LMFDB - Embedded newform 546.2.c.c.337.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(337,546)]

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([0, 0, 1]))

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

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

chi := DirichletCharacter("546.337");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.c (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:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			337.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	546.337
Dual form			546.2.c.c.337.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} -3.00000i q^{11} -1.00000 q^{12} +(3.00000 + 2.00000i) q^{13} +1.00000 q^{14} +1.00000i q^{15} +1.00000 q^{16} +7.00000 q^{17} -1.00000i q^{18} -3.00000i q^{19} -1.00000i q^{20} +1.00000i q^{21} -3.00000 q^{22} +1.00000 q^{23} +1.00000i q^{24} +4.00000 q^{25} +(2.00000 - 3.00000i) q^{26} +1.00000 q^{27} -1.00000i q^{28} -1.00000 q^{29} +1.00000 q^{30} +8.00000i q^{31} -1.00000i q^{32} -3.00000i q^{33} -7.00000i q^{34} -1.00000 q^{35} -1.00000 q^{36} +1.00000i q^{37} -3.00000 q^{38} +(3.00000 + 2.00000i) q^{39} -1.00000 q^{40} -4.00000i q^{41} +1.00000 q^{42} -5.00000 q^{43} +3.00000i q^{44} +1.00000i q^{45} -1.00000i q^{46} +1.00000 q^{48} -1.00000 q^{49} -4.00000i q^{50} +7.00000 q^{51} +(-3.00000 - 2.00000i) q^{52} -6.00000 q^{53} -1.00000i q^{54} +3.00000 q^{55} -1.00000 q^{56} -3.00000i q^{57} +1.00000i q^{58} -10.0000i q^{59} -1.00000i q^{60} -13.0000 q^{61} +8.00000 q^{62} +1.00000i q^{63} -1.00000 q^{64} +(-2.00000 + 3.00000i) q^{65} -3.00000 q^{66} +8.00000i q^{67} -7.00000 q^{68} +1.00000 q^{69} +1.00000i q^{70} -6.00000i q^{71} +1.00000i q^{72} +13.0000i q^{73} +1.00000 q^{74} +4.00000 q^{75} +3.00000i q^{76} +3.00000 q^{77} +(2.00000 - 3.00000i) q^{78} -12.0000 q^{79} +1.00000i q^{80} +1.00000 q^{81} -4.00000 q^{82} -2.00000i q^{83} -1.00000i q^{84} +7.00000i q^{85} +5.00000i q^{86} -1.00000 q^{87} +3.00000 q^{88} -12.0000i q^{89} +1.00000 q^{90} +(-2.00000 + 3.00000i) q^{91} -1.00000 q^{92} +8.00000i q^{93} +3.00000 q^{95} -1.00000i q^{96} -6.00000i q^{97} +1.00000i q^{98} -3.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9	$ 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9} + 2 q^{10} - 2 q^{12} + 6 q^{13} + 2 q^{14} + 2 q^{16} + 14 q^{17} - 6 q^{22} + 2 q^{23} + 8 q^{25} + 4 q^{26} + 2 q^{27} - 2 q^{29} + 2 q^{30} - 2 q^{35} - 2 q^{36} - 6 q^{38} + 6 q^{39} - 2 q^{40} + 2 q^{42} - 10 q^{43} + 2 q^{48} - 2 q^{49} + 14 q^{51} - 6 q^{52} - 12 q^{53} + 6 q^{55} - 2 q^{56} - 26 q^{61} + 16 q^{62} - 2 q^{64} - 4 q^{65} - 6 q^{66} - 14 q^{68} + 2 q^{69} + 2 q^{74} + 8 q^{75} + 6 q^{77} + 4 q^{78} - 24 q^{79} + 2 q^{81} - 8 q^{82} - 2 q^{87} + 6 q^{88} + 2 q^{90} - 4 q^{91} - 2 q^{92} + 6 q^{95}+O(q^{100}) $ 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9 + 2 * q^10 - 2 * q^12 + 6 * q^13 + 2 * q^14 + 2 * q^16 + 14 * q^17 - 6 * q^22 + 2 * q^23 + 8 * q^25 + 4 * q^26 + 2 * q^27 - 2 * q^29 + 2 * q^30 - 2 * q^35 - 2 * q^36 - 6 * q^38 + 6 * q^39 - 2 * q^40 + 2 * q^42 - 10 * q^43 + 2 * q^48 - 2 * q^49 + 14 * q^51 - 6 * q^52 - 12 * q^53 + 6 * q^55 - 2 * q^56 - 26 * q^61 + 16 * q^62 - 2 * q^64 - 4 * q^65 - 6 * q^66 - 14 * q^68 + 2 * q^69 + 2 * q^74 + 8 * q^75 + 6 * q^77 + 4 * q^78 - 24 * q^79 + 2 * q^81 - 8 * q^82 - 2 * q^87 + 6 * q^88 + 2 * q^90 - 4 * q^91 - 2 * q^92 + 6 * q^95

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.00000			−0.500000
$5$			1.00000i			0.447214i	0.974679	+	0.223607i	$0.0717831\pi$
$5$			1.00000i			0.447214i	−0.974679	+	0.223607i	$0.928217\pi$
$6$		−	1.00000i		−	0.408248i
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	1.00000			0.316228
$11$		−	3.00000i		−	0.904534i	−0.891883	−	0.452267i	$-0.850615\pi$
$11$		−	3.00000i		−	0.904534i	0.891883	−	0.452267i	$-0.149385\pi$
$12$	−1.00000			−0.288675
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$13$	3.00000	+	2.00000i	0.832050	+	0.554700i
$14$	1.00000			0.267261
$15$			1.00000i			0.258199i
$16$	1.00000			0.250000
$17$	7.00000			1.69775			0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000			1.69775			0.848875	+	0.528594i	$0.177281\pi$
$18$		−	1.00000i		−	0.235702i
$19$		−	3.00000i		−	0.688247i	−0.938924	−	0.344124i	$-0.888176\pi$
$19$		−	3.00000i		−	0.688247i	0.938924	−	0.344124i	$-0.111824\pi$
$20$		−	1.00000i		−	0.223607i
$21$			1.00000i			0.218218i
$22$	−3.00000			−0.639602
$23$	1.00000			0.208514			0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000			0.208514			0.104257	+	0.994550i	$0.466753\pi$
$24$			1.00000i			0.204124i
$25$	4.00000			0.800000
$26$	2.00000	−	3.00000i	0.392232	−	0.588348i
$27$	1.00000			0.192450
$28$		−	1.00000i		−	0.188982i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$	1.00000			0.182574
$31$			8.00000i			1.43684i	0.695608	+	0.718421i	$0.255135\pi$
$31$			8.00000i			1.43684i	−0.695608	+	0.718421i	$0.744865\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	3.00000i		−	0.522233i
$34$		−	7.00000i		−	1.20049i
$35$	−1.00000			−0.169031
$36$	−1.00000			−0.166667
$37$			1.00000i			0.164399i	0.996616	+	0.0821995i	$0.0261945\pi$
$37$			1.00000i			0.164399i	−0.996616	+	0.0821995i	$0.973806\pi$
$38$	−3.00000			−0.486664
$39$	3.00000	+	2.00000i	0.480384	+	0.320256i
$40$	−1.00000			−0.158114
$41$		−	4.00000i		−	0.624695i	−0.949968	−	0.312348i	$-0.898885\pi$
$41$		−	4.00000i		−	0.624695i	0.949968	−	0.312348i	$-0.101115\pi$
$42$	1.00000			0.154303
$43$	−5.00000			−0.762493			−0.381246	−	0.924473i	$-0.624505\pi$
$43$	−5.00000			−0.762493			−0.381246	+	0.924473i	$0.624505\pi$
$44$			3.00000i			0.452267i
$45$			1.00000i			0.149071i
$46$		−	1.00000i		−	0.147442i
$47$		0			0		1.00000			$0$
$47$		0			0		−1.00000			$\pi$
$48$	1.00000			0.144338
$49$	−1.00000			−0.142857
$50$		−	4.00000i		−	0.565685i
$51$	7.00000			0.980196
$52$	−3.00000	−	2.00000i	−0.416025	−	0.277350i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		−	1.00000i		−	0.136083i
$55$	3.00000			0.404520
$56$	−1.00000			−0.133631
$57$		−	3.00000i		−	0.397360i
$58$			1.00000i			0.131306i
$59$		−	10.0000i		−	1.30189i	−0.759125	−	0.650945i	$-0.774373\pi$
$59$		−	10.0000i		−	1.30189i	0.759125	−	0.650945i	$-0.225627\pi$
$60$		−	1.00000i		−	0.129099i
$61$	−13.0000			−1.66448			−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−13.0000			−1.66448			−0.832240	+	0.554416i	$0.812942\pi$
$62$	8.00000			1.01600
$63$			1.00000i			0.125988i
$64$	−1.00000			−0.125000
$65$	−2.00000	+	3.00000i	−0.248069	+	0.372104i
$66$	−3.00000			−0.369274
$67$			8.00000i			0.977356i	0.872464	+	0.488678i	$0.162521\pi$
$67$			8.00000i			0.977356i	−0.872464	+	0.488678i	$0.837479\pi$
$68$	−7.00000			−0.848875
$69$	1.00000			0.120386
$70$			1.00000i			0.119523i
$71$		−	6.00000i		−	0.712069i	−0.934473	−	0.356034i	$-0.884129\pi$
$71$		−	6.00000i		−	0.712069i	0.934473	−	0.356034i	$-0.115871\pi$
$72$			1.00000i			0.117851i
$73$			13.0000i			1.52153i	0.649025	+	0.760767i	$0.275177\pi$
$73$			13.0000i			1.52153i	−0.649025	+	0.760767i	$0.724823\pi$
$74$	1.00000			0.116248
$75$	4.00000			0.461880
$76$			3.00000i			0.344124i
$77$	3.00000			0.341882
$78$	2.00000	−	3.00000i	0.226455	−	0.339683i
$79$	−12.0000			−1.35011			−0.675053	−	0.737769i	$-0.735879\pi$
$79$	−12.0000			−1.35011			−0.675053	+	0.737769i	$0.735879\pi$
$80$			1.00000i			0.111803i
$81$	1.00000			0.111111
$82$	−4.00000			−0.441726
$83$		−	2.00000i		−	0.219529i	−0.993958	−	0.109764i	$-0.964990\pi$
$83$		−	2.00000i		−	0.219529i	0.993958	−	0.109764i	$-0.0350096\pi$
$84$		−	1.00000i		−	0.109109i
$85$			7.00000i			0.759257i
$86$			5.00000i			0.539164i
$87$	−1.00000			−0.107211
$88$	3.00000			0.319801
$89$		−	12.0000i		−	1.27200i	−0.771690	−	0.635999i	$-0.780588\pi$
$89$		−	12.0000i		−	1.27200i	0.771690	−	0.635999i	$-0.219412\pi$
$90$	1.00000			0.105409
$91$	−2.00000	+	3.00000i	−0.209657	+	0.314485i
$92$	−1.00000			−0.104257
$93$			8.00000i			0.829561i
$94$		0			0
$95$	3.00000			0.307794
$96$		−	1.00000i		−	0.102062i
$97$		−	6.00000i		−	0.609208i	−0.952479	−	0.304604i	$-0.901476\pi$
$97$		−	6.00000i		−	0.609208i	0.952479	−	0.304604i	$-0.0985241\pi$
$98$			1.00000i			0.101015i
$99$		−	3.00000i		−	0.301511i
$100$	−4.00000			−0.400000
$101$	14.0000			1.39305			0.696526	−	0.717532i	$-0.254728\pi$
$101$	14.0000			1.39305			0.696526	+	0.717532i	$0.254728\pi$
$102$		−	7.00000i		−	0.693103i
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	−2.00000	+	3.00000i	−0.196116	+	0.294174i
$105$	−1.00000			−0.0975900
$106$			6.00000i			0.582772i
$107$	2.00000			0.193347			0.0966736	−	0.995316i	$-0.469180\pi$
$107$	2.00000			0.193347			0.0966736	+	0.995316i	$0.469180\pi$
$108$	−1.00000			−0.0962250
$109$		−	7.00000i		−	0.670478i	−0.942133	−	0.335239i	$-0.891183\pi$
$109$		−	7.00000i		−	0.670478i	0.942133	−	0.335239i	$-0.108817\pi$
$110$		−	3.00000i		−	0.286039i
$111$			1.00000i			0.0949158i
$112$			1.00000i			0.0944911i
$113$	−10.0000			−0.940721			−0.470360	−	0.882474i	$-0.655876\pi$
$113$	−10.0000			−0.940721			−0.470360	+	0.882474i	$0.655876\pi$
$114$	−3.00000			−0.280976
$115$			1.00000i			0.0932505i
$116$	1.00000			0.0928477
$117$	3.00000	+	2.00000i	0.277350	+	0.184900i
$118$	−10.0000			−0.920575
$119$			7.00000i			0.641689i
$120$	−1.00000			−0.0912871
$121$	2.00000			0.181818
$122$			13.0000i			1.17696i
$123$		−	4.00000i		−	0.360668i
$124$		−	8.00000i		−	0.718421i
$125$			9.00000i			0.804984i
$126$	1.00000			0.0890871
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$			1.00000i			0.0883883i
$129$	−5.00000			−0.440225
$130$	3.00000	+	2.00000i	0.263117	+	0.175412i
$131$	−17.0000			−1.48530			−0.742648	−	0.669681i	$-0.766431\pi$
$131$	−17.0000			−1.48530			−0.742648	+	0.669681i	$0.766431\pi$
$132$			3.00000i			0.261116i
$133$	3.00000			0.260133
$134$	8.00000			0.691095
$135$			1.00000i			0.0860663i
$136$			7.00000i			0.600245i
$137$			17.0000i			1.45241i	0.687479	+	0.726204i	$0.258717\pi$
$137$			17.0000i			1.45241i	−0.687479	+	0.726204i	$0.741283\pi$
$138$		−	1.00000i		−	0.0851257i
$139$	−8.00000			−0.678551			−0.339276	−	0.940687i	$-0.610182\pi$
$139$	−8.00000			−0.678551			−0.339276	+	0.940687i	$0.610182\pi$
$140$	1.00000			0.0845154
$141$		0			0
$142$	−6.00000			−0.503509
$143$	6.00000	−	9.00000i	0.501745	−	0.752618i
$144$	1.00000			0.0833333
$145$		−	1.00000i		−	0.0830455i
$146$	13.0000			1.07589
$147$	−1.00000			−0.0824786
$148$		−	1.00000i		−	0.0821995i
$149$			22.0000i			1.80231i	0.433497	+	0.901155i	$0.357280\pi$
$149$			22.0000i			1.80231i	−0.433497	+	0.901155i	$0.642720\pi$
$150$		−	4.00000i		−	0.326599i
$151$			11.0000i			0.895167i	0.894242	+	0.447584i	$0.147715\pi$
$151$			11.0000i			0.895167i	−0.894242	+	0.447584i	$0.852285\pi$
$152$	3.00000			0.243332
$153$	7.00000			0.565916
$154$		−	3.00000i		−	0.241747i
$155$	−8.00000			−0.642575
$156$	−3.00000	−	2.00000i	−0.240192	−	0.160128i
$157$	19.0000			1.51637			0.758183	−	0.652042i	$-0.226088\pi$
$157$	19.0000			1.51637			0.758183	+	0.652042i	$0.226088\pi$
$158$			12.0000i			0.954669i
$159$	−6.00000			−0.475831
$160$	1.00000			0.0790569
$161$			1.00000i			0.0788110i
$162$		−	1.00000i		−	0.0785674i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$			4.00000i			0.312348i
$165$	3.00000			0.233550
$166$	−2.00000			−0.155230
$167$		−	15.0000i		−	1.16073i	−0.814355	−	0.580367i	$-0.802909\pi$
$167$		−	15.0000i		−	1.16073i	0.814355	−	0.580367i	$-0.197091\pi$
$168$	−1.00000			−0.0771517
$169$	5.00000	+	12.0000i	0.384615	+	0.923077i
$170$	7.00000			0.536875
$171$		−	3.00000i		−	0.229416i
$172$	5.00000			0.381246
$173$	−6.00000			−0.456172			−0.228086	−	0.973641i	$-0.573247\pi$
$173$	−6.00000			−0.456172			−0.228086	+	0.973641i	$0.573247\pi$
$174$			1.00000i			0.0758098i
$175$			4.00000i			0.302372i
$176$		−	3.00000i		−	0.226134i
$177$		−	10.0000i		−	0.751646i
$178$	−12.0000			−0.899438
$179$	−6.00000			−0.448461			−0.224231	−	0.974536i	$-0.571987\pi$
$179$	−6.00000			−0.448461			−0.224231	+	0.974536i	$0.571987\pi$
$180$		−	1.00000i		−	0.0745356i
$181$	−26.0000			−1.93256			−0.966282	−	0.257485i	$-0.917106\pi$
$181$	−26.0000			−1.93256			−0.966282	+	0.257485i	$0.917106\pi$
$182$	3.00000	+	2.00000i	0.222375	+	0.148250i
$183$	−13.0000			−0.960988
$184$			1.00000i			0.0737210i
$185$	−1.00000			−0.0735215
$186$	8.00000			0.586588
$187$		−	21.0000i		−	1.53567i
$188$		0			0
$189$			1.00000i			0.0727393i
$190$		−	3.00000i		−	0.217643i
$191$	−9.00000			−0.651217			−0.325609	−	0.945505i	$-0.605569\pi$
$191$	−9.00000			−0.651217			−0.325609	+	0.945505i	$0.605569\pi$
$192$	−1.00000			−0.0721688
$193$			8.00000i			0.575853i	0.957653	+	0.287926i	$0.0929658\pi$
$193$			8.00000i			0.575853i	−0.957653	+	0.287926i	$0.907034\pi$
$194$	−6.00000			−0.430775
$195$	−2.00000	+	3.00000i	−0.143223	+	0.214834i
$196$	1.00000			0.0714286
$197$		−	14.0000i		−	0.997459i	−0.866758	−	0.498729i	$-0.833800\pi$
$197$		−	14.0000i		−	0.997459i	0.866758	−	0.498729i	$-0.166200\pi$
$198$	−3.00000			−0.213201
$199$	9.00000			0.637993			0.318997	−	0.947756i	$-0.396654\pi$
$199$	9.00000			0.637993			0.318997	+	0.947756i	$0.396654\pi$
$200$			4.00000i			0.282843i
$201$			8.00000i			0.564276i
$202$		−	14.0000i		−	0.985037i
$203$		−	1.00000i		−	0.0701862i
$204$	−7.00000			−0.490098
$205$	4.00000			0.279372
$206$			1.00000i			0.0696733i
$207$	1.00000			0.0695048
$208$	3.00000	+	2.00000i	0.208013	+	0.138675i
$209$	−9.00000			−0.622543
$210$			1.00000i			0.0690066i
$211$	15.0000			1.03264			0.516321	−	0.856395i	$-0.327301\pi$
$211$	15.0000			1.03264			0.516321	+	0.856395i	$0.327301\pi$
$212$	6.00000			0.412082
$213$		−	6.00000i		−	0.411113i
$214$		−	2.00000i		−	0.136717i
$215$		−	5.00000i		−	0.340997i
$216$			1.00000i			0.0680414i
$217$	−8.00000			−0.543075
$218$	−7.00000			−0.474100
$219$			13.0000i			0.878459i
$220$	−3.00000			−0.202260
$221$	21.0000	+	14.0000i	1.41261	+	0.941742i
$222$	1.00000			0.0671156
$223$		−	4.00000i		−	0.267860i	−0.990991	−	0.133930i	$-0.957240\pi$
$223$		−	4.00000i		−	0.267860i	0.990991	−	0.133930i	$-0.0427597\pi$
$224$	1.00000			0.0668153
$225$	4.00000			0.266667
$226$			10.0000i			0.665190i
$227$		−	20.0000i		−	1.32745i	−0.747978	−	0.663723i	$-0.768975\pi$
$227$		−	20.0000i		−	1.32745i	0.747978	−	0.663723i	$-0.231025\pi$
$228$			3.00000i			0.198680i
$229$		−	10.0000i		−	0.660819i	−0.943838	−	0.330409i	$-0.892813\pi$
$229$		−	10.0000i		−	0.660819i	0.943838	−	0.330409i	$-0.107187\pi$
$230$	1.00000			0.0659380
$231$	3.00000			0.197386
$232$		−	1.00000i		−	0.0656532i
$233$	18.0000			1.17922			0.589610	−	0.807688i	$-0.299282\pi$
$233$	18.0000			1.17922			0.589610	+	0.807688i	$0.299282\pi$
$234$	2.00000	−	3.00000i	0.130744	−	0.196116i
$235$		0			0
$236$			10.0000i			0.650945i
$237$	−12.0000			−0.779484
$238$	7.00000			0.453743
$239$		−	8.00000i		−	0.517477i	−0.965947	−	0.258738i	$-0.916693\pi$
$239$		−	8.00000i		−	0.517477i	0.965947	−	0.258738i	$-0.0833068\pi$
$240$			1.00000i			0.0645497i
$241$		−	26.0000i		−	1.67481i	−0.546585	−	0.837404i	$-0.684072\pi$
$241$		−	26.0000i		−	1.67481i	0.546585	−	0.837404i	$-0.315928\pi$
$242$		−	2.00000i		−	0.128565i
$243$	1.00000			0.0641500
$244$	13.0000			0.832240
$245$		−	1.00000i		−	0.0638877i
$246$	−4.00000			−0.255031
$247$	6.00000	−	9.00000i	0.381771	−	0.572656i
$248$	−8.00000			−0.508001
$249$		−	2.00000i		−	0.126745i
$250$	9.00000			0.569210
$251$	17.0000			1.07303			0.536515	−	0.843891i	$-0.319740\pi$
$251$	17.0000			1.07303			0.536515	+	0.843891i	$0.319740\pi$
$252$		−	1.00000i		−	0.0629941i
$253$		−	3.00000i		−	0.188608i
$254$			4.00000i			0.250982i
$255$			7.00000i			0.438357i
$256$	1.00000			0.0625000
$257$	−6.00000			−0.374270			−0.187135	−	0.982334i	$-0.559920\pi$
$257$	−6.00000			−0.374270			−0.187135	+	0.982334i	$0.559920\pi$
$258$			5.00000i			0.311286i
$259$	−1.00000			−0.0621370
$260$	2.00000	−	3.00000i	0.124035	−	0.186052i
$261$	−1.00000			−0.0618984
$262$			17.0000i			1.05026i
$263$	−24.0000			−1.47990			−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000			−1.47990			−0.739952	+	0.672660i	$0.765152\pi$
$264$	3.00000			0.184637
$265$		−	6.00000i		−	0.368577i
$266$		−	3.00000i		−	0.183942i
$267$		−	12.0000i		−	0.734388i
$268$		−	8.00000i		−	0.488678i
$269$	−4.00000			−0.243884			−0.121942	−	0.992537i	$-0.538912\pi$
$269$	−4.00000			−0.243884			−0.121942	+	0.992537i	$0.538912\pi$
$270$	1.00000			0.0608581
$271$		−	20.0000i		−	1.21491i	−0.794353	−	0.607457i	$-0.792190\pi$
$271$		−	20.0000i		−	1.21491i	0.794353	−	0.607457i	$-0.207810\pi$
$272$	7.00000			0.424437
$273$	−2.00000	+	3.00000i	−0.121046	+	0.181568i
$274$	17.0000			1.02701
$275$		−	12.0000i		−	0.723627i
$276$	−1.00000			−0.0601929
$277$	28.0000			1.68236			0.841178	−	0.540758i	$-0.181862\pi$
$277$	28.0000			1.68236			0.841178	+	0.540758i	$0.181862\pi$
$278$			8.00000i			0.479808i
$279$			8.00000i			0.478947i
$280$		−	1.00000i		−	0.0597614i
$281$			10.0000i			0.596550i	0.954480	+	0.298275i	$0.0964112\pi$
$281$			10.0000i			0.596550i	−0.954480	+	0.298275i	$0.903589\pi$
$282$		0			0
$283$	−14.0000			−0.832214			−0.416107	−	0.909316i	$-0.636606\pi$
$283$	−14.0000			−0.832214			−0.416107	+	0.909316i	$0.636606\pi$
$284$			6.00000i			0.356034i
$285$	3.00000			0.177705
$286$	−9.00000	−	6.00000i	−0.532181	−	0.354787i
$287$	4.00000			0.236113
$288$		−	1.00000i		−	0.0589256i
$289$	32.0000			1.88235
$290$	−1.00000			−0.0587220
$291$		−	6.00000i		−	0.351726i
$292$		−	13.0000i		−	0.760767i
$293$			14.0000i			0.817889i	0.912559	+	0.408944i	$0.134103\pi$
$293$			14.0000i			0.817889i	−0.912559	+	0.408944i	$0.865897\pi$
$294$			1.00000i			0.0583212i
$295$	10.0000			0.582223
$296$	−1.00000			−0.0581238
$297$		−	3.00000i		−	0.174078i
$298$	22.0000			1.27443
$299$	3.00000	+	2.00000i	0.173494	+	0.115663i
$300$	−4.00000			−0.230940
$301$		−	5.00000i		−	0.288195i
$302$	11.0000			0.632979
$303$	14.0000			0.804279
$304$		−	3.00000i		−	0.172062i
$305$		−	13.0000i		−	0.744378i
$306$		−	7.00000i		−	0.400163i
$307$		−	16.0000i		−	0.913168i	−0.889680	−	0.456584i	$-0.849073\pi$
$307$		−	16.0000i		−	0.913168i	0.889680	−	0.456584i	$-0.150927\pi$
$308$	−3.00000			−0.170941
$309$	−1.00000			−0.0568880
$310$			8.00000i			0.454369i
$311$	−4.00000			−0.226819			−0.113410	−	0.993548i	$-0.536177\pi$
$311$	−4.00000			−0.226819			−0.113410	+	0.993548i	$0.536177\pi$
$312$	−2.00000	+	3.00000i	−0.113228	+	0.169842i
$313$	−26.0000			−1.46961			−0.734803	−	0.678280i	$-0.762726\pi$
$313$	−26.0000			−1.46961			−0.734803	+	0.678280i	$0.762726\pi$
$314$		−	19.0000i		−	1.07223i
$315$	−1.00000			−0.0563436
$316$	12.0000			0.675053
$317$		−	24.0000i		−	1.34797i	−0.738743	−	0.673987i	$-0.764580\pi$
$317$		−	24.0000i		−	1.34797i	0.738743	−	0.673987i	$-0.235420\pi$
$318$			6.00000i			0.336463i
$319$			3.00000i			0.167968i
$320$		−	1.00000i		−	0.0559017i
$321$	2.00000			0.111629
$322$	1.00000			0.0557278
$323$		−	21.0000i		−	1.16847i
$324$	−1.00000			−0.0555556
$325$	12.0000	+	8.00000i	0.665640	+	0.443760i
$326$	−4.00000			−0.221540
$327$		−	7.00000i		−	0.387101i
$328$	4.00000			0.220863
$329$		0			0
$330$		−	3.00000i		−	0.165145i
$331$		−	8.00000i		−	0.439720i	−0.975531	−	0.219860i	$-0.929440\pi$
$331$		−	8.00000i		−	0.439720i	0.975531	−	0.219860i	$-0.0705600\pi$
$332$			2.00000i			0.109764i
$333$			1.00000i			0.0547997i
$334$	−15.0000			−0.820763
$335$	−8.00000			−0.437087
$336$			1.00000i			0.0545545i
$337$	−23.0000			−1.25289			−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000			−1.25289			−0.626445	+	0.779466i	$0.715491\pi$
$338$	12.0000	−	5.00000i	0.652714	−	0.271964i
$339$	−10.0000			−0.543125
$340$		−	7.00000i		−	0.379628i
$341$	24.0000			1.29967
$342$	−3.00000			−0.162221
$343$		−	1.00000i		−	0.0539949i
$344$		−	5.00000i		−	0.269582i
$345$			1.00000i			0.0538382i
$346$			6.00000i			0.322562i
$347$	−24.0000			−1.28839			−0.644194	−	0.764862i	$-0.722807\pi$
$347$	−24.0000			−1.28839			−0.644194	+	0.764862i	$0.722807\pi$
$348$	1.00000			0.0536056
$349$			16.0000i			0.856460i	0.903670	+	0.428230i	$0.140863\pi$
$349$			16.0000i			0.856460i	−0.903670	+	0.428230i	$0.859137\pi$
$350$	4.00000			0.213809
$351$	3.00000	+	2.00000i	0.160128	+	0.106752i
$352$	−3.00000			−0.159901
$353$			16.0000i			0.851594i	0.904819	+	0.425797i	$0.140006\pi$
$353$			16.0000i			0.851594i	−0.904819	+	0.425797i	$0.859994\pi$
$354$	−10.0000			−0.531494
$355$	6.00000			0.318447
$356$			12.0000i			0.635999i
$357$			7.00000i			0.370479i
$358$			6.00000i			0.317110i
$359$			26.0000i			1.37223i	0.727494	+	0.686114i	$0.240685\pi$
$359$			26.0000i			1.37223i	−0.727494	+	0.686114i	$0.759315\pi$
$360$	−1.00000			−0.0527046
$361$	10.0000			0.526316
$362$			26.0000i			1.36653i
$363$	2.00000			0.104973
$364$	2.00000	−	3.00000i	0.104828	−	0.157243i
$365$	−13.0000			−0.680451
$366$			13.0000i			0.679521i
$367$	32.0000			1.67039			0.835193	−	0.549957i	$-0.185356\pi$
$367$	32.0000			1.67039			0.835193	+	0.549957i	$0.185356\pi$
$368$	1.00000			0.0521286
$369$		−	4.00000i		−	0.208232i
$370$			1.00000i			0.0519875i
$371$		−	6.00000i		−	0.311504i
$372$		−	8.00000i		−	0.414781i
$373$	6.00000			0.310668			0.155334	−	0.987862i	$-0.450355\pi$
$373$	6.00000			0.310668			0.155334	+	0.987862i	$0.450355\pi$
$374$	−21.0000			−1.08588
$375$			9.00000i			0.464758i
$376$		0			0
$377$	−3.00000	−	2.00000i	−0.154508	−	0.103005i
$378$	1.00000			0.0514344
$379$		−	4.00000i		−	0.205466i	−0.994709	−	0.102733i	$-0.967241\pi$
$379$		−	4.00000i		−	0.205466i	0.994709	−	0.102733i	$-0.0327588\pi$
$380$	−3.00000			−0.153897
$381$	−4.00000			−0.204926
$382$			9.00000i			0.460480i
$383$		−	17.0000i		−	0.868659i	−0.900754	−	0.434330i	$-0.856985\pi$
$383$		−	17.0000i		−	0.868659i	0.900754	−	0.434330i	$-0.143015\pi$
$384$			1.00000i			0.0510310i
$385$			3.00000i			0.152894i
$386$	8.00000			0.407189
$387$	−5.00000			−0.254164
$388$			6.00000i			0.304604i
$389$	−18.0000			−0.912636			−0.456318	−	0.889817i	$-0.650832\pi$
$389$	−18.0000			−0.912636			−0.456318	+	0.889817i	$0.650832\pi$
$390$	3.00000	+	2.00000i	0.151911	+	0.101274i
$391$	7.00000			0.354005
$392$		−	1.00000i		−	0.0505076i
$393$	−17.0000			−0.857537
$394$	−14.0000			−0.705310
$395$		−	12.0000i		−	0.603786i
$396$			3.00000i			0.150756i
$397$		−	8.00000i		−	0.401508i	−0.979642	−	0.200754i	$-0.935661\pi$
$397$		−	8.00000i		−	0.401508i	0.979642	−	0.200754i	$-0.0643393\pi$
$398$		−	9.00000i		−	0.451129i
$399$	3.00000			0.150188
$400$	4.00000			0.200000
$401$			6.00000i			0.299626i	0.988714	+	0.149813i	$0.0478671\pi$
$401$			6.00000i			0.299626i	−0.988714	+	0.149813i	$0.952133\pi$
$402$	8.00000			0.399004
$403$	−16.0000	+	24.0000i	−0.797017	+	1.19553i
$404$	−14.0000			−0.696526
$405$			1.00000i			0.0496904i
$406$	−1.00000			−0.0496292
$407$	3.00000			0.148704
$408$			7.00000i			0.346552i
$409$			29.0000i			1.43396i	0.697095	+	0.716979i	$0.254476\pi$
$409$			29.0000i			1.43396i	−0.697095	+	0.716979i	$0.745524\pi$
$410$		−	4.00000i		−	0.197546i
$411$			17.0000i			0.838548i
$412$	1.00000			0.0492665
$413$	10.0000			0.492068
$414$		−	1.00000i		−	0.0491473i
$415$	2.00000			0.0981761
$416$	2.00000	−	3.00000i	0.0980581	−	0.147087i
$417$	−8.00000			−0.391762
$418$			9.00000i			0.440204i
$419$	−11.0000			−0.537385			−0.268693	−	0.963226i	$-0.586592\pi$
$419$	−11.0000			−0.537385			−0.268693	+	0.963226i	$0.586592\pi$
$420$	1.00000			0.0487950
$421$			34.0000i			1.65706i	0.559946	+	0.828529i	$0.310822\pi$
$421$			34.0000i			1.65706i	−0.559946	+	0.828529i	$0.689178\pi$
$422$		−	15.0000i		−	0.730189i
$423$		0			0
$424$		−	6.00000i		−	0.291386i
$425$	28.0000			1.35820
$426$	−6.00000			−0.290701
$427$		−	13.0000i		−	0.629114i
$428$	−2.00000			−0.0966736
$429$	6.00000	−	9.00000i	0.289683	−	0.434524i
$430$	−5.00000			−0.241121
$431$			14.0000i			0.674356i	0.941441	+	0.337178i	$0.109472\pi$
$431$			14.0000i			0.674356i	−0.941441	+	0.337178i	$0.890528\pi$
$432$	1.00000			0.0481125
$433$	−8.00000			−0.384455			−0.192228	−	0.981350i	$-0.561571\pi$
$433$	−8.00000			−0.384455			−0.192228	+	0.981350i	$0.561571\pi$
$434$			8.00000i			0.384012i
$435$		−	1.00000i		−	0.0479463i
$436$			7.00000i			0.335239i
$437$		−	3.00000i		−	0.143509i
$438$	13.0000			0.621164
$439$	27.0000			1.28864			0.644320	−	0.764756i	$-0.277141\pi$
$439$	27.0000			1.28864			0.644320	+	0.764756i	$0.277141\pi$
$440$			3.00000i			0.143019i
$441$	−1.00000			−0.0476190
$442$	14.0000	−	21.0000i	0.665912	−	0.998868i
$443$	−34.0000			−1.61539			−0.807694	−	0.589601i	$-0.799285\pi$
$443$	−34.0000			−1.61539			−0.807694	+	0.589601i	$0.799285\pi$
$444$		−	1.00000i		−	0.0474579i
$445$	12.0000			0.568855
$446$	−4.00000			−0.189405
$447$			22.0000i			1.04056i
$448$		−	1.00000i		−	0.0472456i
$449$			9.00000i			0.424736i	0.977190	+	0.212368i	$0.0681176\pi$
$449$			9.00000i			0.424736i	−0.977190	+	0.212368i	$0.931882\pi$
$450$		−	4.00000i		−	0.188562i
$451$	−12.0000			−0.565058
$452$	10.0000			0.470360
$453$			11.0000i			0.516825i
$454$	−20.0000			−0.938647
$455$	−3.00000	−	2.00000i	−0.140642	−	0.0937614i
$456$	3.00000			0.140488
$457$		−	28.0000i		−	1.30978i	−0.755722	−	0.654892i	$-0.772714\pi$
$457$		−	28.0000i		−	1.30978i	0.755722	−	0.654892i	$-0.227286\pi$
$458$	−10.0000			−0.467269
$459$	7.00000			0.326732
$460$		−	1.00000i		−	0.0466252i
$461$			27.0000i			1.25752i	0.777601	+	0.628758i	$0.216436\pi$
$461$			27.0000i			1.25752i	−0.777601	+	0.628758i	$0.783564\pi$
$462$		−	3.00000i		−	0.139573i
$463$			15.0000i			0.697109i	0.937288	+	0.348555i	$0.113327\pi$
$463$			15.0000i			0.697109i	−0.937288	+	0.348555i	$0.886673\pi$
$464$	−1.00000			−0.0464238
$465$	−8.00000			−0.370991
$466$		−	18.0000i		−	0.833834i
$467$	9.00000			0.416470			0.208235	−	0.978079i	$-0.433228\pi$
$467$	9.00000			0.416470			0.208235	+	0.978079i	$0.433228\pi$
$468$	−3.00000	−	2.00000i	−0.138675	−	0.0924500i
$469$	−8.00000			−0.369406
$470$		0			0
$471$	19.0000			0.875474
$472$	10.0000			0.460287
$473$			15.0000i			0.689701i
$474$			12.0000i			0.551178i
$475$		−	12.0000i		−	0.550598i
$476$		−	7.00000i		−	0.320844i
$477$	−6.00000			−0.274721
$478$	−8.00000			−0.365911
$479$			3.00000i			0.137073i	0.997649	+	0.0685367i	$0.0218330\pi$
$479$			3.00000i			0.137073i	−0.997649	+	0.0685367i	$0.978167\pi$
$480$	1.00000			0.0456435
$481$	−2.00000	+	3.00000i	−0.0911922	+	0.136788i
$482$	−26.0000			−1.18427
$483$			1.00000i			0.0455016i
$484$	−2.00000			−0.0909091
$485$	6.00000			0.272446
$486$		−	1.00000i		−	0.0453609i
$487$			24.0000i			1.08754i	0.839233	+	0.543772i	$0.183004\pi$
$487$			24.0000i			1.08754i	−0.839233	+	0.543772i	$0.816996\pi$
$488$		−	13.0000i		−	0.588482i
$489$		−	4.00000i		−	0.180886i
$490$	−1.00000			−0.0451754
$491$	−40.0000			−1.80517			−0.902587	−	0.430507i	$-0.858335\pi$
$491$	−40.0000			−1.80517			−0.902587	+	0.430507i	$0.858335\pi$
$492$			4.00000i			0.180334i
$493$	−7.00000			−0.315264
$494$	−9.00000	−	6.00000i	−0.404929	−	0.269953i
$495$	3.00000			0.134840
$496$			8.00000i			0.359211i
$497$	6.00000			0.269137
$498$	−2.00000			−0.0896221
$499$		−	14.0000i		−	0.626726i	−0.949633	−	0.313363i	$-0.898544\pi$
$499$		−	14.0000i		−	0.626726i	0.949633	−	0.313363i	$-0.101456\pi$
$500$		−	9.00000i		−	0.402492i
$501$		−	15.0000i		−	0.670151i
$502$		−	17.0000i		−	0.758747i
$503$	−6.00000			−0.267527			−0.133763	−	0.991013i	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$	−1.00000			−0.0445435
$505$			14.0000i			0.622992i
$506$	−3.00000			−0.133366
$507$	5.00000	+	12.0000i	0.222058	+	0.532939i
$508$	4.00000			0.177471
$509$			27.0000i			1.19675i	0.801215	+	0.598377i	$0.204187\pi$
$509$			27.0000i			1.19675i	−0.801215	+	0.598377i	$0.795813\pi$
$510$	7.00000			0.309965
$511$	−13.0000			−0.575086
$512$		−	1.00000i		−	0.0441942i
$513$		−	3.00000i		−	0.132453i
$514$			6.00000i			0.264649i
$515$		−	1.00000i		−	0.0440653i
$516$	5.00000			0.220113
$517$		0			0
$518$			1.00000i			0.0439375i
$519$	−6.00000			−0.263371
$520$	−3.00000	−	2.00000i	−0.131559	−	0.0877058i
$521$	15.0000			0.657162			0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000			0.657162			0.328581	+	0.944476i	$0.393430\pi$
$522$			1.00000i			0.0437688i
$523$	16.0000			0.699631			0.349816	−	0.936819i	$-0.386244\pi$
$523$	16.0000			0.699631			0.349816	+	0.936819i	$0.386244\pi$
$524$	17.0000			0.742648
$525$			4.00000i			0.174574i
$526$			24.0000i			1.04645i
$527$			56.0000i			2.43940i
$528$		−	3.00000i		−	0.130558i
$529$	−22.0000			−0.956522
$530$	−6.00000			−0.260623
$531$		−	10.0000i		−	0.433963i
$532$	−3.00000			−0.130066
$533$	8.00000	−	12.0000i	0.346518	−	0.519778i
$534$	−12.0000			−0.519291
$535$			2.00000i			0.0864675i
$536$	−8.00000			−0.345547
$537$	−6.00000			−0.258919
$538$			4.00000i			0.172452i
$539$			3.00000i			0.129219i
$540$		−	1.00000i		−	0.0430331i
$541$		−	25.0000i		−	1.07483i	−0.843317	−	0.537417i	$-0.819400\pi$
$541$		−	25.0000i		−	1.07483i	0.843317	−	0.537417i	$-0.180600\pi$
$542$	−20.0000			−0.859074
$543$	−26.0000			−1.11577
$544$		−	7.00000i		−	0.300123i
$545$	7.00000			0.299847
$546$	3.00000	+	2.00000i	0.128388	+	0.0855921i
$547$	28.0000			1.19719			0.598597	−	0.801050i	$-0.295725\pi$
$547$	28.0000			1.19719			0.598597	+	0.801050i	$0.295725\pi$
$548$		−	17.0000i		−	0.726204i
$549$	−13.0000			−0.554826
$550$	−12.0000			−0.511682
$551$			3.00000i			0.127804i
$552$			1.00000i			0.0425628i
$553$		−	12.0000i		−	0.510292i
$554$		−	28.0000i		−	1.18961i
$555$	−1.00000			−0.0424476
$556$	8.00000			0.339276
$557$		−	30.0000i		−	1.27114i	−0.772043	−	0.635570i	$-0.780765\pi$
$557$		−	30.0000i		−	1.27114i	0.772043	−	0.635570i	$-0.219235\pi$
$558$	8.00000			0.338667
$559$	−15.0000	−	10.0000i	−0.634432	−	0.422955i
$560$	−1.00000			−0.0422577
$561$		−	21.0000i		−	0.886621i
$562$	10.0000			0.421825
$563$	41.0000			1.72794			0.863972	−	0.503540i	$-0.167969\pi$
$563$	41.0000			1.72794			0.863972	+	0.503540i	$0.167969\pi$
$564$		0			0
$565$		−	10.0000i		−	0.420703i
$566$			14.0000i			0.588464i
$567$			1.00000i			0.0419961i
$568$	6.00000			0.251754
$569$	−2.00000			−0.0838444			−0.0419222	−	0.999121i	$-0.513348\pi$
$569$	−2.00000			−0.0838444			−0.0419222	+	0.999121i	$0.513348\pi$
$570$		−	3.00000i		−	0.125656i
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$	−6.00000	+	9.00000i	−0.250873	+	0.376309i
$573$	−9.00000			−0.375980
$574$		−	4.00000i		−	0.166957i
$575$	4.00000			0.166812
$576$	−1.00000			−0.0416667
$577$		−	38.0000i		−	1.58196i	−0.611842	−	0.790980i	$-0.709571\pi$
$577$		−	38.0000i		−	1.58196i	0.611842	−	0.790980i	$-0.290429\pi$
$578$		−	32.0000i		−	1.33102i
$579$			8.00000i			0.332469i
$580$			1.00000i			0.0415227i
$581$	2.00000			0.0829740
$582$	−6.00000			−0.248708
$583$			18.0000i			0.745484i
$584$	−13.0000			−0.537944
$585$	−2.00000	+	3.00000i	−0.0826898	+	0.124035i
$586$	14.0000			0.578335
$587$		−	16.0000i		−	0.660391i	−0.943913	−	0.330195i	$-0.892885\pi$
$587$		−	16.0000i		−	0.660391i	0.943913	−	0.330195i	$-0.107115\pi$
$588$	1.00000			0.0412393
$589$	24.0000			0.988903
$590$		−	10.0000i		−	0.411693i
$591$		−	14.0000i		−	0.575883i
$592$			1.00000i			0.0410997i
$593$			16.0000i			0.657041i	0.944497	+	0.328521i	$0.106550\pi$
$593$			16.0000i			0.657041i	−0.944497	+	0.328521i	$0.893450\pi$
$594$	−3.00000			−0.123091
$595$	−7.00000			−0.286972
$596$		−	22.0000i		−	0.901155i
$597$	9.00000			0.368345
$598$	2.00000	−	3.00000i	0.0817861	−	0.122679i
$599$	−3.00000			−0.122577			−0.0612883	−	0.998120i	$-0.519521\pi$
$599$	−3.00000			−0.122577			−0.0612883	+	0.998120i	$0.519521\pi$
$600$			4.00000i			0.163299i
$601$	4.00000			0.163163			0.0815817	−	0.996667i	$-0.474003\pi$
$601$	4.00000			0.163163			0.0815817	+	0.996667i	$0.474003\pi$
$602$	−5.00000			−0.203785
$603$			8.00000i			0.325785i
$604$		−	11.0000i		−	0.447584i
$605$			2.00000i			0.0813116i
$606$		−	14.0000i		−	0.568711i
$607$	−11.0000			−0.446476			−0.223238	−	0.974764i	$-0.571663\pi$
$607$	−11.0000			−0.446476			−0.223238	+	0.974764i	$0.571663\pi$
$608$	−3.00000			−0.121666
$609$		−	1.00000i		−	0.0405220i
$610$	−13.0000			−0.526355
$611$		0			0
$612$	−7.00000			−0.282958
$613$		−	31.0000i		−	1.25208i	−0.779792	−	0.626039i	$-0.784675\pi$
$613$		−	31.0000i		−	1.25208i	0.779792	−	0.626039i	$-0.215325\pi$
$614$	−16.0000			−0.645707
$615$	4.00000			0.161296
$616$			3.00000i			0.120873i
$617$			37.0000i			1.48956i	0.667308	+	0.744782i	$0.267447\pi$
$617$			37.0000i			1.48956i	−0.667308	+	0.744782i	$0.732553\pi$
$618$			1.00000i			0.0402259i
$619$			23.0000i			0.924448i	0.886763	+	0.462224i	$0.152948\pi$
$619$			23.0000i			0.924448i	−0.886763	+	0.462224i	$0.847052\pi$
$620$	8.00000			0.321288
$621$	1.00000			0.0401286
$622$			4.00000i			0.160385i
$623$	12.0000			0.480770
$624$	3.00000	+	2.00000i	0.120096	+	0.0800641i
$625$	11.0000			0.440000
$626$			26.0000i			1.03917i
$627$	−9.00000			−0.359425
$628$	−19.0000			−0.758183
$629$			7.00000i			0.279108i
$630$			1.00000i			0.0398410i
$631$			47.0000i			1.87104i	0.353273	+	0.935520i	$0.385069\pi$
$631$			47.0000i			1.87104i	−0.353273	+	0.935520i	$0.614931\pi$
$632$		−	12.0000i		−	0.477334i
$633$	15.0000			0.596196
$634$	−24.0000			−0.953162
$635$		−	4.00000i		−	0.158735i
$636$	6.00000			0.237915
$637$	−3.00000	−	2.00000i	−0.118864	−	0.0792429i
$638$	3.00000			0.118771
$639$		−	6.00000i		−	0.237356i
$640$	−1.00000			−0.0395285
$641$	12.0000			0.473972			0.236986	−	0.971513i	$-0.423841\pi$
$641$	12.0000			0.473972			0.236986	+	0.971513i	$0.423841\pi$
$642$		−	2.00000i		−	0.0789337i
$643$			39.0000i			1.53801i	0.639243	+	0.769005i	$0.279248\pi$
$643$			39.0000i			1.53801i	−0.639243	+	0.769005i	$0.720752\pi$
$644$		−	1.00000i		−	0.0394055i
$645$		−	5.00000i		−	0.196875i
$646$	−21.0000			−0.826234
$647$	22.0000			0.864909			0.432455	−	0.901656i	$-0.357648\pi$
$647$	22.0000			0.864909			0.432455	+	0.901656i	$0.357648\pi$
$648$			1.00000i			0.0392837i
$649$	−30.0000			−1.17760
$650$	8.00000	−	12.0000i	0.313786	−	0.470679i
$651$	−8.00000			−0.313545
$652$			4.00000i			0.156652i
$653$	−35.0000			−1.36966			−0.684828	−	0.728705i	$-0.740123\pi$
$653$	−35.0000			−1.36966			−0.684828	+	0.728705i	$0.740123\pi$
$654$	−7.00000			−0.273722
$655$		−	17.0000i		−	0.664245i
$656$		−	4.00000i		−	0.156174i
$657$			13.0000i			0.507178i
$658$		0			0
$659$	26.0000			1.01282			0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000			1.01282			0.506408	+	0.862294i	$0.330973\pi$
$660$	−3.00000			−0.116775
$661$			10.0000i			0.388955i	0.980907	+	0.194477i	$0.0623011\pi$
$661$			10.0000i			0.388955i	−0.980907	+	0.194477i	$0.937699\pi$
$662$	−8.00000			−0.310929
$663$	21.0000	+	14.0000i	0.815572	+	0.543715i
$664$	2.00000			0.0776151
$665$			3.00000i			0.116335i
$666$	1.00000			0.0387492
$667$	−1.00000			−0.0387202
$668$			15.0000i			0.580367i
$669$		−	4.00000i		−	0.154649i
$670$			8.00000i			0.309067i
$671$			39.0000i			1.50558i
$672$	1.00000			0.0385758
$673$	−3.00000			−0.115642			−0.0578208	−	0.998327i	$-0.518415\pi$
$673$	−3.00000			−0.115642			−0.0578208	+	0.998327i	$0.518415\pi$
$674$			23.0000i			0.885927i
$675$	4.00000			0.153960
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$			10.0000i			0.384048i
$679$	6.00000			0.230259
$680$	−7.00000			−0.268438
$681$		−	20.0000i		−	0.766402i
$682$		−	24.0000i		−	0.919007i
$683$		−	9.00000i		−	0.344375i	−0.985064	−	0.172188i	$-0.944916\pi$
$683$		−	9.00000i		−	0.344375i	0.985064	−	0.172188i	$-0.0550836\pi$
$684$			3.00000i			0.114708i
$685$	−17.0000			−0.649537
$686$	−1.00000			−0.0381802
$687$		−	10.0000i		−	0.381524i
$688$	−5.00000			−0.190623
$689$	−18.0000	−	12.0000i	−0.685745	−	0.457164i
$690$	1.00000			0.0380693
$691$			16.0000i			0.608669i	0.952565	+	0.304334i	$0.0984340\pi$
$691$			16.0000i			0.608669i	−0.952565	+	0.304334i	$0.901566\pi$
$692$	6.00000			0.228086
$693$	3.00000			0.113961
$694$			24.0000i			0.911028i
$695$		−	8.00000i		−	0.303457i
$696$		−	1.00000i		−	0.0379049i
$697$		−	28.0000i		−	1.06058i
$698$	16.0000			0.605609
$699$	18.0000			0.680823
$700$		−	4.00000i		−	0.151186i
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$	2.00000	−	3.00000i	0.0754851	−	0.113228i
$703$	3.00000			0.113147
$704$			3.00000i			0.113067i
$705$		0			0
$706$	16.0000			0.602168
$707$			14.0000i			0.526524i
$708$			10.0000i			0.375823i
$709$			30.0000i			1.12667i	0.826227	+	0.563337i	$0.190483\pi$
$709$			30.0000i			1.12667i	−0.826227	+	0.563337i	$0.809517\pi$
$710$		−	6.00000i		−	0.225176i
$711$	−12.0000			−0.450035
$712$	12.0000			0.449719
$713$			8.00000i			0.299602i
$714$	7.00000			0.261968
$715$	9.00000	+	6.00000i	0.336581	+	0.224387i
$716$	6.00000			0.224231
$717$		−	8.00000i		−	0.298765i
$718$	26.0000			0.970311
$719$	20.0000			0.745874			0.372937	−	0.927857i	$-0.378351\pi$
$719$	20.0000			0.745874			0.372937	+	0.927857i	$0.378351\pi$
$720$			1.00000i			0.0372678i
$721$		−	1.00000i		−	0.0372419i
$722$		−	10.0000i		−	0.372161i
$723$		−	26.0000i		−	0.966950i
$724$	26.0000			0.966282
$725$	−4.00000			−0.148556
$726$		−	2.00000i		−	0.0742270i
$727$	35.0000			1.29808			0.649039	−	0.760755i	$-0.275171\pi$
$727$	35.0000			1.29808			0.649039	+	0.760755i	$0.275171\pi$
$728$	−3.00000	−	2.00000i	−0.111187	−	0.0741249i
$729$	1.00000			0.0370370
$730$			13.0000i			0.481152i
$731$	−35.0000			−1.29452
$732$	13.0000			0.480494
$733$			8.00000i			0.295487i	0.989026	+	0.147743i	$0.0472010\pi$
$733$			8.00000i			0.295487i	−0.989026	+	0.147743i	$0.952799\pi$
$734$		−	32.0000i		−	1.18114i
$735$		−	1.00000i		−	0.0368856i
$736$		−	1.00000i		−	0.0368605i
$737$	24.0000			0.884051
$738$	−4.00000			−0.147242
$739$		−	16.0000i		−	0.588570i	−0.955718	−	0.294285i	$-0.904919\pi$
$739$		−	16.0000i		−	0.588570i	0.955718	−	0.294285i	$-0.0950814\pi$
$740$	1.00000			0.0367607
$741$	6.00000	−	9.00000i	0.220416	−	0.330623i
$742$	−6.00000			−0.220267
$743$		−	40.0000i		−	1.46746i	−0.679442	−	0.733729i	$-0.737778\pi$
$743$		−	40.0000i		−	1.46746i	0.679442	−	0.733729i	$-0.262222\pi$
$744$	−8.00000			−0.293294
$745$	−22.0000			−0.806018
$746$		−	6.00000i		−	0.219676i
$747$		−	2.00000i		−	0.0731762i
$748$			21.0000i			0.767836i
$749$			2.00000i			0.0730784i
$750$	9.00000			0.328634
$751$	−4.00000			−0.145962			−0.0729810	−	0.997333i	$-0.523251\pi$
$751$	−4.00000			−0.145962			−0.0729810	+	0.997333i	$0.523251\pi$
$752$		0			0
$753$	17.0000			0.619514
$754$	−2.00000	+	3.00000i	−0.0728357	+	0.109254i
$755$	−11.0000			−0.400331
$756$		−	1.00000i		−	0.0363696i
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	−4.00000			−0.145287
$759$		−	3.00000i		−	0.108893i
$760$			3.00000i			0.108821i
$761$			30.0000i			1.08750i	0.839248	+	0.543750i	$0.182996\pi$
$761$			30.0000i			1.08750i	−0.839248	+	0.543750i	$0.817004\pi$
$762$			4.00000i			0.144905i
$763$	7.00000			0.253417
$764$	9.00000			0.325609
$765$			7.00000i			0.253086i
$766$	−17.0000			−0.614235
$767$	20.0000	−	30.0000i	0.722158	−	1.08324i
$768$	1.00000			0.0360844
$769$		−	39.0000i		−	1.40638i	−0.711004	−	0.703188i	$-0.751759\pi$
$769$		−	39.0000i		−	1.40638i	0.711004	−	0.703188i	$-0.248241\pi$
$770$	3.00000			0.108112
$771$	−6.00000			−0.216085
$772$		−	8.00000i		−	0.287926i
$773$		−	21.0000i		−	0.755318i	−0.925945	−	0.377659i	$-0.876729\pi$
$773$		−	21.0000i		−	0.755318i	0.925945	−	0.377659i	$-0.123271\pi$
$774$			5.00000i			0.179721i
$775$			32.0000i			1.14947i
$776$	6.00000			0.215387
$777$	−1.00000			−0.0358748
$778$			18.0000i			0.645331i
$779$	−12.0000			−0.429945
$780$	2.00000	−	3.00000i	0.0716115	−	0.107417i
$781$	−18.0000			−0.644091
$782$		−	7.00000i		−	0.250319i
$783$	−1.00000			−0.0357371
$784$	−1.00000			−0.0357143
$785$			19.0000i			0.678139i
$786$			17.0000i			0.606370i
$787$		−	17.0000i		−	0.605985i	−0.952993	−	0.302992i	$-0.902014\pi$
$787$		−	17.0000i		−	0.605985i	0.952993	−	0.302992i	$-0.0979856\pi$
$788$			14.0000i			0.498729i
$789$	−24.0000			−0.854423
$790$	−12.0000			−0.426941
$791$		−	10.0000i		−	0.355559i
$792$	3.00000			0.106600
$793$	−39.0000	−	26.0000i	−1.38493	−	0.923287i
$794$	−8.00000			−0.283909
$795$		−	6.00000i		−	0.212798i
$796$	−9.00000			−0.318997
$797$	−2.00000			−0.0708436			−0.0354218	−	0.999372i	$-0.511277\pi$
$797$	−2.00000			−0.0708436			−0.0354218	+	0.999372i	$0.511277\pi$
$798$		−	3.00000i		−	0.106199i
$799$		0			0
$800$		−	4.00000i		−	0.141421i
$801$		−	12.0000i		−	0.423999i
$802$	6.00000			0.211867
$803$	39.0000			1.37628
$804$		−	8.00000i		−	0.282138i
$805$	−1.00000			−0.0352454
$806$	24.0000	+	16.0000i	0.845364	+	0.563576i
$807$	−4.00000			−0.140807
$808$			14.0000i			0.492518i
$809$	52.0000			1.82822			0.914111	−	0.405463i	$-0.132890\pi$
$809$	52.0000			1.82822			0.914111	+	0.405463i	$0.132890\pi$
$810$	1.00000			0.0351364
$811$		−	7.00000i		−	0.245803i	−0.992419	−	0.122902i	$-0.960780\pi$
$811$		−	7.00000i		−	0.245803i	0.992419	−	0.122902i	$-0.0392200\pi$
$812$			1.00000i			0.0350931i
$813$		−	20.0000i		−	0.701431i
$814$		−	3.00000i		−	0.105150i
$815$	4.00000			0.140114
$816$	7.00000			0.245049
$817$			15.0000i			0.524784i
$818$	29.0000			1.01396
$819$	−2.00000	+	3.00000i	−0.0698857	+	0.104828i
$820$	−4.00000			−0.139686
$821$		−	36.0000i		−	1.25641i	−0.778048	−	0.628204i	$-0.783790\pi$
$821$		−	36.0000i		−	1.25641i	0.778048	−	0.628204i	$-0.216210\pi$
$822$	17.0000			0.592943
$823$	12.0000			0.418294			0.209147	−	0.977884i	$-0.432931\pi$
$823$	12.0000			0.418294			0.209147	+	0.977884i	$0.432931\pi$
$824$		−	1.00000i		−	0.0348367i
$825$		−	12.0000i		−	0.417786i
$826$		−	10.0000i		−	0.347945i
$827$			9.00000i			0.312961i	0.987681	+	0.156480i	$0.0500148\pi$
$827$			9.00000i			0.312961i	−0.987681	+	0.156480i	$0.949985\pi$
$828$	−1.00000			−0.0347524
$829$	−15.0000			−0.520972			−0.260486	−	0.965478i	$-0.583883\pi$
$829$	−15.0000			−0.520972			−0.260486	+	0.965478i	$0.583883\pi$
$830$		−	2.00000i		−	0.0694210i
$831$	28.0000			0.971309
$832$	−3.00000	−	2.00000i	−0.104006	−	0.0693375i
$833$	−7.00000			−0.242536
$834$			8.00000i			0.277017i
$835$	15.0000			0.519096
$836$	9.00000			0.311272
$837$			8.00000i			0.276520i
$838$			11.0000i			0.379989i
$839$			28.0000i			0.966667i	0.875436	+	0.483334i	$0.160574\pi$
$839$			28.0000i			0.966667i	−0.875436	+	0.483334i	$0.839426\pi$
$840$		−	1.00000i		−	0.0345033i
$841$	−28.0000			−0.965517
$842$	34.0000			1.17172
$843$			10.0000i			0.344418i
$844$	−15.0000			−0.516321
$845$	−12.0000	+	5.00000i	−0.412813	+	0.172005i
$846$		0			0
$847$			2.00000i			0.0687208i
$848$	−6.00000			−0.206041
$849$	−14.0000			−0.480479
$850$		−	28.0000i		−	0.960392i
$851$			1.00000i			0.0342796i
$852$			6.00000i			0.205557i
$853$		−	32.0000i		−	1.09566i	−0.836590	−	0.547830i	$-0.815454\pi$
$853$		−	32.0000i		−	1.09566i	0.836590	−	0.547830i	$-0.184546\pi$
$854$	−13.0000			−0.444851
$855$	3.00000			0.102598
$856$			2.00000i			0.0683586i
$857$	38.0000			1.29806			0.649028	−	0.760765i	$-0.275176\pi$
$857$	38.0000			1.29806			0.649028	+	0.760765i	$0.275176\pi$
$858$	−9.00000	−	6.00000i	−0.307255	−	0.204837i
$859$	22.0000			0.750630			0.375315	−	0.926897i	$-0.377534\pi$
$859$	22.0000			0.750630			0.375315	+	0.926897i	$0.377534\pi$
$860$			5.00000i			0.170499i
$861$	4.00000			0.136320
$862$	14.0000			0.476842
$863$		−	28.0000i		−	0.953131i	−0.879139	−	0.476566i	$-0.841881\pi$
$863$		−	28.0000i		−	0.953131i	0.879139	−	0.476566i	$-0.158119\pi$
$864$		−	1.00000i		−	0.0340207i
$865$		−	6.00000i		−	0.204006i
$866$			8.00000i			0.271851i
$867$	32.0000			1.08678
$868$	8.00000			0.271538
$869$			36.0000i			1.22122i
$870$	−1.00000			−0.0339032
$871$	−16.0000	+	24.0000i	−0.542139	+	0.813209i
$872$	7.00000			0.237050
$873$		−	6.00000i		−	0.203069i
$874$	−3.00000			−0.101477
$875$	−9.00000			−0.304256
$876$		−	13.0000i		−	0.439229i
$877$		−	2.00000i		−	0.0675352i	−0.999430	−	0.0337676i	$-0.989249\pi$
$877$		−	2.00000i		−	0.0675352i	0.999430	−	0.0337676i	$-0.0107506\pi$
$878$		−	27.0000i		−	0.911206i
$879$			14.0000i			0.472208i
$880$	3.00000			0.101130
$881$	51.0000			1.71823			0.859117	−	0.511780i	$-0.171014\pi$
$881$	51.0000			1.71823			0.859117	+	0.511780i	$0.171014\pi$
$882$			1.00000i			0.0336718i
$883$	3.00000			0.100958			0.0504790	−	0.998725i	$-0.483925\pi$
$883$	3.00000			0.100958			0.0504790	+	0.998725i	$0.483925\pi$
$884$	−21.0000	−	14.0000i	−0.706306	−	0.470871i
$885$	10.0000			0.336146
$886$			34.0000i			1.14225i
$887$	42.0000			1.41022			0.705111	−	0.709097i	$-0.250897\pi$
$887$	42.0000			1.41022			0.705111	+	0.709097i	$0.250897\pi$
$888$	−1.00000			−0.0335578
$889$		−	4.00000i		−	0.134156i
$890$		−	12.0000i		−	0.402241i
$891$		−	3.00000i		−	0.100504i
$892$			4.00000i			0.133930i
$893$		0			0
$894$	22.0000			0.735790
$895$		−	6.00000i		−	0.200558i
$896$	−1.00000			−0.0334077
$897$	3.00000	+	2.00000i	0.100167	+	0.0667781i
$898$	9.00000			0.300334
$899$		−	8.00000i		−	0.266815i
$900$	−4.00000			−0.133333
$901$	−42.0000			−1.39922
$902$			12.0000i			0.399556i
$903$		−	5.00000i		−	0.166390i
$904$		−	10.0000i		−	0.332595i
$905$		−	26.0000i		−	0.864269i
$906$	11.0000			0.365451
$907$	28.0000			0.929725			0.464862	−	0.885383i	$-0.346104\pi$
$907$	28.0000			0.929725			0.464862	+	0.885383i	$0.346104\pi$
$908$			20.0000i			0.663723i
$909$	14.0000			0.464351
$910$	−2.00000	+	3.00000i	−0.0662994	+	0.0994490i
$911$	57.0000			1.88849			0.944247	−	0.329238i	$-0.106792\pi$
$911$	57.0000			1.88849			0.944247	+	0.329238i	$0.106792\pi$
$912$		−	3.00000i		−	0.0993399i
$913$	−6.00000			−0.198571
$914$	−28.0000			−0.926158
$915$		−	13.0000i		−	0.429767i
$916$			10.0000i			0.330409i
$917$		−	17.0000i		−	0.561389i
$918$		−	7.00000i		−	0.231034i
$919$	−30.0000			−0.989609			−0.494804	−	0.869004i	$-0.664760\pi$
$919$	−30.0000			−0.989609			−0.494804	+	0.869004i	$0.664760\pi$
$920$	−1.00000			−0.0329690
$921$		−	16.0000i		−	0.527218i
$922$	27.0000			0.889198
$923$	12.0000	−	18.0000i	0.394985	−	0.592477i
$924$	−3.00000			−0.0986928
$925$			4.00000i			0.131519i
$926$	15.0000			0.492931
$927$	−1.00000			−0.0328443
$928$			1.00000i			0.0328266i
$929$			42.0000i			1.37798i	0.724773	+	0.688988i	$0.241945\pi$
$929$			42.0000i			1.37798i	−0.724773	+	0.688988i	$0.758055\pi$
$930$			8.00000i			0.262330i
$931$			3.00000i			0.0983210i
$932$	−18.0000			−0.589610
$933$	−4.00000			−0.130954
$934$		−	9.00000i		−	0.294489i
$935$	21.0000			0.686773
$936$	−2.00000	+	3.00000i	−0.0653720	+	0.0980581i
$937$	4.00000			0.130674			0.0653372	−	0.997863i	$-0.479188\pi$
$937$	4.00000			0.130674			0.0653372	+	0.997863i	$0.479188\pi$
$938$			8.00000i			0.261209i
$939$	−26.0000			−0.848478
$940$		0			0
$941$		−	38.0000i		−	1.23876i	−0.785090	−	0.619382i	$-0.787383\pi$
$941$		−	38.0000i		−	1.23876i	0.785090	−	0.619382i	$-0.212617\pi$
$942$		−	19.0000i		−	0.619053i
$943$		−	4.00000i		−	0.130258i
$944$		−	10.0000i		−	0.325472i
$945$	−1.00000			−0.0325300
$946$	15.0000			0.487692
$947$			25.0000i			0.812391i	0.913786	+	0.406195i	$0.133145\pi$
$947$			25.0000i			0.812391i	−0.913786	+	0.406195i	$0.866855\pi$
$948$	12.0000			0.389742
$949$	−26.0000	+	39.0000i	−0.843996	+	1.26599i
$950$	−12.0000			−0.389331
$951$		−	24.0000i		−	0.778253i
$952$	−7.00000			−0.226871
$953$	−30.0000			−0.971795			−0.485898	−	0.874016i	$-0.661507\pi$
$953$	−30.0000			−0.971795			−0.485898	+	0.874016i	$0.661507\pi$
$954$			6.00000i			0.194257i
$955$		−	9.00000i		−	0.291233i
$956$			8.00000i			0.258738i
$957$			3.00000i			0.0969762i
$958$	3.00000			0.0969256
$959$	−17.0000			−0.548959
$960$		−	1.00000i		−	0.0322749i
$961$	−33.0000			−1.06452
$962$	3.00000	+	2.00000i	0.0967239	+	0.0644826i
$963$	2.00000			0.0644491
$964$			26.0000i			0.837404i
$965$	−8.00000			−0.257529
$966$	1.00000			0.0321745
$967$			43.0000i			1.38279i	0.722478	+	0.691393i	$0.243003\pi$
$967$			43.0000i			1.38279i	−0.722478	+	0.691393i	$0.756997\pi$
$968$			2.00000i			0.0642824i
$969$		−	21.0000i		−	0.674617i
$970$		−	6.00000i		−	0.192648i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$	−1.00000			−0.0320750
$973$		−	8.00000i		−	0.256468i
$974$	24.0000			0.769010
$975$	12.0000	+	8.00000i	0.384308	+	0.256205i
$976$	−13.0000			−0.416120
$977$		−	15.0000i		−	0.479893i	−0.970786	−	0.239946i	$-0.922870\pi$
$977$		−	15.0000i		−	0.479893i	0.970786	−	0.239946i	$-0.0771298\pi$
$978$	−4.00000			−0.127906
$979$	−36.0000			−1.15056
$980$			1.00000i			0.0319438i
$981$		−	7.00000i		−	0.223493i
$982$			40.0000i			1.27645i
$983$			51.0000i			1.62665i	0.581811	+	0.813324i	$0.302344\pi$
$983$			51.0000i			1.62665i	−0.581811	+	0.813324i	$0.697656\pi$
$984$	4.00000			0.127515
$985$	14.0000			0.446077
$986$			7.00000i			0.222925i
$987$		0			0
$988$	−6.00000	+	9.00000i	−0.190885	+	0.286328i
$989$	−5.00000			−0.158991
$990$		−	3.00000i		−	0.0953463i
$991$	−20.0000			−0.635321			−0.317660	−	0.948205i	$-0.602897\pi$
$991$	−20.0000			−0.635321			−0.317660	+	0.948205i	$0.602897\pi$
$992$	8.00000			0.254000
$993$		−	8.00000i		−	0.253872i
$994$		−	6.00000i		−	0.190308i
$995$			9.00000i			0.285319i
$996$			2.00000i			0.0633724i
$997$	18.0000			0.570066			0.285033	−	0.958518i	$-0.407995\pi$
$997$	18.0000			0.570066			0.285033	+	0.958518i	$0.407995\pi$
$998$	−14.0000			−0.443162
$999$			1.00000i			0.0316386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.c.c.337.1	✓	2
3.2	odd	2		1638.2.c.e.883.2		2
4.3	odd	2		4368.2.h.h.337.2		2
7.6	odd	2		3822.2.c.b.883.1		2
13.5	odd	4		7098.2.a.o.1.1		1
13.8	odd	4		7098.2.a.y.1.1		1
13.12	even	2	inner	546.2.c.c.337.2	yes	2
39.38	odd	2		1638.2.c.e.883.1		2
52.51	odd	2		4368.2.h.h.337.1		2
91.90	odd	2		3822.2.c.b.883.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.c.c.337.1	✓	2	1.1	even	1	trivial
546.2.c.c.337.2	yes	2	13.12	even	2	inner
1638.2.c.e.883.1		2	39.38	odd	2
1638.2.c.e.883.2		2	3.2	odd	2
3822.2.c.b.883.1		2	7.6	odd	2
3822.2.c.b.883.2		2	91.90	odd	2
4368.2.h.h.337.1		2	52.51	odd	2
4368.2.h.h.337.2		2	4.3	odd	2
7098.2.a.o.1.1		1	13.5	odd	4
7098.2.a.y.1.1		1	13.8	odd	4

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.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +1.00000 q^{3} -1.00000 q^{4} +1.00000i q^{5} -1.00000i q^{6} +1.00000i q^{7} +1.00000i q^{8} +1.00000 q^{9} +1.00000 q^{10} -3.00000i q^{11} -1.00000 q^{12} +(3.00000 + 2.00000i) q^{13} +1.00000 q^{14} +1.00000i q^{15} +1.00000 q^{16} +7.00000 q^{17} -1.00000i q^{18} -3.00000i q^{19} -1.00000i q^{20} +1.00000i q^{21} -3.00000 q^{22} +1.00000 q^{23} +1.00000i q^{24} +4.00000 q^{25} +(2.00000 - 3.00000i) q^{26} +1.00000 q^{27} -1.00000i q^{28} -1.00000 q^{29} +1.00000 q^{30} +8.00000i q^{31} -1.00000i q^{32} -3.00000i q^{33} -7.00000i q^{34} -1.00000 q^{35} -1.00000 q^{36} +1.00000i q^{37} -3.00000 q^{38} +(3.00000 + 2.00000i) q^{39} -1.00000 q^{40} -4.00000i q^{41} +1.00000 q^{42} -5.00000 q^{43} +3.00000i q^{44} +1.00000i q^{45} -1.00000i q^{46} +1.00000 q^{48} -1.00000 q^{49} -4.00000i q^{50} +7.00000 q^{51} +(-3.00000 - 2.00000i) q^{52} -6.00000 q^{53} -1.00000i q^{54} +3.00000 q^{55} -1.00000 q^{56} -3.00000i q^{57} +1.00000i q^{58} -10.0000i q^{59} -1.00000i q^{60} -13.0000 q^{61} +8.00000 q^{62} +1.00000i q^{63} -1.00000 q^{64} +(-2.00000 + 3.00000i) q^{65} -3.00000 q^{66} +8.00000i q^{67} -7.00000 q^{68} +1.00000 q^{69} +1.00000i q^{70} -6.00000i q^{71} +1.00000i q^{72} +13.0000i q^{73} +1.00000 q^{74} +4.00000 q^{75} +3.00000i q^{76} +3.00000 q^{77} +(2.00000 - 3.00000i) q^{78} -12.0000 q^{79} +1.00000i q^{80} +1.00000 q^{81} -4.00000 q^{82} -2.00000i q^{83} -1.00000i q^{84} +7.00000i q^{85} +5.00000i q^{86} -1.00000 q^{87} +3.00000 q^{88} -12.0000i q^{89} +1.00000 q^{90} +(-2.00000 + 3.00000i) q^{91} -1.00000 q^{92} +8.00000i q^{93} +3.00000 q^{95} -1.00000i q^{96} -6.00000i q^{97} +1.00000i q^{98} -3.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9	\( 2 q + 2 q^{3} - 2 q^{4} + 2 q^{9} + 2 q^{10} - 2 q^{12} + 6 q^{13} + 2 q^{14} + 2 q^{16} + 14 q^{17} - 6 q^{22} + 2 q^{23} + 8 q^{25} + 4 q^{26} + 2 q^{27} - 2 q^{29} + 2 q^{30} - 2 q^{35} - 2 q^{36} - 6 q^{38} + 6 q^{39} - 2 q^{40} + 2 q^{42} - 10 q^{43} + 2 q^{48} - 2 q^{49} + 14 q^{51} - 6 q^{52} - 12 q^{53} + 6 q^{55} - 2 q^{56} - 26 q^{61} + 16 q^{62} - 2 q^{64} - 4 q^{65} - 6 q^{66} - 14 q^{68} + 2 q^{69} + 2 q^{74} + 8 q^{75} + 6 q^{77} + 4 q^{78} - 24 q^{79} + 2 q^{81} - 8 q^{82} - 2 q^{87} + 6 q^{88} + 2 q^{90} - 4 q^{91} - 2 q^{92} + 6 q^{95}+O(q^{100}) \) 2 * q + 2 * q^3 - 2 * q^4 + 2 * q^9 + 2 * q^10 - 2 * q^12 + 6 * q^13 + 2 * q^14 + 2 * q^16 + 14 * q^17 - 6 * q^22 + 2 * q^23 + 8 * q^25 + 4 * q^26 + 2 * q^27 - 2 * q^29 + 2 * q^30 - 2 * q^35 - 2 * q^36 - 6 * q^38 + 6 * q^39 - 2 * q^40 + 2 * q^42 - 10 * q^43 + 2 * q^48 - 2 * q^49 + 14 * q^51 - 6 * q^52 - 12 * q^53 + 6 * q^55 - 2 * q^56 - 26 * q^61 + 16 * q^62 - 2 * q^64 - 4 * q^65 - 6 * q^66 - 14 * q^68 + 2 * q^69 + 2 * q^74 + 8 * q^75 + 6 * q^77 + 4 * q^78 - 24 * q^79 + 2 * q^81 - 8 * q^82 - 2 * q^87 + 6 * q^88 + 2 * q^90 - 4 * q^91 - 2 * q^92 + 6 * q^95

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