	0.945768i	$0.605312\pi$
$308$	−13.4041	+	1.86367i	−0.763772	+	0.106192i
$309$	−4.72931	−	11.4176i	−0.269041	−	0.649522i
$310$	8.34674	+	0.300211i	0.474063	+	0.0170508i
$311$	19.0300	−	5.09907i	1.07909	−	0.289142i	0.324868	−	0.945759i	$-0.394680\pi$
$311$	19.0300	−	5.09907i	1.07909	−	0.289142i	0.754224	+	0.656618i	$0.228013\pi$
$312$	0.665440	−	0.404917i	0.0376731	−	0.0229239i
$313$	18.4611	+	4.94665i	1.04349	+	0.279601i	0.739557	−	0.673094i	$-0.235035\pi$
$313$	18.4611	+	4.94665i	1.04349	+	0.279601i	0.303928	+	0.952695i	$0.401702\pi$
$314$	2.76527	+	12.0351i	0.156053	+	0.679179i
$315$	−1.23338	−	5.78510i	−0.0694933	−	0.325954i
$316$	−6.83984	−	2.37115i	−0.384771	−	0.133388i
$317$	−15.2607	+	2.00911i	−0.857126	+	0.112843i	−0.546265	−	0.837613i	$-0.683951\pi$
$317$	−15.2607	+	2.00911i	−0.857126	+	0.112843i	−0.310861	+	0.950455i	$0.600617\pi$
$318$	0.908362	+	9.53819i	0.0509384	+	0.534875i
$319$	−4.30791	+	7.46152i	−0.241197	+	0.417765i
$320$	7.53561	+	0.640645i	0.421253	+	0.0358131i
$321$	−14.7777			−0.824808
$322$	8.41844	+	18.0737i	0.469142	+	1.00721i
$323$	−4.77246	+	11.5217i	−0.265547	+	0.641086i
$324$	−1.39222	−	7.24314i	−0.0773453	−	0.402397i
$325$	−0.185231	+	1.40697i	−0.0102748	+	0.0780446i
$326$	−0.878900	−	0.269712i	−0.0486778	−	0.0149379i
$327$	5.73333	+	1.53624i	0.317054	+	0.0849543i
$328$	10.9337	−	19.9877i	0.603713	−	1.10363i
$329$	1.55490	+	19.6027i	0.0857245	+	1.08073i
$330$	1.44632	−	2.30921i	0.0796170	−	0.127118i
$331$	−5.41496	+	7.05691i	−0.297633	+	0.387883i	−0.918099	−	0.396350i	$-0.870277\pi$
$331$	−5.41496	+	7.05691i	−0.297633	+	0.387883i	0.620466	+	0.784233i	$0.286943\pi$
$332$	9.48466	+	28.5449i	0.520538	+	1.56660i
$333$	−0.911185	+	0.699177i	−0.0499326	+	0.0383146i
$334$	−5.66600	+	2.11168i	−0.310029	+	0.115546i
$335$			0.203416i			0.0111138i
$336$	−0.558294	−	8.41508i	−0.0304574	−	0.459080i
$337$			30.3107i			1.65113i	0.564309	+	0.825564i	$0.309143\pi$
$337$			30.3107i			1.65113i	−0.564309	+	0.825564i	$0.690857\pi$
$338$	−6.36149	−	17.0690i	−0.346020	−	0.928429i
$339$	−6.18736	+	4.74773i	−0.336051	+	0.257861i
$340$	−2.46418	+	4.91662i	−0.133639	+	0.266641i
$341$	−9.72647	+	12.6758i	−0.526718	+	0.686432i
$342$	−12.1526	−	7.61147i	−0.657138	−	0.411581i
$343$	18.0005	−	4.35671i	0.971937	−	0.235240i
$344$	−16.1526	+	12.9964i	−0.870888	+	0.700720i
$345$	−3.87756	−	1.03899i	−0.208761	−	0.0559373i
$346$	5.43258	−	17.7030i	0.292057	−	0.951717i
$347$	−0.284274	+	2.15927i	−0.0152606	+	0.115916i	−0.997380	−	0.0723450i	$-0.976952\pi$
$347$	−0.284274	+	2.15927i	−0.0152606	+	0.115916i	0.982119	+	0.188261i	$0.0602851\pi$
$348$	−4.44501	−	3.01173i	−0.238277	−	0.161446i
$349$	11.5292	−	27.8339i	0.617142	−	1.48991i	−0.237865	−	0.971298i	$-0.576448\pi$
$349$	11.5292	−	27.8339i	0.617142	−	1.48991i	0.855008	−	0.518616i	$-0.173552\pi$
$350$	12.5820	+	8.81808i	0.672537	+	0.471346i
$351$	−1.47752			−0.0788640
$352$	−9.35731	+	11.0340i	−0.498746	+	0.588113i
$353$	3.24375	−	5.61835i	0.172648	−	0.299034i	−0.766697	−	0.642009i	$-0.778101\pi$
$353$	3.24375	−	5.61835i	0.172648	−	0.299034i	0.939345	+	0.342975i	$0.111434\pi$
$354$	−4.00539	+	0.381450i	−0.212884	+	0.0202739i
$355$	4.19111	−	0.551770i	0.222441	−	0.0292849i
$356$	3.90078	+	8.04040i	0.206741	+	0.426140i
$357$	5.83380	+	1.89155i	0.308758	+	0.100111i
$358$	3.52160	−	0.809148i	0.186122	−	0.0427648i
$359$	23.8719	+	6.39646i	1.25991	+	0.337592i	0.826157	−	0.563440i	$-0.190522\pi$
$359$	23.8719	+	6.39646i	1.25991	+	0.337592i	0.433753	+	0.901032i	$0.357189\pi$
$360$	−5.10416	−	3.73290i	−0.269013	−	0.196741i
$361$	0.597002	−	0.159966i	0.0314212	−	0.00841928i
$362$	0.570223	−	15.8539i	0.0299702	−	0.833261i
$363$	−1.35986	−	3.28298i	−0.0713739	−	0.172312i
$364$	1.81474	+	0.225540i	0.0951181	+	0.0118215i
$365$	3.14393	+	1.30226i	0.164561	+	0.0681632i
$366$	−5.10592	−	13.7000i	−0.266891	−	0.716113i
$367$	32.2338	+	18.6102i	1.68259	+	0.971445i	0.959929	+	0.280243i	$0.0904151\pi$
$367$	32.2338	+	18.6102i	1.68259	+	0.971445i	0.722662	+	0.691201i	$0.242918\pi$
$368$	19.5853	+	8.41030i	1.02096	+	0.438417i
$369$	−16.4973	+	9.52474i	−0.858817	+	0.495838i
$370$	−0.107830	+	0.640252i	−0.00560579	+	0.0332851i
$371$	−12.2392	+	18.8722i	−0.635430	+	0.979796i
$372$	−7.44346	−	6.61321i	−0.385925	−	0.342879i
$373$	2.69062	−	3.50648i	0.139315	−	0.181559i	−0.718485	−	0.695542i	$-0.755164\pi$
$373$	2.69062	−	3.50648i	0.139315	−	0.181559i	0.857800	+	0.513984i	$0.171831\pi$
$374$	−4.92940	−	9.29427i	−0.254893	−	0.480596i
$375$	−6.62646	+	1.77555i	−0.342189	+	0.0916892i
$376$	15.2033	+	14.5183i	0.784052	+	0.748724i
$377$	0.823242	−	0.823242i	0.0423991	−	0.0423991i
$378$	−7.39259	+	14.1861i	−0.380234	+	0.729657i
$379$	−5.63592	+	2.33447i	−0.289498	+	0.119914i	−0.522706	−	0.852513i	$-0.675078\pi$
$379$	−5.63592	+	2.33447i	−0.289498	+	0.119914i	0.233209	+	0.972427i	$0.425078\pi$
$380$	−7.96049	+	1.53010i	−0.408365	+	0.0784924i
$381$	−2.41460	−	3.14677i	−0.123704	−	0.161214i
$382$	−0.548160	−	5.75592i	−0.0280463	−	0.294498i
$383$	2.42892	+	4.20701i	0.124112	+	0.214968i	0.921385	−	0.388650i	$-0.127059\pi$
$383$	2.42892	+	4.20701i	0.124112	+	0.214968i	−0.797274	+	0.603618i	$0.793725\pi$
$384$	−6.43948	−	6.31024i	−0.328613	−	0.322018i
$385$	6.02852	−	2.13899i	0.307242	−	0.109013i
$386$	5.90212	−	4.20064i	0.300410	−	0.213807i
$387$	17.1864	−	2.26264i	0.873635	−	0.115016i
$388$	14.8292	+	17.1312i	0.752836	+	0.869705i
$389$	2.48283	−	18.8589i	0.125884	−	0.956187i	−0.805614	−	0.592441i	$-0.798164\pi$
$389$	2.48283	−	18.8589i	0.125884	−	0.956187i	0.931498	−	0.363746i	$-0.118502\pi$
$390$	−0.269540	+	0.250824i	−0.0136487	+	0.0127010i
$391$	−10.9600	+	10.9600i	−0.554273	+	0.554273i
$392$	11.2453	−	16.2955i	0.567975	−	0.823046i
$393$	8.23412	+	8.23412i	0.415357	+	0.415357i
$394$	5.13201	+	0.184585i	0.258547	+	0.00929927i
$395$	3.39250	+	0.446631i	0.170695	+	0.0224725i
$396$	11.4797	−	3.81438i	0.576875	−	0.191680i
$397$	3.55440	+	26.9984i	0.178390	+	1.35501i	0.813039	+	0.582209i	$0.197812\pi$
$397$	3.55440	+	26.9984i	0.178390	+	1.35501i	−0.634649	+	0.772801i	$0.718855\pi$
$398$	0.563161	−	3.34384i	0.0282287	−	0.167612i
$399$	3.02271	+	8.51921i	0.151325	+	0.426494i
$400$	16.3111	−	1.93355i	0.815553	−	0.0966776i
$401$	−6.34660	+	3.66421i	−0.316934	+	0.182982i	−0.650025	−	0.759913i	$-0.725242\pi$
$401$	−6.34660	+	3.66421i	−0.316934	+	0.182982i	0.333091	+	0.942895i	$0.391908\pi$
$402$	0.154444	−	0.186957i	0.00770296	−	0.00932456i
$403$	1.71286	−	1.31432i	0.0853234	−	0.0654709i
$404$	−23.0634	+	15.1961i	−1.14744	+	0.756032i
$405$	1.33416	+	3.22094i	0.0662947	+	0.160050i
$406$	−3.78523	−	12.0232i	−0.187858	−	0.596703i
$407$	−0.878254	−	0.878254i	−0.0435334	−	0.0435334i
$408$	5.99775	−	2.64787i	0.296933	−	0.131089i
$409$	−8.81882	−	32.9123i	−0.436063	−	1.62741i	−0.738510	−	0.674242i	$-0.764470\pi$
$409$	−8.81882	−	32.9123i	−0.436063	−	1.62741i	0.302448	−	0.953166i	$-0.402196\pi$
$410$	−3.15926	+	10.2950i	−0.156025	+	0.508432i
$411$	7.43523	+	5.70525i	0.366753	+	0.281419i
$412$	−13.5382	−	27.9053i	−0.666979	−	1.37480i
$413$	−7.92505	−	5.13965i	−0.389966	−	0.252906i
$414$	−10.3341	−	14.5200i	−0.507896	−	0.713620i
$415$	−7.10887	−	12.3129i	−0.348961	−	0.604418i
$416$	1.60725	−	1.11294i	0.0788019	−	0.0545661i
$417$	−5.24934	+	9.09212i	−0.257061	+	0.445243i
$418$	6.44540	−	14.1041i	0.315255	−	0.689852i
$419$	−6.02138	+	14.5369i	−0.294164	+	0.710174i	0.705835	+	0.708377i	$0.250572\pi$
$419$	−6.02138	+	14.5369i	−0.294164	+	0.710174i	−0.999998	+	0.00179743i	$0.999428\pi$
$420$	1.05963	+	3.84292i	0.0517049	+	0.187515i
$421$	23.4733	−	9.72296i	1.14402	−	0.473868i	0.271495	−	0.962440i	$-0.412482\pi$
$421$	23.4733	−	9.72296i	1.14402	−	0.473868i	0.872524	+	0.488572i	$0.162482\pi$
$422$	−20.9447	−	22.5076i	−1.01957	−	1.09565i
$423$	−4.54932	−	16.9783i	−0.221196	−	0.825513i
$424$	3.68722	+	23.7622i	0.179067	+	1.15400i
$425$	−3.09140	+	11.5373i	−0.149955	+	0.559640i
$426$	−4.27093	−	2.67499i	−0.206927	−	0.129603i
$427$	10.5866	−	32.6504i	0.512319	−	1.58007i
$428$	−37.0234	+	2.18677i	−1.78959	+	0.105701i
$429$	−0.0919351	−	0.698317i	−0.00443867	−	0.0337150i
$430$	6.24112	−	7.55497i	0.300973	−	0.364333i
$431$	−0.252149	−	0.145578i	−0.0121456	−	0.00701227i	0.493915	−	0.869510i	$-0.335565\pi$
$431$	−0.252149	−	0.145578i	−0.0121456	−	0.00701227i	−0.506061	+	0.862498i	$0.668899\pi$
$432$	4.21256	+	16.5743i	0.202677	+	0.797433i
$433$		−	16.6421i		−	0.799766i	−0.916566	−	0.399883i	$-0.869051\pi$
$433$		−	16.6421i		−	0.799766i	0.916566	−	0.399883i	$-0.130949\pi$
$434$	−4.04916	−	23.0218i	−0.194366	−	1.10508i
$435$	2.34471	+	0.971211i	0.112420	+	0.0465660i
$436$	14.5914	+	3.00044i	0.698802	+	0.143695i
$437$	−22.6508	−	2.98204i	−1.08354	−	0.142650i
$438$	−1.90080	−	3.58392i	−0.0908239	−	0.171246i
$439$	−10.4758	+	39.0961i	−0.499981	+	1.86596i	0.000138064		1.00000i	$0.499956\pi$
$439$	−10.4758	+	39.0961i	−0.499981	+	1.86596i	−0.500120	+	0.865956i	$0.666711\pi$
$440$	3.28183	−	5.99944i	0.156455	−	0.286012i
$441$	−15.1151	+	6.75200i	−0.719769	+	0.321524i
$442$	0.318348	+	1.38552i	0.0151423	+	0.0659026i
$443$	0.0211647	+	0.0162402i	0.00100556	+	0.000771597i	0.609264	−	0.792967i	$-0.291465\pi$
$443$	0.0211647	+	0.0162402i	0.00100556	+	0.000771597i	−0.608259	+	0.793739i	$0.708132\pi$
$444$	0.585218	−	0.506578i	0.0277732	−	0.0240411i
$445$	−2.57149	−	3.35123i	−0.121900	−	0.158864i
$446$	29.1497	+	13.3211i	1.38028	+	0.630772i
$447$	17.2463			0.815722
$448$	−2.64397	−	21.0002i	−0.124916	−	0.992167i
$449$	−12.8409			−0.605999			−0.303000	−	0.952991i	$-0.597988\pi$
$449$	−12.8409			−0.605999			−0.303000	+	0.952991i	$0.597988\pi$
$450$	−12.4912	−	5.70836i	−0.588843	−	0.269095i
$451$	−12.5408	−	16.3435i	−0.590523	−	0.769585i
$452$	−14.7990	+	12.8104i	−0.696088	+	0.602550i
$453$	−11.7246	−	8.99660i	−0.550870	−	0.422697i
$454$	−4.45716	−	19.3986i	−0.209185	−	0.910421i
$455$	−0.861673	+	0.0683488i	−0.0403959	+	0.00320424i
$456$	8.47812	+	4.63773i	0.397025	+	0.217182i
$457$	−10.4697	+	39.0734i	−0.489752	+	1.82778i	0.0678843	+	0.997693i	$0.478375\pi$
$457$	−10.4697	+	39.0734i	−0.489752	+	1.82778i	−0.557636	+	0.830085i	$0.688292\pi$
$458$	−2.16664	−	4.08515i	−0.101240	−	0.190887i
$459$	−12.3295	−	1.62320i	−0.575490	−	0.0757647i
$460$	−9.86846	−	2.02925i	−0.460119	−	0.0946145i
$461$	−30.7733	−	12.7467i	−1.43325	−	0.593673i	−0.475101	−	0.879931i	$-0.657588\pi$
$461$	−30.7733	−	12.7467i	−1.43325	−	0.593673i	−0.958152	+	0.286258i	$0.907588\pi$
$462$	−7.16477	−	2.61125i	−0.333335	−	0.121486i
$463$		−	8.76827i		−	0.407496i	−0.979023	−	0.203748i	$-0.934688\pi$
$463$		−	8.76827i		−	0.407496i	0.979023	−	0.203748i	$-0.0653123\pi$
$464$	−11.5820	−	6.88773i	−0.537682	−	0.319755i
$465$	4.07583	+	2.35318i	0.189012	+	0.109126i
$466$	27.0838	−	32.7853i	1.25463	−	1.51875i
$467$	−1.53776	−	11.6805i	−0.0711591	−	0.540507i	−0.989480	−	0.144670i	$-0.953788\pi$
$467$	−1.53776	−	11.6805i	−0.0711591	−	0.540507i	0.918321	−	0.395837i	$-0.129545\pi$
$468$	−1.63177	+	0.0963797i	−0.0754287	+	0.00445515i
$469$	0.556786	−	0.118707i	0.0257100	−	0.00548137i
$470$	−8.42115	−	5.27437i	−0.388439	−	0.243288i
$471$	−1.80096	+	6.72128i	−0.0829840	+	0.309700i
$472$	−9.97853	+	1.54838i	−0.459299	+	0.0712701i
$473$	4.85186	+	18.1074i	0.223089	+	0.832579i
$474$	−2.77890	−	2.98626i	−0.127639	−	0.137163i
$475$	−16.2653	+	6.73733i	−0.746305	+	0.309130i
$476$	14.8957	+	3.87575i	0.682744	+	0.177645i
$477$	7.69433	−	18.5758i	0.352299	−	0.850526i
$478$	10.2142	−	22.3510i	0.467186	−	1.02231i
$479$	−3.21469	+	5.56801i	−0.146883	+	0.254409i	−0.930074	−	0.367372i	$-0.880257\pi$
$479$	−3.21469	+	5.56801i	−0.146883	+	0.254409i	0.783191	+	0.621781i	$0.213591\pi$
$480$	3.58216	+	2.30850i	0.163502	+	0.105368i
$481$	0.0839171	+	0.145349i	0.00382629	+	0.00662733i
$482$	12.1301	+	17.0434i	0.552510	+	0.776306i
$483$	−0.581088	+	11.2199i	−0.0264404	+	0.510525i
$484$	−3.89274	−	8.02384i	−0.176943	−	0.364720i
$485$	−8.49668	−	6.51973i	−0.385814	−	0.296046i
$486$	6.54066	−	21.3138i	0.296690	−	0.966814i
$487$	2.16645	+	8.08530i	0.0981712	+	0.366380i	0.997481	−	0.0709319i	$-0.0225973\pi$
$487$	2.16645	+	8.08530i	0.0981712	+	0.366380i	−0.899310	+	0.437312i	$0.855931\pi$
$488$	−14.8195	−	33.5680i	−0.670847	−	1.51955i
$489$	−0.366315	−	0.366315i	−0.0165654	−	0.0165654i
$490$	−3.65505	+	8.61520i	−0.165118	+	0.389195i
$491$	10.2917	+	24.8464i	0.464458	+	1.12130i	0.966548	+	0.256486i	$0.0825647\pi$
$491$	10.2917	+	24.8464i	0.464458	+	1.12130i	−0.502090	+	0.864815i	$0.667435\pi$
$492$	10.7201	−	7.06331i	0.483300	−	0.318439i
$493$	7.77414	−	5.96531i	0.350130	−	0.268664i
$494$	−1.33455	+	1.61549i	−0.0600442	+	0.0726845i
$495$	−4.95180	+	2.85892i	−0.222567	+	0.128499i
$496$	−19.6272	−	15.4670i	−0.881286	−	0.694490i
$497$	−3.95609	−	11.1498i	−0.177455	−	0.500139i
$498$	−2.81494	+	16.7141i	−0.126141	+	0.748976i
$499$	2.04233	+	15.5130i	0.0914271	+	0.694458i	0.974366	+	0.224970i	$0.0722283\pi$
$499$	2.04233	+	15.5130i	0.0914271	+	0.694458i	−0.882939	+	0.469488i	$0.844438\pi$
$500$	−16.3389	+	5.42898i	−0.730700	+	0.242791i
$501$	−3.37812	−	0.444738i	−0.150923	−	0.0198694i
$502$	−5.21424	−	0.187543i	−0.232723	−	0.00837044i
$503$	−3.88871	−	3.88871i	−0.173389	−	0.173389i	0.615078	−	0.788467i	$-0.289125\pi$
$503$	−3.88871	−	3.88871i	−0.173389	−	0.173389i	−0.788467	+	0.615078i	$0.789125\pi$
$504$	−7.23903	+	16.1494i	−0.322452	+	0.719354i
$505$	9.23131	−	9.23131i	0.410788	−	0.410788i
$506$	14.1092	−	13.1295i	0.627231	−	0.583678i
$507$	1.33979	−	10.1767i	0.0595020	−	0.451963i
$508$	−6.51511	−	7.52650i	−0.289061	−	0.333934i
$509$	−24.3140	+	3.20100i	−1.07770	+	0.141882i	−0.648415	−	0.761287i	$-0.724568\pi$
$509$	−24.3140	+	3.20100i	−1.07770	+	0.141882i	−0.429285	+	0.903169i	$0.641234\pi$
$510$	−2.52480	+	1.79694i	−0.111800	+	0.0795699i
$511$	1.72983	−	9.36547i	0.0765230	−	0.414304i
$512$	−17.0670	−	14.8566i	−0.754262	−	0.656573i
$513$	−9.16504	−	15.8743i	−0.404646	−	0.700868i
$514$	3.75816	+	39.4623i	0.165765	+	1.74061i
$515$	8.92472	+	11.6309i	0.393270	+	0.512519i
$516$	−11.4723	+	2.20510i	−0.505039	+	0.0970742i
$517$	17.5615	−	7.27420i	0.772353	−	0.319919i
$518$	1.81541	−	0.0784809i	0.0797647	−	0.00344825i
$519$	7.37839	−	7.37839i	0.323875	−	0.323875i
$520$	−0.638180	+	0.668292i	−0.0279861	+	0.0293065i
$521$	−7.55629	+	2.02470i	−0.331047	+	0.0887038i	−0.420514	−	0.907286i	$-0.638150\pi$
$521$	−7.55629	+	2.02470i	−0.331047	+	0.0887038i	0.0894670	+	0.995990i	$0.471484\pi$
$522$	5.27924	+	9.95388i	0.231066	+	0.435670i
$523$	17.5968	−	22.9326i	0.769456	−	1.00277i	−0.230106	−	0.973166i	$-0.573907\pi$
$523$	17.5968	−	22.9326i	0.769456	−	1.00277i	0.999562	−	0.0296085i	$-0.00942604\pi$
$524$	21.8479	+	19.4110i	0.954432	+	0.847974i
$525$	3.93528	+	7.71168i	0.171750	+	0.336565i
$526$	1.78212	−	10.5815i	0.0777040	−	0.461377i
$527$	15.7372	−	9.08589i	0.685524	−	0.395788i
$528$	−7.57139	+	3.02228i	−0.329502	+	0.131528i
$529$	−4.67212	−	2.69745i	−0.203135	−	0.117280i
$530$	−3.96940	−	10.6506i	−0.172420	−	0.462631i
$531$	7.80056	+	3.23110i	0.338516	+	0.140218i
$532$	8.83365	+	20.8964i	0.382987	+	0.905975i
$533$	1.06528	+	2.57181i	0.0461424	+	0.111398i
$534$	−0.181006	+	5.03249i	−0.00783288	+	0.217777i
$535$	16.9332	−	4.53723i	0.732085	−	0.196162i
$536$	0.359273	−	0.491249i	0.0155182	−	0.0212187i
$537$	1.96672	+	0.526981i	0.0848703	+	0.0227409i
$538$	26.8489	−	6.16899i	1.15754	−	0.265964i
$539$	−9.37286	−	15.2529i	−0.403717	−	0.656990i
$540$	−3.52831	−	7.27265i	−0.151834	−	0.312965i
$541$	38.4403	−	5.06077i	1.65268	−	0.217579i	0.754215	−	0.656627i	$-0.228017\pi$
$541$	38.4403	−	5.06077i	1.65268	−	0.217579i	0.898464	+	0.439048i	$0.144684\pi$
$542$	−15.9986	+	1.52362i	−0.687200	+	0.0654449i
$543$	4.46966	−	7.74167i	0.191811	−	0.332227i
$544$	14.6347	−	7.52141i	0.627459	−	0.322478i
$545$	−7.04129			−0.301616
$546$	0.843848	+	0.591409i	0.0361133	+	0.0253100i
$547$	2.27375	−	5.48932i	0.0972186	−	0.234706i	−0.867787	−	0.496937i	$-0.834458\pi$
$547$	2.27375	−	5.48932i	0.0972186	−	0.234706i	0.965005	+	0.262230i	$0.0844581\pi$
$548$	19.4722	+	13.1935i	0.831812	+	0.563598i
$549$	−4.00467	+	30.4185i	−0.170915	+	1.29823i
$550$	4.35715	−	14.1985i	0.185789	−	0.605426i
$551$	13.9514	+	3.73827i	0.594351	+	0.159256i
$552$	7.52926	+	9.35772i	0.320467	+	0.398291i
$553$	−0.757242	−	9.54655i	−0.0322012	−	0.405961i
$554$	−0.102278	−	0.0640591i	−0.00434538	−	0.00272161i
$555$	−0.222720	+	0.290254i	−0.00945394	+	0.0123206i
$556$	−11.8061	+	23.5559i	−0.500689	+	0.998991i
$557$	−1.19267	+	0.915169i	−0.0505351	+	0.0387769i	−0.633720	−	0.773562i	$-0.718473\pi$
$557$	−1.19267	+	0.915169i	−0.0505351	+	0.0387769i	0.583185	+	0.812339i	$0.301806\pi$
$558$	7.29688	+	19.5788i	0.308902	+	0.828835i
$559$		−	2.53313i		−	0.107140i
$560$	3.22344	+	9.47112i	0.136215	+	0.400228i
$561$		−	5.92826i		−	0.250291i
$562$	−26.3347	+	9.81476i	−1.11086	+	0.414011i
$563$	−26.4422	+	20.2898i	−1.11441	+	0.855115i	−0.990546	−	0.137184i	$-0.956195\pi$
$563$	−26.4422	+	20.2898i	−1.11441	+	0.855115i	−0.123862	+	0.992299i	$0.539528\pi$
$564$	3.73520	+	11.2414i	0.157280	+	0.473348i
$565$	5.63216	−	7.33998i	0.236947	−	0.308795i
$566$	−14.2010	+	22.6736i	−0.596914	+	0.953044i
$567$	8.03774	−	5.53147i	0.337553	−	0.232300i
$568$	−11.0961	−	6.06981i	−0.465581	−	0.254684i
$569$	30.1294	+	8.07314i	1.26309	+	0.338444i	0.827379	−	0.561644i	$-0.189831\pi$
$569$	30.1294	+	8.07314i	1.26309	+	0.338444i	0.435710	+	0.900087i	$0.356497\pi$
$570$	−4.36680	−	1.34006i	−0.182905	−	0.0561288i
$571$	−3.38167	+	25.6863i	−0.141518	+	1.07494i	0.762361	+	0.647152i	$0.224040\pi$
$571$	−3.38167	+	25.6863i	−0.141518	+	1.07494i	−0.903880	+	0.427787i	$0.859293\pi$
$572$	−0.333666	−	1.73593i	−0.0139513	−	0.0725830i
$573$	1.24682	−	3.01008i	0.0520865	−	0.125748i
$574$	30.0229	+	2.63967i	1.25313	+	0.110178i
$575$	−21.8813			−0.912512
$576$	5.73352	+	18.0299i	0.238897	+	0.751248i
$577$	17.1767	−	29.7510i	0.715076	−	1.23855i	−0.247854	−	0.968797i	$-0.579725\pi$
$577$	17.1767	−	29.7510i	0.715076	−	1.23855i	0.962930	−	0.269751i	$-0.0869414\pi$
$578$	−1.14489	−	12.0218i	−0.0476210	−	0.500041i
$579$	4.04720	−	0.532824i	0.168196	−	0.0221434i
$580$	6.01807	+	2.08627i	0.249887	+	0.0866278i
$581$	−29.5543	+	26.6437i	−1.22612	+	1.10537i
$582$	2.85907	+	12.4433i	0.118512	+	0.515793i
$583$	21.0025	+	5.62759i	0.869833	+	0.233071i
$584$	−5.29255	−	8.69776i	−0.219007	−	0.359916i
$585$	0.746314	−	0.199974i	0.0308563	−	0.00826792i
$586$	−7.38614	−	0.265660i	−0.305119	−	0.0109743i
$587$	−8.92523	−	21.5474i	−0.368384	−	0.889357i	−0.994016	−	0.109239i	$-0.965159\pi$
$587$	−8.92523	−	21.5474i	−0.368384	−	0.889357i	0.625632	−	0.780118i	$-0.284841\pi$
$588$	9.90043	−	5.14302i	0.408287	−	0.212095i
$589$	24.7458	+	10.2500i	1.01963	+	0.422346i
$590$	4.47252	−	1.66688i	0.184131	−	0.0686244i
$591$	2.50603	+	1.44686i	0.103084	+	0.0595159i
$592$	1.39122	−	1.35576i	0.0571789	−	0.0557215i
$593$	5.61968	−	3.24453i	0.230773	−	0.133237i	−0.380156	−	0.924922i	$-0.624130\pi$
$593$	5.61968	−	3.24453i	0.230773	−	0.133237i	0.610928	+	0.791686i	$0.290796\pi$
$594$	15.2485	+	2.56812i	0.625655	+	0.105371i
$595$	−7.26551	−	0.376286i	−0.297857	−	0.0154262i
$596$	43.2083	−	2.55207i	1.76988	−	0.104537i
$597$	1.16320	−	1.51591i	0.0476066	−	0.0620421i
$598$	−2.30078	+	1.22026i	−0.0940858	+	0.0499002i
$599$	8.61833	−	2.30927i	0.352135	−	0.0943544i	−0.0784153	−	0.996921i	$-0.524986\pi$
$599$	8.61833	−	2.30927i	0.352135	−	0.0943544i	0.430551	+	0.902566i	$0.358319\pi$
$600$	8.63032	+	3.34396i	0.352331	+	0.136516i
$601$	−30.4718	+	30.4718i	−1.24297	+	1.24297i	−0.284208	+	0.958763i	$0.591731\pi$
$601$	−30.4718	+	30.4718i	−1.24297	+	1.24297i	−0.958763	+	0.284208i	$0.908269\pi$
$602$	−24.3215	−	12.6743i	−0.991270	−	0.516564i
$603$	−0.470143	+	0.194740i	−0.0191457	+	0.00793041i
$604$	−30.7057	−	20.8048i	−1.24940	−	0.846535i
$605$	2.56620	+	3.34433i	0.104331	+	0.135966i
$606$	−15.4933	+	1.47549i	−0.629372	+	0.0599377i
$607$	−13.8976	−	24.0714i	−0.564086	−	0.977026i	−0.997134	−	0.0756553i	$-0.975895\pi$
$607$	−13.8976	−	24.0714i	−0.564086	−	0.977026i	0.433048	−	0.901371i	$-0.357438\pi$
$608$	21.9271	+	10.3646i	0.889260	+	0.420341i
$609$	1.29009	−	6.98468i	0.0522770	−	0.283034i
$610$	10.0571	+	14.1307i	0.407198	+	0.572135i
$611$	−2.54659	+	0.335266i	−0.103024	+	0.0135634i
$612$	−13.7226	−	0.988410i	−0.554702	−	0.0399541i
$613$	3.11669	−	23.6736i	0.125882	−	0.956168i	−0.805620	−	0.592432i	$-0.798168\pi$
$613$	3.11669	−	23.6736i	0.125882	−	0.956168i	0.931502	−	0.363736i	$-0.118499\pi$
$614$	2.08686	+	2.24258i	0.0842189	+	0.0905032i
$615$	−4.29082	+	4.29082i	−0.173023	+	0.173023i
$616$	−18.3368	−	5.48191i	−0.738810	−	0.220872i
$617$	−3.10367	−	3.10367i	−0.124949	−	0.124949i	0.641867	−	0.766816i	$-0.278160\pi$
$617$	−3.10367	−	3.10367i	−0.124949	−	0.124949i	−0.766816	+	0.641867i	$0.778160\pi$
$618$	0.628205	−	17.4660i	0.0252701	−	0.702584i
$619$	40.4180	+	5.32113i	1.62454	+	0.213874i	0.887112	−	0.461555i	$-0.152708\pi$
$619$	40.4180	+	5.32113i	1.62454	+	0.213874i	0.737425	+	0.675429i	$0.236042\pi$
$620$	10.5597	+	5.29245i	0.424086	+	0.212550i
$621$	−2.97363	−	22.5869i	−0.119328	−	0.906383i
$622$	27.4749	+	4.62725i	1.10164	+	0.185536i
$623$	−7.67231	+	8.99432i	−0.307385	+	0.360350i
$624$	1.09395	−	0.129679i	0.0437929	−	0.00519132i
$625$	−10.7330	+	6.19670i	−0.429320	+	0.247868i
$626$	20.8382	+	17.2143i	0.832864	+	0.688023i
$627$	6.93239	−	5.31941i	0.276853	−	0.212437i
$628$	−3.51747	+	17.1058i	−0.140362	+	0.682594i
$629$	0.540585	+	1.30509i	0.0215545	+	0.0520372i
$630$	1.81408	−	8.16618i	0.0722747	−	0.325348i
$631$	0.0370594	+	0.0370594i	0.00147531	+	0.00147531i	0.707844	−	0.706369i	$-0.249668\pi$
$631$	0.0370594	+	0.0370594i	0.00147531	+	0.00147531i	−0.706369	+	0.707844i	$0.749668\pi$
$632$	−7.40406	−	7.07045i	−0.294518	−	0.281247i
$633$	−4.48397	−	16.7344i	−0.178222	−	0.665134i
$634$	−20.8103	−	6.38613i	−0.826482	−	0.253626i
$635$	3.73297	+	2.86441i	0.148138	+	0.113670i
$636$	−4.43825	+	12.8026i	−0.175988	+	0.507656i
$637$	0.689928	+	2.31867i	0.0273359	+	0.0918692i
$638$	−9.92707	+	7.06527i	−0.393017	+	0.279717i
$639$	5.28763	+	9.15844i	0.209175	+	0.362302i
$640$	9.31622	+	5.25354i	0.368256	+	0.207665i
$641$	7.76024	−	13.4411i	0.306511	−	0.530893i	−0.671086	−	0.741380i	$-0.734172\pi$
$641$	7.76024	−	13.4411i	0.306511	−	0.530893i	0.977597	+	0.210487i	$0.0675050\pi$
$642$	−19.0080	−	8.68645i	−0.750186	−	0.342827i
$643$	−10.7794	+	26.0237i	−0.425096	+	1.02627i	0.555725	+	0.831366i	$0.312441\pi$
$643$	−10.7794	+	26.0237i	−0.425096	+	1.02627i	−0.980822	+	0.194907i	$0.937559\pi$
$644$	0.204466	+	28.1960i	0.00805708	+	1.11108i
$645$	5.10158	−	2.11314i	0.200875	−	0.0832050i
$646$	−12.9112	+	12.0147i	−0.507986	+	0.472713i
$647$	−10.4918	−	39.1558i	−0.412474	−	1.53937i	−0.789842	−	0.613311i	$-0.789837\pi$
$647$	−10.4918	−	39.1558i	−0.412474	−	1.53937i	0.377368	−	0.926063i	$-0.376829\pi$
$648$	2.46683	−	10.1350i	0.0969062	−	0.398139i
$649$	−2.36321	+	8.81961i	−0.0927640	+	0.346200i
$650$	−1.06529	+	1.70085i	−0.0417839	+	0.0667130i
$651$	4.06257	−	12.5296i	0.159225	−	0.491072i
$652$	−0.971960	−	0.863547i	−0.0380649	−	0.0338191i
$653$	4.85359	+	36.8667i	0.189936	+	1.44271i	0.775125	+	0.631808i	$0.217687\pi$
$653$	4.85359	+	36.8667i	0.189936	+	1.44271i	−0.585189	+	0.810897i	$0.698980\pi$
$654$	6.47157	+	5.34612i	0.253058	+	0.209050i
$655$	−11.9633	−	6.90704i	−0.467446	−	0.269880i
$656$	25.8126	−	19.2825i	1.00781	−	0.752855i
$657$			8.51309i			0.332127i
$658$	−9.52261	+	26.1282i	−0.371230	+	1.01858i
$659$	41.0672	+	17.0106i	1.59975	+	0.662639i	0.991380	−	0.131014i	$-0.0418234\pi$
$659$	41.0672	+	17.0106i	1.59975	+	0.662639i	0.608371	+	0.793653i	$0.291823\pi$
$660$	3.21772	−	2.12010i	0.125250	−	0.0825249i
$661$	−17.0240	−	2.24125i	−0.662157	−	0.0871746i	−0.208045	−	0.978119i	$-0.566710\pi$
$661$	−17.0240	−	2.24125i	−0.662157	−	0.0871746i	−0.454112	+	0.890945i	$0.650043\pi$
$662$	−11.1132	+	5.89410i	−0.431927	+	0.229081i
$663$	−0.207333	+	0.773779i	−0.00805216	+	0.0300511i
$664$	−4.57914	+	42.2914i	−0.177705	+	1.64123i
$665$	−6.07930	−	8.83378i	−0.235745	−	0.342559i
$666$	−1.58301	+	0.363724i	−0.0613403	+	0.0140940i
$667$	14.2418	+	10.9281i	0.551446	+	0.423139i
$668$	−8.52924	−	0.614344i	−0.330006	−	0.0237697i
$669$	10.9939	+	14.3276i	0.425050	+	0.553936i
$670$	−0.119570	+	0.261646i	−0.00461938	+	0.0101083i
$671$	−33.1791			−1.28086
$672$	4.22835	−	11.1522i	0.163112	−	0.430205i
$673$	−32.8126			−1.26483			−0.632417	−	0.774628i	$-0.717937\pi$
$673$	−32.8126			−1.26483			−0.632417	+	0.774628i	$0.717937\pi$
$674$	−17.8169	+	38.9876i	−0.686282	+	1.50175i
$675$	−10.6873	−	13.9280i	−0.411355	−	0.536088i
$676$	1.85073	−	25.6946i	0.0711818	−	0.988253i
$677$	−27.9425	−	21.4410i	−1.07392	−	0.824046i	−0.0888214	−	0.996048i	$-0.528310\pi$
$677$	−27.9425	−	21.4410i	−1.07392	−	0.824046i	−0.985097	+	0.172001i	$0.944977\pi$
$678$	−10.7494	+	2.46985i	−0.412826	+	0.0948540i
$679$	−12.8873	+	27.0617i	−0.494570	+	1.03853i
$680$	−6.05963	+	4.87561i	−0.232376	+	0.186971i
$681$	2.90286	−	10.8336i	0.111238	−	0.415145i
$682$	−19.9618	+	10.5871i	−0.764376	+	0.405402i
$683$	−5.73809	−	0.755434i	−0.219562	−	0.0289059i	0.0199426	−	0.999801i	$-0.493652\pi$
$683$	−5.73809	−	0.755434i	−0.219562	−	0.0289059i	−0.239504	+	0.970895i	$0.576985\pi$
$684$	−11.1574	−	16.9338i	−0.426614	−	0.647480i
$685$	−10.2715	−	4.25458i	−0.392453	−	0.162559i
$686$	25.7144	+	4.97700i	0.981780	+	0.190023i
$687$		−	2.60567i		−	0.0994127i
$688$	−28.4159	+	7.22223i	−1.08335	+	0.275345i
$689$	−2.54450	−	1.46907i	−0.0969378	−	0.0559671i
$690$	−4.37685	−	3.61569i	−0.166624	−	0.137647i
$691$	−2.81203	−	21.3595i	−0.106975	−	0.812554i	−0.957867	−	0.287213i	$-0.907271\pi$
$691$	−2.81203	−	21.3595i	−0.106975	−	0.812554i	0.850892	−	0.525341i	$-0.176062\pi$
$692$	17.3937	−	19.5774i	0.661210	−	0.744221i
$693$	10.7151	+	11.8856i	0.407033	+	0.451497i
$694$	−1.63489	+	2.61030i	−0.0620597	+	0.0990856i
$695$	3.22344	−	12.0301i	0.122272	−	0.456326i
$696$	−3.94713	−	6.48671i	−0.149616	−	0.245878i
$697$	6.06406	+	22.6314i	0.229693	+	0.857225i
$698$	31.1906	−	29.0248i	1.18058	−	1.09861i
$699$	22.1387	−	9.17014i	0.837361	−	0.346846i
$700$	11.0005	+	18.7382i	0.415778	+	0.708238i
$701$	−1.97468	+	4.76730i	−0.0745827	+	0.180059i	−0.956774	−	0.290833i	$-0.906068\pi$
$701$	−1.97468	+	4.76730i	−0.0745827	+	0.180059i	0.882191	+	0.470891i	$0.156068\pi$
$702$	−1.90048	−	0.868498i	−0.0717289	−	0.0327794i
$703$	−1.04108	+	1.80320i	−0.0392650	+	0.0680089i
$704$	−18.5219	+	8.69230i	−0.698069	+	0.327603i
$705$	−2.79958	−	4.84902i	−0.105438	−	0.182624i
$706$	7.47485	−	5.31998i	0.281320	−	0.200220i
$707$	−30.6549	−	19.8807i	−1.15290	−	0.747692i
$708$	−5.37622	−	1.86376i	−0.202051	−	0.0700445i
$709$	−28.1803	−	21.6235i	−1.05833	−	0.812087i	−0.0756037	−	0.997138i	$-0.524088\pi$
$709$	−28.1803	−	21.6235i	−1.05833	−	0.812087i	−0.982729	+	0.185051i	$0.940755\pi$
$710$	5.71521	+	1.75385i	0.214488	+	0.0658209i
$711$	2.21553	+	8.26848i	0.0830890	+	0.310092i
$712$	0.291212	+	12.6350i	0.0109136	+	0.473517i
$713$	23.5394	+	23.5394i	0.881558	+	0.881558i
$714$	6.39195	+	5.86220i	0.239213	+	0.219387i
$715$	0.319752	+	0.771949i	0.0119580	+	0.0288692i
$716$	5.00533	+	1.02925i	0.187058	+	0.0384648i
$717$	10.9859	−	8.42980i	0.410277	−	0.314817i
$718$	26.9457	+	22.2597i	1.00560	+	0.830724i
$719$	−18.5252	+	10.6955i	−0.690873	+	0.398876i	−0.803939	−	0.594712i	$-0.797266\pi$
$719$	−18.5252	+	10.6955i	−0.690873	+	0.398876i	0.113066	+	0.993587i	$0.463933\pi$
$720$	−4.37107	−	7.80178i	−0.162900	−	0.290755i
$721$	26.6278	−	31.2160i	0.991672	−	1.16255i
$722$	0.861934	+	0.145165i	0.0320778	+	0.00540247i
$723$	1.53862	+	11.6870i	0.0572220	+	0.434644i
$724$	10.0525	−	20.0571i	0.373599	−	0.745417i
$725$	13.7151	+	1.80563i	0.509367	+	0.0670595i
$726$	0.180633	−	5.02213i	0.00670391	−	0.186389i
$727$	−15.8509	−	15.8509i	−0.587879	−	0.587879i	0.349178	−	0.937056i	$-0.386461\pi$
$727$	−15.8509	−	15.8509i	−0.587879	−	0.587879i	−0.937056	+	0.349178i	$0.886461\pi$
$728$	2.20166	+	1.35682i	0.0815990	+	0.0502873i
$729$	1.06021	−	1.06021i	0.0392671	−	0.0392671i
$730$	3.27845	+	3.52308i	0.121341	+	0.130395i
$731$	2.78291	−	21.1383i	0.102930	−	0.781828i
$732$	1.48545	−	20.6232i	0.0549037	−	0.762255i
$733$	43.5018	−	5.72712i	1.60678	−	0.211536i	0.726902	−	0.686741i	$-0.240960\pi$
$733$	43.5018	−	5.72712i	1.60678	−	0.211536i	0.879875	+	0.475205i	$0.157626\pi$
$734$	30.5220	+	42.8850i	1.12659	+	1.58291i
$735$	−4.09414	+	3.32372i	−0.151014	+	0.122597i
$736$	20.2483	+	22.3303i	0.746362	+	0.823107i
$737$	−0.275156	−	0.476585i	−0.0101355	−	0.0175552i
$738$	−26.8187	+	2.55406i	−0.987210	+	0.0940161i
$739$	−27.6554	−	36.0413i	−1.01732	−	1.32580i	−0.944520	−	0.328453i	$-0.893473\pi$
$739$	−27.6554	−	36.0413i	−1.01732	−	1.32580i	−0.0728019	−	0.997346i	$-0.523194\pi$
$740$	−0.515044	+	0.760151i	−0.0189334	+	0.0279437i
$741$	−1.09088	+	0.451858i	−0.0400745	+	0.0165994i
$742$	−26.8362	+	17.0803i	−0.985188	+	0.627038i
$743$	26.4880	−	26.4880i	0.971751	−	0.971751i	−0.0278610	−	0.999612i	$-0.508870\pi$
$743$	26.4880	−	26.4880i	0.971751	−	0.971751i	0.999612	+	0.0278610i	$0.00886956\pi$
$744$	−5.68696	−	12.8817i	−0.208494	−	0.472265i
$745$	−19.7619	+	5.29519i	−0.724020	+	0.194001i
$746$	5.52199	−	2.92869i	0.202174	−	0.107227i
$747$	21.6525	−	28.2181i	0.792224	−	1.03245i
$748$	−0.877252	−	14.8525i	−0.0320755	−	0.543060i
$749$	−22.3009	−	43.7015i	−0.814858	−	1.59682i
$750$	−9.56707	−	1.61126i	−0.349340	−	0.0588350i
$751$	−24.7921	+	14.3137i	−0.904678	+	0.522316i	−0.878715	−	0.477347i	$-0.841598\pi$
$751$	−24.7921	+	14.3137i	−0.904678	+	0.522316i	−0.0259628	+	0.999663i	$0.508265\pi$
$752$	11.0215	+	27.6111i	0.401914	+	1.00687i
$753$	−2.54619	−	1.47004i	−0.0927882	−	0.0535713i
$754$	1.54282	−	0.574998i	0.0561861	−	0.0209402i
$755$	16.1971	+	6.70904i	0.589471	+	0.244167i
$756$	−17.8476	+	13.9017i	−0.649111	+	0.505601i
$757$	10.4492	+	25.2266i	0.379783	+	0.916878i	0.992006	+	0.126192i	$0.0402757\pi$
$757$	10.4492	+	25.2266i	0.379783	+	0.916878i	−0.612223	+	0.790686i	$0.709724\pi$
$758$	−8.62152	−	0.310094i	−0.313148	−	0.0112631i
$759$	10.4902	−	2.81084i	0.380771	−	0.102027i
$760$	−11.1387	−	2.71114i	−0.404044	−	0.0983434i
$761$	47.0914	+	12.6181i	1.70706	+	0.457406i	0.974701	−	0.223513i	$-0.0717524\pi$
$761$	47.0914	+	12.6181i	1.70706	+	0.457406i	0.732360	+	0.680918i	$0.238419\pi$
$762$	−1.25612	−	5.46691i	−0.0455043	−	0.198045i
$763$	4.10907	+	19.2733i	0.148758	+	0.697741i
$764$	2.67830	−	7.72585i	0.0968977	−	0.279512i
$765$	6.44748	−	0.848827i	0.233109	−	0.0306894i
$766$	0.651313	+	6.83907i	0.0235329	+	0.247106i
$767$	0.616909	−	1.06852i	0.0222753	−	0.0385820i
$768$	−4.57366	−	11.9018i	−0.165038	−	0.429470i
$769$	0.145002			0.00522889			0.00261445	−	0.999997i	$-0.499168\pi$
$769$	0.145002			0.00522889			0.00261445	+	0.999997i	$0.499168\pi$
$770$	9.01159	+	0.792316i	0.324755	+	0.0285531i
$771$	−8.54812	+	20.6370i	−0.307853	+	0.743223i
$772$	10.0609	−	1.93381i	0.362098	−	0.0695995i
$773$	−3.02302	+	22.9621i	−0.108731	+	0.825890i	0.846989	+	0.531611i	$0.178413\pi$
$773$	−3.02302	+	22.9621i	−0.108731	+	0.825890i	−0.955719	+	0.294280i	$0.904920\pi$
$774$	23.4363	+	7.19200i	0.842401	+	0.258511i
$775$	24.7792	+	6.63956i	0.890094	+	0.238500i
$776$	9.00435	+	30.7520i	0.323237	+	1.10393i
$777$	0.924453	+	0.440243i	0.0331646	+	0.0157936i
$778$	14.2790	−	22.7982i	0.511929	−	0.817355i
$779$	−21.0234	+	27.3983i	−0.753242	+	0.981644i
$780$	−0.494137	+	0.164188i	−0.0176930	+	0.00587888i
$781$	−9.07303	+	6.96198i	−0.324659	+	0.249119i
$782$	−20.5399	+	7.65511i	−0.734507	+	0.273746i
$783$			14.4028i			0.514715i
$784$	24.0431	−	14.3502i	0.858683	−	0.512507i
$785$		−	8.25463i		−	0.294620i
$786$	5.75117	+	15.4314i	0.205138	+	0.550419i
$787$	4.23286	−	3.24799i	0.150885	−	0.115778i	−0.530560	−	0.847647i	$-0.678018\pi$
$787$	4.23286	−	3.24799i	0.150885	−	0.115778i	0.681445	+	0.731869i	$0.261352\pi$
$788$	6.49263	+	3.25407i	0.231290	+	0.115922i
$789$	3.68093	−	4.79708i	0.131045	−	0.170781i
$790$	4.10112	+	2.56863i	0.145911	+	0.0913878i
$791$	−23.3776	−	11.1329i	−0.831213	−	0.395840i
$792$	17.0080	+	1.84156i	0.604354	+	0.0654370i
$793$	4.33066	+	1.16040i	0.153786	+	0.0412069i
$794$	−11.2980	+	36.8164i	−0.400951	+	1.30657i
$795$	0.835991	−	6.34998i	0.0296495	−	0.225211i
$796$	2.68992	−	3.97004i	0.0953416	−	0.140714i
$797$	1.68123	−	4.05884i	0.0595521	−	0.143771i	−0.891303	−	0.453409i	$-0.850208\pi$
$797$	1.68123	−	4.05884i	0.0595521	−	0.143771i	0.950855	+	0.309638i	$0.100208\pi$
$798$	−1.11966	+	12.7347i	−0.0396356	+	0.450805i
$799$	−21.6190			−0.764824
$800$	22.1169	+	7.10074i	0.781951	+	0.251049i
$801$	5.28370	−	9.15164i	0.186690	−	0.323357i
$802$	−10.3173	+	0.982556i	−0.364315	+	0.0346953i
$803$	−9.12748	+	1.20166i	−0.322102	+	0.0424055i
$804$	0.308551	−	0.149693i	0.0108817	−	0.00527925i
$805$	−2.77905	−	13.0349i	−0.0979485	−	0.459421i
$806$	2.97576	−	0.683732i	0.104817	−	0.0240834i
$807$	14.9944	+	4.01774i	0.527828	+	0.141431i
$808$	−38.5980	+	5.98930i	−1.35787	+	0.210703i
$809$	−1.09295	+	0.292855i	−0.0384260	+	0.0102962i	−0.277981	−	0.960587i	$-0.589665\pi$
$809$	−1.09295	+	0.292855i	−0.0384260	+	0.0102962i	0.239555	+	0.970883i	$0.422999\pi$
$810$	−0.177219	+	4.92721i	−0.00622684	+	0.173125i
$811$	−11.8518	−	28.6128i	−0.416174	−	1.00473i	−0.983446	−	0.181202i	$-0.942001\pi$
$811$	−11.8518	−	28.6128i	−0.416174	−	1.00473i	0.567272	−	0.823530i	$-0.307999\pi$
$812$	2.19856	−	17.6901i	0.0771544	−	0.620800i
$813$	−8.36656	−	3.46554i	−0.293428	−	0.121542i
$814$	−0.613422	−	1.64591i	−0.0215004	−	0.0576892i
$815$	0.532219	+	0.307277i	0.0186428	+	0.0107634i
$816$	9.27115	+	0.119678i	0.324555	+	0.00418956i
$817$	27.2158	−	15.7130i	0.952159	−	0.549729i
$818$	8.00281	−	47.5177i	0.279812	−	1.66142i
$819$	−0.982892	−	1.92610i	−0.0343450	−	0.0673035i
$820$	−10.1151	+	11.3850i	−0.353236	+	0.397582i
$821$	−0.170058	+	0.221624i	−0.00593506	+	0.00773473i	−0.796311	−	0.604887i	$-0.793218\pi$
$821$	−0.170058	+	0.221624i	−0.00593506	+	0.00773473i	0.790376	+	0.612622i	$0.209885\pi$
$822$	6.21008	+	11.7090i	0.216601	+	0.408397i
$823$	−38.8603	+	10.4126i	−1.35459	+	0.362960i	−0.861826	−	0.507205i	$-0.830679\pi$
$823$	−38.8603	+	10.4126i	−1.35459	+	0.362960i	−0.492761	+	0.870165i	$0.664012\pi$
$824$	−1.01069	−	43.8515i	−0.0352092	−	1.52764i
$825$	5.91777	−	5.91777i	0.206030	−	0.206030i
$826$	−7.17258	−	11.2694i	−0.249566	−	0.392112i
$827$	8.92722	−	3.69778i	0.310430	−	0.128584i	−0.222029	−	0.975040i	$-0.571268\pi$
$827$	8.92722	−	3.69778i	0.310430	−	0.128584i	0.532459	+	0.846456i	$0.321268\pi$
$828$	−4.75745	−	24.7511i	−0.165333	−	0.860161i
$829$	22.0306	+	28.7109i	0.765156	+	0.997170i	0.999686	+	0.0250616i	$0.00797818\pi$
$829$	22.0306	+	28.7109i	0.765156	+	0.997170i	−0.234530	+	0.972109i	$0.575355\pi$
$830$	−1.90624	−	20.0164i	−0.0661666	−	0.694778i
$831$	−0.0340019	−	0.0588931i	−0.00117951	−	0.00204298i
$832$	2.72154	−	0.486773i	0.0943526	−	0.0168758i
$833$	3.20996	+	20.1067i	0.111218	+	0.696654i
$834$	−12.0965	+	8.60927i	−0.418867	+	0.298115i
$835$	4.00742	−	0.527587i	0.138682	−	0.0182579i
$836$	16.5810	−	14.3529i	0.573466	−	0.496405i
$837$	−3.48624	+	26.4806i	−0.120502	+	0.915304i
$838$	−16.2900	+	15.1589i	−0.562730	+	0.523655i
$839$	−8.42872	+	8.42872i	−0.290992	+	0.290992i	−0.837472	−	0.546480i	$-0.815967\pi$
$839$	−8.42872	+	8.42872i	−0.290992	+	0.290992i	0.546480	+	0.837472i	$0.315967\pi$
$840$	−0.895936	+	5.56588i	−0.0309127	+	0.192041i
$841$	12.4811	+	12.4811i	0.430384	+	0.430384i
$842$	35.9082	+	1.29152i	1.23748	+	0.0445088i
$843$	−15.7010	−	2.06708i	−0.540771	−	0.0711939i
$844$	−13.7103	−	41.2623i	−0.471929	−	1.42031i
$845$	1.58937	+	12.0725i	0.0546760	+	0.415305i
$846$	4.12837	−	24.5127i	0.141936	−	0.842766i
$847$	7.65651	−	8.97580i	0.263081	−	0.308412i
$848$	−9.22493	+	32.7319i	−0.316785	+	1.12402i
$849$	−13.0558	+	7.53776i	−0.448074	+	0.258695i
$850$	−10.7581	+	13.0228i	−0.368999	+	0.446680i
$851$	−2.05307	+	1.57538i	−0.0703784	+	0.0540032i
$852$	−3.92117	−	5.95124i	−0.134337	−	0.203886i
$853$	18.5412	+	44.7623i	0.634837	+	1.53263i	0.833473	+	0.552560i	$0.186349\pi$
$853$	18.5412	+	44.7623i	0.634837	+	1.53263i	−0.198636	+	0.980073i	$0.563651\pi$
$854$	32.8094	−	35.7743i	1.12271	−	1.22417i
$855$	6.77790	+	6.77790i	0.231799	+	0.231799i
$856$	−48.9074	−	18.9500i	−1.67162	−	0.647696i
$857$	−7.92654	−	29.5823i	−0.270765	−	1.01051i	−0.958626	−	0.284668i	$-0.908117\pi$
$857$	−7.92654	−	29.5823i	−0.270765	−	1.01051i	0.687861	−	0.725843i	$-0.258550\pi$
$858$	0.292224	−	0.952261i	0.00997637	−	0.0325097i
$859$	−13.6851	−	10.5010i	−0.466931	−	0.358289i	0.348340	−	0.937368i	$-0.386745\pi$
$859$	−13.6851	−	10.5010i	−0.466931	−	0.358289i	−0.815271	+	0.579079i	$0.803412\pi$
$860$	12.4686	−	6.04912i	0.425176	−	0.206273i
$861$	14.2488	+	9.24080i	0.485597	+	0.314926i
$862$	−0.238759	−	0.335468i	−0.00813215	−	0.0114261i
$863$	−24.3733	−	42.2158i	−0.829676	−	1.43704i	−0.898293	−	0.439398i	$-0.855192\pi$
$863$	−24.3733	−	42.2158i	−0.829676	−	1.43704i	0.0686167	−	0.997643i	$-0.478141\pi$
$864$	−4.32409	+	23.7952i	−0.147108	+	0.809528i
$865$	−6.18922	+	10.7200i	−0.210440	+	0.364492i
$866$	9.78236	−	21.4061i	0.332418	−	0.727409i
$867$	2.60410	−	6.28685i	0.0884398	−	0.213513i
$868$	8.32413	−	31.9923i	0.282539	−	1.08589i
$869$	−8.55248	+	3.54255i	−0.290123	+	0.120173i
$870$	2.44503	+	2.62748i	0.0828944	+	0.0890799i
$871$	0.0192465	+	0.0718289i	0.000652143	+	0.00243383i
$872$	17.0047	+	12.4363i	0.575853	+	0.421147i
$873$	6.93440	−	25.8795i	0.234694	−	0.875890i
$874$	−27.3821	−	17.1501i	−0.926214	−	0.580110i
$875$	−15.2508	−	16.9167i	−0.515570	−	0.571890i
$876$	−0.338273	−	5.72719i	−0.0114292	−	0.193504i
$877$	5.16367	+	39.2220i	0.174365	+	1.32443i	0.825039	+	0.565075i	$0.191153\pi$
$877$	5.16367	+	39.2220i	0.174365	+	1.32443i	−0.650674	+	0.759357i	$0.725514\pi$
$878$	−36.4557	+	44.1303i	−1.23032	+	1.48932i
$879$	−3.60676	−	2.08236i	−0.121653	−	0.0702363i
$880$	7.74784	−	5.78779i	0.261180	−	0.195106i
$881$		−	31.0093i		−	1.04473i	−0.852722	−	0.522365i	$-0.825050\pi$
$881$		−	31.0093i		−	1.04473i	0.852722	−	0.522365i	$-0.174950\pi$
$882$	−23.4110	−	0.199960i	−0.788289	−	0.00673299i
$883$	29.8384	+	12.3595i	1.00414	+	0.415929i	0.823314	−	0.567586i	$-0.192123\pi$
$883$	29.8384	+	12.3595i	1.00414	+	0.415929i	0.180827	+	0.983515i	$0.442123\pi$
$884$	−0.404944	+	1.96928i	−0.0136197	+	0.0662340i
$885$	2.66656	+	0.351059i	0.0896355	+	0.0118007i
$886$	0.0176773	+	0.0333301i	0.000593879	+	0.00111975i
$887$	−1.44556	+	5.39492i	−0.0485373	+	0.181144i	−0.985939	−	0.167107i	$-0.946557\pi$
$887$	−1.44556	+	5.39492i	−0.0485373	+	0.181144i	0.937401	+	0.348251i	$0.113224\pi$
$888$	1.05052	−	0.307597i	0.0352531	−	0.0103223i
$889$	5.66197	−	11.8894i	0.189897	−	0.398758i
$890$	−1.33773	−	5.82212i	−0.0448410	−	0.195158i
$891$	−7.48271	−	5.74169i	−0.250680	−	0.192354i
$892$	29.6640	+	34.2690i	0.993224	+	1.14741i
$893$	−19.3986	−	25.2808i	−0.649150	−	0.845989i
$894$	22.1833	+	10.1375i	0.741921	+	0.339050i
$895$	−2.41540			−0.0807378
$896$	8.94328	−	28.5660i	0.298774	−	0.954324i
$897$	−1.46753			−0.0489993
$898$	−16.5168	−	7.54800i	−0.551173	−	0.251880i
$899$	−12.8120	−	16.6969i	−0.427304	−	0.556873i
$900$	−12.7116	−	14.6849i	−0.423721	−	0.489498i
$901$	−19.6192	−	15.0544i	−0.653612	−	0.501534i
$902$	−6.52394	−	28.3937i	−0.217224	−	0.945406i
$903$	−8.76119	−	12.7308i	−0.291554	−	0.423655i
$904$	−26.5656	+	7.77854i	−0.883557	+	0.258710i
$905$	−2.74467	+	10.2432i	−0.0912358	+	0.340497i
$906$	−9.79266	−	18.4639i	−0.325339	−	0.613421i
$907$	24.2485	+	3.19237i	0.805158	+	0.106001i	0.521860	−	0.853031i	$-0.325238\pi$
$907$	24.2485	+	3.19237i	0.805158	+	0.106001i	0.283297	+	0.959032i	$0.408572\pi$
$908$	5.66958	−	27.5717i	0.188152	−	0.914999i
$909$	30.1734	+	12.4982i	1.00079	+	0.414540i
$910$	−1.14852	−	0.418585i	−0.0380730	−	0.0138760i
$911$		−	20.4352i		−	0.677050i	−0.940957	−	0.338525i	$-0.890072\pi$
$911$		−	20.4352i		−	0.677050i	0.940957	−	0.338525i	$-0.109928\pi$
$912$	8.17902	+	10.9489i	0.270834	+	0.362554i
$913$	33.3109	+	19.2321i	1.10243	+	0.636489i
$914$	−36.4346	+	44.1046i	−1.20515	+	1.45885i
$915$	1.27567	+	9.68970i	0.0421725	+	0.320332i
$916$	−0.385582	−	6.52816i	−0.0127400	−	0.215697i
$917$	−11.9244	+	36.7766i	−0.393779	+	1.21447i
$918$	−14.9048	−	9.33525i	−0.491933	−	0.308109i
$919$	−11.9791	+	44.7065i	−0.395153	+	1.47473i	0.426367	+	0.904550i	$0.359793\pi$
$919$	−11.9791	+	44.7065i	−0.395153	+	1.47473i	−0.821520	+	0.570180i	$0.806873\pi$
$920$	−11.5006	−	8.41094i	−0.379165	−	0.277300i
$921$	0.446768	+	1.66736i	0.0147215	+	0.0549414i
$922$	−32.0900	−	34.4845i	−1.05683	−	1.13569i
$923$	1.42773	−	0.591386i	0.0469944	−	0.0194657i
$924$	−7.68088	−	7.57029i	−0.252682	−	0.249044i
$925$	−0.763149	+	1.84240i	−0.0250922	+	0.0605779i
$926$	5.15407	−	11.2783i	0.169373	−	0.370629i
$927$	−18.3378	+	31.7620i	−0.602293	+	1.04320i
$928$	−10.8489	−	15.6675i	−0.356132	−	0.514310i
$929$	−8.48001	−	14.6878i	−0.278220	−	0.481891i	0.692722	−	0.721204i	$-0.256411\pi$
$929$	−8.48001	−	14.6878i	−0.278220	−	0.481891i	−0.970942	+	0.239313i	$0.923078\pi$
$930$	3.85938	+	5.42263i	0.126554	+	0.177815i
$931$	−20.6320	+	21.7953i	−0.676187	+	0.714312i
$932$	54.1085	−	26.2506i	1.77238	−	0.859866i
$933$	12.4556	+	9.55751i	0.407778	+	0.312899i
$934$	4.88791	−	15.9281i	0.159937	−	0.521183i
$935$	1.82017	+	6.79298i	0.0595261	+	0.222154i
$936$	−2.15555	−	0.835202i	−0.0704562	−	0.0272994i
$937$	−0.494513	−	0.494513i	−0.0161550	−	0.0161550i	0.698983	−	0.715138i	$-0.253636\pi$
$937$	−0.494513	−	0.494513i	−0.0161550	−	0.0161550i	−0.715138	+	0.698983i	$0.753636\pi$
$938$	0.785952	+	0.174596i	0.0256622	+	0.00570076i
$939$	5.82851	+	14.0713i	0.190206	+	0.459198i
$940$	−7.73152	−	11.7343i	−0.252174	−	0.382730i
$941$	37.4358	−	28.7255i	1.22037	−	0.936425i	0.221127	−	0.975245i	$-0.429026\pi$
$941$	37.4358	−	28.7255i	1.22037	−	0.936425i	0.999246	+	0.0388197i	$0.0123598\pi$
$942$	−6.26735	+	7.58673i	−0.204201	+	0.247189i
$943$	−37.1716	+	21.4610i	−1.21047	+	0.698868i
$944$	−13.7452	−	3.87384i	−0.447368	−	0.126083i
$945$	6.93971	−	8.13549i	0.225749	−	0.264647i
$946$	−4.40292	+	26.1429i	−0.143151	+	0.849979i
$947$	1.57326	+	11.9501i	0.0511240	+	0.388325i	0.997809	+	0.0661638i	$0.0210760\pi$
$947$	1.57326	+	11.9501i	0.0511240	+	0.388325i	−0.946685	+	0.322161i	$0.895591\pi$
$948$	−1.81905	−	5.47459i	−0.0590801	−	0.177806i
$949$	1.23338	+	0.162378i	0.0400372	+	0.00527100i
$950$	−24.8818	−	0.894935i	−0.807273	−	0.0290355i
$951$	−8.67348	−	8.67348i	−0.281257	−	0.281257i
$952$	16.8816	+	13.7411i	0.547137	+	0.445351i
$953$	38.3195	−	38.3195i	1.24129	−	1.24129i	0.281824	−	0.959466i	$-0.409060\pi$
$953$	38.3195	−	38.3195i	1.24129	−	1.24129i	0.959466	−	0.281824i	$-0.0909395\pi$
$954$	20.8160	−	19.3706i	0.673942	−	0.627145i
$955$	−0.504487	+	3.83196i	−0.0163248	+	0.123999i
$956$	26.2763	−	22.7454i	0.849837	−	0.735638i
$957$	−6.80719	+	0.896184i	−0.220045	+	0.0289695i
$958$	−7.40788	+	5.27232i	−0.239338	+	0.170341i
$959$	−5.65148	+	30.5978i	−0.182496	+	0.988053i
$960$	3.25065	+	5.07497i	0.104914	+	0.163794i
$961$	−4.01422	−	6.95283i	−0.129491	−	0.224285i
$962$	0.0225023	+	0.236284i	0.000725505	+	0.00761812i
$963$	26.6976	+	34.7930i	0.860318	+	1.12119i
$964$	5.58423	+	29.0525i	0.179856	+	0.935719i
$965$	−4.47395	+	1.85317i	−0.144021	+	0.0596556i
$966$	−7.34262	+	14.0903i	−0.236245	+	0.453346i
$967$	−2.47601	+	2.47601i	−0.0796230	+	0.0796230i	−0.745797	−	0.666174i	$-0.767931\pi$
$967$	−2.47601	+	2.47601i	−0.0796230	+	0.0796230i	0.666174	+	0.745797i	$0.267931\pi$
$968$	−0.290613	−	12.6090i	−0.00934065	−	0.405268i
$969$	−9.59951	+	2.57218i	−0.308381	+	0.0826304i
$970$	−7.09662	−	13.3805i	−0.227859	−	0.429623i
$971$	−12.0088	+	15.6502i	−0.385381	+	0.502239i	−0.945252	−	0.326341i	$-0.894184\pi$
$971$	−12.0088	+	15.6502i	−0.385381	+	0.502239i	0.559871	+	0.828580i	$0.310851\pi$
$972$	20.9415	−	23.5706i	0.671699	−	0.756026i
$973$	−34.8096	−	1.80281i	−1.11594	−	0.0577955i
$974$	−1.96599	+	11.6733i	−0.0629943	+	0.374037i
$975$	−0.979375	+	0.565443i	−0.0313651	+	0.0181087i
$976$	0.669809	−	51.8884i	0.0214401	−	1.66091i
$977$	−22.8540	−	13.1948i	−0.731164	−	0.422138i	0.0876837	−	0.996148i	$-0.472054\pi$
$977$	−22.8540	−	13.1948i	−0.731164	−	0.422138i	−0.818848	+	0.574011i	$0.805387\pi$
$978$	−0.255855	−	0.686503i	−0.00818135	−	0.0219519i
$979$	10.5579	+	4.37324i	0.337433	+	0.139769i
$980$	−9.76546	+	8.93297i	−0.311946	+	0.285353i
$981$	−6.74097	−	16.2741i	−0.215223	−	0.519593i
$982$	−1.36707	+	38.0086i	−0.0436250	+	1.21290i
$983$	−17.1517	+	4.59578i	−0.547054	+	0.146583i	−0.521752	−	0.853097i	$-0.674721\pi$
$983$	−17.1517	+	4.59578i	−0.547054	+	0.146583i	−0.0253020	+	0.999680i	$0.508055\pi$
$984$	17.9408	−	2.78390i	0.571932	−	0.0887475i
$985$	−3.31581	−	0.888468i	−0.105650	−	0.0283090i
$986$	13.5061	−	3.10326i	0.430121	−	0.0988279i
$987$	−11.6389	+	10.4927i	−0.370471	+	0.333986i
$988$	−2.66619	+	1.29349i	−0.0848228	+	0.0411515i
$989$	38.7243	−	5.09815i	1.23136	−	0.162112i
$990$	−8.04983	+	0.766619i	−0.255840	+	0.0243647i
$991$	25.0110	−	43.3204i	0.794502	−	1.37612i	−0.128653	−	0.991690i	$-0.541065\pi$
$991$	25.0110	−	43.3204i	0.794502	−	1.37612i	0.923155	−	0.384428i	$-0.125601\pi$
$992$	−16.1541	−	31.4318i	−0.512893	−	0.997959i
$993$	−7.08844			−0.224945
$994$	1.46540	−	16.6671i	0.0464797	−	0.528648i
$995$	−0.867434	+	2.09417i	−0.0274995	+	0.0663897i
$996$	−13.4455	+	19.8441i	−0.426036	+	0.628785i
$997$	−0.571643	+	4.34206i	−0.0181041	+	0.137514i	−0.998110	−	0.0614547i	$-0.980426\pi$
$997$	−0.571643	+	4.34206i	−0.0181041	+	0.137514i	0.980006	+	0.198969i	$0.0637593\pi$
$998$	−6.49172	+	21.1544i	−0.205492	+	0.669630i
$999$	−2.00553	−	0.537381i	−0.0634523	−	0.0170020i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.bd.a.109.26	yes	240
4.3	odd	2		896.2.bh.a.529.13		240
7.2	even	3	inner	224.2.bd.a.205.15	yes	240
28.23	odd	6		896.2.bh.a.401.18		240
32.5	even	8	inner	224.2.bd.a.165.15	yes	240
32.27	odd	8		896.2.bh.a.753.18		240
224.37	even	24	inner	224.2.bd.a.37.26	✓	240
224.219	odd	24		896.2.bh.a.625.13		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.bd.a.37.26	✓	240	224.37	even	24	inner
224.2.bd.a.109.26	yes	240	1.1	even	1	trivial
224.2.bd.a.165.15	yes	240	32.5	even	8	inner
224.2.bd.a.205.15	yes	240	7.2	even	3	inner
896.2.bh.a.401.18		240	28.23	odd	6
896.2.bh.a.529.13		240	4.3	odd	2
896.2.bh.a.625.13		240	224.219	odd	24
896.2.bh.a.753.18		240	32.27	odd	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.bd (of order \(24\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28627 + 0.587810i) q^{2} +(0.485121 + 0.632222i) q^{3} +(1.30896 + 1.51216i) q^{4} +(-0.749996 - 0.575492i) q^{5} +(0.252368 + 1.09836i) q^{6} +(-1.13756 + 2.38872i) q^{7} +(0.794808 + 2.71446i) q^{8} +(0.612095 - 2.28437i) q^{9} +(-0.626414 - 1.18109i) q^{10} +(2.53563 + 0.333822i) q^{11} +(-0.321016 + 1.56113i) q^{12} +(-0.319285 - 0.132252i) q^{13} +(-2.86731 + 2.40386i) q^{14} -0.753347i q^{15} +(-0.573250 + 3.95871i) q^{16} +(-2.51905 - 1.45438i) q^{17} +(2.13009 - 2.57851i) q^{18} +(-0.559620 - 4.25074i) q^{19} +(-0.111479 - 1.88741i) q^{20} +(-2.06205 + 0.439629i) q^{21} +(3.06527 + 1.91985i) q^{22} +(1.37917 - 5.14712i) q^{23} +(-1.33056 + 1.81934i) q^{24} +(-1.06279 - 3.96640i) q^{25} +(-0.332946 - 0.357790i) q^{26} +(3.94988 - 1.63609i) q^{27} +(-5.10113 + 1.40657i) q^{28} +(-1.28920 + 3.11239i) q^{29} +(0.442825 - 0.969004i) q^{30} +(-3.12364 + 5.41030i) q^{31} +(-3.06432 + 4.75499i) q^{32} +(1.01904 + 1.76503i) q^{33} +(-2.38528 - 3.35144i) q^{34} +(2.22785 - 1.13687i) q^{35} +(4.25554 - 2.06456i) q^{36} +(-0.385287 - 0.295641i) q^{37} +(1.77880 - 5.79653i) q^{38} +(-0.0712791 - 0.266017i) q^{39} +(0.966046 - 2.49324i) q^{40} +(-5.69568 - 5.69568i) q^{41} +(-2.91076 - 0.646614i) q^{42} +(2.80501 + 6.77189i) q^{43} +(2.81425 + 4.27124i) q^{44} +(-1.77370 + 1.36101i) q^{45} +(4.79950 - 5.80987i) q^{46} +(6.43663 - 3.71619i) q^{47} +(-2.78088 + 1.55803i) q^{48} +(-4.41194 - 5.43460i) q^{49} +(0.964452 - 5.72656i) q^{50} +(-0.302557 - 2.29815i) q^{51} +(-0.217945 - 0.655923i) q^{52} +(8.42902 + 1.10970i) q^{53} +(6.04231 + 0.217326i) q^{54} +(-1.70960 - 1.70960i) q^{55} +(-7.38821 - 1.18927i) q^{56} +(2.41593 - 2.41593i) q^{57} +(-3.48774 + 3.24556i) q^{58} +(-0.466000 + 3.53962i) q^{59} +(1.13918 - 0.986101i) q^{60} +(-12.8622 + 1.69334i) q^{61} +(-7.19805 + 5.12298i) q^{62} +(4.76042 + 4.06072i) q^{63} +(-6.73656 + 4.31495i) q^{64} +(0.163352 + 0.282935i) q^{65} +(0.273255 + 2.86929i) q^{66} +(-0.130990 - 0.170710i) q^{67} +(-1.09809 - 5.71293i) q^{68} +(3.92318 - 1.62503i) q^{69} +(3.53387 - 0.152770i) q^{70} +(-3.16194 + 3.16194i) q^{71} +(6.68732 - 0.154130i) q^{72} +(-3.47703 + 0.931668i) q^{73} +(-0.321800 - 0.606748i) q^{74} +(1.99206 - 2.59610i) q^{75} +(5.69527 - 6.41028i) q^{76} +(-3.68183 + 5.67716i) q^{77} +(0.0646837 - 0.384068i) q^{78} +(-3.13466 + 1.80979i) q^{79} +(2.70814 - 2.63911i) q^{80} +(-3.19378 - 1.84393i) q^{81} +(-3.97818 - 10.6741i) q^{82} +(13.8948 + 5.75543i) q^{83} +(-3.36393 - 2.54269i) q^{84} +(1.05230 + 2.54047i) q^{85} +(-0.372596 + 10.3593i) q^{86} +(-2.59314 + 0.694829i) q^{87} +(1.10919 + 7.14819i) q^{88} +(4.31608 + 1.15649i) q^{89} +(-3.08147 + 0.708022i) q^{90} +(0.679118 - 0.612238i) q^{91} +(9.58853 - 4.65185i) q^{92} +(-4.93585 + 0.649817i) q^{93} +(10.4636 - 0.996495i) q^{94} +(-2.02655 + 3.51009i) q^{95} +(-4.49278 + 0.369416i) q^{96} +11.3290 q^{97} +(-2.48041 - 9.58371i) q^{98} +(2.31462 - 5.58799i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} - 16 q^{6} - 8 q^{7} - 16 q^{8} - 4 q^{9} - 4 q^{10} - 4 q^{11} - 4 q^{12} - 16 q^{13} + 24 q^{14} - 24 q^{16} - 24 q^{18} - 4 q^{19} - 48 q^{20} - 8 q^{21}+ \cdots + 8 q^{99}+O(q^{100}) \) 240 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 16 * q^6 - 8 * q^7 - 16 * q^8 - 4 * q^9 - 4 * q^10 - 4 * q^11 - 4 * q^12 - 16 * q^13 + 24 * q^14 - 24 * q^16 - 24 * q^18 - 4 * q^19 - 48 * q^20 - 8 * q^21 - 24 * q^22 - 12 * q^23 + 36 * q^24 - 4 * q^25 - 4 * q^26 - 16 * q^27 + 12 * q^28 - 16 * q^29 + 44 * q^30 - 56 * q^31 - 4 * q^32 - 8 * q^33 - 32 * q^34 - 32 * q^35 - 96 * q^36 - 4 * q^37 + 36 * q^38 - 4 * q^39 - 68 * q^40 - 16 * q^41 - 28 * q^42 + 44 * q^44 + 8 * q^45 - 4 * q^46 - 16 * q^48 + 8 * q^50 - 28 * q^51 - 28 * q^52 - 20 * q^53 - 92 * q^54 - 16 * q^55 - 48 * q^56 - 16 * q^57 + 28 * q^58 - 36 * q^59 + 60 * q^60 - 4 * q^61 - 16 * q^63 + 56 * q^64 - 8 * q^65 - 36 * q^66 + 36 * q^67 - 36 * q^68 - 16 * q^69 - 44 * q^70 + 48 * q^71 - 4 * q^72 - 4 * q^73 + 68 * q^74 + 16 * q^75 - 16 * q^76 - 8 * q^77 - 120 * q^78 - 16 * q^80 - 44 * q^82 - 96 * q^83 - 28 * q^84 - 56 * q^85 - 4 * q^86 - 4 * q^87 + 40 * q^88 - 4 * q^89 + 224 * q^90 - 56 * q^91 - 80 * q^92 + 20 * q^93 + 4 * q^94 - 8 * q^95 - 32 * q^96 - 32 * q^97 + 96 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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