LMFDB - Embedded newform 1110.2.i.o.211.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1110,2,Mod(121,1110)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1110, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1110.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1110 = 2 \cdot 3 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1110.i (of order $3$, degree $2$, 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:	$8.86339462436$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.45911232.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 11x^{4} - 4x^{3} + 121x^{2} - 22x + 4 $ x^6 + 11x^4 - 4x^3 + 121x^2 - 22x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.2
Root			$1.61084 + 2.79005i$ of defining polynomial
Character	$\chi$	$=$	1110.211
Dual form			1110.2.i.o.121.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.210618 + 0.364801i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.210618 + 0.364801i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -3.22168 q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.500000 + 0.866025i) q^{13} +0.421236 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.28938 - 2.23328i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.11084 - 3.65608i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.210618 + 0.364801i) q^{21} +(1.61084 + 2.79005i) q^{22} -5.60088 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} -1.00000 q^{27} +(-0.210618 - 0.364801i) q^{28} -7.24380 q^{29} +(-0.500000 + 0.866025i) q^{30} -2.44335 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.61084 + 2.79005i) q^{33} +(-1.28938 + 2.23328i) q^{34} +(0.210618 + 0.364801i) q^{35} +1.00000 q^{36} +(-2.07876 - 5.71653i) q^{37} -4.22168 q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +(5.12190 - 8.87139i) q^{41} +(0.210618 - 0.364801i) q^{42} +0.842472 q^{43} +(1.61084 - 2.79005i) q^{44} -1.00000 q^{45} +(2.80044 + 4.85051i) q^{46} -8.82256 q^{47} -1.00000 q^{48} +(3.41128 + 5.90851i) q^{49} +(-0.500000 + 0.866025i) q^{50} -2.57876 q^{51} +(-0.500000 - 0.866025i) q^{52} +(1.32146 + 2.28883i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.61084 + 2.79005i) q^{55} +(-0.210618 + 0.364801i) q^{56} +(-2.11084 - 3.65608i) q^{57} +(3.62190 + 6.27331i) q^{58} +(1.03207 + 1.78761i) q^{59} +1.00000 q^{60} +(0.900221 - 1.55923i) q^{61} +(1.22168 + 2.11601i) q^{62} +0.421236 q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +3.22168 q^{66} +(1.93230 - 3.34683i) q^{67} +2.57876 q^{68} +(-2.80044 + 4.85051i) q^{69} +(0.210618 - 0.364801i) q^{70} +(3.58982 - 6.21776i) q^{71} +(-0.500000 - 0.866025i) q^{72} -8.44335 q^{73} +(-3.91128 + 4.65853i) q^{74} -1.00000 q^{75} +(2.11084 + 3.65608i) q^{76} +(0.678543 - 1.17527i) q^{77} +(0.500000 - 0.866025i) q^{78} +(-7.37921 + 12.7812i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -10.2438 q^{82} +(-7.01106 - 12.1435i) q^{83} -0.421236 q^{84} -2.57876 q^{85} +(-0.421236 - 0.729602i) q^{86} +(-3.62190 + 6.27331i) q^{87} -3.22168 q^{88} +(-3.42124 - 5.92575i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-0.210618 - 0.364801i) q^{91} +(2.80044 - 4.85051i) q^{92} +(-1.22168 + 2.11601i) q^{93} +(4.41128 + 7.64056i) q^{94} +(-2.11084 - 3.65608i) q^{95} +(0.500000 + 0.866025i) q^{96} +2.00000 q^{97} +(3.41128 - 5.90851i) q^{98} +(1.61084 + 2.79005i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - 3 q^{9} - 6 q^{10} + 3 q^{12} - 3 q^{13} + 2 q^{14} - 3 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 3 q^{19} + 3 q^{20} + q^{21} + 4 q^{23} + 3 q^{24} - 3 q^{25} + 6 q^{26} - 6 q^{27} - q^{28} + 14 q^{29} - 3 q^{30} + 24 q^{31} - 3 q^{32} - 8 q^{34} + q^{35} + 6 q^{36} - 13 q^{37} - 6 q^{38} + 3 q^{39} + 3 q^{40} + 2 q^{41} + q^{42} + 4 q^{43} - 6 q^{45} - 2 q^{46} + 4 q^{47} - 6 q^{48} - 8 q^{49} - 3 q^{50} - 16 q^{51} - 3 q^{52} - 2 q^{53} + 3 q^{54} - q^{56} - 3 q^{57} - 7 q^{58} - 4 q^{59} + 6 q^{60} - 4 q^{61} - 12 q^{62} + 2 q^{63} + 6 q^{64} + 3 q^{65} - 8 q^{67} + 16 q^{68} + 2 q^{69} + q^{70} + 3 q^{71} - 3 q^{72} - 12 q^{73} + 5 q^{74} - 6 q^{75} + 3 q^{76} + 14 q^{77} + 3 q^{78} - 26 q^{79} - 6 q^{80} - 3 q^{81} - 4 q^{82} - 23 q^{83} - 2 q^{84} - 16 q^{85} - 2 q^{86} + 7 q^{87} - 20 q^{89} + 3 q^{90} - q^{91} - 2 q^{92} + 12 q^{93} - 2 q^{94} - 3 q^{95} + 3 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - 3 * q^9 - 6 * q^10 + 3 * q^12 - 3 * q^13 + 2 * q^14 - 3 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 3 * q^19 + 3 * q^20 + q^21 + 4 * q^23 + 3 * q^24 - 3 * q^25 + 6 * q^26 - 6 * q^27 - q^28 + 14 * q^29 - 3 * q^30 + 24 * q^31 - 3 * q^32 - 8 * q^34 + q^35 + 6 * q^36 - 13 * q^37 - 6 * q^38 + 3 * q^39 + 3 * q^40 + 2 * q^41 + q^42 + 4 * q^43 - 6 * q^45 - 2 * q^46 + 4 * q^47 - 6 * q^48 - 8 * q^49 - 3 * q^50 - 16 * q^51 - 3 * q^52 - 2 * q^53 + 3 * q^54 - q^56 - 3 * q^57 - 7 * q^58 - 4 * q^59 + 6 * q^60 - 4 * q^61 - 12 * q^62 + 2 * q^63 + 6 * q^64 + 3 * q^65 - 8 * q^67 + 16 * q^68 + 2 * q^69 + q^70 + 3 * q^71 - 3 * q^72 - 12 * q^73 + 5 * q^74 - 6 * q^75 + 3 * q^76 + 14 * q^77 + 3 * q^78 - 26 * q^79 - 6 * q^80 - 3 * q^81 - 4 * q^82 - 23 * q^83 - 2 * q^84 - 16 * q^85 - 2 * q^86 + 7 * q^87 - 20 * q^89 + 3 * q^90 - q^91 - 2 * q^92 + 12 * q^93 - 2 * q^94 - 3 * q^95 + 3 * q^96 + 12 * q^97 - 8 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1110\mathbb{Z}\right)^\times$.

$n$	$371$	$631$	$667$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.00000			−0.408248
$7$	−0.210618	+	0.364801i	−0.0796061	+	0.137882i	−0.903080	−	0.429472i	$-0.858700\pi$
$7$	−0.210618	+	0.364801i	−0.0796061	+	0.137882i	0.823474	+	0.567354i	$0.192033\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−1.00000			−0.316228
$11$	−3.22168			−0.971372			−0.485686	−	0.874133i	$-0.661430\pi$
$11$	−3.22168			−0.971372			−0.485686	+	0.874133i	$0.661430\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$	0.421236			0.112580
$15$	−0.500000	−	0.866025i	−0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.28938	−	2.23328i	−0.312721	−	0.541649i	0.666229	−	0.745747i	$-0.267907\pi$
$17$	−1.28938	−	2.23328i	−0.312721	−	0.541649i	−0.978950	+	0.204098i	$0.934574\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	2.11084	−	3.65608i	0.484260	−	0.838762i	−0.515577	−	0.856843i	$-0.672422\pi$
$19$	2.11084	−	3.65608i	0.484260	−	0.838762i	0.999837	+	0.0180811i	$0.00575569\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	0.210618	+	0.364801i	0.0459606	+	0.0796061i
$22$	1.61084	+	2.79005i	0.343432	+	0.594842i
$23$	−5.60088			−1.16786			−0.583932	−	0.811802i	$-0.698487\pi$
$23$	−5.60088			−1.16786			−0.583932	+	0.811802i	$0.698487\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	1.00000			0.196116
$27$	−1.00000			−0.192450
$28$	−0.210618	−	0.364801i	−0.0398031	−	0.0689409i
$29$	−7.24380			−1.34514			−0.672570	−	0.740034i	$-0.734809\pi$
$29$	−7.24380			−1.34514			−0.672570	+	0.740034i	$0.734809\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	−2.44335			−0.438839			−0.219420	−	0.975631i	$-0.570416\pi$
$31$	−2.44335			−0.438839			−0.219420	+	0.975631i	$0.570416\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.61084	+	2.79005i	−0.280411	+	0.485686i
$34$	−1.28938	+	2.23328i	−0.221127	+	0.383004i
$35$	0.210618	+	0.364801i	0.0356009	+	0.0616626i
$36$	1.00000			0.166667
$37$	−2.07876	−	5.71653i	−0.341747	−	0.939792i
$37$	−2.07876	−	5.71653i	−0.341747	−	0.939792i
$38$	−4.22168			−0.684847
$39$	0.500000	+	0.866025i	0.0800641	+	0.138675i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	5.12190	−	8.87139i	0.799906	−	1.38548i	−0.119771	−	0.992802i	$-0.538216\pi$
$41$	5.12190	−	8.87139i	0.799906	−	1.38548i	0.919677	−	0.392676i	$-0.128451\pi$
$42$	0.210618	−	0.364801i	0.0324991	−	0.0562900i
$43$	0.842472			0.128476			0.0642379	−	0.997935i	$-0.479538\pi$
$43$	0.842472			0.128476			0.0642379	+	0.997935i	$0.479538\pi$
$44$	1.61084	−	2.79005i	0.242843	−	0.420617i
$45$	−1.00000			−0.149071
$46$	2.80044	+	4.85051i	0.412903	+	0.715168i
$47$	−8.82256			−1.28690			−0.643451	−	0.765487i	$-0.722498\pi$
$47$	−8.82256			−1.28690			−0.643451	+	0.765487i	$0.722498\pi$
$48$	−1.00000			−0.144338
$49$	3.41128	+	5.90851i	0.487326	+	0.844073i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−2.57876			−0.361099
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	1.32146	+	2.28883i	0.181516	+	0.314395i	0.942397	−	0.334496i	$-0.108566\pi$
$53$	1.32146	+	2.28883i	0.181516	+	0.314395i	−0.760881	+	0.648891i	$0.775233\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$	−1.61084	+	2.79005i	−0.217205	+	0.376211i
$56$	−0.210618	+	0.364801i	−0.0281450	+	0.0487486i
$57$	−2.11084	−	3.65608i	−0.279587	−	0.484260i
$58$	3.62190	+	6.27331i	0.475579	+	0.823726i
$59$	1.03207	+	1.78761i	0.134365	+	0.232726i	0.925355	−	0.379103i	$-0.123767\pi$
$59$	1.03207	+	1.78761i	0.134365	+	0.232726i	−0.790990	+	0.611829i	$0.790434\pi$
$60$	1.00000			0.129099
$61$	0.900221	−	1.55923i	0.115261	−	0.199639i	−0.802623	−	0.596487i	$-0.796563\pi$
$61$	0.900221	−	1.55923i	0.115261	−	0.199639i	0.917884	+	0.396848i	$0.129896\pi$
$62$	1.22168	+	2.11601i	0.155153	+	0.268733i
$63$	0.421236			0.0530707
$64$	1.00000			0.125000
$65$	0.500000	+	0.866025i	0.0620174	+	0.107417i
$66$	3.22168			0.396561
$67$	1.93230	−	3.34683i	0.236067	−	0.408881i	−0.723515	−	0.690309i	$-0.757475\pi$
$67$	1.93230	−	3.34683i	0.236067	−	0.408881i	0.959582	+	0.281428i	$0.0908080\pi$
$68$	2.57876			0.312721
$69$	−2.80044	+	4.85051i	−0.337134	+	0.583932i
$70$	0.210618	−	0.364801i	0.0251737	−	0.0436021i
$71$	3.58982	−	6.21776i	0.426034	−	0.737912i	−0.570483	−	0.821310i	$-0.693244\pi$
$71$	3.58982	−	6.21776i	0.426034	−	0.737912i	0.996516	+	0.0833977i	$0.0265772\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−8.44335			−0.988220			−0.494110	−	0.869399i	$-0.664506\pi$
$73$	−8.44335			−0.988220			−0.494110	+	0.869399i	$0.664506\pi$
$74$	−3.91128	+	4.65853i	−0.454677	+	0.541543i
$75$	−1.00000			−0.115470
$76$	2.11084	+	3.65608i	0.242130	+	0.419381i
$77$	0.678543	−	1.17527i	0.0773272	−	0.133935i
$78$	0.500000	−	0.866025i	0.0566139	−	0.0980581i
$79$	−7.37921	+	12.7812i	−0.830225	+	1.43799i	0.0676338	+	0.997710i	$0.478455\pi$
$79$	−7.37921	+	12.7812i	−0.830225	+	1.43799i	−0.897859	+	0.440282i	$0.854878\pi$
$80$	−1.00000			−0.111803
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−10.2438			−1.13124
$83$	−7.01106	−	12.1435i	−0.769564	−	1.33292i	−0.937800	−	0.347177i	$-0.887140\pi$
$83$	−7.01106	−	12.1435i	−0.769564	−	1.33292i	0.168236	−	0.985747i	$-0.446193\pi$
$84$	−0.421236			−0.0459606
$85$	−2.57876			−0.279706
$86$	−0.421236	−	0.729602i	−0.0454230	−	0.0786750i
$87$	−3.62190	+	6.27331i	−0.388308	+	0.672570i
$88$	−3.22168			−0.343432
$89$	−3.42124	−	5.92575i	−0.362650	−	0.628129i	0.625746	−	0.780027i	$-0.284795\pi$
$89$	−3.42124	−	5.92575i	−0.362650	−	0.628129i	−0.988396	+	0.151898i	$0.951461\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−0.210618	−	0.364801i	−0.0220788	−	0.0382415i
$92$	2.80044	−	4.85051i	0.291966	−	0.505700i
$93$	−1.22168	+	2.11601i	−0.126682	+	0.219420i
$94$	4.41128	+	7.64056i	0.454989	+	0.788064i
$95$	−2.11084	−	3.65608i	−0.216567	−	0.375106i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	2.00000			0.203069			0.101535	−	0.994832i	$-0.467625\pi$
$97$	2.00000			0.203069			0.101535	+	0.994832i	$0.467625\pi$
$98$	3.41128	−	5.90851i	0.344591	−	0.596850i
$99$	1.61084	+	2.79005i	0.161895	+	0.280411i
$100$	1.00000			0.100000
$101$	10.1796			1.01291			0.506456	−	0.862266i	$-0.330955\pi$
$101$	10.1796			1.01291			0.506456	+	0.862266i	$0.330955\pi$
$102$	1.28938	+	2.23328i	0.127668	+	0.221127i
$103$	6.86459			0.676388			0.338194	−	0.941076i	$-0.390184\pi$
$103$	6.86459			0.676388			0.338194	+	0.941076i	$0.390184\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$	0.421236			0.0411084
$106$	1.32146	−	2.28883i	0.128351	−	0.222311i
$107$	−8.76481	+	15.1811i	−0.847326	+	1.46761i	0.0362592	+	0.999342i	$0.488456\pi$
$107$	−8.76481	+	15.1811i	−0.847326	+	1.46761i	−0.883586	+	0.468270i	$0.844878\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	10.1440	+	17.5700i	0.971621	+	1.68290i	0.690664	+	0.723176i	$0.257318\pi$
$109$	10.1440	+	17.5700i	0.971621	+	1.68290i	0.280957	+	0.959720i	$0.409348\pi$
$110$	3.22168			0.307175
$111$	−5.99004	−	1.05800i	−0.568550	−	0.100421i
$112$	0.421236			0.0398031
$113$	−1.20066	−	2.07961i	−0.112949	−	0.195633i	0.804009	−	0.594617i	$-0.202696\pi$
$113$	−1.20066	−	2.07961i	−0.112949	−	0.195633i	−0.916958	+	0.398984i	$0.869363\pi$
$114$	−2.11084	+	3.65608i	−0.197698	+	0.342423i
$115$	−2.80044	+	4.85051i	−0.261143	+	0.452312i
$116$	3.62190	−	6.27331i	0.336285	−	0.582462i
$117$	1.00000			0.0924500
$118$	1.03207	−	1.78761i	0.0950102	−	0.164562i
$119$	1.08627			0.0995780
$120$	−0.500000	−	0.866025i	−0.0456435	−	0.0790569i
$121$	−0.620795			−0.0564359
$122$	−1.80044			−0.163004
$123$	−5.12190	−	8.87139i	−0.461826	−	0.799906i
$124$	1.22168	−	2.11601i	0.109710	−	0.190023i
$125$	−1.00000			−0.0894427
$126$	−0.210618	−	0.364801i	−0.0187633	−	0.0324991i
$127$	−1.58982	−	2.75365i	−0.141074	−	0.244347i	0.786827	−	0.617173i	$-0.211722\pi$
$127$	−1.58982	−	2.75365i	−0.141074	−	0.244347i	−0.927901	+	0.372826i	$0.878389\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	0.421236	−	0.729602i	0.0370878	−	0.0642379i
$130$	0.500000	−	0.866025i	0.0438529	−	0.0759555i
$131$	0.810397	+	1.40365i	0.0708047	+	0.122637i	0.899254	−	0.437426i	$-0.144110\pi$
$131$	0.810397	+	1.40365i	0.0708047	+	0.122637i	−0.828449	+	0.560064i	$0.810777\pi$
$132$	−1.61084	−	2.79005i	−0.140206	−	0.242843i
$133$	0.889161	+	1.54007i	0.0771001	+	0.133541i
$134$	−3.86459			−0.333850
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	−1.28938	−	2.23328i	−0.110564	−	0.191502i
$137$	15.6429			1.33646			0.668232	−	0.743953i	$-0.267051\pi$
$137$	15.6429			1.33646			0.668232	+	0.743953i	$0.267051\pi$
$138$	5.60088			0.476779
$139$	4.95797	+	8.58745i	0.420529	+	0.728378i	0.995991	−	0.0894502i	$-0.0285110\pi$
$139$	4.95797	+	8.58745i	0.420529	+	0.728378i	−0.575462	+	0.817829i	$0.695178\pi$
$140$	−0.421236			−0.0356009
$141$	−4.41128	+	7.64056i	−0.371497	+	0.643451i
$142$	−7.17965			−0.602503
$143$	1.61084	−	2.79005i	0.134705	−	0.233316i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.62190	+	6.27331i	−0.300782	+	0.520970i
$146$	4.22168	+	7.31216i	0.349389	+	0.605159i
$147$	6.82256			0.562715
$148$	5.99004	+	1.05800i	0.492379	+	0.0869674i
$149$	−5.19956			−0.425964			−0.212982	−	0.977056i	$-0.568318\pi$
$149$	−5.19956			−0.425964			−0.212982	+	0.977056i	$0.568318\pi$
$150$	0.500000	+	0.866025i	0.0408248	+	0.0707107i
$151$	0.620795	−	1.07525i	0.0505195	−	0.0875024i	−0.839660	−	0.543113i	$-0.817246\pi$
$151$	0.620795	−	1.07525i	0.0505195	−	0.0875024i	0.890179	+	0.455610i	$0.150579\pi$
$152$	2.11084	−	3.65608i	0.171212	−	0.296547i
$153$	−1.28938	+	2.23328i	−0.104240	+	0.180550i
$154$	−1.35709			−0.109357
$155$	−1.22168	+	2.11601i	−0.0981275	+	0.169962i
$156$	−1.00000			−0.0800641
$157$	−9.16503	−	15.8743i	−0.731449	−	1.26691i	−0.956264	−	0.292506i	$-0.905511\pi$
$157$	−9.16503	−	15.8743i	−0.731449	−	1.26691i	0.224815	−	0.974402i	$-0.427822\pi$
$158$	14.7584			1.17412
$159$	2.64291			0.209597
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	1.17965	−	2.04321i	0.0929692	−	0.161027i
$162$	1.00000			0.0785674
$163$	−1.06770	−	1.84932i	−0.0836291	−	0.144850i	0.821177	−	0.570673i	$-0.193318\pi$
$163$	−1.06770	−	1.84932i	−0.0836291	−	0.144850i	−0.904806	+	0.425824i	$0.859984\pi$
$164$	5.12190	+	8.87139i	0.399953	+	0.692739i
$165$	1.61084	+	2.79005i	0.125404	+	0.217205i
$166$	−7.01106	+	12.1435i	−0.544164	+	0.942519i
$167$	8.25375	−	14.2959i	0.638695	−	1.10625i	−0.347025	−	0.937856i	$-0.612808\pi$
$167$	8.25375	−	14.2959i	0.638695	−	1.10625i	0.985720	−	0.168395i	$-0.0538586\pi$
$168$	0.210618	+	0.364801i	0.0162495	+	0.0281450i
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	1.28938	+	2.23328i	0.0988911	+	0.171284i
$171$	−4.22168			−0.322840
$172$	−0.421236	+	0.729602i	−0.0321189	+	0.0556316i
$173$	−9.34358	−	16.1835i	−0.710379	−	1.23041i	−0.964715	−	0.263296i	$-0.915190\pi$
$173$	−9.34358	−	16.1835i	−0.710379	−	1.23041i	0.254336	−	0.967116i	$-0.418143\pi$
$174$	7.24380			0.549151
$175$	0.421236			0.0318424
$176$	1.61084	+	2.79005i	0.121422	+	0.210308i
$177$	2.06415			0.155151
$178$	−3.42124	+	5.92575i	−0.256432	+	0.444154i
$179$	5.15753			0.385492			0.192746	−	0.981249i	$-0.438261\pi$
$179$	5.15753			0.385492			0.192746	+	0.981249i	$0.438261\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	8.60088	−	14.8972i	0.639299	−	1.10730i	−0.346288	−	0.938128i	$-0.612558\pi$
$181$	8.60088	−	14.8972i	0.639299	−	1.10730i	0.985587	−	0.169170i	$-0.0541085\pi$
$182$	−0.210618	+	0.364801i	−0.0156120	+	0.0270409i
$183$	−0.900221	−	1.55923i	−0.0665462	−	0.115261i
$184$	−5.60088			−0.412903
$185$	−5.99004	−	1.05800i	−0.440397	−	0.0777860i
$186$	2.44335			0.179155
$187$	4.15397	+	7.19489i	0.303769	+	0.526143i
$188$	4.41128	−	7.64056i	0.321726	−	0.557245i
$189$	0.210618	−	0.364801i	0.0153202	−	0.0265354i
$190$	−2.11084	+	3.65608i	−0.153136	+	0.265240i
$191$	−0.243796			−0.0176405			−0.00882024	−	0.999961i	$-0.502808\pi$
$191$	−0.243796			−0.0176405			−0.00882024	+	0.999961i	$0.502808\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	9.71638			0.699400			0.349700	−	0.936862i	$-0.386283\pi$
$193$	9.71638			0.699400			0.349700	+	0.936862i	$0.386283\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$	1.00000			0.0716115
$196$	−6.82256			−0.487326
$197$	−12.0863	−	20.9340i	−0.861111	−	1.49149i	−0.870858	−	0.491535i	$-0.836436\pi$
$197$	−12.0863	−	20.9340i	−0.861111	−	1.49149i	0.00974662	−	0.999953i	$-0.496898\pi$
$198$	1.61084	−	2.79005i	0.114477	−	0.198281i
$199$	−4.97788			−0.352873			−0.176436	−	0.984312i	$-0.556457\pi$
$199$	−4.97788			−0.352873			−0.176436	+	0.984312i	$0.556457\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	−1.93230	−	3.34683i	−0.136294	−	0.236067i
$202$	−5.08982	−	8.81583i	−0.358119	−	0.620280i
$203$	1.52567	−	2.64254i	0.107081	−	0.185470i
$204$	1.28938	−	2.23328i	0.0902748	−	0.156361i
$205$	−5.12190	−	8.87139i	−0.357729	−	0.619605i
$206$	−3.43230	−	5.94491i	−0.239139	−	0.414202i
$207$	2.80044	+	4.85051i	0.194644	+	0.337134i
$208$	1.00000			0.0693375
$209$	−6.80044	+	11.7787i	−0.470396	+	0.814750i
$210$	−0.210618	−	0.364801i	−0.0145340	−	0.0251737i
$211$	12.5367			0.863064			0.431532	−	0.902098i	$-0.357973\pi$
$211$	12.5367			0.863064			0.431532	+	0.902098i	$0.357973\pi$
$212$	−2.64291			−0.181516
$213$	−3.58982	−	6.21776i	−0.245971	−	0.426034i
$214$	17.5296			1.19830
$215$	0.421236	−	0.729602i	0.0287281	−	0.0497585i
$216$	−1.00000			−0.0680414
$217$	0.514615	−	0.891339i	0.0349343	−	0.0605080i
$218$	10.1440	−	17.5700i	0.687040	−	1.18999i
$219$	−4.22168	+	7.31216i	−0.285275	+	0.494110i
$220$	−1.61084	−	2.79005i	−0.108603	−	0.188105i
$221$	2.57876			0.173466
$222$	2.07876	+	5.71653i	0.139518	+	0.383669i
$223$	−12.8867			−0.862958			−0.431479	−	0.902123i	$-0.642008\pi$
$223$	−12.8867			−0.862958			−0.431479	+	0.902123i	$0.642008\pi$
$224$	−0.210618	−	0.364801i	−0.0140725	−	0.0243743i
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$	−1.20066	+	2.07961i	−0.0798669	+	0.138333i
$227$	1.01106	−	1.75121i	0.0671064	−	0.116232i	−0.830520	−	0.556989i	$-0.811957\pi$
$227$	1.01106	−	1.75121i	0.0671064	−	0.116232i	0.897626	+	0.440757i	$0.145290\pi$
$228$	4.22168			0.279587
$229$	−1.09978	+	1.90487i	−0.0726755	+	0.125878i	−0.900073	−	0.435739i	$-0.856487\pi$
$229$	−1.09978	+	1.90487i	−0.0726755	+	0.125878i	0.827398	+	0.561617i	$0.189820\pi$
$230$	5.60088			0.369311
$231$	−0.678543	−	1.17527i	−0.0446449	−	0.0773272i
$232$	−7.24380			−0.475579
$233$	23.8226			1.56067			0.780334	−	0.625363i	$-0.215049\pi$
$233$	23.8226			1.56067			0.780334	+	0.625363i	$0.215049\pi$
$234$	−0.500000	−	0.866025i	−0.0326860	−	0.0566139i
$235$	−4.41128	+	7.64056i	−0.287760	+	0.498415i
$236$	−2.06415			−0.134365
$237$	7.37921	+	12.7812i	0.479331	+	0.830225i
$238$	−0.543134	−	0.940736i	−0.0352062	−	0.0609789i
$239$	−3.11084	−	5.38813i	−0.201223	−	0.348529i	0.747699	−	0.664037i	$-0.231158\pi$
$239$	−3.11084	−	5.38813i	−0.201223	−	0.348529i	−0.948923	+	0.315508i	$0.897825\pi$
$240$	−0.500000	+	0.866025i	−0.0322749	+	0.0559017i
$241$	11.9900	−	20.7674i	0.772347	−	1.33774i	−0.163927	−	0.986472i	$-0.552416\pi$
$241$	11.9900	−	20.7674i	0.772347	−	1.33774i	0.936274	−	0.351271i	$-0.114250\pi$
$242$	0.310397	+	0.537624i	0.0199531	+	0.0345598i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	0.900221	+	1.55923i	0.0576307	+	0.0998193i
$245$	6.82256			0.435877
$246$	−5.12190	+	8.87139i	−0.326560	+	0.565619i
$247$	2.11084	+	3.65608i	0.134309	+	0.232631i
$248$	−2.44335			−0.155153
$249$	−14.0221			−0.888616
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	17.2659			1.08981			0.544907	−	0.838496i	$-0.316565\pi$
$251$	17.2659			1.08981			0.544907	+	0.838496i	$0.316565\pi$
$252$	−0.210618	+	0.364801i	−0.0132677	+	0.0229803i
$253$	18.0442			1.13443
$254$	−1.58982	+	2.75365i	−0.0997544	+	0.172780i
$255$	−1.28938	+	2.23328i	−0.0807442	+	0.139853i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−1.64402	−	2.84752i	−0.102551	−	0.177623i	0.810184	−	0.586176i	$-0.199367\pi$
$257$	−1.64402	−	2.84752i	−0.102551	−	0.177623i	−0.912735	+	0.408552i	$0.866034\pi$
$258$	−0.842472			−0.0524500
$259$	2.52322	+	0.445669i	0.156785	+	0.0276925i
$260$	−1.00000			−0.0620174
$261$	3.62190	+	6.27331i	0.224190	+	0.388308i
$262$	0.810397	−	1.40365i	0.0500665	−	0.0867177i
$263$	−11.8867	+	20.5884i	−0.732966	+	1.26953i	0.222644	+	0.974900i	$0.428531\pi$
$263$	−11.8867	+	20.5884i	−0.732966	+	1.26953i	−0.955610	+	0.294634i	$0.904802\pi$
$264$	−1.61084	+	2.79005i	−0.0991403	+	0.171716i
$265$	2.64291			0.162353
$266$	0.889161	−	1.54007i	0.0545180	−	0.0944279i
$267$	−6.84247			−0.418752
$268$	1.93230	+	3.34683i	0.118034	+	0.204440i
$269$	30.7933			1.87750			0.938751	−	0.344595i	$-0.111984\pi$
$269$	30.7933			1.87750			0.938751	+	0.344595i	$0.111984\pi$
$270$	1.00000			0.0608581
$271$	−9.51106	−	16.4736i	−0.577756	−	1.00070i	−0.995736	−	0.0922463i	$-0.970595\pi$
$271$	−9.51106	−	16.4736i	−0.577756	−	1.00070i	0.417981	−	0.908456i	$-0.362738\pi$
$272$	−1.28938	+	2.23328i	−0.0781803	+	0.135412i
$273$	−0.421236			−0.0254944
$274$	−7.82146	−	13.5472i	−0.472511	−	0.818414i
$275$	1.61084	+	2.79005i	0.0971372	+	0.168247i
$276$	−2.80044	−	4.85051i	−0.168567	−	0.291966i
$277$	5.90132	−	10.2214i	0.354576	−	0.614144i	−0.632469	−	0.774586i	$-0.717958\pi$
$277$	5.90132	−	10.2214i	0.354576	−	0.614144i	0.987045	+	0.160442i	$0.0512918\pi$
$278$	4.95797	−	8.58745i	0.297359	−	0.515041i
$279$	1.22168	+	2.11601i	0.0731399	+	0.126682i
$280$	0.210618	+	0.364801i	0.0125868	+	0.0218010i
$281$	−9.02212	−	15.6268i	−0.538214	−	0.932215i	−0.999000	−	0.0447035i	$-0.985766\pi$
$281$	−9.02212	−	15.6268i	−0.538214	−	0.932215i	0.460786	−	0.887511i	$-0.347568\pi$
$282$	8.82256			0.525376
$283$	1.73274	−	3.00119i	0.103001	−	0.178402i	−0.809919	−	0.586542i	$-0.800489\pi$
$283$	1.73274	−	3.00119i	0.103001	−	0.178402i	0.912920	+	0.408140i	$0.133822\pi$
$284$	3.58982	+	6.21776i	0.213017	+	0.368956i
$285$	−4.22168			−0.250071
$286$	−3.22168			−0.190502
$287$	2.15753	+	3.73695i	0.127355	+	0.220585i
$288$	1.00000			0.0589256
$289$	5.17499	−	8.96334i	0.304411	−	0.527255i
$290$	7.24380			0.425370
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	4.22168	−	7.31216i	0.247055	−	0.427912i
$293$	3.95797	−	6.85540i	0.231227	−	0.400497i	−0.726942	−	0.686698i	$-0.759059\pi$
$293$	3.95797	−	6.85540i	0.231227	−	0.400497i	0.958169	+	0.286201i	$0.0923926\pi$
$294$	−3.41128	−	5.90851i	−0.198950	−	0.344591i
$295$	2.06415			0.120179
$296$	−2.07876	−	5.71653i	−0.120826	−	0.332267i
$297$	3.22168			0.186941
$298$	2.59978	+	4.50295i	0.150601	+	0.260849i
$299$	2.80044	−	4.85051i	0.161954	−	0.280512i
$300$	0.500000	−	0.866025i	0.0288675	−	0.0500000i
$301$	−0.177440	+	0.307335i	−0.0102275	+	0.0177145i
$302$	−1.24159			−0.0714454
$303$	5.08982	−	8.81583i	0.292403	−	0.506456i
$304$	−4.22168			−0.242130
$305$	−0.900221	−	1.55923i	−0.0515465	−	0.0892811i
$306$	2.57876			0.147418
$307$	−0.128299			−0.00732241			−0.00366120	−	0.999993i	$-0.501165\pi$
$307$	−0.128299			−0.00732241			−0.00366120	+	0.999993i	$0.501165\pi$
$308$	0.678543	+	1.17527i	0.0386636	+	0.0669673i
$309$	3.43230	−	5.94491i	0.195256	−	0.338194i
$310$	2.44335			0.138773
$311$	−11.3436	−	19.6476i	−0.643235	−	1.11412i	−0.984706	−	0.174224i	$-0.944258\pi$
$311$	−11.3436	−	19.6476i	−0.643235	−	1.11412i	0.341471	−	0.939892i	$-0.389075\pi$
$312$	0.500000	+	0.866025i	0.0283069	+	0.0490290i
$313$	−5.86459	−	10.1578i	−0.331486	−	0.574151i	0.651317	−	0.758806i	$-0.274217\pi$
$313$	−5.86459	−	10.1578i	−0.331486	−	0.574151i	−0.982804	+	0.184654i	$0.940883\pi$
$314$	−9.16503	+	15.8743i	−0.517213	+	0.895839i
$315$	0.210618	−	0.364801i	0.0118670	−	0.0205542i
$316$	−7.37921	−	12.7812i	−0.415113	−	0.718996i
$317$	10.7228	+	18.5724i	0.602251	+	1.04313i	0.992479	+	0.122412i	$0.0390628\pi$
$317$	10.7228	+	18.5724i	0.602251	+	1.04313i	−0.390228	+	0.920718i	$0.627604\pi$
$318$	−1.32146	−	2.28883i	−0.0741036	−	0.128351i
$319$	23.3372			1.30663
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	8.76481	+	15.1811i	0.489204	+	0.847326i
$322$	−2.35929			−0.131478
$323$	−10.8867			−0.605753
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	1.00000			0.0554700
$326$	−1.06770	+	1.84932i	−0.0591347	+	0.102424i
$327$	20.2880			1.12193
$328$	5.12190	−	8.87139i	0.282810	−	0.489840i
$329$	1.85819	−	3.21848i	0.102445	−	0.177441i
$330$	1.61084	−	2.79005i	0.0886738	−	0.153587i
$331$	8.05309	+	13.9484i	0.442638	+	0.766671i	0.997884	−	0.0650146i	$-0.0207094\pi$
$331$	8.05309	+	13.9484i	0.442638	+	0.766671i	−0.555246	+	0.831686i	$0.687376\pi$
$332$	14.0221			0.769564
$333$	−3.91128	+	4.65853i	−0.214337	+	0.255286i
$334$	−16.5075			−0.903250
$335$	−1.93230	−	3.34683i	−0.105573	−	0.182857i
$336$	0.210618	−	0.364801i	0.0114902	−	0.0199015i
$337$	12.4591	−	21.5797i	0.678689	−	1.17552i	−0.296687	−	0.954975i	$-0.595882\pi$
$337$	12.4591	−	21.5797i	0.678689	−	1.17552i	0.975376	−	0.220549i	$-0.0707849\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$	−2.40132			−0.130422
$340$	1.28938	−	2.23328i	0.0699266	−	0.121116i
$341$	7.87170			0.426277
$342$	2.11084	+	3.65608i	0.114141	+	0.197698i
$343$	−5.82256			−0.314389
$344$	0.842472			0.0454230
$345$	2.80044	+	4.85051i	0.150771	+	0.261143i
$346$	−9.34358	+	16.1835i	−0.502314	+	0.870033i
$347$	−6.49250			−0.348535			−0.174268	−	0.984698i	$-0.555756\pi$
$347$	−6.49250			−0.348535			−0.174268	+	0.984698i	$0.555756\pi$
$348$	−3.62190	−	6.27331i	−0.194154	−	0.336285i
$349$	11.6009	+	20.0933i	0.620981	+	1.07557i	0.989303	+	0.145873i	$0.0465989\pi$
$349$	11.6009	+	20.0933i	0.620981	+	1.07557i	−0.368322	+	0.929698i	$0.620068\pi$
$350$	−0.210618	−	0.364801i	−0.0112580	−	0.0194994i
$351$	0.500000	−	0.866025i	0.0266880	−	0.0462250i
$352$	1.61084	−	2.79005i	0.0858580	−	0.148710i
$353$	−2.31040	−	4.00173i	−0.122970	−	0.212990i	0.797968	−	0.602700i	$-0.205909\pi$
$353$	−2.31040	−	4.00173i	−0.122970	−	0.212990i	−0.920938	+	0.389710i	$0.872575\pi$
$354$	−1.03207	−	1.78761i	−0.0548542	−	0.0950102i
$355$	−3.58982	−	6.21776i	−0.190528	−	0.330004i
$356$	6.84247			0.362650
$357$	0.543134	−	0.940736i	0.0287457	−	0.0497890i
$358$	−2.57876	−	4.46655i	−0.136292	−	0.236065i
$359$	−7.42344			−0.391794			−0.195897	−	0.980624i	$-0.562762\pi$
$359$	−7.42344			−0.391794			−0.195897	+	0.980624i	$0.562762\pi$
$360$	−1.00000			−0.0527046
$361$	0.588720	+	1.01969i	0.0309853	+	0.0536680i
$362$	−17.2018			−0.904105
$363$	−0.310397	+	0.537624i	−0.0162916	+	0.0282179i
$364$	0.421236			0.0220788
$365$	−4.22168	+	7.31216i	−0.220973	+	0.382736i
$366$	−0.900221	+	1.55923i	−0.0470553	+	0.0815022i
$367$	−2.49004	+	4.31288i	−0.129979	+	0.225131i	−0.923668	−	0.383193i	$-0.874824\pi$
$367$	−2.49004	+	4.31288i	−0.129979	+	0.225131i	0.793689	+	0.608324i	$0.208158\pi$
$368$	2.80044	+	4.85051i	0.145983	+	0.252850i
$369$	−10.2438			−0.533271
$370$	2.07876	+	5.71653i	0.108070	+	0.297188i
$371$	−1.11329			−0.0577992
$372$	−1.22168	−	2.11601i	−0.0633410	−	0.109710i
$373$	14.1971	−	24.5901i	0.735098	−	1.27323i	−0.219582	−	0.975594i	$-0.570469\pi$
$373$	14.1971	−	24.5901i	0.735098	−	1.27323i	0.954680	−	0.297634i	$-0.0961974\pi$
$374$	4.15397	−	7.19489i	0.214797	−	0.372039i
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	−8.82256			−0.454989
$377$	3.62190	−	6.27331i	0.186537	−	0.323092i
$378$	−0.421236			−0.0216660
$379$	−0.410177	−	0.710447i	−0.0210694	−	0.0364932i	0.855298	−	0.518136i	$-0.173374\pi$
$379$	−0.410177	−	0.710447i	−0.0210694	−	0.0364932i	−0.876368	+	0.481642i	$0.840040\pi$
$380$	4.22168			0.216567
$381$	−3.17965			−0.162898
$382$	0.121898	+	0.211134i	0.00623685	+	0.0108025i
$383$	−2.56881	+	4.44931i	−0.131260	+	0.227349i	−0.924163	−	0.382000i	$-0.875236\pi$
$383$	−2.56881	+	4.44931i	−0.131260	+	0.227349i	0.792903	+	0.609348i	$0.208569\pi$
$384$	−1.00000			−0.0510310
$385$	−0.678543	−	1.17527i	−0.0345818	−	0.0598974i
$386$	−4.85819	−	8.41463i	−0.247275	−	0.428293i
$387$	−0.421236	−	0.729602i	−0.0214126	−	0.0370878i
$388$	−1.00000	+	1.73205i	−0.0507673	+	0.0879316i
$389$	−15.5343	+	26.9062i	−0.787619	+	1.36420i	0.139802	+	0.990179i	$0.455353\pi$
$389$	−15.5343	+	26.9062i	−0.787619	+	1.36420i	−0.927422	+	0.374017i	$0.877980\pi$
$390$	−0.500000	−	0.866025i	−0.0253185	−	0.0438529i
$391$	7.22168	+	12.5083i	0.365216	+	0.632573i
$392$	3.41128	+	5.90851i	0.172296	+	0.298425i
$393$	1.62079			0.0817583
$394$	−12.0863	+	20.9340i	−0.608897	+	1.05464i
$395$	7.37921	+	12.7812i	0.371288	+	0.643090i
$396$	−3.22168			−0.161895
$397$	12.3792			0.621295			0.310647	−	0.950525i	$-0.399454\pi$
$397$	12.3792			0.621295			0.310647	+	0.950525i	$0.399454\pi$
$398$	2.48894	+	4.31097i	0.124759	+	0.216089i
$399$	1.77832			0.0890275
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	−8.32786			−0.415873			−0.207937	−	0.978142i	$-0.566675\pi$
$401$	−8.32786			−0.415873			−0.207937	+	0.978142i	$0.566675\pi$
$402$	−1.93230	+	3.34683i	−0.0963741	+	0.166925i
$403$	1.22168	−	2.11601i	0.0608561	−	0.105406i
$404$	−5.08982	+	8.81583i	−0.253228	+	0.438604i
$405$	0.500000	+	0.866025i	0.0248452	+	0.0430331i
$406$	−3.05135			−0.151436
$407$	6.69711	+	18.4168i	0.331963	+	0.912888i
$408$	−2.57876			−0.127668
$409$	2.30044	+	3.98448i	0.113750	+	0.197020i	0.917279	−	0.398245i	$-0.130381\pi$
$409$	2.30044	+	3.98448i	0.113750	+	0.197020i	−0.803530	+	0.595265i	$0.797047\pi$
$410$	−5.12190	+	8.87139i	−0.252953	+	0.438127i
$411$	7.82146	−	13.5472i	0.385804	−	0.668232i
$412$	−3.43230	+	5.94491i	−0.169097	+	0.292885i
$413$	−0.869494			−0.0427850
$414$	2.80044	−	4.85051i	0.137634	−	0.238389i
$415$	−14.0221			−0.688319
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	9.91594			0.485586
$418$	13.6009			0.665241
$419$	−11.0221	−	19.0909i	−0.538466	−	0.932650i	−0.998987	−	0.0450013i	$-0.985671\pi$
$419$	−11.0221	−	19.0909i	−0.538466	−	0.932650i	0.460521	−	0.887649i	$-0.347663\pi$
$420$	−0.210618	+	0.364801i	−0.0102771	+	0.0178005i
$421$	−25.8004			−1.25744			−0.628718	−	0.777633i	$-0.716420\pi$
$421$	−25.8004			−1.25744			−0.628718	+	0.777633i	$0.716420\pi$
$422$	−6.26837	−	10.8571i	−0.305139	−	0.528517i
$423$	4.41128	+	7.64056i	0.214484	+	0.371497i
$424$	1.32146	+	2.28883i	0.0641756	+	0.111155i
$425$	−1.28938	+	2.23328i	−0.0625442	+	0.108330i
$426$	−3.58982	+	6.21776i	−0.173928	+	0.301251i
$427$	0.379205	+	0.656803i	0.0183510	+	0.0317849i
$428$	−8.76481	−	15.1811i	−0.423663	−	0.733806i
$429$	−1.61084	−	2.79005i	−0.0777720	−	0.134705i
$430$	−0.842472			−0.0406276
$431$	−2.94691	+	5.10420i	−0.141948	+	0.245861i	−0.928230	−	0.372007i	$-0.878670\pi$
$431$	−2.94691	+	5.10420i	−0.141948	+	0.245861i	0.786282	+	0.617867i	$0.212003\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	14.3151			0.687938			0.343969	−	0.938981i	$-0.388229\pi$
$433$	14.3151			0.687938			0.343969	+	0.938981i	$0.388229\pi$
$434$	−1.02923			−0.0494046
$435$	3.62190	+	6.27331i	0.173657	+	0.300782i
$436$	−20.2880			−0.971621
$437$	−11.8226	+	20.4773i	−0.565550	+	0.979561i
$438$	8.44335			0.403439
$439$	0.553090	−	0.957980i	0.0263975	−	0.0457219i	−0.852525	−	0.522687i	$-0.824930\pi$
$439$	0.553090	−	0.957980i	0.0263975	−	0.0457219i	0.878922	+	0.476965i	$0.158263\pi$
$440$	−1.61084	+	2.79005i	−0.0767937	+	0.133011i
$441$	3.41128	−	5.90851i	0.162442	−	0.281358i
$442$	−1.28938	−	2.23328i	−0.0613296	−	0.106226i
$443$	−14.6522			−0.696148			−0.348074	−	0.937467i	$-0.613164\pi$
$443$	−14.6522			−0.696148			−0.348074	+	0.937467i	$0.613164\pi$
$444$	3.91128	−	4.65853i	0.185621	−	0.221084i
$445$	−6.84247			−0.324364
$446$	6.44335	+	11.1602i	0.305102	+	0.528452i
$447$	−2.59978	+	4.50295i	−0.122965	+	0.212982i
$448$	−0.210618	+	0.364801i	−0.00995077	+	0.0172352i
$449$	−7.60088	+	13.1651i	−0.358708	+	0.621300i	−0.987745	−	0.156075i	$-0.950116\pi$
$449$	−7.60088	+	13.1651i	−0.358708	+	0.621300i	0.629037	+	0.777375i	$0.283449\pi$
$450$	1.00000			0.0471405
$451$	−16.5011	+	28.5807i	−0.777007	+	1.34581i
$452$	2.40132			0.112949
$453$	−0.620795	−	1.07525i	−0.0291675	−	0.0505195i
$454$	−2.02212			−0.0949027
$455$	−0.421236			−0.0197478
$456$	−2.11084	−	3.65608i	−0.0988491	−	0.171212i
$457$	1.97788	−	3.42579i	0.0925214	−	0.160252i	−0.816050	−	0.577981i	$-0.803841\pi$
$457$	1.97788	−	3.42579i	0.0925214	−	0.160252i	0.908571	+	0.417729i	$0.137174\pi$
$458$	2.19956			0.102779
$459$	1.28938	+	2.23328i	0.0601832	+	0.104240i
$460$	−2.80044	−	4.85051i	−0.130571	−	0.226156i
$461$	19.4024	+	33.6060i	0.903661	+	1.56519i	0.822704	+	0.568469i	$0.192464\pi$
$461$	19.4024	+	33.6060i	0.903661	+	1.56519i	0.0809567	+	0.996718i	$0.474202\pi$
$462$	−0.678543	+	1.17527i	−0.0315687	+	0.0546786i
$463$	−0.132958	+	0.230289i	−0.00617906	+	0.0107024i	−0.869098	−	0.494639i	$-0.835300\pi$
$463$	−0.132958	+	0.230289i	−0.00617906	+	0.0107024i	0.862919	+	0.505342i	$0.168634\pi$
$464$	3.62190	+	6.27331i	0.168142	+	0.291231i
$465$	1.22168	+	2.11601i	0.0566539	+	0.0981275i
$466$	−11.9113	−	20.6309i	−0.551779	−	0.955710i
$467$	−7.77832			−0.359938			−0.179969	−	0.983672i	$-0.557600\pi$
$467$	−7.77832			−0.359938			−0.179969	+	0.983672i	$0.557600\pi$
$468$	−0.500000	+	0.866025i	−0.0231125	+	0.0400320i
$469$	0.813952	+	1.40981i	0.0375848	+	0.0650988i
$470$	8.82256			0.406954
$471$	−18.3301			−0.844605
$472$	1.03207	+	1.78761i	0.0475051	+	0.0822812i
$473$	−2.71417			−0.124798
$474$	7.37921	−	12.7812i	0.338938	−	0.587058i
$475$	−4.22168			−0.193704
$476$	−0.543134	+	0.940736i	−0.0248945	+	0.0431186i
$477$	1.32146	−	2.28883i	0.0605053	−	0.104798i
$478$	−3.11084	+	5.38813i	−0.142286	+	0.246447i
$479$	4.06415	+	7.03931i	0.185696	+	0.321634i	0.943811	−	0.330486i	$-0.107213\pi$
$479$	4.06415	+	7.03931i	0.185696	+	0.321634i	−0.758115	+	0.652121i	$0.773879\pi$
$480$	1.00000			0.0456435
$481$	5.99004	+	1.05800i	0.273123	+	0.0482408i
$482$	−23.9801			−1.09226
$483$	−1.17965	−	2.04321i	−0.0536758	−	0.0929692i
$484$	0.310397	−	0.537624i	0.0141090	−	0.0244375i
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−21.2951			−0.964975			−0.482488	−	0.875903i	$-0.660267\pi$
$487$	−21.2951			−0.964975			−0.482488	+	0.875903i	$0.660267\pi$
$488$	0.900221	−	1.55923i	0.0407511	−	0.0705829i
$489$	−2.13541			−0.0965665
$490$	−3.41128	−	5.90851i	−0.154106	−	0.266919i
$491$	17.6009			0.794317			0.397158	−	0.917750i	$-0.369996\pi$
$491$	17.6009			0.794317			0.397158	+	0.917750i	$0.369996\pi$
$492$	10.2438			0.461826
$493$	9.34002	+	16.1774i	0.420653	+	0.728593i
$494$	2.11084	−	3.65608i	0.0949711	−	0.164495i
$495$	3.22168			0.144804
$496$	1.22168	+	2.11601i	0.0548549	+	0.0950115i
$497$	1.51216	+	2.61914i	0.0678298	+	0.117485i
$498$	7.01106	+	12.1435i	0.314173	+	0.544164i
$499$	−4.81150	+	8.33376i	−0.215392	+	0.373071i	−0.953394	−	0.301729i	$-0.902436\pi$
$499$	−4.81150	+	8.33376i	−0.215392	+	0.373071i	0.738002	+	0.674799i	$0.235770\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	−8.25375	−	14.2959i	−0.368750	−	0.638695i
$502$	−8.63296	−	14.9527i	−0.385308	−	0.667373i
$503$	5.21172	+	9.02697i	0.232379	+	0.402493i	0.958508	−	0.285066i	$-0.0920156\pi$
$503$	5.21172	+	9.02697i	0.232379	+	0.402493i	−0.726129	+	0.687559i	$0.758682\pi$
$504$	0.421236			0.0187633
$505$	5.08982	−	8.81583i	0.226494	−	0.392299i
$506$	−9.02212	−	15.6268i	−0.401082	−	0.694695i
$507$	12.0000			0.532939
$508$	3.17965			0.141074
$509$	3.33252	+	5.77209i	0.147711	+	0.255843i	0.930381	−	0.366594i	$-0.119476\pi$
$509$	3.33252	+	5.77209i	0.147711	+	0.255843i	−0.782670	+	0.622437i	$0.786143\pi$
$510$	2.57876			0.114190
$511$	1.77832	−	3.08015i	0.0786684	−	0.136258i
$512$	1.00000			0.0441942
$513$	−2.11084	+	3.65608i	−0.0931958	+	0.161420i
$514$	−1.64402	+	2.84752i	−0.0725145	+	0.125599i
$515$	3.43230	−	5.94491i	0.151245	−	0.261964i
$516$	0.421236	+	0.729602i	0.0185439	+	0.0321189i
$517$	28.4234			1.25006
$518$	−0.875650	−	2.40801i	−0.0384739	−	0.105802i
$519$	−18.6872			−0.820275
$520$	0.500000	+	0.866025i	0.0219265	+	0.0379777i
$521$	8.19956	−	14.2021i	0.359229	−	0.622203i	−0.628603	−	0.777726i	$-0.716373\pi$
$521$	8.19956	−	14.2021i	0.359229	−	0.622203i	0.987832	+	0.155523i	$0.0497063\pi$
$522$	3.62190	−	6.27331i	0.158526	−	0.274575i
$523$	−17.0863	+	29.5943i	−0.747130	+	1.29407i	0.202062	+	0.979373i	$0.435236\pi$
$523$	−17.0863	+	29.5943i	−0.747130	+	1.29407i	−0.949193	+	0.314695i	$0.898098\pi$
$524$	−1.62079			−0.0708047
$525$	0.210618	−	0.364801i	0.00919212	−	0.0159212i
$526$	23.7734			1.03657
$527$	3.15042	+	5.45668i	0.137234	+	0.237697i
$528$	3.22168			0.140206
$529$	8.36989			0.363908
$530$	−1.32146	−	2.28883i	−0.0574004	−	0.0994204i
$531$	1.03207	−	1.78761i	0.0447882	−	0.0775755i
$532$	−1.77832			−0.0771001
$533$	5.12190	+	8.87139i	0.221854	+	0.384262i
$534$	3.42124	+	5.92575i	0.148051	+	0.256432i
$535$	8.76481	+	15.1811i	0.378936	+	0.656336i
$536$	1.93230	−	3.34683i	0.0834625	−	0.144561i
$537$	2.57876	−	4.46655i	0.111282	−	0.192746i
$538$	−15.3967	−	26.6678i	−0.663797	−	1.14973i
$539$	−10.9900	−	19.0353i	−0.473375	−	0.819909i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	17.4013			0.748141			0.374071	−	0.927400i	$-0.377962\pi$
$541$	17.4013			0.748141			0.374071	+	0.927400i	$0.377962\pi$
$542$	−9.51106	+	16.4736i	−0.408535	+	0.707603i
$543$	−8.60088	−	14.8972i	−0.369099	−	0.639299i
$544$	2.57876			0.110564
$545$	20.2880			0.869044
$546$	0.210618	+	0.364801i	0.00901362	+	0.0156120i
$547$	−44.9752			−1.92300			−0.961500	−	0.274805i	$-0.911387\pi$
$547$	−44.9752			−1.92300			−0.961500	+	0.274805i	$0.911387\pi$
$548$	−7.82146	+	13.5472i	−0.334116	+	0.578706i
$549$	−1.80044			−0.0768410
$550$	1.61084	−	2.79005i	0.0686864	−	0.118968i
$551$	−15.2905	+	26.4839i	−0.651397	+	1.12825i
$552$	−2.80044	+	4.85051i	−0.119195	+	0.206451i
$553$	−3.10839	−	5.38388i	−0.132182	−	0.228946i
$554$	−11.8026			−0.501446
$555$	−3.91128	+	4.65853i	−0.166025	+	0.197744i
$556$	−9.91594			−0.420529
$557$	10.6009	+	18.3613i	0.449174	+	0.777992i	0.998332	−	0.0577263i	$-0.0183851\pi$
$557$	10.6009	+	18.3613i	0.449174	+	0.777992i	−0.549159	+	0.835718i	$0.685052\pi$
$558$	1.22168	−	2.11601i	0.0517177	−	0.0895777i
$559$	−0.421236	+	0.729602i	−0.0178164	+	0.0308589i
$560$	0.210618	−	0.364801i	0.00890024	−	0.0154157i
$561$	8.30795			0.350762
$562$	−9.02212	+	15.6268i	−0.380575	+	0.659175i
$563$	−9.09559			−0.383333			−0.191667	−	0.981460i	$-0.561389\pi$
$563$	−9.09559			−0.383333			−0.191667	+	0.981460i	$0.561389\pi$
$564$	−4.41128	−	7.64056i	−0.185748	−	0.321726i
$565$	−2.40132			−0.101024
$566$	−3.46547			−0.145665
$567$	−0.210618	−	0.364801i	−0.00884512	−	0.0153202i
$568$	3.58982	−	6.21776i	0.150626	−	0.260891i
$569$	−38.7314			−1.62370			−0.811852	−	0.583863i	$-0.801540\pi$
$569$	−38.7314			−1.62370			−0.811852	+	0.583863i	$0.801540\pi$
$570$	2.11084	+	3.65608i	0.0884133	+	0.153136i
$571$	0.847131	+	1.46727i	0.0354513	+	0.0614035i	0.883207	−	0.468984i	$-0.155380\pi$
$571$	0.847131	+	1.46727i	0.0354513	+	0.0614035i	−0.847755	+	0.530387i	$0.822046\pi$
$572$	1.61084	+	2.79005i	0.0673525	+	0.116658i
$573$	−0.121898	+	0.211134i	−0.00509237	+	0.00882024i
$574$	2.15753	−	3.73695i	0.0900535	−	0.155977i
$575$	2.80044	+	4.85051i	0.116786	+	0.202280i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−17.5874	−	30.4622i	−0.732172	−	1.26816i	−0.955953	−	0.293519i	$-0.905173\pi$
$577$	−17.5874	−	30.4622i	−0.732172	−	1.26816i	0.223781	−	0.974639i	$-0.428160\pi$
$578$	−10.3500			−0.430502
$579$	4.85819	−	8.41463i	0.201899	−	0.349700i
$580$	−3.62190	−	6.27331i	−0.150391	−	0.260485i
$581$	5.90662			0.245048
$582$	−2.00000			−0.0829027
$583$	−4.25731	−	7.37387i	−0.176320	−	0.305395i
$584$	−8.44335			−0.349389
$585$	0.500000	−	0.866025i	0.0206725	−	0.0358057i
$586$	−7.91594			−0.327004
$587$	1.11724	−	1.93512i	0.0461134	−	0.0798708i	−0.842047	−	0.539403i	$-0.818650\pi$
$587$	1.11724	−	1.93512i	0.0461134	−	0.0798708i	0.888161	+	0.459533i	$0.151983\pi$
$588$	−3.41128	+	5.90851i	−0.140679	+	0.243663i
$589$	−5.15753	+	8.93310i	−0.212512	+	0.368082i
$590$	−1.03207	−	1.78761i	−0.0424898	−	0.0735946i
$591$	−24.1725			−0.994325
$592$	−3.91128	+	4.65853i	−0.160753	+	0.191464i
$593$	−33.7805			−1.38720			−0.693600	−	0.720360i	$-0.743976\pi$
$593$	−33.7805			−1.38720			−0.693600	+	0.720360i	$0.743976\pi$
$594$	−1.61084	−	2.79005i	−0.0660935	−	0.114477i
$595$	0.543134	−	0.940736i	0.0222663	−	0.0385664i
$596$	2.59978	−	4.50295i	0.106491	−	0.184448i
$597$	−2.48894	+	4.31097i	−0.101866	+	0.176436i
$598$	−5.60088			−0.229037
$599$	−6.05309	+	10.4843i	−0.247323	+	0.428375i	−0.962782	−	0.270279i	$-0.912884\pi$
$599$	−6.05309	+	10.4843i	−0.247323	+	0.428375i	0.715459	+	0.698654i	$0.246217\pi$
$600$	−1.00000			−0.0408248
$601$	−1.23163	−	2.13325i	−0.0502394	−	0.0870171i	0.839812	−	0.542877i	$-0.182665\pi$
$601$	−1.23163	−	2.13325i	−0.0502394	−	0.0870171i	−0.890051	+	0.455860i	$0.849332\pi$
$602$	0.354880			0.0144638
$603$	−3.86459			−0.157378
$604$	0.620795	+	1.07525i	0.0252598	+	0.0437512i
$605$	−0.310397	+	0.537624i	−0.0126194	+	0.0218575i
$606$	−10.1796			−0.413520
$607$	−13.2905	−	23.0198i	−0.539444	−	0.934345i	−0.998934	−	0.0461617i	$-0.985301\pi$
$607$	−13.2905	−	23.0198i	−0.539444	−	0.934345i	0.459490	−	0.888183i	$-0.348032\pi$
$608$	2.11084	+	3.65608i	0.0856058	+	0.148274i
$609$	−1.52567	−	2.64254i	−0.0618234	−	0.107081i
$610$	−0.900221	+	1.55923i	−0.0364489	+	0.0631313i
$611$	4.41128	−	7.64056i	0.178461	−	0.309104i
$612$	−1.28938	−	2.23328i	−0.0521202	−	0.0902748i
$613$	1.30044	+	2.25243i	0.0525243	+	0.0909748i	0.891092	−	0.453822i	$-0.149940\pi$
$613$	1.30044	+	2.25243i	0.0525243	+	0.0909748i	−0.838568	+	0.544797i	$0.816607\pi$
$614$	0.0641495	+	0.111110i	0.00258886	+	0.00448404i
$615$	−10.2438			−0.413070
$616$	0.678543	−	1.17527i	0.0273393	−	0.0473530i
$617$	8.75731	+	15.1681i	0.352556	+	0.610645i	0.986697	−	0.162573i	$-0.0519793\pi$
$617$	8.75731	+	15.1681i	0.352556	+	0.610645i	−0.634141	+	0.773218i	$0.718646\pi$
$618$	−6.86459			−0.276134
$619$	−6.43055			−0.258466			−0.129233	−	0.991614i	$-0.541251\pi$
$619$	−6.43055			−0.258466			−0.129233	+	0.991614i	$0.541251\pi$
$620$	−1.22168	−	2.11601i	−0.0490637	−	0.0849809i
$621$	5.60088			0.224756
$622$	−11.3436	+	19.6476i	−0.454836	+	0.787799i
$623$	2.88230			0.115477
$624$	0.500000	−	0.866025i	0.0200160	−	0.0346688i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.86459	+	10.1578i	−0.234396	+	0.405986i
$627$	6.80044	+	11.7787i	0.271583	+	0.470396i
$628$	18.3301			0.731449
$629$	−10.0863	+	12.0132i	−0.402166	+	0.478999i
$630$	−0.421236			−0.0167824
$631$	−16.9345	−	29.3314i	−0.674152	−	1.16767i	−0.976716	−	0.214536i	$-0.931176\pi$
$631$	−16.9345	−	29.3314i	−0.674152	−	1.16767i	0.302564	−	0.953129i	$-0.402157\pi$
$632$	−7.37921	+	12.7812i	−0.293529	+	0.508407i
$633$	6.26837	−	10.8571i	0.249145	−	0.431532i
$634$	10.7228	−	18.5724i	0.425856	−	0.737604i
$635$	−3.17965			−0.126180
$636$	−1.32146	+	2.28883i	−0.0523992	+	0.0907580i
$637$	−6.82256			−0.270320
$638$	−11.6686	−	20.2106i	−0.461964	−	0.800145i
$639$	−7.17965			−0.284022
$640$	−1.00000			−0.0395285
$641$	4.36569	+	7.56160i	0.172435	+	0.298665i	0.939270	−	0.343178i	$-0.111503\pi$
$641$	4.36569	+	7.56160i	0.172435	+	0.298665i	−0.766836	+	0.641843i	$0.778170\pi$
$642$	8.76481	−	15.1811i	0.345920	−	0.599150i
$643$	8.66724			0.341803			0.170901	−	0.985288i	$-0.445332\pi$
$643$	8.66724			0.341803			0.170901	+	0.985288i	$0.445332\pi$
$644$	1.17965	+	2.04321i	0.0464846	+	0.0805137i
$645$	−0.421236	−	0.729602i	−0.0165862	−	0.0287281i
$646$	5.44335	+	9.42817i	0.214166	+	0.370946i
$647$	−19.2117	+	33.2757i	−0.755291	+	1.30820i	0.189939	+	0.981796i	$0.439171\pi$
$647$	−19.2117	+	33.2757i	−0.755291	+	1.30820i	−0.945230	+	0.326406i	$0.894162\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−3.32501	−	5.75909i	−0.130518	−	0.226064i
$650$	−0.500000	−	0.866025i	−0.0196116	−	0.0339683i
$651$	−0.514615	−	0.891339i	−0.0201693	−	0.0349343i
$652$	2.13541			0.0836291
$653$	−15.9381	+	27.6055i	−0.623704	+	1.08029i	0.365085	+	0.930974i	$0.381040\pi$
$653$	−15.9381	+	27.6055i	−0.623704	+	1.08029i	−0.988790	+	0.149314i	$0.952294\pi$
$654$	−10.1440	−	17.5700i	−0.396662	−	0.687040i
$655$	1.62079			0.0633297
$656$	−10.2438			−0.399953
$657$	4.22168	+	7.31216i	0.164703	+	0.285275i
$658$	−3.71638			−0.144880
$659$	8.96793	−	15.5329i	0.349341	−	0.605076i	−0.636792	−	0.771036i	$-0.719739\pi$
$659$	8.96793	−	15.5329i	0.349341	−	0.605076i	0.986133	+	0.165960i	$0.0530722\pi$
$660$	−3.22168			−0.125404
$661$	7.62300	−	13.2034i	0.296500	−	0.513554i	−0.678832	−	0.734293i	$-0.737514\pi$
$661$	7.62300	−	13.2034i	0.296500	−	0.513554i	0.975333	+	0.220739i	$0.0708471\pi$
$662$	8.05309	−	13.9484i	0.312992	−	0.542118i
$663$	1.28938	−	2.23328i	0.0500754	−	0.0867332i
$664$	−7.01106	−	12.1435i	−0.272082	−	0.471260i
$665$	1.77832			0.0689604
$666$	5.99004	+	1.05800i	0.232109	+	0.0409968i
$667$	40.5717			1.57094
$668$	8.25375	+	14.2959i	0.319347	+	0.553126i
$669$	−6.44335	+	11.1602i	−0.249114	+	0.431479i
$670$	−1.93230	+	3.34683i	−0.0746511	+	0.129299i
$671$	−2.90022	+	5.02333i	−0.111962	+	0.193923i
$672$	−0.421236			−0.0162495
$673$	3.25731	−	5.64182i	0.125560	−	0.217476i	−0.796392	−	0.604781i	$-0.793261\pi$
$673$	3.25731	−	5.64182i	0.125560	−	0.217476i	0.921952	+	0.387305i	$0.126594\pi$
$674$	−24.9181			−0.959811
$675$	0.500000	+	0.866025i	0.0192450	+	0.0333333i
$676$	−12.0000			−0.461538
$677$	38.0172			1.46112			0.730560	−	0.682848i	$-0.239259\pi$
$677$	38.0172			1.46112			0.730560	+	0.682848i	$0.239259\pi$
$678$	1.20066	+	2.07961i	0.0461112	+	0.0798669i
$679$	−0.421236	+	0.729602i	−0.0161656	+	0.0279996i
$680$	−2.57876			−0.0988911
$681$	−1.01106	−	1.75121i	−0.0387439	−	0.0671064i
$682$	−3.93585	−	6.81709i	−0.150712	−	0.261040i
$683$	−16.3079	−	28.2462i	−0.624006	−	1.08081i	−0.988732	−	0.149696i	$-0.952171\pi$
$683$	−16.3079	−	28.2462i	−0.624006	−	1.08081i	0.364726	−	0.931115i	$-0.381163\pi$
$684$	2.11084	−	3.65608i	0.0807099	−	0.139794i
$685$	7.82146	−	13.5472i	0.298842	−	0.517610i
$686$	2.91128	+	5.04249i	0.111153	+	0.192523i
$687$	1.09978	+	1.90487i	0.0419592	+	0.0726755i
$688$	−0.421236	−	0.729602i	−0.0160595	−	0.0278158i
$689$	−2.64291			−0.100687
$690$	2.80044	−	4.85051i	0.106611	−	0.184656i
$691$	12.1551	+	21.0532i	0.462401	+	0.800902i	0.999080	−	0.0428846i	$-0.0136548\pi$
$691$	12.1551	+	21.0532i	0.462401	+	0.800902i	−0.536679	+	0.843786i	$0.680321\pi$
$692$	18.6872			0.710379
$693$	−1.35709			−0.0515515
$694$	3.24625	+	5.62267i	0.123226	+	0.213433i
$695$	9.91594			0.376133
$696$	−3.62190	+	6.27331i	−0.137288	+	0.237789i
$697$	−26.4163			−1.00059
$698$	11.6009	−	20.0933i	0.439100	−	0.760543i
$699$	11.9113	−	20.6309i	0.450526	−	0.780334i
$700$	−0.210618	+	0.364801i	−0.00796061	+	0.0137882i
$701$	18.1119	+	31.3708i	0.684079	+	1.18486i	0.973725	+	0.227725i	$0.0731288\pi$
$701$	18.1119	+	31.3708i	0.684079	+	1.18486i	−0.289647	+	0.957134i	$0.593538\pi$
$702$	−1.00000			−0.0377426
$703$	−25.2880	−	4.46655i	−0.953756	−	0.168459i
$704$	−3.22168			−0.121422
$705$	4.41128	+	7.64056i	0.166138	+	0.287760i
$706$	−2.31040	+	4.00173i	−0.0869529	+	0.150607i
$707$	−2.14402	+	3.71355i	−0.0806341	+	0.139662i
$708$	−1.03207	+	1.78761i	−0.0387877	+	0.0671823i
$709$	−37.2146			−1.39762			−0.698811	−	0.715306i	$-0.746287\pi$
$709$	−37.2146			−1.39762			−0.698811	+	0.715306i	$0.746287\pi$
$710$	−3.58982	+	6.21776i	−0.134724	+	0.233348i
$711$	14.7584			0.553484
$712$	−3.42124	−	5.92575i	−0.128216	−	0.222077i
$713$	13.6849			0.512505
$714$	−1.08627			−0.0406526
$715$	−1.61084	−	2.79005i	−0.0602420	−	0.104342i
$716$	−2.57876	+	4.46655i	−0.0963729	+	0.166923i
$717$	−6.22168			−0.232353
$718$	3.71172	+	6.42889i	0.138520	+	0.239924i
$719$	−19.5920	−	33.9344i	−0.730659	−	1.26554i	−0.956602	−	0.291399i	$-0.905879\pi$
$719$	−19.5920	−	33.9344i	−0.730659	−	1.26554i	0.225942	−	0.974141i	$-0.427454\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	−1.44581	+	2.50421i	−0.0538446	+	0.0932617i
$722$	0.588720	−	1.01969i	0.0219099	−	0.0379490i
$723$	−11.9900	−	20.7674i	−0.445915	−	0.772347i
$724$	8.60088	+	14.8972i	0.319649	+	0.553649i
$725$	3.62190	+	6.27331i	0.134514	+	0.232985i
$726$	0.620795			0.0230398
$727$	−22.7117	+	39.3379i	−0.842331	+	1.45896i	0.0455878	+	0.998960i	$0.485484\pi$
$727$	−22.7117	+	39.3379i	−0.842331	+	1.45896i	−0.887919	+	0.460000i	$0.847849\pi$
$728$	−0.210618	−	0.364801i	−0.00780602	−	0.0135204i
$729$	1.00000			0.0370370
$730$	8.44335			0.312503
$731$	−1.08627	−	1.88147i	−0.0401771	−	0.0695887i
$732$	1.80044			0.0665462
$733$	−1.87455	+	3.24681i	−0.0692380	+	0.119924i	−0.898566	−	0.438838i	$-0.855390\pi$
$733$	−1.87455	+	3.24681i	−0.0692380	+	0.119924i	0.829328	+	0.558762i	$0.188723\pi$
$734$	4.98009			0.183818
$735$	3.41128	−	5.90851i	0.125827	−	0.217939i
$736$	2.80044	−	4.85051i	0.103226	−	0.178792i
$737$	−6.22523	+	10.7824i	−0.229309	+	0.397176i
$738$	5.12190	+	8.87139i	0.188540	+	0.326560i
$739$	36.3986			1.33895			0.669473	−	0.742837i	$-0.266520\pi$
$739$	36.3986			1.33895			0.669473	+	0.742837i	$0.266520\pi$
$740$	3.91128	−	4.65853i	0.143782	−	0.171251i
$741$	4.22168			0.155087
$742$	0.556645	+	0.964138i	0.0204351	+	0.0353946i
$743$	−22.0564	+	38.2028i	−0.809171	+	1.40153i	0.104268	+	0.994549i	$0.466750\pi$
$743$	−22.0564	+	38.2028i	−0.809171	+	1.40153i	−0.913439	+	0.406976i	$0.866583\pi$
$744$	−1.22168	+	2.11601i	−0.0447889	+	0.0775766i
$745$	−2.59978	+	4.50295i	−0.0952485	+	0.164975i
$746$	−28.3942			−1.03959
$747$	−7.01106	+	12.1435i	−0.256521	+	0.444308i
$748$	−8.30795			−0.303769
$749$	−3.69205	−	6.39483i	−0.134905	−	0.233662i
$750$	1.00000			0.0365148
$751$	47.2389			1.72377			0.861886	−	0.507102i	$-0.169283\pi$
$751$	47.2389			1.72377			0.861886	+	0.507102i	$0.169283\pi$
$752$	4.41128	+	7.64056i	0.160863	+	0.278623i
$753$	8.63296	−	14.9527i	0.314602	−	0.544907i
$754$	−7.24380			−0.263803
$755$	−0.620795	−	1.07525i	−0.0225930	−	0.0391323i
$756$	0.210618	+	0.364801i	0.00766010	+	0.0132677i
$757$	−16.2263	−	28.1048i	−0.589756	−	1.02149i	−0.994264	−	0.106953i	$-0.965890\pi$
$757$	−16.2263	−	28.1048i	−0.589756	−	1.02149i	0.404508	−	0.914535i	$-0.367443\pi$
$758$	−0.410177	+	0.710447i	−0.0148983	+	0.0258046i
$759$	9.02212	−	15.6268i	0.327482	−	0.567216i
$760$	−2.11084	−	3.65608i	−0.0765682	−	0.132620i
$761$	−1.70066	−	2.94563i	−0.0616490	−	0.106779i	0.833554	−	0.552439i	$-0.186303\pi$
$761$	−1.70066	−	2.94563i	−0.0616490	−	0.106779i	−0.895203	+	0.445659i	$0.852969\pi$
$762$	1.58982	+	2.75365i	0.0575932	+	0.0997544i
$763$	−8.54605			−0.309388
$764$	0.121898	−	0.211134i	0.00441012	−	0.00763855i
$765$	1.28938	+	2.23328i	0.0466177	+	0.0807442i
$766$	5.13762			0.185630
$767$	−2.06415			−0.0745321
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	35.3195			1.27365			0.636826	−	0.771007i	$-0.280247\pi$
$769$	35.3195			1.27365			0.636826	+	0.771007i	$0.280247\pi$
$770$	−0.678543	+	1.17527i	−0.0244530	+	0.0423538i
$771$	−3.28803			−0.118416
$772$	−4.85819	+	8.41463i	−0.174850	+	0.302849i
$773$	−22.1860	+	38.4274i	−0.797977	+	1.38214i	0.122955	+	0.992412i	$0.460763\pi$
$773$	−22.1860	+	38.4274i	−0.797977	+	1.38214i	−0.920932	+	0.389724i	$0.872570\pi$
$774$	−0.421236	+	0.729602i	−0.0151410	+	0.0262250i
$775$	1.22168	+	2.11601i	0.0438839	+	0.0760092i
$776$	2.00000			0.0717958
$777$	1.64757	−	1.96234i	0.0591063	−	0.0703986i
$778$	31.0686			1.11386
$779$	−21.6230	−	37.4521i	−0.774724	−	1.34186i
$780$	−0.500000	+	0.866025i	−0.0179029	+	0.0310087i
$781$	−11.5653	+	20.0316i	−0.413837	+	0.716787i
$782$	7.22168	−	12.5083i	0.258247	−	0.447296i
$783$	7.24380			0.258872
$784$	3.41128	−	5.90851i	0.121831	−	0.211018i
$785$	−18.3301			−0.654228
$786$	−0.810397	−	1.40365i	−0.0289059	−	0.0500665i
$787$	24.9823			0.890523			0.445261	−	0.895401i	$-0.353111\pi$
$787$	24.9823			0.890523			0.445261	+	0.895401i	$0.353111\pi$
$788$	24.1725			0.861111
$789$	11.8867	+	20.5884i	0.423178	+	0.732966i
$790$	7.37921	−	12.7812i	0.262540	−	0.454733i
$791$	1.01152			0.0359657
$792$	1.61084	+	2.79005i	0.0572387	+	0.0991403i
$793$	0.900221	+	1.55923i	0.0319678	+	0.0553698i
$794$	−6.18960	−	10.7207i	−0.219661	−	0.380464i
$795$	1.32146	−	2.28883i	0.0468672	−	0.0811764i
$796$	2.48894	−	4.31097i	0.0882182	−	0.152798i
$797$	5.69426	+	9.86275i	0.201701	+	0.349357i	0.949077	−	0.315045i	$-0.102020\pi$
$797$	5.69426	+	9.86275i	0.201701	+	0.349357i	−0.747376	+	0.664402i	$0.768686\pi$
$798$	−0.889161	−	1.54007i	−0.0314760	−	0.0545180i
$799$	11.3757	+	19.7032i	0.402442	+	0.697049i
$800$	1.00000			0.0353553
$801$	−3.42124	+	5.92575i	−0.120883	+	0.209376i
$802$	4.16393	+	7.21214i	0.147033	+	0.254669i
$803$	27.2018			0.959929
$804$	3.86459			0.136294
$805$	−1.17965	−	2.04321i	−0.0415771	−	0.0720136i
$806$	−2.44335			−0.0860635
$807$	15.3967	−	26.6678i	0.541988	−	0.938751i
$808$	10.1796			0.358119
$809$	23.0221	−	39.8755i	0.809415	−	1.40195i	−0.103855	−	0.994592i	$-0.533118\pi$
$809$	23.0221	−	39.8755i	0.809415	−	1.40195i	0.913270	−	0.407355i	$-0.133549\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	8.96437	−	15.5267i	0.314782	−	0.545218i	−0.664609	−	0.747191i	$-0.731402\pi$
$811$	8.96437	−	15.5267i	0.314782	−	0.545218i	0.979391	+	0.201973i	$0.0647354\pi$
$812$	1.52567	+	2.64254i	0.0535407	+	0.0927351i
$813$	−19.0221			−0.667135
$814$	12.6009	−	15.0083i	0.441661	−	0.526040i
$815$	−2.13541			−0.0748001
$816$	1.28938	+	2.23328i	0.0451374	+	0.0781803i
$817$	1.77832	−	3.08015i	0.0622156	−	0.107761i
$818$	2.30044	−	3.98448i	0.0804330	−	0.139314i
$819$	−0.210618	+	0.364801i	−0.00735959	+	0.0127472i
$820$	10.2438			0.357729
$821$	7.94976	−	13.7694i	0.277448	−	0.480555i	−0.693302	−	0.720648i	$-0.743845\pi$
$821$	7.94976	−	13.7694i	0.277448	−	0.480555i	0.970750	+	0.240093i	$0.0771779\pi$
$822$	−15.6429			−0.545609
$823$	−13.9177	−	24.1061i	−0.485140	−	0.840287i	0.514714	−	0.857362i	$-0.327898\pi$
$823$	−13.9177	−	24.1061i	−0.485140	−	0.840287i	−0.999854	+	0.0170748i	$0.994565\pi$
$824$	6.86459			0.239139
$825$	3.22168			0.112164
$826$	0.434747	+	0.753004i	0.0151268	+	0.0262004i
$827$	2.00466	−	3.47217i	0.0697088	−	0.120739i	−0.829064	−	0.559153i	$-0.811126\pi$
$827$	2.00466	−	3.47217i	0.0697088	−	0.120739i	0.898773	+	0.438414i	$0.144460\pi$
$828$	−5.60088			−0.194644
$829$	−7.36349	−	12.7539i	−0.255744	−	0.442962i	0.709353	−	0.704853i	$-0.248987\pi$
$829$	−7.36349	−	12.7539i	−0.255744	−	0.442962i	−0.965097	+	0.261891i	$0.915654\pi$
$830$	7.01106	+	12.1435i	0.243357	+	0.421507i
$831$	−5.90132	−	10.2214i	−0.204715	−	0.354576i
$832$	−0.500000	+	0.866025i	−0.0173344	+	0.0300240i
$833$	8.79689	−	15.2367i	0.304794	−	0.527919i
$834$	−4.95797	−	8.58745i	−0.171680	−	0.297359i
$835$	−8.25375	−	14.2959i	−0.285633	−	0.494731i
$836$	−6.80044	−	11.7787i	−0.235198	−	0.407375i
$837$	2.44335			0.0844547
$838$	−11.0221	+	19.0909i	−0.380753	+	0.659483i
$839$	20.0577	+	34.7410i	0.692470	+	1.19939i	0.971026	+	0.238974i	$0.0768110\pi$
$839$	20.0577	+	34.7410i	0.692470	+	1.19939i	−0.278556	+	0.960420i	$0.589856\pi$
$840$	0.421236			0.0145340
$841$	23.4726			0.809399
$842$	12.9002	+	22.3438i	0.444571	+	0.770019i
$843$	−18.0442			−0.621477
$844$	−6.26837	+	10.8571i	−0.215766	+	0.373718i
$845$	12.0000			0.412813
$846$	4.41128	−	7.64056i	0.151663	−	0.262688i
$847$	0.130751	−	0.226467i	0.00449264	−	0.00778148i
$848$	1.32146	−	2.28883i	0.0453790	−	0.0785988i
$849$	−1.73274	−	3.00119i	−0.0594674	−	0.103001i
$850$	2.57876			0.0884509
$851$	11.6429	+	32.0176i	0.399114	+	1.09755i
$852$	7.17965			0.245971
$853$	9.34713	+	16.1897i	0.320040	+	0.554325i	0.980496	−	0.196540i	$-0.0629704\pi$
$853$	9.34713	+	16.1897i	0.320040	+	0.554325i	−0.660456	+	0.750865i	$0.729637\pi$
$854$	0.379205	−	0.656803i	0.0129761	−	0.0224753i
$855$	−2.11084	+	3.65608i	−0.0721892	+	0.125035i
$856$	−8.76481	+	15.1811i	−0.299575	+	0.518879i
$857$	3.15973			0.107934			0.0539672	−	0.998543i	$-0.482813\pi$
$857$	3.15973			0.107934			0.0539672	+	0.998543i	$0.482813\pi$
$858$	−1.61084	+	2.79005i	−0.0549931	+	0.0952509i
$859$	−2.99289			−0.102116			−0.0510580	−	0.998696i	$-0.516259\pi$
$859$	−2.99289			−0.102116			−0.0510580	+	0.998696i	$0.516259\pi$
$860$	0.421236	+	0.729602i	0.0143640	+	0.0248792i
$861$	4.31506			0.147057
$862$	5.89382			0.200744
$863$	1.69711	+	2.93948i	0.0577702	+	0.100061i	0.893464	−	0.449134i	$-0.148268\pi$
$863$	1.69711	+	2.93948i	0.0577702	+	0.100061i	−0.835694	+	0.549195i	$0.814934\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$	−18.6872			−0.635382
$866$	−7.15753	−	12.3972i	−0.243223	−	0.421274i
$867$	−5.17499	−	8.96334i	−0.175752	−	0.304411i
$868$	0.514615	+	0.891339i	0.0174672	+	0.0302540i
$869$	23.7734	−	41.1768i	0.806458	−	1.39683i
$870$	3.62190	−	6.27331i	0.122794	−	0.212685i
$871$	1.93230	+	3.34683i	0.0654733	+	0.113403i
$872$	10.1440	+	17.5700i	0.343520	+	0.594994i
$873$	−1.00000	−	1.73205i	−0.0338449	−	0.0586210i
$874$	23.6451			0.799808
$875$	0.210618	−	0.364801i	0.00712019	−	0.0123325i
$876$	−4.22168	−	7.31216i	−0.142637	−	0.247055i
$877$	27.7584			0.937335			0.468667	−	0.883375i	$-0.344734\pi$
$877$	27.7584			0.937335			0.468667	+	0.883375i	$0.344734\pi$
$878$	−1.10618			−0.0373318
$879$	−3.95797	−	6.85540i	−0.133499	−	0.231227i
$880$	3.22168			0.108603
$881$	7.42344	−	12.8578i	0.250102	−	0.433190i	−0.713452	−	0.700705i	$-0.752869\pi$
$881$	7.42344	−	12.8578i	0.250102	−	0.433190i	0.963554	+	0.267515i	$0.0862025\pi$
$882$	−6.82256			−0.229728
$883$	−8.55309	+	14.8144i	−0.287834	+	0.498544i	−0.973293	−	0.229568i	$-0.926269\pi$
$883$	−8.55309	+	14.8144i	−0.287834	+	0.498544i	0.685458	+	0.728112i	$0.259602\pi$
$884$	−1.28938	+	2.23328i	−0.0433666	+	0.0751132i
$885$	1.03207	−	1.78761i	0.0346928	−	0.0600897i
$886$	7.32612	+	12.6892i	0.246126	+	0.426302i
$887$	9.95576			0.334282			0.167141	−	0.985933i	$-0.446547\pi$
$887$	9.95576			0.334282			0.167141	+	0.985933i	$0.446547\pi$
$888$	−5.99004	−	1.05800i	−0.201013	−	0.0355043i
$889$	1.33938			0.0449214
$890$	3.42124	+	5.92575i	0.114680	+	0.198632i
$891$	1.61084	−	2.79005i	0.0539651	−	0.0934703i
$892$	6.44335	−	11.1602i	0.215739	−	0.373672i
$893$	−18.6230	+	32.2560i	−0.623195	+	1.07941i
$894$	5.19956			0.173899
$895$	2.57876	−	4.46655i	0.0861986	−	0.149300i
$896$	0.421236			0.0140725
$897$	−2.80044	−	4.85051i	−0.0935040	−	0.161954i
$898$	15.2018			0.507289
$899$	17.6992			0.590300
$900$	−0.500000	−	0.866025i	−0.0166667	−	0.0288675i
$901$	3.40772	−	5.90235i	0.113528	−	0.196636i
$902$	33.0022			1.09885
$903$	0.177440	+	0.307335i	0.00590483	+	0.0102275i
$904$	−1.20066	−	2.07961i	−0.0399334	−	0.0691667i
$905$	−8.60088	−	14.8972i	−0.285903	−	0.495199i
$906$	−0.620795	+	1.07525i	−0.0206245	+	0.0357227i
$907$	7.24159	−	12.5428i	0.240453	−	0.416477i	−0.720390	−	0.693569i	$-0.756037\pi$
$907$	7.24159	−	12.5428i	0.240453	−	0.416477i	0.960843	+	0.277092i	$0.0893707\pi$
$908$	1.01106	+	1.75121i	0.0335532	+	0.0581158i
$909$	−5.08982	−	8.81583i	−0.168819	−	0.292403i
$910$	0.210618	+	0.364801i	0.00698192	+	0.0120930i
$911$	15.2367			0.504814			0.252407	−	0.967621i	$-0.418778\pi$
$911$	15.2367			0.504814			0.252407	+	0.967621i	$0.418778\pi$
$912$	−2.11084	+	3.65608i	−0.0698969	+	0.121065i
$913$	22.5874	+	39.1225i	0.747533	+	1.29476i
$914$	−3.95576			−0.130845
$915$	−1.80044			−0.0595208
$916$	−1.09978	−	1.90487i	−0.0363377	−	0.0629388i
$917$	−0.682737			−0.0225460
$918$	1.28938	−	2.23328i	0.0425559	−	0.0737091i
$919$	−1.10618			−0.0364895			−0.0182448	−	0.999834i	$-0.505808\pi$
$919$	−1.10618			−0.0364895			−0.0182448	+	0.999834i	$0.505808\pi$
$920$	−2.80044	+	4.85051i	−0.0923278	+	0.159916i
$921$	−0.0641495	+	0.111110i	−0.00211380	+	0.00366120i
$922$	19.4024	−	33.6060i	0.638985	−	1.10675i
$923$	3.58982	+	6.21776i	0.118160	+	0.204660i
$924$	1.35709			0.0446449
$925$	−3.91128	+	4.65853i	−0.128602	+	0.153171i
$926$	0.265915			0.00873851
$927$	−3.43230	−	5.94491i	−0.112731	−	0.195256i
$928$	3.62190	−	6.27331i	0.118895	−	0.205932i
$929$	4.02212	−	6.96651i	0.131961	−	0.228564i	−0.792471	−	0.609909i	$-0.791206\pi$
$929$	4.02212	−	6.96651i	0.131961	−	0.228564i	0.924433	+	0.381345i	$0.124539\pi$
$930$	1.22168	−	2.11601i	0.0400604	−	0.0693866i
$931$	28.8026			0.943969
$932$	−11.9113	+	20.6309i	−0.390167	+	0.675789i
$933$	−22.6872			−0.742744
$934$	3.88916	+	6.73622i	0.127257	+	0.220416i
$935$	8.30795			0.271699
$936$	1.00000			0.0326860
$937$	−21.7670	−	37.7016i	−0.711098	−	1.23166i	−0.964446	−	0.264282i	$-0.914865\pi$
$937$	−21.7670	−	37.7016i	−0.711098	−	1.23166i	0.253348	−	0.967375i	$-0.418468\pi$
$938$	0.813952	−	1.40981i	0.0265765	−	0.0460318i
$939$	−11.7292			−0.382767
$940$	−4.41128	−	7.64056i	−0.143880	−	0.249208i
$941$	−19.9533	−	34.5601i	−0.650459	−	1.12663i	−0.983012	−	0.183544i	$-0.941243\pi$
$941$	−19.9533	−	34.5601i	−0.650459	−	1.12663i	0.332552	−	0.943085i	$-0.392090\pi$
$942$	9.16503	+	15.8743i	0.298613	+	0.517213i
$943$	−28.6872	+	49.6876i	−0.934182	+	1.61805i
$944$	1.03207	−	1.78761i	0.0335912	−	0.0581816i
$945$	−0.210618	−	0.364801i	−0.00685140	−	0.0118670i
$946$	1.35709	+	2.35054i	0.0441227	+	0.0764227i
$947$	6.53207	+	11.3139i	0.212264	+	0.367652i	0.952423	−	0.304780i	$-0.0985830\pi$
$947$	6.53207	+	11.3139i	0.212264	+	0.367652i	−0.740159	+	0.672432i	$0.765250\pi$
$948$	−14.7584			−0.479331
$949$	4.22168	−	7.31216i	0.137041	−	0.237363i
$950$	2.11084	+	3.65608i	0.0684847	+	0.118619i
$951$	21.4456			0.695420
$952$	1.08627			0.0352062
$953$	19.2449	+	33.3331i	0.623403	+	1.07977i	0.988847	+	0.148933i	$0.0475839\pi$
$953$	19.2449	+	33.3331i	0.623403	+	1.07977i	−0.365444	+	0.930833i	$0.619083\pi$
$954$	−2.64291			−0.0855675
$955$	−0.121898	+	0.211134i	−0.00394453	+	0.00683213i
$956$	6.22168			0.201223
$957$	11.6686	−	20.2106i	0.377192	−	0.653315i
$958$	4.06415	−	7.03931i	0.131307	−	0.227430i
$959$	−3.29468	+	5.70655i	−0.106391	+	0.184274i
$960$	−0.500000	−	0.866025i	−0.0161374	−	0.0279508i
$961$	−25.0300			−0.807420
$962$	−2.07876	−	5.71653i	−0.0670220	−	0.184308i
$963$	17.5296			0.564884
$964$	11.9900	+	20.7674i	0.386173	+	0.668872i
$965$	4.85819	−	8.41463i	0.156391	−	0.270877i
$966$	−1.17965	+	2.04321i	−0.0379545	+	0.0657391i
$967$	−1.54559	+	2.67703i	−0.0497027	+	0.0860876i	−0.889806	−	0.456338i	$-0.849161\pi$
$967$	−1.54559	+	2.67703i	−0.0497027	+	0.0860876i	0.840104	+	0.542426i	$0.182494\pi$
$968$	−0.620795			−0.0199531
$969$	−5.44335	+	9.42817i	−0.174866	+	0.302876i
$970$	−2.00000			−0.0642161
$971$	−20.3792	−	35.2978i	−0.654000	−	1.13276i	−0.982144	−	0.188133i	$-0.939756\pi$
$971$	−20.3792	−	35.2978i	−0.654000	−	1.13276i	0.328144	−	0.944628i	$-0.393577\pi$
$972$	−1.00000			−0.0320750
$973$	−4.17695			−0.133907
$974$	10.6476	+	18.4421i	0.341170	+	0.590924i
$975$	0.500000	−	0.866025i	0.0160128	−	0.0277350i
$976$	−1.80044			−0.0576307
$977$	−6.55775	−	11.3584i	−0.209801	−	0.363386i	0.741851	−	0.670565i	$-0.233948\pi$
$977$	−6.55775	−	11.3584i	−0.209801	−	0.363386i	−0.951652	+	0.307179i	$0.900615\pi$
$978$	1.06770	+	1.84932i	0.0341414	+	0.0591347i
$979$	11.0221	+	19.0909i	0.352268	+	0.610147i
$980$	−3.41128	+	5.90851i	−0.108969	+	0.188740i
$981$	10.1440	−	17.5700i	0.323874	−	0.560965i
$982$	−8.80044	−	15.2428i	−0.280833	−	0.486418i
$983$	−19.0221	−	32.9473i	−0.606711	−	1.05085i	−0.991779	−	0.127966i	$-0.959155\pi$
$983$	−19.0221	−	32.9473i	−0.606711	−	1.05085i	0.385067	−	0.922889i	$-0.374178\pi$
$984$	−5.12190	−	8.87139i	−0.163280	−	0.282810i
$985$	−24.1725			−0.770201
$986$	9.34002	−	16.1774i	0.297447	−	0.515193i
$987$	−1.85819	−	3.21848i	−0.0591468	−	0.102445i
$988$	−4.22168			−0.134309
$989$	−4.71859			−0.150042
$990$	−1.61084	−	2.79005i	−0.0511958	−	0.0886738i
$991$	7.06636			0.224470			0.112235	−	0.993682i	$-0.464199\pi$
$991$	7.06636			0.224470			0.112235	+	0.993682i	$0.464199\pi$
$992$	1.22168	−	2.11601i	0.0387883	−	0.0671833i
$993$	16.1062			0.511114
$994$	1.51216	−	2.61914i	0.0479629	−	0.0830742i
$995$	−2.48894	+	4.31097i	−0.0789047	+	0.136667i
$996$	7.01106	−	12.1435i	0.222154	−	0.384782i
$997$	5.20706	+	9.01890i	0.164909	+	0.285631i	0.936623	−	0.350339i	$-0.113934\pi$
$997$	5.20706	+	9.01890i	0.164909	+	0.285631i	−0.771714	+	0.635970i	$0.780600\pi$
$998$	9.62300			0.304611
$999$	2.07876	+	5.71653i	0.0657692	+	0.180863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1110.2.i.o.211.2	yes	6
37.10	even	3	inner	1110.2.i.o.121.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1110.2.i.o.121.2	✓	6	37.10	even	3	inner
1110.2.i.o.211.2	yes	6	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:	\( N \)	\(=\)	\( 1110 = 2 \cdot 3 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1110.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.210618 + 0.364801i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} -1.00000 q^{6} +(-0.210618 + 0.364801i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} -1.00000 q^{10} -3.22168 q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.500000 + 0.866025i) q^{13} +0.421236 q^{14} +(-0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.28938 - 2.23328i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(2.11084 - 3.65608i) q^{19} +(0.500000 + 0.866025i) q^{20} +(0.210618 + 0.364801i) q^{21} +(1.61084 + 2.79005i) q^{22} -5.60088 q^{23} +(0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{26} -1.00000 q^{27} +(-0.210618 - 0.364801i) q^{28} -7.24380 q^{29} +(-0.500000 + 0.866025i) q^{30} -2.44335 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.61084 + 2.79005i) q^{33} +(-1.28938 + 2.23328i) q^{34} +(0.210618 + 0.364801i) q^{35} +1.00000 q^{36} +(-2.07876 - 5.71653i) q^{37} -4.22168 q^{38} +(0.500000 + 0.866025i) q^{39} +(0.500000 - 0.866025i) q^{40} +(5.12190 - 8.87139i) q^{41} +(0.210618 - 0.364801i) q^{42} +0.842472 q^{43} +(1.61084 - 2.79005i) q^{44} -1.00000 q^{45} +(2.80044 + 4.85051i) q^{46} -8.82256 q^{47} -1.00000 q^{48} +(3.41128 + 5.90851i) q^{49} +(-0.500000 + 0.866025i) q^{50} -2.57876 q^{51} +(-0.500000 - 0.866025i) q^{52} +(1.32146 + 2.28883i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-1.61084 + 2.79005i) q^{55} +(-0.210618 + 0.364801i) q^{56} +(-2.11084 - 3.65608i) q^{57} +(3.62190 + 6.27331i) q^{58} +(1.03207 + 1.78761i) q^{59} +1.00000 q^{60} +(0.900221 - 1.55923i) q^{61} +(1.22168 + 2.11601i) q^{62} +0.421236 q^{63} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +3.22168 q^{66} +(1.93230 - 3.34683i) q^{67} +2.57876 q^{68} +(-2.80044 + 4.85051i) q^{69} +(0.210618 - 0.364801i) q^{70} +(3.58982 - 6.21776i) q^{71} +(-0.500000 - 0.866025i) q^{72} -8.44335 q^{73} +(-3.91128 + 4.65853i) q^{74} -1.00000 q^{75} +(2.11084 + 3.65608i) q^{76} +(0.678543 - 1.17527i) q^{77} +(0.500000 - 0.866025i) q^{78} +(-7.37921 + 12.7812i) q^{79} -1.00000 q^{80} +(-0.500000 + 0.866025i) q^{81} -10.2438 q^{82} +(-7.01106 - 12.1435i) q^{83} -0.421236 q^{84} -2.57876 q^{85} +(-0.421236 - 0.729602i) q^{86} +(-3.62190 + 6.27331i) q^{87} -3.22168 q^{88} +(-3.42124 - 5.92575i) q^{89} +(0.500000 + 0.866025i) q^{90} +(-0.210618 - 0.364801i) q^{91} +(2.80044 - 4.85051i) q^{92} +(-1.22168 + 2.11601i) q^{93} +(4.41128 + 7.64056i) q^{94} +(-2.11084 - 3.65608i) q^{95} +(0.500000 + 0.866025i) q^{96} +2.00000 q^{97} +(3.41128 - 5.90851i) q^{98} +(1.61084 + 2.79005i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{5} - 6 q^{6} - q^{7} + 6 q^{8} - 3 q^{9} - 6 q^{10} + 3 q^{12} - 3 q^{13} + 2 q^{14} - 3 q^{15} - 3 q^{16} - 8 q^{17} - 3 q^{18} + 3 q^{19} + 3 q^{20} + q^{21} + 4 q^{23} + 3 q^{24} - 3 q^{25} + 6 q^{26} - 6 q^{27} - q^{28} + 14 q^{29} - 3 q^{30} + 24 q^{31} - 3 q^{32} - 8 q^{34} + q^{35} + 6 q^{36} - 13 q^{37} - 6 q^{38} + 3 q^{39} + 3 q^{40} + 2 q^{41} + q^{42} + 4 q^{43} - 6 q^{45} - 2 q^{46} + 4 q^{47} - 6 q^{48} - 8 q^{49} - 3 q^{50} - 16 q^{51} - 3 q^{52} - 2 q^{53} + 3 q^{54} - q^{56} - 3 q^{57} - 7 q^{58} - 4 q^{59} + 6 q^{60} - 4 q^{61} - 12 q^{62} + 2 q^{63} + 6 q^{64} + 3 q^{65} - 8 q^{67} + 16 q^{68} + 2 q^{69} + q^{70} + 3 q^{71} - 3 q^{72} - 12 q^{73} + 5 q^{74} - 6 q^{75} + 3 q^{76} + 14 q^{77} + 3 q^{78} - 26 q^{79} - 6 q^{80} - 3 q^{81} - 4 q^{82} - 23 q^{83} - 2 q^{84} - 16 q^{85} - 2 q^{86} + 7 q^{87} - 20 q^{89} + 3 q^{90} - q^{91} - 2 q^{92} + 12 q^{93} - 2 q^{94} - 3 q^{95} + 3 q^{96} + 12 q^{97} - 8 q^{98}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^5 - 6 * q^6 - q^7 + 6 * q^8 - 3 * q^9 - 6 * q^10 + 3 * q^12 - 3 * q^13 + 2 * q^14 - 3 * q^15 - 3 * q^16 - 8 * q^17 - 3 * q^18 + 3 * q^19 + 3 * q^20 + q^21 + 4 * q^23 + 3 * q^24 - 3 * q^25 + 6 * q^26 - 6 * q^27 - q^28 + 14 * q^29 - 3 * q^30 + 24 * q^31 - 3 * q^32 - 8 * q^34 + q^35 + 6 * q^36 - 13 * q^37 - 6 * q^38 + 3 * q^39 + 3 * q^40 + 2 * q^41 + q^42 + 4 * q^43 - 6 * q^45 - 2 * q^46 + 4 * q^47 - 6 * q^48 - 8 * q^49 - 3 * q^50 - 16 * q^51 - 3 * q^52 - 2 * q^53 + 3 * q^54 - q^56 - 3 * q^57 - 7 * q^58 - 4 * q^59 + 6 * q^60 - 4 * q^61 - 12 * q^62 + 2 * q^63 + 6 * q^64 + 3 * q^65 - 8 * q^67 + 16 * q^68 + 2 * q^69 + q^70 + 3 * q^71 - 3 * q^72 - 12 * q^73 + 5 * q^74 - 6 * q^75 + 3 * q^76 + 14 * q^77 + 3 * q^78 - 26 * q^79 - 6 * q^80 - 3 * q^81 - 4 * q^82 - 23 * q^83 - 2 * q^84 - 16 * q^85 - 2 * q^86 + 7 * q^87 - 20 * q^89 + 3 * q^90 - q^91 - 2 * q^92 + 12 * q^93 - 2 * q^94 - 3 * q^95 + 3 * q^96 + 12 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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