LMFDB - Embedded newform 441.2.g.h.79.2

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			79.2
Character	$\chi$	$=$	441.79
Dual form			441.2.g.h.67.2

$q$-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 $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−1.08816	−	1.88474i	−0.769442	−	1.33271i	−0.937866	−	0.346998i	$-0.887201\pi$
$2$	−1.08816	−	1.88474i	−0.769442	−	1.33271i	0.168424	−	0.985715i	$-0.446132\pi$
$3$	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	$-0.591528\pi$
$5$	−1.26829			−0.567196			−0.283598	+	0.958943i	$0.591528\pi$
$6$	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	−0.981117	−	0.193417i	$-0.938043\pi$
$13$	−2.37268	−	4.10960i	−0.658062	−	1.13980i	0.323054	−	0.946380i	$-0.395290\pi$
$14$		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	−0.994990	−	0.0999785i	$-0.968123\pi$
$17$	−2.40822	−	4.17116i	−0.584079	−	1.01165i	0.410911	−	0.911676i	$-0.365211\pi$
$18$	5.87181	−	2.85461i	1.38400	−	0.672838i
$19$	2.69059	−	4.66025i	0.617265	−	1.06913i	−0.372718	−	0.927945i	$-0.621574\pi$
$19$	2.69059	−	4.66025i	0.617265	−	1.06913i	0.989983	−	0.141189i	$-0.0450925\pi$
$20$	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	−0.615781	−	0.787917i	$-0.711159\pi$
$29$	2.01656	−	3.49278i	0.374466	−	0.648594i	0.990247	+	0.139324i	$0.0444928\pi$
$30$	−1.40068	+	4.57100i	−0.255729	+	0.834547i
$31$	−0.732093	+	1.26802i	−0.131488	+	0.227744i	−0.924250	−	0.381787i	$-0.875309\pi$
$31$	−0.732093	+	1.26802i	−0.131488	+	0.227744i	0.792763	+	0.609531i	$0.208642\pi$
$32$	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	−0.934034	−	0.357184i	$-0.883737\pi$
$37$	−0.959170	+	1.66133i	−0.157687	+	0.273121i	0.776347	+	0.630305i	$0.217070\pi$
$38$	−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	$-0.0682644\pi$
$41$	1.94808	+	3.37418i	0.304239	+	0.526958i	−0.672852	+	0.739777i	$0.734931\pi$
$42$		0			0
$43$	−1.66016	+	2.87549i	−0.253173	+	0.438508i	−0.964398	−	0.264457i	$-0.914807\pi$
$43$	−1.66016	+	2.87549i	−0.253173	+	0.438508i	0.711225	+	0.702964i	$0.248141\pi$
$44$	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	$-0.0927498\pi$
$47$	1.57773	+	2.73271i	0.230135	+	0.398606i	−0.727712	+	0.685882i	$0.759416\pi$
$48$	−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	0.999941	−	0.0108405i	$-0.00345071\pi$
$53$	3.57149	+	6.18601i	0.490582	+	0.849714i	−0.509359	+	0.860554i	$0.670117\pi$
$54$	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	$-0.826937\pi$
$59$	0.154341	−	0.267327i	0.0200935	−	0.0348030i	0.875897	+	0.482498i	$0.160270\pi$
$60$	5.85781	−	1.34845i	0.756240	−	0.174084i
$61$	5.17143	+	8.95719i	0.662134	+	1.14685i	0.980054	+	0.198732i	$0.0636825\pi$
$61$	5.17143	+	8.95719i	0.662134	+	1.14685i	−0.317920	+	0.948118i	$0.602984\pi$
$62$	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	−0.969689	−	0.244342i	$-0.921428\pi$
$67$	−2.23655	+	3.87382i	−0.273238	+	0.473262i	0.696451	+	0.717604i	$0.254761\pi$
$68$	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	−0.989957	−	0.141371i	$-0.954849\pi$
$73$	−5.27515	−	9.13683i	−0.617409	−	1.06938i	0.372547	−	0.928013i	$-0.378484\pi$
$74$	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	0.999965	+	0.00835000i	$0.00265792\pi$
$79$	4.50822	+	7.80846i	0.507214	+	0.878520i	−0.492751	+	0.870170i	$0.664009\pi$
$80$	−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	−0.440066	−	0.897965i	$-0.645045\pi$
$83$	5.08023	−	8.79921i	0.557627	−	0.965839i	0.997694	−	0.0678739i	$-0.0216216\pi$
$84$		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	$-0.744536\pi$
$89$	2.59776	−	4.49945i	0.275362	−	0.476941i	0.970226	+	0.242200i	$0.0778690\pi$
$90$	−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	$-0.752135\pi$
$97$	2.48521	−	4.30451i	0.252335	−	0.437057i	0.964168	+	0.265291i	$0.0854682\pi$
$98$		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	$-0.500085\pi$
$101$	−0.00533808			−0.000531159			−0.000265580		1.00000i	$0.500085\pi$
$102$	−17.6927	+	4.07281i	−1.75184	+	0.403268i
$103$	−13.0348			−1.28436			−0.642180	−	0.766554i	$-0.721970\pi$
$103$	−13.0348			−1.28436			−0.642180	+	0.766554i	$0.721970\pi$
$104$	−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	−0.998712	−	0.0507430i	$-0.983841\pi$
$107$	−4.71081	+	8.15936i	−0.455411	+	0.788795i	0.543301	+	0.839538i	$0.317174\pi$
$108$	−2.19738	−	14.0476i	−0.211443	−	1.35173i
$109$	−8.44513	−	14.6274i	−0.808896	−	1.40105i	−0.913629	−	0.406549i	$-0.866732\pi$
$109$	−8.44513	−	14.6274i	−0.808896	−	1.40105i	0.104732	−	0.994500i	$-0.466601\pi$
$110$	−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	0.684499	−	0.729014i	$-0.260021\pi$
$113$	−3.07313	−	5.32281i	−0.289095	−	0.500728i	−0.973594	+	0.228286i	$0.926688\pi$
$114$	−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	$-0.497509\pi$
$131$	0.179156			0.0156529			0.00782645	+	0.999969i	$0.497509\pi$
$132$	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	−0.919798	−	0.392392i	$-0.871648\pi$
$139$	−9.42857	−	16.3308i	−0.799721	−	1.38516i	0.120077	−	0.992765i	$-0.461686\pi$
$140$		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	$-0.815593\pi$
$157$	0.697976	−	1.20893i	0.0557045	−	0.0964830i	0.892533	+	0.450982i	$0.148926\pi$
$158$	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	−0.202969	−	0.979185i	$-0.565059\pi$
$163$	9.53086	−	16.5079i	0.746515	−	1.29300i	0.949484	−	0.313816i	$-0.101608\pi$
$164$	−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	$-0.188162\pi$
$167$	−0.872003	−	1.51035i	−0.0674776	−	0.116875i	−0.897790	+	0.440423i	$0.854828\pi$
$168$		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	$-0.291785\pi$
$173$	−5.03794	−	8.72598i	−0.383028	−	0.663424i	−0.991493	+	0.130157i	$0.958452\pi$
$174$	−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	0.970863	+	0.239634i	$0.0770275\pi$
$179$	9.27118	+	16.0582i	0.692961	+	1.20024i	−0.277902	+	0.960609i	$0.589639\pi$
$180$	8.62399	+	5.83297i	0.642794	+	0.434764i
$181$	8.80982			0.654829			0.327414	−	0.944881i	$-0.393823\pi$
$181$	8.80982			0.654829			0.327414	+	0.944881i	$0.393823\pi$
$182$		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	0.763448	−	0.645869i	$-0.223505\pi$
$191$	−2.45469	−	4.25165i	−0.177615	−	0.307639i	−0.941063	+	0.338231i	$0.890172\pi$
$192$	−14.6459	−	15.7259i	−1.05698	−	1.13492i
$193$	4.88380	−	8.45899i	0.351544	−	0.608892i	−0.634976	−	0.772531i	$-0.718990\pi$
$193$	4.88380	−	8.45899i	0.351544	−	0.608892i	0.986520	+	0.163640i	$0.0523235\pi$
$194$	−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	$-0.0380948\pi$
$199$	5.54432	+	9.60304i	0.393026	+	0.680742i	−0.599821	+	0.800134i	$0.704761\pi$
$200$	−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	0.712043	−	0.702136i	$-0.247770\pi$
$211$	−3.66118	−	6.34135i	−0.252046	−	0.436557i	−0.964089	+	0.265579i	$0.914437\pi$
$212$	−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	$-0.876688\pi$
$223$	−2.02765	+	3.51199i	−0.135782	+	0.235181i	0.790114	+	0.612960i	$0.210021\pi$
$224$		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	$-0.514098\pi$
$227$	−1.33417			−0.0885522			−0.0442761	+	0.999019i	$0.514098\pi$
$228$	−7.47218	+	24.3848i	−0.494857	+	1.61492i
$229$	15.9966			1.05709			0.528544	−	0.848906i	$-0.322738\pi$
$229$	15.9966			1.05709			0.528544	+	0.848906i	$0.322738\pi$
$230$	−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	−0.967912	−	0.251288i	$-0.919146\pi$
$233$	−4.06542	+	7.04151i	−0.266334	+	0.461305i	0.701578	+	0.712593i	$0.252479\pi$
$234$	−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	0.963028	+	0.269403i	$0.0868262\pi$
$239$	11.0509	+	19.1407i	0.714823	+	1.23811i	−0.248204	+	0.968708i	$0.579840\pi$
$240$	1.27766	−	4.16952i	0.0824725	−	0.269141i
$241$	−27.5947			−1.77753			−0.888765	−	0.458362i	$-0.848436\pi$
$241$	−27.5947			−1.77753			−0.888765	+	0.458362i	$0.848436\pi$
$242$	−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	$-0.324939\pi$
$251$	16.5610			1.04532			0.522661	+	0.852541i	$0.324939\pi$
$252$		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	$-0.520522\pi$
$257$	−2.06573			−0.128857			−0.0644285	+	0.997922i	$0.520522\pi$
$258$	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	$-0.318930\pi$
$269$	−7.54972	−	13.0765i	−0.460315	−	0.797289i	−0.998976	+	0.0452336i	$0.985597\pi$
$270$	−13.3799	−	5.16545i	−0.814275	−	0.314359i
$271$	−14.4026	+	24.9459i	−0.874893	+	1.51536i	−0.0180156	+	0.999838i	$0.505735\pi$
$271$	−14.4026	+	24.9459i	−0.874893	+	1.51536i	−0.856877	+	0.515521i	$0.827598\pi$
$272$	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	−0.930094	−	0.367321i	$-0.880275\pi$
$281$	−2.46312	+	4.26626i	−0.146938	+	0.254503i	0.783157	+	0.621825i	$0.213608\pi$
$282$	11.5913	−	2.66828i	0.690251	−	0.158894i
$283$	1.79079	−	3.10173i	0.106451	−	0.184379i	−0.807879	−	0.589348i	$-0.799385\pi$
$283$	1.79079	−	3.10173i	0.106451	−	0.184379i	0.914330	+	0.404969i	$0.132718\pi$
$284$	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	−0.963928	−	0.266164i	$-0.914244\pi$
$293$	−12.1955	−	21.1232i	−0.712469	−	1.23403i	0.251459	−	0.967868i	$-0.419090\pi$
$294$		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	$-0.261070\pi$
$307$	23.9025			1.36419			0.682094	+	0.731265i	$0.261070\pi$
$308$		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	$-0.952923\pi$
$311$	−6.47082	+	11.2078i	−0.366926	+	0.635535i	0.622157	+	0.782893i	$0.286257\pi$
$312$	3.85889	−	12.5931i	0.218467	−	0.712946i
$313$	−13.4340	−	23.2684i	−0.759336	−	1.31521i	−0.943189	−	0.332255i	$-0.892190\pi$
$313$	−13.4340	−	23.2684i	−0.759336	−	1.31521i	0.183853	−	0.982954i	$-0.441143\pi$
$314$	−3.03802			−0.171446
$315$		0			0
$316$	−24.6719			−1.38790
$317$	−4.15584	−	7.19813i	−0.233415	−	0.404287i	0.725396	−	0.688332i	$-0.241657\pi$
$317$	−4.15584	−	7.19813i	−0.233415	−	0.404287i	−0.958811	+	0.284045i	$0.908324\pi$
$318$	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	0.643845	−	0.765156i	$-0.277338\pi$
$331$	−6.19889	−	10.7368i	−0.340722	−	0.590147i	−0.984567	+	0.175009i	$0.944005\pi$
$332$	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	−0.966361	−	0.257189i	$-0.917204\pi$
$337$	−12.9588	−	22.4454i	−0.705913	−	1.22268i	0.260448	−	0.965488i	$-0.416130\pi$
$338$	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	−0.546292	−	0.837595i	$-0.683961\pi$
$347$	8.42415	−	14.5911i	0.452232	−	0.783289i	0.998524	+	0.0543058i	$0.0172946\pi$
$348$	−5.60028	+	18.2760i	−0.300207	+	0.979698i
$349$	−15.5503	+	26.9340i	−0.832390	+	1.44174i	0.0637477	+	0.997966i	$0.479695\pi$
$349$	−15.5503	+	26.9340i	−0.832390	+	1.44174i	−0.896138	+	0.443776i	$0.853639\pi$
$350$		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	$-0.522546\pi$
$353$	−2.65938			−0.141544			−0.0707722	+	0.997493i	$0.522546\pi$
$354$	−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	−0.0143230	−	0.999897i	$-0.504559\pi$
$359$	16.2715	−	28.1830i	0.858775	−	1.48744i	0.873098	−	0.487545i	$-0.162107\pi$
$360$	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	$-0.620438\pi$
$367$	−14.1536			−0.738809			−0.369405	+	0.929269i	$0.620438\pi$
$368$	−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	$-0.426241\pi$
$383$	8.98880			0.459306			0.229653	+	0.973273i	$0.426241\pi$
$384$	−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	−0.212066	−	0.977255i	$-0.568019\pi$
$397$	14.7503	−	25.5482i	0.740295	−	1.28223i	0.952361	−	0.304973i	$-0.0986475\pi$
$398$	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	$-0.745789\pi$
$409$	5.49225	−	9.51286i	0.271574	−	0.470381i	0.969265	+	0.246018i	$0.0791224\pi$
$410$	−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	$-0.114620\pi$
$419$	3.33207	+	5.77132i	0.162782	+	0.281947i	−0.773083	+	0.634305i	$0.781286\pi$
$420$		0			0
$421$	−17.0430	+	29.5193i	−0.830625	+	1.43868i	0.0669186	+	0.997758i	$0.478683\pi$
$421$	−17.0430	+	29.5193i	−0.830625	+	1.43868i	−0.897543	+	0.440926i	$0.854650\pi$
$422$	−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	0.837535	−	0.546384i	$-0.183996\pi$
$431$	−1.12969	−	1.95669i	−0.0544155	−	0.0942504i	−0.891950	+	0.452134i	$0.850663\pi$
$432$	−9.62298	−	3.71505i	−0.462986	−	0.178740i
$433$	−34.3904			−1.65270			−0.826348	−	0.563160i	$-0.809585\pi$
$433$	−34.3904			−1.65270			−0.826348	+	0.563160i	$0.809585\pi$
$434$		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	$-0.120999\pi$
$439$	2.99569	+	5.18869i	0.142977	+	0.247643i	−0.785640	+	0.618684i	$0.787666\pi$
$440$	11.1322			0.530706
$441$		0			0
$442$	49.7411			2.36594
$443$	19.7190	+	34.1543i	0.936879	+	1.62272i	0.771249	+	0.636534i	$0.219632\pi$
$443$	19.7190	+	34.1543i	0.936879	+	1.62272i	0.165630	+	0.986188i	$0.447034\pi$
$444$	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	0.707871	−	0.706342i	$-0.249656\pi$
$457$	−5.51058	−	9.54461i	−0.257774	−	0.446478i	−0.965645	+	0.259864i	$0.916322\pi$
$458$	−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	0.291711	+	0.956506i	$0.405775\pi$
$461$	−14.6540	+	25.3814i	−0.682503	+	1.18213i	−0.974215	+	0.225624i	$0.927558\pi$
$462$		0			0
$463$	0.593566	+	1.02809i	0.0275853	+	0.0477792i	0.879489	−	0.475920i	$-0.157885\pi$
$463$	0.593566	+	1.02809i	0.0275853	+	0.0477792i	−0.851903	+	0.523699i	$0.824552\pi$
$464$	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	−0.488236	−	0.872712i	$-0.662359\pi$
$467$	11.0573	−	19.1519i	0.511673	−	0.886243i	0.999908	−	0.0135313i	$-0.00430729\pi$
$468$	−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	$-0.305234\pi$
$479$	25.1428			1.14880			0.574402	+	0.818573i	$0.305234\pi$
$480$	−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	0.670205	−	0.742176i	$-0.266206\pi$
$487$	−6.78904	−	11.7590i	−0.307641	−	0.532849i	−0.977846	+	0.209327i	$0.932873\pi$
$488$	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	0.981969	−	0.189044i	$-0.0605387\pi$
$491$	7.25177	+	12.5604i	0.327268	+	0.566844i	−0.654701	+	0.755888i	$0.727205\pi$
$492$	−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	$-0.718247\pi$
$503$	−28.4011			−1.26634			−0.633171	+	0.774012i	$0.718247\pi$
$504$		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	$-0.475568\pi$
$509$	3.45993			0.153359			0.0766794	+	0.997056i	$0.475568\pi$
$510$	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	$-0.116705\pi$
$521$	3.56797	+	6.17991i	0.156316	+	0.270747i	−0.777222	+	0.629227i	$0.783372\pi$
$522$	1.87032	−	26.2655i	0.0818616	−	1.14961i
$523$	−6.53235	+	11.3144i	−0.285640	+	0.494743i	−0.972764	−	0.231797i	$-0.925539\pi$
$523$	−6.53235	+	11.3144i	−0.285640	+	0.494743i	0.687124	+	0.726540i	$0.258873\pi$
$524$	−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	−0.914188	−	0.405290i	$-0.867171\pi$
$541$	−2.46788	+	4.27450i	−0.106103	+	0.183775i	0.808086	+	0.589065i	$0.200504\pi$
$542$	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	−0.853806	−	0.520591i	$-0.825712\pi$
$547$	0.559964	−	0.969887i	0.0239423	−	0.0414694i	0.877748	+	0.479122i	$0.159045\pi$
$548$	−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	0.958433	−	0.285318i	$-0.0920992\pi$
$557$	5.47832	+	9.48873i	0.232124	+	0.402050i	−0.726309	+	0.687368i	$0.758766\pi$
$558$	−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	$-0.865322\pi$
$563$	−2.38048	+	4.12311i	−0.100325	+	0.173768i	0.811493	+	0.584361i	$0.198655\pi$
$564$	−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	0.827013	−	0.562183i	$-0.190038\pi$
$569$	−1.74988	−	3.03088i	−0.0733588	−	0.127061i	−0.900371	+	0.435122i	$0.856705\pi$
$570$	17.5333	+	18.8262i	0.734390	+	0.788545i
$571$	−3.53051	+	6.11501i	−0.147747	+	0.255905i	−0.930394	−	0.366560i	$-0.880535\pi$
$571$	−3.53051	+	6.11501i	−0.147747	+	0.255905i	0.782647	+	0.622465i	$0.213869\pi$
$572$	−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	$-0.0802502\pi$
$577$	6.44149	+	11.1570i	0.268163	+	0.464472i	−0.700225	+	0.713923i	$0.746917\pi$
$578$	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	−0.111235	−	0.993794i	$-0.535481\pi$
$587$	19.5044	−	33.7826i	0.805034	−	1.39436i	0.916268	−	0.400565i	$-0.131186\pi$
$588$		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	−0.0724676	−	0.997371i	$-0.523087\pi$
$593$	20.1513	−	34.9031i	0.827515	−	1.43330i	0.899982	−	0.435927i	$-0.143579\pi$
$594$	−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	−0.705412	−	0.708797i	$-0.749238\pi$
$599$	6.39103	−	11.0696i	0.261130	−	0.452291i	0.966543	+	0.256506i	$0.0825715\pi$
$600$	−6.41541	−	6.88848i	−0.261908	−	0.281221i
$601$	4.86311	−	8.42316i	0.198371	−	0.343588i	−0.749630	−	0.661858i	$-0.769768\pi$
$601$	4.86311	−	8.42316i	0.198371	−	0.343588i	0.948000	+	0.318270i	$0.103102\pi$
$602$		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	$-0.818598\pi$
$607$	−41.4873			−1.68392			−0.841959	+	0.539541i	$0.818598\pi$
$608$	−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	0.669228	−	0.743057i	$-0.266625\pi$
$613$	−7.64783	−	13.2464i	−0.308893	−	0.535018i	−0.978120	+	0.208039i	$0.933292\pi$
$614$	−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	0.807367	−	0.590049i	$-0.200892\pi$
$617$	−2.66563	−	4.61700i	−0.107314	−	0.185873i	−0.914681	+	0.404176i	$0.867558\pi$
$618$	−14.3955	+	46.9784i	−0.579072	+	1.88975i
$619$	12.6841			0.509817			0.254908	−	0.966965i	$-0.417955\pi$
$619$	12.6841			0.509817			0.254908	+	0.966965i	$0.417955\pi$
$620$	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	0.794180	+	0.607682i	$0.207900\pi$
$643$	23.4140	+	40.5542i	0.923358	+	1.59930i	0.129178	+	0.991621i	$0.458766\pi$
$644$		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	−0.937900	−	0.346905i	$-0.887233\pi$
$647$	−19.5701	−	33.8964i	−0.769379	−	1.33260i	0.168521	−	0.985698i	$-0.446101\pi$
$648$	−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	−0.791238	−	0.611508i	$-0.790563\pi$
$659$	3.43895	−	5.95643i	0.133962	−	0.232030i	0.925201	+	0.379478i	$0.123897\pi$
$660$	−32.0852	+	7.38590i	−1.24891	+	0.287496i
$661$	19.3835	−	33.5733i	0.753932	−	1.30585i	−0.191971	−	0.981401i	$-0.561488\pi$
$661$	19.3835	−	33.5733i	0.753932	−	1.30585i	0.945903	−	0.324449i	$-0.105179\pi$
$662$	−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	−0.277248	−	0.960798i	$-0.589422\pi$
$673$	17.9897	−	31.1591i	0.693452	−	1.20109i	0.970700	−	0.240295i	$-0.0772443\pi$
$674$	−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	$-0.139312\pi$
$677$	2.23329	+	3.86817i	0.0858322	+	0.148666i	−0.819913	+	0.572488i	$0.805978\pi$
$678$	−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	0.999929	+	0.0119046i	$0.00378945\pi$
$683$	13.3356	+	23.0980i	0.510274	+	0.883821i	−0.489655	+	0.871916i	$0.662877\pi$
$684$	−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	−0.931538	−	0.363644i	$-0.881532\pi$
$691$	−20.5220	−	35.5452i	−0.780694	−	1.35220i	0.150844	−	0.988558i	$-0.451801\pi$
$692$	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	0.945402	−	0.325907i	$-0.105670\pi$
$709$	5.07131	+	8.78376i	0.190457	+	0.329881i	−0.754945	+	0.655788i	$0.772336\pi$
$710$	−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	0.165400	+	0.986227i	$0.447109\pi$
$719$	−20.6844	+	35.8264i	−0.771397	+	1.33610i	−0.936797	+	0.349873i	$0.886225\pi$
$720$	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	$-0.775599\pi$
$727$	4.86372	−	8.42422i	0.180386	−	0.312437i	0.942012	+	0.335580i	$0.108932\pi$
$728$		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	$-0.679282\pi$
$733$	−28.9108			−1.06784			−0.533922	+	0.845534i	$0.679282\pi$
$734$	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	0.962281	−	0.272058i	$-0.0877041\pi$
$739$	6.67467	+	11.5609i	0.245532	+	0.425273i	−0.716749	+	0.697331i	$0.754371\pi$
$740$	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	0.956702	+	0.291071i	$0.0940115\pi$
$743$	19.9100	+	34.4851i	0.730425	+	1.26513i	−0.226276	+	0.974063i	$0.572655\pi$
$744$	−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	$-0.897419\pi$
$761$	−52.3321			−1.89704			−0.948519	+	0.316719i	$0.897419\pi$
$762$	−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	$-0.180142\pi$
$769$	−1.17360	−	2.03274i	−0.0423212	−	0.0733025i	−0.886410	+	0.462901i	$0.846809\pi$
$770$		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	0.982158	+	0.188057i	$0.0602189\pi$
$773$	18.1814	+	31.4912i	0.653941	+	1.13266i	−0.328217	+	0.944602i	$0.606448\pi$
$774$	−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	0.430711	+	0.902490i	$0.358263\pi$
$787$	−15.8846	+	27.5129i	−0.566224	+	0.980729i	−0.996935	+	0.0782386i	$0.975070\pi$
$788$	−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	$-0.0816245\pi$
$797$	7.45306	+	12.9091i	0.264001	+	0.457263i	−0.703301	+	0.710893i	$0.748291\pi$
$798$		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	−0.889604	−	0.456733i	$-0.849020\pi$
$809$	−23.9018	−	41.3992i	−0.840344	−	1.45552i	0.0492597	−	0.998786i	$-0.484314\pi$
$810$	−9.24711	−	23.0565i	−0.324910	−	0.810123i
$811$	32.1131			1.12764			0.563821	−	0.825897i	$-0.309331\pi$
$811$	32.1131			1.12764			0.563821	+	0.825897i	$0.309331\pi$
$812$		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	−0.904174	−	0.427165i	$-0.859512\pi$
$821$	−23.5535	−	40.7958i	−0.822023	−	1.42378i	0.0821512	−	0.996620i	$-0.473821\pi$
$822$	3.48110	−	11.3602i	0.121417	−	0.396234i
$823$	−16.8955	+	29.2639i	−0.588941	+	1.02008i	0.405431	+	0.914126i	$0.367122\pi$
$823$	−16.8955	+	29.2639i	−0.588941	+	1.02008i	−0.994372	+	0.105950i	$0.966212\pi$
$824$	−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	$-0.132998\pi$
$829$	3.03978	+	5.26506i	0.105576	+	0.182863i	−0.808397	+	0.588637i	$0.799665\pi$
$830$	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	$-0.853772\pi$
$839$	−1.85858	+	3.21915i	−0.0641653	+	0.111138i	0.832158	+	0.554538i	$0.187105\pi$
$840$		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	$-0.827297\pi$
$853$	0.553861	−	0.959315i	0.0189638	−	0.0328463i	0.875352	+	0.483487i	$0.160630\pi$
$854$		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	$-0.271445\pi$
$857$	38.5195			1.31580			0.657900	+	0.753105i	$0.271445\pi$
$858$	95.4788	−	21.9789i	3.25959	−	0.750348i
$859$	34.8874			1.19034			0.595171	−	0.803599i	$-0.297084\pi$
$859$	34.8874			1.19034			0.595171	+	0.803599i	$0.297084\pi$
$860$	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	−0.883810	−	0.467847i	$-0.845030\pi$
$863$	−1.07924	+	1.86931i	−0.0367379	+	0.0636319i	0.847072	+	0.531478i	$0.178363\pi$
$864$	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	$-0.397877\pi$
$881$	18.7203			0.630704			0.315352	+	0.948975i	$0.397877\pi$
$882$		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	$-0.743550\pi$
$887$	−41.2568			−1.38527			−0.692633	+	0.721290i	$0.743550\pi$
$888$	−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	−0.917346	−	0.398091i	$-0.869673\pi$
$911$	−3.43831	+	5.95533i	−0.113916	+	0.197309i	0.803430	+	0.595400i	$0.203006\pi$
$912$	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	0.375245	+	0.926926i	$0.377559\pi$
$919$	−18.6473	+	32.2981i	−0.615119	+	1.06542i	−0.990364	+	0.138491i	$0.955775\pi$
$920$	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	$-0.261963\pi$
$929$	−8.98933	−	15.5700i	−0.294930	−	0.510834i	−0.974969	+	0.222342i	$0.928630\pi$
$930$	−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	$-0.692016\pi$
$937$	−34.7312			−1.13462			−0.567310	+	0.823504i	$0.692016\pi$
$938$		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	−0.260588	−	0.965450i	$-0.583917\pi$
$941$	21.6512	−	37.5010i	0.705810	−	1.22250i	0.966398	−	0.257049i	$-0.0827501\pi$
$942$	−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	−0.989183	−	0.146687i	$-0.953139\pi$
$947$	−19.1295	−	33.1333i	−0.621626	−	1.07669i	0.367557	−	0.930001i	$-0.380194\pi$
$948$	−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	1.00000		0.000339469i	$0.000108056\pi$
$967$	15.5575	+	26.9463i	0.500294	+	0.866535i	−0.499706	+	0.866195i	$0.666559\pi$
$968$	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	$-0.671941\pi$
$971$	15.1312	−	26.2080i	0.485583	−	0.841055i	0.999863	+	0.0165676i	$0.00527387\pi$
$972$	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	0.379622	+	0.925142i	$0.376054\pi$
$977$	−19.1101	+	33.0996i	−0.611385	+	1.05895i	−0.991007	+	0.133808i	$0.957279\pi$
$978$	−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	$-0.703372\pi$
$983$	−37.3929			−1.19265			−0.596324	+	0.802744i	$0.703372\pi$
$984$	−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	0.990912	−	0.134512i	$-0.0429468\pi$
$991$	11.9299	+	20.6631i	0.378965	+	0.656386i	−0.611947	+	0.790899i	$0.709613\pi$
$992$	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	$-0.194860\pi$
$997$	51.6826			1.63681			0.818403	+	0.574645i	$0.194860\pi$
$998$	−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.79.2		24
3.2	odd	2		1323.2.g.h.667.12		24
7.2	even	3		441.2.f.h.295.1	yes	24
7.3	odd	6		441.2.h.h.214.11		24
7.4	even	3		441.2.h.h.214.12		24
7.5	odd	6		441.2.f.h.295.2	yes	24
7.6	odd	2	inner	441.2.g.h.79.1		24
9.4	even	3		441.2.h.h.373.12		24
9.5	odd	6		1323.2.h.h.226.1		24
21.2	odd	6		1323.2.f.h.883.11		24
21.5	even	6		1323.2.f.h.883.12		24
21.11	odd	6		1323.2.h.h.802.1		24
21.17	even	6		1323.2.h.h.802.2		24
21.20	even	2		1323.2.g.h.667.11		24
63.2	odd	6		3969.2.a.bi.1.2		12
63.4	even	3	inner	441.2.g.h.67.2		24
63.5	even	6		1323.2.f.h.442.12		24
63.13	odd	6		441.2.h.h.373.11		24
63.16	even	3		3969.2.a.bh.1.11		12
63.23	odd	6		1323.2.f.h.442.11		24
63.31	odd	6	inner	441.2.g.h.67.1		24
63.32	odd	6		1323.2.g.h.361.12		24
63.40	odd	6		441.2.f.h.148.2	yes	24
63.41	even	6		1323.2.h.h.226.2		24
63.47	even	6		3969.2.a.bi.1.1		12
63.58	even	3		441.2.f.h.148.1	✓	24
63.59	even	6		1323.2.g.h.361.11		24
63.61	odd	6		3969.2.a.bh.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.1	✓	24	63.58	even	3
441.2.f.h.148.2	yes	24	63.40	odd	6
441.2.f.h.295.1	yes	24	7.2	even	3
441.2.f.h.295.2	yes	24	7.5	odd	6
441.2.g.h.67.1		24	63.31	odd	6	inner
441.2.g.h.67.2		24	63.4	even	3	inner
441.2.g.h.79.1		24	7.6	odd	2	inner
441.2.g.h.79.2		24	1.1	even	1	trivial
441.2.h.h.214.11		24	7.3	odd	6
441.2.h.h.214.12		24	7.4	even	3
441.2.h.h.373.11		24	63.13	odd	6
441.2.h.h.373.12		24	9.4	even	3
1323.2.f.h.442.11		24	63.23	odd	6
1323.2.f.h.442.12		24	63.5	even	6
1323.2.f.h.883.11		24	21.2	odd	6
1323.2.f.h.883.12		24	21.5	even	6
1323.2.g.h.361.11		24	63.59	even	6
1323.2.g.h.361.12		24	63.32	odd	6
1323.2.g.h.667.11		24	21.20	even	2
1323.2.g.h.667.12		24	3.2	odd	2
1323.2.h.h.226.1		24	9.5	odd	6
1323.2.h.h.226.2		24	63.41	even	6
1323.2.h.h.802.1		24	21.11	odd	6
1323.2.h.h.802.2		24	21.17	even	6
3969.2.a.bh.1.11		12	63.16	even	3
3969.2.a.bh.1.12		12	63.61	odd	6
3969.2.a.bi.1.1		12	63.47	even	6
3969.2.a.bi.1.2		12	63.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
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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