LMFDB - Embedded newform 640.2.j.c.543.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(543,640)]

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([2, 1, 3]))

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

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

chi := DirichletCharacter("640.543");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.j (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:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{13} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			543.2
Root			$0.0376504 + 1.41371i$ of defining polynomial
Character	$\chi$	$=$	640.543
Dual form			640.2.j.c.607.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55161i q^{3} +(-1.66635 - 1.49107i) q^{5} +(-2.40368 + 2.40368i) q^{7} -3.51070 q^{9} +O(q^{10})$	\(q-2.55161i q^{3} +(-1.66635 - 1.49107i) q^{5} +(-2.40368 + 2.40368i) q^{7} -3.51070 q^{9} +(-2.67707 + 2.67707i) q^{11} +2.40164 q^{13} +(-3.80462 + 4.25187i) q^{15} +(-0.0750544 + 0.0750544i) q^{17} +(-2.67236 + 2.67236i) q^{19} +(6.13324 + 6.13324i) q^{21} +(-2.12375 - 2.12375i) q^{23} +(0.553442 + 4.96928i) q^{25} +1.30310i q^{27} +(-3.95795 - 3.95795i) q^{29} +1.65367i q^{31} +(6.83083 + 6.83083i) q^{33} +(7.58941 - 0.421324i) q^{35} +2.53082 q^{37} -6.12803i q^{39} +1.70882i q^{41} -3.84601 q^{43} +(5.85005 + 5.23469i) q^{45} +(2.15264 + 2.15264i) q^{47} -4.55532i q^{49} +(0.191509 + 0.191509i) q^{51} +1.29475i q^{53} +(8.45262 - 0.469246i) q^{55} +(6.81881 + 6.81881i) q^{57} +(-5.29614 - 5.29614i) q^{59} +(-10.2413 + 10.2413i) q^{61} +(8.43858 - 8.43858i) q^{63} +(-4.00197 - 3.58100i) q^{65} -10.6230 q^{67} +(-5.41898 + 5.41898i) q^{69} -2.27322 q^{71} +(9.99096 - 9.99096i) q^{73} +(12.6796 - 1.41217i) q^{75} -12.8696i q^{77} -8.70617 q^{79} -7.20709 q^{81} +11.1310i q^{83} +(0.236978 - 0.0131558i) q^{85} +(-10.0991 + 10.0991i) q^{87} -15.6390 q^{89} +(-5.77276 + 5.77276i) q^{91} +4.21952 q^{93} +(8.43775 - 0.468420i) q^{95} +(5.00672 - 5.00672i) q^{97} +(9.39839 - 9.39839i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^5 - 2 * q^7 - 10 * q^9	$ 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9} - 2 q^{11} - 20 q^{15} - 6 q^{17} + 2 q^{19} + 16 q^{21} + 2 q^{23} + 6 q^{25} + 14 q^{29} - 8 q^{33} - 6 q^{35} - 8 q^{37} - 44 q^{43} + 4 q^{45} + 38 q^{47} + 8 q^{51} + 6 q^{55} + 24 q^{57} - 10 q^{59} - 14 q^{61} - 6 q^{63} + 12 q^{67} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 64 q^{75} - 16 q^{79} + 2 q^{81} + 10 q^{85} - 24 q^{87} - 12 q^{89} - 16 q^{93} + 34 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^5 - 2 * q^7 - 10 * q^9 - 2 * q^11 - 20 * q^15 - 6 * q^17 + 2 * q^19 + 16 * q^21 + 2 * q^23 + 6 * q^25 + 14 * q^29 - 8 * q^33 - 6 * q^35 - 8 * q^37 - 44 * q^43 + 4 * q^45 + 38 * q^47 + 8 * q^51 + 6 * q^55 + 24 * q^57 - 10 * q^59 - 14 * q^61 - 6 * q^63 + 12 * q^67 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 64 * q^75 - 16 * q^79 + 2 * q^81 + 10 * q^85 - 24 * q^87 - 12 * q^89 - 16 * q^93 + 34 * q^95 + 18 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$257$	$261$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$	$-1$

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
$3$		−	2.55161i		−	1.47317i	−0.676344	−	0.736586i	$-0.736437\pi$
$3$		−	2.55161i		−	1.47317i	0.676344	−	0.736586i	$-0.263563\pi$
$4$		0			0
$5$	−1.66635	−	1.49107i	−0.745214	−	0.666825i
$5$	−1.66635	−	1.49107i	−0.745214	−	0.666825i
$6$		0			0
$7$	−2.40368	+	2.40368i	−0.908504	+	0.908504i	−0.996152	−	0.0876474i	$-0.972065\pi$
$7$	−2.40368	+	2.40368i	−0.908504	+	0.908504i	0.0876474	+	0.996152i	$0.472065\pi$
$8$		0			0
$9$	−3.51070			−1.17023
$10$		0			0
$11$	−2.67707	+	2.67707i	−0.807167	+	0.807167i	−0.984204	−	0.177037i	$-0.943349\pi$
$11$	−2.67707	+	2.67707i	−0.807167	+	0.807167i	0.177037	+	0.984204i	$0.443349\pi$
$12$		0			0
$13$	2.40164			0.666094			0.333047	−	0.942910i	$-0.391923\pi$
$13$	2.40164			0.666094			0.333047	+	0.942910i	$0.391923\pi$
$14$		0			0
$15$	−3.80462	+	4.25187i	−0.982348	+	1.09783i
$16$		0			0
$17$	−0.0750544	+	0.0750544i	−0.0182034	+	0.0182034i	−0.716150	−	0.697947i	$-0.754097\pi$
$17$	−0.0750544	+	0.0750544i	−0.0182034	+	0.0182034i	0.697947	+	0.716150i	$0.254097\pi$
$18$		0			0
$19$	−2.67236	+	2.67236i	−0.613081	+	0.613081i	−0.943748	−	0.330666i	$-0.892726\pi$
$19$	−2.67236	+	2.67236i	−0.613081	+	0.613081i	0.330666	+	0.943748i	$0.392726\pi$
$20$		0			0
$21$	6.13324	+	6.13324i	1.33838	+	1.33838i
$22$		0			0
$23$	−2.12375	−	2.12375i	−0.442833	−	0.442833i	0.450130	−	0.892963i	$-0.351378\pi$
$23$	−2.12375	−	2.12375i	−0.442833	−	0.442833i	−0.892963	+	0.450130i	$0.851378\pi$
$24$		0			0
$25$	0.553442	+	4.96928i	0.110688	+	0.993855i
$26$		0			0
$27$			1.30310i			0.250783i
$28$		0			0
$29$	−3.95795	−	3.95795i	−0.734974	−	0.734974i	0.236627	−	0.971601i	$-0.423958\pi$
$29$	−3.95795	−	3.95795i	−0.734974	−	0.734974i	−0.971601	+	0.236627i	$0.923958\pi$
$30$		0			0
$31$			1.65367i			0.297008i	0.988912	+	0.148504i	$0.0474458\pi$
$31$			1.65367i			0.297008i	−0.988912	+	0.148504i	$0.952554\pi$
$32$		0			0
$33$	6.83083	+	6.83083i	1.18909	+	1.18909i
$34$		0			0
$35$	7.58941	−	0.421324i	1.28284	−	0.0712168i
$36$		0			0
$37$	2.53082			0.416064			0.208032	−	0.978122i	$-0.433294\pi$
$37$	2.53082			0.416064			0.208032	+	0.978122i	$0.433294\pi$
$38$		0			0
$39$		−	6.12803i		−	0.981271i
$40$		0			0
$41$			1.70882i			0.266873i	0.991057	+	0.133436i	$0.0426012\pi$
$41$			1.70882i			0.266873i	−0.991057	+	0.133436i	$0.957399\pi$
$42$		0			0
$43$	−3.84601			−0.586510			−0.293255	−	0.956034i	$-0.594739\pi$
$43$	−3.84601			−0.586510			−0.293255	+	0.956034i	$0.594739\pi$
$44$		0			0
$45$	5.85005	+	5.23469i	0.872074	+	0.780341i
$46$		0			0
$47$	2.15264	+	2.15264i	0.313995	+	0.313995i	0.846455	−	0.532460i	$-0.178732\pi$
$47$	2.15264	+	2.15264i	0.313995	+	0.313995i	−0.532460	+	0.846455i	$0.678732\pi$
$48$		0			0
$49$		−	4.55532i		−	0.650760i
$50$		0			0
$51$	0.191509	+	0.191509i	0.0268167	+	0.0268167i
$52$		0			0
$53$			1.29475i			0.177848i	0.996038	+	0.0889239i	$0.0283428\pi$
$53$			1.29475i			0.177848i	−0.996038	+	0.0889239i	$0.971657\pi$
$54$		0			0
$55$	8.45262	−	0.469246i	1.13975	−	0.0632731i
$56$		0			0
$57$	6.81881	+	6.81881i	0.903174	+	0.903174i
$58$		0			0
$59$	−5.29614	−	5.29614i	−0.689499	−	0.689499i	0.272622	−	0.962121i	$-0.412109\pi$
$59$	−5.29614	−	5.29614i	−0.689499	−	0.689499i	−0.962121	+	0.272622i	$0.912109\pi$
$60$		0			0
$61$	−10.2413	+	10.2413i	−1.31126	+	1.31126i	−0.390780	+	0.920484i	$0.627795\pi$
$61$	−10.2413	+	10.2413i	−1.31126	+	1.31126i	−0.920484	+	0.390780i	$0.872205\pi$
$62$		0			0
$63$	8.43858	−	8.43858i	1.06316	−	1.06316i
$64$		0			0
$65$	−4.00197	−	3.58100i	−0.496383	−	0.444168i
$66$		0			0
$67$	−10.6230			−1.29780			−0.648901	−	0.760873i	$-0.724771\pi$
$67$	−10.6230			−1.29780			−0.648901	+	0.760873i	$0.724771\pi$
$68$		0			0
$69$	−5.41898	+	5.41898i	−0.652369	+	0.652369i
$70$		0			0
$71$	−2.27322			−0.269781			−0.134891	−	0.990860i	$-0.543068\pi$
$71$	−2.27322			−0.269781			−0.134891	+	0.990860i	$0.543068\pi$
$72$		0			0
$73$	9.99096	−	9.99096i	1.16935	−	1.16935i	0.186992	−	0.982361i	$-0.440126\pi$
$73$	9.99096	−	9.99096i	1.16935	−	1.16935i	0.982361	−	0.186992i	$-0.0598739\pi$
$74$		0			0
$75$	12.6796	−	1.41217i	1.46412	−	0.163063i
$76$		0			0
$77$		−	12.8696i		−	1.46663i
$78$		0			0
$79$	−8.70617			−0.979520			−0.489760	−	0.871857i	$-0.662916\pi$
$79$	−8.70617			−0.979520			−0.489760	+	0.871857i	$0.662916\pi$
$80$		0			0
$81$	−7.20709			−0.800787
$82$		0			0
$83$			11.1310i			1.22178i	0.791715	+	0.610890i	$0.209188\pi$
$83$			11.1310i			1.22178i	−0.791715	+	0.610890i	$0.790812\pi$
$84$		0			0
$85$	0.236978	−	0.0131558i	0.0257039	−	0.00142695i
$86$		0			0
$87$	−10.0991	+	10.0991i	−1.08274	+	1.08274i
$88$		0			0
$89$	−15.6390			−1.65773			−0.828866	−	0.559447i	$-0.811014\pi$
$89$	−15.6390			−1.65773			−0.828866	+	0.559447i	$0.811014\pi$
$90$		0			0
$91$	−5.77276	+	5.77276i	−0.605149	+	0.605149i
$92$		0			0
$93$	4.21952			0.437544
$94$		0			0
$95$	8.43775	−	0.468420i	0.865695	−	0.0480589i
$96$		0			0
$97$	5.00672	−	5.00672i	0.508355	−	0.508355i	−0.405666	−	0.914021i	$-0.632960\pi$
$97$	5.00672	−	5.00672i	0.508355	−	0.508355i	0.914021	+	0.405666i	$0.132960\pi$
$98$		0			0
$99$	9.39839	−	9.39839i	0.944573	−	0.944573i
$100$		0			0
$101$	−6.37101	−	6.37101i	−0.633939	−	0.633939i	0.315115	−	0.949054i	$-0.397957\pi$
$101$	−6.37101	−	6.37101i	−0.633939	−	0.633939i	−0.949054	+	0.315115i	$0.897957\pi$
$102$		0			0
$103$	1.93695	+	1.93695i	0.190854	+	0.190854i	0.796065	−	0.605211i	$-0.206911\pi$
$103$	1.93695	+	1.93695i	0.190854	+	0.190854i	−0.605211	+	0.796065i	$0.706911\pi$
$104$		0			0
$105$	−1.07505	−	19.3652i	−0.104915	−	1.88985i
$106$		0			0
$107$		−	6.97778i		−	0.674568i	−0.941403	−	0.337284i	$-0.890492\pi$
$107$		−	6.97778i		−	0.674568i	0.941403	−	0.337284i	$-0.109508\pi$
$108$		0			0
$109$	0.277748	+	0.277748i	0.0266034	+	0.0266034i	0.720283	−	0.693680i	$-0.244012\pi$
$109$	0.277748	+	0.277748i	0.0266034	+	0.0266034i	−0.693680	+	0.720283i	$0.744012\pi$
$110$		0			0
$111$		−	6.45766i		−	0.612934i
$112$		0			0
$113$	−8.75577	−	8.75577i	−0.823674	−	0.823674i	0.162959	−	0.986633i	$-0.447896\pi$
$113$	−8.75577	−	8.75577i	−0.823674	−	0.823674i	−0.986633	+	0.162959i	$0.947896\pi$
$114$		0			0
$115$	0.372258	+	6.70557i	0.0347133	+	0.625298i
$116$		0			0
$117$	−8.43142			−0.779485
$118$		0			0
$119$		−	0.360813i		−	0.0330757i
$120$		0			0
$121$		−	3.33340i		−	0.303036i
$122$		0			0
$123$	4.36024			0.393149
$124$		0			0
$125$	6.48729	−	9.10577i	0.580241	−	0.814445i
$126$		0			0
$127$	−0.679502	−	0.679502i	−0.0602961	−	0.0602961i	0.676316	−	0.736612i	$-0.263576\pi$
$127$	−0.679502	−	0.679502i	−0.0602961	−	0.0602961i	−0.736612	+	0.676316i	$0.763576\pi$
$128$		0			0
$129$			9.81350i			0.864030i
$130$		0			0
$131$	−5.43859	−	5.43859i	−0.475172	−	0.475172i	0.428412	−	0.903584i	$-0.359073\pi$
$131$	−5.43859	−	5.43859i	−0.475172	−	0.475172i	−0.903584	+	0.428412i	$0.859073\pi$
$132$		0			0
$133$		−	12.8470i		−	1.11397i
$134$		0			0
$135$	1.94302	−	2.17143i	0.167228	−	0.186887i
$136$		0			0
$137$	7.47496	+	7.47496i	0.638629	+	0.638629i	0.950217	−	0.311588i	$-0.100861\pi$
$137$	7.47496	+	7.47496i	0.638629	+	0.638629i	−0.311588	+	0.950217i	$0.600861\pi$
$138$		0			0
$139$	11.5307	+	11.5307i	0.978023	+	0.978023i	0.999764	−	0.0217404i	$-0.00692074\pi$
$139$	11.5307	+	11.5307i	0.978023	+	0.978023i	−0.0217404	+	0.999764i	$0.506921\pi$
$140$		0			0
$141$	5.49270	−	5.49270i	0.462568	−	0.462568i
$142$		0			0
$143$	−6.42935	+	6.42935i	−0.537649	+	0.537649i
$144$		0			0
$145$	0.693763	+	12.4969i	0.0576139	+	1.03781i
$146$		0			0
$147$	−11.6234			−0.958680
$148$		0			0
$149$	5.51174	−	5.51174i	0.451539	−	0.451539i	−0.444326	−	0.895865i	$-0.646557\pi$
$149$	5.51174	−	5.51174i	0.451539	−	0.451539i	0.895865	+	0.444326i	$0.146557\pi$
$150$		0			0
$151$	4.13617			0.336597			0.168299	−	0.985736i	$-0.446173\pi$
$151$	4.13617			0.336597			0.168299	+	0.985736i	$0.446173\pi$
$152$		0			0
$153$	0.263494	−	0.263494i	0.0213022	−	0.0213022i
$154$		0			0
$155$	2.46573	−	2.75559i	0.198052	−	0.221335i
$156$		0			0
$157$			20.2700i			1.61772i	0.587999	+	0.808861i	$0.299916\pi$
$157$			20.2700i			1.61772i	−0.587999	+	0.808861i	$0.700084\pi$
$158$		0			0
$159$	3.30370			0.262000
$160$		0			0
$161$	10.2096			0.804631
$162$		0			0
$163$		−	13.1835i		−	1.03262i	−0.856403	−	0.516308i	$-0.827306\pi$
$163$		−	13.1835i		−	1.03262i	0.856403	−	0.516308i	$-0.172694\pi$
$164$		0			0
$165$	−1.19733	−	21.5678i	−0.0932121	−	1.67905i
$166$		0			0
$167$	11.8190	−	11.8190i	0.914585	−	0.914585i	−0.0820441	−	0.996629i	$-0.526145\pi$
$167$	11.8190	−	11.8190i	0.914585	−	0.914585i	0.996629	+	0.0820441i	$0.0261448\pi$
$168$		0			0
$169$	−7.23214			−0.556319
$170$		0			0
$171$	9.38185	−	9.38185i	0.717448	−	0.717448i
$172$		0			0
$173$	−15.5763			−1.18424			−0.592120	−	0.805849i	$-0.701709\pi$
$173$	−15.5763			−1.18424			−0.592120	+	0.805849i	$0.701709\pi$
$174$		0			0
$175$	−13.2748	−	10.6142i	−1.00348	−	0.802361i
$176$		0			0
$177$	−13.5137	+	13.5137i	−1.01575	+	1.01575i
$178$		0			0
$179$	15.5963	−	15.5963i	1.16572	−	1.16572i	0.182523	−	0.983202i	$-0.441574\pi$
$179$	15.5963	−	15.5963i	1.16572	−	1.16572i	0.983202	−	0.182523i	$-0.0584265\pi$
$180$		0			0
$181$	−2.98705	−	2.98705i	−0.222026	−	0.222026i	0.587325	−	0.809351i	$-0.300181\pi$
$181$	−2.98705	−	2.98705i	−0.222026	−	0.222026i	−0.809351	+	0.587325i	$0.800181\pi$
$182$		0			0
$183$	26.1318	+	26.1318i	1.93172	+	1.93172i
$184$		0			0
$185$	−4.21723	−	3.77362i	−0.310057	−	0.277442i
$186$		0			0
$187$		−	0.401852i		−	0.0293863i
$188$		0			0
$189$	−3.13224	−	3.13224i	−0.227837	−	0.227837i
$190$		0			0
$191$		−	6.47168i		−	0.468274i	−0.972204	−	0.234137i	$-0.924774\pi$
$191$		−	6.47168i		−	0.468274i	0.972204	−	0.234137i	$-0.0752264\pi$
$192$		0			0
$193$	−11.1131	−	11.1131i	−0.799936	−	0.799936i	0.183149	−	0.983085i	$-0.441371\pi$
$193$	−11.1131	−	11.1131i	−0.799936	−	0.799936i	−0.983085	+	0.183149i	$0.941371\pi$
$194$		0			0
$195$	−9.13730	+	10.2114i	−0.654336	+	0.731257i
$196$		0			0
$197$	25.0927			1.78778			0.893889	−	0.448288i	$-0.147966\pi$
$197$	25.0927			1.78778			0.893889	+	0.448288i	$0.147966\pi$
$198$		0			0
$199$		−	18.7579i		−	1.32972i	−0.746970	−	0.664858i	$-0.768492\pi$
$199$		−	18.7579i		−	1.32972i	0.746970	−	0.664858i	$-0.231508\pi$
$200$		0			0
$201$			27.1056i			1.91188i
$202$		0			0
$203$	19.0273			1.33545
$204$		0			0
$205$	2.54796	−	2.84749i	0.177958	−	0.198877i
$206$		0			0
$207$	7.45586	+	7.45586i	0.518218	+	0.518218i
$208$		0			0
$209$		−	14.3082i		−	0.989718i
$210$		0			0
$211$	6.38863	+	6.38863i	0.439811	+	0.439811i	0.891948	−	0.452137i	$-0.149338\pi$
$211$	6.38863	+	6.38863i	0.439811	+	0.439811i	−0.452137	+	0.891948i	$0.649338\pi$
$212$		0			0
$213$			5.80036i			0.397434i
$214$		0			0
$215$	6.40879	+	5.73465i	0.437076	+	0.391100i
$216$		0			0
$217$	−3.97489	−	3.97489i	−0.269833	−	0.269833i
$218$		0			0
$219$	−25.4930	−	25.4930i	−1.72266	−	1.72266i
$220$		0			0
$221$	−0.180253	+	0.180253i	−0.0121252	+	0.0121252i
$222$		0			0
$223$	−4.29779	+	4.29779i	−0.287801	+	0.287801i	−0.836210	−	0.548409i	$-0.815234\pi$
$223$	−4.29779	+	4.29779i	−0.287801	+	0.287801i	0.548409	+	0.836210i	$0.315234\pi$
$224$		0			0
$225$	−1.94297	−	17.4456i	−0.129531	−	1.16304i
$226$		0			0
$227$	29.1029			1.93163			0.965813	−	0.259241i	$-0.0834724\pi$
$227$	29.1029			1.93163			0.965813	+	0.259241i	$0.0834724\pi$
$228$		0			0
$229$	−18.3405	+	18.3405i	−1.21198	+	1.21198i	−0.241600	+	0.970376i	$0.577672\pi$
$229$	−18.3405	+	18.3405i	−1.21198	+	1.21198i	−0.970376	+	0.241600i	$0.922328\pi$
$230$		0			0
$231$	−32.8382			−2.16060
$232$		0			0
$233$	−1.46663	+	1.46663i	−0.0960824	+	0.0960824i	−0.753514	−	0.657432i	$-0.771643\pi$
$233$	−1.46663	+	1.46663i	−0.0960824	+	0.0960824i	0.657432	+	0.753514i	$0.271643\pi$
$234$		0			0
$235$	−0.377322	−	6.79678i	−0.0246138	−	0.443373i
$236$		0			0
$237$			22.2147i			1.44300i
$238$		0			0
$239$	12.5432			0.811352			0.405676	−	0.914017i	$-0.367036\pi$
$239$	12.5432			0.811352			0.405676	+	0.914017i	$0.367036\pi$
$240$		0			0
$241$	14.8870			0.958954			0.479477	−	0.877554i	$-0.340826\pi$
$241$	14.8870			0.958954			0.479477	+	0.877554i	$0.340826\pi$
$242$		0			0
$243$			22.2990i			1.43048i
$244$		0			0
$245$	−6.79228	+	7.59075i	−0.433943	+	0.484955i
$246$		0			0
$247$	−6.41803	+	6.41803i	−0.408370	+	0.408370i
$248$		0			0
$249$	28.4018			1.79989
$250$		0			0
$251$	−5.38459	+	5.38459i	−0.339872	+	0.339872i	−0.856319	−	0.516447i	$-0.827254\pi$
$251$	−5.38459	+	5.38459i	−0.339872	+	0.339872i	0.516447	+	0.856319i	$0.327254\pi$
$252$		0			0
$253$	11.3709			0.714880
$254$		0			0
$255$	−0.0335684	−	0.604675i	−0.00210214	−	0.0378662i
$256$		0			0
$257$	−3.88657	+	3.88657i	−0.242437	+	0.242437i	−0.817858	−	0.575420i	$-0.804838\pi$
$257$	−3.88657	+	3.88657i	−0.242437	+	0.242437i	0.575420	+	0.817858i	$0.304838\pi$
$258$		0			0
$259$	−6.08327	+	6.08327i	−0.377996	+	0.377996i
$260$		0			0
$261$	13.8952	+	13.8952i	0.860090	+	0.860090i
$262$		0			0
$263$	−16.9658	−	16.9658i	−1.04615	−	1.04615i	−0.998882	−	0.0472716i	$-0.984947\pi$
$263$	−16.9658	−	16.9658i	−1.04615	−	1.04615i	−0.0472716	−	0.998882i	$-0.515053\pi$
$264$		0			0
$265$	1.93056	−	2.15751i	0.118593	−	0.132535i
$266$		0			0
$267$			39.9046i			2.44212i
$268$		0			0
$269$	2.55482	+	2.55482i	0.155770	+	0.155770i	0.780689	−	0.624919i	$-0.214868\pi$
$269$	2.55482	+	2.55482i	0.155770	+	0.155770i	−0.624919	+	0.780689i	$0.714868\pi$
$270$		0			0
$271$			3.33684i			0.202698i	0.994851	+	0.101349i	$0.0323159\pi$
$271$			3.33684i			0.202698i	−0.994851	+	0.101349i	$0.967684\pi$
$272$		0			0
$273$	14.7298	+	14.7298i	0.891488	+	0.891488i
$274$		0			0
$275$	−14.7847	−	11.8215i	−0.891551	−	0.712863i
$276$		0			0
$277$	−4.60736			−0.276830			−0.138415	−	0.990374i	$-0.544201\pi$
$277$	−4.60736			−0.276830			−0.138415	+	0.990374i	$0.544201\pi$
$278$		0			0
$279$		−	5.80554i		−	0.347569i
$280$		0			0
$281$		−	22.1178i		−	1.31944i	−0.751513	−	0.659718i	$-0.770676\pi$
$281$		−	22.1178i		−	1.31944i	0.751513	−	0.659718i	$-0.229324\pi$
$282$		0			0
$283$	−10.8629			−0.645734			−0.322867	−	0.946444i	$-0.604647\pi$
$283$	−10.8629			−0.645734			−0.322867	+	0.946444i	$0.604647\pi$
$284$		0			0
$285$	−1.19522	−	21.5298i	−0.0707990	−	1.27532i
$286$		0			0
$287$	−4.10745	−	4.10745i	−0.242455	−	0.242455i
$288$		0			0
$289$			16.9887i			0.999337i
$290$		0			0
$291$	−12.7752	−	12.7752i	−0.748895	−	0.748895i
$292$		0			0
$293$			18.4067i			1.07533i	0.843159	+	0.537665i	$0.180693\pi$
$293$			18.4067i			1.07533i	−0.843159	+	0.537665i	$0.819307\pi$
$294$		0			0
$295$	0.928326	+	16.7221i	0.0540492	+	0.973600i
$296$		0			0
$297$	−3.48850	−	3.48850i	−0.202423	−	0.202423i
$298$		0			0
$299$	−5.10048	−	5.10048i	−0.294968	−	0.294968i
$300$		0			0
$301$	9.24455	−	9.24455i	0.532847	−	0.532847i
$302$		0			0
$303$	−16.2563	+	16.2563i	−0.933900	+	0.933900i
$304$		0			0
$305$	32.3360	−	1.79513i	1.85156	−	0.102789i
$306$		0			0
$307$	−6.60872			−0.377180			−0.188590	−	0.982056i	$-0.560392\pi$
$307$	−6.60872			−0.377180			−0.188590	+	0.982056i	$0.560392\pi$
$308$		0			0
$309$	4.94234	−	4.94234i	0.281160	−	0.281160i
$310$		0			0
$311$	0.606102			0.0343689			0.0171845	−	0.999852i	$-0.494530\pi$
$311$	0.606102			0.0343689			0.0171845	+	0.999852i	$0.494530\pi$
$312$		0			0
$313$	−19.3708	+	19.3708i	−1.09490	+	1.09490i	−0.0999032	+	0.994997i	$0.531853\pi$
$313$	−19.3708	+	19.3708i	−1.09490	+	1.09490i	−0.994997	+	0.0999032i	$0.968147\pi$
$314$		0			0
$315$	−26.6441	+	1.47914i	−1.50123	+	0.0833403i
$316$		0			0
$317$		−	7.04328i		−	0.395590i	−0.980243	−	0.197795i	$-0.936622\pi$
$317$		−	7.04328i		−	0.395590i	0.980243	−	0.197795i	$-0.0633780\pi$
$318$		0			0
$319$	21.1914			1.18649
$320$		0			0
$321$	−17.8046			−0.993753
$322$		0			0
$323$		−	0.401145i		−	0.0223203i
$324$		0			0
$325$	1.32917	+	11.9344i	0.0737290	+	0.662001i
$326$		0			0
$327$	0.708703	−	0.708703i	0.0391914	−	0.0391914i
$328$		0			0
$329$	−10.3485			−0.570532
$330$		0			0
$331$	−13.2275	+	13.2275i	−0.727047	+	0.727047i	−0.970031	−	0.242983i	$-0.921874\pi$
$331$	−13.2275	+	13.2275i	−0.727047	+	0.727047i	0.242983	+	0.970031i	$0.421874\pi$
$332$		0			0
$333$	−8.88495			−0.486892
$334$		0			0
$335$	17.7016	+	15.8395i	0.967140	+	0.865407i
$336$		0			0
$337$	7.73287	−	7.73287i	0.421236	−	0.421236i	−0.464393	−	0.885629i	$-0.653727\pi$
$337$	7.73287	−	7.73287i	0.421236	−	0.421236i	0.885629	+	0.464393i	$0.153727\pi$
$338$		0			0
$339$	−22.3413	+	22.3413i	−1.21341	+	1.21341i
$340$		0			0
$341$	−4.42699	−	4.42699i	−0.239735	−	0.239735i
$342$		0			0
$343$	−5.87623	−	5.87623i	−0.317286	−	0.317286i
$344$		0			0
$345$	17.1100	−	0.949857i	0.921170	−	0.0511386i
$346$		0			0
$347$			11.3945i			0.611691i	0.952081	+	0.305845i	$0.0989391\pi$
$347$			11.3945i			0.611691i	−0.952081	+	0.305845i	$0.901061\pi$
$348$		0			0
$349$	−12.0508	−	12.0508i	−0.645066	−	0.645066i	0.306730	−	0.951796i	$-0.400765\pi$
$349$	−12.0508	−	12.0508i	−0.645066	−	0.645066i	−0.951796	+	0.306730i	$0.900765\pi$
$350$		0			0
$351$			3.12958i			0.167045i
$352$		0			0
$353$	−6.47876	−	6.47876i	−0.344830	−	0.344830i	0.513350	−	0.858179i	$-0.328404\pi$
$353$	−6.47876	−	6.47876i	−0.344830	−	0.344830i	−0.858179	+	0.513350i	$0.828404\pi$
$354$		0			0
$355$	3.78798	+	3.38952i	0.201045	+	0.179897i
$356$		0			0
$357$	−0.920653			−0.0487261
$358$		0			0
$359$		−	3.25098i		−	0.171580i	−0.996313	−	0.0857902i	$-0.972659\pi$
$359$		−	3.25098i		−	0.171580i	0.996313	−	0.0857902i	$-0.0273415\pi$
$360$		0			0
$361$			4.71699i			0.248263i
$362$		0			0
$363$	−8.50553			−0.446424
$364$		0			0
$365$	−31.5456	+	1.75125i	−1.65117	+	0.0916646i
$366$		0			0
$367$	−12.7038	−	12.7038i	−0.663132	−	0.663132i	0.292985	−	0.956117i	$-0.405351\pi$
$367$	−12.7038	−	12.7038i	−0.663132	−	0.663132i	−0.956117	+	0.292985i	$0.905351\pi$
$368$		0			0
$369$		−	5.99916i		−	0.312304i
$370$		0			0
$371$	−3.11216	−	3.11216i	−0.161575	−	0.161575i
$372$		0			0
$373$		−	21.9761i		−	1.13788i	−0.822379	−	0.568939i	$-0.807354\pi$
$373$		−	21.9761i		−	1.13788i	0.822379	−	0.568939i	$-0.192646\pi$
$374$		0			0
$375$	−23.2343	−	16.5530i	−1.19982	−	0.854794i
$376$		0			0
$377$	−9.50557	−	9.50557i	−0.489562	−	0.489562i
$378$		0			0
$379$	17.0642	+	17.0642i	0.876527	+	0.876527i	0.993174	−	0.116646i	$-0.0372144\pi$
$379$	17.0642	+	17.0642i	0.876527	+	0.876527i	−0.116646	+	0.993174i	$0.537214\pi$
$380$		0			0
$381$	−1.73382	+	1.73382i	−0.0888264	+	0.0888264i
$382$		0			0
$383$	−0.228058	+	0.228058i	−0.0116532	+	0.0116532i	−0.712909	−	0.701256i	$-0.752623\pi$
$383$	−0.228058	+	0.228058i	−0.0116532	+	0.0116532i	0.701256	+	0.712909i	$0.252623\pi$
$384$		0			0
$385$	−19.1894	+	21.4453i	−0.977985	+	1.09295i
$386$		0			0
$387$	13.5022			0.686354
$388$		0			0
$389$	−14.3036	+	14.3036i	−0.725221	+	0.725221i	−0.969664	−	0.244443i	$-0.921395\pi$
$389$	−14.3036	+	14.3036i	−0.725221	+	0.725221i	0.244443	+	0.969664i	$0.421395\pi$
$390$		0			0
$391$	0.318794			0.0161221
$392$		0			0
$393$	−13.8771	+	13.8771i	−0.700009	+	0.700009i
$394$		0			0
$395$	14.5075	+	12.9815i	0.729953	+	0.653169i
$396$		0			0
$397$			5.11618i			0.256774i	0.991724	+	0.128387i	$0.0409799\pi$
$397$			5.11618i			0.256774i	−0.991724	+	0.128387i	$0.959020\pi$
$398$		0			0
$399$	−32.7804			−1.64107
$400$		0			0
$401$	−16.2837			−0.813170			−0.406585	−	0.913613i	$-0.633281\pi$
$401$	−16.2837			−0.813170			−0.406585	+	0.913613i	$0.633281\pi$
$402$		0			0
$403$			3.97152i			0.197835i
$404$		0			0
$405$	12.0095	+	10.7462i	0.596758	+	0.533985i
$406$		0			0
$407$	−6.77518	+	6.77518i	−0.335833	+	0.335833i
$408$		0			0
$409$	17.4256			0.861640			0.430820	−	0.902438i	$-0.358224\pi$
$409$	17.4256			0.861640			0.430820	+	0.902438i	$0.358224\pi$
$410$		0			0
$411$	19.0732	−	19.0732i	0.940810	−	0.940810i
$412$		0			0
$413$	25.4604			1.25283
$414$		0			0
$415$	16.5970	−	18.5481i	0.814714	−	0.910488i
$416$		0			0
$417$	29.4219	−	29.4219i	1.44080	−	1.44080i
$418$		0			0
$419$	11.7257	−	11.7257i	0.572837	−	0.572837i	−0.360083	−	0.932920i	$-0.617252\pi$
$419$	11.7257	−	11.7257i	0.572837	−	0.572837i	0.932920	+	0.360083i	$0.117252\pi$
$420$		0			0
$421$	23.5406	+	23.5406i	1.14730	+	1.14730i	0.987082	+	0.160216i	$0.0512191\pi$
$421$	23.5406	+	23.5406i	1.14730	+	1.14730i	0.160216	+	0.987082i	$0.448781\pi$
$422$		0			0
$423$	−7.55728	−	7.55728i	−0.367447	−	0.367447i
$424$		0			0
$425$	−0.414505	−	0.331428i	−0.0201064	−	0.0160766i
$426$		0			0
$427$		−	49.2335i		−	2.38258i
$428$		0			0
$429$	16.4052	+	16.4052i	0.792049	+	0.792049i
$430$		0			0
$431$			35.0243i			1.68706i	0.537079	+	0.843532i	$0.319528\pi$
$431$			35.0243i			1.68706i	−0.537079	+	0.843532i	$0.680472\pi$
$432$		0			0
$433$	10.1094	+	10.1094i	0.485828	+	0.485828i	0.906987	−	0.421159i	$-0.138376\pi$
$433$	10.1094	+	10.1094i	0.485828	+	0.485828i	−0.421159	+	0.906987i	$0.638376\pi$
$434$		0			0
$435$	31.8872	−	1.77021i	1.52887	−	0.0848752i
$436$		0			0
$437$	11.3509			0.542985
$438$		0			0
$439$			22.6071i			1.07898i	0.841993	+	0.539488i	$0.181382\pi$
$439$			22.6071i			1.07898i	−0.841993	+	0.539488i	$0.818618\pi$
$440$		0			0
$441$			15.9923i			0.761540i
$442$		0			0
$443$	−10.9178			−0.518721			−0.259360	−	0.965781i	$-0.583512\pi$
$443$	−10.9178			−0.518721			−0.259360	+	0.965781i	$0.583512\pi$
$444$		0			0
$445$	26.0601	+	23.3188i	1.23537	+	1.10542i
$446$		0			0
$447$	−14.0638	−	14.0638i	−0.665195	−	0.665195i
$448$		0			0
$449$			28.8112i			1.35969i	0.733358	+	0.679843i	$0.237952\pi$
$449$			28.8112i			1.35969i	−0.733358	+	0.679843i	$0.762048\pi$
$450$		0			0
$451$	−4.57463	−	4.57463i	−0.215411	−	0.215411i
$452$		0			0
$453$		−	10.5539i		−	0.495865i
$454$		0			0
$455$	18.2270	−	1.01187i	0.854495	−	0.0474371i
$456$		0			0
$457$	19.1653	+	19.1653i	0.896513	+	0.896513i	0.995126	−	0.0986128i	$-0.0314405\pi$
$457$	19.1653	+	19.1653i	0.896513	+	0.896513i	−0.0986128	+	0.995126i	$0.531441\pi$
$458$		0			0
$459$	−0.0978038	−	0.0978038i	−0.00456509	−	0.00456509i
$460$		0			0
$461$	−4.43227	+	4.43227i	−0.206431	+	0.206431i	−0.802749	−	0.596317i	$-0.796630\pi$
$461$	−4.43227	+	4.43227i	−0.206431	+	0.206431i	0.596317	+	0.802749i	$0.296630\pi$
$462$		0			0
$463$	20.1518	−	20.1518i	0.936534	−	0.936534i	−0.0615691	−	0.998103i	$-0.519610\pi$
$463$	20.1518	−	20.1518i	0.936534	−	0.936534i	0.998103	+	0.0615691i	$0.0196105\pi$
$464$		0			0
$465$	−7.03120	−	6.29158i	−0.326064	−	0.291765i
$466$		0			0
$467$	−3.89858			−0.180405			−0.0902025	−	0.995923i	$-0.528751\pi$
$467$	−3.89858			−0.180405			−0.0902025	+	0.995923i	$0.528751\pi$
$468$		0			0
$469$	25.5342	−	25.5342i	1.17906	−	1.17906i
$470$		0			0
$471$	51.7211			2.38318
$472$		0			0
$473$	10.2960	−	10.2960i	0.473412	−	0.473412i
$474$		0			0
$475$	−14.7587	−	11.8007i	−0.677175	−	0.541453i
$476$		0			0
$477$		−	4.54548i		−	0.208123i
$478$		0			0
$479$	9.85299			0.450194			0.225097	−	0.974336i	$-0.427730\pi$
$479$	9.85299			0.450194			0.225097	+	0.974336i	$0.427730\pi$
$480$		0			0
$481$	6.07811			0.277138
$482$		0			0
$483$		−	26.0510i		−	1.18536i
$484$		0			0
$485$	−15.8083	+	0.877595i	−0.717818	+	0.0398495i
$486$		0			0
$487$	13.9164	−	13.9164i	0.630611	−	0.630611i	−0.317610	−	0.948221i	$-0.602880\pi$
$487$	13.9164	−	13.9164i	0.630611	−	0.630611i	0.948221	+	0.317610i	$0.102880\pi$
$488$		0			0
$489$	−33.6392			−1.52122
$490$		0			0
$491$	2.39213	−	2.39213i	0.107955	−	0.107955i	−0.651066	−	0.759021i	$-0.725678\pi$
$491$	2.39213	−	2.39213i	0.107955	−	0.107955i	0.759021	+	0.651066i	$0.225678\pi$
$492$		0			0
$493$	0.594124			0.0267580
$494$		0			0
$495$	−29.6746	+	1.64738i	−1.33377	+	0.0740443i
$496$		0			0
$497$	5.46408	−	5.46408i	0.245098	−	0.245098i
$498$		0			0
$499$	9.87034	−	9.87034i	0.441857	−	0.441857i	−0.450779	−	0.892636i	$-0.648854\pi$
$499$	9.87034	−	9.87034i	0.441857	−	0.441857i	0.892636	+	0.450779i	$0.148854\pi$
$500$		0			0
$501$	−30.1575	−	30.1575i	−1.34734	−	1.34734i
$502$		0			0
$503$	−9.29035	−	9.29035i	−0.414236	−	0.414236i	0.468975	−	0.883211i	$-0.344623\pi$
$503$	−9.29035	−	9.29035i	−0.414236	−	0.414236i	−0.883211	+	0.468975i	$0.844623\pi$
$504$		0			0
$505$	1.11673	+	20.1159i	0.0496939	+	0.895146i
$506$		0			0
$507$			18.4536i			0.819553i
$508$		0			0
$509$	−6.53818	−	6.53818i	−0.289800	−	0.289800i	0.547201	−	0.837001i	$-0.315693\pi$
$509$	−6.53818	−	6.53818i	−0.289800	−	0.289800i	−0.837001	+	0.547201i	$0.815693\pi$
$510$		0			0
$511$			48.0301i			2.12473i
$512$		0			0
$513$	−3.48236	−	3.48236i	−0.153750	−	0.153750i
$514$		0			0
$515$	−0.339516	−	6.11577i	−0.0149608	−	0.269493i
$516$		0			0
$517$	−11.5255			−0.506893
$518$		0			0
$519$			39.7445i			1.74459i
$520$		0			0
$521$			14.2961i			0.626324i	0.949700	+	0.313162i	$0.101388\pi$
$521$			14.2961i			0.626324i	−0.949700	+	0.313162i	$0.898612\pi$
$522$		0			0
$523$	16.0319			0.701027			0.350513	−	0.936558i	$-0.386007\pi$
$523$	16.0319			0.701027			0.350513	+	0.936558i	$0.386007\pi$
$524$		0			0
$525$	−27.0834	+	33.8721i	−1.18201	+	1.47830i
$526$		0			0
$527$	−0.124115	−	0.124115i	−0.00540655	−	0.00540655i
$528$		0			0
$529$		−	13.9794i		−	0.607798i
$530$		0			0
$531$	18.5932	+	18.5932i	0.806875	+	0.806875i
$532$		0			0
$533$			4.10397i			0.177762i
$534$		0			0
$535$	−10.4043	+	11.6274i	−0.449819	+	0.502697i
$536$		0			0
$537$	−39.7957	−	39.7957i	−1.71731	−	1.71731i
$538$		0			0
$539$	12.1949	+	12.1949i	0.525271	+	0.525271i
$540$		0			0
$541$	14.3926	−	14.3926i	0.618785	−	0.618785i	−0.326435	−	0.945220i	$-0.605847\pi$
$541$	14.3926	−	14.3926i	0.618785	−	0.618785i	0.945220	+	0.326435i	$0.105847\pi$
$542$		0			0
$543$	−7.62178	+	7.62178i	−0.327082	+	0.327082i
$544$		0			0
$545$	−0.0486846	−	0.876965i	−0.00208542	−	0.0375651i
$546$		0			0
$547$	−11.6741			−0.499148			−0.249574	−	0.968356i	$-0.580291\pi$
$547$	−11.6741			−0.499148			−0.249574	+	0.968356i	$0.580291\pi$
$548$		0			0
$549$	35.9541	−	35.9541i	1.53448	−	1.53448i
$550$		0			0
$551$	21.1541			0.901197
$552$		0			0
$553$	20.9268	−	20.9268i	0.889898	−	0.889898i
$554$		0			0
$555$	−9.62880	+	10.7607i	−0.408720	+	0.456767i
$556$		0			0
$557$		−	39.6712i		−	1.68092i	−0.541873	−	0.840460i	$-0.682285\pi$
$557$		−	39.6712i		−	1.68092i	0.541873	−	0.840460i	$-0.317715\pi$
$558$		0			0
$559$	−9.23671			−0.390671
$560$		0			0
$561$	−1.02537			−0.0432911
$562$		0			0
$563$		−	12.4534i		−	0.524850i	−0.964952	−	0.262425i	$-0.915478\pi$
$563$		−	12.4534i		−	0.524850i	0.964952	−	0.262425i	$-0.0845222\pi$
$564$		0			0
$565$	1.53474	+	27.6456i	0.0645671	+	1.16306i
$566$		0			0
$567$	17.3235	−	17.3235i	0.727519	−	0.727519i
$568$		0			0
$569$	5.62622			0.235863			0.117932	−	0.993022i	$-0.462374\pi$
$569$	5.62622			0.235863			0.117932	+	0.993022i	$0.462374\pi$
$570$		0			0
$571$	23.1808	−	23.1808i	0.970086	−	0.970086i	−0.0294797	−	0.999565i	$-0.509385\pi$
$571$	23.1808	−	23.1808i	0.970086	−	0.970086i	0.999565	+	0.0294797i	$0.00938505\pi$
$572$		0			0
$573$	−16.5132			−0.689848
$574$		0			0
$575$	9.37814	−	11.7289i	0.391095	−	0.489128i
$576$		0			0
$577$	−25.6307	+	25.6307i	−1.06702	+	1.06702i	−0.0694322	+	0.997587i	$0.522119\pi$
$577$	−25.6307	+	25.6307i	−1.06702	+	1.06702i	−0.997587	+	0.0694322i	$0.977881\pi$
$578$		0			0
$579$	−28.3562	+	28.3562i	−1.17844	+	1.17844i
$580$		0			0
$581$	−26.7552	−	26.7552i	−1.10999	−	1.10999i
$582$		0			0
$583$	−3.46614	−	3.46614i	−0.143553	−	0.143553i
$584$		0			0
$585$	14.0497	+	12.5718i	0.580884	+	0.519780i
$586$		0			0
$587$		−	25.5579i		−	1.05489i	−0.849590	−	0.527444i	$-0.823151\pi$
$587$		−	25.5579i		−	1.05489i	0.849590	−	0.527444i	$-0.176849\pi$
$588$		0			0
$589$	−4.41920	−	4.41920i	−0.182090	−	0.182090i
$590$		0			0
$591$		−	64.0266i		−	2.63370i
$592$		0			0
$593$	2.96607	+	2.96607i	0.121802	+	0.121802i	0.765380	−	0.643578i	$-0.222551\pi$
$593$	2.96607	+	2.96607i	0.121802	+	0.121802i	−0.643578	+	0.765380i	$0.722551\pi$
$594$		0			0
$595$	−0.537996	+	0.601241i	−0.0220557	+	0.0246485i
$596$		0			0
$597$	−47.8629			−1.95890
$598$		0			0
$599$			5.14724i			0.210311i	0.994456	+	0.105155i	$0.0335340\pi$
$599$			5.14724i			0.210311i	−0.994456	+	0.105155i	$0.966466\pi$
$600$		0			0
$601$		−	33.5619i		−	1.36902i	−0.729005	−	0.684509i	$-0.760017\pi$
$601$		−	33.5619i		−	1.36902i	0.729005	−	0.684509i	$-0.239983\pi$
$602$		0			0
$603$	37.2940			1.51873
$604$		0			0
$605$	−4.97032	+	5.55461i	−0.202072	+	0.225827i
$606$		0			0
$607$	−3.29572	−	3.29572i	−0.133769	−	0.133769i	0.637052	−	0.770821i	$-0.280154\pi$
$607$	−3.29572	−	3.29572i	−0.133769	−	0.133769i	−0.770821	+	0.637052i	$0.780154\pi$
$608$		0			0
$609$		−	48.5501i		−	1.96735i
$610$		0			0
$611$	5.16986	+	5.16986i	0.209150	+	0.209150i
$612$		0			0
$613$		−	0.261903i		−	0.0105781i	−0.999986	−	0.00528907i	$-0.998316\pi$
$613$		−	0.261903i		−	0.0105781i	0.999986	−	0.00528907i	$-0.00168357\pi$
$614$		0			0
$615$	−7.26568	−	6.50140i	−0.292981	−	0.262162i
$616$		0			0
$617$	−12.1529	−	12.1529i	−0.489259	−	0.489259i	0.418813	−	0.908072i	$-0.362446\pi$
$617$	−12.1529	−	12.1529i	−0.489259	−	0.489259i	−0.908072	+	0.418813i	$0.862446\pi$
$618$		0			0
$619$	12.1134	+	12.1134i	0.486877	+	0.486877i	0.907319	−	0.420442i	$-0.138125\pi$
$619$	12.1134	+	12.1134i	0.486877	+	0.486877i	−0.420442	+	0.907319i	$0.638125\pi$
$620$		0			0
$621$	2.76747	−	2.76747i	0.111055	−	0.111055i
$622$		0			0
$623$	37.5911	−	37.5911i	1.50606	−	1.50606i
$624$		0			0
$625$	−24.3874	+	5.50042i	−0.975496	+	0.220017i
$626$		0			0
$627$	−36.5089			−1.45802
$628$		0			0
$629$	−0.189949	+	0.189949i	−0.00757377	+	0.00757377i
$630$		0			0
$631$	−49.8568			−1.98477			−0.992384	−	0.123179i	$-0.960691\pi$
$631$	−49.8568			−1.98477			−0.992384	+	0.123179i	$0.960691\pi$
$632$		0			0
$633$	16.3013	−	16.3013i	0.647917	−	0.647917i
$634$		0			0
$635$	0.119105	+	2.14547i	0.00472656	+	0.0851404i
$636$		0			0
$637$		−	10.9402i		−	0.433467i
$638$		0			0
$639$	7.98059			0.315707
$640$		0			0
$641$	−4.10036			−0.161954			−0.0809772	−	0.996716i	$-0.525804\pi$
$641$	−4.10036			−0.161954			−0.0809772	+	0.996716i	$0.525804\pi$
$642$		0			0
$643$		−	18.7451i		−	0.739233i	−0.929184	−	0.369617i	$-0.879489\pi$
$643$		−	18.7451i		−	0.739233i	0.929184	−	0.369617i	$-0.120511\pi$
$644$		0			0
$645$	14.6326	−	16.3527i	0.576157	−	0.643888i
$646$		0			0
$647$	−5.46529	+	5.46529i	−0.214863	+	0.214863i	−0.806330	−	0.591467i	$-0.798549\pi$
$647$	−5.46529	+	5.46529i	−0.214863	+	0.214863i	0.591467	+	0.806330i	$0.298549\pi$
$648$		0			0
$649$	28.3563			1.11308
$650$		0			0
$651$	−10.1424	+	10.1424i	−0.397510	+	0.397510i
$652$		0			0
$653$	33.9219			1.32747			0.663733	−	0.747970i	$-0.268971\pi$
$653$	33.9219			1.32747			0.663733	+	0.747970i	$0.268971\pi$
$654$		0			0
$655$	0.953294	+	17.1719i	0.0372483	+	0.670961i
$656$		0			0
$657$	−35.0753	+	35.0753i	−1.36842	+	1.36842i
$658$		0			0
$659$	−26.4961	+	26.4961i	−1.03214	+	1.03214i	−0.0326746	+	0.999466i	$0.510402\pi$
$659$	−26.4961	+	26.4961i	−1.03214	+	1.03214i	−0.999466	+	0.0326746i	$0.989598\pi$
$660$		0			0
$661$	−10.6974	−	10.6974i	−0.416081	−	0.416081i	0.467769	−	0.883851i	$-0.345058\pi$
$661$	−10.6974	−	10.6974i	−0.416081	−	0.416081i	−0.883851	+	0.467769i	$0.845058\pi$
$662$		0			0
$663$	0.459936	+	0.459936i	0.0178624	+	0.0178624i
$664$		0			0
$665$	−19.1557	+	21.4075i	−0.742826	+	0.830149i
$666$		0			0
$667$			16.8114i			0.650941i
$668$		0			0
$669$	10.9663	+	10.9663i	0.423980	+	0.423980i
$670$		0			0
$671$		−	54.8333i		−	2.11682i
$672$		0			0
$673$	−6.70854	−	6.70854i	−0.258595	−	0.258595i	0.565887	−	0.824483i	$-0.308534\pi$
$673$	−6.70854	−	6.70854i	−0.258595	−	0.258595i	−0.824483	+	0.565887i	$0.808534\pi$
$674$		0			0
$675$	−6.47549	+	0.721194i	−0.249242	+	0.0277588i
$676$		0			0
$677$	−13.1970			−0.507200			−0.253600	−	0.967309i	$-0.581615\pi$
$677$	−13.1970			−0.507200			−0.253600	+	0.967309i	$0.581615\pi$
$678$		0			0
$679$			24.0691i			0.923686i
$680$		0			0
$681$		−	74.2591i		−	2.84561i
$682$		0			0
$683$	−37.9089			−1.45054			−0.725272	−	0.688462i	$-0.758286\pi$
$683$	−37.9089			−1.45054			−0.725272	+	0.688462i	$0.758286\pi$
$684$		0			0
$685$	−1.31024	−	23.6016i	−0.0500616	−	0.901770i
$686$		0			0
$687$	46.7978	+	46.7978i	1.78545	+	1.78545i
$688$		0			0
$689$			3.10952i			0.118463i
$690$		0			0
$691$	20.8280	+	20.8280i	0.792335	+	0.792335i	0.981873	−	0.189538i	$-0.0606991\pi$
$691$	20.8280	+	20.8280i	0.792335	+	0.792335i	−0.189538	+	0.981873i	$0.560699\pi$
$692$		0			0
$693$			45.1813i			1.71630i
$694$		0			0
$695$	−2.02114	−	36.4073i	−0.0766664	−	1.38101i
$696$		0			0
$697$	−0.128255	−	0.128255i	−0.00485799	−	0.00485799i
$698$		0			0
$699$	3.74227	+	3.74227i	0.141546	+	0.141546i
$700$		0			0
$701$	−19.9053	+	19.9053i	−0.751812	+	0.751812i	−0.974817	−	0.223005i	$-0.928413\pi$
$701$	−19.9053	+	19.9053i	−0.751812	+	0.751812i	0.223005	+	0.974817i	$0.428413\pi$
$702$		0			0
$703$	−6.76326	+	6.76326i	−0.255081	+	0.255081i
$704$		0			0
$705$	−17.3427	+	0.962778i	−0.653165	+	0.0362603i
$706$		0			0
$707$	30.6277			1.15187
$708$		0			0
$709$	−8.57112	+	8.57112i	−0.321895	+	0.321895i	−0.849494	−	0.527599i	$-0.823092\pi$
$709$	−8.57112	+	8.57112i	−0.321895	+	0.321895i	0.527599	+	0.849494i	$0.323092\pi$
$710$		0			0
$711$	30.5647			1.14627
$712$		0			0
$713$	3.51199	−	3.51199i	0.131525	−	0.131525i
$714$		0			0
$715$	20.3001	−	1.12696i	0.759182	−	0.0421458i
$716$		0			0
$717$		−	32.0053i		−	1.19526i
$718$		0			0
$719$	−33.1900			−1.23778			−0.618889	−	0.785478i	$-0.712417\pi$
$719$	−33.1900			−1.23778			−0.618889	+	0.785478i	$0.712417\pi$
$720$		0			0
$721$	−9.31162			−0.346783
$722$		0			0
$723$		−	37.9857i		−	1.41270i
$724$		0			0
$725$	17.4777	−	21.8587i	0.649104	−	0.811810i
$726$		0			0
$727$	−5.06503	+	5.06503i	−0.187852	+	0.187852i	−0.794767	−	0.606915i	$-0.792407\pi$
$727$	−5.06503	+	5.06503i	−0.187852	+	0.187852i	0.606915	+	0.794767i	$0.292407\pi$
$728$		0			0
$729$	35.2770			1.30655
$730$		0			0
$731$	0.288660	−	0.288660i	0.0106765	−	0.0106765i
$732$		0			0
$733$	−43.0744			−1.59099			−0.795494	−	0.605961i	$-0.792789\pi$
$733$	−43.0744			−1.59099			−0.795494	+	0.605961i	$0.792789\pi$
$734$		0			0
$735$	19.3686	+	17.3312i	0.714422	+	0.639272i
$736$		0			0
$737$	28.4384	−	28.4384i	1.04754	−	1.04754i
$738$		0			0
$739$	−11.3838	+	11.3838i	−0.418762	+	0.418762i	−0.884777	−	0.466015i	$-0.845689\pi$
$739$	−11.3838	+	11.3838i	−0.418762	+	0.418762i	0.466015	+	0.884777i	$0.345689\pi$
$740$		0			0
$741$	16.3763	+	16.3763i	0.601599	+	0.601599i
$742$		0			0
$743$	−1.54795	−	1.54795i	−0.0567888	−	0.0567888i	0.678142	−	0.734931i	$-0.262785\pi$
$743$	−1.54795	−	1.54795i	−0.0567888	−	0.0567888i	−0.734931	+	0.678142i	$0.762785\pi$
$744$		0			0
$745$	−17.4029	+	0.966116i	−0.637591	+	0.0353958i
$746$		0			0
$747$		−	39.0774i		−	1.42977i
$748$		0			0
$749$	16.7723	+	16.7723i	0.612847	+	0.612847i
$750$		0			0
$751$		−	1.49244i		−	0.0544600i	−0.999629	−	0.0272300i	$-0.991331\pi$
$751$		−	1.49244i		−	0.0544600i	0.999629	−	0.0272300i	$-0.00866865\pi$
$752$		0			0
$753$	13.7394	+	13.7394i	0.500690	+	0.500690i
$754$		0			0
$755$	−6.89231	−	6.16731i	−0.250837	−	0.224451i
$756$		0			0
$757$	22.7030			0.825154			0.412577	−	0.910923i	$-0.364629\pi$
$757$	22.7030			0.825154			0.412577	+	0.910923i	$0.364629\pi$
$758$		0			0
$759$		−	29.0140i		−	1.05314i
$760$		0			0
$761$			33.6599i			1.22017i	0.792335	+	0.610086i	$0.208865\pi$
$761$			33.6599i			1.22017i	−0.792335	+	0.610086i	$0.791135\pi$
$762$		0			0
$763$	−1.33523			−0.0483386
$764$		0			0
$765$	−0.831959	+	0.0461860i	−0.0300795	+	0.00166986i
$766$		0			0
$767$	−12.7194	−	12.7194i	−0.459271	−	0.459271i
$768$		0			0
$769$		−	10.1943i		−	0.367615i	−0.982962	−	0.183808i	$-0.941158\pi$
$769$		−	10.1943i		−	0.367615i	0.982962	−	0.183808i	$-0.0588423\pi$
$770$		0			0
$771$	9.91699	+	9.91699i	0.357152	+	0.357152i
$772$		0			0
$773$		−	7.34419i		−	0.264152i	−0.991240	−	0.132076i	$-0.957836\pi$
$773$		−	7.34419i		−	0.264152i	0.991240	−	0.132076i	$-0.0421643\pi$
$774$		0			0
$775$	−8.21755	+	0.915212i	−0.295183	+	0.0328754i
$776$		0			0
$777$	15.5221	+	15.5221i	0.556853	+	0.556853i
$778$		0			0
$779$	−4.56658	−	4.56658i	−0.163615	−	0.163615i
$780$		0			0
$781$	6.08556	−	6.08556i	0.217759	−	0.217759i
$782$		0			0
$783$	5.15763	−	5.15763i	0.184319	−	0.184319i
$784$		0			0
$785$	30.2239	−	33.7769i	1.07874	−	1.20555i
$786$		0			0
$787$	29.4359			1.04928			0.524638	−	0.851326i	$-0.324201\pi$
$787$	29.4359			1.04928			0.524638	+	0.851326i	$0.324201\pi$
$788$		0			0
$789$	−43.2900	+	43.2900i	−1.54116	+	1.54116i
$790$		0			0
$791$	42.0921			1.49662
$792$		0			0
$793$	−24.5959	+	24.5959i	−0.873425	+	0.873425i
$794$		0			0
$795$	−5.50511	−	4.92603i	−0.195246	−	0.174708i
$796$		0			0
$797$			50.3934i			1.78503i	0.451022	+	0.892513i	$0.351060\pi$
$797$			50.3934i			1.78503i	−0.451022	+	0.892513i	$0.648940\pi$
$798$		0			0
$799$	−0.323131			−0.0114315
$800$		0			0
$801$	54.9039			1.93993
$802$		0			0
$803$			53.4930i			1.88773i
$804$		0			0
$805$	−17.0128	−	15.2232i	−0.599623	−	0.536548i
$806$		0			0
$807$	6.51890	−	6.51890i	0.229476	−	0.229476i
$808$		0			0
$809$	27.1588			0.954851			0.477426	−	0.878672i	$-0.341570\pi$
$809$	27.1588			0.954851			0.477426	+	0.878672i	$0.341570\pi$
$810$		0			0
$811$	−11.5416	+	11.5416i	−0.405280	+	0.405280i	−0.880089	−	0.474809i	$-0.842517\pi$
$811$	−11.5416	+	11.5416i	−0.405280	+	0.405280i	0.474809	+	0.880089i	$0.342517\pi$
$812$		0			0
$813$	8.51429			0.298609
$814$		0			0
$815$	−19.6575	+	21.9684i	−0.688574	+	0.769520i
$816$		0			0
$817$	10.2779	−	10.2779i	0.359579	−	0.359579i
$818$		0			0
$819$	20.2664	−	20.2664i	0.708166	−	0.708166i
$820$		0			0
$821$	20.2900	+	20.2900i	0.708126	+	0.708126i	0.966141	−	0.258015i	$-0.0830684\pi$
$821$	20.2900	+	20.2900i	0.708126	+	0.708126i	−0.258015	+	0.966141i	$0.583068\pi$
$822$		0			0
$823$	31.4540	+	31.4540i	1.09642	+	1.09642i	0.994826	+	0.101592i	$0.0323936\pi$
$823$	31.4540	+	31.4540i	1.09642	+	1.09642i	0.101592	+	0.994826i	$0.467606\pi$
$824$		0			0
$825$	−30.1638	+	37.7247i	−1.05017	+	1.31341i
$826$		0			0
$827$		−	15.3304i		−	0.533090i	−0.963822	−	0.266545i	$-0.914118\pi$
$827$		−	15.3304i		−	0.533090i	0.963822	−	0.266545i	$-0.0858822\pi$
$828$		0			0
$829$	−0.896046	−	0.896046i	−0.0311210	−	0.0311210i	0.691375	−	0.722496i	$-0.257005\pi$
$829$	−0.896046	−	0.896046i	−0.0311210	−	0.0311210i	−0.722496	+	0.691375i	$0.757005\pi$
$830$		0			0
$831$			11.7562i			0.407817i
$832$		0			0
$833$	0.341897	+	0.341897i	0.0118460	+	0.0118460i
$834$		0			0
$835$	−37.3176	+	2.07168i	−1.29143	+	0.0716935i
$836$		0			0
$837$	−2.15491			−0.0744845
$838$		0			0
$839$			48.1891i			1.66367i	0.555021	+	0.831837i	$0.312710\pi$
$839$			48.1891i			1.66367i	−0.555021	+	0.831837i	$0.687290\pi$
$840$		0			0
$841$			2.33080i			0.0803723i
$842$		0			0
$843$	−56.4359			−1.94376
$844$		0			0
$845$	12.0513	+	10.7836i	0.414577	+	0.370967i
$846$		0			0
$847$	8.01241	+	8.01241i	0.275310	+	0.275310i
$848$		0			0
$849$			27.7179i			0.951277i
$850$		0			0
$851$	−5.37484	−	5.37484i	−0.184247	−	0.184247i
$852$		0			0
$853$			13.7426i			0.470537i	0.971930	+	0.235268i	$0.0755969\pi$
$853$			13.7426i			0.470537i	−0.971930	+	0.235268i	$0.924403\pi$
$854$		0			0
$855$	−29.6224	+	1.64448i	−1.01306	+	0.0562401i
$856$		0			0
$857$	13.4366	+	13.4366i	0.458986	+	0.458986i	0.898323	−	0.439336i	$-0.144786\pi$
$857$	13.4366	+	13.4366i	0.458986	+	0.458986i	−0.439336	+	0.898323i	$0.644786\pi$
$858$		0			0
$859$	−7.00719	−	7.00719i	−0.239082	−	0.239082i	0.577388	−	0.816470i	$-0.304072\pi$
$859$	−7.00719	−	7.00719i	−0.239082	−	0.239082i	−0.816470	+	0.577388i	$0.804072\pi$
$860$		0			0
$861$	−10.4806	+	10.4806i	−0.357178	+	0.357178i
$862$		0			0
$863$	−41.4708	+	41.4708i	−1.41168	+	1.41168i	−0.663560	+	0.748123i	$0.730955\pi$
$863$	−41.4708	+	41.4708i	−1.41168	+	1.41168i	−0.748123	+	0.663560i	$0.769045\pi$
$864$		0			0
$865$	25.9555	+	23.2252i	0.882513	+	0.789682i
$866$		0			0
$867$	43.3486			1.47219
$868$		0			0
$869$	23.3070	−	23.3070i	0.790636	−	0.790636i
$870$		0			0
$871$	−25.5125			−0.864458
$872$		0			0
$873$	−17.5771	+	17.5771i	−0.594894	+	0.594894i
$874$		0			0
$875$	6.29398	+	37.4807i	0.212775	+	1.26708i
$876$		0			0
$877$		−	5.34168i		−	0.180376i	−0.995925	−	0.0901879i	$-0.971253\pi$
$877$		−	5.34168i		−	0.180376i	0.995925	−	0.0901879i	$-0.0287468\pi$
$878$		0			0
$879$	46.9666			1.58414
$880$		0			0
$881$	−45.9723			−1.54885			−0.774423	−	0.632668i	$-0.781960\pi$
$881$	−45.9723			−1.54885			−0.774423	+	0.632668i	$0.781960\pi$
$882$		0			0
$883$			2.64739i			0.0890918i	0.999007	+	0.0445459i	$0.0141841\pi$
$883$			2.64739i			0.0890918i	−0.999007	+	0.0445459i	$0.985816\pi$
$884$		0			0
$885$	42.6683	−	2.36872i	1.43428	−	0.0796238i
$886$		0			0
$887$	−3.87171	+	3.87171i	−0.129999	+	0.129999i	−0.769113	−	0.639113i	$-0.779301\pi$
$887$	−3.87171	+	3.87171i	−0.129999	+	0.129999i	0.639113	+	0.769113i	$0.279301\pi$
$888$		0			0
$889$	3.26661			0.109558
$890$		0			0
$891$	19.2939	−	19.2939i	0.646369	−	0.646369i
$892$		0			0
$893$	−11.5053			−0.385009
$894$		0			0
$895$	−49.2441	+	2.73378i	−1.64605	+	0.0913801i
$896$		0			0
$897$	−13.0144	+	13.0144i	−0.434539	+	0.434539i
$898$		0			0
$899$	6.54516	−	6.54516i	0.218293	−	0.218293i
$900$		0			0
$901$	−0.0971768	−	0.0971768i	−0.00323743	−	0.00323743i
$902$		0			0
$903$	−23.5885	−	23.5885i	−0.784975	−	0.784975i
$904$		0			0
$905$	0.523580	+	9.43136i	0.0174044	+	0.313509i
$906$		0			0
$907$		−	26.2062i		−	0.870163i	−0.900391	−	0.435081i	$-0.856720\pi$
$907$		−	26.2062i		−	0.870163i	0.900391	−	0.435081i	$-0.143280\pi$
$908$		0			0
$909$	22.3667	+	22.3667i	0.741856	+	0.741856i
$910$		0			0
$911$		−	24.2898i		−	0.804757i	−0.915473	−	0.402378i	$-0.868184\pi$
$911$		−	24.2898i		−	0.804757i	0.915473	−	0.402378i	$-0.131816\pi$
$912$		0			0
$913$	−29.7983	−	29.7983i	−0.986181	−	0.986181i
$914$		0			0
$915$	−4.58047	−	82.5089i	−0.151426	−	2.72766i
$916$		0			0
$917$	26.1452			0.863391
$918$		0			0
$919$		−	41.1294i		−	1.35673i	−0.734723	−	0.678367i	$-0.762688\pi$
$919$		−	41.1294i		−	1.35673i	0.734723	−	0.678367i	$-0.237312\pi$
$920$		0			0
$921$			16.8629i			0.555650i
$922$		0			0
$923$	−5.45944			−0.179700
$924$		0			0
$925$	1.40066	+	12.5763i	0.0460535	+	0.413508i
$926$		0			0
$927$	−6.80006	−	6.80006i	−0.223343	−	0.223343i
$928$		0			0
$929$			43.4799i			1.42653i	0.700894	+	0.713265i	$0.252785\pi$
$929$			43.4799i			1.42653i	−0.700894	+	0.713265i	$0.747215\pi$
$930$		0			0
$931$	12.1734	+	12.1734i	0.398968	+	0.398968i
$932$		0			0
$933$		−	1.54653i		−	0.0506313i
$934$		0			0
$935$	−0.599188	+	0.669626i	−0.0195955	+	0.0218991i
$936$		0			0
$937$	−13.0565	−	13.0565i	−0.426537	−	0.426537i	0.460910	−	0.887447i	$-0.347523\pi$
$937$	−13.0565	−	13.0565i	−0.426537	−	0.426537i	−0.887447	+	0.460910i	$0.847523\pi$
$938$		0			0
$939$	49.4266	+	49.4266i	1.61298	+	1.61298i
$940$		0			0
$941$	5.53494	−	5.53494i	0.180434	−	0.180434i	−0.611111	−	0.791545i	$-0.709277\pi$
$941$	5.53494	−	5.53494i	0.180434	−	0.180434i	0.791545	+	0.611111i	$0.209277\pi$
$942$		0			0
$943$	3.62911	−	3.62911i	0.118180	−	0.118180i
$944$		0			0
$945$	0.549030	+	9.88979i	0.0178599	+	0.321715i
$946$		0			0
$947$	−31.6905			−1.02980			−0.514902	−	0.857249i	$-0.672172\pi$
$947$	−31.6905			−1.02980			−0.514902	+	0.857249i	$0.672172\pi$
$948$		0			0
$949$	23.9947	−	23.9947i	0.778900	−	0.778900i
$950$		0			0
$951$	−17.9717			−0.582772
$952$		0			0
$953$	−2.85543	+	2.85543i	−0.0924965	+	0.0924965i	−0.751841	−	0.659344i	$-0.770834\pi$
$953$	−2.85543	+	2.85543i	−0.0924965	+	0.0924965i	0.659344	+	0.751841i	$0.270834\pi$
$954$		0			0
$955$	−9.64970	+	10.7841i	−0.312257	+	0.348964i
$956$		0			0
$957$		−	54.0722i		−	1.74791i
$958$		0			0
$959$	−35.9348			−1.16039
$960$		0			0
$961$	28.2654			0.911786
$962$		0			0
$963$			24.4969i			0.789401i
$964$		0			0
$965$	1.94793	+	35.0886i	0.0627062	+	1.12954i
$966$		0			0
$967$	40.1144	−	40.1144i	1.28999	−	1.28999i	0.355202	−	0.934790i	$-0.384412\pi$
$967$	40.1144	−	40.1144i	1.28999	−	1.28999i	0.934790	−	0.355202i	$-0.115588\pi$
$968$		0			0
$969$	−1.02356			−0.0328816
$970$		0			0
$971$	−17.3439	+	17.3439i	−0.556592	+	0.556592i	−0.928335	−	0.371743i	$-0.878760\pi$
$971$	−17.3439	+	17.3439i	−0.556592	+	0.556592i	0.371743	+	0.928335i	$0.378760\pi$
$972$		0			0
$973$	−55.4322			−1.77708
$974$		0			0
$975$	30.4519	−	3.39151i	0.975241	−	0.108615i
$976$		0			0
$977$	−12.2234	+	12.2234i	−0.391060	+	0.391060i	−0.875065	−	0.484005i	$-0.839182\pi$
$977$	−12.2234	+	12.2234i	−0.391060	+	0.391060i	0.484005	+	0.875065i	$0.339182\pi$
$978$		0			0
$979$	41.8667	−	41.8667i	1.33807	−	1.33807i
$980$		0			0
$981$	−0.975089	−	0.975089i	−0.0311322	−	0.0311322i
$982$		0			0
$983$	−13.6091	−	13.6091i	−0.434063	−	0.434063i	0.455945	−	0.890008i	$-0.349301\pi$
$983$	−13.6091	−	13.6091i	−0.434063	−	0.434063i	−0.890008	+	0.455945i	$0.849301\pi$
$984$		0			0
$985$	−41.8132	−	37.4148i	−1.33228	−	1.19214i
$986$		0			0
$987$			26.4053i			0.840491i
$988$		0			0
$989$	8.16797	+	8.16797i	0.259726	+	0.259726i
$990$		0			0
$991$			52.9400i			1.68169i	0.541273	+	0.840847i	$0.317942\pi$
$991$			52.9400i			1.68169i	−0.541273	+	0.840847i	$0.682058\pi$
$992$		0			0
$993$	33.7513	+	33.7513i	1.07107	+	1.07107i
$994$		0			0
$995$	−27.9693	+	31.2573i	−0.886688	+	0.990923i
$996$		0			0
$997$	−3.67381			−0.116351			−0.0581754	−	0.998306i	$-0.518528\pi$
$997$	−3.67381			−0.116351			−0.0581754	+	0.998306i	$0.518528\pi$
$998$		0			0
$999$			3.29792i			0.104342i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.j.c.543.2		18
4.3	odd	2		640.2.j.d.543.8		18
5.2	odd	4		640.2.s.c.287.2		18
8.3	odd	2		80.2.j.b.43.4	✓	18
8.5	even	2		320.2.j.b.143.8		18
16.3	odd	4		640.2.s.c.223.2		18
16.5	even	4		80.2.s.b.3.2	yes	18
16.11	odd	4		320.2.s.b.303.8		18
16.13	even	4		640.2.s.d.223.8		18
20.7	even	4		640.2.s.d.287.8		18
24.11	even	2		720.2.bd.g.523.6		18
40.3	even	4		400.2.s.d.107.8		18
40.13	odd	4		1600.2.s.d.207.2		18
40.19	odd	2		400.2.j.d.43.6		18
40.27	even	4		80.2.s.b.27.2	yes	18
40.29	even	2		1600.2.j.d.143.2		18
40.37	odd	4		320.2.s.b.207.8		18
48.5	odd	4		720.2.z.g.163.8		18
80.27	even	4		320.2.j.b.47.2		18
80.37	odd	4		80.2.j.b.67.4	yes	18
80.43	even	4		1600.2.j.d.1007.8		18
80.53	odd	4		400.2.j.d.307.6		18
80.59	odd	4		1600.2.s.d.943.2		18
80.67	even	4	inner	640.2.j.c.607.8		18
80.69	even	4		400.2.s.d.243.8		18
80.77	odd	4		640.2.j.d.607.2		18
120.107	odd	4		720.2.z.g.667.8		18
240.197	even	4		720.2.bd.g.307.6		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.4	✓	18	8.3	odd	2
80.2.j.b.67.4	yes	18	80.37	odd	4
80.2.s.b.3.2	yes	18	16.5	even	4
80.2.s.b.27.2	yes	18	40.27	even	4
320.2.j.b.47.2		18	80.27	even	4
320.2.j.b.143.8		18	8.5	even	2
320.2.s.b.207.8		18	40.37	odd	4
320.2.s.b.303.8		18	16.11	odd	4
400.2.j.d.43.6		18	40.19	odd	2
400.2.j.d.307.6		18	80.53	odd	4
400.2.s.d.107.8		18	40.3	even	4
400.2.s.d.243.8		18	80.69	even	4
640.2.j.c.543.2		18	1.1	even	1	trivial
640.2.j.c.607.8		18	80.67	even	4	inner
640.2.j.d.543.8		18	4.3	odd	2
640.2.j.d.607.2		18	80.77	odd	4
640.2.s.c.223.2		18	16.3	odd	4
640.2.s.c.287.2		18	5.2	odd	4
640.2.s.d.223.8		18	16.13	even	4
640.2.s.d.287.8		18	20.7	even	4
720.2.z.g.163.8		18	48.5	odd	4
720.2.z.g.667.8		18	120.107	odd	4
720.2.bd.g.307.6		18	240.197	even	4
720.2.bd.g.523.6		18	24.11	even	2
1600.2.j.d.143.2		18	40.29	even	2
1600.2.j.d.1007.8		18	80.43	even	4
1600.2.s.d.207.2		18	40.13	odd	4
1600.2.s.d.943.2		18	80.59	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.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.55161i q^{3} +(-1.66635 - 1.49107i) q^{5} +(-2.40368 + 2.40368i) q^{7} -3.51070 q^{9} +O(q^{10})\)	\(q-2.55161i q^{3} +(-1.66635 - 1.49107i) q^{5} +(-2.40368 + 2.40368i) q^{7} -3.51070 q^{9} +(-2.67707 + 2.67707i) q^{11} +2.40164 q^{13} +(-3.80462 + 4.25187i) q^{15} +(-0.0750544 + 0.0750544i) q^{17} +(-2.67236 + 2.67236i) q^{19} +(6.13324 + 6.13324i) q^{21} +(-2.12375 - 2.12375i) q^{23} +(0.553442 + 4.96928i) q^{25} +1.30310i q^{27} +(-3.95795 - 3.95795i) q^{29} +1.65367i q^{31} +(6.83083 + 6.83083i) q^{33} +(7.58941 - 0.421324i) q^{35} +2.53082 q^{37} -6.12803i q^{39} +1.70882i q^{41} -3.84601 q^{43} +(5.85005 + 5.23469i) q^{45} +(2.15264 + 2.15264i) q^{47} -4.55532i q^{49} +(0.191509 + 0.191509i) q^{51} +1.29475i q^{53} +(8.45262 - 0.469246i) q^{55} +(6.81881 + 6.81881i) q^{57} +(-5.29614 - 5.29614i) q^{59} +(-10.2413 + 10.2413i) q^{61} +(8.43858 - 8.43858i) q^{63} +(-4.00197 - 3.58100i) q^{65} -10.6230 q^{67} +(-5.41898 + 5.41898i) q^{69} -2.27322 q^{71} +(9.99096 - 9.99096i) q^{73} +(12.6796 - 1.41217i) q^{75} -12.8696i q^{77} -8.70617 q^{79} -7.20709 q^{81} +11.1310i q^{83} +(0.236978 - 0.0131558i) q^{85} +(-10.0991 + 10.0991i) q^{87} -15.6390 q^{89} +(-5.77276 + 5.77276i) q^{91} +4.21952 q^{93} +(8.43775 - 0.468420i) q^{95} +(5.00672 - 5.00672i) q^{97} +(9.39839 - 9.39839i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^5 - 2 * q^7 - 10 * q^9	\( 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9} - 2 q^{11} - 20 q^{15} - 6 q^{17} + 2 q^{19} + 16 q^{21} + 2 q^{23} + 6 q^{25} + 14 q^{29} - 8 q^{33} - 6 q^{35} - 8 q^{37} - 44 q^{43} + 4 q^{45} + 38 q^{47} + 8 q^{51} + 6 q^{55} + 24 q^{57} - 10 q^{59} - 14 q^{61} - 6 q^{63} + 12 q^{67} - 32 q^{69} - 24 q^{71} + 14 q^{73} + 64 q^{75} - 16 q^{79} + 2 q^{81} + 10 q^{85} - 24 q^{87} - 12 q^{89} - 16 q^{93} + 34 q^{95} + 18 q^{97} - 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^5 - 2 * q^7 - 10 * q^9 - 2 * q^11 - 20 * q^15 - 6 * q^17 + 2 * q^19 + 16 * q^21 + 2 * q^23 + 6 * q^25 + 14 * q^29 - 8 * q^33 - 6 * q^35 - 8 * q^37 - 44 * q^43 + 4 * q^45 + 38 * q^47 + 8 * q^51 + 6 * q^55 + 24 * q^57 - 10 * q^59 - 14 * q^61 - 6 * q^63 + 12 * q^67 - 32 * q^69 - 24 * q^71 + 14 * q^73 + 64 * q^75 - 16 * q^79 + 2 * q^81 + 10 * q^85 - 24 * q^87 - 12 * q^89 - 16 * q^93 + 34 * q^95 + 18 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more