LMFDB - Embedded newform 605.2.g.d.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(81,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("605.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.g (of order $5$, degree $4$, not 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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			81.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	605.81
Dual form			605.2.g.d.366.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 + 0.587785i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.42705 + 1.76336i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-4.85410 - 3.52671i) q^{9} +O(q^{10})$	\(q+(0.809017 + 0.587785i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.42705 + 1.76336i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-4.85410 - 3.52671i) q^{9} -1.00000 q^{10} +3.00000 q^{12} +(-3.23607 - 2.35114i) q^{13} +(0.927051 - 2.85317i) q^{14} +(-0.927051 - 2.85317i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.85410 - 5.70634i) q^{18} +(1.23607 - 3.80423i) q^{19} +(0.809017 + 0.587785i) q^{20} +9.00000 q^{21} -8.00000 q^{23} +(7.28115 + 5.29007i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-1.23607 - 3.80423i) q^{26} +(7.28115 - 5.29007i) q^{27} +(-2.42705 + 1.76336i) q^{28} +(1.85410 + 5.70634i) q^{29} +(0.927051 - 2.85317i) q^{30} +(1.61803 + 1.17557i) q^{31} -5.00000 q^{32} +(2.42705 + 1.76336i) q^{35} +(-1.85410 + 5.70634i) q^{36} +(-2.47214 - 7.60845i) q^{37} +(3.23607 - 2.35114i) q^{38} +(9.70820 - 7.05342i) q^{39} +(0.927051 + 2.85317i) q^{40} +(-1.54508 + 4.75528i) q^{41} +(7.28115 + 5.29007i) q^{42} +5.00000 q^{43} +6.00000 q^{45} +(-6.47214 - 4.70228i) q^{46} +(-0.927051 + 2.85317i) q^{47} +(0.927051 + 2.85317i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-1.23607 + 3.80423i) q^{52} +(-3.23607 - 2.35114i) q^{53} +9.00000 q^{54} -9.00000 q^{56} +(9.70820 + 7.05342i) q^{57} +(-1.85410 + 5.70634i) q^{58} +(-0.618034 - 1.90211i) q^{59} +(-2.42705 + 1.76336i) q^{60} +(8.89919 - 6.46564i) q^{61} +(0.618034 + 1.90211i) q^{62} +(-5.56231 + 17.1190i) q^{63} +(-5.66312 - 4.11450i) q^{64} +4.00000 q^{65} -13.0000 q^{67} +(7.41641 - 22.8254i) q^{69} +(0.927051 + 2.85317i) q^{70} +(-1.61803 + 1.17557i) q^{71} +(-14.5623 + 10.5801i) q^{72} +(-2.47214 - 7.60845i) q^{73} +(2.47214 - 7.60845i) q^{74} +(2.42705 + 1.76336i) q^{75} -4.00000 q^{76} +12.0000 q^{78} +(-8.09017 - 5.87785i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-4.04508 + 2.93893i) q^{82} +(-3.23607 + 2.35114i) q^{83} +(-2.78115 - 8.55951i) q^{84} +(4.04508 + 2.93893i) q^{86} -18.0000 q^{87} +1.00000 q^{89} +(4.85410 + 3.52671i) q^{90} +(-3.70820 + 11.4127i) q^{91} +(2.47214 + 7.60845i) q^{92} +(-4.85410 + 3.52671i) q^{93} +(-2.42705 + 1.76336i) q^{94} +(1.23607 + 3.80423i) q^{95} +(4.63525 - 14.2658i) q^{96} +(6.47214 + 4.70228i) q^{97} -2.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} + 3 q^{3} + q^{4} - q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q + q^2 + 3 * q^3 + q^4 - q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^9	$ 4 q + q^{2} + 3 q^{3} + q^{4} - q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{9} - 4 q^{10} + 12 q^{12} - 4 q^{13} - 3 q^{14} + 3 q^{15} + q^{16} + 6 q^{18} - 4 q^{19} + q^{20} + 36 q^{21} - 32 q^{23} + 9 q^{24} - q^{25} + 4 q^{26} + 9 q^{27} - 3 q^{28} - 6 q^{29} - 3 q^{30} + 2 q^{31} - 20 q^{32} + 3 q^{35} + 6 q^{36} + 8 q^{37} + 4 q^{38} + 12 q^{39} - 3 q^{40} + 5 q^{41} + 9 q^{42} + 20 q^{43} + 24 q^{45} - 8 q^{46} + 3 q^{47} - 3 q^{48} - 2 q^{49} + q^{50} + 4 q^{52} - 4 q^{53} + 36 q^{54} - 36 q^{56} + 12 q^{57} + 6 q^{58} + 2 q^{59} - 3 q^{60} + 11 q^{61} - 2 q^{62} + 18 q^{63} - 7 q^{64} + 16 q^{65} - 52 q^{67} - 24 q^{69} - 3 q^{70} - 2 q^{71} - 18 q^{72} + 8 q^{73} - 8 q^{74} + 3 q^{75} - 16 q^{76} + 48 q^{78} - 10 q^{79} + q^{80} - 9 q^{81} - 5 q^{82} - 4 q^{83} + 9 q^{84} + 5 q^{86} - 72 q^{87} + 4 q^{89} + 6 q^{90} + 12 q^{91} - 8 q^{92} - 6 q^{93} - 3 q^{94} - 4 q^{95} - 15 q^{96} + 8 q^{97} - 8 q^{98}+O(q^{100}) $ 4 * q + q^2 + 3 * q^3 + q^4 - q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^9 - 4 * q^10 + 12 * q^12 - 4 * q^13 - 3 * q^14 + 3 * q^15 + q^16 + 6 * q^18 - 4 * q^19 + q^20 + 36 * q^21 - 32 * q^23 + 9 * q^24 - q^25 + 4 * q^26 + 9 * q^27 - 3 * q^28 - 6 * q^29 - 3 * q^30 + 2 * q^31 - 20 * q^32 + 3 * q^35 + 6 * q^36 + 8 * q^37 + 4 * q^38 + 12 * q^39 - 3 * q^40 + 5 * q^41 + 9 * q^42 + 20 * q^43 + 24 * q^45 - 8 * q^46 + 3 * q^47 - 3 * q^48 - 2 * q^49 + q^50 + 4 * q^52 - 4 * q^53 + 36 * q^54 - 36 * q^56 + 12 * q^57 + 6 * q^58 + 2 * q^59 - 3 * q^60 + 11 * q^61 - 2 * q^62 + 18 * q^63 - 7 * q^64 + 16 * q^65 - 52 * q^67 - 24 * q^69 - 3 * q^70 - 2 * q^71 - 18 * q^72 + 8 * q^73 - 8 * q^74 + 3 * q^75 - 16 * q^76 + 48 * q^78 - 10 * q^79 + q^80 - 9 * q^81 - 5 * q^82 - 4 * q^83 + 9 * q^84 + 5 * q^86 - 72 * q^87 + 4 * q^89 + 6 * q^90 + 12 * q^91 - 8 * q^92 - 6 * q^93 - 3 * q^94 - 4 * q^95 - 15 * q^96 + 8 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/605\mathbb{Z}\right)^\times$.

$n$	$122$	$486$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

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 $

$2$	0.809017	+	0.587785i	0.572061	+	0.415627i	0.835853	−	0.548953i	$-0.184973\pi$
$2$	0.809017	+	0.587785i	0.572061	+	0.415627i	−0.263792	+	0.964580i	$0.584973\pi$
$3$	−0.927051	+	2.85317i	−0.535233	+	1.64728i	0.207912	+	0.978148i	$0.433333\pi$
$3$	−0.927051	+	2.85317i	−0.535233	+	1.64728i	−0.743145	+	0.669131i	$0.766667\pi$
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$5$	−0.809017	+	0.587785i	−0.361803	+	0.262866i
$6$	−2.42705	+	1.76336i	−0.990839	+	0.719887i
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	−0.958633	−	0.284644i	$-0.908125\pi$
$7$	−0.927051	−	2.85317i	−0.350392	−	1.07840i	0.608241	−	0.793752i	$-0.291875\pi$
$8$	0.927051	−	2.85317i	0.327762	−	1.00875i
$9$	−4.85410	−	3.52671i	−1.61803	−	1.17557i
$10$	−1.00000			−0.316228
$11$		0			0
$11$		0			0
$12$	3.00000			0.866025
$13$	−3.23607	−	2.35114i	−0.897524	−	0.652089i	0.0403050	−	0.999187i	$-0.487167\pi$
$13$	−3.23607	−	2.35114i	−0.897524	−	0.652089i	−0.937829	+	0.347098i	$0.887167\pi$
$14$	0.927051	−	2.85317i	0.247765	−	0.762542i
$15$	−0.927051	−	2.85317i	−0.239364	−	0.736685i
$16$	0.809017	−	0.587785i	0.202254	−	0.146946i
$17$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$17$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$18$	−1.85410	−	5.70634i	−0.437016	−	1.34500i
$19$	1.23607	−	3.80423i	0.283573	−	0.872749i	−0.703249	−	0.710943i	$-0.748268\pi$
$19$	1.23607	−	3.80423i	0.283573	−	0.872749i	0.986823	−	0.161806i	$-0.0517318\pi$
$20$	0.809017	+	0.587785i	0.180902	+	0.131433i
$21$	9.00000			1.96396
$22$		0			0
$23$	−8.00000			−1.66812			−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000			−1.66812			−0.834058	+	0.551677i	$0.813988\pi$
$24$	7.28115	+	5.29007i	1.48626	+	1.07983i
$25$	0.309017	−	0.951057i	0.0618034	−	0.190211i
$26$	−1.23607	−	3.80423i	−0.242413	−	0.746070i
$27$	7.28115	−	5.29007i	1.40126	−	1.01807i
$28$	−2.42705	+	1.76336i	−0.458670	+	0.333243i
$29$	1.85410	+	5.70634i	0.344298	+	1.05964i	0.961958	+	0.273196i	$0.0880806\pi$
$29$	1.85410	+	5.70634i	0.344298	+	1.05964i	−0.617660	+	0.786445i	$0.711919\pi$
$30$	0.927051	−	2.85317i	0.169256	−	0.520915i
$31$	1.61803	+	1.17557i	0.290607	+	0.211139i	0.723531	−	0.690292i	$-0.242518\pi$
$31$	1.61803	+	1.17557i	0.290607	+	0.211139i	−0.432923	+	0.901431i	$0.642518\pi$
$32$	−5.00000			−0.883883
$33$		0			0
$34$		0			0
$35$	2.42705	+	1.76336i	0.410246	+	0.298062i
$36$	−1.85410	+	5.70634i	−0.309017	+	0.951057i
$37$	−2.47214	−	7.60845i	−0.406417	−	1.25082i	−0.919707	−	0.392607i	$-0.871573\pi$
$37$	−2.47214	−	7.60845i	−0.406417	−	1.25082i	0.513290	−	0.858215i	$-0.328427\pi$
$38$	3.23607	−	2.35114i	0.524960	−	0.381405i
$39$	9.70820	−	7.05342i	1.55456	−	1.12945i
$40$	0.927051	+	2.85317i	0.146580	+	0.451126i
$41$	−1.54508	+	4.75528i	−0.241302	+	0.742650i	0.754921	+	0.655816i	$0.227675\pi$
$41$	−1.54508	+	4.75528i	−0.241302	+	0.742650i	−0.996223	+	0.0868346i	$0.972325\pi$
$42$	7.28115	+	5.29007i	1.12351	+	0.816275i
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$		0			0
$45$	6.00000			0.894427
$46$	−6.47214	−	4.70228i	−0.954264	−	0.693314i
$47$	−0.927051	+	2.85317i	−0.135224	+	0.416178i	−0.995625	−	0.0934408i	$-0.970213\pi$
$47$	−0.927051	+	2.85317i	−0.135224	+	0.416178i	0.860401	+	0.509618i	$0.170213\pi$
$48$	0.927051	+	2.85317i	0.133808	+	0.411820i
$49$	−1.61803	+	1.17557i	−0.231148	+	0.167939i
$50$	0.809017	−	0.587785i	0.114412	−	0.0831254i
$51$		0			0
$52$	−1.23607	+	3.80423i	−0.171412	+	0.527551i
$53$	−3.23607	−	2.35114i	−0.444508	−	0.322954i	0.342916	−	0.939366i	$-0.388586\pi$
$53$	−3.23607	−	2.35114i	−0.444508	−	0.322954i	−0.787424	+	0.616412i	$0.788586\pi$
$54$	9.00000			1.22474
$55$		0			0
$56$	−9.00000			−1.20268
$57$	9.70820	+	7.05342i	1.28588	+	0.934249i
$58$	−1.85410	+	5.70634i	−0.243456	+	0.749279i
$59$	−0.618034	−	1.90211i	−0.0804612	−	0.247634i	0.902732	−	0.430204i	$-0.141558\pi$
$59$	−0.618034	−	1.90211i	−0.0804612	−	0.247634i	−0.983193	+	0.182570i	$0.941558\pi$
$60$	−2.42705	+	1.76336i	−0.313331	+	0.227648i
$61$	8.89919	−	6.46564i	1.13942	−	0.827840i	0.152385	−	0.988321i	$-0.451305\pi$
$61$	8.89919	−	6.46564i	1.13942	−	0.827840i	0.987039	+	0.160481i	$0.0513046\pi$
$62$	0.618034	+	1.90211i	0.0784904	+	0.241569i
$63$	−5.56231	+	17.1190i	−0.700785	+	2.15679i
$64$	−5.66312	−	4.11450i	−0.707890	−	0.514312i
$65$	4.00000			0.496139
$66$		0			0
$67$	−13.0000			−1.58820			−0.794101	−	0.607785i	$-0.792058\pi$
$67$	−13.0000			−1.58820			−0.794101	+	0.607785i	$0.792058\pi$
$68$		0			0
$69$	7.41641	−	22.8254i	0.892831	−	2.74785i
$70$	0.927051	+	2.85317i	0.110804	+	0.341019i
$71$	−1.61803	+	1.17557i	−0.192025	+	0.139515i	−0.679644	−	0.733542i	$-0.737866\pi$
$71$	−1.61803	+	1.17557i	−0.192025	+	0.139515i	0.487619	+	0.873057i	$0.337866\pi$
$72$	−14.5623	+	10.5801i	−1.71618	+	1.24688i
$73$	−2.47214	−	7.60845i	−0.289342	−	0.890502i	−0.985064	−	0.172191i	$-0.944915\pi$
$73$	−2.47214	−	7.60845i	−0.289342	−	0.890502i	0.695722	−	0.718311i	$-0.255085\pi$
$74$	2.47214	−	7.60845i	0.287380	−	0.884465i
$75$	2.42705	+	1.76336i	0.280252	+	0.203615i
$76$	−4.00000			−0.458831
$77$		0			0
$78$	12.0000			1.35873
$79$	−8.09017	−	5.87785i	−0.910215	−	0.661310i	0.0308541	−	0.999524i	$-0.490177\pi$
$79$	−8.09017	−	5.87785i	−0.910215	−	0.661310i	−0.941069	+	0.338214i	$0.890177\pi$
$80$	−0.309017	+	0.951057i	−0.0345492	+	0.106331i
$81$	2.78115	+	8.55951i	0.309017	+	0.951057i
$82$	−4.04508	+	2.93893i	−0.446705	+	0.324550i
$83$	−3.23607	+	2.35114i	−0.355205	+	0.258071i	−0.751049	−	0.660246i	$-0.770452\pi$
$83$	−3.23607	+	2.35114i	−0.355205	+	0.258071i	0.395845	+	0.918318i	$0.370452\pi$
$84$	−2.78115	−	8.55951i	−0.303449	−	0.933919i
$85$		0			0
$86$	4.04508	+	2.93893i	0.436193	+	0.316913i
$87$	−18.0000			−1.92980
$88$		0			0
$89$	1.00000			0.106000			0.0529999	−	0.998595i	$-0.483122\pi$
$89$	1.00000			0.106000			0.0529999	+	0.998595i	$0.483122\pi$
$90$	4.85410	+	3.52671i	0.511667	+	0.371748i
$91$	−3.70820	+	11.4127i	−0.388725	+	1.19637i
$92$	2.47214	+	7.60845i	0.257738	+	0.793236i
$93$	−4.85410	+	3.52671i	−0.503347	+	0.365703i
$94$	−2.42705	+	1.76336i	−0.250331	+	0.181876i
$95$	1.23607	+	3.80423i	0.126818	+	0.390305i
$96$	4.63525	−	14.2658i	0.473084	−	1.45600i
$97$	6.47214	+	4.70228i	0.657146	+	0.477444i	0.865698	−	0.500567i	$-0.166875\pi$
$97$	6.47214	+	4.70228i	0.657146	+	0.477444i	−0.208552	+	0.978011i	$0.566875\pi$
$98$	−2.00000			−0.202031
$99$		0			0
$100$	−1.00000			−0.100000
$101$	4.04508	+	2.93893i	0.402501	+	0.292434i	0.770559	−	0.637369i	$-0.219977\pi$
$101$	4.04508	+	2.93893i	0.402501	+	0.292434i	−0.368058	+	0.929803i	$0.619977\pi$
$102$		0			0
$103$	2.47214	+	7.60845i	0.243587	+	0.749683i	0.995866	+	0.0908382i	$0.0289546\pi$
$103$	2.47214	+	7.60845i	0.243587	+	0.749683i	−0.752279	+	0.658845i	$0.771045\pi$
$104$	−9.70820	+	7.05342i	−0.951968	+	0.691645i
$105$	−7.28115	+	5.29007i	−0.710568	+	0.516258i
$106$	−1.23607	−	3.80423i	−0.120058	−	0.369499i
$107$	2.78115	−	8.55951i	0.268864	−	0.827479i	−0.721914	−	0.691983i	$-0.756737\pi$
$107$	2.78115	−	8.55951i	0.268864	−	0.827479i	0.990778	−	0.135496i	$-0.0432627\pi$
$108$	−7.28115	−	5.29007i	−0.700629	−	0.509037i
$109$	−9.00000			−0.862044			−0.431022	−	0.902342i	$-0.641847\pi$
$109$	−9.00000			−0.862044			−0.431022	+	0.902342i	$0.641847\pi$
$110$		0			0
$111$	24.0000			2.27798
$112$	−2.42705	−	1.76336i	−0.229335	−	0.166621i
$113$	1.85410	−	5.70634i	0.174419	−	0.536807i	−0.825187	−	0.564859i	$-0.808930\pi$
$113$	1.85410	−	5.70634i	0.174419	−	0.536807i	0.999606	+	0.0280521i	$0.00893043\pi$
$114$	3.70820	+	11.4127i	0.347305	+	1.06890i
$115$	6.47214	−	4.70228i	0.603530	−	0.438490i
$116$	4.85410	−	3.52671i	0.450692	−	0.327447i
$117$	7.41641	+	22.8254i	0.685647	+	2.11020i
$118$	0.618034	−	1.90211i	0.0568946	−	0.175104i
$119$		0			0
$120$	−9.00000			−0.821584
$121$		0			0
$122$	11.0000			0.995893
$123$	−12.1353	−	8.81678i	−1.09420	−	0.794982i
$124$	0.618034	−	1.90211i	0.0555011	−	0.170815i
$125$	0.309017	+	0.951057i	0.0276393	+	0.0850651i
$126$	−14.5623	+	10.5801i	−1.29731	+	0.942553i
$127$	−8.89919	+	6.46564i	−0.789675	+	0.573733i	−0.907867	−	0.419258i	$-0.862290\pi$
$127$	−8.89919	+	6.46564i	−0.789675	+	0.573733i	0.118192	+	0.992991i	$0.462290\pi$
$128$	0.927051	+	2.85317i	0.0819405	+	0.252187i
$129$	−4.63525	+	14.2658i	−0.408111	+	1.25604i
$130$	3.23607	+	2.35114i	0.283822	+	0.206209i
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$		0			0
$133$	−12.0000			−1.04053
$134$	−10.5172	−	7.64121i	−0.908550	−	0.660100i
$135$	−2.78115	+	8.55951i	−0.239364	+	0.736685i
$136$		0			0
$137$		0			0		−0.587785	−	0.809017i	$-0.700000\pi$
$137$		0			0		0.587785	+	0.809017i	$0.300000\pi$
$138$	19.4164	−	14.1068i	1.65283	−	1.20085i
$139$	−5.56231	−	17.1190i	−0.471789	−	1.45202i	−0.850240	−	0.526395i	$-0.823543\pi$
$139$	−5.56231	−	17.1190i	−0.471789	−	1.45202i	0.378452	−	0.925621i	$-0.376457\pi$
$140$	0.927051	−	2.85317i	0.0783501	−	0.241137i
$141$	−7.28115	−	5.29007i	−0.613184	−	0.445504i
$142$	−2.00000			−0.167836
$143$		0			0
$144$	−6.00000			−0.500000
$145$	−4.85410	−	3.52671i	−0.403111	−	0.292877i
$146$	2.47214	−	7.60845i	0.204595	−	0.629680i
$147$	−1.85410	−	5.70634i	−0.152924	−	0.470651i
$148$	−6.47214	+	4.70228i	−0.532006	+	0.386525i
$149$	13.7533	−	9.99235i	1.12671	−	0.818605i	0.141500	−	0.989938i	$-0.454807\pi$
$149$	13.7533	−	9.99235i	1.12671	−	0.818605i	0.985213	+	0.171333i	$0.0548074\pi$
$150$	0.927051	+	2.85317i	0.0756934	+	0.232960i
$151$	−4.32624	+	13.3148i	−0.352064	+	1.08354i	0.605628	+	0.795748i	$0.292922\pi$
$151$	−4.32624	+	13.3148i	−0.352064	+	1.08354i	−0.957692	+	0.287794i	$0.907078\pi$
$152$	−9.70820	−	7.05342i	−0.787439	−	0.572108i
$153$		0			0
$154$		0			0
$155$	−2.00000			−0.160644
$156$	−9.70820	−	7.05342i	−0.777278	−	0.564726i
$157$	−2.47214	+	7.60845i	−0.197298	+	0.607221i	0.802644	+	0.596458i	$0.203426\pi$
$157$	−2.47214	+	7.60845i	−0.197298	+	0.607221i	−0.999942	+	0.0107624i	$0.996574\pi$
$158$	−3.09017	−	9.51057i	−0.245841	−	0.756620i
$159$	9.70820	−	7.05342i	0.769911	−	0.559373i
$160$	4.04508	−	2.93893i	0.319792	−	0.232343i
$161$	7.41641	+	22.8254i	0.584495	+	1.79889i
$162$	−2.78115	+	8.55951i	−0.218508	+	0.672499i
$163$	13.7533	+	9.99235i	1.07724	+	0.782661i	0.977200	−	0.212322i	$-0.0681026\pi$
$163$	13.7533	+	9.99235i	1.07724	+	0.782661i	0.100041	+	0.994983i	$0.468103\pi$
$164$	5.00000			0.390434
$165$		0			0
$166$	−4.00000			−0.310460
$167$	5.66312	+	4.11450i	0.438225	+	0.318389i	0.784929	−	0.619585i	$-0.212699\pi$
$167$	5.66312	+	4.11450i	0.438225	+	0.318389i	−0.346704	+	0.937975i	$0.612699\pi$
$168$	8.34346	−	25.6785i	0.643712	−	1.98114i
$169$	0.927051	+	2.85317i	0.0713116	+	0.219475i
$170$		0			0
$171$	−19.4164	+	14.1068i	−1.48481	+	1.07878i
$172$	−1.54508	−	4.75528i	−0.117812	−	0.362587i
$173$	7.41641	−	22.8254i	0.563859	−	1.73538i	−0.107458	−	0.994210i	$-0.534271\pi$
$173$	7.41641	−	22.8254i	0.563859	−	1.73538i	0.671317	−	0.741170i	$-0.265729\pi$
$174$	−14.5623	−	10.5801i	−1.10397	−	0.802078i
$175$	−3.00000			−0.226779
$176$		0			0
$177$	6.00000			0.450988
$178$	0.809017	+	0.587785i	0.0606384	+	0.0440564i
$179$	−8.03444	+	24.7275i	−0.600522	+	1.84822i	−0.0754697	+	0.997148i	$0.524046\pi$
$179$	−8.03444	+	24.7275i	−0.600522	+	1.84822i	−0.525053	+	0.851070i	$0.675954\pi$
$180$	−1.85410	−	5.70634i	−0.138197	−	0.425325i
$181$	15.3713	−	11.1679i	1.14254	−	0.830105i	0.155070	−	0.987903i	$-0.450440\pi$
$181$	15.3713	−	11.1679i	1.14254	−	0.830105i	0.987471	+	0.157799i	$0.0504397\pi$
$182$	−9.70820	+	7.05342i	−0.719620	+	0.522834i
$183$	10.1976	+	31.3849i	0.753825	+	2.32004i
$184$	−7.41641	+	22.8254i	−0.546745	+	1.68271i
$185$	6.47214	+	4.70228i	0.475841	+	0.345719i
$186$	−6.00000			−0.439941
$187$		0			0
$188$	3.00000			0.218797
$189$	−21.8435	−	15.8702i	−1.58888	−	1.15439i
$190$	−1.23607	+	3.80423i	−0.0896738	+	0.275988i
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	0.999789	−	0.0205267i	$-0.00653431\pi$
$191$	2.47214	+	7.60845i	0.178877	+	0.550528i	−0.820912	+	0.571055i	$0.806534\pi$
$192$	16.9894	−	12.3435i	1.22610	−	0.890815i
$193$	8.09017	−	5.87785i	0.582343	−	0.423097i	−0.257225	−	0.966352i	$-0.582808\pi$
$193$	8.09017	−	5.87785i	0.582343	−	0.423097i	0.839568	+	0.543254i	$0.182808\pi$
$194$	2.47214	+	7.60845i	0.177489	+	0.546255i
$195$	−3.70820	+	11.4127i	−0.265550	+	0.817279i
$196$	1.61803	+	1.17557i	0.115574	+	0.0839693i
$197$	−14.0000			−0.997459			−0.498729	−	0.866758i	$-0.666200\pi$
$197$	−14.0000			−0.997459			−0.498729	+	0.866758i	$0.666200\pi$
$198$		0			0
$199$	−6.00000			−0.425329			−0.212664	−	0.977125i	$-0.568214\pi$
$199$	−6.00000			−0.425329			−0.212664	+	0.977125i	$0.568214\pi$
$200$	−2.42705	−	1.76336i	−0.171618	−	0.124688i
$201$	12.0517	−	37.0912i	0.850059	−	2.61621i
$202$	1.54508	+	4.75528i	0.108712	+	0.334581i
$203$	14.5623	−	10.5801i	1.02207	−	0.742580i
$204$		0			0
$205$	−1.54508	−	4.75528i	−0.107913	−	0.332123i
$206$	−2.47214	+	7.60845i	−0.172242	+	0.530106i
$207$	38.8328	+	28.2137i	2.69907	+	1.96099i
$208$	−4.00000			−0.277350
$209$		0			0
$210$	−9.00000			−0.621059
$211$	17.7984	+	12.9313i	1.22529	+	0.890226i	0.996528	−	0.0832566i	$-0.0265321\pi$
$211$	17.7984	+	12.9313i	1.22529	+	0.890226i	0.228762	+	0.973482i	$0.426532\pi$
$212$	−1.23607	+	3.80423i	−0.0848935	+	0.261275i
$213$	−1.85410	−	5.70634i	−0.127041	−	0.390992i
$214$	7.28115	−	5.29007i	0.497729	−	0.361622i
$215$	−4.04508	+	2.93893i	−0.275873	+	0.200433i
$216$	−8.34346	−	25.6785i	−0.567700	−	1.74720i
$217$	1.85410	−	5.70634i	0.125865	−	0.387372i
$218$	−7.28115	−	5.29007i	−0.493142	−	0.358289i
$219$	24.0000			1.62177
$220$		0			0
$221$		0			0
$222$	19.4164	+	14.1068i	1.30314	+	0.946790i
$223$	1.54508	−	4.75528i	0.103467	−	0.318437i	−0.885901	−	0.463874i	$-0.846459\pi$
$223$	1.54508	−	4.75528i	0.103467	−	0.318437i	0.989367	+	0.145437i	$0.0464589\pi$
$224$	4.63525	+	14.2658i	0.309706	+	0.953177i
$225$	−4.85410	+	3.52671i	−0.323607	+	0.235114i
$226$	4.85410	−	3.52671i	0.322890	−	0.234593i
$227$	−0.309017	−	0.951057i	−0.0205102	−	0.0631238i	0.940278	−	0.340409i	$-0.110565\pi$
$227$	−0.309017	−	0.951057i	−0.0205102	−	0.0631238i	−0.960788	+	0.277285i	$0.910565\pi$
$228$	3.70820	−	11.4127i	0.245582	−	0.755823i
$229$	0.809017	+	0.587785i	0.0534613	+	0.0388419i	0.614195	−	0.789154i	$-0.289481\pi$
$229$	0.809017	+	0.587785i	0.0534613	+	0.0388419i	−0.560734	+	0.827996i	$0.689481\pi$
$230$	8.00000			0.527504
$231$		0			0
$232$	18.0000			1.18176
$233$	19.4164	+	14.1068i	1.27201	+	0.924170i	0.999281	−	0.0379203i	$-0.0120733\pi$
$233$	19.4164	+	14.1068i	1.27201	+	0.924170i	0.272730	+	0.962090i	$0.412073\pi$
$234$	−7.41641	+	22.8254i	−0.484826	+	1.49214i
$235$	−0.927051	−	2.85317i	−0.0604741	−	0.186120i
$236$	−1.61803	+	1.17557i	−0.105325	+	0.0765231i
$237$	24.2705	−	17.6336i	1.57654	−	1.14542i
$238$		0			0
$239$	1.23607	−	3.80423i	0.0799546	−	0.246075i	−0.903087	−	0.429458i	$-0.858705\pi$
$239$	1.23607	−	3.80423i	0.0799546	−	0.246075i	0.983042	+	0.183383i	$0.0587048\pi$
$240$	−2.42705	−	1.76336i	−0.156665	−	0.113824i
$241$	23.0000			1.48156			0.740780	−	0.671748i	$-0.234456\pi$
$241$	23.0000			1.48156			0.740780	+	0.671748i	$0.234456\pi$
$242$		0			0
$243$		0			0
$244$	−8.89919	−	6.46564i	−0.569712	−	0.413920i
$245$	0.618034	−	1.90211i	0.0394847	−	0.121522i
$246$	−4.63525	−	14.2658i	−0.295533	−	0.909557i
$247$	−12.9443	+	9.40456i	−0.823624	+	0.598398i
$248$	4.85410	−	3.52671i	0.308236	−	0.223946i
$249$	−3.70820	−	11.4127i	−0.234998	−	0.723249i
$250$	−0.309017	+	0.951057i	−0.0195440	+	0.0601501i
$251$	−14.5623	−	10.5801i	−0.919165	−	0.667812i	0.0241513	−	0.999708i	$-0.492312\pi$
$251$	−14.5623	−	10.5801i	−0.919165	−	0.667812i	−0.943316	+	0.331896i	$0.892312\pi$
$252$	18.0000			1.13389
$253$		0			0
$254$	−11.0000			−0.690201
$255$		0			0
$256$	−5.25329	+	16.1680i	−0.328331	+	1.01050i
$257$	−1.85410	−	5.70634i	−0.115656	−	0.355952i	0.876428	−	0.481534i	$-0.159920\pi$
$257$	−1.85410	−	5.70634i	−0.115656	−	0.355952i	−0.992083	+	0.125582i	$0.959920\pi$
$258$	−12.1353	+	8.81678i	−0.755508	+	0.548909i
$259$	−19.4164	+	14.1068i	−1.20648	+	0.876557i
$260$	−1.23607	−	3.80423i	−0.0766577	−	0.235928i
$261$	11.1246	−	34.2380i	0.688596	−	2.11928i
$262$		0			0
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$		0			0
$265$	4.00000			0.245718
$266$	−9.70820	−	7.05342i	−0.595248	−	0.432473i
$267$	−0.927051	+	2.85317i	−0.0567346	+	0.174611i
$268$	4.01722	+	12.3637i	0.245391	+	0.755235i
$269$	−16.9894	+	12.3435i	−1.03586	+	0.752596i	−0.969473	−	0.245198i	$-0.921147\pi$
$269$	−16.9894	+	12.3435i	−1.03586	+	0.752596i	−0.0663864	+	0.997794i	$0.521147\pi$
$270$	−7.28115	+	5.29007i	−0.443117	+	0.321943i
$271$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$271$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$272$		0			0
$273$	−29.1246	−	21.1603i	−1.76270	−	1.28068i
$274$		0			0
$275$		0			0
$276$	−24.0000			−1.44463
$277$	−11.3262	−	8.22899i	−0.680528	−	0.494432i	0.193005	−	0.981198i	$-0.438177\pi$
$277$	−11.3262	−	8.22899i	−0.680528	−	0.494432i	−0.873533	+	0.486765i	$0.838177\pi$
$278$	5.56231	−	17.1190i	0.333605	−	1.02673i
$279$	−3.70820	−	11.4127i	−0.222004	−	0.683259i
$280$	7.28115	−	5.29007i	0.435132	−	0.316142i
$281$	4.85410	−	3.52671i	0.289571	−	0.210386i	−0.433510	−	0.901149i	$-0.642725\pi$
$281$	4.85410	−	3.52671i	0.289571	−	0.210386i	0.723081	+	0.690763i	$0.242725\pi$
$282$	−2.78115	−	8.55951i	−0.165615	−	0.509711i
$283$	−4.01722	+	12.3637i	−0.238799	+	0.734948i	0.757796	+	0.652492i	$0.226276\pi$
$283$	−4.01722	+	12.3637i	−0.238799	+	0.734948i	−0.996595	+	0.0824559i	$0.973724\pi$
$284$	1.61803	+	1.17557i	0.0960127	+	0.0697573i
$285$	−12.0000			−0.710819
$286$		0			0
$287$	15.0000			0.885422
$288$	24.2705	+	17.6336i	1.43015	+	1.03907i
$289$	−5.25329	+	16.1680i	−0.309017	+	0.951057i
$290$	−1.85410	−	5.70634i	−0.108877	−	0.335088i
$291$	−19.4164	+	14.1068i	−1.13821	+	0.826958i
$292$	−6.47214	+	4.70228i	−0.378753	+	0.275180i
$293$	−10.5066	−	32.3359i	−0.613801	−	1.88908i	−0.418023	−	0.908436i	$-0.637277\pi$
$293$	−10.5066	−	32.3359i	−0.613801	−	1.88908i	−0.195778	−	0.980648i	$-0.562723\pi$
$294$	1.85410	−	5.70634i	0.108133	−	0.332800i
$295$	1.61803	+	1.17557i	0.0942056	+	0.0684444i
$296$	−24.0000			−1.39497
$297$		0			0
$298$	17.0000			0.984784
$299$	25.8885	+	18.8091i	1.49717	+	1.08776i
$300$	0.927051	−	2.85317i	0.0535233	−	0.164728i
$301$	−4.63525	−	14.2658i	−0.267172	−	0.822270i
$302$	−11.3262	+	8.22899i	−0.651752	+	0.473525i
$303$	−12.1353	+	8.81678i	−0.697152	+	0.506511i
$304$	−1.23607	−	3.80423i	−0.0708934	−	0.218187i
$305$	−3.39919	+	10.4616i	−0.194637	+	0.599031i
$306$		0			0
$307$	−8.00000			−0.456584			−0.228292	−	0.973593i	$-0.573314\pi$
$307$	−8.00000			−0.456584			−0.228292	+	0.973593i	$0.573314\pi$
$308$		0			0
$309$	−24.0000			−1.36531
$310$	−1.61803	−	1.17557i	−0.0918982	−	0.0667679i
$311$	7.41641	−	22.8254i	0.420546	−	1.29431i	−0.486649	−	0.873597i	$-0.661781\pi$
$311$	7.41641	−	22.8254i	0.420546	−	1.29431i	0.907195	−	0.420710i	$-0.138219\pi$
$312$	−11.1246	−	34.2380i	−0.629807	−	1.93835i
$313$	−6.47214	+	4.70228i	−0.365827	+	0.265789i	−0.755478	−	0.655174i	$-0.772595\pi$
$313$	−6.47214	+	4.70228i	−0.365827	+	0.265789i	0.389652	+	0.920962i	$0.372595\pi$
$314$	−6.47214	+	4.70228i	−0.365244	+	0.265365i
$315$	−5.56231	−	17.1190i	−0.313400	−	0.964547i
$316$	−3.09017	+	9.51057i	−0.173836	+	0.535011i
$317$	−14.5623	−	10.5801i	−0.817901	−	0.594240i	0.0982098	−	0.995166i	$-0.468688\pi$
$317$	−14.5623	−	10.5801i	−0.817901	−	0.594240i	−0.916110	+	0.400926i	$0.868688\pi$
$318$	12.0000			0.672927
$319$		0			0
$320$	7.00000			0.391312
$321$	21.8435	+	15.8702i	1.21918	+	0.885788i
$322$	−7.41641	+	22.8254i	−0.413300	+	1.27201i
$323$		0			0
$324$	7.28115	−	5.29007i	0.404508	−	0.293893i
$325$	−3.23607	+	2.35114i	−0.179505	+	0.130418i
$326$	5.25329	+	16.1680i	0.290953	+	0.895461i
$327$	8.34346	−	25.6785i	0.461394	−	1.42003i
$328$	12.1353	+	8.81678i	0.670057	+	0.486825i
$329$	9.00000			0.496186
$330$		0			0
$331$	−20.0000			−1.09930			−0.549650	−	0.835395i	$-0.685239\pi$
$331$	−20.0000			−1.09930			−0.549650	+	0.835395i	$0.685239\pi$
$332$	3.23607	+	2.35114i	0.177602	+	0.129036i
$333$	−14.8328	+	45.6507i	−0.812833	+	2.50164i
$334$	2.16312	+	6.65740i	0.118361	+	0.364276i
$335$	10.5172	−	7.64121i	0.574617	−	0.417484i
$336$	7.28115	−	5.29007i	0.397219	−	0.288597i
$337$	−3.70820	−	11.4127i	−0.201999	−	0.621688i	−0.999823	−	0.0187985i	$-0.994016\pi$
$337$	−3.70820	−	11.4127i	−0.201999	−	0.621688i	0.797825	−	0.602890i	$-0.205984\pi$
$338$	−0.927051	+	2.85317i	−0.0504249	+	0.155192i
$339$	14.5623	+	10.5801i	0.790916	+	0.574634i
$340$		0			0
$341$		0			0
$342$	−24.0000			−1.29777
$343$	−12.1353	−	8.81678i	−0.655242	−	0.476061i
$344$	4.63525	−	14.2658i	0.249916	−	0.769163i
$345$	7.41641	+	22.8254i	0.399286	+	1.22888i
$346$	19.4164	−	14.1068i	1.04383	−	0.758389i
$347$	−5.66312	+	4.11450i	−0.304012	+	0.220878i	−0.729323	−	0.684170i	$-0.760165\pi$
$347$	−5.66312	+	4.11450i	−0.304012	+	0.220878i	0.425311	+	0.905047i	$0.360165\pi$
$348$	5.56231	+	17.1190i	0.298171	+	0.917676i
$349$	6.79837	−	20.9232i	0.363909	−	1.12000i	−0.586753	−	0.809766i	$-0.699594\pi$
$349$	6.79837	−	20.9232i	0.363909	−	1.12000i	0.950662	−	0.310230i	$-0.100406\pi$
$350$	−2.42705	−	1.76336i	−0.129731	−	0.0942553i
$351$	−36.0000			−1.92154
$352$		0			0
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$	4.85410	+	3.52671i	0.257993	+	0.187443i
$355$	0.618034	−	1.90211i	0.0328018	−	0.100954i
$356$	−0.309017	−	0.951057i	−0.0163779	−	0.0504059i
$357$		0			0
$358$	−21.0344	+	15.2824i	−1.11170	+	0.807701i
$359$	−8.65248	−	26.6296i	−0.456660	−	1.40546i	−0.869175	−	0.494505i	$-0.835349\pi$
$359$	−8.65248	−	26.6296i	−0.456660	−	1.40546i	0.412515	−	0.910951i	$-0.364651\pi$
$360$	5.56231	−	17.1190i	0.293159	−	0.902251i
$361$	2.42705	+	1.76336i	0.127740	+	0.0928082i
$362$	19.0000			0.998618
$363$		0			0
$364$	12.0000			0.628971
$365$	6.47214	+	4.70228i	0.338767	+	0.246129i
$366$	−10.1976	+	31.3849i	−0.533035	+	1.64051i
$367$	0.309017	+	0.951057i	0.0161306	+	0.0496447i	0.958798	−	0.284089i	$-0.0916912\pi$
$367$	0.309017	+	0.951057i	0.0161306	+	0.0496447i	−0.942667	+	0.333734i	$0.891691\pi$
$368$	−6.47214	+	4.70228i	−0.337383	+	0.245123i
$369$	24.2705	−	17.6336i	1.26347	−	0.917966i
$370$	2.47214	+	7.60845i	0.128520	+	0.395545i
$371$	−3.70820	+	11.4127i	−0.192520	+	0.592517i
$372$	4.85410	+	3.52671i	0.251673	+	0.182851i
$373$	18.0000			0.932005			0.466002	−	0.884783i	$-0.345694\pi$
$373$	18.0000			0.932005			0.466002	+	0.884783i	$0.345694\pi$
$374$		0			0
$375$	−3.00000			−0.154919
$376$	7.28115	+	5.29007i	0.375497	+	0.272814i
$377$	7.41641	−	22.8254i	0.381964	−	1.17557i
$378$	−8.34346	−	25.6785i	−0.429141	−	1.32076i
$379$	17.7984	−	12.9313i	0.914241	−	0.664235i	−0.0278428	−	0.999612i	$-0.508864\pi$
$379$	17.7984	−	12.9313i	0.914241	−	0.664235i	0.942084	+	0.335377i	$0.108864\pi$
$380$	3.23607	−	2.35114i	0.166007	−	0.120611i
$381$	−10.1976	−	31.3849i	−0.522437	−	1.60790i
$382$	−2.47214	+	7.60845i	−0.126485	+	0.389282i
$383$		0			0		0.587785	−	0.809017i	$-0.300000\pi$
$383$		0			0		−0.587785	+	0.809017i	$0.700000\pi$
$384$	−9.00000			−0.459279
$385$		0			0
$386$	10.0000			0.508987
$387$	−24.2705	−	17.6336i	−1.23374	−	0.896364i
$388$	2.47214	−	7.60845i	0.125504	−	0.386261i
$389$	−0.927051	−	2.85317i	−0.0470034	−	0.144661i	0.924800	−	0.380453i	$-0.124232\pi$
$389$	−0.927051	−	2.85317i	−0.0470034	−	0.144661i	−0.971804	+	0.235791i	$0.924232\pi$
$390$	−9.70820	+	7.05342i	−0.491594	+	0.357164i
$391$		0			0
$392$	1.85410	+	5.70634i	0.0936463	+	0.288214i
$393$		0			0
$394$	−11.3262	−	8.22899i	−0.570608	−	0.414571i
$395$	10.0000			0.503155
$396$		0			0
$397$	−12.0000			−0.602263			−0.301131	−	0.953583i	$-0.597364\pi$
$397$	−12.0000			−0.602263			−0.301131	+	0.953583i	$0.597364\pi$
$398$	−4.85410	−	3.52671i	−0.243314	−	0.176778i
$399$	11.1246	−	34.2380i	0.556927	−	1.71405i
$400$	−0.309017	−	0.951057i	−0.0154508	−	0.0475528i
$401$	29.9336	−	21.7481i	1.49481	−	1.08605i	0.522424	−	0.852686i	$-0.325028\pi$
$401$	29.9336	−	21.7481i	1.49481	−	1.08605i	0.972390	−	0.233360i	$-0.0749720\pi$
$402$	31.5517	−	22.9236i	1.57365	−	1.14333i
$403$	−2.47214	−	7.60845i	−0.123146	−	0.379004i
$404$	1.54508	−	4.75528i	0.0768709	−	0.236584i
$405$	−7.28115	−	5.29007i	−0.361803	−	0.262866i
$406$	18.0000			0.893325
$407$		0			0
$408$		0			0
$409$	−16.9894	−	12.3435i	−0.840070	−	0.610346i	0.0823205	−	0.996606i	$-0.473767\pi$
$409$	−16.9894	−	12.3435i	−0.840070	−	0.610346i	−0.922390	+	0.386260i	$0.873767\pi$
$410$	1.54508	−	4.75528i	0.0763063	−	0.234847i
$411$		0			0
$412$	6.47214	−	4.70228i	0.318859	−	0.231665i
$413$	−4.85410	+	3.52671i	−0.238855	+	0.173538i
$414$	14.8328	+	45.6507i	0.728993	+	2.24361i
$415$	1.23607	−	3.80423i	0.0606762	−	0.186742i
$416$	16.1803	+	11.7557i	0.793306	+	0.576371i
$417$	54.0000			2.64439
$418$		0			0
$419$	32.0000			1.56330			0.781651	−	0.623716i	$-0.214378\pi$
$419$	32.0000			1.56330			0.781651	+	0.623716i	$0.214378\pi$
$420$	7.28115	+	5.29007i	0.355284	+	0.258129i
$421$	0.927051	−	2.85317i	0.0451817	−	0.139055i	−0.925921	−	0.377718i	$-0.876709\pi$
$421$	0.927051	−	2.85317i	0.0451817	−	0.139055i	0.971103	+	0.238663i	$0.0767090\pi$
$422$	6.79837	+	20.9232i	0.330940	+	1.01853i
$423$	14.5623	−	10.5801i	0.708044	−	0.514424i
$424$	−9.70820	+	7.05342i	−0.471472	+	0.342545i
$425$		0			0
$426$	1.85410	−	5.70634i	0.0898315	−	0.276473i
$427$	−26.6976	−	19.3969i	−1.29199	−	0.938682i
$428$	−9.00000			−0.435031
$429$		0			0
$430$	−5.00000			−0.241121
$431$	−14.5623	−	10.5801i	−0.701442	−	0.509627i	0.178960	−	0.983856i	$-0.442727\pi$
$431$	−14.5623	−	10.5801i	−0.701442	−	0.509627i	−0.880401	+	0.474229i	$0.842727\pi$
$432$	2.78115	−	8.55951i	0.133808	−	0.411820i
$433$	4.32624	+	13.3148i	0.207906	+	0.639868i	0.999582	+	0.0289266i	$0.00920891\pi$
$433$	4.32624	+	13.3148i	0.207906	+	0.639868i	−0.791676	+	0.610941i	$0.790791\pi$
$434$	4.85410	−	3.52671i	0.233004	−	0.169288i
$435$	14.5623	−	10.5801i	0.698209	−	0.507279i
$436$	2.78115	+	8.55951i	0.133193	+	0.409926i
$437$	−9.88854	+	30.4338i	−0.473033	+	1.45585i
$438$	19.4164	+	14.1068i	0.927752	+	0.674051i
$439$	8.00000			0.381819			0.190910	−	0.981608i	$-0.438856\pi$
$439$	8.00000			0.381819			0.190910	+	0.981608i	$0.438856\pi$
$440$		0			0
$441$	12.0000			0.571429
$442$		0			0
$443$	−7.72542	+	23.7764i	−0.367046	+	1.12965i	0.581644	+	0.813444i	$0.302410\pi$
$443$	−7.72542	+	23.7764i	−0.367046	+	1.12965i	−0.948690	+	0.316208i	$0.897590\pi$
$444$	−7.41641	−	22.8254i	−0.351967	−	1.08324i
$445$	−0.809017	+	0.587785i	−0.0383511	+	0.0278637i
$446$	4.04508	−	2.93893i	0.191540	−	0.139162i
$447$	15.7599	+	48.5039i	0.745416	+	2.29415i
$448$	−6.48936	+	19.9722i	−0.306593	+	0.943597i
$449$	10.5172	+	7.64121i	0.496338	+	0.360611i	0.807617	−	0.589708i	$-0.200757\pi$
$449$	10.5172	+	7.64121i	0.496338	+	0.360611i	−0.311278	+	0.950319i	$0.600757\pi$
$450$	−6.00000			−0.282843
$451$		0			0
$452$	−6.00000			−0.282216
$453$	−33.9787	−	24.6870i	−1.59646	−	1.15990i
$454$	0.309017	−	0.951057i	0.0145029	−	0.0446353i
$455$	−3.70820	−	11.4127i	−0.173843	−	0.535035i
$456$	29.1246	−	21.1603i	1.36388	−	0.990920i
$457$	−21.0344	+	15.2824i	−0.983950	+	0.714881i	−0.958588	−	0.284797i	$-0.908074\pi$
$457$	−21.0344	+	15.2824i	−0.983950	+	0.714881i	−0.0253618	+	0.999678i	$0.508074\pi$
$458$	0.309017	+	0.951057i	0.0144394	+	0.0444400i
$459$		0			0
$460$	−6.47214	−	4.70228i	−0.301765	−	0.219245i
$461$	7.00000			0.326023			0.163011	−	0.986624i	$-0.447879\pi$
$461$	7.00000			0.326023			0.163011	+	0.986624i	$0.447879\pi$
$462$		0			0
$463$	−15.0000			−0.697109			−0.348555	−	0.937288i	$-0.613327\pi$
$463$	−15.0000			−0.697109			−0.348555	+	0.937288i	$0.613327\pi$
$464$	4.85410	+	3.52671i	0.225346	+	0.163723i
$465$	1.85410	−	5.70634i	0.0859819	−	0.264625i
$466$	7.41641	+	22.8254i	0.343558	+	1.05736i
$467$	−21.8435	+	15.8702i	−1.01079	+	0.734385i	−0.964376	−	0.264537i	$-0.914781\pi$
$467$	−21.8435	+	15.8702i	−1.01079	+	0.734385i	−0.0464191	+	0.998922i	$0.514781\pi$
$468$	19.4164	−	14.1068i	0.897524	−	0.652089i
$469$	12.0517	+	37.0912i	0.556494	+	1.71271i
$470$	0.927051	−	2.85317i	0.0427617	−	0.131607i
$471$	−19.4164	−	14.1068i	−0.894661	−	0.650009i
$472$	−6.00000			−0.276172
$473$		0			0
$474$	30.0000			1.37795
$475$	−3.23607	−	2.35114i	−0.148481	−	0.107878i
$476$		0			0
$477$	7.41641	+	22.8254i	0.339574	+	1.04510i
$478$	3.23607	−	2.35114i	0.148014	−	0.107539i
$479$	−4.85410	+	3.52671i	−0.221790	+	0.161140i	−0.693132	−	0.720811i	$-0.743770\pi$
$479$	−4.85410	+	3.52671i	−0.221790	+	0.161140i	0.471342	+	0.881950i	$0.343770\pi$
$480$	4.63525	+	14.2658i	0.211569	+	0.651144i
$481$	−9.88854	+	30.4338i	−0.450879	+	1.38766i
$482$	18.6074	+	13.5191i	0.847543	+	0.615776i
$483$	−72.0000			−3.27611
$484$		0			0
$485$	−8.00000			−0.363261
$486$		0			0
$487$	−2.47214	+	7.60845i	−0.112023	+	0.344772i	−0.991315	−	0.131512i	$-0.958017\pi$
$487$	−2.47214	+	7.60845i	−0.112023	+	0.344772i	0.879291	+	0.476284i	$0.158017\pi$
$488$	−10.1976	−	31.3849i	−0.461622	−	1.42073i
$489$	−41.2599	+	29.9770i	−1.86584	+	1.35561i
$490$	1.61803	−	1.17557i	0.0730953	−	0.0531069i
$491$	6.79837	+	20.9232i	0.306806	+	0.944253i	0.978997	+	0.203875i	$0.0653535\pi$
$491$	6.79837	+	20.9232i	0.306806	+	0.944253i	−0.672191	+	0.740378i	$0.734646\pi$
$492$	−4.63525	+	14.2658i	−0.208973	+	0.643154i
$493$		0			0
$494$	−16.0000			−0.719874
$495$		0			0
$496$	2.00000			0.0898027
$497$	4.85410	+	3.52671i	0.217736	+	0.158195i
$498$	3.70820	−	11.4127i	0.166169	−	0.511414i
$499$	−12.9787	−	39.9444i	−0.581007	−	1.78816i	−0.614746	−	0.788725i	$-0.710742\pi$
$499$	−12.9787	−	39.9444i	−0.581007	−	1.78816i	0.0337391	−	0.999431i	$-0.489258\pi$
$500$	0.809017	−	0.587785i	0.0361803	−	0.0262866i
$501$	−16.9894	+	12.3435i	−0.759028	+	0.551466i
$502$	−5.56231	−	17.1190i	−0.248258	−	0.764059i
$503$	4.01722	−	12.3637i	0.179119	−	0.551272i	−0.820679	−	0.571390i	$-0.806404\pi$
$503$	4.01722	−	12.3637i	0.179119	−	0.551272i	0.999798	+	0.0201184i	$0.00640433\pi$
$504$	43.6869	+	31.7404i	1.94597	+	1.41383i
$505$	−5.00000			−0.222497
$506$		0			0
$507$	−9.00000			−0.399704
$508$	8.89919	+	6.46564i	0.394838	+	0.286866i
$509$	7.10739	−	21.8743i	0.315030	−	0.969561i	−0.660713	−	0.750639i	$-0.729746\pi$
$509$	7.10739	−	21.8743i	0.315030	−	0.969561i	0.975742	−	0.218922i	$-0.0702542\pi$
$510$		0			0
$511$	−19.4164	+	14.1068i	−0.858931	+	0.624050i
$512$	−8.89919	+	6.46564i	−0.393292	+	0.285744i
$513$	−11.1246	−	34.2380i	−0.491164	−	1.51165i
$514$	1.85410	−	5.70634i	0.0817809	−	0.251696i
$515$	−6.47214	−	4.70228i	−0.285196	−	0.207207i
$516$	15.0000			0.660338
$517$		0			0
$518$	−24.0000			−1.05450
$519$	58.2492	+	42.3205i	2.55686	+	1.85767i
$520$	3.70820	−	11.4127i	0.162615	−	0.500479i
$521$	4.63525	+	14.2658i	0.203074	+	0.624998i	0.999787	+	0.0206400i	$0.00657038\pi$
$521$	4.63525	+	14.2658i	0.203074	+	0.624998i	−0.796713	+	0.604358i	$0.793430\pi$
$522$	29.1246	−	21.1603i	1.27475	−	0.926160i
$523$	3.23607	−	2.35114i	0.141503	−	0.102808i	−0.514782	−	0.857321i	$-0.672127\pi$
$523$	3.23607	−	2.35114i	0.141503	−	0.102808i	0.656285	+	0.754513i	$0.272127\pi$
$524$		0			0
$525$	2.78115	−	8.55951i	0.121379	−	0.373568i
$526$	9.70820	+	7.05342i	0.423298	+	0.307544i
$527$		0			0
$528$		0			0
$529$	41.0000			1.78261
$530$	3.23607	+	2.35114i	0.140566	+	0.102127i
$531$	−3.70820	+	11.4127i	−0.160922	+	0.495268i
$532$	3.70820	+	11.4127i	0.160771	+	0.494802i
$533$	16.1803	−	11.7557i	0.700848	−	0.509196i
$534$	−2.42705	+	1.76336i	−0.105029	+	0.0763079i
$535$	2.78115	+	8.55951i	0.120240	+	0.370060i
$536$	−12.0517	+	37.0912i	−0.520553	+	1.60210i
$537$	−63.1033	−	45.8472i	−2.72311	−	1.97845i
$538$	−21.0000			−0.905374
$539$		0			0
$540$	9.00000			0.387298
$541$	−25.0795	−	18.2213i	−1.07825	−	0.783397i	−0.100876	−	0.994899i	$-0.532164\pi$
$541$	−25.0795	−	18.2213i	−1.07825	−	0.783397i	−0.977377	+	0.211502i	$0.932164\pi$
$542$		0			0
$543$	17.6140	+	54.2102i	0.755888	+	2.32638i
$544$		0			0
$545$	7.28115	−	5.29007i	0.311890	−	0.226602i
$546$	−11.1246	−	34.2380i	−0.476089	−	1.46525i
$547$	11.1246	−	34.2380i	0.475654	−	1.46391i	−0.369420	−	0.929263i	$-0.620443\pi$
$547$	11.1246	−	34.2380i	0.475654	−	1.46391i	0.845074	−	0.534650i	$-0.179557\pi$
$548$		0			0
$549$	−66.0000			−2.81681
$550$		0			0
$551$	24.0000			1.02243
$552$	−58.2492	−	42.3205i	−2.47925	−	1.80128i
$553$	−9.27051	+	28.5317i	−0.394222	+	1.21329i
$554$	−4.32624	−	13.3148i	−0.183804	−	0.565691i
$555$	−19.4164	+	14.1068i	−0.824181	+	0.598802i
$556$	−14.5623	+	10.5801i	−0.617579	+	0.448698i
$557$	−8.65248	−	26.6296i	−0.366617	−	1.12833i	−0.948962	−	0.315390i	$-0.897865\pi$
$557$	−8.65248	−	26.6296i	−0.366617	−	1.12833i	0.582345	−	0.812942i	$-0.302135\pi$
$558$	3.70820	−	11.4127i	0.156981	−	0.483137i
$559$	−16.1803	−	11.7557i	−0.684355	−	0.497213i
$560$	3.00000			0.126773
$561$		0			0
$562$	6.00000			0.253095
$563$	−16.9894	−	12.3435i	−0.716016	−	0.520216i	0.169093	−	0.985600i	$-0.445916\pi$
$563$	−16.9894	−	12.3435i	−0.716016	−	0.520216i	−0.885109	+	0.465384i	$0.845916\pi$
$564$	−2.78115	+	8.55951i	−0.117108	+	0.360420i
$565$	1.85410	+	5.70634i	0.0780027	+	0.240067i
$566$	−10.5172	+	7.64121i	−0.442072	+	0.321184i
$567$	21.8435	−	15.8702i	0.917339	−	0.666486i
$568$	1.85410	+	5.70634i	0.0777964	+	0.239433i
$569$	−3.39919	+	10.4616i	−0.142501	+	0.438574i	−0.996681	−	0.0814036i	$-0.974060\pi$
$569$	−3.39919	+	10.4616i	−0.142501	+	0.438574i	0.854180	+	0.519978i	$0.174060\pi$
$570$	−9.70820	−	7.05342i	−0.406632	−	0.295435i
$571$	−18.0000			−0.753277			−0.376638	−	0.926360i	$-0.622920\pi$
$571$	−18.0000			−0.753277			−0.376638	+	0.926360i	$0.622920\pi$
$572$		0			0
$573$	−24.0000			−1.00261
$574$	12.1353	+	8.81678i	0.506516	+	0.368005i
$575$	−2.47214	+	7.60845i	−0.103095	+	0.317294i
$576$	12.9787	+	39.9444i	0.540780	+	1.66435i
$577$	−11.3262	+	8.22899i	−0.471517	+	0.342577i	−0.798032	−	0.602615i	$-0.794126\pi$
$577$	−11.3262	+	8.22899i	−0.471517	+	0.342577i	0.326515	+	0.945192i	$0.394126\pi$
$578$	−13.7533	+	9.99235i	−0.572061	+	0.415627i
$579$	9.27051	+	28.5317i	0.385269	+	1.18574i
$580$	−1.85410	+	5.70634i	−0.0769874	+	0.236943i
$581$	9.70820	+	7.05342i	0.402764	+	0.292625i
$582$	−24.0000			−0.994832
$583$		0			0
$584$	−24.0000			−0.993127
$585$	−19.4164	−	14.1068i	−0.802770	−	0.583246i
$586$	10.5066	−	32.3359i	0.434023	−	1.33578i
$587$	6.48936	+	19.9722i	0.267844	+	0.824340i	0.991024	+	0.133681i	$0.0426797\pi$
$587$	6.48936	+	19.9722i	0.267844	+	0.824340i	−0.723180	+	0.690660i	$0.757320\pi$
$588$	−4.85410	+	3.52671i	−0.200180	+	0.145439i
$589$	6.47214	−	4.70228i	0.266680	−	0.193754i
$590$	0.618034	+	1.90211i	0.0254441	+	0.0783088i
$591$	12.9787	−	39.9444i	0.533873	−	1.64309i
$592$	−6.47214	−	4.70228i	−0.266003	−	0.193263i
$593$	44.0000			1.80686			0.903432	−	0.428732i	$-0.141040\pi$
$593$	44.0000			1.80686			0.903432	+	0.428732i	$0.141040\pi$
$594$		0			0
$595$		0			0
$596$	−13.7533	−	9.99235i	−0.563357	−	0.409303i
$597$	5.56231	−	17.1190i	0.227650	−	0.700635i
$598$	9.88854	+	30.4338i	0.404373	+	1.24453i
$599$	−19.4164	+	14.1068i	−0.793333	+	0.576390i	−0.908951	−	0.416904i	$-0.863115\pi$
$599$	−19.4164	+	14.1068i	−0.793333	+	0.576390i	0.115618	+	0.993294i	$0.463115\pi$
$600$	7.28115	−	5.29007i	0.297252	−	0.215966i
$601$	−0.618034	−	1.90211i	−0.0252101	−	0.0775888i	0.937660	−	0.347554i	$-0.112988\pi$
$601$	−0.618034	−	1.90211i	−0.0252101	−	0.0775888i	−0.962870	+	0.269965i	$0.912988\pi$
$602$	4.63525	−	14.2658i	0.188919	−	0.581433i
$603$	63.1033	+	45.8472i	2.56977	+	1.86704i
$604$	14.0000			0.569652
$605$		0			0
$606$	−15.0000			−0.609333
$607$	32.3607	+	23.5114i	1.31348	+	0.954299i	0.999989	+	0.00470738i	$0.00149841\pi$
$607$	32.3607	+	23.5114i	1.31348	+	0.954299i	0.313491	+	0.949591i	$0.398502\pi$
$608$	−6.18034	+	19.0211i	−0.250646	+	0.771409i
$609$	16.6869	+	51.3571i	0.676188	+	2.08109i
$610$	−8.89919	+	6.46564i	−0.360318	+	0.261786i
$611$	9.70820	−	7.05342i	0.392752	−	0.285351i
$612$		0			0
$613$	−6.79837	+	20.9232i	−0.274584	+	0.845082i	0.714745	+	0.699385i	$0.246543\pi$
$613$	−6.79837	+	20.9232i	−0.274584	+	0.845082i	−0.989329	+	0.145697i	$0.953457\pi$
$614$	−6.47214	−	4.70228i	−0.261194	−	0.189769i
$615$	15.0000			0.604858
$616$		0			0
$617$	26.0000			1.04672			0.523360	−	0.852111i	$-0.324678\pi$
$617$	26.0000			1.04672			0.523360	+	0.852111i	$0.324678\pi$
$618$	−19.4164	−	14.1068i	−0.781042	−	0.567461i
$619$	−2.47214	+	7.60845i	−0.0993635	+	0.305810i	−0.988366	−	0.152092i	$-0.951399\pi$
$619$	−2.47214	+	7.60845i	−0.0993635	+	0.305810i	0.889003	+	0.457902i	$0.151399\pi$
$620$	0.618034	+	1.90211i	0.0248208	+	0.0763907i
$621$	−58.2492	+	42.3205i	−2.33746	+	1.69826i
$622$	19.4164	−	14.1068i	0.778527	−	0.565633i
$623$	−0.927051	−	2.85317i	−0.0371415	−	0.114310i
$624$	3.70820	−	11.4127i	0.148447	−	0.456873i
$625$	−0.809017	−	0.587785i	−0.0323607	−	0.0235114i
$626$	−8.00000			−0.319744
$627$		0			0
$628$	8.00000			0.319235
$629$		0			0
$630$	5.56231	−	17.1190i	0.221608	−	0.682038i
$631$	−13.5967	−	41.8465i	−0.541278	−	1.66588i	−0.729679	−	0.683790i	$-0.760330\pi$
$631$	−13.5967	−	41.8465i	−0.541278	−	1.66588i	0.188401	−	0.982092i	$-0.439670\pi$
$632$	−24.2705	+	17.6336i	−0.965429	+	0.701425i
$633$	−53.3951	+	38.7938i	−2.12227	+	1.54192i
$634$	−5.56231	−	17.1190i	−0.220907	−	0.679883i
$635$	3.39919	−	10.4616i	0.134893	−	0.415157i
$636$	−9.70820	−	7.05342i	−0.384955	−	0.279686i
$637$	8.00000			0.316972
$638$		0			0
$639$	12.0000			0.474713
$640$	−2.42705	−	1.76336i	−0.0959376	−	0.0697028i
$641$	−4.32624	+	13.3148i	−0.170876	+	0.525903i	−0.999421	−	0.0340198i	$-0.989169\pi$
$641$	−4.32624	+	13.3148i	−0.170876	+	0.525903i	0.828545	+	0.559922i	$0.189169\pi$
$642$	8.34346	+	25.6785i	0.329290	+	1.01345i
$643$	−28.3156	+	20.5725i	−1.11666	+	0.811300i	−0.983699	−	0.179822i	$-0.942448\pi$
$643$	−28.3156	+	20.5725i	−1.11666	+	0.811300i	−0.132959	+	0.991122i	$0.542448\pi$
$644$	19.4164	−	14.1068i	0.765114	−	0.555888i
$645$	−4.63525	−	14.2658i	−0.182513	−	0.561717i
$646$		0			0
$647$	20.2254	+	14.6946i	0.795143	+	0.577706i	0.909485	−	0.415736i	$-0.136476\pi$
$647$	20.2254	+	14.6946i	0.795143	+	0.577706i	−0.114342	+	0.993441i	$0.536476\pi$
$648$	27.0000			1.06066
$649$		0			0
$650$	−4.00000			−0.156893
$651$	14.5623	+	10.5801i	0.570742	+	0.414668i
$652$	5.25329	−	16.1680i	0.205735	−	0.633186i
$653$	−10.5066	−	32.3359i	−0.411154	−	1.26540i	−0.915646	−	0.401986i	$-0.868320\pi$
$653$	−10.5066	−	32.3359i	−0.411154	−	1.26540i	0.504492	−	0.863417i	$-0.331680\pi$
$654$	21.8435	−	15.8702i	0.854147	−	0.620574i
$655$		0			0
$656$	1.54508	+	4.75528i	0.0603254	+	0.185663i
$657$	−14.8328	+	45.6507i	−0.578683	+	1.78100i
$658$	7.28115	+	5.29007i	0.283849	+	0.206228i
$659$	−42.0000			−1.63609			−0.818044	−	0.575156i	$-0.804941\pi$
$659$	−42.0000			−1.63609			−0.818044	+	0.575156i	$0.804941\pi$
$660$		0			0
$661$	−37.0000			−1.43913			−0.719567	−	0.694423i	$-0.755660\pi$
$661$	−37.0000			−1.43913			−0.719567	+	0.694423i	$0.755660\pi$
$662$	−16.1803	−	11.7557i	−0.628867	−	0.456898i
$663$		0			0
$664$	3.70820	+	11.4127i	0.143906	+	0.442898i
$665$	9.70820	−	7.05342i	0.376468	−	0.273520i
$666$	−38.8328	+	28.2137i	−1.50474	+	1.09326i
$667$	−14.8328	−	45.6507i	−0.574329	−	1.76760i
$668$	2.16312	−	6.65740i	0.0836936	−	0.257582i
$669$	12.1353	+	8.81678i	0.469176	+	0.340876i
$670$	13.0000			0.502234
$671$		0			0
$672$	−45.0000			−1.73591
$673$	8.09017	+	5.87785i	0.311853	+	0.226575i	0.732691	−	0.680561i	$-0.238264\pi$
$673$	8.09017	+	5.87785i	0.311853	+	0.226575i	−0.420838	+	0.907136i	$0.638264\pi$
$674$	3.70820	−	11.4127i	0.142835	−	0.439600i
$675$	−2.78115	−	8.55951i	−0.107047	−	0.329456i
$676$	2.42705	−	1.76336i	0.0933481	−	0.0678214i
$677$	22.6525	−	16.4580i	0.870605	−	0.632532i	−0.0601440	−	0.998190i	$-0.519156\pi$
$677$	22.6525	−	16.4580i	0.870605	−	0.632532i	0.930749	+	0.365658i	$0.119156\pi$
$678$	5.56231	+	17.1190i	0.213619	+	0.657452i
$679$	7.41641	−	22.8254i	0.284616	−	0.875957i
$680$		0			0
$681$	3.00000			0.114960
$682$		0			0
$683$	47.0000			1.79841			0.899203	−	0.437533i	$-0.144148\pi$
$683$	47.0000			1.79841			0.899203	+	0.437533i	$0.144148\pi$
$684$	19.4164	+	14.1068i	0.742405	+	0.539389i
$685$		0			0
$686$	−4.63525	−	14.2658i	−0.176975	−	0.544673i
$687$	−2.42705	+	1.76336i	−0.0925978	+	0.0672762i
$688$	4.04508	−	2.93893i	0.154217	−	0.112046i
$689$	4.94427	+	15.2169i	0.188362	+	0.579718i
$690$	−7.41641	+	22.8254i	−0.282338	+	0.868946i
$691$	32.3607	+	23.5114i	1.23106	+	0.894416i	0.996969	−	0.0777989i	$-0.0247892\pi$
$691$	32.3607	+	23.5114i	1.23106	+	0.894416i	0.234089	+	0.972215i	$0.424789\pi$
$692$	−24.0000			−0.912343
$693$		0			0
$694$	−7.00000			−0.265716
$695$	14.5623	+	10.5801i	0.552380	+	0.401327i
$696$	−16.6869	+	51.3571i	−0.632516	+	1.94668i
$697$		0			0
$698$	17.7984	−	12.9313i	0.673678	−	0.489456i
$699$	−58.2492	+	42.3205i	−2.20319	+	1.60071i
$700$	0.927051	+	2.85317i	0.0350392	+	0.107840i
$701$	11.7426	−	36.1401i	0.443514	−	1.36499i	−0.440592	−	0.897707i	$-0.645231\pi$
$701$	11.7426	−	36.1401i	0.443514	−	1.36499i	0.884106	−	0.467287i	$-0.154769\pi$
$702$	−29.1246	−	21.1603i	−1.09924	−	0.798643i
$703$	−32.0000			−1.20690
$704$		0			0
$705$	9.00000			0.338960
$706$	4.85410	+	3.52671i	0.182687	+	0.132730i
$707$	4.63525	−	14.2658i	0.174327	−	0.536522i
$708$	−1.85410	−	5.70634i	−0.0696814	−	0.214457i
$709$	20.2254	−	14.6946i	0.759582	−	0.551868i	−0.139200	−	0.990264i	$-0.544453\pi$
$709$	20.2254	−	14.6946i	0.759582	−	0.551868i	0.898782	+	0.438396i	$0.144453\pi$
$710$	1.61803	−	1.17557i	0.0607237	−	0.0441184i
$711$	18.5410	+	57.0634i	0.695343	+	2.14004i
$712$	0.927051	−	2.85317i	0.0347427	−	0.106927i
$713$	−12.9443	−	9.40456i	−0.484767	−	0.352204i
$714$		0			0
$715$		0			0
$716$	26.0000			0.971666
$717$	9.70820	+	7.05342i	0.362560	+	0.263415i
$718$	8.65248	−	26.6296i	0.322908	−	0.993807i
$719$		0			0		0.951057	−	0.309017i	$-0.100000\pi$
$719$		0			0		−0.951057	+	0.309017i	$0.900000\pi$
$720$	4.85410	−	3.52671i	0.180902	−	0.131433i
$721$	19.4164	−	14.1068i	0.723105	−	0.525366i
$722$	0.927051	+	2.85317i	0.0345013	+	0.106184i
$723$	−21.3222	+	65.6229i	−0.792980	+	2.44054i
$724$	−15.3713	−	11.1679i	−0.571271	−	0.415052i
$725$	6.00000			0.222834
$726$		0			0
$727$	−17.0000			−0.630495			−0.315248	−	0.949009i	$-0.602088\pi$
$727$	−17.0000			−0.630495			−0.315248	+	0.949009i	$0.602088\pi$
$728$	29.1246	+	21.1603i	1.07943	+	0.784252i
$729$	−8.34346	+	25.6785i	−0.309017	+	0.951057i
$730$	2.47214	+	7.60845i	0.0914979	+	0.281601i
$731$		0			0
$732$	26.6976	−	19.3969i	0.986770	−	0.716931i
$733$	11.1246	+	34.2380i	0.410897	+	1.26461i	0.915870	+	0.401475i	$0.131502\pi$
$733$	11.1246	+	34.2380i	0.410897	+	1.26461i	−0.504973	+	0.863135i	$0.668498\pi$
$734$	−0.309017	+	0.951057i	−0.0114060	+	0.0351041i
$735$	4.85410	+	3.52671i	0.179046	+	0.130085i
$736$	40.0000			1.47442
$737$		0			0
$738$	30.0000			1.10432
$739$	8.09017	+	5.87785i	0.297602	+	0.216220i	0.726558	−	0.687105i	$-0.241119\pi$
$739$	8.09017	+	5.87785i	0.297602	+	0.216220i	−0.428957	+	0.903325i	$0.641119\pi$
$740$	2.47214	−	7.60845i	0.0908775	−	0.279692i
$741$	−14.8328	−	45.6507i	−0.544897	−	1.67702i
$742$	−9.70820	+	7.05342i	−0.356399	+	0.258939i
$743$	5.66312	−	4.11450i	0.207760	−	0.150946i	−0.479040	−	0.877793i	$-0.659015\pi$
$743$	5.66312	−	4.11450i	0.207760	−	0.150946i	0.686799	+	0.726847i	$0.259015\pi$
$744$	5.56231	+	17.1190i	0.203924	+	0.627614i
$745$	−5.25329	+	16.1680i	−0.192466	+	0.592348i
$746$	14.5623	+	10.5801i	0.533164	+	0.387366i
$747$	24.0000			0.878114
$748$		0			0
$749$	−27.0000			−0.986559
$750$	−2.42705	−	1.76336i	−0.0886234	−	0.0643886i
$751$	3.09017	−	9.51057i	0.112762	−	0.347045i	−0.878712	−	0.477353i	$-0.841596\pi$
$751$	3.09017	−	9.51057i	0.112762	−	0.347045i	0.991474	+	0.130307i	$0.0415964\pi$
$752$	0.927051	+	2.85317i	0.0338061	+	0.104044i
$753$	43.6869	−	31.7404i	1.59204	−	1.15668i
$754$	19.4164	−	14.1068i	0.707104	−	0.513741i
$755$	−4.32624	−	13.3148i	−0.157448	−	0.484575i
$756$	−8.34346	+	25.6785i	−0.303449	+	0.933919i
$757$	9.70820	+	7.05342i	0.352851	+	0.256361i	0.750064	−	0.661365i	$-0.230023\pi$
$757$	9.70820	+	7.05342i	0.352851	+	0.256361i	−0.397213	+	0.917726i	$0.630023\pi$
$758$	22.0000			0.799076
$759$		0			0
$760$	12.0000			0.435286
$761$	−21.0344	−	15.2824i	−0.762498	−	0.553987i	0.137178	−	0.990546i	$-0.456197\pi$
$761$	−21.0344	−	15.2824i	−0.762498	−	0.553987i	−0.899675	+	0.436559i	$0.856197\pi$
$762$	10.1976	−	31.3849i	0.369419	−	1.13695i
$763$	8.34346	+	25.6785i	0.302053	+	0.929625i
$764$	6.47214	−	4.70228i	0.234154	−	0.170123i
$765$		0			0
$766$		0			0
$767$	−2.47214	+	7.60845i	−0.0892637	+	0.274725i
$768$	−41.2599	−	29.9770i	−1.48884	−	1.08170i
$769$	−26.0000			−0.937584			−0.468792	−	0.883309i	$-0.655311\pi$
$769$	−26.0000			−0.937584			−0.468792	+	0.883309i	$0.655311\pi$
$770$		0			0
$771$	18.0000			0.648254
$772$	−8.09017	−	5.87785i	−0.291172	−	0.211549i
$773$	−6.79837	+	20.9232i	−0.244521	+	0.752557i	0.751194	+	0.660081i	$0.229478\pi$
$773$	−6.79837	+	20.9232i	−0.244521	+	0.752557i	−0.995715	+	0.0924757i	$0.970522\pi$
$774$	−9.27051	−	28.5317i	−0.333222	−	1.02555i
$775$	1.61803	−	1.17557i	0.0581215	−	0.0422277i
$776$	19.4164	−	14.1068i	0.697008	−	0.506406i
$777$	−22.2492	−	68.4761i	−0.798186	−	2.45657i
$778$	0.927051	−	2.85317i	0.0332364	−	0.102291i
$779$	16.1803	+	11.7557i	0.579721	+	0.421192i
$780$	12.0000			0.429669
$781$		0			0
$782$		0			0
$783$	43.6869	+	31.7404i	1.56124	+	1.13431i
$784$	−0.618034	+	1.90211i	−0.0220726	+	0.0679326i
$785$	−2.47214	−	7.60845i	−0.0882343	−	0.271557i
$786$		0			0
$787$	34.7877	−	25.2748i	1.24005	−	0.900948i	0.242447	−	0.970165i	$-0.422050\pi$
$787$	34.7877	−	25.2748i	1.24005	−	0.900948i	0.997602	+	0.0692165i	$0.0220499\pi$
$788$	4.32624	+	13.3148i	0.154116	+	0.474320i
$789$	−11.1246	+	34.2380i	−0.396047	+	1.21891i
$790$	8.09017	+	5.87785i	0.287835	+	0.209125i
$791$	−18.0000			−0.640006
$792$		0			0
$793$	−44.0000			−1.56249
$794$	−9.70820	−	7.05342i	−0.344531	−	0.250317i
$795$	−3.70820	+	11.4127i	−0.131516	+	0.404766i
$796$	1.85410	+	5.70634i	0.0657169	+	0.202256i
$797$	40.4508	−	29.3893i	1.43284	−	1.04102i	0.443364	−	0.896342i	$-0.353785\pi$
$797$	40.4508	−	29.3893i	1.43284	−	1.04102i	0.989479	−	0.144679i	$-0.0462151\pi$
$798$	29.1246	−	21.1603i	1.03100	−	0.749065i
$799$		0			0
$800$	−1.54508	+	4.75528i	−0.0546270	+	0.168125i
$801$	−4.85410	−	3.52671i	−0.171511	−	0.124610i
$802$	37.0000			1.30652
$803$		0			0
$804$	−39.0000			−1.37542
$805$	−19.4164	−	14.1068i	−0.684338	−	0.497201i
$806$	2.47214	−	7.60845i	0.0870773	−	0.267996i
$807$	−19.4681	−	59.9166i	−0.685309	−	2.10916i
$808$	12.1353	−	8.81678i	0.426917	−	0.310173i
$809$	−43.6869	+	31.7404i	−1.53595	+	1.11593i	−0.583138	+	0.812373i	$0.698175\pi$
$809$	−43.6869	+	31.7404i	−1.53595	+	1.11593i	−0.952812	+	0.303560i	$0.901825\pi$
$810$	−2.78115	−	8.55951i	−0.0977198	−	0.300750i
$811$	12.9787	−	39.9444i	0.455744	−	1.40264i	−0.414515	−	0.910043i	$-0.636049\pi$
$811$	12.9787	−	39.9444i	0.455744	−	1.40264i	0.870259	−	0.492594i	$-0.163951\pi$
$812$	−14.5623	−	10.5801i	−0.511037	−	0.371290i
$813$		0			0
$814$		0			0
$815$	−17.0000			−0.595484
$816$		0			0
$817$	6.18034	−	19.0211i	0.216223	−	0.665465i
$818$	−6.48936	−	19.9722i	−0.226895	−	0.698311i
$819$	58.2492	−	42.3205i	2.03539	−	1.47880i
$820$	−4.04508	+	2.93893i	−0.141260	+	0.102632i
$821$	−0.927051	−	2.85317i	−0.0323543	−	0.0995763i	0.933575	−	0.358381i	$-0.116671\pi$
$821$	−0.927051	−	2.85317i	−0.0323543	−	0.0995763i	−0.965930	+	0.258805i	$0.916671\pi$
$822$		0			0
$823$	−41.2599	−	29.9770i	−1.43823	−	1.04493i	−0.988409	−	0.151815i	$-0.951488\pi$
$823$	−41.2599	−	29.9770i	−1.43823	−	1.04493i	−0.449820	−	0.893119i	$-0.648512\pi$
$824$	24.0000			0.836080
$825$		0			0
$826$	−6.00000			−0.208767
$827$	−36.4058	−	26.4503i	−1.26595	−	0.919768i	−0.266919	−	0.963719i	$-0.586006\pi$
$827$	−36.4058	−	26.4503i	−1.26595	−	0.919768i	−0.999034	+	0.0439507i	$0.986006\pi$
$828$	14.8328	−	45.6507i	0.515476	−	1.58647i
$829$	4.01722	+	12.3637i	0.139524	+	0.429410i	0.996266	−	0.0863344i	$-0.0275153\pi$
$829$	4.01722	+	12.3637i	0.139524	+	0.429410i	−0.856742	+	0.515745i	$0.827515\pi$
$830$	3.23607	−	2.35114i	0.112326	−	0.0816093i
$831$	33.9787	−	24.6870i	1.17871	−	0.856382i
$832$	8.65248	+	26.6296i	0.299971	+	0.923215i
$833$		0			0
$834$	43.6869	+	31.7404i	1.51275	+	1.09908i
$835$	−7.00000			−0.242245
$836$		0			0
$837$	18.0000			0.622171
$838$	25.8885	+	18.8091i	0.894305	+	0.649751i
$839$	−4.32624	+	13.3148i	−0.149358	+	0.459678i	−0.997546	−	0.0700187i	$-0.977694\pi$
$839$	−4.32624	+	13.3148i	−0.149358	+	0.459678i	0.848187	+	0.529696i	$0.177694\pi$
$840$	8.34346	+	25.6785i	0.287877	+	0.885993i
$841$	−5.66312	+	4.11450i	−0.195280	+	0.141879i
$842$	2.42705	−	1.76336i	0.0836417	−	0.0607693i
$843$	5.56231	+	17.1190i	0.191576	+	0.589610i
$844$	6.79837	−	20.9232i	0.234010	−	0.720208i
$845$	−2.42705	−	1.76336i	−0.0834931	−	0.0606613i
$846$	18.0000			0.618853
$847$		0			0
$848$	−4.00000			−0.137361
$849$	−31.5517	−	22.9236i	−1.08285	−	0.786737i
$850$		0			0
$851$	19.7771	+	60.8676i	0.677950	+	2.08652i
$852$	−4.85410	+	3.52671i	−0.166299	+	0.120823i
$853$	25.8885	−	18.8091i	0.886407	−	0.644012i	−0.0485318	−	0.998822i	$-0.515454\pi$
$853$	25.8885	−	18.8091i	0.886407	−	0.644012i	0.934939	+	0.354809i	$0.115454\pi$
$854$	−10.1976	−	31.3849i	−0.348953	−	1.07397i
$855$	7.41641	−	22.8254i	0.253636	−	0.780611i
$856$	−21.8435	−	15.8702i	−0.746594	−	0.542432i
$857$	−18.0000			−0.614868			−0.307434	−	0.951569i	$-0.599470\pi$
$857$	−18.0000			−0.614868			−0.307434	+	0.951569i	$0.599470\pi$
$858$		0			0
$859$	4.00000			0.136478			0.0682391	−	0.997669i	$-0.478262\pi$
$859$	4.00000			0.136478			0.0682391	+	0.997669i	$0.478262\pi$
$860$	4.04508	+	2.93893i	0.137936	+	0.100217i
$861$	−13.9058	+	42.7975i	−0.473907	+	1.45854i
$862$	−5.56231	−	17.1190i	−0.189453	−	0.583076i
$863$	−25.0795	+	18.2213i	−0.853717	+	0.620262i	−0.926168	−	0.377110i	$-0.876918\pi$
$863$	−25.0795	+	18.2213i	−0.853717	+	0.620262i	0.0724514	+	0.997372i	$0.476918\pi$
$864$	−36.4058	+	26.4503i	−1.23855	+	0.899859i
$865$	7.41641	+	22.8254i	0.252165	+	0.776085i
$866$	−4.32624	+	13.3148i	−0.147012	+	0.452455i
$867$	−41.2599	−	29.9770i	−1.40126	−	1.01807i
$868$	−6.00000			−0.203653
$869$		0			0
$870$	18.0000			0.610257
$871$	42.0689	+	30.5648i	1.42545	+	1.03565i
$872$	−8.34346	+	25.6785i	−0.282545	+	0.869585i
$873$	−14.8328	−	45.6507i	−0.502015	−	1.54504i
$874$	−25.8885	+	18.8091i	−0.875693	+	0.636228i
$875$	2.42705	−	1.76336i	0.0820493	−	0.0596123i
$876$	−7.41641	−	22.8254i	−0.250577	−	0.771197i
$877$	6.79837	−	20.9232i	0.229565	−	0.706528i	−0.768231	−	0.640172i	$-0.778863\pi$
$877$	6.79837	−	20.9232i	0.229565	−	0.706528i	0.997796	−	0.0663553i	$-0.0211371\pi$
$878$	6.47214	+	4.70228i	0.218424	+	0.158694i
$879$	102.000			3.44037
$880$		0			0
$881$	−15.0000			−0.505363			−0.252681	−	0.967550i	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$	9.70820	+	7.05342i	0.326892	+	0.237501i
$883$	6.18034	−	19.0211i	0.207985	−	0.640112i	−0.791593	−	0.611049i	$-0.790748\pi$
$883$	6.18034	−	19.0211i	0.207985	−	0.640112i	0.999578	−	0.0290628i	$-0.00925227\pi$
$884$		0			0
$885$	−4.85410	+	3.52671i	−0.163169	+	0.118549i
$886$	−20.2254	+	14.6946i	−0.679486	+	0.493676i
$887$	0.309017	+	0.951057i	0.0103758	+	0.0319334i	0.956110	−	0.293007i	$-0.0946558\pi$
$887$	0.309017	+	0.951057i	0.0103758	+	0.0319334i	−0.945735	+	0.324940i	$0.894656\pi$
$888$	22.2492	−	68.4761i	0.746635	−	2.29791i
$889$	26.6976	+	19.3969i	0.895407	+	0.650552i
$890$	−1.00000			−0.0335201
$891$		0			0
$892$	−5.00000			−0.167412
$893$	9.70820	+	7.05342i	0.324873	+	0.236034i
$894$	−15.7599	+	48.5039i	−0.527089	+	1.62221i
$895$	−8.03444	−	24.7275i	−0.268562	−	0.826548i
$896$	7.28115	−	5.29007i	0.243246	−	0.176729i
$897$	−77.6656	+	56.4274i	−2.59318	+	1.88406i
$898$	4.01722	+	12.3637i	0.134056	+	0.412583i
$899$	−3.70820	+	11.4127i	−0.123676	+	0.380634i
$900$	4.85410	+	3.52671i	0.161803	+	0.117557i
$901$		0			0
$902$		0			0
$903$	45.0000			1.49751
$904$	−14.5623	−	10.5801i	−0.484335	−	0.351890i
$905$	−5.87132	+	18.0701i	−0.195169	+	0.600670i
$906$	−12.9787	−	39.9444i	−0.431189	−	1.32706i
$907$	34.7877	−	25.2748i	1.15511	−	0.839235i	0.165956	−	0.986133i	$-0.446929\pi$
$907$	34.7877	−	25.2748i	1.15511	−	0.839235i	0.989152	+	0.146898i	$0.0469290\pi$
$908$	−0.809017	+	0.587785i	−0.0268482	+	0.0195063i
$909$	−9.27051	−	28.5317i	−0.307483	−	0.946337i
$910$	3.70820	−	11.4127i	0.122926	−	0.378327i
$911$	27.5066	+	19.9847i	0.911334	+	0.662123i	0.941352	−	0.337427i	$-0.109557\pi$
$911$	27.5066	+	19.9847i	0.911334	+	0.662123i	−0.0300182	+	0.999549i	$0.509557\pi$
$912$	12.0000			0.397360
$913$		0			0
$914$	−26.0000			−0.860004
$915$	−26.6976	−	19.3969i	−0.882594	−	0.641242i
$916$	0.309017	−	0.951057i	0.0102102	−	0.0314238i
$917$		0			0
$918$		0			0
$919$	−9.70820	+	7.05342i	−0.320244	+	0.232671i	−0.736280	−	0.676677i	$-0.763419\pi$
$919$	−9.70820	+	7.05342i	−0.320244	+	0.232671i	0.416036	+	0.909348i	$0.363419\pi$
$920$	−7.41641	−	22.8254i	−0.244512	−	0.752530i
$921$	7.41641	−	22.8254i	0.244379	−	0.752121i
$922$	5.66312	+	4.11450i	0.186505	+	0.135504i
$923$	8.00000			0.263323
$924$		0			0
$925$	−8.00000			−0.263038
$926$	−12.1353	−	8.81678i	−0.398789	−	0.289737i
$927$	14.8328	−	45.6507i	0.487174	−	1.49937i
$928$	−9.27051	−	28.5317i	−0.304319	−	0.936599i
$929$	21.0344	−	15.2824i	0.690118	−	0.501400i	−0.186581	−	0.982440i	$-0.559741\pi$
$929$	21.0344	−	15.2824i	0.690118	−	0.501400i	0.876699	+	0.481040i	$0.159741\pi$
$930$	4.85410	−	3.52671i	0.159172	−	0.115645i
$931$	2.47214	+	7.60845i	0.0810210	+	0.249357i
$932$	7.41641	−	22.8254i	0.242933	−	0.747669i
$933$	58.2492	+	42.3205i	1.90699	+	1.38551i
$934$	−27.0000			−0.883467
$935$		0			0
$936$	72.0000			2.35339
$937$	14.5623	+	10.5801i	0.475730	+	0.345638i	0.799670	−	0.600440i	$-0.205008\pi$
$937$	14.5623	+	10.5801i	0.475730	+	0.345638i	−0.323940	+	0.946078i	$0.605008\pi$
$938$	−12.0517	+	37.0912i	−0.393501	+	1.21107i
$939$	−7.41641	−	22.8254i	−0.242025	−	0.744877i
$940$	−2.42705	+	1.76336i	−0.0791617	+	0.0575143i
$941$	10.5172	−	7.64121i	0.342852	−	0.249096i	−0.403012	−	0.915195i	$-0.632037\pi$
$941$	10.5172	−	7.64121i	0.342852	−	0.249096i	0.745864	+	0.666098i	$0.232037\pi$
$942$	−7.41641	−	22.8254i	−0.241640	−	0.743690i
$943$	12.3607	−	38.0423i	0.402519	−	1.23883i
$944$	−1.61803	−	1.17557i	−0.0526625	−	0.0382616i
$945$	27.0000			0.878310
$946$		0			0
$947$	−12.0000			−0.389948			−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000			−0.389948			−0.194974	+	0.980808i	$0.562462\pi$
$948$	−24.2705	−	17.6336i	−0.788270	−	0.572711i
$949$	−9.88854	+	30.4338i	−0.320996	+	0.987923i
$950$	−1.23607	−	3.80423i	−0.0401033	−	0.123425i
$951$	43.6869	−	31.7404i	1.41665	−	1.02925i
$952$		0			0
$953$	−11.1246	−	34.2380i	−0.360362	−	1.10908i	−0.952835	−	0.303489i	$-0.901849\pi$
$953$	−11.1246	−	34.2380i	−0.360362	−	1.10908i	0.592473	−	0.805590i	$-0.298151\pi$
$954$	−7.41641	+	22.8254i	−0.240115	+	0.738998i
$955$	−6.47214	−	4.70228i	−0.209433	−	0.152162i
$956$	−4.00000			−0.129369
$957$		0			0
$958$	−6.00000			−0.193851
$959$		0			0
$960$	−6.48936	+	19.9722i	−0.209443	+	0.644600i
$961$	−8.34346	−	25.6785i	−0.269144	−	0.828340i
$962$	−25.8885	+	18.8091i	−0.834680	+	0.606431i
$963$	−43.6869	+	31.7404i	−1.40779	+	1.02282i
$964$	−7.10739	−	21.8743i	−0.228914	−	0.704524i
$965$	−3.09017	+	9.51057i	−0.0994761	+	0.306156i
$966$	−58.2492	−	42.3205i	−1.87414	−	1.36164i
$967$	−32.0000			−1.02905			−0.514525	−	0.857475i	$-0.672032\pi$
$967$	−32.0000			−1.02905			−0.514525	+	0.857475i	$0.672032\pi$
$968$		0			0
$969$		0			0
$970$	−6.47214	−	4.70228i	−0.207808	−	0.150981i
$971$	3.70820	−	11.4127i	0.119002	−	0.366250i	−0.873759	−	0.486360i	$-0.838325\pi$
$971$	3.70820	−	11.4127i	0.119002	−	0.366250i	0.992761	+	0.120109i	$0.0383245\pi$
$972$		0			0
$973$	−43.6869	+	31.7404i	−1.40054	+	1.01755i
$974$	−6.47214	+	4.70228i	−0.207381	+	0.150671i
$975$	−3.70820	−	11.4127i	−0.118758	−	0.365498i
$976$	3.39919	−	10.4616i	0.108805	−	0.334868i
$977$	−22.6525	−	16.4580i	−0.724717	−	0.526538i	0.163171	−	0.986598i	$-0.447828\pi$
$977$	−22.6525	−	16.4580i	−0.724717	−	0.526538i	−0.887888	+	0.460060i	$0.847828\pi$
$978$	−51.0000			−1.63080
$979$		0			0
$980$	−2.00000			−0.0638877
$981$	43.6869	+	31.7404i	1.39482	+	1.01339i
$982$	−6.79837	+	20.9232i	−0.216945	+	0.667688i
$983$	−18.8500	−	58.0144i	−0.601223	−	1.85037i	−0.520925	−	0.853603i	$-0.674413\pi$
$983$	−18.8500	−	58.0144i	−0.601223	−	1.85037i	−0.0802981	−	0.996771i	$-0.525587\pi$
$984$	−36.4058	+	26.4503i	−1.16057	+	0.843206i
$985$	11.3262	−	8.22899i	0.360884	−	0.262198i
$986$		0			0
$987$	−8.34346	+	25.6785i	−0.265575	+	0.817356i
$988$	12.9443	+	9.40456i	0.411812	+	0.299199i
$989$	−40.0000			−1.27193
$990$		0			0
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	−8.09017	−	5.87785i	−0.256863	−	0.186622i
$993$	18.5410	−	57.0634i	0.588381	−	1.81085i
$994$	1.85410	+	5.70634i	0.0588085	+	0.180994i
$995$	4.85410	−	3.52671i	0.153885	−	0.111804i
$996$	−9.70820	+	7.05342i	−0.307616	+	0.223496i
$997$	16.0689	+	49.4549i	0.508907	+	1.56625i	0.794102	+	0.607784i	$0.207941\pi$
$997$	16.0689	+	49.4549i	0.508907	+	1.56625i	−0.285196	+	0.958469i	$0.592059\pi$
$998$	12.9787	−	39.9444i	0.410834	−	1.26442i
$999$	−58.2492	−	42.3205i	−1.84292	−	1.33896i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.g.d.81.1		4
11.2	odd	10		605.2.g.b.511.1		4
11.3	even	5	inner	605.2.g.d.366.1		4
11.4	even	5	inner	605.2.g.d.251.1		4
11.5	even	5		605.2.a.a.1.1	✓	1
11.6	odd	10		605.2.a.c.1.1	yes	1
11.7	odd	10		605.2.g.b.251.1		4
11.8	odd	10		605.2.g.b.366.1		4
11.9	even	5	inner	605.2.g.d.511.1		4
11.10	odd	2		605.2.g.b.81.1		4
33.5	odd	10		5445.2.a.h.1.1		1
33.17	even	10		5445.2.a.d.1.1		1
44.27	odd	10		9680.2.a.bf.1.1		1
44.39	even	10		9680.2.a.be.1.1		1
55.39	odd	10		3025.2.a.c.1.1		1
55.49	even	10		3025.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.a.a.1.1	✓	1	11.5	even	5
605.2.a.c.1.1	yes	1	11.6	odd	10
605.2.g.b.81.1		4	11.10	odd	2
605.2.g.b.251.1		4	11.7	odd	10
605.2.g.b.366.1		4	11.8	odd	10
605.2.g.b.511.1		4	11.2	odd	10
605.2.g.d.81.1		4	1.1	even	1	trivial
605.2.g.d.251.1		4	11.4	even	5	inner
605.2.g.d.366.1		4	11.3	even	5	inner
605.2.g.d.511.1		4	11.9	even	5	inner
3025.2.a.c.1.1		1	55.39	odd	10
3025.2.a.g.1.1		1	55.49	even	10
5445.2.a.d.1.1		1	33.17	even	10
5445.2.a.h.1.1		1	33.5	odd	10
9680.2.a.be.1.1		1	44.39	even	10
9680.2.a.bf.1.1		1	44.27	odd	10

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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.42705 + 1.76336i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-4.85410 - 3.52671i) q^{9} +O(q^{10})\)	\(q+(0.809017 + 0.587785i) q^{2} +(-0.927051 + 2.85317i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-0.809017 + 0.587785i) q^{5} +(-2.42705 + 1.76336i) q^{6} +(-0.927051 - 2.85317i) q^{7} +(0.927051 - 2.85317i) q^{8} +(-4.85410 - 3.52671i) q^{9} -1.00000 q^{10} +3.00000 q^{12} +(-3.23607 - 2.35114i) q^{13} +(0.927051 - 2.85317i) q^{14} +(-0.927051 - 2.85317i) q^{15} +(0.809017 - 0.587785i) q^{16} +(-1.85410 - 5.70634i) q^{18} +(1.23607 - 3.80423i) q^{19} +(0.809017 + 0.587785i) q^{20} +9.00000 q^{21} -8.00000 q^{23} +(7.28115 + 5.29007i) q^{24} +(0.309017 - 0.951057i) q^{25} +(-1.23607 - 3.80423i) q^{26} +(7.28115 - 5.29007i) q^{27} +(-2.42705 + 1.76336i) q^{28} +(1.85410 + 5.70634i) q^{29} +(0.927051 - 2.85317i) q^{30} +(1.61803 + 1.17557i) q^{31} -5.00000 q^{32} +(2.42705 + 1.76336i) q^{35} +(-1.85410 + 5.70634i) q^{36} +(-2.47214 - 7.60845i) q^{37} +(3.23607 - 2.35114i) q^{38} +(9.70820 - 7.05342i) q^{39} +(0.927051 + 2.85317i) q^{40} +(-1.54508 + 4.75528i) q^{41} +(7.28115 + 5.29007i) q^{42} +5.00000 q^{43} +6.00000 q^{45} +(-6.47214 - 4.70228i) q^{46} +(-0.927051 + 2.85317i) q^{47} +(0.927051 + 2.85317i) q^{48} +(-1.61803 + 1.17557i) q^{49} +(0.809017 - 0.587785i) q^{50} +(-1.23607 + 3.80423i) q^{52} +(-3.23607 - 2.35114i) q^{53} +9.00000 q^{54} -9.00000 q^{56} +(9.70820 + 7.05342i) q^{57} +(-1.85410 + 5.70634i) q^{58} +(-0.618034 - 1.90211i) q^{59} +(-2.42705 + 1.76336i) q^{60} +(8.89919 - 6.46564i) q^{61} +(0.618034 + 1.90211i) q^{62} +(-5.56231 + 17.1190i) q^{63} +(-5.66312 - 4.11450i) q^{64} +4.00000 q^{65} -13.0000 q^{67} +(7.41641 - 22.8254i) q^{69} +(0.927051 + 2.85317i) q^{70} +(-1.61803 + 1.17557i) q^{71} +(-14.5623 + 10.5801i) q^{72} +(-2.47214 - 7.60845i) q^{73} +(2.47214 - 7.60845i) q^{74} +(2.42705 + 1.76336i) q^{75} -4.00000 q^{76} +12.0000 q^{78} +(-8.09017 - 5.87785i) q^{79} +(-0.309017 + 0.951057i) q^{80} +(2.78115 + 8.55951i) q^{81} +(-4.04508 + 2.93893i) q^{82} +(-3.23607 + 2.35114i) q^{83} +(-2.78115 - 8.55951i) q^{84} +(4.04508 + 2.93893i) q^{86} -18.0000 q^{87} +1.00000 q^{89} +(4.85410 + 3.52671i) q^{90} +(-3.70820 + 11.4127i) q^{91} +(2.47214 + 7.60845i) q^{92} +(-4.85410 + 3.52671i) q^{93} +(-2.42705 + 1.76336i) q^{94} +(1.23607 + 3.80423i) q^{95} +(4.63525 - 14.2658i) q^{96} +(6.47214 + 4.70228i) q^{97} -2.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} + 3 q^{3} + q^{4} - q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q + q^2 + 3 * q^3 + q^4 - q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^9	\( 4 q + q^{2} + 3 q^{3} + q^{4} - q^{5} - 3 q^{6} + 3 q^{7} - 3 q^{8} - 6 q^{9} - 4 q^{10} + 12 q^{12} - 4 q^{13} - 3 q^{14} + 3 q^{15} + q^{16} + 6 q^{18} - 4 q^{19} + q^{20} + 36 q^{21} - 32 q^{23} + 9 q^{24} - q^{25} + 4 q^{26} + 9 q^{27} - 3 q^{28} - 6 q^{29} - 3 q^{30} + 2 q^{31} - 20 q^{32} + 3 q^{35} + 6 q^{36} + 8 q^{37} + 4 q^{38} + 12 q^{39} - 3 q^{40} + 5 q^{41} + 9 q^{42} + 20 q^{43} + 24 q^{45} - 8 q^{46} + 3 q^{47} - 3 q^{48} - 2 q^{49} + q^{50} + 4 q^{52} - 4 q^{53} + 36 q^{54} - 36 q^{56} + 12 q^{57} + 6 q^{58} + 2 q^{59} - 3 q^{60} + 11 q^{61} - 2 q^{62} + 18 q^{63} - 7 q^{64} + 16 q^{65} - 52 q^{67} - 24 q^{69} - 3 q^{70} - 2 q^{71} - 18 q^{72} + 8 q^{73} - 8 q^{74} + 3 q^{75} - 16 q^{76} + 48 q^{78} - 10 q^{79} + q^{80} - 9 q^{81} - 5 q^{82} - 4 q^{83} + 9 q^{84} + 5 q^{86} - 72 q^{87} + 4 q^{89} + 6 q^{90} + 12 q^{91} - 8 q^{92} - 6 q^{93} - 3 q^{94} - 4 q^{95} - 15 q^{96} + 8 q^{97} - 8 q^{98}+O(q^{100}) \) 4 * q + q^2 + 3 * q^3 + q^4 - q^5 - 3 * q^6 + 3 * q^7 - 3 * q^8 - 6 * q^9 - 4 * q^10 + 12 * q^12 - 4 * q^13 - 3 * q^14 + 3 * q^15 + q^16 + 6 * q^18 - 4 * q^19 + q^20 + 36 * q^21 - 32 * q^23 + 9 * q^24 - q^25 + 4 * q^26 + 9 * q^27 - 3 * q^28 - 6 * q^29 - 3 * q^30 + 2 * q^31 - 20 * q^32 + 3 * q^35 + 6 * q^36 + 8 * q^37 + 4 * q^38 + 12 * q^39 - 3 * q^40 + 5 * q^41 + 9 * q^42 + 20 * q^43 + 24 * q^45 - 8 * q^46 + 3 * q^47 - 3 * q^48 - 2 * q^49 + q^50 + 4 * q^52 - 4 * q^53 + 36 * q^54 - 36 * q^56 + 12 * q^57 + 6 * q^58 + 2 * q^59 - 3 * q^60 + 11 * q^61 - 2 * q^62 + 18 * q^63 - 7 * q^64 + 16 * q^65 - 52 * q^67 - 24 * q^69 - 3 * q^70 - 2 * q^71 - 18 * q^72 + 8 * q^73 - 8 * q^74 + 3 * q^75 - 16 * q^76 + 48 * q^78 - 10 * q^79 + q^80 - 9 * q^81 - 5 * q^82 - 4 * q^83 + 9 * q^84 + 5 * q^86 - 72 * q^87 + 4 * q^89 + 6 * q^90 + 12 * q^91 - 8 * q^92 - 6 * q^93 - 3 * q^94 - 4 * q^95 - 15 * q^96 + 8 * q^97 - 8 * q^98

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