LMFDB - Embedded newform 525.2.n.c.316.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(106,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4, 0]))

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

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

chi := DirichletCharacter("525.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			316.6
Character	$\chi$	$=$	525.316
Dual form			525.2.n.c.211.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.74122 + 1.26507i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.813418 + 2.50344i) q^{4} +(-0.783736 + 2.09422i) q^{5} +(-0.665089 + 2.04693i) q^{6} +1.00000 q^{7} +(-0.420520 + 1.29423i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.74122 + 1.26507i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.813418 + 2.50344i) q^{4} +(-0.783736 + 2.09422i) q^{5} +(-0.665089 + 2.04693i) q^{6} +1.00000 q^{7} +(-0.420520 + 1.29423i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-4.01400 + 2.65502i) q^{10} +(-0.101817 - 0.0739744i) q^{11} +(-2.12956 + 1.54721i) q^{12} +(0.0107405 - 0.00780342i) q^{13} +(1.74122 + 1.26507i) q^{14} +(-2.23391 - 0.0982272i) q^{15} +(1.88960 - 1.37287i) q^{16} +(-0.670192 + 2.06264i) q^{17} -2.15227 q^{18} +(-0.494144 + 1.52082i) q^{19} +(-5.88027 - 0.258561i) q^{20} +(0.309017 + 0.951057i) q^{21} +(-0.0837033 - 0.257612i) q^{22} +(0.0892177 + 0.0648204i) q^{23} -1.36083 q^{24} +(-3.77152 - 3.28263i) q^{25} +0.0285735 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.813418 + 2.50344i) q^{28} +(-1.01997 - 3.13914i) q^{29} +(-3.76547 - 2.99710i) q^{30} +(1.50888 - 4.64386i) q^{31} +7.74867 q^{32} +(0.0388906 - 0.119693i) q^{33} +(-3.77634 + 2.74367i) q^{34} +(-0.783736 + 2.09422i) q^{35} +(-2.12956 - 1.54721i) q^{36} +(7.39723 - 5.37440i) q^{37} +(-2.78437 + 2.02296i) q^{38} +(0.0107405 + 0.00780342i) q^{39} +(-2.38082 - 1.89499i) q^{40} +(3.54267 - 2.57390i) q^{41} +(-0.665089 + 2.04693i) q^{42} -3.94017 q^{43} +(0.102371 - 0.315065i) q^{44} +(-0.596896 - 2.15493i) q^{45} +(0.0733454 + 0.225734i) q^{46} +(2.71568 + 8.35799i) q^{47} +(1.88960 + 1.37287i) q^{48} +1.00000 q^{49} +(-2.41429 - 10.4870i) q^{50} -2.16879 q^{51} +(0.0282719 + 0.0205408i) q^{52} +(1.64638 + 5.06703i) q^{53} +(-0.665089 - 2.04693i) q^{54} +(0.234716 - 0.155251i) q^{55} +(-0.420520 + 1.29423i) q^{56} -1.59909 q^{57} +(2.19525 - 6.75628i) q^{58} +(-6.59335 + 4.79035i) q^{59} +(-1.57120 - 5.67237i) q^{60} +(7.37464 + 5.35799i) q^{61} +(8.50214 - 6.17716i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(9.71297 + 7.05689i) q^{64} +(0.00792438 + 0.0286088i) q^{65} +(0.219138 - 0.159213i) q^{66} +(4.16811 - 12.8281i) q^{67} -5.70884 q^{68} +(-0.0340781 + 0.104882i) q^{69} +(-4.01400 + 2.65502i) q^{70} +(-1.60605 - 4.94290i) q^{71} +(-0.420520 - 1.29423i) q^{72} +(4.51194 + 3.27812i) q^{73} +19.6793 q^{74} +(1.95650 - 4.60131i) q^{75} -4.20923 q^{76} +(-0.101817 - 0.0739744i) q^{77} +(0.00882970 + 0.0271750i) q^{78} +(-0.519206 - 1.59795i) q^{79} +(1.39416 + 5.03321i) q^{80} +(0.309017 - 0.951057i) q^{81} +9.42477 q^{82} +(0.521981 - 1.60649i) q^{83} +(-2.12956 + 1.54721i) q^{84} +(-3.79436 - 3.02009i) q^{85} +(-6.86072 - 4.98460i) q^{86} +(2.67031 - 1.94009i) q^{87} +(0.138556 - 0.100667i) q^{88} +(0.143290 + 0.104106i) q^{89} +(1.68681 - 4.50733i) q^{90} +(0.0107405 - 0.00780342i) q^{91} +(-0.0897030 + 0.276078i) q^{92} +4.88285 q^{93} +(-5.84487 + 17.9887i) q^{94} +(-2.79765 - 2.22677i) q^{95} +(2.39447 + 7.36942i) q^{96} +(-3.79281 - 11.6731i) q^{97} +(1.74122 + 1.26507i) q^{98} +0.125853 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) $ 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	1.74122	+	1.26507i	1.23123	+	0.894542i	0.996982	−	0.0776340i	$-0.0247366\pi$
$2$	1.74122	+	1.26507i	1.23123	+	0.894542i	0.234250	+	0.972176i	$0.424737\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	0.813418	+	2.50344i	0.406709	+	1.25172i
$5$	−0.783736	+	2.09422i	−0.350497	+	0.936564i
$5$	−0.783736	+	2.09422i	−0.350497	+	0.936564i
$6$	−0.665089	+	2.04693i	−0.271521	+	0.835657i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.420520	+	1.29423i	−0.148676	+	0.457578i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	−4.01400	+	2.65502i	−1.26934	+	0.839593i
$11$	−0.101817	−	0.0739744i	−0.0306990	−	0.0223041i	0.572330	−	0.820023i	$-0.306040\pi$
$11$	−0.101817	−	0.0739744i	−0.0306990	−	0.0223041i	−0.603029	+	0.797719i	$0.706040\pi$
$12$	−2.12956	+	1.54721i	−0.614750	+	0.446642i
$13$	0.0107405	−	0.00780342i	0.00297887	−	0.00216428i	−0.586295	−	0.810098i	$-0.699414\pi$
$13$	0.0107405	−	0.00780342i	0.00297887	−	0.00216428i	0.589274	+	0.807933i	$0.299414\pi$
$14$	1.74122	+	1.26507i	0.465362	+	0.338105i
$15$	−2.23391	−	0.0982272i	−0.576793	−	0.0253622i
$16$	1.88960	−	1.37287i	0.472400	−	0.343219i
$17$	−0.670192	+	2.06264i	−0.162545	+	0.500263i	−0.998847	−	0.0480064i	$-0.984713\pi$
$17$	−0.670192	+	2.06264i	−0.162545	+	0.500263i	0.836302	+	0.548270i	$0.184713\pi$
$18$	−2.15227			−0.507295
$19$	−0.494144	+	1.52082i	−0.113365	+	0.348900i	−0.991602	−	0.129324i	$-0.958719\pi$
$19$	−0.494144	+	1.52082i	−0.113365	+	0.348900i	0.878238	+	0.478224i	$0.158719\pi$
$20$	−5.88027	−	0.258561i	−1.31487	−	0.0578160i
$21$	0.309017	+	0.951057i	0.0674330	+	0.207538i
$22$	−0.0837033	−	0.257612i	−0.0178456	−	0.0549231i
$23$	0.0892177	+	0.0648204i	0.0186032	+	0.0135160i	0.597048	−	0.802206i	$-0.296340\pi$
$23$	0.0892177	+	0.0648204i	0.0186032	+	0.0135160i	−0.578445	+	0.815722i	$0.696340\pi$
$24$	−1.36083			−0.277778
$25$	−3.77152	−	3.28263i	−0.754303	−	0.656526i
$26$	0.0285735			0.00560372
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	0.813418	+	2.50344i	0.153722	+	0.473106i
$29$	−1.01997	−	3.13914i	−0.189403	−	0.582923i	0.810593	−	0.585610i	$-0.199145\pi$
$29$	−1.01997	−	3.13914i	−0.189403	−	0.582923i	−0.999996	+	0.00268645i	$0.999145\pi$
$30$	−3.76547	−	2.99710i	−0.687478	−	0.547192i
$31$	1.50888	−	4.64386i	0.271003	−	0.834063i	−0.719246	−	0.694756i	$-0.755513\pi$
$31$	1.50888	−	4.64386i	0.271003	−	0.834063i	0.990249	−	0.139307i	$-0.0444875\pi$
$32$	7.74867			1.36978
$33$	0.0388906	−	0.119693i	0.00676999	−	0.0208359i
$34$	−3.77634	+	2.74367i	−0.647638	+	0.470536i
$35$	−0.783736	+	2.09422i	−0.132476	+	0.353988i
$36$	−2.12956	−	1.54721i	−0.354926	−	0.257869i
$37$	7.39723	−	5.37440i	1.21610	−	0.883546i	0.220327	−	0.975426i	$-0.429288\pi$
$37$	7.39723	−	5.37440i	1.21610	−	0.883546i	0.995770	+	0.0918798i	$0.0292876\pi$
$38$	−2.78437	+	2.02296i	−0.451684	+	0.328168i
$39$	0.0107405	+	0.00780342i	0.00171985	+	0.00124955i
$40$	−2.38082	−	1.89499i	−0.376441	−	0.299625i
$41$	3.54267	−	2.57390i	0.553272	−	0.401976i	−0.275718	−	0.961239i	$-0.588916\pi$
$41$	3.54267	−	2.57390i	0.553272	−	0.401976i	0.828991	+	0.559263i	$0.188916\pi$
$42$	−0.665089	+	2.04693i	−0.102625	+	0.315849i
$43$	−3.94017			−0.600870			−0.300435	−	0.953802i	$-0.597132\pi$
$43$	−3.94017			−0.600870			−0.300435	+	0.953802i	$0.597132\pi$
$44$	0.102371	−	0.315065i	0.0154330	−	0.0474979i
$45$	−0.596896	−	2.15493i	−0.0889801	−	0.321238i
$46$	0.0733454	+	0.225734i	0.0108142	+	0.0332826i
$47$	2.71568	+	8.35799i	0.396122	+	1.21914i	0.928084	+	0.372370i	$0.121455\pi$
$47$	2.71568	+	8.35799i	0.396122	+	1.21914i	−0.531962	+	0.846768i	$0.678545\pi$
$48$	1.88960	+	1.37287i	0.272740	+	0.198157i
$49$	1.00000			0.142857
$50$	−2.41429	−	10.4870i	−0.341432	−	1.48309i
$51$	−2.16879			−0.303691
$52$	0.0282719	+	0.0205408i	0.00392061	+	0.00284849i
$53$	1.64638	+	5.06703i	0.226147	+	0.696010i	0.998173	+	0.0604188i	$0.0192436\pi$
$53$	1.64638	+	5.06703i	0.226147	+	0.696010i	−0.772026	+	0.635591i	$0.780756\pi$
$54$	−0.665089	−	2.04693i	−0.0905071	−	0.278552i
$55$	0.234716	−	0.155251i	0.0316491	−	0.0209340i
$56$	−0.420520	+	1.29423i	−0.0561943	+	0.172948i
$57$	−1.59909			−0.211804
$58$	2.19525	−	6.75628i	0.288250	−	0.887143i
$59$	−6.59335	+	4.79035i	−0.858381	+	0.623651i	−0.927444	−	0.373962i	$-0.877999\pi$
$59$	−6.59335	+	4.79035i	−0.858381	+	0.623651i	0.0690627	+	0.997612i	$0.477999\pi$
$60$	−1.57120	−	5.67237i	−0.202841	−	0.732299i
$61$	7.37464	+	5.35799i	0.944226	+	0.686020i	0.949434	−	0.313966i	$-0.101658\pi$
$61$	7.37464	+	5.35799i	0.944226	+	0.686020i	−0.00520857	+	0.999986i	$0.501658\pi$
$62$	8.50214	−	6.17716i	1.07977	−	0.784501i
$63$	−0.809017	+	0.587785i	−0.101927	+	0.0740540i
$64$	9.71297	+	7.05689i	1.21412	+	0.882111i
$65$	0.00792438	+	0.0286088i	0.000982898	+	0.00354848i
$66$	0.219138	−	0.159213i	0.0269740	−	0.0195978i
$67$	4.16811	−	12.8281i	0.509215	−	1.56720i	−0.284351	−	0.958720i	$-0.591778\pi$
$67$	4.16811	−	12.8281i	0.509215	−	1.56720i	0.793567	−	0.608483i	$-0.208222\pi$
$68$	−5.70884			−0.692299
$69$	−0.0340781	+	0.104882i	−0.00410252	+	0.0126263i
$70$	−4.01400	+	2.65502i	−0.479765	+	0.317336i
$71$	−1.60605	−	4.94290i	−0.190603	−	0.586614i	0.809397	−	0.587262i	$-0.199794\pi$
$71$	−1.60605	−	4.94290i	−0.190603	−	0.586614i	−1.00000		0.000647173i	$0.999794\pi$
$72$	−0.420520	−	1.29423i	−0.0495587	−	0.152526i
$73$	4.51194	+	3.27812i	0.528083	+	0.383675i	0.819640	−	0.572879i	$-0.194173\pi$
$73$	4.51194	+	3.27812i	0.528083	+	0.383675i	−0.291557	+	0.956553i	$0.594173\pi$
$74$	19.6793			2.28767
$75$	1.95650	−	4.60131i	0.225918	−	0.531314i
$76$	−4.20923			−0.482832
$77$	−0.101817	−	0.0739744i	−0.0116031	−	0.00843016i
$78$	0.00882970	+	0.0271750i	0.000999766	+	0.00307696i
$79$	−0.519206	−	1.59795i	−0.0584153	−	0.179784i	0.917591	−	0.397525i	$-0.130131\pi$
$79$	−0.519206	−	1.59795i	−0.0584153	−	0.179784i	−0.976006	+	0.217742i	$0.930131\pi$
$80$	1.39416	+	5.03321i	0.155871	+	0.562730i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	9.42477			1.04079
$83$	0.521981	−	1.60649i	0.0572949	−	0.176335i	−0.918313	−	0.395854i	$-0.870449\pi$
$83$	0.521981	−	1.60649i	0.0572949	−	0.176335i	0.975608	+	0.219519i	$0.0704486\pi$
$84$	−2.12956	+	1.54721i	−0.232354	+	0.168815i
$85$	−3.79436	−	3.02009i	−0.411557	−	0.327575i
$86$	−6.86072	−	4.98460i	−0.739810	−	0.537504i
$87$	2.67031	−	1.94009i	0.286287	−	0.208000i
$88$	0.138556	−	0.100667i	0.0147701	−	0.0107311i
$89$	0.143290	+	0.104106i	0.0151887	+	0.0110352i	0.595354	−	0.803464i	$-0.297012\pi$
$89$	0.143290	+	0.104106i	0.0151887	+	0.0110352i	−0.580165	+	0.814499i	$0.697012\pi$
$90$	1.68681	−	4.50733i	0.177806	−	0.475115i
$91$	0.0107405	−	0.00780342i	0.00112591	−	0.000818021i
$92$	−0.0897030	+	0.276078i	−0.00935219	+	0.0287831i
$93$	4.88285			0.506328
$94$	−5.84487	+	17.9887i	−0.602853	+	1.85539i
$95$	−2.79765	−	2.22677i	−0.287033	−	0.228462i
$96$	2.39447	+	7.36942i	0.244385	+	0.752138i
$97$	−3.79281	−	11.6731i	−0.385101	−	1.18522i	−0.936407	−	0.350916i	$-0.885870\pi$
$97$	−3.79281	−	11.6731i	−0.385101	−	1.18522i	0.551306	−	0.834303i	$-0.314130\pi$
$98$	1.74122	+	1.26507i	0.175890	+	0.127792i
$99$	0.125853			0.0126487
$100$	5.15006	−	12.1119i	0.515006	−	1.21119i
$101$	−10.1988			−1.01482			−0.507410	−	0.861705i	$-0.669397\pi$
$101$	−10.1988			−1.01482			−0.507410	+	0.861705i	$0.669397\pi$
$102$	−3.77634	−	2.74367i	−0.373914	−	0.271664i
$103$	−2.55055	−	7.84979i	−0.251313	−	0.773463i	−0.994534	−	0.104416i	$-0.966703\pi$
$103$	−2.55055	−	7.84979i	−0.251313	−	0.773463i	0.743220	−	0.669047i	$-0.233297\pi$
$104$	0.00558281	+	0.0171821i	0.000547439	+	0.00168485i
$105$	−2.23391	−	0.0982272i	−0.218007	−	0.00958600i
$106$	−3.54345	+	10.9056i	−0.344171	+	1.05925i
$107$	15.2913			1.47827			0.739133	−	0.673560i	$-0.235236\pi$
$107$	15.2913			1.47827			0.739133	+	0.673560i	$0.235236\pi$
$108$	0.813418	−	2.50344i	0.0782712	−	0.240894i
$109$	−12.8553	+	9.33989i	−1.23131	+	0.894599i	−0.996988	−	0.0775595i	$-0.975287\pi$
$109$	−12.8553	+	9.33989i	−1.23131	+	0.894599i	−0.234323	+	0.972159i	$0.575287\pi$
$110$	0.605098	+	0.0266068i	0.0576938	+	0.00253685i
$111$	7.39723	+	5.37440i	0.702114	+	0.510116i
$112$	1.88960	−	1.37287i	0.178550	−	0.129724i
$113$	−12.7294	+	9.24848i	−1.19748	+	0.870023i	−0.994035	−	0.109062i	$-0.965215\pi$
$113$	−12.7294	+	9.24848i	−1.19748	+	0.870023i	−0.203449	+	0.979085i	$0.565215\pi$
$114$	−2.78437	−	2.02296i	−0.260780	−	0.189468i
$115$	−0.205671	+	0.136039i	−0.0191790	+	0.0126857i
$116$	7.02899	−	5.10686i	0.652626	−	0.474160i
$117$	−0.00410250	+	0.0126262i	−0.000379276	+	0.00116729i
$118$	−17.5407			−1.61475
$119$	−0.670192	+	2.06264i	−0.0614364	+	0.189082i
$120$	1.06653	−	2.84988i	0.0973606	−	0.260157i
$121$	−3.39429	−	10.4466i	−0.308572	−	0.949687i
$122$	6.06265	+	18.6589i	0.548887	+	1.68930i
$123$	3.54267	+	2.57390i	0.319432	+	0.232081i
$124$	12.8530			1.15423
$125$	9.83042	−	5.32567i	0.879260	−	0.476343i
$126$	−2.15227			−0.191740
$127$	−11.8368	−	8.59991i	−1.05034	−	0.763118i	−0.0780646	−	0.996948i	$-0.524874\pi$
$127$	−11.8368	−	8.59991i	−1.05034	−	0.763118i	−0.972277	+	0.233830i	$0.924874\pi$
$128$	3.19605	+	9.83642i	0.282493	+	0.869425i
$129$	−1.21758	−	3.74732i	−0.107202	−	0.329933i
$130$	−0.0223941	+	0.0598392i	−0.00196409	+	0.00524825i
$131$	−4.37429	+	13.4627i	−0.382184	+	1.17624i	0.556319	+	0.830969i	$0.312213\pi$
$131$	−4.37429	+	13.4627i	−0.382184	+	1.17624i	−0.938503	+	0.345272i	$0.887787\pi$
$132$	0.331279			0.0288342
$133$	−0.494144	+	1.52082i	−0.0428478	+	0.131872i
$134$	23.4861	−	17.0637i	2.02889	−	1.47408i
$135$	1.86501	−	1.23359i	0.160514	−	0.106171i
$136$	−2.38769	−	1.73476i	−0.204743	−	0.148754i
$137$	12.0667	−	8.76695i	1.03092	−	0.749011i	0.0624314	−	0.998049i	$-0.480115\pi$
$137$	12.0667	−	8.76695i	1.03092	−	0.749011i	0.968494	+	0.249038i	$0.0801146\pi$
$138$	−0.192021	+	0.139511i	−0.0163459	+	0.0118760i
$139$	−13.4880	−	9.79961i	−1.14404	−	0.831192i	−0.156361	−	0.987700i	$-0.549976\pi$
$139$	−13.4880	−	9.79961i	−1.14404	−	0.831192i	−0.987677	+	0.156508i	$0.949976\pi$
$140$	−5.88027	−	0.258561i	−0.496973	−	0.0218524i
$141$	−7.10973	+	5.16552i	−0.598747	+	0.435015i
$142$	3.45665	−	10.6385i	0.290075	−	0.892760i
$143$	−0.00167082			−0.000139721
$144$	−0.721763	+	2.22136i	−0.0601469	+	0.185113i
$145$	7.37343	+	0.324217i	0.612330	+	0.0269248i
$146$	3.70924	+	11.4159i	0.306979	+	0.944785i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	19.4716	+	14.1469i	1.60055	+	1.16287i
$149$	−1.90723			−0.156246			−0.0781232	−	0.996944i	$-0.524893\pi$
$149$	−1.90723			−0.156246			−0.0781232	+	0.996944i	$0.524893\pi$
$150$	9.22772	−	5.53680i	0.753440	−	0.452078i
$151$	−5.90754			−0.480749			−0.240375	−	0.970680i	$-0.577270\pi$
$151$	−5.90754			−0.480749			−0.240375	+	0.970680i	$0.577270\pi$
$152$	−1.76049	−	1.27907i	−0.142795	−	0.103746i
$153$	−0.670192	−	2.06264i	−0.0541818	−	0.166754i
$154$	−0.0837033	−	0.257612i	−0.00674500	−	0.0207590i
$155$	8.54271	+	6.79949i	0.686167	+	0.546149i
$156$	−0.0107989	+	0.0332356i	−0.000864605	+	0.00266098i
$157$	−3.49281			−0.278756			−0.139378	−	0.990239i	$-0.544510\pi$
$157$	−3.49281			−0.278756			−0.139378	+	0.990239i	$0.544510\pi$
$158$	1.11747	−	3.43923i	0.0889014	−	0.273610i
$159$	−4.31027	+	3.13160i	−0.341827	+	0.248352i
$160$	−6.07291	+	16.2274i	−0.480106	+	1.28289i
$161$	0.0892177	+	0.0648204i	0.00703134	+	0.00510857i
$162$	1.74122	−	1.26507i	0.136804	−	0.0993936i
$163$	6.68916	−	4.85996i	0.523936	−	0.380661i	−0.294149	−	0.955760i	$-0.595036\pi$
$163$	6.68916	−	4.85996i	0.523936	−	0.380661i	0.818084	+	0.575098i	$0.195036\pi$
$164$	9.32529	+	6.77522i	0.728183	+	0.529056i
$165$	0.220184	+	0.175253i	0.0171413	+	0.0136435i
$166$	2.94122	−	2.13692i	0.228283	−	0.165857i
$167$	2.23746	−	6.88619i	0.173140	−	0.532869i	−0.826404	−	0.563078i	$-0.809617\pi$
$167$	2.23746	−	6.88619i	0.173140	−	0.532869i	0.999544	+	0.0302085i	$0.00961712\pi$
$168$	−1.36083			−0.104990
$169$	−4.01717	+	12.3636i	−0.309013	+	0.951044i
$170$	−2.78620	−	10.0588i	−0.213692	−	0.771476i
$171$	−0.494144	−	1.52082i	−0.0377882	−	0.116300i
$172$	−3.20500	−	9.86399i	−0.244379	−	0.752122i
$173$	−7.45561	−	5.41682i	−0.566840	−	0.411833i	0.267116	−	0.963664i	$-0.413929\pi$
$173$	−7.45561	−	5.41682i	−0.566840	−	0.411833i	−0.833956	+	0.551831i	$0.813929\pi$
$174$	7.10397			0.538551
$175$	−3.77152	−	3.28263i	−0.285100	−	0.248144i
$176$	−0.293951			−0.0221574
$177$	−6.59335	−	4.79035i	−0.495587	−	0.360065i
$178$	0.117798	+	0.362544i	0.00882931	+	0.0271738i
$179$	−2.73743	−	8.42494i	−0.204605	−	0.629709i	−0.999729	−	0.0232630i	$-0.992595\pi$
$179$	−2.73743	−	8.42494i	−0.204605	−	0.629709i	0.795124	−	0.606446i	$-0.207405\pi$
$180$	4.90921	−	3.24715i	0.365911	−	0.242029i
$181$	−7.44723	+	22.9202i	−0.553548	+	1.70365i	0.146199	+	0.989255i	$0.453296\pi$
$181$	−7.44723	+	22.9202i	−0.553548	+	1.70365i	−0.699747	+	0.714391i	$0.746704\pi$
$182$	0.0285735			0.00211801
$183$	−2.81686	+	8.66941i	−0.208228	+	0.640861i
$184$	−0.121410	+	0.0882096i	−0.00895047	+	0.00650290i
$185$	5.45771	+	19.7035i	0.401259	+	1.44863i
$186$	8.50214	+	6.17716i	0.623407	+	0.452932i
$187$	0.220819	−	0.160435i	0.0161479	−	0.0117321i
$188$	−18.7148	+	13.5971i	−1.36492	+	0.991669i
$189$	−0.809017	−	0.587785i	−0.0588473	−	0.0427551i
$190$	−2.05432	−	7.41654i	−0.149036	−	0.538053i
$191$	5.65247	−	4.10676i	0.408998	−	0.297155i	−0.364198	−	0.931322i	$-0.618657\pi$
$191$	5.65247	−	4.10676i	0.408998	−	0.297155i	0.773196	+	0.634167i	$0.218657\pi$
$192$	−3.71003	+	11.4183i	−0.267748	+	0.824044i
$193$	−10.4169			−0.749822			−0.374911	−	0.927061i	$-0.622327\pi$
$193$	−10.4169			−0.749822			−0.374911	+	0.927061i	$0.622327\pi$
$194$	8.16315	−	25.1236i	0.586080	−	1.80377i
$195$	−0.0247598	+	0.0163771i	−0.00177308	+	0.00117279i
$196$	0.813418	+	2.50344i	0.0581013	+	0.178817i
$197$	2.62448	+	8.07731i	0.186986	+	0.575485i	0.999977	−	0.00679201i	$-0.00216198\pi$
$197$	2.62448	+	8.07731i	0.186986	+	0.575485i	−0.812991	+	0.582277i	$0.802162\pi$
$198$	0.219138	+	0.159213i	0.0155735	+	0.0113148i
$199$	−17.0147			−1.20614			−0.603069	−	0.797689i	$-0.706056\pi$
$199$	−17.0147			−1.20614			−0.603069	+	0.797689i	$0.706056\pi$
$200$	5.83447	−	3.50079i	0.412559	−	0.247543i
$201$	13.4883			0.951390
$202$	−17.7584	−	12.9022i	−1.24948	−	0.907799i
$203$	−1.01997	−	3.13914i	−0.0715877	−	0.220324i
$204$	−1.76413	−	5.42943i	−0.123514	−	0.380136i
$205$	2.61380	+	9.43640i	0.182556	+	0.659066i
$206$	5.48948	−	16.8949i	0.382470	−	1.17712i
$207$	−0.110279			−0.00766493
$208$	0.00958210	−	0.0294907i	0.000664399	−	0.00204481i
$209$	0.162814	−	0.118291i	0.0112621	−	0.00818238i
$210$	−3.76547	−	2.99710i	−0.259842	−	0.206819i
$211$	17.9487	+	13.0405i	1.23564	+	0.897745i	0.997300	−	0.0734372i	$-0.0233969\pi$
$211$	17.9487	+	13.0405i	1.23564	+	0.897745i	0.238340	+	0.971182i	$0.423397\pi$
$212$	−11.3458	+	8.24323i	−0.779235	+	0.566147i
$213$	4.20468	−	3.05488i	0.288100	−	0.209317i
$214$	26.6256	+	19.3446i	1.82009	+	1.32237i
$215$	3.08805	−	8.25158i	0.210603	−	0.562753i
$216$	1.10094	−	0.799876i	0.0749091	−	0.0544247i
$217$	1.50888	−	4.64386i	0.102430	−	0.315246i
$218$	−34.1995			−2.31629
$219$	−1.72341	+	5.30411i	−0.116457	+	0.358418i
$220$	0.579584	+	0.461315i	0.0390756	+	0.0311019i
$221$	0.00889744	+	0.0273835i	0.000598507	+	0.00184201i
$222$	6.08122	+	18.7161i	0.408145	+	1.25614i
$223$	−2.09371	−	1.52117i	−0.140205	−	0.101865i	0.515472	−	0.856906i	$-0.327617\pi$
$223$	−2.09371	−	1.52117i	−0.140205	−	0.101865i	−0.655677	+	0.755042i	$0.727617\pi$
$224$	7.74867			0.517730
$225$	4.98070	+	0.438862i	0.332047	+	0.0292574i
$226$	−33.8648			−2.25265
$227$	−3.41380	−	2.48027i	−0.226582	−	0.164622i	0.468702	−	0.883356i	$-0.344722\pi$
$227$	−3.41380	−	2.48027i	−0.226582	−	0.164622i	−0.695285	+	0.718735i	$0.744722\pi$
$228$	−1.30072	−	4.00322i	−0.0861426	−	0.265120i
$229$	−6.43748	−	19.8125i	−0.425401	−	1.30925i	−0.902610	−	0.430459i	$-0.858352\pi$
$229$	−6.43748	−	19.8125i	−0.425401	−	1.30925i	0.477209	−	0.878790i	$-0.341648\pi$
$230$	−0.530220	−	0.0233143i	−0.0349617	−	0.00153730i
$231$	0.0388906	−	0.119693i	0.00255882	−	0.00787523i
$232$	4.49167			0.294893
$233$	0.592618	−	1.82389i	0.0388237	−	0.119487i	−0.929766	−	0.368150i	$-0.879991\pi$
$233$	0.592618	−	1.82389i	0.0388237	−	0.119487i	0.968590	+	0.248663i	$0.0799912\pi$
$234$	−0.0231164	+	0.0167951i	−0.00151117	+	0.00109793i
$235$	−19.6318	−	0.863232i	−1.28064	−	0.0563110i
$236$	−17.3555	−	12.6095i	−1.12975	−	0.820810i
$237$	1.35930	−	0.987589i	0.0882960	−	0.0641508i
$238$	−3.77634	+	2.74367i	−0.244784	+	0.177846i
$239$	−3.24014	−	2.35410i	−0.209587	−	0.152274i	0.478040	−	0.878338i	$-0.341347\pi$
$239$	−3.24014	−	2.35410i	−0.209587	−	0.152274i	−0.687627	+	0.726064i	$0.741347\pi$
$240$	−4.35605	+	2.88127i	−0.281182	+	0.185985i
$241$	−2.42920	+	1.76492i	−0.156479	+	0.113688i	−0.663269	−	0.748381i	$-0.730832\pi$
$241$	−2.42920	+	1.76492i	−0.156479	+	0.113688i	0.506791	+	0.862069i	$0.330832\pi$
$242$	7.30544	−	22.4838i	0.469612	−	1.44532i
$243$	1.00000			0.0641500
$244$	−7.41476	+	22.8203i	−0.474681	+	1.46092i
$245$	−0.783736	+	2.09422i	−0.0500710	+	0.133795i
$246$	2.91241	+	8.96349i	0.185689	+	0.571491i
$247$	0.00656025	+	0.0201904i	0.000417419	+	0.00128468i
$248$	5.37570	+	3.90567i	0.341357	+	0.248011i
$249$	1.68917			0.107047
$250$	23.8543	+	3.16302i	1.50868	+	0.200047i
$251$	24.9606			1.57550			0.787748	−	0.615997i	$-0.211247\pi$
$251$	24.9606			1.57550			0.787748	+	0.615997i	$0.211247\pi$
$252$	−2.12956	−	1.54721i	−0.134149	−	0.0974653i
$253$	−0.00428883	−	0.0131996i	−0.000269636	−	0.000829855i
$254$	−9.73094	−	29.9487i	−0.610573	−	1.87915i
$255$	1.69975	−	4.54191i	0.106443	−	0.284426i
$256$	0.541291	−	1.66592i	0.0338307	−	0.104120i
$257$	−18.8415			−1.17530			−0.587651	−	0.809114i	$-0.699947\pi$
$257$	−18.8415			−1.17530			−0.587651	+	0.809114i	$0.699947\pi$
$258$	2.62056	−	8.06526i	0.163149	−	0.502121i
$259$	7.39723	−	5.37440i	0.459641	−	0.333949i
$260$	−0.0651746	+	0.0431091i	−0.00404196	+	0.00267351i
$261$	2.67031	+	1.94009i	0.165288	+	0.120089i
$262$	−24.6479	+	17.9078i	−1.52275	+	1.10635i
$263$	3.15912	−	2.29524i	0.194800	−	0.141530i	−0.486110	−	0.873898i	$-0.661585\pi$
$263$	3.15912	−	2.29524i	0.194800	−	0.141530i	0.680910	+	0.732367i	$0.261585\pi$
$264$	0.138556	+	0.100667i	0.00852751	+	0.00619560i
$265$	−11.9018	−	0.523334i	−0.731122	−	0.0321482i
$266$	−2.78437	+	2.02296i	−0.170720	+	0.124036i
$267$	−0.0547318	+	0.168447i	−0.00334953	+	0.0103088i
$268$	35.5049			2.16881
$269$	−4.80497	+	14.7882i	−0.292964	+	0.901652i	0.690933	+	0.722919i	$0.257200\pi$
$269$	−4.80497	+	14.7882i	−0.292964	+	0.901652i	−0.983898	+	0.178733i	$0.942800\pi$
$270$	4.80798	+	0.211412i	0.292604	+	0.0128661i
$271$	−1.91707	−	5.90015i	−0.116454	−	0.358409i	0.875794	−	0.482686i	$-0.160339\pi$
$271$	−1.91707	−	5.90015i	−0.116454	−	0.358409i	−0.992248	+	0.124277i	$0.960339\pi$
$272$	1.56535	+	4.81765i	0.0949133	+	0.292113i
$273$	0.0107405	+	0.00780342i	0.000650044	+	0.000472284i
$274$	32.1016			1.93933
$275$	0.141174	+	0.613223i	0.00851311	+	0.0369788i
$276$	−0.290285			−0.0174731
$277$	−8.91777	−	6.47914i	−0.535817	−	0.389294i	0.286712	−	0.958017i	$-0.407438\pi$
$277$	−8.91777	−	6.47914i	−0.535817	−	0.389294i	−0.822529	+	0.568723i	$0.807438\pi$
$278$	−11.0884	−	34.1266i	−0.665039	−	2.04678i
$279$	1.50888	+	4.64386i	0.0903345	+	0.278021i
$280$	−2.38082	−	1.89499i	−0.142281	−	0.113247i
$281$	−10.3087	+	31.7269i	−0.614965	+	1.89267i	−0.212819	+	0.977092i	$0.568265\pi$
$281$	−10.3087	+	31.7269i	−0.614965	+	1.89267i	−0.402146	+	0.915576i	$0.631735\pi$
$282$	−18.9144			−1.12634
$283$	7.09613	−	21.8397i	0.421821	−	1.29823i	−0.484184	−	0.874966i	$-0.660883\pi$
$283$	7.09613	−	21.8397i	0.421821	−	1.29823i	0.906005	−	0.423266i	$-0.139117\pi$
$284$	11.0679	−	8.04129i	0.656758	−	0.477163i
$285$	1.25326	−	3.34884i	0.0742367	−	0.198368i
$286$	−0.00290927	−	0.00211371i	−0.000172029	−	0.000124986i
$287$	3.54267	−	2.57390i	0.209117	−	0.151933i
$288$	−6.26880	+	4.55455i	−0.369393	+	0.268380i
$289$	9.94797	+	7.22762i	0.585175	+	0.425154i
$290$	12.4286	+	9.89247i	0.729835	+	0.580906i
$291$	9.92970	−	7.21435i	0.582089	−	0.422913i
$292$	−4.53649	+	13.9619i	−0.265478	+	0.817057i
$293$	−18.1404			−1.05977			−0.529887	−	0.848069i	$-0.677766\pi$
$293$	−18.1404			−1.05977			−0.529887	+	0.848069i	$0.677766\pi$
$294$	−0.665089	+	2.04693i	−0.0387888	+	0.119380i
$295$	−4.86460	−	17.5623i	−0.283228	−	1.02252i
$296$	3.84501	+	11.8337i	0.223487	+	0.687822i
$297$	0.0388906	+	0.119693i	0.00225666	+	0.00694530i
$298$	−3.32092	−	2.41279i	−0.192376	−	0.139769i
$299$	0.00146406			8.46689e−5
$300$	13.1106	+	1.15520i	0.756940	+	0.0666958i
$301$	−3.94017			−0.227108
$302$	−10.2864	−	7.47348i	−0.591914	−	0.430050i
$303$	−3.15161	−	9.69965i	−0.181055	−	0.557230i
$304$	1.15416	+	3.55214i	0.0661957	+	0.203729i
$305$	−17.0006	+	11.2449i	−0.973450	+	0.643879i
$306$	1.44243	−	4.43936i	0.0824585	−	0.253781i
$307$	9.69836			0.553514			0.276757	−	0.960940i	$-0.410740\pi$
$307$	9.69836			0.553514			0.276757	+	0.960940i	$0.410740\pi$
$308$	0.102371	−	0.315065i	0.00583312	−	0.0179525i
$309$	6.67743	−	4.85144i	0.379866	−	0.275989i
$310$	6.27291	+	22.6466i	0.356278	+	1.28624i
$311$	−23.9841	−	17.4255i	−1.36001	−	0.988108i	−0.998444	−	0.0557626i	$-0.982241\pi$
$311$	−23.9841	−	17.4255i	−1.36001	−	0.988108i	−0.361570	−	0.932345i	$-0.617759\pi$
$312$	−0.0146160	+	0.0106191i	−0.000827467	+	0.000601190i
$313$	7.46378	−	5.42275i	0.421878	−	0.306512i	−0.356515	−	0.934290i	$-0.616035\pi$
$313$	7.46378	−	5.42275i	0.421878	−	0.306512i	0.778393	+	0.627777i	$0.216035\pi$
$314$	−6.08176	−	4.41866i	−0.343214	−	0.249359i
$315$	−0.596896	−	2.15493i	−0.0336313	−	0.121416i
$316$	3.57805	−	2.59961i	0.201281	−	0.146239i
$317$	−7.35842	+	22.6469i	−0.413290	+	1.27198i	0.500482	+	0.865747i	$0.333156\pi$
$317$	−7.35842	+	22.6469i	−0.413290	+	1.27198i	−0.913772	+	0.406228i	$0.866844\pi$
$318$	−11.4669			−0.643029
$319$	−0.128366	+	0.395069i	−0.00718710	+	0.0221196i
$320$	−22.3911	+	14.8104i	−1.25170	+	0.827925i
$321$	4.72527	+	14.5429i	0.263739	+	0.811705i
$322$	0.0733454	+	0.225734i	0.00408738	+	0.0125797i
$323$	−2.80573	−	2.03848i	−0.156115	−	0.113424i
$324$	2.63228			0.146238
$325$	−0.0661237	−	0.00582631i	−0.00366788	−	0.000323186i
$326$	17.7955			0.985604
$327$	−12.8553	−	9.33989i	−0.710897	−	0.516497i
$328$	1.84145	+	5.66740i	0.101677	+	0.312930i
$329$	2.71568	+	8.35799i	0.149720	+	0.460791i
$330$	0.161681	+	0.583704i	0.00890024	+	0.0321319i
$331$	−3.97532	+	12.2348i	−0.218503	+	0.672484i	0.780383	+	0.625302i	$0.215024\pi$
$331$	−3.97532	+	12.2348i	−0.218503	+	0.672484i	−0.998886	+	0.0471822i	$0.984976\pi$
$332$	4.44635			0.244025
$333$	−2.82549	+	8.69597i	−0.154836	+	0.476536i
$334$	12.6075	−	9.15985i	0.689849	−	0.501205i
$335$	23.5982	+	18.7828i	1.28931	+	1.02621i
$336$	1.88960	+	1.37287i	0.103086	+	0.0748965i
$337$	−17.1788	+	12.4812i	−0.935791	+	0.679892i	−0.947404	−	0.320040i	$-0.896304\pi$
$337$	−17.1788	+	12.4812i	−0.935791	+	0.679892i	0.0116125	+	0.999933i	$0.496304\pi$
$338$	−22.6356	+	16.4457i	−1.23122	+	0.894530i
$339$	−12.7294	−	9.24848i	−0.691368	−	0.502308i
$340$	4.47422	−	11.9556i	0.242649	−	0.648382i
$341$	−0.497157	+	0.361206i	−0.0269226	+	0.0195604i
$342$	1.06353	−	3.27322i	0.0575093	−	0.176995i
$343$	1.00000			0.0539949
$344$	1.65692	−	5.09947i	0.0893351	−	0.274945i
$345$	−0.192937	−	0.153567i	−0.0103874	−	0.00826775i
$346$	−6.12922	−	18.8638i	−0.329509	−	1.01412i
$347$	6.10456	+	18.7879i	0.327710	+	1.00859i	0.970202	+	0.242296i	$0.0779004\pi$
$347$	6.10456	+	18.7879i	0.327710	+	1.00859i	−0.642492	+	0.766292i	$0.722100\pi$
$348$	7.02899	+	5.10686i	0.376794	+	0.273757i
$349$	29.4592			1.57691			0.788457	−	0.615089i	$-0.210880\pi$
$349$	29.4592			1.57691			0.788457	+	0.615089i	$0.210880\pi$
$350$	−2.41429	−	10.4870i	−0.129049	−	0.560556i
$351$	−0.0132760			−0.000708619
$352$	−0.788946	−	0.573203i	−0.0420510	−	0.0305518i
$353$	−7.54038	−	23.2069i	−0.401334	−	1.23518i	−0.923918	−	0.382591i	$-0.875032\pi$
$353$	−7.54038	−	23.2069i	−0.401334	−	1.23518i	0.522583	−	0.852588i	$-0.324968\pi$
$354$	−5.42036	−	16.6822i	−0.288089	−	0.886647i
$355$	11.6102	+	0.510514i	0.616207	+	0.0270953i
$356$	−0.144069	+	0.443399i	−0.00763565	+	0.0235001i
$357$	−2.16879			−0.114784
$358$	5.89169	−	18.1328i	0.311385	−	0.958346i
$359$	−20.0988	+	14.6027i	−1.06078	+	0.770699i	−0.974232	−	0.225549i	$-0.927582\pi$
$359$	−20.0988	+	14.6027i	−1.06078	+	0.770699i	−0.0865439	+	0.996248i	$0.527582\pi$
$360$	3.03997	+	0.133671i	0.160221	+	0.00704506i
$361$	13.3026	+	9.66491i	0.700137	+	0.508679i
$362$	−41.9631	+	30.4879i	−2.20553	+	1.60241i
$363$	8.88637	−	6.45633i	0.466414	−	0.338869i
$364$	0.0282719	+	0.0205408i	0.00148185	+	0.00107663i
$365$	−10.4013	+	6.87982i	−0.544427	+	0.360106i
$366$	−15.8722	+	11.5318i	−0.829655	+	0.602779i
$367$	−2.25726	+	6.94712i	−0.117828	+	0.362637i	−0.992526	−	0.122031i	$-0.961059\pi$
$367$	−2.25726	+	6.94712i	−0.117828	+	0.362637i	0.874698	+	0.484667i	$0.161059\pi$
$368$	0.257576			0.0134271
$369$	−1.35318	+	4.16466i	−0.0704438	+	0.216804i
$370$	−15.4233	+	41.2127i	−0.801821	+	2.14255i
$371$	1.64638	+	5.06703i	0.0854757	+	0.263067i
$372$	3.97180	+	12.2239i	0.205928	+	0.633781i
$373$	29.3324	+	21.3112i	1.51877	+	1.10345i	0.962090	+	0.272731i	$0.0879268\pi$
$373$	29.3324	+	21.3112i	1.51877	+	1.10345i	0.556685	+	0.830724i	$0.312073\pi$
$374$	0.587458			0.0303767
$375$	8.10278	+	7.70356i	0.418426	+	0.397810i
$376$	−11.9591			−0.616745
$377$	−0.0354510	−	0.0257566i	−0.00182582	−	0.00132653i
$378$	−0.665089	−	2.04693i	−0.0342085	−	0.105283i
$379$	−4.26481	−	13.1257i	−0.219068	−	0.674223i	−0.998840	−	0.0481588i	$-0.984665\pi$
$379$	−4.26481	−	13.1257i	−0.219068	−	0.674223i	0.779771	−	0.626065i	$-0.215335\pi$
$380$	3.29893	−	8.81506i	0.169231	−	0.452203i
$381$	4.52124	−	13.9149i	0.231630	−	0.712884i
$382$	15.0376			0.769390
$383$	4.18027	−	12.8655i	0.213602	−	0.657399i	−0.785648	−	0.618674i	$-0.787670\pi$
$383$	4.18027	−	12.8655i	0.213602	−	0.657399i	0.999250	−	0.0387250i	$-0.0123296\pi$
$384$	−8.36736	+	6.07924i	−0.426995	+	0.310230i
$385$	0.234716	−	0.155251i	0.0119623	−	0.00791232i
$386$	−18.1381	−	13.1781i	−0.923204	−	0.670747i
$387$	3.18766	−	2.31597i	0.162038	−	0.117728i
$388$	26.1377	−	18.9902i	1.32694	−	0.964079i
$389$	15.8616	+	11.5241i	0.804214	+	0.584296i	0.912147	−	0.409862i	$-0.134423\pi$
$389$	15.8616	+	11.5241i	0.804214	+	0.584296i	−0.107933	+	0.994158i	$0.534423\pi$
$390$	−0.0638306	−	0.00280670i	−0.00323219	−	0.000142123i
$391$	−0.193494	+	0.140582i	−0.00978541	+	0.00710952i
$392$	−0.420520	+	1.29423i	−0.0212395	+	0.0653683i
$393$	−14.1555			−0.714051
$394$	−5.64859	+	17.3846i	−0.284572	+	0.875823i
$395$	3.75339	+	0.165040i	0.188853	+	0.00830407i
$396$	0.102371	+	0.315065i	0.00514433	+	0.0158326i
$397$	0.0613325	+	0.188762i	0.00307819	+	0.00947370i	0.952584	−	0.304276i	$-0.0984146\pi$
$397$	0.0613325	+	0.188762i	0.00307819	+	0.00947370i	−0.949506	+	0.313750i	$0.898415\pi$
$398$	−29.6264	−	21.5248i	−1.48504	−	1.07894i
$399$	−1.59909			−0.0800544
$400$	−11.6333	−	1.02504i	−0.581665	−	0.0512519i
$401$	16.8671			0.842302			0.421151	−	0.906990i	$-0.361626\pi$
$401$	16.8671			0.842302			0.421151	+	0.906990i	$0.361626\pi$
$402$	23.4861	+	17.0637i	1.17138	+	0.851058i
$403$	−0.0200319	−	0.0616518i	−0.000997859	−	0.00307109i
$404$	−8.29590	−	25.5321i	−0.412736	−	1.27027i
$405$	1.74953	+	1.39253i	0.0869351	+	0.0691952i
$406$	2.19525	−	6.75628i	0.108948	−	0.335309i
$407$	−1.15073			−0.0570397
$408$	0.912017	−	2.80690i	0.0451516	−	0.138962i
$409$	3.95652	−	2.87458i	0.195637	−	0.142139i	−0.485654	−	0.874151i	$-0.661419\pi$
$409$	3.95652	−	2.87458i	0.195637	−	0.142139i	0.681291	+	0.732012i	$0.261419\pi$
$410$	−7.38653	+	19.7375i	−0.364794	+	0.974767i
$411$	12.0667	+	8.76695i	0.595205	+	0.432442i
$412$	17.5769	−	12.7703i	0.865949	−	0.629149i
$413$	−6.59335	+	4.79035i	−0.324438	+	0.235718i
$414$	−0.192021	−	0.139511i	−0.00943730	−	0.00685660i
$415$	2.95525	+	2.35221i	0.145068	+	0.115465i
$416$	0.0832245	−	0.0604661i	0.00408041	−	0.00296459i
$417$	5.15196	−	15.8561i	0.252293	−	0.776476i
$418$	0.433143			0.0211857
$419$	−5.77622	+	17.7774i	−0.282187	+	0.868482i	0.705041	+	0.709167i	$0.250929\pi$
$419$	−5.77622	+	17.7774i	−0.282187	+	0.868482i	−0.987228	+	0.159315i	$0.949071\pi$
$420$	−1.57120	−	5.67237i	−0.0766665	−	0.276783i
$421$	4.99663	+	15.3780i	0.243521	+	0.749480i	0.995876	+	0.0907226i	$0.0289177\pi$
$421$	4.99663	+	15.3780i	0.243521	+	0.749480i	−0.752355	+	0.658757i	$0.771082\pi$
$422$	14.7555	+	45.4129i	0.718288	+	2.21066i
$423$	−7.10973	−	5.16552i	−0.345687	−	0.251156i
$424$	−7.25022			−0.352102
$425$	9.29852	−	5.57928i	0.451044	−	0.270635i
$426$	11.1859			0.541961
$427$	7.37464	+	5.35799i	0.356884	+	0.259291i
$428$	12.4382	+	38.2809i	0.601224	+	1.85038i
$429$	−0.000516311	−	0.00158904i	−2.49277e−5	−	7.67197e-5i
$430$	15.8158	−	10.4612i	0.762708	−	0.504486i
$431$	2.81709	−	8.67010i	0.135694	−	0.417624i	−0.860003	−	0.510289i	$-0.829539\pi$
$431$	2.81709	−	8.67010i	0.135694	−	0.417624i	0.995697	+	0.0926649i	$0.0295385\pi$
$432$	−2.33567			−0.112375
$433$	−6.55368	+	20.1702i	−0.314950	+	0.969316i	0.660825	+	0.750540i	$0.270206\pi$
$433$	−6.55368	+	20.1702i	−0.314950	+	0.969316i	−0.975775	+	0.218776i	$0.929794\pi$
$434$	8.50214	−	6.17716i	0.408116	−	0.296513i
$435$	1.97017	+	7.11274i	0.0944623	+	0.341030i
$436$	−33.8386	−	24.5852i	−1.62057	−	1.17742i
$437$	−0.142667	+	0.103653i	−0.00682467	+	0.00495841i
$438$	−9.71093	+	7.05540i	−0.464006	+	0.337120i
$439$	6.89982	+	5.01301i	0.329310	+	0.239258i	0.740138	−	0.672455i	$-0.234760\pi$
$439$	6.89982	+	5.01301i	0.329310	+	0.239258i	−0.410828	+	0.911713i	$0.634760\pi$
$440$	0.102227	+	0.369062i	0.00487348	+	0.0175944i
$441$	−0.809017	+	0.587785i	−0.0385246	+	0.0279898i
$442$	−0.0191497	+	0.0589368i	−0.000910859	+	0.00280334i
$443$	19.2440			0.914311			0.457155	−	0.889387i	$-0.348868\pi$
$443$	19.2440			0.914311			0.457155	+	0.889387i	$0.348868\pi$
$444$	−7.43747	+	22.8902i	−0.352967	+	1.08632i
$445$	−0.330322	+	0.218489i	−0.0156588	+	0.0103573i
$446$	−1.72122	−	5.29738i	−0.0815023	−	0.250838i
$447$	−0.589366	−	1.81388i	−0.0278761	−	0.0857937i
$448$	9.71297	+	7.05689i	0.458895	+	0.333407i
$449$	−34.0935			−1.60897			−0.804486	−	0.593972i	$-0.797559\pi$
$449$	−34.0935			−1.60897			−0.804486	+	0.593972i	$0.797559\pi$
$450$	8.11733	+	7.06511i	0.382655	+	0.333053i
$451$	−0.551107			−0.0259506
$452$	−33.5074	−	24.3445i	−1.57605	−	1.14507i
$453$	−1.82553	−	5.61841i	−0.0857709	−	0.263976i
$454$	−2.80647	−	8.63743i	−0.131714	−	0.405375i
$455$	0.00792438	+	0.0286088i	0.000371501	+	0.00134120i
$456$	0.672447	−	2.06958i	0.0314902	−	0.0969169i
$457$	36.4541			1.70525			0.852626	−	0.522522i	$-0.175009\pi$
$457$	36.4541			1.70525			0.852626	+	0.522522i	$0.175009\pi$
$458$	13.8552	−	42.6420i	0.647412	−	1.99253i
$459$	1.75458	−	1.27478i	0.0818970	−	0.0595016i
$460$	−0.507864	−	0.404230i	−0.0236793	−	0.0188473i
$461$	10.2369	+	7.43753i	0.476779	+	0.346400i	0.800077	−	0.599897i	$-0.204792\pi$
$461$	10.2369	+	7.43753i	0.476779	+	0.346400i	−0.323298	+	0.946297i	$0.604792\pi$
$462$	0.219138	−	0.159213i	0.0101952	−	0.00740726i
$463$	31.4196	−	22.8277i	1.46019	−	1.06089i	0.476883	−	0.878967i	$-0.341767\pi$
$463$	31.4196	−	22.8277i	1.46019	−	1.06089i	0.983312	−	0.181927i	$-0.0582334\pi$
$464$	−6.23698	−	4.53143i	−0.289544	−	0.210366i
$465$	−3.82686	+	10.2258i	−0.177466	+	0.474208i
$466$	3.33924	−	2.42610i	0.154687	−	0.112387i
$467$	8.88760	−	27.3532i	0.411269	−	1.26576i	−0.504276	−	0.863542i	$-0.668241\pi$
$467$	8.88760	−	27.3532i	0.411269	−	1.26576i	0.915546	−	0.402214i	$-0.131759\pi$
$468$	−0.0349460			−0.00161538
$469$	4.16811	−	12.8281i	0.192465	−	0.592347i
$470$	−33.0914	−	26.3388i	−1.52639	−	1.21492i
$471$	−1.07934	−	3.32186i	−0.0497332	−	0.153063i
$472$	−3.42717	−	10.5477i	−0.157748	−	0.485499i
$473$	0.401176	+	0.291472i	0.0184461	+	0.0134019i
$474$	3.61622			0.166098
$475$	6.85596	−	4.11371i	0.314573	−	0.188750i
$476$	−5.70884			−0.261664
$477$	−4.31027	−	3.13160i	−0.197354	−	0.143386i
$478$	−2.66370	−	8.19803i	−0.121835	−	0.374969i
$479$	−5.98813	−	18.4296i	−0.273605	−	0.842068i	−0.989585	−	0.143948i	$-0.954020\pi$
$479$	−5.98813	−	18.4296i	−0.273605	−	0.842068i	0.715981	−	0.698120i	$-0.245980\pi$
$480$	−17.3098	−	0.761130i	−0.790082	−	0.0347407i
$481$	0.0375111	−	0.115447i	0.00171036	−	0.00526395i
$482$	−6.46254			−0.294360
$483$	−0.0340781	+	0.104882i	−0.00155061	+	0.00477228i
$484$	23.3914	−	16.9948i	1.06324	−	0.772493i
$485$	27.4185	+	1.20562i	1.24501	+	0.0547444i
$486$	1.74122	+	1.26507i	0.0789836	+	0.0573849i
$487$	−8.90891	+	6.47270i	−0.403701	+	0.293306i	−0.771047	−	0.636778i	$-0.780267\pi$
$487$	−8.90891	+	6.47270i	−0.403701	+	0.293306i	0.367346	+	0.930085i	$0.380267\pi$
$488$	−10.0356	+	7.29131i	−0.454292	+	0.330062i
$489$	6.68916	+	4.85996i	0.302494	+	0.219775i
$490$	−4.01400	+	2.65502i	−0.181334	+	0.119942i
$491$	−5.43546	+	3.94909i	−0.245299	+	0.178220i	−0.703641	−	0.710556i	$-0.748444\pi$
$491$	−5.43546	+	3.94909i	−0.245299	+	0.178220i	0.458342	+	0.888776i	$0.348444\pi$
$492$	−3.56194	+	10.9625i	−0.160585	+	0.494229i
$493$	7.15848			0.322402
$494$	−0.0141194	+	0.0434552i	−0.000635264	+	0.00195514i
$495$	−0.0986353	+	0.263563i	−0.00443333	+	0.0118463i
$496$	−3.52426	−	10.8466i	−0.158244	−	0.487025i
$497$	−1.60605	−	4.94290i	−0.0720410	−	0.221719i
$498$	2.94122	+	2.13692i	0.131799	+	0.0957577i
$499$	6.36993			0.285157			0.142579	−	0.989783i	$-0.454461\pi$
$499$	6.36993			0.285157			0.142579	+	0.989783i	$0.454461\pi$
$500$	21.3288	+	20.2779i	0.953851	+	0.906856i
$501$	7.24057			0.323485
$502$	43.4620	+	31.5770i	1.93980	+	1.40935i
$503$	−1.13411	−	3.49043i	−0.0505674	−	0.155631i	0.922584	−	0.385796i	$-0.126073\pi$
$503$	−1.13411	−	3.49043i	−0.0505674	−	0.155631i	−0.973151	+	0.230166i	$0.926073\pi$
$504$	−0.420520	−	1.29423i	−0.0187314	−	0.0576494i
$505$	7.99317	−	21.3586i	0.355691	−	0.950443i
$506$	0.00923072	−	0.0284092i	0.000410356	−	0.00126294i
$507$	−12.9998			−0.577342
$508$	11.9011	−	36.6280i	0.528028	−	1.62510i
$509$	−28.1955	+	20.4852i	−1.24974	+	0.907991i	−0.998207	−	0.0598572i	$-0.980935\pi$
$509$	−28.1955	+	20.4852i	−1.24974	+	0.907991i	−0.251535	+	0.967848i	$0.580935\pi$
$510$	8.70551	−	5.75818i	0.385487	−	0.254977i
$511$	4.51194	+	3.27812i	0.199597	+	0.145015i
$512$	19.7847	−	14.3745i	0.874370	−	0.635267i
$513$	1.29369	−	0.939919i	0.0571177	−	0.0414984i
$514$	−32.8073	−	23.8359i	−1.44707	−	1.05136i
$515$	18.4382	+	0.810744i	0.812482	+	0.0357257i
$516$	8.39081	−	6.09628i	0.369385	−	0.268374i
$517$	0.341775	−	1.05188i	0.0150313	−	0.0462615i
$518$	19.6793			0.864657
$519$	2.84779	−	8.76460i	0.125004	−	0.384723i
$520$	−0.0403586	−	0.00177461i	−0.00176984	−	7.78217e-5i
$521$	−7.35881	−	22.6481i	−0.322395	−	0.992231i	−0.972603	−	0.232474i	$-0.925318\pi$
$521$	−7.35881	−	22.6481i	−0.322395	−	0.992231i	0.650207	−	0.759757i	$-0.274682\pi$
$522$	2.19525	+	6.75628i	0.0960834	+	0.295714i
$523$	34.2257	+	24.8664i	1.49659	+	1.08733i	0.971717	+	0.236150i	$0.0758858\pi$
$523$	34.2257	+	24.8664i	1.49659	+	1.08733i	0.524869	+	0.851183i	$0.324114\pi$
$524$	−37.2612			−1.62776
$525$	1.95650	−	4.60131i	0.0853888	−	0.200818i
$526$	8.40438			0.366449
$527$	8.56737	+	6.22456i	0.373200	+	0.271146i
$528$	−0.0908359	−	0.279564i	−0.00395312	−	0.0121665i
$529$	−7.10363	−	21.8627i	−0.308854	−	0.950554i
$530$	−20.0617	−	15.9679i	−0.871423	−	0.693601i
$531$	2.51844	−	7.75095i	0.109291	−	0.336363i
$532$	−4.20923			−0.182493
$533$	0.0179648	−	0.0552899i	0.000778141	−	0.00239487i
$534$	−0.308398	+	0.224065i	−0.0133457	+	0.00969622i
$535$	−11.9843	+	32.0233i	−0.518128	+	1.38449i
$536$	14.8497	+	10.7890i	0.641410	+	0.466012i
$537$	7.16668	−	5.20690i	0.309265	−	0.224694i
$538$	−27.0747	+	19.6709i	−1.16727	+	0.848073i
$539$	−0.101817	−	0.0739744i	−0.00438557	−	0.00318630i
$540$	4.60526	+	3.66551i	0.198179	+	0.157739i
$541$	−5.69164	+	4.13522i	−0.244703	+	0.177787i	−0.703376	−	0.710818i	$-0.748325\pi$
$541$	−5.69164	+	4.13522i	−0.244703	+	0.177787i	0.458673	+	0.888605i	$0.348325\pi$
$542$	4.12607	−	12.6987i	0.177230	−	0.545457i
$543$	−24.0997			−1.03422
$544$	−5.19309	+	15.9827i	−0.222652	+	0.685252i
$545$	−9.48467	−	34.2417i	−0.406278	−	1.46676i
$546$	0.00882970	+	0.0271750i	0.000377876	+	0.00116298i
$547$	−13.0502	−	40.1644i	−0.557986	−	1.71730i	−0.687925	−	0.725782i	$-0.741478\pi$
$547$	−13.0502	−	40.1644i	−0.557986	−	1.71730i	0.129939	−	0.991522i	$-0.458522\pi$
$548$	31.7628	+	23.0770i	1.35684	+	0.985802i
$549$	−9.11555			−0.389042
$550$	−0.529957	+	1.24636i	−0.0225974	+	0.0531448i
$551$	5.27808			0.224854
$552$	−0.121410	−	0.0882096i	−0.00516756	−	0.00375445i
$553$	−0.519206	−	1.59795i	−0.0220789	−	0.0679519i
$554$	−7.33125	−	22.5633i	−0.311475	−	0.958622i
$555$	−17.0527	+	11.2793i	−0.723845	+	0.478780i
$556$	13.5614	−	41.7376i	0.575131	−	1.77007i
$557$	19.1036			0.809444			0.404722	−	0.914440i	$-0.367368\pi$
$557$	19.1036			0.809444			0.404722	+	0.914440i	$0.367368\pi$
$558$	−3.24753	+	9.99486i	−0.137479	+	0.423116i
$559$	−0.0423193	+	0.0307468i	−0.00178992	+	0.00130045i
$560$	1.39416	+	5.03321i	0.0589138	+	0.212692i
$561$	0.220819	+	0.160435i	0.00932300	+	0.00677355i
$562$	−58.0866	+	42.2024i	−2.45024	+	1.78020i
$563$	33.9289	−	24.6508i	1.42993	−	1.03891i	0.439903	−	0.898045i	$-0.355013\pi$
$563$	33.9289	−	24.6508i	1.42993	−	1.03891i	0.990029	−	0.140861i	$-0.0449871\pi$
$564$	−18.7148	−	13.5971i	−0.788034	−	0.572540i
$565$	−9.39183	−	33.9066i	−0.395117	−	1.42646i
$566$	39.9847	−	29.0506i	1.68068	−	1.22109i
$567$	0.309017	−	0.951057i	0.0129775	−	0.0399406i
$568$	7.07261			0.296760
$569$	2.68086	−	8.25085i	0.112388	−	0.345894i	−0.879006	−	0.476812i	$-0.841792\pi$
$569$	2.68086	−	8.25085i	0.112388	−	0.345894i	0.991393	+	0.130918i	$0.0417924\pi$
$570$	6.41873	−	4.24561i	0.268851	−	0.177829i
$571$	−6.51699	−	20.0572i	−0.272728	−	0.839369i	−0.989812	−	0.142382i	$-0.954524\pi$
$571$	−6.51699	−	20.0572i	−0.272728	−	0.839369i	0.717084	−	0.696987i	$-0.245476\pi$
$572$	−0.00135907	−	0.00418280i	−5.68257e−5	−	0.000174892i
$573$	5.65247	+	4.10676i	0.236135	+	0.171562i
$574$	9.42477			0.393382
$575$	−0.123704	−	0.537340i	−0.00515883	−	0.0224086i
$576$	−12.0059			−0.500246
$577$	21.9622	+	15.9564i	0.914297	+	0.664275i	0.942098	−	0.335338i	$-0.108851\pi$
$577$	21.9622	+	15.9564i	0.914297	+	0.664275i	−0.0278012	+	0.999613i	$0.508851\pi$
$578$	8.17818	+	25.1698i	0.340167	+	1.04693i
$579$	−3.21899	−	9.90702i	−0.133776	−	0.411722i
$580$	5.18602	+	18.7227i	0.215338	+	0.777418i
$581$	0.521981	−	1.60649i	0.0216554	−	0.0666485i
$582$	26.4165			1.09500
$583$	0.207201	−	0.637700i	0.00858140	−	0.0264108i
$584$	−6.13999	+	4.46096i	−0.254075	+	0.184596i
$585$	−0.0232268	−	0.0184871i	−0.000960308	−	0.000764349i
$586$	−31.5865	−	22.9489i	−1.30483	−	0.948012i
$587$	−3.41483	+	2.48102i	−0.140945	+	0.102403i	−0.656023	−	0.754741i	$-0.727763\pi$
$587$	−3.41483	+	2.48102i	−0.140945	+	0.102403i	0.515078	+	0.857143i	$0.327763\pi$
$588$	−2.12956	+	1.54721i	−0.0878214	+	0.0638060i
$589$	6.31688	+	4.58948i	0.260282	+	0.189106i
$590$	13.7472	−	36.7340i	0.565965	−	1.51231i
$591$	−6.87097	+	4.99205i	−0.282634	+	0.205346i
$592$	6.59943	−	20.3109i	0.271235	−	0.834775i
$593$	42.3129			1.73758			0.868791	−	0.495180i	$-0.164898\pi$
$593$	42.3129			1.73758			0.868791	+	0.495180i	$0.164898\pi$
$594$	−0.0837033	+	0.257612i	−0.00343439	+	0.0105700i
$595$	−3.79436	−	3.02009i	−0.155554	−	0.123812i
$596$	−1.55138	−	4.77464i	−0.0635468	−	0.195577i
$597$	−5.25783	−	16.1819i	−0.215188	−	0.662282i
$598$	0.00254926	+	0.00185215i	0.000104247	+	7.57399e-5i
$599$	−19.4630			−0.795236			−0.397618	−	0.917551i	$-0.630163\pi$
$599$	−19.4630			−0.795236			−0.397618	+	0.917551i	$0.630163\pi$
$600$	5.13240	+	4.46710i	0.209529	+	0.182369i
$601$	8.80231			0.359054			0.179527	−	0.983753i	$-0.442543\pi$
$601$	8.80231			0.359054			0.179527	+	0.983753i	$0.442543\pi$
$602$	−6.86072	−	4.98460i	−0.279622	−	0.203157i
$603$	4.16811	+	12.8281i	0.169738	+	0.522401i
$604$	−4.80530	−	14.7892i	−0.195525	−	0.601764i
$605$	24.5376	+	1.07894i	0.997596	+	0.0438653i
$606$	6.78311	−	20.8763i	0.275545	−	0.848041i
$607$	10.2483			0.415966			0.207983	−	0.978132i	$-0.433310\pi$
$607$	10.2483			0.415966			0.207983	+	0.978132i	$0.433310\pi$
$608$	−3.82896	+	11.7843i	−0.155285	+	0.477918i
$609$	2.67031	−	1.94009i	0.108206	−	0.0786166i
$610$	−43.8274	−	1.92714i	−1.77452	−	0.0780274i
$611$	0.0943886	+	0.0685773i	0.00381855	+	0.00277434i
$612$	4.61855	−	3.35557i	0.186694	−	0.135641i
$613$	−24.9576	+	18.1327i	−1.00803	+	0.732375i	−0.963794	−	0.266647i	$-0.914084\pi$
$613$	−24.9576	+	18.1327i	−1.00803	+	0.732375i	−0.0442329	+	0.999021i	$0.514084\pi$
$614$	16.8870	+	12.2691i	0.681505	+	0.495142i
$615$	−8.16684	+	5.40188i	−0.329319	+	0.217825i
$616$	0.138556	−	0.100667i	0.00558257	−	0.00405597i
$617$	−0.792966	+	2.44050i	−0.0319236	+	0.0982507i	−0.965749	−	0.259479i	$-0.916449\pi$
$617$	−0.792966	+	2.44050i	−0.0319236	+	0.0982507i	0.933825	+	0.357730i	$0.116449\pi$
$618$	17.7643			0.714587
$619$	−5.43461	+	16.7260i	−0.218436	+	0.672276i	0.780456	+	0.625210i	$0.214987\pi$
$619$	−5.43461	+	16.7260i	−0.218436	+	0.672276i	−0.998892	+	0.0470652i	$0.985013\pi$
$620$	−10.0734	+	26.9170i	−0.404556	+	1.08101i
$621$	−0.0340781	−	0.104882i	−0.00136751	−	0.00420876i
$622$	−19.7172	−	60.6833i	−0.790588	−	2.43318i
$623$	0.143290	+	0.104106i	0.00574078	+	0.00417092i
$624$	0.0310083			0.00124133
$625$	3.44868	+	24.7610i	0.137947	+	0.990440i
$626$	19.8563			0.793617
$627$	0.162814	+	0.118291i	0.00650217	+	0.00472410i
$628$	−2.84111	−	8.74405i	−0.113373	−	0.348926i
$629$	6.12788	+	18.8597i	0.244335	+	0.751985i
$630$	1.68681	−	4.50733i	0.0672042	−	0.179576i
$631$	−0.766383	+	2.35868i	−0.0305092	+	0.0938978i	−0.965152	−	0.261691i	$-0.915720\pi$
$631$	−0.766383	+	2.35868i	−0.0305092	+	0.0938978i	0.934642	+	0.355589i	$0.115720\pi$
$632$	2.28645			0.0909501
$633$	−6.85579	+	21.1000i	−0.272493	+	0.838648i
$634$	−41.4626	+	30.1244i	−1.64669	+	1.19639i
$635$	27.2870	−	18.0487i	1.08285	−	0.716242i
$636$	−11.3458	−	8.24323i	−0.449891	−	0.326865i
$637$	0.0107405	−	0.00780342i	0.000425554	−	0.000309183i
$638$	−0.723305	+	0.525512i	−0.0286359	+	0.0208052i
$639$	4.20468	+	3.05488i	0.166335	+	0.120849i
$640$	−23.1045	−	1.01593i	−0.913285	−	0.0401580i
$641$	−20.1620	+	14.6486i	−0.796353	+	0.578584i	−0.909842	−	0.414955i	$-0.863797\pi$
$641$	−20.1620	+	14.6486i	−0.796353	+	0.578584i	0.113489	+	0.993539i	$0.463797\pi$
$642$	−10.1701	+	31.3002i	−0.401380	+	1.23532i
$643$	26.1096			1.02966			0.514832	−	0.857291i	$-0.327854\pi$
$643$	26.1096			1.02966			0.514832	+	0.857291i	$0.327854\pi$
$644$	−0.0897030	+	0.276078i	−0.00353479	+	0.0108790i
$645$	8.80198	+	0.387032i	0.346578	+	0.0152394i
$646$	−2.30658	−	7.09891i	−0.0907510	−	0.279303i
$647$	−5.12213	−	15.7643i	−0.201372	−	0.619758i	−0.999843	−	0.0177252i	$-0.994358\pi$
$647$	−5.12213	−	15.7643i	−0.201372	−	0.619758i	0.798471	−	0.602033i	$-0.205642\pi$
$648$	1.10094	+	0.799876i	0.0432488	+	0.0314221i
$649$	1.02568			0.0402614
$650$	−0.107765	−	0.0937962i	−0.00422691	−	0.00367899i
$651$	4.88285			0.191374
$652$	17.6077	+	12.7928i	0.689572	+	0.501003i
$653$	8.88204	+	27.3361i	0.347581	+	1.06974i	0.960187	+	0.279357i	$0.0901211\pi$
$653$	8.88204	+	27.3361i	0.347581	+	1.06974i	−0.612606	+	0.790388i	$0.709879\pi$
$654$	−10.5682	−	32.5257i	−0.413251	−	1.27186i
$655$	−24.7656	−	19.7119i	−0.967670	−	0.770209i
$656$	3.16059	−	9.72729i	0.123400	−	0.379787i
$657$	−5.57707			−0.217582
$658$	−5.84487	+	17.9887i	−0.227857	+	0.701271i
$659$	5.72898	−	4.16235i	0.223169	−	0.162142i	−0.470583	−	0.882356i	$-0.655956\pi$
$659$	5.72898	−	4.16235i	0.223169	−	0.162142i	0.693752	+	0.720214i	$0.255956\pi$
$660$	−0.259635	+	0.693772i	−0.0101063	+	0.0270050i
$661$	15.2267	+	11.0629i	0.592251	+	0.430295i	0.843120	−	0.537726i	$-0.180716\pi$
$661$	15.2267	+	11.0629i	0.592251	+	0.430295i	−0.250869	+	0.968021i	$0.580716\pi$
$662$	−22.3998	+	16.2744i	−0.870594	+	0.632523i
$663$	−0.0232938	+	0.0169239i	−0.000904657	+	0.000657272i
$664$	1.85966	+	1.35112i	0.0721689	+	0.0524338i
$665$	−2.79765	−	2.22677i	−0.108488	−	0.0863504i
$666$	−15.9209	+	11.5672i	−0.616921	+	0.448219i
$667$	0.112481	−	0.346181i	0.00435529	−	0.0134042i
$668$	19.0592			0.737422
$669$	0.799724	−	2.46130i	0.0309191	−	0.0951593i
$670$	17.3282	+	62.5585i	0.669446	+	2.41685i
$671$	−0.354510	−	1.09107i	−0.0136857	−	0.0421202i
$672$	2.39447	+	7.36942i	0.0923687	+	0.284282i
$673$	30.4634	+	22.1329i	1.17428	+	0.853161i	0.991515	−	0.129996i	$-0.0414964\pi$
$673$	30.4634	+	22.1329i	1.17428	+	0.853161i	0.182761	+	0.983157i	$0.441496\pi$
$674$	−45.7018			−1.76037
$675$	1.12174	+	4.87255i	0.0431758	+	0.187544i
$676$	−34.2191			−1.31612
$677$	−28.0611	−	20.3876i	−1.07848	−	0.783559i	−0.101060	−	0.994880i	$-0.532223\pi$
$677$	−28.0611	−	20.3876i	−1.07848	−	0.783559i	−0.977417	+	0.211321i	$0.932223\pi$
$678$	−10.4648	−	32.2074i	−0.401898	−	1.23692i
$679$	−3.79281	−	11.6731i	−0.145555	−	0.447971i
$680$	5.50429	−	3.64076i	0.211080	−	0.139617i
$681$	1.30396	−	4.01317i	0.0499677	−	0.153785i
$682$	−1.32261			−0.0506455
$683$	0.726964	−	2.23737i	0.0278165	−	0.0856104i	−0.936184	−	0.351509i	$-0.885669\pi$
$683$	0.726964	−	2.23737i	0.0278165	−	0.0856104i	0.964001	+	0.265899i	$0.0856686\pi$
$684$	3.40534	−	2.47413i	0.130206	−	0.0946006i
$685$	8.90284	+	32.1412i	0.340160	+	1.22805i
$686$	1.74122	+	1.26507i	0.0664803	+	0.0483007i
$687$	16.8535	−	12.2448i	0.643003	−	0.467169i
$688$	−7.44534	+	5.40936i	−0.283851	+	0.206230i
$689$	0.0572231	+	0.0415750i	0.00218002	+	0.00158388i
$690$	−0.141674	−	0.511474i	−0.00539343	−	0.0194715i
$691$	−22.7536	+	16.5315i	−0.865588	+	0.628887i	−0.929400	−	0.369075i	$-0.879674\pi$
$691$	−22.7536	+	16.5315i	−0.865588	+	0.628887i	0.0638111	+	0.997962i	$0.479674\pi$
$692$	7.49617	−	23.0708i	0.284962	−	0.877022i
$693$	0.125853			0.00478075
$694$	−13.1387	+	40.4367i	−0.498737	+	1.53496i
$695$	31.0936	−	20.5665i	1.17945	−	0.780134i
$696$	1.38800	+	4.27184i	0.0526121	+	0.161923i
$697$	2.93476	+	9.03226i	0.111162	+	0.342121i
$698$	51.2951	+	37.2681i	1.94155	+	1.41062i
$699$	1.91775			0.0725361
$700$	5.15006	−	12.1119i	0.194654	−	0.457788i
$701$	14.0281			0.529835			0.264917	−	0.964271i	$-0.414655\pi$
$701$	14.0281			0.529835			0.264917	+	0.964271i	$0.414655\pi$
$702$	−0.0231164	−	0.0167951i	−0.000872474	−	0.000633890i
$703$	4.51820	+	13.9056i	0.170407	+	0.524459i
$704$	−0.466917	−	1.43702i	−0.0175976	−	0.0541598i
$705$	−5.24559	−	18.9377i	−0.197560	−	0.713237i
$706$	16.2290	−	49.9476i	0.610785	−	1.87980i
$707$	−10.1988			−0.383566
$708$	6.62922	−	20.4026i	0.249141	−	0.766778i
$709$	15.8181	−	11.4925i	0.594062	−	0.431611i	−0.249704	−	0.968322i	$-0.580333\pi$
$709$	15.8181	−	11.4925i	0.594062	−	0.431611i	0.843766	+	0.536711i	$0.180333\pi$
$710$	19.5702	+	15.5767i	0.734456	+	0.584584i
$711$	1.35930	+	0.987589i	0.0509777	+	0.0370375i
$712$	−0.194993	+	0.141671i	−0.00730767	+	0.00530933i
$713$	0.435636	−	0.316508i	0.0163147	−	0.0118533i
$714$	−3.77634	−	2.74367i	−0.141326	−	0.102679i
$715$	0.00130948	−	0.00349906i	4.89717e−5	−	0.000130857i
$716$	18.8647	−	13.7060i	0.705006	−	0.512217i
$717$	1.23762	−	3.80901i	0.0462198	−	0.142250i
$718$	−53.4700			−1.99548
$719$	−8.74342	+	26.9095i	−0.326075	+	1.00355i	0.644879	+	0.764285i	$0.276908\pi$
$719$	−8.74342	+	26.9095i	−0.326075	+	1.00355i	−0.970953	+	0.239269i	$0.923092\pi$
$720$	−4.08634	−	3.25249i	−0.152289	−	0.121213i
$721$	−2.55055	−	7.84979i	−0.0949875	−	0.292342i
$722$	10.9360	+	33.6576i	0.406996	+	1.25260i
$723$	−2.42920	−	1.76492i	−0.0903429	−	0.0656380i
$724$	−63.4372			−2.35762
$725$	−6.45780	+	15.1875i	−0.239837	+	0.564049i
$726$	23.6409			0.877396
$727$	11.3645	+	8.25676i	0.421484	+	0.306226i	0.778235	−	0.627973i	$-0.216115\pi$
$727$	11.3645	+	8.25676i	0.421484	+	0.306226i	−0.356750	+	0.934200i	$0.616115\pi$
$728$	0.00558281	+	0.0171821i	0.000206913	+	0.000636812i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−26.8144	−	1.17906i	−0.992447	−	0.0436389i
$731$	2.64067	−	8.12714i	0.0976686	−	0.300593i
$732$	−23.9947			−0.886868
$733$	−12.9879	+	39.9727i	−0.479720	+	1.47643i	0.359765	+	0.933043i	$0.382857\pi$
$733$	−12.9879	+	39.9727i	−0.479720	+	1.47643i	−0.839485	+	0.543383i	$0.817143\pi$
$734$	−12.7190	+	9.24091i	−0.469467	+	0.341088i
$735$	−2.23391	−	0.0982272i	−0.0823990	−	0.00362317i
$736$	0.691318	+	0.502272i	0.0254823	+	0.0185140i
$737$	−1.37334	+	0.997787i	−0.0505875	+	0.0367540i
$738$	−7.62480	+	5.53974i	−0.280673	+	0.203921i
$739$	17.2014	+	12.4975i	0.632762	+	0.459729i	0.857356	−	0.514724i	$-0.172106\pi$
$739$	17.2014	+	12.4975i	0.632762	+	0.459729i	−0.224594	+	0.974452i	$0.572106\pi$
$740$	−44.8873	+	29.6903i	−1.65009	+	1.09144i
$741$	−0.0171750	+	0.0124783i	−0.000630938	+	0.000458403i
$742$	−3.54345	+	10.9056i	−0.130084	+	0.400358i
$743$	−10.8259			−0.397164			−0.198582	−	0.980084i	$-0.563634\pi$
$743$	−10.8259			−0.397164			−0.198582	+	0.980084i	$0.563634\pi$
$744$	−2.05333	+	6.31951i	−0.0752789	+	0.231685i
$745$	1.49476	−	3.99416i	0.0547639	−	0.146335i
$746$	24.1140	+	74.2154i	0.882877	+	2.71722i
$747$	0.521981	+	1.60649i	0.0190983	+	0.0587785i
$748$	0.581257	+	0.422308i	0.0212529	+	0.0154411i
$749$	15.2913			0.558732
$750$	4.36319	+	23.6643i	0.159321	+	0.864097i
$751$	−51.1600			−1.86686			−0.933428	−	0.358764i	$-0.883198\pi$
$751$	−51.1600			−1.86686			−0.933428	+	0.358764i	$0.883198\pi$
$752$	16.6060	+	12.0650i	0.605559	+	0.439964i
$753$	7.71324	+	23.7389i	0.281086	+	0.865094i
$754$	−0.0291441	−	0.0896962i	−0.00106136	−	0.00326654i
$755$	4.62995	−	12.3717i	0.168501	−	0.450252i
$756$	0.813418	−	2.50344i	0.0295837	−	0.0910494i
$757$	−29.0520			−1.05591			−0.527957	−	0.849271i	$-0.677042\pi$
$757$	−29.0520			−1.05591			−0.527957	+	0.849271i	$0.677042\pi$
$758$	9.17903	−	28.2501i	0.333397	−	1.02609i
$759$	0.0112283	−	0.00815783i	0.000407561	−	0.000296110i
$760$	4.05841	−	2.68440i	0.147214	−	0.0973734i
$761$	−23.9720	−	17.4167i	−0.868984	−	0.631354i	0.0613302	−	0.998118i	$-0.480466\pi$
$761$	−23.9720	−	17.4167i	−0.868984	−	0.631354i	−0.930314	+	0.366764i	$0.880466\pi$
$762$	25.4759	−	18.5093i	0.922895	−	0.670523i
$763$	−12.8553	+	9.33989i	−0.465392	+	0.338127i
$764$	14.8789	+	10.8101i	0.538298	+	0.391097i
$765$	4.84487	+	0.213034i	0.175167	+	0.00770225i
$766$	23.5546	−	17.1135i	0.851064	−	0.618334i
$767$	−0.0334347	+	0.102901i	−0.00120726	+	0.00371555i
$768$	1.75165			0.0632074
$769$	7.59125	−	23.3635i	0.273747	−	0.842508i	−0.715801	−	0.698305i	$-0.753938\pi$
$769$	7.59125	−	23.3635i	0.273747	−	0.842508i	0.989548	−	0.144203i	$-0.0460619\pi$
$770$	0.605098	+	0.0266068i	0.0218062	+	0.000958841i
$771$	−5.82235	−	17.9194i	−0.209687	−	0.645350i
$772$	−8.47326	−	26.0780i	−0.304959	−	0.938568i
$773$	6.73928	+	4.89637i	0.242395	+	0.176110i	0.702350	−	0.711832i	$-0.252134\pi$
$773$	6.73928	+	4.89637i	0.242395	+	0.176110i	−0.459955	+	0.887942i	$0.652134\pi$
$774$	8.48031			0.304819
$775$	−20.9349	+	12.5613i	−0.752003	+	0.451215i
$776$	16.7025			0.599586
$777$	7.39723	+	5.37440i	0.265374	+	0.192806i
$778$	13.0397	+	40.1321i	0.467497	+	1.43881i
$779$	2.16385	+	6.65965i	0.0775280	+	0.238607i
$780$	−0.0611393	−	0.0486633i	−0.00218914	−	0.00174242i
$781$	−0.202125	+	0.622078i	−0.00723261	+	0.0222597i
$782$	−0.514763			−0.0184079
$783$	−1.01997	+	3.13914i	−0.0364507	+	0.112184i
$784$	1.88960	−	1.37287i	0.0674857	−	0.0490312i
$785$	2.73744	−	7.31471i	0.0977034	−	0.261073i
$786$	−24.6479	−	17.9078i	−0.879163	−	0.638749i
$787$	−40.6502	+	29.5341i	−1.44902	+	1.05278i	−0.462963	+	0.886378i	$0.653214\pi$
$787$	−40.6502	+	29.5341i	−1.44902	+	1.05278i	−0.986059	+	0.166398i	$0.946786\pi$
$788$	−18.0863	+	13.1405i	−0.644298	+	0.468110i
$789$	3.15912	+	2.29524i	0.112468	+	0.0817126i
$790$	6.32670	+	5.03568i	0.225094	+	0.179162i
$791$	−12.7294	+	9.24848i	−0.452607	+	0.328838i
$792$	−0.0529236	+	0.162882i	−0.00188056	+	0.00578776i
$793$	0.121018			0.00429747
$794$	−0.132004	+	0.406267i	−0.00468466	+	0.0144179i
$795$	−3.18014	−	11.4810i	−0.112788	−	0.407189i
$796$	−13.8401	−	42.5953i	−0.490548	−	1.50975i
$797$	−7.45615	−	22.9477i	−0.264110	−	0.812848i	−0.991897	−	0.127044i	$-0.959451\pi$
$797$	−7.45615	−	22.9477i	−0.264110	−	0.812848i	0.727787	−	0.685804i	$-0.240549\pi$
$798$	−2.78437	−	2.02296i	−0.0985655	−	0.0716120i
$799$	−19.0595			−0.674278
$800$	−29.2242	−	25.4360i	−1.03323	−	0.899299i
$801$	−0.177116			−0.00625808
$802$	29.3694	+	21.3381i	1.03707	+	0.753475i
$803$	−0.216896	−	0.667536i	−0.00765408	−	0.0235568i
$804$	10.9716	+	33.7671i	0.386939	+	1.19088i
$805$	−0.205671	+	0.136039i	−0.00724896	+	0.00479476i
$806$	0.0431141	−	0.132691i	0.00151863	−	0.00467386i
$807$	−15.5492			−0.547359
$808$	4.28880	−	13.1996i	0.150880	−	0.464359i
$809$	−13.8901	+	10.0917i	−0.488349	+	0.354806i	−0.804549	−	0.593886i	$-0.797593\pi$
$809$	−13.8901	+	10.0917i	−0.488349	+	0.354806i	0.316200	+	0.948693i	$0.397593\pi$
$810$	1.28468	+	4.63799i	0.0451392	+	0.162962i
$811$	8.01259	+	5.82148i	0.281360	+	0.204420i	0.719510	−	0.694482i	$-0.244366\pi$
$811$	8.01259	+	5.82148i	0.281360	+	0.204420i	−0.438150	+	0.898902i	$0.644366\pi$
$812$	7.02899	−	5.10686i	0.246669	−	0.179216i
$813$	5.01897	−	3.64649i	0.176023	−	0.127888i
$814$	−2.00368	−	1.45576i	−0.0702291	−	0.0510244i
$815$	4.93529	+	17.8175i	0.172876	+	0.624120i
$816$	−4.09814	+	2.97747i	−0.143464	+	0.104232i
$817$	1.94701	−	5.99229i	0.0681173	−	0.209644i
$818$	10.5257			0.368024
$819$	−0.00410250	+	0.0126262i	−0.000143353	+	0.000441195i
$820$	−21.4974	+	14.2192i	−0.750721	+	0.496557i
$821$	−2.86014	−	8.80260i	−0.0998195	−	0.307213i	0.888660	−	0.458566i	$-0.151637\pi$
$821$	−2.86014	−	8.80260i	−0.0998195	−	0.307213i	−0.988480	+	0.151353i	$0.951637\pi$
$822$	9.91995	+	30.5305i	0.345998	+	1.06487i
$823$	−9.27827	−	6.74106i	−0.323420	−	0.234978i	0.414213	−	0.910180i	$-0.364057\pi$
$823$	−9.27827	−	6.74106i	−0.323420	−	0.234978i	−0.737633	+	0.675201i	$0.764057\pi$
$824$	11.2320			0.391284
$825$	−0.539585	+	0.323761i	−0.0187859	+	0.0112719i
$826$	−17.5407			−0.610318
$827$	21.6959	+	15.7630i	0.754442	+	0.548134i	0.897200	−	0.441624i	$-0.145597\pi$
$827$	21.6959	+	15.7630i	0.754442	+	0.548134i	−0.142759	+	0.989758i	$0.545597\pi$
$828$	−0.0897030	−	0.276078i	−0.00311740	−	0.00959436i
$829$	13.8662	+	42.6757i	0.481592	+	1.48219i	0.836857	+	0.547421i	$0.184391\pi$
$829$	13.8662	+	42.6757i	0.481592	+	1.48219i	−0.355265	+	0.934765i	$0.615609\pi$
$830$	2.17004	+	7.83434i	0.0753233	+	0.271934i
$831$	3.40629	−	10.4835i	0.118163	−	0.363668i
$832$	0.159390			0.00552585
$833$	−0.670192	+	2.06264i	−0.0232208	+	0.0714662i
$834$	29.0299	−	21.0914i	1.00522	−	0.730336i
$835$	12.6676	+	10.0827i	0.438381	+	0.348926i
$836$	0.428572	+	0.311376i	0.0148225	+	0.0107691i
$837$	−3.95031	+	2.87007i	−0.136543	+	0.0992040i
$838$	−32.5474	+	23.6471i	−1.12433	+	0.816874i
$839$	−22.7435	−	16.5241i	−0.785192	−	0.570475i	0.121341	−	0.992611i	$-0.461281\pi$
$839$	−22.7435	−	16.5241i	−0.785192	−	0.570475i	−0.906533	+	0.422136i	$0.861281\pi$
$840$	1.06653	−	2.84988i	0.0367988	−	0.0983302i
$841$	14.6476	−	10.6421i	0.505091	−	0.366970i
$842$	−10.7541	+	33.0977i	−0.370611	+	1.14062i
$843$	−33.3596			−1.14897
$844$	−18.0463	+	55.5409i	−0.621181	+	1.91180i
$845$	−22.7436	−	18.1026i	−0.782405	−	0.622748i
$846$	−5.84487	−	17.9887i	−0.200951	−	0.618463i
$847$	−3.39429	−	10.4466i	−0.116629	−	0.358948i
$848$	10.0674	+	7.31439i	0.345716	+	0.251177i
$849$	22.9636			0.788108
$850$	23.2490	+	2.04853i	0.797435	+	0.0702638i
$851$	1.00833			0.0345653
$852$	11.0679	+	8.04129i	0.379180	+	0.275490i
$853$	−7.98374	−	24.5714i	−0.273358	−	0.841310i	−0.989649	−	0.143508i	$-0.954162\pi$
$853$	−7.98374	−	24.5714i	−0.273358	−	0.841310i	0.716291	−	0.697802i	$-0.245838\pi$
$854$	6.06265	+	18.6589i	0.207460	+	0.638495i
$855$	3.57221	+	0.157074i	0.122167	+	0.00537181i
$856$	−6.43029	+	19.7904i	−0.219783	+	0.676422i
$857$	−11.2285			−0.383559			−0.191780	−	0.981438i	$-0.561426\pi$
$857$	−11.2285			−0.383559			−0.191780	+	0.981438i	$0.561426\pi$
$858$	0.00111124	−	0.00342005i	3.79372e−5	−	0.000116759i
$859$	−42.4969	+	30.8758i	−1.44998	+	1.05347i	−0.464139	+	0.885762i	$0.653636\pi$
$859$	−42.4969	+	30.8758i	−1.44998	+	1.05347i	−0.985837	+	0.167707i	$0.946364\pi$
$860$	23.1692	+	1.01877i	0.790064	+	0.0347399i
$861$	3.54267	+	2.57390i	0.120734	+	0.0877184i
$862$	15.8735	−	11.5328i	0.540653	−	0.392808i
$863$	−26.9706	+	19.5953i	−0.918091	+	0.667032i	−0.943048	−	0.332656i	$-0.892055\pi$
$863$	−26.9706	+	19.5953i	−0.918091	+	0.667032i	0.0249568	+	0.999689i	$0.492055\pi$
$864$	−6.26880	−	4.55455i	−0.213269	−	0.154949i
$865$	17.1872	−	11.3683i	0.584384	−	0.386535i
$866$	−36.9282	+	26.8299i	−1.25487	+	0.911717i
$867$	−3.79979	+	11.6945i	−0.129048	+	0.397167i
$868$	12.8530			0.436259
$869$	−0.0653436	+	0.201107i	−0.00221663	+	0.00682208i
$870$	−5.56764	+	14.8773i	−0.188761	+	0.504387i
$871$	−0.0553357	−	0.170306i	−0.00187498	−	0.00577059i
$872$	−6.68205	−	20.5652i	−0.226283	−	0.696427i
$873$	9.92970	+	7.21435i	0.336069	+	0.244169i
$874$	−0.379544			−0.0128383
$875$	9.83042	−	5.32567i	0.332329	−	0.180041i
$876$	−14.6804			−0.496004
$877$	6.63376	+	4.81971i	0.224006	+	0.162750i	0.694128	−	0.719852i	$-0.255790\pi$
$877$	6.63376	+	4.81971i	0.224006	+	0.162750i	−0.470122	+	0.882601i	$0.655790\pi$
$878$	5.67230	+	17.4576i	0.191431	+	0.589164i
$879$	−5.60569	−	17.2525i	−0.189075	−	0.581914i
$880$	0.230380	−	0.615598i	0.00776611	−	0.0207518i
$881$	−4.59982	+	14.1568i	−0.154972	+	0.476954i	−0.998158	−	0.0606673i	$-0.980677\pi$
$881$	−4.59982	+	14.1568i	−0.154972	+	0.476954i	0.843186	+	0.537622i	$0.180677\pi$
$882$	−2.15227			−0.0724708
$883$	11.8582	−	36.4957i	0.399059	−	1.22818i	−0.526696	−	0.850054i	$-0.676569\pi$
$883$	11.8582	−	36.4957i	0.399059	−	1.22818i	0.925755	−	0.378124i	$-0.123431\pi$
$884$	−0.0613157	+	0.0445485i	−0.00206227	+	0.00149833i
$885$	15.1995	−	10.0536i	0.510925	−	0.337947i
$886$	33.5082	+	24.3451i	1.12573	+	0.817890i
$887$	−17.8071	+	12.9376i	−0.597903	+	0.434402i	−0.845134	−	0.534554i	$-0.820479\pi$
$887$	−17.8071	+	12.9376i	−0.597903	+	0.434402i	0.247231	+	0.968957i	$0.420479\pi$
$888$	−10.0664	+	7.31365i	−0.337805	+	0.245430i
$889$	−11.8368	−	8.59991i	−0.396992	−	0.288432i
$890$	−0.851569	−	0.0374444i	−0.0285447	−	0.00125514i
$891$	−0.101817	+	0.0739744i	−0.00341100	+	0.00247824i
$892$	2.10510	−	6.47882i	0.0704838	−	0.216927i
$893$	−14.0529			−0.470264
$894$	1.26848	−	3.90397i	0.0424242	−	0.130568i
$895$	19.7891	+	0.870146i	0.661476	+	0.0290858i
$896$	3.19605	+	9.83642i	0.106772	+	0.328612i
$897$	0.000452420		0.00139241i	1.51059e−5		4.64911e-5i
$898$	−59.3644	−	43.1308i	−1.98102	−	1.43929i
$899$	−16.1167			−0.537523
$900$	2.95273	+	12.8259i	0.0984243	+	0.427530i
$901$	−11.5548			−0.384947
$902$	−0.959602	−	0.697191i	−0.0319512	−	0.0232139i
$903$	−1.21758	−	3.74732i	−0.0405185	−	0.124703i
$904$	−6.61665	−	20.3639i	−0.220066	−	0.677295i
$905$	−42.1633	−	33.5595i	−1.40156	−	1.11556i
$906$	3.92904	−	12.0923i	0.130534	−	0.401741i
$907$	28.3503			0.941358			0.470679	−	0.882305i	$-0.344009\pi$
$907$	28.3503			0.941358			0.470679	+	0.882305i	$0.344009\pi$
$908$	3.43238	−	10.5638i	0.113907	−	0.350571i
$909$	8.25101	−	5.99471i	0.273669	−	0.198832i
$910$	−0.0223941	+	0.0598392i	−0.000742356	+	0.00198365i
$911$	21.8318	+	15.8618i	0.723321	+	0.525524i	0.887444	−	0.460916i	$-0.152479\pi$
$911$	21.8318	+	15.8618i	0.723321	+	0.525524i	−0.164122	+	0.986440i	$0.552479\pi$
$912$	−3.02163	+	2.19534i	−0.100056	+	0.0726951i
$913$	−0.171986	+	0.124955i	−0.00569190	+	0.00413541i
$914$	63.4748	+	46.1172i	2.09956	+	1.52542i
$915$	−15.9480	−	12.6936i	−0.527224	−	0.419639i
$916$	44.3632	−	32.2317i	1.46580	−	1.06497i
$917$	−4.37429	+	13.4627i	−0.144452	+	0.444577i
$918$	4.66782			0.154061
$919$	17.4398	−	53.6742i	0.575286	−	1.77055i	−0.0599189	−	0.998203i	$-0.519084\pi$
$919$	17.4398	−	53.6742i	0.575286	−	1.77055i	0.635205	−	0.772344i	$-0.280916\pi$
$920$	−0.0895769	−	0.323393i	−0.00295326	−	0.0106619i
$921$	2.99696	+	9.22368i	0.0987531	+	0.303931i
$922$	8.41569	+	25.9008i	0.277156	+	0.852998i
$923$	−0.0558212	−	0.0405565i	−0.00183738	−	0.00133493i
$924$	0.331279			0.0108983
$925$	−45.5410	−	4.01272i	−1.49738	−	0.131937i
$926$	83.5874			2.74685
$927$	6.67743	+	4.85144i	0.219316	+	0.159342i
$928$	−7.90339	−	24.3241i	−0.259442	−	0.798479i
$929$	17.2497	+	53.0893i	0.565946	+	1.74180i	0.665125	+	0.746732i	$0.268378\pi$
$929$	17.2497	+	53.0893i	0.565946	+	1.74180i	−0.0991787	+	0.995070i	$0.531622\pi$
$930$	−19.5998	+	12.9641i	−0.642702	+	0.425109i
$931$	−0.494144	+	1.52082i	−0.0161949	+	0.0498429i
$932$	5.04806			0.165355
$933$	9.16111	−	28.1950i	0.299921	−	0.923063i
$934$	50.0792	−	36.3847i	1.63864	−	1.19054i
$935$	0.162921	+	0.588183i	0.00532810	+	0.0192356i
$936$	−0.0146160	−	0.0106191i	−0.000477738	−	0.000347097i
$937$	22.4308	−	16.2970i	0.732784	−	0.532398i	−0.157659	−	0.987494i	$-0.550395\pi$
$937$	22.4308	−	16.2970i	0.732784	−	0.532398i	0.890443	+	0.455095i	$0.150395\pi$
$938$	23.4861	−	17.0637i	0.766849	−	0.557149i
$939$	7.46378	+	5.42275i	0.243571	+	0.176965i
$940$	−13.8078	−	49.8494i	−0.450362	−	1.62591i
$941$	−43.2552	+	31.4267i	−1.41008	+	1.02448i	−0.416767	+	0.909013i	$0.636837\pi$
$941$	−43.2552	+	31.4267i	−1.41008	+	1.02448i	−0.993311	+	0.115468i	$0.963163\pi$
$942$	2.32303	−	7.14954i	0.0756883	−	0.232945i
$943$	0.482910			0.0157257
$944$	−5.88225	+	18.1037i	−0.191451	+	0.589225i
$945$	1.86501	−	1.23359i	0.0606687	−	0.0401287i
$946$	0.329805	+	1.01504i	0.0107229	+	0.0330016i
$947$	12.4652	+	38.3639i	0.405064	+	1.24666i	0.920842	+	0.389936i	$0.127503\pi$
$947$	12.4652	+	38.3639i	0.405064	+	1.24666i	−0.515778	+	0.856722i	$0.672497\pi$
$948$	3.57805	+	2.59961i	0.116210	+	0.0844313i
$949$	0.0740410			0.00240347
$950$	17.1419	+	1.51042i	0.556157	+	0.0490043i
$951$	−23.8123			−0.772168
$952$	−2.38769	−	1.73476i	−0.0773856	−	0.0562239i
$953$	11.9158	+	36.6730i	0.385990	+	1.18795i	0.935760	+	0.352638i	$0.114715\pi$
$953$	11.9158	+	36.6730i	0.385990	+	1.18795i	−0.549770	+	0.835316i	$0.685285\pi$
$954$	−3.54345	−	10.9056i	−0.114724	−	0.353083i
$955$	4.17042	+	15.0561i	0.134952	+	0.487205i
$956$	3.25776	−	10.0264i	0.105364	−	0.324276i
$957$	−0.415400			−0.0134280
$958$	12.8881	−	39.6654i	0.416395	−	1.28153i
$959$	12.0667	−	8.76695i	0.389653	−	0.283099i
$960$	−21.0047	−	16.7185i	−0.677925	−	0.539588i
$961$	5.79078	+	4.20725i	0.186799	+	0.135718i
$962$	0.211365	−	0.153565i	0.00681467	−	0.00495115i
$963$	−12.3709	+	8.98800i	−0.398647	+	0.289634i
$964$	−6.39433	−	4.64575i	−0.205947	−	0.149630i
$965$	8.16406	−	21.8152i	0.262810	−	0.702256i
$966$	−0.192021	+	0.139511i	−0.00617817	+	0.00448870i
$967$	−11.3076	+	34.8012i	−0.363628	+	1.11913i	0.587207	+	0.809437i	$0.300227\pi$
$967$	−11.3076	+	34.8012i	−0.363628	+	1.11913i	−0.950836	+	0.309696i	$0.899773\pi$
$968$	14.9476			0.480434
$969$	1.07169	−	3.29833i	0.0344278	−	0.105958i
$970$	46.2166	+	36.7857i	1.48393	+	1.18112i
$971$	−12.0174	−	36.9858i	−0.385657	−	1.18693i	−0.936003	−	0.351993i	$-0.885504\pi$
$971$	−12.0174	−	36.9858i	−0.385657	−	1.18693i	0.550346	−	0.834937i	$-0.314496\pi$
$972$	0.813418	+	2.50344i	0.0260904	+	0.0802980i
$973$	−13.4880	−	9.79961i	−0.432406	−	0.314161i
$974$	−23.7009			−0.759425
$975$	−0.0148922	−	0.0646878i	−0.000476932	−	0.00207167i
$976$	21.2910			0.681507
$977$	−43.9133	−	31.9049i	−1.40491	−	1.02073i	−0.994038	−	0.109036i	$-0.965224\pi$
$977$	−43.9133	−	31.9049i	−1.40491	−	1.02073i	−0.410874	−	0.911692i	$-0.634776\pi$
$978$	5.49913	+	16.9246i	0.175843	+	0.541188i
$979$	−0.00688815	−	0.0211995i	−0.000220146	−	0.000677540i
$980$	−5.88027	−	0.258561i	−0.187838	−	0.00825944i
$981$	4.91027	−	15.1123i	0.156773	−	0.482497i
$982$	−14.4603			−0.461445
$983$	9.49397	−	29.2194i	0.302811	−	0.931956i	−0.677674	−	0.735362i	$-0.737012\pi$
$983$	9.49397	−	29.2194i	0.302811	−	0.931956i	0.980485	−	0.196594i	$-0.0629879\pi$
$984$	−4.82098	+	3.50264i	−0.153687	+	0.111660i
$985$	−18.9726	−	0.834243i	−0.604516	−	0.0265812i
$986$	12.4645	+	9.05600i	0.396951	+	0.288402i
$987$	−7.10973	+	5.16552i	−0.226305	+	0.164420i
$988$	−0.0452092	+	0.0328464i	−0.00143830	+	0.00104498i
$989$	−0.351533	−	0.255403i	−0.0111781	−	0.00812136i
$990$	−0.505173	+	0.334142i	−0.0160555	+	0.0106197i
$991$	−22.5729	+	16.4002i	−0.717052	+	0.520968i	−0.885441	−	0.464752i	$-0.846143\pi$
$991$	−22.5729	+	16.4002i	−0.717052	+	0.520968i	0.168389	+	0.985721i	$0.446143\pi$
$992$	11.6918	−	35.9838i	0.371216	−	1.14249i
$993$	−12.8644			−0.408239
$994$	3.45665	−	10.6385i	0.109638	−	0.337432i
$995$	13.3350	−	35.6325i	0.422748	−	1.12963i
$996$	1.37400	+	4.22873i	0.0435368	+	0.133992i
$997$	−5.31683	−	16.3635i	−0.168386	−	0.518238i	0.830884	−	0.556445i	$-0.187835\pi$
$997$	−5.31683	−	16.3635i	−0.168386	−	0.518238i	−0.999270	+	0.0382077i	$0.987835\pi$
$998$	11.0915	+	8.05844i	0.351095	+	0.255085i
$999$	−9.14348			−0.289287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.n.c.316.6	yes	24
25.11	even	5	inner	525.2.n.c.211.6	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.n.c.211.6	✓	24	25.11	even	5	inner
525.2.n.c.316.6	yes	24	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.74122 + 1.26507i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.813418 + 2.50344i) q^{4} +(-0.783736 + 2.09422i) q^{5} +(-0.665089 + 2.04693i) q^{6} +1.00000 q^{7} +(-0.420520 + 1.29423i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.74122 + 1.26507i) q^{2} +(0.309017 + 0.951057i) q^{3} +(0.813418 + 2.50344i) q^{4} +(-0.783736 + 2.09422i) q^{5} +(-0.665089 + 2.04693i) q^{6} +1.00000 q^{7} +(-0.420520 + 1.29423i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(-4.01400 + 2.65502i) q^{10} +(-0.101817 - 0.0739744i) q^{11} +(-2.12956 + 1.54721i) q^{12} +(0.0107405 - 0.00780342i) q^{13} +(1.74122 + 1.26507i) q^{14} +(-2.23391 - 0.0982272i) q^{15} +(1.88960 - 1.37287i) q^{16} +(-0.670192 + 2.06264i) q^{17} -2.15227 q^{18} +(-0.494144 + 1.52082i) q^{19} +(-5.88027 - 0.258561i) q^{20} +(0.309017 + 0.951057i) q^{21} +(-0.0837033 - 0.257612i) q^{22} +(0.0892177 + 0.0648204i) q^{23} -1.36083 q^{24} +(-3.77152 - 3.28263i) q^{25} +0.0285735 q^{26} +(-0.809017 - 0.587785i) q^{27} +(0.813418 + 2.50344i) q^{28} +(-1.01997 - 3.13914i) q^{29} +(-3.76547 - 2.99710i) q^{30} +(1.50888 - 4.64386i) q^{31} +7.74867 q^{32} +(0.0388906 - 0.119693i) q^{33} +(-3.77634 + 2.74367i) q^{34} +(-0.783736 + 2.09422i) q^{35} +(-2.12956 - 1.54721i) q^{36} +(7.39723 - 5.37440i) q^{37} +(-2.78437 + 2.02296i) q^{38} +(0.0107405 + 0.00780342i) q^{39} +(-2.38082 - 1.89499i) q^{40} +(3.54267 - 2.57390i) q^{41} +(-0.665089 + 2.04693i) q^{42} -3.94017 q^{43} +(0.102371 - 0.315065i) q^{44} +(-0.596896 - 2.15493i) q^{45} +(0.0733454 + 0.225734i) q^{46} +(2.71568 + 8.35799i) q^{47} +(1.88960 + 1.37287i) q^{48} +1.00000 q^{49} +(-2.41429 - 10.4870i) q^{50} -2.16879 q^{51} +(0.0282719 + 0.0205408i) q^{52} +(1.64638 + 5.06703i) q^{53} +(-0.665089 - 2.04693i) q^{54} +(0.234716 - 0.155251i) q^{55} +(-0.420520 + 1.29423i) q^{56} -1.59909 q^{57} +(2.19525 - 6.75628i) q^{58} +(-6.59335 + 4.79035i) q^{59} +(-1.57120 - 5.67237i) q^{60} +(7.37464 + 5.35799i) q^{61} +(8.50214 - 6.17716i) q^{62} +(-0.809017 + 0.587785i) q^{63} +(9.71297 + 7.05689i) q^{64} +(0.00792438 + 0.0286088i) q^{65} +(0.219138 - 0.159213i) q^{66} +(4.16811 - 12.8281i) q^{67} -5.70884 q^{68} +(-0.0340781 + 0.104882i) q^{69} +(-4.01400 + 2.65502i) q^{70} +(-1.60605 - 4.94290i) q^{71} +(-0.420520 - 1.29423i) q^{72} +(4.51194 + 3.27812i) q^{73} +19.6793 q^{74} +(1.95650 - 4.60131i) q^{75} -4.20923 q^{76} +(-0.101817 - 0.0739744i) q^{77} +(0.00882970 + 0.0271750i) q^{78} +(-0.519206 - 1.59795i) q^{79} +(1.39416 + 5.03321i) q^{80} +(0.309017 - 0.951057i) q^{81} +9.42477 q^{82} +(0.521981 - 1.60649i) q^{83} +(-2.12956 + 1.54721i) q^{84} +(-3.79436 - 3.02009i) q^{85} +(-6.86072 - 4.98460i) q^{86} +(2.67031 - 1.94009i) q^{87} +(0.138556 - 0.100667i) q^{88} +(0.143290 + 0.104106i) q^{89} +(1.68681 - 4.50733i) q^{90} +(0.0107405 - 0.00780342i) q^{91} +(-0.0897030 + 0.276078i) q^{92} +4.88285 q^{93} +(-5.84487 + 17.9887i) q^{94} +(-2.79765 - 2.22677i) q^{95} +(2.39447 + 7.36942i) q^{96} +(-3.79281 - 11.6731i) q^{97} +(1.74122 + 1.26507i) q^{98} +0.125853 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9}+O(q^{10}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9	\( 24 q + q^{2} - 6 q^{3} - 9 q^{4} - q^{5} + q^{6} + 24 q^{7} + 9 q^{8} - 6 q^{9} - 16 q^{10} + 2 q^{11} + q^{12} + 8 q^{13} + q^{14} - 6 q^{15} + 13 q^{16} + 12 q^{17} - 4 q^{18} + 19 q^{19} + 11 q^{20} - 6 q^{21} - 19 q^{22} - 6 q^{24} + 9 q^{25} - 14 q^{26} - 6 q^{27} - 9 q^{28} + 5 q^{29} - 6 q^{30} + 17 q^{31} - 26 q^{32} + 7 q^{33} - 7 q^{34} - q^{35} + q^{36} + 22 q^{37} - 16 q^{38} + 8 q^{39} + 3 q^{40} + 37 q^{41} + q^{42} + 8 q^{43} + 13 q^{44} + 4 q^{45} + 24 q^{46} - 24 q^{47} + 13 q^{48} + 24 q^{49} - 21 q^{50} - 8 q^{51} + 23 q^{52} - 24 q^{53} + q^{54} - 55 q^{55} + 9 q^{56} - 26 q^{57} + 8 q^{58} - 39 q^{60} + 24 q^{62} - 6 q^{63} - q^{64} - 34 q^{65} + 16 q^{66} + 34 q^{67} + 22 q^{68} + 10 q^{69} - 16 q^{70} - 24 q^{71} + 9 q^{72} + 46 q^{73} + 10 q^{74} + 24 q^{75} - 20 q^{76} + 2 q^{77} - 14 q^{78} + 10 q^{79} + 6 q^{80} - 6 q^{81} - 78 q^{82} + 42 q^{83} + q^{84} - 22 q^{85} - 96 q^{86} - 10 q^{87} - 39 q^{88} + 29 q^{89} + 14 q^{90} + 8 q^{91} + 42 q^{92} - 58 q^{93} + 54 q^{94} - 42 q^{95} + 9 q^{96} - 32 q^{97} + q^{98} - 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - 6 * q^3 - 9 * q^4 - q^5 + q^6 + 24 * q^7 + 9 * q^8 - 6 * q^9 - 16 * q^10 + 2 * q^11 + q^12 + 8 * q^13 + q^14 - 6 * q^15 + 13 * q^16 + 12 * q^17 - 4 * q^18 + 19 * q^19 + 11 * q^20 - 6 * q^21 - 19 * q^22 - 6 * q^24 + 9 * q^25 - 14 * q^26 - 6 * q^27 - 9 * q^28 + 5 * q^29 - 6 * q^30 + 17 * q^31 - 26 * q^32 + 7 * q^33 - 7 * q^34 - q^35 + q^36 + 22 * q^37 - 16 * q^38 + 8 * q^39 + 3 * q^40 + 37 * q^41 + q^42 + 8 * q^43 + 13 * q^44 + 4 * q^45 + 24 * q^46 - 24 * q^47 + 13 * q^48 + 24 * q^49 - 21 * q^50 - 8 * q^51 + 23 * q^52 - 24 * q^53 + q^54 - 55 * q^55 + 9 * q^56 - 26 * q^57 + 8 * q^58 - 39 * q^60 + 24 * q^62 - 6 * q^63 - q^64 - 34 * q^65 + 16 * q^66 + 34 * q^67 + 22 * q^68 + 10 * q^69 - 16 * q^70 - 24 * q^71 + 9 * q^72 + 46 * q^73 + 10 * q^74 + 24 * q^75 - 20 * q^76 + 2 * q^77 - 14 * q^78 + 10 * q^79 + 6 * q^80 - 6 * q^81 - 78 * q^82 + 42 * q^83 + q^84 - 22 * q^85 - 96 * q^86 - 10 * q^87 - 39 * q^88 + 29 * q^89 + 14 * q^90 + 8 * q^91 + 42 * q^92 - 58 * q^93 + 54 * q^94 - 42 * q^95 + 9 * q^96 - 32 * q^97 + q^98 - 18 * q^99

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