LMFDB - Embedded newform 640.2.j.c.543.5

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			543.5
Root			$-1.37691 - 0.322680i$ of defining polynomial
Character	$\chi$	$=$	640.543
Dual form			640.2.j.c.607.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.614566i q^{3} +(2.07551 - 0.832020i) q^{5} +(-2.83610 + 2.83610i) q^{7} +2.62231 q^{9} +O(q^{10})$	\(q+0.614566i q^{3} +(2.07551 - 0.832020i) q^{5} +(-2.83610 + 2.83610i) q^{7} +2.62231 q^{9} +(1.95928 - 1.95928i) q^{11} +2.05493 q^{13} +(0.511331 + 1.27554i) q^{15} +(-4.06774 + 4.06774i) q^{17} +(0.683479 - 0.683479i) q^{19} +(-1.74297 - 1.74297i) q^{21} +(4.95014 + 4.95014i) q^{23} +(3.61549 - 3.45373i) q^{25} +3.45528i q^{27} +(0.835439 + 0.835439i) q^{29} -2.35978i q^{31} +(1.20411 + 1.20411i) q^{33} +(-3.52666 + 8.24604i) q^{35} +4.54384 q^{37} +1.26289i q^{39} +5.07255i q^{41} -0.849753 q^{43} +(5.44263 - 2.18181i) q^{45} +(-2.72646 - 2.72646i) q^{47} -9.08690i q^{49} +(-2.49989 - 2.49989i) q^{51} -5.17605i q^{53} +(2.43634 - 5.69666i) q^{55} +(0.420043 + 0.420043i) q^{57} +(4.16328 + 4.16328i) q^{59} +(-5.55706 + 5.55706i) q^{61} +(-7.43712 + 7.43712i) q^{63} +(4.26502 - 1.70974i) q^{65} -1.73609 q^{67} +(-3.04219 + 3.04219i) q^{69} -2.33526 q^{71} +(4.39686 - 4.39686i) q^{73} +(2.12255 + 2.22195i) q^{75} +11.1134i q^{77} +14.0993 q^{79} +5.74343 q^{81} -2.75725i q^{83} +(-5.05819 + 11.8271i) q^{85} +(-0.513433 + 0.513433i) q^{87} -11.6448 q^{89} +(-5.82797 + 5.82797i) q^{91} +1.45024 q^{93} +(0.849899 - 1.98724i) q^{95} +(-3.52933 + 3.52933i) q^{97} +(5.13783 - 5.13783i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$			0.614566i			0.354820i	0.984137	+	0.177410i	$0.0567718\pi$
$3$			0.614566i			0.354820i	−0.984137	+	0.177410i	$0.943228\pi$
$4$		0			0
$5$	2.07551	−	0.832020i	0.928196	−	0.372091i
$5$	2.07551	−	0.832020i	0.928196	−	0.372091i
$6$		0			0
$7$	−2.83610	+	2.83610i	−1.07194	+	1.07194i	−0.0747413	+	0.997203i	$0.523813\pi$
$7$	−2.83610	+	2.83610i	−1.07194	+	1.07194i	−0.997203	+	0.0747413i	$0.976187\pi$
$8$		0			0
$9$	2.62231			0.874103
$10$		0			0
$11$	1.95928	−	1.95928i	0.590745	−	0.590745i	−0.347088	−	0.937833i	$-0.612829\pi$
$11$	1.95928	−	1.95928i	0.590745	−	0.590745i	0.937833	+	0.347088i	$0.112829\pi$
$12$		0			0
$13$	2.05493			0.569934			0.284967	−	0.958537i	$-0.408017\pi$
$13$	2.05493			0.569934			0.284967	+	0.958537i	$0.408017\pi$
$14$		0			0
$15$	0.511331	+	1.27554i	0.132025	+	0.329343i
$16$		0			0
$17$	−4.06774	+	4.06774i	−0.986571	+	0.986571i	−0.999911	−	0.0133401i	$-0.995754\pi$
$17$	−4.06774	+	4.06774i	−0.986571	+	0.986571i	0.0133401	+	0.999911i	$0.495754\pi$
$18$		0			0
$19$	0.683479	−	0.683479i	0.156801	−	0.156801i	−0.624347	−	0.781147i	$-0.714635\pi$
$19$	0.683479	−	0.683479i	0.156801	−	0.156801i	0.781147	+	0.624347i	$0.214635\pi$
$20$		0			0
$21$	−1.74297	−	1.74297i	−0.380347	−	0.380347i
$22$		0			0
$23$	4.95014	+	4.95014i	1.03218	+	1.03218i	0.999465	+	0.0327113i	$0.0104142\pi$
$23$	4.95014	+	4.95014i	1.03218	+	1.03218i	0.0327113	+	0.999465i	$0.489586\pi$
$24$		0			0
$25$	3.61549	−	3.45373i	0.723097	−	0.690746i
$26$		0			0
$27$			3.45528i			0.664969i
$28$		0			0
$29$	0.835439	+	0.835439i	0.155137	+	0.155137i	0.780408	−	0.625271i	$-0.215011\pi$
$29$	0.835439	+	0.835439i	0.155137	+	0.155137i	−0.625271	+	0.780408i	$0.715011\pi$
$30$		0			0
$31$		−	2.35978i		−	0.423829i	−0.977288	−	0.211915i	$-0.932030\pi$
$31$		−	2.35978i		−	0.423829i	0.977288	−	0.211915i	$-0.0679698\pi$
$32$		0			0
$33$	1.20411	+	1.20411i	0.209608	+	0.209608i
$34$		0			0
$35$	−3.52666	+	8.24604i	−0.596114	+	1.39384i
$36$		0			0
$37$	4.54384			0.747002			0.373501	−	0.927630i	$-0.378157\pi$
$37$	4.54384			0.747002			0.373501	+	0.927630i	$0.378157\pi$
$38$		0			0
$39$			1.26289i			0.202224i
$40$		0			0
$41$			5.07255i			0.792199i	0.918208	+	0.396100i	$0.129636\pi$
$41$			5.07255i			0.792199i	−0.918208	+	0.396100i	$0.870364\pi$
$42$		0			0
$43$	−0.849753			−0.129586			−0.0647930	−	0.997899i	$-0.520639\pi$
$43$	−0.849753			−0.129586			−0.0647930	+	0.997899i	$0.520639\pi$
$44$		0			0
$45$	5.44263	−	2.18181i	0.811339	−	0.325245i
$46$		0			0
$47$	−2.72646	−	2.72646i	−0.397696	−	0.397696i	0.479724	−	0.877419i	$-0.340737\pi$
$47$	−2.72646	−	2.72646i	−0.397696	−	0.397696i	−0.877419	+	0.479724i	$0.840737\pi$
$48$		0			0
$49$		−	9.08690i		−	1.29813i
$50$		0			0
$51$	−2.49989	−	2.49989i	−0.350055	−	0.350055i
$52$		0			0
$53$		−	5.17605i		−	0.710985i	−0.934679	−	0.355492i	$-0.884313\pi$
$53$		−	5.17605i		−	0.710985i	0.934679	−	0.355492i	$-0.115687\pi$
$54$		0			0
$55$	2.43634	−	5.69666i	0.328517	−	0.768138i
$56$		0			0
$57$	0.420043	+	0.420043i	0.0556360	+	0.0556360i
$58$		0			0
$59$	4.16328	+	4.16328i	0.542013	+	0.542013i	0.924119	−	0.382105i	$-0.124801\pi$
$59$	4.16328	+	4.16328i	0.542013	+	0.542013i	−0.382105	+	0.924119i	$0.624801\pi$
$60$		0			0
$61$	−5.55706	+	5.55706i	−0.711509	+	0.711509i	−0.966851	−	0.255342i	$-0.917812\pi$
$61$	−5.55706	+	5.55706i	−0.711509	+	0.711509i	0.255342	+	0.966851i	$0.417812\pi$
$62$		0			0
$63$	−7.43712	+	7.43712i	−0.936990	+	0.936990i
$64$		0			0
$65$	4.26502	−	1.70974i	0.529011	−	0.212067i
$66$		0			0
$67$	−1.73609			−0.212097			−0.106048	−	0.994361i	$-0.533820\pi$
$67$	−1.73609			−0.212097			−0.106048	+	0.994361i	$0.533820\pi$
$68$		0			0
$69$	−3.04219	+	3.04219i	−0.366237	+	0.366237i
$70$		0			0
$71$	−2.33526			−0.277144			−0.138572	−	0.990352i	$-0.544251\pi$
$71$	−2.33526			−0.277144			−0.138572	+	0.990352i	$0.544251\pi$
$72$		0			0
$73$	4.39686	−	4.39686i	0.514613	−	0.514613i	−0.401323	−	0.915936i	$-0.631450\pi$
$73$	4.39686	−	4.39686i	0.514613	−	0.514613i	0.915936	+	0.401323i	$0.131450\pi$
$74$		0			0
$75$	2.12255	+	2.22195i	0.245091	+	0.256569i
$76$		0			0
$77$			11.1134i			1.26649i
$78$		0			0
$79$	14.0993			1.58629			0.793146	−	0.609032i	$-0.208442\pi$
$79$	14.0993			1.58629			0.793146	+	0.609032i	$0.208442\pi$
$80$		0			0
$81$	5.74343			0.638159
$82$		0			0
$83$		−	2.75725i		−	0.302648i	−0.988484	−	0.151324i	$-0.951646\pi$
$83$		−	2.75725i		−	0.302648i	0.988484	−	0.151324i	$-0.0483536\pi$
$84$		0			0
$85$	−5.05819	+	11.8271i	−0.548638	+	1.28283i
$86$		0			0
$87$	−0.513433	+	0.513433i	−0.0550458	+	0.0550458i
$88$		0			0
$89$	−11.6448			−1.23435			−0.617173	−	0.786828i	$-0.711722\pi$
$89$	−11.6448			−1.23435			−0.617173	+	0.786828i	$0.711722\pi$
$90$		0			0
$91$	−5.82797	+	5.82797i	−0.610937	+	0.610937i
$92$		0			0
$93$	1.45024			0.150383
$94$		0			0
$95$	0.849899	−	1.98724i	0.0871978	−	0.203886i
$96$		0			0
$97$	−3.52933	+	3.52933i	−0.358349	+	0.358349i	−0.863204	−	0.504855i	$-0.831546\pi$
$97$	−3.52933	+	3.52933i	−0.358349	+	0.358349i	0.504855	+	0.863204i	$0.331546\pi$
$98$		0			0
$99$	5.13783	−	5.13783i	0.516372	−	0.516372i
$100$		0			0
$101$	−7.39467	−	7.39467i	−0.735797	−	0.735797i	0.235964	−	0.971762i	$-0.424175\pi$
$101$	−7.39467	−	7.39467i	−0.735797	−	0.735797i	−0.971762	+	0.235964i	$0.924175\pi$
$102$		0			0
$103$	−3.72605	−	3.72605i	−0.367139	−	0.367139i	0.499294	−	0.866433i	$-0.333593\pi$
$103$	−3.72605	−	3.72605i	−0.367139	−	0.367139i	−0.866433	+	0.499294i	$0.833593\pi$
$104$		0			0
$105$	−5.06774	−	2.16737i	−0.494560	−	0.211513i
$106$		0			0
$107$		−	16.4605i		−	1.59130i	−0.605758	−	0.795649i	$-0.707130\pi$
$107$		−	16.4605i		−	1.59130i	0.605758	−	0.795649i	$-0.292870\pi$
$108$		0			0
$109$	−12.8554	−	12.8554i	−1.23133	−	1.23133i	−0.963455	−	0.267870i	$-0.913680\pi$
$109$	−12.8554	−	12.8554i	−1.23133	−	1.23133i	−0.267870	−	0.963455i	$-0.586320\pi$
$110$		0			0
$111$			2.79249i			0.265051i
$112$		0			0
$113$	0.863630	+	0.863630i	0.0812435	+	0.0812435i	0.746561	−	0.665317i	$-0.231704\pi$
$113$	0.863630	+	0.863630i	0.0812435	+	0.0812435i	−0.665317	+	0.746561i	$0.731704\pi$
$114$		0			0
$115$	14.3927	+	6.15546i	1.34213	+	0.573999i
$116$		0			0
$117$	5.38865			0.498181
$118$		0			0
$119$		−	23.0730i		−	2.11510i
$120$		0			0
$121$			3.32246i			0.302042i
$122$		0			0
$123$	−3.11742			−0.281088
$124$		0			0
$125$	4.63041	−	10.1764i	0.414156	−	0.910206i
$126$		0			0
$127$	−11.7944	−	11.7944i	−1.04659	−	1.04659i	−0.998860	−	0.0477265i	$-0.984802\pi$
$127$	−11.7944	−	11.7944i	−1.04659	−	1.04659i	−0.0477265	−	0.998860i	$-0.515198\pi$
$128$		0			0
$129$		−	0.522229i		−	0.0459797i
$130$		0			0
$131$	−15.9756	−	15.9756i	−1.39579	−	1.39579i	−0.811659	−	0.584132i	$-0.801435\pi$
$131$	−15.9756	−	15.9756i	−1.39579	−	1.39579i	−0.584132	−	0.811659i	$-0.698565\pi$
$132$		0			0
$133$			3.87683i			0.336163i
$134$		0			0
$135$	2.87486	+	7.17147i	0.247429	+	0.617222i
$136$		0			0
$137$	−1.29423	−	1.29423i	−0.110573	−	0.110573i	0.649655	−	0.760229i	$-0.274913\pi$
$137$	−1.29423	−	1.29423i	−0.110573	−	0.110573i	−0.760229	+	0.649655i	$0.774913\pi$
$138$		0			0
$139$	−8.61413	−	8.61413i	−0.730641	−	0.730641i	0.240106	−	0.970747i	$-0.422818\pi$
$139$	−8.61413	−	8.61413i	−0.730641	−	0.730641i	−0.970747	+	0.240106i	$0.922818\pi$
$140$		0			0
$141$	1.67559	−	1.67559i	0.141110	−	0.141110i
$142$		0			0
$143$	4.02617	−	4.02617i	0.336685	−	0.336685i
$144$		0			0
$145$	2.42906	+	1.03886i	0.201723	+	0.0862727i
$146$		0			0
$147$	5.58450			0.460602
$148$		0			0
$149$	0.0806133	−	0.0806133i	0.00660410	−	0.00660410i	−0.703797	−	0.710401i	$-0.748514\pi$
$149$	0.0806133	−	0.0806133i	0.00660410	−	0.00660410i	0.710401	+	0.703797i	$0.248514\pi$
$150$		0			0
$151$	3.25198			0.264643			0.132321	−	0.991207i	$-0.457757\pi$
$151$	3.25198			0.264643			0.132321	+	0.991207i	$0.457757\pi$
$152$		0			0
$153$	−10.6669	+	10.6669i	−0.862364	+	0.862364i
$154$		0			0
$155$	−1.96338	−	4.89775i	−0.157703	−	0.393397i
$156$		0			0
$157$		−	9.06652i		−	0.723587i	−0.932258	−	0.361793i	$-0.882165\pi$
$157$		−	9.06652i		−	0.723587i	0.932258	−	0.361793i	$-0.117835\pi$
$158$		0			0
$159$	3.18102			0.252271
$160$		0			0
$161$	−28.0782			−2.21287
$162$		0			0
$163$			3.93313i			0.308067i	0.988066	+	0.154033i	$0.0492263\pi$
$163$			3.93313i			0.308067i	−0.988066	+	0.154033i	$0.950774\pi$
$164$		0			0
$165$	3.50097	+	1.49729i	0.272550	+	0.116564i
$166$		0			0
$167$	−8.13216	+	8.13216i	−0.629285	+	0.629285i	−0.947888	−	0.318603i	$-0.896786\pi$
$167$	−8.13216	+	8.13216i	−0.629285	+	0.629285i	0.318603	+	0.947888i	$0.396786\pi$
$168$		0			0
$169$	−8.77728			−0.675175
$170$		0			0
$171$	1.79229	−	1.79229i	0.137060	−	0.137060i
$172$		0			0
$173$	−6.86735			−0.522115			−0.261057	−	0.965323i	$-0.584071\pi$
$173$	−6.86735			−0.522115			−0.261057	+	0.965323i	$0.584071\pi$
$174$		0			0
$175$	−0.458751	+	20.0490i	−0.0346784	+	1.51556i
$176$		0			0
$177$	−2.55861	+	2.55861i	−0.192317	+	0.192317i
$178$		0			0
$179$	15.7117	−	15.7117i	1.17435	−	1.17435i	0.193183	−	0.981163i	$-0.438119\pi$
$179$	15.7117	−	15.7117i	1.17435	−	1.17435i	0.981163	−	0.193183i	$-0.0618811\pi$
$180$		0			0
$181$	13.9112	+	13.9112i	1.03401	+	1.03401i	0.999401	+	0.0346142i	$0.0110202\pi$
$181$	13.9112	+	13.9112i	1.03401	+	1.03401i	0.0346142	+	0.999401i	$0.488980\pi$
$182$		0			0
$183$	−3.41518	−	3.41518i	−0.252458	−	0.252458i
$184$		0			0
$185$	9.43078	−	3.78056i	0.693365	−	0.277953i
$186$		0			0
$187$			15.9397i			1.16562i
$188$		0			0
$189$	−9.79951	−	9.79951i	−0.712810	−	0.712810i
$190$		0			0
$191$		−	10.3393i		−	0.748123i	−0.927404	−	0.374061i	$-0.877965\pi$
$191$		−	10.3393i		−	0.748123i	0.927404	−	0.374061i	$-0.122035\pi$
$192$		0			0
$193$	13.2080	+	13.2080i	0.950734	+	0.950734i	0.998842	−	0.0481079i	$-0.0153191\pi$
$193$	13.2080	+	13.2080i	0.950734	+	0.950734i	−0.0481079	+	0.998842i	$0.515319\pi$
$194$		0			0
$195$	1.05075	+	2.62114i	0.0752456	+	0.187704i
$196$		0			0
$197$	−15.2437			−1.08607			−0.543036	−	0.839709i	$-0.682725\pi$
$197$	−15.2437			−1.08607			−0.543036	+	0.839709i	$0.682725\pi$
$198$		0			0
$199$			4.98761i			0.353562i	0.984250	+	0.176781i	$0.0565684\pi$
$199$			4.98761i			0.353562i	−0.984250	+	0.176781i	$0.943432\pi$
$200$		0			0
$201$		−	1.06694i		−	0.0752561i
$202$		0			0
$203$	−4.73878			−0.332597
$204$		0			0
$205$	4.22046	+	10.5281i	0.294770	+	0.735316i
$206$		0			0
$207$	12.9808	+	12.9808i	0.902228	+	0.902228i
$208$		0			0
$209$		−	2.67825i		−	0.185258i
$210$		0			0
$211$	10.3803	+	10.3803i	0.714608	+	0.714608i	0.967496	−	0.252887i	$-0.0813802\pi$
$211$	10.3803	+	10.3803i	0.714608	+	0.714608i	−0.252887	+	0.967496i	$0.581380\pi$
$212$		0			0
$213$		−	1.43517i		−	0.0983362i
$214$		0			0
$215$	−1.76367	+	0.707011i	−0.120281	+	0.0482178i
$216$		0			0
$217$	6.69257	+	6.69257i	0.454321	+	0.454321i
$218$		0			0
$219$	2.70216	+	2.70216i	0.182595	+	0.182595i
$220$		0			0
$221$	−8.35890	+	8.35890i	−0.562280	+	0.562280i
$222$		0			0
$223$	1.49853	−	1.49853i	0.100349	−	0.100349i	−0.655150	−	0.755499i	$-0.727395\pi$
$223$	1.49853	−	1.49853i	0.100349	−	0.100349i	0.755499	+	0.655150i	$0.227395\pi$
$224$		0			0
$225$	9.48092	−	9.05675i	0.632061	−	0.603783i
$226$		0			0
$227$	−15.6346			−1.03771			−0.518853	−	0.854864i	$-0.673641\pi$
$227$	−15.6346			−1.03771			−0.518853	+	0.854864i	$0.673641\pi$
$228$		0			0
$229$	9.74097	−	9.74097i	0.643702	−	0.643702i	−0.307762	−	0.951463i	$-0.599580\pi$
$229$	9.74097	−	9.74097i	0.643702	−	0.643702i	0.951463	+	0.307762i	$0.0995800\pi$
$230$		0			0
$231$	−6.82992			−0.449376
$232$		0			0
$233$	0.509123	−	0.509123i	0.0333538	−	0.0333538i	−0.690233	−	0.723587i	$-0.742492\pi$
$233$	0.509123	−	0.509123i	0.0333538	−	0.0333538i	0.723587	+	0.690233i	$0.242492\pi$
$234$		0			0
$235$	−7.92727	−	3.39033i	−0.517118	−	0.221161i
$236$		0			0
$237$			8.66493i			0.562848i
$238$		0			0
$239$	−8.19486			−0.530081			−0.265041	−	0.964237i	$-0.585385\pi$
$239$	−8.19486			−0.530081			−0.265041	+	0.964237i	$0.585385\pi$
$240$		0			0
$241$	5.66775			0.365092			0.182546	−	0.983197i	$-0.441566\pi$
$241$	5.66775			0.365092			0.182546	+	0.983197i	$0.441566\pi$
$242$		0			0
$243$			13.8956i			0.891400i
$244$		0			0
$245$	−7.56048	−	18.8600i	−0.483022	−	1.20492i
$246$		0			0
$247$	1.40450	−	1.40450i	0.0893661	−	0.0893661i
$248$		0			0
$249$	1.69451			0.107385
$250$		0			0
$251$	14.7484	−	14.7484i	0.930911	−	0.930911i	−0.0668521	−	0.997763i	$-0.521296\pi$
$251$	14.7484	−	14.7484i	0.930911	−	0.930911i	0.997763	+	0.0668521i	$0.0212956\pi$
$252$		0			0
$253$	19.3974			1.21951
$254$		0			0
$255$	−7.26851	−	3.10859i	−0.455172	−	0.194668i
$256$		0			0
$257$	3.61143	−	3.61143i	0.225275	−	0.225275i	−0.585440	−	0.810715i	$-0.699078\pi$
$257$	3.61143	−	3.61143i	0.225275	−	0.225275i	0.810715	+	0.585440i	$0.199078\pi$
$258$		0			0
$259$	−12.8868	+	12.8868i	−0.800745	+	0.800745i
$260$		0			0
$261$	2.19078	+	2.19078i	0.135606	+	0.135606i
$262$		0			0
$263$	6.80041	+	6.80041i	0.419331	+	0.419331i	0.884973	−	0.465642i	$-0.154177\pi$
$263$	6.80041	+	6.80041i	0.419331	+	0.419331i	−0.465642	+	0.884973i	$0.654177\pi$
$264$		0			0
$265$	−4.30657	−	10.7429i	−0.264551	−	0.659933i
$266$		0			0
$267$		−	7.15650i		−	0.437970i
$268$		0			0
$269$	1.20010	+	1.20010i	0.0731711	+	0.0731711i	0.742745	−	0.669574i	$-0.233523\pi$
$269$	1.20010	+	1.20010i	0.0731711	+	0.0731711i	−0.669574	+	0.742745i	$0.733523\pi$
$270$		0			0
$271$		−	2.79591i		−	0.169840i	−0.996388	−	0.0849199i	$-0.972937\pi$
$271$		−	2.79591i		−	0.169840i	0.996388	−	0.0849199i	$-0.0270634\pi$
$272$		0			0
$273$	−3.58167	−	3.58167i	−0.216773	−	0.216773i
$274$		0			0
$275$	0.316922	−	13.8506i	0.0191111	−	0.835220i
$276$		0			0
$277$	−13.8115			−0.829852			−0.414926	−	0.909855i	$-0.636193\pi$
$277$	−13.8115			−0.829852			−0.414926	+	0.909855i	$0.636193\pi$
$278$		0			0
$279$		−	6.18807i		−	0.370470i
$280$		0			0
$281$		−	7.21718i		−	0.430541i	−0.976554	−	0.215270i	$-0.930937\pi$
$281$		−	7.21718i		−	0.430541i	0.976554	−	0.215270i	$-0.0690633\pi$
$282$		0			0
$283$	25.2988			1.50386			0.751930	−	0.659243i	$-0.229123\pi$
$283$	25.2988			1.50386			0.751930	+	0.659243i	$0.229123\pi$
$284$		0			0
$285$	1.22129	+	0.522319i	0.0723428	+	0.0309395i
$286$		0			0
$287$	−14.3862	−	14.3862i	−0.849193	−	0.849193i
$288$		0			0
$289$		−	16.0930i		−	0.946644i
$290$		0			0
$291$	−2.16901	−	2.16901i	−0.127149	−	0.127149i
$292$		0			0
$293$			14.1276i			0.825344i	0.910880	+	0.412672i	$0.135404\pi$
$293$			14.1276i			0.825344i	−0.910880	+	0.412672i	$0.864596\pi$
$294$		0			0
$295$	12.1049	+	5.17700i	0.704773	+	0.301417i
$296$		0			0
$297$	6.76985	+	6.76985i	0.392827	+	0.392827i
$298$		0			0
$299$	10.1722	+	10.1722i	0.588272	+	0.588272i
$300$		0			0
$301$	2.40998	−	2.40998i	0.138909	−	0.138909i
$302$		0			0
$303$	4.54451	−	4.54451i	0.261076	−	0.261076i
$304$		0			0
$305$	−6.91016	+	16.1573i	−0.395674	+	0.925166i
$306$		0			0
$307$	−22.6081			−1.29031			−0.645156	−	0.764051i	$-0.723208\pi$
$307$	−22.6081			−1.29031			−0.645156	+	0.764051i	$0.723208\pi$
$308$		0			0
$309$	2.28990	−	2.28990i	0.130268	−	0.130268i
$310$		0			0
$311$	10.7903			0.611859			0.305929	−	0.952054i	$-0.401033\pi$
$311$	10.7903			0.611859			0.305929	+	0.952054i	$0.401033\pi$
$312$		0			0
$313$	20.6842	−	20.6842i	1.16914	−	1.16914i	0.186727	−	0.982412i	$-0.440212\pi$
$313$	20.6842	−	20.6842i	1.16914	−	1.16914i	0.982412	−	0.186727i	$-0.0597879\pi$
$314$		0			0
$315$	−9.24799	+	21.6237i	−0.521065	+	1.21836i
$316$		0			0
$317$			23.8207i			1.33791i	0.743305	+	0.668953i	$0.233257\pi$
$317$			23.8207i			1.33791i	−0.743305	+	0.668953i	$0.766743\pi$
$318$		0			0
$319$	3.27372			0.183293
$320$		0			0
$321$	10.1161			0.564624
$322$		0			0
$323$			5.56042i			0.309390i
$324$		0			0
$325$	7.42956	−	7.09716i	0.412118	−	0.393680i
$326$		0			0
$327$	7.90050	−	7.90050i	0.436899	−	0.436899i
$328$		0			0
$329$	15.4650			0.852615
$330$		0			0
$331$	−19.7688	+	19.7688i	−1.08659	+	1.08659i	−0.0907155	+	0.995877i	$0.528915\pi$
$331$	−19.7688	+	19.7688i	−1.08659	+	1.08659i	−0.995877	+	0.0907155i	$0.971085\pi$
$332$		0			0
$333$	11.9153			0.652957
$334$		0			0
$335$	−3.60326	+	1.44446i	−0.196867	+	0.0789191i
$336$		0			0
$337$	7.26955	−	7.26955i	0.395998	−	0.395998i	−0.480821	−	0.876819i	$-0.659661\pi$
$337$	7.26955	−	7.26955i	0.395998	−	0.395998i	0.876819	+	0.480821i	$0.159661\pi$
$338$		0			0
$339$	−0.530758	+	0.530758i	−0.0288268	+	0.0288268i
$340$		0			0
$341$	−4.62347	−	4.62347i	−0.250375	−	0.250375i
$342$		0			0
$343$	5.91866	+	5.91866i	0.319578	+	0.319578i
$344$		0			0
$345$	−3.78293	+	8.84526i	−0.203666	+	0.476213i
$346$		0			0
$347$			23.4667i			1.25976i	0.776692	+	0.629880i	$0.216896\pi$
$347$			23.4667i			1.25976i	−0.776692	+	0.629880i	$0.783104\pi$
$348$		0			0
$349$	23.2089	+	23.2089i	1.24234	+	1.24234i	0.959027	+	0.283315i	$0.0914342\pi$
$349$	23.2089	+	23.2089i	1.24234	+	1.24234i	0.283315	+	0.959027i	$0.408566\pi$
$350$		0			0
$351$			7.10035i			0.378988i
$352$		0			0
$353$	−13.3220	−	13.3220i	−0.709059	−	0.709059i	0.257278	−	0.966337i	$-0.417174\pi$
$353$	−13.3220	−	13.3220i	−0.709059	−	0.709059i	−0.966337	+	0.257278i	$0.917174\pi$
$354$		0			0
$355$	−4.84685	+	1.94298i	−0.257244	+	0.103123i
$356$		0			0
$357$	14.1799			0.750479
$358$		0			0
$359$			26.9902i			1.42449i	0.701932	+	0.712244i	$0.252321\pi$
$359$			26.9902i			1.42449i	−0.701932	+	0.712244i	$0.747679\pi$
$360$		0			0
$361$			18.0657i			0.950827i
$362$		0			0
$363$	−2.04187			−0.107170
$364$		0			0
$365$	5.46745	−	12.7840i	0.286179	−	0.669145i
$366$		0			0
$367$	19.4758	+	19.4758i	1.01663	+	1.01663i	0.999859	+	0.0167684i	$0.00533781\pi$
$367$	19.4758	+	19.4758i	1.01663	+	1.01663i	0.0167684	+	0.999859i	$0.494662\pi$
$368$		0			0
$369$			13.3018i			0.692464i
$370$		0			0
$371$	14.6798	+	14.6798i	0.762136	+	0.762136i
$372$		0			0
$373$		−	4.87069i		−	0.252195i	−0.992018	−	0.126097i	$-0.959755\pi$
$373$		−	4.87069i		−	0.252195i	0.992018	−	0.126097i	$-0.0402452\pi$
$374$		0			0
$375$	6.25408	+	2.84569i	0.322959	+	0.146951i
$376$		0			0
$377$	1.71677	+	1.71677i	0.0884180	+	0.0884180i
$378$		0			0
$379$	2.54450	+	2.54450i	0.130702	+	0.130702i	0.769432	−	0.638729i	$-0.220540\pi$
$379$	2.54450	+	2.54450i	0.130702	+	0.130702i	−0.638729	+	0.769432i	$0.720540\pi$
$380$		0			0
$381$	7.24846	−	7.24846i	0.371350	−	0.371350i
$382$		0			0
$383$	−0.193238	+	0.193238i	−0.00987399	+	0.00987399i	−0.712027	−	0.702153i	$-0.752222\pi$
$383$	−0.193238	+	0.193238i	−0.00987399	+	0.00987399i	0.702153	+	0.712027i	$0.252222\pi$
$384$		0			0
$385$	9.24658	+	23.0660i	0.471249	+	1.17555i
$386$		0			0
$387$	−2.22831			−0.113272
$388$		0			0
$389$	−2.01528	+	2.01528i	−0.102179	+	0.102179i	−0.756348	−	0.654169i	$-0.773018\pi$
$389$	−2.01528	+	2.01528i	−0.102179	+	0.102179i	0.654169	+	0.756348i	$0.273018\pi$
$390$		0			0
$391$	−40.2718			−2.03663
$392$		0			0
$393$	9.81803	−	9.81803i	0.495254	−	0.495254i
$394$		0			0
$395$	29.2632	−	11.7309i	1.47239	−	0.590244i
$396$		0			0
$397$		−	21.5509i		−	1.08161i	−0.841149	−	0.540804i	$-0.818120\pi$
$397$		−	21.5509i		−	1.08161i	0.841149	−	0.540804i	$-0.181880\pi$
$398$		0			0
$399$	−2.38257			−0.119277
$400$		0			0
$401$	−10.3965			−0.519176			−0.259588	−	0.965719i	$-0.583587\pi$
$401$	−10.3965			−0.519176			−0.259588	+	0.965719i	$0.583587\pi$
$402$		0			0
$403$		−	4.84917i		−	0.241555i
$404$		0			0
$405$	11.9205	−	4.77865i	0.592337	−	0.237453i
$406$		0			0
$407$	8.90264	−	8.90264i	0.441288	−	0.441288i
$408$		0			0
$409$	−0.330732			−0.0163536			−0.00817682	−	0.999967i	$-0.502603\pi$
$409$	−0.330732			−0.0163536			−0.00817682	+	0.999967i	$0.502603\pi$
$410$		0			0
$411$	0.795389	−	0.795389i	0.0392337	−	0.0392337i
$412$		0			0
$413$	−23.6150			−1.16202
$414$		0			0
$415$	−2.29409	−	5.72270i	−0.112612	−	0.280917i
$416$		0			0
$417$	5.29395	−	5.29395i	0.259246	−	0.259246i
$418$		0			0
$419$	−6.71354	+	6.71354i	−0.327978	+	0.327978i	−0.851817	−	0.523839i	$-0.824499\pi$
$419$	−6.71354	+	6.71354i	−0.327978	+	0.327978i	0.523839	+	0.851817i	$0.324499\pi$
$420$		0			0
$421$	−2.99831	−	2.99831i	−0.146129	−	0.146129i	0.630258	−	0.776386i	$-0.282949\pi$
$421$	−2.99831	−	2.99831i	−0.146129	−	0.146129i	−0.776386	+	0.630258i	$0.782949\pi$
$422$		0			0
$423$	−7.14963	−	7.14963i	−0.347627	−	0.347627i
$424$		0			0
$425$	−0.657974	+	28.7557i	−0.0319164	+	1.39486i
$426$		0			0
$427$		−	31.5208i		−	1.52540i
$428$		0			0
$429$	2.47435	+	2.47435i	0.119463	+	0.119463i
$430$		0			0
$431$		−	19.9548i		−	0.961191i	−0.876942	−	0.480596i	$-0.840420\pi$
$431$		−	19.9548i		−	0.961191i	0.876942	−	0.480596i	$-0.159580\pi$
$432$		0			0
$433$	−16.1910	−	16.1910i	−0.778092	−	0.778092i	0.201414	−	0.979506i	$-0.435446\pi$
$433$	−16.1910	−	16.1910i	−0.778092	−	0.778092i	−0.979506	+	0.201414i	$0.935446\pi$
$434$		0			0
$435$	−0.638449	+	1.49282i	−0.0306113	+	0.0715753i
$436$		0			0
$437$	6.76664			0.323692
$438$		0			0
$439$			29.3734i			1.40191i	0.713204	+	0.700957i	$0.247243\pi$
$439$			29.3734i			1.40191i	−0.713204	+	0.700957i	$0.752757\pi$
$440$		0			0
$441$		−	23.8287i		−	1.13470i
$442$		0			0
$443$	−19.8713			−0.944115			−0.472057	−	0.881568i	$-0.656489\pi$
$443$	−19.8713			−0.944115			−0.472057	+	0.881568i	$0.656489\pi$
$444$		0			0
$445$	−24.1689	+	9.68870i	−1.14572	+	0.459288i
$446$		0			0
$447$	0.0495422	+	0.0495422i	0.00234326	+	0.00234326i
$448$		0			0
$449$			16.7577i			0.790844i	0.918500	+	0.395422i	$0.129402\pi$
$449$			16.7577i			0.790844i	−0.918500	+	0.395422i	$0.870598\pi$
$450$		0			0
$451$	9.93854	+	9.93854i	0.467987	+	0.467987i
$452$		0			0
$453$			1.99856i			0.0939005i
$454$		0			0
$455$	−7.24703	+	16.9450i	−0.339746	+	0.794394i
$456$		0			0
$457$	−5.00267	−	5.00267i	−0.234015	−	0.234015i	0.580351	−	0.814366i	$-0.302915\pi$
$457$	−5.00267	−	5.00267i	−0.234015	−	0.234015i	−0.814366	+	0.580351i	$0.802915\pi$
$458$		0			0
$459$	−14.0552	−	14.0552i	−0.656039	−	0.656039i
$460$		0			0
$461$	−2.71518	+	2.71518i	−0.126459	+	0.126459i	−0.767503	−	0.641045i	$-0.778501\pi$
$461$	−2.71518	+	2.71518i	−0.126459	+	0.126459i	0.641045	+	0.767503i	$0.278501\pi$
$462$		0			0
$463$	−9.18551	+	9.18551i	−0.426887	+	0.426887i	−0.887566	−	0.460680i	$-0.847606\pi$
$463$	−9.18551	+	9.18551i	−0.426887	+	0.426887i	0.460680	+	0.887566i	$0.347606\pi$
$464$		0			0
$465$	3.00999	−	1.20663i	0.139585	−	0.0559561i
$466$		0			0
$467$	−1.06405			−0.0492385			−0.0246193	−	0.999697i	$-0.507837\pi$
$467$	−1.06405			−0.0492385			−0.0246193	+	0.999697i	$0.507837\pi$
$468$		0			0
$469$	4.92371	−	4.92371i	0.227356	−	0.227356i
$470$		0			0
$471$	5.57197			0.256743
$472$		0			0
$473$	−1.66490	+	1.66490i	−0.0765523	+	0.0765523i
$474$		0			0
$475$	0.110556	−	4.83166i	0.00507265	−	0.221692i
$476$		0			0
$477$		−	13.5732i		−	0.621474i
$478$		0			0
$479$	−15.8658			−0.724926			−0.362463	−	0.931998i	$-0.618064\pi$
$479$	−15.8658			−0.724926			−0.362463	+	0.931998i	$0.618064\pi$
$480$		0			0
$481$	9.33725			0.425742
$482$		0			0
$483$		−	17.2559i		−	0.785170i
$484$		0			0
$485$	−4.38869	+	10.2616i	−0.199280	+	0.465957i
$486$		0			0
$487$	13.7947	−	13.7947i	0.625099	−	0.625099i	−0.321732	−	0.946831i	$-0.604265\pi$
$487$	13.7947	−	13.7947i	0.625099	−	0.625099i	0.946831	+	0.321732i	$0.104265\pi$
$488$		0			0
$489$	−2.41717			−0.109308
$490$		0			0
$491$	19.4471	−	19.4471i	0.877637	−	0.877637i	−0.115652	−	0.993290i	$-0.536896\pi$
$491$	19.4471	−	19.4471i	0.877637	−	0.877637i	0.993290	+	0.115652i	$0.0368958\pi$
$492$		0			0
$493$	−6.79669			−0.306108
$494$		0			0
$495$	6.38885	−	14.9384i	0.287157	−	0.671431i
$496$		0			0
$497$	6.62302	−	6.62302i	0.297083	−	0.297083i
$498$		0			0
$499$	23.0141	−	23.0141i	1.03025	−	1.03025i	0.0307258	−	0.999528i	$-0.490218\pi$
$499$	23.0141	−	23.0141i	1.03025	−	1.03025i	0.999528	−	0.0307258i	$-0.00978185\pi$
$500$		0			0
$501$	−4.99775	−	4.99775i	−0.223283	−	0.223283i
$502$		0			0
$503$	−6.63364	−	6.63364i	−0.295780	−	0.295780i	0.543579	−	0.839358i	$-0.317069\pi$
$503$	−6.63364	−	6.63364i	−0.295780	−	0.295780i	−0.839358	+	0.543579i	$0.817069\pi$
$504$		0			0
$505$	−21.5002	−	9.19520i	−0.956748	−	0.409181i
$506$		0			0
$507$		−	5.39422i		−	0.239566i
$508$		0			0
$509$	−8.04140	−	8.04140i	−0.356429	−	0.356429i	0.506066	−	0.862495i	$-0.331099\pi$
$509$	−8.04140	−	8.04140i	−0.356429	−	0.356429i	−0.862495	+	0.506066i	$0.831099\pi$
$510$		0			0
$511$			24.9398i			1.10327i
$512$		0			0
$513$	2.36161	+	2.36161i	0.104268	+	0.104268i
$514$		0			0
$515$	−10.8336	−	4.63331i	−0.477386	−	0.204168i
$516$		0			0
$517$	−10.6838			−0.469873
$518$		0			0
$519$		−	4.22044i		−	0.185257i
$520$		0			0
$521$		−	32.8549i		−	1.43940i	−0.694285	−	0.719700i	$-0.744279\pi$
$521$		−	32.8549i		−	1.43940i	0.694285	−	0.719700i	$-0.255721\pi$
$522$		0			0
$523$	−2.46341			−0.107717			−0.0538587	−	0.998549i	$-0.517152\pi$
$523$	−2.46341			−0.107717			−0.0538587	+	0.998549i	$0.517152\pi$
$524$		0			0
$525$	−12.3214	−	0.281933i	−0.537751	−	0.0123046i
$526$		0			0
$527$	9.59896	+	9.59896i	0.418137	+	0.418137i
$528$		0			0
$529$			26.0078i			1.13078i
$530$		0			0
$531$	10.9174	+	10.9174i	0.473775	+	0.473775i
$532$		0			0
$533$			10.4237i			0.451501i
$534$		0			0
$535$	−13.6955	−	34.1640i	−0.592107	−	1.47704i
$536$		0			0
$537$	9.65586	+	9.65586i	0.416681	+	0.416681i
$538$		0			0
$539$	−17.8038	−	17.8038i	−0.766863	−	0.766863i
$540$		0			0
$541$	18.0772	−	18.0772i	0.777198	−	0.777198i	−0.202156	−	0.979353i	$-0.564795\pi$
$541$	18.0772	−	18.0772i	0.777198	−	0.777198i	0.979353	+	0.202156i	$0.0647947\pi$
$542$		0			0
$543$	−8.54938	+	8.54938i	−0.366889	+	0.366889i
$544$		0			0
$545$	−37.3775	−	15.9856i	−1.60108	−	0.684747i
$546$		0			0
$547$	43.6742			1.86738			0.933688	−	0.358089i	$-0.116572\pi$
$547$	43.6742			1.86738			0.933688	+	0.358089i	$0.116572\pi$
$548$		0			0
$549$	−14.5723	+	14.5723i	−0.621932	+	0.621932i
$550$		0			0
$551$	1.14201			0.0486513
$552$		0			0
$553$	−39.9869	+	39.9869i	−1.70042	+	1.70042i
$554$		0			0
$555$	2.32341	+	5.79584i	0.0986231	+	0.246020i
$556$		0			0
$557$		−	5.18948i		−	0.219885i	−0.993938	−	0.109943i	$-0.964933\pi$
$557$		−	5.18948i		−	0.219885i	0.993938	−	0.109943i	$-0.0350667\pi$
$558$		0			0
$559$	−1.74618			−0.0738555
$560$		0			0
$561$	−9.79597			−0.413586
$562$		0			0
$563$			11.3756i			0.479423i	0.970844	+	0.239711i	$0.0770528\pi$
$563$			11.3756i			0.479423i	−0.970844	+	0.239711i	$0.922947\pi$
$564$		0			0
$565$	2.51103	+	1.07392i	0.105640	+	0.0451800i
$566$		0			0
$567$	−16.2889	+	16.2889i	−0.684071	+	0.684071i
$568$		0			0
$569$	−7.51787			−0.315165			−0.157583	−	0.987506i	$-0.550370\pi$
$569$	−7.51787			−0.315165			−0.157583	+	0.987506i	$0.550370\pi$
$570$		0			0
$571$	−7.76889	+	7.76889i	−0.325118	+	0.325118i	−0.850726	−	0.525609i	$-0.823838\pi$
$571$	−7.76889	+	7.76889i	−0.325118	+	0.325118i	0.525609	+	0.850726i	$0.323838\pi$
$572$		0			0
$573$	6.35416			0.265449
$574$		0			0
$575$	34.9936	+	0.800708i	1.45934	+	0.0333918i
$576$		0			0
$577$	−9.84819	+	9.84819i	−0.409986	+	0.409986i	−0.881733	−	0.471748i	$-0.843623\pi$
$577$	−9.84819	+	9.84819i	−0.409986	+	0.409986i	0.471748	+	0.881733i	$0.343623\pi$
$578$		0			0
$579$	−8.11720	+	8.11720i	−0.337339	+	0.337339i
$580$		0			0
$581$	7.81984	+	7.81984i	0.324421	+	0.324421i
$582$		0			0
$583$	−10.1413	−	10.1413i	−0.420010	−	0.420010i
$584$		0			0
$585$	11.1842	−	4.48346i	0.462410	−	0.185368i
$586$		0			0
$587$			33.0447i			1.36390i	0.731398	+	0.681951i	$0.238868\pi$
$587$			33.0447i			1.36390i	−0.731398	+	0.681951i	$0.761132\pi$
$588$		0			0
$589$	−1.61286	−	1.61286i	−0.0664567	−	0.0664567i
$590$		0			0
$591$		−	9.36829i		−	0.385360i
$592$		0			0
$593$	18.5424	+	18.5424i	0.761445	+	0.761445i	0.976584	−	0.215139i	$-0.0690203\pi$
$593$	18.5424	+	18.5424i	0.761445	+	0.761445i	−0.215139	+	0.976584i	$0.569020\pi$
$594$		0			0
$595$	−19.1972	−	47.8882i	−0.787008	−	1.96323i
$596$		0			0
$597$	−3.06521			−0.125451
$598$		0			0
$599$		−	28.3117i		−	1.15678i	−0.815759	−	0.578392i	$-0.803681\pi$
$599$		−	28.3117i		−	1.15678i	0.815759	−	0.578392i	$-0.196319\pi$
$600$		0			0
$601$			41.7630i			1.70355i	0.523909	+	0.851774i	$0.324473\pi$
$601$			41.7630i			1.70355i	−0.523909	+	0.851774i	$0.675527\pi$
$602$		0			0
$603$	−4.55255			−0.185394
$604$		0			0
$605$	2.76435	+	6.89579i	0.112387	+	0.280354i
$606$		0			0
$607$	−4.01973	−	4.01973i	−0.163156	−	0.163156i	0.620807	−	0.783963i	$-0.286805\pi$
$607$	−4.01973	−	4.01973i	−0.163156	−	0.163156i	−0.783963	+	0.620807i	$0.786805\pi$
$608$		0			0
$609$		−	2.91229i		−	0.118012i
$610$		0			0
$611$	−5.60268	−	5.60268i	−0.226660	−	0.226660i
$612$		0			0
$613$		−	21.5230i		−	0.869305i	−0.900598	−	0.434652i	$-0.856871\pi$
$613$		−	21.5230i		−	0.869305i	0.900598	−	0.434652i	$-0.143129\pi$
$614$		0			0
$615$	−6.47023	+	2.59375i	−0.260905	+	0.104590i
$616$		0			0
$617$	−26.4655	−	26.4655i	−1.06546	−	1.06546i	−0.997702	−	0.0677580i	$-0.978415\pi$
$617$	−26.4655	−	26.4655i	−1.06546	−	1.06546i	−0.0677580	−	0.997702i	$-0.521585\pi$
$618$		0			0
$619$	21.7935	+	21.7935i	0.875955	+	0.875955i	0.993113	−	0.117158i	$-0.0373784\pi$
$619$	21.7935	+	21.7935i	0.875955	+	0.875955i	−0.117158	+	0.993113i	$0.537378\pi$
$620$		0			0
$621$	−17.1041	+	17.1041i	−0.686365	+	0.686365i
$622$		0			0
$623$	33.0258	−	33.0258i	1.32315	−	1.32315i
$624$		0			0
$625$	1.14348	−	24.9738i	0.0457391	−	0.998953i
$626$		0			0
$627$	1.64596			0.0657334
$628$		0			0
$629$	−18.4831	+	18.4831i	−0.736971	+	0.736971i
$630$		0			0
$631$	42.7412			1.70150			0.850751	−	0.525570i	$-0.176148\pi$
$631$	42.7412			1.70150			0.850751	+	0.525570i	$0.176148\pi$
$632$		0			0
$633$	−6.37937	+	6.37937i	−0.253557	+	0.253557i
$634$		0			0
$635$	−34.2927	−	14.6663i	−1.36086	−	0.582013i
$636$		0			0
$637$		−	18.6729i		−	0.739848i
$638$		0			0
$639$	−6.12376			−0.242252
$640$		0			0
$641$	45.4930			1.79687			0.898433	−	0.439110i	$-0.144706\pi$
$641$	45.4930			1.79687			0.898433	+	0.439110i	$0.144706\pi$
$642$		0			0
$643$		−	31.3531i		−	1.23645i	−0.786002	−	0.618224i	$-0.787853\pi$
$643$		−	31.3531i		−	1.23645i	0.786002	−	0.618224i	$-0.212147\pi$
$644$		0			0
$645$	−0.434505	−	1.08389i	−0.0171086	−	0.0426782i
$646$		0			0
$647$	24.0355	−	24.0355i	0.944932	−	0.944932i	−0.0536292	−	0.998561i	$-0.517079\pi$
$647$	24.0355	−	24.0355i	0.944932	−	0.944932i	0.998561	+	0.0536292i	$0.0170789\pi$
$648$		0			0
$649$	16.3141			0.640383
$650$		0			0
$651$	−4.11303	+	4.11303i	−0.161202	+	0.161202i
$652$		0			0
$653$	−15.4153			−0.603248			−0.301624	−	0.953427i	$-0.597529\pi$
$653$	−15.4153			−0.603248			−0.301624	+	0.953427i	$0.597529\pi$
$654$		0			0
$655$	−46.4494	−	19.8654i	−1.81493	−	0.776207i
$656$		0			0
$657$	11.5299	−	11.5299i	0.449825	−	0.449825i
$658$		0			0
$659$	−30.4355	+	30.4355i	−1.18560	+	1.18560i	−0.207327	+	0.978272i	$0.566476\pi$
$659$	−30.4355	+	30.4355i	−1.18560	+	1.18560i	−0.978272	+	0.207327i	$0.933524\pi$
$660$		0			0
$661$	11.2208	+	11.2208i	0.436437	+	0.436437i	0.890811	−	0.454374i	$-0.150137\pi$
$661$	11.2208	+	11.2208i	0.436437	+	0.436437i	−0.454374	+	0.890811i	$0.650137\pi$
$662$		0			0
$663$	−5.13709	−	5.13709i	−0.199508	−	0.199508i
$664$		0			0
$665$	3.22560	+	8.04639i	0.125083	+	0.312026i
$666$		0			0
$667$			8.27109i			0.320258i
$668$		0			0
$669$	0.920946	+	0.920946i	0.0356058	+	0.0356058i
$670$		0			0
$671$			21.7757i			0.840640i
$672$		0			0
$673$	−29.2965	−	29.2965i	−1.12930	−	1.12930i	−0.990291	−	0.139006i	$-0.955609\pi$
$673$	−29.2965	−	29.2965i	−1.12930	−	1.12930i	−0.139006	−	0.990291i	$-0.544391\pi$
$674$		0			0
$675$	11.9336	+	12.4925i	0.459325	+	0.480837i
$676$		0			0
$677$	−2.74511			−0.105503			−0.0527516	−	0.998608i	$-0.516799\pi$
$677$	−2.74511			−0.105503			−0.0527516	+	0.998608i	$0.516799\pi$
$678$		0			0
$679$		−	20.0191i		−	0.768261i
$680$		0			0
$681$		−	9.60850i		−	0.368199i
$682$		0			0
$683$	−33.0796			−1.26576			−0.632878	−	0.774251i	$-0.718127\pi$
$683$	−33.0796			−1.26576			−0.632878	+	0.774251i	$0.718127\pi$
$684$		0			0
$685$	−3.76301	−	1.60936i	−0.143777	−	0.0614905i
$686$		0			0
$687$	5.98647	+	5.98647i	0.228398	+	0.228398i
$688$		0			0
$689$		−	10.6364i		−	0.405214i
$690$		0			0
$691$	−30.8216	−	30.8216i	−1.17251	−	1.17251i	−0.981610	−	0.190899i	$-0.938860\pi$
$691$	−30.8216	−	30.8216i	−1.17251	−	1.17251i	−0.190899	−	0.981610i	$-0.561140\pi$
$692$		0			0
$693$			29.1428i			1.10704i
$694$		0			0
$695$	−25.0458	−	10.7116i	−0.950043	−	0.406314i
$696$		0			0
$697$	−20.6338	−	20.6338i	−0.781561	−	0.781561i
$698$		0			0
$699$	0.312890	+	0.312890i	0.0118346	+	0.0118346i
$700$		0			0
$701$	22.1242	−	22.1242i	0.835619	−	0.835619i	−0.152660	−	0.988279i	$-0.548784\pi$
$701$	22.1242	−	22.1242i	0.835619	−	0.835619i	0.988279	+	0.152660i	$0.0487838\pi$
$702$		0			0
$703$	3.10562	−	3.10562i	0.117131	−	0.117131i
$704$		0			0
$705$	2.08358	−	4.87183i	0.0784723	−	0.183484i
$706$		0			0
$707$	41.9440			1.57747
$708$		0			0
$709$	7.09244	−	7.09244i	0.266362	−	0.266362i	−0.561270	−	0.827632i	$-0.689687\pi$
$709$	7.09244	−	7.09244i	0.266362	−	0.266362i	0.827632	+	0.561270i	$0.189687\pi$
$710$		0			0
$711$	36.9726			1.38658
$712$		0			0
$713$	11.6812	−	11.6812i	0.437466	−	0.437466i
$714$		0			0
$715$	5.00651	−	11.7062i	0.187233	−	0.437788i
$716$		0			0
$717$		−	5.03628i		−	0.188083i
$718$		0			0
$719$	−30.2949			−1.12981			−0.564905	−	0.825156i	$-0.691087\pi$
$719$	−30.2949			−1.12981			−0.564905	+	0.825156i	$0.691087\pi$
$720$		0			0
$721$	21.1349			0.787104
$722$		0			0
$723$			3.48320i			0.129542i
$724$		0			0
$725$	5.90590	+	0.135136i	0.219340	+	0.00501883i
$726$		0			0
$727$	−15.9503	+	15.9503i	−0.591566	+	0.591566i	−0.938054	−	0.346489i	$-0.887374\pi$
$727$	−15.9503	+	15.9503i	−0.591566	+	0.591566i	0.346489	+	0.938054i	$0.387374\pi$
$728$		0			0
$729$	8.69055			0.321872
$730$		0			0
$731$	3.45657	−	3.45657i	0.127846	−	0.127846i
$732$		0			0
$733$	−35.8535			−1.32428			−0.662140	−	0.749380i	$-0.730352\pi$
$733$	−35.8535			−1.32428			−0.662140	+	0.749380i	$0.730352\pi$
$734$		0			0
$735$	11.5907	−	4.64642i	0.427529	−	0.171386i
$736$		0			0
$737$	−3.40147	+	3.40147i	−0.125295	+	0.125295i
$738$		0			0
$739$	−21.4532	+	21.4532i	−0.789168	+	0.789168i	−0.981358	−	0.192190i	$-0.938441\pi$
$739$	−21.4532	+	21.4532i	−0.789168	+	0.789168i	0.192190	+	0.981358i	$0.438441\pi$
$740$		0			0
$741$	0.863157	+	0.863157i	0.0317089	+	0.0317089i
$742$		0			0
$743$	−13.0311	−	13.0311i	−0.478063	−	0.478063i	0.426449	−	0.904512i	$-0.359765\pi$
$743$	−13.0311	−	13.0311i	−0.478063	−	0.478063i	−0.904512	+	0.426449i	$0.859765\pi$
$744$		0			0
$745$	0.100242	−	0.234385i	0.00367258	−	0.00858722i
$746$		0			0
$747$		−	7.23036i		−	0.264545i
$748$		0			0
$749$	46.6836	+	46.6836i	1.70578	+	1.70578i
$750$		0			0
$751$			22.4879i			0.820595i	0.911952	+	0.410297i	$0.134575\pi$
$751$			22.4879i			0.820595i	−0.911952	+	0.410297i	$0.865425\pi$
$752$		0			0
$753$	9.06387	+	9.06387i	0.330306	+	0.330306i
$754$		0			0
$755$	6.74952	−	2.70571i	0.245640	−	0.0984710i
$756$		0			0
$757$	−15.8781			−0.577100			−0.288550	−	0.957465i	$-0.593173\pi$
$757$	−15.8781			−0.577100			−0.288550	+	0.957465i	$0.593173\pi$
$758$		0			0
$759$			11.9210i			0.432705i
$760$		0			0
$761$			19.5227i			0.707696i	0.935303	+	0.353848i	$0.115127\pi$
$761$			19.5227i			0.707696i	−0.935303	+	0.353848i	$0.884873\pi$
$762$		0			0
$763$	72.9184			2.63982
$764$		0			0
$765$	−13.2641	+	31.0142i	−0.479566	+	1.12132i
$766$		0			0
$767$	8.55524	+	8.55524i	0.308912	+	0.308912i
$768$		0			0
$769$			8.03843i			0.289873i	0.989441	+	0.144937i	$0.0462978\pi$
$769$			8.03843i			0.289873i	−0.989441	+	0.144937i	$0.953702\pi$
$770$		0			0
$771$	2.21946	+	2.21946i	0.0799320	+	0.0799320i
$772$		0			0
$773$		−	40.5118i		−	1.45711i	−0.684988	−	0.728554i	$-0.740193\pi$
$773$		−	40.5118i		−	1.45711i	0.684988	−	0.728554i	$-0.259807\pi$
$774$		0			0
$775$	−8.15005	−	8.53175i	−0.292758	−	0.306470i
$776$		0			0
$777$	−7.91977	−	7.91977i	−0.284120	−	0.284120i
$778$		0			0
$779$	3.46698	+	3.46698i	0.124217	+	0.124217i
$780$		0			0
$781$	−4.57542	+	4.57542i	−0.163721	+	0.163721i
$782$		0			0
$783$	−2.88668	+	2.88668i	−0.103161	+	0.103161i
$784$		0			0
$785$	−7.54352	−	18.8176i	−0.269240	−	0.671631i
$786$		0			0
$787$	15.8333			0.564396			0.282198	−	0.959356i	$-0.408937\pi$
$787$	15.8333			0.564396			0.282198	+	0.959356i	$0.408937\pi$
$788$		0			0
$789$	−4.17930	+	4.17930i	−0.148787	+	0.148787i
$790$		0			0
$791$	−4.89868			−0.174177
$792$		0			0
$793$	−11.4194	+	11.4194i	−0.405513	+	0.405513i
$794$		0			0
$795$	6.60224	−	2.64667i	0.234157	−	0.0938678i
$796$		0			0
$797$		−	10.2670i		−	0.363674i	−0.983329	−	0.181837i	$-0.941796\pi$
$797$		−	10.2670i		−	0.363674i	0.983329	−	0.181837i	$-0.0582044\pi$
$798$		0			0
$799$	22.1811			0.784710
$800$		0			0
$801$	−30.5362			−1.07895
$802$		0			0
$803$		−	17.2293i		−	0.608010i
$804$		0			0
$805$	−58.2766	+	23.3616i	−2.05398	+	0.823388i
$806$		0			0
$807$	−0.737538	+	0.737538i	−0.0259626	+	0.0259626i
$808$		0			0
$809$	−9.16442			−0.322204			−0.161102	−	0.986938i	$-0.551505\pi$
$809$	−9.16442			−0.322204			−0.161102	+	0.986938i	$0.551505\pi$
$810$		0			0
$811$	−22.1702	+	22.1702i	−0.778502	+	0.778502i	−0.979576	−	0.201074i	$-0.935557\pi$
$811$	−22.1702	+	22.1702i	−0.778502	+	0.778502i	0.201074	+	0.979576i	$0.435557\pi$
$812$		0			0
$813$	1.71827			0.0602625
$814$		0			0
$815$	3.27245	+	8.16326i	0.114629	+	0.285947i
$816$		0			0
$817$	−0.580788	+	0.580788i	−0.0203192	+	0.0203192i
$818$		0			0
$819$	−15.2827	+	15.2827i	−0.534022	+	0.534022i
$820$		0			0
$821$	−13.3258	−	13.3258i	−0.465074	−	0.465074i	0.435240	−	0.900314i	$-0.356663\pi$
$821$	−13.3258	−	13.3258i	−0.465074	−	0.465074i	−0.900314	+	0.435240i	$0.856663\pi$
$822$		0			0
$823$	34.7796	+	34.7796i	1.21234	+	1.21234i	0.970255	+	0.242084i	$0.0778308\pi$
$823$	34.7796	+	34.7796i	1.21234	+	1.21234i	0.242084	+	0.970255i	$0.422169\pi$
$824$		0			0
$825$	8.51209	+	0.194769i	0.296353	+	0.00678100i
$826$		0			0
$827$		−	16.5717i		−	0.576253i	−0.957592	−	0.288127i	$-0.906968\pi$
$827$		−	16.5717i		−	0.576253i	0.957592	−	0.288127i	$-0.0930324\pi$
$828$		0			0
$829$	11.9869	+	11.9869i	0.416321	+	0.416321i	0.883933	−	0.467613i	$-0.154886\pi$
$829$	11.9869	+	11.9869i	0.416321	+	0.416321i	−0.467613	+	0.883933i	$0.654886\pi$
$830$		0			0
$831$		−	8.48807i		−	0.294448i
$832$		0			0
$833$	36.9631	+	36.9631i	1.28070	+	1.28070i
$834$		0			0
$835$	−10.1123	+	23.6445i	−0.349949	+	0.818252i
$836$		0			0
$837$	8.15370			0.281833
$838$		0			0
$839$			4.44215i			0.153360i	0.997056	+	0.0766800i	$0.0244320\pi$
$839$			4.44215i			0.153360i	−0.997056	+	0.0766800i	$0.975568\pi$
$840$		0			0
$841$		−	27.6041i		−	0.951865i
$842$		0			0
$843$	4.43543			0.152764
$844$		0			0
$845$	−18.2173	+	7.30287i	−0.626695	+	0.251226i
$846$		0			0
$847$	−9.42281	−	9.42281i	−0.323772	−	0.323772i
$848$		0			0
$849$			15.5478i			0.533599i
$850$		0			0
$851$	22.4926	+	22.4926i	0.771038	+	0.771038i
$852$		0			0
$853$		−	35.6748i		−	1.22148i	−0.791830	−	0.610742i	$-0.790871\pi$
$853$		−	35.6748i		−	1.22148i	0.791830	−	0.610742i	$-0.209129\pi$
$854$		0			0
$855$	2.22870	−	5.21114i	0.0762199	−	0.178217i
$856$		0			0
$857$	−13.8568	−	13.8568i	−0.473340	−	0.473340i	0.429654	−	0.902994i	$-0.358636\pi$
$857$	−13.8568	−	13.8568i	−0.473340	−	0.473340i	−0.902994	+	0.429654i	$0.858636\pi$
$858$		0			0
$859$	−19.4217	−	19.4217i	−0.662660	−	0.662660i	0.293346	−	0.956006i	$-0.405231\pi$
$859$	−19.4217	−	19.4217i	−0.662660	−	0.662660i	−0.956006	+	0.293346i	$0.905231\pi$
$860$		0			0
$861$	8.84130	−	8.84130i	0.301311	−	0.301311i
$862$		0			0
$863$	−9.22041	+	9.22041i	−0.313866	+	0.313866i	−0.846405	−	0.532539i	$-0.821238\pi$
$863$	−9.22041	+	9.22041i	−0.313866	+	0.313866i	0.532539	+	0.846405i	$0.321238\pi$
$864$		0			0
$865$	−14.2532	+	5.71377i	−0.484625	+	0.194274i
$866$		0			0
$867$	9.89018			0.335888
$868$		0			0
$869$	27.6244	−	27.6244i	0.937093	−	0.937093i
$870$		0			0
$871$	−3.56753			−0.120881
$872$		0			0
$873$	−9.25500	+	9.25500i	−0.313234	+	0.313234i
$874$		0			0
$875$	15.7290	+	41.9936i	0.531738	+	1.41964i
$876$		0			0
$877$			10.4267i			0.352084i	0.984383	+	0.176042i	$0.0563295\pi$
$877$			10.4267i			0.352084i	−0.984383	+	0.176042i	$0.943670\pi$
$878$		0			0
$879$	−8.68236			−0.292849
$880$		0			0
$881$	−12.7405			−0.429239			−0.214619	−	0.976698i	$-0.568851\pi$
$881$	−12.7405			−0.429239			−0.214619	+	0.976698i	$0.568851\pi$
$882$		0			0
$883$			27.9073i			0.939156i	0.882891	+	0.469578i	$0.155594\pi$
$883$			27.9073i			0.939156i	−0.882891	+	0.469578i	$0.844406\pi$
$884$		0			0
$885$	−3.18161	+	7.43924i	−0.106949	+	0.250067i
$886$		0			0
$887$	−41.7449	+	41.7449i	−1.40166	+	1.40166i	−0.606811	+	0.794846i	$0.707552\pi$
$887$	−41.7449	+	41.7449i	−1.40166	+	1.40166i	−0.794846	+	0.606811i	$0.792448\pi$
$888$		0			0
$889$	66.9004			2.24377
$890$		0			0
$891$	11.2530	−	11.2530i	0.376989	−	0.376989i
$892$		0			0
$893$	−3.72696			−0.124718
$894$		0			0
$895$	19.5373	−	45.6822i	0.653061	−	1.52699i
$896$		0			0
$897$	−6.25148	+	6.25148i	−0.208731	+	0.208731i
$898$		0			0
$899$	1.97145	−	1.97145i	0.0657516	−	0.0657516i
$900$		0			0
$901$	21.0548	+	21.0548i	0.701437	+	0.701437i
$902$		0			0
$903$	1.48109	+	1.48109i	0.0492877	+	0.0492877i
$904$		0			0
$905$	40.4474	+	17.2985i	1.34452	+	0.575022i
$906$		0			0
$907$		−	26.7614i		−	0.888597i	−0.895879	−	0.444298i	$-0.853453\pi$
$907$		−	26.7614i		−	0.888597i	0.895879	−	0.444298i	$-0.146547\pi$
$908$		0			0
$909$	−19.3911	−	19.3911i	−0.643163	−	0.643163i
$910$		0			0
$911$			19.2403i			0.637459i	0.947846	+	0.318729i	$0.103256\pi$
$911$			19.2403i			0.637459i	−0.947846	+	0.318729i	$0.896744\pi$
$912$		0			0
$913$	−5.40222	−	5.40222i	−0.178787	−	0.178787i
$914$		0			0
$915$	−9.92975	−	4.24675i	−0.328267	−	0.140393i
$916$		0			0
$917$	90.6165			2.99242
$918$		0			0
$919$			42.6903i			1.40822i	0.710090	+	0.704111i	$0.248654\pi$
$919$			42.6903i			1.40822i	−0.710090	+	0.704111i	$0.751346\pi$
$920$		0			0
$921$		−	13.8942i		−	0.457828i
$922$		0			0
$923$	−4.79878			−0.157954
$924$		0			0
$925$	16.4282	−	15.6932i	0.540155	−	0.515989i
$926$		0			0
$927$	−9.77085	−	9.77085i	−0.320917	−	0.320917i
$928$		0			0
$929$		−	5.58037i		−	0.183086i	−0.995801	−	0.0915430i	$-0.970820\pi$
$929$		−	5.58037i		−	0.183086i	0.995801	−	0.0915430i	$-0.0291799\pi$
$930$		0			0
$931$	−6.21070	−	6.21070i	−0.203548	−	0.203548i
$932$		0			0
$933$			6.63132i			0.217100i
$934$		0			0
$935$	13.2621	+	33.0829i	0.433717	+	1.08193i
$936$		0			0
$937$	41.0680	+	41.0680i	1.34163	+	1.34163i	0.894435	+	0.447197i	$0.147578\pi$
$937$	41.0680	+	41.0680i	1.34163	+	1.34163i	0.447197	+	0.894435i	$0.352422\pi$
$938$		0			0
$939$	12.7118	+	12.7118i	0.414834	+	0.414834i
$940$		0			0
$941$	31.5476	−	31.5476i	1.02842	−	1.02842i	0.0288377	−	0.999584i	$-0.490819\pi$
$941$	31.5476	−	31.5476i	1.02842	−	1.02842i	0.999584	−	0.0288377i	$-0.00918061\pi$
$942$		0			0
$943$	−25.1098	+	25.1098i	−0.817689	+	0.817689i
$944$		0			0
$945$	−28.4924	−	12.1856i	−0.926857	−	0.396398i
$946$		0			0
$947$	−34.7892			−1.13050			−0.565248	−	0.824921i	$-0.691220\pi$
$947$	−34.7892			−1.13050			−0.565248	+	0.824921i	$0.691220\pi$
$948$		0			0
$949$	9.03522	−	9.03522i	0.293296	−	0.293296i
$950$		0			0
$951$	−14.6394			−0.474715
$952$		0			0
$953$	26.7047	−	26.7047i	0.865050	−	0.865050i	−0.126870	−	0.991919i	$-0.540493\pi$
$953$	26.7047	−	26.7047i	0.865050	−	0.865050i	0.991919	+	0.126870i	$0.0404931\pi$
$954$		0			0
$955$	−8.60247	−	21.4592i	−0.278369	−	0.694405i
$956$		0			0
$957$			2.01191i			0.0650360i
$958$		0			0
$959$	7.34112			0.237057
$960$		0			0
$961$	25.4314			0.820369
$962$		0			0
$963$		−	43.1645i		−	1.39096i
$964$		0			0
$965$	38.4027	+	16.4241i	1.23623	+	0.528709i
$966$		0			0
$967$	12.8711	−	12.8711i	0.413906	−	0.413906i	−0.469191	−	0.883097i	$-0.655454\pi$
$967$	12.8711	−	12.8711i	0.413906	−	0.413906i	0.883097	+	0.469191i	$0.155454\pi$
$968$		0			0
$969$	−3.41725			−0.109778
$970$		0			0
$971$	−23.9028	+	23.9028i	−0.767078	+	0.767078i	−0.977591	−	0.210513i	$-0.932487\pi$
$971$	−23.9028	+	23.9028i	−0.767078	+	0.767078i	0.210513	+	0.977591i	$0.432487\pi$
$972$		0			0
$973$	48.8610			1.56641
$974$		0			0
$975$	4.36168	+	4.56595i	0.139685	+	0.146228i
$976$		0			0
$977$	2.71449	−	2.71449i	0.0868441	−	0.0868441i	−0.662350	−	0.749194i	$-0.730441\pi$
$977$	2.71449	−	2.71449i	0.0868441	−	0.0868441i	0.749194	+	0.662350i	$0.230441\pi$
$978$		0			0
$979$	−22.8154	+	22.8154i	−0.729183	+	0.729183i
$980$		0			0
$981$	−33.7109	−	33.7109i	−1.07630	−	1.07630i
$982$		0			0
$983$	13.7542	+	13.7542i	0.438692	+	0.438692i	0.891572	−	0.452880i	$-0.149603\pi$
$983$	13.7542	+	13.7542i	0.438692	+	0.438692i	−0.452880	+	0.891572i	$0.649603\pi$
$984$		0			0
$985$	−31.6386	+	12.6831i	−1.00809	+	0.404117i
$986$		0			0
$987$			9.50428i			0.302525i
$988$		0			0
$989$	−4.20640	−	4.20640i	−0.133756	−	0.133756i
$990$		0			0
$991$			26.5971i			0.844883i	0.906390	+	0.422442i	$0.138827\pi$
$991$			26.5971i			0.844883i	−0.906390	+	0.422442i	$0.861173\pi$
$992$		0			0
$993$	−12.1492	−	12.1492i	−0.385545	−	0.385545i
$994$		0			0
$995$	4.14979	+	10.3518i	0.131557	+	0.328175i
$996$		0			0
$997$	25.4590			0.806295			0.403148	−	0.915135i	$-0.367916\pi$
$997$	25.4590			0.806295			0.403148	+	0.915135i	$0.367916\pi$
$998$		0			0
$999$			15.7002i			0.496733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.j.c.543.5		18
4.3	odd	2		640.2.j.d.543.5		18
5.2	odd	4		640.2.s.c.287.5		18
8.3	odd	2		80.2.j.b.43.7	✓	18
8.5	even	2		320.2.j.b.143.5		18
16.3	odd	4		640.2.s.c.223.5		18
16.5	even	4		80.2.s.b.3.3	yes	18
16.11	odd	4		320.2.s.b.303.5		18
16.13	even	4		640.2.s.d.223.5		18
20.7	even	4		640.2.s.d.287.5		18
24.11	even	2		720.2.bd.g.523.3		18
40.3	even	4		400.2.s.d.107.7		18
40.13	odd	4		1600.2.s.d.207.5		18
40.19	odd	2		400.2.j.d.43.3		18
40.27	even	4		80.2.s.b.27.3	yes	18
40.29	even	2		1600.2.j.d.143.5		18
40.37	odd	4		320.2.s.b.207.5		18
48.5	odd	4		720.2.z.g.163.7		18
80.27	even	4		320.2.j.b.47.5		18
80.37	odd	4		80.2.j.b.67.7	yes	18
80.43	even	4		1600.2.j.d.1007.5		18
80.53	odd	4		400.2.j.d.307.3		18
80.59	odd	4		1600.2.s.d.943.5		18
80.67	even	4	inner	640.2.j.c.607.5		18
80.69	even	4		400.2.s.d.243.7		18
80.77	odd	4		640.2.j.d.607.5		18
120.107	odd	4		720.2.z.g.667.7		18
240.197	even	4		720.2.bd.g.307.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.7	✓	18	8.3	odd	2
80.2.j.b.67.7	yes	18	80.37	odd	4
80.2.s.b.3.3	yes	18	16.5	even	4
80.2.s.b.27.3	yes	18	40.27	even	4
320.2.j.b.47.5		18	80.27	even	4
320.2.j.b.143.5		18	8.5	even	2
320.2.s.b.207.5		18	40.37	odd	4
320.2.s.b.303.5		18	16.11	odd	4
400.2.j.d.43.3		18	40.19	odd	2
400.2.j.d.307.3		18	80.53	odd	4
400.2.s.d.107.7		18	40.3	even	4
400.2.s.d.243.7		18	80.69	even	4
640.2.j.c.543.5		18	1.1	even	1	trivial
640.2.j.c.607.5		18	80.67	even	4	inner
640.2.j.d.543.5		18	4.3	odd	2
640.2.j.d.607.5		18	80.77	odd	4
640.2.s.c.223.5		18	16.3	odd	4
640.2.s.c.287.5		18	5.2	odd	4
640.2.s.d.223.5		18	16.13	even	4
640.2.s.d.287.5		18	20.7	even	4
720.2.z.g.163.7		18	48.5	odd	4
720.2.z.g.667.7		18	120.107	odd	4
720.2.bd.g.307.3		18	240.197	even	4
720.2.bd.g.523.3		18	24.11	even	2
1600.2.j.d.143.5		18	40.29	even	2
1600.2.j.d.1007.5		18	80.43	even	4
1600.2.s.d.207.5		18	40.13	odd	4
1600.2.s.d.943.5		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)

\(f(q)\)	\(=\)	\(q+0.614566i q^{3} +(2.07551 - 0.832020i) q^{5} +(-2.83610 + 2.83610i) q^{7} +2.62231 q^{9} +O(q^{10})\)	\(q+0.614566i q^{3} +(2.07551 - 0.832020i) q^{5} +(-2.83610 + 2.83610i) q^{7} +2.62231 q^{9} +(1.95928 - 1.95928i) q^{11} +2.05493 q^{13} +(0.511331 + 1.27554i) q^{15} +(-4.06774 + 4.06774i) q^{17} +(0.683479 - 0.683479i) q^{19} +(-1.74297 - 1.74297i) q^{21} +(4.95014 + 4.95014i) q^{23} +(3.61549 - 3.45373i) q^{25} +3.45528i q^{27} +(0.835439 + 0.835439i) q^{29} -2.35978i q^{31} +(1.20411 + 1.20411i) q^{33} +(-3.52666 + 8.24604i) q^{35} +4.54384 q^{37} +1.26289i q^{39} +5.07255i q^{41} -0.849753 q^{43} +(5.44263 - 2.18181i) q^{45} +(-2.72646 - 2.72646i) q^{47} -9.08690i q^{49} +(-2.49989 - 2.49989i) q^{51} -5.17605i q^{53} +(2.43634 - 5.69666i) q^{55} +(0.420043 + 0.420043i) q^{57} +(4.16328 + 4.16328i) q^{59} +(-5.55706 + 5.55706i) q^{61} +(-7.43712 + 7.43712i) q^{63} +(4.26502 - 1.70974i) q^{65} -1.73609 q^{67} +(-3.04219 + 3.04219i) q^{69} -2.33526 q^{71} +(4.39686 - 4.39686i) q^{73} +(2.12255 + 2.22195i) q^{75} +11.1134i q^{77} +14.0993 q^{79} +5.74343 q^{81} -2.75725i q^{83} +(-5.05819 + 11.8271i) q^{85} +(-0.513433 + 0.513433i) q^{87} -11.6448 q^{89} +(-5.82797 + 5.82797i) q^{91} +1.45024 q^{93} +(0.849899 - 1.98724i) q^{95} +(-3.52933 + 3.52933i) q^{97} +(5.13783 - 5.13783i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) \) 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

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