LMFDB - Embedded newform 429.2.n.b.157.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, degree $4$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 4 x^{18} + 4 x^{17} + 37 x^{16} - 74 x^{15} + 398 x^{14} - 224 x^{13} + 978 x^{12} + \cdots + 121 $ x^20 - x^19 + 4x^18 + 4x^17 + 37x^16 - 74x^15 + 398x^14 - 224x^13 + 978x^12 + 115x^11 + 1963x^10 + 323x^9 + 3007x^8 + 1828x^7 + 6736x^6 + 4512x^5 + 5197x^4 + 2152x^3 + 1259x^2 + 495x + 121
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.4
Root			$1.21086 + 0.879744i$ of defining polynomial
Character	$\chi$	$=$	429.157
Dual form			429.2.n.b.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.21086 - 0.879744i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.0742075 - 0.228387i) q^{4} +(2.08500 + 1.51484i) q^{5} +(-1.21086 - 0.879744i) q^{6} +(-0.780732 + 2.40285i) q^{7} +(0.813950 + 2.50508i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.21086 - 0.879744i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.0742075 - 0.228387i) q^{4} +(2.08500 + 1.51484i) q^{5} +(-1.21086 - 0.879744i) q^{6} +(-0.780732 + 2.40285i) q^{7} +(0.813950 + 2.50508i) q^{8} +(-0.809017 + 0.587785i) q^{9} +3.85732 q^{10} +(3.27879 + 0.499525i) q^{11} -0.240141 q^{12} +(0.809017 - 0.587785i) q^{13} +(1.16853 + 3.59636i) q^{14} +(0.796398 - 2.45106i) q^{15} +(3.57797 + 2.59955i) q^{16} +(-0.636560 - 0.462488i) q^{17} +(-0.462509 + 1.42346i) q^{18} +(-1.94870 - 5.99747i) q^{19} +(0.500693 - 0.363774i) q^{20} +2.52650 q^{21} +(4.40962 - 2.27964i) q^{22} -4.00166 q^{23} +(2.13095 - 1.54823i) q^{24} +(0.507391 + 1.56159i) q^{25} +(0.462509 - 1.42346i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.490843 + 0.356618i) q^{28} +(1.37968 - 4.24621i) q^{29} +(-1.19198 - 3.66853i) q^{30} +(-5.52347 + 4.01303i) q^{31} +1.35137 q^{32} +(-0.538126 - 3.27268i) q^{33} -1.17766 q^{34} +(-5.26775 + 3.82724i) q^{35} +(0.0742075 + 0.228387i) q^{36} +(1.79363 - 5.52023i) q^{37} +(-7.63585 - 5.54777i) q^{38} +(-0.809017 - 0.587785i) q^{39} +(-2.09771 + 6.45609i) q^{40} +(-0.313930 - 0.966178i) q^{41} +(3.05925 - 2.22267i) q^{42} +6.60286 q^{43} +(0.357396 - 0.711766i) q^{44} -2.57720 q^{45} +(-4.84546 + 3.52043i) q^{46} +(-0.938497 - 2.88840i) q^{47} +(1.36666 - 4.20616i) q^{48} +(0.498996 + 0.362542i) q^{49} +(1.98818 + 1.44450i) q^{50} +(-0.243144 + 0.748321i) q^{51} +(-0.0742075 - 0.228387i) q^{52} +(4.00297 - 2.90833i) q^{53} +1.49671 q^{54} +(6.07957 + 6.00835i) q^{55} -6.65480 q^{56} +(-5.10176 + 3.70664i) q^{57} +(-2.06498 - 6.35535i) q^{58} +(-0.304974 + 0.938613i) q^{59} +(-0.500693 - 0.363774i) q^{60} +(7.67014 + 5.57268i) q^{61} +(-3.15772 + 9.71847i) q^{62} +(-0.780732 - 2.40285i) q^{63} +(-5.51961 + 4.01023i) q^{64} +2.57720 q^{65} +(-3.53072 - 3.48935i) q^{66} +1.72262 q^{67} +(-0.152864 + 0.111062i) q^{68} +(1.23658 + 3.80580i) q^{69} +(-3.01153 + 9.26854i) q^{70} +(-5.68259 - 4.12864i) q^{71} +(-2.13095 - 1.54823i) q^{72} +(2.33618 - 7.19003i) q^{73} +(-2.68455 - 8.26218i) q^{74} +(1.32837 - 0.965115i) q^{75} -1.51435 q^{76} +(-3.76014 + 7.48843i) q^{77} -1.49671 q^{78} +(-3.55700 + 2.58431i) q^{79} +(3.52216 + 10.8401i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.23012 - 0.893731i) q^{82} +(-11.6460 - 8.46131i) q^{83} +(0.187485 - 0.577021i) q^{84} +(-0.626631 - 1.92857i) q^{85} +(7.99516 - 5.80882i) q^{86} -4.46473 q^{87} +(1.41742 + 8.62023i) q^{88} -12.7162 q^{89} +(-3.12064 + 2.26727i) q^{90} +(0.780732 + 2.40285i) q^{91} +(-0.296953 + 0.913927i) q^{92} +(5.52347 + 4.01303i) q^{93} +(-3.67744 - 2.67182i) q^{94} +(5.02218 - 15.4567i) q^{95} +(-0.417597 - 1.28523i) q^{96} +(-8.68009 + 6.30645i) q^{97} +0.923160 q^{98} +(-2.94621 + 1.52310i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	1.21086	−	0.879744i	0.856210	−	0.622073i	−0.0706412	−	0.997502i	$-0.522505\pi$
$2$	1.21086	−	0.879744i	0.856210	−	0.622073i	0.926851	+	0.375429i	$0.122505\pi$
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$3$	−0.309017	−	0.951057i	−0.178411	−	0.549093i
$4$	0.0742075	−	0.228387i	0.0371038	−	0.114194i
$5$	2.08500	+	1.51484i	0.932439	+	0.677457i	0.946589	−	0.322443i	$-0.104504\pi$
$5$	2.08500	+	1.51484i	0.932439	+	0.677457i	−0.0141497	+	0.999900i	$0.504504\pi$
$6$	−1.21086	−	0.879744i	−0.494333	−	0.359154i
$7$	−0.780732	+	2.40285i	−0.295089	+	0.908190i	0.688103	+	0.725613i	$0.258444\pi$
$7$	−0.780732	+	2.40285i	−0.295089	+	0.908190i	−0.983192	+	0.182577i	$0.941556\pi$
$8$	0.813950	+	2.50508i	0.287775	+	0.885680i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	3.85732			1.21979
$11$	3.27879	+	0.499525i	0.988593	+	0.150612i
$11$	3.27879	+	0.499525i	0.988593	+	0.150612i
$12$	−0.240141			−0.0693226
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	1.16853	+	3.59636i	0.312302	+	0.961168i
$15$	0.796398	−	2.45106i	0.205629	−	0.632861i
$16$	3.57797	+	2.59955i	0.894492	+	0.649887i
$17$	−0.636560	−	0.462488i	−0.154388	−	0.112170i	0.507909	−	0.861411i	$-0.330419\pi$
$17$	−0.636560	−	0.462488i	−0.154388	−	0.112170i	−0.662298	+	0.749241i	$0.730419\pi$
$18$	−0.462509	+	1.42346i	−0.109014	+	0.335512i
$19$	−1.94870	−	5.99747i	−0.447062	−	1.37591i	−0.880207	−	0.474590i	$-0.842596\pi$
$19$	−1.94870	−	5.99747i	−0.447062	−	1.37591i	0.433145	−	0.901324i	$-0.357404\pi$
$20$	0.500693	−	0.363774i	0.111958	−	0.0813424i
$21$	2.52650			0.551328
$22$	4.40962	−	2.27964i	0.940135	−	0.486021i
$23$	−4.00166			−0.834403			−0.417201	−	0.908814i	$-0.636989\pi$
$23$	−4.00166			−0.834403			−0.417201	+	0.908814i	$0.636989\pi$
$24$	2.13095	−	1.54823i	0.434978	−	0.316030i
$25$	0.507391	+	1.56159i	0.101478	+	0.312318i
$26$	0.462509	−	1.42346i	0.0907054	−	0.279163i
$27$	0.809017	+	0.587785i	0.155695	+	0.113119i
$28$	0.490843	+	0.356618i	0.0927606	+	0.0673945i
$29$	1.37968	−	4.24621i	0.256200	−	0.788502i	−0.737391	−	0.675466i	$-0.763943\pi$
$29$	1.37968	−	4.24621i	0.256200	−	0.788502i	0.993591	−	0.113036i	$-0.0360575\pi$
$30$	−1.19198	−	3.66853i	−0.217624	−	0.669779i
$31$	−5.52347	+	4.01303i	−0.992044	+	0.720762i	−0.960368	−	0.278736i	$-0.910085\pi$
$31$	−5.52347	+	4.01303i	−0.992044	+	0.720762i	−0.0316762	+	0.999498i	$0.510085\pi$
$32$	1.35137			0.238891
$33$	−0.538126	−	3.27268i	−0.0936757	−	0.569700i
$34$	−1.17766			−0.201967
$35$	−5.26775	+	3.82724i	−0.890412	+	0.646922i
$36$	0.0742075	+	0.228387i	0.0123679	+	0.0380645i
$37$	1.79363	−	5.52023i	0.294871	−	0.907520i	−0.688394	−	0.725337i	$-0.741684\pi$
$37$	1.79363	−	5.52023i	0.294871	−	0.907520i	0.983265	−	0.182183i	$-0.0583162\pi$
$38$	−7.63585	−	5.54777i	−1.23870	−	0.899967i
$39$	−0.809017	−	0.587785i	−0.129546	−	0.0941210i
$40$	−2.09771	+	6.45609i	−0.331677	+	1.02080i
$41$	−0.313930	−	0.966178i	−0.0490277	−	0.150892i	0.923545	−	0.383489i	$-0.125278\pi$
$41$	−0.313930	−	0.966178i	−0.0490277	−	0.150892i	−0.972573	+	0.232597i	$0.925278\pi$
$42$	3.05925	−	2.22267i	0.472052	−	0.342966i
$43$	6.60286			1.00693			0.503463	−	0.864017i	$-0.332059\pi$
$43$	6.60286			1.00693			0.503463	+	0.864017i	$0.332059\pi$
$44$	0.357396	−	0.711766i	0.0538795	−	0.107303i
$45$	−2.57720			−0.384186
$46$	−4.84546	+	3.52043i	−0.714424	+	0.519059i
$47$	−0.938497	−	2.88840i	−0.136894	−	0.421316i	0.858986	−	0.511999i	$-0.171095\pi$
$47$	−0.938497	−	2.88840i	−0.136894	−	0.421316i	−0.995880	+	0.0906832i	$0.971095\pi$
$48$	1.36666	−	4.20616i	0.197261	−	0.607106i
$49$	0.498996	+	0.362542i	0.0712851	+	0.0517917i
$50$	1.98818	+	1.44450i	0.281171	+	0.204283i
$51$	−0.243144	+	0.748321i	−0.0340470	+	0.104786i
$52$	−0.0742075	−	0.228387i	−0.0102907	−	0.0316716i
$53$	4.00297	−	2.90833i	0.549850	−	0.399490i	−0.277880	−	0.960616i	$-0.589632\pi$
$53$	4.00297	−	2.90833i	0.549850	−	0.399490i	0.827730	+	0.561126i	$0.189632\pi$
$54$	1.49671			0.203676
$55$	6.07957	+	6.00835i	0.819769	+	0.810166i
$56$	−6.65480			−0.889285
$57$	−5.10176	+	3.70664i	−0.675744	+	0.490957i
$58$	−2.06498	−	6.35535i	−0.271145	−	0.834498i
$59$	−0.304974	+	0.938613i	−0.0397042	+	0.122197i	−0.968944	−	0.247280i	$-0.920463\pi$
$59$	−0.304974	+	0.938613i	−0.0397042	+	0.122197i	0.929240	+	0.369477i	$0.120463\pi$
$60$	−0.500693	−	0.363774i	−0.0646391	−	0.0469631i
$61$	7.67014	+	5.57268i	0.982061	+	0.713509i	0.958168	−	0.286206i	$-0.0923941\pi$
$61$	7.67014	+	5.57268i	0.982061	+	0.713509i	0.0238924	+	0.999715i	$0.492394\pi$
$62$	−3.15772	+	9.71847i	−0.401031	+	1.23425i
$63$	−0.780732	−	2.40285i	−0.0983630	−	0.302730i
$64$	−5.51961	+	4.01023i	−0.689952	+	0.501279i
$65$	2.57720			0.319662
$66$	−3.53072	−	3.48935i	−0.434601	−	0.429510i
$67$	1.72262			0.210452			0.105226	−	0.994448i	$-0.466443\pi$
$67$	1.72262			0.210452			0.105226	+	0.994448i	$0.466443\pi$
$68$	−0.152864	+	0.111062i	−0.0185375	+	0.0134683i
$69$	1.23658	+	3.80580i	0.148867	+	0.458165i
$70$	−3.01153	+	9.26854i	−0.359947	+	1.10780i
$71$	−5.68259	−	4.12864i	−0.674400	−	0.489980i	0.197095	−	0.980384i	$-0.436849\pi$
$71$	−5.68259	−	4.12864i	−0.674400	−	0.489980i	−0.871495	+	0.490404i	$0.836849\pi$
$72$	−2.13095	−	1.54823i	−0.251135	−	0.182460i
$73$	2.33618	−	7.19003i	0.273429	−	0.841529i	−0.716201	−	0.697894i	$-0.754121\pi$
$73$	2.33618	−	7.19003i	0.273429	−	0.841529i	0.989631	−	0.143635i	$-0.0458792\pi$
$74$	−2.68455	−	8.26218i	−0.312072	−	0.960459i
$75$	1.32837	−	0.965115i	0.153387	−	0.111442i
$76$	−1.51435			−0.173708
$77$	−3.76014	+	7.48843i	−0.428507	+	0.853386i
$78$	−1.49671			−0.169469
$79$	−3.55700	+	2.58431i	−0.400194	+	0.290758i	−0.769620	−	0.638502i	$-0.779554\pi$
$79$	−3.55700	+	2.58431i	−0.400194	+	0.290758i	0.369426	+	0.929260i	$0.379554\pi$
$80$	3.52216	+	10.8401i	0.393790	+	1.21196i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−1.23012	−	0.893731i	−0.135844	−	0.0986961i
$83$	−11.6460	−	8.46131i	−1.27831	−	0.928749i	−0.278813	−	0.960345i	$-0.589941\pi$
$83$	−11.6460	−	8.46131i	−1.27831	−	0.928749i	−0.999501	+	0.0315959i	$0.989941\pi$
$84$	0.187485	−	0.577021i	0.0204563	−	0.0629581i
$85$	−0.626631	−	1.92857i	−0.0679677	−	0.209183i
$86$	7.99516	−	5.80882i	0.862140	−	0.626382i
$87$	−4.46473			−0.478669
$88$	1.41742	+	8.62023i	0.151098	+	0.918920i
$89$	−12.7162			−1.34791			−0.673957	−	0.738770i	$-0.735407\pi$
$89$	−12.7162			−1.34791			−0.673957	+	0.738770i	$0.735407\pi$
$90$	−3.12064	+	2.26727i	−0.328944	+	0.238992i
$91$	0.780732	+	2.40285i	0.0818429	+	0.251887i
$92$	−0.296953	+	0.913927i	−0.0309595	+	0.0952835i
$93$	5.52347	+	4.01303i	0.572757	+	0.416132i
$94$	−3.67744	−	2.67182i	−0.379299	−	0.275577i
$95$	5.02218	−	15.4567i	0.515265	−	1.58582i
$96$	−0.417597	−	1.28523i	−0.0426208	−	0.131173i
$97$	−8.68009	+	6.30645i	−0.881329	+	0.640323i	−0.933603	−	0.358310i	$-0.883353\pi$
$97$	−8.68009	+	6.30645i	−0.881329	+	0.640323i	0.0522735	+	0.998633i	$0.483353\pi$
$98$	0.923160			0.0932533
$99$	−2.94621	+	1.52310i	−0.296105	+	0.153077i
$100$	0.394299			0.0394299
$101$	−7.27443	+	5.28518i	−0.723832	+	0.525895i	−0.887606	−	0.460603i	$-0.847633\pi$
$101$	−7.27443	+	5.28518i	−0.723832	+	0.525895i	0.163774	+	0.986498i	$0.447633\pi$
$102$	0.363916	+	1.12002i	0.0360331	+	0.110898i
$103$	−3.70916	+	11.4156i	−0.365474	+	1.12481i	0.584209	+	0.811603i	$0.301405\pi$
$103$	−3.70916	+	11.4156i	−0.365474	+	1.12481i	−0.949684	+	0.313211i	$0.898595\pi$
$104$	2.13095	+	1.54823i	0.208957	+	0.151816i
$105$	5.26775	+	3.82724i	0.514080	+	0.373501i
$106$	2.28847	−	7.04318i	0.222276	−	0.684094i
$107$	0.0952089	+	0.293023i	0.00920419	+	0.0283276i	0.955553	−	0.294819i	$-0.0952593\pi$
$107$	0.0952089	+	0.293023i	0.00920419	+	0.0283276i	−0.946349	+	0.323147i	$0.895259\pi$
$108$	0.194278	−	0.141151i	0.0186944	−	0.0135823i
$109$	18.6020			1.78175			0.890873	−	0.454253i	$-0.150094\pi$
$109$	18.6020			1.78175			0.890873	+	0.454253i	$0.150094\pi$
$110$	12.6473	+	1.92683i	1.20588	+	0.183716i
$111$	−5.80431			−0.550921
$112$	−9.03974	+	6.56776i	−0.854175	+	0.620595i
$113$	−0.153595	−	0.472717i	−0.0144490	−	0.0444694i	0.943572	−	0.331167i	$-0.107442\pi$
$113$	−0.153595	−	0.472717i	−0.0144490	−	0.0444694i	−0.958021	+	0.286698i	$0.907442\pi$
$114$	−2.91663	+	8.97648i	−0.273168	+	0.840724i
$115$	−8.34344	−	6.06186i	−0.778030	−	0.565272i
$116$	−0.867398	−	0.630202i	−0.0805359	−	0.0585128i
$117$	−0.309017	+	0.951057i	−0.0285686	+	0.0879252i
$118$	0.456458	+	1.40483i	0.0420203	+	0.129325i
$119$	1.60827	−	1.16848i	0.147430	−	0.107114i
$120$	6.78834			0.619688
$121$	10.5009	+	3.27568i	0.954632	+	0.297789i
$122$	14.1900			1.28470
$123$	−0.821880	+	0.597131i	−0.0741064	+	0.0538415i
$124$	0.506643	+	1.55929i	0.0454979	+	0.140028i
$125$	2.67434	−	8.23078i	0.239201	−	0.736184i
$126$	−3.05925	−	2.22267i	−0.272540	−	0.198012i
$127$	−14.2137	−	10.3269i	−1.26126	−	0.916362i	−0.262445	−	0.964947i	$-0.584529\pi$
$127$	−14.2137	−	10.3269i	−1.26126	−	0.916362i	−0.998819	+	0.0485845i	$0.984529\pi$
$128$	−3.99071	+	12.2822i	−0.352733	+	1.08560i
$129$	−2.04039	−	6.27969i	−0.179647	−	0.552896i
$130$	3.12064	−	2.26727i	0.273698	−	0.198853i
$131$	3.92092			0.342572			0.171286	−	0.985221i	$-0.445208\pi$
$131$	3.92092			0.342572			0.171286	+	0.985221i	$0.445208\pi$
$132$	−0.787371	−	0.119956i	−0.0685319	−	0.0104409i
$133$	15.9324			1.38152
$134$	2.08586	−	1.51547i	0.180191	−	0.130917i
$135$	0.796398	+	2.45106i	0.0685430	+	0.210954i
$136$	0.640442	−	1.97108i	0.0549174	−	0.169018i
$137$	4.92718	+	3.57980i	0.420957	+	0.305843i	0.778023	−	0.628236i	$-0.216223\pi$
$137$	4.92718	+	3.57980i	0.420957	+	0.305843i	−0.357066	+	0.934079i	$0.616223\pi$
$138$	4.84546	+	3.52043i	0.412473	+	0.299679i
$139$	6.86259	−	21.1209i	0.582077	−	1.79145i	−0.0286265	−	0.999590i	$-0.509113\pi$
$139$	6.86259	−	21.1209i	0.582077	−	1.79145i	0.610704	−	0.791859i	$-0.290887\pi$
$140$	0.483187	+	1.48710i	0.0408368	+	0.125683i
$141$	−2.45702	+	1.78513i	−0.206918	+	0.150335i
$142$	−10.5130			−0.882231
$143$	2.94621	−	1.52310i	0.246375	−	0.127368i
$144$	−4.42261			−0.368551
$145$	9.30895	−	6.76335i	0.773066	−	0.561666i
$146$	−3.49658	−	10.7614i	−0.289379	−	0.890618i
$147$	0.190600	−	0.586605i	0.0157204	−	0.0483824i
$148$	−1.12765	−	0.819285i	−0.0926922	−	0.0673448i
$149$	0.888277	+	0.645371i	0.0727705	+	0.0528708i	0.623576	−	0.781763i	$-0.285679\pi$
$149$	0.888277	+	0.645371i	0.0727705	+	0.0528708i	−0.550805	+	0.834634i	$0.685679\pi$
$150$	0.759417	−	2.33725i	0.0620062	−	0.190835i
$151$	3.87162	+	11.9156i	0.315068	+	0.969679i	0.975727	+	0.218993i	$0.0702770\pi$
$151$	3.87162	+	11.9156i	0.315068	+	0.969679i	−0.660659	+	0.750686i	$0.729723\pi$
$152$	13.4380	−	9.76329i	1.08997	−	0.791908i
$153$	0.786831			0.0636115
$154$	2.03489	+	12.3754i	0.163976	+	0.997241i
$155$	−17.5955			−1.41331
$156$	−0.194278	+	0.141151i	−0.0155547	+	0.0113011i
$157$	−0.282532	−	0.869545i	−0.0225485	−	0.0693973i	0.939149	−	0.343510i	$-0.111616\pi$
$157$	−0.282532	−	0.869545i	−0.0225485	−	0.0693973i	−0.961698	+	0.274113i	$0.911616\pi$
$158$	−2.03351	+	6.25850i	−0.161777	+	0.497900i
$159$	−4.00297	−	2.90833i	−0.317456	−	0.230646i
$160$	2.81761	+	2.04711i	0.222751	+	0.161838i
$161$	3.12422	−	9.61536i	0.246223	−	0.757796i
$162$	−0.462509	−	1.42346i	−0.0363381	−	0.111837i
$163$	−15.6319	+	11.3572i	−1.22438	+	0.889566i	−0.996456	−	0.0841125i	$-0.973194\pi$
$163$	−15.6319	+	11.3572i	−1.22438	+	0.889566i	−0.227926	+	0.973678i	$0.573194\pi$
$164$	−0.243959			−0.0190500
$165$	3.83559	−	7.63870i	0.298600	−	0.594672i
$166$	−21.5455			−1.67226
$167$	−0.107360	+	0.0780013i	−0.00830774	+	0.00603592i	−0.591931	−	0.805988i	$-0.701634\pi$
$167$	−0.107360	+	0.0780013i	−0.00830774	+	0.00603592i	0.583624	+	0.812024i	$0.301634\pi$
$168$	2.05645	+	6.32909i	0.158658	+	0.488300i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−2.45541	−	1.78396i	−0.188322	−	0.136824i
$171$	5.10176	+	3.70664i	0.390141	+	0.283454i
$172$	0.489982	−	1.50801i	0.0373608	−	0.114985i
$173$	−5.25161	−	16.1628i	−0.399273	−	1.22884i	−0.925584	−	0.378543i	$-0.876425\pi$
$173$	−5.25161	−	16.1628i	−0.399273	−	1.22884i	0.526311	−	0.850292i	$-0.323575\pi$
$174$	−5.40618	+	3.92782i	−0.409841	+	0.297767i
$175$	−4.14839			−0.313589
$176$	10.4329	+	10.3107i	0.786408	+	0.777195i
$177$	0.986916			0.0741812
$178$	−15.3976	+	11.1870i	−1.15410	+	0.838501i
$179$	−7.87357	−	24.2324i	−0.588498	−	1.81121i	−0.584743	−	0.811218i	$-0.698805\pi$
$179$	−7.87357	−	24.2324i	−0.588498	−	1.81121i	−0.00375489	−	0.999993i	$-0.501195\pi$
$180$	−0.191248	+	0.588599i	−0.0142547	+	0.0438716i
$181$	14.1473	+	10.2786i	1.05156	+	0.764004i	0.972509	−	0.232866i	$-0.0748104\pi$
$181$	14.1473	+	10.2786i	1.05156	+	0.764004i	0.0790528	+	0.996870i	$0.474810\pi$
$182$	3.05925	+	2.22267i	0.226767	+	0.164756i
$183$	2.92973	−	9.01679i	0.216572	−	0.666540i
$184$	−3.25715	−	10.0245i	−0.240120	−	0.739014i
$185$	12.1020	−	8.79260i	0.889755	−	0.646445i
$186$	10.2186			0.749265
$187$	−1.85612	−	1.83438i	−0.135733	−	0.134143i
$188$	−0.729317			−0.0531909
$189$	−2.04398	+	1.48504i	−0.148678	+	0.108021i
$190$	−7.51675	−	23.1342i	−0.545322	−	1.67833i
$191$	−8.26130	+	25.4257i	−0.597766	+	1.83974i	−0.0573231	+	0.998356i	$0.518257\pi$
$191$	−8.26130	+	25.4257i	−0.597766	+	1.83974i	−0.540443	+	0.841380i	$0.681743\pi$
$192$	5.51961	+	4.01023i	0.398344	+	0.289414i
$193$	1.70485	+	1.23865i	0.122718	+	0.0891599i	0.647451	−	0.762107i	$-0.275835\pi$
$193$	1.70485	+	1.23865i	0.122718	+	0.0891599i	−0.524733	+	0.851267i	$0.675835\pi$
$194$	−4.96234	+	15.2725i	−0.356275	+	1.09650i
$195$	−0.796398	−	2.45106i	−0.0570313	−	0.175524i
$196$	0.119829	−	0.0870610i	0.00855923	−	0.00621864i
$197$	−5.21648			−0.371659			−0.185829	−	0.982582i	$-0.559497\pi$
$197$	−5.21648			−0.371659			−0.185829	+	0.982582i	$0.559497\pi$
$198$	−2.22752	+	4.43618i	−0.158303	+	0.315266i
$199$	1.84268			0.130624			0.0653121	−	0.997865i	$-0.479196\pi$
$199$	1.84268			0.130624			0.0653121	+	0.997865i	$0.479196\pi$
$200$	−3.49892	+	2.54211i	−0.247411	+	0.179754i
$201$	−0.532320	−	1.63831i	−0.0375470	−	0.115558i
$202$	−4.15873	+	12.7993i	−0.292607	+	0.900553i
$203$	9.12583	+	6.63030i	0.640508	+	0.465356i
$204$	0.152864	+	0.111062i	0.0107026	+	0.00777590i
$205$	0.809060	−	2.49003i	0.0565072	−	0.173911i
$206$	5.55153	+	17.0859i	0.386794	+	1.19043i
$207$	3.23741	−	2.35211i	0.225015	−	0.163483i
$208$	4.42261			0.306653
$209$	−3.39348	−	20.6379i	−0.234732	−	1.42755i
$210$	9.74552			0.672505
$211$	6.02665	−	4.37862i	0.414892	−	0.301437i	−0.360687	−	0.932687i	$-0.617458\pi$
$211$	6.02665	−	4.37862i	0.414892	−	0.301437i	0.775579	+	0.631250i	$0.217458\pi$
$212$	−0.367175	−	1.13005i	−0.0252177	−	0.0776120i
$213$	−2.17056	+	6.68029i	−0.148724	+	0.457726i
$214$	0.373070	+	0.271051i	0.0255025	+	0.0185287i
$215$	13.7669	+	10.0023i	0.938897	+	0.682149i
$216$	−0.813950	+	2.50508i	−0.0553823	+	0.170449i
$217$	−5.33035	−	16.4051i	−0.361848	−	1.11365i
$218$	22.5245	−	16.3650i	1.52555	−	1.10838i
$219$	−7.56004			−0.510860
$220$	1.82338	−	0.942632i	0.122932	−	0.0635522i
$221$	−0.786831			−0.0529280
$222$	−7.02823	+	5.10631i	−0.471704	+	0.342713i
$223$	4.31503	+	13.2803i	0.288956	+	0.889314i	0.985185	+	0.171495i	$0.0548596\pi$
$223$	4.31503	+	13.2803i	0.288956	+	0.889314i	−0.696230	+	0.717819i	$0.745140\pi$
$224$	−1.05506	+	3.24714i	−0.0704941	+	0.216958i
$225$	−1.32837	−	0.965115i	−0.0885578	−	0.0643410i
$226$	−0.601852	−	0.437271i	−0.0400346	−	0.0290868i
$227$	−1.74994	+	5.38575i	−0.116147	+	0.357465i	−0.992185	−	0.124779i	$-0.960178\pi$
$227$	−1.74994	+	5.38575i	−0.116147	+	0.357465i	0.876037	+	0.482243i	$0.160178\pi$
$228$	0.467961	+	1.44024i	0.0309915	+	0.0953820i
$229$	13.3810	−	9.72188i	0.884242	−	0.642440i	−0.0501280	−	0.998743i	$-0.515963\pi$
$229$	13.3810	−	9.72188i	0.884242	−	0.642440i	0.934370	+	0.356303i	$0.115963\pi$
$230$	−15.4357			−1.01780
$231$	8.28387	+	1.26205i	0.545039	+	0.0830368i
$232$	11.7601			0.772088
$233$	−22.2953	+	16.1985i	−1.46061	+	1.06120i	−0.477409	+	0.878681i	$0.658424\pi$
$233$	−22.2953	+	16.1985i	−1.46061	+	1.06120i	−0.983203	+	0.182515i	$0.941576\pi$
$234$	0.462509	+	1.42346i	0.0302351	+	0.0930542i
$235$	2.41869	−	7.44397i	0.157778	−	0.485591i
$236$	0.191736	+	0.139304i	0.0124810	+	0.00906794i
$237$	3.55700	+	2.58431i	0.231052	+	0.167869i
$238$	0.919435	−	2.82973i	0.0595981	−	0.183424i
$239$	−1.46600	−	4.51188i	−0.0948276	−	0.291849i	0.892381	−	0.451283i	$-0.149033\pi$
$239$	−1.46600	−	4.51188i	−0.0948276	−	0.291849i	−0.987209	+	0.159433i	$0.949033\pi$
$240$	9.22114	−	6.69955i	0.595222	−	0.432454i
$241$	−1.91794			−0.123546			−0.0617728	−	0.998090i	$-0.519675\pi$
$241$	−1.91794			−0.123546			−0.0617728	+	0.998090i	$0.519675\pi$
$242$	15.5970	−	5.27175i	1.00261	−	0.338881i
$243$	−1.00000			−0.0641500
$244$	1.84191	−	1.33823i	0.117916	−	0.0856712i
$245$	0.491213	+	1.51180i	0.0313824	+	0.0965852i
$246$	−0.469862	+	1.44609i	−0.0299573	+	0.0921992i
$247$	−5.10176	−	3.70664i	−0.324617	−	0.235848i
$248$	−14.5488	−	10.5703i	−0.923850	−	0.671216i
$249$	−4.44837	+	13.6907i	−0.281904	+	0.867612i
$250$	−4.00272	−	12.3191i	−0.253154	−	0.779128i
$251$	−10.8532	+	7.88533i	−0.685049	+	0.497718i	−0.875029	−	0.484071i	$-0.839158\pi$
$251$	−10.8532	+	7.88533i	−0.685049	+	0.497718i	0.189980	+	0.981788i	$0.439158\pi$
$252$	−0.606715			−0.0382195
$253$	−13.1206	−	1.99893i	−0.824885	−	0.125671i
$254$	−26.2959			−1.64995
$255$	−1.64054	+	1.19192i	−0.102735	+	0.0746411i
$256$	1.75633	+	5.40543i	0.109771	+	0.337840i
$257$	1.33137	−	4.09752i	0.0830483	−	0.255596i	−0.900907	−	0.434013i	$-0.857097\pi$
$257$	1.33137	−	4.09752i	0.0830483	−	0.255596i	0.983955	+	0.178416i	$0.0570974\pi$
$258$	−7.99516	−	5.80882i	−0.497757	−	0.361642i
$259$	11.8639	+	8.61963i	0.737187	+	0.535598i
$260$	0.191248	−	0.588599i	0.0118607	−	0.0365034i
$261$	1.37968	+	4.24621i	0.0853999	+	0.262834i
$262$	4.74770	−	3.44940i	0.293314	−	0.213105i
$263$	24.0820			1.48496			0.742481	−	0.669867i	$-0.233649\pi$
$263$	24.0820			1.48496			0.742481	+	0.669867i	$0.233649\pi$
$264$	7.76032	−	4.01185i	0.477615	−	0.246912i
$265$	12.7518			0.783339
$266$	19.2920	−	14.0164i	1.18287	−	0.859403i
$267$	3.92952	+	12.0938i	0.240483	+	0.740130i
$268$	0.127832	−	0.393426i	0.00780857	−	0.0240323i
$269$	20.1805	+	14.6620i	1.23043	+	0.893959i	0.996922	−	0.0783960i	$-0.0249799\pi$
$269$	20.1805	+	14.6620i	1.23043	+	0.893959i	0.233507	+	0.972355i	$0.424980\pi$
$270$	3.12064	+	2.26727i	0.189916	+	0.137982i
$271$	7.02276	−	21.6138i	0.426602	−	1.31295i	−0.474850	−	0.880067i	$-0.657498\pi$
$271$	7.02276	−	21.6138i	0.426602	−	1.31295i	0.901452	−	0.432879i	$-0.142502\pi$
$272$	−1.07533	−	3.30954i	−0.0652017	−	0.200670i
$273$	2.04398	−	1.48504i	0.123707	−	0.0898787i
$274$	9.11545			0.550684
$275$	0.883577	+	5.37358i	0.0532817	+	0.324039i
$276$	0.960960			0.0578430
$277$	17.2781	−	12.5533i	1.03814	−	0.754255i	0.0682205	−	0.997670i	$-0.478268\pi$
$277$	17.2781	−	12.5533i	1.03814	−	0.754255i	0.969922	+	0.243415i	$0.0782678\pi$
$278$	−10.2713	−	31.6118i	−0.616032	−	1.89595i
$279$	2.10978	−	6.49322i	0.126309	−	0.388739i
$280$	−13.8752	−	10.0810i	−0.829204	−	0.602452i
$281$	26.0099	+	18.8973i	1.55162	+	1.12732i	0.942484	+	0.334250i	$0.108483\pi$
$281$	26.0099	+	18.8973i	1.55162	+	1.12732i	0.609135	+	0.793067i	$0.291517\pi$
$282$	−1.40466	+	4.32309i	−0.0836461	+	0.257436i
$283$	−4.30005	−	13.2342i	−0.255611	−	0.786690i	−0.993709	−	0.111996i	$-0.964276\pi$
$283$	−4.30005	−	13.2342i	−0.255611	−	0.786690i	0.738097	−	0.674694i	$-0.235724\pi$
$284$	−1.36462	+	0.991455i	−0.0809754	+	0.0588320i
$285$	−16.2521			−0.962692
$286$	2.22752	−	4.43618i	0.131716	−	0.262317i
$287$	2.56667			0.151506
$288$	−1.09328	+	0.794316i	−0.0644223	+	0.0468055i
$289$	−5.06198	−	15.5792i	−0.297763	−	0.916421i
$290$	5.32186	−	16.3790i	0.312510	−	0.961807i
$291$	8.68009	+	6.30645i	0.508836	+	0.369691i
$292$	−1.46875	−	1.06711i	−0.0859520	−	0.0624478i
$293$	−5.85996	+	18.0351i	−0.342343	+	1.05362i	0.620648	+	0.784089i	$0.286870\pi$
$293$	−5.85996	+	18.0351i	−0.342343	+	1.05362i	−0.962991	+	0.269534i	$0.913130\pi$
$294$	−0.285272	−	0.877978i	−0.0166374	−	0.0512047i
$295$	−2.05772	+	1.49502i	−0.119805	+	0.0870434i
$296$	15.2886			0.888629
$297$	2.35898	+	2.33135i	0.136882	+	0.135279i
$298$	1.64334			0.0951963
$299$	−3.23741	+	2.35211i	−0.187224	+	0.136026i
$300$	−0.121845	−	0.375001i	−0.00703474	−	0.0216507i
$301$	−5.15506	+	15.8656i	−0.297133	+	0.914480i
$302$	15.1707	+	11.0222i	0.872975	+	0.634254i
$303$	7.27443	+	5.28518i	0.417905	+	0.303626i
$304$	8.61833	−	26.5245i	0.494295	−	1.52128i
$305$	7.55050	+	23.2381i	0.432340	+	1.33061i
$306$	0.952746	−	0.692210i	0.0544648	−	0.0395710i
$307$	−18.8271			−1.07452			−0.537260	−	0.843416i	$-0.680541\pi$
$307$	−18.8271			−1.07452			−0.537260	+	0.843416i	$0.680541\pi$
$308$	1.43123	+	1.41447i	0.0815520	+	0.0805967i
$309$	12.0031			0.682832
$310$	−21.3058	+	15.4795i	−1.21009	+	0.879179i
$311$	1.72527	+	5.30982i	0.0978309	+	0.301093i	0.987981	−	0.154575i	$-0.0494007\pi$
$311$	1.72527	+	5.30982i	0.0978309	+	0.301093i	−0.890150	+	0.455667i	$0.849401\pi$
$312$	0.813950	−	2.50508i	0.0460809	−	0.141822i
$313$	4.03844	+	2.93410i	0.228266	+	0.165845i	0.696040	−	0.718003i	$-0.254944\pi$
$313$	4.03844	+	2.93410i	0.228266	+	0.165845i	−0.467774	+	0.883848i	$0.654944\pi$
$314$	−1.10709	−	0.804345i	−0.0624765	−	0.0453918i
$315$	2.01210	−	6.19261i	0.113369	−	0.348914i
$316$	0.326268	+	1.00415i	0.0183540	+	0.0564878i
$317$	−26.8077	+	19.4770i	−1.50567	+	1.09393i	−0.537620	+	0.843187i	$0.680676\pi$
$317$	−26.8077	+	19.4770i	−1.50567	+	1.09393i	−0.968053	+	0.250747i	$0.919324\pi$
$318$	−7.40564			−0.415288
$319$	6.64476	−	13.2333i	0.372035	−	0.740920i
$320$	−17.5832			−0.982933
$321$	0.249260	−	0.181098i	0.0139123	−	0.0101079i
$322$	−4.67605	−	14.3914i	−0.260586	−	0.802002i
$323$	−1.53330	+	4.71900i	−0.0853149	+	0.262572i
$324$	−0.194278	−	0.141151i	−0.0107932	−	0.00784173i
$325$	1.32837	+	0.965115i	0.0736845	+	0.0535350i
$326$	−8.93662	+	27.5041i	−0.494954	+	1.52331i
$327$	−5.74833	−	17.6915i	−0.317883	−	0.978344i
$328$	2.16483	−	1.57284i	0.119533	−	0.0868456i
$329$	7.67308			0.423031
$330$	−2.07572	−	12.6238i	−0.114265	−	0.694915i
$331$	25.4014			1.39619			0.698095	−	0.716005i	$-0.254031\pi$
$331$	25.4014			1.39619			0.698095	+	0.716005i	$0.254031\pi$
$332$	−2.79668	+	2.03190i	−0.153488	+	0.111515i
$333$	1.79363	+	5.52023i	0.0982904	+	0.302507i
$334$	−0.0613767	+	0.188898i	−0.00335838	+	0.0103360i
$335$	3.59167	+	2.60950i	0.196234	+	0.142572i
$336$	9.03974	+	6.56776i	0.493158	+	0.358301i
$337$	−6.33578	+	19.4995i	−0.345132	+	1.06221i	0.616381	+	0.787448i	$0.288598\pi$
$337$	−6.33578	+	19.4995i	−0.345132	+	1.06221i	−0.961513	+	0.274759i	$0.911402\pi$
$338$	−0.462509	−	1.42346i	−0.0251572	−	0.0774258i
$339$	−0.402117	+	0.292155i	−0.0218400	+	0.0158677i
$340$	−0.486962			−0.0264092
$341$	−20.1149	+	10.3988i	−1.08928	+	0.563126i
$342$	9.43843			0.510372
$343$	−15.5686	+	11.3112i	−0.840625	+	0.610750i
$344$	5.37440	+	16.5407i	0.289768	+	0.891815i
$345$	−3.18691	+	9.80830i	−0.171578	+	0.528061i
$346$	−20.5781	−	14.9509i	−1.10629	−	0.803764i
$347$	24.3865	+	17.7178i	1.30914	+	0.951143i	1.00000		0.000125173i	$3.98439e-5\pi$
$347$	24.3865	+	17.7178i	1.30914	+	0.951143i	0.309136	+	0.951018i	$0.399960\pi$
$348$	−0.331317	+	1.01969i	−0.0177604	+	0.0546610i
$349$	0.402163	+	1.23773i	0.0215273	+	0.0662542i	0.961243	−	0.275702i	$-0.0889104\pi$
$349$	0.402163	+	1.23773i	0.0215273	+	0.0662542i	−0.939716	+	0.341957i	$0.888910\pi$
$350$	−5.02314	+	3.64952i	−0.268498	+	0.195075i
$351$	1.00000			0.0533761
$352$	4.43087	+	0.675044i	0.236166	+	0.0359800i
$353$	−36.2892			−1.93148			−0.965741	−	0.259509i	$-0.916439\pi$
$353$	−36.2892			−1.93148			−0.965741	+	0.259509i	$0.916439\pi$
$354$	1.19502	−	0.868234i	0.0635147	−	0.0461461i
$355$	−5.59396	−	17.2164i	−0.296896	−	0.913753i
$356$	−0.943638	+	2.90422i	−0.0500127	+	0.153923i
$357$	−1.60827	−	1.16848i	−0.0851186	−	0.0618423i
$358$	−30.8521	−	22.4154i	−1.63058	−	1.18469i
$359$	−2.84294	+	8.74966i	−0.150044	+	0.461789i	−0.997625	−	0.0688772i	$-0.978058\pi$
$359$	−2.84294	+	8.74966i	−0.150044	+	0.461789i	0.847581	+	0.530667i	$0.178058\pi$
$360$	−2.09771	−	6.45609i	−0.110559	−	0.340266i
$361$	−16.8009	+	12.2066i	−0.884260	+	0.642452i
$362$	26.1730			1.37562
$363$	−0.129618	−	10.9992i	−0.00680318	−	0.577310i
$364$	0.606715			0.0318005
$365$	15.7627	−	11.4522i	0.825055	−	0.599438i
$366$	−4.38496	−	13.4955i	−0.229205	−	0.705422i
$367$	−10.0540	+	30.9430i	−0.524814	+	1.61521i	0.239870	+	0.970805i	$0.422895\pi$
$367$	−10.0540	+	30.9430i	−0.524814	+	1.61521i	−0.764684	+	0.644405i	$0.777105\pi$
$368$	−14.3178	−	10.4025i	−0.746367	−	0.542267i
$369$	0.821880	+	0.597131i	0.0427854	+	0.0310854i
$370$	6.91861	−	21.2933i	0.359681	−	1.10698i
$371$	3.86302	+	11.8891i	0.200558	+	0.617254i
$372$	1.32641	−	0.963692i	0.0687711	−	0.0499651i
$373$	22.7456			1.17772			0.588862	−	0.808234i	$-0.299576\pi$
$373$	22.7456			1.17772			0.588862	+	0.808234i	$0.299576\pi$
$374$	−3.86130	−	0.588270i	−0.199663	−	0.0304187i
$375$	−8.65436			−0.446909
$376$	6.47178	−	4.70202i	0.333757	−	0.242488i
$377$	−1.37968	−	4.24621i	−0.0710570	−	0.218691i
$378$	−1.16853	+	3.59636i	−0.0601026	+	0.184977i
$379$	8.26267	+	6.00318i	0.424425	+	0.308363i	0.779416	−	0.626507i	$-0.215516\pi$
$379$	8.26267	+	6.00318i	0.424425	+	0.308363i	−0.354991	+	0.934870i	$0.615516\pi$
$380$	−3.15743	−	2.29400i	−0.161973	−	0.117680i
$381$	−5.42916	+	16.7092i	−0.278144	+	0.856040i
$382$	12.3648	+	38.0548i	0.632636	+	1.94705i
$383$	−14.6436	+	10.6392i	−0.748252	+	0.543637i	−0.895284	−	0.445495i	$-0.853028\pi$
$383$	−14.6436	+	10.6392i	−0.748252	+	0.543637i	0.147033	+	0.989132i	$0.453028\pi$
$384$	12.9142			0.659026
$385$	−19.1837	+	9.91736i	−0.977689	+	0.505435i
$386$	3.15404			0.160536
$387$	−5.34182	+	3.88106i	−0.271540	+	0.197285i
$388$	0.796186	+	2.45041i	0.0404202	+	0.124401i
$389$	2.47817	−	7.62701i	0.125648	−	0.386705i	−0.868371	−	0.495916i	$-0.834832\pi$
$389$	2.47817	−	7.62701i	0.125648	−	0.386705i	0.994019	+	0.109211i	$0.0348324\pi$
$390$	−3.12064	−	2.26727i	−0.158020	−	0.114808i
$391$	2.54729	+	1.85072i	0.128822	+	0.0935948i
$392$	−0.502039	+	1.54512i	−0.0253568	+	0.0780402i
$393$	−1.21163	−	3.72901i	−0.0611186	−	0.188104i
$394$	−6.31645	+	4.58917i	−0.318218	+	0.231199i
$395$	−11.3312			−0.570133
$396$	0.129226	+	0.785903i	0.00649384	+	0.0394931i
$397$	−25.1675			−1.26312			−0.631560	−	0.775327i	$-0.717585\pi$
$397$	−25.1675			−1.26312			−0.631560	+	0.775327i	$0.717585\pi$
$398$	2.23124	−	1.62109i	0.111842	−	0.0812578i
$399$	−4.92339	−	15.1526i	−0.246478	−	0.758580i
$400$	−2.24399	+	6.90631i	−0.112200	+	0.345315i
$401$	1.25845	+	0.914315i	0.0628438	+	0.0456587i	0.618764	−	0.785577i	$-0.287634\pi$
$401$	1.25845	+	0.914315i	0.0628438	+	0.0456587i	−0.555920	+	0.831236i	$0.687634\pi$
$402$	−2.08586	−	1.51547i	−0.104033	−	0.0755847i
$403$	−2.10978	+	6.49322i	−0.105095	+	0.323451i
$404$	0.667251	+	2.05359i	0.0331970	+	0.102170i
$405$	2.08500	−	1.51484i	0.103604	−	0.0752730i
$406$	16.8831			0.837895
$407$	8.63843	−	17.2037i	0.428191	−	0.852756i
$408$	−2.07251			−0.102605
$409$	23.5517	−	17.1113i	1.16456	−	0.846099i	0.174209	−	0.984709i	$-0.444263\pi$
$409$	23.5517	−	17.1113i	1.16456	−	0.846099i	0.990347	+	0.138610i	$0.0442633\pi$
$410$	−1.21093	−	3.72685i	−0.0598035	−	0.184056i
$411$	1.88201	−	5.79224i	0.0928329	−	0.285710i
$412$	2.33193	+	1.69425i	0.114886	+	0.0834697i
$413$	−2.01724	−	1.46561i	−0.0992619	−	0.0721180i
$414$	1.85080	−	5.69618i	0.0909619	−	0.279952i
$415$	−11.4643	−	35.2836i	−0.562762	−	1.73200i
$416$	1.09328	−	0.794316i	0.0536026	−	0.0389446i
$417$	−22.2078			−1.08752
$418$	−22.2651	−	22.0043i	−1.08902	−	1.07626i
$419$	−34.6970			−1.69506			−0.847529	−	0.530749i	$-0.821911\pi$
$419$	−34.6970			−1.69506			−0.847529	+	0.530749i	$0.821911\pi$
$420$	1.26500	−	0.919076i	0.0617257	−	0.0448463i
$421$	6.76690	+	20.8264i	0.329799	+	1.01502i	0.969228	+	0.246166i	$0.0791707\pi$
$421$	6.76690	+	20.8264i	0.329799	+	1.01502i	−0.639429	+	0.768850i	$0.720829\pi$
$422$	3.44539	−	10.6038i	0.167719	−	0.516186i
$423$	2.45702	+	1.78513i	0.119464	+	0.0867959i
$424$	10.5438	+	7.66054i	0.512053	+	0.372029i
$425$	0.399231	−	1.22871i	0.0193656	−	0.0596011i
$426$	3.24869	+	9.99845i	0.157400	+	0.484427i
$427$	−19.3786	+	14.0794i	−0.937797	+	0.681349i
$428$	0.0739879			0.00357634
$429$	−2.35898	−	2.33135i	−0.113893	−	0.112559i
$430$	25.4693			1.22824
$431$	29.8366	−	21.6775i	1.43718	−	1.04417i	0.448554	−	0.893756i	$-0.351939\pi$
$431$	29.8366	−	21.6775i	1.43718	−	1.04417i	0.988623	−	0.150415i	$-0.0480609\pi$
$432$	1.36666	+	4.20616i	0.0657536	+	0.202369i
$433$	−0.535787	+	1.64898i	−0.0257483	+	0.0792451i	−0.963105	−	0.269126i	$-0.913265\pi$
$433$	−0.535787	+	1.64898i	−0.0257483	+	0.0792451i	0.937357	+	0.348371i	$0.113265\pi$
$434$	−20.8867	−	15.1750i	−1.00259	−	0.728425i
$435$	−9.30895	−	6.76335i	−0.446330	−	0.324278i
$436$	1.38041	−	4.24845i	0.0661095	−	0.203464i
$437$	7.79801	+	23.9998i	0.373030	+	1.14807i
$438$	−9.15418	+	6.65090i	−0.437404	+	0.317792i
$439$	17.1581			0.818912			0.409456	−	0.912330i	$-0.365719\pi$
$439$	17.1581			0.818912			0.409456	+	0.912330i	$0.365719\pi$
$440$	−10.1029	+	20.1203i	−0.481639	+	0.959199i
$441$	−0.616793			−0.0293711
$442$	−0.952746	+	0.692210i	−0.0453175	+	0.0329251i
$443$	−2.84288	−	8.74947i	−0.135069	−	0.415700i	0.860532	−	0.509397i	$-0.170132\pi$
$443$	−2.84288	−	8.74947i	−0.135069	−	0.415700i	−0.995601	+	0.0936970i	$0.970132\pi$
$444$	−0.430724	+	1.32563i	−0.0204412	+	0.0629117i
$445$	−26.5132	−	19.2630i	−1.25685	−	0.913154i
$446$	16.9082	+	12.2845i	0.800625	+	0.581688i
$447$	0.339292	−	1.04423i	0.0160479	−	0.0493905i
$448$	−5.32663	−	16.3937i	−0.251660	−	0.774529i
$449$	12.7423	−	9.25785i	0.601348	−	0.436905i	−0.245009	−	0.969521i	$-0.578791\pi$
$449$	12.7423	−	9.25785i	0.601348	−	0.436905i	0.846357	+	0.532616i	$0.178791\pi$
$450$	−2.45753			−0.115849
$451$	−0.546682	−	3.32471i	−0.0257422	−	0.156555i
$452$	−0.119360			−0.00561424
$453$	10.1360	−	7.36425i	0.476232	−	0.346003i
$454$	2.61915	+	8.06090i	0.122923	+	0.378317i
$455$	−2.01210	+	6.19261i	−0.0943287	+	0.290314i
$456$	−13.4380	−	9.76329i	−0.629293	−	0.457208i
$457$	−27.6474	−	20.0870i	−1.29329	−	0.939632i	−0.293426	−	0.955982i	$-0.594795\pi$
$457$	−27.6474	−	20.0870i	−1.29329	−	0.939632i	−0.999866	+	0.0163504i	$0.994795\pi$
$458$	7.64982	−	23.5437i	0.357453	−	1.10013i
$459$	−0.243144	−	0.748321i	−0.0113490	−	0.0349286i
$460$	−2.00360	+	1.45570i	−0.0934183	+	0.0678724i
$461$	−1.31549			−0.0612686			−0.0306343	−	0.999531i	$-0.509753\pi$
$461$	−1.31549			−0.0612686			−0.0306343	+	0.999531i	$0.509753\pi$
$462$	11.1409	−	5.75951i	0.518322	−	0.267957i
$463$	−18.4328			−0.856645			−0.428323	−	0.903626i	$-0.640895\pi$
$463$	−18.4328			−0.856645			−0.428323	+	0.903626i	$0.640895\pi$
$464$	15.9747	−	11.6063i	0.741605	−	0.538808i
$465$	5.43731	+	16.7343i	0.252149	+	0.776036i
$466$	−12.7460	+	39.2283i	−0.590449	+	1.81721i
$467$	−21.1961	−	15.3999i	−0.980841	−	0.712622i	−0.0229443	−	0.999737i	$-0.507304\pi$
$467$	−21.1961	−	15.3999i	−0.980841	−	0.712622i	−0.957896	+	0.287114i	$0.907304\pi$
$468$	0.194278	+	0.141151i	0.00898050	+	0.00652471i
$469$	−1.34491	+	4.13920i	−0.0621021	+	0.191131i
$470$	−3.62008	−	11.1415i	−0.166982	−	0.513917i
$471$	−0.739680	+	0.537409i	−0.0340826	+	0.0247625i
$472$	−2.59954			−0.119653
$473$	21.6494	+	3.29829i	0.995440	+	0.151656i
$474$	6.58058			0.302256
$475$	8.37684	−	6.08613i	0.384356	−	0.279251i
$476$	−0.147519	−	0.454018i	−0.00676154	−	0.0208099i
$477$	−1.52900	+	4.70578i	−0.0700081	+	0.215463i
$478$	−5.74442	−	4.17357i	−0.262744	−	0.190895i
$479$	−21.2370	−	15.4296i	−0.970343	−	0.704995i	−0.0148130	−	0.999890i	$-0.504715\pi$
$479$	−21.2370	−	15.4296i	−0.970343	−	0.704995i	−0.955530	+	0.294895i	$0.904715\pi$
$480$	1.07623	−	3.31230i	0.0491230	−	0.151185i
$481$	−1.79363	−	5.52023i	−0.0817825	−	0.251701i
$482$	−2.32237	+	1.68730i	−0.105781	+	0.0768544i
$483$	−10.1102			−0.460029
$484$	1.52737	−	2.15520i	0.0694260	−	0.0979638i
$485$	−27.6512			−1.25558
$486$	−1.21086	+	0.879744i	−0.0549259	+	0.0399060i
$487$	6.40981	+	19.7274i	0.290456	+	0.893932i	0.984710	+	0.174202i	$0.0557346\pi$
$487$	6.40981	+	19.7274i	0.290456	+	0.893932i	−0.694254	+	0.719730i	$0.744265\pi$
$488$	−7.71691	+	23.7502i	−0.349328	+	1.07512i
$489$	15.6319	+	11.3572i	0.706898	+	0.513591i
$490$	1.92479	+	1.39844i	0.0869530	+	0.0631750i
$491$	−2.55768	+	7.87173i	−0.115426	+	0.355246i	−0.992036	−	0.125957i	$-0.959800\pi$
$491$	−2.55768	+	7.87173i	−0.115426	+	0.355246i	0.876609	+	0.481203i	$0.159800\pi$
$492$	0.0753874	+	0.232018i	0.00339873	+	0.0104602i
$493$	−2.84207	+	2.06488i	−0.128000	+	0.0929977i
$494$	−9.43843			−0.424655
$495$	−8.45010	−	1.28738i	−0.379804	−	0.0578632i
$496$	−30.1949			−1.35579
$497$	14.3571	−	10.4310i	0.644003	−	0.467895i
$498$	6.65793	+	20.4910i	0.298349	+	0.918223i
$499$	−10.5136	+	32.3576i	−0.470654	+	1.44852i	0.381076	+	0.924544i	$0.375554\pi$
$499$	−10.5136	+	32.3576i	−0.470654	+	1.44852i	−0.851730	+	0.523981i	$0.824446\pi$
$500$	−1.68135	−	1.22157i	−0.0751922	−	0.0546304i
$501$	0.107360	+	0.0780013i	0.00479647	+	0.00348484i
$502$	−6.20470	+	19.0961i	−0.276930	+	0.852301i
$503$	−0.938272	−	2.88771i	−0.0418355	−	0.128756i	0.927957	−	0.372686i	$-0.121563\pi$
$503$	−0.938272	−	2.88771i	−0.0418355	−	0.128756i	−0.969793	+	0.243930i	$0.921563\pi$
$504$	5.38385	−	3.91159i	0.239816	−	0.174236i
$505$	−23.1734			−1.03120
$506$	−17.6458	+	9.12234i	−0.784451	+	0.405537i
$507$	−1.00000			−0.0444116
$508$	−3.41329	+	2.47990i	−0.151440	+	0.110028i
$509$	6.32076	+	19.4533i	0.280163	+	0.862252i	0.987807	+	0.155683i	$0.0497579\pi$
$509$	6.32076	+	19.4533i	0.280163	+	0.862252i	−0.707644	+	0.706569i	$0.750242\pi$
$510$	−0.937885	+	2.88651i	−0.0415302	+	0.127817i
$511$	15.4526	+	11.2270i	0.683582	+	0.496652i
$512$	−14.0136	−	10.1815i	−0.619318	−	0.449961i
$513$	1.94870	−	5.99747i	0.0860371	−	0.264795i
$514$	−1.99267	−	6.13280i	−0.0878928	−	0.270506i
$515$	−25.0264	+	18.1828i	−1.10280	+	0.801228i
$516$	−1.58561			−0.0698028
$517$	−1.63431	−	9.93925i	−0.0718769	−	0.437128i
$518$	21.9486			0.964368
$519$	−13.7489	+	9.98916i	−0.603510	+	0.438476i
$520$	2.09771	+	6.45609i	0.0919908	+	0.283118i
$521$	7.24433	−	22.2958i	0.317380	−	0.976795i	−0.657384	−	0.753556i	$-0.728337\pi$
$521$	7.24433	−	22.2958i	0.317380	−	0.976795i	0.974764	−	0.223239i	$-0.0716630\pi$
$522$	5.40618	+	3.92782i	0.236622	+	0.171916i
$523$	−22.3314	−	16.2247i	−0.976485	−	0.709458i	−0.0195649	−	0.999809i	$-0.506228\pi$
$523$	−22.3314	−	16.2247i	−0.976485	−	0.709458i	−0.956920	+	0.290351i	$0.906228\pi$
$524$	0.290962	−	0.895488i	0.0127107	−	0.0391196i
$525$	1.28192	+	3.94536i	0.0559478	+	0.172189i
$526$	29.1601	−	21.1860i	1.27144	−	0.923755i
$527$	5.37200			0.234008
$528$	6.58208	−	13.1084i	0.286448	−	0.570471i
$529$	−6.98675			−0.303772
$530$	15.4407	−	11.2184i	0.670703	−	0.487294i
$531$	−0.304974	−	0.938613i	−0.0132347	−	0.0407323i
$532$	1.18230	−	3.63876i	0.0512594	−	0.157760i
$533$	−0.821880	−	0.597131i	−0.0355996	−	0.0258646i
$534$	15.3976	+	11.1870i	0.666319	+	0.484109i
$535$	−0.245372	+	0.755178i	−0.0106084	+	0.0326492i
$536$	1.40213	+	4.31532i	0.0605628	+	0.186393i
$537$	−20.6133	+	14.9764i	−0.889528	+	0.646280i
$538$	37.3347			1.60961
$539$	1.45501	+	1.43796i	0.0626715	+	0.0619373i
$540$	0.618890			0.0266328
$541$	8.69559	−	6.31771i	0.373853	−	0.271620i	−0.384954	−	0.922936i	$-0.625783\pi$
$541$	8.69559	−	6.31771i	0.373853	−	0.271620i	0.758807	+	0.651316i	$0.225783\pi$
$542$	−10.5110	−	32.3496i	−0.451487	−	1.38954i
$543$	5.40379	−	16.6312i	0.231899	−	0.713712i
$544$	−0.860229	−	0.624993i	−0.0368820	−	0.0267964i
$545$	38.7851	+	28.1790i	1.66137	+	1.20706i
$546$	1.16853	−	3.59636i	0.0500084	−	0.153910i
$547$	12.3897	+	38.1315i	0.529745	+	1.63039i	0.754738	+	0.656026i	$0.227764\pi$
$547$	12.3897	+	38.1315i	0.529745	+	1.63039i	−0.224993	+	0.974360i	$0.572236\pi$
$548$	1.18321	−	0.859656i	0.0505444	−	0.0367227i
$549$	−9.48081			−0.404631
$550$	5.79727	+	5.72935i	0.247196	+	0.244300i
$551$	−28.1551			−1.19945
$552$	−8.52733	+	6.19547i	−0.362947	+	0.263697i
$553$	−3.43264	−	10.5646i	−0.145971	−	0.449252i
$554$	9.87778	−	30.4007i	0.419667	−	1.29160i
$555$	−12.1020	−	8.79260i	−0.513700	−	0.373225i
$556$	−4.31448	−	3.13466i	−0.182975	−	0.132939i
$557$	−3.24879	+	9.99875i	−0.137656	+	0.423661i	−0.995994	−	0.0894241i	$-0.971497\pi$
$557$	−3.24879	+	9.99875i	−0.137656	+	0.423661i	0.858338	+	0.513085i	$0.171497\pi$
$558$	−3.15772	−	9.71847i	−0.133677	−	0.411416i
$559$	5.34182	−	3.88106i	0.225935	−	0.164151i
$560$	−28.7969			−1.21689
$561$	−1.17102	+	2.33213i	−0.0494407	+	0.0984627i
$562$	48.1192			2.02979
$563$	12.5032	−	9.08408i	0.526945	−	0.382848i	−0.292269	−	0.956336i	$-0.594410\pi$
$563$	12.5032	−	9.08408i	0.526945	−	0.382848i	0.819214	+	0.573488i	$0.194410\pi$
$564$	0.225371	+	0.693621i	0.00948984	+	0.0292067i
$565$	0.395845	−	1.21828i	0.0166533	−	0.0512536i
$566$	−16.8495	−	12.2418i	−0.708236	−	0.514563i
$567$	2.04398	+	1.48504i	0.0858392	+	0.0623658i
$568$	5.71724	−	17.5959i	0.239890	−	0.738306i
$569$	0.962449	+	2.96211i	0.0403480	+	0.124178i	0.969202	−	0.246269i	$-0.0792045\pi$
$569$	0.962449	+	2.96211i	0.0403480	+	0.124178i	−0.928854	+	0.370447i	$0.879205\pi$
$570$	−19.6791	+	14.2977i	−0.824267	+	0.598865i
$571$	19.5964			0.820083			0.410041	−	0.912067i	$-0.365514\pi$
$571$	19.5964			0.820083			0.410041	+	0.912067i	$0.365514\pi$
$572$	−0.129226	−	0.785903i	−0.00540321	−	0.0328603i
$573$	26.7341			1.11683
$574$	3.10789	−	2.25801i	0.129721	−	0.0942476i
$575$	−2.03040	−	6.24894i	−0.0846737	−	0.260599i
$576$	2.10830	−	6.48869i	0.0878460	−	0.270362i
$577$	15.6484	+	11.3692i	0.651450	+	0.473306i	0.863765	−	0.503895i	$-0.168100\pi$
$577$	15.6484	+	11.3692i	0.651450	+	0.473306i	−0.212315	+	0.977201i	$0.568100\pi$
$578$	−19.8350	−	14.4110i	−0.825029	−	0.599418i
$579$	0.651196	−	2.00418i	0.0270628	−	0.0832907i
$580$	−0.853869	−	2.62794i	−0.0354550	−	0.109119i
$581$	29.4236	−	21.3775i	1.22070	−	0.886888i
$582$	16.0585			0.665645
$583$	14.5777	−	7.53622i	0.603746	−	0.312118i
$584$	19.9131			0.824011
$585$	−2.08500	+	1.51484i	−0.0862040	+	0.0626309i
$586$	8.77067	+	26.9933i	0.362313	+	1.11508i
$587$	10.8912	−	33.5197i	0.449529	−	1.38351i	−0.427911	−	0.903821i	$-0.640750\pi$
$587$	10.8912	−	33.5197i	0.449529	−	1.38351i	0.877440	−	0.479687i	$-0.159250\pi$
$588$	−0.119829	−	0.0870610i	−0.00494167	−	0.00359034i
$589$	34.8316	+	25.3067i	1.43521	+	1.04274i
$590$	−1.17638	+	3.62053i	−0.0484309	+	0.149055i
$591$	1.61198	+	4.96117i	0.0663080	+	0.204075i
$592$	20.7677	−	15.0886i	0.853545	−	0.620137i
$593$	−46.9684			−1.92876			−0.964381	−	0.264517i	$-0.914788\pi$
$593$	−46.9684			−1.92876			−0.964381	+	0.264517i	$0.914788\pi$
$594$	4.90740	+	0.747644i	0.201353	+	0.0306762i
$595$	5.12329			0.210034
$596$	0.213311	−	0.154980i	0.00873757	−	0.00634822i
$597$	−0.569420	−	1.75249i	−0.0233048	−	0.0717248i
$598$	−1.85080	+	5.69618i	−0.0756849	+	0.232934i
$599$	1.22277	+	0.888395i	0.0499611	+	0.0362988i	0.612486	−	0.790482i	$-0.290170\pi$
$599$	1.22277	+	0.888395i	0.0499611	+	0.0362988i	−0.562524	+	0.826781i	$0.690170\pi$
$600$	3.49892	+	2.54211i	0.142843	+	0.103781i
$601$	−1.50614	+	4.63543i	−0.0614369	+	0.189083i	−0.977064	−	0.212945i	$-0.931695\pi$
$601$	−1.50614	+	4.63543i	−0.0614369	+	0.189083i	0.915627	+	0.402028i	$0.131695\pi$
$602$	7.71563	+	23.7463i	0.314466	+	0.967825i
$603$	−1.39363	+	1.01253i	−0.0567531	+	0.0412336i
$604$	3.00868			0.122421
$605$	16.9323	+	22.7370i	0.688397	+	0.924392i
$606$	13.4579			0.546692
$607$	38.6199	−	28.0590i	1.56753	−	1.13888i	0.638060	−	0.769986i	$-0.279737\pi$
$607$	38.6199	−	28.0590i	1.56753	−	1.13888i	0.929472	−	0.368892i	$-0.120263\pi$
$608$	−2.63341	−	8.10482i	−0.106799	−	0.328694i
$609$	3.48576	−	10.7281i	0.141250	−	0.434723i
$610$	29.5862	+	21.4956i	1.19791	+	0.870332i
$611$	−2.45702	−	1.78513i	−0.0994003	−	0.0722185i
$612$	0.0583888	−	0.179702i	0.00236023	−	0.00726403i
$613$	14.1056	+	43.4124i	0.569718	+	1.75341i	0.653498	+	0.756928i	$0.273301\pi$
$613$	14.1056	+	43.4124i	0.569718	+	1.75341i	−0.0837800	+	0.996484i	$0.526699\pi$
$614$	−22.7971	+	16.5630i	−0.920015	+	0.668430i
$615$	−2.61817			−0.105575
$616$	−21.8197	−	3.32424i	−0.879141	−	0.133937i
$617$	38.3854			1.54534			0.772668	−	0.634810i	$-0.218922\pi$
$617$	38.3854			1.54534			0.772668	+	0.634810i	$0.218922\pi$
$618$	14.5341	−	10.5596i	0.584648	−	0.424771i
$619$	−4.11630	−	12.6687i	−0.165448	−	0.509196i	0.833621	−	0.552337i	$-0.186264\pi$
$619$	−4.11630	−	12.6687i	−0.165448	−	0.509196i	−0.999069	+	0.0431404i	$0.986264\pi$
$620$	−1.30572	+	4.01859i	−0.0524390	+	0.161391i
$621$	−3.23741	−	2.35211i	−0.129913	−	0.0943871i
$622$	6.76035	+	4.91168i	0.271065	+	0.196940i
$623$	9.92794	−	30.5551i	0.397755	−	1.22416i
$624$	−1.36666	−	4.20616i	−0.0547103	−	0.168381i
$625$	24.6861	−	17.9355i	0.987446	−	0.717421i
$626$	7.47125			0.298611
$627$	−18.5792	+	9.60485i	−0.741980	+	0.383581i
$628$	−0.219559			−0.00876137
$629$	−3.69479	+	2.68442i	−0.147321	+	0.107035i
$630$	−3.01153	−	9.26854i	−0.119982	−	0.369267i
$631$	−10.0808	+	31.0256i	−0.401311	+	1.23511i	0.522625	+	0.852563i	$0.324953\pi$
$631$	−10.0808	+	31.0256i	−0.401311	+	1.23511i	−0.923936	+	0.382546i	$0.875047\pi$
$632$	−9.36914	−	6.80708i	−0.372684	−	0.270771i
$633$	−6.02665	−	4.37862i	−0.239538	−	0.174035i
$634$	−15.3258	+	47.1679i	−0.608664	+	1.87328i
$635$	−13.9920	−	43.0630i	−0.555257	−	1.70890i
$636$	−0.961276	+	0.698408i	−0.0381171	+	0.0276937i
$637$	0.616793			0.0244382
$638$	−3.59598	−	21.8694i	−0.142366	−	0.865816i
$639$	7.02407			0.277868
$640$	−26.9261	+	19.5630i	−1.06435	+	0.773294i
$641$	−8.68835	−	26.7400i	−0.343169	−	1.05617i	−0.962557	−	0.271081i	$-0.912619\pi$
$641$	−8.68835	−	26.7400i	−0.343169	−	1.05617i	0.619388	−	0.785085i	$-0.287381\pi$
$642$	0.142500	−	0.438570i	0.00562403	−	0.0173090i
$643$	6.06096	+	4.40355i	0.239021	+	0.173659i	0.700847	−	0.713312i	$-0.252806\pi$
$643$	6.06096	+	4.40355i	0.239021	+	0.173659i	−0.461826	+	0.886971i	$0.652806\pi$
$644$	−1.96419	−	1.42706i	−0.0773997	−	0.0562342i
$645$	5.25850	−	16.1840i	0.207053	−	0.637245i
$646$	2.29490	+	7.06297i	0.0902916	+	0.277889i
$647$	17.8456	−	12.9656i	0.701584	−	0.509731i	−0.178864	−	0.983874i	$-0.557242\pi$
$647$	17.8456	−	12.9656i	0.701584	−	0.509731i	0.880448	+	0.474143i	$0.157242\pi$
$648$	2.63400			0.103473
$649$	−1.46881	+	2.92518i	−0.0576557	+	0.114823i
$650$	2.45753			0.0963921
$651$	−13.9550	+	10.1389i	−0.546941	+	0.397376i
$652$	1.43384	+	4.41291i	0.0561536	+	0.172823i
$653$	0.341741	−	1.05177i	0.0133733	−	0.0411589i	−0.944147	−	0.329524i	$-0.893112\pi$
$653$	0.341741	−	1.05177i	0.0133733	−	0.0411589i	0.957521	+	0.288365i	$0.0931117\pi$
$654$	−22.5245	−	16.3650i	−0.880776	−	0.639921i
$655$	8.17510	+	5.93956i	0.319428	+	0.232078i
$656$	1.38839	−	4.27303i	0.0542076	−	0.166834i
$657$	2.33618	+	7.19003i	0.0911431	+	0.280510i
$658$	9.29106	−	6.75035i	0.362203	−	0.263156i
$659$	−13.9168			−0.542120			−0.271060	−	0.962562i	$-0.587374\pi$
$659$	−13.9168			−0.542120			−0.271060	+	0.962562i	$0.587374\pi$
$660$	−1.45995	−	1.44285i	−0.0568286	−	0.0561628i
$661$	19.8349			0.771490			0.385745	−	0.922605i	$-0.373944\pi$
$661$	19.8349			0.771490			0.385745	+	0.922605i	$0.373944\pi$
$662$	30.7577	−	22.3468i	1.19543	−	0.868532i
$663$	0.243144	+	0.748321i	0.00944294	+	0.0290624i
$664$	11.7170	−	36.0613i	0.454708	−	1.39945i
$665$	33.2190	+	24.1350i	1.28818	+	0.935917i
$666$	7.02823	+	5.10631i	0.272338	+	0.197865i
$667$	−5.52099	+	16.9919i	−0.213774	+	0.657928i
$668$	0.00984762	+	0.0303079i	0.000381016	+	0.00117265i
$669$	11.2969	−	8.20767i	0.436763	−	0.317327i
$670$	6.64471			0.256708
$671$	22.3651	+	22.1031i	0.863395	+	0.853280i
$672$	3.41424			0.131707
$673$	2.45143	−	1.78107i	0.0944958	−	0.0686552i	−0.539534	−	0.841964i	$-0.681400\pi$
$673$	2.45143	−	1.78107i	0.0944958	−	0.0686552i	0.634030	+	0.773309i	$0.281400\pi$
$674$	9.48282	+	29.1851i	0.365265	+	1.12417i
$675$	−0.507391	+	1.56159i	−0.0195295	+	0.0601056i
$676$	−0.194278	−	0.141151i	−0.00747222	−	0.00542889i
$677$	−15.7011	−	11.4075i	−0.603442	−	0.438427i	0.243657	−	0.969862i	$-0.421653\pi$
$677$	−15.7011	−	11.4075i	−0.603442	−	0.438427i	−0.847099	+	0.531435i	$0.821653\pi$
$678$	−0.229887	+	0.707520i	−0.00882876	+	0.0271721i
$679$	−8.37661	−	25.7806i	−0.321465	−	0.989367i
$680$	4.32118	−	3.13952i	0.165710	−	0.120395i
$681$	5.66291			0.217003
$682$	−15.2081	+	30.2875i	−0.582350	+	1.15977i
$683$	41.2470			1.57827			0.789135	−	0.614219i	$-0.210529\pi$
$683$	41.2470			1.57827			0.789135	+	0.614219i	$0.210529\pi$
$684$	1.22514	−	0.890115i	0.0468443	−	0.0340344i
$685$	4.85032	+	14.9278i	0.185321	+	0.570360i
$686$	−8.90044	+	27.3927i	−0.339820	+	1.04586i
$687$	−13.3810	−	9.72188i	−0.510518	−	0.370913i
$688$	23.6248	+	17.1644i	0.900688	+	0.654388i
$689$	1.52900	−	4.70578i	0.0582502	−	0.179276i
$690$	4.76988	+	14.6802i	0.181586	+	0.558865i
$691$	−26.3668	+	19.1566i	−1.00304	+	0.728751i	−0.962738	−	0.270437i	$-0.912832\pi$
$691$	−26.3668	+	19.1566i	−1.00304	+	0.728751i	−0.0403018	+	0.999188i	$0.512832\pi$
$692$	−4.08109			−0.155140
$693$	−1.35958	−	8.26842i	−0.0516460	−	0.314091i
$694$	45.1159			1.71258
$695$	46.3032	−	33.6413i	1.75638	−	1.27609i
$696$	−3.63407	−	11.1845i	−0.137749	−	0.423948i
$697$	−0.247010	+	0.760219i	−0.00935617	+	0.0287953i
$698$	1.57585	+	1.14492i	0.0596468	+	0.0433359i
$699$	22.2953	+	16.1985i	0.843285	+	0.612682i
$700$	−0.307842	+	0.947440i	−0.0116353	+	0.0358099i
$701$	−1.46314	−	4.50308i	−0.0552620	−	0.170079i	0.919616	−	0.392819i	$-0.128500\pi$
$701$	−1.46314	−	4.50308i	−0.0552620	−	0.170079i	−0.974878	+	0.222740i	$0.928500\pi$
$702$	1.21086	−	0.879744i	0.0457011	−	0.0332038i
$703$	−36.6027			−1.38050
$704$	−20.1009	+	10.3915i	−0.757580	+	0.391646i
$705$	−7.82705			−0.294784
$706$	−43.9413	+	31.9252i	−1.65375	+	1.20152i
$707$	−7.02009	−	21.6056i	−0.264018	−	0.812563i
$708$	0.0732366	−	0.225399i	0.00275240	−	0.00847102i
$709$	−28.4917	−	20.7004i	−1.07003	−	0.777420i	−0.0941103	−	0.995562i	$-0.530001\pi$
$709$	−28.4917	−	20.7004i	−1.07003	−	0.777420i	−0.975917	+	0.218141i	$0.930001\pi$
$710$	−21.9196	−	15.9255i	−0.822627	−	0.597673i
$711$	1.35865	−	4.18151i	0.0509535	−	0.156819i
$712$	−10.3504	−	31.8551i	−0.387896	−	1.19382i
$713$	22.1030	−	16.0588i	0.827764	−	0.601406i
$714$	−2.97536			−0.111350
$715$	8.45010	+	1.28738i	0.316016	+	0.0481451i
$716$	−6.11864			−0.228664
$717$	−3.83803	+	2.78850i	−0.143334	+	0.104138i
$718$	4.25505	+	13.0957i	0.158797	+	0.488727i
$719$	−3.10717	+	9.56287i	−0.115878	+	0.356635i	−0.992129	−	0.125219i	$-0.960037\pi$
$719$	−3.10717	+	9.56287i	−0.115878	+	0.356635i	0.876251	+	0.481854i	$0.160037\pi$
$720$	−9.22114	−	6.69955i	−0.343652	−	0.249677i
$721$	−24.5341	−	17.8251i	−0.913698	−	0.663840i
$722$	−9.60497	+	29.5611i	−0.357460	+	1.10015i
$723$	0.592677	+	1.82407i	0.0220419	+	0.0678380i
$724$	3.39734	−	2.46832i	0.126261	−	0.0917342i
$725$	7.33087			0.272262
$726$	−9.83346	−	13.2045i	−0.364954	−	0.490067i
$727$	18.5456			0.687817			0.343909	−	0.939003i	$-0.388249\pi$
$727$	18.5456			0.687817			0.343909	+	0.939003i	$0.388249\pi$
$728$	−5.38385	+	3.91159i	−0.199539	+	0.144973i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	9.01139	−	27.7342i	0.333527	−	1.02649i
$731$	−4.20311	−	3.05374i	−0.155458	−	0.112947i
$732$	−1.84191	−	1.33823i	−0.0680790	−	0.0494623i
$733$	−2.72093	+	8.37416i	−0.100500	+	0.309307i	−0.988648	−	0.150251i	$-0.951992\pi$
$733$	−2.72093	+	8.37416i	−0.100500	+	0.309307i	0.888148	+	0.459557i	$0.151992\pi$
$734$	15.0479	+	46.3127i	0.555428	+	1.70943i
$735$	1.28601	−	0.934342i	0.0474353	−	0.0344637i
$736$	−5.40772			−0.199331
$737$	5.64813	+	0.860494i	0.208051	+	0.0316967i
$738$	1.52051			0.0559706
$739$	0.243954	−	0.177243i	0.00897398	−	0.00651998i	−0.583289	−	0.812265i	$-0.698235\pi$
$739$	0.243954	−	0.177243i	0.00897398	−	0.00651998i	0.592263	+	0.805745i	$0.298235\pi$
$740$	−1.11006	−	3.41641i	−0.0408066	−	0.125590i
$741$	−1.94870	+	5.99747i	−0.0715872	+	0.220323i
$742$	15.1370	+	10.9977i	0.555697	+	0.403737i
$743$	−4.67561	−	3.39703i	−0.171531	−	0.124625i	0.498707	−	0.866770i	$-0.333808\pi$
$743$	−4.67561	−	3.39703i	−0.171531	−	0.124625i	−0.670239	+	0.742146i	$0.733808\pi$
$744$	−5.55715	+	17.1031i	−0.203735	+	0.627032i
$745$	0.874422	+	2.69119i	0.0320363	+	0.0985977i
$746$	27.5419	−	20.0103i	1.00838	−	0.732630i
$747$	14.3952			0.526694
$748$	−0.556687	+	0.287790i	−0.0203545	+	0.0105227i
$749$	−0.778421			−0.0284429
$750$	−10.4792	+	7.61362i	−0.382648	+	0.278010i
$751$	5.19207	+	15.9796i	0.189461	+	0.583102i	0.999997	−	0.00258759i	$-0.000823656\pi$
$751$	5.19207	+	15.9796i	0.189461	+	0.583102i	−0.810535	+	0.585690i	$0.800824\pi$
$752$	4.15061	−	12.7743i	0.151357	−	0.465829i
$753$	10.8532	+	7.88533i	0.395513	+	0.287357i
$754$	−5.40618	−	3.92782i	−0.196881	−	0.143043i
$755$	−9.97793	+	30.7089i	−0.363134	+	1.11761i
$756$	0.187485	+	0.577021i	0.00681878	+	0.0209860i
$757$	−22.8984	+	16.6366i	−0.832255	+	0.604669i	−0.920196	−	0.391457i	$-0.871971\pi$
$757$	−22.8984	+	16.6366i	−0.832255	+	0.604669i	0.0879412	+	0.996126i	$0.471971\pi$
$758$	15.2862			0.555221
$759$	2.15339	+	13.0961i	0.0781633	+	0.475359i
$760$	42.8081			1.55281
$761$	−6.88215	+	5.00017i	−0.249478	+	0.181256i	−0.705495	−	0.708715i	$-0.749275\pi$
$761$	−6.88215	+	5.00017i	−0.249478	+	0.181256i	0.456018	+	0.889971i	$0.349275\pi$
$762$	8.12588	+	25.0089i	0.294370	+	0.905976i
$763$	−14.5232	+	44.6977i	−0.525773	+	1.61816i
$764$	5.19385	+	3.77355i	0.187907	+	0.136522i
$765$	1.64054	+	1.19192i	0.0593139	+	0.0430941i
$766$	−8.37162	+	25.7652i	−0.302479	+	0.930934i
$767$	0.304974	+	0.938613i	0.0110120	+	0.0338914i
$768$	4.59814	−	3.34074i	0.165921	−	0.120549i
$769$	−17.1995			−0.620230			−0.310115	−	0.950699i	$-0.600368\pi$
$769$	−17.1995			−0.620230			−0.310115	+	0.950699i	$0.600368\pi$
$770$	−14.5040	+	28.8853i	−0.522690	+	1.04095i
$771$	−4.30839			−0.155163
$772$	0.409405	−	0.297450i	0.0147348	−	0.0107055i
$773$	−0.709074	−	2.18231i	−0.0255036	−	0.0784921i	0.937495	−	0.348000i	$-0.113139\pi$
$773$	−0.709074	−	2.18231i	−0.0255036	−	0.0784921i	−0.962998	+	0.269508i	$0.913139\pi$
$774$	−3.05388	+	9.39887i	−0.109769	+	0.337836i
$775$	−9.06927	−	6.58921i	−0.325778	−	0.236691i
$776$	−22.8633	−	16.6112i	−0.820746	−	0.596307i
$777$	4.53161	−	13.9469i	0.162571	−	0.500341i
$778$	−3.70910	−	11.4154i	−0.132978	−	0.409263i
$779$	−5.18287	+	3.76558i	−0.185696	+	0.134916i
$780$	−0.618890			−0.0221598
$781$	−16.5697	−	16.3756i	−0.592910	−	0.585964i
$782$	4.71258			0.168522
$783$	3.61204	−	2.62430i	0.129084	−	0.0937849i
$784$	0.842948	+	2.59433i	0.0301053	+	0.0926545i
$785$	0.728142	−	2.24099i	0.0259885	−	0.0799844i
$786$	−4.74770	−	3.44940i	−0.169345	−	0.123036i
$787$	12.6954	+	9.22376i	0.452543	+	0.328791i	0.790599	−	0.612334i	$-0.209769\pi$
$787$	12.6954	+	9.22376i	0.452543	+	0.328791i	−0.338056	+	0.941126i	$0.609769\pi$
$788$	−0.387102	+	1.19138i	−0.0137899	+	0.0424411i
$789$	−7.44176	−	22.9034i	−0.264934	−	0.815382i
$790$	−13.7205	+	9.96852i	−0.488153	+	0.354664i
$791$	1.25578			0.0446504
$792$	−6.21356	−	6.14077i	−0.220789	−	0.218203i
$793$	9.48081			0.336674
$794$	−30.4744	+	22.1409i	−1.08150	+	0.785753i
$795$	−3.94053	−	12.1277i	−0.139756	−	0.430126i
$796$	0.136741	−	0.420845i	0.00484665	−	0.0149165i
$797$	12.3240	+	8.95391i	0.436538	+	0.317164i	0.784258	−	0.620435i	$-0.213044\pi$
$797$	12.3240	+	8.95391i	0.436538	+	0.317164i	−0.347720	+	0.937599i	$0.613044\pi$
$798$	−19.2920	−	14.0164i	−0.682929	−	0.496177i
$799$	−0.738439	+	2.27268i	−0.0261241	+	0.0804017i
$800$	0.685674	+	2.11029i	0.0242422	+	0.0746099i
$801$	10.2876	−	7.47440i	0.363495	−	0.264095i
$802$	2.32817			0.0822105
$803$	11.2514	−	22.4076i	0.397055	−	0.790748i
$804$	−0.413672			−0.0145891
$805$	21.0797	−	15.3153i	0.742962	−	0.539794i
$806$	3.15772	+	9.71847i	0.111226	+	0.342319i
$807$	7.70828	−	23.7236i	0.271344	−	0.835112i
$808$	−19.1608	−	13.9212i	−0.674076	−	0.489745i
$809$	−12.2510	−	8.90091i	−0.430724	−	0.312939i	0.351214	−	0.936295i	$-0.385769\pi$
$809$	−12.2510	−	8.90091i	−0.430724	−	0.312939i	−0.781938	+	0.623356i	$0.785769\pi$
$810$	1.19198	−	3.66853i	0.0418818	−	0.128899i
$811$	6.23603	+	19.1925i	0.218977	+	0.673941i	0.998847	+	0.0480004i	$0.0152849\pi$
$811$	6.23603	+	19.1925i	0.218977	+	0.673941i	−0.779871	+	0.625941i	$0.784715\pi$
$812$	2.19148	−	1.59221i	0.0769060	−	0.0558754i
$813$	−22.7261			−0.797040
$814$	−4.67490	−	28.4310i	−0.163855	−	0.996505i
$815$	−49.7968			−1.74430
$816$	−2.81526	+	2.04541i	−0.0985538	+	0.0716035i
$817$	−12.8670	−	39.6005i	−0.450158	−	1.38544i
$818$	13.4643	−	41.4389i	0.470769	−	1.44888i
$819$	−2.04398	−	1.48504i	−0.0714225	−	0.0518915i
$820$	−0.508653	−	0.369558i	−0.0177629	−	0.0129055i
$821$	−5.57560	+	17.1599i	−0.194590	+	0.598886i	0.805391	+	0.592743i	$0.201955\pi$
$821$	−5.57560	+	17.1599i	−0.194590	+	0.598886i	−0.999981	+	0.00614234i	$0.998045\pi$
$822$	−2.81683	−	8.66931i	−0.0982482	−	0.302377i
$823$	−10.6805	+	7.75987i	−0.372300	+	0.270492i	−0.758164	−	0.652064i	$-0.773903\pi$
$823$	−10.6805	+	7.75987i	−0.372300	+	0.270492i	0.385864	+	0.922556i	$0.373903\pi$
$824$	−31.6161			−1.10140
$825$	4.83754	−	2.50086i	0.168421	−	0.0870687i
$826$	−3.73196			−0.129852
$827$	7.27395	−	5.28484i	0.252940	−	0.183772i	−0.454089	−	0.890956i	$-0.650035\pi$
$827$	7.27395	−	5.28484i	0.252940	−	0.183772i	0.707029	+	0.707185i	$0.250035\pi$
$828$	−0.296953	−	0.913927i	−0.0103198	−	0.0317612i
$829$	8.90009	−	27.3917i	0.309113	−	0.951352i	−0.668997	−	0.743265i	$-0.733276\pi$
$829$	8.90009	−	27.3917i	0.309113	−	0.951352i	0.978110	−	0.208087i	$-0.0667238\pi$
$830$	−44.9223	−	32.6380i	−1.55928	−	1.13288i
$831$	−17.2781	−	12.5533i	−0.599372	−	0.435469i
$832$	−2.10830	+	6.48869i	−0.0730923	+	0.224955i
$833$	−0.149970	−	0.461559i	−0.00519614	−	0.0159921i
$834$	−26.8906	+	19.5372i	−0.931146	+	0.676517i
$835$	−0.342004			−0.0118355
$836$	−4.96525	−	0.756458i	−0.171727	−	0.0261626i
$837$	−6.82738			−0.235989
$838$	−42.0133	+	30.5245i	−1.45133	+	1.05445i
$839$	−16.0617	−	49.4329i	−0.554512	−	1.70661i	−0.697229	−	0.716849i	$-0.745584\pi$
$839$	−16.0617	−	49.4329i	−0.554512	−	1.70661i	0.142717	−	0.989764i	$-0.454416\pi$
$840$	−5.29987	+	16.3113i	−0.182863	+	0.562794i
$841$	7.33469	+	5.32897i	0.252920	+	0.183757i
$842$	26.5157	+	19.2648i	0.913791	+	0.663908i
$843$	9.93489	−	30.5764i	0.342176	−	1.05311i
$844$	−0.552798	−	1.70134i	−0.0190281	−	0.0585625i
$845$	2.08500	−	1.51484i	0.0717261	−	0.0521121i
$846$	4.54557			0.156280
$847$	−16.0694	+	22.6747i	−0.552150	+	0.779113i
$848$	21.8829			0.751460
$849$	−11.2577	+	8.17917i	−0.386362	+	0.280708i
$850$	−0.597533	−	1.83902i	−0.0204952	−	0.0630778i
$851$	−7.17749	+	22.0901i	−0.246041	+	0.757237i
$852$	1.36462	+	0.991455i	0.0467511	+	0.0339667i
$853$	−31.4599	−	22.8569i	−1.07717	−	0.782607i	−0.0999794	−	0.994990i	$-0.531878\pi$
$853$	−31.4599	−	22.8569i	−1.07717	−	0.782607i	−0.977187	+	0.212383i	$0.931878\pi$
$854$	−11.0786	+	34.0964i	−0.379102	+	1.16676i
$855$	5.02218	+	15.4567i	0.171755	+	0.528607i
$856$	−0.656551	+	0.477012i	−0.0224404	+	0.0163039i
$857$	33.2845			1.13698			0.568488	−	0.822691i	$-0.307528\pi$
$857$	33.2845			1.13698			0.568488	+	0.822691i	$0.307528\pi$
$858$	−4.90740	−	0.747644i	−0.167536	−	0.0255241i
$859$	−20.7140			−0.706751			−0.353376	−	0.935482i	$-0.614966\pi$
$859$	−20.7140			−0.706751			−0.353376	+	0.935482i	$0.614966\pi$
$860$	3.30600	−	2.40195i	0.112734	−	0.0819058i
$861$	−0.793145	−	2.44105i	−0.0270303	−	0.0831907i
$862$	17.0573	−	52.4971i	0.580975	−	1.78806i
$863$	−1.71780	−	1.24805i	−0.0584744	−	0.0424842i	0.558164	−	0.829731i	$-0.311506\pi$
$863$	−1.71780	−	1.24805i	−0.0584744	−	0.0424842i	−0.616639	+	0.787246i	$0.711506\pi$
$864$	1.09328	+	0.794316i	0.0371942	+	0.0270232i
$865$	13.5344	−	41.6548i	0.460185	−	1.41630i
$866$	0.801918	+	2.46805i	0.0272503	+	0.0838677i
$867$	−13.2524	+	9.62845i	−0.450076	+	0.326999i
$868$	−4.14228			−0.140598
$869$	−12.9536	+	6.69661i	−0.439421	+	0.227167i
$870$	−17.2219			−0.583877
$871$	1.39363	−	1.01253i	0.0472214	−	0.0343084i
$872$	15.1411	+	46.5995i	0.512742	+	1.57806i
$873$	3.31550	−	10.2041i	0.112213	−	0.345355i
$874$	30.5560	+	22.2003i	1.03357	+	0.750935i
$875$	17.6894	+	12.8521i	0.598009	+	0.434479i
$876$	−0.561012	+	1.72662i	−0.0189548	+	0.0583370i
$877$	−5.49001	−	16.8965i	−0.185384	−	0.570555i	0.814570	−	0.580065i	$-0.196973\pi$
$877$	−5.49001	−	16.8965i	−0.185384	−	0.570555i	−0.999955	+	0.00951020i	$0.996973\pi$
$878$	20.7761	−	15.0947i	0.701160	−	0.509423i
$879$	18.9632			0.639614
$880$	6.13353	+	37.3018i	0.206761	+	1.25744i
$881$	−17.5451			−0.591108			−0.295554	−	0.955326i	$-0.595504\pi$
$881$	−17.5451			−0.591108			−0.295554	+	0.955326i	$0.595504\pi$
$882$	−0.746852	+	0.542620i	−0.0251478	+	0.0182710i
$883$	−2.72238	−	8.37862i	−0.0916154	−	0.281963i	0.894741	−	0.446584i	$-0.147360\pi$
$883$	−2.72238	−	8.37862i	−0.0916154	−	0.281963i	−0.986357	+	0.164621i	$0.947360\pi$
$884$	−0.0583888	+	0.179702i	−0.00196383	+	0.00604404i
$885$	2.05772	+	1.49502i	0.0691694	+	0.0502545i
$886$	−11.1396	−	8.09342i	−0.374243	−	0.271904i
$887$	−1.66611	+	5.12777i	−0.0559426	+	0.172174i	−0.975124	−	0.221662i	$-0.928852\pi$
$887$	−1.66611	+	5.12777i	−0.0559426	+	0.172174i	0.919181	+	0.393835i	$0.128852\pi$
$888$	−4.72442	−	14.5403i	−0.158541	−	0.487940i
$889$	35.9110	−	26.0909i	1.20442	−	0.875060i
$890$	−49.0504			−1.64417
$891$	1.48828	−	2.96395i	0.0498592	−	0.0992962i
$892$	3.35326			0.112275
$893$	−15.4942	+	11.2572i	−0.518495	+	0.376709i
$894$	−0.507821	−	1.56291i	−0.0169841	−	0.0522716i
$895$	20.2918	−	62.4516i	0.678278	−	2.08753i
$896$	−26.3964	−	19.1781i	−0.881843	−	0.640696i
$897$	3.23741	+	2.35211i	0.108094	+	0.0785348i
$898$	7.28470	−	22.4200i	0.243093	−	0.748165i
$899$	9.41958	+	28.9905i	0.314161	+	0.966887i
$900$	−0.318995	+	0.231763i	−0.0106332	+	0.00772545i
$901$	−3.89320			−0.129701
$902$	−3.58685	−	3.54483i	−0.119429	−	0.118030i
$903$	16.6821			0.555146
$904$	1.05918	−	0.769536i	0.0352276	−	0.0255944i
$905$	13.9266	+	42.8618i	0.462937	+	1.42477i
$906$	5.79469	−	17.8342i	0.192516	−	0.592502i
$907$	−7.29194	−	5.29791i	−0.242125	−	0.175914i	0.460104	−	0.887865i	$-0.347812\pi$
$907$	−7.29194	−	5.29791i	−0.242125	−	0.175914i	−0.702229	+	0.711951i	$0.747812\pi$
$908$	1.10018	+	0.799326i	0.0365107	+	0.0265266i
$909$	2.77858	−	8.55160i	0.0921598	−	0.283639i
$910$	3.01153	+	9.26854i	0.0998313	+	0.307249i
$911$	44.1540	−	32.0798i	1.46289	−	1.06285i	0.480289	−	0.877110i	$-0.340532\pi$
$911$	44.1540	−	32.0798i	1.46289	−	1.06285i	0.982599	−	0.185740i	$-0.0594684\pi$
$912$	−27.8895			−0.923514
$913$	−33.9582	−	33.5603i	−1.12385	−	1.11069i
$914$	−51.1487			−1.69185
$915$	19.7675	−	14.3619i	0.653492	−	0.474790i
$916$	−1.22738	−	3.77749i	−0.0405538	−	0.124812i
$917$	−3.06118	+	9.42136i	−0.101089	+	0.311121i
$918$	−0.952746	−	0.692210i	−0.0314453	−	0.0228463i
$919$	33.8520	+	24.5949i	1.11668	+	0.811312i	0.983702	−	0.179807i	$-0.0575474\pi$
$919$	33.8520	+	24.5949i	1.11668	+	0.811312i	0.132974	+	0.991120i	$0.457547\pi$
$920$	8.39432	−	25.8351i	0.276753	−	0.851757i
$921$	5.81790	+	17.9057i	0.191706	+	0.590011i
$922$	−1.59288	+	1.15730i	−0.0524588	+	0.0381135i
$923$	−7.02407			−0.231200
$924$	0.902962	−	1.79828i	0.0297053	−	0.0591590i
$925$	9.53040			0.313358
$926$	−22.3196	+	16.2161i	−0.733468	+	0.532896i
$927$	−3.70916	−	11.4156i	−0.121825	−	0.374938i
$928$	1.86446	−	5.73821i	0.0612038	−	0.188366i
$929$	31.0263	+	22.5419i	1.01794	+	0.739577i	0.965860	−	0.259066i	$-0.0834148\pi$
$929$	31.0263	+	22.5419i	1.01794	+	0.739577i	0.0520803	+	0.998643i	$0.483415\pi$
$930$	21.3058	+	15.4795i	0.698644	+	0.507594i
$931$	1.20194	−	3.69920i	0.0393921	−	0.121236i
$932$	2.04505	+	6.29400i	0.0669877	+	0.206167i
$933$	4.51681	−	3.28165i	0.147874	−	0.107436i
$934$	−39.2136			−1.28311
$935$	−1.09122	−	6.63640i	−0.0356868	−	0.217034i
$936$	−2.63400			−0.0860950
$937$	7.48417	−	5.43757i	0.244497	−	0.177638i	−0.458787	−	0.888546i	$-0.651716\pi$
$937$	7.48417	−	5.43757i	0.244497	−	0.177638i	0.703284	+	0.710909i	$0.251716\pi$
$938$	2.01294	+	6.19518i	0.0657247	+	0.202280i
$939$	1.54255	−	4.74747i	0.0503391	−	0.154928i
$940$	−1.52062	−	1.10480i	−0.0495973	−	0.0360345i
$941$	−34.4916	−	25.0596i	−1.12440	−	0.816921i	−0.139526	−	0.990218i	$-0.544558\pi$
$941$	−34.4916	−	25.0596i	−1.12440	−	0.816921i	−0.984870	+	0.173297i	$0.944558\pi$
$942$	−0.422869	+	1.30146i	−0.0137778	+	0.0424038i
$943$	1.25624	+	3.86631i	0.0409088	+	0.125904i
$944$	−3.53116	+	2.56554i	−0.114929	+	0.0835011i
$945$	−6.51129			−0.211812
$946$	29.1161	−	15.0521i	0.946647	−	0.489387i
$947$	−20.8660			−0.678054			−0.339027	−	0.940777i	$-0.610098\pi$
$947$	−20.8660			−0.678054			−0.339027	+	0.940777i	$0.610098\pi$
$948$	0.854181	−	0.620599i	0.0277425	−	0.0201561i
$949$	−2.33618	−	7.19003i	−0.0758356	−	0.233398i
$950$	4.78897	−	14.7389i	0.155375	−	0.478195i
$951$	26.8077	+	19.4770i	0.869300	+	0.631584i
$952$	4.23618	+	3.07776i	0.137295	+	0.0997509i
$953$	0.513840	−	1.58144i	0.0166449	−	0.0512278i	−0.942389	−	0.334519i	$-0.891426\pi$
$953$	0.513840	−	1.58144i	0.0166449	−	0.0512278i	0.959034	+	0.283291i	$0.0914262\pi$
$954$	2.28847	+	7.04318i	0.0740919	+	0.228031i
$955$	−55.7406	+	40.4979i	−1.80372	+	1.31048i
$956$	−1.13924			−0.0368458
$957$	−14.6389	−	2.23024i	−0.473209	−	0.0720936i
$958$	−39.2892			−1.26938
$959$	−12.4485	+	9.04437i	−0.401983	+	0.292058i
$960$	5.43352	+	16.7227i	0.175366	+	0.539721i
$961$	4.82472	−	14.8490i	0.155636	−	0.478999i
$962$	−7.02823	−	5.10631i	−0.226599	−	0.164634i
$963$	−0.249260	−	0.181098i	−0.00803230	−	0.00583580i
$964$	−0.142326	+	0.438034i	−0.00458401	+	0.0141081i
$965$	1.67826	+	5.16516i	0.0540252	+	0.166272i
$966$	−12.2421	+	8.89438i	−0.393882	+	0.286172i
$967$	−23.8509			−0.766993			−0.383497	−	0.923542i	$-0.625280\pi$
$967$	−23.8509			−0.766993			−0.383497	+	0.923542i	$0.625280\pi$
$968$	0.341414	+	28.9720i	0.0109735	+	0.931195i
$969$	4.96185			0.159398
$970$	−33.4819	+	24.3260i	−1.07504	+	0.781061i
$971$	1.16214	+	3.57671i	0.0372949	+	0.114782i	0.967971	−	0.251063i	$-0.0807801\pi$
$971$	1.16214	+	3.57671i	0.0372949	+	0.114782i	−0.930676	+	0.365845i	$0.880780\pi$
$972$	−0.0742075	+	0.228387i	−0.00238021	+	0.00732553i
$973$	45.3924	+	32.9795i	1.45521	+	1.05727i
$974$	25.1164	+	18.2482i	0.804783	+	0.584709i
$975$	0.507391	−	1.56159i	0.0162495	−	0.0500109i
$976$	12.9571	+	39.8778i	0.414746	+	1.27646i
$977$	−3.87039	+	2.81200i	−0.123825	+	0.0899640i	−0.647974	−	0.761663i	$-0.724383\pi$
$977$	−3.87039	+	2.81200i	−0.123825	+	0.0899640i	0.524149	+	0.851626i	$0.324383\pi$
$978$	28.9195			0.924744
$979$	−41.6938	−	6.35206i	−1.33254	−	0.203013i
$980$	0.381727			0.0121938
$981$	−15.0493	+	10.9340i	−0.480488	+	0.349095i
$982$	3.82810	+	11.7817i	0.122160	+	0.375969i
$983$	10.3454	−	31.8399i	0.329968	−	1.01554i	−0.639180	−	0.769057i	$-0.720726\pi$
$983$	10.3454	−	31.8399i	0.329968	−	1.01554i	0.969148	−	0.246479i	$-0.0792737\pi$
$984$	−2.16483	−	1.57284i	−0.0690123	−	0.0501404i
$985$	−10.8763	−	7.90213i	−0.346549	−	0.251783i
$986$	−1.62479	+	5.00059i	−0.0517438	+	0.159251i
$987$	−2.37111	−	7.29754i	−0.0754734	−	0.232283i
$988$	−1.22514	+	0.890115i	−0.0389769	+	0.0283183i
$989$	−26.4224			−0.840182
$990$	−11.3645	+	5.87509i	−0.361187	+	0.186723i
$991$	31.8102			1.01048			0.505242	−	0.862978i	$-0.331403\pi$
$991$	31.8102			1.01048			0.505242	+	0.862978i	$0.331403\pi$
$992$	−7.46426	+	5.42310i	−0.236990	+	0.172184i
$993$	−7.84948	−	24.1582i	−0.249096	−	0.766637i
$994$	8.20783	−	25.2611i	0.260337	−	0.801233i
$995$	3.84199	+	2.79137i	0.121799	+	0.0884923i
$996$	2.79668	+	2.03190i	0.0886161	+	0.0643834i
$997$	−1.51411	+	4.65996i	−0.0479524	+	0.147582i	−0.972166	−	0.234294i	$-0.924722\pi$
$997$	−1.51411	+	4.65996i	−0.0479524	+	0.147582i	0.924213	+	0.381877i	$0.124722\pi$
$998$	15.7358	+	48.4299i	0.498109	+	1.53302i
$999$	4.69579	−	3.41169i	0.148568	−	0.107941i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.b.157.4	✓	20
11.2	odd	10		4719.2.a.bi.1.9		10
11.4	even	5	inner	429.2.n.b.235.4	yes	20
11.9	even	5		4719.2.a.bn.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.b.157.4	✓	20	1.1	even	1	trivial
429.2.n.b.235.4	yes	20	11.4	even	5	inner
4719.2.a.bi.1.9		10	11.2	odd	10
4719.2.a.bn.1.2		10	11.9	even	5

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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.21086 - 0.879744i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.0742075 - 0.228387i) q^{4} +(2.08500 + 1.51484i) q^{5} +(-1.21086 - 0.879744i) q^{6} +(-0.780732 + 2.40285i) q^{7} +(0.813950 + 2.50508i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.21086 - 0.879744i) q^{2} +(-0.309017 - 0.951057i) q^{3} +(0.0742075 - 0.228387i) q^{4} +(2.08500 + 1.51484i) q^{5} +(-1.21086 - 0.879744i) q^{6} +(-0.780732 + 2.40285i) q^{7} +(0.813950 + 2.50508i) q^{8} +(-0.809017 + 0.587785i) q^{9} +3.85732 q^{10} +(3.27879 + 0.499525i) q^{11} -0.240141 q^{12} +(0.809017 - 0.587785i) q^{13} +(1.16853 + 3.59636i) q^{14} +(0.796398 - 2.45106i) q^{15} +(3.57797 + 2.59955i) q^{16} +(-0.636560 - 0.462488i) q^{17} +(-0.462509 + 1.42346i) q^{18} +(-1.94870 - 5.99747i) q^{19} +(0.500693 - 0.363774i) q^{20} +2.52650 q^{21} +(4.40962 - 2.27964i) q^{22} -4.00166 q^{23} +(2.13095 - 1.54823i) q^{24} +(0.507391 + 1.56159i) q^{25} +(0.462509 - 1.42346i) q^{26} +(0.809017 + 0.587785i) q^{27} +(0.490843 + 0.356618i) q^{28} +(1.37968 - 4.24621i) q^{29} +(-1.19198 - 3.66853i) q^{30} +(-5.52347 + 4.01303i) q^{31} +1.35137 q^{32} +(-0.538126 - 3.27268i) q^{33} -1.17766 q^{34} +(-5.26775 + 3.82724i) q^{35} +(0.0742075 + 0.228387i) q^{36} +(1.79363 - 5.52023i) q^{37} +(-7.63585 - 5.54777i) q^{38} +(-0.809017 - 0.587785i) q^{39} +(-2.09771 + 6.45609i) q^{40} +(-0.313930 - 0.966178i) q^{41} +(3.05925 - 2.22267i) q^{42} +6.60286 q^{43} +(0.357396 - 0.711766i) q^{44} -2.57720 q^{45} +(-4.84546 + 3.52043i) q^{46} +(-0.938497 - 2.88840i) q^{47} +(1.36666 - 4.20616i) q^{48} +(0.498996 + 0.362542i) q^{49} +(1.98818 + 1.44450i) q^{50} +(-0.243144 + 0.748321i) q^{51} +(-0.0742075 - 0.228387i) q^{52} +(4.00297 - 2.90833i) q^{53} +1.49671 q^{54} +(6.07957 + 6.00835i) q^{55} -6.65480 q^{56} +(-5.10176 + 3.70664i) q^{57} +(-2.06498 - 6.35535i) q^{58} +(-0.304974 + 0.938613i) q^{59} +(-0.500693 - 0.363774i) q^{60} +(7.67014 + 5.57268i) q^{61} +(-3.15772 + 9.71847i) q^{62} +(-0.780732 - 2.40285i) q^{63} +(-5.51961 + 4.01023i) q^{64} +2.57720 q^{65} +(-3.53072 - 3.48935i) q^{66} +1.72262 q^{67} +(-0.152864 + 0.111062i) q^{68} +(1.23658 + 3.80580i) q^{69} +(-3.01153 + 9.26854i) q^{70} +(-5.68259 - 4.12864i) q^{71} +(-2.13095 - 1.54823i) q^{72} +(2.33618 - 7.19003i) q^{73} +(-2.68455 - 8.26218i) q^{74} +(1.32837 - 0.965115i) q^{75} -1.51435 q^{76} +(-3.76014 + 7.48843i) q^{77} -1.49671 q^{78} +(-3.55700 + 2.58431i) q^{79} +(3.52216 + 10.8401i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-1.23012 - 0.893731i) q^{82} +(-11.6460 - 8.46131i) q^{83} +(0.187485 - 0.577021i) q^{84} +(-0.626631 - 1.92857i) q^{85} +(7.99516 - 5.80882i) q^{86} -4.46473 q^{87} +(1.41742 + 8.62023i) q^{88} -12.7162 q^{89} +(-3.12064 + 2.26727i) q^{90} +(0.780732 + 2.40285i) q^{91} +(-0.296953 + 0.913927i) q^{92} +(5.52347 + 4.01303i) q^{93} +(-3.67744 - 2.67182i) q^{94} +(5.02218 - 15.4567i) q^{95} +(-0.417597 - 1.28523i) q^{96} +(-8.68009 + 6.30645i) q^{97} +0.923160 q^{98} +(-2.94621 + 1.52310i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9	\( 20 q + q^{2} + 5 q^{3} + 3 q^{4} + 4 q^{5} - q^{6} - 3 q^{7} - 7 q^{8} - 5 q^{9} - 2 q^{10} + 14 q^{11} - 18 q^{12} + 5 q^{13} - q^{14} - 4 q^{15} - 35 q^{16} + 2 q^{17} - 4 q^{18} - 2 q^{19} + 45 q^{20} - 2 q^{21} + 11 q^{22} + 6 q^{23} + 2 q^{24} - 7 q^{25} + 4 q^{26} + 5 q^{27} + 12 q^{28} + 26 q^{29} - 3 q^{30} + 20 q^{31} + 42 q^{32} + q^{33} - 24 q^{34} - 18 q^{35} + 3 q^{36} - 6 q^{37} - 3 q^{38} - 5 q^{39} - 26 q^{41} - 9 q^{42} + 28 q^{43} - 38 q^{44} - 16 q^{45} - 17 q^{46} + 8 q^{47} - 20 q^{48} + 2 q^{49} - 29 q^{50} + 3 q^{51} - 3 q^{52} + q^{53} - 6 q^{54} - 36 q^{56} - 8 q^{57} + 22 q^{58} - 21 q^{59} - 45 q^{60} + 26 q^{61} - 10 q^{62} - 3 q^{63} - 87 q^{64} + 16 q^{65} + 14 q^{66} + 56 q^{67} + 65 q^{68} + 4 q^{69} - 24 q^{70} - 28 q^{71} - 2 q^{72} + 45 q^{73} - 29 q^{74} - 3 q^{75} + 60 q^{76} + 4 q^{77} + 6 q^{78} - 15 q^{79} - 7 q^{80} - 5 q^{81} - 46 q^{82} + 36 q^{83} + 8 q^{84} + 39 q^{86} + 24 q^{87} + 73 q^{88} - 126 q^{89} - 2 q^{90} + 3 q^{91} + 2 q^{92} - 20 q^{93} - 3 q^{94} + 47 q^{95} - 47 q^{96} + 18 q^{97} - 54 q^{98} - 16 q^{99}+O(q^{100}) \) 20 * q + q^2 + 5 * q^3 + 3 * q^4 + 4 * q^5 - q^6 - 3 * q^7 - 7 * q^8 - 5 * q^9 - 2 * q^10 + 14 * q^11 - 18 * q^12 + 5 * q^13 - q^14 - 4 * q^15 - 35 * q^16 + 2 * q^17 - 4 * q^18 - 2 * q^19 + 45 * q^20 - 2 * q^21 + 11 * q^22 + 6 * q^23 + 2 * q^24 - 7 * q^25 + 4 * q^26 + 5 * q^27 + 12 * q^28 + 26 * q^29 - 3 * q^30 + 20 * q^31 + 42 * q^32 + q^33 - 24 * q^34 - 18 * q^35 + 3 * q^36 - 6 * q^37 - 3 * q^38 - 5 * q^39 - 26 * q^41 - 9 * q^42 + 28 * q^43 - 38 * q^44 - 16 * q^45 - 17 * q^46 + 8 * q^47 - 20 * q^48 + 2 * q^49 - 29 * q^50 + 3 * q^51 - 3 * q^52 + q^53 - 6 * q^54 - 36 * q^56 - 8 * q^57 + 22 * q^58 - 21 * q^59 - 45 * q^60 + 26 * q^61 - 10 * q^62 - 3 * q^63 - 87 * q^64 + 16 * q^65 + 14 * q^66 + 56 * q^67 + 65 * q^68 + 4 * q^69 - 24 * q^70 - 28 * q^71 - 2 * q^72 + 45 * q^73 - 29 * q^74 - 3 * q^75 + 60 * q^76 + 4 * q^77 + 6 * q^78 - 15 * q^79 - 7 * q^80 - 5 * q^81 - 46 * q^82 + 36 * q^83 + 8 * q^84 + 39 * q^86 + 24 * q^87 + 73 * q^88 - 126 * q^89 - 2 * q^90 + 3 * q^91 + 2 * q^92 - 20 * q^93 - 3 * q^94 + 47 * q^95 - 47 * q^96 + 18 * q^97 - 54 * q^98 - 16 * q^99

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