LMFDB - Embedded newform 180.2.x.a.43.32

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(7,180)] 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("180.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 8, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.x (of order $12$, degree $4$, 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:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$32$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			43.32
Character	$\chi$	$=$	180.43
Dual form			180.2.x.a.67.32

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.41320 - 0.0534584i) q^{2} +(1.72686 - 0.133985i) q^{3} +(1.99428 - 0.151095i) q^{4} +(-2.20762 - 0.355578i) q^{5} +(2.43324 - 0.281664i) q^{6} +(-2.46165 + 0.659597i) q^{7} +(2.81025 - 0.320139i) q^{8} +(2.96410 - 0.462748i) q^{9} +(-3.13882 - 0.384488i) q^{10} +(-3.01796 - 1.74242i) q^{11} +(3.42361 - 0.528125i) q^{12} +(-1.36518 + 5.09493i) q^{13} +(-3.44355 + 1.06374i) q^{14} +(-3.85989 - 0.318245i) q^{15} +(3.95434 - 0.602653i) q^{16} +(2.16382 - 2.16382i) q^{17} +(4.16413 - 0.812413i) q^{18} -3.88577 q^{19} +(-4.45634 - 0.375564i) q^{20} +(-4.16255 + 1.46886i) q^{21} +(-4.35813 - 2.30106i) q^{22} +(-3.70190 - 0.991920i) q^{23} +(4.81002 - 0.929369i) q^{24} +(4.74713 + 1.56996i) q^{25} +(-1.65691 + 7.27315i) q^{26} +(5.05658 - 1.19625i) q^{27} +(-4.80957 + 1.68737i) q^{28} +(3.85118 + 2.22348i) q^{29} +(-5.47181 - 0.243402i) q^{30} +(1.86992 - 1.07960i) q^{31} +(5.55607 - 1.06306i) q^{32} +(-5.44505 - 2.60455i) q^{33} +(2.94224 - 3.17359i) q^{34} +(5.66891 - 0.580828i) q^{35} +(5.84133 - 1.37071i) q^{36} +(3.67542 - 3.67542i) q^{37} +(-5.49138 + 0.207727i) q^{38} +(-1.67483 + 8.98115i) q^{39} +(-6.31779 - 0.292519i) q^{40} +(-4.04792 - 7.01121i) q^{41} +(-5.80400 + 2.29832i) q^{42} +(1.36185 + 5.08248i) q^{43} +(-6.28194 - 3.01888i) q^{44} +(-6.70813 - 0.0323966i) q^{45} +(-5.28456 - 1.20389i) q^{46} +(0.231550 - 0.0620436i) q^{47} +(6.74785 - 1.57052i) q^{48} +(-0.437526 + 0.252606i) q^{49} +(6.79258 + 1.96490i) q^{50} +(3.44669 - 4.02653i) q^{51} +(-1.95274 + 10.3670i) q^{52} +(0.265818 + 0.265818i) q^{53} +(7.08202 - 1.96086i) q^{54} +(6.04292 + 4.91971i) q^{55} +(-6.70669 + 2.64170i) q^{56} +(-6.71018 + 0.520636i) q^{57} +(5.56137 + 2.93635i) q^{58} +(-5.69158 - 9.85810i) q^{59} +(-7.74580 - 0.0514614i) q^{60} +(-4.61792 + 7.99848i) q^{61} +(2.58487 - 1.62566i) q^{62} +(-6.99134 + 3.09423i) q^{63} +(7.79502 - 1.79934i) q^{64} +(4.82544 - 10.7622i) q^{65} +(-7.83420 - 3.38968i) q^{66} +(-0.192807 + 0.719566i) q^{67} +(3.98832 - 4.64221i) q^{68} +(-6.52556 - 1.21691i) q^{69} +(7.98027 - 1.12388i) q^{70} -2.06980i q^{71} +(8.18171 - 2.24936i) q^{72} +(8.97449 + 8.97449i) q^{73} +(4.99763 - 5.39060i) q^{74} +(8.40798 + 2.07505i) q^{75} +(-7.74933 + 0.587121i) q^{76} +(8.57845 + 2.29859i) q^{77} +(-1.88676 + 12.7817i) q^{78} +(7.56173 - 13.0973i) q^{79} +(-8.94395 - 0.0756494i) q^{80} +(8.57173 - 2.74326i) q^{81} +(-6.09534 - 9.69186i) q^{82} +(4.01723 + 14.9925i) q^{83} +(-8.07937 + 3.55826i) q^{84} +(-5.54628 + 4.00747i) q^{85} +(2.19627 + 7.10978i) q^{86} +(6.94837 + 3.32364i) q^{87} +(-9.03903 - 3.93047i) q^{88} +3.61495i q^{89} +(-9.48167 + 0.312823i) q^{90} -13.4424i q^{91} +(-7.53251 - 1.41883i) q^{92} +(3.08444 - 2.11486i) q^{93} +(0.323910 - 0.100059i) q^{94} +(8.57828 + 1.38169i) q^{95} +(9.45212 - 2.58020i) q^{96} +(-0.818990 - 3.05651i) q^{97} +(-0.604809 + 0.380373i) q^{98} +(-9.75182 - 3.76814i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 2 q^{2} - 4 q^{5} - 8 q^{6} - 8 q^{8} - 8 q^{10} + 2 q^{12} - 4 q^{13} - 4 q^{16} - 16 q^{17} - 36 q^{18} - 18 q^{20} - 24 q^{21} - 10 q^{22} - 4 q^{25} - 48 q^{26} + 8 q^{28} - 14 q^{30} + 18 q^{32}+ \cdots + 164 q^{98}+O(q^{100}) $ 128 * q - 2 * q^2 - 4 * q^5 - 8 * q^6 - 8 * q^8 - 8 * q^10 + 2 * q^12 - 4 * q^13 - 4 * q^16 - 16 * q^17 - 36 * q^18 - 18 * q^20 - 24 * q^21 - 10 * q^22 - 4 * q^25 - 48 * q^26 + 8 * q^28 - 14 * q^30 + 18 * q^32 - 20 * q^33 - 40 * q^36 - 16 * q^37 - 34 * q^38 - 2 * q^40 - 8 * q^41 + 34 * q^42 - 28 * q^45 - 40 * q^46 - 22 * q^48 + 38 * q^50 - 18 * q^52 - 64 * q^53 - 32 * q^56 - 48 * q^57 - 10 * q^58 + 74 * q^60 - 8 * q^61 + 44 * q^62 + 12 * q^65 - 36 * q^66 + 58 * q^68 - 22 * q^70 + 78 * q^72 - 16 * q^73 - 32 * q^76 - 60 * q^77 + 114 * q^78 + 132 * q^80 + 24 * q^81 - 4 * q^85 + 32 * q^86 - 10 * q^88 + 138 * q^90 + 52 * q^92 - 68 * q^93 + 52 * q^96 - 4 * q^97 + 164 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.41320	−	0.0534584i	0.999285	−	0.0378008i
$2$	1.41320	−	0.0534584i	0.999285	−	0.0378008i
$3$	1.72686	−	0.133985i	0.997003	−	0.0773565i
$3$	1.72686	−	0.133985i	0.997003	−	0.0773565i
$4$	1.99428	−	0.151095i	0.997142	−	0.0755476i
$5$	−2.20762	−	0.355578i	−0.987275	−	0.159019i
$5$	−2.20762	−	0.355578i	−0.987275	−	0.159019i
$6$	2.43324	−	0.281664i	0.993367	−	0.114989i
$7$	−2.46165	+	0.659597i	−0.930416	+	0.249304i	−0.692032	−	0.721867i	$-0.743284\pi$
$7$	−2.46165	+	0.659597i	−0.930416	+	0.249304i	−0.238384	+	0.971171i	$0.576618\pi$
$8$	2.81025	−	0.320139i	0.993574	−	0.113186i
$9$	2.96410	−	0.462748i	0.988032	−	0.154249i
$10$	−3.13882	−	0.384488i	−0.992581	−	0.121586i
$11$	−3.01796	−	1.74242i	−0.909948	−	0.525359i	−0.0295338	−	0.999564i	$-0.509402\pi$
$11$	−3.01796	−	1.74242i	−0.909948	−	0.525359i	−0.880415	+	0.474205i	$0.842736\pi$
$12$	3.42361	−	0.528125i	0.988310	−	0.152457i
$13$	−1.36518	+	5.09493i	−0.378634	+	1.41308i	0.469329	+	0.883024i	$0.344496\pi$
$13$	−1.36518	+	5.09493i	−0.378634	+	1.41308i	−0.847962	+	0.530057i	$0.822171\pi$
$14$	−3.44355	+	1.06374i	−0.920327	+	0.284297i
$15$	−3.85989	−	0.318245i	−0.996618	−	0.0821706i
$16$	3.95434	−	0.602653i	0.988585	−	0.150663i
$17$	2.16382	−	2.16382i	0.524802	−	0.524802i	−0.394216	−	0.919018i	$-0.628984\pi$
$17$	2.16382	−	2.16382i	0.524802	−	0.524802i	0.919018	+	0.394216i	$0.128984\pi$
$18$	4.16413	−	0.812413i	0.981495	−	0.191488i
$19$	−3.88577			−0.891456			−0.445728	−	0.895168i	$-0.647055\pi$
$19$	−3.88577			−0.891456			−0.445728	+	0.895168i	$0.647055\pi$
$20$	−4.45634	−	0.375564i	−0.996468	−	0.0839786i
$21$	−4.16255	+	1.46886i	−0.908343	+	0.320531i
$22$	−4.35813	−	2.30106i	−0.929157	−	0.490587i
$23$	−3.70190	−	0.991920i	−0.771899	−	0.206830i	−0.148689	−	0.988884i	$-0.547505\pi$
$23$	−3.70190	−	0.991920i	−0.771899	−	0.206830i	−0.623210	+	0.782054i	$0.714172\pi$
$24$	4.81002	−	0.929369i	0.981841	−	0.189707i
$25$	4.74713	+	1.56996i	0.949426	+	0.313992i
$26$	−1.65691	+	7.27315i	−0.324947	+	1.42638i
$27$	5.05658	−	1.19625i	0.973139	−	0.230218i
$28$	−4.80957	+	1.68737i	−0.908923	+	0.318883i
$29$	3.85118	+	2.22348i	0.715147	+	0.412890i	0.812964	−	0.582314i	$-0.197853\pi$
$29$	3.85118	+	2.22348i	0.715147	+	0.412890i	−0.0978169	+	0.995204i	$0.531186\pi$
$30$	−5.47181	−	0.243402i	−0.999012	−	0.0444389i
$31$	1.86992	−	1.07960i	0.335848	−	0.193902i	−0.322586	−	0.946540i	$-0.604552\pi$
$31$	1.86992	−	1.07960i	0.335848	−	0.193902i	0.658434	+	0.752638i	$0.271219\pi$
$32$	5.55607	−	1.06306i	0.982183	−	0.187925i
$33$	−5.44505	−	2.60455i	−0.947862	−	0.453394i
$34$	2.94224	−	3.17359i	0.504589	−	0.544265i
$35$	5.66891	−	0.580828i	0.958221	−	0.0981779i
$36$	5.84133	−	1.37071i	0.973555	−	0.228452i
$37$	3.67542	−	3.67542i	0.604235	−	0.604235i	−0.337198	−	0.941434i	$-0.609479\pi$
$37$	3.67542	−	3.67542i	0.604235	−	0.604235i	0.941434	+	0.337198i	$0.109479\pi$
$38$	−5.49138	+	0.207727i	−0.890819	+	0.0336978i
$39$	−1.67483	+	8.98115i	−0.268188	+	1.43814i
$40$	−6.31779	−	0.292519i	−0.998930	−	0.0462513i
$41$	−4.04792	−	7.01121i	−0.632179	−	1.09497i	−0.987105	−	0.160072i	$-0.948827\pi$
$41$	−4.04792	−	7.01121i	−0.632179	−	1.09497i	0.354926	−	0.934894i	$-0.384506\pi$
$42$	−5.80400	+	2.29832i	−0.895577	+	0.354638i
$43$	1.36185	+	5.08248i	0.207680	+	0.775071i	0.988616	+	0.150461i	$0.0480757\pi$
$43$	1.36185	+	5.08248i	0.207680	+	0.775071i	−0.780936	+	0.624611i	$0.785258\pi$
$44$	−6.28194	−	3.01888i	−0.947037	−	0.455113i
$45$	−6.70813	−	0.0323966i	−0.999988	−	0.00482940i
$46$	−5.28456	−	1.20389i	−0.779165	−	0.177503i
$47$	0.231550	−	0.0620436i	0.0337750	−	0.00904999i	−0.241892	−	0.970303i	$-0.577768\pi$
$47$	0.231550	−	0.0620436i	0.0337750	−	0.00904999i	0.275667	+	0.961253i	$0.411101\pi$
$48$	6.74785	−	1.57052i	0.973968	−	0.226685i
$49$	−0.437526	+	0.252606i	−0.0625037	+	0.0360865i
$50$	6.79258	+	1.96490i	0.960616	+	0.277878i
$51$	3.44669	−	4.02653i	0.482633	−	0.563827i
$52$	−1.95274	+	10.3670i	−0.270797	+	1.43765i
$53$	0.265818	+	0.265818i	0.0365129	+	0.0365129i	0.725127	−	0.688615i	$-0.241781\pi$
$53$	0.265818	+	0.265818i	0.0365129	+	0.0365129i	−0.688615	+	0.725127i	$0.741781\pi$
$54$	7.08202	−	1.96086i	0.963741	−	0.266839i
$55$	6.04292	+	4.91971i	0.814827	+	0.663373i
$56$	−6.70669	+	2.64170i	−0.896219	+	0.353013i
$57$	−6.71018	+	0.520636i	−0.888785	+	0.0689600i
$58$	5.56137	+	2.93635i	0.730243	+	0.385562i
$59$	−5.69158	−	9.85810i	−0.740980	−	1.28342i	−0.952049	−	0.305944i	$-0.901028\pi$
$59$	−5.69158	−	9.85810i	−0.740980	−	1.28342i	0.211069	−	0.977471i	$-0.432305\pi$
$60$	−7.74580	−	0.0514614i	−0.999978	−	0.00664364i
$61$	−4.61792	+	7.99848i	−0.591264	+	1.02410i	0.402798	+	0.915289i	$0.368038\pi$
$61$	−4.61792	+	7.99848i	−0.591264	+	1.02410i	−0.994062	+	0.108811i	$0.965296\pi$
$62$	2.58487	−	1.62566i	0.328278	−	0.206459i
$63$	−6.99134	+	3.09423i	−0.880826	+	0.389837i
$64$	7.79502	−	1.79934i	0.974378	−	0.224918i
$65$	4.82544	−	10.7622i	0.598523	−	1.33489i
$66$	−7.83420	−	3.38968i	−0.964323	−	0.417240i
$67$	−0.192807	+	0.719566i	−0.0235551	+	0.0879089i	−0.976703	−	0.214596i	$-0.931156\pi$
$67$	−0.192807	+	0.719566i	−0.0235551	+	0.0879089i	0.953148	+	0.302505i	$0.0978230\pi$
$68$	3.98832	−	4.64221i	0.483655	−	0.562950i
$69$	−6.52556	−	1.21691i	−0.785585	−	0.146498i
$70$	7.98027	−	1.12388i	0.953825	−	0.134329i
$71$		−	2.06980i		−	0.245640i	−0.992429	−	0.122820i	$-0.960806\pi$
$71$		−	2.06980i		−	0.245640i	0.992429	−	0.122820i	$-0.0391938\pi$
$72$	8.18171	−	2.24936i	0.964224	−	0.265090i
$73$	8.97449	+	8.97449i	1.05038	+	1.05038i	0.998661	+	0.0517232i	$0.0164714\pi$
$73$	8.97449	+	8.97449i	1.05038	+	1.05038i	0.0517232	+	0.998661i	$0.483529\pi$
$74$	4.99763	−	5.39060i	0.580963	−	0.626644i
$75$	8.40798	+	2.07505i	0.970870	+	0.239607i
$76$	−7.74933	+	0.587121i	−0.888909	+	0.0673474i
$77$	8.57845	+	2.29859i	0.977605	+	0.261948i
$78$	−1.88676	+	12.7817i	−0.213634	+	1.44725i
$79$	7.56173	−	13.0973i	0.850761	−	1.47356i	−0.0297623	−	0.999557i	$-0.509475\pi$
$79$	7.56173	−	13.0973i	0.850761	−	1.47356i	0.880523	−	0.474004i	$-0.157192\pi$
$80$	−8.94395	−	0.0756494i	−0.999964	−	0.00845786i
$81$	8.57173	−	2.74326i	0.952414	−	0.304807i
$82$	−6.09534	−	9.69186i	−0.673118	−	1.07029i
$83$	4.01723	+	14.9925i	0.440949	+	1.64564i	0.726417	+	0.687255i	$0.241184\pi$
$83$	4.01723	+	14.9925i	0.440949	+	1.64564i	−0.285468	+	0.958388i	$0.592149\pi$
$84$	−8.07937	+	3.55826i	−0.881532	+	0.388238i
$85$	−5.54628	+	4.00747i	−0.601578	+	0.434671i
$86$	2.19627	+	7.10978i	0.236830	+	0.766667i
$87$	6.94837	+	3.32364i	0.744944	+	0.356332i
$88$	−9.03903	−	3.93047i	−0.963564	−	0.418989i
$89$			3.61495i			0.383184i	0.981475	+	0.191592i	$0.0613650\pi$
$89$			3.61495i			0.383184i	−0.981475	+	0.191592i	$0.938635\pi$
$90$	−9.48167	+	0.312823i	−0.999456	+	0.0329744i
$91$		−	13.4424i		−	1.40915i
$92$	−7.53251	−	1.41883i	−0.785318	−	0.147923i
$93$	3.08444	−	2.11486i	0.319842	−	0.219301i
$94$	0.323910	−	0.100059i	0.0334088	−	0.0103203i
$95$	8.57828	+	1.38169i	0.880113	+	0.141759i
$96$	9.45212	−	2.58020i	0.964703	−	0.263340i
$97$	−0.818990	−	3.05651i	−0.0831559	−	0.310342i	0.911803	−	0.410629i	$-0.134691\pi$
$97$	−0.818990	−	3.05651i	−0.0831559	−	0.310342i	−0.994959	+	0.100287i	$0.968024\pi$
$98$	−0.604809	+	0.380373i	−0.0610949	+	0.0384234i
$99$	−9.75182	−	3.76814i	−0.980094	−	0.378712i
$100$	9.70434	+	2.41368i	0.970434	+	0.241368i
$101$	2.15969	−	3.74069i	0.214897	−	0.372213i	−0.738344	−	0.674425i	$-0.764392\pi$
$101$	2.15969	−	3.74069i	0.214897	−	0.372213i	0.953241	+	0.302212i	$0.0977250\pi$
$102$	4.65562	−	5.87456i	0.460975	−	0.581668i
$103$	−1.31939	−	0.353529i	−0.130003	−	0.0348342i	0.193231	−	0.981153i	$-0.438103\pi$
$103$	−1.31939	−	0.353529i	−0.130003	−	0.0348342i	−0.323234	+	0.946319i	$0.604770\pi$
$104$	−2.20542	+	14.7551i	−0.216259	+	1.44686i
$105$	9.71160	−	1.76256i	0.947755	−	0.172008i
$106$	0.389864	+	0.361444i	0.0378670	+	0.0351065i
$107$	5.32781	+	5.32781i	0.515059	+	0.515059i	0.916072	−	0.401013i	$-0.131342\pi$
$107$	5.32781	+	5.32781i	0.515059	+	0.515059i	−0.401013	+	0.916072i	$0.631342\pi$
$108$	9.90351	−	3.14968i	0.952966	−	0.303078i
$109$		−	14.1851i		−	1.35869i	−0.733820	−	0.679344i	$-0.762264\pi$
$109$		−	14.1851i		−	1.35869i	0.733820	−	0.679344i	$-0.237736\pi$
$110$	8.80287	+	6.62950i	0.839321	+	0.632098i
$111$	5.85449	−	6.83939i	0.555683	−	0.649166i
$112$	−9.33669	+	4.09179i	−0.882235	+	0.386638i
$113$	−0.117242	+	0.437551i	−0.0110292	+	0.0411614i	−0.971221	−	0.238180i	$-0.923449\pi$
$113$	−0.117242	+	0.437551i	−0.0110292	+	0.0411614i	0.960192	+	0.279341i	$0.0901160\pi$
$114$	−9.45501	+	1.09448i	−0.885543	+	0.102507i
$115$	7.81966	+	3.50609i	0.729187	+	0.326945i
$116$	8.01631	+	3.85236i	0.744296	+	0.357683i
$117$	−1.68886	+	15.7336i	−0.156135	+	1.45457i
$118$	−8.57035	−	13.6272i	−0.788965	−	1.25449i
$119$	−3.89931	+	6.75380i	−0.357449	+	0.619120i
$120$	−10.9491	+	0.341353i	−0.999514	+	0.0311611i
$121$	0.572043	+	0.990808i	0.0520040	+	0.0900735i
$122$	−6.09848	+	11.5503i	−0.552130	+	1.04572i
$123$	−7.92960	−	11.5650i	−0.714988	−	1.04278i
$124$	3.56603	−	2.43557i	0.320239	−	0.218720i
$125$	−9.92159	−	5.15384i	−0.887414	−	0.460973i
$126$	−9.71477	+	4.74653i	−0.865460	+	0.422854i
$127$	−2.66261	−	2.66261i	−0.236269	−	0.236269i	0.579034	−	0.815303i	$-0.303430\pi$
$127$	−2.66261	−	2.66261i	−0.236269	−	0.236269i	−0.815303	+	0.579034i	$0.803430\pi$
$128$	10.9198	−	2.95955i	0.965179	−	0.261590i
$129$	3.03270	+	8.59427i	0.267014	+	0.756683i
$130$	6.24400	−	15.4672i	0.547635	−	1.35656i
$131$	−10.6177	+	6.13011i	−0.927670	+	0.535590i	−0.886074	−	0.463544i	$-0.846578\pi$
$131$	−10.6177	+	6.13011i	−0.927670	+	0.535590i	−0.0415959	+	0.999135i	$0.513244\pi$
$132$	−11.2525	−	4.37150i	−0.979406	−	0.380490i
$133$	9.56540	−	2.56304i	0.829425	−	0.222244i
$134$	−0.234009	+	1.02720i	−0.0202153	+	0.0887365i
$135$	−11.5883	+	0.842847i	−0.997365	+	0.0725407i
$136$	5.38814	−	6.77359i	0.462029	−	0.580830i
$137$	2.39423	+	8.93538i	0.204553	+	0.763401i	0.989585	+	0.143947i	$0.0459794\pi$
$137$	2.39423	+	8.93538i	0.204553	+	0.763401i	−0.785033	+	0.619454i	$0.787354\pi$
$138$	−9.28700	−	1.37089i	−0.790562	−	0.116698i
$139$	8.95460	+	15.5098i	0.759520	+	1.31553i	0.943096	+	0.332521i	$0.107899\pi$
$139$	8.95460	+	15.5098i	0.759520	+	1.31553i	−0.183576	+	0.983005i	$0.558767\pi$
$140$	11.2177	−	2.01488i	0.948066	−	0.170289i
$141$	0.391542	−	0.138165i	0.0329738	−	0.0116356i
$142$	−0.110648	−	2.92504i	−0.00928539	−	0.245464i
$143$	12.9976	−	12.9976i	1.08691	−	1.08691i
$144$	11.4422	−	3.61619i	0.953514	−	0.301349i
$145$	−7.71131	−	6.27799i	−0.640389	−	0.521359i
$146$	13.1625	+	12.2030i	1.08934	+	1.00993i
$147$	−0.721701	+	0.494837i	−0.0595249	+	0.0408135i
$148$	6.77450	−	7.88517i	0.556860	−	0.648157i
$149$	−2.39752	+	1.38421i	−0.196413	+	0.113399i	−0.594981	−	0.803740i	$-0.702840\pi$
$149$	−2.39752	+	1.38421i	−0.196413	+	0.113399i	0.398568	+	0.917139i	$0.369507\pi$
$150$	11.9931	+	2.48299i	0.979234	+	0.202736i
$151$	−6.51667	−	3.76240i	−0.530319	−	0.306180i	0.210827	−	0.977523i	$-0.432384\pi$
$151$	−6.51667	−	3.76240i	−0.530319	−	0.306180i	−0.741146	+	0.671343i	$0.765718\pi$
$152$	−10.9200	+	1.24399i	−0.885728	+	0.100901i
$153$	5.41246	−	7.41506i	0.437571	−	0.599472i
$154$	12.2460	+	2.78978i	0.986808	+	0.224807i
$155$	−4.51195	+	1.71844i	−0.362409	+	0.138028i
$156$	−1.98309	+	18.1640i	−0.158774	+	1.45429i
$157$	−3.61744	−	0.969291i	−0.288703	−	0.0773578i	0.111561	−	0.993758i	$-0.464415\pi$
$157$	−3.61744	−	0.969291i	−0.288703	−	0.0773578i	−0.400264	+	0.916400i	$0.631082\pi$
$158$	9.98609	−	18.9134i	0.794451	−	1.50467i
$159$	0.494646	+	0.423414i	0.0392279	+	0.0335789i
$160$	−12.6437	+	0.371222i	−0.999569	+	0.0293476i
$161$	9.76704			0.769751
$162$	11.9669	−	4.33502i	0.940212	−	0.340591i
$163$	−6.76935	+	6.76935i	−0.530216	+	0.530216i	−0.920637	−	0.390420i	$-0.872330\pi$
$163$	−6.76935	+	6.76935i	−0.530216	+	0.530216i	0.390420	+	0.920637i	$0.372330\pi$
$164$	−9.13207	−	13.3707i	−0.713095	−	1.04408i
$165$	11.0945	+	7.68599i	0.863702	+	0.598353i
$166$	6.47864	+	20.9727i	0.502840	+	1.62780i
$167$	−0.957423	+	3.57315i	−0.0740876	+	0.276499i	−0.993025	−	0.117905i	$-0.962382\pi$
$167$	−0.957423	+	3.57315i	−0.0740876	+	0.276499i	0.918937	+	0.394404i	$0.129049\pi$
$168$	−11.2276	+	5.46045i	−0.866226	+	0.421283i
$169$	−12.8363	−	7.41103i	−0.987406	−	0.570079i
$170$	−7.62378	+	5.95986i	−0.584717	+	0.457100i
$171$	−11.5178	+	1.79813i	−0.880787	+	0.137507i
$172$	3.48385	+	9.93015i	0.265641	+	0.757167i
$173$	−22.3985	+	6.00167i	−1.70293	+	0.456299i	−0.973674	−	0.227943i	$-0.926800\pi$
$173$	−22.3985	+	6.00167i	−1.70293	+	0.456299i	−0.729255	+	0.684242i	$0.760133\pi$
$174$	9.99714	+	4.32553i	0.757881	+	0.327918i
$175$	−12.7213	−	0.733496i	−0.961641	−	0.0554470i
$176$	−12.9841	−	5.07133i	−0.978714	−	0.382266i
$177$	−11.1494	−	16.2610i	−0.838041	−	1.22225i
$178$	0.193249	+	5.10866i	0.0144847	+	0.382910i
$179$	−10.0185			−0.748819			−0.374410	−	0.927263i	$-0.622155\pi$
$179$	−10.0185			−0.748819			−0.374410	+	0.927263i	$0.622155\pi$
$180$	−13.3828	+	0.948957i	−0.997495	+	0.0707311i
$181$	−19.9811			−1.48518			−0.742590	−	0.669746i	$-0.766403\pi$
$181$	−19.9811			−1.48518			−0.742590	+	0.669746i	$0.766403\pi$
$182$	−0.718610	−	18.9969i	−0.0532669	−	1.40814i
$183$	−6.90283	+	14.4310i	−0.510272	+	1.06677i
$184$	−10.7208	−	1.60242i	−0.790349	−	0.118132i
$185$	−9.42081	+	6.80702i	−0.692632	+	0.500462i
$186$	4.24589	−	3.15362i	0.311324	−	0.231234i
$187$	−10.3006	+	2.76003i	−0.753253	+	0.201833i
$188$	0.452402	−	0.158719i	0.0329948	−	0.0115758i
$189$	−11.6585	+	6.28005i	−0.848030	+	0.456806i
$190$	12.1967	+	1.49403i	0.884843	+	0.108388i
$191$	13.5705	+	7.83490i	0.981923	+	0.566914i	0.902850	−	0.429955i	$-0.141471\pi$
$191$	13.5705	+	7.83490i	0.981923	+	0.566914i	0.0790731	+	0.996869i	$0.474804\pi$
$192$	13.2198	−	4.15164i	0.954059	−	0.299619i
$193$	5.58592	−	20.8469i	0.402083	−	1.50060i	−0.407289	−	0.913299i	$-0.633526\pi$
$193$	5.58592	−	20.8469i	0.402083	−	1.50060i	0.809372	−	0.587296i	$-0.199807\pi$
$194$	−1.32080	−	4.27569i	−0.0948276	−	0.306977i
$195$	6.89089	−	19.2314i	0.493467	−	1.37719i
$196$	−0.834384	+	0.569876i	−0.0595988	+	0.0407054i
$197$	−9.44630	+	9.44630i	−0.673021	+	0.673021i	−0.958411	−	0.285390i	$-0.907877\pi$
$197$	−9.44630	+	9.44630i	−0.673021	+	0.673021i	0.285390	+	0.958411i	$0.407877\pi$
$198$	−13.9827	−	4.80383i	−0.993709	−	0.341393i
$199$	−2.06079			−0.146085			−0.0730427	−	0.997329i	$-0.523271\pi$
$199$	−2.06079			−0.146085			−0.0730427	+	0.997329i	$0.523271\pi$
$200$	13.8432	+	2.89223i	0.978864	+	0.204512i
$201$	−0.236540	+	1.26842i	−0.0166842	+	0.0894677i
$202$	2.85211	−	5.40181i	0.200674	−	0.380070i
$203$	−10.9469	−	2.93320i	−0.768320	−	0.205871i
$204$	6.26529	−	8.55082i	0.438658	−	0.598677i
$205$	6.44322	+	16.9174i	0.450014	+	1.18156i
$206$	−1.88346	−	0.429076i	−0.131227	−	0.0298951i
$207$	−11.4318	−	1.22710i	−0.794564	−	0.0852893i
$208$	−2.32792	+	20.9698i	−0.161412	+	1.45400i
$209$	11.7271	+	6.77063i	0.811179	+	0.468335i
$210$	13.6302	−	3.01002i	0.940576	−	0.207711i
$211$	−1.99458	+	1.15157i	−0.137313	+	0.0792776i	−0.567083	−	0.823661i	$-0.691928\pi$
$211$	−1.99458	+	1.15157i	−0.137313	+	0.0792776i	0.429770	+	0.902938i	$0.358595\pi$
$212$	0.570280	+	0.489952i	0.0391670	+	0.0336500i
$213$	−0.277323	−	3.57425i	−0.0190019	−	0.244904i
$214$	7.81409	+	7.24446i	0.534161	+	0.495221i
$215$	−1.19922	−	11.7044i	−0.0817858	−	0.798234i
$216$	13.8273	−	4.98057i	0.940828	−	0.338885i
$217$	−3.89099	+	3.89099i	−0.264138	+	0.264138i
$218$	−0.758314	−	20.0465i	−0.0513595	−	1.35772i
$219$	16.7001	+	14.2952i	1.12849	+	0.965983i
$220$	12.7946	+	8.89824i	0.862615	+	0.599919i
$221$	8.07049	+	13.9785i	0.542880	+	0.940296i
$222$	7.90795	−	9.97842i	0.530747	−	0.669708i
$223$	−4.32002	−	16.1225i	−0.289290	−	1.07964i	−0.945647	−	0.325194i	$-0.894570\pi$
$223$	−4.32002	−	16.1225i	−0.289290	−	1.07964i	0.656357	−	0.754450i	$-0.272096\pi$
$224$	−12.9759	+	6.28166i	−0.866989	+	0.419711i
$225$	14.7974	+	2.45678i	0.986496	+	0.163785i
$226$	−0.142295	+	0.624617i	−0.00946534	+	0.0415489i
$227$	−4.86933	+	1.30473i	−0.323189	+	0.0865981i	−0.416766	−	0.909014i	$-0.636836\pi$
$227$	−4.86933	+	1.30473i	−0.323189	+	0.0865981i	0.0935772	+	0.995612i	$0.470170\pi$
$228$	−13.3033	+	2.05217i	−0.881035	+	0.135908i
$229$	6.71866	−	3.87902i	0.443981	−	0.256333i	−0.261304	−	0.965257i	$-0.584152\pi$
$229$	6.71866	−	3.87902i	0.443981	−	0.256333i	0.705285	+	0.708924i	$0.250819\pi$
$230$	11.2382	+	4.53679i	0.741024	+	0.299147i
$231$	15.1218	+	2.81995i	0.994939	+	0.185539i
$232$	11.5346	+	5.01563i	0.757285	+	0.329292i
$233$	−4.15335	−	4.15335i	−0.272095	−	0.272095i	0.557848	−	0.829943i	$-0.311627\pi$
$233$	−4.15335	−	4.15335i	−0.272095	−	0.272095i	−0.829943	+	0.557848i	$0.811627\pi$
$234$	−1.54561	+	22.3251i	−0.101040	+	1.45943i
$235$	−0.533235	+	0.0546344i	−0.0347844	+	0.00356396i
$236$	−12.8401	−	18.7999i	−0.835822	−	1.22377i
$237$	11.3032	−	23.6304i	0.734222	−	1.53496i
$238$	−5.14947	+	9.75295i	−0.333791	+	0.632190i
$239$	−1.28058	−	2.21802i	−0.0828335	−	0.143472i	0.821632	−	0.570018i	$-0.193064\pi$
$239$	−1.28058	−	2.21802i	−0.0828335	−	0.143472i	−0.904466	+	0.426546i	$0.859730\pi$
$240$	−15.4551	+	1.06772i	−0.997622	+	0.0689213i
$241$	6.89420	−	11.9411i	0.444094	−	0.769194i	−0.553894	−	0.832587i	$-0.686859\pi$
$241$	6.89420	−	11.9411i	0.444094	−	0.769194i	0.997989	+	0.0633929i	$0.0201921\pi$
$242$	0.861381	+	1.36963i	0.0553716	+	0.0880433i
$243$	14.4346	−	5.88572i	0.925981	−	0.377569i
$244$	−8.00092	+	16.6490i	−0.512206	+	1.06584i
$245$	1.05571	−	0.402082i	0.0674468	−	0.0256881i
$246$	−11.8244	−	15.9198i	−0.753895	−	1.01501i
$247$	5.30478	−	19.7977i	0.337535	−	1.25970i
$248$	4.90933	−	3.63258i	0.311743	−	0.230669i
$249$	8.94598	+	25.3517i	0.566929	+	1.60660i
$250$	−14.2967	−	6.75303i	−0.904205	−	0.427099i
$251$		−	11.4799i		−	0.724602i	−0.932061	−	0.362301i	$-0.881991\pi$
$251$		−	11.4799i		−	0.724602i	0.932061	−	0.362301i	$-0.118009\pi$
$252$	−13.4752	+	7.22714i	−0.848857	+	0.455267i
$253$	9.44382	+	9.44382i	0.593728	+	0.593728i
$254$	−3.90515	−	3.62047i	−0.245031	−	0.227169i
$255$	−9.04071	+	7.66346i	−0.566151	+	0.479904i
$256$	15.2736	−	4.76619i	0.954601	−	0.297887i
$257$	14.1728	+	3.79760i	0.884077	+	0.236888i	0.672165	−	0.740401i	$-0.265364\pi$
$257$	14.1728	+	3.79760i	0.884077	+	0.236888i	0.211912	+	0.977289i	$0.432031\pi$
$258$	4.74525	+	11.9833i	0.295427	+	0.746049i
$259$	−6.62330	+	11.4719i	−0.411552	+	0.712829i
$260$	7.99719	−	22.1920i	0.495965	−	1.37629i
$261$	12.4442	+	4.80848i	0.770276	+	0.297638i
$262$	−14.6772	+	9.23070i	−0.906761	+	0.570274i
$263$	0.474777	+	1.77189i	0.0292760	+	0.109259i	0.979018	−	0.203775i	$-0.0653211\pi$
$263$	0.474777	+	1.77189i	0.0292760	+	0.109259i	−0.949742	+	0.313034i	$0.898654\pi$
$264$	−16.1358	−	5.57627i	−0.993088	−	0.343196i
$265$	−0.492304	−	0.681342i	−0.0302420	−	0.0418545i
$266$	13.3808	−	4.13345i	0.820432	−	0.253438i
$267$	0.484351	+	6.24252i	0.0296418	+	0.382036i
$268$	−0.275789	+	1.46415i	−0.0168465	+	0.0894372i
$269$		−	13.4031i		−	0.817201i	−0.912713	−	0.408600i	$-0.866017\pi$
$269$		−	13.4031i		−	0.817201i	0.912713	−	0.408600i	$-0.133983\pi$
$270$	−16.3316	+	1.81061i	−0.993911	+	0.110190i
$271$			19.1919i			1.16582i	0.812536	+	0.582911i	$0.198086\pi$
$271$			19.1919i			1.16582i	−0.812536	+	0.582911i	$0.801914\pi$
$272$	7.25243	−	9.86050i	0.439743	−	0.597880i
$273$	−1.80109	−	23.2132i	−0.109007	−	1.40493i
$274$	3.86120	+	12.4995i	0.233264	+	0.755123i
$275$	−11.5911	−	13.0096i	−0.698970	−	0.784505i
$276$	−13.1977	−	1.44088i	−0.794408	−	0.0867307i
$277$	−1.93430	−	7.21889i	−0.116221	−	0.433741i	0.883155	−	0.469082i	$-0.155415\pi$
$277$	−1.93430	−	7.21889i	−0.116221	−	0.433741i	−0.999375	+	0.0353406i	$0.988748\pi$
$278$	13.4838	+	21.4398i	0.808705	+	1.28588i
$279$	5.04305	−	4.06534i	0.301919	−	0.243386i
$280$	15.7451	−	3.44712i	0.940951	−	0.206005i
$281$	−6.99536	+	12.1163i	−0.417308	+	0.722799i	−0.995668	−	0.0929831i	$-0.970360\pi$
$281$	−6.99536	+	12.1163i	−0.417308	+	0.722799i	0.578360	+	0.815782i	$0.303693\pi$
$282$	0.545942	−	0.216186i	0.0325104	−	0.0128737i
$283$	1.79491	+	0.480944i	0.106696	+	0.0285891i	0.311772	−	0.950157i	$-0.399077\pi$
$283$	1.79491	+	0.480944i	0.106696	+	0.0285891i	−0.205076	+	0.978746i	$0.565744\pi$
$284$	−0.312737	−	4.12777i	−0.0185575	−	0.244938i
$285$	14.9986	+	1.23663i	0.888442	+	0.0732515i
$286$	17.6734	−	19.0630i	1.04505	−	1.12722i
$287$	14.5891	+	14.5891i	0.861170	+	0.861170i
$288$	15.9768	−	5.72209i	0.941441	−	0.337177i
$289$			7.63580i			0.449165i
$290$	−11.2333	−	8.45984i	−0.659640	−	0.496779i
$291$	−1.82381	−	5.16844i	−0.106914	−	0.302979i
$292$	19.2537	+	16.5417i	1.12674	+	0.968029i
$293$	−6.82756	+	25.4808i	−0.398870	+	1.48860i	0.416217	+	0.909266i	$0.363356\pi$
$293$	−6.82756	+	25.4808i	−0.398870	+	1.48860i	−0.815087	+	0.579339i	$0.803311\pi$
$294$	−0.993456	+	0.737886i	−0.0579396	+	0.0430344i
$295$	9.05949	+	23.7867i	0.527464	+	1.38491i
$296$	9.15221	−	11.5055i	0.531961	−	0.668744i
$297$	−17.3449	−	5.20045i	−1.00645	−	0.301761i
$298$	−3.31419	+	2.08434i	−0.191986	+	0.120742i
$299$	10.1075	−	17.5068i	0.584534	−	1.01244i
$300$	17.0814	+	2.86784i	0.986197	+	0.165575i
$301$	−6.70478	−	11.6130i	−0.386457	−	0.669363i
$302$	−9.41051	−	4.96867i	−0.541514	−	0.285915i
$303$	3.22828	−	6.74902i	0.185460	−	0.387721i
$304$	−15.3657	+	2.34177i	−0.881280	+	0.134310i
$305$	13.0387	−	16.0155i	0.746593	−	0.917046i
$306$	7.25250	−	10.7683i	0.414598	−	0.615584i
$307$	13.9421	+	13.9421i	0.795717	+	0.795717i	0.982417	−	0.186700i	$-0.0597792\pi$
$307$	13.9421	+	13.9421i	0.795717	+	0.795717i	−0.186700	+	0.982417i	$0.559779\pi$
$308$	17.4552	+	3.28788i	0.994601	+	0.187344i
$309$	−2.32577	−	0.433717i	−0.132308	−	0.0246733i
$310$	−6.28444	+	2.66970i	−0.356932	+	0.151629i
$311$	−0.701482	+	0.405001i	−0.0397774	+	0.0229655i	−0.519757	−	0.854314i	$-0.673977\pi$
$311$	−0.701482	+	0.405001i	−0.0397774	+	0.0229655i	0.479979	+	0.877280i	$0.340644\pi$
$312$	−1.83148	+	25.7755i	−0.103687	+	1.45925i
$313$	6.11329	−	1.63805i	0.345544	−	0.0925882i	−0.0818732	−	0.996643i	$-0.526090\pi$
$313$	6.11329	−	1.63805i	0.345544	−	0.0925882i	0.427417	+	0.904055i	$0.359424\pi$
$314$	−5.16400	−	1.17642i	−0.291421	−	0.0663893i
$315$	16.5344	−	4.34491i	0.931609	−	0.244808i
$316$	13.1013	−	27.2623i	0.737005	−	1.53362i
$317$	−5.23297	−	19.5297i	−0.293913	−	1.09690i	−0.942077	−	0.335397i	$-0.891129\pi$
$317$	−5.23297	−	19.5297i	−0.293913	−	1.09690i	0.648164	−	0.761501i	$-0.275537\pi$
$318$	0.721670	+	0.571927i	0.0404692	+	0.0320721i
$319$	−7.74847	−	13.4207i	−0.433831	−	0.751418i
$320$	−17.8482	+	1.20052i	−0.997746	+	0.0671112i
$321$	9.91424	+	8.48654i	0.553359	+	0.473672i
$322$	13.8028	−	0.522130i	0.769200	−	0.0290972i
$323$	−8.40809	+	8.40809i	−0.467838	+	0.467838i
$324$	16.6800	−	6.76599i	0.926665	−	0.375888i
$325$	−14.4795	+	22.0430i	−0.803180	+	1.22273i
$326$	−9.20458	+	9.92834i	−0.509795	+	0.549880i
$327$	−1.90060	−	24.4957i	−0.105103	−	1.35462i
$328$	−13.6202	−	18.4073i	−0.752052	−	1.01638i
$329$	−0.529071	+	0.305459i	−0.0291686	+	0.0168405i
$330$	16.0896	+	10.2688i	0.885703	+	0.565277i
$331$	16.9166	+	9.76680i	0.929821	+	0.536832i	0.886755	−	0.462240i	$-0.152954\pi$
$331$	16.9166	+	9.76680i	0.929821	+	0.536832i	0.0430657	+	0.999072i	$0.486288\pi$
$332$	10.2768	+	29.2924i	0.564013	+	1.60763i
$333$	9.19350	−	12.5951i	0.503801	−	0.690207i
$334$	−1.16202	+	5.10077i	−0.0635828	+	0.279102i
$335$	0.681505	−	1.51997i	0.0372346	−	0.0830446i
$336$	−15.5749	+	8.31694i	−0.849682	+	0.453726i
$337$	9.77024	+	2.61793i	0.532219	+	0.142608i	0.514913	−	0.857243i	$-0.327824\pi$
$337$	9.77024	+	2.61793i	0.532219	+	0.142608i	0.0173061	+	0.999850i	$0.494491\pi$
$338$	−18.5365	−	9.78708i	−1.00825	−	0.532347i
$339$	−0.143834	+	0.771299i	−0.00781201	+	0.0418912i
$340$	−10.4553	+	8.83005i	−0.567021	+	0.478876i
$341$	−7.52446			−0.407472
$342$	−16.1808	+	3.15685i	−0.874960	+	0.170703i
$343$	13.5248	−	13.5248i	0.730270	−	0.730270i
$344$	5.45423	+	13.8471i	0.294073	+	0.746584i
$345$	13.9732	+	5.00681i	0.752293	+	0.269558i
$346$	−31.3328	+	9.67897i	−1.68446	+	0.520345i
$347$	6.50347	−	24.2713i	0.349125	−	1.30295i	−0.538594	−	0.842565i	$-0.681044\pi$
$347$	6.50347	−	24.2713i	0.349125	−	1.30295i	0.887719	−	0.460386i	$-0.152289\pi$
$348$	14.3592	+	5.57842i	0.769735	+	0.299035i
$349$	−15.0315	−	8.67844i	−0.804617	−	0.464546i	0.0404658	−	0.999181i	$-0.487116\pi$
$349$	−15.0315	−	8.67844i	−0.804617	−	0.464546i	−0.845083	+	0.534635i	$0.820449\pi$
$350$	−18.0170	−	0.356517i	−0.963049	−	0.0190566i
$351$	−0.808354	+	27.3960i	−0.0431467	+	1.46229i
$352$	−18.6203	−	6.47271i	−0.992464	−	0.344997i
$353$	−28.8445	+	7.72886i	−1.53524	+	0.411366i	−0.924723	−	0.380640i	$-0.875704\pi$
$353$	−28.8445	+	7.72886i	−1.53524	+	0.411366i	−0.610514	+	0.792006i	$0.709037\pi$
$354$	−16.6257	−	22.3840i	−0.883644	−	1.18970i
$355$	−0.735975	+	4.56932i	−0.0390615	+	0.242514i
$356$	0.546201	+	7.20924i	0.0289486	+	0.382089i
$357$	−5.82865	+	12.1853i	−0.308485	+	0.644916i
$358$	−14.1582	+	0.535574i	−0.748284	+	0.0283060i
$359$	26.1394			1.37959			0.689794	−	0.724006i	$-0.257701\pi$
$359$	26.1394			1.37959			0.689794	+	0.724006i	$0.257701\pi$
$360$	−18.8619	+	2.05649i	−0.994109	+	0.108387i
$361$	−3.90081			−0.205306
$362$	−28.2373	+	1.06816i	−1.48412	+	0.0561410i
$363$	1.12059	+	1.63434i	0.0588159	+	0.0857807i
$364$	−2.03108	−	26.8080i	−0.106458	−	1.40512i
$365$	−16.6211	−	23.0034i	−0.869988	−	1.20405i
$366$	−8.98364	+	20.7629i	−0.469582	+	1.08530i
$367$	−22.2128	+	5.95191i	−1.15950	+	0.310687i	−0.786766	−	0.617251i	$-0.788246\pi$
$367$	−22.2128	+	5.95191i	−1.15950	+	0.310687i	−0.372734	+	0.927938i	$0.621580\pi$
$368$	−15.2363	−	1.69143i	−0.794249	−	0.0881718i
$369$	−15.2429	−	18.9087i	−0.793511	−	0.984348i
$370$	−12.9496	+	10.1233i	−0.673219	+	0.526286i
$371$	−0.829682	−	0.479017i	−0.0430750	−	0.0248693i
$372$	5.83172	−	4.68368i	0.302360	−	0.242838i
$373$	−3.44016	+	12.8388i	−0.178125	+	0.664770i	0.817874	+	0.575398i	$0.195153\pi$
$373$	−3.44016	+	12.8388i	−0.178125	+	0.664770i	−0.995998	+	0.0893722i	$0.971514\pi$
$374$	−14.4093	+	4.45114i	−0.745085	+	0.230163i
$375$	−17.8237	−	7.57061i	−0.920414	−	0.390945i
$376$	0.630851	−	0.248486i	0.0325337	−	0.0128147i
$377$	−16.5861	+	16.5861i	−0.854226	+	0.854226i
$378$	−16.1401	+	9.49823i	−0.830156	+	0.488536i
$379$	−12.7657			−0.655730			−0.327865	−	0.944725i	$-0.606329\pi$
$379$	−12.7657			−0.655730			−0.327865	+	0.944725i	$0.606329\pi$
$380$	17.3163	+	1.45935i	0.888307	+	0.0748632i
$381$	−4.95471	−	4.24121i	−0.253838	−	0.217284i
$382$	19.5966	+	10.3469i	1.00265	+	0.529391i
$383$	33.9365	+	9.09327i	1.73408	+	0.464644i	0.981116	−	0.193422i	$-0.0619586\pi$
$383$	33.9365	+	9.09327i	1.73408	+	0.464644i	0.752960	+	0.658066i	$0.228625\pi$
$384$	18.4604	−	6.57381i	0.942051	−	0.335469i
$385$	−18.1206	−	8.12470i	−0.923510	−	0.414073i
$386$	6.77959	−	29.7596i	0.345072	−	1.51472i
$387$	6.38856	+	14.4348i	0.324749	+	0.733761i
$388$	−2.09512	−	5.97181i	−0.106364	−	0.303173i
$389$	15.4675	+	8.93019i	0.784236	+	0.452779i	0.837929	−	0.545779i	$-0.183766\pi$
$389$	15.4675	+	8.93019i	0.784236	+	0.452779i	−0.0536937	+	0.998557i	$0.517099\pi$
$390$	8.71014	−	27.5462i	0.441055	−	1.39486i
$391$	−10.1566	+	5.86389i	−0.513639	+	0.296550i
$392$	−1.14869	+	0.849955i	−0.0580175	+	0.0429292i
$393$	−17.5139	+	12.0085i	−0.883459	+	0.605747i
$394$	−12.8446	+	13.8545i	−0.647099	+	0.697981i
$395$	−21.3505	+	26.2250i	−1.07426	+	1.31952i
$396$	−20.0172	−	6.04129i	−1.00590	−	0.303586i
$397$	22.9050	−	22.9050i	1.14957	−	1.14957i	0.162934	−	0.986637i	$-0.447904\pi$
$397$	22.9050	−	22.9050i	1.14957	−	1.14957i	0.986637	−	0.162934i	$-0.0520959\pi$
$398$	−2.91231	+	0.110166i	−0.145981	+	0.00552215i
$399$	16.1747	−	5.70764i	0.809748	−	0.285739i
$400$	19.7179	+	3.34728i	0.985895	+	0.167364i
$401$	−15.2608	−	26.4324i	−0.762087	−	1.31997i	−0.941773	−	0.336249i	$-0.890841\pi$
$401$	−15.2608	−	26.4324i	−0.762087	−	1.31997i	0.179686	−	0.983724i	$-0.442492\pi$
$402$	−0.266471	+	1.80518i	−0.0132903	+	0.0900344i
$403$	2.94770	+	11.0010i	0.146836	+	0.547998i
$404$	3.74183	−	7.78632i	0.186163	−	0.387384i
$405$	−19.8985	+	3.00815i	−0.988765	+	0.149476i
$406$	−15.6270	−	3.56001i	−0.775553	−	0.176680i
$407$	−17.4964	+	4.68814i	−0.867263	+	0.232383i
$408$	8.39701	−	12.4190i	0.415714	−	0.614831i
$409$	14.2191	−	8.20942i	0.703091	−	0.405930i	−0.105407	−	0.994429i	$-0.533614\pi$
$409$	14.2191	−	8.20942i	0.703091	−	0.405930i	0.808498	+	0.588499i	$0.200281\pi$
$410$	10.0100	+	23.5633i	0.494357	+	1.16371i
$411$	5.33171	+	15.1094i	0.262994	+	0.745290i
$412$	−2.68465	−	0.505684i	−0.132263	−	0.0249133i
$413$	20.5130	+	20.5130i	1.00938	+	1.00938i
$414$	−16.2210	−	1.12302i	−0.797220	−	0.0551932i
$415$	−3.53750	−	34.5262i	−0.173649	−	1.69482i
$416$	−2.16881	+	29.7591i	−0.106335	+	1.45906i
$417$	17.5414	+	25.5835i	0.859008	+	1.25283i
$418$	16.9347	+	8.94137i	0.828303	+	0.437337i
$419$	5.01036	+	8.67820i	0.244772	+	0.423958i	0.962068	−	0.272811i	$-0.0879535\pi$
$419$	5.01036	+	8.67820i	0.244772	+	0.423958i	−0.717295	+	0.696769i	$0.754620\pi$
$420$	19.1014	−	4.98242i	0.932052	−	0.243117i
$421$	−3.68335	+	6.37975i	−0.179515	+	0.310930i	−0.941715	−	0.336413i	$-0.890786\pi$
$421$	−3.68335	+	6.37975i	−0.179515	+	0.310930i	0.762199	+	0.647342i	$0.224120\pi$
$422$	−2.75719	+	1.73403i	−0.134218	+	0.0844115i
$423$	0.657626	−	0.291053i	0.0319749	−	0.0141515i
$424$	0.832113	+	0.661915i	0.0404110	+	0.0321455i
$425$	13.6690	−	6.87481i	0.663045	−	0.333477i
$426$	−0.582987	−	5.03632i	−0.0282458	−	0.244010i
$427$	6.09194	−	22.7354i	0.294810	−	1.10024i
$428$	11.4302	+	9.82017i	0.552499	+	0.474676i
$429$	20.7035	−	24.1865i	0.999575	−	1.16773i
$430$	−2.32043	−	16.4766i	−0.111901	−	0.794572i
$431$			16.4473i			0.792237i	0.918199	+	0.396119i	$0.129643\pi$
$431$			16.4473i			0.792237i	−0.918199	+	0.396119i	$0.870357\pi$
$432$	19.2745	−	7.77774i	0.927345	−	0.374206i
$433$	−3.78112	−	3.78112i	−0.181709	−	0.181709i	0.610391	−	0.792100i	$-0.291012\pi$
$433$	−3.78112	−	3.78112i	−0.181709	−	0.181709i	−0.792100	+	0.610391i	$0.791012\pi$
$434$	−5.29076	+	5.70677i	−0.253964	+	0.273934i
$435$	−14.1575	−	9.80801i	−0.678801	−	0.470258i
$436$	−2.14330	−	28.2892i	−0.102646	−	1.35481i
$437$	14.3847	+	3.85437i	0.688114	+	0.184380i
$438$	24.3649	+	19.3093i	1.16420	+	0.922635i
$439$	18.4104	−	31.8878i	0.878683	−	1.52192i	0.0258954	−	0.999665i	$-0.491756\pi$
$439$	18.4104	−	31.8878i	0.878683	−	1.52192i	0.852787	−	0.522258i	$-0.174910\pi$
$440$	18.5571	+	11.8910i	0.884676	+	0.566883i
$441$	−1.17998	+	0.951212i	−0.0561893	+	0.0452958i
$442$	12.1525	+	19.3230i	0.578036	+	0.919102i
$443$	−3.13302	−	11.6926i	−0.148854	−	0.555532i	−0.999554	−	0.0298790i	$-0.990488\pi$
$443$	−3.13302	−	11.6926i	−0.148854	−	0.555532i	0.850699	−	0.525653i	$-0.176179\pi$
$444$	10.6421	−	14.5243i	0.505052	−	0.689292i
$445$	1.28540	−	7.98042i	0.0609336	−	0.378308i
$446$	−6.96695	−	22.5535i	−0.329895	−	1.06794i
$447$	−3.95472	+	2.71157i	−0.187052	+	0.128253i
$448$	−18.0018	+	9.57093i	−0.850504	+	0.452184i
$449$			1.04828i			0.0494715i	0.999694	+	0.0247357i	$0.00787443\pi$
$449$			1.04828i			0.0494715i	−0.999694	+	0.0247357i	$0.992126\pi$
$450$	21.0431	+	2.68088i	0.991982	+	0.126378i
$451$			28.2127i			1.32848i
$452$	−0.167701	+	0.890317i	−0.00788800	+	0.0418770i
$453$	−11.7575	−	5.62401i	−0.552415	−	0.264239i
$454$	−6.81160	+	2.10416i	−0.319684	+	0.0987530i
$455$	−4.77982	+	29.6757i	−0.224082	+	1.39122i
$456$	−18.6906	+	3.61131i	−0.875268	+	0.169115i
$457$	3.52188	+	13.1438i	0.164747	+	0.614843i	0.998072	+	0.0620609i	$0.0197673\pi$
$457$	3.52188	+	13.1438i	0.164747	+	0.614843i	−0.833326	+	0.552782i	$0.813566\pi$
$458$	9.28746	−	5.84101i	0.433974	−	0.272932i
$459$	8.35305	−	13.5300i	0.389887	−	0.631525i
$460$	16.1244	+	5.81063i	0.751803	+	0.270922i
$461$	5.72422	−	9.91464i	0.266604	−	0.461771i	−0.701379	−	0.712789i	$-0.747432\pi$
$461$	5.72422	−	9.91464i	0.266604	−	0.461771i	0.967983	+	0.251018i	$0.0807652\pi$
$462$	21.5209	+	3.17678i	1.00124	+	0.147797i
$463$	−4.53841	−	1.21606i	−0.210918	−	0.0565153i	0.151813	−	0.988409i	$-0.451489\pi$
$463$	−4.53841	−	1.21606i	−0.210918	−	0.0565153i	−0.362731	+	0.931894i	$0.618156\pi$
$464$	16.5689	+	6.47148i	0.769191	+	0.300431i
$465$	−7.56127	+	3.57204i	−0.350645	+	0.165649i
$466$	−6.09155	−	5.64749i	−0.282186	−	0.261615i
$467$	−25.5411	−	25.5411i	−1.18190	−	1.18190i	−0.979251	−	0.202651i	$-0.935044\pi$
$467$	−25.5411	−	25.5411i	−1.18190	−	1.18190i	−0.202651	−	0.979251i	$-0.564956\pi$
$468$	−0.990798	+	31.6325i	−0.0457997	+	1.46221i
$469$		−	1.89849i		−	0.0876643i
$470$	−0.750648	+	0.105715i	−0.0346248	+	0.00487629i
$471$	−6.37669	−	1.18915i	−0.293822	−	0.0547929i
$472$	−19.1507	−	25.8816i	−0.881484	−	1.19130i
$473$	4.74581	−	17.7116i	0.218213	−	0.814381i
$474$	14.7105	−	33.9987i	0.675674	−	1.56161i
$475$	−18.4462	−	6.10049i	−0.846372	−	0.279910i
$476$	−6.75587	+	14.0582i	−0.309655	+	0.644355i
$477$	0.910915	+	0.664902i	0.0417080	+	0.0304438i
$478$	−1.92828	−	3.06606i	−0.0881977	−	0.140238i
$479$	−6.06234	+	10.5003i	−0.276995	+	0.479770i	−0.970637	−	0.240551i	$-0.922672\pi$
$479$	−6.06234	+	10.5003i	−0.276995	+	0.479770i	0.693641	+	0.720321i	$0.256005\pi$
$480$	−21.7841	+	2.33511i	−0.994304	+	0.106583i
$481$	13.7084	+	23.7436i	0.625049	+	1.08262i
$482$	9.10455	−	17.2438i	0.414701	−	0.785431i
$483$	16.8663	−	1.30864i	0.767444	−	0.0595452i
$484$	1.29052	+	1.88952i	0.0586602	+	0.0858873i
$485$	0.721187	+	7.03882i	0.0327474	+	0.319616i
$486$	20.0844	−	9.08936i	0.911047	−	0.412302i
$487$	12.5621	+	12.5621i	0.569243	+	0.569243i	0.931916	−	0.362673i	$-0.118136\pi$
$487$	12.5621	+	12.5621i	0.569243	+	0.569243i	−0.362673	+	0.931916i	$0.618136\pi$
$488$	−10.4169	+	23.9561i	−0.471551	+	1.08444i
$489$	−10.7827	+	12.5967i	−0.487612	+	0.569643i
$490$	1.47044	−	0.624659i	0.0664276	−	0.0282192i
$491$	0.109289	−	0.0630982i	0.00493215	−	0.00284758i	−0.497532	−	0.867446i	$-0.665760\pi$
$491$	0.109289	−	0.0630982i	0.00493215	−	0.00284758i	0.502464	+	0.864598i	$0.332427\pi$
$492$	−17.5613	−	21.8658i	−0.791724	−	0.985786i
$493$	13.1445	−	3.52205i	0.591997	−	0.158625i
$494$	6.43838	−	28.2618i	0.289677	−	1.27156i
$495$	20.1884	+	11.7861i	0.907401	+	0.529747i
$496$	6.74369	−	5.39602i	0.302800	−	0.242289i
$497$	1.36523	+	5.09512i	0.0612391	+	0.228547i
$498$	13.9978	+	35.3489i	0.627254	+	1.58402i
$499$	20.2868	+	35.1377i	0.908161	+	1.57298i	0.816618	+	0.577179i	$0.195847\pi$
$499$	20.2868	+	35.1377i	0.908161	+	1.57298i	0.0915430	+	0.995801i	$0.470820\pi$
$500$	−20.5652	−	8.77911i	−0.919703	−	0.392614i
$501$	−1.17459	+	6.29862i	−0.0524766	+	0.281401i
$502$	−0.613695	−	16.2234i	−0.0273905	−	0.724084i
$503$	6.97397	−	6.97397i	0.310954	−	0.310954i	−0.534325	−	0.845279i	$-0.679434\pi$
$503$	6.97397	−	6.97397i	0.310954	−	0.310954i	0.845279	+	0.534325i	$0.179434\pi$
$504$	−18.6568	+	10.9338i	−0.831041	+	0.487029i
$505$	−6.09787	+	7.49007i	−0.271352	+	0.333304i
$506$	13.8509	+	12.8412i	0.615747	+	0.570860i
$507$	−23.1594	−	11.0779i	−1.02855	−	0.491989i
$508$	−5.71231	−	4.90770i	−0.253443	−	0.217744i
$509$	27.6387	−	15.9572i	1.22507	−	0.707292i	0.259072	−	0.965858i	$-0.416583\pi$
$509$	27.6387	−	15.9572i	1.22507	−	0.707292i	0.965994	+	0.258566i	$0.0832499\pi$
$510$	−12.3667	+	11.3133i	−0.547606	+	0.500962i
$511$	−28.0116	−	16.1725i	−1.23916	−	0.715430i
$512$	21.3299	−	7.55210i	0.942658	−	0.333759i
$513$	−19.6487	+	4.64834i	−0.867511	+	0.205229i
$514$	20.2321	+	4.60912i	0.892400	+	0.203300i
$515$	2.78699	+	1.24960i	0.122810	+	0.0550640i
$516$	7.34662	+	16.6812i	0.323417	+	0.734349i
$517$	−0.806914	−	0.216212i	−0.0354880	−	0.00950899i
$518$	−8.74680	+	16.5662i	−0.384312	+	0.727876i
$519$	−37.8750	+	13.3651i	−1.66253	+	0.586664i
$520$	10.1153	−	31.7894i	0.443585	−	1.39406i
$521$	34.5815			1.51504			0.757521	−	0.652811i	$-0.226410\pi$
$521$	34.5815			1.51504			0.757521	+	0.652811i	$0.226410\pi$
$522$	17.8432	+	6.13012i	0.780977	+	0.268308i
$523$	31.6445	−	31.6445i	1.38372	−	1.38372i	0.545801	−	0.837915i	$-0.316225\pi$
$523$	31.6445	−	31.6445i	1.38372	−	1.38372i	0.837915	−	0.545801i	$-0.183775\pi$
$524$	−20.2484	+	13.8295i	−0.884556	+	0.604143i
$525$	−22.0662	+	0.437826i	−0.963048	+	0.0191083i
$526$	0.765678	+	2.47866i	0.0333851	+	0.108075i
$527$	1.71011	−	6.38222i	0.0744936	−	0.278014i
$528$	−23.1012	−	7.01780i	−1.00535	−	0.305411i
$529$	−7.19846	−	4.15603i	−0.312976	−	0.180697i
$530$	−0.732149	−	0.936556i	−0.0318025	−	0.0406814i
$531$	−21.4322	−	26.5866i	−0.930078	−	1.15376i
$532$	18.6889	−	6.55672i	0.810265	−	0.284270i
$533$	41.2478	−	11.0523i	1.78664	−	0.478729i
$534$	1.01820	+	8.79605i	0.0440619	+	0.380642i
$535$	−9.86731	−	13.6562i	−0.426601	−	0.590409i
$536$	−0.311475	+	2.08389i	−0.0134537	+	0.0900101i
$537$	−17.3006	+	1.34234i	−0.746575	+	0.0579261i
$538$	−0.716508	−	18.9413i	−0.0308908	−	0.816617i
$539$	1.76058			0.0758335
$540$	−22.9831	+	3.43182i	−0.989035	+	0.147682i
$541$	35.6814			1.53407			0.767033	−	0.641608i	$-0.221732\pi$
$541$	35.6814			1.53407			0.767033	+	0.641608i	$0.221732\pi$
$542$	1.02597	+	27.1220i	0.0440690	+	1.16499i
$543$	−34.5045	+	2.67717i	−1.48073	+	0.114888i
$544$	9.72203	−	14.3226i	0.416829	−	0.614076i
$545$	−5.04392	+	31.3153i	−0.216058	+	1.34140i
$546$	−3.78624	−	32.7086i	−0.162036	−	1.39980i
$547$	15.9487	−	4.27345i	0.681919	−	0.182720i	0.0988010	−	0.995107i	$-0.468499\pi$
$547$	15.9487	−	4.27345i	0.681919	−	0.182720i	0.583118	+	0.812388i	$0.301833\pi$
$548$	6.12487	+	17.4579i	0.261641	+	0.745766i
$549$	−9.98668	+	25.8452i	−0.426221	+	1.10305i
$550$	−17.0761	−	17.7655i	−0.728125	−	0.757523i
$551$	−14.9648	−	8.63994i	−0.637522	−	0.368074i
$552$	−18.7280	−	1.33073i	−0.797119	−	0.0566395i
$553$	−9.97538	+	37.2286i	−0.424197	+	1.58312i
$554$	−3.11946	−	10.0984i	−0.132533	−	0.429038i
$555$	−15.3564	+	13.0170i	−0.651842	+	0.552542i
$556$	20.2015	+	29.5780i	0.856734	+	1.25439i
$557$	1.96120	−	1.96120i	0.0830989	−	0.0830989i	−0.664336	−	0.747434i	$-0.731285\pi$
$557$	1.96120	−	1.96120i	0.0830989	−	0.0830989i	0.747434	+	0.664336i	$0.231285\pi$
$558$	6.90952	−	6.01475i	0.292503	−	0.254625i
$559$	−27.7541			−1.17387
$560$	22.0668	−	5.71318i	0.932492	−	0.241426i
$561$	−17.4179	+	6.14632i	−0.735383	+	0.259498i
$562$	−9.23814	+	17.4968i	−0.389687	+	0.738057i
$563$	−12.8024	−	3.43039i	−0.539557	−	0.144574i	−0.0212589	−	0.999774i	$-0.506767\pi$
$563$	−12.8024	−	3.43039i	−0.539557	−	0.144574i	−0.518298	+	0.855200i	$0.673434\pi$
$564$	0.759969	−	0.334700i	0.0320005	−	0.0140934i
$565$	0.414408	−	0.924257i	0.0174343	−	0.0388838i
$566$	2.56228	+	0.583718i	0.107701	+	0.0245355i
$567$	−19.2911	+	12.4068i	−0.810152	+	0.521038i
$568$	−0.662624	−	5.81665i	−0.0278031	−	0.244061i
$569$	−9.89594	−	5.71342i	−0.414859	−	0.239519i	0.278016	−	0.960576i	$-0.410323\pi$
$569$	−9.89594	−	5.71342i	−0.414859	−	0.239519i	−0.692876	+	0.721057i	$0.743656\pi$
$570$	21.2622	+	0.945802i	0.890576	+	0.0396153i
$571$	32.2228	−	18.6038i	1.34848	−	0.778546i	0.360447	−	0.932780i	$-0.382624\pi$
$571$	32.2228	−	18.6038i	1.34848	−	0.778546i	0.988034	+	0.154234i	$0.0492908\pi$
$572$	23.9570	−	27.8847i	1.00169	−	1.16592i
$573$	24.4840	+	11.7115i	1.02284	+	0.489257i
$574$	21.3973	+	19.8375i	0.893107	+	0.828001i
$575$	−16.0161	−	10.5206i	−0.667918	−	0.438739i
$576$	22.2725	−	8.94056i	0.928023	−	0.372523i
$577$	−8.63696	+	8.63696i	−0.359561	+	0.359561i	−0.863651	−	0.504090i	$-0.831828\pi$
$577$	−8.63696	+	8.63696i	−0.359561	+	0.359561i	0.504090	+	0.863651i	$0.331828\pi$
$578$	0.408198	+	10.7909i	0.0169788	+	0.448844i
$579$	6.85292	−	36.7482i	0.284798	−	1.52720i
$580$	−16.3271	−	11.3550i	−0.677947	−	0.471489i
$581$	−19.7780	−	34.2566i	−0.820532	−	1.42120i
$582$	−2.85371	−	7.20655i	−0.118290	−	0.298721i
$583$	−0.339061	−	1.26539i	−0.0140425	−	0.0524072i
$584$	28.0937	+	22.3475i	1.16252	+	0.924745i
$585$	9.32288	−	34.1332i	0.385454	−	1.41124i
$586$	−8.28656	+	36.3745i	−0.342315	+	1.50262i
$587$	7.66180	−	2.05297i	0.316236	−	0.0847352i	−0.0972097	−	0.995264i	$-0.530992\pi$
$587$	7.66180	−	2.05297i	0.316236	−	0.0847352i	0.413446	+	0.910529i	$0.364325\pi$
$588$	−1.36451	+	1.09589i	−0.0562714	+	0.0451938i
$589$	−7.26609	+	4.19508i	−0.299394	+	0.172855i
$590$	14.0745	+	33.1311i	0.579438	+	1.36399i
$591$	−15.0468	+	17.5781i	−0.618942	+	0.723067i
$592$	12.3189	−	16.7489i	0.506302	−	0.688374i
$593$	−17.4824	−	17.4824i	−0.717918	−	0.717918i	0.250261	−	0.968178i	$-0.419484\pi$
$593$	−17.4824	−	17.4824i	−0.717918	−	0.717918i	−0.968178	+	0.250261i	$0.919484\pi$
$594$	−24.7899	−	6.42206i	−1.01714	−	0.263500i
$595$	11.0097	−	13.5233i	0.451353	−	0.554401i
$596$	−4.57219	+	3.12276i	−0.187284	+	0.127913i
$597$	−3.55869	+	0.276116i	−0.145648	+	0.0113007i
$598$	13.3481	−	25.2809i	0.545845	−	1.03381i
$599$	15.1365	+	26.2172i	0.618461	+	1.07121i	0.989767	+	0.142696i	$0.0455770\pi$
$599$	15.1365	+	26.2172i	0.618461	+	1.07121i	−0.371305	+	0.928511i	$0.621090\pi$
$600$	24.2928	+	3.13969i	0.991751	+	0.128177i
$601$	−1.15030	+	1.99238i	−0.0469219	+	0.0812710i	−0.888532	−	0.458814i	$-0.848275\pi$
$601$	−1.15030	+	1.99238i	−0.0469219	+	0.0812710i	0.841611	+	0.540085i	$0.181608\pi$
$602$	−10.0960	−	16.0531i	−0.411483	−	0.654277i
$603$	−0.238521	+	2.22208i	−0.00971331	+	0.0904902i
$604$	−13.5646	−	6.51866i	−0.551935	−	0.265241i
$605$	−0.910542	−	2.39073i	−0.0370188	−	0.0971970i
$606$	4.20143	−	9.71031i	0.170671	−	0.394455i
$607$	−11.3362	+	42.3071i	−0.460120	+	1.71719i	0.212461	+	0.977170i	$0.431852\pi$
$607$	−11.3362	+	42.3071i	−0.460120	+	1.71719i	−0.672581	+	0.740023i	$0.734815\pi$
$608$	−21.5896	+	4.13082i	−0.875574	+	0.167527i
$609$	−19.2967	−	3.59851i	−0.781943	−	0.145819i
$610$	17.5701	−	23.3302i	0.711394	−	0.944613i
$611$			1.26443i			0.0511535i
$612$	9.67360	−	15.6055i	0.391032	−	0.630816i
$613$	5.01756	+	5.01756i	0.202657	+	0.202657i	0.801138	−	0.598480i	$-0.204228\pi$
$613$	5.01756	+	5.01756i	0.202657	+	0.202657i	−0.598480	+	0.801138i	$0.704228\pi$
$614$	20.4483	+	18.9577i	0.825227	+	0.765070i
$615$	13.3932	+	28.3507i	0.540067	+	1.14321i
$616$	24.8435	+	3.71331i	1.00097	+	0.149614i
$617$	−6.92773	−	1.85628i	−0.278900	−	0.0747310i	0.116658	−	0.993172i	$-0.462782\pi$
$617$	−6.92773	−	1.85628i	−0.278900	−	0.0747310i	−0.395558	+	0.918441i	$0.629449\pi$
$618$	−3.30997	−	0.488598i	−0.133146	−	0.0196543i
$619$	−6.11352	+	10.5889i	−0.245723	+	0.425605i	−0.962335	−	0.271868i	$-0.912359\pi$
$619$	−6.11352	+	10.5889i	−0.245723	+	0.425605i	0.716612	+	0.697473i	$0.245692\pi$
$620$	−8.73847	+	4.10879i	−0.350945	+	0.165013i
$621$	−19.9055	−	0.587337i	−0.798781	−	0.0235690i
$622$	−0.969686	+	0.609848i	−0.0388809	+	0.0244527i
$623$	−2.38441	−	8.89874i	−0.0955294	−	0.356521i
$624$	−1.21034	+	36.5239i	−0.0484524	+	1.46213i
$625$	20.0705	+	14.9056i	0.802818	+	0.596224i
$626$	8.55176	−	2.64171i	0.341797	−	0.105584i
$627$	21.1582	+	10.1207i	0.844977	+	0.404181i
$628$	−7.36066	−	1.38646i	−0.293723	−	0.0553259i
$629$		−	15.9059i		−	0.634208i
$630$	23.1342	−	7.02414i	0.921690	−	0.279849i
$631$			8.53598i			0.339812i	0.985460	+	0.169906i	$0.0543464\pi$
$631$			8.53598i			0.339812i	−0.985460	+	0.169906i	$0.945654\pi$
$632$	17.0574	−	39.2275i	0.678506	−	1.56039i
$633$	−3.29008	+	2.25585i	−0.130769	+	0.0896621i
$634$	−8.43928	−	27.3197i	−0.335167	−	1.08500i
$635$	4.93126	+	6.82479i	0.195691	+	0.270833i
$636$	1.05044	+	0.769670i	0.0416527	+	0.0305194i
$637$	−0.689706	−	2.57402i	−0.0273272	−	0.101986i
$638$	−11.6676	−	18.5520i	−0.461925	−	0.734481i
$639$	−0.957796	−	6.13508i	−0.0378898	−	0.242700i
$640$	−25.1590	+	2.65072i	−0.994496	+	0.104779i
$641$	5.32828	−	9.22886i	0.210454	−	0.364518i	−0.741402	−	0.671061i	$-0.765839\pi$
$641$	5.32828	−	9.22886i	0.210454	−	0.364518i	0.951857	+	0.306543i	$0.0991723\pi$
$642$	14.4645	+	11.4632i	0.570869	+	0.452416i
$643$	0.317383	+	0.0850425i	0.0125164	+	0.00335375i	0.265072	−	0.964229i	$-0.414604\pi$
$643$	0.317383	+	0.0850425i	0.0125164	+	0.00335375i	−0.252555	+	0.967582i	$0.581271\pi$
$644$	19.4783	−	1.47575i	0.767551	−	0.0581528i
$645$	−3.63910	−	20.0512i	−0.143289	−	0.789515i
$646$	−11.4328	+	12.3318i	−0.449819	+	0.485189i
$647$	−1.08970	−	1.08970i	−0.0428405	−	0.0428405i	0.685362	−	0.728203i	$-0.259644\pi$
$647$	−1.08970	−	1.08970i	−0.0428405	−	0.0428405i	−0.728203	+	0.685362i	$0.759644\pi$
$648$	23.2105	−	10.4534i	0.911794	−	0.410648i
$649$			39.6684i			1.55712i
$650$	−19.2841	+	31.9253i	−0.756386	+	1.25221i
$651$	−6.19787	+	7.24054i	−0.242914	+	0.283779i
$652$	−12.4772	+	14.5228i	−0.488644	+	0.568758i
$653$	5.92931	−	22.1285i	0.232032	−	0.865954i	−0.747433	−	0.664337i	$-0.768714\pi$
$653$	5.92931	−	22.1285i	0.232032	−	0.865954i	0.979465	−	0.201617i	$-0.0646195\pi$
$654$	−3.99544	−	34.5158i	−0.156234	−	1.34968i
$655$	25.6195	−	9.75752i	1.00103	−	0.381258i
$656$	−20.2322	−	25.2852i	−0.789934	−	0.987221i
$657$	30.7542	+	22.4483i	1.19983	+	0.875792i
$658$	−0.731356	+	0.459959i	−0.0285112	+	0.0179311i
$659$	6.24819	−	10.8222i	0.243395	−	0.421572i	−0.718284	−	0.695750i	$-0.755072\pi$
$659$	6.24819	−	10.8222i	0.243395	−	0.421572i	0.961679	+	0.274177i	$0.0884055\pi$
$660$	23.2868	+	13.6517i	0.906438	+	0.531393i
$661$	−2.84081	−	4.92043i	−0.110495	−	0.191382i	0.805475	−	0.592630i	$-0.201910\pi$
$661$	−2.84081	−	4.92043i	−0.110495	−	0.191382i	−0.915970	+	0.401247i	$0.868577\pi$
$662$	24.4287	+	12.8981i	0.949449	+	0.501300i
$663$	15.8095	+	23.0576i	0.613991	+	0.895483i
$664$	16.0891	+	40.8467i	0.624379	+	1.58516i
$665$	−22.0281	+	2.25696i	−0.854212	+	0.0875213i
$666$	12.3190	−	18.2909i	0.477350	−	0.708758i
$667$	−12.0512	−	12.0512i	−0.466623	−	0.466623i
$668$	−1.36949	+	7.27054i	−0.0529871	+	0.281306i
$669$	−9.62026	−	27.2625i	−0.371941	−	1.05403i
$670$	0.881850	−	2.18445i	0.0340689	−	0.0843928i
$671$	27.8734	−	16.0927i	1.07604	−	0.621252i
$672$	−21.5659	+	12.5861i	−0.831924	+	0.485521i
$673$	−28.9286	+	7.75138i	−1.11511	+	0.298794i	−0.768905	−	0.639363i	$-0.779198\pi$
$673$	−28.9286	+	7.75138i	−1.11511	+	0.298794i	−0.346209	+	0.938157i	$0.612531\pi$
$674$	13.9473	+	3.17736i	0.537229	+	0.122387i
$675$	25.8823	+	2.25988i	0.996210	+	0.0869827i
$676$	−26.7190	−	12.8402i	−1.02765	−	0.493854i
$677$	−0.688499	−	2.56951i	−0.0264612	−	0.0987544i	0.951432	−	0.307858i	$-0.0996121\pi$
$677$	−0.688499	−	2.56951i	−0.0264612	−	0.0987544i	−0.977894	+	0.209103i	$0.932945\pi$
$678$	−0.162035	+	1.09769i	−0.00622290	+	0.0421566i
$679$	4.03213	+	6.98386i	0.154739	+	0.268016i
$680$	−14.3035	+	13.0376i	−0.548514	+	0.499968i
$681$	−8.23384	+	2.90551i	−0.315521	+	0.111339i
$682$	−10.6336	+	0.402246i	−0.407181	+	0.0154028i
$683$	−31.3443	+	31.3443i	−1.19936	+	1.19936i	−0.224999	+	0.974359i	$0.572238\pi$
$683$	−31.3443	+	31.3443i	−1.19936	+	1.19936i	−0.974359	+	0.224999i	$0.927762\pi$
$684$	−22.6981	+	5.32627i	−0.867882	+	0.203655i
$685$	−2.10831	−	20.5772i	−0.0805544	−	0.786215i
$686$	18.3903	−	19.8363i	0.702143	−	0.757353i
$687$	11.0825	−	7.59873i	0.422822	−	0.289909i
$688$	8.44818	+	19.2771i	0.322084	+	0.734934i
$689$	−1.71721	+	0.991433i	−0.0654206	+	0.0377706i
$690$	20.0147	+	6.32865i	0.761945	+	0.240928i
$691$	−1.44150	−	0.832251i	−0.0548373	−	0.0316603i	0.472331	−	0.881421i	$-0.343413\pi$
$691$	−1.44150	−	0.832251i	−0.0548373	−	0.0316603i	−0.527168	+	0.849761i	$0.676746\pi$
$692$	−43.7622	+	15.3534i	−1.66359	+	0.583647i
$693$	26.4910	+	2.84357i	1.00631	+	0.108018i
$694$	7.89322	−	34.6479i	0.299623	−	1.31522i
$695$	−14.2534	−	37.4238i	−0.540661	−	1.41957i
$696$	20.5907	+	7.11582i	0.780488	+	0.269724i
$697$	−23.9299	−	6.41200i	−0.906410	−	0.242872i
$698$	−21.7065	−	11.4608i	−0.821603	−	0.433799i
$699$	−7.72874	−	6.61576i	−0.292328	−	0.250231i
$700$	−25.4807	+	0.459330i	−0.963081	+	0.0173610i
$701$	−6.95642			−0.262740			−0.131370	−	0.991333i	$-0.541938\pi$
$701$	−6.95642			−0.262740			−0.131370	+	0.991333i	$0.541938\pi$
$702$	0.322180	+	38.7594i	0.0121599	+	1.46288i
$703$	−14.2818	+	14.2818i	−0.538649	+	0.538649i
$704$	−26.6603	−	8.15185i	−1.00480	−	0.307234i
$705$	−0.913502	+	0.165792i	−0.0344045	+	0.00624408i
$706$	−40.3499	+	12.4644i	−1.51859	+	0.469105i
$707$	−2.84905	+	10.6328i	−0.107150	+	0.399888i
$708$	−24.6920	−	30.7444i	−0.927984	−	1.15545i
$709$	41.5369	+	23.9814i	1.55995	+	0.900639i	0.997260	+	0.0739729i	$0.0235678\pi$
$709$	41.5369	+	23.9814i	1.55995	+	0.900639i	0.562693	+	0.826666i	$0.309765\pi$
$710$	−0.795813	+	6.49672i	−0.0298663	+	0.243817i
$711$	16.3529	−	42.3208i	0.613283	−	1.58715i
$712$	1.15729	+	10.1589i	0.0433712	+	0.380722i
$713$	−7.99314	+	2.14175i	−0.299345	+	0.0802093i
$714$	−7.58566	+	17.5319i	−0.283886	+	0.656116i
$715$	−33.3153	+	24.0720i	−1.24592	+	0.900241i
$716$	−19.9798	+	1.51375i	−0.746679	+	0.0565715i
$717$	−2.50856	−	3.65864i	−0.0936838	−	0.136634i
$718$	36.9403	−	1.39737i	1.37860	−	0.0521495i
$719$	−27.9555			−1.04257			−0.521283	−	0.853384i	$-0.674546\pi$
$719$	−27.9555			−1.04257			−0.521283	+	0.853384i	$0.674546\pi$
$720$	−26.5457	+	3.91457i	−0.989301	+	0.145887i
$721$	3.48106			0.129641
$722$	−5.51263	+	0.208531i	−0.205159	+	0.00776072i
$723$	10.3054	−	21.5443i	0.383261	−	0.801243i
$724$	−39.8479	+	3.01904i	−1.48094	+	0.112202i
$725$	14.7913	+	16.6014i	0.549335	+	0.616559i
$726$	1.67100	+	2.24975i	0.0620164	+	0.0834961i
$727$	32.2018	−	8.62843i	1.19430	−	0.320011i	0.393714	−	0.919233i	$-0.371190\pi$
$727$	32.2018	−	8.62843i	1.19430	−	0.320011i	0.800583	+	0.599222i	$0.204523\pi$
$728$	−4.30345	−	37.7766i	−0.159496	−	1.40009i
$729$	24.1380	−	12.0978i	0.893999	−	0.448068i
$730$	−24.7187	−	31.6199i	−0.914880	−	1.17030i
$731$	13.9443	+	8.05077i	0.515750	+	0.297768i
$732$	−11.5858	+	29.8225i	−0.428222	+	1.10227i
$733$	−0.439391	+	1.63983i	−0.0162293	+	0.0605685i	−0.973566	−	0.228408i	$-0.926648\pi$
$733$	−0.439391	+	1.63983i	−0.0162293	+	0.0605685i	0.957336	+	0.288976i	$0.0933148\pi$
$734$	−31.0731	+	9.59872i	−1.14693	+	0.354295i
$735$	1.76919	−	0.835789i	0.0652576	−	0.0308285i
$736$	−21.6225	−	1.57582i	−0.797014	−	0.0580856i
$737$	1.83567	−	1.83567i	0.0676177	−	0.0676177i
$738$	−22.5521	−	25.9070i	−0.830153	−	0.953650i
$739$	−48.7588			−1.79362			−0.896811	−	0.442414i	$-0.854122\pi$
$739$	−48.7588			−1.79362			−0.896811	+	0.442414i	$0.854122\pi$
$740$	−17.7593	+	14.9986i	−0.652844	+	0.551358i
$741$	6.50802	−	34.8987i	0.239078	−	1.28204i
$742$	−1.19812	−	0.632595i	−0.0439843	−	0.0232233i
$743$	−20.5756	−	5.51322i	−0.754846	−	0.202260i	−0.139179	−	0.990267i	$-0.544446\pi$
$743$	−20.5756	−	5.51322i	−0.754846	−	0.202260i	−0.615667	+	0.788007i	$0.711113\pi$
$744$	7.99101	−	6.93074i	0.292965	−	0.254093i
$745$	5.78500	−	2.20330i	0.211946	−	0.0807225i
$746$	−4.17530	+	18.3278i	−0.152868	+	0.671028i
$747$	18.8452	+	42.5803i	0.689511	+	1.55793i
$748$	−20.1253	+	7.06065i	−0.735852	+	0.258163i
$749$	−16.6294	−	9.60100i	−0.607626	−	0.350813i
$750$	−25.5933	−	9.74598i	−0.934534	−	0.355873i
$751$	30.0558	−	17.3527i	1.09675	−	0.633209i	0.161385	−	0.986892i	$-0.448404\pi$
$751$	30.0558	−	17.3527i	1.09675	−	0.633209i	0.935366	+	0.353682i	$0.115071\pi$
$752$	0.878237	−	0.384886i	0.0320260	−	0.0140354i
$753$	−1.53813	−	19.8241i	−0.0560527	−	0.722431i
$754$	−22.5528	+	24.3261i	−0.821325	+	0.885906i
$755$	13.0485	+	10.6231i	0.474883	+	0.386615i
$756$	−22.3015	+	14.2857i	−0.811096	+	0.519567i
$757$	21.6732	−	21.6732i	0.787727	−	0.787727i	−0.193394	−	0.981121i	$-0.561950\pi$
$757$	21.6732	−	21.6732i	0.787727	−	0.787727i	0.981121	+	0.193394i	$0.0619496\pi$
$758$	−18.0405	+	0.682434i	−0.655262	+	0.0247871i
$759$	17.5735	+	15.0428i	0.637878	+	0.546020i
$760$	24.5495	+	1.13666i	0.890502	+	0.0412310i
$761$	13.2539	+	22.9564i	0.480452	+	0.832167i	0.999748	−	0.0224270i	$-0.00713933\pi$
$761$	13.2539	+	22.9564i	0.480452	+	0.832167i	−0.519297	+	0.854594i	$0.673806\pi$
$762$	−7.22874	−	5.72882i	−0.261870	−	0.207533i
$763$	9.35647	+	34.9188i	0.338727	+	1.26415i
$764$	28.2472	+	13.5746i	1.02195	+	0.491112i
$765$	−14.5853	+	14.4450i	−0.527331	+	0.522262i
$766$	48.4453	+	11.0364i	1.75040	+	0.398763i
$767$	57.9964	−	15.5401i	2.09413	−	0.561120i
$768$	25.7368	−	10.2770i	0.928697	−	0.370839i
$769$	10.2142	−	5.89716i	0.368333	−	0.212657i	−0.304397	−	0.952545i	$-0.598455\pi$
$769$	10.2142	−	5.89716i	0.368333	−	0.212657i	0.672730	+	0.739888i	$0.265122\pi$
$770$	−26.0424	−	10.5132i	−0.938503	−	0.378868i
$771$	24.9833	+	4.65897i	0.899753	+	0.167789i
$772$	7.99004	−	42.4187i	0.287568	−	1.52668i
$773$	7.36402	+	7.36402i	0.264865	+	0.264865i	0.827027	−	0.562162i	$-0.190030\pi$
$773$	7.36402	+	7.36402i	0.264865	+	0.264865i	−0.562162	+	0.827027i	$0.690030\pi$
$774$	9.79998	+	20.0577i	0.352253	+	0.720960i
$775$	10.5717	−	2.18930i	0.379746	−	0.0786420i
$776$	−3.28008	−	8.32738i	−0.117748	−	0.298935i
$777$	−9.90045	+	20.6978i	−0.355177	+	0.742529i
$778$	22.3362	+	11.7933i	0.800791	+	0.422810i
$779$	15.7293	+	27.2439i	0.563560	+	0.976115i
$780$	10.8366	−	39.3941i	0.388013	−	1.41053i
$781$	−3.60645	+	6.24656i	−0.129049	+	0.223520i
$782$	−14.0398	+	8.82982i	−0.502062	+	0.315754i
$783$	22.1337	+	6.63624i	0.790992	+	0.237160i
$784$	−1.57789	+	1.26257i	−0.0563533	+	0.0450916i
$785$	7.64126	+	3.42610i	0.272728	+	0.122283i
$786$	−24.1087	+	17.9067i	−0.859929	+	0.638709i
$787$	7.95656	−	29.6943i	0.283621	−	1.05849i	−0.666220	−	0.745755i	$-0.732089\pi$
$787$	7.95656	−	29.6943i	0.283621	−	1.05849i	0.949841	−	0.312733i	$-0.101244\pi$
$788$	−17.4113	+	20.2659i	−0.620253	+	0.721943i
$789$	1.05728	+	2.99619i	0.0376402	+	0.106667i
$790$	−28.7706	+	38.2026i	−1.02361	+	1.35919i
$791$		−	1.15443i		−	0.0410468i
$792$	−28.6114	−	7.46748i	−1.01666	−	0.265345i
$793$	−34.4474	−	34.4474i	−1.22326	−	1.22326i
$794$	31.1450	−	33.5939i	1.10529	−	1.19220i
$795$	−0.941430	−	1.11062i	−0.0333891	−	0.0393897i
$796$	−4.10980	+	0.311375i	−0.145668	+	0.0110364i
$797$	−17.8210	−	4.77511i	−0.631251	−	0.169143i	−0.0710135	−	0.997475i	$-0.522623\pi$
$797$	−17.8210	−	4.77511i	−0.631251	−	0.169143i	−0.560237	+	0.828332i	$0.689290\pi$
$798$	22.5530	−	8.93073i	0.798368	−	0.316144i
$799$	0.366781	−	0.635283i	0.0129758	−	0.0224747i
$800$	28.0443	+	3.67629i	0.991517	+	0.129977i
$801$	1.67281	+	10.7151i	0.0591059	+	0.378598i
$802$	−22.9796	−	36.5386i	−0.811438	−	1.29022i
$803$	−11.4473	−	42.7219i	−0.403967	−	1.50762i
$804$	−0.280075	+	2.56534i	−0.00987747	+	0.0904724i
$805$	−21.5619	−	3.47294i	−0.759956	−	0.122405i
$806$	4.75380	+	15.3890i	0.167445	+	0.542056i
$807$	−1.79582	−	23.1453i	−0.0632158	−	0.814752i
$808$	4.87173	−	11.2037i	0.171387	−	0.394144i
$809$			45.3459i			1.59428i	0.603798	+	0.797138i	$0.293653\pi$
$809$			45.3459i			1.59428i	−0.603798	+	0.797138i	$0.706347\pi$
$810$	−27.9598	+	5.31487i	−0.982408	+	0.186745i
$811$			32.6505i			1.14652i	0.819375	+	0.573258i	$0.194321\pi$
$811$			32.6505i			1.14652i	−0.819375	+	0.573258i	$0.805679\pi$
$812$	−22.2744	−	4.19563i	−0.781677	−	0.147238i
$813$	2.57143	+	33.1417i	0.0901840	+	1.16233i
$814$	−24.4753	+	7.56062i	−0.857859	+	0.265000i
$815$	17.3511	−	12.5371i	0.607784	−	0.439155i
$816$	11.2028	−	17.9994i	0.392176	−	0.630106i
$817$	−5.29182	−	19.7493i	−0.185137	−	0.690942i
$818$	19.6557	−	12.3617i	0.687244	−	0.432217i
$819$	−6.22045	−	39.8446i	−0.217360	−	1.39228i
$820$	15.4058	+	32.7646i	0.537992	+	1.14419i
$821$	−14.0278	+	24.2968i	−0.489572	+	0.847964i	−0.999928	−	0.0119995i	$-0.996180\pi$
$821$	−14.0278	+	24.2968i	−0.489572	+	0.847964i	0.510356	+	0.859963i	$0.329514\pi$
$822$	8.34251	+	21.0676i	0.290978	+	0.734816i
$823$	−33.5290	−	8.98407i	−1.16875	−	0.313165i	−0.378293	−	0.925686i	$-0.623489\pi$
$823$	−33.5290	−	8.98407i	−1.16875	−	0.313165i	−0.790454	+	0.612521i	$0.790156\pi$
$824$	−3.82099	−	0.571117i	−0.133111	−	0.0198958i
$825$	−21.7593	−	20.9126i	−0.757562	−	0.728085i
$826$	30.0857	+	27.8925i	1.04682	+	0.970504i
$827$	−0.244245	−	0.244245i	−0.00849323	−	0.00849323i	0.702847	−	0.711341i	$-0.251912\pi$
$827$	−0.244245	−	0.244245i	−0.00849323	−	0.00849323i	−0.711341	+	0.702847i	$0.751912\pi$
$828$	−22.9836	−	0.719898i	−0.798737	−	0.0250182i
$829$		−	24.5821i		−	0.853771i	−0.904306	−	0.426885i	$-0.859611\pi$
$829$		−	24.5821i		−	0.853771i	0.904306	−	0.426885i	$-0.140389\pi$
$830$	−6.84491	−	48.6033i	−0.237590	−	1.68705i
$831$	−4.30749	−	12.2069i	−0.149425	−	0.423451i
$832$	−1.47409	+	42.1715i	−0.0511050	+	1.46204i
$833$	−0.400133	+	1.49332i	−0.0138638	+	0.0517404i
$834$	26.1573	+	35.2170i	0.905752	+	1.21946i
$835$	3.38416	−	7.54770i	0.117114	−	0.261199i
$836$	24.4101	+	11.7307i	0.844243	+	0.405713i
$837$	8.16394	−	7.69597i	0.282187	−	0.266012i
$838$	7.54458	+	11.9962i	0.260623	+	0.414402i
$839$	4.08967	−	7.08351i	0.141191	−	0.244550i	−0.786754	−	0.617266i	$-0.788240\pi$
$839$	4.08967	−	7.08351i	0.141191	−	0.244550i	0.927945	+	0.372716i	$0.121574\pi$
$840$	26.7278	−	8.06231i	0.922196	−	0.278176i
$841$	−4.61225	−	7.98866i	−0.159043	−	0.275471i
$842$	−4.86427	+	9.21278i	−0.167634	+	0.317493i
$843$	−10.4566	+	21.8605i	−0.360144	+	0.752914i
$844$	−3.80377	+	2.59794i	−0.130931	+	0.0894247i
$845$	25.7024	+	20.9250i	0.884189	+	0.719842i
$846$	0.913799	−	0.446472i	0.0314171	−	0.0153500i
$847$	−2.06171	−	2.06171i	−0.0708410	−	0.0708410i
$848$	1.21133	+	0.890937i	0.0415972	+	0.0305949i
$849$	3.16399	+	0.590032i	0.108588	+	0.0202498i
$850$	18.9496	−	10.4462i	0.649965	−	0.358303i
$851$	−17.2517	+	9.96030i	−0.591382	+	0.341435i
$852$	−1.09311	−	7.08618i	−0.0374494	−	0.242768i
$853$	26.9342	−	7.21700i	0.922210	−	0.247105i	0.233680	−	0.972314i	$-0.424923\pi$
$853$	26.9342	−	7.21700i	0.922210	−	0.247105i	0.688530	+	0.725208i	$0.258257\pi$
$854$	7.39374	−	32.4554i	0.253009	−	1.11060i
$855$	26.0662	+	0.125886i	0.891446	+	0.00430520i
$856$	16.6781	+	13.2668i	0.570047	+	0.453451i
$857$	−11.3944	−	42.5245i	−0.389226	−	1.45261i	−0.831397	−	0.555679i	$-0.812458\pi$
$857$	−11.3944	−	42.5245i	−0.389226	−	1.45261i	0.442171	−	0.896931i	$-0.354208\pi$
$858$	27.9653	−	35.2872i	0.954719	−	1.20468i
$859$	1.47011	+	2.54630i	0.0501593	+	0.0868785i	0.890015	−	0.455931i	$-0.150694\pi$
$859$	1.47011	+	2.54630i	0.0501593	+	0.0868785i	−0.839856	+	0.542810i	$0.817360\pi$
$860$	−4.16006	−	23.1607i	−0.141857	−	0.789774i
$861$	27.1481	+	23.2387i	0.925206	+	0.791972i
$862$	0.879245	+	23.2433i	0.0299472	+	0.791671i
$863$	−7.13386	+	7.13386i	−0.242839	+	0.242839i	−0.818024	−	0.575184i	$-0.804930\pi$
$863$	−7.13386	+	7.13386i	−0.242839	+	0.242839i	0.575184	+	0.818024i	$0.304930\pi$
$864$	26.8230	−	12.0219i	0.912537	−	0.408993i
$865$	51.5814	−	5.28495i	1.75382	−	0.179694i
$866$	−5.54562	−	5.14136i	−0.188448	−	0.174710i
$867$	1.02309	+	13.1860i	0.0347458	+	0.447819i
$868$	−7.17184	+	8.34766i	−0.243428	+	0.283338i
$869$	−45.6419	+	26.3514i	−1.54830	+	0.893909i
$870$	−20.5318	−	13.1039i	−0.696092	−	0.444263i
$871$	−3.40292	−	1.96468i	−0.115304	−	0.0665706i
$872$	−4.54122	−	39.8638i	−0.153785	−	1.34996i
$873$	−3.84196	−	8.68081i	−0.130031	−	0.293801i
$874$	20.5346	+	4.67802i	0.694592	+	0.158237i
$875$	27.8229	+	6.14269i	0.940587	+	0.207661i
$876$	35.4648	+	25.9855i	1.19824	+	0.877968i
$877$	−22.5386	−	6.03921i	−0.761076	−	0.203930i	−0.142650	−	0.989773i	$-0.545562\pi$
$877$	−22.5386	−	6.03921i	−0.761076	−	0.203930i	−0.618426	+	0.785843i	$0.712229\pi$
$878$	24.3130	−	46.0482i	0.820525	−	1.55405i
$879$	−8.37619	+	44.9166i	−0.282522	+	1.51500i
$880$	26.8607	+	15.8124i	0.905472	+	0.533036i
$881$	−42.4590			−1.43048			−0.715241	−	0.698878i	$-0.753683\pi$
$881$	−42.4590			−1.43048			−0.715241	+	0.698878i	$0.753683\pi$
$882$	−1.61669	+	1.40734i	−0.0544370	+	0.0473874i
$883$	−7.64008	+	7.64008i	−0.257109	+	0.257109i	−0.823877	−	0.566768i	$-0.808193\pi$
$883$	−7.64008	+	7.64008i	−0.257109	+	0.257109i	0.566768	+	0.823877i	$0.308193\pi$
$884$	18.2069	+	26.6577i	0.612366	+	0.896595i
$885$	18.8315	+	39.8625i	0.633016	+	1.33996i
$886$	−5.05266	−	16.3565i	−0.169747	−	0.549508i
$887$	−1.25685	+	4.69064i	−0.0422010	+	0.157496i	−0.983811	−	0.179209i	$-0.942646\pi$
$887$	−1.25685	+	4.69064i	−0.0422010	+	0.157496i	0.941610	+	0.336706i	$0.109313\pi$
$888$	14.2630	−	21.0947i	0.478636	−	0.707890i
$889$	8.31067	+	4.79817i	0.278731	+	0.160925i
$890$	1.38991	−	11.3467i	0.0465897	−	0.380341i
$891$	−30.6490	−	6.65649i	−1.02678	−	0.223001i
$892$	−11.0514	−	31.5002i	−0.370028	−	1.05470i
$893$	−0.899750	+	0.241087i	−0.0301090	+	0.00806768i
$894$	−5.44387	+	4.04341i	−0.182070	+	0.135232i
$895$	22.1170	+	3.56236i	0.739291	+	0.119077i
$896$	−24.9285	+	14.4880i	−0.832803	+	0.484010i
$897$	15.1086	−	31.5860i	0.504463	−	1.05463i
$898$	0.0560395	+	1.48143i	0.00187006	+	0.0494361i
$899$	9.60189			0.320241
$900$	29.8815	+	2.66370i	0.996050	+	0.0887899i
$901$	1.15036			0.0383241
$902$	1.50821	+	39.8703i	0.0502178	+	1.32753i
$903$	−13.1342	−	19.1557i	−0.437079	−	0.637463i
$904$	−0.189401	+	1.26716i	−0.00629938	+	0.0421452i
$905$	44.1105	+	7.10483i	1.46628	+	0.236172i
$906$	−16.9164	−	7.31932i	−0.562009	−	0.243168i
$907$	−58.1113	+	15.5709i	−1.92955	+	0.517022i	−0.952154	+	0.305620i	$0.901136\pi$
$907$	−58.1113	+	15.5709i	−1.92955	+	0.517022i	−0.977399	+	0.211402i	$0.932197\pi$
$908$	−9.51369	+	3.33774i	−0.315723	+	0.110767i
$909$	4.67053	−	12.0872i	0.154912	−	0.400906i
$910$	−5.16845	+	42.1933i	−0.171332	+	1.39869i
$911$	−2.72513	−	1.57335i	−0.0902875	−	0.0521275i	0.454176	−	0.890912i	$-0.349934\pi$
$911$	−2.72513	−	1.57335i	−0.0902875	−	0.0521275i	−0.544464	+	0.838784i	$0.683267\pi$
$912$	−26.2206	+	6.10269i	−0.868250	+	0.202080i
$913$	13.9994	−	52.2465i	0.463313	−	1.72911i
$914$	5.67979	+	18.3867i	0.187871	+	0.608176i
$915$	20.3701	−	29.4036i	0.673416	−	0.972052i
$916$	12.8128	−	8.75102i	0.423347	−	0.289142i
$917$	22.0936	−	22.0936i	0.729594	−	0.729594i
$918$	11.0813	−	19.5671i	0.365736	−	0.645811i
$919$	31.3326			1.03357			0.516783	−	0.856116i	$-0.327129\pi$
$919$	31.3326			1.03357			0.516783	+	0.856116i	$0.327129\pi$
$920$	23.0976	+	7.34961i	0.761506	+	0.242310i
$921$	25.9441	+	22.2080i	0.854887	+	0.731779i
$922$	7.55947	−	14.3174i	0.248958	−	0.471519i
$923$	10.5455	+	2.82565i	0.347109	+	0.0930075i
$924$	30.5832	+	3.33897i	1.00611	+	0.109844i
$925$	23.2180	−	11.6774i	0.763401	−	0.383952i
$926$	−6.47871	−	1.47593i	−0.212904	−	0.0485020i
$927$	−4.07439	−	0.437349i	−0.133820	−	0.0143644i
$928$	23.7611	+	8.25976i	0.779998	+	0.271140i
$929$	−10.8495	−	6.26399i	−0.355962	−	0.205515i	0.311346	−	0.950297i	$-0.399220\pi$
$929$	−10.8495	−	6.26399i	−0.355962	−	0.205515i	−0.667308	+	0.744782i	$0.732554\pi$
$930$	−10.4946	+	5.45223i	−0.344133	+	0.178786i
$931$	1.70012	−	0.981567i	0.0557193	−	0.0321696i
$932$	−8.91050	−	7.65540i	−0.291873	−	0.250761i
$933$	−1.15710	+	0.793368i	−0.0378817	+	0.0259737i
$934$	−37.4602	−	34.7294i	−1.22573	−	1.13638i
$935$	23.7211	−	2.43043i	0.775763	−	0.0794835i
$936$	0.290822	+	44.7561i	0.00950583	+	1.46290i
$937$	−27.1824	+	27.1824i	−0.888011	+	0.888011i	−0.994332	−	0.106321i	$-0.966093\pi$
$937$	−27.1824	+	27.1824i	−0.888011	+	0.888011i	0.106321	+	0.994332i	$0.466093\pi$
$938$	−0.101490	−	2.68296i	−0.00331378	−	0.0876016i
$939$	10.3373	−	3.64778i	0.337346	−	0.119041i
$940$	−1.05517	+	0.189526i	−0.0344157	+	0.00618165i
$941$	12.5030	+	21.6558i	0.407585	+	0.705957i	0.994619	−	0.103605i	$-0.0330378\pi$
$941$	12.5030	+	21.6558i	0.407585	+	0.705957i	−0.587034	+	0.809562i	$0.699704\pi$
$942$	−9.07513	−	1.33962i	−0.295684	−	0.0436471i
$943$	8.03043	+	29.9700i	0.261507	+	0.975956i
$944$	−28.4475	−	35.5522i	−0.925886	−	1.15713i
$945$	27.9705	−	9.71843i	0.909880	−	0.316141i
$946$	5.75996	−	25.2838i	0.187273	−	0.822048i
$947$	−58.2038	+	15.5957i	−1.89137	+	0.506791i	−0.892979	+	0.450098i	$0.851389\pi$
$947$	−58.2038	+	15.5957i	−1.89137	+	0.506791i	−0.998392	+	0.0566928i	$0.981944\pi$
$948$	18.9714	−	48.8335i	0.616161	−	1.58604i
$949$	−57.9762	+	33.4726i	−1.88199	+	1.08657i
$950$	−26.3944	−	7.63513i	−0.856348	−	0.247716i
$951$	−11.6533	−	33.0240i	−0.377885	−	1.07088i
$952$	−8.79588	+	20.2282i	−0.285076	+	0.655600i
$953$	7.86673	+	7.86673i	0.254828	+	0.254828i	0.822947	−	0.568118i	$-0.192328\pi$
$953$	7.86673	+	7.86673i	0.254828	+	0.254828i	−0.568118	+	0.822947i	$0.692328\pi$
$954$	1.32285	+	0.890945i	0.0428289	+	0.0288454i
$955$	−27.1724	−	22.1218i	−0.879279	−	0.715845i
$956$	−2.88896	−	4.22988i	−0.0934357	−	0.136804i
$957$	−15.1787	−	22.1376i	−0.490658	−	0.715606i
$958$	−8.00599	+	15.1631i	−0.258662	+	0.489898i
$959$	−11.7875	−	20.4166i	−0.380638	−	0.659285i
$960$	−30.6605	+	4.46453i	−0.989564	+	0.144092i
$961$	−13.1689	+	22.8092i	−0.424804	+	0.735782i
$962$	20.6420	+	32.8218i	0.665526	+	1.05822i
$963$	18.2576	+	13.3267i	0.588342	+	0.429447i
$964$	11.9448	−	24.8556i	0.384715	−	0.800546i
$965$	−19.7443	+	44.0358i	−0.635591	+	1.41756i
$966$	23.7656	−	2.75102i	0.764645	−	0.0885127i
$967$	−4.17163	+	15.5687i	−0.134151	+	0.500657i	0.865849	+	0.500305i	$0.166779\pi$
$967$	−4.17163	+	15.5687i	−0.134151	+	0.500657i	−1.00000		0.000352232i	$0.999888\pi$
$968$	1.92478	+	2.60129i	0.0618649	+	0.0836085i
$969$	−13.3930	+	15.6462i	−0.430246	+	0.502627i
$970$	1.39547	+	9.90872i	0.0448057	+	0.318150i
$971$		−	51.3038i		−	1.64642i	−0.567739	−	0.823209i	$-0.692182\pi$
$971$		−	51.3038i		−	1.64642i	0.567739	−	0.823209i	$-0.307818\pi$
$972$	27.8974	−	13.9188i	0.894811	−	0.446446i
$973$	−32.2733	−	32.2733i	−1.03464	−	1.03464i
$974$	18.4243	+	17.0812i	0.590354	+	0.547318i
$975$	−22.0507	+	40.0053i	−0.706187	+	1.28119i
$976$	−13.4405	+	34.4117i	−0.430221	+	1.10149i
$977$	1.37730	+	0.369048i	0.0440639	+	0.0118069i	0.280784	−	0.959771i	$-0.409406\pi$
$977$	1.37730	+	0.369048i	0.0440639	+	0.0118069i	−0.236720	+	0.971578i	$0.576072\pi$
$978$	−14.5648	+	18.3781i	−0.465730	+	0.587668i
$979$	6.29876	−	10.9098i	0.201309	−	0.348678i
$980$	2.04463	−	0.961378i	0.0653134	−	0.0307101i
$981$	−6.56414	−	42.0461i	−0.209577	−	1.34243i
$982$	0.151075	−	0.0950129i	0.00482099	−	0.00303198i
$983$	11.8993	+	44.4088i	0.379529	+	1.41642i	0.846614	+	0.532208i	$0.178638\pi$
$983$	11.8993	+	44.4088i	0.379529	+	1.41642i	−0.467085	+	0.884212i	$0.654696\pi$
$984$	−25.9866	−	29.9620i	−0.828422	−	0.955154i
$985$	24.2127	−	17.4949i	0.771481	−	0.557434i
$986$	18.3875	−	5.68005i	0.585577	−	0.180890i
$987$	−0.872705	+	0.598374i	−0.0277785	+	0.0190464i
$988$	7.58791	−	40.2838i	0.241404	−	1.28160i
$989$		−	20.1657i		−	0.641231i
$990$	29.1604	+	15.5770i	0.926777	+	0.495068i
$991$		−	47.4822i		−	1.50832i	−0.656689	−	0.754161i	$-0.728044\pi$
$991$		−	47.4822i		−	1.50832i	0.656689	−	0.754161i	$-0.271956\pi$
$992$	9.24173	−	7.98618i	0.293425	−	0.253561i
$993$	30.5212	+	14.5993i	0.968562	+	0.463296i
$994$	2.20173	+	7.12745i	0.0698346	+	0.226069i
$995$	4.54943	+	0.732771i	0.144227	+	0.0232304i
$996$	21.6714	+	49.2069i	0.686683	+	1.55918i
$997$	14.6874	+	54.8142i	0.465156	+	1.73598i	0.656373	+	0.754436i	$0.272090\pi$
$997$	14.6874	+	54.8142i	0.465156	+	1.73598i	−0.191218	+	0.981548i	$0.561244\pi$
$998$	30.5477	+	48.5722i	0.966971	+	1.53753i
$999$	14.1883	−	22.9818i	0.448899	−	0.727111i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.x.a.43.32	yes	128
3.2	odd	2		540.2.y.a.343.1		128
4.3	odd	2	inner	180.2.x.a.43.5	yes	128
5.2	odd	4	inner	180.2.x.a.7.18	yes	128
5.3	odd	4		900.2.bf.e.7.15		128
5.4	even	2		900.2.bf.e.43.1		128
9.4	even	3	inner	180.2.x.a.103.12	yes	128
9.5	odd	6		540.2.y.a.523.21		128
12.11	even	2		540.2.y.a.343.28		128
15.2	even	4		540.2.y.a.127.15		128
20.3	even	4		900.2.bf.e.7.21		128
20.7	even	4	inner	180.2.x.a.7.12	✓	128
20.19	odd	2		900.2.bf.e.43.28		128
36.23	even	6		540.2.y.a.523.15		128
36.31	odd	6	inner	180.2.x.a.103.18	yes	128
45.4	even	6		900.2.bf.e.643.21		128
45.13	odd	12		900.2.bf.e.607.28		128
45.22	odd	12	inner	180.2.x.a.67.5	yes	128
45.32	even	12		540.2.y.a.307.28		128
60.47	odd	4		540.2.y.a.127.21		128
180.67	even	12	inner	180.2.x.a.67.32	yes	128
180.103	even	12		900.2.bf.e.607.1		128
180.139	odd	6		900.2.bf.e.643.15		128
180.167	odd	12		540.2.y.a.307.1		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.x.a.7.12	✓	128	20.7	even	4	inner
180.2.x.a.7.18	yes	128	5.2	odd	4	inner
180.2.x.a.43.5	yes	128	4.3	odd	2	inner
180.2.x.a.43.32	yes	128	1.1	even	1	trivial
180.2.x.a.67.5	yes	128	45.22	odd	12	inner
180.2.x.a.67.32	yes	128	180.67	even	12	inner
180.2.x.a.103.12	yes	128	9.4	even	3	inner
180.2.x.a.103.18	yes	128	36.31	odd	6	inner
540.2.y.a.127.15		128	15.2	even	4
540.2.y.a.127.21		128	60.47	odd	4
540.2.y.a.307.1		128	180.167	odd	12
540.2.y.a.307.28		128	45.32	even	12
540.2.y.a.343.1		128	3.2	odd	2
540.2.y.a.343.28		128	12.11	even	2
540.2.y.a.523.15		128	36.23	even	6
540.2.y.a.523.21		128	9.5	odd	6
900.2.bf.e.7.15		128	5.3	odd	4
900.2.bf.e.7.21		128	20.3	even	4
900.2.bf.e.43.1		128	5.4	even	2
900.2.bf.e.43.28		128	20.19	odd	2
900.2.bf.e.607.1		128	180.103	even	12
900.2.bf.e.607.28		128	45.13	odd	12
900.2.bf.e.643.15		128	180.139	odd	6
900.2.bf.e.643.21		128	45.4	even	6

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.x (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.41320 - 0.0534584i) q^{2} +(1.72686 - 0.133985i) q^{3} +(1.99428 - 0.151095i) q^{4} +(-2.20762 - 0.355578i) q^{5} +(2.43324 - 0.281664i) q^{6} +(-2.46165 + 0.659597i) q^{7} +(2.81025 - 0.320139i) q^{8} +(2.96410 - 0.462748i) q^{9} +(-3.13882 - 0.384488i) q^{10} +(-3.01796 - 1.74242i) q^{11} +(3.42361 - 0.528125i) q^{12} +(-1.36518 + 5.09493i) q^{13} +(-3.44355 + 1.06374i) q^{14} +(-3.85989 - 0.318245i) q^{15} +(3.95434 - 0.602653i) q^{16} +(2.16382 - 2.16382i) q^{17} +(4.16413 - 0.812413i) q^{18} -3.88577 q^{19} +(-4.45634 - 0.375564i) q^{20} +(-4.16255 + 1.46886i) q^{21} +(-4.35813 - 2.30106i) q^{22} +(-3.70190 - 0.991920i) q^{23} +(4.81002 - 0.929369i) q^{24} +(4.74713 + 1.56996i) q^{25} +(-1.65691 + 7.27315i) q^{26} +(5.05658 - 1.19625i) q^{27} +(-4.80957 + 1.68737i) q^{28} +(3.85118 + 2.22348i) q^{29} +(-5.47181 - 0.243402i) q^{30} +(1.86992 - 1.07960i) q^{31} +(5.55607 - 1.06306i) q^{32} +(-5.44505 - 2.60455i) q^{33} +(2.94224 - 3.17359i) q^{34} +(5.66891 - 0.580828i) q^{35} +(5.84133 - 1.37071i) q^{36} +(3.67542 - 3.67542i) q^{37} +(-5.49138 + 0.207727i) q^{38} +(-1.67483 + 8.98115i) q^{39} +(-6.31779 - 0.292519i) q^{40} +(-4.04792 - 7.01121i) q^{41} +(-5.80400 + 2.29832i) q^{42} +(1.36185 + 5.08248i) q^{43} +(-6.28194 - 3.01888i) q^{44} +(-6.70813 - 0.0323966i) q^{45} +(-5.28456 - 1.20389i) q^{46} +(0.231550 - 0.0620436i) q^{47} +(6.74785 - 1.57052i) q^{48} +(-0.437526 + 0.252606i) q^{49} +(6.79258 + 1.96490i) q^{50} +(3.44669 - 4.02653i) q^{51} +(-1.95274 + 10.3670i) q^{52} +(0.265818 + 0.265818i) q^{53} +(7.08202 - 1.96086i) q^{54} +(6.04292 + 4.91971i) q^{55} +(-6.70669 + 2.64170i) q^{56} +(-6.71018 + 0.520636i) q^{57} +(5.56137 + 2.93635i) q^{58} +(-5.69158 - 9.85810i) q^{59} +(-7.74580 - 0.0514614i) q^{60} +(-4.61792 + 7.99848i) q^{61} +(2.58487 - 1.62566i) q^{62} +(-6.99134 + 3.09423i) q^{63} +(7.79502 - 1.79934i) q^{64} +(4.82544 - 10.7622i) q^{65} +(-7.83420 - 3.38968i) q^{66} +(-0.192807 + 0.719566i) q^{67} +(3.98832 - 4.64221i) q^{68} +(-6.52556 - 1.21691i) q^{69} +(7.98027 - 1.12388i) q^{70} -2.06980i q^{71} +(8.18171 - 2.24936i) q^{72} +(8.97449 + 8.97449i) q^{73} +(4.99763 - 5.39060i) q^{74} +(8.40798 + 2.07505i) q^{75} +(-7.74933 + 0.587121i) q^{76} +(8.57845 + 2.29859i) q^{77} +(-1.88676 + 12.7817i) q^{78} +(7.56173 - 13.0973i) q^{79} +(-8.94395 - 0.0756494i) q^{80} +(8.57173 - 2.74326i) q^{81} +(-6.09534 - 9.69186i) q^{82} +(4.01723 + 14.9925i) q^{83} +(-8.07937 + 3.55826i) q^{84} +(-5.54628 + 4.00747i) q^{85} +(2.19627 + 7.10978i) q^{86} +(6.94837 + 3.32364i) q^{87} +(-9.03903 - 3.93047i) q^{88} +3.61495i q^{89} +(-9.48167 + 0.312823i) q^{90} -13.4424i q^{91} +(-7.53251 - 1.41883i) q^{92} +(3.08444 - 2.11486i) q^{93} +(0.323910 - 0.100059i) q^{94} +(8.57828 + 1.38169i) q^{95} +(9.45212 - 2.58020i) q^{96} +(-0.818990 - 3.05651i) q^{97} +(-0.604809 + 0.380373i) q^{98} +(-9.75182 - 3.76814i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 2 q^{2} - 4 q^{5} - 8 q^{6} - 8 q^{8} - 8 q^{10} + 2 q^{12} - 4 q^{13} - 4 q^{16} - 16 q^{17} - 36 q^{18} - 18 q^{20} - 24 q^{21} - 10 q^{22} - 4 q^{25} - 48 q^{26} + 8 q^{28} - 14 q^{30} + 18 q^{32}+ \cdots + 164 q^{98}+O(q^{100}) \) 128 * q - 2 * q^2 - 4 * q^5 - 8 * q^6 - 8 * q^8 - 8 * q^10 + 2 * q^12 - 4 * q^13 - 4 * q^16 - 16 * q^17 - 36 * q^18 - 18 * q^20 - 24 * q^21 - 10 * q^22 - 4 * q^25 - 48 * q^26 + 8 * q^28 - 14 * q^30 + 18 * q^32 - 20 * q^33 - 40 * q^36 - 16 * q^37 - 34 * q^38 - 2 * q^40 - 8 * q^41 + 34 * q^42 - 28 * q^45 - 40 * q^46 - 22 * q^48 + 38 * q^50 - 18 * q^52 - 64 * q^53 - 32 * q^56 - 48 * q^57 - 10 * q^58 + 74 * q^60 - 8 * q^61 + 44 * q^62 + 12 * q^65 - 36 * q^66 + 58 * q^68 - 22 * q^70 + 78 * q^72 - 16 * q^73 - 32 * q^76 - 60 * q^77 + 114 * q^78 + 132 * q^80 + 24 * q^81 - 4 * q^85 + 32 * q^86 - 10 * q^88 + 138 * q^90 + 52 * q^92 - 68 * q^93 + 52 * q^96 - 4 * q^97 + 164 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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