LMFDB - Embedded newform 1530.2.m.c.647.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1530,2,Mod(647,1530)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1530, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("1530.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1530.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$12.2171115093$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			647.2
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1530.647
Dual form			1530.2.m.c.953.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.00000 - 1.00000i) q^{10} -5.65685i q^{11} -1.41421 q^{14} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} -4.00000i q^{19} +(0.707107 - 2.12132i) q^{20} +(-4.00000 - 4.00000i) q^{22} +(4.00000 + 3.00000i) q^{25} +(-1.00000 + 1.00000i) q^{28} -1.41421 q^{29} -6.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.00000i q^{34} +(-1.41421 - 2.82843i) q^{35} +(1.00000 + 1.00000i) q^{37} +(-2.82843 - 2.82843i) q^{38} +(-1.00000 - 2.00000i) q^{40} -5.65685i q^{41} +(7.00000 - 7.00000i) q^{43} -5.65685 q^{44} +(-2.82843 + 2.82843i) q^{47} -5.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(7.07107 + 7.07107i) q^{53} +(4.00000 - 12.0000i) q^{55} +1.41421i q^{56} +(-1.00000 + 1.00000i) q^{58} -1.41421 q^{59} +4.00000 q^{61} +(-4.24264 + 4.24264i) q^{62} +1.00000i q^{64} +(-5.00000 - 5.00000i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-3.00000 - 1.00000i) q^{70} +9.89949i q^{71} +(10.0000 - 10.0000i) q^{73} +1.41421 q^{74} -4.00000 q^{76} +(-5.65685 + 5.65685i) q^{77} -8.00000i q^{79} +(-2.12132 - 0.707107i) q^{80} +(-4.00000 - 4.00000i) q^{82} +(1.41421 + 1.41421i) q^{83} +(-2.00000 + 1.00000i) q^{85} -9.89949i q^{86} +(-4.00000 + 4.00000i) q^{88} -1.41421 q^{89} +4.00000i q^{94} +(2.82843 - 8.48528i) q^{95} +(4.00000 + 4.00000i) q^{97} +(-3.53553 - 3.53553i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{7}+O(q^{10}) $ 4 * q - 4 * q^7	$ 4 q - 4 q^{7} + 8 q^{10} - 4 q^{16} - 16 q^{22} + 16 q^{25} - 4 q^{28} - 24 q^{31} + 4 q^{37} - 4 q^{40} + 28 q^{43} + 16 q^{55} - 4 q^{58} + 16 q^{61} - 20 q^{67} - 12 q^{70} + 40 q^{73} - 16 q^{76} - 16 q^{82} - 8 q^{85} - 16 q^{88} + 16 q^{97}+O(q^{100}) $ 4 * q - 4 * q^7 + 8 * q^10 - 4 * q^16 - 16 * q^22 + 16 * q^25 - 4 * q^28 - 24 * q^31 + 4 * q^37 - 4 * q^40 + 28 * q^43 + 16 * q^55 - 4 * q^58 + 16 * q^61 - 20 * q^67 - 12 * q^70 + 40 * q^73 - 16 * q^76 - 16 * q^82 - 8 * q^85 - 16 * q^88 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times$.

$n$	$307$	$1261$	$1361$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$

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 $

$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$2$	0.707107	−	0.707107i	0.500000	−	0.500000i
$3$		0			0
$3$		0			0
$4$		−	1.00000i		−	0.500000i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$5$	2.12132	+	0.707107i	0.948683	+	0.316228i
$6$		0			0
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$	−0.707107	−	0.707107i	−0.250000	−	0.250000i
$9$		0			0
$10$	2.00000	−	1.00000i	0.632456	−	0.316228i
$11$		−	5.65685i		−	1.70561i	−0.522233	−	0.852803i	$-0.674901\pi$
$11$		−	5.65685i		−	1.70561i	0.522233	−	0.852803i	$-0.325099\pi$
$12$		0			0
$13$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$13$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$14$	−1.41421			−0.377964
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$17$	−0.707107	+	0.707107i	−0.171499	+	0.171499i
$18$		0			0
$19$		−	4.00000i		−	0.917663i	−0.888523	−	0.458831i	$-0.848268\pi$
$19$		−	4.00000i		−	0.917663i	0.888523	−	0.458831i	$-0.151732\pi$
$20$	0.707107	−	2.12132i	0.158114	−	0.474342i
$21$		0			0
$22$	−4.00000	−	4.00000i	−0.852803	−	0.852803i
$23$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$23$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$24$		0			0
$25$	4.00000	+	3.00000i	0.800000	+	0.600000i
$26$		0			0
$27$		0			0
$28$	−1.00000	+	1.00000i	−0.188982	+	0.188982i
$29$	−1.41421			−0.262613			−0.131306	−	0.991342i	$-0.541917\pi$
$29$	−1.41421			−0.262613			−0.131306	+	0.991342i	$0.541917\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$		0			0
$34$			1.00000i			0.171499i
$35$	−1.41421	−	2.82843i	−0.239046	−	0.478091i
$36$		0			0
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	0.784512	−	0.620113i	$-0.212913\pi$
$37$	1.00000	+	1.00000i	0.164399	+	0.164399i	−0.620113	+	0.784512i	$0.712913\pi$
$38$	−2.82843	−	2.82843i	−0.458831	−	0.458831i
$39$		0			0
$40$	−1.00000	−	2.00000i	−0.158114	−	0.316228i
$41$		−	5.65685i		−	0.883452i	−0.897150	−	0.441726i	$-0.854366\pi$
$41$		−	5.65685i		−	0.883452i	0.897150	−	0.441726i	$-0.145634\pi$
$42$		0			0
$43$	7.00000	−	7.00000i	1.06749	−	1.06749i	0.0699387	−	0.997551i	$-0.477720\pi$
$43$	7.00000	−	7.00000i	1.06749	−	1.06749i	0.997551	−	0.0699387i	$-0.0222804\pi$
$44$	−5.65685			−0.852803
$45$		0			0
$46$		0			0
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	−0.882632	−	0.470064i	$-0.844231\pi$
$47$	−2.82843	+	2.82843i	−0.412568	+	0.412568i	0.470064	+	0.882632i	$0.344231\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$	4.94975	−	0.707107i	0.700000	−	0.100000i
$51$		0			0
$52$		0			0
$53$	7.07107	+	7.07107i	0.971286	+	0.971286i	0.999599	−	0.0283132i	$-0.00901359\pi$
$53$	7.07107	+	7.07107i	0.971286	+	0.971286i	−0.0283132	+	0.999599i	$0.509014\pi$
$54$		0			0
$55$	4.00000	−	12.0000i	0.539360	−	1.61808i
$56$			1.41421i			0.188982i
$57$		0			0
$58$	−1.00000	+	1.00000i	−0.131306	+	0.131306i
$59$	−1.41421			−0.184115			−0.0920575	−	0.995754i	$-0.529344\pi$
$59$	−1.41421			−0.184115			−0.0920575	+	0.995754i	$0.529344\pi$
$60$		0			0
$61$	4.00000			0.512148			0.256074	−	0.966657i	$-0.417571\pi$
$61$	4.00000			0.512148			0.256074	+	0.966657i	$0.417571\pi$
$62$	−4.24264	+	4.24264i	−0.538816	+	0.538816i
$63$		0			0
$64$			1.00000i			0.125000i
$65$		0			0
$66$		0			0
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	0.332320	−	0.943167i	$-0.392169\pi$
$67$	−5.00000	−	5.00000i	−0.610847	−	0.610847i	−0.943167	+	0.332320i	$0.892169\pi$
$68$	0.707107	+	0.707107i	0.0857493	+	0.0857493i
$69$		0			0
$70$	−3.00000	−	1.00000i	−0.358569	−	0.119523i
$71$			9.89949i			1.17485i	0.809277	+	0.587427i	$0.199859\pi$
$71$			9.89949i			1.17485i	−0.809277	+	0.587427i	$0.800141\pi$
$72$		0			0
$73$	10.0000	−	10.0000i	1.17041	−	1.17041i	0.188300	−	0.982112i	$-0.439702\pi$
$73$	10.0000	−	10.0000i	1.17041	−	1.17041i	0.982112	−	0.188300i	$-0.0602977\pi$
$74$	1.41421			0.164399
$75$		0			0
$76$	−4.00000			−0.458831
$77$	−5.65685	+	5.65685i	−0.644658	+	0.644658i
$78$		0			0
$79$		−	8.00000i		−	0.900070i	−0.893011	−	0.450035i	$-0.851411\pi$
$79$		−	8.00000i		−	0.900070i	0.893011	−	0.450035i	$-0.148589\pi$
$80$	−2.12132	−	0.707107i	−0.237171	−	0.0790569i
$81$		0			0
$82$	−4.00000	−	4.00000i	−0.441726	−	0.441726i
$83$	1.41421	+	1.41421i	0.155230	+	0.155230i	0.780449	−	0.625219i	$-0.214990\pi$
$83$	1.41421	+	1.41421i	0.155230	+	0.155230i	−0.625219	+	0.780449i	$0.714990\pi$
$84$		0			0
$85$	−2.00000	+	1.00000i	−0.216930	+	0.108465i
$86$		−	9.89949i		−	1.06749i
$87$		0			0
$88$	−4.00000	+	4.00000i	−0.426401	+	0.426401i
$89$	−1.41421			−0.149906			−0.0749532	−	0.997187i	$-0.523881\pi$
$89$	−1.41421			−0.149906			−0.0749532	+	0.997187i	$0.523881\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$		0			0
$94$			4.00000i			0.412568i
$95$	2.82843	−	8.48528i	0.290191	−	0.870572i
$96$		0			0
$97$	4.00000	+	4.00000i	0.406138	+	0.406138i	0.880390	−	0.474251i	$-0.157281\pi$
$97$	4.00000	+	4.00000i	0.406138	+	0.406138i	−0.474251	+	0.880390i	$0.657281\pi$
$98$	−3.53553	−	3.53553i	−0.357143	−	0.357143i
$99$		0			0
$100$	3.00000	−	4.00000i	0.300000	−	0.400000i
$101$			14.1421i			1.40720i	0.710599	+	0.703598i	$0.248424\pi$
$101$			14.1421i			1.40720i	−0.710599	+	0.703598i	$0.751576\pi$
$102$		0			0
$103$	14.0000	−	14.0000i	1.37946	−	1.37946i	0.533936	−	0.845525i	$-0.320712\pi$
$103$	14.0000	−	14.0000i	1.37946	−	1.37946i	0.845525	−	0.533936i	$-0.179288\pi$
$104$		0			0
$105$		0			0
$106$	10.0000			0.971286
$107$	−5.65685	+	5.65685i	−0.546869	+	0.546869i	−0.925534	−	0.378665i	$-0.876383\pi$
$107$	−5.65685	+	5.65685i	−0.546869	+	0.546869i	0.378665	+	0.925534i	$0.376383\pi$
$108$		0			0
$109$			6.00000i			0.574696i	0.957826	+	0.287348i	$0.0927736\pi$
$109$			6.00000i			0.574696i	−0.957826	+	0.287348i	$0.907226\pi$
$110$	−5.65685	−	11.3137i	−0.539360	−	1.07872i
$111$		0			0
$112$	1.00000	+	1.00000i	0.0944911	+	0.0944911i
$113$	−7.07107	−	7.07107i	−0.665190	−	0.665190i	0.291409	−	0.956599i	$-0.405876\pi$
$113$	−7.07107	−	7.07107i	−0.665190	−	0.665190i	−0.956599	+	0.291409i	$0.905876\pi$
$114$		0			0
$115$		0			0
$116$			1.41421i			0.131306i
$117$		0			0
$118$	−1.00000	+	1.00000i	−0.0920575	+	0.0920575i
$119$	1.41421			0.129641
$120$		0			0
$121$	−21.0000			−1.90909
$122$	2.82843	−	2.82843i	0.256074	−	0.256074i
$123$		0			0
$124$			6.00000i			0.538816i
$125$	6.36396	+	9.19239i	0.569210	+	0.822192i
$126$		0			0
$127$	6.00000	+	6.00000i	0.532414	+	0.532414i	0.921290	−	0.388876i	$-0.127137\pi$
$127$	6.00000	+	6.00000i	0.532414	+	0.532414i	−0.388876	+	0.921290i	$0.627137\pi$
$128$	0.707107	+	0.707107i	0.0625000	+	0.0625000i
$129$		0			0
$130$		0			0
$131$		−	2.82843i		−	0.247121i	−0.992337	−	0.123560i	$-0.960569\pi$
$131$		−	2.82843i		−	0.247121i	0.992337	−	0.123560i	$-0.0394313\pi$
$132$		0			0
$133$	−4.00000	+	4.00000i	−0.346844	+	0.346844i
$134$	−7.07107			−0.610847
$135$		0			0
$136$	1.00000			0.0857493
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$		0			0
$139$			16.0000i			1.35710i	0.734553	+	0.678551i	$0.237392\pi$
$139$			16.0000i			1.35710i	−0.734553	+	0.678551i	$0.762608\pi$
$140$	−2.82843	+	1.41421i	−0.239046	+	0.119523i
$141$		0			0
$142$	7.00000	+	7.00000i	0.587427	+	0.587427i
$143$		0			0
$144$		0			0
$145$	−3.00000	−	1.00000i	−0.249136	−	0.0830455i
$146$		−	14.1421i		−	1.17041i
$147$		0			0
$148$	1.00000	−	1.00000i	0.0821995	−	0.0821995i
$149$	−8.48528			−0.695141			−0.347571	−	0.937654i	$-0.612993\pi$
$149$	−8.48528			−0.695141			−0.347571	+	0.937654i	$0.612993\pi$
$150$		0			0
$151$	−16.0000			−1.30206			−0.651031	−	0.759051i	$-0.725663\pi$
$151$	−16.0000			−1.30206			−0.651031	+	0.759051i	$0.725663\pi$
$152$	−2.82843	+	2.82843i	−0.229416	+	0.229416i
$153$		0			0
$154$			8.00000i			0.644658i
$155$	−12.7279	−	4.24264i	−1.02233	−	0.340777i
$156$		0			0
$157$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$157$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$158$	−5.65685	−	5.65685i	−0.450035	−	0.450035i
$159$		0			0
$160$	−2.00000	+	1.00000i	−0.158114	+	0.0790569i
$161$		0			0
$162$		0			0
$163$	6.00000	−	6.00000i	0.469956	−	0.469956i	−0.431944	−	0.901900i	$-0.642172\pi$
$163$	6.00000	−	6.00000i	0.469956	−	0.469956i	0.901900	+	0.431944i	$0.142172\pi$
$164$	−5.65685			−0.441726
$165$		0			0
$166$	2.00000			0.155230
$167$	−7.07107	+	7.07107i	−0.547176	+	0.547176i	−0.925623	−	0.378447i	$-0.876458\pi$
$167$	−7.07107	+	7.07107i	−0.547176	+	0.547176i	0.378447	+	0.925623i	$0.376458\pi$
$168$		0			0
$169$			13.0000i			1.00000i
$170$	−0.707107	+	2.12132i	−0.0542326	+	0.162698i
$171$		0			0
$172$	−7.00000	−	7.00000i	−0.533745	−	0.533745i
$173$	5.65685	+	5.65685i	0.430083	+	0.430083i	0.888656	−	0.458574i	$-0.151639\pi$
$173$	5.65685	+	5.65685i	0.430083	+	0.430083i	−0.458574	+	0.888656i	$0.651639\pi$
$174$		0			0
$175$	−1.00000	−	7.00000i	−0.0755929	−	0.529150i
$176$			5.65685i			0.426401i
$177$		0			0
$178$	−1.00000	+	1.00000i	−0.0749532	+	0.0749532i
$179$	24.0416			1.79696			0.898478	−	0.439019i	$-0.144674\pi$
$179$	24.0416			1.79696			0.898478	+	0.439019i	$0.144674\pi$
$180$		0			0
$181$	−6.00000			−0.445976			−0.222988	−	0.974821i	$-0.571581\pi$
$181$	−6.00000			−0.445976			−0.222988	+	0.974821i	$0.571581\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.41421	+	2.82843i	0.103975	+	0.207950i
$186$		0			0
$187$	4.00000	+	4.00000i	0.292509	+	0.292509i
$188$	2.82843	+	2.82843i	0.206284	+	0.206284i
$189$		0			0
$190$	−4.00000	−	8.00000i	−0.290191	−	0.580381i
$191$		−	2.82843i		−	0.204658i	−0.994751	−	0.102329i	$-0.967371\pi$
$191$		−	2.82843i		−	0.204658i	0.994751	−	0.102329i	$-0.0326294\pi$
$192$		0			0
$193$	16.0000	−	16.0000i	1.15171	−	1.15171i	0.165494	−	0.986211i	$-0.447078\pi$
$193$	16.0000	−	16.0000i	1.15171	−	1.15171i	0.986211	−	0.165494i	$-0.0529220\pi$
$194$	5.65685			0.406138
$195$		0			0
$196$	−5.00000			−0.357143
$197$	−8.48528	+	8.48528i	−0.604551	+	0.604551i	−0.941517	−	0.336966i	$-0.890599\pi$
$197$	−8.48528	+	8.48528i	−0.604551	+	0.604551i	0.336966	+	0.941517i	$0.390599\pi$
$198$		0			0
$199$		−	2.00000i		−	0.141776i	−0.997484	−	0.0708881i	$-0.977417\pi$
$199$		−	2.00000i		−	0.141776i	0.997484	−	0.0708881i	$-0.0225833\pi$
$200$	−0.707107	−	4.94975i	−0.0500000	−	0.350000i
$201$		0			0
$202$	10.0000	+	10.0000i	0.703598	+	0.703598i
$203$	1.41421	+	1.41421i	0.0992583	+	0.0992583i
$204$		0			0
$205$	4.00000	−	12.0000i	0.279372	−	0.838116i
$206$		−	19.7990i		−	1.37946i
$207$		0			0
$208$		0			0
$209$	−22.6274			−1.56517
$210$		0			0
$211$	12.0000			0.826114			0.413057	−	0.910705i	$-0.364461\pi$
$211$	12.0000			0.826114			0.413057	+	0.910705i	$0.364461\pi$
$212$	7.07107	−	7.07107i	0.485643	−	0.485643i
$213$		0			0
$214$			8.00000i			0.546869i
$215$	19.7990	−	9.89949i	1.35028	−	0.675140i
$216$		0			0
$217$	6.00000	+	6.00000i	0.407307	+	0.407307i
$218$	4.24264	+	4.24264i	0.287348	+	0.287348i
$219$		0			0
$220$	−12.0000	−	4.00000i	−0.809040	−	0.269680i
$221$		0			0
$222$		0			0
$223$	−2.00000	+	2.00000i	−0.133930	+	0.133930i	−0.770894	−	0.636964i	$-0.780190\pi$
$223$	−2.00000	+	2.00000i	−0.133930	+	0.133930i	0.636964	+	0.770894i	$0.280190\pi$
$224$	1.41421			0.0944911
$225$		0			0
$226$	−10.0000			−0.665190
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	−0.367024	−	0.930212i	$-0.619623\pi$
$227$	8.48528	−	8.48528i	0.563188	−	0.563188i	0.930212	+	0.367024i	$0.119623\pi$
$228$		0			0
$229$			26.0000i			1.71813i	0.511868	+	0.859064i	$0.328954\pi$
$229$			26.0000i			1.71813i	−0.511868	+	0.859064i	$0.671046\pi$
$230$		0			0
$231$		0			0
$232$	1.00000	+	1.00000i	0.0656532	+	0.0656532i
$233$	12.7279	+	12.7279i	0.833834	+	0.833834i	0.988039	−	0.154205i	$-0.0492816\pi$
$233$	12.7279	+	12.7279i	0.833834	+	0.833834i	−0.154205	+	0.988039i	$0.549282\pi$
$234$		0			0
$235$	−8.00000	+	4.00000i	−0.521862	+	0.260931i
$236$			1.41421i			0.0920575i
$237$		0			0
$238$	1.00000	−	1.00000i	0.0648204	−	0.0648204i
$239$	22.6274			1.46365			0.731823	−	0.681495i	$-0.238670\pi$
$239$	22.6274			1.46365			0.731823	+	0.681495i	$0.238670\pi$
$240$		0			0
$241$	14.0000			0.901819			0.450910	−	0.892570i	$-0.351100\pi$
$241$	14.0000			0.901819			0.450910	+	0.892570i	$0.351100\pi$
$242$	−14.8492	+	14.8492i	−0.954545	+	0.954545i
$243$		0			0
$244$		−	4.00000i		−	0.256074i
$245$	3.53553	−	10.6066i	0.225877	−	0.677631i
$246$		0			0
$247$		0			0
$248$	4.24264	+	4.24264i	0.269408	+	0.269408i
$249$		0			0
$250$	11.0000	+	2.00000i	0.695701	+	0.126491i
$251$			9.89949i			0.624851i	0.949942	+	0.312425i	$0.101141\pi$
$251$			9.89949i			0.624851i	−0.949942	+	0.312425i	$0.898859\pi$
$252$		0			0
$253$		0			0
$254$	8.48528			0.532414
$255$		0			0
$256$	1.00000			0.0625000
$257$	−21.2132	+	21.2132i	−1.32324	+	1.32324i	−0.412108	+	0.911135i	$0.635208\pi$
$257$	−21.2132	+	21.2132i	−1.32324	+	1.32324i	−0.911135	+	0.412108i	$0.864792\pi$
$258$		0			0
$259$		−	2.00000i		−	0.124274i
$260$		0			0
$261$		0			0
$262$	−2.00000	−	2.00000i	−0.123560	−	0.123560i
$263$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$263$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$264$		0			0
$265$	10.0000	+	20.0000i	0.614295	+	1.22859i
$266$			5.65685i			0.346844i
$267$		0			0
$268$	−5.00000	+	5.00000i	−0.305424	+	0.305424i
$269$	−29.6985			−1.81075			−0.905374	−	0.424614i	$-0.860410\pi$
$269$	−29.6985			−1.81075			−0.905374	+	0.424614i	$0.860410\pi$
$270$		0			0
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	0.707107	−	0.707107i	0.0428746	−	0.0428746i
$273$		0			0
$274$		0			0
$275$	16.9706	−	22.6274i	1.02336	−	1.36448i
$276$		0			0
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	0.611213	−	0.791466i	$-0.290682\pi$
$277$	−3.00000	−	3.00000i	−0.180253	−	0.180253i	−0.791466	+	0.611213i	$0.790682\pi$
$278$	11.3137	+	11.3137i	0.678551	+	0.678551i
$279$		0			0
$280$	−1.00000	+	3.00000i	−0.0597614	+	0.179284i
$281$		−	1.41421i		−	0.0843649i	−0.999110	−	0.0421825i	$-0.986569\pi$
$281$		−	1.41421i		−	0.0843649i	0.999110	−	0.0421825i	$-0.0134311\pi$
$282$		0			0
$283$	−12.0000	+	12.0000i	−0.713326	+	0.713326i	−0.967230	−	0.253904i	$-0.918285\pi$
$283$	−12.0000	+	12.0000i	−0.713326	+	0.713326i	0.253904	+	0.967230i	$0.418285\pi$
$284$	9.89949			0.587427
$285$		0			0
$286$		0			0
$287$	−5.65685	+	5.65685i	−0.333914	+	0.333914i
$288$		0			0
$289$		−	1.00000i		−	0.0588235i
$290$	−2.82843	+	1.41421i	−0.166091	+	0.0830455i
$291$		0			0
$292$	−10.0000	−	10.0000i	−0.585206	−	0.585206i
$293$	−1.41421	−	1.41421i	−0.0826192	−	0.0826192i	0.664589	−	0.747209i	$-0.268606\pi$
$293$	−1.41421	−	1.41421i	−0.0826192	−	0.0826192i	−0.747209	+	0.664589i	$0.768606\pi$
$294$		0			0
$295$	−3.00000	−	1.00000i	−0.174667	−	0.0582223i
$296$		−	1.41421i		−	0.0821995i
$297$		0			0
$298$	−6.00000	+	6.00000i	−0.347571	+	0.347571i
$299$		0			0
$300$		0			0
$301$	−14.0000			−0.806947
$302$	−11.3137	+	11.3137i	−0.651031	+	0.651031i
$303$		0			0
$304$			4.00000i			0.229416i
$305$	8.48528	+	2.82843i	0.485866	+	0.161955i
$306$		0			0
$307$	15.0000	+	15.0000i	0.856095	+	0.856095i	0.990876	−	0.134780i	$-0.0430329\pi$
$307$	15.0000	+	15.0000i	0.856095	+	0.856095i	−0.134780	+	0.990876i	$0.543033\pi$
$308$	5.65685	+	5.65685i	0.322329	+	0.322329i
$309$		0			0
$310$	−12.0000	+	6.00000i	−0.681554	+	0.340777i
$311$			26.8701i			1.52366i	0.647776	+	0.761831i	$0.275699\pi$
$311$			26.8701i			1.52366i	−0.647776	+	0.761831i	$0.724301\pi$
$312$		0			0
$313$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$313$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$314$		0			0
$315$		0			0
$316$	−8.00000			−0.450035
$317$	21.2132	−	21.2132i	1.19145	−	1.19145i	0.214792	−	0.976660i	$-0.431092\pi$
$317$	21.2132	−	21.2132i	1.19145	−	1.19145i	0.976660	−	0.214792i	$-0.0689075\pi$
$318$		0			0
$319$			8.00000i			0.447914i
$320$	−0.707107	+	2.12132i	−0.0395285	+	0.118585i
$321$		0			0
$322$		0			0
$323$	2.82843	+	2.82843i	0.157378	+	0.157378i
$324$		0			0
$325$		0			0
$326$		−	8.48528i		−	0.469956i
$327$		0			0
$328$	−4.00000	+	4.00000i	−0.220863	+	0.220863i
$329$	5.65685			0.311872
$330$		0			0
$331$	−14.0000			−0.769510			−0.384755	−	0.923019i	$-0.625714\pi$
$331$	−14.0000			−0.769510			−0.384755	+	0.923019i	$0.625714\pi$
$332$	1.41421	−	1.41421i	0.0776151	−	0.0776151i
$333$		0			0
$334$			10.0000i			0.547176i
$335$	−7.07107	−	14.1421i	−0.386334	−	0.772667i
$336$		0			0
$337$	6.00000	+	6.00000i	0.326841	+	0.326841i	0.851384	−	0.524543i	$-0.175764\pi$
$337$	6.00000	+	6.00000i	0.326841	+	0.326841i	−0.524543	+	0.851384i	$0.675764\pi$
$338$	9.19239	+	9.19239i	0.500000	+	0.500000i
$339$		0			0
$340$	1.00000	+	2.00000i	0.0542326	+	0.108465i
$341$			33.9411i			1.83801i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$	−9.89949			−0.533745
$345$		0			0
$346$	8.00000			0.430083
$347$	19.7990	−	19.7990i	1.06287	−	1.06287i	0.0649788	−	0.997887i	$-0.479302\pi$
$347$	19.7990	−	19.7990i	1.06287	−	1.06287i	0.997887	−	0.0649788i	$-0.0206980\pi$
$348$		0			0
$349$			14.0000i			0.749403i	0.927146	+	0.374701i	$0.122255\pi$
$349$			14.0000i			0.749403i	−0.927146	+	0.374701i	$0.877745\pi$
$350$	−5.65685	−	4.24264i	−0.302372	−	0.226779i
$351$		0			0
$352$	4.00000	+	4.00000i	0.213201	+	0.213201i
$353$	19.7990	+	19.7990i	1.05379	+	1.05379i	0.998468	+	0.0553255i	$0.0176197\pi$
$353$	19.7990	+	19.7990i	1.05379	+	1.05379i	0.0553255	+	0.998468i	$0.482380\pi$
$354$		0			0
$355$	−7.00000	+	21.0000i	−0.371521	+	1.11456i
$356$			1.41421i			0.0749532i
$357$		0			0
$358$	17.0000	−	17.0000i	0.898478	−	0.898478i
$359$	2.82843			0.149279			0.0746393	−	0.997211i	$-0.476219\pi$
$359$	2.82843			0.149279			0.0746393	+	0.997211i	$0.476219\pi$
$360$		0			0
$361$	3.00000			0.157895
$362$	−4.24264	+	4.24264i	−0.222988	+	0.222988i
$363$		0			0
$364$		0			0
$365$	28.2843	−	14.1421i	1.48047	−	0.740233i
$366$		0			0
$367$	−15.0000	−	15.0000i	−0.782994	−	0.782994i	0.197341	−	0.980335i	$-0.436769\pi$
$367$	−15.0000	−	15.0000i	−0.782994	−	0.782994i	−0.980335	+	0.197341i	$0.936769\pi$
$368$		0			0
$369$		0			0
$370$	3.00000	+	1.00000i	0.155963	+	0.0519875i
$371$		−	14.1421i		−	0.734223i
$372$		0			0
$373$	6.00000	−	6.00000i	0.310668	−	0.310668i	−0.534500	−	0.845168i	$-0.679500\pi$
$373$	6.00000	−	6.00000i	0.310668	−	0.310668i	0.845168	+	0.534500i	$0.179500\pi$
$374$	5.65685			0.292509
$375$		0			0
$376$	4.00000			0.206284
$377$		0			0
$378$		0			0
$379$		−	8.00000i		−	0.410932i	−0.978664	−	0.205466i	$-0.934129\pi$
$379$		−	8.00000i		−	0.410932i	0.978664	−	0.205466i	$-0.0658711\pi$
$380$	−8.48528	−	2.82843i	−0.435286	−	0.145095i
$381$		0			0
$382$	−2.00000	−	2.00000i	−0.102329	−	0.102329i
$383$	25.4558	+	25.4558i	1.30073	+	1.30073i	0.927898	+	0.372835i	$0.121614\pi$
$383$	25.4558	+	25.4558i	1.30073	+	1.30073i	0.372835	+	0.927898i	$0.378386\pi$
$384$		0			0
$385$	−16.0000	+	8.00000i	−0.815436	+	0.407718i
$386$		−	22.6274i		−	1.15171i
$387$		0			0
$388$	4.00000	−	4.00000i	0.203069	−	0.203069i
$389$	19.7990			1.00385			0.501924	−	0.864912i	$-0.332626\pi$
$389$	19.7990			1.00385			0.501924	+	0.864912i	$0.332626\pi$
$390$		0			0
$391$		0			0
$392$	−3.53553	+	3.53553i	−0.178571	+	0.178571i
$393$		0			0
$394$			12.0000i			0.604551i
$395$	5.65685	−	16.9706i	0.284627	−	0.853882i
$396$		0			0
$397$	1.00000	+	1.00000i	0.0501886	+	0.0501886i	0.731756	−	0.681567i	$-0.238701\pi$
$397$	1.00000	+	1.00000i	0.0501886	+	0.0501886i	−0.681567	+	0.731756i	$0.738701\pi$
$398$	−1.41421	−	1.41421i	−0.0708881	−	0.0708881i
$399$		0			0
$400$	−4.00000	−	3.00000i	−0.200000	−	0.150000i
$401$		−	31.1127i		−	1.55369i	−0.629689	−	0.776847i	$-0.716818\pi$
$401$		−	31.1127i		−	1.55369i	0.629689	−	0.776847i	$-0.283182\pi$
$402$		0			0
$403$		0			0
$404$	14.1421			0.703598
$405$		0			0
$406$	2.00000			0.0992583
$407$	5.65685	−	5.65685i	0.280400	−	0.280400i
$408$		0			0
$409$		−	10.0000i		−	0.494468i	−0.968956	−	0.247234i	$-0.920478\pi$
$409$		−	10.0000i		−	0.494468i	0.968956	−	0.247234i	$-0.0795217\pi$
$410$	−5.65685	−	11.3137i	−0.279372	−	0.558744i
$411$		0			0
$412$	−14.0000	−	14.0000i	−0.689730	−	0.689730i
$413$	1.41421	+	1.41421i	0.0695889	+	0.0695889i
$414$		0			0
$415$	2.00000	+	4.00000i	0.0981761	+	0.196352i
$416$		0			0
$417$		0			0
$418$	−16.0000	+	16.0000i	−0.782586	+	0.782586i
$419$	−8.48528			−0.414533			−0.207267	−	0.978285i	$-0.566457\pi$
$419$	−8.48528			−0.414533			−0.207267	+	0.978285i	$0.566457\pi$
$420$		0			0
$421$	−30.0000			−1.46211			−0.731055	−	0.682318i	$-0.760972\pi$
$421$	−30.0000			−1.46211			−0.731055	+	0.682318i	$0.760972\pi$
$422$	8.48528	−	8.48528i	0.413057	−	0.413057i
$423$		0			0
$424$		−	10.0000i		−	0.485643i
$425$	−4.94975	+	0.707107i	−0.240098	+	0.0342997i
$426$		0			0
$427$	−4.00000	−	4.00000i	−0.193574	−	0.193574i
$428$	5.65685	+	5.65685i	0.273434	+	0.273434i
$429$		0			0
$430$	7.00000	−	21.0000i	0.337570	−	1.01271i
$431$			4.24264i			0.204361i	0.994766	+	0.102180i	$0.0325819\pi$
$431$			4.24264i			0.204361i	−0.994766	+	0.102180i	$0.967418\pi$
$432$		0			0
$433$	9.00000	−	9.00000i	0.432512	−	0.432512i	−0.456970	−	0.889482i	$-0.651065\pi$
$433$	9.00000	−	9.00000i	0.432512	−	0.432512i	0.889482	+	0.456970i	$0.151065\pi$
$434$	8.48528			0.407307
$435$		0			0
$436$	6.00000			0.287348
$437$		0			0
$438$		0			0
$439$		−	16.0000i		−	0.763638i	−0.924237	−	0.381819i	$-0.875298\pi$
$439$		−	16.0000i		−	0.763638i	0.924237	−	0.381819i	$-0.124702\pi$
$440$	−11.3137	+	5.65685i	−0.539360	+	0.269680i
$441$		0			0
$442$		0			0
$443$	24.0416	+	24.0416i	1.14225	+	1.14225i	0.988037	+	0.154215i	$0.0492849\pi$
$443$	24.0416	+	24.0416i	1.14225	+	1.14225i	0.154215	+	0.988037i	$0.450715\pi$
$444$		0			0
$445$	−3.00000	−	1.00000i	−0.142214	−	0.0474045i
$446$			2.82843i			0.133930i
$447$		0			0
$448$	1.00000	−	1.00000i	0.0472456	−	0.0472456i
$449$	−36.7696			−1.73526			−0.867631	−	0.497208i	$-0.834358\pi$
$449$	−36.7696			−1.73526			−0.867631	+	0.497208i	$0.834358\pi$
$450$		0			0
$451$	−32.0000			−1.50682
$452$	−7.07107	+	7.07107i	−0.332595	+	0.332595i
$453$		0			0
$454$		−	12.0000i		−	0.563188i
$455$		0			0
$456$		0			0
$457$	−5.00000	−	5.00000i	−0.233890	−	0.233890i	0.580424	−	0.814314i	$-0.302887\pi$
$457$	−5.00000	−	5.00000i	−0.233890	−	0.233890i	−0.814314	+	0.580424i	$0.802887\pi$
$458$	18.3848	+	18.3848i	0.859064	+	0.859064i
$459$		0			0
$460$		0			0
$461$		−	33.9411i		−	1.58080i	−0.612594	−	0.790398i	$-0.709874\pi$
$461$		−	33.9411i		−	1.58080i	0.612594	−	0.790398i	$-0.290126\pi$
$462$		0			0
$463$	−18.0000	+	18.0000i	−0.836531	+	0.836531i	−0.988401	−	0.151870i	$-0.951471\pi$
$463$	−18.0000	+	18.0000i	−0.836531	+	0.836531i	0.151870	+	0.988401i	$0.451471\pi$
$464$	1.41421			0.0656532
$465$		0			0
$466$	18.0000			0.833834
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	−0.875632	−	0.482980i	$-0.839555\pi$
$467$	−8.48528	+	8.48528i	−0.392652	+	0.392652i	0.482980	+	0.875632i	$0.339555\pi$
$468$		0			0
$469$			10.0000i			0.461757i
$470$	−2.82843	+	8.48528i	−0.130466	+	0.391397i
$471$		0			0
$472$	1.00000	+	1.00000i	0.0460287	+	0.0460287i
$473$	−39.5980	−	39.5980i	−1.82072	−	1.82072i
$474$		0			0
$475$	12.0000	−	16.0000i	0.550598	−	0.734130i
$476$		−	1.41421i		−	0.0648204i
$477$		0			0
$478$	16.0000	−	16.0000i	0.731823	−	0.731823i
$479$	−18.3848			−0.840022			−0.420011	−	0.907519i	$-0.637974\pi$
$479$	−18.3848			−0.840022			−0.420011	+	0.907519i	$0.637974\pi$
$480$		0			0
$481$		0			0
$482$	9.89949	−	9.89949i	0.450910	−	0.450910i
$483$		0			0
$484$			21.0000i			0.954545i
$485$	5.65685	+	11.3137i	0.256865	+	0.513729i
$486$		0			0
$487$	−11.0000	−	11.0000i	−0.498458	−	0.498458i	0.412500	−	0.910958i	$-0.364656\pi$
$487$	−11.0000	−	11.0000i	−0.498458	−	0.498458i	−0.910958	+	0.412500i	$0.864656\pi$
$488$	−2.82843	−	2.82843i	−0.128037	−	0.128037i
$489$		0			0
$490$	−5.00000	−	10.0000i	−0.225877	−	0.451754i
$491$		−	12.7279i		−	0.574403i	−0.957870	−	0.287202i	$-0.907275\pi$
$491$		−	12.7279i		−	0.574403i	0.957870	−	0.287202i	$-0.0927249\pi$
$492$		0			0
$493$	1.00000	−	1.00000i	0.0450377	−	0.0450377i
$494$		0			0
$495$		0			0
$496$	6.00000			0.269408
$497$	9.89949	−	9.89949i	0.444053	−	0.444053i
$498$		0			0
$499$			20.0000i			0.895323i	0.894203	+	0.447661i	$0.147743\pi$
$499$			20.0000i			0.895323i	−0.894203	+	0.447661i	$0.852257\pi$
$500$	9.19239	−	6.36396i	0.411096	−	0.284605i
$501$		0			0
$502$	7.00000	+	7.00000i	0.312425	+	0.312425i
$503$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$503$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$504$		0			0
$505$	−10.0000	+	30.0000i	−0.444994	+	1.33498i
$506$		0			0
$507$		0			0
$508$	6.00000	−	6.00000i	0.266207	−	0.266207i
$509$	−31.1127			−1.37905			−0.689523	−	0.724264i	$-0.742180\pi$
$509$	−31.1127			−1.37905			−0.689523	+	0.724264i	$0.742180\pi$
$510$		0			0
$511$	−20.0000			−0.884748
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$		0			0
$514$			30.0000i			1.32324i
$515$	39.5980	−	19.7990i	1.74490	−	0.872448i
$516$		0			0
$517$	16.0000	+	16.0000i	0.703679	+	0.703679i
$518$	−1.41421	−	1.41421i	−0.0621370	−	0.0621370i
$519$		0			0
$520$		0			0
$521$			14.1421i			0.619578i	0.950805	+	0.309789i	$0.100258\pi$
$521$			14.1421i			0.619578i	−0.950805	+	0.309789i	$0.899742\pi$
$522$		0			0
$523$	19.0000	−	19.0000i	0.830812	−	0.830812i	−0.156816	−	0.987628i	$-0.550123\pi$
$523$	19.0000	−	19.0000i	0.830812	−	0.830812i	0.987628	+	0.156816i	$0.0501229\pi$
$524$	−2.82843			−0.123560
$525$		0			0
$526$		0			0
$527$	4.24264	−	4.24264i	0.184812	−	0.184812i
$528$		0			0
$529$		−	23.0000i		−	1.00000i
$530$	21.2132	+	7.07107i	0.921443	+	0.307148i
$531$		0			0
$532$	4.00000	+	4.00000i	0.173422	+	0.173422i
$533$		0			0
$534$		0			0
$535$	−16.0000	+	8.00000i	−0.691740	+	0.345870i
$536$			7.07107i			0.305424i
$537$		0			0
$538$	−21.0000	+	21.0000i	−0.905374	+	0.905374i
$539$	−28.2843			−1.21829
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	14.1421	−	14.1421i	0.607457	−	0.607457i
$543$		0			0
$544$		−	1.00000i		−	0.0428746i
$545$	−4.24264	+	12.7279i	−0.181735	+	0.545204i
$546$		0			0
$547$	20.0000	+	20.0000i	0.855138	+	0.855138i	0.990761	−	0.135622i	$-0.0433034\pi$
$547$	20.0000	+	20.0000i	0.855138	+	0.855138i	−0.135622	+	0.990761i	$0.543303\pi$
$548$		0			0
$549$		0			0
$550$	−4.00000	−	28.0000i	−0.170561	−	1.19392i
$551$			5.65685i			0.240990i
$552$		0			0
$553$	−8.00000	+	8.00000i	−0.340195	+	0.340195i
$554$	−4.24264			−0.180253
$555$		0			0
$556$	16.0000			0.678551
$557$	−9.89949	+	9.89949i	−0.419455	+	0.419455i	−0.885016	−	0.465561i	$-0.845853\pi$
$557$	−9.89949	+	9.89949i	−0.419455	+	0.419455i	0.465561	+	0.885016i	$0.345853\pi$
$558$		0			0
$559$		0			0
$560$	1.41421	+	2.82843i	0.0597614	+	0.119523i
$561$		0			0
$562$	−1.00000	−	1.00000i	−0.0421825	−	0.0421825i
$563$	−12.7279	−	12.7279i	−0.536418	−	0.536418i	0.386057	−	0.922475i	$-0.373837\pi$
$563$	−12.7279	−	12.7279i	−0.536418	−	0.536418i	−0.922475	+	0.386057i	$0.873837\pi$
$564$		0			0
$565$	−10.0000	−	20.0000i	−0.420703	−	0.841406i
$566$			16.9706i			0.713326i
$567$		0			0
$568$	7.00000	−	7.00000i	0.293713	−	0.293713i
$569$	−24.0416			−1.00788			−0.503939	−	0.863739i	$-0.668116\pi$
$569$	−24.0416			−1.00788			−0.503939	+	0.863739i	$0.668116\pi$
$570$		0			0
$571$	−40.0000			−1.67395			−0.836974	−	0.547243i	$-0.815677\pi$
$571$	−40.0000			−1.67395			−0.836974	+	0.547243i	$0.815677\pi$
$572$		0			0
$573$		0			0
$574$			8.00000i			0.333914i
$575$		0			0
$576$		0			0
$577$	27.0000	+	27.0000i	1.12402	+	1.12402i	0.991130	+	0.132895i	$0.0424272\pi$
$577$	27.0000	+	27.0000i	1.12402	+	1.12402i	0.132895	+	0.991130i	$0.457573\pi$
$578$	−0.707107	−	0.707107i	−0.0294118	−	0.0294118i
$579$		0			0
$580$	−1.00000	+	3.00000i	−0.0415227	+	0.124568i
$581$		−	2.82843i		−	0.117343i
$582$		0			0
$583$	40.0000	−	40.0000i	1.65663	−	1.65663i
$584$	−14.1421			−0.585206
$585$		0			0
$586$	−2.00000			−0.0826192
$587$	12.7279	−	12.7279i	0.525338	−	0.525338i	−0.393841	−	0.919179i	$-0.628854\pi$
$587$	12.7279	−	12.7279i	0.525338	−	0.525338i	0.919179	+	0.393841i	$0.128854\pi$
$588$		0			0
$589$			24.0000i			0.988903i
$590$	−2.82843	+	1.41421i	−0.116445	+	0.0582223i
$591$		0			0
$592$	−1.00000	−	1.00000i	−0.0410997	−	0.0410997i
$593$	21.2132	+	21.2132i	0.871122	+	0.871122i	0.992595	−	0.121473i	$-0.0387618\pi$
$593$	21.2132	+	21.2132i	0.871122	+	0.871122i	−0.121473	+	0.992595i	$0.538762\pi$
$594$		0			0
$595$	3.00000	+	1.00000i	0.122988	+	0.0409960i
$596$			8.48528i			0.347571i
$597$		0			0
$598$		0			0
$599$	−2.82843			−0.115566			−0.0577832	−	0.998329i	$-0.518403\pi$
$599$	−2.82843			−0.115566			−0.0577832	+	0.998329i	$0.518403\pi$
$600$		0			0
$601$	30.0000			1.22373			0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000			1.22373			0.611863	+	0.790964i	$0.290420\pi$
$602$	−9.89949	+	9.89949i	−0.403473	+	0.403473i
$603$		0			0
$604$			16.0000i			0.651031i
$605$	−44.5477	−	14.8492i	−1.81112	−	0.603708i
$606$		0			0
$607$	−21.0000	−	21.0000i	−0.852364	−	0.852364i	0.138060	−	0.990424i	$-0.455913\pi$
$607$	−21.0000	−	21.0000i	−0.852364	−	0.852364i	−0.990424	+	0.138060i	$0.955913\pi$
$608$	2.82843	+	2.82843i	0.114708	+	0.114708i
$609$		0			0
$610$	8.00000	−	4.00000i	0.323911	−	0.161955i
$611$		0			0
$612$		0			0
$613$	26.0000	−	26.0000i	1.05013	−	1.05013i	0.0514548	−	0.998675i	$-0.483614\pi$
$613$	26.0000	−	26.0000i	1.05013	−	1.05013i	0.998675	−	0.0514548i	$-0.0163858\pi$
$614$	21.2132			0.856095
$615$		0			0
$616$	8.00000			0.322329
$617$	−4.24264	+	4.24264i	−0.170802	+	0.170802i	−0.787332	−	0.616530i	$-0.788538\pi$
$617$	−4.24264	+	4.24264i	−0.170802	+	0.170802i	0.616530	+	0.787332i	$0.288538\pi$
$618$		0			0
$619$		−	44.0000i		−	1.76851i	−0.467005	−	0.884255i	$-0.654667\pi$
$619$		−	44.0000i		−	1.76851i	0.467005	−	0.884255i	$-0.345333\pi$
$620$	−4.24264	+	12.7279i	−0.170389	+	0.511166i
$621$		0			0
$622$	19.0000	+	19.0000i	0.761831	+	0.761831i
$623$	1.41421	+	1.41421i	0.0566593	+	0.0566593i
$624$		0			0
$625$	7.00000	+	24.0000i	0.280000	+	0.960000i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−1.41421			−0.0563884
$630$		0			0
$631$	−44.0000			−1.75161			−0.875806	−	0.482663i	$-0.839670\pi$
$631$	−44.0000			−1.75161			−0.875806	+	0.482663i	$0.839670\pi$
$632$	−5.65685	+	5.65685i	−0.225018	+	0.225018i
$633$		0			0
$634$		−	30.0000i		−	1.19145i
$635$	8.48528	+	16.9706i	0.336728	+	0.673456i
$636$		0			0
$637$		0			0
$638$	5.65685	+	5.65685i	0.223957	+	0.223957i
$639$		0			0
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$		−	42.4264i		−	1.67574i	−0.545868	−	0.837871i	$-0.683800\pi$
$641$		−	42.4264i		−	1.67574i	0.545868	−	0.837871i	$-0.316200\pi$
$642$		0			0
$643$	18.0000	−	18.0000i	0.709851	−	0.709851i	−0.256653	−	0.966504i	$-0.582620\pi$
$643$	18.0000	−	18.0000i	0.709851	−	0.709851i	0.966504	+	0.256653i	$0.0826197\pi$
$644$		0			0
$645$		0			0
$646$	4.00000			0.157378
$647$	−19.7990	+	19.7990i	−0.778379	+	0.778379i	−0.979555	−	0.201176i	$-0.935524\pi$
$647$	−19.7990	+	19.7990i	−0.778379	+	0.778379i	0.201176	+	0.979555i	$0.435524\pi$
$648$		0			0
$649$			8.00000i			0.314027i
$650$		0			0
$651$		0			0
$652$	−6.00000	−	6.00000i	−0.234978	−	0.234978i
$653$	−8.48528	−	8.48528i	−0.332055	−	0.332055i	0.521312	−	0.853366i	$-0.325443\pi$
$653$	−8.48528	−	8.48528i	−0.332055	−	0.332055i	−0.853366	+	0.521312i	$0.825443\pi$
$654$		0			0
$655$	2.00000	−	6.00000i	0.0781465	−	0.234439i
$656$			5.65685i			0.220863i
$657$		0			0
$658$	4.00000	−	4.00000i	0.155936	−	0.155936i
$659$	7.07107			0.275450			0.137725	−	0.990471i	$-0.456021\pi$
$659$	7.07107			0.275450			0.137725	+	0.990471i	$0.456021\pi$
$660$		0			0
$661$	30.0000			1.16686			0.583432	−	0.812162i	$-0.301709\pi$
$661$	30.0000			1.16686			0.583432	+	0.812162i	$0.301709\pi$
$662$	−9.89949	+	9.89949i	−0.384755	+	0.384755i
$663$		0			0
$664$		−	2.00000i		−	0.0776151i
$665$	−11.3137	+	5.65685i	−0.438727	+	0.219363i
$666$		0			0
$667$		0			0
$668$	7.07107	+	7.07107i	0.273588	+	0.273588i
$669$		0			0
$670$	−15.0000	−	5.00000i	−0.579501	−	0.193167i
$671$		−	22.6274i		−	0.873522i
$672$		0			0
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	−0.997386	−	0.0722542i	$-0.976981\pi$
$673$	−24.0000	+	24.0000i	−0.925132	+	0.925132i	0.0722542	+	0.997386i	$0.476981\pi$
$674$	8.48528			0.326841
$675$		0			0
$676$	13.0000			0.500000
$677$	4.24264	−	4.24264i	0.163058	−	0.163058i	−0.620862	−	0.783920i	$-0.713217\pi$
$677$	4.24264	−	4.24264i	0.163058	−	0.163058i	0.783920	+	0.620862i	$0.213217\pi$
$678$		0			0
$679$		−	8.00000i		−	0.307012i
$680$	2.12132	+	0.707107i	0.0813489	+	0.0271163i
$681$		0			0
$682$	24.0000	+	24.0000i	0.919007	+	0.919007i
$683$	−28.2843	−	28.2843i	−1.08227	−	1.08227i	−0.996298	−	0.0859698i	$-0.972601\pi$
$683$	−28.2843	−	28.2843i	−1.08227	−	1.08227i	−0.0859698	−	0.996298i	$-0.527399\pi$
$684$		0			0
$685$		0			0
$686$			16.9706i			0.647939i
$687$		0			0
$688$	−7.00000	+	7.00000i	−0.266872	+	0.266872i
$689$		0			0
$690$		0			0
$691$		0			0			−	1.00000i	$-0.5\pi$
$691$		0			0				1.00000i	$0.5\pi$
$692$	5.65685	−	5.65685i	0.215041	−	0.215041i
$693$		0			0
$694$		−	28.0000i		−	1.06287i
$695$	−11.3137	+	33.9411i	−0.429153	+	1.28746i
$696$		0			0
$697$	4.00000	+	4.00000i	0.151511	+	0.151511i
$698$	9.89949	+	9.89949i	0.374701	+	0.374701i
$699$		0			0
$700$	−7.00000	+	1.00000i	−0.264575	+	0.0377964i
$701$			39.5980i			1.49560i	0.663927	+	0.747798i	$0.268889\pi$
$701$			39.5980i			1.49560i	−0.663927	+	0.747798i	$0.731111\pi$
$702$		0			0
$703$	4.00000	−	4.00000i	0.150863	−	0.150863i
$704$	5.65685			0.213201
$705$		0			0
$706$	28.0000			1.05379
$707$	14.1421	−	14.1421i	0.531870	−	0.531870i
$708$		0			0
$709$		−	38.0000i		−	1.42712i	−0.700594	−	0.713560i	$-0.747082\pi$
$709$		−	38.0000i		−	1.42712i	0.700594	−	0.713560i	$-0.252918\pi$
$710$	9.89949	+	19.7990i	0.371521	+	0.743043i
$711$		0			0
$712$	1.00000	+	1.00000i	0.0374766	+	0.0374766i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		−	24.0416i		−	0.898478i
$717$		0			0
$718$	2.00000	−	2.00000i	0.0746393	−	0.0746393i
$719$	15.5563			0.580154			0.290077	−	0.957003i	$-0.406319\pi$
$719$	15.5563			0.580154			0.290077	+	0.957003i	$0.406319\pi$
$720$		0			0
$721$	−28.0000			−1.04277
$722$	2.12132	−	2.12132i	0.0789474	−	0.0789474i
$723$		0			0
$724$			6.00000i			0.222988i
$725$	−5.65685	−	4.24264i	−0.210090	−	0.157568i
$726$		0			0
$727$	18.0000	+	18.0000i	0.667583	+	0.667583i	0.957156	−	0.289573i	$-0.0935133\pi$
$727$	18.0000	+	18.0000i	0.667583	+	0.667583i	−0.289573	+	0.957156i	$0.593513\pi$
$728$		0			0
$729$		0			0
$730$	10.0000	−	30.0000i	0.370117	−	1.11035i
$731$			9.89949i			0.366146i
$732$		0			0
$733$	−6.00000	+	6.00000i	−0.221615	+	0.221615i	−0.809178	−	0.587563i	$-0.800087\pi$
$733$	−6.00000	+	6.00000i	−0.221615	+	0.221615i	0.587563	+	0.809178i	$0.300087\pi$
$734$	−21.2132			−0.782994
$735$		0			0
$736$		0			0
$737$	−28.2843	+	28.2843i	−1.04186	+	1.04186i
$738$		0			0
$739$			34.0000i			1.25071i	0.780340	+	0.625355i	$0.215046\pi$
$739$			34.0000i			1.25071i	−0.780340	+	0.625355i	$0.784954\pi$
$740$	2.82843	−	1.41421i	0.103975	−	0.0519875i
$741$		0			0
$742$	−10.0000	−	10.0000i	−0.367112	−	0.367112i
$743$	1.41421	+	1.41421i	0.0518825	+	0.0518825i	0.732572	−	0.680690i	$-0.238320\pi$
$743$	1.41421	+	1.41421i	0.0518825	+	0.0518825i	−0.680690	+	0.732572i	$0.738320\pi$
$744$		0			0
$745$	−18.0000	−	6.00000i	−0.659469	−	0.219823i
$746$		−	8.48528i		−	0.310668i
$747$		0			0
$748$	4.00000	−	4.00000i	0.146254	−	0.146254i
$749$	11.3137			0.413394
$750$		0			0
$751$		0			0			−	1.00000i	$-0.5\pi$
$751$		0			0				1.00000i	$0.5\pi$
$752$	2.82843	−	2.82843i	0.103142	−	0.103142i
$753$		0			0
$754$		0			0
$755$	−33.9411	−	11.3137i	−1.23524	−	0.411748i
$756$		0			0
$757$	24.0000	+	24.0000i	0.872295	+	0.872295i	0.992722	−	0.120427i	$-0.0384265\pi$
$757$	24.0000	+	24.0000i	0.872295	+	0.872295i	−0.120427	+	0.992722i	$0.538426\pi$
$758$	−5.65685	−	5.65685i	−0.205466	−	0.205466i
$759$		0			0
$760$	−8.00000	+	4.00000i	−0.290191	+	0.145095i
$761$			9.89949i			0.358856i	0.983771	+	0.179428i	$0.0574248\pi$
$761$			9.89949i			0.358856i	−0.983771	+	0.179428i	$0.942575\pi$
$762$		0			0
$763$	6.00000	−	6.00000i	0.217215	−	0.217215i
$764$	−2.82843			−0.102329
$765$		0			0
$766$	36.0000			1.30073
$767$		0			0
$768$		0			0
$769$		−	18.0000i		−	0.649097i	−0.945869	−	0.324548i	$-0.894788\pi$
$769$		−	18.0000i		−	0.649097i	0.945869	−	0.324548i	$-0.105212\pi$
$770$	−5.65685	+	16.9706i	−0.203859	+	0.611577i
$771$		0			0
$772$	−16.0000	−	16.0000i	−0.575853	−	0.575853i
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.997499	−	0.0706813i	$-0.977483\pi$
$773$	−29.6985	−	29.6985i	−1.06818	−	1.06818i	−0.0706813	−	0.997499i	$-0.522517\pi$
$774$		0			0
$775$	−24.0000	−	18.0000i	−0.862105	−	0.646579i
$776$		−	5.65685i		−	0.203069i
$777$		0			0
$778$	14.0000	−	14.0000i	0.501924	−	0.501924i
$779$	−22.6274			−0.810711
$780$		0			0
$781$	56.0000			2.00384
$782$		0			0
$783$		0			0
$784$			5.00000i			0.178571i
$785$		0			0
$786$		0			0
$787$	−2.00000	−	2.00000i	−0.0712923	−	0.0712923i	0.670562	−	0.741854i	$-0.266053\pi$
$787$	−2.00000	−	2.00000i	−0.0712923	−	0.0712923i	−0.741854	+	0.670562i	$0.766053\pi$
$788$	8.48528	+	8.48528i	0.302276	+	0.302276i
$789$		0			0
$790$	−8.00000	−	16.0000i	−0.284627	−	0.569254i
$791$			14.1421i			0.502836i
$792$		0			0
$793$		0			0
$794$	1.41421			0.0501886
$795$		0			0
$796$	−2.00000			−0.0708881
$797$	−15.5563	+	15.5563i	−0.551034	+	0.551034i	−0.926739	−	0.375705i	$-0.877401\pi$
$797$	−15.5563	+	15.5563i	−0.551034	+	0.551034i	0.375705	+	0.926739i	$0.377401\pi$
$798$		0			0
$799$		−	4.00000i		−	0.141510i
$800$	−4.94975	+	0.707107i	−0.175000	+	0.0250000i
$801$		0			0
$802$	−22.0000	−	22.0000i	−0.776847	−	0.776847i
$803$	−56.5685	−	56.5685i	−1.99626	−	1.99626i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	10.0000	−	10.0000i	0.351799	−	0.351799i
$809$	−39.5980			−1.39219			−0.696095	−	0.717949i	$-0.745081\pi$
$809$	−39.5980			−1.39219			−0.696095	+	0.717949i	$0.745081\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	1.41421	−	1.41421i	0.0496292	−	0.0496292i
$813$		0			0
$814$		−	8.00000i		−	0.280400i
$815$	16.9706	−	8.48528i	0.594453	−	0.297226i
$816$		0			0
$817$	−28.0000	−	28.0000i	−0.979596	−	0.979596i
$818$	−7.07107	−	7.07107i	−0.247234	−	0.247234i
$819$		0			0
$820$	−12.0000	−	4.00000i	−0.419058	−	0.139686i
$821$		−	29.6985i		−	1.03648i	−0.855234	−	0.518242i	$-0.826587\pi$
$821$		−	29.6985i		−	1.03648i	0.855234	−	0.518242i	$-0.173413\pi$
$822$		0			0
$823$	15.0000	−	15.0000i	0.522867	−	0.522867i	−0.395569	−	0.918436i	$-0.629453\pi$
$823$	15.0000	−	15.0000i	0.522867	−	0.522867i	0.918436	+	0.395569i	$0.129453\pi$
$824$	−19.7990			−0.689730
$825$		0			0
$826$	2.00000			0.0695889
$827$	8.48528	−	8.48528i	0.295062	−	0.295062i	−0.544014	−	0.839076i	$-0.683096\pi$
$827$	8.48528	−	8.48528i	0.295062	−	0.295062i	0.839076	+	0.544014i	$0.183096\pi$
$828$		0			0
$829$		−	46.0000i		−	1.59765i	−0.601566	−	0.798823i	$-0.705456\pi$
$829$		−	46.0000i		−	1.59765i	0.601566	−	0.798823i	$-0.294544\pi$
$830$	4.24264	+	1.41421i	0.147264	+	0.0490881i
$831$		0			0
$832$		0			0
$833$	3.53553	+	3.53553i	0.122499	+	0.122499i
$834$		0			0
$835$	−20.0000	+	10.0000i	−0.692129	+	0.346064i
$836$			22.6274i			0.782586i
$837$		0			0
$838$	−6.00000	+	6.00000i	−0.207267	+	0.207267i
$839$	24.0416			0.830009			0.415005	−	0.909819i	$-0.363780\pi$
$839$	24.0416			0.830009			0.415005	+	0.909819i	$0.363780\pi$
$840$		0			0
$841$	−27.0000			−0.931034
$842$	−21.2132	+	21.2132i	−0.731055	+	0.731055i
$843$		0			0
$844$		−	12.0000i		−	0.413057i
$845$	−9.19239	+	27.5772i	−0.316228	+	0.948683i
$846$		0			0
$847$	21.0000	+	21.0000i	0.721569	+	0.721569i
$848$	−7.07107	−	7.07107i	−0.242821	−	0.242821i
$849$		0			0
$850$	−3.00000	+	4.00000i	−0.102899	+	0.137199i
$851$		0			0
$852$		0			0
$853$	−25.0000	+	25.0000i	−0.855984	+	0.855984i	−0.990862	−	0.134878i	$-0.956936\pi$
$853$	−25.0000	+	25.0000i	−0.855984	+	0.855984i	0.134878	+	0.990862i	$0.456936\pi$
$854$	−5.65685			−0.193574
$855$		0			0
$856$	8.00000			0.273434
$857$	−9.89949	+	9.89949i	−0.338160	+	0.338160i	−0.855675	−	0.517514i	$-0.826857\pi$
$857$	−9.89949	+	9.89949i	−0.338160	+	0.338160i	0.517514	+	0.855675i	$0.326857\pi$
$858$		0			0
$859$			6.00000i			0.204717i	0.994748	+	0.102359i	$0.0326389\pi$
$859$			6.00000i			0.204717i	−0.994748	+	0.102359i	$0.967361\pi$
$860$	−9.89949	−	19.7990i	−0.337570	−	0.675140i
$861$		0			0
$862$	3.00000	+	3.00000i	0.102180	+	0.102180i
$863$	16.9706	+	16.9706i	0.577685	+	0.577685i	0.934265	−	0.356580i	$-0.116057\pi$
$863$	16.9706	+	16.9706i	0.577685	+	0.577685i	−0.356580	+	0.934265i	$0.616057\pi$
$864$		0			0
$865$	8.00000	+	16.0000i	0.272008	+	0.544016i
$866$		−	12.7279i		−	0.432512i
$867$		0			0
$868$	6.00000	−	6.00000i	0.203653	−	0.203653i
$869$	−45.2548			−1.53517
$870$		0			0
$871$		0			0
$872$	4.24264	−	4.24264i	0.143674	−	0.143674i
$873$		0			0
$874$		0			0
$875$	2.82843	−	15.5563i	0.0956183	−	0.525901i
$876$		0			0
$877$	−27.0000	−	27.0000i	−0.911725	−	0.911725i	0.0846827	−	0.996408i	$-0.473012\pi$
$877$	−27.0000	−	27.0000i	−0.911725	−	0.911725i	−0.996408	+	0.0846827i	$0.973012\pi$
$878$	−11.3137	−	11.3137i	−0.381819	−	0.381819i
$879$		0			0
$880$	−4.00000	+	12.0000i	−0.134840	+	0.404520i
$881$		−	2.82843i		−	0.0952921i	−0.998864	−	0.0476461i	$-0.984828\pi$
$881$		−	2.82843i		−	0.0952921i	0.998864	−	0.0476461i	$-0.0151720\pi$
$882$		0			0
$883$	−33.0000	+	33.0000i	−1.11054	+	1.11054i	−0.117461	+	0.993078i	$0.537475\pi$
$883$	−33.0000	+	33.0000i	−1.11054	+	1.11054i	−0.993078	+	0.117461i	$0.962525\pi$
$884$		0			0
$885$		0			0
$886$	34.0000			1.14225
$887$	22.6274	−	22.6274i	0.759754	−	0.759754i	−0.216523	−	0.976277i	$-0.569472\pi$
$887$	22.6274	−	22.6274i	0.759754	−	0.759754i	0.976277	+	0.216523i	$0.0694717\pi$
$888$		0			0
$889$		−	12.0000i		−	0.402467i
$890$	−2.82843	+	1.41421i	−0.0948091	+	0.0474045i
$891$		0			0
$892$	2.00000	+	2.00000i	0.0669650	+	0.0669650i
$893$	11.3137	+	11.3137i	0.378599	+	0.378599i
$894$		0			0
$895$	51.0000	+	17.0000i	1.70474	+	0.568247i
$896$		−	1.41421i		−	0.0472456i
$897$		0			0
$898$	−26.0000	+	26.0000i	−0.867631	+	0.867631i
$899$	8.48528			0.283000
$900$		0			0
$901$	−10.0000			−0.333148
$902$	−22.6274	+	22.6274i	−0.753411	+	0.753411i
$903$		0			0
$904$			10.0000i			0.332595i
$905$	−12.7279	−	4.24264i	−0.423090	−	0.141030i
$906$		0			0
$907$	−22.0000	−	22.0000i	−0.730498	−	0.730498i	0.240220	−	0.970718i	$-0.422780\pi$
$907$	−22.0000	−	22.0000i	−0.730498	−	0.730498i	−0.970718	+	0.240220i	$0.922780\pi$
$908$	−8.48528	−	8.48528i	−0.281594	−	0.281594i
$909$		0			0
$910$		0			0
$911$		−	35.3553i		−	1.17137i	−0.810537	−	0.585687i	$-0.800825\pi$
$911$		−	35.3553i		−	1.17137i	0.810537	−	0.585687i	$-0.199175\pi$
$912$		0			0
$913$	8.00000	−	8.00000i	0.264761	−	0.264761i
$914$	−7.07107			−0.233890
$915$		0			0
$916$	26.0000			0.859064
$917$	−2.82843	+	2.82843i	−0.0934029	+	0.0934029i
$918$		0			0
$919$		−	48.0000i		−	1.58337i	−0.610927	−	0.791687i	$-0.709203\pi$
$919$		−	48.0000i		−	1.58337i	0.610927	−	0.791687i	$-0.290797\pi$
$920$		0			0
$921$		0			0
$922$	−24.0000	−	24.0000i	−0.790398	−	0.790398i
$923$		0			0
$924$		0			0
$925$	1.00000	+	7.00000i	0.0328798	+	0.230159i
$926$			25.4558i			0.836531i
$927$		0			0
$928$	1.00000	−	1.00000i	0.0328266	−	0.0328266i
$929$	−5.65685			−0.185595			−0.0927977	−	0.995685i	$-0.529581\pi$
$929$	−5.65685			−0.185595			−0.0927977	+	0.995685i	$0.529581\pi$
$930$		0			0
$931$	−20.0000			−0.655474
$932$	12.7279	−	12.7279i	0.416917	−	0.416917i
$933$		0			0
$934$			12.0000i			0.392652i
$935$	5.65685	+	11.3137i	0.184999	+	0.369998i
$936$		0			0
$937$	25.0000	+	25.0000i	0.816714	+	0.816714i	0.985630	−	0.168916i	$-0.0540267\pi$
$937$	25.0000	+	25.0000i	0.816714	+	0.816714i	−0.168916	+	0.985630i	$0.554027\pi$
$938$	7.07107	+	7.07107i	0.230879	+	0.230879i
$939$		0			0
$940$	4.00000	+	8.00000i	0.130466	+	0.260931i
$941$			18.3848i			0.599327i	0.954045	+	0.299663i	$0.0968743\pi$
$941$			18.3848i			0.599327i	−0.954045	+	0.299663i	$0.903126\pi$
$942$		0			0
$943$		0			0
$944$	1.41421			0.0460287
$945$		0			0
$946$	−56.0000			−1.82072
$947$	−36.7696	+	36.7696i	−1.19485	+	1.19485i	−0.219161	+	0.975689i	$0.570332\pi$
$947$	−36.7696	+	36.7696i	−1.19485	+	1.19485i	−0.975689	+	0.219161i	$0.929668\pi$
$948$		0			0
$949$		0			0
$950$	−2.82843	−	19.7990i	−0.0917663	−	0.642364i
$951$		0			0
$952$	−1.00000	−	1.00000i	−0.0324102	−	0.0324102i
$953$	33.9411	+	33.9411i	1.09946	+	1.09946i	0.994474	+	0.104987i	$0.0334802\pi$
$953$	33.9411	+	33.9411i	1.09946	+	1.09946i	0.104987	+	0.994474i	$0.466520\pi$
$954$		0			0
$955$	2.00000	−	6.00000i	0.0647185	−	0.194155i
$956$		−	22.6274i		−	0.731823i
$957$		0			0
$958$	−13.0000	+	13.0000i	−0.420011	+	0.420011i
$959$		0			0
$960$		0			0
$961$	5.00000			0.161290
$962$		0			0
$963$		0			0
$964$		−	14.0000i		−	0.450910i
$965$	45.2548	−	22.6274i	1.45680	−	0.728402i
$966$		0			0
$967$	−12.0000	−	12.0000i	−0.385894	−	0.385894i	0.487326	−	0.873220i	$-0.337972\pi$
$967$	−12.0000	−	12.0000i	−0.385894	−	0.385894i	−0.873220	+	0.487326i	$0.837972\pi$
$968$	14.8492	+	14.8492i	0.477273	+	0.477273i
$969$		0			0
$970$	12.0000	+	4.00000i	0.385297	+	0.128432i
$971$		−	57.9828i		−	1.86076i	−0.366603	−	0.930378i	$-0.619479\pi$
$971$		−	57.9828i		−	1.86076i	0.366603	−	0.930378i	$-0.380521\pi$
$972$		0			0
$973$	16.0000	−	16.0000i	0.512936	−	0.512936i
$974$	−15.5563			−0.498458
$975$		0			0
$976$	−4.00000			−0.128037
$977$	31.1127	−	31.1127i	0.995383	−	0.995383i	−0.00460599	−	0.999989i	$-0.501466\pi$
$977$	31.1127	−	31.1127i	0.995383	−	0.995383i	0.999989	+	0.00460599i	$0.00146614\pi$
$978$		0			0
$979$			8.00000i			0.255681i
$980$	−10.6066	−	3.53553i	−0.338815	−	0.112938i
$981$		0			0
$982$	−9.00000	−	9.00000i	−0.287202	−	0.287202i
$983$	−7.07107	−	7.07107i	−0.225532	−	0.225532i	0.585291	−	0.810823i	$-0.300980\pi$
$983$	−7.07107	−	7.07107i	−0.225532	−	0.225532i	−0.810823	+	0.585291i	$0.800980\pi$
$984$		0			0
$985$	−24.0000	+	12.0000i	−0.764704	+	0.382352i
$986$		−	1.41421i		−	0.0450377i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$	42.0000			1.33417			0.667087	−	0.744980i	$-0.267541\pi$
$991$	42.0000			1.33417			0.667087	+	0.744980i	$0.267541\pi$
$992$	4.24264	−	4.24264i	0.134704	−	0.134704i
$993$		0			0
$994$		−	14.0000i		−	0.444053i
$995$	1.41421	−	4.24264i	0.0448336	−	0.134501i
$996$		0			0
$997$	15.0000	+	15.0000i	0.475055	+	0.475055i	0.903546	−	0.428491i	$-0.140955\pi$
$997$	15.0000	+	15.0000i	0.475055	+	0.475055i	−0.428491	+	0.903546i	$0.640955\pi$
$998$	14.1421	+	14.1421i	0.447661	+	0.447661i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1530.2.m.c.647.2	yes	4
3.2	odd	2	inner	1530.2.m.c.647.1	✓	4
5.3	odd	4	inner	1530.2.m.c.953.1	yes	4
15.8	even	4	inner	1530.2.m.c.953.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1530.2.m.c.647.1	✓	4	3.2	odd	2	inner
1530.2.m.c.647.2	yes	4	1.1	even	1	trivial
1530.2.m.c.953.1	yes	4	5.3	odd	4	inner
1530.2.m.c.953.2	yes	4	15.8	even	4	inner

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:	\( N \)	\(=\)	\( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1530.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 - 0.707107i) q^{2} -1.00000i q^{4} +(2.12132 + 0.707107i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(2.00000 - 1.00000i) q^{10} -5.65685i q^{11} -1.41421 q^{14} -1.00000 q^{16} +(-0.707107 + 0.707107i) q^{17} -4.00000i q^{19} +(0.707107 - 2.12132i) q^{20} +(-4.00000 - 4.00000i) q^{22} +(4.00000 + 3.00000i) q^{25} +(-1.00000 + 1.00000i) q^{28} -1.41421 q^{29} -6.00000 q^{31} +(-0.707107 + 0.707107i) q^{32} +1.00000i q^{34} +(-1.41421 - 2.82843i) q^{35} +(1.00000 + 1.00000i) q^{37} +(-2.82843 - 2.82843i) q^{38} +(-1.00000 - 2.00000i) q^{40} -5.65685i q^{41} +(7.00000 - 7.00000i) q^{43} -5.65685 q^{44} +(-2.82843 + 2.82843i) q^{47} -5.00000i q^{49} +(4.94975 - 0.707107i) q^{50} +(7.07107 + 7.07107i) q^{53} +(4.00000 - 12.0000i) q^{55} +1.41421i q^{56} +(-1.00000 + 1.00000i) q^{58} -1.41421 q^{59} +4.00000 q^{61} +(-4.24264 + 4.24264i) q^{62} +1.00000i q^{64} +(-5.00000 - 5.00000i) q^{67} +(0.707107 + 0.707107i) q^{68} +(-3.00000 - 1.00000i) q^{70} +9.89949i q^{71} +(10.0000 - 10.0000i) q^{73} +1.41421 q^{74} -4.00000 q^{76} +(-5.65685 + 5.65685i) q^{77} -8.00000i q^{79} +(-2.12132 - 0.707107i) q^{80} +(-4.00000 - 4.00000i) q^{82} +(1.41421 + 1.41421i) q^{83} +(-2.00000 + 1.00000i) q^{85} -9.89949i q^{86} +(-4.00000 + 4.00000i) q^{88} -1.41421 q^{89} +4.00000i q^{94} +(2.82843 - 8.48528i) q^{95} +(4.00000 + 4.00000i) q^{97} +(-3.53553 - 3.53553i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{7}+O(q^{10}) \) 4 * q - 4 * q^7	\( 4 q - 4 q^{7} + 8 q^{10} - 4 q^{16} - 16 q^{22} + 16 q^{25} - 4 q^{28} - 24 q^{31} + 4 q^{37} - 4 q^{40} + 28 q^{43} + 16 q^{55} - 4 q^{58} + 16 q^{61} - 20 q^{67} - 12 q^{70} + 40 q^{73} - 16 q^{76} - 16 q^{82} - 8 q^{85} - 16 q^{88} + 16 q^{97}+O(q^{100}) \) 4 * q - 4 * q^7 + 8 * q^10 - 4 * q^16 - 16 * q^22 + 16 * q^25 - 4 * q^28 - 24 * q^31 + 4 * q^37 - 4 * q^40 + 28 * q^43 + 16 * q^55 - 4 * q^58 + 16 * q^61 - 20 * q^67 - 12 * q^70 + 40 * q^73 - 16 * q^76 - 16 * q^82 - 8 * q^85 - 16 * q^88 + 16 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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