LMFDB - Embedded newform 546.2.l.i.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.i.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.56155 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.56155 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.78078 - 3.08440i) q^{10} +(-1.28078 + 2.21837i) q^{11} +1.00000 q^{12} +(-0.500000 - 3.57071i) q^{13} -1.00000 q^{14} +(1.78078 - 3.08440i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(-3.84233 - 6.65511i) q^{19} +(1.78078 + 3.08440i) q^{20} -1.00000 q^{21} +(-1.28078 - 2.21837i) q^{22} +(4.56155 - 7.90084i) q^{23} +(-0.500000 + 0.866025i) q^{24} +7.68466 q^{25} +(3.34233 + 1.35234i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(0.500000 - 0.866025i) q^{29} +(1.78078 + 3.08440i) q^{30} +5.12311 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.28078 - 2.21837i) q^{33} -5.00000 q^{34} +(-1.78078 - 3.08440i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.90388 - 8.49377i) q^{37} +7.68466 q^{38} +(3.34233 + 1.35234i) q^{39} -3.56155 q^{40} +(-2.06155 + 3.57071i) q^{41} +(0.500000 - 0.866025i) q^{42} +(1.43845 + 2.49146i) q^{43} +2.56155 q^{44} +(1.78078 + 3.08440i) q^{45} +(4.56155 + 7.90084i) q^{46} -7.68466 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-3.84233 + 6.65511i) q^{50} -5.00000 q^{51} +(-2.84233 + 2.21837i) q^{52} -3.87689 q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.56155 - 7.90084i) q^{55} +(0.500000 + 0.866025i) q^{56} +7.68466 q^{57} +(0.500000 + 0.866025i) q^{58} +(-6.56155 - 11.3649i) q^{59} -3.56155 q^{60} +(0.500000 + 0.866025i) q^{61} +(-2.56155 + 4.43674i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.78078 + 12.7173i) q^{65} +2.56155 q^{66} +(-0.561553 + 0.972638i) q^{67} +(2.50000 - 4.33013i) q^{68} +(4.56155 + 7.90084i) q^{69} +3.56155 q^{70} +(2.00000 + 3.46410i) q^{71} +(-0.500000 - 0.866025i) q^{72} -2.43845 q^{73} +(4.90388 + 8.49377i) q^{74} +(-3.84233 + 6.65511i) q^{75} +(-3.84233 + 6.65511i) q^{76} -2.56155 q^{77} +(-2.84233 + 2.21837i) q^{78} +1.43845 q^{79} +(1.78078 - 3.08440i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.06155 - 3.57071i) q^{82} -10.2462 q^{83} +(0.500000 + 0.866025i) q^{84} +(-8.90388 - 15.4220i) q^{85} -2.87689 q^{86} +(0.500000 + 0.866025i) q^{87} +(-1.28078 + 2.21837i) q^{88} +(4.84233 - 8.38716i) q^{89} -3.56155 q^{90} +(2.84233 - 2.21837i) q^{91} -9.12311 q^{92} +(-2.56155 + 4.43674i) q^{93} +(3.84233 - 6.65511i) q^{94} +(13.6847 + 23.7025i) q^{95} +1.00000 q^{96} +(-6.12311 - 10.6055i) q^{97} +(-0.500000 - 0.866025i) q^{98} +2.56155 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 6 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 - 6 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 3 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 4 q^{14} + 3 q^{15} - 2 q^{16} + 10 q^{17} + 4 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} - q^{22} + 10 q^{23} - 2 q^{24} + 6 q^{25} + q^{26} + 4 q^{27} + 2 q^{28} + 2 q^{29} + 3 q^{30} + 4 q^{31} - 2 q^{32} - q^{33} - 20 q^{34} - 3 q^{35} - 2 q^{36} - q^{37} + 6 q^{38} + q^{39} - 6 q^{40} + 2 q^{42} + 14 q^{43} + 2 q^{44} + 3 q^{45} + 10 q^{46} - 6 q^{47} - 2 q^{48} - 2 q^{49} - 3 q^{50} - 20 q^{51} + q^{52} - 32 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 6 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 2 q^{61} - 2 q^{62} + 2 q^{63} + 4 q^{64} + 3 q^{65} + 2 q^{66} + 6 q^{67} + 10 q^{68} + 10 q^{69} + 6 q^{70} + 8 q^{71} - 2 q^{72} - 18 q^{73} - q^{74} - 3 q^{75} - 3 q^{76} - 2 q^{77} + q^{78} + 14 q^{79} + 3 q^{80} - 2 q^{81} - 8 q^{83} + 2 q^{84} - 15 q^{85} - 28 q^{86} + 2 q^{87} - q^{88} + 7 q^{89} - 6 q^{90} - q^{91} - 20 q^{92} - 2 q^{93} + 3 q^{94} + 30 q^{95} + 4 q^{96} - 8 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 3 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 4 * q^14 + 3 * q^15 - 2 * q^16 + 10 * q^17 + 4 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 - q^22 + 10 * q^23 - 2 * q^24 + 6 * q^25 + q^26 + 4 * q^27 + 2 * q^28 + 2 * q^29 + 3 * q^30 + 4 * q^31 - 2 * q^32 - q^33 - 20 * q^34 - 3 * q^35 - 2 * q^36 - q^37 + 6 * q^38 + q^39 - 6 * q^40 + 2 * q^42 + 14 * q^43 + 2 * q^44 + 3 * q^45 + 10 * q^46 - 6 * q^47 - 2 * q^48 - 2 * q^49 - 3 * q^50 - 20 * q^51 + q^52 - 32 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 6 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 2 * q^61 - 2 * q^62 + 2 * q^63 + 4 * q^64 + 3 * q^65 + 2 * q^66 + 6 * q^67 + 10 * q^68 + 10 * q^69 + 6 * q^70 + 8 * q^71 - 2 * q^72 - 18 * q^73 - q^74 - 3 * q^75 - 3 * q^76 - 2 * q^77 + q^78 + 14 * q^79 + 3 * q^80 - 2 * q^81 - 8 * q^83 + 2 * q^84 - 15 * q^85 - 28 * q^86 + 2 * q^87 - q^88 + 7 * q^89 - 6 * q^90 - q^91 - 20 * q^92 - 2 * q^93 + 3 * q^94 + 30 * q^95 + 4 * q^96 - 8 * 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
$5$	−3.56155			−1.59277			−0.796387	−	0.604787i	$-0.793258\pi$
$5$	−3.56155			−1.59277			−0.796387	+	0.604787i	$0.793258\pi$
$6$	−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
$10$	1.78078	−	3.08440i	0.563131	−	0.975371i
$11$	−1.28078	+	2.21837i	−0.386169	+	0.668864i	−0.991931	−	0.126782i	$-0.959535\pi$
$11$	−1.28078	+	2.21837i	−0.386169	+	0.668864i	0.605762	+	0.795646i	$0.292868\pi$
$12$	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
$15$	1.78078	−	3.08440i	0.459794	−	0.796387i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	0.991838	+	0.127502i	$0.0406959\pi$
$17$	2.50000	+	4.33013i	0.606339	+	1.05021i	−0.385499	+	0.922708i	$0.625971\pi$
$18$	1.00000			0.235702
$19$	−3.84233	−	6.65511i	−0.881491	−	1.52679i	−0.849684	−	0.527293i	$-0.823207\pi$
$19$	−3.84233	−	6.65511i	−0.881491	−	1.52679i	−0.0318071	−	0.999494i	$-0.510126\pi$
$20$	1.78078	+	3.08440i	0.398194	+	0.689692i
$21$	−1.00000			−0.218218
$22$	−1.28078	−	2.21837i	−0.273062	−	0.472958i
$23$	4.56155	−	7.90084i	0.951150	−	1.64744i	0.208206	−	0.978085i	$-0.433237\pi$
$23$	4.56155	−	7.90084i	0.951150	−	1.64744i	0.742943	−	0.669354i	$-0.233429\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	7.68466			1.53693
$26$	3.34233	+	1.35234i	0.655485	+	0.265217i
$27$	1.00000			0.192450
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$	1.78078	+	3.08440i	0.325124	+	0.563131i
$31$	5.12311			0.920137			0.460068	−	0.887883i	$-0.347825\pi$
$31$	5.12311			0.920137			0.460068	+	0.887883i	$0.347825\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.28078	−	2.21837i	−0.222955	−	0.386169i
$34$	−5.00000			−0.857493
$35$	−1.78078	−	3.08440i	−0.301006	−	0.521358i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	4.90388	−	8.49377i	0.806193	−	1.39637i	−0.109289	−	0.994010i	$-0.534857\pi$
$37$	4.90388	−	8.49377i	0.806193	−	1.39637i	0.915483	−	0.402358i	$-0.131809\pi$
$38$	7.68466			1.24662
$39$	3.34233	+	1.35234i	0.535201	+	0.216548i
$40$	−3.56155			−0.563131
$41$	−2.06155	+	3.57071i	−0.321960	+	0.557652i	−0.980892	−	0.194551i	$-0.937675\pi$
$41$	−2.06155	+	3.57071i	−0.321960	+	0.557652i	0.658932	+	0.752202i	$0.271008\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	1.43845	+	2.49146i	0.219361	+	0.379945i	0.954613	−	0.297850i	$-0.0962694\pi$
$43$	1.43845	+	2.49146i	0.219361	+	0.379945i	−0.735252	+	0.677794i	$0.762936\pi$
$44$	2.56155			0.386169
$45$	1.78078	+	3.08440i	0.265462	+	0.459794i
$46$	4.56155	+	7.90084i	0.672564	+	1.16492i
$47$	−7.68466			−1.12092			−0.560461	−	0.828181i	$-0.689376\pi$
$47$	−7.68466			−1.12092			−0.560461	+	0.828181i	$0.689376\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−3.84233	+	6.65511i	−0.543387	+	0.941175i
$51$	−5.00000			−0.700140
$52$	−2.84233	+	2.21837i	−0.394160	+	0.307633i
$53$	−3.87689			−0.532532			−0.266266	−	0.963900i	$-0.585790\pi$
$53$	−3.87689			−0.532532			−0.266266	+	0.963900i	$0.585790\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	4.56155	−	7.90084i	0.615080	−	1.06535i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	7.68466			1.01786
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	−6.56155	−	11.3649i	−0.854241	−	1.47959i	−0.877347	−	0.479857i	$-0.840689\pi$
$59$	−6.56155	−	11.3649i	−0.854241	−	1.47959i	0.0231056	−	0.999733i	$-0.492645\pi$
$60$	−3.56155			−0.459794
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	−2.56155	+	4.43674i	−0.325318	+	0.563466i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	1.78078	+	12.7173i	0.220878	+	1.57739i
$66$	2.56155			0.315305
$67$	−0.561553	+	0.972638i	−0.0686046	+	0.118827i	−0.898287	−	0.439409i	$-0.855188\pi$
$67$	−0.561553	+	0.972638i	−0.0686046	+	0.118827i	0.829683	+	0.558235i	$0.188521\pi$
$68$	2.50000	−	4.33013i	0.303170	−	0.525105i
$69$	4.56155	+	7.90084i	0.549146	+	0.951150i
$70$	3.56155			0.425687
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	0.959955	−	0.280155i	$-0.0903858\pi$
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	−0.722599	+	0.691268i	$0.757052\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−2.43845			−0.285399			−0.142699	−	0.989766i	$-0.545578\pi$
$73$	−2.43845			−0.285399			−0.142699	+	0.989766i	$0.545578\pi$
$74$	4.90388	+	8.49377i	0.570065	+	0.987381i
$75$	−3.84233	+	6.65511i	−0.443674	+	0.768466i
$76$	−3.84233	+	6.65511i	−0.440745	+	0.763393i
$77$	−2.56155			−0.291916
$78$	−2.84233	+	2.21837i	−0.321830	+	0.251181i
$79$	1.43845			0.161838			0.0809190	−	0.996721i	$-0.474214\pi$
$79$	1.43845			0.161838			0.0809190	+	0.996721i	$0.474214\pi$
$80$	1.78078	−	3.08440i	0.199097	−	0.344846i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.06155	−	3.57071i	−0.227660	−	0.394319i
$83$	−10.2462			−1.12467			−0.562334	−	0.826910i	$-0.690096\pi$
$83$	−10.2462			−1.12467			−0.562334	+	0.826910i	$0.690096\pi$
$84$	0.500000	+	0.866025i	0.0545545	+	0.0944911i
$85$	−8.90388	−	15.4220i	−0.965762	−	1.67275i
$86$	−2.87689			−0.310223
$87$	0.500000	+	0.866025i	0.0536056	+	0.0928477i
$88$	−1.28078	+	2.21837i	−0.136531	+	0.236479i
$89$	4.84233	−	8.38716i	0.513286	−	0.889037i	−0.486595	−	0.873627i	$-0.661761\pi$
$89$	4.84233	−	8.38716i	0.513286	−	0.889037i	0.999881	−	0.0154098i	$-0.00490527\pi$
$90$	−3.56155			−0.375421
$91$	2.84233	−	2.21837i	0.297957	−	0.232548i
$92$	−9.12311			−0.951150
$93$	−2.56155	+	4.43674i	−0.265621	+	0.460068i
$94$	3.84233	−	6.65511i	0.396306	−	0.686422i
$95$	13.6847	+	23.7025i	1.40402	+	2.43183i
$96$	1.00000			0.102062
$97$	−6.12311	−	10.6055i	−0.621707	−	1.07683i	−0.989168	−	0.146789i	$-0.953106\pi$
$97$	−6.12311	−	10.6055i	−0.621707	−	1.07683i	0.367461	−	0.930039i	$-0.380227\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	2.56155			0.257446
$100$	−3.84233	−	6.65511i	−0.384233	−	0.665511i
$101$	9.78078	−	16.9408i	0.973224	−	1.68567i	0.287547	−	0.957767i	$-0.407160\pi$
$101$	9.78078	−	16.9408i	0.973224	−	1.68567i	0.685677	−	0.727906i	$-0.259506\pi$
$102$	2.50000	−	4.33013i	0.247537	−	0.428746i
$103$	−11.3693			−1.12025			−0.560126	−	0.828407i	$-0.689247\pi$
$103$	−11.3693			−1.12025			−0.560126	+	0.828407i	$0.689247\pi$
$104$	−0.500000	−	3.57071i	−0.0490290	−	0.350137i
$105$	3.56155			0.347572
$106$	1.93845	−	3.35749i	0.188279	−	0.326108i
$107$	4.71922	−	8.17394i	0.456225	−	0.790204i	−0.542533	−	0.840034i	$-0.682535\pi$
$107$	4.71922	−	8.17394i	0.456225	−	0.790204i	0.998758	+	0.0498303i	$0.0158680\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	0.876894			0.0839912			0.0419956	−	0.999118i	$-0.486628\pi$
$109$	0.876894			0.0839912			0.0419956	+	0.999118i	$0.486628\pi$
$110$	4.56155	+	7.90084i	0.434927	+	0.753316i
$111$	4.90388	+	8.49377i	0.465456	+	0.806193i
$112$	−1.00000			−0.0944911
$113$	−8.46543	−	14.6626i	−0.796361	−	1.37934i	−0.921971	−	0.387258i	$-0.873422\pi$
$113$	−8.46543	−	14.6626i	−0.796361	−	1.37934i	0.125610	−	0.992080i	$-0.459911\pi$
$114$	−3.84233	+	6.65511i	−0.359867	+	0.623308i
$115$	−16.2462	+	28.1393i	−1.51497	+	2.62400i
$116$	−1.00000			−0.0928477
$117$	−2.84233	+	2.21837i	−0.262773	+	0.205088i
$118$	13.1231			1.20808
$119$	−2.50000	+	4.33013i	−0.229175	+	0.396942i
$120$	1.78078	−	3.08440i	0.162562	−	0.281565i
$121$	2.21922	+	3.84381i	0.201748	+	0.349437i
$122$	−1.00000			−0.0905357
$123$	−2.06155	−	3.57071i	−0.185884	−	0.321960i
$124$	−2.56155	−	4.43674i	−0.230034	−	0.398431i
$125$	−9.56155			−0.855211
$126$	0.500000	+	0.866025i	0.0445435	+	0.0771517i
$127$	−1.12311	+	1.94528i	−0.0996595	+	0.172615i	−0.911544	−	0.411203i	$-0.865109\pi$
$127$	−1.12311	+	1.94528i	−0.0996595	+	0.172615i	0.811884	+	0.583818i	$0.198442\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.87689			−0.253296
$130$	−11.9039	−	4.81645i	−1.04404	−	0.422430i
$131$	−16.4924			−1.44095			−0.720475	−	0.693481i	$-0.756076\pi$
$131$	−16.4924			−1.44095			−0.720475	+	0.693481i	$0.756076\pi$
$132$	−1.28078	+	2.21837i	−0.111477	+	0.193084i
$133$	3.84233	−	6.65511i	0.333172	−	0.577071i
$134$	−0.561553	−	0.972638i	−0.0485108	−	0.0840231i
$135$	−3.56155			−0.306530
$136$	2.50000	+	4.33013i	0.214373	+	0.371305i
$137$	2.90388	+	5.02967i	0.248095	+	0.429714i	0.962997	−	0.269511i	$-0.0868620\pi$
$137$	2.90388	+	5.02967i	0.248095	+	0.429714i	−0.714902	+	0.699225i	$0.753529\pi$
$138$	−9.12311			−0.776610
$139$	3.84233	+	6.65511i	0.325902	+	0.564479i	0.981695	−	0.190462i	$-0.0609987\pi$
$139$	3.84233	+	6.65511i	0.325902	+	0.564479i	−0.655792	+	0.754941i	$0.727665\pi$
$140$	−1.78078	+	3.08440i	−0.150503	+	0.260679i
$141$	3.84233	−	6.65511i	0.323582	−	0.560461i
$142$	−4.00000			−0.335673
$143$	8.56155	+	3.46410i	0.715953	+	0.289683i
$144$	1.00000			0.0833333
$145$	−1.78078	+	3.08440i	−0.147885	+	0.256145i
$146$	1.21922	−	2.11176i	0.100904	−	0.174770i
$147$	−0.500000	−	0.866025i	−0.0412393	−	0.0714286i
$148$	−9.80776			−0.806193
$149$	8.90388	+	15.4220i	0.729434	+	1.26342i	0.957123	+	0.289683i	$0.0935500\pi$
$149$	8.90388	+	15.4220i	0.729434	+	1.26342i	−0.227688	+	0.973734i	$0.573117\pi$
$150$	−3.84233	−	6.65511i	−0.313725	−	0.543387i
$151$	−17.4384			−1.41912			−0.709560	−	0.704645i	$-0.751106\pi$
$151$	−17.4384			−1.41912			−0.709560	+	0.704645i	$0.751106\pi$
$152$	−3.84233	−	6.65511i	−0.311654	−	0.539801i
$153$	2.50000	−	4.33013i	0.202113	−	0.350070i
$154$	1.28078	−	2.21837i	0.103208	−	0.178761i
$155$	−18.2462			−1.46557
$156$	−0.500000	−	3.57071i	−0.0400320	−	0.285886i
$157$	−5.80776			−0.463510			−0.231755	−	0.972774i	$-0.574447\pi$
$157$	−5.80776			−0.463510			−0.231755	+	0.972774i	$0.574447\pi$
$158$	−0.719224	+	1.24573i	−0.0572184	+	0.0991051i
$159$	1.93845	−	3.35749i	0.153729	−	0.266266i
$160$	1.78078	+	3.08440i	0.140783	+	0.243843i
$161$	9.12311			0.719001
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	0.561553	+	0.972638i	0.0439842	+	0.0761829i	0.887179	−	0.461425i	$-0.152662\pi$
$163$	0.561553	+	0.972638i	0.0439842	+	0.0761829i	−0.843195	+	0.537608i	$0.819328\pi$
$164$	4.12311			0.321960
$165$	4.56155	+	7.90084i	0.355116	+	0.615080i
$166$	5.12311	−	8.87348i	0.397630	−	0.688716i
$167$	−10.2462	+	17.7470i	−0.792876	+	1.37330i	0.131304	+	0.991342i	$0.458084\pi$
$167$	−10.2462	+	17.7470i	−0.792876	+	1.37330i	−0.924179	+	0.381959i	$0.875250\pi$
$168$	−1.00000			−0.0771517
$169$	−12.5000	+	3.57071i	−0.961538	+	0.274670i
$170$	17.8078			1.36579
$171$	−3.84233	+	6.65511i	−0.293830	+	0.508929i
$172$	1.43845	−	2.49146i	0.109681	−	0.189972i
$173$	2.43845	+	4.22351i	0.185392	+	0.321108i	0.943708	−	0.330778i	$-0.107311\pi$
$173$	2.43845	+	4.22351i	0.185392	+	0.321108i	−0.758317	+	0.651886i	$0.773978\pi$
$174$	−1.00000			−0.0758098
$175$	3.84233	+	6.65511i	0.290453	+	0.503079i
$176$	−1.28078	−	2.21837i	−0.0965422	−	0.167216i
$177$	13.1231			0.986393
$178$	4.84233	+	8.38716i	0.362948	+	0.628644i
$179$	8.24621	−	14.2829i	0.616351	−	1.06755i	−0.373795	−	0.927511i	$-0.621944\pi$
$179$	8.24621	−	14.2829i	0.616351	−	1.06755i	0.990146	−	0.140040i	$-0.0447230\pi$
$180$	1.78078	−	3.08440i	0.132731	−	0.229897i
$181$	13.2462			0.984583			0.492292	−	0.870430i	$-0.336159\pi$
$181$	13.2462			0.984583			0.492292	+	0.870430i	$0.336159\pi$
$182$	0.500000	+	3.57071i	0.0370625	+	0.264679i
$183$	−1.00000			−0.0739221
$184$	4.56155	−	7.90084i	0.336282	−	0.582458i
$185$	−17.4654	+	30.2510i	−1.28408	+	2.22410i
$186$	−2.56155	−	4.43674i	−0.187822	−	0.325318i
$187$	−12.8078			−0.936596
$188$	3.84233	+	6.65511i	0.280231	+	0.485374i
$189$	0.500000	+	0.866025i	0.0363696	+	0.0629941i
$190$	−27.3693			−1.98558
$191$	−2.87689	−	4.98293i	−0.208165	−	0.360552i	0.742972	−	0.669323i	$-0.233416\pi$
$191$	−2.87689	−	4.98293i	−0.208165	−	0.360552i	−0.951136	+	0.308771i	$0.900082\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	10.1847	−	17.6403i	0.733108	−	1.26978i	−0.222441	−	0.974946i	$-0.571402\pi$
$193$	10.1847	−	17.6403i	0.733108	−	1.26978i	0.955549	−	0.294834i	$-0.0952642\pi$
$194$	12.2462			0.879227
$195$	−11.9039	−	4.81645i	−0.852455	−	0.344913i
$196$	1.00000			0.0714286
$197$	0.280776	−	0.486319i	0.0200045	−	0.0346488i	−0.855850	−	0.517224i	$-0.826965\pi$
$197$	0.280776	−	0.486319i	0.0200045	−	0.0346488i	0.875854	+	0.482576i	$0.160299\pi$
$198$	−1.28078	+	2.21837i	−0.0910208	+	0.157653i
$199$	8.80776	+	15.2555i	0.624366	+	1.08143i	0.988663	+	0.150151i	$0.0479759\pi$
$199$	8.80776	+	15.2555i	0.624366	+	1.08143i	−0.364297	+	0.931283i	$0.618691\pi$
$200$	7.68466			0.543387
$201$	−0.561553	−	0.972638i	−0.0396089	−	0.0686046i
$202$	9.78078	+	16.9408i	0.688173	+	1.19195i
$203$	1.00000			0.0701862
$204$	2.50000	+	4.33013i	0.175035	+	0.303170i
$205$	7.34233	−	12.7173i	0.512811	−	0.888214i
$206$	5.68466	−	9.84612i	0.396069	−	0.686011i
$207$	−9.12311			−0.634100
$208$	3.34233	+	1.35234i	0.231749	+	0.0937682i
$209$	19.6847			1.36162
$210$	−1.78078	+	3.08440i	−0.122885	+	0.212843i
$211$	1.43845	−	2.49146i	0.0990268	−	0.171519i	−0.812255	−	0.583302i	$-0.801760\pi$
$211$	1.43845	−	2.49146i	0.0990268	−	0.171519i	0.911282	+	0.411783i	$0.135094\pi$
$212$	1.93845	+	3.35749i	0.133133	+	0.230593i
$213$	−4.00000			−0.274075
$214$	4.71922	+	8.17394i	0.322599	+	0.558759i
$215$	−5.12311	−	8.87348i	−0.349393	−	0.605166i
$216$	1.00000			0.0680414
$217$	2.56155	+	4.43674i	0.173890	+	0.301186i
$218$	−0.438447	+	0.759413i	−0.0296954	+	0.0514339i
$219$	1.21922	−	2.11176i	0.0823875	−	0.142699i
$220$	−9.12311			−0.615080
$221$	14.2116	−	11.0918i	0.955979	−	0.746119i
$222$	−9.80776			−0.658254
$223$	8.24621	−	14.2829i	0.552207	−	0.956451i	−0.445908	−	0.895079i	$-0.647119\pi$
$223$	8.24621	−	14.2829i	0.552207	−	0.956451i	0.998115	−	0.0613719i	$-0.0195476\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	−3.84233	−	6.65511i	−0.256155	−	0.443674i
$226$	16.9309			1.12622
$227$	−6.56155	−	11.3649i	−0.435506	−	0.754318i	0.561831	−	0.827252i	$-0.310097\pi$
$227$	−6.56155	−	11.3649i	−0.435506	−	0.754318i	−0.997337	+	0.0729341i	$0.976764\pi$
$228$	−3.84233	−	6.65511i	−0.254464	−	0.440745i
$229$	22.8078			1.50718			0.753590	−	0.657345i	$-0.228321\pi$
$229$	22.8078			1.50718			0.753590	+	0.657345i	$0.228321\pi$
$230$	−16.2462	−	28.1393i	−1.07124	−	1.85545i
$231$	1.28078	−	2.21837i	0.0842689	−	0.145958i
$232$	0.500000	−	0.866025i	0.0328266	−	0.0568574i
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$	−0.500000	−	3.57071i	−0.0326860	−	0.233425i
$235$	27.3693			1.78538
$236$	−6.56155	+	11.3649i	−0.427121	+	0.739795i
$237$	−0.719224	+	1.24573i	−0.0467186	+	0.0809190i
$238$	−2.50000	−	4.33013i	−0.162051	−	0.280680i
$239$	4.00000			0.258738			0.129369	−	0.991596i	$-0.458705\pi$
$239$	4.00000			0.258738			0.129369	+	0.991596i	$0.458705\pi$
$240$	1.78078	+	3.08440i	0.114949	+	0.199097i
$241$	−5.65767	−	9.79937i	−0.364443	−	0.631233i	0.624244	−	0.781229i	$-0.285407\pi$
$241$	−5.65767	−	9.79937i	−0.364443	−	0.631233i	−0.988687	+	0.149996i	$0.952074\pi$
$242$	−4.43845			−0.285314
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$	1.78078	−	3.08440i	0.113770	−	0.197055i
$246$	4.12311			0.262880
$247$	−21.8423	+	17.0474i	−1.38979	+	1.08470i
$248$	5.12311			0.325318
$249$	5.12311	−	8.87348i	0.324664	−	0.562334i
$250$	4.78078	−	8.28055i	0.302363	−	0.523708i
$251$	−4.24621	−	7.35465i	−0.268018	−	0.464222i	0.700332	−	0.713818i	$-0.253035\pi$
$251$	−4.24621	−	7.35465i	−0.268018	−	0.464222i	−0.968350	+	0.249596i	$0.919702\pi$
$252$	−1.00000			−0.0629941
$253$	11.6847	+	20.2384i	0.734608	+	1.27238i
$254$	−1.12311	−	1.94528i	−0.0704699	−	0.122057i
$255$	17.8078			1.11517
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.37689	−	12.7772i	0.460158	−	0.797017i	−0.538810	−	0.842427i	$-0.681126\pi$
$257$	7.37689	−	12.7772i	0.460158	−	0.797017i	0.998968	+	0.0454100i	$0.0144594\pi$
$258$	1.43845	−	2.49146i	0.0895538	−	0.155112i
$259$	9.80776			0.609425
$260$	10.1231	−	7.90084i	0.627808	−	0.489989i
$261$	−1.00000			−0.0618984
$262$	8.24621	−	14.2829i	0.509453	−	0.882398i
$263$	10.2462	−	17.7470i	0.631808	−	1.09432i	−0.355373	−	0.934724i	$-0.615646\pi$
$263$	10.2462	−	17.7470i	0.631808	−	1.09432i	0.987182	−	0.159600i	$-0.0510204\pi$
$264$	−1.28078	−	2.21837i	−0.0788263	−	0.136531i
$265$	13.8078			0.848204
$266$	3.84233	+	6.65511i	0.235588	+	0.408051i
$267$	4.84233	+	8.38716i	0.296346	+	0.513286i
$268$	1.12311			0.0686046
$269$	2.43845	+	4.22351i	0.148675	+	0.257512i	0.930738	−	0.365687i	$-0.119166\pi$
$269$	2.43845	+	4.22351i	0.148675	+	0.257512i	−0.782063	+	0.623199i	$0.785833\pi$
$270$	1.78078	−	3.08440i	0.108375	−	0.187710i
$271$	−6.56155	+	11.3649i	−0.398586	+	0.690371i	−0.993552	−	0.113380i	$-0.963832\pi$
$271$	−6.56155	+	11.3649i	−0.398586	+	0.690371i	0.594966	+	0.803751i	$0.297166\pi$
$272$	−5.00000			−0.303170
$273$	0.500000	+	3.57071i	0.0302614	+	0.216109i
$274$	−5.80776			−0.350860
$275$	−9.84233	+	17.0474i	−0.593515	+	1.02800i
$276$	4.56155	−	7.90084i	0.274573	−	0.475575i
$277$	1.78078	+	3.08440i	0.106996	+	0.185323i	0.914552	−	0.404468i	$-0.132543\pi$
$277$	1.78078	+	3.08440i	0.106996	+	0.185323i	−0.807556	+	0.589791i	$0.799210\pi$
$278$	−7.68466			−0.460895
$279$	−2.56155	−	4.43674i	−0.153356	−	0.265621i
$280$	−1.78078	−	3.08440i	−0.106422	−	0.184328i
$281$	7.80776			0.465772			0.232886	−	0.972504i	$-0.425183\pi$
$281$	7.80776			0.465772			0.232886	+	0.972504i	$0.425183\pi$
$282$	3.84233	+	6.65511i	0.228807	+	0.396306i
$283$	−4.24621	+	7.35465i	−0.252411	+	0.437189i	−0.964189	−	0.265216i	$-0.914557\pi$
$283$	−4.24621	+	7.35465i	−0.252411	+	0.437189i	0.711778	+	0.702404i	$0.247890\pi$
$284$	2.00000	−	3.46410i	0.118678	−	0.205557i
$285$	−27.3693			−1.62122
$286$	−7.28078	+	5.68247i	−0.430521	+	0.336012i
$287$	−4.12311			−0.243379
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$	−1.78078	−	3.08440i	−0.104571	−	0.181122i
$291$	12.2462			0.717886
$292$	1.21922	+	2.11176i	0.0713497	+	0.123581i
$293$	2.34233	+	4.05703i	0.136840	+	0.237014i	0.926299	−	0.376789i	$-0.122972\pi$
$293$	2.34233	+	4.05703i	0.136840	+	0.237014i	−0.789459	+	0.613804i	$0.789639\pi$
$294$	1.00000			0.0583212
$295$	23.3693	+	40.4768i	1.36061	+	2.35665i
$296$	4.90388	−	8.49377i	0.285032	−	0.493691i
$297$	−1.28078	+	2.21837i	−0.0743182	+	0.128723i
$298$	−17.8078			−1.03158
$299$	−30.4924	−	12.3376i	−1.76342	−	0.713501i
$300$	7.68466			0.443674
$301$	−1.43845	+	2.49146i	−0.0829107	+	0.143606i
$302$	8.71922	−	15.1021i	0.501735	−	0.869030i
$303$	9.78078	+	16.9408i	0.561891	+	0.973224i
$304$	7.68466			0.440745
$305$	−1.78078	−	3.08440i	−0.101967	−	0.176612i
$306$	2.50000	+	4.33013i	0.142915	+	0.247537i
$307$	−33.9309			−1.93654			−0.968269	−	0.249912i	$-0.919598\pi$
$307$	−33.9309			−1.93654			−0.968269	+	0.249912i	$0.919598\pi$
$308$	1.28078	+	2.21837i	0.0729790	+	0.126403i
$309$	5.68466	−	9.84612i	0.323389	−	0.560126i
$310$	9.12311	−	15.8017i	0.518158	−	0.897475i
$311$	22.5616			1.27935			0.639674	−	0.768646i	$-0.279069\pi$
$311$	22.5616			1.27935			0.639674	+	0.768646i	$0.279069\pi$
$312$	3.34233	+	1.35234i	0.189222	+	0.0765614i
$313$	27.6155			1.56092			0.780461	−	0.625205i	$-0.214984\pi$
$313$	27.6155			1.56092			0.780461	+	0.625205i	$0.214984\pi$
$314$	2.90388	−	5.02967i	0.163876	−	0.283841i
$315$	−1.78078	+	3.08440i	−0.100335	+	0.173786i
$316$	−0.719224	−	1.24573i	−0.0404595	−	0.0700779i
$317$	−11.5616			−0.649362			−0.324681	−	0.945824i	$-0.605257\pi$
$317$	−11.5616			−0.649362			−0.324681	+	0.945824i	$0.605257\pi$
$318$	1.93845	+	3.35749i	0.108703	+	0.188279i
$319$	1.28078	+	2.21837i	0.0717097	+	0.124205i
$320$	−3.56155			−0.199097
$321$	4.71922	+	8.17394i	0.263401	+	0.456225i
$322$	−4.56155	+	7.90084i	−0.254205	+	0.440297i
$323$	19.2116	−	33.2755i	1.06896	−	1.85150i
$324$	1.00000			0.0555556
$325$	−3.84233	−	27.4397i	−0.213134	−	1.52208i
$326$	−1.12311			−0.0622031
$327$	−0.438447	+	0.759413i	−0.0242462	+	0.0419956i
$328$	−2.06155	+	3.57071i	−0.113830	+	0.197160i
$329$	−3.84233	−	6.65511i	−0.211834	−	0.366908i
$330$	−9.12311			−0.502210
$331$	17.6847	+	30.6307i	0.972037	+	1.68362i	0.689386	+	0.724394i	$0.257880\pi$
$331$	17.6847	+	30.6307i	0.972037	+	1.68362i	0.282651	+	0.959223i	$0.408786\pi$
$332$	5.12311	+	8.87348i	0.281167	+	0.486995i
$333$	−9.80776			−0.537462
$334$	−10.2462	−	17.7470i	−0.560648	−	0.971070i
$335$	2.00000	−	3.46410i	0.109272	−	0.189264i
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	−29.4924			−1.60655			−0.803277	−	0.595605i	$-0.796912\pi$
$337$	−29.4924			−1.60655			−0.803277	+	0.595605i	$0.796912\pi$
$338$	3.15767	−	12.6107i	0.171755	−	0.685930i
$339$	16.9309			0.919559
$340$	−8.90388	+	15.4220i	−0.482881	+	0.836374i
$341$	−6.56155	+	11.3649i	−0.355328	+	0.615446i
$342$	−3.84233	−	6.65511i	−0.207769	−	0.359867i
$343$	−1.00000			−0.0539949
$344$	1.43845	+	2.49146i	0.0775559	+	0.134331i
$345$	−16.2462	−	28.1393i	−0.874667	−	1.51497i
$346$	−4.87689			−0.262183
$347$	0.157671	+	0.273094i	0.00846421	+	0.0146604i	0.870226	−	0.492652i	$-0.163972\pi$
$347$	0.157671	+	0.273094i	0.00846421	+	0.0146604i	−0.861762	+	0.507312i	$0.830639\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	3.24621	−	5.62260i	0.173766	−	0.300971i	−0.765968	−	0.642879i	$-0.777740\pi$
$349$	3.24621	−	5.62260i	0.173766	−	0.300971i	0.939733	+	0.341908i	$0.111073\pi$
$350$	−7.68466			−0.410762
$351$	−0.500000	−	3.57071i	−0.0266880	−	0.190591i
$352$	2.56155			0.136531
$353$	4.90388	−	8.49377i	0.261007	−	0.452078i	−0.705503	−	0.708707i	$-0.749279\pi$
$353$	4.90388	−	8.49377i	0.261007	−	0.452078i	0.966510	+	0.256629i	$0.0826120\pi$
$354$	−6.56155	+	11.3649i	−0.348743	+	0.604040i
$355$	−7.12311	−	12.3376i	−0.378055	−	0.654811i
$356$	−9.68466			−0.513286
$357$	−2.50000	−	4.33013i	−0.132314	−	0.229175i
$358$	8.24621	+	14.2829i	0.435826	+	0.754872i
$359$	−4.63068			−0.244398			−0.122199	−	0.992506i	$-0.538995\pi$
$359$	−4.63068			−0.244398			−0.122199	+	0.992506i	$0.538995\pi$
$360$	1.78078	+	3.08440i	0.0938552	+	0.162562i
$361$	−20.0270	+	34.6878i	−1.05405	+	1.82567i
$362$	−6.62311	+	11.4716i	−0.348103	+	0.602932i
$363$	−4.43845			−0.232958
$364$	−3.34233	−	1.35234i	−0.175186	−	0.0708821i
$365$	8.68466			0.454576
$366$	0.500000	−	0.866025i	0.0261354	−	0.0452679i
$367$	−5.68466	+	9.84612i	−0.296737	+	0.513963i	−0.975387	−	0.220498i	$-0.929232\pi$
$367$	−5.68466	+	9.84612i	−0.296737	+	0.513963i	0.678651	+	0.734461i	$0.262565\pi$
$368$	4.56155	+	7.90084i	0.237787	+	0.411860i
$369$	4.12311			0.214640
$370$	−17.4654	−	30.2510i	−0.907985	−	1.57268i
$371$	−1.93845	−	3.35749i	−0.100639	−	0.174312i
$372$	5.12311			0.265621
$373$	−10.7808	−	18.6729i	−0.558207	−	0.966844i	−0.997646	−	0.0685711i	$-0.978156\pi$
$373$	−10.7808	−	18.6729i	−0.558207	−	0.966844i	0.439439	−	0.898273i	$-0.355177\pi$
$374$	6.40388	−	11.0918i	0.331137	−	0.573546i
$375$	4.78078	−	8.28055i	0.246878	−	0.427606i
$376$	−7.68466			−0.396306
$377$	−3.34233	−	1.35234i	−0.172139	−	0.0696493i
$378$	−1.00000			−0.0514344
$379$	−0.246211	+	0.426450i	−0.0126470	+	0.0219053i	−0.872280	−	0.489007i	$-0.837359\pi$
$379$	−0.246211	+	0.426450i	−0.0126470	+	0.0219053i	0.859633	+	0.510913i	$0.170692\pi$
$380$	13.6847	−	23.7025i	0.702008	−	1.21591i
$381$	−1.12311	−	1.94528i	−0.0575384	−	0.0996595i
$382$	5.75379			0.294389
$383$	−4.15767	−	7.20130i	−0.212447	−	0.367969i	0.740033	−	0.672571i	$-0.234810\pi$
$383$	−4.15767	−	7.20130i	−0.212447	−	0.367969i	−0.952480	+	0.304602i	$0.901477\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	9.12311			0.464957
$386$	10.1847	+	17.6403i	0.518385	+	0.897870i
$387$	1.43845	−	2.49146i	0.0731204	−	0.126648i
$388$	−6.12311	+	10.6055i	−0.310854	+	0.538414i
$389$	18.6847			0.947350			0.473675	−	0.880700i	$-0.342927\pi$
$389$	18.6847			0.947350			0.473675	+	0.880700i	$0.342927\pi$
$390$	10.1231	−	7.90084i	0.512603	−	0.400075i
$391$	45.6155			2.30688
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	8.24621	−	14.2829i	0.415966	−	0.720475i
$394$	0.280776	+	0.486319i	0.0141453	+	0.0245004i
$395$	−5.12311			−0.257771
$396$	−1.28078	−	2.21837i	−0.0643614	−	0.111477i
$397$	−0.842329	−	1.45896i	−0.0422753	−	0.0732230i	0.844114	−	0.536164i	$-0.180127\pi$
$397$	−0.842329	−	1.45896i	−0.0422753	−	0.0732230i	−0.886389	+	0.462942i	$0.846794\pi$
$398$	−17.6155			−0.882987
$399$	3.84233	+	6.65511i	0.192357	+	0.333172i
$400$	−3.84233	+	6.65511i	−0.192116	+	0.332755i
$401$	−7.58854	+	13.1437i	−0.378954	+	0.656367i	−0.990910	−	0.134524i	$-0.957049\pi$
$401$	−7.58854	+	13.1437i	−0.378954	+	0.656367i	0.611957	+	0.790891i	$0.290383\pi$
$402$	1.12311			0.0560154
$403$	−2.56155	−	18.2931i	−0.127600	−	0.911247i
$404$	−19.5616			−0.973224
$405$	1.78078	−	3.08440i	0.0884875	−	0.153265i
$406$	−0.500000	+	0.866025i	−0.0248146	+	0.0429801i
$407$	12.5616	+	21.7572i	0.622653	+	1.07847i
$408$	−5.00000			−0.247537
$409$	15.2192	+	26.3605i	0.752542	+	1.30344i	0.946587	+	0.322449i	$0.104506\pi$
$409$	15.2192	+	26.3605i	0.752542	+	1.30344i	−0.194045	+	0.980993i	$0.562161\pi$
$410$	7.34233	+	12.7173i	0.362612	+	0.628062i
$411$	−5.80776			−0.286476
$412$	5.68466	+	9.84612i	0.280063	+	0.485083i
$413$	6.56155	−	11.3649i	0.322873	−	0.559232i
$414$	4.56155	−	7.90084i	0.224188	−	0.388305i
$415$	36.4924			1.79134
$416$	−2.84233	+	2.21837i	−0.139357	+	0.108765i
$417$	−7.68466			−0.376319
$418$	−9.84233	+	17.0474i	−0.481404	+	0.833816i
$419$	−11.3693	+	19.6922i	−0.555427	+	0.962029i	0.442443	+	0.896797i	$0.354112\pi$
$419$	−11.3693	+	19.6922i	−0.555427	+	0.962029i	−0.997870	+	0.0652318i	$0.979221\pi$
$420$	−1.78078	−	3.08440i	−0.0868930	−	0.150503i
$421$	8.43845			0.411265			0.205632	−	0.978629i	$-0.434075\pi$
$421$	8.43845			0.411265			0.205632	+	0.978629i	$0.434075\pi$
$422$	1.43845	+	2.49146i	0.0700225	+	0.121283i
$423$	3.84233	+	6.65511i	0.186820	+	0.323582i
$424$	−3.87689			−0.188279
$425$	19.2116	+	33.2755i	0.931902	+	1.61410i
$426$	2.00000	−	3.46410i	0.0969003	−	0.167836i
$427$	−0.500000	+	0.866025i	−0.0241967	+	0.0419099i
$428$	−9.43845			−0.456225
$429$	−7.28078	+	5.68247i	−0.351519	+	0.274352i
$430$	10.2462			0.494116
$431$	9.36932	−	16.2281i	0.451304	−	0.781682i	−0.547163	−	0.837026i	$-0.684292\pi$
$431$	9.36932	−	16.2281i	0.451304	−	0.781682i	0.998467	+	0.0553443i	$0.0176256\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	2.65767	+	4.60322i	0.127720	+	0.221217i	0.922793	−	0.385297i	$-0.125901\pi$
$433$	2.65767	+	4.60322i	0.127720	+	0.221217i	−0.795073	+	0.606514i	$0.792568\pi$
$434$	−5.12311			−0.245917
$435$	−1.78078	−	3.08440i	−0.0853817	−	0.147885i
$436$	−0.438447	−	0.759413i	−0.0209978	−	0.0363693i
$437$	−70.1080			−3.35372
$438$	1.21922	+	2.11176i	0.0582568	+	0.100904i
$439$	14.2462	−	24.6752i	0.679935	−	1.17768i	−0.295066	−	0.955477i	$-0.595342\pi$
$439$	14.2462	−	24.6752i	0.679935	−	1.17768i	0.975000	−	0.222204i	$-0.0713252\pi$
$440$	4.56155	−	7.90084i	0.217463	−	0.376658i
$441$	1.00000			0.0476190
$442$	2.50000	+	17.8536i	0.118913	+	0.849208i
$443$	−34.4233			−1.63550			−0.817750	−	0.575574i	$-0.804779\pi$
$443$	−34.4233			−1.63550			−0.817750	+	0.575574i	$0.804779\pi$
$444$	4.90388	−	8.49377i	0.232728	−	0.403097i
$445$	−17.2462	+	29.8713i	−0.817549	+	1.41604i
$446$	8.24621	+	14.2829i	0.390469	+	0.676313i
$447$	−17.8078			−0.842278
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	0.571660	−	0.820491i	$-0.306300\pi$
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	−0.996396	+	0.0848262i	$0.972967\pi$
$450$	7.68466			0.362258
$451$	−5.28078	−	9.14657i	−0.248662	−	0.430695i
$452$	−8.46543	+	14.6626i	−0.398181	+	0.689669i
$453$	8.71922	−	15.1021i	0.409665	−	0.709560i
$454$	13.1231			0.615898
$455$	−10.1231	+	7.90084i	−0.474579	+	0.370397i
$456$	7.68466			0.359867
$457$	6.65767	−	11.5314i	0.311433	−	0.539417i	−0.667240	−	0.744843i	$-0.732524\pi$
$457$	6.65767	−	11.5314i	0.311433	−	0.539417i	0.978673	+	0.205425i	$0.0658578\pi$
$458$	−11.4039	+	19.7521i	−0.532868	+	0.922955i
$459$	2.50000	+	4.33013i	0.116690	+	0.202113i
$460$	32.4924			1.51497
$461$	−15.0270	−	26.0275i	−0.699877	−	1.21222i	−0.968509	−	0.248979i	$-0.919905\pi$
$461$	−15.0270	−	26.0275i	−0.699877	−	1.21222i	0.268632	−	0.963243i	$-0.413428\pi$
$462$	1.28078	+	2.21837i	0.0595871	+	0.103208i
$463$	−11.6847			−0.543032			−0.271516	−	0.962434i	$-0.587525\pi$
$463$	−11.6847			−0.543032			−0.271516	+	0.962434i	$0.587525\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$	9.12311	−	15.8017i	0.423074	−	0.732785i
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	28.0000			1.29569			0.647843	−	0.761774i	$-0.275671\pi$
$467$	28.0000			1.29569			0.647843	+	0.761774i	$0.275671\pi$
$468$	3.34233	+	1.35234i	0.154499	+	0.0625121i
$469$	−1.12311			−0.0518602
$470$	−13.6847	+	23.7025i	−0.631226	+	1.09332i
$471$	2.90388	−	5.02967i	0.133804	−	0.231755i
$472$	−6.56155	−	11.3649i	−0.302020	−	0.523114i
$473$	−7.36932			−0.338842
$474$	−0.719224	−	1.24573i	−0.0330350	−	0.0572184i
$475$	−29.5270	−	51.1422i	−1.35479	−	2.34657i
$476$	5.00000			0.229175
$477$	1.93845	+	3.35749i	0.0887554	+	0.153729i
$478$	−2.00000	+	3.46410i	−0.0914779	+	0.158444i
$479$	1.28078	−	2.21837i	0.0585202	−	0.101360i	−0.835281	−	0.549823i	$-0.814695\pi$
$479$	1.28078	−	2.21837i	0.0585202	−	0.101360i	0.893801	+	0.448463i	$0.148028\pi$
$480$	−3.56155			−0.162562
$481$	−32.7808	−	13.2635i	−1.49467	−	0.604762i
$482$	11.3153			0.515400
$483$	−4.56155	+	7.90084i	−0.207558	+	0.359501i
$484$	2.21922	−	3.84381i	0.100874	−	0.174719i
$485$	21.8078	+	37.7722i	0.990240	+	1.71515i
$486$	1.00000			0.0453609
$487$	−11.8423	−	20.5115i	−0.536627	−	0.929466i	−0.999083	−	0.0428230i	$-0.986365\pi$
$487$	−11.8423	−	20.5115i	−0.536627	−	0.929466i	0.462456	−	0.886642i	$-0.346968\pi$
$488$	0.500000	+	0.866025i	0.0226339	+	0.0392031i
$489$	−1.12311			−0.0507886
$490$	1.78078	+	3.08440i	0.0804473	+	0.139339i
$491$	0.876894	−	1.51883i	0.0395737	−	0.0685436i	−0.845560	−	0.533880i	$-0.820733\pi$
$491$	0.876894	−	1.51883i	0.0395737	−	0.0685436i	0.885134	+	0.465337i	$0.154067\pi$
$492$	−2.06155	+	3.57071i	−0.0929420	+	0.160980i
$493$	5.00000			0.225189
$494$	−3.84233	−	27.4397i	−0.172875	−	1.23457i
$495$	−9.12311			−0.410053
$496$	−2.56155	+	4.43674i	−0.115017	+	0.199215i
$497$	−2.00000	+	3.46410i	−0.0897123	+	0.155386i
$498$	5.12311	+	8.87348i	0.229572	+	0.397630i
$499$	−27.3693			−1.22522			−0.612609	−	0.790386i	$-0.709880\pi$
$499$	−27.3693			−1.22522			−0.612609	+	0.790386i	$0.709880\pi$
$500$	4.78078	+	8.28055i	0.213803	+	0.370317i
$501$	−10.2462	−	17.7470i	−0.457767	−	0.792876i
$502$	8.49242			0.379035
$503$	−10.2462	−	17.7470i	−0.456856	−	0.791298i	0.541937	−	0.840419i	$-0.317691\pi$
$503$	−10.2462	−	17.7470i	−0.456856	−	0.791298i	−0.998793	+	0.0491215i	$0.984358\pi$
$504$	0.500000	−	0.866025i	0.0222718	−	0.0385758i
$505$	−34.8348	+	60.3356i	−1.55013	+	2.68490i
$506$	−23.3693			−1.03889
$507$	3.15767	−	12.6107i	0.140237	−	0.560060i
$508$	2.24621			0.0996595
$509$	−13.6577	+	23.6558i	−0.605366	+	1.04852i	0.386628	+	0.922236i	$0.373640\pi$
$509$	−13.6577	+	23.6558i	−0.605366	+	1.04852i	−0.991994	+	0.126288i	$0.959694\pi$
$510$	−8.90388	+	15.4220i	−0.394271	+	0.682897i
$511$	−1.21922	−	2.11176i	−0.0539353	−	0.0934186i
$512$	1.00000			0.0441942
$513$	−3.84233	−	6.65511i	−0.169643	−	0.293830i
$514$	7.37689	+	12.7772i	0.325381	+	0.563576i
$515$	40.4924			1.78431
$516$	1.43845	+	2.49146i	0.0633241	+	0.109681i
$517$	9.84233	−	17.0474i	0.432865	−	0.749744i
$518$	−4.90388	+	8.49377i	−0.215464	+	0.373195i
$519$	−4.87689			−0.214072
$520$	1.78078	+	12.7173i	0.0780922	+	0.557690i
$521$	−17.0000			−0.744784			−0.372392	−	0.928076i	$-0.621462\pi$
$521$	−17.0000			−0.744784			−0.372392	+	0.928076i	$0.621462\pi$
$522$	0.500000	−	0.866025i	0.0218844	−	0.0379049i
$523$	−7.59612	+	13.1569i	−0.332155	+	0.575309i	−0.982934	−	0.183958i	$-0.941109\pi$
$523$	−7.59612	+	13.1569i	−0.332155	+	0.575309i	0.650779	+	0.759267i	$0.274442\pi$
$524$	8.24621	+	14.2829i	0.360237	+	0.623949i
$525$	−7.68466			−0.335386
$526$	10.2462	+	17.7470i	0.446756	+	0.773804i
$527$	12.8078	+	22.1837i	0.557915	+	0.966337i
$528$	2.56155			0.111477
$529$	−30.1155	−	52.1616i	−1.30937	−	2.26790i
$530$	−6.90388	+	11.9579i	−0.299885	+	0.519417i
$531$	−6.56155	+	11.3649i	−0.284747	+	0.493197i
$532$	−7.68466			−0.333172
$533$	13.7808	+	5.57586i	0.596912	+	0.241517i
$534$	−9.68466			−0.419096
$535$	−16.8078	+	29.1119i	−0.726663	+	1.25862i
$536$	−0.561553	+	0.972638i	−0.0242554	+	0.0420116i
$537$	8.24621	+	14.2829i	0.355850	+	0.616351i
$538$	−4.87689			−0.210258
$539$	−1.28078	−	2.21837i	−0.0551669	−	0.0955520i
$540$	1.78078	+	3.08440i	0.0766324	+	0.132731i
$541$	1.56155			0.0671364			0.0335682	−	0.999436i	$-0.489313\pi$
$541$	1.56155			0.0671364			0.0335682	+	0.999436i	$0.489313\pi$
$542$	−6.56155	−	11.3649i	−0.281843	−	0.488166i
$543$	−6.62311	+	11.4716i	−0.284225	+	0.492292i
$544$	2.50000	−	4.33013i	0.107187	−	0.185653i
$545$	−3.12311			−0.133779
$546$	−3.34233	−	1.35234i	−0.143038	−	0.0578750i
$547$	−22.7386			−0.972234			−0.486117	−	0.873894i	$-0.661587\pi$
$547$	−22.7386			−0.972234			−0.486117	+	0.873894i	$0.661587\pi$
$548$	2.90388	−	5.02967i	0.124048	−	0.214857i
$549$	0.500000	−	0.866025i	0.0213395	−	0.0369611i
$550$	−9.84233	−	17.0474i	−0.419678	−	0.726904i
$551$	−7.68466			−0.327377
$552$	4.56155	+	7.90084i	0.194153	+	0.336282i
$553$	0.719224	+	1.24573i	0.0305845	+	0.0529739i
$554$	−3.56155			−0.151316
$555$	−17.4654	−	30.2510i	−0.741366	−	1.28408i
$556$	3.84233	−	6.65511i	0.162951	−	0.282240i
$557$	−10.8693	+	18.8262i	−0.460548	+	0.797692i	−0.998988	−	0.0449714i	$-0.985680\pi$
$557$	−10.8693	+	18.8262i	−0.460548	+	0.797692i	0.538441	+	0.842664i	$0.319014\pi$
$558$	5.12311			0.216878
$559$	8.17708	−	6.38202i	0.345854	−	0.269930i
$560$	3.56155			0.150503
$561$	6.40388	−	11.0918i	0.270372	−	0.468298i
$562$	−3.90388	+	6.76172i	−0.164675	+	0.285226i
$563$	0.315342	+	0.546188i	0.0132901	+	0.0230191i	0.872594	−	0.488446i	$-0.162436\pi$
$563$	0.315342	+	0.546188i	0.0132901	+	0.0230191i	−0.859304	+	0.511465i	$0.829103\pi$
$564$	−7.68466			−0.323582
$565$	30.1501	+	52.2215i	1.26842	+	2.19697i
$566$	−4.24621	−	7.35465i	−0.178482	−	0.309139i
$567$	−1.00000			−0.0419961
$568$	2.00000	+	3.46410i	0.0839181	+	0.145350i
$569$	−5.80776	+	10.0593i	−0.243474	+	0.421710i	−0.961702	−	0.274099i	$-0.911620\pi$
$569$	−5.80776	+	10.0593i	−0.243474	+	0.421710i	0.718227	+	0.695808i	$0.244954\pi$
$570$	13.6847	−	23.7025i	0.573187	−	0.992789i
$571$	13.7538			0.575578			0.287789	−	0.957694i	$-0.407080\pi$
$571$	13.7538			0.575578			0.287789	+	0.957694i	$0.407080\pi$
$572$	−1.28078	−	9.14657i	−0.0535520	−	0.382437i
$573$	5.75379			0.240368
$574$	2.06155	−	3.57071i	0.0860476	−	0.149039i
$575$	35.0540	−	60.7153i	1.46185	−	2.53200i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	31.3153			1.30367			0.651837	−	0.758359i	$-0.273998\pi$
$577$	31.3153			1.30367			0.651837	+	0.758359i	$0.273998\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	10.1847	+	17.6403i	0.423260	+	0.733108i
$580$	3.56155			0.147885
$581$	−5.12311	−	8.87348i	−0.212542	−	0.368134i
$582$	−6.12311	+	10.6055i	−0.253811	+	0.439613i
$583$	4.96543	−	8.60039i	0.205647	−	0.356192i
$584$	−2.43845			−0.100904
$585$	10.1231	−	7.90084i	0.418539	−	0.326660i
$586$	−4.68466			−0.193521
$587$	−15.6847	+	27.1666i	−0.647375	+	1.12129i	0.336372	+	0.941729i	$0.390800\pi$
$587$	−15.6847	+	27.1666i	−0.647375	+	1.12129i	−0.983747	+	0.179558i	$0.942533\pi$
$588$	−0.500000	+	0.866025i	−0.0206197	+	0.0357143i
$589$	−19.6847	−	34.0948i	−0.811092	−	1.40485i
$590$	−46.7386			−1.92420
$591$	0.280776	+	0.486319i	0.0115496	+	0.0200045i
$592$	4.90388	+	8.49377i	0.201548	+	0.349092i
$593$	32.6155			1.33936			0.669680	−	0.742650i	$-0.266431\pi$
$593$	32.6155			1.33936			0.669680	+	0.742650i	$0.266431\pi$
$594$	−1.28078	−	2.21837i	−0.0525509	−	0.0910208i
$595$	8.90388	−	15.4220i	0.365024	−	0.632239i
$596$	8.90388	−	15.4220i	0.364717	−	0.631709i
$597$	−17.6155			−0.720956
$598$	25.9309	−	20.2384i	1.06039	−	0.827611i
$599$	−22.8769			−0.934725			−0.467362	−	0.884066i	$-0.654796\pi$
$599$	−22.8769			−0.934725			−0.467362	+	0.884066i	$0.654796\pi$
$600$	−3.84233	+	6.65511i	−0.156862	+	0.271694i
$601$	−18.4654	+	31.9831i	−0.753221	+	1.30462i	0.193033	+	0.981192i	$0.438167\pi$
$601$	−18.4654	+	31.9831i	−0.753221	+	1.30462i	−0.946254	+	0.323424i	$0.895166\pi$
$602$	−1.43845	−	2.49146i	−0.0586267	−	0.101544i
$603$	1.12311			0.0457364
$604$	8.71922	+	15.1021i	0.354780	+	0.614497i
$605$	−7.90388	−	13.6899i	−0.321339	−	0.556575i
$606$	−19.5616			−0.794634
$607$	−10.5616	−	18.2931i	−0.428680	−	0.742496i	0.568076	−	0.822976i	$-0.307688\pi$
$607$	−10.5616	−	18.2931i	−0.428680	−	0.742496i	−0.996756	+	0.0804802i	$0.974355\pi$
$608$	−3.84233	+	6.65511i	−0.155827	+	0.269900i
$609$	−0.500000	+	0.866025i	−0.0202610	+	0.0350931i
$610$	3.56155			0.144203
$611$	3.84233	+	27.4397i	0.155444	+	1.11009i
$612$	−5.00000			−0.202113
$613$	−18.1501	+	31.4369i	−0.733075	+	1.26972i	0.222487	+	0.974936i	$0.428582\pi$
$613$	−18.1501	+	31.4369i	−0.733075	+	1.26972i	−0.955563	+	0.294788i	$0.904751\pi$
$614$	16.9654	−	29.3850i	0.684669	−	1.18588i
$615$	7.34233	+	12.7173i	0.296071	+	0.512811i
$616$	−2.56155			−0.103208
$617$	13.7116	+	23.7493i	0.552010	+	0.956110i	0.998129	+	0.0611360i	$0.0194723\pi$
$617$	13.7116	+	23.7493i	0.552010	+	0.956110i	−0.446119	+	0.894973i	$0.647194\pi$
$618$	5.68466	+	9.84612i	0.228670	+	0.396069i
$619$	4.31534			0.173448			0.0867241	−	0.996232i	$-0.472360\pi$
$619$	4.31534			0.173448			0.0867241	+	0.996232i	$0.472360\pi$
$620$	9.12311	+	15.8017i	0.366393	+	0.634611i
$621$	4.56155	−	7.90084i	0.183049	−	0.317050i
$622$	−11.2808	+	19.5389i	−0.452318	+	0.783438i
$623$	9.68466			0.388008
$624$	−2.84233	+	2.21837i	−0.113784	+	0.0888059i
$625$	−4.36932			−0.174773
$626$	−13.8078	+	23.9157i	−0.551869	+	0.955866i
$627$	−9.84233	+	17.0474i	−0.393065	+	0.680808i
$628$	2.90388	+	5.02967i	0.115878	+	0.200706i
$629$	49.0388			1.95531
$630$	−1.78078	−	3.08440i	−0.0709478	−	0.122885i
$631$	−11.5961	−	20.0851i	−0.461634	−	0.799574i	0.537408	−	0.843322i	$-0.319403\pi$
$631$	−11.5961	−	20.0851i	−0.461634	−	0.799574i	−0.999043	+	0.0437483i	$0.986070\pi$
$632$	1.43845			0.0572184
$633$	1.43845	+	2.49146i	0.0571731	+	0.0990268i
$634$	5.78078	−	10.0126i	0.229584	−	0.397651i
$635$	4.00000	−	6.92820i	0.158735	−	0.274937i
$636$	−3.87689			−0.153729
$637$	3.34233	+	1.35234i	0.132428	+	0.0535818i
$638$	−2.56155			−0.101413
$639$	2.00000	−	3.46410i	0.0791188	−	0.137038i
$640$	1.78078	−	3.08440i	0.0703914	−	0.121921i
$641$	−18.4654	−	31.9831i	−0.729341	−	1.26326i	−0.957162	−	0.289552i	$-0.906494\pi$
$641$	−18.4654	−	31.9831i	−0.729341	−	1.26326i	0.227821	−	0.973703i	$-0.426840\pi$
$642$	−9.43845			−0.372506
$643$	13.2808	+	23.0030i	0.523743	+	0.907149i	0.999618	+	0.0276362i	$0.00879800\pi$
$643$	13.2808	+	23.0030i	0.523743	+	0.907149i	−0.475875	+	0.879513i	$0.657869\pi$
$644$	−4.56155	−	7.90084i	−0.179750	−	0.311337i
$645$	10.2462			0.403444
$646$	19.2116	+	33.2755i	0.755872	+	1.30921i
$647$	10.4039	−	18.0201i	0.409019	−	0.708441i	−0.585761	−	0.810484i	$-0.699204\pi$
$647$	10.4039	−	18.0201i	0.409019	−	0.708441i	0.994780	+	0.102042i	$0.0325377\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	33.6155			1.31952
$650$	25.6847	+	10.3923i	1.00744	+	0.407620i
$651$	−5.12311			−0.200790
$652$	0.561553	−	0.972638i	0.0219921	−	0.0380914i
$653$	9.40388	−	16.2880i	0.368002	−	0.637399i	−0.621251	−	0.783612i	$-0.713375\pi$
$653$	9.40388	−	16.2880i	0.368002	−	0.637399i	0.989253	+	0.146213i	$0.0467085\pi$
$654$	−0.438447	−	0.759413i	−0.0171446	−	0.0296954i
$655$	58.7386			2.29511
$656$	−2.06155	−	3.57071i	−0.0804901	−	0.139413i
$657$	1.21922	+	2.11176i	0.0475664	+	0.0823875i
$658$	7.68466			0.299579
$659$	14.1577	+	24.5218i	0.551505	+	0.955234i	0.998166	+	0.0605310i	$0.0192794\pi$
$659$	14.1577	+	24.5218i	0.551505	+	0.955234i	−0.446662	+	0.894703i	$0.647387\pi$
$660$	4.56155	−	7.90084i	0.177558	−	0.307540i
$661$	4.90388	−	8.49377i	0.190739	−	0.330369i	−0.754756	−	0.656005i	$-0.772245\pi$
$661$	4.90388	−	8.49377i	0.190739	−	0.330369i	0.945495	+	0.325636i	$0.105578\pi$
$662$	−35.3693			−1.37467
$663$	2.50000	+	17.8536i	0.0970920	+	0.693375i
$664$	−10.2462			−0.397630
$665$	−13.6847	+	23.7025i	−0.530668	+	0.919144i
$666$	4.90388	−	8.49377i	0.190022	−	0.329127i
$667$	−4.56155	−	7.90084i	−0.176624	−	0.305922i
$668$	20.4924			0.792876
$669$	8.24621	+	14.2829i	0.318817	+	0.552207i
$670$	2.00000	+	3.46410i	0.0772667	+	0.133830i
$671$	−2.56155			−0.0988876
$672$	0.500000	+	0.866025i	0.0192879	+	0.0334077i
$673$	−4.37689	+	7.58100i	−0.168717	+	0.292226i	−0.937969	−	0.346719i	$-0.887296\pi$
$673$	−4.37689	+	7.58100i	−0.168717	+	0.292226i	0.769252	+	0.638945i	$0.220629\pi$
$674$	14.7462	−	25.5412i	0.568003	−	0.983810i
$675$	7.68466			0.295783
$676$	9.34233	+	9.03996i	0.359320	+	0.347691i
$677$	−8.38447			−0.322241			−0.161121	−	0.986935i	$-0.551511\pi$
$677$	−8.38447			−0.322241			−0.161121	+	0.986935i	$0.551511\pi$
$678$	−8.46543	+	14.6626i	−0.325113	+	0.563112i
$679$	6.12311	−	10.6055i	0.234983	−	0.407003i
$680$	−8.90388	−	15.4220i	−0.341448	−	0.591406i
$681$	13.1231			0.502879
$682$	−6.56155	−	11.3649i	−0.251255	−	0.435186i
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	0.825222	−	0.564809i	$-0.191050\pi$
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	−0.901750	+	0.432259i	$0.857717\pi$
$684$	7.68466			0.293830
$685$	−10.3423	−	17.9134i	−0.395160	−	0.684437i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	−11.4039	+	19.7521i	−0.435085	+	0.753590i
$688$	−2.87689			−0.109681
$689$	1.93845	+	13.8433i	0.0738490	+	0.527387i
$690$	32.4924			1.23697
$691$	14.2462	−	24.6752i	0.541951	−	0.938687i	−0.456841	−	0.889549i	$-0.651019\pi$
$691$	14.2462	−	24.6752i	0.541951	−	0.938687i	0.998792	−	0.0491388i	$-0.0156477\pi$
$692$	2.43845	−	4.22351i	0.0926959	−	0.160554i
$693$	1.28078	+	2.21837i	0.0486527	+	0.0842689i
$694$	−0.315342			−0.0119702
$695$	−13.6847	−	23.7025i	−0.519089	−	0.899088i
$696$	0.500000	+	0.866025i	0.0189525	+	0.0328266i
$697$	−20.6155			−0.780869
$698$	3.24621	+	5.62260i	0.122871	+	0.212819i
$699$	3.00000	−	5.19615i	0.113470	−	0.196537i
$700$	3.84233	−	6.65511i	0.145226	−	0.251539i
$701$	9.05398			0.341964			0.170982	−	0.985274i	$-0.445306\pi$
$701$	9.05398			0.341964			0.170982	+	0.985274i	$0.445306\pi$
$702$	3.34233	+	1.35234i	0.126148	+	0.0510410i
$703$	−75.3693			−2.84261
$704$	−1.28078	+	2.21837i	−0.0482711	+	0.0836080i
$705$	−13.6847	+	23.7025i	−0.515394	+	0.892689i
$706$	4.90388	+	8.49377i	0.184560	+	0.319667i
$707$	19.5616			0.735688
$708$	−6.56155	−	11.3649i	−0.246598	−	0.427121i
$709$	−10.1501	−	17.5805i	−0.381195	−	0.660249i	0.610039	−	0.792372i	$-0.291154\pi$
$709$	−10.1501	−	17.5805i	−0.381195	−	0.660249i	−0.991233	+	0.132123i	$0.957821\pi$
$710$	14.2462			0.534651
$711$	−0.719224	−	1.24573i	−0.0269730	−	0.0467186i
$712$	4.84233	−	8.38716i	0.181474	−	0.314322i
$713$	23.3693	−	40.4768i	0.875188	−	1.51587i
$714$	5.00000			0.187120
$715$	−30.4924	−	12.3376i	−1.14035	−	0.461399i
$716$	−16.4924			−0.616351
$717$	−2.00000	+	3.46410i	−0.0746914	+	0.129369i
$718$	2.31534	−	4.01029i	0.0864078	−	0.149663i
$719$	−10.9654	−	18.9927i	−0.408942	−	0.708308i	0.585830	−	0.810434i	$-0.300769\pi$
$719$	−10.9654	−	18.9927i	−0.408942	−	0.708308i	−0.994771	+	0.102126i	$0.967435\pi$
$720$	−3.56155			−0.132731
$721$	−5.68466	−	9.84612i	−0.211708	−	0.366689i
$722$	−20.0270	−	34.6878i	−0.745327	−	1.29094i
$723$	11.3153			0.420822
$724$	−6.62311	−	11.4716i	−0.246146	−	0.426337i
$725$	3.84233	−	6.65511i	0.142701	−	0.247165i
$726$	2.21922	−	3.84381i	0.0823631	−	0.142657i
$727$	50.2462			1.86353			0.931764	−	0.363063i	$-0.118269\pi$
$727$	50.2462			1.86353			0.931764	+	0.363063i	$0.118269\pi$
$728$	2.84233	−	2.21837i	0.105344	−	0.0822183i
$729$	1.00000			0.0370370
$730$	−4.34233	+	7.52113i	−0.160717	+	0.278370i
$731$	−7.19224	+	12.4573i	−0.266014	+	0.460751i
$732$	0.500000	+	0.866025i	0.0184805	+	0.0320092i
$733$	32.6155			1.20468			0.602341	−	0.798239i	$-0.294235\pi$
$733$	32.6155			1.20468			0.602341	+	0.798239i	$0.294235\pi$
$734$	−5.68466	−	9.84612i	−0.209825	−	0.363427i
$735$	1.78078	+	3.08440i	0.0656849	+	0.113770i
$736$	−9.12311			−0.336282
$737$	−1.43845	−	2.49146i	−0.0529859	−	0.0917742i
$738$	−2.06155	+	3.57071i	−0.0758868	+	0.131440i
$739$	−23.6847	+	41.0230i	−0.871254	+	1.50906i	−0.0105542	+	0.999944i	$0.503360\pi$
$739$	−23.6847	+	41.0230i	−0.871254	+	1.50906i	−0.860700	+	0.509112i	$0.829974\pi$
$740$	34.9309			1.28408
$741$	−3.84233	−	27.4397i	−0.141151	−	1.00802i
$742$	3.87689			0.142325
$743$	−4.31534	+	7.47439i	−0.158315	+	0.274209i	−0.934261	−	0.356590i	$-0.883939\pi$
$743$	−4.31534	+	7.47439i	−0.158315	+	0.274209i	0.775946	+	0.630799i	$0.217273\pi$
$744$	−2.56155	+	4.43674i	−0.0939111	+	0.162659i
$745$	−31.7116	−	54.9262i	−1.16182	−	2.01234i
$746$	21.5616			0.789425
$747$	5.12311	+	8.87348i	0.187445	+	0.324664i
$748$	6.40388	+	11.0918i	0.234149	+	0.405558i
$749$	9.43845			0.344873
$750$	4.78078	+	8.28055i	0.174569	+	0.302363i
$751$	0.403882	−	0.699544i	0.0147379	−	0.0255267i	−0.858562	−	0.512709i	$-0.828642\pi$
$751$	0.403882	−	0.699544i	0.0147379	−	0.0255267i	0.873300	+	0.487182i	$0.161975\pi$
$752$	3.84233	−	6.65511i	0.140115	−	0.242687i
$753$	8.49242			0.309481
$754$	2.84233	−	2.21837i	0.103512	−	0.0807883i
$755$	62.1080			2.26034
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	3.56155	−	6.16879i	0.129447	−	0.224209i	−0.794016	−	0.607897i	$-0.792013\pi$
$757$	3.56155	−	6.16879i	0.129447	−	0.224209i	0.923462	+	0.383689i	$0.125347\pi$
$758$	−0.246211	−	0.426450i	−0.00894280	−	0.0154894i
$759$	−23.3693			−0.848252
$760$	13.6847	+	23.7025i	0.496395	+	0.859781i
$761$	21.2462	+	36.7995i	0.770175	+	1.33398i	0.937467	+	0.348074i	$0.113164\pi$
$761$	21.2462	+	36.7995i	0.770175	+	1.33398i	−0.167292	+	0.985907i	$0.553502\pi$
$762$	2.24621			0.0813716
$763$	0.438447	+	0.759413i	0.0158729	+	0.0274926i
$764$	−2.87689	+	4.98293i	−0.104082	+	0.180276i
$765$	−8.90388	+	15.4220i	−0.321921	+	0.557583i
$766$	8.31534			0.300446
$767$	−37.3002	+	29.1119i	−1.34683	+	1.05117i
$768$	1.00000			0.0360844
$769$	11.4924	−	19.9055i	0.414427	−	0.717809i	−0.580941	−	0.813946i	$-0.697315\pi$
$769$	11.4924	−	19.9055i	0.414427	−	0.717809i	0.995368	+	0.0961366i	$0.0306486\pi$
$770$	−4.56155	+	7.90084i	−0.164387	+	0.284727i
$771$	7.37689	+	12.7772i	0.265672	+	0.460158i
$772$	−20.3693			−0.733108
$773$	−13.2462	−	22.9431i	−0.476433	−	0.825206i	0.523202	−	0.852209i	$-0.324737\pi$
$773$	−13.2462	−	22.9431i	−0.476433	−	0.825206i	−0.999635	+	0.0270022i	$0.991404\pi$
$774$	1.43845	+	2.49146i	0.0517039	+	0.0895538i
$775$	39.3693			1.41419
$776$	−6.12311	−	10.6055i	−0.219807	−	0.380716i
$777$	−4.90388	+	8.49377i	−0.175926	+	0.304712i
$778$	−9.34233	+	16.1814i	−0.334939	+	0.580131i
$779$	31.6847			1.13522
$780$	1.78078	+	12.7173i	0.0637620	+	0.455352i
$781$	−10.2462			−0.366638
$782$	−22.8078	+	39.5042i	−0.815604	+	1.41267i
$783$	0.500000	−	0.866025i	0.0178685	−	0.0309492i
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	20.6847			0.738267
$786$	8.24621	+	14.2829i	0.294133	+	0.509453i
$787$	−0.403882	−	0.699544i	−0.0143968	−	0.0249361i	0.858737	−	0.512416i	$-0.171249\pi$
$787$	−0.403882	−	0.699544i	−0.0143968	−	0.0249361i	−0.873134	+	0.487480i	$0.837916\pi$
$788$	−0.561553			−0.0200045
$789$	10.2462	+	17.7470i	0.364775	+	0.631808i
$790$	2.56155	−	4.43674i	0.0911360	−	0.157852i
$791$	8.46543	−	14.6626i	0.300996	−	0.521341i
$792$	2.56155			0.0910208
$793$	2.84233	−	2.21837i	0.100934	−	0.0787766i
$794$	1.68466			0.0597863
$795$	−6.90388	+	11.9579i	−0.244855	+	0.424102i
$796$	8.80776	−	15.2555i	0.312183	−	0.540717i
$797$	12.0540	+	20.8781i	0.426974	+	0.739540i	0.996602	−	0.0823619i	$-0.0262463\pi$
$797$	12.0540	+	20.8781i	0.426974	+	0.739540i	−0.569629	+	0.821902i	$0.692913\pi$
$798$	−7.68466			−0.272034
$799$	−19.2116	−	33.2755i	−0.679659	−	1.17720i
$800$	−3.84233	−	6.65511i	−0.135847	−	0.235294i
$801$	−9.68466			−0.342191
$802$	−7.58854	−	13.1437i	−0.267961	−	0.464122i
$803$	3.12311	−	5.40938i	0.110212	−	0.190893i
$804$	−0.561553	+	0.972638i	−0.0198044	+	0.0343023i
$805$	−32.4924			−1.14521
$806$	17.1231	+	6.92820i	0.603136	+	0.244036i
$807$	−4.87689			−0.171675
$808$	9.78078	−	16.9408i	0.344087	−	0.595975i
$809$	5.46543	−	9.46641i	0.192154	−	0.332821i	−0.753810	−	0.657093i	$-0.771786\pi$
$809$	5.46543	−	9.46641i	0.192154	−	0.332821i	0.945964	+	0.324272i	$0.105119\pi$
$810$	1.78078	+	3.08440i	0.0625701	+	0.108375i
$811$	5.75379			0.202043			0.101021	−	0.994884i	$-0.467789\pi$
$811$	5.75379			0.202043			0.101021	+	0.994884i	$0.467789\pi$
$812$	−0.500000	−	0.866025i	−0.0175466	−	0.0303915i
$813$	−6.56155	−	11.3649i	−0.230124	−	0.398586i
$814$	−25.1231			−0.880564
$815$	−2.00000	−	3.46410i	−0.0700569	−	0.121342i
$816$	2.50000	−	4.33013i	0.0875175	−	0.151585i
$817$	11.0540	−	19.1460i	0.386730	−	0.669835i
$818$	−30.4384			−1.06426
$819$	−3.34233	−	1.35234i	−0.116790	−	0.0472547i
$820$	−14.6847			−0.512811
$821$	6.03457	−	10.4522i	0.210608	−	0.364783i	−0.741297	−	0.671177i	$-0.765789\pi$
$821$	6.03457	−	10.4522i	0.210608	−	0.364783i	0.951905	+	0.306394i	$0.0991224\pi$
$822$	2.90388	−	5.02967i	0.101285	−	0.175430i
$823$	−7.12311	−	12.3376i	−0.248296	−	0.430061i	0.714757	−	0.699373i	$-0.246537\pi$
$823$	−7.12311	−	12.3376i	−0.248296	−	0.430061i	−0.963053	+	0.269312i	$0.913204\pi$
$824$	−11.3693			−0.396069
$825$	−9.84233	−	17.0474i	−0.342666	−	0.593515i
$826$	6.56155	+	11.3649i	0.228306	+	0.395437i
$827$	−11.5076			−0.400158			−0.200079	−	0.979780i	$-0.564120\pi$
$827$	−11.5076			−0.400158			−0.200079	+	0.979780i	$0.564120\pi$
$828$	4.56155	+	7.90084i	0.158525	+	0.274573i
$829$	−14.5540	+	25.2082i	−0.505480	+	0.875518i	0.494499	+	0.869178i	$0.335351\pi$
$829$	−14.5540	+	25.2082i	−0.505480	+	0.875518i	−0.999980	+	0.00633989i	$0.997982\pi$
$830$	−18.2462	+	31.6034i	−0.633335	+	1.09697i
$831$	−3.56155			−0.123549
$832$	−0.500000	−	3.57071i	−0.0173344	−	0.123792i
$833$	−5.00000			−0.173240
$834$	3.84233	−	6.65511i	0.133049	−	0.230448i
$835$	36.4924	−	63.2067i	1.26287	−	2.18736i
$836$	−9.84233	−	17.0474i	−0.340404	−	0.589597i
$837$	5.12311			0.177080
$838$	−11.3693	−	19.6922i	−0.392747	−	0.680257i
$839$	−4.00000	−	6.92820i	−0.138095	−	0.239188i	0.788680	−	0.614804i	$-0.210765\pi$
$839$	−4.00000	−	6.92820i	−0.138095	−	0.239188i	−0.926776	+	0.375615i	$0.877431\pi$
$840$	3.56155			0.122885
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	−4.21922	+	7.30791i	−0.145404	+	0.251847i
$843$	−3.90388	+	6.76172i	−0.134457	+	0.232886i
$844$	−2.87689			−0.0990268
$845$	44.5194	−	12.7173i	1.53151	−	0.437488i
$846$	−7.68466			−0.264204
$847$	−2.21922	+	3.84381i	−0.0762534	+	0.132075i
$848$	1.93845	−	3.35749i	0.0665665	−	0.115297i
$849$	−4.24621	−	7.35465i	−0.145730	−	0.252411i
$850$	−38.4233			−1.31791
$851$	−44.7386	−	77.4896i	−1.53362	−	2.65631i
$852$	2.00000	+	3.46410i	0.0685189	+	0.118678i
$853$	−0.369317			−0.0126452			−0.00632258	−	0.999980i	$-0.502013\pi$
$853$	−0.369317			−0.0126452			−0.00632258	+	0.999980i	$0.502013\pi$
$854$	−0.500000	−	0.866025i	−0.0171096	−	0.0296348i
$855$	13.6847	−	23.7025i	0.468005	−	0.810609i
$856$	4.71922	−	8.17394i	0.161300	−	0.279379i
$857$	−22.3002			−0.761760			−0.380880	−	0.924625i	$-0.624379\pi$
$857$	−22.3002			−0.761760			−0.380880	+	0.924625i	$0.624379\pi$
$858$	−1.28078	−	9.14657i	−0.0437250	−	0.312259i
$859$	−36.8078			−1.25586			−0.627932	−	0.778268i	$-0.716099\pi$
$859$	−36.8078			−1.25586			−0.627932	+	0.778268i	$0.716099\pi$
$860$	−5.12311	+	8.87348i	−0.174696	+	0.302583i
$861$	2.06155	−	3.57071i	0.0702575	−	0.121690i
$862$	9.36932	+	16.2281i	0.319120	+	0.552732i
$863$	26.1080			0.888725			0.444362	−	0.895847i	$-0.353430\pi$
$863$	26.1080			0.888725			0.444362	+	0.895847i	$0.353430\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−8.68466	−	15.0423i	−0.295287	−	0.511453i
$866$	−5.31534			−0.180623
$867$	−4.00000	−	6.92820i	−0.135847	−	0.235294i
$868$	2.56155	−	4.43674i	0.0869448	−	0.150593i
$869$	−1.84233	+	3.19101i	−0.0624967	+	0.108248i
$870$	3.56155			0.120748
$871$	3.75379	+	1.51883i	0.127192	+	0.0514634i
$872$	0.876894			0.0296954
$873$	−6.12311	+	10.6055i	−0.207236	+	0.358943i
$874$	35.0540	−	60.7153i	1.18572	−	2.05372i
$875$	−4.78078	−	8.28055i	−0.161620	−	0.279934i
$876$	−2.43845			−0.0823875
$877$	−4.15009	−	7.18817i	−0.140139	−	0.242727i	0.787410	−	0.616430i	$-0.211422\pi$
$877$	−4.15009	−	7.18817i	−0.140139	−	0.242727i	−0.927549	+	0.373702i	$0.878088\pi$
$878$	14.2462	+	24.6752i	0.480786	+	0.832746i
$879$	−4.68466			−0.158010
$880$	4.56155	+	7.90084i	0.153770	+	0.266337i
$881$	−23.5885	+	40.8566i	−0.794718	+	1.37649i	0.128300	+	0.991735i	$0.459048\pi$
$881$	−23.5885	+	40.8566i	−0.794718	+	1.37649i	−0.923018	+	0.384757i	$0.874285\pi$
$882$	−0.500000	+	0.866025i	−0.0168359	+	0.0291606i
$883$	17.1231			0.576238			0.288119	−	0.957595i	$-0.406970\pi$
$883$	17.1231			0.576238			0.288119	+	0.957595i	$0.406970\pi$
$884$	−16.7116	−	6.76172i	−0.562073	−	0.227421i
$885$	−46.7386			−1.57110
$886$	17.2116	−	29.8114i	0.578237	−	1.00154i
$887$	−2.71922	+	4.70983i	−0.0913026	+	0.158141i	−0.908059	−	0.418841i	$-0.862436\pi$
$887$	−2.71922	+	4.70983i	−0.0913026	+	0.158141i	0.816757	+	0.576982i	$0.195770\pi$
$888$	4.90388	+	8.49377i	0.164564	+	0.285032i
$889$	−2.24621			−0.0753355
$890$	−17.2462	−	29.8713i	−0.578094	−	1.00129i
$891$	−1.28078	−	2.21837i	−0.0429076	−	0.0743182i
$892$	−16.4924			−0.552207
$893$	29.5270	+	51.1422i	0.988083	+	1.71141i
$894$	8.90388	−	15.4220i	0.297790	−	0.515788i
$895$	−29.3693	+	50.8691i	−0.981708	+	1.70037i
$896$	−1.00000			−0.0334077
$897$	25.9309	−	20.2384i	0.865807	−	0.675741i
$898$	18.0000			0.600668
$899$	2.56155	−	4.43674i	0.0854326	−	0.147974i
$900$	−3.84233	+	6.65511i	−0.128078	+	0.221837i
$901$	−9.69224	−	16.7874i	−0.322895	−	0.559271i
$902$	10.5616			0.351661
$903$	−1.43845	−	2.49146i	−0.0478685	−	0.0829107i
$904$	−8.46543	−	14.6626i	−0.281556	−	0.487670i
$905$	−47.1771			−1.56822
$906$	8.71922	+	15.1021i	0.289677	+	0.501735i
$907$	−11.4384	+	19.8120i	−0.379807	+	0.657846i	−0.991034	−	0.133610i	$-0.957343\pi$
$907$	−11.4384	+	19.8120i	−0.379807	+	0.657846i	0.611227	+	0.791456i	$0.290676\pi$
$908$	−6.56155	+	11.3649i	−0.217753	+	0.377159i
$909$	−19.5616			−0.648816
$910$	−1.78078	−	12.7173i	−0.0590322	−	0.421574i
$911$	−5.26137			−0.174317			−0.0871584	−	0.996194i	$-0.527779\pi$
$911$	−5.26137			−0.174317			−0.0871584	+	0.996194i	$0.527779\pi$
$912$	−3.84233	+	6.65511i	−0.127232	+	0.220373i
$913$	13.1231	−	22.7299i	0.434311	−	0.752249i
$914$	6.65767	+	11.5314i	0.220216	+	0.381426i
$915$	3.56155			0.117741
$916$	−11.4039	−	19.7521i	−0.376795	−	0.652628i
$917$	−8.24621	−	14.2829i	−0.272314	−	0.471661i
$918$	−5.00000			−0.165025
$919$	−3.28078	−	5.68247i	−0.108223	−	0.187447i	0.806828	−	0.590787i	$-0.201183\pi$
$919$	−3.28078	−	5.68247i	−0.108223	−	0.187447i	−0.915050	+	0.403340i	$0.867849\pi$
$920$	−16.2462	+	28.1393i	−0.535622	+	0.927724i
$921$	16.9654	−	29.3850i	0.559030	−	0.968269i
$922$	30.0540			0.989775
$923$	11.3693	−	8.87348i	0.374226	−	0.292074i
$924$	−2.56155			−0.0842689
$925$	37.6847	−	65.2717i	1.23906	−	2.14612i
$926$	5.84233	−	10.1192i	0.191991	−	0.332538i
$927$	5.68466	+	9.84612i	0.186709	+	0.323389i
$928$	−1.00000			−0.0328266
$929$	3.30776	+	5.72922i	0.108524	+	0.187969i	0.915173	−	0.403062i	$-0.132054\pi$
$929$	3.30776	+	5.72922i	0.108524	+	0.187969i	−0.806648	+	0.591032i	$0.798721\pi$
$930$	9.12311	+	15.8017i	0.299158	+	0.518158i
$931$	7.68466			0.251855
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$	−11.2808	+	19.5389i	−0.369316	+	0.639674i
$934$	−14.0000	+	24.2487i	−0.458094	+	0.793442i
$935$	45.6155			1.49179
$936$	−2.84233	+	2.21837i	−0.0929044	+	0.0725097i
$937$	13.5616			0.443037			0.221518	−	0.975156i	$-0.428899\pi$
$937$	13.5616			0.443037			0.221518	+	0.975156i	$0.428899\pi$
$938$	0.561553	−	0.972638i	0.0183353	−	0.0317578i
$939$	−13.8078	+	23.9157i	−0.450599	+	0.780461i
$940$	−13.6847	−	23.7025i	−0.446344	−	0.773091i
$941$	53.3693			1.73979			0.869895	−	0.493237i	$-0.164186\pi$
$941$	53.3693			1.73979			0.869895	+	0.493237i	$0.164186\pi$
$942$	2.90388	+	5.02967i	0.0946136	+	0.163876i
$943$	18.8078	+	32.5760i	0.612465	+	1.06082i
$944$	13.1231			0.427121
$945$	−1.78078	−	3.08440i	−0.0579287	−	0.100335i
$946$	3.68466	−	6.38202i	0.119799	−	0.207497i
$947$	0.157671	−	0.273094i	0.00512361	−	0.00887436i	−0.863452	−	0.504431i	$-0.831702\pi$
$947$	0.157671	−	0.273094i	0.00512361	−	0.00887436i	0.868576	+	0.495556i	$0.165036\pi$
$948$	1.43845			0.0467186
$949$	1.21922	+	8.70700i	0.0395777	+	0.282641i
$950$	59.0540			1.91596
$951$	5.78078	−	10.0126i	0.187455	−	0.324681i
$952$	−2.50000	+	4.33013i	−0.0810255	+	0.140340i
$953$	26.3693	+	45.6730i	0.854186	+	1.47949i	0.877398	+	0.479763i	$0.159277\pi$
$953$	26.3693	+	45.6730i	0.854186	+	1.47949i	−0.0232122	+	0.999731i	$0.507389\pi$
$954$	−3.87689			−0.125519
$955$	10.2462	+	17.7470i	0.331560	+	0.574278i
$956$	−2.00000	−	3.46410i	−0.0646846	−	0.112037i
$957$	−2.56155			−0.0828032
$958$	1.28078	+	2.21837i	0.0413800	+	0.0716723i
$959$	−2.90388	+	5.02967i	−0.0937712	+	0.162417i
$960$	1.78078	−	3.08440i	0.0574743	−	0.0995484i
$961$	−4.75379			−0.153348
$962$	27.8769	−	21.7572i	0.898787	−	0.701482i
$963$	−9.43845			−0.304150
$964$	−5.65767	+	9.79937i	−0.182221	+	0.315617i
$965$	−36.2732	+	62.8270i	−1.16768	+	2.02247i
$966$	−4.56155	−	7.90084i	−0.146766	−	0.254205i
$967$	−4.49242			−0.144467			−0.0722333	−	0.997388i	$-0.523013\pi$
$967$	−4.49242			−0.144467			−0.0722333	+	0.997388i	$0.523013\pi$
$968$	2.21922	+	3.84381i	0.0713285	+	0.123545i
$969$	19.2116	+	33.2755i	0.617167	+	1.06896i
$970$	−43.6155			−1.40041
$971$	5.43845	+	9.41967i	0.174528	+	0.302291i	0.939998	−	0.341180i	$-0.110827\pi$
$971$	5.43845	+	9.41967i	0.174528	+	0.302291i	−0.765470	+	0.643472i	$0.777493\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−3.84233	+	6.65511i	−0.123179	+	0.213353i
$974$	23.6847			0.758905
$975$	25.6847	+	10.3923i	0.822567	+	0.332820i
$976$	−1.00000			−0.0320092
$977$	−1.02699	+	1.77879i	−0.0328562	+	0.0569087i	−0.881986	−	0.471276i	$-0.843794\pi$
$977$	−1.02699	+	1.77879i	−0.0328562	+	0.0569087i	0.849130	+	0.528184i	$0.177127\pi$
$978$	0.561553	−	0.972638i	0.0179565	−	0.0311015i
$979$	12.4039	+	21.4842i	0.396430	+	0.686637i
$980$	−3.56155			−0.113770
$981$	−0.438447	−	0.759413i	−0.0139985	−	0.0242462i
$982$	0.876894	+	1.51883i	0.0279828	+	0.0484677i
$983$	55.2311			1.76160			0.880799	−	0.473491i	$-0.157006\pi$
$983$	55.2311			1.76160			0.880799	+	0.473491i	$0.157006\pi$
$984$	−2.06155	−	3.57071i	−0.0657199	−	0.113830i
$985$	−1.00000	+	1.73205i	−0.0318626	+	0.0551877i
$986$	−2.50000	+	4.33013i	−0.0796162	+	0.137899i
$987$	7.68466			0.244605
$988$	25.6847	+	10.3923i	0.817138	+	0.330623i
$989$	26.2462			0.834581
$990$	4.56155	−	7.90084i	0.144976	−	0.251105i
$991$	0.719224	−	1.24573i	0.0228469	−	0.0395720i	−0.854376	−	0.519655i	$-0.826060\pi$
$991$	0.719224	−	1.24573i	0.0228469	−	0.0395720i	0.877223	+	0.480084i	$0.159394\pi$
$992$	−2.56155	−	4.43674i	−0.0813294	−	0.140867i
$993$	−35.3693			−1.12241
$994$	−2.00000	−	3.46410i	−0.0634361	−	0.109875i
$995$	−31.3693	−	54.3333i	−0.994474	−	1.72248i
$996$	−10.2462			−0.324664
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	0.968655	−	0.248410i	$-0.0799082\pi$
$997$	8.50000	+	14.7224i	0.269198	+	0.466264i	−0.699457	+	0.714675i	$0.746575\pi$
$998$	13.6847	−	23.7025i	0.433180	−	0.750290i
$999$	4.90388	−	8.49377i	0.155152	−	0.268731i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.56155 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -3.56155 q^{5} +(-0.500000 - 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.78078 - 3.08440i) q^{10} +(-1.28078 + 2.21837i) q^{11} +1.00000 q^{12} +(-0.500000 - 3.57071i) q^{13} -1.00000 q^{14} +(1.78078 - 3.08440i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.50000 + 4.33013i) q^{17} +1.00000 q^{18} +(-3.84233 - 6.65511i) q^{19} +(1.78078 + 3.08440i) q^{20} -1.00000 q^{21} +(-1.28078 - 2.21837i) q^{22} +(4.56155 - 7.90084i) q^{23} +(-0.500000 + 0.866025i) q^{24} +7.68466 q^{25} +(3.34233 + 1.35234i) q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(0.500000 - 0.866025i) q^{29} +(1.78078 + 3.08440i) q^{30} +5.12311 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.28078 - 2.21837i) q^{33} -5.00000 q^{34} +(-1.78078 - 3.08440i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(4.90388 - 8.49377i) q^{37} +7.68466 q^{38} +(3.34233 + 1.35234i) q^{39} -3.56155 q^{40} +(-2.06155 + 3.57071i) q^{41} +(0.500000 - 0.866025i) q^{42} +(1.43845 + 2.49146i) q^{43} +2.56155 q^{44} +(1.78078 + 3.08440i) q^{45} +(4.56155 + 7.90084i) q^{46} -7.68466 q^{47} +(-0.500000 - 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(-3.84233 + 6.65511i) q^{50} -5.00000 q^{51} +(-2.84233 + 2.21837i) q^{52} -3.87689 q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.56155 - 7.90084i) q^{55} +(0.500000 + 0.866025i) q^{56} +7.68466 q^{57} +(0.500000 + 0.866025i) q^{58} +(-6.56155 - 11.3649i) q^{59} -3.56155 q^{60} +(0.500000 + 0.866025i) q^{61} +(-2.56155 + 4.43674i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(1.78078 + 12.7173i) q^{65} +2.56155 q^{66} +(-0.561553 + 0.972638i) q^{67} +(2.50000 - 4.33013i) q^{68} +(4.56155 + 7.90084i) q^{69} +3.56155 q^{70} +(2.00000 + 3.46410i) q^{71} +(-0.500000 - 0.866025i) q^{72} -2.43845 q^{73} +(4.90388 + 8.49377i) q^{74} +(-3.84233 + 6.65511i) q^{75} +(-3.84233 + 6.65511i) q^{76} -2.56155 q^{77} +(-2.84233 + 2.21837i) q^{78} +1.43845 q^{79} +(1.78078 - 3.08440i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-2.06155 - 3.57071i) q^{82} -10.2462 q^{83} +(0.500000 + 0.866025i) q^{84} +(-8.90388 - 15.4220i) q^{85} -2.87689 q^{86} +(0.500000 + 0.866025i) q^{87} +(-1.28078 + 2.21837i) q^{88} +(4.84233 - 8.38716i) q^{89} -3.56155 q^{90} +(2.84233 - 2.21837i) q^{91} -9.12311 q^{92} +(-2.56155 + 4.43674i) q^{93} +(3.84233 - 6.65511i) q^{94} +(13.6847 + 23.7025i) q^{95} +1.00000 q^{96} +(-6.12311 - 10.6055i) q^{97} +(-0.500000 - 0.866025i) q^{98} +2.56155 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} - 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 3 q^{10} - q^{11} + 4 q^{12} - 2 q^{13} - 4 q^{14} + 3 q^{15} - 2 q^{16} + 10 q^{17} + 4 q^{18} - 3 q^{19} + 3 q^{20} - 4 q^{21} - q^{22} + 10 q^{23} - 2 q^{24} + 6 q^{25} + q^{26} + 4 q^{27} + 2 q^{28} + 2 q^{29} + 3 q^{30} + 4 q^{31} - 2 q^{32} - q^{33} - 20 q^{34} - 3 q^{35} - 2 q^{36} - q^{37} + 6 q^{38} + q^{39} - 6 q^{40} + 2 q^{42} + 14 q^{43} + 2 q^{44} + 3 q^{45} + 10 q^{46} - 6 q^{47} - 2 q^{48} - 2 q^{49} - 3 q^{50} - 20 q^{51} + q^{52} - 32 q^{53} - 2 q^{54} + 10 q^{55} + 2 q^{56} + 6 q^{57} + 2 q^{58} - 18 q^{59} - 6 q^{60} + 2 q^{61} - 2 q^{62} + 2 q^{63} + 4 q^{64} + 3 q^{65} + 2 q^{66} + 6 q^{67} + 10 q^{68} + 10 q^{69} + 6 q^{70} + 8 q^{71} - 2 q^{72} - 18 q^{73} - q^{74} - 3 q^{75} - 3 q^{76} - 2 q^{77} + q^{78} + 14 q^{79} + 3 q^{80} - 2 q^{81} - 8 q^{83} + 2 q^{84} - 15 q^{85} - 28 q^{86} + 2 q^{87} - q^{88} + 7 q^{89} - 6 q^{90} - q^{91} - 20 q^{92} - 2 q^{93} + 3 q^{94} + 30 q^{95} + 4 q^{96} - 8 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 3 * q^10 - q^11 + 4 * q^12 - 2 * q^13 - 4 * q^14 + 3 * q^15 - 2 * q^16 + 10 * q^17 + 4 * q^18 - 3 * q^19 + 3 * q^20 - 4 * q^21 - q^22 + 10 * q^23 - 2 * q^24 + 6 * q^25 + q^26 + 4 * q^27 + 2 * q^28 + 2 * q^29 + 3 * q^30 + 4 * q^31 - 2 * q^32 - q^33 - 20 * q^34 - 3 * q^35 - 2 * q^36 - q^37 + 6 * q^38 + q^39 - 6 * q^40 + 2 * q^42 + 14 * q^43 + 2 * q^44 + 3 * q^45 + 10 * q^46 - 6 * q^47 - 2 * q^48 - 2 * q^49 - 3 * q^50 - 20 * q^51 + q^52 - 32 * q^53 - 2 * q^54 + 10 * q^55 + 2 * q^56 + 6 * q^57 + 2 * q^58 - 18 * q^59 - 6 * q^60 + 2 * q^61 - 2 * q^62 + 2 * q^63 + 4 * q^64 + 3 * q^65 + 2 * q^66 + 6 * q^67 + 10 * q^68 + 10 * q^69 + 6 * q^70 + 8 * q^71 - 2 * q^72 - 18 * q^73 - q^74 - 3 * q^75 - 3 * q^76 - 2 * q^77 + q^78 + 14 * q^79 + 3 * q^80 - 2 * q^81 - 8 * q^83 + 2 * q^84 - 15 * q^85 - 28 * q^86 + 2 * q^87 - q^88 + 7 * q^89 - 6 * q^90 - q^91 - 20 * q^92 - 2 * q^93 + 3 * q^94 + 30 * q^95 + 4 * q^96 - 8 * q^97 - 2 * q^98 + 2 * q^99

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