LMFDB - Embedded newform 420.2.l.f.239.2

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			239.2
Root			$1.40961 + 0.114062i$ of defining polynomial
Character	$\chi$	$=$	420.239
Dual form			420.2.l.f.239.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40961 + 0.114062i) q^{2} +(-1.47398 - 0.909606i) q^{3} +(1.97398 - 0.321565i) q^{4} +(1.00000 + 2.00000i) q^{5} +(2.18148 + 1.11406i) q^{6} +1.00000 q^{7} +(-2.74586 + 0.678435i) q^{8} +(1.34523 + 2.68148i) q^{9} +O(q^{10})$	\(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} +(2.18148 + 1.11406i) 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} +(-3.20210 - 1.32156i) q^{12} +1.36297i q^{13} +(-1.40961 + 0.114062i) q^{14} +(0.345233 - 3.85757i) q^{15} +(3.79319 - 1.26952i) q^{16} -2.69047 q^{17} +(-2.20210 - 3.62639i) 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} +(4.66445 + 1.49765i) 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} +(-0.0466412 + 5.47703i) 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} +(3.51773 + 4.86061i) 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} +(2.18148 + 1.11406i) q^{42} -2.25749 q^{43} +(-5.81921 + 0.947960i) q^{44} +(-4.01773 + 5.37195i) q^{45} +(-0.819213 - 10.1240i) q^{46} +1.81921i q^{47} +(-6.74586 - 1.57906i) 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} +(-0.0527356 + 7.34828i) 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} +(-0.558974 - 7.72577i) 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} +(-6.43092 - 3.28421i) 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} +(-5.51303 - 6.45031i) q^{72} -8.00000i q^{73} +(-1.12875 - 13.9493i) q^{74} +(8.06036 - 3.16710i) q^{75} +(-1.13955 - 6.99530i) q^{76} -2.94796 q^{77} +(-1.51843 + 2.97328i) 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} +(-3.20210 - 1.32156i) 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} +(5.05069 - 8.03060i) 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} +(9.68911 + 1.45641i) 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} + 4 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 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9	$ 8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{12} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 6 q^{18} + 10 q^{20} + 2 q^{21} + 6 q^{22} + 6 q^{24} - 24 q^{25} + 26 q^{26} + 8 q^{27} + 2 q^{28} - 16 q^{30} - 30 q^{32} + 26 q^{33} + 30 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{38} + 18 q^{39} - 14 q^{40} + 4 q^{42} - 8 q^{43} - 24 q^{44} - 14 q^{45} + 16 q^{46} - 38 q^{48} + 8 q^{49} - 8 q^{50} - 14 q^{51} + 16 q^{52} + 8 q^{54} + 4 q^{55} - 6 q^{56} + 20 q^{57} - 26 q^{58} + 8 q^{59} + 10 q^{60} - 16 q^{61} - 40 q^{62} + 2 q^{63} + 26 q^{64} + 32 q^{65} - 6 q^{66} - 24 q^{67} + 12 q^{68} + 24 q^{69} - 4 q^{70} - 64 q^{71} + 22 q^{72} - 4 q^{74} - 22 q^{75} - 28 q^{76} + 4 q^{77} + 42 q^{78} - 38 q^{80} + 2 q^{81} + 4 q^{82} - 14 q^{84} - 4 q^{85} - 24 q^{86} - 18 q^{87} + 24 q^{88} - 6 q^{90} + 36 q^{92} + 32 q^{93} - 2 q^{94} + 48 q^{95} - 14 q^{96} + 14 q^{99}+O(q^{100}) $ 8 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^11 - 14 * q^12 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 6 * q^18 + 10 * q^20 + 2 * q^21 + 6 * q^22 + 6 * q^24 - 24 * q^25 + 26 * q^26 + 8 * q^27 + 2 * q^28 - 16 * q^30 - 30 * q^32 + 26 * q^33 + 30 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^38 + 18 * q^39 - 14 * q^40 + 4 * q^42 - 8 * q^43 - 24 * q^44 - 14 * q^45 + 16 * q^46 - 38 * q^48 + 8 * q^49 - 8 * q^50 - 14 * q^51 + 16 * q^52 + 8 * q^54 + 4 * q^55 - 6 * q^56 + 20 * q^57 - 26 * q^58 + 8 * q^59 + 10 * q^60 - 16 * q^61 - 40 * q^62 + 2 * q^63 + 26 * q^64 + 32 * q^65 - 6 * q^66 - 24 * q^67 + 12 * q^68 + 24 * q^69 - 4 * q^70 - 64 * q^71 + 22 * q^72 - 4 * q^74 - 22 * q^75 - 28 * q^76 + 4 * q^77 + 42 * q^78 - 38 * q^80 + 2 * q^81 + 4 * q^82 - 14 * q^84 - 4 * q^85 - 24 * q^86 - 18 * q^87 + 24 * q^88 - 6 * q^90 + 36 * q^92 + 32 * q^93 - 2 * q^94 + 48 * q^95 - 14 * 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
$6$	2.18148	+	1.11406i	0.890587	+	0.454814i
$7$	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	$-0.646591\pi$
$11$	−2.94796			−0.888843			−0.444422	+	0.895818i	$0.646591\pi$
$12$	−3.20210	−	1.32156i	−0.924368	−	0.381503i
$13$			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
$15$	0.345233	−	3.85757i	0.0891387	−	0.996019i
$16$	3.79319	−	1.26952i	0.948298	−	0.317381i
$17$	−2.69047			−0.652534			−0.326267	−	0.945278i	$-0.605791\pi$
$17$	−2.69047			−0.652534			−0.326267	+	0.945278i	$0.605791\pi$
$18$	−2.20210	−	3.62639i	−0.519041	−	0.854749i
$19$		−	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	$0.269367\pi$
$23$			7.18218i			1.49759i	−0.662803	+	0.748794i	$0.730633\pi$
$24$	4.66445	+	1.49765i	0.952126	+	0.305706i
$25$	−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	$-0.959610\pi$
$29$		−	1.36297i		−	0.253096i	0.991960	−	0.126548i	$-0.0403898\pi$
$30$	−0.0466412	+	5.47703i	−0.00851547	+	0.999964i
$31$			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
$36$	3.51773	+	4.86061i	0.586289	+	0.810102i
$37$			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	$0.152292\pi$
$41$			5.89592i			0.920788i	−0.887715	+	0.460394i	$0.847708\pi$
$42$	2.18148	+	1.11406i	0.336610	+	0.171903i
$43$	−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
$45$	−4.01773	+	5.37195i	−0.598928	+	0.800803i
$46$	−0.819213	−	10.1240i	−0.120786	−	1.49271i
$47$			1.81921i			0.265359i	0.991159	+	0.132680i	$0.0423582\pi$
$47$			1.81921i			0.265359i	−0.991159	+	0.132680i	$0.957642\pi$
$48$	−6.74586	−	1.57906i	−0.973680	−	0.227917i
$49$	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	$-0.103872\pi$
$53$	13.7918			1.89445			0.947227	+	0.320563i	$0.103872\pi$
$54$	−0.0527356	+	7.34828i	−0.00717640	+	0.999974i
$55$	−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	$-0.353847\pi$
$59$	6.80841			0.886380			0.443190	+	0.896428i	$0.353847\pi$
$60$	−0.558974	−	7.72577i	−0.0721633	−	0.997393i
$61$	−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
$66$	−6.43092	−	3.28421i	−0.791592	−	0.404258i
$67$	−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	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$	−5.51303	−	6.45031i	−0.649717	−	0.760177i
$73$		−	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
$75$	8.06036	−	3.16710i	0.930731	−	0.365705i
$76$	−1.13955	−	6.99530i	−0.130715	−	0.802415i
$77$	−2.94796			−0.335951
$78$	−1.51843	+	2.97328i	−0.171928	+	0.336658i
$79$			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	$-0.896197\pi$
$83$		−	5.83718i		−	0.640714i	0.947297	−	0.320357i	$-0.103803\pi$
$84$	−3.20210	−	1.32156i	−0.349378	−	0.144195i
$85$	−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	$-0.917599\pi$
$89$		−	4.83001i		−	0.511980i	0.966679	−	0.255990i	$-0.0824014\pi$
$90$	5.05069	−	8.03060i	0.532389	−	0.846500i
$91$			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
$96$	9.68911	+	1.45641i	0.988891	+	0.148644i
$97$		−	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	$-0.744711\pi$
$101$		−	14.4468i		−	1.43751i	0.695261	−	0.718757i	$-0.255289\pi$
$102$	−5.86920	−	2.99735i	−0.581138	−	0.296781i
$103$	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
$105$	0.345233	−	3.85757i	0.0336913	−	0.376460i
$106$	−19.4411	+	1.57312i	−1.88828	+	0.152795i
$107$			6.71374i			0.649042i	0.945879	+	0.324521i	$0.105203\pi$
$107$			6.71374i			0.649042i	−0.945879	+	0.324521i	$0.894797\pi$
$108$	−0.763822	−	10.3642i	−0.0734988	−	0.997295i
$109$	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	$-0.457503\pi$
$113$	2.83001			0.266225			0.133113	+	0.991101i	$0.457503\pi$
$114$	3.94796	−	7.73063i	0.369760	−	0.724040i
$115$	−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
$120$	1.66915	+	10.8265i	0.152372	+	0.988323i
$121$	−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
$126$	−2.20210	−	3.62639i	−0.196179	−	0.323065i
$127$	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	$-0.749352\pi$
$131$	−16.1534			−1.41133			−0.705665	+	0.708546i	$0.749352\pi$
$132$	9.43967	+	3.89592i	0.821618	+	0.339096i
$133$		−	3.54375i		−	0.307282i
$134$	11.9372	−	0.965926i	1.03121	−	0.0834433i
$135$	10.8084	−	4.26359i	0.930240	−	0.366951i
$136$	7.38763	−	1.82531i	0.633484	−	0.156519i
$137$	2.55092			0.217940			0.108970	−	0.994045i	$-0.465245\pi$
$137$	2.55092			0.217940			0.108970	+	0.994045i	$0.465245\pi$
$138$	−8.00139	+	15.6678i	−0.681124	+	1.33373i
$139$			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
$144$	8.50693	+	8.46357i	0.708911	+	0.705298i
$145$	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	$-0.896597\pi$
$149$		−	7.79184i		−	0.638332i	0.947699	−	0.319166i	$-0.103403\pi$
$150$	−11.0007	+	5.38374i	−0.898203	+	0.439581i
$151$			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
$156$	1.80125	−	4.36436i	0.144215	−	0.349428i
$157$		−	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
$162$	6.76177	−	10.7832i	0.531255	−	0.847212i
$163$	−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
$165$	−1.01773	+	11.3719i	−0.0792304	+	0.885305i
$166$	0.665799	+	8.22812i	0.0516761	+	0.638626i
$167$		−	13.4217i		−	1.03860i	−0.854591	−	0.519301i	$-0.826192\pi$
$167$		−	13.4217i		−	1.03860i	0.854591	−	0.519301i	$-0.173808\pi$
$168$	4.66445	+	1.49765i	0.359870	+	0.115546i
$169$	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	$-0.484148\pi$
$173$	1.30953			0.0995621			0.0497810	+	0.998760i	$0.484148\pi$
$174$	1.51843	−	2.97328i	0.115112	−	0.225404i
$175$	−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	$-0.185007\pi$
$179$	22.3644			1.67159			0.835795	+	0.549041i	$0.185007\pi$
$180$	−6.20349	+	11.8961i	−0.462381	+	0.886681i
$181$	−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
$186$	−9.01797	+	17.6584i	−0.661229	+	1.29478i
$187$	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	$-0.515118\pi$
$191$	−1.31231			−0.0949558			−0.0474779	+	0.998872i	$0.515118\pi$
$192$	−13.8240	−	0.947801i	−0.997658	−	0.0684016i
$193$		−	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
$195$	5.25773	+	0.470540i	0.376514	+	0.0336961i
$196$	1.97398	−	0.321565i	0.140999	−	0.0229689i
$197$	−7.34500			−0.523310			−0.261655	−	0.965162i	$-0.584268\pi$
$197$	−7.34500			−0.523310			−0.261655	+	0.965162i	$0.584268\pi$
$198$	6.49171	+	10.6905i	0.461346	+	0.759738i
$199$		−	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
$204$	8.61515	+	3.55562i	0.603181	+	0.248943i
$205$	−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
$210$	−0.0466412	+	5.47703i	−0.00321855	+	0.377951i
$211$		−	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
$216$	2.25885	+	14.5223i	0.153695	+	0.988118i
$217$			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
$222$	−11.0247	+	21.5878i	−0.739927	+	1.44888i
$223$	−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
$225$	−14.7616	−	2.66352i	−0.984109	−	0.177568i
$226$	−3.98920	+	0.322796i	−0.265358	+	0.0214721i
$227$		−	1.81921i		−	0.120745i	−0.998176	−	0.0603727i	$-0.980771\pi$
$227$		−	1.81921i		−	0.120745i	0.998176	−	0.0603727i	$-0.0192289\pi$
$228$	−4.68330	+	11.3475i	−0.310159	+	0.751504i
$229$	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	$-0.441746\pi$
$233$	5.55594			0.363982			0.181991	+	0.983300i	$0.441746\pi$
$234$	4.94265	−	3.00139i	0.323111	−	0.196207i
$235$	−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	$-0.173989\pi$
$239$	26.4142			1.70859			0.854295	+	0.519789i	$0.173989\pi$
$240$	−3.58774	−	15.0708i	−0.231588	−	0.972814i
$241$	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
$246$	−6.56842	+	12.8618i	−0.418787	+	0.820041i
$247$	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	$-0.431067\pi$
$251$	6.80841			0.429743			0.214872	+	0.976642i	$0.431067\pi$
$252$	3.51773	+	4.86061i	0.221596	+	0.306190i
$253$		−	21.1728i		−	1.33112i
$254$	−19.5878	+	1.58499i	−1.22905	+	0.0994514i
$255$	−0.928837	+	10.3786i	−0.0581660	+	0.649936i
$256$	12.7766	−	9.63110i	0.798539	−	0.601944i
$257$	−0.339978			−0.0212072			−0.0106036	−	0.999944i	$-0.503375\pi$
$257$	−0.339978			−0.0212072			−0.0106036	+	0.999944i	$0.503375\pi$
$258$	−4.92468	−	2.51499i	−0.306597	−	0.156576i
$259$			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	$0.0572409\pi$
$263$			5.80125i			0.357720i	−0.983875	+	0.178860i	$0.942759\pi$
$264$	−13.7506	−	4.41501i	−0.846291	−	0.271725i
$265$	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	$0.130407\pi$
$269$			13.0659i			0.796642i	−0.917246	+	0.398321i	$0.869593\pi$
$270$	−14.7493	+	7.24281i	−0.897614	+	0.440783i
$271$		−	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
$276$	9.49171	−	22.9981i	0.571334	−	1.38432i
$277$		−	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	$0.170978\pi$
$281$			17.1548i			1.02337i	−0.859173	+	0.511685i	$0.829022\pi$
$282$	−2.02672	+	3.96858i	−0.120689	+	0.236326i
$283$	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
$285$	−13.6703	−	1.22342i	−0.809756	−	0.0724691i
$286$	0.458297	+	5.66375i	0.0270997	+	0.334905i
$287$			5.89592i			0.348025i
$288$	−12.9568	−	10.9600i	−0.763487	−	0.645824i
$289$	−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	$-0.343705\pi$
$293$	16.1423			0.943045			0.471522	+	0.881854i	$0.343705\pi$
$294$	2.18148	+	1.11406i	0.127227	+	0.0649734i
$295$	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
$300$	14.8926	−	8.84372i	0.859823	−	0.510592i
$301$	−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
$306$	5.92468	+	9.75669i	0.338692	+	0.557753i
$307$	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	$-0.371450\pi$
$311$	13.8600			0.785928			0.392964	+	0.919554i	$0.371450\pi$
$312$	−2.04124	+	6.35748i	−0.115563	+	0.359921i
$313$			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
$315$	−4.01773	+	5.37195i	−0.226374	+	0.302675i
$316$	5.20406	+	31.9460i	0.292751	+	1.79710i
$317$	−7.38093			−0.414554			−0.207277	−	0.978282i	$-0.566460\pi$
$317$	−7.38093			−0.414554			−0.207277	+	0.978282i	$0.566460\pi$
$318$	30.0867	+	15.3650i	1.68718	+	0.861624i
$319$			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
$324$	−8.30148	+	15.9714i	−0.461193	+	0.887300i
$325$	−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
$330$	0.137496	−	16.1461i	0.00756892	−	0.888811i
$331$			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
$336$	−6.74586	−	1.57906i	−0.368017	−	0.0861447i
$337$			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
$342$	−12.8510	+	7.80371i	−0.694905	+	0.421976i
$343$	1.00000			0.0539949
$344$	6.19875	−	1.53156i	0.334214	−	0.0825764i
$345$	27.7057	+	2.47952i	1.49163	+	0.133493i
$346$	−1.84593	+	0.149368i	−0.0992377	+	0.00803007i
$347$			5.96286i			0.320103i	0.987109	+	0.160051i	$0.0511660\pi$
$347$			5.96286i			0.320103i	−0.987109	+	0.160051i	$0.948834\pi$
$348$	−1.80125	+	4.36436i	−0.0965569	+	0.233954i
$349$	−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	$-0.457259\pi$
$353$	5.03044			0.267743			0.133872	+	0.990999i	$0.457259\pi$
$354$	14.8524	+	7.58499i	0.789398	+	0.403138i
$355$	−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	$-0.384487\pi$
$359$	13.4519			0.709962			0.354981	+	0.934874i	$0.384487\pi$
$360$	7.38760	−	17.4764i	0.389360	−	0.921085i
$361$	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
$366$	−14.2907	−	7.29813i	−0.746988	−	0.381479i
$367$	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
$372$	10.6976	−	25.9200i	0.554646	−	1.34389i
$373$		−	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
$375$	14.3946	+	12.9536i	0.743332	+	0.668923i
$376$	−1.23422	−	4.99530i	−0.0636499	−	0.257613i
$377$	1.85767			0.0956751
$378$	−0.0527356	+	7.34828i	−0.00271243	+	0.377955i
$379$		−	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	$-0.708279\pi$
$383$		−	31.0565i		−	1.58691i	0.608627	−	0.793457i	$-0.291721\pi$
$384$	19.5944	−	0.240760i	0.999925	−	0.0122862i
$385$	−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	$-0.809525\pi$
$389$		−	22.2207i		−	1.12663i	0.826241	−	0.563317i	$-0.190475\pi$
$390$	−7.46500	−	0.0635703i	−0.378005	−	0.00321901i
$391$		−	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
$396$	−10.3701	−	14.3289i	−0.521119	−	0.720054i
$397$			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	$-0.858784\pi$
$401$		−	17.1907i		−	0.858464i	0.903194	−	0.429232i	$-0.141216\pi$
$402$	−18.4737	−	9.43436i	−0.921387	−	0.470543i
$403$	−11.0328			−0.549581
$404$	−4.64559	−	28.5178i	−0.231127	−	1.41881i
$405$	−19.8096	−	3.54696i	−0.984345	−	0.176250i
$406$	0.155462	+	1.92124i	0.00771547	+	0.0953497i
$407$		−	29.1728i		−	1.44604i
$408$	−12.5495	−	4.02937i	−0.621294	−	0.199484i
$409$	−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
$414$	26.0454	−	15.8159i	1.28006	−	0.777309i
$415$	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	$-0.586725\pi$
$419$	−11.0166			−0.538195			−0.269097	+	0.963113i	$0.586725\pi$
$420$	−0.558974	−	7.72577i	−0.0272751	−	0.376979i
$421$	−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
$426$	−17.4519	−	8.91249i	−0.845545	−	0.431812i
$427$	−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	$-0.732717\pi$
$431$	−27.7232			−1.33538			−0.667690	+	0.744439i	$0.732717\pi$
$432$	−4.84053	−	20.2131i	−0.232890	−	0.972503i
$433$			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
$435$	−5.25773	−	0.470540i	−0.252089	−	0.0225607i
$436$	13.2068	−	2.15142i	0.632493	−	0.103034i
$437$	25.4519			1.21753
$438$	8.91249	−	17.4519i	0.425855	−	0.833882i
$439$		−	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	$0.0533994\pi$
$443$			7.02876i			0.333947i	−0.985961	+	0.166973i	$0.946601\pi$
$444$	13.0781	−	31.6878i	0.620659	−	1.50383i
$445$	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	$0.299631\pi$
$449$			34.2566i			1.61667i	−0.588722	+	0.808335i	$0.700369\pi$
$450$	21.1119	+	2.07077i	0.995224	+	0.0976171i
$451$		−	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
$456$	5.30729	−	16.5296i	0.248537	−	0.774071i
$457$			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	$0.211527\pi$
$461$			26.4818i			1.23338i	−0.787205	+	0.616691i	$0.788473\pi$
$462$	−6.43092	−	3.28421i	−0.299194	−	0.152795i
$463$	−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
$465$	31.2257	+	2.79455i	1.44806	+	0.129594i
$466$	−7.83169	+	0.633721i	−0.362796	+	0.0293566i
$467$			9.97263i			0.461478i	0.973016	+	0.230739i	$0.0741144\pi$
$467$			9.97263i			0.461478i	−0.973016	+	0.230739i	$0.925886\pi$
$468$	−6.62485	+	4.79455i	−0.306234	+	0.221628i
$469$	−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
$474$	−18.0295	+	35.3042i	−0.828122	+	1.62157i
$475$	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	$-0.441230\pi$
$479$	8.03593			0.367171			0.183586	+	0.983004i	$0.441230\pi$
$480$	6.77630	+	20.8346i	0.309294	+	0.950966i
$481$	−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
$486$	−19.7752	+	9.74374i	−0.897022	+	0.441985i
$487$	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	$-0.541125\pi$
$491$	−5.70982			−0.257681			−0.128840	+	0.991665i	$0.541125\pi$
$492$	7.79184	−	18.8793i	0.351283	−	0.851147i
$493$			3.66701i			0.165154i
$494$	−6.80841	+	0.550920i	−0.306325	+	0.0247871i
$495$	11.8441	−	15.8363i	0.532353	−	0.711788i
$496$	10.2764	+	30.7047i	0.461423	+	1.37868i
$497$	−8.00000			−0.358849
$498$	6.50298	−	12.7337i	0.291405	−	0.570611i
$499$		−	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	$0.392891\pi$
$503$			42.3398i			1.88784i	−0.330179	+	0.943918i	$0.607109\pi$
$504$	−5.51303	−	6.45031i	−0.245570	−	0.287320i
$505$	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	$0.00898902\pi$
$509$			1.27407i			0.0564721i	−0.999601	+	0.0282361i	$0.991011\pi$
$510$	0.125486	−	14.7358i	0.00555663	−	0.652510i
$511$		−	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
$516$	7.22873	+	2.98342i	0.318227	+	0.131338i
$517$		−	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	$0.213848\pi$
$521$			28.4137i			1.24483i	−0.782689	+	0.622413i	$0.786152\pi$
$522$	−4.94265	+	3.00139i	−0.216334	+	0.131367i
$523$	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
$525$	8.06036	−	3.16710i	0.351783	−	0.138224i
$526$	−0.661701	−	8.17747i	−0.0288515	−	0.356555i
$527$		−	21.7784i		−	0.948684i
$528$	19.8865	+	4.65500i	0.865449	+	0.202583i
$529$	−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
$534$	5.38093	−	10.5366i	0.232856	−	0.455963i
$535$	−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
$540$	19.9646	−	11.8918i	0.859138	−	0.511743i
$541$	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
$546$	−1.51843	+	2.97328i	−0.0649827	+	0.127245i
$547$	−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
$552$	−10.7564	+	33.5009i	−0.457822	+	1.42589i
$553$			16.1836i			0.688195i
$554$	2.32033	+	28.6753i	0.0985815	+	1.21830i
$555$	38.1742	+	3.41640i	1.62040	+	0.145018i
$556$	0.756374	+	4.64313i	0.0320774	+	0.196913i
$557$	−21.9346			−0.929400			−0.464700	−	0.885468i	$-0.653838\pi$
$557$	−21.9346			−0.929400			−0.464700	+	0.885468i	$0.653838\pi$
$558$	29.3545	−	17.8253i	1.24267	−	0.754605i
$559$		−	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	$-0.904823\pi$
$563$		−	13.9790i		−	0.589146i	0.955629	−	0.294573i	$-0.0951774\pi$
$564$	2.40421	−	5.82531i	0.101235	−	0.245290i
$565$	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	$0.125641\pi$
$569$			18.3455i			0.769085i	−0.923107	+	0.384542i	$0.874359\pi$
$570$	19.4092	+	0.165285i	0.812963	+	0.00692302i
$571$			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
$576$	19.5141	+	13.9714i	0.813088	+	0.582141i
$577$		−	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
$582$	4.12531	−	8.07791i	0.170999	−	0.334840i
$583$	−40.6578			−1.68387
$584$	5.42748	+	21.9668i	0.224591	+	0.908995i
$585$	−7.32178	−	5.47603i	−0.302718	−	0.226406i
$586$	−22.7543	+	1.84122i	−0.939972	+	0.0760603i
$587$			36.2015i			1.49420i	0.664713	+	0.747099i	$0.268554\pi$
$587$			36.2015i			1.49420i	−0.664713	+	0.747099i	$0.731446\pi$
$588$	−3.20210	−	1.32156i	−0.132053	−	0.0545004i
$589$	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	$-0.590978\pi$
$593$	−13.7314			−0.563882			−0.281941	+	0.959432i	$0.590978\pi$
$594$	0.155462	−	21.6624i	0.00637870	−	0.888820i
$595$	−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	$-0.288540\pi$
$599$	30.1783			1.23305			0.616525	+	0.787335i	$0.288540\pi$
$600$	−19.9839	+	14.1648i	−0.815840	+	0.578277i
$601$	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
$606$	16.0947	−	31.5155i	0.653801	−	1.28023i
$607$	−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
$612$	−9.46434	−	13.0773i	−0.382573	−	0.528619i
$613$			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
$615$	22.7439	+	2.03546i	0.917122	+	0.0820779i
$616$	8.09467	−	2.00000i	0.326144	−	0.0805823i
$617$	−33.2769			−1.33968			−0.669838	−	0.742507i	$-0.733636\pi$
$617$	−33.2769			−1.33968			−0.669838	+	0.742507i	$0.733636\pi$
$618$	21.8922	+	11.1801i	0.880633	+	0.449731i
$619$			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
$624$	2.15220	−	9.19437i	0.0861570	−	0.368069i
$625$	−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
$630$	5.05069	−	8.03060i	0.201224	−	0.319947i
$631$		−	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
$636$	−44.1629	−	18.2268i	−1.75117	−	0.722740i
$637$			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	$-0.723138\pi$
$641$		−	38.6956i		−	1.52838i	0.644990	−	0.764191i	$-0.276862\pi$
$642$	−7.47952	+	14.6459i	−0.295193	+	0.578028i
$643$	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
$645$	−0.779361	+	8.70843i	−0.0306873	+	0.342894i
$646$	−1.08751	−	13.4397i	−0.0427873	−	0.528777i
$647$			28.4840i			1.11982i	0.828553	+	0.559910i	$0.189164\pi$
$647$			28.4840i			1.11982i	−0.828553	+	0.559910i	$0.810836\pi$
$648$	9.88009	−	23.4603i	0.388127	−	0.921606i
$649$	−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	$-0.526838\pi$
$653$	−4.30405			−0.168430			−0.0842152	+	0.996448i	$0.526838\pi$
$654$	14.5951	+	7.45359i	0.570715	+	0.291459i
$655$	−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	$-0.572123\pi$
$659$	−11.5339			−0.449296			−0.224648	+	0.974440i	$0.572123\pi$
$660$	1.64783	+	22.7753i	0.0641418	+	0.886526i
$661$	−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
$666$	35.8865	−	21.7918i	1.39057	−	0.844417i
$667$	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
$672$	9.68911	+	1.45641i	0.373766	+	0.0561821i
$673$		−	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
$675$	19.3356	+	17.3532i	0.744227	+	0.667927i
$676$	21.9947	−	3.58298i	0.845951	−	0.137807i
$677$	18.2741			0.702332			0.351166	−	0.936313i	$-0.385785\pi$
$677$	18.2741			0.702332			0.351166	+	0.936313i	$0.385785\pi$
$678$	6.17362	+	3.15281i	0.237096	+	0.121083i
$679$		−	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	$-0.875839\pi$
$683$		−	19.8750i		−	0.760494i	0.924885	−	0.380247i	$-0.124161\pi$
$684$	17.2248	−	12.4660i	0.658607	−	0.476648i
$685$	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
$690$	−39.3370	−	0.334985i	−1.49753	−	0.0127527i
$691$			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
$696$	2.04124	−	6.35748i	0.0773731	−	0.240980i
$697$		−	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	$-0.949700\pi$
$701$		−	8.33299i		−	0.314733i	0.987540	−	0.157366i	$-0.0503003\pi$
$702$	−10.0154	−	0.0718767i	−0.378009	−	0.00271281i
$703$	35.0687			1.32264
$704$	−20.8699	+	10.9834i	−0.786565	+	0.413953i
$705$	7.01773	+	0.628052i	0.264303	+	0.0236538i
$706$	−7.09094	+	0.573782i	−0.266871	+	0.0215946i
$707$		−	14.4468i		−	0.543329i
$708$	−21.8012	−	8.99776i	−0.819341	−	0.338157i
$709$	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
$714$	−5.86920	−	2.99735i	−0.219649	−	0.112173i
$715$	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	$-0.295161\pi$
$719$	32.1778			1.20003			0.600015	+	0.799989i	$0.295161\pi$
$720$	−8.42021	+	25.4774i	−0.313803	+	0.949488i
$721$	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
$726$	−5.03821	−	2.57296i	−0.186985	−	0.0954917i
$727$	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
$732$	20.9767	+	8.65746i	0.775322	+	0.319989i
$733$			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
$735$	0.345233	−	3.85757i	0.0127341	−	0.142288i
$736$	−15.9601	−	37.3624i	−0.588299	−	1.37720i
$737$	24.9646			0.919583
$738$	21.3809	−	12.9834i	0.787043	−	0.477926i
$739$		−	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	$-0.861001\pi$
$743$		−	23.0565i		−	0.845861i	0.906162	−	0.422930i	$-0.138999\pi$
$744$	−12.1230	+	37.7572i	−0.444450	+	1.38424i
$745$	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
$750$	−21.7682	−	16.6176i	−0.794862	−	0.606791i
$751$			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
$756$	−0.763822	−	10.3642i	−0.0277799	−	0.376942i
$757$		−	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	$0.0659401\pi$
$761$			11.3478i			0.411357i	−0.978620	+	0.205678i	$0.934060\pi$
$762$	30.3137	+	15.4809i	1.09815	+	0.560814i
$763$	6.69047			0.242211
$764$	−2.59048	+	0.421994i	−0.0937204	+	0.0152672i
$765$	10.8096	−	14.4530i	0.390821	−	0.522551i
$766$	3.54236	+	43.7774i	0.127991	+	1.58174i
$767$			9.27963i			0.335068i
$768$	−27.5930	+	2.57435i	−0.995676	+	0.0928940i
$769$	−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	$-0.687083\pi$
$773$	−30.8323			−1.10896			−0.554481	+	0.832197i	$0.687083\pi$
$774$	4.97124	+	8.18656i	0.178687	+	0.294260i
$775$	−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
$780$	10.5300	−	0.761862i	0.377033	−	0.0272790i
$781$	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
$786$	−35.2384	−	17.9959i	−1.25691	−	0.641893i
$787$	−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
$792$	16.2522	+	19.0153i	0.577496	+	0.675678i
$793$		−	8.92868i		−	0.317067i
$794$	−3.64047	−	44.9899i	−0.129196	−	1.59663i
$795$	4.76139	−	53.2029i	0.168869	−	1.88691i
$796$	−1.87703	−	11.5225i	−0.0665296	−	0.408403i
$797$	1.38140			0.0489317			0.0244658	−	0.999701i	$-0.492212\pi$
$797$	1.38140			0.0489317			0.0244658	+	0.999701i	$0.492212\pi$
$798$	3.94796	−	7.73063i	0.139756	−	0.273661i
$799$		−	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
$804$	27.1168	+	11.1916i	0.956336	+	0.394697i
$805$	−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	$0.0205333\pi$
$809$			3.66701i			0.128925i	−0.997920	+	0.0644626i	$0.979467\pi$
$810$	28.3283	+	2.74030i	0.995354	+	0.0962843i
$811$		−	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
$816$	18.1495	+	4.24840i	0.635359	+	0.148724i
$817$			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	$0.177286\pi$
$821$			30.2926i			1.05722i	−0.848865	+	0.528609i	$0.822714\pi$
$822$	5.56479	+	2.84188i	0.194094	+	0.0991220i
$823$	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
$825$	−23.7616	+	9.33648i	−0.827274	+	0.325055i
$826$	−9.59718	+	0.776580i	−0.333929	+	0.0270207i
$827$			41.0233i			1.42652i	0.700899	+	0.713261i	$0.252782\pi$
$827$			41.0233i			1.42652i	−0.700899	+	0.713261i	$0.747218\pi$
$828$	−34.9098	+	25.2650i	−1.21320	+	0.878019i
$829$	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
$834$	−2.62046	+	5.13121i	−0.0907391	+	0.177679i
$835$	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	$-0.579693\pi$
$839$	−14.3528			−0.495514			−0.247757	+	0.968822i	$0.579693\pi$
$840$	1.66915	+	10.8265i	0.0575911	+	0.373551i
$841$	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
$846$	6.59718	−	4.00609i	0.226816	−	0.137732i
$847$	−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
$852$	25.6168	+	10.5725i	0.877618	+	0.362208i
$853$			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
$855$	19.0369	+	14.2378i	0.651047	+	0.486924i
$856$	−4.55484	−	18.4350i	−0.155681	−	0.630094i
$857$	22.1419			0.756351			0.378176	−	0.925734i	$-0.376552\pi$
$857$	22.1419			0.756351			0.378176	+	0.925734i	$0.376552\pi$
$858$	4.47626	−	8.76512i	0.152817	−	0.299236i
$859$			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	$0.205514\pi$
$863$			35.3527i			1.20342i	−0.798715	+	0.601710i	$0.794486\pi$
$864$	9.12878	+	27.9404i	0.310568	+	0.950551i
$865$	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
$870$	7.46500	+	0.0635703i	0.253087	+	0.00215523i
$871$		−	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
$876$	−10.5725	+	25.6168i	−0.357212	+	0.865512i
$877$		−	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	$-0.577279\pi$
$881$		−	57.6224i		−	1.94135i	0.240400	−	0.970674i	$-0.422721\pi$
$882$	−2.20210	−	3.62639i	−0.0741487	−	0.122107i
$883$	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
$885$	2.35049	−	26.2639i	0.0790108	−	0.882852i
$886$	−0.801714	−	9.90779i	−0.0269341	−	0.332859i
$887$		−	34.6834i		−	1.16455i	−0.812991	−	0.582277i	$-0.802162\pi$
$887$		−	34.6834i		−	1.16455i	0.812991	−	0.582277i	$-0.197838\pi$
$888$	−14.8206	+	46.1590i	−0.497347	+	1.54899i
$889$	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
$894$	8.68059	−	16.9978i	0.290322	−	0.568490i
$895$	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
$900$	−29.9956	−	0.510910i	−0.999855	−	0.0170303i
$901$	−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
$906$	−23.0595	+	45.1535i	−0.766100	+	1.50013i
$907$	−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	$-0.0859040\pi$
$911$	58.1806			1.92761			0.963804	+	0.266611i	$0.0859040\pi$
$912$	−5.59579	+	23.9056i	−0.185295	+	0.791595i
$913$			17.2078i			0.569494i
$914$	−4.07503	−	50.3603i	−0.134790	−	1.66577i
$915$	−2.26159	+	25.2706i	−0.0747659	+	0.835420i
$916$	23.4114	−	3.81375i	0.773534	−	0.126010i
$917$	−16.1534			−0.533433
$918$	0.141883	−	19.7703i	0.00468285	−	0.652517i
$919$		−	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
$924$	9.43967	+	3.89592i	0.310542	+	0.128166i
$925$	−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	$-0.928484\pi$
$929$		−	13.5809i		−	0.445575i	0.974867	−	0.222787i	$-0.0715156\pi$
$930$	−44.3347	−	0.377545i	−1.45379	−	0.0123802i
$931$		−	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
$936$	8.79155	−	7.51407i	0.287361	−	0.245605i
$937$		−	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	$0.189347\pi$
$941$			34.3805i			1.12077i	−0.828231	+	0.560387i	$0.810653\pi$
$942$	8.68059	−	16.9978i	0.282829	−	0.553817i
$943$	−42.3455			−1.37896
$944$	25.8256	−	8.64345i	0.840552	−	0.281320i
$945$	10.8084	−	4.26359i	0.351598	−	0.138695i
$946$	−9.38093	+	0.759082i	−0.305000	+	0.0246799i
$947$		−	4.63404i		−	0.150586i	−0.997161	−	0.0752930i	$-0.976011\pi$
$947$		−	4.63404i		−	0.150586i	0.997161	−	0.0752930i	$-0.0239892\pi$
$948$	21.3876	−	51.8215i	0.694638	−	1.68308i
$949$	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	$-0.618256\pi$
$953$	−22.4137			−0.726051			−0.363025	+	0.931779i	$0.618256\pi$
$954$	−30.3711	−	50.0147i	−0.983299	−	1.61928i
$955$	−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
$960$	−11.9284	−	28.5957i	−0.384986	−	0.922922i
$961$	−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
$966$	−8.00139	+	15.6678i	−0.257441	+	0.504103i
$967$	−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	$-0.599805\pi$
$971$	−19.2221			−0.616867			−0.308433	+	0.951246i	$0.599805\pi$
$972$	26.7639	−	15.9904i	0.858452	−	0.512893i
$973$			2.35217i			0.0754070i
$974$	−33.7384	+	2.73003i	−1.08105	+	0.0874758i
$975$	4.31665	+	10.9860i	0.138243	+	0.351833i
$976$	−24.8489	+	8.31655i	−0.795394	+	0.266206i
$977$	29.3128			0.937799			0.468899	−	0.883252i	$-0.344651\pi$
$977$	29.3128			0.937799			0.468899	+	0.883252i	$0.344651\pi$
$978$	−32.3043	−	16.4975i	−1.03298	−	0.527532i
$979$			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	$0.00574661\pi$
$983$			1.13200i			0.0361050i	−0.999837	+	0.0180525i	$0.994253\pi$
$984$	−8.83001	+	27.5012i	−0.281490	+	0.876706i
$985$	−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
$990$	−14.8892	+	23.6739i	−0.473210	+	0.752406i
$991$		−	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
$996$	−7.71421	+	18.6913i	−0.244434	+	0.592255i
$997$		−	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.f.239.2	yes	8
3.2	odd	2		420.2.l.e.239.7	yes	8
4.3	odd	2		420.2.l.d.239.1	yes	8
5.4	even	2		420.2.l.c.239.7	✓	8
12.11	even	2		420.2.l.c.239.8	yes	8
15.14	odd	2		420.2.l.d.239.2	yes	8
20.19	odd	2		420.2.l.e.239.8	yes	8
60.59	even	2	inner	420.2.l.f.239.1	yes	8

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

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)

\(f(q)\)	\(=\)	\(q+(-1.40961 + 0.114062i) q^{2} +(-1.47398 - 0.909606i) q^{3} +(1.97398 - 0.321565i) q^{4} +(1.00000 + 2.00000i) q^{5} +(2.18148 + 1.11406i) q^{6} +1.00000 q^{7} +(-2.74586 + 0.678435i) q^{8} +(1.34523 + 2.68148i) q^{9} +O(q^{10})\)	\(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} +(2.18148 + 1.11406i) 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} +(-3.20210 - 1.32156i) q^{12} +1.36297i q^{13} +(-1.40961 + 0.114062i) q^{14} +(0.345233 - 3.85757i) q^{15} +(3.79319 - 1.26952i) q^{16} -2.69047 q^{17} +(-2.20210 - 3.62639i) 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} +(4.66445 + 1.49765i) 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} +(-0.0466412 + 5.47703i) 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} +(3.51773 + 4.86061i) 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} +(2.18148 + 1.11406i) q^{42} -2.25749 q^{43} +(-5.81921 + 0.947960i) q^{44} +(-4.01773 + 5.37195i) q^{45} +(-0.819213 - 10.1240i) q^{46} +1.81921i q^{47} +(-6.74586 - 1.57906i) 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} +(-0.0527356 + 7.34828i) 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} +(-0.558974 - 7.72577i) 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} +(-6.43092 - 3.28421i) 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} +(-5.51303 - 6.45031i) q^{72} -8.00000i q^{73} +(-1.12875 - 13.9493i) q^{74} +(8.06036 - 3.16710i) q^{75} +(-1.13955 - 6.99530i) q^{76} -2.94796 q^{77} +(-1.51843 + 2.97328i) 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} +(-3.20210 - 1.32156i) 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} +(5.05069 - 8.03060i) 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} +(9.68911 + 1.45641i) q^{96} -3.70294i q^{97} +(-1.40961 + 0.114062i) q^{98} +(-3.96569 - 7.90490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9	\( 8 q + 2 q^{3} + 2 q^{4} + 8 q^{5} + 4 q^{6} + 8 q^{7} - 6 q^{8} + 2 q^{9} - 4 q^{10} + 4 q^{11} - 14 q^{12} - 6 q^{15} - 6 q^{16} - 4 q^{17} - 6 q^{18} + 10 q^{20} + 2 q^{21} + 6 q^{22} + 6 q^{24} - 24 q^{25} + 26 q^{26} + 8 q^{27} + 2 q^{28} - 16 q^{30} - 30 q^{32} + 26 q^{33} + 30 q^{34} + 8 q^{35} + 10 q^{36} - 20 q^{38} + 18 q^{39} - 14 q^{40} + 4 q^{42} - 8 q^{43} - 24 q^{44} - 14 q^{45} + 16 q^{46} - 38 q^{48} + 8 q^{49} - 8 q^{50} - 14 q^{51} + 16 q^{52} + 8 q^{54} + 4 q^{55} - 6 q^{56} + 20 q^{57} - 26 q^{58} + 8 q^{59} + 10 q^{60} - 16 q^{61} - 40 q^{62} + 2 q^{63} + 26 q^{64} + 32 q^{65} - 6 q^{66} - 24 q^{67} + 12 q^{68} + 24 q^{69} - 4 q^{70} - 64 q^{71} + 22 q^{72} - 4 q^{74} - 22 q^{75} - 28 q^{76} + 4 q^{77} + 42 q^{78} - 38 q^{80} + 2 q^{81} + 4 q^{82} - 14 q^{84} - 4 q^{85} - 24 q^{86} - 18 q^{87} + 24 q^{88} - 6 q^{90} + 36 q^{92} + 32 q^{93} - 2 q^{94} + 48 q^{95} - 14 q^{96} + 14 q^{99}+O(q^{100}) \) 8 * q + 2 * q^3 + 2 * q^4 + 8 * q^5 + 4 * q^6 + 8 * q^7 - 6 * q^8 + 2 * q^9 - 4 * q^10 + 4 * q^11 - 14 * q^12 - 6 * q^15 - 6 * q^16 - 4 * q^17 - 6 * q^18 + 10 * q^20 + 2 * q^21 + 6 * q^22 + 6 * q^24 - 24 * q^25 + 26 * q^26 + 8 * q^27 + 2 * q^28 - 16 * q^30 - 30 * q^32 + 26 * q^33 + 30 * q^34 + 8 * q^35 + 10 * q^36 - 20 * q^38 + 18 * q^39 - 14 * q^40 + 4 * q^42 - 8 * q^43 - 24 * q^44 - 14 * q^45 + 16 * q^46 - 38 * q^48 + 8 * q^49 - 8 * q^50 - 14 * q^51 + 16 * q^52 + 8 * q^54 + 4 * q^55 - 6 * q^56 + 20 * q^57 - 26 * q^58 + 8 * q^59 + 10 * q^60 - 16 * q^61 - 40 * q^62 + 2 * q^63 + 26 * q^64 + 32 * q^65 - 6 * q^66 - 24 * q^67 + 12 * q^68 + 24 * q^69 - 4 * q^70 - 64 * q^71 + 22 * q^72 - 4 * q^74 - 22 * q^75 - 28 * q^76 + 4 * q^77 + 42 * q^78 - 38 * q^80 + 2 * q^81 + 4 * q^82 - 14 * q^84 - 4 * q^85 - 24 * q^86 - 18 * q^87 + 24 * q^88 - 6 * q^90 + 36 * q^92 + 32 * q^93 - 2 * q^94 + 48 * q^95 - 14 * q^96 + 14 * q^99

Introduction

L-functions

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