LMFDB - Embedded newform 686.2.e.b.99.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(99,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([10]))

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

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

chi := DirichletCharacter("686.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.e (of order $7$, degree $6$, not 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:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 37 x^{16} + 557 x^{14} + 4495 x^{12} + 21331 x^{10} + 60904 x^{8} + 101893 x^{6} + 91665 x^{4} + \cdots + 5103 $ x^18 + 37x^16 + 557x^14 + 4495x^12 + 21331x^10 + 60904x^8 + 101893x^6 + 91665x^4 + 36855x^2 + 5103
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 7 $
Twist minimal:	no (minimal twist has level 98)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			99.3
Root			$3.48640i$ of defining polynomial
Character	$\chi$	$=$	686.99
Dual form			686.2.e.b.589.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.222521 - 0.974928i) q^{2} +(1.91682 - 2.40361i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(1.88629 - 2.36534i) q^{5} +(-1.91682 - 2.40361i) q^{6} +(-0.623490 + 0.781831i) q^{8} +(-1.43560 - 6.28979i) q^{9} +O(q^{10})$	\(q+(0.222521 - 0.974928i) q^{2} +(1.91682 - 2.40361i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(1.88629 - 2.36534i) q^{5} +(-1.91682 - 2.40361i) q^{6} +(-0.623490 + 0.781831i) q^{8} +(-1.43560 - 6.28979i) q^{9} +(-1.88629 - 2.36534i) q^{10} +(-0.673210 + 2.94953i) q^{11} +(-2.76988 + 1.33390i) q^{12} +(-0.532118 + 2.33136i) q^{13} +(-2.06968 - 9.06784i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-0.579338 + 0.278994i) q^{17} -6.45155 q^{18} -0.629295 q^{19} +(-2.72577 + 1.31266i) q^{20} +(2.72577 + 1.31266i) q^{22} +(8.46635 + 4.07718i) q^{23} +(0.684104 + 2.99726i) q^{24} +(-0.924113 - 4.04880i) q^{25} +(2.15450 + 1.03755i) q^{26} +(-9.56038 - 4.60404i) q^{27} +(-3.84228 + 1.85034i) q^{29} -9.30104 q^{30} +2.51075 q^{31} +(0.900969 - 0.433884i) q^{32} +(5.79910 + 7.27184i) q^{33} +(0.143085 + 0.626894i) q^{34} +(-1.43560 + 6.28979i) q^{36} +(5.78775 - 2.78724i) q^{37} +(-0.140031 + 0.613517i) q^{38} +(4.58372 + 5.74780i) q^{39} +(0.673210 + 2.94953i) q^{40} +(-1.29087 + 1.61870i) q^{41} +(0.845798 + 1.06060i) q^{43} +(1.88629 - 2.36534i) q^{44} +(-17.5855 - 8.46871i) q^{45} +(5.85889 - 7.34682i) q^{46} +(0.235928 - 1.03367i) q^{47} +3.07434 q^{48} -4.15293 q^{50} +(-0.439890 + 1.92728i) q^{51} +(1.49096 - 1.86961i) q^{52} +(-4.22215 - 2.03328i) q^{53} +(-6.61599 + 8.29618i) q^{54} +(5.70676 + 7.15605i) q^{55} +(-1.20624 + 1.51258i) q^{57} +(0.948965 + 4.15769i) q^{58} +(-1.96057 - 2.45848i) q^{59} +(-2.06968 + 9.06784i) q^{60} +(-4.86234 + 2.34158i) q^{61} +(0.558695 - 2.44780i) q^{62} +(-0.222521 - 0.974928i) q^{64} +(4.51073 + 5.65627i) q^{65} +(8.37995 - 4.03557i) q^{66} +6.32287 q^{67} +0.643016 q^{68} +(26.0284 - 12.5346i) q^{69} +(-12.7586 - 6.14419i) q^{71} +(5.81264 + 2.79922i) q^{72} +(0.925455 + 4.05468i) q^{73} +(-1.42946 - 6.26286i) q^{74} +(-11.5031 - 5.53961i) q^{75} +(0.566975 + 0.273041i) q^{76} +(6.62367 - 3.18979i) q^{78} -11.2211 q^{79} +3.02538 q^{80} +(-11.9539 + 5.75669i) q^{81} +(1.29087 + 1.61870i) q^{82} +(1.69664 + 7.43348i) q^{83} +(-0.432885 + 1.89659i) q^{85} +(1.22221 - 0.588587i) q^{86} +(-2.91744 + 12.7821i) q^{87} +(-1.88629 - 2.36534i) q^{88} +(0.265089 + 1.16143i) q^{89} +(-12.1695 + 15.2601i) q^{90} +(-5.85889 - 7.34682i) q^{92} +(4.81265 - 6.03488i) q^{93} +(-0.955254 - 0.460026i) q^{94} +(-1.18704 + 1.48850i) q^{95} +(0.684104 - 2.99726i) q^{96} -16.3992 q^{97} +19.5184 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 3 q^{2} + 5 q^{3} - 3 q^{4} - 5 q^{6} + 3 q^{8} - 10 q^{9}+O(q^{10}) $ 18 * q + 3 * q^2 + 5 * q^3 - 3 * q^4 - 5 * q^6 + 3 * q^8 - 10 * q^9	$ 18 q + 3 q^{2} + 5 q^{3} - 3 q^{4} - 5 q^{6} + 3 q^{8} - 10 q^{9} + 7 q^{11} - 2 q^{12} + 10 q^{13} + 7 q^{15} - 3 q^{16} - q^{17} - 32 q^{18} + 44 q^{19} - 7 q^{20} + 7 q^{22} + 21 q^{23} + 2 q^{24} + q^{25} - 3 q^{26} - 10 q^{27} + 11 q^{29} + 24 q^{31} + 3 q^{32} + 14 q^{33} + q^{34} - 10 q^{36} - 13 q^{37} + 19 q^{38} - 3 q^{39} - 7 q^{40} - 8 q^{41} - 24 q^{43} - 98 q^{45} + 21 q^{46} - 40 q^{47} - 2 q^{48} - 50 q^{50} + 36 q^{51} - 18 q^{52} + 10 q^{53} - 4 q^{54} - 49 q^{55} + 19 q^{57} + 24 q^{58} - 13 q^{59} + 7 q^{60} - 27 q^{61} + 11 q^{62} - 3 q^{64} + 21 q^{66} - 86 q^{67} + 34 q^{68} + 91 q^{69} + 3 q^{72} - 5 q^{73} + 13 q^{74} + 3 q^{75} + 2 q^{76} + 38 q^{78} - 66 q^{79} - 2 q^{81} + 8 q^{82} - 55 q^{83} - 49 q^{85} - 18 q^{86} + 110 q^{87} - 62 q^{89} - 21 q^{90} - 21 q^{92} + 46 q^{93} - 23 q^{94} - 7 q^{95} + 2 q^{96} + 32 q^{97} + 14 q^{99}+O(q^{100}) $ 18 * q + 3 * q^2 + 5 * q^3 - 3 * q^4 - 5 * q^6 + 3 * q^8 - 10 * q^9 + 7 * q^11 - 2 * q^12 + 10 * q^13 + 7 * q^15 - 3 * q^16 - q^17 - 32 * q^18 + 44 * q^19 - 7 * q^20 + 7 * q^22 + 21 * q^23 + 2 * q^24 + q^25 - 3 * q^26 - 10 * q^27 + 11 * q^29 + 24 * q^31 + 3 * q^32 + 14 * q^33 + q^34 - 10 * q^36 - 13 * q^37 + 19 * q^38 - 3 * q^39 - 7 * q^40 - 8 * q^41 - 24 * q^43 - 98 * q^45 + 21 * q^46 - 40 * q^47 - 2 * q^48 - 50 * q^50 + 36 * q^51 - 18 * q^52 + 10 * q^53 - 4 * q^54 - 49 * q^55 + 19 * q^57 + 24 * q^58 - 13 * q^59 + 7 * q^60 - 27 * q^61 + 11 * q^62 - 3 * q^64 + 21 * q^66 - 86 * q^67 + 34 * q^68 + 91 * q^69 + 3 * q^72 - 5 * q^73 + 13 * q^74 + 3 * q^75 + 2 * q^76 + 38 * q^78 - 66 * q^79 - 2 * q^81 + 8 * q^82 - 55 * q^83 - 49 * q^85 - 18 * q^86 + 110 * q^87 - 62 * q^89 - 21 * q^90 - 21 * q^92 + 46 * q^93 - 23 * q^94 - 7 * q^95 + 2 * q^96 + 32 * q^97 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{7}\right)$

Coefficient data

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

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

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

$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$2$	0.222521	−	0.974928i	0.157346	−	0.689378i
$3$	1.91682	−	2.40361i	1.10668	−	1.38773i	0.193040	−	0.981191i	$-0.438165\pi$
$3$	1.91682	−	2.40361i	1.10668	−	1.38773i	0.913635	−	0.406536i	$-0.133263\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	1.88629	−	2.36534i	0.843576	−	1.05781i	−0.153989	−	0.988073i	$-0.549212\pi$
$5$	1.88629	−	2.36534i	0.843576	−	1.05781i	0.997565	−	0.0697386i	$-0.0222165\pi$
$6$	−1.91682	−	2.40361i	−0.782538	−	0.981271i
$7$		0			0
$7$		0			0
$8$	−0.623490	+	0.781831i	−0.220437	+	0.276419i
$9$	−1.43560	−	6.28979i	−0.478535	−	2.09660i
$10$	−1.88629	−	2.36534i	−0.596498	−	0.747985i
$11$	−0.673210	+	2.94953i	−0.202981	+	0.889316i	0.766129	+	0.642687i	$0.222180\pi$
$11$	−0.673210	+	2.94953i	−0.202981	+	0.889316i	−0.969110	+	0.246630i	$0.920677\pi$
$12$	−2.76988	+	1.33390i	−0.799596	+	0.385065i
$13$	−0.532118	+	2.33136i	−0.147583	+	0.646603i	0.845970	+	0.533231i	$0.179022\pi$
$13$	−0.532118	+	2.33136i	−0.147583	+	0.646603i	−0.993553	+	0.113372i	$0.963835\pi$
$14$		0			0
$15$	−2.06968	−	9.06784i	−0.534388	−	2.34131i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−0.579338	+	0.278994i	−0.140510	+	0.0676661i	−0.502818	−	0.864393i	$-0.667703\pi$
$17$	−0.579338	+	0.278994i	−0.140510	+	0.0676661i	0.362308	+	0.932059i	$0.381989\pi$
$18$	−6.45155			−1.52064
$19$	−0.629295			−0.144370			−0.0721851	−	0.997391i	$-0.522997\pi$
$19$	−0.629295			−0.144370			−0.0721851	+	0.997391i	$0.522997\pi$
$20$	−2.72577	+	1.31266i	−0.609501	+	0.293520i
$21$		0			0
$22$	2.72577	+	1.31266i	0.581137	+	0.279861i
$23$	8.46635	+	4.07718i	1.76536	+	0.850150i	0.969662	+	0.244451i	$0.0786078\pi$
$23$	8.46635	+	4.07718i	1.76536	+	0.850150i	0.795694	+	0.605699i	$0.207107\pi$
$24$	0.684104	+	2.99726i	0.139642	+	0.611812i
$25$	−0.924113	−	4.04880i	−0.184823	−	0.809761i
$26$	2.15450	+	1.03755i	0.422533	+	0.203481i
$27$	−9.56038	−	4.60404i	−1.83990	−	0.886047i
$28$		0			0
$29$	−3.84228	+	1.85034i	−0.713493	+	0.343600i	−0.755168	−	0.655531i	$-0.772445\pi$
$29$	−3.84228	+	1.85034i	−0.713493	+	0.343600i	0.0416749	+	0.999131i	$0.486731\pi$
$30$	−9.30104			−1.69813
$31$	2.51075			0.450944			0.225472	−	0.974250i	$-0.427608\pi$
$31$	2.51075			0.450944			0.225472	+	0.974250i	$0.427608\pi$
$32$	0.900969	−	0.433884i	0.159270	−	0.0767005i
$33$	5.79910	+	7.27184i	1.00949	+	1.26587i
$34$	0.143085	+	0.626894i	0.0245388	+	0.107512i
$35$		0			0
$36$	−1.43560	+	6.28979i	−0.239267	+	1.04830i
$37$	5.78775	−	2.78724i	0.951501	−	0.458219i	0.107289	−	0.994228i	$-0.465783\pi$
$37$	5.78775	−	2.78724i	0.951501	−	0.458219i	0.844212	+	0.536009i	$0.180069\pi$
$38$	−0.140031	+	0.613517i	−0.0227161	+	0.0995256i
$39$	4.58372	+	5.74780i	0.733982	+	0.920385i
$40$	0.673210	+	2.94953i	0.106444	+	0.466361i
$41$	−1.29087	+	1.61870i	−0.201600	+	0.252798i	−0.872346	−	0.488889i	$-0.837402\pi$
$41$	−1.29087	+	1.61870i	−0.201600	+	0.252798i	0.670747	+	0.741687i	$0.265974\pi$
$42$		0			0
$43$	0.845798	+	1.06060i	0.128983	+	0.161740i	0.842129	−	0.539276i	$-0.181302\pi$
$43$	0.845798	+	1.06060i	0.128983	+	0.161740i	−0.713146	+	0.701015i	$0.752730\pi$
$44$	1.88629	−	2.36534i	0.284369	−	0.356588i
$45$	−17.5855	−	8.46871i	−2.62149	−	1.26244i
$46$	5.85889	−	7.34682i	0.863847	−	1.08323i
$47$	0.235928	−	1.03367i	0.0344137	−	0.150776i	−0.954802	−	0.297243i	$-0.903933\pi$
$47$	0.235928	−	1.03367i	0.0344137	−	0.150776i	0.989216	+	0.146467i	$0.0467901\pi$
$48$	3.07434			0.443742
$49$		0			0
$50$	−4.15293			−0.587313
$51$	−0.439890	+	1.92728i	−0.0615969	+	0.269874i
$52$	1.49096	−	1.86961i	0.206759	−	0.259268i
$53$	−4.22215	−	2.03328i	−0.579957	−	0.279293i	0.120818	−	0.992675i	$-0.461448\pi$
$53$	−4.22215	−	2.03328i	−0.579957	−	0.279293i	−0.700775	+	0.713382i	$0.747162\pi$
$54$	−6.61599	+	8.29618i	−0.900322	+	1.12897i
$55$	5.70676	+	7.15605i	0.769499	+	0.964921i
$56$		0			0
$57$	−1.20624	+	1.51258i	−0.159771	+	0.200346i
$58$	0.948965	+	4.15769i	0.124605	+	0.545931i
$59$	−1.96057	−	2.45848i	−0.255245	−	0.320067i	0.637655	−	0.770322i	$-0.279905\pi$
$59$	−1.96057	−	2.45848i	−0.255245	−	0.320067i	−0.892900	+	0.450255i	$0.851333\pi$
$60$	−2.06968	+	9.06784i	−0.267194	+	1.17065i
$61$	−4.86234	+	2.34158i	−0.622559	+	0.299809i	−0.718445	−	0.695584i	$-0.755146\pi$
$61$	−4.86234	+	2.34158i	−0.622559	+	0.299809i	0.0958862	+	0.995392i	$0.469432\pi$
$62$	0.558695	−	2.44780i	0.0709543	−	0.310871i
$63$		0			0
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	4.51073	+	5.65627i	0.559487	+	0.701574i
$66$	8.37995	−	4.03557i	1.03150	−	0.496744i
$67$	6.32287			0.772462			0.386231	−	0.922402i	$-0.373777\pi$
$67$	6.32287			0.772462			0.386231	+	0.922402i	$0.373777\pi$
$68$	0.643016			0.0779772
$69$	26.0284	−	12.5346i	3.13345	−	1.50899i
$70$		0			0
$71$	−12.7586	−	6.14419i	−1.51416	−	0.729182i	−0.521860	−	0.853031i	$-0.674762\pi$
$71$	−12.7586	−	6.14419i	−1.51416	−	0.729182i	−0.992301	+	0.123849i	$0.960476\pi$
$72$	5.81264	+	2.79922i	0.685027	+	0.329891i
$73$	0.925455	+	4.05468i	0.108316	+	0.474565i	0.999770	+	0.0214527i	$0.00682914\pi$
$73$	0.925455	+	4.05468i	0.108316	+	0.474565i	−0.891454	+	0.453112i	$0.850314\pi$
$74$	−1.42946	−	6.26286i	−0.166171	−	0.728043i
$75$	−11.5031	−	5.53961i	−1.32827	−	0.639659i
$76$	0.566975	+	0.273041i	0.0650365	+	0.0313199i
$77$		0			0
$78$	6.62367	−	3.18979i	0.749982	−	0.361173i
$79$	−11.2211			−1.26247			−0.631236	−	0.775590i	$-0.717452\pi$
$79$	−11.2211			−1.26247			−0.631236	+	0.775590i	$0.717452\pi$
$80$	3.02538			0.338248
$81$	−11.9539	+	5.75669i	−1.32821	+	0.639632i
$82$	1.29087	+	1.61870i	0.142552	+	0.178755i
$83$	1.69664	+	7.43348i	0.186231	+	0.815930i	0.978581	+	0.205864i	$0.0660003\pi$
$83$	1.69664	+	7.43348i	0.186231	+	0.815930i	−0.792350	+	0.610067i	$0.791143\pi$
$84$		0			0
$85$	−0.432885	+	1.89659i	−0.0469530	+	0.205715i
$86$	1.22221	−	0.588587i	0.131795	−	0.0634690i
$87$	−2.91744	+	12.7821i	−0.312782	+	1.37039i
$88$	−1.88629	−	2.36534i	−0.201080	−	0.252146i
$89$	0.265089	+	1.16143i	0.0280994	+	0.123112i	0.987032	−	0.160521i	$-0.0513175\pi$
$89$	0.265089	+	1.16143i	0.0280994	+	0.123112i	−0.958933	+	0.283633i	$0.908460\pi$
$90$	−12.1695	+	15.2601i	−1.28278	+	1.60855i
$91$		0			0
$92$	−5.85889	−	7.34682i	−0.610832	−	0.765959i
$93$	4.81265	−	6.03488i	0.499049	−	0.625787i
$94$	−0.955254	−	0.460026i	−0.0985269	−	0.0474481i
$95$	−1.18704	+	1.48850i	−0.121787	+	0.152716i
$96$	0.684104	−	2.99726i	0.0698211	−	0.305906i
$97$	−16.3992			−1.66509			−0.832543	−	0.553961i	$-0.813116\pi$
$97$	−16.3992			−1.66509			−0.832543	+	0.553961i	$0.813116\pi$
$98$		0			0
$99$	19.5184			1.96167
$100$	−0.924113	+	4.04880i	−0.0924113	+	0.404880i
$101$	−8.95938	+	11.2347i	−0.891492	+	1.11790i	0.100915	+	0.994895i	$0.467823\pi$
$101$	−8.95938	+	11.2347i	−0.891492	+	1.11790i	−0.992407	+	0.123000i	$0.960748\pi$
$102$	1.78108	+	0.857722i	0.176353	+	0.0849272i
$103$	10.1830	−	12.7691i	1.00336	−	1.25817i	0.0374497	−	0.999299i	$-0.488077\pi$
$103$	10.1830	−	12.7691i	1.00336	−	1.25817i	0.965911	−	0.258876i	$-0.0833520\pi$
$104$	−1.49096	−	1.86961i	−0.146201	−	0.183330i
$105$		0			0
$106$	−2.92182	+	3.66385i	−0.283792	+	0.355864i
$107$	−3.71249	−	16.2655i	−0.358900	−	1.57244i	−0.755939	−	0.654642i	$-0.772820\pi$
$107$	−3.71249	−	16.2655i	−0.358900	−	1.57244i	0.397039	−	0.917802i	$-0.370038\pi$
$108$	6.61599	+	8.29618i	0.636624	+	0.798301i
$109$	−0.370529	+	1.62339i	−0.0354902	+	0.155493i	−0.989568	−	0.144066i	$-0.953982\pi$
$109$	−0.370529	+	1.62339i	−0.0354902	+	0.155493i	0.954078	+	0.299559i	$0.0968394\pi$
$110$	8.24650	−	3.97131i	0.786273	−	0.378649i
$111$	4.39463	−	19.2541i	0.417120	−	1.82752i
$112$		0			0
$113$	2.05961	+	9.02372i	0.193751	+	0.848880i	0.974563	+	0.224114i	$0.0719487\pi$
$113$	2.05961	+	9.02372i	0.193751	+	0.848880i	−0.780812	+	0.624767i	$0.785194\pi$
$114$	1.20624	+	1.51258i	0.112975	+	0.141666i
$115$	25.6139	−	12.3350i	2.38851	−	1.15025i
$116$	4.26461			0.395959
$117$	15.4277			1.42629
$118$	−2.83311	+	1.36435i	−0.260809	+	0.125599i
$119$		0			0
$120$	8.37995	+	4.03557i	0.764981	+	0.368395i
$121$	1.66416	+	0.801415i	0.151287	+	0.0728559i
$122$	1.20090	+	5.26148i	0.108724	+	0.476352i
$123$	1.41636	+	6.20549i	0.127709	+	0.559530i
$124$	−2.26211	−	1.08937i	−0.203143	−	0.0978287i
$125$	2.30893	+	1.11192i	0.206517	+	0.0994533i
$126$		0			0
$127$	12.0689	−	5.81208i	1.07094	−	0.515739i	0.186532	−	0.982449i	$-0.440275\pi$
$127$	12.0689	−	5.81208i	1.07094	−	0.515739i	0.884410	+	0.466710i	$0.154561\pi$
$128$	−1.00000			−0.0883883
$129$	4.17051			0.367193
$130$	6.51819	−	3.13899i	0.571683	−	0.275308i
$131$	−12.1193	−	15.1971i	−1.05887	−	1.32778i	−0.942364	−	0.334588i	$-0.891403\pi$
$131$	−12.1193	−	15.1971i	−1.05887	−	1.32778i	−0.116503	−	0.993190i	$-0.537169\pi$
$132$	−2.06968	−	9.06784i	−0.180142	−	0.789254i
$133$		0			0
$134$	1.40697	−	6.16435i	0.121544	−	0.532518i
$135$	−28.9238	+	13.9290i	−2.48936	+	1.19881i
$136$	0.143085	−	0.626894i	0.0122694	−	0.0537558i
$137$	4.91692	+	6.16562i	0.420081	+	0.526764i	0.946172	−	0.323663i	$-0.104915\pi$
$137$	4.91692	+	6.16562i	0.420081	+	0.526764i	−0.526092	+	0.850428i	$0.676343\pi$
$138$	−6.42848	−	28.1650i	−0.547229	−	2.39757i
$139$	0.182803	−	0.229228i	0.0155052	−	0.0194428i	−0.774018	−	0.633163i	$-0.781756\pi$
$139$	0.182803	−	0.229228i	0.0155052	−	0.0194428i	0.789524	+	0.613720i	$0.210328\pi$
$140$		0			0
$141$	−2.03231	−	2.54844i	−0.171151	−	0.214617i
$142$	−8.82919	+	11.0715i	−0.740929	+	0.929096i
$143$	−6.51819	−	3.13899i	−0.545078	−	0.262496i
$144$	4.02247	−	5.04402i	0.335206	−	0.420335i
$145$	−2.87098	+	12.5786i	−0.238422	+	1.04459i
$146$	4.15896			0.344198
$147$		0			0
$148$	−6.42392			−0.528043
$149$	1.57842	−	6.91551i	0.129309	−	0.566540i	−0.868213	−	0.496191i	$-0.834732\pi$
$149$	1.57842	−	6.91551i	0.129309	−	0.566540i	0.997522	−	0.0703492i	$-0.0224114\pi$
$150$	−7.96040	+	9.98203i	−0.649964	+	0.815029i
$151$	−10.6287	−	5.11852i	−0.864953	−	0.416539i	−0.0518469	−	0.998655i	$-0.516511\pi$
$151$	−10.6287	−	5.11852i	−0.864953	−	0.416539i	−0.813106	+	0.582116i	$0.802225\pi$
$152$	0.392359	−	0.492003i	0.0318245	−	0.0399067i
$153$	2.58652	+	3.24339i	0.209107	+	0.262212i
$154$		0			0
$155$	4.73601	−	5.93877i	0.380406	−	0.477014i
$156$	−1.63591	−	7.16739i	−0.130978	−	0.573851i
$157$	8.20330	+	10.2866i	0.654695	+	0.820961i	0.992754	−	0.120164i	$-0.0383419\pi$
$157$	8.20330	+	10.2866i	0.654695	+	0.820961i	−0.338059	+	0.941125i	$0.609770\pi$
$158$	−2.49693	+	10.9398i	−0.198645	+	0.870321i
$159$	−12.9803	+	6.25099i	−1.02941	+	0.495736i
$160$	0.673210	−	2.94953i	0.0532220	−	0.233181i
$161$		0			0
$162$	2.95237	+	12.9352i	0.231960	+	1.01628i
$163$	8.36144	+	10.4849i	0.654918	+	0.821241i	0.992779	−	0.119954i	$-0.0382749\pi$
$163$	8.36144	+	10.4849i	0.654918	+	0.821241i	−0.337861	+	0.941196i	$0.609703\pi$
$164$	1.86536	−	0.898309i	0.145660	−	0.0701461i
$165$	28.1392			2.19063
$166$	7.62465			0.591787
$167$	−8.54332	+	4.11425i	−0.661102	+	0.318370i	−0.734179	−	0.678956i	$-0.762433\pi$
$167$	−8.54332	+	4.11425i	−0.661102	+	0.318370i	0.0730766	+	0.997326i	$0.476718\pi$
$168$		0			0
$169$	6.56050	+	3.15937i	0.504654	+	0.243028i
$170$	1.75272	+	0.844064i	0.134427	+	0.0647367i
$171$	0.903419	+	3.95814i	0.0690861	+	0.302686i
$172$	−0.301862	−	1.32254i	−0.0230168	−	0.100843i
$173$	−0.948259	−	0.456658i	−0.0720948	−	0.0347190i	0.397489	−	0.917607i	$-0.369882\pi$
$173$	−0.948259	−	0.456658i	−0.0720948	−	0.0347190i	−0.469584	+	0.882888i	$0.655596\pi$
$174$	11.8125	+	5.68858i	0.895500	+	0.431250i
$175$		0			0
$176$	−2.72577	+	1.31266i	−0.205463	+	0.0989457i
$177$	−9.66730			−0.726639
$178$	1.19130			0.0892917
$179$	9.18269	−	4.42215i	0.686347	−	0.330527i	−0.0580037	−	0.998316i	$-0.518474\pi$
$179$	9.18269	−	4.42215i	0.686347	−	0.330527i	0.744350	+	0.667789i	$0.232759\pi$
$180$	12.1695	+	15.2601i	0.907062	+	1.13742i
$181$	3.08835	+	13.5309i	0.229555	+	1.00575i	0.950004	+	0.312238i	$0.101079\pi$
$181$	3.08835	+	13.5309i	0.229555	+	1.00575i	−0.720449	+	0.693508i	$0.756064\pi$
$182$		0			0
$183$	−3.69197	+	16.1756i	−0.272918	+	1.19573i
$184$	−8.46635	+	4.07718i	−0.624147	+	0.300574i
$185$	4.32465	−	18.9475i	0.317955	−	1.39305i
$186$	−4.81265	−	6.03488i	−0.352881	−	0.442499i
$187$	−0.432885	−	1.89659i	−0.0316557	−	0.138693i
$188$	−0.661056	+	0.828938i	−0.0482125	+	0.0604565i
$189$		0			0
$190$	1.18704	+	1.48850i	0.0861166	+	0.107987i
$191$	4.19109	−	5.25546i	0.303257	−	0.380272i	−0.606731	−	0.794907i	$-0.707519\pi$
$191$	4.19109	−	5.25546i	0.303257	−	0.380272i	0.909988	+	0.414635i	$0.136091\pi$
$192$	−2.76988	−	1.33390i	−0.199899	−	0.0962663i
$193$	−1.44686	+	1.81431i	−0.104147	+	0.130597i	−0.831174	−	0.556013i	$-0.812330\pi$
$193$	−1.44686	+	1.81431i	−0.104147	+	0.130597i	0.727026	+	0.686610i	$0.240902\pi$
$194$	−3.64916	+	15.9880i	−0.261995	+	1.14787i
$195$	22.2417			1.59276
$196$		0			0
$197$	8.72306			0.621492			0.310746	−	0.950493i	$-0.399421\pi$
$197$	8.72306			0.621492			0.310746	+	0.950493i	$0.399421\pi$
$198$	4.34325	−	19.0290i	0.308661	−	1.35233i
$199$	6.65827	−	8.34921i	0.471992	−	0.591860i	−0.487665	−	0.873031i	$-0.662151\pi$
$199$	6.65827	−	8.34921i	0.471992	−	0.591860i	0.959658	+	0.281171i	$0.0907228\pi$
$200$	3.74166	+	1.80189i	0.264575	+	0.127413i
$201$	12.1198	−	15.1977i	0.854865	−	1.07197i
$202$	8.95938	+	11.2347i	0.630380	+	0.790472i
$203$		0			0
$204$	1.23254	−	1.54556i	0.0862954	−	0.108211i
$205$	1.39381	+	6.10667i	0.0973478	+	0.426509i
$206$	−10.1830	−	12.7691i	−0.709483	−	0.889663i
$207$	13.4903	−	59.1048i	0.937639	−	4.10807i
$208$	−2.15450	+	1.03755i	−0.149388	+	0.0719414i
$209$	0.423648	−	1.85612i	0.0293043	−	0.128391i
$210$		0			0
$211$	3.16480	+	13.8659i	0.217874	+	0.954566i	0.959046	+	0.283251i	$0.0914131\pi$
$211$	3.16480	+	13.8659i	0.217874	+	0.954566i	−0.741172	+	0.671315i	$0.765730\pi$
$212$	2.92182	+	3.66385i	0.200671	+	0.251634i
$213$	−39.2241	+	18.8893i	−2.68759	+	1.29428i
$214$	−16.6838			−1.14048
$215$	4.10410			0.279897
$216$	9.56038	−	4.60404i	0.650501	−	0.313265i
$217$		0			0
$218$	1.50024	+	0.722477i	0.101609	+	0.0489323i
$219$	11.5198	+	5.54765i	0.778437	+	0.374876i
$220$	−2.03672	−	8.92344i	−0.137315	−	0.601618i
$221$	−0.342161	−	1.49910i	−0.0230162	−	0.100841i
$222$	−17.7935	−	8.56890i	−1.19422	−	0.575107i
$223$	−8.73560	−	4.20684i	−0.584979	−	0.281711i	0.117894	−	0.993026i	$-0.462386\pi$
$223$	−8.73560	−	4.20684i	−0.584979	−	0.281711i	−0.702873	+	0.711315i	$0.748100\pi$
$224$		0			0
$225$	−24.1395	+	11.6250i	−1.60930	+	0.774997i
$226$	9.25578			0.615686
$227$	6.19599			0.411242			0.205621	−	0.978632i	$-0.434079\pi$
$227$	6.19599			0.411242			0.205621	+	0.978632i	$0.434079\pi$
$228$	1.74307	−	0.839420i	0.115438	−	0.0555919i
$229$	−0.341248	−	0.427912i	−0.0225503	−	0.0282772i	0.770428	−	0.637526i	$-0.220042\pi$
$229$	−0.341248	−	0.427912i	−0.0225503	−	0.0282772i	−0.792979	+	0.609249i	$0.791471\pi$
$230$	−6.32612	−	27.7165i	−0.417132	−	1.82757i
$231$		0			0
$232$	0.948965	−	4.15769i	0.0623026	−	0.272965i
$233$	−6.10655	+	2.94076i	−0.400053	+	0.192656i	−0.623082	−	0.782156i	$-0.714120\pi$
$233$	−6.10655	+	2.94076i	−0.400053	+	0.192656i	0.223029	+	0.974812i	$0.428406\pi$
$234$	3.43299	−	15.0409i	0.224421	−	0.983254i
$235$	−1.99995	−	2.50785i	−0.130462	−	0.163594i
$236$	0.699721	+	3.06568i	0.0455479	+	0.199559i
$237$	−21.5088	+	26.9712i	−1.39715	+	1.75197i
$238$		0			0
$239$	−4.24070	−	5.31767i	−0.274308	−	0.343971i	0.625526	−	0.780203i	$-0.284884\pi$
$239$	−4.24070	−	5.31767i	−0.274308	−	0.343971i	−0.899834	+	0.436232i	$0.856313\pi$
$240$	5.79910	−	7.27184i	0.374330	−	0.469396i
$241$	23.4832	+	11.3089i	1.51269	+	0.728471i	0.992113	−	0.125347i	$-0.0400043\pi$
$241$	23.4832	+	11.3089i	1.51269	+	0.728471i	0.520572	+	0.853818i	$0.325719\pi$
$242$	1.15163	−	1.44410i	0.0740297	−	0.0928303i
$243$	−1.99292	+	8.73154i	−0.127846	+	0.560129i
$244$	5.39679			0.345494
$245$		0			0
$246$	6.36508			0.405822
$247$	0.334859	−	1.46711i	0.0213066	−	0.0933502i
$248$	−1.56543	+	1.96298i	−0.0994048	+	0.124650i
$249$	21.1194	+	10.1706i	1.33839	+	0.644533i
$250$	1.59783	−	2.00361i	0.101056	−	0.126720i
$251$	16.3304	+	20.4777i	1.03077	+	1.29254i	0.955378	+	0.295386i	$0.0954484\pi$
$251$	16.3304	+	20.4777i	1.03077	+	1.29254i	0.0753889	+	0.997154i	$0.475980\pi$
$252$		0			0
$253$	−17.7254	+	22.2269i	−1.11439	+	1.39739i
$254$	−2.98077	−	13.0596i	−0.187030	−	0.819434i
$255$	3.72892	+	4.67591i	0.233514	+	0.292817i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	12.0796	−	5.81722i	0.753504	−	0.362868i	−0.0173758	−	0.999849i	$-0.505531\pi$
$257$	12.0796	−	5.81722i	0.753504	−	0.362868i	0.770880	+	0.636981i	$0.219817\pi$
$258$	0.928025	−	4.06594i	0.0577763	−	0.253135i
$259$		0			0
$260$	−1.60986	−	7.05326i	−0.0998393	−	0.437424i
$261$	17.1543	+	21.5108i	1.06182	+	1.33148i
$262$	−17.5129	+	8.43376i	−1.08195	+	0.521040i
$263$	−10.5626			−0.651320			−0.325660	−	0.945487i	$-0.605586\pi$
$263$	−10.5626			−0.651320			−0.325660	+	0.945487i	$0.605586\pi$
$264$	−9.30104			−0.572439
$265$	−12.7736	+	6.15145i	−0.784677	+	0.377880i
$266$		0			0
$267$	3.29976	+	1.58908i	0.201942	+	0.0972502i
$268$	−5.69671	−	2.74339i	−0.347982	−	0.167579i
$269$	−2.65240	−	11.6209i	−0.161720	−	0.708540i	−0.989142	−	0.146960i	$-0.953051\pi$
$269$	−2.65240	−	11.6209i	−0.161720	−	0.708540i	0.827423	−	0.561579i	$-0.189806\pi$
$270$	7.14358	+	31.2981i	0.434745	+	1.90474i
$271$	22.4071	+	10.7907i	1.36114	+	0.655489i	0.964890	−	0.262656i	$-0.0845983\pi$
$271$	22.4071	+	10.7907i	1.36114	+	0.655489i	0.396246	+	0.918144i	$0.370313\pi$
$272$	−0.579338	−	0.278994i	−0.0351275	−	0.0169165i
$273$		0			0
$274$	7.10515	−	3.42166i	0.429238	−	0.206710i
$275$	12.5642			0.757649
$276$	−28.8893			−1.73893
$277$	−25.0286	+	12.0531i	−1.50382	+	0.724202i	−0.990946	−	0.134262i	$-0.957134\pi$
$277$	−25.0286	+	12.0531i	−1.50382	+	0.724202i	−0.512875	+	0.858464i	$0.671419\pi$
$278$	−0.182803	−	0.229228i	−0.0109638	−	0.0137482i
$279$	−3.60445	−	15.7921i	−0.215793	−	0.945449i
$280$		0			0
$281$	6.94033	−	30.4076i	0.414025	−	1.81396i	−0.150574	−	0.988599i	$-0.548112\pi$
$281$	6.94033	−	30.4076i	0.414025	−	1.81396i	0.564600	−	0.825365i	$-0.309031\pi$
$282$	−2.93677	+	1.41427i	−0.174882	+	0.0842188i
$283$	−4.22408	+	18.5069i	−0.251096	+	1.10012i	0.679385	+	0.733782i	$0.262246\pi$
$283$	−4.22408	+	18.5069i	−0.251096	+	1.10012i	−0.930481	+	0.366340i	$0.880611\pi$
$284$	8.82919	+	11.0715i	0.523916	+	0.656970i
$285$	1.30244	+	5.70635i	0.0771497	+	0.338015i
$286$	−4.51073	+	5.65627i	−0.266725	+	0.334462i
$287$		0			0
$288$	−4.02247	−	5.04402i	−0.237027	−	0.297222i
$289$	−10.3415	+	12.9679i	−0.608325	+	0.762816i
$290$	11.6244	+	5.59800i	0.682606	+	0.328726i
$291$	−31.4343	+	39.4173i	−1.84271	+	2.31068i
$292$	0.925455	−	4.05468i	0.0541582	−	0.237282i
$293$	−19.6220			−1.14633			−0.573163	−	0.819441i	$-0.694284\pi$
$293$	−19.6220			−1.14633			−0.573163	+	0.819441i	$0.694284\pi$
$294$		0			0
$295$	−9.51336			−0.553889
$296$	−1.42946	+	6.26286i	−0.0830855	+	0.364021i
$297$	20.0159	−	25.0991i	1.16144	−	1.45640i
$298$	−6.39089	−	3.07769i	−0.370214	−	0.178286i
$299$	−14.0105	+	17.5686i	−0.810247	+	1.01602i
$300$	7.96040	+	9.98203i	0.459594	+	0.576313i
$301$		0			0
$302$	−7.35530	+	9.22326i	−0.423250	+	0.530739i
$303$	9.83040	+	43.0698i	0.564742	+	2.47429i
$304$	−0.392359	−	0.492003i	−0.0225033	−	0.0282183i
$305$	−3.63318	+	15.9180i	−0.208035	+	0.911461i
$306$	3.73762	−	1.79994i	0.213666	−	0.102896i
$307$	4.68518	−	20.5271i	0.267397	−	1.17154i	−0.645632	−	0.763649i	$-0.723406\pi$
$307$	4.68518	−	20.5271i	0.267397	−	1.17154i	0.913029	−	0.407895i	$-0.133737\pi$
$308$		0			0
$309$	−11.1730	−	48.9520i	−0.635608	−	2.78478i
$310$	−4.73601	−	5.93877i	−0.268988	−	0.337300i
$311$	−10.6094	+	5.10920i	−0.601602	+	0.289716i	−0.709789	−	0.704414i	$-0.751210\pi$
$311$	−10.6094	+	5.10920i	−0.601602	+	0.289716i	0.108187	+	0.994131i	$0.465496\pi$
$312$	−7.35171			−0.416209
$313$	−21.4522			−1.21255			−0.606275	−	0.795255i	$-0.707337\pi$
$313$	−21.4522			−1.21255			−0.606275	+	0.795255i	$0.707337\pi$
$314$	11.8541	−	5.70864i	0.668966	−	0.322157i
$315$		0			0
$316$	10.1099	+	4.86865i	0.568724	+	0.273883i
$317$	−26.7438	−	12.8791i	−1.50208	−	0.723363i	−0.511370	−	0.859360i	$-0.670862\pi$
$317$	−26.7438	−	12.8791i	−1.50208	−	0.723363i	−0.990709	+	0.135997i	$0.956576\pi$
$318$	3.20587	+	14.0458i	0.179776	+	0.787652i
$319$	−2.87098	−	12.5786i	−0.160744	−	0.704265i
$320$	−2.72577	−	1.31266i	−0.152375	−	0.0733801i
$321$	−46.2121	−	22.2546i	−2.57931	−	1.24213i
$322$		0			0
$323$	0.364574	−	0.175570i	0.0202855	−	0.00976896i
$324$	13.2678			0.737101
$325$	9.93096			0.550871
$326$	12.0826	−	5.81869i	0.669195	−	0.322267i
$327$	3.19177	+	4.00235i	0.176505	+	0.221331i
$328$	−0.460705	−	2.01848i	−0.0254382	−	0.111452i
$329$		0			0
$330$	6.26156	−	27.4337i	0.344687	−	1.51017i
$331$	0.739639	−	0.356191i	0.0406542	−	0.0195780i	−0.413446	−	0.910529i	$-0.635675\pi$
$331$	0.739639	−	0.356191i	0.0406542	−	0.0195780i	0.454100	+	0.890951i	$0.349961\pi$
$332$	1.69664	−	7.43348i	0.0931154	−	0.407965i
$333$	−25.8401	−	32.4024i	−1.41603	−	1.77564i
$334$	2.11003	+	9.24463i	0.115455	+	0.505844i
$335$	11.9268	−	14.9557i	0.651631	−	0.817119i
$336$		0			0
$337$	2.24830	+	2.81928i	0.122473	+	0.153576i	0.839288	−	0.543687i	$-0.182972\pi$
$337$	2.24830	+	2.81928i	0.122473	+	0.153576i	−0.716815	+	0.697263i	$0.754401\pi$
$338$	4.54001	−	5.69299i	0.246944	−	0.309658i
$339$	25.6374	+	12.3463i	1.39243	+	0.670561i
$340$	1.21292	−	1.52095i	0.0657797	−	0.0824851i
$341$	−1.69026	+	7.40553i	−0.0915329	+	0.401032i
$342$	4.05993			0.219536
$343$		0			0
$344$	−1.35656			−0.0731406
$345$	19.4486	−	85.2099i	1.04708	−	4.58755i
$346$	−0.656216	+	0.822869i	−0.0352784	+	0.0442377i
$347$	14.9046	+	7.17767i	0.800120	+	0.385317i	0.788824	−	0.614619i	$-0.210690\pi$
$347$	14.9046	+	7.17767i	0.800120	+	0.385317i	0.0112956	+	0.999936i	$0.496404\pi$
$348$	8.17448	−	10.2505i	0.438198	−	0.549483i
$349$	−1.47185	−	1.84565i	−0.0787865	−	0.0987951i	0.740876	−	0.671642i	$-0.234411\pi$
$349$	−1.47185	−	1.84565i	−0.0787865	−	0.0987951i	−0.819663	+	0.572847i	$0.805839\pi$
$350$		0			0
$351$	15.8209	−	19.8388i	0.844458	−	1.05892i
$352$	0.673210	+	2.94953i	0.0358822	+	0.157210i
$353$	2.36737	+	2.96859i	0.126003	+	0.158002i	0.840831	−	0.541297i	$-0.182067\pi$
$353$	2.36737	+	2.96859i	0.126003	+	0.158002i	−0.714829	+	0.699300i	$0.753495\pi$
$354$	−2.15118	+	9.42492i	−0.114334	+	0.500929i
$355$	−38.5995	+	18.5885i	−2.04865	+	0.986577i
$356$	0.265089	−	1.16143i	0.0140497	−	0.0615558i
$357$		0			0
$358$	−2.26794	−	9.93649i	−0.119864	−	0.525160i
$359$	−17.4182	−	21.8418i	−0.919299	−	1.15276i	−0.987896	−	0.155120i	$-0.950424\pi$
$359$	−17.4182	−	21.8418i	−0.919299	−	1.15276i	0.0685967	−	0.997644i	$-0.478148\pi$
$360$	17.5855	−	8.46871i	0.926835	−	0.446340i
$361$	−18.6040			−0.979157
$362$	13.8789			0.729459
$363$	5.11617	−	2.46382i	0.268530	−	0.129317i
$364$		0			0
$365$	11.3364	+	5.45931i	0.593373	+	0.285753i
$366$	14.9485	+	7.19880i	0.781369	+	0.376287i
$367$	−6.93948	−	30.4038i	−0.362238	−	1.58707i	−0.747501	−	0.664260i	$-0.768747\pi$
$367$	−6.93948	−	30.4038i	−0.362238	−	1.58707i	0.385264	−	0.922807i	$-0.374110\pi$
$368$	2.09101	+	9.16134i	0.109002	+	0.477568i
$369$	12.0344	+	5.79548i	0.626488	+	0.301701i
$370$	−17.5102	−	8.43245i	−0.910310	−	0.438382i
$371$		0			0
$372$	−6.95448	+	3.34910i	−0.360573	+	0.173643i
$373$	−16.2454			−0.841155			−0.420578	−	0.907257i	$-0.638173\pi$
$373$	−16.2454			−0.841155			−0.420578	+	0.907257i	$0.638173\pi$
$374$	−1.94537			−0.100593
$375$	7.09843	−	3.41842i	0.366561	−	0.176527i
$376$	0.661056	+	0.828938i	0.0340914	+	0.0427492i
$377$	−2.26928	−	9.94235i	−0.116874	−	0.512057i
$378$		0			0
$379$	−6.55969	+	28.7399i	−0.336949	+	1.47627i	0.468426	+	0.883503i	$0.344821\pi$
$379$	−6.55969	+	28.7399i	−0.336949	+	1.47627i	−0.805375	+	0.592766i	$0.798036\pi$
$380$	1.71532	−	0.826052i	0.0879938	−	0.0423756i
$381$	9.16390	−	40.1497i	0.469481	−	2.05693i
$382$	−4.19109	−	5.25546i	−0.214435	−	0.268893i
$383$	−3.73776	−	16.3762i	−0.190991	−	0.836784i	−0.976082	−	0.217404i	$-0.930241\pi$
$383$	−3.73776	−	16.3762i	−0.190991	−	0.836784i	0.785091	−	0.619380i	$-0.212616\pi$
$384$	−1.91682	+	2.40361i	−0.0978172	+	0.122659i
$385$		0			0
$386$	1.44686	+	1.81431i	0.0736433	+	0.0923458i
$387$	5.45671	−	6.84250i	0.277380	−	0.347824i
$388$	14.7752	+	7.11534i	0.750095	+	0.361227i
$389$	−7.22891	+	9.06477i	−0.366520	+	0.459602i	−0.930557	−	0.366148i	$-0.880676\pi$
$389$	−7.22891	+	9.06477i	−0.366520	+	0.459602i	0.564036	+	0.825750i	$0.309248\pi$
$390$	4.94925	−	21.6841i	0.250615	−	1.09802i
$391$	−6.04238			−0.305576
$392$		0			0
$393$	−59.7585			−3.01442
$394$	1.94106	−	8.50435i	0.0977893	−	0.428443i
$395$	−21.1663	+	26.5417i	−1.06499	+	1.33546i
$396$	−17.5855	−	8.46871i	−0.883702	−	0.425569i
$397$	−8.51285	+	10.6748i	−0.427247	+	0.535751i	−0.948132	−	0.317875i	$-0.897031\pi$
$397$	−8.51285	+	10.6748i	−0.427247	+	0.535751i	0.520885	+	0.853627i	$0.325602\pi$
$398$	−6.65827	−	8.34921i	−0.333749	−	0.418508i
$399$		0			0
$400$	2.58931	−	3.24689i	0.129465	−	0.162344i
$401$	−2.68854	−	11.7792i	−0.134259	−	0.588228i	−0.996636	−	0.0819601i	$-0.973882\pi$
$401$	−2.68854	−	11.7792i	−0.134259	−	0.588228i	0.862377	−	0.506267i	$-0.168975\pi$
$402$	−12.1198	−	15.1977i	−0.604481	−	0.757995i
$403$	−1.33602	+	5.85347i	−0.0665517	+	0.291582i
$404$	12.9467	−	6.23479i	0.644122	−	0.310193i
$405$	−8.93203	+	39.1338i	−0.443836	+	1.94457i
$406$		0			0
$407$	4.32465	+	18.9475i	0.214365	+	0.939195i
$408$	−1.23254	−	1.54556i	−0.0610201	−	0.0765167i
$409$	−22.6745	+	10.9195i	−1.12118	+	0.539933i	−0.900257	−	0.435358i	$-0.856622\pi$
$409$	−22.6745	+	10.9195i	−1.12118	+	0.539933i	−0.220924	+	0.975291i	$0.570907\pi$
$410$	6.26372			0.309343
$411$	24.2446			1.19590
$412$	−14.7149	+	7.08630i	−0.724949	+	0.349117i
$413$		0			0
$414$	−54.6210	−	26.3041i	−2.68448	−	1.29278i
$415$	20.7831	+	10.0086i	1.02020	+	0.491303i
$416$	0.532118	+	2.33136i	0.0260892	+	0.114304i
$417$	−0.200575	−	0.878776i	−0.00982219	−	0.0430338i
$418$	−1.71532	−	0.826052i	−0.0838988	−	0.0404035i
$419$	19.3992	+	9.34214i	0.947711	+	0.456393i	0.842883	−	0.538097i	$-0.180857\pi$
$419$	19.3992	+	9.34214i	0.947711	+	0.456393i	0.104828	+	0.994490i	$0.466571\pi$
$420$		0			0
$421$	25.2231	−	12.1468i	1.22930	−	0.591998i	0.297411	−	0.954750i	$-0.403877\pi$
$421$	25.2231	−	12.1468i	1.22930	−	0.591998i	0.931886	+	0.362751i	$0.118163\pi$
$422$	14.2225			0.692339
$423$	−6.84026			−0.332585
$424$	4.22215	−	2.03328i	0.205046	−	0.0987448i
$425$	1.66497	+	2.08780i	0.0807628	+	0.101273i
$426$	9.68755	+	42.4439i	0.469363	+	2.05642i
$427$		0			0
$428$	−3.71249	+	16.2655i	−0.179450	+	0.786222i
$429$	−20.0391	+	9.65033i	−0.967497	+	0.465922i
$430$	0.913247	−	4.00120i	0.0440407	−	0.192955i
$431$	−11.0229	−	13.8223i	−0.530956	−	0.665798i	0.441939	−	0.897045i	$-0.354291\pi$
$431$	−11.0229	−	13.8223i	−0.530956	−	0.665798i	−0.972895	+	0.231247i	$0.925719\pi$
$432$	−2.36122	−	10.3452i	−0.113604	−	0.497732i
$433$	0.735843	−	0.922718i	0.0353624	−	0.0443430i	−0.763836	−	0.645411i	$-0.776686\pi$
$433$	0.735843	−	0.922718i	0.0353624	−	0.0443430i	0.799198	+	0.601068i	$0.205258\pi$
$434$		0			0
$435$	24.7309	+	31.0116i	1.18576	+	1.48689i
$436$	1.03820	−	1.30186i	0.0497207	−	0.0623478i
$437$	−5.32783	−	2.56575i	−0.254865	−	0.122736i
$438$	7.97196	−	9.99653i	0.380915	−	0.477653i
$439$	−4.75079	+	20.8146i	−0.226743	+	0.993424i	0.725534	+	0.688187i	$0.241593\pi$
$439$	−4.75079	+	20.8146i	−0.226743	+	0.993424i	−0.952276	+	0.305238i	$0.901264\pi$
$440$	−9.15293			−0.436349
$441$		0			0
$442$	−1.53766			−0.0731388
$443$	−1.91875	+	8.40661i	−0.0911627	+	0.399410i	−0.999836	−	0.0180974i	$-0.994239\pi$
$443$	−1.91875	+	8.40661i	−0.0911627	+	0.399410i	0.908673	+	0.417507i	$0.137096\pi$
$444$	−12.3135	+	15.4406i	−0.584372	+	0.732780i
$445$	3.24721	+	1.56378i	0.153933	+	0.0741301i
$446$	−6.04522	+	7.58047i	−0.286249	+	0.358946i
$447$	−13.5967	−	17.0497i	−0.643100	−	0.806422i
$448$		0			0
$449$	10.4421	−	13.0940i	0.492794	−	0.617944i	−0.471793	−	0.881710i	$-0.656393\pi$
$449$	10.4421	−	13.0940i	0.492794	−	0.617944i	0.964587	+	0.263765i	$0.0849644\pi$
$450$	5.96196	+	26.1211i	0.281049	+	1.23136i
$451$	−3.90536	−	4.89717i	−0.183896	−	0.230599i
$452$	2.05961	−	9.02372i	0.0968757	−	0.424440i
$453$	−32.6763	+	15.7361i	−1.53526	+	0.739345i
$454$	1.37874	−	6.04064i	0.0647073	−	0.283501i
$455$		0			0
$456$	−0.430503	−	1.88616i	−0.0201602	−	0.0883275i
$457$	4.99775	+	6.26698i	0.233785	+	0.293157i	0.884861	−	0.465856i	$-0.154253\pi$
$457$	4.99775	+	6.26698i	0.233785	+	0.293157i	−0.651076	+	0.759013i	$0.725682\pi$
$458$	−0.493118	+	0.237473i	−0.0230419	+	0.0110964i
$459$	6.82319			0.318479
$460$	−28.4293			−1.32552
$461$	16.3204	−	7.85951i	0.760118	−	0.366054i	−0.0133316	−	0.999911i	$-0.504244\pi$
$461$	16.3204	−	7.85951i	0.760118	−	0.366054i	0.773450	+	0.633857i	$0.218529\pi$
$462$		0			0
$463$	−4.79374	−	2.30855i	−0.222784	−	0.107287i	0.319163	−	0.947700i	$-0.396598\pi$
$463$	−4.79374	−	2.30855i	−0.222784	−	0.107287i	−0.541947	+	0.840413i	$0.682313\pi$
$464$	−3.84228	−	1.85034i	−0.178373	−	0.0859001i
$465$	−5.19644	−	22.7671i	−0.240979	−	1.05580i
$466$	1.50819	+	6.60783i	0.0698657	+	0.306102i
$467$	−30.2327	−	14.5593i	−1.39900	−	0.673724i	−0.426043	−	0.904703i	$-0.640093\pi$
$467$	−30.2327	−	14.5593i	−1.39900	−	0.673724i	−0.972959	+	0.230979i	$0.925807\pi$
$468$	−13.8999	−	6.69383i	−0.642522	−	0.309422i
$469$		0			0
$470$	−2.89001	+	1.39175i	−0.133306	+	0.0641968i
$471$	40.4493			1.86380
$472$	3.14452			0.144738
$473$	−3.69766	+	1.78070i	−0.170019	+	0.0818767i
$474$	21.5088	+	26.9712i	0.987932	+	1.23883i
$475$	0.581540	+	2.54789i	0.0266829	+	0.116905i
$476$		0			0
$477$	−6.72758	+	29.4754i	−0.308035	+	1.34959i
$478$	−6.12799	+	2.95108i	−0.280288	+	0.134979i
$479$	−3.72555	+	16.3227i	−0.170225	+	0.745804i	0.815681	+	0.578502i	$0.196363\pi$
$479$	−3.72555	+	16.3227i	−0.170225	+	0.745804i	−0.985906	+	0.167302i	$0.946495\pi$
$480$	−5.79910	−	7.27184i	−0.264692	−	0.331913i
$481$	3.41829	+	14.9765i	0.155860	+	0.682869i
$482$	16.2509	−	20.3780i	0.740207	−	0.928190i
$483$		0			0
$484$	−1.15163	−	1.44410i	−0.0523469	−	0.0656409i
$485$	−30.9337	+	38.7896i	−1.40463	+	1.76135i
$486$	8.06916	+	3.88590i	0.366024	+	0.176268i
$487$	16.6150	−	20.8346i	0.752899	−	0.944105i	−0.246789	−	0.969069i	$-0.579376\pi$
$487$	16.6150	−	20.8346i	0.752899	−	0.944105i	0.999688	+	0.0249638i	$0.00794704\pi$
$488$	1.20090	−	5.26148i	0.0543621	−	0.238176i
$489$	41.2290			1.86444
$490$		0			0
$491$	7.56655			0.341474			0.170737	−	0.985317i	$-0.445385\pi$
$491$	7.56655			0.341474			0.170737	+	0.985317i	$0.445385\pi$
$492$	1.41636	−	6.20549i	0.0638546	−	0.279765i
$493$	1.70974	−	2.14395i	0.0770029	−	0.0965586i
$494$	−1.35582	−	0.652927i	−0.0610011	−	0.0293766i
$495$	36.8174	−	46.1676i	1.65482	−	2.07508i
$496$	1.56543	+	1.96298i	0.0702898	+	0.0881406i
$497$		0			0
$498$	14.6151	−	18.3267i	0.654916	−	0.821239i
$499$	2.33363	+	10.2243i	0.104468	+	0.457702i	0.999921	+	0.0125476i	$0.00399412\pi$
$499$	2.33363	+	10.2243i	0.104468	+	0.457702i	−0.895454	+	0.445155i	$0.853149\pi$
$500$	−1.59783	−	2.00361i	−0.0714571	−	0.0896044i
$501$	−6.48693	+	28.4211i	−0.289815	+	1.26976i
$502$	23.5981	−	11.3643i	1.05324	−	0.507212i
$503$	−0.109148	+	0.478210i	−0.00486668	+	0.0213223i	−0.977303	−	0.211846i	$-0.932052\pi$
$503$	−0.109148	+	0.478210i	−0.00486668	+	0.0213223i	0.972436	+	0.233169i	$0.0749095\pi$
$504$		0			0
$505$	9.67386	+	42.3839i	0.430481	+	1.88606i
$506$	17.7254	+	22.2269i	0.787989	+	0.988107i
$507$	20.1692	−	9.71296i	0.895745	−	0.431368i
$508$	−13.3955			−0.594328
$509$	15.9439			0.706703			0.353351	−	0.935491i	$-0.385042\pi$
$509$	15.9439			0.706703			0.353351	+	0.935491i	$0.385042\pi$
$510$	5.38844	−	2.59494i	0.238604	−	0.114906i
$511$		0			0
$512$	0.900969	+	0.433884i	0.0398176	+	0.0191751i
$513$	6.01630	+	2.89730i	0.265626	+	0.127919i
$514$	−2.98341	−	13.0712i	−0.131593	−	0.576545i
$515$	−10.9950	−	48.1724i	−0.484500	−	2.12273i
$516$	−3.75750	−	1.80952i	−0.165415	−	0.0796595i
$517$	2.89001	+	1.39175i	0.127102	+	0.0612093i
$518$		0			0
$519$	−2.91527	+	1.40392i	−0.127966	+	0.0616252i
$520$	−7.23464			−0.317260
$521$	−31.8495			−1.39535			−0.697677	−	0.716413i	$-0.745783\pi$
$521$	−31.8495			−1.39535			−0.697677	+	0.716413i	$0.745783\pi$
$522$	24.7886	−	11.9376i	1.08497	−	0.522494i
$523$	26.4558	+	33.1745i	1.15683	+	1.45062i	0.870282	+	0.492554i	$0.163937\pi$
$523$	26.4558	+	33.1745i	1.15683	+	1.45062i	0.286549	+	0.958066i	$0.407492\pi$
$524$	4.32533	+	18.9505i	0.188953	+	0.827856i
$525$		0			0
$526$	−2.35041	+	10.2978i	−0.102483	+	0.449006i
$527$	−1.45457	+	0.700485i	−0.0633622	+	0.0305136i
$528$	−2.06968	+	9.06784i	−0.0900711	+	0.394627i
$529$	40.7154	+	51.0555i	1.77023	+	2.21980i
$530$	3.15482	+	13.8222i	0.137037	+	0.600397i
$531$	−12.6487	+	15.8610i	−0.548908	+	0.688309i
$532$		0			0
$533$	−3.08687	−	3.87082i	−0.133707	−	0.167664i
$534$	2.28351	−	2.86342i	0.0988169	−	0.123913i
$535$	−45.4762	−	21.9002i	−1.96611	−	0.946827i
$536$	−3.94225	+	4.94342i	−0.170279	+	0.213523i
$537$	6.97241	−	30.5481i	0.300881	−	1.31825i
$538$	−11.9198			−0.513898
$539$		0			0
$540$	32.1030			1.38149
$541$	−1.45562	+	6.37750i	−0.0625821	+	0.274190i	−0.996532	−	0.0832148i	$-0.973481\pi$
$541$	−1.45562	+	6.37750i	−0.0625821	+	0.274190i	0.933950	+	0.357405i	$0.116338\pi$
$542$	15.5062	−	19.4442i	0.666049	−	0.835199i
$543$	38.4429	+	18.5131i	1.64974	+	0.794475i
$544$	−0.400914	+	0.502730i	−0.0171890	+	0.0215544i
$545$	3.14094	+	3.93862i	0.134543	+	0.168712i
$546$		0			0
$547$	11.3933	−	14.2867i	0.487141	−	0.610856i	−0.476134	−	0.879373i	$-0.657962\pi$
$547$	11.3933	−	14.2867i	0.487141	−	0.610856i	0.963275	+	0.268517i	$0.0865336\pi$
$548$	−1.75483	−	7.68840i	−0.0749625	−	0.328432i
$549$	21.7084	+	27.2215i	0.926494	+	1.16179i
$550$	2.79579	−	12.2492i	0.119213	−	0.522306i
$551$	2.41793	−	1.16441i	0.103007	−	0.0496056i
$552$	−6.42848	+	28.1650i	−0.273614	+	1.19878i
$553$		0			0
$554$	6.18154	+	27.0831i	0.262629	+	1.15065i
$555$	−37.2530	−	46.7138i	−1.58130	−	1.98289i
$556$	−0.264158	+	0.127212i	−0.0112028	+	0.00539498i
$557$	−36.4469			−1.54431			−0.772153	−	0.635436i	$-0.780820\pi$
$557$	−36.4469			−1.54431			−0.772153	+	0.635436i	$0.780820\pi$
$558$	−16.1982			−0.685726
$559$	−2.92270	+	1.40750i	−0.123617	+	0.0595309i
$560$		0			0
$561$	−5.38844	−	2.59494i	−0.227500	−	0.109558i
$562$	−28.1008	−	13.5326i	−1.18536	−	0.570840i
$563$	1.36966	+	6.00086i	0.0577242	+	0.252906i	0.995554	−	0.0941881i	$-0.0300255\pi$
$563$	1.36966	+	6.00086i	0.0577242	+	0.252906i	−0.937830	+	0.347094i	$0.887168\pi$
$564$	0.725323	+	3.17785i	0.0305416	+	0.133811i
$565$	25.2292	+	12.1497i	1.06140	+	0.511143i
$566$	17.1030	+	8.23635i	0.718891	+	0.346200i
$567$		0			0
$568$	12.7586	−	6.14419i	0.535337	−	0.257805i
$569$	8.41931			0.352956			0.176478	−	0.984305i	$-0.443530\pi$
$569$	8.41931			0.352956			0.176478	+	0.984305i	$0.443530\pi$
$570$	5.85310			0.245159
$571$	31.5658	−	15.2013i	1.32099	−	0.636155i	0.365398	−	0.930851i	$-0.380933\pi$
$571$	31.5658	−	15.2013i	1.32099	−	0.636155i	0.955591	+	0.294696i	$0.0952185\pi$
$572$	4.51073	+	5.65627i	0.188603	+	0.236501i
$573$	−4.59854	−	20.1475i	−0.192107	−	0.841675i
$574$		0			0
$575$	8.68383	−	38.0464i	0.362141	−	1.58664i
$576$	−5.81264	+	2.79922i	−0.242193	+	0.116634i
$577$	−7.74498	+	33.9330i	−0.322428	+	1.41265i	0.510791	+	0.859705i	$0.329352\pi$
$577$	−7.74498	+	33.9330i	−0.322428	+	1.41265i	−0.833219	+	0.552943i	$0.813505\pi$
$578$	10.3415	+	12.9679i	0.430151	+	0.539392i
$579$	1.58752	+	6.95539i	0.0659752	+	0.289056i
$580$	8.04430	−	10.0872i	0.334022	−	0.418850i
$581$		0			0
$582$	31.4343	+	39.4173i	1.30299	+	1.63390i
$583$	8.83961	−	11.0845i	0.366099	−	0.459074i
$584$	−3.74709	−	1.80450i	−0.155056	−	0.0746709i
$585$	29.1012	−	36.4917i	1.20319	−	1.50875i
$586$	−4.36629	+	19.1300i	−0.180370	+	0.790253i
$587$	−19.8051			−0.817443			−0.408722	−	0.912659i	$-0.634025\pi$
$587$	−19.8051			−0.817443			−0.408722	+	0.912659i	$0.634025\pi$
$588$		0			0
$589$	−1.58000			−0.0651029
$590$	−2.11692	+	9.27484i	−0.0871523	+	0.381839i
$591$	16.7205	−	20.9669i	0.687790	−	0.862461i
$592$	5.78775	+	2.78724i	0.237875	+	0.114555i
$593$	−6.57004	+	8.23857i	−0.269799	+	0.338317i	−0.898212	−	0.439563i	$-0.855133\pi$
$593$	−6.57004	+	8.23857i	−0.269799	+	0.338317i	0.628413	+	0.777880i	$0.283705\pi$
$594$	−20.0159	−	25.0991i	−0.821261	−	1.02983i
$595$		0			0
$596$	−4.42263	+	5.54581i	−0.181158	+	0.227165i
$597$	−7.30558	−	32.0078i	−0.298997	−	1.30999i
$598$	14.0105	+	17.5686i	0.572931	+	0.718433i
$599$	0.828100	−	3.62814i	0.0338352	−	0.148242i	−0.955189	−	0.295998i	$-0.904348\pi$
$599$	0.828100	−	3.62814i	0.0338352	−	0.148242i	0.989024	+	0.147756i	$0.0472050\pi$
$600$	11.5031	−	5.53961i	0.469613	−	0.226154i
$601$	0.0432317	−	0.189411i	0.00176346	−	0.00772622i	−0.974039	−	0.226382i	$-0.927310\pi$
$601$	0.0432317	−	0.189411i	0.00176346	−	0.00772622i	0.975802	+	0.218656i	$0.0701673\pi$
$602$		0			0
$603$	−9.07715	−	39.7696i	−0.369650	−	1.61954i
$604$	7.35530	+	9.22326i	0.299283	+	0.375289i
$605$	5.03470	−	2.42459i	0.204690	−	0.0985734i
$606$	44.1774			1.79458
$607$	20.2928			0.823658			0.411829	−	0.911261i	$-0.364890\pi$
$607$	20.2928			0.823658			0.411829	+	0.911261i	$0.364890\pi$
$608$	−0.566975	+	0.273041i	−0.0229939	+	0.0110733i
$609$		0			0
$610$	14.7104	+	7.08417i	0.595608	+	0.286830i
$611$	2.28431	+	1.10007i	0.0924135	+	0.0445040i
$612$	−0.923117	−	4.04444i	−0.0373148	−	0.163487i
$613$	−3.25039	−	14.2409i	−0.131282	−	0.575185i	−0.997186	−	0.0749735i	$-0.976113\pi$
$613$	−3.25039	−	14.2409i	−0.131282	−	0.575185i	0.865903	−	0.500211i	$-0.166744\pi$
$614$	−18.9699	−	9.13542i	−0.765563	−	0.368675i
$615$	17.3498	+	8.35520i	0.699610	+	0.336914i
$616$		0			0
$617$	−10.5371	+	5.07442i	−0.424209	+	0.204288i	−0.633794	−	0.773502i	$-0.718503\pi$
$617$	−10.5371	+	5.07442i	−0.424209	+	0.204288i	0.209584	+	0.977791i	$0.432789\pi$
$618$	−50.2109			−2.01978
$619$	37.4631			1.50577			0.752885	−	0.658152i	$-0.228662\pi$
$619$	37.4631			1.50577			0.752885	+	0.658152i	$0.228662\pi$
$620$	−6.84374	+	3.29577i	−0.274851	+	0.132361i
$621$	−62.1700	−	77.9587i	−2.49480	−	3.12838i
$622$	2.62030	+	11.4803i	0.105064	+	0.460317i
$623$		0			0
$624$	−1.63591	+	7.16739i	−0.0654888	+	0.286925i
$625$	25.6937	−	12.3734i	1.02775	−	0.494937i
$626$	−4.77356	+	20.9143i	−0.190790	+	0.835905i
$627$	−3.64935	−	4.57614i	−0.145741	−	0.182753i
$628$	−2.92772	−	12.8272i	−0.116829	−	0.511861i
$629$	−2.57544	+	3.22950i	−0.102690	+	0.128769i
$630$		0			0
$631$	−8.17143	−	10.2467i	−0.325300	−	0.407913i	0.592110	−	0.805857i	$-0.298295\pi$
$631$	−8.17143	−	10.2467i	−0.325300	−	0.407913i	−0.917410	+	0.397944i	$0.869724\pi$
$632$	6.99624	−	8.77301i	0.278296	−	0.348972i
$633$	39.3945	+	18.9714i	1.56579	+	0.754046i
$634$	−18.5073	+	23.2074i	−0.735017	+	0.921682i
$635$	9.01798	−	39.5103i	0.357867	−	1.56792i
$636$	14.4071			0.571277
$637$		0			0
$638$	−12.9021			−0.510798
$639$	−20.3295	+	89.0693i	−0.804222	+	3.52353i
$640$	−1.88629	+	2.36534i	−0.0745623	+	0.0934982i
$641$	10.3864	+	5.00184i	0.410239	+	0.197561i	0.627609	−	0.778528i	$-0.284034\pi$
$641$	10.3864	+	5.00184i	0.410239	+	0.197561i	−0.217370	+	0.976089i	$0.569748\pi$
$642$	−31.9798	+	40.1013i	−1.26214	+	1.58267i
$643$	14.3138	+	17.9489i	0.564481	+	0.707836i	0.979379	−	0.202031i	$-0.0647543\pi$
$643$	14.3138	+	17.9489i	0.564481	+	0.707836i	−0.414898	+	0.909868i	$0.636183\pi$
$644$		0			0
$645$	7.86680	−	9.86466i	0.309755	−	0.388421i
$646$	−0.0900424	−	0.394502i	−0.00354267	−	0.0155215i
$647$	−1.62204	−	2.03397i	−0.0637689	−	0.0799636i	0.748924	−	0.662656i	$-0.230571\pi$
$647$	−1.62204	−	2.03397i	−0.0637689	−	0.0799636i	−0.812693	+	0.582692i	$0.801999\pi$
$648$	2.95237	−	12.9352i	0.115980	−	0.508141i
$649$	8.57124	−	4.12769i	0.336451	−	0.162026i
$650$	2.20985	−	9.68197i	0.0866773	−	0.379758i
$651$		0			0
$652$	−2.98416	−	13.0745i	−0.116869	−	0.512036i
$653$	22.0743	+	27.6803i	0.863835	+	1.08321i	0.995763	+	0.0919555i	$0.0293117\pi$
$653$	22.0743	+	27.6803i	0.863835	+	1.08321i	−0.131928	+	0.991259i	$0.542117\pi$
$654$	4.61224	−	2.22114i	0.180353	−	0.0868534i
$655$	−58.8069			−2.29777
$656$	−2.07039			−0.0808351
$657$	24.1745	−	11.6418i	0.943139	−	0.454192i
$658$		0			0
$659$	24.6402	+	11.8661i	0.959847	+	0.462238i	0.847128	−	0.531389i	$-0.178330\pi$
$659$	24.6402	+	11.8661i	0.959847	+	0.462238i	0.112719	+	0.993627i	$0.464044\pi$
$660$	−25.3525	−	12.2091i	−0.986846	−	0.475240i
$661$	0.769109	+	3.36968i	0.0299149	+	0.131066i	0.987680	−	0.156485i	$-0.0500162\pi$
$661$	0.769109	+	3.36968i	0.0299149	+	0.131066i	−0.957765	+	0.287550i	$0.907159\pi$
$662$	−0.182676	−	0.800355i	−0.00709989	−	0.0311067i
$663$	−4.25912	−	2.05109i	−0.165411	−	0.0796576i
$664$	−6.86957	−	3.30821i	−0.266591	−	0.128383i
$665$		0			0
$666$	−37.3400	+	17.9820i	−1.44689	+	0.696788i
$667$	−40.0743			−1.55168
$668$	9.48237			0.366884
$669$	−26.8562	+	12.9332i	−1.03832	+	0.500028i
$670$	−11.9268	−	14.9557i	−0.460772	−	0.577790i
$671$	−3.63318	−	15.9180i	−0.140257	−	0.614507i
$672$		0			0
$673$	4.76589	−	20.8807i	0.183712	−	0.804893i	−0.796131	−	0.605124i	$-0.793124\pi$
$673$	4.76589	−	20.8807i	0.183712	−	0.804893i	0.979843	−	0.199769i	$-0.0640192\pi$
$674$	3.24888	−	1.56458i	0.125142	−	0.0602654i
$675$	−9.80597	+	42.9627i	−0.377432	+	1.65364i
$676$	−4.54001	−	5.69299i	−0.174616	−	0.218961i
$677$	−4.14397	−	18.1559i	−0.159266	−	0.697789i	−0.989994	−	0.141111i	$-0.954933\pi$
$677$	−4.14397	−	18.1559i	−0.159266	−	0.697789i	0.830728	−	0.556679i	$-0.187924\pi$
$678$	17.7416	−	22.2473i	0.681364	−	0.854403i
$679$		0			0
$680$	−1.21292	−	1.52095i	−0.0465133	−	0.0583258i
$681$	11.8766	−	14.8928i	0.455111	−	0.570692i
$682$	6.84374	+	3.29577i	0.262060	+	0.126202i
$683$	−3.88430	+	4.87076i	−0.148629	+	0.186374i	−0.850572	−	0.525858i	$-0.823744\pi$
$683$	−3.88430	+	4.87076i	−0.148629	+	0.186374i	0.701944	+	0.712232i	$0.252316\pi$
$684$	0.903419	−	3.95814i	0.0345431	−	0.151343i
$685$	23.8585			0.911587
$686$		0			0
$687$	−1.68264			−0.0641969
$688$	−0.301862	+	1.32254i	−0.0115084	+	0.0504215i
$689$	6.98700	−	8.76142i	0.266183	−	0.333783i
$690$	−78.7458	−	37.9220i	−2.99780	−	1.44367i
$691$	14.0148	−	17.5739i	0.533146	−	0.668544i	−0.440196	−	0.897902i	$-0.645091\pi$
$691$	14.0148	−	17.5739i	0.533146	−	0.668544i	0.973342	+	0.229357i	$0.0736625\pi$
$692$	0.656216	+	0.822869i	0.0249456	+	0.0312808i
$693$		0			0
$694$	10.3143	−	12.9337i	0.391525	−	0.490957i
$695$	−0.197381	−	0.864782i	−0.00748708	−	0.0328030i
$696$	−8.17448	−	10.2505i	−0.309853	−	0.388543i
$697$	0.296241	−	1.29792i	0.0112209	−	0.0491621i
$698$	−2.12689	+	1.02426i	−0.0805039	+	0.0387687i
$699$	−4.63669	+	20.3147i	−0.175376	+	0.768372i
$700$		0			0
$701$	5.47281	+	23.9779i	0.206705	+	0.905634i	0.966742	+	0.255754i	$0.0823237\pi$
$701$	5.47281	+	23.9779i	0.206705	+	0.905634i	−0.760037	+	0.649880i	$0.774819\pi$
$702$	−15.8209	−	19.8388i	−0.597122	−	0.748768i
$703$	−3.64220	+	1.75399i	−0.137368	+	0.0661531i
$704$	3.02538			0.114023
$705$	−9.86144			−0.371403
$706$	3.42095	−	1.64744i	0.128749	−	0.0620024i
$707$		0			0
$708$	8.70994	+	4.19448i	0.327340	+	0.157638i
$709$	−3.78492	−	1.82272i	−0.142146	−	0.0684538i	0.361459	−	0.932388i	$-0.382279\pi$
$709$	−3.78492	−	1.82272i	−0.142146	−	0.0684538i	−0.503605	+	0.863934i	$0.667993\pi$
$710$	9.53328	+	41.7680i	0.357778	+	1.56753i
$711$	16.1091	+	70.5784i	0.604137	+	2.64690i
$712$	−1.07332	−	0.516886i	−0.0402245	−	0.0193711i
$713$	21.2569	+	10.2368i	0.796077	+	0.383370i
$714$		0			0
$715$	−19.7200	+	9.49665i	−0.737486	+	0.355155i
$716$	−10.1920			−0.380894
$717$	−20.9103			−0.780908
$718$	−25.1701	+	12.1213i	−0.939339	+	0.452362i
$719$	−28.8282	−	36.1494i	−1.07511	−	1.34815i	−0.933644	−	0.358203i	$-0.883390\pi$
$719$	−28.8282	−	36.1494i	−1.07511	−	1.34815i	−0.141467	−	0.989943i	$-0.545182\pi$
$720$	−4.34325	−	19.0290i	−0.161863	−	0.709170i
$721$		0			0
$722$	−4.13978	+	18.1375i	−0.154067	+	0.675010i
$723$	72.1952	−	34.7674i	2.68497	−	1.29301i
$724$	3.08835	−	13.5309i	0.114778	−	0.502873i
$725$	11.0424	+	13.8467i	0.410104	+	0.514254i
$726$	−1.26359	−	5.53615i	−0.0468963	−	0.205466i
$727$	−0.337641	+	0.423389i	−0.0125224	+	0.0157026i	−0.788053	−	0.615607i	$-0.788911\pi$
$727$	−0.337641	+	0.423389i	−0.0125224	+	0.0157026i	0.775531	+	0.631310i	$0.217482\pi$
$728$		0			0
$729$	−7.64986	−	9.59262i	−0.283328	−	0.355282i
$730$	7.84502	−	9.83734i	0.290357	−	0.364096i
$731$	−0.785903	−	0.378471i	−0.0290677	−	0.0139983i
$732$	10.3447	−	12.9718i	0.382350	−	0.479451i
$733$	3.74578	−	16.4114i	0.138354	−	0.606167i	−0.857443	−	0.514579i	$-0.827948\pi$
$733$	3.74578	−	16.4114i	0.138354	−	0.606167i	0.995797	−	0.0915886i	$-0.0291945\pi$
$734$	−31.1857			−1.15109
$735$		0			0
$736$	9.39694			0.346376
$737$	−4.25663	+	18.6495i	−0.156795	+	0.686963i
$738$	8.32809	−	10.4431i	0.306561	−	0.384416i
$739$	12.0260	+	5.79140i	0.442382	+	0.213040i	0.641796	−	0.766875i	$-0.278189\pi$
$739$	12.0260	+	5.79140i	0.442382	+	0.213040i	−0.199414	+	0.979915i	$0.563904\pi$
$740$	−12.1174	+	15.1947i	−0.445445	+	0.558570i
$741$	−2.88451	−	3.61706i	−0.105965	−	0.132876i
$742$		0			0
$743$	−25.2863	+	31.7080i	−0.927663	+	1.16325i	0.0586353	+	0.998279i	$0.481325\pi$
$743$	−25.2863	+	31.7080i	−0.927663	+	1.16325i	−0.986298	+	0.164973i	$0.947246\pi$
$744$	1.71762	+	7.52537i	0.0629709	+	0.275893i
$745$	−13.3801	−	16.7782i	−0.490211	−	0.614705i
$746$	−3.61494	+	15.8381i	−0.132352	+	0.579874i
$747$	44.3193	−	21.3431i	1.62156	−	0.780902i
$748$	−0.432885	+	1.89659i	−0.0158279	+	0.0693464i
$749$		0			0
$750$	−1.75317	−	7.68113i	−0.0640166	−	0.280475i
$751$	−13.8236	−	17.3343i	−0.504431	−	0.632536i	0.462792	−	0.886467i	$-0.346848\pi$
$751$	−13.8236	−	17.3343i	−0.504431	−	0.632536i	−0.967222	+	0.253931i	$0.918276\pi$
$752$	0.955254	−	0.460026i	0.0348345	−	0.0167754i
$753$	80.5229			2.93442
$754$	−10.1980			−0.371390
$755$	−32.1559	+	15.4855i	−1.17027	+	0.563574i
$756$		0			0
$757$	−16.4965	−	7.94430i	−0.599576	−	0.288740i	0.109373	−	0.994001i	$-0.465116\pi$
$757$	−16.4965	−	7.94430i	−0.599576	−	0.288740i	−0.708948	+	0.705260i	$0.750830\pi$
$758$	26.5597	+	12.7905i	0.964690	+	0.464570i
$759$	19.4486	+	85.2099i	0.705940	+	3.09292i
$760$	−0.423648	−	1.85612i	−0.0153673	−	0.0673287i
$761$	23.8595	+	11.4902i	0.864908	+	0.416518i	0.813089	−	0.582139i	$-0.197784\pi$
$761$	23.8595	+	11.4902i	0.864908	+	0.416518i	0.0518185	+	0.998657i	$0.483498\pi$
$762$	−37.1039	−	17.8683i	−1.34413	−	0.647300i
$763$		0			0
$764$	−6.05630	+	2.91656i	−0.219109	+	0.105518i
$765$	12.5506			0.453769
$766$	−16.7973			−0.606912
$767$	6.77487	−	3.26260i	0.244626	−	0.117806i
$768$	1.91682	+	2.40361i	0.0691672	+	0.0867329i
$769$	−11.1387	−	48.8018i	−0.401671	−	1.75984i	−0.620631	−	0.784103i	$-0.713123\pi$
$769$	−11.1387	−	48.8018i	−0.401671	−	1.75984i	0.218960	−	0.975734i	$-0.429734\pi$
$770$		0			0
$771$	9.17201	−	40.1852i	0.330322	−	1.44724i
$772$	2.09078	−	1.00686i	0.0752486	−	0.0362378i
$773$	−2.10947	+	9.24219i	−0.0758723	+	0.332418i	−0.998592	−	0.0530541i	$-0.983104\pi$
$773$	−2.10947	+	9.24219i	−0.0758723	+	0.332418i	0.922719	+	0.385473i	$0.125962\pi$
$774$	−5.45671	−	6.84250i	−0.196137	−	0.245948i
$775$	−2.32022	−	10.1655i	−0.0833447	−	0.365157i
$776$	10.2247	−	12.8214i	0.367046	−	0.460261i
$777$		0			0
$778$	7.22891	+	9.06477i	0.259169	+	0.324988i
$779$	0.812336	−	1.01864i	0.0291050	−	0.0364965i
$780$	−20.0391	−	9.65033i	−0.717515	−	0.345537i
$781$	26.7117	−	33.4954i	0.955819	−	1.19856i
$782$	−1.34456	+	5.89089i	−0.0480812	+	0.210658i
$783$	45.2527			1.61720
$784$		0			0
$785$	39.8052			1.42071
$786$	−13.2975	+	58.2602i	−0.474307	+	2.07807i
$787$	27.1997	−	34.1074i	0.969565	−	1.21580i	−0.00686820	−	0.999976i	$-0.502186\pi$
$787$	27.1997	−	34.1074i	0.969565	−	1.21580i	0.976433	−	0.215820i	$-0.0692423\pi$
$788$	−7.85920	−	3.78479i	−0.279972	−	0.134828i
$789$	−20.2466	+	25.3885i	−0.720800	+	0.903854i
$790$	21.1663	+	26.5417i	0.753063	+	0.944311i
$791$		0			0
$792$	−12.1695	+	15.2601i	−0.432425	+	0.542244i
$793$	−2.87173	−	12.5819i	−0.101978	−	0.446795i
$794$	8.51285	+	10.6748i	0.302110	+	0.378833i
$795$	−9.69898	+	42.4940i	−0.343988	+	1.50711i
$796$	−9.62148	+	4.63346i	−0.341024	+	0.164229i
$797$	−1.46387	+	6.41362i	−0.0518528	+	0.227182i	−0.994214	−	0.107414i	$-0.965743\pi$
$797$	−1.46387	+	6.41362i	−0.0518528	+	0.227182i	0.942362	+	0.334596i	$0.108600\pi$
$798$		0			0
$799$	0.151706	+	0.664666i	0.00536696	+	0.0235142i
$800$	−2.58931	−	3.24689i	−0.0915458	−	0.114795i
$801$	6.92460	−	3.33471i	0.244669	−	0.117826i
$802$	−12.0822			−0.426636
$803$	−12.5824			−0.444024
$804$	−17.5136	+	8.43411i	−0.617658	+	0.297448i
$805$		0			0
$806$	5.40942	+	2.60504i	0.190539	+	0.0917586i
$807$	−33.0163	−	15.8998i	−1.16223	−	0.559701i
$808$	−3.19757	−	14.0095i	−0.112490	−	0.492851i
$809$	−7.97579	−	34.9442i	−0.280414	−	1.22857i	−0.897265	−	0.441493i	$-0.854449\pi$
$809$	−7.97579	−	34.9442i	−0.280414	−	1.22857i	0.616851	−	0.787080i	$-0.288408\pi$
$810$	36.1651	+	17.4162i	1.27071	+	0.611942i
$811$	23.6835	+	11.4054i	0.831642	+	0.400498i	0.800731	−	0.599025i	$-0.204445\pi$
$811$	23.6835	+	11.4054i	0.831642	+	0.400498i	0.0309111	+	0.999522i	$0.490159\pi$
$812$		0			0
$813$	68.8871	−	33.1743i	2.41597	−	1.16347i
$814$	19.4348			0.681190
$815$	40.5725			1.42119
$816$	−1.78108	+	0.857722i	−0.0623502	+	0.0300263i
$817$	−0.532257	−	0.667429i	−0.0186213	−	0.0233504i
$818$	5.60014	+	24.5358i	0.195804	+	0.857874i
$819$		0			0
$820$	1.39381	−	6.10667i	0.0486739	−	0.213254i
$821$	−31.5369	+	15.1874i	−1.10065	+	0.530043i	−0.893861	−	0.448344i	$-0.852014\pi$
$821$	−31.5369	+	15.1874i	−1.10065	+	0.530043i	−0.206784	+	0.978387i	$0.566300\pi$
$822$	5.39493	−	23.6367i	0.188170	−	0.824426i
$823$	16.8693	+	21.1534i	0.588026	+	0.737361i	0.983458	−	0.181134i	$-0.0579767\pi$
$823$	16.8693	+	21.1534i	0.588026	+	0.737361i	−0.395433	+	0.918495i	$0.629405\pi$
$824$	3.63427	+	15.9228i	0.126606	+	0.554696i
$825$	24.0832	−	30.1994i	0.838471	−	1.05141i
$826$		0			0
$827$	−19.5888	−	24.5635i	−0.681168	−	0.854157i	0.314293	−	0.949326i	$-0.398232\pi$
$827$	−19.5888	−	24.5635i	−0.681168	−	0.854157i	−0.995461	+	0.0951686i	$0.969661\pi$
$828$	−37.7989	+	47.3984i	−1.31360	+	1.64721i
$829$	−17.2214	−	8.29339i	−0.598124	−	0.288041i	0.110222	−	0.993907i	$-0.464844\pi$
$829$	−17.2214	−	8.29339i	−0.598124	−	0.288041i	−0.708346	+	0.705866i	$0.750558\pi$
$830$	14.3823	−	18.0349i	0.499218	−	0.625999i
$831$	−19.0041	+	83.2626i	−0.659247	+	2.88835i
$832$	2.39132			0.0829040
$833$		0			0
$834$	−0.901375			−0.0312121
$835$	−6.38363	+	27.9685i	−0.220915	+	0.967890i
$836$	−1.18704	+	1.48850i	−0.0410545	+	0.0514807i
$837$	−24.0037	−	11.5596i	−0.829690	−	0.399558i
$838$	13.4246	−	16.8340i	0.463746	−	0.581519i
$839$	−6.82417	−	8.55724i	−0.235597	−	0.295429i	0.649952	−	0.759975i	$-0.274789\pi$
$839$	−6.82417	−	8.55724i	−0.235597	−	0.295429i	−0.885549	+	0.464546i	$0.846217\pi$
$840$		0			0
$841$	−6.74187	+	8.45403i	−0.232478	+	0.291518i
$842$	−6.22958	−	27.2936i	−0.214686	−	0.940599i
$843$	−59.7847	−	74.9676i	−2.05909	−	2.58202i
$844$	3.16480	−	13.8659i	0.108937	−	0.477283i
$845$	19.8480	−	9.55829i	0.682792	−	0.328815i
$846$	−1.52210	+	6.66876i	−0.0523309	+	0.229277i
$847$		0			0
$848$	−1.04279	−	4.56874i	−0.0358094	−	0.156891i
$849$	36.3867	+	45.6274i	1.24879	+	1.56593i
$850$	2.40595	−	1.15864i	0.0825233	−	0.0397411i
$851$	60.3652			2.06929
$852$	43.5355			1.49150
$853$	−44.1593	+	21.2660i	−1.51199	+	0.728134i	−0.992023	−	0.126056i	$-0.959768\pi$
$853$	−44.1593	+	21.2660i	−1.51199	+	0.728134i	−0.519962	+	0.854189i	$0.674054\pi$
$854$		0			0
$855$	11.0664	+	5.32932i	0.378464	+	0.182259i
$856$	15.0316	+	7.23882i	0.513768	+	0.247418i
$857$	−2.46292	−	10.7908i	−0.0841317	−	0.368605i	0.915283	−	0.402811i	$-0.131967\pi$
$857$	−2.46292	−	10.7908i	−0.0841317	−	0.368605i	−0.999415	+	0.0342061i	$0.989110\pi$
$858$	4.94925	+	21.6841i	0.168965	+	0.740282i
$859$	−13.3149	−	6.41211i	−0.454298	−	0.218778i	0.192719	−	0.981254i	$-0.438269\pi$
$859$	−13.3149	−	6.41211i	−0.454298	−	0.218778i	−0.647017	+	0.762476i	$0.723984\pi$
$860$	−3.69766	−	1.78070i	−0.126089	−	0.0607214i
$861$		0			0
$862$	−15.9286	+	7.67081i	−0.542530	+	0.261269i
$863$	−7.06992			−0.240663			−0.120331	−	0.992734i	$-0.538396\pi$
$863$	−7.06992			−0.240663			−0.120331	+	0.992734i	$0.538396\pi$
$864$	−10.6112			−0.361001
$865$	−2.86885	+	1.38156i	−0.0975437	+	0.0469745i
$866$	−0.735843	−	0.922718i	−0.0250050	−	0.0313552i
$867$	11.3469	+	49.7141i	0.385361	+	1.68838i
$868$		0			0
$869$	7.55417	−	33.0970i	0.256258	−	1.12274i
$870$	35.7372	−	17.2101i	1.21160	−	0.583478i
$871$	−3.36452	+	14.7409i	−0.114002	+	0.499477i
$872$	−1.03820	−	1.30186i	−0.0351578	−	0.0440865i
$873$	23.5427	+	103.148i	0.796801	+	3.49101i
$874$	−3.68697	+	4.62332i	−0.124714	+	0.156386i
$875$		0			0
$876$	−7.97196	−	9.99653i	−0.269348	−	0.337751i
$877$	30.0485	−	37.6796i	1.01467	−	1.27235i	0.0528650	−	0.998602i	$-0.483165\pi$
$877$	30.0485	−	37.6796i	1.01467	−	1.27235i	0.961801	−	0.273749i	$-0.0882639\pi$
$878$	19.2355	+	9.26335i	0.649168	+	0.312623i
$879$	−37.6117	+	47.1636i	−1.26861	+	1.59079i
$880$	−2.03672	+	8.92344i	−0.0686577	+	0.300809i
$881$	−5.91801			−0.199383			−0.0996915	−	0.995018i	$-0.531786\pi$
$881$	−5.91801			−0.199383			−0.0996915	+	0.995018i	$0.531786\pi$
$882$		0			0
$883$	−29.4616			−0.991461			−0.495730	−	0.868477i	$-0.665100\pi$
$883$	−29.4616			−0.991461			−0.495730	+	0.868477i	$0.665100\pi$
$884$	−0.342161	+	1.49910i	−0.0115081	+	0.0504203i
$885$	−18.2354	+	22.8664i	−0.612975	+	0.768647i
$886$	7.76887	+	3.74129i	0.261000	+	0.125691i
$887$	−14.4965	+	18.1781i	−0.486746	+	0.610360i	−0.963182	−	0.268849i	$-0.913357\pi$
$887$	−14.4965	+	18.1781i	−0.486746	+	0.610360i	0.476437	+	0.879209i	$0.341928\pi$
$888$	12.3135	+	15.4406i	0.413214	+	0.518154i
$889$		0			0
$890$	2.24714	−	2.81783i	0.0753244	−	0.0944538i
$891$	−8.93203	−	39.1338i	−0.299234	−	1.31103i
$892$	6.04522	+	7.58047i	0.202409	+	0.253813i
$893$	−0.148468	+	0.650483i	−0.00496831	+	0.0217676i
$894$	−19.6477	+	9.46186i	−0.657119	+	0.316452i
$895$	6.86137	−	30.0616i	0.229350	−	1.00485i
$896$		0			0
$897$	15.3725	+	67.3515i	0.513274	+	2.24880i
$898$	−10.4421	−	13.0940i	−0.348458	−	0.436953i
$899$	−9.64701	+	4.64575i	−0.321746	+	0.154945i
$900$	26.7928			0.893093
$901$	3.01332			0.100388
$902$	−5.64341	+	2.71773i	−0.187905	+	0.0904903i
$903$		0			0
$904$	−8.33917	−	4.01593i	−0.277357	−	0.133568i
$905$	37.8308	+	18.2183i	1.25754	+	0.605598i
$906$	8.07037	+	35.3586i	0.268120	+	1.17471i
$907$	−3.76041	−	16.4754i	−0.124862	−	0.547057i	−0.998202	−	0.0599450i	$-0.980907\pi$
$907$	−3.76041	−	16.4754i	−0.124862	−	0.547057i	0.873339	−	0.487112i	$-0.161950\pi$
$908$	−5.58239	−	2.68834i	−0.185258	−	0.0892156i
$909$	83.5261	+	40.2241i	2.77039	+	1.33415i
$910$		0			0
$911$	−43.4454	+	20.9222i	−1.43941	+	0.693183i	−0.980721	−	0.195415i	$-0.937395\pi$
$911$	−43.4454	+	20.9222i	−1.43941	+	0.693183i	−0.458688	+	0.888597i	$0.651680\pi$
$912$	−1.93466			−0.0640632
$913$	−23.0675			−0.763421
$914$	7.22195	−	3.47791i	0.238881	−	0.115039i
$915$	31.2965	+	39.2446i	1.03463	+	1.29739i
$916$	0.121790	+	0.533597i	0.00402406	+	0.0176305i
$917$		0			0
$918$	1.51830	−	6.65211i	0.0501114	−	0.219552i
$919$	9.46409	−	4.55767i	0.312192	−	0.150344i	−0.271226	−	0.962516i	$-0.587429\pi$
$919$	9.46409	−	4.55767i	0.312192	−	0.150344i	0.583418	+	0.812172i	$0.301715\pi$
$920$	−6.32612	+	27.7165i	−0.208566	+	0.913787i
$921$	−40.3586	−	50.6081i	−1.32986	−	1.66759i
$922$	−4.03081	−	17.6602i	−0.132748	−	0.581606i
$923$	21.1134	−	26.4754i	0.694956	−	0.871447i
$924$		0			0
$925$	−16.6335	−	20.8578i	−0.546906	−	0.685799i
$926$	−3.31737	+	4.15985i	−0.109016	+	0.136701i
$927$	−94.9336	−	45.7176i	−3.11803	−	1.50156i
$928$	−2.65894	+	3.33421i	−0.0872840	+	0.109451i
$929$	7.82533	−	34.2850i	0.256741	−	1.12485i	−0.667971	−	0.744187i	$-0.732837\pi$
$929$	7.82533	−	34.2850i	0.256741	−	1.12485i	0.924712	−	0.380668i	$-0.124306\pi$
$930$	−23.3526			−0.765762
$931$		0			0
$932$	6.77776			0.222013
$933$	−8.05568	+	35.2942i	−0.263731	+	1.15548i
$934$	−20.9217	+	26.2349i	−0.684578	+	0.858434i
$935$	−5.30263	−	2.55361i	−0.173415	−	0.0835121i
$936$	−9.61901	+	12.0619i	−0.314407	+	0.394254i
$937$	−16.0560	−	20.1336i	−0.524527	−	0.657736i	0.447036	−	0.894516i	$-0.352480\pi$
$937$	−16.0560	−	20.1336i	−0.524527	−	0.657736i	−0.971563	+	0.236779i	$0.923908\pi$
$938$		0			0
$939$	−41.1200	+	51.5628i	−1.34190	+	1.68269i
$940$	0.713773	+	3.12724i	0.0232807	+	0.101999i
$941$	0.647819	+	0.812339i	0.0211183	+	0.0264815i	0.792278	−	0.610160i	$-0.208895\pi$
$941$	0.647819	+	0.812339i	0.0211183	+	0.0264815i	−0.771160	+	0.636641i	$0.780323\pi$
$942$	9.00081	−	39.4351i	0.293262	−	1.28487i
$943$	−17.5286	+	8.44135i	−0.570811	+	0.274888i
$944$	0.699721	−	3.06568i	0.0227740	−	0.0997793i
$945$		0			0
$946$	0.913247	+	4.00120i	0.0296922	+	0.130090i
$947$	−21.3235	−	26.7389i	−0.692922	−	0.868897i	0.303551	−	0.952815i	$-0.401828\pi$
$947$	−21.3235	−	26.7389i	−0.692922	−	0.868897i	−0.996473	+	0.0839185i	$0.973256\pi$
$948$	31.0811	−	14.9679i	1.00947	−	0.486134i
$949$	−9.94539			−0.322841
$950$	2.61342			0.0847904
$951$	−82.2194	+	39.5948i	−2.66615	+	1.28395i
$952$		0			0
$953$	19.4727	+	9.37756i	0.630783	+	0.303769i	0.721822	−	0.692078i	$-0.243305\pi$
$953$	19.4727	+	9.37756i	0.630783	+	0.303769i	−0.0910396	+	0.995847i	$0.529019\pi$
$954$	27.2394	+	13.1178i	0.881908	+	0.424705i
$955$	−4.52531	−	19.8267i	−0.146436	−	0.641577i
$956$	1.51349	+	6.63103i	0.0489497	+	0.214463i
$957$	−35.7372	−	17.2101i	−1.15522	−	0.556324i
$958$	15.0845	+	7.26429i	0.487357	+	0.234699i
$959$		0			0
$960$	−8.37995	+	4.03557i	−0.270462	+	0.130247i
$961$	−24.6961			−0.796649
$962$	15.3616			0.495279
$963$	−96.9768	+	46.7016i	−3.12503	+	1.50494i
$964$	−16.2509	−	20.3780i	−0.523405	−	0.656330i
$965$	1.56224	+	6.84463i	0.0502904	+	0.220336i
$966$		0			0
$967$	6.95133	−	30.4558i	0.223540	−	0.979392i	−0.731250	−	0.682110i	$-0.761063\pi$
$967$	6.95133	−	30.4558i	0.223540	−	0.979392i	0.954790	−	0.297282i	$-0.0960802\pi$
$968$	−1.66416	+	0.801415i	−0.0534880	+	0.0257585i
$969$	0.276821	−	1.21283i	0.00889276	−	0.0389617i
$970$	30.9337	+	38.7896i	0.993221	+	1.24546i
$971$	1.89102	+	8.28509i	0.0606857	+	0.265881i	0.996164	−	0.0875019i	$-0.0278884\pi$
$971$	1.89102	+	8.28509i	0.0606857	+	0.265881i	−0.935479	+	0.353383i	$0.885031\pi$
$972$	5.58403	−	7.00215i	0.179108	−	0.224594i
$973$		0			0
$974$	−16.6150	−	20.8346i	−0.532380	−	0.667583i
$975$	19.0358	−	23.8702i	0.609635	−	0.764458i
$976$	−4.86234	−	2.34158i	−0.155640	−	0.0749521i
$977$	1.35686	−	1.70145i	0.0434097	−	0.0544341i	−0.759653	−	0.650329i	$-0.774631\pi$
$977$	1.35686	−	1.70145i	0.0434097	−	0.0544341i	0.803062	+	0.595895i	$0.203203\pi$
$978$	9.17432	−	40.1953i	0.293362	−	1.28530i
$979$	−3.60414			−0.115189
$980$		0			0
$981$	10.7427			0.342989
$982$	1.68372	−	7.37684i	0.0537295	−	0.235404i
$983$	17.1419	−	21.4952i	0.546741	−	0.685591i	−0.429304	−	0.903160i	$-0.641241\pi$
$983$	17.1419	−	21.4952i	0.546741	−	0.685591i	0.976045	+	0.217569i	$0.0698126\pi$
$984$	−5.73474	−	2.76170i	−0.182817	−	0.0880399i
$985$	16.4542	−	20.6330i	0.524276	−	0.657421i
$986$	−1.70974	−	2.14395i	−0.0544493	−	0.0682772i
$987$		0			0
$988$	−0.938255	+	1.17653i	−0.0298499	+	0.0374305i
$989$	2.83658	+	12.4279i	0.0901979	+	0.395183i
$990$	−36.8174	−	46.1676i	−1.17013	−	1.46730i
$991$	0.140427	−	0.615250i	0.00446080	−	0.0195440i	−0.972649	−	0.232282i	$-0.925381\pi$
$991$	0.140427	−	0.615250i	0.00446080	−	0.0195440i	0.977109	+	0.212738i	$0.0682380\pi$
$992$	2.26211	−	1.08937i	0.0718220	−	0.0345877i
$993$	0.561607	−	2.46056i	0.0178220	−	0.0780835i
$994$		0			0
$995$	−7.18924	−	31.4981i	−0.227914	−	0.998558i
$996$	−14.6151	−	18.3267i	−0.463096	−	0.580704i
$997$	18.4649	−	8.89223i	0.584789	−	0.281620i	−0.118005	−	0.993013i	$-0.537650\pi$
$997$	18.4649	−	8.89223i	0.584789	−	0.281620i	0.702794	+	0.711393i	$0.251936\pi$
$998$	10.4872			0.331967
$999$	−68.1657			−2.15667

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.e.b.99.3		18
7.2	even	3		686.2.g.g.67.3		36
7.3	odd	6		686.2.g.h.177.3		36
7.4	even	3		686.2.g.g.177.1		36
7.5	odd	6		686.2.g.h.67.1		36
7.6	odd	2		98.2.e.b.15.1	✓	18
21.20	even	2		882.2.u.g.505.3		18
28.27	even	2		784.2.u.d.113.3		18
49.2	even	21		686.2.g.g.655.1		36
49.6	odd	14		4802.2.a.d.1.1		9
49.11	even	21		686.2.g.g.471.3		36
49.13	odd	14		98.2.e.b.85.1	yes	18
49.36	even	7	inner	686.2.e.b.589.3		18
49.38	odd	42		686.2.g.h.471.1		36
49.43	even	7		4802.2.a.c.1.9		9
49.47	odd	42		686.2.g.h.655.3		36
147.62	even	14		882.2.u.g.379.3		18
196.111	even	14		784.2.u.d.673.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.2.e.b.15.1	✓	18	7.6	odd	2
98.2.e.b.85.1	yes	18	49.13	odd	14
686.2.e.b.99.3		18	1.1	even	1	trivial
686.2.e.b.589.3		18	49.36	even	7	inner
686.2.g.g.67.3		36	7.2	even	3
686.2.g.g.177.1		36	7.4	even	3
686.2.g.g.471.3		36	49.11	even	21
686.2.g.g.655.1		36	49.2	even	21
686.2.g.h.67.1		36	7.5	odd	6
686.2.g.h.177.3		36	7.3	odd	6
686.2.g.h.471.1		36	49.38	odd	42
686.2.g.h.655.3		36	49.47	odd	42
784.2.u.d.113.3		18	28.27	even	2
784.2.u.d.673.3		18	196.111	even	14
882.2.u.g.379.3		18	147.62	even	14
882.2.u.g.505.3		18	21.20	even	2
4802.2.a.c.1.9		9	49.43	even	7
4802.2.a.d.1.1		9	49.6	odd	14

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:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.e (of order \(7\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.222521 - 0.974928i) q^{2} +(1.91682 - 2.40361i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(1.88629 - 2.36534i) q^{5} +(-1.91682 - 2.40361i) q^{6} +(-0.623490 + 0.781831i) q^{8} +(-1.43560 - 6.28979i) q^{9} +O(q^{10})\)	\(q+(0.222521 - 0.974928i) q^{2} +(1.91682 - 2.40361i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(1.88629 - 2.36534i) q^{5} +(-1.91682 - 2.40361i) q^{6} +(-0.623490 + 0.781831i) q^{8} +(-1.43560 - 6.28979i) q^{9} +(-1.88629 - 2.36534i) q^{10} +(-0.673210 + 2.94953i) q^{11} +(-2.76988 + 1.33390i) q^{12} +(-0.532118 + 2.33136i) q^{13} +(-2.06968 - 9.06784i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-0.579338 + 0.278994i) q^{17} -6.45155 q^{18} -0.629295 q^{19} +(-2.72577 + 1.31266i) q^{20} +(2.72577 + 1.31266i) q^{22} +(8.46635 + 4.07718i) q^{23} +(0.684104 + 2.99726i) q^{24} +(-0.924113 - 4.04880i) q^{25} +(2.15450 + 1.03755i) q^{26} +(-9.56038 - 4.60404i) q^{27} +(-3.84228 + 1.85034i) q^{29} -9.30104 q^{30} +2.51075 q^{31} +(0.900969 - 0.433884i) q^{32} +(5.79910 + 7.27184i) q^{33} +(0.143085 + 0.626894i) q^{34} +(-1.43560 + 6.28979i) q^{36} +(5.78775 - 2.78724i) q^{37} +(-0.140031 + 0.613517i) q^{38} +(4.58372 + 5.74780i) q^{39} +(0.673210 + 2.94953i) q^{40} +(-1.29087 + 1.61870i) q^{41} +(0.845798 + 1.06060i) q^{43} +(1.88629 - 2.36534i) q^{44} +(-17.5855 - 8.46871i) q^{45} +(5.85889 - 7.34682i) q^{46} +(0.235928 - 1.03367i) q^{47} +3.07434 q^{48} -4.15293 q^{50} +(-0.439890 + 1.92728i) q^{51} +(1.49096 - 1.86961i) q^{52} +(-4.22215 - 2.03328i) q^{53} +(-6.61599 + 8.29618i) q^{54} +(5.70676 + 7.15605i) q^{55} +(-1.20624 + 1.51258i) q^{57} +(0.948965 + 4.15769i) q^{58} +(-1.96057 - 2.45848i) q^{59} +(-2.06968 + 9.06784i) q^{60} +(-4.86234 + 2.34158i) q^{61} +(0.558695 - 2.44780i) q^{62} +(-0.222521 - 0.974928i) q^{64} +(4.51073 + 5.65627i) q^{65} +(8.37995 - 4.03557i) q^{66} +6.32287 q^{67} +0.643016 q^{68} +(26.0284 - 12.5346i) q^{69} +(-12.7586 - 6.14419i) q^{71} +(5.81264 + 2.79922i) q^{72} +(0.925455 + 4.05468i) q^{73} +(-1.42946 - 6.26286i) q^{74} +(-11.5031 - 5.53961i) q^{75} +(0.566975 + 0.273041i) q^{76} +(6.62367 - 3.18979i) q^{78} -11.2211 q^{79} +3.02538 q^{80} +(-11.9539 + 5.75669i) q^{81} +(1.29087 + 1.61870i) q^{82} +(1.69664 + 7.43348i) q^{83} +(-0.432885 + 1.89659i) q^{85} +(1.22221 - 0.588587i) q^{86} +(-2.91744 + 12.7821i) q^{87} +(-1.88629 - 2.36534i) q^{88} +(0.265089 + 1.16143i) q^{89} +(-12.1695 + 15.2601i) q^{90} +(-5.85889 - 7.34682i) q^{92} +(4.81265 - 6.03488i) q^{93} +(-0.955254 - 0.460026i) q^{94} +(-1.18704 + 1.48850i) q^{95} +(0.684104 - 2.99726i) q^{96} -16.3992 q^{97} +19.5184 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 3 q^{2} + 5 q^{3} - 3 q^{4} - 5 q^{6} + 3 q^{8} - 10 q^{9}+O(q^{10}) \) 18 * q + 3 * q^2 + 5 * q^3 - 3 * q^4 - 5 * q^6 + 3 * q^8 - 10 * q^9	\( 18 q + 3 q^{2} + 5 q^{3} - 3 q^{4} - 5 q^{6} + 3 q^{8} - 10 q^{9} + 7 q^{11} - 2 q^{12} + 10 q^{13} + 7 q^{15} - 3 q^{16} - q^{17} - 32 q^{18} + 44 q^{19} - 7 q^{20} + 7 q^{22} + 21 q^{23} + 2 q^{24} + q^{25} - 3 q^{26} - 10 q^{27} + 11 q^{29} + 24 q^{31} + 3 q^{32} + 14 q^{33} + q^{34} - 10 q^{36} - 13 q^{37} + 19 q^{38} - 3 q^{39} - 7 q^{40} - 8 q^{41} - 24 q^{43} - 98 q^{45} + 21 q^{46} - 40 q^{47} - 2 q^{48} - 50 q^{50} + 36 q^{51} - 18 q^{52} + 10 q^{53} - 4 q^{54} - 49 q^{55} + 19 q^{57} + 24 q^{58} - 13 q^{59} + 7 q^{60} - 27 q^{61} + 11 q^{62} - 3 q^{64} + 21 q^{66} - 86 q^{67} + 34 q^{68} + 91 q^{69} + 3 q^{72} - 5 q^{73} + 13 q^{74} + 3 q^{75} + 2 q^{76} + 38 q^{78} - 66 q^{79} - 2 q^{81} + 8 q^{82} - 55 q^{83} - 49 q^{85} - 18 q^{86} + 110 q^{87} - 62 q^{89} - 21 q^{90} - 21 q^{92} + 46 q^{93} - 23 q^{94} - 7 q^{95} + 2 q^{96} + 32 q^{97} + 14 q^{99}+O(q^{100}) \) 18 * q + 3 * q^2 + 5 * q^3 - 3 * q^4 - 5 * q^6 + 3 * q^8 - 10 * q^9 + 7 * q^11 - 2 * q^12 + 10 * q^13 + 7 * q^15 - 3 * q^16 - q^17 - 32 * q^18 + 44 * q^19 - 7 * q^20 + 7 * q^22 + 21 * q^23 + 2 * q^24 + q^25 - 3 * q^26 - 10 * q^27 + 11 * q^29 + 24 * q^31 + 3 * q^32 + 14 * q^33 + q^34 - 10 * q^36 - 13 * q^37 + 19 * q^38 - 3 * q^39 - 7 * q^40 - 8 * q^41 - 24 * q^43 - 98 * q^45 + 21 * q^46 - 40 * q^47 - 2 * q^48 - 50 * q^50 + 36 * q^51 - 18 * q^52 + 10 * q^53 - 4 * q^54 - 49 * q^55 + 19 * q^57 + 24 * q^58 - 13 * q^59 + 7 * q^60 - 27 * q^61 + 11 * q^62 - 3 * q^64 + 21 * q^66 - 86 * q^67 + 34 * q^68 + 91 * q^69 + 3 * q^72 - 5 * q^73 + 13 * q^74 + 3 * q^75 + 2 * q^76 + 38 * q^78 - 66 * q^79 - 2 * q^81 + 8 * q^82 - 55 * q^83 - 49 * q^85 - 18 * q^86 + 110 * q^87 - 62 * q^89 - 21 * q^90 - 21 * q^92 + 46 * q^93 - 23 * q^94 - 7 * q^95 + 2 * q^96 + 32 * q^97 + 14 * q^99

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