LMFDB - Embedded newform 840.2.da.b.689.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [840,2,Mod(89,840)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(840, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 3, 3, 5]))

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

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

chi := DirichletCharacter("840.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	840.da (of order $6$, 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:	$6.70743376979$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			689.21
Character	$\chi$	$=$	840.689
Dual form			840.2.da.b.89.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.59188 - 0.682575i) q^{3} +(2.06723 - 0.852393i) q^{5} +(-2.55997 + 0.668258i) q^{7} +(2.06818 - 2.17316i) q^{9} +O(q^{10})$	\(q+(1.59188 - 0.682575i) q^{3} +(2.06723 - 0.852393i) q^{5} +(-2.55997 + 0.668258i) q^{7} +(2.06818 - 2.17316i) q^{9} +(-2.74776 - 1.58642i) q^{11} +3.04832 q^{13} +(2.70896 - 2.76795i) q^{15} +(3.15456 + 1.82129i) q^{17} +(3.68634 - 2.12831i) q^{19} +(-3.61903 + 2.81116i) q^{21} +(-2.75984 - 4.78018i) q^{23} +(3.54685 - 3.52418i) q^{25} +(1.80896 - 4.87110i) q^{27} -7.12076i q^{29} +(7.11211 + 4.10618i) q^{31} +(-5.45696 - 0.649843i) q^{33} +(-4.72241 + 3.56354i) q^{35} +(-2.21569 + 1.27923i) q^{37} +(4.85257 - 2.08071i) q^{39} +0.652545 q^{41} +9.40132i q^{43} +(2.42302 - 6.25532i) q^{45} +(-7.25360 + 4.18787i) q^{47} +(6.10686 - 3.42144i) q^{49} +(6.26486 + 0.746050i) q^{51} +(-5.86407 + 10.1569i) q^{53} +(-7.03250 - 0.937318i) q^{55} +(4.41550 - 5.90423i) q^{57} +(0.725991 - 1.25745i) q^{59} +(-8.46753 + 4.88873i) q^{61} +(-3.84225 + 6.94529i) q^{63} +(6.30158 - 2.59837i) q^{65} +(-8.85778 - 5.11404i) q^{67} +(-7.65618 - 5.72569i) q^{69} -7.34623i q^{71} +(-3.14081 + 5.44005i) q^{73} +(3.24066 - 8.03107i) q^{75} +(8.09431 + 2.22497i) q^{77} +(3.17806 + 5.50456i) q^{79} +(-0.445242 - 8.98898i) q^{81} +0.397748i q^{83} +(8.07364 + 1.07609i) q^{85} +(-4.86045 - 11.3354i) q^{87} +(3.15120 + 5.45804i) q^{89} +(-7.80361 + 2.03707i) q^{91} +(14.1244 + 1.68201i) q^{93} +(5.80635 - 7.54192i) q^{95} +17.1688 q^{97} +(-9.13041 + 2.69031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 3 q^{3} + 3 q^{5} - q^{9}+O(q^{10}) $ 48 * q + 3 * q^3 + 3 * q^5 - q^9	$ 48 q + 3 q^{3} + 3 q^{5} - q^{9} + 6 q^{15} + 5 q^{21} + 2 q^{23} + q^{25} + 6 q^{31} + 24 q^{33} - 4 q^{35} + 2 q^{39} - 21 q^{45} + 12 q^{51} - 6 q^{53} + 20 q^{57} + 18 q^{61} - 26 q^{63} + 10 q^{65} - 51 q^{75} + 2 q^{77} + 2 q^{79} - 9 q^{81} - 15 q^{87} + 24 q^{91} + 8 q^{93} + 6 q^{95} - 12 q^{99}+O(q^{100}) $ 48 * q + 3 * q^3 + 3 * q^5 - q^9 + 6 * q^15 + 5 * q^21 + 2 * q^23 + q^25 + 6 * q^31 + 24 * q^33 - 4 * q^35 + 2 * q^39 - 21 * q^45 + 12 * q^51 - 6 * q^53 + 20 * q^57 + 18 * q^61 - 26 * q^63 + 10 * q^65 - 51 * q^75 + 2 * q^77 + 2 * q^79 - 9 * q^81 - 15 * q^87 + 24 * q^91 + 8 * q^93 + 6 * q^95 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$-1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.59188	−	0.682575i	0.919074	−	0.394085i
$3$	1.59188	−	0.682575i	0.919074	−	0.394085i
$4$		0			0
$5$	2.06723	−	0.852393i	0.924492	−	0.381202i
$5$	2.06723	−	0.852393i	0.924492	−	0.381202i
$6$		0			0
$7$	−2.55997	+	0.668258i	−0.967577	+	0.252578i
$7$	−2.55997	+	0.668258i	−0.967577	+	0.252578i
$8$		0			0
$9$	2.06818	−	2.17316i	0.689394	−	0.724386i
$10$		0			0
$11$	−2.74776	−	1.58642i	−0.828481	−	0.478324i	0.0248513	−	0.999691i	$-0.492089\pi$
$11$	−2.74776	−	1.58642i	−0.828481	−	0.478324i	−0.853332	+	0.521367i	$0.825422\pi$
$12$		0			0
$13$	3.04832			0.845453			0.422726	−	0.906257i	$-0.361073\pi$
$13$	3.04832			0.845453			0.422726	+	0.906257i	$0.361073\pi$
$14$		0			0
$15$	2.70896	−	2.76795i	0.699451	−	0.714681i
$16$		0			0
$17$	3.15456	+	1.82129i	0.765093	+	0.441727i	0.831121	−	0.556091i	$-0.187699\pi$
$17$	3.15456	+	1.82129i	0.765093	+	0.441727i	−0.0660282	+	0.997818i	$0.521033\pi$
$18$		0			0
$19$	3.68634	−	2.12831i	0.845705	−	0.488268i	−0.0134942	−	0.999909i	$-0.504295\pi$
$19$	3.68634	−	2.12831i	0.845705	−	0.488268i	0.859199	+	0.511641i	$0.170962\pi$
$20$		0			0
$21$	−3.61903	+	2.81116i	−0.789738	+	0.613445i
$22$		0			0
$23$	−2.75984	−	4.78018i	−0.575466	−	0.996737i	−0.995991	−	0.0894559i	$-0.971487\pi$
$23$	−2.75984	−	4.78018i	−0.575466	−	0.996737i	0.420524	−	0.907281i	$-0.361846\pi$
$24$		0			0
$25$	3.54685	−	3.52418i	0.709370	−	0.704836i
$26$		0			0
$27$	1.80896	−	4.87110i	0.348135	−	0.937445i
$28$		0			0
$29$		−	7.12076i		−	1.32229i	−0.750257	−	0.661146i	$-0.770070\pi$
$29$		−	7.12076i		−	1.32229i	0.750257	−	0.661146i	$-0.229930\pi$
$30$		0			0
$31$	7.11211	+	4.10618i	1.27737	+	0.737491i	0.976364	−	0.216131i	$-0.0693437\pi$
$31$	7.11211	+	4.10618i	1.27737	+	0.737491i	0.301008	+	0.953622i	$0.402677\pi$
$32$		0			0
$33$	−5.45696	−	0.649843i	−0.949936	−	0.113123i
$34$		0			0
$35$	−4.72241	+	3.56354i	−0.798234	+	0.602348i
$36$		0			0
$37$	−2.21569	+	1.27923i	−0.364257	+	0.210304i	−0.670947	−	0.741506i	$-0.734112\pi$
$37$	−2.21569	+	1.27923i	−0.364257	+	0.210304i	0.306689	+	0.951810i	$0.400779\pi$
$38$		0			0
$39$	4.85257	−	2.08071i	0.777034	−	0.333180i
$40$		0			0
$41$	0.652545			0.101910			0.0509552	−	0.998701i	$-0.483773\pi$
$41$	0.652545			0.101910			0.0509552	+	0.998701i	$0.483773\pi$
$42$		0			0
$43$			9.40132i			1.43369i	0.697234	+	0.716844i	$0.254414\pi$
$43$			9.40132i			1.43369i	−0.697234	+	0.716844i	$0.745586\pi$
$44$		0			0
$45$	2.42302	−	6.25532i	0.361202	−	0.932488i
$46$		0			0
$47$	−7.25360	+	4.18787i	−1.05805	+	0.610863i	−0.924891	−	0.380232i	$-0.875844\pi$
$47$	−7.25360	+	4.18787i	−1.05805	+	0.610863i	−0.133155	+	0.991095i	$0.542511\pi$
$48$		0			0
$49$	6.10686	−	3.42144i	0.872409	−	0.488776i
$50$		0			0
$51$	6.26486	+	0.746050i	0.877255	+	0.104468i
$52$		0			0
$53$	−5.86407	+	10.1569i	−0.805492	+	1.39515i	0.110466	+	0.993880i	$0.464766\pi$
$53$	−5.86407	+	10.1569i	−0.805492	+	1.39515i	−0.915958	+	0.401274i	$0.868568\pi$
$54$		0			0
$55$	−7.03250	−	0.937318i	−0.948262	−	0.126388i
$56$		0			0
$57$	4.41550	−	5.90423i	0.584847	−	0.782034i
$58$		0			0
$59$	0.725991	−	1.25745i	0.0945159	−	0.163706i	−0.814891	−	0.579615i	$-0.803203\pi$
$59$	0.725991	−	1.25745i	0.0945159	−	0.163706i	0.909406	+	0.415908i	$0.136536\pi$
$60$		0			0
$61$	−8.46753	+	4.88873i	−1.08416	+	0.625938i	−0.932015	−	0.362421i	$-0.881950\pi$
$61$	−8.46753	+	4.88873i	−1.08416	+	0.625938i	−0.152142	+	0.988359i	$0.548617\pi$
$62$		0			0
$63$	−3.84225	+	6.94529i	−0.484078	+	0.875025i
$64$		0			0
$65$	6.30158	−	2.59837i	0.781614	−	0.322288i
$66$		0			0
$67$	−8.85778	−	5.11404i	−1.08215	−	0.624779i	−0.150674	−	0.988583i	$-0.548144\pi$
$67$	−8.85778	−	5.11404i	−1.08215	−	0.624779i	−0.931475	+	0.363804i	$0.881478\pi$
$68$		0			0
$69$	−7.65618	−	5.72569i	−0.921695	−	0.689293i
$70$		0			0
$71$		−	7.34623i		−	0.871837i	−0.899986	−	0.435918i	$-0.856424\pi$
$71$		−	7.34623i		−	0.871837i	0.899986	−	0.435918i	$-0.143576\pi$
$72$		0			0
$73$	−3.14081	+	5.44005i	−0.367604	+	0.636709i	−0.989190	−	0.146637i	$-0.953155\pi$
$73$	−3.14081	+	5.44005i	−0.367604	+	0.636709i	0.621586	+	0.783346i	$0.286489\pi$
$74$		0			0
$75$	3.24066	−	8.03107i	0.374199	−	0.927349i
$76$		0			0
$77$	8.09431	+	2.22497i	0.922433	+	0.253559i
$78$		0			0
$79$	3.17806	+	5.50456i	0.357559	+	0.619311i	0.987553	−	0.157290i	$-0.0502756\pi$
$79$	3.17806	+	5.50456i	0.357559	+	0.619311i	−0.629993	+	0.776601i	$0.716942\pi$
$80$		0			0
$81$	−0.445242	−	8.98898i	−0.0494713	−	0.998776i
$82$		0			0
$83$			0.397748i			0.0436585i	0.999762	+	0.0218292i	$0.00694902\pi$
$83$			0.397748i			0.0436585i	−0.999762	+	0.0218292i	$0.993051\pi$
$84$		0			0
$85$	8.07364	+	1.07609i	0.875710	+	0.116718i
$86$		0			0
$87$	−4.86045	−	11.3354i	−0.521095	−	1.21528i
$88$		0			0
$89$	3.15120	+	5.45804i	0.334027	+	0.578551i	0.983297	−	0.182006i	$-0.0582591\pi$
$89$	3.15120	+	5.45804i	0.334027	+	0.578551i	−0.649271	+	0.760557i	$0.724926\pi$
$90$		0			0
$91$	−7.80361	+	2.03707i	−0.818040	+	0.213542i
$92$		0			0
$93$	14.1244	+	1.68201i	1.46463	+	0.174416i
$94$		0			0
$95$	5.80635	−	7.54192i	0.595719	−	0.773784i
$96$		0			0
$97$	17.1688			1.74322			0.871612	−	0.490196i	$-0.163075\pi$
$97$	17.1688			1.74322			0.871612	+	0.490196i	$0.163075\pi$
$98$		0			0
$99$	−9.13041	+	2.69031i	−0.917641	+	0.270387i
$100$		0			0
$101$	−1.55824	+	2.69896i	−0.155051	+	0.268556i	−0.933078	−	0.359675i	$-0.882888\pi$
$101$	−1.55824	+	2.69896i	−0.155051	+	0.268556i	0.778027	+	0.628231i	$0.216221\pi$
$102$		0			0
$103$	4.33234	+	7.50383i	0.426878	+	0.739375i	0.996594	−	0.0824672i	$-0.0262800\pi$
$103$	4.33234	+	7.50383i	0.426878	+	0.739375i	−0.569716	+	0.821842i	$0.692947\pi$
$104$		0			0
$105$	−5.08515	+	8.89614i	−0.496260	+	0.868174i
$106$		0			0
$107$	−2.81910	−	4.88283i	−0.272533	−	0.472041i	0.696977	−	0.717094i	$-0.254528\pi$
$107$	−2.81910	−	4.88283i	−0.272533	−	0.472041i	−0.969510	+	0.245053i	$0.921195\pi$
$108$		0			0
$109$	−5.50964	+	9.54298i	−0.527728	+	0.914052i	0.471750	+	0.881733i	$0.343623\pi$
$109$	−5.50964	+	9.54298i	−0.527728	+	0.914052i	−0.999478	+	0.0323192i	$0.989711\pi$
$110$		0			0
$111$	−2.65395	+	3.54876i	−0.251902	+	0.336833i
$112$		0			0
$113$	0.884131			0.0831721			0.0415860	−	0.999135i	$-0.486759\pi$
$113$	0.884131			0.0831721			0.0415860	+	0.999135i	$0.486759\pi$
$114$		0			0
$115$	−9.77981	−	7.52925i	−0.911972	−	0.702107i
$116$		0			0
$117$	6.30449	−	6.62449i	0.582850	−	0.612434i
$118$		0			0
$119$	−9.29266	−	2.55437i	−0.851857	−	0.234159i
$120$		0			0
$121$	−0.466541	−	0.808072i	−0.0424128	−	0.0734611i
$122$		0			0
$123$	1.03878	−	0.445411i	0.0936633	−	0.0401614i
$124$		0			0
$125$	4.32816	−	10.3086i	0.387122	−	0.922028i
$126$		0			0
$127$			21.9000i			1.94331i	0.236396	+	0.971657i	$0.424034\pi$
$127$			21.9000i			1.94331i	−0.236396	+	0.971657i	$0.575966\pi$
$128$		0			0
$129$	6.41711	+	14.9658i	0.564995	+	1.31767i
$130$		0			0
$131$	4.01734	+	6.95824i	0.350997	+	0.607945i	0.986424	−	0.164216i	$-0.0525094\pi$
$131$	4.01734	+	6.95824i	0.350997	+	0.607945i	−0.635427	+	0.772161i	$0.719176\pi$
$132$		0			0
$133$	−8.01466	+	7.91184i	−0.694959	+	0.686043i
$134$		0			0
$135$	−0.412565	−	11.6116i	−0.0355080	−	0.999369i
$136$		0			0
$137$	4.31600	−	7.47553i	0.368741	−	0.638677i	−0.620628	−	0.784105i	$-0.713122\pi$
$137$	4.31600	−	7.47553i	0.368741	−	0.638677i	0.989369	+	0.145427i	$0.0464557\pi$
$138$		0			0
$139$		−	4.29376i		−	0.364192i	−0.983281	−	0.182096i	$-0.941712\pi$
$139$		−	4.29376i		−	0.364192i	0.983281	−	0.182096i	$-0.0582882\pi$
$140$		0			0
$141$	−8.68835	+	11.6177i	−0.731691	+	0.978389i
$142$		0			0
$143$	−8.37606	−	4.83592i	−0.700442	−	0.404400i
$144$		0			0
$145$	−6.06968	−	14.7202i	−0.504060	−	1.22245i
$146$		0			0
$147$	7.38603	−	9.61492i	0.609189	−	0.793025i
$148$		0			0
$149$	14.4601	−	8.34856i	1.18462	−	0.683940i	0.227541	−	0.973769i	$-0.426931\pi$
$149$	14.4601	−	8.34856i	1.18462	−	0.683940i	0.957079	+	0.289828i	$0.0935981\pi$
$150$		0			0
$151$	−0.351881	+	0.609476i	−0.0286357	+	0.0495984i	−0.879988	−	0.474996i	$-0.842450\pi$
$151$	−0.351881	+	0.609476i	−0.0286357	+	0.0495984i	0.851352	+	0.524594i	$0.175783\pi$
$152$		0			0
$153$	10.4822	−	3.08861i	0.847432	−	0.249699i
$154$		0			0
$155$	18.2024	+	2.42609i	1.46205	+	0.194868i
$156$		0			0
$157$	−5.95210	+	10.3093i	−0.475029	+	0.822774i	−0.999591	−	0.0285978i	$-0.990896\pi$
$157$	−5.95210	+	10.3093i	−0.475029	+	0.822774i	0.524562	+	0.851372i	$0.324229\pi$
$158$		0			0
$159$	−2.40209	+	20.1712i	−0.190498	+	1.59968i
$160$		0			0
$161$	10.2595	+	10.3928i	0.808561	+	0.819070i
$162$		0			0
$163$	−5.85283	+	3.37913i	−0.458429	+	0.264674i	−0.711383	−	0.702804i	$-0.751931\pi$
$163$	−5.85283	+	3.37913i	−0.458429	+	0.264674i	0.252954	+	0.967478i	$0.418598\pi$
$164$		0			0
$165$	−11.8347	+	3.30811i	−0.921330	+	0.257536i
$166$		0			0
$167$		−	1.53620i		−	0.118875i	−0.998232	−	0.0594373i	$-0.981069\pi$
$167$		−	1.53620i		−	0.118875i	0.998232	−	0.0594373i	$-0.0189306\pi$
$168$		0			0
$169$	−3.70773			−0.285210
$170$		0			0
$171$	2.99887	−	12.4127i	0.229329	−	0.949227i
$172$		0			0
$173$	−21.3044	+	12.3001i	−1.61974	+	0.935158i	−0.632755	+	0.774352i	$0.718076\pi$
$173$	−21.3044	+	12.3001i	−1.61974	+	0.935158i	−0.986986	+	0.160806i	$0.948591\pi$
$174$		0			0
$175$	−6.72476	+	11.3920i	−0.508344	+	0.861154i
$176$		0			0
$177$	0.297386	−	2.49726i	0.0223529	−	0.187706i
$178$		0			0
$179$	−11.4366	−	6.60295i	−0.854815	−	0.493528i	0.00745752	−	0.999972i	$-0.497626\pi$
$179$	−11.4366	−	6.60295i	−0.854815	−	0.493528i	−0.862273	+	0.506444i	$0.830960\pi$
$180$		0			0
$181$		−	2.40852i		−	0.179024i	−0.995986	−	0.0895120i	$-0.971469\pi$
$181$		−	2.40852i		−	0.179024i	0.995986	−	0.0895120i	$-0.0285308\pi$
$182$		0			0
$183$	−10.1424	+	13.5620i	−0.749747	+	1.00253i
$184$		0			0
$185$	−3.48993	+	4.53310i	−0.256585	+	0.333280i
$186$		0			0
$187$	−5.77865	−	10.0089i	−0.422577	−	0.731925i
$188$		0			0
$189$	−1.37573	+	13.6787i	−0.100069	+	0.994980i
$190$		0			0
$191$	−21.0445	+	12.1501i	−1.52273	+	0.879148i	−0.523089	+	0.852278i	$0.675221\pi$
$191$	−21.0445	+	12.1501i	−1.52273	+	0.879148i	−0.999639	+	0.0268696i	$0.991446\pi$
$192$		0			0
$193$	13.4236	+	7.75013i	0.966253	+	0.557866i	0.898092	−	0.439808i	$-0.144954\pi$
$193$	13.4236	+	7.75013i	0.966253	+	0.557866i	0.0681609	+	0.997674i	$0.478287\pi$
$194$		0			0
$195$	8.25779	−	8.43760i	0.591352	−	0.604229i
$196$		0			0
$197$	15.1239			1.07753			0.538767	−	0.842455i	$-0.318890\pi$
$197$	15.1239			1.07753			0.538767	+	0.842455i	$0.318890\pi$
$198$		0			0
$199$	−19.3565	−	11.1755i	−1.37215	−	0.792211i	−0.380951	−	0.924595i	$-0.624403\pi$
$199$	−19.3565	−	11.1755i	−1.37215	−	0.792211i	−0.991198	+	0.132385i	$0.957737\pi$
$200$		0			0
$201$	−17.5913	−	2.09486i	−1.24079	−	0.147760i
$202$		0			0
$203$	4.75850	+	18.2289i	0.333981	+	1.27942i
$204$		0			0
$205$	1.34896	−	0.556225i	0.0942154	−	0.0388484i
$206$		0			0
$207$	−16.0960	−	3.88872i	−1.11875	−	0.270285i
$208$		0			0
$209$	−13.5056			−0.934201
$210$		0			0
$211$	15.8956			1.09430			0.547150	−	0.837034i	$-0.315713\pi$
$211$	15.8956			1.09430			0.547150	+	0.837034i	$0.315713\pi$
$212$		0			0
$213$	−5.01435	−	11.6943i	−0.343578	−	0.801283i
$214$		0			0
$215$	8.01362	+	19.4347i	0.546524	+	1.32543i
$216$		0			0
$217$	−20.9507	−	5.75896i	−1.42223	−	0.390944i
$218$		0			0
$219$	−1.28657	+	10.8038i	−0.0869380	+	0.730050i
$220$		0			0
$221$	9.61612	+	5.55187i	0.646850	+	0.373459i
$222$		0			0
$223$	19.1954			1.28542			0.642711	−	0.766109i	$-0.277810\pi$
$223$	19.1954			1.28542			0.642711	+	0.766109i	$0.277810\pi$
$224$		0			0
$225$	−0.323065	−	14.9965i	−0.0215377	−	0.999768i
$226$		0			0
$227$	5.97779	+	3.45128i	0.396760	+	0.229070i	0.685085	−	0.728463i	$-0.259765\pi$
$227$	5.97779	+	3.45128i	0.396760	+	0.229070i	−0.288325	+	0.957533i	$0.593098\pi$
$228$		0			0
$229$	−3.15289	+	1.82032i	−0.208349	+	0.120290i	−0.600544	−	0.799592i	$-0.705049\pi$
$229$	−3.15289	+	1.82032i	−0.208349	+	0.120290i	0.392195	+	0.919882i	$0.371716\pi$
$230$		0			0
$231$	14.4039	−	1.98308i	0.947708	−	0.130477i
$232$		0			0
$233$	−0.525603	−	0.910371i	−0.0344334	−	0.0596404i	0.848295	−	0.529524i	$-0.177629\pi$
$233$	−0.525603	−	0.910371i	−0.0344334	−	0.0596404i	−0.882729	+	0.469883i	$0.844296\pi$
$234$		0			0
$235$	−11.4251	+	14.8402i	−0.745293	+	0.968067i
$236$		0			0
$237$	8.81637	+	6.59335i	0.572685	+	0.428284i
$238$		0			0
$239$			6.54292i			0.423226i	0.977354	+	0.211613i	$0.0678717\pi$
$239$			6.54292i			0.423226i	−0.977354	+	0.211613i	$0.932128\pi$
$240$		0			0
$241$	−17.4296	−	10.0630i	−1.12274	−	0.648215i	−0.180642	−	0.983549i	$-0.557818\pi$
$241$	−17.4296	−	10.0630i	−1.12274	−	0.648215i	−0.942099	+	0.335334i	$0.891151\pi$
$242$		0			0
$243$	−6.84443	−	14.0055i	−0.439070	−	0.898453i
$244$		0			0
$245$	9.70786	−	12.2783i	0.620213	−	0.784434i
$246$		0			0
$247$	11.2372	−	6.48778i	0.715004	−	0.412808i
$248$		0			0
$249$	0.271493	+	0.633168i	0.0172051	+	0.0401254i
$250$		0			0
$251$	8.21881			0.518767			0.259383	−	0.965774i	$-0.416481\pi$
$251$	8.21881			0.518767			0.259383	+	0.965774i	$0.416481\pi$
$252$		0			0
$253$			17.5131i			1.10104i
$254$		0			0
$255$	13.5868	−	3.79786i	0.850839	−	0.237831i
$256$		0			0
$257$	−10.2293	+	5.90590i	−0.638087	+	0.368400i	−0.783877	−	0.620916i	$-0.786761\pi$
$257$	−10.2293	+	5.90590i	−0.638087	+	0.368400i	0.145790	+	0.989316i	$0.453428\pi$
$258$		0			0
$259$	4.81724	−	4.75544i	0.299329	−	0.295489i
$260$		0			0
$261$	−15.4745	−	14.7270i	−0.957850	−	0.911580i
$262$		0			0
$263$	−14.1109	+	24.4407i	−0.870113	+	1.50708i	−0.00823401	+	0.999966i	$0.502621\pi$
$263$	−14.1109	+	24.4407i	−0.870113	+	1.50708i	−0.861879	+	0.507114i	$0.830712\pi$
$264$		0			0
$265$	−3.46472	+	25.9951i	−0.212836	+	1.59686i
$266$		0			0
$267$	8.74187	+	6.53763i	0.534994	+	0.400097i
$268$		0			0
$269$	8.31723	−	14.4059i	0.507110	−	0.878341i	−0.492856	−	0.870111i	$-0.664047\pi$
$269$	8.31723	−	14.4059i	0.507110	−	0.878341i	0.999966	−	0.00822992i	$-0.00261969\pi$
$270$		0			0
$271$	12.6459	−	7.30109i	0.768182	−	0.443510i	−0.0640439	−	0.997947i	$-0.520400\pi$
$271$	12.6459	−	7.30109i	0.768182	−	0.443510i	0.832226	+	0.554437i	$0.187066\pi$
$272$		0			0
$273$	−11.0320	+	8.56932i	−0.667686	+	0.518639i
$274$		0			0
$275$	−15.3367	+	4.05680i	−0.924840	+	0.244634i
$276$		0			0
$277$	−12.9793	−	7.49363i	−0.779853	−	0.450249i	0.0565249	−	0.998401i	$-0.481998\pi$
$277$	−12.9793	−	7.49363i	−0.779853	−	0.450249i	−0.836378	+	0.548153i	$0.815331\pi$
$278$		0			0
$279$	23.6325	−	6.96342i	1.41484	−	0.416889i
$280$		0			0
$281$			23.3608i			1.39359i	0.717271	+	0.696794i	$0.245391\pi$
$281$			23.3608i			1.39359i	−0.717271	+	0.696794i	$0.754609\pi$
$282$		0			0
$283$	15.3145	−	26.5255i	0.910353	−	1.57678i	0.0967878	−	0.995305i	$-0.469143\pi$
$283$	15.3145	−	26.5255i	0.910353	−	1.57678i	0.813566	−	0.581473i	$-0.197523\pi$
$284$		0			0
$285$	4.09511	−	15.9691i	0.242573	−	0.945929i
$286$		0			0
$287$	−1.67049	+	0.436068i	−0.0986062	+	0.0257403i
$288$		0			0
$289$	−1.86583	−	3.23172i	−0.109755	−	0.190101i
$290$		0			0
$291$	27.3307	−	11.7190i	1.60215	−	0.686979i
$292$		0			0
$293$		−	12.4515i		−	0.727422i	−0.931512	−	0.363711i	$-0.881510\pi$
$293$		−	12.4515i		−	0.727422i	0.931512	−	0.363711i	$-0.118490\pi$
$294$		0			0
$295$	0.428943	−	3.21827i	0.0249740	−	0.187375i
$296$		0			0
$297$	−12.6982	+	10.5149i	−0.736825	+	0.610134i
$298$		0			0
$299$	−8.41288	−	14.5715i	−0.486530	−	0.842694i
$300$		0			0
$301$	−6.28250	−	24.0671i	−0.362117	−	1.38720i
$302$		0			0
$303$	−0.638300	+	5.36004i	−0.0366694	+	0.307926i
$304$		0			0
$305$	−13.3372	+	17.3238i	−0.763685	+	0.991957i
$306$		0			0
$307$	10.5062			0.599620			0.299810	−	0.953999i	$-0.403077\pi$
$307$	10.5062			0.599620			0.299810	+	0.953999i	$0.403077\pi$
$308$		0			0
$309$	12.0185	+	8.98808i	0.683709	+	0.511314i
$310$		0			0
$311$	3.75631	−	6.50613i	0.213001	−	0.368929i	−0.739651	−	0.672990i	$-0.765010\pi$
$311$	3.75631	−	6.50613i	0.213001	−	0.368929i	0.952652	+	0.304062i	$0.0983429\pi$
$312$		0			0
$313$	0.351263	+	0.608406i	0.0198546	+	0.0343891i	0.875782	−	0.482707i	$-0.160346\pi$
$313$	0.351263	+	0.608406i	0.0198546	+	0.0343891i	−0.855927	+	0.517096i	$0.827013\pi$
$314$		0			0
$315$	−2.02268	+	17.6326i	−0.113965	+	0.993485i
$316$		0			0
$317$	−8.03766	−	13.9216i	−0.451440	−	0.781917i	0.547036	−	0.837109i	$-0.315756\pi$
$317$	−8.03766	−	13.9216i	−0.451440	−	0.781917i	−0.998476	+	0.0551923i	$0.982423\pi$
$318$		0			0
$319$	−11.2965	+	19.5661i	−0.632483	+	1.09549i
$320$		0			0
$321$	−7.82058	−	5.84864i	−0.436502	−	0.326439i
$322$		0			0
$323$	15.5051			0.862725
$324$		0			0
$325$	10.8120	−	10.7428i	0.599739	−	0.595905i
$326$		0			0
$327$	−2.25691	+	18.9521i	−0.124807	+	1.04805i
$328$		0			0
$329$	15.7704	−	15.5681i	0.869451	−	0.858296i
$330$		0			0
$331$	15.2517	+	26.4168i	0.838311	+	1.45200i	0.891306	+	0.453402i	$0.149790\pi$
$331$	15.2517	+	26.4168i	0.838311	+	1.45200i	−0.0529954	+	0.998595i	$0.516877\pi$
$332$		0			0
$333$	−1.80248	+	7.46073i	−0.0987755	+	0.408845i
$334$		0			0
$335$	−22.6702	−	3.02157i	−1.23861	−	0.165086i
$336$		0			0
$337$			3.18432i			0.173461i	0.996232	+	0.0867306i	$0.0276419\pi$
$337$			3.18432i			0.173461i	−0.996232	+	0.0867306i	$0.972358\pi$
$338$		0			0
$339$	1.40743	−	0.603486i	0.0764413	−	0.0327769i
$340$		0			0
$341$	−13.0282	−	22.5656i	−0.705519	−	1.22199i
$342$		0			0
$343$	−13.3470	+	12.8397i	−0.720669	+	0.693280i
$344$		0			0
$345$	−20.7076	−	5.31024i	−1.11486	−	0.285893i
$346$		0			0
$347$	6.38275	−	11.0552i	0.342644	−	0.593476i	−0.642279	−	0.766471i	$-0.722011\pi$
$347$	6.38275	−	11.0552i	0.342644	−	0.593476i	0.984923	+	0.172994i	$0.0553443\pi$
$348$		0			0
$349$		−	0.203714i		−	0.0109046i	−0.999985	−	0.00545228i	$-0.998264\pi$
$349$		−	0.203714i		−	0.0109046i	0.999985	−	0.00545228i	$-0.00173552\pi$
$350$		0			0
$351$	5.51430	−	14.8487i	0.294331	−	0.792565i
$352$		0			0
$353$	−1.55975	−	0.900520i	−0.0830169	−	0.0479298i	0.457917	−	0.888995i	$-0.348596\pi$
$353$	−1.55975	−	0.900520i	−0.0830169	−	0.0479298i	−0.540934	+	0.841065i	$0.681929\pi$
$354$		0			0
$355$	−6.26187	−	15.1863i	−0.332346	−	0.806006i
$356$		0			0
$357$	−16.5364	+	2.27667i	−0.875198	+	0.120494i
$358$		0			0
$359$	−2.86938	+	1.65664i	−0.151440	+	0.0874340i	−0.573805	−	0.818992i	$-0.694533\pi$
$359$	−2.86938	+	1.65664i	−0.151440	+	0.0874340i	0.422365	+	0.906426i	$0.361200\pi$
$360$		0			0
$361$	−0.440579	+	0.763106i	−0.0231884	+	0.0401635i
$362$		0			0
$363$	−1.29425	−	0.967907i	−0.0679304	−	0.0508019i
$364$		0			0
$365$	−1.85571	+	13.9230i	−0.0971324	+	0.728764i
$366$		0			0
$367$	−2.13660	+	3.70069i	−0.111529	+	0.193175i	−0.916387	−	0.400293i	$-0.868908\pi$
$367$	−2.13660	+	3.70069i	−0.111529	+	0.193175i	0.804858	+	0.593468i	$0.202242\pi$
$368$		0			0
$369$	1.34958	−	1.41808i	0.0702565	−	0.0738225i
$370$		0			0
$371$	8.22443	−	29.9200i	0.426991	−	1.55337i
$372$		0			0
$373$	−14.6641	+	8.46634i	−0.759280	+	0.438370i	−0.829037	−	0.559194i	$-0.811111\pi$
$373$	−14.6641	+	8.46634i	−0.759280	+	0.438370i	0.0697574	+	0.997564i	$0.477777\pi$
$374$		0			0
$375$	−0.146461	−	19.3644i	−0.00756321	−	0.999971i
$376$		0			0
$377$		−	21.7064i		−	1.11794i
$378$		0			0
$379$	9.54142			0.490110			0.245055	−	0.969509i	$-0.421194\pi$
$379$	9.54142			0.490110			0.245055	+	0.969509i	$0.421194\pi$
$380$		0			0
$381$	14.9484	+	34.8623i	0.765831	+	1.78605i
$382$		0			0
$383$	−13.5710	+	7.83524i	−0.693447	+	0.400362i	−0.804902	−	0.593407i	$-0.797782\pi$
$383$	−13.5710	+	7.83524i	−0.693447	+	0.400362i	0.111455	+	0.993769i	$0.464449\pi$
$384$		0			0
$385$	18.6293	−	2.30002i	0.949439	−	0.117220i
$386$		0			0
$387$	20.4306	+	19.4436i	1.03854	+	0.988376i
$388$		0			0
$389$	−0.554210	−	0.319974i	−0.0280996	−	0.0162233i	0.485884	−	0.874023i	$-0.338498\pi$
$389$	−0.554210	−	0.319974i	−0.0280996	−	0.0162233i	−0.513984	+	0.857800i	$0.671831\pi$
$390$		0			0
$391$		−	20.1058i		−	1.01680i
$392$		0			0
$393$	11.1447	+	8.33457i	0.562174	+	0.420424i
$394$		0			0
$395$	11.2618	+	8.67021i	0.566643	+	0.436246i
$396$		0			0
$397$	−6.64284	−	11.5057i	−0.333395	−	0.577456i	0.649781	−	0.760122i	$-0.274861\pi$
$397$	−6.64284	−	11.5057i	−0.333395	−	0.577456i	−0.983175	+	0.182666i	$0.941527\pi$
$398$		0			0
$399$	−7.35798	+	18.0653i	−0.368360	+	0.904397i
$400$		0			0
$401$	−10.4362	+	6.02536i	−0.521160	+	0.300892i	−0.737409	−	0.675446i	$-0.763951\pi$
$401$	−10.4362	+	6.02536i	−0.521160	+	0.300892i	0.216249	+	0.976338i	$0.430618\pi$
$402$		0			0
$403$	21.6800	+	12.5170i	1.07996	+	0.623514i
$404$		0			0
$405$	−8.58256	−	18.2027i	−0.426471	−	0.904501i
$406$		0			0
$407$	8.11758			0.402374
$408$		0			0
$409$	2.24844	+	1.29814i	0.111178	+	0.0641888i	0.554558	−	0.832145i	$-0.312887\pi$
$409$	2.24844	+	1.29814i	0.111178	+	0.0641888i	−0.443380	+	0.896334i	$0.646221\pi$
$410$		0			0
$411$	1.76795	−	14.8462i	0.0872068	−	0.732307i
$412$		0			0
$413$	−1.01821	+	3.70419i	−0.0501028	+	0.182271i
$414$		0			0
$415$	0.339037	+	0.822235i	0.0166427	+	0.0403619i
$416$		0			0
$417$	−2.93081	−	6.83516i	−0.143523	−	0.334719i
$418$		0			0
$419$	2.04634			0.0999703			0.0499851	−	0.998750i	$-0.484083\pi$
$419$	2.04634			0.0999703			0.0499851	+	0.998750i	$0.484083\pi$
$420$		0			0
$421$	19.8163			0.965785			0.482892	−	0.875680i	$-0.339586\pi$
$421$	19.8163			0.965785			0.482892	+	0.875680i	$0.339586\pi$
$422$		0			0
$423$	−5.90087	+	24.4245i	−0.286910	+	1.18756i
$424$		0			0
$425$	17.6073	−	4.65740i	0.854079	−	0.225917i
$426$		0			0
$427$	18.4097	−	18.1735i	0.890907	−	0.879477i
$428$		0			0
$429$	−16.6346	−	1.98093i	−0.803126	−	0.0956402i
$430$		0			0
$431$	18.2561	+	10.5402i	0.879367	+	0.507703i	0.870450	−	0.492257i	$-0.163828\pi$
$431$	18.2561	+	10.5402i	0.879367	+	0.507703i	0.00891735	+	0.999960i	$0.497161\pi$
$432$		0			0
$433$	−7.07414			−0.339961			−0.169981	−	0.985447i	$-0.554371\pi$
$433$	−7.07414			−0.339961			−0.169981	+	0.985447i	$0.554371\pi$
$434$		0			0
$435$	−19.7099	−	19.2899i	−0.945017	−	0.924878i
$436$		0			0
$437$	−20.3474	−	11.7476i	−0.973350	−	0.561964i
$438$		0			0
$439$	24.3862	−	14.0794i	1.16389	−	0.671973i	0.211658	−	0.977344i	$-0.432114\pi$
$439$	24.3862	−	14.0794i	1.16389	−	0.671973i	0.952234	+	0.305371i	$0.0987804\pi$
$440$		0			0
$441$	5.19479	−	20.3473i	0.247371	−	0.968921i
$442$		0			0
$443$	−2.85933	−	4.95251i	−0.135851	−	0.235301i	0.790071	−	0.613015i	$-0.210044\pi$
$443$	−2.85933	−	4.95251i	−0.135851	−	0.235301i	−0.925922	+	0.377714i	$0.876710\pi$
$444$		0			0
$445$	11.1666	+	8.59695i	0.529350	+	0.407534i
$446$		0			0
$447$	17.3203	−	23.1600i	0.819223	−	1.09543i
$448$		0			0
$449$		−	30.7201i		−	1.44977i	−0.688869	−	0.724886i	$-0.741893\pi$
$449$		−	30.7201i		−	1.44977i	0.688869	−	0.724886i	$-0.258107\pi$
$450$		0			0
$451$	−1.79304	−	1.03521i	−0.0844309	−	0.0487462i
$452$		0			0
$453$	−0.144140	+	1.21040i	−0.00677231	+	0.0568695i
$454$		0			0
$455$	−14.3954	+	10.8628i	−0.674869	+	0.509257i
$456$		0			0
$457$	33.9899	−	19.6241i	1.58998	−	0.917976i	0.596672	−	0.802485i	$-0.296489\pi$
$457$	33.9899	−	19.6241i	1.58998	−	0.917976i	0.993309	−	0.115490i	$-0.0368439\pi$
$458$		0			0
$459$	14.5782	−	12.0716i	0.680450	−	0.563452i
$460$		0			0
$461$	20.3916			0.949733			0.474867	−	0.880058i	$-0.342496\pi$
$461$	20.3916			0.949733			0.474867	+	0.880058i	$0.342496\pi$
$462$		0			0
$463$		−	26.4790i		−	1.23058i	−0.788299	−	0.615292i	$-0.789038\pi$
$463$		−	26.4790i		−	1.23058i	0.788299	−	0.615292i	$-0.210962\pi$
$464$		0			0
$465$	30.6321	−	8.56247i	1.42053	−	0.397075i
$466$		0			0
$467$	22.5176	−	13.0005i	1.04199	−	0.601593i	0.121594	−	0.992580i	$-0.461200\pi$
$467$	22.5176	−	13.0005i	1.04199	−	0.601593i	0.920396	+	0.390987i	$0.127866\pi$
$468$		0			0
$469$	26.0931	+	7.17250i	1.20487	+	0.331195i
$470$		0			0
$471$	−2.43815	+	20.4740i	−0.112344	+	0.943392i
$472$		0			0
$473$	14.9144	−	25.8326i	0.685767	−	1.18778i
$474$		0			0
$475$	5.57436	−	20.5401i	0.255769	−	0.942446i
$476$		0			0
$477$	9.94453	+	33.7498i	0.455329	+	1.54530i
$478$		0			0
$479$	12.7113	−	22.0167i	0.580795	−	1.00597i	−0.414590	−	0.910008i	$-0.636075\pi$
$479$	12.7113	−	22.0167i	0.580795	−	1.00597i	0.995385	−	0.0959586i	$-0.0305916\pi$
$480$		0			0
$481$	−6.75414	+	3.89951i	−0.307962	+	0.177802i
$482$		0			0
$483$	23.4258	+	9.54129i	1.06591	+	0.434144i
$484$		0			0
$485$	35.4917	−	14.6345i	1.61160	−	0.664520i
$486$		0			0
$487$	−28.7329	−	16.5890i	−1.30201	−	0.751717i	−0.321263	−	0.946990i	$-0.604107\pi$
$487$	−28.7329	−	16.5890i	−1.30201	−	0.751717i	−0.980749	+	0.195273i	$0.937441\pi$
$488$		0			0
$489$	−7.01051	+	9.37418i	−0.317026	+	0.423915i
$490$		0			0
$491$		−	3.43666i		−	0.155094i	−0.996989	−	0.0775471i	$-0.975291\pi$
$491$		−	3.43666i		−	0.155094i	0.996989	−	0.0775471i	$-0.0247088\pi$
$492$		0			0
$493$	12.9689	−	22.4629i	0.584092	−	1.01168i
$494$		0			0
$495$	−16.5814	+	13.3442i	−0.745280	+	0.599777i
$496$		0			0
$497$	4.90917	+	18.8061i	0.220207	+	0.843569i
$498$		0			0
$499$	−12.8499	−	22.2567i	−0.575240	−	0.996345i	−0.996016	−	0.0891801i	$-0.971575\pi$
$499$	−12.8499	−	22.2567i	−0.575240	−	0.996345i	0.420775	−	0.907165i	$-0.361758\pi$
$500$		0			0
$501$	−1.04857	−	2.44545i	−0.0468467	−	0.109255i
$502$		0			0
$503$		−	0.789804i		−	0.0352156i	−0.999845	−	0.0176078i	$-0.994395\pi$
$503$		−	0.789804i		−	0.0352156i	0.999845	−	0.0176078i	$-0.00560503\pi$
$504$		0			0
$505$	−0.920670	+	6.90759i	−0.0409693	+	0.307384i
$506$		0			0
$507$	−5.90226	+	2.53080i	−0.262129	+	0.112397i
$508$		0			0
$509$	−19.5947	−	33.9390i	−0.868519	−	1.50432i	−0.863510	−	0.504331i	$-0.831739\pi$
$509$	−19.5947	−	33.9390i	−0.868519	−	1.50432i	−0.00500861	−	0.999987i	$-0.501594\pi$
$510$		0			0
$511$	4.40502	−	16.0252i	0.194867	−	0.708914i
$512$		0			0
$513$	−3.69878	−	21.8066i	−0.163305	−	0.962785i
$514$		0			0
$515$	15.3521	+	11.8193i	0.676496	+	0.520819i
$516$		0			0
$517$	26.5749			1.16876
$518$		0			0
$519$	−25.5183	+	34.1221i	−1.12013	+	1.49779i
$520$		0			0
$521$	−21.5008	+	37.2405i	−0.941966	+	1.63153i	−0.180252	+	0.983620i	$0.557691\pi$
$521$	−21.5008	+	37.2405i	−0.941966	+	1.63153i	−0.761714	+	0.647913i	$0.775642\pi$
$522$		0			0
$523$	−18.9905	−	32.8926i	−0.830398	−	1.43829i	−0.897723	−	0.440561i	$-0.854780\pi$
$523$	−18.9905	−	32.8926i	−0.830398	−	1.43829i	0.0673245	−	0.997731i	$-0.478554\pi$
$524$		0			0
$525$	−2.92915	+	22.7249i	−0.127838	+	0.991795i
$526$		0			0
$527$	14.9570	+	25.9064i	0.651539	+	1.12850i
$528$		0			0
$529$	−3.73344	+	6.46650i	−0.162323	+	0.281152i
$530$		0			0
$531$	−1.23116	−	4.17833i	−0.0534279	−	0.181324i
$532$		0			0
$533$	1.98917			0.0861605
$534$		0			0
$535$	−9.98981	−	7.69093i	−0.431897	−	0.332508i
$536$		0			0
$537$	−22.7128	−	2.70476i	−0.980130	−	0.116719i
$538$		0			0
$539$	−22.2080	−	0.286768i	−0.956568	−	0.0123520i
$540$		0			0
$541$	3.12618	+	5.41470i	0.134405	+	0.232796i	0.925370	−	0.379065i	$-0.123754\pi$
$541$	3.12618	+	5.41470i	0.134405	+	0.232796i	−0.790965	+	0.611861i	$0.790421\pi$
$542$		0			0
$543$	−1.64400	−	3.83409i	−0.0705507	−	0.164536i
$544$		0			0
$545$	−3.25531	+	24.4239i	−0.139442	+	1.04620i
$546$		0			0
$547$		−	0.731095i		−	0.0312594i	−0.999878	−	0.0156297i	$-0.995025\pi$
$547$		−	0.731095i		−	0.0312594i	0.999878	−	0.0156297i	$-0.00497529\pi$
$548$		0			0
$549$	−6.88841	+	28.5121i	−0.293990	+	1.21687i
$550$		0			0
$551$	−15.1552	−	26.2496i	−0.645633	−	1.11827i
$552$		0			0
$553$	−11.8142	−	11.9677i	−0.502390	−	0.508919i
$554$		0			0
$555$	−2.46138	+	9.59830i	−0.104480	+	0.407425i
$556$		0			0
$557$	−2.75616	+	4.77382i	−0.116782	+	0.202273i	−0.918491	−	0.395442i	$-0.870591\pi$
$557$	−2.75616	+	4.77382i	−0.116782	+	0.202273i	0.801708	+	0.597715i	$0.203925\pi$
$558$		0			0
$559$			28.6583i			1.21212i
$560$		0			0
$561$	−16.0308	−	11.9887i	−0.676820	−	0.506162i
$562$		0			0
$563$	−4.76090	−	2.74871i	−0.200648	−	0.115844i	0.396310	−	0.918117i	$-0.370291\pi$
$563$	−4.76090	−	2.74871i	−0.200648	−	0.115844i	−0.596958	+	0.802273i	$0.703624\pi$
$564$		0			0
$565$	1.82770	−	0.753627i	0.0768919	−	0.0317053i
$566$		0			0
$567$	7.14676	+	22.7140i	0.300136	+	0.953897i
$568$		0			0
$569$	4.98266	−	2.87674i	0.208884	−	0.120599i	−0.391909	−	0.920004i	$-0.628185\pi$
$569$	4.98266	−	2.87674i	0.208884	−	0.120599i	0.600793	+	0.799405i	$0.294852\pi$
$570$		0			0
$571$	−8.32468	+	14.4188i	−0.348377	+	0.603407i	−0.985961	−	0.166974i	$-0.946600\pi$
$571$	−8.32468	+	14.4188i	−0.348377	+	0.603407i	0.637584	+	0.770381i	$0.279934\pi$
$572$		0			0
$573$	−25.2071	+	33.7059i	−1.05304	+	1.40809i
$574$		0			0
$575$	−26.6350	−	7.22843i	−1.11075	−	0.301446i
$576$		0			0
$577$	−11.3941	+	19.7352i	−0.474344	+	0.821588i	−0.999568	−	0.0293759i	$-0.990648\pi$
$577$	−11.3941	+	19.7352i	−0.474344	+	0.821588i	0.525225	+	0.850964i	$0.323981\pi$
$578$		0			0
$579$	26.6589	+	3.17467i	1.10790	+	0.131935i
$580$		0			0
$581$	−0.265798	−	1.01822i	−0.0110272	−	0.0422429i
$582$		0			0
$583$	32.2261	−	18.6058i	1.33467	−	0.770572i
$584$		0			0
$585$	7.38614	−	19.0682i	0.305379	−	0.788374i
$586$		0			0
$587$			18.4977i			0.763483i	0.924269	+	0.381741i	$0.124676\pi$
$587$			18.4977i			0.763483i	−0.924269	+	0.381741i	$0.875324\pi$
$588$		0			0
$589$	34.9569			1.44037
$590$		0			0
$591$	24.0755	−	10.3232i	0.990333	−	0.424640i
$592$		0			0
$593$	−0.729403	+	0.421121i	−0.0299530	+	0.0172934i	−0.514902	−	0.857249i	$-0.672172\pi$
$593$	−0.729403	+	0.421121i	−0.0299530	+	0.0172934i	0.484949	+	0.874543i	$0.338838\pi$
$594$		0			0
$595$	−21.3874	+	2.64053i	−0.876796	+	0.108251i
$596$		0			0
$597$	−38.4415	−	4.57780i	−1.57330	−	0.187357i
$598$		0			0
$599$	−2.43748	−	1.40728i	−0.0995929	−	0.0575000i	0.449376	−	0.893343i	$-0.351646\pi$
$599$	−2.43748	−	1.40728i	−0.0995929	−	0.0575000i	−0.548969	+	0.835843i	$0.684980\pi$
$600$		0			0
$601$			15.2185i			0.620775i	0.950610	+	0.310388i	$0.100459\pi$
$601$			15.2185i			0.620775i	−0.950610	+	0.310388i	$0.899541\pi$
$602$		0			0
$603$	−29.4331	+	8.67259i	−1.19861	+	0.353175i
$604$		0			0
$605$	−1.65324	−	1.27279i	−0.0672138	−	0.0517463i
$606$		0			0
$607$	5.84912	+	10.1310i	0.237409	+	0.411204i	0.959970	−	0.280103i	$-0.0903686\pi$
$607$	5.84912	+	10.1310i	0.237409	+	0.411204i	−0.722561	+	0.691307i	$0.757035\pi$
$608$		0			0
$609$	20.0176	+	25.7703i	0.811153	+	1.04426i
$610$		0			0
$611$	−22.1113	+	12.7660i	−0.894528	+	0.516456i
$612$		0			0
$613$	−35.0567	−	20.2400i	−1.41593	−	0.817486i	−0.419989	−	0.907529i	$-0.637966\pi$
$613$	−35.0567	−	20.2400i	−1.41593	−	0.817486i	−0.995938	+	0.0900434i	$0.971299\pi$
$614$		0			0
$615$	1.76772	−	1.80621i	0.0712813	−	0.0728335i
$616$		0			0
$617$	−48.3959			−1.94835			−0.974174	−	0.225801i	$-0.927500\pi$
$617$	−48.3959			−1.94835			−0.974174	+	0.225801i	$0.927500\pi$
$618$		0			0
$619$	−0.952353	−	0.549841i	−0.0382783	−	0.0221000i	0.480739	−	0.876864i	$-0.340369\pi$
$619$	−0.952353	−	0.549841i	−0.0382783	−	0.0221000i	−0.519017	+	0.854764i	$0.673702\pi$
$620$		0			0
$621$	−28.2772	+	4.79631i	−1.13473	+	0.192469i
$622$		0			0
$623$	−11.7144	−	11.8666i	−0.469326	−	0.475425i
$624$		0			0
$625$	0.160319	−	24.9995i	0.00641275	−	0.999979i
$626$		0			0
$627$	−21.4993	+	9.21858i	−0.858600	+	0.368155i
$628$		0			0
$629$	−9.31937			−0.371588
$630$		0			0
$631$	21.5811			0.859132			0.429566	−	0.903036i	$-0.358667\pi$
$631$	21.5811			0.859132			0.429566	+	0.903036i	$0.358667\pi$
$632$		0			0
$633$	25.3040	−	10.8500i	1.00574	−	0.431247i
$634$		0			0
$635$	18.6674	+	45.2723i	0.740795	+	1.79658i
$636$		0			0
$637$	18.6157	−	10.4296i	0.737581	−	0.413237i
$638$		0			0
$639$	−15.9645	−	15.1933i	−0.631547	−	0.601039i
$640$		0			0
$641$	31.5677	+	18.2256i	1.24685	+	0.719870i	0.970480	−	0.241181i	$-0.0775349\pi$
$641$	31.5677	+	18.2256i	1.24685	+	0.719870i	0.276371	+	0.961051i	$0.410868\pi$
$642$		0			0
$643$	9.47060			0.373484			0.186742	−	0.982409i	$-0.440207\pi$
$643$	9.47060			0.373484			0.186742	+	0.982409i	$0.440207\pi$
$644$		0			0
$645$	26.0224	+	25.4678i	1.02463	+	1.00279i
$646$		0			0
$647$	−30.1254	−	17.3929i	−1.18435	−	0.683785i	−0.227334	−	0.973817i	$-0.573001\pi$
$647$	−30.1254	−	17.3929i	−1.18435	−	0.683785i	−0.957017	+	0.290032i	$0.906334\pi$
$648$		0			0
$649$	−3.98970	+	2.30345i	−0.156609	+	0.0904184i
$650$		0			0
$651$	−37.2820	+	5.13287i	−1.46120	+	0.201173i
$652$		0			0
$653$	13.7213	+	23.7661i	0.536958	+	0.930038i	0.999066	+	0.0432146i	$0.0137599\pi$
$653$	13.7213	+	23.7661i	0.536958	+	0.930038i	−0.462108	+	0.886824i	$0.652907\pi$
$654$		0			0
$655$	14.2359	+	10.9599i	0.556243	+	0.428239i
$656$		0			0
$657$	5.32631	+	18.0765i	0.207799	+	0.705231i
$658$		0			0
$659$		−	28.4082i		−	1.10663i	−0.832973	−	0.553313i	$-0.813363\pi$
$659$		−	28.4082i		−	1.10663i	0.832973	−	0.553313i	$-0.186637\pi$
$660$		0			0
$661$	−33.8007	−	19.5148i	−1.31469	−	0.759039i	−0.331824	−	0.943341i	$-0.607664\pi$
$661$	−33.8007	−	19.5148i	−1.31469	−	0.759039i	−0.982870	+	0.184302i	$0.940997\pi$
$662$		0			0
$663$	19.0973	+	2.27420i	0.741678	+	0.0883227i
$664$		0			0
$665$	−9.82412	+	23.1872i	−0.380963	+	0.899161i
$666$		0			0
$667$	−34.0385	+	19.6522i	−1.31798	+	0.760934i
$668$		0			0
$669$	30.5569	−	13.1023i	1.18140	−	0.506565i
$670$		0			0
$671$	31.0223			1.19760
$672$		0			0
$673$			0.880844i			0.0339540i	0.999856	+	0.0169770i	$0.00540421\pi$
$673$			0.880844i			0.0339540i	−0.999856	+	0.0169770i	$0.994596\pi$
$674$		0			0
$675$	−10.7505	−	23.6522i	−0.413788	−	0.910373i
$676$		0			0
$677$	1.33147	−	0.768723i	0.0511724	−	0.0295444i	−0.474196	−	0.880420i	$-0.657261\pi$
$677$	1.33147	−	0.768723i	0.0511724	−	0.0295444i	0.525368	+	0.850875i	$0.323928\pi$
$678$		0			0
$679$	−43.9515	+	11.4732i	−1.68670	+	0.440300i
$680$		0			0
$681$	11.8717	+	1.41374i	0.454925	+	0.0541747i
$682$		0			0
$683$	14.5363	−	25.1776i	0.556215	−	0.963393i	−0.441592	−	0.897216i	$-0.645586\pi$
$683$	14.5363	−	25.1776i	0.556215	−	0.963393i	0.997808	−	0.0661777i	$-0.0210804\pi$
$684$		0			0
$685$	2.55006	−	19.1325i	0.0974327	−	0.731017i
$686$		0			0
$687$	−3.77653	+	5.04983i	−0.144084	+	0.192663i
$688$		0			0
$689$	−17.8756	+	30.9614i	−0.681006	+	1.17954i
$690$		0			0
$691$	−37.5335	+	21.6700i	−1.42784	+	0.824365i	−0.996950	−	0.0780383i	$-0.975134\pi$
$691$	−37.5335	+	21.6700i	−1.42784	+	0.824365i	−0.430892	+	0.902403i	$0.641801\pi$
$692$		0			0
$693$	21.5757	−	12.9886i	0.819595	−	0.493396i
$694$		0			0
$695$	−3.65997	−	8.87618i	−0.138831	−	0.336693i
$696$		0			0
$697$	2.05849	+	1.18847i	0.0779710	+	0.0450166i
$698$		0			0
$699$	−1.45810	−	1.09044i	−0.0551502	−	0.0412443i
$700$		0			0
$701$			25.8766i			0.977345i	0.872467	+	0.488673i	$0.162519\pi$
$701$			25.8766i			0.977345i	−0.872467	+	0.488673i	$0.837481\pi$
$702$		0			0
$703$	−5.44520	+	9.43136i	−0.205370	+	0.355711i
$704$		0			0
$705$	−8.05792	+	31.4224i	−0.303479	+	1.18343i
$706$		0			0
$707$	2.18545	−	7.95055i	0.0821924	−	0.299011i
$708$		0			0
$709$	−5.64504	−	9.77749i	−0.212004	−	0.367201i	0.740338	−	0.672235i	$-0.234666\pi$
$709$	−5.64504	−	9.77749i	−0.212004	−	0.367201i	−0.952342	+	0.305034i	$0.901332\pi$
$710$		0			0
$711$	18.5351	+	4.47800i	0.695120	+	0.167938i
$712$		0			0
$713$		−	45.3296i		−	1.69761i
$714$		0			0
$715$	−21.4373	−	2.85725i	−0.801711	−	0.106855i
$716$		0			0
$717$	4.46603	+	10.4156i	0.166787	+	0.388976i
$718$		0			0
$719$	14.0562	+	24.3461i	0.524208	+	0.907956i	0.999603	+	0.0281828i	$0.00897206\pi$
$719$	14.0562	+	24.3461i	0.524208	+	0.907956i	−0.475394	+	0.879773i	$0.657695\pi$
$720$		0			0
$721$	−16.1051	−	16.3144i	−0.599787	−	0.607582i
$722$		0			0
$723$	−34.6147	−	4.12209i	−1.28733	−	0.153302i
$724$		0			0
$725$	−25.0948	−	25.2563i	−0.931999	−	0.937995i
$726$		0			0
$727$	9.22579			0.342165			0.171083	−	0.985257i	$-0.445273\pi$
$727$	9.22579			0.342165			0.171083	+	0.985257i	$0.445273\pi$
$728$		0			0
$729$	−20.4553	−	17.6233i	−0.757605	−	0.652714i
$730$		0			0
$731$	−17.1225	+	29.6570i	−0.633298	+	1.09690i
$732$		0			0
$733$	8.89992	+	15.4151i	0.328726	+	0.569370i	0.982259	−	0.187528i	$-0.0600474\pi$
$733$	8.89992	+	15.4151i	0.328726	+	0.569370i	−0.653533	+	0.756898i	$0.726714\pi$
$734$		0			0
$735$	7.07290	−	26.1720i	0.260888	−	0.965369i
$736$		0			0
$737$	16.2260	+	28.1043i	0.597694	+	1.03524i
$738$		0			0
$739$	3.15829	−	5.47033i	0.116180	−	0.201229i	−0.802071	−	0.597229i	$-0.796268\pi$
$739$	3.15829	−	5.47033i	0.116180	−	0.201229i	0.918251	+	0.395999i	$0.129602\pi$
$740$		0			0
$741$	13.4599	−	17.9980i	0.494460	−	0.661173i
$742$		0			0
$743$	50.3390			1.84676			0.923379	−	0.383890i	$-0.125416\pi$
$743$	50.3390			1.84676			0.923379	+	0.383890i	$0.125416\pi$
$744$		0			0
$745$	22.7761	−	29.5841i	0.834452	−	1.08388i
$746$		0			0
$747$	0.864369	+	0.822615i	0.0316256	+	0.0300979i
$748$		0			0
$749$	10.4798	+	10.6160i	0.382923	+	0.387900i
$750$		0			0
$751$	23.0281	+	39.8858i	0.840306	+	1.45545i	0.889636	+	0.456670i	$0.150958\pi$
$751$	23.0281	+	39.8858i	0.840306	+	1.45545i	−0.0493301	+	0.998783i	$0.515709\pi$
$752$		0			0
$753$	13.0834	−	5.60995i	0.476785	−	0.204438i
$754$		0			0
$755$	−0.207905	+	1.55987i	−0.00756643	+	0.0567693i
$756$		0			0
$757$		−	49.4487i		−	1.79724i	−0.438725	−	0.898621i	$-0.644570\pi$
$757$		−	49.4487i		−	1.79724i	0.438725	−	0.898621i	$-0.355430\pi$
$758$		0			0
$759$	11.9540	+	27.8788i	0.433902	+	1.01193i
$760$		0			0
$761$	−16.4488	−	28.4901i	−0.596268	−	1.03277i	−0.993367	−	0.114990i	$-0.963316\pi$
$761$	−16.4488	−	28.4901i	−0.596268	−	1.03277i	0.397099	−	0.917776i	$-0.370017\pi$
$762$		0			0
$763$	7.72733	−	28.1116i	0.279748	−	1.01771i
$764$		0			0
$765$	19.0363	−	15.3198i	0.688258	−	0.553887i
$766$		0			0
$767$	2.21305	−	3.83312i	0.0799087	−	0.138406i
$768$		0			0
$769$			15.3215i			0.552507i	0.961085	+	0.276254i	$0.0890929\pi$
$769$			15.3215i			0.552507i	−0.961085	+	0.276254i	$0.910907\pi$
$770$		0			0
$771$	−12.2527	+	16.3838i	−0.441269	+	0.590047i
$772$		0			0
$773$	20.1944	+	11.6592i	0.726342	+	0.419354i	0.817082	−	0.576521i	$-0.195590\pi$
$773$	20.1944	+	11.6592i	0.726342	+	0.419354i	−0.0907407	+	0.995875i	$0.528923\pi$
$774$		0			0
$775$	39.6965	−	10.5003i	1.42594	−	0.377183i
$776$		0			0
$777$	4.42254	−	10.8582i	0.158658	−	0.389537i
$778$		0			0
$779$	2.40551	−	1.38882i	0.0861862	−	0.0497596i
$780$		0			0
$781$	−11.6542	+	20.1857i	−0.417020	+	0.722300i
$782$		0			0
$783$	−34.6860	−	12.8812i	−1.23958	−	0.460335i
$784$		0			0
$785$	−3.51673	+	26.3853i	−0.125517	+	0.941730i
$786$		0			0
$787$	−15.4172	+	26.7033i	−0.549563	+	0.951871i	0.448741	+	0.893662i	$0.351872\pi$
$787$	−15.4172	+	26.7033i	−0.549563	+	0.951871i	−0.998304	+	0.0582094i	$0.981461\pi$
$788$		0			0
$789$	−5.78021	+	48.5385i	−0.205781	+	1.72802i
$790$		0			0
$791$	−2.26335	+	0.590827i	−0.0804753	+	0.0210074i
$792$		0			0
$793$	−25.8118	+	14.9024i	−0.916603	+	0.529201i
$794$		0			0
$795$	12.2281	+	43.7460i	0.433688	+	1.55151i
$796$		0			0
$797$			20.1623i			0.714186i	0.934069	+	0.357093i	$0.116232\pi$
$797$			20.1623i			0.714186i	−0.934069	+	0.357093i	$0.883768\pi$
$798$		0			0
$799$	−30.5092			−1.07934
$800$		0			0
$801$	18.3785	+	4.44016i	0.649371	+	0.156885i
$802$		0			0
$803$	17.2604	−	9.96530i	0.609106	−	0.351668i
$804$		0			0
$805$	30.0675	+	12.7392i	1.05974	+	0.448998i
$806$		0			0
$807$	3.40697	−	28.6096i	0.119931	−	1.00710i
$808$		0			0
$809$	−28.2278	−	16.2974i	−0.992438	−	0.572985i	−0.0864360	−	0.996257i	$-0.527548\pi$
$809$	−28.2278	−	16.2974i	−0.992438	−	0.572985i	−0.906002	+	0.423273i	$0.860881\pi$
$810$		0			0
$811$			27.4529i			0.964003i	0.876170	+	0.482001i	$0.160090\pi$
$811$			27.4529i			0.964003i	−0.876170	+	0.482001i	$0.839910\pi$
$812$		0			0
$813$	15.1472	−	20.2542i	0.531235	−	0.710347i
$814$		0			0
$815$	−9.21878	+	11.9743i	−0.322920	+	0.419443i
$816$		0			0
$817$	20.0089	+	34.6565i	0.700024	+	1.21248i
$818$		0			0
$819$	−11.7124	+	21.1715i	−0.409265	+	0.739792i
$820$		0			0
$821$	−19.3028	+	11.1445i	−0.673671	+	0.388944i	−0.797466	−	0.603364i	$-0.793827\pi$
$821$	−19.3028	+	11.1445i	−0.673671	+	0.388944i	0.123795	+	0.992308i	$0.460493\pi$
$822$		0			0
$823$	5.11467	+	2.95296i	0.178286	+	0.102934i	0.586487	−	0.809958i	$-0.300510\pi$
$823$	5.11467	+	2.95296i	0.178286	+	0.102934i	−0.408201	+	0.912892i	$0.633844\pi$
$824$		0			0
$825$	−21.6452	+	16.9264i	−0.753589	+	0.589303i
$826$		0			0
$827$	−0.636826			−0.0221446			−0.0110723	−	0.999939i	$-0.503524\pi$
$827$	−0.636826			−0.0221446			−0.0110723	+	0.999939i	$0.503524\pi$
$828$		0			0
$829$	−31.3706	−	18.1118i	−1.08955	−	0.629050i	−0.156090	−	0.987743i	$-0.549889\pi$
$829$	−31.3706	−	18.1118i	−1.08955	−	0.629050i	−0.933455	+	0.358693i	$0.883222\pi$
$830$		0			0
$831$	−25.7766	−	3.06960i	−0.894179	−	0.106483i
$832$		0			0
$833$	25.4959	+	0.329223i	0.883380	+	0.0114069i
$834$		0			0
$835$	−1.30945	−	3.17567i	−0.0453152	−	0.109899i
$836$		0			0
$837$	32.8671	−	27.2159i	1.13605	−	0.940719i
$838$		0			0
$839$	28.0342			0.967848			0.483924	−	0.875110i	$-0.339211\pi$
$839$	28.0342			0.967848			0.483924	+	0.875110i	$0.339211\pi$
$840$		0			0
$841$	−21.7052			−0.748455
$842$		0			0
$843$	15.9455	+	37.1877i	0.549192	+	1.28081i
$844$		0			0
$845$	−7.66471	+	3.16044i	−0.263674	+	0.108722i
$846$		0			0
$847$	1.73433	+	1.75687i	0.0595922	+	0.0603667i
$848$		0			0
$849$	6.27326	−	52.6788i	0.215298	−	1.80793i
$850$		0			0
$851$	12.2299	+	7.06094i	0.419236	+	0.242046i
$852$		0			0
$853$	−13.7679			−0.471403			−0.235702	−	0.971825i	$-0.575739\pi$
$853$	−13.7679			−0.471403			−0.235702	+	0.971825i	$0.575739\pi$
$854$		0			0
$855$	−4.38119	−	28.2162i	−0.149834	−	0.964973i
$856$		0			0
$857$	48.7056	+	28.1202i	1.66375	+	0.960567i	0.970900	+	0.239487i	$0.0769791\pi$
$857$	48.7056	+	28.1202i	1.66375	+	0.960567i	0.692851	+	0.721080i	$0.256354\pi$
$858$		0			0
$859$	23.4146	−	13.5184i	0.798897	−	0.461243i	−0.0441884	−	0.999023i	$-0.514070\pi$
$859$	23.4146	−	13.5184i	0.798897	−	0.461243i	0.843085	+	0.537780i	$0.180737\pi$
$860$		0			0
$861$	−2.36158	+	1.83441i	−0.0804825	+	0.0625164i
$862$		0			0
$863$	−6.85347	−	11.8706i	−0.233295	−	0.404079i	0.725481	−	0.688242i	$-0.241617\pi$
$863$	−6.85347	−	11.8706i	−0.233295	−	0.404079i	−0.958776	+	0.284164i	$0.908284\pi$
$864$		0			0
$865$	−33.5565	+	43.5868i	−1.14095	+	1.48199i
$866$		0			0
$867$	−5.17608	−	3.87095i	−0.175789	−	0.131464i
$868$		0			0
$869$		−	20.1669i		−	0.684117i
$870$		0			0
$871$	−27.0014	−	15.5892i	−0.914906	−	0.528221i
$872$		0			0
$873$	35.5082	−	37.3105i	1.20177	−	1.26277i
$874$		0			0
$875$	−4.19116	+	29.2820i	−0.141687	+	0.989912i
$876$		0			0
$877$	27.7508	−	16.0219i	0.937079	−	0.541023i	0.0480353	−	0.998846i	$-0.484704\pi$
$877$	27.7508	−	16.0219i	0.937079	−	0.541023i	0.889043	+	0.457823i	$0.151371\pi$
$878$		0			0
$879$	−8.49905	−	19.8213i	−0.286666	−	0.668554i
$880$		0			0
$881$	−58.9479			−1.98601			−0.993003	−	0.118088i	$-0.962324\pi$
$881$	−58.9479			−1.98601			−0.993003	+	0.118088i	$0.962324\pi$
$882$		0			0
$883$		−	23.7884i		−	0.800544i	−0.916396	−	0.400272i	$-0.868916\pi$
$883$		−	23.7884i		−	0.800544i	0.916396	−	0.400272i	$-0.131084\pi$
$884$		0			0
$885$	−1.51388	−	5.41589i	−0.0508886	−	0.182053i
$886$		0			0
$887$	6.86422	−	3.96306i	0.230478	−	0.133066i	−0.380315	−	0.924857i	$-0.624184\pi$
$887$	6.86422	−	3.96306i	0.230478	−	0.133066i	0.610793	+	0.791791i	$0.290851\pi$
$888$		0			0
$889$	−14.6349	−	56.0634i	−0.490838	−	1.88030i
$890$		0			0
$891$	−13.0369	+	25.4059i	−0.436752	+	0.851130i
$892$		0			0
$893$	−17.8262	+	30.8758i	−0.596530	+	1.03322i
$894$		0			0
$895$	−29.2704	−	3.90128i	−0.978403	−	0.130405i
$896$		0			0
$897$	−23.3385	−	17.4538i	−0.779250	−	0.582764i
$898$		0			0
$899$	29.2391	−	50.6436i	0.975178	−	1.68906i
$900$		0			0
$901$	−36.9971	+	21.3603i	−1.23255	+	0.711615i
$902$		0			0
$903$	−26.4286	−	34.0237i	−0.879488	−	1.13224i
$904$		0			0
$905$	−2.05301	−	4.97896i	−0.0682443	−	0.165506i
$906$		0			0
$907$	31.1912	+	18.0083i	1.03569	+	0.597954i	0.918609	−	0.395168i	$-0.129314\pi$
$907$	31.1912	+	18.0083i	1.03569	+	0.597954i	0.117079	+	0.993123i	$0.462647\pi$
$908$		0			0
$909$	2.64253	+	8.96825i	0.0876472	+	0.297458i
$910$		0			0
$911$			6.09716i			0.202008i	0.994886	+	0.101004i	$0.0322055\pi$
$911$			6.09716i			0.202008i	−0.994886	+	0.101004i	$0.967795\pi$
$912$		0			0
$913$	0.630995	−	1.09292i	0.0208829	−	0.0361702i
$914$		0			0
$915$	−9.40646	+	36.6811i	−0.310968	+	1.21264i
$916$		0			0
$917$	−14.9342	−	15.1283i	−0.493170	−	0.499579i
$918$		0			0
$919$	22.3186	+	38.6569i	0.736222	+	1.27517i	0.954185	+	0.299218i	$0.0967256\pi$
$919$	22.3186	+	38.6569i	0.736222	+	1.27517i	−0.217962	+	0.975957i	$0.569941\pi$
$920$		0			0
$921$	16.7246	−	7.17127i	0.551096	−	0.236301i
$922$		0			0
$923$		−	22.3937i		−	0.737097i
$924$		0			0
$925$	−3.35049	+	12.3457i	−0.110164	+	0.405925i
$926$		0			0
$927$	25.2671	+	6.10443i	0.829880	+	0.200496i
$928$		0			0
$929$	30.1915	+	52.2932i	0.990551	+	1.71568i	0.614049	+	0.789268i	$0.289540\pi$
$929$	30.1915	+	52.2932i	0.990551	+	1.71568i	0.376502	+	0.926416i	$0.377127\pi$
$930$		0			0
$931$	15.2301	−	25.6099i	0.499147	−	0.839330i
$932$		0			0
$933$	1.53869	−	12.9210i	0.0503745	−	0.423013i
$934$		0			0
$935$	−20.4773	−	15.7650i	−0.669680	−	0.515571i
$936$		0			0
$937$	−52.5337			−1.71620			−0.858100	−	0.513483i	$-0.828355\pi$
$937$	−52.5337			−1.71620			−0.858100	+	0.513483i	$0.828355\pi$
$938$		0			0
$939$	0.974453	+	0.728747i	0.0318001	+	0.0237818i
$940$		0			0
$941$	22.3326	−	38.6812i	0.728021	−	1.26097i	−0.229697	−	0.973262i	$-0.573774\pi$
$941$	22.3326	−	38.6812i	0.728021	−	1.26097i	0.957718	−	0.287707i	$-0.0928931\pi$
$942$		0			0
$943$	−1.80092	−	3.11929i	−0.0586460	−	0.101578i
$944$		0			0
$945$	8.81571	+	29.4497i	0.286775	+	0.957998i
$946$		0			0
$947$	−12.4350	−	21.5381i	−0.404084	−	0.699894i	0.590131	−	0.807308i	$-0.299076\pi$
$947$	−12.4350	−	21.5381i	−0.404084	−	0.699894i	−0.994214	+	0.107414i	$0.965743\pi$
$948$		0			0
$949$	−9.57421	+	16.5830i	−0.310792	+	0.538308i
$950$		0			0
$951$	−22.2976	−	16.6753i	−0.723048	−	0.540734i
$952$		0			0
$953$	18.9078			0.612484			0.306242	−	0.951954i	$-0.400928\pi$
$953$	18.9078			0.612484			0.306242	+	0.951954i	$0.400928\pi$
$954$		0			0
$955$	−33.1472	+	43.0551i	−1.07262	+	1.39323i
$956$		0			0
$957$	−4.62737	+	38.8577i	−0.149582	+	1.25609i
$958$		0			0
$959$	−6.05323	+	22.0213i	−0.195469	+	0.711105i
$960$		0			0
$961$	18.2214	+	31.5603i	0.587786	+	1.01808i
$962$		0			0
$963$	−16.4416	−	3.97222i	−0.529822	−	0.128003i
$964$		0			0
$965$	34.3558	+	4.57907i	1.10595	+	0.147406i
$966$		0			0
$967$		−	0.439343i		−	0.0141283i	−0.999975	−	0.00706415i	$-0.997751\pi$
$967$		−	0.439343i		−	0.0141283i	0.999975	−	0.00706415i	$-0.00224861\pi$
$968$		0			0
$969$	24.6822	−	10.5834i	0.792908	−	0.339987i
$970$		0			0
$971$	19.5826	+	33.9181i	0.628436	+	1.08848i	0.987866	+	0.155311i	$0.0496381\pi$
$971$	19.5826	+	33.9181i	0.628436	+	1.08848i	−0.359429	+	0.933172i	$0.617029\pi$
$972$		0			0
$973$	2.86934	+	10.9919i	0.0919868	+	0.352384i
$974$		0			0
$975$	9.87857	−	24.4813i	0.316367	−	0.784029i
$976$		0			0
$977$	−12.8878	+	22.3223i	−0.412316	+	0.714153i	−0.995143	−	0.0984441i	$-0.968613\pi$
$977$	−12.8878	+	22.3223i	−0.412316	+	0.714153i	0.582826	+	0.812597i	$0.301947\pi$
$978$		0			0
$979$		−	19.9965i		−	0.639092i
$980$		0			0
$981$	9.34347	+	31.7100i	0.298314	+	1.01242i
$982$		0			0
$983$	−13.4197	−	7.74788i	−0.428023	−	0.247119i	0.270481	−	0.962725i	$-0.412817\pi$
$983$	−13.4197	−	7.74788i	−0.428023	−	0.247119i	−0.698504	+	0.715606i	$0.746151\pi$
$984$		0			0
$985$	31.2645	−	12.8915i	0.996171	−	0.410758i
$986$		0			0
$987$	14.4783	−	35.5470i	0.460848	−	1.13147i
$988$		0			0
$989$	44.9400	−	25.9461i	1.42901	−	0.825039i
$990$		0			0
$991$	16.7689	−	29.0446i	0.532682	−	0.922632i	−0.466590	−	0.884474i	$-0.654518\pi$
$991$	16.7689	−	29.0446i	0.532682	−	0.922632i	0.999272	−	0.0381579i	$-0.0121490\pi$
$992$		0			0
$993$	42.3104	+	31.6420i	1.34268	+	1.00413i
$994$		0			0
$995$	−49.5403	−	6.60292i	−1.57053	−	0.209327i
$996$		0			0
$997$	2.51253	−	4.35182i	0.0795725	−	0.137824i	−0.823493	−	0.567326i	$-0.807978\pi$
$997$	2.51253	−	4.35182i	0.0795725	−	0.137824i	0.903066	+	0.429503i	$0.141311\pi$
$998$		0			0
$999$	2.22317	+	13.1069i	0.0703378	+	0.414685i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	840.2.da.b.689.21	yes	48
3.2	odd	2		840.2.da.a.689.13	yes	48
5.4	even	2		840.2.da.a.689.4	yes	48
7.5	odd	6	inner	840.2.da.b.89.12	yes	48
15.14	odd	2	inner	840.2.da.b.689.12	yes	48
21.5	even	6		840.2.da.a.89.4	✓	48
35.19	odd	6		840.2.da.a.89.13	yes	48
105.89	even	6	inner	840.2.da.b.89.21	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.da.a.89.4	✓	48	21.5	even	6
840.2.da.a.89.13	yes	48	35.19	odd	6
840.2.da.a.689.4	yes	48	5.4	even	2
840.2.da.a.689.13	yes	48	3.2	odd	2
840.2.da.b.89.12	yes	48	7.5	odd	6	inner
840.2.da.b.89.21	yes	48	105.89	even	6	inner
840.2.da.b.689.12	yes	48	15.14	odd	2	inner
840.2.da.b.689.21	yes	48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 840 = 2^{3} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	840.da (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.59188 - 0.682575i) q^{3} +(2.06723 - 0.852393i) q^{5} +(-2.55997 + 0.668258i) q^{7} +(2.06818 - 2.17316i) q^{9} +O(q^{10})\)	\(q+(1.59188 - 0.682575i) q^{3} +(2.06723 - 0.852393i) q^{5} +(-2.55997 + 0.668258i) q^{7} +(2.06818 - 2.17316i) q^{9} +(-2.74776 - 1.58642i) q^{11} +3.04832 q^{13} +(2.70896 - 2.76795i) q^{15} +(3.15456 + 1.82129i) q^{17} +(3.68634 - 2.12831i) q^{19} +(-3.61903 + 2.81116i) q^{21} +(-2.75984 - 4.78018i) q^{23} +(3.54685 - 3.52418i) q^{25} +(1.80896 - 4.87110i) q^{27} -7.12076i q^{29} +(7.11211 + 4.10618i) q^{31} +(-5.45696 - 0.649843i) q^{33} +(-4.72241 + 3.56354i) q^{35} +(-2.21569 + 1.27923i) q^{37} +(4.85257 - 2.08071i) q^{39} +0.652545 q^{41} +9.40132i q^{43} +(2.42302 - 6.25532i) q^{45} +(-7.25360 + 4.18787i) q^{47} +(6.10686 - 3.42144i) q^{49} +(6.26486 + 0.746050i) q^{51} +(-5.86407 + 10.1569i) q^{53} +(-7.03250 - 0.937318i) q^{55} +(4.41550 - 5.90423i) q^{57} +(0.725991 - 1.25745i) q^{59} +(-8.46753 + 4.88873i) q^{61} +(-3.84225 + 6.94529i) q^{63} +(6.30158 - 2.59837i) q^{65} +(-8.85778 - 5.11404i) q^{67} +(-7.65618 - 5.72569i) q^{69} -7.34623i q^{71} +(-3.14081 + 5.44005i) q^{73} +(3.24066 - 8.03107i) q^{75} +(8.09431 + 2.22497i) q^{77} +(3.17806 + 5.50456i) q^{79} +(-0.445242 - 8.98898i) q^{81} +0.397748i q^{83} +(8.07364 + 1.07609i) q^{85} +(-4.86045 - 11.3354i) q^{87} +(3.15120 + 5.45804i) q^{89} +(-7.80361 + 2.03707i) q^{91} +(14.1244 + 1.68201i) q^{93} +(5.80635 - 7.54192i) q^{95} +17.1688 q^{97} +(-9.13041 + 2.69031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 3 q^{3} + 3 q^{5} - q^{9}+O(q^{10}) \) 48 * q + 3 * q^3 + 3 * q^5 - q^9	\( 48 q + 3 q^{3} + 3 q^{5} - q^{9} + 6 q^{15} + 5 q^{21} + 2 q^{23} + q^{25} + 6 q^{31} + 24 q^{33} - 4 q^{35} + 2 q^{39} - 21 q^{45} + 12 q^{51} - 6 q^{53} + 20 q^{57} + 18 q^{61} - 26 q^{63} + 10 q^{65} - 51 q^{75} + 2 q^{77} + 2 q^{79} - 9 q^{81} - 15 q^{87} + 24 q^{91} + 8 q^{93} + 6 q^{95} - 12 q^{99}+O(q^{100}) \) 48 * q + 3 * q^3 + 3 * q^5 - q^9 + 6 * q^15 + 5 * q^21 + 2 * q^23 + q^25 + 6 * q^31 + 24 * q^33 - 4 * q^35 + 2 * q^39 - 21 * q^45 + 12 * q^51 - 6 * q^53 + 20 * q^57 + 18 * q^61 - 26 * q^63 + 10 * q^65 - 51 * q^75 + 2 * q^77 + 2 * q^79 - 9 * q^81 - 15 * q^87 + 24 * q^91 + 8 * q^93 + 6 * q^95 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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