LMFDB - Embedded newform 1520.2.q.c.961.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1520,2,Mod(881,1520)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1520, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1520.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1520 = 2^{4} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1520.q (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.1372611072$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			961.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1520.961
Dual form			1520.2.q.c.881.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} -3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(1.00000 + 1.73205i) q^{15} +(-3.00000 + 5.19615i) q^{17} +(3.50000 + 2.59808i) q^{19} +(-4.00000 + 6.92820i) q^{21} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +7.00000 q^{31} +(3.00000 - 5.19615i) q^{33} +(2.00000 - 3.46410i) q^{35} +8.00000 q^{37} +4.00000 q^{39} +(3.00000 - 5.19615i) q^{41} +(-2.00000 + 3.46410i) q^{43} -1.00000 q^{45} +(3.00000 + 5.19615i) q^{47} +9.00000 q^{49} +(-6.00000 - 10.3923i) q^{51} +(3.00000 + 5.19615i) q^{53} +(-1.50000 + 2.59808i) q^{55} +(-8.00000 + 3.46410i) q^{57} +(-7.50000 + 12.9904i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-2.00000 - 3.46410i) q^{63} -2.00000 q^{65} +(1.00000 + 1.73205i) q^{67} +(-1.50000 + 2.59808i) q^{71} +(-4.00000 + 6.92820i) q^{73} +2.00000 q^{75} -12.0000 q^{77} +(2.50000 - 4.33013i) q^{79} +(5.50000 - 9.52628i) q^{81} -12.0000 q^{83} +(3.00000 + 5.19615i) q^{85} -6.00000 q^{87} +(7.50000 + 12.9904i) q^{89} +(-4.00000 - 6.92820i) q^{91} +(-7.00000 + 12.1244i) q^{93} +(4.00000 - 1.73205i) q^{95} +(-4.00000 + 6.92820i) q^{97} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + q^{5} + 8 q^{7} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^3 + q^5 + 8 * q^7 - q^9	$ 2 q - 2 q^{3} + q^{5} + 8 q^{7} - q^{9} - 6 q^{11} - 2 q^{13} + 2 q^{15} - 6 q^{17} + 7 q^{19} - 8 q^{21} - q^{25} - 8 q^{27} + 3 q^{29} + 14 q^{31} + 6 q^{33} + 4 q^{35} + 16 q^{37} + 8 q^{39} + 6 q^{41} - 4 q^{43} - 2 q^{45} + 6 q^{47} + 18 q^{49} - 12 q^{51} + 6 q^{53} - 3 q^{55} - 16 q^{57} - 15 q^{59} - 5 q^{61} - 4 q^{63} - 4 q^{65} + 2 q^{67} - 3 q^{71} - 8 q^{73} + 4 q^{75} - 24 q^{77} + 5 q^{79} + 11 q^{81} - 24 q^{83} + 6 q^{85} - 12 q^{87} + 15 q^{89} - 8 q^{91} - 14 q^{93} + 8 q^{95} - 8 q^{97} + 3 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + q^5 + 8 * q^7 - q^9 - 6 * q^11 - 2 * q^13 + 2 * q^15 - 6 * q^17 + 7 * q^19 - 8 * q^21 - q^25 - 8 * q^27 + 3 * q^29 + 14 * q^31 + 6 * q^33 + 4 * q^35 + 16 * q^37 + 8 * q^39 + 6 * q^41 - 4 * q^43 - 2 * q^45 + 6 * q^47 + 18 * q^49 - 12 * q^51 + 6 * q^53 - 3 * q^55 - 16 * q^57 - 15 * q^59 - 5 * q^61 - 4 * q^63 - 4 * q^65 + 2 * q^67 - 3 * q^71 - 8 * q^73 + 4 * q^75 - 24 * q^77 + 5 * q^79 + 11 * q^81 - 24 * q^83 + 6 * q^85 - 12 * q^87 + 15 * q^89 - 8 * q^91 - 14 * q^93 + 8 * q^95 - 8 * q^97 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times$.

$n$	$191$	$401$	$1141$	$1217$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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			0
$2$		0			0
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	4.00000			1.51186			0.755929	−	0.654654i	$-0.227186\pi$
$7$	4.00000			1.51186			0.755929	+	0.654654i	$0.227186\pi$
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$		0			0
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	−1.00000	−	1.73205i	−0.277350	−	0.480384i	−0.970725	+	0.240192i	$0.922790\pi$
$14$		0			0
$15$	1.00000	+	1.73205i	0.258199	+	0.447214i
$16$		0			0
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	0.230285	+	0.973123i	$0.426034\pi$
$17$	−3.00000	+	5.19615i	−0.727607	+	1.26025i	−0.957892	+	0.287129i	$0.907299\pi$
$18$		0			0
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$19$	3.50000	+	2.59808i	0.802955	+	0.596040i
$20$		0			0
$21$	−4.00000	+	6.92820i	−0.872872	+	1.51186i
$22$		0			0
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−4.00000			−0.769800
$28$		0			0
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$	7.00000			1.25724			0.628619	−	0.777714i	$-0.283621\pi$
$31$	7.00000			1.25724			0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	3.00000	−	5.19615i	0.522233	−	0.904534i
$34$		0			0
$35$	2.00000	−	3.46410i	0.338062	−	0.585540i
$36$		0			0
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$		0			0
$39$	4.00000			0.640513
$40$		0			0
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		0			0
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	−0.977261	−	0.212041i	$-0.931989\pi$
$43$	−2.00000	+	3.46410i	−0.304997	+	0.528271i	0.672264	+	0.740312i	$0.265322\pi$
$44$		0			0
$45$	−1.00000			−0.149071
$46$		0			0
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	9.00000			1.28571
$50$		0			0
$51$	−6.00000	−	10.3923i	−0.840168	−	1.45521i
$52$		0			0
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	0.995117	−	0.0987002i	$-0.0314685\pi$
$53$	3.00000	+	5.19615i	0.412082	+	0.713746i	−0.583036	+	0.812447i	$0.698135\pi$
$54$		0			0
$55$	−1.50000	+	2.59808i	−0.202260	+	0.350325i
$56$		0			0
$57$	−8.00000	+	3.46410i	−1.05963	+	0.458831i
$58$		0			0
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.301239	+	0.953549i	$0.597400\pi$
$59$	−7.50000	+	12.9904i	−0.976417	+	1.69120i	−0.675178	+	0.737655i	$0.735933\pi$
$60$		0			0
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	0.660415	−	0.750901i	$-0.270381\pi$
$61$	−2.50000	−	4.33013i	−0.320092	−	0.554416i	−0.980507	+	0.196485i	$0.937047\pi$
$62$		0			0
$63$	−2.00000	−	3.46410i	−0.251976	−	0.436436i
$64$		0			0
$65$	−2.00000			−0.248069
$66$		0			0
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	0.920623	−	0.390453i	$-0.127682\pi$
$67$	1.00000	+	1.73205i	0.122169	+	0.211604i	−0.798454	+	0.602056i	$0.794348\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	−0.941201	−	0.337846i	$-0.890302\pi$
$71$	−1.50000	+	2.59808i	−0.178017	+	0.308335i	0.763184	+	0.646181i	$0.223635\pi$
$72$		0			0
$73$	−4.00000	+	6.92820i	−0.468165	+	0.810885i	−0.999338	−	0.0363782i	$-0.988418\pi$
$73$	−4.00000	+	6.92820i	−0.468165	+	0.810885i	0.531174	+	0.847263i	$0.321751\pi$
$74$		0			0
$75$	2.00000			0.230940
$76$		0			0
$77$	−12.0000			−1.36753
$78$		0			0
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	−0.690426	−	0.723403i	$-0.742577\pi$
$79$	2.50000	−	4.33013i	0.281272	−	0.487177i	0.971698	+	0.236225i	$0.0759104\pi$
$80$		0			0
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	3.00000	+	5.19615i	0.325396	+	0.563602i
$86$		0			0
$87$	−6.00000			−0.643268
$88$		0			0
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	0.922840	+	0.385183i	$0.125862\pi$
$89$	7.50000	+	12.9904i	0.794998	+	1.37698i	−0.127842	+	0.991795i	$0.540805\pi$
$90$		0			0
$91$	−4.00000	−	6.92820i	−0.419314	−	0.726273i
$92$		0			0
$93$	−7.00000	+	12.1244i	−0.725866	+	1.25724i
$94$		0			0
$95$	4.00000	−	1.73205i	0.410391	−	0.177705i
$96$		0			0
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	−0.994453	−	0.105180i	$-0.966458\pi$
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	0.588315	+	0.808632i	$0.299792\pi$
$98$		0			0
$99$	1.50000	+	2.59808i	0.150756	+	0.261116i
$100$		0			0
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	−0.949595	−	0.313478i	$-0.898506\pi$
$101$	−7.50000	−	12.9904i	−0.746278	−	1.29259i	0.203317	−	0.979113i	$-0.434828\pi$
$102$		0			0
$103$	16.0000			1.57653			0.788263	−	0.615338i	$-0.210980\pi$
$103$	16.0000			1.57653			0.788263	+	0.615338i	$0.210980\pi$
$104$		0			0
$105$	4.00000	+	6.92820i	0.390360	+	0.676123i
$106$		0			0
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$		0			0
$111$	−8.00000	+	13.8564i	−0.759326	+	1.31519i
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$		0			0
$119$	−12.0000	+	20.7846i	−1.10004	+	1.90532i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$	6.00000	+	10.3923i	0.541002	+	0.937043i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	0.906977	−	0.421180i	$-0.138384\pi$
$127$	1.00000	+	1.73205i	0.0887357	+	0.153695i	−0.818241	+	0.574875i	$0.805051\pi$
$128$		0			0
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$		0			0
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	14.0000	+	10.3923i	1.21395	+	0.901127i
$134$		0			0
$135$	−2.00000	+	3.46410i	−0.172133	+	0.298142i
$136$		0			0
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	0.999893	+	0.0146279i	$0.00465636\pi$
$137$	6.00000	+	10.3923i	0.512615	+	0.887875i	−0.487278	+	0.873247i	$0.662010\pi$
$138$		0			0
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		0			0
$141$	−12.0000			−1.01058
$142$		0			0
$143$	3.00000	+	5.19615i	0.250873	+	0.434524i
$144$		0			0
$145$	3.00000			0.249136
$146$		0			0
$147$	−9.00000	+	15.5885i	−0.742307	+	1.28571i
$148$		0			0
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		0			0
$151$	−17.0000			−1.38344			−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000			−1.38344			−0.691720	+	0.722166i	$0.743147\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	3.50000	−	6.06218i	0.281127	−	0.486926i
$156$		0			0
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$		0			0
$159$	−12.0000			−0.951662
$160$		0			0
$161$		0			0
$162$		0			0
$163$	10.0000			0.783260			0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000			0.783260			0.391630	+	0.920123i	$0.371911\pi$
$164$		0			0
$165$	−3.00000	−	5.19615i	−0.233550	−	0.404520i
$166$		0			0
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	0.500000	−	4.33013i	0.0382360	−	0.331133i
$172$		0			0
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$		0			0
$177$	−15.0000	−	25.9808i	−1.12747	−	1.95283i
$178$		0			0
$179$	9.00000			0.672692			0.336346	−	0.941739i	$-0.390809\pi$
$179$	9.00000			0.672692			0.336346	+	0.941739i	$0.390809\pi$
$180$		0			0
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	0.826465	−	0.562988i	$-0.190348\pi$
$181$	−1.00000	−	1.73205i	−0.0743294	−	0.128742i	−0.900794	+	0.434246i	$0.857015\pi$
$182$		0			0
$183$	10.0000			0.739221
$184$		0			0
$185$	4.00000	−	6.92820i	0.294086	−	0.509372i
$186$		0			0
$187$	9.00000	−	15.5885i	0.658145	−	1.13994i
$188$		0			0
$189$	−16.0000			−1.16383
$190$		0			0
$191$	15.0000			1.08536			0.542681	−	0.839939i	$-0.317409\pi$
$191$	15.0000			1.08536			0.542681	+	0.839939i	$0.317409\pi$
$192$		0			0
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	−0.420096	−	0.907480i	$-0.638004\pi$
$193$	8.00000	−	13.8564i	0.575853	−	0.997406i	0.995948	−	0.0899262i	$-0.0286631\pi$
$194$		0			0
$195$	2.00000	−	3.46410i	0.143223	−	0.248069i
$196$		0			0
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	−9.50000	−	16.4545i	−0.673437	−	1.16643i	−0.976923	−	0.213591i	$-0.931484\pi$
$199$	−9.50000	−	16.4545i	−0.673437	−	1.16643i	0.303486	−	0.952836i	$-0.401849\pi$
$200$		0			0
$201$	−4.00000			−0.282138
$202$		0			0
$203$	6.00000	+	10.3923i	0.421117	+	0.729397i
$204$		0			0
$205$	−3.00000	−	5.19615i	−0.209529	−	0.362915i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−10.5000	−	7.79423i	−0.726300	−	0.539138i
$210$		0			0
$211$	−3.50000	+	6.06218i	−0.240950	+	0.417338i	−0.960985	−	0.276600i	$-0.910792\pi$
$211$	−3.50000	+	6.06218i	−0.240950	+	0.417338i	0.720035	+	0.693938i	$0.244126\pi$
$212$		0			0
$213$	−3.00000	−	5.19615i	−0.205557	−	0.356034i
$214$		0			0
$215$	2.00000	+	3.46410i	0.136399	+	0.236250i
$216$		0			0
$217$	28.0000			1.90076
$218$		0			0
$219$	−8.00000	−	13.8564i	−0.540590	−	0.936329i
$220$		0			0
$221$	12.0000			0.807207
$222$		0			0
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	−0.925188	−	0.379509i	$-0.876093\pi$
$223$	−2.00000	+	3.46410i	−0.133930	+	0.231973i	0.791258	+	0.611482i	$0.209426\pi$
$224$		0			0
$225$	−0.500000	+	0.866025i	−0.0333333	+	0.0577350i
$226$		0			0
$227$	24.0000			1.59294			0.796468	−	0.604681i	$-0.206699\pi$
$227$	24.0000			1.59294			0.796468	+	0.604681i	$0.206699\pi$
$228$		0			0
$229$	−7.00000			−0.462573			−0.231287	−	0.972886i	$-0.574293\pi$
$229$	−7.00000			−0.462573			−0.231287	+	0.972886i	$0.574293\pi$
$230$		0			0
$231$	12.0000	−	20.7846i	0.789542	−	1.36753i
$232$		0			0
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	−0.947403	−	0.320043i	$-0.896303\pi$
$233$	−3.00000	+	5.19615i	−0.196537	+	0.340411i	0.750867	+	0.660454i	$0.229636\pi$
$234$		0			0
$235$	6.00000			0.391397
$236$		0			0
$237$	5.00000	+	8.66025i	0.324785	+	0.562544i
$238$		0			0
$239$	3.00000			0.194054			0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000			0.194054			0.0970269	+	0.995282i	$0.469067\pi$
$240$		0			0
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	0.774202	−	0.632938i	$-0.218151\pi$
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	−0.935242	+	0.354010i	$0.884818\pi$
$242$		0			0
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$		0			0
$245$	4.50000	−	7.79423i	0.287494	−	0.497955i
$246$		0			0
$247$	1.00000	−	8.66025i	0.0636285	−	0.551039i
$248$		0			0
$249$	12.0000	−	20.7846i	0.760469	−	1.31717i
$250$		0			0
$251$	−7.50000	−	12.9904i	−0.473396	−	0.819946i	0.526140	−	0.850398i	$-0.323639\pi$
$251$	−7.50000	−	12.9904i	−0.473396	−	0.819946i	−0.999536	+	0.0304521i	$0.990305\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$	−12.0000			−0.751469
$256$		0			0
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	0.997374	+	0.0724199i	$0.0230722\pi$
$257$	9.00000	+	15.5885i	0.561405	+	0.972381i	−0.435970	+	0.899961i	$0.643595\pi$
$258$		0			0
$259$	32.0000			1.98838
$260$		0			0
$261$	1.50000	−	2.59808i	0.0928477	−	0.160817i
$262$		0			0
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$		0			0
$265$	6.00000			0.368577
$266$		0			0
$267$	−30.0000			−1.83597
$268$		0			0
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	−0.345192	−	0.938532i	$-0.612186\pi$
$269$	10.5000	−	18.1865i	0.640196	−	1.10885i	0.985389	−	0.170321i	$-0.0544803\pi$
$270$		0			0
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	−0.649211	−	0.760609i	$-0.724901\pi$
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	0.983312	+	0.181928i	$0.0582339\pi$
$272$		0			0
$273$	16.0000			0.968364
$274$		0			0
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$		0			0
$277$	8.00000			0.480673			0.240337	−	0.970690i	$-0.422742\pi$
$277$	8.00000			0.480673			0.240337	+	0.970690i	$0.422742\pi$
$278$		0			0
$279$	−3.50000	−	6.06218i	−0.209540	−	0.362933i
$280$		0			0
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$		0			0
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	−0.579437	−	0.815017i	$-0.696728\pi$
$283$	7.00000	−	12.1244i	0.416107	−	0.720718i	0.995544	+	0.0942988i	$0.0300609\pi$
$284$		0			0
$285$	−1.00000	+	8.66025i	−0.0592349	+	0.512989i
$286$		0			0
$287$	12.0000	−	20.7846i	0.708338	−	1.22688i
$288$		0			0
$289$	−9.50000	−	16.4545i	−0.558824	−	0.967911i
$290$		0			0
$291$	−8.00000	−	13.8564i	−0.468968	−	0.812277i
$292$		0			0
$293$	24.0000			1.40209			0.701047	−	0.713115i	$-0.252716\pi$
$293$	24.0000			1.40209			0.701047	+	0.713115i	$0.252716\pi$
$294$		0			0
$295$	7.50000	+	12.9904i	0.436667	+	0.756329i
$296$		0			0
$297$	12.0000			0.696311
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−8.00000	+	13.8564i	−0.461112	+	0.798670i
$302$		0			0
$303$	30.0000			1.72345
$304$		0			0
$305$	−5.00000			−0.286299
$306$		0			0
$307$	−17.0000	+	29.4449i	−0.970241	+	1.68051i	−0.275421	+	0.961324i	$0.588817\pi$
$307$	−17.0000	+	29.4449i	−0.970241	+	1.68051i	−0.694820	+	0.719183i	$0.744516\pi$
$308$		0			0
$309$	−16.0000	+	27.7128i	−0.910208	+	1.57653i
$310$		0			0
$311$	−24.0000			−1.36092			−0.680458	−	0.732787i	$-0.738219\pi$
$311$	−24.0000			−1.36092			−0.680458	+	0.732787i	$0.738219\pi$
$312$		0			0
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$		0			0
$315$	−4.00000			−0.225374
$316$		0			0
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	−0.976764	−	0.214318i	$-0.931247\pi$
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	0.302777	−	0.953062i	$-0.402086\pi$
$318$		0			0
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−24.0000	+	10.3923i	−1.33540	+	0.578243i
$324$		0			0
$325$	−1.00000	+	1.73205i	−0.0554700	+	0.0960769i
$326$		0			0
$327$	−11.0000	−	19.0526i	−0.608301	−	1.05361i
$328$		0			0
$329$	12.0000	+	20.7846i	0.661581	+	1.14589i
$330$		0			0
$331$	4.00000			0.219860			0.109930	−	0.993939i	$-0.464937\pi$
$331$	4.00000			0.219860			0.109930	+	0.993939i	$0.464937\pi$
$332$		0			0
$333$	−4.00000	−	6.92820i	−0.219199	−	0.379663i
$334$		0			0
$335$	2.00000			0.109272
$336$		0			0
$337$	8.00000	−	13.8564i	0.435788	−	0.754807i	−0.561572	−	0.827428i	$-0.689803\pi$
$337$	8.00000	−	13.8564i	0.435788	−	0.754807i	0.997360	+	0.0726214i	$0.0231365\pi$
$338$		0			0
$339$	−6.00000	+	10.3923i	−0.325875	+	0.564433i
$340$		0			0
$341$	−21.0000			−1.13721
$342$		0			0
$343$	8.00000			0.431959
$344$		0			0
$345$		0			0
$346$		0			0
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	14.0000			0.749403			0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000			0.749403			0.374701	+	0.927146i	$0.377745\pi$
$350$		0			0
$351$	4.00000	+	6.92820i	0.213504	+	0.369800i
$352$		0			0
$353$	12.0000			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$354$		0			0
$355$	1.50000	+	2.59808i	0.0796117	+	0.137892i
$356$		0			0
$357$	−24.0000	−	41.5692i	−1.27021	−	2.20008i
$358$		0			0
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	5.50000	+	18.1865i	0.289474	+	0.957186i
$362$		0			0
$363$	2.00000	−	3.46410i	0.104973	−	0.181818i
$364$		0			0
$365$	4.00000	+	6.92820i	0.209370	+	0.362639i
$366$		0			0
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	0.809093	−	0.587680i	$-0.199959\pi$
$367$	−2.00000	−	3.46410i	−0.104399	−	0.180825i	−0.913493	+	0.406855i	$0.866625\pi$
$368$		0			0
$369$	−6.00000			−0.312348
$370$		0			0
$371$	12.0000	+	20.7846i	0.623009	+	1.07908i
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$	1.00000	−	1.73205i	0.0516398	−	0.0894427i
$376$		0			0
$377$	3.00000	−	5.19615i	0.154508	−	0.267615i
$378$		0			0
$379$	37.0000			1.90056			0.950281	−	0.311393i	$-0.100796\pi$
$379$	37.0000			1.90056			0.950281	+	0.311393i	$0.100796\pi$
$380$		0			0
$381$	−4.00000			−0.204926
$382$		0			0
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	−0.173005	−	0.984921i	$-0.555348\pi$
$383$	15.0000	−	25.9808i	0.766464	−	1.32755i	0.939469	−	0.342634i	$-0.111319\pi$
$384$		0			0
$385$	−6.00000	+	10.3923i	−0.305788	+	0.529641i
$386$		0			0
$387$	4.00000			0.203331
$388$		0			0
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	12.0000	+	20.7846i	0.605320	+	1.04844i
$394$		0			0
$395$	−2.50000	−	4.33013i	−0.125789	−	0.217872i
$396$		0			0
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	−0.948772	−	0.315963i	$-0.897673\pi$
$397$	−4.00000	+	6.92820i	−0.200754	+	0.347717i	0.748017	+	0.663679i	$0.231006\pi$
$398$		0			0
$399$	−32.0000	+	13.8564i	−1.60200	+	0.693688i
$400$		0			0
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	−0.0787327	−	0.996896i	$-0.525087\pi$
$401$	16.5000	−	28.5788i	0.823971	−	1.42716i	0.902703	−	0.430263i	$-0.141579\pi$
$402$		0			0
$403$	−7.00000	−	12.1244i	−0.348695	−	0.603957i
$404$		0			0
$405$	−5.50000	−	9.52628i	−0.273297	−	0.473365i
$406$		0			0
$407$	−24.0000			−1.18964
$408$		0			0
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	−0.996701	−	0.0811615i	$-0.974137\pi$
$409$	−11.5000	−	19.9186i	−0.568638	−	0.984911i	0.428063	−	0.903749i	$-0.359196\pi$
$410$		0			0
$411$	−24.0000			−1.18383
$412$		0			0
$413$	−30.0000	+	51.9615i	−1.47620	+	2.55686i
$414$		0			0
$415$	−6.00000	+	10.3923i	−0.294528	+	0.510138i
$416$		0			0
$417$	32.0000			1.56705
$418$		0			0
$419$	3.00000			0.146560			0.0732798	−	0.997311i	$-0.476653\pi$
$419$	3.00000			0.146560			0.0732798	+	0.997311i	$0.476653\pi$
$420$		0			0
$421$	9.50000	−	16.4545i	0.463002	−	0.801942i	−0.536107	−	0.844150i	$-0.680106\pi$
$421$	9.50000	−	16.4545i	0.463002	−	0.801942i	0.999109	+	0.0422075i	$0.0134391\pi$
$422$		0			0
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$		0			0
$425$	6.00000			0.291043
$426$		0			0
$427$	−10.0000	−	17.3205i	−0.483934	−	0.838198i
$428$		0			0
$429$	−12.0000			−0.579365
$430$		0			0
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	0.626907	−	0.779094i	$-0.284321\pi$
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	−0.988169	+	0.153370i	$0.950987\pi$
$432$		0			0
$433$	−4.00000	−	6.92820i	−0.192228	−	0.332948i	0.753760	−	0.657149i	$-0.228238\pi$
$433$	−4.00000	−	6.92820i	−0.192228	−	0.332948i	−0.945988	+	0.324201i	$0.894905\pi$
$434$		0			0
$435$	−3.00000	+	5.19615i	−0.143839	+	0.249136i
$436$		0			0
$437$		0			0
$438$		0			0
$439$	−6.50000	+	11.2583i	−0.310228	+	0.537331i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−6.50000	+	11.2583i	−0.310228	+	0.537331i	0.668184	+	0.743996i	$0.267072\pi$
$440$		0			0
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$		0			0
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	0.687557	−	0.726130i	$-0.258683\pi$
$443$	−6.00000	−	10.3923i	−0.285069	−	0.493753i	−0.972626	+	0.232377i	$0.925350\pi$
$444$		0			0
$445$	15.0000			0.711068
$446$		0			0
$447$	−3.00000	−	5.19615i	−0.141895	−	0.245770i
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	−9.00000	+	15.5885i	−0.423793	+	0.734032i
$452$		0			0
$453$	17.0000	−	29.4449i	0.798730	−	1.38344i
$454$		0			0
$455$	−8.00000			−0.375046
$456$		0			0
$457$	−22.0000			−1.02912			−0.514558	−	0.857455i	$-0.672044\pi$
$457$	−22.0000			−1.02912			−0.514558	+	0.857455i	$0.672044\pi$
$458$		0			0
$459$	12.0000	−	20.7846i	0.560112	−	0.970143i
$460$		0			0
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	−0.741998	−	0.670402i	$-0.766122\pi$
$461$	4.50000	−	7.79423i	0.209586	−	0.363013i	0.951584	+	0.307388i	$0.0994551\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$		0			0
$465$	7.00000	+	12.1244i	0.324617	+	0.562254i
$466$		0			0
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$		0			0
$469$	4.00000	+	6.92820i	0.184703	+	0.319915i
$470$		0			0
$471$	−2.00000	−	3.46410i	−0.0921551	−	0.159617i
$472$		0			0
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$		0			0
$475$	0.500000	−	4.33013i	0.0229416	−	0.198680i
$476$		0			0
$477$	3.00000	−	5.19615i	0.137361	−	0.237915i
$478$		0			0
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	0.984930	−	0.172953i	$-0.0553307\pi$
$479$	7.50000	+	12.9904i	0.342684	+	0.593546i	−0.642246	+	0.766498i	$0.721997\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	4.00000	+	6.92820i	0.181631	+	0.314594i
$486$		0			0
$487$	−2.00000			−0.0906287			−0.0453143	−	0.998973i	$-0.514429\pi$
$487$	−2.00000			−0.0906287			−0.0453143	+	0.998973i	$0.514429\pi$
$488$		0			0
$489$	−10.0000	+	17.3205i	−0.452216	+	0.783260i
$490$		0			0
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	−0.984145	−	0.177365i	$-0.943243\pi$
$491$	−7.50000	+	12.9904i	−0.338470	+	0.586248i	0.645675	+	0.763612i	$0.276576\pi$
$492$		0			0
$493$	−18.0000			−0.810679
$494$		0			0
$495$	3.00000			0.134840
$496$		0			0
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$		0			0
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	−0.550572	−	0.834788i	$-0.685590\pi$
$499$	10.0000	−	17.3205i	0.447661	−	0.775372i	0.998233	+	0.0594153i	$0.0189236\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−21.0000	−	36.3731i	−0.936344	−	1.62179i	−0.772220	−	0.635355i	$-0.780854\pi$
$503$	−21.0000	−	36.3731i	−0.936344	−	1.62179i	−0.164124	−	0.986440i	$-0.552480\pi$
$504$		0			0
$505$	−15.0000			−0.667491
$506$		0			0
$507$	9.00000	+	15.5885i	0.399704	+	0.692308i
$508$		0			0
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	0.993593	−	0.113020i	$-0.0360525\pi$
$509$	9.00000	+	15.5885i	0.398918	+	0.690946i	−0.594675	+	0.803966i	$0.702719\pi$
$510$		0			0
$511$	−16.0000	+	27.7128i	−0.707798	+	1.22594i
$512$		0			0
$513$	−14.0000	−	10.3923i	−0.618115	−	0.458831i
$514$		0			0
$515$	8.00000	−	13.8564i	0.352522	−	0.610586i
$516$		0			0
$517$	−9.00000	−	15.5885i	−0.395820	−	0.685580i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−45.0000			−1.97149			−0.985743	−	0.168259i	$-0.946186\pi$
$521$	−45.0000			−1.97149			−0.985743	+	0.168259i	$0.946186\pi$
$522$		0			0
$523$	13.0000	+	22.5167i	0.568450	+	0.984585i	0.996719	+	0.0809336i	$0.0257902\pi$
$523$	13.0000	+	22.5167i	0.568450	+	0.984585i	−0.428269	+	0.903651i	$0.640876\pi$
$524$		0			0
$525$	8.00000			0.349149
$526$		0			0
$527$	−21.0000	+	36.3731i	−0.914774	+	1.58444i
$528$		0			0
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	15.0000			0.650945
$532$		0			0
$533$	−12.0000			−0.519778
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−9.00000	+	15.5885i	−0.388379	+	0.672692i
$538$		0			0
$539$	−27.0000			−1.16297
$540$		0			0
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	0.922599	+	0.385759i	$0.126061\pi$
$541$	18.5000	+	32.0429i	0.795377	+	1.37763i	−0.127222	+	0.991874i	$0.540606\pi$
$542$		0			0
$543$	4.00000			0.171656
$544$		0			0
$545$	5.50000	+	9.52628i	0.235594	+	0.408061i
$546$		0			0
$547$	−2.00000	−	3.46410i	−0.0855138	−	0.148114i	0.820096	−	0.572226i	$-0.193920\pi$
$547$	−2.00000	−	3.46410i	−0.0855138	−	0.148114i	−0.905610	+	0.424111i	$0.860587\pi$
$548$		0			0
$549$	−2.50000	+	4.33013i	−0.106697	+	0.184805i
$550$		0			0
$551$	−1.50000	+	12.9904i	−0.0639021	+	0.553409i
$552$		0			0
$553$	10.0000	−	17.3205i	0.425243	−	0.736543i
$554$		0			0
$555$	8.00000	+	13.8564i	0.339581	+	0.588172i
$556$		0			0
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	0.710457	−	0.703740i	$-0.248488\pi$
$557$	−6.00000	−	10.3923i	−0.254228	−	0.440336i	−0.964686	+	0.263404i	$0.915155\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$		0			0
$561$	18.0000	+	31.1769i	0.759961	+	1.31629i
$562$		0			0
$563$	−6.00000			−0.252870			−0.126435	−	0.991975i	$-0.540353\pi$
$563$	−6.00000			−0.252870			−0.126435	+	0.991975i	$0.540353\pi$
$564$		0			0
$565$	3.00000	−	5.19615i	0.126211	−	0.218604i
$566$		0			0
$567$	22.0000	−	38.1051i	0.923913	−	1.60026i
$568$		0			0
$569$	39.0000			1.63497			0.817483	−	0.575953i	$-0.195369\pi$
$569$	39.0000			1.63497			0.817483	+	0.575953i	$0.195369\pi$
$570$		0			0
$571$	7.00000			0.292941			0.146470	−	0.989215i	$-0.453209\pi$
$571$	7.00000			0.292941			0.146470	+	0.989215i	$0.453209\pi$
$572$		0			0
$573$	−15.0000	+	25.9808i	−0.626634	+	1.08536i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−16.0000			−0.666089			−0.333044	−	0.942911i	$-0.608076\pi$
$577$	−16.0000			−0.666089			−0.333044	+	0.942911i	$0.608076\pi$
$578$		0			0
$579$	16.0000	+	27.7128i	0.664937	+	1.15171i
$580$		0			0
$581$	−48.0000			−1.99138
$582$		0			0
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$		0			0
$585$	1.00000	+	1.73205i	0.0413449	+	0.0716115i
$586$		0			0
$587$	−18.0000	+	31.1769i	−0.742940	+	1.28681i	0.208212	+	0.978084i	$0.433236\pi$
$587$	−18.0000	+	31.1769i	−0.742940	+	1.28681i	−0.951151	+	0.308725i	$0.900098\pi$
$588$		0			0
$589$	24.5000	+	18.1865i	1.00950	+	0.749363i
$590$		0			0
$591$	18.0000	−	31.1769i	0.740421	−	1.28245i
$592$		0			0
$593$	−6.00000	−	10.3923i	−0.246390	−	0.426761i	0.716131	−	0.697966i	$-0.245911\pi$
$593$	−6.00000	−	10.3923i	−0.246390	−	0.426761i	−0.962522	+	0.271205i	$0.912578\pi$
$594$		0			0
$595$	12.0000	+	20.7846i	0.491952	+	0.852086i
$596$		0			0
$597$	38.0000			1.55524
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−31.0000			−1.26452			−0.632258	−	0.774758i	$-0.717872\pi$
$601$	−31.0000			−1.26452			−0.632258	+	0.774758i	$0.717872\pi$
$602$		0			0
$603$	1.00000	−	1.73205i	0.0407231	−	0.0705346i
$604$		0			0
$605$	−1.00000	+	1.73205i	−0.0406558	+	0.0704179i
$606$		0			0
$607$	−2.00000			−0.0811775			−0.0405887	−	0.999176i	$-0.512923\pi$
$607$	−2.00000			−0.0811775			−0.0405887	+	0.999176i	$0.512923\pi$
$608$		0			0
$609$	−24.0000			−0.972529
$610$		0			0
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$		0			0
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$		0			0
$615$	12.0000			0.483887
$616$		0			0
$617$	−18.0000	−	31.1769i	−0.724653	−	1.25514i	−0.959117	−	0.283011i	$-0.908667\pi$
$617$	−18.0000	−	31.1769i	−0.724653	−	1.25514i	0.234464	−	0.972125i	$-0.424666\pi$
$618$		0			0
$619$	4.00000			0.160774			0.0803868	−	0.996764i	$-0.474384\pi$
$619$	4.00000			0.160774			0.0803868	+	0.996764i	$0.474384\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	30.0000	+	51.9615i	1.20192	+	2.08179i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	24.0000	−	10.3923i	0.958468	−	0.415029i
$628$		0			0
$629$	−24.0000	+	41.5692i	−0.956943	+	1.65747i
$630$		0			0
$631$	−9.50000	−	16.4545i	−0.378189	−	0.655043i	0.612610	−	0.790386i	$-0.290120\pi$
$631$	−9.50000	−	16.4545i	−0.378189	−	0.655043i	−0.990799	+	0.135343i	$0.956786\pi$
$632$		0			0
$633$	−7.00000	−	12.1244i	−0.278225	−	0.481900i
$634$		0			0
$635$	2.00000			0.0793676
$636$		0			0
$637$	−9.00000	−	15.5885i	−0.356593	−	0.617637i
$638$		0			0
$639$	3.00000			0.118678
$640$		0			0
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	−0.941106	−	0.338112i	$-0.890212\pi$
$641$	−4.50000	+	7.79423i	−0.177739	+	0.307854i	0.763367	+	0.645966i	$0.223545\pi$
$642$		0			0
$643$	−17.0000	+	29.4449i	−0.670415	+	1.16119i	0.307372	+	0.951589i	$0.400550\pi$
$643$	−17.0000	+	29.4449i	−0.670415	+	1.16119i	−0.977787	+	0.209603i	$0.932783\pi$
$644$		0			0
$645$	−8.00000			−0.315000
$646$		0			0
$647$	−18.0000			−0.707653			−0.353827	−	0.935311i	$-0.615120\pi$
$647$	−18.0000			−0.707653			−0.353827	+	0.935311i	$0.615120\pi$
$648$		0			0
$649$	22.5000	−	38.9711i	0.883202	−	1.52975i
$650$		0			0
$651$	−28.0000	+	48.4974i	−1.09741	+	1.90076i
$652$		0			0
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$		0			0
$655$	−6.00000	−	10.3923i	−0.234439	−	0.406061i
$656$		0			0
$657$	8.00000			0.312110
$658$		0			0
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	0.813302	−	0.581842i	$-0.197668\pi$
$661$	−2.50000	−	4.33013i	−0.0972387	−	0.168422i	−0.910541	+	0.413419i	$0.864334\pi$
$662$		0			0
$663$	−12.0000	+	20.7846i	−0.466041	+	0.807207i
$664$		0			0
$665$	16.0000	−	6.92820i	0.620453	−	0.268664i
$666$		0			0
$667$		0			0
$668$		0			0
$669$	−4.00000	−	6.92820i	−0.154649	−	0.267860i
$670$		0			0
$671$	7.50000	+	12.9904i	0.289534	+	0.501488i
$672$		0			0
$673$	−4.00000			−0.154189			−0.0770943	−	0.997024i	$-0.524564\pi$
$673$	−4.00000			−0.154189			−0.0770943	+	0.997024i	$0.524564\pi$
$674$		0			0
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$		0			0
$677$	48.0000			1.84479			0.922395	−	0.386248i	$-0.126229\pi$
$677$	48.0000			1.84479			0.922395	+	0.386248i	$0.126229\pi$
$678$		0			0
$679$	−16.0000	+	27.7128i	−0.614024	+	1.06352i
$680$		0			0
$681$	−24.0000	+	41.5692i	−0.919682	+	1.59294i
$682$		0			0
$683$	18.0000			0.688751			0.344375	−	0.938832i	$-0.388091\pi$
$683$	18.0000			0.688751			0.344375	+	0.938832i	$0.388091\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$	7.00000	−	12.1244i	0.267067	−	0.462573i
$688$		0			0
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	37.0000			1.40755			0.703773	−	0.710425i	$-0.251497\pi$
$691$	37.0000			1.40755			0.703773	+	0.710425i	$0.251497\pi$
$692$		0			0
$693$	6.00000	+	10.3923i	0.227921	+	0.394771i
$694$		0			0
$695$	−16.0000			−0.606915
$696$		0			0
$697$	18.0000	+	31.1769i	0.681799	+	1.18091i
$698$		0			0
$699$	−6.00000	−	10.3923i	−0.226941	−	0.393073i
$700$		0			0
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	−0.917102	−	0.398652i	$-0.869478\pi$
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	0.803794	+	0.594908i	$0.202811\pi$
$702$		0			0
$703$	28.0000	+	20.7846i	1.05604	+	0.783906i
$704$		0			0
$705$	−6.00000	+	10.3923i	−0.225973	+	0.391397i
$706$		0			0
$707$	−30.0000	−	51.9615i	−1.12827	−	1.95421i
$708$		0			0
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	0.995228	+	0.0975728i	$0.0311079\pi$
$709$	15.5000	+	26.8468i	0.582115	+	1.00825i	−0.413114	+	0.910679i	$0.635559\pi$
$710$		0			0
$711$	−5.00000			−0.187515
$712$		0			0
$713$		0			0
$714$		0			0
$715$	6.00000			0.224387
$716$		0			0
$717$	−3.00000	+	5.19615i	−0.112037	+	0.194054i
$718$		0			0
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	−0.691608	−	0.722273i	$-0.743097\pi$
$719$	7.50000	−	12.9904i	0.279703	−	0.484459i	0.971311	+	0.237814i	$0.0764307\pi$
$720$		0			0
$721$	64.0000			2.38348
$722$		0			0
$723$	10.0000			0.371904
$724$		0			0
$725$	1.50000	−	2.59808i	0.0557086	−	0.0964901i
$726$		0			0
$727$	7.00000	−	12.1244i	0.259616	−	0.449667i	−0.706523	−	0.707690i	$-0.749737\pi$
$727$	7.00000	−	12.1244i	0.259616	−	0.449667i	0.966139	+	0.258022i	$0.0830708\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$		0			0
$733$	32.0000			1.18195			0.590973	−	0.806691i	$-0.298744\pi$
$733$	32.0000			1.18195			0.590973	+	0.806691i	$0.298744\pi$
$734$		0			0
$735$	9.00000	+	15.5885i	0.331970	+	0.574989i
$736$		0			0
$737$	−3.00000	−	5.19615i	−0.110506	−	0.191403i
$738$		0			0
$739$	17.5000	−	30.3109i	0.643748	−	1.11500i	−0.340841	−	0.940121i	$-0.610712\pi$
$739$	17.5000	−	30.3109i	0.643748	−	1.11500i	0.984589	−	0.174883i	$-0.0559548\pi$
$740$		0			0
$741$	14.0000	+	10.3923i	0.514303	+	0.381771i
$742$		0			0
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	−0.997707	−	0.0676840i	$-0.978439\pi$
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	0.557470	+	0.830197i	$0.311772\pi$
$744$		0			0
$745$	1.50000	+	2.59808i	0.0549557	+	0.0951861i
$746$		0			0
$747$	6.00000	+	10.3923i	0.219529	+	0.380235i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−3.50000	−	6.06218i	−0.127717	−	0.221212i	0.795075	−	0.606511i	$-0.207432\pi$
$751$	−3.50000	−	6.06218i	−0.127717	−	0.221212i	−0.922792	+	0.385299i	$0.874098\pi$
$752$		0			0
$753$	30.0000			1.09326
$754$		0			0
$755$	−8.50000	+	14.7224i	−0.309347	+	0.535804i
$756$		0			0
$757$	5.00000	−	8.66025i	0.181728	−	0.314762i	−0.760741	−	0.649056i	$-0.775164\pi$
$757$	5.00000	−	8.66025i	0.181728	−	0.314762i	0.942469	+	0.334293i	$0.108498\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$		0			0
$763$	−22.0000	+	38.1051i	−0.796453	+	1.37950i
$764$		0			0
$765$	3.00000	−	5.19615i	0.108465	−	0.187867i
$766$		0			0
$767$	30.0000			1.08324
$768$		0			0
$769$	−14.5000	−	25.1147i	−0.522883	−	0.905661i	−0.999645	−	0.0266282i	$-0.991523\pi$
$769$	−14.5000	−	25.1147i	−0.522883	−	0.905661i	0.476762	−	0.879032i	$-0.341810\pi$
$770$		0			0
$771$	−36.0000			−1.29651
$772$		0			0
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	−0.998930	−	0.0462427i	$-0.985275\pi$
$773$	−15.0000	−	25.9808i	−0.539513	−	0.934463i	0.459418	−	0.888220i	$-0.348058\pi$
$774$		0			0
$775$	−3.50000	−	6.06218i	−0.125724	−	0.217760i
$776$		0			0
$777$	−32.0000	+	55.4256i	−1.14799	+	1.98838i
$778$		0			0
$779$	24.0000	−	10.3923i	0.859889	−	0.372343i
$780$		0			0
$781$	4.50000	−	7.79423i	0.161023	−	0.278899i
$782$		0			0
$783$	−6.00000	−	10.3923i	−0.214423	−	0.371391i
$784$		0			0
$785$	1.00000	+	1.73205i	0.0356915	+	0.0618195i
$786$		0			0
$787$	34.0000			1.21197			0.605985	−	0.795476i	$-0.292779\pi$
$787$	34.0000			1.21197			0.605985	+	0.795476i	$0.292779\pi$
$788$		0			0
$789$	−18.0000	−	31.1769i	−0.640817	−	1.10993i
$790$		0			0
$791$	24.0000			0.853342
$792$		0			0
$793$	−5.00000	+	8.66025i	−0.177555	+	0.307535i
$794$		0			0
$795$	−6.00000	+	10.3923i	−0.212798	+	0.368577i
$796$		0			0
$797$	−30.0000			−1.06265			−0.531327	−	0.847167i	$-0.678307\pi$
$797$	−30.0000			−1.06265			−0.531327	+	0.847167i	$0.678307\pi$
$798$		0			0
$799$	−36.0000			−1.27359
$800$		0			0
$801$	7.50000	−	12.9904i	0.264999	−	0.458993i
$802$		0			0
$803$	12.0000	−	20.7846i	0.423471	−	0.733473i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	21.0000	+	36.3731i	0.739235	+	1.28039i
$808$		0			0
$809$	−27.0000			−0.949269			−0.474635	−	0.880183i	$-0.657420\pi$
$809$	−27.0000			−0.949269			−0.474635	+	0.880183i	$0.657420\pi$
$810$		0			0
$811$	−21.5000	−	37.2391i	−0.754967	−	1.30764i	−0.945391	−	0.325939i	$-0.894319\pi$
$811$	−21.5000	−	37.2391i	−0.754967	−	1.30764i	0.190424	−	0.981702i	$-0.439014\pi$
$812$		0			0
$813$	11.0000	+	19.0526i	0.385787	+	0.668202i
$814$		0			0
$815$	5.00000	−	8.66025i	0.175142	−	0.303355i
$816$		0			0
$817$	−16.0000	+	6.92820i	−0.559769	+	0.242387i
$818$		0			0
$819$	−4.00000	+	6.92820i	−0.139771	+	0.242091i
$820$		0			0
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	0.891013	−	0.453978i	$-0.149995\pi$
$821$	1.50000	+	2.59808i	0.0523504	+	0.0906735i	−0.838663	+	0.544651i	$0.816662\pi$
$822$		0			0
$823$	−11.0000	−	19.0526i	−0.383436	−	0.664130i	0.608115	−	0.793849i	$-0.291926\pi$
$823$	−11.0000	−	19.0526i	−0.383436	−	0.664130i	−0.991551	+	0.129719i	$0.958593\pi$
$824$		0			0
$825$	−6.00000			−0.208893
$826$		0			0
$827$	−21.0000	−	36.3731i	−0.730242	−	1.26482i	−0.956780	−	0.290813i	$-0.906074\pi$
$827$	−21.0000	−	36.3731i	−0.730242	−	1.26482i	0.226538	−	0.974002i	$-0.427259\pi$
$828$		0			0
$829$	26.0000			0.903017			0.451509	−	0.892267i	$-0.350886\pi$
$829$	26.0000			0.903017			0.451509	+	0.892267i	$0.350886\pi$
$830$		0			0
$831$	−8.00000	+	13.8564i	−0.277517	+	0.480673i
$832$		0			0
$833$	−27.0000	+	46.7654i	−0.935495	+	1.62032i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−28.0000			−0.967822
$838$		0			0
$839$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$839$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$		0			0
$843$	12.0000			0.413302
$844$		0			0
$845$	−4.50000	−	7.79423i	−0.154805	−	0.268130i
$846$		0			0
$847$	−8.00000			−0.274883
$848$		0			0
$849$	14.0000	+	24.2487i	0.480479	+	0.832214i
$850$		0			0
$851$		0			0
$852$		0			0
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	−0.960621	−	0.277862i	$-0.910374\pi$
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	0.720946	+	0.692992i	$0.243708\pi$
$854$		0			0
$855$	−3.50000	−	2.59808i	−0.119697	−	0.0888523i
$856$		0			0
$857$	−18.0000	+	31.1769i	−0.614868	+	1.06498i	0.375539	+	0.926806i	$0.377458\pi$
$857$	−18.0000	+	31.1769i	−0.614868	+	1.06498i	−0.990408	+	0.138177i	$0.955876\pi$
$858$		0			0
$859$	−3.50000	−	6.06218i	−0.119418	−	0.206839i	0.800119	−	0.599841i	$-0.204770\pi$
$859$	−3.50000	−	6.06218i	−0.119418	−	0.206839i	−0.919537	+	0.393003i	$0.871436\pi$
$860$		0			0
$861$	24.0000	+	41.5692i	0.817918	+	1.41668i
$862$		0			0
$863$	−18.0000			−0.612727			−0.306364	−	0.951915i	$-0.599112\pi$
$863$	−18.0000			−0.612727			−0.306364	+	0.951915i	$0.599112\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	38.0000			1.29055
$868$		0			0
$869$	−7.50000	+	12.9904i	−0.254420	+	0.440668i
$870$		0			0
$871$	2.00000	−	3.46410i	0.0677674	−	0.117377i
$872$		0			0
$873$	8.00000			0.270759
$874$		0			0
$875$	−4.00000			−0.135225
$876$		0			0
$877$	26.0000	−	45.0333i	0.877958	−	1.52067i	0.0243792	−	0.999703i	$-0.492239\pi$
$877$	26.0000	−	45.0333i	0.877958	−	1.52067i	0.853578	−	0.520964i	$-0.174428\pi$
$878$		0			0
$879$	−24.0000	+	41.5692i	−0.809500	+	1.40209i
$880$		0			0
$881$	9.00000			0.303218			0.151609	−	0.988441i	$-0.451555\pi$
$881$	9.00000			0.303218			0.151609	+	0.988441i	$0.451555\pi$
$882$		0			0
$883$	4.00000	+	6.92820i	0.134611	+	0.233153i	0.925449	−	0.378873i	$-0.123688\pi$
$883$	4.00000	+	6.92820i	0.134611	+	0.233153i	−0.790838	+	0.612026i	$0.790355\pi$
$884$		0			0
$885$	−30.0000			−1.00844
$886$		0			0
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$	4.00000	+	6.92820i	0.134156	+	0.232364i
$890$		0			0
$891$	−16.5000	+	28.5788i	−0.552771	+	0.957427i
$892$		0			0
$893$	−3.00000	+	25.9808i	−0.100391	+	0.869413i
$894$		0			0
$895$	4.50000	−	7.79423i	0.150418	−	0.260532i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	10.5000	+	18.1865i	0.350195	+	0.606555i
$900$		0			0
$901$	−36.0000			−1.19933
$902$		0			0
$903$	−16.0000	−	27.7128i	−0.532447	−	0.922225i
$904$		0			0
$905$	−2.00000			−0.0664822
$906$		0			0
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	−0.791944	−	0.610594i	$-0.790931\pi$
$907$	4.00000	−	6.92820i	0.132818	−	0.230047i	0.924762	+	0.380547i	$0.124264\pi$
$908$		0			0
$909$	−7.50000	+	12.9904i	−0.248759	+	0.430864i
$910$		0			0
$911$	−21.0000			−0.695761			−0.347881	−	0.937539i	$-0.613099\pi$
$911$	−21.0000			−0.695761			−0.347881	+	0.937539i	$0.613099\pi$
$912$		0			0
$913$	36.0000			1.19143
$914$		0			0
$915$	5.00000	−	8.66025i	0.165295	−	0.286299i
$916$		0			0
$917$	24.0000	−	41.5692i	0.792550	−	1.37274i
$918$		0			0
$919$	−8.00000			−0.263896			−0.131948	−	0.991257i	$-0.542123\pi$
$919$	−8.00000			−0.263896			−0.131948	+	0.991257i	$0.542123\pi$
$920$		0			0
$921$	−34.0000	−	58.8897i	−1.12034	−	1.94048i
$922$		0			0
$923$	6.00000			0.197492
$924$		0			0
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$		0			0
$927$	−8.00000	−	13.8564i	−0.262754	−	0.455104i
$928$		0			0
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	−0.997905	−	0.0646999i	$-0.979391\pi$
$929$	−13.5000	+	23.3827i	−0.442921	+	0.767161i	0.554984	+	0.831861i	$0.312724\pi$
$930$		0			0
$931$	31.5000	+	23.3827i	1.03237	+	0.766337i
$932$		0			0
$933$	24.0000	−	41.5692i	0.785725	−	1.36092i
$934$		0			0
$935$	−9.00000	−	15.5885i	−0.294331	−	0.509797i
$936$		0			0
$937$	23.0000	+	39.8372i	0.751377	+	1.30142i	0.947155	+	0.320775i	$0.103943\pi$
$937$	23.0000	+	39.8372i	0.751377	+	1.30142i	−0.195778	+	0.980648i	$0.562723\pi$
$938$		0			0
$939$	−20.0000			−0.652675
$940$		0			0
$941$	4.50000	+	7.79423i	0.146696	+	0.254085i	0.930004	−	0.367549i	$-0.119803\pi$
$941$	4.50000	+	7.79423i	0.146696	+	0.254085i	−0.783309	+	0.621633i	$0.786469\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$	−8.00000	+	13.8564i	−0.260240	+	0.450749i
$946$		0			0
$947$	−9.00000	+	15.5885i	−0.292461	+	0.506557i	−0.974391	−	0.224860i	$-0.927807\pi$
$947$	−9.00000	+	15.5885i	−0.292461	+	0.506557i	0.681930	+	0.731417i	$0.261141\pi$
$948$		0			0
$949$	16.0000			0.519382
$950$		0			0
$951$	48.0000			1.55651
$952$		0			0
$953$	6.00000	−	10.3923i	0.194359	−	0.336640i	−0.752331	−	0.658785i	$-0.771071\pi$
$953$	6.00000	−	10.3923i	0.194359	−	0.336640i	0.946690	+	0.322145i	$0.104404\pi$
$954$		0			0
$955$	7.50000	−	12.9904i	0.242694	−	0.420359i
$956$		0			0
$957$	18.0000			0.581857
$958$		0			0
$959$	24.0000	+	41.5692i	0.775000	+	1.34234i
$960$		0			0
$961$	18.0000			0.580645
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−8.00000	−	13.8564i	−0.257529	−	0.446054i
$966$		0			0
$967$	−8.00000	+	13.8564i	−0.257263	+	0.445592i	−0.965508	−	0.260375i	$-0.916154\pi$
$967$	−8.00000	+	13.8564i	−0.257263	+	0.445592i	0.708245	+	0.705967i	$0.249487\pi$
$968$		0			0
$969$	6.00000	−	51.9615i	0.192748	−	1.66924i
$970$		0			0
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$		0			0
$973$	−32.0000	−	55.4256i	−1.02587	−	1.77686i
$974$		0			0
$975$	−2.00000	−	3.46410i	−0.0640513	−	0.110940i
$976$		0			0
$977$	−12.0000			−0.383914			−0.191957	−	0.981403i	$-0.561483\pi$
$977$	−12.0000			−0.383914			−0.191957	+	0.981403i	$0.561483\pi$
$978$		0			0
$979$	−22.5000	−	38.9711i	−0.719103	−	1.24552i
$980$		0			0
$981$	11.0000			0.351203
$982$		0			0
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	0.422027	+	0.906583i	$0.361319\pi$
$983$	−18.0000	+	31.1769i	−0.574111	+	0.994389i	−0.996138	+	0.0878058i	$0.972015\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$	−48.0000			−1.52786
$988$		0			0
$989$		0			0
$990$		0			0
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$		0			0
$993$	−4.00000	+	6.92820i	−0.126936	+	0.219860i
$994$		0			0
$995$	−19.0000			−0.602340
$996$		0			0
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	0.985961	−	0.166978i	$-0.0534008\pi$
$997$	11.0000	+	19.0526i	0.348373	+	0.603401i	−0.637587	+	0.770378i	$0.720067\pi$
$998$		0			0
$999$	−32.0000			−1.01244

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1520.2.q.c.961.1		2
4.3	odd	2		95.2.e.a.11.1	✓	2
12.11	even	2		855.2.k.b.676.1		2
19.7	even	3	inner	1520.2.q.c.881.1		2
20.3	even	4		475.2.j.a.49.2		4
20.7	even	4		475.2.j.a.49.1		4
20.19	odd	2		475.2.e.b.201.1		2
76.7	odd	6		95.2.e.a.26.1	yes	2
76.11	odd	6		1805.2.a.a.1.1		1
76.27	even	6		1805.2.a.b.1.1		1
228.83	even	6		855.2.k.b.406.1		2
380.7	even	12		475.2.j.a.349.2		4
380.83	even	12		475.2.j.a.349.1		4
380.159	odd	6		475.2.e.b.26.1		2
380.179	even	6		9025.2.a.e.1.1		1
380.239	odd	6		9025.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.e.a.11.1	✓	2	4.3	odd	2
95.2.e.a.26.1	yes	2	76.7	odd	6
475.2.e.b.26.1		2	380.159	odd	6
475.2.e.b.201.1		2	20.19	odd	2
475.2.j.a.49.1		4	20.7	even	4
475.2.j.a.49.2		4	20.3	even	4
475.2.j.a.349.1		4	380.83	even	12
475.2.j.a.349.2		4	380.7	even	12
855.2.k.b.406.1		2	228.83	even	6
855.2.k.b.676.1		2	12.11	even	2
1520.2.q.c.881.1		2	19.7	even	3	inner
1520.2.q.c.961.1		2	1.1	even	1	trivial
1805.2.a.a.1.1		1	76.11	odd	6
1805.2.a.b.1.1		1	76.27	even	6
9025.2.a.e.1.1		1	380.179	even	6
9025.2.a.g.1.1		1	380.239	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1520 = 2^{4} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1520.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{3} +(0.500000 - 0.866025i) q^{5} +4.00000 q^{7} +(-0.500000 - 0.866025i) q^{9} -3.00000 q^{11} +(-1.00000 - 1.73205i) q^{13} +(1.00000 + 1.73205i) q^{15} +(-3.00000 + 5.19615i) q^{17} +(3.50000 + 2.59808i) q^{19} +(-4.00000 + 6.92820i) q^{21} +(-0.500000 - 0.866025i) q^{25} -4.00000 q^{27} +(1.50000 + 2.59808i) q^{29} +7.00000 q^{31} +(3.00000 - 5.19615i) q^{33} +(2.00000 - 3.46410i) q^{35} +8.00000 q^{37} +4.00000 q^{39} +(3.00000 - 5.19615i) q^{41} +(-2.00000 + 3.46410i) q^{43} -1.00000 q^{45} +(3.00000 + 5.19615i) q^{47} +9.00000 q^{49} +(-6.00000 - 10.3923i) q^{51} +(3.00000 + 5.19615i) q^{53} +(-1.50000 + 2.59808i) q^{55} +(-8.00000 + 3.46410i) q^{57} +(-7.50000 + 12.9904i) q^{59} +(-2.50000 - 4.33013i) q^{61} +(-2.00000 - 3.46410i) q^{63} -2.00000 q^{65} +(1.00000 + 1.73205i) q^{67} +(-1.50000 + 2.59808i) q^{71} +(-4.00000 + 6.92820i) q^{73} +2.00000 q^{75} -12.0000 q^{77} +(2.50000 - 4.33013i) q^{79} +(5.50000 - 9.52628i) q^{81} -12.0000 q^{83} +(3.00000 + 5.19615i) q^{85} -6.00000 q^{87} +(7.50000 + 12.9904i) q^{89} +(-4.00000 - 6.92820i) q^{91} +(-7.00000 + 12.1244i) q^{93} +(4.00000 - 1.73205i) q^{95} +(-4.00000 + 6.92820i) q^{97} +(1.50000 + 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + q^{5} + 8 q^{7} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^3 + q^5 + 8 * q^7 - q^9	\( 2 q - 2 q^{3} + q^{5} + 8 q^{7} - q^{9} - 6 q^{11} - 2 q^{13} + 2 q^{15} - 6 q^{17} + 7 q^{19} - 8 q^{21} - q^{25} - 8 q^{27} + 3 q^{29} + 14 q^{31} + 6 q^{33} + 4 q^{35} + 16 q^{37} + 8 q^{39} + 6 q^{41} - 4 q^{43} - 2 q^{45} + 6 q^{47} + 18 q^{49} - 12 q^{51} + 6 q^{53} - 3 q^{55} - 16 q^{57} - 15 q^{59} - 5 q^{61} - 4 q^{63} - 4 q^{65} + 2 q^{67} - 3 q^{71} - 8 q^{73} + 4 q^{75} - 24 q^{77} + 5 q^{79} + 11 q^{81} - 24 q^{83} + 6 q^{85} - 12 q^{87} + 15 q^{89} - 8 q^{91} - 14 q^{93} + 8 q^{95} - 8 q^{97} + 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + q^5 + 8 * q^7 - q^9 - 6 * q^11 - 2 * q^13 + 2 * q^15 - 6 * q^17 + 7 * q^19 - 8 * q^21 - q^25 - 8 * q^27 + 3 * q^29 + 14 * q^31 + 6 * q^33 + 4 * q^35 + 16 * q^37 + 8 * q^39 + 6 * q^41 - 4 * q^43 - 2 * q^45 + 6 * q^47 + 18 * q^49 - 12 * q^51 + 6 * q^53 - 3 * q^55 - 16 * q^57 - 15 * q^59 - 5 * q^61 - 4 * q^63 - 4 * q^65 + 2 * q^67 - 3 * q^71 - 8 * q^73 + 4 * q^75 - 24 * q^77 + 5 * q^79 + 11 * q^81 - 24 * q^83 + 6 * q^85 - 12 * q^87 + 15 * q^89 - 8 * q^91 - 14 * q^93 + 8 * q^95 - 8 * q^97 + 3 * q^99

Introduction

L-functions

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Database

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