LMFDB - Embedded newform 435.2.bm.a.247.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(37,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(28))

chi = DirichletCharacter(H, H._module([0, 7, 3]))

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

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

chi := DirichletCharacter("435.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.bm (of order $28$, degree $12$, 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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$180$
Relative dimension:	$15$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			247.9
Character	$\chi$	$=$	435.247
Dual form			435.2.bm.a.118.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.771248 + 0.615050i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(-0.228505 - 1.00114i) q^{4} +(-0.815777 - 2.08195i) q^{5} +(-0.771248 + 0.615050i) q^{6} +(1.37372 - 0.863168i) q^{7} +(1.29554 - 2.69022i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.651335 - 2.10744i) q^{10} +(-5.82151 - 2.03703i) q^{11} +1.02689 q^{12} +(-5.79264 - 2.02693i) q^{13} +(1.59037 + 0.179192i) q^{14} +(2.21128 - 0.332047i) q^{15} +(0.803409 - 0.386902i) q^{16} -2.92431i q^{17} +(-0.428010 - 0.888773i) q^{18} +(6.53435 + 4.10580i) q^{19} +(-1.89792 + 1.29244i) q^{20} +(0.535844 + 1.53135i) q^{21} +(-3.23695 - 5.15158i) q^{22} +(4.87250 + 0.548998i) q^{23} +(2.33448 + 1.86169i) q^{24} +(-3.66902 + 3.39681i) q^{25} +(-3.22090 - 5.12603i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-1.17806 - 1.17806i) q^{28} +(5.30582 - 0.921030i) q^{29} +(1.90967 + 1.10395i) q^{30} +(3.53221 - 0.397985i) q^{31} +(-4.96451 - 1.13312i) q^{32} +(3.28137 - 5.22227i) q^{33} +(1.79860 - 2.25537i) q^{34} +(-2.91772 - 2.15587i) q^{35} +(-0.228505 + 1.00114i) q^{36} +(2.38594 + 1.14901i) q^{37} +(2.51433 + 7.18554i) q^{38} +(3.26510 - 5.19637i) q^{39} +(-6.65777 - 0.502630i) q^{40} +(6.46729 - 6.46729i) q^{41} +(-0.528591 + 1.51063i) q^{42} +(1.53720 + 1.92758i) q^{43} +(-0.709123 + 6.29364i) q^{44} +(-0.168334 + 2.22972i) q^{45} +(3.42024 + 3.42024i) q^{46} +(-2.93787 + 1.41481i) q^{47} +(0.198426 + 0.869360i) q^{48} +(-1.89513 + 3.93527i) q^{49} +(-4.91893 + 0.363157i) q^{50} +(2.85100 + 0.650721i) q^{51} +(-0.705606 + 6.26243i) q^{52} +(0.164450 + 1.45953i) q^{53} +(0.961731 - 0.219509i) q^{54} +(0.508055 + 13.7818i) q^{55} +(-0.542395 - 4.81389i) q^{56} +(-5.45689 + 5.45689i) q^{57} +(4.65858 + 2.55300i) q^{58} -3.52481i q^{59} +(-0.837713 - 2.13793i) q^{60} +(-1.78069 + 1.11888i) q^{61} +(2.96899 + 1.86554i) q^{62} +(-1.61220 + 0.181651i) q^{63} +(-4.24390 - 5.32168i) q^{64} +(0.505536 + 13.7135i) q^{65} +(5.74271 - 2.00946i) q^{66} +(-1.31120 + 0.458808i) q^{67} +(-2.92766 + 0.668219i) q^{68} +(-1.61947 + 4.62817i) q^{69} +(-0.924322 - 3.45726i) q^{70} +(-3.76912 - 7.82665i) q^{71} +(-2.33448 + 1.86169i) q^{72} +(3.04105 - 2.42515i) q^{73} +(1.13346 + 2.35364i) q^{74} +(-2.49521 - 4.33289i) q^{75} +(2.61737 - 7.48002i) q^{76} +(-9.75545 + 2.22662i) q^{77} +(5.71423 - 1.99950i) q^{78} +(13.6922 - 4.79111i) q^{79} +(-1.46091 - 1.35703i) q^{80} +(0.623490 + 0.781831i) q^{81} +(8.96560 - 1.01018i) q^{82} +(-9.68667 - 6.08654i) q^{83} +(1.41066 - 0.886378i) q^{84} +(-6.08827 + 2.38559i) q^{85} +2.43210i q^{86} +(-0.282718 + 5.37774i) q^{87} +(-13.0221 + 13.0221i) q^{88} +(-0.148232 - 1.31559i) q^{89} +(-1.50122 + 1.61614i) q^{90} +(-9.70708 + 2.21558i) q^{91} +(-0.563761 - 5.00352i) q^{92} +(-0.397985 + 3.53221i) q^{93} +(-3.13600 - 0.715773i) q^{94} +(3.21750 - 16.9536i) q^{95} +(2.20942 - 4.58790i) q^{96} +(-0.519112 - 2.27438i) q^{97} +(-3.88200 + 1.86947i) q^{98} +(4.36116 + 4.36116i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 180 q - 30 q^{3} + 30 q^{4} + 10 q^{5} - 30 q^{9} - 4 q^{10} - 30 q^{11} - 180 q^{12} - 20 q^{13} - 10 q^{14} - 4 q^{15} - 14 q^{16} + 8 q^{19} + 2 q^{20} + 36 q^{22} + 64 q^{25} - 36 q^{26} - 30 q^{27}+ \cdots + 12 q^{99}+O(q^{100}) $ 180 * q - 30 * q^3 + 30 * q^4 + 10 * q^5 - 30 * q^9 - 4 * q^10 - 30 * q^11 - 180 * q^12 - 20 * q^13 - 10 * q^14 - 4 * q^15 - 14 * q^16 + 8 * q^19 + 2 * q^20 + 36 * q^22 + 64 * q^25 - 36 * q^26 - 30 * q^27 + 72 * q^28 + 12 * q^29 - 4 * q^30 - 20 * q^31 + 12 * q^33 + 40 * q^34 - 6 * q^35 + 30 * q^36 + 42 * q^37 + 16 * q^38 + 22 * q^39 + 18 * q^40 - 10 * q^41 + 4 * q^42 + 26 * q^43 + 4 * q^44 - 4 * q^45 + 12 * q^46 - 20 * q^47 - 70 * q^48 + 8 * q^50 + 12 * q^52 - 82 * q^53 + 48 * q^55 + 6 * q^56 + 8 * q^57 - 70 * q^58 - 40 * q^60 + 14 * q^61 + 110 * q^62 - 14 * q^63 - 74 * q^64 + 42 * q^65 + 22 * q^66 - 20 * q^67 - 98 * q^68 + 28 * q^69 + 8 * q^70 + 140 * q^71 + 98 * q^73 + 22 * q^75 - 4 * q^76 - 42 * q^77 + 34 * q^78 - 24 * q^79 - 62 * q^80 - 30 * q^81 + 6 * q^82 - 60 * q^83 - 68 * q^84 - 178 * q^85 - 44 * q^87 - 156 * q^88 - 12 * q^89 - 4 * q^90 - 56 * q^91 - 8 * q^92 + 8 * q^93 + 4 * q^95 - 42 * q^97 + 194 * q^98 + 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$e\left(\frac{27}{28}\right)$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	0.771248	+	0.615050i	0.545355	+	0.434906i	0.857018	−	0.515287i	$-0.172315\pi$
$2$	0.771248	+	0.615050i	0.545355	+	0.434906i	−0.311663	+	0.950193i	$0.600886\pi$
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$3$	−0.222521	+	0.974928i	−0.128473	+	0.562875i
$4$	−0.228505	−	1.00114i	−0.114252	−	0.500572i
$5$	−0.815777	−	2.08195i	−0.364827	−	0.931075i
$5$	−0.815777	−	2.08195i	−0.364827	−	0.931075i
$6$	−0.771248	+	0.615050i	−0.314861	+	0.251093i
$7$	1.37372	−	0.863168i	0.519219	−	0.326247i	−0.246798	−	0.969067i	$-0.579379\pi$
$7$	1.37372	−	0.863168i	0.519219	−	0.326247i	0.766017	+	0.642820i	$0.222236\pi$
$8$	1.29554	−	2.69022i	0.458043	−	0.951136i
$9$	−0.900969	−	0.433884i	−0.300323	−	0.144628i
$10$	0.651335	−	2.10744i	0.205970	−	0.666432i
$11$	−5.82151	−	2.03703i	−1.75525	−	0.614189i	−0.756064	−	0.654498i	$-0.772880\pi$
$11$	−5.82151	−	2.03703i	−1.75525	−	0.614189i	−0.999187	+	0.0403088i	$0.987166\pi$
$12$	1.02689			0.296438
$13$	−5.79264	−	2.02693i	−1.60659	−	0.562170i	−0.629872	−	0.776699i	$-0.716893\pi$
$13$	−5.79264	−	2.02693i	−1.60659	−	0.562170i	−0.976718	+	0.214529i	$0.931178\pi$
$14$	1.59037	+	0.179192i	0.425045	+	0.0478911i
$15$	2.21128	−	0.332047i	0.570949	−	0.0857341i
$16$	0.803409	−	0.386902i	0.200852	−	0.0967254i
$17$		−	2.92431i		−	0.709250i	−0.935009	−	0.354625i	$-0.884608\pi$
$17$		−	2.92431i		−	0.709250i	0.935009	−	0.354625i	$-0.115392\pi$
$18$	−0.428010	−	0.888773i	−0.100883	−	0.209486i
$19$	6.53435	+	4.10580i	1.49908	+	0.941936i	0.997023	+	0.0771024i	$0.0245668\pi$
$19$	6.53435	+	4.10580i	1.49908	+	0.941936i	0.502059	+	0.864833i	$0.332576\pi$
$20$	−1.89792	+	1.29244i	−0.424388	+	0.288999i
$21$	0.535844	+	1.53135i	0.116931	+	0.334169i
$22$	−3.23695	−	5.15158i	−0.690120	−	1.09832i
$23$	4.87250	+	0.548998i	1.01599	+	0.114474i	0.604222	−	0.796816i	$-0.293484\pi$
$23$	4.87250	+	0.548998i	1.01599	+	0.114474i	0.411764	+	0.911290i	$0.364913\pi$
$24$	2.33448	+	1.86169i	0.476524	+	0.380016i
$25$	−3.66902	+	3.39681i	−0.733803	+	0.679362i
$26$	−3.22090	−	5.12603i	−0.631670	−	1.00530i
$27$	0.623490	−	0.781831i	0.119991	−	0.150464i
$28$	−1.17806	−	1.17806i	−0.222632	−	0.222632i
$29$	5.30582	−	0.921030i	0.985266	−	0.171031i
$29$	5.30582	−	0.921030i	0.985266	−	0.171031i
$30$	1.90967	+	1.10395i	0.348656	+	0.201554i
$31$	3.53221	−	0.397985i	0.634404	−	0.0714802i	0.211095	−	0.977466i	$-0.432297\pi$
$31$	3.53221	−	0.397985i	0.634404	−	0.0714802i	0.423309	+	0.905985i	$0.360868\pi$
$32$	−4.96451	−	1.13312i	−0.877610	−	0.200309i
$33$	3.28137	−	5.22227i	0.571213	−	0.909080i
$34$	1.79860	−	2.25537i	0.308457	−	0.386793i
$35$	−2.91772	−	2.15587i	−0.493185	−	0.364408i
$36$	−0.228505	+	1.00114i	−0.0380841	+	0.166857i
$37$	2.38594	+	1.14901i	0.392246	+	0.188896i	0.619602	−	0.784916i	$-0.287294\pi$
$37$	2.38594	+	1.14901i	0.392246	+	0.188896i	−0.227356	+	0.973812i	$0.573008\pi$
$38$	2.51433	+	7.18554i	0.407878	+	1.16565i
$39$	3.26510	−	5.19637i	0.522834	−	0.832086i
$40$	−6.65777	−	0.502630i	−1.05269	−	0.0794728i
$41$	6.46729	−	6.46729i	1.01002	−	1.01002i	0.0100724	−	0.999949i	$-0.496794\pi$
$41$	6.46729	−	6.46729i	1.01002	−	1.01002i	0.999949	−	0.0100724i	$-0.00320621\pi$
$42$	−0.528591	+	1.51063i	−0.0815633	+	0.233095i
$43$	1.53720	+	1.92758i	0.234420	+	0.293954i	0.885102	−	0.465397i	$-0.154088\pi$
$43$	1.53720	+	1.92758i	0.234420	+	0.293954i	−0.650682	+	0.759350i	$0.725517\pi$
$44$	−0.709123	+	6.29364i	−0.106904	+	0.948802i
$45$	−0.168334	+	2.22972i	−0.0250937	+	0.332387i
$46$	3.42024	+	3.42024i	0.504287	+	0.504287i
$47$	−2.93787	+	1.41481i	−0.428533	+	0.206371i	−0.635702	−	0.771935i	$-0.719289\pi$
$47$	−2.93787	+	1.41481i	−0.428533	+	0.206371i	0.207169	+	0.978305i	$0.433575\pi$
$48$	0.198426	+	0.869360i	0.0286403	+	0.125481i
$49$	−1.89513	+	3.93527i	−0.270733	+	0.562182i
$50$	−4.91893	+	0.363157i	−0.695642	+	0.0513582i
$51$	2.85100	+	0.650721i	0.399219	+	0.0911192i
$52$	−0.705606	+	6.26243i	−0.0978500	+	0.868443i
$53$	0.164450	+	1.45953i	0.0225889	+	0.200482i	0.999938	−	0.0111522i	$-0.00354994\pi$
$53$	0.164450	+	1.45953i	0.0225889	+	0.200482i	−0.977349	+	0.211634i	$0.932121\pi$
$54$	0.961731	−	0.219509i	0.130875	−	0.0298714i
$55$	0.508055	+	13.7818i	0.0685061	+	1.85834i
$56$	−0.542395	−	4.81389i	−0.0724805	−	0.643282i
$57$	−5.45689	+	5.45689i	−0.722783	+	0.722783i
$58$	4.65858	+	2.55300i	0.611702	+	0.335225i
$59$		−	3.52481i		−	0.458891i	−0.973322	−	0.229445i	$-0.926309\pi$
$59$		−	3.52481i		−	0.458891i	0.973322	−	0.229445i	$-0.0736912\pi$
$60$	−0.837713	−	2.13793i	−0.108148	−	0.276006i
$61$	−1.78069	+	1.11888i	−0.227994	+	0.143258i	−0.641185	−	0.767386i	$-0.721557\pi$
$61$	−1.78069	+	1.11888i	−0.227994	+	0.143258i	0.413191	+	0.910644i	$0.364414\pi$
$62$	2.96899	+	1.86554i	0.377063	+	0.236924i
$63$	−1.61220	+	0.181651i	−0.203118	+	0.0228859i
$64$	−4.24390	−	5.32168i	−0.530488	−	0.665211i
$65$	0.505536	+	13.7135i	0.0627040	+	1.70095i
$66$	5.74271	−	2.00946i	0.706878	−	0.247347i
$67$	−1.31120	+	0.458808i	−0.160188	+	0.0560523i	−0.409182	−	0.912453i	$-0.634186\pi$
$67$	−1.31120	+	0.458808i	−0.160188	+	0.0560523i	0.248994	+	0.968505i	$0.419900\pi$
$68$	−2.92766	+	0.668219i	−0.355031	+	0.0810335i
$69$	−1.61947	+	4.62817i	−0.194961	+	0.557166i
$70$	−0.924322	−	3.45726i	−0.110478	−	0.413221i
$71$	−3.76912	−	7.82665i	−0.447312	−	0.928852i	−0.995701	−	0.0926289i	$-0.970473\pi$
$71$	−3.76912	−	7.82665i	−0.447312	−	0.928852i	0.548389	−	0.836223i	$-0.315241\pi$
$72$	−2.33448	+	1.86169i	−0.275121	+	0.219402i
$73$	3.04105	−	2.42515i	0.355928	−	0.283843i	−0.429159	−	0.903229i	$-0.641190\pi$
$73$	3.04105	−	2.42515i	0.355928	−	0.283843i	0.785086	+	0.619386i	$0.212619\pi$
$74$	1.13346	+	2.35364i	0.131762	+	0.273606i
$75$	−2.49521	−	4.33289i	−0.288122	−	0.500319i
$76$	2.61737	−	7.48002i	0.300233	−	0.858017i
$77$	−9.75545	+	2.22662i	−1.11174	+	0.253747i
$78$	5.71423	−	1.99950i	0.647009	−	0.226398i
$79$	13.6922	−	4.79111i	1.54049	−	0.539042i	0.579347	−	0.815081i	$-0.303307\pi$
$79$	13.6922	−	4.79111i	1.54049	−	0.539042i	0.961147	+	0.276039i	$0.0890218\pi$
$80$	−1.46091	−	1.35703i	−0.163335	−	0.151721i
$81$	0.623490	+	0.781831i	0.0692766	+	0.0868702i
$82$	8.96560	−	1.01018i	0.990085	−	0.111556i
$83$	−9.68667	−	6.08654i	−1.06325	−	0.668084i	−0.117531	−	0.993069i	$-0.537498\pi$
$83$	−9.68667	−	6.08654i	−1.06325	−	0.668084i	−0.945719	+	0.324985i	$0.894641\pi$
$84$	1.41066	−	0.886378i	0.153916	−	0.0967118i
$85$	−6.08827	+	2.38559i	−0.660366	+	0.258753i
$86$			2.43210i			0.262260i
$87$	−0.282718	+	5.37774i	−0.0303105	+	0.576554i
$88$	−13.0221	+	13.0221i	−1.38816	+	1.38816i
$89$	−0.148232	−	1.31559i	−0.0157125	−	0.139452i	0.983407	−	0.181415i	$-0.0580676\pi$
$89$	−0.148232	−	1.31559i	−0.0157125	−	0.139452i	−0.999119	+	0.0419623i	$0.986639\pi$
$90$	−1.50122	+	1.61614i	−0.158242	+	0.170356i
$91$	−9.70708	+	2.21558i	−1.01758	+	0.232256i
$92$	−0.563761	−	5.00352i	−0.0587762	−	0.521653i
$93$	−0.397985	+	3.53221i	−0.0412691	+	0.366274i
$94$	−3.13600	−	0.715773i	−0.323454	−	0.0738263i
$95$	3.21750	−	16.9536i	0.330108	−	1.73940i
$96$	2.20942	−	4.58790i	0.225498	−	0.468251i
$97$	−0.519112	−	2.27438i	−0.0527079	−	0.230928i	0.941712	−	0.336419i	$-0.109216\pi$
$97$	−0.519112	−	2.27438i	−0.0527079	−	0.230928i	−0.994420	+	0.105491i	$0.966359\pi$
$98$	−3.88200	+	1.86947i	−0.392142	+	0.188845i
$99$	4.36116	+	4.36116i	0.438313	+	0.438313i
$100$	4.23908	+	2.89702i	0.423908	+	0.289702i
$101$	−0.514172	+	4.56340i	−0.0511620	+	0.454075i	0.941847	+	0.336041i	$0.109088\pi$
$101$	−0.514172	+	4.56340i	−0.0511620	+	0.454075i	−0.993009	+	0.118035i	$0.962341\pi$
$102$	1.79860	+	2.25537i	0.178088	+	0.223315i
$103$	4.18887	−	11.9711i	0.412742	−	1.17955i	−0.530570	−	0.847641i	$-0.678022\pi$
$103$	4.18887	−	11.9711i	0.412742	−	1.17955i	0.943312	−	0.331907i	$-0.107692\pi$
$104$	−12.9575	+	12.9575i	−1.27059	+	1.27059i
$105$	2.75107	−	2.36484i	0.268477	−	0.230785i
$106$	−0.770854	+	1.22681i	−0.0748719	+	0.119158i
$107$	2.45956	+	7.02903i	0.237775	+	0.679522i	0.999500	+	0.0316212i	$0.0100670\pi$
$107$	2.45956	+	7.02903i	0.237775	+	0.679522i	−0.761725	+	0.647900i	$0.775647\pi$
$108$	−0.925196	−	0.445551i	−0.0890270	−	0.0428732i
$109$	−1.04250	+	4.56748i	−0.0998532	+	0.437486i	0.900145	+	0.435590i	$0.143460\pi$
$109$	−1.04250	+	4.56748i	−0.0998532	+	0.437486i	−0.999998	+	0.00189517i	$0.999397\pi$
$110$	−8.08469	+	10.9417i	−0.770845	+	1.04325i
$111$	−1.65112	+	2.07044i	−0.156718	+	0.196518i
$112$	0.769702	−	1.22497i	0.0727300	−	0.115749i
$113$	−13.7691	−	3.14271i	−1.29529	−	0.295641i	−0.481318	−	0.876546i	$-0.659842\pi$
$113$	−13.7691	−	3.14271i	−1.29529	−	0.295641i	−0.813971	+	0.580905i	$0.802699\pi$
$114$	−7.56488	+	0.852357i	−0.708516	+	0.0798305i
$115$	−2.83189	−	10.5921i	−0.264075	−	0.987723i
$116$	−2.13449	−	5.10143i	−0.198182	−	0.473656i
$117$	4.33954	+	4.33954i	0.401190	+	0.401190i
$118$	2.16793	−	2.71850i	0.199574	−	0.250258i
$119$	−2.52417	−	4.01720i	−0.231391	−	0.368256i
$120$	1.97152	−	6.37900i	0.179974	−	0.582320i
$121$	21.1403	+	16.8588i	1.92185	+	1.53262i
$122$	−2.06152	−	0.232277i	−0.186641	−	0.0210294i
$123$	4.86604	+	7.74425i	0.438756	+	0.698276i
$124$	−1.20557	−	3.44531i	−0.108263	−	0.309398i
$125$	10.0651	+	4.86766i	0.900248	+	0.435377i
$126$	−1.35513	−	0.851484i	−0.120724	−	0.0758562i
$127$	5.08163	+	10.5521i	0.450922	+	0.936349i	0.995239	+	0.0974690i	$0.0310747\pi$
$127$	5.08163	+	10.5521i	0.450922	+	0.936349i	−0.544317	+	0.838880i	$0.683211\pi$
$128$			3.46982i			0.306692i
$129$	−2.22131	+	1.06973i	−0.195576	+	0.0941843i
$130$	−8.04460	+	10.8874i	−0.705558	+	0.954892i
$131$	−5.33078	−	0.600634i	−0.465752	−	0.0524776i	−0.124029	−	0.992279i	$-0.539582\pi$
$131$	−5.33078	−	0.600634i	−0.465752	−	0.0524776i	−0.341723	+	0.939801i	$0.611010\pi$
$132$	−5.97805	−	2.09181i	−0.520322	−	0.182069i
$133$	12.5204			1.08566
$134$	−1.29345	−	0.452598i	−0.111737	−	0.0390985i
$135$	−2.13636	−	0.660273i	−0.183869	−	0.0568273i
$136$	−7.86704	−	3.78857i	−0.674593	−	0.324867i
$137$	7.61764	−	15.8182i	0.650819	−	1.35144i	−0.270533	−	0.962711i	$-0.587200\pi$
$137$	7.61764	−	15.8182i	0.650819	−	1.35144i	0.921352	−	0.388729i	$-0.127086\pi$
$138$	−4.09557	+	2.57341i	−0.348638	+	0.219064i
$139$	10.8333	−	8.63925i	0.918866	−	0.732771i	−0.0450478	−	0.998985i	$-0.514344\pi$
$139$	10.8333	−	8.63925i	0.918866	−	0.732771i	0.963914	+	0.266213i	$0.0857726\pi$
$140$	−1.49162	+	3.41369i	−0.126065	+	0.288509i
$141$	−0.725595	−	3.17904i	−0.0611061	−	0.267723i
$142$	1.90686	−	8.35448i	0.160020	−	0.701093i
$143$	29.5930	+	23.5996i	2.47469	+	1.97350i
$144$	−0.891717			−0.0743098
$145$	−6.24590	−	10.2951i	−0.518694	−	0.854960i
$146$	3.83699			0.317552
$147$	−3.41490	−	2.72329i	−0.281656	−	0.224613i
$148$	0.605125	−	2.65122i	0.0497409	−	0.217929i
$149$	2.32438	+	10.1838i	0.190421	+	0.834287i	0.976389	+	0.216020i	$0.0693077\pi$
$149$	2.32438	+	10.1838i	0.190421	+	0.834287i	−0.785968	+	0.618267i	$0.787835\pi$
$150$	0.740513	−	4.87641i	0.0604626	−	0.398157i
$151$	4.34020	−	3.46119i	0.353200	−	0.281668i	−0.430776	−	0.902459i	$-0.641760\pi$
$151$	4.34020	−	3.46119i	0.353200	−	0.281668i	0.783976	+	0.620791i	$0.213189\pi$
$152$	19.5110	−	12.2596i	1.58255	−	0.994383i
$153$	−1.26881	+	2.63472i	−0.102577	+	0.213004i
$154$	−8.89335	−	4.28281i	−0.716647	−	0.345119i
$155$	−3.71008	−	7.02922i	−0.298001	−	0.564600i
$156$	−5.94841	−	2.08144i	−0.476254	−	0.166648i
$157$	−12.0266			−0.959823			−0.479912	−	0.877317i	$-0.659331\pi$
$157$	−12.0266			−0.959823			−0.479912	+	0.877317i	$0.659331\pi$
$158$	13.5069	+	4.72626i	1.07455	+	0.376001i
$159$	−1.45953	−	0.164450i	−0.115748	−	0.0130417i
$160$	1.69084	+	11.2602i	0.133673	+	0.890200i
$161$	7.16734	−	3.45161i	0.564866	−	0.272025i
$162$			0.986463i			0.0775039i
$163$	0.0881246	+	0.182993i	0.00690245	+	0.0143331i	0.904392	−	0.426703i	$-0.140325\pi$
$163$	0.0881246	+	0.182993i	0.00690245	+	0.0143331i	−0.897489	+	0.441037i	$0.854611\pi$
$164$	−7.95250	−	4.99689i	−0.620986	−	0.390191i
$165$	−13.5494	−	2.57143i	−1.05482	−	0.200186i
$166$	−3.72730	−	10.6520i	−0.289295	−	0.826757i
$167$	3.56010	+	5.66587i	0.275489	+	0.438438i	0.955598	−	0.294673i	$-0.0952106\pi$
$167$	3.56010	+	5.66587i	0.275489	+	0.438438i	−0.680109	+	0.733111i	$0.738068\pi$
$168$	4.81389	+	0.542395i	0.371399	+	0.0418467i
$169$	19.2824	+	15.3772i	1.48326	+	1.18286i
$170$	−6.16282	−	1.90471i	−0.472667	−	0.146085i
$171$	−4.10580	−	6.53435i	−0.313979	−	0.499694i
$172$	1.57853	−	1.97942i	0.120362	−	0.150929i
$173$	−1.70817	−	1.70817i	−0.129870	−	0.129870i	0.639184	−	0.769054i	$-0.279272\pi$
$173$	−1.70817	−	1.70817i	−0.129870	−	0.129870i	−0.769054	+	0.639184i	$0.779272\pi$
$174$	−3.52562	+	3.97369i	−0.267277	+	0.301244i
$175$	−2.10820	+	7.83326i	−0.159365	+	0.592139i
$176$	−5.46519	+	0.615779i	−0.411954	+	0.0464161i
$177$	3.43643	+	0.784343i	0.258298	+	0.0589548i
$178$	0.694831	−	1.10582i	0.0520798	−	0.0828845i
$179$	4.59200	−	5.75818i	0.343222	−	0.430387i	−0.580022	−	0.814601i	$-0.696956\pi$
$179$	4.59200	−	5.75818i	0.343222	−	0.430387i	0.923244	+	0.384214i	$0.125527\pi$
$180$	2.27074	−	0.340976i	0.169251	−	0.0254148i
$181$	−0.741974	+	3.25080i	−0.0551505	+	0.241630i	−0.994988	−	0.0999907i	$-0.968119\pi$
$181$	−0.741974	+	3.25080i	−0.0551505	+	0.241630i	0.939838	+	0.341621i	$0.110976\pi$
$182$	−8.84925	−	4.26158i	−0.655950	−	0.315889i
$183$	−0.694587	−	1.98501i	−0.0513453	−	0.146737i
$184$	7.78944	−	12.3968i	0.574245	−	0.913906i
$185$	0.445780	−	5.90474i	0.0327744	−	0.434125i
$186$	−2.47943	+	2.47943i	−0.181801	+	0.181801i
$187$	−5.95693	+	17.0239i	−0.435614	+	1.24491i
$188$	2.08774	+	2.61794i	0.152264	+	0.190933i
$189$	0.181651	−	1.61220i	0.0132132	−	0.117270i
$190$	12.9088	−	11.0965i	0.936502	−	0.805025i
$191$	−6.76572	−	6.76572i	−0.489550	−	0.489550i	0.418614	−	0.908164i	$-0.362516\pi$
$191$	−6.76572	−	6.76572i	−0.489550	−	0.489550i	−0.908164	+	0.418614i	$0.862516\pi$
$192$	6.13262	−	2.95331i	0.442583	−	0.213137i
$193$	1.26395	+	5.53773i	0.0909811	+	0.398614i	0.999829	−	0.0185142i	$-0.00589359\pi$
$193$	1.26395	+	5.53773i	0.0909811	+	0.398614i	−0.908847	+	0.417129i	$0.863036\pi$
$194$	0.998492	−	2.07339i	0.0716876	−	0.148861i
$195$	−13.4822	−	2.55868i	−0.965478	−	0.183231i
$196$	4.37282	+	0.998067i	0.312344	+	0.0712905i
$197$	−1.58357	+	14.0546i	−0.112825	+	1.00135i	0.801952	+	0.597389i	$0.203795\pi$
$197$	−1.58357	+	14.0546i	−0.112825	+	1.00135i	−0.914777	+	0.403960i	$0.867633\pi$
$198$	0.681206	+	6.04587i	0.0484112	+	0.429661i
$199$	18.2633	−	4.16848i	1.29465	−	0.295496i	0.480935	−	0.876756i	$-0.340297\pi$
$199$	18.2633	−	4.16848i	1.29465	−	0.295496i	0.813718	+	0.581260i	$0.197440\pi$
$200$	4.38480	+	14.2712i	0.310052	+	1.00912i
$201$	−0.155536	−	1.38042i	−0.0109707	−	0.0973672i
$202$	−3.20327	+	3.20327i	−0.225381	+	0.225381i
$203$	6.49373	−	5.84505i	0.455770	−	0.410242i
$204$		−	3.00295i		−	0.210248i
$205$	−18.7404	−	8.18870i	−1.30889	−	0.571924i
$206$	10.5935	−	6.65633i	0.738083	−	0.463768i
$207$	−4.15177	−	2.60873i	−0.288568	−	0.181319i
$208$	−5.43809	+	0.612725i	−0.377063	+	0.0424848i
$209$	−29.6761	−	37.2127i	−2.05274	−	2.57405i
$210$	3.57626	−	0.131835i	0.246785	−	0.00909750i
$211$	−5.28084	+	1.84785i	−0.363548	+	0.127211i	−0.505871	−	0.862609i	$-0.668829\pi$
$211$	−5.28084	+	1.84785i	−0.363548	+	0.127211i	0.142322	+	0.989820i	$0.454543\pi$
$212$	1.42362	−	0.498148i	0.0977749	−	0.0342129i
$213$	8.46912	−	1.93302i	0.580295	−	0.132449i
$214$	−2.42627	+	6.93388i	−0.165856	+	0.473990i
$215$	2.75912	−	4.77284i	0.188170	−	0.325505i
$216$	−1.29554	−	2.69022i	−0.0881504	−	0.183046i
$217$	4.50876	−	3.59562i	0.306074	−	0.244086i
$218$	−3.61326	+	2.88147i	−0.244721	+	0.195158i
$219$	1.68765	+	3.50445i	0.114041	+	0.236809i
$220$	13.6815	−	3.65785i	0.922408	−	0.246612i
$221$	−5.92739	+	16.9395i	−0.398719	+	1.13947i
$222$	−2.54685	+	0.581302i	−0.170933	+	0.0390144i
$223$	−20.4044	+	7.13979i	−1.36638	+	0.478116i	−0.911082	−	0.412225i	$-0.864752\pi$
$223$	−20.4044	+	7.13979i	−1.36638	+	0.478116i	−0.455294	+	0.890341i	$0.650466\pi$
$224$	−7.79794	+	2.72862i	−0.521022	+	0.182313i
$225$	4.77949	−	1.46850i	0.318633	−	0.0978997i
$226$	−8.68648	−	10.8925i	−0.577816	−	0.724558i
$227$	−4.80202	+	0.541058i	−0.318721	+	0.0359113i	−0.269876	−	0.962895i	$-0.586983\pi$
$227$	−4.80202	+	0.541058i	−0.318721	+	0.0359113i	−0.0488453	+	0.998806i	$0.515554\pi$
$228$	6.71006	+	4.21621i	0.444384	+	0.279225i
$229$	−11.9015	+	7.47822i	−0.786475	+	0.494175i	−0.864412	−	0.502783i	$-0.832309\pi$
$229$	−11.9015	+	7.47822i	−0.786475	+	0.494175i	0.0779378	+	0.996958i	$0.475166\pi$
$230$	4.33061	−	9.91092i	0.285552	−	0.653507i
$231$		−	10.0063i		−	0.658368i
$232$	4.39613	−	15.4670i	0.288620	−	1.01546i
$233$	−8.08321	+	8.08321i	−0.529548	+	0.529548i	−0.920438	−	0.390889i	$-0.872168\pi$
$233$	−8.08321	+	8.08321i	−0.529548	+	0.529548i	0.390889	+	0.920438i	$0.372168\pi$
$234$	0.677828	+	6.01589i	0.0443110	+	0.393271i
$235$	5.34220	+	4.96233i	0.348487	+	0.323707i
$236$	−3.52884	+	0.805434i	−0.229708	+	0.0524293i
$237$	1.62418	+	14.4150i	0.105502	+	0.936357i
$238$	0.524014	−	4.65075i	0.0339668	−	0.301463i
$239$	28.5782	+	6.52279i	1.84857	+	0.421924i	0.995071	−	0.0991681i	$-0.0316182\pi$
$239$	28.5782	+	6.52279i	1.84857	+	0.421924i	0.853500	+	0.521092i	$0.174475\pi$
$240$	1.64809	−	1.12232i	0.106384	−	0.0724452i
$241$	9.32986	−	19.3737i	0.600989	−	1.24797i	−0.349420	−	0.936966i	$-0.613621\pi$
$241$	9.32986	−	19.3737i	0.600989	−	1.24797i	0.950410	−	0.311001i	$-0.100664\pi$
$242$	5.93540	+	26.0047i	0.381542	+	1.67165i
$243$	−0.900969	+	0.433884i	−0.0577972	+	0.0278337i
$244$	1.52705	+	1.52705i	0.0977596	+	0.0977596i
$245$	9.73904	+	0.735251i	0.622204	+	0.0469735i
$246$	−1.01018	+	8.96560i	−0.0644067	+	0.571626i
$247$	−29.5290	−	37.0281i	−1.87888	−	2.35604i
$248$	3.50546	−	10.0180i	0.222597	−	0.636145i
$249$	8.08942	−	8.08942i	0.512646	−	0.512646i
$250$	4.76882	+	9.94470i	0.301607	+	0.628958i
$251$	6.54085	−	10.4097i	0.412855	−	0.657054i	−0.573965	−	0.818880i	$-0.694595\pi$
$251$	6.54085	−	10.4097i	0.412855	−	0.657054i	0.986819	+	0.161826i	$0.0517382\pi$
$252$	0.550253	+	1.57253i	0.0346627	+	0.0990603i
$253$	−27.2470	−	13.1214i	−1.71300	−	0.824938i
$254$	−2.57088	+	11.2638i	−0.161311	+	0.706751i
$255$	−0.971009	−	6.46647i	−0.0608070	−	0.404946i
$256$	−10.6219	+	13.3195i	−0.663870	+	0.832466i
$257$	−7.64654	+	12.1694i	−0.476978	+	0.759107i	−0.995378	−	0.0960316i	$-0.969385\pi$
$257$	−7.64654	+	12.1694i	−0.476978	+	0.759107i	0.518400	+	0.855138i	$0.326528\pi$
$258$	−2.37112	−	0.541192i	−0.147619	−	0.0336932i
$259$	4.26941	−	0.481047i	0.265288	−	0.0298908i
$260$	13.6137	−	3.63971i	0.844284	−	0.225725i
$261$	−5.18000	−	1.47229i	−0.320634	−	0.0911324i
$262$	−3.74193	−	3.74193i	−0.231177	−	0.231177i
$263$	11.3844	−	14.2756i	0.701990	−	0.880268i	−0.295180	−	0.955442i	$-0.595380\pi$
$263$	11.3844	−	14.2756i	0.701990	−	0.880268i	0.997170	+	0.0751734i	$0.0239510\pi$
$264$	−9.79789	−	15.5933i	−0.603019	−	0.959699i
$265$	2.90452	−	1.53303i	0.178423	−	0.0941733i
$266$	9.65633	+	7.70066i	0.592067	+	0.472158i
$267$	1.31559	+	0.148232i	0.0805129	+	0.00907163i
$268$	0.758948	+	1.20786i	0.0463601	+	0.0737817i
$269$	9.66100	+	27.6096i	0.589042	+	1.68338i	0.721686	+	0.692221i	$0.243368\pi$
$269$	9.66100	+	27.6096i	0.589042	+	1.68338i	−0.132644	+	0.991164i	$0.542347\pi$
$270$	−1.24156	−	1.82320i	−0.0755592	−	0.110957i
$271$	−15.3211	−	9.62687i	−0.930689	−	0.584790i	−0.0208635	−	0.999782i	$-0.506642\pi$
$271$	−15.3211	−	9.62687i	−0.930689	−	0.584790i	−0.909825	+	0.414992i	$0.863784\pi$
$272$	−1.13142	−	2.34942i	−0.0686025	−	0.142455i
$273$		−	9.95671i		−	0.602608i
$274$	15.6041	−	7.51453i	0.942676	−	0.453969i
$275$	28.2786	−	12.3007i	1.70527	−	0.741758i
$276$	5.00352	+	0.563761i	0.301176	+	0.0339344i
$277$	15.4922	+	5.42094i	0.930834	+	0.325713i	0.752753	−	0.658303i	$-0.228725\pi$
$277$	15.4922	+	5.42094i	0.930834	+	0.325713i	0.178081	+	0.984016i	$0.443011\pi$
$278$	13.6687			0.819795
$279$	−3.35509	−	1.17400i	−0.200864	−	0.0702854i
$280$	−9.57979	+	5.05629i	−0.572502	+	0.302171i
$281$	26.2685	+	12.6502i	1.56705	+	0.754650i	0.997722	−	0.0674634i	$-0.0214906\pi$
$281$	26.2685	+	12.6502i	1.56705	+	0.754650i	0.569324	+	0.822113i	$0.307205\pi$
$282$	1.39565	−	2.89810i	0.0831100	−	0.172580i
$283$	−23.5009	+	14.7666i	−1.39699	+	0.877785i	−0.999212	−	0.0396986i	$-0.987360\pi$
$283$	−23.5009	+	14.7666i	−1.39699	+	0.877785i	−0.397775	+	0.917483i	$0.630217\pi$
$284$	−6.97434	+	5.56185i	−0.413851	+	0.330035i
$285$	15.8126	+	6.90936i	0.936656	+	0.409275i
$286$	8.30859	+	36.4023i	0.491297	+	2.15251i
$287$	3.30192	−	14.4666i	0.194906	−	0.853939i
$288$	3.98123	+	3.17493i	0.234596	+	0.187084i
$289$	8.44839			0.496964
$290$	1.51485	−	11.7816i	0.0889550	−	0.691840i
$291$	2.33287			0.136755
$292$	−3.12282	−	2.49037i	−0.182749	−	0.145738i
$293$	2.55795	−	11.2071i	0.149437	−	0.654728i	−0.843605	−	0.536965i	$-0.819571\pi$
$293$	2.55795	−	11.2071i	0.149437	−	0.654728i	0.993042	−	0.117762i	$-0.0375722\pi$
$294$	−0.958776	−	4.20067i	−0.0559169	−	0.244988i
$295$	−7.33846	+	2.87546i	−0.427262	+	0.167416i
$296$	6.18217	−	4.93012i	0.359331	−	0.286557i
$297$	−5.22227	+	3.28137i	−0.303027	+	0.190404i
$298$	−4.47085	+	9.28382i	−0.258990	+	0.537798i
$299$	−27.1118	−	13.0564i	−1.56792	−	0.755070i
$300$	−3.76767	+	3.48815i	−0.217527	+	0.201389i
$301$	3.77551	+	1.32111i	0.217617	+	0.0761474i
$302$	5.47617			0.315118
$303$	−4.33457	−	1.51673i	−0.249015	−	0.0871340i
$304$	6.83830	+	0.770491i	0.392203	+	0.0441907i
$305$	3.78209	+	2.79454i	0.216562	+	0.160015i
$306$	−2.59905	+	1.25164i	−0.148578	+	0.0715513i
$307$		−	25.2519i		−	1.44120i	−0.693349	−	0.720602i	$-0.743866\pi$
$307$		−	25.2519i		−	1.44120i	0.693349	−	0.720602i	$-0.256134\pi$
$308$	4.45833	+	9.25781i	0.254037	+	0.527513i
$309$	10.7389	+	6.74767i	0.610912	+	0.383861i
$310$	1.46193	−	7.70316i	0.0830318	−	0.437510i
$311$	−2.47873	−	7.08381i	−0.140556	−	0.401686i	0.851990	−	0.523558i	$-0.175396\pi$
$311$	−2.47873	−	7.08381i	−0.140556	−	0.401686i	−0.992546	+	0.121872i	$0.961110\pi$
$312$	−9.74931	−	15.5159i	−0.551946	−	0.878417i
$313$	−7.13831	−	0.804295i	−0.403481	−	0.0454614i	−0.0921078	−	0.995749i	$-0.529360\pi$
$313$	−7.13831	−	0.804295i	−0.403481	−	0.0454614i	−0.311373	+	0.950288i	$0.600789\pi$
$314$	−9.27546	−	7.39693i	−0.523444	−	0.417433i
$315$	1.69338	+	3.20832i	0.0954112	+	0.180769i
$316$	−7.92532	−	12.6131i	−0.445834	−	0.709541i
$317$	−5.60774	+	7.03189i	−0.314962	+	0.394950i	−0.913963	−	0.405799i	$-0.866993\pi$
$317$	−5.60774	+	7.03189i	−0.314962	+	0.394950i	0.599000	+	0.800749i	$0.295565\pi$
$318$	−1.02452	−	1.02452i	−0.0574521	−	0.0574521i
$319$	−32.7640	−	5.44635i	−1.83443	−	0.304937i
$320$	−7.61739	+	13.1769i	−0.425825	+	0.736611i
$321$	−7.40010	+	0.833791i	−0.413033	+	0.0465377i
$322$	7.65071	+	1.74623i	0.426358	+	0.0973133i
$323$	12.0067	−	19.1085i	0.668068	−	1.06322i
$324$	0.640255	−	0.802855i	0.0355697	−	0.0446030i
$325$	28.1384	−	12.2397i	1.56084	−	0.678934i
$326$	−0.0445836	+	0.195334i	−0.00246926	+	0.0108185i
$327$	−4.22099	−	2.03272i	−0.233421	−	0.112410i
$328$	−9.01979	−	25.7771i	−0.498034	−	1.42330i
$329$	−2.81461	+	4.47943i	−0.155175	+	0.246959i
$330$	−8.86836	−	10.3167i	−0.488187	−	0.567918i
$331$	1.51402	−	1.51402i	0.0832183	−	0.0832183i	−0.664272	−	0.747491i	$-0.731258\pi$
$331$	1.51402	−	1.51402i	0.0832183	−	0.0832183i	0.747491	+	0.664272i	$0.231258\pi$
$332$	−3.88005	+	11.0886i	−0.212946	+	0.608563i
$333$	−1.65112	−	2.07044i	−0.0904810	−	0.113460i
$334$	−0.739070	+	6.55943i	−0.0404401	+	0.358916i
$335$	2.02486	+	2.35556i	0.110630	+	0.128698i
$336$	1.02299	+	1.02299i	0.0558084	+	0.0558084i
$337$	−11.2936	+	5.43870i	−0.615200	+	0.296265i	−0.715414	−	0.698701i	$-0.753762\pi$
$337$	−11.2936	+	5.43870i	−0.615200	+	0.296265i	0.100214	+	0.994966i	$0.468047\pi$
$338$	5.41378	+	23.7193i	0.294471	+	1.29016i
$339$	6.12783	−	12.7246i	0.332818	−	0.691104i
$340$	3.77951	+	5.55012i	0.204973	+	0.300997i
$341$	−21.3735	−	4.87837i	−1.15744	−	0.264178i
$342$	0.852357	−	7.56488i	0.0460902	−	0.409062i
$343$	2.06498	+	18.3272i	0.111498	+	0.989574i
$344$	7.17712	−	1.63813i	0.386964	−	0.0883220i
$345$	10.9567	−	0.403910i	0.589891	−	0.0217458i
$346$	−0.266813	−	2.36803i	−0.0143439	−	0.127306i
$347$	−1.61855	+	1.61855i	−0.0868885	+	0.0868885i	−0.749215	−	0.662327i	$-0.769569\pi$
$347$	−1.61855	+	1.61855i	−0.0868885	+	0.0868885i	0.662327	+	0.749215i	$0.269569\pi$
$348$	5.44849	−	0.945796i	0.292070	−	0.0507000i
$349$			0.194023i			0.0103858i	0.999987	+	0.00519290i	$0.00165296\pi$
$349$			0.194023i			0.0103858i	−0.999987	+	0.00519290i	$0.998347\pi$
$350$	−6.44379	+	4.74474i	−0.344435	+	0.253617i
$351$	−5.19637	+	3.26510i	−0.277362	+	0.174278i
$352$	26.5928	+	16.7093i	1.41740	+	0.890611i
$353$	11.1308	−	1.25414i	0.592433	−	0.0667511i	0.189342	−	0.981911i	$-0.439364\pi$
$353$	11.1308	−	1.25414i	0.592433	−	0.0667511i	0.403091	+	0.915160i	$0.367936\pi$
$354$	2.16793	+	2.71850i	0.115224	+	0.144487i
$355$	−13.2199	+	14.2319i	−0.701640	+	0.755351i
$356$	−1.28323	+	0.449020i	−0.0680108	+	0.0237980i
$357$	4.47816	−	1.56698i	0.237009	−	0.0829332i
$358$	7.08314	−	1.61668i	0.374356	−	0.0854442i
$359$	−3.53734	+	10.1091i	−0.186694	+	0.533540i	−0.998747	−	0.0500434i	$-0.984064\pi$
$359$	−3.53734	+	10.1091i	−0.186694	+	0.533540i	0.812053	+	0.583583i	$0.198350\pi$
$360$	5.78036	+	3.34155i	0.304652	+	0.176115i
$361$	17.5963	+	36.5391i	0.926121	+	1.92311i
$362$	−2.57165	+	2.05082i	−0.135163	+	0.107789i
$363$	−21.1403	+	16.8588i	−1.10958	+	0.884860i
$364$	4.43622	+	9.21191i	0.232521	+	0.482835i
$365$	−7.52986	−	4.35292i	−0.394131	−	0.227842i
$366$	0.685184	−	1.95814i	0.0358152	−	0.102354i
$367$	10.6581	−	2.43263i	0.556346	−	0.126982i	0.0649020	−	0.997892i	$-0.479327\pi$
$367$	10.6581	−	2.43263i	0.556346	−	0.126982i	0.491444	+	0.870909i	$0.336469\pi$
$368$	4.12702	−	1.44411i	0.215136	−	0.0752792i
$369$	−8.63288	+	3.02078i	−0.449410	+	0.157255i
$370$	3.97552	−	4.27984i	0.206677	−	0.222499i
$371$	1.48573	+	1.86305i	0.0771353	+	0.0967246i
$372$	3.62720	−	0.408687i	0.188061	−	0.0211894i
$373$	−24.8540	−	15.6168i	−1.28689	−	0.808606i	−0.297616	−	0.954686i	$-0.596192\pi$
$373$	−24.8540	−	15.6168i	−1.28689	−	0.808606i	−0.989273	+	0.146079i	$0.953335\pi$
$374$	−15.0648	+	9.46586i	−0.778984	+	0.489468i
$375$	−6.98531	+	8.72958i	−0.360720	+	0.450793i
$376$			9.73646i			0.502119i
$377$	−32.6016	−	5.41934i	−1.67907	−	0.279110i
$378$	1.13168	−	1.13168i	0.0582073	−	0.0582073i
$379$	−3.03713	−	26.9553i	−0.156007	−	1.38460i	−0.790875	−	0.611978i	$-0.790374\pi$
$379$	−3.03713	−	26.9553i	−0.156007	−	1.38460i	0.634868	−	0.772621i	$-0.281055\pi$
$380$	−17.7082	+	0.652796i	−0.908411	+	0.0334877i
$381$	−11.4183	+	2.60616i	−0.584978	+	0.133517i
$382$	−1.05679	−	9.37930i	−0.0540703	−	0.479887i
$383$	−1.22417	+	10.8648i	−0.0625522	+	0.555166i	0.922879	+	0.385090i	$0.125830\pi$
$383$	−1.22417	+	10.8648i	−0.0625522	+	0.555166i	−0.985431	+	0.170076i	$0.945599\pi$
$384$	−3.38283	−	0.772108i	−0.172629	−	0.0394015i
$385$	12.5940	+	18.4939i	0.641848	+	0.942537i
$386$	−2.43116	+	5.04836i	−0.123743	+	0.256955i
$387$	−0.548619	−	2.40366i	−0.0278879	−	0.122185i
$388$	−2.15836	+	1.03941i	−0.109574	+	0.0527681i
$389$	14.0972	+	14.0972i	0.714754	+	0.714754i	0.967526	−	0.252772i	$-0.0813422\pi$
$389$	14.0972	+	14.0972i	0.714754	+	0.714754i	−0.252772	+	0.967526i	$0.581342\pi$
$390$	−8.82438	−	10.2656i	−0.446840	−	0.519818i
$391$	1.60544	−	14.2487i	0.0811908	−	0.720588i
$392$	8.13153	+	10.1966i	0.410704	+	0.515007i
$393$	1.77178	−	5.06347i	0.0893747	−	0.255418i
$394$	−9.86561	+	9.86561i	−0.497022	+	0.497022i
$395$	−21.1446	−	24.5980i	−1.06390	−	1.23766i
$396$	3.36961	−	5.36270i	0.169329	−	0.269486i
$397$	4.80013	+	13.7180i	0.240911	+	0.688485i	0.999326	+	0.0367127i	$0.0116886\pi$
$397$	4.80013	+	13.7180i	0.240911	+	0.688485i	−0.758414	+	0.651773i	$0.774026\pi$
$398$	16.6494	+	8.01792i	0.834558	+	0.401902i
$399$	−2.78605	+	12.2065i	−0.139477	+	0.611088i
$400$	−1.63349	+	4.14858i	−0.0816745	+	0.207429i
$401$	−2.74728	+	3.44498i	−0.137192	+	0.172034i	−0.845682	−	0.533688i	$-0.820806\pi$
$401$	−2.74728	+	3.44498i	−0.137192	+	0.172034i	0.708489	+	0.705722i	$0.249377\pi$
$402$	0.729070	−	1.16031i	0.0363627	−	0.0578709i
$403$	−21.2675	−	4.85418i	−1.05941	−	0.241804i
$404$	4.68611	−	0.527998i	0.233143	−	0.0262689i
$405$	1.11910	−	1.93587i	0.0556087	−	0.0961943i
$406$	8.60327	−	0.514021i	0.426973	−	0.0255104i
$407$	−11.5492	−	11.5492i	−0.572473	−	0.572473i
$408$	5.44416	−	6.82676i	0.269526	−	0.337975i
$409$	−6.00578	−	9.55814i	−0.296967	−	0.472620i	0.664597	−	0.747202i	$-0.268603\pi$
$409$	−6.00578	−	9.55814i	−0.296967	−	0.472620i	−0.961564	+	0.274582i	$0.911460\pi$
$410$	−9.41707	−	17.8418i	−0.465076	−	0.881145i
$411$	13.7265	+	10.9465i	0.677079	+	0.539953i
$412$	−12.9420	−	1.45821i	−0.637605	−	0.0718409i
$413$	−3.04250	−	4.84211i	−0.149712	−	0.238265i
$414$	−1.59754	−	4.56552i	−0.0785150	−	0.224383i
$415$	−4.76969	+	25.1324i	−0.234135	+	1.23370i
$416$	26.4609	+	16.6265i	1.29735	+	0.815181i
$417$	6.01201	+	12.4841i	0.294410	+	0.611348i
$418$		−	46.9525i		−	2.29652i
$419$	−3.72408	+	1.79342i	−0.181933	+	0.0876143i	−0.522633	−	0.852558i	$-0.675050\pi$
$419$	−3.72408	+	1.79342i	−0.181933	+	0.0876143i	0.340700	+	0.940172i	$0.389336\pi$
$420$	−2.99618	−	2.21384i	−0.146199	−	0.108024i
$421$	28.0089	+	3.15585i	1.36507	+	0.153807i	0.763910	−	0.645322i	$-0.223277\pi$
$421$	28.0089	+	3.15585i	1.36507	+	0.153807i	0.601160	+	0.799129i	$0.294705\pi$
$422$	−5.20936	−	1.82283i	−0.253588	−	0.0887342i
$423$	3.26079			0.158545
$424$	4.13951	+	1.44848i	0.201032	+	0.0703443i
$425$	9.93334	+	10.7294i	0.481838	+	0.520450i
$426$	7.72070	+	3.71809i	0.374069	+	0.180142i
$427$	−1.48039	+	3.07406i	−0.0716411	+	0.148764i
$428$	6.47504	−	4.06854i	0.312983	−	0.196660i
$429$	−29.5930	+	23.5996i	−1.42876	+	1.13940i
$430$	5.06350	−	1.98405i	0.244184	−	0.0956793i
$431$	4.88852	+	21.4180i	0.235472	+	1.03167i	0.945020	+	0.327012i	$0.106042\pi$
$431$	4.88852	+	21.4180i	0.235472	+	1.03167i	−0.709549	+	0.704656i	$0.751101\pi$
$432$	0.198426	−	0.869360i	0.00954676	−	0.0418271i
$433$	4.76512	+	3.80005i	0.228997	+	0.182619i	0.731266	−	0.682093i	$-0.238930\pi$
$433$	4.76512	+	3.80005i	0.228997	+	0.182619i	−0.502269	+	0.864711i	$0.667501\pi$
$434$	5.68885			0.273074
$435$	11.4268	−	3.79843i	0.547873	−	0.182121i
$436$	4.81092			0.230401
$437$	29.5845	+	23.5929i	1.41522	+	1.12860i
$438$	−0.853811	+	3.74079i	−0.0407967	+	0.178742i
$439$	2.56207	+	11.2252i	0.122281	+	0.535748i	0.998545	+	0.0539176i	$0.0171708\pi$
$439$	2.56207	+	11.2252i	0.122281	+	0.535748i	−0.876264	+	0.481831i	$0.839972\pi$
$440$	37.7344	+	16.4882i	1.79892	+	0.786042i
$441$	3.41490	−	2.72329i	0.162614	−	0.129681i
$442$	−14.9901	+	9.41892i	−0.713008	+	0.448012i
$443$	12.2182	−	25.3714i	0.580506	−	1.20543i	−0.379431	−	0.925220i	$-0.623880\pi$
$443$	12.2182	−	25.3714i	0.580506	−	1.20543i	0.959938	−	0.280214i	$-0.0904053\pi$
$444$	2.45010	+	1.17991i	0.116277	+	0.0559959i
$445$	−2.61807	+	1.38184i	−0.124108	+	0.0655055i
$446$	−20.1281	−	7.04314i	−0.953095	−	0.333502i
$447$	−10.4457			−0.494063
$448$	−10.4235	−	3.64732i	−0.492462	−	0.172320i
$449$	−3.90006	−	0.439431i	−0.184055	−	0.0207380i	0.0194558	−	0.999811i	$-0.493807\pi$
$449$	−3.90006	−	0.439431i	−0.184055	−	0.0207380i	−0.203511	+	0.979073i	$0.565235\pi$
$450$	4.58937	+	1.80705i	0.216345	+	0.0851852i
$451$	−50.8235	+	24.4753i	−2.39319	+	1.15250i
$452$			14.5030i			0.682163i
$453$	2.40863	+	5.00156i	0.113167	+	0.234994i
$454$	−4.03633	−	2.53619i	−0.189434	−	0.119029i
$455$	12.5315	+	18.4022i	0.587487	+	0.862709i
$456$	7.61060	+	21.7498i	0.356399	+	1.01853i
$457$	11.2383	+	17.8857i	0.525706	+	0.836656i	0.999021	−	0.0442370i	$-0.0140857\pi$
$457$	11.2383	+	17.8857i	0.525706	+	0.836656i	−0.473315	+	0.880893i	$0.656943\pi$
$458$	−13.7785	−	1.55246i	−0.643827	−	0.0725419i
$459$	−2.28632	−	1.82328i	−0.106716	−	0.0851034i
$460$	−9.95716	+	5.25548i	−0.464255	+	0.245038i
$461$	−11.7938	−	18.7698i	−0.549294	−	0.874196i	0.450534	−	0.892759i	$-0.351234\pi$
$461$	−11.7938	−	18.7698i	−0.549294	−	0.874196i	−0.999828	+	0.0185632i	$0.994091\pi$
$462$	6.15439	−	7.71736i	0.286328	−	0.359044i
$463$	4.22333	+	4.22333i	0.196275	+	0.196275i	0.798401	−	0.602126i	$-0.205680\pi$
$463$	4.22333	+	4.22333i	0.196275	+	0.196275i	−0.602126	+	0.798401i	$0.705680\pi$
$464$	3.90640	−	2.79279i	0.181350	−	0.129652i
$465$	7.67855	−	2.05292i	0.356084	−	0.0952017i
$466$	−11.2057	+	1.26258i	−0.519096	+	0.0584880i
$467$	37.0649	+	8.45982i	1.71516	+	0.391474i	0.963422	−	0.267989i	$-0.0863590\pi$
$467$	37.0649	+	8.45982i	1.71516	+	0.391474i	0.751737	+	0.659463i	$0.229216\pi$
$468$	3.35290	−	5.33610i	0.154988	−	0.246661i
$469$	−1.40520	+	1.76206i	−0.0648859	+	0.0813644i
$470$	1.06808	+	7.11291i	0.0492668	+	0.328094i
$471$	2.67616	−	11.7250i	0.123311	−	0.540260i
$472$	−9.48250	−	4.56653i	−0.436467	−	0.210192i
$473$	−5.02225	−	14.3528i	−0.230923	−	0.659941i
$474$	−7.61332	+	12.1165i	−0.349691	+	0.556531i
$475$	−37.9213	+	7.13169i	−1.73995	+	0.327225i
$476$	−3.44501	+	3.44501i	−0.157902	+	0.157902i
$477$	0.485103	−	1.38635i	0.0222114	−	0.0634764i
$478$	18.0291	+	22.6077i	0.824630	+	1.03405i
$479$	−3.97471	+	35.2765i	−0.181609	+	1.61182i	0.490547	+	0.871415i	$0.336797\pi$
$479$	−3.97471	+	35.2765i	−0.181609	+	1.61182i	−0.672156	+	0.740409i	$0.734632\pi$
$480$	−11.3542	−	0.857186i	−0.518244	−	0.0391250i
$481$	−11.4919	−	11.4919i	−0.523988	−	0.523988i
$482$	19.1114	−	9.20357i	0.870501	−	0.419211i
$483$	1.77019	+	7.75570i	0.0805463	+	0.352896i
$484$	12.0475	−	25.0168i	0.547612	−	1.13713i
$485$	−4.31166	+	2.93615i	−0.195782	+	0.133324i
$486$	−0.961731	−	0.219509i	−0.0436250	−	0.00995712i
$487$	−0.109269	+	0.969787i	−0.00495144	+	0.0439453i	−0.995945	−	0.0899645i	$-0.971325\pi$
$487$	−0.109269	+	0.969787i	−0.00495144	+	0.0439453i	0.990994	+	0.133910i	$0.0427532\pi$
$488$	0.703078	+	6.23999i	0.0318268	+	0.282471i
$489$	−0.198014	+	0.0451954i	−0.00895451	+	0.00204381i
$490$	7.05900	+	6.55705i	0.318893	+	0.296218i
$491$	2.67003	+	23.6971i	0.120497	+	1.06944i	0.897828	+	0.440346i	$0.145144\pi$
$491$	2.67003	+	23.6971i	0.120497	+	1.06944i	−0.777332	+	0.629091i	$0.783427\pi$
$492$	6.64120	−	6.64120i	0.299408	−	0.299408i
$493$	−2.69338	−	15.5159i	−0.121304	−	0.698800i
$494$		−	46.7197i		−	2.10202i
$495$	5.52198	−	12.6375i	0.248194	−	0.568011i
$496$	2.68383	−	1.68636i	0.120508	−	0.0757200i
$497$	−11.9334	−	7.49827i	−0.535288	−	0.336344i
$498$	11.2144	−	1.26355i	0.502527	−	0.0566212i
$499$	−10.9262	−	13.7010i	−0.489122	−	0.613340i	0.474615	−	0.880193i	$-0.342587\pi$
$499$	−10.9262	−	13.7010i	−0.489122	−	0.613340i	−0.963737	+	0.266854i	$0.914016\pi$
$500$	2.57331	−	11.1889i	0.115082	−	0.500382i
$501$	−6.31601	+	2.21007i	−0.282179	+	0.0987386i
$502$	11.4471	−	4.00551i	0.510909	−	0.178775i
$503$	−37.0405	+	8.45426i	−1.65156	+	0.376957i	−0.944063	−	0.329764i	$-0.893031\pi$
$503$	−37.0405	+	8.45426i	−1.65156	+	0.376957i	−0.707493	+	0.706721i	$0.750174\pi$
$504$	−1.59999	+	4.57250i	−0.0712690	+	0.203675i
$505$	9.92021	−	2.65224i	0.441444	−	0.118023i
$506$	−12.9438	−	26.8781i	−0.575423	−	1.19488i
$507$	−19.2824	+	15.3772i	−0.856363	+	0.682927i
$508$	9.40301	−	7.49865i	0.417191	−	0.332699i
$509$	−16.3265	−	33.9023i	−0.723658	−	1.50269i	−0.859046	−	0.511899i	$-0.828942\pi$
$509$	−16.3265	−	33.9023i	−0.723658	−	1.50269i	0.135387	−	0.990793i	$-0.456772\pi$
$510$	3.22831	−	5.58447i	0.142952	−	0.247285i
$511$	2.08424	−	5.95642i	0.0922015	−	0.263497i
$512$	−9.61861	+	2.19539i	−0.425087	+	0.0970233i
$513$	7.28414	−	2.54883i	0.321603	−	0.112534i
$514$	−13.3822	+	4.68263i	−0.590262	+	0.206542i
$515$	−28.3404	+	1.04474i	−1.24883	+	0.0460369i
$516$	1.57853	+	1.97942i	0.0694909	+	0.0871389i
$517$	19.9849	−	2.25175i	0.878933	−	0.0990320i
$518$	3.58865	+	2.25490i	0.157676	+	0.0990744i
$519$	2.04544	−	1.28524i	0.0897850	−	0.0564156i
$520$	37.5473	+	16.4064i	1.64656	+	0.719468i
$521$			36.7474i			1.60993i	0.593319	+	0.804967i	$0.297817\pi$
$521$			36.7474i			1.60993i	−0.593319	+	0.804967i	$0.702183\pi$
$522$	−3.08953	−	4.32146i	−0.135225	−	0.189145i
$523$	23.8782	−	23.8782i	1.04412	−	1.04412i	0.0451380	−	0.998981i	$-0.485627\pi$
$523$	23.8782	−	23.8782i	1.04412	−	1.04412i	0.998981	−	0.0451380i	$-0.0143727\pi$
$524$	0.616785	+	5.47412i	0.0269444	+	0.239138i
$525$	−7.16774	−	3.79840i	−0.312826	−	0.165776i
$526$	17.5604	−	4.00804i	0.765668	−	0.174759i
$527$	−1.16383	−	10.3293i	−0.0506974	−	0.449952i
$528$	0.615779	−	5.46519i	0.0267983	−	0.237842i
$529$	1.01648	+	0.232005i	0.0441948	+	0.0100872i
$530$	3.18299	+	0.604077i	0.138260	+	0.0262394i
$531$	−1.52936	+	3.17574i	−0.0663684	+	0.137815i
$532$	−2.86096	−	12.5347i	−0.124039	−	0.543448i
$533$	−50.5715	+	24.3539i	−2.19049	+	1.05489i
$534$	0.923478	+	0.923478i	0.0399628	+	0.0399628i
$535$	12.6276	−	10.8548i	0.545939	−	0.469294i
$536$	−0.464417	+	4.12181i	−0.0200598	+	0.178035i
$537$	4.59200	+	5.75818i	0.198159	+	0.248484i
$538$	−9.53023	+	27.2358i	−0.410877	+	1.17422i
$539$	19.0488	−	19.0488i	0.820490	−	0.820490i
$540$	−0.172860	+	2.28968i	−0.00743871	+	0.0985321i
$541$	−21.4943	+	34.2079i	−0.924110	+	1.47071i	−0.0423022	+	0.999105i	$0.513469\pi$
$541$	−21.4943	+	34.2079i	−0.924110	+	1.47071i	−0.881808	+	0.471608i	$0.843674\pi$
$542$	−5.89534	−	16.8479i	−0.253227	−	0.723680i
$543$	−3.00419	−	1.44674i	−0.128922	−	0.0620857i
$544$	−3.31359	+	14.5178i	−0.142069	+	0.622446i
$545$	10.3597	−	1.55562i	0.443761	−	0.0666355i
$546$	6.12387	−	7.67909i	0.262078	−	0.328635i
$547$	−2.03786	+	3.24324i	−0.0871326	+	0.138671i	−0.887447	−	0.460910i	$-0.847523\pi$
$547$	−2.03786	+	3.24324i	−0.0871326	+	0.138671i	0.800314	+	0.599581i	$0.204666\pi$
$548$	−17.5770	−	4.01182i	−0.750850	−	0.171377i
$549$	2.08981	−	0.235465i	0.0891908	−	0.0100494i
$550$	29.3754	+	7.90591i	1.25257	+	0.337109i
$551$	38.4516	+	15.7663i	1.63809	+	0.671667i
$552$	10.3527	+	10.3527i	0.440640	+	0.440640i
$553$	14.6738	−	18.4003i	0.623993	−	0.782462i
$554$	8.61415	+	13.7093i	0.365980	+	0.582454i
$555$	5.65750	+	1.74853i	0.240148	+	0.0742211i
$556$	−11.1246	−	8.87156i	−0.471787	−	0.376238i
$557$	9.66427	+	1.08890i	0.409488	+	0.0461382i	0.314306	−	0.949322i	$-0.398228\pi$
$557$	9.66427	+	1.08890i	0.409488	+	0.0461382i	0.0951820	+	0.995460i	$0.469657\pi$
$558$	−1.86554	−	2.96899i	−0.0789747	−	0.125688i
$559$	−4.99734	−	14.2816i	−0.211365	−	0.604047i
$560$	−3.17824	−	0.603174i	−0.134305	−	0.0254887i
$561$	−15.2716	−	9.59575i	−0.644766	−	0.405133i
$562$	12.4790	+	25.9129i	0.526394	+	1.09307i
$563$		−	13.4447i		−	0.566628i	−0.959027	−	0.283314i	$-0.908566\pi$
$563$		−	13.4447i		−	0.566628i	0.959027	−	0.283314i	$-0.0914338\pi$
$564$	−3.01687	+	1.45285i	−0.127033	+	0.0611760i
$565$	4.68957	+	31.2303i	0.197292	+	1.31387i
$566$	−27.2073	−	3.06552i	−1.14361	−	0.128854i
$567$	1.53135	+	0.535844i	0.0643109	+	0.0225033i
$568$	−25.9384			−1.08835
$569$	18.7652	+	6.56622i	0.786677	+	0.275270i	0.693573	−	0.720386i	$-0.256035\pi$
$569$	18.7652	+	6.56622i	0.786677	+	0.275270i	0.0931041	+	0.995656i	$0.470321\pi$
$570$	7.94582	+	15.0543i	0.332814	+	0.630557i
$571$	32.4110	+	15.6083i	1.35636	+	0.653188i	0.963822	−	0.266548i	$-0.0858831\pi$
$571$	32.4110	+	15.6083i	1.35636	+	0.653188i	0.392537	+	0.919736i	$0.371597\pi$
$572$	16.8645	−	35.0195i	0.705139	−	1.46424i
$573$	8.10160	−	5.09058i	0.338449	−	0.212662i
$574$	11.4443	−	9.12652i	0.477676	−	0.380934i
$575$	−19.7421	+	14.5367i	−0.823303	+	0.606221i
$576$	1.51463	+	6.63603i	0.0631096	+	0.276501i
$577$	5.95956	−	26.1105i	0.248100	−	1.08700i	−0.685330	−	0.728233i	$-0.740342\pi$
$577$	5.95956	−	26.1105i	0.248100	−	1.08700i	0.933429	−	0.358762i	$-0.116801\pi$
$578$	6.51580	+	5.19618i	0.271022	+	0.216133i
$579$	−5.68014			−0.236059
$580$	−8.87964	+	8.60552i	−0.368707	+	0.357325i
$581$	−18.5605			−0.770020
$582$	1.79922	+	1.43483i	0.0745801	+	0.0594757i
$583$	2.01577	−	8.83167i	0.0834848	−	0.365771i
$584$	−2.58439	−	11.3230i	−0.106943	−	0.468547i
$585$	5.49460	−	12.5748i	0.227174	−	0.519903i
$586$	8.86576	−	7.07021i	0.366241	−	0.292068i
$587$	3.44682	−	2.16578i	0.142265	−	0.0893913i	−0.459019	−	0.888427i	$-0.651799\pi$
$587$	3.44682	−	2.16578i	0.142265	−	0.0893913i	0.601284	+	0.799035i	$0.294656\pi$
$588$	−1.94609	+	4.04109i	−0.0802553	+	0.166652i
$589$	24.7148	+	11.9020i	1.01835	+	0.490413i
$590$	−7.42833	−	2.29583i	−0.305819	−	0.0945179i
$591$	−13.3499	−	4.67132i	−0.549140	−	0.192152i
$592$	2.36144			0.0970547
$593$	−17.9885	−	6.29446i	−0.738700	−	0.258482i	−0.0654077	−	0.997859i	$-0.520835\pi$
$593$	−17.9885	−	6.29446i	−0.738700	−	0.258482i	−0.673292	+	0.739376i	$0.735120\pi$
$594$	−6.04587	−	0.681206i	−0.248065	−	0.0279502i
$595$	−6.30444	+	8.53234i	−0.258457	+	0.349792i
$596$	9.66429	−	4.65408i	0.395865	−	0.190638i
$597$			18.7330i			0.766691i
$598$	−12.8796	−	26.7448i	−0.526688	−	1.09368i
$599$	11.0401	+	6.93698i	0.451088	+	0.283437i	0.738354	−	0.674414i	$-0.235603\pi$
$599$	11.0401	+	6.93698i	0.451088	+	0.283437i	−0.287266	+	0.957851i	$0.592746\pi$
$600$	−14.8891	+	1.09924i	−0.607843	+	0.0448761i
$601$	−1.37792	−	3.93788i	−0.0562067	−	0.160629i	0.912357	−	0.409396i	$-0.134261\pi$
$601$	−1.37792	−	3.93788i	−0.0562067	−	0.160629i	−0.968563	+	0.248767i	$0.919975\pi$
$602$	2.09931	+	3.34103i	0.0855614	+	0.136170i
$603$	1.38042	+	0.155536i	0.0562150	+	0.00633391i
$604$	−4.45690	−	3.55426i	−0.181349	−	0.144621i
$605$	17.8534	−	57.7661i	0.725846	−	2.34853i
$606$	−2.41016	−	3.83575i	−0.0979062	−	0.155817i
$607$	14.6985	−	18.4314i	0.596594	−	0.748106i	−0.388248	−	0.921555i	$-0.626920\pi$
$607$	14.6985	−	18.4314i	0.596594	−	0.748106i	0.984843	+	0.173449i	$0.0554912\pi$
$608$	−27.7875	−	27.7875i	−1.12693	−	1.12693i
$609$	4.25352	+	7.63156i	0.172361	+	0.309246i
$610$	1.19815	+	4.48146i	0.0485117	+	0.181449i
$611$	19.8858	−	2.24059i	0.804492	−	0.0906445i
$612$	2.92766	+	0.668219i	0.118344	+	0.0270112i
$613$	12.0671	−	19.2047i	0.487387	−	0.775672i	−0.508985	−	0.860775i	$-0.669979\pi$
$613$	12.0671	−	19.2047i	0.487387	−	0.775672i	0.996372	+	0.0851032i	$0.0271220\pi$
$614$	15.5312	−	19.4755i	0.626788	−	0.785967i
$615$	12.1535	−	16.4484i	0.490078	−	0.663264i
$616$	−6.64849	+	29.1290i	−0.267875	+	1.17364i
$617$	−32.5338	−	15.6674i	−1.30976	−	0.630747i	−0.356895	−	0.934144i	$-0.616165\pi$
$617$	−32.5338	−	15.6674i	−1.30976	−	0.630747i	−0.952864	+	0.303397i	$0.901879\pi$
$618$	4.13217	+	11.8091i	0.166220	+	0.475030i
$619$	−10.3311	+	16.4419i	−0.415242	+	0.660855i	−0.987211	−	0.159421i	$-0.949037\pi$
$619$	−10.3311	+	16.4419i	−0.415242	+	0.660855i	0.571968	+	0.820276i	$0.306180\pi$
$620$	−6.18949	+	5.32053i	−0.248576	+	0.213678i
$621$	3.46718	−	3.46718i	0.139133	−	0.139133i
$622$	2.44518	−	6.98792i	0.0980427	−	0.280190i
$623$	−1.33921	−	1.67931i	−0.0536542	−	0.0672802i
$624$	0.612725	−	5.43809i	0.0245286	−	0.217698i
$625$	1.92335	−	24.9259i	0.0769338	−	0.997036i
$626$	−5.01073	−	5.01073i	−0.200269	−	0.200269i
$627$	42.8832	−	20.6515i	1.71259	−	0.824740i
$628$	2.74812	+	12.0403i	0.109662	+	0.480461i
$629$	3.36006	−	6.97724i	0.133975	−	0.278201i
$630$	−0.667262	+	3.51593i	−0.0265843	+	0.140078i
$631$	−3.34424	−	0.763302i	−0.133132	−	0.0303866i	0.155436	−	0.987846i	$-0.450322\pi$
$631$	−3.34424	−	0.763302i	−0.133132	−	0.0303866i	−0.288568	+	0.957459i	$0.593179\pi$
$632$	4.84968	−	43.0421i	0.192910	−	1.71212i
$633$	−0.626420	−	5.55963i	−0.0248979	−	0.220975i
$634$	−8.64992	+	1.97429i	−0.343532	+	0.0784090i
$635$	17.8235	−	19.1879i	0.707303	−	0.761447i
$636$	0.168872	+	1.49878i	0.00669621	+	0.0594305i
$637$	18.9543	−	18.9543i	0.750998	−	0.750998i
$638$	−21.9194	−	24.3520i	−0.867798	−	0.964105i
$639$			8.68692i			0.343649i
$640$	7.22399	−	2.83060i	0.285553	−	0.111889i
$641$	−30.9526	+	19.4488i	−1.22256	+	0.768182i	−0.979424	−	0.201811i	$-0.935317\pi$
$641$	−30.9526	+	19.4488i	−1.22256	+	0.768182i	−0.243131	+	0.969994i	$0.578174\pi$
$642$	−6.22014	−	3.90837i	−0.245489	−	0.154251i
$643$	33.3226	−	3.75456i	1.31412	−	0.148065i	0.573063	−	0.819511i	$-0.305755\pi$
$643$	33.3226	−	3.75456i	1.31412	−	0.148065i	0.741054	+	0.671446i	$0.234326\pi$
$644$	−5.09333	−	6.38683i	−0.200705	−	0.251676i
$645$	4.03921	+	3.75200i	0.159044	+	0.147735i
$646$	21.0128	−	7.35269i	0.826737	−	0.289288i
$647$	−24.9771	+	8.73988i	−0.981953	+	0.343600i	−0.773056	−	0.634337i	$-0.781273\pi$
$647$	−24.9771	+	8.73988i	−0.981953	+	0.343600i	−0.208897	+	0.977938i	$0.566987\pi$
$648$	2.91105	−	0.664429i	0.114357	−	0.0261012i
$649$	−7.18015	+	20.5197i	−0.281846	+	0.805468i
$650$	29.2297	+	7.86670i	1.14648	+	0.308557i
$651$	2.50217	+	5.19581i	0.0980679	+	0.203640i
$652$	0.163065	−	0.130040i	0.00638612	−	0.00509276i
$653$	−5.90804	+	4.71151i	−0.231200	+	0.184375i	−0.732237	−	0.681050i	$-0.761523\pi$
$653$	−5.90804	+	4.71151i	−0.231200	+	0.184375i	0.501037	+	0.865426i	$0.332952\pi$
$654$	−2.00521	−	4.16385i	−0.0784097	−	0.162819i
$655$	3.09824	+	11.5884i	0.121058	+	0.452796i
$656$	2.69368	−	7.69809i	0.105170	−	0.300560i
$657$	−3.79212	+	0.865527i	−0.147945	+	0.0337674i
$658$	−4.92584	+	1.72362i	−0.192029	+	0.0671939i
$659$	−8.35393	+	2.92317i	−0.325423	+	0.113870i	−0.488046	−	0.872818i	$-0.662290\pi$
$659$	−8.35393	+	2.92317i	−0.325423	+	0.113870i	0.162623	+	0.986688i	$0.448005\pi$
$660$	0.521717	+	14.1524i	0.0203078	+	0.550883i
$661$	−6.95527	−	8.72163i	−0.270529	−	0.339232i	0.627947	−	0.778256i	$-0.283896\pi$
$661$	−6.95527	−	8.72163i	−0.270529	−	0.339232i	−0.898475	+	0.439024i	$0.855324\pi$
$662$	2.09889	−	0.236488i	0.0815756	−	0.00919137i
$663$	−15.1958	−	9.54817i	−0.590157	−	0.370820i
$664$	−28.9236	+	18.1739i	−1.12245	+	0.705284i
$665$	−10.2138	−	26.0668i	−0.396076	−	1.01083i
$666$		−	2.61235i		−	0.101226i
$667$	26.3582	−	1.57483i	1.02059	−	0.0609776i
$668$	4.85885	−	4.85885i	0.187995	−	0.187995i
$669$	−2.42039	−	21.4815i	−0.0935775	−	0.830524i
$670$	0.112882	+	3.06211i	0.00436101	+	0.118300i
$671$	12.6455	−	2.88625i	0.488173	−	0.111422i
$672$	−0.925001	−	8.20961i	−0.0356827	−	0.316692i
$673$	−2.75509	+	24.4521i	−0.106201	+	0.942558i	0.821748	+	0.569851i	$0.192999\pi$
$673$	−2.75509	+	24.4521i	−0.106201	+	0.942558i	−0.927949	+	0.372707i	$0.878430\pi$
$674$	−12.0552	−	2.75152i	−0.464349	−	0.105985i
$675$	0.368140	+	4.98643i	0.0141697	+	0.191928i
$676$	10.9887	−	22.8183i	0.422642	−	0.877625i
$677$	−6.95966	−	30.4923i	−0.267482	−	1.17191i	−0.912932	−	0.408111i	$-0.866188\pi$
$677$	−6.95966	−	30.4923i	−0.267482	−	1.17191i	0.645451	−	0.763802i	$-0.276670\pi$
$678$	12.5523	−	6.04488i	0.482069	−	0.232152i
$679$	−2.67629	−	2.67629i	−0.102707	−	0.102707i
$680$	−1.46985	+	19.4694i	−0.0563661	+	0.746617i
$681$	0.541058	−	4.80202i	0.0207334	−	0.184014i
$682$	−13.4839	−	16.9082i	−0.516323	−	0.647449i
$683$	−6.40472	+	18.3036i	−0.245070	+	0.700370i	0.753984	+	0.656892i	$0.228129\pi$
$683$	−6.40472	+	18.3036i	−0.245070	+	0.700370i	−0.999054	+	0.0434774i	$0.986156\pi$
$684$	−5.60363	+	5.60363i	−0.214260	+	0.214260i
$685$	−39.1470	−	2.95541i	−1.49573	−	0.112920i
$686$	−9.67952	+	15.4049i	−0.369566	+	0.588160i
$687$	−4.64239	−	13.2672i	−0.177118	−	0.506175i
$688$	1.98078	+	0.953894i	0.0755166	+	0.0363669i
$689$	2.00578	−	8.78788i	0.0764140	−	0.334792i
$690$	8.69878	+	6.42742i	0.331157	+	0.244688i
$691$	−5.12898	+	6.43153i	−0.195115	+	0.244667i	−0.869759	−	0.493477i	$-0.835726\pi$
$691$	−5.12898	+	6.43153i	−0.195115	+	0.244667i	0.674644	+	0.738144i	$0.264297\pi$
$692$	−1.31980	+	2.10044i	−0.0501711	+	0.0798469i
$693$	9.75545	+	2.22662i	0.370579	+	0.0845822i
$694$	−2.24380	+	0.252815i	−0.0851734	+	0.00959674i
$695$	−26.8240	−	15.5066i	−1.01749	−	0.588199i
$696$	14.1010	+	7.72765i	0.534498	+	0.292916i
$697$	−18.9124	−	18.9124i	−0.716358	−	0.716358i
$698$	−0.119334	+	0.149640i	−0.00451685	+	0.00566395i
$699$	−6.08186	−	9.67923i	−0.230037	−	0.366102i
$700$	8.32395	+	0.320672i	0.314616	+	0.0121203i
$701$	−18.1924	−	14.5079i	−0.687117	−	0.547957i	0.216509	−	0.976281i	$-0.430533\pi$
$701$	−18.1924	−	14.5079i	−0.687117	−	0.547957i	−0.903626	+	0.428323i	$0.859104\pi$
$702$	−6.01589	−	0.677828i	−0.227055	−	0.0255830i
$703$	10.8730	+	17.3042i	0.410082	+	0.652642i
$704$	13.8655	+	39.6252i	0.522574	+	1.49343i
$705$	−6.02667	+	4.10404i	−0.226977	+	0.154567i
$706$	9.35597	+	5.87875i	0.352117	+	0.221249i
$707$	3.23265	+	6.71267i	0.121576	+	0.252456i
$708$		−	3.61959i		−	0.136032i
$709$	42.0709	−	20.2603i	1.58000	−	0.760890i	0.581396	−	0.813621i	$-0.302507\pi$
$709$	42.0709	−	20.2603i	1.58000	−	0.760890i	0.998609	+	0.0527308i	$0.0167925\pi$
$710$	−18.9492	+	2.84542i	−0.711150	+	0.106787i
$711$	−14.4150	−	1.62418i	−0.540606	−	0.0609117i
$712$	−3.73127	−	1.30563i	−0.139835	−	0.0489305i
$713$	17.4292			0.652728
$714$	4.41754	+	1.54577i	0.165322	+	0.0578488i
$715$	24.9919	−	80.8631i	0.934644	−	3.02411i
$716$	−6.81406	−	3.28148i	−0.254653	−	0.122635i
$717$	−12.7185	+	26.4102i	−0.474981	+	0.986309i
$718$	−8.94579	+	5.62101i	−0.333854	+	0.209774i
$719$	−25.7922	+	20.5686i	−0.961885	+	0.767078i	−0.972509	−	0.232866i	$-0.925190\pi$
$719$	−25.7922	+	20.5686i	−0.961885	+	0.767078i	0.0106235	+	0.999944i	$0.496618\pi$
$720$	0.727442	+	1.85651i	0.0271102	+	0.0691880i
$721$	−4.57872	−	20.0607i	−0.170521	−	0.747099i
$722$	−8.90225	+	39.0033i	−0.331307	+	1.45155i
$723$	16.8118	+	13.4070i	0.625239	+	0.498611i
$724$	3.42406			0.127254
$725$	−16.3386	+	21.4021i	−0.606799	+	0.794855i
$726$	−26.6735			−0.989945
$727$	15.8914	+	12.6729i	0.589378	+	0.470013i	0.872193	−	0.489161i	$-0.162697\pi$
$727$	15.8914	+	12.6729i	0.589378	+	0.470013i	−0.282816	+	0.959174i	$0.591269\pi$
$728$	−6.61553	+	28.9845i	−0.245188	+	1.07424i
$729$	−0.222521	−	0.974928i	−0.00824152	−	0.0361084i
$730$	−3.13013	−	7.98842i	−0.115851	−	0.295665i
$731$	5.63686	−	4.49524i	0.208487	−	0.166263i
$732$	−1.82857	+	1.14897i	−0.0675858	+	0.0424670i
$733$	−20.0608	+	41.6567i	−0.740963	+	1.53863i	0.0984567	+	0.995141i	$0.468609\pi$
$733$	−20.0608	+	41.6567i	−0.740963	+	1.53863i	−0.839420	+	0.543484i	$0.817105\pi$
$734$	9.71619	+	4.67907i	0.358631	+	0.172708i
$735$	−2.88396	+	9.33125i	−0.106376	+	0.344188i
$736$	−23.5675	−	8.24662i	−0.868710	−	0.303975i
$737$	8.56776			0.315598
$738$	−8.51602	−	2.97989i	−0.313479	−	0.109691i
$739$	13.4858	+	1.51949i	0.496084	+	0.0558952i	0.356462	−	0.934310i	$-0.383983\pi$
$739$	13.4858	+	1.51949i	0.496084	+	0.0558952i	0.139622	+	0.990205i	$0.455411\pi$
$740$	−6.01336	+	0.902970i	−0.221055	+	0.0331938i
$741$	42.6706	−	20.5491i	1.56754	−	0.754889i
$742$			2.35067i			0.0862958i
$743$	−8.61864	−	17.8968i	−0.316187	−	0.656569i	0.680938	−	0.732341i	$-0.261572\pi$
$743$	−8.61864	−	17.8968i	−0.316187	−	0.656569i	−0.997125	+	0.0757717i	$0.975858\pi$
$744$	8.98682	+	5.64679i	0.329473	+	0.207021i
$745$	19.3059	−	13.1469i	0.707314	−	0.481666i
$746$	−9.56347	−	27.3308i	−0.350144	−	1.00065i
$747$	6.08654	+	9.68667i	0.222695	+	0.354417i
$748$	18.4046	+	2.07370i	0.672938	+	0.0758219i
$749$	9.44599	+	7.53293i	0.345149	+	0.275247i
$750$	−10.7565	+	2.43636i	−0.392773	+	0.0889632i
$751$	20.0116	+	31.8483i	0.730235	+	1.16216i	0.980980	+	0.194109i	$0.0621816\pi$
$751$	20.0116	+	31.8483i	0.730235	+	1.16216i	−0.250745	+	0.968053i	$0.580676\pi$
$752$	−1.81292	+	2.27334i	−0.0661106	+	0.0829000i
$753$	8.69323	+	8.69323i	0.316799	+	0.316799i
$754$	−21.8107	−	24.2313i	−0.794300	−	0.882450i
$755$	−10.7467	−	6.21250i	−0.391111	−	0.226096i
$756$	−1.65555	+	0.186536i	−0.0602117	+	0.00678423i
$757$	−12.3874	−	2.82735i	−0.450229	−	0.102762i	−0.00860702	−	0.999963i	$-0.502740\pi$
$757$	−12.3874	−	2.82735i	−0.450229	−	0.102762i	−0.441622	+	0.897201i	$0.645597\pi$
$758$	14.2365	−	22.6572i	0.517091	−	0.822946i
$759$	18.8555	−	23.6440i	0.684411	−	0.858224i
$760$	−41.4405	−	30.6198i	−1.50320	−	1.11070i
$761$	4.01323	−	17.5831i	0.145480	−	0.637388i	−0.848628	−	0.528990i	$-0.822571\pi$
$761$	4.01323	−	17.5831i	0.145480	−	0.637388i	0.994108	−	0.108398i	$-0.0345720\pi$
$762$	−10.4093	−	5.01284i	−0.377088	−	0.181596i
$763$	2.51040	+	7.17431i	0.0908826	+	0.259728i
$764$	−5.22746	+	8.31946i	−0.189123	+	0.300987i
$765$	6.52041	+	0.492260i	0.235746	+	0.0177977i
$766$	−7.62654	+	7.62654i	−0.275558	+	0.275558i
$767$	−7.14455	+	20.4179i	−0.257975	+	0.737249i
$768$	−10.6219	−	13.3195i	−0.383285	−	0.480625i
$769$	4.29703	−	38.1372i	0.154955	−	1.37526i	−0.639898	−	0.768460i	$-0.721024\pi$
$769$	4.29703	−	38.1372i	0.154955	−	1.37526i	0.794853	−	0.606802i	$-0.207548\pi$
$770$	−1.66160	+	22.0093i	−0.0598799	+	0.793161i
$771$	−10.1628	−	10.1628i	−0.366003	−	0.366003i
$772$	5.25524	−	2.53079i	0.189140	−	0.0910852i
$773$	5.26761	+	23.0789i	0.189463	+	0.830091i	0.976900	+	0.213696i	$0.0685503\pi$
$773$	5.26761	+	23.0789i	0.189463	+	0.830091i	−0.787437	+	0.616395i	$0.788593\pi$
$774$	1.05525	−	2.19124i	0.0379301	−	0.0787626i
$775$	−11.6079	+	13.4585i	−0.416967	+	0.483443i
$776$	−6.79111	−	1.55003i	−0.243786	−	0.0556427i
$777$	−0.481047	+	4.26941i	−0.0172575	+	0.153164i
$778$	2.20195	+	19.5429i	0.0789438	+	0.700645i
$779$	68.8130	−	15.7061i	2.46548	−	0.562730i
$780$	0.519130	+	14.0823i	0.0185878	+	0.504226i
$781$	5.99879	+	53.2407i	0.214654	+	1.90510i
$782$	10.0019	−	10.0019i	0.357666	−	0.357666i
$783$	2.58803	−	4.72251i	0.0924888	−	0.168769i
$784$			3.89486i			0.139102i
$785$	9.81099	+	25.0387i	0.350169	+	0.893668i
$786$	4.48077	−	2.81545i	0.159824	−	0.100424i
$787$	−36.9616	−	23.2245i	−1.31754	−	0.827864i	−0.324526	−	0.945877i	$-0.605205\pi$
$787$	−36.9616	−	23.2245i	−1.31754	−	0.827864i	−0.993012	+	0.118012i	$0.962348\pi$
$788$	14.4325	−	1.62616i	0.514138	−	0.0579294i
$789$	11.3844	+	14.2756i	0.405294	+	0.508223i
$790$	−1.17877	−	31.9762i	−0.0419388	−	1.13766i
$791$	−21.6276	+	7.56784i	−0.768991	+	0.269081i
$792$	17.3825	−	6.08241i	0.617662	−	0.216129i
$793$	12.5828	−	2.87194i	0.446827	−	0.101985i
$794$	−4.73515	+	13.5323i	−0.168044	+	0.480243i
$795$	0.848278	+	3.17283i	0.0300853	+	0.112529i
$796$	−8.34650	−	17.3317i	−0.295834	−	0.614306i
$797$	−5.10153	+	4.06833i	−0.180705	+	0.144108i	−0.709665	−	0.704539i	$-0.751154\pi$
$797$	−5.10153	+	4.06833i	−0.180705	+	0.144108i	0.528960	+	0.848647i	$0.322582\pi$
$798$	−9.65633	+	7.70066i	−0.341830	+	0.272600i
$799$	4.13733	+	8.59126i	0.146368	+	0.303937i
$800$	22.0639	−	12.7061i	0.780075	−	0.449228i
$801$	−0.437262	+	1.24962i	−0.0154499	+	0.0441532i
$802$	−4.23766	+	0.967219i	−0.149637	+	0.0341537i
$803$	−22.6436	+	7.92334i	−0.799075	+	0.279609i
$804$	−1.34646	+	0.471146i	−0.0474859	+	0.0166160i
$805$	−13.0330	−	12.1063i	−0.459354	−	0.426691i
$806$	−13.4170	−	16.8244i	−0.472593	−	0.592613i
$807$	−29.0671	+	3.27508i	−1.02321	+	0.115288i
$808$	11.6104	+	7.29530i	0.408453	+	0.256648i
$809$	38.1488	−	23.9705i	1.34124	−	0.842757i	0.345815	−	0.938303i	$-0.387602\pi$
$809$	38.1488	−	23.9705i	1.34124	−	0.842757i	0.995425	+	0.0955455i	$0.0304595\pi$
$810$	2.05377	−	0.804734i	0.0721620	−	0.0282755i
$811$		−	43.9263i		−	1.54246i	−0.636556	−	0.771231i	$-0.719641\pi$
$811$		−	43.9263i		−	1.54246i	0.636556	−	0.771231i	$-0.280359\pi$
$812$	−7.33558	−	5.16553i	−0.257429	−	0.181275i
$813$	12.7948	−	12.7948i	0.448732	−	0.448732i
$814$	−1.80397	−	16.0107i	−0.0632290	−	0.561173i
$815$	0.309091	−	0.332752i	0.0108270	−	0.0116558i
$816$	2.54228	−	0.580259i	0.0889977	−	0.0203131i
$817$	2.13030	+	18.9069i	0.0745297	+	0.661469i
$818$	1.24679	−	11.0656i	0.0435929	−	0.386898i
$819$	9.70708	+	2.21558i	0.339193	+	0.0774185i
$820$	−3.91579	+	20.6330i	−0.136745	+	0.720537i
$821$	−7.13211	+	14.8100i	−0.248912	+	0.516872i	−0.987564	−	0.157215i	$-0.949748\pi$
$821$	−7.13211	+	14.8100i	−0.248912	+	0.516872i	0.738652	+	0.674087i	$0.235463\pi$
$822$	3.85389	+	16.8850i	0.134420	+	0.588931i
$823$	6.30682	−	3.03721i	0.219842	−	0.105870i	−0.320722	−	0.947174i	$-0.603925\pi$
$823$	6.30682	−	3.03721i	0.219842	−	0.105870i	0.540563	+	0.841303i	$0.318211\pi$
$824$	−26.7780	−	26.7780i	−0.932857	−	0.932857i
$825$	5.69967	+	30.3068i	0.198437	+	1.05515i
$826$	0.631617	−	5.60576i	0.0219768	−	0.195049i
$827$	11.7979	+	14.7941i	0.410254	+	0.514442i	0.943434	−	0.331560i	$-0.107575\pi$
$827$	11.7979	+	14.7941i	0.410254	+	0.514442i	−0.533181	+	0.846001i	$0.679003\pi$
$828$	−1.66301	+	4.75262i	−0.0577937	+	0.165165i
$829$	−6.44961	+	6.44961i	−0.224004	+	0.224004i	−0.810182	−	0.586178i	$-0.800632\pi$
$829$	−6.44961	+	6.44961i	−0.224004	+	0.224004i	0.586178	+	0.810182i	$0.300632\pi$
$830$	−19.1363	+	16.4497i	−0.664231	+	0.570978i
$831$	−8.73236	+	13.8975i	−0.302922	+	0.482098i
$832$	13.7967	+	39.4287i	0.478315	+	1.36694i
$833$	11.5080	+	5.54195i	0.398728	+	0.192017i
$834$	−3.04157	+	13.3260i	−0.105321	+	0.461442i
$835$	8.89180	−	12.0340i	0.307713	−	0.416455i
$836$	−30.4741	+	38.2133i	−1.05397	+	1.32163i
$837$	1.89114	−	3.00974i	0.0653674	−	0.104032i
$838$	−3.97523	−	0.907320i	−0.137322	−	0.0313429i
$839$	−20.0256	+	2.25634i	−0.691359	+	0.0778975i	−0.450651	−	0.892700i	$-0.648808\pi$
$839$	−20.0256	+	2.25634i	−0.691359	+	0.0778975i	−0.240708	+	0.970598i	$0.577380\pi$
$840$	−2.79782	−	10.4647i	−0.0965340	−	0.361068i
$841$	27.3034	−	9.77363i	0.941497	−	0.337022i
$842$	19.6608	+	19.6608i	0.677556	+	0.677556i
$843$	−18.1784	+	22.7949i	−0.626096	+	0.785099i
$844$	3.05666	+	4.86464i	0.105214	+	0.167448i
$845$	16.2844	−	52.6894i	0.560201	−	1.81257i
$846$	2.51488	+	2.00555i	0.0864634	+	0.0689522i
$847$	43.5930	+	4.91175i	1.49787	+	0.168770i
$848$	0.696816	+	1.10898i	0.0239288	+	0.0380824i
$849$	−9.16694	−	26.1976i	−0.314609	−	0.899100i
$850$	1.06199	+	14.3845i	0.0364258	+	0.493384i
$851$	10.9947	+	6.90842i	0.376893	+	0.236818i
$852$	−3.87047	−	8.03711i	−0.132600	−	0.275347i
$853$		−	27.4289i		−	0.939149i	−0.882893	−	0.469575i	$-0.844407\pi$
$853$		−	27.4289i		−	0.939149i	0.882893	−	0.469575i	$-0.155593\pi$
$854$	−3.03245	+	1.46035i	−0.103768	+	0.0499722i
$855$	−10.2548	+	13.8786i	−0.350705	+	0.474639i
$856$	22.0961	+	2.48963i	0.755228	+	0.0850938i
$857$	37.5943	+	13.1548i	1.28420	+	0.449360i	0.884179	−	0.467148i	$-0.154718\pi$
$857$	37.5943	+	13.1548i	1.28420	+	0.449360i	0.400017	+	0.916508i	$0.369004\pi$
$858$	−37.3385			−1.27471
$859$	6.03153	+	2.11052i	0.205793	+	0.0720102i	0.431207	−	0.902253i	$-0.358088\pi$
$859$	6.03153	+	2.11052i	0.205793	+	0.0720102i	−0.225414	+	0.974263i	$0.572373\pi$
$860$	−5.40877	−	1.67166i	−0.184437	−	0.0570031i
$861$	13.3692	+	6.43826i	0.455621	+	0.219415i
$862$	−9.40287	+	19.5253i	−0.320263	+	0.665033i
$863$	30.6440	−	19.2549i	1.04314	−	0.655445i	0.102454	−	0.994738i	$-0.467331\pi$
$863$	30.6440	−	19.2549i	1.04314	−	0.655445i	0.940681	+	0.339293i	$0.110188\pi$
$864$	−3.98123	+	3.17493i	−0.135444	+	0.108013i
$865$	−2.16283	+	4.94980i	−0.0735385	+	0.168298i
$866$	1.33786	+	5.86157i	0.0454625	+	0.199184i
$867$	−1.87994	+	8.23657i	−0.0638462	+	0.279729i
$868$	−4.63000	−	3.69230i	−0.157152	−	0.125325i
$869$	−89.4690			−3.03503
$870$	11.1491	+	4.09852i	0.377991	+	0.138953i
$871$	8.52528			0.288868
$872$	10.9369	+	8.72191i	0.370371	+	0.295361i
$873$	−0.519112	+	2.27438i	−0.0175693	+	0.0769761i
$874$	8.30621	+	36.3919i	0.280962	+	1.23097i
$875$	18.0283	−	2.00104i	0.609466	−	0.0676475i
$876$	3.12282	−	2.49037i	0.105510	−	0.0841417i
$877$	−36.5304	+	22.9535i	−1.23354	+	0.775086i	−0.981283	−	0.192573i	$-0.938317\pi$
$877$	−36.5304	+	22.9535i	−1.23354	+	0.775086i	−0.252260	+	0.967659i	$0.581174\pi$
$878$	−4.92805	+	10.2332i	−0.166314	+	0.345354i
$879$	10.3569	+	4.98764i	0.349331	+	0.168229i
$880$	5.74039	+	10.8759i	0.193509	+	0.366626i
$881$	8.39509	+	2.93757i	0.282838	+	0.0989692i	0.467970	−	0.883744i	$-0.344986\pi$
$881$	8.39509	+	2.93757i	0.282838	+	0.0989692i	−0.185132	+	0.982714i	$0.559271\pi$
$882$	4.30870			0.145081
$883$	15.1970	+	5.31767i	0.511421	+	0.178954i	0.573638	−	0.819109i	$-0.305532\pi$
$883$	15.1970	+	5.31767i	0.511421	+	0.178954i	−0.0622175	+	0.998063i	$0.519817\pi$
$884$	18.3133	+	2.06342i	0.615943	+	0.0694002i
$885$	−1.17040	−	7.79432i	−0.0393426	−	0.262003i
$886$	25.0280	−	12.0528i	0.840832	−	0.404923i
$887$			27.9769i			0.939373i	0.882833	+	0.469686i	$0.155633\pi$
$887$			27.9769i			0.939373i	−0.882833	+	0.469686i	$0.844367\pi$
$888$	3.43085	+	7.12422i	0.115132	+	0.239073i
$889$	16.0890	+	10.1094i	0.539608	+	0.339058i
$890$	−2.86908	−	0.544502i	−0.0961719	−	0.0182517i
$891$	−2.03703	−	5.82151i	−0.0682432	−	0.195028i
$892$	11.8104	+	18.7962i	0.395443	+	0.629344i
$893$	−25.0060	−	2.81750i	−0.836794	−	0.0942840i
$894$	−8.05620	−	6.42461i	−0.269440	−	0.214871i
$895$	−15.7343	−	4.86291i	−0.525939	−	0.162549i
$896$	2.99504	+	4.76658i	0.100057	+	0.159240i
$897$	18.7620	−	23.5268i	0.626444	−	0.785536i
$898$	−2.73764	−	2.73764i	−0.0913562	−	0.0913562i
$899$	18.3747	−	5.36491i	0.612831	−	0.178930i
$900$	−2.56231	−	4.44940i	−0.0854103	−	0.148313i
$901$	4.26813	−	0.480903i	0.142192	−	0.0160212i
$902$	−54.2511	−	12.3825i	−1.80636	−	0.412291i
$903$	−2.12812	+	3.38688i	−0.0708192	+	0.112708i
$904$	−26.2930	+	32.9704i	−0.874493	+	1.09658i
$905$	7.37329	−	1.10718i	0.245096	−	0.0368038i
$906$	−1.21856	+	5.33887i	−0.0404840	+	0.177372i
$907$	41.2822	+	19.8805i	1.37075	+	0.660120i	0.967007	−	0.254751i	$-0.0819935\pi$
$907$	41.2822	+	19.8805i	1.37075	+	0.660120i	0.403746	+	0.914871i	$0.367708\pi$
$908$	1.63896	+	4.68388i	0.0543908	+	0.155440i
$909$	2.44324	−	3.88839i	0.0810371	−	0.128970i
$910$	−1.65336	+	21.9002i	−0.0548084	+	0.725984i
$911$	−0.370618	+	0.370618i	−0.0122791	+	0.0122791i	−0.713220	−	0.700941i	$-0.752764\pi$
$911$	−0.370618	+	0.370618i	−0.0122791	+	0.0122791i	0.700941	+	0.713220i	$0.252764\pi$
$912$	−2.27284	+	6.49540i	−0.0752612	+	0.215084i
$913$	43.9926	+	55.1649i	1.45594	+	1.82569i
$914$	−2.33305	+	20.7064i	−0.0771705	+	0.684907i
$915$	−3.56607	+	3.06542i	−0.117891	+	0.101340i
$916$	10.2063	+	10.2063i	0.337226	+	0.337226i
$917$	−7.84146	+	3.77625i	−0.258948	+	0.124703i
$918$	−0.641913	−	2.81240i	−0.0211863	−	0.0928231i
$919$	−5.93966	+	12.3338i	−0.195931	+	0.406855i	−0.975668	−	0.219252i	$-0.929638\pi$
$919$	−5.93966	+	12.3338i	−0.195931	+	0.406855i	0.779737	+	0.626107i	$0.215353\pi$
$920$	−32.1640	−	6.10417i	−1.06042	−	0.201248i
$921$	24.6188	+	5.61908i	0.811217	+	0.185155i
$922$	2.44838	−	21.7300i	0.0806331	−	0.715638i
$923$	5.96904	+	52.9767i	0.196473	+	1.74375i
$924$	−10.0178	+	2.28649i	−0.329561	+	0.0752200i
$925$	−12.6570	+	3.88886i	−0.416160	+	0.127865i
$926$	0.659677	+	5.85479i	0.0216783	+	0.192400i
$927$	−8.96811	+	8.96811i	−0.294551	+	0.294551i
$928$	−27.3844	−	1.43965i	−0.898938	−	0.0472589i
$929$			5.47807i			0.179730i	0.995954	+	0.0898648i	$0.0286435\pi$
$929$			5.47807i			0.179730i	−0.995954	+	0.0898648i	$0.971357\pi$
$930$	7.18472	+	3.13939i	0.235596	+	0.102945i
$931$	−28.5409	+	17.9334i	−0.935390	+	0.587744i
$932$	9.93950	+	6.24540i	0.325579	+	0.204575i
$933$	7.45777	−	0.840289i	0.244157	−	0.0275098i
$934$	23.3830	+	29.3214i	0.765116	+	0.959425i
$935$	40.3024	−	1.48571i	1.31803	−	0.0485880i
$936$	17.2963	−	6.05225i	0.565349	−	0.197824i
$937$	−44.9429	+	15.7262i	−1.46822	+	0.513753i	−0.941713	−	0.336418i	$-0.890785\pi$
$937$	−44.9429	+	15.7262i	−1.46822	+	0.513753i	−0.526508	+	0.850170i	$0.676499\pi$
$938$	−2.16751	+	0.494720i	−0.0707717	+	0.0161532i
$939$	2.37255	−	6.78037i	0.0774253	−	0.221269i
$940$	3.74729	−	6.48223i	0.122223	−	0.211427i
$941$	7.56808	+	15.7153i	0.246712	+	0.512304i	0.987145	−	0.159827i	$-0.0510936\pi$
$941$	7.56808	+	15.7153i	0.246712	+	0.512304i	−0.740433	+	0.672131i	$0.765379\pi$
$942$	9.27546	−	7.39693i	0.302211	−	0.241005i
$943$	35.0624	−	27.9613i	1.14179	−	0.910546i
$944$	−1.36375	−	2.83186i	−0.0443864	−	0.0921693i
$945$	−3.50470	+	0.937006i	−0.114008	+	0.0304808i
$946$	4.95426	−	14.1585i	0.161077	−	0.460332i
$947$	−29.8098	+	6.80390i	−0.968690	+	0.221097i	−0.677463	−	0.735557i	$-0.736921\pi$
$947$	−29.8098	+	6.80390i	−0.968690	+	0.221097i	−0.291227	+	0.956654i	$0.594063\pi$
$948$	14.0604	−	4.91994i	0.456660	−	0.159792i
$949$	−22.5313	+	7.88405i	−0.731398	+	0.255927i
$950$	−33.6330	−	17.8232i	−1.09120	−	0.578260i
$951$	−5.60774	−	7.03189i	−0.181844	−	0.228025i
$952$	−14.0773	+	1.58613i	−0.456248	+	0.0514068i
$953$	−14.3457	−	9.01403i	−0.464704	−	0.291993i	0.279256	−	0.960217i	$-0.409912\pi$
$953$	−14.3457	−	9.01403i	−0.464704	−	0.291993i	−0.743961	+	0.668224i	$0.767055\pi$
$954$	1.22681	−	0.770854i	0.0397193	−	0.0249573i
$955$	−8.56656	+	19.6052i	−0.277207	+	0.634409i
$956$		−	30.1014i		−	0.973548i
$957$	12.6005	−	30.7307i	0.407316	−	0.993381i
$958$	−24.7623	+	24.7623i	−0.800033	+	0.800033i
$959$	−3.18922	−	28.3051i	−0.102985	−	0.914021i
$960$	−11.1515	−	10.3585i	−0.359913	−	0.334320i
$961$	−17.9046	+	4.08661i	−0.577568	+	0.131826i
$962$	−1.79502	−	15.9313i	−0.0578738	−	0.513644i
$963$	0.833791	−	7.40010i	0.0268685	−	0.238465i
$964$	−21.5277	−	4.91356i	−0.693362	−	0.158255i
$965$	10.4982	−	7.14903i	0.337948	−	0.230135i
$966$	−3.40489	+	7.07032i	−0.109550	+	0.227484i
$967$	−6.04326	−	26.4773i	−0.194338	−	0.851452i	−0.974234	−	0.225542i	$-0.927585\pi$
$967$	−6.04326	−	26.4773i	−0.194338	−	0.851452i	0.779895	−	0.625910i	$-0.215272\pi$
$968$	72.7421	−	35.0307i	2.33802	−	1.12593i
$969$	15.9577	+	15.9577i	0.512634	+	0.512634i
$970$	−5.13124	−	0.387384i	−0.164754	−	0.0124382i
$971$	1.02088	−	9.06054i	0.0327615	−	0.290766i	−0.966639	−	0.256143i	$-0.917548\pi$
$971$	1.02088	−	9.06054i	0.0327615	−	0.290766i	0.999400	−	0.0346235i	$-0.0110232\pi$
$972$	0.640255	+	0.802855i	0.0205362	+	0.0257516i
$973$	7.42481	−	21.2189i	0.238028	−	0.680246i
$974$	−0.680741	+	0.680741i	−0.0218123	+	0.0218123i
$975$	5.67141	+	30.1565i	0.181630	+	0.965781i
$976$	−0.997724	+	1.58787i	−0.0319364	+	0.0508264i
$977$	1.83761	+	5.25159i	0.0587904	+	0.168013i	0.969533	−	0.244962i	$-0.0787754\pi$
$977$	1.83761	+	5.25159i	0.0587904	+	0.168013i	−0.910742	+	0.412975i	$0.864490\pi$
$978$	−0.180515	−	0.0869316i	−0.00577225	−	0.00277977i
$979$	−1.81697	+	7.96068i	−0.0580708	+	0.254425i
$980$	−1.48932	−	9.91818i	−0.0475746	−	0.316825i
$981$	2.92102	−	3.66284i	0.0932609	−	0.116945i
$982$	−12.5157	+	19.9186i	−0.399391	+	0.635627i
$983$	28.6906	+	6.54845i	0.915089	+	0.208863i	0.654038	−	0.756462i	$-0.273074\pi$
$983$	28.6906	+	6.54845i	0.915089	+	0.208863i	0.261051	+	0.965325i	$0.415931\pi$
$984$	27.1379	−	3.05770i	0.865124	−	0.0974761i
$985$	30.5528	−	8.16851i	0.973493	−	0.260270i
$986$	7.46577	−	13.6232i	0.237759	−	0.433850i
$987$	−3.74081	−	3.74081i	−0.119071	−	0.119071i
$988$	−30.3230	+	38.0238i	−0.964703	+	1.20970i
$989$	6.43174	+	10.2361i	0.204517	+	0.325488i
$990$	12.0315	−	6.35032i	0.382385	−	0.201826i
$991$	−13.7806	−	10.9897i	−0.437756	−	0.349099i	0.379680	−	0.925118i	$-0.376034\pi$
$991$	−13.7806	−	10.9897i	−0.437756	−	0.349099i	−0.817436	+	0.576019i	$0.804606\pi$
$992$	−17.9867	−	2.02661i	−0.571078	−	0.0643450i
$993$	1.13916	+	1.81297i	0.0361502	+	0.0575328i
$994$	−4.59183	−	13.1227i	−0.145644	−	0.416226i
$995$	−23.5774	−	34.6227i	−0.747453	−	1.09761i
$996$	−9.94715	−	6.25021i	−0.315187	−	0.198045i
$997$	−27.0099	−	56.0867i	−0.855414	−	1.77628i	−0.579193	−	0.815190i	$-0.696632\pi$
$997$	−27.0099	−	56.0867i	−0.855414	−	1.77628i	−0.276221	−	0.961094i	$-0.589082\pi$
$998$		−	17.2870i		−	0.547210i
$999$	2.38594	−	1.14901i	0.0754879	−	0.0363530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.bm.a.247.9	yes	180
5.3	odd	4		435.2.bd.b.73.9	✓	180
29.2	odd	28		435.2.bd.b.292.9	yes	180
145.118	even	28	inner	435.2.bm.a.118.9	yes	180

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.bd.b.73.9	✓	180	5.3	odd	4
435.2.bd.b.292.9	yes	180	29.2	odd	28
435.2.bm.a.118.9	yes	180	145.118	even	28	inner
435.2.bm.a.247.9	yes	180	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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.bm (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.771248 + 0.615050i) q^{2} +(-0.222521 + 0.974928i) q^{3} +(-0.228505 - 1.00114i) q^{4} +(-0.815777 - 2.08195i) q^{5} +(-0.771248 + 0.615050i) q^{6} +(1.37372 - 0.863168i) q^{7} +(1.29554 - 2.69022i) q^{8} +(-0.900969 - 0.433884i) q^{9} +(0.651335 - 2.10744i) q^{10} +(-5.82151 - 2.03703i) q^{11} +1.02689 q^{12} +(-5.79264 - 2.02693i) q^{13} +(1.59037 + 0.179192i) q^{14} +(2.21128 - 0.332047i) q^{15} +(0.803409 - 0.386902i) q^{16} -2.92431i q^{17} +(-0.428010 - 0.888773i) q^{18} +(6.53435 + 4.10580i) q^{19} +(-1.89792 + 1.29244i) q^{20} +(0.535844 + 1.53135i) q^{21} +(-3.23695 - 5.15158i) q^{22} +(4.87250 + 0.548998i) q^{23} +(2.33448 + 1.86169i) q^{24} +(-3.66902 + 3.39681i) q^{25} +(-3.22090 - 5.12603i) q^{26} +(0.623490 - 0.781831i) q^{27} +(-1.17806 - 1.17806i) q^{28} +(5.30582 - 0.921030i) q^{29} +(1.90967 + 1.10395i) q^{30} +(3.53221 - 0.397985i) q^{31} +(-4.96451 - 1.13312i) q^{32} +(3.28137 - 5.22227i) q^{33} +(1.79860 - 2.25537i) q^{34} +(-2.91772 - 2.15587i) q^{35} +(-0.228505 + 1.00114i) q^{36} +(2.38594 + 1.14901i) q^{37} +(2.51433 + 7.18554i) q^{38} +(3.26510 - 5.19637i) q^{39} +(-6.65777 - 0.502630i) q^{40} +(6.46729 - 6.46729i) q^{41} +(-0.528591 + 1.51063i) q^{42} +(1.53720 + 1.92758i) q^{43} +(-0.709123 + 6.29364i) q^{44} +(-0.168334 + 2.22972i) q^{45} +(3.42024 + 3.42024i) q^{46} +(-2.93787 + 1.41481i) q^{47} +(0.198426 + 0.869360i) q^{48} +(-1.89513 + 3.93527i) q^{49} +(-4.91893 + 0.363157i) q^{50} +(2.85100 + 0.650721i) q^{51} +(-0.705606 + 6.26243i) q^{52} +(0.164450 + 1.45953i) q^{53} +(0.961731 - 0.219509i) q^{54} +(0.508055 + 13.7818i) q^{55} +(-0.542395 - 4.81389i) q^{56} +(-5.45689 + 5.45689i) q^{57} +(4.65858 + 2.55300i) q^{58} -3.52481i q^{59} +(-0.837713 - 2.13793i) q^{60} +(-1.78069 + 1.11888i) q^{61} +(2.96899 + 1.86554i) q^{62} +(-1.61220 + 0.181651i) q^{63} +(-4.24390 - 5.32168i) q^{64} +(0.505536 + 13.7135i) q^{65} +(5.74271 - 2.00946i) q^{66} +(-1.31120 + 0.458808i) q^{67} +(-2.92766 + 0.668219i) q^{68} +(-1.61947 + 4.62817i) q^{69} +(-0.924322 - 3.45726i) q^{70} +(-3.76912 - 7.82665i) q^{71} +(-2.33448 + 1.86169i) q^{72} +(3.04105 - 2.42515i) q^{73} +(1.13346 + 2.35364i) q^{74} +(-2.49521 - 4.33289i) q^{75} +(2.61737 - 7.48002i) q^{76} +(-9.75545 + 2.22662i) q^{77} +(5.71423 - 1.99950i) q^{78} +(13.6922 - 4.79111i) q^{79} +(-1.46091 - 1.35703i) q^{80} +(0.623490 + 0.781831i) q^{81} +(8.96560 - 1.01018i) q^{82} +(-9.68667 - 6.08654i) q^{83} +(1.41066 - 0.886378i) q^{84} +(-6.08827 + 2.38559i) q^{85} +2.43210i q^{86} +(-0.282718 + 5.37774i) q^{87} +(-13.0221 + 13.0221i) q^{88} +(-0.148232 - 1.31559i) q^{89} +(-1.50122 + 1.61614i) q^{90} +(-9.70708 + 2.21558i) q^{91} +(-0.563761 - 5.00352i) q^{92} +(-0.397985 + 3.53221i) q^{93} +(-3.13600 - 0.715773i) q^{94} +(3.21750 - 16.9536i) q^{95} +(2.20942 - 4.58790i) q^{96} +(-0.519112 - 2.27438i) q^{97} +(-3.88200 + 1.86947i) q^{98} +(4.36116 + 4.36116i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 180 q - 30 q^{3} + 30 q^{4} + 10 q^{5} - 30 q^{9} - 4 q^{10} - 30 q^{11} - 180 q^{12} - 20 q^{13} - 10 q^{14} - 4 q^{15} - 14 q^{16} + 8 q^{19} + 2 q^{20} + 36 q^{22} + 64 q^{25} - 36 q^{26} - 30 q^{27}+ \cdots + 12 q^{99}+O(q^{100}) \) 180 * q - 30 * q^3 + 30 * q^4 + 10 * q^5 - 30 * q^9 - 4 * q^10 - 30 * q^11 - 180 * q^12 - 20 * q^13 - 10 * q^14 - 4 * q^15 - 14 * q^16 + 8 * q^19 + 2 * q^20 + 36 * q^22 + 64 * q^25 - 36 * q^26 - 30 * q^27 + 72 * q^28 + 12 * q^29 - 4 * q^30 - 20 * q^31 + 12 * q^33 + 40 * q^34 - 6 * q^35 + 30 * q^36 + 42 * q^37 + 16 * q^38 + 22 * q^39 + 18 * q^40 - 10 * q^41 + 4 * q^42 + 26 * q^43 + 4 * q^44 - 4 * q^45 + 12 * q^46 - 20 * q^47 - 70 * q^48 + 8 * q^50 + 12 * q^52 - 82 * q^53 + 48 * q^55 + 6 * q^56 + 8 * q^57 - 70 * q^58 - 40 * q^60 + 14 * q^61 + 110 * q^62 - 14 * q^63 - 74 * q^64 + 42 * q^65 + 22 * q^66 - 20 * q^67 - 98 * q^68 + 28 * q^69 + 8 * q^70 + 140 * q^71 + 98 * q^73 + 22 * q^75 - 4 * q^76 - 42 * q^77 + 34 * q^78 - 24 * q^79 - 62 * q^80 - 30 * q^81 + 6 * q^82 - 60 * q^83 - 68 * q^84 - 178 * q^85 - 44 * q^87 - 156 * q^88 - 12 * q^89 - 4 * q^90 - 56 * q^91 - 8 * q^92 + 8 * q^93 + 4 * q^95 - 42 * q^97 + 194 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

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Database

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