LMFDB - Embedded newform 546.2.g.c.209.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(209,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("546.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.g (of order $2$, degree $1$, 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:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 4x^{10} - 8x^{8} + 26x^{7} - 50x^{6} + 78x^{5} - 72x^{4} + 324x^{2} - 486x + 729 $ x^12 - 2x^11 + 4x^10 - 8x^8 + 26x^7 - 50x^6 + 78x^5 - 72x^4 + 324x^2 - 486*x + 729
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.5
Root			$1.07299 - 1.35967i$ of defining polynomial
Character	$\chi$	$=$	546.209
Dual form			546.2.g.c.209.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.35967 - 1.07299i) q^{3} -1.00000 q^{4} -0.745238 q^{5} +(-1.07299 - 1.35967i) q^{6} +(-2.35778 - 1.20037i) q^{7} +1.00000i q^{8} +(0.697395 - 2.91781i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.35967 - 1.07299i) q^{3} -1.00000 q^{4} -0.745238 q^{5} +(-1.07299 - 1.35967i) q^{6} +(-2.35778 - 1.20037i) q^{7} +1.00000i q^{8} +(0.697395 - 2.91781i) q^{9} +0.745238i q^{10} -2.89121i q^{11} +(-1.35967 + 1.07299i) q^{12} -1.00000i q^{13} +(-1.20037 + 2.35778i) q^{14} +(-1.01328 + 0.799631i) q^{15} +1.00000 q^{16} -2.53678 q^{17} +(-2.91781 - 0.697395i) q^{18} +4.50115i q^{19} +0.745238 q^{20} +(-4.49378 + 0.897763i) q^{21} -2.89121 q^{22} -5.62123i q^{23} +(1.07299 + 1.35967i) q^{24} -4.44462 q^{25} -1.00000 q^{26} +(-2.18255 - 4.71556i) q^{27} +(2.35778 + 1.20037i) q^{28} -7.30263i q^{29} +(0.799631 + 1.01328i) q^{30} +6.18608i q^{31} -1.00000i q^{32} +(-3.10224 - 3.93109i) q^{33} +2.53678i q^{34} +(1.75711 + 0.894561i) q^{35} +(-0.697395 + 2.91781i) q^{36} +9.19762 q^{37} +4.50115 q^{38} +(-1.07299 - 1.35967i) q^{39} -0.745238i q^{40} -3.79553 q^{41} +(0.897763 + 4.49378i) q^{42} -5.86153 q^{43} +2.89121i q^{44} +(-0.519725 + 2.17447i) q^{45} -5.62123 q^{46} +12.0866 q^{47} +(1.35967 - 1.07299i) q^{48} +(4.11823 + 5.66040i) q^{49} +4.44462i q^{50} +(-3.44918 + 2.72194i) q^{51} +1.00000i q^{52} -5.09343i q^{53} +(-4.71556 + 2.18255i) q^{54} +2.15464i q^{55} +(1.20037 - 2.35778i) q^{56} +(4.82968 + 6.12007i) q^{57} -7.30263 q^{58} +12.0957 q^{59} +(1.01328 - 0.799631i) q^{60} -9.20452i q^{61} +6.18608 q^{62} +(-5.14675 + 6.04243i) q^{63} -1.00000 q^{64} +0.745238i q^{65} +(-3.93109 + 3.10224i) q^{66} +3.54888 q^{67} +2.53678 q^{68} +(-6.03151 - 7.64300i) q^{69} +(0.894561 - 1.75711i) q^{70} +0.765844i q^{71} +(2.91781 + 0.697395i) q^{72} +6.83961i q^{73} -9.19762i q^{74} +(-6.04321 + 4.76902i) q^{75} -4.50115i q^{76} +(-3.47052 + 6.81684i) q^{77} +(-1.35967 + 1.07299i) q^{78} +14.3002 q^{79} -0.745238 q^{80} +(-8.02728 - 4.06974i) q^{81} +3.79553i q^{82} -8.53210 q^{83} +(4.49378 - 0.897763i) q^{84} +1.89051 q^{85} +5.86153i q^{86} +(-7.83563 - 9.92915i) q^{87} +2.89121 q^{88} +1.62733 q^{89} +(2.17447 + 0.519725i) q^{90} +(-1.20037 + 2.35778i) q^{91} +5.62123i q^{92} +(6.63758 + 8.41101i) q^{93} -12.0866i q^{94} -3.35443i q^{95} +(-1.07299 - 1.35967i) q^{96} -1.89413i q^{97} +(5.66040 - 4.11823i) q^{98} +(-8.43602 - 2.01632i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{3} - 12 q^{4} + 4 q^{5} - 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) $ 12 * q - 2 * q^3 - 12 * q^4 + 4 * q^5 - 2 * q^6 - 8 * q^7 + 4 * q^9	$ 12 q - 2 q^{3} - 12 q^{4} + 4 q^{5} - 2 q^{6} - 8 q^{7} + 4 q^{9} + 2 q^{12} - 10 q^{14} + 4 q^{15} + 12 q^{16} - 12 q^{17} + 8 q^{18} - 4 q^{20} + 2 q^{24} + 20 q^{25} - 12 q^{26} - 8 q^{27} + 8 q^{28} + 14 q^{30} - 46 q^{33} + 22 q^{35} - 4 q^{36} + 16 q^{37} + 8 q^{38} - 2 q^{39} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 24 q^{46} + 68 q^{47} - 2 q^{48} + 26 q^{49} - 50 q^{51} - 16 q^{54} + 10 q^{56} - 28 q^{57} - 24 q^{58} - 8 q^{59} - 4 q^{60} - 16 q^{62} + 2 q^{63} - 12 q^{64} + 12 q^{66} + 8 q^{67} + 12 q^{68} + 24 q^{69} - 28 q^{70} - 8 q^{72} - 92 q^{75} + 8 q^{77} + 2 q^{78} + 36 q^{79} + 4 q^{80} + 16 q^{81} + 32 q^{83} - 8 q^{87} + 48 q^{89} - 2 q^{90} - 10 q^{91} + 8 q^{93} - 2 q^{96} - 16 q^{98}+O(q^{100}) $ 12 * q - 2 * q^3 - 12 * q^4 + 4 * q^5 - 2 * q^6 - 8 * q^7 + 4 * q^9 + 2 * q^12 - 10 * q^14 + 4 * q^15 + 12 * q^16 - 12 * q^17 + 8 * q^18 - 4 * q^20 + 2 * q^24 + 20 * q^25 - 12 * q^26 - 8 * q^27 + 8 * q^28 + 14 * q^30 - 46 * q^33 + 22 * q^35 - 4 * q^36 + 16 * q^37 + 8 * q^38 - 2 * q^39 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 24 * q^46 + 68 * q^47 - 2 * q^48 + 26 * q^49 - 50 * q^51 - 16 * q^54 + 10 * q^56 - 28 * q^57 - 24 * q^58 - 8 * q^59 - 4 * q^60 - 16 * q^62 + 2 * q^63 - 12 * q^64 + 12 * q^66 + 8 * q^67 + 12 * q^68 + 24 * q^69 - 28 * q^70 - 8 * q^72 - 92 * q^75 + 8 * q^77 + 2 * q^78 + 36 * q^79 + 4 * q^80 + 16 * q^81 + 32 * q^83 - 8 * q^87 + 48 * q^89 - 2 * q^90 - 10 * q^91 + 8 * q^93 - 2 * q^96 - 16 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.35967	−	1.07299i	0.785005	−	0.619490i
$3$	1.35967	−	1.07299i	0.785005	−	0.619490i
$4$	−1.00000			−0.500000
$5$	−0.745238			−0.333281			−0.166640	−	0.986018i	$-0.553292\pi$
$5$	−0.745238			−0.333281			−0.166640	+	0.986018i	$0.553292\pi$
$6$	−1.07299	−	1.35967i	−0.438045	−	0.555082i
$7$	−2.35778	−	1.20037i	−0.891156	−	0.453697i
$7$	−2.35778	−	1.20037i	−0.891156	−	0.453697i
$8$			1.00000i			0.353553i
$9$	0.697395	−	2.91781i	0.232465	−	0.972605i
$10$			0.745238i			0.235665i
$11$		−	2.89121i		−	0.871734i	−0.900011	−	0.435867i	$-0.856442\pi$
$11$		−	2.89121i		−	0.871734i	0.900011	−	0.435867i	$-0.143558\pi$
$12$	−1.35967	+	1.07299i	−0.392502	+	0.309745i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−1.20037	+	2.35778i	−0.320812	+	0.630143i
$15$	−1.01328	+	0.799631i	−0.261627	+	0.206464i
$16$	1.00000			0.250000
$17$	−2.53678			−0.615260			−0.307630	−	0.951506i	$-0.599536\pi$
$17$	−2.53678			−0.615260			−0.307630	+	0.951506i	$0.599536\pi$
$18$	−2.91781	−	0.697395i	−0.687735	−	0.164378i
$19$			4.50115i			1.03264i	0.856397	+	0.516318i	$0.172698\pi$
$19$			4.50115i			1.03264i	−0.856397	+	0.516318i	$0.827302\pi$
$20$	0.745238			0.166640
$21$	−4.49378	+	0.897763i	−0.980622	+	0.195908i
$22$	−2.89121			−0.616409
$23$		−	5.62123i		−	1.17211i	−0.810272	−	0.586053i	$-0.800681\pi$
$23$		−	5.62123i		−	1.17211i	0.810272	−	0.586053i	$-0.199319\pi$
$24$	1.07299	+	1.35967i	0.219023	+	0.277541i
$25$	−4.44462			−0.888924
$26$	−1.00000			−0.196116
$27$	−2.18255	−	4.71556i	−0.420033	−	0.907509i
$28$	2.35778	+	1.20037i	0.445578	+	0.226848i
$29$		−	7.30263i		−	1.35606i	−0.735032	−	0.678032i	$-0.762833\pi$
$29$		−	7.30263i		−	1.35606i	0.735032	−	0.678032i	$-0.237167\pi$
$30$	0.799631	+	1.01328i	0.145992	+	0.184998i
$31$			6.18608i			1.11105i	0.831499	+	0.555526i	$0.187483\pi$
$31$			6.18608i			1.11105i	−0.831499	+	0.555526i	$0.812517\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−3.10224	−	3.93109i	−0.540030	−	0.684315i
$34$			2.53678i			0.435055i
$35$	1.75711	+	0.894561i	0.297005	+	0.151208i
$36$	−0.697395	+	2.91781i	−0.116232	+	0.486302i
$37$	9.19762			1.51208			0.756040	−	0.654526i	$-0.227132\pi$
$37$	9.19762			1.51208			0.756040	+	0.654526i	$0.227132\pi$
$38$	4.50115			0.730183
$39$	−1.07299	−	1.35967i	−0.171816	−	0.217721i
$40$		−	0.745238i		−	0.117833i
$41$	−3.79553			−0.592762			−0.296381	−	0.955070i	$-0.595780\pi$
$41$	−3.79553			−0.592762			−0.296381	+	0.955070i	$0.595780\pi$
$42$	0.897763	+	4.49378i	0.138528	+	0.693405i
$43$	−5.86153			−0.893875			−0.446938	−	0.894565i	$-0.647485\pi$
$43$	−5.86153			−0.893875			−0.446938	+	0.894565i	$0.647485\pi$
$44$			2.89121i			0.435867i
$45$	−0.519725	+	2.17447i	−0.0774761	+	0.324150i
$46$	−5.62123			−0.828805
$47$	12.0866			1.76301			0.881507	−	0.472172i	$-0.156530\pi$
$47$	12.0866			1.76301			0.881507	+	0.472172i	$0.156530\pi$
$48$	1.35967	−	1.07299i	0.196251	−	0.154872i
$49$	4.11823	+	5.66040i	0.588319	+	0.808629i
$50$			4.44462i			0.628564i
$51$	−3.44918	+	2.72194i	−0.482982	+	0.381147i
$52$			1.00000i			0.138675i
$53$		−	5.09343i		−	0.699636i	−0.936818	−	0.349818i	$-0.886243\pi$
$53$		−	5.09343i		−	0.699636i	0.936818	−	0.349818i	$-0.113757\pi$
$54$	−4.71556	+	2.18255i	−0.641706	+	0.297008i
$55$			2.15464i			0.290532i
$56$	1.20037	−	2.35778i	0.160406	−	0.315071i
$57$	4.82968	+	6.12007i	0.639707	+	0.810624i
$58$	−7.30263			−0.958882
$59$	12.0957			1.57473			0.787365	−	0.616487i	$-0.211445\pi$
$59$	12.0957			1.57473			0.787365	+	0.616487i	$0.211445\pi$
$60$	1.01328	−	0.799631i	0.130813	−	0.103232i
$61$		−	9.20452i		−	1.17852i	−0.807944	−	0.589259i	$-0.799420\pi$
$61$		−	9.20452i		−	1.17852i	0.807944	−	0.589259i	$-0.200580\pi$
$62$	6.18608			0.785633
$63$	−5.14675	+	6.04243i	−0.648430	+	0.761274i
$64$	−1.00000			−0.125000
$65$			0.745238i			0.0924354i
$66$	−3.93109	+	3.10224i	−0.483884	+	0.381859i
$67$	3.54888			0.433565			0.216782	−	0.976220i	$-0.430444\pi$
$67$	3.54888			0.433565			0.216782	+	0.976220i	$0.430444\pi$
$68$	2.53678			0.307630
$69$	−6.03151	−	7.64300i	−0.726108	−	0.920109i
$70$	0.894561	−	1.75711i	0.106920	−	0.210014i
$71$			0.765844i			0.0908889i	0.998967	+	0.0454445i	$0.0144704\pi$
$71$			0.765844i			0.0908889i	−0.998967	+	0.0454445i	$0.985530\pi$
$72$	2.91781	+	0.697395i	0.343868	+	0.0821888i
$73$			6.83961i			0.800516i	0.916403	+	0.400258i	$0.131079\pi$
$73$			6.83961i			0.800516i	−0.916403	+	0.400258i	$0.868921\pi$
$74$		−	9.19762i		−	1.06920i
$75$	−6.04321	+	4.76902i	−0.697810	+	0.550679i
$76$		−	4.50115i		−	0.516318i
$77$	−3.47052	+	6.81684i	−0.395503	+	0.776851i
$78$	−1.35967	+	1.07299i	−0.153952	+	0.121492i
$79$	14.3002			1.60890			0.804449	−	0.594021i	$-0.202461\pi$
$79$	14.3002			1.60890			0.804449	+	0.594021i	$0.202461\pi$
$80$	−0.745238			−0.0833202
$81$	−8.02728	−	4.06974i	−0.891920	−	0.452193i
$82$			3.79553i			0.419146i
$83$	−8.53210			−0.936519			−0.468260	−	0.883591i	$-0.655119\pi$
$83$	−8.53210			−0.936519			−0.468260	+	0.883591i	$0.655119\pi$
$84$	4.49378	−	0.897763i	0.490311	−	0.0979540i
$85$	1.89051			0.205054
$86$			5.86153i			0.632065i
$87$	−7.83563	−	9.92915i	−0.840068	−	1.06452i
$88$	2.89121			0.308204
$89$	1.62733			0.172497			0.0862484	−	0.996274i	$-0.472512\pi$
$89$	1.62733			0.172497			0.0862484	+	0.996274i	$0.472512\pi$
$90$	2.17447	+	0.519725i	0.229209	+	0.0547839i
$91$	−1.20037	+	2.35778i	−0.125833	+	0.247162i
$92$			5.62123i			0.586053i
$93$	6.63758	+	8.41101i	0.688285	+	0.872181i
$94$		−	12.0866i		−	1.24664i
$95$		−	3.35443i		−	0.344157i
$96$	−1.07299	−	1.35967i	−0.109511	−	0.138771i
$97$		−	1.89413i		−	0.192319i	−0.995366	−	0.0961597i	$-0.969344\pi$
$97$		−	1.89413i		−	0.192319i	0.995366	−	0.0961597i	$-0.0306560\pi$
$98$	5.66040	−	4.11823i	0.571787	−	0.416004i
$99$	−8.43602	−	2.01632i	−0.847852	−	0.202648i
$100$	4.44462			0.444462
$101$	−1.61770			−0.160967			−0.0804837	−	0.996756i	$-0.525646\pi$
$101$	−1.61770			−0.160967			−0.0804837	+	0.996756i	$0.525646\pi$
$102$	2.72194	+	3.44918i	0.269512	+	0.341520i
$103$		−	12.1254i		−	1.19475i	−0.801961	−	0.597376i	$-0.796210\pi$
$103$		−	12.1254i		−	1.19475i	0.801961	−	0.597376i	$-0.203790\pi$
$104$	1.00000			0.0980581
$105$	3.34893	−	0.669048i	0.326822	−	0.0652924i
$106$	−5.09343			−0.494717
$107$			5.02216i			0.485511i	0.970088	+	0.242755i	$0.0780513\pi$
$107$			5.02216i			0.485511i	−0.970088	+	0.242755i	$0.921949\pi$
$108$	2.18255	+	4.71556i	0.210016	+	0.453755i
$109$	−6.16260			−0.590270			−0.295135	−	0.955456i	$-0.595365\pi$
$109$	−6.16260			−0.590270			−0.295135	+	0.955456i	$0.595365\pi$
$110$	2.15464			0.205437
$111$	12.5057	−	9.86893i	1.18699	−	0.936718i
$112$	−2.35778	−	1.20037i	−0.222789	−	0.113424i
$113$			6.81623i			0.641217i	0.947212	+	0.320608i	$0.103887\pi$
$113$			6.81623i			0.641217i	−0.947212	+	0.320608i	$0.896113\pi$
$114$	6.12007	−	4.82968i	0.573197	−	0.452341i
$115$			4.18915i			0.390640i
$116$			7.30263i			0.678032i
$117$	−2.91781	−	0.697395i	−0.269752	−	0.0644742i
$118$		−	12.0957i		−	1.11350i
$119$	5.98117	+	3.04507i	0.548293	+	0.279142i
$120$	−0.799631	−	1.01328i	−0.0729960	−	0.0924991i
$121$	2.64088			0.240080
$122$	−9.20452			−0.833338
$123$	−5.16066	+	4.07255i	−0.465321	+	0.367210i
$124$		−	6.18608i		−	0.555526i
$125$	7.03849			0.629542
$126$	6.04243	+	5.14675i	0.538302	+	0.458509i
$127$	17.1017			1.51753			0.758764	−	0.651365i	$-0.225803\pi$
$127$	17.1017			1.51753			0.758764	+	0.651365i	$0.225803\pi$
$128$			1.00000i			0.0883883i
$129$	−7.96974	+	6.28935i	−0.701696	+	0.553746i
$130$	0.745238			0.0653617
$131$	12.6919			1.10889			0.554447	−	0.832219i	$-0.312930\pi$
$131$	12.6919			1.10889			0.554447	+	0.832219i	$0.312930\pi$
$132$	3.10224	+	3.93109i	0.270015	+	0.342158i
$133$	5.40304	−	10.6127i	0.468503	−	0.920239i
$134$		−	3.54888i		−	0.306576i
$135$	1.62652	+	3.51421i	0.139989	+	0.302455i
$136$		−	2.53678i		−	0.217527i
$137$		−	10.2742i		−	0.877781i	−0.898541	−	0.438890i	$-0.855372\pi$
$137$		−	10.2742i		−	0.877781i	0.898541	−	0.438890i	$-0.144628\pi$
$138$	−7.64300	+	6.03151i	−0.650616	+	0.513436i
$139$			12.2986i			1.04316i	0.853203	+	0.521579i	$0.174657\pi$
$139$			12.2986i			1.04316i	−0.853203	+	0.521579i	$0.825343\pi$
$140$	−1.75711	−	0.894561i	−0.148503	−	0.0756042i
$141$	16.4338	−	12.9688i	1.38397	−	1.09217i
$142$	0.765844			0.0642682
$143$	−2.89121			−0.241775
$144$	0.697395	−	2.91781i	0.0581162	−	0.243151i
$145$			5.44220i			0.451950i
$146$	6.83961			0.566050
$147$	11.6730	+	3.27746i	0.962770	+	0.270320i
$148$	−9.19762			−0.756040
$149$		−	13.3876i		−	1.09675i	−0.836232	−	0.548376i	$-0.815246\pi$
$149$		−	13.3876i		−	1.09675i	0.836232	−	0.548376i	$-0.184754\pi$
$150$	4.76902	+	6.04321i	0.389389	+	0.493426i
$151$	−8.09890			−0.659079			−0.329540	−	0.944142i	$-0.606894\pi$
$151$	−8.09890			−0.659079			−0.329540	+	0.944142i	$0.606894\pi$
$152$	−4.50115			−0.365092
$153$	−1.76914	+	7.40186i	−0.143026	+	0.598405i
$154$	6.81684	+	3.47052i	0.549317	+	0.279663i
$155$		−	4.61010i		−	0.370292i
$156$	1.07299	+	1.35967i	0.0859078	+	0.108861i
$157$		−	15.5084i		−	1.23770i	−0.785508	−	0.618851i	$-0.787598\pi$
$157$		−	15.5084i		−	1.23770i	0.785508	−	0.618851i	$-0.212402\pi$
$158$		−	14.3002i		−	1.13766i
$159$	−5.46518	−	6.92537i	−0.433417	−	0.549217i
$160$			0.745238i			0.0589163i
$161$	−6.74754	+	13.2536i	−0.531781	+	1.04453i
$162$	−4.06974	+	8.02728i	−0.319749	+	0.630683i
$163$	−2.92915			−0.229429			−0.114714	−	0.993399i	$-0.536595\pi$
$163$	−2.92915			−0.229429			−0.114714	+	0.993399i	$0.536595\pi$
$164$	3.79553			0.296381
$165$	2.31191	+	2.92960i	0.179982	+	0.228069i
$166$			8.53210i			0.662219i
$167$	−19.6297			−1.51899			−0.759495	−	0.650513i	$-0.774554\pi$
$167$	−19.6297			−1.51899			−0.759495	+	0.650513i	$0.774554\pi$
$168$	−0.897763	−	4.49378i	−0.0692640	−	0.346702i
$169$	−1.00000			−0.0769231
$170$		−	1.89051i		−	0.144995i
$171$	13.1335	+	3.13908i	1.00435	+	0.240051i
$172$	5.86153			0.446938
$173$	23.5070			1.78720			0.893601	−	0.448862i	$-0.148170\pi$
$173$	23.5070			1.78720			0.893601	+	0.448862i	$0.148170\pi$
$174$	−9.92915	+	7.83563i	−0.752727	+	0.594017i
$175$	10.4794	+	5.33518i	0.792170	+	0.403302i
$176$		−	2.89121i		−	0.217933i
$177$	16.4462	−	12.9786i	1.23617	−	0.975529i
$178$		−	1.62733i		−	0.121974i
$179$			11.0408i			0.825225i	0.910907	+	0.412612i	$0.135384\pi$
$179$			11.0408i			0.825225i	−0.910907	+	0.412612i	$0.864616\pi$
$180$	0.519725	−	2.17447i	0.0387380	−	0.162075i
$181$			7.45611i			0.554208i	0.960840	+	0.277104i	$0.0893746\pi$
$181$			7.45611i			0.554208i	−0.960840	+	0.277104i	$0.910625\pi$
$182$	2.35778	+	1.20037i	0.174770	+	0.0889772i
$183$	−9.87633	−	12.5151i	−0.730080	−	0.925142i
$184$	5.62123			0.414402
$185$	−6.85442			−0.503947
$186$	8.41101	−	6.63758i	0.616725	−	0.486691i
$187$			7.33438i			0.536343i
$188$	−12.0866			−0.881507
$189$	−0.514429	+	13.7381i	−0.0374192	+	0.999300i
$190$	−3.35443			−0.243356
$191$			20.0993i			1.45433i	0.686462	+	0.727165i	$0.259163\pi$
$191$			20.0993i			1.45433i	−0.686462	+	0.727165i	$0.740837\pi$
$192$	−1.35967	+	1.07299i	−0.0981256	+	0.0774362i
$193$	−14.8165			−1.06651			−0.533257	−	0.845953i	$-0.679032\pi$
$193$	−14.8165			−1.06651			−0.533257	+	0.845953i	$0.679032\pi$
$194$	−1.89413			−0.135990
$195$	0.799631	+	1.01328i	0.0572628	+	0.0725622i
$196$	−4.11823	−	5.66040i	−0.294159	−	0.404315i
$197$		−	10.6416i		−	0.758181i	−0.925360	−	0.379090i	$-0.876237\pi$
$197$		−	10.6416i		−	0.758181i	0.925360	−	0.379090i	$-0.123763\pi$
$198$	−2.01632	+	8.43602i	−0.143293	+	0.599522i
$199$			0.863102i			0.0611837i	0.999532	+	0.0305918i	$0.00973920\pi$
$199$			0.863102i			0.0611837i	−0.999532	+	0.0305918i	$0.990261\pi$
$200$		−	4.44462i		−	0.314282i
$201$	4.82530	−	3.80790i	0.340350	−	0.268589i
$202$			1.61770i			0.113821i
$203$	−8.76584	+	17.2180i	−0.615242	+	1.20846i
$204$	3.44918	−	2.72194i	0.241491	−	0.190574i
$205$	2.82857			0.197556
$206$	−12.1254			−0.844818
$207$	−16.4017	−	3.92021i	−1.14000	−	0.272474i
$208$		−	1.00000i		−	0.0693375i
$209$	13.0138			0.900183
$210$	−0.669048	−	3.34893i	−0.0461687	−	0.231098i
$211$	−22.1657			−1.52595			−0.762973	−	0.646430i	$-0.776261\pi$
$211$	−22.1657			−1.52595			−0.762973	+	0.646430i	$0.776261\pi$
$212$			5.09343i			0.349818i
$213$	0.821741	+	1.04129i	0.0563048	+	0.0713483i
$214$	5.02216			0.343308
$215$	4.36824			0.297911
$216$	4.71556	−	2.18255i	0.320853	−	0.148504i
$217$	7.42557	−	14.5854i	0.504081	−	0.990121i
$218$			6.16260i			0.417384i
$219$	7.33882	+	9.29960i	0.495911	+	0.628409i
$220$		−	2.15464i		−	0.145266i
$221$			2.53678i			0.170642i
$222$	−9.86893	−	12.5057i	−0.662360	−	0.839328i
$223$			18.1611i			1.21616i	0.793876	+	0.608079i	$0.208060\pi$
$223$			18.1611i			1.21616i	−0.793876	+	0.608079i	$0.791940\pi$
$224$	−1.20037	+	2.35778i	−0.0802030	+	0.157536i
$225$	−3.09966	+	12.9686i	−0.206644	+	0.864572i
$226$	6.81623			0.453409
$227$	20.1759			1.33912			0.669562	−	0.742756i	$-0.266482\pi$
$227$	20.1759			1.33912			0.669562	+	0.742756i	$0.266482\pi$
$228$	−4.82968	−	6.12007i	−0.319853	−	0.405312i
$229$			18.7567i			1.23948i	0.784809	+	0.619738i	$0.212761\pi$
$229$			18.7567i			1.23948i	−0.784809	+	0.619738i	$0.787239\pi$
$230$	4.18915			0.276225
$231$	2.59563	+	12.9925i	0.170780	+	0.854841i
$232$	7.30263			0.479441
$233$		−	13.8783i		−	0.909195i	−0.890697	−	0.454597i	$-0.849783\pi$
$233$		−	13.8783i		−	0.909195i	0.890697	−	0.454597i	$-0.150217\pi$
$234$	−0.697395	+	2.91781i	−0.0455901	+	0.190743i
$235$	−9.00740			−0.587578
$236$	−12.0957			−0.787365
$237$	19.4435	−	15.3439i	1.26299	−	0.996696i
$238$	3.04507	−	5.98117i	0.197383	−	0.387702i
$239$		−	1.08541i		−	0.0702091i	−0.999384	−	0.0351045i	$-0.988824\pi$
$239$		−	1.08541i		−	0.0702091i	0.999384	−	0.0351045i	$-0.0111764\pi$
$240$	−1.01328	+	0.799631i	−0.0654067	+	0.0516160i
$241$		−	27.1249i		−	1.74727i	−0.486581	−	0.873636i	$-0.661756\pi$
$241$		−	27.1249i		−	1.74727i	0.486581	−	0.873636i	$-0.338244\pi$
$242$		−	2.64088i		−	0.169762i
$243$	−15.2812	+	3.07968i	−0.980290	+	0.197562i
$244$			9.20452i			0.589259i
$245$	−3.06906	−	4.21835i	−0.196075	−	0.269500i
$246$	4.07255	+	5.16066i	0.259657	+	0.329031i
$247$	4.50115			0.286401
$248$	−6.18608			−0.392816
$249$	−11.6008	+	9.15484i	−0.735172	+	0.580164i
$250$		−	7.03849i		−	0.445153i
$251$	−20.8040			−1.31314			−0.656570	−	0.754266i	$-0.727993\pi$
$251$	−20.8040			−1.31314			−0.656570	+	0.754266i	$0.727993\pi$
$252$	5.14675	−	6.04243i	0.324215	−	0.380637i
$253$	−16.2522			−1.02176
$254$		−	17.1017i		−	1.07305i
$255$	2.57046	−	2.02849i	0.160969	−	0.127029i
$256$	1.00000			0.0625000
$257$	−11.1048			−0.692695			−0.346348	−	0.938106i	$-0.612578\pi$
$257$	−11.1048			−0.692695			−0.346348	+	0.938106i	$0.612578\pi$
$258$	6.28935	+	7.96974i	0.391558	+	0.496174i
$259$	−21.6859	−	11.0405i	−1.34750	−	0.686026i
$260$		−	0.745238i		−	0.0462177i
$261$	−21.3077	−	5.09281i	−1.31891	−	0.315237i
$262$		−	12.6919i		−	0.784107i
$263$		−	12.9490i		−	0.798470i	−0.916849	−	0.399235i	$-0.869276\pi$
$263$		−	12.9490i		−	0.798470i	0.916849	−	0.399235i	$-0.130724\pi$
$264$	3.93109	−	3.10224i	0.241942	−	0.190929i
$265$			3.79581i			0.233175i
$266$	−10.6127	−	5.40304i	−0.650707	−	0.331282i
$267$	2.21263	−	1.74611i	0.135411	−	0.106860i
$268$	−3.54888			−0.216782
$269$	−5.35266			−0.326357			−0.163179	−	0.986597i	$-0.552175\pi$
$269$	−5.35266			−0.326357			−0.163179	+	0.986597i	$0.552175\pi$
$270$	3.51421	−	1.62652i	0.213868	−	0.0989870i
$271$			17.6940i			1.07484i	0.843316	+	0.537418i	$0.180600\pi$
$271$			17.6940i			1.07484i	−0.843316	+	0.537418i	$0.819400\pi$
$272$	−2.53678			−0.153815
$273$	0.897763	+	4.49378i	0.0543351	+	0.271976i
$274$	−10.2742			−0.620685
$275$			12.8503i			0.774905i
$276$	6.03151	+	7.64300i	0.363054	+	0.460055i
$277$	−10.6053			−0.637208			−0.318604	−	0.947888i	$-0.603214\pi$
$277$	−10.6053			−0.637208			−0.318604	+	0.947888i	$0.603214\pi$
$278$	12.2986			0.737624
$279$	18.0498	+	4.31414i	1.08061	+	0.258281i
$280$	−0.894561	+	1.75711i	−0.0534602	+	0.105007i
$281$		−	0.996077i		−	0.0594210i	−0.999559	−	0.0297105i	$-0.990541\pi$
$281$		−	0.996077i		−	0.0594210i	0.999559	−	0.0297105i	$-0.00945853\pi$
$282$	−12.9688	−	16.4338i	−0.772280	−	0.978617i
$283$			5.85438i			0.348007i	0.984745	+	0.174003i	$0.0556704\pi$
$283$			5.85438i			0.348007i	−0.984745	+	0.174003i	$0.944330\pi$
$284$		−	0.765844i		−	0.0454445i
$285$	−3.59926	−	4.56091i	−0.213202	−	0.270165i
$286$			2.89121i			0.170961i
$287$	8.94901	+	4.55603i	0.528243	+	0.268934i
$288$	−2.91781	−	0.697395i	−0.171934	−	0.0410944i
$289$	−10.5647			−0.621455
$290$	5.44220			0.319577
$291$	−2.03237	−	2.57538i	−0.119140	−	0.150972i
$292$		−	6.83961i		−	0.400258i
$293$	−8.86431			−0.517858			−0.258929	−	0.965896i	$-0.583370\pi$
$293$	−8.86431			−0.517858			−0.258929	+	0.965896i	$0.583370\pi$
$294$	3.27746	−	11.6730i	0.191145	−	0.680781i
$295$	−9.01420			−0.524827
$296$			9.19762i			0.534601i
$297$	−13.6337	+	6.31023i	−0.791106	+	0.366157i
$298$	−13.3876			−0.775520
$299$	−5.62123			−0.325084
$300$	6.04321	−	4.76902i	0.348905	−	0.275340i
$301$	13.8202	+	7.03600i	0.796582	+	0.405548i
$302$			8.09890i			0.466039i
$303$	−2.19954	+	1.73577i	−0.126360	+	0.0997176i
$304$			4.50115i			0.258159i
$305$			6.85956i			0.392777i
$306$	7.40186	+	1.76914i	0.423136	+	0.101135i
$307$			11.9193i			0.680269i	0.940377	+	0.340135i	$0.110473\pi$
$307$			11.9193i			0.680269i	−0.940377	+	0.340135i	$0.889527\pi$
$308$	3.47052	−	6.81684i	0.197751	−	0.388425i
$309$	−13.0104	−	16.4865i	−0.740137	−	0.937886i
$310$	−4.61010			−0.261836
$311$	−17.9300			−1.01671			−0.508357	−	0.861146i	$-0.669747\pi$
$311$	−17.9300			−1.01671			−0.508357	+	0.861146i	$0.669747\pi$
$312$	1.35967	−	1.07299i	0.0769760	−	0.0607460i
$313$		−	13.3465i		−	0.754388i	−0.926134	−	0.377194i	$-0.876889\pi$
$313$		−	13.3465i		−	0.754388i	0.926134	−	0.377194i	$-0.123111\pi$
$314$	−15.5084			−0.875188
$315$	3.83556	−	4.50305i	0.216109	−	0.253718i
$316$	−14.3002			−0.804449
$317$			0.0995628i			0.00559201i	0.999996	+	0.00279600i	$0.000889997\pi$
$317$			0.0995628i			0.00559201i	−0.999996	+	0.00279600i	$0.999110\pi$
$318$	−6.92537	+	5.46518i	−0.388355	+	0.306472i
$319$	−21.1135			−1.18213
$320$	0.745238			0.0416601
$321$	5.38872	+	6.82848i	0.300769	+	0.381128i
$322$	13.2536	+	6.74754i	0.738594	+	0.376026i
$323$		−	11.4184i		−	0.635339i
$324$	8.02728	+	4.06974i	0.445960	+	0.226097i
$325$			4.44462i			0.246543i
$326$			2.92915i			0.162231i
$327$	−8.37909	+	6.61239i	−0.463365	+	0.365666i
$328$		−	3.79553i		−	0.209573i
$329$	−28.4975	−	14.5084i	−1.57112	−	0.799873i
$330$	2.92960	−	2.31191i	0.161269	−	0.127266i
$331$	−6.19404			−0.340455			−0.170228	−	0.985405i	$-0.554450\pi$
$331$	−6.19404			−0.340455			−0.170228	+	0.985405i	$0.554450\pi$
$332$	8.53210			0.468260
$333$	6.41437	−	26.8370i	0.351506	−	1.47066i
$334$			19.6297i			1.07409i
$335$	−2.64476			−0.144499
$336$	−4.49378	+	0.897763i	−0.245156	+	0.0489770i
$337$	34.0537			1.85502			0.927511	−	0.373796i	$-0.121944\pi$
$337$	34.0537			1.85502			0.927511	+	0.373796i	$0.121944\pi$
$338$			1.00000i			0.0543928i
$339$	7.31373	+	9.26781i	0.397227	+	0.503358i
$340$	−1.89051			−0.102527
$341$	17.8853			0.968542
$342$	3.13908	−	13.1335i	0.169742	−	0.710180i
$343$	−2.91530	−	18.2894i	−0.157411	−	0.987533i
$344$		−	5.86153i		−	0.316033i
$345$	4.49491	+	5.69586i	0.241998	+	0.306655i
$346$		−	23.5070i		−	1.26374i
$347$			25.9291i			1.39195i	0.718068	+	0.695973i	$0.245027\pi$
$347$			25.9291i			1.39195i	−0.718068	+	0.695973i	$0.754973\pi$
$348$	7.83563	+	9.92915i	0.420034	+	0.532258i
$349$			17.8663i			0.956362i	0.878261	+	0.478181i	$0.158704\pi$
$349$			17.8663i			0.956362i	−0.878261	+	0.478181i	$0.841296\pi$
$350$	5.33518	−	10.4794i	0.285177	−	0.560149i
$351$	−4.71556	+	2.18255i	−0.251698	+	0.116496i
$352$	−2.89121			−0.154102
$353$	−1.77567			−0.0945092			−0.0472546	−	0.998883i	$-0.515047\pi$
$353$	−1.77567			−0.0945092			−0.0472546	+	0.998883i	$0.515047\pi$
$354$	−12.9786	−	16.4462i	−0.689803	−	0.874105i
$355$		−	0.570736i		−	0.0302915i
$356$	−1.62733			−0.0862484
$357$	11.3997	−	2.27743i	0.603338	−	0.120534i
$358$	11.0408			0.583522
$359$			20.3922i			1.07626i	0.842862	+	0.538130i	$0.180869\pi$
$359$			20.3922i			1.07626i	−0.842862	+	0.538130i	$0.819131\pi$
$360$	−2.17447	−	0.519725i	−0.114604	−	0.0273919i
$361$	−1.26037			−0.0663354
$362$	7.45611			0.391884
$363$	3.59073	−	2.83364i	0.188464	−	0.148727i
$364$	1.20037	−	2.35778i	0.0629164	−	0.123581i
$365$		−	5.09714i		−	0.266796i
$366$	−12.5151	+	9.87633i	−0.654174	+	0.516244i
$367$			2.20568i			0.115135i	0.998342	+	0.0575677i	$0.0183345\pi$
$367$			2.20568i			0.115135i	−0.998342	+	0.0575677i	$0.981665\pi$
$368$		−	5.62123i		−	0.293027i
$369$	−2.64698	+	11.0746i	−0.137796	+	0.576523i
$370$			6.85442i			0.356344i
$371$	−6.11399	+	12.0092i	−0.317422	+	0.623485i
$372$	−6.63758	−	8.41101i	−0.344143	−	0.436091i
$373$	8.13564			0.421247			0.210624	−	0.977567i	$-0.432451\pi$
$373$	8.13564			0.421247			0.210624	+	0.977567i	$0.432451\pi$
$374$	7.33438			0.379252
$375$	9.57001	−	7.55221i	0.494193	−	0.389995i
$376$			12.0866i			0.623319i
$377$	−7.30263			−0.376104
$378$	13.7381	+	0.514429i	0.706612	+	0.0264594i
$379$	30.4346			1.56332			0.781661	−	0.623703i	$-0.214373\pi$
$379$	30.4346			1.56332			0.781661	+	0.623703i	$0.214373\pi$
$380$			3.35443i			0.172079i
$381$	23.2526	−	18.3499i	1.19127	−	0.940093i
$382$	20.0993			1.02837
$383$	−33.4014			−1.70673			−0.853365	−	0.521314i	$-0.825442\pi$
$383$	−33.4014			−1.70673			−0.853365	+	0.521314i	$0.825442\pi$
$384$	1.07299	+	1.35967i	0.0547557	+	0.0693853i
$385$	2.58637	−	5.08017i	0.131813	−	0.258909i
$386$			14.8165i			0.754139i
$387$	−4.08780	+	17.1029i	−0.207795	+	0.869387i
$388$			1.89413i			0.0961597i
$389$			17.5558i			0.890112i	0.895503	+	0.445056i	$0.146816\pi$
$389$			17.5558i			0.890112i	−0.895503	+	0.445056i	$0.853184\pi$
$390$	1.01328	−	0.799631i	0.0513093	−	0.0404909i
$391$			14.2598i			0.721151i
$392$	−5.66040	+	4.11823i	−0.285894	+	0.208002i
$393$	17.2567	−	13.6182i	0.870488	−	0.686949i
$394$	−10.6416			−0.536115
$395$	−10.6571			−0.536215
$396$	8.43602	+	2.01632i	0.423926	+	0.101324i
$397$		−	14.8027i		−	0.742926i	−0.928448	−	0.371463i	$-0.878856\pi$
$397$		−	14.8027i		−	0.742926i	0.928448	−	0.371463i	$-0.121144\pi$
$398$	0.863102			0.0432634
$399$	−4.04097	−	20.2272i	−0.202302	−	1.01263i
$400$	−4.44462			−0.222231
$401$			21.0341i			1.05039i	0.850982	+	0.525195i	$0.176008\pi$
$401$			21.0341i			1.05039i	−0.850982	+	0.525195i	$0.823992\pi$
$402$	−3.80790	−	4.82530i	−0.189921	−	0.240664i
$403$	6.18608			0.308150
$404$	1.61770			0.0804837
$405$	5.98224	+	3.03292i	0.297260	+	0.150707i
$406$	17.2180	+	8.76584i	0.854513	+	0.435042i
$407$		−	26.5923i		−	1.31813i
$408$	−2.72194	−	3.44918i	−0.134756	−	0.170760i
$409$			11.9264i			0.589724i	0.955540	+	0.294862i	$0.0952737\pi$
$409$			11.9264i			0.589724i	−0.955540	+	0.294862i	$0.904726\pi$
$410$		−	2.82857i		−	0.139693i
$411$	−11.0241	−	13.9695i	−0.543776	−	0.689062i
$412$			12.1254i			0.597376i
$413$	−28.5190	−	14.5193i	−1.40333	−	0.714450i
$414$	−3.92021	+	16.4017i	−0.192668	+	0.806099i
$415$	6.35844			0.312124
$416$	−1.00000			−0.0490290
$417$	13.1963	+	16.7221i	0.646225	+	0.818884i
$418$		−	13.0138i		−	0.636525i
$419$	27.8270			1.35944			0.679718	−	0.733473i	$-0.262102\pi$
$419$	27.8270			1.35944			0.679718	+	0.733473i	$0.262102\pi$
$420$	−3.34893	+	0.669048i	−0.163411	+	0.0326462i
$421$	23.0110			1.12149			0.560744	−	0.827989i	$-0.310515\pi$
$421$	23.0110			1.12149			0.560744	+	0.827989i	$0.310515\pi$
$422$			22.1657i			1.07901i
$423$	8.42914	−	35.2665i	0.409839	−	1.71472i
$424$	5.09343			0.247359
$425$	11.2750			0.546920
$426$	1.04129	−	0.821741i	0.0504508	−	0.0398135i
$427$	−11.0488	+	21.7022i	−0.534690	+	1.05024i
$428$		−	5.02216i		−	0.242755i
$429$	−3.93109	+	3.10224i	−0.189795	+	0.149777i
$430$		−	4.36824i		−	0.210655i
$431$		−	27.1332i		−	1.30696i	−0.756945	−	0.653479i	$-0.773309\pi$
$431$		−	27.1332i		−	1.30696i	0.756945	−	0.653479i	$-0.226691\pi$
$432$	−2.18255	−	4.71556i	−0.105008	−	0.226877i
$433$		−	16.2543i		−	0.781131i	−0.920575	−	0.390566i	$-0.872279\pi$
$433$		−	16.2543i		−	0.781131i	0.920575	−	0.390566i	$-0.127721\pi$
$434$	−14.5854	−	7.42557i	−0.700121	−	0.356439i
$435$	5.83941	+	7.39958i	0.279978	+	0.354783i
$436$	6.16260			0.295135
$437$	25.3020			1.21036
$438$	9.29960	−	7.33882i	0.444352	−	0.350662i
$439$			23.1348i			1.10416i	0.833790	+	0.552081i	$0.186166\pi$
$439$			23.1348i			1.10416i	−0.833790	+	0.552081i	$0.813834\pi$
$440$	−2.15464			−0.102719
$441$	19.3880	−	8.06870i	0.923240	−	0.384224i
$442$	2.53678			0.120662
$443$		−	9.47712i		−	0.450272i	−0.974327	−	0.225136i	$-0.927717\pi$
$443$		−	9.47712i		−	0.450272i	0.974327	−	0.225136i	$-0.0722826\pi$
$444$	−12.5057	+	9.86893i	−0.593495	+	0.468359i
$445$	−1.21275			−0.0574898
$446$	18.1611			0.859954
$447$	−14.3647	−	18.2026i	−0.679426	−	0.860955i
$448$	2.35778	+	1.20037i	0.111395	+	0.0567121i
$449$		−	20.4786i		−	0.966446i	−0.875497	−	0.483223i	$-0.839466\pi$
$449$		−	20.4786i		−	0.966446i	0.875497	−	0.483223i	$-0.160534\pi$
$450$	12.9686	+	3.09966i	0.611345	+	0.146119i
$451$			10.9737i			0.516730i
$452$		−	6.81623i		−	0.320608i
$453$	−11.0118	+	8.69002i	−0.517380	+	0.408293i
$454$		−	20.1759i		−	0.946903i
$455$	0.894561	−	1.75711i	0.0419376	−	0.0823744i
$456$	−6.12007	+	4.82968i	−0.286599	+	0.226171i
$457$	−4.36199			−0.204045			−0.102023	−	0.994782i	$-0.532531\pi$
$457$	−4.36199			−0.204045			−0.102023	+	0.994782i	$0.532531\pi$
$458$	18.7567			0.876441
$459$	5.53666	+	11.9623i	0.258429	+	0.558354i
$460$		−	4.18915i		−	0.195320i
$461$	3.18865			0.148510			0.0742552	−	0.997239i	$-0.476342\pi$
$461$	3.18865			0.148510			0.0742552	+	0.997239i	$0.476342\pi$
$462$	12.9925	−	2.59563i	0.604464	−	0.120759i
$463$	27.1033			1.25960			0.629798	−	0.776759i	$-0.283137\pi$
$463$	27.1033			1.25960			0.629798	+	0.776759i	$0.283137\pi$
$464$		−	7.30263i		−	0.339016i
$465$	−4.94658	−	6.26821i	−0.229392	−	0.290681i
$466$	−13.8783			−0.642898
$467$	25.0637			1.15981			0.579905	−	0.814684i	$-0.303090\pi$
$467$	25.0637			1.15981			0.579905	+	0.814684i	$0.303090\pi$
$468$	2.91781	+	0.697395i	0.134876	+	0.0322371i
$469$	−8.36747	−	4.25996i	−0.386374	−	0.196707i
$470$			9.00740i			0.415481i
$471$	−16.6403	−	21.0862i	−0.766744	−	0.971602i
$472$			12.0957i			0.556751i
$473$			16.9469i			0.779221i
$474$	−15.3439	−	19.4435i	−0.704771	−	0.893071i
$475$		−	20.0059i		−	0.917934i
$476$	−5.98117	−	3.04507i	−0.274146	−	0.139571i
$477$	−14.8617	−	3.55213i	−0.680469	−	0.162641i
$478$	−1.08541			−0.0496453
$479$	−7.15238			−0.326800			−0.163400	−	0.986560i	$-0.552246\pi$
$479$	−7.15238			−0.326800			−0.163400	+	0.986560i	$0.552246\pi$
$480$	0.799631	+	1.01328i	0.0364980	+	0.0462495i
$481$		−	9.19762i		−	0.419375i
$482$	−27.1249			−1.23551
$483$	5.04653	+	25.2605i	0.229625	+	1.14939i
$484$	−2.64088			−0.120040
$485$			1.41158i			0.0640963i
$486$	3.07968	+	15.2812i	0.139697	+	0.693170i
$487$	38.9956			1.76706			0.883531	−	0.468373i	$-0.155160\pi$
$487$	38.9956			1.76706			0.883531	+	0.468373i	$0.155160\pi$
$488$	9.20452			0.416669
$489$	−3.98267	+	3.14294i	−0.180103	+	0.142129i
$490$	−4.21835	+	3.06906i	−0.190566	+	0.138646i
$491$			31.2995i			1.41252i	0.707950	+	0.706262i	$0.249620\pi$
$491$			31.2995i			1.41252i	−0.707950	+	0.706262i	$0.750380\pi$
$492$	5.16066	−	4.07255i	0.232660	−	0.183605i
$493$			18.5252i			0.834332i
$494$		−	4.50115i		−	0.202516i
$495$	6.28685	+	1.50264i	0.282573	+	0.0675385i
$496$			6.18608i			0.277763i
$497$	0.919295	−	1.80569i	0.0412360	−	0.0809962i
$498$	9.15484	+	11.6008i	0.410238	+	0.519845i
$499$	−5.92951			−0.265441			−0.132721	−	0.991153i	$-0.542371\pi$
$499$	−5.92951			−0.265441			−0.132721	+	0.991153i	$0.542371\pi$
$500$	−7.03849			−0.314771
$501$	−26.6898	+	21.0624i	−1.19241	+	0.940999i
$502$			20.8040i			0.928530i
$503$	−29.8706			−1.33186			−0.665932	−	0.746012i	$-0.731966\pi$
$503$	−29.8706			−1.33186			−0.665932	+	0.746012i	$0.731966\pi$
$504$	−6.04243	−	5.14675i	−0.269151	−	0.229255i
$505$	1.20557			0.0536473
$506$			16.2522i			0.722497i
$507$	−1.35967	+	1.07299i	−0.0603850	+	0.0476531i
$508$	−17.1017			−0.758764
$509$	−18.5104			−0.820458			−0.410229	−	0.911983i	$-0.634551\pi$
$509$	−18.5104			−0.820458			−0.410229	+	0.911983i	$0.634551\pi$
$510$	−2.02849	−	2.57046i	−0.0898231	−	0.113822i
$511$	8.21005	−	16.1263i	0.363191	−	0.713385i
$512$		−	1.00000i		−	0.0441942i
$513$	21.2254	−	9.82401i	0.937126	−	0.433740i
$514$			11.1048i			0.489810i
$515$			9.03632i			0.398188i
$516$	7.96974	−	6.28935i	0.350848	−	0.276873i
$517$		−	34.9450i		−	1.53688i
$518$	−11.0405	+	21.6859i	−0.485093	+	0.952826i
$519$	31.9617	−	25.2227i	1.40296	−	1.10715i
$520$	−0.745238			−0.0326809
$521$	2.37866			0.104211			0.0521054	−	0.998642i	$-0.483407\pi$
$521$	2.37866			0.104211			0.0521054	+	0.998642i	$0.483407\pi$
$522$	−5.09281	+	21.3077i	−0.222906	+	0.932613i
$523$		−	21.0743i		−	0.921513i	−0.887527	−	0.460756i	$-0.847578\pi$
$523$		−	21.0743i		−	0.921513i	0.887527	−	0.460756i	$-0.152422\pi$
$524$	−12.6919			−0.554447
$525$	19.9731	−	3.99022i	0.871699	−	0.174147i
$526$	−12.9490			−0.564604
$527$		−	15.6927i		−	0.683586i
$528$	−3.10224	−	3.93109i	−0.135008	−	0.171079i
$529$	−8.59818			−0.373834
$530$	3.79581			0.164880
$531$	8.43550	−	35.2931i	0.366069	−	1.53159i
$532$	−5.40304	+	10.6127i	−0.234252	+	0.460120i
$533$			3.79553i			0.164403i
$534$	−1.74611	−	2.21263i	−0.0755614	−	0.0957499i
$535$		−	3.74271i		−	0.161811i
$536$			3.54888i			0.153288i
$537$	11.8466	+	15.0118i	0.511218	+	0.647805i
$538$			5.35266i			0.230769i
$539$	16.3654	−	11.9067i	0.704909	−	0.512857i
$540$	−1.62652	−	3.51421i	−0.0699944	−	0.151228i
$541$	−4.70136			−0.202127			−0.101064	−	0.994880i	$-0.532225\pi$
$541$	−4.70136			−0.202127			−0.101064	+	0.994880i	$0.532225\pi$
$542$	17.6940			0.760024
$543$	8.00031	+	10.1378i	0.343326	+	0.435056i
$544$			2.53678i			0.108764i
$545$	4.59260			0.196726
$546$	4.49378	−	0.897763i	0.192316	−	0.0384207i
$547$	7.85564			0.335883			0.167941	−	0.985797i	$-0.446288\pi$
$547$	7.85564			0.335883			0.167941	+	0.985797i	$0.446288\pi$
$548$			10.2742i			0.438890i
$549$	−26.8571	−	6.41918i	−1.14623	−	0.273964i
$550$	12.8503			0.547941
$551$	32.8702			1.40032
$552$	7.64300	−	6.03151i	0.325308	−	0.256718i
$553$	−33.7167	−	17.1655i	−1.43378	−	0.729952i
$554$			10.6053i			0.450574i
$555$	−9.31973	+	7.35471i	−0.395601	+	0.312190i
$556$		−	12.2986i		−	0.521579i
$557$			17.9543i			0.760748i	0.924833	+	0.380374i	$0.124205\pi$
$557$			17.9543i			0.760748i	−0.924833	+	0.380374i	$0.875795\pi$
$558$	4.31414	−	18.0498i	0.182632	−	0.764110i
$559$			5.86153i			0.247916i
$560$	1.75711	+	0.894561i	0.0742513	+	0.0378021i
$561$	7.86970	+	9.97232i	0.332259	+	0.421032i
$562$	−0.996077			−0.0420170
$563$	1.06591			0.0449226			0.0224613	−	0.999748i	$-0.492850\pi$
$563$	1.06591			0.0449226			0.0224613	+	0.999748i	$0.492850\pi$
$564$	−16.4338	+	12.9688i	−0.691987	+	0.546084i
$565$		−	5.07971i		−	0.213705i
$566$	5.85438			0.246078
$567$	14.0414	+	19.2312i	0.589682	+	0.807636i
$568$	−0.765844			−0.0321341
$569$		−	14.4896i		−	0.607434i	−0.952762	−	0.303717i	$-0.901772\pi$
$569$		−	14.4896i		−	0.607434i	0.952762	−	0.303717i	$-0.0982278\pi$
$570$	−4.56091	+	3.59926i	−0.191036	+	0.150757i
$571$	25.9732			1.08694			0.543471	−	0.839428i	$-0.317110\pi$
$571$	25.9732			1.08694			0.543471	+	0.839428i	$0.317110\pi$
$572$	2.89121			0.120888
$573$	21.5663	+	27.3283i	0.900943	+	1.14166i
$574$	4.55603	−	8.94901i	0.190165	−	0.373524i
$575$			24.9842i			1.04191i
$576$	−0.697395	+	2.91781i	−0.0290581	+	0.121576i
$577$			19.7337i			0.821523i	0.911743	+	0.410762i	$0.134737\pi$
$577$			19.7337i			0.821523i	−0.911743	+	0.410762i	$0.865263\pi$
$578$			10.5647i			0.439435i
$579$	−20.1455	+	15.8979i	−0.837219	+	0.660694i
$580$		−	5.44220i		−	0.225975i
$581$	20.1168	+	10.2417i	0.834585	+	0.424896i
$582$	−2.57538	+	2.03237i	−0.106753	+	0.0842446i
$583$	−14.7262			−0.609896
$584$	−6.83961			−0.283025
$585$	2.17447	+	0.519725i	0.0899031	+	0.0214880i
$586$			8.86431i			0.366181i
$587$	4.66288			0.192458			0.0962289	−	0.995359i	$-0.469322\pi$
$587$	4.66288			0.192458			0.0962289	+	0.995359i	$0.469322\pi$
$588$	−11.6730	−	3.27746i	−0.481385	−	0.135160i
$589$	−27.8445			−1.14731
$590$			9.01420i			0.371109i
$591$	−11.4183	−	14.4690i	−0.469685	−	0.595176i
$592$	9.19762			0.378020
$593$	−8.37579			−0.343952			−0.171976	−	0.985101i	$-0.555015\pi$
$593$	−8.37579			−0.343952			−0.171976	+	0.985101i	$0.555015\pi$
$594$	6.31023	+	13.6337i	0.258912	+	0.559397i
$595$	−4.45740	−	2.26931i	−0.182735	−	0.0930325i
$596$			13.3876i			0.548376i
$597$	0.926098	+	1.17353i	0.0379027	+	0.0480295i
$598$			5.62123i			0.229869i
$599$		−	12.5079i		−	0.511061i	−0.966801	−	0.255530i	$-0.917750\pi$
$599$		−	12.5079i		−	0.511061i	0.966801	−	0.255530i	$-0.0822501\pi$
$600$	−4.76902	−	6.04321i	−0.194695	−	0.246713i
$601$		−	31.6598i		−	1.29143i	−0.763578	−	0.645715i	$-0.776559\pi$
$601$		−	31.6598i		−	1.29143i	0.763578	−	0.645715i	$-0.223441\pi$
$602$	7.03600	−	13.8202i	0.286766	−	0.563269i
$603$	2.47497	−	10.3550i	0.100789	−	0.421687i
$604$	8.09890			0.329540
$605$	−1.96809			−0.0800141
$606$	1.73577	+	2.19954i	0.0705110	+	0.0893501i
$607$		−	44.3394i		−	1.79968i	−0.436221	−	0.899840i	$-0.643683\pi$
$607$		−	44.3394i		−	1.79968i	0.436221	−	0.899840i	$-0.356317\pi$
$608$	4.50115			0.182546
$609$	6.55603	+	32.8164i	0.265664	+	1.32979i
$610$	6.85956			0.277735
$611$		−	12.0866i		−	0.488972i
$612$	1.76914	−	7.40186i	0.0715132	−	0.299203i
$613$	13.0630			0.527610			0.263805	−	0.964576i	$-0.415022\pi$
$613$	13.0630			0.527610			0.263805	+	0.964576i	$0.415022\pi$
$614$	11.9193			0.481023
$615$	3.84592	−	3.03502i	0.155082	−	0.122384i
$616$	−6.81684	−	3.47052i	−0.274658	−	0.139831i
$617$		−	18.2937i		−	0.736477i	−0.929731	−	0.368238i	$-0.879961\pi$
$617$		−	18.2937i		−	0.736477i	0.929731	−	0.368238i	$-0.120039\pi$
$618$	−16.4865	+	13.0104i	−0.663186	+	0.523356i
$619$		−	29.4925i		−	1.18540i	−0.805422	−	0.592701i	$-0.798062\pi$
$619$		−	29.4925i		−	1.18540i	0.805422	−	0.592701i	$-0.201938\pi$
$620$			4.61010i			0.185146i
$621$	−26.5072	+	12.2686i	−1.06370	+	0.492323i
$622$			17.9300i			0.718926i
$623$	−3.83689	−	1.95340i	−0.153722	−	0.0782612i
$624$	−1.07299	−	1.35967i	−0.0429539	−	0.0544303i
$625$	16.9777			0.679110
$626$	−13.3465			−0.533433
$627$	17.6944	−	13.9636i	0.706648	−	0.557654i
$628$			15.5084i			0.618851i
$629$	−23.3324			−0.930322
$630$	−4.50305	−	3.83556i	−0.179406	−	0.152812i
$631$	33.3500			1.32764			0.663822	−	0.747891i	$-0.268933\pi$
$631$	33.3500			1.32764			0.663822	+	0.747891i	$0.268933\pi$
$632$			14.3002i			0.568832i
$633$	−30.1379	+	23.7835i	−1.19788	+	0.945308i
$634$	0.0995628			0.00395415
$635$	−12.7448			−0.505763
$636$	5.46518	+	6.92537i	0.216709	+	0.274609i
$637$	5.66040	−	4.11823i	0.224273	−	0.163170i
$638$			21.1135i			0.835890i
$639$	2.23459	+	0.534096i	0.0883990	+	0.0211285i
$640$		−	0.745238i		−	0.0294581i
$641$		−	16.2279i		−	0.640963i	−0.947255	−	0.320481i	$-0.896155\pi$
$641$		−	16.2279i		−	0.640963i	0.947255	−	0.320481i	$-0.103845\pi$
$642$	6.82848	−	5.38872i	0.269498	−	0.212676i
$643$			6.49351i			0.256079i	0.991769	+	0.128040i	$0.0408684\pi$
$643$			6.49351i			0.256079i	−0.991769	+	0.128040i	$0.959132\pi$
$644$	6.74754	−	13.2536i	0.265890	−	0.522265i
$645$	5.93935	−	4.68706i	0.233862	−	0.184553i
$646$	−11.4184			−0.449253
$647$	13.3079			0.523187			0.261594	−	0.965178i	$-0.415752\pi$
$647$	13.3079			0.523187			0.261594	+	0.965178i	$0.415752\pi$
$648$	4.06974	−	8.02728i	0.159874	−	0.315341i
$649$		−	34.9713i		−	1.37275i
$650$	4.44462			0.174332
$651$	−5.55363	−	27.7988i	−0.217664	−	1.08952i
$652$	2.92915			0.114714
$653$			14.6545i			0.573475i	0.958009	+	0.286738i	$0.0925708\pi$
$653$			14.6545i			0.573475i	−0.958009	+	0.286738i	$0.907429\pi$
$654$	6.61239	+	8.37909i	0.258565	+	0.327648i
$655$	−9.45847			−0.369573
$656$	−3.79553			−0.148190
$657$	19.9567	+	4.76991i	0.778586	+	0.186092i
$658$	−14.5084	+	28.4975i	−0.565596	+	1.11095i
$659$		−	14.5472i		−	0.566679i	−0.959020	−	0.283340i	$-0.908558\pi$
$659$		−	14.5472i		−	0.566679i	0.959020	−	0.283340i	$-0.0914424\pi$
$660$	−2.31191	−	2.92960i	−0.0899908	−	0.114034i
$661$			28.1459i			1.09475i	0.836888	+	0.547375i	$0.184373\pi$
$661$			28.1459i			1.09475i	−0.836888	+	0.547375i	$0.815627\pi$
$662$			6.19404i			0.240738i
$663$	2.72194	+	3.44918i	0.105711	+	0.133955i
$664$		−	8.53210i		−	0.331110i
$665$	−4.02655	+	7.90900i	−0.156143	+	0.306698i
$666$	−26.8370	−	6.41437i	−1.03991	−	0.248552i
$667$	−41.0497			−1.58945
$668$	19.6297			0.759495
$669$	19.4867	+	24.6931i	0.753398	+	0.954691i
$670$			2.64476i			0.102176i
$671$	−26.6122			−1.02735
$672$	0.897763	+	4.49378i	0.0346320	+	0.173351i
$673$	−14.8492			−0.572393			−0.286197	−	0.958171i	$-0.592391\pi$
$673$	−14.8492			−0.572393			−0.286197	+	0.958171i	$0.592391\pi$
$674$		−	34.0537i		−	1.31170i
$675$	9.70062	+	20.9589i	0.373377	+	0.806707i
$676$	1.00000			0.0384615
$677$	37.8192			1.45351			0.726756	−	0.686896i	$-0.241027\pi$
$677$	37.8192			1.45351			0.726756	+	0.686896i	$0.241027\pi$
$678$	9.26781	−	7.31373i	0.355928	−	0.280882i
$679$	−2.27365	+	4.46593i	−0.0872547	+	0.171387i
$680$			1.89051i			0.0724977i
$681$	27.4326	−	21.6485i	1.05122	−	0.829573i
$682$		−	17.8853i		−	0.684862i
$683$			1.79952i			0.0688569i	0.999407	+	0.0344285i	$0.0109611\pi$
$683$			1.79952i			0.0688569i	−0.999407	+	0.0344285i	$0.989039\pi$
$684$	−13.1335	−	3.13908i	−0.502173	−	0.120026i
$685$			7.65670i			0.292547i
$686$	−18.2894	+	2.91530i	−0.698291	+	0.111307i
$687$	20.1257	+	25.5028i	0.767842	+	0.972994i
$688$	−5.86153			−0.223469
$689$	−5.09343			−0.194044
$690$	5.69586	−	4.49491i	0.216838	−	0.171118i
$691$			16.4766i			0.626798i	0.949622	+	0.313399i	$0.101468\pi$
$691$			16.4766i			0.626798i	−0.949622	+	0.313399i	$0.898532\pi$
$692$	−23.5070			−0.893601
$693$	17.4699	+	14.8804i	0.663628	+	0.565258i
$694$	25.9291			0.984255
$695$		−	9.16542i		−	0.347664i
$696$	9.92915	−	7.83563i	0.376363	−	0.297009i
$697$	9.62843			0.364703
$698$	17.8663			0.676250
$699$	−14.8912	−	18.8698i	−0.563237	−	0.713722i
$700$	−10.4794	−	5.33518i	−0.396085	−	0.201651i
$701$			24.5236i			0.926244i	0.886294	+	0.463122i	$0.153271\pi$
$701$			24.5236i			0.926244i	−0.886294	+	0.463122i	$0.846729\pi$
$702$	2.18255	+	4.71556i	0.0823752	+	0.177977i
$703$			41.3999i			1.56143i
$704$			2.89121i			0.108967i
$705$	−12.2471	+	9.66483i	−0.461252	+	0.363999i
$706$			1.77567i			0.0668281i
$707$	3.81418	+	1.94184i	0.143447	+	0.0730304i
$708$	−16.4462	+	12.9786i	−0.618085	+	0.487765i
$709$	7.07319			0.265639			0.132820	−	0.991140i	$-0.457597\pi$
$709$	7.07319			0.265639			0.132820	+	0.991140i	$0.457597\pi$
$710$	−0.570736			−0.0214193
$711$	9.97289	−	41.7253i	0.374013	−	1.56482i
$712$			1.62733i			0.0609868i
$713$	34.7733			1.30227
$714$	−2.27743	−	11.3997i	−0.0852307	−	0.426624i
$715$	2.15464			0.0805791
$716$		−	11.0408i		−	0.412612i
$717$	−1.16463	−	1.47579i	−0.0434938	−	0.0551145i
$718$	20.3922			0.761030
$719$	−13.7168			−0.511550			−0.255775	−	0.966736i	$-0.582331\pi$
$719$	−13.7168			−0.511550			−0.255775	+	0.966736i	$0.582331\pi$
$720$	−0.519725	+	2.17447i	−0.0193690	+	0.0810376i
$721$	−14.5550	+	28.5890i	−0.542055	+	1.06471i
$722$			1.26037i			0.0469062i
$723$	−29.1047	−	36.8809i	−1.08242	−	1.37162i
$724$		−	7.45611i		−	0.277104i
$725$			32.4574i			1.20544i
$726$	−2.83364	−	3.59073i	−0.105166	−	0.133264i
$727$		−	6.39156i		−	0.237050i	−0.992951	−	0.118525i	$-0.962183\pi$
$727$		−	6.39156i		−	0.237050i	0.992951	−	0.118525i	$-0.0378166\pi$
$728$	−2.35778	−	1.20037i	−0.0873851	−	0.0444886i
$729$	−17.4729	+	20.5839i	−0.647145	+	0.762367i
$730$	−5.09714			−0.188654
$731$	14.8694			0.549966
$732$	9.87633	+	12.5151i	0.365040	+	0.462571i
$733$			12.7382i			0.470494i	0.971936	+	0.235247i	$0.0755900\pi$
$733$			12.7382i			0.470494i	−0.971936	+	0.235247i	$0.924410\pi$
$734$	2.20568			0.0814131
$735$	−8.69914	−	2.44249i	−0.320873	−	0.0900926i
$736$	−5.62123			−0.207201
$737$		−	10.2606i		−	0.377953i
$738$	11.0746	+	2.64698i	0.407663	+	0.0974367i
$739$	−39.4798			−1.45229			−0.726143	−	0.687543i	$-0.758689\pi$
$739$	−39.4798			−1.45229			−0.726143	+	0.687543i	$0.758689\pi$
$740$	6.85442			0.251973
$741$	6.12007	−	4.82968i	0.224827	−	0.177423i
$742$	12.0092	+	6.11399i	0.440870	+	0.224452i
$743$		−	38.3960i		−	1.40861i	−0.709897	−	0.704306i	$-0.751258\pi$
$743$		−	38.3960i		−	1.40861i	0.709897	−	0.704306i	$-0.248742\pi$
$744$	−8.41101	+	6.63758i	−0.308363	+	0.243346i
$745$			9.97692i			0.365526i
$746$		−	8.13564i		−	0.297867i
$747$	−5.95024	+	24.8951i	−0.217708	+	0.910863i
$748$		−	7.33438i		−	0.268172i
$749$	6.02845	−	11.8411i	0.220275	−	0.432666i
$750$	−7.55221	−	9.57001i	−0.275768	−	0.349447i
$751$	12.3556			0.450864			0.225432	−	0.974259i	$-0.427621\pi$
$751$	12.3556			0.450864			0.225432	+	0.974259i	$0.427621\pi$
$752$	12.0866			0.440753
$753$	−28.2866	+	22.3225i	−1.03082	+	0.813476i
$754$			7.30263i			0.265946i
$755$	6.03561			0.219658
$756$	0.514429	−	13.7381i	0.0187096	−	0.499650i
$757$	−27.9201			−1.01477			−0.507386	−	0.861719i	$-0.669388\pi$
$757$	−27.9201			−1.01477			−0.507386	+	0.861719i	$0.669388\pi$
$758$		−	30.4346i		−	1.10544i
$759$	−22.0975	+	17.4384i	−0.802090	+	0.632973i
$760$	3.35443			0.121678
$761$	−49.1587			−1.78200			−0.891001	−	0.454001i	$-0.849996\pi$
$761$	−49.1587			−1.78200			−0.891001	+	0.454001i	$0.849996\pi$
$762$	−18.3499	−	23.2526i	−0.664746	−	0.842353i
$763$	14.5300	+	7.39739i	0.526023	+	0.267804i
$764$		−	20.0993i		−	0.727165i
$765$	1.31843	−	5.51615i	0.0476679	−	0.199437i
$766$			33.4014i			1.20684i
$767$		−	12.0957i		−	0.436751i
$768$	1.35967	−	1.07299i	0.0490628	−	0.0387181i
$769$		−	13.3903i		−	0.482868i	−0.970417	−	0.241434i	$-0.922382\pi$
$769$		−	13.3903i		−	0.482868i	0.970417	−	0.241434i	$-0.0776178\pi$
$770$	−5.08017	−	2.58637i	−0.183077	−	0.0932061i
$771$	−15.0988	+	11.9153i	−0.543769	+	0.429118i
$772$	14.8165			0.533257
$773$	−14.5011			−0.521570			−0.260785	−	0.965397i	$-0.583981\pi$
$773$	−14.5011			−0.521570			−0.260785	+	0.965397i	$0.583981\pi$
$774$	17.1029	+	4.08780i	0.614750	+	0.146933i
$775$		−	27.4948i		−	0.987641i
$776$	1.89413			0.0679952
$777$	−41.3320	+	8.25729i	−1.48278	+	0.296229i
$778$	17.5558			0.629404
$779$		−	17.0842i		−	0.612107i
$780$	−0.799631	−	1.01328i	−0.0286314	−	0.0362811i
$781$	2.21422			0.0792310
$782$	14.2598			0.509930
$783$	−34.4359	+	15.9384i	−1.23064	+	0.569591i
$784$	4.11823	+	5.66040i	0.147080	+	0.202157i
$785$			11.5574i			0.412502i
$786$	−13.6182	−	17.2567i	−0.485746	−	0.615528i
$787$		−	25.2642i		−	0.900572i	−0.892884	−	0.450286i	$-0.851322\pi$
$787$		−	25.2642i		−	0.900572i	0.892884	−	0.450286i	$-0.148678\pi$
$788$			10.6416i			0.379090i
$789$	−13.8941	−	17.6064i	−0.494644	−	0.626803i
$790$			10.6571i			0.379161i
$791$	8.18199	−	16.0711i	0.290918	−	0.571424i
$792$	2.01632	−	8.43602i	0.0716467	−	0.299761i
$793$	−9.20452			−0.326862
$794$	−14.8027			−0.525328
$795$	4.07286	+	5.16105i	0.144450	+	0.183044i
$796$		−	0.863102i		−	0.0305918i
$797$	21.5622			0.763771			0.381885	−	0.924210i	$-0.375275\pi$
$797$	21.5622			0.763771			0.381885	+	0.924210i	$0.375275\pi$
$798$	−20.2272	+	4.04097i	−0.716034	+	0.143049i
$799$	−30.6611			−1.08471
$800$			4.44462i			0.157141i
$801$	1.13489	−	4.74825i	0.0400995	−	0.167771i
$802$	21.0341			0.742738
$803$	19.7748			0.697837
$804$	−4.82530	+	3.80790i	−0.170175	+	0.134294i
$805$	5.02853	−	9.87709i	0.177232	−	0.348122i
$806$		−	6.18608i		−	0.217895i
$807$	−7.27784	+	5.74334i	−0.256192	+	0.202175i
$808$		−	1.61770i		−	0.0569106i
$809$			34.3664i			1.20826i	0.796886	+	0.604130i	$0.206479\pi$
$809$			34.3664i			1.20826i	−0.796886	+	0.604130i	$0.793521\pi$
$810$	3.03292	−	5.98224i	0.106566	−	0.210194i
$811$			38.9516i			1.36778i	0.729587	+	0.683888i	$0.239712\pi$
$811$			38.9516i			1.36778i	−0.729587	+	0.683888i	$0.760288\pi$
$812$	8.76584	−	17.2180i	0.307621	−	0.604232i
$813$	18.9855	+	24.0580i	0.665850	+	0.843751i
$814$	−26.5923			−0.932059
$815$	2.18291			0.0764641
$816$	−3.44918	+	2.72194i	−0.120746	+	0.0952868i
$817$		−	26.3836i		−	0.923047i
$818$	11.9264			0.416998
$819$	6.04243	+	5.14675i	0.211139	+	0.179842i
$820$	−2.82857			−0.0987780
$821$		−	52.3941i		−	1.82857i	−0.405076	−	0.914283i	$-0.632755\pi$
$821$		−	52.3941i		−	1.82857i	0.405076	−	0.914283i	$-0.367245\pi$
$822$	−13.9695	+	11.0241i	−0.487241	+	0.384508i
$823$	37.3531			1.30205			0.651024	−	0.759058i	$-0.274340\pi$
$823$	37.3531			1.30205			0.651024	+	0.759058i	$0.274340\pi$
$824$	12.1254			0.422409
$825$	13.7883	+	17.4722i	0.480046	+	0.608304i
$826$	−14.5193	+	28.5190i	−0.505192	+	0.992304i
$827$			49.2863i			1.71385i	0.515438	+	0.856927i	$0.327629\pi$
$827$			49.2863i			1.71385i	−0.515438	+	0.856927i	$0.672371\pi$
$828$	16.4017	+	3.92021i	0.569998	+	0.136237i
$829$		−	32.8306i		−	1.14025i	−0.821557	−	0.570127i	$-0.806894\pi$
$829$		−	32.8306i		−	1.14025i	0.821557	−	0.570127i	$-0.193106\pi$
$830$		−	6.35844i		−	0.220705i
$831$	−14.4196	+	11.3793i	−0.500211	+	0.394744i
$832$			1.00000i			0.0346688i
$833$	−10.4471	−	14.3592i	−0.361969	−	0.497517i
$834$	16.7221	−	13.1963i	0.579038	−	0.456950i
$835$	14.6288			0.506250
$836$	−13.0138			−0.450091
$837$	29.1708	−	13.5014i	1.00829	−	0.466678i
$838$		−	27.8270i		−	0.961267i
$839$	12.3867			0.427638			0.213819	−	0.976873i	$-0.431410\pi$
$839$	12.3867			0.427638			0.213819	+	0.976873i	$0.431410\pi$
$840$	0.669048	+	3.34893i	0.0230843	+	0.115549i
$841$	−24.3284			−0.838909
$842$		−	23.0110i		−	0.793011i
$843$	−1.06878	−	1.35433i	−0.0368107	−	0.0466457i
$844$	22.1657			0.762973
$845$	0.745238			0.0256370
$846$	−35.2665	−	8.42914i	−1.21249	−	0.289800i
$847$	−6.22662	−	3.17003i	−0.213949	−	0.108924i
$848$		−	5.09343i		−	0.174909i
$849$	6.28168	+	7.96001i	0.215587	+	0.273187i
$850$		−	11.2750i		−	0.386731i
$851$		−	51.7019i		−	1.77232i
$852$	−0.821741	−	1.04129i	−0.0281524	−	0.0356741i
$853$		−	27.3192i		−	0.935392i	−0.883889	−	0.467696i	$-0.845084\pi$
$853$		−	27.3192i		−	0.935392i	0.883889	−	0.467696i	$-0.154916\pi$
$854$	21.7022	+	11.0488i	0.742634	+	0.378083i
$855$	−9.78761	−	2.33936i	−0.334729	−	0.0800045i
$856$	−5.02216			−0.171654
$857$	3.26290			0.111458			0.0557292	−	0.998446i	$-0.482252\pi$
$857$	3.26290			0.111458			0.0557292	+	0.998446i	$0.482252\pi$
$858$	3.10224	+	3.93109i	0.105909	+	0.134205i
$859$		−	1.64488i		−	0.0561225i	−0.999606	−	0.0280612i	$-0.991067\pi$
$859$		−	1.64488i		−	0.0561225i	0.999606	−	0.0280612i	$-0.00893334\pi$
$860$	−4.36824			−0.148956
$861$	17.0562	−	3.40749i	0.581275	−	0.116127i
$862$	−27.1332			−0.924159
$863$		−	42.3485i		−	1.44156i	−0.693164	−	0.720780i	$-0.743784\pi$
$863$		−	42.3485i		−	1.44156i	0.693164	−	0.720780i	$-0.256216\pi$
$864$	−4.71556	+	2.18255i	−0.160426	+	0.0742520i
$865$	−17.5183			−0.595640
$866$	−16.2543			−0.552343
$867$	−14.3645	+	11.3358i	−0.487845	+	0.384985i
$868$	−7.42557	+	14.5854i	−0.252040	+	0.495061i
$869$		−	41.3449i		−	1.40253i
$870$	7.39958	−	5.83941i	0.250869	−	0.197975i
$871$		−	3.54888i		−	0.120249i
$872$		−	6.16260i		−	0.208692i
$873$	−5.52671	−	1.32095i	−0.187051	−	0.0447075i
$874$		−	25.3020i		−	0.855853i
$875$	−16.5952	−	8.44878i	−0.561020	−	0.285621i
$876$	−7.33882	−	9.29960i	−0.247956	−	0.314204i
$877$	−31.5059			−1.06388			−0.531939	−	0.846783i	$-0.678536\pi$
$877$	−31.5059			−1.06388			−0.531939	+	0.846783i	$0.678536\pi$
$878$	23.1348			0.780761
$879$	−12.0525	+	9.51129i	−0.406521	+	0.320808i
$880$			2.15464i			0.0726330i
$881$	−58.0766			−1.95665			−0.978325	−	0.207076i	$-0.933605\pi$
$881$	−58.0766			−1.95665			−0.978325	+	0.207076i	$0.933605\pi$
$882$	−8.06870	−	19.3880i	−0.271687	−	0.652829i
$883$	7.31671			0.246227			0.123113	−	0.992393i	$-0.460712\pi$
$883$	7.31671			0.246227			0.123113	+	0.992393i	$0.460712\pi$
$884$		−	2.53678i		−	0.0853212i
$885$	−12.2563	+	9.67213i	−0.411992	+	0.325125i
$886$	−9.47712			−0.318390
$887$	12.3390			0.414303			0.207151	−	0.978309i	$-0.433581\pi$
$887$	12.3390			0.414303			0.207151	+	0.978309i	$0.433581\pi$
$888$	9.86893	+	12.5057i	0.331180	+	0.419664i
$889$	−40.3220	−	20.5283i	−1.35235	−	0.688498i
$890$			1.21275i			0.0406515i
$891$	−11.7665	+	23.2086i	−0.394192	+	0.777517i
$892$		−	18.1611i		−	0.608079i
$893$			54.4037i			1.82055i
$894$	−18.2026	+	14.3647i	−0.608787	+	0.480427i
$895$		−	8.22799i		−	0.275031i
$896$	1.20037	−	2.35778i	0.0401015	−	0.0787678i
$897$	−7.64300	+	6.03151i	−0.255192	+	0.201386i
$898$	−20.4786			−0.683381
$899$	45.1746			1.50666
$900$	3.09966	−	12.9686i	0.103322	−	0.432286i
$901$			12.9209i			0.430458i
$902$	10.9737			0.365384
$903$	26.3404	−	5.26227i	0.876554	−	0.175117i
$904$	−6.81623			−0.226704
$905$		−	5.55657i		−	0.184707i
$906$	8.69002	+	11.0118i	0.288707	+	0.365843i
$907$	35.1817			1.16819			0.584095	−	0.811685i	$-0.301449\pi$
$907$	35.1817			1.16819			0.584095	+	0.811685i	$0.301449\pi$
$908$	−20.1759			−0.669562
$909$	−1.12818	+	4.72015i	−0.0374193	+	0.156558i
$910$	−1.75711	−	0.894561i	−0.0582475	−	0.0296544i
$911$		−	59.9053i		−	1.98475i	−0.123248	−	0.992376i	$-0.539331\pi$
$911$		−	59.9053i		−	1.98475i	0.123248	−	0.992376i	$-0.460669\pi$
$912$	4.82968	+	6.12007i	0.159927	+	0.202656i
$913$			24.6681i			0.816396i
$914$			4.36199i			0.144282i
$915$	7.36022	+	9.32672i	0.243321	+	0.308332i
$916$		−	18.7567i		−	0.619738i
$917$	−29.9246	−	15.2349i	−0.988198	−	0.503102i
$918$	11.9623	−	5.53666i	0.394816	−	0.182737i
$919$	−23.2733			−0.767715			−0.383857	−	0.923392i	$-0.625405\pi$
$919$	−23.2733			−0.767715			−0.383857	+	0.923392i	$0.625405\pi$
$920$	−4.18915			−0.138112
$921$	12.7892	+	16.2063i	0.421420	+	0.534015i
$922$		−	3.18865i		−	0.105013i
$923$	0.765844			0.0252081
$924$	−2.59563	−	12.9925i	−0.0853898	−	0.427421i
$925$	−40.8799			−1.34412
$926$		−	27.1033i		−	0.890670i
$927$	−35.3797	−	8.45620i	−1.16202	−	0.277738i
$928$	−7.30263			−0.239720
$929$	51.1917			1.67955			0.839773	−	0.542937i	$-0.182688\pi$
$929$	51.1917			1.67955			0.839773	+	0.542937i	$0.182688\pi$
$930$	−6.26821	+	4.94658i	−0.205543	+	0.162205i
$931$	−25.4783	+	18.5368i	−0.835019	+	0.607519i
$932$			13.8783i			0.454597i
$933$	−24.3788	+	19.2386i	−0.798126	+	0.629844i
$934$		−	25.0637i		−	0.820109i
$935$		−	5.46586i		−	0.178753i
$936$	0.697395	−	2.91781i	0.0227951	−	0.0953717i
$937$		−	26.4402i		−	0.863762i	−0.901931	−	0.431881i	$-0.857850\pi$
$937$		−	26.4402i		−	0.863762i	0.901931	−	0.431881i	$-0.142150\pi$
$938$	−4.25996	+	8.36747i	−0.139093	+	0.273208i
$939$	−14.3206	−	18.1468i	−0.467336	−	0.592199i
$940$	9.00740			0.293789
$941$	33.5496			1.09369			0.546843	−	0.837235i	$-0.315829\pi$
$941$	33.5496			1.09369			0.546843	+	0.837235i	$0.315829\pi$
$942$	−21.0862	+	16.6403i	−0.687026	+	0.542170i
$943$			21.3355i			0.694780i
$944$	12.0957			0.393682
$945$	0.383372	−	10.2382i	0.0124711	−	0.333047i
$946$	16.9469			0.550992
$947$			40.0622i			1.30185i	0.759144	+	0.650923i	$0.225618\pi$
$947$			40.0622i			1.30185i	−0.759144	+	0.650923i	$0.774382\pi$
$948$	−19.4435	+	15.3439i	−0.631497	+	0.498348i
$949$	6.83961			0.222023
$950$	−20.0059			−0.649078
$951$	0.106830	+	0.135372i	0.00346419	+	0.00438975i
$952$	−3.04507	+	5.98117i	−0.0986914	+	0.193851i
$953$			5.98543i			0.193887i	0.995290	+	0.0969435i	$0.0309066\pi$
$953$			5.98543i			0.193887i	−0.995290	+	0.0969435i	$0.969093\pi$
$954$	−3.55213	+	14.8617i	−0.115004	+	0.481164i
$955$		−	14.9787i		−	0.484700i
$956$			1.08541i			0.0351045i
$957$	−28.7073	+	22.6545i	−0.927975	+	0.732315i
$958$			7.15238i			0.231083i
$959$	−12.3328	+	24.2242i	−0.398246	+	0.782240i
$960$	1.01328	−	0.799631i	0.0327034	−	0.0258080i
$961$	−7.26755			−0.234437
$962$	−9.19762			−0.296543
$963$	14.6537	+	3.50243i	0.472210	+	0.112864i
$964$			27.1249i			0.873636i
$965$	11.0418			0.355448
$966$	25.2605	−	5.04653i	0.812744	−	0.162369i
$967$	14.6261			0.470345			0.235173	−	0.971954i	$-0.424434\pi$
$967$	14.6261			0.470345			0.235173	+	0.971954i	$0.424434\pi$
$968$			2.64088i			0.0848812i
$969$	−12.2519	−	15.5253i	−0.393586	−	0.498744i
$970$	1.41158			0.0453230
$971$	−17.3611			−0.557146			−0.278573	−	0.960415i	$-0.589861\pi$
$971$	−17.3611			−0.557146			−0.278573	+	0.960415i	$0.589861\pi$
$972$	15.2812	−	3.07968i	0.490145	−	0.0987808i
$973$	14.7629	−	28.9975i	0.473277	−	0.929616i
$974$		−	38.9956i		−	1.24950i
$975$	4.76902	+	6.04321i	0.152731	+	0.193538i
$976$		−	9.20452i		−	0.294629i
$977$			28.5214i			0.912479i	0.889857	+	0.456240i	$0.150804\pi$
$977$			28.5214i			0.912479i	−0.889857	+	0.456240i	$0.849196\pi$
$978$	3.14294	+	3.98267i	0.100500	+	0.127352i
$979$		−	4.70496i		−	0.150371i
$980$	3.06906	+	4.21835i	0.0980376	+	0.134750i
$981$	−4.29776	+	17.9813i	−0.137217	+	0.574099i
$982$	31.2995			0.998806
$983$	32.7357			1.04411			0.522053	−	0.852913i	$-0.325166\pi$
$983$	32.7357			1.04411			0.522053	+	0.852913i	$0.325166\pi$
$984$	−4.07255	−	5.16066i	−0.129828	−	0.164516i
$985$			7.93051i			0.252687i
$986$	18.5252			0.589962
$987$	−54.3145	+	10.8509i	−1.72885	+	0.345388i
$988$	−4.50115			−0.143201
$989$			32.9490i			1.04772i
$990$	1.50264	−	6.28685i	0.0477569	−	0.199809i
$991$	37.5448			1.19265			0.596325	−	0.802743i	$-0.296627\pi$
$991$	37.5448			1.19265			0.596325	+	0.802743i	$0.296627\pi$
$992$	6.18608			0.196408
$993$	−8.42184	+	6.64613i	−0.267259	+	0.210909i
$994$	−1.80569	−	0.919295i	−0.0572730	−	0.0291583i
$995$		−	0.643217i		−	0.0203913i
$996$	11.6008	−	9.15484i	0.367586	−	0.290082i
$997$			17.4300i			0.552014i	0.961156	+	0.276007i	$0.0890113\pi$
$997$			17.4300i			0.552014i	−0.961156	+	0.276007i	$0.910989\pi$
$998$			5.92951i			0.187695i
$999$	−20.0743	−	43.3719i	−0.635123	−	1.37223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.g.c.209.5	✓	12
3.2	odd	2		546.2.g.d.209.8	yes	12
7.6	odd	2		546.2.g.d.209.2	yes	12
21.20	even	2	inner	546.2.g.c.209.11	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.g.c.209.5	✓	12	1.1	even	1	trivial
546.2.g.c.209.11	yes	12	21.20	even	2	inner
546.2.g.d.209.2	yes	12	7.6	odd	2
546.2.g.d.209.8	yes	12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.35967 - 1.07299i) q^{3} -1.00000 q^{4} -0.745238 q^{5} +(-1.07299 - 1.35967i) q^{6} +(-2.35778 - 1.20037i) q^{7} +1.00000i q^{8} +(0.697395 - 2.91781i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.35967 - 1.07299i) q^{3} -1.00000 q^{4} -0.745238 q^{5} +(-1.07299 - 1.35967i) q^{6} +(-2.35778 - 1.20037i) q^{7} +1.00000i q^{8} +(0.697395 - 2.91781i) q^{9} +0.745238i q^{10} -2.89121i q^{11} +(-1.35967 + 1.07299i) q^{12} -1.00000i q^{13} +(-1.20037 + 2.35778i) q^{14} +(-1.01328 + 0.799631i) q^{15} +1.00000 q^{16} -2.53678 q^{17} +(-2.91781 - 0.697395i) q^{18} +4.50115i q^{19} +0.745238 q^{20} +(-4.49378 + 0.897763i) q^{21} -2.89121 q^{22} -5.62123i q^{23} +(1.07299 + 1.35967i) q^{24} -4.44462 q^{25} -1.00000 q^{26} +(-2.18255 - 4.71556i) q^{27} +(2.35778 + 1.20037i) q^{28} -7.30263i q^{29} +(0.799631 + 1.01328i) q^{30} +6.18608i q^{31} -1.00000i q^{32} +(-3.10224 - 3.93109i) q^{33} +2.53678i q^{34} +(1.75711 + 0.894561i) q^{35} +(-0.697395 + 2.91781i) q^{36} +9.19762 q^{37} +4.50115 q^{38} +(-1.07299 - 1.35967i) q^{39} -0.745238i q^{40} -3.79553 q^{41} +(0.897763 + 4.49378i) q^{42} -5.86153 q^{43} +2.89121i q^{44} +(-0.519725 + 2.17447i) q^{45} -5.62123 q^{46} +12.0866 q^{47} +(1.35967 - 1.07299i) q^{48} +(4.11823 + 5.66040i) q^{49} +4.44462i q^{50} +(-3.44918 + 2.72194i) q^{51} +1.00000i q^{52} -5.09343i q^{53} +(-4.71556 + 2.18255i) q^{54} +2.15464i q^{55} +(1.20037 - 2.35778i) q^{56} +(4.82968 + 6.12007i) q^{57} -7.30263 q^{58} +12.0957 q^{59} +(1.01328 - 0.799631i) q^{60} -9.20452i q^{61} +6.18608 q^{62} +(-5.14675 + 6.04243i) q^{63} -1.00000 q^{64} +0.745238i q^{65} +(-3.93109 + 3.10224i) q^{66} +3.54888 q^{67} +2.53678 q^{68} +(-6.03151 - 7.64300i) q^{69} +(0.894561 - 1.75711i) q^{70} +0.765844i q^{71} +(2.91781 + 0.697395i) q^{72} +6.83961i q^{73} -9.19762i q^{74} +(-6.04321 + 4.76902i) q^{75} -4.50115i q^{76} +(-3.47052 + 6.81684i) q^{77} +(-1.35967 + 1.07299i) q^{78} +14.3002 q^{79} -0.745238 q^{80} +(-8.02728 - 4.06974i) q^{81} +3.79553i q^{82} -8.53210 q^{83} +(4.49378 - 0.897763i) q^{84} +1.89051 q^{85} +5.86153i q^{86} +(-7.83563 - 9.92915i) q^{87} +2.89121 q^{88} +1.62733 q^{89} +(2.17447 + 0.519725i) q^{90} +(-1.20037 + 2.35778i) q^{91} +5.62123i q^{92} +(6.63758 + 8.41101i) q^{93} -12.0866i q^{94} -3.35443i q^{95} +(-1.07299 - 1.35967i) q^{96} -1.89413i q^{97} +(5.66040 - 4.11823i) q^{98} +(-8.43602 - 2.01632i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{3} - 12 q^{4} + 4 q^{5} - 2 q^{6} - 8 q^{7} + 4 q^{9}+O(q^{10}) \) 12 * q - 2 * q^3 - 12 * q^4 + 4 * q^5 - 2 * q^6 - 8 * q^7 + 4 * q^9	\( 12 q - 2 q^{3} - 12 q^{4} + 4 q^{5} - 2 q^{6} - 8 q^{7} + 4 q^{9} + 2 q^{12} - 10 q^{14} + 4 q^{15} + 12 q^{16} - 12 q^{17} + 8 q^{18} - 4 q^{20} + 2 q^{24} + 20 q^{25} - 12 q^{26} - 8 q^{27} + 8 q^{28} + 14 q^{30} - 46 q^{33} + 22 q^{35} - 4 q^{36} + 16 q^{37} + 8 q^{38} - 2 q^{39} - 28 q^{41} + 2 q^{42} - 8 q^{43} + 24 q^{46} + 68 q^{47} - 2 q^{48} + 26 q^{49} - 50 q^{51} - 16 q^{54} + 10 q^{56} - 28 q^{57} - 24 q^{58} - 8 q^{59} - 4 q^{60} - 16 q^{62} + 2 q^{63} - 12 q^{64} + 12 q^{66} + 8 q^{67} + 12 q^{68} + 24 q^{69} - 28 q^{70} - 8 q^{72} - 92 q^{75} + 8 q^{77} + 2 q^{78} + 36 q^{79} + 4 q^{80} + 16 q^{81} + 32 q^{83} - 8 q^{87} + 48 q^{89} - 2 q^{90} - 10 q^{91} + 8 q^{93} - 2 q^{96} - 16 q^{98}+O(q^{100}) \) 12 * q - 2 * q^3 - 12 * q^4 + 4 * q^5 - 2 * q^6 - 8 * q^7 + 4 * q^9 + 2 * q^12 - 10 * q^14 + 4 * q^15 + 12 * q^16 - 12 * q^17 + 8 * q^18 - 4 * q^20 + 2 * q^24 + 20 * q^25 - 12 * q^26 - 8 * q^27 + 8 * q^28 + 14 * q^30 - 46 * q^33 + 22 * q^35 - 4 * q^36 + 16 * q^37 + 8 * q^38 - 2 * q^39 - 28 * q^41 + 2 * q^42 - 8 * q^43 + 24 * q^46 + 68 * q^47 - 2 * q^48 + 26 * q^49 - 50 * q^51 - 16 * q^54 + 10 * q^56 - 28 * q^57 - 24 * q^58 - 8 * q^59 - 4 * q^60 - 16 * q^62 + 2 * q^63 - 12 * q^64 + 12 * q^66 + 8 * q^67 + 12 * q^68 + 24 * q^69 - 28 * q^70 - 8 * q^72 - 92 * q^75 + 8 * q^77 + 2 * q^78 + 36 * q^79 + 4 * q^80 + 16 * q^81 + 32 * q^83 - 8 * q^87 + 48 * q^89 - 2 * q^90 - 10 * q^91 + 8 * q^93 - 2 * q^96 - 16 * q^98

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