LMFDB - Embedded newform 546.2.l.l.295.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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, 0, 2]))

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

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{17})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 5x^{2} + 4x + 16 $ x^4 - x^3 + 5x^2 + 4x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.1
Root			$1.28078 + 2.21837i$ of defining polynomial
Character	$\chi$	$=$	546.295
Dual form			546.2.l.l.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.56155 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.56155 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.28078 - 2.21837i) q^{10} +(-0.780776 + 1.35234i) q^{11} -1.00000 q^{12} +(-0.500000 + 3.57071i) q^{13} +1.00000 q^{14} +(-1.28078 + 2.21837i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.06155 + 7.03482i) q^{17} +1.00000 q^{18} +(-0.780776 - 1.35234i) q^{19} +(1.28078 + 2.21837i) q^{20} -1.00000 q^{21} +(-0.780776 - 1.35234i) q^{22} +(-3.56155 + 6.16879i) q^{23} +(0.500000 - 0.866025i) q^{24} +1.56155 q^{25} +(-2.84233 - 2.21837i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-1.06155 + 1.83866i) q^{29} +(-1.28078 - 2.21837i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(0.780776 + 1.35234i) q^{33} -8.12311 q^{34} +(1.28078 + 2.21837i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.28078 - 5.68247i) q^{37} +1.56155 q^{38} +(2.84233 + 2.21837i) q^{39} -2.56155 q^{40} +(-2.62311 + 4.54335i) q^{41} +(0.500000 - 0.866025i) q^{42} +(4.00000 + 6.92820i) q^{43} +1.56155 q^{44} +(1.28078 + 2.21837i) q^{45} +(-3.56155 - 6.16879i) q^{46} -12.6847 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.780776 + 1.35234i) q^{50} +8.12311 q^{51} +(3.34233 - 1.35234i) q^{52} +7.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(2.00000 - 3.46410i) q^{55} +(-0.500000 - 0.866025i) q^{56} -1.56155 q^{57} +(-1.06155 - 1.83866i) q^{58} +(1.56155 + 2.70469i) q^{59} +2.56155 q^{60} +(-2.62311 - 4.54335i) q^{61} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(1.28078 - 9.14657i) q^{65} -1.56155 q^{66} +(-0.438447 + 0.759413i) q^{67} +(4.06155 - 7.03482i) q^{68} +(3.56155 + 6.16879i) q^{69} -2.56155 q^{70} +(-6.68466 - 11.5782i) q^{71} +(-0.500000 - 0.866025i) q^{72} -6.56155 q^{73} +(3.28078 + 5.68247i) q^{74} +(0.780776 - 1.35234i) q^{75} +(-0.780776 + 1.35234i) q^{76} +1.56155 q^{77} +(-3.34233 + 1.35234i) q^{78} -2.43845 q^{79} +(1.28078 - 2.21837i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.62311 - 4.54335i) q^{82} +3.12311 q^{83} +(0.500000 + 0.866025i) q^{84} +(-10.4039 - 18.0201i) q^{85} -8.00000 q^{86} +(1.06155 + 1.83866i) q^{87} +(-0.780776 + 1.35234i) q^{88} +(-3.78078 + 6.54850i) q^{89} -2.56155 q^{90} +(3.34233 - 1.35234i) q^{91} +7.12311 q^{92} +(6.34233 - 10.9852i) q^{94} +(2.00000 + 3.46410i) q^{95} -1.00000 q^{96} +(4.56155 + 7.90084i) q^{97} +(-0.500000 - 0.866025i) q^{98} +1.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} + q^{19} + q^{20} - 4 q^{21} + q^{22} - 6 q^{23} + 2 q^{24} - 2 q^{25} + q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{29} - q^{30} - 2 q^{32} - q^{33} - 16 q^{34} + q^{35} - 2 q^{36} + 9 q^{37} - 2 q^{38} - q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 16 q^{43} - 2 q^{44} + q^{45} - 6 q^{46} - 26 q^{47} + 2 q^{48} - 2 q^{49} + q^{50} + 16 q^{51} + q^{52} + 28 q^{53} + 2 q^{54} + 8 q^{55} - 2 q^{56} + 2 q^{57} + 4 q^{58} - 2 q^{59} + 2 q^{60} + 6 q^{61} - 2 q^{63} + 4 q^{64} + q^{65} + 2 q^{66} - 10 q^{67} + 8 q^{68} + 6 q^{69} - 2 q^{70} - 2 q^{71} - 2 q^{72} - 18 q^{73} + 9 q^{74} - q^{75} + q^{76} - 2 q^{77} - q^{78} - 18 q^{79} + q^{80} - 2 q^{81} + 6 q^{82} - 4 q^{83} + 2 q^{84} - 21 q^{85} - 32 q^{86} - 4 q^{87} + q^{88} - 11 q^{89} - 2 q^{90} + q^{91} + 12 q^{92} + 13 q^{94} + 8 q^{95} - 4 q^{96} + 10 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + q^11 - 4 * q^12 - 2 * q^13 + 4 * q^14 - q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 + q^19 + q^20 - 4 * q^21 + q^22 - 6 * q^23 + 2 * q^24 - 2 * q^25 + q^26 - 4 * q^27 - 2 * q^28 + 4 * q^29 - q^30 - 2 * q^32 - q^33 - 16 * q^34 + q^35 - 2 * q^36 + 9 * q^37 - 2 * q^38 - q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 16 * q^43 - 2 * q^44 + q^45 - 6 * q^46 - 26 * q^47 + 2 * q^48 - 2 * q^49 + q^50 + 16 * q^51 + q^52 + 28 * q^53 + 2 * q^54 + 8 * q^55 - 2 * q^56 + 2 * q^57 + 4 * q^58 - 2 * q^59 + 2 * q^60 + 6 * q^61 - 2 * q^63 + 4 * q^64 + q^65 + 2 * q^66 - 10 * q^67 + 8 * q^68 + 6 * q^69 - 2 * q^70 - 2 * q^71 - 2 * q^72 - 18 * q^73 + 9 * q^74 - q^75 + q^76 - 2 * q^77 - q^78 - 18 * q^79 + q^80 - 2 * q^81 + 6 * q^82 - 4 * q^83 + 2 * q^84 - 21 * q^85 - 32 * q^86 - 4 * q^87 + q^88 - 11 * q^89 - 2 * q^90 + q^91 + 12 * q^92 + 13 * q^94 + 8 * q^95 - 4 * q^96 + 10 * q^97 - 2 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	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
$5$	−2.56155			−1.14556			−0.572781	−	0.819709i	$-0.694135\pi$
$5$	−2.56155			−1.14556			−0.572781	+	0.819709i	$0.694135\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.28078	−	2.21837i	0.405017	−	0.701510i
$11$	−0.780776	+	1.35234i	−0.235413	+	0.407747i	−0.959393	−	0.282074i	$-0.908978\pi$
$11$	−0.780776	+	1.35234i	−0.235413	+	0.407747i	0.723980	+	0.689821i	$0.242311\pi$
$12$	−1.00000			−0.288675
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$13$	−0.500000	+	3.57071i	−0.138675	+	0.990338i
$14$	1.00000			0.267261
$15$	−1.28078	+	2.21837i	−0.330695	+	0.572781i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	4.06155	+	7.03482i	0.985071	+	1.70619i	0.641619	+	0.767023i	$0.278263\pi$
$17$	4.06155	+	7.03482i	0.985071	+	1.70619i	0.343452	+	0.939170i	$0.388404\pi$
$18$	1.00000			0.235702
$19$	−0.780776	−	1.35234i	−0.179122	−	0.310249i	0.762458	−	0.647038i	$-0.223992\pi$
$19$	−0.780776	−	1.35234i	−0.179122	−	0.310249i	−0.941580	+	0.336789i	$0.890659\pi$
$20$	1.28078	+	2.21837i	0.286390	+	0.496043i
$21$	−1.00000			−0.218218
$22$	−0.780776	−	1.35234i	−0.166462	−	0.288321i
$23$	−3.56155	+	6.16879i	−0.742635	+	1.28628i	0.208656	+	0.977989i	$0.433091\pi$
$23$	−3.56155	+	6.16879i	−0.742635	+	1.28628i	−0.951292	+	0.308293i	$0.900242\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	1.56155			0.312311
$26$	−2.84233	−	2.21837i	−0.557427	−	0.435058i
$27$	−1.00000			−0.192450
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	−1.06155	+	1.83866i	−0.197125	+	0.341431i	−0.947595	−	0.319474i	$-0.896494\pi$
$29$	−1.06155	+	1.83866i	−0.197125	+	0.341431i	0.750470	+	0.660905i	$0.229827\pi$
$30$	−1.28078	−	2.21837i	−0.233837	−	0.405017i
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	0.780776	+	1.35234i	0.135916	+	0.235413i
$34$	−8.12311			−1.39310
$35$	1.28078	+	2.21837i	0.216491	+	0.374973i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	3.28078	−	5.68247i	0.539356	−	0.934193i	−0.459582	−	0.888135i	$-0.652001\pi$
$37$	3.28078	−	5.68247i	0.539356	−	0.934193i	0.998939	−	0.0460575i	$-0.0146657\pi$
$38$	1.56155			0.253317
$39$	2.84233	+	2.21837i	0.455137	+	0.355223i
$40$	−2.56155			−0.405017
$41$	−2.62311	+	4.54335i	−0.409660	+	0.709552i	−0.994852	−	0.101343i	$-0.967686\pi$
$41$	−2.62311	+	4.54335i	−0.409660	+	0.709552i	0.585191	+	0.810895i	$0.301019\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	0.991241	+	0.132068i	$0.0421616\pi$
$43$	4.00000	+	6.92820i	0.609994	+	1.05654i	−0.381246	+	0.924473i	$0.624505\pi$
$44$	1.56155			0.235413
$45$	1.28078	+	2.21837i	0.190927	+	0.330695i
$46$	−3.56155	−	6.16879i	−0.525122	−	0.909539i
$47$	−12.6847			−1.85025			−0.925124	−	0.379666i	$-0.876039\pi$
$47$	−12.6847			−1.85025			−0.925124	+	0.379666i	$0.876039\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−0.780776	+	1.35234i	−0.110418	+	0.191250i
$51$	8.12311			1.13746
$52$	3.34233	−	1.35234i	0.463498	−	0.187536i
$53$	7.00000			0.961524			0.480762	−	0.876851i	$-0.340360\pi$
$53$	7.00000			0.961524			0.480762	+	0.876851i	$0.340360\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	2.00000	−	3.46410i	0.269680	−	0.467099i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−1.56155			−0.206833
$58$	−1.06155	−	1.83866i	−0.139389	−	0.241428i
$59$	1.56155	+	2.70469i	0.203297	+	0.352120i	0.949589	−	0.313498i	$-0.101501\pi$
$59$	1.56155	+	2.70469i	0.203297	+	0.352120i	−0.746292	+	0.665619i	$0.768168\pi$
$60$	2.56155			0.330695
$61$	−2.62311	−	4.54335i	−0.335854	−	0.581717i	0.647794	−	0.761815i	$-0.275692\pi$
$61$	−2.62311	−	4.54335i	−0.335854	−	0.581717i	−0.983649	+	0.180099i	$0.942358\pi$
$62$		0			0
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	1.28078	−	9.14657i	0.158861	−	1.13449i
$66$	−1.56155			−0.192214
$67$	−0.438447	+	0.759413i	−0.0535648	+	0.0927770i	−0.891565	−	0.452894i	$-0.850392\pi$
$67$	−0.438447	+	0.759413i	−0.0535648	+	0.0927770i	0.838000	+	0.545671i	$0.183725\pi$
$68$	4.06155	−	7.03482i	0.492536	−	0.853097i
$69$	3.56155	+	6.16879i	0.428761	+	0.742635i
$70$	−2.56155			−0.306164
$71$	−6.68466	−	11.5782i	−0.793323	−	1.37408i	−0.923899	−	0.382637i	$-0.875016\pi$
$71$	−6.68466	−	11.5782i	−0.793323	−	1.37408i	0.130576	−	0.991438i	$-0.458317\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−6.56155			−0.767972			−0.383986	−	0.923339i	$-0.625449\pi$
$73$	−6.56155			−0.767972			−0.383986	+	0.923339i	$0.625449\pi$
$74$	3.28078	+	5.68247i	0.381383	+	0.660574i
$75$	0.780776	−	1.35234i	0.0901563	−	0.156155i
$76$	−0.780776	+	1.35234i	−0.0895612	+	0.155125i
$77$	1.56155			0.177955
$78$	−3.34233	+	1.35234i	−0.378444	+	0.153123i
$79$	−2.43845			−0.274347			−0.137173	−	0.990547i	$-0.543802\pi$
$79$	−2.43845			−0.274347			−0.137173	+	0.990547i	$0.543802\pi$
$80$	1.28078	−	2.21837i	0.143195	−	0.248021i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.62311	−	4.54335i	−0.289674	−	0.501729i
$83$	3.12311			0.342805			0.171403	−	0.985201i	$-0.445170\pi$
$83$	3.12311			0.342805			0.171403	+	0.985201i	$0.445170\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	−10.4039	−	18.0201i	−1.12846	−	1.95455i
$86$	−8.00000			−0.862662
$87$	1.06155	+	1.83866i	0.113810	+	0.197125i
$88$	−0.780776	+	1.35234i	−0.0832310	+	0.144160i
$89$	−3.78078	+	6.54850i	−0.400761	+	0.694139i	−0.993818	−	0.111022i	$-0.964588\pi$
$89$	−3.78078	+	6.54850i	−0.400761	+	0.694139i	0.593056	+	0.805161i	$0.297921\pi$
$90$	−2.56155			−0.270011
$91$	3.34233	−	1.35234i	0.350371	−	0.141764i
$92$	7.12311			0.742635
$93$		0			0
$94$	6.34233	−	10.9852i	0.654161	−	1.13304i
$95$	2.00000	+	3.46410i	0.205196	+	0.355409i
$96$	−1.00000			−0.102062
$97$	4.56155	+	7.90084i	0.463156	+	0.802209i	0.999116	−	0.0420341i	$-0.0133838\pi$
$97$	4.56155	+	7.90084i	0.463156	+	0.802209i	−0.535961	+	0.844243i	$0.680050\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	1.56155			0.156942
$100$	−0.780776	−	1.35234i	−0.0780776	−	0.135234i
$101$	−7.40388	+	12.8239i	−0.736714	+	1.27603i	0.217254	+	0.976115i	$0.430290\pi$
$101$	−7.40388	+	12.8239i	−0.736714	+	1.27603i	−0.953967	+	0.299911i	$0.903043\pi$
$102$	−4.06155	+	7.03482i	−0.402154	+	0.696551i
$103$	−10.2462			−1.00959			−0.504795	−	0.863239i	$-0.668432\pi$
$103$	−10.2462			−1.00959			−0.504795	+	0.863239i	$0.668432\pi$
$104$	−0.500000	+	3.57071i	−0.0490290	+	0.350137i
$105$	2.56155			0.249982
$106$	−3.50000	+	6.06218i	−0.339950	+	0.588811i
$107$	7.46543	−	12.9305i	0.721711	−	1.25004i	−0.238603	−	0.971117i	$-0.576689\pi$
$107$	7.46543	−	12.9305i	0.721711	−	1.25004i	0.960314	−	0.278923i	$-0.0899773\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	4.24621			0.406713			0.203357	−	0.979105i	$-0.434815\pi$
$109$	4.24621			0.406713			0.203357	+	0.979105i	$0.434815\pi$
$110$	2.00000	+	3.46410i	0.190693	+	0.330289i
$111$	−3.28078	−	5.68247i	−0.311398	−	0.539356i
$112$	1.00000			0.0944911
$113$	1.28078	+	2.21837i	0.120485	+	0.208687i	0.919959	−	0.392014i	$-0.128222\pi$
$113$	1.28078	+	2.21837i	0.120485	+	0.208687i	−0.799474	+	0.600701i	$0.794888\pi$
$114$	0.780776	−	1.35234i	0.0731264	−	0.126659i
$115$	9.12311	−	15.8017i	0.850734	−	1.47351i
$116$	2.12311			0.197125
$117$	3.34233	−	1.35234i	0.308998	−	0.125024i
$118$	−3.12311			−0.287505
$119$	4.06155	−	7.03482i	0.372322	−	0.644881i
$120$	−1.28078	+	2.21837i	−0.116918	+	0.202509i
$121$	4.28078	+	7.41452i	0.389161	+	0.674047i
$122$	5.24621			0.474970
$123$	2.62311	+	4.54335i	0.236517	+	0.409660i
$124$		0			0
$125$	8.80776			0.787790
$126$	−0.500000	−	0.866025i	−0.0445435	−	0.0771517i
$127$	10.2462	−	17.7470i	0.909204	−	1.57479i	0.0940321	−	0.995569i	$-0.470024\pi$
$127$	10.2462	−	17.7470i	0.909204	−	1.57479i	0.815172	−	0.579219i	$-0.196642\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	8.00000			0.704361
$130$	7.28078	+	5.68247i	0.638566	+	0.498386i
$131$	−2.24621			−0.196252			−0.0981262	−	0.995174i	$-0.531285\pi$
$131$	−2.24621			−0.196252			−0.0981262	+	0.995174i	$0.531285\pi$
$132$	0.780776	−	1.35234i	0.0679579	−	0.117706i
$133$	−0.780776	+	1.35234i	−0.0677019	+	0.117263i
$134$	−0.438447	−	0.759413i	−0.0378761	−	0.0656033i
$135$	2.56155			0.220463
$136$	4.06155	+	7.03482i	0.348275	+	0.603230i
$137$	−8.28078	−	14.3427i	−0.707474	−	1.22538i	−0.965791	−	0.259321i	$-0.916501\pi$
$137$	−8.28078	−	14.3427i	−0.707474	−	1.22538i	0.258317	−	0.966060i	$-0.416832\pi$
$138$	−7.12311			−0.606359
$139$	4.78078	+	8.28055i	0.405500	+	0.702347i	0.994380	−	0.105874i	$-0.0337640\pi$
$139$	4.78078	+	8.28055i	0.405500	+	0.702347i	−0.588879	+	0.808221i	$0.700431\pi$
$140$	1.28078	−	2.21837i	0.108245	−	0.187486i
$141$	−6.34233	+	10.9852i	−0.534120	+	0.925124i
$142$	13.3693			1.12193
$143$	−4.43845	−	3.46410i	−0.371162	−	0.289683i
$144$	1.00000			0.0833333
$145$	2.71922	−	4.70983i	0.225819	−	0.391130i
$146$	3.28078	−	5.68247i	0.271519	−	0.470285i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$	−6.56155			−0.539356
$149$	5.71922	+	9.90599i	0.468537	+	0.811530i	0.999353	−	0.0359569i	$-0.0114479\pi$
$149$	5.71922	+	9.90599i	0.468537	+	0.811530i	−0.530816	+	0.847487i	$0.678115\pi$
$150$	0.780776	+	1.35234i	0.0637501	+	0.110418i
$151$	6.93087			0.564026			0.282013	−	0.959411i	$-0.408998\pi$
$151$	6.93087			0.564026			0.282013	+	0.959411i	$0.408998\pi$
$152$	−0.780776	−	1.35234i	−0.0633293	−	0.109690i
$153$	4.06155	−	7.03482i	0.328357	−	0.568731i
$154$	−0.780776	+	1.35234i	−0.0629168	+	0.108975i
$155$		0			0
$156$	0.500000	−	3.57071i	0.0400320	−	0.285886i
$157$	−13.6847			−1.09215			−0.546077	−	0.837735i	$-0.683880\pi$
$157$	−13.6847			−1.09215			−0.546077	+	0.837735i	$0.683880\pi$
$158$	1.21922	−	2.11176i	0.0969962	−	0.168002i
$159$	3.50000	−	6.06218i	0.277568	−	0.480762i
$160$	1.28078	+	2.21837i	0.101254	+	0.175378i
$161$	7.12311			0.561379
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	4.24621	+	7.35465i	0.332589	+	0.576061i	0.983019	−	0.183505i	$-0.0587445\pi$
$163$	4.24621	+	7.35465i	0.332589	+	0.576061i	−0.650430	+	0.759566i	$0.725411\pi$
$164$	5.24621			0.409660
$165$	−2.00000	−	3.46410i	−0.155700	−	0.269680i
$166$	−1.56155	+	2.70469i	−0.121200	+	0.209925i
$167$	10.2462	−	17.7470i	0.792876	−	1.37330i	−0.131304	−	0.991342i	$-0.541916\pi$
$167$	10.2462	−	17.7470i	0.792876	−	1.37330i	0.924179	−	0.381959i	$-0.124750\pi$
$168$	−1.00000			−0.0771517
$169$	−12.5000	−	3.57071i	−0.961538	−	0.274670i
$170$	20.8078			1.59588
$171$	−0.780776	+	1.35234i	−0.0597075	+	0.103416i
$172$	4.00000	−	6.92820i	0.304997	−	0.528271i
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	0.973670	+	0.227964i	$0.0732068\pi$
$173$	9.00000	+	15.5885i	0.684257	+	1.18517i	−0.289412	+	0.957205i	$0.593460\pi$
$174$	−2.12311			−0.160952
$175$	−0.780776	−	1.35234i	−0.0590211	−	0.102228i
$176$	−0.780776	−	1.35234i	−0.0588532	−	0.101937i
$177$	3.12311			0.234747
$178$	−3.78078	−	6.54850i	−0.283381	−	0.490831i
$179$	9.12311	−	15.8017i	0.681893	−	1.18107i	−0.292510	−	0.956263i	$-0.594490\pi$
$179$	9.12311	−	15.8017i	0.681893	−	1.18107i	0.974402	−	0.224811i	$-0.0721763\pi$
$180$	1.28078	−	2.21837i	0.0954634	−	0.165348i
$181$	−3.24621			−0.241289			−0.120644	−	0.992696i	$-0.538496\pi$
$181$	−3.24621			−0.241289			−0.120644	+	0.992696i	$0.538496\pi$
$182$	−0.500000	+	3.57071i	−0.0370625	+	0.264679i
$183$	−5.24621			−0.387811
$184$	−3.56155	+	6.16879i	−0.262561	+	0.454769i
$185$	−8.40388	+	14.5560i	−0.617866	+	1.07017i
$186$		0			0
$187$	−12.6847			−0.927594
$188$	6.34233	+	10.9852i	0.462562	+	0.801181i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	−4.00000			−0.290191
$191$	−1.56155	−	2.70469i	−0.112990	−	0.195704i	0.803984	−	0.594650i	$-0.202709\pi$
$191$	−1.56155	−	2.70469i	−0.112990	−	0.195704i	−0.916974	+	0.398946i	$0.869376\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	4.06155	−	7.03482i	0.292357	−	0.506377i	−0.682010	−	0.731343i	$-0.738894\pi$
$193$	4.06155	−	7.03482i	0.292357	−	0.506377i	0.974367	+	0.224966i	$0.0722271\pi$
$194$	−9.12311			−0.655001
$195$	−7.28078	−	5.68247i	−0.521387	−	0.406930i
$196$	1.00000			0.0714286
$197$	−4.21922	+	7.30791i	−0.300607	+	0.520667i	−0.976274	−	0.216541i	$-0.930523\pi$
$197$	−4.21922	+	7.30791i	−0.300607	+	0.520667i	0.675666	+	0.737208i	$0.263856\pi$
$198$	−0.780776	+	1.35234i	−0.0554874	+	0.0961069i
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	0.996850	+	0.0793045i	$0.0252700\pi$
$199$	8.00000	+	13.8564i	0.567105	+	0.982255i	−0.429745	+	0.902950i	$0.641397\pi$
$200$	1.56155			0.110418
$201$	0.438447	+	0.759413i	0.0309257	+	0.0535648i
$202$	−7.40388	−	12.8239i	−0.520935	−	0.902286i
$203$	2.12311			0.149013
$204$	−4.06155	−	7.03482i	−0.284366	−	0.492536i
$205$	6.71922	−	11.6380i	0.469291	−	0.812836i
$206$	5.12311	−	8.87348i	0.356944	−	0.618245i
$207$	7.12311			0.495090
$208$	−2.84233	−	2.21837i	−0.197080	−	0.153816i
$209$	2.43845			0.168671
$210$	−1.28078	+	2.21837i	−0.0883820	+	0.153082i
$211$	1.56155	−	2.70469i	0.107502	−	0.186198i	−0.807256	−	0.590202i	$-0.799048\pi$
$211$	1.56155	−	2.70469i	0.107502	−	0.186198i	0.914758	+	0.404003i	$0.132382\pi$
$212$	−3.50000	−	6.06218i	−0.240381	−	0.416352i
$213$	−13.3693			−0.916050
$214$	7.46543	+	12.9305i	0.510327	+	0.883912i
$215$	−10.2462	−	17.7470i	−0.698786	−	1.21033i
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−2.12311	+	3.67733i	−0.143795	+	0.249060i
$219$	−3.28078	+	5.68247i	−0.221694	+	0.383986i
$220$	−4.00000			−0.269680
$221$	−27.1501	+	10.9852i	−1.82631	+	0.738947i
$222$	6.56155			0.440383
$223$	−13.1231	+	22.7299i	−0.878788	+	1.52211i	−0.0261163	+	0.999659i	$0.508314\pi$
$223$	−13.1231	+	22.7299i	−0.878788	+	1.52211i	−0.852672	+	0.522447i	$0.825019\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	−0.780776	−	1.35234i	−0.0520518	−	0.0901563i
$226$	−2.56155			−0.170392
$227$	9.56155	+	16.5611i	0.634623	+	1.09920i	0.986595	+	0.163188i	$0.0521778\pi$
$227$	9.56155	+	16.5611i	0.634623	+	1.09920i	−0.351972	+	0.936010i	$0.614489\pi$
$228$	0.780776	+	1.35234i	0.0517082	+	0.0895612i
$229$	−20.0540			−1.32520			−0.662602	−	0.748972i	$-0.730548\pi$
$229$	−20.0540			−1.32520			−0.662602	+	0.748972i	$0.730548\pi$
$230$	9.12311	+	15.8017i	0.601560	+	1.04193i
$231$	0.780776	−	1.35234i	0.0513713	−	0.0889777i
$232$	−1.06155	+	1.83866i	−0.0696944	+	0.120714i
$233$	−23.3693			−1.53097			−0.765487	−	0.643451i	$-0.777502\pi$
$233$	−23.3693			−1.53097			−0.765487	+	0.643451i	$0.777502\pi$
$234$	−0.500000	+	3.57071i	−0.0326860	+	0.233425i
$235$	32.4924			2.11957
$236$	1.56155	−	2.70469i	0.101648	−	0.176060i
$237$	−1.21922	+	2.11176i	−0.0791971	+	0.137173i
$238$	4.06155	+	7.03482i	0.263271	+	0.455999i
$239$	−5.36932			−0.347312			−0.173656	−	0.984806i	$-0.555558\pi$
$239$	−5.36932			−0.347312			−0.173656	+	0.984806i	$0.555558\pi$
$240$	−1.28078	−	2.21837i	−0.0826738	−	0.143195i
$241$	10.4039	+	18.0201i	0.670173	+	1.16077i	0.977855	+	0.209284i	$0.0671134\pi$
$241$	10.4039	+	18.0201i	0.670173	+	1.16077i	−0.307682	+	0.951489i	$0.599553\pi$
$242$	−8.56155			−0.550357
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−2.62311	+	4.54335i	−0.167927	+	0.290858i
$245$	1.28078	−	2.21837i	0.0818258	−	0.141726i
$246$	−5.24621			−0.334486
$247$	5.21922	−	2.11176i	0.332091	−	0.134368i
$248$		0			0
$249$	1.56155	−	2.70469i	0.0989594	−	0.171403i
$250$	−4.40388	+	7.62775i	−0.278526	+	0.482421i
$251$	−13.8078	−	23.9157i	−0.871538	−	1.50955i	−0.860405	−	0.509611i	$-0.829789\pi$
$251$	−13.8078	−	23.9157i	−0.871538	−	1.50955i	−0.0111332	−	0.999938i	$-0.503544\pi$
$252$	1.00000			0.0629941
$253$	−5.56155	−	9.63289i	−0.349652	−	0.605615i
$254$	10.2462	+	17.7470i	0.642904	+	1.11354i
$255$	−20.8078			−1.30303
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.184658	+	0.319838i	−0.0115187	+	0.0199509i	−0.871727	−	0.489991i	$-0.837000\pi$
$257$	−0.184658	+	0.319838i	−0.0115187	+	0.0199509i	0.860209	+	0.509942i	$0.170333\pi$
$258$	−4.00000	+	6.92820i	−0.249029	+	0.431331i
$259$	−6.56155			−0.407715
$260$	−8.56155	+	3.46410i	−0.530965	+	0.214834i
$261$	2.12311			0.131417
$262$	1.12311	−	1.94528i	0.0693857	−	0.120180i
$263$	1.56155	−	2.70469i	0.0962895	−	0.166778i	−0.813857	−	0.581066i	$-0.802636\pi$
$263$	1.56155	−	2.70469i	0.0962895	−	0.166778i	0.910146	+	0.414288i	$0.135969\pi$
$264$	0.780776	+	1.35234i	0.0480535	+	0.0832310i
$265$	−17.9309			−1.10148
$266$	−0.780776	−	1.35234i	−0.0478725	−	0.0829176i
$267$	3.78078	+	6.54850i	0.231380	+	0.400761i
$268$	0.876894			0.0535648
$269$	−9.43845	−	16.3479i	−0.575472	−	0.996747i	−0.995990	−	0.0894630i	$-0.971485\pi$
$269$	−9.43845	−	16.3479i	−0.575472	−	0.996747i	0.420518	−	0.907284i	$-0.361848\pi$
$270$	−1.28078	+	2.21837i	−0.0779456	+	0.135006i
$271$	−13.3693	+	23.1563i	−0.812128	+	1.40665i	0.0992436	+	0.995063i	$0.468358\pi$
$271$	−13.3693	+	23.1563i	−0.812128	+	1.40665i	−0.911372	+	0.411584i	$0.864976\pi$
$272$	−8.12311			−0.492536
$273$	0.500000	−	3.57071i	0.0302614	−	0.216109i
$274$	16.5616			1.00052
$275$	−1.21922	+	2.11176i	−0.0735219	+	0.127344i
$276$	3.56155	−	6.16879i	0.214380	−	0.371318i
$277$	7.71922	+	13.3701i	0.463803	+	0.803331i	0.999147	−	0.0413038i	$-0.0131511\pi$
$277$	7.71922	+	13.3701i	0.463803	+	0.803331i	−0.535343	+	0.844634i	$0.679818\pi$
$278$	−9.56155			−0.573464
$279$		0			0
$280$	1.28078	+	2.21837i	0.0765410	+	0.132573i
$281$	−15.9309			−0.950356			−0.475178	−	0.879890i	$-0.657616\pi$
$281$	−15.9309			−0.950356			−0.475178	+	0.879890i	$0.657616\pi$
$282$	−6.34233	−	10.9852i	−0.377680	−	0.654161i
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	−0.399188	−	0.916869i	$-0.630708\pi$
$283$	10.0000	−	17.3205i	0.594438	−	1.02960i	0.993626	−	0.112728i	$-0.0359589\pi$
$284$	−6.68466	+	11.5782i	−0.396662	+	0.687038i
$285$	4.00000			0.236940
$286$	5.21922	−	2.11176i	0.308619	−	0.124871i
$287$	5.24621			0.309674
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−24.4924	+	42.4221i	−1.44073	+	2.49542i
$290$	2.71922	+	4.70983i	0.159678	+	0.276571i
$291$	9.12311			0.534806
$292$	3.28078	+	5.68247i	0.191993	+	0.332541i
$293$	−10.9654	−	18.9927i	−0.640608	−	1.10956i	−0.985297	−	0.170848i	$-0.945349\pi$
$293$	−10.9654	−	18.9927i	−0.640608	−	1.10956i	0.344690	−	0.938717i	$-0.387984\pi$
$294$	−1.00000			−0.0583212
$295$	−4.00000	−	6.92820i	−0.232889	−	0.403376i
$296$	3.28078	−	5.68247i	0.190691	−	0.330287i
$297$	0.780776	−	1.35234i	0.0453052	−	0.0784710i
$298$	−11.4384			−0.662611
$299$	−20.2462	−	15.8017i	−1.17087	−	0.913835i
$300$	−1.56155			−0.0901563
$301$	4.00000	−	6.92820i	0.230556	−	0.399335i
$302$	−3.46543	+	6.00231i	−0.199413	+	0.345394i
$303$	7.40388	+	12.8239i	0.425342	+	0.736714i
$304$	1.56155			0.0895612
$305$	6.71922	+	11.6380i	0.384742	+	0.666392i
$306$	4.06155	+	7.03482i	0.232184	+	0.402154i
$307$	18.9309			1.08044			0.540221	−	0.841523i	$-0.318341\pi$
$307$	18.9309			1.08044			0.540221	+	0.841523i	$0.318341\pi$
$308$	−0.780776	−	1.35234i	−0.0444889	−	0.0770570i
$309$	−5.12311	+	8.87348i	−0.291443	+	0.504795i
$310$		0			0
$311$	−6.93087			−0.393014			−0.196507	−	0.980502i	$-0.562960\pi$
$311$	−6.93087			−0.393014			−0.196507	+	0.980502i	$0.562960\pi$
$312$	2.84233	+	2.21837i	0.160915	+	0.125590i
$313$	−6.00000			−0.339140			−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000			−0.339140			−0.169570	+	0.985518i	$0.554238\pi$
$314$	6.84233	−	11.8513i	0.386135	−	0.668805i
$315$	1.28078	−	2.21837i	0.0721636	−	0.124991i
$316$	1.21922	+	2.11176i	0.0685867	+	0.118796i
$317$	16.5616			0.930189			0.465095	−	0.885261i	$-0.346020\pi$
$317$	16.5616			0.930189			0.465095	+	0.885261i	$0.346020\pi$
$318$	3.50000	+	6.06218i	0.196270	+	0.339950i
$319$	−1.65767	−	2.87117i	−0.0928117	−	0.160755i
$320$	−2.56155			−0.143195
$321$	−7.46543	−	12.9305i	−0.416680	−	0.721711i
$322$	−3.56155	+	6.16879i	−0.198478	+	0.343773i
$323$	6.34233	−	10.9852i	0.352897	−	0.611235i
$324$	1.00000			0.0555556
$325$	−0.780776	+	5.57586i	−0.0433097	+	0.309293i
$326$	−8.49242			−0.470352
$327$	2.12311	−	3.67733i	0.117408	−	0.203357i
$328$	−2.62311	+	4.54335i	−0.144837	+	0.250865i
$329$	6.34233	+	10.9852i	0.349664	+	0.605636i
$330$	4.00000			0.220193
$331$	2.68466	+	4.64996i	0.147562	+	0.255585i	0.930326	−	0.366734i	$-0.119524\pi$
$331$	2.68466	+	4.64996i	0.147562	+	0.255585i	−0.782764	+	0.622319i	$0.786191\pi$
$332$	−1.56155	−	2.70469i	−0.0857013	−	0.148439i
$333$	−6.56155			−0.359571
$334$	10.2462	+	17.7470i	0.560648	+	0.971070i
$335$	1.12311	−	1.94528i	0.0613618	−	0.106282i
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	19.4924			1.06182			0.530910	−	0.847428i	$-0.321850\pi$
$337$	19.4924			1.06182			0.530910	+	0.847428i	$0.321850\pi$
$338$	9.34233	−	9.03996i	0.508156	−	0.491709i
$339$	2.56155			0.139124
$340$	−10.4039	+	18.0201i	−0.564230	+	0.977275i
$341$		0			0
$342$	−0.780776	−	1.35234i	−0.0422196	−	0.0731264i
$343$	1.00000			0.0539949
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$	−9.12311	−	15.8017i	−0.491171	−	0.850734i
$346$	−18.0000			−0.967686
$347$	11.0270	+	19.0993i	0.591960	+	1.02530i	0.993968	+	0.109668i	$0.0349789\pi$
$347$	11.0270	+	19.0993i	0.591960	+	1.02530i	−0.402009	+	0.915636i	$0.631688\pi$
$348$	1.06155	−	1.83866i	0.0569052	−	0.0985627i
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	−0.518022	−	0.855367i	$-0.673331\pi$
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	0.999781	+	0.0209364i	$0.00666475\pi$
$350$	1.56155			0.0834685
$351$	0.500000	−	3.57071i	0.0266880	−	0.190591i
$352$	1.56155			0.0832310
$353$	6.59612	−	11.4248i	0.351076	−	0.608081i	−0.635362	−	0.772214i	$-0.719149\pi$
$353$	6.59612	−	11.4248i	0.351076	−	0.608081i	0.986438	+	0.164133i	$0.0524826\pi$
$354$	−1.56155	+	2.70469i	−0.0829956	+	0.143753i
$355$	17.1231	+	29.6581i	0.908800	+	1.57409i
$356$	7.56155			0.400761
$357$	−4.06155	−	7.03482i	−0.214960	−	0.372322i
$358$	9.12311	+	15.8017i	0.482171	+	0.835145i
$359$	−18.2462			−0.962998			−0.481499	−	0.876447i	$-0.659908\pi$
$359$	−18.2462			−0.962998			−0.481499	+	0.876447i	$0.659908\pi$
$360$	1.28078	+	2.21837i	0.0675028	+	0.116918i
$361$	8.28078	−	14.3427i	0.435830	−	0.754880i
$362$	1.62311	−	2.81130i	0.0853085	−	0.147759i
$363$	8.56155			0.449365
$364$	−2.84233	−	2.21837i	−0.148979	−	0.116274i
$365$	16.8078			0.879759
$366$	2.62311	−	4.54335i	0.137112	−	0.237485i
$367$	13.8078	−	23.9157i	0.720759	−	1.24839i	−0.239936	−	0.970789i	$-0.577127\pi$
$367$	13.8078	−	23.9157i	0.720759	−	1.24839i	0.960696	−	0.277603i	$-0.0895401\pi$
$368$	−3.56155	−	6.16879i	−0.185659	−	0.321570i
$369$	5.24621			0.273107
$370$	−8.40388	−	14.5560i	−0.436897	−	0.756728i
$371$	−3.50000	−	6.06218i	−0.181711	−	0.314733i
$372$		0			0
$373$	15.9654	+	27.6529i	0.826659	+	1.43182i	0.900645	+	0.434556i	$0.143095\pi$
$373$	15.9654	+	27.6529i	0.826659	+	1.43182i	−0.0739860	+	0.997259i	$0.523572\pi$
$374$	6.34233	−	10.9852i	0.327954	−	0.568033i
$375$	4.40388	−	7.62775i	0.227415	−	0.393895i
$376$	−12.6847			−0.654161
$377$	−6.03457	−	4.70983i	−0.310796	−	0.242569i
$378$	−1.00000			−0.0514344
$379$	1.80776	−	3.13114i	0.0928586	−	0.160836i	−0.815854	−	0.578258i	$-0.803733\pi$
$379$	1.80776	−	3.13114i	0.0928586	−	0.160836i	0.908713	+	0.417422i	$0.137066\pi$
$380$	2.00000	−	3.46410i	0.102598	−	0.177705i
$381$	−10.2462	−	17.7470i	−0.524929	−	0.909204i
$382$	3.12311			0.159792
$383$	−3.90388	−	6.76172i	−0.199479	−	0.345508i	0.748881	−	0.662705i	$-0.230592\pi$
$383$	−3.90388	−	6.76172i	−0.199479	−	0.345508i	−0.948360	+	0.317197i	$0.897258\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−4.00000			−0.203859
$386$	4.06155	+	7.03482i	0.206728	+	0.358063i
$387$	4.00000	−	6.92820i	0.203331	−	0.352180i
$388$	4.56155	−	7.90084i	0.231578	−	0.401104i
$389$	−17.6847			−0.896648			−0.448324	−	0.893871i	$-0.647979\pi$
$389$	−17.6847			−0.896648			−0.448324	+	0.893871i	$0.647979\pi$
$390$	8.56155	−	3.46410i	0.433531	−	0.175412i
$391$	−57.8617			−2.92619
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−1.12311	+	1.94528i	−0.0566532	+	0.0981262i
$394$	−4.21922	−	7.30791i	−0.212561	−	0.368167i
$395$	6.24621			0.314281
$396$	−0.780776	−	1.35234i	−0.0392355	−	0.0679579i
$397$	0.465435	+	0.806157i	0.0233595	+	0.0404598i	0.877469	−	0.479634i	$-0.159230\pi$
$397$	0.465435	+	0.806157i	0.0233595	+	0.0404598i	−0.854109	+	0.520093i	$0.825897\pi$
$398$	−16.0000			−0.802008
$399$	0.780776	+	1.35234i	0.0390877	+	0.0677019i
$400$	−0.780776	+	1.35234i	−0.0390388	+	0.0676172i
$401$	−9.40388	+	16.2880i	−0.469607	+	0.813384i	−0.999396	−	0.0347457i	$-0.988938\pi$
$401$	−9.40388	+	16.2880i	−0.469607	+	0.813384i	0.529789	+	0.848130i	$0.322271\pi$
$402$	−0.876894			−0.0437355
$403$		0			0
$404$	14.8078			0.736714
$405$	1.28078	−	2.21837i	0.0636423	−	0.110232i
$406$	−1.06155	+	1.83866i	−0.0526840	+	0.0912513i
$407$	5.12311	+	8.87348i	0.253943	+	0.439842i
$408$	8.12311			0.402154
$409$	3.71922	+	6.44188i	0.183904	+	0.318531i	0.943207	−	0.332207i	$-0.107793\pi$
$409$	3.71922	+	6.44188i	0.183904	+	0.318531i	−0.759303	+	0.650737i	$0.774460\pi$
$410$	6.71922	+	11.6380i	0.331839	+	0.574762i
$411$	−16.5616			−0.816921
$412$	5.12311	+	8.87348i	0.252397	+	0.437165i
$413$	1.56155	−	2.70469i	0.0768390	−	0.133089i
$414$	−3.56155	+	6.16879i	−0.175041	+	0.303180i
$415$	−8.00000			−0.392705
$416$	3.34233	−	1.35234i	0.163871	−	0.0663041i
$417$	9.56155			0.468231
$418$	−1.21922	+	2.11176i	−0.0596342	+	0.103289i
$419$	0.684658	−	1.18586i	0.0334478	−	0.0579332i	−0.848817	−	0.528687i	$-0.822685\pi$
$419$	0.684658	−	1.18586i	0.0334478	−	0.0579332i	0.882265	+	0.470754i	$0.156018\pi$
$420$	−1.28078	−	2.21837i	−0.0624955	−	0.108245i
$421$	31.3002			1.52548			0.762739	−	0.646707i	$-0.223854\pi$
$421$	31.3002			1.52548			0.762739	+	0.646707i	$0.223854\pi$
$422$	1.56155	+	2.70469i	0.0760152	+	0.131662i
$423$	6.34233	+	10.9852i	0.308375	+	0.534120i
$424$	7.00000			0.339950
$425$	6.34233	+	10.9852i	0.307648	+	0.532862i
$426$	6.68466	−	11.5782i	0.323873	−	0.560964i
$427$	−2.62311	+	4.54335i	−0.126941	+	0.219868i
$428$	−14.9309			−0.721711
$429$	−5.21922	+	2.11176i	−0.251986	+	0.101957i
$430$	20.4924			0.988232
$431$	2.68466	−	4.64996i	0.129315	−	0.223981i	−0.794096	−	0.607792i	$-0.792055\pi$
$431$	2.68466	−	4.64996i	0.129315	−	0.223981i	0.923412	+	0.383811i	$0.125389\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	16.8423	+	29.1718i	0.809391	+	1.40191i	0.913287	+	0.407318i	$0.133536\pi$
$433$	16.8423	+	29.1718i	0.809391	+	1.40191i	−0.103896	+	0.994588i	$0.533131\pi$
$434$		0			0
$435$	−2.71922	−	4.70983i	−0.130377	−	0.225819i
$436$	−2.12311	−	3.67733i	−0.101678	−	0.176112i
$437$	11.1231			0.532090
$438$	−3.28078	−	5.68247i	−0.156762	−	0.271519i
$439$	4.87689	−	8.44703i	0.232761	−	0.403155i	−0.725858	−	0.687844i	$-0.758557\pi$
$439$	4.87689	−	8.44703i	0.232761	−	0.403155i	0.958620	+	0.284690i	$0.0918905\pi$
$440$	2.00000	−	3.46410i	0.0953463	−	0.165145i
$441$	1.00000			0.0476190
$442$	4.06155	−	29.0053i	0.193188	−	1.37964i
$443$	10.0540			0.477679			0.238839	−	0.971059i	$-0.423233\pi$
$443$	10.0540			0.477679			0.238839	+	0.971059i	$0.423233\pi$
$444$	−3.28078	+	5.68247i	−0.155699	+	0.269678i
$445$	9.68466	−	16.7743i	0.459097	−	0.795179i
$446$	−13.1231	−	22.7299i	−0.621397	−	1.07629i
$447$	11.4384			0.541020
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	15.6847	+	27.1666i	0.740205	+	1.28207i	0.952402	+	0.304845i	$0.0986048\pi$
$449$	15.6847	+	27.1666i	0.740205	+	1.28207i	−0.212197	+	0.977227i	$0.568062\pi$
$450$	1.56155			0.0736123
$451$	−4.09612	−	7.09468i	−0.192879	−	0.334076i
$452$	1.28078	−	2.21837i	0.0602427	−	0.104343i
$453$	3.46543	−	6.00231i	0.162820	−	0.282013i
$454$	−19.1231			−0.897492
$455$	−8.56155	+	3.46410i	−0.401372	+	0.162400i
$456$	−1.56155			−0.0731264
$457$	−0.0345652	+	0.0598686i	−0.00161689	+	0.00280054i	−0.866833	−	0.498599i	$-0.833848\pi$
$457$	−0.0345652	+	0.0598686i	−0.00161689	+	0.00280054i	0.865216	+	0.501400i	$0.167181\pi$
$458$	10.0270	−	17.3673i	0.468530	−	0.811518i
$459$	−4.06155	−	7.03482i	−0.189577	−	0.328357i
$460$	−18.2462			−0.850734
$461$	15.5270	+	26.8935i	0.723164	+	1.25256i	0.959725	+	0.280940i	$0.0906462\pi$
$461$	15.5270	+	26.8935i	0.723164	+	1.25256i	−0.236561	+	0.971617i	$0.576020\pi$
$462$	0.780776	+	1.35234i	0.0363250	+	0.0629168i
$463$	24.6847			1.14719			0.573597	−	0.819138i	$-0.305548\pi$
$463$	24.6847			1.14719			0.573597	+	0.819138i	$0.305548\pi$
$464$	−1.06155	−	1.83866i	−0.0492814	−	0.0853578i
$465$		0			0
$466$	11.6847	−	20.2384i	0.541281	−	0.937527i
$467$	28.9848			1.34126			0.670629	−	0.741793i	$-0.266024\pi$
$467$	28.9848			1.34126			0.670629	+	0.741793i	$0.266024\pi$
$468$	−2.84233	−	2.21837i	−0.131387	−	0.102544i
$469$	0.876894			0.0404912
$470$	−16.2462	+	28.1393i	−0.749382	+	1.29797i
$471$	−6.84233	+	11.8513i	−0.315278	+	0.546077i
$472$	1.56155	+	2.70469i	0.0718763	+	0.124493i
$473$	−12.4924			−0.574402
$474$	−1.21922	−	2.11176i	−0.0560008	−	0.0969962i
$475$	−1.21922	−	2.11176i	−0.0559418	−	0.0968941i
$476$	−8.12311			−0.372322
$477$	−3.50000	−	6.06218i	−0.160254	−	0.277568i
$478$	2.68466	−	4.64996i	0.122793	−	0.212684i
$479$	−13.4654	+	23.3228i	−0.615251	+	1.06565i	0.375089	+	0.926989i	$0.377612\pi$
$479$	−13.4654	+	23.3228i	−0.615251	+	1.06565i	−0.990340	+	0.138658i	$0.955721\pi$
$480$	2.56155			0.116918
$481$	18.6501	+	14.5560i	0.850371	+	0.663694i
$482$	−20.8078			−0.947768
$483$	3.56155	−	6.16879i	0.162056	−	0.280690i
$484$	4.28078	−	7.41452i	0.194581	−	0.337024i
$485$	−11.6847	−	20.2384i	−0.530573	−	0.918979i
$486$	−1.00000			−0.0453609
$487$	−5.65767	−	9.79937i	−0.256374	−	0.444052i	0.708894	−	0.705315i	$-0.249194\pi$
$487$	−5.65767	−	9.79937i	−0.256374	−	0.444052i	−0.965268	+	0.261263i	$0.915861\pi$
$488$	−2.62311	−	4.54335i	−0.118742	−	0.205668i
$489$	8.49242			0.384041
$490$	1.28078	+	2.21837i	0.0578596	+	0.100216i
$491$	−8.24621	+	14.2829i	−0.372146	+	0.644576i	−0.989895	−	0.141799i	$-0.954711\pi$
$491$	−8.24621	+	14.2829i	−0.372146	+	0.644576i	0.617749	+	0.786375i	$0.288045\pi$
$492$	2.62311	−	4.54335i	0.118259	−	0.204830i
$493$	−17.2462			−0.776730
$494$	−0.780776	+	5.57586i	−0.0351288	+	0.250870i
$495$	−4.00000			−0.179787
$496$		0			0
$497$	−6.68466	+	11.5782i	−0.299848	+	0.519352i
$498$	1.56155	+	2.70469i	0.0699749	+	0.121200i
$499$	13.7538			0.615704			0.307852	−	0.951434i	$-0.400390\pi$
$499$	13.7538			0.615704			0.307852	+	0.951434i	$0.400390\pi$
$500$	−4.40388	−	7.62775i	−0.196948	−	0.341123i
$501$	−10.2462	−	17.7470i	−0.457767	−	0.792876i
$502$	27.6155			1.23254
$503$	−2.24621	−	3.89055i	−0.100154	−	0.173471i	0.811594	−	0.584222i	$-0.198600\pi$
$503$	−2.24621	−	3.89055i	−0.100154	−	0.173471i	−0.911748	+	0.410750i	$0.865267\pi$
$504$	−0.500000	+	0.866025i	−0.0222718	+	0.0385758i
$505$	18.9654	−	32.8491i	0.843951	−	1.46177i
$506$	11.1231			0.494482
$507$	−9.34233	+	9.03996i	−0.414907	+	0.401479i
$508$	−20.4924			−0.909204
$509$	10.5961	−	18.3530i	0.469665	−	0.813483i	−0.529734	−	0.848164i	$-0.677708\pi$
$509$	10.5961	−	18.3530i	0.469665	−	0.813483i	0.999398	+	0.0346809i	$0.0110415\pi$
$510$	10.4039	−	18.0201i	0.460692	−	0.797941i
$511$	3.28078	+	5.68247i	0.145133	+	0.251378i
$512$	1.00000			0.0441942
$513$	0.780776	+	1.35234i	0.0344721	+	0.0597075i
$514$	−0.184658	−	0.319838i	−0.00814493	−	0.0141074i
$515$	26.2462			1.15655
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	9.90388	−	17.1540i	0.435572	−	0.754433i
$518$	3.28078	−	5.68247i	0.144149	−	0.249673i
$519$	18.0000			0.790112
$520$	1.28078	−	9.14657i	0.0561658	−	0.401104i
$521$	34.1231			1.49496			0.747480	−	0.664284i	$-0.231263\pi$
$521$	34.1231			1.49496			0.747480	+	0.664284i	$0.231263\pi$
$522$	−1.06155	+	1.83866i	−0.0464629	+	0.0804761i
$523$	−1.90388	+	3.29762i	−0.0832509	+	0.144195i	−0.904645	−	0.426167i	$-0.859864\pi$
$523$	−1.90388	+	3.29762i	−0.0832509	+	0.144195i	0.821394	+	0.570362i	$0.193197\pi$
$524$	1.12311	+	1.94528i	0.0490631	+	0.0849798i
$525$	−1.56155			−0.0681518
$526$	1.56155	+	2.70469i	0.0680869	+	0.117930i
$527$		0			0
$528$	−1.56155			−0.0679579
$529$	−13.8693	−	24.0224i	−0.603014	−	1.04445i
$530$	8.96543	−	15.5286i	0.389434	−	0.674519i
$531$	1.56155	−	2.70469i	0.0677656	−	0.117373i
$532$	1.56155			0.0677019
$533$	−14.9115	−	11.6380i	−0.645887	−	0.504099i
$534$	−7.56155			−0.327220
$535$	−19.1231	+	33.1222i	−0.826764	+	1.43200i
$536$	−0.438447	+	0.759413i	−0.0189380	+	0.0328016i
$537$	−9.12311	−	15.8017i	−0.393691	−	0.681893i
$538$	18.8769			0.813841
$539$	−0.780776	−	1.35234i	−0.0336304	−	0.0582496i
$540$	−1.28078	−	2.21837i	−0.0551158	−	0.0954634i
$541$	−26.1771			−1.12544			−0.562720	−	0.826647i	$-0.690245\pi$
$541$	−26.1771			−1.12544			−0.562720	+	0.826647i	$0.690245\pi$
$542$	−13.3693	−	23.1563i	−0.574261	−	0.994650i
$543$	−1.62311	+	2.81130i	−0.0696541	+	0.120644i
$544$	4.06155	−	7.03482i	0.174138	−	0.301615i
$545$	−10.8769			−0.465915
$546$	2.84233	+	2.21837i	0.121640	+	0.0949375i
$547$	7.61553			0.325616			0.162808	−	0.986658i	$-0.447945\pi$
$547$	7.61553			0.325616			0.162808	+	0.986658i	$0.447945\pi$
$548$	−8.28078	+	14.3427i	−0.353737	+	0.612691i
$549$	−2.62311	+	4.54335i	−0.111951	+	0.193906i
$550$	−1.21922	−	2.11176i	−0.0519879	−	0.0900456i
$551$	3.31534			0.141238
$552$	3.56155	+	6.16879i	0.151590	+	0.262561i
$553$	1.21922	+	2.11176i	0.0518467	+	0.0898011i
$554$	−15.4384			−0.655917
$555$	8.40388	+	14.5560i	0.356725	+	0.617866i
$556$	4.78078	−	8.28055i	0.202750	−	0.351173i
$557$	−1.93845	+	3.35749i	−0.0821346	+	0.142261i	−0.904167	−	0.427180i	$-0.859507\pi$
$557$	−1.93845	+	3.35749i	−0.0821346	+	0.142261i	0.822032	+	0.569441i	$0.192840\pi$
$558$		0			0
$559$	−26.7386	+	10.8188i	−1.13092	+	0.457585i
$560$	−2.56155			−0.108245
$561$	−6.34233	+	10.9852i	−0.267773	+	0.463797i
$562$	7.96543	−	13.7965i	0.336002	−	0.581972i
$563$	11.1231	+	19.2658i	0.468783	+	0.811956i	0.999363	−	0.0356787i	$-0.0113593\pi$
$563$	11.1231	+	19.2658i	0.468783	+	0.811956i	−0.530580	+	0.847635i	$0.678026\pi$
$564$	12.6847			0.534120
$565$	−3.28078	−	5.68247i	−0.138023	−	0.239063i
$566$	10.0000	+	17.3205i	0.420331	+	0.728035i
$567$	1.00000			0.0419961
$568$	−6.68466	−	11.5782i	−0.280482	−	0.485809i
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	−0.537874	−	0.843025i	$-0.680772\pi$
$569$	11.0000	−	19.0526i	0.461144	−	0.798725i	0.999018	+	0.0443003i	$0.0141058\pi$
$570$	−2.00000	+	3.46410i	−0.0837708	+	0.145095i
$571$	−12.8769			−0.538881			−0.269441	−	0.963017i	$-0.586839\pi$
$571$	−12.8769			−0.538881			−0.269441	+	0.963017i	$0.586839\pi$
$572$	−0.780776	+	5.57586i	−0.0326459	+	0.233138i
$573$	−3.12311			−0.130470
$574$	−2.62311	+	4.54335i	−0.109486	+	0.189636i
$575$	−5.56155	+	9.63289i	−0.231933	+	0.401719i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−31.4384			−1.30880			−0.654400	−	0.756149i	$-0.727079\pi$
$577$	−31.4384			−1.30880			−0.654400	+	0.756149i	$0.727079\pi$
$578$	−24.4924	−	42.4221i	−1.01875	−	1.76453i
$579$	−4.06155	−	7.03482i	−0.168792	−	0.292357i
$580$	−5.43845			−0.225819
$581$	−1.56155	−	2.70469i	−0.0647841	−	0.112209i
$582$	−4.56155	+	7.90084i	−0.189082	+	0.327500i
$583$	−5.46543	+	9.46641i	−0.226355	+	0.392059i
$584$	−6.56155			−0.271519
$585$	−8.56155	+	3.46410i	−0.353977	+	0.143223i
$586$	21.9309			0.905956
$587$	7.12311	−	12.3376i	0.294002	−	0.509226i	−0.680750	−	0.732516i	$-0.738346\pi$
$587$	7.12311	−	12.3376i	0.294002	−	0.509226i	0.974752	+	0.223289i	$0.0716794\pi$
$588$	0.500000	−	0.866025i	0.0206197	−	0.0357143i
$589$		0			0
$590$	8.00000			0.329355
$591$	4.21922	+	7.30791i	0.173556	+	0.300607i
$592$	3.28078	+	5.68247i	0.134839	+	0.233548i
$593$	31.9848			1.31346			0.656730	−	0.754126i	$-0.271939\pi$
$593$	31.9848			1.31346			0.656730	+	0.754126i	$0.271939\pi$
$594$	0.780776	+	1.35234i	0.0320356	+	0.0554874i
$595$	−10.4039	+	18.0201i	−0.426518	+	0.738750i
$596$	5.71922	−	9.90599i	0.234269	−	0.405765i
$597$	16.0000			0.654836
$598$	23.8078	−	9.63289i	0.973572	−	0.393918i
$599$	−33.8617			−1.38355			−0.691777	−	0.722112i	$-0.743172\pi$
$599$	−33.8617			−1.38355			−0.691777	+	0.722112i	$0.743172\pi$
$600$	0.780776	−	1.35234i	0.0318751	−	0.0552092i
$601$	12.6501	−	21.9106i	0.516008	−	0.893752i	−0.483819	−	0.875168i	$-0.660751\pi$
$601$	12.6501	−	21.9106i	0.516008	−	0.893752i	0.999827	−	0.0185842i	$-0.00591589\pi$
$602$	4.00000	+	6.92820i	0.163028	+	0.282372i
$603$	0.876894			0.0357099
$604$	−3.46543	−	6.00231i	−0.141007	−	0.244230i
$605$	−10.9654	−	18.9927i	−0.445808	−	0.772163i
$606$	−14.8078			−0.601524
$607$	−8.49242	−	14.7093i	−0.344697	−	0.597032i	0.640602	−	0.767873i	$-0.278685\pi$
$607$	−8.49242	−	14.7093i	−0.344697	−	0.597032i	−0.985299	+	0.170841i	$0.945352\pi$
$608$	−0.780776	+	1.35234i	−0.0316647	+	0.0548448i
$609$	1.06155	−	1.83866i	0.0430163	−	0.0745064i
$610$	−13.4384			−0.544107
$611$	6.34233	−	45.2933i	0.256583	−	1.83237i
$612$	−8.12311			−0.328357
$613$	−8.71922	+	15.1021i	−0.352166	+	0.609970i	−0.986629	−	0.162984i	$-0.947888\pi$
$613$	−8.71922	+	15.1021i	−0.352166	+	0.609970i	0.634463	+	0.772954i	$0.281221\pi$
$614$	−9.46543	+	16.3946i	−0.381994	+	0.661633i
$615$	−6.71922	−	11.6380i	−0.270945	−	0.469291i
$616$	1.56155			0.0629168
$617$	11.0885	+	19.2059i	0.446408	+	0.773201i	0.998149	−	0.0608143i	$-0.0193697\pi$
$617$	11.0885	+	19.2059i	0.446408	+	0.773201i	−0.551741	+	0.834015i	$0.686036\pi$
$618$	−5.12311	−	8.87348i	−0.206082	−	0.356944i
$619$	30.9309			1.24322			0.621608	−	0.783328i	$-0.286480\pi$
$619$	30.9309			1.24322			0.621608	+	0.783328i	$0.286480\pi$
$620$		0			0
$621$	3.56155	−	6.16879i	0.142920	−	0.247545i
$622$	3.46543	−	6.00231i	0.138951	−	0.240671i
$623$	7.56155			0.302947
$624$	−3.34233	+	1.35234i	−0.133800	+	0.0541371i
$625$	−30.3693			−1.21477
$626$	3.00000	−	5.19615i	0.119904	−	0.207680i
$627$	1.21922	−	2.11176i	0.0486911	−	0.0843355i
$628$	6.84233	+	11.8513i	0.273039	+	0.472917i
$629$	53.3002			2.12522
$630$	1.28078	+	2.21837i	0.0510274	+	0.0883820i
$631$	19.4654	+	33.7151i	0.774907	+	1.34218i	0.934847	+	0.355051i	$0.115537\pi$
$631$	19.4654	+	33.7151i	0.774907	+	1.34218i	−0.159940	+	0.987127i	$0.551130\pi$
$632$	−2.43845			−0.0969962
$633$	−1.56155	−	2.70469i	−0.0620662	−	0.107502i
$634$	−8.28078	+	14.3427i	−0.328872	+	0.569622i
$635$	−26.2462	+	45.4598i	−1.04155	+	1.80402i
$636$	−7.00000			−0.277568
$637$	−2.84233	−	2.21837i	−0.112617	−	0.0878950i
$638$	3.31534			0.131256
$639$	−6.68466	+	11.5782i	−0.264441	+	0.458025i
$640$	1.28078	−	2.21837i	0.0506271	−	0.0876888i
$641$	−6.28078	−	10.8786i	−0.248076	−	0.429680i	0.714916	−	0.699210i	$-0.246465\pi$
$641$	−6.28078	−	10.8786i	−0.248076	−	0.429680i	−0.962992	+	0.269530i	$0.913132\pi$
$642$	14.9309			0.589274
$643$	−17.6577	−	30.5840i	−0.696351	−	1.20611i	−0.969723	−	0.244206i	$-0.921473\pi$
$643$	−17.6577	−	30.5840i	−0.696351	−	1.20611i	0.273373	−	0.961908i	$-0.411861\pi$
$644$	−3.56155	−	6.16879i	−0.140345	−	0.243084i
$645$	−20.4924			−0.806888
$646$	6.34233	+	10.9852i	0.249536	+	0.432208i
$647$	23.0270	−	39.8839i	0.905284	−	1.56800i	0.0847492	−	0.996402i	$-0.472991\pi$
$647$	23.0270	−	39.8839i	0.905284	−	1.56800i	0.820535	−	0.571596i	$-0.193676\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−4.87689			−0.191435
$650$	−4.43845	−	3.46410i	−0.174090	−	0.135873i
$651$		0			0
$652$	4.24621	−	7.35465i	0.166294	−	0.288030i
$653$	−8.21922	+	14.2361i	−0.321643	+	0.557102i	−0.980827	−	0.194879i	$-0.937568\pi$
$653$	−8.21922	+	14.2361i	−0.321643	+	0.557102i	0.659184	+	0.751982i	$0.270902\pi$
$654$	2.12311	+	3.67733i	0.0830200	+	0.143795i
$655$	5.75379			0.224819
$656$	−2.62311	−	4.54335i	−0.102415	−	0.177388i
$657$	3.28078	+	5.68247i	0.127995	+	0.221694i
$658$	−12.6847			−0.494499
$659$	−15.4654	−	26.7869i	−0.602448	−	1.04347i	−0.992449	−	0.122656i	$-0.960859\pi$
$659$	−15.4654	−	26.7869i	−0.602448	−	1.04347i	0.390001	−	0.920814i	$-0.372475\pi$
$660$	−2.00000	+	3.46410i	−0.0778499	+	0.134840i
$661$	−8.52699	+	14.7692i	−0.331661	+	0.574454i	−0.982838	−	0.184472i	$-0.940942\pi$
$661$	−8.52699	+	14.7692i	−0.331661	+	0.574454i	0.651176	+	0.758926i	$0.274276\pi$
$662$	−5.36932			−0.208684
$663$	−4.06155	+	29.0053i	−0.157738	+	1.12647i
$664$	3.12311			0.121200
$665$	2.00000	−	3.46410i	0.0775567	−	0.134332i
$666$	3.28078	−	5.68247i	0.127128	−	0.220191i
$667$	−7.56155	−	13.0970i	−0.292784	−	0.507118i
$668$	−20.4924			−0.792876
$669$	13.1231	+	22.7299i	0.507369	+	0.878788i
$670$	1.12311	+	1.94528i	0.0433894	+	0.0751526i
$671$	8.19224			0.316258
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	9.62311	−	16.6677i	0.370943	−	0.642493i	−0.618767	−	0.785574i	$-0.712368\pi$
$673$	9.62311	−	16.6677i	0.370943	−	0.642493i	0.989711	+	0.143081i	$0.0457010\pi$
$674$	−9.74621	+	16.8809i	−0.375410	+	0.650229i
$675$	−1.56155			−0.0601042
$676$	3.15767	+	12.6107i	0.121449	+	0.485026i
$677$	24.7386			0.950783			0.475391	−	0.879774i	$-0.342306\pi$
$677$	24.7386			0.950783			0.475391	+	0.879774i	$0.342306\pi$
$678$	−1.28078	+	2.21837i	−0.0491879	+	0.0851960i
$679$	4.56155	−	7.90084i	0.175056	−	0.303206i
$680$	−10.4039	−	18.0201i	−0.398971	−	0.691037i
$681$	19.1231			0.732799
$682$		0			0
$683$	−3.75379	−	6.50175i	−0.143635	−	0.248783i	0.785228	−	0.619207i	$-0.212546\pi$
$683$	−3.75379	−	6.50175i	−0.143635	−	0.248783i	−0.928863	+	0.370424i	$0.879212\pi$
$684$	1.56155			0.0597075
$685$	21.2116	+	36.7396i	0.810455	+	1.40375i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−10.0270	+	17.3673i	−0.382553	+	0.662602i
$688$	−8.00000			−0.304997
$689$	−3.50000	+	24.9950i	−0.133339	+	0.952234i
$690$	18.2462			0.694621
$691$	−16.4924	+	28.5657i	−0.627401	+	1.08669i	0.360670	+	0.932694i	$0.382548\pi$
$691$	−16.4924	+	28.5657i	−0.627401	+	1.08669i	−0.988071	+	0.153997i	$0.950785\pi$
$692$	9.00000	−	15.5885i	0.342129	−	0.592584i
$693$	−0.780776	−	1.35234i	−0.0296592	−	0.0513713i
$694$	−22.0540			−0.837157
$695$	−12.2462	−	21.2111i	−0.464525	−	0.804581i
$696$	1.06155	+	1.83866i	0.0402381	+	0.0696944i
$697$	−42.6155			−1.61418
$698$	9.00000	+	15.5885i	0.340655	+	0.590032i
$699$	−11.6847	+	20.2384i	−0.441954	+	0.765487i
$700$	−0.780776	+	1.35234i	−0.0295106	+	0.0511138i
$701$	14.3002			0.540111			0.270055	−	0.962845i	$-0.412958\pi$
$701$	14.3002			0.540111			0.270055	+	0.962845i	$0.412958\pi$
$702$	2.84233	+	2.21837i	0.107277	+	0.0837270i
$703$	−10.2462			−0.386443
$704$	−0.780776	+	1.35234i	−0.0294266	+	0.0509684i
$705$	16.2462	−	28.1393i	0.611868	−	1.05979i
$706$	6.59612	+	11.4248i	0.248248	+	0.429978i
$707$	14.8078			0.556903
$708$	−1.56155	−	2.70469i	−0.0586867	−	0.101648i
$709$	−7.65009	−	13.2504i	−0.287305	−	0.497627i	0.685860	−	0.727733i	$-0.259426\pi$
$709$	−7.65009	−	13.2504i	−0.287305	−	0.497627i	−0.973166	+	0.230106i	$0.926093\pi$
$710$	−34.2462			−1.28524
$711$	1.21922	+	2.11176i	0.0457245	+	0.0791971i
$712$	−3.78078	+	6.54850i	−0.141691	+	0.245415i
$713$		0			0
$714$	8.12311			0.304000
$715$	11.3693	+	8.87348i	0.425188	+	0.331849i
$716$	−18.2462			−0.681893
$717$	−2.68466	+	4.64996i	−0.100260	+	0.173656i
$718$	9.12311	−	15.8017i	0.340471	−	0.589714i
$719$	9.90388	+	17.1540i	0.369352	+	0.639737i	0.989464	−	0.144776i	$-0.0462462\pi$
$719$	9.90388	+	17.1540i	0.369352	+	0.639737i	−0.620112	+	0.784513i	$0.712913\pi$
$720$	−2.56155			−0.0954634
$721$	5.12311	+	8.87348i	0.190794	+	0.330466i
$722$	8.28078	+	14.3427i	0.308179	+	0.533781i
$723$	20.8078			0.773849
$724$	1.62311	+	2.81130i	0.0603222	+	0.104481i
$725$	−1.65767	+	2.87117i	−0.0615643	+	0.106633i
$726$	−4.28078	+	7.41452i	−0.158875	+	0.275179i
$727$	40.0000			1.48352			0.741759	−	0.670667i	$-0.233992\pi$
$727$	40.0000			1.48352			0.741759	+	0.670667i	$0.233992\pi$
$728$	3.34233	−	1.35234i	0.123875	−	0.0501212i
$729$	1.00000			0.0370370
$730$	−8.40388	+	14.5560i	−0.311042	+	0.538740i
$731$	−32.4924	+	56.2785i	−1.20178	+	2.08154i
$732$	2.62311	+	4.54335i	0.0969528	+	0.167927i
$733$	28.8617			1.06603			0.533016	−	0.846105i	$-0.321058\pi$
$733$	28.8617			1.06603			0.533016	+	0.846105i	$0.321058\pi$
$734$	13.8078	+	23.9157i	0.509654	+	0.882746i
$735$	−1.28078	−	2.21837i	−0.0472421	−	0.0818258i
$736$	7.12311			0.262561
$737$	−0.684658	−	1.18586i	−0.0252197	−	0.0436818i
$738$	−2.62311	+	4.54335i	−0.0965579	+	0.167243i
$739$	4.68466	−	8.11407i	0.172328	−	0.298481i	−0.766905	−	0.641760i	$-0.778204\pi$
$739$	4.68466	−	8.11407i	0.172328	−	0.298481i	0.939233	+	0.343279i	$0.111538\pi$
$740$	16.8078			0.617866
$741$	0.780776	−	5.57586i	0.0286825	−	0.204834i
$742$	7.00000			0.256978
$743$	−14.2462	+	24.6752i	−0.522643	+	0.905244i	0.477010	+	0.878898i	$0.341721\pi$
$743$	−14.2462	+	24.6752i	−0.522643	+	0.905244i	−0.999653	+	0.0263461i	$0.991613\pi$
$744$		0			0
$745$	−14.6501	−	25.3747i	−0.536738	−	0.929657i
$746$	−31.9309			−1.16907
$747$	−1.56155	−	2.70469i	−0.0571342	−	0.0989594i
$748$	6.34233	+	10.9852i	0.231899	+	0.401660i
$749$	−14.9309			−0.545562
$750$	4.40388	+	7.62775i	0.160807	+	0.278526i
$751$	10.0961	−	17.4870i	0.368413	−	0.638109i	−0.620905	−	0.783886i	$-0.713235\pi$
$751$	10.0961	−	17.4870i	0.368413	−	0.638109i	0.989318	+	0.145777i	$0.0465681\pi$
$752$	6.34233	−	10.9852i	0.231281	−	0.400590i
$753$	−27.6155			−1.00637
$754$	7.09612	−	2.87117i	0.258425	−	0.104562i
$755$	−17.7538			−0.646127
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	−1.63068	+	2.82443i	−0.0592682	+	0.102656i	−0.894137	−	0.447793i	$-0.852210\pi$
$757$	−1.63068	+	2.82443i	−0.0592682	+	0.102656i	0.834869	+	0.550449i	$0.185543\pi$
$758$	1.80776	+	3.13114i	0.0656609	+	0.113728i
$759$	−11.1231			−0.403743
$760$	2.00000	+	3.46410i	0.0725476	+	0.125656i
$761$	7.49242	+	12.9773i	0.271600	+	0.470425i	0.969272	−	0.245993i	$-0.0791139\pi$
$761$	7.49242	+	12.9773i	0.271600	+	0.470425i	−0.697672	+	0.716418i	$0.745781\pi$
$762$	20.4924			0.742362
$763$	−2.12311	−	3.67733i	−0.0768616	−	0.133128i
$764$	−1.56155	+	2.70469i	−0.0564950	+	0.0978522i
$765$	−10.4039	+	18.0201i	−0.376153	+	0.651516i
$766$	7.80776			0.282106
$767$	−10.4384	+	4.22351i	−0.376910	+	0.152502i
$768$	−1.00000			−0.0360844
$769$	−6.56155	+	11.3649i	−0.236616	+	0.409830i	−0.959741	−	0.280887i	$-0.909372\pi$
$769$	−6.56155	+	11.3649i	−0.236616	+	0.409830i	0.723125	+	0.690717i	$0.242705\pi$
$770$	2.00000	−	3.46410i	0.0720750	−	0.124838i
$771$	0.184658	+	0.319838i	0.00665031	+	0.0115187i
$772$	−8.12311			−0.292357
$773$	14.3693	+	24.8884i	0.516828	+	0.895173i	0.999809	+	0.0195420i	$0.00622081\pi$
$773$	14.3693	+	24.8884i	0.516828	+	0.895173i	−0.482981	+	0.875631i	$0.660446\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$		0			0
$776$	4.56155	+	7.90084i	0.163750	+	0.283624i
$777$	−3.28078	+	5.68247i	−0.117697	+	0.203858i
$778$	8.84233	−	15.3154i	0.317013	−	0.549082i
$779$	8.19224			0.293517
$780$	−1.28078	+	9.14657i	−0.0458592	+	0.327500i
$781$	20.8769			0.747034
$782$	28.9309	−	50.1097i	1.03457	−	1.79192i
$783$	1.06155	−	1.83866i	0.0379368	−	0.0657085i
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	35.0540			1.25113
$786$	−1.12311	−	1.94528i	−0.0400599	−	0.0693857i
$787$	−22.5885	−	39.1245i	−0.805195	−	1.39464i	−0.916160	−	0.400814i	$-0.868728\pi$
$787$	−22.5885	−	39.1245i	−0.805195	−	1.39464i	0.110965	−	0.993824i	$-0.464606\pi$
$788$	8.43845			0.300607
$789$	−1.56155	−	2.70469i	−0.0555928	−	0.0962895i
$790$	−3.12311	+	5.40938i	−0.111115	+	0.192457i
$791$	1.28078	−	2.21837i	0.0455392	−	0.0788762i
$792$	1.56155			0.0554874
$793$	17.5346	−	7.09468i	0.622671	−	0.251940i
$794$	−0.930870			−0.0330353
$795$	−8.96543	+	15.5286i	−0.317971	+	0.550742i
$796$	8.00000	−	13.8564i	0.283552	−	0.491127i
$797$	−8.75379	−	15.1620i	−0.310075	−	0.537066i	0.668303	−	0.743889i	$-0.267021\pi$
$797$	−8.75379	−	15.1620i	−0.310075	−	0.537066i	−0.978378	+	0.206823i	$0.933688\pi$
$798$	−1.56155			−0.0552784
$799$	−51.5194	−	89.2342i	−1.82263	−	3.15688i
$800$	−0.780776	−	1.35234i	−0.0276046	−	0.0478126i
$801$	7.56155			0.267174
$802$	−9.40388	−	16.2880i	−0.332063	−	0.575149i
$803$	5.12311	−	8.87348i	0.180790	−	0.313138i
$804$	0.438447	−	0.759413i	0.0154628	−	0.0267824i
$805$	−18.2462			−0.643094
$806$		0			0
$807$	−18.8769			−0.664498
$808$	−7.40388	+	12.8239i	−0.260468	+	0.451143i
$809$	9.96543	−	17.2606i	0.350366	−	0.606852i	−0.635948	−	0.771732i	$-0.719391\pi$
$809$	9.96543	−	17.2606i	0.350366	−	0.606852i	0.986314	+	0.164881i	$0.0527239\pi$
$810$	1.28078	+	2.21837i	0.0450019	+	0.0779456i
$811$	24.0000			0.842754			0.421377	−	0.906886i	$-0.361547\pi$
$811$	24.0000			0.842754			0.421377	+	0.906886i	$0.361547\pi$
$812$	−1.06155	−	1.83866i	−0.0372532	−	0.0645244i
$813$	13.3693	+	23.1563i	0.468882	+	0.812128i
$814$	−10.2462			−0.359130
$815$	−10.8769	−	18.8393i	−0.381001	−	0.659913i
$816$	−4.06155	+	7.03482i	−0.142183	+	0.246268i
$817$	6.24621	−	10.8188i	0.218527	−	0.378500i
$818$	−7.43845			−0.260079
$819$	−2.84233	−	2.21837i	−0.0993190	−	0.0775161i
$820$	−13.4384			−0.469291
$821$	13.1501	−	22.7766i	0.458941	−	0.794910i	−0.539964	−	0.841688i	$-0.681562\pi$
$821$	13.1501	−	22.7766i	0.458941	−	0.794910i	0.998905	+	0.0467783i	$0.0148954\pi$
$822$	8.28078	−	14.3427i	0.288825	−	0.500260i
$823$	10.8769	+	18.8393i	0.379145	+	0.656698i	0.990938	−	0.134320i	$-0.0428849\pi$
$823$	10.8769	+	18.8393i	0.379145	+	0.656698i	−0.611793	+	0.791018i	$0.709552\pi$
$824$	−10.2462			−0.356944
$825$	1.21922	+	2.11176i	0.0424479	+	0.0735219i
$826$	1.56155	+	2.70469i	0.0543334	+	0.0941082i
$827$	17.7538			0.617360			0.308680	−	0.951166i	$-0.400113\pi$
$827$	17.7538			0.617360			0.308680	+	0.951166i	$0.400113\pi$
$828$	−3.56155	−	6.16879i	−0.123773	−	0.214380i
$829$	−12.1847	+	21.1044i	−0.423191	+	0.732988i	−0.996250	−	0.0865264i	$-0.972423\pi$
$829$	−12.1847	+	21.1044i	−0.423191	+	0.732988i	0.573059	+	0.819514i	$0.305757\pi$
$830$	4.00000	−	6.92820i	0.138842	−	0.240481i
$831$	15.4384			0.535554
$832$	−0.500000	+	3.57071i	−0.0173344	+	0.123792i
$833$	−8.12311			−0.281449
$834$	−4.78078	+	8.28055i	−0.165545	+	0.286732i
$835$	−26.2462	+	45.4598i	−0.908288	+	1.57320i
$836$	−1.21922	−	2.11176i	−0.0421677	−	0.0730367i
$837$		0			0
$838$	0.684658	+	1.18586i	0.0236511	+	0.0409650i
$839$	−0.876894	−	1.51883i	−0.0302738	−	0.0524357i	0.850492	−	0.525989i	$-0.176305\pi$
$839$	−0.876894	−	1.51883i	−0.0302738	−	0.0524357i	−0.880765	+	0.473553i	$0.842971\pi$
$840$	2.56155			0.0883820
$841$	12.2462	+	21.2111i	0.422283	+	0.731416i
$842$	−15.6501	+	27.1068i	−0.539338	+	0.934161i
$843$	−7.96543	+	13.7965i	−0.274344	+	0.475178i
$844$	−3.12311			−0.107502
$845$	32.0194	+	9.14657i	1.10150	+	0.314652i
$846$	−12.6847			−0.436108
$847$	4.28078	−	7.41452i	0.147089	−	0.254766i
$848$	−3.50000	+	6.06218i	−0.120190	+	0.208176i
$849$	−10.0000	−	17.3205i	−0.343199	−	0.594438i
$850$	−12.6847			−0.435080
$851$	23.3693	+	40.4768i	0.801090	+	1.38753i
$852$	6.68466	+	11.5782i	0.229013	+	0.396662i
$853$	5.63068			0.192791			0.0963955	−	0.995343i	$-0.469269\pi$
$853$	5.63068			0.192791			0.0963955	+	0.995343i	$0.469269\pi$
$854$	−2.62311	−	4.54335i	−0.0897608	−	0.155470i
$855$	2.00000	−	3.46410i	0.0683986	−	0.118470i
$856$	7.46543	−	12.9305i	0.255163	−	0.441956i
$857$	20.5616			0.702369			0.351185	−	0.936306i	$-0.385779\pi$
$857$	20.5616			0.702369			0.351185	+	0.936306i	$0.385779\pi$
$858$	0.780776	−	5.57586i	0.0266553	−	0.190357i
$859$	−10.9309			−0.372956			−0.186478	−	0.982459i	$-0.559707\pi$
$859$	−10.9309			−0.372956			−0.186478	+	0.982459i	$0.559707\pi$
$860$	−10.2462	+	17.7470i	−0.349393	+	0.605166i
$861$	2.62311	−	4.54335i	0.0893952	−	0.154837i
$862$	2.68466	+	4.64996i	0.0914398	+	0.158378i
$863$	32.8769			1.11914			0.559571	−	0.828782i	$-0.310966\pi$
$863$	32.8769			1.11914			0.559571	+	0.828782i	$0.310966\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	−23.0540	−	39.9307i	−0.783859	−	1.35768i
$866$	−33.6847			−1.14465
$867$	24.4924	+	42.4221i	0.831806	+	1.44073i
$868$		0			0
$869$	1.90388	−	3.29762i	0.0645848	−	0.111864i
$870$	5.43845			0.184381
$871$	−2.49242	−	1.94528i	−0.0844525	−	0.0659132i
$872$	4.24621			0.143795
$873$	4.56155	−	7.90084i	0.154385	−	0.267403i
$874$	−5.56155	+	9.63289i	−0.188122	+	0.325837i
$875$	−4.40388	−	7.62775i	−0.148878	−	0.257865i
$876$	6.56155			0.221694
$877$	−20.7732	−	35.9802i	−0.701461	−	1.21497i	−0.967954	−	0.251129i	$-0.919198\pi$
$877$	−20.7732	−	35.9802i	−0.701461	−	1.21497i	0.266492	−	0.963837i	$-0.414135\pi$
$878$	4.87689	+	8.44703i	0.164587	+	0.285073i
$879$	−21.9309			−0.739710
$880$	2.00000	+	3.46410i	0.0674200	+	0.116775i
$881$	−28.5270	+	49.4102i	−0.961099	+	1.66467i	−0.241348	+	0.970439i	$0.577590\pi$
$881$	−28.5270	+	49.4102i	−0.961099	+	1.66467i	−0.719750	+	0.694233i	$0.755744\pi$
$882$	−0.500000	+	0.866025i	−0.0168359	+	0.0291606i
$883$	−20.0000			−0.673054			−0.336527	−	0.941674i	$-0.609252\pi$
$883$	−20.0000			−0.673054			−0.336527	+	0.941674i	$0.609252\pi$
$884$	23.0885	+	18.0201i	0.776552	+	0.606080i
$885$	−8.00000			−0.268917
$886$	−5.02699	+	8.70700i	−0.168885	+	0.292517i
$887$	23.0270	−	39.8839i	0.773171	−	1.33917i	−0.162646	−	0.986684i	$-0.552003\pi$
$887$	23.0270	−	39.8839i	0.773171	−	1.33917i	0.935817	−	0.352486i	$-0.114664\pi$
$888$	−3.28078	−	5.68247i	−0.110096	−	0.190691i
$889$	−20.4924			−0.687294
$890$	9.68466	+	16.7743i	0.324630	+	0.562276i
$891$	−0.780776	−	1.35234i	−0.0261570	−	0.0453052i
$892$	26.2462			0.878788
$893$	9.90388	+	17.1540i	0.331421	+	0.574038i
$894$	−5.71922	+	9.90599i	−0.191279	+	0.331306i
$895$	−23.3693	+	40.4768i	−0.781150	+	1.35299i
$896$	1.00000			0.0334077
$897$	−23.8078	+	9.63289i	−0.794918	+	0.321633i
$898$	−31.3693			−1.04681
$899$		0			0
$900$	−0.780776	+	1.35234i	−0.0260259	+	0.0450781i
$901$	28.4309	+	49.2437i	0.947170	+	1.64055i
$902$	8.19224			0.272772
$903$	−4.00000	−	6.92820i	−0.133112	−	0.230556i
$904$	1.28078	+	2.21837i	0.0425980	+	0.0737819i
$905$	8.31534			0.276411
$906$	3.46543	+	6.00231i	0.115131	+	0.199413i
$907$	−3.56155	+	6.16879i	−0.118259	+	0.204831i	−0.919078	−	0.394076i	$-0.871065\pi$
$907$	−3.56155	+	6.16879i	−0.118259	+	0.204831i	0.800819	+	0.598907i	$0.204398\pi$
$908$	9.56155	−	16.5611i	0.317311	−	0.549599i
$909$	14.8078			0.491143
$910$	1.28078	−	9.14657i	0.0424573	−	0.303206i
$911$	−27.6155			−0.914943			−0.457472	−	0.889224i	$-0.651245\pi$
$911$	−27.6155			−0.914943			−0.457472	+	0.889224i	$0.651245\pi$
$912$	0.780776	−	1.35234i	0.0258541	−	0.0447806i
$913$	−2.43845	+	4.22351i	−0.0807008	+	0.139778i
$914$	−0.0345652	−	0.0598686i	−0.00114331	−	0.00198028i
$915$	13.4384			0.444261
$916$	10.0270	+	17.3673i	0.331301	+	0.573830i
$917$	1.12311	+	1.94528i	0.0370882	+	0.0642387i
$918$	8.12311			0.268102
$919$	8.53457	+	14.7823i	0.281529	+	0.487623i	0.971762	−	0.235965i	$-0.0758250\pi$
$919$	8.53457	+	14.7823i	0.281529	+	0.487623i	−0.690232	+	0.723588i	$0.742492\pi$
$920$	9.12311	−	15.8017i	0.300780	−	0.520966i
$921$	9.46543	−	16.3946i	0.311897	−	0.540221i
$922$	−31.0540			−1.02271
$923$	44.6847	−	18.0799i	1.47081	−	0.595108i
$924$	−1.56155			−0.0513713
$925$	5.12311	−	8.87348i	0.168447	−	0.291758i
$926$	−12.3423	+	21.3775i	−0.405594	+	0.702510i
$927$	5.12311	+	8.87348i	0.168265	+	0.291443i
$928$	2.12311			0.0696944
$929$	9.62311	+	16.6677i	0.315724	+	0.546850i	0.979591	−	0.201001i	$-0.0644193\pi$
$929$	9.62311	+	16.6677i	0.315724	+	0.546850i	−0.663867	+	0.747850i	$0.731086\pi$
$930$		0			0
$931$	1.56155			0.0511778
$932$	11.6847	+	20.2384i	0.382744	+	0.662932i
$933$	−3.46543	+	6.00231i	−0.113453	+	0.196507i
$934$	−14.4924	+	25.1016i	−0.474207	+	0.821350i
$935$	32.4924			1.06262
$936$	3.34233	−	1.35234i	0.109247	−	0.0442028i
$937$	−38.5616			−1.25975			−0.629876	−	0.776696i	$-0.716894\pi$
$937$	−38.5616			−1.25975			−0.629876	+	0.776696i	$0.716894\pi$
$938$	−0.438447	+	0.759413i	−0.0143158	+	0.0247957i
$939$	−3.00000	+	5.19615i	−0.0979013	+	0.169570i
$940$	−16.2462	−	28.1393i	−0.529893	−	0.917802i
$941$	−35.3693			−1.15301			−0.576503	−	0.817095i	$-0.695583\pi$
$941$	−35.3693			−1.15301			−0.576503	+	0.817095i	$0.695583\pi$
$942$	−6.84233	−	11.8513i	−0.222935	−	0.386135i
$943$	−18.6847	−	32.3628i	−0.608456	−	1.05388i
$944$	−3.12311			−0.101648
$945$	−1.28078	−	2.21837i	−0.0416637	−	0.0721636i
$946$	6.24621	−	10.8188i	0.203082	−	0.351748i
$947$	−27.2192	+	47.1451i	−0.884506	+	1.53201i	−0.0382270	+	0.999269i	$0.512171\pi$
$947$	−27.2192	+	47.1451i	−0.884506	+	1.53201i	−0.846279	+	0.532740i	$0.821162\pi$
$948$	2.43845			0.0791971
$949$	3.28078	−	23.4294i	0.106499	−	0.760551i
$950$	2.43845			0.0791137
$951$	8.28078	−	14.3427i	0.268523	−	0.465095i
$952$	4.06155	−	7.03482i	0.131636	−	0.228000i
$953$	−10.5616	−	18.2931i	−0.342122	−	0.592573i	0.642704	−	0.766114i	$-0.277812\pi$
$953$	−10.5616	−	18.2931i	−0.342122	−	0.592573i	−0.984827	+	0.173541i	$0.944479\pi$
$954$	7.00000			0.226633
$955$	4.00000	+	6.92820i	0.129437	+	0.224191i
$956$	2.68466	+	4.64996i	0.0868281	+	0.150391i
$957$	−3.31534			−0.107170
$958$	−13.4654	−	23.3228i	−0.435048	−	0.753526i
$959$	−8.28078	+	14.3427i	−0.267400	+	0.463151i
$960$	−1.28078	+	2.21837i	−0.0413369	+	0.0715976i
$961$	−31.0000			−1.00000
$962$	−21.9309	+	8.87348i	−0.707080	+	0.286092i
$963$	−14.9309			−0.481141
$964$	10.4039	−	18.0201i	0.335086	−	0.580387i
$965$	−10.4039	+	18.0201i	−0.334913	+	0.580086i
$966$	3.56155	+	6.16879i	0.114591	+	0.198478i
$967$	4.49242			0.144467			0.0722333	−	0.997388i	$-0.476987\pi$
$967$	4.49242			0.144467			0.0722333	+	0.997388i	$0.476987\pi$
$968$	4.28078	+	7.41452i	0.137589	+	0.238312i
$969$	−6.34233	−	10.9852i	−0.203745	−	0.352897i
$970$	23.3693			0.750344
$971$	−0.192236	−	0.332962i	−0.00616914	−	0.0106853i	0.862924	−	0.505333i	$-0.168630\pi$
$971$	−0.192236	−	0.332962i	−0.00616914	−	0.0106853i	−0.869093	+	0.494648i	$0.835297\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	4.78078	−	8.28055i	0.153265	−	0.265462i
$974$	11.3153			0.362567
$975$	4.43845	+	3.46410i	0.142144	+	0.110940i
$976$	5.24621			0.167927
$977$	−2.08854	+	3.61746i	−0.0668183	+	0.115733i	−0.897499	−	0.441016i	$-0.854618\pi$
$977$	−2.08854	+	3.61746i	−0.0668183	+	0.115733i	0.830681	+	0.556749i	$0.187951\pi$
$978$	−4.24621	+	7.35465i	−0.135779	+	0.235176i
$979$	−5.90388	−	10.2258i	−0.188689	−	0.326819i
$980$	−2.56155			−0.0818258
$981$	−2.12311	−	3.67733i	−0.0677855	−	0.117408i
$982$	−8.24621	−	14.2829i	−0.263147	−	0.455784i
$983$	−30.7386			−0.980410			−0.490205	−	0.871607i	$-0.663078\pi$
$983$	−30.7386			−0.980410			−0.490205	+	0.871607i	$0.663078\pi$
$984$	2.62311	+	4.54335i	0.0836216	+	0.144837i
$985$	10.8078	−	18.7196i	0.344364	−	0.596456i
$986$	8.62311	−	14.9357i	0.274616	−	0.475648i
$987$	12.6847			0.403757
$988$	−4.43845	−	3.46410i	−0.141206	−	0.110208i
$989$	−56.9848			−1.81201
$990$	2.00000	−	3.46410i	0.0635642	−	0.110096i
$991$	−24.8348	+	43.0151i	−0.788902	+	1.36642i	0.137738	+	0.990469i	$0.456017\pi$
$991$	−24.8348	+	43.0151i	−0.788902	+	1.36642i	−0.926640	+	0.375949i	$0.877317\pi$
$992$		0			0
$993$	5.36932			0.170390
$994$	−6.68466	−	11.5782i	−0.212024	−	0.367237i
$995$	−20.4924	−	35.4939i	−0.649653	−	1.12523i
$996$	−3.12311			−0.0989594
$997$	−11.9924	−	20.7715i	−0.379804	−	0.657840i	0.611230	−	0.791453i	$-0.290675\pi$
$997$	−11.9924	−	20.7715i	−0.379804	−	0.657840i	−0.991033	+	0.133614i	$0.957342\pi$
$998$	−6.87689	+	11.9111i	−0.217684	+	0.377040i
$999$	−3.28078	+	5.68247i	−0.103799	+	0.179785i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.l.295.1	yes	4
3.2	odd	2		1638.2.r.y.1387.2		4
13.3	even	3	inner	546.2.l.l.211.1	✓	4
13.4	even	6		7098.2.a.bi.1.2		2
13.9	even	3		7098.2.a.bt.1.1		2
39.29	odd	6		1638.2.r.y.757.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.l.211.1	✓	4	13.3	even	3	inner
546.2.l.l.295.1	yes	4	1.1	even	1	trivial
1638.2.r.y.757.2		4	39.29	odd	6
1638.2.r.y.1387.2		4	3.2	odd	2
7098.2.a.bi.1.2		2	13.4	even	6
7098.2.a.bt.1.1		2	13.9	even	3

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.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.56155 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.56155 q^{5} +(0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.28078 - 2.21837i) q^{10} +(-0.780776 + 1.35234i) q^{11} -1.00000 q^{12} +(-0.500000 + 3.57071i) q^{13} +1.00000 q^{14} +(-1.28078 + 2.21837i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(4.06155 + 7.03482i) q^{17} +1.00000 q^{18} +(-0.780776 - 1.35234i) q^{19} +(1.28078 + 2.21837i) q^{20} -1.00000 q^{21} +(-0.780776 - 1.35234i) q^{22} +(-3.56155 + 6.16879i) q^{23} +(0.500000 - 0.866025i) q^{24} +1.56155 q^{25} +(-2.84233 - 2.21837i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-1.06155 + 1.83866i) q^{29} +(-1.28078 - 2.21837i) q^{30} +(-0.500000 - 0.866025i) q^{32} +(0.780776 + 1.35234i) q^{33} -8.12311 q^{34} +(1.28078 + 2.21837i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(3.28078 - 5.68247i) q^{37} +1.56155 q^{38} +(2.84233 + 2.21837i) q^{39} -2.56155 q^{40} +(-2.62311 + 4.54335i) q^{41} +(0.500000 - 0.866025i) q^{42} +(4.00000 + 6.92820i) q^{43} +1.56155 q^{44} +(1.28078 + 2.21837i) q^{45} +(-3.56155 - 6.16879i) q^{46} -12.6847 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-0.780776 + 1.35234i) q^{50} +8.12311 q^{51} +(3.34233 - 1.35234i) q^{52} +7.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(2.00000 - 3.46410i) q^{55} +(-0.500000 - 0.866025i) q^{56} -1.56155 q^{57} +(-1.06155 - 1.83866i) q^{58} +(1.56155 + 2.70469i) q^{59} +2.56155 q^{60} +(-2.62311 - 4.54335i) q^{61} +(-0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(1.28078 - 9.14657i) q^{65} -1.56155 q^{66} +(-0.438447 + 0.759413i) q^{67} +(4.06155 - 7.03482i) q^{68} +(3.56155 + 6.16879i) q^{69} -2.56155 q^{70} +(-6.68466 - 11.5782i) q^{71} +(-0.500000 - 0.866025i) q^{72} -6.56155 q^{73} +(3.28078 + 5.68247i) q^{74} +(0.780776 - 1.35234i) q^{75} +(-0.780776 + 1.35234i) q^{76} +1.56155 q^{77} +(-3.34233 + 1.35234i) q^{78} -2.43845 q^{79} +(1.28078 - 2.21837i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.62311 - 4.54335i) q^{82} +3.12311 q^{83} +(0.500000 + 0.866025i) q^{84} +(-10.4039 - 18.0201i) q^{85} -8.00000 q^{86} +(1.06155 + 1.83866i) q^{87} +(-0.780776 + 1.35234i) q^{88} +(-3.78078 + 6.54850i) q^{89} -2.56155 q^{90} +(3.34233 - 1.35234i) q^{91} +7.12311 q^{92} +(6.34233 - 10.9852i) q^{94} +(2.00000 + 3.46410i) q^{95} -1.00000 q^{96} +(4.56155 + 7.90084i) q^{97} +(-0.500000 - 0.866025i) q^{98} +1.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} + 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{9} + q^{10} + q^{11} - 4 q^{12} - 2 q^{13} + 4 q^{14} - q^{15} - 2 q^{16} + 8 q^{17} + 4 q^{18} + q^{19} + q^{20} - 4 q^{21} + q^{22} - 6 q^{23} + 2 q^{24} - 2 q^{25} + q^{26} - 4 q^{27} - 2 q^{28} + 4 q^{29} - q^{30} - 2 q^{32} - q^{33} - 16 q^{34} + q^{35} - 2 q^{36} + 9 q^{37} - 2 q^{38} - q^{39} - 2 q^{40} + 6 q^{41} + 2 q^{42} + 16 q^{43} - 2 q^{44} + q^{45} - 6 q^{46} - 26 q^{47} + 2 q^{48} - 2 q^{49} + q^{50} + 16 q^{51} + q^{52} + 28 q^{53} + 2 q^{54} + 8 q^{55} - 2 q^{56} + 2 q^{57} + 4 q^{58} - 2 q^{59} + 2 q^{60} + 6 q^{61} - 2 q^{63} + 4 q^{64} + q^{65} + 2 q^{66} - 10 q^{67} + 8 q^{68} + 6 q^{69} - 2 q^{70} - 2 q^{71} - 2 q^{72} - 18 q^{73} + 9 q^{74} - q^{75} + q^{76} - 2 q^{77} - q^{78} - 18 q^{79} + q^{80} - 2 q^{81} + 6 q^{82} - 4 q^{83} + 2 q^{84} - 21 q^{85} - 32 q^{86} - 4 q^{87} + q^{88} - 11 q^{89} - 2 q^{90} + q^{91} + 12 q^{92} + 13 q^{94} + 8 q^{95} - 4 q^{96} + 10 q^{97} - 2 q^{98} - 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 + 2 * q^6 - 2 * q^7 + 4 * q^8 - 2 * q^9 + q^10 + q^11 - 4 * q^12 - 2 * q^13 + 4 * q^14 - q^15 - 2 * q^16 + 8 * q^17 + 4 * q^18 + q^19 + q^20 - 4 * q^21 + q^22 - 6 * q^23 + 2 * q^24 - 2 * q^25 + q^26 - 4 * q^27 - 2 * q^28 + 4 * q^29 - q^30 - 2 * q^32 - q^33 - 16 * q^34 + q^35 - 2 * q^36 + 9 * q^37 - 2 * q^38 - q^39 - 2 * q^40 + 6 * q^41 + 2 * q^42 + 16 * q^43 - 2 * q^44 + q^45 - 6 * q^46 - 26 * q^47 + 2 * q^48 - 2 * q^49 + q^50 + 16 * q^51 + q^52 + 28 * q^53 + 2 * q^54 + 8 * q^55 - 2 * q^56 + 2 * q^57 + 4 * q^58 - 2 * q^59 + 2 * q^60 + 6 * q^61 - 2 * q^63 + 4 * q^64 + q^65 + 2 * q^66 - 10 * q^67 + 8 * q^68 + 6 * q^69 - 2 * q^70 - 2 * q^71 - 2 * q^72 - 18 * q^73 + 9 * q^74 - q^75 + q^76 - 2 * q^77 - q^78 - 18 * q^79 + q^80 - 2 * q^81 + 6 * q^82 - 4 * q^83 + 2 * q^84 - 21 * q^85 - 32 * q^86 - 4 * q^87 + q^88 - 11 * q^89 - 2 * q^90 + q^91 + 12 * q^92 + 13 * q^94 + 8 * q^95 - 4 * q^96 + 10 * q^97 - 2 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more