LMFDB - Embedded newform 1764.2.b.m.1567.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1764,2,Mod(1567,1764)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1764, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1764.1567");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1764.b (of order $2$, degree $1$, 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:	$14.0856109166$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.15911316233388032.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 4 x^{11} + 10 x^{10} - 20 x^{9} + 35 x^{8} - 56 x^{7} + 84 x^{6} - 112 x^{5} + 140 x^{4} + \cdots + 64 $ x^12 - 4x^11 + 10x^10 - 20x^9 + 35x^8 - 56x^7 + 84x^6 - 112x^5 + 140x^4 - 160x^3 + 160x^2 - 128*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 588)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			1567.9
Root			$-0.476589 - 1.33149i$ of defining polynomial
Character	$\chi$	$=$	1764.1567
Dual form			1764.2.b.m.1567.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.476589 - 1.33149i) q^{2} +(-1.54572 - 1.26915i) q^{4} +0.509876i q^{5} +(-2.42653 + 1.45325i) q^{8} +O(q^{10})$	\(q+(0.476589 - 1.33149i) q^{2} +(-1.54572 - 1.26915i) q^{4} +0.509876i q^{5} +(-2.42653 + 1.45325i) q^{8} +(0.678894 + 0.243001i) q^{10} +4.12734i q^{11} -3.97722i q^{13} +(0.778531 + 3.92350i) q^{16} +4.93843i q^{17} -5.05234 q^{19} +(0.647107 - 0.788127i) q^{20} +(5.49550 + 1.96705i) q^{22} -2.91930i q^{23} +4.74003 q^{25} +(-5.29562 - 1.89550i) q^{26} +5.82102 q^{29} +5.71997 q^{31} +(5.59514 + 0.833296i) q^{32} +(6.57546 + 2.35360i) q^{34} +10.0074 q^{37} +(-2.40789 + 6.72713i) q^{38} +(-0.740978 - 1.23723i) q^{40} +11.7494i q^{41} +9.84649i q^{43} +(5.23820 - 6.37973i) q^{44} +(-3.88701 - 1.39131i) q^{46} -7.87161 q^{47} +(2.25905 - 6.31129i) q^{50} +(-5.04767 + 6.14768i) q^{52} -1.23873 q^{53} -2.10443 q^{55} +(2.77424 - 7.75063i) q^{58} +4.65379 q^{59} -0.543314i q^{61} +(2.72608 - 7.61607i) q^{62} +(3.77611 - 7.05273i) q^{64} +2.02789 q^{65} +7.02106i q^{67} +(6.26759 - 7.63345i) q^{68} -1.06587i q^{71} +0.837037i q^{73} +(4.76943 - 13.3248i) q^{74} +(7.80952 + 6.41216i) q^{76} -1.25800i q^{79} +(-2.00050 + 0.396954i) q^{80} +(15.6442 + 5.59964i) q^{82} +13.7332 q^{83} -2.51798 q^{85} +(13.1105 + 4.69273i) q^{86} +(-5.99807 - 10.0151i) q^{88} -4.68906i q^{89} +(-3.70502 + 4.51243i) q^{92} +(-3.75153 + 10.4810i) q^{94} -2.57606i q^{95} +1.80904i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8}+O(q^{10}) $ 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8	$ 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} + 24 q^{20} - 12 q^{25} - 24 q^{26} - 32 q^{29} + 16 q^{31} - 4 q^{32} + 32 q^{34} + 32 q^{37} + 24 q^{38} - 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} + 32 q^{52} + 32 q^{53} + 16 q^{55} + 16 q^{58} + 16 q^{59} - 8 q^{62} - 4 q^{64} + 8 q^{68} + 32 q^{74} - 32 q^{76} + 16 q^{80} + 32 q^{82} + 16 q^{83} + 16 q^{85} + 24 q^{86} + 24 q^{88}+O(q^{100}) $ 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 + 24 * q^20 - 12 * q^25 - 24 * q^26 - 32 * q^29 + 16 * q^31 - 4 * q^32 + 32 * q^34 + 32 * q^37 + 24 * q^38 - 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 + 32 * q^52 + 32 * q^53 + 16 * q^55 + 16 * q^58 + 16 * q^59 - 8 * q^62 - 4 * q^64 + 8 * q^68 + 32 * q^74 - 32 * q^76 + 16 * q^80 + 32 * q^82 + 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times$.

$n$	$785$	$883$	$1081$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	0.476589	−	1.33149i	0.337000	−	0.941505i
$2$	0.476589	−	1.33149i	0.337000	−	0.941505i
$3$		0			0
$3$		0			0
$4$	−1.54572	−	1.26915i	−0.772862	−	0.634574i
$5$			0.509876i			0.228023i	0.993479	+	0.114012i	$0.0363701\pi$
$5$			0.509876i			0.228023i	−0.993479	+	0.114012i	$0.963630\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−2.42653	+	1.45325i	−0.857908	+	0.513803i
$9$		0			0
$10$	0.678894	+	0.243001i	0.214685	+	0.0768438i
$11$			4.12734i			1.24444i	0.782843	+	0.622220i	$0.213769\pi$
$11$			4.12734i			1.24444i	−0.782843	+	0.622220i	$0.786231\pi$
$12$		0			0
$13$		−	3.97722i		−	1.10308i	−0.834148	−	0.551541i	$-0.814040\pi$
$13$		−	3.97722i		−	1.10308i	0.834148	−	0.551541i	$-0.185960\pi$
$14$		0			0
$15$		0			0
$16$	0.778531	+	3.92350i	0.194633	+	0.980876i
$17$			4.93843i			1.19774i	0.800844	+	0.598872i	$0.204384\pi$
$17$			4.93843i			1.19774i	−0.800844	+	0.598872i	$0.795616\pi$
$18$		0			0
$19$	−5.05234			−1.15909			−0.579543	−	0.814942i	$-0.696769\pi$
$19$	−5.05234			−1.15909			−0.579543	+	0.814942i	$0.696769\pi$
$20$	0.647107	−	0.788127i	0.144698	−	0.176231i
$21$		0			0
$22$	5.49550	+	1.96705i	1.17165	+	0.419376i
$23$		−	2.91930i		−	0.608715i	−0.952558	−	0.304358i	$-0.901558\pi$
$23$		−	2.91930i		−	0.608715i	0.952558	−	0.304358i	$-0.0984418\pi$
$24$		0			0
$25$	4.74003			0.948005
$26$	−5.29562	−	1.89550i	−1.03856	−	0.371738i
$27$		0			0
$28$		0			0
$29$	5.82102			1.08094			0.540469	−	0.841364i	$-0.318247\pi$
$29$	5.82102			1.08094			0.540469	+	0.841364i	$0.318247\pi$
$30$		0			0
$31$	5.71997			1.02734			0.513668	−	0.857989i	$-0.328286\pi$
$31$	5.71997			1.02734			0.513668	+	0.857989i	$0.328286\pi$
$32$	5.59514	+	0.833296i	0.989091	+	0.147307i
$33$		0			0
$34$	6.57546	+	2.35360i	1.12768	+	0.403640i
$35$		0			0
$36$		0			0
$37$	10.0074			1.64521			0.822604	−	0.568614i	$-0.192520\pi$
$37$	10.0074			1.64521			0.822604	+	0.568614i	$0.192520\pi$
$38$	−2.40789	+	6.72713i	−0.390612	+	1.09128i
$39$		0			0
$40$	−0.740978	−	1.23723i	−0.117159	−	0.195623i
$41$			11.7494i			1.83495i	0.397797	+	0.917474i	$0.369775\pi$
$41$			11.7494i			1.83495i	−0.397797	+	0.917474i	$0.630225\pi$
$42$		0			0
$43$			9.84649i			1.50158i	0.660544	+	0.750788i	$0.270326\pi$
$43$			9.84649i			1.50158i	−0.660544	+	0.750788i	$0.729674\pi$
$44$	5.23820	−	6.37973i	0.789688	−	0.961780i
$45$		0			0
$46$	−3.88701	−	1.39131i	−0.573108	−	0.205137i
$47$	−7.87161			−1.14819			−0.574096	−	0.818788i	$-0.694646\pi$
$47$	−7.87161			−1.14819			−0.574096	+	0.818788i	$0.694646\pi$
$48$		0			0
$49$		0			0
$50$	2.25905	−	6.31129i	0.319477	−	0.892552i
$51$		0			0
$52$	−5.04767	+	6.14768i	−0.699986	+	0.852530i
$53$	−1.23873			−0.170152			−0.0850761	−	0.996374i	$-0.527113\pi$
$53$	−1.23873			−0.170152			−0.0850761	+	0.996374i	$0.527113\pi$
$54$		0			0
$55$	−2.10443			−0.283761
$56$		0			0
$57$		0			0
$58$	2.77424	−	7.75063i	0.364275	−	1.01771i
$59$	4.65379			0.605872			0.302936	−	0.953011i	$-0.402033\pi$
$59$	4.65379			0.605872			0.302936	+	0.953011i	$0.402033\pi$
$60$		0			0
$61$		−	0.543314i		−	0.0695643i	−0.999395	−	0.0347821i	$-0.988926\pi$
$61$		−	0.543314i		−	0.0695643i	0.999395	−	0.0347821i	$-0.0110737\pi$
$62$	2.72608	−	7.61607i	0.346212	−	0.967242i
$63$		0			0
$64$	3.77611	−	7.05273i	0.472014	−	0.881591i
$65$	2.02789			0.251528
$66$		0			0
$67$			7.02106i			0.857758i	0.903362	+	0.428879i	$0.141091\pi$
$67$			7.02106i			0.857758i	−0.903362	+	0.428879i	$0.858909\pi$
$68$	6.26759	−	7.63345i	0.760057	−	0.925692i
$69$		0			0
$70$		0			0
$71$		−	1.06587i		−	0.126496i	−0.997998	−	0.0632478i	$-0.979854\pi$
$71$		−	1.06587i		−	0.126496i	0.997998	−	0.0632478i	$-0.0201458\pi$
$72$		0			0
$73$			0.837037i			0.0979678i	0.998800	+	0.0489839i	$0.0155983\pi$
$73$			0.837037i			0.0979678i	−0.998800	+	0.0489839i	$0.984402\pi$
$74$	4.76943	−	13.3248i	0.554435	−	1.54897i
$75$		0			0
$76$	7.80952	+	6.41216i	0.895814	+	0.735525i
$77$		0			0
$78$		0			0
$79$		−	1.25800i		−	0.141536i	−0.997493	−	0.0707682i	$-0.977455\pi$
$79$		−	1.25800i		−	0.141536i	0.997493	−	0.0707682i	$-0.0225450\pi$
$80$	−2.00050	+	0.396954i	−0.223663	+	0.0443808i
$81$		0			0
$82$	15.6442	+	5.59964i	1.72761	+	0.618377i
$83$	13.7332			1.50741			0.753705	−	0.657213i	$-0.228265\pi$
$83$	13.7332			1.50741			0.753705	+	0.657213i	$0.228265\pi$
$84$		0			0
$85$	−2.51798			−0.273114
$86$	13.1105	+	4.69273i	1.41374	+	0.506030i
$87$		0			0
$88$	−5.99807	−	10.0151i	−0.639396	−	1.06761i
$89$		−	4.68906i		−	0.497040i	−0.968627	−	0.248520i	$-0.920056\pi$
$89$		−	4.68906i		−	0.497040i	0.968627	−	0.248520i	$-0.0799441\pi$
$90$		0			0
$91$		0			0
$92$	−3.70502	+	4.51243i	−0.386275	+	0.470453i
$93$		0			0
$94$	−3.75153	+	10.4810i	−0.386940	+	1.08103i
$95$		−	2.57606i		−	0.264299i
$96$		0			0
$97$			1.80904i			0.183680i	0.995774	+	0.0918402i	$0.0292749\pi$
$97$			1.80904i			0.183680i	−0.995774	+	0.0918402i	$0.970725\pi$
$98$		0			0
$99$		0			0
$100$	−7.32678	−	6.01579i	−0.732678	−	0.601579i
$101$		−	5.96314i		−	0.593354i	−0.954978	−	0.296677i	$-0.904122\pi$
$101$		−	5.96314i		−	0.593354i	0.954978	−	0.296677i	$-0.0958785\pi$
$102$		0			0
$103$	−11.0937			−1.09309			−0.546545	−	0.837430i	$-0.684057\pi$
$103$	−11.0937			−1.09309			−0.546545	+	0.837430i	$0.684057\pi$
$104$	5.77990	+	9.65084i	0.566766	+	0.946343i
$105$		0			0
$106$	−0.590364	+	1.64935i	−0.0573412	+	0.160199i
$107$		−	0.629229i		−	0.0608299i	−0.999537	−	0.0304150i	$-0.990317\pi$
$107$		−	0.629229i		−	0.0608299i	0.999537	−	0.0304150i	$-0.00968287\pi$
$108$		0			0
$109$	15.8175			1.51505			0.757523	−	0.652809i	$-0.226410\pi$
$109$	15.8175			1.51505			0.757523	+	0.652809i	$0.226410\pi$
$110$	−1.00295	+	2.80202i	−0.0956274	+	0.267162i
$111$		0			0
$112$		0			0
$113$	3.72346			0.350273			0.175137	−	0.984544i	$-0.443963\pi$
$113$	3.72346			0.350273			0.175137	+	0.984544i	$0.443963\pi$
$114$		0			0
$115$	1.48848			0.138801
$116$	−8.99770	−	7.38774i	−0.835416	−	0.685934i
$117$		0			0
$118$	2.21795	−	6.19647i	0.204179	−	0.570431i
$119$		0			0
$120$		0			0
$121$	−6.03492			−0.548629
$122$	−0.723417	−	0.258938i	−0.0654951	−	0.0234431i
$123$		0			0
$124$	−8.84150	−	7.25948i	−0.793990	−	0.651921i
$125$			4.96620i			0.444191i
$126$		0			0
$127$		−	14.0834i		−	1.24970i	−0.780746	−	0.624848i	$-0.785161\pi$
$127$		−	14.0834i		−	1.24970i	0.780746	−	0.624848i	$-0.214839\pi$
$128$	−7.59098	−	8.38910i	−0.670954	−	0.741499i
$129$		0			0
$130$	0.966469	−	2.70011i	0.0847649	−	0.236815i
$131$	−3.36363			−0.293882			−0.146941	−	0.989145i	$-0.546943\pi$
$131$	−3.36363			−0.293882			−0.146941	+	0.989145i	$0.546943\pi$
$132$		0			0
$133$		0			0
$134$	9.34846	+	3.34616i	0.807584	+	0.289064i
$135$		0			0
$136$	−7.17679	−	11.9833i	−0.615405	−	1.02756i
$137$	0.487457			0.0416462			0.0208231	−	0.999783i	$-0.493371\pi$
$137$	0.487457			0.0416462			0.0208231	+	0.999783i	$0.493371\pi$
$138$		0			0
$139$	−16.2489			−1.37821			−0.689105	−	0.724662i	$-0.741996\pi$
$139$	−16.2489			−1.37821			−0.689105	+	0.724662i	$0.741996\pi$
$140$		0			0
$141$		0			0
$142$	−1.41920	−	0.507983i	−0.119096	−	0.0426290i
$143$	16.4153			1.37272
$144$		0			0
$145$			2.96800i			0.246479i
$146$	1.11451	+	0.398923i	0.0922372	+	0.0330151i
$147$		0			0
$148$	−15.4687	−	12.7009i	−1.27152	−	1.04401i
$149$	15.7474			1.29008			0.645040	−	0.764149i	$-0.276841\pi$
$149$	15.7474			1.29008			0.645040	+	0.764149i	$0.276841\pi$
$150$		0			0
$151$			24.2825i			1.97608i	0.154191	+	0.988041i	$0.450723\pi$
$151$			24.2825i			1.97608i	−0.154191	+	0.988041i	$0.549277\pi$
$152$	12.2597	−	7.34233i	0.994389	−	0.595541i
$153$		0			0
$154$		0			0
$155$			2.91647i			0.234257i
$156$		0			0
$157$		−	3.75846i		−	0.299958i	−0.988689	−	0.149979i	$-0.952079\pi$
$157$		−	3.75846i		−	0.299958i	0.988689	−	0.149979i	$-0.0479206\pi$
$158$	−1.67502	−	0.599551i	−0.133257	−	0.0476977i
$159$		0			0
$160$	−0.424877	+	2.85283i	−0.0335895	+	0.225536i
$161$		0			0
$162$		0			0
$163$		−	8.08975i		−	0.633638i	−0.948486	−	0.316819i	$-0.897385\pi$
$163$		−	8.08975i		−	0.633638i	0.948486	−	0.316819i	$-0.102615\pi$
$164$	14.9117	−	18.1613i	1.16441	−	1.41816i
$165$		0			0
$166$	6.54508	−	18.2856i	0.507997	−	1.41923i
$167$	−23.7606			−1.83865			−0.919327	−	0.393495i	$-0.871266\pi$
$167$	−23.7606			−1.83865			−0.919327	+	0.393495i	$0.871266\pi$
$168$		0			0
$169$	−2.81825			−0.216789
$170$	−1.20004	+	3.35267i	−0.0920392	+	0.257138i
$171$		0			0
$172$	12.4966	−	15.2200i	0.952860	−	1.16051i
$173$			8.73293i			0.663953i	0.943288	+	0.331976i	$0.107715\pi$
$173$			8.73293i			0.663953i	−0.943288	+	0.331976i	$0.892285\pi$
$174$		0			0
$175$		0			0
$176$	−16.1936	+	3.21326i	−1.22064	+	0.242209i
$177$		0			0
$178$	−6.24343	−	2.23476i	−0.467965	−	0.167502i
$179$			10.7957i			0.806911i	0.914999	+	0.403456i	$0.132191\pi$
$179$			10.7957i			0.806911i	−0.914999	+	0.403456i	$0.867809\pi$
$180$		0			0
$181$			26.0627i			1.93722i	0.248580	+	0.968611i	$0.420036\pi$
$181$			26.0627i			1.93722i	−0.248580	+	0.968611i	$0.579964\pi$
$182$		0			0
$183$		0			0
$184$	4.24248	+	7.08376i	0.312760	+	0.522222i
$185$			5.10254i			0.375146i
$186$		0			0
$187$	−20.3826			−1.49052
$188$	12.1673	+	9.99023i	0.887395	+	0.728612i
$189$		0			0
$190$	−3.43000	−	1.22772i	−0.248838	−	0.0890685i
$191$		−	1.75467i		−	0.126964i	−0.997983	−	0.0634819i	$-0.979779\pi$
$191$		−	1.75467i		−	0.126964i	0.997983	−	0.0634819i	$-0.0202205\pi$
$192$		0			0
$193$	−14.9268			−1.07446			−0.537229	−	0.843437i	$-0.680529\pi$
$193$	−14.9268			−1.07446			−0.537229	+	0.843437i	$0.680529\pi$
$194$	2.40872	+	0.862171i	0.172936	+	0.0619003i
$195$		0			0
$196$		0			0
$197$	−12.1669			−0.866855			−0.433428	−	0.901188i	$-0.642696\pi$
$197$	−12.1669			−0.866855			−0.433428	+	0.901188i	$0.642696\pi$
$198$		0			0
$199$	21.4536			1.52080			0.760401	−	0.649453i	$-0.225002\pi$
$199$	21.4536			1.52080			0.760401	+	0.649453i	$0.225002\pi$
$200$	−11.5018	+	6.88846i	−0.813302	+	0.487088i
$201$		0			0
$202$	−7.93985	−	2.84197i	−0.558646	−	0.199960i
$203$		0			0
$204$		0			0
$205$	−5.99073			−0.418411
$206$	−5.28712	+	14.7711i	−0.368371	+	1.02915i
$207$		0			0
$208$	15.6046	−	3.09639i	1.08199	−	0.214696i
$209$		−	20.8527i		−	1.44241i
$210$		0			0
$211$			9.90704i			0.682029i	0.940058	+	0.341014i	$0.110770\pi$
$211$			9.90704i			0.682029i	−0.940058	+	0.341014i	$0.889230\pi$
$212$	1.91473	+	1.57213i	0.131504	+	0.107974i
$213$		0			0
$214$	−0.837812	−	0.299884i	−0.0572716	−	0.0204997i
$215$	−5.02048			−0.342394
$216$		0			0
$217$		0			0
$218$	7.53847	−	21.0609i	0.510570	−	1.42642i
$219$		0			0
$220$	3.25287	+	2.67083i	0.219308	+	0.180067i
$221$	19.6412			1.32121
$222$		0			0
$223$	5.67517			0.380037			0.190019	−	0.981780i	$-0.439145\pi$
$223$	5.67517			0.380037			0.190019	+	0.981780i	$0.439145\pi$
$224$		0			0
$225$		0			0
$226$	1.77456	−	4.95774i	0.118042	−	0.329784i
$227$	−2.04705			−0.135867			−0.0679337	−	0.997690i	$-0.521641\pi$
$227$	−2.04705			−0.135867			−0.0679337	+	0.997690i	$0.521641\pi$
$228$		0			0
$229$			4.65100i			0.307347i	0.988122	+	0.153673i	$0.0491104\pi$
$229$			4.65100i			0.307347i	−0.988122	+	0.153673i	$0.950890\pi$
$230$	0.709393	−	1.98189i	0.0467760	−	0.130682i
$231$		0			0
$232$	−14.1249	+	8.45942i	−0.927345	+	0.555388i
$233$	−4.24354			−0.278003			−0.139002	−	0.990292i	$-0.544389\pi$
$233$	−4.24354			−0.278003			−0.139002	+	0.990292i	$0.544389\pi$
$234$		0			0
$235$		−	4.01354i		−	0.261815i
$236$	−7.19348	−	5.90634i	−0.468255	−	0.384470i
$237$		0			0
$238$		0			0
$239$			11.6610i			0.754289i	0.926154	+	0.377145i	$0.123094\pi$
$239$			11.6610i			0.754289i	−0.926154	+	0.377145i	$0.876906\pi$
$240$		0			0
$241$		−	9.97522i		−	0.642560i	−0.946984	−	0.321280i	$-0.895887\pi$
$241$		−	9.97522i		−	0.642560i	0.946984	−	0.321280i	$-0.104113\pi$
$242$	−2.87618	+	8.03543i	−0.184888	+	0.516537i
$243$		0			0
$244$	−0.689546	+	0.839814i	−0.0441436	+	0.0537636i
$245$		0			0
$246$		0			0
$247$			20.0942i			1.27857i
$248$	−13.8797	+	8.31256i	−0.881361	+	0.527848i
$249$		0			0
$250$	6.61244	+	2.36684i	0.418208	+	0.149692i
$251$	−11.8869			−0.750292			−0.375146	−	0.926966i	$-0.622407\pi$
$251$	−11.8869			−0.750292			−0.375146	+	0.926966i	$0.622407\pi$
$252$		0			0
$253$	12.0489			0.757509
$254$	−18.7518	−	6.71198i	−1.17659	−	0.421147i
$255$		0			0
$256$	−14.7878	+	6.10914i	−0.924236	+	0.381821i
$257$		−	20.7566i		−	1.29476i	−0.762166	−	0.647381i	$-0.775864\pi$
$257$		−	20.7566i		−	1.29476i	0.762166	−	0.647381i	$-0.224136\pi$
$258$		0			0
$259$		0			0
$260$	−3.13455	−	2.57368i	−0.194397	−	0.159613i
$261$		0			0
$262$	−1.60307	+	4.47863i	−0.0990380	+	0.276691i
$263$			1.36520i			0.0841817i	0.999114	+	0.0420908i	$0.0134019\pi$
$263$			1.36520i			0.0841817i	−0.999114	+	0.0420908i	$0.986598\pi$
$264$		0			0
$265$		−	0.631597i		−	0.0387987i
$266$		0			0
$267$		0			0
$268$	8.91075	−	10.8526i	0.544311	−	0.662929i
$269$		−	23.3960i		−	1.42648i	−0.700922	−	0.713238i	$-0.747228\pi$
$269$		−	23.3960i		−	1.42648i	0.700922	−	0.713238i	$-0.252772\pi$
$270$		0			0
$271$	20.9191			1.27075			0.635373	−	0.772205i	$-0.280846\pi$
$271$	20.9191			1.27075			0.635373	+	0.772205i	$0.280846\pi$
$272$	−19.3759	+	3.84472i	−1.17484	+	0.233120i
$273$		0			0
$274$	0.232317	−	0.649043i	0.0140348	−	0.0392101i
$275$			19.5637i			1.17974i
$276$		0			0
$277$	−18.4472			−1.10838			−0.554192	−	0.832389i	$-0.686973\pi$
$277$	−18.4472			−1.10838			−0.554192	+	0.832389i	$0.686973\pi$
$278$	−7.74403	+	21.6352i	−0.464456	+	1.29759i
$279$		0			0
$280$		0			0
$281$	−19.9336			−1.18914			−0.594569	−	0.804044i	$-0.702677\pi$
$281$	−19.9336			−1.18914			−0.594569	+	0.804044i	$0.702677\pi$
$282$		0			0
$283$	20.2957			1.20645			0.603227	−	0.797569i	$-0.293881\pi$
$283$	20.2957			1.20645			0.603227	+	0.797569i	$0.293881\pi$
$284$	−1.35275	+	1.64754i	−0.0802708	+	0.0977637i
$285$		0			0
$286$	7.82337	−	21.8568i	0.462605	−	1.29242i
$287$		0			0
$288$		0			0
$289$	−7.38808			−0.434593
$290$	3.95186	+	1.41452i	0.232061	+	0.0830633i
$291$		0			0
$292$	1.06232	−	1.29383i	0.0621678	−	0.0757156i
$293$		−	2.69416i		−	0.157394i	−0.996899	−	0.0786972i	$-0.974924\pi$
$293$		−	2.69416i		−	0.157394i	0.996899	−	0.0786972i	$-0.0250760\pi$
$294$		0			0
$295$			2.37285i			0.138153i
$296$	−24.2833	+	14.5433i	−1.41144	+	0.845312i
$297$		0			0
$298$	7.50506	−	20.9675i	0.434757	−	1.21462i
$299$	−11.6107			−0.671462
$300$		0			0
$301$		0			0
$302$	32.3319	+	11.5728i	1.86049	+	0.665939i
$303$		0			0
$304$	−3.93340	−	19.8229i	−0.225596	−	1.13692i
$305$	0.277023			0.0158623
$306$		0			0
$307$	−6.99511			−0.399232			−0.199616	−	0.979874i	$-0.563969\pi$
$307$	−6.99511			−0.399232			−0.199616	+	0.979874i	$0.563969\pi$
$308$		0			0
$309$		0			0
$310$	3.88325	+	1.38996i	0.220554	+	0.0789444i
$311$	−22.0212			−1.24870			−0.624352	−	0.781143i	$-0.714637\pi$
$311$	−22.0212			−1.24870			−0.624352	+	0.781143i	$0.714637\pi$
$312$		0			0
$313$			1.73737i			0.0982021i	0.998794	+	0.0491010i	$0.0156356\pi$
$313$			1.73737i			0.0982021i	−0.998794	+	0.0491010i	$0.984364\pi$
$314$	−5.00435	−	1.79124i	−0.282412	−	0.101086i
$315$		0			0
$316$	−1.59659	+	1.94453i	−0.0898152	+	0.109388i
$317$	−32.1296			−1.80458			−0.902288	−	0.431133i	$-0.858114\pi$
$317$	−32.1296			−1.80458			−0.902288	+	0.431133i	$0.858114\pi$
$318$		0			0
$319$			24.0253i			1.34516i
$320$	3.59601	+	1.92535i	0.201023	+	0.107630i
$321$		0			0
$322$		0			0
$323$		−	24.9506i		−	1.38829i
$324$		0			0
$325$		−	18.8521i		−	1.04573i
$326$	−10.7714	−	3.85549i	−0.596573	−	0.213536i
$327$		0			0
$328$	−17.0748	−	28.5103i	−0.942801	−	1.57422i
$329$		0			0
$330$		0			0
$331$			11.4233i			0.627882i	0.949442	+	0.313941i	$0.101649\pi$
$331$			11.4233i			0.627882i	−0.949442	+	0.313941i	$0.898351\pi$
$332$	−21.2277	−	17.4294i	−1.16502	−	0.956563i
$333$		0			0
$334$	−11.3241	+	31.6370i	−0.619625	+	1.73110i
$335$	−3.57986			−0.195589
$336$		0			0
$337$	7.08667			0.386036			0.193018	−	0.981195i	$-0.438172\pi$
$337$	7.08667			0.386036			0.193018	+	0.981195i	$0.438172\pi$
$338$	−1.34315	+	3.75247i	−0.0730577	+	0.204107i
$339$		0			0
$340$	3.89211	+	3.19569i	0.211079	+	0.173311i
$341$			23.6082i			1.27846i
$342$		0			0
$343$		0			0
$344$	−14.3094	−	23.8928i	−0.771513	−	1.28821i
$345$		0			0
$346$	11.6278	+	4.16202i	0.625114	+	0.223752i
$347$			20.9062i			1.12230i	0.827713	+	0.561151i	$0.189641\pi$
$347$			20.9062i			1.12230i	−0.827713	+	0.561151i	$0.810359\pi$
$348$		0			0
$349$			1.67904i			0.0898768i	0.998990	+	0.0449384i	$0.0143092\pi$
$349$			1.67904i			0.0898768i	−0.998990	+	0.0449384i	$0.985691\pi$
$350$		0			0
$351$		0			0
$352$	−3.43929	+	23.0930i	−0.183315	+	1.23086i
$353$			6.21344i			0.330708i	0.986234	+	0.165354i	$0.0528766\pi$
$353$			6.21344i			0.330708i	−0.986234	+	0.165354i	$0.947123\pi$
$354$		0			0
$355$	0.543462			0.0288439
$356$	−5.95111	+	7.24800i	−0.315408	+	0.384143i
$357$		0			0
$358$	14.3744	+	5.14513i	0.759711	+	0.271929i
$359$		−	22.5485i		−	1.19007i	−0.803701	−	0.595033i	$-0.797139\pi$
$359$		−	22.5485i		−	1.19007i	0.803701	−	0.595033i	$-0.202861\pi$
$360$		0			0
$361$	6.52612			0.343480
$362$	34.7021	+	12.4212i	1.82390	+	0.652843i
$363$		0			0
$364$		0			0
$365$	−0.426785			−0.0223389
$366$		0			0
$367$	−22.2898			−1.16352			−0.581760	−	0.813361i	$-0.697636\pi$
$367$	−22.2898			−1.16352			−0.581760	+	0.813361i	$0.697636\pi$
$368$	11.4539	−	2.27276i	0.597074	−	0.118476i
$369$		0			0
$370$	6.79397	+	2.43181i	0.353202	+	0.126424i
$371$		0			0
$372$		0			0
$373$	−3.16466			−0.163860			−0.0819300	−	0.996638i	$-0.526108\pi$
$373$	−3.16466			−0.163860			−0.0819300	+	0.996638i	$0.526108\pi$
$374$	−9.71412	+	27.1392i	−0.502305	+	1.40333i
$375$		0			0
$376$	19.1007	−	11.4394i	0.985044	−	0.589944i
$377$		−	23.1515i		−	1.19236i
$378$		0			0
$379$			7.23505i			0.371640i	0.982584	+	0.185820i	$0.0594941\pi$
$379$			7.23505i			0.371640i	−0.982584	+	0.185820i	$0.940506\pi$
$380$	−3.26940	+	3.98189i	−0.167717	+	0.204266i
$381$		0			0
$382$	−2.33633	−	0.836260i	−0.119537	−	0.0427868i
$383$	25.1864			1.28696			0.643482	−	0.765461i	$-0.277489\pi$
$383$	25.1864			1.28696			0.643482	+	0.765461i	$0.277489\pi$
$384$		0			0
$385$		0			0
$386$	−7.11398	+	19.8749i	−0.362092	+	1.01161i
$387$		0			0
$388$	2.29594	−	2.79628i	0.116559	−	0.141960i
$389$	8.18501			0.414997			0.207498	−	0.978235i	$-0.433468\pi$
$389$	8.18501			0.414997			0.207498	+	0.978235i	$0.433468\pi$
$390$		0			0
$391$	14.4167			0.729086
$392$		0			0
$393$		0			0
$394$	−5.79861	+	16.2001i	−0.292130	+	0.816149i
$395$	0.641425			0.0322736
$396$		0			0
$397$			33.5216i			1.68240i	0.540724	+	0.841200i	$0.318150\pi$
$397$			33.5216i			1.68240i	−0.540724	+	0.841200i	$0.681850\pi$
$398$	10.2245	−	28.5652i	0.512510	−	1.43184i
$399$		0			0
$400$	3.69026	+	18.5975i	0.184513	+	0.929876i
$401$	7.05553			0.352336			0.176168	−	0.984360i	$-0.443630\pi$
$401$	7.05553			0.352336			0.176168	+	0.984360i	$0.443630\pi$
$402$		0			0
$403$		−	22.7496i		−	1.13324i
$404$	−7.56810	+	9.21737i	−0.376527	+	0.458581i
$405$		0			0
$406$		0			0
$407$			41.3040i			2.04736i
$408$		0			0
$409$			25.7115i			1.27135i	0.771955	+	0.635677i	$0.219279\pi$
$409$			25.7115i			1.27135i	−0.771955	+	0.635677i	$0.780721\pi$
$410$	−2.85512	+	7.97659i	−0.141004	+	0.393936i
$411$		0			0
$412$	17.1477	+	14.0795i	0.844808	+	0.693646i
$413$		0			0
$414$		0			0
$415$			7.00220i			0.343725i
$416$	3.31420	−	22.2531i	0.162492	−	1.09105i
$417$		0			0
$418$	−27.7651	−	9.93818i	−1.35804	−	0.486092i
$419$	16.0117			0.782223			0.391111	−	0.920343i	$-0.372091\pi$
$419$	16.0117			0.782223			0.391111	+	0.920343i	$0.372091\pi$
$420$		0			0
$421$	6.19958			0.302149			0.151075	−	0.988522i	$-0.451727\pi$
$421$	6.19958			0.302149			0.151075	+	0.988522i	$0.451727\pi$
$422$	13.1911	+	4.72159i	0.642133	+	0.229843i
$423$		0			0
$424$	3.00581	−	1.80018i	0.145975	−	0.0874247i
$425$			23.4083i			1.13547i
$426$		0			0
$427$		0			0
$428$	−0.798585	+	0.972616i	−0.0386010	+	0.0470131i
$429$		0			0
$430$	−2.39271	+	6.68472i	−0.115387	+	0.322366i
$431$		−	30.5495i		−	1.47152i	−0.677245	−	0.735758i	$-0.736826\pi$
$431$		−	30.5495i		−	1.47152i	0.677245	−	0.735758i	$-0.263174\pi$
$432$		0			0
$433$		−	23.2309i		−	1.11641i	−0.829704	−	0.558204i	$-0.811491\pi$
$433$		−	23.2309i		−	1.11641i	0.829704	−	0.558204i	$-0.188509\pi$
$434$		0			0
$435$		0			0
$436$	−24.4496	−	20.0748i	−1.17092	−	0.961408i
$437$			14.7493i			0.705553i
$438$		0			0
$439$	−2.40651			−0.114856			−0.0574282	−	0.998350i	$-0.518290\pi$
$439$	−2.40651			−0.114856			−0.0574282	+	0.998350i	$0.518290\pi$
$440$	5.10646	−	3.05827i	0.243441	−	0.145797i
$441$		0			0
$442$	9.36079	−	26.1520i	0.445247	−	1.24393i
$443$			7.61212i			0.361663i	0.983514	+	0.180831i	$0.0578788\pi$
$443$			7.61212i			0.361663i	−0.983514	+	0.180831i	$0.942121\pi$
$444$		0			0
$445$	2.39084			0.113337
$446$	2.70472	−	7.55642i	0.128072	−	0.357807i
$447$		0			0
$448$		0			0
$449$	16.8969			0.797414			0.398707	−	0.917078i	$-0.369459\pi$
$449$	16.8969			0.797414			0.398707	+	0.917078i	$0.369459\pi$
$450$		0			0
$451$	−48.4937			−2.28348
$452$	−5.75544	−	4.72562i	−0.270713	−	0.222274i
$453$		0			0
$454$	−0.975602	+	2.72562i	−0.0457873	+	0.127920i
$455$		0			0
$456$		0			0
$457$	7.67859			0.359189			0.179595	−	0.983741i	$-0.442521\pi$
$457$	7.67859			0.359189			0.179595	+	0.983741i	$0.442521\pi$
$458$	6.19275	+	2.21662i	0.289368	+	0.103576i
$459$		0			0
$460$	−2.30078	−	1.88910i	−0.107274	−	0.0880796i
$461$		−	4.29773i		−	0.200165i	−0.994979	−	0.100083i	$-0.968089\pi$
$461$		−	4.29773i		−	0.200165i	0.994979	−	0.100083i	$-0.0319107\pi$
$462$		0			0
$463$		−	2.92047i		−	0.135726i	−0.997695	−	0.0678628i	$-0.978382\pi$
$463$		−	2.92047i		−	0.135726i	0.997695	−	0.0678628i	$-0.0216180\pi$
$464$	4.53185	+	22.8388i	0.210386	+	1.06027i
$465$		0			0
$466$	−2.02242	+	5.65022i	−0.0936870	+	0.261741i
$467$	40.1511			1.85797			0.928985	−	0.370118i	$-0.120683\pi$
$467$	40.1511			1.85797			0.928985	+	0.370118i	$0.120683\pi$
$468$		0			0
$469$		0			0
$470$	−5.34399	−	1.91281i	−0.246500	−	0.0882314i
$471$		0			0
$472$	−11.2926	+	6.76313i	−0.519782	+	0.311298i
$473$	−40.6398			−1.86862
$474$		0			0
$475$	−23.9482			−1.09882
$476$		0			0
$477$		0			0
$478$	15.5265	+	5.55752i	0.710167	+	0.254195i
$479$	−22.0231			−1.00626			−0.503132	−	0.864210i	$-0.667819\pi$
$479$	−22.0231			−1.00626			−0.503132	+	0.864210i	$0.667819\pi$
$480$		0			0
$481$		−	39.8016i		−	1.81480i
$482$	−13.2819	−	4.75408i	−0.604974	−	0.216543i
$483$		0			0
$484$	9.32833	+	7.65920i	0.424015	+	0.348146i
$485$	−0.922387			−0.0418834
$486$		0			0
$487$		−	19.9191i		−	0.902621i	−0.892367	−	0.451310i	$-0.850957\pi$
$487$		−	19.9191i		−	0.902621i	0.892367	−	0.451310i	$-0.149043\pi$
$488$	0.789573	+	1.31837i	0.0357423	+	0.0596798i
$489$		0			0
$490$		0			0
$491$		−	22.4901i		−	1.01496i	−0.861662	−	0.507482i	$-0.830576\pi$
$491$		−	22.4901i		−	1.01496i	0.861662	−	0.507482i	$-0.169424\pi$
$492$		0			0
$493$			28.7467i			1.29469i
$494$	26.7553	+	9.57670i	1.20378	+	0.430876i
$495$		0			0
$496$	4.45317	+	22.4423i	0.199953	+	1.00769i
$497$		0			0
$498$		0			0
$499$		−	26.0278i		−	1.16516i	−0.812773	−	0.582581i	$-0.802043\pi$
$499$		−	26.0278i		−	1.16516i	0.812773	−	0.582581i	$-0.197957\pi$
$500$	6.30284	−	7.67638i	0.281872	−	0.343298i
$501$		0			0
$502$	−5.66515	+	15.8272i	−0.252848	+	0.706404i
$503$	−21.9468			−0.978561			−0.489281	−	0.872126i	$-0.662741\pi$
$503$	−21.9468			−0.978561			−0.489281	+	0.872126i	$0.662741\pi$
$504$		0			0
$505$	3.04046			0.135299
$506$	5.74239	−	16.0430i	0.255280	−	0.713199i
$507$		0			0
$508$	−17.8739	+	21.7690i	−0.793024	+	0.965843i
$509$			6.16635i			0.273318i	0.990618	+	0.136659i	$0.0436365\pi$
$509$			6.16635i			0.273318i	−0.990618	+	0.136659i	$0.956363\pi$
$510$		0			0
$511$		0			0
$512$	1.08655	+	22.6013i	0.0480193	+	0.998846i
$513$		0			0
$514$	−27.6372	−	9.89239i	−1.21903	−	0.436334i
$515$		−	5.65638i		−	0.249250i
$516$		0			0
$517$		−	32.4888i		−	1.42886i
$518$		0			0
$519$		0			0
$520$	−4.92073	+	2.94703i	−0.215788	+	0.129236i
$521$		−	12.9458i		−	0.567167i	−0.958948	−	0.283583i	$-0.908477\pi$
$521$		−	12.9458i		−	0.567167i	0.958948	−	0.283583i	$-0.0915233\pi$
$522$		0			0
$523$	23.3047			1.01904			0.509521	−	0.860458i	$-0.329823\pi$
$523$	23.3047			1.01904			0.509521	+	0.860458i	$0.329823\pi$
$524$	5.19924	+	4.26894i	0.227130	+	0.186489i
$525$		0			0
$526$	1.81775	+	0.650639i	0.0792575	+	0.0283692i
$527$			28.2477i			1.23049i
$528$		0			0
$529$	14.4777			0.629466
$530$	−0.840964	−	0.301012i	−0.0365291	−	0.0130751i
$531$		0			0
$532$		0			0
$533$	46.7299			2.02410
$534$		0			0
$535$	0.320829			0.0138706
$536$	−10.2034	−	17.0368i	−0.440719	−	0.735878i
$537$		0			0
$538$	−31.1515	−	11.1503i	−1.34303	−	0.480722i
$539$		0			0
$540$		0			0
$541$	−9.41398			−0.404739			−0.202369	−	0.979309i	$-0.564864\pi$
$541$	−9.41398			−0.404739			−0.202369	+	0.979309i	$0.564864\pi$
$542$	9.96984	−	27.8536i	0.428241	−	1.19641i
$543$		0			0
$544$	−4.11517	+	27.6312i	−0.176437	+	1.18468i
$545$			8.06497i			0.345466i
$546$		0			0
$547$		−	15.9880i		−	0.683598i	−0.939773	−	0.341799i	$-0.888964\pi$
$547$		−	15.9880i		−	0.683598i	0.939773	−	0.341799i	$-0.111036\pi$
$548$	−0.753474	−	0.618654i	−0.0321868	−	0.0264276i
$549$		0			0
$550$	26.0488	+	9.32385i	1.11073	+	0.397570i
$551$	−29.4098			−1.25290
$552$		0			0
$553$		0			0
$554$	−8.79173	+	24.5622i	−0.373525	+	1.04355i
$555$		0			0
$556$	25.1163	+	20.6222i	1.06517	+	0.874576i
$557$	5.07655			0.215100			0.107550	−	0.994200i	$-0.465699\pi$
$557$	5.07655			0.215100			0.107550	+	0.994200i	$0.465699\pi$
$558$		0			0
$559$	39.1616			1.65636
$560$		0			0
$561$		0			0
$562$	−9.50014	+	26.5414i	−0.400739	+	1.11958i
$563$	25.0392			1.05527			0.527637	−	0.849470i	$-0.323078\pi$
$563$	25.0392			1.05527			0.527637	+	0.849470i	$0.323078\pi$
$564$		0			0
$565$			1.89850i			0.0798705i
$566$	9.67272	−	27.0235i	0.406575	−	1.13588i
$567$		0			0
$568$	1.54898	+	2.58637i	0.0649938	+	0.108522i
$569$	−13.7147			−0.574951			−0.287476	−	0.957788i	$-0.592816\pi$
$569$	−13.7147			−0.574951			−0.287476	+	0.957788i	$0.592816\pi$
$570$		0			0
$571$		−	12.7496i		−	0.533555i	−0.963758	−	0.266778i	$-0.914041\pi$
$571$		−	12.7496i		−	0.533555i	0.963758	−	0.266778i	$-0.0859589\pi$
$572$	−25.3736	−	20.8335i	−1.06092	−	0.871090i
$573$		0			0
$574$		0			0
$575$		−	13.8375i		−	0.577065i
$576$		0			0
$577$		−	17.7665i		−	0.739628i	−0.929106	−	0.369814i	$-0.879421\pi$
$577$		−	17.7665i		−	0.739628i	0.929106	−	0.369814i	$-0.120579\pi$
$578$	−3.52108	+	9.83715i	−0.146458	+	0.409171i
$579$		0			0
$580$	3.76683	−	4.58771i	0.156409	−	0.190494i
$581$		0			0
$582$		0			0
$583$		−	5.11265i		−	0.211744i
$584$	−1.21643	−	2.03110i	−0.0503361	−	0.0840474i
$585$		0			0
$586$	−3.58724	−	1.28401i	−0.148188	−	0.0530419i
$587$	43.2377			1.78461			0.892306	−	0.451431i	$-0.149086\pi$
$587$	43.2377			1.78461			0.892306	+	0.451431i	$0.149086\pi$
$588$		0			0
$589$	−28.8992			−1.19077
$590$	3.15943	+	1.13088i	0.130072	+	0.0465575i
$591$		0			0
$592$	7.79108	+	39.2641i	0.320212	+	1.61375i
$593$		−	30.8684i		−	1.26761i	−0.773491	−	0.633807i	$-0.781491\pi$
$593$		−	30.8684i		−	1.26761i	0.773491	−	0.633807i	$-0.218509\pi$
$594$		0			0
$595$		0			0
$596$	−24.3412	−	19.9858i	−0.997055	−	0.818651i
$597$		0			0
$598$	−5.53352	+	15.4595i	−0.226283	+	0.632185i
$599$			0.155501i			0.00635360i	0.999995	+	0.00317680i	$0.00101121\pi$
$599$			0.155501i			0.00635360i	−0.999995	+	0.00317680i	$0.998989\pi$
$600$		0			0
$601$		−	22.4797i		−	0.916967i	−0.888703	−	0.458484i	$-0.848393\pi$
$601$		−	22.4797i		−	0.916967i	0.888703	−	0.458484i	$-0.151607\pi$
$602$		0			0
$603$		0			0
$604$	30.8181	−	37.5341i	1.25397	−	1.52724i
$605$		−	3.07706i		−	0.125100i
$606$		0			0
$607$	−14.9029			−0.604888			−0.302444	−	0.953167i	$-0.597803\pi$
$607$	−14.9029			−0.604888			−0.302444	+	0.953167i	$0.597803\pi$
$608$	−28.2686	−	4.21009i	−1.14644	−	0.170742i
$609$		0			0
$610$	0.132026	−	0.368853i	0.00534558	−	0.0149344i
$611$			31.3071i			1.26655i
$612$		0			0
$613$	37.5154			1.51523			0.757617	−	0.652700i	$-0.226364\pi$
$613$	37.5154			1.51523			0.757617	+	0.652700i	$0.226364\pi$
$614$	−3.33380	+	9.31391i	−0.134541	+	0.375879i
$615$		0			0
$616$		0			0
$617$	−10.8459			−0.436641			−0.218321	−	0.975877i	$-0.570058\pi$
$617$	−10.8459			−0.436641			−0.218321	+	0.975877i	$0.570058\pi$
$618$		0			0
$619$	23.1198			0.929263			0.464632	−	0.885504i	$-0.346187\pi$
$619$	23.1198			0.929263			0.464632	+	0.885504i	$0.346187\pi$
$620$	3.70143	−	4.50806i	0.148653	−	0.181048i
$621$		0			0
$622$	−10.4950	+	29.3209i	−0.420813	+	1.17566i
$623$		0			0
$624$		0			0
$625$	21.1680			0.846720
$626$	2.31329	+	0.828013i	0.0924577	+	0.0330941i
$627$		0			0
$628$	−4.77004	+	5.80955i	−0.190346	+	0.231826i
$629$			49.4209i			1.97054i
$630$		0			0
$631$			12.0123i			0.478200i	0.970995	+	0.239100i	$0.0768524\pi$
$631$			12.0123i			0.478200i	−0.970995	+	0.239100i	$0.923148\pi$
$632$	1.82820	+	3.05258i	0.0727217	+	0.121425i
$633$		0			0
$634$	−15.3126	+	42.7802i	−0.608142	+	1.69902i
$635$	7.18076			0.284960
$636$		0			0
$637$		0			0
$638$	31.9895	+	11.4502i	1.26648	+	0.453319i
$639$		0			0
$640$	4.27740	−	3.87045i	0.169079	−	0.152993i
$641$	−48.9806			−1.93462			−0.967308	−	0.253603i	$-0.918384\pi$
$641$	−48.9806			−1.93462			−0.967308	+	0.253603i	$0.918384\pi$
$642$		0			0
$643$	−16.4052			−0.646958			−0.323479	−	0.946235i	$-0.604853\pi$
$643$	−16.4052			−0.646958			−0.323479	+	0.946235i	$0.604853\pi$
$644$		0			0
$645$		0			0
$646$	−33.2215	−	11.8912i	−1.30708	−	0.467853i
$647$	18.5101			0.727708			0.363854	−	0.931456i	$-0.381461\pi$
$647$	18.5101			0.727708			0.363854	+	0.931456i	$0.381461\pi$
$648$		0			0
$649$			19.2078i			0.753970i
$650$	−25.1014	−	8.98472i	−0.984557	−	0.352410i
$651$		0			0
$652$	−10.2671	+	12.5045i	−0.402090	+	0.489715i
$653$	12.4786			0.488325			0.244163	−	0.969734i	$-0.421487\pi$
$653$	12.4786			0.488325			0.244163	+	0.969734i	$0.421487\pi$
$654$		0			0
$655$		−	1.71503i		−	0.0670118i
$656$	−46.0988	+	9.14727i	−1.79986	+	0.357141i
$657$		0			0
$658$		0			0
$659$			28.5032i			1.11033i	0.831741	+	0.555163i	$0.187344\pi$
$659$			28.5032i			1.11033i	−0.831741	+	0.555163i	$0.812656\pi$
$660$		0			0
$661$			4.58439i			0.178312i	0.996018	+	0.0891561i	$0.0284170\pi$
$661$			4.58439i			0.178312i	−0.996018	+	0.0891561i	$0.971583\pi$
$662$	15.2100	+	5.44423i	0.591154	+	0.211596i
$663$		0			0
$664$	−33.3240	+	19.9578i	−1.29322	+	0.774512i
$665$		0			0
$666$		0			0
$667$		−	16.9933i		−	0.657983i
$668$	36.7274	+	30.1557i	1.42103	+	1.16676i
$669$		0			0
$670$	−1.70613	+	4.76655i	−0.0659134	+	0.184148i
$671$	2.24244			0.0865685
$672$		0			0
$673$	−35.9408			−1.38542			−0.692708	−	0.721219i	$-0.743582\pi$
$673$	−35.9408			−1.38542			−0.692708	+	0.721219i	$0.743582\pi$
$674$	3.37743	−	9.43582i	0.130094	−	0.363454i
$675$		0			0
$676$	4.35624	+	3.57677i	0.167548	+	0.137568i
$677$			10.1754i			0.391073i	0.980696	+	0.195537i	$0.0626448\pi$
$677$			10.1754i			0.391073i	−0.980696	+	0.195537i	$0.937355\pi$
$678$		0			0
$679$		0			0
$680$	6.10997	−	3.65927i	0.234307	−	0.140327i
$681$		0			0
$682$	31.4341	+	11.2514i	1.20367	+	0.430840i
$683$			9.71979i			0.371918i	0.982558	+	0.185959i	$0.0595391\pi$
$683$			9.71979i			0.371918i	−0.982558	+	0.185959i	$0.940461\pi$
$684$		0			0
$685$			0.248542i			0.00949631i
$686$		0			0
$687$		0			0
$688$	−38.6327	+	7.66580i	−1.47286	+	0.292256i
$689$			4.92669i			0.187692i
$690$		0			0
$691$	36.1912			1.37678			0.688389	−	0.725341i	$-0.258318\pi$
$691$	36.1912			1.37678			0.688389	+	0.725341i	$0.258318\pi$
$692$	11.0834	−	13.4987i	0.421327	−	0.513144i
$693$		0			0
$694$	27.8363	+	9.96366i	1.05665	+	0.378216i
$695$		−	8.28489i		−	0.314264i
$696$		0			0
$697$	−58.0235			−2.19780
$698$	2.23562	+	0.800212i	0.0846195	+	0.0302885i
$699$		0			0
$700$		0			0
$701$	−28.4159			−1.07325			−0.536626	−	0.843820i	$-0.680301\pi$
$701$	−28.4159			−1.07325			−0.536626	+	0.843820i	$0.680301\pi$
$702$		0			0
$703$	−50.5608			−1.90694
$704$	29.1090	+	15.5853i	1.09709	+	0.587392i
$705$		0			0
$706$	8.27312	+	2.96126i	0.311363	+	0.111448i
$707$		0			0
$708$		0			0
$709$	−0.498957			−0.0187387			−0.00936937	−	0.999956i	$-0.502982\pi$
$709$	−0.498957			−0.0187387			−0.00936937	+	0.999956i	$0.502982\pi$
$710$	0.259008	−	0.723613i	0.00972040	−	0.0271567i
$711$		0			0
$712$	6.81440	+	11.3782i	0.255380	+	0.426414i
$713$		−	16.6983i		−	0.625356i
$714$		0			0
$715$			8.36977i			0.313012i
$716$	13.7014	−	16.6872i	0.512045	−	0.623631i
$717$		0			0
$718$	−30.0231	−	10.7464i	−1.12045	−	0.401052i
$719$	−6.36688			−0.237445			−0.118722	−	0.992928i	$-0.537880\pi$
$719$	−6.36688			−0.237445			−0.118722	+	0.992928i	$0.537880\pi$
$720$		0			0
$721$		0			0
$722$	3.11028	−	8.68945i	0.115753	−	0.323388i
$723$		0			0
$724$	33.0774	−	40.2857i	1.22931	−	1.49721i
$725$	27.5918			1.02473
$726$		0			0
$727$	18.5763			0.688958			0.344479	−	0.938794i	$-0.388056\pi$
$727$	18.5763			0.688958			0.344479	+	0.938794i	$0.388056\pi$
$728$		0			0
$729$		0			0
$730$	−0.203401	+	0.568259i	−0.00752822	+	0.0210322i
$731$	−48.6262			−1.79850
$732$		0			0
$733$		−	36.2451i		−	1.33874i	−0.742927	−	0.669372i	$-0.766563\pi$
$733$		−	36.2451i		−	1.33874i	0.742927	−	0.669372i	$-0.233437\pi$
$734$	−10.6231	+	29.6786i	−0.392106	+	1.09546i
$735$		0			0
$736$	2.43264	−	16.3339i	0.0896682	−	0.602075i
$737$	−28.9783			−1.06743
$738$		0			0
$739$		−	46.8692i		−	1.72411i	−0.506813	−	0.862056i	$-0.669177\pi$
$739$		−	46.8692i		−	1.72411i	0.506813	−	0.862056i	$-0.330823\pi$
$740$	6.47587	−	7.88712i	0.238058	−	0.289936i
$741$		0			0
$742$		0			0
$743$		−	38.5048i		−	1.41260i	−0.707911	−	0.706302i	$-0.750362\pi$
$743$		−	38.5048i		−	1.41260i	0.707911	−	0.706302i	$-0.249638\pi$
$744$		0			0
$745$			8.02923i			0.294168i
$746$	−1.50824	+	4.21371i	−0.0552208	+	0.154275i
$747$		0			0
$748$	31.5058	+	25.8685i	1.15197	+	0.945845i
$749$		0			0
$750$		0			0
$751$		−	1.00038i		−	0.0365044i	−0.999833	−	0.0182522i	$-0.994190\pi$
$751$		−	1.00038i		−	0.0365044i	0.999833	−	0.0182522i	$-0.00581017\pi$
$752$	−6.12829	−	30.8843i	−0.223476	−	1.12623i
$753$		0			0
$754$	−30.8259	−	11.0337i	−1.12261	−	0.401825i
$755$	−12.3811			−0.450593
$756$		0			0
$757$	−13.8254			−0.502491			−0.251246	−	0.967923i	$-0.580840\pi$
$757$	−13.8254			−0.502491			−0.251246	+	0.967923i	$0.580840\pi$
$758$	9.63339	+	3.44815i	0.349900	+	0.125242i
$759$		0			0
$760$	3.74367	+	6.25090i	0.135797	+	0.226744i
$761$		−	29.4968i		−	1.06926i	−0.845087	−	0.534629i	$-0.820451\pi$
$761$		−	29.4968i		−	1.06926i	0.845087	−	0.534629i	$-0.179549\pi$
$762$		0			0
$763$		0			0
$764$	−2.22694	+	2.71224i	−0.0805679	+	0.0981256i
$765$		0			0
$766$	12.0036	−	33.5354i	0.433707	−	1.21168i
$767$		−	18.5091i		−	0.668326i
$768$		0			0
$769$			33.1479i			1.19534i	0.801741	+	0.597672i	$0.203907\pi$
$769$			33.1479i			1.19534i	−0.801741	+	0.597672i	$0.796093\pi$
$770$		0			0
$771$		0			0
$772$	23.0728	+	18.9444i	0.830408	+	0.681822i
$773$			8.26988i			0.297447i	0.988879	+	0.148723i	$0.0475164\pi$
$773$			8.26988i			0.297447i	−0.988879	+	0.148723i	$0.952484\pi$
$774$		0			0
$775$	27.1128			0.973921
$776$	−2.62900	−	4.38970i	−0.0943755	−	0.157581i
$777$		0			0
$778$	3.90089	−	10.8983i	0.139854	−	0.390721i
$779$		−	59.3619i		−	2.12686i
$780$		0			0
$781$	4.39921			0.157416
$782$	6.87086	−	19.1957i	0.245702	−	0.686438i
$783$		0			0
$784$		0			0
$785$	1.91635			0.0683974
$786$		0			0
$787$	−7.54751			−0.269040			−0.134520	−	0.990911i	$-0.542949\pi$
$787$	−7.54751			−0.269040			−0.134520	+	0.990911i	$0.542949\pi$
$788$	18.8067	+	15.4416i	0.669960	+	0.550084i
$789$		0			0
$790$	0.305696	−	0.854050i	0.0108762	−	0.0303857i
$791$		0			0
$792$		0			0
$793$	−2.16088			−0.0767350
$794$	44.6336	+	15.9760i	1.58399	+	0.566968i
$795$		0			0
$796$	−33.1613	−	27.2277i	−1.17537	−	0.965061i
$797$			36.4436i			1.29090i	0.763803	+	0.645450i	$0.223330\pi$
$797$			36.4436i			1.29090i	−0.763803	+	0.645450i	$0.776670\pi$
$798$		0			0
$799$		−	38.8734i		−	1.37524i
$800$	26.5211	+	3.94984i	0.937663	+	0.139648i
$801$		0			0
$802$	3.36259	−	9.39436i	0.118737	−	0.331726i
$803$	−3.45474			−0.121915
$804$		0			0
$805$		0			0
$806$	−30.2908	−	10.8422i	−1.06695	−	0.381900i
$807$		0			0
$808$	8.66595	+	14.4697i	0.304867	+	0.509043i
$809$	−25.2478			−0.887665			−0.443832	−	0.896110i	$-0.646381\pi$
$809$	−25.2478			−0.887665			−0.443832	+	0.896110i	$0.646381\pi$
$810$		0			0
$811$	15.1794			0.533021			0.266510	−	0.963832i	$-0.414129\pi$
$811$	15.1794			0.533021			0.266510	+	0.963832i	$0.414129\pi$
$812$		0			0
$813$		0			0
$814$	54.9958	+	19.6850i	1.92760	+	0.689960i
$815$	4.12477			0.144484
$816$		0			0
$817$		−	49.7478i		−	1.74045i
$818$	34.2346	+	12.2539i	1.19699	+	0.428446i
$819$		0			0
$820$	9.26002	+	7.60312i	0.323374	+	0.265512i
$821$	46.6651			1.62862			0.814311	−	0.580429i	$-0.197115\pi$
$821$	46.6651			1.62862			0.814311	+	0.580429i	$0.197115\pi$
$822$		0			0
$823$		−	24.3757i		−	0.849682i	−0.905268	−	0.424841i	$-0.860330\pi$
$823$		−	24.3757i		−	0.849682i	0.905268	−	0.424841i	$-0.139670\pi$
$824$	26.9191	−	16.1219i	0.937771	−	0.561633i
$825$		0			0
$826$		0			0
$827$		−	42.9409i		−	1.49320i	−0.665273	−	0.746600i	$-0.731685\pi$
$827$		−	42.9409i		−	1.49320i	0.665273	−	0.746600i	$-0.268315\pi$
$828$		0			0
$829$		−	48.8194i		−	1.69557i	−0.530341	−	0.847784i	$-0.677936\pi$
$829$		−	48.8194i		−	1.69557i	0.530341	−	0.847784i	$-0.322064\pi$
$830$	9.32336	+	3.33718i	0.323618	+	0.115835i
$831$		0			0
$832$	−28.0502	−	15.0184i	−0.972467	−	0.520670i
$833$		0			0
$834$		0			0
$835$		−	12.1150i		−	0.419256i
$836$	−26.4652	+	32.2326i	−0.915317	+	1.11479i
$837$		0			0
$838$	7.63101	−	21.3194i	0.263609	−	0.736467i
$839$	42.1517			1.45524			0.727620	−	0.685981i	$-0.240626\pi$
$839$	42.1517			1.45524			0.727620	+	0.685981i	$0.240626\pi$
$840$		0			0
$841$	4.88432			0.168425
$842$	2.95466	−	8.25468i	0.101824	−	0.284475i
$843$		0			0
$844$	12.5735	−	15.3136i	0.432797	−	0.527114i
$845$		−	1.43696i		−	0.0494328i
$846$		0			0
$847$		0			0
$848$	−0.964387	−	4.86015i	−0.0331172	−	0.166898i
$849$		0			0
$850$	31.1679	+	11.1561i	1.06905	+	0.382653i
$851$		−	29.2146i		−	1.00146i
$852$		0			0
$853$			13.5733i			0.464741i	0.972627	+	0.232370i	$0.0746481\pi$
$853$			13.5733i			0.464741i	−0.972627	+	0.232370i	$0.925352\pi$
$854$		0			0
$855$		0			0
$856$	0.914430	+	1.52684i	0.0312546	+	0.0521865i
$857$			50.9071i			1.73895i	0.493973	+	0.869477i	$0.335544\pi$
$857$			50.9071i			1.73895i	−0.493973	+	0.869477i	$0.664456\pi$
$858$		0			0
$859$	−12.8182			−0.437351			−0.218676	−	0.975798i	$-0.570174\pi$
$859$	−12.8182			−0.437351			−0.218676	+	0.975798i	$0.570174\pi$
$860$	7.76028	+	6.37173i	0.264624	+	0.217274i
$861$		0			0
$862$	−40.6763	−	14.5595i	−1.38544	−	0.495900i
$863$		−	51.9246i		−	1.76753i	−0.467926	−	0.883767i	$-0.654999\pi$
$863$		−	51.9246i		−	1.76753i	0.467926	−	0.883767i	$-0.345001\pi$
$864$		0			0
$865$	−4.45271			−0.151397
$866$	−30.9317	−	11.0716i	−1.05110	−	0.376229i
$867$		0			0
$868$		0			0
$869$	5.19220			0.176133
$870$		0			0
$871$	27.9243			0.946177
$872$	−38.3817	+	22.9869i	−1.29977	+	0.778434i
$873$		0			0
$874$	19.6385	+	7.02935i	0.664282	+	0.237771i
$875$		0			0
$876$		0			0
$877$	18.1994			0.614550			0.307275	−	0.951621i	$-0.400583\pi$
$877$	18.1994			0.614550			0.307275	+	0.951621i	$0.400583\pi$
$878$	−1.14692	+	3.20424i	−0.0387065	+	0.108138i
$879$		0			0
$880$	−1.63836	−	8.25674i	−0.0552292	−	0.278335i
$881$			12.1271i			0.408571i	0.978911	+	0.204286i	$0.0654872\pi$
$881$			12.1271i			0.408571i	−0.978911	+	0.204286i	$0.934513\pi$
$882$		0			0
$883$		−	28.6986i		−	0.965786i	−0.875679	−	0.482893i	$-0.839586\pi$
$883$		−	28.6986i		−	0.965786i	0.875679	−	0.482893i	$-0.160414\pi$
$884$	−30.3599	−	24.9276i	−1.02111	−	0.838405i
$885$		0			0
$886$	10.1354	+	3.62786i	0.340507	+	0.121880i
$887$	13.0638			0.438639			0.219320	−	0.975653i	$-0.429616\pi$
$887$	13.0638			0.438639			0.219320	+	0.975653i	$0.429616\pi$
$888$		0			0
$889$		0			0
$890$	1.13945	−	3.18337i	0.0381944	−	0.106707i
$891$		0			0
$892$	−8.77224	−	7.20262i	−0.293716	−	0.241162i
$893$	39.7700			1.33085
$894$		0			0
$895$	−5.50448			−0.183995
$896$		0			0
$897$		0			0
$898$	8.05289	−	22.4980i	0.268728	−	0.750770i
$899$	33.2961			1.11049
$900$		0			0
$901$		−	6.11737i		−	0.203799i
$902$	−23.1116	+	64.5689i	−0.769532	+	2.14991i
$903$		0			0
$904$	−9.03509	+	5.41113i	−0.300503	+	0.179971i
$905$	−13.2887			−0.441732
$906$		0			0
$907$		−	27.2879i		−	0.906080i	−0.891490	−	0.453040i	$-0.850339\pi$
$907$		−	27.2879i		−	0.906080i	0.891490	−	0.453040i	$-0.149661\pi$
$908$	3.16417	+	2.59801i	0.105007	+	0.0862178i
$909$		0			0
$910$		0			0
$911$			39.9753i			1.32444i	0.749309	+	0.662221i	$0.230386\pi$
$911$			39.9753i			1.32444i	−0.749309	+	0.662221i	$0.769614\pi$
$912$		0			0
$913$			56.6814i			1.87588i
$914$	3.65954	−	10.2240i	0.121047	−	0.338178i
$915$		0			0
$916$	5.90280	−	7.18917i	0.195034	−	0.237537i
$917$		0			0
$918$		0			0
$919$			31.2841i			1.03197i	0.856599	+	0.515983i	$0.172573\pi$
$919$			31.2841i			1.03197i	−0.856599	+	0.515983i	$0.827427\pi$
$920$	−3.61184	+	2.16314i	−0.119079	+	0.0713165i
$921$		0			0
$922$	−5.72238	−	2.04825i	−0.188457	−	0.0674557i
$923$	−4.23920			−0.139535
$924$		0			0
$925$	47.4354			1.55967
$926$	−3.88857	−	1.39186i	−0.127786	−	0.0457395i
$927$		0			0
$928$	32.5695	+	4.85063i	1.06914	+	0.159230i
$929$		−	15.9768i		−	0.524181i	−0.965043	−	0.262090i	$-0.915588\pi$
$929$		−	15.9768i		−	0.524181i	0.965043	−	0.262090i	$-0.0844119\pi$
$930$		0			0
$931$		0			0
$932$	6.55934	+	5.38567i	0.214858	+	0.176414i
$933$		0			0
$934$	19.1356	−	53.4607i	0.626135	−	1.74929i
$935$		−	10.3926i		−	0.339873i
$936$		0			0
$937$			18.3690i			0.600089i	0.953925	+	0.300045i	$0.0970016\pi$
$937$			18.3690i			0.600089i	−0.953925	+	0.300045i	$0.902998\pi$
$938$		0			0
$939$		0			0
$940$	−5.09377	+	6.20383i	−0.166141	+	0.202347i
$941$		−	35.7695i		−	1.16605i	−0.812454	−	0.583026i	$-0.801869\pi$
$941$		−	35.7695i		−	1.16605i	0.812454	−	0.583026i	$-0.198131\pi$
$942$		0			0
$943$	34.3000			1.11696
$944$	3.62312	+	18.2592i	0.117922	+	0.594285i
$945$		0			0
$946$	−19.3685	+	54.1114i	−0.629724	+	1.75931i
$947$		−	12.7872i		−	0.415527i	−0.978179	−	0.207763i	$-0.933382\pi$
$947$		−	12.7872i		−	0.415527i	0.978179	−	0.207763i	$-0.0666184\pi$
$948$		0			0
$949$	3.32908			0.108066
$950$	−11.4135	+	31.8868i	−0.370302	+	1.03454i
$951$		0			0
$952$		0			0
$953$	−23.6660			−0.766616			−0.383308	−	0.923621i	$-0.625215\pi$
$953$	−23.6660			−0.766616			−0.383308	+	0.923621i	$0.625215\pi$
$954$		0			0
$955$	0.894666			0.0289507
$956$	14.7996	−	18.0247i	0.478652	−	0.582962i
$957$		0			0
$958$	−10.4960	+	29.3236i	−0.339110	+	0.947402i
$959$		0			0
$960$		0			0
$961$	1.71804			0.0554208
$962$	−52.9954	−	18.9690i	−1.70864	−	0.611587i
$963$		0			0
$964$	−12.6600	+	15.4189i	−0.407752	+	0.496611i
$965$		−	7.61083i		−	0.245001i
$966$		0			0
$967$		−	9.30274i		−	0.299156i	−0.988750	−	0.149578i	$-0.952208\pi$
$967$		−	9.30274i		−	0.299156i	0.988750	−	0.149578i	$-0.0477915\pi$
$968$	14.6439	−	8.77027i	0.470674	−	0.281887i
$969$		0			0
$970$	−0.439600	+	1.22815i	−0.0141147	+	0.0394334i
$971$	24.8749			0.798273			0.399136	−	0.916892i	$-0.369310\pi$
$971$	24.8749			0.798273			0.399136	+	0.916892i	$0.369310\pi$
$972$		0			0
$973$		0			0
$974$	−26.5221	−	9.49323i	−0.849822	−	0.304183i
$975$		0			0
$976$	2.13170	−	0.422987i	0.0682339	−	0.0135395i
$977$	35.0896			1.12262			0.561308	−	0.827607i	$-0.310298\pi$
$977$	35.0896			1.12262			0.561308	+	0.827607i	$0.310298\pi$
$978$		0			0
$979$	19.3533			0.618536
$980$		0			0
$981$		0			0
$982$	−29.9453	−	10.7186i	−0.955594	−	0.342043i
$983$	−50.3218			−1.60502			−0.802508	−	0.596642i	$-0.796501\pi$
$983$	−50.3218			−1.60502			−0.802508	+	0.596642i	$0.796501\pi$
$984$		0			0
$985$		−	6.20360i		−	0.197663i
$986$	38.2759	+	13.7004i	1.21895	+	0.436309i
$987$		0			0
$988$	25.5025	−	31.0602i	0.811344	−	0.988156i
$989$	28.7448			0.914032
$990$		0			0
$991$		−	31.1543i		−	0.989648i	−0.868993	−	0.494824i	$-0.835233\pi$
$991$		−	31.1543i		−	0.989648i	0.868993	−	0.494824i	$-0.164767\pi$
$992$	32.0040	+	4.76642i	1.01613	+	0.151334i
$993$		0			0
$994$		0			0
$995$			10.9386i			0.346778i
$996$		0			0
$997$		−	31.3979i		−	0.994381i	−0.867641	−	0.497191i	$-0.834365\pi$
$997$		−	31.3979i		−	0.994381i	0.867641	−	0.497191i	$-0.165635\pi$
$998$	−34.6557	−	12.4046i	−1.09701	−	0.392659i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1764.2.b.m.1567.9		12
3.2	odd	2		588.2.b.d.391.4	yes	12
4.3	odd	2		1764.2.b.l.1567.10		12
7.6	odd	2		1764.2.b.l.1567.9		12
12.11	even	2		588.2.b.c.391.3	✓	12
21.2	odd	6		588.2.o.e.31.12		24
21.5	even	6		588.2.o.f.31.12		24
21.11	odd	6		588.2.o.e.19.5		24
21.17	even	6		588.2.o.f.19.5		24
21.20	even	2		588.2.b.c.391.4	yes	12
28.27	even	2	inner	1764.2.b.m.1567.10		12
84.11	even	6		588.2.o.f.19.12		24
84.23	even	6		588.2.o.f.31.5		24
84.47	odd	6		588.2.o.e.31.5		24
84.59	odd	6		588.2.o.e.19.12		24
84.83	odd	2		588.2.b.d.391.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
588.2.b.c.391.3	✓	12	12.11	even	2
588.2.b.c.391.4	yes	12	21.20	even	2
588.2.b.d.391.3	yes	12	84.83	odd	2
588.2.b.d.391.4	yes	12	3.2	odd	2
588.2.o.e.19.5		24	21.11	odd	6
588.2.o.e.19.12		24	84.59	odd	6
588.2.o.e.31.5		24	84.47	odd	6
588.2.o.e.31.12		24	21.2	odd	6
588.2.o.f.19.5		24	21.17	even	6
588.2.o.f.19.12		24	84.11	even	6
588.2.o.f.31.5		24	84.23	even	6
588.2.o.f.31.12		24	21.5	even	6
1764.2.b.l.1567.9		12	7.6	odd	2
1764.2.b.l.1567.10		12	4.3	odd	2
1764.2.b.m.1567.9		12	1.1	even	1	trivial
1764.2.b.m.1567.10		12	28.27	even	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1764.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.476589 - 1.33149i) q^{2} +(-1.54572 - 1.26915i) q^{4} +0.509876i q^{5} +(-2.42653 + 1.45325i) q^{8} +O(q^{10})\)	\(q+(0.476589 - 1.33149i) q^{2} +(-1.54572 - 1.26915i) q^{4} +0.509876i q^{5} +(-2.42653 + 1.45325i) q^{8} +(0.678894 + 0.243001i) q^{10} +4.12734i q^{11} -3.97722i q^{13} +(0.778531 + 3.92350i) q^{16} +4.93843i q^{17} -5.05234 q^{19} +(0.647107 - 0.788127i) q^{20} +(5.49550 + 1.96705i) q^{22} -2.91930i q^{23} +4.74003 q^{25} +(-5.29562 - 1.89550i) q^{26} +5.82102 q^{29} +5.71997 q^{31} +(5.59514 + 0.833296i) q^{32} +(6.57546 + 2.35360i) q^{34} +10.0074 q^{37} +(-2.40789 + 6.72713i) q^{38} +(-0.740978 - 1.23723i) q^{40} +11.7494i q^{41} +9.84649i q^{43} +(5.23820 - 6.37973i) q^{44} +(-3.88701 - 1.39131i) q^{46} -7.87161 q^{47} +(2.25905 - 6.31129i) q^{50} +(-5.04767 + 6.14768i) q^{52} -1.23873 q^{53} -2.10443 q^{55} +(2.77424 - 7.75063i) q^{58} +4.65379 q^{59} -0.543314i q^{61} +(2.72608 - 7.61607i) q^{62} +(3.77611 - 7.05273i) q^{64} +2.02789 q^{65} +7.02106i q^{67} +(6.26759 - 7.63345i) q^{68} -1.06587i q^{71} +0.837037i q^{73} +(4.76943 - 13.3248i) q^{74} +(7.80952 + 6.41216i) q^{76} -1.25800i q^{79} +(-2.00050 + 0.396954i) q^{80} +(15.6442 + 5.59964i) q^{82} +13.7332 q^{83} -2.51798 q^{85} +(13.1105 + 4.69273i) q^{86} +(-5.99807 - 10.0151i) q^{88} -4.68906i q^{89} +(-3.70502 + 4.51243i) q^{92} +(-3.75153 + 10.4810i) q^{94} -2.57606i q^{95} +1.80904i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8}+O(q^{10}) \) 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8	\( 12 q - 4 q^{2} - 4 q^{4} - 4 q^{8} - 4 q^{16} + 24 q^{20} - 12 q^{25} - 24 q^{26} - 32 q^{29} + 16 q^{31} - 4 q^{32} + 32 q^{34} + 32 q^{37} + 24 q^{38} - 32 q^{40} + 24 q^{44} + 24 q^{46} + 28 q^{50} + 32 q^{52} + 32 q^{53} + 16 q^{55} + 16 q^{58} + 16 q^{59} - 8 q^{62} - 4 q^{64} + 8 q^{68} + 32 q^{74} - 32 q^{76} + 16 q^{80} + 32 q^{82} + 16 q^{83} + 16 q^{85} + 24 q^{86} + 24 q^{88}+O(q^{100}) \) 12 * q - 4 * q^2 - 4 * q^4 - 4 * q^8 - 4 * q^16 + 24 * q^20 - 12 * q^25 - 24 * q^26 - 32 * q^29 + 16 * q^31 - 4 * q^32 + 32 * q^34 + 32 * q^37 + 24 * q^38 - 32 * q^40 + 24 * q^44 + 24 * q^46 + 28 * q^50 + 32 * q^52 + 32 * q^53 + 16 * q^55 + 16 * q^58 + 16 * q^59 - 8 * q^62 - 4 * q^64 + 8 * q^68 + 32 * q^74 - 32 * q^76 + 16 * q^80 + 32 * q^82 + 16 * q^83 + 16 * q^85 + 24 * q^86 + 24 * q^88

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