LMFDB - Embedded newform 546.2.k.e.445.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 15x^{8} + 14x^{7} + 110x^{6} + 36x^{5} + 233x^{4} + 164x^{3} + 345x^{2} + 76x + 16 $ x^10 - 2x^9 + 15x^8 + 14x^7 + 110x^6 + 36x^5 + 233x^4 + 164x^3 + 345x^2 + 76*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			445.4
Root			$-0.623307 + 1.07960i$ of defining polynomial
Character	$\chi$	$=$	546.445
Dual form			546.2.k.e.373.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.623307 + 1.07960i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.27938 - 1.34329i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.623307 + 1.07960i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.27938 - 1.34329i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.24661 q^{10} -2.49532 q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.785103 - 3.51904i) q^{13} +(-2.30301 + 1.30235i) q^{14} +(-0.623307 - 1.07960i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.247662 - 0.428963i) q^{17} +(0.500000 - 0.866025i) q^{18} -7.67156 q^{19} +(0.623307 - 1.07960i) q^{20} +(2.27938 + 1.34329i) q^{21} +(-1.24766 + 2.16101i) q^{22} +(-0.224026 + 0.388024i) q^{23} +1.00000 q^{24} +(1.72298 - 2.98428i) q^{25} +(-3.44013 - 1.07960i) q^{26} -1.00000 q^{27} +(-0.0236360 + 2.64565i) q^{28} +(-3.71142 - 6.42837i) q^{29} -1.24661 q^{30} +(-4.06448 + 7.03989i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.49532 q^{33} -0.495324 q^{34} +(0.0294650 - 3.29810i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.37097 + 2.37459i) q^{37} +(-3.83578 + 6.64376i) q^{38} +(0.785103 + 3.51904i) q^{39} +(-0.623307 - 1.07960i) q^{40} +(-1.87097 - 3.24061i) q^{41} +(2.30301 - 1.30235i) q^{42} +(1.47532 - 2.55532i) q^{43} +(1.24766 + 2.16101i) q^{44} +(0.623307 + 1.07960i) q^{45} +(0.224026 + 0.388024i) q^{46} +(3.29729 + 5.71107i) q^{47} +(0.500000 - 0.866025i) q^{48} +(3.39113 + 6.12374i) q^{49} +(-1.72298 - 2.98428i) q^{50} +(0.247662 + 0.428963i) q^{51} +(-2.65502 + 2.43944i) q^{52} +(3.86750 - 6.69870i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.55535 - 2.69395i) q^{55} +(2.27938 + 1.34329i) q^{56} +7.67156 q^{57} -7.42285 q^{58} +(0.727653 + 1.26033i) q^{59} +(-0.623307 + 1.07960i) q^{60} -4.19934 q^{61} +(4.06448 + 7.03989i) q^{62} +(-2.27938 - 1.34329i) q^{63} +1.00000 q^{64} +(3.30979 - 3.04103i) q^{65} +(1.24766 - 2.16101i) q^{66} +0.0276094 q^{67} +(-0.247662 + 0.428963i) q^{68} +(0.224026 - 0.388024i) q^{69} +(-2.84150 - 1.67457i) q^{70} +(4.68884 - 8.12130i) q^{71} -1.00000 q^{72} +(-5.07151 + 8.78412i) q^{73} +(1.37097 + 2.37459i) q^{74} +(-1.72298 + 2.98428i) q^{75} +(3.83578 + 6.64376i) q^{76} +(5.68779 + 3.35195i) q^{77} +(3.44013 + 1.07960i) q^{78} +(-4.93545 - 8.54845i) q^{79} -1.24661 q^{80} +1.00000 q^{81} -3.74194 q^{82} +7.42285 q^{83} +(0.0236360 - 2.64565i) q^{84} +(0.308739 - 0.534751i) q^{85} +(-1.47532 - 2.55532i) q^{86} +(3.71142 + 6.42837i) q^{87} +2.49532 q^{88} +(5.74056 - 9.94294i) q^{89} +1.24661 q^{90} +(-2.93755 + 9.07584i) q^{91} +0.448052 q^{92} +(4.06448 - 7.03989i) q^{93} +6.59458 q^{94} +(-4.78173 - 8.28221i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(-0.509831 + 0.883054i) q^{97} +(6.99888 + 0.125065i) q^{98} -2.49532 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9} - 4 q^{10} - 12 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 5 q^{18} - 6 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} + 6 q^{23} + 10 q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{31} + 5 q^{32} + 12 q^{33} + 8 q^{34} - 2 q^{35} - 5 q^{36} + q^{37} - 3 q^{38} + 4 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} + 3 q^{43} + 6 q^{44} - 2 q^{45} - 6 q^{46} - 15 q^{47} + 5 q^{48} - 20 q^{49} + q^{50} - 4 q^{51} + 2 q^{52} - 17 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{56} + 6 q^{57} + 2 q^{59} + 2 q^{60} - 22 q^{61} + 10 q^{62} + 4 q^{63} + 10 q^{64} + 41 q^{65} + 6 q^{66} + 2 q^{67} + 4 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} - 10 q^{72} + 12 q^{73} - q^{74} + q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} + 4 q^{80} + 10 q^{81} - 8 q^{82} + 2 q^{84} + q^{85} - 3 q^{86} + 12 q^{88} + 7 q^{89} - 4 q^{90} - 4 q^{91} - 12 q^{92} + 10 q^{93} - 30 q^{94} + 24 q^{95} - 5 q^{96} - 6 q^{97} - 16 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9 - 4 * q^10 - 12 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 5 * q^18 - 6 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 + 6 * q^23 + 10 * q^24 - q^25 - 2 * q^26 - 10 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^31 + 5 * q^32 + 12 * q^33 + 8 * q^34 - 2 * q^35 - 5 * q^36 + q^37 - 3 * q^38 + 4 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 + 3 * q^43 + 6 * q^44 - 2 * q^45 - 6 * q^46 - 15 * q^47 + 5 * q^48 - 20 * q^49 + q^50 - 4 * q^51 + 2 * q^52 - 17 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^56 + 6 * q^57 + 2 * q^59 + 2 * q^60 - 22 * q^61 + 10 * q^62 + 4 * q^63 + 10 * q^64 + 41 * q^65 + 6 * q^66 + 2 * q^67 + 4 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 - 10 * q^72 + 12 * q^73 - q^74 + q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 + 4 * q^80 + 10 * q^81 - 8 * q^82 + 2 * q^84 + q^85 - 3 * q^86 + 12 * q^88 + 7 * q^89 - 4 * q^90 - 4 * q^91 - 12 * q^92 + 10 * q^93 - 30 * q^94 + 24 * q^95 - 5 * q^96 - 6 * q^97 - 16 * q^98 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.623307	+	1.07960i	0.278751	+	0.482811i	0.971075	−	0.238776i	$-0.0767462\pi$
$5$	0.623307	+	1.07960i	0.278751	+	0.482811i	−0.692323	+	0.721587i	$0.743413\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−2.27938	−	1.34329i	−0.861524	−	0.507717i
$7$	−2.27938	−	1.34329i	−0.861524	−	0.507717i
$8$	−1.00000			−0.353553
$9$	1.00000			0.333333
$10$	1.24661			0.394214
$11$	−2.49532			−0.752369			−0.376184	−	0.926545i	$-0.622764\pi$
$11$	−2.49532			−0.752369			−0.376184	+	0.926545i	$0.622764\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−0.785103	−	3.51904i	−0.217748	−	0.976005i
$13$	−0.785103	−	3.51904i	−0.217748	−	0.976005i
$14$	−2.30301	+	1.30235i	−0.615506	+	0.348069i
$15$	−0.623307	−	1.07960i	−0.160937	−	0.278751i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.247662	−	0.428963i	−0.0600669	−	0.104039i	0.834428	−	0.551117i	$-0.185798\pi$
$17$	−0.247662	−	0.428963i	−0.0600669	−	0.104039i	−0.894495	+	0.447078i	$0.852465\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−7.67156			−1.75998			−0.879988	−	0.474996i	$-0.842450\pi$
$19$	−7.67156			−1.75998			−0.879988	+	0.474996i	$0.842450\pi$
$20$	0.623307	−	1.07960i	0.139376	−	0.241406i
$21$	2.27938	+	1.34329i	0.497401	+	0.293130i
$22$	−1.24766	+	2.16101i	−0.266002	+	0.460730i
$23$	−0.224026	+	0.388024i	−0.0467127	+	0.0809087i	−0.888436	−	0.459000i	$-0.848208\pi$
$23$	−0.224026	+	0.388024i	−0.0467127	+	0.0809087i	0.841724	+	0.539909i	$0.181541\pi$
$24$	1.00000			0.204124
$25$	1.72298	−	2.98428i	0.344595	−	0.596857i
$26$	−3.44013	−	1.07960i	−0.674664	−	0.211727i
$27$	−1.00000			−0.192450
$28$	−0.0236360	+	2.64565i	−0.00446679	+	0.499980i
$29$	−3.71142	−	6.42837i	−0.689194	−	1.19372i	−0.972099	−	0.234571i	$-0.924631\pi$
$29$	−3.71142	−	6.42837i	−0.689194	−	1.19372i	0.282905	−	0.959148i	$-0.408702\pi$
$30$	−1.24661			−0.227599
$31$	−4.06448	+	7.03989i	−0.730002	+	1.26440i	0.226879	+	0.973923i	$0.427148\pi$
$31$	−4.06448	+	7.03989i	−0.730002	+	1.26440i	−0.956882	+	0.290478i	$0.906186\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.49532			0.434380
$34$	−0.495324			−0.0849474
$35$	0.0294650	−	3.29810i	0.00498050	−	0.557480i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.37097	+	2.37459i	−0.225386	+	0.390380i	−0.956435	−	0.291945i	$-0.905698\pi$
$37$	−1.37097	+	2.37459i	−0.225386	+	0.390380i	0.731049	+	0.682325i	$0.239031\pi$
$38$	−3.83578	+	6.64376i	−0.622246	+	1.07776i
$39$	0.785103	+	3.51904i	0.125717	+	0.563497i
$40$	−0.623307	−	1.07960i	−0.0985534	−	0.170700i
$41$	−1.87097	−	3.24061i	−0.292196	−	0.506099i	0.682133	−	0.731229i	$-0.261053\pi$
$41$	−1.87097	−	3.24061i	−0.292196	−	0.506099i	−0.974329	+	0.225130i	$0.927719\pi$
$42$	2.30301	−	1.30235i	0.355363	−	0.200958i
$43$	1.47532	−	2.55532i	0.224983	−	0.389683i	−0.731331	−	0.682023i	$-0.761101\pi$
$43$	1.47532	−	2.55532i	0.224983	−	0.389683i	0.956314	+	0.292340i	$0.0944339\pi$
$44$	1.24766	+	2.16101i	0.188092	+	0.325785i
$45$	0.623307	+	1.07960i	0.0929171	+	0.160937i
$46$	0.224026	+	0.388024i	0.0330308	+	0.0572111i
$47$	3.29729	+	5.71107i	0.480959	+	0.833046i	0.999761	−	0.0218486i	$-0.00695519\pi$
$47$	3.29729	+	5.71107i	0.480959	+	0.833046i	−0.518802	+	0.854894i	$0.673622\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	3.39113	+	6.12374i	0.484447	+	0.874820i
$50$	−1.72298	−	2.98428i	−0.243666	−	0.422042i
$51$	0.247662	+	0.428963i	0.0346796	+	0.0600669i
$52$	−2.65502	+	2.43944i	−0.368185	+	0.338289i
$53$	3.86750	−	6.69870i	0.531241	−	0.920137i	−0.468094	−	0.883679i	$-0.655059\pi$
$53$	3.86750	−	6.69870i	0.531241	−	0.920137i	0.999335	−	0.0364583i	$-0.0116076\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−1.55535	−	2.69395i	−0.209724	−	0.363252i
$56$	2.27938	+	1.34329i	0.304595	+	0.179505i
$57$	7.67156			1.01612
$58$	−7.42285			−0.974668
$59$	0.727653	+	1.26033i	0.0947324	+	0.164081i	0.909497	−	0.415711i	$-0.136467\pi$
$59$	0.727653	+	1.26033i	0.0947324	+	0.164081i	−0.814764	+	0.579792i	$0.803134\pi$
$60$	−0.623307	+	1.07960i	−0.0804686	+	0.139376i
$61$	−4.19934			−0.537671			−0.268835	−	0.963186i	$-0.586639\pi$
$61$	−4.19934			−0.537671			−0.268835	+	0.963186i	$0.586639\pi$
$62$	4.06448	+	7.03989i	0.516190	+	0.894067i
$63$	−2.27938	−	1.34329i	−0.287175	−	0.169239i
$64$	1.00000			0.125000
$65$	3.30979	−	3.04103i	0.410529	−	0.377194i
$66$	1.24766	−	2.16101i	0.153577	−	0.266002i
$67$	0.0276094			0.00337303			0.00168652	−	0.999999i	$-0.499463\pi$
$67$	0.0276094			0.00337303			0.00168652	+	0.999999i	$0.499463\pi$
$68$	−0.247662	+	0.428963i	−0.0300334	+	0.0520194i
$69$	0.224026	−	0.388024i	0.0269696	−	0.0467127i
$70$	−2.84150	−	1.67457i	−0.339625	−	0.200149i
$71$	4.68884	−	8.12130i	0.556463	−	0.963821i	−0.441326	−	0.897347i	$-0.645492\pi$
$71$	4.68884	−	8.12130i	0.556463	−	0.963821i	0.997788	−	0.0664743i	$-0.0211751\pi$
$72$	−1.00000			−0.117851
$73$	−5.07151	+	8.78412i	−0.593576	+	1.02810i	0.400170	+	0.916441i	$0.368951\pi$
$73$	−5.07151	+	8.78412i	−0.593576	+	1.02810i	−0.993746	+	0.111663i	$0.964382\pi$
$74$	1.37097	+	2.37459i	0.159372	+	0.276040i
$75$	−1.72298	+	2.98428i	−0.198952	+	0.344595i
$76$	3.83578	+	6.64376i	0.439994	+	0.762092i
$77$	5.68779	+	3.35195i	0.648184	+	0.381990i
$78$	3.44013	+	1.07960i	0.389518	+	0.122241i
$79$	−4.93545	−	8.54845i	−0.555282	−	0.961776i	−0.997882	−	0.0650567i	$-0.979277\pi$
$79$	−4.93545	−	8.54845i	−0.555282	−	0.961776i	0.442600	−	0.896719i	$-0.354056\pi$
$80$	−1.24661			−0.139376
$81$	1.00000			0.111111
$82$	−3.74194			−0.413228
$83$	7.42285			0.814763			0.407382	−	0.913258i	$-0.366442\pi$
$83$	7.42285			0.814763			0.407382	+	0.913258i	$0.366442\pi$
$84$	0.0236360	−	2.64565i	0.00257890	−	0.288664i
$85$	0.308739	−	0.534751i	0.0334874	−	0.0580019i
$86$	−1.47532	−	2.55532i	−0.159087	−	0.275547i
$87$	3.71142	+	6.42837i	0.397906	+	0.689194i
$88$	2.49532			0.266002
$89$	5.74056	−	9.94294i	0.608498	−	1.05395i	−0.382990	−	0.923753i	$-0.625106\pi$
$89$	5.74056	−	9.94294i	0.608498	−	1.05395i	0.991488	−	0.130197i	$-0.0415611\pi$
$90$	1.24661			0.131405
$91$	−2.93755	+	9.07584i	−0.307939	+	0.951406i
$92$	0.448052			0.0467127
$93$	4.06448	−	7.03989i	0.421467	−	0.730002i
$94$	6.59458			0.680179
$95$	−4.78173	−	8.28221i	−0.490596	−	0.849736i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−0.509831	+	0.883054i	−0.0517655	+	0.0896605i	−0.890747	−	0.454499i	$-0.849818\pi$
$97$	−0.509831	+	0.883054i	−0.0517655	+	0.0896605i	0.838982	+	0.544160i	$0.183152\pi$
$98$	6.99888	+	0.125065i	0.706994	+	0.0126335i
$99$	−2.49532			−0.250790
$100$	−3.44595			−0.344595
$101$	17.9425			1.78535			0.892675	−	0.450701i	$-0.148826\pi$
$101$	17.9425			1.78535			0.892675	+	0.450701i	$0.148826\pi$
$102$	0.495324			0.0490444
$103$	0.524685	+	0.908780i	0.0516987	+	0.0895448i	0.890717	−	0.454559i	$-0.150203\pi$
$103$	0.524685	+	0.908780i	0.0516987	+	0.0895448i	−0.839018	+	0.544104i	$0.816870\pi$
$104$	0.785103	+	3.51904i	0.0769857	+	0.345070i
$105$	−0.0294650	+	3.29810i	−0.00287549	+	0.321861i
$106$	−3.86750	−	6.69870i	−0.375644	−	0.650635i
$107$	5.09152	−	8.81877i	0.492216	−	0.852543i	−0.507744	−	0.861508i	$-0.669520\pi$
$107$	5.09152	−	8.81877i	0.492216	−	0.852543i	0.999960	+	0.00896501i	$0.00285369\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	9.92285	−	17.1869i	0.950436	−	1.64620i	0.205955	−	0.978562i	$-0.433970\pi$
$109$	9.92285	−	17.1869i	0.950436	−	1.64620i	0.744482	−	0.667643i	$-0.232697\pi$
$110$	−3.11070			−0.296594
$111$	1.37097	−	2.37459i	0.130127	−	0.225386i
$112$	2.30301	−	1.30235i	0.217614	−	0.123061i
$113$	−7.93440	+	13.7428i	−0.746406	+	1.29281i	0.203129	+	0.979152i	$0.434889\pi$
$113$	−7.93440	+	13.7428i	−0.746406	+	1.29281i	−0.949535	+	0.313661i	$0.898445\pi$
$114$	3.83578	−	6.64376i	0.359254	−	0.622246i
$115$	−0.558548			−0.0520848
$116$	−3.71142	+	6.42837i	−0.344597	+	0.596860i
$117$	−0.785103	−	3.51904i	−0.0725828	−	0.325335i
$118$	1.45531			0.133972
$119$	−0.0117075	+	1.31045i	−0.00107322	+	0.120129i
$120$	0.623307	+	1.07960i	0.0568999	+	0.0985534i
$121$	−4.77336			−0.433942
$122$	−2.09967	+	3.63674i	−0.190095	+	0.329255i
$123$	1.87097	+	3.24061i	0.168700	+	0.292196i
$124$	8.12896			0.730002
$125$	10.5288			0.941728
$126$	−2.30301	+	1.30235i	−0.205169	+	0.116023i
$127$	4.23846	+	7.34124i	0.376103	+	0.651429i	0.990491	−	0.137574i	$-0.0439306\pi$
$127$	4.23846	+	7.34124i	0.376103	+	0.651429i	−0.614389	+	0.789004i	$0.710597\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−1.47532	+	2.55532i	−0.129894	+	0.224983i
$130$	−0.978720	−	4.38688i	−0.0858394	−	0.384755i
$131$	−8.26678	−	14.3185i	−0.722272	−	1.25101i	−0.960087	−	0.279701i	$-0.909765\pi$
$131$	−8.26678	−	14.3185i	−0.722272	−	1.25101i	0.237816	−	0.971310i	$-0.423569\pi$
$132$	−1.24766	−	2.16101i	−0.108595	−	0.188092i
$133$	17.4864	+	10.3051i	1.51626	+	0.893569i
$134$	0.0138047	−	0.0239105i	0.00119255	−	0.00206555i
$135$	−0.623307	−	1.07960i	−0.0536457	−	0.0929171i
$136$	0.247662	+	0.428963i	0.0212368	+	0.0367833i
$137$	0.428418	+	0.742042i	0.0366023	+	0.0633970i	0.883746	−	0.467966i	$-0.155013\pi$
$137$	0.428418	+	0.742042i	0.0366023	+	0.0633970i	−0.847144	+	0.531363i	$0.821680\pi$
$138$	−0.224026	−	0.388024i	−0.0190704	−	0.0330308i
$139$	4.74886	−	8.22528i	0.402793	−	0.697659i	−0.591268	−	0.806475i	$-0.701373\pi$
$139$	4.74886	−	8.22528i	0.402793	−	0.697659i	0.994062	+	0.108816i	$0.0347060\pi$
$140$	−2.87097	+	1.62353i	−0.242641	+	0.137213i
$141$	−3.29729	−	5.71107i	−0.277682	−	0.480959i
$142$	−4.68884	−	8.12130i	−0.393478	−	0.681525i
$143$	1.95909	+	8.78114i	0.163827	+	0.734315i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	4.62671	−	8.01370i	0.384227	−	0.665501i
$146$	5.07151	+	8.78412i	0.419721	+	0.726979i
$147$	−3.39113	−	6.12374i	−0.279696	−	0.505078i
$148$	2.74194			0.225386
$149$	−4.73744			−0.388106			−0.194053	−	0.980991i	$-0.562163\pi$
$149$	−4.73744			−0.388106			−0.194053	+	0.980991i	$0.562163\pi$
$150$	1.72298	+	2.98428i	0.140681	+	0.243666i
$151$	−3.56085	+	6.16758i	−0.289778	+	0.501911i	−0.973757	−	0.227592i	$-0.926915\pi$
$151$	−3.56085	+	6.16758i	−0.289778	+	0.501911i	0.683978	+	0.729502i	$0.260248\pi$
$152$	7.67156			0.622246
$153$	−0.247662	−	0.428963i	−0.0200223	−	0.0346796i
$154$	5.74677	−	3.24979i	0.463088	−	0.261876i
$155$	−10.1337			−0.813956
$156$	2.65502	−	2.43944i	0.212572	−	0.195311i
$157$	−7.52147	+	13.0276i	−0.600279	+	1.03971i	0.392500	+	0.919752i	$0.371610\pi$
$157$	−7.52147	+	13.0276i	−0.600279	+	1.03971i	−0.992779	+	0.119961i	$0.961723\pi$
$158$	−9.87090			−0.785287
$159$	−3.86750	+	6.69870i	−0.306712	+	0.531241i
$160$	−0.623307	+	1.07960i	−0.0492767	+	0.0853498i
$161$	1.03187	−	0.583522i	0.0813228	−	0.0459880i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−9.02971			−0.707261			−0.353631	−	0.935385i	$-0.615053\pi$
$163$	−9.02971			−0.707261			−0.353631	+	0.935385i	$0.615053\pi$
$164$	−1.87097	+	3.24061i	−0.146098	+	0.253049i
$165$	1.55535	+	2.69395i	0.121084	+	0.209724i
$166$	3.71142	−	6.42837i	0.288062	−	0.498939i
$167$	1.42442	+	2.46716i	0.110225	+	0.190915i	0.915861	−	0.401496i	$-0.131510\pi$
$167$	1.42442	+	2.46716i	0.110225	+	0.190915i	−0.805636	+	0.592411i	$0.798176\pi$
$168$	−2.27938	−	1.34329i	−0.175858	−	0.103637i
$169$	−11.7672	+	5.52561i	−0.905171	+	0.425047i
$170$	−0.308739	−	0.534751i	−0.0236792	−	0.0410136i
$171$	−7.67156			−0.586659
$172$	−2.95063			−0.224983
$173$	−25.4875			−1.93778			−0.968891	−	0.247487i	$-0.920395\pi$
$173$	−25.4875			−1.93778			−0.968891	+	0.247487i	$0.920395\pi$
$174$	7.42285			0.562725
$175$	−7.93608	+	4.48785i	−0.599912	+	0.339250i
$176$	1.24766	−	2.16101i	0.0940461	−	0.162893i
$177$	−0.727653	−	1.26033i	−0.0546938	−	0.0947324i
$178$	−5.74056	−	9.94294i	−0.430273	−	0.745255i
$179$	18.2006			1.36038			0.680189	−	0.733037i	$-0.261898\pi$
$179$	18.2006			1.36038			0.680189	+	0.733037i	$0.261898\pi$
$180$	0.623307	−	1.07960i	0.0464585	−	0.0804686i
$181$	−13.7305			−1.02058			−0.510290	−	0.860003i	$-0.670462\pi$
$181$	−13.7305			−1.02058			−0.510290	+	0.860003i	$0.670462\pi$
$182$	6.39113	+	7.08191i	0.473742	+	0.524946i
$183$	4.19934			0.310424
$184$	0.224026	−	0.388024i	0.0165154	−	0.0286055i
$185$	−3.41814			−0.251306
$186$	−4.06448	−	7.03989i	−0.298022	−	0.516190i
$187$	0.617997	+	1.07040i	0.0451924	+	0.0782756i
$188$	3.29729	−	5.71107i	0.240480	−	0.416523i
$189$	2.27938	+	1.34329i	0.165800	+	0.0977101i
$190$	−9.56347			−0.693807
$191$	5.28588			0.382473			0.191236	−	0.981544i	$-0.438750\pi$
$191$	5.28588			0.382473			0.191236	+	0.981544i	$0.438750\pi$
$192$	−1.00000			−0.0721688
$193$	4.81197			0.346373			0.173187	−	0.984889i	$-0.444594\pi$
$193$	4.81197			0.346373			0.173187	+	0.984889i	$0.444594\pi$
$194$	0.509831	+	0.883054i	0.0366038	+	0.0633996i
$195$	−3.30979	+	3.04103i	−0.237019	+	0.217773i
$196$	3.60775	−	5.99868i	0.257696	−	0.428477i
$197$	11.7743	+	20.3937i	0.838883	+	1.45299i	0.890829	+	0.454339i	$0.150124\pi$
$197$	11.7743	+	20.3937i	0.838883	+	1.45299i	−0.0519458	+	0.998650i	$0.516542\pi$
$198$	−1.24766	+	2.16101i	−0.0886675	+	0.153577i
$199$	−5.63984	−	9.76849i	−0.399798	−	0.692470i	0.593903	−	0.804537i	$-0.297586\pi$
$199$	−5.63984	−	9.76849i	−0.399798	−	0.692470i	−0.993701	+	0.112067i	$0.964253\pi$
$200$	−1.72298	+	2.98428i	−0.121833	+	0.211021i
$201$	−0.0276094			−0.00194742
$202$	8.97127	−	15.5387i	0.631217	−	1.09330i
$203$	−0.175447	+	19.6382i	−0.0123139	+	1.37833i
$204$	0.247662	−	0.428963i	0.0173398	−	0.0300334i
$205$	2.33237	−	4.03979i	0.162900	−	0.282151i
$206$	1.04937			0.0731130
$207$	−0.224026	+	0.388024i	−0.0155709	+	0.0269696i
$208$	3.44013	+	1.07960i	0.238530	+	0.0748567i
$209$	19.1430			1.32415
$210$	2.84150	+	1.67457i	0.196082	+	0.115556i
$211$	−6.22021	−	10.7737i	−0.428217	−	0.741693i	0.568498	−	0.822685i	$-0.307525\pi$
$211$	−6.22021	−	10.7737i	−0.428217	−	0.741693i	−0.996715	+	0.0809915i	$0.974191\pi$
$212$	−7.73499			−0.531241
$213$	−4.68884	+	8.12130i	−0.321274	+	0.556463i
$214$	−5.09152	−	8.81877i	−0.348049	−	0.602839i
$215$	3.67830			0.250858
$216$	1.00000			0.0680414
$217$	18.7211	−	10.5868i	1.27087	−	0.718678i
$218$	−9.92285	−	17.1869i	−0.672060	−	1.16404i
$219$	5.07151	−	8.78412i	0.342701	−	0.593576i
$220$	−1.55535	+	2.69395i	−0.104862	+	0.181626i
$221$	−1.31510	+	1.20831i	−0.0884630	+	0.0812799i
$222$	−1.37097	−	2.37459i	−0.0920134	−	0.159372i
$223$	−10.4651	−	18.1260i	−0.700793	−	1.21381i	−0.968188	−	0.250222i	$-0.919496\pi$
$223$	−10.4651	−	18.1260i	−0.700793	−	1.21381i	0.267396	−	0.963587i	$-0.413837\pi$
$224$	0.0236360	−	2.64565i	0.00157925	−	0.176770i
$225$	1.72298	−	2.98428i	0.114865	−	0.198952i
$226$	7.93440	+	13.7428i	0.527789	+	0.914157i
$227$	−8.79052	−	15.2256i	−0.583447	−	1.01056i	−0.995067	−	0.0992044i	$-0.968370\pi$
$227$	−8.79052	−	15.2256i	−0.583447	−	1.01056i	0.411620	−	0.911356i	$-0.364963\pi$
$228$	−3.83578	−	6.64376i	−0.254031	−	0.439994i
$229$	7.24620	+	12.5508i	0.478842	+	0.829379i	0.999706	−	0.0242609i	$-0.00772324\pi$
$229$	7.24620	+	12.5508i	0.478842	+	0.829379i	−0.520863	+	0.853640i	$0.674390\pi$
$230$	−0.279274	+	0.483717i	−0.0184148	+	0.0318953i
$231$	−5.68779	−	3.35195i	−0.374229	−	0.220542i
$232$	3.71142	+	6.42837i	0.243667	+	0.422043i
$233$	−7.24897	−	12.5556i	−0.474896	−	0.822544i	0.524691	−	0.851293i	$-0.324181\pi$
$233$	−7.24897	−	12.5556i	−0.474896	−	0.822544i	−0.999587	+	0.0287492i	$0.990848\pi$
$234$	−3.44013	−	1.07960i	−0.224888	−	0.0705756i
$235$	−4.11045	+	7.11950i	−0.268136	+	0.464425i
$236$	0.727653	−	1.26033i	0.0473662	−	0.0820407i
$237$	4.93545	+	8.54845i	0.320592	+	0.555282i
$238$	1.12903	+	0.665365i	0.0731842	+	0.0431292i
$239$	3.15093			0.203817			0.101908	−	0.994794i	$-0.467505\pi$
$239$	3.15093			0.203817			0.101908	+	0.994794i	$0.467505\pi$
$240$	1.24661			0.0804686
$241$	12.4223	+	21.5160i	0.800189	+	1.38597i	0.919491	+	0.393111i	$0.128601\pi$
$241$	12.4223	+	21.5160i	0.800189	+	1.38597i	−0.119302	+	0.992858i	$0.538066\pi$
$242$	−2.38668	+	4.13385i	−0.153422	+	0.265734i
$243$	−1.00000			−0.0641500
$244$	2.09967	+	3.63674i	0.134418	+	0.232818i
$245$	−4.49747	+	7.47803i	−0.287333	+	0.477754i
$246$	3.74194			0.238577
$247$	6.02296	+	26.9965i	0.383232	+	1.71775i
$248$	4.06448	−	7.03989i	0.258095	−	0.447033i
$249$	−7.42285			−0.470404
$250$	5.26442	−	9.11824i	0.332951	−	0.576688i
$251$	−3.69421	+	6.39857i	−0.233177	+	0.403874i	−0.958741	−	0.284280i	$-0.908245\pi$
$251$	−3.69421	+	6.39857i	−0.233177	+	0.403874i	0.725564	+	0.688154i	$0.241579\pi$
$252$	−0.0236360	+	2.64565i	−0.00148893	+	0.166660i
$253$	0.559018	−	0.968247i	0.0351451	−	0.0608732i
$254$	8.47693			0.531890
$255$	−0.308739	+	0.534751i	−0.0193340	+	0.0334874i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.4446	+	23.2867i	−0.838650	+	1.45258i	0.0523740	+	0.998628i	$0.483321\pi$
$257$	−13.4446	+	23.2867i	−0.838650	+	1.45258i	−0.891024	+	0.453957i	$0.850012\pi$
$258$	1.47532	+	2.55532i	0.0918491	+	0.159087i
$259$	6.31472	−	3.57097i	0.392378	−	0.221889i
$260$	−4.28851	−	1.34584i	−0.265962	−	0.0834656i
$261$	−3.71142	−	6.42837i	−0.229731	−	0.397906i
$262$	−16.5336			−1.02145
$263$	−2.93123			−0.180748			−0.0903738	−	0.995908i	$-0.528806\pi$
$263$	−2.93123			−0.180748			−0.0903738	+	0.995908i	$0.528806\pi$
$264$	−2.49532			−0.153577
$265$	9.64254			0.592337
$266$	17.6677	−	9.99108i	1.08328	−	0.612592i
$267$	−5.74056	+	9.94294i	−0.351317	+	0.608498i
$268$	−0.0138047	−	0.0239105i	−0.000843258	−	0.00146056i
$269$	−1.07222	−	1.85713i	−0.0653741	−	0.113231i	0.831486	−	0.555546i	$-0.187491\pi$
$269$	−1.07222	−	1.85713i	−0.0653741	−	0.113231i	−0.896860	+	0.442315i	$0.854157\pi$
$270$	−1.24661			−0.0758665
$271$	−8.64220	+	14.9687i	−0.524976	+	0.909285i	0.474601	+	0.880201i	$0.342592\pi$
$271$	−8.64220	+	14.9687i	−0.524976	+	0.909285i	−0.999577	+	0.0290842i	$0.990741\pi$
$272$	0.495324			0.0300334
$273$	2.93755	−	9.07584i	0.177788	−	0.549295i
$274$	0.856837			0.0517634
$275$	−4.29939	+	7.44676i	−0.259263	+	0.449056i
$276$	−0.448052			−0.0269696
$277$	1.41690	+	2.45415i	0.0851336	+	0.147456i	0.905448	−	0.424457i	$-0.139535\pi$
$277$	1.41690	+	2.45415i	0.0851336	+	0.147456i	−0.820315	+	0.571913i	$0.806202\pi$
$278$	−4.74886	−	8.22528i	−0.284818	−	0.493319i
$279$	−4.06448	+	7.03989i	−0.243334	+	0.421467i
$280$	−0.0294650	+	3.29810i	−0.00176087	+	0.197099i
$281$	−28.5254			−1.70168			−0.850842	−	0.525422i	$-0.823907\pi$
$281$	−28.5254			−1.70168			−0.850842	+	0.525422i	$0.823907\pi$
$282$	−6.59458			−0.392702
$283$	−4.59802			−0.273324			−0.136662	−	0.990618i	$-0.543637\pi$
$283$	−4.59802			−0.273324			−0.136662	+	0.990618i	$0.543637\pi$
$284$	−9.37767			−0.556463
$285$	4.78173	+	8.28221i	0.283245	+	0.490596i
$286$	8.58423	+	2.69395i	0.507596	+	0.159297i
$287$	−0.0884446	+	9.89984i	−0.00522072	+	0.584369i
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	8.37733	−	14.5100i	0.492784	−	0.853527i
$290$	−4.62671	−	8.01370i	−0.271690	−	0.470581i
$291$	0.509831	−	0.883054i	0.0298868	−	0.0517655i
$292$	10.1430			0.593576
$293$	3.19384	−	5.53189i	0.186586	−	0.323177i	−0.757524	−	0.652808i	$-0.773591\pi$
$293$	3.19384	−	5.53189i	0.186586	−	0.323177i	0.944110	+	0.329631i	$0.106924\pi$
$294$	−6.99888	−	0.125065i	−0.408183	−	0.00729395i
$295$	−0.907102	+	1.57115i	−0.0528135	+	0.0914757i
$296$	1.37097	−	2.37459i	0.0796859	−	0.138020i
$297$	2.49532			0.144793
$298$	−2.36872	+	4.10274i	−0.137216	+	0.237665i
$299$	1.54136	+	0.483717i	0.0891389	+	0.0279740i
$300$	3.44595			0.198952
$301$	−6.79535	+	3.84276i	−0.391677	+	0.221493i
$302$	3.56085	+	6.16758i	0.204904	+	0.354904i
$303$	−17.9425			−1.03077
$304$	3.83578	−	6.64376i	0.219997	−	0.381046i
$305$	−2.61748	−	4.53360i	−0.149876	−	0.259593i
$306$	−0.495324			−0.0283158
$307$	−1.39899			−0.0798446			−0.0399223	−	0.999203i	$-0.512711\pi$
$307$	−1.39899			−0.0798446			−0.0399223	+	0.999203i	$0.512711\pi$
$308$	0.0589796	−	6.60174i	0.00336067	−	0.376169i
$309$	−0.524685	−	0.908780i	−0.0298483	−	0.0516987i
$310$	−5.06684	+	8.77602i	−0.287777	+	0.498444i
$311$	−8.55183	+	14.8122i	−0.484930	+	0.839923i	−0.999850	−	0.0173150i	$-0.994488\pi$
$311$	−8.55183	+	14.8122i	−0.484930	+	0.839923i	0.514920	+	0.857238i	$0.327822\pi$
$312$	−0.785103	−	3.51904i	−0.0444477	−	0.199226i
$313$	−5.81247	−	10.0675i	−0.328540	−	0.569048i	0.653682	−	0.756769i	$-0.273223\pi$
$313$	−5.81247	−	10.0675i	−0.328540	−	0.569048i	−0.982222	+	0.187721i	$0.939890\pi$
$314$	7.52147	+	13.0276i	0.424461	+	0.735188i
$315$	0.0294650	−	3.29810i	0.00166017	−	0.185827i
$316$	−4.93545	+	8.54845i	−0.277641	+	0.480888i
$317$	−3.29277	−	5.70324i	−0.184940	−	0.320326i	0.758616	−	0.651538i	$-0.225876\pi$
$317$	−3.29277	−	5.70324i	−0.184940	−	0.320326i	−0.943556	+	0.331212i	$0.892543\pi$
$318$	3.86750	+	6.69870i	0.216878	+	0.375644i
$319$	9.26121	+	16.0409i	0.518528	+	0.898117i
$320$	0.623307	+	1.07960i	0.0348439	+	0.0603514i
$321$	−5.09152	+	8.81877i	−0.284181	+	0.492216i
$322$	0.0105902	−	1.18539i	0.000590168	−	0.0660590i
$323$	1.89995	+	3.29082i	0.105716	+	0.183106i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−11.8545	−	3.72025i	−0.657570	−	0.206362i
$326$	−4.51485	+	7.81996i	−0.250055	+	0.433107i
$327$	−9.92285	+	17.1869i	−0.548735	+	0.950436i
$328$	1.87097	+	3.24061i	0.103307	+	0.178933i
$329$	0.155870	−	17.4469i	0.00859338	−	0.961880i
$330$	3.11070			0.171239
$331$	−23.2685			−1.27895			−0.639477	−	0.768810i	$-0.720849\pi$
$331$	−23.2685			−1.27895			−0.639477	+	0.768810i	$0.720849\pi$
$332$	−3.71142	−	6.42837i	−0.203691	−	0.352803i
$333$	−1.37097	+	2.37459i	−0.0751286	+	0.130127i
$334$	2.84883			0.155881
$335$	0.0172092	+	0.0298071i	0.000940236	+	0.00162854i
$336$	−2.30301	+	1.30235i	−0.125640	+	0.0710492i
$337$	19.4320			1.05853			0.529263	−	0.848458i	$-0.322468\pi$
$337$	19.4320			1.05853			0.529263	+	0.848458i	$0.322468\pi$
$338$	−1.09829	+	12.9535i	−0.0597394	+	0.704579i
$339$	7.93440	−	13.7428i	0.430938	−	0.746406i
$340$	−0.617478			−0.0334874
$341$	10.1422	−	17.5668i	0.549231	−	0.951296i
$342$	−3.83578	+	6.64376i	−0.207415	+	0.359254i
$343$	0.496304	−	18.5136i	0.0267979	−	0.999641i
$344$	−1.47532	+	2.55532i	−0.0795437	+	0.137774i
$345$	0.558548			0.0300712
$346$	−12.7438	+	22.0729i	−0.685110	+	1.18664i
$347$	−14.8354	−	25.6956i	−0.796404	−	1.37941i	−0.921944	−	0.387324i	$-0.873400\pi$
$347$	−14.8354	−	25.6956i	−0.796404	−	1.37941i	0.125540	−	0.992089i	$-0.459934\pi$
$348$	3.71142	−	6.42837i	0.198953	−	0.344597i
$349$	−13.3023	−	23.0403i	−0.712058	−	1.23332i	−0.964083	−	0.265600i	$-0.914430\pi$
$349$	−13.3023	−	23.0403i	−0.712058	−	1.23332i	0.252025	−	0.967721i	$-0.418904\pi$
$350$	−0.0814487	+	9.11678i	−0.00435362	+	0.487312i
$351$	0.785103	+	3.51904i	0.0419057	+	0.187832i
$352$	−1.24766	−	2.16101i	−0.0665006	−	0.115182i
$353$	−13.8188			−0.735499			−0.367750	−	0.929925i	$-0.619872\pi$
$353$	−13.8188			−0.735499			−0.367750	+	0.929925i	$0.619872\pi$
$354$	−1.45531			−0.0773487
$355$	11.6903			0.620458
$356$	−11.4811			−0.608498
$357$	0.0117075	−	1.31045i	0.000619627	−	0.0693565i
$358$	9.10030	−	15.7622i	0.480966	−	0.833058i
$359$	1.38095	+	2.39188i	0.0728840	+	0.126239i	0.900164	−	0.435551i	$-0.143446\pi$
$359$	1.38095	+	2.39188i	0.0728840	+	0.126239i	−0.827280	+	0.561790i	$0.810113\pi$
$360$	−0.623307	−	1.07960i	−0.0328511	−	0.0568999i
$361$	39.8528			2.09752
$362$	−6.86524	+	11.8910i	−0.360829	+	0.624975i
$363$	4.77336			0.250536
$364$	9.32868	−	1.99393i	0.488956	−	0.104510i
$365$	−12.6444			−0.661840
$366$	2.09967	−	3.63674i	0.109752	−	0.190095i
$367$	−10.9230			−0.570177			−0.285089	−	0.958501i	$-0.592023\pi$
$367$	−10.9230			−0.570177			−0.285089	+	0.958501i	$0.592023\pi$
$368$	−0.224026	−	0.388024i	−0.0116782	−	0.0202272i
$369$	−1.87097	−	3.24061i	−0.0973987	−	0.168700i
$370$	−1.70907	+	2.96019i	−0.0888502	+	0.153893i
$371$	−17.8138	+	10.0737i	−0.924846	+	0.523000i
$372$	−8.12896			−0.421467
$373$	19.6861			1.01931			0.509653	−	0.860380i	$-0.329774\pi$
$373$	19.6861			1.01931			0.509653	+	0.860380i	$0.329774\pi$
$374$	1.23599			0.0639117
$375$	−10.5288			−0.543707
$376$	−3.29729	−	5.71107i	−0.170045	−	0.294526i
$377$	−19.7078	+	18.1076i	−1.01501	+	0.932587i
$378$	2.30301	−	1.30235i	0.118454	−	0.0669858i
$379$	−8.31713	−	14.4057i	−0.427222	−	0.739970i	0.569403	−	0.822059i	$-0.307174\pi$
$379$	−8.31713	−	14.4057i	−0.427222	−	0.739970i	−0.996625	+	0.0820882i	$0.973841\pi$
$380$	−4.78173	+	8.28221i	−0.245298	+	0.424868i
$381$	−4.23846	−	7.34124i	−0.217143	−	0.376103i
$382$	2.64294	−	4.57771i	0.135225	−	0.234216i
$383$	36.3667			1.85825			0.929127	−	0.369761i	$-0.120560\pi$
$383$	36.3667			1.85825			0.929127	+	0.369761i	$0.120560\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−0.0735247	+	8.22982i	−0.00374717	+	0.419431i
$386$	2.40599	−	4.16729i	0.122461	−	0.212109i
$387$	1.47532	−	2.55532i	0.0749945	−	0.129894i
$388$	1.01966			0.0517655
$389$	8.89008	−	15.3981i	0.450745	−	0.780713i	−0.547687	−	0.836683i	$-0.684492\pi$
$389$	8.89008	−	15.3981i	0.450745	−	0.780713i	0.998432	+	0.0559696i	$0.0178250\pi$
$390$	0.978720	+	4.38688i	0.0495594	+	0.222138i
$391$	0.221931			0.0112235
$392$	−3.39113	−	6.12374i	−0.171278	−	0.309296i
$393$	8.26678	+	14.3185i	0.417004	+	0.722272i
$394$	23.5486			1.18636
$395$	6.15260	−	10.6566i	0.309571	−	0.536192i
$396$	1.24766	+	2.16101i	0.0626974	+	0.108595i
$397$	8.87904			0.445626			0.222813	−	0.974861i	$-0.428476\pi$
$397$	8.87904			0.445626			0.222813	+	0.974861i	$0.428476\pi$
$398$	−11.2797			−0.565400
$399$	−17.4864	−	10.3051i	−0.875414	−	0.515903i
$400$	1.72298	+	2.98428i	0.0861489	+	0.149214i
$401$	15.0815	−	26.1219i	0.753134	−	1.30447i	−0.193163	−	0.981167i	$-0.561874\pi$
$401$	15.0815	−	26.1219i	0.753134	−	1.30447i	0.946297	−	0.323300i	$-0.104792\pi$
$402$	−0.0138047	+	0.0239105i	−0.000688517	+	0.00119255i
$403$	27.9647	+	8.77602i	1.39302	+	0.437165i
$404$	−8.97127	−	15.5387i	−0.446338	−	0.773079i
$405$	0.623307	+	1.07960i	0.0309724	+	0.0536457i
$406$	16.9195	+	9.97105i	0.839700	+	0.494855i
$407$	3.42101	−	5.92537i	0.169573	−	0.293709i
$408$	−0.247662	−	0.428963i	−0.0122611	−	0.0212368i
$409$	−8.38601	−	14.5250i	−0.414662	−	0.718215i	0.580731	−	0.814095i	$-0.302767\pi$
$409$	−8.38601	−	14.5250i	−0.414662	−	0.718215i	−0.995393	+	0.0958804i	$0.969433\pi$
$410$	−2.33237	−	4.03979i	−0.115188	−	0.199511i
$411$	−0.428418	−	0.742042i	−0.0211323	−	0.0366023i
$412$	0.524685	−	0.908780i	0.0258494	−	0.0447724i
$413$	0.0343977	−	3.85023i	0.00169260	−	0.189457i
$414$	0.224026	+	0.388024i	0.0110103	+	0.0190704i
$415$	4.62671	+	8.01370i	0.227116	+	0.393377i
$416$	2.65502	−	2.43944i	0.130173	−	0.119603i
$417$	−4.74886	+	8.22528i	−0.232553	+	0.402793i
$418$	9.57151	−	16.5783i	0.468158	−	0.810873i
$419$	−19.8098	−	34.3115i	−0.967770	−	1.67623i	−0.701982	−	0.712195i	$-0.747701\pi$
$419$	−19.8098	−	34.3115i	−0.967770	−	1.67623i	−0.265788	−	0.964031i	$-0.585632\pi$
$420$	2.87097	−	1.62353i	0.140089	−	0.0792202i
$421$	−32.2271			−1.57065			−0.785326	−	0.619083i	$-0.787505\pi$
$421$	−32.2271			−1.57065			−0.785326	+	0.619083i	$0.787505\pi$
$422$	−12.4404			−0.605590
$423$	3.29729	+	5.71107i	0.160320	+	0.277682i
$424$	−3.86750	+	6.69870i	−0.187822	+	0.325318i
$425$	−1.70686			−0.0827951
$426$	4.68884	+	8.12130i	0.227175	+	0.393478i
$427$	9.57189	+	5.64094i	0.463216	+	0.272984i
$428$	−10.1830			−0.492216
$429$	−1.95909	−	8.78114i	−0.0945856	−	0.423957i
$430$	1.83915	−	3.18550i	0.0886916	−	0.153618i
$431$	11.0013			0.529912			0.264956	−	0.964260i	$-0.414642\pi$
$431$	11.0013			0.529912			0.264956	+	0.964260i	$0.414642\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	15.9643	−	27.6509i	0.767193	−	1.32882i	−0.171886	−	0.985117i	$-0.554986\pi$
$433$	15.9643	−	27.6509i	0.767193	−	1.32882i	0.939079	−	0.343701i	$-0.111681\pi$
$434$	0.192136	−	21.5064i	0.00922285	−	1.03234i
$435$	−4.62671	+	8.01370i	−0.221834	+	0.384227i
$436$	−19.8457			−0.950436
$437$	1.71863	−	2.97675i	0.0822132	−	0.142397i
$438$	−5.07151	−	8.78412i	−0.242326	−	0.419721i
$439$	0.717628	−	1.24297i	0.0342505	−	0.0593236i	−0.848392	−	0.529368i	$-0.822429\pi$
$439$	0.717628	−	1.24297i	0.0342505	−	0.0593236i	0.882643	+	0.470045i	$0.155762\pi$
$440$	1.55535	+	2.69395i	0.0741485	+	0.128429i
$441$	3.39113	+	6.12374i	0.161482	+	0.291607i
$442$	0.388880	+	1.74306i	0.0184972	+	0.0829091i
$443$	5.72758	+	9.92047i	0.272126	+	0.471336i	0.969406	−	0.245463i	$-0.0789400\pi$
$443$	5.72758	+	9.92047i	0.272126	+	0.471336i	−0.697280	+	0.716799i	$0.745607\pi$
$444$	−2.74194			−0.130127
$445$	14.3125			0.678479
$446$	−20.9301			−0.991071
$447$	4.73744			0.224073
$448$	−2.27938	−	1.34329i	−0.107691	−	0.0634646i
$449$	−17.3713	+	30.0880i	−0.819803	+	1.41994i	0.0860243	+	0.996293i	$0.472584\pi$
$449$	−17.3713	+	30.0880i	−0.819803	+	1.41994i	−0.905827	+	0.423647i	$0.860750\pi$
$450$	−1.72298	−	2.98428i	−0.0812219	−	0.140681i
$451$	4.66867	+	8.08638i	0.219839	+	0.380773i
$452$	15.8688			0.746406
$453$	3.56085	−	6.16758i	0.167304	−	0.289778i
$454$	−17.5810			−0.825119
$455$	−11.6293	+	2.48566i	−0.545188	+	0.116529i
$456$	−7.67156			−0.359254
$457$	−18.4024	+	31.8739i	−0.860829	+	1.49100i	0.0103007	+	0.999947i	$0.496721\pi$
$457$	−18.4024	+	31.8739i	−0.860829	+	1.49100i	−0.871130	+	0.491053i	$0.836612\pi$
$458$	14.4924			0.677185
$459$	0.247662	+	0.428963i	0.0115599	+	0.0200223i
$460$	0.279274	+	0.483717i	0.0130212	+	0.0225534i
$461$	−3.99129	+	6.91311i	−0.185893	+	0.321976i	−0.943877	−	0.330297i	$-0.892851\pi$
$461$	−3.99129	+	6.91311i	−0.185893	+	0.321976i	0.757984	+	0.652273i	$0.226184\pi$
$462$	−5.74677	+	3.24979i	−0.267364	+	0.151194i
$463$	26.4799			1.23063			0.615314	−	0.788282i	$-0.289029\pi$
$463$	26.4799			1.23063			0.615314	+	0.788282i	$0.289029\pi$
$464$	7.42285			0.344597
$465$	10.1337			0.469938
$466$	−14.4979			−0.671604
$467$	−3.12210	−	5.40764i	−0.144474	−	0.250236i	0.784703	−	0.619872i	$-0.212816\pi$
$467$	−3.12210	−	5.40764i	−0.144474	−	0.250236i	−0.929176	+	0.369636i	$0.879482\pi$
$468$	−2.65502	+	2.43944i	−0.122728	+	0.112763i
$469$	−0.0629324	−	0.0370876i	−0.00290595	−	0.00171254i
$470$	4.11045	+	7.11950i	0.189601	+	0.328398i
$471$	7.52147	−	13.0276i	0.346571	−	0.600279i
$472$	−0.727653	−	1.26033i	−0.0334930	−	0.0580115i
$473$	−3.68139	+	6.37635i	−0.169270	+	0.293185i
$474$	9.87090			0.453385
$475$	−13.2179	+	22.8941i	−0.606480	+	1.05045i
$476$	1.14074	−	0.645087i	0.0522857	−	0.0295675i
$477$	3.86750	−	6.69870i	0.177080	−	0.306712i
$478$	1.57547	−	2.72879i	0.0720601	−	0.124812i
$479$	21.5725			0.985671			0.492836	−	0.870122i	$-0.335960\pi$
$479$	21.5725			0.985671			0.492836	+	0.870122i	$0.335960\pi$
$480$	0.623307	−	1.07960i	0.0284499	−	0.0492767i
$481$	9.43261	+	2.96019i	0.430090	+	0.134973i
$482$	24.8446			1.13164
$483$	−1.03187	+	0.583522i	−0.0469517	+	0.0265512i
$484$	2.38668	+	4.13385i	0.108485	+	0.187902i
$485$	−1.27113			−0.0577188
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−6.80757	−	11.7911i	−0.308481	−	0.534304i	0.669550	−	0.742767i	$-0.266487\pi$
$487$	−6.80757	−	11.7911i	−0.308481	−	0.534304i	−0.978030	+	0.208463i	$0.933154\pi$
$488$	4.19934			0.190095
$489$	9.02971			0.408337
$490$	4.22743	+	7.63394i	0.190976	+	0.344866i
$491$	6.14512	+	10.6437i	0.277326	+	0.480342i	0.970719	−	0.240217i	$-0.0772186\pi$
$491$	6.14512	+	10.6437i	0.277326	+	0.480342i	−0.693394	+	0.720559i	$0.743885\pi$
$492$	1.87097	−	3.24061i	0.0843498	−	0.146098i
$493$	−1.83836	+	3.18413i	−0.0827955	+	0.143406i
$494$	26.3911	+	8.28221i	1.18739	+	0.372634i
$495$	−1.55535	−	2.69395i	−0.0699079	−	0.121084i
$496$	−4.06448	−	7.03989i	−0.182501	−	0.316100i
$497$	−21.5969	+	12.2130i	−0.968754	+	0.547830i
$498$	−3.71142	+	6.42837i	−0.166313	+	0.288062i
$499$	−7.11789	−	12.3285i	−0.318640	−	0.551901i	0.661564	−	0.749889i	$-0.269893\pi$
$499$	−7.11789	−	12.3285i	−0.318640	−	0.551901i	−0.980205	+	0.197987i	$0.936560\pi$
$500$	−5.26442	−	9.11824i	−0.235432	−	0.407780i
$501$	−1.42442	−	2.46716i	−0.0636382	−	0.110225i
$502$	3.69421	+	6.39857i	0.164881	+	0.285582i
$503$	10.4692	−	18.1332i	0.466798	−	0.808518i	−0.532482	−	0.846441i	$-0.678741\pi$
$503$	10.4692	−	18.1332i	0.466798	−	0.808518i	0.999281	+	0.0379227i	$0.0120741\pi$
$504$	2.27938	+	1.34329i	0.101532	+	0.0598350i
$505$	11.1837	+	19.3708i	0.497669	+	0.861987i
$506$	−0.559018	−	0.968247i	−0.0248514	−	0.0430438i
$507$	11.7672	−	5.52561i	0.522601	−	0.245401i
$508$	4.23846	−	7.34124i	0.188051	−	0.325715i
$509$	−6.96485	+	12.0635i	−0.308711	+	0.534704i	−0.978081	−	0.208226i	$-0.933231\pi$
$509$	−6.96485	+	12.0635i	−0.308711	+	0.534704i	0.669369	+	0.742930i	$0.266564\pi$
$510$	0.308739	+	0.534751i	0.0136712	+	0.0236792i
$511$	23.3595	−	13.2098i	1.03336	−	0.584367i
$512$	−1.00000			−0.0441942
$513$	7.67156			0.338708
$514$	13.4446	+	23.2867i	0.593015	+	1.02713i
$515$	−0.654079	+	1.13290i	−0.0288222	+	0.0499214i
$516$	2.95063			0.129894
$517$	−8.22781	−	14.2510i	−0.361859	−	0.626757i
$518$	0.0648086	−	7.25420i	0.00284752	−	0.318731i
$519$	25.4875			1.11878
$520$	−3.30979	+	3.04103i	−0.145144	+	0.133358i
$521$	11.1502	−	19.3128i	0.488501	−	0.846109i	−0.511412	−	0.859336i	$-0.670877\pi$
$521$	11.1502	−	19.3128i	0.488501	−	0.846109i	0.999913	+	0.0132274i	$0.00421053\pi$
$522$	−7.42285			−0.324889
$523$	13.8516	−	23.9917i	0.605689	−	1.04908i	−0.386254	−	0.922393i	$-0.626231\pi$
$523$	13.8516	−	23.9917i	0.605689	−	1.04908i	0.991942	−	0.126691i	$-0.0404357\pi$
$524$	−8.26678	+	14.3185i	−0.361136	+	0.625506i
$525$	7.93608	−	4.48785i	0.346359	−	0.195866i
$526$	−1.46562	+	2.53852i	−0.0639040	+	0.110685i
$527$	4.02647			0.175396
$528$	−1.24766	+	2.16101i	−0.0542975	+	0.0940461i
$529$	11.3996	+	19.7447i	0.495636	+	0.858466i
$530$	4.82127	−	8.35069i	0.209423	−	0.362731i
$531$	0.727653	+	1.26033i	0.0315775	+	0.0546938i
$532$	0.181325	−	20.2962i	0.00786145	−	0.879953i
$533$	−9.93493	+	9.12822i	−0.430330	+	0.395387i
$534$	5.74056	+	9.94294i	0.248418	+	0.430273i
$535$	12.6943			0.548823
$536$	−0.0276094			−0.00119255
$537$	−18.2006			−0.785414
$538$	−2.14443			−0.0924530
$539$	−8.46197	−	15.2807i	−0.364483	−	0.658187i
$540$	−0.623307	+	1.07960i	−0.0268229	+	0.0464585i
$541$	7.32108	+	12.6805i	0.314758	+	0.545177i	0.979386	−	0.201998i	$-0.0647434\pi$
$541$	7.32108	+	12.6805i	0.314758	+	0.545177i	−0.664628	+	0.747174i	$0.731410\pi$
$542$	8.64220	+	14.9687i	0.371214	+	0.642962i
$543$	13.7305			0.589232
$544$	0.247662	−	0.428963i	0.0106184	−	0.0183916i
$545$	24.7399			1.05974
$546$	−6.39113	−	7.08191i	−0.273515	−	0.303078i
$547$	21.7401			0.929542			0.464771	−	0.885431i	$-0.346137\pi$
$547$	21.7401			0.929542			0.464771	+	0.885431i	$0.346137\pi$
$548$	0.428418	−	0.742042i	0.0183011	−	0.0316985i
$549$	−4.19934			−0.179224
$550$	4.29939	+	7.44676i	0.183326	+	0.317531i
$551$	28.4724	+	49.3157i	1.21297	+	2.10092i
$552$	−0.224026	+	0.388024i	−0.00953518	+	0.0165154i
$553$	−0.233309	+	26.1149i	−0.00992131	+	1.11052i
$554$	2.83381			0.120397
$555$	3.41814			0.145092
$556$	−9.49773			−0.402793
$557$	4.47177			0.189475			0.0947375	−	0.995502i	$-0.469799\pi$
$557$	4.47177			0.189475			0.0947375	+	0.995502i	$0.469799\pi$
$558$	4.06448	+	7.03989i	0.172063	+	0.298022i
$559$	−10.1505	−	3.18550i	−0.429322	−	0.134732i
$560$	2.84150	+	1.67457i	0.120075	+	0.0707633i
$561$	−0.617997	−	1.07040i	−0.0260919	−	0.0451924i
$562$	−14.2627	+	24.7037i	−0.601636	+	1.04206i
$563$	5.57899	+	9.66309i	0.235126	+	0.407251i	0.959309	−	0.282357i	$-0.0911163\pi$
$563$	5.57899	+	9.66309i	0.235126	+	0.407251i	−0.724183	+	0.689608i	$0.757783\pi$
$564$	−3.29729	+	5.71107i	−0.138841	+	0.240480i
$565$	−19.7823			−0.832246
$566$	−2.29901	+	3.98201i	−0.0966347	+	0.167376i
$567$	−2.27938	−	1.34329i	−0.0957249	−	0.0564130i
$568$	−4.68884	+	8.12130i	−0.196739	+	0.340762i
$569$	18.4409	−	31.9406i	0.773083	−	1.33902i	−0.162782	−	0.986662i	$-0.552047\pi$
$569$	18.4409	−	31.9406i	0.773083	−	1.33902i	0.935865	−	0.352358i	$-0.114620\pi$
$570$	9.56347			0.400570
$571$	0.101526	−	0.175849i	0.00424874	−	0.00735904i	−0.863893	−	0.503675i	$-0.831981\pi$
$571$	0.101526	−	0.175849i	0.00424874	−	0.00735904i	0.868142	+	0.496316i	$0.165314\pi$
$572$	6.62514	−	6.08719i	0.277011	−	0.254518i
$573$	−5.28588			−0.220821
$574$	8.52929	+	5.02652i	0.356006	+	0.209803i
$575$	0.771984	+	1.33711i	0.0321939	+	0.0557615i
$576$	1.00000			0.0416667
$577$	10.4151	−	18.0396i	0.433588	−	0.750997i	−0.563591	−	0.826054i	$-0.690581\pi$
$577$	10.4151	−	18.0396i	0.433588	−	0.750997i	0.997179	+	0.0750570i	$0.0239139\pi$
$578$	−8.37733	−	14.5100i	−0.348451	−	0.603535i
$579$	−4.81197			−0.199979
$580$	−9.25342			−0.384227
$581$	−16.9195	−	9.97105i	−0.701938	−	0.413669i
$582$	−0.509831	−	0.883054i	−0.0211332	−	0.0366038i
$583$	−9.65066	+	16.7154i	−0.399689	+	0.692282i
$584$	5.07151	−	8.78412i	0.209861	−	0.363489i
$585$	3.30979	−	3.04103i	0.136843	−	0.125731i
$586$	−3.19384	−	5.53189i	−0.131936	−	0.228520i
$587$	−8.25511	−	14.2983i	−0.340725	−	0.590153i	0.643843	−	0.765158i	$-0.277339\pi$
$587$	−8.25511	−	14.2983i	−0.340725	−	0.590153i	−0.984568	+	0.175005i	$0.944006\pi$
$588$	−3.60775	+	5.99868i	−0.148781	+	0.247381i
$589$	31.1809	−	54.0069i	1.28479	−	2.22532i
$590$	0.907102	+	1.57115i	0.0373448	+	0.0646831i
$591$	−11.7743	−	20.3937i	−0.484329	−	0.838883i
$592$	−1.37097	−	2.37459i	−0.0563465	−	0.0975950i
$593$	5.86959	+	10.1664i	0.241035	+	0.417485i	0.961009	−	0.276515i	$-0.0891797\pi$
$593$	5.86959	+	10.1664i	0.241035	+	0.417485i	−0.719974	+	0.694001i	$0.755846\pi$
$594$	1.24766	−	2.16101i	0.0511922	−	0.0886675i
$595$	−1.42206	+	0.804174i	−0.0582988	+	0.0329679i
$596$	2.36872	+	4.10274i	0.0970264	+	0.168055i
$597$	5.63984	+	9.76849i	0.230823	+	0.399798i
$598$	1.18959	−	1.09299i	0.0486459	−	0.0446959i
$599$	−21.8486	+	37.8430i	−0.892711	+	1.54622i	−0.0560993	+	0.998425i	$0.517866\pi$
$599$	−21.8486	+	37.8430i	−0.892711	+	1.54622i	−0.836612	+	0.547796i	$0.815467\pi$
$600$	1.72298	−	2.98428i	0.0703403	−	0.121833i
$601$	2.84613	+	4.92964i	0.116096	+	0.201084i	0.918217	−	0.396077i	$-0.129629\pi$
$601$	2.84613	+	4.92964i	0.116096	+	0.201084i	−0.802121	+	0.597161i	$0.796295\pi$
$602$	−0.0697412	+	7.80632i	−0.00284244	+	0.318162i
$603$	0.0276094			0.00112434
$604$	7.12171			0.289778
$605$	−2.97527	−	5.15331i	−0.120962	−	0.209512i
$606$	−8.97127	+	15.5387i	−0.364433	+	0.631217i
$607$	−25.0986			−1.01872			−0.509360	−	0.860553i	$-0.670118\pi$
$607$	−25.0986			−1.01872			−0.509360	+	0.860553i	$0.670118\pi$
$608$	−3.83578	−	6.64376i	−0.155561	−	0.269440i
$609$	0.175447	−	19.6382i	0.00710946	−	0.795781i
$610$	−5.23496			−0.211957
$611$	17.5088	−	16.0871i	0.708329	−	0.650813i
$612$	−0.247662	+	0.428963i	−0.0100111	+	0.0173398i
$613$	2.59331			0.104743			0.0523715	−	0.998628i	$-0.483322\pi$
$613$	2.59331			0.104743			0.0523715	+	0.998628i	$0.483322\pi$
$614$	−0.699495	+	1.21156i	−0.0282293	+	0.0488947i
$615$	−2.33237	+	4.03979i	−0.0940504	+	0.162900i
$616$	−5.68779	−	3.35195i	−0.229168	−	0.135054i
$617$	8.83438	−	15.3016i	0.355659	−	0.616019i	−0.631572	−	0.775318i	$-0.717590\pi$
$617$	8.83438	−	15.3016i	0.355659	−	0.616019i	0.987231	+	0.159298i	$0.0509231\pi$
$618$	−1.04937			−0.0422118
$619$	20.4642	−	35.4450i	0.822525	−	1.42465i	−0.0812719	−	0.996692i	$-0.525898\pi$
$619$	20.4642	−	35.4450i	0.822525	−	1.42465i	0.903797	−	0.427962i	$-0.140768\pi$
$620$	5.06684	+	8.77602i	0.203489	+	0.352453i
$621$	0.224026	−	0.388024i	0.00898986	−	0.0155709i
$622$	8.55183	+	14.8122i	0.342897	+	0.593915i
$623$	−26.4412	+	14.9525i	−1.05934	+	0.599058i
$624$	−3.44013	−	1.07960i	−0.137715	−	0.0432185i
$625$	−2.05219	−	3.55450i	−0.0820876	−	0.142180i
$626$	−11.6249			−0.464626
$627$	−19.1430			−0.764499
$628$	15.0429			0.600279
$629$	1.35815			0.0541529
$630$	−2.84150	−	1.67457i	−0.113208	−	0.0667163i
$631$	3.58097	−	6.20242i	0.142556	−	0.246914i	−0.785902	−	0.618351i	$-0.787801\pi$
$631$	3.58097	−	6.20242i	0.142556	−	0.246914i	0.928459	+	0.371436i	$0.121135\pi$
$632$	4.93545	+	8.54845i	0.196322	+	0.340039i
$633$	6.22021	+	10.7737i	0.247231	+	0.428217i
$634$	−6.58554			−0.261545
$635$	−5.28373	+	9.15168i	−0.209678	+	0.363173i
$636$	7.73499			0.306712
$637$	18.8873	−	16.7413i	0.748341	−	0.663314i
$638$	18.5224			0.733309
$639$	4.68884	−	8.12130i	0.185488	−	0.321274i
$640$	1.24661			0.0492767
$641$	−1.62960	−	2.82254i	−0.0643652	−	0.111484i	0.832047	−	0.554705i	$-0.187169\pi$
$641$	−1.62960	−	2.82254i	−0.0643652	−	0.111484i	−0.896412	+	0.443221i	$0.853836\pi$
$642$	5.09152	+	8.81877i	0.200946	+	0.348049i
$643$	−9.17027	+	15.8834i	−0.361640	+	0.626379i	−0.988231	−	0.152969i	$-0.951116\pi$
$643$	−9.17027	+	15.8834i	−0.361640	+	0.626379i	0.626591	+	0.779348i	$0.284450\pi$
$644$	−1.02128	−	0.601865i	−0.0402441	−	0.0237168i
$645$	−3.67830			−0.144833
$646$	3.79991			0.149505
$647$	43.8685			1.72465			0.862325	−	0.506355i	$-0.169008\pi$
$647$	43.8685			1.72465			0.862325	+	0.506355i	$0.169008\pi$
$648$	−1.00000			−0.0392837
$649$	−1.81573	−	3.14494i	−0.0712737	−	0.123450i
$650$	−9.14909	+	8.40619i	−0.358857	+	0.329718i
$651$	−18.7211	+	10.5868i	−0.733738	+	0.414929i
$652$	4.51485	+	7.81996i	0.176815	+	0.306253i
$653$	−6.64022	+	11.5012i	−0.259852	+	0.450077i	−0.966202	−	0.257786i	$-0.917007\pi$
$653$	−6.64022	+	11.5012i	−0.259852	+	0.450077i	0.706350	+	0.707863i	$0.250340\pi$
$654$	9.92285	+	17.1869i	0.388014	+	0.672060i
$655$	10.3055	−	17.8496i	0.402668	−	0.697442i
$656$	3.74194			0.146098
$657$	−5.07151	+	8.78412i	−0.197859	+	0.342701i
$658$	−15.0315	−	8.85845i	−0.585991	−	0.345338i
$659$	1.53479	−	2.65834i	0.0597871	−	0.103554i	−0.834583	−	0.550883i	$-0.814291\pi$
$659$	1.53479	−	2.65834i	0.0597871	−	0.103554i	0.894370	+	0.447328i	$0.147624\pi$
$660$	1.55535	−	2.69395i	0.0605420	−	0.104862i
$661$	−29.6068			−1.15157			−0.575785	−	0.817601i	$-0.695304\pi$
$661$	−29.6068			−1.15157			−0.575785	+	0.817601i	$0.695304\pi$
$662$	−11.6343	+	20.1512i	−0.452179	+	0.783197i
$663$	1.31510	−	1.20831i	0.0510741	−	0.0469270i
$664$	−7.42285			−0.288062
$665$	−0.226043	+	25.3015i	−0.00876555	+	0.981152i
$666$	1.37097	+	2.37459i	0.0531240	+	0.0920134i
$667$	3.32582			0.128776
$668$	1.42442	−	2.46716i	0.0551123	−	0.0954573i
$669$	10.4651	+	18.1260i	0.404603	+	0.700793i
$670$	0.0344183			0.00132970
$671$	10.4787			0.404526
$672$	−0.0236360	+	2.64565i	−0.000911780	+	0.102058i
$673$	−4.54511	−	7.87235i	−0.175201	−	0.303457i	0.765030	−	0.643995i	$-0.222724\pi$
$673$	−4.54511	−	7.87235i	−0.175201	−	0.303457i	−0.940231	+	0.340538i	$0.889391\pi$
$674$	9.71598	−	16.8286i	0.374246	−	0.648212i
$675$	−1.72298	+	2.98428i	−0.0663174	+	0.114865i
$676$	10.6689	+	7.42791i	0.410344	+	0.285689i
$677$	8.92163	+	15.4527i	0.342886	+	0.593896i	0.984967	−	0.172741i	$-0.0552622\pi$
$677$	8.92163	+	15.4527i	0.342886	+	0.593896i	−0.642081	+	0.766636i	$0.721929\pi$
$678$	−7.93440	−	13.7428i	−0.304719	−	0.527789i
$679$	2.34830	−	1.32796i	0.0901194	−	0.0509625i
$680$	−0.308739	+	0.534751i	−0.0118396	+	0.0205068i
$681$	8.79052	+	15.2256i	0.336853	+	0.583447i
$682$	−10.1422	−	17.5668i	−0.388365	−	0.672668i
$683$	6.15898	+	10.6677i	0.235667	+	0.408187i	0.959466	−	0.281824i	$-0.0909393\pi$
$683$	6.15898	+	10.6677i	0.235667	+	0.408187i	−0.723800	+	0.690010i	$0.757606\pi$
$684$	3.83578	+	6.64376i	0.146665	+	0.254031i
$685$	−0.534072	+	0.925040i	−0.0204058	+	0.0353440i
$686$	−15.7851	−	9.68662i	−0.602678	−	0.369837i
$687$	−7.24620	−	12.5508i	−0.276460	−	0.478842i
$688$	1.47532	+	2.55532i	0.0562459	+	0.0974207i
$689$	−26.6093	−	8.35069i	−1.01374	−	0.318136i
$690$	0.279274	−	0.483717i	0.0106318	−	0.0184148i
$691$	13.5881	−	23.5353i	0.516916	−	0.895325i	−0.482891	−	0.875681i	$-0.660413\pi$
$691$	13.5881	−	23.5353i	0.516916	−	0.895325i	0.999807	−	0.0196447i	$-0.00625351\pi$
$692$	12.7438	+	22.0729i	0.484446	+	0.839084i
$693$	5.68779	+	3.35195i	0.216061	+	0.127330i
$694$	−29.6707			−1.12629
$695$	11.8400			0.449117
$696$	−3.71142	−	6.42837i	−0.140681	−	0.243667i
$697$	−0.926736	+	1.60515i	−0.0351026	+	0.0607995i
$698$	−26.6047			−1.00700
$699$	7.24897	+	12.5556i	0.274181	+	0.474896i
$700$	7.85464	+	4.62892i	0.296877	+	0.174957i
$701$	38.0704			1.43790			0.718950	−	0.695062i	$-0.244623\pi$
$701$	38.0704			1.43790			0.718950	+	0.695062i	$0.244623\pi$
$702$	3.44013	+	1.07960i	0.129839	+	0.0407468i
$703$	10.5175	−	18.2168i	0.396674	−	0.687059i
$704$	−2.49532			−0.0940461
$705$	4.11045	−	7.11950i	0.154808	−	0.268136i
$706$	−6.90939	+	11.9674i	−0.260038	+	0.450400i
$707$	−40.8979	−	24.1021i	−1.53812	−	0.906452i
$708$	−0.727653	+	1.26033i	−0.0273469	+	0.0473662i
$709$	−41.5249			−1.55950			−0.779750	−	0.626091i	$-0.784654\pi$
$709$	−41.5249			−1.55950			−0.779750	+	0.626091i	$0.784654\pi$
$710$	5.84517	−	10.1241i	0.219365	−	0.379952i
$711$	−4.93545	−	8.54845i	−0.185094	−	0.320592i
$712$	−5.74056	+	9.94294i	−0.215137	+	0.372628i
$713$	−1.82110	−	3.15424i	−0.0682007	−	0.118127i
$714$	−1.12903	−	0.665365i	−0.0422529	−	0.0249007i
$715$	−8.25899	+	7.58837i	−0.308869	+	0.283789i
$716$	−9.10030	−	15.7622i	−0.340094	−	0.589061i
$717$	−3.15093			−0.117674
$718$	2.76191			0.103074
$719$	16.6093			0.619421			0.309710	−	0.950831i	$-0.399768\pi$
$719$	16.6093			0.619421			0.309710	+	0.950831i	$0.399768\pi$
$720$	−1.24661			−0.0464585
$721$	0.0248029	−	2.77626i	0.000923710	−	0.103393i
$722$	19.9264	−	34.5135i	0.741584	−	1.28446i
$723$	−12.4223	−	21.5160i	−0.461990	−	0.800189i
$724$	6.86524	+	11.8910i	0.255145	+	0.441924i
$725$	−25.5788			−0.949973
$726$	2.38668	−	4.13385i	0.0885780	−	0.153422i
$727$	−20.2421			−0.750737			−0.375368	−	0.926876i	$-0.622484\pi$
$727$	−20.2421			−0.750737			−0.375368	+	0.926876i	$0.622484\pi$
$728$	2.93755	−	9.07584i	0.108873	−	0.336373i
$729$	1.00000			0.0370370
$730$	−6.32222	+	10.9504i	−0.233996	+	0.405292i
$731$	−1.46152			−0.0540562
$732$	−2.09967	−	3.63674i	−0.0776061	−	0.134418i
$733$	−8.42173	−	14.5869i	−0.311064	−	0.538778i	0.667529	−	0.744584i	$-0.267352\pi$
$733$	−8.42173	−	14.5869i	−0.311064	−	0.538778i	−0.978593	+	0.205805i	$0.934019\pi$
$734$	−5.46151	+	9.45961i	−0.201588	+	0.349161i
$735$	4.49747	−	7.47803i	0.165892	−	0.275831i
$736$	−0.448052			−0.0165154
$737$	−0.0688945			−0.00253776
$738$	−3.74194			−0.137743
$739$	−48.1193			−1.77010			−0.885049	−	0.465498i	$-0.845875\pi$
$739$	−48.1193			−1.77010			−0.885049	+	0.465498i	$0.845875\pi$
$740$	1.70907	+	2.96019i	0.0628266	+	0.108819i
$741$	−6.02296	−	26.9965i	−0.221259	−	0.991741i
$742$	−0.182825	+	20.4640i	−0.00671170	+	0.751259i
$743$	2.98460	+	5.16948i	0.109494	+	0.189650i	0.915566	−	0.402169i	$-0.131744\pi$
$743$	2.98460	+	5.16948i	0.109494	+	0.189650i	−0.806071	+	0.591819i	$0.798410\pi$
$744$	−4.06448	+	7.03989i	−0.149011	+	0.258095i
$745$	−2.95288	−	5.11453i	−0.108185	−	0.187382i
$746$	9.84303	−	17.0486i	0.360379	−	0.624195i
$747$	7.42285			0.271588
$748$	0.617997	−	1.07040i	0.0225962	−	0.0391378i
$749$	−23.4517	+	13.2619i	−0.856906	+	0.484580i
$750$	−5.26442	+	9.11824i	−0.192229	+	0.332951i
$751$	−18.1527	+	31.4414i	−0.662401	+	1.14731i	0.317582	+	0.948231i	$0.397129\pi$
$751$	−18.1527	+	31.4414i	−0.662401	+	1.14731i	−0.979983	+	0.199081i	$0.936204\pi$
$752$	−6.59458			−0.240480
$753$	3.69421	−	6.39857i	0.134625	−	0.233177i
$754$	5.82770	+	26.1213i	0.212232	+	0.951280i
$755$	−8.87802			−0.323104
$756$	0.0236360	−	2.64565i	0.000859635	−	0.0962212i
$757$	−3.48399	−	6.03445i	−0.126628	−	0.219326i	0.795740	−	0.605638i	$-0.207082\pi$
$757$	−3.48399	−	6.03445i	−0.126628	−	0.219326i	−0.922368	+	0.386312i	$0.873749\pi$
$758$	−16.6343			−0.604183
$759$	−0.559018	+	0.968247i	−0.0202911	+	0.0351451i
$760$	4.78173	+	8.28221i	0.173452	+	0.300427i
$761$	−2.95124			−0.106982			−0.0534912	−	0.998568i	$-0.517035\pi$
$761$	−2.95124			−0.106982			−0.0534912	+	0.998568i	$0.517035\pi$
$762$	−8.47693			−0.307087
$763$	−45.7049	+	25.8461i	−1.65463	+	0.935692i
$764$	−2.64294	−	4.57771i	−0.0956182	−	0.165616i
$765$	0.308739	−	0.534751i	0.0111625	−	0.0193340i
$766$	18.1834	−	31.4945i	0.656992	−	1.13794i
$767$	3.86387	−	3.55013i	0.139516	−	0.128188i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	−21.0168	−	36.4022i	−0.757885	−	1.31270i	−0.943927	−	0.330154i	$-0.892899\pi$
$769$	−21.0168	−	36.4022i	−0.757885	−	1.31270i	0.186042	−	0.982542i	$-0.440434\pi$
$770$	7.09047	+	4.17859i	0.255523	+	0.150586i
$771$	13.4446	−	23.2867i	0.484195	−	0.838650i
$772$	−2.40599	−	4.16729i	−0.0865933	−	0.149984i
$773$	21.8155	+	37.7856i	0.784650	+	1.35905i	0.929208	+	0.369557i	$0.120490\pi$
$773$	21.8155	+	37.7856i	0.784650	+	1.35905i	−0.144559	+	0.989496i	$0.546176\pi$
$774$	−1.47532	−	2.55532i	−0.0530291	−	0.0918491i
$775$	14.0060	+	24.2591i	0.503111	+	0.871414i
$776$	0.509831	−	0.883054i	0.0183019	−	0.0316998i
$777$	−6.31472	+	3.57097i	−0.226539	+	0.128108i
$778$	−8.89008	−	15.3981i	−0.318725	−	0.552048i
$779$	14.3532	+	24.8606i	0.514258	+	0.890722i
$780$	4.28851	+	1.34584i	0.153553	+	0.0481889i
$781$	−11.7002	+	20.2653i	−0.418665	+	0.725149i
$782$	0.110966	−	0.192198i	0.00396812	−	0.00687298i
$783$	3.71142	+	6.42837i	0.132635	+	0.229731i
$784$	−6.99888	−	0.125065i	−0.249960	−	0.00446661i
$785$	−18.7527			−0.669314
$786$	16.5336			0.589732
$787$	−12.1660	−	21.0721i	−0.433671	−	0.751140i	0.563515	−	0.826106i	$-0.309449\pi$
$787$	−12.1660	−	21.0721i	−0.433671	−	0.751140i	−0.997186	+	0.0749659i	$0.976115\pi$
$788$	11.7743	−	20.3937i	0.419442	−	0.726494i
$789$	2.93123			0.104355
$790$	−6.15260	−	10.6566i	−0.218900	−	0.379145i
$791$	36.5461	−	20.6668i	1.29943	−	0.734826i
$792$	2.49532			0.0886675
$793$	3.29691	+	14.7776i	0.117077	+	0.524769i
$794$	4.43952	−	7.68948i	0.157553	−	0.272889i
$795$	−9.64254			−0.341986
$796$	−5.63984	+	9.76849i	−0.199899	+	0.346235i
$797$	−13.8223	+	23.9408i	−0.489609	+	0.848028i	−0.999929	−	0.0119569i	$-0.996194\pi$
$797$	−13.8223	+	23.9408i	−0.489609	+	0.848028i	0.510319	+	0.859985i	$0.329527\pi$
$798$	−17.6677	+	9.99108i	−0.625430	+	0.353680i
$799$	1.63323	−	2.82883i	0.0577794	−	0.100077i
$800$	3.44595			0.121833
$801$	5.74056	−	9.94294i	0.202833	−	0.351317i
$802$	−15.0815	−	26.1219i	−0.532546	−	0.922397i
$803$	12.6551	−	21.9192i	0.446588	−	0.773513i
$804$	0.0138047	+	0.0239105i	0.000486855	+	0.000843258i
$805$	1.27314	+	0.750293i	0.0448723	+	0.0264443i
$806$	21.5826	−	19.8301i	0.760214	−	0.698485i
$807$	1.07222	+	1.85713i	0.0377438	+	0.0653741i
$808$	−17.9425			−0.631217
$809$	−46.7670			−1.64424			−0.822119	−	0.569315i	$-0.807208\pi$
$809$	−46.7670			−1.64424			−0.822119	+	0.569315i	$0.807208\pi$
$810$	1.24661			0.0438015
$811$	−33.4037			−1.17296			−0.586481	−	0.809963i	$-0.699487\pi$
$811$	−33.4037			−1.17296			−0.586481	+	0.809963i	$0.699487\pi$
$812$	17.0949	−	9.66717i	0.599914	−	0.339251i
$813$	8.64220	−	14.9687i	0.303095	−	0.524976i
$814$	−3.42101	−	5.92537i	−0.119906	−	0.207684i
$815$	−5.62828	−	9.74846i	−0.197150	−	0.341474i
$816$	−0.495324			−0.0173398
$817$	−11.3180	+	19.6033i	−0.395966	+	0.685833i
$818$	−16.7720			−0.586420
$819$	−2.93755	+	9.07584i	−0.102646	+	0.317135i
$820$	−4.66475			−0.162900
$821$	−18.7437	+	32.4651i	−0.654160	+	1.13304i	0.327943	+	0.944697i	$0.393645\pi$
$821$	−18.7437	+	32.4651i	−0.654160	+	1.13304i	−0.982104	+	0.188342i	$0.939689\pi$
$822$	−0.856837			−0.0298856
$823$	24.8772	+	43.0886i	0.867166	+	1.50198i	0.864881	+	0.501978i	$0.167394\pi$
$823$	24.8772	+	43.0886i	0.867166	+	1.50198i	0.00228512	+	0.999997i	$0.499273\pi$
$824$	−0.524685	−	0.908780i	−0.0182783	−	0.0316589i
$825$	4.29939	−	7.44676i	0.149685	−	0.259263i
$826$	−3.31719	−	1.95490i	−0.115420	−	0.0680197i
$827$	3.32250			0.115534			0.0577672	−	0.998330i	$-0.481602\pi$
$827$	3.32250			0.115534			0.0577672	+	0.998330i	$0.481602\pi$
$828$	0.448052			0.0155709
$829$	−16.5097			−0.573405			−0.286703	−	0.958020i	$-0.592559\pi$
$829$	−16.5097			−0.573405			−0.286703	+	0.958020i	$0.592559\pi$
$830$	9.25342			0.321191
$831$	−1.41690	−	2.45415i	−0.0491519	−	0.0851336i
$832$	−0.785103	−	3.51904i	−0.0272185	−	0.122001i
$833$	1.78701	−	2.97129i	0.0619161	−	0.102949i
$834$	4.74886	+	8.22528i	0.164440	+	0.284818i
$835$	−1.77570	+	3.07560i	−0.0614505	+	0.106435i
$836$	−9.57151	−	16.5783i	−0.331038	−	0.573374i
$837$	4.06448	−	7.03989i	0.140489	−	0.243334i
$838$	−39.6195			−1.36863
$839$	8.35299	−	14.4678i	0.288377	−	0.499484i	−0.685045	−	0.728500i	$-0.740218\pi$
$839$	8.35299	−	14.4678i	0.288377	−	0.499484i	0.973423	+	0.229016i	$0.0735510\pi$
$840$	0.0294650	−	3.29810i	0.00101664	−	0.113795i
$841$	−13.0493	+	22.6021i	−0.449977	+	0.779383i
$842$	−16.1135	+	27.9095i	−0.555309	+	0.961824i
$843$	28.5254			0.982467
$844$	−6.22021	+	10.7737i	−0.214108	+	0.370847i
$845$	−13.3000	−	9.25974i	−0.457535	−	0.318545i
$846$	6.59458			0.226726
$847$	10.8803	+	6.41201i	0.373851	+	0.220319i
$848$	3.86750	+	6.69870i	0.132810	+	0.230034i
$849$	4.59802			0.157804
$850$	−0.853432	+	1.47819i	−0.0292725	+	0.0507014i
$851$	−0.614265	−	1.06394i	−0.0210567	−	0.0364714i
$852$	9.37767			0.321274
$853$	27.5476			0.943212			0.471606	−	0.881809i	$-0.343674\pi$
$853$	27.5476			0.943212			0.471606	+	0.881809i	$0.343674\pi$
$854$	9.67114	−	5.46903i	0.330940	−	0.187146i
$855$	−4.78173	−	8.28221i	−0.163532	−	0.283245i
$856$	−5.09152	+	8.81877i	−0.174025	+	0.301419i
$857$	−9.17302	+	15.8881i	−0.313344	+	0.542729i	−0.979084	−	0.203455i	$-0.934783\pi$
$857$	−9.17302	+	15.8881i	−0.313344	+	0.542729i	0.665740	+	0.746184i	$0.268116\pi$
$858$	−8.58423	−	2.69395i	−0.293061	−	0.0919699i
$859$	−21.5684	−	37.3575i	−0.735903	−	1.27462i	−0.954326	−	0.298767i	$-0.903425\pi$
$859$	−21.5684	−	37.3575i	−0.735903	−	1.27462i	0.218423	−	0.975854i	$-0.429909\pi$
$860$	−1.83915	−	3.18550i	−0.0627144	−	0.108625i
$861$	0.0884446	−	9.89984i	0.00301418	−	0.337386i
$862$	5.50063	−	9.52738i	0.187352	−	0.324504i
$863$	22.5095	+	38.9876i	0.766233	+	1.32715i	0.939592	+	0.342296i	$0.111204\pi$
$863$	22.5095	+	38.9876i	0.766233	+	1.32715i	−0.173359	+	0.984859i	$0.555462\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−15.8866	−	27.5163i	−0.540159	−	0.935583i
$866$	−15.9643	−	27.6509i	−0.542488	−	0.939616i
$867$	−8.37733	+	14.5100i	−0.284509	+	0.492784i
$868$	−18.5290	−	10.9196i	−0.628915	−	0.370634i
$869$	12.3155	+	21.3312i	0.417776	+	0.723610i
$870$	4.62671	+	8.01370i	0.156860	+	0.271690i
$871$	−0.0216763	−	0.0971586i	−0.000734472	−	0.00329209i
$872$	−9.92285	+	17.1869i	−0.336030	+	0.582021i
$873$	−0.509831	+	0.883054i	−0.0172552	+	0.0298868i
$874$	−1.71863	−	2.97675i	−0.0581335	−	0.100690i
$875$	−23.9992	−	14.1433i	−0.811321	−	0.478131i
$876$	−10.1430			−0.342701
$877$	−21.8595			−0.738142			−0.369071	−	0.929401i	$-0.620324\pi$
$877$	−21.8595			−0.738142			−0.369071	+	0.929401i	$0.620324\pi$
$878$	−0.717628	−	1.24297i	−0.0242188	−	0.0419481i
$879$	−3.19384	+	5.53189i	−0.107726	+	0.186586i
$880$	3.11070			0.104862
$881$	0.975574	+	1.68974i	0.0328679	+	0.0569289i	0.881991	−	0.471265i	$-0.156203\pi$
$881$	0.975574	+	1.68974i	0.0328679	+	0.0569289i	−0.849124	+	0.528194i	$0.822869\pi$
$882$	6.99888	+	0.125065i	0.235665	+	0.00421116i
$883$	−20.9397			−0.704677			−0.352338	−	0.935873i	$-0.614613\pi$
$883$	−20.9397			−0.704677			−0.352338	+	0.935873i	$0.614613\pi$
$884$	1.70398	+	0.534751i	0.0573110	+	0.0179856i
$885$	0.907102	−	1.57115i	0.0304919	−	0.0528135i
$886$	11.4552			0.384844
$887$	−11.7886	+	20.4185i	−0.395823	+	0.685586i	−0.993206	−	0.116370i	$-0.962874\pi$
$887$	−11.7886	+	20.4185i	−0.395823	+	0.685586i	0.597383	+	0.801956i	$0.296207\pi$
$888$	−1.37097	+	2.37459i	−0.0460067	+	0.0796859i
$889$	0.200361	−	22.4270i	0.00671989	−	0.752176i
$890$	7.15626	−	12.3950i	0.239878	−	0.415482i
$891$	−2.49532			−0.0835965
$892$	−10.4651	+	18.1260i	−0.350396	+	0.606904i
$893$	−25.2954	−	43.8128i	−0.846477	−	1.46614i
$894$	2.36872	−	4.10274i	0.0792218	−	0.137216i
$895$	11.3446	+	19.6494i	0.379207	+	0.656806i
$896$	−2.30301	+	1.30235i	−0.0769383	+	0.0435086i
$897$	−1.54136	−	0.483717i	−0.0514644	−	0.0161508i
$898$	17.3713	+	30.0880i	0.579688	+	1.00405i
$899$	60.3401			2.01245
$900$	−3.44595			−0.114865
$901$	−3.83133			−0.127640
$902$	9.33735			0.310900
$903$	6.79535	−	3.84276i	0.226135	−	0.127879i
$904$	7.93440	−	13.7428i	0.263894	−	0.457078i
$905$	−8.55831	−	14.8234i	−0.284488	−	0.492747i
$906$	−3.56085	−	6.16758i	−0.118301	−	0.204904i
$907$	0.141508			0.00469870			0.00234935	−	0.999997i	$-0.499252\pi$
$907$	0.141508			0.00469870			0.00234935	+	0.999997i	$0.499252\pi$
$908$	−8.79052	+	15.2256i	−0.291724	+	0.505280i
$909$	17.9425			0.595117
$910$	−3.66199	+	11.3141i	−0.121394	+	0.375057i
$911$	48.1769			1.59617			0.798086	−	0.602543i	$-0.205846\pi$
$911$	48.1769			1.59617			0.798086	+	0.602543i	$0.205846\pi$
$912$	−3.83578	+	6.64376i	−0.127015	+	0.219997i
$913$	−18.5224			−0.613002
$914$	18.4024	+	31.8739i	0.608698	+	1.05430i
$915$	2.61748	+	4.53360i	0.0865311	+	0.149876i
$916$	7.24620	−	12.5508i	0.239421	−	0.414690i
$917$	−0.390788	+	43.7419i	−0.0129049	+	1.44449i
$918$	0.495324			0.0163481
$919$	39.6180			1.30688			0.653439	−	0.756980i	$-0.273326\pi$
$919$	39.6180			1.30688			0.653439	+	0.756980i	$0.273326\pi$
$920$	0.558548			0.0184148
$921$	1.39899			0.0460983
$922$	3.99129	+	6.91311i	0.131446	+	0.227671i
$923$	−32.2604	−	10.1241i	−1.06186	−	0.333240i
$924$	−0.0589796	+	6.60174i	−0.00194029	+	0.217181i
$925$	4.72430	+	8.18272i	0.155334	+	0.269046i
$926$	13.2400	−	22.9323i	0.435093	−	0.753602i
$927$	0.524685	+	0.908780i	0.0172329	+	0.0298483i
$928$	3.71142	−	6.42837i	0.121833	−	0.211022i
$929$	36.0334			1.18222			0.591109	−	0.806592i	$-0.298690\pi$
$929$	36.0334			1.18222			0.591109	+	0.806592i	$0.298690\pi$
$930$	5.06684	−	8.77602i	0.166148	−	0.287777i
$931$	−26.0153	−	46.9787i	−0.852616	−	1.53966i
$932$	−7.24897	+	12.5556i	−0.237448	+	0.411272i
$933$	8.55183	−	14.8122i	0.279974	−	0.484930i
$934$	−6.24421			−0.204317
$935$	−0.770404	+	1.33438i	−0.0251949	+	0.0436388i
$936$	0.785103	+	3.51904i	0.0256619	+	0.115023i
$937$	−2.37671			−0.0776439			−0.0388219	−	0.999246i	$-0.512361\pi$
$937$	−2.37671			−0.0776439			−0.0388219	+	0.999246i	$0.512361\pi$
$938$	−0.0635849	+	0.0359573i	−0.00207612	+	0.00117405i
$939$	5.81247	+	10.0675i	0.189683	+	0.328540i
$940$	8.22089			0.268136
$941$	−19.3411	+	33.4998i	−0.630503	+	1.09206i	0.356946	+	0.934125i	$0.383818\pi$
$941$	−19.3411	+	33.4998i	−0.630503	+	1.09206i	−0.987449	+	0.157938i	$0.949515\pi$
$942$	−7.52147	−	13.0276i	−0.245063	−	0.424461i
$943$	1.67658			0.0545971
$944$	−1.45531			−0.0473662
$945$	−0.0294650	+	3.29810i	−0.000958497	+	0.107287i
$946$	3.68139	+	6.37635i	0.119692	+	0.207313i
$947$	7.37320	−	12.7708i	0.239597	−	0.414994i	−0.721002	−	0.692933i	$-0.756318\pi$
$947$	7.37320	−	12.7708i	0.239597	−	0.414994i	0.960599	+	0.277939i	$0.0896514\pi$
$948$	4.93545	−	8.54845i	0.160296	−	0.277641i
$949$	34.8933	+	10.9504i	1.13268	+	0.355465i
$950$	13.2179	+	22.8941i	0.428846	+	0.742783i
$951$	3.29277	+	5.70324i	0.106775	+	0.184940i
$952$	0.0117075	−	1.31045i	0.000379442	−	0.0424720i
$953$	8.54843	−	14.8063i	0.276911	−	0.479623i	−0.693705	−	0.720259i	$-0.744023\pi$
$953$	8.54843	−	14.8063i	0.276911	−	0.479623i	0.970615	+	0.240636i	$0.0773561\pi$
$954$	−3.86750	−	6.69870i	−0.125215	−	0.216878i
$955$	3.29473	+	5.70663i	0.106615	+	0.184662i
$956$	−1.57547	−	2.72879i	−0.0509542	−	0.0882553i
$957$	−9.26121	−	16.0409i	−0.299372	−	0.518528i
$958$	10.7862	−	18.6823i	0.348487	−	0.603598i
$959$	0.0202522	−	2.26689i	0.000653979	−	0.0732016i
$960$	−0.623307	−	1.07960i	−0.0201171	−	0.0348439i
$961$	−17.5400	−	30.3802i	−0.565807	−	0.980006i
$962$	7.27991	−	6.68878i	0.234714	−	0.215655i
$963$	5.09152	−	8.81877i	0.164072	−	0.284181i
$964$	12.4223	−	21.5160i	0.400095	−	0.692984i
$965$	2.99933	+	5.19500i	0.0965520	+	0.167233i
$966$	−0.0105902	+	1.18539i	−0.000340733	+	0.0381392i
$967$	−7.90857			−0.254323			−0.127161	−	0.991882i	$-0.540587\pi$
$967$	−7.90857			−0.254323			−0.127161	+	0.991882i	$0.540587\pi$
$968$	4.77336			0.153422
$969$	−1.89995	−	3.29082i	−0.0610353	−	0.105716i
$970$	−0.635563	+	1.10083i	−0.0204067	+	0.0353454i
$971$	3.90099			0.125189			0.0625944	−	0.998039i	$-0.480063\pi$
$971$	3.90099			0.125189			0.0625944	+	0.998039i	$0.480063\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−21.8734	+	12.3694i	−0.701229	+	0.396545i
$974$	−13.6151			−0.436257
$975$	11.8545	+	3.72025i	0.379648	+	0.119143i
$976$	2.09967	−	3.63674i	0.0672088	−	0.116409i
$977$	−51.3897			−1.64410			−0.822051	−	0.569414i	$-0.807170\pi$
$977$	−51.3897			−1.64410			−0.822051	+	0.569414i	$0.807170\pi$
$978$	4.51485	−	7.81996i	0.144369	−	0.250055i
$979$	−14.3246	+	24.8109i	−0.457815	+	0.792959i
$980$	8.72490	+	0.155908i	0.278707	+	0.00498030i
$981$	9.92285	−	17.1869i	0.316812	−	0.548735i
$982$	12.2902			0.392198
$983$	7.32146	−	12.6811i	0.233518	−	0.404465i	−0.725323	−	0.688409i	$-0.758310\pi$
$983$	7.32146	−	12.6811i	0.233518	−	0.404465i	0.958841	+	0.283944i	$0.0916428\pi$
$984$	−1.87097	−	3.24061i	−0.0596443	−	0.103307i
$985$	−14.6780	+	25.4230i	−0.467680	+	0.810045i
$986$	1.83836	+	3.18413i	0.0585452	+	0.101403i
$987$	−0.155870	+	17.4469i	−0.00496139	+	0.555342i
$988$	20.3682	−	18.7143i	0.647998	−	0.595381i
$989$	0.661018	+	1.14492i	0.0210192	+	0.0364062i
$990$	−3.11070			−0.0988647
$991$	−22.5329			−0.715780			−0.357890	−	0.933764i	$-0.616504\pi$
$991$	−22.5329			−0.715780			−0.357890	+	0.933764i	$0.616504\pi$
$992$	−8.12896			−0.258095
$993$	23.2685			0.738405
$994$	−0.221651	+	24.8100i	−0.00703035	+	0.786925i
$995$	7.03070	−	12.1775i	0.222888	−	0.386054i
$996$	3.71142	+	6.42837i	0.117601	+	0.203691i
$997$	12.3016	+	21.3071i	0.389597	+	0.674801i	0.992395	−	0.123092i	$-0.0392810\pi$
$997$	12.3016	+	21.3071i	0.389597	+	0.674801i	−0.602798	+	0.797893i	$0.705948\pi$
$998$	−14.2358			−0.450626
$999$	1.37097	−	2.37459i	0.0433755	−	0.0751286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.e.445.4	yes	10
3.2	odd	2		1638.2.p.j.991.2		10
7.2	even	3		546.2.j.e.289.4	✓	10
13.9	even	3		546.2.j.e.529.4	yes	10
21.2	odd	6		1638.2.m.k.289.2		10
39.35	odd	6		1638.2.m.k.1621.2		10
91.9	even	3	inner	546.2.k.e.373.4	yes	10
273.191	odd	6		1638.2.p.j.919.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.e.289.4	✓	10	7.2	even	3
546.2.j.e.529.4	yes	10	13.9	even	3
546.2.k.e.373.4	yes	10	91.9	even	3	inner
546.2.k.e.445.4	yes	10	1.1	even	1	trivial
1638.2.m.k.289.2		10	21.2	odd	6
1638.2.m.k.1621.2		10	39.35	odd	6
1638.2.p.j.919.2		10	273.191	odd	6
1638.2.p.j.991.2		10	3.2	odd	2

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.623307 + 1.07960i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.27938 - 1.34329i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.623307 + 1.07960i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.27938 - 1.34329i) q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.24661 q^{10} -2.49532 q^{11} +(0.500000 + 0.866025i) q^{12} +(-0.785103 - 3.51904i) q^{13} +(-2.30301 + 1.30235i) q^{14} +(-0.623307 - 1.07960i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.247662 - 0.428963i) q^{17} +(0.500000 - 0.866025i) q^{18} -7.67156 q^{19} +(0.623307 - 1.07960i) q^{20} +(2.27938 + 1.34329i) q^{21} +(-1.24766 + 2.16101i) q^{22} +(-0.224026 + 0.388024i) q^{23} +1.00000 q^{24} +(1.72298 - 2.98428i) q^{25} +(-3.44013 - 1.07960i) q^{26} -1.00000 q^{27} +(-0.0236360 + 2.64565i) q^{28} +(-3.71142 - 6.42837i) q^{29} -1.24661 q^{30} +(-4.06448 + 7.03989i) q^{31} +(0.500000 + 0.866025i) q^{32} +2.49532 q^{33} -0.495324 q^{34} +(0.0294650 - 3.29810i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.37097 + 2.37459i) q^{37} +(-3.83578 + 6.64376i) q^{38} +(0.785103 + 3.51904i) q^{39} +(-0.623307 - 1.07960i) q^{40} +(-1.87097 - 3.24061i) q^{41} +(2.30301 - 1.30235i) q^{42} +(1.47532 - 2.55532i) q^{43} +(1.24766 + 2.16101i) q^{44} +(0.623307 + 1.07960i) q^{45} +(0.224026 + 0.388024i) q^{46} +(3.29729 + 5.71107i) q^{47} +(0.500000 - 0.866025i) q^{48} +(3.39113 + 6.12374i) q^{49} +(-1.72298 - 2.98428i) q^{50} +(0.247662 + 0.428963i) q^{51} +(-2.65502 + 2.43944i) q^{52} +(3.86750 - 6.69870i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(-1.55535 - 2.69395i) q^{55} +(2.27938 + 1.34329i) q^{56} +7.67156 q^{57} -7.42285 q^{58} +(0.727653 + 1.26033i) q^{59} +(-0.623307 + 1.07960i) q^{60} -4.19934 q^{61} +(4.06448 + 7.03989i) q^{62} +(-2.27938 - 1.34329i) q^{63} +1.00000 q^{64} +(3.30979 - 3.04103i) q^{65} +(1.24766 - 2.16101i) q^{66} +0.0276094 q^{67} +(-0.247662 + 0.428963i) q^{68} +(0.224026 - 0.388024i) q^{69} +(-2.84150 - 1.67457i) q^{70} +(4.68884 - 8.12130i) q^{71} -1.00000 q^{72} +(-5.07151 + 8.78412i) q^{73} +(1.37097 + 2.37459i) q^{74} +(-1.72298 + 2.98428i) q^{75} +(3.83578 + 6.64376i) q^{76} +(5.68779 + 3.35195i) q^{77} +(3.44013 + 1.07960i) q^{78} +(-4.93545 - 8.54845i) q^{79} -1.24661 q^{80} +1.00000 q^{81} -3.74194 q^{82} +7.42285 q^{83} +(0.0236360 - 2.64565i) q^{84} +(0.308739 - 0.534751i) q^{85} +(-1.47532 - 2.55532i) q^{86} +(3.71142 + 6.42837i) q^{87} +2.49532 q^{88} +(5.74056 - 9.94294i) q^{89} +1.24661 q^{90} +(-2.93755 + 9.07584i) q^{91} +0.448052 q^{92} +(4.06448 - 7.03989i) q^{93} +6.59458 q^{94} +(-4.78173 - 8.28221i) q^{95} +(-0.500000 - 0.866025i) q^{96} +(-0.509831 + 0.883054i) q^{97} +(6.99888 + 0.125065i) q^{98} -2.49532 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9	\( 10 q + 5 q^{2} - 10 q^{3} - 5 q^{4} - 2 q^{5} - 5 q^{6} + 4 q^{7} - 10 q^{8} + 10 q^{9} - 4 q^{10} - 12 q^{11} + 5 q^{12} - 4 q^{13} + 2 q^{14} + 2 q^{15} - 5 q^{16} + 4 q^{17} + 5 q^{18} - 6 q^{19} - 2 q^{20} - 4 q^{21} - 6 q^{22} + 6 q^{23} + 10 q^{24} - q^{25} - 2 q^{26} - 10 q^{27} - 2 q^{28} + 4 q^{30} - 10 q^{31} + 5 q^{32} + 12 q^{33} + 8 q^{34} - 2 q^{35} - 5 q^{36} + q^{37} - 3 q^{38} + 4 q^{39} + 2 q^{40} - 4 q^{41} - 2 q^{42} + 3 q^{43} + 6 q^{44} - 2 q^{45} - 6 q^{46} - 15 q^{47} + 5 q^{48} - 20 q^{49} + q^{50} - 4 q^{51} + 2 q^{52} - 17 q^{53} - 5 q^{54} + 3 q^{55} - 4 q^{56} + 6 q^{57} + 2 q^{59} + 2 q^{60} - 22 q^{61} + 10 q^{62} + 4 q^{63} + 10 q^{64} + 41 q^{65} + 6 q^{66} + 2 q^{67} + 4 q^{68} - 6 q^{69} - 16 q^{70} + 18 q^{71} - 10 q^{72} + 12 q^{73} - q^{74} + q^{75} + 3 q^{76} + 18 q^{77} + 2 q^{78} - 4 q^{79} + 4 q^{80} + 10 q^{81} - 8 q^{82} + 2 q^{84} + q^{85} - 3 q^{86} + 12 q^{88} + 7 q^{89} - 4 q^{90} - 4 q^{91} - 12 q^{92} + 10 q^{93} - 30 q^{94} + 24 q^{95} - 5 q^{96} - 6 q^{97} - 16 q^{98} - 12 q^{99}+O(q^{100}) \) 10 * q + 5 * q^2 - 10 * q^3 - 5 * q^4 - 2 * q^5 - 5 * q^6 + 4 * q^7 - 10 * q^8 + 10 * q^9 - 4 * q^10 - 12 * q^11 + 5 * q^12 - 4 * q^13 + 2 * q^14 + 2 * q^15 - 5 * q^16 + 4 * q^17 + 5 * q^18 - 6 * q^19 - 2 * q^20 - 4 * q^21 - 6 * q^22 + 6 * q^23 + 10 * q^24 - q^25 - 2 * q^26 - 10 * q^27 - 2 * q^28 + 4 * q^30 - 10 * q^31 + 5 * q^32 + 12 * q^33 + 8 * q^34 - 2 * q^35 - 5 * q^36 + q^37 - 3 * q^38 + 4 * q^39 + 2 * q^40 - 4 * q^41 - 2 * q^42 + 3 * q^43 + 6 * q^44 - 2 * q^45 - 6 * q^46 - 15 * q^47 + 5 * q^48 - 20 * q^49 + q^50 - 4 * q^51 + 2 * q^52 - 17 * q^53 - 5 * q^54 + 3 * q^55 - 4 * q^56 + 6 * q^57 + 2 * q^59 + 2 * q^60 - 22 * q^61 + 10 * q^62 + 4 * q^63 + 10 * q^64 + 41 * q^65 + 6 * q^66 + 2 * q^67 + 4 * q^68 - 6 * q^69 - 16 * q^70 + 18 * q^71 - 10 * q^72 + 12 * q^73 - q^74 + q^75 + 3 * q^76 + 18 * q^77 + 2 * q^78 - 4 * q^79 + 4 * q^80 + 10 * q^81 - 8 * q^82 + 2 * q^84 + q^85 - 3 * q^86 + 12 * q^88 + 7 * q^89 - 4 * q^90 - 4 * q^91 - 12 * q^92 + 10 * q^93 - 30 * q^94 + 24 * q^95 - 5 * q^96 - 6 * q^97 - 16 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more