LMFDB - Embedded newform 546.2.z.b.131.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(131,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("546.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.z (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.9
Character	$\chi$	$=$	546.131
Dual form			546.2.z.b.521.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(-1.43878 - 0.964322i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.85995 - 3.22152i) q^{5} +(-0.763858 - 1.55452i) q^{6} +(-1.49982 - 2.17958i) q^{7} +1.00000i q^{8} +(1.14017 + 2.77489i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(-1.43878 - 0.964322i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.85995 - 3.22152i) q^{5} +(-0.763858 - 1.55452i) q^{6} +(-1.49982 - 2.17958i) q^{7} +1.00000i q^{8} +(1.14017 + 2.77489i) q^{9} +(3.22152 - 1.85995i) q^{10} +(-0.553597 + 0.319619i) q^{11} +(0.115738 - 1.72818i) q^{12} +1.00000i q^{13} +(-0.209090 - 2.63748i) q^{14} +(-5.78264 + 2.84147i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.63964 - 6.30404i) q^{17} +(-0.400031 + 2.97321i) q^{18} +(-4.62720 - 2.67151i) q^{19} +3.71990 q^{20} +(0.0560891 + 4.58223i) q^{21} -0.639239 q^{22} +(4.07685 + 2.35377i) q^{23} +(0.964322 - 1.43878i) q^{24} +(-4.41881 - 7.65361i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(1.03544 - 5.09194i) q^{27} +(1.13766 - 2.38867i) q^{28} +2.98058i q^{29} +(-6.42865 - 0.430532i) q^{30} +(0.608107 - 0.351091i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.10472 + 0.0739840i) q^{33} -7.27927i q^{34} +(-9.81114 + 0.777791i) q^{35} +(-1.83304 + 2.37486i) q^{36} +(5.21987 - 9.04107i) q^{37} +(-2.67151 - 4.62720i) q^{38} +(0.964322 - 1.43878i) q^{39} +(3.22152 + 1.85995i) q^{40} +11.6843 q^{41} +(-2.24254 + 3.99637i) q^{42} -3.57757 q^{43} +(-0.553597 - 0.319619i) q^{44} +(11.0600 + 1.48807i) q^{45} +(2.35377 + 4.07685i) q^{46} +(-3.53495 + 6.12272i) q^{47} +(1.55452 - 0.763858i) q^{48} +(-2.50111 + 6.53792i) q^{49} -8.83762i q^{50} +(-0.842486 + 12.5799i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(6.65923 - 3.84471i) q^{53} +(3.44269 - 3.89203i) q^{54} +2.37790i q^{55} +(2.17958 - 1.49982i) q^{56} +(4.08131 + 8.30582i) q^{57} +(-1.49029 + 2.58126i) q^{58} +(-1.35119 - 2.34033i) q^{59} +(-5.35211 - 3.58718i) q^{60} +(10.0041 + 5.77587i) q^{61} +0.702181 q^{62} +(4.33805 - 6.64691i) q^{63} -1.00000 q^{64} +(3.22152 + 1.85995i) q^{65} +(0.919723 + 0.616432i) q^{66} +(-1.15384 - 1.99852i) q^{67} +(3.63964 - 6.30404i) q^{68} +(-3.59590 - 7.31796i) q^{69} +(-8.88559 - 4.23198i) q^{70} -10.9092i q^{71} +(-2.77489 + 1.14017i) q^{72} +(-8.28825 + 4.78522i) q^{73} +(9.04107 - 5.21987i) q^{74} +(-1.02285 + 15.2730i) q^{75} -5.34303i q^{76} +(1.52693 + 0.727237i) q^{77} +(1.55452 - 0.763858i) q^{78} +(-5.00806 + 8.67422i) q^{79} +(1.85995 + 3.22152i) q^{80} +(-6.40003 + 6.32768i) q^{81} +(10.1189 + 5.84214i) q^{82} +6.70374 q^{83} +(-3.94029 + 2.33969i) q^{84} -27.0781 q^{85} +(-3.09826 - 1.78878i) q^{86} +(2.87423 - 4.28839i) q^{87} +(-0.319619 - 0.553597i) q^{88} +(1.95052 - 3.37839i) q^{89} +(8.83423 + 6.81872i) q^{90} +(2.17958 - 1.49982i) q^{91} +4.70754i q^{92} +(-1.21350 - 0.0812688i) q^{93} +(-6.12272 + 3.53495i) q^{94} +(-17.2127 + 9.93775i) q^{95} +(1.72818 + 0.115738i) q^{96} +3.50071i q^{97} +(-5.43499 + 4.41145i) q^{98} +(-1.51810 - 1.17175i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	$ 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) $ 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−1.43878	−	0.964322i	−0.830679	−	0.556751i
$3$	−1.43878	−	0.964322i	−0.830679	−	0.556751i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	1.85995	−	3.22152i	0.831794	−	1.44071i	−0.0648203	−	0.997897i	$-0.520647\pi$
$5$	1.85995	−	3.22152i	0.831794	−	1.44071i	0.896614	−	0.442812i	$-0.146019\pi$
$6$	−0.763858	−	1.55452i	−0.311844	−	0.634629i
$7$	−1.49982	−	2.17958i	−0.566877	−	0.823803i
$7$	−1.49982	−	2.17958i	−0.566877	−	0.823803i
$8$			1.00000i			0.353553i
$9$	1.14017	+	2.77489i	0.380056	+	0.924963i
$10$	3.22152	−	1.85995i	1.01874	−	0.588167i
$11$	−0.553597	+	0.319619i	−0.166916	+	0.0963689i	−0.581131	−	0.813810i	$-0.697390\pi$
$11$	−0.553597	+	0.319619i	−0.166916	+	0.0963689i	0.414215	+	0.910179i	$0.364056\pi$
$12$	0.115738	−	1.72818i	0.0334106	−	0.498882i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−0.209090	−	2.63748i	−0.0558815	−	0.704895i
$15$	−5.78264	+	2.84147i	−1.49307	+	0.733665i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.63964	−	6.30404i	−0.882742	−	1.52895i	−0.848280	−	0.529548i	$-0.822362\pi$
$17$	−3.63964	−	6.30404i	−0.882742	−	1.52895i	−0.0344615	−	0.999406i	$-0.510972\pi$
$18$	−0.400031	+	2.97321i	−0.0942881	+	0.700792i
$19$	−4.62720	−	2.67151i	−1.06155	−	0.612887i	−0.135691	−	0.990751i	$-0.543325\pi$
$19$	−4.62720	−	2.67151i	−1.06155	−	0.612887i	−0.925861	+	0.377864i	$0.876659\pi$
$20$	3.71990			0.831794
$21$	0.0560891	+	4.58223i	0.0122396	+	0.999925i
$22$	−0.639239			−0.136286
$23$	4.07685	+	2.35377i	0.850083	+	0.490795i	0.860679	−	0.509148i	$-0.170040\pi$
$23$	4.07685	+	2.35377i	0.850083	+	0.490795i	−0.0105961	+	0.999944i	$0.503373\pi$
$24$	0.964322	−	1.43878i	0.196841	−	0.293689i
$25$	−4.41881	−	7.65361i	−0.883762	−	1.53072i
$26$	−0.500000	+	0.866025i	−0.0980581	+	0.169842i
$27$	1.03544	−	5.09194i	0.199270	−	0.979945i
$28$	1.13766	−	2.38867i	0.214998	−	0.451415i
$29$			2.98058i			0.553479i	0.960945	+	0.276740i	$0.0892540\pi$
$29$			2.98058i			0.553479i	−0.960945	+	0.276740i	$0.910746\pi$
$30$	−6.42865	−	0.430532i	−1.17371	−	0.0786040i
$31$	0.608107	−	0.351091i	0.109219	−	0.0630577i	−0.444395	−	0.895831i	$-0.646581\pi$
$31$	0.608107	−	0.351091i	0.109219	−	0.0630577i	0.553615	+	0.832773i	$0.313248\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	1.10472	+	0.0739840i	0.192307	+	0.0128790i
$34$		−	7.27927i		−	1.24839i
$35$	−9.81114	+	0.777791i	−1.65838	+	0.131471i
$36$	−1.83304	+	2.37486i	−0.305507	+	0.395810i
$37$	5.21987	−	9.04107i	0.858141	−	1.48634i	−0.0155596	−	0.999879i	$-0.504953\pi$
$37$	5.21987	−	9.04107i	0.858141	−	1.48634i	0.873700	−	0.486465i	$-0.161714\pi$
$38$	−2.67151	−	4.62720i	−0.433377	−	0.750630i
$39$	0.964322	−	1.43878i	0.154415	−	0.230389i
$40$	3.22152	+	1.85995i	0.509368	+	0.294084i
$41$	11.6843			1.82478			0.912389	−	0.409325i	$-0.134236\pi$
$41$	11.6843			1.82478			0.912389	+	0.409325i	$0.134236\pi$
$42$	−2.24254	+	3.99637i	−0.346032	+	0.616654i
$43$	−3.57757			−0.545574			−0.272787	−	0.962075i	$-0.587945\pi$
$43$	−3.57757			−0.545574			−0.272787	+	0.962075i	$0.587945\pi$
$44$	−0.553597	−	0.319619i	−0.0834579	−	0.0481844i
$45$	11.0600	+	1.48807i	1.64873	+	0.221829i
$46$	2.35377	+	4.07685i	0.347045	+	0.601099i
$47$	−3.53495	+	6.12272i	−0.515626	+	0.893090i	0.484210	+	0.874952i	$0.339107\pi$
$47$	−3.53495	+	6.12272i	−0.515626	+	0.893090i	−0.999835	+	0.0181379i	$0.994226\pi$
$48$	1.55452	−	0.763858i	0.224375	−	0.110253i
$49$	−2.50111	+	6.53792i	−0.357301	+	0.933989i
$50$		−	8.83762i		−	1.24983i
$51$	−0.842486	+	12.5799i	−0.117972	+	1.76154i
$52$	−0.866025	+	0.500000i	−0.120096	+	0.0693375i
$53$	6.65923	−	3.84471i	0.914715	−	0.528111i	0.0327700	−	0.999463i	$-0.489567\pi$
$53$	6.65923	−	3.84471i	0.914715	−	0.528111i	0.881945	+	0.471352i	$0.156234\pi$
$54$	3.44269	−	3.89203i	0.468490	−	0.529639i
$55$			2.37790i			0.320636i
$56$	2.17958	−	1.49982i	0.291258	−	0.200421i
$57$	4.08131	+	8.30582i	0.540583	+	1.10013i
$58$	−1.49029	+	2.58126i	−0.195684	+	0.338935i
$59$	−1.35119	−	2.34033i	−0.175910	−	0.304685i	0.764566	−	0.644546i	$-0.222953\pi$
$59$	−1.35119	−	2.34033i	−0.175910	−	0.304685i	−0.940476	+	0.339861i	$0.889620\pi$
$60$	−5.35211	−	3.58718i	−0.690954	−	0.463102i
$61$	10.0041	+	5.77587i	1.28089	+	0.739524i	0.977012	−	0.213186i	$-0.0683841\pi$
$61$	10.0041	+	5.77587i	1.28089	+	0.739524i	0.303881	+	0.952710i	$0.401717\pi$
$62$	0.702181			0.0891771
$63$	4.33805	−	6.64691i	0.546542	−	0.837431i
$64$	−1.00000			−0.125000
$65$	3.22152	+	1.85995i	0.399581	+	0.230698i
$66$	0.919723	+	0.616432i	0.113210	+	0.0758775i
$67$	−1.15384	−	1.99852i	−0.140965	−	0.244158i	0.786896	−	0.617086i	$-0.211687\pi$
$67$	−1.15384	−	1.99852i	−0.140965	−	0.244158i	−0.927860	+	0.372928i	$0.878354\pi$
$68$	3.63964	−	6.30404i	0.441371	−	0.764477i
$69$	−3.59590	−	7.31796i	−0.432895	−	0.880978i
$70$	−8.88559	−	4.23198i	−1.06203	−	0.505819i
$71$		−	10.9092i		−	1.29468i	−0.762201	−	0.647340i	$-0.775881\pi$
$71$		−	10.9092i		−	1.29468i	0.762201	−	0.647340i	$-0.224119\pi$
$72$	−2.77489	+	1.14017i	−0.327024	+	0.134370i
$73$	−8.28825	+	4.78522i	−0.970066	+	0.560068i	−0.899256	−	0.437422i	$-0.855892\pi$
$73$	−8.28825	+	4.78522i	−0.970066	+	0.560068i	−0.0708097	+	0.997490i	$0.522558\pi$
$74$	9.04107	−	5.21987i	1.05100	−	0.606797i
$75$	−1.02285	+	15.2730i	−0.118108	+	1.76357i
$76$		−	5.34303i		−	0.612887i
$77$	1.52693	+	0.727237i	0.174010	+	0.0828764i
$78$	1.55452	−	0.763858i	0.176014	−	0.0864899i
$79$	−5.00806	+	8.67422i	−0.563451	+	0.975926i	0.433741	+	0.901038i	$0.357193\pi$
$79$	−5.00806	+	8.67422i	−0.563451	+	0.975926i	−0.997192	+	0.0748885i	$0.976140\pi$
$80$	1.85995	+	3.22152i	0.207948	+	0.360177i
$81$	−6.40003	+	6.32768i	−0.711115	+	0.703076i
$82$	10.1189	+	5.84214i	1.11744	+	0.645156i
$83$	6.70374			0.735831			0.367916	−	0.929859i	$-0.380072\pi$
$83$	6.70374			0.735831			0.367916	+	0.929859i	$0.380072\pi$
$84$	−3.94029	+	2.33969i	−0.429920	+	0.255281i
$85$	−27.0781			−2.93704
$86$	−3.09826	−	1.78878i	−0.334094	−	0.192889i
$87$	2.87423	−	4.28839i	0.308150	−	0.459764i
$88$	−0.319619	−	0.553597i	−0.0340716	−	0.0590137i
$89$	1.95052	−	3.37839i	0.206754	−	0.358109i	−0.743936	−	0.668251i	$-0.767043\pi$
$89$	1.95052	−	3.37839i	0.206754	−	0.358109i	0.950690	+	0.310142i	$0.100377\pi$
$90$	8.83423	+	6.81872i	0.931210	+	0.718757i
$91$	2.17958	−	1.49982i	0.228482	−	0.157223i
$92$			4.70754i			0.490795i
$93$	−1.21350	−	0.0812688i	−0.125834	−	0.00842718i
$94$	−6.12272	+	3.53495i	−0.631510	+	0.364602i
$95$	−17.2127	+	9.93775i	−1.76598	+	1.01959i
$96$	1.72818	+	0.115738i	0.176382	+	0.0118124i
$97$			3.50071i			0.355443i	0.984081	+	0.177721i	$0.0568726\pi$
$97$			3.50071i			0.355443i	−0.984081	+	0.177721i	$0.943127\pi$
$98$	−5.43499	+	4.41145i	−0.549017	+	0.445624i
$99$	−1.51810	−	1.17175i	−0.152575	−	0.117765i
$100$	4.41881	−	7.65361i	0.441881	−	0.765361i
$101$	0.886720	+	1.53584i	0.0882319	+	0.152822i	0.906764	−	0.421639i	$-0.138545\pi$
$101$	0.886720	+	1.53584i	0.0882319	+	0.152822i	−0.818532	+	0.574461i	$0.805212\pi$
$102$	−7.01956	+	10.4733i	−0.695040	+	1.03701i
$103$	7.16629	+	4.13746i	0.706115	+	0.407676i	0.809621	−	0.586953i	$-0.199673\pi$
$103$	7.16629	+	4.13746i	0.706115	+	0.407676i	−0.103506	+	0.994629i	$0.533006\pi$
$104$	−1.00000			−0.0980581
$105$	14.8661	+	8.34202i	1.45078	+	0.814098i
$106$	7.68941			0.746862
$107$	14.4332	+	8.33299i	1.39531	+	0.805580i	0.993896	−	0.110318i	$-0.0351869\pi$
$107$	14.4332	+	8.33299i	1.39531	+	0.805580i	0.401410	+	0.915898i	$0.368520\pi$
$108$	4.92747	−	1.64926i	0.474146	−	0.158700i
$109$	5.02724	+	8.70744i	0.481523	+	0.834022i	0.999775	−	0.0212061i	$-0.00675061\pi$
$109$	5.02724	+	8.70744i	0.481523	+	0.834022i	−0.518253	+	0.855228i	$0.673417\pi$
$110$	−1.18895	+	2.05932i	−0.113362	+	0.196349i
$111$	−16.2287	+	7.97447i	−1.54036	+	0.756904i
$112$	2.63748	−	0.209090i	0.249218	−	0.0197571i
$113$		−	9.55689i		−	0.899036i	−0.893271	−	0.449518i	$-0.851596\pi$
$113$		−	9.55689i		−	0.899036i	0.893271	−	0.449518i	$-0.148404\pi$
$114$	−0.618389	+	9.23371i	−0.0579174	+	0.864816i
$115$	15.1655	−	8.75579i	1.41419	−	0.816481i
$116$	−2.58126	+	1.49029i	−0.239664	+	0.138370i
$117$	−2.77489	+	1.14017i	−0.256539	+	0.105409i
$118$		−	2.70238i		−	0.248774i
$119$	−8.28135	+	17.3878i	−0.759150	+	1.59393i
$120$	−2.84147	−	5.78264i	−0.259390	−	0.527880i
$121$	−5.29569	+	9.17240i	−0.481426	+	0.833854i
$122$	5.77587	+	10.0041i	0.522922	+	0.905728i
$123$	−16.8111	−	11.2674i	−1.51580	−	1.01595i
$124$	0.608107	+	0.351091i	0.0546096	+	0.0315289i
$125$	−14.2756			−1.27684
$126$	7.08031	−	3.58737i	0.630764	−	0.319588i
$127$	2.68673			0.238409			0.119204	−	0.992870i	$-0.461966\pi$
$127$	2.68673			0.238409			0.119204	+	0.992870i	$0.461966\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	5.14732	+	3.44992i	0.453197	+	0.303749i
$130$	1.85995	+	3.22152i	0.163128	+	0.282546i
$131$	3.14262	−	5.44318i	0.274572	−	0.475573i	−0.695455	−	0.718570i	$-0.744797\pi$
$131$	3.14262	−	5.44318i	0.274572	−	0.475573i	0.970027	+	0.242997i	$0.0781305\pi$
$132$	0.488288	+	0.993707i	0.0425000	+	0.0864911i
$133$	1.11717	+	14.0921i	0.0968710	+	1.22194i
$134$		−	2.30769i		−	0.199354i
$135$	−14.4780	−	12.8064i	−1.24606	−	1.10220i
$136$	6.30404	−	3.63964i	0.540567	−	0.312096i
$137$	12.5020	−	7.21801i	1.06811	−	0.616676i	0.140449	−	0.990088i	$-0.455145\pi$
$137$	12.5020	−	7.21801i	1.06811	−	0.616676i	0.927666	+	0.373411i	$0.121812\pi$
$138$	0.544840	−	8.13548i	0.0463799	−	0.692538i
$139$			8.02304i			0.680505i	0.940334	+	0.340253i	$0.110513\pi$
$139$			8.02304i			0.680505i	−0.940334	+	0.340253i	$0.889487\pi$
$140$	−5.57916	−	8.10780i	−0.471525	−	0.685234i
$141$	10.9903	−	5.40040i	0.925548	−	0.454796i
$142$	5.45459	−	9.44762i	0.457739	−	0.792827i
$143$	−0.319619	−	0.553597i	−0.0267279	−	0.0462941i
$144$	−2.97321	−	0.400031i	−0.247767	−	0.0333359i
$145$	9.60200	+	5.54372i	0.797403	+	0.460381i
$146$	−9.57044			−0.792056
$147$	9.90320	−	6.99475i	0.816803	−	0.576917i
$148$	10.4397			0.858141
$149$	12.9471	+	7.47499i	1.06066	+	0.612375i	0.925616	−	0.378464i	$-0.123548\pi$
$149$	12.9471	+	7.47499i	1.06066	+	0.612375i	0.135048	+	0.990839i	$0.456881\pi$
$150$	−8.52231	+	12.7154i	−0.695844	+	1.03821i
$151$	2.84087	+	4.92054i	0.231187	+	0.400428i	0.958158	−	0.286241i	$-0.0924058\pi$
$151$	2.84087	+	4.92054i	0.231187	+	0.400428i	−0.726971	+	0.686668i	$0.759072\pi$
$152$	2.67151	−	4.62720i	0.216688	−	0.375315i
$153$	13.3432	−	17.2873i	1.07873	−	1.39759i
$154$	0.958740	+	1.39327i	0.0772575	+	0.112273i
$155$		−	2.61204i		−	0.209804i
$156$	1.72818	+	0.115738i	0.138365	+	0.00926642i
$157$	−3.76719	+	2.17499i	−0.300654	+	0.173583i	−0.642737	−	0.766087i	$-0.722201\pi$
$157$	−3.76719	+	2.17499i	−0.300654	+	0.173583i	0.342083	+	0.939670i	$0.388868\pi$
$158$	−8.67422	+	5.00806i	−0.690084	+	0.398420i
$159$	−13.2887	−	0.889954i	−1.05386	−	0.0705780i
$160$			3.71990i			0.294084i
$161$	−0.984298	−	12.4160i	−0.0775736	−	0.978521i
$162$	−8.70643	+	2.27992i	−0.684042	+	0.179127i
$163$	11.6978	−	20.2611i	0.916240	−	1.58697i	0.111163	−	0.993802i	$-0.464542\pi$
$163$	11.6978	−	20.2611i	0.916240	−	1.58697i	0.805076	−	0.593171i	$-0.202124\pi$
$164$	5.84214	+	10.1189i	0.456194	+	0.790152i
$165$	2.29306	−	3.42127i	0.178515	−	0.266346i
$166$	5.80561	+	3.35187i	0.450603	+	0.260156i
$167$	2.43964			0.188785			0.0943923	−	0.995535i	$-0.469909\pi$
$167$	2.43964			0.188785			0.0943923	+	0.995535i	$0.469909\pi$
$168$	−4.58223	+	0.0560891i	−0.353527	+	0.00432737i
$169$	−1.00000			−0.0769231
$170$	−23.4504	−	13.5391i	−1.79856	−	1.03840i
$171$	2.13737	−	15.8859i	0.163449	−	1.21483i
$172$	−1.78878	−	3.09826i	−0.136393	−	0.236240i
$173$	−1.18592	+	2.05407i	−0.0901638	+	0.156168i	−0.907580	−	0.419879i	$-0.862072\pi$
$173$	−1.18592	+	2.05407i	−0.0901638	+	0.156168i	0.817416	+	0.576048i	$0.195406\pi$
$174$	4.63336	−	2.27674i	0.351254	−	0.172599i
$175$	−10.0542	+	21.1101i	−0.760028	+	1.59578i
$176$		−	0.639239i		−	0.0481844i
$177$	−0.312767	+	4.67020i	−0.0235090	+	0.351034i
$178$	3.37839	−	1.95052i	0.253221	−	0.146197i
$179$	−8.34373	+	4.81725i	−0.623639	+	0.360058i	−0.778285	−	0.627912i	$-0.783910\pi$
$179$	−8.34373	+	4.81725i	−0.623639	+	0.360058i	0.154645	+	0.987970i	$0.450577\pi$
$180$	4.24131	+	10.3223i	0.316128	+	0.769379i
$181$		−	10.6638i		−	0.792636i	−0.918113	−	0.396318i	$-0.870288\pi$
$181$		−	10.6638i		−	0.792636i	0.918113	−	0.396318i	$-0.129712\pi$
$182$	2.63748	−	0.209090i	0.195503	−	0.0154987i
$183$	−8.82388	−	17.9574i	−0.652280	−	1.32745i
$184$	−2.35377	+	4.07685i	−0.173522	+	0.300550i
$185$	−19.4174	−	33.6319i	−1.42759	−	2.47266i
$186$	−1.01028	−	0.677129i	−0.0740776	−	0.0496495i
$187$	4.02979	+	2.32660i	0.294687	+	0.170138i
$188$	−7.06990			−0.515626
$189$	−12.6512	+	5.38016i	−0.920242	+	0.391349i
$190$	−19.8755			−1.44192
$191$	−8.44258	−	4.87433i	−0.610884	−	0.352694i	0.162428	−	0.986720i	$-0.448068\pi$
$191$	−8.44258	−	4.87433i	−0.610884	−	0.352694i	−0.773311	+	0.634027i	$0.781401\pi$
$192$	1.43878	+	0.964322i	0.103835	+	0.0695939i
$193$	−1.46371	−	2.53522i	−0.105360	−	0.182489i	0.808525	−	0.588462i	$-0.200266\pi$
$193$	−1.46371	−	2.53522i	−0.105360	−	0.182489i	−0.913885	+	0.405972i	$0.866933\pi$
$194$	−1.75035	+	3.03170i	−0.125668	+	0.217663i
$195$	−2.84147	−	5.78264i	−0.203482	−	0.414103i
$196$	−6.91256	+	1.10294i	−0.493755	+	0.0787812i
$197$			2.60658i			0.185711i	0.995680	+	0.0928556i	$0.0295995\pi$
$197$			2.60658i			0.185711i	−0.995680	+	0.0928556i	$0.970400\pi$
$198$	−0.728840	−	1.77382i	−0.0517964	−	0.126060i
$199$	−9.74629	+	5.62702i	−0.690896	+	0.398889i	−0.803948	−	0.594700i	$-0.797271\pi$
$199$	−9.74629	+	5.62702i	−0.690896	+	0.398889i	0.113052	+	0.993589i	$0.463937\pi$
$200$	7.65361	−	4.41881i	0.541192	−	0.312457i
$201$	−0.267086	+	3.98810i	−0.0188388	+	0.281299i
$202$			1.77344i			0.124779i
$203$	6.49640	−	4.47031i	0.455958	−	0.313755i
$204$	−11.3158	+	5.56033i	−0.792261	+	0.389301i
$205$	21.7321	−	37.6412i	1.51784	−	2.62897i
$206$	4.13746	+	7.16629i	0.288270	+	0.499299i
$207$	−1.88316	+	13.9965i	−0.130889	+	0.972825i
$208$	−0.866025	−	0.500000i	−0.0600481	−	0.0346688i
$209$	3.41547			0.236253
$210$	8.70341	+	14.6574i	0.600592	+	1.01146i
$211$	0.972576			0.0669549			0.0334775	−	0.999439i	$-0.489342\pi$
$211$	0.972576			0.0669549			0.0334775	+	0.999439i	$0.489342\pi$
$212$	6.65923	+	3.84471i	0.457358	+	0.264056i
$213$	−10.5199	+	15.6959i	−0.720815	+	1.07546i
$214$	8.33299	+	14.4332i	0.569631	+	0.986631i
$215$	−6.65408	+	11.5252i	−0.453805	+	0.786013i
$216$	5.09194	+	1.03544i	0.346463	+	0.0704526i
$217$	−1.67728	−	0.798845i	−0.113861	−	0.0542291i
$218$			10.0545i			0.680976i
$219$	16.5394	+	1.10766i	1.11763	+	0.0748487i
$220$	−2.05932	+	1.18895i	−0.138840	+	0.0801591i
$221$	6.30404	−	3.63964i	0.424055	−	0.244829i
$222$	−18.0417	−	1.20827i	−1.21088	−	0.0810937i
$223$		−	11.7623i		−	0.787661i	−0.919183	−	0.393830i	$-0.871150\pi$
$223$		−	11.7623i		−	0.787661i	0.919183	−	0.393830i	$-0.128850\pi$
$224$	2.38867	+	1.13766i	0.159599	+	0.0760132i
$225$	16.1997	−	20.9881i	1.07998	−	1.39921i
$226$	4.77844	−	8.27651i	0.317857	−	0.550545i
$227$	3.46041	+	5.99360i	0.229675	+	0.397809i	0.957712	−	0.287729i	$-0.0929003\pi$
$227$	3.46041	+	5.99360i	0.229675	+	0.397809i	−0.728037	+	0.685538i	$0.759567\pi$
$228$	−5.15240	+	7.68743i	−0.341226	+	0.509113i
$229$	−8.65357	−	4.99614i	−0.571844	−	0.330154i	0.186042	−	0.982542i	$-0.440434\pi$
$229$	−8.65357	−	4.99614i	−0.571844	−	0.330154i	−0.757885	+	0.652388i	$0.773767\pi$
$230$	17.5116			1.15468
$231$	−1.49562	−	2.51878i	−0.0984047	−	0.165724i
$232$	−2.98058			−0.195684
$233$	−1.71349	−	0.989282i	−0.112254	−	0.0648100i	0.442822	−	0.896610i	$-0.353977\pi$
$233$	−1.71349	−	0.989282i	−0.112254	−	0.0648100i	−0.555076	+	0.831800i	$0.687311\pi$
$234$	−2.97321	−	0.400031i	−0.194365	−	0.0261508i
$235$	13.1496	+	22.7759i	0.857789	+	1.48573i
$236$	1.35119	−	2.34033i	0.0879550	−	0.152343i
$237$	15.5702	−	7.65090i	1.01140	−	0.496979i
$238$	−15.8657	+	10.9176i	−1.02842	+	0.707681i
$239$		−	10.7072i		−	0.692588i	−0.938126	−	0.346294i	$-0.887440\pi$
$239$		−	10.7072i		−	0.692588i	0.938126	−	0.346294i	$-0.112560\pi$
$240$	0.430532	−	6.42865i	0.0277907	−	0.414967i
$241$	−17.1442	+	9.89818i	−1.10435	+	0.637598i	−0.937361	−	0.348360i	$-0.886739\pi$
$241$	−17.1442	+	9.89818i	−1.10435	+	0.637598i	−0.166991	+	0.985958i	$0.553405\pi$
$242$	−9.17240	+	5.29569i	−0.589624	+	0.340420i
$243$	15.3102	−	2.93245i	0.982147	−	0.188116i
$244$			11.5517i			0.739524i
$245$	16.4101	+	20.2176i	1.04841	+	1.29165i
$246$	−8.92513	−	18.1634i	−0.569046	−	1.15806i
$247$	2.67151	−	4.62720i	0.169984	−	0.294421i
$248$	0.351091	+	0.608107i	0.0222943	+	0.0386148i
$249$	−9.64520	−	6.46456i	−0.611240	−	0.409675i
$250$	−12.3630	−	7.13778i	−0.781905	−	0.451433i
$251$	27.2102			1.71749			0.858747	−	0.512400i	$-0.171244\pi$
$251$	27.2102			1.71749			0.858747	+	0.512400i	$0.171244\pi$
$252$	7.92541	+	0.433404i	0.499254	+	0.0273019i
$253$	−3.00925			−0.189190
$254$	2.32678	+	1.34337i	0.145995	+	0.0842903i
$255$	38.9595	+	26.1120i	2.43974	+	1.63520i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.3753	+	19.7025i	−0.709569	+	1.22901i	0.255447	+	0.966823i	$0.417777\pi$
$257$	−11.3753	+	19.7025i	−0.709569	+	1.22901i	−0.965017	+	0.262187i	$0.915556\pi$
$258$	2.73275	+	5.56138i	0.170134	+	0.346237i
$259$	−27.5345	+	2.18284i	−1.71091	+	0.135635i
$260$			3.71990i			0.230698i
$261$	−8.27078	+	3.39836i	−0.511948	+	0.210353i
$262$	5.44318	−	3.14262i	0.336281	−	0.194152i
$263$	1.66747	−	0.962712i	0.102820	−	0.0593634i	−0.447708	−	0.894180i	$-0.647760\pi$
$263$	1.66747	−	0.962712i	0.102820	−	0.0593634i	0.550528	+	0.834816i	$0.314426\pi$
$264$	−0.0739840	+	1.10472i	−0.00455340	+	0.0679908i
$265$		−	28.6038i		−	1.75712i
$266$	−6.07855	+	12.7627i	−0.372700	+	0.782532i
$267$	−6.06422	+	2.97983i	−0.371124	+	0.182363i
$268$	1.15384	−	1.99852i	0.0704823	−	0.122079i
$269$	−9.29729	−	16.1034i	−0.566866	−	0.981840i	−0.996873	−	0.0790149i	$-0.974823\pi$
$269$	−9.29729	−	16.1034i	−0.566866	−	0.981840i	0.430008	−	0.902825i	$-0.358511\pi$
$270$	−6.13506	−	18.3297i	−0.373368	−	1.11551i
$271$	−5.08642	−	2.93665i	−0.308978	−	0.178389i	0.337491	−	0.941329i	$-0.390422\pi$
$271$	−5.08642	−	2.93665i	−0.308978	−	0.178389i	−0.646469	+	0.762940i	$0.723755\pi$
$272$	7.27927			0.441371
$273$	−4.58223	+	0.0560891i	−0.277329	+	0.00339467i
$274$	14.4360			0.872112
$275$	4.89248	+	2.82468i	0.295028	+	0.170334i
$276$	4.53959	−	6.77312i	0.273251	−	0.407694i
$277$	−3.58404	−	6.20773i	−0.215344	−	0.372987i	0.738035	−	0.674762i	$-0.235754\pi$
$277$	−3.58404	−	6.20773i	−0.215344	−	0.372987i	−0.953379	+	0.301776i	$0.902421\pi$
$278$	−4.01152	+	6.94815i	−0.240595	+	0.416723i
$279$	1.66758	+	1.28713i	0.0998355	+	0.0770583i
$280$	−0.777791	−	9.81114i	−0.0464819	−	0.586328i
$281$			1.56977i			0.0936448i	0.998903	+	0.0468224i	$0.0149095\pi$
$281$			1.56977i			0.0936448i	−0.998903	+	0.0468224i	$0.985091\pi$
$282$	12.2181	+	0.818254i	0.727575	+	0.0487263i
$283$	17.3559	−	10.0204i	1.03170	−	0.595653i	0.114230	−	0.993454i	$-0.463560\pi$
$283$	17.3559	−	10.0204i	1.03170	−	0.595653i	0.917472	+	0.397801i	$0.130227\pi$
$284$	9.44762	−	5.45459i	0.560613	−	0.323670i
$285$	34.3484	+	2.30034i	2.03463	+	0.136261i
$286$		−	0.639239i		−	0.0377990i
$287$	−17.5243	−	25.4668i	−1.03442	−	1.50326i
$288$	−2.37486	−	1.83304i	−0.139940	−	0.108013i
$289$	−17.9939	+	31.1664i	−1.05847	+	1.83332i
$290$	5.54372	+	9.60200i	0.325538	+	0.563849i
$291$	3.37581	−	5.03674i	0.197893	−	0.295259i
$292$	−8.28825	−	4.78522i	−0.485033	−	0.280034i
$293$	−17.0764			−0.997617			−0.498808	−	0.866712i	$-0.666229\pi$
$293$	−17.0764			−0.997617			−0.498808	+	0.866712i	$0.666229\pi$
$294$	12.0738	−	1.10603i	0.704158	−	0.0645050i
$295$	−10.0526			−0.585284
$296$	9.04107	+	5.21987i	0.525502	+	0.303399i
$297$	1.05427	+	3.14983i	0.0611749	+	0.182772i
$298$	7.47499	+	12.9471i	0.433014	+	0.750003i
$299$	−2.35377	+	4.07685i	−0.136122	+	0.235771i
$300$	−13.7382	+	6.75069i	−0.793177	+	0.389751i
$301$	5.36569	+	7.79758i	0.309273	+	0.449445i
$302$			5.68175i			0.326948i
$303$	0.205254	−	3.06482i	0.0117915	−	0.176069i
$304$	4.62720	−	2.67151i	0.265388	−	0.153222i
$305$	37.2142	−	21.4856i	2.13088	−	1.23026i
$306$	20.1992	−	8.29960i	1.15471	−	0.474456i
$307$			2.27545i			0.129867i	0.997890	+	0.0649335i	$0.0206835\pi$
$307$			2.27545i			0.129867i	−0.997890	+	0.0649335i	$0.979316\pi$
$308$	0.133658	+	1.68598i	0.00761588	+	0.0960675i
$309$	−6.32086	−	12.8635i	−0.359581	−	0.731778i
$310$	1.30602	−	2.26209i	0.0741770	−	0.128478i
$311$	−10.8605	−	18.8110i	−0.615844	−	1.06667i	−0.990236	−	0.139402i	$-0.955482\pi$
$311$	−10.8605	−	18.8110i	−0.615844	−	1.06667i	0.374392	−	0.927270i	$-0.377851\pi$
$312$	1.43878	+	0.964322i	0.0814548	+	0.0545940i
$313$	−14.3547	−	8.28769i	−0.811376	−	0.468448i	0.0360575	−	0.999350i	$-0.488520\pi$
$313$	−14.3547	−	8.28769i	−0.811376	−	0.468448i	−0.847434	+	0.530902i	$0.821853\pi$
$314$	−4.34997			−0.245483
$315$	−13.3446	−	26.3380i	−0.751885	−	1.48398i
$316$	−10.0161			−0.563451
$317$	7.12729	+	4.11494i	0.400308	+	0.231118i	0.686617	−	0.727019i	$-0.259095\pi$
$317$	7.12729	+	4.11494i	0.400308	+	0.231118i	−0.286309	+	0.958137i	$0.592428\pi$
$318$	−11.0634	−	7.41507i	−0.620403	−	0.415816i
$319$	−0.952651	−	1.65004i	−0.0533382	−	0.0923845i
$320$	−1.85995	+	3.22152i	−0.103974	+	0.180089i
$321$	−12.7304	−	25.9075i	−0.710544	−	1.44602i
$322$	5.35559	−	11.2448i	0.298455	−	0.626646i
$323$			38.8934i			2.16408i
$324$	−8.67995	−	2.37875i	−0.482219	−	0.132153i
$325$	7.65361	−	4.41881i	0.424546	−	0.245112i
$326$	20.2611	−	11.6978i	1.12216	−	0.647879i
$327$	1.16368	−	17.3760i	0.0643518	−	0.960893i
$328$			11.6843i			0.645156i
$329$	18.6467	−	1.47824i	1.02803	−	0.0814982i
$330$	3.69649	−	1.81638i	0.203485	−	0.0999884i
$331$	−11.3043	+	19.5795i	−0.621338	+	1.07619i	0.367899	+	0.929866i	$0.380077\pi$
$331$	−11.3043	+	19.5795i	−0.621338	+	1.07619i	−0.989237	+	0.146323i	$0.953256\pi$
$332$	3.35187	+	5.80561i	0.183958	+	0.318624i
$333$	31.0395	+	4.17621i	1.70095	+	0.228855i
$334$	2.11279	+	1.21982i	0.115607	+	0.0667455i
$335$	−8.58436			−0.469014
$336$	−3.99637	−	2.24254i	−0.218020	−	0.122341i
$337$	1.33284			0.0726044			0.0363022	−	0.999341i	$-0.488442\pi$
$337$	1.33284			0.0726044			0.0363022	+	0.999341i	$0.488442\pi$
$338$	−0.866025	−	0.500000i	−0.0471056	−	0.0271964i
$339$	−9.21591	+	13.7502i	−0.500540	+	0.746811i
$340$	−13.5391	−	23.4504i	−0.734259	−	1.27177i
$341$	−0.224431	+	0.388726i	−0.0121536	+	0.0210507i
$342$	9.79399	−	12.6889i	0.529598	−	0.686139i
$343$	18.0011	−	4.35432i	0.971969	−	0.235111i
$344$		−	3.57757i		−	0.192889i
$345$	−30.2631	−	2.02675i	−1.62931	−	0.109116i
$346$	−2.05407	+	1.18592i	−0.110428	+	0.0637554i
$347$	−19.2344	+	11.1050i	−1.03255	+	0.596146i	−0.917716	−	0.397238i	$-0.869969\pi$
$347$	−19.2344	+	11.1050i	−1.03255	+	0.596146i	−0.114839	+	0.993384i	$0.536635\pi$
$348$	5.15097	+	0.344965i	0.276121	+	0.0184921i
$349$			17.4181i			0.932371i	0.884687	+	0.466185i	$0.154372\pi$
$349$			17.4181i			0.932371i	−0.884687	+	0.466185i	$0.845628\pi$
$350$	−19.2623	+	13.2548i	−1.02961	+	0.708499i
$351$	5.09194	+	1.03544i	0.271788	+	0.0552675i
$352$	0.319619	−	0.553597i	0.0170358	−	0.0295068i
$353$	−14.4605	−	25.0463i	−0.769653	−	1.33308i	−0.937751	−	0.347307i	$-0.887096\pi$
$353$	−14.4605	−	25.0463i	−0.769653	−	1.33308i	0.168099	−	0.985770i	$-0.446237\pi$
$354$	−2.60596	+	3.88813i	−0.138505	+	0.206652i
$355$	−35.1442	−	20.2905i	−1.86526	−	1.07691i
$356$	3.90103			0.206754
$357$	28.6824	−	17.0313i	1.51803	−	0.901389i
$358$	−9.63450			−0.509199
$359$	−3.51757	−	2.03087i	−0.185650	−	0.107185i	0.404294	−	0.914629i	$-0.367517\pi$
$359$	−3.51757	−	2.03087i	−0.185650	−	0.107185i	−0.589945	+	0.807444i	$0.700850\pi$
$360$	−1.48807	+	11.0600i	−0.0784283	+	0.582915i
$361$	4.77397	+	8.26875i	0.251261	+	0.435198i
$362$	5.33192	−	9.23515i	0.280239	−	0.485389i
$363$	16.4645	−	8.09031i	0.864160	−	0.424631i
$364$	2.38867	+	1.13766i	0.125200	+	0.0596297i
$365$			35.6011i			1.86344i
$366$	1.33697	−	19.9635i	0.0698845	−	1.04351i
$367$	8.01993	−	4.63031i	0.418637	−	0.241700i	−0.275857	−	0.961199i	$-0.588962\pi$
$367$	8.01993	−	4.63031i	0.418637	−	0.241700i	0.694494	+	0.719499i	$0.255628\pi$
$368$	−4.07685	+	2.35377i	−0.212521	+	0.122699i
$369$	13.3220	+	32.4226i	0.693518	+	1.68785i
$370$		−	38.8347i		−	2.01892i
$371$	−18.3674	−	8.74795i	−0.953590	−	0.454171i
$372$	−0.536367	−	1.09155i	−0.0278093	−	0.0565943i
$373$	−3.06884	+	5.31539i	−0.158899	+	0.275220i	−0.934472	−	0.356037i	$-0.884128\pi$
$373$	−3.06884	+	5.31539i	−0.158899	+	0.275220i	0.775573	+	0.631258i	$0.217461\pi$
$374$	2.32660	+	4.02979i	0.120306	+	0.208375i
$375$	20.5394	+	13.7662i	1.06065	+	0.710885i
$376$	−6.12272	−	3.53495i	−0.315755	−	0.182301i
$377$	−2.98058			−0.153508
$378$	−13.6464	−	1.66627i	−0.701894	−	0.0857036i
$379$	15.9194			0.817725			0.408863	−	0.912596i	$-0.365926\pi$
$379$	15.9194			0.817725			0.408863	+	0.912596i	$0.365926\pi$
$380$	−17.2127	−	9.93775i	−0.882992	−	0.509796i
$381$	−3.86561	−	2.59087i	−0.198041	−	0.132734i
$382$	−4.87433	−	8.44258i	−0.249392	−	0.431960i
$383$	−13.7676	+	23.8462i	−0.703491	+	1.21848i	0.263742	+	0.964593i	$0.415043\pi$
$383$	−13.7676	+	23.8462i	−0.703491	+	1.21848i	−0.967233	+	0.253889i	$0.918290\pi$
$384$	0.763858	+	1.55452i	0.0389805	+	0.0793286i
$385$	5.18282	−	3.56641i	0.264141	−	0.181761i
$386$		−	2.92742i		−	0.149002i
$387$	−4.07903	−	9.92735i	−0.207349	−	0.504636i
$388$	−3.03170	+	1.75035i	−0.153911	+	0.0888607i
$389$	−16.1727	+	9.33731i	−0.819988	+	0.473420i	−0.850412	−	0.526117i	$-0.823648\pi$
$389$	−16.1727	+	9.33731i	−0.819988	+	0.473420i	0.0304242	+	0.999537i	$0.490314\pi$
$390$	0.430532	−	6.42865i	0.0218008	−	0.325527i
$391$		−	34.2675i		−	1.73298i
$392$	−6.53792	−	2.50111i	−0.330215	−	0.126325i
$393$	−9.77051	+	4.80103i	−0.492857	+	0.242180i
$394$	−1.30329	+	2.25737i	−0.0656589	+	0.113724i
$395$	18.6295	+	32.2672i	0.937351	+	1.62354i
$396$	0.255715	−	1.90059i	0.0128502	−	0.0955083i
$397$	−2.58988	−	1.49527i	−0.129982	−	0.0750452i	0.433599	−	0.901106i	$-0.357243\pi$
$397$	−2.58988	−	1.49527i	−0.129982	−	0.0750452i	−0.563581	+	0.826061i	$0.690577\pi$
$398$	−11.2540			−0.564114
$399$	11.9820	−	21.3527i	0.599848	−	1.06897i
$400$	8.83762			0.441881
$401$	−8.68481	−	5.01418i	−0.433699	−	0.250396i	0.267222	−	0.963635i	$-0.413894\pi$
$401$	−8.68481	−	5.01418i	−0.433699	−	0.250396i	−0.700921	+	0.713239i	$0.747228\pi$
$402$	−2.22535	+	3.32025i	−0.110991	+	0.165599i
$403$	0.351091	+	0.608107i	0.0174891	+	0.0302920i
$404$	−0.886720	+	1.53584i	−0.0441160	+	0.0764111i
$405$	8.48105	+	32.3870i	0.421427	+	1.60932i
$406$	7.86120	−	0.623208i	0.390145	−	0.0309293i
$407$			6.67348i			0.330792i
$408$	−12.5799	−	0.842486i	−0.622798	−	0.0417093i
$409$	28.0742	−	16.2086i	1.38818	−	0.801466i	0.395069	−	0.918651i	$-0.370721\pi$
$409$	28.0742	−	16.2086i	1.38818	−	0.801466i	0.993110	+	0.117186i	$0.0373873\pi$
$410$	37.6412	−	21.7321i	1.85897	−	1.07327i
$411$	−24.9480	−	1.67079i	−1.23060	−	0.0824140i
$412$			8.27492i			0.407676i
$413$	−3.07440	+	6.45509i	−0.151281	+	0.317634i
$414$	−8.62913	+	11.1798i	−0.424098	+	0.549455i
$415$	12.4686	−	21.5963i	0.612060	−	1.06012i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	7.73679	−	11.5434i	0.378872	−	0.565281i
$418$	2.95788	+	1.70774i	0.144675	+	0.0835281i
$419$	−35.0674			−1.71315			−0.856577	−	0.516019i	$-0.827413\pi$
$419$	−35.0674			−1.71315			−0.856577	+	0.516019i	$0.827413\pi$
$420$	0.208646	+	17.0454i	0.0101809	+	0.831732i
$421$	12.0494			0.587249			0.293625	−	0.955921i	$-0.405138\pi$
$421$	12.0494			0.587249			0.293625	+	0.955921i	$0.405138\pi$
$422$	0.842276	+	0.486288i	0.0410013	+	0.0236721i
$423$	−21.0203	−	2.82818i	−1.02204	−	0.137511i
$424$	3.84471	+	6.65923i	0.186715	+	0.323401i
$425$	−32.1657	+	55.7127i	−1.56027	+	2.70246i
$426$	−16.9585	+	8.33306i	−0.821641	+	0.403738i
$427$	−2.41535	−	30.4674i	−0.116887	−	1.47442i
$428$			16.6660i			0.805580i
$429$	−0.0739840	+	1.10472i	−0.00357198	+	0.0533364i
$430$	−11.5252	+	6.65408i	−0.555795	+	0.320888i
$431$	12.1267	−	7.00133i	0.584121	−	0.337242i	−0.178649	−	0.983913i	$-0.557173\pi$
$431$	12.1267	−	7.00133i	0.584121	−	0.337242i	0.762769	+	0.646671i	$0.223839\pi$
$432$	3.89203	+	3.44269i	0.187255	+	0.165636i
$433$			23.7265i			1.14022i	0.821568	+	0.570110i	$0.193100\pi$
$433$			23.7265i			1.14022i	−0.821568	+	0.570110i	$0.806900\pi$
$434$	−1.05314	−	1.53046i	−0.0505524	−	0.0734643i
$435$	−8.46923	−	17.2356i	−0.406068	−	0.826384i
$436$	−5.02724	+	8.70744i	−0.240761	+	0.417011i
$437$	−12.5763	−	21.7827i	−0.601605	−	1.04201i
$438$	13.7698	+	9.22899i	0.657944	+	0.440978i
$439$	−23.8048	−	13.7437i	−1.13614	−	0.655950i	−0.190668	−	0.981655i	$-0.561065\pi$
$439$	−23.8048	−	13.7437i	−1.13614	−	0.655950i	−0.945472	+	0.325704i	$0.894399\pi$
$440$	−2.37790			−0.113362
$441$	−20.9937	+	0.514027i	−0.999700	+	0.0244775i
$442$	7.27927			0.346240
$443$	19.7056	+	11.3770i	0.936242	+	0.540540i	0.888780	−	0.458334i	$-0.151553\pi$
$443$	19.7056	+	11.3770i	0.936242	+	0.540540i	0.0474616	+	0.998873i	$0.484887\pi$
$444$	−15.0205	−	10.0673i	−0.712840	−	0.477771i
$445$	−7.25571	−	12.5673i	−0.343954	−	0.595746i
$446$	5.88114	−	10.1864i	0.278480	−	0.482342i
$447$	−11.4197	−	23.2400i	−0.540131	−	1.09921i
$448$	1.49982	+	2.17958i	0.0708596	+	0.102975i
$449$		−	12.2342i		−	0.577368i	−0.957425	−	0.288684i	$-0.906782\pi$
$449$		−	12.2342i		−	0.577368i	0.957425	−	0.288684i	$-0.0932176\pi$
$450$	24.5234	−	10.0764i	1.15605	−	0.475005i
$451$	−6.46838	+	3.73452i	−0.304584	+	0.175852i
$452$	8.27651	−	4.77844i	0.389294	−	0.224759i
$453$	0.657592	−	9.81908i	0.0308963	−	0.461340i
$454$			6.92081i			0.324810i
$455$	−0.777791	−	9.81114i	−0.0364634	−	0.459953i
$456$	−8.30582	+	4.08131i	−0.388956	+	0.191125i
$457$	−9.42161	+	16.3187i	−0.440724	+	0.763357i	−0.997743	−	0.0671429i	$-0.978612\pi$
$457$	−9.42161	+	16.3187i	−0.440724	+	0.763357i	0.557019	+	0.830500i	$0.311945\pi$
$458$	−4.99614	−	8.65357i	−0.233454	−	0.404355i
$459$	−35.8684	+	12.0054i	−1.67419	+	0.560364i
$460$	15.1655	+	8.75579i	0.707094	+	0.408241i
$461$	18.7725			0.874324			0.437162	−	0.899383i	$-0.355984\pi$
$461$	18.7725			0.874324			0.437162	+	0.899383i	$0.355984\pi$
$462$	−0.0358543	−	2.92914i	−0.00166810	−	0.136276i
$463$	21.8455			1.01525			0.507624	−	0.861579i	$-0.330524\pi$
$463$	21.8455			1.01525			0.507624	+	0.861579i	$0.330524\pi$
$464$	−2.58126	−	1.49029i	−0.119832	−	0.0691849i
$465$	−2.51885	+	3.75815i	−0.116809	+	0.174280i
$466$	−0.989282	−	1.71349i	−0.0458276	−	0.0793758i
$467$	13.6271	−	23.6028i	0.630586	−	1.09221i	−0.356846	−	0.934163i	$-0.616148\pi$
$467$	13.6271	−	23.6028i	0.630586	−	1.09221i	0.987432	−	0.158043i	$-0.0505186\pi$
$468$	−2.37486	−	1.83304i	−0.109778	−	0.0847324i
$469$	−2.62537	+	5.51230i	−0.121228	+	0.254534i
$470$			26.2993i			1.21310i
$471$	7.51753	+	0.503455i	0.346390	+	0.0231980i
$472$	2.34033	−	1.35119i	0.107722	−	0.0621936i
$473$	1.98053	−	1.14346i	0.0910649	−	0.0525763i
$474$	17.3097	+	1.15924i	0.795060	+	0.0532458i
$475$			47.2197i			2.16659i
$476$	−19.1989	+	1.52202i	−0.879981	+	0.0697617i
$477$	18.2613	+	14.0950i	0.836127	+	0.645366i
$478$	5.35358	−	9.27267i	0.244867	−	0.424122i
$479$	4.07896	+	7.06496i	0.186372	+	0.322806i	0.944038	−	0.329836i	$-0.106994\pi$
$479$	4.07896	+	7.06496i	0.186372	+	0.322806i	−0.757666	+	0.652643i	$0.773660\pi$
$480$	3.58718	−	5.35211i	0.163731	−	0.244289i
$481$	9.04107	+	5.21987i	0.412237	+	0.238005i
$482$	−19.7964			−0.901700
$483$	−10.5569	+	18.8131i	−0.480354	+	0.856026i
$484$	−10.5914			−0.481426
$485$	11.2776	+	6.51113i	0.512090	+	0.295655i
$486$	14.7252	+	5.11550i	0.667949	+	0.232044i
$487$	15.7854	+	27.3411i	0.715304	+	1.23894i	0.962842	+	0.270065i	$0.0870453\pi$
$487$	15.7854	+	27.3411i	0.715304	+	1.23894i	−0.247538	+	0.968878i	$0.579621\pi$
$488$	−5.77587	+	10.0041i	−0.261461	+	0.452864i
$489$	−36.3687	+	17.8709i	−1.64465	+	0.808148i
$490$	4.10281	+	25.7140i	0.185346	+	1.16164i
$491$		−	10.4465i		−	0.471445i	−0.971820	−	0.235722i	$-0.924254\pi$
$491$		−	10.4465i		−	0.471445i	0.971820	−	0.235722i	$-0.0757456\pi$
$492$	1.35231	−	20.1925i	0.0609669	−	0.910350i
$493$	18.7897	−	10.8482i	0.846244	−	0.488579i
$494$	4.62720	−	2.67151i	0.208187	−	0.120197i
$495$	−6.59842	+	2.71121i	−0.296577	+	0.121860i
$496$			0.702181i			0.0315289i
$497$	−23.7774	+	16.3617i	−1.06656	+	0.733924i
$498$	−5.12071	−	10.4211i	−0.229464	−	0.466979i
$499$	−9.01724	+	15.6183i	−0.403667	+	0.699172i	−0.994165	−	0.107867i	$-0.965598\pi$
$499$	−9.01724	+	15.6183i	−0.403667	+	0.699172i	0.590498	+	0.807039i	$0.298931\pi$
$500$	−7.13778	−	12.3630i	−0.319211	−	0.552890i
$501$	−3.51010	−	2.35259i	−0.156820	−	0.105106i
$502$	23.5647	+	13.6051i	1.05175	+	0.607226i
$503$	1.94837			0.0868734			0.0434367	−	0.999056i	$-0.486169\pi$
$503$	1.94837			0.0868734			0.0434367	+	0.999056i	$0.486169\pi$
$504$	6.64691	+	4.33805i	0.296077	+	0.193232i
$505$	6.59701			0.293563
$506$	−2.60608	−	1.50462i	−0.115855	−	0.0668887i
$507$	1.43878	+	0.964322i	0.0638984	+	0.0428270i
$508$	1.34337	+	2.32678i	0.0596022	+	0.103234i
$509$	−9.25943	+	16.0378i	−0.410417	+	0.710863i	−0.994935	−	0.100517i	$-0.967950\pi$
$509$	−9.25943	+	16.0378i	−0.410417	+	0.710863i	0.584518	+	0.811381i	$0.301284\pi$
$510$	20.6839	+	42.0934i	0.915897	+	1.86393i
$511$	22.8606	+	10.8879i	1.01129	+	0.481653i
$512$		−	1.00000i		−	0.0441942i
$513$	−18.3944	+	20.7952i	−0.812131	+	0.918132i
$514$	−19.7025	+	11.3753i	−0.869042	+	0.501741i
$515$	26.6578	−	15.3909i	1.17468	−	0.678205i
$516$	−0.414059	+	6.18268i	−0.0182279	+	0.272177i
$517$		−	4.51936i		−	0.198761i
$518$	−24.9370	−	11.8769i	−1.09567	−	0.521840i
$519$	3.68706	−	1.81175i	0.161844	−	0.0795269i
$520$	−1.85995	+	3.22152i	−0.0815641	+	0.141273i
$521$	11.1032	+	19.2313i	0.486441	+	0.842541i	0.999879	−	0.0155863i	$-0.00496148\pi$
$521$	11.1032	+	19.2313i	0.486441	+	0.842541i	−0.513437	+	0.858127i	$0.671628\pi$
$522$	−8.86188	−	1.19232i	−0.387874	−	0.0521865i
$523$	12.1280	+	7.00210i	0.530320	+	0.306181i	0.741147	−	0.671343i	$-0.234282\pi$
$523$	12.1280	+	7.00210i	0.530320	+	0.306181i	−0.210827	+	0.977523i	$0.567616\pi$
$524$	6.28524			0.274572
$525$	34.8228	−	20.6773i	1.51979	−	0.902432i
$526$	1.92542			0.0839525
$527$	−4.42658	−	2.55569i	−0.192825	−	0.111327i
$528$	−0.616432	+	0.919723i	−0.0268268	+	0.0400258i
$529$	−0.419511	−	0.726614i	−0.0182396	−	0.0315919i
$530$	14.3019	−	24.7716i	0.621235	−	1.07601i
$531$	4.95358	−	6.41778i	0.214967	−	0.278508i
$532$	−11.6455	+	8.01355i	−0.504898	+	0.347432i
$533$			11.6843i			0.506102i
$534$	−6.74168	−	0.451496i	−0.291741	−	0.0195381i
$535$	53.6899	−	30.9978i	2.32121	−	1.34015i
$536$	1.99852	−	1.15384i	0.0863228	−	0.0498385i
$537$	16.6502	+	1.11507i	0.718507	+	0.0481190i
$538$		−	18.5946i		−	0.801669i
$539$	−0.705041	−	4.41878i	−0.0303682	−	0.190330i
$540$	3.85172	−	18.9415i	0.165752	−	0.815112i
$541$	4.23557	−	7.33622i	0.182101	−	0.315409i	−0.760495	−	0.649344i	$-0.775043\pi$
$541$	4.23557	−	7.33622i	0.182101	−	0.315409i	0.942596	+	0.333935i	$0.108377\pi$
$542$	−2.93665	−	5.08642i	−0.126140	−	0.218481i
$543$	−10.2834	+	15.3429i	−0.441301	+	0.658427i
$544$	6.30404	+	3.63964i	0.270283	+	0.156048i
$545$	37.4016			1.60211
$546$	−3.99637	−	2.24254i	−0.171029	−	0.0959719i
$547$	−15.3032			−0.654318			−0.327159	−	0.944969i	$-0.606091\pi$
$547$	−15.3032			−0.654318			−0.327159	+	0.944969i	$0.606091\pi$
$548$	12.5020	+	7.21801i	0.534057	+	0.308338i
$549$	−4.62105	+	34.3457i	−0.197221	+	1.46584i
$550$	2.82468	+	4.89248i	0.120445	+	0.208616i
$551$	7.96265	−	13.7917i	0.339220	−	0.587547i
$552$	7.31796	−	3.59590i	0.311473	−	0.153052i
$553$	26.4173	−	2.09427i	1.12338	−	0.0890573i
$554$		−	7.16807i		−	0.304542i
$555$	−4.49464	+	67.1134i	−0.190787	+	2.84880i
$556$	−6.94815	+	4.01152i	−0.294667	+	0.170126i
$557$	−5.44584	+	3.14416i	−0.230748	+	0.133222i	−0.610917	−	0.791695i	$-0.709199\pi$
$557$	−5.44584	+	3.14416i	−0.230748	+	0.133222i	0.380169	+	0.924917i	$0.375866\pi$
$558$	0.800605	+	1.94848i	0.0338923	+	0.0824856i
$559$		−	3.57757i		−	0.151315i
$560$	4.23198	−	8.88559i	0.178834	−	0.375485i
$561$	−3.55438	−	7.23347i	−0.150066	−	0.305397i
$562$	−0.784886	+	1.35946i	−0.0331084	+	0.0573455i
$563$	−9.26195	−	16.0422i	−0.390344	−	0.676096i	0.602150	−	0.798383i	$-0.294311\pi$
$563$	−9.26195	−	16.0422i	−0.390344	−	0.676096i	−0.992495	+	0.122286i	$0.960977\pi$
$564$	10.1720	+	6.81766i	0.428320	+	0.287075i
$565$	−30.7877	−	17.7753i	−1.29525	−	0.747813i
$566$	20.0409			0.842381
$567$	23.3905	+	4.45901i	0.982310	+	0.187261i
$568$	10.9092			0.457739
$569$	13.7196	+	7.92099i	0.575154	+	0.332065i	0.759205	−	0.650852i	$-0.225588\pi$
$569$	13.7196	+	7.92099i	0.575154	+	0.332065i	−0.184051	+	0.982917i	$0.558921\pi$
$570$	28.5964	+	19.1664i	1.19777	+	0.802791i
$571$	11.5912	+	20.0765i	0.485075	+	0.840174i	0.999853	−	0.0171491i	$-0.00545899\pi$
$571$	11.5912	+	20.0765i	0.485075	+	0.840174i	−0.514778	+	0.857324i	$0.672126\pi$
$572$	0.319619	−	0.553597i	0.0133640	−	0.0231471i
$573$	7.44659	+	15.1544i	0.311086	+	0.633086i
$574$	−2.44306	−	30.8170i	−0.101971	−	1.28628i
$575$		−	41.6035i		−	1.73499i
$576$	−1.14017	−	2.77489i	−0.0475070	−	0.115620i
$577$	−18.4472	+	10.6505i	−0.767968	+	0.443386i	−0.832149	−	0.554552i	$-0.812890\pi$
$577$	−18.4472	+	10.6505i	−0.767968	+	0.443386i	0.0641814	+	0.997938i	$0.479556\pi$
$578$	−31.1664	+	17.9939i	−1.29635	+	0.748448i
$579$	−0.338813	+	5.05911i	−0.0140806	+	0.210249i
$580$			11.0874i			0.460381i
$581$	−10.0544	−	14.6113i	−0.417126	−	0.606180i
$582$	5.44191	−	2.67404i	0.225574	−	0.110843i
$583$	−2.45769	+	4.25684i	−0.101787	+	0.176300i
$584$	−4.78522	−	8.28825i	−0.198014	−	0.342970i
$585$	−1.48807	+	11.0600i	−0.0615242	+	0.457276i
$586$	−14.7886	−	8.53822i	−0.610913	−	0.352711i
$587$	33.7288			1.39214			0.696068	−	0.717976i	$-0.254931\pi$
$587$	33.7288			1.39214			0.696068	+	0.717976i	$0.254931\pi$
$588$	11.0092	+	5.07905i	0.454013	+	0.209457i
$589$	−3.75177			−0.154589
$590$	−8.70579	−	5.02629i	−0.358412	−	0.206929i
$591$	2.51358	−	3.75029i	0.103395	−	0.154267i
$592$	5.21987	+	9.04107i	0.214535	+	0.371586i
$593$	17.5003	−	30.3114i	0.718651	−	1.24474i	−0.242884	−	0.970055i	$-0.578093\pi$
$593$	17.5003	−	30.3114i	0.718651	−	1.24474i	0.961534	−	0.274684i	$-0.0885734\pi$
$594$	−0.661892	+	3.25497i	−0.0271577	+	0.133553i
$595$	40.6122	+	59.0189i	1.66494	+	2.41954i
$596$			14.9500i			0.612375i
$597$	19.4490	+	1.30252i	0.795995	+	0.0533084i
$598$	−4.07685	+	2.35377i	−0.166715	+	0.0962529i
$599$	−2.10938	+	1.21785i	−0.0861871	+	0.0497601i	−0.542474	−	0.840072i	$-0.682512\pi$
$599$	−2.10938	+	1.21785i	−0.0861871	+	0.0497601i	0.456287	+	0.889833i	$0.349179\pi$
$600$	−15.2730	−	1.02285i	−0.623518	−	0.0417575i
$601$		−	3.59313i		−	0.146567i	−0.997311	−	0.0732833i	$-0.976652\pi$
$601$		−	3.59313i		−	0.146567i	0.997311	−	0.0732833i	$-0.0233477\pi$
$602$	0.748031	+	9.43574i	0.0304875	+	0.384572i
$603$	4.23009	−	5.48044i	0.172263	−	0.223181i
$604$	−2.84087	+	4.92054i	−0.115593	+	0.200214i
$605$	19.6994	+	34.1204i	0.800895	+	1.38719i
$606$	1.71017	−	2.55159i	0.0694707	−	0.103651i
$607$	−37.0768	−	21.4063i	−1.50490	−	0.868856i	−0.999984	−	0.00568830i	$-0.998189\pi$
$607$	−37.0768	−	21.4063i	−1.50490	−	0.868856i	−0.504918	−	0.863167i	$-0.668477\pi$
$608$	5.34303			0.216688
$609$	−13.6577	+	0.167178i	−0.553438	+	0.00677439i
$610$	42.9712			1.73985
$611$	−6.12272	−	3.53495i	−0.247699	−	0.143009i
$612$	21.6428	+	2.91193i	0.874859	+	0.117708i
$613$	−6.21541	−	10.7654i	−0.251038	−	0.434811i	0.712774	−	0.701394i	$-0.247439\pi$
$613$	−6.21541	−	10.7654i	−0.251038	−	0.434811i	−0.963812	+	0.266583i	$0.914105\pi$
$614$	−1.13773	+	1.97060i	−0.0459149	+	0.0795270i
$615$	−67.5660	+	33.2006i	−2.72452	+	1.33878i
$616$	−0.727237	+	1.52693i	−0.0293012	+	0.0615217i
$617$			38.6142i			1.55455i	0.629161	+	0.777275i	$0.283399\pi$
$617$			38.6142i			1.55455i	−0.629161	+	0.777275i	$0.716601\pi$
$618$	0.957719	−	14.3005i	0.0385251	−	0.575252i
$619$	−6.51713	+	3.76267i	−0.261946	+	0.151234i	−0.625222	−	0.780447i	$-0.714991\pi$
$619$	−6.51713	+	3.76267i	−0.261946	+	0.151234i	0.363276	+	0.931681i	$0.381658\pi$
$620$	2.26209	−	1.30602i	0.0908479	−	0.0524510i
$621$	16.2066	−	18.3219i	0.650348	−	0.735233i
$622$		−	21.7210i		−	0.870935i
$623$	−10.2889	+	0.815665i	−0.412215	+	0.0326789i
$624$	0.763858	+	1.55452i	0.0305788	+	0.0622305i
$625$	−4.45773	+	7.72102i	−0.178309	+	0.308841i
$626$	−8.28769	−	14.3547i	−0.331243	−	0.573729i
$627$	−4.91411	−	3.29361i	−0.196251	−	0.131534i
$628$	−3.76719	−	2.17499i	−0.150327	−	0.0867914i
$629$	−75.9937			−3.03007
$630$	1.61222	−	29.4817i	0.0642324	−	1.17458i
$631$	−28.1181			−1.11936			−0.559682	−	0.828707i	$-0.689077\pi$
$631$	−28.1181			−1.11936			−0.559682	+	0.828707i	$0.689077\pi$
$632$	−8.67422	−	5.00806i	−0.345042	−	0.199210i
$633$	−1.39932	−	0.937876i	−0.0556181	−	0.0372772i
$634$	4.11494	+	7.12729i	0.163425	+	0.283061i
$635$	4.99718	−	8.65537i	0.198307	−	0.343478i
$636$	−5.87362	−	11.9533i	−0.232904	−	0.473980i
$637$	−6.53792	−	2.50111i	−0.259042	−	0.0990976i
$638$		−	1.90530i		−	0.0754316i
$639$	30.2718	−	12.4383i	1.19753	−	0.492051i
$640$	−3.22152	+	1.85995i	−0.127342	+	0.0735209i
$641$	−35.4835	+	20.4864i	−1.40151	+	0.809164i	−0.994548	−	0.104279i	$-0.966746\pi$
$641$	−35.4835	+	20.4864i	−1.40151	+	0.809164i	−0.406965	+	0.913444i	$0.633413\pi$
$642$	1.92888	−	28.8018i	0.0761268	−	1.13672i
$643$			13.7897i			0.543812i	0.962324	+	0.271906i	$0.0876539\pi$
$643$			13.7897i			0.543812i	−0.962324	+	0.271906i	$0.912346\pi$
$644$	10.2605	−	7.06045i	0.404319	−	0.278221i
$645$	20.6878	−	10.1656i	0.814580	−	0.400268i
$646$	−19.4467	+	33.6826i	−0.765119	+	1.32523i
$647$	12.9910	+	22.5010i	0.510728	+	0.884607i	0.999923	+	0.0124324i	$0.00395746\pi$
$647$	12.9910	+	22.5010i	0.510728	+	0.884607i	−0.489195	+	0.872175i	$0.662709\pi$
$648$	−6.32768	−	6.40003i	−0.248575	−	0.251417i
$649$	1.49603	+	0.863734i	0.0587243	+	0.0339045i
$650$	8.83762			0.346640
$651$	1.64289	+	2.76679i	0.0643898	+	0.108439i
$652$	23.3955			0.916240
$653$	−7.09560	−	4.09665i	−0.277672	−	0.160314i	0.354697	−	0.934981i	$-0.384584\pi$
$653$	−7.09560	−	4.09665i	−0.277672	−	0.160314i	−0.632369	+	0.774667i	$0.717917\pi$
$654$	9.69576	−	14.4662i	0.379134	−	0.565672i
$655$	−11.6902	−	20.2481i	−0.456775	−	0.791157i
$656$	−5.84214	+	10.1189i	−0.228097	+	0.395076i
$657$	−22.7285	−	17.5430i	−0.886722	−	0.684419i
$658$	16.8876	+	8.04315i	0.658349	+	0.313555i
$659$			12.0959i			0.471188i	0.971852	+	0.235594i	$0.0757035\pi$
$659$			12.0959i			0.471188i	−0.971852	+	0.235594i	$0.924296\pi$
$660$	4.10944	+	0.275213i	0.159960	+	0.0107126i
$661$	−41.8718	+	24.1747i	−1.62862	+	0.940287i	−0.644121	+	0.764924i	$0.722777\pi$
$661$	−41.8718	+	24.1747i	−1.62862	+	0.940287i	−0.984504	+	0.175363i	$0.943890\pi$
$662$	−19.5795	+	11.3043i	−0.760981	+	0.439352i
$663$	−12.5799	−	0.842486i	−0.488563	−	0.0327194i
$664$			6.70374i			0.260156i
$665$	47.4759	+	22.6116i	1.84104	+	0.876840i
$666$	24.7929	+	19.1365i	0.960705	+	0.741523i
$667$	−7.01560	+	12.1514i	−0.271645	+	0.470503i
$668$	1.21982	+	2.11279i	0.0471962	+	0.0817462i
$669$	−11.3426	+	16.9233i	−0.438531	+	0.654293i
$670$	−7.43427	−	4.29218i	−0.287211	−	0.165821i
$671$	−7.38432			−0.285068
$672$	−2.33969	−	3.94029i	−0.0902555	−	0.152000i
$673$	−37.0135			−1.42677			−0.713383	−	0.700774i	$-0.752838\pi$
$673$	−37.0135			−1.42677			−0.713383	+	0.700774i	$0.752838\pi$
$674$	1.15427	+	0.666420i	0.0444609	+	0.0256695i
$675$	−43.5471	+	14.5755i	−1.67613	+	0.561011i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−3.06663	+	5.31156i	−0.117860	+	0.204140i	−0.918919	−	0.394445i	$-0.870937\pi$
$677$	−3.06663	+	5.31156i	−0.117860	+	0.204140i	0.801059	+	0.598585i	$0.204270\pi$
$678$	−14.8563	+	7.30011i	−0.570554	+	0.280359i
$679$	7.63006	−	5.25041i	0.292815	−	0.201492i
$680$		−	27.0781i		−	1.03840i
$681$	0.800998	−	11.9604i	0.0306943	−	0.458324i
$682$	−0.388726	+	0.224431i	−0.0148851	+	0.00859390i
$683$	−3.42887	+	1.97966i	−0.131202	+	0.0757496i	−0.564164	−	0.825662i	$-0.690802\pi$
$683$	−3.42887	+	1.97966i	−0.131202	+	0.0757496i	0.432962	+	0.901412i	$0.357468\pi$
$684$	14.8263	−	6.09195i	0.566898	−	0.232931i
$685$		−	53.7005i		−	2.05179i
$686$	17.7666	+	5.22961i	0.678331	+	0.199667i
$687$	7.63268	+	15.5332i	0.291205	+	0.592627i
$688$	1.78878	−	3.09826i	0.0681967	−	0.118120i
$689$	3.84471	+	6.65923i	0.146472	+	0.253696i
$690$	−25.1953	−	16.8868i	−0.959168	−	0.642869i
$691$	33.1863	+	19.1601i	1.26247	+	0.728885i	0.973551	−	0.228470i	$-0.0733723\pi$
$691$	33.1863	+	19.1601i	1.26247	+	0.728885i	0.288915	+	0.957355i	$0.406706\pi$
$692$	−2.37184			−0.0901638
$693$	−0.277049	+	5.06623i	−0.0105242	+	0.192450i
$694$	−22.2099			−0.843078
$695$	25.8464	+	14.9224i	0.980410	+	0.566040i
$696$	4.28839	+	2.87423i	0.162551	+	0.108948i
$697$	−42.5265	−	73.6581i	−1.61081	−	2.79000i
$698$	−8.70906	+	15.0845i	−0.329643	+	0.570958i
$699$	1.51134	+	3.07571i	0.0571642	+	0.116334i
$700$	−23.3090	+	1.84785i	−0.880998	+	0.0698423i
$701$			13.5430i			0.511511i	0.966741	+	0.255756i	$0.0823243\pi$
$701$			13.5430i			0.511511i	−0.966741	+	0.255756i	$0.917676\pi$
$702$	3.89203	+	3.44269i	0.146895	+	0.129936i
$703$	−48.3067	+	27.8899i	−1.82192	+	1.05189i
$704$	0.553597	−	0.319619i	0.0208645	−	0.0120461i
$705$	3.04382	−	45.4499i	0.114637	−	1.71174i
$706$		−	28.9209i		−	1.08845i
$707$	2.01757	−	4.23616i	0.0758787	−	0.159317i
$708$	−4.20090	+	2.06424i	−0.157879	+	0.0775787i
$709$	1.67931	−	2.90864i	0.0630677	−	0.109236i	−0.832768	−	0.553623i	$-0.813245\pi$
$709$	1.67931	−	2.90864i	0.0630677	−	0.109236i	0.895835	+	0.444386i	$0.146578\pi$
$710$	−20.2905	−	35.1442i	−0.761488	−	1.31894i
$711$	−29.7801	−	4.00676i	−1.11684	−	0.150265i
$712$	3.37839	+	1.95052i	0.126611	+	0.0730987i
$713$	3.30555			0.123794
$714$	33.3553	−	0.408288i	1.24829	−	0.0152798i
$715$	−2.37790			−0.0889285
$716$	−8.34373	−	4.81725i	−0.311820	−	0.180029i
$717$	−10.3251	+	15.4052i	−0.385600	+	0.575319i
$718$	−2.03087	−	3.51757i	−0.0757914	−	0.131275i
$719$	5.76707	−	9.98887i	0.215076	−	0.372522i	−0.738220	−	0.674560i	$-0.764334\pi$
$719$	5.76707	−	9.98887i	0.215076	−	0.372522i	0.953296	+	0.302038i	$0.0976669\pi$
$720$	−6.81872	+	8.83423i	−0.254119	+	0.329232i
$721$	−1.73020	−	21.8249i	−0.0644360	−	0.812802i
$722$			9.54793i			0.355337i
$723$	34.2117	+	2.29118i	1.27235	+	0.0852100i
$724$	9.23515	−	5.33192i	0.343222	−	0.198159i
$725$	22.8122	−	13.1706i	0.847223	−	0.489144i
$726$	18.3038	+	1.22582i	0.679318	+	0.0454944i
$727$			22.1982i			0.823284i	0.911346	+	0.411642i	$0.135045\pi$
$727$			22.1982i			0.823284i	−0.911346	+	0.411642i	$0.864955\pi$
$728$	1.49982	+	2.17958i	0.0555868	+	0.0807805i
$729$	−24.8557	−	10.5448i	−0.920583	−	0.390547i
$730$	−17.8005	+	30.8314i	−0.658827	+	1.14112i
$731$	13.0210	+	22.5531i	0.481601	+	0.834157i
$732$	11.1396	−	16.6204i	0.411731	−	0.614307i
$733$	17.0396	+	9.83784i	0.629373	+	0.363369i	0.780509	−	0.625144i	$-0.214960\pi$
$733$	17.0396	+	9.83784i	0.629373	+	0.363369i	−0.151136	+	0.988513i	$0.548293\pi$
$734$	9.26062			0.341816
$735$	−4.11432	−	44.9133i	−0.151759	−	1.65665i
$736$	−4.70754			−0.173522
$737$	1.27753	+	0.737582i	0.0470584	+	0.0271692i
$738$	−4.67407	+	34.7398i	−0.172055	+	1.27879i
$739$	−4.31359	−	7.47135i	−0.158678	−	0.274838i	0.775714	−	0.631084i	$-0.217390\pi$
$739$	−4.31359	−	7.47135i	−0.158678	−	0.274838i	−0.934392	+	0.356246i	$0.884056\pi$
$740$	19.4174	−	33.6319i	0.713796	−	1.23633i
$741$	−8.30582	+	4.08131i	−0.305122	+	0.149931i
$742$	−11.5327	−	16.7597i	−0.423379	−	0.615267i
$743$		−	11.8689i		−	0.435428i	−0.976013	−	0.217714i	$-0.930140\pi$
$743$		−	11.8689i		−	0.435428i	0.976013	−	0.217714i	$-0.0698601\pi$
$744$	0.0812688	−	1.21350i	0.00297946	−	0.0444889i
$745$	48.1617	−	27.8062i	1.76451	−	1.01874i
$746$	−5.31539	+	3.06884i	−0.194610	+	0.112358i
$747$	7.64339	+	18.6021i	0.279657	+	0.680617i
$748$			4.65320i			0.170138i
$749$	−3.48468	−	43.9561i	−0.127327	−	1.60612i
$750$	10.9045	+	22.1916i	0.398176	+	0.810322i
$751$	22.4815	−	38.9390i	0.820360	−	1.42091i	−0.0850545	−	0.996376i	$-0.527106\pi$
$751$	22.4815	−	38.9390i	0.820360	−	1.42091i	0.905414	−	0.424529i	$-0.139560\pi$
$752$	−3.53495	−	6.12272i	−0.128906	−	0.223272i
$753$	−39.1495	−	26.2394i	−1.42669	−	0.956217i
$754$	−2.58126	−	1.49029i	−0.0940038	−	0.0542731i
$755$	21.1355			0.769200
$756$	−10.9850	−	8.26622i	−0.399520	−	0.300639i
$757$	23.3891			0.850093			0.425046	−	0.905172i	$-0.360258\pi$
$757$	23.3891			0.850093			0.425046	+	0.905172i	$0.360258\pi$
$758$	13.7866	+	7.95971i	0.500752	+	0.289110i
$759$	4.32964	+	2.90188i	0.157156	+	0.105332i
$760$	−9.93775	−	17.2127i	−0.360480	−	0.624370i
$761$	23.3116	−	40.3768i	0.845044	−	1.46366i	−0.0405392	−	0.999178i	$-0.512908\pi$
$761$	23.3116	−	40.3768i	0.845044	−	1.46366i	0.885583	−	0.464481i	$-0.153759\pi$
$762$	−2.05228	−	4.17657i	−0.0743463	−	0.151301i
$763$	11.4386	−	24.0168i	0.414105	−	0.869467i
$764$		−	9.74865i		−	0.352694i
$765$	−30.8736	−	75.1389i	−1.11624	−	2.71665i
$766$	−23.8462	+	13.7676i	−0.861597	+	0.497443i
$767$	2.34033	−	1.35119i	0.0845045	−	0.0487887i
$768$	−0.115738	+	1.72818i	−0.00417632	+	0.0623603i
$769$			29.3721i			1.05918i	0.848252	+	0.529592i	$0.177655\pi$
$769$			29.3721i			1.05918i	−0.848252	+	0.529592i	$0.822345\pi$
$770$	6.27166	−	0.497194i	0.226015	−	0.0179176i
$771$	35.3661	−	17.3782i	1.27368	−	0.625860i
$772$	1.46371	−	2.53522i	0.0526801	−	0.0912446i
$773$	−27.2086	−	47.1267i	−0.978626	−	1.69503i	−0.667411	−	0.744690i	$-0.732597\pi$
$773$	−27.2086	−	47.1267i	−0.978626	−	1.69503i	−0.311215	−	0.950340i	$-0.600736\pi$
$774$	1.43114	−	10.6369i	0.0514411	−	0.382334i
$775$	−5.37422	−	3.10281i	−0.193048	−	0.111456i
$776$	−3.50071			−0.125668
$777$	41.7211	+	23.4115i	1.49674	+	0.839884i
$778$	−18.6746			−0.669518
$779$	−54.0655	−	31.2147i	−1.93710	−	1.11838i
$780$	3.58718	−	5.35211i	0.128441	−	0.191636i
$781$	3.48678	+	6.03929i	0.124767	+	0.216103i
$782$	17.1338	−	29.6765i	0.612702	−	1.06123i
$783$	15.1769	+	3.08620i	0.542379	+	0.110292i
$784$	−4.41145	−	5.43499i	−0.157552	−	0.194107i
$785$			16.1814i			0.577540i
$786$	−10.8620	−	0.727439i	−0.387436	−	0.0259469i
$787$	−1.22692	+	0.708362i	−0.0437349	+	0.0252504i	−0.521708	−	0.853124i	$-0.674705\pi$
$787$	−1.22692	+	0.708362i	−0.0437349	+	0.0252504i	0.477973	+	0.878374i	$0.341372\pi$
$788$	−2.25737	+	1.30329i	−0.0804153	+	0.0464278i
$789$	−3.32748	−	0.222844i	−0.118461	−	0.00793345i
$790$			37.2590i			1.32561i
$791$	−20.8300	+	14.3336i	−0.740628	+	0.509643i
$792$	1.17175	−	1.51810i	0.0416364	−	0.0539434i
$793$	−5.77587	+	10.0041i	−0.205107	+	0.355256i
$794$	−1.49527	−	2.58988i	−0.0530650	−	0.0919113i
$795$	−27.5833	+	41.1546i	−0.978278	+	1.45960i
$796$	−9.74629	−	5.62702i	−0.345448	−	0.199445i
$797$	−22.8484			−0.809331			−0.404665	−	0.914465i	$-0.632612\pi$
$797$	−22.8484			−0.809331			−0.404665	+	0.914465i	$0.632612\pi$
$798$	21.0530	−	12.5010i	0.745270	−	0.442532i
$799$	51.4638			1.82066
$800$	7.65361	+	4.41881i	0.270596	+	0.156229i
$801$	11.5986	+	1.56053i	0.409816	+	0.0551387i
$802$	−5.01418	−	8.68481i	−0.177057	−	0.306671i
$803$	3.05890	−	5.29817i	0.107946	−	0.186968i
$804$	−3.58734	+	1.76275i	−0.126516	+	0.0621673i
$805$	−41.8293	−	19.9222i	−1.47429	−	0.702167i
$806$			0.702181i			0.0247333i
$807$	−2.15209	+	32.1348i	−0.0757572	+	1.13120i
$808$	−1.53584	+	0.886720i	−0.0540308	+	0.0311947i
$809$	−16.9162	+	9.76655i	−0.594740	+	0.343374i	−0.766970	−	0.641683i	$-0.778236\pi$
$809$	−16.9162	+	9.76655i	−0.594740	+	0.343374i	0.172229	+	0.985057i	$0.444903\pi$
$810$	−8.84870	+	32.2885i	−0.310912	+	1.13450i
$811$			44.6035i			1.56624i	0.621870	+	0.783120i	$0.286373\pi$
$811$			44.6035i			1.56624i	−0.621870	+	0.783120i	$0.713627\pi$
$812$	7.11960	+	3.39089i	0.249849	+	0.118997i
$813$	4.48637	+	9.13014i	0.157344	+	0.320208i
$814$	−3.33674	+	5.77941i	−0.116953	+	0.202568i
$815$	−43.5145	−	75.3693i	−1.52425	−	2.64007i
$816$	−10.4733	−	7.01956i	−0.366638	−	0.245734i
$817$	16.5541	+	9.55751i	0.579155	+	0.334375i
$818$	32.4173			1.13344
$819$	6.64691	+	4.33805i	0.232262	+	0.151584i
$820$	43.4643			1.51784
$821$	30.6156	+	17.6759i	1.06849	+	0.616894i	0.927769	−	0.373155i	$-0.121724\pi$
$821$	30.6156	+	17.6759i	1.06849	+	0.616894i	0.140723	+	0.990049i	$0.455057\pi$
$822$	−20.7702	−	13.9210i	−0.724446	−	0.485550i
$823$	−28.0658	−	48.6113i	−0.978311	−	1.69448i	−0.668544	−	0.743672i	$-0.733082\pi$
$823$	−28.0658	−	48.6113i	−0.978311	−	1.69448i	−0.309767	−	0.950813i	$-0.600251\pi$
$824$	−4.13746	+	7.16629i	−0.144135	+	0.249649i
$825$	−4.31530	−	8.78201i	−0.150240	−	0.305750i
$826$	−5.89005	+	4.05307i	−0.204941	+	0.141024i
$827$		−	5.37342i		−	0.186852i	−0.995626	−	0.0934261i	$-0.970218\pi$
$827$		−	5.37342i		−	0.186852i	0.995626	−	0.0934261i	$-0.0297819\pi$
$828$	−13.0629	+	5.36739i	−0.453968	+	0.186530i
$829$	22.5316	−	13.0086i	0.782554	−	0.451808i	−0.0547805	−	0.998498i	$-0.517446\pi$
$829$	22.5316	−	13.0086i	0.782554	−	0.451808i	0.837335	+	0.546691i	$0.184113\pi$
$830$	21.5963	−	12.4686i	0.749617	−	0.432792i
$831$	−0.829615	+	12.3877i	−0.0287790	+	0.429725i
$832$		−	1.00000i		−	0.0346688i
$833$	50.3184	−	8.02858i	1.74343	−	0.278174i
$834$	12.4719	−	6.12846i	0.431868	−	0.212211i
$835$	4.53760	−	7.85935i	0.157030	−	0.271984i
$836$	1.70774	+	2.95788i	0.0590633	+	0.102301i
$837$	−1.15808	−	3.45998i	−0.0400290	−	0.119594i
$838$	−30.3692	−	17.5337i	−1.04909	−	0.605691i
$839$	33.1916			1.14590			0.572950	−	0.819590i	$-0.305799\pi$
$839$	33.1916			1.14590			0.572950	+	0.819590i	$0.305799\pi$
$840$	−8.34202	+	14.8661i	−0.287827	+	0.512929i
$841$	20.1162			0.693661
$842$	10.4350	+	6.02468i	0.359615	+	0.207624i
$843$	1.51377	−	2.25855i	0.0521368	−	0.0777888i
$844$	0.486288	+	0.842276i	0.0167387	+	0.0289923i
$845$	−1.85995	+	3.22152i	−0.0639841	+	0.110824i
$846$	−16.7900	−	12.9594i	−0.577253	−	0.445554i
$847$	27.9345	−	2.21455i	0.959841	−	0.0760927i
$848$			7.68941i			0.264056i
$849$	−34.6342	−	2.31948i	−1.18864	−	0.0796044i
$850$	−55.7127	+	32.1657i	−1.91093	+	1.10328i
$851$	42.5613	−	24.5728i	1.45898	−	0.842343i
$852$	−18.8530	−	1.26260i	−0.645893	−	0.0432560i
$853$			45.1819i			1.54700i	0.633797	+	0.773499i	$0.281495\pi$
$853$			45.1819i			1.54700i	−0.633797	+	0.773499i	$0.718505\pi$
$854$	13.1420	−	27.5932i	0.449709	−	0.944221i
$855$	−47.2015	−	36.4326i	−1.61426	−	1.24597i
$856$	−8.33299	+	14.4332i	−0.284816	+	0.493315i
$857$	16.9269	+	29.3183i	0.578212	+	1.00149i	0.995684	+	0.0928029i	$0.0295827\pi$
$857$	16.9269	+	29.3183i	0.578212	+	1.00149i	−0.417473	+	0.908690i	$0.637084\pi$
$858$	−0.616432	+	0.919723i	−0.0210446	+	0.0313988i
$859$	48.6477	+	28.0868i	1.65984	+	0.958309i	0.972787	+	0.231700i	$0.0744288\pi$
$859$	48.6477	+	28.0868i	1.65984	+	0.958309i	0.687052	+	0.726608i	$0.258905\pi$
$860$	−13.3082			−0.453805
$861$	0.655361	+	53.5401i	0.0223346	+	1.82464i
$862$	14.0027			0.476933
$863$	−13.2859	−	7.67064i	−0.452258	−	0.261111i	0.256525	−	0.966538i	$-0.417422\pi$
$863$	−13.2859	−	7.67064i	−0.452258	−	0.261111i	−0.708784	+	0.705426i	$0.750756\pi$
$864$	1.64926	+	4.92747i	0.0561088	+	0.167636i
$865$	4.41150	+	7.64093i	0.149995	+	0.259800i
$866$	−11.8632	+	20.5477i	−0.403129	+	0.698240i
$867$	55.9437	−	27.4896i	1.89995	−	0.933596i
$868$	−0.146819	−	1.85199i	−0.00498335	−	0.0628605i
$869$		−	6.40270i		−	0.217197i
$870$	1.28323	−	19.1611i	0.0435057	−	0.649622i
$871$	1.99852	−	1.15384i	0.0677172	−	0.0390965i
$872$	−8.70744	+	5.02724i	−0.294871	+	0.170244i
$873$	−9.71408	+	3.99139i	−0.328772	+	0.135088i
$874$		−	25.1525i		−	0.850797i
$875$	21.4107	+	31.1147i	0.723814	+	1.05187i
$876$	7.31046	+	14.8774i	0.246998	+	0.502661i
$877$	27.0824	−	46.9081i	0.914508	−	1.58397i	0.106888	−	0.994271i	$-0.465912\pi$
$877$	27.0824	−	46.9081i	0.914508	−	1.58397i	0.807620	−	0.589703i	$-0.200755\pi$
$878$	−13.7437	−	23.8048i	−0.463827	−	0.803372i
$879$	24.5692	+	16.4672i	0.828699	+	0.555424i
$880$	−2.05932	−	1.18895i	−0.0694198	−	0.0400795i
$881$	−33.5277			−1.12958			−0.564788	−	0.825236i	$-0.691042\pi$
$881$	−33.5277			−1.12958			−0.564788	+	0.825236i	$0.691042\pi$
$882$	−18.4381	−	10.0517i	−0.620843	−	0.338458i
$883$	18.1979			0.612407			0.306203	−	0.951966i	$-0.400941\pi$
$883$	18.1979			0.612407			0.306203	+	0.951966i	$0.400941\pi$
$884$	6.30404	+	3.63964i	0.212028	+	0.122414i
$885$	14.4634	+	9.69392i	0.486183	+	0.325857i
$886$	11.3770	+	19.7056i	0.382219	+	0.662023i
$887$	3.80995	−	6.59903i	0.127926	−	0.221574i	−0.794947	−	0.606679i	$-0.792501\pi$
$887$	3.80995	−	6.59903i	0.127926	−	0.221574i	0.922873	+	0.385105i	$0.125835\pi$
$888$	−7.97447	−	16.2287i	−0.267606	−	0.544601i
$889$	−4.02960	−	5.85594i	−0.135148	−	0.196402i
$890$		−	14.5114i		−	0.486424i
$891$	1.52059	−	5.54856i	0.0509417	−	0.185884i
$892$	10.1864	−	5.88114i	0.341067	−	0.196915i
$893$	32.7138	−	18.8873i	1.09473	−	0.632041i
$894$	1.73027	−	25.8362i	0.0578690	−	0.864093i
$895$			35.8394i			1.19798i
$896$	0.209090	+	2.63748i	0.00698519	+	0.0881119i
$897$	7.31796	−	3.59590i	0.244339	−	0.120063i
$898$	6.11710	−	10.5951i	0.204130	−	0.353564i
$899$	1.04645	+	1.81251i	0.0349012	+	0.0604506i
$900$	26.2761	+	3.53532i	0.875870	+	0.117844i
$901$	−48.4743	−	27.9867i	−1.61491	−	0.932371i
$902$	−7.46905			−0.248692
$903$	−0.200662	−	16.3932i	−0.00667763	−	0.545533i
$904$	9.55689			0.317857
$905$	−34.3538	−	19.8342i	−1.14196	−	0.659310i
$906$	5.47903	−	8.17477i	0.182029	−	0.271589i
$907$	−14.0093	−	24.2648i	−0.465171	−	0.805700i	0.534038	−	0.845460i	$-0.320674\pi$
$907$	−14.0093	−	24.2648i	−0.465171	−	0.805700i	−0.999209	+	0.0397603i	$0.987341\pi$
$908$	−3.46041	+	5.99360i	−0.114838	+	0.198905i
$909$	−3.25079	+	4.21167i	−0.107822	+	0.139692i
$910$	4.23198	−	8.88559i	0.140289	−	0.294554i
$911$		−	10.0668i		−	0.333529i	−0.985997	−	0.166765i	$-0.946668\pi$
$911$		−	10.0668i		−	0.333529i	0.985997	−	0.166765i	$-0.0533320\pi$
$912$	−9.23371	−	0.618389i	−0.305759	−	0.0204769i
$913$	−3.71117	+	2.14265i	−0.122822	+	0.0709112i
$914$	−16.3187	+	9.42161i	−0.539775	+	0.311639i
$915$	−74.2620	−	4.97339i	−2.45503	−	0.164415i
$916$		−	9.99228i		−	0.330154i
$917$	−16.5772	+	1.31418i	−0.547427	+	0.0433980i
$918$	−37.0656	−	7.53723i	−1.22335	−	0.248766i
$919$	2.87061	−	4.97204i	0.0946926	−	0.164012i	−0.814788	−	0.579759i	$-0.803147\pi$
$919$	2.87061	−	4.97204i	0.0946926	−	0.164012i	0.909480	+	0.415747i	$0.136480\pi$
$920$	8.75579	+	15.1655i	0.288670	+	0.499991i
$921$	2.19427	−	3.27388i	0.0723037	−	0.107878i
$922$	16.2575	+	9.38627i	0.535412	+	0.309120i
$923$	10.9092			0.359080
$924$	1.43352	−	2.55464i	0.0471593	−	0.0840414i
$925$	−92.2624			−3.03357
$926$	18.9188	+	10.9228i	0.621710	+	0.358944i
$927$	−3.31022	+	24.6031i	−0.108722	+	0.808071i
$928$	−1.49029	−	2.58126i	−0.0489211	−	0.0847339i
$929$	19.1734	−	33.2093i	0.629058	−	1.08956i	−0.358683	−	0.933460i	$-0.616774\pi$
$929$	19.1734	−	33.2093i	0.629058	−	1.08956i	0.987741	−	0.156101i	$-0.0498926\pi$
$930$	−4.06046	+	1.99523i	−0.133148	+	0.0654261i
$931$	29.0393	−	23.5705i	0.951724	−	0.772492i
$932$		−	1.97856i		−	0.0648100i
$933$	−2.51394	+	37.5379i	−0.0823027	+	1.22893i
$934$	23.6028	−	13.6271i	0.772307	−	0.445891i
$935$	14.9904	−	8.65470i	0.490238	−	0.283039i
$936$	−1.14017	−	2.77489i	−0.0372676	−	0.0907001i
$937$		−	5.20813i		−	0.170142i	−0.996375	−	0.0850711i	$-0.972888\pi$
$937$		−	5.20813i		−	0.170142i	0.996375	−	0.0850711i	$-0.0271117\pi$
$938$	−5.02978	+	3.46111i	−0.164228	+	0.113009i
$939$	12.6612	+	25.7667i	0.413184	+	0.840865i
$940$	−13.1496	+	22.7759i	−0.428894	+	0.742867i
$941$	16.0739	+	27.8409i	0.523995	+	0.907586i	0.999610	+	0.0279326i	$0.00889238\pi$
$941$	16.0739	+	27.8409i	0.523995	+	0.907586i	−0.475615	+	0.879654i	$0.657774\pi$
$942$	6.25864	+	4.19477i	0.203918	+	0.136673i
$943$	47.6351	+	27.5021i	1.55121	+	0.895593i
$944$	2.70238			0.0879550
$945$	−6.19835	+	50.7631i	−0.201632	+	1.65132i
$946$	2.28692			0.0743542
$947$	23.4484	+	13.5380i	0.761971	+	0.439924i	0.830003	−	0.557759i	$-0.188339\pi$
$947$	23.4484	+	13.5380i	0.761971	+	0.439924i	−0.0680317	+	0.997683i	$0.521672\pi$
$948$	14.4110	+	9.65877i	0.468047	+	0.313702i
$949$	−4.78522	−	8.28825i	−0.155335	−	0.269048i
$950$	−23.6098	+	40.8934i	−0.766004	+	1.32676i
$951$	−6.28646	−	12.7935i	−0.203852	−	0.414857i
$952$	−17.3878	−	8.28135i	−0.563540	−	0.268400i
$953$			8.80705i			0.285288i	0.989774	+	0.142644i	$0.0455604\pi$
$953$			8.80705i			0.285288i	−0.989774	+	0.142644i	$0.954440\pi$
$954$	8.76722	+	21.3373i	0.283849	+	0.690820i
$955$	−31.4055	+	18.1320i	−1.01626	+	0.586737i
$956$	9.27267	−	5.35358i	0.299900	−	0.173147i
$957$	−0.220515	+	3.29270i	−0.00712824	+	0.106438i
$958$			8.15791i			0.263570i
$959$	−34.4828	−	16.4233i	−1.11351	−	0.530336i
$960$	5.78264	−	2.84147i	0.186634	−	0.0917081i
$961$	−15.2535	+	26.4198i	−0.492047	+	0.852251i
$962$	5.21987	+	9.04107i	0.168295	+	0.291496i
$963$	−6.66690	+	49.5514i	−0.214838	+	1.59677i
$964$	−17.1442	−	9.89818i	−0.552176	−	0.318799i
$965$	−10.8897			−0.350552
$966$	−18.5491	+	11.0142i	−0.596807	+	0.354376i
$967$	48.3827			1.55588			0.777942	−	0.628336i	$-0.216264\pi$
$967$	48.3827			1.55588			0.777942	+	0.628336i	$0.216264\pi$
$968$	−9.17240	−	5.29569i	−0.294812	−	0.170210i
$969$	37.5057	−	55.9589i	1.20486	−	1.79766i
$970$	6.51113	+	11.2776i	0.209060	+	0.362102i
$971$	0.914961	−	1.58476i	0.0293625	−	0.0508574i	−0.850971	−	0.525213i	$-0.823986\pi$
$971$	0.914961	−	1.58476i	0.0293625	−	0.0508574i	0.880333	+	0.474356i	$0.157319\pi$
$972$	10.1946	+	11.7928i	0.326993	+	0.378253i
$973$	17.4868	−	12.0331i	0.560602	−	0.385763i
$974$			31.5708i			1.01159i
$975$	−15.2730	−	1.02285i	−0.489127	−	0.0327573i
$976$	−10.0041	+	5.77587i	−0.320223	+	0.184881i
$977$	27.4543	−	15.8507i	0.878341	−	0.507110i	0.00822977	−	0.999966i	$-0.497380\pi$
$977$	27.4543	−	15.8507i	0.878341	−	0.507110i	0.870111	+	0.492856i	$0.164047\pi$
$978$	−40.4317	−	2.70774i	−1.29286	−	0.0865840i
$979$			2.49369i			0.0796987i
$980$	−9.30387	+	24.3204i	−0.297201	+	0.776887i
$981$	−18.4303	+	23.8780i	−0.588434	+	0.762366i
$982$	5.22326	−	9.04695i	0.166681	−	0.288700i
$983$	−1.09220	−	1.89174i	−0.0348357	−	0.0603372i	0.848082	−	0.529865i	$-0.177757\pi$
$983$	−1.09220	−	1.89174i	−0.0348357	−	0.0603372i	−0.882918	+	0.469528i	$0.844424\pi$
$984$	11.2674	−	16.8111i	0.359192	−	0.535918i
$985$	8.39717	+	4.84811i	0.267556	+	0.154474i
$986$	21.6964			0.690955
$987$	−28.2540	−	15.8546i	−0.899334	−	0.504656i
$988$	5.34303			0.169984
$989$	−14.5852	−	8.42077i	−0.463783	−	0.267765i
$990$	−7.07000	−	0.951234i	−0.224699	−	0.0302322i
$991$	3.92400	+	6.79656i	0.124650	+	0.215900i	0.921596	−	0.388150i	$-0.126886\pi$
$991$	3.92400	+	6.79656i	0.124650	+	0.215900i	−0.796946	+	0.604050i	$0.793553\pi$
$992$	−0.351091	+	0.608107i	−0.0111471	+	0.0193074i
$993$	35.1453	−	17.2697i	1.11530	−	0.548037i
$994$	−28.7727	+	2.28099i	−0.912614	+	0.0723487i
$995$			41.8639i			1.32717i
$996$	0.775875	−	11.5853i	0.0245845	−	0.367093i
$997$	42.0066	−	24.2525i	1.33036	−	0.768085i	0.345008	−	0.938600i	$-0.387876\pi$
$997$	42.0066	−	24.2525i	1.33036	−	0.768085i	0.985355	+	0.170514i	$0.0545429\pi$
$998$	−15.6183	+	9.01724i	−0.494389	+	0.285436i
$999$	−40.6318	−	35.9407i	−1.28553	−	1.13711i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.z.b.131.9	yes	32
3.2	odd	2		546.2.z.a.131.5	✓	32
7.3	odd	6		546.2.z.a.521.5	yes	32
21.17	even	6	inner	546.2.z.b.521.9	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.z.a.131.5	✓	32	3.2	odd	2
546.2.z.a.521.5	yes	32	7.3	odd	6
546.2.z.b.131.9	yes	32	1.1	even	1	trivial
546.2.z.b.521.9	yes	32	21.17	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.z (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.43878 - 0.964322i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.85995 - 3.22152i) q^{5} +(-0.763858 - 1.55452i) q^{6} +(-1.49982 - 2.17958i) q^{7} +1.00000i q^{8} +(1.14017 + 2.77489i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(-1.43878 - 0.964322i) q^{3} +(0.500000 + 0.866025i) q^{4} +(1.85995 - 3.22152i) q^{5} +(-0.763858 - 1.55452i) q^{6} +(-1.49982 - 2.17958i) q^{7} +1.00000i q^{8} +(1.14017 + 2.77489i) q^{9} +(3.22152 - 1.85995i) q^{10} +(-0.553597 + 0.319619i) q^{11} +(0.115738 - 1.72818i) q^{12} +1.00000i q^{13} +(-0.209090 - 2.63748i) q^{14} +(-5.78264 + 2.84147i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-3.63964 - 6.30404i) q^{17} +(-0.400031 + 2.97321i) q^{18} +(-4.62720 - 2.67151i) q^{19} +3.71990 q^{20} +(0.0560891 + 4.58223i) q^{21} -0.639239 q^{22} +(4.07685 + 2.35377i) q^{23} +(0.964322 - 1.43878i) q^{24} +(-4.41881 - 7.65361i) q^{25} +(-0.500000 + 0.866025i) q^{26} +(1.03544 - 5.09194i) q^{27} +(1.13766 - 2.38867i) q^{28} +2.98058i q^{29} +(-6.42865 - 0.430532i) q^{30} +(0.608107 - 0.351091i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(1.10472 + 0.0739840i) q^{33} -7.27927i q^{34} +(-9.81114 + 0.777791i) q^{35} +(-1.83304 + 2.37486i) q^{36} +(5.21987 - 9.04107i) q^{37} +(-2.67151 - 4.62720i) q^{38} +(0.964322 - 1.43878i) q^{39} +(3.22152 + 1.85995i) q^{40} +11.6843 q^{41} +(-2.24254 + 3.99637i) q^{42} -3.57757 q^{43} +(-0.553597 - 0.319619i) q^{44} +(11.0600 + 1.48807i) q^{45} +(2.35377 + 4.07685i) q^{46} +(-3.53495 + 6.12272i) q^{47} +(1.55452 - 0.763858i) q^{48} +(-2.50111 + 6.53792i) q^{49} -8.83762i q^{50} +(-0.842486 + 12.5799i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(6.65923 - 3.84471i) q^{53} +(3.44269 - 3.89203i) q^{54} +2.37790i q^{55} +(2.17958 - 1.49982i) q^{56} +(4.08131 + 8.30582i) q^{57} +(-1.49029 + 2.58126i) q^{58} +(-1.35119 - 2.34033i) q^{59} +(-5.35211 - 3.58718i) q^{60} +(10.0041 + 5.77587i) q^{61} +0.702181 q^{62} +(4.33805 - 6.64691i) q^{63} -1.00000 q^{64} +(3.22152 + 1.85995i) q^{65} +(0.919723 + 0.616432i) q^{66} +(-1.15384 - 1.99852i) q^{67} +(3.63964 - 6.30404i) q^{68} +(-3.59590 - 7.31796i) q^{69} +(-8.88559 - 4.23198i) q^{70} -10.9092i q^{71} +(-2.77489 + 1.14017i) q^{72} +(-8.28825 + 4.78522i) q^{73} +(9.04107 - 5.21987i) q^{74} +(-1.02285 + 15.2730i) q^{75} -5.34303i q^{76} +(1.52693 + 0.727237i) q^{77} +(1.55452 - 0.763858i) q^{78} +(-5.00806 + 8.67422i) q^{79} +(1.85995 + 3.22152i) q^{80} +(-6.40003 + 6.32768i) q^{81} +(10.1189 + 5.84214i) q^{82} +6.70374 q^{83} +(-3.94029 + 2.33969i) q^{84} -27.0781 q^{85} +(-3.09826 - 1.78878i) q^{86} +(2.87423 - 4.28839i) q^{87} +(-0.319619 - 0.553597i) q^{88} +(1.95052 - 3.37839i) q^{89} +(8.83423 + 6.81872i) q^{90} +(2.17958 - 1.49982i) q^{91} +4.70754i q^{92} +(-1.21350 - 0.0812688i) q^{93} +(-6.12272 + 3.53495i) q^{94} +(-17.2127 + 9.93775i) q^{95} +(1.72818 + 0.115738i) q^{96} +3.50071i q^{97} +(-5.43499 + 4.41145i) q^{98} +(-1.51810 - 1.17175i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9}+O(q^{10}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9	\( 32 q + 16 q^{4} + 2 q^{7} + 2 q^{9} + 6 q^{10} + 24 q^{11} - 4 q^{14} - 12 q^{15} - 16 q^{16} - 4 q^{17} - 24 q^{18} + 4 q^{21} - 12 q^{22} - 6 q^{24} - 18 q^{25} - 16 q^{26} + 6 q^{27} - 2 q^{28} - 8 q^{30} - 6 q^{31} + 14 q^{33} - 48 q^{35} + 4 q^{36} - 16 q^{38} - 6 q^{39} + 6 q^{40} - 16 q^{41} + 14 q^{42} + 32 q^{43} + 24 q^{44} + 20 q^{45} + 16 q^{46} - 20 q^{47} - 26 q^{49} - 46 q^{51} + 60 q^{53} + 6 q^{54} - 8 q^{56} - 8 q^{57} - 10 q^{58} - 8 q^{59} - 6 q^{60} + 36 q^{61} - 36 q^{62} + 84 q^{63} - 32 q^{64} + 6 q^{65} + 36 q^{66} + 4 q^{68} + 36 q^{69} - 18 q^{70} - 24 q^{72} - 48 q^{73} + 84 q^{74} - 2 q^{75} - 52 q^{77} + 18 q^{79} - 74 q^{81} - 24 q^{83} + 8 q^{84} - 32 q^{85} + 24 q^{86} + 14 q^{87} - 6 q^{88} + 20 q^{89} + 6 q^{90} - 8 q^{91} - 40 q^{93} + 72 q^{95} - 6 q^{96} - 32 q^{98}+O(q^{100}) \) 32 * q + 16 * q^4 + 2 * q^7 + 2 * q^9 + 6 * q^10 + 24 * q^11 - 4 * q^14 - 12 * q^15 - 16 * q^16 - 4 * q^17 - 24 * q^18 + 4 * q^21 - 12 * q^22 - 6 * q^24 - 18 * q^25 - 16 * q^26 + 6 * q^27 - 2 * q^28 - 8 * q^30 - 6 * q^31 + 14 * q^33 - 48 * q^35 + 4 * q^36 - 16 * q^38 - 6 * q^39 + 6 * q^40 - 16 * q^41 + 14 * q^42 + 32 * q^43 + 24 * q^44 + 20 * q^45 + 16 * q^46 - 20 * q^47 - 26 * q^49 - 46 * q^51 + 60 * q^53 + 6 * q^54 - 8 * q^56 - 8 * q^57 - 10 * q^58 - 8 * q^59 - 6 * q^60 + 36 * q^61 - 36 * q^62 + 84 * q^63 - 32 * q^64 + 6 * q^65 + 36 * q^66 + 4 * q^68 + 36 * q^69 - 18 * q^70 - 24 * q^72 - 48 * q^73 + 84 * q^74 - 2 * q^75 - 52 * q^77 + 18 * q^79 - 74 * q^81 - 24 * q^83 + 8 * q^84 - 32 * q^85 + 24 * q^86 + 14 * q^87 - 6 * q^88 + 20 * q^89 + 6 * q^90 - 8 * q^91 - 40 * q^93 + 72 * q^95 - 6 * q^96 - 32 * q^98

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