LMFDB - Embedded newform 855.2.n.d.818.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(647,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("855.647");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.n (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 101x^{16} + 2922x^{12} + 18746x^{8} + 4405x^{4} + 1 $ x^20 + 101x^16 + 2922x^12 + 18746x^8 + 4405x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			818.3
Root			$-1.20930 - 1.20930i$ of defining polynomial
Character	$\chi$	$=$	855.818
Dual form			855.2.n.d.647.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20930 - 1.20930i) q^{2} +0.924801i q^{4} +(-1.20930 - 1.88085i) q^{5} +(2.18506 - 2.18506i) q^{7} +(-1.30024 + 1.30024i) q^{8} +O(q^{10})$	\(q+(-1.20930 - 1.20930i) q^{2} +0.924801i q^{4} +(-1.20930 - 1.88085i) q^{5} +(2.18506 - 2.18506i) q^{7} +(-1.30024 + 1.30024i) q^{8} +(-0.812108 + 3.73691i) q^{10} +6.39552i q^{11} +(3.18506 + 3.18506i) q^{13} -5.28479 q^{14} +4.99435 q^{16} +(4.92813 + 4.92813i) q^{17} +1.00000i q^{19} +(1.73941 - 1.11836i) q^{20} +(7.73408 - 7.73408i) q^{22} +(1.62276 - 1.62276i) q^{23} +(-2.07520 + 4.54902i) q^{25} -7.70338i q^{26} +(2.02075 + 2.02075i) q^{28} -2.20338 q^{29} -1.59617 q^{31} +(-3.43918 - 3.43918i) q^{32} -11.9191i q^{34} +(-6.75217 - 1.46739i) q^{35} +(-6.56977 + 6.56977i) q^{37} +(1.20930 - 1.20930i) q^{38} +(4.01792 + 0.873178i) q^{40} -5.32003i q^{41} +(4.02075 + 4.02075i) q^{43} -5.91458 q^{44} -3.92480 q^{46} +(2.10370 + 2.10370i) q^{47} -2.54902i q^{49} +(8.01065 - 2.99158i) q^{50} +(-2.94555 + 2.94555i) q^{52} +(7.08100 - 7.08100i) q^{53} +(12.0290 - 7.73408i) q^{55} +5.68220i q^{56} +(2.66454 + 2.66454i) q^{58} +4.04550 q^{59} -2.29493 q^{61} +(1.93024 + 1.93024i) q^{62} -1.67071i q^{64} +(2.13894 - 9.84232i) q^{65} +(-3.38470 + 3.38470i) q^{67} +(-4.55754 + 4.55754i) q^{68} +(6.39088 + 9.93989i) q^{70} -10.9670i q^{71} +(5.68484 + 5.68484i) q^{73} +15.8896 q^{74} -0.924801 q^{76} +(13.9746 + 13.9746i) q^{77} -0.156054i q^{79} +(-6.03965 - 9.39362i) q^{80} +(-6.43350 + 6.43350i) q^{82} +(-8.12862 + 8.12862i) q^{83} +(3.30950 - 15.2286i) q^{85} -9.72456i q^{86} +(-8.31568 - 8.31568i) q^{88} -14.9439 q^{89} +13.9191 q^{91} +(1.50073 + 1.50073i) q^{92} -5.08800i q^{94} +(1.88085 - 1.20930i) q^{95} +(0.439151 - 0.439151i) q^{97} +(-3.08252 + 3.08252i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q+O(q^{10}) $ 20 * q	$ 20 q + 28 q^{10} + 20 q^{13} - 76 q^{16} + 32 q^{22} - 32 q^{25} - 16 q^{28} - 16 q^{31} + 4 q^{37} - 64 q^{40} + 24 q^{43} - 88 q^{46} - 12 q^{52} + 40 q^{55} + 116 q^{58} + 32 q^{61} + 24 q^{67} - 16 q^{70} + 20 q^{73} - 28 q^{76} + 92 q^{82} - 16 q^{85} - 32 q^{88} + 112 q^{91} - 36 q^{97}+O(q^{100}) $ 20 * q + 28 * q^10 + 20 * q^13 - 76 * q^16 + 32 * q^22 - 32 * q^25 - 16 * q^28 - 16 * q^31 + 4 * q^37 - 64 * q^40 + 24 * q^43 - 88 * q^46 - 12 * q^52 + 40 * q^55 + 116 * q^58 + 32 * q^61 + 24 * q^67 - 16 * q^70 + 20 * q^73 - 28 * q^76 + 92 * q^82 - 16 * q^85 - 32 * q^88 + 112 * q^91 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.20930	−	1.20930i	−0.855102	−	0.855102i	0.135654	−	0.990756i	$-0.456686\pi$
$2$	−1.20930	−	1.20930i	−0.855102	−	0.855102i	−0.990756	+	0.135654i	$0.956686\pi$
$3$		0			0
$3$		0			0
$4$			0.924801i			0.462400i
$5$	−1.20930	−	1.88085i	−0.540814	−	0.841142i
$5$	−1.20930	−	1.88085i	−0.540814	−	0.841142i
$6$		0			0
$7$	2.18506	−	2.18506i	0.825877	−	0.825877i	−0.161067	−	0.986944i	$-0.551493\pi$
$7$	2.18506	−	2.18506i	0.825877	−	0.825877i	0.986944	+	0.161067i	$0.0514934\pi$
$8$	−1.30024	+	1.30024i	−0.459703	+	0.459703i
$9$		0			0
$10$	−0.812108	+	3.73691i	−0.256811	+	1.18171i
$11$			6.39552i			1.92832i	0.265320	+	0.964160i	$0.414522\pi$
$11$			6.39552i			1.92832i	−0.265320	+	0.964160i	$0.585478\pi$
$12$		0			0
$13$	3.18506	+	3.18506i	0.883378	+	0.883378i	0.993876	−	0.110498i	$-0.0352447\pi$
$13$	3.18506	+	3.18506i	0.883378	+	0.883378i	−0.110498	+	0.993876i	$0.535245\pi$
$14$	−5.28479			−1.41242
$15$		0			0
$16$	4.99435			1.24859
$17$	4.92813	+	4.92813i	1.19525	+	1.19525i	0.975574	+	0.219673i	$0.0704991\pi$
$17$	4.92813	+	4.92813i	1.19525	+	1.19525i	0.219673	+	0.975574i	$0.429501\pi$
$18$		0			0
$19$			1.00000i			0.229416i
$19$			1.00000i			0.229416i
$20$	1.73941	−	1.11836i	0.388944	−	0.250073i
$21$		0			0
$22$	7.73408	−	7.73408i	1.64891	−	1.64891i
$23$	1.62276	−	1.62276i	0.338369	−	0.338369i	−0.517384	−	0.855753i	$-0.673094\pi$
$23$	1.62276	−	1.62276i	0.338369	−	0.338369i	0.855753	+	0.517384i	$0.173094\pi$
$24$		0			0
$25$	−2.07520	+	4.54902i	−0.415040	+	0.909803i
$26$		−	7.70338i		−	1.51076i
$27$		0			0
$28$	2.02075	+	2.02075i	0.381886	+	0.381886i
$29$	−2.20338			−0.409157			−0.204578	−	0.978850i	$-0.565582\pi$
$29$	−2.20338			−0.409157			−0.204578	+	0.978850i	$0.565582\pi$
$30$		0			0
$31$	−1.59617			−0.286680			−0.143340	−	0.989673i	$-0.545784\pi$
$31$	−1.59617			−0.286680			−0.143340	+	0.989673i	$0.545784\pi$
$32$	−3.43918	−	3.43918i	−0.607966	−	0.607966i
$33$		0			0
$34$		−	11.9191i		−	2.04412i
$35$	−6.75217	−	1.46739i	−1.14133	−	0.248034i
$36$		0			0
$37$	−6.56977	+	6.56977i	−1.08006	+	1.08006i	−0.0835600	+	0.996503i	$0.526629\pi$
$37$	−6.56977	+	6.56977i	−1.08006	+	1.08006i	−0.996503	+	0.0835600i	$0.973371\pi$
$38$	1.20930	−	1.20930i	0.196174	−	0.196174i
$39$		0			0
$40$	4.01792	+	0.873178i	0.635289	+	0.138062i
$41$		−	5.32003i		−	0.830849i	−0.909628	−	0.415424i	$-0.863633\pi$
$41$		−	5.32003i		−	0.830849i	0.909628	−	0.415424i	$-0.136367\pi$
$42$		0			0
$43$	4.02075	+	4.02075i	0.613158	+	0.613158i	0.943768	−	0.330609i	$-0.107254\pi$
$43$	4.02075	+	4.02075i	0.613158	+	0.613158i	−0.330609	+	0.943768i	$0.607254\pi$
$44$	−5.91458			−0.891656
$45$		0			0
$46$	−3.92480			−0.578680
$47$	2.10370	+	2.10370i	0.306856	+	0.306856i	0.843689	−	0.536833i	$-0.180379\pi$
$47$	2.10370	+	2.10370i	0.306856	+	0.306856i	−0.536833	+	0.843689i	$0.680379\pi$
$48$		0			0
$49$		−	2.54902i		−	0.364145i
$50$	8.01065	−	2.99158i	1.13288	−	0.423073i
$51$		0			0
$52$	−2.94555	+	2.94555i	−0.408474	+	0.408474i
$53$	7.08100	−	7.08100i	0.972651	−	0.972651i	−0.0269852	−	0.999636i	$-0.508591\pi$
$53$	7.08100	−	7.08100i	0.972651	−	0.972651i	0.999636	+	0.0269852i	$0.00859071\pi$
$54$		0			0
$55$	12.0290	−	7.73408i	1.62199	−	1.04286i
$56$			5.68220i			0.759316i
$57$		0			0
$58$	2.66454	+	2.66454i	0.349871	+	0.349871i
$59$	4.04550			0.526680			0.263340	−	0.964703i	$-0.415176\pi$
$59$	4.04550			0.526680			0.263340	+	0.964703i	$0.415176\pi$
$60$		0			0
$61$	−2.29493			−0.293836			−0.146918	−	0.989149i	$-0.546935\pi$
$61$	−2.29493			−0.293836			−0.146918	+	0.989149i	$0.546935\pi$
$62$	1.93024	+	1.93024i	0.245141	+	0.245141i
$63$		0			0
$64$		−	1.67071i		−	0.208839i
$65$	2.13894	−	9.84232i	0.265303	−	1.22079i
$66$		0			0
$67$	−3.38470	+	3.38470i	−0.413507	+	0.413507i	−0.882958	−	0.469451i	$-0.844452\pi$
$67$	−3.38470	+	3.38470i	−0.413507	+	0.413507i	0.469451	+	0.882958i	$0.344452\pi$
$68$	−4.55754	+	4.55754i	−0.552682	+	0.552682i
$69$		0			0
$70$	6.39088	+	9.93989i	0.763856	+	1.18804i
$71$		−	10.9670i		−	1.30154i	−0.759274	−	0.650771i	$-0.774446\pi$
$71$		−	10.9670i		−	1.30154i	0.759274	−	0.650771i	$-0.225554\pi$
$72$		0			0
$73$	5.68484	+	5.68484i	0.665361	+	0.665361i	0.956639	−	0.291278i	$-0.0940804\pi$
$73$	5.68484	+	5.68484i	0.665361	+	0.665361i	−0.291278	+	0.956639i	$0.594080\pi$
$74$	15.8896			1.84713
$75$		0			0
$76$	−0.924801			−0.106082
$77$	13.9746	+	13.9746i	1.59256	+	1.59256i
$78$		0			0
$79$		−	0.156054i		−	0.0175574i	−0.999961	−	0.00877871i	$-0.997206\pi$
$79$		−	0.156054i		−	0.0175574i	0.999961	−	0.00877871i	$-0.00279439\pi$
$80$	−6.03965	−	9.39362i	−0.675253	−	1.05024i
$81$		0			0
$82$	−6.43350	+	6.43350i	−0.710461	+	0.710461i
$83$	−8.12862	+	8.12862i	−0.892232	+	0.892232i	−0.994733	−	0.102501i	$-0.967316\pi$
$83$	−8.12862	+	8.12862i	−0.892232	+	0.892232i	0.102501	+	0.994733i	$0.467316\pi$
$84$		0			0
$85$	3.30950	−	15.2286i	0.358966	−	1.65178i
$86$		−	9.72456i		−	1.04863i
$87$		0			0
$88$	−8.31568	−	8.31568i	−0.886454	−	0.886454i
$89$	−14.9439			−1.58405			−0.792025	−	0.610488i	$-0.790973\pi$
$89$	−14.9439			−1.58405			−0.792025	+	0.610488i	$0.790973\pi$
$90$		0			0
$91$	13.9191			1.45912
$92$	1.50073	+	1.50073i	0.156462	+	0.156462i
$93$		0			0
$94$		−	5.08800i		−	0.524787i
$95$	1.88085	−	1.20930i	0.192971	−	0.124071i
$96$		0			0
$97$	0.439151	−	0.439151i	0.0445890	−	0.0445890i	−0.684461	−	0.729050i	$-0.739962\pi$
$97$	0.439151	−	0.439151i	0.0445890	−	0.0445890i	0.729050	+	0.684461i	$0.239962\pi$
$98$	−3.08252	+	3.08252i	−0.311381	+	0.311381i
$99$		0			0
$100$	−4.20693	−	1.91915i	−0.420693	−	0.191915i
$101$			10.9317i			1.08775i	0.839166	+	0.543875i	$0.183043\pi$
$101$			10.9317i			1.08775i	−0.839166	+	0.543875i	$0.816957\pi$
$102$		0			0
$103$	2.29493	+	2.29493i	0.226126	+	0.226126i	0.811072	−	0.584946i	$-0.198884\pi$
$103$	2.29493	+	2.29493i	0.226126	+	0.226126i	−0.584946	+	0.811072i	$0.698884\pi$
$104$	−8.28267			−0.812183
$105$		0			0
$106$	−17.1261			−1.66343
$107$	6.24014	+	6.24014i	0.603257	+	0.603257i	0.941176	−	0.337918i	$-0.109723\pi$
$107$	6.24014	+	6.24014i	0.603257	+	0.603257i	−0.337918	+	0.941176i	$0.609723\pi$
$108$		0			0
$109$		−	2.54967i		−	0.244214i	−0.992517	−	0.122107i	$-0.961035\pi$
$109$		−	2.54967i		−	0.244214i	0.992517	−	0.122107i	$-0.0389651\pi$
$110$	−23.8995	−	5.19385i	−2.27872	−	0.495214i
$111$		0			0
$112$	10.9130	−	10.9130i	1.03118	−	1.03118i
$113$	13.5354	−	13.5354i	1.27331	−	1.27331i	0.328965	−	0.944342i	$-0.393300\pi$
$113$	13.5354	−	13.5354i	1.27331	−	1.27331i	0.944342	−	0.328965i	$-0.106700\pi$
$114$		0			0
$115$	−5.01457	−	1.08977i	−0.467611	−	0.101622i
$116$		−	2.03768i		−	0.189194i
$117$		0			0
$118$	−4.89222	−	4.89222i	−0.450365	−	0.450365i
$119$	21.5366			1.97425
$120$		0			0
$121$	−29.9026			−2.71842
$122$	2.77525	+	2.77525i	0.251260	+	0.251260i
$123$		0			0
$124$		−	1.47614i		−	0.132561i
$125$	11.0656	−	1.59797i	0.989733	−	0.142927i
$126$		0			0
$127$	11.0089	−	11.0089i	0.976883	−	0.976883i	−0.0228555	−	0.999739i	$-0.507276\pi$
$127$	11.0089	−	11.0089i	0.976883	−	0.976883i	0.999739	+	0.0228555i	$0.00727575\pi$
$128$	−8.89874	+	8.89874i	−0.786545	+	0.786545i
$129$		0			0
$130$	−14.4889	+	9.31568i	−1.27076	+	0.817039i
$131$			7.61764i			0.665556i	0.943005	+	0.332778i	$0.107986\pi$
$131$			7.61764i			0.665556i	−0.943005	+	0.332778i	$0.892014\pi$
$132$		0			0
$133$	2.18506	+	2.18506i	0.189469	+	0.189469i
$134$	8.18622			0.707182
$135$		0			0
$136$	−12.8155			−1.09892
$137$	−10.5524	−	10.5524i	−0.901554	−	0.901554i	0.0940170	−	0.995571i	$-0.470029\pi$
$137$	−10.5524	−	10.5524i	−0.901554	−	0.901554i	−0.995571	+	0.0940170i	$0.970029\pi$
$138$		0			0
$139$		−	6.57750i		−	0.557897i	−0.960306	−	0.278948i	$-0.910014\pi$
$139$		−	6.57750i		−	0.557897i	0.960306	−	0.278948i	$-0.0899858\pi$
$140$	1.35704	−	6.24441i	0.114691	−	0.527749i
$141$		0			0
$142$	−13.2623	+	13.2623i	−1.11295	+	1.11295i
$143$	−20.3701	+	20.3701i	−1.70344	+	1.70344i
$144$		0			0
$145$	2.66454	+	4.14422i	0.221278	+	0.344159i
$146$		−	13.7493i		−	1.13790i
$147$		0			0
$148$	−6.07572	−	6.07572i	−0.499421	−	0.499421i
$149$	19.4713			1.59515			0.797577	−	0.603218i	$-0.206115\pi$
$149$	19.4713			1.59515			0.797577	+	0.603218i	$0.206115\pi$
$150$		0			0
$151$	−9.59051			−0.780465			−0.390232	−	0.920716i	$-0.627605\pi$
$151$	−9.59051			−0.780465			−0.390232	+	0.920716i	$0.627605\pi$
$152$	−1.30024	−	1.30024i	−0.105463	−	0.105463i
$153$		0			0
$154$		−	33.7989i		−	2.72360i
$155$	1.93024	+	3.00216i	0.155041	+	0.241139i
$156$		0			0
$157$	7.41319	−	7.41319i	0.591637	−	0.591637i	−0.346437	−	0.938073i	$-0.612608\pi$
$157$	7.41319	−	7.41319i	0.591637	−	0.591637i	0.938073	+	0.346437i	$0.112608\pi$
$158$	−0.188715	+	0.188715i	−0.0150134	+	0.0150134i
$159$		0			0
$160$	−2.30959	+	10.6276i	−0.182589	+	0.840183i
$161$		−	7.09167i		−	0.558902i
$162$		0			0
$163$	7.43915	+	7.43915i	0.582679	+	0.582679i	0.935639	−	0.352959i	$-0.114825\pi$
$163$	7.43915	+	7.43915i	0.582679	+	0.582679i	−0.352959	+	0.935639i	$0.614825\pi$
$164$	4.91996			0.384185
$165$		0			0
$166$	19.6598			1.52590
$167$	6.44469	+	6.44469i	0.498705	+	0.498705i	0.911035	−	0.412330i	$-0.135285\pi$
$167$	6.44469	+	6.44469i	0.498705	+	0.498705i	−0.412330	+	0.911035i	$0.635285\pi$
$168$		0			0
$169$			7.28928i			0.560713i
$170$	−22.4181	+	14.4138i	−1.71939	+	1.10549i
$171$		0			0
$172$	−3.71839	+	3.71839i	−0.283525	+	0.283525i
$173$	−1.85514	+	1.85514i	−0.141044	+	0.141044i	−0.774103	−	0.633060i	$-0.781799\pi$
$173$	−1.85514	+	1.85514i	−0.141044	+	0.141044i	0.633060	+	0.774103i	$0.281799\pi$
$174$		0			0
$175$	5.40545	+	14.4743i	0.408614	+	1.09416i
$176$			31.9414i			2.40767i
$177$		0			0
$178$	18.0716	+	18.0716i	1.35453	+	1.35453i
$179$	5.73817			0.428891			0.214446	−	0.976736i	$-0.431206\pi$
$179$	5.73817			0.428891			0.214446	+	0.976736i	$0.431206\pi$
$180$		0			0
$181$	−14.0124			−1.04153			−0.520765	−	0.853700i	$-0.674353\pi$
$181$	−14.0124			−1.04153			−0.520765	+	0.853700i	$0.674353\pi$
$182$	−16.8324	−	16.8324i	−1.24770	−	1.24770i
$183$		0			0
$184$			4.21994i			0.311098i
$185$	20.3015	+	4.41195i	1.49260	+	0.324373i
$186$		0			0
$187$	−31.5179	+	31.5179i	−2.30482	+	2.30482i
$188$	−1.94550	+	1.94550i	−0.141890	+	0.141890i
$189$		0			0
$190$	−3.73691	−	0.812108i	−0.271104	−	0.0589165i
$191$			3.99218i			0.288864i	0.989515	+	0.144432i	$0.0461355\pi$
$191$			3.99218i			0.288864i	−0.989515	+	0.144432i	$0.953865\pi$
$192$		0			0
$193$	14.2551	+	14.2551i	1.02610	+	1.02610i	0.999650	+	0.0264509i	$0.00842056\pi$
$193$	14.2551	+	14.2551i	1.02610	+	1.02610i	0.0264509	+	0.999650i	$0.491579\pi$
$194$	−1.06213			−0.0762563
$195$		0			0
$196$	2.35733			0.168381
$197$	3.62026	+	3.62026i	0.257933	+	0.257933i	0.824213	−	0.566280i	$-0.191618\pi$
$197$	3.62026	+	3.62026i	0.257933	+	0.257933i	−0.566280	+	0.824213i	$0.691618\pi$
$198$		0			0
$199$		−	0.999558i		−	0.0708568i	−0.999372	−	0.0354284i	$-0.988720\pi$
$199$		−	0.999558i		−	0.0708568i	0.999372	−	0.0354284i	$-0.0112796\pi$
$200$	−3.21655	−	8.61304i	−0.227444	−	0.609034i
$201$		0			0
$202$	13.2197	−	13.2197i	0.930137	−	0.930137i
$203$	−4.81452	+	4.81452i	−0.337913	+	0.337913i
$204$		0			0
$205$	−10.0062	+	6.43350i	−0.698862	+	0.449335i
$206$		−	5.55051i		−	0.386722i
$207$		0			0
$208$	15.9073	+	15.9073i	1.10297	+	1.10297i
$209$	−6.39552			−0.442387
$210$		0			0
$211$	10.2847			0.708029			0.354015	−	0.935240i	$-0.384816\pi$
$211$	10.2847			0.708029			0.354015	+	0.935240i	$0.384816\pi$
$212$	6.54852	+	6.54852i	0.449754	+	0.449754i
$213$		0			0
$214$		−	15.0924i		−	1.03169i
$215$	2.70015	−	12.4247i	0.184149	−	0.847358i
$216$		0			0
$217$	−3.48773	+	3.48773i	−0.236763	+	0.236763i
$218$	−3.08331	+	3.08331i	−0.208828	+	0.208828i
$219$		0			0
$220$	7.15248	+	11.1244i	0.482220	+	0.750009i
$221$			31.3928i			2.11171i
$222$		0			0
$223$	−5.24256	−	5.24256i	−0.351068	−	0.351068i	0.509439	−	0.860507i	$-0.329853\pi$
$223$	−5.24256	−	5.24256i	−0.351068	−	0.351068i	−0.860507	+	0.509439i	$0.829853\pi$
$224$	−15.0296			−1.00421
$225$		0			0
$226$	−32.7367			−2.17762
$227$	−14.1300	−	14.1300i	−0.937840	−	0.937840i	0.0603377	−	0.998178i	$-0.480782\pi$
$227$	−14.1300	−	14.1300i	−0.937840	−	0.937840i	−0.998178	+	0.0603377i	$0.980782\pi$
$228$		0			0
$229$		−	29.1157i		−	1.92402i	−0.273021	−	0.962008i	$-0.588023\pi$
$229$		−	29.1157i		−	1.92402i	0.273021	−	0.962008i	$-0.411977\pi$
$230$	4.74625	+	7.38196i	0.312959	+	0.486752i
$231$		0			0
$232$	2.86491	−	2.86491i	0.188090	−	0.188090i
$233$	−15.5695	+	15.5695i	−1.01999	+	1.01999i	−0.0201964	+	0.999796i	$0.506429\pi$
$233$	−15.5695	+	15.5695i	−1.01999	+	1.01999i	−0.999796	+	0.0201964i	$0.993571\pi$
$234$		0			0
$235$	1.41275	−	6.50074i	0.0921574	−	0.424062i
$236$			3.74128i			0.243537i
$237$		0			0
$238$	−26.0441	−	26.0441i	−1.68819	−	1.68819i
$239$	5.52295			0.357250			0.178625	−	0.983917i	$-0.442835\pi$
$239$	5.52295			0.357250			0.178625	+	0.983917i	$0.442835\pi$
$240$		0			0
$241$	−10.4116			−0.670672			−0.335336	−	0.942099i	$-0.608850\pi$
$241$	−10.4116			−0.670672			−0.335336	+	0.942099i	$0.608850\pi$
$242$	36.1612	+	36.1612i	2.32453	+	2.32453i
$243$		0			0
$244$		−	2.12235i		−	0.135870i
$245$	−4.79432	+	3.08252i	−0.306298	+	0.196935i
$246$		0			0
$247$	−3.18506	+	3.18506i	−0.202661	+	0.202661i
$248$	2.07540	−	2.07540i	0.131788	−	0.131788i
$249$		0			0
$250$	−15.3140	−	11.4491i	−0.968541	−	0.724106i
$251$		−	7.99887i		−	0.504884i	−0.967612	−	0.252442i	$-0.918766\pi$
$251$		−	7.99887i		−	0.504884i	0.967612	−	0.252442i	$-0.0812337\pi$
$252$		0			0
$253$	10.3784	+	10.3784i	0.652484	+	0.652484i
$254$	−26.6261			−1.67067
$255$		0			0
$256$	18.1810			1.13631
$257$	−9.46626	−	9.46626i	−0.590489	−	0.590489i	0.347275	−	0.937763i	$-0.387107\pi$
$257$	−9.46626	−	9.46626i	−0.590489	−	0.590489i	−0.937763	+	0.347275i	$0.887107\pi$
$258$		0			0
$259$			28.7107i			1.78400i
$260$	9.10219	+	1.97809i	0.564494	+	0.122676i
$261$		0			0
$262$	9.21199	−	9.21199i	0.569119	−	0.569119i
$263$	6.95805	−	6.95805i	0.429052	−	0.429052i	−0.459254	−	0.888305i	$-0.651883\pi$
$263$	6.95805	−	6.95805i	0.429052	−	0.429052i	0.888305	+	0.459254i	$0.151883\pi$
$264$		0			0
$265$	−21.8813	−	4.75527i	−1.34416	−	0.292114i
$266$		−	5.28479i		−	0.324031i
$267$		0			0
$268$	−3.13017	−	3.13017i	−0.191206	−	0.191206i
$269$	−28.3286			−1.72722			−0.863611	−	0.504158i	$-0.831803\pi$
$269$	−28.3286			−1.72722			−0.863611	+	0.504158i	$0.831803\pi$
$270$		0			0
$271$	2.87830			0.174844			0.0874222	−	0.996171i	$-0.472137\pi$
$271$	2.87830			0.174844			0.0874222	+	0.996171i	$0.472137\pi$
$272$	24.6128	+	24.6128i	1.49237	+	1.49237i
$273$		0			0
$274$			25.5220i			1.54184i
$275$	−29.0933	−	13.2720i	−1.75439	−	0.800330i
$276$		0			0
$277$	5.49248	−	5.49248i	0.330011	−	0.330011i	−0.522579	−	0.852591i	$-0.675030\pi$
$277$	5.49248	−	5.49248i	0.330011	−	0.330011i	0.852591	+	0.522579i	$0.175030\pi$
$278$	−7.95416	+	7.95416i	−0.477059	+	0.477059i
$279$		0			0
$280$	10.6874	−	6.87147i	0.638692	−	0.410649i
$281$			28.3007i			1.68828i	0.536124	+	0.844139i	$0.319888\pi$
$281$			28.3007i			1.68828i	−0.536124	+	0.844139i	$0.680112\pi$
$282$		0			0
$283$	9.55454	+	9.55454i	0.567958	+	0.567958i	0.931556	−	0.363598i	$-0.118452\pi$
$283$	9.55454	+	9.55454i	0.567958	+	0.567958i	−0.363598	+	0.931556i	$0.618452\pi$
$284$	10.1423			0.601833
$285$		0			0
$286$	49.2671			2.91322
$287$	−11.6246	−	11.6246i	−0.686179	−	0.686179i
$288$		0			0
$289$			31.5729i			1.85723i
$290$	1.78938	−	8.23381i	0.105076	−	0.483506i
$291$		0			0
$292$	−5.25735	+	5.25735i	−0.307663	+	0.307663i
$293$	−5.30807	+	5.30807i	−0.310101	+	0.310101i	−0.844948	−	0.534848i	$-0.820369\pi$
$293$	−5.30807	+	5.30807i	−0.310101	+	0.310101i	0.534848	+	0.844948i	$0.320369\pi$
$294$		0			0
$295$	−4.89222	−	7.60899i	−0.284836	−	0.443013i
$296$		−	17.0845i		−	0.993016i
$297$		0			0
$298$	−23.5466	−	23.5466i	−1.36402	−	1.36402i
$299$	10.3372			0.597815
$300$		0			0
$301$	17.5712			1.01279
$302$	11.5978	+	11.5978i	0.667378	+	0.667378i
$303$		0			0
$304$			4.99435i			0.286445i
$305$	2.77525	+	4.31642i	0.158911	+	0.247158i
$306$		0			0
$307$	14.2836	−	14.2836i	0.815209	−	0.815209i	−0.170200	−	0.985409i	$-0.554441\pi$
$307$	14.2836	−	14.2836i	0.815209	−	0.815209i	0.985409	+	0.170200i	$0.0544415\pi$
$308$	−12.9237	+	12.9237i	−0.736398	+	0.736398i
$309$		0			0
$310$	1.29626	−	5.96474i	0.0736227	−	0.338774i
$311$		−	21.2935i		−	1.20744i	−0.797196	−	0.603721i	$-0.793684\pi$
$311$		−	21.2935i		−	1.20744i	0.797196	−	0.603721i	$-0.206316\pi$
$312$		0			0
$313$	1.68594	+	1.68594i	0.0952949	+	0.0952949i	0.753147	−	0.657852i	$-0.228535\pi$
$313$	1.68594	+	1.68594i	0.0952949	+	0.0952949i	−0.657852	+	0.753147i	$0.728535\pi$
$314$	−17.9295			−1.01182
$315$		0			0
$316$	0.144319			0.00811856
$317$	7.57258	+	7.57258i	0.425318	+	0.425318i	0.887030	−	0.461712i	$-0.152765\pi$
$317$	7.57258	+	7.57258i	0.425318	+	0.425318i	−0.461712	+	0.887030i	$0.652765\pi$
$318$		0			0
$319$		−	14.0917i		−	0.788985i
$320$	−3.14236	+	2.02039i	−0.175664	+	0.112943i
$321$		0			0
$322$	−8.57594	+	8.57594i	−0.477919	+	0.477919i
$323$	−4.92813	+	4.92813i	−0.274208	+	0.274208i
$324$		0			0
$325$	−21.0986	+	7.87927i	−1.17034	+	0.437063i
$326$		−	17.9923i		−	0.996501i
$327$		0			0
$328$	6.91729	+	6.91729i	0.381943	+	0.381943i
$329$	9.19344			0.506851
$330$		0			0
$331$	−13.6766			−0.751736			−0.375868	−	0.926673i	$-0.622655\pi$
$331$	−13.6766			−0.751736			−0.375868	+	0.926673i	$0.622655\pi$
$332$	−7.51736	−	7.51736i	−0.412568	−	0.412568i
$333$		0			0
$334$		−	15.5871i		−	0.852888i
$335$	10.4592	+	2.27301i	0.571449	+	0.124188i
$336$		0			0
$337$	−0.979251	+	0.979251i	−0.0533432	+	0.0533432i	−0.733275	−	0.679932i	$-0.762009\pi$
$337$	−0.979251	+	0.979251i	−0.0533432	+	0.0533432i	0.679932	+	0.733275i	$0.262009\pi$
$338$	8.81490	−	8.81490i	0.479467	−	0.479467i
$339$		0			0
$340$	14.0835	+	3.06063i	0.763783	+	0.165986i
$341$		−	10.2083i		−	0.552812i
$342$		0			0
$343$	9.72569	+	9.72569i	0.525138	+	0.525138i
$344$	−10.4558			−0.563741
$345$		0			0
$346$	4.48683			0.241213
$347$	−17.5039	−	17.5039i	−0.939661	−	0.939661i	0.0586196	−	0.998280i	$-0.481330\pi$
$347$	−17.5039	−	17.5039i	−0.939661	−	0.939661i	−0.998280	+	0.0586196i	$0.981330\pi$
$348$		0			0
$349$			4.89631i			0.262094i	0.991376	+	0.131047i	$0.0418338\pi$
$349$			4.89631i			0.262094i	−0.991376	+	0.131047i	$0.958166\pi$
$350$	10.9670	−	24.0406i	0.586210	−	1.28502i
$351$		0			0
$352$	21.9953	−	21.9953i	1.17235	−	1.17235i
$353$	−5.87829	+	5.87829i	−0.312870	+	0.312870i	−0.846020	−	0.533151i	$-0.821008\pi$
$353$	−5.87829	+	5.87829i	−0.312870	+	0.312870i	0.533151	+	0.846020i	$0.321008\pi$
$354$		0			0
$355$	−20.6273	+	13.2623i	−1.09478	+	0.703892i
$356$		−	13.8201i		−	0.732466i
$357$		0			0
$358$	−6.93916	−	6.93916i	−0.366746	−	0.366746i
$359$	32.5369			1.71723			0.858616	−	0.512620i	$-0.171325\pi$
$359$	32.5369			1.71723			0.858616	+	0.512620i	$0.171325\pi$
$360$		0			0
$361$	−1.00000			−0.0526316
$362$	16.9451	+	16.9451i	0.890615	+	0.890615i
$363$		0			0
$364$			12.8724i			0.674699i
$365$	3.81768	−	17.5670i	0.199826	−	0.919499i
$366$		0			0
$367$	11.4654	−	11.4654i	0.598490	−	0.598490i	−0.341420	−	0.939911i	$-0.610908\pi$
$367$	11.4654	−	11.4654i	0.598490	−	0.598490i	0.939911	+	0.341420i	$0.110908\pi$
$368$	8.10463	−	8.10463i	0.422483	−	0.422483i
$369$		0			0
$370$	−19.2153	−	29.8860i	−0.998953	−	1.55370i
$371$		−	30.9449i		−	1.60658i
$372$		0			0
$373$	−7.73452	−	7.73452i	−0.400478	−	0.400478i	0.477923	−	0.878402i	$-0.341390\pi$
$373$	−7.73452	−	7.73452i	−0.400478	−	0.400478i	−0.878402	+	0.477923i	$0.841390\pi$
$374$	76.2291			3.94171
$375$		0			0
$376$	−5.47061			−0.282125
$377$	−7.01789	−	7.01789i	−0.361440	−	0.361440i
$378$		0			0
$379$			27.8974i			1.43299i	0.697590	+	0.716497i	$0.254256\pi$
$379$			27.8974i			1.43299i	−0.697590	+	0.716497i	$0.745744\pi$
$380$	1.11836	+	1.73941i	0.0573706	+	0.0892299i
$381$		0			0
$382$	4.82773	−	4.82773i	0.247008	−	0.247008i
$383$	22.3282	−	22.3282i	1.14092	−	1.14092i	0.152638	−	0.988282i	$-0.451223\pi$
$383$	22.3282	−	22.3282i	1.14092	−	1.14092i	0.988282	−	0.152638i	$-0.0487768\pi$
$384$		0			0
$385$	9.38470	−	43.1836i	0.478289	−	2.20084i
$386$		−	34.4772i		−	1.75484i
$387$		0			0
$388$	0.406127	+	0.406127i	0.0206180	+	0.0206180i
$389$	11.8101			0.598796			0.299398	−	0.954128i	$-0.403214\pi$
$389$	11.8101			0.598796			0.299398	+	0.954128i	$0.403214\pi$
$390$		0			0
$391$	15.9943			0.808869
$392$	3.31432	+	3.31432i	0.167399	+	0.167399i
$393$		0			0
$394$		−	8.75595i		−	0.441118i
$395$	−0.293514	+	0.188715i	−0.0147683	+	0.00949531i
$396$		0			0
$397$	−6.62987	+	6.62987i	−0.332744	+	0.332744i	−0.853628	−	0.520884i	$-0.825602\pi$
$397$	−6.62987	+	6.62987i	−0.332744	+	0.332744i	0.520884	+	0.853628i	$0.325602\pi$
$398$	−1.20876	+	1.20876i	−0.0605898	+	0.0605898i
$399$		0			0
$400$	−10.3643	+	22.7194i	−0.518213	+	1.13597i
$401$		−	19.4459i		−	0.971080i	−0.874214	−	0.485540i	$-0.838623\pi$
$401$		−	19.4459i		−	0.971080i	0.874214	−	0.485540i	$-0.161377\pi$
$402$		0			0
$403$	−5.08390	−	5.08390i	−0.253247	−	0.253247i
$404$	−10.1097			−0.502976
$405$		0			0
$406$	11.6444			0.577900
$407$	−42.0170	−	42.0170i	−2.08271	−	2.08271i
$408$		0			0
$409$		−	19.8272i		−	0.980390i	−0.871613	−	0.490195i	$-0.836926\pi$
$409$		−	19.8272i		−	0.980390i	0.871613	−	0.490195i	$-0.163074\pi$
$410$	19.8805	+	4.32044i	0.981826	+	0.213371i
$411$		0			0
$412$	−2.12235	+	2.12235i	−0.104561	+	0.104561i
$413$	8.83969	−	8.83969i	0.434973	−	0.434973i
$414$		0			0
$415$	25.1187	+	5.45880i	1.23303	+	0.267962i
$416$		−	21.9080i		−	1.07413i
$417$		0			0
$418$	7.73408	+	7.73408i	0.378286	+	0.378286i
$419$	36.6414			1.79005			0.895026	−	0.446015i	$-0.147157\pi$
$419$	36.6414			1.79005			0.895026	+	0.446015i	$0.147157\pi$
$420$		0			0
$421$	−17.9548			−0.875062			−0.437531	−	0.899203i	$-0.644147\pi$
$421$	−17.9548			−0.875062			−0.437531	+	0.899203i	$0.644147\pi$
$422$	−12.4373	−	12.4373i	−0.605437	−	0.605437i
$423$		0			0
$424$			18.4139i			0.894260i
$425$	−32.6450	+	12.1913i	−1.58351	+	0.591364i
$426$		0			0
$427$	−5.01457	+	5.01457i	−0.242672	+	0.242672i
$428$	−5.77089	+	5.77089i	−0.278946	+	0.278946i
$429$		0			0
$430$	−18.2905	+	11.7599i	−0.882044	+	0.567112i
$431$			40.3285i			1.94256i	0.237947	+	0.971278i	$0.423526\pi$
$431$			40.3285i			1.94256i	−0.237947	+	0.971278i	$0.576474\pi$
$432$		0			0
$433$	−7.97138	−	7.97138i	−0.383080	−	0.383080i	0.489130	−	0.872211i	$-0.337314\pi$
$433$	−7.97138	−	7.97138i	−0.383080	−	0.383080i	−0.872211	+	0.489130i	$0.837314\pi$
$434$	8.43541			0.404913
$435$		0			0
$436$	2.35794			0.112925
$437$	1.62276	+	1.62276i	0.0776272	+	0.0776272i
$438$		0			0
$439$		−	15.3684i		−	0.733493i	−0.930321	−	0.366746i	$-0.880472\pi$
$439$		−	15.3684i		−	0.733493i	0.930321	−	0.366746i	$-0.119528\pi$
$440$	−5.58442	+	25.6967i	−0.266227	+	1.22504i
$441$		0			0
$442$	37.9633	−	37.9633i	1.80573	−	1.80573i
$443$	18.5975	−	18.5975i	0.883594	−	0.883594i	−0.110304	−	0.993898i	$-0.535182\pi$
$443$	18.5975	−	18.5975i	0.883594	−	0.883594i	0.993898	+	0.110304i	$0.0351823\pi$
$444$		0			0
$445$	18.0716	+	28.1073i	0.856677	+	1.33241i
$446$			12.6796i			0.600398i
$447$		0			0
$448$	−3.65062	−	3.65062i	−0.172476	−	0.172476i
$449$	−8.21864			−0.387861			−0.193931	−	0.981015i	$-0.562124\pi$
$449$	−8.21864			−0.387861			−0.193931	+	0.981015i	$0.562124\pi$
$450$		0			0
$451$	34.0243			1.60214
$452$	12.5176	+	12.5176i	0.588778	+	0.588778i
$453$		0			0
$454$			34.1747i			1.60390i
$455$	−16.8324	−	26.1798i	−0.789114	−	1.22733i
$456$		0			0
$457$	10.5986	−	10.5986i	0.495780	−	0.495780i	−0.414342	−	0.910121i	$-0.635988\pi$
$457$	10.5986	−	10.5986i	0.495780	−	0.495780i	0.910121	+	0.414342i	$0.135988\pi$
$458$	−35.2095	+	35.2095i	−1.64523	+	1.64523i
$459$		0			0
$460$	1.00782	−	4.63748i	0.0469899	−	0.216224i
$461$			17.6356i			0.821372i	0.911777	+	0.410686i	$0.134711\pi$
$461$			17.6356i			0.821372i	−0.911777	+	0.410686i	$0.865289\pi$
$462$		0			0
$463$	−21.0147	−	21.0147i	−0.976634	−	0.976634i	0.0230994	−	0.999733i	$-0.492647\pi$
$463$	−21.0147	−	21.0147i	−0.976634	−	0.976634i	−0.999733	+	0.0230994i	$0.992647\pi$
$464$	−11.0044			−0.510867
$465$		0			0
$466$	37.6563			1.74440
$467$	1.31306	+	1.31306i	0.0607613	+	0.0607613i	0.736834	−	0.676073i	$-0.236320\pi$
$467$	1.31306	+	1.31306i	0.0607613	+	0.0607613i	−0.676073	+	0.736834i	$0.736320\pi$
$468$		0			0
$469$			14.7916i			0.683012i
$470$	−9.56976	+	6.15290i	−0.441420	+	0.283812i
$471$		0			0
$472$	−5.26011	+	5.26011i	−0.242116	+	0.242116i
$473$	−25.7148	+	25.7148i	−1.18237	+	1.18237i
$474$		0			0
$475$	−4.54902	−	2.07520i	−0.208723	−	0.0952167i
$476$			19.9170i			0.912895i
$477$		0			0
$478$	−6.67889	−	6.67889i	−0.305486	−	0.305486i
$479$	6.28928			0.287364			0.143682	−	0.989624i	$-0.454106\pi$
$479$	6.28928			0.287364			0.143682	+	0.989624i	$0.454106\pi$
$480$		0			0
$481$	−41.8503			−1.90821
$482$	12.5908	+	12.5908i	0.573493	+	0.573493i
$483$		0			0
$484$		−	27.6540i		−	1.25700i
$485$	−1.35704	−	0.294913i	−0.0616201	−	0.0133913i
$486$		0			0
$487$	25.1874	−	25.1874i	1.14135	−	1.14135i	0.153144	−	0.988204i	$-0.451060\pi$
$487$	25.1874	−	25.1874i	1.14135	−	1.14135i	0.988204	−	0.153144i	$-0.0489400\pi$
$488$	2.98395	−	2.98395i	0.135077	−	0.135077i
$489$		0			0
$490$	9.52544	+	2.07008i	0.430315	+	0.0935165i
$491$		−	17.0077i		−	0.767547i	−0.923427	−	0.383773i	$-0.874624\pi$
$491$		−	17.0077i		−	0.767547i	0.923427	−	0.383773i	$-0.125376\pi$
$492$		0			0
$493$	−10.8585	−	10.8585i	−0.489043	−	0.489043i
$494$	7.70338			0.346592
$495$		0			0
$496$	−7.97182			−0.357945
$497$	−23.9636	−	23.9636i	−1.07491	−	1.07491i
$498$		0			0
$499$			12.3888i			0.554601i	0.960783	+	0.277300i	$0.0894397\pi$
$499$			12.3888i			0.554601i	−0.960783	+	0.277300i	$0.910560\pi$
$500$	1.47781	+	10.2334i	0.0660895	+	0.457653i
$501$		0			0
$502$	−9.67301	+	9.67301i	−0.431728	+	0.431728i
$503$	9.81969	−	9.81969i	0.437838	−	0.437838i	−0.453446	−	0.891284i	$-0.649805\pi$
$503$	9.81969	−	9.81969i	0.437838	−	0.437838i	0.891284	+	0.453446i	$0.149805\pi$
$504$		0			0
$505$	20.5610	−	13.2197i	0.914952	−	0.588270i
$506$		−	25.1011i		−	1.11588i
$507$		0			0
$508$	10.1811	+	10.1811i	0.451711	+	0.451711i
$509$	−9.12486			−0.404452			−0.202226	−	0.979339i	$-0.564818\pi$
$509$	−9.12486			−0.404452			−0.202226	+	0.979339i	$0.564818\pi$
$510$		0			0
$511$	24.8435			1.09901
$512$	−4.18878	−	4.18878i	−0.185120	−	0.185120i
$513$		0			0
$514$			22.8950i			1.00986i
$515$	1.54117	−	7.09167i	0.0679120	−	0.312497i
$516$		0			0
$517$	−13.4542	+	13.4542i	−0.591717	+	0.591717i
$518$	34.7198	−	34.7198i	1.52550	−	1.52550i
$519$		0			0
$520$	10.0162	+	15.5785i	0.439240	+	0.683161i
$521$			21.2160i			0.929491i	0.885444	+	0.464746i	$0.153854\pi$
$521$			21.2160i			0.929491i	−0.885444	+	0.464746i	$0.846146\pi$
$522$		0			0
$523$	−6.23842	−	6.23842i	−0.272787	−	0.272787i	0.557434	−	0.830221i	$-0.311786\pi$
$523$	−6.23842	−	6.23842i	−0.272787	−	0.272787i	−0.830221	+	0.557434i	$0.811786\pi$
$524$	−7.04480			−0.307753
$525$		0			0
$526$	−16.8287			−0.733766
$527$	−7.86613	−	7.86613i	−0.342654	−	0.342654i
$528$		0			0
$529$			17.7333i			0.771013i
$530$	20.7105	+	32.2116i	0.899608	+	1.39918i
$531$		0			0
$532$	−2.02075	+	2.02075i	−0.0876106	+	0.0876106i
$533$	16.9446	−	16.9446i	0.733954	−	0.733954i
$534$		0			0
$535$	4.19059	−	19.2830i	0.181175	−	0.833675i
$536$		−	8.80182i		−	0.380181i
$537$		0			0
$538$	34.2577	+	34.2577i	1.47695	+	1.47695i
$539$	16.3023			0.702189
$540$		0			0
$541$	−0.261229			−0.0112311			−0.00561556	−	0.999984i	$-0.501787\pi$
$541$	−0.261229			−0.0112311			−0.00561556	+	0.999984i	$0.501787\pi$
$542$	−3.48072	−	3.48072i	−0.149510	−	0.149510i
$543$		0			0
$544$		−	33.8974i		−	1.45334i
$545$	−4.79555	+	3.08331i	−0.205419	+	0.132074i
$546$		0			0
$547$	7.61835	−	7.61835i	0.325737	−	0.325737i	−0.525226	−	0.850963i	$-0.676019\pi$
$547$	7.61835	−	7.61835i	0.325737	−	0.325737i	0.850963	+	0.525226i	$0.176019\pi$
$548$	9.75888	−	9.75888i	0.416879	−	0.416879i
$549$		0			0
$550$	19.1327	+	51.2322i	0.815821	+	2.18455i
$551$		−	2.20338i		−	0.0938670i
$552$		0			0
$553$	−0.340988	−	0.340988i	−0.0145003	−	0.0145003i
$554$	−13.2841			−0.564387
$555$		0			0
$556$	6.08288			0.257972
$557$	−3.56267	−	3.56267i	−0.150955	−	0.150955i	0.627589	−	0.778544i	$-0.284042\pi$
$557$	−3.56267	−	3.56267i	−0.150955	−	0.150955i	−0.778544	+	0.627589i	$0.784042\pi$
$558$		0			0
$559$			25.6127i			1.08330i
$560$	−33.7227	−	7.32864i	−1.42504	−	0.309692i
$561$		0			0
$562$	34.2240	−	34.2240i	1.44365	−	1.44365i
$563$	2.50019	−	2.50019i	0.105370	−	0.105370i	−0.652456	−	0.757826i	$-0.726261\pi$
$563$	2.50019	−	2.50019i	0.105370	−	0.105370i	0.757826	+	0.652456i	$0.226261\pi$
$564$		0			0
$565$	−41.8265	−	9.08977i	−1.75965	−	0.382410i
$566$		−	23.1086i		−	0.971325i
$567$		0			0
$568$	14.2597	+	14.2597i	0.598322	+	0.598322i
$569$	11.7470			0.492461			0.246231	−	0.969211i	$-0.420808\pi$
$569$	11.7470			0.492461			0.246231	+	0.969211i	$0.420808\pi$
$570$		0			0
$571$	−0.0111305			−0.000465796			−0.000232898	−	1.00000i	$-0.500074\pi$
$571$	−0.0111305			−0.000465796			−0.000232898		1.00000i	$0.500074\pi$
$572$	−18.8383	−	18.8383i	−0.787669	−	0.787669i
$573$		0			0
$574$			28.1152i			1.17351i
$575$	4.01441	+	10.7495i	0.167413	+	0.448286i
$576$		0			0
$577$	−19.1867	+	19.1867i	−0.798753	+	0.798753i	−0.982899	−	0.184146i	$-0.941048\pi$
$577$	−19.1867	+	19.1867i	−0.798753	+	0.798753i	0.184146	+	0.982899i	$0.441048\pi$
$578$	38.1810	−	38.1810i	1.58812	−	1.58812i
$579$		0			0
$580$	−3.83258	+	2.46416i	−0.159139	+	0.102319i
$581$			35.5231i			1.47375i
$582$		0			0
$583$	45.2867	+	45.2867i	1.87558	+	1.87558i
$584$	−14.7833			−0.611736
$585$		0			0
$586$	12.8381			0.530335
$587$	26.8789	+	26.8789i	1.10941	+	1.10941i	0.993228	+	0.116185i	$0.0370666\pi$
$587$	26.8789	+	26.8789i	1.10941	+	1.10941i	0.116185	+	0.993228i	$0.462933\pi$
$588$		0			0
$589$		−	1.59617i		−	0.0657690i
$590$	−3.28539	+	15.1177i	−0.135257	+	0.622385i
$591$		0			0
$592$	−32.8117	+	32.8117i	−1.34855	+	1.34855i
$593$	−6.59487	+	6.59487i	−0.270819	+	0.270819i	−0.829430	−	0.558611i	$-0.811334\pi$
$593$	−6.59487	+	6.59487i	−0.270819	+	0.270819i	0.558611	+	0.829430i	$0.311334\pi$
$594$		0			0
$595$	−26.0441	−	40.5071i	−1.06770	−	1.66063i
$596$			18.0071i			0.737599i
$597$		0			0
$598$	−12.5007	−	12.5007i	−0.511193	−	0.511193i
$599$	−21.8982			−0.894737			−0.447368	−	0.894350i	$-0.647639\pi$
$599$	−21.8982			−0.894737			−0.447368	+	0.894350i	$0.647639\pi$
$600$		0			0
$601$	32.9509			1.34409			0.672047	−	0.740508i	$-0.265415\pi$
$601$	32.9509			1.34409			0.672047	+	0.740508i	$0.265415\pi$
$602$	−21.2488	−	21.2488i	−0.866036	−	0.866036i
$603$		0			0
$604$		−	8.86931i		−	0.360887i
$605$	36.1612	+	56.2424i	1.47016	+	2.28658i
$606$		0			0
$607$	20.1956	−	20.1956i	0.819714	−	0.819714i	−0.166352	−	0.986066i	$-0.553199\pi$
$607$	20.1956	−	20.1956i	0.819714	−	0.819714i	0.986066	+	0.166352i	$0.0531989\pi$
$608$	3.43918	−	3.43918i	0.139477	−	0.139477i
$609$		0			0
$610$	1.86373	−	8.57594i	0.0754602	−	0.347230i
$611$			13.4008i			0.542140i
$612$		0			0
$613$	−19.4951	−	19.4951i	−0.787399	−	0.787399i	0.193668	−	0.981067i	$-0.437962\pi$
$613$	−19.4951	−	19.4951i	−0.787399	−	0.787399i	−0.981067	+	0.193668i	$0.937962\pi$
$614$	−34.5463			−1.39417
$615$		0			0
$616$	−36.3406			−1.46420
$617$	−17.7580	−	17.7580i	−0.714909	−	0.714909i	0.252649	−	0.967558i	$-0.418698\pi$
$617$	−17.7580	−	17.7580i	−0.714909	−	0.714909i	−0.967558	+	0.252649i	$0.918698\pi$
$618$		0			0
$619$		−	47.3008i		−	1.90118i	−0.310450	−	0.950590i	$-0.600480\pi$
$619$		−	47.3008i		−	1.90118i	0.310450	−	0.950590i	$-0.399520\pi$
$620$	−2.77640	+	1.78509i	−0.111503	+	0.0716910i
$621$		0			0
$622$	−25.7501	+	25.7501i	−1.03249	+	1.03249i
$623$	−32.6534	+	32.6534i	−1.30823	+	1.30823i
$624$		0			0
$625$	−16.3871	−	18.8802i	−0.655484	−	0.755209i
$626$		−	4.07761i		−	0.162974i
$627$		0			0
$628$	6.85572	+	6.85572i	0.273573	+	0.273573i
$629$	−64.7533			−2.58188
$630$		0			0
$631$	−31.6544			−1.26014			−0.630071	−	0.776538i	$-0.716974\pi$
$631$	−31.6544			−1.26014			−0.630071	+	0.776538i	$0.716974\pi$
$632$	0.202907	+	0.202907i	0.00807120	+	0.00807120i
$633$		0			0
$634$		−	18.3150i		−	0.727382i
$635$	−34.0192	−	7.39307i	−1.35001	−	0.293385i
$636$		0			0
$637$	8.11878	−	8.11878i	0.321678	−	0.321678i
$638$	−17.0411	+	17.0411i	−0.674663	+	0.674663i
$639$		0			0
$640$	27.4984	+	5.97598i	1.08697	+	0.236221i
$641$			40.9546i			1.61761i	0.588078	+	0.808804i	$0.299885\pi$
$641$			40.9546i			1.61761i	−0.588078	+	0.808804i	$0.700115\pi$
$642$		0			0
$643$	20.0553	+	20.0553i	0.790903	+	0.790903i	0.981641	−	0.190738i	$-0.0610880\pi$
$643$	20.0553	+	20.0553i	0.790903	+	0.790903i	−0.190738	+	0.981641i	$0.561088\pi$
$644$	6.55838			0.258437
$645$		0			0
$646$	11.9191			0.468953
$647$	−7.34757	−	7.34757i	−0.288863	−	0.288863i	0.547768	−	0.836631i	$-0.315478\pi$
$647$	−7.34757	−	7.34757i	−0.288863	−	0.288863i	−0.836631	+	0.547768i	$0.815478\pi$
$648$		0			0
$649$			25.8731i			1.01561i
$650$	35.0428	+	15.9861i	1.37449	+	0.627025i
$651$		0			0
$652$	−6.87973	+	6.87973i	−0.269431	+	0.269431i
$653$	5.51837	−	5.51837i	0.215950	−	0.215950i	−0.590839	−	0.806789i	$-0.701203\pi$
$653$	5.51837	−	5.51837i	0.215950	−	0.215950i	0.806789	+	0.590839i	$0.201203\pi$
$654$		0			0
$655$	14.3276	−	9.21199i	0.559827	−	0.359942i
$656$		−	26.5701i		−	1.03739i
$657$		0			0
$658$	−11.1176	−	11.1176i	−0.433409	−	0.433409i
$659$	−15.2922			−0.595701			−0.297850	−	0.954613i	$-0.596270\pi$
$659$	−15.2922			−0.595701			−0.297850	+	0.954613i	$0.596270\pi$
$660$		0			0
$661$	−13.1834			−0.512777			−0.256388	−	0.966574i	$-0.582533\pi$
$661$	−13.1834			−0.512777			−0.256388	+	0.966574i	$0.582533\pi$
$662$	16.5391	+	16.5391i	0.642811	+	0.642811i
$663$		0			0
$664$		−	21.1383i		−	0.820323i
$665$	1.46739	−	6.75217i	0.0569028	−	0.261838i
$666$		0			0
$667$	−3.57555	+	3.57555i	−0.138446	+	0.138446i
$668$	−5.96005	+	5.96005i	−0.230601	+	0.230601i
$669$		0			0
$670$	−9.89957	−	15.3971i	−0.382454	−	0.594840i
$671$		−	14.6773i		−	0.566609i
$672$		0			0
$673$	−14.4137	−	14.4137i	−0.555608	−	0.555608i	0.372446	−	0.928054i	$-0.378519\pi$
$673$	−14.4137	−	14.4137i	−0.555608	−	0.555608i	−0.928054	+	0.372446i	$0.878519\pi$
$674$	2.36841			0.0912278
$675$		0			0
$676$	−6.74113			−0.259274
$677$	2.47514	+	2.47514i	0.0951275	+	0.0951275i	0.753069	−	0.657942i	$-0.228573\pi$
$677$	2.47514	+	2.47514i	0.0951275	+	0.0951275i	−0.657942	+	0.753069i	$0.728573\pi$
$678$		0			0
$679$		−	1.91915i		−	0.0736500i
$680$	15.4977	+	24.1040i	0.594310	+	0.924345i
$681$		0			0
$682$	−12.3449	+	12.3449i	−0.472711	+	0.472711i
$683$	12.4204	−	12.4204i	0.475255	−	0.475255i	−0.428355	−	0.903610i	$-0.640907\pi$
$683$	12.4204	−	12.4204i	0.475255	−	0.475255i	0.903610	+	0.428355i	$0.140907\pi$
$684$		0			0
$685$	−7.08651	+	32.6085i	−0.270762	+	1.24591i
$686$		−	23.5225i		−	0.898093i
$687$		0			0
$688$	20.0810	+	20.0810i	0.765581	+	0.765581i
$689$	45.1069			1.71844
$690$		0			0
$691$	47.1413			1.79334			0.896669	−	0.442701i	$-0.145980\pi$
$691$	47.1413			1.79334			0.896669	+	0.442701i	$0.145980\pi$
$692$	−1.71563	−	1.71563i	−0.0652186	−	0.0652186i
$693$		0			0
$694$			42.3349i			1.60701i
$695$	−12.3713	+	7.95416i	−0.469270	+	0.301718i
$696$		0			0
$697$	26.2178	−	26.2178i	0.993069	−	0.993069i
$698$	5.92110	−	5.92110i	0.224117	−	0.224117i
$699$		0			0
$700$	−13.3859	+	4.99896i	−0.505939	+	0.188943i
$701$		−	17.3056i		−	0.653624i	−0.945089	−	0.326812i	$-0.894026\pi$
$701$		−	17.3056i		−	0.653624i	0.945089	−	0.326812i	$-0.105974\pi$
$702$		0			0
$703$	−6.56977	−	6.56977i	−0.247783	−	0.247783i
$704$	10.6851			0.402709
$705$		0			0
$706$	14.2172			0.535071
$707$	23.8866	+	23.8866i	0.898347	+	0.898347i
$708$		0			0
$709$			35.1056i			1.31842i	0.751960	+	0.659209i	$0.229109\pi$
$709$			35.1056i			1.31842i	−0.751960	+	0.659209i	$0.770891\pi$
$710$	40.9826	+	8.90637i	1.53805	+	0.334250i
$711$		0			0
$712$	19.4306	−	19.4306i	0.728193	−	0.728193i
$713$	−2.59020	+	2.59020i	−0.0970038	+	0.0970038i
$714$		0			0
$715$	62.9467	+	13.6796i	2.35407	+	0.511589i
$716$			5.30667i			0.198319i
$717$		0			0
$718$	−39.3468	−	39.3468i	−1.46841	−	1.46841i
$719$	−25.7773			−0.961331			−0.480666	−	0.876904i	$-0.659605\pi$
$719$	−25.7773			−0.961331			−0.480666	+	0.876904i	$0.659605\pi$
$720$		0			0
$721$	10.0291			0.373505
$722$	1.20930	+	1.20930i	0.0450054	+	0.0450054i
$723$		0			0
$724$		−	12.9586i		−	0.481604i
$725$	4.57244	−	10.0232i	0.169816	−	0.372252i
$726$		0			0
$727$	11.6889	−	11.6889i	0.433516	−	0.433516i	−0.456307	−	0.889823i	$-0.650828\pi$
$727$	11.6889	−	11.6889i	0.433516	−	0.433516i	0.889823	+	0.456307i	$0.150828\pi$
$728$	−18.0982	+	18.0982i	−0.670763	+	0.670763i
$729$		0			0
$730$	−25.8604	+	16.6270i	−0.957138	+	0.615394i
$731$			39.6295i			1.46575i
$732$		0			0
$733$	−25.0206	−	25.0206i	−0.924158	−	0.924158i	0.0731624	−	0.997320i	$-0.476691\pi$
$733$	−25.0206	−	25.0206i	−0.924158	−	0.924158i	−0.997320	+	0.0731624i	$0.976691\pi$
$734$	−27.7302			−1.02354
$735$		0			0
$736$	−11.1619			−0.411434
$737$	−21.6469	−	21.6469i	−0.797374	−	0.797374i
$738$		0			0
$739$		−	23.1672i		−	0.852219i	−0.904672	−	0.426109i	$-0.859884\pi$
$739$		−	23.1672i		−	0.852219i	0.904672	−	0.426109i	$-0.140116\pi$
$740$	−4.08017	+	18.7749i	−0.149990	+	0.690178i
$741$		0			0
$742$	−37.4216	+	37.4216i	−1.37379	+	1.37379i
$743$	−26.0695	+	26.0695i	−0.956395	+	0.956395i	−0.999088	−	0.0426929i	$-0.986406\pi$
$743$	−26.0695	+	26.0695i	−0.956395	+	0.956395i	0.0426929	+	0.999088i	$0.486406\pi$
$744$		0			0
$745$	−23.5466	−	36.6227i	−0.862681	−	1.34175i
$746$			18.7067i			0.684900i
$747$		0			0
$748$	−29.1478	−	29.1478i	−1.06575	−	1.06575i
$749$	27.2702			0.996433
$750$		0			0
$751$	−29.3705			−1.07175			−0.535873	−	0.844299i	$-0.680017\pi$
$751$	−29.3705			−1.07175			−0.535873	+	0.844299i	$0.680017\pi$
$752$	10.5066	+	10.5066i	0.383136	+	0.383136i
$753$		0			0
$754$			16.9734i			0.618136i
$755$	11.5978	+	18.0383i	0.422087	+	0.656482i
$756$		0			0
$757$	−16.5892	+	16.5892i	−0.602945	+	0.602945i	−0.941093	−	0.338148i	$-0.890200\pi$
$757$	−16.5892	+	16.5892i	−0.602945	+	0.602945i	0.338148	+	0.941093i	$0.390200\pi$
$758$	33.7363	−	33.7363i	1.22536	−	1.22536i
$759$		0			0
$760$	−0.873178	+	4.01792i	−0.0316735	+	0.145745i
$761$		−	2.62004i		−	0.0949765i	−0.998872	−	0.0474882i	$-0.984878\pi$
$761$		−	2.62004i		−	0.0949765i	0.998872	−	0.0474882i	$-0.0151217\pi$
$762$		0			0
$763$	−5.57119	−	5.57119i	−0.201691	−	0.201691i
$764$	−3.69197			−0.133571
$765$		0			0
$766$	−54.0030			−1.95121
$767$	12.8852	+	12.8852i	0.465257	+	0.465257i
$768$		0			0
$769$		−	23.0002i		−	0.829408i	−0.909956	−	0.414704i	$-0.863885\pi$
$769$		−	23.0002i		−	0.829408i	0.909956	−	0.414704i	$-0.136115\pi$
$770$	−63.5708	+	40.8730i	−2.29093	+	1.47296i
$771$		0			0
$772$	−13.1831	+	13.1831i	−0.474469	+	0.474469i
$773$	9.06485	−	9.06485i	0.326040	−	0.326040i	−0.525039	−	0.851078i	$-0.675949\pi$
$773$	9.06485	−	9.06485i	0.326040	−	0.326040i	0.851078	+	0.525039i	$0.175949\pi$
$774$		0			0
$775$	3.31237	−	7.26100i	0.118984	−	0.260823i
$776$			1.14200i			0.0409954i
$777$		0			0
$778$	−14.2819	−	14.2819i	−0.512032	−	0.512032i
$779$	5.32003			0.190610
$780$		0			0
$781$	70.1395			2.50979
$782$	−19.3419	−	19.3419i	−0.691666	−	0.691666i
$783$		0			0
$784$		−	12.7307i		−	0.454667i
$785$	−22.9079	−	4.97835i	−0.817616	−	0.177685i
$786$		0			0
$787$	−23.8659	+	23.8659i	−0.850726	+	0.850726i	−0.990223	−	0.139496i	$-0.955452\pi$
$787$	−23.8659	+	23.8659i	−0.850726	+	0.850726i	0.139496	+	0.990223i	$0.455452\pi$
$788$	−3.34802	+	3.34802i	−0.119268	+	0.119268i
$789$		0			0
$790$	0.583159	+	0.126733i	0.0207479	+	0.00450894i
$791$		−	59.1516i		−	2.10319i
$792$		0			0
$793$	−7.30950	−	7.30950i	−0.259568	−	0.259568i
$794$	16.0350			0.569060
$795$		0			0
$796$	0.924392			0.0327642
$797$	36.2931	+	36.2931i	1.28557	+	1.28557i	0.937452	+	0.348115i	$0.113178\pi$
$797$	36.2931	+	36.2931i	1.28557	+	1.28557i	0.348115	+	0.937452i	$0.386822\pi$
$798$		0			0
$799$			20.7346i			0.733538i
$800$	22.7818	−	8.50789i	0.805460	−	0.300799i
$801$		0			0
$802$	−23.5158	+	23.5158i	−0.830373	+	0.830373i
$803$	−36.3575	+	36.3575i	−1.28303	+	1.28303i
$804$		0			0
$805$	−13.3384	+	8.57594i	−0.470116	+	0.302262i
$806$			12.2959i			0.433105i
$807$		0			0
$808$	−14.2138	−	14.2138i	−0.500041	−	0.500041i
$809$	−13.2271			−0.465039			−0.232520	−	0.972592i	$-0.574697\pi$
$809$	−13.2271			−0.465039			−0.232520	+	0.972592i	$0.574697\pi$
$810$		0			0
$811$	−18.4012			−0.646154			−0.323077	−	0.946373i	$-0.604717\pi$
$811$	−18.4012			−0.646154			−0.323077	+	0.946373i	$0.604717\pi$
$812$	−4.45247	−	4.45247i	−0.156251	−	0.156251i
$813$		0			0
$814$			101.622i			3.56186i
$815$	4.99579	−	22.9881i	0.174995	−	0.805237i
$816$		0			0
$817$	−4.02075	+	4.02075i	−0.140668	+	0.140668i
$818$	−23.9769	+	23.9769i	−0.838334	+	0.838334i
$819$		0			0
$820$	−5.94970	−	9.25372i	−0.207773	−	0.323154i
$821$		−	6.38333i		−	0.222780i	−0.993777	−	0.111390i	$-0.964470\pi$
$821$		−	6.38333i		−	0.222780i	0.993777	−	0.111390i	$-0.0355302\pi$
$822$		0			0
$823$	32.6349	+	32.6349i	1.13758	+	1.13758i	0.988882	+	0.148700i	$0.0475088\pi$
$823$	32.6349	+	32.6349i	1.13758	+	1.13758i	0.148700	+	0.988882i	$0.452491\pi$
$824$	−5.96790			−0.207902
$825$		0			0
$826$	−21.3796			−0.743892
$827$	−12.6859	−	12.6859i	−0.441131	−	0.441131i	0.451261	−	0.892392i	$-0.350974\pi$
$827$	−12.6859	−	12.6859i	−0.441131	−	0.441131i	−0.892392	+	0.451261i	$0.850974\pi$
$828$		0			0
$829$			24.2254i			0.841382i	0.907204	+	0.420691i	$0.138212\pi$
$829$			24.2254i			0.841382i	−0.907204	+	0.420691i	$0.861788\pi$
$830$	−23.7746	−	36.9772i	−0.825228	−	1.28350i
$831$		0			0
$832$	5.32133	−	5.32133i	0.184484	−	0.184484i
$833$	12.5619	−	12.5619i	0.435243	−	0.435243i
$834$		0			0
$835$	4.32795	−	19.9151i	0.149775	−	0.689189i
$836$		−	5.91458i		−	0.204560i
$837$		0			0
$838$	−44.3104	−	44.3104i	−1.53068	−	1.53068i
$839$	35.9297			1.24043			0.620215	−	0.784432i	$-0.287045\pi$
$839$	35.9297			1.24043			0.620215	+	0.784432i	$0.287045\pi$
$840$		0			0
$841$	−24.1451			−0.832591
$842$	21.7127	+	21.7127i	0.748268	+	0.748268i
$843$		0			0
$844$			9.51131i			0.327393i
$845$	13.7100	−	8.81490i	0.471640	−	0.303242i
$846$		0			0
$847$	−65.3392	+	65.3392i	−2.24508	+	2.24508i
$848$	35.3650	−	35.3650i	1.21444	−	1.21444i
$849$		0			0
$850$	54.2204	+	24.7346i	1.85974	+	0.848390i
$851$			21.3223i			0.730919i
$852$		0			0
$853$	7.89045	+	7.89045i	0.270164	+	0.270164i	0.829166	−	0.559002i	$-0.188816\pi$
$853$	7.89045	+	7.89045i	0.270164	+	0.270164i	−0.559002	+	0.829166i	$0.688816\pi$
$854$	12.1282			0.415019
$855$		0			0
$856$	−16.2273			−0.554638
$857$	11.8794	+	11.8794i	0.405792	+	0.405792i	0.880268	−	0.474476i	$-0.157363\pi$
$857$	11.8794	+	11.8794i	0.405792	+	0.405792i	−0.474476	+	0.880268i	$0.657363\pi$
$858$		0			0
$859$		−	49.1067i		−	1.67550i	−0.546056	−	0.837749i	$-0.683871\pi$
$859$		−	49.1067i		−	1.67550i	0.546056	−	0.837749i	$-0.316129\pi$
$860$	11.4904	+	2.49710i	0.391819	+	0.0851503i
$861$		0			0
$862$	48.7692	−	48.7692i	1.66108	−	1.66108i
$863$	−22.8690	+	22.8690i	−0.778471	+	0.778471i	−0.979571	−	0.201100i	$-0.935548\pi$
$863$	−22.8690	+	22.8690i	−0.778471	+	0.778471i	0.201100	+	0.979571i	$0.435548\pi$
$864$		0			0
$865$	5.73265	+	1.24582i	0.194916	+	0.0423593i
$866$			19.2795i			0.655146i
$867$		0			0
$868$	−3.22546	−	3.22546i	−0.109479	−	0.109479i
$869$	0.998045			0.0338563
$870$		0			0
$871$	−21.5610			−0.730566
$872$	3.31517	+	3.31517i	0.112266	+	0.112266i
$873$		0			0
$874$		−	3.92480i		−	0.132758i
$875$	20.6873	−	27.6706i	0.699358	−	0.935438i
$876$		0			0
$877$	−24.9799	+	24.9799i	−0.843511	+	0.843511i	−0.989314	−	0.145802i	$-0.953424\pi$
$877$	−24.9799	+	24.9799i	−0.843511	+	0.843511i	0.145802	+	0.989314i	$0.453424\pi$
$878$	−18.5849	+	18.5849i	−0.627211	+	0.627211i
$879$		0			0
$880$	60.0770	−	38.6267i	2.02520	−	1.30210i
$881$			5.29063i			0.178246i	0.996021	+	0.0891229i	$0.0284064\pi$
$881$			5.29063i			0.178246i	−0.996021	+	0.0891229i	$0.971594\pi$
$882$		0			0
$883$	−1.33371	−	1.33371i	−0.0448830	−	0.0448830i	0.684309	−	0.729192i	$-0.260104\pi$
$883$	−1.33371	−	1.33371i	−0.0448830	−	0.0448830i	−0.729192	+	0.684309i	$0.760104\pi$
$884$	−29.0321			−0.976455
$885$		0			0
$886$	−44.9798			−1.51113
$887$	−8.13572	−	8.13572i	−0.273171	−	0.273171i	0.557205	−	0.830375i	$-0.311874\pi$
$887$	−8.13572	−	8.13572i	−0.273171	−	0.273171i	−0.830375	+	0.557205i	$0.811874\pi$
$888$		0			0
$889$		−	48.1104i		−	1.61357i
$890$	12.1361	−	55.8440i	0.406802	−	1.87190i
$891$		0			0
$892$	4.84833	−	4.84833i	0.162334	−	0.162334i
$893$	−2.10370	+	2.10370i	−0.0703976	+	0.0703976i
$894$		0			0
$895$	−6.93916	−	10.7926i	−0.231951	−	0.360758i
$896$			38.8887i			1.29918i
$897$		0			0
$898$	9.93878	+	9.93878i	0.331661	+	0.331661i
$899$	3.51696			0.117297
$900$		0			0
$901$	69.7922			2.32511
$902$	−41.1455	−	41.1455i	−1.37000	−	1.37000i
$903$		0			0
$904$			35.1985i			1.17069i
$905$	16.9451	+	26.3552i	0.563274	+	0.876075i
$906$		0			0
$907$	3.43185	−	3.43185i	0.113953	−	0.113953i	−0.647831	−	0.761784i	$-0.724324\pi$
$907$	3.43185	−	3.43185i	0.113953	−	0.113953i	0.761784	+	0.647831i	$0.224324\pi$
$908$	13.0674	−	13.0674i	0.433658	−	0.433658i
$909$		0			0
$910$	−11.3038	+	52.0146i	−0.374719	+	1.72427i
$911$			32.6667i			1.08230i	0.840927	+	0.541149i	$0.182010\pi$
$911$			32.6667i			1.08230i	−0.840927	+	0.541149i	$0.817990\pi$
$912$		0			0
$913$	−51.9867	−	51.9867i	−1.72051	−	1.72051i
$914$	−25.6336			−0.847885
$915$		0			0
$916$	26.9262			0.889666
$917$	16.6450	+	16.6450i	0.549668	+	0.549668i
$918$		0			0
$919$		−	47.1389i		−	1.55497i	−0.628902	−	0.777485i	$-0.716495\pi$
$919$		−	47.1389i		−	1.55497i	0.628902	−	0.777485i	$-0.283505\pi$
$920$	7.93708	−	5.10317i	0.261678	−	0.168246i
$921$		0			0
$922$	21.3267	−	21.3267i	0.702357	−	0.702357i
$923$	34.9306	−	34.9306i	1.14975	−	1.14975i
$924$		0			0
$925$	−16.2524	−	43.5195i	−0.534375	−	1.43091i
$926$			50.8259i			1.67024i
$927$		0			0
$928$	7.57780	+	7.57780i	0.248753	+	0.248753i
$929$	−41.9076			−1.37494			−0.687471	−	0.726211i	$-0.741279\pi$
$929$	−41.9076			−1.37494			−0.687471	+	0.726211i	$0.741279\pi$
$930$		0			0
$931$	2.54902			0.0835406
$932$	−14.3987	−	14.3987i	−0.471645	−	0.471645i
$933$		0			0
$934$		−	3.17577i		−	0.103914i
$935$	97.3951	+	21.1660i	3.18516	+	0.692201i
$936$		0			0
$937$	4.49144	−	4.49144i	0.146729	−	0.146729i	−0.629926	−	0.776655i	$-0.716915\pi$
$937$	4.49144	−	4.49144i	0.146729	−	0.146729i	0.776655	+	0.629926i	$0.216915\pi$
$938$	17.8874	−	17.8874i	0.584045	−	0.584045i
$939$		0			0
$940$	6.01189	+	1.30651i	0.196086	+	0.0426136i
$941$			8.57988i			0.279696i	0.990173	+	0.139848i	$0.0446614\pi$
$941$			8.57988i			0.279696i	−0.990173	+	0.139848i	$0.955339\pi$
$942$		0			0
$943$	−8.63313	−	8.63313i	−0.281133	−	0.281133i
$944$	20.2046			0.657605
$945$		0			0
$946$	62.1936			2.02209
$947$	−12.8953	−	12.8953i	−0.419042	−	0.419042i	0.465832	−	0.884873i	$-0.345755\pi$
$947$	−12.8953	−	12.8953i	−0.419042	−	0.419042i	−0.884873	+	0.465832i	$0.845755\pi$
$948$		0			0
$949$			36.2132i			1.17553i
$950$	2.99158	+	8.01065i	0.0970597	+	0.259900i
$951$		0			0
$952$	−28.0026	+	28.0026i	−0.907570	+	0.907570i
$953$	20.1541	−	20.1541i	0.652854	−	0.652854i	−0.300825	−	0.953679i	$-0.597262\pi$
$953$	20.1541	−	20.1541i	0.652854	−	0.652854i	0.953679	+	0.300825i	$0.0972621\pi$
$954$		0			0
$955$	7.50870	−	4.82773i	0.242976	−	0.156222i
$956$			5.10763i			0.165193i
$957$		0			0
$958$	−7.60561	−	7.60561i	−0.245726	−	0.245726i
$959$	−46.1154			−1.48914
$960$		0			0
$961$	−28.4522			−0.917814
$962$	50.6094	+	50.6094i	1.63171	+	1.63171i
$963$		0			0
$964$		−	9.62868i		−	0.310119i
$965$	9.57303	−	44.0502i	0.308167	−	1.41803i
$966$		0			0
$967$	9.56041	−	9.56041i	0.307442	−	0.307442i	−0.536475	−	0.843917i	$-0.680244\pi$
$967$	9.56041	−	9.56041i	0.307442	−	0.307442i	0.843917	+	0.536475i	$0.180244\pi$
$968$	38.8805	−	38.8805i	1.24967	−	1.24967i
$969$		0			0
$970$	1.28443	+	1.99770i	0.0412405	+	0.0641424i
$971$		−	29.6220i		−	0.950615i	−0.879820	−	0.475308i	$-0.842337\pi$
$971$		−	29.6220i		−	0.950615i	0.879820	−	0.475308i	$-0.157663\pi$
$972$		0			0
$973$	−14.3723	−	14.3723i	−0.460754	−	0.460754i
$974$	−60.9180			−1.95194
$975$		0			0
$976$	−11.4617			−0.366879
$977$	−1.69779	−	1.69779i	−0.0543172	−	0.0543172i	0.679426	−	0.733744i	$-0.262229\pi$
$977$	−1.69779	−	1.69779i	−0.0543172	−	0.0543172i	−0.733744	+	0.679426i	$0.762229\pi$
$978$		0			0
$979$		−	95.5740i		−	3.05456i
$980$	−2.85071	−	4.43379i	−0.0910628	−	0.141632i
$981$		0			0
$982$	−20.5674	+	20.5674i	−0.656331	+	0.656331i
$983$	26.6829	−	26.6829i	0.851051	−	0.851051i	−0.139212	−	0.990263i	$-0.544457\pi$
$983$	26.6829	−	26.6829i	0.851051	−	0.851051i	0.990263	+	0.139212i	$0.0444569\pi$
$984$		0			0
$985$	2.43120	−	11.1871i	0.0774645	−	0.356452i
$986$			26.2624i			0.836364i
$987$		0			0
$988$	−2.94555	−	2.94555i	−0.0937104	−	0.0937104i
$989$	13.0494			0.414948
$990$		0			0
$991$	4.11083			0.130585			0.0652924	−	0.997866i	$-0.479202\pi$
$991$	4.11083			0.130585			0.0652924	+	0.997866i	$0.479202\pi$
$992$	5.48951	+	5.48951i	0.174292	+	0.174292i
$993$		0			0
$994$			57.9582i			1.83832i
$995$	−1.88002	+	1.20876i	−0.0596007	+	0.0383204i
$996$		0			0
$997$	−5.53028	+	5.53028i	−0.175146	+	0.175146i	−0.789236	−	0.614090i	$-0.789523\pi$
$997$	−5.53028	+	5.53028i	−0.175146	+	0.175146i	0.614090	+	0.789236i	$0.289523\pi$
$998$	14.9818	−	14.9818i	0.474241	−	0.474241i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.n.d.818.3	yes	20
3.2	odd	2	inner	855.2.n.d.818.8	yes	20
5.2	odd	4	inner	855.2.n.d.647.8	yes	20
15.2	even	4	inner	855.2.n.d.647.3	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
855.2.n.d.647.3	✓	20	15.2	even	4	inner
855.2.n.d.647.8	yes	20	5.2	odd	4	inner
855.2.n.d.818.3	yes	20	1.1	even	1	trivial
855.2.n.d.818.8	yes	20	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.n (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20930 - 1.20930i) q^{2} +0.924801i q^{4} +(-1.20930 - 1.88085i) q^{5} +(2.18506 - 2.18506i) q^{7} +(-1.30024 + 1.30024i) q^{8} +O(q^{10})\)	\(q+(-1.20930 - 1.20930i) q^{2} +0.924801i q^{4} +(-1.20930 - 1.88085i) q^{5} +(2.18506 - 2.18506i) q^{7} +(-1.30024 + 1.30024i) q^{8} +(-0.812108 + 3.73691i) q^{10} +6.39552i q^{11} +(3.18506 + 3.18506i) q^{13} -5.28479 q^{14} +4.99435 q^{16} +(4.92813 + 4.92813i) q^{17} +1.00000i q^{19} +(1.73941 - 1.11836i) q^{20} +(7.73408 - 7.73408i) q^{22} +(1.62276 - 1.62276i) q^{23} +(-2.07520 + 4.54902i) q^{25} -7.70338i q^{26} +(2.02075 + 2.02075i) q^{28} -2.20338 q^{29} -1.59617 q^{31} +(-3.43918 - 3.43918i) q^{32} -11.9191i q^{34} +(-6.75217 - 1.46739i) q^{35} +(-6.56977 + 6.56977i) q^{37} +(1.20930 - 1.20930i) q^{38} +(4.01792 + 0.873178i) q^{40} -5.32003i q^{41} +(4.02075 + 4.02075i) q^{43} -5.91458 q^{44} -3.92480 q^{46} +(2.10370 + 2.10370i) q^{47} -2.54902i q^{49} +(8.01065 - 2.99158i) q^{50} +(-2.94555 + 2.94555i) q^{52} +(7.08100 - 7.08100i) q^{53} +(12.0290 - 7.73408i) q^{55} +5.68220i q^{56} +(2.66454 + 2.66454i) q^{58} +4.04550 q^{59} -2.29493 q^{61} +(1.93024 + 1.93024i) q^{62} -1.67071i q^{64} +(2.13894 - 9.84232i) q^{65} +(-3.38470 + 3.38470i) q^{67} +(-4.55754 + 4.55754i) q^{68} +(6.39088 + 9.93989i) q^{70} -10.9670i q^{71} +(5.68484 + 5.68484i) q^{73} +15.8896 q^{74} -0.924801 q^{76} +(13.9746 + 13.9746i) q^{77} -0.156054i q^{79} +(-6.03965 - 9.39362i) q^{80} +(-6.43350 + 6.43350i) q^{82} +(-8.12862 + 8.12862i) q^{83} +(3.30950 - 15.2286i) q^{85} -9.72456i q^{86} +(-8.31568 - 8.31568i) q^{88} -14.9439 q^{89} +13.9191 q^{91} +(1.50073 + 1.50073i) q^{92} -5.08800i q^{94} +(1.88085 - 1.20930i) q^{95} +(0.439151 - 0.439151i) q^{97} +(-3.08252 + 3.08252i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q+O(q^{10}) \) 20 * q	\( 20 q + 28 q^{10} + 20 q^{13} - 76 q^{16} + 32 q^{22} - 32 q^{25} - 16 q^{28} - 16 q^{31} + 4 q^{37} - 64 q^{40} + 24 q^{43} - 88 q^{46} - 12 q^{52} + 40 q^{55} + 116 q^{58} + 32 q^{61} + 24 q^{67} - 16 q^{70} + 20 q^{73} - 28 q^{76} + 92 q^{82} - 16 q^{85} - 32 q^{88} + 112 q^{91} - 36 q^{97}+O(q^{100}) \) 20 * q + 28 * q^10 + 20 * q^13 - 76 * q^16 + 32 * q^22 - 32 * q^25 - 16 * q^28 - 16 * q^31 + 4 * q^37 - 64 * q^40 + 24 * q^43 - 88 * q^46 - 12 * q^52 + 40 * q^55 + 116 * q^58 + 32 * q^61 + 24 * q^67 - 16 * q^70 + 20 * q^73 - 28 * q^76 + 92 * q^82 - 16 * q^85 - 32 * q^88 + 112 * q^91 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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