LMFDB - Embedded newform 819.2.y.h.307.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(307,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("819.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.y (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 35x^{8} + 295x^{4} + 169 $ x^12 + 35x^8 + 295x^4 + 169
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.6
Root			$-0.626770 - 0.626770i$ of defining polynomial
Character	$\chi$	$=$	819.307
Dual form			819.2.y.h.811.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45161 + 1.45161i) q^{2} +2.21432i q^{4} +(2.01464 - 2.01464i) q^{5} +(-1.13594 + 2.38948i) q^{7} +(-0.311108 + 0.311108i) q^{8} +O(q^{10})$	\(q+(1.45161 + 1.45161i) q^{2} +2.21432i q^{4} +(2.01464 - 2.01464i) q^{5} +(-1.13594 + 2.38948i) q^{7} +(-0.311108 + 0.311108i) q^{8} +5.84892 q^{10} +(-0.451606 + 0.451606i) q^{11} +(3.40251 - 1.19288i) q^{13} +(-5.11753 + 1.81964i) q^{14} +3.52543 q^{16} +4.32672 q^{17} +(-3.40251 + 3.40251i) q^{19} +(4.46105 + 4.46105i) q^{20} -1.31111 q^{22} +0.933323i q^{23} -3.11753i q^{25} +(6.67068 + 3.20751i) q^{26} +(-5.29108 - 2.51534i) q^{28} -6.33185 q^{29} +(5.47781 - 5.47781i) q^{31} +(5.73975 + 5.73975i) q^{32} +(6.28070 + 6.28070i) q^{34} +(2.52543 + 7.10246i) q^{35} +(2.14050 - 2.14050i) q^{37} -9.87820 q^{38} +1.25354i q^{40} +(-1.81964 + 1.81964i) q^{41} +10.4795i q^{43} +(-1.00000 - 1.00000i) q^{44} +(-1.35482 + 1.35482i) q^{46} +(-5.90958 - 5.90958i) q^{47} +(-4.41926 - 5.42864i) q^{49} +(4.52543 - 4.52543i) q^{50} +(2.64141 + 7.53424i) q^{52} -3.36196 q^{53} +1.81964i q^{55} +(-0.389986 - 1.09679i) q^{56} +(-9.19135 - 9.19135i) q^{58} +(0.255657 + 0.255657i) q^{59} -7.78989i q^{61} +15.9032 q^{62} +9.61285i q^{64} +(4.45161 - 9.25803i) q^{65} +(7.28100 + 7.28100i) q^{67} +9.58075i q^{68} +(-6.64405 + 13.9759i) q^{70} +(-5.56914 - 5.56914i) q^{71} +(-8.86144 - 8.86144i) q^{73} +6.21432 q^{74} +(-7.53424 - 7.53424i) q^{76} +(-0.566106 - 1.59210i) q^{77} -13.7971 q^{79} +(7.10246 - 7.10246i) q^{80} -5.28281 q^{82} +(-4.30785 + 4.30785i) q^{83} +(8.71678 - 8.71678i) q^{85} +(-15.2121 + 15.2121i) q^{86} -0.280996i q^{88} +(-5.61214 - 5.61214i) q^{89} +(-1.01470 + 9.48527i) q^{91} -2.06668 q^{92} -17.1568i q^{94} +13.7096i q^{95} +(-0.236784 + 0.236784i) q^{97} +(1.46522 - 14.2953i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 - 8 * q^7 - 4 * q^8	$ 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8} + 8 q^{11} - 8 q^{14} + 16 q^{16} - 16 q^{22} - 20 q^{28} + 4 q^{29} + 16 q^{32} + 4 q^{35} + 12 q^{37} - 12 q^{44} + 24 q^{46} + 28 q^{50} + 12 q^{53} - 44 q^{58} + 40 q^{65} + 60 q^{67} + 4 q^{70} + 48 q^{74} - 4 q^{79} + 12 q^{85} - 36 q^{86} - 32 q^{91} - 24 q^{92} + 28 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 - 8 * q^7 - 4 * q^8 + 8 * q^11 - 8 * q^14 + 16 * q^16 - 16 * q^22 - 20 * q^28 + 4 * q^29 + 16 * q^32 + 4 * q^35 + 12 * q^37 - 12 * q^44 + 24 * q^46 + 28 * q^50 + 12 * q^53 - 44 * q^58 + 40 * q^65 + 60 * q^67 + 4 * q^70 + 48 * q^74 - 4 * q^79 + 12 * q^85 - 36 * q^86 - 32 * q^91 - 24 * q^92 + 28 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.45161	+	1.45161i	1.02644	+	1.02644i	0.999641	+	0.0267996i	$0.00853160\pi$
$2$	1.45161	+	1.45161i	1.02644	+	1.02644i	0.0267996	+	0.999641i	$0.491468\pi$
$3$		0			0
$3$		0			0
$4$			2.21432i			1.10716i
$5$	2.01464	−	2.01464i	0.900973	−	0.900973i	−0.0945469	−	0.995520i	$-0.530140\pi$
$5$	2.01464	−	2.01464i	0.900973	−	0.900973i	0.995520	+	0.0945469i	$0.0301402\pi$
$6$		0			0
$7$	−1.13594	+	2.38948i	−0.429347	+	0.903140i
$7$	−1.13594	+	2.38948i	−0.429347	+	0.903140i
$8$	−0.311108	+	0.311108i	−0.109993	+	0.109993i
$9$		0			0
$10$	5.84892			1.84959
$11$	−0.451606	+	0.451606i	−0.136164	+	0.136164i	−0.771904	−	0.635739i	$-0.780695\pi$
$11$	−0.451606	+	0.451606i	−0.136164	+	0.136164i	0.635739	+	0.771904i	$0.280695\pi$
$12$		0			0
$13$	3.40251	−	1.19288i	0.943685	−	0.330844i
$13$	3.40251	−	1.19288i	0.943685	−	0.330844i
$14$	−5.11753	+	1.81964i	−1.36772	+	0.486321i
$15$		0			0
$16$	3.52543			0.881357
$17$	4.32672			1.04938			0.524692	−	0.851292i	$-0.324180\pi$
$17$	4.32672			1.04938			0.524692	+	0.851292i	$0.324180\pi$
$18$		0			0
$19$	−3.40251	+	3.40251i	−0.780588	+	0.780588i	−0.979930	−	0.199342i	$-0.936120\pi$
$19$	−3.40251	+	3.40251i	−0.780588	+	0.780588i	0.199342	+	0.979930i	$0.436120\pi$
$20$	4.46105	+	4.46105i	0.997522	+	0.997522i
$21$		0			0
$22$	−1.31111			−0.279529
$23$			0.933323i			0.194611i	0.995255	+	0.0973057i	$0.0310225\pi$
$23$			0.933323i			0.194611i	−0.995255	+	0.0973057i	$0.968978\pi$
$24$		0			0
$25$		−	3.11753i		−	0.623506i
$26$	6.67068	+	3.20751i	1.30823	+	0.629045i
$27$		0			0
$28$	−5.29108	−	2.51534i	−0.999920	−	0.475355i
$29$	−6.33185			−1.17580			−0.587898	−	0.808935i	$-0.700044\pi$
$29$	−6.33185			−1.17580			−0.587898	+	0.808935i	$0.700044\pi$
$30$		0			0
$31$	5.47781	−	5.47781i	0.983843	−	0.983843i	−0.0160282	−	0.999872i	$-0.505102\pi$
$31$	5.47781	−	5.47781i	0.983843	−	0.983843i	0.999872	+	0.0160282i	$0.00510215\pi$
$32$	5.73975	+	5.73975i	1.01465	+	1.01465i
$33$		0			0
$34$	6.28070	+	6.28070i	1.07713	+	1.07713i
$35$	2.52543	+	7.10246i	0.426875	+	1.20053i
$36$		0			0
$37$	2.14050	−	2.14050i	0.351896	−	0.351896i	−0.508919	−	0.860815i	$-0.669955\pi$
$37$	2.14050	−	2.14050i	0.351896	−	0.351896i	0.860815	+	0.508919i	$0.169955\pi$
$38$	−9.87820			−1.60246
$39$		0			0
$40$			1.25354i			0.198202i
$41$	−1.81964	+	1.81964i	−0.284181	+	0.284181i	−0.834774	−	0.550593i	$-0.814402\pi$
$41$	−1.81964	+	1.81964i	−0.284181	+	0.284181i	0.550593	+	0.834774i	$0.314402\pi$
$42$		0			0
$43$			10.4795i			1.59811i	0.601259	+	0.799054i	$0.294666\pi$
$43$			10.4795i			1.59811i	−0.601259	+	0.799054i	$0.705334\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$		0			0
$46$	−1.35482	+	1.35482i	−0.199757	+	0.199757i
$47$	−5.90958	−	5.90958i	−0.862002	−	0.862002i	0.129569	−	0.991570i	$-0.458641\pi$
$47$	−5.90958	−	5.90958i	−0.862002	−	0.862002i	−0.991570	+	0.129569i	$0.958641\pi$
$48$		0			0
$49$	−4.41926	−	5.42864i	−0.631323	−	0.775520i
$50$	4.52543	−	4.52543i	0.639992	−	0.639992i
$51$		0			0
$52$	2.64141	+	7.53424i	0.366297	+	1.04481i
$53$	−3.36196			−0.461801			−0.230901	−	0.972977i	$-0.574167\pi$
$53$	−3.36196			−0.461801			−0.230901	+	0.972977i	$0.574167\pi$
$54$		0			0
$55$			1.81964i			0.245361i
$56$	−0.389986	−	1.09679i	−0.0521141	−	0.146564i
$57$		0			0
$58$	−9.19135	−	9.19135i	−1.20688	−	1.20688i
$59$	0.255657	+	0.255657i	0.0332837	+	0.0332837i	0.723553	−	0.690269i	$-0.242508\pi$
$59$	0.255657	+	0.255657i	0.0332837	+	0.0332837i	−0.690269	+	0.723553i	$0.742508\pi$
$60$		0			0
$61$		−	7.78989i		−	0.997394i	−0.866776	−	0.498697i	$-0.833812\pi$
$61$		−	7.78989i		−	0.997394i	0.866776	−	0.498697i	$-0.166188\pi$
$62$	15.9032			2.01971
$63$		0			0
$64$			9.61285i			1.20161i
$65$	4.45161	−	9.25803i	0.552154	−	1.14832i
$66$		0			0
$67$	7.28100	+	7.28100i	0.889515	+	0.889515i	0.994476	−	0.104961i	$-0.0334718\pi$
$67$	7.28100	+	7.28100i	0.889515	+	0.889515i	−0.104961	+	0.994476i	$0.533472\pi$
$68$			9.58075i			1.16184i
$69$		0			0
$70$	−6.64405	+	13.9759i	−0.794116	+	1.67044i
$71$	−5.56914	−	5.56914i	−0.660935	−	0.660935i	0.294665	−	0.955600i	$-0.404792\pi$
$71$	−5.56914	−	5.56914i	−0.660935	−	0.660935i	−0.955600	+	0.294665i	$0.904792\pi$
$72$		0			0
$73$	−8.86144	−	8.86144i	−1.03715	−	1.03715i	−0.999283	−	0.0378706i	$-0.987943\pi$
$73$	−8.86144	−	8.86144i	−1.03715	−	1.03715i	−0.0378706	−	0.999283i	$-0.512057\pi$
$74$	6.21432			0.722400
$75$		0			0
$76$	−7.53424	−	7.53424i	−0.864236	−	0.864236i
$77$	−0.566106	−	1.59210i	−0.0645137	−	0.181437i
$78$		0			0
$79$	−13.7971			−1.55229			−0.776145	−	0.630554i	$-0.782828\pi$
$79$	−13.7971			−1.55229			−0.776145	+	0.630554i	$0.782828\pi$
$80$	7.10246	−	7.10246i	0.794079	−	0.794079i
$81$		0			0
$82$	−5.28281			−0.583389
$83$	−4.30785	+	4.30785i	−0.472848	+	0.472848i	−0.902835	−	0.429987i	$-0.858518\pi$
$83$	−4.30785	+	4.30785i	−0.472848	+	0.472848i	0.429987	+	0.902835i	$0.358518\pi$
$84$		0			0
$85$	8.71678	−	8.71678i	0.945468	−	0.945468i
$86$	−15.2121	+	15.2121i	−1.64036	+	1.64036i
$87$		0			0
$88$		−	0.280996i		−	0.0299543i
$89$	−5.61214	−	5.61214i	−0.594885	−	0.594885i	0.344062	−	0.938947i	$-0.388197\pi$
$89$	−5.61214	−	5.61214i	−0.594885	−	0.594885i	−0.938947	+	0.344062i	$0.888197\pi$
$90$		0			0
$91$	−1.01470	+	9.48527i	−0.106370	+	0.994327i
$92$	−2.06668			−0.215466
$93$		0			0
$94$		−	17.1568i		−	1.76959i
$95$			13.7096i			1.40658i
$96$		0			0
$97$	−0.236784	+	0.236784i	−0.0240417	+	0.0240417i	−0.719025	−	0.694984i	$-0.755412\pi$
$97$	−0.236784	+	0.236784i	−0.0240417	+	0.0240417i	0.694984	+	0.719025i	$0.255412\pi$
$98$	1.46522	−	14.2953i	0.148009	−	1.44404i
$99$		0			0
$100$	6.90321			0.690321
$101$	−9.21955			−0.917380			−0.458690	−	0.888596i	$-0.651681\pi$
$101$	−9.21955			−0.917380			−0.458690	+	0.888596i	$0.651681\pi$
$102$		0			0
$103$	−2.50708			−0.247030			−0.123515	−	0.992343i	$-0.539417\pi$
$103$	−2.50708			−0.247030			−0.123515	+	0.992343i	$0.539417\pi$
$104$	−0.687433	+	1.42966i	−0.0674084	+	0.140190i
$105$		0			0
$106$	−4.88025	−	4.88025i	−0.474011	−	0.474011i
$107$	−2.88247			−0.278659			−0.139329	−	0.990246i	$-0.544495\pi$
$107$	−2.88247			−0.278659			−0.139329	+	0.990246i	$0.544495\pi$
$108$		0			0
$109$	−3.54839	−	3.54839i	−0.339875	−	0.339875i	0.516446	−	0.856320i	$-0.327255\pi$
$109$	−3.54839	−	3.54839i	−0.339875	−	0.339875i	−0.856320	+	0.516446i	$0.827255\pi$
$110$	−2.64141	+	2.64141i	−0.251848	+	0.251848i
$111$		0			0
$112$	−4.00469	+	8.42395i	−0.378408	+	0.795989i
$113$	16.3526			1.53832			0.769161	−	0.639055i	$-0.220674\pi$
$113$	16.3526			1.53832			0.769161	+	0.639055i	$0.220674\pi$
$114$		0			0
$115$	1.88031	+	1.88031i	0.175340	+	0.175340i
$116$		−	14.0207i		−	1.30179i
$117$		0			0
$118$			0.742226i			0.0683274i
$119$	−4.91492	+	10.3386i	−0.450550	+	0.947741i
$120$		0			0
$121$			10.5921i			0.962919i
$122$	11.3079	−	11.3079i	1.02377	−	1.02377i
$123$		0			0
$124$	12.1296	+	12.1296i	1.08927	+	1.08927i
$125$	3.79249	+	3.79249i	0.339211	+	0.339211i
$126$		0			0
$127$		−	13.8272i		−	1.22696i	−0.789709	−	0.613481i	$-0.789769\pi$
$127$		−	13.8272i		−	1.22696i	0.789709	−	0.613481i	$-0.210231\pi$
$128$	−2.47457	+	2.47457i	−0.218723	+	0.218723i
$129$		0			0
$130$	19.9010	−	6.97703i	1.74543	−	0.611926i
$131$		−	12.8301i		−	1.12097i	−0.828166	−	0.560483i	$-0.810615\pi$
$131$		−	12.8301i		−	1.12097i	0.828166	−	0.560483i	$-0.189385\pi$
$132$		0			0
$133$	−4.26517	−	11.9953i	−0.369838	−	1.04012i
$134$			21.1383i			1.82607i
$135$		0			0
$136$	−1.34608	+	1.34608i	−0.115425	+	0.115425i
$137$	−2.40075	+	2.40075i	−0.205110	+	0.205110i	−0.802185	−	0.597075i	$-0.796329\pi$
$137$	−2.40075	+	2.40075i	−0.205110	+	0.205110i	0.597075	+	0.802185i	$0.296329\pi$
$138$		0			0
$139$		−	3.34184i		−	0.283451i	−0.989906	−	0.141726i	$-0.954735\pi$
$139$		−	3.34184i		−	0.283451i	0.989906	−	0.141726i	$-0.0452651\pi$
$140$	−15.7271	+	5.59210i	−1.32918	+	0.472619i
$141$		0			0
$142$		−	16.1684i		−	1.35682i
$143$	−0.997882	+	2.07530i	−0.0834471	+	0.173545i
$144$		0			0
$145$	−12.7564	+	12.7564i	−1.05936	+	1.05936i
$146$		−	25.7266i		−	2.12915i
$147$		0			0
$148$	4.73975	+	4.73975i	0.389605	+	0.389605i
$149$	−2.62936	−	2.62936i	−0.215406	−	0.215406i	0.591153	−	0.806559i	$-0.298673\pi$
$149$	−2.62936	−	2.62936i	−0.215406	−	0.215406i	−0.806559	+	0.591153i	$0.798673\pi$
$150$		0			0
$151$	−4.78346	+	4.78346i	−0.389272	+	0.389272i	−0.874428	−	0.485156i	$-0.838763\pi$
$151$	−4.78346	+	4.78346i	−0.389272	+	0.389272i	0.485156	+	0.874428i	$0.338763\pi$
$152$		−	2.11709i		−	0.171719i
$153$		0			0
$154$	1.48935	−	3.13287i	0.120015	−	0.252454i
$155$		−	22.0716i		−	1.77283i
$156$		0			0
$157$		−	3.42542i		−	0.273379i	−0.990614	−	0.136689i	$-0.956354\pi$
$157$		−	3.42542i		−	0.273379i	0.990614	−	0.136689i	$-0.0436462\pi$
$158$	−20.0279	−	20.0279i	−1.59333	−	1.59333i
$159$		0			0
$160$	23.1270			1.82835
$161$	−2.23016	−	1.06020i	−0.175761	−	0.0835557i
$162$		0			0
$163$	10.4494	−	10.4494i	0.818459	−	0.818459i	−0.167426	−	0.985885i	$-0.553545\pi$
$163$	10.4494	−	10.4494i	0.818459	−	0.818459i	0.985885	+	0.167426i	$0.0535455\pi$
$164$	−4.02928	−	4.02928i	−0.314634	−	0.314634i
$165$		0			0
$166$	−12.5066			−0.970701
$167$	16.2326	+	16.2326i	1.25611	+	1.25611i	0.952933	+	0.303180i	$0.0980483\pi$
$167$	16.2326	+	16.2326i	1.25611	+	1.25611i	0.303180	+	0.952933i	$0.401952\pi$
$168$		0			0
$169$	10.1541	−	8.11753i	0.781084	−	0.624426i
$170$	25.3067			1.94093
$171$		0			0
$172$	−23.2050			−1.76936
$173$	−14.3810			−1.09337			−0.546685	−	0.837338i	$-0.684111\pi$
$173$	−14.3810			−1.09337			−0.546685	+	0.837338i	$0.684111\pi$
$174$		0			0
$175$	7.44929	+	3.54134i	0.563113	+	0.267700i
$176$	−1.59210	+	1.59210i	−0.120009	+	0.120009i
$177$		0			0
$178$		−	16.2932i		−	1.22123i
$179$			4.11108i			0.307276i	0.988127	+	0.153638i	$0.0490990\pi$
$179$			4.11108i			0.307276i	−0.988127	+	0.153638i	$0.950901\pi$
$180$		0			0
$181$	21.5760			1.60373			0.801867	−	0.597502i	$-0.203840\pi$
$181$	21.5760			1.60373			0.801867	+	0.597502i	$0.203840\pi$
$182$	−15.2418	+	12.2959i	−1.12980	+	0.911435i
$183$		0			0
$184$	−0.290364	−	0.290364i	−0.0214059	−	0.0214059i
$185$		−	8.62466i		−	0.634097i
$186$		0			0
$187$	−1.95397	+	1.95397i	−0.142889	+	0.142889i
$188$	13.0857	−	13.0857i	0.954373	−	0.954373i
$189$		0			0
$190$	−19.9010	+	19.9010i	−1.44377	+	1.44377i
$191$	−10.3017			−0.745408			−0.372704	−	0.927950i	$-0.621569\pi$
$191$	−10.3017			−0.745408			−0.372704	+	0.927950i	$0.621569\pi$
$192$		0			0
$193$	6.28592	−	6.28592i	0.452470	−	0.452470i	−0.443703	−	0.896174i	$-0.646336\pi$
$193$	6.28592	−	6.28592i	0.452470	−	0.452470i	0.896174	+	0.443703i	$0.146336\pi$
$194$	−0.687433			−0.0493548
$195$		0			0
$196$	12.0207	−	9.78566i	0.858625	−	0.698976i
$197$	3.25088	+	3.25088i	0.231616	+	0.231616i	0.813367	−	0.581751i	$-0.197632\pi$
$197$	3.25088	+	3.25088i	0.231616	+	0.231616i	−0.581751	+	0.813367i	$0.697632\pi$
$198$		0			0
$199$	−6.20116			−0.439589			−0.219794	−	0.975546i	$-0.570539\pi$
$199$	−6.20116			−0.439589			−0.219794	+	0.975546i	$0.570539\pi$
$200$	0.969888	+	0.969888i	0.0685815	+	0.0685815i
$201$		0			0
$202$	−13.3832	−	13.3832i	−0.941636	−	0.941636i
$203$	7.19263	−	15.1299i	0.504824	−	1.06191i
$204$		0			0
$205$			7.33185i			0.512079i
$206$	−3.63929	−	3.63929i	−0.253561	−	0.253561i
$207$		0			0
$208$	11.9953	−	4.20540i	0.831724	−	0.291592i
$209$		−	3.07318i		−	0.212577i
$210$		0			0
$211$	−9.55554			−0.657830			−0.328915	−	0.944359i	$-0.606683\pi$
$211$	−9.55554			−0.657830			−0.328915	+	0.944359i	$0.606683\pi$
$212$		−	7.44446i		−	0.511288i
$213$		0			0
$214$	−4.18421	−	4.18421i	−0.286027	−	0.286027i
$215$	21.1124	+	21.1124i	1.43985	+	1.43985i
$216$		0			0
$217$	6.86665	+	19.3116i	0.466138	+	1.31096i
$218$		−	10.3017i		−	0.697722i
$219$		0			0
$220$	−4.02928			−0.271654
$221$	14.7217	−	5.16124i	0.990289	−	0.347183i
$222$		0			0
$223$	−2.58074	+	2.58074i	−0.172819	+	0.172819i	−0.788217	−	0.615398i	$-0.788995\pi$
$223$	−2.58074	+	2.58074i	−0.172819	+	0.172819i	0.615398	+	0.788217i	$0.288995\pi$
$224$	−20.2351	+	7.19500i	−1.35201	+	0.480736i
$225$		0			0
$226$	23.7375	+	23.7375i	1.57900	+	1.57900i
$227$	−5.25403	+	5.25403i	−0.348722	+	0.348722i	−0.859633	−	0.510911i	$-0.829308\pi$
$227$	−5.25403	+	5.25403i	−0.348722	+	0.348722i	0.510911	+	0.859633i	$0.329308\pi$
$228$		0			0
$229$	−0.729224	−	0.729224i	−0.0481885	−	0.0481885i	0.682602	−	0.730790i	$-0.260848\pi$
$229$	−0.729224	−	0.729224i	−0.0481885	−	0.0481885i	−0.730790	+	0.682602i	$0.760848\pi$
$230$			5.45893i			0.359952i
$231$		0			0
$232$	1.96989	−	1.96989i	0.129330	−	0.129330i
$233$			24.6128i			1.61244i	0.591615	+	0.806221i	$0.298491\pi$
$233$			24.6128i			1.61244i	−0.591615	+	0.806221i	$0.701509\pi$
$234$		0			0
$235$	−23.8113			−1.55328
$236$	−0.566106	+	0.566106i	−0.0368503	+	0.0368503i
$237$		0			0
$238$	−22.1421	+	7.87310i	−1.43526	+	0.510337i
$239$	6.52543	+	6.52543i	0.422095	+	0.422095i	0.885924	−	0.463830i	$-0.153525\pi$
$239$	6.52543	+	6.52543i	0.422095	+	0.422095i	−0.463830	+	0.885924i	$0.653525\pi$
$240$		0			0
$241$	20.1563	+	20.1563i	1.29838	+	1.29838i	0.929461	+	0.368920i	$0.120272\pi$
$241$	20.1563	+	20.1563i	1.29838	+	1.29838i	0.368920	+	0.929461i	$0.379728\pi$
$242$	−15.3756	+	15.3756i	−0.988379	+	0.988379i
$243$		0			0
$244$	17.2493			1.10427
$245$	−19.8400	−	2.03353i	−1.26753	−	0.129918i
$246$		0			0
$247$	−7.51828	+	15.6358i	−0.478377	+	0.994883i
$248$			3.40838i			0.216432i
$249$		0			0
$250$			11.0104i			0.696359i
$251$	14.4448			0.911747			0.455873	−	0.890045i	$-0.349327\pi$
$251$	14.4448			0.911747			0.455873	+	0.890045i	$0.349327\pi$
$252$		0			0
$253$	−0.421494	−	0.421494i	−0.0264991	−	0.0264991i
$254$	20.0716	−	20.0716i	1.25940	−	1.25940i
$255$		0			0
$256$	12.0415			0.752593
$257$	−14.6237			−0.912201			−0.456101	−	0.889928i	$-0.650754\pi$
$257$	−14.6237			−0.912201			−0.456101	+	0.889928i	$0.650754\pi$
$258$		0			0
$259$	2.68320	+	7.54617i	0.166726	+	0.468896i
$260$	20.5002	+	9.85728i	1.27137	+	0.611322i
$261$		0			0
$262$	18.6242	−	18.6242i	1.15061	−	1.15061i
$263$	2.61729			0.161389			0.0806946	−	0.996739i	$-0.474286\pi$
$263$	2.61729			0.161389			0.0806946	+	0.996739i	$0.474286\pi$
$264$		0			0
$265$	−6.77314	+	6.77314i	−0.416071	+	0.416071i
$266$	11.2211	−	23.6038i	0.688009	−	1.44724i
$267$		0			0
$268$	−16.1225	+	16.1225i	−0.984836	+	0.984836i
$269$			9.82340i			0.598944i	0.954105	+	0.299472i	$0.0968104\pi$
$269$			9.82340i			0.598944i	−0.954105	+	0.299472i	$0.903190\pi$
$270$		0			0
$271$	−3.43438	−	3.43438i	−0.208624	−	0.208624i	0.595059	−	0.803682i	$-0.297129\pi$
$271$	−3.43438	−	3.43438i	−0.208624	−	0.208624i	−0.803682	+	0.595059i	$0.797129\pi$
$272$	15.2535			0.924882
$273$		0			0
$274$	−6.96989			−0.421066
$275$	1.40790	+	1.40790i	0.0848993	+	0.0848993i
$276$		0			0
$277$			5.89877i			0.354423i	0.984173	+	0.177211i	$0.0567076\pi$
$277$			5.89877i			0.354423i	−0.984173	+	0.177211i	$0.943292\pi$
$278$	4.85104	−	4.85104i	0.290946	−	0.290946i
$279$		0			0
$280$	−2.99531	−	1.42395i	−0.179004	−	0.0850973i
$281$	−9.23729	+	9.23729i	−0.551050	+	0.551050i	−0.926744	−	0.375694i	$-0.877405\pi$
$281$	−9.23729	+	9.23729i	−0.551050	+	0.551050i	0.375694	+	0.926744i	$0.377405\pi$
$282$		0			0
$283$	8.32721			0.495001			0.247501	−	0.968888i	$-0.420391\pi$
$283$	8.32721			0.495001			0.247501	+	0.968888i	$0.420391\pi$
$284$	12.3319	−	12.3319i	0.731761	−	0.731761i
$285$		0			0
$286$	−4.46105	+	1.56399i	−0.263788	+	0.0924806i
$287$	−2.28100	−	6.41503i	−0.134643	−	0.378667i
$288$		0			0
$289$	1.72054			0.101208
$290$	−37.0345			−2.17474
$291$		0			0
$292$	19.6221	−	19.6221i	1.14829	−	1.14829i
$293$	−15.4903	−	15.4903i	−0.904955	−	0.904955i	0.0909047	−	0.995860i	$-0.471024\pi$
$293$	−15.4903	−	15.4903i	−0.904955	−	0.904955i	−0.995860	+	0.0909047i	$0.971024\pi$
$294$		0			0
$295$	1.03011			0.0599754
$296$			1.33185i			0.0774123i
$297$		0			0
$298$		−	7.63359i		−	0.442202i
$299$	1.11334	+	3.17564i	0.0643860	+	0.183652i
$300$		0			0
$301$	−25.0406	−	11.9041i	−1.44331	−	0.686142i
$302$	−13.8874			−0.799130
$303$		0			0
$304$	−11.9953	+	11.9953i	−0.687977	+	0.687977i
$305$	−15.6938	−	15.6938i	−0.898625	−	0.898625i
$306$		0			0
$307$	−5.77526	−	5.77526i	−0.329611	−	0.329611i	0.522827	−	0.852439i	$-0.324877\pi$
$307$	−5.77526	−	5.77526i	−0.329611	−	0.329611i	−0.852439	+	0.522827i	$0.824877\pi$
$308$	3.52543	−	1.25354i	0.200880	−	0.0714270i
$309$		0			0
$310$	32.0393	−	32.0393i	1.81971	−	1.81971i
$311$	−2.62562			−0.148885			−0.0744426	−	0.997225i	$-0.523718\pi$
$311$	−2.62562			−0.148885			−0.0744426	+	0.997225i	$0.523718\pi$
$312$		0			0
$313$		−	19.8489i		−	1.12193i	−0.827840	−	0.560964i	$-0.810431\pi$
$313$		−	19.8489i		−	1.12193i	0.827840	−	0.560964i	$-0.189569\pi$
$314$	4.97237	−	4.97237i	0.280607	−	0.280607i
$315$		0			0
$316$		−	30.5511i		−	1.71863i
$317$	−1.14764	−	1.14764i	−0.0644581	−	0.0644581i	0.674143	−	0.738601i	$-0.264513\pi$
$317$	−1.14764	−	1.14764i	−0.0644581	−	0.0644581i	−0.738601	+	0.674143i	$0.764513\pi$
$318$		0			0
$319$	2.85950	−	2.85950i	0.160101	−	0.160101i
$320$	19.3664	+	19.3664i	1.08262	+	1.08262i
$321$		0			0
$322$	−1.69832	−	4.77631i	−0.0946435	−	0.266173i
$323$	−14.7217	+	14.7217i	−0.819137	+	0.819137i
$324$		0			0
$325$	−3.71883	−	10.6074i	−0.206283	−	0.588394i
$326$	30.3368			1.68020
$327$		0			0
$328$		−	1.13221i		−	0.0625159i
$329$	20.8338	−	7.40790i	1.14861	−	0.408411i
$330$		0			0
$331$	−2.90321	−	2.90321i	−0.159575	−	0.159575i	0.622803	−	0.782378i	$-0.285994\pi$
$331$	−2.90321	−	2.90321i	−0.159575	−	0.159575i	−0.782378	+	0.622803i	$0.785994\pi$
$332$	−9.53896	−	9.53896i	−0.523518	−	0.523518i
$333$		0			0
$334$			47.1266i			2.57865i
$335$	29.3371			1.60286
$336$		0			0
$337$		−	4.47304i		−	0.243662i	−0.992551	−	0.121831i	$-0.961123\pi$
$337$		−	4.47304i		−	0.243662i	0.992551	−	0.121831i	$-0.0388766\pi$
$338$	26.5232	+	2.95629i	1.44267	+	0.160801i
$339$		0			0
$340$	19.3017	+	19.3017i	1.04678	+	1.04678i
$341$			4.94762i			0.267929i
$342$		0			0
$343$	17.9917	−	4.39312i	0.971459	−	0.237206i
$344$	−3.26025	−	3.26025i	−0.175781	−	0.175781i
$345$		0			0
$346$	−20.8756	−	20.8756i	−1.12228	−	1.12228i
$347$	−8.81135			−0.473018			−0.236509	−	0.971629i	$-0.576003\pi$
$347$	−8.81135			−0.473018			−0.236509	+	0.971629i	$0.576003\pi$
$348$		0			0
$349$	11.8133	+	11.8133i	0.632351	+	0.632351i	0.948657	−	0.316306i	$-0.102443\pi$
$349$	11.8133	+	11.8133i	0.632351	+	0.632351i	−0.316306	+	0.948657i	$0.602443\pi$
$350$	5.67280	+	15.9541i	0.303224	+	0.852781i
$351$		0			0
$352$	−5.18421			−0.276319
$353$	−2.91007	+	2.91007i	−0.154887	+	0.154887i	−0.780297	−	0.625410i	$-0.784932\pi$
$353$	−2.91007	+	2.91007i	−0.154887	+	0.154887i	0.625410	+	0.780297i	$0.284932\pi$
$354$		0			0
$355$	−22.4396			−1.19097
$356$	12.4271	−	12.4271i	0.658633	−	0.658633i
$357$		0			0
$358$	−5.96767	+	5.96767i	−0.315401	+	0.315401i
$359$	−3.52320	+	3.52320i	−0.185948	+	0.185948i	−0.793942	−	0.607994i	$-0.791974\pi$
$359$	−3.52320	+	3.52320i	−0.185948	+	0.185948i	0.607994	+	0.793942i	$0.291974\pi$
$360$		0			0
$361$		−	4.15410i		−	0.218637i
$362$	31.3199	+	31.3199i	1.64614	+	1.64614i
$363$		0			0
$364$	−21.0034	−	2.24687i	−1.10088	−	0.117768i
$365$	−35.7052			−1.86890
$366$		0			0
$367$			19.8112i			1.03414i	0.855944	+	0.517068i	$0.172976\pi$
$367$			19.8112i			1.03414i	−0.855944	+	0.517068i	$0.827024\pi$
$368$			3.29036i			0.171522i
$369$		0			0
$370$	12.5196	−	12.5196i	0.650863	−	0.650863i
$371$	3.81900	−	8.03335i	0.198273	−	0.417071i
$372$		0			0
$373$	−24.5368			−1.27047			−0.635234	−	0.772320i	$-0.719096\pi$
$373$	−24.5368			−1.27047			−0.635234	+	0.772320i	$0.719096\pi$
$374$	−5.67280			−0.293334
$375$		0			0
$376$	3.67704			0.189629
$377$	−21.5442	+	7.55311i	−1.10958	+	0.389005i
$378$		0			0
$379$	−8.78346	−	8.78346i	−0.451176	−	0.451176i	0.444569	−	0.895745i	$-0.353357\pi$
$379$	−8.78346	−	8.78346i	−0.451176	−	0.451176i	−0.895745	+	0.444569i	$0.853357\pi$
$380$	−30.3575			−1.55731
$381$		0			0
$382$	−14.9541	−	14.9541i	−0.765117	−	0.765117i
$383$	−17.8990	+	17.8990i	−0.914596	+	0.914596i	−0.996630	−	0.0820333i	$-0.973859\pi$
$383$	−17.8990	+	17.8990i	−0.914596	+	0.914596i	0.0820333	+	0.996630i	$0.473859\pi$
$384$		0			0
$385$	−4.34801	−	2.06702i	−0.221595	−	0.105345i
$386$	18.2494			0.928868
$387$		0			0
$388$	−0.524315	−	0.524315i	−0.0266181	−	0.0266181i
$389$		−	12.0667i		−	0.611805i	−0.952063	−	0.305902i	$-0.901042\pi$
$389$		−	12.0667i		−	0.611805i	0.952063	−	0.305902i	$-0.0989581\pi$
$390$		0			0
$391$			4.03823i			0.204222i
$392$	3.06376	+	0.314025i	0.154743	+	0.0158607i
$393$		0			0
$394$			9.43801i			0.475480i
$395$	−27.7961	+	27.7961i	−1.39857	+	1.39857i
$396$		0			0
$397$	−7.82177	−	7.82177i	−0.392563	−	0.392563i	0.483037	−	0.875600i	$-0.339534\pi$
$397$	−7.82177	−	7.82177i	−0.392563	−	0.392563i	−0.875600	+	0.483037i	$0.839534\pi$
$398$	−9.00164	−	9.00164i	−0.451212	−	0.451212i
$399$		0			0
$400$		−	10.9906i		−	0.549532i
$401$	17.6178	−	17.6178i	0.879789	−	0.879789i	−0.113723	−	0.993512i	$-0.536278\pi$
$401$	17.6178	−	17.6178i	0.879789	−	0.879789i	0.993512	+	0.113723i	$0.0362777\pi$
$402$		0			0
$403$	12.1039	−	25.1726i	0.602940	−	1.25394i
$404$		−	20.4150i		−	1.01569i
$405$		0			0
$406$	32.4035	−	11.5217i	1.60816	−	0.571813i
$407$			1.93332i			0.0958313i
$408$		0			0
$409$	−24.0225	+	24.0225i	−1.18783	+	1.18783i	−0.210169	+	0.977665i	$0.567401\pi$
$409$	−24.0225	+	24.0225i	−1.18783	+	1.18783i	−0.977665	+	0.210169i	$0.932599\pi$
$410$	−10.6430	+	10.6430i	−0.525618	+	0.525618i
$411$		0			0
$412$		−	5.55147i		−	0.273501i
$413$	−0.901299	+	0.320476i	−0.0443500	+	0.0157696i
$414$		0			0
$415$			17.3575i			0.852047i
$416$	26.3763	+	12.6827i	1.29321	+	0.621822i
$417$		0			0
$418$	4.46105	−	4.46105i	0.218197	−	0.218197i
$419$			19.6899i			0.961912i	0.876745	+	0.480956i	$0.159710\pi$
$419$			19.6899i			0.961912i	−0.876745	+	0.480956i	$0.840290\pi$
$420$		0			0
$421$	26.6042	+	26.6042i	1.29661	+	1.29661i	0.930619	+	0.365989i	$0.119269\pi$
$421$	26.6042	+	26.6042i	1.29661	+	1.29661i	0.365989	+	0.930619i	$0.380731\pi$
$422$	−13.8709	−	13.8709i	−0.675224	−	0.675224i
$423$		0			0
$424$	1.04593	−	1.04593i	0.0507950	−	0.0507950i
$425$		−	13.4887i		−	0.654298i
$426$		0			0
$427$	18.6138	+	8.84888i	0.900786	+	0.428228i
$428$		−	6.38271i		−	0.308520i
$429$		0			0
$430$			61.2937i			2.95585i
$431$	4.81135	+	4.81135i	0.231754	+	0.231754i	0.813425	−	0.581670i	$-0.197601\pi$
$431$	4.81135	+	4.81135i	0.231754	+	0.231754i	−0.581670	+	0.813425i	$0.697601\pi$
$432$		0			0
$433$	−8.34704			−0.401133			−0.200567	−	0.979680i	$-0.564278\pi$
$433$	−8.34704			−0.401133			−0.200567	+	0.979680i	$0.564278\pi$
$434$	−18.0652	+	38.0005i	−0.867157	+	1.82408i
$435$		0			0
$436$	7.85728	−	7.85728i	0.376295	−	0.376295i
$437$	−3.17564	−	3.17564i	−0.151911	−	0.151911i
$438$		0			0
$439$	−2.42350			−0.115667			−0.0578336	−	0.998326i	$-0.518419\pi$
$439$	−2.42350			−0.115667			−0.0578336	+	0.998326i	$0.518419\pi$
$440$	−0.566106	−	0.566106i	−0.0269880	−	0.0269880i
$441$		0			0
$442$	28.8622	+	13.8780i	1.37283	+	0.660110i
$443$	−13.7763			−0.654532			−0.327266	−	0.944932i	$-0.606127\pi$
$443$	−13.7763			−0.654532			−0.327266	+	0.944932i	$0.606127\pi$
$444$		0			0
$445$	−22.6128			−1.07195
$446$	−7.49245			−0.354778
$447$		0			0
$448$	−22.9697	−	10.9197i	−1.08522	−	0.515905i
$449$	24.7447	−	24.7447i	1.16777	−	1.16777i	0.185043	−	0.982730i	$-0.440758\pi$
$449$	24.7447	−	24.7447i	1.16777	−	1.16777i	0.982730	−	0.185043i	$-0.0592423\pi$
$450$		0			0
$451$		−	1.64353i		−	0.0773906i
$452$			36.2099i			1.70317i
$453$		0			0
$454$	−15.2535			−0.715885
$455$	17.0651	+	21.1536i	0.800026	+	0.991698i
$456$		0			0
$457$	−2.84521	−	2.84521i	−0.133093	−	0.133093i	0.637422	−	0.770515i	$-0.280001\pi$
$457$	−2.84521	−	2.84521i	−0.133093	−	0.133093i	−0.770515	+	0.637422i	$0.780001\pi$
$458$		−	2.11709i		−	0.0989252i
$459$		0			0
$460$	−4.16360	+	4.16360i	−0.194129	+	0.194129i
$461$	2.38575	−	2.38575i	0.111115	−	0.111115i	−0.649363	−	0.760479i	$-0.724964\pi$
$461$	2.38575	−	2.38575i	0.111115	−	0.111115i	0.760479	+	0.649363i	$0.224964\pi$
$462$		0			0
$463$	17.5899	−	17.5899i	0.817471	−	0.817471i	−0.168270	−	0.985741i	$-0.553818\pi$
$463$	17.5899	−	17.5899i	0.817471	−	0.817471i	0.985741	+	0.168270i	$0.0538180\pi$
$464$	−22.3225			−1.03630
$465$		0			0
$466$	−35.7282	+	35.7282i	−1.65507	+	1.65507i
$467$	21.4287			0.991602			0.495801	−	0.868436i	$-0.334874\pi$
$467$	21.4287			0.991602			0.495801	+	0.868436i	$0.334874\pi$
$468$		0			0
$469$	−25.6686	+	9.12701i	−1.18527	+	0.421446i
$470$	−34.5647	−	34.5647i	−1.59435	−	1.59435i
$471$		0			0
$472$	−0.159074			−0.00732196
$473$	−4.73260	−	4.73260i	−0.217605	−	0.217605i
$474$		0			0
$475$	10.6074	+	10.6074i	0.486702	+	0.486702i
$476$	−22.8930	−	10.8832i	−1.04930	−	0.498830i
$477$		0			0
$478$			18.9447i			0.866510i
$479$	−4.61425	−	4.61425i	−0.210831	−	0.210831i	0.593790	−	0.804620i	$-0.297631\pi$
$479$	−4.61425	−	4.61425i	−0.210831	−	0.210831i	−0.804620	+	0.593790i	$0.797631\pi$
$480$		0			0
$481$	4.72971	−	9.83641i	0.215656	−	0.448501i
$482$			58.5180i			2.66542i
$483$		0			0
$484$	−23.4543			−1.06610
$485$			0.954067i			0.0433220i
$486$		0			0
$487$	9.62867	+	9.62867i	0.436317	+	0.436317i	0.890770	−	0.454454i	$-0.150166\pi$
$487$	9.62867	+	9.62867i	0.436317	+	0.436317i	−0.454454	+	0.890770i	$0.650166\pi$
$488$	2.42350	+	2.42350i	0.109707	+	0.109707i
$489$		0			0
$490$	−25.8479	−	31.7517i	−1.16769	−	1.43439i
$491$			9.21924i			0.416059i	0.978123	+	0.208029i	$0.0667049\pi$
$491$			9.21924i			0.416059i	−0.978123	+	0.208029i	$0.933295\pi$
$492$		0			0
$493$	−27.3962			−1.23386
$494$	−33.6106	+	11.7835i	−1.51221	+	0.530163i
$495$		0			0
$496$	19.3116	−	19.3116i	0.867117	−	0.867117i
$497$	19.6336	−	6.98113i	0.880687	−	0.313147i
$498$		0			0
$499$	−6.65947	−	6.65947i	−0.298119	−	0.298119i	0.542158	−	0.840277i	$-0.317608\pi$
$499$	−6.65947	−	6.65947i	−0.298119	−	0.298119i	−0.840277	+	0.542158i	$0.817608\pi$
$500$	−8.39779	+	8.39779i	−0.375561	+	0.375561i
$501$		0			0
$502$	20.9681	+	20.9681i	0.935854	+	0.935854i
$503$			1.81069i			0.0807346i	0.999185	+	0.0403673i	$0.0128528\pi$
$503$			1.81069i			0.0807346i	−0.999185	+	0.0403673i	$0.987147\pi$
$504$		0			0
$505$	−18.5741	+	18.5741i	−0.826535	+	0.826535i
$506$		−	1.22369i		−	0.0543996i
$507$		0			0
$508$	30.6178			1.35844
$509$	22.2864	−	22.2864i	0.987827	−	0.987827i	−0.0121000	−	0.999927i	$-0.503852\pi$
$509$	22.2864	−	22.2864i	0.987827	−	0.987827i	0.999927	+	0.0121000i	$0.00385163\pi$
$510$		0			0
$511$	31.2404	−	11.1082i	1.38199	−	0.491396i
$512$	22.4286	+	22.4286i	0.991215	+	0.991215i
$513$		0			0
$514$	−21.2278	−	21.2278i	−0.936320	−	0.936320i
$515$	−5.05086	+	5.05086i	−0.222567	+	0.222567i
$516$		0			0
$517$	5.33761			0.234748
$518$	−7.05912	+	14.8490i	−0.310160	+	0.652428i
$519$		0			0
$520$	1.49532	+	4.26517i	0.0655739	+	0.187040i
$521$			15.8744i			0.695472i	0.937592	+	0.347736i	$0.113049\pi$
$521$			15.8744i			0.695472i	−0.937592	+	0.347736i	$0.886951\pi$
$522$		0			0
$523$		−	3.90795i		−	0.170883i	−0.996343	−	0.0854413i	$-0.972770\pi$
$523$		−	3.90795i		−	0.170883i	0.996343	−	0.0854413i	$-0.0272300\pi$
$524$	28.4098			1.24109
$525$		0			0
$526$	3.79928	+	3.79928i	0.165656	+	0.165656i
$527$	23.7010	−	23.7010i	1.03243	−	1.03243i
$528$		0			0
$529$	22.1289			0.962126
$530$	−19.6639			−0.854143
$531$		0			0
$532$	26.5614	−	9.44446i	1.15158	−	0.409469i
$533$	−4.02074	+	8.36196i	−0.174158	+	0.362197i
$534$		0			0
$535$	−5.80713	+	5.80713i	−0.251064	+	0.251064i
$536$	−4.53035			−0.195681
$537$		0			0
$538$	−14.2597	+	14.2597i	−0.614780	+	0.614780i
$539$	4.44737	+	0.455841i	0.191562	+	0.0196345i
$540$		0			0
$541$	8.57406	−	8.57406i	0.368628	−	0.368628i	−0.498349	−	0.866977i	$-0.666060\pi$
$541$	8.57406	−	8.57406i	0.368628	−	0.368628i	0.866977	+	0.498349i	$0.166060\pi$
$542$		−	9.97073i		−	0.428280i
$543$		0			0
$544$	24.8343	+	24.8343i	1.06476	+	1.06476i
$545$	−14.2975			−0.612436
$546$		0			0
$547$	−4.72546			−0.202046			−0.101023	−	0.994884i	$-0.532212\pi$
$547$	−4.72546			−0.202046			−0.101023	+	0.994884i	$0.532212\pi$
$548$	−5.31603	−	5.31603i	−0.227090	−	0.227090i
$549$		0			0
$550$			4.08742i			0.174288i
$551$	21.5442	−	21.5442i	0.917812	−	0.917812i
$552$		0			0
$553$	15.6727	−	32.9678i	0.666470	−	1.40193i
$554$	−8.56268	+	8.56268i	−0.363794	+	0.363794i
$555$		0			0
$556$	7.39991			0.313826
$557$	23.8415	−	23.8415i	1.01019	−	1.01019i	0.0102475	−	0.999947i	$-0.496738\pi$
$557$	23.8415	−	23.8415i	1.01019	−	1.01019i	0.999947	−	0.0102475i	$-0.00326193\pi$
$558$		0			0
$559$	12.5007	+	35.6565i	0.528725	+	1.50811i
$560$	8.90321	+	25.0392i	0.376229	+	1.05810i
$561$		0			0
$562$	−26.8178			−1.13124
$563$	41.2776			1.73965			0.869823	−	0.493365i	$-0.164233\pi$
$563$	41.2776			1.73965			0.869823	+	0.493365i	$0.164233\pi$
$564$		0			0
$565$	32.9446	−	32.9446i	1.38599	−	1.38599i
$566$	12.0878	+	12.0878i	0.508089	+	0.508089i
$567$		0			0
$568$	3.46520			0.145397
$569$			43.5402i			1.82530i	0.408742	+	0.912650i	$0.365968\pi$
$569$			43.5402i			1.82530i	−0.408742	+	0.912650i	$0.634032\pi$
$570$		0			0
$571$			21.2701i			0.890126i	0.895499	+	0.445063i	$0.146819\pi$
$571$			21.2701i			0.890126i	−0.895499	+	0.445063i	$0.853181\pi$
$572$	−4.59538	−	2.20963i	−0.192143	−	0.0923893i
$573$		0			0
$574$	6.00098	−	12.6232i	0.250476	−	0.526882i
$575$	2.90967			0.121341
$576$		0			0
$577$	8.73703	−	8.73703i	0.363727	−	0.363727i	−0.501456	−	0.865183i	$-0.667202\pi$
$577$	8.73703	−	8.73703i	0.363727	−	0.363727i	0.865183	+	0.501456i	$0.167202\pi$
$578$	2.49754	+	2.49754i	0.103884	+	0.103884i
$579$		0			0
$580$	−28.2467	−	28.2467i	−1.17288	−	1.17288i
$581$	−5.40006	−	15.1870i	−0.224032	−	0.630064i
$582$		0			0
$583$	1.51828	−	1.51828i	0.0628808	−	0.0628808i
$584$	5.51373			0.228160
$585$		0			0
$586$		−	44.9717i		−	1.85776i
$587$	30.6931	−	30.6931i	1.26684	−	1.26684i	0.319131	−	0.947711i	$-0.396609\pi$
$587$	30.6931	−	30.6931i	1.26684	−	1.26684i	0.947711	−	0.319131i	$-0.103391\pi$
$588$		0			0
$589$			37.2766i			1.53595i
$590$	1.49532	+	1.49532i	0.0615612	+	0.0615612i
$591$		0			0
$592$	7.54617	−	7.54617i	0.310146	−	0.310146i
$593$	5.18036	+	5.18036i	0.212732	+	0.212732i	0.805427	−	0.592695i	$-0.201936\pi$
$593$	5.18036	+	5.18036i	0.212732	+	0.212732i	−0.592695	+	0.805427i	$0.701936\pi$
$594$		0			0
$595$	10.9268	+	30.7304i	0.447956	+	1.25982i
$596$	5.82225	−	5.82225i	0.238488	−	0.238488i
$597$		0			0
$598$	−2.99365	+	6.22591i	−0.122419	+	0.254596i
$599$	18.5254			0.756928			0.378464	−	0.925616i	$-0.376452\pi$
$599$	18.5254			0.756928			0.378464	+	0.925616i	$0.376452\pi$
$600$		0			0
$601$			30.9807i			1.26373i	0.775079	+	0.631864i	$0.217710\pi$
$601$			30.9807i			1.26373i	−0.775079	+	0.631864i	$0.782290\pi$
$602$	−19.0690	−	53.6291i	−0.777193	−	2.18576i
$603$		0			0
$604$	−10.5921	−	10.5921i	−0.430987	−	0.430987i
$605$	21.3393	+	21.3393i	0.867564	+	0.867564i
$606$		0			0
$607$		−	29.4674i		−	1.19605i	−0.801479	−	0.598023i	$-0.795953\pi$
$607$		−	29.4674i		−	1.19605i	0.801479	−	0.598023i	$-0.204047\pi$
$608$	−39.0591			−1.58405
$609$		0			0
$610$		−	45.5625i		−	1.84477i
$611$	−27.1568	−	13.0580i	−1.09865	−	0.528270i
$612$		0			0
$613$	13.9398	+	13.9398i	0.563022	+	0.563022i	0.930165	−	0.367142i	$-0.119664\pi$
$613$	13.9398	+	13.9398i	0.563022	+	0.563022i	−0.367142	+	0.930165i	$0.619664\pi$
$614$		−	16.7668i		−	0.676653i
$615$		0			0
$616$	0.671436	+	0.319196i	0.0270529	+	0.0128608i
$617$	27.7052	+	27.7052i	1.11537	+	1.11537i	0.992412	+	0.122957i	$0.0392377\pi$
$617$	27.7052	+	27.7052i	1.11537	+	1.11537i	0.122957	+	0.992412i	$0.460762\pi$
$618$		0			0
$619$	4.58642	+	4.58642i	0.184344	+	0.184344i	0.793246	−	0.608902i	$-0.208390\pi$
$619$	4.58642	+	4.58642i	0.184344	+	0.184344i	−0.608902	+	0.793246i	$0.708390\pi$
$620$	48.8736			1.96281
$621$		0			0
$622$	−3.81137	−	3.81137i	−0.152822	−	0.152822i
$623$	19.7852	−	7.03503i	0.792677	−	0.281853i
$624$		0			0
$625$	30.8687			1.23475
$626$	28.8128	−	28.8128i	1.15159	−	1.15159i
$627$		0			0
$628$	7.58498			0.302674
$629$	9.26134	−	9.26134i	0.369274	−	0.369274i
$630$		0			0
$631$	11.1175	−	11.1175i	0.442582	−	0.442582i	−0.450297	−	0.892879i	$-0.648682\pi$
$631$	11.1175	−	11.1175i	0.442582	−	0.442582i	0.892879	+	0.450297i	$0.148682\pi$
$632$	4.29237	−	4.29237i	0.170741	−	0.170741i
$633$		0			0
$634$		−	3.33185i		−	0.132325i
$635$	−27.8567	−	27.8567i	−1.10546	−	1.10546i
$636$		0			0
$637$	−21.5123	−	13.1994i	−0.852347	−	0.522977i
$638$	8.30174			0.328669
$639$		0			0
$640$			9.97073i			0.394128i
$641$			22.3590i			0.883129i	0.897229	+	0.441565i	$0.145576\pi$
$641$			22.3590i			0.883129i	−0.897229	+	0.441565i	$0.854424\pi$
$642$		0			0
$643$	−5.69880	+	5.69880i	−0.224739	+	0.224739i	−0.810491	−	0.585752i	$-0.800799\pi$
$643$	−5.69880	+	5.69880i	−0.224739	+	0.224739i	0.585752	+	0.810491i	$0.300799\pi$
$644$	2.34763	−	4.93829i	0.0925096	−	0.194596i
$645$		0			0
$646$	−42.7402			−1.68159
$647$	−7.73510			−0.304098			−0.152049	−	0.988373i	$-0.548587\pi$
$647$	−7.73510			−0.304098			−0.152049	+	0.988373i	$0.548587\pi$
$648$		0			0
$649$	−0.230912			−0.00906410
$650$	9.99952	−	20.7961i	0.392214	−	0.815689i
$651$		0			0
$652$	23.1383	+	23.1383i	0.906165	+	0.906165i
$653$	−21.3921			−0.837137			−0.418568	−	0.908185i	$-0.637468\pi$
$653$	−21.3921			−0.837137			−0.418568	+	0.908185i	$0.637468\pi$
$654$		0			0
$655$	−25.8479	−	25.8479i	−1.00996	−	1.00996i
$656$	−6.41503	+	6.41503i	−0.250465	+	0.250465i
$657$		0			0
$658$	40.9958	+	19.4891i	1.59818	+	0.759766i
$659$	1.68445			0.0656167			0.0328084	−	0.999462i	$-0.489555\pi$
$659$	1.68445			0.0656167			0.0328084	+	0.999462i	$0.489555\pi$
$660$		0			0
$661$	−23.4056	−	23.4056i	−0.910372	−	0.910372i	0.0859290	−	0.996301i	$-0.472614\pi$
$661$	−23.4056	−	23.4056i	−0.910372	−	0.910372i	−0.996301	+	0.0859290i	$0.972614\pi$
$662$		−	8.42864i		−	0.327588i
$663$		0			0
$664$		−	2.68041i		−	0.104020i
$665$	−32.7589	−	15.5734i	−1.27034	−	0.603910i
$666$		0			0
$667$		−	5.90967i		−	0.228823i
$668$	−35.9441	+	35.9441i	−1.39072	+	1.39072i
$669$		0			0
$670$	42.5860	+	42.5860i	1.64524	+	1.64524i
$671$	3.51796	+	3.51796i	0.135809	+	0.135809i
$672$		0			0
$673$			26.2464i			1.01173i	0.862614	+	0.505863i	$0.168826\pi$
$673$			26.2464i			1.01173i	−0.862614	+	0.505863i	$0.831174\pi$
$674$	6.49309	−	6.49309i	0.250105	−	0.250105i
$675$		0			0
$676$	17.9748	+	22.4844i	0.691339	+	0.864785i
$677$		−	36.7658i		−	1.41303i	−0.707700	−	0.706513i	$-0.750267\pi$
$677$		−	36.7658i		−	1.41303i	0.707700	−	0.706513i	$-0.249733\pi$
$678$		0			0
$679$	−0.296818	−	0.834764i	−0.0113908	−	0.0320353i
$680$			5.42372i			0.207990i
$681$		0			0
$682$	−7.18200	+	7.18200i	−0.275013	+	0.275013i
$683$	14.5812	−	14.5812i	0.557934	−	0.557934i	−0.370785	−	0.928719i	$-0.620911\pi$
$683$	14.5812	−	14.5812i	0.557934	−	0.557934i	0.928719	+	0.370785i	$0.120911\pi$
$684$		0			0
$685$			9.67329i			0.369597i
$686$	32.4939	+	19.7397i	1.24062	+	0.753667i
$687$		0			0
$688$			36.9447i			1.40850i
$689$	−11.4391	+	4.01040i	−0.435795	+	0.152784i
$690$		0			0
$691$	30.4663	−	30.4663i	1.15899	−	1.15899i	0.174299	−	0.984693i	$-0.444234\pi$
$691$	30.4663	−	30.4663i	1.15899	−	1.15899i	0.984693	−	0.174299i	$-0.0557658\pi$
$692$		−	31.8442i		−	1.21054i
$693$		0			0
$694$	−12.7906	−	12.7906i	−0.485525	−	0.485525i
$695$	−6.73260	−	6.73260i	−0.255382	−	0.255382i
$696$		0			0
$697$	−7.87310	+	7.87310i	−0.298215	+	0.298215i
$698$			34.2965i			1.29814i
$699$		0			0
$700$	−7.84166	+	16.4951i	−0.296387	+	0.623457i
$701$			17.7368i			0.669911i	0.942234	+	0.334955i	$0.108721\pi$
$701$			17.7368i			0.669911i	−0.942234	+	0.334955i	$0.891279\pi$
$702$		0			0
$703$			14.5661i			0.549371i
$704$	−4.34122	−	4.34122i	−0.163616	−	0.163616i
$705$		0			0
$706$	−8.44854			−0.317965
$707$	10.4729	−	22.0300i	0.393874	−	0.828522i
$708$		0			0
$709$	19.2422	−	19.2422i	0.722656	−	0.722656i	−0.246489	−	0.969146i	$-0.579277\pi$
$709$	19.2422	−	19.2422i	0.722656	−	0.722656i	0.969146	+	0.246489i	$0.0792770\pi$
$710$	−32.5734	−	32.5734i	−1.22246	−	1.22246i
$711$		0			0
$712$	3.49196			0.130867
$713$	5.11257	+	5.11257i	0.191467	+	0.191467i
$714$		0			0
$715$	2.17061	+	6.19135i	0.0811762	+	0.231543i
$716$	−9.10324			−0.340204
$717$		0			0
$718$	−10.2286			−0.381728
$719$	−42.3551			−1.57958			−0.789789	−	0.613379i	$-0.789810\pi$
$719$	−42.3551			−1.57958			−0.789789	+	0.613379i	$0.789810\pi$
$720$		0			0
$721$	2.84790	−	5.99062i	0.106061	−	0.223102i
$722$	6.03011	−	6.03011i	0.224418	−	0.224418i
$723$		0			0
$724$			47.7762i			1.77559i
$725$			19.7397i			0.733116i
$726$		0			0
$727$	23.2484			0.862234			0.431117	−	0.902296i	$-0.358120\pi$
$727$	23.2484			0.862234			0.431117	+	0.902296i	$0.358120\pi$
$728$	−2.63526	−	3.26662i	−0.0976693	−	0.121069i
$729$		0			0
$730$	−51.8299	−	51.8299i	−1.91831	−	1.91831i
$731$			45.3419i			1.67703i
$732$		0			0
$733$	24.1280	−	24.1280i	0.891188	−	0.891188i	−0.103447	−	0.994635i	$-0.532987\pi$
$733$	24.1280	−	24.1280i	0.891188	−	0.891188i	0.994635	+	0.103447i	$0.0329873\pi$
$734$	−28.7580	+	28.7580i	−1.06148	+	1.06148i
$735$		0			0
$736$	−5.35704	+	5.35704i	−0.197463	+	0.197463i
$737$	−6.57628			−0.242240
$738$		0			0
$739$	4.46590	−	4.46590i	0.164281	−	0.164281i	−0.620179	−	0.784460i	$-0.712940\pi$
$739$	4.46590	−	4.46590i	0.164281	−	0.164281i	0.784460	+	0.620179i	$0.212940\pi$
$740$	19.0977			0.702047
$741$		0			0
$742$	17.2050	−	6.11758i	0.631614	−	0.224583i
$743$	−10.0114	−	10.0114i	−0.367282	−	0.367282i	0.499203	−	0.866485i	$-0.333626\pi$
$743$	−10.0114	−	10.0114i	−0.367282	−	0.367282i	−0.866485	+	0.499203i	$0.833626\pi$
$744$		0			0
$745$	−10.5944			−0.388149
$746$	−35.6178	−	35.6178i	−1.30406	−	1.30406i
$747$		0			0
$748$	−4.32672	−	4.32672i	−0.158201	−	0.158201i
$749$	3.27432	−	6.88761i	0.119641	−	0.251668i
$750$		0			0
$751$			8.16686i			0.298013i	0.988836	+	0.149006i	$0.0476075\pi$
$751$			8.16686i			0.298013i	−0.988836	+	0.149006i	$0.952392\pi$
$752$	−20.8338	−	20.8338i	−0.759731	−	0.759731i
$753$		0			0
$754$	−42.2378	−	20.3095i	−1.53821	−	0.739628i
$755$			19.2739i			0.701448i
$756$		0			0
$757$	10.5210			0.382392			0.191196	−	0.981552i	$-0.438763\pi$
$757$	10.5210			0.382392			0.191196	+	0.981552i	$0.438763\pi$
$758$		−	25.5002i		−	0.926210i
$759$		0			0
$760$	−4.26517	−	4.26517i	−0.154714	−	0.154714i
$761$	−5.95138	−	5.95138i	−0.215737	−	0.215737i	0.590962	−	0.806699i	$-0.298748\pi$
$761$	−5.95138	−	5.95138i	−0.215737	−	0.215737i	−0.806699	+	0.590962i	$0.798748\pi$
$762$		0			0
$763$	12.5096	−	4.44805i	0.452878	−	0.161030i
$764$		−	22.8113i		−	0.825286i
$765$		0			0
$766$	−51.9646			−1.87756
$767$	1.17484	+	0.564907i	0.0424210	+	0.0203976i
$768$		0			0
$769$	9.73800	−	9.73800i	0.351161	−	0.351161i	−0.509380	−	0.860541i	$-0.670125\pi$
$769$	9.73800	−	9.73800i	0.351161	−	0.351161i	0.860541	+	0.509380i	$0.170125\pi$
$770$	−3.31111	−	9.31209i	−0.119324	−	0.335584i
$771$		0			0
$772$	13.9190	+	13.9190i	0.500957	+	0.500957i
$773$	16.0246	−	16.0246i	0.576364	−	0.576364i	−0.357536	−	0.933899i	$-0.616383\pi$
$773$	16.0246	−	16.0246i	0.576364	−	0.576364i	0.933899	+	0.357536i	$0.116383\pi$
$774$		0			0
$775$	−17.0772	−	17.0772i	−0.613433	−	0.613433i
$776$		−	0.147331i		−	0.00528886i
$777$		0			0
$778$	17.5161	−	17.5161i	0.627981	−	0.627981i
$779$		−	12.3827i		−	0.443657i
$780$		0			0
$781$	5.03011			0.179992
$782$	−5.86192	+	5.86192i	−0.209622	+	0.209622i
$783$		0			0
$784$	−15.5798	−	19.1383i	−0.556421	−	0.683510i
$785$	−6.90099	−	6.90099i	−0.246307	−	0.246307i
$786$		0			0
$787$	−17.9844	−	17.9844i	−0.641075	−	0.641075i	0.309745	−	0.950820i	$-0.399756\pi$
$787$	−17.9844	−	17.9844i	−0.641075	−	0.641075i	−0.950820	+	0.309745i	$0.899756\pi$
$788$	−7.19850	+	7.19850i	−0.256436	+	0.256436i
$789$		0			0
$790$	−80.6979			−2.87110
$791$	−18.5756	+	39.0743i	−0.660474	+	1.38932i
$792$		0			0
$793$	−9.29237	−	26.5052i	−0.329982	−	0.941226i
$794$		−	22.7082i		−	0.805886i
$795$		0			0
$796$		−	13.7314i		−	0.486695i
$797$	−43.9698			−1.55749			−0.778745	−	0.627341i	$-0.784143\pi$
$797$	−43.9698			−1.55749			−0.778745	+	0.627341i	$0.784143\pi$
$798$		0			0
$799$	−25.5691	−	25.5691i	−0.904571	−	0.904571i
$800$	17.8938	−	17.8938i	0.632643	−	0.632643i
$801$		0			0
$802$	51.1481			1.80610
$803$	8.00376			0.282447
$804$		0			0
$805$	−6.62889	+	2.35704i	−0.233638	+	0.0830748i
$806$	54.1109	−	18.9706i	1.90597	−	0.668210i
$807$		0			0
$808$	2.86827	−	2.86827i	0.100906	−	0.100906i
$809$	−12.0509			−0.423686			−0.211843	−	0.977304i	$-0.567946\pi$
$809$	−12.0509			−0.423686			−0.211843	+	0.977304i	$0.567946\pi$
$810$		0			0
$811$	−1.07742	+	1.07742i	−0.0378333	+	0.0378333i	−0.725770	−	0.687937i	$-0.758517\pi$
$811$	−1.07742	+	1.07742i	−0.0378333	+	0.0378333i	0.687937	+	0.725770i	$0.258517\pi$
$812$	33.5023	+	15.9268i	1.17570	+	0.558920i
$813$		0			0
$814$	−2.80642	+	2.80642i	−0.0983651	+	0.0983651i
$815$		−	42.1034i		−	1.47482i
$816$		0			0
$817$	−35.6565	−	35.6565i	−1.24746	−	1.24746i
$818$	−69.7423			−2.43848
$819$		0			0
$820$	−16.2351			−0.566953
$821$	34.1847	+	34.1847i	1.19305	+	1.19305i	0.976205	+	0.216848i	$0.0695777\pi$
$821$	34.1847	+	34.1847i	1.19305	+	1.19305i	0.216848	+	0.976205i	$0.430422\pi$
$822$		0			0
$823$			4.71609i			0.164393i	0.996616	+	0.0821963i	$0.0261934\pi$
$823$			4.71609i			0.164393i	−0.996616	+	0.0821963i	$0.973807\pi$
$824$	0.779972	−	0.779972i	0.0271716	−	0.0271716i
$825$		0			0
$826$	−1.77354	−	0.843127i	−0.0617092	−	0.0293361i
$827$	−24.0939	+	24.0939i	−0.837826	+	0.837826i	−0.988572	−	0.150746i	$-0.951832\pi$
$827$	−24.0939	+	24.0939i	−0.837826	+	0.837826i	0.150746	+	0.988572i	$0.451832\pi$
$828$		0			0
$829$	−12.4689			−0.433061			−0.216531	−	0.976276i	$-0.569474\pi$
$829$	−12.4689			−0.433061			−0.216531	+	0.976276i	$0.569474\pi$
$830$	−25.1963	+	25.1963i	−0.874575	+	0.874575i
$831$		0			0
$832$	11.4669	+	32.7078i	0.397544	+	1.13394i
$833$	−19.1209	−	23.4882i	−0.662501	−	0.813819i
$834$		0			0
$835$	65.4055			2.26345
$836$	6.80501			0.235356
$837$		0			0
$838$	−28.5819	+	28.5819i	−0.987346	+	0.987346i
$839$	26.1454	+	26.1454i	0.902640	+	0.902640i	0.995664	−	0.0930239i	$-0.0296533\pi$
$839$	26.1454	+	26.1454i	0.902640	+	0.902640i	−0.0930239	+	0.995664i	$0.529653\pi$
$840$		0			0
$841$	11.0923			0.382495
$842$			77.2375i			2.66178i
$843$		0			0
$844$		−	21.1590i		−	0.728323i
$845$	4.10294	−	36.8107i	0.141145	−	1.26633i
$846$		0			0
$847$	−25.3097	−	12.0320i	−0.869650	−	0.413426i
$848$	−11.8524			−0.407012
$849$		0			0
$850$	19.5803	−	19.5803i	0.671598	−	0.671598i
$851$	1.99778	+	1.99778i	0.0684829	+	0.0684829i
$852$		0			0
$853$	−15.4396	−	15.4396i	−0.528641	−	0.528641i	0.391526	−	0.920167i	$-0.371947\pi$
$853$	−15.4396	−	15.4396i	−0.528641	−	0.528641i	−0.920167	+	0.391526i	$0.871947\pi$
$854$	14.1748	+	39.8650i	0.485053	+	1.36415i
$855$		0			0
$856$	0.896758	−	0.896758i	0.0306506	−	0.0306506i
$857$	−35.9311			−1.22738			−0.613691	−	0.789546i	$-0.710316\pi$
$857$	−35.9311			−1.22738			−0.613691	+	0.789546i	$0.710316\pi$
$858$		0			0
$859$			6.05104i			0.206459i	0.994658	+	0.103229i	$0.0329176\pi$
$859$			6.05104i			0.206459i	−0.994658	+	0.103229i	$0.967082\pi$
$860$	−46.7496	+	46.7496i	−1.59415	+	1.59415i
$861$		0			0
$862$			13.9684i			0.475764i
$863$	11.8524	+	11.8524i	0.403459	+	0.403459i	0.879450	−	0.475991i	$-0.157911\pi$
$863$	11.8524	+	11.8524i	0.403459	+	0.403459i	−0.475991	+	0.879450i	$0.657911\pi$
$864$		0			0
$865$	−28.9726	+	28.9726i	−0.985098	+	0.985098i
$866$	−12.1166	−	12.1166i	−0.411739	−	0.411739i
$867$		0			0
$868$	−42.7621	+	15.2050i	−1.45144	+	0.516090i
$869$	6.23083	−	6.23083i	0.211367	−	0.211367i
$870$		0			0
$871$	33.4590	+	16.0883i	1.13371	+	0.545132i
$872$	2.20787			0.0747678
$873$		0			0
$874$		−	9.21955i		−	0.311856i
$875$	−13.3702	+	4.75404i	−0.451994	+	0.160716i
$876$		0			0
$877$	29.7741	+	29.7741i	1.00540	+	1.00540i	0.999985	+	0.00541422i	$0.00172341\pi$
$877$	29.7741	+	29.7741i	1.00540	+	1.00540i	0.00541422	+	0.999985i	$0.498277\pi$
$878$	−3.51796	−	3.51796i	−0.118725	−	0.118725i
$879$		0			0
$880$			6.41503i			0.216251i
$881$	−18.8928			−0.636516			−0.318258	−	0.948004i	$-0.603098\pi$
$881$	−18.8928			−0.636516			−0.318258	+	0.948004i	$0.603098\pi$
$882$		0			0
$883$			7.28391i			0.245123i	0.992461	+	0.122562i	$0.0391109\pi$
$883$			7.28391i			0.245123i	−0.992461	+	0.122562i	$0.960889\pi$
$884$	11.4286	+	32.5986i	0.384387	+	1.09641i
$885$		0			0
$886$	−19.9978	−	19.9978i	−0.671838	−	0.671838i
$887$		−	36.5520i		−	1.22730i	−0.789580	−	0.613648i	$-0.789702\pi$
$887$		−	36.5520i		−	1.22730i	0.789580	−	0.613648i	$-0.210298\pi$
$888$		0			0
$889$	33.0398	+	15.7069i	1.10812	+	0.526792i
$890$	−32.8249	−	32.8249i	−1.10029	−	1.10029i
$891$		0			0
$892$	−5.71459	−	5.71459i	−0.191339	−	0.191339i
$893$	40.2148			1.34574
$894$		0			0
$895$	8.28233	+	8.28233i	0.276848	+	0.276848i
$896$	−3.10197	−	8.72393i	−0.103630	−	0.291446i
$897$		0			0
$898$	71.8390			2.39730
$899$	−34.6847	+	34.6847i	−1.15680	+	1.15680i
$900$		0			0
$901$	−14.5463			−0.484607
$902$	2.38575	−	2.38575i	0.0794368	−	0.0794368i
$903$		0			0
$904$	−5.08742	+	5.08742i	−0.169205	+	0.169205i
$905$	43.4679	−	43.4679i	1.44492	−	1.44492i
$906$		0			0
$907$			8.45875i			0.280868i	0.990090	+	0.140434i	$0.0448498\pi$
$907$			8.45875i			0.280868i	−0.990090	+	0.140434i	$0.955150\pi$
$908$	−11.6341	−	11.6341i	−0.386091	−	0.386091i
$909$		0			0
$910$	−5.93491	+	55.4786i	−0.196740	+	1.83910i
$911$	11.0973			0.367669			0.183834	−	0.982957i	$-0.441149\pi$
$911$	11.0973			0.367669			0.183834	+	0.982957i	$0.441149\pi$
$912$		0			0
$913$		−	3.89090i		−	0.128770i
$914$		−	8.26025i		−	0.273225i
$915$		0			0
$916$	1.61474	−	1.61474i	0.0533524	−	0.0533524i
$917$	30.6572	+	14.5742i	1.01239	+	0.481283i
$918$		0			0
$919$	−30.7225			−1.01344			−0.506722	−	0.862110i	$-0.669143\pi$
$919$	−30.7225			−1.01344			−0.506722	+	0.862110i	$0.669143\pi$
$920$	−1.16996			−0.0385724
$921$		0			0
$922$	6.92634			0.228107
$923$	−25.5923	−	12.3057i	−0.842381	−	0.405048i
$924$		0			0
$925$	−6.67307	−	6.67307i	−0.219409	−	0.219409i
$926$	51.0672			1.67817
$927$		0			0
$928$	−36.3432	−	36.3432i	−1.19302	−	1.19302i
$929$	24.7606	−	24.7606i	0.812370	−	0.812370i	−0.172619	−	0.984989i	$-0.555223\pi$
$929$	24.7606	−	24.7606i	0.812370	−	0.812370i	0.984989	+	0.172619i	$0.0552228\pi$
$930$		0			0
$931$	33.5075	+	3.43441i	1.09817	+	0.112558i
$932$	−54.5007			−1.78523
$933$		0			0
$934$	31.1060	+	31.1060i	1.01782	+	1.01782i
$935$			7.87310i			0.257478i
$936$		0			0
$937$		−	18.9594i		−	0.619376i	−0.950838	−	0.309688i	$-0.899775\pi$
$937$		−	18.9594i		−	0.619376i	0.950838	−	0.309688i	$-0.100225\pi$
$938$	−50.5096	−	24.0119i	−1.64920	−	0.784016i
$939$		0			0
$940$		−	52.7259i		−	1.71973i
$941$	32.7842	−	32.7842i	1.06874	−	1.06874i	0.0712788	−	0.997456i	$-0.477292\pi$
$941$	32.7842	−	32.7842i	1.06874	−	1.06874i	0.997456	−	0.0712788i	$-0.0227080\pi$
$942$		0			0
$943$	−1.69832	−	1.69832i	−0.0553048	−	0.0553048i
$944$	0.901299	+	0.901299i	0.0293348	+	0.0293348i
$945$		0			0
$946$		−	13.7397i		−	0.446718i
$947$	29.9748	−	29.9748i	0.974050	−	0.974050i	−0.0256213	−	0.999672i	$-0.508156\pi$
$947$	29.9748	−	29.9748i	0.974050	−	0.974050i	0.999672	+	0.0256213i	$0.00815639\pi$
$948$		0			0
$949$	−40.7217	−	19.5805i	−1.32188	−	0.635610i
$950$			30.7956i			0.999141i
$951$		0			0
$952$	−1.68736	−	4.74550i	−0.0546877	−	0.153802i
$953$		−	41.0785i		−	1.33066i	−0.746548	−	0.665332i	$-0.768290\pi$
$953$		−	41.0785i		−	1.33066i	0.746548	−	0.665332i	$-0.231710\pi$
$954$		0			0
$955$	−20.7543	+	20.7543i	−0.671593	+	0.671593i
$956$	−14.4494	+	14.4494i	−0.467326	+	0.467326i
$957$		0			0
$958$		−	13.3962i		−	0.432810i
$959$	−3.00944	−	8.46367i	−0.0971797	−	0.273306i
$960$		0			0
$961$		−	29.0128i		−	0.935895i
$962$	21.1443	−	7.41291i	0.681718	−	0.239002i
$963$		0			0
$964$	−44.6325	+	44.6325i	−1.43752	+	1.43752i
$965$		−	25.3277i		−	0.815327i
$966$		0			0
$967$	−43.8412	−	43.8412i	−1.40984	−	1.40984i	−0.760492	−	0.649347i	$-0.775042\pi$
$967$	−43.8412	−	43.8412i	−1.40984	−	1.40984i	−0.649347	−	0.760492i	$-0.724958\pi$
$968$	−3.29529	−	3.29529i	−0.105915	−	0.105915i
$969$		0			0
$970$	−1.38493	+	1.38493i	−0.0444674	+	0.0444674i
$971$		−	44.2843i		−	1.42115i	−0.703621	−	0.710575i	$-0.748435\pi$
$971$		−	44.2843i		−	1.42115i	0.703621	−	0.710575i	$-0.251565\pi$
$972$		0			0
$973$	7.98528	+	3.79615i	0.255996	+	0.121699i
$974$			27.9541i			0.895706i
$975$		0			0
$976$		−	27.4627i		−	0.879060i
$977$	−7.01207	−	7.01207i	−0.224336	−	0.224336i	0.585986	−	0.810321i	$-0.300708\pi$
$977$	−7.01207	−	7.01207i	−0.224336	−	0.224336i	−0.810321	+	0.585986i	$0.800708\pi$
$978$		0			0
$979$	5.06895			0.162004
$980$	4.50289	−	43.9320i	0.143839	−	1.40336i
$981$		0			0
$982$	−13.3827	+	13.3827i	−0.427059	+	0.427059i
$983$	31.8034	+	31.8034i	1.01437	+	1.01437i	0.999895	+	0.0144754i	$0.00460781\pi$
$983$	31.8034	+	31.8034i	1.01437	+	1.01437i	0.0144754	+	0.999895i	$0.495392\pi$
$984$		0			0
$985$	13.0987			0.417360
$986$	−39.7684	−	39.7684i	−1.26649	−	1.26649i
$987$		0			0
$988$	−34.6227	−	16.6479i	−1.10149	−	0.529640i
$989$	−9.78076			−0.311010
$990$		0			0
$991$	42.1367			1.33852			0.669259	−	0.743029i	$-0.266612\pi$
$991$	42.1367			1.33852			0.669259	+	0.743029i	$0.266612\pi$
$992$	62.8825			1.99652
$993$		0			0
$994$	38.6341	+	18.3664i	1.22540	+	0.582546i
$995$	−12.4931	+	12.4931i	−0.396058	+	0.396058i
$996$		0			0
$997$		−	27.7314i		−	0.878261i	−0.898423	−	0.439131i	$-0.855287\pi$
$997$		−	27.7314i		−	0.878261i	0.898423	−	0.439131i	$-0.144713\pi$
$998$		−	19.3339i		−	0.612003i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.y.h.307.6		12
3.2	odd	2		91.2.i.a.34.2	yes	12
7.6	odd	2	inner	819.2.y.h.307.5		12
13.5	odd	4	inner	819.2.y.h.811.5		12
21.2	odd	6		637.2.bc.a.619.1		24
21.5	even	6		637.2.bc.a.619.2		24
21.11	odd	6		637.2.bc.a.411.6		24
21.17	even	6		637.2.bc.a.411.5		24
21.20	even	2		91.2.i.a.34.1	✓	12
39.5	even	4		91.2.i.a.83.2	yes	12
91.83	even	4	inner	819.2.y.h.811.6		12
273.5	odd	12		637.2.bc.a.31.6		24
273.44	even	12		637.2.bc.a.31.5		24
273.83	odd	4		91.2.i.a.83.1	yes	12
273.122	odd	12		637.2.bc.a.460.1		24
273.200	even	12		637.2.bc.a.460.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.i.a.34.1	✓	12	21.20	even	2
91.2.i.a.34.2	yes	12	3.2	odd	2
91.2.i.a.83.1	yes	12	273.83	odd	4
91.2.i.a.83.2	yes	12	39.5	even	4
637.2.bc.a.31.5		24	273.44	even	12
637.2.bc.a.31.6		24	273.5	odd	12
637.2.bc.a.411.5		24	21.17	even	6
637.2.bc.a.411.6		24	21.11	odd	6
637.2.bc.a.460.1		24	273.122	odd	12
637.2.bc.a.460.2		24	273.200	even	12
637.2.bc.a.619.1		24	21.2	odd	6
637.2.bc.a.619.2		24	21.5	even	6
819.2.y.h.307.5		12	7.6	odd	2	inner
819.2.y.h.307.6		12	1.1	even	1	trivial
819.2.y.h.811.5		12	13.5	odd	4	inner
819.2.y.h.811.6		12	91.83	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.y (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45161 + 1.45161i) q^{2} +2.21432i q^{4} +(2.01464 - 2.01464i) q^{5} +(-1.13594 + 2.38948i) q^{7} +(-0.311108 + 0.311108i) q^{8} +O(q^{10})\)	\(q+(1.45161 + 1.45161i) q^{2} +2.21432i q^{4} +(2.01464 - 2.01464i) q^{5} +(-1.13594 + 2.38948i) q^{7} +(-0.311108 + 0.311108i) q^{8} +5.84892 q^{10} +(-0.451606 + 0.451606i) q^{11} +(3.40251 - 1.19288i) q^{13} +(-5.11753 + 1.81964i) q^{14} +3.52543 q^{16} +4.32672 q^{17} +(-3.40251 + 3.40251i) q^{19} +(4.46105 + 4.46105i) q^{20} -1.31111 q^{22} +0.933323i q^{23} -3.11753i q^{25} +(6.67068 + 3.20751i) q^{26} +(-5.29108 - 2.51534i) q^{28} -6.33185 q^{29} +(5.47781 - 5.47781i) q^{31} +(5.73975 + 5.73975i) q^{32} +(6.28070 + 6.28070i) q^{34} +(2.52543 + 7.10246i) q^{35} +(2.14050 - 2.14050i) q^{37} -9.87820 q^{38} +1.25354i q^{40} +(-1.81964 + 1.81964i) q^{41} +10.4795i q^{43} +(-1.00000 - 1.00000i) q^{44} +(-1.35482 + 1.35482i) q^{46} +(-5.90958 - 5.90958i) q^{47} +(-4.41926 - 5.42864i) q^{49} +(4.52543 - 4.52543i) q^{50} +(2.64141 + 7.53424i) q^{52} -3.36196 q^{53} +1.81964i q^{55} +(-0.389986 - 1.09679i) q^{56} +(-9.19135 - 9.19135i) q^{58} +(0.255657 + 0.255657i) q^{59} -7.78989i q^{61} +15.9032 q^{62} +9.61285i q^{64} +(4.45161 - 9.25803i) q^{65} +(7.28100 + 7.28100i) q^{67} +9.58075i q^{68} +(-6.64405 + 13.9759i) q^{70} +(-5.56914 - 5.56914i) q^{71} +(-8.86144 - 8.86144i) q^{73} +6.21432 q^{74} +(-7.53424 - 7.53424i) q^{76} +(-0.566106 - 1.59210i) q^{77} -13.7971 q^{79} +(7.10246 - 7.10246i) q^{80} -5.28281 q^{82} +(-4.30785 + 4.30785i) q^{83} +(8.71678 - 8.71678i) q^{85} +(-15.2121 + 15.2121i) q^{86} -0.280996i q^{88} +(-5.61214 - 5.61214i) q^{89} +(-1.01470 + 9.48527i) q^{91} -2.06668 q^{92} -17.1568i q^{94} +13.7096i q^{95} +(-0.236784 + 0.236784i) q^{97} +(1.46522 - 14.2953i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 - 8 * q^7 - 4 * q^8	\( 12 q + 4 q^{2} - 8 q^{7} - 4 q^{8} + 8 q^{11} - 8 q^{14} + 16 q^{16} - 16 q^{22} - 20 q^{28} + 4 q^{29} + 16 q^{32} + 4 q^{35} + 12 q^{37} - 12 q^{44} + 24 q^{46} + 28 q^{50} + 12 q^{53} - 44 q^{58} + 40 q^{65} + 60 q^{67} + 4 q^{70} + 48 q^{74} - 4 q^{79} + 12 q^{85} - 36 q^{86} - 32 q^{91} - 24 q^{92} + 28 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 - 8 * q^7 - 4 * q^8 + 8 * q^11 - 8 * q^14 + 16 * q^16 - 16 * q^22 - 20 * q^28 + 4 * q^29 + 16 * q^32 + 4 * q^35 + 12 * q^37 - 12 * q^44 + 24 * q^46 + 28 * q^50 + 12 * q^53 - 44 * q^58 + 40 * q^65 + 60 * q^67 + 4 * q^70 + 48 * q^74 - 4 * q^79 + 12 * q^85 - 36 * q^86 - 32 * q^91 - 24 * q^92 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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