LMFDB - Embedded newform 441.2.g.h.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(67,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("441.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.g (of order $3$, degree $2$, not 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Character	$\chi$	$=$	441.67
Dual form			441.2.g.h.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08816 + 1.88474i) q^{2} +(-1.18045 + 1.26749i) q^{3} +(-1.36816 - 2.36973i) q^{4} +1.26829 q^{5} +(-1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-0.213085 - 2.99242i) q^{9} +O(q^{10})$	\(q+(-1.08816 + 1.88474i) q^{2} +(-1.18045 + 1.26749i) q^{3} +(-1.36816 - 2.36973i) q^{4} +1.26829 q^{5} +(-1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-0.213085 - 2.99242i) q^{9} +(-1.38010 + 2.39040i) q^{10} -5.47733 q^{11} +(4.61867 + 1.06320i) q^{12} +(2.37268 - 4.10960i) q^{13} +(-1.49715 + 1.60755i) q^{15} +(0.992580 - 1.71920i) q^{16} +(2.40822 - 4.17116i) q^{17} +(5.87181 + 2.85461i) q^{18} +(-2.69059 - 4.66025i) q^{19} +(-1.73523 - 3.00550i) q^{20} +(5.96019 - 10.3233i) q^{22} -5.17631 q^{23} +(-1.89165 + 2.03114i) q^{24} -3.39144 q^{25} +(5.16368 + 8.94376i) q^{26} +(4.04442 + 3.26231i) q^{27} +(2.01656 + 3.49278i) q^{29} +(-1.40068 - 4.57100i) q^{30} +(0.732093 + 1.26802i) q^{31} +(3.76264 + 6.51709i) q^{32} +(6.46570 - 6.94249i) q^{33} +(5.24103 + 9.07773i) q^{34} +(-6.79970 + 4.59908i) q^{36} +(-0.959170 - 1.66133i) q^{37} +11.7111 q^{38} +(2.40807 + 7.85852i) q^{39} +2.03241 q^{40} +(-1.94808 + 3.37418i) q^{41} +(-1.66016 - 2.87549i) q^{43} +(7.49389 + 12.9798i) q^{44} +(-0.270254 - 3.79526i) q^{45} +(5.63263 - 9.75600i) q^{46} +(-1.57773 + 2.73271i) q^{47} +(1.00739 + 3.28752i) q^{48} +(3.69042 - 6.39199i) q^{50} +(2.44414 + 7.97624i) q^{51} -12.9849 q^{52} +(3.57149 - 6.18601i) q^{53} +(-10.5496 + 4.07277i) q^{54} -6.94684 q^{55} +(9.08294 + 2.09086i) q^{57} -8.77732 q^{58} +(-0.154341 - 0.267327i) q^{59} +(5.85781 + 1.34845i) q^{60} +(-5.17143 + 8.95719i) q^{61} -3.18652 q^{62} -12.4070 q^{64} +(3.00924 - 5.21216i) q^{65} +(6.04910 + 19.7407i) q^{66} +(-2.23655 - 3.87382i) q^{67} -13.1794 q^{68} +(6.11037 - 6.56095i) q^{69} -1.96688 q^{71} +(-0.341465 - 4.79530i) q^{72} +(5.27515 - 9.13683i) q^{73} +4.17491 q^{74} +(4.00342 - 4.29863i) q^{75} +(-7.36235 + 12.7520i) q^{76} +(-17.4316 - 4.01270i) q^{78} +(4.50822 - 7.80846i) q^{79} +(1.25888 - 2.18044i) q^{80} +(-8.90919 + 1.27528i) q^{81} +(-4.23963 - 7.34326i) q^{82} +(-5.08023 - 8.79921i) q^{83} +(3.05432 - 5.29023i) q^{85} +7.22607 q^{86} +(-6.80753 - 1.56707i) q^{87} -8.77732 q^{88} +(-2.59776 - 4.49945i) q^{89} +(7.44716 + 3.62047i) q^{90} +(7.08205 + 12.2665i) q^{92} +(-2.47141 - 0.568910i) q^{93} +(-3.43363 - 5.94722i) q^{94} +(-3.41245 - 5.91054i) q^{95} +(-12.7020 - 2.92396i) q^{96} +(-2.48521 - 4.30451i) q^{97} +(1.16714 + 16.3905i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} - 8 q^{51} + 32 q^{53} - 12 q^{57} + 56 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} - 168 q^{72} - 136 q^{74} - 60 q^{78} + 12 q^{79} - 40 q^{81} + 12 q^{85} - 152 q^{86} + 16 q^{92} + 112 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−1.08816	+	1.88474i	−0.769442	+	1.33271i	0.168424	+	0.985715i	$0.446132\pi$
$2$	−1.08816	+	1.88474i	−0.769442	+	1.33271i	−0.937866	+	0.346998i	$0.887201\pi$
$3$	−1.18045	+	1.26749i	−0.681532	+	0.731788i
$3$	−1.18045	+	1.26749i	−0.681532	+	0.731788i
$4$	−1.36816	−	2.36973i	−0.684082	−	1.18487i
$5$	1.26829			0.567196			0.283598	−	0.958943i	$-0.408472\pi$
$5$	1.26829			0.567196			0.283598	+	0.958943i	$0.408472\pi$
$6$	−1.10439	−	3.60407i	−0.450864	−	1.47136i
$7$		0			0
$7$		0			0
$8$	1.60248			0.566563
$9$	−0.213085	−	2.99242i	−0.0710284	−	0.997474i
$10$	−1.38010	+	2.39040i	−0.436425	+	0.755910i
$11$	−5.47733			−1.65148			−0.825739	−	0.564053i	$-0.809241\pi$
$11$	−5.47733			−1.65148			−0.825739	+	0.564053i	$0.809241\pi$
$12$	4.61867	+	1.06320i	1.33329	+	0.306920i
$13$	2.37268	−	4.10960i	0.658062	−	1.13980i	−0.323054	−	0.946380i	$-0.604710\pi$
$13$	2.37268	−	4.10960i	0.658062	−	1.13980i	0.981117	−	0.193417i	$-0.0619570\pi$
$14$		0			0
$15$	−1.49715	+	1.60755i	−0.386562	+	0.415068i
$16$	0.992580	−	1.71920i	0.248145	−	0.429800i
$17$	2.40822	−	4.17116i	0.584079	−	1.01165i	−0.410911	−	0.911676i	$-0.634789\pi$
$17$	2.40822	−	4.17116i	0.584079	−	1.01165i	0.994990	−	0.0999785i	$-0.0318774\pi$
$18$	5.87181	+	2.85461i	1.38400	+	0.672838i
$19$	−2.69059	−	4.66025i	−0.617265	−	1.06913i	−0.989983	−	0.141189i	$-0.954907\pi$
$19$	−2.69059	−	4.66025i	−0.617265	−	1.06913i	0.372718	−	0.927945i	$-0.378426\pi$
$20$	−1.73523	−	3.00550i	−0.388009	−	0.672051i
$21$		0			0
$22$	5.96019	−	10.3233i	1.27072	−	2.20095i
$23$	−5.17631			−1.07934			−0.539668	−	0.841878i	$-0.681450\pi$
$23$	−5.17631			−1.07934			−0.539668	+	0.841878i	$0.681450\pi$
$24$	−1.89165	+	2.03114i	−0.386131	+	0.414604i
$25$	−3.39144			−0.678288
$26$	5.16368	+	8.94376i	1.01268	+	1.75402i
$27$	4.04442	+	3.26231i	0.778348	+	0.627833i
$28$		0			0
$29$	2.01656	+	3.49278i	0.374466	+	0.648594i	0.990247	−	0.139324i	$-0.0444928\pi$
$29$	2.01656	+	3.49278i	0.374466	+	0.648594i	−0.615781	+	0.787917i	$0.711159\pi$
$30$	−1.40068	−	4.57100i	−0.255729	−	0.834547i
$31$	0.732093	+	1.26802i	0.131488	+	0.227744i	0.924250	−	0.381787i	$-0.124691\pi$
$31$	0.732093	+	1.26802i	0.131488	+	0.227744i	−0.792763	+	0.609531i	$0.791358\pi$
$32$	3.76264	+	6.51709i	0.665148	+	1.15207i
$33$	6.46570	−	6.94249i	1.12553	−	1.20853i
$34$	5.24103	+	9.07773i	0.898830	+	1.55682i
$35$		0			0
$36$	−6.79970	+	4.59908i	−1.13328	+	0.766514i
$37$	−0.959170	−	1.66133i	−0.157687	−	0.273121i	0.776347	−	0.630305i	$-0.217070\pi$
$37$	−0.959170	−	1.66133i	−0.157687	−	0.273121i	−0.934034	+	0.357184i	$0.883737\pi$
$38$	11.7111			1.89980
$39$	2.40807	+	7.85852i	0.385600	+	1.25837i
$40$	2.03241			0.321352
$41$	−1.94808	+	3.37418i	−0.304239	+	0.526958i	−0.977092	−	0.212819i	$-0.931736\pi$
$41$	−1.94808	+	3.37418i	−0.304239	+	0.526958i	0.672852	+	0.739777i	$0.265069\pi$
$42$		0			0
$43$	−1.66016	−	2.87549i	−0.253173	−	0.438508i	0.711225	−	0.702964i	$-0.248141\pi$
$43$	−1.66016	−	2.87549i	−0.253173	−	0.438508i	−0.964398	+	0.264457i	$0.914807\pi$
$44$	7.49389	+	12.9798i	1.12975	+	1.95678i
$45$	−0.270254	−	3.79526i	−0.0402871	−	0.565764i
$46$	5.63263	−	9.75600i	0.830486	−	1.43844i
$47$	−1.57773	+	2.73271i	−0.230135	+	0.398606i	−0.957848	−	0.287276i	$-0.907250\pi$
$47$	−1.57773	+	2.73271i	−0.230135	+	0.398606i	0.727712	+	0.685882i	$0.240584\pi$
$48$	1.00739	+	3.28752i	0.145404	+	0.474512i
$49$		0			0
$50$	3.69042	−	6.39199i	0.521904	−	0.903964i
$51$	2.44414	+	7.97624i	0.342248	+	1.11690i
$52$	−12.9849			−1.80068
$53$	3.57149	−	6.18601i	0.490582	−	0.849714i	−0.509359	−	0.860554i	$-0.670117\pi$
$53$	3.57149	−	6.18601i	0.490582	−	0.849714i	0.999941	+	0.0108405i	$0.00345071\pi$
$54$	−10.5496	+	4.07277i	−1.43561	+	0.554234i
$55$	−6.94684			−0.936712
$56$		0			0
$57$	9.08294	+	2.09086i	1.20307	+	0.276942i
$58$	−8.77732			−1.15252
$59$	−0.154341	−	0.267327i	−0.0200935	−	0.0348030i	0.855804	−	0.517301i	$-0.173063\pi$
$59$	−0.154341	−	0.267327i	−0.0200935	−	0.0348030i	−0.875897	+	0.482498i	$0.839730\pi$
$60$	5.85781	+	1.34845i	0.756240	+	0.174084i
$61$	−5.17143	+	8.95719i	−0.662134	+	1.14685i	0.317920	+	0.948118i	$0.397016\pi$
$61$	−5.17143	+	8.95719i	−0.662134	+	1.14685i	−0.980054	+	0.198732i	$0.936318\pi$
$62$	−3.18652			−0.404689
$63$		0			0
$64$	−12.4070			−1.55088
$65$	3.00924	−	5.21216i	0.373250	−	0.646489i
$66$	6.04910	+	19.7407i	0.744592	+	2.42991i
$67$	−2.23655	−	3.87382i	−0.273238	−	0.473262i	0.696451	−	0.717604i	$-0.254761\pi$
$67$	−2.23655	−	3.87382i	−0.273238	−	0.473262i	−0.969689	+	0.244342i	$0.921428\pi$
$68$	−13.1794			−1.59823
$69$	6.11037	−	6.56095i	0.735602	−	0.789845i
$70$		0			0
$71$	−1.96688			−0.233426			−0.116713	−	0.993166i	$-0.537236\pi$
$71$	−1.96688			−0.233426			−0.116713	+	0.993166i	$0.537236\pi$
$72$	−0.341465	−	4.79530i	−0.0402421	−	0.565132i
$73$	5.27515	−	9.13683i	0.617409	−	1.06938i	−0.372547	−	0.928013i	$-0.621516\pi$
$73$	5.27515	−	9.13683i	0.617409	−	1.06938i	0.989957	−	0.141371i	$-0.0451512\pi$
$74$	4.17491			0.485323
$75$	4.00342	−	4.29863i	0.462275	−	0.496364i
$76$	−7.36235	+	12.7520i	−0.844520	+	1.46275i
$77$		0			0
$78$	−17.4316	−	4.01270i	−1.97374	−	0.454349i
$79$	4.50822	−	7.80846i	0.507214	−	0.878520i	−0.492751	−	0.870170i	$-0.664009\pi$
$79$	4.50822	−	7.80846i	0.507214	−	0.878520i	0.999965	−	0.00835000i	$-0.00265792\pi$
$80$	1.25888	−	2.18044i	0.140747	−	0.243781i
$81$	−8.90919	+	1.27528i	−0.989910	+	0.141698i
$82$	−4.23963	−	7.34326i	−0.468189	−	0.810927i
$83$	−5.08023	−	8.79921i	−0.557627	−	0.965839i	−0.997694	−	0.0678739i	$-0.978378\pi$
$83$	−5.08023	−	8.79921i	−0.557627	−	0.965839i	0.440066	−	0.897965i	$-0.354955\pi$
$84$		0			0
$85$	3.05432	−	5.29023i	0.331287	−	0.573806i
$86$	7.22607			0.779207
$87$	−6.80753	−	1.56707i	−0.729844	−	0.168008i
$88$	−8.77732			−0.935666
$89$	−2.59776	−	4.49945i	−0.275362	−	0.476941i	0.694864	−	0.719141i	$-0.255464\pi$
$89$	−2.59776	−	4.49945i	−0.275362	−	0.476941i	−0.970226	+	0.242200i	$0.922131\pi$
$90$	7.44716	+	3.62047i	0.784999	+	0.381631i
$91$		0			0
$92$	7.08205	+	12.2665i	0.738354	+	1.27887i
$93$	−2.47141	−	0.568910i	−0.256273	−	0.0589932i
$94$	−3.43363	−	5.94722i	−0.354152	−	0.613409i
$95$	−3.41245	−	5.91054i	−0.350110	−	0.606409i
$96$	−12.7020	−	2.92396i	−1.29639	−	0.298425i
$97$	−2.48521	−	4.30451i	−0.252335	−	0.437057i	0.711833	−	0.702348i	$-0.247865\pi$
$97$	−2.48521	−	4.30451i	−0.252335	−	0.437057i	−0.964168	+	0.265291i	$0.914532\pi$
$98$		0			0
$99$	1.16714	+	16.3905i	0.117302	+	1.64731i
$100$	4.64005	+	8.03680i	0.464005	+	0.803680i
$101$	0.00533808			0.000531159			0.000265580	−	1.00000i	$-0.499915\pi$
$101$	0.00533808			0.000531159			0.000265580		1.00000i	$0.499915\pi$
$102$	−17.6927	−	4.07281i	−1.75184	−	0.403268i
$103$	13.0348			1.28436			0.642180	−	0.766554i	$-0.278030\pi$
$103$	13.0348			1.28436			0.642180	+	0.766554i	$0.278030\pi$
$104$	3.80217	−	6.58555i	0.372834	−	0.645767i
$105$		0			0
$106$	7.77268	+	13.4627i	0.754950	+	1.30761i
$107$	−4.71081	−	8.15936i	−0.455411	−	0.788795i	0.543301	−	0.839538i	$-0.317174\pi$
$107$	−4.71081	−	8.15936i	−0.455411	−	0.788795i	−0.998712	+	0.0507430i	$0.983841\pi$
$108$	2.19738	−	14.0476i	0.211443	−	1.35173i
$109$	−8.44513	+	14.6274i	−0.808896	+	1.40105i	0.104732	+	0.994500i	$0.466601\pi$
$109$	−8.44513	+	14.6274i	−0.808896	+	1.40105i	−0.913629	+	0.406549i	$0.866732\pi$
$110$	7.55924	−	13.0930i	0.720746	−	1.24837i
$111$	3.23798	+	0.745372i	0.307335	+	0.0707476i
$112$		0			0
$113$	−3.07313	+	5.32281i	−0.289095	+	0.500728i	−0.973594	−	0.228286i	$-0.926688\pi$
$113$	−3.07313	+	5.32281i	−0.289095	+	0.500728i	0.684499	+	0.729014i	$0.260021\pi$
$114$	−13.8244	+	14.8438i	−1.29477	+	1.39025i
$115$	−6.56506			−0.612195
$116$	5.51797	−	9.55741i	0.512331	−	0.887383i
$117$	−12.8032	−	6.22436i	−1.18366	−	0.575442i
$118$	0.671790			0.0618432
$119$		0			0
$120$	−2.39915	+	2.57607i	−0.219012	+	0.235162i
$121$	19.0012			1.72738
$122$	−11.2546	−	19.4936i	−1.01895	−	1.76487i
$123$	−1.97714	−	6.45222i	−0.178273	−	0.581777i
$124$	2.00325	−	3.46973i	0.179897	−	0.311591i
$125$	−10.6428			−0.951919
$126$		0			0
$127$	−13.9305			−1.23613			−0.618065	−	0.786127i	$-0.712083\pi$
$127$	−13.9305			−1.23613			−0.618065	+	0.786127i	$0.712083\pi$
$128$	5.97551	−	10.3499i	0.528165	−	0.914809i
$129$	5.60440	+	1.29012i	0.493440	+	0.113588i
$130$	6.54905	+	11.3433i	0.574389	+	0.994871i
$131$	−0.179156			−0.0156529			−0.00782645	−	0.999969i	$-0.502491\pi$
$131$	−0.179156			−0.0156529			−0.00782645	+	0.999969i	$0.502491\pi$
$132$	−25.2980	−	5.82351i	−2.20191	−	0.506872i
$133$		0			0
$134$	9.73486			0.840964
$135$	5.12949	+	4.13756i	0.441476	+	0.356104i
$136$	3.85913	−	6.68420i	0.330917	−	0.573166i
$137$	3.15206			0.269299			0.134649	−	0.990893i	$-0.457009\pi$
$137$	3.15206			0.269299			0.134649	+	0.990893i	$0.457009\pi$
$138$	5.71665	+	18.6558i	0.486634	+	1.58809i
$139$	9.42857	−	16.3308i	0.799721	−	1.38516i	−0.120077	−	0.992765i	$-0.538314\pi$
$139$	9.42857	−	16.3308i	0.799721	−	1.38516i	0.919798	−	0.392392i	$-0.128352\pi$
$140$		0			0
$141$	−1.60126	−	5.22558i	−0.134851	−	0.440073i
$142$	2.14027	−	3.70706i	0.179608	−	0.311090i
$143$	−12.9959	+	22.5096i	−1.08677	+	1.88235i
$144$	−5.35608	−	2.60388i	−0.446340	−	0.216990i
$145$	2.55758	+	4.42986i	0.212396	+	0.367880i
$146$	11.4804	+	19.8846i	0.950122	+	1.64566i
$147$		0			0
$148$	−2.62461	+	4.54595i	−0.215741	+	0.373675i
$149$	−21.2740			−1.74284			−0.871418	−	0.490541i	$-0.836799\pi$
$149$	−21.2740			−1.74284			−0.871418	+	0.490541i	$0.836799\pi$
$150$	3.74547	+	12.2230i	0.305816	+	0.998003i
$151$	6.36561			0.518026			0.259013	−	0.965874i	$-0.416603\pi$
$151$	6.36561			0.518026			0.259013	+	0.965874i	$0.416603\pi$
$152$	−4.31163	−	7.46796i	−0.349719	−	0.605731i
$153$	−12.9950	−	6.31759i	−1.05059	−	0.510747i
$154$		0			0
$155$	0.928506	+	1.60822i	0.0745794	+	0.129175i
$156$	15.3279	−	16.4582i	1.22722	−	1.31771i
$157$	−0.697976	−	1.20893i	−0.0557045	−	0.0964830i	0.836828	−	0.547465i	$-0.184407\pi$
$157$	−0.697976	−	1.20893i	−0.0557045	−	0.0964830i	−0.892533	+	0.450982i	$0.851074\pi$
$158$	9.81128	+	16.9936i	0.780543	+	1.35194i
$159$	3.62477	+	11.8291i	0.287463	+	0.938110i
$160$	4.77212	+	8.26556i	0.377269	+	0.653450i
$161$		0			0
$162$	7.29101	−	18.1792i	0.572836	−	1.42829i
$163$	9.53086	+	16.5079i	0.746515	+	1.29300i	0.949484	+	0.313816i	$0.101608\pi$
$163$	9.53086	+	16.5079i	0.746515	+	1.29300i	−0.202969	+	0.979185i	$0.565059\pi$
$164$	10.6612			0.832499
$165$	8.20038	−	8.80508i	0.638399	−	0.685475i
$166$	22.1123			1.71625
$167$	0.872003	−	1.51035i	0.0674776	−	0.116875i	−0.830313	−	0.557298i	$-0.811838\pi$
$167$	0.872003	−	1.51035i	0.0674776	−	0.116875i	0.897790	+	0.440423i	$0.145172\pi$
$168$		0			0
$169$	−4.75919	−	8.24317i	−0.366092	−	0.634090i
$170$	6.64715	+	11.5132i	0.509813	+	0.883022i
$171$	−13.3721	+	9.04443i	−1.02259	+	0.691645i
$172$	−4.54276	+	7.86828i	−0.346382	+	0.599951i
$173$	5.03794	−	8.72598i	0.383028	−	0.663424i	−0.608466	−	0.793580i	$-0.708215\pi$
$173$	5.03794	−	8.72598i	0.383028	−	0.663424i	0.991493	+	0.130157i	$0.0415480\pi$
$174$	10.3612	−	11.1252i	0.785478	−	0.843400i
$175$		0			0
$176$	−5.43669	+	9.41662i	−0.409806	+	0.709805i
$177$	0.521028	+	0.119939i	0.0391628	+	0.00901516i
$178$	11.3071			0.847500
$179$	9.27118	−	16.0582i	0.692961	−	1.20024i	−0.277902	−	0.960609i	$-0.589639\pi$
$179$	9.27118	−	16.0582i	0.692961	−	1.20024i	0.970863	−	0.239634i	$-0.0770275\pi$
$180$	−8.62399	+	5.83297i	−0.642794	+	0.434764i
$181$	−8.80982			−0.654829			−0.327414	−	0.944881i	$-0.606177\pi$
$181$	−8.80982			−0.654829			−0.327414	+	0.944881i	$0.606177\pi$
$182$		0			0
$183$	−5.24858	−	17.1283i	−0.387986	−	1.26616i
$184$	−8.29494			−0.611511
$185$	−1.21651	−	2.10705i	−0.0894393	−	0.154913i
$186$	3.76153	−	4.03890i	0.275808	−	0.296147i
$187$	−13.1906	+	22.8468i	−0.964593	+	1.67072i
$188$	8.63437			0.629726
$189$		0			0
$190$	14.8531			1.07756
$191$	−2.45469	+	4.25165i	−0.177615	+	0.307639i	−0.941063	−	0.338231i	$-0.890172\pi$
$191$	−2.45469	+	4.25165i	−0.177615	+	0.307639i	0.763448	+	0.645869i	$0.223505\pi$
$192$	14.6459	−	15.7259i	1.05698	−	1.13492i
$193$	4.88380	+	8.45899i	0.351544	+	0.608892i	0.986520	−	0.163640i	$-0.0523235\pi$
$193$	4.88380	+	8.45899i	0.351544	+	0.608892i	−0.634976	+	0.772531i	$0.718990\pi$
$194$	10.8172			0.776629
$195$	3.05413	+	9.96688i	0.218711	+	0.713743i
$196$		0			0
$197$	3.31445			0.236145			0.118073	−	0.993005i	$-0.462328\pi$
$197$	3.31445			0.236145			0.118073	+	0.993005i	$0.462328\pi$
$198$	−32.1618	−	15.6356i	−2.28564	−	1.11118i
$199$	−5.54432	+	9.60304i	−0.393026	+	0.680742i	−0.992847	−	0.119393i	$-0.961905\pi$
$199$	−5.54432	+	9.60304i	−0.393026	+	0.680742i	0.599821	+	0.800134i	$0.295239\pi$
$200$	−5.43472			−0.384293
$201$	7.55018	+	1.73803i	0.532548	+	0.122591i
$202$	−0.00580866	+	0.0100609i	−0.000408696	+	0.000707883i
$203$		0			0
$204$	15.5575	−	16.7048i	1.08925	−	1.16957i
$205$	−2.47073	+	4.27943i	−0.172563	+	0.298889i
$206$	−14.1839	+	24.5673i	−0.988240	+	1.71168i
$207$	1.10300	+	15.4897i	0.0766635	+	1.07661i
$208$	−4.71014	−	8.15821i	−0.326590	−	0.565670i
$209$	14.7373	+	25.5257i	1.01940	+	1.76565i
$210$		0			0
$211$	−3.66118	+	6.34135i	−0.252046	+	0.436557i	−0.964089	−	0.265579i	$-0.914437\pi$
$211$	−3.66118	+	6.34135i	−0.252046	+	0.436557i	0.712043	+	0.702136i	$0.247770\pi$
$212$	−19.5456			−1.34240
$213$	2.32180	−	2.49301i	0.159087	−	0.170818i
$214$	20.5044			1.40165
$215$	−2.10557	−	3.64695i	−0.143599	−	0.248720i
$216$	6.48110	+	5.22780i	0.440983	+	0.355707i
$217$		0			0
$218$	−18.3792	−	31.8337i	−1.24480	−	2.15605i
$219$	5.35384	+	17.4718i	0.361779	+	1.18063i
$220$	9.50442	+	16.4621i	0.640788	+	1.10988i
$221$	−11.4278	−	19.7936i	−0.768720	−	1.33146i
$222$	−4.92826	+	5.29167i	−0.330763	+	0.355154i
$223$	2.02765	+	3.51199i	0.135782	+	0.235181i	0.925896	−	0.377779i	$-0.123312\pi$
$223$	2.02765	+	3.51199i	0.135782	+	0.235181i	−0.790114	+	0.612960i	$0.789979\pi$
$224$		0			0
$225$	0.722667	+	10.1486i	0.0481778	+	0.676575i
$226$	−6.68808	−	11.5841i	−0.444884	−	0.770562i
$227$	1.33417			0.0885522			0.0442761	−	0.999019i	$-0.485902\pi$
$227$	1.33417			0.0885522			0.0442761	+	0.999019i	$0.485902\pi$
$228$	−7.47218	−	24.3848i	−0.494857	−	1.61492i
$229$	−15.9966			−1.05709			−0.528544	−	0.848906i	$-0.677262\pi$
$229$	−15.9966			−1.05709			−0.528544	+	0.848906i	$0.677262\pi$
$230$	7.14381	−	12.3734i	0.471049	−	0.815880i
$231$		0			0
$232$	3.23150	+	5.59712i	0.212158	+	0.367469i
$233$	−4.06542	−	7.04151i	−0.266334	−	0.461305i	0.701578	−	0.712593i	$-0.252479\pi$
$233$	−4.06542	−	7.04151i	−0.266334	−	0.461305i	−0.967912	+	0.251288i	$0.919146\pi$
$234$	25.6632	−	17.3577i	1.67766	−	1.13471i
$235$	−2.00102	+	3.46586i	−0.130532	+	0.226088i
$236$	−0.422329	+	0.731495i	−0.0274913	+	0.0476163i
$237$	4.57547	+	14.9316i	0.297208	+	0.969913i
$238$		0			0
$239$	11.0509	−	19.1407i	0.714823	−	1.23811i	−0.248204	−	0.968708i	$-0.579840\pi$
$239$	11.0509	−	19.1407i	0.714823	−	1.23811i	0.963028	−	0.269403i	$-0.0868262\pi$
$240$	1.27766	+	4.16952i	0.0824725	+	0.269141i
$241$	27.5947			1.77753			0.888765	−	0.458362i	$-0.151564\pi$
$241$	27.5947			1.77753			0.888765	+	0.458362i	$0.151564\pi$
$242$	−20.6762	+	35.8122i	−1.32912	+	2.30210i
$243$	8.90042	−	12.7978i	0.570962	−	0.820976i
$244$	28.3015			1.81182
$245$		0			0
$246$	14.3122	+	3.29462i	0.912513	+	0.210057i
$247$	−25.5356			−1.62479
$248$	1.17317	+	2.03198i	0.0744961	+	0.129031i
$249$	17.1499	+	3.94785i	1.08683	+	0.250185i
$250$	11.5810	−	20.0589i	0.732447	−	1.26863i
$251$	−16.5610			−1.04532			−0.522661	−	0.852541i	$-0.675061\pi$
$251$	−16.5610			−1.04532			−0.522661	+	0.852541i	$0.675061\pi$
$252$		0			0
$253$	28.3524			1.78250
$254$	15.1585	−	26.2553i	0.951130	−	1.64741i
$255$	3.09988	+	10.1162i	0.194122	+	0.633500i
$256$	0.597516	+	1.03493i	0.0373448	+	0.0646831i
$257$	2.06573			0.128857			0.0644285	−	0.997922i	$-0.479478\pi$
$257$	2.06573			0.128857			0.0644285	+	0.997922i	$0.479478\pi$
$258$	−8.53000	+	9.15900i	−0.531054	+	0.570214i
$259$		0			0
$260$	−16.4686			−1.02134
$261$	10.0222	−	6.77866i	0.620358	−	0.419589i
$262$	0.194949	−	0.337662i	0.0120440	−	0.0208608i
$263$	10.1296			0.624620			0.312310	−	0.949980i	$-0.398897\pi$
$263$	10.1296			0.624620			0.312310	+	0.949980i	$0.398897\pi$
$264$	10.3612	−	11.1252i	0.637686	−	0.684709i
$265$	4.52969	−	7.84565i	0.278257	−	0.481954i
$266$		0			0
$267$	8.76955	+	2.01872i	0.536688	+	0.123544i
$268$	−6.11994	+	10.6000i	−0.373835	+	0.647501i
$269$	7.54972	−	13.0765i	0.460315	−	0.797289i	−0.538662	−	0.842522i	$-0.681070\pi$
$269$	7.54972	−	13.0765i	0.460315	−	0.797289i	0.998976	+	0.0452336i	$0.0144032\pi$
$270$	−13.3799	+	5.16545i	−0.814275	+	0.314359i
$271$	14.4026	+	24.9459i	0.874893	+	1.51536i	0.856877	+	0.515521i	$0.172402\pi$
$271$	14.4026	+	24.9459i	0.874893	+	1.51536i	0.0180156	+	0.999838i	$0.494265\pi$
$272$	−4.78070	−	8.28041i	−0.289872	−	0.502074i
$273$		0			0
$274$	−3.42993	+	5.94082i	−0.207210	+	0.358898i
$275$	18.5760			1.12018
$276$	−23.9077	−	5.50347i	−1.43907	−	0.331270i
$277$	−2.69963			−0.162205			−0.0811026	−	0.996706i	$-0.525844\pi$
$277$	−2.69963			−0.162205			−0.0811026	+	0.996706i	$0.525844\pi$
$278$	20.5195	+	35.5408i	1.23068	+	2.13160i
$279$	3.63846	−	2.46093i	0.217829	−	0.147332i
$280$		0			0
$281$	−2.46312	−	4.26626i	−0.146938	−	0.254503i	0.783157	−	0.621825i	$-0.213608\pi$
$281$	−2.46312	−	4.26626i	−0.146938	−	0.254503i	−0.930094	+	0.367321i	$0.880275\pi$
$282$	11.5913	+	2.66828i	0.690251	+	0.158894i
$283$	−1.79079	−	3.10173i	−0.106451	−	0.184379i	0.807879	−	0.589348i	$-0.200615\pi$
$283$	−1.79079	−	3.10173i	−0.106451	−	0.184379i	−0.914330	+	0.404969i	$0.867282\pi$
$284$	2.69102	+	4.66098i	0.159682	+	0.276578i
$285$	11.5198	+	2.65182i	0.682374	+	0.157080i
$286$	−28.2832	−	48.9879i	−1.67242	−	2.89672i
$287$		0			0
$288$	18.7001	−	12.6481i	1.10192	−	0.745298i
$289$	−3.09903	−	5.36768i	−0.182296	−	0.315746i
$290$	−11.1322			−0.653704
$291$	8.38961	+	1.93126i	0.491808	+	0.113212i
$292$	−28.8691			−1.68944
$293$	12.1955	−	21.1232i	0.712469	−	1.23403i	−0.251459	−	0.967868i	$-0.580910\pi$
$293$	12.1955	−	21.1232i	0.712469	−	1.23403i	0.963928	−	0.266164i	$-0.0857563\pi$
$294$		0			0
$295$	−0.195750	−	0.339048i	−0.0113970	−	0.0197401i
$296$	−1.53705	−	2.66225i	−0.0893394	−	0.154740i
$297$	−22.1526	−	17.8688i	−1.28542	−	1.03685i
$298$	23.1494	−	40.0960i	1.34101	−	2.32270i
$299$	−12.2817	+	21.2726i	−0.710270	+	1.23022i
$300$	−15.6639	−	3.60579i	−0.904358	−	0.208180i
$301$		0			0
$302$	−6.92678	+	11.9975i	−0.398591	+	0.690380i
$303$	−0.00630133	+	0.00676599i	−0.000362002	+	0.000388696i
$304$	−10.6825			−0.612685
$305$	−6.55887	+	11.3603i	−0.375560	+	0.650489i
$306$	26.0476	−	17.6177i	1.48904	−	1.00714i
$307$	−23.9025			−1.36419			−0.682094	−	0.731265i	$-0.738930\pi$
$307$	−23.9025			−1.36419			−0.682094	+	0.731265i	$0.738930\pi$
$308$		0			0
$309$	−15.3869	+	16.5216i	−0.875332	+	0.939879i
$310$	−4.04143			−0.229538
$311$	6.47082	+	11.2078i	0.366926	+	0.635535i	0.989083	−	0.147357i	$-0.0470768\pi$
$311$	6.47082	+	11.2078i	0.366926	+	0.635535i	−0.622157	+	0.782893i	$0.713743\pi$
$312$	3.85889	+	12.5931i	0.218467	+	0.712946i
$313$	13.4340	−	23.2684i	0.759336	−	1.31521i	−0.183853	−	0.982954i	$-0.558857\pi$
$313$	13.4340	−	23.2684i	0.759336	−	1.31521i	0.943189	−	0.332255i	$-0.107810\pi$
$314$	3.03802			0.171446
$315$		0			0
$316$	−24.6719			−1.38790
$317$	−4.15584	+	7.19813i	−0.233415	+	0.404287i	−0.958811	−	0.284045i	$-0.908324\pi$
$317$	−4.15584	+	7.19813i	−0.233415	+	0.404287i	0.725396	+	0.688332i	$0.241657\pi$
$318$	−26.2391	−	6.04016i	−1.47142	−	0.338715i
$319$	−11.0454	−	19.1311i	−0.618422	−	1.07114i
$320$	−15.7357			−0.879654
$321$	15.9028	+	3.66078i	0.887608	+	0.204325i
$322$		0			0
$323$	−25.9182			−1.44212
$324$	15.2113	+	19.3676i	0.845073	+	1.07598i
$325$	−8.04680	+	13.9375i	−0.446356	+	0.773111i
$326$	−41.4842			−2.29760
$327$	−8.57110	−	27.9710i	−0.473983	−	1.54680i
$328$	−3.12177	+	5.40706i	−0.172371	+	0.298555i
$329$		0			0
$330$	7.67201	+	25.0369i	0.422330	+	1.37824i
$331$	−6.19889	+	10.7368i	−0.340722	+	0.590147i	−0.984567	−	0.175009i	$-0.944005\pi$
$331$	−6.19889	+	10.7368i	−0.340722	+	0.590147i	0.643845	+	0.765156i	$0.277338\pi$
$332$	−13.9012	+	24.0775i	−0.762926	+	1.32143i
$333$	−4.76702	+	3.22425i	−0.261231	+	0.176688i
$334$	1.89775	+	3.28700i	0.103840	+	0.179857i
$335$	−2.83659	−	4.91312i	−0.154980	−	0.268433i
$336$		0			0
$337$	−12.9588	+	22.4454i	−0.705913	+	1.22268i	0.260448	+	0.965488i	$0.416130\pi$
$337$	−12.9588	+	22.4454i	−0.705913	+	1.22268i	−0.966361	+	0.257189i	$0.917204\pi$
$338$	20.7150			1.12675
$339$	−3.11897	−	10.1785i	−0.169399	−	0.552819i
$340$	−16.7152			−0.906511
$341$	−4.00992	−	6.94538i	−0.217149	−	0.376113i
$342$	−2.49547	−	35.0447i	−0.134940	−	1.89500i
$343$		0			0
$344$	−2.66038	−	4.60792i	−0.143438	−	0.248442i
$345$	7.74971	−	8.32118i	0.417230	−	0.447997i
$346$	10.9641	+	18.9904i	0.589435	+	1.02093i
$347$	8.42415	+	14.5911i	0.452232	+	0.783289i	0.998524	−	0.0543058i	$-0.0172946\pi$
$347$	8.42415	+	14.5911i	0.452232	+	0.783289i	−0.546292	+	0.837595i	$0.683961\pi$
$348$	5.60028	+	18.2760i	0.300207	+	0.979698i
$349$	15.5503	+	26.9340i	0.832390	+	1.44174i	0.896138	+	0.443776i	$0.146361\pi$
$349$	15.5503	+	26.9340i	0.832390	+	1.44174i	−0.0637477	+	0.997966i	$0.520305\pi$
$350$		0			0
$351$	23.0029	−	8.88050i	1.22780	−	0.474006i
$352$	−20.6092	−	35.6963i	−1.09848	−	1.90262i
$353$	2.65938			0.141544			0.0707722	−	0.997493i	$-0.477454\pi$
$353$	2.65938			0.141544			0.0707722	+	0.997493i	$0.477454\pi$
$354$	−0.793013	+	0.851490i	−0.0421481	+	0.0452562i
$355$	−2.49457			−0.132398
$356$	−7.10833	+	12.3120i	−0.376741	+	0.652534i
$357$		0			0
$358$	20.1770	+	34.9476i	1.06639	+	1.84704i
$359$	16.2715	+	28.1830i	0.858775	+	1.48744i	0.873098	+	0.487545i	$0.162107\pi$
$359$	16.2715	+	28.1830i	0.858775	+	1.48744i	−0.0143230	+	0.999897i	$0.504559\pi$
$360$	−0.433077	−	6.08183i	−0.0228252	−	0.320541i
$361$	−4.97859	+	8.62318i	−0.262031	+	0.453852i
$362$	9.58646	−	16.6042i	0.503853	−	0.872699i
$363$	−22.4299	+	24.0839i	−1.17726	+	1.26407i
$364$		0			0
$365$	6.69042	−	11.5881i	0.350192	−	0.606551i
$366$	37.9936	+	8.74600i	1.98596	+	0.457161i
$367$	14.1536			0.738809			0.369405	−	0.929269i	$-0.379562\pi$
$367$	14.1536			0.738809			0.369405	+	0.929269i	$0.379562\pi$
$368$	−5.13790	+	8.89911i	−0.267832	+	0.463898i
$369$	10.5121	+	5.11050i	0.547237	+	0.266042i
$370$	5.29499			0.275273
$371$		0			0
$372$	2.03313	+	6.63494i	0.105413	+	0.344005i
$373$	2.67628			0.138573			0.0692863	−	0.997597i	$-0.477928\pi$
$373$	2.67628			0.138573			0.0692863	+	0.997597i	$0.477928\pi$
$374$	−28.7069	−	49.7217i	−1.48440	−	2.57105i
$375$	12.5632	−	13.4897i	0.648763	−	0.696603i
$376$	−2.52828	+	4.37911i	−0.130386	+	0.225835i
$377$	19.1386			0.985687
$378$		0			0
$379$	−0.312929			−0.0160741			−0.00803705	−	0.999968i	$-0.502558\pi$
$379$	−0.312929			−0.0160741			−0.00803705	+	0.999968i	$0.502558\pi$
$380$	−9.33759	+	16.1732i	−0.479008	+	0.829667i
$381$	16.4442	−	17.6568i	0.842462	−	0.904586i
$382$	−5.34218	−	9.25292i	−0.273330	−	0.473421i
$383$	−8.98880			−0.459306			−0.229653	−	0.973273i	$-0.573759\pi$
$383$	−8.98880			−0.459306			−0.229653	+	0.973273i	$0.573759\pi$
$384$	6.06465	+	19.7914i	0.309485	+	1.00998i
$385$		0			0
$386$	−21.2573			−1.08197
$387$	−8.25092	+	5.58064i	−0.419418	+	0.283680i
$388$	−6.80036	+	11.7786i	−0.345236	+	0.597966i
$389$	−26.9869			−1.36829			−0.684144	−	0.729347i	$-0.739824\pi$
$389$	−26.9869			−1.36829			−0.684144	+	0.729347i	$0.739824\pi$
$390$	−22.1084	−	5.08927i	−1.11950	−	0.257705i
$391$	−12.4657	+	21.5912i	−0.630417	+	1.09191i
$392$		0			0
$393$	0.211484	−	0.227079i	0.0106680	−	0.0114546i
$394$	−3.60664	+	6.24689i	−0.181700	+	0.314714i
$395$	5.71772	−	9.90339i	0.287690	−	0.498293i
$396$	37.2442	−	25.1907i	1.87159	−	1.26588i
$397$	−14.7503	−	25.5482i	−0.740295	−	1.28223i	−0.952361	−	0.304973i	$-0.901352\pi$
$397$	−14.7503	−	25.5482i	−0.740295	−	1.28223i	0.212066	−	0.977255i	$-0.431981\pi$
$398$	−12.0662	−	20.8992i	−0.604822	−	1.04758i
$399$		0			0
$400$	−3.36628	+	5.83056i	−0.168314	+	0.291528i
$401$	−34.2784			−1.71178			−0.855891	−	0.517156i	$-0.826991\pi$
$401$	−34.2784			−1.71178			−0.855891	+	0.517156i	$0.826991\pi$
$402$	−11.4915	+	12.3389i	−0.573144	+	0.615407i
$403$	6.94808			0.346109
$404$	−0.00730338	−	0.0126498i	−0.000363357	−	0.000629352i
$405$	−11.2994	+	1.61743i	−0.561473	+	0.0803706i
$406$		0			0
$407$	5.25369	+	9.09966i	0.260416	+	0.451054i
$408$	3.91669	+	12.7818i	0.193905	+	0.632792i
$409$	−5.49225	−	9.51286i	−0.271574	−	0.470381i	0.697691	−	0.716399i	$-0.254211\pi$
$409$	−5.49225	−	9.51286i	−0.271574	−	0.470381i	−0.969265	+	0.246018i	$0.920878\pi$
$410$	−5.37708	−	9.31338i	−0.265555	−	0.459955i
$411$	−3.72084	+	3.99522i	−0.183536	+	0.197070i
$412$	−17.8338	−	30.8890i	−0.878608	−	1.52179i
$413$		0			0
$414$	−30.3943	−	14.7764i	−1.49380	−	0.726218i
$415$	−6.44320	−	11.1599i	−0.316284	−	0.547820i
$416$	35.7102			1.75083
$417$	9.56921	+	31.2283i	0.468606	+	1.52925i
$418$	−64.1458			−3.13747
$419$	−3.33207	+	5.77132i	−0.162782	+	0.281947i	−0.935866	−	0.352357i	$-0.885380\pi$
$419$	−3.33207	+	5.77132i	−0.162782	+	0.281947i	0.773083	+	0.634305i	$0.218714\pi$
$420$		0			0
$421$	−17.0430	−	29.5193i	−0.830625	−	1.43868i	−0.897543	−	0.440926i	$-0.854650\pi$
$421$	−17.0430	−	29.5193i	−0.830625	−	1.43868i	0.0669186	−	0.997758i	$-0.478683\pi$
$422$	−7.96787	−	13.8008i	−0.387870	−	0.671810i
$423$	8.51360	+	4.13893i	0.413946	+	0.201242i
$424$	5.72325	−	9.91297i	0.277946	−	0.481416i
$425$	−8.16733	+	14.1462i	−0.396174	+	0.686193i
$426$	2.17220	+	7.08877i	0.105243	+	0.343452i
$427$		0			0
$428$	−12.8903	+	22.3267i	−0.623077	+	1.07920i
$429$	−13.1898	−	43.0437i	−0.636810	−	2.07817i
$430$	9.16474			0.441963
$431$	−1.12969	+	1.95669i	−0.0544155	+	0.0942504i	−0.891950	−	0.452134i	$-0.850663\pi$
$431$	−1.12969	+	1.95669i	−0.0544155	+	0.0942504i	0.837535	+	0.546384i	$0.183996\pi$
$432$	9.62298	−	3.71505i	0.462986	−	0.178740i
$433$	34.3904			1.65270			0.826348	−	0.563160i	$-0.190415\pi$
$433$	34.3904			1.65270			0.826348	+	0.563160i	$0.190415\pi$
$434$		0			0
$435$	−8.63392	−	1.98750i	−0.413965	−	0.0952933i
$436$	46.2173			2.21341
$437$	13.9274	+	24.1229i	0.666236	+	1.15395i
$438$	−38.7556	−	8.92140i	−1.85181	−	0.426281i
$439$	−2.99569	+	5.18869i	−0.142977	+	0.247643i	−0.928616	−	0.371042i	$-0.879001\pi$
$439$	−2.99569	+	5.18869i	−0.142977	+	0.247643i	0.785640	+	0.618684i	$0.212334\pi$
$440$	−11.1322			−0.530706
$441$		0			0
$442$	49.7411			2.36594
$443$	19.7190	−	34.1543i	0.936879	−	1.62272i	0.165630	−	0.986188i	$-0.447034\pi$
$443$	19.7190	−	34.1543i	0.936879	−	1.62272i	0.771249	−	0.636534i	$-0.219632\pi$
$444$	−2.66376	−	8.69293i	−0.126416	−	0.412548i
$445$	−3.29471	−	5.70661i	−0.156184	−	0.270519i
$446$	−8.82560			−0.417904
$447$	25.1129	−	26.9647i	1.18780	−	1.27539i
$448$		0			0
$449$	2.45092			0.115666			0.0578330	−	0.998326i	$-0.481581\pi$
$449$	2.45092			0.115666			0.0578330	+	0.998326i	$0.481581\pi$
$450$	−19.9139	−	9.68125i	−0.938750	−	0.456378i
$451$	10.6703	−	18.4815i	0.502444	−	0.870259i
$452$	16.8182			0.791060
$453$	−7.51428	+	8.06838i	−0.353052	+	0.379086i
$454$	−1.45179	+	2.51457i	−0.0681358	+	0.118015i
$455$		0			0
$456$	14.5552	+	3.35057i	0.681612	+	0.156905i
$457$	−5.51058	+	9.54461i	−0.257774	+	0.446478i	−0.965645	−	0.259864i	$-0.916322\pi$
$457$	−5.51058	+	9.54461i	−0.257774	+	0.446478i	0.707871	+	0.706342i	$0.249656\pi$
$458$	17.4068	−	30.1495i	0.813368	−	1.40879i
$459$	23.3475	−	9.01353i	1.08977	−	0.420715i
$460$	8.98208	+	15.5574i	0.418792	+	0.725369i
$461$	14.6540	+	25.3814i	0.682503	+	1.18213i	0.974215	+	0.225624i	$0.0724420\pi$
$461$	14.6540	+	25.3814i	0.682503	+	1.18213i	−0.291711	+	0.956506i	$0.594225\pi$
$462$		0			0
$463$	0.593566	−	1.02809i	0.0275853	−	0.0477792i	−0.851903	−	0.523699i	$-0.824552\pi$
$463$	0.593566	−	1.02809i	0.0275853	−	0.0477792i	0.879489	+	0.475920i	$0.157885\pi$
$464$	8.00639			0.371687
$465$	−3.13446	−	0.721543i	−0.145357	−	0.0334608i
$466$	17.6952			0.819715
$467$	−11.0573	−	19.1519i	−0.511673	−	0.886243i	−0.999908	−	0.0135313i	$-0.995693\pi$
$467$	−11.0573	−	19.1519i	−0.511673	−	0.886243i	0.488236	−	0.872712i	$-0.337641\pi$
$468$	2.76688	+	38.8562i	0.127899	+	1.79613i
$469$		0			0
$470$	−4.35483	−	7.54280i	−0.200874	−	0.347923i
$471$	2.35623	+	0.542398i	0.108570	+	0.0249924i
$472$	−0.247329	−	0.428387i	−0.0113842	−	0.0197181i
$473$	9.09327	+	15.7500i	0.418109	+	0.724186i
$474$	−33.1210	−	7.62436i	−1.52130	−	0.350198i
$475$	9.12499	+	15.8050i	0.418683	+	0.725181i
$476$		0			0
$477$	−19.2722	−	9.36927i	−0.882413	−	0.428990i
$478$	24.0502	+	41.6562i	1.10003	+	1.90531i
$479$	−25.1428			−1.14880			−0.574402	−	0.818573i	$-0.694766\pi$
$479$	−25.1428			−1.14880			−0.574402	+	0.818573i	$0.694766\pi$
$480$	−16.1098	−	3.70842i	−0.735308	−	0.169266i
$481$	−9.10321			−0.415071
$482$	−30.0273	+	52.0088i	−1.36771	+	2.36894i
$483$		0			0
$484$	−25.9967	−	45.0276i	−1.18167	−	2.04671i
$485$	−3.15197	−	5.45937i	−0.143123	−	0.247897i
$486$	14.4354	+	30.7009i	0.654803	+	1.39262i
$487$	−6.78904	+	11.7590i	−0.307641	+	0.532849i	−0.977846	−	0.209327i	$-0.932873\pi$
$487$	−6.78904	+	11.7590i	−0.307641	+	0.532849i	0.670205	+	0.742176i	$0.266206\pi$
$488$	−8.28713	+	14.3537i	−0.375141	+	0.649763i
$489$	−32.1744	−	7.40644i	−1.45498	−	0.334931i
$490$		0			0
$491$	7.25177	−	12.5604i	0.327268	−	0.566844i	−0.654701	−	0.755888i	$-0.727205\pi$
$491$	7.25177	−	12.5604i	0.327268	−	0.566844i	0.981969	+	0.189044i	$0.0605387\pi$
$492$	−12.5850	+	13.5130i	−0.567375	+	0.609213i
$493$	19.4253			0.874870
$494$	27.7868	−	48.1281i	1.25019	−	2.16538i
$495$	1.48027	+	20.7879i	0.0665332	+	0.934346i
$496$	2.90664			0.130512
$497$		0			0
$498$	−26.1024	+	28.0272i	−1.16968	+	1.25593i
$499$	13.9915			0.626345			0.313172	−	0.949696i	$-0.398608\pi$
$499$	13.9915			0.626345			0.313172	+	0.949696i	$0.398608\pi$
$500$	14.5611	+	25.2205i	0.651191	+	1.12790i
$501$	0.885011	+	2.88815i	0.0395394	+	0.129033i
$502$	18.0209	−	31.2132i	0.804314	−	1.39311i
$503$	28.4011			1.26634			0.633171	−	0.774012i	$-0.281753\pi$
$503$	28.4011			1.26634			0.633171	+	0.774012i	$0.281753\pi$
$504$		0			0
$505$	0.00677023			0.000301271
$506$	−30.8518	+	53.4369i	−1.37153	+	2.37556i
$507$	16.0661	+	3.69837i	0.713523	+	0.164251i
$508$	19.0592	+	33.0115i	0.845615	+	1.46465i
$509$	−3.45993			−0.153359			−0.0766794	−	0.997056i	$-0.524432\pi$
$509$	−3.45993			−0.153359			−0.0766794	+	0.997056i	$0.524432\pi$
$510$	−22.4395	−	5.16550i	−0.993639	−	0.228732i
$511$		0			0
$512$	21.3013			0.941392
$513$	4.32131	−	27.6255i	0.190790	−	1.21970i
$514$	−2.24784	+	3.89337i	−0.0991480	+	0.171729i
$515$	16.5319			0.728484
$516$	−4.61052	−	15.0460i	−0.202967	−	0.662364i
$517$	8.64174	−	14.9679i	0.380063	−	0.658289i
$518$		0			0
$519$	5.11310	+	16.6861i	0.224440	+	0.732440i
$520$	4.82225	−	8.35239i	0.211470	−	0.366276i
$521$	−3.56797	+	6.17991i	−0.156316	+	0.270747i	−0.933537	−	0.358480i	$-0.883295\pi$
$521$	−3.56797	+	6.17991i	−0.156316	+	0.270747i	0.777222	+	0.629227i	$0.216628\pi$
$522$	1.87032	+	26.2655i	0.0818616	+	1.14961i
$523$	6.53235	+	11.3144i	0.285640	+	0.494743i	0.972764	−	0.231797i	$-0.0744606\pi$
$523$	6.53235	+	11.3144i	0.285640	+	0.494743i	−0.687124	+	0.726540i	$0.741127\pi$
$524$	0.245114	+	0.424551i	0.0107079	+	0.0185466i
$525$		0			0
$526$	−11.0226	+	19.0917i	−0.480609	+	0.832439i
$527$	7.05216			0.307197
$528$	−5.51779	−	18.0068i	−0.240131	−	0.783646i
$529$	3.79420			0.164965
$530$	9.85801	+	17.0746i	0.428205	+	0.741672i
$531$	−0.767068	+	0.518818i	−0.0332879	+	0.0225148i
$532$		0			0
$533$	9.24434	+	16.0117i	0.400417	+	0.693542i
$534$	−13.3474	+	14.3316i	−0.577599	+	0.620191i
$535$	−5.97467	−	10.3484i	−0.258308	−	0.447402i
$536$	−3.58403	−	6.20772i	−0.154807	−	0.268133i
$537$	9.40948	+	30.7070i	0.406049	+	1.32510i
$538$	16.4305	+	28.4585i	0.708371	+	1.22693i
$539$		0			0
$540$	2.78691	−	17.8164i	0.119930	−	0.766695i
$541$	−2.46788	−	4.27450i	−0.106103	−	0.183775i	0.808086	−	0.589065i	$-0.200504\pi$
$541$	−2.46788	−	4.27450i	−0.106103	−	0.183775i	−0.914188	+	0.405290i	$0.867171\pi$
$542$	−62.6889			−2.69272
$543$	10.3995	−	11.1664i	0.446287	−	0.479196i
$544$	36.2451			1.55399
$545$	−10.7109	+	18.5518i	−0.458803	+	0.794670i
$546$		0			0
$547$	0.559964	+	0.969887i	0.0239423	+	0.0414694i	0.877748	−	0.479122i	$-0.159045\pi$
$547$	0.559964	+	0.969887i	0.0239423	+	0.0414694i	−0.853806	+	0.520591i	$0.825712\pi$
$548$	−4.31254	−	7.46954i	−0.184223	−	0.319083i
$549$	27.9056	+	13.5665i	1.19098	+	0.579003i
$550$	−20.2136	+	35.0110i	−0.861912	+	1.49288i
$551$	10.8515	−	18.7953i	0.462289	−	0.800708i
$552$	9.79175	−	10.5138i	0.416764	−	0.447497i
$553$		0			0
$554$	2.93762	−	5.08811i	0.124808	−	0.216173i
$555$	4.10670	+	0.945348i	0.174320	+	0.0401278i
$556$	−51.5993			−2.18830
$557$	5.47832	−	9.48873i	0.232124	−	0.402050i	−0.726309	−	0.687368i	$-0.758766\pi$
$557$	5.47832	−	9.48873i	0.232124	−	0.402050i	0.958433	+	0.285318i	$0.0920992\pi$
$558$	0.679001	+	9.53543i	0.0287444	+	0.403667i
$559$	−15.7561			−0.666413
$560$		0			0
$561$	−13.3874	−	43.6885i	−0.565215	−	1.84453i
$562$	10.7210			0.452240
$563$	2.38048	+	4.12311i	0.100325	+	0.173768i	0.911819	−	0.410593i	$-0.134678\pi$
$563$	2.38048	+	4.12311i	0.100325	+	0.173768i	−0.811493	+	0.584361i	$0.801345\pi$
$564$	−10.1924	+	10.9440i	−0.429179	+	0.460826i
$565$	−3.89761	+	6.75087i	−0.163974	+	0.284011i
$566$	7.79462			0.327632
$567$		0			0
$568$	−3.15189			−0.132250
$569$	−1.74988	+	3.03088i	−0.0733588	+	0.127061i	−0.900371	−	0.435122i	$-0.856705\pi$
$569$	−1.74988	+	3.03088i	−0.0733588	+	0.127061i	0.827013	+	0.562183i	$0.190038\pi$
$570$	−17.5333	+	18.8262i	−0.734390	+	0.788545i
$571$	−3.53051	−	6.11501i	−0.147747	−	0.255905i	0.782647	−	0.622465i	$-0.213869\pi$
$571$	−3.53051	−	6.11501i	−0.147747	−	0.255905i	−0.930394	+	0.366560i	$0.880535\pi$
$572$	71.1223			2.97377
$573$	−2.49131	−	8.13017i	−0.104076	−	0.339643i
$574$		0			0
$575$	17.5552			0.732101
$576$	2.64376	+	37.1271i	0.110157	+	1.54696i
$577$	−6.44149	+	11.1570i	−0.268163	+	0.464472i	−0.968387	−	0.249451i	$-0.919750\pi$
$577$	−6.44149	+	11.1570i	−0.268163	+	0.464472i	0.700225	+	0.713923i	$0.253083\pi$
$578$	13.4889			0.561064
$579$	−16.4868	−	3.79521i	−0.685168	−	0.157723i
$580$	6.99838	−	12.1216i	0.290592	−	0.503320i
$581$		0			0
$582$	−12.7691	+	13.7107i	−0.529297	+	0.568328i
$583$	−19.5623	+	33.8828i	−0.810186	+	1.40328i
$584$	8.45333	−	14.6416i	0.349801	−	0.605874i
$585$	−16.2382	−	7.89429i	−0.671367	−	0.326389i
$586$	26.5412	+	45.9707i	1.09641	+	1.89903i
$587$	−19.5044	−	33.7826i	−0.805034	−	1.39436i	−0.916268	−	0.400565i	$-0.868814\pi$
$587$	−19.5044	−	33.7826i	−0.805034	−	1.39436i	0.111235	−	0.993794i	$-0.464519\pi$
$588$		0			0
$589$	3.93953	−	6.82347i	0.162326	−	0.281156i
$590$	0.852024			0.0350773
$591$	−3.91254	+	4.20105i	−0.160940	+	0.172808i
$592$	−3.80821			−0.156517
$593$	−20.1513	−	34.9031i	−0.827515	−	1.43330i	−0.899982	−	0.435927i	$-0.856421\pi$
$593$	−20.1513	−	34.9031i	−0.827515	−	1.43330i	0.0724676	−	0.997371i	$-0.476913\pi$
$594$	57.7835	−	22.3079i	2.37089	−	0.915304i
$595$		0			0
$596$	29.1064	+	50.4137i	1.19224	+	2.06503i
$597$	−5.62703	−	18.3633i	−0.230299	−	0.751559i
$598$	−26.7288	−	46.2957i	−1.09302	−	1.89317i
$599$	6.39103	+	11.0696i	0.261130	+	0.452291i	0.966543	−	0.256506i	$-0.0825715\pi$
$599$	6.39103	+	11.0696i	0.261130	+	0.452291i	−0.705412	+	0.708797i	$0.749238\pi$
$600$	6.41541	−	6.88848i	0.261908	−	0.281221i
$601$	−4.86311	−	8.42316i	−0.198371	−	0.343588i	0.749630	−	0.661858i	$-0.230232\pi$
$601$	−4.86311	−	8.42316i	−0.198371	−	0.343588i	−0.948000	+	0.318270i	$0.896898\pi$
$602$		0			0
$603$	−11.1155	+	7.51816i	−0.452659	+	0.306163i
$604$	−8.70921	−	15.0848i	−0.354373	−	0.613792i
$605$	24.0990			0.979762
$606$	−0.00589531	−	0.0192388i	−0.000239481	−	0.000781524i
$607$	41.4873			1.68392			0.841959	−	0.539541i	$-0.181402\pi$
$607$	41.4873			1.68392			0.841959	+	0.539541i	$0.181402\pi$
$608$	20.2475	−	35.0697i	0.821145	−	1.42226i
$609$		0			0
$610$	−14.2742	−	24.7236i	−0.577943	−	1.00103i
$611$	7.48688	+	12.9677i	0.302887	+	0.524615i
$612$	2.80833	+	39.4382i	0.113520	+	1.59420i
$613$	−7.64783	+	13.2464i	−0.308893	+	0.535018i	−0.978120	−	0.208039i	$-0.933292\pi$
$613$	−7.64783	+	13.2464i	−0.308893	+	0.535018i	0.669228	+	0.743057i	$0.266625\pi$
$614$	26.0096	−	45.0500i	1.04966	−	1.81807i
$615$	−2.50759	−	8.18329i	−0.101116	−	0.329982i
$616$		0			0
$617$	−2.66563	+	4.61700i	−0.107314	+	0.185873i	−0.914681	−	0.404176i	$-0.867558\pi$
$617$	−2.66563	+	4.61700i	−0.107314	+	0.185873i	0.807367	+	0.590049i	$0.200892\pi$
$618$	−14.3955	−	46.9784i	−0.579072	−	1.88975i
$619$	−12.6841			−0.509817			−0.254908	−	0.966965i	$-0.582045\pi$
$619$	−12.6841			−0.509817			−0.254908	+	0.966965i	$0.582045\pi$
$620$	2.54070	−	4.40062i	0.102037	−	0.176733i
$621$	−20.9352	−	16.8868i	−0.840099	−	0.677642i
$622$	−28.1650			−1.12931
$623$		0			0
$624$	15.9006	+	3.66026i	0.636532	+	0.146528i
$625$	3.45909			0.138363
$626$	29.2366	+	50.6393i	1.16853	+	2.02395i
$627$	−49.7503	−	11.4524i	−1.98683	−	0.457363i
$628$	−1.90989	+	3.30803i	−0.0762129	+	0.132005i
$629$	−9.23957			−0.368406
$630$		0			0
$631$	0.123764			0.00492698			0.00246349	−	0.999997i	$-0.499216\pi$
$631$	0.123764			0.00492698			0.00246349	+	0.999997i	$0.499216\pi$
$632$	7.22433	−	12.5129i	0.287369	−	0.497737i
$633$	−3.71580	−	12.1262i	−0.147690	−	0.481972i
$634$	−9.04441	−	15.6654i	−0.359199	−	0.622151i
$635$	−17.6679			−0.701128
$636$	23.0725	−	24.7739i	0.914885	−	0.982349i
$637$		0			0
$638$	48.0763			1.90336
$639$	0.419113	+	5.88574i	0.0165799	+	0.232836i
$640$	7.57868	−	13.1267i	0.299573	−	0.518876i
$641$	5.93177			0.234291			0.117145	−	0.993115i	$-0.462626\pi$
$641$	5.93177			0.234291			0.117145	+	0.993115i	$0.462626\pi$
$642$	−24.2043	+	25.9892i	−0.955269	+	1.02571i
$643$	−23.4140	+	40.5542i	−0.923358	+	1.59930i	−0.129178	+	0.991621i	$0.541234\pi$
$643$	−23.4140	+	40.5542i	−0.923358	+	1.59930i	−0.794180	+	0.607682i	$0.792100\pi$
$644$		0			0
$645$	7.10801	+	1.63624i	0.279877	+	0.0644269i
$646$	28.2030	−	48.8490i	1.10963	−	1.92194i
$647$	19.5701	−	33.8964i	0.769379	−	1.33260i	−0.168521	−	0.985698i	$-0.553899\pi$
$647$	19.5701	−	33.8964i	0.769379	−	1.33260i	0.937900	−	0.346905i	$-0.112767\pi$
$648$	−14.2768	+	2.04362i	−0.560846	+	0.0802809i
$649$	0.845379	+	1.46424i	0.0331840	+	0.0574764i
$650$	−17.5123	−	30.3322i	−0.686890	−	1.18973i
$651$		0			0
$652$	26.0796	−	45.1711i	1.02135	−	1.76904i
$653$	43.3281			1.69556			0.847779	−	0.530350i	$-0.177939\pi$
$653$	43.3281			1.69556			0.847779	+	0.530350i	$0.177939\pi$
$654$	62.0448	+	14.2825i	2.42614	+	0.558491i
$655$	−0.227221			−0.00887827
$656$	3.86726	+	6.69828i	0.150991	+	0.261524i
$657$	−28.4653	−	13.8386i	−1.11054	−	0.539893i
$658$		0			0
$659$	3.43895	+	5.95643i	0.133962	+	0.232030i	0.925201	−	0.379478i	$-0.123897\pi$
$659$	3.43895	+	5.95643i	0.133962	+	0.232030i	−0.791238	+	0.611508i	$0.790563\pi$
$660$	−32.0852	−	7.38590i	−1.24891	−	0.287496i
$661$	−19.3835	−	33.5733i	−0.753932	−	1.30585i	−0.945903	−	0.324449i	$-0.894821\pi$
$661$	−19.3835	−	33.5733i	−0.753932	−	1.30585i	0.191971	−	0.981401i	$-0.438512\pi$
$662$	−13.4907	−	23.3666i	−0.524331	−	0.908168i
$663$	38.5783	+	8.88059i	1.49826	+	0.344894i
$664$	−8.14097	−	14.1006i	−0.315931	−	0.547209i
$665$		0			0
$666$	−0.889611	−	12.4931i	−0.0344717	−	0.484097i
$667$	−10.4383	−	18.0797i	−0.404174	−	0.700050i
$668$	−4.77217			−0.184641
$669$	−6.84497	−	1.57569i	−0.264642	−	0.0609197i
$670$	12.3466			0.476991
$671$	28.3257	−	49.0615i	1.09350	−	1.89400i
$672$		0			0
$673$	17.9897	+	31.1591i	0.693452	+	1.20109i	0.970700	+	0.240295i	$0.0772443\pi$
$673$	17.9897	+	31.1591i	0.693452	+	1.20109i	−0.277248	+	0.960798i	$0.589422\pi$
$674$	−28.2025	−	48.8481i	−1.08632	−	1.88156i
$675$	−13.7164	−	11.0640i	−0.527945	−	0.425852i
$676$	−13.0227	+	22.5560i	−0.500874	+	0.867539i
$677$	−2.23329	+	3.86817i	−0.0858322	+	0.148666i	−0.905746	−	0.423822i	$-0.860688\pi$
$677$	−2.23329	+	3.86817i	−0.0858322	+	0.148666i	0.819913	+	0.572488i	$0.194022\pi$
$678$	22.5777	+	5.19731i	0.867092	+	0.199602i
$679$		0			0
$680$	4.89449	−	8.47750i	0.187695	−	0.325097i
$681$	−1.57492	+	1.69106i	−0.0603511	+	0.0648015i
$682$	17.4536			0.668335
$683$	13.3356	−	23.0980i	0.510274	−	0.883821i	−0.489655	−	0.871916i	$-0.662877\pi$
$683$	13.3356	−	23.0980i	0.510274	−	0.883821i	0.999929	−	0.0119046i	$-0.00378945\pi$
$684$	39.7281	+	19.3140i	1.51904	+	0.738490i
$685$	3.99773			0.152745
$686$		0			0
$687$	18.8832	−	20.2757i	0.720439	−	0.773565i
$688$	−6.59138			−0.251294
$689$	−16.9480	−	29.3548i	−0.645668	−	1.11833i
$690$	7.25037	+	23.6609i	0.276017	+	0.900756i
$691$	20.5220	−	35.5452i	0.780694	−	1.35220i	−0.150844	−	0.988558i	$-0.548199\pi$
$691$	20.5220	−	35.5452i	0.780694	−	1.35220i	0.931538	−	0.363644i	$-0.118468\pi$
$692$	−27.5709			−1.04809
$693$		0			0
$694$	−36.6671			−1.39187
$695$	11.9582	−	20.7121i	0.453599	−	0.785656i
$696$	−10.9089	−	2.51120i	−0.413502	−	0.0951869i
$697$	9.38281	+	16.2515i	0.355399	+	0.615570i
$698$	−67.6847			−2.56190
$699$	13.7241	+	3.15924i	0.519093	+	0.119493i
$700$		0			0
$701$	9.63355			0.363854			0.181927	−	0.983312i	$-0.441767\pi$
$701$	9.63355			0.363854			0.181927	+	0.983312i	$0.441767\pi$
$702$	−8.29328	+	53.0179i	−0.313010	+	2.00103i
$703$	−5.16148	+	8.93994i	−0.194669	+	0.337176i
$704$	67.9575			2.56125
$705$	−2.03087	−	6.62755i	−0.0764869	−	0.249608i
$706$	−2.89382	+	5.01224i	−0.108910	+	0.188638i
$707$		0			0
$708$	−0.428629	−	1.39879i	−0.0161089	−	0.0525698i
$709$	5.07131	−	8.78376i	0.190457	−	0.329881i	−0.754945	−	0.655788i	$-0.772336\pi$
$709$	5.07131	−	8.78376i	0.190457	−	0.329881i	0.945402	+	0.325907i	$0.105670\pi$
$710$	2.71448	−	4.70162i	0.101873	−	0.176449i
$711$	−24.3268	−	11.8266i	−0.912328	−	0.443533i
$712$	−4.16286	−	7.21029i	−0.156010	−	0.270217i
$713$	−3.78954	−	6.56368i	−0.141919	−	0.245812i
$714$		0			0
$715$	−16.4826	+	28.5487i	−0.616415	+	1.06766i
$716$	−50.7380			−1.89617
$717$	11.2157	+	36.6016i	0.418860	+	1.36691i
$718$	−70.8235			−2.64311
$719$	20.6844	+	35.8264i	0.771397	+	1.33610i	0.936797	+	0.349873i	$0.113775\pi$
$719$	20.6844	+	35.8264i	0.771397	+	1.33610i	−0.165400	+	0.986227i	$0.552891\pi$
$720$	−6.79305	−	3.30248i	−0.253162	−	0.123076i
$721$		0			0
$722$	−10.8350	−	18.7667i	−0.403236	−	0.698425i
$723$	−32.5741	+	34.9761i	−1.21144	+	1.30078i
$724$	12.0533	+	20.8769i	0.447957	+	0.775884i
$725$	−6.83904	−	11.8456i	−0.253996	−	0.439934i
$726$	−20.9846	−	68.4815i	−0.778813	−	2.54159i
$727$	−4.86372	−	8.42422i	−0.180386	−	0.312437i	0.761626	−	0.648016i	$-0.224401\pi$
$727$	−4.86372	−	8.42422i	−0.180386	−	0.312437i	−0.942012	+	0.335580i	$0.891068\pi$
$728$		0			0
$729$	5.71460	+	26.3883i	0.211652	+	0.977345i
$730$	14.5604	+	25.2194i	0.538906	+	0.933412i
$731$	−15.9921			−0.591491
$732$	−33.4084	+	35.8720i	−1.23481	+	1.32587i
$733$	28.9108			1.06784			0.533922	−	0.845534i	$-0.320718\pi$
$733$	28.9108			1.06784			0.533922	+	0.845534i	$0.320718\pi$
$734$	−15.4013	+	26.6758i	−0.568471	+	0.984621i
$735$		0			0
$736$	−19.4766	−	33.7345i	−0.717918	−	1.24347i
$737$	12.2503	+	21.2182i	0.451247	+	0.781582i
$738$	−21.0707	+	14.2515i	−0.775624	+	0.524605i
$739$	6.67467	−	11.5609i	0.245532	−	0.425273i	−0.716749	−	0.697331i	$-0.754371\pi$
$739$	6.67467	−	11.5609i	0.245532	−	0.425273i	0.962281	+	0.272058i	$0.0877041\pi$
$740$	−3.32876	+	5.76558i	−0.122368	+	0.211947i
$741$	30.1435	−	32.3663i	1.10735	−	1.18901i
$742$		0			0
$743$	19.9100	−	34.4851i	0.730425	−	1.26513i	−0.226276	−	0.974063i	$-0.572655\pi$
$743$	19.9100	−	34.4851i	0.730425	−	1.26513i	0.956702	−	0.291071i	$-0.0940115\pi$
$744$	−3.96039	−	0.911668i	−0.145195	−	0.0334234i
$745$	−26.9816			−0.988530
$746$	−2.91221	+	5.04410i	−0.106624	+	0.184678i
$747$	−25.2484	+	17.0772i	−0.923792	+	0.624821i
$748$	72.1877			2.63944
$749$		0			0
$750$	11.7538	+	38.3573i	0.429186	+	1.40061i
$751$	−38.4345			−1.40250			−0.701248	−	0.712917i	$-0.747374\pi$
$751$	−38.4345			−1.40250			−0.701248	+	0.712917i	$0.747374\pi$
$752$	3.13204	+	5.42486i	0.114214	+	0.197824i
$753$	19.5494	−	20.9910i	0.712420	−	0.764954i
$754$	−20.8258	+	36.0713i	−0.758429	+	1.31364i
$755$	8.07344			0.293823
$756$		0			0
$757$	−5.66698			−0.205970			−0.102985	−	0.994683i	$-0.532839\pi$
$757$	−5.66698			−0.205970			−0.102985	+	0.994683i	$0.532839\pi$
$758$	0.340516	−	0.589791i	0.0123681	−	0.0214222i
$759$	−33.4685	+	35.9365i	−1.21483	+	1.30441i
$760$	−5.46839	−	9.47153i	−0.198359	−	0.343569i
$761$	52.3321			1.89704			0.948519	−	0.316719i	$-0.102581\pi$
$761$	52.3321			1.89704			0.948519	+	0.316719i	$0.102581\pi$
$762$	15.3846	+	50.2064i	0.557327	+	1.81879i
$763$		0			0
$764$	13.4337			0.486014
$765$	−16.4814	−	8.01254i	−0.595888	−	0.289694i
$766$	9.78121	−	16.9416i	0.353410	−	0.612123i
$767$	−1.46481			−0.0528912
$768$	−2.01710	−	0.464331i	−0.0727860	−	0.0167551i
$769$	1.17360	−	2.03274i	0.0423212	−	0.0733025i	−0.844089	−	0.536203i	$-0.819858\pi$
$769$	1.17360	−	2.03274i	0.0423212	−	0.0733025i	0.886410	+	0.462901i	$0.153191\pi$
$770$		0			0
$771$	−2.43849	+	2.61831i	−0.0878201	+	0.0942960i
$772$	13.3637	−	23.1466i	0.480970	−	0.833064i
$773$	−18.1814	+	31.4912i	−0.653941	+	1.13266i	0.328217	+	0.944602i	$0.393552\pi$
$773$	−18.1814	+	31.4912i	−0.653941	+	1.13266i	−0.982158	+	0.188057i	$0.939781\pi$
$774$	−1.53977	−	21.6234i	−0.0553458	−	0.777239i
$775$	−2.48285	−	4.30042i	−0.0891866	−	0.154476i
$776$	−3.98251	−	6.89790i	−0.142964	−	0.247620i
$777$		0			0
$778$	29.3659	−	50.8633i	1.05282	−	1.82354i
$779$	20.9660			0.751185
$780$	19.4403	−	20.8738i	0.696073	−	0.747402i
$781$	10.7733			0.385497
$782$	−27.1292	−	46.9892i	−0.970139	−	1.68033i
$783$	−3.23875	+	20.7049i	−0.115744	+	0.739934i
$784$		0			0
$785$	−0.885235	−	1.53327i	−0.0315954	−	0.0547248i
$786$	0.197857	+	0.645689i	0.00705734	+	0.0230310i
$787$	15.8846	+	27.5129i	0.566224	+	0.980729i	0.996935	+	0.0782386i	$0.0249296\pi$
$787$	15.8846	+	27.5129i	0.566224	+	0.980729i	−0.430711	+	0.902490i	$0.641737\pi$
$788$	−4.53472	−	7.85437i	−0.161543	−	0.279800i
$789$	−11.9575	+	12.8393i	−0.425698	+	0.457090i
$790$	12.4435	+	21.5528i	0.442721	+	0.766816i
$791$		0			0
$792$	1.87032	+	26.2655i	0.0664589	+	0.933302i
$793$	24.5403	+	42.5050i	0.871451	+	1.50940i
$794$	64.2024			2.27846
$795$	4.59726	+	15.0027i	0.163048	+	0.532092i
$796$	30.3422			1.07545
$797$	−7.45306	+	12.9091i	−0.264001	+	0.457263i	−0.967301	−	0.253630i	$-0.918375\pi$
$797$	−7.45306	+	12.9091i	−0.264001	+	0.457263i	0.703301	+	0.710893i	$0.251709\pi$
$798$		0			0
$799$	7.59903	+	13.1619i	0.268834	+	0.465635i
$800$	−12.7608	−	22.1023i	−0.451162	−	0.781436i
$801$	−12.9107	+	8.73236i	−0.456178	+	0.308543i
$802$	37.3002	−	64.6059i	1.31712	−	2.28131i
$803$	−28.8937	+	50.0454i	−1.01964	+	1.76606i
$804$	−6.21123	−	20.2698i	−0.219053	−	0.714860i
$805$		0			0
$806$	−7.56059	+	13.0953i	−0.266311	+	0.461263i
$807$	7.66234	+	25.0054i	0.269727	+	0.880231i
$808$	0.00855418			0.000300935
$809$	−23.9018	+	41.3992i	−0.840344	+	1.45552i	0.0492597	+	0.998786i	$0.484314\pi$
$809$	−23.9018	+	41.3992i	−0.840344	+	1.45552i	−0.889604	+	0.456733i	$0.849020\pi$
$810$	9.24711	−	23.0565i	0.324910	−	0.810123i
$811$	−32.1131			−1.12764			−0.563821	−	0.825897i	$-0.690669\pi$
$811$	−32.1131			−1.12764			−0.563821	+	0.825897i	$0.690669\pi$
$812$		0			0
$813$	−48.6203	−	11.1922i	−1.70519	−	0.392529i
$814$	−22.8673			−0.801500
$815$	12.0879	+	20.9368i	0.423420	+	0.733385i
$816$	16.1387	+	3.71509i	0.564969	+	0.130054i
$817$	−8.93366	+	15.4735i	−0.312549	+	0.541351i
$818$	23.9057			0.835843
$819$		0			0
$820$	13.5215			0.472190
$821$	−23.5535	+	40.7958i	−0.822023	+	1.42378i	0.0821512	+	0.996620i	$0.473821\pi$
$821$	−23.5535	+	40.7958i	−0.822023	+	1.42378i	−0.904174	+	0.427165i	$0.859512\pi$
$822$	−3.48110	−	11.3602i	−0.121417	−	0.396234i
$823$	−16.8955	−	29.2639i	−0.588941	−	1.02008i	−0.994372	−	0.105950i	$-0.966212\pi$
$823$	−16.8955	−	29.2639i	−0.588941	−	1.02008i	0.405431	−	0.914126i	$-0.367122\pi$
$824$	20.8881			0.727670
$825$	−21.9281	+	23.5450i	−0.763437	+	0.819733i
$826$		0			0
$827$	2.98023			0.103633			0.0518164	−	0.998657i	$-0.483499\pi$
$827$	2.98023			0.103633			0.0518164	+	0.998657i	$0.483499\pi$
$828$	35.1974	−	23.8063i	1.22319	−	0.827325i
$829$	−3.03978	+	5.26506i	−0.105576	+	0.182863i	−0.913973	−	0.405774i	$-0.867002\pi$
$829$	−3.03978	+	5.26506i	−0.105576	+	0.182863i	0.808397	+	0.588637i	$0.200335\pi$
$830$	28.0448			0.973450
$831$	3.18678	−	3.42177i	0.110548	−	0.118700i
$832$	−29.4379	+	50.9880i	−1.02058	+	1.76769i
$833$		0			0
$834$	−69.2700	−	15.9457i	−2.39862	−	0.552155i
$835$	1.10595	−	1.91557i	0.0382731	−	0.0662909i
$836$	40.3260	−	69.8467i	1.39471	−	2.41570i
$837$	−1.17580	+	7.51673i	−0.0406416	+	0.259816i
$838$	−7.25163	−	12.5602i	−0.250503	−	0.433885i
$839$	1.85858	+	3.21915i	0.0641653	+	0.111138i	0.896323	−	0.443401i	$-0.146228\pi$
$839$	1.85858	+	3.21915i	0.0641653	+	0.111138i	−0.832158	+	0.554538i	$0.812895\pi$
$840$		0			0
$841$	6.36697	−	11.0279i	0.219551	−	0.380273i
$842$	74.1817			2.55647
$843$	8.31505	+	1.91410i	0.286385	+	0.0659250i
$844$	20.0364			0.689681
$845$	−6.03604	−	10.4547i	−0.207646	−	0.359653i
$846$	−17.0649	+	11.5421i	−0.586705	+	0.396827i
$847$		0			0
$848$	−7.08999	−	12.2802i	−0.243471	−	0.421705i
$849$	6.04536	+	1.39162i	0.207476	+	0.0477604i
$850$	−17.7747	−	30.7866i	−0.609666	−	1.05597i
$851$	4.96496	+	8.59957i	0.170197	+	0.294789i
$852$	−9.08437	−	2.09119i	−0.311225	−	0.0716431i
$853$	−0.553861	−	0.959315i	−0.0189638	−	0.0328463i	0.856388	−	0.516333i	$-0.172703\pi$
$853$	−0.553861	−	0.959315i	−0.0189638	−	0.0328463i	−0.875352	+	0.483487i	$0.839370\pi$
$854$		0			0
$855$	−16.9597	+	11.4709i	−0.580009	+	0.392298i
$856$	−7.54899	−	13.0752i	−0.258019	−	0.446902i
$857$	−38.5195			−1.31580			−0.657900	−	0.753105i	$-0.728555\pi$
$857$	−38.5195			−1.31580			−0.657900	+	0.753105i	$0.728555\pi$
$858$	95.4788	+	21.9789i	3.25959	+	0.750348i
$859$	−34.8874			−1.19034			−0.595171	−	0.803599i	$-0.702916\pi$
$859$	−34.8874			−1.19034			−0.595171	+	0.803599i	$0.702916\pi$
$860$	−5.76153	+	9.97926i	−0.196467	+	0.340290i
$861$		0			0
$862$	−2.45857	−	4.25836i	−0.0837391	−	0.145040i
$863$	−1.07924	−	1.86931i	−0.0367379	−	0.0636319i	0.847072	−	0.531478i	$-0.178363\pi$
$863$	−1.07924	−	1.86931i	−0.0367379	−	0.0636319i	−0.883810	+	0.467847i	$0.845030\pi$
$864$	−6.04310	+	38.6328i	−0.205591	+	1.31431i
$865$	6.38957	−	11.0671i	0.217252	−	0.376291i
$866$	−37.4221	+	64.8169i	−1.27165	+	2.20257i
$867$	10.4617	+	2.40826i	0.355299	+	0.0817888i
$868$		0			0
$869$	−24.6930	+	42.7695i	−0.837652	+	1.45086i
$870$	13.1410	−	14.1100i	0.445520	−	0.478373i
$871$	−21.2264			−0.719231
$872$	−13.5332	+	23.4401i	−0.458291	+	0.793783i
$873$	−12.3514	+	8.35403i	−0.418030	+	0.282741i
$874$	−60.6205			−2.05052
$875$		0			0
$876$	34.0785	−	36.5914i	1.15140	−	1.23631i
$877$	18.8790			0.637499			0.318749	−	0.947839i	$-0.396737\pi$
$877$	18.8790			0.637499			0.318749	+	0.947839i	$0.396737\pi$
$878$	−6.51956	−	11.2922i	−0.220025	−	0.381094i
$879$	12.3774	+	40.3926i	0.417480	+	1.36241i
$880$	−6.89530	+	11.9430i	−0.232440	+	0.402599i
$881$	−18.7203			−0.630704			−0.315352	−	0.948975i	$-0.602123\pi$
$881$	−18.7203			−0.630704			−0.315352	+	0.948975i	$0.602123\pi$
$882$		0			0
$883$	−13.3717			−0.449993			−0.224996	−	0.974360i	$-0.572237\pi$
$883$	−13.3717			−0.449993			−0.224996	+	0.974360i	$0.572237\pi$
$884$	−31.2704	+	54.1618i	−1.05174	+	1.82166i
$885$	0.660814	+	0.152117i	0.0222130	+	0.00511336i
$886$	42.9147	+	74.3305i	1.44175	+	2.49718i
$887$	41.2568			1.38527			0.692633	−	0.721290i	$-0.256450\pi$
$887$	41.2568			1.38527			0.692633	+	0.721290i	$0.256450\pi$
$888$	5.18880	+	1.19445i	0.174125	+	0.0400830i
$889$		0			0
$890$	14.3406			0.480699
$891$	48.7986	−	6.98515i	1.63481	−	0.234011i
$892$	5.54832	−	9.60997i	0.185772	−	0.321766i
$893$	16.9801			0.568218
$894$	23.4948	+	76.6731i	0.785783	+	2.56433i
$895$	11.7585	−	20.3664i	0.393045	−	0.680774i
$896$		0			0
$897$	−12.4649	−	40.6782i	−0.416192	−	1.35820i
$898$	−2.66698	+	4.61934i	−0.0889982	+	0.154149i
$899$	−2.95262	+	5.11408i	−0.0984753	+	0.170564i
$900$	23.0608	−	15.5975i	0.768693	−	0.519917i
$901$	−17.2019	−	29.7945i	−0.573078	−	0.992599i
$902$	23.2219	+	40.2215i	0.773204	+	1.33923i
$903$		0			0
$904$	−4.92463	+	8.52971i	−0.163791	+	0.283694i
$905$	−11.1734			−0.371416
$906$	−7.03011	−	22.9421i	−0.233560	−	0.762201i
$907$	3.69037			0.122537			0.0612684	−	0.998121i	$-0.480485\pi$
$907$	3.69037			0.122537			0.0612684	+	0.998121i	$0.480485\pi$
$908$	−1.82537	−	3.16163i	−0.0605770	−	0.104922i
$909$	−0.00113747	−	0.0159738i	−3.77274e−5	−	0.000529818i
$910$		0			0
$911$	−3.43831	−	5.95533i	−0.113916	−	0.197309i	0.803430	−	0.595400i	$-0.203006\pi$
$911$	−3.43831	−	5.95533i	−0.113916	−	0.197309i	−0.917346	+	0.398091i	$0.869673\pi$
$912$	12.6102	−	13.5400i	0.417564	−	0.448356i
$913$	27.8261	+	48.1962i	0.920909	+	1.59506i
$914$	−11.9927	−	20.7720i	−0.396685	−	0.687078i
$915$	−6.65671	−	21.7236i	−0.220064	−	0.718160i
$916$	21.8860	+	37.9077i	0.723135	+	1.25251i
$917$		0			0
$918$	−8.41751	+	53.8120i	−0.277819	+	1.77606i
$919$	−18.6473	−	32.2981i	−0.615119	−	1.06542i	−0.990364	−	0.138491i	$-0.955775\pi$
$919$	−18.6473	−	32.2981i	−0.615119	−	1.06542i	0.375245	−	0.926926i	$-0.377559\pi$
$920$	−10.5204			−0.346847
$921$	28.2156	−	30.2963i	0.929737	−	0.998296i
$922$	−63.7832			−2.10059
$923$	−4.66677	+	8.08309i	−0.153609	+	0.266058i
$924$		0			0
$925$	3.25297	+	5.63431i	0.106957	+	0.185255i
$926$	1.29178	+	2.23743i	0.0424506	+	0.0735267i
$927$	−2.77753	−	39.0057i	−0.0912261	−	1.28112i
$928$	−15.1752	+	26.2842i	−0.498150	+	0.862821i
$929$	8.98933	−	15.5700i	0.294930	−	0.510834i	−0.680038	−	0.733177i	$-0.738037\pi$
$929$	8.98933	−	15.5700i	0.294930	−	0.510834i	0.974969	+	0.222342i	$0.0713702\pi$
$930$	4.77070	−	5.12250i	0.156438	−	0.167973i
$931$		0			0
$932$	−11.1243	+	19.2679i	−0.364389	+	0.631141i
$933$	−21.8443	−	5.02848i	−0.715149	−	0.164625i
$934$	48.1284			1.57481
$935$	−16.7295	+	28.9764i	−0.547113	+	0.947628i
$936$	−20.5170	−	9.97442i	−0.670617	−	0.326024i
$937$	34.7312			1.13462			0.567310	−	0.823504i	$-0.307984\pi$
$937$	34.7312			1.13462			0.567310	+	0.823504i	$0.307984\pi$
$938$		0			0
$939$	13.6344	+	44.4947i	0.444943	+	1.45203i
$940$	10.9509			0.357178
$941$	−21.6512	−	37.5010i	−0.705810	−	1.22250i	−0.966398	−	0.257049i	$-0.917250\pi$
$941$	−21.6512	−	37.5010i	−0.705810	−	1.22250i	0.260588	−	0.965450i	$-0.416083\pi$
$942$	−3.58623	+	3.85068i	−0.116846	+	0.125462i
$943$	10.0839	−	17.4658i	0.328376	−	0.568764i
$944$	−0.612785			−0.0199444
$945$		0			0
$946$	−39.5796			−1.28684
$947$	−19.1295	+	33.1333i	−0.621626	+	1.07669i	0.367557	+	0.930001i	$0.380194\pi$
$947$	−19.1295	+	33.1333i	−0.621626	+	1.07669i	−0.989183	+	0.146687i	$0.953139\pi$
$948$	29.1239	−	31.2715i	0.945901	−	1.01565i
$949$	−25.0325	−	43.3575i	−0.812588	−	1.40744i
$950$	−39.7176			−1.28861
$951$	−4.21784	−	13.7645i	−0.136773	−	0.446345i
$952$		0			0
$953$	−47.8757			−1.55085			−0.775423	−	0.631442i	$-0.782463\pi$
$953$	−47.8757			−1.55085			−0.775423	+	0.631442i	$0.782463\pi$
$954$	38.6298	−	26.1279i	1.25069	−	0.845920i
$955$	−3.11326	+	5.39233i	−0.100743	+	0.174492i
$956$	−60.4778			−1.95599
$957$	37.2871	+	8.58337i	1.20532	+	0.277461i
$958$	27.3593	−	47.3877i	0.883939	−	1.53103i
$959$		0			0
$960$	18.5752	−	19.9450i	0.599512	−	0.643721i
$961$	14.4281	−	24.9902i	0.465422	−	0.806134i
$962$	9.90570	−	17.1572i	0.319373	−	0.553170i
$963$	−23.4125	+	15.8354i	−0.754456	+	0.510288i
$964$	−37.7541	−	65.3920i	−1.21598	−	2.10613i
$965$	6.19407	+	10.7284i	0.199394	+	0.345361i
$966$		0			0
$967$	15.5575	−	26.9463i	0.500294	−	0.866535i	−0.499706	−	0.866195i	$-0.666559\pi$
$967$	15.5575	−	26.9463i	0.500294	−	0.866535i	1.00000		0.000339469i	$-0.000108056\pi$
$968$	30.4490			0.978668
$969$	30.5950	−	32.8511i	0.982854	−	1.05533i
$970$	13.7193			0.440501
$971$	−15.1312	−	26.2080i	−0.485583	−	0.841055i	0.514279	−	0.857623i	$-0.328059\pi$
$971$	−15.1312	−	26.2080i	−0.485583	−	0.841055i	−0.999863	+	0.0165676i	$0.994726\pi$
$972$	−42.5045	−	3.58216i	−1.36333	−	0.114898i
$973$		0			0
$974$	−14.7751	−	25.5911i	−0.473423	−	0.819993i
$975$	−8.16683	−	26.6517i	−0.261548	−	0.853538i
$976$	10.2661	+	17.7815i	0.328611	+	0.569170i
$977$	−19.1101	−	33.0996i	−0.611385	−	1.05895i	−0.991007	−	0.133808i	$-0.957279\pi$
$977$	−19.1101	−	33.0996i	−0.611385	−	1.05895i	0.379622	−	0.925142i	$-0.376054\pi$
$978$	48.9700	−	52.5810i	1.56589	−	1.68136i
$979$	14.2288	+	24.6450i	0.454754	+	0.787657i
$980$		0			0
$981$	45.5709	+	22.1545i	1.45497	+	0.707339i
$982$	15.7821	+	27.3354i	0.503627	+	0.872308i
$983$	37.3929			1.19265			0.596324	−	0.802744i	$-0.296628\pi$
$983$	37.3929			1.19265			0.596324	+	0.802744i	$0.296628\pi$
$984$	−3.16833	−	10.3396i	−0.101003	−	0.329613i
$985$	4.20369			0.133941
$986$	−21.1377	+	36.6116i	−0.673162	+	1.16595i
$987$		0			0
$988$	34.9370	+	60.5126i	1.11149	+	1.92516i
$989$	8.59353	+	14.8844i	0.273258	+	0.473297i
$990$	−40.7905	−	19.8305i	−1.29641	−	0.630256i
$991$	11.9299	−	20.6631i	0.378965	−	0.656386i	−0.611947	−	0.790899i	$-0.709613\pi$
$991$	11.9299	−	20.6631i	0.378965	−	0.656386i	0.990912	+	0.134512i	$0.0429468\pi$
$992$	−5.50921	+	9.54223i	−0.174918	+	0.302966i
$993$	−6.29136	−	20.5313i	−0.199650	−	0.651540i
$994$		0			0
$995$	−7.03180	+	12.1794i	−0.222923	+	0.386114i
$996$	−14.1085	−	46.0420i	−0.447046	−	1.45890i
$997$	−51.6826			−1.63681			−0.818403	−	0.574645i	$-0.805140\pi$
$997$	−51.6826			−1.63681			−0.818403	+	0.574645i	$0.805140\pi$
$998$	−15.2249	+	26.3703i	−0.481936	+	0.834738i
$999$	1.54050	−	9.84823i	0.0487394	−	0.311584i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.g.h.67.1		24
3.2	odd	2		1323.2.g.h.361.11		24
7.2	even	3		441.2.h.h.373.11		24
7.3	odd	6		441.2.f.h.148.1	✓	24
7.4	even	3		441.2.f.h.148.2	yes	24
7.5	odd	6		441.2.h.h.373.12		24
7.6	odd	2	inner	441.2.g.h.67.2		24
9.2	odd	6		1323.2.h.h.802.2		24
9.7	even	3		441.2.h.h.214.11		24
21.2	odd	6		1323.2.h.h.226.2		24
21.5	even	6		1323.2.h.h.226.1		24
21.11	odd	6		1323.2.f.h.442.12		24
21.17	even	6		1323.2.f.h.442.11		24
21.20	even	2		1323.2.g.h.361.12		24
63.2	odd	6		1323.2.g.h.667.11		24
63.4	even	3		3969.2.a.bh.1.12		12
63.11	odd	6		1323.2.f.h.883.12		24
63.16	even	3	inner	441.2.g.h.79.1		24
63.20	even	6		1323.2.h.h.802.1		24
63.25	even	3		441.2.f.h.295.2	yes	24
63.31	odd	6		3969.2.a.bh.1.11		12
63.32	odd	6		3969.2.a.bi.1.1		12
63.34	odd	6		441.2.h.h.214.12		24
63.38	even	6		1323.2.f.h.883.11		24
63.47	even	6		1323.2.g.h.667.12		24
63.52	odd	6		441.2.f.h.295.1	yes	24
63.59	even	6		3969.2.a.bi.1.2		12
63.61	odd	6	inner	441.2.g.h.79.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.1	✓	24	7.3	odd	6
441.2.f.h.148.2	yes	24	7.4	even	3
441.2.f.h.295.1	yes	24	63.52	odd	6
441.2.f.h.295.2	yes	24	63.25	even	3
441.2.g.h.67.1		24	1.1	even	1	trivial
441.2.g.h.67.2		24	7.6	odd	2	inner
441.2.g.h.79.1		24	63.16	even	3	inner
441.2.g.h.79.2		24	63.61	odd	6	inner
441.2.h.h.214.11		24	9.7	even	3
441.2.h.h.214.12		24	63.34	odd	6
441.2.h.h.373.11		24	7.2	even	3
441.2.h.h.373.12		24	7.5	odd	6
1323.2.f.h.442.11		24	21.17	even	6
1323.2.f.h.442.12		24	21.11	odd	6
1323.2.f.h.883.11		24	63.38	even	6
1323.2.f.h.883.12		24	63.11	odd	6
1323.2.g.h.361.11		24	3.2	odd	2
1323.2.g.h.361.12		24	21.20	even	2
1323.2.g.h.667.11		24	63.2	odd	6
1323.2.g.h.667.12		24	63.47	even	6
1323.2.h.h.226.1		24	21.5	even	6
1323.2.h.h.226.2		24	21.2	odd	6
1323.2.h.h.802.1		24	63.20	even	6
1323.2.h.h.802.2		24	9.2	odd	6
3969.2.a.bh.1.11		12	63.31	odd	6
3969.2.a.bh.1.12		12	63.4	even	3
3969.2.a.bi.1.1		12	63.32	odd	6
3969.2.a.bi.1.2		12	63.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.g (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.08816 + 1.88474i) q^{2} +(-1.18045 + 1.26749i) q^{3} +(-1.36816 - 2.36973i) q^{4} +1.26829 q^{5} +(-1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-0.213085 - 2.99242i) q^{9} +O(q^{10})\)	\(q+(-1.08816 + 1.88474i) q^{2} +(-1.18045 + 1.26749i) q^{3} +(-1.36816 - 2.36973i) q^{4} +1.26829 q^{5} +(-1.10439 - 3.60407i) q^{6} +1.60248 q^{8} +(-0.213085 - 2.99242i) q^{9} +(-1.38010 + 2.39040i) q^{10} -5.47733 q^{11} +(4.61867 + 1.06320i) q^{12} +(2.37268 - 4.10960i) q^{13} +(-1.49715 + 1.60755i) q^{15} +(0.992580 - 1.71920i) q^{16} +(2.40822 - 4.17116i) q^{17} +(5.87181 + 2.85461i) q^{18} +(-2.69059 - 4.66025i) q^{19} +(-1.73523 - 3.00550i) q^{20} +(5.96019 - 10.3233i) q^{22} -5.17631 q^{23} +(-1.89165 + 2.03114i) q^{24} -3.39144 q^{25} +(5.16368 + 8.94376i) q^{26} +(4.04442 + 3.26231i) q^{27} +(2.01656 + 3.49278i) q^{29} +(-1.40068 - 4.57100i) q^{30} +(0.732093 + 1.26802i) q^{31} +(3.76264 + 6.51709i) q^{32} +(6.46570 - 6.94249i) q^{33} +(5.24103 + 9.07773i) q^{34} +(-6.79970 + 4.59908i) q^{36} +(-0.959170 - 1.66133i) q^{37} +11.7111 q^{38} +(2.40807 + 7.85852i) q^{39} +2.03241 q^{40} +(-1.94808 + 3.37418i) q^{41} +(-1.66016 - 2.87549i) q^{43} +(7.49389 + 12.9798i) q^{44} +(-0.270254 - 3.79526i) q^{45} +(5.63263 - 9.75600i) q^{46} +(-1.57773 + 2.73271i) q^{47} +(1.00739 + 3.28752i) q^{48} +(3.69042 - 6.39199i) q^{50} +(2.44414 + 7.97624i) q^{51} -12.9849 q^{52} +(3.57149 - 6.18601i) q^{53} +(-10.5496 + 4.07277i) q^{54} -6.94684 q^{55} +(9.08294 + 2.09086i) q^{57} -8.77732 q^{58} +(-0.154341 - 0.267327i) q^{59} +(5.85781 + 1.34845i) q^{60} +(-5.17143 + 8.95719i) q^{61} -3.18652 q^{62} -12.4070 q^{64} +(3.00924 - 5.21216i) q^{65} +(6.04910 + 19.7407i) q^{66} +(-2.23655 - 3.87382i) q^{67} -13.1794 q^{68} +(6.11037 - 6.56095i) q^{69} -1.96688 q^{71} +(-0.341465 - 4.79530i) q^{72} +(5.27515 - 9.13683i) q^{73} +4.17491 q^{74} +(4.00342 - 4.29863i) q^{75} +(-7.36235 + 12.7520i) q^{76} +(-17.4316 - 4.01270i) q^{78} +(4.50822 - 7.80846i) q^{79} +(1.25888 - 2.18044i) q^{80} +(-8.90919 + 1.27528i) q^{81} +(-4.23963 - 7.34326i) q^{82} +(-5.08023 - 8.79921i) q^{83} +(3.05432 - 5.29023i) q^{85} +7.22607 q^{86} +(-6.80753 - 1.56707i) q^{87} -8.77732 q^{88} +(-2.59776 - 4.49945i) q^{89} +(7.44716 + 3.62047i) q^{90} +(7.08205 + 12.2665i) q^{92} +(-2.47141 - 0.568910i) q^{93} +(-3.43363 - 5.94722i) q^{94} +(-3.41245 - 5.91054i) q^{95} +(-12.7020 - 2.92396i) q^{96} +(-2.48521 - 4.30451i) q^{97} +(1.16714 + 16.3905i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} - 4 q^{9} - 40 q^{11} + 4 q^{15} - 12 q^{16} + 28 q^{18} - 64 q^{23} + 24 q^{25} + 16 q^{29} + 84 q^{30} + 48 q^{32} - 4 q^{36} - 12 q^{37} - 40 q^{39} + 56 q^{44} + 24 q^{46} - 4 q^{50} - 8 q^{51} + 32 q^{53} - 12 q^{57} + 56 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} - 168 q^{72} - 136 q^{74} - 60 q^{78} + 12 q^{79} - 40 q^{81} + 12 q^{85} - 152 q^{86} + 16 q^{92} + 112 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 - 4 * q^9 - 40 * q^11 + 4 * q^15 - 12 * q^16 + 28 * q^18 - 64 * q^23 + 24 * q^25 + 16 * q^29 + 84 * q^30 + 48 * q^32 - 4 * q^36 - 12 * q^37 - 40 * q^39 + 56 * q^44 + 24 * q^46 - 4 * q^50 - 8 * q^51 + 32 * q^53 - 12 * q^57 + 56 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 - 168 * q^72 - 136 * q^74 - 60 * q^78 + 12 * q^79 - 40 * q^81 + 12 * q^85 - 152 * q^86 + 16 * q^92 + 112 * q^93 + 64 * q^95 + 20 * q^99

Introduction

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