LMFDB - Embedded newform 1008.2.v.a.323.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(323,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1008.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.v (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:	$8.04892052375$
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:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.2
Root			$0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.a.827.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.41421i q^{2} -2.00000 q^{4} +(1.41421 + 1.41421i) q^{5} +1.00000 q^{7} -2.82843i q^{8} +O(q^{10})$	\(q+1.41421i q^{2} -2.00000 q^{4} +(1.41421 + 1.41421i) q^{5} +1.00000 q^{7} -2.82843i q^{8} +(-2.00000 + 2.00000i) q^{10} +(2.82843 - 2.82843i) q^{11} +(4.00000 + 4.00000i) q^{13} +1.41421i q^{14} +4.00000 q^{16} -5.65685i q^{17} +(4.00000 - 4.00000i) q^{19} +(-2.82843 - 2.82843i) q^{20} +(4.00000 + 4.00000i) q^{22} -1.41421i q^{23} -1.00000i q^{25} +(-5.65685 + 5.65685i) q^{26} -2.00000 q^{28} +(-5.65685 + 5.65685i) q^{29} +5.65685i q^{32} +8.00000 q^{34} +(1.41421 + 1.41421i) q^{35} +(-5.00000 + 5.00000i) q^{37} +(5.65685 + 5.65685i) q^{38} +(4.00000 - 4.00000i) q^{40} +8.48528 q^{41} +(7.00000 + 7.00000i) q^{43} +(-5.65685 + 5.65685i) q^{44} +2.00000 q^{46} +1.00000 q^{49} +1.41421 q^{50} +(-8.00000 - 8.00000i) q^{52} +(-7.07107 - 7.07107i) q^{53} +8.00000 q^{55} -2.82843i q^{56} +(-8.00000 - 8.00000i) q^{58} +(-5.65685 + 5.65685i) q^{59} +(4.00000 + 4.00000i) q^{61} -8.00000 q^{64} +11.3137i q^{65} +(7.00000 - 7.00000i) q^{67} +11.3137i q^{68} +(-2.00000 + 2.00000i) q^{70} +7.07107i q^{71} +6.00000i q^{73} +(-7.07107 - 7.07107i) q^{74} +(-8.00000 + 8.00000i) q^{76} +(2.82843 - 2.82843i) q^{77} +(5.65685 + 5.65685i) q^{80} +12.0000i q^{82} +(-2.82843 - 2.82843i) q^{83} +(8.00000 - 8.00000i) q^{85} +(-9.89949 + 9.89949i) q^{86} +(-8.00000 - 8.00000i) q^{88} -16.9706 q^{89} +(4.00000 + 4.00000i) q^{91} +2.82843i q^{92} +11.3137 q^{95} -10.0000 q^{97} +1.41421i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{4} + 4 q^{7}+O(q^{10}) $ 4 * q - 8 * q^4 + 4 * q^7	$ 4 q - 8 q^{4} + 4 q^{7} - 8 q^{10} + 16 q^{13} + 16 q^{16} + 16 q^{19} + 16 q^{22} - 8 q^{28} + 32 q^{34} - 20 q^{37} + 16 q^{40} + 28 q^{43} + 8 q^{46} + 4 q^{49} - 32 q^{52} + 32 q^{55} - 32 q^{58} + 16 q^{61} - 32 q^{64} + 28 q^{67} - 8 q^{70} - 32 q^{76} + 32 q^{85} - 32 q^{88} + 16 q^{91} - 40 q^{97}+O(q^{100}) $ 4 * q - 8 * q^4 + 4 * q^7 - 8 * q^10 + 16 * q^13 + 16 * q^16 + 16 * q^19 + 16 * q^22 - 8 * q^28 + 32 * q^34 - 20 * q^37 + 16 * q^40 + 28 * q^43 + 8 * q^46 + 4 * q^49 - 32 * q^52 + 32 * q^55 - 32 * q^58 + 16 * q^61 - 32 * q^64 + 28 * q^67 - 8 * q^70 - 32 * q^76 + 32 * q^85 - 32 * q^88 + 16 * q^91 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$			1.41421i			1.00000i
$2$			1.41421i			1.00000i
$3$		0			0
$3$		0			0
$4$	−2.00000			−1.00000
$5$	1.41421	+	1.41421i	0.632456	+	0.632456i	0.948683	−	0.316228i	$-0.102416\pi$
$5$	1.41421	+	1.41421i	0.632456	+	0.632456i	−0.316228	+	0.948683i	$0.602416\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$		−	2.82843i		−	1.00000i
$9$		0			0
$10$	−2.00000	+	2.00000i	−0.632456	+	0.632456i
$11$	2.82843	−	2.82843i	0.852803	−	0.852803i	−0.137675	−	0.990478i	$-0.543963\pi$
$11$	2.82843	−	2.82843i	0.852803	−	0.852803i	0.990478	+	0.137675i	$0.0439628\pi$
$12$		0			0
$13$	4.00000	+	4.00000i	1.10940	+	1.10940i	0.993229	+	0.116171i	$0.0370621\pi$
$13$	4.00000	+	4.00000i	1.10940	+	1.10940i	0.116171	+	0.993229i	$0.462938\pi$
$14$			1.41421i			0.377964i
$15$		0			0
$16$	4.00000			1.00000
$17$		−	5.65685i		−	1.37199i	−0.727607	−	0.685994i	$-0.759367\pi$
$17$		−	5.65685i		−	1.37199i	0.727607	−	0.685994i	$-0.240633\pi$
$18$		0			0
$19$	4.00000	−	4.00000i	0.917663	−	0.917663i	−0.0791961	−	0.996859i	$-0.525235\pi$
$19$	4.00000	−	4.00000i	0.917663	−	0.917663i	0.996859	+	0.0791961i	$0.0252353\pi$
$20$	−2.82843	−	2.82843i	−0.632456	−	0.632456i
$21$		0			0
$22$	4.00000	+	4.00000i	0.852803	+	0.852803i
$23$		−	1.41421i		−	0.294884i	−0.989071	−	0.147442i	$-0.952896\pi$
$23$		−	1.41421i		−	0.294884i	0.989071	−	0.147442i	$-0.0471040\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	−5.65685	+	5.65685i	−1.10940	+	1.10940i
$27$		0			0
$28$	−2.00000			−0.377964
$29$	−5.65685	+	5.65685i	−1.05045	+	1.05045i	−0.0517937	+	0.998658i	$0.516494\pi$
$29$	−5.65685	+	5.65685i	−1.05045	+	1.05045i	−0.998658	+	0.0517937i	$0.983506\pi$
$30$		0			0
$31$		0			0		1.00000			$0$
$31$		0			0		−1.00000			$\pi$
$32$			5.65685i			1.00000i
$33$		0			0
$34$	8.00000			1.37199
$35$	1.41421	+	1.41421i	0.239046	+	0.239046i
$36$		0			0
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$	−5.00000	+	5.00000i	−0.821995	+	0.821995i	0.164399	+	0.986394i	$0.447432\pi$
$38$	5.65685	+	5.65685i	0.917663	+	0.917663i
$39$		0			0
$40$	4.00000	−	4.00000i	0.632456	−	0.632456i
$41$	8.48528			1.32518			0.662589	−	0.748983i	$-0.269458\pi$
$41$	8.48528			1.32518			0.662589	+	0.748983i	$0.269458\pi$
$42$		0			0
$43$	7.00000	+	7.00000i	1.06749	+	1.06749i	0.997551	+	0.0699387i	$0.0222804\pi$
$43$	7.00000	+	7.00000i	1.06749	+	1.06749i	0.0699387	+	0.997551i	$0.477720\pi$
$44$	−5.65685	+	5.65685i	−0.852803	+	0.852803i
$45$		0			0
$46$	2.00000			0.294884
$47$		0			0			−	1.00000i	$-0.5\pi$
$47$		0			0				1.00000i	$0.5\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	1.41421			0.200000
$51$		0			0
$52$	−8.00000	−	8.00000i	−1.10940	−	1.10940i
$53$	−7.07107	−	7.07107i	−0.971286	−	0.971286i	0.0283132	−	0.999599i	$-0.490986\pi$
$53$	−7.07107	−	7.07107i	−0.971286	−	0.971286i	−0.999599	+	0.0283132i	$0.990986\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$		−	2.82843i		−	0.377964i
$57$		0			0
$58$	−8.00000	−	8.00000i	−1.05045	−	1.05045i
$59$	−5.65685	+	5.65685i	−0.736460	+	0.736460i	−0.971891	−	0.235431i	$-0.924350\pi$
$59$	−5.65685	+	5.65685i	−0.736460	+	0.736460i	0.235431	+	0.971891i	$0.424350\pi$
$60$		0			0
$61$	4.00000	+	4.00000i	0.512148	+	0.512148i	0.915184	−	0.403036i	$-0.132045\pi$
$61$	4.00000	+	4.00000i	0.512148	+	0.512148i	−0.403036	+	0.915184i	$0.632045\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$			11.3137i			1.40329i
$66$		0			0
$67$	7.00000	−	7.00000i	0.855186	−	0.855186i	−0.135580	−	0.990766i	$-0.543290\pi$
$67$	7.00000	−	7.00000i	0.855186	−	0.855186i	0.990766	+	0.135580i	$0.0432899\pi$
$68$			11.3137i			1.37199i
$69$		0			0
$70$	−2.00000	+	2.00000i	−0.239046	+	0.239046i
$71$			7.07107i			0.839181i	0.907713	+	0.419591i	$0.137826\pi$
$71$			7.07107i			0.839181i	−0.907713	+	0.419591i	$0.862174\pi$
$72$		0			0
$73$			6.00000i			0.702247i	0.936329	+	0.351123i	$0.114200\pi$
$73$			6.00000i			0.702247i	−0.936329	+	0.351123i	$0.885800\pi$
$74$	−7.07107	−	7.07107i	−0.821995	−	0.821995i
$75$		0			0
$76$	−8.00000	+	8.00000i	−0.917663	+	0.917663i
$77$	2.82843	−	2.82843i	0.322329	−	0.322329i
$78$		0			0
$79$		0			0		1.00000			$0$
$79$		0			0		−1.00000			$\pi$
$80$	5.65685	+	5.65685i	0.632456	+	0.632456i
$81$		0			0
$82$			12.0000i			1.32518i
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	0.534628	−	0.845088i	$-0.320452\pi$
$83$	−2.82843	−	2.82843i	−0.310460	−	0.310460i	−0.845088	+	0.534628i	$0.820452\pi$
$84$		0			0
$85$	8.00000	−	8.00000i	0.867722	−	0.867722i
$86$	−9.89949	+	9.89949i	−1.06749	+	1.06749i
$87$		0			0
$88$	−8.00000	−	8.00000i	−0.852803	−	0.852803i
$89$	−16.9706			−1.79888			−0.899438	−	0.437048i	$-0.856024\pi$
$89$	−16.9706			−1.79888			−0.899438	+	0.437048i	$0.856024\pi$
$90$		0			0
$91$	4.00000	+	4.00000i	0.419314	+	0.419314i
$92$			2.82843i			0.294884i
$93$		0			0
$94$		0			0
$95$	11.3137			1.16076
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$			1.41421i			0.142857i
$99$		0			0
$100$			2.00000i			0.200000i
$101$	−7.07107	−	7.07107i	−0.703598	−	0.703598i	0.261583	−	0.965181i	$-0.415755\pi$
$101$	−7.07107	−	7.07107i	−0.703598	−	0.703598i	−0.965181	+	0.261583i	$0.915755\pi$
$102$		0			0
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$	11.3137	−	11.3137i	1.10940	−	1.10940i
$105$		0			0
$106$	10.0000	−	10.0000i	0.971286	−	0.971286i
$107$	7.07107	−	7.07107i	0.683586	−	0.683586i	−0.277220	−	0.960806i	$-0.589413\pi$
$107$	7.07107	−	7.07107i	0.683586	−	0.683586i	0.960806	+	0.277220i	$0.0894132\pi$
$108$		0			0
$109$	13.0000	+	13.0000i	1.24517	+	1.24517i	0.957826	+	0.287348i	$0.0927736\pi$
$109$	13.0000	+	13.0000i	1.24517	+	1.24517i	0.287348	+	0.957826i	$0.407226\pi$
$110$			11.3137i			1.07872i
$111$		0			0
$112$	4.00000			0.377964
$113$		−	1.41421i		−	0.133038i	−0.997785	−	0.0665190i	$-0.978811\pi$
$113$		−	1.41421i		−	0.133038i	0.997785	−	0.0665190i	$-0.0211893\pi$
$114$		0			0
$115$	2.00000	−	2.00000i	0.186501	−	0.186501i
$116$	11.3137	−	11.3137i	1.05045	−	1.05045i
$117$		0			0
$118$	−8.00000	−	8.00000i	−0.736460	−	0.736460i
$119$		−	5.65685i		−	0.518563i
$120$		0			0
$121$		−	5.00000i		−	0.454545i
$122$	−5.65685	+	5.65685i	−0.512148	+	0.512148i
$123$		0			0
$124$		0			0
$125$	8.48528	−	8.48528i	0.758947	−	0.758947i
$126$		0			0
$127$			18.0000i			1.59724i	0.601834	+	0.798621i	$0.294437\pi$
$127$			18.0000i			1.59724i	−0.601834	+	0.798621i	$0.705563\pi$
$128$		−	11.3137i		−	1.00000i
$129$		0			0
$130$	−16.0000			−1.40329
$131$	14.1421	+	14.1421i	1.23560	+	1.23560i	0.961780	+	0.273824i	$0.0882887\pi$
$131$	14.1421	+	14.1421i	1.23560	+	1.23560i	0.273824	+	0.961780i	$0.411711\pi$
$132$		0			0
$133$	4.00000	−	4.00000i	0.346844	−	0.346844i
$134$	9.89949	+	9.89949i	0.855186	+	0.855186i
$135$		0			0
$136$	−16.0000			−1.37199
$137$	−4.24264			−0.362473			−0.181237	−	0.983440i	$-0.558010\pi$
$137$	−4.24264			−0.362473			−0.181237	+	0.983440i	$0.558010\pi$
$138$		0			0
$139$	−14.0000	−	14.0000i	−1.18746	−	1.18746i	−0.977766	−	0.209698i	$-0.932752\pi$
$139$	−14.0000	−	14.0000i	−1.18746	−	1.18746i	−0.209698	−	0.977766i	$-0.567248\pi$
$140$	−2.82843	−	2.82843i	−0.239046	−	0.239046i
$141$		0			0
$142$	−10.0000			−0.839181
$143$	22.6274			1.89220
$144$		0			0
$145$	−16.0000			−1.32873
$146$	−8.48528			−0.702247
$147$		0			0
$148$	10.0000	−	10.0000i	0.821995	−	0.821995i
$149$	−11.3137	−	11.3137i	−0.926855	−	0.926855i	0.0706463	−	0.997501i	$-0.477494\pi$
$149$	−11.3137	−	11.3137i	−0.926855	−	0.926855i	−0.997501	+	0.0706463i	$0.977494\pi$
$150$		0			0
$151$	−10.0000			−0.813788			−0.406894	−	0.913475i	$-0.633388\pi$
$151$	−10.0000			−0.813788			−0.406894	+	0.913475i	$0.633388\pi$
$152$	−11.3137	−	11.3137i	−0.917663	−	0.917663i
$153$		0			0
$154$	4.00000	+	4.00000i	0.322329	+	0.322329i
$155$		0			0
$156$		0			0
$157$	−2.00000	−	2.00000i	−0.159617	−	0.159617i	0.622780	−	0.782397i	$-0.286003\pi$
$157$	−2.00000	−	2.00000i	−0.159617	−	0.159617i	−0.782397	+	0.622780i	$0.786003\pi$
$158$		0			0
$159$		0			0
$160$	−8.00000	+	8.00000i	−0.632456	+	0.632456i
$161$		−	1.41421i		−	0.111456i
$162$		0			0
$163$	13.0000	−	13.0000i	1.01824	−	1.01824i	0.0184080	−	0.999831i	$-0.494140\pi$
$163$	13.0000	−	13.0000i	1.01824	−	1.01824i	0.999831	−	0.0184080i	$-0.00585979\pi$
$164$	−16.9706			−1.32518
$165$		0			0
$166$	4.00000	−	4.00000i	0.310460	−	0.310460i
$167$		−	14.1421i		−	1.09435i	−0.837018	−	0.547176i	$-0.815703\pi$
$167$		−	14.1421i		−	1.09435i	0.837018	−	0.547176i	$-0.184297\pi$
$168$		0			0
$169$			19.0000i			1.46154i
$170$	11.3137	+	11.3137i	0.867722	+	0.867722i
$171$		0			0
$172$	−14.0000	−	14.0000i	−1.06749	−	1.06749i
$173$	−1.41421	+	1.41421i	−0.107521	+	0.107521i	−0.758820	−	0.651300i	$-0.774224\pi$
$173$	−1.41421	+	1.41421i	−0.107521	+	0.107521i	0.651300	+	0.758820i	$0.274224\pi$
$174$		0			0
$175$		−	1.00000i		−	0.0755929i
$176$	11.3137	−	11.3137i	0.852803	−	0.852803i
$177$		0			0
$178$		−	24.0000i		−	1.79888i
$179$	−7.07107	−	7.07107i	−0.528516	−	0.528516i	0.391613	−	0.920130i	$-0.371917\pi$
$179$	−7.07107	−	7.07107i	−0.528516	−	0.528516i	−0.920130	+	0.391613i	$0.871917\pi$
$180$		0			0
$181$	−8.00000	+	8.00000i	−0.594635	+	0.594635i	−0.938880	−	0.344245i	$-0.888135\pi$
$181$	−8.00000	+	8.00000i	−0.594635	+	0.594635i	0.344245	+	0.938880i	$0.388135\pi$
$182$	−5.65685	+	5.65685i	−0.419314	+	0.419314i
$183$		0			0
$184$	−4.00000			−0.294884
$185$	−14.1421			−1.03975
$186$		0			0
$187$	−16.0000	−	16.0000i	−1.17004	−	1.17004i
$188$		0			0
$189$		0			0
$190$			16.0000i			1.16076i
$191$	12.7279			0.920960			0.460480	−	0.887670i	$-0.347677\pi$
$191$	12.7279			0.920960			0.460480	+	0.887670i	$0.347677\pi$
$192$		0			0
$193$	14.0000			1.00774			0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000			1.00774			0.503871	+	0.863779i	$0.331909\pi$
$194$		−	14.1421i		−	1.01535i
$195$		0			0
$196$	−2.00000			−0.142857
$197$	−2.82843	−	2.82843i	−0.201517	−	0.201517i	0.599133	−	0.800650i	$-0.295512\pi$
$197$	−2.82843	−	2.82843i	−0.201517	−	0.201517i	−0.800650	+	0.599133i	$0.795512\pi$
$198$		0			0
$199$	−16.0000			−1.13421			−0.567105	−	0.823646i	$-0.691937\pi$
$199$	−16.0000			−1.13421			−0.567105	+	0.823646i	$0.691937\pi$
$200$	−2.82843			−0.200000
$201$		0			0
$202$	10.0000	−	10.0000i	0.703598	−	0.703598i
$203$	−5.65685	+	5.65685i	−0.397033	+	0.397033i
$204$		0			0
$205$	12.0000	+	12.0000i	0.838116	+	0.838116i
$206$		−	5.65685i		−	0.394132i
$207$		0			0
$208$	16.0000	+	16.0000i	1.10940	+	1.10940i
$209$		−	22.6274i		−	1.56517i
$210$		0			0
$211$	19.0000	−	19.0000i	1.30801	−	1.30801i	0.385167	−	0.922847i	$-0.374144\pi$
$211$	19.0000	−	19.0000i	1.30801	−	1.30801i	0.922847	−	0.385167i	$-0.125856\pi$
$212$	14.1421	+	14.1421i	0.971286	+	0.971286i
$213$		0			0
$214$	10.0000	+	10.0000i	0.683586	+	0.683586i
$215$			19.7990i			1.35028i
$216$		0			0
$217$		0			0
$218$	−18.3848	+	18.3848i	−1.24517	+	1.24517i
$219$		0			0
$220$	−16.0000			−1.07872
$221$	22.6274	−	22.6274i	1.52208	−	1.52208i
$222$		0			0
$223$		−	12.0000i		−	0.803579i	−0.915732	−	0.401790i	$-0.868388\pi$
$223$		−	12.0000i		−	0.803579i	0.915732	−	0.401790i	$-0.131612\pi$
$224$			5.65685i			0.377964i
$225$		0			0
$226$	2.00000			0.133038
$227$	5.65685	+	5.65685i	0.375459	+	0.375459i	0.869461	−	0.494002i	$-0.164466\pi$
$227$	5.65685	+	5.65685i	0.375459	+	0.375459i	−0.494002	+	0.869461i	$0.664466\pi$
$228$		0			0
$229$	4.00000	−	4.00000i	0.264327	−	0.264327i	−0.562482	−	0.826809i	$-0.690153\pi$
$229$	4.00000	−	4.00000i	0.264327	−	0.264327i	0.826809	+	0.562482i	$0.190153\pi$
$230$	2.82843	+	2.82843i	0.186501	+	0.186501i
$231$		0			0
$232$	16.0000	+	16.0000i	1.05045	+	1.05045i
$233$	−4.24264			−0.277945			−0.138972	−	0.990296i	$-0.544380\pi$
$233$	−4.24264			−0.277945			−0.138972	+	0.990296i	$0.544380\pi$
$234$		0			0
$235$		0			0
$236$	11.3137	−	11.3137i	0.736460	−	0.736460i
$237$		0			0
$238$	8.00000			0.518563
$239$	−4.24264			−0.274434			−0.137217	−	0.990541i	$-0.543816\pi$
$239$	−4.24264			−0.274434			−0.137217	+	0.990541i	$0.543816\pi$
$240$		0			0
$241$	−10.0000			−0.644157			−0.322078	−	0.946713i	$-0.604381\pi$
$241$	−10.0000			−0.644157			−0.322078	+	0.946713i	$0.604381\pi$
$242$	7.07107			0.454545
$243$		0			0
$244$	−8.00000	−	8.00000i	−0.512148	−	0.512148i
$245$	1.41421	+	1.41421i	0.0903508	+	0.0903508i
$246$		0			0
$247$	32.0000			2.03611
$248$		0			0
$249$		0			0
$250$	12.0000	+	12.0000i	0.758947	+	0.758947i
$251$	2.82843	−	2.82843i	0.178529	−	0.178529i	−0.612185	−	0.790714i	$-0.709709\pi$
$251$	2.82843	−	2.82843i	0.178529	−	0.178529i	0.790714	+	0.612185i	$0.209709\pi$
$252$		0			0
$253$	−4.00000	−	4.00000i	−0.251478	−	0.251478i
$254$	−25.4558			−1.59724
$255$		0			0
$256$	16.0000			1.00000
$257$			11.3137i			0.705730i	0.935674	+	0.352865i	$0.114792\pi$
$257$			11.3137i			0.705730i	−0.935674	+	0.352865i	$0.885208\pi$
$258$		0			0
$259$	−5.00000	+	5.00000i	−0.310685	+	0.310685i
$260$		−	22.6274i		−	1.40329i
$261$		0			0
$262$	−20.0000	+	20.0000i	−1.23560	+	1.23560i
$263$		−	9.89949i		−	0.610429i	−0.952284	−	0.305215i	$-0.901272\pi$
$263$		−	9.89949i		−	0.610429i	0.952284	−	0.305215i	$-0.0987282\pi$
$264$		0			0
$265$		−	20.0000i		−	1.22859i
$266$	5.65685	+	5.65685i	0.346844	+	0.346844i
$267$		0			0
$268$	−14.0000	+	14.0000i	−0.855186	+	0.855186i
$269$	−1.41421	+	1.41421i	−0.0862261	+	0.0862261i	−0.748904	−	0.662678i	$-0.769420\pi$
$269$	−1.41421	+	1.41421i	−0.0862261	+	0.0862261i	0.662678	+	0.748904i	$0.269420\pi$
$270$		0			0
$271$			12.0000i			0.728948i	0.931214	+	0.364474i	$0.118751\pi$
$271$			12.0000i			0.728948i	−0.931214	+	0.364474i	$0.881249\pi$
$272$		−	22.6274i		−	1.37199i
$273$		0			0
$274$		−	6.00000i		−	0.362473i
$275$	−2.82843	−	2.82843i	−0.170561	−	0.170561i
$276$		0			0
$277$	−11.0000	+	11.0000i	−0.660926	+	0.660926i	−0.955598	−	0.294672i	$-0.904789\pi$
$277$	−11.0000	+	11.0000i	−0.660926	+	0.660926i	0.294672	+	0.955598i	$0.404789\pi$
$278$	19.7990	−	19.7990i	1.18746	−	1.18746i
$279$		0			0
$280$	4.00000	−	4.00000i	0.239046	−	0.239046i
$281$	4.24264			0.253095			0.126547	−	0.991961i	$-0.459610\pi$
$281$	4.24264			0.253095			0.126547	+	0.991961i	$0.459610\pi$
$282$		0			0
$283$	−2.00000	−	2.00000i	−0.118888	−	0.118888i	0.645160	−	0.764048i	$-0.276791\pi$
$283$	−2.00000	−	2.00000i	−0.118888	−	0.118888i	−0.764048	+	0.645160i	$0.776791\pi$
$284$		−	14.1421i		−	0.839181i
$285$		0			0
$286$			32.0000i			1.89220i
$287$	8.48528			0.500870
$288$		0			0
$289$	−15.0000			−0.882353
$290$		−	22.6274i		−	1.32873i
$291$		0			0
$292$		−	12.0000i		−	0.702247i
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	0.934444	−	0.356110i	$-0.115897\pi$
$293$	9.89949	+	9.89949i	0.578335	+	0.578335i	−0.356110	+	0.934444i	$0.615897\pi$
$294$		0			0
$295$	−16.0000			−0.931556
$296$	14.1421	+	14.1421i	0.821995	+	0.821995i
$297$		0			0
$298$	16.0000	−	16.0000i	0.926855	−	0.926855i
$299$	5.65685	−	5.65685i	0.327144	−	0.327144i
$300$		0			0
$301$	7.00000	+	7.00000i	0.403473	+	0.403473i
$302$		−	14.1421i		−	0.813788i
$303$		0			0
$304$	16.0000	−	16.0000i	0.917663	−	0.917663i
$305$			11.3137i			0.647821i
$306$		0			0
$307$	−8.00000	+	8.00000i	−0.456584	+	0.456584i	−0.897532	−	0.440948i	$-0.854642\pi$
$307$	−8.00000	+	8.00000i	−0.456584	+	0.456584i	0.440948	+	0.897532i	$0.354642\pi$
$308$	−5.65685	+	5.65685i	−0.322329	+	0.322329i
$309$		0			0
$310$		0			0
$311$			11.3137i			0.641542i	0.947157	+	0.320771i	$0.103942\pi$
$311$			11.3137i			0.641542i	−0.947157	+	0.320771i	$0.896058\pi$
$312$		0			0
$313$		−	18.0000i		−	1.01742i	−0.860938	−	0.508710i	$-0.830123\pi$
$313$		−	18.0000i		−	1.01742i	0.860938	−	0.508710i	$-0.169877\pi$
$314$	2.82843	−	2.82843i	0.159617	−	0.159617i
$315$		0			0
$316$		0			0
$317$	−1.41421	+	1.41421i	−0.0794301	+	0.0794301i	−0.745706	−	0.666276i	$-0.767887\pi$
$317$	−1.41421	+	1.41421i	−0.0794301	+	0.0794301i	0.666276	+	0.745706i	$0.267887\pi$
$318$		0			0
$319$			32.0000i			1.79166i
$320$	−11.3137	−	11.3137i	−0.632456	−	0.632456i
$321$		0			0
$322$	2.00000			0.111456
$323$	−22.6274	−	22.6274i	−1.25902	−	1.25902i
$324$		0			0
$325$	4.00000	−	4.00000i	0.221880	−	0.221880i
$326$	18.3848	+	18.3848i	1.01824	+	1.01824i
$327$		0			0
$328$		−	24.0000i		−	1.32518i
$329$		0			0
$330$		0			0
$331$	13.0000	+	13.0000i	0.714545	+	0.714545i	0.967483	−	0.252938i	$-0.0813968\pi$
$331$	13.0000	+	13.0000i	0.714545	+	0.714545i	−0.252938	+	0.967483i	$0.581397\pi$
$332$	5.65685	+	5.65685i	0.310460	+	0.310460i
$333$		0			0
$334$	20.0000			1.09435
$335$	19.7990			1.08173
$336$		0			0
$337$	−22.0000			−1.19842			−0.599208	−	0.800593i	$-0.704518\pi$
$337$	−22.0000			−1.19842			−0.599208	+	0.800593i	$0.704518\pi$
$338$	−26.8701			−1.46154
$339$		0			0
$340$	−16.0000	+	16.0000i	−0.867722	+	0.867722i
$341$		0			0
$342$		0			0
$343$	1.00000			0.0539949
$344$	19.7990	−	19.7990i	1.06749	−	1.06749i
$345$		0			0
$346$	−2.00000	−	2.00000i	−0.107521	−	0.107521i
$347$	7.07107	−	7.07107i	0.379595	−	0.379595i	−0.491361	−	0.870956i	$-0.663500\pi$
$347$	7.07107	−	7.07107i	0.379595	−	0.379595i	0.870956	+	0.491361i	$0.163500\pi$
$348$		0			0
$349$	−2.00000	−	2.00000i	−0.107058	−	0.107058i	0.651549	−	0.758607i	$-0.274119\pi$
$349$	−2.00000	−	2.00000i	−0.107058	−	0.107058i	−0.758607	+	0.651549i	$0.774119\pi$
$350$	1.41421			0.0755929
$351$		0			0
$352$	16.0000	+	16.0000i	0.852803	+	0.852803i
$353$			2.82843i			0.150542i	0.997163	+	0.0752710i	$0.0239822\pi$
$353$			2.82843i			0.150542i	−0.997163	+	0.0752710i	$0.976018\pi$
$354$		0			0
$355$	−10.0000	+	10.0000i	−0.530745	+	0.530745i
$356$	33.9411			1.79888
$357$		0			0
$358$	10.0000	−	10.0000i	0.528516	−	0.528516i
$359$			32.5269i			1.71670i	0.513061	+	0.858352i	$0.328512\pi$
$359$			32.5269i			1.71670i	−0.513061	+	0.858352i	$0.671488\pi$
$360$		0			0
$361$		−	13.0000i		−	0.684211i
$362$	−11.3137	−	11.3137i	−0.594635	−	0.594635i
$363$		0			0
$364$	−8.00000	−	8.00000i	−0.419314	−	0.419314i
$365$	−8.48528	+	8.48528i	−0.444140	+	0.444140i
$366$		0			0
$367$		−	24.0000i		−	1.25279i	−0.779506	−	0.626395i	$-0.784530\pi$
$367$		−	24.0000i		−	1.25279i	0.779506	−	0.626395i	$-0.215470\pi$
$368$		−	5.65685i		−	0.294884i
$369$		0			0
$370$		−	20.0000i		−	1.03975i
$371$	−7.07107	−	7.07107i	−0.367112	−	0.367112i
$372$		0			0
$373$	−5.00000	+	5.00000i	−0.258890	+	0.258890i	−0.824603	−	0.565712i	$-0.808601\pi$
$373$	−5.00000	+	5.00000i	−0.258890	+	0.258890i	0.565712	+	0.824603i	$0.308601\pi$
$374$	22.6274	−	22.6274i	1.17004	−	1.17004i
$375$		0			0
$376$		0			0
$377$	−45.2548			−2.33074
$378$		0			0
$379$	−17.0000	−	17.0000i	−0.873231	−	0.873231i	0.119592	−	0.992823i	$-0.461841\pi$
$379$	−17.0000	−	17.0000i	−0.873231	−	0.873231i	−0.992823	+	0.119592i	$0.961841\pi$
$380$	−22.6274			−1.16076
$381$		0			0
$382$			18.0000i			0.920960i
$383$	−8.48528			−0.433578			−0.216789	−	0.976219i	$-0.569558\pi$
$383$	−8.48528			−0.433578			−0.216789	+	0.976219i	$0.569558\pi$
$384$		0			0
$385$	8.00000			0.407718
$386$			19.7990i			1.00774i
$387$		0			0
$388$	20.0000			1.01535
$389$	−7.07107	−	7.07107i	−0.358517	−	0.358517i	0.504749	−	0.863266i	$-0.331585\pi$
$389$	−7.07107	−	7.07107i	−0.358517	−	0.358517i	−0.863266	+	0.504749i	$0.831585\pi$
$390$		0			0
$391$	−8.00000			−0.404577
$392$		−	2.82843i		−	0.142857i
$393$		0			0
$394$	4.00000	−	4.00000i	0.201517	−	0.201517i
$395$		0			0
$396$		0			0
$397$	−2.00000	−	2.00000i	−0.100377	−	0.100377i	0.655135	−	0.755512i	$-0.272612\pi$
$397$	−2.00000	−	2.00000i	−0.100377	−	0.100377i	−0.755512	+	0.655135i	$0.772612\pi$
$398$		−	22.6274i		−	1.13421i
$399$		0			0
$400$		−	4.00000i		−	0.200000i
$401$			24.0416i			1.20058i	0.799782	+	0.600291i	$0.204949\pi$
$401$			24.0416i			1.20058i	−0.799782	+	0.600291i	$0.795051\pi$
$402$		0			0
$403$		0			0
$404$	14.1421	+	14.1421i	0.703598	+	0.703598i
$405$		0			0
$406$	−8.00000	−	8.00000i	−0.397033	−	0.397033i
$407$			28.2843i			1.40200i
$408$		0			0
$409$			18.0000i			0.890043i	0.895520	+	0.445021i	$0.146804\pi$
$409$			18.0000i			0.890043i	−0.895520	+	0.445021i	$0.853196\pi$
$410$	−16.9706	+	16.9706i	−0.838116	+	0.838116i
$411$		0			0
$412$	8.00000			0.394132
$413$	−5.65685	+	5.65685i	−0.278356	+	0.278356i
$414$		0			0
$415$		−	8.00000i		−	0.392705i
$416$	−22.6274	+	22.6274i	−1.10940	+	1.10940i
$417$		0			0
$418$	32.0000			1.56517
$419$	−2.82843	−	2.82843i	−0.138178	−	0.138178i	0.634635	−	0.772812i	$-0.281151\pi$
$419$	−2.82843	−	2.82843i	−0.138178	−	0.138178i	−0.772812	+	0.634635i	$0.781151\pi$
$420$		0			0
$421$	1.00000	−	1.00000i	0.0487370	−	0.0487370i	−0.682318	−	0.731055i	$-0.739028\pi$
$421$	1.00000	−	1.00000i	0.0487370	−	0.0487370i	0.731055	+	0.682318i	$0.239028\pi$
$422$	26.8701	+	26.8701i	1.30801	+	1.30801i
$423$		0			0
$424$	−20.0000	+	20.0000i	−0.971286	+	0.971286i
$425$	−5.65685			−0.274398
$426$		0			0
$427$	4.00000	+	4.00000i	0.193574	+	0.193574i
$428$	−14.1421	+	14.1421i	−0.683586	+	0.683586i
$429$		0			0
$430$	−28.0000			−1.35028
$431$	−21.2132			−1.02180			−0.510902	−	0.859639i	$-0.670689\pi$
$431$	−21.2132			−1.02180			−0.510902	+	0.859639i	$0.670689\pi$
$432$		0			0
$433$	−34.0000			−1.63394			−0.816968	−	0.576683i	$-0.804347\pi$
$433$	−34.0000			−1.63394			−0.816968	+	0.576683i	$0.804347\pi$
$434$		0			0
$435$		0			0
$436$	−26.0000	−	26.0000i	−1.24517	−	1.24517i
$437$	−5.65685	−	5.65685i	−0.270604	−	0.270604i
$438$		0			0
$439$	−28.0000			−1.33637			−0.668184	−	0.743996i	$-0.732928\pi$
$439$	−28.0000			−1.33637			−0.668184	+	0.743996i	$0.732928\pi$
$440$		−	22.6274i		−	1.07872i
$441$		0			0
$442$	32.0000	+	32.0000i	1.52208	+	1.52208i
$443$	−14.1421	+	14.1421i	−0.671913	+	0.671913i	−0.958157	−	0.286244i	$-0.907593\pi$
$443$	−14.1421	+	14.1421i	−0.671913	+	0.671913i	0.286244	+	0.958157i	$0.407593\pi$
$444$		0			0
$445$	−24.0000	−	24.0000i	−1.13771	−	1.13771i
$446$	16.9706			0.803579
$447$		0			0
$448$	−8.00000			−0.377964
$449$			32.5269i			1.53504i	0.641025	+	0.767520i	$0.278509\pi$
$449$			32.5269i			1.53504i	−0.641025	+	0.767520i	$0.721491\pi$
$450$		0			0
$451$	24.0000	−	24.0000i	1.13012	−	1.13012i
$452$			2.82843i			0.133038i
$453$		0			0
$454$	−8.00000	+	8.00000i	−0.375459	+	0.375459i
$455$			11.3137i			0.530395i
$456$		0			0
$457$			36.0000i			1.68401i	0.539471	+	0.842004i	$0.318624\pi$
$457$			36.0000i			1.68401i	−0.539471	+	0.842004i	$0.681376\pi$
$458$	5.65685	+	5.65685i	0.264327	+	0.264327i
$459$		0			0
$460$	−4.00000	+	4.00000i	−0.186501	+	0.186501i
$461$	7.07107	−	7.07107i	0.329332	−	0.329332i	−0.523000	−	0.852333i	$-0.675187\pi$
$461$	7.07107	−	7.07107i	0.329332	−	0.329332i	0.852333	+	0.523000i	$0.175187\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$	−22.6274	+	22.6274i	−1.05045	+	1.05045i
$465$		0			0
$466$		−	6.00000i		−	0.277945i
$467$	−11.3137	−	11.3137i	−0.523536	−	0.523536i	0.395101	−	0.918637i	$-0.370709\pi$
$467$	−11.3137	−	11.3137i	−0.523536	−	0.523536i	−0.918637	+	0.395101i	$0.870709\pi$
$468$		0			0
$469$	7.00000	−	7.00000i	0.323230	−	0.323230i
$470$		0			0
$471$		0			0
$472$	16.0000	+	16.0000i	0.736460	+	0.736460i
$473$	39.5980			1.82072
$474$		0			0
$475$	−4.00000	−	4.00000i	−0.183533	−	0.183533i
$476$			11.3137i			0.518563i
$477$		0			0
$478$		−	6.00000i		−	0.274434i
$479$	33.9411			1.55081			0.775405	−	0.631464i	$-0.217546\pi$
$479$	33.9411			1.55081			0.775405	+	0.631464i	$0.217546\pi$
$480$		0			0
$481$	−40.0000			−1.82384
$482$		−	14.1421i		−	0.644157i
$483$		0			0
$484$			10.0000i			0.454545i
$485$	−14.1421	−	14.1421i	−0.642161	−	0.642161i
$486$		0			0
$487$	38.0000			1.72194			0.860972	−	0.508652i	$-0.169856\pi$
$487$	38.0000			1.72194			0.860972	+	0.508652i	$0.169856\pi$
$488$	11.3137	−	11.3137i	0.512148	−	0.512148i
$489$		0			0
$490$	−2.00000	+	2.00000i	−0.0903508	+	0.0903508i
$491$	−14.1421	+	14.1421i	−0.638226	+	0.638226i	−0.950118	−	0.311892i	$-0.899037\pi$
$491$	−14.1421	+	14.1421i	−0.638226	+	0.638226i	0.311892	+	0.950118i	$0.399037\pi$
$492$		0			0
$493$	32.0000	+	32.0000i	1.44121	+	1.44121i
$494$			45.2548i			2.03611i
$495$		0			0
$496$		0			0
$497$			7.07107i			0.317181i
$498$		0			0
$499$	13.0000	−	13.0000i	0.581960	−	0.581960i	−0.353482	−	0.935441i	$-0.615002\pi$
$499$	13.0000	−	13.0000i	0.581960	−	0.581960i	0.935441	+	0.353482i	$0.115002\pi$
$500$	−16.9706	+	16.9706i	−0.758947	+	0.758947i
$501$		0			0
$502$	4.00000	+	4.00000i	0.178529	+	0.178529i
$503$		−	31.1127i		−	1.38725i	−0.720338	−	0.693623i	$-0.756013\pi$
$503$		−	31.1127i		−	1.38725i	0.720338	−	0.693623i	$-0.243987\pi$
$504$		0			0
$505$		−	20.0000i		−	0.889988i
$506$	5.65685	−	5.65685i	0.251478	−	0.251478i
$507$		0			0
$508$		−	36.0000i		−	1.59724i
$509$	−9.89949	+	9.89949i	−0.438787	+	0.438787i	−0.891604	−	0.452816i	$-0.850419\pi$
$509$	−9.89949	+	9.89949i	−0.438787	+	0.438787i	0.452816	+	0.891604i	$0.350419\pi$
$510$		0			0
$511$			6.00000i			0.265424i
$512$			22.6274i			1.00000i
$513$		0			0
$514$	−16.0000			−0.705730
$515$	−5.65685	−	5.65685i	−0.249271	−	0.249271i
$516$		0			0
$517$		0			0
$518$	−7.07107	−	7.07107i	−0.310685	−	0.310685i
$519$		0			0
$520$	32.0000			1.40329
$521$	−33.9411			−1.48699			−0.743494	−	0.668743i	$-0.766833\pi$
$521$	−33.9411			−1.48699			−0.743494	+	0.668743i	$0.766833\pi$
$522$		0			0
$523$	−20.0000	−	20.0000i	−0.874539	−	0.874539i	0.118424	−	0.992963i	$-0.462216\pi$
$523$	−20.0000	−	20.0000i	−0.874539	−	0.874539i	−0.992963	+	0.118424i	$0.962216\pi$
$524$	−28.2843	−	28.2843i	−1.23560	−	1.23560i
$525$		0			0
$526$	14.0000			0.610429
$527$		0			0
$528$		0			0
$529$	21.0000			0.913043
$530$	28.2843			1.22859
$531$		0			0
$532$	−8.00000	+	8.00000i	−0.346844	+	0.346844i
$533$	33.9411	+	33.9411i	1.47015	+	1.47015i
$534$		0			0
$535$	20.0000			0.864675
$536$	−19.7990	−	19.7990i	−0.855186	−	0.855186i
$537$		0			0
$538$	−2.00000	−	2.00000i	−0.0862261	−	0.0862261i
$539$	2.82843	−	2.82843i	0.121829	−	0.121829i
$540$		0			0
$541$	7.00000	+	7.00000i	0.300954	+	0.300954i	0.841387	−	0.540433i	$-0.181740\pi$
$541$	7.00000	+	7.00000i	0.300954	+	0.300954i	−0.540433	+	0.841387i	$0.681740\pi$
$542$	−16.9706			−0.728948
$543$		0			0
$544$	32.0000			1.37199
$545$			36.7696i			1.57503i
$546$		0			0
$547$	−17.0000	+	17.0000i	−0.726868	+	0.726868i	−0.969994	−	0.243127i	$-0.921827\pi$
$547$	−17.0000	+	17.0000i	−0.726868	+	0.726868i	0.243127	+	0.969994i	$0.421827\pi$
$548$	8.48528			0.362473
$549$		0			0
$550$	4.00000	−	4.00000i	0.170561	−	0.170561i
$551$			45.2548i			1.92792i
$552$		0			0
$553$		0			0
$554$	−15.5563	−	15.5563i	−0.660926	−	0.660926i
$555$		0			0
$556$	28.0000	+	28.0000i	1.18746	+	1.18746i
$557$	11.3137	−	11.3137i	0.479377	−	0.479377i	−0.425555	−	0.904932i	$-0.639921\pi$
$557$	11.3137	−	11.3137i	0.479377	−	0.479377i	0.904932	+	0.425555i	$0.139921\pi$
$558$		0			0
$559$			56.0000i			2.36855i
$560$	5.65685	+	5.65685i	0.239046	+	0.239046i
$561$		0			0
$562$			6.00000i			0.253095i
$563$	5.65685	+	5.65685i	0.238408	+	0.238408i	0.816191	−	0.577783i	$-0.196082\pi$
$563$	5.65685	+	5.65685i	0.238408	+	0.238408i	−0.577783	+	0.816191i	$0.696082\pi$
$564$		0			0
$565$	2.00000	−	2.00000i	0.0841406	−	0.0841406i
$566$	2.82843	−	2.82843i	0.118888	−	0.118888i
$567$		0			0
$568$	20.0000			0.839181
$569$	12.7279			0.533582			0.266791	−	0.963754i	$-0.414037\pi$
$569$	12.7279			0.533582			0.266791	+	0.963754i	$0.414037\pi$
$570$		0			0
$571$	−11.0000	−	11.0000i	−0.460336	−	0.460336i	0.438430	−	0.898765i	$-0.355535\pi$
$571$	−11.0000	−	11.0000i	−0.460336	−	0.460336i	−0.898765	+	0.438430i	$0.855535\pi$
$572$	−45.2548			−1.89220
$573$		0			0
$574$			12.0000i			0.500870i
$575$	−1.41421			−0.0589768
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$		−	21.2132i		−	0.882353i
$579$		0			0
$580$	32.0000			1.32873
$581$	−2.82843	−	2.82843i	−0.117343	−	0.117343i
$582$		0			0
$583$	−40.0000			−1.65663
$584$	16.9706			0.702247
$585$		0			0
$586$	−14.0000	+	14.0000i	−0.578335	+	0.578335i
$587$	−31.1127	+	31.1127i	−1.28416	+	1.28416i	−0.345880	+	0.938279i	$0.612419\pi$
$587$	−31.1127	+	31.1127i	−1.28416	+	1.28416i	−0.938279	+	0.345880i	$0.887581\pi$
$588$		0			0
$589$		0			0
$590$		−	22.6274i		−	0.931556i
$591$		0			0
$592$	−20.0000	+	20.0000i	−0.821995	+	0.821995i
$593$			19.7990i			0.813047i	0.913640	+	0.406524i	$0.133259\pi$
$593$			19.7990i			0.813047i	−0.913640	+	0.406524i	$0.866741\pi$
$594$		0			0
$595$	8.00000	−	8.00000i	0.327968	−	0.327968i
$596$	22.6274	+	22.6274i	0.926855	+	0.926855i
$597$		0			0
$598$	8.00000	+	8.00000i	0.327144	+	0.327144i
$599$		−	1.41421i		−	0.0577832i	−0.999583	−	0.0288916i	$-0.990802\pi$
$599$		−	1.41421i		−	0.0577832i	0.999583	−	0.0288916i	$-0.00919776\pi$
$600$		0			0
$601$		−	30.0000i		−	1.22373i	−0.790964	−	0.611863i	$-0.790420\pi$
$601$		−	30.0000i		−	1.22373i	0.790964	−	0.611863i	$-0.209580\pi$
$602$	−9.89949	+	9.89949i	−0.403473	+	0.403473i
$603$		0			0
$604$	20.0000			0.813788
$605$	7.07107	−	7.07107i	0.287480	−	0.287480i
$606$		0			0
$607$		−	12.0000i		−	0.487065i	−0.969893	−	0.243532i	$-0.921694\pi$
$607$		−	12.0000i		−	0.487065i	0.969893	−	0.243532i	$-0.0783062\pi$
$608$	22.6274	+	22.6274i	0.917663	+	0.917663i
$609$		0			0
$610$	−16.0000			−0.647821
$611$		0			0
$612$		0			0
$613$	25.0000	−	25.0000i	1.00974	−	1.00974i	0.00978840	−	0.999952i	$-0.496884\pi$
$613$	25.0000	−	25.0000i	1.00974	−	1.00974i	0.999952	−	0.00978840i	$-0.00311579\pi$
$614$	−11.3137	−	11.3137i	−0.456584	−	0.456584i
$615$		0			0
$616$	−8.00000	−	8.00000i	−0.322329	−	0.322329i
$617$	21.2132			0.854011			0.427006	−	0.904249i	$-0.359568\pi$
$617$	21.2132			0.854011			0.427006	+	0.904249i	$0.359568\pi$
$618$		0			0
$619$	−8.00000	−	8.00000i	−0.321547	−	0.321547i	0.527813	−	0.849360i	$-0.323012\pi$
$619$	−8.00000	−	8.00000i	−0.321547	−	0.321547i	−0.849360	+	0.527813i	$0.823012\pi$
$620$		0			0
$621$		0			0
$622$	−16.0000			−0.641542
$623$	−16.9706			−0.679911
$624$		0			0
$625$	19.0000			0.760000
$626$	25.4558			1.01742
$627$		0			0
$628$	4.00000	+	4.00000i	0.159617	+	0.159617i
$629$	28.2843	+	28.2843i	1.12777	+	1.12777i
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$		0			0
$633$		0			0
$634$	−2.00000	−	2.00000i	−0.0794301	−	0.0794301i
$635$	−25.4558	+	25.4558i	−1.01018	+	1.01018i
$636$		0			0
$637$	4.00000	+	4.00000i	0.158486	+	0.158486i
$638$	−45.2548			−1.79166
$639$		0			0
$640$	16.0000	−	16.0000i	0.632456	−	0.632456i
$641$			15.5563i			0.614439i	0.951639	+	0.307219i	$0.0993986\pi$
$641$			15.5563i			0.614439i	−0.951639	+	0.307219i	$0.900601\pi$
$642$		0			0
$643$	10.0000	−	10.0000i	0.394362	−	0.394362i	−0.481877	−	0.876239i	$-0.660045\pi$
$643$	10.0000	−	10.0000i	0.394362	−	0.394362i	0.876239	+	0.481877i	$0.160045\pi$
$644$			2.82843i			0.111456i
$645$		0			0
$646$	32.0000	−	32.0000i	1.25902	−	1.25902i
$647$		−	31.1127i		−	1.22317i	−0.791180	−	0.611583i	$-0.790533\pi$
$647$		−	31.1127i		−	1.22317i	0.791180	−	0.611583i	$-0.209467\pi$
$648$		0			0
$649$			32.0000i			1.25611i
$650$	5.65685	+	5.65685i	0.221880	+	0.221880i
$651$		0			0
$652$	−26.0000	+	26.0000i	−1.01824	+	1.01824i
$653$	2.82843	−	2.82843i	0.110685	−	0.110685i	−0.649595	−	0.760280i	$-0.725062\pi$
$653$	2.82843	−	2.82843i	0.110685	−	0.110685i	0.760280	+	0.649595i	$0.225062\pi$
$654$		0			0
$655$			40.0000i			1.56293i
$656$	33.9411			1.32518
$657$		0			0
$658$		0			0
$659$	9.89949	+	9.89949i	0.385630	+	0.385630i	0.873125	−	0.487496i	$-0.162090\pi$
$659$	9.89949	+	9.89949i	0.385630	+	0.385630i	−0.487496	+	0.873125i	$0.662090\pi$
$660$		0			0
$661$	−20.0000	+	20.0000i	−0.777910	+	0.777910i	−0.979475	−	0.201565i	$-0.935397\pi$
$661$	−20.0000	+	20.0000i	−0.777910	+	0.777910i	0.201565	+	0.979475i	$0.435397\pi$
$662$	−18.3848	+	18.3848i	−0.714545	+	0.714545i
$663$		0			0
$664$	−8.00000	+	8.00000i	−0.310460	+	0.310460i
$665$	11.3137			0.438727
$666$		0			0
$667$	8.00000	+	8.00000i	0.309761	+	0.309761i
$668$			28.2843i			1.09435i
$669$		0			0
$670$			28.0000i			1.08173i
$671$	22.6274			0.873522
$672$		0			0
$673$	−28.0000			−1.07932			−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000			−1.07932			−0.539660	+	0.841883i	$0.681447\pi$
$674$		−	31.1127i		−	1.19842i
$675$		0			0
$676$		−	38.0000i		−	1.46154i
$677$	−24.0416	−	24.0416i	−0.923995	−	0.923995i	0.0733140	−	0.997309i	$-0.476642\pi$
$677$	−24.0416	−	24.0416i	−0.923995	−	0.923995i	−0.997309	+	0.0733140i	$0.976642\pi$
$678$		0			0
$679$	−10.0000			−0.383765
$680$	−22.6274	−	22.6274i	−0.867722	−	0.867722i
$681$		0			0
$682$		0			0
$683$	−14.1421	+	14.1421i	−0.541134	+	0.541134i	−0.923861	−	0.382727i	$-0.874985\pi$
$683$	−14.1421	+	14.1421i	−0.541134	+	0.541134i	0.382727	+	0.923861i	$0.374985\pi$
$684$		0			0
$685$	−6.00000	−	6.00000i	−0.229248	−	0.229248i
$686$			1.41421i			0.0539949i
$687$		0			0
$688$	28.0000	+	28.0000i	1.06749	+	1.06749i
$689$		−	56.5685i		−	2.15509i
$690$		0			0
$691$	22.0000	−	22.0000i	0.836919	−	0.836919i	−0.151533	−	0.988452i	$-0.548421\pi$
$691$	22.0000	−	22.0000i	0.836919	−	0.836919i	0.988452	+	0.151533i	$0.0484209\pi$
$692$	2.82843	−	2.82843i	0.107521	−	0.107521i
$693$		0			0
$694$	10.0000	+	10.0000i	0.379595	+	0.379595i
$695$		−	39.5980i		−	1.50204i
$696$		0			0
$697$		−	48.0000i		−	1.81813i
$698$	2.82843	−	2.82843i	0.107058	−	0.107058i
$699$		0			0
$700$			2.00000i			0.0755929i
$701$	15.5563	−	15.5563i	0.587555	−	0.587555i	−0.349413	−	0.936969i	$-0.613619\pi$
$701$	15.5563	−	15.5563i	0.587555	−	0.587555i	0.936969	+	0.349413i	$0.113619\pi$
$702$		0			0
$703$			40.0000i			1.50863i
$704$	−22.6274	+	22.6274i	−0.852803	+	0.852803i
$705$		0			0
$706$	−4.00000			−0.150542
$707$	−7.07107	−	7.07107i	−0.265935	−	0.265935i
$708$		0			0
$709$	31.0000	−	31.0000i	1.16423	−	1.16423i	0.180689	−	0.983540i	$-0.442167\pi$
$709$	31.0000	−	31.0000i	1.16423	−	1.16423i	0.983540	−	0.180689i	$-0.0578328\pi$
$710$	−14.1421	−	14.1421i	−0.530745	−	0.530745i
$711$		0			0
$712$			48.0000i			1.79888i
$713$		0			0
$714$		0			0
$715$	32.0000	+	32.0000i	1.19673	+	1.19673i
$716$	14.1421	+	14.1421i	0.528516	+	0.528516i
$717$		0			0
$718$	−46.0000			−1.71670
$719$	−42.4264			−1.58224			−0.791119	−	0.611662i	$-0.790501\pi$
$719$	−42.4264			−1.58224			−0.791119	+	0.611662i	$0.790501\pi$
$720$		0			0
$721$	−4.00000			−0.148968
$722$	18.3848			0.684211
$723$		0			0
$724$	16.0000	−	16.0000i	0.594635	−	0.594635i
$725$	5.65685	+	5.65685i	0.210090	+	0.210090i
$726$		0			0
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$	11.3137	−	11.3137i	0.419314	−	0.419314i
$729$		0			0
$730$	−12.0000	−	12.0000i	−0.444140	−	0.444140i
$731$	39.5980	−	39.5980i	1.46458	−	1.46458i
$732$		0			0
$733$	−26.0000	−	26.0000i	−0.960332	−	0.960332i	0.0389108	−	0.999243i	$-0.487611\pi$
$733$	−26.0000	−	26.0000i	−0.960332	−	0.960332i	−0.999243	+	0.0389108i	$0.987611\pi$
$734$	33.9411			1.25279
$735$		0			0
$736$	8.00000			0.294884
$737$		−	39.5980i		−	1.45861i
$738$		0			0
$739$	−29.0000	+	29.0000i	−1.06678	+	1.06678i	−0.0691779	+	0.997604i	$0.522038\pi$
$739$	−29.0000	+	29.0000i	−1.06678	+	1.06678i	−0.997604	+	0.0691779i	$0.977962\pi$
$740$	28.2843			1.03975
$741$		0			0
$742$	10.0000	−	10.0000i	0.367112	−	0.367112i
$743$		−	26.8701i		−	0.985767i	−0.870095	−	0.492883i	$-0.835943\pi$
$743$		−	26.8701i		−	0.985767i	0.870095	−	0.492883i	$-0.164057\pi$
$744$		0			0
$745$		−	32.0000i		−	1.17239i
$746$	−7.07107	−	7.07107i	−0.258890	−	0.258890i
$747$		0			0
$748$	32.0000	+	32.0000i	1.17004	+	1.17004i
$749$	7.07107	−	7.07107i	0.258371	−	0.258371i
$750$		0			0
$751$			24.0000i			0.875772i	0.899030	+	0.437886i	$0.144273\pi$
$751$			24.0000i			0.875772i	−0.899030	+	0.437886i	$0.855727\pi$
$752$		0			0
$753$		0			0
$754$		−	64.0000i		−	2.33074i
$755$	−14.1421	−	14.1421i	−0.514685	−	0.514685i
$756$		0			0
$757$	37.0000	−	37.0000i	1.34479	−	1.34479i	0.453564	−	0.891224i	$-0.350152\pi$
$757$	37.0000	−	37.0000i	1.34479	−	1.34479i	0.891224	−	0.453564i	$-0.149848\pi$
$758$	24.0416	−	24.0416i	0.873231	−	0.873231i
$759$		0			0
$760$		−	32.0000i		−	1.16076i
$761$	42.4264			1.53796			0.768978	−	0.639275i	$-0.220766\pi$
$761$	42.4264			1.53796			0.768978	+	0.639275i	$0.220766\pi$
$762$		0			0
$763$	13.0000	+	13.0000i	0.470632	+	0.470632i
$764$	−25.4558			−0.920960
$765$		0			0
$766$		−	12.0000i		−	0.433578i
$767$	−45.2548			−1.63406
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$			11.3137i			0.407718i
$771$		0			0
$772$	−28.0000			−1.00774
$773$	−32.5269	−	32.5269i	−1.16991	−	1.16991i	−0.982230	−	0.187682i	$-0.939903\pi$
$773$	−32.5269	−	32.5269i	−1.16991	−	1.16991i	−0.187682	−	0.982230i	$-0.560097\pi$
$774$		0			0
$775$		0			0
$776$			28.2843i			1.01535i
$777$		0			0
$778$	10.0000	−	10.0000i	0.358517	−	0.358517i
$779$	33.9411	−	33.9411i	1.21607	−	1.21607i
$780$		0			0
$781$	20.0000	+	20.0000i	0.715656	+	0.715656i
$782$		−	11.3137i		−	0.404577i
$783$		0			0
$784$	4.00000			0.142857
$785$		−	5.65685i		−	0.201902i
$786$		0			0
$787$	−2.00000	+	2.00000i	−0.0712923	+	0.0712923i	−0.741854	−	0.670562i	$-0.766053\pi$
$787$	−2.00000	+	2.00000i	−0.0712923	+	0.0712923i	0.670562	+	0.741854i	$0.266053\pi$
$788$	5.65685	+	5.65685i	0.201517	+	0.201517i
$789$		0			0
$790$		0			0
$791$		−	1.41421i		−	0.0502836i
$792$		0			0
$793$			32.0000i			1.13635i
$794$	2.82843	−	2.82843i	0.100377	−	0.100377i
$795$		0			0
$796$	32.0000			1.13421
$797$	−1.41421	+	1.41421i	−0.0500940	+	0.0500940i	−0.731710	−	0.681616i	$-0.761277\pi$
$797$	−1.41421	+	1.41421i	−0.0500940	+	0.0500940i	0.681616	+	0.731710i	$0.261277\pi$
$798$		0			0
$799$		0			0
$800$	5.65685			0.200000
$801$		0			0
$802$	−34.0000			−1.20058
$803$	16.9706	+	16.9706i	0.598878	+	0.598878i
$804$		0			0
$805$	2.00000	−	2.00000i	0.0704907	−	0.0704907i
$806$		0			0
$807$		0			0
$808$	−20.0000	+	20.0000i	−0.703598	+	0.703598i
$809$	4.24264			0.149163			0.0745817	−	0.997215i	$-0.476238\pi$
$809$	4.24264			0.149163			0.0745817	+	0.997215i	$0.476238\pi$
$810$		0			0
$811$	−8.00000	−	8.00000i	−0.280918	−	0.280918i	0.552557	−	0.833475i	$-0.313652\pi$
$811$	−8.00000	−	8.00000i	−0.280918	−	0.280918i	−0.833475	+	0.552557i	$0.813652\pi$
$812$	11.3137	−	11.3137i	0.397033	−	0.397033i
$813$		0			0
$814$	−40.0000			−1.40200
$815$	36.7696			1.28798
$816$		0			0
$817$	56.0000			1.95919
$818$	−25.4558			−0.890043
$819$		0			0
$820$	−24.0000	−	24.0000i	−0.838116	−	0.838116i
$821$	26.8701	+	26.8701i	0.937771	+	0.937771i	0.998174	−	0.0604026i	$-0.0192385\pi$
$821$	26.8701	+	26.8701i	0.937771	+	0.937771i	−0.0604026	+	0.998174i	$0.519238\pi$
$822$		0			0
$823$	14.0000			0.488009			0.244005	−	0.969774i	$-0.421539\pi$
$823$	14.0000			0.488009			0.244005	+	0.969774i	$0.421539\pi$
$824$			11.3137i			0.394132i
$825$		0			0
$826$	−8.00000	−	8.00000i	−0.278356	−	0.278356i
$827$	−9.89949	+	9.89949i	−0.344239	+	0.344239i	−0.857958	−	0.513719i	$-0.828267\pi$
$827$	−9.89949	+	9.89949i	−0.344239	+	0.344239i	0.513719	+	0.857958i	$0.328267\pi$
$828$		0			0
$829$	22.0000	+	22.0000i	0.764092	+	0.764092i	0.977059	−	0.212968i	$-0.0683129\pi$
$829$	22.0000	+	22.0000i	0.764092	+	0.764092i	−0.212968	+	0.977059i	$0.568313\pi$
$830$	11.3137			0.392705
$831$		0			0
$832$	−32.0000	−	32.0000i	−1.10940	−	1.10940i
$833$		−	5.65685i		−	0.195998i
$834$		0			0
$835$	20.0000	−	20.0000i	0.692129	−	0.692129i
$836$			45.2548i			1.56517i
$837$		0			0
$838$	4.00000	−	4.00000i	0.138178	−	0.138178i
$839$			2.82843i			0.0976481i	0.998807	+	0.0488241i	$0.0155474\pi$
$839$			2.82843i			0.0976481i	−0.998807	+	0.0488241i	$0.984453\pi$
$840$		0			0
$841$		−	35.0000i		−	1.20690i
$842$	1.41421	+	1.41421i	0.0487370	+	0.0487370i
$843$		0			0
$844$	−38.0000	+	38.0000i	−1.30801	+	1.30801i
$845$	−26.8701	+	26.8701i	−0.924358	+	0.924358i
$846$		0			0
$847$		−	5.00000i		−	0.171802i
$848$	−28.2843	−	28.2843i	−0.971286	−	0.971286i
$849$		0			0
$850$		−	8.00000i		−	0.274398i
$851$	7.07107	+	7.07107i	0.242393	+	0.242393i
$852$		0			0
$853$	10.0000	−	10.0000i	0.342393	−	0.342393i	−0.514873	−	0.857266i	$-0.672161\pi$
$853$	10.0000	−	10.0000i	0.342393	−	0.342393i	0.857266	+	0.514873i	$0.172161\pi$
$854$	−5.65685	+	5.65685i	−0.193574	+	0.193574i
$855$		0			0
$856$	−20.0000	−	20.0000i	−0.683586	−	0.683586i
$857$	8.48528			0.289852			0.144926	−	0.989443i	$-0.453706\pi$
$857$	8.48528			0.289852			0.144926	+	0.989443i	$0.453706\pi$
$858$		0			0
$859$	28.0000	+	28.0000i	0.955348	+	0.955348i	0.999045	−	0.0436972i	$-0.0139137\pi$
$859$	28.0000	+	28.0000i	0.955348	+	0.955348i	−0.0436972	+	0.999045i	$0.513914\pi$
$860$		−	39.5980i		−	1.35028i
$861$		0			0
$862$		−	30.0000i		−	1.02180i
$863$	−29.6985			−1.01095			−0.505474	−	0.862842i	$-0.668682\pi$
$863$	−29.6985			−1.01095			−0.505474	+	0.862842i	$0.668682\pi$
$864$		0			0
$865$	−4.00000			−0.136004
$866$		−	48.0833i		−	1.63394i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	56.0000			1.89749
$872$	36.7696	−	36.7696i	1.24517	−	1.24517i
$873$		0			0
$874$	8.00000	−	8.00000i	0.270604	−	0.270604i
$875$	8.48528	−	8.48528i	0.286855	−	0.286855i
$876$		0			0
$877$	1.00000	+	1.00000i	0.0337676	+	0.0337676i	0.723789	−	0.690021i	$-0.242399\pi$
$877$	1.00000	+	1.00000i	0.0337676	+	0.0337676i	−0.690021	+	0.723789i	$0.742399\pi$
$878$		−	39.5980i		−	1.33637i
$879$		0			0
$880$	32.0000			1.07872
$881$		−	31.1127i		−	1.04821i	−0.851653	−	0.524107i	$-0.824399\pi$
$881$		−	31.1127i		−	1.04821i	0.851653	−	0.524107i	$-0.175601\pi$
$882$		0			0
$883$	−35.0000	+	35.0000i	−1.17784	+	1.17784i	−0.197551	+	0.980293i	$0.563299\pi$
$883$	−35.0000	+	35.0000i	−1.17784	+	1.17784i	−0.980293	+	0.197551i	$0.936701\pi$
$884$	−45.2548	+	45.2548i	−1.52208	+	1.52208i
$885$		0			0
$886$	−20.0000	−	20.0000i	−0.671913	−	0.671913i
$887$		−	14.1421i		−	0.474846i	−0.971406	−	0.237423i	$-0.923697\pi$
$887$		−	14.1421i		−	0.474846i	0.971406	−	0.237423i	$-0.0763028\pi$
$888$		0			0
$889$			18.0000i			0.603701i
$890$	33.9411	−	33.9411i	1.13771	−	1.13771i
$891$		0			0
$892$			24.0000i			0.803579i
$893$		0			0
$894$		0			0
$895$		−	20.0000i		−	0.668526i
$896$		−	11.3137i		−	0.377964i
$897$		0			0
$898$	−46.0000			−1.53504
$899$		0			0
$900$		0			0
$901$	−40.0000	+	40.0000i	−1.33259	+	1.33259i
$902$	33.9411	+	33.9411i	1.13012	+	1.13012i
$903$		0			0
$904$	−4.00000			−0.133038
$905$	−22.6274			−0.752161
$906$		0			0
$907$	−17.0000	−	17.0000i	−0.564476	−	0.564476i	0.366100	−	0.930576i	$-0.380693\pi$
$907$	−17.0000	−	17.0000i	−0.564476	−	0.564476i	−0.930576	+	0.366100i	$0.880693\pi$
$908$	−11.3137	−	11.3137i	−0.375459	−	0.375459i
$909$		0			0
$910$	−16.0000			−0.530395
$911$	−21.2132			−0.702825			−0.351412	−	0.936221i	$-0.614298\pi$
$911$	−21.2132			−0.702825			−0.351412	+	0.936221i	$0.614298\pi$
$912$		0			0
$913$	−16.0000			−0.529523
$914$	−50.9117			−1.68401
$915$		0			0
$916$	−8.00000	+	8.00000i	−0.264327	+	0.264327i
$917$	14.1421	+	14.1421i	0.467014	+	0.467014i
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$	−5.65685	−	5.65685i	−0.186501	−	0.186501i
$921$		0			0
$922$	10.0000	+	10.0000i	0.329332	+	0.329332i
$923$	−28.2843	+	28.2843i	−0.930988	+	0.930988i
$924$		0			0
$925$	5.00000	+	5.00000i	0.164399	+	0.164399i
$926$	33.9411			1.11537
$927$		0			0
$928$	−32.0000	−	32.0000i	−1.05045	−	1.05045i
$929$			53.7401i			1.76316i	0.472038	+	0.881578i	$0.343518\pi$
$929$			53.7401i			1.76316i	−0.472038	+	0.881578i	$0.656482\pi$
$930$		0			0
$931$	4.00000	−	4.00000i	0.131095	−	0.131095i
$932$	8.48528			0.277945
$933$		0			0
$934$	16.0000	−	16.0000i	0.523536	−	0.523536i
$935$		−	45.2548i		−	1.47999i
$936$		0			0
$937$		−	18.0000i		−	0.588034i	−0.955800	−	0.294017i	$-0.905008\pi$
$937$		−	18.0000i		−	0.588034i	0.955800	−	0.294017i	$-0.0949923\pi$
$938$	9.89949	+	9.89949i	0.323230	+	0.323230i
$939$		0			0
$940$		0			0
$941$	7.07107	−	7.07107i	0.230510	−	0.230510i	−0.582395	−	0.812906i	$-0.697884\pi$
$941$	7.07107	−	7.07107i	0.230510	−	0.230510i	0.812906	+	0.582395i	$0.197884\pi$
$942$		0			0
$943$		−	12.0000i		−	0.390774i
$944$	−22.6274	+	22.6274i	−0.736460	+	0.736460i
$945$		0			0
$946$			56.0000i			1.82072i
$947$	1.41421	+	1.41421i	0.0459558	+	0.0459558i	0.729711	−	0.683755i	$-0.239654\pi$
$947$	1.41421	+	1.41421i	0.0459558	+	0.0459558i	−0.683755	+	0.729711i	$0.739654\pi$
$948$		0			0
$949$	−24.0000	+	24.0000i	−0.779073	+	0.779073i
$950$	5.65685	−	5.65685i	0.183533	−	0.183533i
$951$		0			0
$952$	−16.0000			−0.518563
$953$	12.7279			0.412298			0.206149	−	0.978521i	$-0.433907\pi$
$953$	12.7279			0.412298			0.206149	+	0.978521i	$0.433907\pi$
$954$		0			0
$955$	18.0000	+	18.0000i	0.582466	+	0.582466i
$956$	8.48528			0.274434
$957$		0			0
$958$			48.0000i			1.55081i
$959$	−4.24264			−0.137002
$960$		0			0
$961$	31.0000			1.00000
$962$		−	56.5685i		−	1.82384i
$963$		0			0
$964$	20.0000			0.644157
$965$	19.7990	+	19.7990i	0.637352	+	0.637352i
$966$		0			0
$967$	−40.0000			−1.28631			−0.643157	−	0.765735i	$-0.722376\pi$
$967$	−40.0000			−1.28631			−0.643157	+	0.765735i	$0.722376\pi$
$968$	−14.1421			−0.454545
$969$		0			0
$970$	20.0000	−	20.0000i	0.642161	−	0.642161i
$971$	19.7990	−	19.7990i	0.635380	−	0.635380i	−0.314032	−	0.949412i	$-0.601680\pi$
$971$	19.7990	−	19.7990i	0.635380	−	0.635380i	0.949412	+	0.314032i	$0.101680\pi$
$972$		0			0
$973$	−14.0000	−	14.0000i	−0.448819	−	0.448819i
$974$			53.7401i			1.72194i
$975$		0			0
$976$	16.0000	+	16.0000i	0.512148	+	0.512148i
$977$		−	1.41421i		−	0.0452447i	−0.999744	−	0.0226224i	$-0.992798\pi$
$977$		−	1.41421i		−	0.0452447i	0.999744	−	0.0226224i	$-0.00720153\pi$
$978$		0			0
$979$	−48.0000	+	48.0000i	−1.53409	+	1.53409i
$980$	−2.82843	−	2.82843i	−0.0903508	−	0.0903508i
$981$		0			0
$982$	−20.0000	−	20.0000i	−0.638226	−	0.638226i
$983$			28.2843i			0.902128i	0.892492	+	0.451064i	$0.148955\pi$
$983$			28.2843i			0.902128i	−0.892492	+	0.451064i	$0.851045\pi$
$984$		0			0
$985$		−	8.00000i		−	0.254901i
$986$	−45.2548	+	45.2548i	−1.44121	+	1.44121i
$987$		0			0
$988$	−64.0000			−2.03611
$989$	9.89949	−	9.89949i	0.314786	−	0.314786i
$990$		0			0
$991$		−	30.0000i		−	0.952981i	−0.879180	−	0.476491i	$-0.841909\pi$
$991$		−	30.0000i		−	0.952981i	0.879180	−	0.476491i	$-0.158091\pi$
$992$		0			0
$993$		0			0
$994$	−10.0000			−0.317181
$995$	−22.6274	−	22.6274i	−0.717337	−	0.717337i
$996$		0			0
$997$	−20.0000	+	20.0000i	−0.633406	+	0.633406i	−0.948921	−	0.315514i	$-0.897823\pi$
$997$	−20.0000	+	20.0000i	−0.633406	+	0.633406i	0.315514	+	0.948921i	$0.397823\pi$
$998$	18.3848	+	18.3848i	0.581960	+	0.581960i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.a.323.2	yes	4
3.2	odd	2	inner	1008.2.v.a.323.1	✓	4
4.3	odd	2		4032.2.v.b.1583.2		4
12.11	even	2		4032.2.v.b.1583.1		4
16.5	even	4		4032.2.v.b.3599.1		4
16.11	odd	4	inner	1008.2.v.a.827.2	yes	4
48.5	odd	4		4032.2.v.b.3599.2		4
48.11	even	4	inner	1008.2.v.a.827.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.a.323.1	✓	4	3.2	odd	2	inner
1008.2.v.a.323.2	yes	4	1.1	even	1	trivial
1008.2.v.a.827.1	yes	4	48.11	even	4	inner
1008.2.v.a.827.2	yes	4	16.11	odd	4	inner
4032.2.v.b.1583.1		4	12.11	even	2
4032.2.v.b.1583.2		4	4.3	odd	2
4032.2.v.b.3599.1		4	16.5	even	4
4032.2.v.b.3599.2		4	48.5	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(1.41421 + 1.41421i) q^{5} +1.00000 q^{7} -2.82843i q^{8} +O(q^{10})\)	\(q+1.41421i q^{2} -2.00000 q^{4} +(1.41421 + 1.41421i) q^{5} +1.00000 q^{7} -2.82843i q^{8} +(-2.00000 + 2.00000i) q^{10} +(2.82843 - 2.82843i) q^{11} +(4.00000 + 4.00000i) q^{13} +1.41421i q^{14} +4.00000 q^{16} -5.65685i q^{17} +(4.00000 - 4.00000i) q^{19} +(-2.82843 - 2.82843i) q^{20} +(4.00000 + 4.00000i) q^{22} -1.41421i q^{23} -1.00000i q^{25} +(-5.65685 + 5.65685i) q^{26} -2.00000 q^{28} +(-5.65685 + 5.65685i) q^{29} +5.65685i q^{32} +8.00000 q^{34} +(1.41421 + 1.41421i) q^{35} +(-5.00000 + 5.00000i) q^{37} +(5.65685 + 5.65685i) q^{38} +(4.00000 - 4.00000i) q^{40} +8.48528 q^{41} +(7.00000 + 7.00000i) q^{43} +(-5.65685 + 5.65685i) q^{44} +2.00000 q^{46} +1.00000 q^{49} +1.41421 q^{50} +(-8.00000 - 8.00000i) q^{52} +(-7.07107 - 7.07107i) q^{53} +8.00000 q^{55} -2.82843i q^{56} +(-8.00000 - 8.00000i) q^{58} +(-5.65685 + 5.65685i) q^{59} +(4.00000 + 4.00000i) q^{61} -8.00000 q^{64} +11.3137i q^{65} +(7.00000 - 7.00000i) q^{67} +11.3137i q^{68} +(-2.00000 + 2.00000i) q^{70} +7.07107i q^{71} +6.00000i q^{73} +(-7.07107 - 7.07107i) q^{74} +(-8.00000 + 8.00000i) q^{76} +(2.82843 - 2.82843i) q^{77} +(5.65685 + 5.65685i) q^{80} +12.0000i q^{82} +(-2.82843 - 2.82843i) q^{83} +(8.00000 - 8.00000i) q^{85} +(-9.89949 + 9.89949i) q^{86} +(-8.00000 - 8.00000i) q^{88} -16.9706 q^{89} +(4.00000 + 4.00000i) q^{91} +2.82843i q^{92} +11.3137 q^{95} -10.0000 q^{97} +1.41421i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{4} + 4 q^{7}+O(q^{10}) \) 4 * q - 8 * q^4 + 4 * q^7	\( 4 q - 8 q^{4} + 4 q^{7} - 8 q^{10} + 16 q^{13} + 16 q^{16} + 16 q^{19} + 16 q^{22} - 8 q^{28} + 32 q^{34} - 20 q^{37} + 16 q^{40} + 28 q^{43} + 8 q^{46} + 4 q^{49} - 32 q^{52} + 32 q^{55} - 32 q^{58} + 16 q^{61} - 32 q^{64} + 28 q^{67} - 8 q^{70} - 32 q^{76} + 32 q^{85} - 32 q^{88} + 16 q^{91} - 40 q^{97}+O(q^{100}) \) 4 * q - 8 * q^4 + 4 * q^7 - 8 * q^10 + 16 * q^13 + 16 * q^16 + 16 * q^19 + 16 * q^22 - 8 * q^28 + 32 * q^34 - 20 * q^37 + 16 * q^40 + 28 * q^43 + 8 * q^46 + 4 * q^49 - 32 * q^52 + 32 * q^55 - 32 * q^58 + 16 * q^61 - 32 * q^64 + 28 * q^67 - 8 * q^70 - 32 * q^76 + 32 * q^85 - 32 * q^88 + 16 * q^91 - 40 * q^97

Introduction

L-functions

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