LMFDB - Embedded newform 640.2.q.f.609.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(289,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("640.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.q (of order $4$, 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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	16.0.534694406811304329216.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2x^{14} - 2x^{12} + 4x^{10} + 4x^{8} + 16x^{6} - 32x^{4} - 128x^{2} + 256 $ x^16 - 2x^14 - 2x^12 + 4x^10 + 4x^8 + 16x^6 - 32x^4 - 128*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			609.6
Root			$-0.841995 + 1.13624i$ of defining polynomial
Character	$\chi$	$=$	640.609
Dual form			640.2.q.f.289.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.734294 + 0.734294i) q^{3} +(1.17216 - 1.90421i) q^{5} -1.71452 q^{7} -1.92163i q^{9} +(2.82684 + 2.82684i) q^{11} +(2.59462 + 2.59462i) q^{13} +(2.25896 - 0.537540i) q^{15} -1.89939i q^{17} +(2.89623 - 2.89623i) q^{19} +(-1.25896 - 1.25896i) q^{21} -2.00613 q^{23} +(-2.25207 - 4.46410i) q^{25} +(3.61392 - 3.61392i) q^{27} +(6.72307 - 6.72307i) q^{29} +7.11778 q^{31} +4.15146i q^{33} +(-2.00970 + 3.26482i) q^{35} +(-2.25207 + 2.25207i) q^{37} +3.81042i q^{39} -1.59630i q^{41} +(-8.06886 + 8.06886i) q^{43} +(-3.65919 - 2.25246i) q^{45} +4.43823i q^{47} -4.06040 q^{49} +(1.39471 - 1.39471i) q^{51} +(-0.481758 + 0.481758i) q^{53} +(8.69642 - 2.06939i) q^{55} +4.25336 q^{57} +(3.08580 + 3.08580i) q^{59} +(-3.46410 + 3.46410i) q^{61} +3.29468i q^{63} +(7.98203 - 1.89939i) q^{65} +(1.80454 + 1.80454i) q^{67} +(-1.47309 - 1.47309i) q^{69} +0.379150i q^{71} +8.37718 q^{73} +(1.62428 - 4.93164i) q^{75} +(-4.84668 - 4.84668i) q^{77} -11.2566 q^{79} -0.457524 q^{81} +(-8.24890 - 8.24890i) q^{83} +(-3.61685 - 2.22640i) q^{85} +9.87341 q^{87} +11.9820i q^{89} +(-4.44854 - 4.44854i) q^{91} +(5.22654 + 5.22654i) q^{93} +(-2.12019 - 8.90989i) q^{95} -6.50543i q^{97} +(5.43213 - 5.43213i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{5} + 8 q^{11} - 8 q^{19} + 16 q^{21} + 16 q^{29} - 16 q^{31} - 24 q^{35} - 8 q^{45} + 16 q^{49} - 16 q^{51} - 24 q^{59} - 32 q^{69} + 48 q^{75} - 16 q^{79} - 16 q^{81} - 16 q^{91} - 32 q^{95}+ \cdots + 88 q^{99}+O(q^{100}) $ 16 * q + 8 * q^5 + 8 * q^11 - 8 * q^19 + 16 * q^21 + 16 * q^29 - 16 * q^31 - 24 * q^35 - 8 * q^45 + 16 * q^49 - 16 * q^51 - 24 * q^59 - 32 * q^69 + 48 * q^75 - 16 * q^79 - 16 * q^81 - 16 * q^91 - 32 * q^95 + 88 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	0.734294	+	0.734294i	0.423945	+	0.423945i	0.886559	−	0.462615i	$-0.153089\pi$
$3$	0.734294	+	0.734294i	0.423945	+	0.423945i	−0.462615	+	0.886559i	$0.653089\pi$
$4$		0			0
$5$	1.17216	−	1.90421i	0.524207	−	0.851591i
$5$	1.17216	−	1.90421i	0.524207	−	0.851591i
$6$		0			0
$7$	−1.71452			−0.648029			−0.324015	−	0.946052i	$-0.605033\pi$
$7$	−1.71452			−0.648029			−0.324015	+	0.946052i	$0.605033\pi$
$8$		0			0
$9$		−	1.92163i		−	0.640542i
$10$		0			0
$11$	2.82684	+	2.82684i	0.852324	+	0.852324i	0.990419	−	0.138095i	$-0.0440980\pi$
$11$	2.82684	+	2.82684i	0.852324	+	0.852324i	−0.138095	+	0.990419i	$0.544098\pi$
$12$		0			0
$13$	2.59462	+	2.59462i	0.719618	+	0.719618i	0.968527	−	0.248909i	$-0.0800720\pi$
$13$	2.59462	+	2.59462i	0.719618	+	0.719618i	−0.248909	+	0.968527i	$0.580072\pi$
$14$		0			0
$15$	2.25896	−	0.537540i	0.583262	−	0.138792i
$16$		0			0
$17$		−	1.89939i		−	0.460671i	−0.973111	−	0.230335i	$-0.926018\pi$
$17$		−	1.89939i		−	0.460671i	0.973111	−	0.230335i	$-0.0739823\pi$
$18$		0			0
$19$	2.89623	−	2.89623i	0.664440	−	0.664440i	−0.291983	−	0.956423i	$-0.594315\pi$
$19$	2.89623	−	2.89623i	0.664440	−	0.664440i	0.956423	+	0.291983i	$0.0943151\pi$
$20$		0			0
$21$	−1.25896	−	1.25896i	−0.274729	−	0.274729i
$22$		0			0
$23$	−2.00613			−0.418306			−0.209153	−	0.977883i	$-0.567071\pi$
$23$	−2.00613			−0.418306			−0.209153	+	0.977883i	$0.567071\pi$
$24$		0			0
$25$	−2.25207	−	4.46410i	−0.450413	−	0.892820i
$26$		0			0
$27$	3.61392	−	3.61392i	0.695499	−	0.695499i
$28$		0			0
$29$	6.72307	−	6.72307i	1.24844	−	1.24844i	0.292034	−	0.956408i	$-0.405668\pi$
$29$	6.72307	−	6.72307i	1.24844	−	1.24844i	0.956408	−	0.292034i	$-0.0943321\pi$
$30$		0			0
$31$	7.11778			1.27839			0.639195	−	0.769044i	$-0.279268\pi$
$31$	7.11778			1.27839			0.639195	+	0.769044i	$0.279268\pi$
$32$		0			0
$33$			4.15146i			0.722676i
$34$		0			0
$35$	−2.00970	+	3.26482i	−0.339702	+	0.551856i
$36$		0			0
$37$	−2.25207	+	2.25207i	−0.370237	+	0.370237i	−0.867564	−	0.497326i	$-0.834315\pi$
$37$	−2.25207	+	2.25207i	−0.370237	+	0.370237i	0.497326	+	0.867564i	$0.334315\pi$
$38$		0			0
$39$			3.81042i			0.610156i
$40$		0			0
$41$		−	1.59630i		−	0.249301i	−0.992201	−	0.124650i	$-0.960219\pi$
$41$		−	1.59630i		−	0.249301i	0.992201	−	0.124650i	$-0.0397809\pi$
$42$		0			0
$43$	−8.06886	+	8.06886i	−1.23049	+	1.23049i	−0.266715	+	0.963776i	$0.585938\pi$
$43$	−8.06886	+	8.06886i	−1.23049	+	1.23049i	−0.963776	+	0.266715i	$0.914062\pi$
$44$		0			0
$45$	−3.65919	−	2.25246i	−0.545480	−	0.335777i
$46$		0			0
$47$			4.43823i			0.647383i	0.946163	+	0.323691i	$0.104924\pi$
$47$			4.43823i			0.647383i	−0.946163	+	0.323691i	$0.895076\pi$
$48$		0			0
$49$	−4.06040			−0.580058
$50$		0			0
$51$	1.39471	−	1.39471i	0.195299	−	0.195299i
$52$		0			0
$53$	−0.481758	+	0.481758i	−0.0661746	+	0.0661746i	−0.739420	−	0.673245i	$-0.764900\pi$
$53$	−0.481758	+	0.481758i	−0.0661746	+	0.0661746i	0.673245	+	0.739420i	$0.264900\pi$
$54$		0			0
$55$	8.69642	−	2.06939i	1.17263	−	0.279036i
$56$		0			0
$57$	4.25336			0.563372
$58$		0			0
$59$	3.08580	+	3.08580i	0.401737	+	0.401737i	0.878845	−	0.477108i	$-0.158315\pi$
$59$	3.08580	+	3.08580i	0.401737	+	0.401737i	−0.477108	+	0.878845i	$0.658315\pi$
$60$		0			0
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	−0.893197	−	0.449665i	$-0.851543\pi$
$61$	−3.46410	+	3.46410i	−0.443533	+	0.443533i	0.449665	+	0.893197i	$0.351543\pi$
$62$		0			0
$63$			3.29468i			0.415090i
$64$		0			0
$65$	7.98203	−	1.89939i	0.990049	−	0.235591i
$66$		0			0
$67$	1.80454	+	1.80454i	0.220460	+	0.220460i	0.808692	−	0.588232i	$-0.200176\pi$
$67$	1.80454	+	1.80454i	0.220460	+	0.220460i	−0.588232	+	0.808692i	$0.700176\pi$
$68$		0			0
$69$	−1.47309	−	1.47309i	−0.177339	−	0.177339i
$70$		0			0
$71$			0.379150i			0.0449969i	0.999747	+	0.0224984i	$0.00716208\pi$
$71$			0.379150i			0.0449969i	−0.999747	+	0.0224984i	$0.992838\pi$
$72$		0			0
$73$	8.37718			0.980475			0.490237	−	0.871589i	$-0.336910\pi$
$73$	8.37718			0.980475			0.490237	+	0.871589i	$0.336910\pi$
$74$		0			0
$75$	1.62428	−	4.93164i	0.187556	−	0.569456i
$76$		0			0
$77$	−4.84668	−	4.84668i	−0.552331	−	0.552331i
$78$		0			0
$79$	−11.2566			−1.26646			−0.633231	−	0.773963i	$-0.718272\pi$
$79$	−11.2566			−1.26646			−0.633231	+	0.773963i	$0.718272\pi$
$80$		0			0
$81$	−0.457524			−0.0508360
$82$		0			0
$83$	−8.24890	−	8.24890i	−0.905435	−	0.905435i	0.0904649	−	0.995900i	$-0.471165\pi$
$83$	−8.24890	−	8.24890i	−0.905435	−	0.905435i	−0.995900	+	0.0904649i	$0.971165\pi$
$84$		0			0
$85$	−3.61685	−	2.22640i	−0.392303	−	0.241487i
$86$		0			0
$87$	9.87341			1.05854
$88$		0			0
$89$			11.9820i			1.27009i	0.772474	+	0.635046i	$0.219019\pi$
$89$			11.9820i			1.27009i	−0.772474	+	0.635046i	$0.780981\pi$
$90$		0			0
$91$	−4.44854	−	4.44854i	−0.466334	−	0.466334i
$92$		0			0
$93$	5.22654	+	5.22654i	0.541967	+	0.541967i
$94$		0			0
$95$	−2.12019	−	8.90989i	−0.217526	−	0.914136i
$96$		0			0
$97$		−	6.50543i		−	0.660526i	−0.943889	−	0.330263i	$-0.892863\pi$
$97$		−	6.50543i		−	0.660526i	0.943889	−	0.330263i	$-0.107137\pi$
$98$		0			0
$99$	5.43213	−	5.43213i	0.545949	−	0.545949i
$100$		0			0
$101$	6.72307	+	6.72307i	0.668970	+	0.668970i	0.957478	−	0.288508i	$-0.0931590\pi$
$101$	6.72307	+	6.72307i	0.668970	+	0.668970i	−0.288508	+	0.957478i	$0.593159\pi$
$102$		0			0
$103$	−15.1733			−1.49506			−0.747532	−	0.664225i	$-0.768762\pi$
$103$	−15.1733			−1.49506			−0.747532	+	0.664225i	$0.768762\pi$
$104$		0			0
$105$	−3.87305	+	0.921626i	−0.377971	+	0.0899415i
$106$		0			0
$107$	−1.69781	+	1.69781i	−0.164134	+	0.164134i	−0.784395	−	0.620262i	$-0.787026\pi$
$107$	−1.69781	+	1.69781i	−0.164134	+	0.164134i	0.620262	+	0.784395i	$0.287026\pi$
$108$		0			0
$109$	−3.11120	+	3.11120i	−0.297999	+	0.297999i	−0.840230	−	0.542231i	$-0.817580\pi$
$109$	−3.11120	+	3.11120i	−0.297999	+	0.297999i	0.542231	+	0.840230i	$0.317580\pi$
$110$		0			0
$111$	−3.30735			−0.313920
$112$		0			0
$113$			15.8259i			1.48877i	0.667748	+	0.744387i	$0.267258\pi$
$113$			15.8259i			1.48877i	−0.667748	+	0.744387i	$0.732742\pi$
$114$		0			0
$115$	−2.35151	+	3.82010i	−0.219279	+	0.356226i
$116$		0			0
$117$	4.98589	−	4.98589i	0.460946	−	0.460946i
$118$		0			0
$119$			3.25656i			0.298528i
$120$		0			0
$121$			4.98203i			0.452912i
$122$		0			0
$123$	1.17216	−	1.17216i	0.105690	−	0.105690i
$124$		0			0
$125$	−11.1404	−	0.944243i	−0.996427	−	0.0844556i
$126$		0			0
$127$		−	18.3239i		−	1.62598i	−0.582276	−	0.812991i	$-0.697838\pi$
$127$		−	18.3239i		−	1.62598i	0.582276	−	0.812991i	$-0.302162\pi$
$128$		0			0
$129$	−11.8498			−1.04332
$130$		0			0
$131$	−10.2036	+	10.2036i	−0.891491	+	0.891491i	−0.994663	−	0.103172i	$-0.967101\pi$
$131$	−10.2036	+	10.2036i	−0.891491	+	0.891491i	0.103172	+	0.994663i	$0.467101\pi$
$132$		0			0
$133$	−4.96565	+	4.96565i	−0.430577	+	0.430577i
$134$		0			0
$135$	−2.64557	−	11.1178i	−0.227695	−	0.956866i
$136$		0			0
$137$	−14.9845			−1.28021			−0.640107	−	0.768286i	$-0.721110\pi$
$137$	−14.9845			−1.28021			−0.640107	+	0.768286i	$0.721110\pi$
$138$		0			0
$139$	−8.29094	−	8.29094i	−0.703228	−	0.703228i	0.261874	−	0.965102i	$-0.415660\pi$
$139$	−8.29094	−	8.29094i	−0.703228	−	0.703228i	−0.965102	+	0.261874i	$0.915660\pi$
$140$		0			0
$141$	−3.25896	+	3.25896i	−0.274454	+	0.274454i
$142$		0			0
$143$			14.6691i			1.22670i
$144$		0			0
$145$	−4.92163	−	20.6827i	−0.408719	−	1.71760i
$146$		0			0
$147$	−2.98153	−	2.98153i	−0.245912	−	0.245912i
$148$		0			0
$149$	7.30735	+	7.30735i	0.598642	+	0.598642i	0.939951	−	0.341309i	$-0.110870\pi$
$149$	7.30735	+	7.30735i	0.598642	+	0.598642i	−0.341309	+	0.939951i	$0.610870\pi$
$150$		0			0
$151$		−	4.56873i		−	0.371798i	−0.982569	−	0.185899i	$-0.940480\pi$
$151$		−	4.56873i		−	0.371798i	0.982569	−	0.185899i	$-0.0595197\pi$
$152$		0			0
$153$	−3.64992			−0.295079
$154$		0			0
$155$	8.34320	−	13.5538i	0.670142	−	1.08867i
$156$		0			0
$157$	1.52966	+	1.52966i	0.122080	+	0.122080i	0.765507	−	0.643427i	$-0.222488\pi$
$157$	1.52966	+	1.52966i	0.122080	+	0.122080i	−0.643427	+	0.765507i	$0.722488\pi$
$158$		0			0
$159$	−0.707504			−0.0561087
$160$		0			0
$161$	3.43955			0.271075
$162$		0			0
$163$	10.1361	+	10.1361i	0.793918	+	0.793918i	0.982129	−	0.188211i	$-0.0602689\pi$
$163$	10.1361	+	10.1361i	0.793918	+	0.793918i	−0.188211	+	0.982129i	$0.560269\pi$
$164$		0			0
$165$	7.90527	+	4.86619i	0.615424	+	0.378832i
$166$		0			0
$167$	−2.57967			−0.199621			−0.0998105	−	0.995006i	$-0.531824\pi$
$167$	−2.57967			−0.199621			−0.0998105	+	0.995006i	$0.531824\pi$
$168$		0			0
$169$			0.464102i			0.0357001i
$170$		0			0
$171$	−5.56547	−	5.56547i	−0.425602	−	0.425602i
$172$		0			0
$173$	14.1773	+	14.1773i	1.07788	+	1.07788i	0.996700	+	0.0811779i	$0.0258682\pi$
$173$	14.1773	+	14.1773i	1.07788	+	1.07788i	0.0811779	+	0.996700i	$0.474132\pi$
$174$		0			0
$175$	3.86122	+	7.65381i	0.291881	+	0.578574i
$176$		0			0
$177$			4.53177i			0.340629i
$178$		0			0
$179$	−9.88067	+	9.88067i	−0.738516	+	0.738516i	−0.972291	−	0.233775i	$-0.924892\pi$
$179$	−9.88067	+	9.88067i	−0.738516	+	0.738516i	0.233775	+	0.972291i	$0.424892\pi$
$180$		0			0
$181$	−6.20514	−	6.20514i	−0.461224	−	0.461224i	0.437832	−	0.899057i	$-0.355746\pi$
$181$	−6.20514	−	6.20514i	−0.461224	−	0.461224i	−0.899057	+	0.437832i	$0.855746\pi$
$182$		0			0
$183$	−5.08733			−0.376067
$184$		0			0
$185$	1.64863	+	6.92820i	0.121209	+	0.509372i
$186$		0			0
$187$	5.36928	−	5.36928i	0.392641	−	0.392641i
$188$		0			0
$189$	−6.19615	+	6.19615i	−0.450704	+	0.450704i
$190$		0			0
$191$	−18.9282			−1.36960			−0.684798	−	0.728733i	$-0.740110\pi$
$191$	−18.9282			−1.36960			−0.684798	+	0.728733i	$0.740110\pi$
$192$		0			0
$193$			4.42987i			0.318869i	0.987209	+	0.159434i	$0.0509670\pi$
$193$			4.42987i			0.318869i	−0.987209	+	0.159434i	$0.949033\pi$
$194$		0			0
$195$	7.25587	+	4.46644i	0.519603	+	0.319849i
$196$		0			0
$197$	6.39341	−	6.39341i	0.455511	−	0.455511i	−0.441667	−	0.897179i	$-0.645613\pi$
$197$	6.39341	−	6.39341i	0.455511	−	0.455511i	0.897179	+	0.441667i	$0.145613\pi$
$198$		0			0
$199$		−	5.85641i		−	0.415150i	−0.978219	−	0.207575i	$-0.933443\pi$
$199$		−	5.85641i		−	0.415150i	0.978219	−	0.207575i	$-0.0665570\pi$
$200$		0			0
$201$			2.65013i			0.186926i
$202$		0			0
$203$	−11.5269	+	11.5269i	−0.809027	+	0.809027i
$204$		0			0
$205$	−3.03970	−	1.87113i	−0.212302	−	0.130685i
$206$		0			0
$207$			3.85503i			0.267943i
$208$		0			0
$209$	16.3743			1.13264
$210$		0			0
$211$	7.60373	−	7.60373i	0.523462	−	0.523462i	−0.395153	−	0.918615i	$-0.629308\pi$
$211$	7.60373	−	7.60373i	0.523462	−	0.523462i	0.918615	+	0.395153i	$0.129308\pi$
$212$		0			0
$213$	−0.278408	+	0.278408i	−0.0190762	+	0.0190762i
$214$		0			0
$215$	5.90682	+	24.8229i	0.402842	+	1.69291i
$216$		0			0
$217$	−12.2036			−0.828435
$218$		0			0
$219$	6.15131	+	6.15131i	0.415667	+	0.415667i
$220$		0			0
$221$	4.92820	−	4.92820i	0.331507	−	0.331507i
$222$		0			0
$223$		−	9.22430i		−	0.617705i	−0.951110	−	0.308853i	$-0.900055\pi$
$223$		−	9.22430i		−	0.617705i	0.951110	−	0.308853i	$-0.0999450\pi$
$224$		0			0
$225$	−8.57833	+	4.32763i	−0.571889	+	0.288508i
$226$		0			0
$227$	9.21725	+	9.21725i	0.611770	+	0.611770i	0.943407	−	0.331637i	$-0.107601\pi$
$227$	9.21725	+	9.21725i	0.611770	+	0.611770i	−0.331637	+	0.943407i	$0.607601\pi$
$228$		0			0
$229$	−1.63811	−	1.63811i	−0.108250	−	0.108250i	0.650907	−	0.759157i	$-0.274389\pi$
$229$	−1.63811	−	1.63811i	−0.108250	−	0.108250i	−0.759157	+	0.650907i	$0.774389\pi$
$230$		0			0
$231$		−	7.11778i		−	0.468315i
$232$		0			0
$233$	12.3798			0.811026			0.405513	−	0.914089i	$-0.367093\pi$
$233$	12.3798			0.811026			0.405513	+	0.914089i	$0.367093\pi$
$234$		0			0
$235$	8.45134	+	5.20233i	0.551305	+	0.339363i
$236$		0			0
$237$	−8.26562	−	8.26562i	−0.536910	−	0.536910i
$238$		0			0
$239$	7.77449			0.502890			0.251445	−	0.967872i	$-0.419094\pi$
$239$	7.77449			0.502890			0.251445	+	0.967872i	$0.419094\pi$
$240$		0			0
$241$	−3.47068			−0.223566			−0.111783	−	0.993733i	$-0.535656\pi$
$241$	−3.47068			−0.223566			−0.111783	+	0.993733i	$0.535656\pi$
$242$		0			0
$243$	−11.1777	−	11.1777i	−0.717051	−	0.717051i
$244$		0			0
$245$	−4.75946	+	7.73188i	−0.304071	+	0.493972i
$246$		0			0
$247$	15.0292			0.956286
$248$		0			0
$249$		−	12.1142i		−	0.767708i
$250$		0			0
$251$	8.94765	+	8.94765i	0.564771	+	0.564771i	0.930659	−	0.365888i	$-0.119235\pi$
$251$	8.94765	+	8.94765i	0.564771	+	0.564771i	−0.365888	+	0.930659i	$0.619235\pi$
$252$		0			0
$253$	−5.67100	−	5.67100i	−0.356533	−	0.356533i
$254$		0			0
$255$	−1.02100	−	4.29066i	−0.0639375	−	0.268692i
$256$		0			0
$257$			3.62228i			0.225952i	0.993598	+	0.112976i	$0.0360383\pi$
$257$			3.62228i			0.225952i	−0.993598	+	0.112976i	$0.963962\pi$
$258$		0			0
$259$	3.86122	−	3.86122i	0.239925	−	0.239925i
$260$		0			0
$261$	−12.9192	−	12.9192i	−0.799680	−	0.799680i
$262$		0			0
$263$	−13.7416			−0.847345			−0.423673	−	0.905815i	$-0.639259\pi$
$263$	−13.7416			−0.847345			−0.423673	+	0.905815i	$0.639259\pi$
$264$		0			0
$265$	0.352672	+	1.48207i	0.0216644	+	0.0910429i
$266$		0			0
$267$	−8.79833	+	8.79833i	−0.538449	+	0.538449i
$268$		0			0
$269$	4.22240	−	4.22240i	0.257444	−	0.257444i	−0.566570	−	0.824014i	$-0.691730\pi$
$269$	4.22240	−	4.22240i	0.257444	−	0.257444i	0.824014	+	0.566570i	$0.191730\pi$
$270$		0			0
$271$	5.40015			0.328036			0.164018	−	0.986457i	$-0.447555\pi$
$271$	5.40015			0.328036			0.164018	+	0.986457i	$0.447555\pi$
$272$		0			0
$273$		−	6.53307i		−	0.395399i
$274$		0			0
$275$	6.25307	−	18.9855i	0.377074	−	1.14487i
$276$		0			0
$277$	−5.08733	+	5.08733i	−0.305668	+	0.305668i	−0.843227	−	0.537558i	$-0.819347\pi$
$277$	−5.08733	+	5.08733i	−0.305668	+	0.305668i	0.537558	+	0.843227i	$0.319347\pi$
$278$		0			0
$279$		−	13.6777i		−	0.818863i
$280$		0			0
$281$		−	21.2780i		−	1.26934i	−0.772784	−	0.634669i	$-0.781136\pi$
$281$		−	21.2780i		−	1.26934i	0.772784	−	0.634669i	$-0.218864\pi$
$282$		0			0
$283$	−4.08521	+	4.08521i	−0.242840	+	0.242840i	−0.818024	−	0.575184i	$-0.804931\pi$
$283$	−4.08521	+	4.08521i	−0.242840	+	0.242840i	0.575184	+	0.818024i	$0.304931\pi$
$284$		0			0
$285$	4.98564	−	8.09931i	0.295324	−	0.479762i
$286$		0			0
$287$			2.73690i			0.161554i
$288$		0			0
$289$	13.3923			0.787783
$290$		0			0
$291$	4.77689	−	4.77689i	0.280026	−	0.280026i
$292$		0			0
$293$	−7.40400	+	7.40400i	−0.432547	+	0.432547i	−0.889494	−	0.456947i	$-0.848943\pi$
$293$	−7.40400	+	7.40400i	−0.432547	+	0.432547i	0.456947	+	0.889494i	$0.348943\pi$
$294$		0			0
$295$	9.49310	−	2.25896i	0.552709	−	0.131522i
$296$		0			0
$297$	20.4319			1.18558
$298$		0			0
$299$	−5.20514	−	5.20514i	−0.301021	−	0.301021i
$300$		0			0
$301$	13.8343	−	13.8343i	0.797394	−	0.797394i
$302$		0			0
$303$			9.87341i			0.567212i
$304$		0			0
$305$	2.53590	+	10.6569i	0.145205	+	0.610212i
$306$		0			0
$307$	−16.6634	−	16.6634i	−0.951030	−	0.951030i	0.0478262	−	0.998856i	$-0.484771\pi$
$307$	−16.6634	−	16.6634i	−0.951030	−	0.951030i	−0.998856	+	0.0478262i	$0.984771\pi$
$308$		0			0
$309$	−11.1416	−	11.1416i	−0.633825	−	0.633825i
$310$		0			0
$311$			21.9072i			1.24224i	0.783714	+	0.621122i	$0.213323\pi$
$311$			21.9072i			1.24224i	−0.783714	+	0.621122i	$0.786677\pi$
$312$		0			0
$313$	12.4820			0.705525			0.352763	−	0.935713i	$-0.385242\pi$
$313$	12.4820			0.705525			0.352763	+	0.935713i	$0.385242\pi$
$314$		0			0
$315$	6.27377	+	3.86190i	0.353487	+	0.217593i
$316$		0			0
$317$	4.24325	+	4.24325i	0.238324	+	0.238324i	0.816156	−	0.577832i	$-0.196101\pi$
$317$	4.24325	+	4.24325i	0.238324	+	0.238324i	−0.577832	+	0.816156i	$0.696101\pi$
$318$		0			0
$319$	38.0100			2.12815
$320$		0			0
$321$	−2.49338			−0.139167
$322$		0			0
$323$	−5.50108	−	5.50108i	−0.306088	−	0.306088i
$324$		0			0
$325$	5.73939	−	17.4259i	0.318364	−	0.966615i
$326$		0			0
$327$	−4.56907			−0.252670
$328$		0			0
$329$		−	7.60946i		−	0.419523i
$330$		0			0
$331$	1.10377	+	1.10377i	0.0606688	+	0.0606688i	0.736790	−	0.676121i	$-0.236341\pi$
$331$	1.10377	+	1.10377i	0.0606688	+	0.0606688i	−0.676121	+	0.736790i	$0.736341\pi$
$332$		0			0
$333$	4.32763	+	4.32763i	0.237152	+	0.237152i
$334$		0			0
$335$	5.55146	−	1.32102i	0.303309	−	0.0721749i
$336$		0			0
$337$		−	7.47635i		−	0.407263i	−0.979048	−	0.203631i	$-0.934726\pi$
$337$		−	7.47635i		−	0.407263i	0.979048	−	0.203631i	$-0.0652744\pi$
$338$		0			0
$339$	−11.6208	+	11.6208i	−0.631158	+	0.631158i
$340$		0			0
$341$	20.1208	+	20.1208i	1.08960	+	1.08960i
$342$		0			0
$343$	18.9633			1.02392
$344$		0			0
$345$	−4.53177	+	1.07837i	−0.243982	+	0.0580577i
$346$		0			0
$347$	8.56074	−	8.56074i	0.459565	−	0.459565i	−0.438948	−	0.898512i	$-0.644649\pi$
$347$	8.56074	−	8.56074i	0.459565	−	0.459565i	0.898512	+	0.438948i	$0.144649\pi$
$348$		0			0
$349$	−7.91567	+	7.91567i	−0.423716	+	0.423716i	−0.886481	−	0.462765i	$-0.846857\pi$
$349$	−7.91567	+	7.91567i	−0.423716	+	0.423716i	0.462765	+	0.886481i	$0.346857\pi$
$350$		0			0
$351$	18.7535			1.00099
$352$		0			0
$353$		−	9.67314i		−	0.514849i	−0.966298	−	0.257425i	$-0.917126\pi$
$353$		−	9.67314i		−	0.514849i	0.966298	−	0.257425i	$-0.0828739\pi$
$354$		0			0
$355$	0.721984	+	0.444426i	0.0383189	+	0.0235877i
$356$		0			0
$357$	−2.39127	+	2.39127i	−0.126559	+	0.126559i
$358$		0			0
$359$			17.0867i			0.901799i	0.892575	+	0.450900i	$0.148897\pi$
$359$			17.0867i			0.901799i	−0.892575	+	0.450900i	$0.851103\pi$
$360$		0			0
$361$			2.22373i			0.117038i
$362$		0			0
$363$	−3.65827	+	3.65827i	−0.192010	+	0.192010i
$364$		0			0
$365$	9.81943	−	15.9519i	0.513972	−	0.834963i
$366$		0			0
$367$			13.4500i			0.702086i	0.936359	+	0.351043i	$0.114173\pi$
$367$			13.4500i			0.702086i	−0.936359	+	0.351043i	$0.885827\pi$
$368$		0			0
$369$	−3.06750			−0.159688
$370$		0			0
$371$	0.825987	−	0.825987i	0.0428831	−	0.0428831i
$372$		0			0
$373$	12.0271	−	12.0271i	0.622740	−	0.622740i	−0.323491	−	0.946231i	$-0.604857\pi$
$373$	12.0271	−	12.0271i	0.622740	−	0.622740i	0.946231	+	0.323491i	$0.104857\pi$
$374$		0			0
$375$	−7.48697	−	8.87367i	−0.386625	−	0.458234i
$376$		0			0
$377$	34.8876			1.79680
$378$		0			0
$379$	19.1552	+	19.1552i	0.983936	+	0.983936i	0.999873	−	0.0159369i	$-0.00507308\pi$
$379$	19.1552	+	19.1552i	0.983936	+	0.983936i	−0.0159369	+	0.999873i	$0.505073\pi$
$380$		0			0
$381$	13.4551	−	13.4551i	0.689327	−	0.689327i
$382$		0			0
$383$		−	17.7503i		−	0.907000i	−0.891256	−	0.453500i	$-0.850175\pi$
$383$		−	17.7503i		−	0.907000i	0.891256	−	0.453500i	$-0.149825\pi$
$384$		0			0
$385$	−14.9102	+	3.54802i	−0.759896	+	0.180824i
$386$		0			0
$387$	15.5053	+	15.5053i	0.788181	+	0.788181i
$388$		0			0
$389$	1.18654	+	1.18654i	0.0601602	+	0.0601602i	0.736547	−	0.676387i	$-0.236455\pi$
$389$	1.18654	+	1.18654i	0.0601602	+	0.0601602i	−0.676387	+	0.736547i	$0.736455\pi$
$390$		0			0
$391$			3.81042i			0.192701i
$392$		0			0
$393$	−14.9848			−0.755886
$394$		0			0
$395$	−13.1945	+	21.4349i	−0.663889	+	1.07851i
$396$		0			0
$397$	4.74478	+	4.74478i	0.238134	+	0.238134i	0.816077	−	0.577943i	$-0.196145\pi$
$397$	4.74478	+	4.74478i	0.238134	+	0.238134i	−0.577943	+	0.816077i	$0.696145\pi$
$398$		0			0
$399$	−7.29250			−0.365081
$400$		0			0
$401$	0.632677			0.0315944			0.0157972	−	0.999875i	$-0.494971\pi$
$401$	0.632677			0.0315944			0.0157972	+	0.999875i	$0.494971\pi$
$402$		0			0
$403$	18.4679	+	18.4679i	0.919953	+	0.919953i
$404$		0			0
$405$	−0.536293	+	0.871224i	−0.0266486	+	0.0432915i
$406$		0			0
$407$	−12.7324			−0.631124
$408$		0			0
$409$		−	26.3809i		−	1.30445i	−0.758024	−	0.652226i	$-0.773835\pi$
$409$		−	26.3809i		−	1.30445i	0.758024	−	0.652226i	$-0.226165\pi$
$410$		0			0
$411$	−11.0030	−	11.0030i	−0.542739	−	0.542739i
$412$		0			0
$413$	−5.29069	−	5.29069i	−0.260338	−	0.260338i
$414$		0			0
$415$	−25.3767	+	6.03862i	−1.24570	+	0.296424i
$416$		0			0
$417$		−	12.1760i		−	0.596260i
$418$		0			0
$419$	−1.37589	+	1.37589i	−0.0672167	+	0.0672167i	−0.739916	−	0.672699i	$-0.765135\pi$
$419$	−1.37589	+	1.37589i	−0.0672167	+	0.0672167i	0.672699	+	0.739916i	$0.265135\pi$
$420$		0			0
$421$	−6.65671	−	6.65671i	−0.324428	−	0.324428i	0.526035	−	0.850463i	$-0.323678\pi$
$421$	−6.65671	−	6.65671i	−0.324428	−	0.324428i	−0.850463	+	0.526035i	$0.823678\pi$
$422$		0			0
$423$	8.52862			0.414676
$424$		0			0
$425$	−8.47908	+	4.27756i	−0.411296	+	0.207492i
$426$		0			0
$427$	5.93929	−	5.93929i	0.287422	−	0.287422i
$428$		0			0
$429$	−10.7715	+	10.7715i	−0.520051	+	0.520051i
$430$		0			0
$431$	−4.08798			−0.196911			−0.0984556	−	0.995141i	$-0.531390\pi$
$431$	−4.08798			−0.196911			−0.0984556	+	0.995141i	$0.531390\pi$
$432$		0			0
$433$			29.2913i			1.40765i	0.710373	+	0.703826i	$0.248526\pi$
$433$			29.2913i			1.40765i	−0.710373	+	0.703826i	$0.751474\pi$
$434$		0			0
$435$	11.5732	−	18.8011i	0.554895	−	0.901443i
$436$		0			0
$437$	−5.81020	+	5.81020i	−0.277940	+	0.277940i
$438$		0			0
$439$		−	26.9790i		−	1.28764i	−0.765178	−	0.643819i	$-0.777349\pi$
$439$		−	26.9790i		−	1.28764i	0.765178	−	0.643819i	$-0.222651\pi$
$440$		0			0
$441$			7.80258i			0.371551i
$442$		0			0
$443$	14.5286	−	14.5286i	0.690276	−	0.690276i	−0.272017	−	0.962293i	$-0.587691\pi$
$443$	14.5286	−	14.5286i	0.690276	−	0.690276i	0.962293	+	0.272017i	$0.0876906\pi$
$444$		0			0
$445$	22.8164	+	14.0449i	1.08160	+	0.665792i
$446$		0			0
$447$			10.7315i			0.507582i
$448$		0			0
$449$	23.1572			1.09286			0.546428	−	0.837506i	$-0.315987\pi$
$449$	23.1572			1.09286			0.546428	+	0.837506i	$0.315987\pi$
$450$		0			0
$451$	4.51249	−	4.51249i	0.212485	−	0.212485i
$452$		0			0
$453$	3.35479	−	3.35479i	0.157622	−	0.157622i
$454$		0			0
$455$	−13.6854	+	3.25656i	−0.641581	+	0.152670i
$456$		0			0
$457$	−37.7026			−1.76365			−0.881827	−	0.471572i	$-0.843687\pi$
$457$	−37.7026			−1.76365			−0.881827	+	0.471572i	$0.843687\pi$
$458$		0			0
$459$	−6.86425	−	6.86425i	−0.320396	−	0.320396i
$460$		0			0
$461$	−11.3737	+	11.3737i	−0.529727	+	0.529727i	−0.920491	−	0.390764i	$-0.872211\pi$
$461$	−11.3737	+	11.3737i	−0.529727	+	0.529727i	0.390764	+	0.920491i	$0.372211\pi$
$462$		0			0
$463$			7.94895i			0.369419i	0.982793	+	0.184710i	$0.0591344\pi$
$463$			7.94895i			0.369419i	−0.982793	+	0.184710i	$0.940866\pi$
$464$		0			0
$465$	16.0788	−	3.82609i	0.745637	−	0.177431i
$466$		0			0
$467$	5.34999	+	5.34999i	0.247568	+	0.247568i	0.819972	−	0.572404i	$-0.193989\pi$
$467$	5.34999	+	5.34999i	0.247568	+	0.247568i	−0.572404	+	0.819972i	$0.693989\pi$
$468$		0			0
$469$	−3.09394	−	3.09394i	−0.142865	−	0.142865i
$470$		0			0
$471$			2.24643i			0.103510i
$472$		0			0
$473$	−45.6187			−2.09755
$474$		0			0
$475$	−19.4515	−	6.40656i	−0.892498	−	0.293953i
$476$		0			0
$477$	0.925759	+	0.925759i	0.0423876	+	0.0423876i
$478$		0			0
$479$	9.58973			0.438166			0.219083	−	0.975706i	$-0.429693\pi$
$479$	9.58973			0.438166			0.219083	+	0.975706i	$0.429693\pi$
$480$		0			0
$481$	−11.6865			−0.532859
$482$		0			0
$483$	2.52564	+	2.52564i	0.114921	+	0.114921i
$484$		0			0
$485$	−12.3877	−	7.62543i	−0.562498	−	0.346253i
$486$		0			0
$487$	−36.6487			−1.66071			−0.830357	−	0.557232i	$-0.811863\pi$
$487$	−36.6487			−1.66071			−0.830357	+	0.557232i	$0.811863\pi$
$488$		0			0
$489$			14.8857i			0.673154i
$490$		0			0
$491$	23.4273	+	23.4273i	1.05726	+	1.05726i	0.998258	+	0.0590019i	$0.0187918\pi$
$491$	23.4273	+	23.4273i	1.05726	+	1.05726i	0.0590019	+	0.998258i	$0.481208\pi$
$492$		0			0
$493$	−12.7697	−	12.7697i	−0.575120	−	0.575120i
$494$		0			0
$495$	−3.97659	−	16.7113i	−0.178735	−	0.751116i
$496$		0			0
$497$		−	0.650063i		−	0.0291593i
$498$		0			0
$499$	−9.50152	+	9.50152i	−0.425346	+	0.425346i	−0.887040	−	0.461693i	$-0.847242\pi$
$499$	−9.50152	+	9.50152i	−0.425346	+	0.425346i	0.461693	+	0.887040i	$0.347242\pi$
$500$		0			0
$501$	−1.89424	−	1.89424i	−0.0846283	−	0.0846283i
$502$		0			0
$503$	20.6875			0.922411			0.461206	−	0.887293i	$-0.347417\pi$
$503$	20.6875			0.922411			0.461206	+	0.887293i	$0.347417\pi$
$504$		0			0
$505$	20.6827	−	4.92163i	0.920368	−	0.219009i
$506$		0			0
$507$	−0.340787	+	0.340787i	−0.0151349	+	0.0151349i
$508$		0			0
$509$	−11.6381	+	11.6381i	−0.515850	+	0.515850i	−0.916313	−	0.400463i	$-0.868849\pi$
$509$	−11.6381	+	11.6381i	−0.515850	+	0.515850i	0.400463	+	0.916313i	$0.368849\pi$
$510$		0			0
$511$	−14.3629			−0.635377
$512$		0			0
$513$		−	20.9335i		−	0.924235i
$514$		0			0
$515$	−17.7855	+	28.8931i	−0.783724	+	1.27318i
$516$		0			0
$517$	−12.5462	+	12.5462i	−0.551780	+	0.551780i
$518$		0			0
$519$			20.8205i			0.913921i
$520$		0			0
$521$			5.18654i			0.227227i	0.993525	+	0.113613i	$0.0362425\pi$
$521$			5.18654i			0.227227i	−0.993525	+	0.113613i	$0.963758\pi$
$522$		0			0
$523$	26.9589	−	26.9589i	1.17883	−	1.17883i	0.198788	−	0.980043i	$-0.436300\pi$
$523$	26.9589	−	26.9589i	1.17883	−	1.17883i	0.980043	−	0.198788i	$-0.0637004\pi$
$524$		0			0
$525$	−2.78488	+	8.45542i	−0.121542	+	0.369025i
$526$		0			0
$527$		−	13.5195i		−	0.588917i
$528$		0			0
$529$	−18.9755			−0.825020
$530$		0			0
$531$	5.92976	−	5.92976i	0.257330	−	0.257330i
$532$		0			0
$533$	4.14180	−	4.14180i	0.179401	−	0.179401i
$534$		0			0
$535$	1.24288	+	5.22311i	0.0537345	+	0.225815i
$536$		0			0
$537$	−14.5106			−0.626179
$538$		0			0
$539$	−11.4781	−	11.4781i	−0.494397	−	0.494397i
$540$		0			0
$541$	−27.4945	+	27.4945i	−1.18208	+	1.18208i	−0.202878	+	0.979204i	$0.565029\pi$
$541$	−27.4945	+	27.4945i	−1.18208	+	1.18208i	−0.979204	+	0.202878i	$0.934971\pi$
$542$		0			0
$543$		−	9.11278i		−	0.391067i
$544$		0			0
$545$	2.27756	+	9.57123i	0.0975598	+	0.409986i
$546$		0			0
$547$	−22.5197	−	22.5197i	−0.962873	−	0.962873i	0.0364619	−	0.999335i	$-0.488391\pi$
$547$	−22.5197	−	22.5197i	−0.962873	−	0.962873i	−0.999335	+	0.0364619i	$0.988391\pi$
$548$		0			0
$549$	6.65671	+	6.65671i	0.284101	+	0.284101i
$550$		0			0
$551$		−	38.9431i		−	1.65903i
$552$		0			0
$553$	19.2996			0.820704
$554$		0			0
$555$	−3.87676	+	6.29791i	−0.164559	+	0.267331i
$556$		0			0
$557$	13.7333	+	13.7333i	0.581897	+	0.581897i	0.935424	−	0.353527i	$-0.115018\pi$
$557$	13.7333	+	13.7333i	0.581897	+	0.581897i	−0.353527	+	0.935424i	$0.615018\pi$
$558$		0			0
$559$	−41.8713			−1.77097
$560$		0			0
$561$	7.88525			0.332916
$562$		0			0
$563$	0.229223	+	0.229223i	0.00966061	+	0.00966061i	0.711921	−	0.702260i	$-0.247826\pi$
$563$	0.229223	+	0.229223i	0.00966061	+	0.00966061i	−0.702260	+	0.711921i	$0.747826\pi$
$564$		0			0
$565$	30.1359	+	18.5505i	1.26783	+	0.780427i
$566$		0			0
$567$	0.784437			0.0329433
$568$		0			0
$569$			23.0376i			0.965787i	0.875679	+	0.482894i	$0.160414\pi$
$569$			23.0376i			0.965787i	−0.875679	+	0.482894i	$0.839586\pi$
$570$		0			0
$571$	−11.8610	−	11.8610i	−0.496367	−	0.496367i	0.413938	−	0.910305i	$-0.364153\pi$
$571$	−11.8610	−	11.8610i	−0.496367	−	0.496367i	−0.910305	+	0.413938i	$0.864153\pi$
$572$		0			0
$573$	−13.8989	−	13.8989i	−0.580633	−	0.580633i
$574$		0			0
$575$	4.51793	+	8.95556i	0.188411	+	0.373473i
$576$		0			0
$577$			39.7168i			1.65343i	0.562621	+	0.826715i	$0.309793\pi$
$577$			39.7168i			1.65343i	−0.562621	+	0.826715i	$0.690207\pi$
$578$		0			0
$579$	−3.25282	+	3.25282i	−0.135183	+	0.135183i
$580$		0			0
$581$	14.1429	+	14.1429i	0.586748	+	0.586748i
$582$		0			0
$583$	−2.72371			−0.112804
$584$		0			0
$585$	−3.64992	−	15.3385i	−0.150906	−	0.634168i
$586$		0			0
$587$	−8.63887	+	8.63887i	−0.356564	+	0.356564i	−0.862545	−	0.505980i	$-0.831131\pi$
$587$	−8.63887	+	8.63887i	−0.356564	+	0.356564i	0.505980	+	0.862545i	$0.331131\pi$
$588$		0			0
$589$	20.6147	−	20.6147i	0.849414	−	0.849414i
$590$		0			0
$591$	9.38927			0.386223
$592$		0			0
$593$		−	45.8229i		−	1.88172i	−0.338795	−	0.940860i	$-0.610019\pi$
$593$		−	45.8229i		−	1.88172i	0.338795	−	0.940860i	$-0.389981\pi$
$594$		0			0
$595$	6.20118	+	3.81722i	0.254224	+	0.156491i
$596$		0			0
$597$	4.30032	−	4.30032i	0.176000	−	0.176000i
$598$		0			0
$599$		−	17.0609i		−	0.697090i	−0.937292	−	0.348545i	$-0.886676\pi$
$599$		−	17.0609i		−	0.697090i	0.937292	−	0.348545i	$-0.113324\pi$
$600$		0			0
$601$			38.0363i			1.55153i	0.631020	+	0.775766i	$0.282636\pi$
$601$			38.0363i			1.55153i	−0.631020	+	0.775766i	$0.717364\pi$
$602$		0			0
$603$	3.46766	−	3.46766i	0.141214	−	0.141214i
$604$		0			0
$605$	9.48685	+	5.83975i	0.385695	+	0.237420i
$606$		0			0
$607$		−	8.67169i		−	0.351973i	−0.984393	−	0.175987i	$-0.943688\pi$
$607$		−	8.67169i		−	0.351973i	0.984393	−	0.175987i	$-0.0563115\pi$
$608$		0			0
$609$	−16.9282			−0.685965
$610$		0			0
$611$	−11.5155	+	11.5155i	−0.465868	+	0.465868i
$612$		0			0
$613$	13.9739	−	13.9739i	0.564401	−	0.564401i	−0.366153	−	0.930554i	$-0.619325\pi$
$613$	13.9739	−	13.9739i	0.564401	−	0.564401i	0.930554	+	0.366153i	$0.119325\pi$
$614$		0			0
$615$	−0.858077	−	3.60599i	−0.0346010	−	0.145408i
$616$		0			0
$617$	37.3904			1.50528			0.752641	−	0.658431i	$-0.228780\pi$
$617$	37.3904			1.50528			0.752641	+	0.658431i	$0.228780\pi$
$618$		0			0
$619$	−23.2754	−	23.2754i	−0.935516	−	0.935516i	0.0625269	−	0.998043i	$-0.480084\pi$
$619$	−23.2754	−	23.2754i	−0.935516	−	0.935516i	−0.998043	+	0.0625269i	$0.980084\pi$
$620$		0			0
$621$	−7.24998	+	7.24998i	−0.290932	+	0.290932i
$622$		0			0
$623$		−	20.5435i		−	0.823058i
$624$		0			0
$625$	−14.8564	+	20.1069i	−0.594256	+	0.804276i
$626$		0			0
$627$	12.0236	+	12.0236i	0.480175	+	0.480175i
$628$		0			0
$629$	4.27756	+	4.27756i	0.170557	+	0.170557i
$630$		0			0
$631$			19.1834i			0.763680i	0.924228	+	0.381840i	$0.124710\pi$
$631$			19.1834i			0.763680i	−0.924228	+	0.381840i	$0.875290\pi$
$632$		0			0
$633$	11.1667			0.443838
$634$		0			0
$635$	−34.8926	−	21.4786i	−1.38467	−	0.852352i
$636$		0			0
$637$	−10.5352	−	10.5352i	−0.417420	−	0.417420i
$638$		0			0
$639$	0.728585			0.0288224
$640$		0			0
$641$	−16.1765			−0.638933			−0.319466	−	0.947598i	$-0.603504\pi$
$641$	−16.1765			−0.638933			−0.319466	+	0.947598i	$0.603504\pi$
$642$		0			0
$643$	−15.0289	−	15.0289i	−0.592681	−	0.592681i	0.345674	−	0.938355i	$-0.387650\pi$
$643$	−15.0289	−	15.0289i	−0.592681	−	0.592681i	−0.938355	+	0.345674i	$0.887650\pi$
$644$		0			0
$645$	−13.8899	+	22.5646i	−0.546916	+	0.888481i
$646$		0			0
$647$	49.3812			1.94138			0.970688	−	0.240345i	$-0.0772606\pi$
$647$	49.3812			1.94138			0.970688	+	0.240345i	$0.0772606\pi$
$648$		0			0
$649$			17.4461i			0.684821i
$650$		0			0
$651$	−8.96103	−	8.96103i	−0.351210	−	0.351210i
$652$		0			0
$653$	−19.8685	−	19.8685i	−0.777514	−	0.777514i	0.201893	−	0.979408i	$-0.435291\pi$
$653$	−19.8685	−	19.8685i	−0.777514	−	0.777514i	−0.979408	+	0.201893i	$0.935291\pi$
$654$		0			0
$655$	7.46954	+	31.3901i	0.291859	+	1.22651i
$656$		0			0
$657$		−	16.0978i		−	0.628035i
$658$		0			0
$659$	4.94765	−	4.94765i	0.192733	−	0.192733i	−0.604143	−	0.796876i	$-0.706484\pi$
$659$	4.94765	−	4.94765i	0.192733	−	0.192733i	0.796876	+	0.604143i	$0.206484\pi$
$660$		0			0
$661$	−12.1602	−	12.1602i	−0.472977	−	0.472977i	0.429899	−	0.902877i	$-0.358549\pi$
$661$	−12.1602	−	12.1602i	−0.472977	−	0.472977i	−0.902877	+	0.429899i	$0.858549\pi$
$662$		0			0
$663$	7.23750			0.281081
$664$		0			0
$665$	3.63511	+	15.2762i	0.140964	+	0.592387i
$666$		0			0
$667$	−13.4873	+	13.4873i	−0.522231	+	0.522231i
$668$		0			0
$669$	6.77335	−	6.77335i	0.261873	−	0.261873i
$670$		0			0
$671$	−19.5849			−0.756067
$672$		0			0
$673$		−	32.9882i		−	1.27160i	−0.771853	−	0.635801i	$-0.780670\pi$
$673$		−	32.9882i		−	1.27160i	0.771853	−	0.635801i	$-0.219330\pi$
$674$		0			0
$675$	−24.2717	−	7.99412i	−0.934217	−	0.307694i
$676$		0			0
$677$	18.4610	−	18.4610i	0.709513	−	0.709513i	−0.256920	−	0.966433i	$-0.582708\pi$
$677$	18.4610	−	18.4610i	0.709513	−	0.709513i	0.966433	+	0.256920i	$0.0827076\pi$
$678$		0			0
$679$			11.1537i			0.428040i
$680$		0			0
$681$			13.5363i			0.518713i
$682$		0			0
$683$	12.2374	−	12.2374i	0.468251	−	0.468251i	−0.433097	−	0.901347i	$-0.642579\pi$
$683$	12.2374	−	12.2374i	0.468251	−	0.468251i	0.901347	+	0.433097i	$0.142579\pi$
$684$		0			0
$685$	−17.5643	+	28.5337i	−0.671097	+	1.09022i
$686$		0			0
$687$		−	2.40571i		−	0.0917837i
$688$		0			0
$689$	−2.49996			−0.0952409
$690$		0			0
$691$	−9.46014	+	9.46014i	−0.359881	+	0.359881i	−0.863769	−	0.503888i	$-0.831902\pi$
$691$	−9.46014	+	9.46014i	−0.359881	+	0.359881i	0.503888	+	0.863769i	$0.331902\pi$
$692$		0			0
$693$	−9.31352	+	9.31352i	−0.353791	+	0.353791i
$694$		0			0
$695$	−25.5061	+	6.06939i	−0.967500	+	0.230225i
$696$		0			0
$697$	−3.03201			−0.114845
$698$		0			0
$699$	9.09039	+	9.09039i	0.343830	+	0.343830i
$700$		0			0
$701$	5.14714	−	5.14714i	0.194405	−	0.194405i	−0.603192	−	0.797596i	$-0.706105\pi$
$701$	5.14714	−	5.14714i	0.194405	−	0.194405i	0.797596	+	0.603192i	$0.206105\pi$
$702$		0			0
$703$			13.0450i			0.492001i
$704$		0			0
$705$	2.38573	+	10.0258i	0.0898517	+	0.377594i
$706$		0			0
$707$	−11.5269	−	11.5269i	−0.433512	−	0.433512i
$708$		0			0
$709$	18.0125	+	18.0125i	0.676472	+	0.676472i	0.959200	−	0.282728i	$-0.0912395\pi$
$709$	18.0125	+	18.0125i	0.676472	+	0.676472i	−0.282728	+	0.959200i	$0.591239\pi$
$710$		0			0
$711$			21.6309i			0.811222i
$712$		0			0
$713$	−14.2792			−0.534759
$714$		0			0
$715$	27.9332	+	17.1946i	1.04464	+	0.643043i
$716$		0			0
$717$	5.70875	+	5.70875i	0.213197	+	0.213197i
$718$		0			0
$719$	−34.5017			−1.28669			−0.643347	−	0.765574i	$-0.722455\pi$
$719$	−34.5017			−1.28669			−0.643347	+	0.765574i	$0.722455\pi$
$720$		0			0
$721$	26.0149			0.968846
$722$		0			0
$723$	−2.54850	−	2.54850i	−0.0947796	−	0.0947796i
$724$		0			0
$725$	−45.1532	−	14.8717i	−1.67695	−	0.552320i
$726$		0			0
$727$	−12.8421			−0.476288			−0.238144	−	0.971230i	$-0.576539\pi$
$727$	−12.8421			−0.476288			−0.238144	+	0.971230i	$0.576539\pi$
$728$		0			0
$729$		−	15.0429i		−	0.557143i
$730$		0			0
$731$	15.3259	+	15.3259i	0.566851	+	0.566851i
$732$		0			0
$733$	−24.1490	−	24.1490i	−0.891965	−	0.891965i	0.102743	−	0.994708i	$-0.467238\pi$
$733$	−24.1490	−	24.1490i	−0.891965	−	0.891965i	−0.994708	+	0.102743i	$0.967238\pi$
$734$		0			0
$735$	−9.17231	+	2.18263i	−0.338326	+	0.0805075i
$736$		0			0
$737$			10.2023i			0.375807i
$738$		0			0
$739$	35.9398	−	35.9398i	1.32207	−	1.32207i	0.409966	−	0.912101i	$-0.365540\pi$
$739$	35.9398	−	35.9398i	1.32207	−	1.32207i	0.912101	−	0.409966i	$-0.134460\pi$
$740$		0			0
$741$	11.0359	+	11.0359i	0.405412	+	0.405412i
$742$		0			0
$743$	45.9502			1.68575			0.842875	−	0.538109i	$-0.180861\pi$
$743$	45.9502			1.68575			0.842875	+	0.538109i	$0.180861\pi$
$744$		0			0
$745$	22.4802	−	5.34935i	0.823610	−	0.195985i
$746$		0			0
$747$	−15.8513	+	15.8513i	−0.579969	+	0.579969i
$748$		0			0
$749$	2.91094	−	2.91094i	0.106363	−	0.106363i
$750$		0			0
$751$	24.4820			0.893361			0.446680	−	0.894694i	$-0.352606\pi$
$751$	24.4820			0.893361			0.446680	+	0.894694i	$0.352606\pi$
$752$		0			0
$753$			13.1404i			0.478863i
$754$		0			0
$755$	−8.69983	−	5.35529i	−0.316619	−	0.194899i
$756$		0			0
$757$	−17.0328	+	17.0328i	−0.619067	+	0.619067i	−0.945292	−	0.326225i	$-0.894223\pi$
$757$	−17.0328	+	17.0328i	−0.619067	+	0.619067i	0.326225	+	0.945292i	$0.394223\pi$
$758$		0			0
$759$		−	8.32835i		−	0.302300i
$760$		0			0
$761$		−	8.53590i		−	0.309426i	−0.987959	−	0.154713i	$-0.950555\pi$
$761$		−	8.53590i		−	0.309426i	0.987959	−	0.154713i	$-0.0494453\pi$
$762$		0			0
$763$	5.33423	−	5.33423i	0.193112	−	0.193112i
$764$		0			0
$765$	−4.27831	+	6.95024i	−0.154683	+	0.251286i
$766$		0			0
$767$			16.0130i			0.578195i
$768$		0			0
$769$	−1.87438			−0.0675917			−0.0337959	−	0.999429i	$-0.510760\pi$
$769$	−1.87438			−0.0675917			−0.0337959	+	0.999429i	$0.510760\pi$
$770$		0			0
$771$	−2.65982	+	2.65982i	−0.0957911	+	0.0957911i
$772$		0			0
$773$	−21.5374	+	21.5374i	−0.774645	+	0.774645i	−0.978915	−	0.204270i	$-0.934518\pi$
$773$	−21.5374	+	21.5374i	−0.774645	+	0.774645i	0.204270	+	0.978915i	$0.434518\pi$
$774$		0			0
$775$	−16.0297	−	31.7745i	−0.575804	−	1.14137i
$776$		0			0
$777$	5.67054			0.203429
$778$		0			0
$779$	−4.62326	−	4.62326i	−0.165645	−	0.165645i
$780$		0			0
$781$	−1.07180	+	1.07180i	−0.0383519	+	0.0383519i
$782$		0			0
$783$		−	48.5932i		−	1.73658i
$784$		0			0
$785$	4.70580	−	1.11979i	0.167957	−	0.0399669i
$786$		0			0
$787$	−7.03687	−	7.03687i	−0.250837	−	0.250837i	0.570477	−	0.821314i	$-0.306759\pi$
$787$	−7.03687	−	7.03687i	−0.250837	−	0.250837i	−0.821314	+	0.570477i	$0.806759\pi$
$788$		0			0
$789$	−10.0904	−	10.0904i	−0.359227	−	0.359227i
$790$		0			0
$791$		−	27.1339i		−	0.964770i
$792$		0			0
$793$	−17.9761			−0.638348
$794$		0			0
$795$	−0.829311	+	1.34724i	−0.0294126	+	0.0477817i
$796$		0			0
$797$	8.07933	+	8.07933i	0.286185	+	0.286185i	0.835569	−	0.549385i	$-0.185138\pi$
$797$	8.07933	+	8.07933i	0.286185	+	0.286185i	−0.549385	+	0.835569i	$0.685138\pi$
$798$		0			0
$799$	8.42995			0.298230
$800$		0			0
$801$	23.0250			0.813548
$802$		0			0
$803$	23.6809	+	23.6809i	0.835682	+	0.835682i
$804$		0			0
$805$	4.03172	−	6.54965i	0.142099	−	0.230845i
$806$		0			0
$807$	6.20097			0.218284
$808$		0			0
$809$		−	5.40185i		−	0.189919i	−0.995481	−	0.0949595i	$-0.969728\pi$
$809$		−	5.40185i		−	0.189919i	0.995481	−	0.0949595i	$-0.0302722\pi$
$810$		0			0
$811$	−10.3478	−	10.3478i	−0.363360	−	0.363360i	0.501688	−	0.865049i	$-0.332712\pi$
$811$	−10.3478	−	10.3478i	−0.363360	−	0.363360i	−0.865049	+	0.501688i	$0.832712\pi$
$812$		0			0
$813$	3.96530	+	3.96530i	0.139069	+	0.139069i
$814$		0			0
$815$	31.1824	−	7.42011i	1.09227	−	0.259915i
$816$		0			0
$817$			46.7385i			1.63517i
$818$		0			0
$819$	−8.54843	+	8.54843i	−0.298706	+	0.298706i
$820$		0			0
$821$	−10.7321	−	10.7321i	−0.374551	−	0.374551i	0.494581	−	0.869132i	$-0.335322\pi$
$821$	−10.7321	−	10.7321i	−0.374551	−	0.374551i	−0.869132	+	0.494581i	$0.835322\pi$
$822$		0			0
$823$	3.51588			0.122556			0.0612780	−	0.998121i	$-0.480482\pi$
$823$	3.51588			0.122556			0.0612780	+	0.998121i	$0.480482\pi$
$824$		0			0
$825$	18.5325	−	9.34935i	0.645220	−	0.325503i
$826$		0			0
$827$	−27.7375	+	27.7375i	−0.964529	+	0.964529i	−0.999392	−	0.0348631i	$-0.988900\pi$
$827$	−27.7375	+	27.7375i	−0.964529	+	0.964529i	0.0348631	+	0.999392i	$0.488900\pi$
$828$		0			0
$829$	19.5849	−	19.5849i	0.680212	−	0.680212i	−0.279836	−	0.960048i	$-0.590280\pi$
$829$	19.5849	−	19.5849i	0.680212	−	0.680212i	0.960048	+	0.279836i	$0.0902800\pi$
$830$		0			0
$831$	−7.47119			−0.259173
$832$		0			0
$833$			7.71231i			0.267216i
$834$		0			0
$835$	−3.02380	+	4.91225i	−0.104643	+	0.169995i
$836$		0			0
$837$	25.7231	−	25.7231i	0.889119	−	0.889119i
$838$		0			0
$839$			40.0520i			1.38275i	0.722496	+	0.691375i	$0.242995\pi$
$839$			40.0520i			1.38275i	−0.722496	+	0.691375i	$0.757005\pi$
$840$		0			0
$841$		−	61.3992i		−	2.11722i
$842$		0			0
$843$	15.6243	−	15.6243i	0.538129	−	0.538129i
$844$		0			0
$845$	0.883749	+	0.544003i	0.0304019	+	0.0187143i
$846$		0			0
$847$		−	8.54182i		−	0.293500i
$848$		0			0
$849$	−5.99948			−0.205902
$850$		0			0
$851$	4.51793	−	4.51793i	0.154873	−	0.154873i
$852$		0			0
$853$	13.7328	−	13.7328i	0.470202	−	0.470202i	−0.431778	−	0.901980i	$-0.642114\pi$
$853$	13.7328	−	13.7328i	0.470202	−	0.470202i	0.901980	+	0.431778i	$0.142114\pi$
$854$		0			0
$855$	−17.1215	+	4.07420i	−0.585542	+	0.139335i
$856$		0			0
$857$	−39.9485			−1.36462			−0.682308	−	0.731065i	$-0.739024\pi$
$857$	−39.9485			−1.36462			−0.682308	+	0.731065i	$0.739024\pi$
$858$		0			0
$859$	33.6366	+	33.6366i	1.14766	+	1.14766i	0.987011	+	0.160654i	$0.0513602\pi$
$859$	33.6366	+	33.6366i	1.14766	+	1.14766i	0.160654	+	0.987011i	$0.448640\pi$
$860$		0			0
$861$	−2.00969	+	2.00969i	−0.0684900	+	0.0684900i
$862$		0			0
$863$			16.5303i			0.562697i	0.959606	+	0.281349i	$0.0907817\pi$
$863$			16.5303i			0.562697i	−0.959606	+	0.281349i	$0.909218\pi$
$864$		0			0
$865$	43.6146	−	10.3785i	1.48294	−	0.352879i
$866$		0			0
$867$	9.83388	+	9.83388i	0.333976	+	0.333976i
$868$		0			0
$869$	−31.8205	−	31.8205i	−1.07944	−	1.07944i
$870$		0			0
$871$			9.36421i			0.317294i
$872$		0			0
$873$	−12.5010			−0.423095
$874$		0			0
$875$	19.1005	+	1.61893i	0.645714	+	0.0547297i
$876$		0			0
$877$	−9.66381	−	9.66381i	−0.326324	−	0.326324i	0.524863	−	0.851187i	$-0.324117\pi$
$877$	−9.66381	−	9.66381i	−0.326324	−	0.326324i	−0.851187	+	0.524863i	$0.824117\pi$
$878$		0			0
$879$	−10.8734			−0.366752
$880$		0			0
$881$	−43.4299			−1.46319			−0.731596	−	0.681739i	$-0.761224\pi$
$881$	−43.4299			−1.46319			−0.731596	+	0.681739i	$0.761224\pi$
$882$		0			0
$883$	22.3879	+	22.3879i	0.753413	+	0.753413i	0.975115	−	0.221701i	$-0.0711610\pi$
$883$	22.3879	+	22.3879i	0.753413	+	0.753413i	−0.221701	+	0.975115i	$0.571161\pi$
$884$		0			0
$885$	8.62946	+	5.31198i	0.290076	+	0.178560i
$886$		0			0
$887$	−31.6913			−1.06409			−0.532045	−	0.846716i	$-0.678576\pi$
$887$	−31.6913			−1.06409			−0.532045	+	0.846716i	$0.678576\pi$
$888$		0			0
$889$			31.4168i			1.05368i
$890$		0			0
$891$	−1.29335	−	1.29335i	−0.0433288	−	0.0433288i
$892$		0			0
$893$	12.8541	+	12.8541i	0.430147	+	0.430147i
$894$		0			0
$895$	7.23315	+	30.3967i	0.241778	+	1.01605i
$896$		0			0
$897$		−	7.64420i		−	0.255232i
$898$		0			0
$899$	47.8533	−	47.8533i	1.59600	−	1.59600i
$900$		0			0
$901$	0.915049	+	0.915049i	0.0304847	+	0.0304847i
$902$		0			0
$903$	20.3168			0.676102
$904$		0			0
$905$	−19.0893	+	4.54248i	−0.634551	+	0.150997i
$906$		0			0
$907$	24.9184	−	24.9184i	0.827401	−	0.827401i	−0.159755	−	0.987157i	$-0.551071\pi$
$907$	24.9184	−	24.9184i	0.827401	−	0.827401i	0.987157	+	0.159755i	$0.0510705\pi$
$908$		0			0
$909$	12.9192	−	12.9192i	0.428503	−	0.428503i
$910$		0			0
$911$	47.0459			1.55870			0.779350	−	0.626589i	$-0.215549\pi$
$911$	47.0459			1.55870			0.779350	+	0.626589i	$0.215549\pi$
$912$		0			0
$913$		−	46.6366i		−	1.54345i
$914$		0			0
$915$	−5.96319	+	9.68738i	−0.197137	+	0.320255i
$916$		0			0
$917$	17.4943	−	17.4943i	0.577712	−	0.577712i
$918$		0			0
$919$			12.5442i			0.413796i	0.978362	+	0.206898i	$0.0663369\pi$
$919$			12.5442i			0.413796i	−0.978362	+	0.206898i	$0.933663\pi$
$920$		0			0
$921$		−	24.4716i		−	0.806368i
$922$		0			0
$923$	−0.983751	+	0.983751i	−0.0323806	+	0.0323806i
$924$		0			0
$925$	15.1252	+	4.98165i	0.497315	+	0.163796i
$926$		0			0
$927$			29.1573i			0.957652i
$928$		0			0
$929$	−26.7421			−0.877380			−0.438690	−	0.898639i	$-0.644557\pi$
$929$	−26.7421			−0.877380			−0.438690	+	0.898639i	$0.644557\pi$
$930$		0			0
$931$	−11.7599	+	11.7599i	−0.385414	+	0.385414i
$932$		0			0
$933$	−16.0863	+	16.0863i	−0.526642	+	0.526642i
$934$		0			0
$935$	−3.93058	−	16.5179i	−0.128544	−	0.540194i
$936$		0			0
$937$	−3.06580			−0.100155			−0.0500777	−	0.998745i	$-0.515947\pi$
$937$	−3.06580			−0.100155			−0.0500777	+	0.998745i	$0.515947\pi$
$938$		0			0
$939$	9.16546	+	9.16546i	0.299104	+	0.299104i
$940$		0			0
$941$	14.6023	−	14.6023i	0.476020	−	0.476020i	−0.427836	−	0.903856i	$-0.640724\pi$
$941$	14.6023	−	14.6023i	0.476020	−	0.476020i	0.903856	+	0.427836i	$0.140724\pi$
$942$		0			0
$943$			3.20239i			0.104284i
$944$		0			0
$945$	4.53590	+	19.0617i	0.147553	+	0.620077i
$946$		0			0
$947$	29.4872	+	29.4872i	0.958204	+	0.958204i	0.999161	−	0.0409570i	$-0.0130407\pi$
$947$	29.4872	+	29.4872i	0.958204	+	0.958204i	−0.0409570	+	0.999161i	$0.513041\pi$
$948$		0			0
$949$	21.7356	+	21.7356i	0.705567	+	0.705567i
$950$		0			0
$951$			6.23158i			0.202073i
$952$		0			0
$953$	33.6807			1.09103			0.545513	−	0.838103i	$-0.316335\pi$
$953$	33.6807			1.09103			0.545513	+	0.838103i	$0.316335\pi$
$954$		0			0
$955$	−22.1870	+	36.0434i	−0.717953	+	1.16634i
$956$		0			0
$957$	27.9105	+	27.9105i	0.902219	+	0.902219i
$958$		0			0
$959$	25.6913			0.829616
$960$		0			0
$961$	19.6628			0.634283
$962$		0			0
$963$	3.26256	+	3.26256i	0.105134	+	0.105134i
$964$		0			0
$965$	8.43541	+	5.19253i	0.271546	+	0.167153i
$966$		0			0
$967$	−8.70089			−0.279802			−0.139901	−	0.990166i	$-0.544678\pi$
$967$	−8.70089			−0.279802			−0.139901	+	0.990166i	$0.544678\pi$
$968$		0			0
$969$		−	8.07881i		−	0.259529i
$970$		0			0
$971$	−5.87523	−	5.87523i	−0.188545	−	0.188545i	0.606522	−	0.795067i	$-0.292564\pi$
$971$	−5.87523	−	5.87523i	−0.188545	−	0.188545i	−0.795067	+	0.606522i	$0.792564\pi$
$972$		0			0
$973$	14.2150	+	14.2150i	0.455713	+	0.455713i
$974$		0			0
$975$	17.0101	−	8.58132i	0.544760	−	0.274822i
$976$		0			0
$977$		−	41.8541i		−	1.33903i	−0.742798	−	0.669516i	$-0.766502\pi$
$977$		−	41.8541i		−	1.33903i	0.742798	−	0.669516i	$-0.233498\pi$
$978$		0			0
$979$	−33.8713	+	33.8713i	−1.08253	+	1.08253i
$980$		0			0
$981$	5.97856	+	5.97856i	0.190881	+	0.190881i
$982$		0			0
$983$	−57.4539			−1.83250			−0.916248	−	0.400612i	$-0.868797\pi$
$983$	−57.4539			−1.83250			−0.916248	+	0.400612i	$0.868797\pi$
$984$		0			0
$985$	−4.68030	−	19.6685i	−0.149127	−	0.626692i
$986$		0			0
$987$	5.58758	−	5.58758i	0.177854	−	0.177854i
$988$		0			0
$989$	16.1872	−	16.1872i	0.514722	−	0.514722i
$990$		0			0
$991$	−12.8205			−0.407258			−0.203629	−	0.979048i	$-0.565274\pi$
$991$	−12.8205			−0.407258			−0.203629	+	0.979048i	$0.565274\pi$
$992$		0			0
$993$			1.62099i			0.0514404i
$994$		0			0
$995$	−11.1519	−	6.86467i	−0.353538	−	0.217625i
$996$		0			0
$997$	−15.0860	+	15.0860i	−0.477777	+	0.477777i	−0.904420	−	0.426643i	$-0.859696\pi$
$997$	−15.0860	+	15.0860i	−0.477777	+	0.477777i	0.426643	+	0.904420i	$0.359696\pi$
$998$		0			0
$999$			16.2776i			0.514999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.q.f.609.6		16
4.3	odd	2		640.2.q.e.609.3		16
5.4	even	2	inner	640.2.q.f.609.3		16
8.3	odd	2		80.2.q.c.69.4	yes	16
8.5	even	2		320.2.q.c.49.3		16
16.3	odd	4		640.2.q.e.289.6		16
16.5	even	4		320.2.q.c.209.6		16
16.11	odd	4		80.2.q.c.29.5	yes	16
16.13	even	4	inner	640.2.q.f.289.3		16
20.19	odd	2		640.2.q.e.609.6		16
24.11	even	2		720.2.bm.f.469.5		16
40.3	even	4		400.2.l.i.101.8		16
40.13	odd	4		1600.2.l.h.1201.6		16
40.19	odd	2		80.2.q.c.69.5	yes	16
40.27	even	4		400.2.l.i.101.1		16
40.29	even	2		320.2.q.c.49.6		16
40.37	odd	4		1600.2.l.h.1201.3		16
48.11	even	4		720.2.bm.f.109.4		16
80.19	odd	4		640.2.q.e.289.3		16
80.27	even	4		400.2.l.i.301.1		16
80.29	even	4	inner	640.2.q.f.289.6		16
80.37	odd	4		1600.2.l.h.401.3		16
80.43	even	4		400.2.l.i.301.8		16
80.53	odd	4		1600.2.l.h.401.6		16
80.59	odd	4		80.2.q.c.29.4	✓	16
80.69	even	4		320.2.q.c.209.3		16
120.59	even	2		720.2.bm.f.469.4		16
240.59	even	4		720.2.bm.f.109.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.q.c.29.4	✓	16	80.59	odd	4
80.2.q.c.29.5	yes	16	16.11	odd	4
80.2.q.c.69.4	yes	16	8.3	odd	2
80.2.q.c.69.5	yes	16	40.19	odd	2
320.2.q.c.49.3		16	8.5	even	2
320.2.q.c.49.6		16	40.29	even	2
320.2.q.c.209.3		16	80.69	even	4
320.2.q.c.209.6		16	16.5	even	4
400.2.l.i.101.1		16	40.27	even	4
400.2.l.i.101.8		16	40.3	even	4
400.2.l.i.301.1		16	80.27	even	4
400.2.l.i.301.8		16	80.43	even	4
640.2.q.e.289.3		16	80.19	odd	4
640.2.q.e.289.6		16	16.3	odd	4
640.2.q.e.609.3		16	4.3	odd	2
640.2.q.e.609.6		16	20.19	odd	2
640.2.q.f.289.3		16	16.13	even	4	inner
640.2.q.f.289.6		16	80.29	even	4	inner
640.2.q.f.609.3		16	5.4	even	2	inner
640.2.q.f.609.6		16	1.1	even	1	trivial
720.2.bm.f.109.4		16	48.11	even	4
720.2.bm.f.109.5		16	240.59	even	4
720.2.bm.f.469.4		16	120.59	even	2
720.2.bm.f.469.5		16	24.11	even	2
1600.2.l.h.401.3		16	80.37	odd	4
1600.2.l.h.401.6		16	80.53	odd	4
1600.2.l.h.1201.3		16	40.37	odd	4
1600.2.l.h.1201.6		16	40.13	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.q (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.734294 + 0.734294i) q^{3} +(1.17216 - 1.90421i) q^{5} -1.71452 q^{7} -1.92163i q^{9} +(2.82684 + 2.82684i) q^{11} +(2.59462 + 2.59462i) q^{13} +(2.25896 - 0.537540i) q^{15} -1.89939i q^{17} +(2.89623 - 2.89623i) q^{19} +(-1.25896 - 1.25896i) q^{21} -2.00613 q^{23} +(-2.25207 - 4.46410i) q^{25} +(3.61392 - 3.61392i) q^{27} +(6.72307 - 6.72307i) q^{29} +7.11778 q^{31} +4.15146i q^{33} +(-2.00970 + 3.26482i) q^{35} +(-2.25207 + 2.25207i) q^{37} +3.81042i q^{39} -1.59630i q^{41} +(-8.06886 + 8.06886i) q^{43} +(-3.65919 - 2.25246i) q^{45} +4.43823i q^{47} -4.06040 q^{49} +(1.39471 - 1.39471i) q^{51} +(-0.481758 + 0.481758i) q^{53} +(8.69642 - 2.06939i) q^{55} +4.25336 q^{57} +(3.08580 + 3.08580i) q^{59} +(-3.46410 + 3.46410i) q^{61} +3.29468i q^{63} +(7.98203 - 1.89939i) q^{65} +(1.80454 + 1.80454i) q^{67} +(-1.47309 - 1.47309i) q^{69} +0.379150i q^{71} +8.37718 q^{73} +(1.62428 - 4.93164i) q^{75} +(-4.84668 - 4.84668i) q^{77} -11.2566 q^{79} -0.457524 q^{81} +(-8.24890 - 8.24890i) q^{83} +(-3.61685 - 2.22640i) q^{85} +9.87341 q^{87} +11.9820i q^{89} +(-4.44854 - 4.44854i) q^{91} +(5.22654 + 5.22654i) q^{93} +(-2.12019 - 8.90989i) q^{95} -6.50543i q^{97} +(5.43213 - 5.43213i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{5} + 8 q^{11} - 8 q^{19} + 16 q^{21} + 16 q^{29} - 16 q^{31} - 24 q^{35} - 8 q^{45} + 16 q^{49} - 16 q^{51} - 24 q^{59} - 32 q^{69} + 48 q^{75} - 16 q^{79} - 16 q^{81} - 16 q^{91} - 32 q^{95}+ \cdots + 88 q^{99}+O(q^{100}) \) 16 * q + 8 * q^5 + 8 * q^11 - 8 * q^19 + 16 * q^21 + 16 * q^29 - 16 * q^31 - 24 * q^35 - 8 * q^45 + 16 * q^49 - 16 * q^51 - 24 * q^59 - 32 * q^69 + 48 * q^75 - 16 * q^79 - 16 * q^81 - 16 * q^91 - 32 * q^95 + 88 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more