LMFDB - Embedded newform 420.2.l.e.239.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [420,2,Mod(239,420)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(420, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 1, 0]))

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

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

chi := DirichletCharacter("420.239");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	420.l (of order $2$, degree $1$, 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:	$3.35371688489$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.386672896.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{6} - 2x^{5} + 2x^{4} - 4x^{3} - 4x^{2} + 16 $ x^8 - x^6 - 2x^5 + 2x^4 - 4x^3 - 4x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.7
Root			$1.40961 + 0.114062i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.e.239.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.40961 - 0.114062i) q^{2} +(-1.47398 + 0.909606i) q^{3} +(1.97398 - 0.321565i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-1.97398 + 1.45031i) q^{6} +1.00000 q^{7} +(2.74586 - 0.678435i) q^{8} +(1.34523 - 2.68148i) q^{9} +O(q^{10})$	\(q+(1.40961 - 0.114062i) q^{2} +(-1.47398 + 0.909606i) q^{3} +(1.97398 - 0.321565i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-1.97398 + 1.45031i) q^{6} +1.00000 q^{7} +(2.74586 - 0.678435i) q^{8} +(1.34523 - 2.68148i) q^{9} +(-1.63773 - 2.70515i) q^{10} +2.94796 q^{11} +(-2.61711 + 2.26952i) q^{12} +1.36297i q^{13} +(1.40961 - 0.114062i) q^{14} +(3.29319 + 2.03835i) q^{15} +(3.79319 - 1.26952i) q^{16} +2.69047 q^{17} +(1.59039 - 3.93327i) q^{18} -3.54375i q^{19} +(-2.61711 - 3.62639i) q^{20} +(-1.47398 + 0.909606i) q^{21} +(4.15546 - 0.336250i) q^{22} -7.18218i q^{23} +(-3.43023 + 3.49765i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(0.155462 + 1.92124i) q^{26} +(0.456247 + 5.17608i) q^{27} +(1.97398 - 0.321565i) q^{28} +1.36297i q^{29} +(4.87460 + 2.49765i) q^{30} +8.09467i q^{31} +(5.20210 - 2.22219i) q^{32} +(-4.34523 + 2.68148i) q^{33} +(3.79250 - 0.306880i) q^{34} +(-1.00000 - 2.00000i) q^{35} +(1.79319 - 5.72577i) q^{36} +9.89592i q^{37} +(-0.404207 - 4.99530i) q^{38} +(-1.23976 - 2.00898i) q^{39} +(-4.10273 - 4.81328i) q^{40} -5.89592i q^{41} +(-1.97398 + 1.45031i) q^{42} -2.25749 q^{43} +(5.81921 - 0.947960i) q^{44} +(-6.70820 - 0.00898303i) q^{45} +(-0.819213 - 10.1240i) q^{46} -1.81921i q^{47} +(-4.43632 + 5.32156i) q^{48} +1.00000 q^{49} +(-3.77257 + 5.98061i) q^{50} +(-3.96569 + 2.44726i) q^{51} +(0.438281 + 2.69047i) q^{52} -13.7918 q^{53} +(1.23352 + 7.24420i) q^{54} +(-2.94796 - 5.89592i) q^{55} +(2.74586 - 0.678435i) q^{56} +(3.22342 + 5.22342i) q^{57} +(0.155462 + 1.92124i) q^{58} -6.80841 q^{59} +(7.15616 + 2.96469i) q^{60} -6.55092 q^{61} +(0.923293 + 11.4103i) q^{62} +(1.34523 - 2.68148i) q^{63} +(7.07945 - 3.72577i) q^{64} +(2.72593 - 1.36297i) q^{65} +(-5.81921 + 4.27546i) q^{66} -8.46844 q^{67} +(5.31092 - 0.865159i) q^{68} +(6.53295 + 10.5864i) q^{69} +(-1.63773 - 2.70515i) q^{70} +8.00000 q^{71} +(1.87460 - 8.27562i) q^{72} -8.00000i q^{73} +(1.12875 + 13.9493i) q^{74} +(0.783514 - 8.62474i) q^{75} +(-1.13955 - 6.99530i) q^{76} +2.94796 q^{77} +(-1.97672 - 2.69047i) q^{78} +16.1836i q^{79} +(-6.33224 - 6.31686i) q^{80} +(-5.38070 - 7.21444i) q^{81} +(-0.672500 - 8.31092i) q^{82} +5.83718i q^{83} +(-2.61711 + 2.26952i) q^{84} +(-2.69047 - 5.38093i) q^{85} +(-3.18218 + 0.257494i) q^{86} +(-1.23976 - 2.00898i) q^{87} +(8.09467 - 2.00000i) q^{88} +4.83001i q^{89} +(-9.45694 + 0.752487i) q^{90} +1.36297i q^{91} +(-2.30953 - 14.1775i) q^{92} +(-7.36297 - 11.9314i) q^{93} +(-0.207503 - 2.56437i) q^{94} +(-7.08751 + 3.54375i) q^{95} +(-5.64648 + 8.00733i) q^{96} -3.70294i q^{97} +(1.40961 - 0.114062i) q^{98} +(3.96569 - 7.90490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 2 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q + 2 * q^3 + 2 * q^4 - 8 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9	$ 8 q + 2 q^{3} + 2 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9} - 4 q^{10} - 4 q^{11} - 10 q^{12} - 10 q^{15} - 6 q^{16} + 4 q^{17} + 24 q^{18} - 10 q^{20} + 2 q^{21} + 6 q^{22} - 18 q^{24} - 24 q^{25} - 26 q^{26} + 8 q^{27} + 2 q^{28} + 18 q^{30} + 30 q^{32} - 26 q^{33} + 30 q^{34} - 8 q^{35} - 22 q^{36} + 20 q^{38} - 18 q^{39} - 14 q^{40} - 2 q^{42} - 8 q^{43} + 24 q^{44} - 18 q^{45} + 16 q^{46} - 2 q^{48} + 8 q^{49} + 8 q^{50} + 14 q^{51} + 16 q^{52} + 24 q^{54} + 4 q^{55} + 6 q^{56} - 20 q^{57} - 26 q^{58} - 8 q^{59} - 6 q^{60} - 16 q^{61} + 40 q^{62} + 2 q^{63} + 26 q^{64} - 32 q^{65} - 24 q^{66} - 24 q^{67} - 12 q^{68} + 24 q^{69} - 4 q^{70} + 64 q^{71} - 6 q^{72} + 4 q^{74} + 10 q^{75} - 28 q^{76} - 4 q^{77} - 4 q^{78} + 38 q^{80} + 2 q^{81} + 4 q^{82} - 10 q^{84} - 4 q^{85} + 24 q^{86} - 18 q^{87} + 24 q^{88} - 44 q^{90} - 36 q^{92} - 32 q^{93} - 2 q^{94} - 48 q^{95} - 22 q^{96} - 14 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^4 - 8 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9 - 4 * q^10 - 4 * q^11 - 10 * q^12 - 10 * q^15 - 6 * q^16 + 4 * q^17 + 24 * q^18 - 10 * q^20 + 2 * q^21 + 6 * q^22 - 18 * q^24 - 24 * q^25 - 26 * q^26 + 8 * q^27 + 2 * q^28 + 18 * q^30 + 30 * q^32 - 26 * q^33 + 30 * q^34 - 8 * q^35 - 22 * q^36 + 20 * q^38 - 18 * q^39 - 14 * q^40 - 2 * q^42 - 8 * q^43 + 24 * q^44 - 18 * q^45 + 16 * q^46 - 2 * q^48 + 8 * q^49 + 8 * q^50 + 14 * q^51 + 16 * q^52 + 24 * q^54 + 4 * q^55 + 6 * q^56 - 20 * q^57 - 26 * q^58 - 8 * q^59 - 6 * q^60 - 16 * q^61 + 40 * q^62 + 2 * q^63 + 26 * q^64 - 32 * q^65 - 24 * q^66 - 24 * q^67 - 12 * q^68 + 24 * q^69 - 4 * q^70 + 64 * q^71 - 6 * q^72 + 4 * q^74 + 10 * q^75 - 28 * q^76 - 4 * q^77 - 4 * q^78 + 38 * q^80 + 2 * q^81 + 4 * q^82 - 10 * q^84 - 4 * q^85 + 24 * q^86 - 18 * q^87 + 24 * q^88 - 44 * q^90 - 36 * q^92 - 32 * q^93 - 2 * q^94 - 48 * q^95 - 22 * q^96 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/420\mathbb{Z}\right)^\times$.

$n$	$211$	$241$	$281$	$337$
$\chi(n)$	$-1$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	1.40961	−	0.114062i	0.996742	−	0.0806539i
$2$	1.40961	−	0.114062i	0.996742	−	0.0806539i
$3$	−1.47398	+	0.909606i	−0.851003	+	0.525161i
$3$	−1.47398	+	0.909606i	−0.851003	+	0.525161i
$4$	1.97398	−	0.321565i	0.986990	−	0.160782i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$5$	−1.00000	−	2.00000i	−0.447214	−	0.894427i
$6$	−1.97398	+	1.45031i	−0.805874	+	0.592087i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.74586	−	0.678435i	0.970807	−	0.239863i
$9$	1.34523	−	2.68148i	0.448411	−	0.893828i
$10$	−1.63773	−	2.70515i	−0.517896	−	0.855444i
$11$	2.94796			0.888843			0.444422	−	0.895818i	$-0.353409\pi$
$11$	2.94796			0.888843			0.444422	+	0.895818i	$0.353409\pi$
$12$	−2.61711	+	2.26952i	−0.755494	+	0.655155i
$13$			1.36297i			0.378019i	0.981975	+	0.189009i	$0.0605276\pi$
$13$			1.36297i			0.378019i	−0.981975	+	0.189009i	$0.939472\pi$
$14$	1.40961	−	0.114062i	0.376733	−	0.0304843i
$15$	3.29319	+	2.03835i	0.850299	+	0.526301i
$16$	3.79319	−	1.26952i	0.948298	−	0.317381i
$17$	2.69047			0.652534			0.326267	−	0.945278i	$-0.394209\pi$
$17$	2.69047			0.652534			0.326267	+	0.945278i	$0.394209\pi$
$18$	1.59039	−	3.93327i	0.374859	−	0.927082i
$19$		−	3.54375i		−	0.812993i	−0.913652	−	0.406496i	$-0.866750\pi$
$19$		−	3.54375i		−	0.812993i	0.913652	−	0.406496i	$-0.133250\pi$
$20$	−2.61711	−	3.62639i	−0.585203	−	0.810887i
$21$	−1.47398	+	0.909606i	−0.321649	+	0.198492i
$22$	4.15546	−	0.336250i	0.885948	−	0.0716887i
$23$		−	7.18218i		−	1.49759i	−0.662803	−	0.748794i	$-0.730633\pi$
$23$		−	7.18218i		−	1.49759i	0.662803	−	0.748794i	$-0.269367\pi$
$24$	−3.43023	+	3.49765i	−0.700192	+	0.713954i
$25$	−3.00000	+	4.00000i	−0.600000	+	0.800000i
$26$	0.155462	+	1.92124i	0.0304887	+	0.376787i
$27$	0.456247	+	5.17608i	0.0878049	+	0.996138i
$28$	1.97398	−	0.321565i	0.373047	−	0.0607700i
$29$			1.36297i			0.253096i	0.991960	+	0.126548i	$0.0403898\pi$
$29$			1.36297i			0.253096i	−0.991960	+	0.126548i	$0.959610\pi$
$30$	4.87460	+	2.49765i	0.889977	+	0.456006i
$31$			8.09467i			1.45385i	0.686719	+	0.726923i	$0.259050\pi$
$31$			8.09467i			1.45385i	−0.686719	+	0.726923i	$0.740950\pi$
$32$	5.20210	−	2.22219i	0.919611	−	0.392831i
$33$	−4.34523	+	2.68148i	−0.756408	+	0.466786i
$34$	3.79250	−	0.306880i	0.650408	−	0.0526294i
$35$	−1.00000	−	2.00000i	−0.169031	−	0.338062i
$36$	1.79319	−	5.72577i	0.298865	−	0.954295i
$37$			9.89592i			1.62688i	0.581649	+	0.813440i	$0.302408\pi$
$37$			9.89592i			1.62688i	−0.581649	+	0.813440i	$0.697592\pi$
$38$	−0.404207	−	4.99530i	−0.0655710	−	0.810344i
$39$	−1.23976	−	2.00898i	−0.198521	−	0.321695i
$40$	−4.10273	−	4.81328i	−0.648698	−	0.761046i
$41$		−	5.89592i		−	0.920788i	−0.887715	−	0.460394i	$-0.847708\pi$
$41$		−	5.89592i		−	0.920788i	0.887715	−	0.460394i	$-0.152292\pi$
$42$	−1.97398	+	1.45031i	−0.304592	+	0.223788i
$43$	−2.25749			−0.344265			−0.172132	−	0.985074i	$-0.555066\pi$
$43$	−2.25749			−0.344265			−0.172132	+	0.985074i	$0.555066\pi$
$44$	5.81921	−	0.947960i	0.877279	−	0.142910i
$45$	−6.70820	−	0.00898303i	−0.999999	−	0.00133911i
$46$	−0.819213	−	10.1240i	−0.120786	−	1.49271i
$47$		−	1.81921i		−	0.265359i	−0.991159	−	0.132680i	$-0.957642\pi$
$47$		−	1.81921i		−	0.265359i	0.991159	−	0.132680i	$-0.0423582\pi$
$48$	−4.43632	+	5.32156i	−0.640328	+	0.768102i
$49$	1.00000			0.142857
$50$	−3.77257	+	5.98061i	−0.533522	+	0.845786i
$51$	−3.96569	+	2.44726i	−0.555308	+	0.342686i
$52$	0.438281	+	2.69047i	0.0607787	+	0.373100i
$53$	−13.7918			−1.89445			−0.947227	−	0.320563i	$-0.896128\pi$
$53$	−13.7918			−1.89445			−0.947227	+	0.320563i	$0.896128\pi$
$54$	1.23352	+	7.24420i	0.167861	+	0.985811i
$55$	−2.94796	−	5.89592i	−0.397503	−	0.795006i
$56$	2.74586	−	0.678435i	0.366930	−	0.0906597i
$57$	3.22342	+	5.22342i	0.426952	+	0.691859i
$58$	0.155462	+	1.92124i	0.0204132	+	0.252272i
$59$	−6.80841			−0.886380			−0.443190	−	0.896428i	$-0.646153\pi$
$59$	−6.80841			−0.886380			−0.443190	+	0.896428i	$0.646153\pi$
$60$	7.15616	+	2.96469i	0.923856	+	0.382740i
$61$	−6.55092			−0.838759			−0.419380	−	0.907811i	$-0.637752\pi$
$61$	−6.55092			−0.838759			−0.419380	+	0.907811i	$0.637752\pi$
$62$	0.923293	+	11.4103i	0.117258	+	1.44911i
$63$	1.34523	−	2.68148i	0.169483	−	0.337835i
$64$	7.07945	−	3.72577i	0.884931	−	0.465721i
$65$	2.72593	−	1.36297i	0.338110	−	0.169055i
$66$	−5.81921	+	4.27546i	−0.716296	+	0.526273i
$67$	−8.46844			−1.03458			−0.517292	−	0.855809i	$-0.673060\pi$
$67$	−8.46844			−1.03458			−0.517292	+	0.855809i	$0.673060\pi$
$68$	5.31092	−	0.865159i	0.644044	−	0.104916i
$69$	6.53295	+	10.5864i	0.786475	+	1.27445i
$70$	−1.63773	−	2.70515i	−0.195746	−	0.323327i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$	1.87460	−	8.27562i	0.220924	−	0.975291i
$73$		−	8.00000i		−	0.936329i	−0.883641	−	0.468165i	$-0.844915\pi$
$73$		−	8.00000i		−	0.936329i	0.883641	−	0.468165i	$-0.155085\pi$
$74$	1.12875	+	13.9493i	0.131214	+	1.62158i
$75$	0.783514	−	8.62474i	0.0904724	−	0.995899i
$76$	−1.13955	−	6.99530i	−0.130715	−	0.802415i
$77$	2.94796			0.335951
$78$	−1.97672	−	2.69047i	−0.223820	−	0.304635i
$79$			16.1836i			1.82079i	0.413736	+	0.910397i	$0.364224\pi$
$79$			16.1836i			1.82079i	−0.413736	+	0.910397i	$0.635776\pi$
$80$	−6.33224	−	6.31686i	−0.707966	−	0.706246i
$81$	−5.38070	−	7.21444i	−0.597855	−	0.801604i
$82$	−0.672500	−	8.31092i	−0.0742651	−	0.917788i
$83$			5.83718i			0.640714i	0.947297	+	0.320357i	$0.103803\pi$
$83$			5.83718i			0.640714i	−0.947297	+	0.320357i	$0.896197\pi$
$84$	−2.61711	+	2.26952i	−0.285550	+	0.247625i
$85$	−2.69047	−	5.38093i	−0.291822	−	0.583644i
$86$	−3.18218	+	0.257494i	−0.343143	+	0.0277663i
$87$	−1.23976	−	2.00898i	−0.132916	−	0.215386i
$88$	8.09467	−	2.00000i	0.862895	−	0.213201i
$89$			4.83001i			0.511980i	0.966679	+	0.255990i	$0.0824014\pi$
$89$			4.83001i			0.511980i	−0.966679	+	0.255990i	$0.917599\pi$
$90$	−9.45694	+	0.752487i	−0.996849	+	0.0793191i
$91$			1.36297i			0.142878i
$92$	−2.30953	−	14.1775i	−0.240786	−	1.47810i
$93$	−7.36297	−	11.9314i	−0.763504	−	1.23723i
$94$	−0.207503	−	2.56437i	−0.0214023	−	0.264495i
$95$	−7.08751	+	3.54375i	−0.727163	+	0.363581i
$96$	−5.64648	+	8.00733i	−0.576291	+	0.817244i
$97$		−	3.70294i		−	0.375977i	−0.982171	−	0.187988i	$-0.939803\pi$
$97$		−	3.70294i		−	0.375977i	0.982171	−	0.187988i	$-0.0601968\pi$
$98$	1.40961	−	0.114062i	0.142392	−	0.0115220i
$99$	3.96569	−	7.90490i	0.398567	−	0.794473i
$100$	−4.63568	+	8.86061i	−0.463568	+	0.886061i
$101$			14.4468i			1.43751i	0.695261	+	0.718757i	$0.255289\pi$
$101$			14.4468i			1.43751i	−0.695261	+	0.718757i	$0.744711\pi$
$102$	−5.31092	+	3.90201i	−0.525860	+	0.386357i
$103$	10.0355			0.988824			0.494412	−	0.869228i	$-0.335383\pi$
$103$	10.0355			0.988824			0.494412	+	0.869228i	$0.335383\pi$
$104$	0.924684	+	3.74251i	0.0906727	+	0.366983i
$105$	3.29319	+	2.03835i	0.321383	+	0.198923i
$106$	−19.4411	+	1.57312i	−1.88828	+	0.152795i
$107$		−	6.71374i		−	0.649042i	−0.945879	−	0.324521i	$-0.894797\pi$
$107$		−	6.71374i		−	0.649042i	0.945879	−	0.324521i	$-0.105203\pi$
$108$	2.56507	+	10.0708i	0.246824	+	0.969060i
$109$	6.69047			0.640830			0.320415	−	0.947277i	$-0.396178\pi$
$109$	6.69047			0.640830			0.320415	+	0.947277i	$0.396178\pi$
$110$	−4.82796	−	7.97467i	−0.460328	−	0.760355i
$111$	−9.00139	−	14.5864i	−0.854374	−	1.38448i
$112$	3.79319	−	1.26952i	0.358423	−	0.119959i
$113$	−2.83001			−0.266225			−0.133113	−	0.991101i	$-0.542497\pi$
$113$	−2.83001			−0.266225			−0.133113	+	0.991101i	$0.542497\pi$
$114$	5.13955	+	6.99530i	0.481363	+	0.655169i
$115$	−14.3644	+	7.18218i	−1.33948	+	0.669742i
$116$	0.438281	+	2.69047i	0.0406934	+	0.249803i
$117$	3.65477	+	1.83351i	0.337883	+	0.169508i
$118$	−9.59718	+	0.776580i	−0.883492	+	0.0714900i
$119$	2.69047			0.246635
$120$	10.4255	+	3.36281i	0.951716	+	0.306981i
$121$	−2.30953			−0.209958
$122$	−9.23422	+	0.747210i	−0.836027	+	0.0676492i
$123$	5.36297	+	8.69047i	0.483562	+	0.783593i
$124$	2.60296	+	15.9787i	0.233753	+	1.43493i
$125$	11.0000	+	2.00000i	0.983870	+	0.178885i
$126$	1.59039	−	3.93327i	0.141684	−	0.350404i
$127$	13.8959			1.23306			0.616532	−	0.787330i	$-0.288537\pi$
$127$	13.8959			1.23306			0.616532	+	0.787330i	$0.288537\pi$
$128$	9.55427	−	6.05937i	0.844486	−	0.535577i
$129$	3.32750	−	2.05343i	0.292970	−	0.180794i
$130$	3.68703	−	2.23217i	0.323374	−	0.195774i
$131$	16.1534			1.41133			0.705665	−	0.708546i	$-0.250648\pi$
$131$	16.1534			1.41133			0.705665	+	0.708546i	$0.250648\pi$
$132$	−7.71513	+	6.69047i	−0.671516	+	0.582330i
$133$		−	3.54375i		−	0.307282i
$134$	−11.9372	+	0.965926i	−1.03121	+	0.0834433i
$135$	9.89592	−	6.08858i	0.851705	−	0.524021i
$136$	7.38763	−	1.82531i	0.633484	−	0.156519i
$137$	−2.55092			−0.217940			−0.108970	−	0.994045i	$-0.534755\pi$
$137$	−2.55092			−0.217940			−0.108970	+	0.994045i	$0.534755\pi$
$138$	10.4164	+	14.1775i	0.886702	+	1.20687i
$139$			2.35217i			0.199508i	0.995012	+	0.0997541i	$0.0318056\pi$
$139$			2.35217i			0.199508i	−0.995012	+	0.0997541i	$0.968194\pi$
$140$	−2.61711	−	3.62639i	−0.221186	−	0.306486i
$141$	1.65477	+	2.68148i	0.139357	+	0.225822i
$142$	11.2769	−	0.912495i	0.946332	−	0.0765749i
$143$			4.01797i			0.335999i
$144$	1.69852	−	11.8792i	0.141543	−	0.989932i
$145$	2.72593	−	1.36297i	0.226376	−	0.113188i
$146$	−0.912495	−	11.2769i	−0.0755186	−	0.933279i
$147$	−1.47398	+	0.909606i	−0.121572	+	0.0750231i
$148$	3.18218	+	19.5343i	0.261573	+	1.60571i
$149$			7.79184i			0.638332i	0.947699	+	0.319166i	$0.103403\pi$
$149$			7.79184i			0.638332i	−0.947699	+	0.319166i	$0.896597\pi$
$150$	0.120693	−	12.2469i	0.00985453	−	0.999951i
$151$			20.6986i			1.68442i	0.539146	+	0.842212i	$0.318747\pi$
$151$			20.6986i			1.68442i	−0.539146	+	0.842212i	$0.681253\pi$
$152$	−2.40421	−	9.73063i	−0.195007	−	0.789259i
$153$	3.61930	−	7.21444i	0.292603	−	0.583253i
$154$	4.15546	−	0.336250i	0.334857	−	0.0270958i
$155$	16.1893	−	8.09467i	1.30036	−	0.650180i
$156$	−3.09328	−	3.56703i	−0.247661	−	0.285591i
$157$		−	7.79184i		−	0.621856i	−0.950433	−	0.310928i	$-0.899360\pi$
$157$		−	7.79184i		−	0.621856i	0.950433	−	0.310928i	$-0.100640\pi$
$158$	1.84593	+	22.8125i	0.146854	+	1.81486i
$159$	20.3289	−	12.5451i	1.61219	−	0.994895i
$160$	−9.64648	−	8.18202i	−0.762621	−	0.646845i
$161$		−	7.18218i		−	0.566035i
$162$	−8.40756	−	9.55578i	−0.660560	−	0.750773i
$163$	−14.8084			−1.15988			−0.579942	−	0.814658i	$-0.696925\pi$
$163$	−14.8084			−1.15988			−0.579942	+	0.814658i	$0.696925\pi$
$164$	−1.89592	−	11.6384i	−0.148046	−	0.908808i
$165$	9.70820	+	6.00898i	0.755782	+	0.467799i
$166$	0.665799	+	8.22812i	0.0516761	+	0.638626i
$167$			13.4217i			1.03860i	0.854591	+	0.519301i	$0.173808\pi$
$167$			13.4217i			1.03860i	−0.854591	+	0.519301i	$0.826192\pi$
$168$	−3.43023	+	3.49765i	−0.264648	+	0.269849i
$169$	11.1423			0.857102
$170$	−4.40626	−	7.27811i	−0.337944	−	0.558206i
$171$	−9.50251	−	4.76717i	−0.726675	−	0.364555i
$172$	−4.45625	+	0.725930i	−0.339786	+	0.0553517i
$173$	−1.30953			−0.0995621			−0.0497810	−	0.998760i	$-0.515852\pi$
$173$	−1.30953			−0.0995621			−0.0497810	+	0.998760i	$0.515852\pi$
$174$	−1.97672	−	2.69047i	−0.149855	−	0.203964i
$175$	−3.00000	+	4.00000i	−0.226779	+	0.302372i
$176$	11.1822	−	3.74251i	0.842888	−	0.282102i
$177$	10.0355	−	6.19298i	0.754312	−	0.465493i
$178$	0.550920	+	6.80841i	0.0412932	+	0.510312i
$179$	−22.3644			−1.67159			−0.835795	−	0.549041i	$-0.814993\pi$
$179$	−22.3644			−1.67159			−0.835795	+	0.549041i	$0.814993\pi$
$180$	−13.2447	+	2.13939i	−0.987204	+	0.159460i
$181$	−9.27685			−0.689543			−0.344771	−	0.938687i	$-0.612044\pi$
$181$	−9.27685			−0.689543			−0.344771	+	0.938687i	$0.612044\pi$
$182$	0.155462	+	1.92124i	0.0115236	+	0.142412i
$183$	9.65592	−	5.95876i	0.713786	−	0.440484i
$184$	−4.87264	−	19.7212i	−0.359216	−	1.45387i
$185$	19.7918	−	9.89592i	1.45512	−	0.727562i
$186$	−11.7398	−	15.9787i	−0.860804	−	1.17162i
$187$	7.93138			0.580000
$188$	−0.584994	−	3.59109i	−0.0426651	−	0.261907i
$189$	0.456247	+	5.17608i	0.0331871	+	0.376505i
$190$	−9.58638	+	5.80371i	−0.695469	+	0.421045i
$191$	1.31231			0.0949558			0.0474779	−	0.998872i	$-0.484882\pi$
$191$	1.31231			0.0949558			0.0474779	+	0.998872i	$0.484882\pi$
$192$	−7.04598	+	11.9312i	−0.508500	+	0.861062i
$193$		−	9.34500i		−	0.672668i	−0.941743	−	0.336334i	$-0.890813\pi$
$193$		−	9.34500i		−	0.672668i	0.941743	−	0.336334i	$-0.109187\pi$
$194$	−0.422365	−	5.21969i	−0.0303240	−	0.374752i
$195$	−2.77820	+	4.48851i	−0.198951	+	0.321429i
$196$	1.97398	−	0.321565i	0.140999	−	0.0229689i
$197$	7.34500			0.523310			0.261655	−	0.965162i	$-0.415732\pi$
$197$	7.34500			0.523310			0.261655	+	0.965162i	$0.415732\pi$
$198$	4.68842	−	11.5951i	0.333191	−	0.824030i
$199$		−	5.83718i		−	0.413787i	−0.978364	−	0.206893i	$-0.933665\pi$
$199$		−	5.83718i		−	0.413787i	0.978364	−	0.206893i	$-0.0663353\pi$
$200$	−5.52383	+	13.0187i	−0.390594	+	0.920563i
$201$	12.4823	−	7.70294i	0.880434	−	0.543324i
$202$	1.64783	+	20.3644i	0.115941	+	1.43283i
$203$			1.36297i			0.0956614i
$204$	−7.04124	+	6.10608i	−0.492986	+	0.427511i
$205$	−11.7918	+	5.89592i	−0.823578	+	0.411789i
$206$	14.1461	−	1.14466i	0.985602	−	0.0797525i
$207$	−19.2589	−	9.66170i	−1.33858	−	0.671535i
$208$	1.73032	+	5.16999i	0.119976	+	0.358474i
$209$		−	10.4468i		−	0.722623i
$210$	4.87460	+	2.49765i	0.336380	+	0.172354i
$211$		−	13.4217i		−	0.923988i	−0.886883	−	0.461994i	$-0.847134\pi$
$211$		−	13.4217i		−	0.923988i	0.886883	−	0.461994i	$-0.152866\pi$
$212$	−27.2248	+	4.43497i	−1.86981	+	0.304595i
$213$	−11.7918	+	7.27685i	−0.807963	+	0.498602i
$214$	−0.765782	−	9.46373i	−0.0523478	−	0.646927i
$215$	2.25749	+	4.51499i	0.153960	+	0.307920i
$216$	4.76443	+	13.9032i	0.324178	+	0.945996i
$217$			8.09467i			0.549502i
$218$	9.43092	−	0.763127i	0.638743	−	0.0516855i
$219$	7.27685	+	11.7918i	0.491724	+	0.796819i
$220$	−7.71513	−	10.6905i	−0.520154	−	0.720751i
$221$			3.66701i			0.246670i
$222$	−14.3522	−	19.5343i	−0.963254	−	1.31106i
$223$	−25.0332			−1.67635			−0.838174	−	0.545402i	$-0.816377\pi$
$223$	−25.0332			−1.67635			−0.838174	+	0.545402i	$0.816377\pi$
$224$	5.20210	−	2.22219i	0.347580	−	0.148476i
$225$	6.69023	+	13.4254i	0.446015	+	0.895025i
$226$	−3.98920	+	0.322796i	−0.265358	+	0.0214721i
$227$			1.81921i			0.120745i	0.998176	+	0.0603727i	$0.0192289\pi$
$227$			1.81921i			0.120745i	−0.998176	+	0.0603727i	$0.980771\pi$
$228$	8.04263	+	9.27439i	0.532636	+	0.614211i
$229$	11.8600			0.783730			0.391865	−	0.920023i	$-0.371830\pi$
$229$	11.8600			0.783730			0.391865	+	0.920023i	$0.371830\pi$
$230$	−19.4289	+	11.7625i	−1.28110	+	0.775594i
$231$	−4.34523	+	2.68148i	−0.285895	+	0.176429i
$232$	0.924684	+	3.74251i	0.0607085	+	0.245708i
$233$	−5.55594			−0.363982			−0.181991	−	0.983300i	$-0.558254\pi$
$233$	−5.55594			−0.363982			−0.181991	+	0.983300i	$0.558254\pi$
$234$	5.36092	+	2.16765i	0.350454	+	0.141704i
$235$	−3.63843	+	1.81921i	−0.237345	+	0.118672i
$236$	−13.4397	+	2.18935i	−0.874848	+	0.142514i
$237$	−14.7207	−	23.8543i	−0.956211	−	1.54950i
$238$	3.79250	−	0.306880i	0.245831	−	0.0198920i
$239$	−26.4142			−1.70859			−0.854295	−	0.519789i	$-0.826011\pi$
$239$	−26.4142			−1.70859			−0.854295	+	0.519789i	$0.826011\pi$
$240$	15.0795	+	3.55108i	0.973374	+	0.229221i
$241$	25.8987			1.66828			0.834141	−	0.551551i	$-0.185964\pi$
$241$	25.8987			1.66828			0.834141	+	0.551551i	$0.185964\pi$
$242$	−3.25553	+	0.263430i	−0.209274	+	0.0169339i
$243$	14.4933	+	5.73962i	0.929748	+	0.368197i
$244$	−12.9314	+	2.10654i	−0.827847	+	0.134858i
$245$	−1.00000	−	2.00000i	−0.0638877	−	0.127775i
$246$	8.55092	+	11.6384i	0.545187	+	0.742039i
$247$	4.83001			0.307326
$248$	5.49171	+	22.2268i	0.348724	+	1.41140i
$249$	−5.30953	−	8.60388i	−0.336478	−	0.545249i
$250$	15.7338	+	1.56453i	0.995092	+	0.0989497i
$251$	−6.80841			−0.429743			−0.214872	−	0.976642i	$-0.568933\pi$
$251$	−6.80841			−0.429743			−0.214872	+	0.976642i	$0.568933\pi$
$252$	1.79319	−	5.72577i	0.112961	−	0.360690i
$253$		−	21.1728i		−	1.33112i
$254$	19.5878	−	1.58499i	1.22905	−	0.0994514i
$255$	8.86022	+	5.48412i	0.554849	+	0.343429i
$256$	12.7766	−	9.63110i	0.798539	−	0.601944i
$257$	0.339978			0.0212072			0.0106036	−	0.999944i	$-0.496625\pi$
$257$	0.339978			0.0212072			0.0106036	+	0.999944i	$0.496625\pi$
$258$	4.45625	−	3.27407i	0.277434	−	0.203835i
$259$			9.89592i			0.614902i
$260$	4.94265	−	3.56703i	0.306530	−	0.221218i
$261$	3.65477	+	1.83351i	0.226224	+	0.113491i
$262$	22.7700	−	1.84249i	1.40673	−	0.113829i
$263$		−	5.80125i		−	0.357720i	−0.983875	−	0.178860i	$-0.942759\pi$
$263$		−	5.80125i		−	0.357720i	0.983875	−	0.178860i	$-0.0572409\pi$
$264$	−10.1122	+	10.3109i	−0.622361	+	0.634594i
$265$	13.7918	+	27.5837i	0.847226	+	1.69445i
$266$	−0.404207	−	4.99530i	−0.0247835	−	0.306281i
$267$	−4.39341	−	7.11934i	−0.268872	−	0.435696i
$268$	−16.7165	+	2.72315i	−1.02112	+	0.166343i
$269$		−	13.0659i		−	0.796642i	−0.917246	−	0.398321i	$-0.869593\pi$
$269$		−	13.0659i		−	0.796642i	0.917246	−	0.398321i	$-0.130407\pi$
$270$	13.2549	−	9.71125i	0.806666	−	0.591008i
$271$		−	28.9768i		−	1.76022i	−0.474774	−	0.880108i	$-0.657470\pi$
$271$		−	28.9768i		−	1.76022i	0.474774	−	0.880108i	$-0.342530\pi$
$272$	10.2055	−	3.41561i	0.618797	−	0.207102i
$273$	−1.23976	−	2.00898i	−0.0750338	−	0.121589i
$274$	−3.59579	+	0.290963i	−0.217230	+	0.0175777i
$275$	−8.84388	+	11.7918i	−0.533306	+	0.711075i
$276$	16.3001	+	18.7965i	0.981152	+	1.13142i
$277$		−	20.3428i		−	1.22228i	−0.791523	−	0.611139i	$-0.790712\pi$
$277$		−	20.3428i		−	1.22228i	0.791523	−	0.611139i	$-0.209288\pi$
$278$	0.268293	+	3.31563i	0.0160911	+	0.198858i
$279$	21.7057	+	10.8892i	1.29949	+	0.651920i
$280$	−4.10273	−	4.81328i	−0.245185	−	0.287648i
$281$		−	17.1548i		−	1.02337i	−0.859173	−	0.511685i	$-0.829022\pi$
$281$		−	17.1548i		−	1.02337i	0.859173	−	0.511685i	$-0.170978\pi$
$282$	2.63843	+	3.59109i	0.157116	+	0.213846i
$283$	20.3289			1.20843			0.604214	−	0.796822i	$-0.293487\pi$
$283$	20.3289			1.20843			0.604214	+	0.796822i	$0.293487\pi$
$284$	15.7918	−	2.57252i	0.937073	−	0.152651i
$285$	7.22342	−	11.6703i	0.427878	−	0.691286i
$286$	0.458297	+	5.66375i	0.0270997	+	0.334905i
$287$		−	5.89592i		−	0.348025i
$288$	1.03928	−	16.9387i	0.0612403	−	0.998123i
$289$	−9.76139			−0.574200
$290$	3.68703	−	2.23217i	0.216510	−	0.131077i
$291$	3.36822	+	5.45806i	0.197449	+	0.319957i
$292$	−2.57252	−	15.7918i	−0.150545	−	0.924147i
$293$	−16.1423			−0.943045			−0.471522	−	0.881854i	$-0.656295\pi$
$293$	−16.1423			−0.943045			−0.471522	+	0.881854i	$0.656295\pi$
$294$	−1.97398	+	1.45031i	−0.115125	+	0.0845839i
$295$	6.80841	+	13.6168i	0.396401	+	0.792802i
$296$	6.71374	+	27.1728i	0.390228	+	1.57939i
$297$	1.34500	+	15.2589i	0.0780448	+	0.885410i
$298$	0.888752	+	10.9834i	0.0514840	+	0.636253i
$299$	9.78906			0.566116
$300$	−1.22677	−	17.2770i	−0.0708276	−	0.997489i
$301$	−2.25749			−0.130120
$302$	2.36092	+	29.1768i	0.135855	+	1.67894i
$303$	−13.1409	−	21.2943i	−0.754927	−	1.22333i
$304$	−4.49888	−	13.4421i	−0.258028	−	0.770959i
$305$	6.55092	+	13.1018i	0.375105	+	0.750209i
$306$	4.27890	−	10.5823i	0.244608	−	0.604952i
$307$	22.0166			1.25656			0.628278	−	0.777989i	$-0.283760\pi$
$307$	22.0166			1.25656			0.628278	+	0.777989i	$0.283760\pi$
$308$	5.81921	−	0.947960i	0.331580	−	0.0540150i
$309$	−14.7921	+	9.12832i	−0.841492	+	0.519292i
$310$	21.8973	−	13.2569i	1.24368	−	0.752941i
$311$	−13.8600			−0.785928			−0.392964	−	0.919554i	$-0.628550\pi$
$311$	−13.8600			−0.785928			−0.392964	+	0.919554i	$0.628550\pi$
$312$	−4.76717	−	4.67528i	−0.269888	−	0.264686i
$313$			1.15480i			0.0652733i	0.999467	+	0.0326367i	$0.0103904\pi$
$313$			1.15480i			0.0652733i	−0.999467	+	0.0326367i	$0.989610\pi$
$314$	−0.888752	−	10.9834i	−0.0501552	−	0.619830i
$315$	−6.70820	−	0.00898303i	−0.377964	−	0.000506137i
$316$	5.20406	+	31.9460i	0.292751	+	1.79710i
$317$	7.38093			0.414554			0.207277	−	0.978282i	$-0.433540\pi$
$317$	7.38093			0.414554			0.207277	+	0.978282i	$0.433540\pi$
$318$	27.2248	−	20.0025i	1.52669	−	1.12168i
$319$			4.01797i			0.224963i
$320$	−14.5310	−	10.4331i	−0.812307	−	0.583230i
$321$	6.10686	+	9.89592i	0.340852	+	0.552336i
$322$	−0.819213	−	10.1240i	−0.0456529	−	0.564191i
$323$		−	9.53434i		−	0.530505i
$324$	−12.9413	−	12.5109i	−0.718961	−	0.695051i
$325$	−5.45186	−	4.08890i	−0.302415	−	0.226811i
$326$	−20.8740	+	1.68908i	−1.15611	+	0.0935492i
$327$	−9.86161	+	6.08569i	−0.545348	+	0.336539i
$328$	−4.00000	−	16.1893i	−0.220863	−	0.893907i
$329$		−	1.81921i		−	0.100296i
$330$	14.3701	+	7.36297i	0.791050	+	0.405318i
$331$			8.52718i			0.468696i	0.972153	+	0.234348i	$0.0752955\pi$
$331$			8.52718i			0.468696i	−0.972153	+	0.234348i	$0.924704\pi$
$332$	1.87703	+	11.5225i	0.103015	+	0.632378i
$333$	26.5357	+	13.3123i	1.45415	+	0.729510i
$334$	1.53090	+	18.9193i	0.0837674	+	1.03522i
$335$	8.46844	+	16.9369i	0.462680	+	0.925360i
$336$	−4.43632	+	5.32156i	−0.242021	+	0.290315i
$337$			7.96407i			0.433830i	0.976190	+	0.216915i	$0.0695995\pi$
$337$			7.96407i			0.433830i	−0.976190	+	0.216915i	$0.930400\pi$
$338$	15.7063	−	1.27091i	0.854310	−	0.0691286i
$339$	4.17138	−	2.57420i	0.226558	−	0.139811i
$340$	−7.04124	−	9.75669i	−0.381865	−	0.529131i
$341$			23.8628i			1.29224i
$342$	−13.9386	−	5.63596i	−0.753711	−	0.304758i
$343$	1.00000			0.0539949
$344$	−6.19875	+	1.53156i	−0.334214	+	0.0825764i
$345$	14.6398	−	23.6523i	0.788181	−	1.27340i
$346$	−1.84593	+	0.149368i	−0.0992377	+	0.00803007i
$347$		−	5.96286i		−	0.320103i	−0.987109	−	0.160051i	$-0.948834\pi$
$347$		−	5.96286i		−	0.320103i	0.987109	−	0.160051i	$-0.0511660\pi$
$348$	−3.09328	−	3.56703i	−0.165817	−	0.191213i
$349$	−28.0028			−1.49895			−0.749477	−	0.662030i	$-0.769695\pi$
$349$	−28.0028			−1.49895			−0.749477	+	0.662030i	$0.769695\pi$
$350$	−3.77257	+	5.98061i	−0.201652	+	0.319677i
$351$	−7.05482	+	0.621849i	−0.376558	+	0.0331919i
$352$	15.3356	−	6.55092i	0.817390	−	0.349165i
$353$	−5.03044			−0.267743			−0.133872	−	0.990999i	$-0.542741\pi$
$353$	−5.03044			−0.267743			−0.133872	+	0.990999i	$0.542741\pi$
$354$	13.4397	−	9.87432i	0.714310	−	0.524814i
$355$	−8.00000	−	16.0000i	−0.424596	−	0.849192i
$356$	1.55316	+	9.53434i	0.0823174	+	0.505319i
$357$	−3.96569	+	2.44726i	−0.209887	+	0.129523i
$358$	−31.5249	+	2.55092i	−1.66614	+	0.134820i
$359$	−13.4519			−0.709962			−0.354981	−	0.934874i	$-0.615513\pi$
$359$	−13.4519			−0.709962			−0.354981	+	0.934874i	$0.615513\pi$
$360$	−18.4258	+	4.52641i	−0.971127	+	0.238563i
$361$	6.44182			0.339043
$362$	−13.0767	+	1.05813i	−0.687296	+	0.0556143i
$363$	3.40421	−	2.10077i	0.178675	−	0.110262i
$364$	0.438281	+	2.69047i	0.0229722	+	0.141019i
$365$	−16.0000	+	8.00000i	−0.837478	+	0.418739i
$366$	12.9314	−	9.50088i	0.675934	−	0.496619i
$367$	2.20043			0.114862			0.0574308	−	0.998349i	$-0.481709\pi$
$367$	2.20043			0.114862			0.0574308	+	0.998349i	$0.481709\pi$
$368$	−9.11795	−	27.2434i	−0.475306	−	1.42016i
$369$	−15.8098	−	7.93138i	−0.823026	−	0.412891i
$370$	26.7700	−	16.2068i	1.39170	−	0.842554i
$371$	−13.7918			−0.716037
$372$	−18.3711	−	21.1846i	−0.952495	−	1.09837i
$373$		−	2.96183i		−	0.153358i	−0.997056	−	0.0766788i	$-0.975568\pi$
$373$		−	2.96183i		−	0.153358i	0.997056	−	0.0766788i	$-0.0244316\pi$
$374$	11.1801	−	0.904668i	0.578111	−	0.0467793i
$375$	−18.0330	+	7.05771i	−0.931220	+	0.364459i
$376$	−1.23422	−	4.99530i	−0.0636499	−	0.257613i
$377$	−1.85767			−0.0956751
$378$	1.23352	+	7.24420i	0.0634456	+	0.372601i
$379$		−	20.5084i		−	1.05344i	−0.850038	−	0.526722i	$-0.823421\pi$
$379$		−	20.5084i		−	1.05344i	0.850038	−	0.526722i	$-0.176579\pi$
$380$	−12.8510	+	9.27439i	−0.659245	+	0.475766i
$381$	−20.4823	+	12.6398i	−1.04934	+	0.647557i
$382$	1.84985	−	0.149685i	0.0946464	−	0.00765856i
$383$			31.0565i			1.58691i	0.608627	+	0.793457i	$0.291721\pi$
$383$			31.0565i			1.58691i	−0.608627	+	0.793457i	$0.708279\pi$
$384$	−8.57116	+	17.6220i	−0.437395	+	0.899269i
$385$	−2.94796	−	5.89592i	−0.150242	−	0.300484i
$386$	−1.06591	−	13.1728i	−0.0542533	−	0.670476i
$387$	−3.03685	+	6.05343i	−0.154372	+	0.307713i
$388$	−1.19074	−	7.30953i	−0.0604504	−	0.371085i
$389$			22.2207i			1.12663i	0.826241	+	0.563317i	$0.190475\pi$
$389$			22.2207i			1.12663i	−0.826241	+	0.563317i	$0.809525\pi$
$390$	−3.40421	+	6.64391i	−0.172379	+	0.336428i
$391$		−	19.3234i		−	0.977226i
$392$	2.74586	−	0.678435i	0.138687	−	0.0342662i
$393$	−23.8098	+	14.6932i	−1.20105	+	0.741176i
$394$	10.3536	−	0.837784i	0.521605	−	0.0422070i
$395$	32.3671	−	16.1836i	1.62857	−	0.814284i
$396$	5.28626	−	16.8793i	0.265644	−	0.848219i
$397$			31.9167i			1.60185i	0.598764	+	0.800926i	$0.295659\pi$
$397$			31.9167i			1.60185i	−0.598764	+	0.800926i	$0.704341\pi$
$398$	−0.665799	−	8.22812i	−0.0333735	−	0.412439i
$399$	3.22342	+	5.22342i	0.161373	+	0.261498i
$400$	−6.30148	+	18.9813i	−0.315074	+	0.949067i
$401$			17.1907i			0.858464i	0.903194	+	0.429232i	$0.141216\pi$
$401$			17.1907i			0.858464i	−0.903194	+	0.429232i	$0.858784\pi$
$402$	16.7165	−	12.2819i	0.833744	−	0.612564i
$403$	−11.0328			−0.549581
$404$	4.64559	+	28.5178i	0.231127	+	1.41881i
$405$	−9.04818	+	17.9758i	−0.449607	+	0.893226i
$406$	0.155462	+	1.92124i	0.00771547	+	0.0953497i
$407$			29.1728i			1.44604i
$408$	−9.22891	+	9.41030i	−0.456899	+	0.465879i
$409$	−16.4109			−0.811467			−0.405734	−	0.913991i	$-0.632984\pi$
$409$	−16.4109			−0.811467			−0.405734	+	0.913991i	$0.632984\pi$
$410$	−15.9493	+	9.65592i	−0.787682	+	0.476872i
$411$	3.76000	−	2.32033i	0.185467	−	0.114454i
$412$	19.8098	−	3.22705i	0.975959	−	0.158985i
$413$	−6.80841			−0.335020
$414$	−28.2495	−	11.4225i	−1.38839	−	0.561385i
$415$	11.6744	−	5.83718i	0.573072	−	0.286536i
$416$	3.02876	+	7.09029i	0.148497	+	0.347630i
$417$	−2.13955	−	3.46705i	−0.104774	−	0.169782i
$418$	−1.19159	−	14.7259i	−0.0582824	−	0.720269i
$419$	11.0166			0.538195			0.269097	−	0.963113i	$-0.413275\pi$
$419$	11.0166			0.538195			0.269097	+	0.963113i	$0.413275\pi$
$420$	7.15616	+	2.96469i	0.349185	+	0.144662i
$421$	−14.4823			−0.705824			−0.352912	−	0.935656i	$-0.614809\pi$
$421$	−14.4823			−0.705824			−0.352912	+	0.935656i	$0.614809\pi$
$422$	−1.53090	−	18.9193i	−0.0745233	−	0.920978i
$423$	−4.87819	−	2.44726i	−0.237186	−	0.118990i
$424$	−37.8704	+	9.35687i	−1.83915	+	0.454410i
$425$	−8.07140	+	10.7619i	−0.391520	+	0.522027i
$426$	−15.7918	+	11.6025i	−0.765117	+	0.562143i
$427$	−6.55092			−0.317021
$428$	−2.15890	−	13.2528i	−0.104354	−	0.640598i
$429$	−3.65477	−	5.92240i	−0.176454	−	0.285936i
$430$	3.69717	+	6.10686i	0.178293	+	0.294499i
$431$	27.7232			1.33538			0.667690	−	0.744439i	$-0.267283\pi$
$431$	27.7232			1.33538			0.667690	+	0.744439i	$0.267283\pi$
$432$	8.30180	+	19.0547i	0.399420	+	0.916768i
$433$			25.1018i			1.20632i	0.797621	+	0.603159i	$0.206091\pi$
$433$			25.1018i			1.20632i	−0.797621	+	0.603159i	$0.793909\pi$
$434$	0.923293	+	11.4103i	0.0443195	+	0.547712i
$435$	−2.77820	+	4.48851i	−0.133205	+	0.215207i
$436$	13.2068	−	2.15142i	0.632493	−	0.103034i
$437$	−25.4519			−1.21753
$438$	11.6025	+	15.7918i	0.554389	+	0.754563i
$439$		−	14.8672i		−	0.709571i	−0.934948	−	0.354785i	$-0.884554\pi$
$439$		−	14.8672i		−	0.709571i	0.934948	−	0.354785i	$-0.115446\pi$
$440$	−12.0947	−	14.1893i	−0.576591	−	0.676450i
$441$	1.34523	−	2.68148i	0.0640587	−	0.127690i
$442$	0.418266	+	5.16904i	0.0198949	+	0.245866i
$443$		−	7.02876i		−	0.333947i	−0.985961	−	0.166973i	$-0.946601\pi$
$443$		−	7.02876i		−	0.333947i	0.985961	−	0.166973i	$-0.0533994\pi$
$444$	−22.4590	−	25.8987i	−1.06586	−	1.22910i
$445$	9.66002	−	4.83001i	0.457929	−	0.228964i
$446$	−35.2870	+	2.85534i	−1.67089	+	0.135204i
$447$	−7.08751	−	11.4850i	−0.335227	−	0.543222i
$448$	7.07945	−	3.72577i	0.334473	−	0.176026i
$449$		−	34.2566i		−	1.61667i	−0.588722	−	0.808335i	$-0.700369\pi$
$449$		−	34.2566i		−	1.61667i	0.588722	−	0.808335i	$-0.299631\pi$
$450$	10.9619	+	18.1614i	0.516750	+	0.856137i
$451$		−	17.3809i		−	0.818436i
$452$	−5.58638	+	0.910032i	−0.262761	+	0.0428043i
$453$	−18.8275	−	30.5093i	−0.884595	−	1.43345i
$454$	0.207503	+	2.56437i	0.00973859	+	0.120352i
$455$	2.72593	−	1.36297i	0.127794	−	0.0638968i
$456$	12.3948	+	12.1559i	0.580440	+	0.569251i
$457$			35.7265i			1.67121i	0.549328	+	0.835607i	$0.314884\pi$
$457$			35.7265i			1.67121i	−0.549328	+	0.835607i	$0.685116\pi$
$458$	16.7179	−	1.35277i	0.781177	−	0.0632109i
$459$	1.22752	+	13.9261i	0.0572956	+	0.650013i
$460$	−26.0454	+	18.7965i	−1.21437	+	0.876393i
$461$		−	26.4818i		−	1.23338i	−0.787205	−	0.616691i	$-0.788473\pi$
$461$		−	26.4818i		−	1.23338i	0.787205	−	0.616691i	$-0.211527\pi$
$462$	−5.81921	+	4.27546i	−0.270734	+	0.198912i
$463$	−18.2819			−0.849631			−0.424815	−	0.905280i	$-0.639661\pi$
$463$	−18.2819			−0.849631			−0.424815	+	0.905280i	$0.639661\pi$
$464$	1.73032	+	5.16999i	0.0803280	+	0.240011i
$465$	−16.4998	+	26.6573i	−0.765160	+	1.23620i
$466$	−7.83169	+	0.633721i	−0.362796	+	0.0293566i
$467$		−	9.97263i		−	0.461478i	−0.973016	−	0.230739i	$-0.925886\pi$
$467$		−	9.97263i		−	0.461478i	0.973016	−	0.230739i	$-0.0741144\pi$
$468$	7.80403	+	2.44406i	0.360741	+	0.112977i
$469$	−8.46844			−0.391036
$470$	−4.92124	+	2.97938i	−0.227000	+	0.137429i
$471$	7.08751	+	11.4850i	0.326575	+	0.529201i
$472$	−18.6949	+	4.61907i	−0.860504	+	0.212610i
$473$	−6.65500			−0.305997
$474$	−23.4712	−	31.9460i	−1.07807	−	1.46733i
$475$	14.1750	+	10.6313i	0.650394	+	0.487796i
$476$	5.31092	−	0.865159i	0.243426	−	0.0396545i
$477$	−18.5532	+	36.9826i	−0.849494	+	1.69332i
$478$	−37.2336	+	3.01285i	−1.70302	+	0.137804i
$479$	−8.03593			−0.367171			−0.183586	−	0.983004i	$-0.558770\pi$
$479$	−8.03593			−0.367171			−0.183586	+	0.983004i	$0.558770\pi$
$480$	21.6611	+	3.28563i	0.988691	+	0.149968i
$481$	−13.4878			−0.614990
$482$	36.5070	−	2.95405i	1.66285	−	0.134553i
$483$	6.53295	+	10.5864i	0.297260	+	0.481697i
$484$	−4.55897	+	0.742665i	−0.207226	+	0.0337575i
$485$	−7.40589	+	3.70294i	−0.336284	+	0.168142i
$486$	21.0846	+	6.43746i	0.956415	+	0.292009i
$487$	23.9346			1.08458			0.542291	−	0.840191i	$-0.317557\pi$
$487$	23.9346			1.08458			0.542291	+	0.840191i	$0.317557\pi$
$488$	−17.9879	+	4.44438i	−0.814273	+	0.201187i
$489$	21.8273	−	13.4698i	0.987065	−	0.609127i
$490$	−1.63773	−	2.70515i	−0.0739851	−	0.122206i
$491$	5.70982			0.257681			0.128840	−	0.991665i	$-0.458875\pi$
$491$	5.70982			0.257681			0.128840	+	0.991665i	$0.458875\pi$
$492$	13.3809	+	15.4303i	0.603259	+	0.695650i
$493$			3.66701i			0.165154i
$494$	6.80841	−	0.550920i	0.306325	−	0.0247871i
$495$	−19.7755	−	0.0264816i	−0.888842	−	0.00119026i
$496$	10.2764	+	30.7047i	0.461423	+	1.37868i
$497$	8.00000			0.358849
$498$	−8.46573	−	11.5225i	−0.379358	−	0.516334i
$499$		−	17.2495i		−	0.772193i	−0.922458	−	0.386096i	$-0.873823\pi$
$499$		−	17.2495i		−	0.772193i	0.922458	−	0.386096i	$-0.126177\pi$
$500$	22.3569	+	0.410748i	0.999831	+	0.0183692i
$501$	−12.2085	−	19.7833i	−0.545434	−	0.883854i
$502$	−9.59718	+	0.776580i	−0.428343	+	0.0346605i
$503$		−	42.3398i		−	1.88784i	−0.330179	−	0.943918i	$-0.607109\pi$
$503$		−	42.3398i		−	1.88784i	0.330179	−	0.943918i	$-0.392891\pi$
$504$	1.87460	−	8.27562i	0.0835015	−	0.368625i
$505$	28.8937	−	14.4468i	1.28575	−	0.642876i
$506$	−2.41501	−	29.8453i	−0.107360	−	1.32678i
$507$	−16.4236	+	10.1351i	−0.729396	+	0.450117i
$508$	27.4303	−	4.46844i	1.21702	−	0.198255i
$509$		−	1.27407i		−	0.0564721i	−0.999601	−	0.0282361i	$-0.991011\pi$
$509$		−	1.27407i		−	0.0564721i	0.999601	−	0.0282361i	$-0.00898902\pi$
$510$	13.1150	+	6.71984i	0.580740	+	0.297559i
$511$		−	8.00000i		−	0.353899i
$512$	16.9115	−	15.0334i	0.747388	−	0.664388i
$513$	18.3428	−	1.61683i	0.809853	−	0.0713847i
$514$	0.479235	−	0.0387785i	0.0211381	−	0.00171045i
$515$	−10.0355	−	20.0709i	−0.442215	−	0.884431i
$516$	5.90811	−	5.12344i	0.260090	−	0.225547i
$517$		−	5.36297i		−	0.235863i
$518$	1.12875	+	13.9493i	0.0495943	+	0.612899i
$519$	1.93023	−	1.19116i	0.0847276	−	0.0522862i
$520$	6.56033	−	5.59187i	0.287689	−	0.245220i
$521$		−	28.4137i		−	1.24483i	−0.782689	−	0.622413i	$-0.786152\pi$
$521$		−	28.4137i		−	1.24483i	0.782689	−	0.622413i	$-0.213848\pi$
$522$	5.36092	+	2.16765i	0.234641	+	0.0948755i
$523$	36.9181			1.61431			0.807157	−	0.590337i	$-0.201005\pi$
$523$	36.9181			1.61431			0.807157	+	0.590337i	$0.201005\pi$
$524$	31.8865	−	5.19437i	1.39297	−	0.226917i
$525$	0.783514	−	8.62474i	0.0341954	−	0.376414i
$526$	−0.661701	−	8.17747i	−0.0288515	−	0.356555i
$527$			21.7784i			0.948684i
$528$	−13.0781	+	15.6878i	−0.569151	+	0.682722i
$529$	−28.5837			−1.24277
$530$	22.5873	+	37.3090i	0.981130	+	1.62060i
$531$	−9.15890	+	18.2566i	−0.397462	+	0.792271i
$532$	−1.13955	−	6.99530i	−0.0494056	−	0.303285i
$533$	8.03593			0.348075
$534$	−7.00502	−	9.53434i	−0.303137	−	0.412591i
$535$	−13.4275	+	6.71374i	−0.580521	+	0.290260i
$536$	−23.2531	+	5.74529i	−1.00438	+	0.248159i
$537$	32.9646	−	20.3428i	1.42253	−	0.877855i
$538$	−1.49032	−	18.4178i	−0.0642523	−	0.794047i
$539$	2.94796			0.126978
$540$	17.5765	−	15.2009i	0.756371	−	0.654143i
$541$	14.4114			0.619593			0.309797	−	0.950803i	$-0.399739\pi$
$541$	14.4114			0.619593			0.309797	+	0.950803i	$0.399739\pi$
$542$	−3.30515	−	40.8459i	−0.141968	−	1.75448i
$543$	13.6739	−	8.43828i	0.586803	−	0.362121i
$544$	13.9961	−	5.97872i	0.600077	−	0.256336i
$545$	−6.69047	−	13.3809i	−0.286588	−	0.573176i
$546$	−1.97672	−	2.69047i	−0.0845960	−	0.115141i
$547$	−0.432504			−0.0184925			−0.00924627	−	0.999957i	$-0.502943\pi$
$547$	−0.432504			−0.0184925			−0.00924627	+	0.999957i	$0.502943\pi$
$548$	−5.03546	+	0.820286i	−0.215104	+	0.0350409i
$549$	−8.81251	+	17.5662i	−0.376109	+	0.749706i
$550$	−11.1214	+	17.6306i	−0.474218	+	0.751771i
$551$	4.83001			0.205765
$552$	25.1207	+	24.6365i	1.06921	+	1.04860i
$553$			16.1836i			0.688195i
$554$	−2.32033	−	28.6753i	−0.0985815	−	1.21830i
$555$	−20.1714	+	32.5892i	−0.856227	+	1.38333i
$556$	0.756374	+	4.64313i	0.0320774	+	0.196913i
$557$	21.9346			0.929400			0.464700	−	0.885468i	$-0.346162\pi$
$557$	21.9346			0.929400			0.464700	+	0.885468i	$0.346162\pi$
$558$	31.8386	+	12.8737i	1.34783	+	0.544988i
$559$		−	3.07689i		−	0.130138i
$560$	−6.33224	−	6.31686i	−0.267586	−	0.266936i
$561$	−11.6907	+	7.21444i	−0.493582	+	0.304594i
$562$	−1.95671	−	24.1815i	−0.0825388	−	1.02004i
$563$			13.9790i			0.589146i	0.955629	+	0.294573i	$0.0951774\pi$
$563$			13.9790i			0.589146i	−0.955629	+	0.294573i	$0.904823\pi$
$564$	4.12875	+	4.76108i	0.173852	+	0.200478i
$565$	2.83001	+	5.66002i	0.119059	+	0.238119i
$566$	28.6557	−	2.31875i	1.20449	−	0.0974644i
$567$	−5.38070	−	7.21444i	−0.225968	−	0.302978i
$568$	21.9668	−	5.42748i	0.921708	−	0.227732i
$569$		−	18.3455i		−	0.769085i	−0.923107	−	0.384542i	$-0.874359\pi$
$569$		−	18.3455i		−	0.769085i	0.923107	−	0.384542i	$-0.125641\pi$
$570$	8.85105	−	17.2744i	0.370730	−	0.723544i
$571$			30.8672i			1.29175i	0.763443	+	0.645875i	$0.223507\pi$
$571$			30.8672i			1.29175i	−0.763443	+	0.645875i	$0.776493\pi$
$572$	1.29204	+	7.93138i	0.0540227	+	0.331628i
$573$	−1.93433	+	1.19369i	−0.0808076	+	0.0498671i
$574$	−0.672500	−	8.31092i	−0.0280696	−	0.346891i
$575$	28.7287	+	21.5465i	1.19807	+	0.898553i
$576$	−0.467082	−	23.9955i	−0.0194618	−	0.999811i
$577$		−	25.1548i		−	1.04721i	−0.851962	−	0.523604i	$-0.824587\pi$
$577$		−	25.1548i		−	1.04721i	0.851962	−	0.523604i	$-0.175413\pi$
$578$	−13.7597	+	1.11340i	−0.572329	+	0.0463115i
$579$	8.50027	+	13.7743i	0.353259	+	0.572442i
$580$	4.94265	−	3.56703i	0.205232	−	0.148113i
$581$			5.83718i			0.242167i
$582$	5.37042	+	7.30953i	0.222611	+	0.302990i
$583$	−40.6578			−1.68387
$584$	−5.42748	−	21.9668i	−0.224591	−	0.908995i
$585$	0.0122436	−	9.14304i	0.000506209	−	0.378018i
$586$	−22.7543	+	1.84122i	−0.939972	+	0.0760603i
$587$		−	36.2015i		−	1.49420i	−0.664713	−	0.747099i	$-0.731446\pi$
$587$		−	36.2015i		−	1.49420i	0.664713	−	0.747099i	$-0.268554\pi$
$588$	−2.61711	+	2.26952i	−0.107928	+	0.0935936i
$589$	28.6855			1.18197
$590$	11.1503	+	18.4178i	0.459052	+	0.758248i
$591$	−10.8264	+	6.68106i	−0.445338	+	0.274822i
$592$	12.5631	+	37.5371i	0.516341	+	1.54277i
$593$	13.7314			0.563882			0.281941	−	0.959432i	$-0.409022\pi$
$593$	13.7314			0.563882			0.281941	+	0.959432i	$0.409022\pi$
$594$	3.63638	+	21.3556i	0.149202	+	0.876231i
$595$	−2.69047	−	5.38093i	−0.110298	−	0.220597i
$596$	2.50558	+	15.3809i	0.102633	+	0.630027i
$597$	5.30953	+	8.60388i	0.217305	+	0.352134i
$598$	13.7987	−	1.11656i	0.564272	−	0.0456595i
$599$	−30.1783			−1.23305			−0.616525	−	0.787335i	$-0.711460\pi$
$599$	−30.1783			−1.23305			−0.616525	+	0.787335i	$0.711460\pi$
$600$	−3.69991	−	24.2139i	−0.151048	−	0.988526i
$601$	26.4928			1.08066			0.540332	−	0.841452i	$-0.318299\pi$
$601$	26.4928			1.08066			0.540332	+	0.841452i	$0.318299\pi$
$602$	−3.18218	+	0.257494i	−0.129696	+	0.0104947i
$603$	−11.3920	+	22.7080i	−0.463919	+	0.924740i
$604$	6.65592	+	40.8585i	0.270826	+	1.66251i
$605$	2.30953	+	4.61907i	0.0938959	+	0.187792i
$606$	−20.9524	−	28.5178i	−0.851134	−	1.15846i
$607$	−10.4142			−0.422698			−0.211349	−	0.977411i	$-0.567786\pi$
$607$	−10.4142			−0.422698			−0.211349	+	0.977411i	$0.567786\pi$
$608$	−7.87488	−	18.4350i	−0.319369	−	0.747637i
$609$	−1.23976	−	2.00898i	−0.0502377	−	0.0814081i
$610$	10.7286	+	17.7212i	0.434390	+	0.717511i
$611$	2.47952			0.100311
$612$	4.82452	−	15.4050i	0.195020	−	0.622710i
$613$			20.3068i			0.820185i	0.912044	+	0.410092i	$0.134504\pi$
$613$			20.3068i			0.820185i	−0.912044	+	0.410092i	$0.865496\pi$
$614$	31.0348	−	2.51126i	1.25246	−	0.101346i
$615$	12.0180	−	19.4164i	0.484611	−	0.782945i
$616$	8.09467	−	2.00000i	0.326144	−	0.0805823i
$617$	33.2769			1.33968			0.669838	−	0.742507i	$-0.266364\pi$
$617$	33.2769			1.33968			0.669838	+	0.742507i	$0.266364\pi$
$618$	−19.8098	+	14.5546i	−0.796867	+	0.585470i
$619$			25.0072i			1.00512i	0.864541	+	0.502561i	$0.167609\pi$
$619$			25.0072i			1.00512i	−0.864541	+	0.502561i	$0.832391\pi$
$620$	29.3545	−	21.1846i	1.17890	−	0.850796i
$621$	37.1756	−	3.27685i	1.49180	−	0.131495i
$622$	−19.5371	+	1.58090i	−0.783367	+	0.0633882i
$623$			4.83001i			0.193510i
$624$	−7.25311	−	6.04655i	−0.290357	−	0.242056i
$625$	−7.00000	−	24.0000i	−0.280000	−	0.960000i
$626$	0.131719	+	1.62782i	0.00526455	+	0.0650607i
$627$	9.50251	+	15.3984i	0.379494	+	0.614954i
$628$	−2.50558	−	15.3809i	−0.0999835	−	0.613766i
$629$			26.6246i			1.06159i
$630$	−9.45694	+	0.752487i	−0.376774	+	0.0299798i
$631$		−	3.51517i		−	0.139937i	−0.997549	−	0.0699683i	$-0.977710\pi$
$631$		−	3.51517i		−	0.139937i	0.997549	−	0.0699683i	$-0.0222898\pi$
$632$	10.9795	+	44.4377i	0.436741	+	1.76764i
$633$	12.2085	+	19.7833i	0.485243	+	0.786316i
$634$	10.4042	−	0.841883i	0.413204	−	0.0334354i
$635$	−13.8959	−	27.7918i	−0.551443	−	1.10289i
$636$	36.0947	−	31.3009i	1.43125	−	1.24116i
$637$			1.36297i			0.0540026i
$638$	0.458297	+	5.66375i	0.0181441	+	0.224230i
$639$	10.7619	−	21.4519i	0.425733	−	0.848622i
$640$	−21.6730	−	13.0492i	−0.856701	−	0.515814i
$641$			38.6956i			1.52838i	0.644990	+	0.764191i	$0.276862\pi$
$641$			38.6956i			1.52838i	−0.644990	+	0.764191i	$0.723138\pi$
$642$	9.73702	+	13.2528i	0.384289	+	0.523046i
$643$	14.2957			0.563769			0.281884	−	0.959448i	$-0.409041\pi$
$643$	14.2957			0.563769			0.281884	+	0.959448i	$0.409041\pi$
$644$	−2.30953	−	14.1775i	−0.0910084	−	0.558671i
$645$	−7.43436	−	4.60157i	−0.292728	−	0.181187i
$646$	−1.08751	−	13.4397i	−0.0427873	−	0.528777i
$647$		−	28.4840i		−	1.11982i	−0.828553	−	0.559910i	$-0.810836\pi$
$647$		−	28.4840i		−	1.11982i	0.828553	−	0.559910i	$-0.189164\pi$
$648$	−19.6691	−	16.1593i	−0.772677	−	0.634799i
$649$	−20.0709			−0.787853
$650$	−8.15136	−	5.14188i	−0.319723	−	0.201681i
$651$	−7.36297	−	11.9314i	−0.288577	−	0.467628i
$652$	−29.2315	+	4.76186i	−1.14479	+	0.186489i
$653$	4.30405			0.168430			0.0842152	−	0.996448i	$-0.473162\pi$
$653$	4.30405			0.168430			0.0842152	+	0.996448i	$0.473162\pi$
$654$	−13.2068	+	9.70326i	−0.516428	+	0.379427i
$655$	−16.1534	−	32.3068i	−0.631166	−	1.26233i
$656$	−7.48501	−	22.3644i	−0.292241	−	0.873181i
$657$	−21.4519	−	10.7619i	−0.836917	−	0.419860i
$658$	−0.207503	−	2.56437i	−0.00808930	−	0.0999697i
$659$	11.5339			0.449296			0.224648	−	0.974440i	$-0.427877\pi$
$659$	11.5339			0.449296			0.224648	+	0.974440i	$0.427877\pi$
$660$	21.0961	+	8.73980i	0.821163	+	0.340196i
$661$	−19.6878			−0.765765			−0.382883	−	0.923797i	$-0.625069\pi$
$661$	−19.6878			−0.765765			−0.382883	+	0.923797i	$0.625069\pi$
$662$	0.972626	+	12.0200i	0.0378022	+	0.467169i
$663$	−3.33554	−	5.40510i	−0.129541	−	0.209917i
$664$	3.96015	+	16.0281i	0.153684	+	0.622009i
$665$	−7.08751	+	3.54375i	−0.274842	+	0.137421i
$666$	38.9234	+	15.7384i	1.50825	+	0.609851i
$667$	9.78906			0.379034
$668$	4.31595	+	26.4942i	0.166989	+	1.02509i
$669$	36.8985	−	22.7704i	1.42658	−	0.880354i
$670$	13.8690	+	22.9084i	0.535807	+	0.885029i
$671$	−19.3118			−0.745526
$672$	−5.64648	+	8.00733i	−0.217818	+	0.308889i
$673$		−	38.4524i		−	1.48223i	−0.671377	−	0.741116i	$-0.734297\pi$
$673$		−	38.4524i		−	1.48223i	0.671377	−	0.741116i	$-0.265703\pi$
$674$	0.908396	+	11.2262i	0.0349901	+	0.432417i
$675$	−22.0731	−	13.7033i	−0.849593	−	0.527439i
$676$	21.9947	−	3.58298i	0.845951	−	0.137807i
$677$	−18.2741			−0.702332			−0.351166	−	0.936313i	$-0.614215\pi$
$677$	−18.2741			−0.702332			−0.351166	+	0.936313i	$0.614215\pi$
$678$	5.58638	−	4.10440i	0.214544	−	0.157628i
$679$		−	3.70294i		−	0.142106i
$680$	−11.0382	−	12.9500i	−0.423297	−	0.496608i
$681$	−1.65477	−	2.68148i	−0.0634108	−	0.102755i
$682$	2.72183	+	33.6371i	0.104224	+	1.28803i
$683$			19.8750i			0.760494i	0.924885	+	0.380247i	$0.124161\pi$
$683$			19.8750i			0.760494i	−0.924885	+	0.380247i	$0.875839\pi$
$684$	−20.2907	−	6.35463i	−0.775835	−	0.242975i
$685$	2.55092	+	5.10184i	0.0974656	+	0.194931i
$686$	1.40961	−	0.114062i	0.0538190	−	0.00435490i
$687$	−17.4814	+	10.7879i	−0.666956	+	0.411585i
$688$	−8.56311	+	2.86594i	−0.326465	+	0.109263i
$689$		−	18.7978i		−	0.716139i
$690$	17.9386	−	35.0103i	0.682909	−	1.33282i
$691$			33.5931i			1.27794i	0.769231	+	0.638971i	$0.220639\pi$
$691$			33.5931i			1.27794i	−0.769231	+	0.638971i	$0.779361\pi$
$692$	−2.58499	+	0.421100i	−0.0982667	+	0.0160078i
$693$	3.96569	−	7.90490i	0.150644	−	0.300282i
$694$	−0.680135	−	8.40528i	−0.0258176	−	0.319060i
$695$	4.70433	−	2.35217i	0.178446	−	0.0892228i
$696$	−4.76717	−	4.67528i	−0.180699	−	0.177216i
$697$		−	15.8628i		−	0.600845i
$698$	−39.4729	+	3.19405i	−1.49407	+	0.120897i
$699$	8.18935	−	5.05372i	0.309749	−	0.191149i
$700$	−4.63568	+	8.86061i	−0.175212	+	0.334900i
$701$			8.33299i			0.314733i	0.987540	+	0.157366i	$0.0503003\pi$
$701$			8.33299i			0.314733i	−0.987540	+	0.157366i	$0.949700\pi$
$702$	−9.87359	+	1.68125i	−0.372655	+	0.0634546i
$703$	35.0687			1.32264
$704$	20.8699	−	10.9834i	0.786565	−	0.413953i
$705$	3.70820	−	5.99102i	0.139659	−	0.225635i
$706$	−7.09094	+	0.573782i	−0.266871	+	0.0215946i
$707$			14.4468i			0.543329i
$708$	17.8184	−	15.4519i	0.669655	−	0.580716i
$709$	27.7914			1.04373			0.521863	−	0.853029i	$-0.325237\pi$
$709$	27.7914			1.04373			0.521863	+	0.853029i	$0.325237\pi$
$710$	−13.1018	−	21.6412i	−0.491703	−	0.812180i
$711$	43.3960	+	21.7707i	1.62748	+	0.816464i
$712$	3.27685	+	13.2625i	0.122805	+	0.497034i
$713$	58.1374			2.17726
$714$	−5.31092	+	3.90201i	−0.198756	+	0.146029i
$715$	8.03593	−	4.01797i	0.300527	−	0.150263i
$716$	−44.1468	+	7.19159i	−1.64984	+	0.268762i
$717$	38.9339	−	24.0265i	1.45401	−	0.897285i
$718$	−18.9618	+	1.53434i	−0.707649	+	0.0572612i
$719$	−32.1778			−1.20003			−0.600015	−	0.799989i	$-0.704839\pi$
$719$	−32.1778			−1.20003			−0.600015	+	0.799989i	$0.704839\pi$
$720$	−25.4569	+	8.48215i	−0.948722	+	0.316111i
$721$	10.0355			0.373740
$722$	9.08043	−	0.734766i	0.337939	−	0.0273452i
$723$	−38.1742	+	23.5576i	−1.41971	+	0.876117i
$724$	−18.3123	+	2.98311i	−0.680572	+	0.110866i
$725$	−5.45186	−	4.08890i	−0.202477	−	0.151858i
$726$	4.55897	−	3.34954i	0.169199	−	0.124313i
$727$	13.4519			0.498902			0.249451	−	0.968387i	$-0.419750\pi$
$727$	13.4519			0.498902			0.249451	+	0.968387i	$0.419750\pi$
$728$	0.924684	+	3.74251i	0.0342711	+	0.138707i
$729$	−26.5837	+	4.72315i	−0.984581	+	0.174931i
$730$	−21.6412	+	13.1018i	−0.800977	+	0.484921i
$731$	−6.07371			−0.224644
$732$	17.1445	−	14.8675i	0.633678	−	0.549518i
$733$			21.1907i			0.782698i	0.920242	+	0.391349i	$0.127991\pi$
$733$			21.1907i			0.782698i	−0.920242	+	0.391349i	$0.872009\pi$
$734$	3.10174	−	0.250985i	0.114487	−	0.00926404i
$735$	3.29319	+	2.03835i	0.121471	+	0.0751858i
$736$	−15.9601	−	37.3624i	−0.588299	−	1.37720i
$737$	−24.9646			−0.919583
$738$	−23.1903	−	9.37683i	−0.853646	−	0.345166i
$739$		−	41.2854i		−	1.51871i	−0.650678	−	0.759354i	$-0.725515\pi$
$739$		−	41.2854i		−	1.51871i	0.650678	−	0.759354i	$-0.274485\pi$
$740$	35.8865	−	25.8987i	1.31921	−	0.952055i
$741$	−7.11934	+	4.39341i	−0.261535	+	0.161396i
$742$	−19.4411	+	1.57312i	−0.713704	+	0.0577512i
$743$			23.0565i			0.845861i	0.906162	+	0.422930i	$0.138999\pi$
$743$			23.0565i			0.845861i	−0.906162	+	0.422930i	$0.861001\pi$
$744$	−28.3123	−	27.7666i	−1.03798	−	1.01797i
$745$	15.5837	−	7.79184i	0.570942	−	0.285471i
$746$	−0.337832	−	4.17501i	−0.0123689	−	0.152858i
$747$	15.6523	+	7.85236i	0.572687	+	0.287303i
$748$	15.6564	−	2.55045i	0.572454	−	0.0932538i
$749$		−	6.71374i		−	0.245315i
$750$	−24.6144	+	12.0055i	−0.898791	+	0.438378i
$751$			23.5895i			0.860791i	0.902640	+	0.430396i	$0.141626\pi$
$751$			23.5895i			0.860791i	−0.902640	+	0.430396i	$0.858374\pi$
$752$	−2.30953	−	6.90062i	−0.0842201	−	0.251640i
$753$	10.0355	−	6.19298i	0.365713	−	0.225685i
$754$	−2.61859	+	0.211890i	−0.0953634	+	0.00771657i
$755$	41.3971	−	20.6986i	1.50660	−	0.753298i
$756$	2.56507	+	10.0708i	0.0932906	+	0.366270i
$757$		−	40.7287i		−	1.48031i	−0.672436	−	0.740155i	$-0.734752\pi$
$757$		−	40.7287i		−	1.48031i	0.672436	−	0.740155i	$-0.265248\pi$
$758$	−2.33922	−	28.9087i	−0.0849644	−	1.05001i
$759$	19.2589	+	31.2082i	0.699053	+	1.13279i
$760$	−17.0571	+	14.5390i	−0.618725	+	0.527387i
$761$		−	11.3478i		−	0.411357i	−0.978620	−	0.205678i	$-0.934060\pi$
$761$		−	11.3478i		−	0.411357i	0.978620	−	0.205678i	$-0.0659401\pi$
$762$	−27.4303	+	20.1534i	−0.993694	+	0.730081i
$763$	6.69047			0.242211
$764$	2.59048	−	0.421994i	0.0937204	−	0.0152672i
$765$	−18.0482	−	0.0241685i	−0.652533	−	0.000873815i
$766$	3.54236	+	43.7774i	0.127991	+	1.58174i
$767$		−	9.27963i		−	0.335068i
$768$	−10.0720	+	25.8177i	−0.363441	+	0.931617i
$769$	−34.7564			−1.25335			−0.626675	−	0.779281i	$-0.715585\pi$
$769$	−34.7564			−1.25335			−0.626675	+	0.779281i	$0.715585\pi$
$770$	−4.82796	−	7.97467i	−0.173988	−	0.287387i
$771$	−0.501120	+	0.309246i	−0.0180474	+	0.0111372i
$772$	−3.00502	−	18.4468i	−0.108153	−	0.663916i
$773$	30.8323			1.10896			0.554481	−	0.832197i	$-0.312917\pi$
$773$	30.8323			1.10896			0.554481	+	0.832197i	$0.312917\pi$
$774$	−3.59030	+	8.87934i	−0.129051	+	0.319161i
$775$	−32.3787	−	24.2840i	−1.16308	−	0.872308i
$776$	−2.51221	−	10.1677i	−0.0901830	−	0.365001i
$777$	−9.00139	−	14.5864i	−0.322923	−	0.523284i
$778$	2.53454	+	31.3225i	0.0908675	+	1.12296i
$779$	−20.8937			−0.748594
$780$	−4.04077	+	9.75359i	−0.144683	+	0.349235i
$781$	23.5837			0.843890
$782$	−2.20406	−	27.2384i	−0.0788171	−	0.974043i
$783$	−7.05482	+	0.621849i	−0.252119	+	0.0222231i
$784$	3.79319	−	1.26952i	0.135471	−	0.0453402i
$785$	−15.5837	+	7.79184i	−0.556205	+	0.278103i
$786$	−31.8865	+	23.4275i	−1.13735	+	0.835631i
$787$	−38.4607			−1.37098			−0.685488	−	0.728084i	$-0.740411\pi$
$787$	−38.4607			−1.37098			−0.685488	+	0.728084i	$0.740411\pi$
$788$	14.4989	−	2.36189i	0.516501	−	0.0841389i
$789$	5.27685	+	8.55092i	0.187861	+	0.304421i
$790$	43.7790	−	26.5043i	1.55759	−	0.942981i
$791$	−2.83001			−0.100624
$792$	5.52625	−	24.3962i	0.196367	−	0.866881i
$793$		−	8.92868i		−	0.317067i
$794$	3.64047	+	44.9899i	0.129196	+	1.59663i
$795$	−45.4192	−	28.1126i	−1.61085	−	0.997053i
$796$	−1.87703	−	11.5225i	−0.0665296	−	0.408403i
$797$	−1.38140			−0.0489317			−0.0244658	−	0.999701i	$-0.507788\pi$
$797$	−1.38140			−0.0489317			−0.0244658	+	0.999701i	$0.507788\pi$
$798$	5.13955	+	6.99530i	0.181938	+	0.247631i
$799$		−	4.89453i		−	0.173156i
$800$	−6.71756	+	27.4750i	−0.237502	+	0.971387i
$801$	12.9516	+	6.49749i	0.457622	+	0.229577i
$802$	1.96081	+	24.2322i	0.0692385	+	0.855668i
$803$		−	23.5837i		−	0.832250i
$804$	22.1628	−	19.2193i	0.781622	−	0.677813i
$805$	−14.3644	+	7.18218i	−0.506277	+	0.253139i
$806$	−15.5518	+	1.25842i	−0.547790	+	0.0443258i
$807$	11.8848	+	19.2589i	0.418366	+	0.677945i
$808$	9.80125	+	39.6689i	0.344807	+	1.39555i
$809$		−	3.66701i		−	0.128925i	−0.997920	−	0.0644626i	$-0.979467\pi$
$809$		−	3.66701i		−	0.128925i	0.997920	−	0.0644626i	$-0.0205333\pi$
$810$	−10.7040	+	26.3709i	−0.376101	+	0.926579i
$811$		−	27.5715i		−	0.968166i	−0.875022	−	0.484083i	$-0.839153\pi$
$811$		−	27.5715i		−	0.968166i	0.875022	−	0.484083i	$-0.160847\pi$
$812$	0.438281	+	2.69047i	0.0153807	+	0.0944168i
$813$	26.3575	+	42.7112i	0.924397	+	1.49795i
$814$	3.32750	+	41.1221i	0.116629	+	1.44133i
$815$	14.8084	+	29.6168i	0.518716	+	1.03743i
$816$	−11.9358	+	14.3175i	−0.417836	+	0.501212i
$817$			8.00000i			0.279885i
$818$	−23.1329	+	1.87186i	−0.808824	+	0.0654480i
$819$	3.65477	+	1.83351i	0.127708	+	0.0640679i
$820$	−21.3809	+	15.4303i	−0.746655	+	0.538848i
$821$		−	30.2926i		−	1.05722i	−0.848865	−	0.528609i	$-0.822714\pi$
$821$		−	30.2926i		−	1.05722i	0.848865	−	0.528609i	$-0.177286\pi$
$822$	5.03546	−	3.69963i	0.175632	−	0.129039i
$823$	44.4414			1.54913			0.774565	−	0.632494i	$-0.217969\pi$
$823$	44.4414			1.54913			0.774565	+	0.632494i	$0.217969\pi$
$824$	27.5559	−	6.80841i	0.959957	−	0.237182i
$825$	2.30977	−	25.4254i	0.0804158	−	0.885198i
$826$	−9.59718	+	0.776580i	−0.333929	+	0.0270207i
$827$		−	41.0233i		−	1.42652i	−0.700899	−	0.713261i	$-0.747218\pi$
$827$		−	41.0233i		−	1.42652i	0.700899	−	0.713261i	$-0.252782\pi$
$828$	−41.1235	−	12.8790i	−1.42914	−	0.447577i
$829$	43.5155			1.51136			0.755678	−	0.654943i	$-0.227307\pi$
$829$	43.5155			1.51136			0.755678	+	0.654943i	$0.227307\pi$
$830$	15.7904	−	9.55972i	0.548094	−	0.331823i
$831$	18.5039	+	29.9848i	0.641893	+	1.04016i
$832$	5.07810	+	9.64904i	0.176051	+	0.334520i
$833$	2.69047			0.0932191
$834$	−3.41137	−	4.64313i	−0.118126	−	0.160778i
$835$	26.8434	−	13.4217i	0.928955	−	0.464477i
$836$	−3.35933	−	20.6218i	−0.116185	−	0.713222i
$837$	−41.8987	+	3.69317i	−1.44823	+	0.127655i
$838$	15.5290	−	1.25657i	0.536442	−	0.0434075i
$839$	14.3528			0.495514			0.247757	−	0.968822i	$-0.420307\pi$
$839$	14.3528			0.495514			0.247757	+	0.968822i	$0.420307\pi$
$840$	10.4255	+	3.36281i	0.359715	+	0.116028i
$841$	27.1423			0.935942
$842$	−20.4143	+	1.65188i	−0.703525	+	0.0569275i
$843$	15.6041	+	25.2858i	0.537434	+	0.870890i
$844$	−4.31595	−	26.4942i	−0.148561	−	0.911967i
$845$	−11.1423	−	22.2847i	−0.383308	−	0.766615i
$846$	−7.15546	−	2.89326i	−0.246010	−	0.0994725i
$847$	−2.30953			−0.0793565
$848$	−52.3151	+	17.5091i	−1.79651	+	0.601264i
$849$	−29.9644	+	18.4913i	−1.02837	+	0.634619i
$850$	−10.1500	+	16.0906i	−0.348141	+	0.551904i
$851$	71.0742			2.43639
$852$	−20.9369	+	18.1562i	−0.717285	+	0.622021i
$853$			5.10184i			0.174684i	0.996178	+	0.0873418i	$0.0278372\pi$
$853$			5.10184i			0.174684i	−0.996178	+	0.0873418i	$0.972163\pi$
$854$	−9.23422	+	0.747210i	−0.315988	+	0.0255690i
$855$	−0.0318336	+	23.7722i	−0.00108869	+	0.812992i
$856$	−4.55484	−	18.4350i	−0.155681	−	0.630094i
$857$	−22.1419			−0.756351			−0.378176	−	0.925734i	$-0.623448\pi$
$857$	−22.1419			−0.756351			−0.378176	+	0.925734i	$0.623448\pi$
$858$	−5.82730	−	7.93138i	−0.198941	−	0.270773i
$859$			30.3218i			1.03457i	0.855814	+	0.517283i	$0.173057\pi$
$859$			30.3218i			1.03457i	−0.855814	+	0.517283i	$0.826943\pi$
$860$	5.90811	+	8.18656i	0.201465	+	0.279160i
$861$	5.36297	+	8.69047i	0.182769	+	0.296170i
$862$	39.0788	−	3.16216i	1.33103	−	0.107704i
$863$		−	35.3527i		−	1.20342i	−0.798715	−	0.601710i	$-0.794486\pi$
$863$		−	35.3527i		−	1.20342i	0.798715	−	0.601710i	$-0.205514\pi$
$864$	13.8757	+	25.9127i	0.472060	+	0.881566i
$865$	1.30953	+	2.61907i	0.0445255	+	0.0890510i
$866$	2.86316	+	35.3837i	0.0972942	+	1.20239i
$867$	14.3881	−	8.87903i	0.488645	−	0.301548i
$868$	2.60296	+	15.9787i	0.0883502	+	0.542353i
$869$			47.7085i			1.61840i
$870$	−3.40421	+	6.64391i	−0.115413	+	0.225250i
$871$		−	11.5422i		−	0.391092i
$872$	18.3711	−	4.53905i	0.622122	−	0.153712i
$873$	−9.92938	−	4.98132i	−0.336058	−	0.168592i
$874$	−35.8771	+	2.90309i	−1.21356	+	0.0981984i
$875$	11.0000	+	2.00000i	0.371868	+	0.0676123i
$876$	18.1562	+	20.9369i	0.613441	+	0.707391i
$877$		−	20.6218i		−	0.696350i	−0.937429	−	0.348175i	$-0.886801\pi$
$877$		−	20.6218i		−	0.696350i	0.937429	−	0.348175i	$-0.113199\pi$
$878$	−1.69578	−	20.9568i	−0.0572296	−	0.707259i
$879$	23.7935	−	14.6832i	0.802534	−	0.495251i
$880$	−18.6672	−	18.6218i	−0.629271	−	0.627742i
$881$			57.6224i			1.94135i	0.240400	+	0.970674i	$0.422721\pi$
$881$			57.6224i			1.94135i	−0.240400	+	0.970674i	$0.577279\pi$
$882$	1.59039	−	3.93327i	0.0535513	−	0.132440i
$883$	17.6993			0.595629			0.297815	−	0.954624i	$-0.403742\pi$
$883$	17.6993			0.595629			0.297815	+	0.954624i	$0.403742\pi$
$884$	1.17918	+	7.23861i	0.0396601	+	0.243461i
$885$	−22.4214	−	13.8780i	−0.753688	−	0.466502i
$886$	−0.801714	−	9.90779i	−0.0269341	−	0.332859i
$887$			34.6834i			1.16455i	0.812991	+	0.582277i	$0.197838\pi$
$887$			34.6834i			1.16455i	−0.812991	+	0.582277i	$0.802162\pi$
$888$	−34.6124	−	33.9453i	−1.16152	−	1.13913i
$889$	13.8959			0.466054
$890$	13.0659	−	7.91025i	0.437970	−	0.265152i
$891$	−15.8621	−	21.2679i	−0.531400	−	0.712500i
$892$	−49.4151	+	8.04980i	−1.65454	+	0.269527i
$893$	−6.44684			−0.215735
$894$	−11.3006	−	15.3809i	−0.377948	−	0.514415i
$895$	22.3644	+	44.7287i	0.747558	+	1.49512i
$896$	9.55427	−	6.05937i	0.319186	−	0.202429i
$897$	−14.4289	+	8.90419i	−0.481766	+	0.297302i
$898$	−3.90738	−	48.2884i	−0.130391	−	1.61140i
$899$	−11.0328			−0.367963
$900$	17.5235	+	24.3501i	0.584117	+	0.811669i
$901$	−37.1065			−1.23620
$902$	−1.98250	−	24.5003i	−0.0660101	−	0.815770i
$903$	3.32750	−	2.05343i	0.110732	−	0.0683339i
$904$	−7.77080	+	1.91998i	−0.258453	+	0.0638576i
$905$	9.27685	+	18.5537i	0.308373	+	0.616746i
$906$	−30.0194	−	40.8585i	−0.997326	−	1.35743i
$907$	−0.948427			−0.0314920			−0.0157460	−	0.999876i	$-0.505012\pi$
$907$	−0.948427			−0.0314920			−0.0157460	+	0.999876i	$0.505012\pi$
$908$	0.584994	+	3.59109i	0.0194137	+	0.119174i
$909$	38.7389	+	19.4344i	1.28489	+	0.644597i
$910$	3.68703	−	2.23217i	0.122224	−	0.0739957i
$911$	−58.1806			−1.92761			−0.963804	−	0.266611i	$-0.914096\pi$
$911$	−58.1806			−1.92761			−0.963804	+	0.266611i	$0.914096\pi$
$912$	18.8583	+	15.7212i	0.624461	+	0.520582i
$913$			17.2078i			0.569494i
$914$	4.07503	+	50.3603i	0.134790	+	1.66577i
$915$	−21.5734	−	13.3531i	−0.713196	−	0.441440i
$916$	23.4114	−	3.81375i	0.773534	−	0.126010i
$917$	16.1534			0.533433
$918$	3.31875	+	19.4903i	0.109535	+	0.643275i
$919$		−	29.6111i		−	0.976778i	−0.872626	−	0.488389i	$-0.837585\pi$
$919$		−	29.6111i		−	0.976778i	0.872626	−	0.488389i	$-0.162415\pi$
$920$	−34.5698	+	29.4665i	−1.13973	+	0.971482i
$921$	−32.4521	+	20.0265i	−1.06933	+	0.659895i
$922$	−3.02057	−	37.3290i	−0.0994771	−	1.22936i
$923$			10.9037i			0.358900i
$924$	−7.71513	+	6.69047i	−0.253809	+	0.220100i
$925$	−39.5837	−	29.6878i	−1.30150	−	0.976127i
$926$	−25.7702	+	2.08526i	−0.846863	+	0.0685260i
$927$	13.5000	−	26.9099i	0.443399	−	0.883838i
$928$	3.02876	+	7.09029i	0.0994241	+	0.232750i
$929$			13.5809i			0.445575i	0.974867	+	0.222787i	$0.0715156\pi$
$929$			13.5809i			0.445575i	−0.974867	+	0.222787i	$0.928484\pi$
$930$	−20.2176	+	39.4583i	−0.662963	+	1.29389i
$931$		−	3.54375i		−	0.116142i
$932$	−10.9673	+	1.78659i	−0.359246	+	0.0585218i
$933$	20.4293	−	12.6071i	0.668827	−	0.412739i
$934$	−1.13750	−	14.0575i	−0.0372200	−	0.459975i
$935$	−7.93138	−	15.8628i	−0.259384	−	0.518768i
$936$	11.2794	+	2.55502i	0.368678	+	0.0835134i
$937$		−	32.0889i		−	1.04830i	−0.851626	−	0.524149i	$-0.824383\pi$
$937$		−	32.0889i		−	1.04830i	0.851626	−	0.524149i	$-0.175617\pi$
$938$	−11.9372	+	0.965926i	−0.389762	+	0.0315386i
$939$	−1.05042	−	1.70216i	−0.0342790	−	0.0555478i
$940$	−6.59718	+	4.76108i	−0.215176	+	0.155289i
$941$		−	34.3805i		−	1.12077i	−0.828231	−	0.560387i	$-0.810653\pi$
$941$		−	34.3805i		−	1.12077i	0.828231	−	0.560387i	$-0.189347\pi$
$942$	11.3006	+	15.3809i	0.368193	+	0.501138i
$943$	−42.3455			−1.37896
$944$	−25.8256	+	8.64345i	−0.840552	+	0.281320i
$945$	9.89592	−	6.08858i	0.321914	−	0.198061i
$946$	−9.38093	+	0.759082i	−0.305000	+	0.0246799i
$947$			4.63404i			0.150586i	0.997161	+	0.0752930i	$0.0239892\pi$
$947$			4.63404i			0.150586i	−0.997161	+	0.0752930i	$0.976011\pi$
$948$	−36.7290	−	42.3542i	−1.19290	−	1.37560i
$949$	10.9037			0.353950
$950$	21.1938	+	13.3691i	0.687618	+	0.433750i
$951$	−10.8793	+	6.71374i	−0.352787	+	0.217708i
$952$	7.38763	−	1.82531i	0.239435	−	0.0591585i
$953$	22.4137			0.726051			0.363025	−	0.931779i	$-0.381744\pi$
$953$	22.4137			0.726051			0.363025	+	0.931779i	$0.381744\pi$
$954$	−21.9345	+	54.2471i	−0.710154	+	1.75631i
$955$	−1.31231	−	2.62463i	−0.0424655	−	0.0849310i
$956$	−52.1410	+	8.49386i	−1.68636	+	0.274711i
$957$	−3.65477	−	5.92240i	−0.118142	−	0.191444i
$958$	−11.3275	+	0.916593i	−0.365975	+	0.0296138i
$959$	−2.55092			−0.0823735
$960$	30.9084	+	2.16074i	0.997565	+	0.0697376i
$961$	−34.5237			−1.11367
$962$	−19.0125	+	1.53844i	−0.612987	+	0.0496014i
$963$	−18.0028	−	9.03155i	−0.580131	−	0.291037i
$964$	51.1235	−	8.32811i	1.64658	−	0.268230i
$965$	−18.6900	+	9.34500i	−0.601652	+	0.300826i
$966$	10.4164	+	14.1775i	0.335142	+	0.456153i
$967$	−9.24370			−0.297257			−0.148629	−	0.988893i	$-0.547486\pi$
$967$	−9.24370			−0.297257			−0.148629	+	0.988893i	$0.547486\pi$
$968$	−6.34165	+	1.56687i	−0.203828	+	0.0503611i
$969$	8.67250	+	14.0534i	0.278601	+	0.451461i
$970$	−10.0170	+	6.06442i	−0.321627	+	0.194717i
$971$	19.2221			0.616867			0.308433	−	0.951246i	$-0.400195\pi$
$971$	19.2221			0.616867			0.308433	+	0.951246i	$0.400195\pi$
$972$	30.4552	+	6.66934i	0.976851	+	0.213919i
$973$			2.35217i			0.0754070i
$974$	33.7384	−	2.73003i	1.08105	−	0.0874758i
$975$	11.7552	+	1.06790i	0.376468	+	0.0342003i
$976$	−24.8489	+	8.31655i	−0.795394	+	0.266206i
$977$	−29.3128			−0.937799			−0.468899	−	0.883252i	$-0.655349\pi$
$977$	−29.3128			−0.937799			−0.468899	+	0.883252i	$0.655349\pi$
$978$	29.2315	−	21.4768i	0.934721	−	0.686753i
$979$			14.2387i			0.455070i
$980$	−2.61711	−	3.62639i	−0.0836005	−	0.115841i
$981$	9.00023	−	17.9404i	0.287355	−	0.572792i
$982$	8.04860	−	0.651273i	0.256841	−	0.0207830i
$983$		−	1.13200i		−	0.0361050i	−0.999837	−	0.0180525i	$-0.994253\pi$
$983$		−	1.13200i		−	0.0361050i	0.999837	−	0.0180525i	$-0.00574661\pi$
$984$	20.6218	+	20.2243i	0.657401	+	0.644728i
$985$	−7.34500	−	14.6900i	−0.234031	−	0.468062i
$986$	0.418266	+	5.16904i	0.0133203	+	0.164616i
$987$	1.65477	+	2.68148i	0.0526718	+	0.0853525i
$988$	9.53434	−	1.55316i	0.303328	−	0.0494126i
$989$			16.2137i			0.515566i
$990$	−27.8787	+	2.21830i	−0.886043	+	0.0705022i
$991$		−	8.90587i		−	0.282904i	−0.989945	−	0.141452i	$-0.954823\pi$
$991$		−	8.90587i		−	0.282904i	0.989945	−	0.141452i	$-0.0451771\pi$
$992$	17.9879	+	42.1093i	0.571116	+	1.33697i
$993$	−7.75637	−	12.5689i	−0.246141	−	0.398862i
$994$	11.2769	−	0.912495i	0.357680	−	0.0289426i
$995$	−11.6744	+	5.83718i	−0.370102	+	0.185051i
$996$	−13.2476	−	15.2765i	−0.419767	−	0.484055i
$997$		−	1.43483i		−	0.0454415i	−0.999742	−	0.0227208i	$-0.992767\pi$
$997$		−	1.43483i		−	0.0454415i	0.999742	−	0.0227208i	$-0.00723286\pi$
$998$	−1.96751	−	24.3150i	−0.0622804	−	0.769677i
$999$	−51.2221	+	4.51499i	−1.62060	+	0.142848i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	420.2.l.e.239.7	yes	8
3.2	odd	2		420.2.l.f.239.2	yes	8
4.3	odd	2		420.2.l.c.239.8	yes	8
5.4	even	2		420.2.l.d.239.2	yes	8
12.11	even	2		420.2.l.d.239.1	yes	8
15.14	odd	2		420.2.l.c.239.7	✓	8
20.19	odd	2		420.2.l.f.239.1	yes	8
60.59	even	2	inner	420.2.l.e.239.8	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
420.2.l.c.239.7	✓	8	15.14	odd	2
420.2.l.c.239.8	yes	8	4.3	odd	2
420.2.l.d.239.1	yes	8	12.11	even	2
420.2.l.d.239.2	yes	8	5.4	even	2
420.2.l.e.239.7	yes	8	1.1	even	1	trivial
420.2.l.e.239.8	yes	8	60.59	even	2	inner
420.2.l.f.239.1	yes	8	20.19	odd	2
420.2.l.f.239.2	yes	8	3.2	odd	2

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:	\( N \)	\(=\)	\( 420 = 2^{2} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	420.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.40961 - 0.114062i) q^{2} +(-1.47398 + 0.909606i) q^{3} +(1.97398 - 0.321565i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-1.97398 + 1.45031i) q^{6} +1.00000 q^{7} +(2.74586 - 0.678435i) q^{8} +(1.34523 - 2.68148i) q^{9} +O(q^{10})\)	\(q+(1.40961 - 0.114062i) q^{2} +(-1.47398 + 0.909606i) q^{3} +(1.97398 - 0.321565i) q^{4} +(-1.00000 - 2.00000i) q^{5} +(-1.97398 + 1.45031i) q^{6} +1.00000 q^{7} +(2.74586 - 0.678435i) q^{8} +(1.34523 - 2.68148i) q^{9} +(-1.63773 - 2.70515i) q^{10} +2.94796 q^{11} +(-2.61711 + 2.26952i) q^{12} +1.36297i q^{13} +(1.40961 - 0.114062i) q^{14} +(3.29319 + 2.03835i) q^{15} +(3.79319 - 1.26952i) q^{16} +2.69047 q^{17} +(1.59039 - 3.93327i) q^{18} -3.54375i q^{19} +(-2.61711 - 3.62639i) q^{20} +(-1.47398 + 0.909606i) q^{21} +(4.15546 - 0.336250i) q^{22} -7.18218i q^{23} +(-3.43023 + 3.49765i) q^{24} +(-3.00000 + 4.00000i) q^{25} +(0.155462 + 1.92124i) q^{26} +(0.456247 + 5.17608i) q^{27} +(1.97398 - 0.321565i) q^{28} +1.36297i q^{29} +(4.87460 + 2.49765i) q^{30} +8.09467i q^{31} +(5.20210 - 2.22219i) q^{32} +(-4.34523 + 2.68148i) q^{33} +(3.79250 - 0.306880i) q^{34} +(-1.00000 - 2.00000i) q^{35} +(1.79319 - 5.72577i) q^{36} +9.89592i q^{37} +(-0.404207 - 4.99530i) q^{38} +(-1.23976 - 2.00898i) q^{39} +(-4.10273 - 4.81328i) q^{40} -5.89592i q^{41} +(-1.97398 + 1.45031i) q^{42} -2.25749 q^{43} +(5.81921 - 0.947960i) q^{44} +(-6.70820 - 0.00898303i) q^{45} +(-0.819213 - 10.1240i) q^{46} -1.81921i q^{47} +(-4.43632 + 5.32156i) q^{48} +1.00000 q^{49} +(-3.77257 + 5.98061i) q^{50} +(-3.96569 + 2.44726i) q^{51} +(0.438281 + 2.69047i) q^{52} -13.7918 q^{53} +(1.23352 + 7.24420i) q^{54} +(-2.94796 - 5.89592i) q^{55} +(2.74586 - 0.678435i) q^{56} +(3.22342 + 5.22342i) q^{57} +(0.155462 + 1.92124i) q^{58} -6.80841 q^{59} +(7.15616 + 2.96469i) q^{60} -6.55092 q^{61} +(0.923293 + 11.4103i) q^{62} +(1.34523 - 2.68148i) q^{63} +(7.07945 - 3.72577i) q^{64} +(2.72593 - 1.36297i) q^{65} +(-5.81921 + 4.27546i) q^{66} -8.46844 q^{67} +(5.31092 - 0.865159i) q^{68} +(6.53295 + 10.5864i) q^{69} +(-1.63773 - 2.70515i) q^{70} +8.00000 q^{71} +(1.87460 - 8.27562i) q^{72} -8.00000i q^{73} +(1.12875 + 13.9493i) q^{74} +(0.783514 - 8.62474i) q^{75} +(-1.13955 - 6.99530i) q^{76} +2.94796 q^{77} +(-1.97672 - 2.69047i) q^{78} +16.1836i q^{79} +(-6.33224 - 6.31686i) q^{80} +(-5.38070 - 7.21444i) q^{81} +(-0.672500 - 8.31092i) q^{82} +5.83718i q^{83} +(-2.61711 + 2.26952i) q^{84} +(-2.69047 - 5.38093i) q^{85} +(-3.18218 + 0.257494i) q^{86} +(-1.23976 - 2.00898i) q^{87} +(8.09467 - 2.00000i) q^{88} +4.83001i q^{89} +(-9.45694 + 0.752487i) q^{90} +1.36297i q^{91} +(-2.30953 - 14.1775i) q^{92} +(-7.36297 - 11.9314i) q^{93} +(-0.207503 - 2.56437i) q^{94} +(-7.08751 + 3.54375i) q^{95} +(-5.64648 + 8.00733i) q^{96} -3.70294i q^{97} +(1.40961 - 0.114062i) q^{98} +(3.96569 - 7.90490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 2 * q^4 - 8 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9	\( 8 q + 2 q^{3} + 2 q^{4} - 8 q^{5} - 2 q^{6} + 8 q^{7} + 6 q^{8} + 2 q^{9} - 4 q^{10} - 4 q^{11} - 10 q^{12} - 10 q^{15} - 6 q^{16} + 4 q^{17} + 24 q^{18} - 10 q^{20} + 2 q^{21} + 6 q^{22} - 18 q^{24} - 24 q^{25} - 26 q^{26} + 8 q^{27} + 2 q^{28} + 18 q^{30} + 30 q^{32} - 26 q^{33} + 30 q^{34} - 8 q^{35} - 22 q^{36} + 20 q^{38} - 18 q^{39} - 14 q^{40} - 2 q^{42} - 8 q^{43} + 24 q^{44} - 18 q^{45} + 16 q^{46} - 2 q^{48} + 8 q^{49} + 8 q^{50} + 14 q^{51} + 16 q^{52} + 24 q^{54} + 4 q^{55} + 6 q^{56} - 20 q^{57} - 26 q^{58} - 8 q^{59} - 6 q^{60} - 16 q^{61} + 40 q^{62} + 2 q^{63} + 26 q^{64} - 32 q^{65} - 24 q^{66} - 24 q^{67} - 12 q^{68} + 24 q^{69} - 4 q^{70} + 64 q^{71} - 6 q^{72} + 4 q^{74} + 10 q^{75} - 28 q^{76} - 4 q^{77} - 4 q^{78} + 38 q^{80} + 2 q^{81} + 4 q^{82} - 10 q^{84} - 4 q^{85} + 24 q^{86} - 18 q^{87} + 24 q^{88} - 44 q^{90} - 36 q^{92} - 32 q^{93} - 2 q^{94} - 48 q^{95} - 22 q^{96} - 14 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^4 - 8 * q^5 - 2 * q^6 + 8 * q^7 + 6 * q^8 + 2 * q^9 - 4 * q^10 - 4 * q^11 - 10 * q^12 - 10 * q^15 - 6 * q^16 + 4 * q^17 + 24 * q^18 - 10 * q^20 + 2 * q^21 + 6 * q^22 - 18 * q^24 - 24 * q^25 - 26 * q^26 + 8 * q^27 + 2 * q^28 + 18 * q^30 + 30 * q^32 - 26 * q^33 + 30 * q^34 - 8 * q^35 - 22 * q^36 + 20 * q^38 - 18 * q^39 - 14 * q^40 - 2 * q^42 - 8 * q^43 + 24 * q^44 - 18 * q^45 + 16 * q^46 - 2 * q^48 + 8 * q^49 + 8 * q^50 + 14 * q^51 + 16 * q^52 + 24 * q^54 + 4 * q^55 + 6 * q^56 - 20 * q^57 - 26 * q^58 - 8 * q^59 - 6 * q^60 - 16 * q^61 + 40 * q^62 + 2 * q^63 + 26 * q^64 - 32 * q^65 - 24 * q^66 - 24 * q^67 - 12 * q^68 + 24 * q^69 - 4 * q^70 + 64 * q^71 - 6 * q^72 + 4 * q^74 + 10 * q^75 - 28 * q^76 - 4 * q^77 - 4 * q^78 + 38 * q^80 + 2 * q^81 + 4 * q^82 - 10 * q^84 - 4 * q^85 + 24 * q^86 - 18 * q^87 + 24 * q^88 - 44 * q^90 - 36 * q^92 - 32 * q^93 - 2 * q^94 - 48 * q^95 - 22 * q^96 - 14 * q^99

Introduction

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