LMFDB - Embedded newform 819.2.bm.e.550.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(478,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 5]))

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

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

chi := DirichletCharacter("819.478");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.bm (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:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.2346760387617129.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + x^{10} + 10 x^{9} - 15 x^{8} - 10 x^{7} + 45 x^{6} - 20 x^{5} - 60 x^{4} + 80 x^{3} + \cdots + 64 $ x^12 - 3x^11 + x^10 + 10x^9 - 15x^8 - 10x^7 + 45x^6 - 20x^5 - 60x^4 + 80x^3 + 16x^2 - 96x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			550.3
Root			$-1.38488 - 0.286553i$ of defining polynomial
Character	$\chi$	$=$	819.550
Dual form			819.2.bm.e.478.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.573107i q^{2} +1.67155 q^{4} +(2.74304 - 1.58369i) q^{5} +(0.0699870 + 2.64483i) q^{7} -2.10419i q^{8} +O(q^{10})$	\(q-0.573107i q^{2} +1.67155 q^{4} +(2.74304 - 1.58369i) q^{5} +(0.0699870 + 2.64483i) q^{7} -2.10419i q^{8} +(-0.907626 - 1.57205i) q^{10} +(0.305703 - 0.176498i) q^{11} +(1.81339 + 3.11635i) q^{13} +(1.51577 - 0.0401100i) q^{14} +2.13717 q^{16} +0.888553 q^{17} +(1.32596 + 0.765541i) q^{19} +(4.58512 - 2.64722i) q^{20} +(-0.101152 - 0.175201i) q^{22} -4.53157 q^{23} +(2.51618 - 4.35815i) q^{25} +(1.78600 - 1.03926i) q^{26} +(0.116987 + 4.42095i) q^{28} +(-0.213739 + 0.370207i) q^{29} +(-7.47692 - 4.31680i) q^{31} -5.43321i q^{32} -0.509236i q^{34} +(4.38057 + 7.14402i) q^{35} +3.33015i q^{37} +(0.438737 - 0.759914i) q^{38} +(-3.33239 - 5.77187i) q^{40} +(4.73839 + 2.73571i) q^{41} +(-0.380909 - 0.659754i) q^{43} +(0.510998 - 0.295025i) q^{44} +2.59708i q^{46} +(-8.53765 + 4.92921i) q^{47} +(-6.99020 + 0.370207i) q^{49} +(-2.49768 - 1.44204i) q^{50} +(3.03117 + 5.20913i) q^{52} +(-2.06487 + 3.57646i) q^{53} +(0.559038 - 0.968281i) q^{55} +(5.56521 - 0.147266i) q^{56} +(0.212168 + 0.122495i) q^{58} -11.5102i q^{59} +(7.57803 - 13.1255i) q^{61} +(-2.47399 + 4.28507i) q^{62} +1.16054 q^{64} +(9.90954 + 5.67641i) q^{65} +(8.10167 - 4.67750i) q^{67} +1.48526 q^{68} +(4.09429 - 2.51054i) q^{70} +(-10.7783 + 6.22283i) q^{71} +(-5.88903 - 3.40003i) q^{73} +1.90853 q^{74} +(2.21640 + 1.27964i) q^{76} +(0.488201 + 0.796179i) q^{77} +(-3.48680 - 6.03932i) q^{79} +(5.86235 - 3.38463i) q^{80} +(1.56785 - 2.71560i) q^{82} -14.9864i q^{83} +(2.43734 - 1.40720i) q^{85} +(-0.378110 + 0.218302i) q^{86} +(-0.371385 - 0.643258i) q^{88} +6.11094i q^{89} +(-8.11528 + 5.01420i) q^{91} -7.57475 q^{92} +(2.82497 + 4.89298i) q^{94} +4.84953 q^{95} +(11.3769 - 6.56845i) q^{97} +(0.212168 + 4.00613i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7	$ 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7} - 7 q^{10} + 18 q^{11} - q^{13} + 16 q^{14} - 6 q^{16} + 9 q^{19} + 27 q^{20} + 7 q^{22} - 32 q^{23} + 10 q^{25} + 7 q^{26} + 36 q^{28} + 5 q^{29} - 15 q^{31} + 2 q^{35} - 24 q^{38} + 21 q^{40} + 15 q^{41} - 13 q^{43} - 30 q^{44} - 9 q^{47} - 3 q^{49} + 63 q^{50} + 32 q^{52} - 18 q^{53} + 13 q^{55} - 3 q^{56} - 57 q^{58} + 26 q^{61} + 13 q^{62} - 4 q^{64} - 10 q^{65} - 24 q^{67} + 42 q^{70} + 15 q^{71} + 18 q^{73} + 76 q^{74} - 30 q^{76} - 20 q^{77} - 4 q^{79} - 39 q^{80} - 14 q^{82} - 12 q^{85} - 15 q^{86} + 16 q^{88} + 4 q^{91} + 40 q^{92} - 3 q^{94} - 56 q^{95} + 45 q^{97} - 57 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7 - 7 * q^10 + 18 * q^11 - q^13 + 16 * q^14 - 6 * q^16 + 9 * q^19 + 27 * q^20 + 7 * q^22 - 32 * q^23 + 10 * q^25 + 7 * q^26 + 36 * q^28 + 5 * q^29 - 15 * q^31 + 2 * q^35 - 24 * q^38 + 21 * q^40 + 15 * q^41 - 13 * q^43 - 30 * q^44 - 9 * q^47 - 3 * q^49 + 63 * q^50 + 32 * q^52 - 18 * q^53 + 13 * q^55 - 3 * q^56 - 57 * q^58 + 26 * q^61 + 13 * q^62 - 4 * q^64 - 10 * q^65 - 24 * q^67 + 42 * q^70 + 15 * q^71 + 18 * q^73 + 76 * q^74 - 30 * q^76 - 20 * q^77 - 4 * q^79 - 39 * q^80 - 14 * q^82 - 12 * q^85 - 15 * q^86 + 16 * q^88 + 4 * q^91 + 40 * q^92 - 3 * q^94 - 56 * q^95 + 45 * q^97 - 57 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$		−	0.573107i		−	0.405248i	−0.979257	−	0.202624i	$-0.935053\pi$
$2$		−	0.573107i		−	0.405248i	0.979257	−	0.202624i	$-0.0649469\pi$
$3$		0			0
$3$		0			0
$4$	1.67155			0.835774
$5$	2.74304	−	1.58369i	1.22672	−	0.708250i	0.260381	−	0.965506i	$-0.416152\pi$
$5$	2.74304	−	1.58369i	1.22672	−	0.708250i	0.966343	+	0.257256i	$0.0828184\pi$
$6$		0			0
$7$	0.0699870	+	2.64483i	0.0264526	+	0.999650i
$7$	0.0699870	+	2.64483i	0.0264526	+	0.999650i
$8$		−	2.10419i		−	0.743943i
$9$		0			0
$10$	−0.907626	−	1.57205i	−0.287017	−	0.497127i
$11$	0.305703	−	0.176498i	0.0921730	−	0.0532161i	−0.453205	−	0.891406i	$-0.649719\pi$
$11$	0.305703	−	0.176498i	0.0921730	−	0.0532161i	0.545378	+	0.838190i	$0.316386\pi$
$12$		0			0
$13$	1.81339	+	3.11635i	0.502943	+	0.864319i
$13$	1.81339	+	3.11635i	0.502943	+	0.864319i
$14$	1.51577	−	0.0401100i	0.405106	−	0.0107198i
$15$		0			0
$16$	2.13717			0.534293
$17$	0.888553			0.215506			0.107753	−	0.994178i	$-0.465634\pi$
$17$	0.888553			0.215506			0.107753	+	0.994178i	$0.465634\pi$
$18$		0			0
$19$	1.32596	+	0.765541i	0.304195	+	0.175627i	0.644326	−	0.764751i	$-0.277138\pi$
$19$	1.32596	+	0.765541i	0.304195	+	0.175627i	−0.340131	+	0.940378i	$0.610471\pi$
$20$	4.58512	−	2.64722i	1.02526	−	0.591937i
$21$		0			0
$22$	−0.101152	−	0.175201i	−0.0215657	−	0.0373529i
$23$	−4.53157			−0.944899			−0.472449	−	0.881358i	$-0.656630\pi$
$23$	−4.53157			−0.944899			−0.472449	+	0.881358i	$0.656630\pi$
$24$		0			0
$25$	2.51618	−	4.35815i	0.503235	−	0.871629i
$26$	1.78600	−	1.03926i	0.350263	−	0.203817i
$27$		0			0
$28$	0.116987	+	4.42095i	0.0221084	+	0.835482i
$29$	−0.213739	+	0.370207i	−0.0396903	+	0.0687457i	−0.885188	−	0.465233i	$-0.845970\pi$
$29$	−0.213739	+	0.370207i	−0.0396903	+	0.0687457i	0.845498	+	0.533979i	$0.179304\pi$
$30$		0			0
$31$	−7.47692	−	4.31680i	−1.34289	−	0.775320i	−0.355663	−	0.934614i	$-0.615745\pi$
$31$	−7.47692	−	4.31680i	−1.34289	−	0.775320i	−0.987231	+	0.159294i	$0.949078\pi$
$32$		−	5.43321i		−	0.960464i
$33$		0			0
$34$		−	0.509236i		−	0.0873332i
$35$	4.38057	+	7.14402i	0.740452	+	1.20756i
$36$		0			0
$37$			3.33015i			0.547473i	0.961805	+	0.273736i	$0.0882596\pi$
$37$			3.33015i			0.547473i	−0.961805	+	0.273736i	$0.911740\pi$
$38$	0.438737	−	0.759914i	0.0711725	−	0.123274i
$39$		0			0
$40$	−3.33239	−	5.77187i	−0.526898	−	0.912613i
$41$	4.73839	+	2.73571i	0.740012	+	0.427246i	0.822074	−	0.569381i	$-0.192817\pi$
$41$	4.73839	+	2.73571i	0.740012	+	0.427246i	−0.0820619	+	0.996627i	$0.526151\pi$
$42$		0			0
$43$	−0.380909	−	0.659754i	−0.0580881	−	0.100612i	0.835519	−	0.549462i	$-0.185167\pi$
$43$	−0.380909	−	0.659754i	−0.0580881	−	0.100612i	−0.893607	+	0.448850i	$0.851834\pi$
$44$	0.510998	−	0.295025i	0.0770359	−	0.0444767i
$45$		0			0
$46$			2.59708i			0.382918i
$47$	−8.53765	+	4.92921i	−1.24534	+	0.719000i	−0.970177	−	0.242397i	$-0.922066\pi$
$47$	−8.53765	+	4.92921i	−1.24534	+	0.719000i	−0.275167	+	0.961397i	$0.588733\pi$
$48$		0			0
$49$	−6.99020	+	0.370207i	−0.998601	+	0.0528867i
$50$	−2.49768	−	1.44204i	−0.353226	−	0.203935i
$51$		0			0
$52$	3.03117	+	5.20913i	0.420347	+	0.722376i
$53$	−2.06487	+	3.57646i	−0.283632	+	0.491265i	−0.972276	−	0.233834i	$-0.924873\pi$
$53$	−2.06487	+	3.57646i	−0.283632	+	0.491265i	0.688645	+	0.725099i	$0.258206\pi$
$54$		0			0
$55$	0.559038	−	0.968281i	0.0753806	−	0.130563i
$56$	5.56521	−	0.147266i	0.743683	−	0.0196792i
$57$		0			0
$58$	0.212168	+	0.122495i	0.0278590	+	0.0160844i
$59$		−	11.5102i		−	1.49850i	−0.662287	−	0.749250i	$-0.730414\pi$
$59$		−	11.5102i		−	1.49850i	0.662287	−	0.749250i	$-0.269586\pi$
$60$		0			0
$61$	7.57803	−	13.1255i	0.970267	−	1.68055i	0.275523	−	0.961294i	$-0.411149\pi$
$61$	7.57803	−	13.1255i	0.970267	−	1.68055i	0.694744	−	0.719257i	$-0.255518\pi$
$62$	−2.47399	+	4.28507i	−0.314197	+	0.544204i
$63$		0			0
$64$	1.16054			0.145067
$65$	9.90954	+	5.67641i	1.22913	+	0.704073i
$66$		0			0
$67$	8.10167	−	4.67750i	0.989777	−	0.571448i	0.0845695	−	0.996418i	$-0.473049\pi$
$67$	8.10167	−	4.67750i	0.989777	−	0.571448i	0.905208	+	0.424970i	$0.139715\pi$
$68$	1.48526			0.180114
$69$		0			0
$70$	4.09429	−	2.51054i	0.489361	−	0.300066i
$71$	−10.7783	+	6.22283i	−1.27914	+	0.738514i	−0.976691	−	0.214651i	$-0.931139\pi$
$71$	−10.7783	+	6.22283i	−1.27914	+	0.738514i	−0.302453	+	0.953164i	$0.597805\pi$
$72$		0			0
$73$	−5.88903	−	3.40003i	−0.689259	−	0.397944i	0.114075	−	0.993472i	$-0.463609\pi$
$73$	−5.88903	−	3.40003i	−0.689259	−	0.397944i	−0.803334	+	0.595528i	$0.796943\pi$
$74$	1.90853			0.221862
$75$		0			0
$76$	2.21640	+	1.27964i	0.254239	+	0.146785i
$77$	0.488201	+	0.796179i	0.0556357	+	0.0907331i
$78$		0			0
$79$	−3.48680	−	6.03932i	−0.392296	−	0.679476i	0.600456	−	0.799658i	$-0.294986\pi$
$79$	−3.48680	−	6.03932i	−0.392296	−	0.679476i	−0.992752	+	0.120182i	$0.961652\pi$
$80$	5.86235	−	3.38463i	0.655430	−	0.378413i
$81$		0			0
$82$	1.56785	−	2.71560i	0.173140	−	0.299888i
$83$		−	14.9864i		−	1.64498i	−0.568782	−	0.822488i	$-0.692585\pi$
$83$		−	14.9864i		−	1.64498i	0.568782	−	0.822488i	$-0.307415\pi$
$84$		0			0
$85$	2.43734	−	1.40720i	0.264366	−	0.152632i
$86$	−0.378110	+	0.218302i	−0.0407726	+	0.0235401i
$87$		0			0
$88$	−0.371385	−	0.643258i	−0.0395898	−	0.0685715i
$89$			6.11094i			0.647759i	0.946098	+	0.323879i	$0.104987\pi$
$89$			6.11094i			0.647759i	−0.946098	+	0.323879i	$0.895013\pi$
$90$		0			0
$91$	−8.11528	+	5.01420i	−0.850713	+	0.525631i
$92$	−7.57475			−0.789722
$93$		0			0
$94$	2.82497	+	4.89298i	0.291373	+	0.504673i
$95$	4.84953			0.497552
$96$		0			0
$97$	11.3769	−	6.56845i	1.15515	−	0.666925i	0.205012	−	0.978759i	$-0.434277\pi$
$97$	11.3769	−	6.56845i	1.15515	−	0.666925i	0.950137	+	0.311834i	$0.100943\pi$
$98$	0.212168	+	4.00613i	0.0214322	+	0.404681i
$99$		0			0
$100$	4.20591	−	7.28485i	0.420591	−	0.728485i
$101$	−6.02344	−	10.4329i	−0.599355	−	1.03811i	−0.992916	−	0.118814i	$-0.962091\pi$
$101$	−6.02344	−	10.4329i	−0.599355	−	1.03811i	0.393562	−	0.919298i	$-0.371243\pi$
$102$		0			0
$103$	6.84541	+	11.8566i	0.674498	+	1.16827i	0.976615	+	0.214995i	$0.0689734\pi$
$103$	6.84541	+	11.8566i	0.674498	+	1.16827i	−0.302117	+	0.953271i	$0.597693\pi$
$104$	6.55739	−	3.81571i	0.643005	−	0.374161i
$105$		0			0
$106$	2.04969	+	1.18339i	0.199084	+	0.114941i
$107$	5.13159			0.496090			0.248045	−	0.968749i	$-0.420212\pi$
$107$	5.13159			0.496090			0.248045	+	0.968749i	$0.420212\pi$
$108$		0			0
$109$	0.865142	+	0.499490i	0.0828656	+	0.0478425i	0.540860	−	0.841112i	$-0.318099\pi$
$109$	0.865142	+	0.499490i	0.0828656	+	0.0478425i	−0.457995	+	0.888955i	$0.651432\pi$
$110$	−0.554929	−	0.320388i	−0.0529104	−	0.0305478i
$111$		0			0
$112$	0.149574	+	5.65245i	0.0141334	+	0.534106i
$113$	1.46152	+	2.53143i	0.137488	+	0.238137i	0.926545	−	0.376183i	$-0.122764\pi$
$113$	1.46152	+	2.53143i	0.137488	+	0.238137i	−0.789057	+	0.614320i	$0.789430\pi$
$114$		0			0
$115$	−12.4303	+	7.17663i	−1.15913	+	0.669224i
$116$	−0.357275	+	0.618818i	−0.0331722	+	0.0574559i
$117$		0			0
$118$	−6.59657			−0.607264
$119$	0.0621871	+	2.35007i	0.00570069	+	0.215430i
$120$		0			0
$121$	−5.43770	+	9.41837i	−0.494336	+	0.856215i
$122$	−7.52233	−	4.34302i	−0.681040	−	0.393198i
$123$		0			0
$124$	−12.4980	−	7.21574i	−1.12236	−	0.647993i
$125$		−	0.102477i		−	0.00916579i
$126$		0			0
$127$	−7.80251	+	13.5143i	−0.692361	+	1.19920i	0.278701	+	0.960378i	$0.410096\pi$
$127$	−7.80251	+	13.5143i	−0.692361	+	1.19920i	−0.971062	+	0.238826i	$0.923237\pi$
$128$		−	11.5315i		−	1.01925i
$129$		0			0
$130$	3.25319	−	5.67922i	0.285324	−	0.498101i
$131$	2.73134	+	4.73083i	0.238639	+	0.413334i	0.960324	−	0.278887i	$-0.0899655\pi$
$131$	2.73134	+	4.73083i	0.238639	+	0.413334i	−0.721685	+	0.692221i	$0.756632\pi$
$132$		0			0
$133$	−1.93192	+	3.56050i	−0.167519	+	0.308735i
$134$	−2.68071	−	4.64312i	−0.231578	−	0.401105i
$135$		0			0
$136$		−	1.86968i		−	0.160324i
$137$			15.7768i			1.34790i	0.738777	+	0.673950i	$0.235404\pi$
$137$			15.7768i			1.34790i	−0.738777	+	0.673950i	$0.764596\pi$
$138$		0			0
$139$	4.66230	+	8.07533i	0.395451	+	0.684941i	0.993159	−	0.116773i	$-0.0372550\pi$
$139$	4.66230	+	8.07533i	0.395451	+	0.684941i	−0.597708	+	0.801714i	$0.703922\pi$
$140$	7.32234	+	11.9416i	0.618851	+	1.00925i
$141$		0			0
$142$	3.56634	+	6.17709i	0.299281	+	0.518370i
$143$	1.10439	+	0.632619i	0.0923535	+	0.0529023i
$144$		0			0
$145$			1.35399i			0.112443i
$146$	−1.94858	+	3.37504i	−0.161266	+	0.279321i
$147$		0			0
$148$			5.56650i			0.457564i
$149$	2.42918	+	1.40249i	0.199006	+	0.114896i	0.596192	−	0.802842i	$-0.296680\pi$
$149$	2.42918	+	1.40249i	0.199006	+	0.114896i	−0.397186	+	0.917738i	$0.630013\pi$
$150$		0			0
$151$	−17.5134	−	10.1114i	−1.42522	−	0.822853i	−0.428484	−	0.903549i	$-0.640952\pi$
$151$	−17.5134	−	10.1114i	−1.42522	−	0.822853i	−0.996739	+	0.0806967i	$0.974285\pi$
$152$	1.61084	−	2.79006i	0.130657	−	0.226304i
$153$		0			0
$154$	0.456296	−	0.279792i	0.0367694	−	0.0225462i
$155$	−27.3460			−2.19648
$156$		0			0
$157$	2.32141	−	4.02080i	0.185269	−	0.320894i	−0.758398	−	0.651791i	$-0.774018\pi$
$157$	2.32141	−	4.02080i	0.185269	−	0.320894i	0.943667	+	0.330897i	$0.107351\pi$
$158$	−3.46117	+	1.99831i	−0.275356	+	0.158977i
$159$		0			0
$160$	−8.60454	−	14.9035i	−0.680249	−	1.17823i
$161$	−0.317151	−	11.9852i	−0.0249950	−	0.944568i
$162$		0			0
$163$	2.82608	+	1.63164i	0.221355	+	0.127800i	0.606578	−	0.795024i	$-0.292542\pi$
$163$	2.82608	+	1.63164i	0.221355	+	0.127800i	−0.385222	+	0.922824i	$0.625875\pi$
$164$	7.92044	+	4.57287i	0.618483	+	0.357081i
$165$		0			0
$166$	−8.58883			−0.666623
$167$	−20.9079	−	12.0712i	−1.61790	−	0.934096i	−0.987462	−	0.157859i	$-0.949541\pi$
$167$	−20.9079	−	12.0712i	−1.61790	−	0.934096i	−0.630441	−	0.776238i	$-0.717126\pi$
$168$		0			0
$169$	−6.42325	+	11.3023i	−0.494096	+	0.869407i
$170$	−0.806474	−	1.39685i	−0.0618537	−	0.107134i
$171$		0			0
$172$	−0.636708	−	1.10281i	−0.0485486	−	0.0840886i
$173$	−9.59569	+	16.6202i	−0.729547	+	1.26361i	0.227528	+	0.973772i	$0.426936\pi$
$173$	−9.59569	+	16.6202i	−0.729547	+	1.26361i	−0.957075	+	0.289841i	$0.906398\pi$
$174$		0			0
$175$	11.7026	+	6.34984i	0.884636	+	0.480002i
$176$	0.653341	−	0.377206i	0.0492474	−	0.0284330i
$177$		0			0
$178$	3.50222			0.262503
$179$	−11.3937	−	19.7345i	−0.851608	−	1.47503i	−0.879756	−	0.475425i	$-0.842294\pi$
$179$	−11.3937	−	19.7345i	−0.851608	−	1.47503i	0.0281482	−	0.999604i	$-0.491039\pi$
$180$		0			0
$181$	1.32420			0.0984270			0.0492135	−	0.998788i	$-0.484329\pi$
$181$	1.32420			0.0984270			0.0492135	+	0.998788i	$0.484329\pi$
$182$	2.87367	+	4.65092i	0.213011	+	0.344749i
$183$		0			0
$184$			9.53529i			0.702951i
$185$	5.27394	+	9.13472i	0.387747	+	0.671598i
$186$		0			0
$187$	0.271634	−	0.156828i	0.0198638	−	0.0114684i
$188$	−14.2711	+	8.23942i	−1.04083	+	0.600921i
$189$		0			0
$190$		−	2.77930i		−	0.201632i
$191$	−3.88818	+	6.73453i	−0.281339	+	0.487293i	−0.971715	−	0.236158i	$-0.924112\pi$
$191$	−3.88818	+	6.73453i	−0.281339	+	0.487293i	0.690376	+	0.723451i	$0.257445\pi$
$192$		0			0
$193$	−9.50295	+	5.48653i	−0.684037	+	0.394929i	−0.801374	−	0.598163i	$-0.795897\pi$
$193$	−9.50295	+	5.48653i	−0.684037	+	0.394929i	0.117337	+	0.993092i	$0.462564\pi$
$194$	−3.76442	−	6.52017i	−0.270270	−	0.468121i
$195$		0			0
$196$	−11.6845	+	0.618818i	−0.834605	+	0.0442013i
$197$	−5.20917	−	3.00752i	−0.371138	−	0.214277i	0.302818	−	0.953049i	$-0.402073\pi$
$197$	−5.20917	−	3.00752i	−0.371138	−	0.214277i	−0.673955	+	0.738772i	$0.735406\pi$
$198$		0			0
$199$	14.8254			1.05095			0.525473	−	0.850811i	$-0.323889\pi$
$199$	14.8254			1.05095			0.525473	+	0.850811i	$0.323889\pi$
$200$	−9.17036	−	5.29451i	−0.648443	−	0.374379i
$201$		0			0
$202$	−5.97917	+	3.45207i	−0.420693	+	0.242887i
$203$	−0.994091	−	0.539392i	−0.0697715	−	0.0378579i
$204$		0			0
$205$	17.3301			1.21039
$206$	6.79510	−	3.92315i	0.473437	−	0.273339i
$207$		0			0
$208$	3.87552	+	6.66017i	0.268719	+	0.461800i
$209$	0.540466			0.0373848
$210$		0			0
$211$	−10.3820	+	17.9821i	−0.714725	+	1.23794i	0.248340	+	0.968673i	$0.420115\pi$
$211$	−10.3820	+	17.9821i	−0.714725	+	1.23794i	−0.963065	+	0.269267i	$0.913218\pi$
$212$	−3.45153	+	5.97823i	−0.237052	+	0.410586i
$213$		0			0
$214$		−	2.94095i		−	0.201039i
$215$	−2.08970	−	1.20649i	−0.142516	−	0.0822818i
$216$		0			0
$217$	10.8939	−	20.0773i	0.739526	−	1.36293i
$218$	0.286261	−	0.495819i	0.0193880	−	0.0335811i
$219$		0			0
$220$	0.934459	−	1.61853i	0.0630012	−	0.109121i
$221$	1.61129	+	2.76904i	0.108387	+	0.186266i
$222$		0			0
$223$	−6.16220	−	3.55775i	−0.412652	−	0.238244i	0.279277	−	0.960211i	$-0.409905\pi$
$223$	−6.16220	−	3.55775i	−0.412652	−	0.238244i	−0.691928	+	0.721966i	$0.743239\pi$
$224$	14.3699	−	0.380254i	0.960128	−	0.0254068i
$225$		0			0
$226$	1.45078	−	0.837607i	0.0965043	−	0.0557168i
$227$		−	3.70996i		−	0.246239i	−0.992392	−	0.123119i	$-0.960710\pi$
$227$		−	3.70996i		−	0.246239i	0.992392	−	0.123119i	$-0.0392898\pi$
$228$		0			0
$229$	11.3004	−	6.52429i	0.746751	−	0.431137i	−0.0777675	−	0.996972i	$-0.524779\pi$
$229$	11.3004	−	6.52429i	0.746751	−	0.431137i	0.824519	+	0.565834i	$0.191446\pi$
$230$	4.11297	+	7.12388i	0.271202	+	0.469735i
$231$		0			0
$232$	0.778985	+	0.449747i	0.0511429	+	0.0295273i
$233$	8.10047	+	14.0304i	0.530679	+	0.919164i	0.999359	+	0.0357956i	$0.0113965\pi$
$233$	8.10047	+	14.0304i	0.530679	+	0.919164i	−0.468680	+	0.883368i	$0.655270\pi$
$234$		0			0
$235$	−15.6127	+	27.0421i	−1.01846	+	1.76403i
$236$		−	19.2399i		−	1.25241i
$237$		0			0
$238$	1.34684	−	0.0356399i	0.0873026	−	0.00231019i
$239$			14.4871i			0.937093i	0.883439	+	0.468547i	$0.155222\pi$
$239$			14.4871i			0.937093i	−0.883439	+	0.468547i	$0.844778\pi$
$240$		0			0
$241$		−	20.6501i		−	1.33019i	−0.746758	−	0.665096i	$-0.768391\pi$
$241$		−	20.6501i		−	1.33019i	0.746758	−	0.665096i	$-0.231609\pi$
$242$	5.39773	+	3.11638i	0.346979	+	0.200329i
$243$		0			0
$244$	12.6670	−	21.9400i	0.810924	−	1.40456i
$245$	−18.5881	+	12.0858i	−1.18755	+	0.772136i
$246$		0			0
$247$	0.0187793	+	5.52036i	0.00119490	+	0.351252i
$248$	−9.08336	+	15.7328i	−0.576794	+	0.999037i
$249$		0			0
$250$	−0.0587300			−0.00371441
$251$	12.9380	+	22.4093i	0.816642	+	1.41447i	0.908143	+	0.418660i	$0.137500\pi$
$251$	12.9380	+	22.4093i	0.816642	+	1.41447i	−0.0915012	+	0.995805i	$0.529167\pi$
$252$		0			0
$253$	−1.38532	+	0.799814i	−0.0870942	+	0.0502838i
$254$	7.74516	+	4.47167i	0.485975	+	0.280578i
$255$		0			0
$256$	−4.28772			−0.267982
$257$	1.89069			0.117938			0.0589689	−	0.998260i	$-0.481219\pi$
$257$	1.89069			0.117938			0.0589689	+	0.998260i	$0.481219\pi$
$258$		0			0
$259$	−8.80766	+	0.233067i	−0.547281	+	0.0144821i
$260$	16.5643	+	9.48840i	1.02727	+	0.588446i
$261$		0			0
$262$	2.71127	−	1.56535i	0.167503	−	0.0967077i
$263$	3.04658	+	5.27683i	0.187860	+	0.325384i	0.944537	−	0.328406i	$-0.106511\pi$
$263$	3.04658	+	5.27683i	0.187860	+	0.325384i	−0.756676	+	0.653790i	$0.773178\pi$
$264$		0			0
$265$			13.0805i			0.803529i
$266$	2.04055	+	1.10720i	0.125114	+	0.0678867i
$267$		0			0
$268$	13.5423	−	7.81868i	0.827230	−	0.477602i
$269$	1.40409			0.0856087			0.0428043	−	0.999083i	$-0.486371\pi$
$269$	1.40409			0.0856087			0.0428043	+	0.999083i	$0.486371\pi$
$270$		0			0
$271$		−	13.2620i		−	0.805608i	−0.915286	−	0.402804i	$-0.868036\pi$
$271$		−	13.2620i		−	0.805608i	0.915286	−	0.402804i	$-0.131964\pi$
$272$	1.89899			0.115143
$273$		0			0
$274$	9.04177			0.546233
$275$		−	1.77640i		−	0.107121i
$276$		0			0
$277$	16.8899			1.01481			0.507407	−	0.861706i	$-0.330604\pi$
$277$	16.8899			1.01481			0.507407	+	0.861706i	$0.330604\pi$
$278$	4.62803	−	2.67199i	0.277571	−	0.160256i
$279$		0			0
$280$	15.0324	−	9.21755i	0.898356	−	0.550854i
$281$			22.5550i			1.34552i	0.739860	+	0.672761i	$0.234892\pi$
$281$			22.5550i			1.34552i	−0.739860	+	0.672761i	$0.765108\pi$
$282$		0			0
$283$	−0.399128	−	0.691311i	−0.0237257	−	0.0410941i	0.853919	−	0.520406i	$-0.174220\pi$
$283$	−0.399128	−	0.691311i	−0.0237257	−	0.0410941i	−0.877644	+	0.479312i	$0.840886\pi$
$284$	−18.0164	+	10.4018i	−1.06908	+	0.617231i
$285$		0			0
$286$	0.362558	−	0.632932i	0.0214385	−	0.0374261i
$287$	−6.90385	+	12.7237i	−0.407521	+	0.751054i
$288$		0			0
$289$	−16.2105			−0.953557
$290$	0.775980			0.0455671
$291$		0			0
$292$	−9.84380	−	5.68332i	−0.576065	−	0.332591i
$293$	26.6711	−	15.3986i	1.55814	−	0.899593i	0.560706	−	0.828015i	$-0.310530\pi$
$293$	26.6711	−	15.3986i	1.55814	−	0.899593i	0.997435	−	0.0715779i	$-0.0228035\pi$
$294$		0			0
$295$	−18.2286	−	31.5729i	−1.06131	−	1.83825i
$296$	7.00726			0.407289
$297$		0			0
$298$	0.803774	−	1.39218i	0.0465614	−	0.0806467i
$299$	−8.21750	−	14.1220i	−0.475230	−	0.816694i
$300$		0			0
$301$	1.71828	−	1.05361i	0.0990398	−	0.0607292i
$302$	−5.79490	+	10.0371i	−0.333459	+	0.577568i
$303$		0			0
$304$	2.83380	+	1.63609i	0.162529	+	0.0938364i
$305$		−	48.0051i		−	2.74877i
$306$		0			0
$307$			21.4161i			1.22228i	0.791522	+	0.611140i	$0.209289\pi$
$307$			21.4161i			1.22228i	−0.791522	+	0.611140i	$0.790711\pi$
$308$	0.816052	+	1.33085i	0.0464989	+	0.0758324i
$309$		0			0
$310$			15.6722i			0.890119i
$311$	9.69378	−	16.7901i	0.549684	−	0.952081i	−0.448612	−	0.893727i	$-0.648081\pi$
$311$	9.69378	−	16.7901i	0.549684	−	0.952081i	0.998296	−	0.0583541i	$-0.0185852\pi$
$312$		0			0
$313$	3.85148	+	6.67096i	0.217699	+	0.377065i	0.954104	−	0.299476i	$-0.0968117\pi$
$313$	3.85148	+	6.67096i	0.217699	+	0.377065i	−0.736405	+	0.676540i	$0.763478\pi$
$314$	−2.30435	−	1.33041i	−0.130042	−	0.0750796i
$315$		0			0
$316$	−5.82836	−	10.0950i	−0.327871	−	0.567889i
$317$	12.7818	−	7.37956i	0.717896	−	0.414477i	−0.0960819	−	0.995373i	$-0.530631\pi$
$317$	12.7818	−	7.37956i	0.717896	−	0.414477i	0.813978	+	0.580896i	$0.197298\pi$
$318$		0			0
$319$			0.150898i			0.00844866i
$320$	3.18340	−	1.83794i	0.177958	−	0.102744i
$321$		0			0
$322$	−6.86881	+	0.181761i	−0.382784	+	0.0101292i
$323$	1.17818	+	0.680224i	0.0655558	+	0.0378487i
$324$		0			0
$325$	18.1443	−	0.0617235i	1.00646	−	0.00342381i
$326$	0.935102	−	1.61964i	0.0517905	−	0.0897038i
$327$		0			0
$328$	5.75645	−	9.97046i	0.317847	−	0.550527i
$329$	−13.6344	−	22.2356i	−0.751691	−	1.22589i
$330$		0			0
$331$	1.43371	+	0.827754i	0.0788040	+	0.0454975i	0.538884	−	0.842380i	$-0.318846\pi$
$331$	1.43371	+	0.827754i	0.0788040	+	0.0454975i	−0.460080	+	0.887877i	$0.652179\pi$
$332$		−	25.0506i		−	1.37483i
$333$		0			0
$334$	−6.91808	+	11.9825i	−0.378540	+	0.655651i
$335$	14.8155	−	25.6612i	0.809456	−	1.40202i
$336$		0			0
$337$	−2.88666			−0.157246			−0.0786231	−	0.996904i	$-0.525052\pi$
$337$	−2.88666			−0.157246			−0.0786231	+	0.996904i	$0.525052\pi$
$338$	6.47742	+	3.68121i	0.352325	+	0.200231i
$339$		0			0
$340$	4.07413	−	2.35220i	0.220950	−	0.127566i
$341$	−3.04762			−0.165038
$342$		0			0
$343$	−1.46836	−	18.4620i	−0.0792837	−	0.996852i
$344$	−1.38825	+	0.801505i	−0.0748493	+	0.0432143i
$345$		0			0
$346$	9.52517	+	5.49936i	0.512076	+	0.295647i
$347$	29.0876			1.56151			0.780753	−	0.624840i	$-0.214836\pi$
$347$	29.0876			1.56151			0.780753	+	0.624840i	$0.214836\pi$
$348$		0			0
$349$	−15.8747	−	9.16529i	−0.849756	−	0.490607i	0.0108128	−	0.999942i	$-0.496558\pi$
$349$	−15.8747	−	9.16529i	−0.849756	−	0.490607i	−0.860568	+	0.509335i	$0.829891\pi$
$350$	3.63913	−	6.70686i	0.194520	−	0.358497i
$351$		0			0
$352$	−0.958950	−	1.66095i	−0.0511122	−	0.0885289i
$353$	−6.19062	+	3.57415i	−0.329493	+	0.190233i	−0.655616	−	0.755094i	$-0.727591\pi$
$353$	−6.19062	+	3.57415i	−0.329493	+	0.190233i	0.326123	+	0.945327i	$0.394258\pi$
$354$		0			0
$355$	−19.7101	+	34.1389i	−1.04610	+	1.81191i
$356$			10.2147i			0.541380i
$357$		0			0
$358$	−11.3100	+	6.52983i	−0.597752	+	0.345112i
$359$	−13.0092	+	7.51088i	−0.686601	+	0.396409i	−0.802337	−	0.596871i	$-0.796410\pi$
$359$	−13.0092	+	7.51088i	−0.686601	+	0.396409i	0.115737	+	0.993280i	$0.463077\pi$
$360$		0			0
$361$	−8.32789	−	14.4243i	−0.438310	−	0.759175i
$362$		−	0.758908i		−	0.0398873i
$363$		0			0
$364$	−13.5651	+	8.38147i	−0.711004	+	0.439309i
$365$	−21.5385			−1.12737
$366$		0			0
$367$	2.02451	+	3.50655i	0.105678	+	0.183040i	0.914015	−	0.405680i	$-0.132965\pi$
$367$	2.02451	+	3.50655i	0.105678	+	0.183040i	−0.808337	+	0.588720i	$0.799632\pi$
$368$	−9.68476			−0.504853
$369$		0			0
$370$	5.23517	−	3.02253i	0.272164	−	0.157134i
$371$	−9.60363	−	5.21092i	−0.498596	−	0.270537i
$372$		0			0
$373$	−9.50471	+	16.4626i	−0.492135	+	0.852403i	−0.999959	−	0.00905764i	$-0.997117\pi$
$373$	−9.50471	+	16.4626i	−0.492135	+	0.852403i	0.507824	+	0.861461i	$0.330450\pi$
$374$	−0.0898790	−	0.155675i	−0.00464753	−	0.00804977i
$375$		0			0
$376$	10.3720	+	17.9648i	0.534895	+	0.926465i
$377$	−1.54128	+	0.00524316i	−0.0793802	+	0.000270037i
$378$		0			0
$379$	14.4405	+	8.33722i	0.741758	+	0.428254i	0.822708	−	0.568464i	$-0.192462\pi$
$379$	14.4405	+	8.33722i	0.741758	+	0.428254i	−0.0809502	+	0.996718i	$0.525795\pi$
$380$	8.10623			0.415841
$381$		0			0
$382$	3.85960	+	2.22834i	0.197474	+	0.114012i
$383$	−7.48326	−	4.32046i	−0.382377	−	0.220765i	0.296475	−	0.955041i	$-0.404189\pi$
$383$	−7.48326	−	4.32046i	−0.382377	−	0.220765i	−0.678852	+	0.734275i	$0.737522\pi$
$384$		0			0
$385$	2.60006	+	1.41079i	0.132511	+	0.0719005i
$386$	3.14437	+	5.44620i	0.160044	+	0.277204i
$387$		0			0
$388$	19.0170	−	10.9795i	0.965443	−	0.557399i
$389$	−3.54047	+	6.13227i	−0.179509	+	0.310918i	−0.941712	−	0.336419i	$-0.890784\pi$
$389$	−3.54047	+	6.13227i	−0.179509	+	0.310918i	0.762204	+	0.647337i	$0.224117\pi$
$390$		0			0
$391$	−4.02654			−0.203631
$392$	0.778985	+	14.7087i	0.0393447	+	0.742902i
$393$		0			0
$394$	−1.72363	+	2.98541i	−0.0868351	+	0.150403i
$395$	−19.1289	−	11.0441i	−0.962478	−	0.555687i
$396$		0			0
$397$	−18.7486	−	10.8245i	−0.940964	−	0.543266i	−0.0507018	−	0.998714i	$-0.516146\pi$
$397$	−18.7486	−	10.8245i	−0.940964	−	0.543266i	−0.890262	+	0.455448i	$0.849479\pi$
$398$		−	8.49654i		−	0.425893i
$399$		0			0
$400$	5.37750	−	9.31411i	0.268875	−	0.465705i
$401$		−	14.7595i		−	0.737053i	−0.929617	−	0.368527i	$-0.879862\pi$
$401$		−	14.7595i		−	0.737053i	0.929617	−	0.368527i	$-0.120138\pi$
$402$		0			0
$403$	−0.105894	−	31.1287i	−0.00527496	−	1.55063i
$404$	−10.0685	−	17.4391i	−0.500925	−	0.867628i
$405$		0			0
$406$	−0.309129	+	0.569720i	−0.0153418	+	0.0282747i
$407$	0.587764	+	1.01804i	0.0291344	+	0.0504622i
$408$		0			0
$409$		−	17.5127i		−	0.865948i	−0.901406	−	0.432974i	$-0.857464\pi$
$409$		−	17.5127i		−	0.865948i	0.901406	−	0.432974i	$-0.142536\pi$
$410$		−	9.93200i		−	0.490507i
$411$		0			0
$412$	11.4424	+	19.8189i	0.563729	+	0.976406i
$413$	30.4425	−	0.805564i	1.49798	−	0.0396392i
$414$		0			0
$415$	−23.7340	−	41.1084i	−1.16505	−	2.01793i
$416$	16.9318	−	9.85251i	0.830148	−	0.483059i
$417$		0			0
$418$		−	0.309745i		−	0.0151501i
$419$	−15.4087	+	26.6887i	−0.752764	+	1.30383i	0.193714	+	0.981058i	$0.437947\pi$
$419$	−15.4087	+	26.6887i	−0.752764	+	1.30383i	−0.946478	+	0.322768i	$0.895387\pi$
$420$		0			0
$421$		−	29.3681i		−	1.43131i	−0.698452	−	0.715657i	$-0.746127\pi$
$421$		−	29.3681i		−	1.43131i	0.698452	−	0.715657i	$-0.253873\pi$
$422$	10.3057	+	5.94998i	0.501672	+	0.289641i
$423$		0			0
$424$	7.52555	+	4.34488i	0.365473	+	0.211006i
$425$	2.23576	−	3.87244i	0.108450	−	0.187841i
$426$		0			0
$427$	35.2451	+	19.1239i	1.70563	+	0.925473i
$428$	8.57770			0.414619
$429$		0			0
$430$	−0.691446	+	1.19762i	−0.0333445	+	0.0577544i
$431$	18.4400	−	10.6463i	0.888224	−	0.512816i	0.0148626	−	0.999890i	$-0.495269\pi$
$431$	18.4400	−	10.6463i	0.888224	−	0.512816i	0.873361	+	0.487073i	$0.161936\pi$
$432$		0			0
$433$	8.80166	+	15.2449i	0.422981	+	0.732624i	0.996229	−	0.0867574i	$-0.0276505\pi$
$433$	8.80166	+	15.2449i	0.422981	+	0.732624i	−0.573249	+	0.819381i	$0.694317\pi$
$434$	−11.5064	−	6.24336i	−0.552325	−	0.299691i
$435$		0			0
$436$	1.44613	+	0.834922i	0.0692569	+	0.0399855i
$437$	−6.00867	−	3.46911i	−0.287434	−	0.165950i
$438$		0			0
$439$	22.8133			1.08882			0.544409	−	0.838820i	$-0.316754\pi$
$439$	22.8133			1.08882			0.544409	+	0.838820i	$0.316754\pi$
$440$	−2.03745	−	1.17632i	−0.0971315	−	0.0560789i
$441$		0			0
$442$	1.58696	−	0.923442i	0.0754838	−	0.0439236i
$443$	19.5291	+	33.8254i	0.927857	+	1.60709i	0.786901	+	0.617079i	$0.211684\pi$
$443$	19.5291	+	33.8254i	0.927857	+	1.60709i	0.140955	+	0.990016i	$0.454983\pi$
$444$		0			0
$445$	9.67787	+	16.7626i	0.458775	+	0.794621i
$446$	−2.03897	+	3.53160i	−0.0965480	+	0.167226i
$447$		0			0
$448$	0.0812225	+	3.06942i	0.00383740	+	0.145016i
$449$	10.3848	−	5.99568i	0.490090	−	0.282954i	−0.234522	−	0.972111i	$-0.575352\pi$
$449$	10.3848	−	5.99568i	0.490090	−	0.282954i	0.724612	+	0.689157i	$0.242019\pi$
$450$		0			0
$451$	1.93139			0.0909455
$452$	2.44300	+	4.23140i	0.114909	+	0.199029i
$453$		0			0
$454$	−2.12620			−0.0997876
$455$	−14.3196	+	26.6063i	−0.671313	+	1.24732i
$456$		0			0
$457$		−	2.49129i		−	0.116538i	−0.998301	−	0.0582689i	$-0.981442\pi$
$457$		−	2.49129i		−	0.116538i	0.998301	−	0.0582689i	$-0.0185581\pi$
$458$	−3.73911	−	6.47633i	−0.174717	−	0.302619i
$459$		0			0
$460$	−20.7778	+	11.9961i	−0.968771	+	0.559320i
$461$	28.0132	−	16.1734i	1.30471	−	0.753273i	0.323499	−	0.946228i	$-0.395141\pi$
$461$	28.0132	−	16.1734i	1.30471	−	0.753273i	0.981207	+	0.192956i	$0.0618074\pi$
$462$		0			0
$463$			23.4856i			1.09147i	0.837958	+	0.545735i	$0.183749\pi$
$463$			23.4856i			1.09147i	−0.837958	+	0.545735i	$0.816251\pi$
$464$	−0.456797	+	0.791195i	−0.0212063	+	0.0367303i
$465$		0			0
$466$	8.04093	−	4.64243i	0.372489	−	0.215057i
$467$	1.27155	+	2.20240i	0.0588405	+	0.101915i	0.893945	−	0.448176i	$-0.147926\pi$
$467$	1.27155	+	2.20240i	0.0588405	+	0.101915i	−0.835105	+	0.550091i	$0.814593\pi$
$468$		0			0
$469$	12.9382	+	21.1002i	0.597430	+	0.974314i
$470$	15.4980	+	8.94776i	0.714869	+	0.412730i
$471$		0			0
$472$	−24.2196			−1.11480
$473$	−0.232891	−	0.134459i	−0.0107083	−	0.00618245i
$474$		0			0
$475$	6.67268	−	3.85247i	0.306164	−	0.176764i
$476$	0.103949	+	3.92825i	0.00476449	+	0.180051i
$477$		0			0
$478$	8.30266			0.379755
$479$	16.9874	−	9.80768i	0.776174	−	0.448124i	−0.0588986	−	0.998264i	$-0.518759\pi$
$479$	16.9874	−	9.80768i	0.776174	−	0.448124i	0.835073	+	0.550140i	$0.185426\pi$
$480$		0			0
$481$	−10.3779	+	6.03885i	−0.473191	+	0.275348i
$482$	−11.8347			−0.539057
$483$		0			0
$484$	−9.08938	+	15.7433i	−0.413153	+	0.715603i
$485$	20.8048	−	36.0350i	0.944699	−	1.63627i
$486$		0			0
$487$			3.52506i			0.159736i	0.996805	+	0.0798678i	$0.0254498\pi$
$487$			3.52506i			0.159736i	−0.996805	+	0.0798678i	$0.974550\pi$
$488$	−27.6186	−	15.9456i	−1.25024	−	0.721824i
$489$		0			0
$490$	6.92648	+	10.6530i	0.312906	+	0.481252i
$491$	8.85905	−	15.3443i	0.399803	−	0.692480i	−0.593898	−	0.804540i	$-0.702412\pi$
$491$	8.85905	−	15.3443i	0.399803	−	0.692480i	0.993701	+	0.112061i	$0.0357451\pi$
$492$		0			0
$493$	−0.189918	+	0.328948i	−0.00855349	+	0.0148151i
$494$	3.16376	−	0.0107625i	0.142344	−	0.000484228i
$495$		0			0
$496$	−15.9795	−	9.22574i	−0.717499	−	0.414248i
$497$	−17.2126	−	28.0711i	−0.772092	−	1.25916i
$498$		0			0
$499$	10.2757	−	5.93271i	0.460006	−	0.265584i	−0.252041	−	0.967717i	$-0.581102\pi$
$499$	10.2757	−	5.93271i	0.460006	−	0.265584i	0.712047	+	0.702132i	$0.247768\pi$
$500$		−	0.171295i		−	0.00766053i
$501$		0			0
$502$	12.8429	−	7.41488i	0.573209	−	0.330942i
$503$	12.6878	+	21.9759i	0.565722	+	0.979858i	0.996982	+	0.0776311i	$0.0247356\pi$
$503$	12.6878	+	21.9759i	0.565722	+	0.979858i	−0.431261	+	0.902227i	$0.641931\pi$
$504$		0			0
$505$	−33.0451	−	19.0786i	−1.47049	−	0.848985i
$506$	0.458378	+	0.793935i	0.0203774	+	0.0352947i
$507$		0			0
$508$	−13.0423	+	22.5899i	−0.578657	+	1.00226i
$509$		−	12.9314i		−	0.573174i	−0.958054	−	0.286587i	$-0.907479\pi$
$509$		−	12.9314i		−	0.573174i	0.958054	−	0.286587i	$-0.0925208\pi$
$510$		0			0
$511$	8.58034	−	15.8134i	0.379572	−	0.699544i
$512$		−	20.6057i		−	0.910653i
$513$		0			0
$514$		−	1.08357i		−	0.0477940i
$515$	37.5545	+	21.6821i	1.65485	+	0.955427i
$516$		0			0
$517$	−1.73999	+	3.01375i	−0.0765247	+	0.132545i
$518$	0.133572	+	5.04773i	0.00586883	+	0.221784i
$519$		0			0
$520$	11.9443	−	20.8515i	0.523790	−	0.914401i
$521$	−11.6491	+	20.1769i	−0.510357	+	0.883964i	0.489571	+	0.871963i	$0.337153\pi$
$521$	−11.6491	+	20.1769i	−0.510357	+	0.883964i	−0.999928	+	0.0120008i	$0.996180\pi$
$522$		0			0
$523$	15.3596			0.671627			0.335813	−	0.941929i	$-0.390989\pi$
$523$	15.3596			0.671627			0.335813	+	0.941929i	$0.390989\pi$
$524$	4.56557	+	7.90781i	0.199448	+	0.345454i
$525$		0			0
$526$	3.02419	−	1.74602i	0.131861	−	0.0761299i
$527$	−6.64364	−	3.83571i	−0.289401	−	0.167086i
$528$		0			0
$529$	−2.46483			−0.107167
$530$	7.49652			0.325628
$531$		0			0
$532$	−3.22930	+	5.95155i	−0.140008	+	0.258032i
$533$	0.0671088	+	19.7274i	0.00290681	+	0.854487i
$534$		0			0
$535$	14.0762	−	8.12687i	0.608565	−	0.351355i
$536$	−9.84235	−	17.0475i	−0.425125	−	0.736338i
$537$		0			0
$538$		−	0.804692i		−	0.0346927i
$539$	−2.07159	+	1.34693i	−0.0892296	+	0.0580164i
$540$		0			0
$541$	27.6990	−	15.9920i	1.19087	−	0.687551i	0.232368	−	0.972628i	$-0.425353\pi$
$541$	27.6990	−	15.9920i	1.19087	−	0.687551i	0.958505	+	0.285077i	$0.0920193\pi$
$542$	−7.60053			−0.326471
$543$		0			0
$544$		−	4.82769i		−	0.206986i
$545$	3.16416			0.135538
$546$		0			0
$547$	−3.77706			−0.161496			−0.0807478	−	0.996735i	$-0.525731\pi$
$547$	−3.77706			−0.161496			−0.0807478	+	0.996735i	$0.525731\pi$
$548$			26.3716i			1.12654i
$549$		0			0
$550$	−1.01807			−0.0434105
$551$	−0.566817	+	0.327252i	−0.0241472	+	0.0139414i
$552$		0			0
$553$	15.7289	−	9.64465i	0.668861	−	0.410132i
$554$		−	9.67971i		−	0.411251i
$555$		0			0
$556$	7.79326	+	13.4983i	0.330508	+	0.572456i
$557$	−4.77707	+	2.75804i	−0.202411	+	0.116862i	−0.597780	−	0.801661i	$-0.703950\pi$
$557$	−4.77707	+	2.75804i	−0.202411	+	0.116862i	0.395369	+	0.918523i	$0.370617\pi$
$558$		0			0
$559$	1.36529	−	2.38344i	0.0577455	−	0.100809i
$560$	9.36204	+	15.2680i	0.395618	+	0.645191i
$561$		0			0
$562$	12.9264			0.545269
$563$	−2.65222			−0.111778			−0.0558888	−	0.998437i	$-0.517799\pi$
$563$	−2.65222			−0.111778			−0.0558888	+	0.998437i	$0.517799\pi$
$564$		0			0
$565$	8.01802	+	4.62920i	0.337321	+	0.194752i
$566$	−0.396195	+	0.228743i	−0.0166533	+	0.00961479i
$567$		0			0
$568$	13.0940	+	22.6795i	0.549412	+	0.951610i
$569$	−29.6363			−1.24242			−0.621210	−	0.783644i	$-0.713359\pi$
$569$	−29.6363			−1.24242			−0.621210	+	0.783644i	$0.713359\pi$
$570$		0			0
$571$	13.1073	−	22.7025i	0.548522	−	0.950068i	−0.449854	−	0.893102i	$-0.648524\pi$
$571$	13.1073	−	22.7025i	0.548522	−	0.950068i	0.998376	−	0.0569662i	$-0.0181427\pi$
$572$	1.84604	+	1.05745i	0.0771867	+	0.0442144i
$573$		0			0
$574$	7.29202	+	3.95664i	0.304363	+	0.165147i
$575$	−11.4022	+	19.7493i	−0.475506	+	0.823601i
$576$		0			0
$577$	−24.6222	−	14.2157i	−1.02504	−	0.591806i	−0.109478	−	0.993989i	$-0.534918\pi$
$577$	−24.6222	−	14.2157i	−1.02504	−	0.591806i	−0.915559	+	0.402183i	$0.868251\pi$
$578$			9.29033i			0.386427i
$579$		0			0
$580$			2.26326i			0.0939767i
$581$	39.6365	−	1.04886i	1.64440	−	0.0435139i
$582$		0			0
$583$			1.45778i			0.0603751i
$584$	−7.15431	+	12.3916i	−0.296048	+	0.512769i
$585$		0			0
$586$	−8.82501	−	15.2854i	−0.364558	−	0.631433i
$587$	−0.721765	−	0.416711i	−0.0297904	−	0.0171995i	0.485031	−	0.874497i	$-0.338808\pi$
$587$	−0.721765	−	0.416711i	−0.0297904	−	0.0171995i	−0.514821	+	0.857298i	$0.672142\pi$
$588$		0			0
$589$	−6.60938	−	11.4478i	−0.272335	−	0.471697i
$590$	−18.0947	+	10.4470i	−0.744945	+	0.430094i
$591$		0			0
$592$			7.11710i			0.292511i
$593$	23.9758	−	13.8424i	0.984566	−	0.568440i	0.0809207	−	0.996721i	$-0.474214\pi$
$593$	23.9758	−	13.8424i	0.984566	−	0.568440i	0.903646	+	0.428281i	$0.140881\pi$
$594$		0			0
$595$	3.89237	+	6.34784i	0.159572	+	0.260236i
$596$	4.06049	+	2.34432i	0.166324	+	0.0960272i
$597$		0			0
$598$	−8.09339	+	4.70950i	−0.330963	+	0.192586i
$599$	−12.4488	+	21.5620i	−0.508645	+	0.881000i	0.491304	+	0.870988i	$0.336520\pi$
$599$	−12.4488	+	21.5620i	−0.508645	+	0.881000i	−0.999950	+	0.0100118i	$0.996813\pi$
$600$		0			0
$601$	15.3339	−	26.5592i	0.625485	−	1.08337i	−0.362962	−	0.931804i	$-0.618235\pi$
$601$	15.3339	−	26.5592i	0.625485	−	1.08337i	0.988447	−	0.151568i	$-0.0484321\pi$
$602$	−0.603833	−	0.984756i	−0.0246104	−	0.0401356i
$603$		0			0
$604$	−29.2746	−	16.9017i	−1.19116	−	0.687719i
$605$			34.4466i			1.40045i
$606$		0			0
$607$	−4.11638	+	7.12977i	−0.167079	+	0.289388i	−0.937391	−	0.348278i	$-0.886767\pi$
$607$	−4.11638	+	7.12977i	−0.167079	+	0.289388i	0.770313	+	0.637666i	$0.220100\pi$
$608$	4.15934	−	7.20419i	0.168684	−	0.292169i
$609$		0			0
$610$	−27.5121			−1.11393
$611$	−30.8432	−	17.6677i	−1.24778	−	0.714759i
$612$		0			0
$613$	−33.7573	+	19.4898i	−1.36344	+	0.787184i	−0.990080	−	0.140502i	$-0.955128\pi$
$613$	−33.7573	+	19.4898i	−1.36344	+	0.787184i	−0.373362	+	0.927686i	$0.621795\pi$
$614$	12.2737			0.495326
$615$		0			0
$616$	1.67531	−	1.02727i	0.0675003	−	0.0413898i
$617$	39.3193	−	22.7010i	1.58293	−	0.913907i	0.588506	−	0.808493i	$-0.299716\pi$
$617$	39.3193	−	22.7010i	1.58293	−	0.913907i	0.994428	−	0.105414i	$-0.0336169\pi$
$618$		0			0
$619$	−20.2395	−	11.6853i	−0.813495	−	0.469672i	0.0346730	−	0.999399i	$-0.488961\pi$
$619$	−20.2395	−	11.6853i	−0.813495	−	0.469672i	−0.848168	+	0.529727i	$0.822294\pi$
$620$	−45.7101			−1.83576
$621$		0			0
$622$	−9.62253	−	5.55557i	−0.385828	−	0.222758i
$623$	−16.1624	+	0.427686i	−0.647532	+	0.0171349i
$624$		0			0
$625$	12.4186	+	21.5096i	0.496744	+	0.860385i
$626$	3.82317	−	2.20731i	0.152805	−	0.0882218i
$627$		0			0
$628$	3.88035	−	6.72096i	0.154843	−	0.268195i
$629$			2.95901i			0.117984i
$630$		0			0
$631$	27.7776	−	16.0374i	1.10581	−	0.638439i	0.168069	−	0.985775i	$-0.446247\pi$
$631$	27.7776	−	16.0374i	1.10581	−	0.638439i	0.937741	+	0.347336i	$0.112914\pi$
$632$	−12.7079	+	7.33689i	−0.505492	+	0.291846i
$633$		0			0
$634$	−4.22927	−	7.32532i	−0.167966	−	0.290926i
$635$			49.4272i			1.96146i
$636$		0			0
$637$	−13.8296	−	21.1126i	−0.547950	−	0.836511i
$638$	0.0864806			0.00342380
$639$		0			0
$640$	−18.2624	−	31.6314i	−0.721885	−	1.25034i
$641$	31.2142			1.23289			0.616444	−	0.787399i	$-0.288573\pi$
$641$	31.2142			1.23289			0.616444	+	0.787399i	$0.288573\pi$
$642$		0			0
$643$	−6.24367	+	3.60479i	−0.246226	+	0.142159i	−0.618035	−	0.786150i	$-0.712071\pi$
$643$	−6.24367	+	3.60479i	−0.246226	+	0.142159i	0.371809	+	0.928309i	$0.378738\pi$
$644$	−0.530134	−	20.0339i	−0.0208902	−	0.789446i
$645$		0			0
$646$	0.389841	−	0.675224i	0.0153381	−	0.0265663i
$647$	−11.5276	−	19.9664i	−0.453196	−	0.784959i	0.545386	−	0.838185i	$-0.316383\pi$
$647$	−11.5276	−	19.9664i	−0.453196	−	0.784959i	−0.998583	+	0.0532257i	$0.983050\pi$
$648$		0			0
$649$	−2.03153	−	3.51871i	−0.0797444	−	0.138121i
$650$	−0.0353742	−	10.3986i	−0.00138749	−	0.407868i
$651$		0			0
$652$	4.72393	+	2.72736i	0.185003	+	0.106812i
$653$	17.4861			0.684284			0.342142	−	0.939648i	$-0.388848\pi$
$653$	17.4861			0.684284			0.342142	+	0.939648i	$0.388848\pi$
$654$		0			0
$655$	14.9844	+	8.65123i	0.585488	+	0.338031i
$656$	10.1267	+	5.84668i	0.395383	+	0.228275i
$657$		0			0
$658$	−12.7434	+	7.81398i	−0.496789	+	0.304621i
$659$	−20.2279	−	35.0357i	−0.787967	−	1.36480i	−0.927211	−	0.374540i	$-0.877801\pi$
$659$	−20.2279	−	35.0357i	−0.787967	−	1.36480i	0.139244	−	0.990258i	$-0.455533\pi$
$660$		0			0
$661$	−38.7038	+	22.3457i	−1.50540	+	0.869146i	−0.505424	+	0.862871i	$0.668664\pi$
$661$	−38.7038	+	22.3457i	−1.50540	+	0.869146i	−0.999980	+	0.00627497i	$0.998003\pi$
$662$	0.474392	−	0.821670i	0.0184378	−	0.0319351i
$663$		0			0
$664$	−31.5343			−1.22377
$665$	0.339404	+	12.8262i	0.0131615	+	0.497378i
$666$		0			0
$667$	0.968574	−	1.67762i	0.0375033	−	0.0649577i
$668$	−34.9486	−	20.1776i	−1.35220	−	0.780694i
$669$		0			0
$670$	−14.7066	−	8.49085i	−0.568165	−	0.328030i
$671$		−	5.35002i		−	0.206535i
$672$		0			0
$673$	6.76618	−	11.7194i	0.260817	−	0.451748i	−0.705642	−	0.708568i	$-0.749341\pi$
$673$	6.76618	−	11.7194i	0.260817	−	0.451748i	0.966459	+	0.256820i	$0.0826748\pi$
$674$			1.65436i			0.0637237i
$675$		0			0
$676$	−10.7368	+	18.8923i	−0.412953	+	0.726628i
$677$	−16.7974	−	29.0939i	−0.645575	−	1.11817i	−0.984168	−	0.177237i	$-0.943284\pi$
$677$	−16.7974	−	29.0939i	−0.645575	−	1.11817i	0.338593	−	0.940933i	$-0.390049\pi$
$678$		0			0
$679$	18.1686	+	29.6302i	0.697249	+	1.13710i
$680$	−2.96101	−	5.12862i	−0.113549	−	0.196673i
$681$		0			0
$682$			1.74661i			0.0668813i
$683$			41.2155i			1.57707i	0.614992	+	0.788533i	$0.289159\pi$
$683$			41.2155i			1.57707i	−0.614992	+	0.788533i	$0.710841\pi$
$684$		0			0
$685$	24.9856	+	43.2763i	0.954650	+	1.65350i
$686$	−10.5807	+	0.841524i	−0.403972	+	0.0321295i
$687$		0			0
$688$	−0.814069	−	1.41001i	−0.0310361	−	0.0537561i
$689$	−14.8899	+	0.0506527i	−0.567260	+	0.00192971i
$690$		0			0
$691$			4.37493i			0.166430i	0.996532	+	0.0832152i	$0.0265189\pi$
$691$			4.37493i			0.166430i	−0.996532	+	0.0832152i	$0.973481\pi$
$692$	−16.0397	+	27.7815i	−0.609737	+	1.05610i
$693$		0			0
$694$		−	16.6703i		−	0.632796i
$695$	25.5777	+	14.7673i	0.970218	+	0.560156i
$696$		0			0
$697$	4.21031	+	2.43082i	0.159477	+	0.0920740i
$698$	−5.25269	+	9.09792i	−0.198817	+	0.344361i
$699$		0			0
$700$	19.5615	+	10.6141i	0.739356	+	0.401174i
$701$	−41.1220			−1.55316			−0.776579	−	0.630020i	$-0.783047\pi$
$701$	−41.1220			−1.55316			−0.776579	+	0.630020i	$0.783047\pi$
$702$		0			0
$703$	−2.54936	+	4.41563i	−0.0961511	+	0.166539i
$704$	0.354780	−	0.204832i	0.0133713	−	0.00771991i
$705$		0			0
$706$	2.04837	+	3.54788i	0.0770915	+	0.133526i
$707$	27.1716	−	16.6611i	1.02189	−	0.626606i
$708$		0			0
$709$	16.5571	+	9.55925i	0.621815	+	0.359005i	0.777575	−	0.628790i	$-0.216449\pi$
$709$	16.5571	+	9.55925i	0.621815	+	0.359005i	−0.155760	+	0.987795i	$0.549783\pi$
$710$	19.5652	+	11.2960i	0.734271	+	0.423931i
$711$		0			0
$712$	12.8586			0.481896
$713$	33.8822	+	19.5619i	1.26890	+	0.732599i
$714$		0			0
$715$	4.03125	−	0.0137136i	0.150760	−	0.000512859i
$716$	−19.0452	−	32.9872i	−0.711752	−	1.23279i
$717$		0			0
$718$	4.30454	+	7.45568i	0.160644	+	0.278243i
$719$	−7.49690	+	12.9850i	−0.279587	+	0.484259i	−0.971282	−	0.237931i	$-0.923531\pi$
$719$	−7.49690	+	12.9850i	−0.279587	+	0.484259i	0.691695	+	0.722190i	$0.256864\pi$
$720$		0			0
$721$	−30.8796	+	18.9347i	−1.15001	+	0.705166i
$722$	−8.26668	+	4.77277i	−0.307654	+	0.177624i
$723$		0			0
$724$	2.21346			0.0822628
$725$	1.07561	+	1.86301i	0.0399471	+	0.0691905i
$726$		0			0
$727$	18.8699			0.699847			0.349923	−	0.936778i	$-0.386208\pi$
$727$	18.8699			0.699847			0.349923	+	0.936778i	$0.386208\pi$
$728$	10.5508	+	17.0761i	0.391039	+	0.632882i
$729$		0			0
$730$			12.3438i			0.456866i
$731$	−0.338458	−	0.586227i	−0.0125183	−	0.0216824i
$732$		0			0
$733$	22.4233	−	12.9461i	0.828225	−	0.478176i	−0.0250198	−	0.999687i	$-0.507965\pi$
$733$	22.4233	−	12.9461i	0.828225	−	0.478176i	0.853244	+	0.521511i	$0.174632\pi$
$734$	2.00962	−	1.16026i	0.0741766	−	0.0428259i
$735$		0			0
$736$			24.6210i			0.907541i
$737$	1.65114	−	2.85986i	0.0608205	−	0.105344i
$738$		0			0
$739$	34.6057	−	19.9796i	1.27299	−	0.734962i	0.297442	−	0.954740i	$-0.403867\pi$
$739$	34.6057	−	19.9796i	1.27299	−	0.734962i	0.975550	+	0.219778i	$0.0705332\pi$
$740$	8.81564	+	15.2691i	0.324069	+	0.561305i
$741$		0			0
$742$	−2.98641	+	5.50391i	−0.109635	+	0.202055i
$743$	10.9942	+	6.34749i	0.403337	+	0.232867i	0.687923	−	0.725784i	$-0.258523\pi$
$743$	10.9942	+	6.34749i	0.403337	+	0.232867i	−0.284586	+	0.958651i	$0.591856\pi$
$744$		0			0
$745$	8.88444			0.325501
$746$	9.43485	+	5.44721i	0.345434	+	0.199437i
$747$		0			0
$748$	0.454049	−	0.262145i	0.0166017	−	0.00958498i
$749$	0.359144	+	13.5722i	0.0131229	+	0.495916i
$750$		0			0
$751$	−37.3088			−1.36142			−0.680709	−	0.732554i	$-0.738328\pi$
$751$	−37.3088			−1.36142			−0.680709	+	0.732554i	$0.738328\pi$
$752$	−18.2464	+	10.5346i	−0.665379	+	0.384157i
$753$		0			0
$754$	0.00300489	+	0.883320i	0.000109432	+	0.0321686i
$755$	−64.0534			−2.33114
$756$		0			0
$757$	12.2949	−	21.2953i	0.446864	−	0.773992i	−0.551316	−	0.834297i	$-0.685874\pi$
$757$	12.2949	−	21.2953i	0.446864	−	0.773992i	0.998180	+	0.0603051i	$0.0192074\pi$
$758$	4.77812	−	8.27594i	0.173549	−	0.300596i
$759$		0			0
$760$		−	10.2043i		−	0.370150i
$761$	−12.4784	−	7.20440i	−0.452341	−	0.261159i	0.256477	−	0.966550i	$-0.417438\pi$
$761$	−12.4784	−	7.20440i	−0.452341	−	0.261159i	−0.708818	+	0.705391i	$0.750771\pi$
$762$		0			0
$763$	−1.26052	+	2.32311i	−0.0456337	+	0.0841021i
$764$	−6.49928	+	11.2571i	−0.235136	+	0.407267i
$765$		0			0
$766$	−2.47609	+	4.28871i	−0.0894646	+	0.154957i
$767$	35.8698	−	20.8724i	1.29518	−	0.753660i
$768$		0			0
$769$	−22.7651	−	13.1435i	−0.820932	−	0.473965i	0.0298056	−	0.999556i	$-0.490511\pi$
$769$	−22.7651	−	13.1435i	−0.820932	−	0.473965i	−0.850738	+	0.525590i	$0.823845\pi$
$770$	0.808533	−	1.49011i	0.0291375	−	0.0536999i
$771$		0			0
$772$	−15.8846	+	9.17100i	−0.571701	+	0.330071i
$773$			43.6593i			1.57032i	0.619295	+	0.785158i	$0.287418\pi$
$773$			43.6593i			1.57032i	−0.619295	+	0.785158i	$0.712582\pi$
$774$		0			0
$775$	−37.6265	+	21.7237i	−1.35158	+	0.780337i
$776$	−13.8213	−	23.9391i	−0.496155	−	0.859365i
$777$		0			0
$778$	3.51444	+	2.02906i	0.125999	+	0.0727455i
$779$	4.18860	+	7.25486i	0.150072	+	0.259932i
$780$		0			0
$781$	−2.19663	+	3.80468i	−0.0786017	+	0.136142i
$782$			2.30764i			0.0825210i
$783$		0			0
$784$	−14.9393	+	0.791195i	−0.533545	+	0.0282570i
$785$		−	14.7056i		−	0.524866i
$786$		0			0
$787$			15.8702i			0.565710i	0.959163	+	0.282855i	$0.0912815\pi$
$787$			15.8702i			0.565710i	−0.959163	+	0.282855i	$0.908718\pi$
$788$	−8.70738	−	5.02721i	−0.310188	−	0.179087i
$789$		0			0
$790$	−6.32942	+	10.9629i	−0.225191	+	0.390042i
$791$	−6.59290	+	4.04263i	−0.234416	+	0.143740i
$792$		0			0
$793$	54.6456	−	0.185894i	1.94052	−	0.00660130i
$794$	−6.20359	+	10.7449i	−0.220157	+	0.381324i
$795$		0			0
$796$	24.7814			0.878353
$797$	−14.7381	−	25.5272i	−0.522051	−	0.904219i	−0.999671	−	0.0256525i	$-0.991834\pi$
$797$	−14.7381	−	25.5272i	−0.522051	−	0.904219i	0.477620	−	0.878567i	$-0.341500\pi$
$798$		0			0
$799$	−7.58615	+	4.37987i	−0.268379	+	0.154949i
$800$	−23.6787	−	13.6709i	−0.837169	−	0.483340i
$801$		0			0
$802$	−8.45876			−0.298689
$803$	−2.40040			−0.0847081
$804$		0			0
$805$	−19.8509	−	32.3737i	−0.699652	−	1.14102i
$806$	−17.8401	+	0.0606886i	−0.628390	+	0.00213766i
$807$		0			0
$808$	−21.9528	+	12.6745i	−0.772297	+	0.445886i
$809$	3.24854	+	5.62663i	0.114212	+	0.197822i	0.917465	−	0.397817i	$-0.130232\pi$
$809$	3.24854	+	5.62663i	0.114212	+	0.197822i	−0.803252	+	0.595639i	$0.796899\pi$
$810$		0			0
$811$			20.7305i			0.727945i	0.931410	+	0.363972i	$0.118580\pi$
$811$			20.7305i			0.727945i	−0.931410	+	0.363972i	$0.881420\pi$
$812$	−1.66167	−	0.901621i	−0.0583132	−	0.0316407i
$813$		0			0
$814$	0.583444	−	0.336851i	0.0204497	−	0.0118066i
$815$	10.3361			0.362056
$816$		0			0
$817$		−	1.16641i		−	0.0408074i
$818$	−10.0367			−0.350924
$819$		0			0
$820$	28.9681			1.01161
$821$		−	25.1122i		−	0.876420i	−0.898873	−	0.438210i	$-0.855613\pi$
$821$		−	25.1122i		−	0.876420i	0.898873	−	0.438210i	$-0.144387\pi$
$822$		0			0
$823$	50.5413			1.76176			0.880880	−	0.473339i	$-0.156952\pi$
$823$	50.5413			1.76176			0.880880	+	0.473339i	$0.156952\pi$
$824$	24.9485	−	14.4040i	0.869123	−	0.501789i
$825$		0			0
$826$	−0.461674	−	17.4468i	−0.0160637	−	0.607051i
$827$		−	7.58852i		−	0.263879i	−0.991258	−	0.131939i	$-0.957880\pi$
$827$		−	7.58852i		−	0.263879i	0.991258	−	0.131939i	$-0.0421204\pi$
$828$		0			0
$829$	19.4095	+	33.6183i	0.674120	+	1.16761i	0.976725	+	0.214495i	$0.0688104\pi$
$829$	19.4095	+	33.6183i	0.674120	+	1.16761i	−0.302605	+	0.953116i	$0.597856\pi$
$830$	−23.5595	+	13.6021i	−0.817763	+	0.472135i
$831$		0			0
$832$	2.10450	+	3.61664i	0.0729606	+	0.125384i
$833$	−6.21117	+	0.328948i	−0.215204	+	0.0113974i
$834$		0			0
$835$	−76.4683			−2.64629
$836$	0.903415			0.0312453
$837$		0			0
$838$	15.2954	+	8.83083i	0.528373	+	0.305056i
$839$	0.124870	−	0.0720936i	0.00431098	−	0.00248895i	−0.497843	−	0.867267i	$-0.665874\pi$
$839$	0.124870	−	0.0720936i	0.00431098	−	0.00248895i	0.502154	+	0.864778i	$0.332541\pi$
$840$		0			0
$841$	14.4086	+	24.9565i	0.496849	+	0.860568i
$842$	−16.8311			−0.580037
$843$		0			0
$844$	−17.3540	+	30.0580i	−0.597349	+	1.03464i
$845$	0.280143	+	41.1751i	0.00963722	+	1.41647i
$846$		0			0
$847$	−25.2905	−	13.7226i	−0.868992	−	0.471514i
$848$	−4.41299	+	7.64351i	−0.151543	+	0.262479i
$849$		0			0
$850$	−2.21932	−	1.28133i	−0.0761222	−	0.0439492i
$851$		−	15.0908i		−	0.517306i
$852$		0			0
$853$			2.84303i			0.0973435i	0.998815	+	0.0486718i	$0.0154988\pi$
$853$			2.84303i			0.0973435i	−0.998815	+	0.0486718i	$0.984501\pi$
$854$	10.9601	−	20.1992i	0.375046	−	0.691202i
$855$		0			0
$856$		−	10.7978i		−	0.369062i
$857$	16.0653	−	27.8259i	0.548779	−	0.950513i	−0.449580	−	0.893240i	$-0.648426\pi$
$857$	16.0653	−	27.8259i	0.548779	−	0.950513i	0.998359	−	0.0572728i	$-0.0182405\pi$
$858$		0			0
$859$	−14.7024	−	25.4653i	−0.501640	−	0.868866i	−0.999998	−	0.00189479i	$-0.999397\pi$
$859$	−14.7024	−	25.4653i	−0.501640	−	0.868866i	0.498358	−	0.866971i	$-0.333936\pi$
$860$	−3.49303	−	2.01670i	−0.119111	−	0.0687690i
$861$		0			0
$862$	−6.10149	−	10.5681i	−0.207818	−	0.359951i
$863$	−36.9726	+	21.3461i	−1.25856	+	0.726631i	−0.972795	−	0.231669i	$-0.925582\pi$
$863$	−36.9726	+	21.3461i	−1.25856	+	0.726631i	−0.285767	+	0.958299i	$0.592248\pi$
$864$		0			0
$865$			60.7866i			2.06681i
$866$	8.73696	−	5.04429i	0.296894	−	0.171412i
$867$		0			0
$868$	18.2097	−	33.5601i	0.618077	−	1.13910i
$869$	−2.13185	−	1.23083i	−0.0723182	−	0.0417529i
$870$		0			0
$871$	29.2682	+	16.7655i	0.991715	+	0.568078i
$872$	1.05102	−	1.82042i	0.0355921	−	0.0616473i
$873$		0			0
$874$	−1.98817	+	3.44361i	−0.0672508	+	0.116482i
$875$	0.271033	−	0.00717203i	0.00916258	−	0.000242459i
$876$		0			0
$877$	−11.3481	−	6.55181i	−0.383197	−	0.221239i	0.296011	−	0.955184i	$-0.404343\pi$
$877$	−11.3481	−	6.55181i	−0.383197	−	0.221239i	−0.679208	+	0.733945i	$0.737677\pi$
$878$		−	13.0744i		−	0.441241i
$879$		0			0
$880$	1.19476	−	2.06938i	0.0402753	−	0.0697589i
$881$	18.9666	−	32.8512i	0.639002	−	1.10678i	−0.346650	−	0.937995i	$-0.612681\pi$
$881$	18.9666	−	32.8512i	0.639002	−	1.10678i	0.985652	−	0.168790i	$-0.0539859\pi$
$882$		0			0
$883$	15.9034			0.535194			0.267597	−	0.963531i	$-0.413770\pi$
$883$	15.9034			0.535194			0.267597	+	0.963531i	$0.413770\pi$
$884$	2.69335	+	4.62859i	0.0905872	+	0.155676i
$885$		0			0
$886$	19.3856	−	11.1923i	0.651271	−	0.376012i
$887$	10.1640			0.341275			0.170637	−	0.985334i	$-0.445417\pi$
$887$	10.1640			0.341275			0.170637	+	0.985334i	$0.445417\pi$
$888$		0			0
$889$	−36.2892	−	19.6905i	−1.21710	−	0.660397i
$890$	9.60673	−	5.54645i	0.322018	−	0.185917i
$891$		0			0
$892$	−10.3004	−	5.94695i	−0.344884	−	0.199119i
$893$	−15.0941			−0.505104
$894$		0			0
$895$	−62.5070	−	36.0884i	−2.08938	−	1.20630i
$896$	30.4989	−	0.807057i	1.01890	−	0.0269619i
$897$		0			0
$898$	−3.43616	−	5.95161i	−0.114666	−	0.198608i
$899$	3.19622	−	1.84534i	0.106600	−	0.0615454i
$900$		0			0
$901$	−1.83475	+	3.17788i	−0.0611243	+	0.105870i
$902$		−	1.10689i		−	0.0368554i
$903$		0			0
$904$	5.32660	−	3.07532i	0.177160	−	0.102283i
$905$	3.63233	−	2.09713i	0.120743	−	0.0697109i
$906$		0			0
$907$	−14.4751	−	25.0717i	−0.480639	−	0.832492i	0.519114	−	0.854705i	$-0.326262\pi$
$907$	−14.4751	−	25.0717i	−0.480639	−	0.832492i	−0.999753	+	0.0222132i	$0.992929\pi$
$908$		−	6.20138i		−	0.205800i
$909$		0			0
$910$	15.2482	+	8.20665i	0.505474	+	0.272048i
$911$	−2.42075			−0.0802032			−0.0401016	−	0.999196i	$-0.512768\pi$
$911$	−2.42075			−0.0802032			−0.0401016	+	0.999196i	$0.512768\pi$
$912$		0			0
$913$	−2.64508	−	4.58141i	−0.0875393	−	0.151622i
$914$	−1.42778			−0.0472267
$915$		0			0
$916$	18.8892	−	10.9057i	0.624116	−	0.360333i
$917$	−12.3211	+	7.55502i	−0.406877	+	0.249489i
$918$		0			0
$919$	−1.55235	+	2.68875i	−0.0512074	+	0.0886937i	−0.890493	−	0.454997i	$-0.849640\pi$
$919$	−1.55235	+	2.68875i	−0.0512074	+	0.0886937i	0.839286	+	0.543691i	$0.182974\pi$
$920$	15.1010	+	26.1557i	0.497865	+	0.862327i
$921$		0			0
$922$	−9.26911	−	16.0546i	−0.305262	−	0.528729i
$923$	−38.9377	−	22.3044i	−1.28165	−	0.734158i
$924$		0			0
$925$	14.5133	+	8.37924i	0.477193	+	0.275508i
$926$	13.4598			0.442316
$927$		0			0
$928$	2.01141	+	1.16129i	0.0660277	+	0.0381211i
$929$	−7.09737	−	4.09767i	−0.232857	−	0.134440i	0.379032	−	0.925383i	$-0.376257\pi$
$929$	−7.09737	−	4.09767i	−0.232857	−	0.134440i	−0.611889	+	0.790943i	$0.709590\pi$
$930$		0			0
$931$	−9.55211	−	4.86041i	−0.313058	−	0.159294i
$932$	13.5403	+	23.4525i	0.443528	+	0.768214i
$933$		0			0
$934$	1.26221	−	0.728736i	0.0413007	−	0.0238450i
$935$	0.496735	−	0.860369i	0.0162450	−	0.0281371i
$936$		0			0
$937$	53.8795			1.76017			0.880084	−	0.474819i	$-0.157486\pi$
$937$	53.8795			1.76017			0.880084	+	0.474819i	$0.157486\pi$
$938$	12.0926	−	7.41497i	0.394839	−	0.242107i
$939$		0			0
$940$	−26.0974	+	45.2021i	−0.851205	+	1.47433i
$941$	2.93824	+	1.69639i	0.0957838	+	0.0553008i	0.547127	−	0.837050i	$-0.315722\pi$
$941$	2.93824	+	1.69639i	0.0957838	+	0.0553008i	−0.451343	+	0.892351i	$0.649055\pi$
$942$		0			0
$943$	−21.4724	−	12.3971i	−0.699236	−	0.403704i
$944$		−	24.5993i		−	0.800638i
$945$		0			0
$946$	−0.0770596	+	0.133471i	−0.00250542	+	0.00433952i
$947$		−	44.1524i		−	1.43476i	−0.696681	−	0.717381i	$-0.745341\pi$
$947$		−	44.1524i		−	1.43476i	0.696681	−	0.717381i	$-0.254659\pi$
$948$		0			0
$949$	−0.0834051	−	24.5178i	−0.00270745	−	0.795883i
$950$	−2.20788	−	3.82416i	−0.0716331	−	0.124072i
$951$		0			0
$952$	4.94499	−	0.130854i	0.160268	−	0.00424099i
$953$	−8.43489	−	14.6097i	−0.273233	−	0.473253i	0.696455	−	0.717601i	$-0.254760\pi$
$953$	−8.43489	−	14.6097i	−0.273233	−	0.473253i	−0.969688	+	0.244347i	$0.921426\pi$
$954$		0			0
$955$			24.6308i			0.797033i
$956$			24.2159i			0.783198i
$957$		0			0
$958$	−5.62085	−	9.73559i	−0.181601	−	0.314543i
$959$	−41.7268	+	1.10417i	−1.34743	+	0.0356555i
$960$		0			0
$961$	21.7695	+	37.7059i	0.702242	+	1.21632i
$962$	3.46090	+	5.94764i	0.111584	+	0.191760i
$963$		0			0
$964$		−	34.5177i		−	1.11174i
$965$	−17.3780	+	30.0995i	−0.559417	+	0.968938i
$966$		0			0
$967$		−	21.6217i		−	0.695308i	−0.937623	−	0.347654i	$-0.886978\pi$
$967$		−	21.6217i		−	0.695308i	0.937623	−	0.347654i	$-0.113022\pi$
$968$	19.8180	+	11.4419i	0.636976	+	0.367758i
$969$		0			0
$970$	−20.6519	−	11.9234i	−0.663093	−	0.382837i
$971$	18.1828	−	31.4936i	0.583515	−	1.01068i	−0.411544	−	0.911390i	$-0.635010\pi$
$971$	18.1828	−	31.4936i	0.583515	−	1.01068i	0.995059	−	0.0992873i	$-0.0316563\pi$
$972$		0			0
$973$	−21.0315	+	12.8961i	−0.674241	+	0.413431i
$974$	2.02023			0.0647325
$975$		0			0
$976$	16.1956	−	28.0515i	0.518407	−	0.897907i
$977$	−10.4549	+	6.03614i	−0.334482	+	0.193113i	−0.657829	−	0.753167i	$-0.728525\pi$
$977$	−10.4549	+	6.03614i	−0.334482	+	0.193113i	0.323347	+	0.946280i	$0.395192\pi$
$978$		0			0
$979$	1.07857	+	1.86814i	0.0344712	+	0.0597059i
$980$	−31.0709	+	20.2021i	−0.992524	+	0.645331i
$981$		0			0
$982$	−8.79393	−	5.07718i	−0.280626	−	0.162019i
$983$	−10.8771	−	6.27988i	−0.346925	−	0.200297i	0.316405	−	0.948624i	$-0.397524\pi$
$983$	−10.8771	−	6.27988i	−0.346925	−	0.200297i	−0.663330	+	0.748327i	$0.730857\pi$
$984$		0			0
$985$	−19.0519			−0.607045
$986$	0.188522	+	0.108843i	0.00600378	+	0.00346628i
$987$		0			0
$988$	0.0313904	+	9.22756i	0.000998663	+	0.293568i
$989$	1.72612	+	2.98973i	0.0548874	+	0.0950678i
$990$		0			0
$991$	4.56723	+	7.91068i	0.145083	+	0.251291i	0.929404	−	0.369064i	$-0.120322\pi$
$991$	4.56723	+	7.91068i	0.145083	+	0.251291i	−0.784321	+	0.620355i	$0.786988\pi$
$992$	−23.4541	+	40.6236i	−0.744667	+	1.28980i
$993$		0			0
$994$	−16.0877	+	9.86468i	−0.510272	+	0.312888i
$995$	40.6667	−	23.4789i	1.28922	−	0.744332i
$996$		0			0
$997$	−14.9919			−0.474798			−0.237399	−	0.971412i	$-0.576295\pi$
$997$	−14.9919			−0.474798			−0.237399	+	0.971412i	$0.576295\pi$
$998$	−3.40007	−	5.88910i	−0.107627	−	0.186416i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.bm.e.550.3		12
3.2	odd	2		273.2.t.c.4.4	✓	12
7.2	even	3		819.2.do.f.667.3		12
13.10	even	6		819.2.do.f.361.3		12
21.2	odd	6		273.2.bl.c.121.4	yes	12
39.23	odd	6		273.2.bl.c.88.4	yes	12
91.23	even	6	inner	819.2.bm.e.478.4		12
273.23	odd	6		273.2.t.c.205.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.t.c.4.4	✓	12	3.2	odd	2
273.2.t.c.205.3	yes	12	273.23	odd	6
273.2.bl.c.88.4	yes	12	39.23	odd	6
273.2.bl.c.121.4	yes	12	21.2	odd	6
819.2.bm.e.478.4		12	91.23	even	6	inner
819.2.bm.e.550.3		12	1.1	even	1	trivial
819.2.do.f.361.3		12	13.10	even	6
819.2.do.f.667.3		12	7.2	even	3

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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.bm (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.573107i q^{2} +1.67155 q^{4} +(2.74304 - 1.58369i) q^{5} +(0.0699870 + 2.64483i) q^{7} -2.10419i q^{8} +O(q^{10})\)	\(q-0.573107i q^{2} +1.67155 q^{4} +(2.74304 - 1.58369i) q^{5} +(0.0699870 + 2.64483i) q^{7} -2.10419i q^{8} +(-0.907626 - 1.57205i) q^{10} +(0.305703 - 0.176498i) q^{11} +(1.81339 + 3.11635i) q^{13} +(1.51577 - 0.0401100i) q^{14} +2.13717 q^{16} +0.888553 q^{17} +(1.32596 + 0.765541i) q^{19} +(4.58512 - 2.64722i) q^{20} +(-0.101152 - 0.175201i) q^{22} -4.53157 q^{23} +(2.51618 - 4.35815i) q^{25} +(1.78600 - 1.03926i) q^{26} +(0.116987 + 4.42095i) q^{28} +(-0.213739 + 0.370207i) q^{29} +(-7.47692 - 4.31680i) q^{31} -5.43321i q^{32} -0.509236i q^{34} +(4.38057 + 7.14402i) q^{35} +3.33015i q^{37} +(0.438737 - 0.759914i) q^{38} +(-3.33239 - 5.77187i) q^{40} +(4.73839 + 2.73571i) q^{41} +(-0.380909 - 0.659754i) q^{43} +(0.510998 - 0.295025i) q^{44} +2.59708i q^{46} +(-8.53765 + 4.92921i) q^{47} +(-6.99020 + 0.370207i) q^{49} +(-2.49768 - 1.44204i) q^{50} +(3.03117 + 5.20913i) q^{52} +(-2.06487 + 3.57646i) q^{53} +(0.559038 - 0.968281i) q^{55} +(5.56521 - 0.147266i) q^{56} +(0.212168 + 0.122495i) q^{58} -11.5102i q^{59} +(7.57803 - 13.1255i) q^{61} +(-2.47399 + 4.28507i) q^{62} +1.16054 q^{64} +(9.90954 + 5.67641i) q^{65} +(8.10167 - 4.67750i) q^{67} +1.48526 q^{68} +(4.09429 - 2.51054i) q^{70} +(-10.7783 + 6.22283i) q^{71} +(-5.88903 - 3.40003i) q^{73} +1.90853 q^{74} +(2.21640 + 1.27964i) q^{76} +(0.488201 + 0.796179i) q^{77} +(-3.48680 - 6.03932i) q^{79} +(5.86235 - 3.38463i) q^{80} +(1.56785 - 2.71560i) q^{82} -14.9864i q^{83} +(2.43734 - 1.40720i) q^{85} +(-0.378110 + 0.218302i) q^{86} +(-0.371385 - 0.643258i) q^{88} +6.11094i q^{89} +(-8.11528 + 5.01420i) q^{91} -7.57475 q^{92} +(2.82497 + 4.89298i) q^{94} +4.84953 q^{95} +(11.3769 - 6.56845i) q^{97} +(0.212168 + 4.00613i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7	\( 12 q - 10 q^{4} + 6 q^{5} - 3 q^{7} - 7 q^{10} + 18 q^{11} - q^{13} + 16 q^{14} - 6 q^{16} + 9 q^{19} + 27 q^{20} + 7 q^{22} - 32 q^{23} + 10 q^{25} + 7 q^{26} + 36 q^{28} + 5 q^{29} - 15 q^{31} + 2 q^{35} - 24 q^{38} + 21 q^{40} + 15 q^{41} - 13 q^{43} - 30 q^{44} - 9 q^{47} - 3 q^{49} + 63 q^{50} + 32 q^{52} - 18 q^{53} + 13 q^{55} - 3 q^{56} - 57 q^{58} + 26 q^{61} + 13 q^{62} - 4 q^{64} - 10 q^{65} - 24 q^{67} + 42 q^{70} + 15 q^{71} + 18 q^{73} + 76 q^{74} - 30 q^{76} - 20 q^{77} - 4 q^{79} - 39 q^{80} - 14 q^{82} - 12 q^{85} - 15 q^{86} + 16 q^{88} + 4 q^{91} + 40 q^{92} - 3 q^{94} - 56 q^{95} + 45 q^{97} - 57 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^5 - 3 * q^7 - 7 * q^10 + 18 * q^11 - q^13 + 16 * q^14 - 6 * q^16 + 9 * q^19 + 27 * q^20 + 7 * q^22 - 32 * q^23 + 10 * q^25 + 7 * q^26 + 36 * q^28 + 5 * q^29 - 15 * q^31 + 2 * q^35 - 24 * q^38 + 21 * q^40 + 15 * q^41 - 13 * q^43 - 30 * q^44 - 9 * q^47 - 3 * q^49 + 63 * q^50 + 32 * q^52 - 18 * q^53 + 13 * q^55 - 3 * q^56 - 57 * q^58 + 26 * q^61 + 13 * q^62 - 4 * q^64 - 10 * q^65 - 24 * q^67 + 42 * q^70 + 15 * q^71 + 18 * q^73 + 76 * q^74 - 30 * q^76 - 20 * q^77 - 4 * q^79 - 39 * q^80 - 14 * q^82 - 12 * q^85 - 15 * q^86 + 16 * q^88 + 4 * q^91 + 40 * q^92 - 3 * q^94 - 56 * q^95 + 45 * q^97 - 57 * q^98

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