LMFDB - Embedded newform 840.2.da.a.89.13

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			89.13
Character	$\chi$	$=$	840.89
Dual form			840.2.da.a.689.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.204814 + 1.71990i) q^{3} +(-2.06723 - 0.852393i) q^{5} +(-2.55997 - 0.668258i) q^{7} +(-2.91610 - 0.704519i) q^{9} +O(q^{10})$	\(q+(-0.204814 + 1.71990i) q^{3} +(-2.06723 - 0.852393i) q^{5} +(-2.55997 - 0.668258i) q^{7} +(-2.91610 - 0.704519i) q^{9} +(2.74776 - 1.58642i) q^{11} +3.04832 q^{13} +(1.88943 - 3.38084i) q^{15} +(-3.15456 + 1.82129i) q^{17} +(3.68634 + 2.12831i) q^{19} +(1.67365 - 4.26602i) q^{21} +(2.75984 - 4.78018i) q^{23} +(3.54685 + 3.52418i) q^{25} +(1.80896 - 4.87110i) q^{27} -7.12076i q^{29} +(7.11211 - 4.10618i) q^{31} +(2.16570 + 5.05079i) q^{33} +(4.72241 + 3.56354i) q^{35} +(-2.21569 - 1.27923i) q^{37} +(-0.624340 + 5.24281i) q^{39} -0.652545 q^{41} -9.40132i q^{43} +(5.42772 + 3.94207i) q^{45} +(7.25360 + 4.18787i) q^{47} +(6.10686 + 3.42144i) q^{49} +(-2.48633 - 5.79855i) q^{51} +(5.86407 + 10.1569i) q^{53} +(-7.03250 + 0.937318i) q^{55} +(-4.41550 + 5.90423i) q^{57} +(-0.725991 - 1.25745i) q^{59} +(-8.46753 - 4.88873i) q^{61} +(6.99433 + 3.75225i) q^{63} +(-6.30158 - 2.59837i) q^{65} +(-8.85778 + 5.11404i) q^{67} +(7.65618 + 5.72569i) q^{69} -7.34623i q^{71} +(-3.14081 - 5.44005i) q^{73} +(-6.78768 + 5.37842i) q^{75} +(-8.09431 + 2.22497i) q^{77} +(3.17806 - 5.50456i) q^{79} +(8.00731 + 4.10890i) q^{81} +0.397748i q^{83} +(8.07364 - 1.07609i) q^{85} +(12.2470 + 1.45843i) q^{87} +(-3.15120 + 5.45804i) q^{89} +(-7.80361 - 2.03707i) q^{91} +(5.60555 + 13.0731i) q^{93} +(-5.80635 - 7.54192i) q^{95} +17.1688 q^{97} +(-9.13041 + 2.69031i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 14 q^{15} + 5 q^{21} - 2 q^{23} + q^{25} + 6 q^{31} - 24 q^{33} + 4 q^{35} + 2 q^{39} - 3 q^{45} + 12 q^{51} + 6 q^{53} - 20 q^{57} + 18 q^{61} + 26 q^{63} - 10 q^{65} - 3 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 - 14 * q^15 + 5 * q^21 - 2 * q^23 + q^25 + 6 * q^31 - 24 * q^33 + 4 * q^35 + 2 * q^39 - 3 * q^45 + 12 * q^51 + 6 * q^53 - 20 * q^57 + 18 * q^61 + 26 * q^63 - 10 * q^65 - 3 * 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 $\left(\mathbb{Z}/840\mathbb{Z}\right)^\times$.

$n$	$241$	$281$	$337$	$421$	$631$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$	$1$

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
$3$	−0.204814	+	1.71990i	−0.118249	+	0.992984i
$3$	−0.204814	+	1.71990i	−0.118249	+	0.992984i
$4$		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
$9$	−2.91610	−	0.704519i	−0.972034	−	0.234840i
$10$		0			0
$11$	2.74776	−	1.58642i	0.828481	−	0.478324i	−0.0248513	−	0.999691i	$-0.507911\pi$
$11$	2.74776	−	1.58642i	0.828481	−	0.478324i	0.853332	+	0.521367i	$0.174578\pi$
$12$		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
$15$	1.88943	−	3.38084i	0.487848	−	0.872929i
$16$		0			0
$17$	−3.15456	+	1.82129i	−0.765093	+	0.441727i	−0.831121	−	0.556091i	$-0.812301\pi$
$17$	−3.15456	+	1.82129i	−0.765093	+	0.441727i	0.0660282	+	0.997818i	$0.478967\pi$
$18$		0			0
$19$	3.68634	+	2.12831i	0.845705	+	0.488268i	0.859199	−	0.511641i	$-0.170962\pi$
$19$	3.68634	+	2.12831i	0.845705	+	0.488268i	−0.0134942	+	0.999909i	$0.504295\pi$
$20$		0			0
$21$	1.67365	−	4.26602i	0.365221	−	0.930921i
$22$		0			0
$23$	2.75984	−	4.78018i	0.575466	−	0.996737i	−0.420524	−	0.907281i	$-0.638154\pi$
$23$	2.75984	−	4.78018i	0.575466	−	0.996737i	0.995991	−	0.0894559i	$-0.0285128\pi$
$24$		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	0.301008	−	0.953622i	$-0.402677\pi$
$31$	7.11211	−	4.10618i	1.27737	−	0.737491i	0.976364	+	0.216131i	$0.0693437\pi$
$32$		0			0
$33$	2.16570	+	5.05079i	0.377000	+	0.879230i
$34$		0			0
$35$	4.72241	+	3.56354i	0.798234	+	0.602348i
$36$		0			0
$37$	−2.21569	−	1.27923i	−0.364257	−	0.210304i	0.306689	−	0.951810i	$-0.400779\pi$
$37$	−2.21569	−	1.27923i	−0.364257	−	0.210304i	−0.670947	+	0.741506i	$0.734112\pi$
$38$		0			0
$39$	−0.624340	+	5.24281i	−0.0999744	+	0.839521i
$40$		0			0
$41$	−0.652545			−0.101910			−0.0509552	−	0.998701i	$-0.516227\pi$
$41$	−0.652545			−0.101910			−0.0509552	+	0.998701i	$0.516227\pi$
$42$		0			0
$43$		−	9.40132i		−	1.43369i	−0.697234	−	0.716844i	$-0.745586\pi$
$43$		−	9.40132i		−	1.43369i	0.697234	−	0.716844i	$-0.254414\pi$
$44$		0			0
$45$	5.42772	+	3.94207i	0.809116	+	0.587649i
$46$		0			0
$47$	7.25360	+	4.18787i	1.05805	+	0.610863i	0.924891	−	0.380232i	$-0.124156\pi$
$47$	7.25360	+	4.18787i	1.05805	+	0.610863i	0.133155	+	0.991095i	$0.457489\pi$
$48$		0			0
$49$	6.10686	+	3.42144i	0.872409	+	0.488776i
$50$		0			0
$51$	−2.48633	−	5.79855i	−0.348156	−	0.811959i
$52$		0			0
$53$	5.86407	+	10.1569i	0.805492	+	1.39515i	0.915958	+	0.401274i	$0.131432\pi$
$53$	5.86407	+	10.1569i	0.805492	+	1.39515i	−0.110466	+	0.993880i	$0.535234\pi$
$54$		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	$-0.196797\pi$
$59$	−0.725991	−	1.25745i	−0.0945159	−	0.163706i	−0.909406	+	0.415908i	$0.863464\pi$
$60$		0			0
$61$	−8.46753	−	4.88873i	−1.08416	−	0.625938i	−0.152142	−	0.988359i	$-0.548617\pi$
$61$	−8.46753	−	4.88873i	−1.08416	−	0.625938i	−0.932015	+	0.362421i	$0.881950\pi$
$62$		0			0
$63$	6.99433	+	3.75225i	0.881202	+	0.472739i
$64$		0			0
$65$	−6.30158	−	2.59837i	−0.781614	−	0.322288i
$66$		0			0
$67$	−8.85778	+	5.11404i	−1.08215	+	0.624779i	−0.931475	−	0.363804i	$-0.881478\pi$
$67$	−8.85778	+	5.11404i	−1.08215	+	0.624779i	−0.150674	+	0.988583i	$0.548144\pi$
$68$		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	0.621586	−	0.783346i	$-0.286489\pi$
$73$	−3.14081	−	5.44005i	−0.367604	−	0.636709i	−0.989190	+	0.146637i	$0.953155\pi$
$74$		0			0
$75$	−6.78768	+	5.37842i	−0.783773	+	0.621047i
$76$		0			0
$77$	−8.09431	+	2.22497i	−0.922433	+	0.253559i
$78$		0			0
$79$	3.17806	−	5.50456i	0.357559	−	0.619311i	−0.629993	−	0.776601i	$-0.716942\pi$
$79$	3.17806	−	5.50456i	0.357559	−	0.619311i	0.987553	+	0.157290i	$0.0502756\pi$
$80$		0			0
$81$	8.00731	+	4.10890i	0.889701	+	0.456544i
$82$		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
$87$	12.2470	+	1.45843i	1.31301	+	0.156360i
$88$		0			0
$89$	−3.15120	+	5.45804i	−0.334027	+	0.578551i	−0.983297	−	0.182006i	$-0.941741\pi$
$89$	−3.15120	+	5.45804i	−0.334027	+	0.578551i	0.649271	+	0.760557i	$0.275074\pi$
$90$		0			0
$91$	−7.80361	−	2.03707i	−0.818040	−	0.213542i
$92$		0			0
$93$	5.60555	+	13.0731i	0.581268	+	1.35562i
$94$		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	$-0.117112\pi$
$101$	1.55824	+	2.69896i	0.155051	+	0.268556i	−0.778027	+	0.628231i	$0.783779\pi$
$102$		0			0
$103$	4.33234	−	7.50383i	0.426878	−	0.739375i	−0.569716	−	0.821842i	$-0.692947\pi$
$103$	4.33234	−	7.50383i	0.426878	−	0.739375i	0.996594	+	0.0824672i	$0.0262800\pi$
$104$		0			0
$105$	−7.09614	+	7.39221i	−0.692513	+	0.721406i
$106$		0			0
$107$	2.81910	−	4.88283i	0.272533	−	0.472041i	−0.696977	−	0.717094i	$-0.745472\pi$
$107$	2.81910	−	4.88283i	0.272533	−	0.472041i	0.969510	+	0.245053i	$0.0788053\pi$
$108$		0			0
$109$	−5.50964	−	9.54298i	−0.527728	−	0.914052i	−0.999478	−	0.0323192i	$-0.989711\pi$
$109$	−5.50964	−	9.54298i	−0.527728	−	0.914052i	0.471750	−	0.881733i	$-0.343623\pi$
$110$		0			0
$111$	2.65395	−	3.54876i	0.251902	−	0.336833i
$112$		0			0
$113$	−0.884131			−0.0831721			−0.0415860	−	0.999135i	$-0.513241\pi$
$113$	−0.884131			−0.0831721			−0.0415860	+	0.999135i	$0.513241\pi$
$114$		0			0
$115$	−9.77981	+	7.52925i	−0.911972	+	0.702107i
$116$		0			0
$117$	−8.88922	−	2.14760i	−0.821809	−	0.198546i
$118$		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
$123$	0.133650	−	1.12231i	0.0120509	−	0.101195i
$124$		0			0
$125$	−4.32816	−	10.3086i	−0.387122	−	0.922028i
$126$		0			0
$127$		−	21.9000i		−	1.94331i	−0.236396	−	0.971657i	$-0.575966\pi$
$127$		−	21.9000i		−	1.94331i	0.236396	−	0.971657i	$-0.424034\pi$
$128$		0			0
$129$	16.1693	+	1.92552i	1.42363	+	0.169533i
$130$		0			0
$131$	−4.01734	+	6.95824i	−0.350997	+	0.607945i	−0.986424	−	0.164216i	$-0.947491\pi$
$131$	−4.01734	+	6.95824i	−0.350997	+	0.607945i	0.635427	+	0.772161i	$0.280824\pi$
$132$		0			0
$133$	−8.01466	−	7.91184i	−0.694959	−	0.686043i
$134$		0			0
$135$	−7.89163	+	8.52773i	−0.679203	+	0.733950i
$136$		0			0
$137$	−4.31600	−	7.47553i	−0.368741	−	0.638677i	0.620628	−	0.784105i	$-0.286878\pi$
$137$	−4.31600	−	7.47553i	−0.368741	−	0.638677i	−0.989369	+	0.145427i	$0.953544\pi$
$138$		0			0
$139$			4.29376i			0.364192i	0.983281	+	0.182096i	$0.0582882\pi$
$139$			4.29376i			0.364192i	−0.983281	+	0.182096i	$0.941712\pi$
$140$		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
$147$	−7.13529	+	9.80243i	−0.588509	+	0.808491i
$148$		0			0
$149$	−14.4601	−	8.34856i	−1.18462	−	0.683940i	−0.227541	−	0.973769i	$-0.573069\pi$
$149$	−14.4601	−	8.34856i	−1.18462	−	0.683940i	−0.957079	+	0.289828i	$0.906402\pi$
$150$		0			0
$151$	−0.351881	−	0.609476i	−0.0286357	−	0.0495984i	0.851352	−	0.524594i	$-0.175783\pi$
$151$	−0.351881	−	0.609476i	−0.0286357	−	0.0495984i	−0.879988	+	0.474996i	$0.842450\pi$
$152$		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	0.524562	−	0.851372i	$-0.324229\pi$
$157$	−5.95210	−	10.3093i	−0.475029	−	0.822774i	−0.999591	+	0.0285978i	$0.990896\pi$
$158$		0			0
$159$	−18.6698	+	8.00534i	−1.48061	+	0.634865i
$160$		0			0
$161$	−10.2595	+	10.3928i	−0.808561	+	0.819070i
$162$		0			0
$163$	−5.85283	−	3.37913i	−0.458429	−	0.264674i	0.252954	−	0.967478i	$-0.418598\pi$
$163$	−5.85283	−	3.37913i	−0.458429	−	0.264674i	−0.711383	+	0.702804i	$0.751931\pi$
$164$		0			0
$165$	−0.171737	−	12.2872i	−0.0133697	−	0.956554i
$166$		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
$171$	−9.25032	−	8.80347i	−0.707390	−	0.673218i
$172$		0			0
$173$	21.3044	+	12.3001i	1.61974	+	0.935158i	0.986986	+	0.160806i	$0.0514093\pi$
$173$	21.3044	+	12.3001i	1.61974	+	0.935158i	0.632755	+	0.774352i	$0.281924\pi$
$174$		0			0
$175$	−6.72476	−	11.3920i	−0.508344	−	0.861154i
$176$		0			0
$177$	2.31138	−	0.991086i	0.173734	−	0.0744946i
$178$		0			0
$179$	11.4366	−	6.60295i	0.854815	−	0.493528i	−0.00745752	−	0.999972i	$-0.502374\pi$
$179$	11.4366	−	6.60295i	0.854815	−	0.493528i	0.862273	+	0.506444i	$0.169040\pi$
$180$		0			0
$181$			2.40852i			0.179024i	0.995986	+	0.0895120i	$0.0285308\pi$
$181$			2.40852i			0.179024i	−0.995986	+	0.0895120i	$0.971469\pi$
$182$		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
$189$	−7.88603	+	11.2610i	−0.573624	+	0.819118i
$190$		0			0
$191$	21.0445	+	12.1501i	1.52273	+	0.879148i	0.999639	+	0.0268696i	$0.00855390\pi$
$191$	21.0445	+	12.1501i	1.52273	+	0.879148i	0.523089	+	0.852278i	$0.324779\pi$
$192$		0			0
$193$	13.4236	−	7.75013i	0.966253	−	0.557866i	0.0681609	−	0.997674i	$-0.478287\pi$
$193$	13.4236	−	7.75013i	0.966253	−	0.557866i	0.898092	+	0.439808i	$0.144954\pi$
$194$		0			0
$195$	5.75958	−	10.3059i	0.412452	−	0.738020i
$196$		0			0
$197$	−15.1239			−1.07753			−0.538767	−	0.842455i	$-0.681110\pi$
$197$	−15.1239			−1.07753			−0.538767	+	0.842455i	$0.681110\pi$
$198$		0			0
$199$	−19.3565	+	11.1755i	−1.37215	+	0.792211i	−0.991198	−	0.132385i	$-0.957737\pi$
$199$	−19.3565	+	11.1755i	−1.37215	+	0.792211i	−0.380951	+	0.924595i	$0.624403\pi$
$200$		0			0
$201$	−6.98143	−	16.2819i	−0.492432	−	1.14844i
$202$		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
$207$	−11.4157	+	11.9951i	−0.793446	+	0.833720i
$208$		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
$213$	12.6348	+	1.50461i	0.865720	+	0.103094i
$214$		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
$219$	9.99961	−	4.28768i	0.675711	−	0.289735i
$220$		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
$225$	−7.86013	−	12.7757i	−0.524009	−	0.851713i
$226$		0			0
$227$	−5.97779	+	3.45128i	−0.396760	+	0.229070i	−0.685085	−	0.728463i	$-0.740235\pi$
$227$	−5.97779	+	3.45128i	−0.396760	+	0.229070i	0.288325	+	0.957533i	$0.406902\pi$
$228$		0			0
$229$	−3.15289	−	1.82032i	−0.208349	−	0.120290i	0.392195	−	0.919882i	$-0.371716\pi$
$229$	−3.15289	−	1.82032i	−0.208349	−	0.120290i	−0.600544	+	0.799592i	$0.705049\pi$
$230$		0			0
$231$	−2.16890	−	14.3771i	−0.142703	−	0.945944i
$232$		0			0
$233$	0.525603	−	0.910371i	0.0344334	−	0.0596404i	−0.848295	−	0.529524i	$-0.822371\pi$
$233$	0.525603	−	0.910371i	0.0344334	−	0.0596404i	0.882729	+	0.469883i	$0.155704\pi$
$234$		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	−0.942099	−	0.335334i	$-0.891151\pi$
$241$	−17.4296	+	10.0630i	−1.12274	+	0.648215i	−0.180642	+	0.983549i	$0.557818\pi$
$242$		0			0
$243$	−8.70690	+	12.9302i	−0.558548	+	0.829472i
$244$		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
$249$	−0.684086	−	0.0814643i	−0.0433522	−	0.00516259i
$250$		0			0
$251$	−8.21881			−0.518767			−0.259383	−	0.965774i	$-0.583519\pi$
$251$	−8.21881			−0.518767			−0.259383	+	0.965774i	$0.583519\pi$
$252$		0			0
$253$		−	17.5131i		−	1.10104i
$254$		0			0
$255$	0.197163	+	14.1062i	0.0123468	+	0.883367i
$256$		0			0
$257$	10.2293	+	5.90590i	0.638087	+	0.368400i	0.783877	−	0.620916i	$-0.213239\pi$
$257$	10.2293	+	5.90590i	0.638087	+	0.368400i	−0.145790	+	0.989316i	$0.546572\pi$
$258$		0			0
$259$	4.81724	+	4.75544i	0.299329	+	0.295489i
$260$		0			0
$261$	−5.01671	+	20.7649i	−0.310527	+	1.28531i
$262$		0			0
$263$	14.1109	+	24.4407i	0.870113	+	1.50708i	0.861879	+	0.507114i	$0.169288\pi$
$263$	14.1109	+	24.4407i	0.870113	+	1.50708i	0.00823401	+	0.999966i	$0.497379\pi$
$264$		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	−0.999966	−	0.00822992i	$-0.997380\pi$
$269$	−8.31723	−	14.4059i	−0.507110	−	0.878341i	0.492856	−	0.870111i	$-0.335953\pi$
$270$		0			0
$271$	12.6459	+	7.30109i	0.768182	+	0.443510i	0.832226	−	0.554437i	$-0.187066\pi$
$271$	12.6459	+	7.30109i	0.768182	+	0.443510i	−0.0640439	+	0.997947i	$0.520400\pi$
$272$		0			0
$273$	5.10183	−	13.0042i	0.308777	−	0.787050i
$274$		0			0
$275$	15.3367	+	4.05680i	0.924840	+	0.244634i
$276$		0			0
$277$	−12.9793	+	7.49363i	−0.779853	+	0.450249i	−0.836378	−	0.548153i	$-0.815331\pi$
$277$	−12.9793	+	7.49363i	−0.779853	+	0.450249i	0.0565249	+	0.998401i	$0.481998\pi$
$278$		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	0.813566	+	0.581473i	$0.197523\pi$
$283$	15.3145	+	26.5255i	0.910353	+	1.57678i	0.0967878	+	0.995305i	$0.469143\pi$
$284$		0			0
$285$	14.1606	−	8.44164i	0.838799	−	0.500040i
$286$		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
$291$	−3.51641	+	29.5286i	−0.206135	+	1.73099i
$292$		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
$297$	−2.75703	−	16.2544i	−0.159979	−	0.943176i
$298$		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
$303$	−4.96108	+	2.12724i	−0.285007	+	0.122207i
$304$		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	$-0.234990\pi$
$311$	−3.75631	−	6.50613i	−0.213001	−	0.368929i	−0.952652	+	0.304062i	$0.901657\pi$
$312$		0			0
$313$	0.351263	−	0.608406i	0.0198546	−	0.0343891i	−0.855927	−	0.517096i	$-0.827013\pi$
$313$	0.351263	−	0.608406i	0.0198546	−	0.0343891i	0.875782	+	0.482707i	$0.160346\pi$
$314$		0			0
$315$	−11.2605	−	13.7187i	−0.634455	−	0.772960i
$316$		0			0
$317$	8.03766	−	13.9216i	0.451440	−	0.781917i	−0.547036	−	0.837109i	$-0.684244\pi$
$317$	8.03766	−	13.9216i	0.451440	−	0.781917i	0.998476	+	0.0551923i	$0.0175772\pi$
$318$		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
$327$	17.5414	−	7.52149i	0.970042	−	0.415939i
$328$		0			0
$329$	−15.7704	−	15.5681i	−0.869451	−	0.858296i
$330$		0			0
$331$	15.2517	−	26.4168i	0.838311	−	1.45200i	−0.0529954	−	0.998595i	$-0.516877\pi$
$331$	15.2517	−	26.4168i	0.838311	−	1.45200i	0.891306	−	0.453402i	$-0.149790\pi$
$332$		0			0
$333$	5.55994	+	5.29136i	0.304683	+	0.289965i
$334$		0			0
$335$	22.6702	−	3.02157i	1.23861	−	0.165086i
$336$		0			0
$337$		−	3.18432i		−	0.173461i	−0.996232	−	0.0867306i	$-0.972358\pi$
$337$		−	3.18432i		−	0.173461i	0.996232	−	0.0867306i	$-0.0276419\pi$
$338$		0			0
$339$	0.181083	−	1.52062i	0.00983505	−	0.0825885i
$340$		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
$345$	−10.9465	−	18.3624i	−0.589340	−	0.988597i
$346$		0			0
$347$	−6.38275	−	11.0552i	−0.342644	−	0.593476i	0.642279	−	0.766471i	$-0.277989\pi$
$347$	−6.38275	−	11.0552i	−0.342644	−	0.593476i	−0.984923	+	0.172994i	$0.944656\pi$
$348$		0			0
$349$			0.203714i			0.0109046i	0.999985	+	0.00545228i	$0.00173552\pi$
$349$			0.203714i			0.0109046i	−0.999985	+	0.00545228i	$0.998264\pi$
$350$		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	$-0.651404\pi$
$353$	1.55975	−	0.900520i	0.0830169	−	0.0479298i	0.540934	+	0.841065i	$0.318071\pi$
$354$		0			0
$355$	−6.26187	+	15.1863i	−0.332346	+	0.806006i
$356$		0			0
$357$	2.49000	+	16.5056i	0.131785	+	0.873569i
$358$		0			0
$359$	2.86938	+	1.65664i	0.151440	+	0.0874340i	0.573805	−	0.818992i	$-0.305467\pi$
$359$	2.86938	+	1.65664i	0.151440	+	0.0874340i	−0.422365	+	0.906426i	$0.638800\pi$
$360$		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	0.804858	−	0.593468i	$-0.202242\pi$
$367$	−2.13660	−	3.70069i	−0.111529	−	0.193175i	−0.916387	+	0.400293i	$0.868908\pi$
$368$		0			0
$369$	1.90289	+	0.459731i	0.0990604	+	0.0239326i
$370$		0			0
$371$	−8.22443	−	29.9200i	−0.426991	−	1.55337i
$372$		0			0
$373$	−14.6641	−	8.46634i	−0.759280	−	0.438370i	0.0697574	−	0.997564i	$-0.477777\pi$
$373$	−14.6641	−	8.46634i	−0.759280	−	0.438370i	−0.829037	+	0.559194i	$0.811111\pi$
$374$		0			0
$375$	18.6162	−	5.33265i	0.961336	−	0.275377i
$376$		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
$381$	37.6658	+	4.48544i	1.92968	+	0.229796i
$382$		0			0
$383$	13.5710	+	7.83524i	0.693447	+	0.400362i	0.804902	−	0.593407i	$-0.202218\pi$
$383$	13.5710	+	7.83524i	0.693447	+	0.400362i	−0.111455	+	0.993769i	$0.535551\pi$
$384$		0			0
$385$	18.6293	+	2.30002i	0.949439	+	0.117220i
$386$		0			0
$387$	−6.62341	+	27.4152i	−0.336687	+	1.39359i
$388$		0			0
$389$	0.554210	−	0.319974i	0.0280996	−	0.0162233i	−0.485884	−	0.874023i	$-0.661502\pi$
$389$	0.554210	−	0.319974i	0.0280996	−	0.0162233i	0.513984	+	0.857800i	$0.328169\pi$
$390$		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	−0.983175	−	0.182666i	$-0.941527\pi$
$397$	−6.64284	+	11.5057i	−0.333395	+	0.577456i	0.649781	+	0.760122i	$0.274861\pi$
$398$		0			0
$399$	15.2491	−	12.1639i	0.763408	−	0.608959i
$400$		0			0
$401$	10.4362	+	6.02536i	0.521160	+	0.300892i	0.737409	−	0.675446i	$-0.236049\pi$
$401$	10.4362	+	6.02536i	0.521160	+	0.300892i	−0.216249	+	0.976338i	$0.569382\pi$
$402$		0			0
$403$	21.6800	−	12.5170i	1.07996	−	0.623514i
$404$		0			0
$405$	−13.0505	−	15.3194i	−0.648485	−	0.761227i
$406$		0			0
$407$	−8.11758			−0.402374
$408$		0			0
$409$	2.24844	−	1.29814i	0.111178	−	0.0641888i	−0.443380	−	0.896334i	$-0.646221\pi$
$409$	2.24844	−	1.29814i	0.111178	−	0.0641888i	0.554558	+	0.832145i	$0.312887\pi$
$410$		0			0
$411$	13.7411	−	5.89199i	0.677800	−	0.290630i
$412$		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
$417$	−7.38483	−	0.879423i	−0.361637	−	0.0430655i
$418$		0			0
$419$	−2.04634			−0.0999703			−0.0499851	−	0.998750i	$-0.515917\pi$
$419$	−2.04634			−0.0999703			−0.0499851	+	0.998750i	$0.515917\pi$
$420$		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
$423$	−18.2018	−	17.3226i	−0.885002	−	0.842251i
$424$		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
$429$	6.60176	+	15.3964i	0.318736	+	0.743347i
$430$		0			0
$431$	−18.2561	+	10.5402i	−0.879367	+	0.507703i	−0.870450	−	0.492257i	$-0.836172\pi$
$431$	−18.2561	+	10.5402i	−0.879367	+	0.507703i	−0.00891735	+	0.999960i	$0.502839\pi$
$432$		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
$435$	−24.0741	−	13.4542i	−1.15427	−	0.645077i
$436$		0			0
$437$	20.3474	−	11.7476i	0.973350	−	0.561964i
$438$		0			0
$439$	24.3862	+	14.0794i	1.16389	+	0.671973i	0.952234	−	0.305371i	$-0.0987804\pi$
$439$	24.3862	+	14.0794i	1.16389	+	0.671973i	0.211658	+	0.977344i	$0.432114\pi$
$440$		0			0
$441$	−15.3978	−	14.2797i	−0.733227	−	0.679984i
$442$		0			0
$443$	2.85933	−	4.95251i	0.135851	−	0.235301i	−0.790071	−	0.613015i	$-0.789956\pi$
$443$	2.85933	−	4.95251i	0.135851	−	0.235301i	0.925922	+	0.377714i	$0.123290\pi$
$444$		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
$453$	1.12031	−	0.480370i	0.0526366	−	0.0225698i
$454$		0			0
$455$	14.3954	+	10.8628i	0.674869	+	0.509257i
$456$		0			0
$457$	33.9899	+	19.6241i	1.58998	+	0.917976i	0.993309	+	0.115490i	$0.0368439\pi$
$457$	33.9899	+	19.6241i	1.58998	+	0.917976i	0.596672	+	0.802485i	$0.296489\pi$
$458$		0			0
$459$	3.16520	+	18.6608i	0.147739	+	0.871013i
$460$		0			0
$461$	−20.3916			−0.949733			−0.474867	−	0.880058i	$-0.657504\pi$
$461$	−20.3916			−0.949733			−0.474867	+	0.880058i	$0.657504\pi$
$462$		0			0
$463$			26.4790i			1.23058i	0.788299	+	0.615292i	$0.210962\pi$
$463$			26.4790i			1.23058i	−0.788299	+	0.615292i	$0.789038\pi$
$464$		0			0
$465$	−0.444513	−	31.8032i	−0.0206138	−	1.47484i
$466$		0			0
$467$	−22.5176	−	13.0005i	−1.04199	−	0.601593i	−0.121594	−	0.992580i	$-0.538800\pi$
$467$	−22.5176	−	13.0005i	−1.04199	−	0.601593i	−0.920396	+	0.390987i	$0.872134\pi$
$468$		0			0
$469$	26.0931	−	7.17250i	1.20487	−	0.331195i
$470$		0			0
$471$	18.9501	−	8.12551i	0.873174	−	0.374404i
$472$		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	−0.995385	−	0.0959586i	$-0.969408\pi$
$479$	−12.7113	−	22.0167i	−0.580795	−	1.00597i	0.414590	−	0.910008i	$-0.363925\pi$
$480$		0			0
$481$	−6.75414	−	3.89951i	−0.307962	−	0.177802i
$482$		0			0
$483$	−15.7733	−	19.7739i	−0.717711	−	0.899743i
$484$		0			0
$485$	−35.4917	−	14.6345i	−1.61160	−	0.664520i
$486$		0			0
$487$	−28.7329	+	16.5890i	−1.30201	+	0.751717i	−0.980749	−	0.195273i	$-0.937441\pi$
$487$	−28.7329	+	16.5890i	−1.30201	+	0.751717i	−0.321263	+	0.946990i	$0.604107\pi$
$488$		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
$495$	21.1678	+	2.22121i	0.951424	+	0.0998361i
$496$		0			0
$497$	−4.90917	+	18.8061i	−0.220207	+	0.843569i
$498$		0			0
$499$	−12.8499	+	22.2567i	−0.575240	+	0.996345i	0.420775	+	0.907165i	$0.361758\pi$
$499$	−12.8499	+	22.2567i	−0.575240	+	0.996345i	−0.996016	+	0.0891801i	$0.971575\pi$
$500$		0			0
$501$	2.64211	+	0.314635i	0.118041	+	0.0140569i
$502$		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
$507$	0.759395	−	6.37691i	0.0337259	−	0.283209i
$508$		0			0
$509$	19.5947	−	33.9390i	0.868519	−	1.50432i	0.00500861	−	0.999987i	$-0.498406\pi$
$509$	19.5947	−	33.9390i	0.868519	−	1.50432i	0.863510	−	0.504331i	$-0.168261\pi$
$510$		0			0
$511$	4.40502	+	16.0252i	0.194867	+	0.708914i
$512$		0			0
$513$	17.0357	−	14.1065i	0.752144	−	0.622819i
$514$		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	0.761714	+	0.647913i	$0.224358\pi$
$521$	21.5008	+	37.2405i	0.941966	+	1.63153i	0.180252	+	0.983620i	$0.442309\pi$
$522$		0			0
$523$	−18.9905	+	32.8926i	−0.830398	+	1.43829i	0.0673245	+	0.997731i	$0.478554\pi$
$523$	−18.9905	+	32.8926i	−0.830398	+	1.43829i	−0.897723	+	0.440561i	$0.854780\pi$
$524$		0			0
$525$	20.9704	−	9.23267i	0.915223	−	0.402947i
$526$		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
$537$	9.01402	+	21.0222i	0.388984	+	0.907177i
$538$		0			0
$539$	22.2080	−	0.286768i	0.956568	−	0.0123520i
$540$		0			0
$541$	3.12618	−	5.41470i	0.134405	−	0.232796i	−0.790965	−	0.611861i	$-0.790421\pi$
$541$	3.12618	−	5.41470i	0.134405	−	0.232796i	0.925370	+	0.379065i	$0.123754\pi$
$542$		0			0
$543$	−4.14241	−	0.493299i	−0.177768	−	0.0211695i
$544$		0			0
$545$	3.25531	+	24.4239i	0.139442	+	1.04620i
$546$		0			0
$547$			0.731095i			0.0312594i	0.999878	+	0.0156297i	$0.00497529\pi$
$547$			0.731095i			0.0312594i	−0.999878	+	0.0156297i	$0.995025\pi$
$548$		0			0
$549$	21.2480	+	20.2216i	0.906842	+	0.863036i
$550$		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
$555$	−8.51125	+	5.07388i	−0.361283	+	0.215374i
$556$		0			0
$557$	2.75616	+	4.77382i	0.116782	+	0.202273i	0.918491	−	0.395442i	$-0.129409\pi$
$557$	2.75616	+	4.77382i	0.116782	+	0.202273i	−0.801708	+	0.597715i	$0.796075\pi$
$558$		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	$-0.629709\pi$
$563$	4.76090	−	2.74871i	0.200648	−	0.115844i	0.596958	+	0.802273i	$0.296376\pi$
$564$		0			0
$565$	1.82770	+	0.753627i	0.0768919	+	0.0317053i
$566$		0			0
$567$	−17.7526	−	15.8696i	−0.745541	−	0.666460i
$568$		0			0
$569$	−4.98266	−	2.87674i	−0.208884	−	0.120599i	0.391909	−	0.920004i	$-0.371815\pi$
$569$	−4.98266	−	2.87674i	−0.208884	−	0.120599i	−0.600793	+	0.799405i	$0.705148\pi$
$570$		0			0
$571$	−8.32468	−	14.4188i	−0.348377	−	0.603407i	0.637584	−	0.770381i	$-0.279934\pi$
$571$	−8.32468	−	14.4188i	−0.348377	−	0.603407i	−0.985961	+	0.166974i	$0.946600\pi$
$572$		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	0.525225	−	0.850964i	$-0.323981\pi$
$577$	−11.3941	−	19.7352i	−0.474344	−	0.821588i	−0.999568	+	0.0293759i	$0.990648\pi$
$578$		0			0
$579$	10.5801	+	24.6746i	0.439693	+	1.02544i
$580$		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
$585$	16.5454	+	12.0167i	0.684070	+	0.496829i
$586$		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
$591$	3.09759	−	26.0116i	0.127418	−	1.06997i
$592$		0			0
$593$	0.729403	+	0.421121i	0.0299530	+	0.0172934i	0.514902	−	0.857249i	$-0.327828\pi$
$593$	0.729403	+	0.421121i	0.0299530	+	0.0172934i	−0.484949	+	0.874543i	$0.661162\pi$
$594$		0			0
$595$	−21.3874	−	2.64053i	−0.876796	−	0.108251i
$596$		0			0
$597$	−15.2562	−	35.5802i	−0.624397	−	1.45620i
$598$		0			0
$599$	2.43748	−	1.40728i	0.0995929	−	0.0575000i	−0.449376	−	0.893343i	$-0.648354\pi$
$599$	2.43748	−	1.40728i	0.0995929	−	0.0575000i	0.548969	+	0.835843i	$0.315020\pi$
$600$		0			0
$601$		−	15.2185i		−	0.620775i	−0.950610	−	0.310388i	$-0.899541\pi$
$601$		−	15.2185i		−	0.620775i	0.950610	−	0.310388i	$-0.100459\pi$
$602$		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	−0.722561	−	0.691307i	$-0.757035\pi$
$607$	5.84912	−	10.1310i	0.237409	−	0.411204i	0.959970	+	0.280103i	$0.0903686\pi$
$608$		0			0
$609$	−30.3773	−	11.9177i	−1.23095	−	0.482929i
$610$		0			0
$611$	22.1113	+	12.7660i	0.894528	+	0.516456i
$612$		0			0
$613$	−35.0567	+	20.2400i	−1.41593	+	0.817486i	−0.995938	−	0.0900434i	$-0.971299\pi$
$613$	−35.0567	+	20.2400i	−1.41593	+	0.817486i	−0.419989	+	0.907529i	$0.637966\pi$
$614$		0			0
$615$	−1.23294	+	2.20615i	−0.0497168	+	0.0889606i
$616$		0			0
$617$	48.3959			1.94835			0.974174	−	0.225801i	$-0.0724998\pi$
$617$	48.3959			1.94835			0.974174	+	0.225801i	$0.0724998\pi$
$618$		0			0
$619$	−0.952353	+	0.549841i	−0.0382783	+	0.0221000i	−0.519017	−	0.854764i	$-0.673702\pi$
$619$	−0.952353	+	0.549841i	−0.0382783	+	0.0221000i	0.480739	+	0.876864i	$0.340369\pi$
$620$		0			0
$621$	−18.2923	−	22.0906i	−0.734046	−	0.886467i
$622$		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
$627$	−2.76614	+	23.2282i	−0.110469	+	0.927647i
$628$		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
$633$	−3.25565	+	27.3389i	−0.129400	+	1.08662i
$634$		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
$639$	−5.17556	+	21.4224i	−0.204742	+	0.847455i
$640$		0			0
$641$	−31.5677	+	18.2256i	−1.24685	+	0.719870i	−0.970480	−	0.241181i	$-0.922465\pi$
$641$	−31.5677	+	18.2256i	−1.24685	+	0.719870i	−0.276371	+	0.961051i	$0.589132\pi$
$642$		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
$645$	−31.7843	−	17.7631i	−1.25151	−	0.699421i
$646$		0			0
$647$	30.1254	−	17.3929i	1.18435	−	0.683785i	0.227334	−	0.973817i	$-0.426999\pi$
$647$	30.1254	−	17.3929i	1.18435	−	0.683785i	0.957017	+	0.290032i	$0.0936659\pi$
$648$		0			0
$649$	−3.98970	−	2.30345i	−0.156609	−	0.0904184i
$650$		0			0
$651$	−5.61382	−	37.2127i	−0.220023	−	1.45848i
$652$		0			0
$653$	−13.7213	+	23.7661i	−0.536958	+	0.930038i	0.462108	+	0.886824i	$0.347093\pi$
$653$	−13.7213	+	23.7661i	−0.536958	+	0.930038i	−0.999066	+	0.0432146i	$0.986240\pi$
$654$		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	−0.982870	−	0.184302i	$-0.940997\pi$
$661$	−33.8007	+	19.5148i	−1.31469	+	0.759039i	−0.331824	+	0.943341i	$0.607664\pi$
$662$		0			0
$663$	−7.57913	−	17.6759i	−0.294349	−	0.686473i
$664$		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
$669$	−3.93150	+	33.0142i	−0.152000	+	1.27640i
$670$		0			0
$671$	−31.0223			−1.19760
$672$		0			0
$673$		−	0.880844i		−	0.0339540i	−0.999856	−	0.0169770i	$-0.994596\pi$
$673$		−	0.880844i		−	0.0339540i	0.999856	−	0.0169770i	$-0.00540421\pi$
$674$		0			0
$675$	23.5828	−	10.9020i	0.907701	−	0.419618i
$676$		0			0
$677$	−1.33147	−	0.768723i	−0.0511724	−	0.0295444i	0.474196	−	0.880420i	$-0.342739\pi$
$677$	−1.33147	−	0.768723i	−0.0511724	−	0.0295444i	−0.525368	+	0.850875i	$0.676072\pi$
$678$		0			0
$679$	−43.9515	−	11.4732i	−1.68670	−	0.440300i
$680$		0			0
$681$	−4.71152	−	10.9881i	−0.180546	−	0.421064i
$682$		0			0
$683$	−14.5363	−	25.1776i	−0.556215	−	0.963393i	−0.997808	−	0.0661777i	$-0.978920\pi$
$683$	−14.5363	−	25.1776i	−0.556215	−	0.963393i	0.441592	−	0.897216i	$-0.354414\pi$
$684$		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	−0.430892	−	0.902403i	$-0.641801\pi$
$691$	−37.5335	−	21.6700i	−1.42784	−	0.824365i	−0.996950	+	0.0780383i	$0.975134\pi$
$692$		0			0
$693$	25.1714	−	0.785647i	0.956182	−	0.0298443i
$694$		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
$705$	27.8637	−	16.6106i	1.04941	−	0.625591i
$706$		0			0
$707$	−2.18545	−	7.95055i	−0.0821924	−	0.299011i
$708$		0			0
$709$	−5.64504	+	9.77749i	−0.212004	+	0.367201i	−0.952342	−	0.305034i	$-0.901332\pi$
$709$	−5.64504	+	9.77749i	−0.212004	+	0.367201i	0.740338	+	0.672235i	$0.234666\pi$
$710$		0			0
$711$	−13.1456	+	13.8128i	−0.492999	+	0.518022i
$712$		0			0
$713$		−	45.3296i		−	1.69761i
$714$		0			0
$715$	−21.4373	+	2.85725i	−0.801711	+	0.106855i
$716$		0			0
$717$	−11.2532	−	1.34008i	−0.420257	−	0.0500463i
$718$		0			0
$719$	−14.0562	+	24.3461i	−0.524208	+	0.907956i	0.475394	+	0.879773i	$0.342305\pi$
$719$	−14.0562	+	24.3461i	−0.524208	+	0.907956i	−0.999603	+	0.0281828i	$0.991028\pi$
$720$		0			0
$721$	−16.1051	+	16.3144i	−0.599787	+	0.607582i
$722$		0			0
$723$	−13.7375	−	32.0383i	−0.510904	−	1.19152i
$724$		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	−0.653533	−	0.756898i	$-0.726714\pi$
$733$	8.89992	−	15.4151i	0.328726	−	0.569370i	0.982259	+	0.187528i	$0.0600474\pi$
$734$		0			0
$735$	23.1058	−	14.1818i	0.852270	−	0.523102i
$736$		0			0
$737$	−16.2260	+	28.1043i	−0.597694	+	1.03524i
$738$		0			0
$739$	3.15829	+	5.47033i	0.116180	+	0.201229i	0.918251	−	0.395999i	$-0.129602\pi$
$739$	3.15829	+	5.47033i	0.116180	+	0.201229i	−0.802071	+	0.597229i	$0.796268\pi$
$740$		0			0
$741$	−13.4599	+	17.9980i	−0.494460	+	0.661173i
$742$		0			0
$743$	−50.3390			−1.84676			−0.923379	−	0.383890i	$-0.874584\pi$
$743$	−50.3390			−1.84676			−0.923379	+	0.383890i	$0.874584\pi$
$744$		0			0
$745$	22.7761	+	29.5841i	0.834452	+	1.08388i
$746$		0			0
$747$	0.280221	−	1.15987i	0.0102527	−	0.0424375i
$748$		0			0
$749$	−10.4798	+	10.6160i	−0.382923	+	0.387900i
$750$		0			0
$751$	23.0281	−	39.8858i	0.840306	−	1.45545i	−0.0493301	−	0.998783i	$-0.515709\pi$
$751$	23.0281	−	39.8858i	0.840306	−	1.45545i	0.889636	−	0.456670i	$-0.150958\pi$
$752$		0			0
$753$	1.68333	−	14.1355i	0.0613439	−	0.515127i
$754$		0			0
$755$	0.207905	+	1.55987i	0.00756643	+	0.0567693i
$756$		0			0
$757$			49.4487i			1.79724i	0.438725	+	0.898621i	$0.355430\pi$
$757$			49.4487i			1.79724i	−0.438725	+	0.898621i	$0.644570\pi$
$758$		0			0
$759$	30.1207	+	3.58692i	1.09331	+	0.130197i
$760$		0			0
$761$	16.4488	−	28.4901i	0.596268	−	1.03277i	−0.397099	−	0.917776i	$-0.629983\pi$
$761$	16.4488	−	28.4901i	0.596268	−	1.03277i	0.993367	−	0.114990i	$-0.0366837\pi$
$762$		0			0
$763$	7.72733	+	28.1116i	0.279748	+	1.01771i
$764$		0			0
$765$	−24.3017	−	2.55006i	−0.878630	−	0.0921975i
$766$		0			0
$767$	−2.21305	−	3.83312i	−0.0799087	−	0.138406i
$768$		0			0
$769$		−	15.3215i		−	0.552507i	−0.961085	−	0.276254i	$-0.910907\pi$
$769$		−	15.3215i		−	0.552507i	0.961085	−	0.276254i	$-0.0890929\pi$
$770$		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	$-0.804410\pi$
$773$	−20.1944	+	11.6592i	−0.726342	+	0.419354i	0.0907407	+	0.995875i	$0.471077\pi$
$774$		0			0
$775$	39.6965	+	10.5003i	1.42594	+	0.377183i
$776$		0			0
$777$	−9.16551	+	7.31118i	−0.328811	+	0.262287i
$778$		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	−0.998304	−	0.0582094i	$-0.981461\pi$
$787$	−15.4172	−	26.7033i	−0.549563	−	0.951871i	0.448741	−	0.893662i	$-0.351872\pi$
$788$		0			0
$789$	−44.9257	+	19.2634i	−1.59940	+	0.685797i
$790$		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
$795$	45.4185	−	0.634813i	1.61083	−	0.0225145i
$796$		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
$801$	13.0345	−	13.6961i	0.460552	−	0.483929i
$802$		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
$807$	26.4801	−	11.3543i	0.932144	−	0.399689i
$808$		0			0
$809$	28.2278	−	16.2974i	0.992438	−	0.572985i	0.0864360	−	0.996257i	$-0.472452\pi$
$809$	28.2278	−	16.2974i	0.992438	−	0.572985i	0.906002	+	0.423273i	$0.139119\pi$
$810$		0			0
$811$		−	27.4529i		−	0.964003i	−0.876170	−	0.482001i	$-0.839910\pi$
$811$		−	27.4529i		−	0.964003i	0.876170	−	0.482001i	$-0.160090\pi$
$812$		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
$819$	21.3210	+	11.4381i	0.745015	+	0.399679i
$820$		0			0
$821$	19.3028	+	11.1445i	0.673671	+	0.388944i	0.797466	−	0.603364i	$-0.206173\pi$
$821$	19.3028	+	11.1445i	0.673671	+	0.388944i	−0.123795	+	0.992308i	$0.539507\pi$
$822$		0			0
$823$	5.11467	−	2.95296i	0.178286	−	0.102934i	−0.408201	−	0.912892i	$-0.633844\pi$
$823$	5.11467	−	2.95296i	0.178286	−	0.102934i	0.586487	+	0.809958i	$0.300510\pi$
$824$		0			0
$825$	−10.1185	+	25.5467i	−0.352280	+	0.889423i
$826$		0			0
$827$	0.636826			0.0221446			0.0110723	−	0.999939i	$-0.496476\pi$
$827$	0.636826			0.0221446			0.0110723	+	0.999939i	$0.496476\pi$
$828$		0			0
$829$	−31.3706	+	18.1118i	−1.08955	+	0.629050i	−0.933455	−	0.358693i	$-0.883222\pi$
$829$	−31.3706	+	18.1118i	−1.08955	+	0.629050i	−0.156090	+	0.987743i	$0.549889\pi$
$830$		0			0
$831$	−10.2299	−	23.8580i	−0.354872	−	0.827624i
$832$		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
$837$	−7.13610	−	42.0717i	−0.246660	−	1.45421i
$838$		0			0
$839$	−28.0342			−0.967848			−0.483924	−	0.875110i	$-0.660789\pi$
$839$	−28.0342			−0.967848			−0.483924	+	0.875110i	$0.660789\pi$
$840$		0			0
$841$	−21.7052			−0.748455
$842$		0			0
$843$	−40.1782	−	4.78462i	−1.38381	−	0.164791i
$844$		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
$849$	−48.7578	+	20.9066i	−1.67336	+	0.717513i
$850$		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
$855$	11.6185	+	26.0837i	0.397344	+	0.892043i
$856$		0			0
$857$	−48.7056	+	28.1202i	−1.66375	+	0.960567i	−0.692851	+	0.721080i	$0.743646\pi$
$857$	−48.7056	+	28.1202i	−1.66375	+	0.960567i	−0.970900	+	0.239487i	$0.923021\pi$
$858$		0			0
$859$	23.4146	+	13.5184i	0.798897	+	0.461243i	0.843085	−	0.537780i	$-0.180737\pi$
$859$	23.4146	+	13.5184i	0.798897	+	0.461243i	−0.0441884	+	0.999023i	$0.514070\pi$
$860$		0			0
$861$	−1.09213	+	2.78377i	−0.0372198	+	0.0948706i
$862$		0			0
$863$	6.85347	−	11.8706i	0.233295	−	0.404079i	−0.725481	−	0.688242i	$-0.758383\pi$
$863$	6.85347	−	11.8706i	0.233295	−	0.404079i	0.958776	+	0.284164i	$0.0917159\pi$
$864$		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
$873$	−50.0659	−	12.0957i	−1.69447	−	0.409378i
$874$		0			0
$875$	4.19116	+	29.2820i	0.141687	+	0.989912i
$876$		0			0
$877$	27.7508	+	16.0219i	0.937079	+	0.541023i	0.889043	−	0.457823i	$-0.151371\pi$
$877$	27.7508	+	16.0219i	0.937079	+	0.541023i	0.0480353	+	0.998846i	$0.484704\pi$
$878$		0			0
$879$	21.4152	+	2.55023i	0.722318	+	0.0860172i
$880$		0			0
$881$	58.9479			1.98601			0.993003	−	0.118088i	$-0.0376764\pi$
$881$	58.9479			1.98601			0.993003	+	0.118088i	$0.0376764\pi$
$882$		0			0
$883$			23.7884i			0.800544i	0.916396	+	0.400272i	$0.131084\pi$
$883$			23.7884i			0.800544i	−0.916396	+	0.400272i	$0.868916\pi$
$884$		0			0
$885$	−5.62295	+	0.0785919i	−0.189013	+	0.00264184i
$886$		0			0
$887$	−6.86422	−	3.96306i	−0.230478	−	0.133066i	0.380315	−	0.924857i	$-0.375816\pi$
$887$	−6.86422	−	3.96306i	−0.230478	−	0.133066i	−0.610793	+	0.791791i	$0.709149\pi$
$888$		0			0
$889$	−14.6349	+	56.0634i	−0.490838	+	1.88030i
$890$		0			0
$891$	28.5206	−	1.41268i	0.955476	−	0.0473266i
$892$		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
$903$	−40.1062	−	15.7345i	−1.33465	−	0.523613i
$904$		0			0
$905$	2.05301	−	4.97896i	0.0682443	−	0.165506i
$906$		0			0
$907$	31.1912	−	18.0083i	1.03569	−	0.597954i	0.117079	−	0.993123i	$-0.462647\pi$
$907$	31.1912	−	18.0083i	1.03569	−	0.597954i	0.918609	+	0.395168i	$0.129314\pi$
$908$		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
$915$	−32.5268	+	19.3905i	−1.07530	+	0.641029i
$916$		0			0
$917$	14.9342	−	15.1283i	0.493170	−	0.499579i
$918$		0			0
$919$	22.3186	−	38.6569i	0.736222	−	1.27517i	−0.217962	−	0.975957i	$-0.569941\pi$
$919$	22.3186	−	38.6569i	0.736222	−	1.27517i	0.954185	−	0.299218i	$-0.0967256\pi$
$920$		0			0
$921$	−2.15182	+	18.0696i	−0.0709048	+	0.595413i
$922$		0			0
$923$		−	22.3937i		−	0.737097i
$924$		0			0
$925$	−3.35049	−	12.3457i	−0.110164	−	0.405925i
$926$		0			0
$927$	−17.9201	+	18.8297i	−0.588575	+	0.618450i
$928$		0			0
$929$	−30.1915	+	52.2932i	−0.990551	+	1.71568i	−0.376502	+	0.926416i	$0.622873\pi$
$929$	−30.1915	+	52.2932i	−0.990551	+	1.71568i	−0.614049	+	0.789268i	$0.710460\pi$
$930$		0			0
$931$	15.2301	+	25.6099i	0.499147	+	0.839330i
$932$		0			0
$933$	11.9592	−	5.12793i	0.391527	−	0.167881i
$934$		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	−0.957718	−	0.287707i	$-0.907107\pi$
$941$	−22.3326	−	38.6812i	−0.728021	−	1.26097i	0.229697	−	0.973262i	$-0.426226\pi$
$942$		0			0
$943$	−1.80092	+	3.11929i	−0.0586460	+	0.101578i
$944$		0			0
$945$	25.9010	−	16.5571i	0.842561	−	0.538602i
$946$		0			0
$947$	12.4350	−	21.5381i	0.404084	−	0.699894i	−0.590131	−	0.807308i	$-0.700924\pi$
$947$	12.4350	−	21.5381i	0.404084	−	0.699894i	0.994214	+	0.107414i	$0.0342571\pi$
$948$		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	$-0.599072\pi$
$953$	−18.9078			−0.612484			−0.306242	+	0.951954i	$0.599072\pi$
$954$		0			0
$955$	−33.1472	−	43.0551i	−1.07262	−	1.39323i
$956$		0			0
$957$	35.9655	−	15.4214i	1.16260	−	0.498504i
$958$		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
$963$	−11.6608	+	12.2527i	−0.375765	+	0.394838i
$964$		0			0
$965$	−34.3558	+	4.57907i	−1.10595	+	0.147406i
$966$		0			0
$967$			0.439343i			0.0141283i	0.999975	+	0.00706415i	$0.00224861\pi$
$967$			0.439343i			0.0141283i	−0.999975	+	0.00706415i	$0.997751\pi$
$968$		0			0
$969$	3.17565	−	26.6671i	0.102017	−	0.856672i
$970$		0			0
$971$	−19.5826	+	33.9181i	−0.628436	+	1.08848i	0.359429	+	0.933172i	$0.382971\pi$
$971$	−19.5826	+	33.9181i	−0.628436	+	1.08848i	−0.987866	+	0.155311i	$0.950362\pi$
$972$		0			0
$973$	2.86934	−	10.9919i	0.0919868	−	0.352384i
$974$		0			0
$975$	−20.6910	+	16.3952i	−0.662643	+	0.525066i
$976$		0			0
$977$	12.8878	+	22.3223i	0.412316	+	0.714153i	0.995143	−	0.0984441i	$-0.0313866\pi$
$977$	12.8878	+	22.3223i	0.412316	+	0.714153i	−0.582826	+	0.812597i	$0.698053\pi$
$978$		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	$-0.587183\pi$
$983$	13.4197	−	7.74788i	0.428023	−	0.247119i	0.698504	+	0.715606i	$0.253849\pi$
$984$		0			0
$985$	31.2645	+	12.8915i	0.996171	+	0.410758i
$986$		0			0
$987$	30.0055	−	23.9349i	0.955086	−	0.761857i
$988$		0			0
$989$	−44.9400	−	25.9461i	−1.42901	−	0.825039i
$990$		0			0
$991$	16.7689	+	29.0446i	0.532682	+	0.922632i	0.999272	+	0.0381579i	$0.0121490\pi$
$991$	16.7689	+	29.0446i	0.532682	+	0.922632i	−0.466590	+	0.884474i	$0.654518\pi$
$992$		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	0.903066	−	0.429503i	$-0.141311\pi$
$997$	2.51253	+	4.35182i	0.0795725	+	0.137824i	−0.823493	+	0.567326i	$0.807978\pi$
$998$		0			0
$999$	−10.2394	+	8.47879i	−0.323959	+	0.268257i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
840.2.da.a.89.4	✓	48	15.14	odd	2	inner
840.2.da.a.89.13	yes	48	1.1	even	1	trivial
840.2.da.a.689.4	yes	48	7.3	odd	6	inner
840.2.da.a.689.13	yes	48	105.59	even	6	inner
840.2.da.b.89.12	yes	48	5.4	even	2
840.2.da.b.89.21	yes	48	3.2	odd	2
840.2.da.b.689.12	yes	48	21.17	even	6
840.2.da.b.689.21	yes	48	35.24	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-0.204814 + 1.71990i) q^{3} +(-2.06723 - 0.852393i) q^{5} +(-2.55997 - 0.668258i) q^{7} +(-2.91610 - 0.704519i) q^{9} +O(q^{10})\)	\(q+(-0.204814 + 1.71990i) q^{3} +(-2.06723 - 0.852393i) q^{5} +(-2.55997 - 0.668258i) q^{7} +(-2.91610 - 0.704519i) q^{9} +(2.74776 - 1.58642i) q^{11} +3.04832 q^{13} +(1.88943 - 3.38084i) q^{15} +(-3.15456 + 1.82129i) q^{17} +(3.68634 + 2.12831i) q^{19} +(1.67365 - 4.26602i) q^{21} +(2.75984 - 4.78018i) q^{23} +(3.54685 + 3.52418i) q^{25} +(1.80896 - 4.87110i) q^{27} -7.12076i q^{29} +(7.11211 - 4.10618i) q^{31} +(2.16570 + 5.05079i) q^{33} +(4.72241 + 3.56354i) q^{35} +(-2.21569 - 1.27923i) q^{37} +(-0.624340 + 5.24281i) q^{39} -0.652545 q^{41} -9.40132i q^{43} +(5.42772 + 3.94207i) q^{45} +(7.25360 + 4.18787i) q^{47} +(6.10686 + 3.42144i) q^{49} +(-2.48633 - 5.79855i) q^{51} +(5.86407 + 10.1569i) q^{53} +(-7.03250 + 0.937318i) q^{55} +(-4.41550 + 5.90423i) q^{57} +(-0.725991 - 1.25745i) q^{59} +(-8.46753 - 4.88873i) q^{61} +(6.99433 + 3.75225i) q^{63} +(-6.30158 - 2.59837i) q^{65} +(-8.85778 + 5.11404i) q^{67} +(7.65618 + 5.72569i) q^{69} -7.34623i q^{71} +(-3.14081 - 5.44005i) q^{73} +(-6.78768 + 5.37842i) q^{75} +(-8.09431 + 2.22497i) q^{77} +(3.17806 - 5.50456i) q^{79} +(8.00731 + 4.10890i) q^{81} +0.397748i q^{83} +(8.07364 - 1.07609i) q^{85} +(12.2470 + 1.45843i) q^{87} +(-3.15120 + 5.45804i) q^{89} +(-7.80361 - 2.03707i) q^{91} +(5.60555 + 13.0731i) q^{93} +(-5.80635 - 7.54192i) q^{95} +17.1688 q^{97} +(-9.13041 + 2.69031i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 3 q^{3} - 3 q^{5} - q^{9}+O(q^{10}) \) 48 * q - 3 * q^3 - 3 * q^5 - q^9	\( 48 q - 3 q^{3} - 3 q^{5} - q^{9} - 14 q^{15} + 5 q^{21} - 2 q^{23} + q^{25} + 6 q^{31} - 24 q^{33} + 4 q^{35} + 2 q^{39} - 3 q^{45} + 12 q^{51} + 6 q^{53} - 20 q^{57} + 18 q^{61} + 26 q^{63} - 10 q^{65} - 3 q^{75} - 2 q^{77} + 2 q^{79} - 9 q^{81} + 15 q^{87} + 24 q^{91} - 8 q^{93} - 6 q^{95} - 12 q^{99}+O(q^{100}) \) 48 * q - 3 * q^3 - 3 * q^5 - q^9 - 14 * q^15 + 5 * q^21 - 2 * q^23 + q^25 + 6 * q^31 - 24 * q^33 + 4 * q^35 + 2 * q^39 - 3 * q^45 + 12 * q^51 + 6 * q^53 - 20 * q^57 + 18 * q^61 + 26 * q^63 - 10 * q^65 - 3 * 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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