LMFDB - Embedded newform 1134.2.f.b.379.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(379,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1134.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.f (of order $3$, degree $2$, not 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:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			379.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.379
Dual form			1134.2.f.b.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +3.00000 q^{10} +(1.50000 - 2.59808i) q^{11} +(2.00000 + 3.46410i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} -7.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -4.00000 q^{26} +1.00000 q^{28} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +3.00000 q^{35} -7.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(5.00000 - 8.66025i) q^{43} -3.00000 q^{44} +3.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(2.00000 - 3.46410i) q^{52} -12.0000 q^{53} -9.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-3.00000 - 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} +5.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{70} -9.00000 q^{71} +2.00000 q^{73} +(3.50000 - 6.06218i) q^{74} +(3.50000 + 6.06218i) q^{76} +(1.50000 + 2.59808i) q^{77} +(5.00000 - 8.66025i) q^{79} +3.00000 q^{80} +9.00000 q^{82} +(-9.00000 - 15.5885i) q^{85} +(5.00000 + 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} -15.0000 q^{89} -4.00000 q^{91} +(-1.50000 + 2.59808i) q^{92} +(3.00000 + 5.19615i) q^{94} +(10.5000 + 18.1865i) q^{95} +(-4.00000 + 6.92820i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8} + 6 q^{10} + 3 q^{11} + 4 q^{13} - q^{14} - q^{16} + 12 q^{17} - 14 q^{19} - 3 q^{20} + 3 q^{22} - 3 q^{23} - 4 q^{25} - 8 q^{26} + 2 q^{28} - 5 q^{31} - q^{32} - 6 q^{34} + 6 q^{35} - 14 q^{37} + 7 q^{38} - 3 q^{40} - 9 q^{41} + 10 q^{43} - 6 q^{44} + 6 q^{46} + 6 q^{47} - q^{49} - 4 q^{50} + 4 q^{52} - 24 q^{53} - 18 q^{55} - q^{56} - 6 q^{59} - 8 q^{61} + 10 q^{62} + 2 q^{64} + 12 q^{65} + 4 q^{67} - 6 q^{68} - 3 q^{70} - 18 q^{71} + 4 q^{73} + 7 q^{74} + 7 q^{76} + 3 q^{77} + 10 q^{79} + 6 q^{80} + 18 q^{82} - 18 q^{85} + 10 q^{86} + 3 q^{88} - 30 q^{89} - 8 q^{91} - 3 q^{92} + 6 q^{94} + 21 q^{95} - 8 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8 + 6 * q^10 + 3 * q^11 + 4 * q^13 - q^14 - q^16 + 12 * q^17 - 14 * q^19 - 3 * q^20 + 3 * q^22 - 3 * q^23 - 4 * q^25 - 8 * q^26 + 2 * q^28 - 5 * q^31 - q^32 - 6 * q^34 + 6 * q^35 - 14 * q^37 + 7 * q^38 - 3 * q^40 - 9 * q^41 + 10 * q^43 - 6 * q^44 + 6 * q^46 + 6 * q^47 - q^49 - 4 * q^50 + 4 * q^52 - 24 * q^53 - 18 * q^55 - q^56 - 6 * q^59 - 8 * q^61 + 10 * q^62 + 2 * q^64 + 12 * q^65 + 4 * q^67 - 6 * q^68 - 3 * q^70 - 18 * q^71 + 4 * q^73 + 7 * q^74 + 7 * q^76 + 3 * q^77 + 10 * q^79 + 6 * q^80 + 18 * q^82 - 18 * q^85 + 10 * q^86 + 3 * q^88 - 30 * q^89 - 8 * q^91 - 3 * q^92 + 6 * q^94 + 21 * q^95 - 8 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−1.50000	−	2.59808i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		0			0
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$	3.00000			0.948683
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	0.997927	+	0.0643593i	$0.0205004\pi$
$13$	2.00000	+	3.46410i	0.554700	+	0.960769i	−0.443227	+	0.896410i	$0.646166\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	6.00000			1.45521			0.727607	−	0.685994i	$-0.240633\pi$
$17$	6.00000			1.45521			0.727607	+	0.685994i	$0.240633\pi$
$18$		0			0
$19$	−7.00000			−1.60591			−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000			−1.60591			−0.802955	+	0.596040i	$0.796740\pi$
$20$	−1.50000	+	2.59808i	−0.335410	+	0.580948i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−1.50000	−	2.59808i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$		0			0
$25$	−2.00000	+	3.46410i	−0.400000	+	0.692820i
$26$	−4.00000			−0.784465
$27$		0			0
$28$	1.00000			0.188982
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.00000	+	5.19615i	−0.514496	+	0.891133i
$35$	3.00000			0.507093
$36$		0			0
$37$	−7.00000			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$38$	3.50000	−	6.06218i	0.567775	−	0.983415i
$39$		0			0
$40$	−1.50000	−	2.59808i	−0.237171	−	0.410792i
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	−0.967486	−	0.252924i	$-0.918608\pi$
$41$	−4.50000	−	7.79423i	−0.702782	−	1.21725i	0.264704	−	0.964330i	$-0.414726\pi$
$42$		0			0
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	−0.179069	−	0.983836i	$-0.557309\pi$
$43$	5.00000	−	8.66025i	0.762493	−	1.32068i	0.941562	−	0.336840i	$-0.109358\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	3.00000			0.442326
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	5.00000			0.635001
$63$		0			0
$64$	1.00000			0.125000
$65$	6.00000	−	10.3923i	0.744208	−	1.28901i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$		0			0
$70$	−1.50000	+	2.59808i	−0.179284	+	0.310530i
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$		0			0
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	3.50000	−	6.06218i	0.406867	−	0.704714i
$75$		0			0
$76$	3.50000	+	6.06218i	0.401478	+	0.695379i
$77$	1.50000	+	2.59808i	0.170941	+	0.296078i
$78$		0			0
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	−0.434730	−	0.900561i	$-0.643156\pi$
$79$	5.00000	−	8.66025i	0.562544	−	0.974355i	0.997274	−	0.0737937i	$-0.0235106\pi$
$80$	3.00000			0.335410
$81$		0			0
$82$	9.00000			0.993884
$83$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$83$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$84$		0			0
$85$	−9.00000	−	15.5885i	−0.976187	−	1.69081i
$86$	5.00000	+	8.66025i	0.539164	+	0.933859i
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$	−4.00000			−0.419314
$92$	−1.50000	+	2.59808i	−0.156386	+	0.270868i
$93$		0			0
$94$	3.00000	+	5.19615i	0.309426	+	0.535942i
$95$	10.5000	+	18.1865i	1.07728	+	1.86590i
$96$		0			0
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	−0.994453	−	0.105180i	$-0.966458\pi$
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	0.588315	+	0.808632i	$0.299792\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	4.00000			0.400000
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$		0			0
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	0.716173	−	0.697923i	$-0.245892\pi$
$103$	−2.50000	−	4.33013i	−0.246332	−	0.426660i	−0.962505	+	0.271263i	$0.912559\pi$
$104$	2.00000	+	3.46410i	0.196116	+	0.339683i
$105$		0			0
$106$	6.00000	−	10.3923i	0.582772	−	1.00939i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	11.0000			1.05361			0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000			1.05361			0.526804	+	0.849987i	$0.323390\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$		0			0
$112$	−0.500000	−	0.866025i	−0.0472456	−	0.0818317i
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	−0.884182	−	0.467143i	$-0.845283\pi$
$113$	−9.00000	−	15.5885i	−0.846649	−	1.46644i	0.0375328	−	0.999295i	$-0.488050\pi$
$114$		0			0
$115$	−4.50000	+	7.79423i	−0.419627	+	0.726816i
$116$		0			0
$117$		0			0
$118$	6.00000			0.552345
$119$	−3.00000	+	5.19615i	−0.275010	+	0.476331i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	−4.00000	−	6.92820i	−0.362143	−	0.627250i
$123$		0			0
$124$	−2.50000	+	4.33013i	−0.224507	+	0.388857i
$125$	−3.00000			−0.268328
$126$		0			0
$127$	20.0000			1.77471			0.887357	−	0.461084i	$-0.152539\pi$
$127$	20.0000			1.77471			0.887357	+	0.461084i	$0.152539\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	6.00000	+	10.3923i	0.526235	+	0.911465i
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$		0			0
$133$	3.50000	−	6.06218i	0.303488	−	0.525657i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	6.00000			0.514496
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	0.938293	−	0.345843i	$-0.112407\pi$
$139$	2.00000	+	3.46410i	0.169638	+	0.293821i	−0.768655	+	0.639664i	$0.779074\pi$
$140$	−1.50000	−	2.59808i	−0.126773	−	0.219578i
$141$		0			0
$142$	4.50000	−	7.79423i	0.377632	−	0.654077i
$143$	12.0000			1.00349
$144$		0			0
$145$		0			0
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$		0			0
$148$	3.50000	+	6.06218i	0.287698	+	0.498308i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	−0.587646	−	0.809118i	$-0.699945\pi$
$151$	5.00000	−	8.66025i	0.406894	−	0.704761i	0.994540	+	0.104357i	$0.0332784\pi$
$152$	−7.00000			−0.567775
$153$		0			0
$154$	−3.00000			−0.241747
$155$	−7.50000	+	12.9904i	−0.602414	+	1.04341i
$156$		0			0
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	0.934731	−	0.355357i	$-0.115641\pi$
$157$	2.00000	+	3.46410i	0.159617	+	0.276465i	−0.775113	+	0.631822i	$0.782307\pi$
$158$	5.00000	+	8.66025i	0.397779	+	0.688973i
$159$		0			0
$160$	−1.50000	+	2.59808i	−0.118585	+	0.205396i
$161$	3.00000			0.236433
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$		0			0
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	−0.969693	−	0.244328i	$-0.921432\pi$
$167$	−9.00000	−	15.5885i	−0.696441	−	1.20627i	0.273252	−	0.961943i	$-0.411901\pi$
$168$		0			0
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	18.0000			1.38054
$171$		0			0
$172$	−10.0000			−0.762493
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872399\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	7.50000	−	12.9904i	0.562149	−	0.973670i
$179$	24.0000			1.79384			0.896922	−	0.442189i	$-0.145798\pi$
$179$	24.0000			1.79384			0.896922	+	0.442189i	$0.145798\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	2.00000	−	3.46410i	0.148250	−	0.256776i
$183$		0			0
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$	10.5000	+	18.1865i	0.771975	+	1.33710i
$186$		0			0
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$	−6.00000			−0.437595
$189$		0			0
$190$	−21.0000			−1.52350
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	−0.456068	−	0.889945i	$-0.650743\pi$
$191$	7.50000	−	12.9904i	0.542681	−	0.939951i	0.998749	−	0.0500060i	$-0.0159241\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	−4.00000	−	6.92820i	−0.287183	−	0.497416i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−7.00000			−0.496217			−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000			−0.496217			−0.248108	+	0.968732i	$0.579809\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	−3.00000	−	5.19615i	−0.211079	−	0.365600i
$203$		0			0
$204$		0			0
$205$	−13.5000	+	23.3827i	−0.942881	+	1.63312i
$206$	5.00000			0.348367
$207$		0			0
$208$	−4.00000			−0.277350
$209$	−10.5000	+	18.1865i	−0.726300	+	1.25799i
$210$		0			0
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	0.517884	−	0.855451i	$-0.326720\pi$
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	−0.999784	+	0.0207756i	$0.993386\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	−30.0000			−2.04598
$216$		0			0
$217$	5.00000			0.339422
$218$	−5.50000	+	9.52628i	−0.372507	+	0.645201i
$219$		0			0
$220$	4.50000	+	7.79423i	0.303390	+	0.525487i
$221$	12.0000	+	20.7846i	0.807207	+	1.39812i
$222$		0			0
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	−0.848799	−	0.528716i	$-0.822674\pi$
$223$	0.500000	−	0.866025i	0.0334825	−	0.0579934i	0.882281	+	0.470723i	$0.156007\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	18.0000			1.19734
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	−0.948242	−	0.317547i	$-0.897141\pi$
$227$	−3.00000	+	5.19615i	−0.199117	+	0.344881i	0.749125	+	0.662428i	$0.230474\pi$
$228$		0			0
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	0.924510	−	0.381157i	$-0.124474\pi$
$229$	2.00000	+	3.46410i	0.132164	+	0.228914i	−0.792347	+	0.610071i	$0.791141\pi$
$230$	−4.50000	−	7.79423i	−0.296721	−	0.513936i
$231$		0			0
$232$		0			0
$233$	−6.00000			−0.393073			−0.196537	−	0.980497i	$-0.562969\pi$
$233$	−6.00000			−0.393073			−0.196537	+	0.980497i	$0.562969\pi$
$234$		0			0
$235$	−18.0000			−1.17419
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$		0			0
$238$	−3.00000	−	5.19615i	−0.194461	−	0.336817i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	0.0546547	+	0.998505i	$0.482594\pi$
$241$	−13.0000	+	22.5167i	−0.837404	+	1.45043i	−0.892058	+	0.451920i	$0.850739\pi$
$242$	−2.00000			−0.128565
$243$		0			0
$244$	8.00000			0.512148
$245$	−1.50000	+	2.59808i	−0.0958315	+	0.165985i
$246$		0			0
$247$	−14.0000	−	24.2487i	−0.890799	−	1.54291i
$248$	−2.50000	−	4.33013i	−0.158750	−	0.274963i
$249$		0			0
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−9.00000			−0.565825
$254$	−10.0000	+	17.3205i	−0.627456	+	1.08679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	−0.981901	−	0.189396i	$-0.939347\pi$
$257$	−10.5000	−	18.1865i	−0.654972	−	1.13444i	0.326929	−	0.945049i	$-0.393986\pi$
$258$		0			0
$259$	3.50000	−	6.06218i	0.217479	−	0.376685i
$260$	−12.0000			−0.744208
$261$		0			0
$262$	−6.00000			−0.370681
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	−0.999083	−	0.0428069i	$-0.986370\pi$
$263$	−7.50000	+	12.9904i	−0.462470	+	0.801021i	0.536614	+	0.843828i	$0.319703\pi$
$264$		0			0
$265$	18.0000	+	31.1769i	1.10573	+	1.91518i
$266$	3.50000	+	6.06218i	0.214599	+	0.371696i
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	15.0000			0.914566			0.457283	−	0.889321i	$-0.348823\pi$
$269$	15.0000			0.914566			0.457283	+	0.889321i	$0.348823\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	−3.00000	+	5.19615i	−0.181902	+	0.315063i
$273$		0			0
$274$	6.00000	+	10.3923i	0.362473	+	0.627822i
$275$	6.00000	+	10.3923i	0.361814	+	0.626680i
$276$		0			0
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$	−4.00000			−0.239904
$279$		0			0
$280$	3.00000			0.179284
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	−0.462174	−	0.886789i	$-0.652930\pi$
$281$	9.00000	−	15.5885i	0.536895	−	0.929929i	0.999069	−	0.0431402i	$-0.0137362\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	4.50000	+	7.79423i	0.267026	+	0.462502i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$	9.00000			0.531253
$288$		0			0
$289$	19.0000			1.11765
$290$		0			0
$291$		0			0
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	0.999549	+	0.0300351i	$0.00956192\pi$
$293$	9.00000	+	15.5885i	0.525786	+	0.910687i	−0.473763	+	0.880652i	$0.657105\pi$
$294$		0			0
$295$	−9.00000	+	15.5885i	−0.524000	+	0.907595i
$296$	−7.00000			−0.406867
$297$		0			0
$298$	−6.00000			−0.347571
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$		0			0
$301$	5.00000	+	8.66025i	0.288195	+	0.499169i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$		0			0
$304$	3.50000	−	6.06218i	0.200739	−	0.347690i
$305$	24.0000			1.37424
$306$		0			0
$307$	29.0000			1.65512			0.827559	−	0.561379i	$-0.189729\pi$
$307$	29.0000			1.65512			0.827559	+	0.561379i	$0.189729\pi$
$308$	1.50000	−	2.59808i	0.0854704	−	0.148039i
$309$		0			0
$310$	−7.50000	−	12.9904i	−0.425971	−	0.737804i
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	14.0000	−	24.2487i	0.791327	−	1.37062i	−0.133819	−	0.991006i	$-0.542724\pi$
$313$	14.0000	−	24.2487i	0.791327	−	1.37062i	0.925146	−	0.379612i	$-0.123943\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−10.0000			−0.562544
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	0.0453045	+	0.998973i	$0.485574\pi$
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	−0.887788	+	0.460252i	$0.847759\pi$
$318$		0			0
$319$		0			0
$320$	−1.50000	−	2.59808i	−0.0838525	−	0.145237i
$321$		0			0
$322$	−1.50000	+	2.59808i	−0.0835917	+	0.144785i
$323$	−42.0000			−2.33694
$324$		0			0
$325$	−16.0000			−0.887520
$326$	8.00000	−	13.8564i	0.443079	−	0.767435i
$327$		0			0
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$	3.00000	+	5.19615i	0.165395	+	0.286473i
$330$		0			0
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	−0.168320	−	0.985732i	$-0.553834\pi$
$331$	14.0000	−	24.2487i	0.769510	−	1.33283i	0.937829	−	0.347097i	$-0.112833\pi$
$332$		0			0
$333$		0			0
$334$	18.0000			0.984916
$335$	6.00000	−	10.3923i	0.327815	−	0.567792i
$336$		0			0
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	0.986960	−	0.160968i	$-0.0514616\pi$
$337$	6.50000	+	11.2583i	0.354078	+	0.613280i	−0.632882	+	0.774248i	$0.718128\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		0			0
$340$	−9.00000	+	15.5885i	−0.488094	+	0.845403i
$341$	−15.0000			−0.812296
$342$		0			0
$343$	1.00000			0.0539949
$344$	5.00000	−	8.66025i	0.269582	−	0.466930i
$345$		0			0
$346$	−10.5000	−	18.1865i	−0.564483	−	0.977714i
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	0.903475	−	0.428640i	$-0.141007\pi$
$347$	1.50000	+	2.59808i	0.0805242	+	0.139472i	−0.822951	+	0.568112i	$0.807674\pi$
$348$		0			0
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	−3.00000			−0.159901
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	−0.438733	−	0.898617i	$-0.644573\pi$
$353$	10.5000	−	18.1865i	0.558859	−	0.967972i	0.997592	−	0.0693543i	$-0.0220939\pi$
$354$		0			0
$355$	13.5000	+	23.3827i	0.716506	+	1.24102i
$356$	7.50000	+	12.9904i	0.397499	+	0.688489i
$357$		0			0
$358$	−12.0000	+	20.7846i	−0.634220	+	1.09850i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	30.0000			1.57895
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$		0			0
$364$	2.00000	+	3.46410i	0.104828	+	0.181568i
$365$	−3.00000	−	5.19615i	−0.157027	−	0.271979i
$366$		0			0
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	−0.997960	−	0.0638362i	$-0.979666\pi$
$367$	−8.50000	+	14.7224i	−0.443696	+	0.768505i	0.554264	+	0.832341i	$0.313000\pi$
$368$	3.00000			0.156386
$369$		0			0
$370$	−21.0000			−1.09174
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$		0			0
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	−0.647225	+	0.762299i	$0.724071\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$		0			0
$376$	3.00000	−	5.19615i	0.154713	−	0.267971i
$377$		0			0
$378$		0			0
$379$	2.00000			0.102733			0.0513665	−	0.998680i	$-0.483642\pi$
$379$	2.00000			0.102733			0.0513665	+	0.998680i	$0.483642\pi$
$380$	10.5000	−	18.1865i	0.538639	−	0.932949i
$381$		0			0
$382$	7.50000	+	12.9904i	0.383733	+	0.664646i
$383$	−15.0000	−	25.9808i	−0.766464	−	1.32755i	−0.939469	−	0.342634i	$-0.888681\pi$
$383$	−15.0000	−	25.9808i	−0.766464	−	1.32755i	0.173005	−	0.984921i	$-0.444652\pi$
$384$		0			0
$385$	4.50000	−	7.79423i	0.229341	−	0.397231i
$386$	14.0000			0.712581
$387$		0			0
$388$	8.00000			0.406138
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	−0.672874	−	0.739758i	$-0.734940\pi$
$389$	6.00000	−	10.3923i	0.304212	−	0.526911i	0.977086	+	0.212847i	$0.0682735\pi$
$390$		0			0
$391$	−9.00000	−	15.5885i	−0.455150	−	0.788342i
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$		0			0
$394$	−9.00000	+	15.5885i	−0.453413	+	0.785335i
$395$	−30.0000			−1.50946
$396$		0			0
$397$	2.00000			0.100377			0.0501886	−	0.998740i	$-0.484018\pi$
$397$	2.00000			0.100377			0.0501886	+	0.998740i	$0.484018\pi$
$398$	3.50000	−	6.06218i	0.175439	−	0.303870i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	0.992932	+	0.118686i	$0.0378683\pi$
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	−0.393680	+	0.919247i	$0.628798\pi$
$402$		0			0
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	6.00000			0.298511
$405$		0			0
$406$		0			0
$407$	−10.5000	+	18.1865i	−0.520466	+	0.901473i
$408$		0			0
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$	−13.5000	−	23.3827i	−0.666717	−	1.15479i
$411$		0			0
$412$	−2.50000	+	4.33013i	−0.123166	+	0.213330i
$413$	6.00000			0.295241
$414$		0			0
$415$		0			0
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$		0			0
$418$	−10.5000	−	18.1865i	−0.513572	−	0.889532i
$419$	9.00000	+	15.5885i	0.439679	+	0.761546i	0.997665	−	0.0683046i	$-0.0217590\pi$
$419$	9.00000	+	15.5885i	0.439679	+	0.761546i	−0.557986	+	0.829851i	$0.688426\pi$
$420$		0			0
$421$	−8.50000	+	14.7224i	−0.414265	+	0.717527i	−0.995351	−	0.0963145i	$-0.969295\pi$
$421$	−8.50000	+	14.7224i	−0.414265	+	0.717527i	0.581086	+	0.813842i	$0.302628\pi$
$422$	14.0000			0.681509
$423$		0			0
$424$	−12.0000			−0.582772
$425$	−12.0000	+	20.7846i	−0.582086	+	1.00820i
$426$		0			0
$427$	−4.00000	−	6.92820i	−0.193574	−	0.335279i
$428$	−6.00000	−	10.3923i	−0.290021	−	0.502331i
$429$		0			0
$430$	15.0000	−	25.9808i	0.723364	−	1.25290i
$431$	−3.00000			−0.144505			−0.0722525	−	0.997386i	$-0.523019\pi$
$431$	−3.00000			−0.144505			−0.0722525	+	0.997386i	$0.523019\pi$
$432$		0			0
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$	−2.50000	+	4.33013i	−0.120004	+	0.207853i
$435$		0			0
$436$	−5.50000	−	9.52628i	−0.263402	−	0.456226i
$437$	10.5000	+	18.1865i	0.502283	+	0.869980i
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	−24.0000			−1.14156
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	−0.899457	−	0.437009i	$-0.856038\pi$
$443$	−1.50000	+	2.59808i	−0.0712672	+	0.123438i	0.828190	+	0.560448i	$0.189371\pi$
$444$		0			0
$445$	22.5000	+	38.9711i	1.06660	+	1.84741i
$446$	0.500000	+	0.866025i	0.0236757	+	0.0410075i
$447$		0			0
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$	−27.0000			−1.27138
$452$	−9.00000	+	15.5885i	−0.423324	+	0.733219i
$453$		0			0
$454$	−3.00000	−	5.19615i	−0.140797	−	0.243868i
$455$	6.00000	+	10.3923i	0.281284	+	0.487199i
$456$		0			0
$457$	9.50000	−	16.4545i	0.444391	−	0.769708i	−0.553618	−	0.832771i	$-0.686753\pi$
$457$	9.50000	−	16.4545i	0.444391	−	0.769708i	0.998010	+	0.0630623i	$0.0200867\pi$
$458$	−4.00000			−0.186908
$459$		0			0
$460$	9.00000			0.419627
$461$	13.5000	−	23.3827i	0.628758	−	1.08904i	−0.359044	−	0.933321i	$-0.616897\pi$
$461$	13.5000	−	23.3827i	0.628758	−	1.08904i	0.987801	−	0.155719i	$-0.0497696\pi$
$462$		0			0
$463$	−7.00000	−	12.1244i	−0.325318	−	0.563467i	0.656259	−	0.754536i	$-0.272138\pi$
$463$	−7.00000	−	12.1244i	−0.325318	−	0.563467i	−0.981577	+	0.191069i	$0.938805\pi$
$464$		0			0
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	−6.00000			−0.277647			−0.138823	−	0.990317i	$-0.544332\pi$
$467$	−6.00000			−0.277647			−0.138823	+	0.990317i	$0.544332\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$	9.00000	−	15.5885i	0.415139	−	0.719042i
$471$		0			0
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	−15.0000	−	25.9808i	−0.689701	−	1.19460i
$474$		0			0
$475$	14.0000	−	24.2487i	0.642364	−	1.11261i
$476$	6.00000			0.275010
$477$		0			0
$478$		0			0
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	0.450098	+	0.892979i	$0.351389\pi$
$479$	−12.0000	+	20.7846i	−0.548294	+	0.949673i	−0.998392	+	0.0566937i	$0.981944\pi$
$480$		0			0
$481$	−14.0000	−	24.2487i	−0.638345	−	1.10565i
$482$	−13.0000	−	22.5167i	−0.592134	−	1.02561i
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	24.0000			1.08978
$486$		0			0
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	−4.00000	+	6.92820i	−0.181071	+	0.313625i
$489$		0			0
$490$	−1.50000	−	2.59808i	−0.0677631	−	0.117369i
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	0.746438	−	0.665455i	$-0.231763\pi$
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	−0.949520	+	0.313707i	$0.898429\pi$
$492$		0			0
$493$		0			0
$494$	28.0000			1.25978
$495$		0			0
$496$	5.00000			0.224507
$497$	4.50000	−	7.79423i	0.201853	−	0.349619i
$498$		0			0
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	0.999962	−	0.00872186i	$-0.00277629\pi$
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	−0.507534	+	0.861632i	$0.669443\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		0			0
$502$		0			0
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	4.50000	−	7.79423i	0.200049	−	0.346496i
$507$		0			0
$508$	−10.0000	−	17.3205i	−0.443678	−	0.768473i
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$	1.00000			0.0441942
$513$		0			0
$514$	21.0000			0.926270
$515$	−7.50000	+	12.9904i	−0.330489	+	0.572425i
$516$		0			0
$517$	−9.00000	−	15.5885i	−0.395820	−	0.685580i
$518$	3.50000	+	6.06218i	0.153781	+	0.266357i
$519$		0			0
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	15.0000			0.657162			0.328581	−	0.944476i	$-0.393430\pi$
$521$	15.0000			0.657162			0.328581	+	0.944476i	$0.393430\pi$
$522$		0			0
$523$	29.0000			1.26808			0.634041	−	0.773300i	$-0.281395\pi$
$523$	29.0000			1.26808			0.634041	+	0.773300i	$0.281395\pi$
$524$	3.00000	−	5.19615i	0.131056	−	0.226995i
$525$		0			0
$526$	−7.50000	−	12.9904i	−0.327016	−	0.566408i
$527$	−15.0000	−	25.9808i	−0.653410	−	1.13174i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$	−36.0000			−1.56374
$531$		0			0
$532$	−7.00000			−0.303488
$533$	18.0000	−	31.1769i	0.779667	−	1.35042i
$534$		0			0
$535$	−18.0000	−	31.1769i	−0.778208	−	1.34790i
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$		0			0
$538$	−7.50000	+	12.9904i	−0.323348	+	0.560055i
$539$	−3.00000			−0.129219
$540$		0			0
$541$	−7.00000			−0.300954			−0.150477	−	0.988614i	$-0.548081\pi$
$541$	−7.00000			−0.300954			−0.150477	+	0.988614i	$0.548081\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$		0			0
$544$	−3.00000	−	5.19615i	−0.128624	−	0.222783i
$545$	−16.5000	−	28.5788i	−0.706782	−	1.22418i
$546$		0			0
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	−0.394432	−	0.918925i	$-0.629059\pi$
$547$	14.0000	−	24.2487i	0.598597	−	1.03680i	0.993028	−	0.117875i	$-0.0376081\pi$
$548$	−12.0000			−0.512615
$549$		0			0
$550$	−12.0000			−0.511682
$551$		0			0
$552$		0			0
$553$	5.00000	+	8.66025i	0.212622	+	0.368271i
$554$	−8.50000	−	14.7224i	−0.361130	−	0.625496i
$555$		0			0
$556$	2.00000	−	3.46410i	0.0848189	−	0.146911i
$557$	42.0000			1.77960			0.889799	−	0.456354i	$-0.150845\pi$
$557$	42.0000			1.77960			0.889799	+	0.456354i	$0.150845\pi$
$558$		0			0
$559$	40.0000			1.69182
$560$	−1.50000	+	2.59808i	−0.0633866	+	0.109789i
$561$		0			0
$562$	9.00000	+	15.5885i	0.379642	+	0.657559i
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$		0			0
$565$	−27.0000	+	46.7654i	−1.13590	+	1.96743i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	−9.00000			−0.377632
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	−7.00000	−	12.1244i	−0.292941	−	0.507388i	0.681563	−	0.731760i	$-0.261301\pi$
$571$	−7.00000	−	12.1244i	−0.292941	−	0.507388i	−0.974504	+	0.224371i	$0.927967\pi$
$572$	−6.00000	−	10.3923i	−0.250873	−	0.434524i
$573$		0			0
$574$	−4.50000	+	7.79423i	−0.187826	+	0.325325i
$575$	12.0000			0.500435
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	−9.50000	+	16.4545i	−0.395148	+	0.684416i
$579$		0			0
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−18.0000	+	31.1769i	−0.745484	+	1.29122i
$584$	2.00000			0.0827606
$585$		0			0
$586$	−18.0000			−0.743573
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	−0.618322	−	0.785925i	$-0.712187\pi$
$587$	9.00000	−	15.5885i	0.371470	−	0.643404i	0.989792	+	0.142520i	$0.0455206\pi$
$588$		0			0
$589$	17.5000	+	30.3109i	0.721075	+	1.24894i
$590$	−9.00000	−	15.5885i	−0.370524	−	0.641767i
$591$		0			0
$592$	3.50000	−	6.06218i	0.143849	−	0.249154i
$593$	−33.0000			−1.35515			−0.677574	−	0.735455i	$-0.736969\pi$
$593$	−33.0000			−1.35515			−0.677574	+	0.735455i	$0.736969\pi$
$594$		0			0
$595$	18.0000			0.737928
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$		0			0
$598$	6.00000	+	10.3923i	0.245358	+	0.424973i
$599$	−16.5000	−	28.5788i	−0.674172	−	1.16770i	−0.976710	−	0.214563i	$-0.931167\pi$
$599$	−16.5000	−	28.5788i	−0.674172	−	1.16770i	0.302539	−	0.953137i	$-0.402166\pi$
$600$		0			0
$601$	14.0000	−	24.2487i	0.571072	−	0.989126i	−0.425384	−	0.905013i	$-0.639861\pi$
$601$	14.0000	−	24.2487i	0.571072	−	0.989126i	0.996456	−	0.0841128i	$-0.0268056\pi$
$602$	−10.0000			−0.407570
$603$		0			0
$604$	−10.0000			−0.406894
$605$	3.00000	−	5.19615i	0.121967	−	0.211254i
$606$		0			0
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	0.903756	−	0.428048i	$-0.140799\pi$
$607$	2.00000	+	3.46410i	0.0811775	+	0.140604i	−0.822578	+	0.568652i	$0.807465\pi$
$608$	3.50000	+	6.06218i	0.141944	+	0.245854i
$609$		0			0
$610$	−12.0000	+	20.7846i	−0.485866	+	0.841544i
$611$	24.0000			0.970936
$612$		0			0
$613$	29.0000			1.17130			0.585649	−	0.810564i	$-0.300840\pi$
$613$	29.0000			1.17130			0.585649	+	0.810564i	$0.300840\pi$
$614$	−14.5000	+	25.1147i	−0.585172	+	1.01355i
$615$		0			0
$616$	1.50000	+	2.59808i	0.0604367	+	0.104679i
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	0.988343	−	0.152242i	$-0.0486493\pi$
$617$	9.00000	+	15.5885i	0.362326	+	0.627568i	−0.626017	+	0.779809i	$0.715316\pi$
$618$		0			0
$619$	−17.5000	+	30.3109i	−0.703384	+	1.21830i	0.263887	+	0.964554i	$0.414995\pi$
$619$	−17.5000	+	30.3109i	−0.703384	+	1.21830i	−0.967271	+	0.253744i	$0.918338\pi$
$620$	15.0000			0.602414
$621$		0			0
$622$	−12.0000			−0.481156
$623$	7.50000	−	12.9904i	0.300481	−	0.520449i
$624$		0			0
$625$	14.5000	+	25.1147i	0.580000	+	1.00459i
$626$	14.0000	+	24.2487i	0.559553	+	0.969173i
$627$		0			0
$628$	2.00000	−	3.46410i	0.0798087	−	0.138233i
$629$	−42.0000			−1.67465
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$	5.00000	−	8.66025i	0.198889	−	0.344486i
$633$		0			0
$634$	−15.0000	−	25.9808i	−0.595726	−	1.03183i
$635$	−30.0000	−	51.9615i	−1.19051	−	2.06203i
$636$		0			0
$637$	2.00000	−	3.46410i	0.0792429	−	0.137253i
$638$		0			0
$639$		0			0
$640$	3.00000			0.118585
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	−0.919171	−	0.393860i	$-0.871140\pi$
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	0.800678	+	0.599095i	$0.204473\pi$
$642$		0			0
$643$	−2.50000	−	4.33013i	−0.0985904	−	0.170764i	0.812511	−	0.582946i	$-0.198100\pi$
$643$	−2.50000	−	4.33013i	−0.0985904	−	0.170764i	−0.911101	+	0.412182i	$0.864767\pi$
$644$	−1.50000	−	2.59808i	−0.0591083	−	0.102379i
$645$		0			0
$646$	21.0000	−	36.3731i	0.826234	−	1.43108i
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$		0			0
$649$	−18.0000			−0.706562
$650$	8.00000	−	13.8564i	0.313786	−	0.543493i
$651$		0			0
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$	9.00000	−	15.5885i	0.351659	−	0.609091i
$656$	9.00000			0.351391
$657$		0			0
$658$	−6.00000			−0.233904
$659$	−4.50000	+	7.79423i	−0.175295	+	0.303620i	−0.940263	−	0.340448i	$-0.889421\pi$
$659$	−4.50000	+	7.79423i	−0.175295	+	0.303620i	0.764968	+	0.644068i	$0.222755\pi$
$660$		0			0
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	0.933144	+	0.359502i	$0.117053\pi$
$661$	20.0000	+	34.6410i	0.777910	+	1.34738i	−0.155235	+	0.987878i	$0.549613\pi$
$662$	14.0000	+	24.2487i	0.544125	+	0.942453i
$663$		0			0
$664$		0			0
$665$	−21.0000			−0.814345
$666$		0			0
$667$		0			0
$668$	−9.00000	+	15.5885i	−0.348220	+	0.603136i
$669$		0			0
$670$	6.00000	+	10.3923i	0.231800	+	0.401490i
$671$	12.0000	+	20.7846i	0.463255	+	0.802381i
$672$		0			0
$673$	23.0000	−	39.8372i	0.886585	−	1.53561i	0.0426985	−	0.999088i	$-0.486405\pi$
$673$	23.0000	−	39.8372i	0.886585	−	1.53561i	0.843886	−	0.536522i	$-0.180262\pi$
$674$	−13.0000			−0.500741
$675$		0			0
$676$	3.00000			0.115385
$677$	7.50000	−	12.9904i	0.288248	−	0.499261i	−0.685143	−	0.728408i	$-0.740260\pi$
$677$	7.50000	−	12.9904i	0.288248	−	0.499261i	0.973392	+	0.229147i	$0.0735938\pi$
$678$		0			0
$679$	−4.00000	−	6.92820i	−0.153506	−	0.265880i
$680$	−9.00000	−	15.5885i	−0.345134	−	0.597790i
$681$		0			0
$682$	7.50000	−	12.9904i	0.287190	−	0.497427i
$683$	15.0000			0.573959			0.286980	−	0.957937i	$-0.407349\pi$
$683$	15.0000			0.573959			0.286980	+	0.957937i	$0.407349\pi$
$684$		0			0
$685$	−36.0000			−1.37549
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	5.00000	+	8.66025i	0.190623	+	0.330169i
$689$	−24.0000	−	41.5692i	−0.914327	−	1.58366i
$690$		0			0
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$	21.0000			0.798300
$693$		0			0
$694$	−3.00000			−0.113878
$695$	6.00000	−	10.3923i	0.227593	−	0.394203i
$696$		0			0
$697$	−27.0000	−	46.7654i	−1.02270	−	1.77136i
$698$	5.00000	+	8.66025i	0.189253	+	0.327795i
$699$		0			0
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	49.0000			1.84807
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	10.5000	+	18.1865i	0.395173	+	0.684459i
$707$	−3.00000	−	5.19615i	−0.112827	−	0.195421i
$708$		0			0
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	0.324104	+	0.946021i	$0.394937\pi$
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	−0.981331	+	0.192328i	$0.938396\pi$
$710$	−27.0000			−1.01329
$711$		0			0
$712$	−15.0000			−0.562149
$713$	−7.50000	+	12.9904i	−0.280877	+	0.486494i
$714$		0			0
$715$	−18.0000	−	31.1769i	−0.673162	−	1.16595i
$716$	−12.0000	−	20.7846i	−0.448461	−	0.776757i
$717$		0			0
$718$	−6.00000	+	10.3923i	−0.223918	+	0.387837i
$719$	30.0000			1.11881			0.559406	−	0.828894i	$-0.311029\pi$
$719$	30.0000			1.11881			0.559406	+	0.828894i	$0.311029\pi$
$720$		0			0
$721$	5.00000			0.186210
$722$	−15.0000	+	25.9808i	−0.558242	+	0.966904i
$723$		0			0
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$		0			0
$726$		0			0
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	−0.930618	−	0.365991i	$-0.880730\pi$
$727$	−4.00000	+	6.92820i	−0.148352	+	0.256953i	0.782267	+	0.622944i	$0.214063\pi$
$728$	−4.00000			−0.148250
$729$		0			0
$730$	6.00000			0.222070
$731$	30.0000	−	51.9615i	1.10959	−	1.92187i
$732$		0			0
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	0.994471	−	0.105010i	$-0.0334875\pi$
$733$	11.0000	+	19.0526i	0.406294	+	0.703722i	−0.588177	+	0.808732i	$0.700154\pi$
$734$	−8.50000	−	14.7224i	−0.313741	−	0.543415i
$735$		0			0
$736$	−1.50000	+	2.59808i	−0.0552907	+	0.0957664i
$737$	12.0000			0.442026
$738$		0			0
$739$	−34.0000			−1.25071			−0.625355	−	0.780340i	$-0.715046\pi$
$739$	−34.0000			−1.25071			−0.625355	+	0.780340i	$0.715046\pi$
$740$	10.5000	−	18.1865i	0.385988	−	0.668550i
$741$		0			0
$742$	6.00000	+	10.3923i	0.220267	+	0.381514i
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	0.936687	−	0.350168i	$-0.113876\pi$
$743$	4.50000	+	7.79423i	0.165089	+	0.285943i	−0.771598	+	0.636111i	$0.780542\pi$
$744$		0			0
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	−13.0000			−0.475964
$747$		0			0
$748$	−18.0000			−0.658145
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$		0			0
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	0.993895	−	0.110333i	$-0.0351919\pi$
$751$	11.0000	+	19.0526i	0.401396	+	0.695238i	−0.592499	+	0.805571i	$0.701859\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$		0			0
$755$	−30.0000			−1.09181
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$	−1.00000	+	1.73205i	−0.0363216	+	0.0629109i
$759$		0			0
$760$	10.5000	+	18.1865i	0.380875	+	0.659695i
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	0.942207	+	0.335032i	$0.108747\pi$
$761$	21.0000	+	36.3731i	0.761249	+	1.31852i	−0.180957	+	0.983491i	$0.557920\pi$
$762$		0			0
$763$	−5.50000	+	9.52628i	−0.199113	+	0.344874i
$764$	−15.0000			−0.542681
$765$		0			0
$766$	30.0000			1.08394
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$		0			0
$769$	2.00000	+	3.46410i	0.0721218	+	0.124919i	0.899831	−	0.436239i	$-0.143690\pi$
$769$	2.00000	+	3.46410i	0.0721218	+	0.124919i	−0.827709	+	0.561157i	$0.810356\pi$
$770$	4.50000	+	7.79423i	0.162169	+	0.280885i
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	−39.0000			−1.40273			−0.701366	−	0.712801i	$-0.747426\pi$
$773$	−39.0000			−1.40273			−0.701366	+	0.712801i	$0.747426\pi$
$774$		0			0
$775$	20.0000			0.718421
$776$	−4.00000	+	6.92820i	−0.143592	+	0.248708i
$777$		0			0
$778$	6.00000	+	10.3923i	0.215110	+	0.372582i
$779$	31.5000	+	54.5596i	1.12860	+	1.95480i
$780$		0			0
$781$	−13.5000	+	23.3827i	−0.483068	+	0.836698i
$782$	18.0000			0.643679
$783$		0			0
$784$	1.00000			0.0357143
$785$	6.00000	−	10.3923i	0.214149	−	0.370917i
$786$		0			0
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	−0.996531	−	0.0832226i	$-0.973479\pi$
$787$	−16.0000	−	27.7128i	−0.570338	−	0.987855i	0.426193	−	0.904632i	$-0.359855\pi$
$788$	−9.00000	−	15.5885i	−0.320612	−	0.555316i
$789$		0			0
$790$	15.0000	−	25.9808i	0.533676	−	0.924354i
$791$	18.0000			0.640006
$792$		0			0
$793$	−32.0000			−1.13635
$794$	−1.00000	+	1.73205i	−0.0354887	+	0.0614682i
$795$		0			0
$796$	3.50000	+	6.06218i	0.124054	+	0.214868i
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	0.999687	−	0.0249984i	$-0.00795805\pi$
$797$	13.5000	+	23.3827i	0.478195	+	0.828257i	−0.521493	+	0.853256i	$0.674625\pi$
$798$		0			0
$799$	18.0000	−	31.1769i	0.636794	−	1.10296i
$800$	4.00000			0.141421
$801$		0			0
$802$	−24.0000			−0.847469
$803$	3.00000	−	5.19615i	0.105868	−	0.183368i
$804$		0			0
$805$	−4.50000	−	7.79423i	−0.158604	−	0.274710i
$806$	10.0000	+	17.3205i	0.352235	+	0.610089i
$807$		0			0
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	24.0000			0.843795			0.421898	−	0.906644i	$-0.361364\pi$
$809$	24.0000			0.843795			0.421898	+	0.906644i	$0.361364\pi$
$810$		0			0
$811$	−25.0000			−0.877869			−0.438934	−	0.898519i	$-0.644644\pi$
$811$	−25.0000			−0.877869			−0.438934	+	0.898519i	$0.644644\pi$
$812$		0			0
$813$		0			0
$814$	−10.5000	−	18.1865i	−0.368025	−	0.637438i
$815$	24.0000	+	41.5692i	0.840683	+	1.45611i
$816$		0			0
$817$	−35.0000	+	60.6218i	−1.22449	+	2.12089i
$818$	−22.0000			−0.769212
$819$		0			0
$820$	27.0000			0.942881
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	0.476122	+	0.879379i	$0.342042\pi$
$821$	−15.0000	+	25.9808i	−0.523504	+	0.906735i	−0.999626	+	0.0273557i	$0.991291\pi$
$822$		0			0
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	−2.50000	−	4.33013i	−0.0870916	−	0.150847i
$825$		0			0
$826$	−3.00000	+	5.19615i	−0.104383	+	0.180797i
$827$	−9.00000			−0.312961			−0.156480	−	0.987681i	$-0.550015\pi$
$827$	−9.00000			−0.312961			−0.156480	+	0.987681i	$0.550015\pi$
$828$		0			0
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$		0			0
$831$		0			0
$832$	2.00000	+	3.46410i	0.0693375	+	0.120096i
$833$	−3.00000	−	5.19615i	−0.103944	−	0.180036i
$834$		0			0
$835$	−27.0000	+	46.7654i	−0.934374	+	1.61838i
$836$	21.0000			0.726300
$837$		0			0
$838$	−18.0000			−0.621800
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−8.50000	−	14.7224i	−0.292929	−	0.507369i
$843$		0			0
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	9.00000			0.309609
$846$		0			0
$847$	−2.00000			−0.0687208
$848$	6.00000	−	10.3923i	0.206041	−	0.356873i
$849$		0			0
$850$	−12.0000	−	20.7846i	−0.411597	−	0.712906i
$851$	10.5000	+	18.1865i	0.359935	+	0.623426i
$852$		0			0
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	−0.926343	−	0.376680i	$-0.877066\pi$
$853$	−4.00000	+	6.92820i	−0.136957	+	0.237217i	0.789386	+	0.613897i	$0.210399\pi$
$854$	8.00000			0.273754
$855$		0			0
$856$	12.0000			0.410152
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	−0.839268	−	0.543718i	$-0.817016\pi$
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	0.890507	+	0.454969i	$0.150350\pi$
$858$		0			0
$859$	15.5000	+	26.8468i	0.528853	+	0.916001i	0.999434	+	0.0336436i	$0.0107111\pi$
$859$	15.5000	+	26.8468i	0.528853	+	0.916001i	−0.470581	+	0.882357i	$0.655956\pi$
$860$	15.0000	+	25.9808i	0.511496	+	0.885937i
$861$		0			0
$862$	1.50000	−	2.59808i	0.0510902	−	0.0884908i
$863$	−24.0000			−0.816970			−0.408485	−	0.912765i	$-0.633943\pi$
$863$	−24.0000			−0.816970			−0.408485	+	0.912765i	$0.633943\pi$
$864$		0			0
$865$	63.0000			2.14206
$866$	8.00000	−	13.8564i	0.271851	−	0.470860i
$867$		0			0
$868$	−2.50000	−	4.33013i	−0.0848555	−	0.146974i
$869$	−15.0000	−	25.9808i	−0.508840	−	0.881337i
$870$		0			0
$871$	−8.00000	+	13.8564i	−0.271070	+	0.469506i
$872$	11.0000			0.372507
$873$		0			0
$874$	−21.0000			−0.710336
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$		0			0
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	0.723298	−	0.690536i	$-0.242625\pi$
$877$	−7.00000	−	12.1244i	−0.236373	−	0.409410i	−0.959671	+	0.281126i	$0.909292\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$		0			0
$880$	4.50000	−	7.79423i	0.151695	−	0.262743i
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$		0			0
$883$	−16.0000			−0.538443			−0.269221	−	0.963078i	$-0.586766\pi$
$883$	−16.0000			−0.538443			−0.269221	+	0.963078i	$0.586766\pi$
$884$	12.0000	−	20.7846i	0.403604	−	0.699062i
$885$		0			0
$886$	−1.50000	−	2.59808i	−0.0503935	−	0.0872841i
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	0.994077	−	0.108678i	$-0.0346618\pi$
$887$	12.0000	+	20.7846i	0.402921	+	0.697879i	−0.591156	+	0.806557i	$0.701328\pi$
$888$		0			0
$889$	−10.0000	+	17.3205i	−0.335389	+	0.580911i
$890$	−45.0000			−1.50840
$891$		0			0
$892$	−1.00000			−0.0334825
$893$	−21.0000	+	36.3731i	−0.702738	+	1.21718i
$894$		0			0
$895$	−36.0000	−	62.3538i	−1.20335	−	2.08426i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	9.00000	−	15.5885i	0.300334	−	0.520194i
$899$		0			0
$900$		0			0
$901$	−72.0000			−2.39867
$902$	13.5000	−	23.3827i	0.449501	−	0.778558i
$903$		0			0
$904$	−9.00000	−	15.5885i	−0.299336	−	0.518464i
$905$	−3.00000	−	5.19615i	−0.0997234	−	0.172726i
$906$		0			0
$907$	23.0000	−	39.8372i	0.763702	−	1.32277i	−0.177227	−	0.984170i	$-0.556713\pi$
$907$	23.0000	−	39.8372i	0.763702	−	1.32277i	0.940930	−	0.338602i	$-0.109954\pi$
$908$	6.00000			0.199117
$909$		0			0
$910$	−12.0000			−0.397796
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$		0			0
$914$	9.50000	+	16.4545i	0.314232	+	0.544266i
$915$		0			0
$916$	2.00000	−	3.46410i	0.0660819	−	0.114457i
$917$	−6.00000			−0.198137
$918$		0			0
$919$	−52.0000			−1.71532			−0.857661	−	0.514216i	$-0.828083\pi$
$919$	−52.0000			−1.71532			−0.857661	+	0.514216i	$0.828083\pi$
$920$	−4.50000	+	7.79423i	−0.148361	+	0.256968i
$921$		0			0
$922$	13.5000	+	23.3827i	0.444599	+	0.770068i
$923$	−18.0000	−	31.1769i	−0.592477	−	1.02620i
$924$		0			0
$925$	14.0000	−	24.2487i	0.460317	−	0.797293i
$926$	14.0000			0.460069
$927$		0			0
$928$		0			0
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$	3.50000	+	6.06218i	0.114708	+	0.198680i
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$		0			0
$934$	3.00000	−	5.19615i	0.0981630	−	0.170023i
$935$	−54.0000			−1.76599
$936$		0			0
$937$	20.0000			0.653372			0.326686	−	0.945133i	$-0.394068\pi$
$937$	20.0000			0.653372			0.326686	+	0.945133i	$0.394068\pi$
$938$	2.00000	−	3.46410i	0.0653023	−	0.113107i
$939$		0			0
$940$	9.00000	+	15.5885i	0.293548	+	0.508439i
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	0.717496	−	0.696563i	$-0.245288\pi$
$941$	−7.50000	−	12.9904i	−0.244493	−	0.423474i	−0.961989	+	0.273088i	$0.911955\pi$
$942$		0			0
$943$	−13.5000	+	23.3827i	−0.439620	+	0.761445i
$944$	6.00000			0.195283
$945$		0			0
$946$	30.0000			0.975384
$947$	−19.5000	+	33.7750i	−0.633665	+	1.09754i	0.353131	+	0.935574i	$0.385117\pi$
$947$	−19.5000	+	33.7750i	−0.633665	+	1.09754i	−0.986796	+	0.161966i	$0.948217\pi$
$948$		0			0
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$	14.0000	+	24.2487i	0.454220	+	0.786732i
$951$		0			0
$952$	−3.00000	+	5.19615i	−0.0972306	+	0.168408i
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$	−45.0000			−1.45617
$956$		0			0
$957$		0			0
$958$	−12.0000	−	20.7846i	−0.387702	−	0.671520i
$959$	6.00000	+	10.3923i	0.193750	+	0.335585i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	28.0000			0.902756
$963$		0			0
$964$	26.0000			0.837404
$965$	−21.0000	+	36.3731i	−0.676014	+	1.17089i
$966$		0			0
$967$	29.0000	+	50.2295i	0.932577	+	1.61527i	0.778898	+	0.627150i	$0.215779\pi$
$967$	29.0000	+	50.2295i	0.932577	+	1.61527i	0.153679	+	0.988121i	$0.450888\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$	−12.0000	+	20.7846i	−0.385297	+	0.667354i
$971$	48.0000			1.54039			0.770197	−	0.637806i	$-0.220158\pi$
$971$	48.0000			1.54039			0.770197	+	0.637806i	$0.220158\pi$
$972$		0			0
$973$	−4.00000			−0.128234
$974$	−1.00000	+	1.73205i	−0.0320421	+	0.0554985i
$975$		0			0
$976$	−4.00000	−	6.92820i	−0.128037	−	0.221766i
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	0.945899	−	0.324462i	$-0.105183\pi$
$977$	6.00000	+	10.3923i	0.191957	+	0.332479i	−0.753942	+	0.656941i	$0.771850\pi$
$978$		0			0
$979$	−22.5000	+	38.9711i	−0.719103	+	1.24552i
$980$	3.00000			0.0958315
$981$		0			0
$982$	9.00000			0.287202
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	−0.909894	−	0.414840i	$-0.863838\pi$
$983$	−3.00000	+	5.19615i	−0.0956851	+	0.165732i	0.814209	+	0.580572i	$0.197171\pi$
$984$		0			0
$985$	−27.0000	−	46.7654i	−0.860292	−	1.49007i
$986$		0			0
$987$		0			0
$988$	−14.0000	+	24.2487i	−0.445399	+	0.771454i
$989$	−30.0000			−0.953945
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$	−2.50000	+	4.33013i	−0.0793751	+	0.137482i
$993$		0			0
$994$	4.50000	+	7.79423i	0.142731	+	0.247218i
$995$	10.5000	+	18.1865i	0.332872	+	0.576552i
$996$		0			0
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$	−22.0000			−0.696398
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.f.b.379.1		2
3.2	odd	2		1134.2.f.o.379.1		2
9.2	odd	6		378.2.a.b.1.1	✓	1
9.4	even	3	inner	1134.2.f.b.757.1		2
9.5	odd	6		1134.2.f.o.757.1		2
9.7	even	3		378.2.a.g.1.1	yes	1
36.7	odd	6		3024.2.a.bb.1.1		1
36.11	even	6		3024.2.a.c.1.1		1
45.29	odd	6		9450.2.a.cu.1.1		1
45.34	even	6		9450.2.a.h.1.1		1
63.20	even	6		2646.2.a.n.1.1		1
63.34	odd	6		2646.2.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.a.b.1.1	✓	1	9.2	odd	6
378.2.a.g.1.1	yes	1	9.7	even	3
1134.2.f.b.379.1		2	1.1	even	1	trivial
1134.2.f.b.757.1		2	9.4	even	3	inner
1134.2.f.o.379.1		2	3.2	odd	2
1134.2.f.o.757.1		2	9.5	odd	6
2646.2.a.n.1.1		1	63.20	even	6
2646.2.a.q.1.1		1	63.34	odd	6
3024.2.a.c.1.1		1	36.11	even	6
3024.2.a.bb.1.1		1	36.7	odd	6
9450.2.a.h.1.1		1	45.34	even	6
9450.2.a.cu.1.1		1	45.29	odd	6

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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 2.59808i) q^{5} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +3.00000 q^{10} +(1.50000 - 2.59808i) q^{11} +(2.00000 + 3.46410i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +6.00000 q^{17} -7.00000 q^{19} +(-1.50000 + 2.59808i) q^{20} +(1.50000 + 2.59808i) q^{22} +(-1.50000 - 2.59808i) q^{23} +(-2.00000 + 3.46410i) q^{25} -4.00000 q^{26} +1.00000 q^{28} +(-2.50000 - 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-3.00000 + 5.19615i) q^{34} +3.00000 q^{35} -7.00000 q^{37} +(3.50000 - 6.06218i) q^{38} +(-1.50000 - 2.59808i) q^{40} +(-4.50000 - 7.79423i) q^{41} +(5.00000 - 8.66025i) q^{43} -3.00000 q^{44} +3.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(2.00000 - 3.46410i) q^{52} -12.0000 q^{53} -9.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-3.00000 - 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} +5.00000 q^{62} +1.00000 q^{64} +(6.00000 - 10.3923i) q^{65} +(2.00000 + 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +(-1.50000 + 2.59808i) q^{70} -9.00000 q^{71} +2.00000 q^{73} +(3.50000 - 6.06218i) q^{74} +(3.50000 + 6.06218i) q^{76} +(1.50000 + 2.59808i) q^{77} +(5.00000 - 8.66025i) q^{79} +3.00000 q^{80} +9.00000 q^{82} +(-9.00000 - 15.5885i) q^{85} +(5.00000 + 8.66025i) q^{86} +(1.50000 - 2.59808i) q^{88} -15.0000 q^{89} -4.00000 q^{91} +(-1.50000 + 2.59808i) q^{92} +(3.00000 + 5.19615i) q^{94} +(10.5000 + 18.1865i) q^{95} +(-4.00000 + 6.92820i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 3 q^{5} - q^{7} + 2 q^{8} + 6 q^{10} + 3 q^{11} + 4 q^{13} - q^{14} - q^{16} + 12 q^{17} - 14 q^{19} - 3 q^{20} + 3 q^{22} - 3 q^{23} - 4 q^{25} - 8 q^{26} + 2 q^{28} - 5 q^{31} - q^{32} - 6 q^{34} + 6 q^{35} - 14 q^{37} + 7 q^{38} - 3 q^{40} - 9 q^{41} + 10 q^{43} - 6 q^{44} + 6 q^{46} + 6 q^{47} - q^{49} - 4 q^{50} + 4 q^{52} - 24 q^{53} - 18 q^{55} - q^{56} - 6 q^{59} - 8 q^{61} + 10 q^{62} + 2 q^{64} + 12 q^{65} + 4 q^{67} - 6 q^{68} - 3 q^{70} - 18 q^{71} + 4 q^{73} + 7 q^{74} + 7 q^{76} + 3 q^{77} + 10 q^{79} + 6 q^{80} + 18 q^{82} - 18 q^{85} + 10 q^{86} + 3 q^{88} - 30 q^{89} - 8 q^{91} - 3 q^{92} + 6 q^{94} + 21 q^{95} - 8 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 3 * q^5 - q^7 + 2 * q^8 + 6 * q^10 + 3 * q^11 + 4 * q^13 - q^14 - q^16 + 12 * q^17 - 14 * q^19 - 3 * q^20 + 3 * q^22 - 3 * q^23 - 4 * q^25 - 8 * q^26 + 2 * q^28 - 5 * q^31 - q^32 - 6 * q^34 + 6 * q^35 - 14 * q^37 + 7 * q^38 - 3 * q^40 - 9 * q^41 + 10 * q^43 - 6 * q^44 + 6 * q^46 + 6 * q^47 - q^49 - 4 * q^50 + 4 * q^52 - 24 * q^53 - 18 * q^55 - q^56 - 6 * q^59 - 8 * q^61 + 10 * q^62 + 2 * q^64 + 12 * q^65 + 4 * q^67 - 6 * q^68 - 3 * q^70 - 18 * q^71 + 4 * q^73 + 7 * q^74 + 7 * q^76 + 3 * q^77 + 10 * q^79 + 6 * q^80 + 18 * q^82 - 18 * q^85 + 10 * q^86 + 3 * q^88 - 30 * q^89 - 8 * q^91 - 3 * q^92 + 6 * q^94 + 21 * q^95 - 8 * q^97 + 2 * q^98

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