LMFDB - Embedded newform 966.2.k.b.229.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(229,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.229");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.k (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:	$7.71354883526$
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			229.14
Character	$\chi$	$=$	966.229
Dual form			966.2.k.b.367.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.28362 - 2.22329i) q^{5} -1.00000i q^{6} +(1.74878 + 1.98539i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.28362 - 2.22329i) q^{5} -1.00000i q^{6} +(1.74878 + 1.98539i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.28362 - 2.22329i) q^{10} +(3.74890 - 2.16443i) q^{11} +(-0.866025 - 0.500000i) q^{12} +5.81269i q^{13} +(2.59379 - 0.521797i) q^{14} -2.56724i q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.22357 + 2.11928i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.00943 - 5.21248i) q^{19} -2.56724 q^{20} +(2.50718 + 0.845003i) q^{21} -4.32885i q^{22} +(2.46490 - 4.11391i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-0.795352 - 1.37759i) q^{25} +(5.03394 + 2.90635i) q^{26} -1.00000i q^{27} +(0.845003 - 2.50718i) q^{28} -3.89593 q^{29} +(-2.22329 - 1.28362i) q^{30} +(-8.38213 + 4.83943i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.16443 - 3.74890i) q^{33} +2.44713 q^{34} +(6.65886 - 1.33958i) q^{35} -1.00000 q^{36} +(-9.58443 - 5.53357i) q^{37} +(-3.00943 - 5.21248i) q^{38} +(2.90635 + 5.03394i) q^{39} +(-1.28362 + 2.22329i) q^{40} -4.24238i q^{41} +(1.98539 - 1.74878i) q^{42} +9.27845i q^{43} +(-3.74890 - 2.16443i) q^{44} +(-1.28362 - 2.22329i) q^{45} +(-2.33030 - 4.19162i) q^{46} +(0.485292 + 0.280183i) q^{47} +1.00000i q^{48} +(-0.883516 + 6.94402i) q^{49} -1.59070 q^{50} +(2.11928 + 1.22357i) q^{51} +(5.03394 - 2.90635i) q^{52} +(-3.03846 + 1.75425i) q^{53} +(-0.866025 - 0.500000i) q^{54} -11.1132i q^{55} +(-1.74878 - 1.98539i) q^{56} -6.01886i q^{57} +(-1.94796 + 3.37397i) q^{58} +(-9.23060 + 5.32929i) q^{59} +(-2.22329 + 1.28362i) q^{60} +(2.79450 - 4.84021i) q^{61} +9.67885i q^{62} +(2.59379 - 0.521797i) q^{63} +1.00000 q^{64} +(12.9233 + 7.46128i) q^{65} +(-2.16443 - 3.74890i) q^{66} +(7.00382 - 4.04366i) q^{67} +(1.22357 - 2.11928i) q^{68} +(0.0777105 - 4.79520i) q^{69} +(2.16932 - 6.43653i) q^{70} -13.9696 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.37567 - 3.10364i) q^{73} +(-9.58443 + 5.53357i) q^{74} +(-1.37759 - 0.795352i) q^{75} -6.01886 q^{76} +(10.8532 + 3.65789i) q^{77} +5.81269 q^{78} +(-3.37662 - 1.94949i) q^{79} +(1.28362 + 2.22329i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.67401 - 2.12119i) q^{82} -0.193800 q^{83} +(-0.521797 - 2.59379i) q^{84} +6.28236 q^{85} +(8.03537 + 4.63923i) q^{86} +(-3.37397 + 1.94796i) q^{87} +(-3.74890 + 2.16443i) q^{88} +(-0.225025 + 0.389754i) q^{89} -2.56724 q^{90} +(-11.5404 + 10.1651i) q^{91} +(-4.79520 - 0.0777105i) q^{92} +(-4.83943 + 8.38213i) q^{93} +(0.485292 - 0.280183i) q^{94} +(-7.72592 - 13.3817i) q^{95} +(0.866025 + 0.500000i) q^{96} -4.63569 q^{97} +(5.57194 + 4.23716i) q^{98} -4.32885i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	$ 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) $ 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	1.28362	−	2.22329i	0.574052	−	0.994287i	−0.422092	−	0.906553i	$-0.638704\pi$
$5$	1.28362	−	2.22329i	0.574052	−	0.994287i	0.996144	−	0.0877337i	$-0.0279625\pi$
$6$		−	1.00000i		−	0.408248i
$7$	1.74878	+	1.98539i	0.660978	+	0.750405i
$7$	1.74878	+	1.98539i	0.660978	+	0.750405i
$8$	−1.00000			−0.353553
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$	−1.28362	−	2.22329i	−0.405916	−	0.703067i
$11$	3.74890	−	2.16443i	1.13033	−	0.652599i	0.186316	−	0.982490i	$-0.440345\pi$
$11$	3.74890	−	2.16443i	1.13033	−	0.652599i	0.944019	+	0.329891i	$0.107012\pi$
$12$	−0.866025	−	0.500000i	−0.250000	−	0.144338i
$13$			5.81269i			1.61215i	0.591813	+	0.806075i	$0.298412\pi$
$13$			5.81269i			1.61215i	−0.591813	+	0.806075i	$0.701588\pi$
$14$	2.59379	−	0.521797i	0.693219	−	0.139456i
$15$		−	2.56724i		−	0.662858i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.22357	+	2.11928i	0.296758	+	0.514000i	0.975392	−	0.220476i	$-0.0707611\pi$
$17$	1.22357	+	2.11928i	0.296758	+	0.514000i	−0.678634	+	0.734476i	$0.737428\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	3.00943	−	5.21248i	0.690410	−	1.19583i	−0.281293	−	0.959622i	$-0.590763\pi$
$19$	3.00943	−	5.21248i	0.690410	−	1.19583i	0.971703	−	0.236204i	$-0.0759034\pi$
$20$	−2.56724			−0.574052
$21$	2.50718	+	0.845003i	0.547112	+	0.184395i
$22$		−	4.32885i		−	0.922914i
$23$	2.46490	−	4.11391i	0.513967	−	0.857810i
$23$	2.46490	−	4.11391i	0.513967	−	0.857810i
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−0.795352	−	1.37759i	−0.159070	−	0.275518i
$26$	5.03394	+	2.90635i	0.987237	+	0.569981i
$27$		−	1.00000i		−	0.192450i
$28$	0.845003	−	2.50718i	0.159691	−	0.473813i
$29$	−3.89593			−0.723455			−0.361728	−	0.932284i	$-0.617813\pi$
$29$	−3.89593			−0.723455			−0.361728	+	0.932284i	$0.617813\pi$
$30$	−2.22329	−	1.28362i	−0.405916	−	0.234356i
$31$	−8.38213	+	4.83943i	−1.50548	+	0.869187i	−0.505496	+	0.862829i	$0.668690\pi$
$31$	−8.38213	+	4.83943i	−1.50548	+	0.869187i	−0.999980	+	0.00635769i	$0.997976\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.16443	−	3.74890i	0.376778	−	0.652599i
$34$	2.44713			0.419679
$35$	6.65886	−	1.33958i	1.12555	−	0.226430i
$36$	−1.00000			−0.166667
$37$	−9.58443	−	5.53357i	−1.57567	−	0.909714i	−0.995453	−	0.0952520i	$-0.969634\pi$
$37$	−9.58443	−	5.53357i	−1.57567	−	0.909714i	−0.580217	−	0.814462i	$-0.697032\pi$
$38$	−3.00943	−	5.21248i	−0.488194	−	0.845577i
$39$	2.90635	+	5.03394i	0.465388	+	0.806075i
$40$	−1.28362	+	2.22329i	−0.202958	+	0.351533i
$41$		−	4.24238i		−	0.662549i	−0.943534	−	0.331274i	$-0.892521\pi$
$41$		−	4.24238i		−	0.662549i	0.943534	−	0.331274i	$-0.107479\pi$
$42$	1.98539	−	1.74878i	0.306352	−	0.269843i
$43$			9.27845i			1.41495i	0.706738	+	0.707475i	$0.250166\pi$
$43$			9.27845i			1.41495i	−0.706738	+	0.707475i	$0.749834\pi$
$44$	−3.74890	−	2.16443i	−0.565167	−	0.326299i
$45$	−1.28362	−	2.22329i	−0.191351	−	0.331429i
$46$	−2.33030	−	4.19162i	−0.343584	−	0.618021i
$47$	0.485292	+	0.280183i	0.0707871	+	0.0408689i	0.534976	−	0.844867i	$-0.320321\pi$
$47$	0.485292	+	0.280183i	0.0707871	+	0.0408689i	−0.464189	+	0.885736i	$0.653654\pi$
$48$			1.00000i			0.144338i
$49$	−0.883516	+	6.94402i	−0.126217	+	0.992003i
$50$	−1.59070			−0.224960
$51$	2.11928	+	1.22357i	0.296758	+	0.171333i
$52$	5.03394	−	2.90635i	0.698082	−	0.403038i
$53$	−3.03846	+	1.75425i	−0.417364	+	0.240965i	−0.693949	−	0.720024i	$-0.744131\pi$
$53$	−3.03846	+	1.75425i	−0.417364	+	0.240965i	0.276585	+	0.960990i	$0.410797\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		−	11.1132i		−	1.49850i
$56$	−1.74878	−	1.98539i	−0.233691	−	0.265308i
$57$		−	6.01886i		−	0.797217i
$58$	−1.94796	+	3.37397i	−0.255780	+	0.443024i
$59$	−9.23060	+	5.32929i	−1.20172	+	0.693815i	−0.960938	−	0.276764i	$-0.910738\pi$
$59$	−9.23060	+	5.32929i	−1.20172	+	0.693815i	−0.240784	+	0.970579i	$0.577405\pi$
$60$	−2.22329	+	1.28362i	−0.287026	+	0.165714i
$61$	2.79450	−	4.84021i	0.357798	−	0.619725i	−0.629794	−	0.776762i	$-0.716861\pi$
$61$	2.79450	−	4.84021i	0.357798	−	0.619725i	0.987593	+	0.157037i	$0.0501942\pi$
$62$			9.67885i			1.22922i
$63$	2.59379	−	0.521797i	0.326786	−	0.0657403i
$64$	1.00000			0.125000
$65$	12.9233	+	7.46128i	1.60294	+	0.925458i
$66$	−2.16443	−	3.74890i	−0.266422	−	0.461457i
$67$	7.00382	−	4.04366i	0.855653	−	0.494011i	−0.00690130	−	0.999976i	$-0.502197\pi$
$67$	7.00382	−	4.04366i	0.855653	−	0.494011i	0.862554	+	0.505965i	$0.168863\pi$
$68$	1.22357	−	2.11928i	0.148379	−	0.257000i
$69$	0.0777105	−	4.79520i	0.00935524	−	0.577274i
$70$	2.16932	−	6.43653i	0.259284	−	0.769313i
$71$	−13.9696			−1.65789			−0.828943	−	0.559333i	$-0.811057\pi$
$71$	−13.9696			−1.65789			−0.828943	+	0.559333i	$0.811057\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	5.37567	−	3.10364i	0.629174	−	0.363254i	−0.151258	−	0.988494i	$-0.548332\pi$
$73$	5.37567	−	3.10364i	0.629174	−	0.363254i	0.780432	+	0.625240i	$0.214999\pi$
$74$	−9.58443	+	5.53357i	−1.11417	+	0.643265i
$75$	−1.37759	−	0.795352i	−0.159070	−	0.0918394i
$76$	−6.01886			−0.690410
$77$	10.8532	+	3.65789i	1.23684	+	0.416856i
$78$	5.81269			0.658158
$79$	−3.37662	−	1.94949i	−0.379899	−	0.219335i	0.297875	−	0.954605i	$-0.403722\pi$
$79$	−3.37662	−	1.94949i	−0.379899	−	0.219335i	−0.677774	+	0.735270i	$0.737055\pi$
$80$	1.28362	+	2.22329i	0.143513	+	0.248572i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−3.67401	−	2.12119i	−0.405727	−	0.234246i
$83$	−0.193800			−0.0212723			−0.0106361	−	0.999943i	$-0.503386\pi$
$83$	−0.193800			−0.0212723			−0.0106361	+	0.999943i	$0.503386\pi$
$84$	−0.521797	−	2.59379i	−0.0569328	−	0.283005i
$85$	6.28236			0.681418
$86$	8.03537	+	4.63923i	0.866477	+	0.500261i
$87$	−3.37397	+	1.94796i	−0.361728	+	0.208844i
$88$	−3.74890	+	2.16443i	−0.399634	+	0.230729i
$89$	−0.225025	+	0.389754i	−0.0238526	+	0.0413139i	−0.877705	−	0.479201i	$-0.840927\pi$
$89$	−0.225025	+	0.389754i	−0.0238526	+	0.0413139i	0.853853	+	0.520515i	$0.174260\pi$
$90$	−2.56724			−0.270611
$91$	−11.5404	+	10.1651i	−1.20977	+	1.06560i
$92$	−4.79520	−	0.0777105i	−0.499934	−	0.00810188i
$93$	−4.83943	+	8.38213i	−0.501825	+	0.869187i
$94$	0.485292	−	0.280183i	0.0500540	−	0.0288987i
$95$	−7.72592	−	13.3817i	−0.792662	−	1.37293i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−4.63569			−0.470683			−0.235342	−	0.971913i	$-0.575621\pi$
$97$	−4.63569			−0.470683			−0.235342	+	0.971913i	$0.575621\pi$
$98$	5.57194	+	4.23716i	0.562851	+	0.428017i
$99$		−	4.32885i		−	0.435066i
$100$	−0.795352	+	1.37759i	−0.0795352	+	0.137759i
$101$	11.9127	−	6.87781i	1.18536	−	0.684367i	0.228111	−	0.973635i	$-0.426745\pi$
$101$	11.9127	−	6.87781i	1.18536	−	0.684367i	0.957248	+	0.289268i	$0.0934119\pi$
$102$	2.11928	−	1.22357i	0.209840	−	0.121151i
$103$	−2.15096	+	3.72558i	−0.211941	+	0.367092i	−0.952322	−	0.305095i	$-0.901312\pi$
$103$	−2.15096	+	3.72558i	−0.211941	+	0.367092i	0.740381	+	0.672187i	$0.234645\pi$
$104$		−	5.81269i		−	0.569981i
$105$	5.09696	−	4.48954i	0.497412	−	0.438134i
$106$			3.50851i			0.340777i
$107$	9.05044	+	5.22527i	0.874939	+	0.505146i	0.868986	−	0.494836i	$-0.164772\pi$
$107$	9.05044	+	5.22527i	0.874939	+	0.505146i	0.00595236	+	0.999982i	$0.498105\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$	−2.84824	+	1.64443i	−0.272812	+	0.157508i	−0.630165	−	0.776461i	$-0.717013\pi$
$109$	−2.84824	+	1.64443i	−0.272812	+	0.157508i	0.357353	+	0.933969i	$0.383679\pi$
$110$	−9.62430	−	5.55659i	−0.917641	−	0.529800i
$111$	−11.0671			−1.05045
$112$	−2.59379	+	0.521797i	−0.245090	+	0.0493052i
$113$			10.8600i			1.02162i	0.859692	+	0.510812i	$0.170655\pi$
$113$			10.8600i			1.02162i	−0.859692	+	0.510812i	$0.829345\pi$
$114$	−5.21248	−	3.00943i	−0.488194	−	0.281859i
$115$	−5.98244	−	10.7609i	−0.557865	−	1.00346i
$116$	1.94796	+	3.37397i	0.180864	+	0.313265i
$117$	5.03394	+	2.90635i	0.465388	+	0.268692i
$118$			10.6586i			0.981202i
$119$	−2.06783	+	6.13540i	−0.189558	+	0.562432i
$120$			2.56724i			0.234356i
$121$	3.86948	−	6.70213i	0.351771	−	0.609285i
$122$	−2.79450	−	4.84021i	−0.253002	−	0.438212i
$123$	−2.12119	−	3.67401i	−0.191261	−	0.331274i
$124$	8.38213	+	4.83943i	0.752738	+	0.434593i
$125$	8.75247			0.782845
$126$	0.845003	−	2.50718i	0.0752789	−	0.223358i
$127$	7.07248			0.627582			0.313791	−	0.949492i	$-0.398401\pi$
$127$	7.07248			0.627582			0.313791	+	0.949492i	$0.398401\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.63923	+	8.03537i	0.408461	+	0.707475i
$130$	12.9233	−	7.46128i	1.13345	−	0.654397i
$131$	10.0401	+	5.79663i	0.877204	+	0.506454i	0.869736	−	0.493518i	$-0.164289\pi$
$131$	10.0401	+	5.79663i	0.877204	+	0.506454i	0.00746865	+	0.999972i	$0.497623\pi$
$132$	−4.32885			−0.376778
$133$	15.6116	−	3.14062i	1.35370	−	0.272327i
$134$		−	8.08732i		−	0.698638i
$135$	−2.22329	−	1.28362i	−0.191351	−	0.110476i
$136$	−1.22357	−	2.11928i	−0.104920	−	0.181727i
$137$	10.7726	−	6.21957i	0.920367	−	0.531374i	0.0366145	−	0.999329i	$-0.488343\pi$
$137$	10.7726	−	6.21957i	0.920367	−	0.531374i	0.883752	+	0.467956i	$0.155009\pi$
$138$	−4.11391	−	2.46490i	−0.350199	−	0.209826i
$139$			11.4894i			0.974519i	0.873257	+	0.487260i	$0.162003\pi$
$139$			11.4894i			0.974519i	−0.873257	+	0.487260i	$0.837997\pi$
$140$	−4.48954	−	5.09696i	−0.379435	−	0.430771i
$141$	0.560367			0.0471914
$142$	−6.98480	+	12.0980i	−0.586151	+	1.01524i
$143$	12.5811	+	21.7912i	1.05209	+	1.82227i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$	−5.00088	+	8.66178i	−0.415301	+	0.719322i
$146$		−	6.20729i		−	0.513719i
$147$	2.70686	+	6.45545i	0.223258	+	0.532437i
$148$			11.0671i			0.909714i
$149$	−14.0614	−	8.11835i	−1.15195	−	0.665081i	−0.202592	−	0.979263i	$-0.564936\pi$
$149$	−14.0614	−	8.11835i	−1.15195	−	0.665081i	−0.949363	+	0.314182i	$0.898270\pi$
$150$	−1.37759	+	0.795352i	−0.112480	+	0.0649402i
$151$	−8.06432	−	13.9678i	−0.656265	−	1.13668i	−0.981575	−	0.191077i	$-0.938802\pi$
$151$	−8.06432	−	13.9678i	−0.656265	−	1.13668i	0.325310	−	0.945607i	$-0.394531\pi$
$152$	−3.00943	+	5.21248i	−0.244097	+	0.422788i
$153$	2.44713			0.197839
$154$	8.59444	−	7.57022i	0.692560	−	0.610026i
$155$			24.8479i			1.99583i
$156$	2.90635	−	5.03394i	0.232694	−	0.403038i
$157$	−2.88092	−	4.98990i	−0.229922	−	0.398237i	0.727862	−	0.685723i	$-0.240514\pi$
$157$	−2.88092	−	4.98990i	−0.229922	−	0.398237i	−0.957785	+	0.287486i	$0.907181\pi$
$158$	−3.37662	+	1.94949i	−0.268629	+	0.155093i
$159$	−1.75425	+	3.03846i	−0.139121	+	0.240965i
$160$	2.56724			0.202958
$161$	12.4783	−	2.30056i	0.983426	−	0.181309i
$162$	−1.00000			−0.0785674
$163$	−4.13276	+	7.15814i	−0.323702	+	0.560669i	−0.981249	−	0.192745i	$-0.938261\pi$
$163$	−4.13276	+	7.15814i	−0.323702	+	0.560669i	0.657546	+	0.753414i	$0.271594\pi$
$164$	−3.67401	+	2.12119i	−0.286892	+	0.165637i
$165$	−5.55659	−	9.62430i	−0.432580	−	0.749251i
$166$	−0.0968999	+	0.167836i	−0.00752089	+	0.0130266i
$167$			11.6758i			0.903498i	0.892145	+	0.451749i	$0.149200\pi$
$167$			11.6758i			0.903498i	−0.892145	+	0.451749i	$0.850800\pi$
$168$	−2.50718	−	0.845003i	−0.193433	−	0.0651934i
$169$	−20.7874			−1.59903
$170$	3.14118	−	5.44069i	0.240918	−	0.417282i
$171$	−3.00943	−	5.21248i	−0.230137	−	0.398609i
$172$	8.03537	−	4.63923i	0.612692	−	0.353738i
$173$	−1.62888	−	0.940436i	−0.123842	−	0.0715001i	0.436799	−	0.899559i	$-0.356112\pi$
$173$	−1.62888	−	0.940436i	−0.123842	−	0.0715001i	−0.560641	+	0.828059i	$0.689445\pi$
$174$			3.89593i			0.295349i
$175$	1.34415	−	3.98819i	0.101608	−	0.301479i
$176$			4.32885i			0.326299i
$177$	−5.32929	+	9.23060i	−0.400574	+	0.693815i
$178$	0.225025	+	0.389754i	0.0168663	+	0.0292133i
$179$	6.18091	+	10.7056i	0.461983	+	0.800178i	0.999060	−	0.0433557i	$-0.0138049\pi$
$179$	6.18091	+	10.7056i	0.461983	+	0.800178i	−0.537077	+	0.843533i	$0.680472\pi$
$180$	−1.28362	+	2.22329i	−0.0956753	+	0.165714i
$181$	5.04841			0.375245			0.187623	−	0.982241i	$-0.439922\pi$
$181$	5.04841			0.375245			0.187623	+	0.982241i	$0.439922\pi$
$182$	3.03305	+	15.0769i	0.224824	+	1.11757i
$183$		−	5.58899i		−	0.413150i
$184$	−2.46490	+	4.11391i	−0.181715	+	0.303282i
$185$	−24.6055	+	14.2060i	−1.80903	+	1.04445i
$186$	4.83943	+	8.38213i	0.354844	+	0.614608i
$187$	9.17404	+	5.29663i	0.670872	+	0.387328i
$188$		−	0.560367i		−	0.0408689i
$189$	1.98539	−	1.74878i	0.144416	−	0.127205i
$190$	−15.4518			−1.12099
$191$	−0.472131	−	0.272585i	−0.0341622	−	0.0197236i	0.482822	−	0.875719i	$-0.339612\pi$
$191$	−0.472131	−	0.272585i	−0.0341622	−	0.0197236i	−0.516984	+	0.855995i	$0.672945\pi$
$192$	0.866025	−	0.500000i	0.0625000	−	0.0360844i
$193$	−10.6461	−	18.4395i	−0.766321	−	1.32731i	−0.939546	−	0.342424i	$-0.888752\pi$
$193$	−10.6461	−	18.4395i	−0.766321	−	1.32731i	0.173225	−	0.984882i	$-0.444581\pi$
$194$	−2.31785	+	4.01463i	−0.166412	+	0.288234i
$195$	14.9226			1.06863
$196$	6.45545	−	2.70686i	0.461104	−	0.193347i
$197$	−1.20861			−0.0861102			−0.0430551	−	0.999073i	$-0.513709\pi$
$197$	−1.20861			−0.0861102			−0.0430551	+	0.999073i	$0.513709\pi$
$198$	−3.74890	−	2.16443i	−0.266422	−	0.153819i
$199$	0.967524	+	1.67580i	0.0685859	+	0.118794i	0.898279	−	0.439425i	$-0.144818\pi$
$199$	0.967524	+	1.67580i	0.0685859	+	0.118794i	−0.829693	+	0.558220i	$0.811485\pi$
$200$	0.795352	+	1.37759i	0.0562399	+	0.0974104i
$201$	4.04366	−	7.00382i	0.285218	−	0.494011i
$202$		−	13.7556i		−	0.967841i
$203$	−6.81313	−	7.73492i	−0.478188	−	0.542885i
$204$		−	2.44713i		−	0.171333i
$205$	−9.43206	−	5.44560i	−0.658763	−	0.380337i
$206$	2.15096	+	3.72558i	0.149865	+	0.259573i
$207$	−2.33030	−	4.19162i	−0.161967	−	0.291338i
$208$	−5.03394	−	2.90635i	−0.349041	−	0.201519i
$209$		−	26.0547i		−	1.80224i
$210$	−1.33958	−	6.65886i	−0.0924396	−	0.459505i
$211$	−1.29856			−0.0893963			−0.0446981	−	0.999001i	$-0.514233\pi$
$211$	−1.29856			−0.0893963			−0.0446981	+	0.999001i	$0.514233\pi$
$212$	3.03846	+	1.75425i	0.208682	+	0.120483i
$213$	−12.0980	+	6.98480i	−0.828943	+	0.478591i
$214$	9.05044	−	5.22527i	0.618675	−	0.357192i
$215$	20.6287	+	11.9100i	1.40687	+	0.812255i
$216$			1.00000i			0.0680414i
$217$	−24.2667	−	8.17866i	−1.64733	−	0.555204i
$218$			3.28887i			0.222750i
$219$	3.10364	−	5.37567i	0.209725	−	0.363254i
$220$	−9.62430	+	5.55659i	−0.648870	+	0.374625i
$221$	−12.3187	+	7.11221i	−0.828646	+	0.478419i
$222$	−5.53357	+	9.58443i	−0.371389	+	0.643265i
$223$		−	3.83544i		−	0.256840i	−0.991720	−	0.128420i	$-0.959009\pi$
$223$		−	3.83544i		−	0.256840i	0.991720	−	0.128420i	$-0.0409906\pi$
$224$	−0.845003	+	2.50718i	−0.0564592	+	0.167518i
$225$	−1.59070			−0.106047
$226$	9.40505	+	5.43001i	0.625615	+	0.361199i
$227$	13.3025	+	23.0406i	0.882918	+	1.52926i	0.848081	+	0.529867i	$0.177758\pi$
$227$	13.3025	+	23.0406i	0.882918	+	1.52926i	0.0348374	+	0.999393i	$0.488909\pi$
$228$	−5.21248	+	3.00943i	−0.345205	+	0.199304i
$229$	−5.28694	+	9.15725i	−0.349371	+	0.605128i	−0.986138	−	0.165928i	$-0.946938\pi$
$229$	−5.28694	+	9.15725i	−0.349371	+	0.605128i	0.636767	+	0.771056i	$0.280271\pi$
$230$	−12.3104	−	0.199501i	−0.811725	−	0.0131547i
$231$	11.2281	−	2.25878i	0.738756	−	0.148617i
$232$	3.89593			0.255780
$233$	−5.96422	+	10.3303i	−0.390729	+	0.676763i	−0.992546	−	0.121871i	$-0.961110\pi$
$233$	−5.96422	+	10.3303i	−0.390729	+	0.676763i	0.601817	+	0.798634i	$0.294444\pi$
$234$	5.03394	−	2.90635i	0.329079	−	0.189994i
$235$	1.24586	−	0.719297i	0.0812709	−	0.0469218i
$236$	9.23060	+	5.32929i	0.600861	+	0.346907i
$237$	−3.89898			−0.253266
$238$	4.27950	+	4.85850i	0.277399	+	0.314930i
$239$	−20.7933			−1.34501			−0.672503	−	0.740094i	$-0.734781\pi$
$239$	−20.7933			−1.34501			−0.672503	+	0.740094i	$0.734781\pi$
$240$	2.22329	+	1.28362i	0.143513	+	0.0828572i
$241$	4.27326	+	7.40151i	0.275265	+	0.476773i	0.970202	−	0.242298i	$-0.0779011\pi$
$241$	4.27326	+	7.40151i	0.275265	+	0.476773i	−0.694937	+	0.719071i	$0.744568\pi$
$242$	−3.86948	−	6.70213i	−0.248740	−	0.430829i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−5.58899			−0.357798
$245$	14.3045	+	10.8778i	0.913880	+	0.694956i
$246$	−4.24238			−0.270484
$247$	30.2986	+	17.4929i	1.92785	+	1.11305i
$248$	8.38213	−	4.83943i	0.532266	−	0.307304i
$249$	−0.167836	+	0.0968999i	−0.0106361	+	0.00614078i
$250$	4.37623	−	7.57986i	0.276777	−	0.479392i
$251$	−1.70245			−0.107458			−0.0537289	−	0.998556i	$-0.517111\pi$
$251$	−1.70245			−0.107458			−0.0537289	+	0.998556i	$0.517111\pi$
$252$	−1.74878	−	1.98539i	−0.110163	−	0.125068i
$253$	0.336397	−	20.7577i	0.0211491	−	1.30503i
$254$	3.53624	−	6.12495i	0.221884	−	0.384314i
$255$	5.44069	−	3.14118i	0.340709	−	0.196708i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	20.0132	+	11.5546i	1.24839	+	0.720758i	0.970788	−	0.239939i	$-0.0771274\pi$
$257$	20.0132	+	11.5546i	1.24839	+	0.720758i	0.277601	+	0.960696i	$0.410461\pi$
$258$	9.27845			0.577651
$259$	−5.77481	−	28.7058i	−0.358829	−	1.78369i
$260$		−	14.9226i		−	0.925458i
$261$	−1.94796	+	3.37397i	−0.120576	+	0.208844i
$262$	10.0401	−	5.79663i	0.620277	−	0.358117i
$263$	−11.6534	+	6.72808i	−0.718578	+	0.414871i	−0.814229	−	0.580544i	$-0.802840\pi$
$263$	−11.6534	+	6.72808i	−0.718578	+	0.414871i	0.0956511	+	0.995415i	$0.469507\pi$
$264$	−2.16443	+	3.74890i	−0.133211	+	0.230729i
$265$			9.00718i			0.553306i
$266$	5.08596	−	15.0904i	0.311840	−	0.925251i
$267$			0.450050i			0.0275426i
$268$	−7.00382	−	4.04366i	−0.427826	−	0.247006i
$269$	2.60844	−	1.50598i	0.159039	−	0.0918213i	−0.418368	−	0.908278i	$-0.637398\pi$
$269$	2.60844	−	1.50598i	0.159039	−	0.0918213i	0.577407	+	0.816456i	$0.304064\pi$
$270$	−2.22329	+	1.28362i	−0.135305	+	0.0781185i
$271$	18.3144	+	10.5738i	1.11252	+	0.642314i	0.939481	−	0.342601i	$-0.111308\pi$
$271$	18.3144	+	10.5738i	1.11252	+	0.642314i	0.173040	+	0.984915i	$0.444641\pi$
$272$	−2.44713			−0.148379
$273$	−4.91174	+	14.5735i	−0.297272	+	0.882028i
$274$		−	12.4391i		−	0.751476i
$275$	−5.96339	−	3.44296i	−0.359606	−	0.207618i
$276$	−4.19162	+	2.33030i	−0.252306	+	0.140268i
$277$	11.1856	+	19.3741i	0.672080	+	1.16408i	0.977313	+	0.211799i	$0.0679321\pi$
$277$	11.1856	+	19.3741i	0.672080	+	1.16408i	−0.305234	+	0.952278i	$0.598735\pi$
$278$	9.95012	+	5.74471i	0.596769	+	0.344545i
$279$			9.67885i			0.579458i
$280$	−6.65886	+	1.33958i	−0.397943	+	0.0800551i
$281$		−	17.2658i		−	1.02999i	−0.857193	−	0.514995i	$-0.827794\pi$
$281$		−	17.2658i		−	1.02999i	0.857193	−	0.514995i	$-0.172206\pi$
$282$	0.280183	−	0.485292i	0.0166847	−	0.0288987i
$283$	−6.55378	−	11.3515i	−0.389582	−	0.674775i	0.602812	−	0.797884i	$-0.294047\pi$
$283$	−6.55378	−	11.3515i	−0.389582	−	0.674775i	−0.992393	+	0.123108i	$0.960714\pi$
$284$	6.98480	+	12.0980i	0.414472	+	0.717886i
$285$	−13.3817	−	7.72592i	−0.792662	−	0.457644i
$286$	25.1623			1.48788
$287$	8.42277	−	7.41901i	0.497180	−	0.437930i
$288$	1.00000			0.0589256
$289$	5.50578	−	9.53628i	0.323869	−	0.560958i
$290$	5.00088	+	8.66178i	0.293662	+	0.508637i
$291$	−4.01463	+	2.31785i	−0.235342	+	0.135875i
$292$	−5.37567	−	3.10364i	−0.314587	−	0.181627i
$293$	17.2617			1.00844			0.504221	−	0.863575i	$-0.331780\pi$
$293$	17.2617			1.00844			0.504221	+	0.863575i	$0.331780\pi$
$294$	6.94402	+	0.883516i	0.404983	+	0.0515277i
$295$			27.3631i			1.59314i
$296$	9.58443	+	5.53357i	0.557084	+	0.321632i
$297$	−2.16443	−	3.74890i	−0.125593	−	0.217533i
$298$	−14.0614	+	8.11835i	−0.814555	+	0.470283i
$299$	23.9129	+	14.3277i	1.38292	+	0.828593i
$300$			1.59070i			0.0918394i
$301$	−18.4213	+	16.2260i	−1.06179	+	0.935251i
$302$	−16.1286			−0.928099
$303$	6.87781	−	11.9127i	0.395120	−	0.684367i
$304$	3.00943	+	5.21248i	0.172603	+	0.298956i
$305$	−7.17413	−	12.4260i	−0.410790	−	0.711508i
$306$	1.22357	−	2.11928i	0.0699466	−	0.121151i
$307$			12.7264i			0.726335i	0.931724	+	0.363168i	$0.118305\pi$
$307$			12.7264i			0.726335i	−0.931724	+	0.363168i	$0.881695\pi$
$308$	−2.25878	−	11.2281i	−0.128706	−	0.639781i
$309$			4.30193i			0.244728i
$310$	21.5189	+	12.4240i	1.22219	+	0.705633i
$311$	22.6887	−	13.0993i	1.28656	−	0.742794i	0.308519	−	0.951218i	$-0.400167\pi$
$311$	22.6887	−	13.0993i	1.28656	−	0.742794i	0.978039	+	0.208424i	$0.0668333\pi$
$312$	−2.90635	−	5.03394i	−0.164539	−	0.284991i
$313$	11.4870	−	19.8960i	0.649281	−	1.12459i	−0.334014	−	0.942568i	$-0.608403\pi$
$313$	11.4870	−	19.8960i	0.649281	−	1.12459i	0.983295	−	0.182020i	$-0.0582634\pi$
$314$	−5.76184			−0.325159
$315$	2.16932	−	6.43653i	0.122228	−	0.362658i
$316$			3.89898i			0.219335i
$317$	3.78659	−	6.55856i	0.212676	−	0.368365i	−0.739875	−	0.672744i	$-0.765116\pi$
$317$	3.78659	−	6.55856i	0.212676	−	0.368365i	0.952551	+	0.304379i	$0.0984488\pi$
$318$	1.75425	+	3.03846i	0.0983737	+	0.170388i
$319$	−14.6054	+	8.43244i	−0.817747	+	0.472126i
$320$	1.28362	−	2.22329i	0.0717564	−	0.124286i
$321$	10.4505			0.583292
$322$	4.24680	−	11.9568i	0.236665	−	0.666326i
$323$	14.7289			0.819540
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	8.00751	−	4.62314i	0.444177	−	0.256446i
$326$	4.13276	+	7.15814i	0.228892	+	0.396453i
$327$	−1.64443	+	2.84824i	−0.0909373	+	0.157508i
$328$			4.24238i			0.234246i
$329$	0.292398	+	1.45347i	0.0161204	+	0.0801325i
$330$	−11.1132			−0.611761
$331$	−15.0498	+	26.0670i	−0.827210	+	1.43277i	0.0730091	+	0.997331i	$0.476740\pi$
$331$	−15.0498	+	26.0670i	−0.827210	+	1.43277i	−0.900219	+	0.435438i	$0.856594\pi$
$332$	0.0968999	+	0.167836i	0.00531807	+	0.00921117i
$333$	−9.58443	+	5.53357i	−0.525223	+	0.303238i
$334$	10.1115	+	5.83788i	0.553277	+	0.319435i
$335$		−	20.7621i		−	1.13435i
$336$	−1.98539	+	1.74878i	−0.108312	+	0.0954039i
$337$		−	35.6664i		−	1.94287i	−0.237298	−	0.971437i	$-0.576262\pi$
$337$		−	35.6664i		−	1.94287i	0.237298	−	0.971437i	$-0.423738\pi$
$338$	−10.3937	+	18.0024i	−0.565343	+	0.979202i
$339$	5.43001	+	9.40505i	0.294918	+	0.510812i
$340$	−3.14118	−	5.44069i	−0.170354	−	0.295063i
$341$	−20.9492	+	36.2850i	−1.13446	+	1.96494i
$342$	−6.01886			−0.325463
$343$	−15.3316	+	10.3895i	−0.827831	+	0.560978i
$344$		−	9.27845i		−	0.500261i
$345$	−10.5614	−	6.32798i	−0.568606	−	0.340687i
$346$	−1.62888	+	0.940436i	−0.0875693	+	0.0505582i
$347$	−14.7747	−	25.5906i	−0.793150	−	1.37378i	−0.924007	−	0.382374i	$-0.875106\pi$
$347$	−14.7747	−	25.5906i	−0.793150	−	1.37378i	0.130858	−	0.991401i	$-0.458227\pi$
$348$	3.37397	+	1.94796i	0.180864	+	0.104422i
$349$			28.0609i			1.50207i	0.660264	+	0.751034i	$0.270445\pi$
$349$			28.0609i			1.50207i	−0.660264	+	0.751034i	$0.729555\pi$
$350$	−2.78180	−	3.15816i	−0.148693	−	0.168811i
$351$	5.81269			0.310259
$352$	3.74890	+	2.16443i	0.199817	+	0.115364i
$353$	−16.2176	+	9.36326i	−0.863178	+	0.498356i	−0.865075	−	0.501642i	$-0.832729\pi$
$353$	−16.2176	+	9.36326i	−0.863178	+	0.498356i	0.00189712	+	0.999998i	$0.499396\pi$
$354$	5.32929	+	9.23060i	0.283249	+	0.490601i
$355$	−17.9316	+	31.0585i	−0.951712	+	1.64841i
$356$	0.450050			0.0238526
$357$	1.27691	+	6.34733i	0.0675810	+	0.335936i
$358$	12.3618			0.653342
$359$	−32.1802	−	18.5793i	−1.69841	−	0.980577i	−0.947273	−	0.320429i	$-0.896173\pi$
$359$	−32.1802	−	18.5793i	−1.69841	−	0.980577i	−0.751136	−	0.660148i	$-0.770494\pi$
$360$	1.28362	+	2.22329i	0.0676526	+	0.117178i
$361$	−8.61333	−	14.9187i	−0.453333	−	0.785196i
$362$	2.52421	−	4.37205i	0.132669	−	0.229790i
$363$		−	7.73896i		−	0.406190i
$364$	14.5735	+	4.91174i	0.763858	+	0.257445i
$365$		−	15.9356i		−	0.834106i
$366$	−4.84021	−	2.79450i	−0.253002	−	0.146071i
$367$	−8.46442	−	14.6608i	−0.441839	−	0.765288i	0.555987	−	0.831191i	$-0.312341\pi$
$367$	−8.46442	−	14.6608i	−0.441839	−	0.765288i	−0.997826	+	0.0659031i	$0.979007\pi$
$368$	2.33030	+	4.19162i	0.121475	+	0.218503i
$369$	−3.67401	−	2.12119i	−0.191261	−	0.110425i
$370$			28.4120i			1.47707i
$371$	−8.79648	−	2.96470i	−0.456690	−	0.153920i
$372$	9.67885			0.501825
$373$	−5.49398	−	3.17195i	−0.284467	−	0.164237i	0.350977	−	0.936384i	$-0.385850\pi$
$373$	−5.49398	−	3.17195i	−0.284467	−	0.164237i	−0.635444	+	0.772147i	$0.719183\pi$
$374$	9.17404	−	5.29663i	0.474378	−	0.273882i
$375$	7.57986	−	4.37623i	0.391422	−	0.225988i
$376$	−0.485292	−	0.280183i	−0.0250270	−	0.0144494i
$377$		−	22.6458i		−	1.16632i
$378$	−0.521797	−	2.59379i	−0.0268384	−	0.133410i
$379$			29.0651i			1.49297i	0.665400	+	0.746487i	$0.268261\pi$
$379$			29.0651i			1.49297i	−0.665400	+	0.746487i	$0.731739\pi$
$380$	−7.72592	+	13.3817i	−0.396331	+	0.686466i
$381$	6.12495	−	3.53624i	0.313791	−	0.181167i
$382$	−0.472131	+	0.272585i	−0.0241563	+	0.0139467i
$383$	4.80504	−	8.32257i	0.245526	−	0.425263i	−0.716753	−	0.697327i	$-0.754373\pi$
$383$	4.80504	−	8.32257i	0.245526	−	0.425263i	0.962279	+	0.272063i	$0.0877060\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	22.0640	−	19.4346i	1.12448	−	0.990477i
$386$	−21.2921			−1.08374
$387$	8.03537	+	4.63923i	0.408461	+	0.235825i
$388$	2.31785	+	4.01463i	0.117671	+	0.203812i
$389$	0.214495	−	0.123838i	0.0108753	−	0.00627886i	−0.494552	−	0.869148i	$-0.664668\pi$
$389$	0.214495	−	0.123838i	0.0108753	−	0.00627886i	0.505428	+	0.862869i	$0.331335\pi$
$390$	7.46128	−	12.9233i	0.377817	−	0.654397i
$391$	11.7345	+	0.190168i	0.593438	+	0.00961719i
$392$	0.883516	−	6.94402i	0.0446243	−	0.350726i
$393$	11.5933			0.584803
$394$	−0.604307	+	1.04669i	−0.0304446	+	0.0527315i
$395$	−8.66858	+	5.00481i	−0.436164	+	0.251819i
$396$	−3.74890	+	2.16443i	−0.188389	+	0.108766i
$397$	−11.4352	−	6.60211i	−0.573916	−	0.331351i	0.184796	−	0.982777i	$-0.440838\pi$
$397$	−11.4352	−	6.60211i	−0.573916	−	0.331351i	−0.758712	+	0.651426i	$0.774171\pi$
$398$	1.93505			0.0969952
$399$	11.9498	−	10.5257i	0.598236	−	0.526943i
$400$	1.59070			0.0795352
$401$	−4.03620	−	2.33030i	−0.201558	−	0.116370i	0.395824	−	0.918326i	$-0.370459\pi$
$401$	−4.03620	−	2.33030i	−0.201558	−	0.116370i	−0.597382	+	0.801957i	$0.703792\pi$
$402$	−4.04366	−	7.00382i	−0.201679	−	0.349319i
$403$	−28.1301	−	48.7228i	−1.40126	−	2.42705i
$404$	−11.9127	−	6.87781i	−0.592679	−	0.342184i
$405$	−2.56724			−0.127567
$406$	−10.1052	+	2.03288i	−0.501513	+	0.100890i
$407$	−47.9080			−2.37471
$408$	−2.11928	−	1.22357i	−0.104920	−	0.0605755i
$409$	−13.0777	+	7.55039i	−0.646648	+	0.373343i	−0.787171	−	0.616735i	$-0.788455\pi$
$409$	−13.0777	+	7.55039i	−0.646648	+	0.373343i	0.140523	+	0.990077i	$0.455122\pi$
$410$	−9.43206	+	5.44560i	−0.465816	+	0.268939i
$411$	6.21957	−	10.7726i	0.306789	−	0.531374i
$412$	4.30193			0.211941
$413$	−26.7230	−	9.00654i	−1.31495	−	0.443183i
$414$	−4.79520	−	0.0777105i	−0.235671	−	0.00381926i
$415$	−0.248765	+	0.430874i	−0.0122114	+	0.0211508i
$416$	−5.03394	+	2.90635i	−0.246809	+	0.142495i
$417$	5.74471	+	9.95012i	0.281319	+	0.487260i
$418$	−22.5641	−	13.0274i	−1.10364	−	0.637190i
$419$	30.6549			1.49759			0.748795	−	0.662802i	$-0.230633\pi$
$419$	30.6549			1.49759			0.748795	+	0.662802i	$0.230633\pi$
$420$	−6.43653	−	2.16932i	−0.314071	−	0.105852i
$421$		−	34.5613i		−	1.68441i	−0.539155	−	0.842206i	$-0.681256\pi$
$421$		−	34.5613i		−	1.68441i	0.539155	−	0.842206i	$-0.318744\pi$
$422$	−0.649278	+	1.12458i	−0.0316064	+	0.0547438i
$423$	0.485292	−	0.280183i	0.0235957	−	0.0136230i
$424$	3.03846	−	1.75425i	0.147561	−	0.0851941i
$425$	1.94633	−	3.37114i	0.0944109	−	0.163524i
$426$			13.9696i			0.676829i
$427$	14.4966	−	2.91632i	0.701542	−	0.141131i
$428$		−	10.4505i		−	0.505146i
$429$	21.7912	+	12.5811i	1.05209	+	0.607423i
$430$	20.6287	−	11.9100i	0.994805	−	0.574351i
$431$	−9.77446	+	5.64329i	−0.470819	+	0.271828i	−0.716583	−	0.697502i	$-0.754295\pi$
$431$	−9.77446	+	5.64329i	−0.470819	+	0.271828i	0.245763	+	0.969330i	$0.420961\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	−26.5677			−1.27676			−0.638382	−	0.769720i	$-0.720396\pi$
$433$	−26.5677			−1.27676			−0.638382	+	0.769720i	$0.720396\pi$
$434$	−19.2163	+	16.9262i	−0.922410	+	0.812484i
$435$			10.0018i			0.479548i
$436$	2.84824	+	1.64443i	0.136406	+	0.0787540i
$437$	−14.0258	−	25.2288i	−0.670943	−	1.20686i
$438$	−3.10364	−	5.37567i	−0.148298	−	0.256859i
$439$	21.8889	+	12.6376i	1.04470	+	0.603159i	0.921162	−	0.389180i	$-0.127242\pi$
$439$	21.8889	+	12.6376i	1.04470	+	0.603159i	0.123541	+	0.992340i	$0.460575\pi$
$440$			11.1132i			0.529800i
$441$	5.57194	+	4.23716i	0.265330	+	0.201769i
$442$			14.2244i			0.676587i
$443$	−9.91152	+	17.1673i	−0.470911	+	0.815641i	−0.999446	−	0.0332700i	$-0.989408\pi$
$443$	−9.91152	+	17.1673i	−0.470911	+	0.815641i	0.528536	+	0.848911i	$0.322741\pi$
$444$	5.53357	+	9.58443i	0.262612	+	0.454857i
$445$	0.577692	+	1.00059i	0.0273852	+	0.0474326i
$446$	−3.32159	−	1.91772i	−0.157282	−	0.0908067i
$447$	−16.2367			−0.767970
$448$	1.74878	+	1.98539i	0.0826222	+	0.0938007i
$449$	−4.45876			−0.210422			−0.105211	−	0.994450i	$-0.533552\pi$
$449$	−4.45876			−0.210422			−0.105211	+	0.994450i	$0.533552\pi$
$450$	−0.795352	+	1.37759i	−0.0374933	+	0.0649402i
$451$	−9.18232	−	15.9042i	−0.432379	−	0.748902i
$452$	9.40505	−	5.43001i	0.442376	−	0.255406i
$453$	−13.9678	−	8.06432i	−0.656265	−	0.378895i
$454$	26.6050			1.24864
$455$	7.78655	+	38.7059i	0.365039	+	1.81456i
$456$			6.01886i			0.281859i
$457$	6.38519	+	3.68649i	0.298687	+	0.172447i	0.641853	−	0.766828i	$-0.278166\pi$
$457$	6.38519	+	3.68649i	0.298687	+	0.172447i	−0.343166	+	0.939275i	$0.611499\pi$
$458$	5.28694	+	9.15725i	0.247043	+	0.427890i
$459$	2.11928	−	1.22357i	0.0989194	−	0.0571111i
$460$	−6.32798	+	10.5614i	−0.295044	+	0.492427i
$461$		−	40.1702i		−	1.87091i	−0.353441	−	0.935457i	$-0.614988\pi$
$461$		−	40.1702i		−	1.87091i	0.353441	−	0.935457i	$-0.385012\pi$
$462$	3.65789	−	10.8532i	0.170181	−	0.504938i
$463$	27.1862			1.26345			0.631725	−	0.775193i	$-0.282347\pi$
$463$	27.1862			1.26345			0.631725	+	0.775193i	$0.282347\pi$
$464$	1.94796	−	3.37397i	0.0904319	−	0.156633i
$465$	12.4240	+	21.5189i	0.576147	+	0.997916i
$466$	5.96422	+	10.3303i	0.276287	+	0.478544i
$467$	20.2473	−	35.0693i	0.936933	−	1.62282i	0.165783	−	0.986162i	$-0.446985\pi$
$467$	20.2473	−	35.0693i	0.936933	−	1.62282i	0.771150	−	0.636654i	$-0.219682\pi$
$468$		−	5.81269i		−	0.268692i
$469$	20.2764	+	6.83381i	0.936276	+	0.315556i
$470$		−	1.43859i		−	0.0663574i
$471$	−4.98990	−	2.88092i	−0.229922	−	0.132746i
$472$	9.23060	−	5.32929i	0.424873	−	0.245301i
$473$	20.0825	+	34.7839i	0.923395	+	1.59937i
$474$	−1.94949	+	3.37662i	−0.0895431	+	0.155093i
$475$	−9.57423			−0.439296
$476$	6.34733	−	1.27691i	0.290930	−	0.0585269i
$477$			3.50851i			0.160644i
$478$	−10.3967	+	18.0075i	−0.475532	+	0.823645i
$479$	−16.6736	−	28.8795i	−0.761835	−	1.31954i	−0.941904	−	0.335883i	$-0.890965\pi$
$479$	−16.6736	−	28.8795i	−0.761835	−	1.31954i	0.180069	−	0.983654i	$-0.442368\pi$
$480$	2.22329	−	1.28362i	0.101479	−	0.0585889i
$481$	32.1650	−	55.7113i	1.46660	−	2.54022i
$482$	8.54652			0.389283
$483$	9.65623	−	8.23148i	0.439374	−	0.374545i
$484$	−7.73896			−0.351771
$485$	−5.95046	+	10.3065i	−0.270197	+	0.467994i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	−10.1369	−	17.5576i	−0.459346	−	0.795611i	0.539580	−	0.841934i	$-0.318583\pi$
$487$	−10.1369	−	17.5576i	−0.459346	−	0.795611i	−0.998926	+	0.0463234i	$0.985250\pi$
$488$	−2.79450	+	4.84021i	−0.126501	+	0.219106i
$489$			8.26551i			0.373779i
$490$	16.5727	−	6.94916i	0.748677	−	0.313931i
$491$	16.9866			0.766593			0.383296	−	0.923625i	$-0.374789\pi$
$491$	16.9866			0.766593			0.383296	+	0.923625i	$0.374789\pi$
$492$	−2.12119	+	3.67401i	−0.0956307	+	0.165637i
$493$	−4.76692	−	8.25655i	−0.214691	−	0.371856i
$494$	30.2986	−	17.4929i	1.36320	−	0.787042i
$495$	−9.62430	−	5.55659i	−0.432580	−	0.249750i
$496$		−	9.67885i		−	0.434593i
$497$	−24.4298	−	27.7351i	−1.09583	−	1.24409i
$498$			0.193800i			0.00868438i
$499$	8.48384	−	14.6944i	0.379789	−	0.657814i	−0.611242	−	0.791443i	$-0.709330\pi$
$499$	8.48384	−	14.6944i	0.379789	−	0.657814i	0.991031	+	0.133630i	$0.0426633\pi$
$500$	−4.37623	−	7.57986i	−0.195711	−	0.338982i
$501$	5.83788	+	10.1115i	0.260817	+	0.451749i
$502$	−0.851226	+	1.47437i	−0.0379921	+	0.0658042i
$503$	−33.6568			−1.50068			−0.750341	−	0.661051i	$-0.770111\pi$
$503$	−33.6568			−1.50068			−0.750341	+	0.661051i	$0.770111\pi$
$504$	−2.59379	+	0.521797i	−0.115536	+	0.0232427i
$505$		−	35.3139i		−	1.57145i
$506$	−17.8085	−	10.6702i	−0.791685	−	0.474348i
$507$	−18.0024	+	10.3937i	−0.799515	+	0.461600i
$508$	−3.53624	−	6.12495i	−0.156895	−	0.271751i
$509$	9.68896	+	5.59392i	0.429455	+	0.247946i	0.699115	−	0.715010i	$-0.253578\pi$
$509$	9.68896	+	5.59392i	0.429455	+	0.247946i	−0.269659	+	0.962956i	$0.586911\pi$
$510$		−	6.28236i		−	0.278188i
$511$	15.5628	+	5.24518i	0.688458	+	0.232033i
$512$	−1.00000			−0.0441942
$513$	−5.21248	−	3.00943i	−0.230137	−	0.132870i
$514$	20.0132	−	11.5546i	0.882744	−	0.509653i
$515$	5.52203	+	9.56444i	0.243330	+	0.421460i
$516$	4.63923	−	8.03537i	0.204231	−	0.353738i
$517$	2.42574			0.106684
$518$	−27.7474	−	9.35178i	−1.21915	−	0.410893i
$519$	−1.88087			−0.0825612
$520$	−12.9233	−	7.46128i	−0.566725	−	0.327199i
$521$	−0.934217	−	1.61811i	−0.0409288	−	0.0708908i	0.844835	−	0.535026i	$-0.179698\pi$
$521$	−0.934217	−	1.61811i	−0.0409288	−	0.0708908i	−0.885764	+	0.464136i	$0.846365\pi$
$522$	1.94796	+	3.37397i	0.0852600	+	0.147675i
$523$	−12.6234	+	21.8644i	−0.551983	+	0.956062i	0.446149	+	0.894959i	$0.352795\pi$
$523$	−12.6234	+	21.8644i	−0.551983	+	0.956062i	−0.998131	+	0.0611033i	$0.980538\pi$
$524$		−	11.5933i		−	0.506454i
$525$	−0.830026	−	4.12595i	−0.0362253	−	0.180071i
$526$			13.4562i			0.586716i
$527$	−20.5122	−	11.8427i	−0.893524	−	0.515876i
$528$	2.16443	+	3.74890i	0.0941945	+	0.163150i
$529$	−10.8485	−	20.2808i	−0.471675	−	0.881772i
$530$	7.80044	+	4.50359i	0.338830	+	0.195623i
$531$			10.6586i			0.462543i
$532$	−10.5257	−	11.9498i	−0.456346	−	0.518088i
$533$	24.6597			1.06813
$534$	0.389754	+	0.225025i	0.0168663	+	0.00973778i
$535$	23.2346	−	13.4145i	1.00452	−	0.579960i
$536$	−7.00382	+	4.04366i	−0.302519	+	0.174659i
$537$	10.7056	+	6.18091i	0.461983	+	0.266726i
$538$		−	3.01196i		−	0.129855i
$539$	11.7176	+	27.9447i	0.504713	+	1.20366i
$540$			2.56724i			0.110476i
$541$	−19.7979	+	34.2910i	−0.851178	+	1.47428i	0.0289680	+	0.999580i	$0.490778\pi$
$541$	−19.7979	+	34.2910i	−0.851178	+	1.47428i	−0.880146	+	0.474703i	$0.842555\pi$
$542$	18.3144	−	10.5738i	0.786671	−	0.454185i
$543$	4.37205	−	2.52421i	0.187623	−	0.108324i
$544$	−1.22357	+	2.11928i	−0.0524599	+	0.0908633i
$545$			8.44330i			0.361671i
$546$	10.1651	+	11.5404i	0.435028	+	0.493885i
$547$	−17.6144			−0.753139			−0.376570	−	0.926388i	$-0.622896\pi$
$547$	−17.6144			−0.753139			−0.376570	+	0.926388i	$0.622896\pi$
$548$	−10.7726	−	6.21957i	−0.460183	−	0.265687i
$549$	−2.79450	−	4.84021i	−0.119266	−	0.206575i
$550$	−5.96339	+	3.44296i	−0.254280	+	0.146808i
$551$	−11.7245	+	20.3075i	−0.499481	+	0.865127i
$552$	−0.0777105	+	4.79520i	−0.00330758	+	0.204097i
$553$	−2.03448	−	10.1131i	−0.0865149	−	0.430054i
$554$	22.3713			0.950464
$555$	−14.2060	+	24.6055i	−0.603011	+	1.04445i
$556$	9.95012	−	5.74471i	0.421979	−	0.243630i
$557$	21.7836	−	12.5768i	0.923000	−	0.532894i	0.0384089	−	0.999262i	$-0.487771\pi$
$557$	21.7836	−	12.5768i	0.923000	−	0.532894i	0.884591	+	0.466368i	$0.154438\pi$
$558$	8.38213	+	4.83943i	0.354844	+	0.204869i
$559$	−53.9328			−2.28111
$560$	−2.16932	+	6.43653i	−0.0916707	+	0.271993i
$561$	10.5933			0.447248
$562$	−14.9526	−	8.63288i	−0.630737	−	0.364156i
$563$	−22.2601	−	38.5556i	−0.938151	−	1.62492i	−0.768917	−	0.639349i	$-0.779204\pi$
$563$	−22.2601	−	38.5556i	−0.938151	−	1.62492i	−0.169234	−	0.985576i	$-0.554129\pi$
$564$	−0.280183	−	0.485292i	−0.0117978	−	0.0204345i
$565$	24.1450	+	13.9401i	1.01579	+	0.586465i
$566$	−13.1076			−0.550952
$567$	0.845003	−	2.50718i	0.0354868	−	0.105292i
$568$	13.9696			0.586151
$569$	22.5541	+	13.0216i	0.945517	+	0.545894i	0.891685	−	0.452656i	$-0.149523\pi$
$569$	22.5541	+	13.0216i	0.945517	+	0.545894i	0.0538315	+	0.998550i	$0.482857\pi$
$570$	−13.3817	+	7.72592i	−0.560497	+	0.323603i
$571$	16.5603	−	9.56112i	0.693029	−	0.400121i	−0.111717	−	0.993740i	$-0.535635\pi$
$571$	16.5603	−	9.56112i	0.693029	−	0.400121i	0.804746	+	0.593620i	$0.202302\pi$
$572$	12.5811	−	21.7912i	0.526044	−	0.911135i
$573$	−0.545170			−0.0227748
$574$	−2.21366	−	11.0038i	−0.0923965	−	0.459291i
$575$	−7.62775	−	0.123614i	−0.318099	−	0.00515508i
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$	−13.1023	+	7.56462i	−0.545456	+	0.314919i	−0.747287	−	0.664501i	$-0.768644\pi$
$577$	−13.1023	+	7.56462i	−0.545456	+	0.314919i	0.201831	+	0.979420i	$0.435311\pi$
$578$	−5.50578	−	9.53628i	−0.229010	−	0.396657i
$579$	−18.4395	−	10.6461i	−0.766321	−	0.442435i
$580$	10.0018			0.415301
$581$	−0.338914	−	0.384768i	−0.0140605	−	0.0159628i
$582$			4.63569i			0.192156i
$583$	−7.59391	+	13.1530i	−0.314508	+	0.544743i
$584$	−5.37567	+	3.10364i	−0.222447	+	0.128430i
$585$	12.9233	−	7.46128i	0.534313	−	0.308486i
$586$	8.63087	−	14.9491i	0.356538	−	0.617542i
$587$		−	9.12775i		−	0.376743i	−0.982098	−	0.188371i	$-0.939679\pi$
$587$		−	9.12775i		−	0.376743i	0.982098	−	0.188371i	$-0.0603209\pi$
$588$	4.23716	−	5.57194i	0.174737	−	0.229783i
$589$			58.2557i			2.40038i
$590$	23.6971	+	13.6816i	0.975596	+	0.563261i
$591$	−1.04669	+	0.604307i	−0.0430551	+	0.0248579i
$592$	9.58443	−	5.53357i	0.393918	−	0.227428i
$593$	−11.7403	−	6.77828i	−0.482117	−	0.278351i	0.239181	−	0.970975i	$-0.423121\pi$
$593$	−11.7403	−	6.77828i	−0.482117	−	0.278351i	−0.721298	+	0.692624i	$0.756454\pi$
$594$	−4.32885			−0.177615
$595$	10.9865	+	12.4729i	0.450402	+	0.511340i
$596$			16.2367i			0.665081i
$597$	1.67580	+	0.967524i	0.0685859	+	0.0395981i
$598$	24.3646	−	13.5453i	0.996343	−	0.553910i
$599$	−1.18590	−	2.05404i	−0.0484547	−	0.0839260i	0.840781	−	0.541376i	$-0.182096\pi$
$599$	−1.18590	−	2.05404i	−0.0484547	−	0.0839260i	−0.889236	+	0.457450i	$0.848763\pi$
$600$	1.37759	+	0.795352i	0.0562399	+	0.0324701i
$601$			0.795513i			0.0324497i	0.999868	+	0.0162248i	$0.00516475\pi$
$601$			0.795513i			0.0324497i	−0.999868	+	0.0162248i	$0.994835\pi$
$602$	4.84147	+	24.0663i	0.197324	+	0.980870i
$603$		−	8.08732i		−	0.329341i
$604$	−8.06432	+	13.9678i	−0.328132	+	0.568342i
$605$	−9.93387	−	17.2060i	−0.403869	−	0.699522i
$606$	−6.87781	−	11.9127i	−0.279392	−	0.483921i
$607$	20.6098	+	11.8990i	0.836524	+	0.482967i	0.856081	−	0.516841i	$-0.172892\pi$
$607$	20.6098	+	11.8990i	0.836524	+	0.482967i	−0.0195571	+	0.999809i	$0.506226\pi$
$608$	6.01886			0.244097
$609$	−9.76780	−	3.29207i	−0.395811	−	0.133401i
$610$	−14.3483			−0.580944
$611$	−1.62862	+	2.82085i	−0.0658869	+	0.114119i
$612$	−1.22357	−	2.11928i	−0.0494597	−	0.0856667i
$613$	−12.6007	+	7.27504i	−0.508939	+	0.293836i	−0.732397	−	0.680877i	$-0.761599\pi$
$613$	−12.6007	+	7.27504i	−0.508939	+	0.293836i	0.223458	+	0.974713i	$0.428265\pi$
$614$	11.0214	+	6.36321i	0.444788	+	0.256798i
$615$	−10.8912			−0.439176
$616$	−10.8532	−	3.65789i	−0.437289	−	0.147381i
$617$		−	17.9658i		−	0.723276i	−0.932319	−	0.361638i	$-0.882218\pi$
$617$		−	17.9658i		−	0.723276i	0.932319	−	0.361638i	$-0.117782\pi$
$618$	3.72558	+	2.15096i	0.149865	+	0.0865244i
$619$	16.6671	+	28.8683i	0.669909	+	1.16032i	0.977929	+	0.208937i	$0.0670003\pi$
$619$	16.6671	+	28.8683i	0.669909	+	1.16032i	−0.308020	+	0.951380i	$0.599666\pi$
$620$	21.5189	−	12.4240i	0.864221	−	0.498958i
$621$	−4.11391	−	2.46490i	−0.165086	−	0.0989130i
$622$		−	26.1986i		−	1.05047i
$623$	−1.16733	+	0.234835i	−0.0467682	+	0.00940846i
$624$	−5.81269			−0.232694
$625$	15.2116	−	26.3472i	0.608464	−	1.05389i
$626$	−11.4870	−	19.8960i	−0.459111	−	0.795204i
$627$	−13.0274	−	22.5641i	−0.520263	−	0.901122i
$628$	−2.88092	+	4.98990i	−0.114961	+	0.199119i
$629$		−	27.0827i		−	1.07986i
$630$	−4.48954	−	5.09696i	−0.178868	−	0.203068i
$631$			9.21018i			0.366652i	0.983052	+	0.183326i	$0.0586863\pi$
$631$			9.21018i			0.366652i	−0.983052	+	0.183326i	$0.941314\pi$
$632$	3.37662	+	1.94949i	0.134315	+	0.0775466i
$633$	−1.12458	+	0.649278i	−0.0446981	+	0.0258065i
$634$	−3.78659	−	6.55856i	−0.150385	−	0.260474i
$635$	9.07837	−	15.7242i	0.360264	−	0.623996i
$636$	3.50851			0.139121
$637$	−40.3634	−	5.13561i	−1.59926	−	0.203480i
$638$			16.8649i			0.667687i
$639$	−6.98480	+	12.0980i	−0.276314	+	0.478591i
$640$	−1.28362	−	2.22329i	−0.0507395	−	0.0878833i
$641$	35.8087	−	20.6742i	1.41436	−	0.816580i	0.418563	−	0.908188i	$-0.362534\pi$
$641$	35.8087	−	20.6742i	1.41436	−	0.816580i	0.995795	+	0.0916075i	$0.0292005\pi$
$642$	5.22527	−	9.05044i	0.206225	−	0.357192i
$643$	−35.3150			−1.39269			−0.696343	−	0.717709i	$-0.745191\pi$
$643$	−35.3150			−1.39269			−0.696343	+	0.717709i	$0.745191\pi$
$644$	−8.23148	−	9.65623i	−0.324366	−	0.380509i
$645$	23.8200			0.937911
$646$	7.36447	−	12.7556i	0.289751	−	0.501863i
$647$	15.3044	−	8.83602i	0.601679	−	0.347380i	−0.168023	−	0.985783i	$-0.553738\pi$
$647$	15.3044	−	8.83602i	0.601679	−	0.347380i	0.769702	+	0.638403i	$0.220405\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−23.0697	+	39.9579i	−0.905566	+	1.56849i
$650$		−	9.24628i		−	0.362669i
$651$	−25.1049	+	5.05040i	−0.983938	+	0.197941i
$652$	8.26551			0.323702
$653$	3.42670	−	5.93521i	0.134097	−	0.232263i	−0.791155	−	0.611616i	$-0.790520\pi$
$653$	3.42670	−	5.93521i	0.134097	−	0.232263i	0.925252	+	0.379353i	$0.123853\pi$
$654$	1.64443	+	2.84824i	0.0643024	+	0.111375i
$655$	25.7752	−	14.8813i	1.00712	−	0.581462i
$656$	3.67401	+	2.12119i	0.143446	+	0.0828186i
$657$		−	6.20729i		−	0.242169i
$658$	1.40494	+	0.473512i	0.0547704	+	0.0184594i
$659$		−	22.6044i		−	0.880541i	−0.897865	−	0.440270i	$-0.854883\pi$
$659$		−	22.6044i		−	0.880541i	0.897865	−	0.440270i	$-0.145117\pi$
$660$	−5.55659	+	9.62430i	−0.216290	+	0.374625i
$661$	9.88411	+	17.1198i	0.384447	+	0.665882i	0.991692	−	0.128633i	$-0.0410588\pi$
$661$	9.88411	+	17.1198i	0.384447	+	0.665882i	−0.607245	+	0.794514i	$0.707725\pi$
$662$	15.0498	+	26.0670i	0.584926	+	1.01312i
$663$	−7.11221	+	12.3187i	−0.276215	+	0.478419i
$664$	0.193800			0.00752089
$665$	13.0569	−	38.7406i	0.506323	−	1.50230i
$666$			11.0671i			0.428843i
$667$	−9.60307	+	16.0275i	−0.371832	+	0.620587i
$668$	10.1115	−	5.83788i	0.391226	−	0.225874i
$669$	−1.91772	−	3.32159i	−0.0741434	−	0.128420i
$670$	−17.9805	−	10.3810i	−0.694646	−	0.401054i
$671$		−	24.1939i		−	0.933996i
$672$	0.521797	+	2.59379i	0.0201288	+	0.100057i
$673$	44.9198			1.73153			0.865765	−	0.500450i	$-0.166832\pi$
$673$	44.9198			1.73153			0.865765	+	0.500450i	$0.166832\pi$
$674$	−30.8880	−	17.8332i	−1.18976	−	0.686910i
$675$	−1.37759	+	0.795352i	−0.0530235	+	0.0306131i
$676$	10.3937	+	18.0024i	0.399758	+	0.692401i
$677$	7.96502	−	13.7958i	0.306121	−	0.530217i	−0.671389	−	0.741105i	$-0.734302\pi$
$677$	7.96502	−	13.7958i	0.306121	−	0.530217i	0.977510	+	0.210888i	$0.0676355\pi$
$678$	10.8600			0.417077
$679$	−8.10682	−	9.20364i	−0.311111	−	0.353203i
$680$	−6.28236			−0.240918
$681$	23.0406	+	13.3025i	0.882918	+	0.509753i
$682$	20.9492	+	36.2850i	0.802185	+	1.38942i
$683$	6.89284	+	11.9387i	0.263747	+	0.456823i	0.967235	−	0.253884i	$-0.0817082\pi$
$683$	6.89284	+	11.9387i	0.263747	+	0.456823i	−0.703487	+	0.710708i	$0.748375\pi$
$684$	−3.00943	+	5.21248i	−0.115068	+	0.199304i
$685$		−	31.9342i		−	1.22014i
$686$	1.33172	+	18.4723i	0.0508452	+	0.705276i
$687$			10.5739i			0.403419i
$688$	−8.03537	−	4.63923i	−0.306346	−	0.176869i
$689$	−10.1969	−	17.6616i	−0.388473	−	0.672854i
$690$	−10.7609	+	5.98244i	−0.409660	+	0.227747i
$691$	−8.29434	−	4.78874i	−0.315531	−	0.182172i	0.333868	−	0.942620i	$-0.391646\pi$
$691$	−8.29434	−	4.78874i	−0.315531	−	0.182172i	−0.649399	+	0.760448i	$0.724979\pi$
$692$			1.88087i			0.0715001i
$693$	8.59444	−	7.57022i	0.326476	−	0.287569i
$694$	−29.5495			−1.12168
$695$	25.5443	+	14.7480i	0.968951	+	0.559424i
$696$	3.37397	−	1.94796i	0.127890	−	0.0738374i
$697$	8.99078	−	5.19083i	0.340550	−	0.196617i
$698$	24.3015	+	14.0305i	0.919825	+	0.531061i
$699$			11.9284i			0.451175i
$700$	−4.12595	+	0.830026i	−0.155946	+	0.0313720i
$701$			25.5339i			0.964402i	0.876061	+	0.482201i	$0.160163\pi$
$701$			25.5339i			0.964402i	−0.876061	+	0.482201i	$0.839837\pi$
$702$	2.90635	−	5.03394i	0.109693	−	0.189994i
$703$	−57.6873	+	33.3058i	−2.17572	+	1.25615i
$704$	3.74890	−	2.16443i	0.141292	−	0.0815749i
$705$	0.719297	−	1.24586i	0.0270903	−	0.0469218i
$706$			18.7265i			0.704782i
$707$	34.4878	+	11.6235i	1.29705	+	0.437148i
$708$	10.6586			0.400574
$709$	−40.9375	−	23.6353i	−1.53744	−	0.887641i	−0.998988	−	0.0449846i	$-0.985676\pi$
$709$	−40.9375	−	23.6353i	−1.53744	−	0.887641i	−0.538452	−	0.842656i	$-0.680991\pi$
$710$	17.9316	+	31.0585i	0.672962	+	1.16561i
$711$	−3.37662	+	1.94949i	−0.126633	+	0.0731117i
$712$	0.225025	−	0.389754i	0.00843316	−	0.0146067i
$713$	−0.752148	+	46.4121i	−0.0281682	+	1.73815i
$714$	6.13540	+	2.06783i	0.229612	+	0.0773867i
$715$	64.5975			2.41581
$716$	6.18091	−	10.7056i	0.230991	−	0.400089i
$717$	−18.0075	+	10.3967i	−0.672503	+	0.388270i
$718$	−32.1802	+	18.5793i	−1.20096	+	0.693372i
$719$	−18.0867	−	10.4423i	−0.674519	−	0.389434i	0.123268	−	0.992373i	$-0.460663\pi$
$719$	−18.0867	−	10.4423i	−0.674519	−	0.389434i	−0.797787	+	0.602940i	$0.793996\pi$
$720$	2.56724			0.0956753
$721$	−11.1583	+	2.24473i	−0.415556	+	0.0835983i
$722$	−17.2267			−0.641110
$723$	7.40151	+	4.27326i	0.275265	+	0.158924i
$724$	−2.52421	−	4.37205i	−0.0938114	−	0.162486i
$725$	3.09863	+	5.36699i	0.115080	+	0.199325i
$726$	−6.70213	−	3.86948i	−0.248740	−	0.143610i
$727$	27.4239			1.01710			0.508549	−	0.861033i	$-0.330182\pi$
$727$	27.4239			1.01710			0.508549	+	0.861033i	$0.330182\pi$
$728$	11.5404	−	10.1651i	0.427717	−	0.376745i
$729$	−1.00000			−0.0370370
$730$	−13.8006	−	7.96779i	−0.510784	−	0.294901i
$731$	−19.6636	+	11.3528i	−0.727285	+	0.419898i
$732$	−4.84021	+	2.79450i	−0.178899	+	0.103288i
$733$	−1.17386	+	2.03318i	−0.0433575	+	0.0750973i	−0.886890	−	0.461981i	$-0.847139\pi$
$733$	−1.17386	+	2.03318i	−0.0433575	+	0.0750973i	0.843532	+	0.537078i	$0.180472\pi$
$734$	−16.9288			−0.624855
$735$	17.8269	+	2.26820i	0.657557	+	0.0836637i
$736$	4.79520	+	0.0777105i	0.176753	+	0.00286445i
$737$	17.5044	−	30.3185i	0.644783	−	1.11680i
$738$	−3.67401	+	2.12119i	−0.135242	+	0.0780821i
$739$	−3.56792	−	6.17982i	−0.131248	−	0.227328i	0.792910	−	0.609339i	$-0.208565\pi$
$739$	−3.56792	−	6.17982i	−0.131248	−	0.227328i	−0.924158	+	0.382011i	$0.875232\pi$
$740$	24.6055	+	14.2060i	0.904516	+	0.522223i
$741$	34.9858			1.28523
$742$	−6.96575	+	6.13562i	−0.255721	+	0.225246i
$743$			26.2939i			0.964630i	0.875998	+	0.482315i	$0.160204\pi$
$743$			26.2939i			0.964630i	−0.875998	+	0.482315i	$0.839796\pi$
$744$	4.83943	−	8.38213i	0.177422	−	0.307304i
$745$	−36.0989	+	20.8417i	−1.32256	+	0.763582i
$746$	−5.49398	+	3.17195i	−0.201149	+	0.116133i
$747$	−0.0968999	+	0.167836i	−0.00354538	+	0.00614078i
$748$		−	10.5933i		−	0.387328i
$749$	5.45307	+	27.1065i	0.199251	+	0.990449i
$750$		−	8.75247i		−	0.319595i
$751$	44.0167	+	25.4130i	1.60619	+	0.927335i	0.990212	+	0.139572i	$0.0445727\pi$
$751$	44.0167	+	25.4130i	1.60619	+	0.927335i	0.615979	+	0.787763i	$0.288761\pi$
$752$	−0.485292	+	0.280183i	−0.0176968	+	0.0102172i
$753$	−1.47437	+	0.851226i	−0.0537289	+	0.0310204i
$754$	−19.6119	−	11.3229i	−0.714222	−	0.412356i
$755$	−41.4060			−1.50692
$756$	−2.50718	−	0.845003i	−0.0911854	−	0.0307325i
$757$		−	27.7521i		−	1.00867i	−0.863509	−	0.504333i	$-0.831738\pi$
$757$		−	27.7521i		−	1.00867i	0.863509	−	0.504333i	$-0.168262\pi$
$758$	25.1711	+	14.5326i	0.914257	+	0.527846i
$759$	−10.0875	−	18.1449i	−0.366154	−	0.658618i
$760$	7.72592	+	13.3817i	0.280248	+	0.485405i
$761$	−17.3853	−	10.0374i	−0.630215	−	0.363855i	0.150620	−	0.988592i	$-0.451873\pi$
$761$	−17.3853	−	10.0374i	−0.630215	−	0.363855i	−0.780835	+	0.624737i	$0.785206\pi$
$762$		−	7.07248i		−	0.256209i
$763$	−8.24579	−	2.77910i	−0.298518	−	0.100610i
$764$			0.545170i			0.0197236i
$765$	3.14118	−	5.44069i	0.113570	−	0.196708i
$766$	−4.80504	−	8.32257i	−0.173613	−	0.300707i
$767$	−30.9775	−	53.6547i	−1.11853	−	1.93736i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	27.8086			1.00280			0.501402	−	0.865214i	$-0.332818\pi$
$769$	27.8086			1.00280			0.501402	+	0.865214i	$0.332818\pi$
$770$	−5.79883	−	28.8252i	−0.208975	−	1.03879i
$771$	23.1093			0.832259
$772$	−10.6461	+	18.4395i	−0.383160	+	0.663653i
$773$	0.192942	+	0.334185i	0.00693963	+	0.0120198i	0.869474	−	0.493978i	$-0.164458\pi$
$773$	0.192942	+	0.334185i	0.00693963	+	0.0120198i	−0.862535	+	0.505998i	$0.831124\pi$
$774$	8.03537	−	4.63923i	0.288826	−	0.166754i
$775$	13.3335	+	7.69810i	0.478953	+	0.276524i
$776$	4.63569			0.166412
$777$	−19.3540	−	21.9726i	−0.694322	−	0.788261i
$778$		−	0.247677i		−	0.00887965i
$779$	−22.1134	−	12.7671i	−0.792293	−	0.457431i
$780$	−7.46128	−	12.9233i	−0.267157	−	0.462729i
$781$	−52.3706	+	30.2362i	−1.87397	+	1.08194i
$782$	6.03193	−	10.0673i	0.215701	−	0.360005i
$783$			3.89593i			0.139229i
$784$	−5.57194	−	4.23716i	−0.198998	−	0.151327i
$785$	−14.7920			−0.527949
$786$	5.79663	−	10.0401i	0.206759	−	0.358117i
$787$	24.3827	+	42.2320i	0.869148	+	1.50541i	0.862869	+	0.505428i	$0.168665\pi$
$787$	24.3827	+	42.2320i	0.869148	+	1.50541i	0.00627880	+	0.999980i	$0.498001\pi$
$788$	0.604307	+	1.04669i	0.0215275	+	0.0372868i
$789$	−6.72808	+	11.6534i	−0.239526	+	0.414871i
$790$			10.0096i			0.356126i
$791$	−21.5613	+	18.9918i	−0.766633	+	0.675271i
$792$			4.32885i			0.153819i
$793$	28.1346	+	16.2435i	0.999090	+	0.576825i
$794$	−11.4352	+	6.60211i	−0.405820	+	0.234300i
$795$	4.50359	+	7.80044i	0.159726	+	0.276653i
$796$	0.967524	−	1.67580i	0.0342930	−	0.0593972i
$797$	30.3242			1.07414			0.537069	−	0.843538i	$-0.319531\pi$
$797$	30.3242			1.07414			0.537069	+	0.843538i	$0.319531\pi$
$798$	−3.14062	−	15.6116i	−0.111177	−	0.552646i
$799$			1.37129i			0.0485128i
$800$	0.795352	−	1.37759i	0.0281200	−	0.0487052i
$801$	0.225025	+	0.389754i	0.00795086	+	0.0137713i
$802$	−4.03620	+	2.33030i	−0.142523	+	0.0822857i
$803$	13.4352	−	23.2705i	0.474118	−	0.821197i
$804$	−8.08732			−0.285218
$805$	10.9025	−	30.6959i	0.384264	−	1.08189i
$806$	−56.2602			−1.98168
$807$	1.50598	−	2.60844i	0.0530131	−	0.0918213i
$808$	−11.9127	+	6.87781i	−0.419088	+	0.241960i
$809$	−7.38075	−	12.7838i	−0.259493	−	0.449456i	0.706613	−	0.707600i	$-0.250222\pi$
$809$	−7.38075	−	12.7838i	−0.259493	−	0.449456i	−0.966106	+	0.258145i	$0.916889\pi$
$810$	−1.28362	+	2.22329i	−0.0451018	+	0.0781185i
$811$			25.7948i			0.905776i	0.891567	+	0.452888i	$0.149606\pi$
$811$			25.7948i			0.905776i	−0.891567	+	0.452888i	$0.850394\pi$
$812$	−3.29207	+	9.76780i	−0.115529	+	0.342783i
$813$	21.1477			0.741681
$814$	−23.9540	+	41.4896i	−0.839588	+	1.45421i
$815$	10.6098	+	18.3767i	0.371644	+	0.643706i
$816$	−2.11928	+	1.22357i	−0.0741895	+	0.0428333i
$817$	48.3638	+	27.9228i	1.69203	+	0.976897i
$818$			15.1008i			0.527986i
$819$	3.03305	+	15.0769i	0.105983	+	0.526829i
$820$			10.8912i			0.380337i
$821$	2.54607	−	4.40991i	0.0888583	−	0.153907i	−0.818171	−	0.574976i	$-0.805012\pi$
$821$	2.54607	−	4.40991i	0.0888583	−	0.153907i	0.907029	+	0.421069i	$0.138345\pi$
$822$	−6.21957	−	10.7726i	−0.216932	−	0.375738i
$823$	22.0765	+	38.2375i	0.769537	+	1.33288i	0.937814	+	0.347137i	$0.112846\pi$
$823$	22.0765	+	38.2375i	0.769537	+	1.33288i	−0.168277	+	0.985740i	$0.553820\pi$
$824$	2.15096	−	3.72558i	0.0749324	−	0.129787i
$825$	−6.88592			−0.239737
$826$	−21.1614	+	18.6395i	−0.736299	+	0.648553i
$827$		−	12.1060i		−	0.420966i	−0.977598	−	0.210483i	$-0.932496\pi$
$827$		−	12.1060i		−	0.420966i	0.977598	−	0.210483i	$-0.0675037\pi$
$828$	−2.46490	+	4.11391i	−0.0856612	+	0.142968i
$829$	22.9977	−	13.2777i	0.798742	−	0.461154i	−0.0442889	−	0.999019i	$-0.514102\pi$
$829$	22.9977	−	13.2777i	0.798742	−	0.461154i	0.843031	+	0.537865i	$0.180769\pi$
$830$	0.248765	+	0.430874i	0.00863476	+	0.0149558i
$831$	19.3741	+	11.1856i	0.672080	+	0.388025i
$832$			5.81269i			0.201519i
$833$	−15.7973	+	6.62404i	−0.547345	+	0.229510i
$834$	11.4894			0.397846
$835$	25.9586	+	14.9872i	0.898336	+	0.518654i
$836$	−22.5641	+	13.0274i	−0.780395	+	0.450561i
$837$	4.83943	+	8.38213i	0.167275	+	0.289729i
$838$	15.3275	−	26.5479i	0.529478	−	0.917083i
$839$	0.141059			0.00486988			0.00243494	−	0.999997i	$-0.499225\pi$
$839$	0.141059			0.00486988			0.00243494	+	0.999997i	$0.499225\pi$
$840$	−5.09696	+	4.48954i	−0.175862	+	0.154904i
$841$	−13.8218			−0.476612
$842$	−29.9309	−	17.2806i	−1.03149	−	0.595530i
$843$	−8.63288	−	14.9526i	−0.297332	−	0.514995i
$844$	0.649278	+	1.12458i	0.0223491	+	0.0387097i
$845$	−26.6831	+	46.2165i	−0.917926	+	1.58989i
$846$		−	0.560367i		−	0.0192658i
$847$	20.0732	−	4.03817i	0.689723	−	0.138753i
$848$		−	3.50851i		−	0.120483i
$849$	−11.3515	−	6.55378i	−0.389582	−	0.224925i
$850$	−1.94633	−	3.37114i	−0.0667586	−	0.115629i
$851$	−46.3893	+	25.7898i	−1.59020	+	0.884063i
$852$	12.0980	+	6.98480i	0.414472	+	0.239295i
$853$			6.14032i			0.210241i	0.994460	+	0.105120i	$0.0335228\pi$
$853$			6.14032i			0.210241i	−0.994460	+	0.105120i	$0.966477\pi$
$854$	4.72272	−	14.0126i	0.161608	−	0.479502i
$855$	−15.4518			−0.528442
$856$	−9.05044	−	5.22527i	−0.309338	−	0.178596i
$857$	8.72321	−	5.03635i	0.297979	−	0.172038i	−0.343556	−	0.939132i	$-0.611631\pi$
$857$	8.72321	−	5.03635i	0.297979	−	0.172038i	0.641535	+	0.767094i	$0.278298\pi$
$858$	21.7912	−	12.5811i	0.743939	−	0.429513i
$859$	−26.3839	−	15.2328i	−0.900208	−	0.519735i	−0.0229403	−	0.999737i	$-0.507303\pi$
$859$	−26.3839	−	15.2328i	−0.900208	−	0.519735i	−0.877268	+	0.480002i	$0.840636\pi$
$860$		−	23.8200i		−	0.812255i
$861$	3.58483	−	10.6364i	0.122171	−	0.362489i
$862$			11.2866i			0.384422i
$863$	−6.10187	+	10.5687i	−0.207710	+	0.359764i	−0.950993	−	0.309213i	$-0.899934\pi$
$863$	−6.10187	+	10.5687i	−0.207710	+	0.359764i	0.743283	+	0.668977i	$0.233268\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$	−4.18173	+	2.41432i	−0.142183	+	0.0820894i
$866$	−13.2839	+	23.0083i	−0.451404	+	0.781855i
$867$		−	11.0116i		−	0.373972i
$868$	5.05040	+	25.1049i	0.171422	+	0.852115i
$869$	−16.8781			−0.572551
$870$	8.66178	+	5.00088i	0.293662	+	0.169546i
$871$	23.5045	+	40.7111i	0.796421	+	1.37944i
$872$	2.84824	−	1.64443i	0.0964536	−	0.0556875i
$873$	−2.31785	+	4.01463i	−0.0784472	+	0.135875i
$874$	−28.8616	−	0.467728i	−0.976260	−	0.0158211i
$875$	15.3062	+	17.3770i	0.517443	+	0.587451i
$876$	−6.20729			−0.209725
$877$	18.8387	−	32.6296i	0.636138	−	1.10182i	−0.350134	−	0.936699i	$-0.613864\pi$
$877$	18.8387	−	32.6296i	0.636138	−	1.10182i	0.986273	−	0.165124i	$-0.0528025\pi$
$878$	21.8889	−	12.6376i	0.738716	−	0.426498i
$879$	14.9491	−	8.63087i	0.504221	−	0.291112i
$880$	9.62430	+	5.55659i	0.324435	+	0.187313i
$881$	−2.20717			−0.0743616			−0.0371808	−	0.999309i	$-0.511838\pi$
$881$	−2.20717			−0.0743616			−0.0371808	+	0.999309i	$0.511838\pi$
$882$	6.45545	−	2.70686i	0.217366	−	0.0911448i
$883$	−0.166875			−0.00561579			−0.00280790	−	0.999996i	$-0.500894\pi$
$883$	−0.166875			−0.00561579			−0.00280790	+	0.999996i	$0.500894\pi$
$884$	12.3187	+	7.11221i	0.414323	+	0.239209i
$885$	13.6816	+	23.6971i	0.459900	+	0.796571i
$886$	9.91152	+	17.1673i	0.332984	+	0.576745i
$887$	23.2555	+	13.4266i	0.780844	+	0.450820i	0.836729	−	0.547617i	$-0.184465\pi$
$887$	23.2555	+	13.4266i	0.780844	+	0.450820i	−0.0558855	+	0.998437i	$0.517798\pi$
$888$	11.0671			0.371389
$889$	12.3682	+	14.0416i	0.414817	+	0.470941i
$890$	1.15538			0.0387286
$891$	−3.74890	−	2.16443i	−0.125593	−	0.0725110i
$892$	−3.32159	+	1.91772i	−0.111215	+	0.0642100i
$893$	2.92090	−	1.68638i	0.0977443	−	0.0564327i
$894$	−8.11835	+	14.0614i	−0.271518	+	0.470283i
$895$	31.7357			1.06081
$896$	2.59379	−	0.521797i	0.0866523	−	0.0174320i
$897$	27.8730	+	0.451707i	0.930654	+	0.0150821i
$898$	−2.22938	+	3.86140i	−0.0743954	+	0.128857i
$899$	32.6562	−	18.8541i	1.08914	−	0.628818i
$900$	0.795352	+	1.37759i	0.0265117	+	0.0459197i
$901$	−7.43550	−	4.29289i	−0.247713	−	0.143017i
$902$	−18.3646			−0.611476
$903$	−7.84032	+	23.2628i	−0.260910	+	0.774137i
$904$		−	10.8600i		−	0.361199i
$905$	6.48023	−	11.2241i	0.215410	−	0.373101i
$906$	−13.9678	+	8.06432i	−0.464049	+	0.267919i
$907$	−27.1839	+	15.6946i	−0.902627	+	0.521132i	−0.878052	−	0.478566i	$-0.841157\pi$
$907$	−27.1839	+	15.6946i	−0.902627	+	0.521132i	−0.0245754	+	0.999698i	$0.507823\pi$
$908$	13.3025	−	23.0406i	0.441459	−	0.764630i
$909$		−	13.7556i		−	0.456245i
$910$	37.4136	+	12.6096i	1.24025	+	0.418005i
$911$		−	23.0351i		−	0.763187i	−0.924330	−	0.381593i	$-0.875375\pi$
$911$		−	23.0351i		−	0.763187i	0.924330	−	0.381593i	$-0.124625\pi$
$912$	5.21248	+	3.00943i	0.172603	+	0.0996522i
$913$	−0.726535	+	0.419465i	−0.0240448	+	0.0138823i
$914$	6.38519	−	3.68649i	0.211203	−	0.121938i
$915$	−12.4260	−	7.17413i	−0.410790	−	0.237169i
$916$	10.5739			0.349371
$917$	6.04934	+	30.0705i	0.199767	+	0.993014i
$918$		−	2.44713i		−	0.0807673i
$919$	−26.6251	−	15.3720i	−0.878282	−	0.507076i	−0.00819045	−	0.999966i	$-0.502607\pi$
$919$	−26.6251	−	15.3720i	−0.878282	−	0.507076i	−0.870092	+	0.492890i	$0.835940\pi$
$920$	5.98244	+	10.7609i	0.197235	+	0.354776i
$921$	6.36321	+	11.0214i	0.209675	+	0.363168i
$922$	−34.7884	−	20.0851i	−1.14570	−	0.661468i
$923$		−	81.2010i		−	2.67276i
$924$	−7.57022	−	8.59444i	−0.249042	−	0.282736i
$925$			17.6046i			0.578834i
$926$	13.5931	−	23.5439i	0.446697	−	0.773702i
$927$	2.15096	+	3.72558i	0.0706469	+	0.122364i
$928$	−1.94796	−	3.37397i	−0.0639450	−	0.110756i
$929$	7.61105	+	4.39424i	0.249710	+	0.144170i	0.619632	−	0.784893i	$-0.287282\pi$
$929$	7.61105	+	4.39424i	0.249710	+	0.144170i	−0.369921	+	0.929063i	$0.620615\pi$
$930$	24.8479			0.814795
$931$	33.5367	+	25.5028i	1.09912	+	0.835822i
$932$	11.9284			0.390729
$933$	13.0993	−	22.6887i	0.428853	−	0.742794i
$934$	−20.2473	−	35.0693i	−0.662512	−	1.14750i
$935$	23.5519	−	13.5977i	0.770230	−	0.444693i
$936$	−5.03394	−	2.90635i	−0.164539	−	0.0949969i
$937$	6.83067			0.223148			0.111574	−	0.993756i	$-0.464411\pi$
$937$	6.83067			0.223148			0.111574	+	0.993756i	$0.464411\pi$
$938$	16.0564	−	14.1430i	0.524261	−	0.461784i
$939$		−	22.9739i		−	0.749725i
$940$	−1.24586	−	0.719297i	−0.0406354	−	0.0234609i
$941$	8.68699	+	15.0463i	0.283188	+	0.490495i	0.972168	−	0.234285i	$-0.0752747\pi$
$941$	8.68699	+	15.0463i	0.283188	+	0.490495i	−0.688980	+	0.724780i	$0.741941\pi$
$942$	−4.98990	+	2.88092i	−0.162580	+	0.0938654i
$943$	−17.4528	−	10.4570i	−0.568341	−	0.340528i
$944$		−	10.6586i		−	0.346907i
$945$	−1.33958	−	6.65886i	−0.0435765	−	0.216613i
$946$	40.1650			1.30588
$947$	−7.98102	+	13.8235i	−0.259348	+	0.449204i	−0.966067	−	0.258290i	$-0.916841\pi$
$947$	−7.98102	+	13.8235i	−0.259348	+	0.449204i	0.706719	+	0.707494i	$0.250174\pi$
$948$	1.94949	+	3.37662i	0.0633166	+	0.109667i
$949$	18.0405	+	31.2471i	0.585620	+	1.01432i
$950$	−4.78711	+	8.29152i	−0.155314	+	0.269013i
$951$		−	7.57317i		−	0.245577i
$952$	2.06783	−	6.13540i	0.0670189	−	0.198850i
$953$			22.2764i			0.721605i	0.932642	+	0.360802i	$0.117497\pi$
$953$			22.2764i			0.721605i	−0.932642	+	0.360802i	$0.882503\pi$
$954$	3.03846	+	1.75425i	0.0983737	+	0.0567961i
$955$	−1.21207	+	0.699791i	−0.0392218	+	0.0226447i
$956$	10.3967	+	18.0075i	0.336252	+	0.582405i
$957$	−8.43244	+	14.6054i	−0.272582	+	0.472126i
$958$	−33.3471			−1.07740
$959$	31.1872	+	10.5111i	1.00709	+	0.339422i
$960$		−	2.56724i		−	0.0828572i
$961$	31.3401	−	54.2827i	1.01097	−	1.75105i
$962$	−32.1650	−	55.7113i	−1.03704	−	1.79621i
$963$	9.05044	−	5.22527i	0.291646	−	0.168382i
$964$	4.27326	−	7.40151i	0.137632	−	0.238386i
$965$	−54.6619			−1.75963
$966$	−2.30056	−	12.4783i	−0.0740193	−	0.401482i
$967$	17.2064			0.553322			0.276661	−	0.960968i	$-0.410772\pi$
$967$	17.2064			0.553322			0.276661	+	0.960968i	$0.410772\pi$
$968$	−3.86948	+	6.70213i	−0.124370	+	0.215415i
$969$	12.7556	−	7.36447i	0.409770	−	0.236581i
$970$	5.95046	+	10.3065i	0.191058	+	0.330922i
$971$	10.4260	−	18.0584i	0.334588	−	0.579523i	−0.648818	−	0.760944i	$-0.724736\pi$
$971$	10.4260	−	18.0584i	0.334588	−	0.579523i	0.983406	+	0.181421i	$0.0580696\pi$
$972$			1.00000i			0.0320750i
$973$	−22.8109	+	20.0925i	−0.731284	+	0.644136i
$974$	−20.2738			−0.649613
$975$	4.62314	−	8.00751i	0.148059	−	0.256446i
$976$	2.79450	+	4.84021i	0.0894496	+	0.154931i
$977$	−28.1832	+	16.2716i	−0.901660	+	0.520574i	−0.877738	−	0.479140i	$-0.840949\pi$
$977$	−28.1832	+	16.2716i	−0.901660	+	0.520574i	−0.0239217	+	0.999714i	$0.507615\pi$
$978$	7.15814	+	4.13276i	0.228892	+	0.132151i
$979$			1.94820i			0.0622647i
$980$	2.26820	−	17.8269i	0.0724548	−	0.569461i
$981$			3.28887i			0.105005i
$982$	8.49328	−	14.7108i	0.271031	−	0.469440i
$983$	18.3170	+	31.7260i	0.584222	+	1.01190i	0.994972	+	0.100155i	$0.0319338\pi$
$983$	18.3170	+	31.7260i	0.584222	+	1.01190i	−0.410749	+	0.911748i	$0.634733\pi$
$984$	2.12119	+	3.67401i	0.0676211	+	0.117123i
$985$	−1.55140	+	2.68710i	−0.0494317	+	0.0856182i
$986$	−9.53384			−0.303619
$987$	0.979960	+	1.11254i	0.0311925	+	0.0354127i
$988$		−	34.9858i		−	1.11305i
$989$	38.1707	+	22.8705i	1.21376	+	0.727238i
$990$	−9.62430	+	5.55659i	−0.305880	+	0.176600i
$991$	−17.2110	−	29.8103i	−0.546724	−	0.946954i	−0.998496	−	0.0548207i	$-0.982541\pi$
$991$	−17.2110	−	29.8103i	−0.546724	−	0.946954i	0.451772	−	0.892133i	$-0.350792\pi$
$992$	−8.38213	−	4.83943i	−0.266133	−	0.153652i
$993$			30.0995i			0.955179i
$994$	−36.2342	+	7.28930i	−1.14928	+	0.231203i
$995$	4.96772			0.157487
$996$	0.167836	+	0.0968999i	0.00531807	+	0.00307039i
$997$	−36.2426	+	20.9247i	−1.14781	+	0.662691i	−0.948354	−	0.317215i	$-0.897252\pi$
$997$	−36.2426	+	20.9247i	−1.14781	+	0.662691i	−0.199460	+	0.979906i	$0.563919\pi$
$998$	−8.48384	−	14.6944i	−0.268551	−	0.465145i
$999$	−5.53357	+	9.58443i	−0.175074	+	0.303238i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.k.b.229.14	yes	32
7.3	odd	6	inner	966.2.k.b.367.11	yes	32
23.22	odd	2	inner	966.2.k.b.229.11	✓	32
161.45	even	6	inner	966.2.k.b.367.14	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.k.b.229.11	✓	32	23.22	odd	2	inner
966.2.k.b.229.14	yes	32	1.1	even	1	trivial
966.2.k.b.367.11	yes	32	7.3	odd	6	inner
966.2.k.b.367.14	yes	32	161.45	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.28362 - 2.22329i) q^{5} -1.00000i q^{6} +(1.74878 + 1.98539i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(1.28362 - 2.22329i) q^{5} -1.00000i q^{6} +(1.74878 + 1.98539i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{9} +(-1.28362 - 2.22329i) q^{10} +(3.74890 - 2.16443i) q^{11} +(-0.866025 - 0.500000i) q^{12} +5.81269i q^{13} +(2.59379 - 0.521797i) q^{14} -2.56724i q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.22357 + 2.11928i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(3.00943 - 5.21248i) q^{19} -2.56724 q^{20} +(2.50718 + 0.845003i) q^{21} -4.32885i q^{22} +(2.46490 - 4.11391i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-0.795352 - 1.37759i) q^{25} +(5.03394 + 2.90635i) q^{26} -1.00000i q^{27} +(0.845003 - 2.50718i) q^{28} -3.89593 q^{29} +(-2.22329 - 1.28362i) q^{30} +(-8.38213 + 4.83943i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.16443 - 3.74890i) q^{33} +2.44713 q^{34} +(6.65886 - 1.33958i) q^{35} -1.00000 q^{36} +(-9.58443 - 5.53357i) q^{37} +(-3.00943 - 5.21248i) q^{38} +(2.90635 + 5.03394i) q^{39} +(-1.28362 + 2.22329i) q^{40} -4.24238i q^{41} +(1.98539 - 1.74878i) q^{42} +9.27845i q^{43} +(-3.74890 - 2.16443i) q^{44} +(-1.28362 - 2.22329i) q^{45} +(-2.33030 - 4.19162i) q^{46} +(0.485292 + 0.280183i) q^{47} +1.00000i q^{48} +(-0.883516 + 6.94402i) q^{49} -1.59070 q^{50} +(2.11928 + 1.22357i) q^{51} +(5.03394 - 2.90635i) q^{52} +(-3.03846 + 1.75425i) q^{53} +(-0.866025 - 0.500000i) q^{54} -11.1132i q^{55} +(-1.74878 - 1.98539i) q^{56} -6.01886i q^{57} +(-1.94796 + 3.37397i) q^{58} +(-9.23060 + 5.32929i) q^{59} +(-2.22329 + 1.28362i) q^{60} +(2.79450 - 4.84021i) q^{61} +9.67885i q^{62} +(2.59379 - 0.521797i) q^{63} +1.00000 q^{64} +(12.9233 + 7.46128i) q^{65} +(-2.16443 - 3.74890i) q^{66} +(7.00382 - 4.04366i) q^{67} +(1.22357 - 2.11928i) q^{68} +(0.0777105 - 4.79520i) q^{69} +(2.16932 - 6.43653i) q^{70} -13.9696 q^{71} +(-0.500000 + 0.866025i) q^{72} +(5.37567 - 3.10364i) q^{73} +(-9.58443 + 5.53357i) q^{74} +(-1.37759 - 0.795352i) q^{75} -6.01886 q^{76} +(10.8532 + 3.65789i) q^{77} +5.81269 q^{78} +(-3.37662 - 1.94949i) q^{79} +(1.28362 + 2.22329i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-3.67401 - 2.12119i) q^{82} -0.193800 q^{83} +(-0.521797 - 2.59379i) q^{84} +6.28236 q^{85} +(8.03537 + 4.63923i) q^{86} +(-3.37397 + 1.94796i) q^{87} +(-3.74890 + 2.16443i) q^{88} +(-0.225025 + 0.389754i) q^{89} -2.56724 q^{90} +(-11.5404 + 10.1651i) q^{91} +(-4.79520 - 0.0777105i) q^{92} +(-4.83943 + 8.38213i) q^{93} +(0.485292 - 0.280183i) q^{94} +(-7.72592 - 13.3817i) q^{95} +(0.866025 + 0.500000i) q^{96} -4.63569 q^{97} +(5.57194 + 4.23716i) q^{98} -4.32885i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9}+O(q^{10}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9	\( 32 q + 16 q^{2} - 16 q^{4} - 32 q^{8} + 16 q^{9} - 16 q^{16} - 16 q^{18} + 4 q^{23} - 40 q^{25} - 12 q^{26} + 24 q^{29} - 24 q^{31} + 16 q^{32} + 12 q^{35} - 32 q^{36} + 8 q^{39} - 4 q^{46} + 12 q^{47} + 24 q^{49} - 80 q^{50} - 12 q^{52} + 12 q^{58} - 12 q^{59} + 32 q^{64} + 24 q^{70} + 16 q^{71} - 16 q^{72} - 84 q^{73} + 12 q^{75} - 40 q^{77} + 16 q^{78} - 16 q^{81} - 36 q^{82} - 112 q^{85} - 48 q^{87} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 24 q^{98}+O(q^{100}) \) 32 * q + 16 * q^2 - 16 * q^4 - 32 * q^8 + 16 * q^9 - 16 * q^16 - 16 * q^18 + 4 * q^23 - 40 * q^25 - 12 * q^26 + 24 * q^29 - 24 * q^31 + 16 * q^32 + 12 * q^35 - 32 * q^36 + 8 * q^39 - 4 * q^46 + 12 * q^47 + 24 * q^49 - 80 * q^50 - 12 * q^52 + 12 * q^58 - 12 * q^59 + 32 * q^64 + 24 * q^70 + 16 * q^71 - 16 * q^72 - 84 * q^73 + 12 * q^75 - 40 * q^77 + 16 * q^78 - 16 * q^81 - 36 * q^82 - 112 * q^85 - 48 * q^87 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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