LMFDB - Embedded newform 441.2.f.h.295.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(148,441)]

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, 0]))

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

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

chi := DirichletCharacter("441.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.52140272914$
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			295.12
Character	$\chi$	$=$	441.295
Dual form			441.2.f.h.148.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.35757 - 2.35137i) q^{2} +(0.521588 - 1.65165i) q^{3} +(-2.68597 - 4.65224i) q^{4} +(0.793197 + 1.37386i) q^{5} +(-3.17555 - 3.46867i) q^{6} -9.15528 q^{8} +(-2.45589 - 1.72296i) q^{9} +O(q^{10})$	\(q+(1.35757 - 2.35137i) q^{2} +(0.521588 - 1.65165i) q^{3} +(-2.68597 - 4.65224i) q^{4} +(0.793197 + 1.37386i) q^{5} +(-3.17555 - 3.46867i) q^{6} -9.15528 q^{8} +(-2.45589 - 1.72296i) q^{9} +4.30727 q^{10} +(0.674376 - 1.16805i) q^{11} +(-9.08484 + 2.00973i) q^{12} +(1.58916 + 2.75251i) q^{13} +(2.68285 - 0.593495i) q^{15} +(-7.05696 + 12.2230i) q^{16} +2.80054 q^{17} +(-7.38536 + 3.43568i) q^{18} +0.625693 q^{19} +(4.26101 - 7.38028i) q^{20} +(-1.83102 - 3.17142i) q^{22} +(0.142434 + 0.246702i) q^{23} +(-4.77529 + 15.1213i) q^{24} +(1.24168 - 2.15065i) q^{25} +8.62957 q^{26} +(-4.12669 + 3.15760i) q^{27} +(2.27396 - 3.93861i) q^{29} +(2.24662 - 7.11410i) q^{30} +(-3.71502 - 6.43461i) q^{31} +(10.0053 + 17.3297i) q^{32} +(-1.57747 - 1.72308i) q^{33} +(3.80191 - 6.58511i) q^{34} +(-1.41918 + 16.0532i) q^{36} +8.02252 q^{37} +(0.849420 - 1.47124i) q^{38} +(5.37507 - 1.18906i) q^{39} +(-7.26194 - 12.5780i) q^{40} +(5.01329 + 8.68327i) q^{41} +(-3.12937 + 5.42022i) q^{43} -7.24542 q^{44} +(0.419098 - 4.74069i) q^{45} +0.773452 q^{46} +(-5.57383 + 9.65415i) q^{47} +(16.5073 + 18.0310i) q^{48} +(-3.37132 - 5.83930i) q^{50} +(1.46073 - 4.62550i) q^{51} +(8.53689 - 14.7863i) q^{52} +2.78698 q^{53} +(1.82243 + 13.9900i) q^{54} +2.13965 q^{55} +(0.326354 - 1.03343i) q^{57} +(-6.17410 - 10.6939i) q^{58} +(-2.28734 - 3.96180i) q^{59} +(-9.96715 - 10.8872i) q^{60} +(0.192507 - 0.333432i) q^{61} -20.1736 q^{62} +26.1036 q^{64} +(-2.52104 + 4.36656i) q^{65} +(-6.19311 + 1.37003i) q^{66} +(1.26958 + 2.19898i) q^{67} +(-7.52217 - 13.0288i) q^{68} +(0.481757 - 0.106573i) q^{69} -1.45208 q^{71} +(22.4844 + 15.7742i) q^{72} -0.468134 q^{73} +(10.8911 - 18.8639i) q^{74} +(-2.90448 - 3.17257i) q^{75} +(-1.68059 - 2.91087i) q^{76} +(4.50108 - 14.2530i) q^{78} +(7.85620 - 13.6073i) q^{79} -22.3902 q^{80} +(3.06281 + 8.46281i) q^{81} +27.2235 q^{82} +(-6.99338 + 12.1129i) q^{83} +(2.22138 + 3.84754i) q^{85} +(8.49665 + 14.7166i) q^{86} +(-5.31914 - 5.81012i) q^{87} +(-6.17410 + 10.6939i) q^{88} -2.58706 q^{89} +(-10.5782 - 7.42126i) q^{90} +(0.765146 - 1.32527i) q^{92} +(-12.5654 + 2.77970i) q^{93} +(15.1337 + 26.2123i) q^{94} +(0.496297 + 0.859612i) q^{95} +(33.8412 - 7.48628i) q^{96} +(7.22962 - 12.5221i) q^{97} +(-3.66871 + 1.70669i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9	$ 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9} + 20 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} + 48 q^{32} - 4 q^{36} + 24 q^{37} + 32 q^{39} - 112 q^{44} - 48 q^{46} - 4 q^{50} - 56 q^{51} - 64 q^{53} - 12 q^{57} - 88 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} + 168 q^{72} + 68 q^{74} - 60 q^{78} + 12 q^{79} + 80 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 80 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9 + 20 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 + 48 * q^32 - 4 * q^36 + 24 * q^37 + 32 * q^39 - 112 * q^44 - 48 * q^46 - 4 * q^50 - 56 * q^51 - 64 * q^53 - 12 * q^57 - 88 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 + 168 * q^72 + 68 * q^74 - 60 * q^78 + 12 * q^79 + 80 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 80 * q^93 + 64 * q^95 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.35757	−	2.35137i	0.959944	−	1.66267i	0.237320	−	0.971432i	$-0.423731\pi$
$2$	1.35757	−	2.35137i	0.959944	−	1.66267i	0.722624	−	0.691241i	$-0.242936\pi$
$3$	0.521588	−	1.65165i	0.301139	−	0.953580i
$3$	0.521588	−	1.65165i	0.301139	−	0.953580i
$4$	−2.68597	−	4.65224i	−1.34299	−	2.32612i
$5$	0.793197	+	1.37386i	0.354728	+	0.614407i	0.987071	−	0.160281i	$-0.0512400\pi$
$5$	0.793197	+	1.37386i	0.354728	+	0.614407i	−0.632343	+	0.774688i	$0.717907\pi$
$6$	−3.17555	−	3.46867i	−1.29641	−	1.41608i
$7$		0			0
$7$		0			0
$8$	−9.15528			−3.23688
$9$	−2.45589	−	1.72296i	−0.818630	−	0.574321i
$10$	4.30727			1.36208
$11$	0.674376	−	1.16805i	0.203332	−	0.352181i	−0.746268	−	0.665646i	$-0.768156\pi$
$11$	0.674376	−	1.16805i	0.203332	−	0.352181i	0.949600	+	0.313464i	$0.101490\pi$
$12$	−9.08484	+	2.00973i	−2.62257	+	0.580159i
$13$	1.58916	+	2.75251i	0.440754	+	0.763409i	0.997746	−	0.0671096i	$-0.0213777\pi$
$13$	1.58916	+	2.75251i	0.440754	+	0.763409i	−0.556991	+	0.830518i	$0.688044\pi$
$14$		0			0
$15$	2.68285	−	0.593495i	0.692709	−	0.153240i
$16$	−7.05696	+	12.2230i	−1.76424	+	3.05575i
$17$	2.80054			0.679230			0.339615	−	0.940565i	$-0.389703\pi$
$17$	2.80054			0.679230			0.339615	+	0.940565i	$0.389703\pi$
$18$	−7.38536	+	3.43568i	−1.74075	+	0.809799i
$19$	0.625693			0.143544			0.0717719	−	0.997421i	$-0.477135\pi$
$19$	0.625693			0.143544			0.0717719	+	0.997421i	$0.477135\pi$
$20$	4.26101	−	7.38028i	0.952791	−	1.65028i
$21$		0			0
$22$	−1.83102	−	3.17142i	−0.390375	−	0.676149i
$23$	0.142434	+	0.246702i	0.0296995	+	0.0514410i	0.880493	−	0.474059i	$-0.157212\pi$
$23$	0.142434	+	0.246702i	0.0296995	+	0.0514410i	−0.850794	+	0.525500i	$0.823878\pi$
$24$	−4.77529	+	15.1213i	−0.974751	+	3.08663i
$25$	1.24168	−	2.15065i	0.248336	−	0.430130i
$26$	8.62957			1.69240
$27$	−4.12669	+	3.15760i	−0.794182	+	0.607679i
$28$		0			0
$29$	2.27396	−	3.93861i	0.422264	−	0.731382i	−0.573897	−	0.818928i	$-0.694569\pi$
$29$	2.27396	−	3.93861i	0.422264	−	0.731382i	0.996161	+	0.0875454i	$0.0279023\pi$
$30$	2.24662	−	7.11410i	0.410175	−	1.29885i
$31$	−3.71502	−	6.43461i	−0.667238	−	1.15569i	−0.978673	−	0.205423i	$-0.934143\pi$
$31$	−3.71502	−	6.43461i	−0.667238	−	1.15569i	0.311435	−	0.950267i	$-0.399190\pi$
$32$	10.0053	+	17.3297i	1.76870	+	3.06348i
$33$	−1.57747	−	1.72308i	−0.274602	−	0.299949i
$34$	3.80191	−	6.58511i	0.652023	−	1.12934i
$35$		0			0
$36$	−1.41918	+	16.0532i	−0.236529	+	2.67554i
$37$	8.02252			1.31889			0.659447	−	0.751751i	$-0.270791\pi$
$37$	8.02252			1.31889			0.659447	+	0.751751i	$0.270791\pi$
$38$	0.849420	−	1.47124i	0.137794	−	0.238666i
$39$	5.37507	−	1.18906i	0.860700	−	0.190402i
$40$	−7.26194	−	12.5780i	−1.14821	−	1.98876i
$41$	5.01329	+	8.68327i	0.782944	+	1.35610i	0.930219	+	0.367004i	$0.119616\pi$
$41$	5.01329	+	8.68327i	0.782944	+	1.35610i	−0.147275	+	0.989096i	$0.547050\pi$
$42$		0			0
$43$	−3.12937	+	5.42022i	−0.477224	+	0.826576i	−0.999659	−	0.0261027i	$-0.991690\pi$
$43$	−3.12937	+	5.42022i	−0.477224	+	0.826576i	0.522435	+	0.852679i	$0.325024\pi$
$44$	−7.24542			−1.09229
$45$	0.419098	−	4.74069i	0.0624754	−	0.706700i
$46$	0.773452			0.114039
$47$	−5.57383	+	9.65415i	−0.813026	+	1.40820i	0.0977106	+	0.995215i	$0.468848\pi$
$47$	−5.57383	+	9.65415i	−0.813026	+	1.40820i	−0.910737	+	0.412988i	$0.864485\pi$
$48$	16.5073	+	18.0310i	2.38262	+	2.60255i
$49$		0			0
$50$	−3.37132	−	5.83930i	−0.476777	−	0.825802i
$51$	1.46073	−	4.62550i	0.204543	−	0.647700i
$52$	8.53689	−	14.7863i	1.18385	−	2.05049i
$53$	2.78698			0.382821			0.191410	−	0.981510i	$-0.438694\pi$
$53$	2.78698			0.382821			0.191410	+	0.981510i	$0.438694\pi$
$54$	1.82243	+	13.9900i	0.248001	+	1.90380i
$55$	2.13965			0.288510
$56$		0			0
$57$	0.326354	−	1.03343i	0.0432266	−	0.136881i
$58$	−6.17410	−	10.6939i	−0.810699	−	1.40417i
$59$	−2.28734	−	3.96180i	−0.297787	−	0.515782i	0.677842	−	0.735207i	$-0.262915\pi$
$59$	−2.28734	−	3.96180i	−0.297787	−	0.515782i	−0.975629	+	0.219425i	$0.929582\pi$
$60$	−9.96715	−	10.8872i	−1.28675	−	1.40553i
$61$	0.192507	−	0.333432i	0.0246480	−	0.0426916i	−0.853438	−	0.521194i	$-0.825487\pi$
$61$	0.192507	−	0.333432i	0.0246480	−	0.0426916i	0.878086	+	0.478502i	$0.158820\pi$
$62$	−20.1736			−2.56205
$63$		0			0
$64$	26.1036			3.26295
$65$	−2.52104	+	4.36656i	−0.312696	+	0.541605i
$66$	−6.19311	+	1.37003i	−0.762320	+	0.168639i
$67$	1.26958	+	2.19898i	0.155104	+	0.268648i	0.933097	−	0.359625i	$-0.117095\pi$
$67$	1.26958	+	2.19898i	0.155104	+	0.268648i	−0.777993	+	0.628273i	$0.783762\pi$
$68$	−7.52217	−	13.0288i	−0.912197	−	1.57997i
$69$	0.481757	−	0.106573i	0.0579968	−	0.0128299i
$70$		0			0
$71$	−1.45208			−0.172330			−0.0861651	−	0.996281i	$-0.527461\pi$
$71$	−1.45208			−0.172330			−0.0861651	+	0.996281i	$0.527461\pi$
$72$	22.4844	+	15.7742i	2.64981	+	1.85901i
$73$	−0.468134			−0.0547909			−0.0273955	−	0.999625i	$-0.508721\pi$
$73$	−0.468134			−0.0547909			−0.0273955	+	0.999625i	$0.508721\pi$
$74$	10.8911	−	18.8639i	1.26606	−	2.19289i
$75$	−2.90448	−	3.17257i	−0.335380	−	0.366337i
$76$	−1.68059	−	2.91087i	−0.192777	−	0.333900i
$77$		0			0
$78$	4.50108	−	14.2530i	0.509647	−	1.61384i
$79$	7.85620	−	13.6073i	0.883892	−	1.53095i	0.0369135	−	0.999318i	$-0.488247\pi$
$79$	7.85620	−	13.6073i	0.883892	−	1.53095i	0.846978	−	0.531627i	$-0.178419\pi$
$80$	−22.3902			−2.50330
$81$	3.06281	+	8.46281i	0.340312	+	0.940313i
$82$	27.2235			3.00633
$83$	−6.99338	+	12.1129i	−0.767623	+	1.32956i	0.171225	+	0.985232i	$0.445228\pi$
$83$	−6.99338	+	12.1129i	−0.767623	+	1.32956i	−0.938848	+	0.344331i	$0.888106\pi$
$84$		0			0
$85$	2.22138	+	3.84754i	0.240942	+	0.417324i
$86$	8.49665	+	14.7166i	0.916217	+	1.58693i
$87$	−5.31914	−	5.81012i	−0.570272	−	0.622910i
$88$	−6.17410	+	10.6939i	−0.658162	+	1.13997i
$89$	−2.58706			−0.274228			−0.137114	−	0.990555i	$-0.543783\pi$
$89$	−2.58706			−0.274228			−0.137114	+	0.990555i	$0.543783\pi$
$90$	−10.5782	−	7.42126i	−1.11504	−	0.782269i
$91$		0			0
$92$	0.765146	−	1.32527i	0.0797719	−	0.138169i
$93$	−12.5654	+	2.77970i	−1.30297	+	0.288241i
$94$	15.1337	+	26.2123i	1.56092	+	2.70359i
$95$	0.496297	+	0.859612i	0.0509190	+	0.0881944i
$96$	33.8412	−	7.48628i	3.45390	−	0.764065i
$97$	7.22962	−	12.5221i	0.734057	−	1.27142i	−0.221079	−	0.975256i	$-0.570958\pi$
$97$	7.22962	−	12.5221i	0.734057	−	1.27142i	0.955136	−	0.296168i	$-0.0957089\pi$
$98$		0			0
$99$	−3.66871	+	1.70669i	−0.368719	+	0.171529i
$100$	−13.3405			−1.33405
$101$	−4.91888	+	8.51975i	−0.489447	+	0.847747i	−0.999926	−	0.0121430i	$-0.996135\pi$
$101$	−4.91888	+	8.51975i	−0.489447	+	0.847747i	0.510479	+	0.859890i	$0.329468\pi$
$102$	−8.89326	−	9.71414i	−0.880564	−	0.961844i
$103$	−5.52897	−	9.57646i	−0.544786	−	0.943597i	−0.998620	−	0.0525110i	$-0.983278\pi$
$103$	−5.52897	−	9.57646i	−0.544786	−	0.943597i	0.453834	−	0.891086i	$-0.350056\pi$
$104$	−14.5492	−	25.2000i	−1.42667	−	2.47106i
$105$		0			0
$106$	3.78350	−	6.55322i	0.367486	−	0.636505i
$107$	−1.92431			−0.186030			−0.0930149	−	0.995665i	$-0.529650\pi$
$107$	−1.92431			−0.186030			−0.0930149	+	0.995665i	$0.529650\pi$
$108$	25.7741	+	10.7172i	2.48011	+	1.03126i
$109$	−18.6068			−1.78221			−0.891105	−	0.453797i	$-0.850069\pi$
$109$	−18.6068			−1.78221			−0.891105	+	0.453797i	$0.850069\pi$
$110$	2.90472	−	5.03112i	0.276954	−	0.479698i
$111$	4.18445	−	13.2504i	0.397170	−	1.25767i
$112$		0			0
$113$	1.59338	+	2.75982i	0.149893	+	0.259622i	0.931188	−	0.364540i	$-0.118774\pi$
$113$	1.59338	+	2.75982i	0.149893	+	0.259622i	−0.781295	+	0.624162i	$0.785440\pi$
$114$	−1.98692	−	2.17032i	−0.186092	−	0.203269i
$115$	−0.225956	+	0.391367i	−0.0210705	+	0.0364951i
$116$	−24.4312			−2.26838
$117$	0.839659	−	9.49793i	0.0776265	−	0.878084i
$118$	−12.4209			−1.14344
$119$		0			0
$120$	−24.5623	+	5.43361i	−2.24222	+	0.496019i
$121$	4.59043	+	7.95086i	0.417312	+	0.722806i
$122$	−0.522682	−	0.905312i	−0.0473214	−	0.0819631i
$123$	16.9566	−	3.75110i	1.52892	−	0.338226i
$124$	−19.9569	+	34.5664i	−1.79218	+	3.10415i
$125$	11.8715			1.06182
$126$		0			0
$127$	−8.37387			−0.743061			−0.371530	−	0.928421i	$-0.621167\pi$
$127$	−8.37387			−0.743061			−0.371530	+	0.928421i	$0.621167\pi$
$128$	15.4267	−	26.7199i	1.36354	−	2.36173i
$129$	7.32007	+	7.99574i	0.644496	+	0.703986i
$130$	6.84495	+	11.8558i	0.600341	+	1.03982i
$131$	5.98629	+	10.3686i	0.523024	+	0.905905i	0.999641	+	0.0267937i	$0.00852971\pi$
$131$	5.98629	+	10.3686i	0.523024	+	0.905905i	−0.476616	+	0.879111i	$0.658137\pi$
$132$	−3.77913	+	11.9669i	−0.328931	+	1.04158i
$133$		0			0
$134$	6.89415			0.595564
$135$	−7.61136	−	3.16489i	−0.655082	−	0.272390i
$136$	−25.6397			−2.19859
$137$	−8.27525	+	14.3332i	−0.707003	+	1.22456i	0.258961	+	0.965888i	$0.416620\pi$
$137$	−8.27525	+	14.3332i	−0.707003	+	1.22456i	−0.965964	+	0.258677i	$0.916714\pi$
$138$	0.403424	−	1.27747i	0.0343417	−	0.108746i
$139$	3.95119	+	6.84367i	0.335136	+	0.580472i	0.983511	−	0.180849i	$-0.0578845\pi$
$139$	3.95119	+	6.84367i	0.335136	+	0.580472i	−0.648375	+	0.761321i	$0.724551\pi$
$140$		0			0
$141$	13.0380	+	14.2415i	1.09800	+	1.19935i
$142$	−1.97130	+	3.41438i	−0.165427	+	0.286529i
$143$	4.28677			0.358478
$144$	38.3909	−	17.8595i	3.19924	−	1.48829i
$145$	7.21479			0.599156
$146$	−0.635523	+	1.10076i	−0.0525962	+	0.0910994i
$147$		0			0
$148$	−21.5483	−	37.3227i	−1.77126	−	3.06791i
$149$	6.83427	+	11.8373i	0.559885	+	0.969749i	0.997505	+	0.0705895i	$0.0224881\pi$
$149$	6.83427	+	11.8373i	0.559885	+	0.969749i	−0.437620	+	0.899160i	$0.644179\pi$
$150$	−11.4029	+	2.52253i	−0.931045	+	0.205964i
$151$	−1.94982	+	3.37718i	−0.158674	+	0.274831i	−0.934391	−	0.356250i	$-0.884055\pi$
$151$	−1.94982	+	3.37718i	−0.158674	+	0.274831i	0.775717	+	0.631081i	$0.217389\pi$
$152$	−5.72839			−0.464634
$153$	−6.87781	−	4.82522i	−0.556038	−	0.390096i
$154$		0			0
$155$	5.89349	−	10.2078i	0.473376	−	0.819912i
$156$	−19.9691	−	21.8123i	−1.59881	−	1.74638i
$157$	0.147176	+	0.254917i	0.0117459	+	0.0203446i	0.871839	−	0.489793i	$-0.162928\pi$
$157$	0.147176	+	0.254917i	0.0117459	+	0.0203446i	−0.860093	+	0.510138i	$0.829594\pi$
$158$	−21.3306	−	36.9457i	−1.69697	−	2.93925i
$159$	1.45365	−	4.60311i	0.115282	−	0.365050i
$160$	−15.8723	+	27.4917i	−1.25482	+	2.17341i
$161$		0			0
$162$	24.0572	+	4.28703i	1.89011	+	0.336821i
$163$	10.7091			0.838802			0.419401	−	0.907801i	$-0.362240\pi$
$163$	10.7091			0.838802			0.419401	+	0.907801i	$0.362240\pi$
$164$	26.9311	−	46.6461i	2.10297	−	3.64245i
$165$	1.11602	−	3.53395i	0.0868818	−	0.275118i
$166$	18.9880	+	32.8881i	1.47375	+	2.55261i
$167$	1.59872	+	2.76907i	0.123713	+	0.214277i	0.921229	−	0.389020i	$-0.127186\pi$
$167$	1.59872	+	2.76907i	0.123713	+	0.214277i	−0.797516	+	0.603298i	$0.793853\pi$
$168$		0			0
$169$	1.44913	−	2.50997i	0.111472	−	0.193074i
$170$	12.0627			0.925164
$171$	−1.53663	−	1.07804i	−0.117509	−	0.0824401i
$172$	33.6216			2.56362
$173$	5.71875	−	9.90517i	0.434789	−	0.753076i	−0.562490	−	0.826804i	$-0.690156\pi$
$173$	5.71875	−	9.90517i	0.434789	−	0.753076i	0.997278	+	0.0737284i	$0.0234898\pi$
$174$	−20.8828	+	4.61966i	−1.58312	+	0.350216i
$175$		0			0
$176$	9.51809	+	16.4858i	0.717453	+	1.24266i
$177$	−7.73655	+	1.71146i	−0.581515	+	0.128642i
$178$	−3.51210	+	6.08314i	−0.263243	+	0.455951i
$179$	1.09855			0.0821095			0.0410547	−	0.999157i	$-0.486928\pi$
$179$	1.09855			0.0821095			0.0410547	+	0.999157i	$0.486928\pi$
$180$	−23.1805	+	10.7836i	−1.72777	+	0.803764i
$181$	3.19013			0.237120			0.118560	−	0.992947i	$-0.462172\pi$
$181$	3.19013			0.237120			0.118560	+	0.992947i	$0.462172\pi$
$182$		0			0
$183$	−0.450303	−	0.491868i	−0.0332874	−	0.0363599i
$184$	−1.30402	−	2.25863i	−0.0961336	−	0.166508i
$185$	6.36343	+	11.0218i	0.467849	+	0.810338i
$186$	−10.5223	+	33.3197i	−0.771532	+	2.44312i
$187$	1.88861	−	3.27118i	0.138109	−	0.239212i
$188$	59.8846			4.36753
$189$		0			0
$190$	2.69503			0.195518
$191$	−1.93407	+	3.34992i	−0.139945	+	0.242391i	−0.927475	−	0.373884i	$-0.878026\pi$
$191$	−1.93407	+	3.34992i	−0.139945	+	0.242391i	0.787531	+	0.616275i	$0.211359\pi$
$192$	13.6153	−	43.1139i	0.982601	−	3.11148i
$193$	2.06793	+	3.58175i	0.148853	+	0.257820i	0.930804	−	0.365520i	$-0.119109\pi$
$193$	2.06793	+	3.58175i	0.148853	+	0.257820i	−0.781951	+	0.623340i	$0.785775\pi$
$194$	−19.6294	−	33.9991i	−1.40931	−	2.44099i
$195$	5.89709	+	6.44141i	0.422299	+	0.461279i
$196$		0			0
$197$	−0.889267			−0.0633576			−0.0316788	−	0.999498i	$-0.510085\pi$
$197$	−0.889267			−0.0633576			−0.0316788	+	0.999498i	$0.510085\pi$
$198$	−0.967449	+	10.9434i	−0.0687536	+	0.777717i
$199$	6.32386			0.448287			0.224143	−	0.974556i	$-0.428042\pi$
$199$	6.32386			0.448287			0.224143	+	0.974556i	$0.428042\pi$
$200$	−11.3679	+	19.6898i	−0.803833	+	1.39228i
$201$	4.29414	−	0.949940i	0.302885	−	0.0670036i
$202$	13.3554	+	23.1323i	0.939684	+	1.62758i
$203$		0			0
$204$	−25.4424	+	5.62833i	−1.78133	+	0.394062i
$205$	−7.95305	+	13.7751i	−0.555465	+	0.962093i
$206$	−30.0238			−2.09186
$207$	0.0752570	−	0.851282i	0.00523073	−	0.0591682i
$208$	−44.8586			−3.11038
$209$	0.421952	−	0.730843i	0.0291870	−	0.0505535i
$210$		0			0
$211$	5.71291	+	9.89505i	0.393293	+	0.681204i	0.992882	−	0.119105i	$-0.0380025\pi$
$211$	5.71291	+	9.89505i	0.393293	+	0.681204i	−0.599589	+	0.800308i	$0.704669\pi$
$212$	−7.48574	−	12.9657i	−0.514123	−	0.890487i
$213$	−0.757388	+	2.39833i	−0.0518954	+	0.164331i
$214$	−2.61237	+	4.52476i	−0.178578	+	0.309307i
$215$	−9.92881			−0.677139
$216$	37.7810	−	28.9087i	2.57067	−	1.96699i
$217$		0			0
$218$	−25.2600	+	43.7516i	−1.71082	+	2.96323i
$219$	−0.244173	+	0.773193i	−0.0164997	+	0.0522475i
$220$	−5.74705	−	9.95417i	−0.387466	−	0.671110i
$221$	4.45051	+	7.70850i	0.299373	+	0.518530i
$222$	−25.4759	−	27.8275i	−1.70983	−	1.86766i
$223$	8.35953	−	14.4791i	0.559796	−	0.969595i	−0.437717	−	0.899113i	$-0.644213\pi$
$223$	8.35953	−	14.4791i	0.559796	−	0.969595i	0.997513	−	0.0704822i	$-0.0224538\pi$
$224$		0			0
$225$	−6.75492	+	3.14240i	−0.450328	+	0.209493i
$226$	8.65250			0.575555
$227$	−8.53501	+	14.7831i	−0.566489	+	0.981187i	0.430421	+	0.902628i	$0.358365\pi$
$227$	−8.53501	+	14.7831i	−0.566489	+	0.981187i	−0.996909	+	0.0785588i	$0.974968\pi$
$228$	−5.68432	+	1.25747i	−0.376453	+	0.0832783i
$229$	−9.89471	−	17.1381i	−0.653861	−	1.13252i	−0.982178	−	0.187953i	$-0.939815\pi$
$229$	−9.89471	−	17.1381i	−0.653861	−	1.13252i	0.328317	−	0.944567i	$-0.393518\pi$
$230$	0.613500	+	1.06261i	0.0404530	+	0.0700666i
$231$		0			0
$232$	−20.8187	+	36.0591i	−1.36682	+	2.36740i
$233$	5.93159			0.388591			0.194296	−	0.980943i	$-0.437758\pi$
$233$	5.93159			0.388591			0.194296	+	0.980943i	$0.437758\pi$
$234$	−21.1933	−	14.8684i	−1.38545	−	0.971979i
$235$	−17.6846			−1.15361
$236$	−12.2875	+	21.2826i	−0.799847	+	1.38538i
$237$	−18.3769	−	20.0731i	−1.19371	−	1.30389i
$238$		0			0
$239$	−10.0277	−	17.3685i	−0.648637	−	1.12347i	−0.983449	−	0.181187i	$-0.942006\pi$
$239$	−10.0277	−	17.3685i	−0.648637	−	1.12347i	0.334812	−	0.942285i	$-0.391327\pi$
$240$	−11.6785	+	36.9808i	−0.753842	+	2.38710i
$241$	−14.6444	+	25.3648i	−0.943326	+	1.63389i	−0.184256	+	0.982878i	$0.558988\pi$
$241$	−14.6444	+	25.3648i	−0.943326	+	1.63389i	−0.759069	+	0.651010i	$0.774346\pi$
$242$	24.9273			1.60239
$243$	15.5751	−	0.644577i	0.999145	−	0.0413497i
$244$	−2.06827			−0.132408
$245$		0			0
$246$	14.1995	−	44.9637i	0.905324	−	2.86678i
$247$	0.994327	+	1.72223i	0.0632675	+	0.109583i
$248$	34.0121	+	58.9107i	2.15977	+	3.74083i
$249$	16.3586	+	17.8686i	1.03668	+	1.13237i
$250$	16.1164	−	27.9144i	1.01929	−	1.76546i
$251$	−22.7856			−1.43821			−0.719106	−	0.694901i	$-0.755448\pi$
$251$	−22.7856			−1.43821			−0.719106	+	0.694901i	$0.755448\pi$
$252$		0			0
$253$	0.384215			0.0241554
$254$	−11.3681	+	19.6901i	−0.713297	+	1.23547i
$255$	7.51342	−	1.66210i	0.470509	−	0.104085i
$256$	−15.7821	−	27.3354i	−0.986381	−	1.70846i
$257$	12.1444	+	21.0348i	0.757550	+	1.31211i	0.944097	+	0.329668i	$0.106937\pi$
$257$	12.1444	+	21.0348i	0.757550	+	1.31211i	−0.186547	+	0.982446i	$0.559730\pi$
$258$	28.7385	−	6.35747i	1.78918	−	0.395798i
$259$		0			0
$260$	27.0857			1.67979
$261$	−12.3707	+	5.75486i	−0.765726	+	0.356217i
$262$	32.5071			2.00830
$263$	4.30578	−	7.45782i	0.265506	−	0.459869i	−0.702190	−	0.711989i	$-0.747794\pi$
$263$	4.30578	−	7.45782i	0.265506	−	0.459869i	0.967696	+	0.252120i	$0.0811278\pi$
$264$	14.4422	+	15.7752i	0.888854	+	0.970899i
$265$	2.21062	+	3.82890i	0.135797	+	0.235208i
$266$		0			0
$267$	−1.34938	+	4.27291i	−0.0825807	+	0.261498i
$268$	6.82011	−	11.8128i	0.416605	−	0.721581i
$269$	−15.2312			−0.928664			−0.464332	−	0.885661i	$-0.653706\pi$
$269$	−15.2312			−0.928664			−0.464332	+	0.885661i	$0.653706\pi$
$270$	−17.7748	+	13.6006i	−1.08174	+	0.827707i
$271$	−4.67820			−0.284181			−0.142090	−	0.989854i	$-0.545382\pi$
$271$	−4.67820			−0.284181			−0.142090	+	0.989854i	$0.545382\pi$
$272$	−19.7633	+	34.2310i	−1.19832	+	2.07556i
$273$		0			0
$274$	22.4684	+	38.9164i	1.35737	+	2.35103i
$275$	−1.67472	−	2.90069i	−0.100989	−	0.174918i
$276$	−1.78979	−	1.95500i	−0.107733	−	0.117677i
$277$	8.19537	−	14.1948i	0.492412	−	0.852883i	−0.507550	−	0.861622i	$-0.669449\pi$
$277$	8.19537	−	14.1948i	0.492412	−	0.852883i	0.999962	+	0.00873986i	$0.00278202\pi$
$278$	21.4560			1.28685
$279$	−1.96289	+	22.2035i	−0.117515	+	1.32929i
$280$		0			0
$281$	1.75702	−	3.04325i	0.104815	−	0.181545i	−0.808848	−	0.588018i	$-0.799908\pi$
$281$	1.75702	−	3.04325i	0.104815	−	0.181545i	0.913663	+	0.406473i	$0.133242\pi$
$282$	51.1871	−	11.3235i	3.04815	−	0.674305i
$283$	−13.0354	−	22.5780i	−0.774874	−	1.34212i	−0.934865	−	0.355002i	$-0.884480\pi$
$283$	−13.0354	−	22.5780i	−0.774874	−	1.34212i	0.159992	−	0.987118i	$-0.448853\pi$
$284$	3.90025	+	6.75543i	0.231437	+	0.400861i
$285$	1.67864	−	0.371346i	0.0994341	−	0.0219966i
$286$	5.81958	−	10.0798i	0.344119	−	0.596031i
$287$		0			0
$288$	5.28645	−	59.7985i	0.311507	−	3.52366i
$289$	−9.15699			−0.538647
$290$	9.79455	−	16.9647i	0.575156	−	0.996199i
$291$	−16.9112	−	18.4722i	−0.991352	−	1.08286i
$292$	1.25740	+	2.17787i	0.0735835	+	0.127450i
$293$	−9.44192	−	16.3539i	−0.551603	−	0.955404i	−0.998159	−	0.0606487i	$-0.980683\pi$
$293$	−9.44192	−	16.3539i	−0.551603	−	0.955404i	0.446556	−	0.894756i	$-0.352650\pi$
$294$		0			0
$295$	3.62863	−	6.28497i	0.211267	−	0.365925i
$296$	−73.4484			−4.26910
$297$	0.905298	+	6.94961i	0.0525307	+	0.403257i
$298$	37.1119			2.14983
$299$	−0.452700	+	0.784099i	−0.0261803	+	0.0453456i
$300$	−6.95823	+	22.0338i	−0.401733	+	1.27212i
$301$		0			0
$302$	5.29401	+	9.16950i	0.304636	+	0.527645i
$303$	11.5060	+	12.5681i	0.661003	+	0.722017i
$304$	−4.41549	+	7.64785i	−0.253246	+	0.438634i
$305$	0.610783			0.0349734
$306$	−20.6830	+	9.62176i	−1.18237	+	0.550039i
$307$	−21.6407			−1.23510			−0.617551	−	0.786531i	$-0.711875\pi$
$307$	−21.6407			−1.23510			−0.617551	+	0.786531i	$0.711875\pi$
$308$		0			0
$309$	−18.7008	+	4.13696i	−1.06385	+	0.235343i
$310$	−16.0016	−	27.7156i	−0.908830	−	1.57414i
$311$	−2.24724	−	3.89234i	−0.127429	−	0.220714i	0.795251	−	0.606281i	$-0.207339\pi$
$311$	−2.24724	−	3.89234i	−0.127429	−	0.220714i	−0.922680	+	0.385567i	$0.874006\pi$
$312$	−49.2103	+	10.8862i	−2.78598	+	0.616309i
$313$	−4.30102	+	7.44958i	−0.243108	+	0.421075i	−0.961598	−	0.274462i	$-0.911500\pi$
$313$	−4.30102	+	7.44958i	−0.243108	+	0.421075i	0.718490	+	0.695537i	$0.244834\pi$
$314$	0.799206			0.0451018
$315$		0			0
$316$	−84.4062			−4.74822
$317$	4.03128	−	6.98237i	0.226419	−	0.392169i	−0.730325	−	0.683100i	$-0.760631\pi$
$317$	4.03128	−	6.98237i	0.226419	−	0.392169i	0.956744	+	0.290930i	$0.0939648\pi$
$318$	−8.85019	−	9.66711i	−0.496294	−	0.542104i
$319$	−3.06701	−	5.31221i	−0.171719	−	0.297427i
$320$	20.7053	+	35.8626i	1.15746	+	2.00478i
$321$	−1.00370	+	3.17828i	−0.0560208	+	0.177394i
$322$		0			0
$323$	1.75228			0.0974992
$324$	31.1444	−	36.9798i	1.73025	−	2.05443i
$325$	7.89291			0.437820
$326$	14.5383	−	25.1811i	0.805203	−	1.39465i
$327$	−9.70510	+	30.7319i	−0.536693	+	1.69948i
$328$	−45.8981	−	79.4978i	−2.53430	−	4.38953i
$329$		0			0
$330$	−6.79458	−	7.42175i	−0.374029	−	0.408554i
$331$	11.4513	−	19.8342i	0.629419	−	1.09019i	−0.358249	−	0.933626i	$-0.616626\pi$
$331$	11.4513	−	19.8342i	0.629419	−	1.09019i	0.987668	−	0.156560i	$-0.0500405\pi$
$332$	75.1361			4.12363
$333$	−19.7024	−	13.8225i	−1.07969	−	0.757468i
$334$	8.68150			0.475030
$335$	−2.01405	+	3.48844i	−0.110039	+	0.190594i
$336$		0			0
$337$	−6.81891	−	11.8107i	−0.371450	−	0.643369i	0.618339	−	0.785911i	$-0.287806\pi$
$337$	−6.81891	−	11.8107i	−0.371450	−	0.643369i	−0.989789	+	0.142542i	$0.954472\pi$
$338$	−3.93458	−	6.81489i	−0.214013	−	0.370681i
$339$	5.38935	−	1.19222i	0.292709	−	0.0647525i
$340$	11.9331	−	20.6688i	0.647164	−	1.12092i
$341$	−10.0213			−0.542683
$342$	−4.62097	+	2.14968i	−0.249873	+	0.116242i
$343$		0			0
$344$	28.6502	−	49.6237i	1.54472	−	2.67553i
$345$	0.528545	+	0.577332i	0.0284559	+	0.0310825i
$346$	−15.5272	−	26.8938i	−0.834746	−	1.44582i
$347$	1.41282	+	2.44707i	0.0758440	+	0.131366i	0.901453	−	0.432877i	$-0.142502\pi$
$347$	1.41282	+	2.44707i	0.0758440	+	0.131366i	−0.825609	+	0.564243i	$0.809168\pi$
$348$	−12.7430	+	40.3517i	−0.683097	+	2.16308i
$349$	−1.81202	+	3.13851i	−0.0969951	+	0.168000i	−0.910440	−	0.413642i	$-0.864256\pi$
$349$	−1.81202	+	3.13851i	−0.0969951	+	0.168000i	0.813444	+	0.581643i	$0.197590\pi$
$350$		0			0
$351$	−15.2493	−	6.34083i	−0.813947	−	0.338448i
$352$	26.9893			1.43854
$353$	1.37701	−	2.38504i	0.0732907	−	0.126943i	−0.827051	−	0.562127i	$-0.809983\pi$
$353$	1.37701	−	2.38504i	0.0732907	−	0.126943i	0.900342	+	0.435184i	$0.143317\pi$
$354$	−6.47859	+	20.5149i	−0.344333	+	1.09036i
$355$	−1.15179	−	1.99495i	−0.0611304	−	0.105881i
$356$	6.94877	+	12.0356i	0.368284	+	0.637887i
$357$		0			0
$358$	1.49135	−	2.58310i	0.0788205	−	0.136521i
$359$	−16.8015			−0.886750			−0.443375	−	0.896336i	$-0.646219\pi$
$359$	−16.8015			−0.886750			−0.443375	+	0.896336i	$0.646219\pi$
$360$	−3.83696	+	43.4024i	−0.202226	+	2.28750i
$361$	−18.6085			−0.979395
$362$	4.33081	−	7.50119i	0.227622	−	0.394254i
$363$	15.5264	−	3.43471i	0.814922	−	0.180276i
$364$		0			0
$365$	−0.371322	−	0.643149i	−0.0194359	−	0.0336640i
$366$	−1.76788	+	0.391087i	−0.0924087	+	0.0204425i
$367$	11.9670	−	20.7274i	0.624670	−	1.08196i	−0.363934	−	0.931425i	$-0.618567\pi$
$367$	11.9670	−	20.7274i	0.624670	−	1.08196i	0.988605	−	0.150536i	$-0.0480999\pi$
$368$	−4.02059			−0.209588
$369$	2.64885	−	29.9629i	0.137894	−	1.55981i
$370$	34.5551			1.79644
$371$		0			0
$372$	46.6822	+	50.9912i	2.42036	+	2.64377i
$373$	9.58030	+	16.5936i	0.496049	+	0.859182i	0.999990	−	0.00455622i	$-0.00145030\pi$
$373$	9.58030	+	16.5936i	0.496049	+	0.859182i	−0.503941	+	0.863738i	$0.668117\pi$
$374$	−5.12784	−	8.88168i	−0.265154	−	0.459261i
$375$	6.19206	−	19.6076i	0.319757	−	1.01253i
$376$	51.0299	−	88.3865i	2.63167	−	4.55818i
$377$	14.4548			0.744458
$378$		0			0
$379$	10.0770			0.517622			0.258811	−	0.965928i	$-0.416669\pi$
$379$	10.0770			0.517622			0.258811	+	0.965928i	$0.416669\pi$
$380$	2.66608	−	4.61779i	0.136767	−	0.236888i
$381$	−4.36771	+	13.8307i	−0.223765	+	0.708568i
$382$	5.25127	+	9.09546i	0.268678	+	0.465364i
$383$	10.0718	+	17.4448i	0.514643	+	0.891388i	0.999856	+	0.0169915i	$0.00540883\pi$
$383$	10.0718	+	17.4448i	0.514643	+	0.891388i	−0.485213	+	0.874396i	$0.661258\pi$
$384$	−36.0855	−	39.4164i	−1.84148	−	2.01146i
$385$		0			0
$386$	11.2294			0.571561
$387$	17.0242	−	7.91970i	0.865390	−	0.402581i
$388$	−77.6743			−3.94332
$389$	−6.69736	+	11.6002i	−0.339570	+	0.588152i	−0.984352	−	0.176215i	$-0.943615\pi$
$389$	−6.69736	+	11.6002i	−0.339570	+	0.588152i	0.644782	+	0.764366i	$0.276948\pi$
$390$	23.1519	−	5.12161i	1.17234	−	0.259343i
$391$	0.398891	+	0.690899i	0.0201728	+	0.0349402i
$392$		0			0
$393$	20.2476	−	4.47913i	1.02136	−	0.225942i
$394$	−1.20724	+	2.09100i	−0.0608198	+	0.105343i
$395$	24.9261			1.25417
$396$	17.7940	+	12.4836i	0.894181	+	0.627324i
$397$	−18.0133			−0.904061			−0.452031	−	0.892002i	$-0.649300\pi$
$397$	−18.0133			−0.904061			−0.452031	+	0.892002i	$0.649300\pi$
$398$	8.58506	−	14.8698i	0.430330	−	0.745354i
$399$		0			0
$400$	17.5249	+	30.3541i	0.876247	+	1.51770i
$401$	−14.4337	−	25.0000i	−0.720787	−	1.24844i	−0.960685	−	0.277642i	$-0.910447\pi$
$401$	−14.4337	−	25.0000i	−0.720787	−	1.24844i	0.239898	−	0.970798i	$-0.422886\pi$
$402$	3.59591	−	11.3867i	0.179348	−	0.567918i
$403$	11.8075	−	20.4513i	0.588176	−	1.01875i
$404$	52.8479			2.62928
$405$	−9.19729	+	10.9205i	−0.457017	+	0.542646i
$406$		0			0
$407$	5.41019	−	9.37073i	0.268173	−	0.464490i
$408$	−13.3734	+	42.3478i	−0.662080	+	2.09653i
$409$	5.42937	+	9.40395i	0.268465	+	0.464995i	0.968466	−	0.249147i	$-0.0801502\pi$
$409$	5.42937	+	9.40395i	0.268465	+	0.464995i	−0.700000	+	0.714142i	$0.746817\pi$
$410$	21.5936	+	37.4012i	1.06643	+	1.84711i
$411$	19.3571	+	21.1438i	0.954814	+	1.04295i
$412$	−29.7014	+	51.4443i	−1.46328	+	2.53448i
$413$		0			0
$414$	−1.89951	−	1.33263i	−0.0933561	−	0.0654951i
$415$	−22.1885			−1.08919
$416$	−31.8001	+	55.0793i	−1.55913	+	2.70049i
$417$	13.3642	−	2.95641i	0.654449	−	0.144776i
$418$	−1.14566	−	1.98434i	−0.0560359	−	0.0970570i
$419$	−0.247572	−	0.428807i	−0.0120947	−	0.0209486i	0.859915	−	0.510438i	$-0.170517\pi$
$419$	−0.247572	−	0.428807i	−0.0120947	−	0.0209486i	−0.872009	+	0.489489i	$0.837183\pi$
$420$		0			0
$421$	9.50320	−	16.4600i	0.463158	−	0.802212i	−0.535959	−	0.844244i	$-0.680050\pi$
$421$	9.50320	−	16.4600i	0.463158	−	0.802212i	0.999116	+	0.0420318i	$0.0133831\pi$
$422$	31.0226			1.51016
$423$	30.3224	−	14.1061i	1.47433	−	0.685860i
$424$	−25.5155			−1.23914
$425$	3.47737	−	6.02298i	0.168677	−	0.292157i
$426$	4.61116	+	5.03679i	0.223411	+	0.244033i
$427$		0			0
$428$	5.16864	+	8.95234i	0.249835	+	0.432728i
$429$	2.23593	−	7.08024i	0.107952	−	0.341837i
$430$	−13.4790	+	23.3464i	−0.650016	+	1.12586i
$431$	−16.9215			−0.815078			−0.407539	−	0.913188i	$-0.633613\pi$
$431$	−16.9215			−0.815078			−0.407539	+	0.913188i	$0.633613\pi$
$432$	−9.47342	−	72.7236i	−0.455790	−	3.49892i
$433$	−33.4740			−1.60866			−0.804330	−	0.594183i	$-0.797476\pi$
$433$	−33.4740			−1.60866			−0.804330	+	0.594183i	$0.797476\pi$
$434$		0			0
$435$	3.76315	−	11.9163i	0.180429	−	0.571343i
$436$	49.9774	+	86.5634i	2.39348	+	4.14564i
$437$	0.0891197	+	0.154360i	0.00426317	+	0.00738403i
$438$	1.48658	+	1.62380i	0.0710318	+	0.0775883i
$439$	−10.4657	+	18.1272i	−0.499502	+	0.865163i	−1.00000		0.000574559i	$-0.999817\pi$
$439$	−10.4657	+	18.1272i	−0.499502	+	0.865163i	0.500498	+	0.865738i	$0.333150\pi$
$440$	−19.5891			−0.933874
$441$		0			0
$442$	24.1674			1.14953
$443$	15.4290	−	26.7238i	0.733054	−	1.26969i	−0.222517	−	0.974929i	$-0.571427\pi$
$443$	15.4290	−	26.7238i	0.733054	−	1.26969i	0.955572	−	0.294759i	$-0.0952393\pi$
$444$	−72.8833	+	16.1231i	−3.45889	+	0.765169i
$445$	−2.05205	−	3.55425i	−0.0972763	−	0.168487i
$446$	−22.6972	−	39.3128i	−1.07475	−	1.86151i
$447$	23.1157	−	5.11362i	1.09334	−	0.241866i
$448$		0			0
$449$	−33.2789			−1.57053			−0.785263	−	0.619162i	$-0.787472\pi$
$449$	−33.2789			−1.57053			−0.785263	+	0.619162i	$0.787472\pi$
$450$	−1.78129	+	20.1493i	−0.0839709	+	0.949849i
$451$	13.5234			0.636791
$452$	8.55957	−	14.8256i	0.402608	−	0.697338i
$453$	4.56092	+	4.98191i	0.214291	+	0.234071i
$454$	23.1737	+	40.1380i	1.08760	+	1.88377i
$455$		0			0
$456$	−2.98786	+	9.46130i	−0.139919	+	0.443066i
$457$	−11.8952	+	20.6031i	−0.556434	+	0.963772i	0.441356	+	0.897332i	$0.354498\pi$
$457$	−11.8952	+	20.6031i	−0.556434	+	0.963772i	−0.997790	+	0.0664402i	$0.978836\pi$
$458$	−53.7309			−2.51068
$459$	−11.5570	+	8.84296i	−0.539432	+	0.412754i
$460$	2.42764			0.113189
$461$	8.53122	−	14.7765i	0.397339	−	0.688211i	−0.596058	−	0.802941i	$-0.703267\pi$
$461$	8.53122	−	14.7765i	0.397339	−	0.688211i	0.993397	+	0.114731i	$0.0366005\pi$
$462$		0			0
$463$	18.1243	+	31.3922i	0.842306	+	1.45892i	0.887940	+	0.459959i	$0.152136\pi$
$463$	18.1243	+	31.3922i	0.842306	+	1.45892i	−0.0456338	+	0.998958i	$0.514531\pi$
$464$	32.0945	+	55.5893i	1.48995	+	2.58067i
$465$	−13.7858	−	15.0583i	−0.639300	−	0.698310i
$466$	8.05253	−	13.9474i	0.373026	−	0.646100i
$467$	−8.19160			−0.379062			−0.189531	−	0.981875i	$-0.560697\pi$
$467$	−8.19160			−0.379062			−0.189531	+	0.981875i	$0.560697\pi$
$468$	−46.4420	+	21.6049i	−2.14678	+	0.998686i
$469$		0			0
$470$	−24.0080	+	41.5830i	−1.10740	+	1.91808i
$471$	0.497798	−	0.110122i	0.0229373	−	0.00507415i
$472$	20.9413	+	36.2714i	0.963900	+	1.66952i
$473$	4.22074	+	7.31054i	0.194070	+	0.336139i
$474$	−72.1472	+	15.9603i	−3.31383	+	0.733079i
$475$	0.776909	−	1.34565i	0.0356470	−	0.0617425i
$476$		0			0
$477$	−6.84451	−	4.80185i	−0.313389	−	0.219862i
$478$	−54.4530			−2.49062
$479$	12.7775	−	22.1312i	0.583817	−	1.01120i	−0.411205	−	0.911543i	$-0.634892\pi$
$479$	12.7775	−	22.1312i	0.583817	−	1.01120i	0.995022	−	0.0996574i	$-0.0317747\pi$
$480$	37.1278	+	40.5549i	1.69464	+	1.85107i
$481$	12.7491	+	22.0820i	0.581308	+	1.00685i
$482$	39.7614	+	68.8687i	1.81108	+	3.13688i
$483$		0			0
$484$	24.6596	−	42.7116i	1.12089	−	1.94144i
$485$	22.9381			1.04156
$486$	19.6286	−	37.4980i	0.890372	−	1.70094i
$487$	−6.92281			−0.313702			−0.156851	−	0.987622i	$-0.550134\pi$
$487$	−6.92281			−0.313702			−0.156851	+	0.987622i	$0.550134\pi$
$488$	−1.76246	+	3.05266i	−0.0797826	+	0.138188i
$489$	5.58574	−	17.6877i	0.252596	−	0.799865i
$490$		0			0
$491$	18.7262	+	32.4348i	0.845103	+	1.46376i	0.885532	+	0.464578i	$0.153794\pi$
$491$	18.7262	+	32.4348i	0.845103	+	1.46376i	−0.0404294	+	0.999182i	$0.512873\pi$
$492$	−62.9960	−	68.8108i	−2.84008	−	3.10223i
$493$	6.36831	−	11.0302i	0.286814	−	0.496777i
$494$	5.39946			0.242933
$495$	−5.25475	−	3.68654i	−0.236183	−	0.165698i
$496$	104.867			4.70867
$497$		0			0
$498$	64.2235	−	14.2074i	2.87793	−	0.636649i
$499$	−12.8125	−	22.1919i	−0.573566	−	0.993446i	−0.996196	−	0.0871432i	$-0.972226\pi$
$499$	−12.8125	−	22.1919i	−0.573566	−	0.993446i	0.422630	−	0.906302i	$-0.361107\pi$
$500$	−31.8867	−	55.2293i	−1.42601	−	2.46993i
$501$	5.40741	−	1.19622i	0.241585	−	0.0534430i
$502$	−30.9329	+	53.5774i	−1.38060	+	2.39127i
$503$	−5.79692			−0.258472			−0.129236	−	0.991614i	$-0.541252\pi$
$503$	−5.79692			−0.258472			−0.129236	+	0.991614i	$0.541252\pi$
$504$		0			0
$505$	−15.6066			−0.694483
$506$	0.521598	−	0.903434i	0.0231878	−	0.0401625i
$507$	−3.38974	−	3.70262i	−0.150543	−	0.164439i
$508$	22.4920	+	38.9573i	0.997921	+	1.72845i
$509$	−12.5697	−	21.7714i	−0.557144	−	0.965002i	−0.997733	−	0.0672931i	$-0.978564\pi$
$509$	−12.5697	−	21.7714i	−0.557144	−	0.965002i	0.440589	−	0.897709i	$-0.354770\pi$
$510$	6.29174	−	19.9233i	0.278603	−	0.882218i
$511$		0			0
$512$	−23.9940			−1.06039
$513$	−2.58204	+	1.97568i	−0.114000	+	0.0872286i
$514$	65.9475			2.90882
$515$	8.77113	−	15.1920i	0.386502	−	0.669441i
$516$	17.5366	−	55.5311i	0.772007	−	2.44462i
$517$	7.51771	+	13.0211i	0.330629	+	0.572665i
$518$		0			0
$519$	−13.3770	−	14.6118i	−0.587186	−	0.641386i
$520$	23.0808	−	39.9771i	1.01216	−	1.75311i
$521$	7.29656			0.319668			0.159834	−	0.987144i	$-0.448904\pi$
$521$	7.29656			0.319668			0.159834	+	0.987144i	$0.448904\pi$
$522$	−3.26218	+	36.9007i	−0.142782	+	1.61510i
$523$	16.7727			0.733421			0.366710	−	0.930335i	$-0.380484\pi$
$523$	16.7727			0.733421			0.366710	+	0.930335i	$0.380484\pi$
$524$	32.1580	−	55.6993i	1.40483	−	2.43324i
$525$		0			0
$526$	−11.6908	−	20.2490i	−0.509741	−	0.882898i
$527$	−10.4041	−	18.0204i	−0.453208	−	0.784979i
$528$	32.1933	−	7.12174i	1.40103	−	0.309934i
$529$	11.4594	−	19.8483i	0.498236	−	0.862970i
$530$	12.0042			0.521431
$531$	−1.20855	+	13.6707i	−0.0524468	+	0.593260i
$532$		0			0
$533$	−15.9339	+	27.5982i	−0.690172	+	1.19541i
$534$	8.21535	+	8.97366i	0.355513	+	0.388328i
$535$	−1.52635	−	2.64372i	−0.0659900	−	0.114298i
$536$	−11.6234	−	20.1322i	−0.502053	−	0.869581i
$537$	0.572991	−	1.81442i	0.0247264	−	0.0782980i
$538$	−20.6774	+	35.8143i	−0.891466	+	1.54406i
$539$		0			0
$540$	5.72007	+	43.9107i	0.246153	+	1.88962i
$541$	−5.29816			−0.227786			−0.113893	−	0.993493i	$-0.536332\pi$
$541$	−5.29816			−0.227786			−0.113893	+	0.993493i	$0.536332\pi$
$542$	−6.35097	+	11.0002i	−0.272798	+	0.472499i
$543$	1.66393	−	5.26898i	0.0714062	−	0.226113i
$544$	28.0202	+	48.5324i	1.20136	+	2.08081i
$545$	−14.7589	−	25.5631i	−0.632200	−	1.09500i
$546$		0			0
$547$	16.4325	−	28.4619i	0.702603	−	1.21694i	−0.264947	−	0.964263i	$-0.585354\pi$
$547$	16.4325	−	28.4619i	0.702603	−	1.21694i	0.967550	−	0.252681i	$-0.0813123\pi$
$548$	88.9084			3.79798
$549$	−1.04727	+	0.487190i	−0.0446962	+	0.0207928i
$550$	−9.09416			−0.387776
$551$	1.42280	−	2.46436i	0.0606133	−	0.104985i
$552$	−4.41062	+	0.975709i	−0.187729	+	0.0415290i
$553$		0			0
$554$	−22.2515	−	38.5408i	−0.945376	−	1.63744i
$555$	21.5232	−	4.76132i	0.913610	−	0.202107i
$556$	21.2256	−	36.7638i	0.900166	−	1.55913i
$557$	−18.8160			−0.797258			−0.398629	−	0.917112i	$-0.630514\pi$
$557$	−18.8160			−0.797258			−0.398629	+	0.917112i	$0.630514\pi$
$558$	49.5441	+	34.7583i	2.09737	+	1.47144i
$559$	−19.8923			−0.841354
$560$		0			0
$561$	−4.41776	−	4.82554i	−0.186518	−	0.203734i
$562$	−4.77054	−	8.26282i	−0.201233	−	0.348546i
$563$	−13.8325	−	23.9586i	−0.582970	−	1.00973i	−0.995125	−	0.0986197i	$-0.968557\pi$
$563$	−13.8325	−	23.9586i	−0.582970	−	1.00973i	0.412155	−	0.911114i	$-0.364776\pi$
$564$	31.2351	−	98.9083i	1.31523	−	4.16479i
$565$	−2.52773	+	4.37816i	−0.106343	+	0.184191i
$566$	−70.7856			−2.97534
$567$		0			0
$568$	13.2942			0.557812
$569$	20.0916	−	34.7996i	0.842282	−	1.45888i	−0.0456782	−	0.998956i	$-0.514545\pi$
$569$	20.0916	−	34.7996i	0.842282	−	1.45888i	0.887961	−	0.459920i	$-0.152122\pi$
$570$	1.40569	−	4.45124i	0.0588780	−	0.186442i
$571$	3.40565	+	5.89875i	0.142522	+	0.246855i	0.928446	−	0.371468i	$-0.121146\pi$
$571$	3.40565	+	5.89875i	0.142522	+	0.246855i	−0.785924	+	0.618323i	$0.787812\pi$
$572$	−11.5142	−	19.9431i	−0.481431	−	0.833863i
$573$	4.52409	+	4.94169i	0.188997	+	0.206442i
$574$		0			0
$575$	0.707427			0.0295017
$576$	−64.1075	−	44.9755i	−2.67115	−	1.87398i
$577$	−36.4222			−1.51628			−0.758138	−	0.652094i	$-0.773891\pi$
$577$	−36.4222			−1.51628			−0.758138	+	0.652094i	$0.773891\pi$
$578$	−12.4312	+	21.5315i	−0.517071	+	0.895593i
$579$	6.99441	−	1.54729i	0.290678	−	0.0643031i
$580$	−19.3787	−	33.5649i	−0.804658	−	1.39371i
$581$		0			0
$582$	−66.3930	+	14.6873i	−2.75208	+	0.608810i
$583$	1.87947	−	3.25534i	0.0778397	−	0.134822i
$584$	4.28590			0.177352
$585$	13.7148	−	6.38015i	0.567037	−	0.263787i
$586$	−51.2721			−2.11803
$587$	5.57943	−	9.66385i	0.230288	−	0.398870i	−0.727605	−	0.685996i	$-0.759367\pi$
$587$	5.57943	−	9.66385i	0.230288	−	0.398870i	0.957893	+	0.287126i	$0.0927000\pi$
$588$		0			0
$589$	−2.32446	−	4.02609i	−0.0957779	−	0.165892i
$590$	−9.85220	−	17.0645i	−0.405609	−	0.702535i
$591$	−0.463831	+	1.46876i	−0.0190795	+	0.0604166i
$592$	−56.6145	+	98.0593i	−2.32684	+	4.03021i
$593$	19.8085			0.813439			0.406720	−	0.913553i	$-0.366673\pi$
$593$	19.8085			0.813439			0.406720	+	0.913553i	$0.366673\pi$
$594$	17.5701	+	7.30586i	0.720911	+	0.299763i
$595$		0			0
$596$	36.7133	−	63.5893i	1.50384	−	2.60472i
$597$	3.29845	−	10.4448i	0.134997	−	0.427477i
$598$	1.22914	+	2.12893i	0.0502633	+	0.0870586i
$599$	9.06600	+	15.7028i	0.370427	+	0.641598i	0.989631	−	0.143632i	$-0.0458781\pi$
$599$	9.06600	+	15.7028i	0.370427	+	0.641598i	−0.619204	+	0.785230i	$0.712545\pi$
$600$	26.5913	+	29.0458i	1.08558	+	1.18579i
$601$	−12.3285	+	21.3536i	−0.502889	+	0.871030i	0.497105	+	0.867690i	$0.334396\pi$
$601$	−12.3285	+	21.3536i	−0.502889	+	0.871030i	−0.999994	+	0.00333942i	$0.998937\pi$
$602$		0			0
$603$	0.670802	−	7.58788i	0.0273172	−	0.309003i
$604$	20.9486			0.852387
$605$	−7.28223	+	12.6132i	−0.296065	+	0.512799i
$606$	45.1724	−	9.99295i	1.83500	−	0.405936i
$607$	−8.63876	−	14.9628i	−0.350637	−	0.607320i	0.635725	−	0.771916i	$-0.280701\pi$
$607$	−8.63876	−	14.9628i	−0.350637	−	0.607320i	−0.986361	+	0.164596i	$0.947368\pi$
$608$	6.26024	+	10.8431i	0.253886	+	0.439744i
$609$		0			0
$610$	0.829179	−	1.43618i	0.0335725	−	0.0581492i
$611$	−35.4308			−1.43338
$612$	−3.97445	+	44.9577i	−0.160658	+	1.81731i
$613$	19.5566			0.789882			0.394941	−	0.918707i	$-0.370765\pi$
$613$	19.5566			0.789882			0.394941	+	0.918707i	$0.370765\pi$
$614$	−29.3787	+	50.8855i	−1.18563	+	2.05357i
$615$	18.6034	+	20.3206i	0.750161	+	0.819404i
$616$		0			0
$617$	10.8723	+	18.8314i	0.437702	+	0.758122i	0.997512	−	0.0704988i	$-0.0224591\pi$
$617$	10.8723	+	18.8314i	0.437702	+	0.758122i	−0.559810	+	0.828621i	$0.689126\pi$
$618$	−15.6601	+	49.5888i	−0.629940	+	1.99475i
$619$	−16.9024	+	29.2758i	−0.679366	+	1.17670i	0.295807	+	0.955248i	$0.404412\pi$
$619$	−16.9024	+	29.2758i	−0.679366	+	1.17670i	−0.975172	+	0.221448i	$0.928922\pi$
$620$	−63.3190			−2.54295
$621$	−1.36677	−	0.568317i	−0.0548464	−	0.0228058i
$622$	−12.2031			−0.489300
$623$		0			0
$624$	−23.3977	+	74.0906i	−0.936658	+	2.96600i
$625$	3.20808	+	5.55655i	0.128323	+	0.222262i
$626$	11.6778	+	20.2266i	0.466740	+	0.808418i
$627$	−0.987011	−	1.07812i	−0.0394174	−	0.0430558i
$628$	0.790623	−	1.36940i	0.0315493	−	0.0546450i
$629$	22.4674			0.895832
$630$		0			0
$631$	−23.6410			−0.941134			−0.470567	−	0.882364i	$-0.655951\pi$
$631$	−23.6410			−0.941134			−0.470567	+	0.882364i	$0.655951\pi$
$632$	−71.9258	+	124.579i	−2.86105	+	4.95549i
$633$	19.3229	−	4.27458i	0.768018	−	0.169899i
$634$	−10.9454	−	18.9581i	−0.434699	−	0.752921i
$635$	−6.64213	−	11.5045i	−0.263585	−	0.456542i
$636$	−25.3192	+	5.60107i	−1.00397	+	0.222097i
$637$		0			0
$638$	−16.6547			−0.659365
$639$	3.56615	+	2.50188i	0.141075	+	0.0989728i
$640$	48.9458			1.93475
$641$	−7.95901	+	13.7854i	−0.314362	+	0.544491i	−0.979302	−	0.202406i	$-0.935124\pi$
$641$	−7.95901	+	13.7854i	−0.314362	+	0.544491i	0.664940	+	0.746897i	$0.268457\pi$
$642$	6.11074	+	6.67479i	0.241172	+	0.263433i
$643$	−13.2527	−	22.9544i	−0.522636	−	0.905231i	−0.999653	−	0.0263376i	$-0.991616\pi$
$643$	−13.2527	−	22.9544i	−0.522636	−	0.905231i	0.477017	−	0.878894i	$-0.341718\pi$
$644$		0			0
$645$	−5.17875	+	16.3989i	−0.203913	+	0.645707i
$646$	2.37883	−	4.12026i	0.0935938	−	0.162109i
$647$	0.0160392			0.000630565			0.000315282	−	1.00000i	$-0.499900\pi$
$647$	0.0160392			0.000630565			0.000315282		1.00000i	$0.499900\pi$
$648$	−28.0408	−	77.4794i	−1.10155	−	3.04368i
$649$	−6.17012			−0.242198
$650$	10.7152	−	18.5592i	0.420283	−	0.727951i
$651$		0			0
$652$	−28.7644	−	49.8214i	−1.12650	−	1.95115i
$653$	16.6440	+	28.8282i	0.651328	+	1.12813i	0.982801	+	0.184669i	$0.0591212\pi$
$653$	16.6440	+	28.8282i	0.651328	+	1.12813i	−0.331473	+	0.943465i	$0.607545\pi$
$654$	59.0870	+	64.5410i	2.31048	+	2.52375i
$655$	−9.49661	+	16.4486i	−0.371063	+	0.642700i
$656$	−141.514			−5.52520
$657$	1.14969	+	0.806577i	0.0448535	+	0.0314676i
$658$		0			0
$659$	19.4156	−	33.6288i	0.756324	−	1.30999i	−0.188389	−	0.982094i	$-0.560327\pi$
$659$	19.4156	−	33.6288i	0.756324	−	1.30999i	0.944713	−	0.327897i	$-0.106340\pi$
$660$	−19.4384	+	4.30012i	−0.756639	+	0.167382i
$661$	−2.65322	−	4.59551i	−0.103198	−	0.178745i	0.809802	−	0.586703i	$-0.199574\pi$
$661$	−2.65322	−	4.59551i	−0.103198	−	0.178745i	−0.913001	+	0.407958i	$0.866241\pi$
$662$	−31.0917	−	53.8525i	−1.20842	−	2.09304i
$663$	15.0531	−	3.33001i	0.584613	−	0.129327i
$664$	64.0264	−	110.897i	2.48471	−	4.30364i
$665$		0			0
$666$	−59.2492	+	27.5628i	−2.29586	+	1.06804i
$667$	1.29555			0.0501640
$668$	8.58826	−	14.8753i	0.332290	−	0.575543i
$669$	−19.5542	−	21.3592i	−0.756010	−	0.825793i
$670$	5.46842	+	9.47158i	0.211263	+	0.365919i
$671$	−0.259644	−	0.449717i	−0.0100235	−	0.0173611i
$672$		0			0
$673$	−3.03565	+	5.25789i	−0.117016	+	0.202677i	−0.918584	−	0.395227i	$-0.870666\pi$
$673$	−3.03565	+	5.25789i	−0.117016	+	0.202677i	0.801568	+	0.597903i	$0.203999\pi$
$674$	−37.0285			−1.42628
$675$	1.66686	+	12.7958i	0.0641574	+	0.492510i
$676$	−15.5693			−0.598819
$677$	17.3925	−	30.1247i	0.668449	−	1.15779i	−0.309889	−	0.950773i	$-0.600292\pi$
$677$	17.3925	−	30.1247i	0.668449	−	1.15779i	0.978338	−	0.207014i	$-0.0663747\pi$
$678$	4.51304	−	14.2909i	0.173322	−	0.548838i
$679$		0			0
$680$	−20.3373	−	35.2253i	−0.779901	−	1.35083i
$681$	19.9647	+	21.8075i	0.765049	+	0.835666i
$682$	−13.6046	+	23.5638i	−0.520946	+	0.902305i
$683$	19.4241			0.743243			0.371622	−	0.928384i	$-0.378802\pi$
$683$	19.4241			0.743243			0.371622	+	0.928384i	$0.378802\pi$
$684$	−0.887968	+	10.0444i	−0.0339523	+	0.384057i
$685$	−26.2556			−1.00318
$686$		0			0
$687$	−33.4672	+	7.40354i	−1.27685	+	0.282463i
$688$	−44.1676	−	76.5006i	−1.68387	−	2.91656i
$689$	4.42895	+	7.67117i	0.168730	+	0.292248i
$690$	2.07506	−	0.459040i	0.0789961	−	0.0174754i
$691$	3.31837	−	5.74759i	0.126237	−	0.218649i	−0.795979	−	0.605324i	$-0.793043\pi$
$691$	3.31837	−	5.74759i	0.126237	−	0.218649i	0.922216	+	0.386676i	$0.126377\pi$
$692$	−61.4416			−2.33566
$693$		0			0
$694$	7.67197			0.291224
$695$	−6.26814	+	10.8567i	−0.237764	+	0.411820i
$696$	48.6982	+	53.1933i	1.84590	+	2.01629i
$697$	14.0399	+	24.3178i	0.531799	+	0.921103i
$698$	4.91987	+	8.52147i	0.186220	+	0.322542i
$699$	3.09385	−	9.79690i	0.117020	−	0.370553i
$700$		0			0
$701$	−13.9153			−0.525574			−0.262787	−	0.964854i	$-0.584642\pi$
$701$	−13.9153			−0.525574			−0.262787	+	0.964854i	$0.584642\pi$
$702$	−35.6116	+	27.2487i	−1.34407	+	1.02844i
$703$	5.01963			0.189319
$704$	17.6036	−	30.4904i	0.663462	−	1.14915i
$705$	−9.22406	+	29.2087i	−0.347398	+	1.10006i
$706$	−3.73876	−	6.47571i	−0.140710	−	0.243717i
$707$		0			0
$708$	28.7423	+	31.3954i	1.08020	+	1.17991i
$709$	−17.0778	+	29.5796i	−0.641370	+	1.11089i	0.343757	+	0.939059i	$0.388300\pi$
$709$	−17.0778	+	29.5796i	−0.641370	+	1.11089i	−0.985127	+	0.171827i	$0.945033\pi$
$710$	−6.25450			−0.234727
$711$	−42.7389	+	19.8822i	−1.60283	+	0.745642i
$712$	23.6852			0.887642
$713$	1.05829	−	1.83301i	0.0396332	−	0.0686467i
$714$		0			0
$715$	3.40025	+	5.88941i	0.127162	+	0.220251i
$716$	−2.95068	−	5.11072i	−0.110272	−	0.190997i
$717$	−33.9169	+	7.50303i	−1.26665	+	0.280206i
$718$	−22.8092	+	39.5066i	−0.851231	+	1.47437i
$719$	−44.2900			−1.65174			−0.825870	−	0.563861i	$-0.809316\pi$
$719$	−44.2900			−1.65174			−0.825870	+	0.563861i	$0.809316\pi$
$720$	54.9879	+	38.5775i	2.04928	+	1.43770i
$721$		0			0
$722$	−25.2623	+	43.7556i	−0.940165	+	1.62841i
$723$	34.2554	+	37.4173i	1.27397	+	1.39156i
$724$	−8.56860	−	14.8413i	−0.318450	−	0.551571i
$725$	−5.64705	−	9.78099i	−0.209726	−	0.363257i
$726$	13.0018	−	41.1711i	0.482541	−	1.52800i
$727$	14.1247	−	24.4647i	0.523857	−	0.907346i	−0.475758	−	0.879576i	$-0.657826\pi$
$727$	14.1247	−	24.4647i	0.523857	−	0.907346i	0.999614	−	0.0277700i	$-0.00884060\pi$
$728$		0			0
$729$	7.05919	−	26.0608i	0.261451	−	0.965217i
$730$	−2.01638			−0.0746295
$731$	−8.76391	+	15.1795i	−0.324145	+	0.561435i
$732$	−1.07879	+	3.41606i	−0.0398731	+	0.126261i
$733$	12.5084	+	21.6653i	0.462010	+	0.800225i	0.999061	−	0.0433249i	$-0.0137951\pi$
$733$	12.5084	+	21.6653i	0.462010	+	0.800225i	−0.537051	+	0.843550i	$0.680462\pi$
$734$	−32.4919	−	56.2776i	−1.19930	−	2.07724i
$735$		0			0
$736$	−2.85018	+	4.93666i	−0.105059	+	0.181968i
$737$	3.42470			0.126150
$738$	−66.8579	−	46.9050i	−2.46107	−	1.72660i
$739$	32.0230			1.17798			0.588992	−	0.808139i	$-0.299525\pi$
$739$	32.0230			1.17798			0.588992	+	0.808139i	$0.299525\pi$
$740$	34.1840	−	59.2084i	1.25663	−	2.17655i
$741$	3.36314	−	0.743987i	0.123548	−	0.0273311i
$742$		0			0
$743$	19.4031	+	33.6072i	0.711833	+	1.23293i	0.964169	+	0.265290i	$0.0854678\pi$
$743$	19.4031	+	33.6072i	0.711833	+	1.23293i	−0.252336	+	0.967640i	$0.581199\pi$
$744$	115.040	−	25.4489i	4.21757	−	0.933003i
$745$	−10.8418	+	18.7786i	−0.397214	+	0.687995i
$746$	52.0236			1.90472
$747$	38.0450	−	17.6986i	1.39200	−	0.647559i
$748$	−20.2911			−0.741915
$749$		0			0
$750$	−37.6987	−	41.1785i	−1.37656	−	1.50363i
$751$	−10.8495	−	18.7920i	−0.395905	−	0.685728i	0.597311	−	0.802010i	$-0.296236\pi$
$751$	−10.8495	−	18.7920i	−0.395905	−	0.685728i	−0.993216	+	0.116282i	$0.962903\pi$
$752$	−78.6685	−	136.258i	−2.86874	−	4.96881i
$753$	−11.8847	+	37.6337i	−0.433102	+	1.37145i
$754$	19.6233	−	33.9885i	0.714638	−	1.23779i
$755$	−6.18635			−0.225144
$756$		0			0
$757$	33.5242			1.21846			0.609229	−	0.792995i	$-0.291479\pi$
$757$	33.5242			1.21846			0.609229	+	0.792995i	$0.291479\pi$
$758$	13.6802	−	23.6949i	0.496889	−	0.860637i
$759$	0.200402	−	0.634589i	0.00727414	−	0.0230341i
$760$	−4.54374	−	7.86999i	−0.164819	−	0.285475i
$761$	6.66048	+	11.5363i	0.241442	+	0.418190i	0.961125	−	0.276113i	$-0.0890462\pi$
$761$	6.66048	+	11.5363i	0.241442	+	0.418190i	−0.719683	+	0.694303i	$0.755713\pi$
$762$	26.5917	+	29.0462i	0.963315	+	1.05223i
$763$		0			0
$764$	20.7795			0.751775
$765$	1.17370	−	13.2765i	0.0424352	−	0.480012i
$766$	54.6923			1.97611
$767$	7.26992	−	12.5919i	0.262502	−	0.454666i
$768$	−53.3802	+	11.8087i	−1.92619	+	0.426109i
$769$	27.3568	+	47.3833i	0.986510	+	1.70869i	0.635022	+	0.772494i	$0.280991\pi$
$769$	27.3568	+	47.3833i	0.986510	+	1.70869i	0.351488	+	0.936192i	$0.385676\pi$
$770$		0			0
$771$	41.0765	−	9.08686i	1.47933	−	0.327255i
$772$	11.1088	−	19.2410i	0.399814	−	0.692498i
$773$	2.36042			0.0848983			0.0424491	−	0.999099i	$-0.486484\pi$
$773$	2.36042			0.0848983			0.0424491	+	0.999099i	$0.486484\pi$
$774$	4.48934	−	50.7818i	0.161366	−	1.82532i
$775$	−18.4515			−0.662796
$776$	−66.1892	+	114.643i	−2.37606	+	4.11545i
$777$		0			0
$778$	18.1842	+	31.4960i	0.651936	+	1.12919i
$779$	3.13678	+	5.43306i	0.112387	+	0.194660i
$780$	14.1276	−	44.7361i	0.505849	−	1.60181i
$781$	−0.979248	+	1.69611i	−0.0350403	+	0.0606915i
$782$	2.16608			0.0774589
$783$	3.05261	+	23.4337i	0.109092	+	0.837452i
$784$		0			0
$785$	−0.233479	+	0.404398i	−0.00833323	+	0.0144336i
$786$	16.9553	−	53.6904i	0.604777	−	1.91507i
$787$	0.833971	+	1.44448i	0.0297278	+	0.0514901i	0.880507	−	0.474034i	$-0.157203\pi$
$787$	0.833971	+	1.44448i	0.0297278	+	0.0514901i	−0.850779	+	0.525524i	$0.823869\pi$
$788$	2.38855	+	4.13708i	0.0850884	+	0.147377i
$789$	−10.0719	−	11.0015i	−0.358568	−	0.391665i
$790$	33.8388	−	58.6105i	1.20393	−	2.08527i
$791$		0			0
$792$	33.5880	−	15.6252i	1.19350	−	0.555218i
$793$	1.22370			0.0434548
$794$	−24.4542	+	42.3560i	−0.867848	+	1.50316i
$795$	7.47704	−	1.65406i	0.265183	−	0.0586633i
$796$	−16.9857	−	29.4201i	−0.602043	−	1.04277i
$797$	−14.3148	−	24.7939i	−0.507055	−	0.878244i	−0.999967	−	0.00816511i	$-0.997401\pi$
$797$	−14.3148	−	24.7939i	−0.507055	−	0.878244i	0.492912	−	0.870079i	$-0.335932\pi$
$798$		0			0
$799$	−15.6097	+	27.0368i	−0.552232	+	0.956493i
$800$	49.6934			1.75693
$801$	6.35353	+	4.45740i	0.224491	+	0.157495i
$802$	−78.3791			−2.76766
$803$	−0.315698	+	0.546805i	−0.0111408	+	0.0192963i
$804$	−15.9533	−	17.4258i	−0.562629	−	0.614562i
$805$		0			0
$806$	−32.0591	−	55.5279i	−1.12923	−	1.95589i
$807$	−7.94443	+	25.1566i	−0.279657	+	0.885556i
$808$	45.0337	−	78.0007i	1.58428	−	2.74406i
$809$	−2.85691			−0.100444			−0.0502219	−	0.998738i	$-0.515993\pi$
$809$	−2.85691			−0.100444			−0.0502219	+	0.998738i	$0.515993\pi$
$810$	13.1923	+	36.4516i	0.463531	+	1.28078i
$811$	26.2917			0.923225			0.461613	−	0.887082i	$-0.347271\pi$
$811$	26.2917			0.923225			0.461613	+	0.887082i	$0.347271\pi$
$812$		0			0
$813$	−2.44010	+	7.72675i	−0.0855779	+	0.270989i
$814$	−14.6894	−	25.4428i	−0.514863	−	0.891769i
$815$	8.49443	+	14.7128i	0.297547	+	0.515366i
$816$	46.2293	+	50.4965i	1.61835	+	1.76773i
$817$	−1.95802	+	3.39139i	−0.0685025	+	0.118650i
$818$	29.4829			1.03085
$819$		0			0
$820$	85.4467			2.98393
$821$	1.32925	−	2.30232i	0.0463910	−	0.0803517i	−0.841897	−	0.539638i	$-0.818561\pi$
$821$	1.32925	−	2.30232i	0.0463910	−	0.0803517i	0.888289	+	0.459286i	$0.151895\pi$
$822$	75.9956	−	16.8116i	2.65065	−	0.586371i
$823$	6.10769	+	10.5788i	0.212901	+	0.368755i	0.952621	−	0.304160i	$-0.0983756\pi$
$823$	6.10769	+	10.5788i	0.212901	+	0.368755i	−0.739721	+	0.672914i	$0.765042\pi$
$824$	50.6193	+	87.6752i	1.76341	+	3.05431i
$825$	−5.66444	+	1.25308i	−0.197211	+	0.0436265i
$826$		0			0
$827$	9.15812			0.318459			0.159230	−	0.987242i	$-0.449099\pi$
$827$	9.15812			0.318459			0.159230	+	0.987242i	$0.449099\pi$
$828$	−4.16251	+	1.93641i	−0.144657	+	0.0672947i
$829$	18.3431			0.637083			0.318541	−	0.947909i	$-0.396807\pi$
$829$	18.3431			0.637083			0.318541	+	0.947909i	$0.396807\pi$
$830$	−30.1224	+	52.1735i	−1.04556	+	1.81097i
$831$	−19.1702	−	20.9397i	−0.665007	−	0.726391i
$832$	41.4828	+	71.8503i	1.43816	+	2.49096i
$833$		0			0
$834$	11.1912	−	35.4378i	0.387520	−	1.22711i
$835$	−2.53620	+	4.39284i	−0.0877690	+	0.152020i
$836$	−4.53341			−0.156791
$837$	35.6487	+	14.8231i	1.23220	+	0.512362i
$838$	−1.34438			−0.0464409
$839$	−9.47055	+	16.4035i	−0.326960	+	0.566311i	−0.981907	−	0.189364i	$-0.939357\pi$
$839$	−9.47055	+	16.4035i	−0.326960	+	0.566311i	0.654947	+	0.755675i	$0.272691\pi$
$840$		0			0
$841$	4.15821	+	7.20224i	0.143387	+	0.248353i
$842$	−25.8024	−	44.6911i	−0.889211	−	1.54016i
$843$	−4.10994	−	4.48930i	−0.141554	−	0.154620i
$844$	30.6895	−	53.1557i	1.05637	−	1.82969i
$845$	4.59778			0.158168
$846$	7.99612	−	90.4493i	0.274912	−	3.10971i
$847$		0			0
$848$	−19.6676	+	34.0652i	−0.675387	+	1.16980i
$849$	−44.0900	+	9.75350i	−1.51316	+	0.334739i
$850$	−9.44151	−	16.3532i	−0.323841	−	0.560909i
$851$	1.14268	+	1.97917i	0.0391704	+	0.0678452i
$852$	13.1919	−	2.91829i	0.451948	−	0.0999790i
$853$	−9.97922	+	17.2845i	−0.341682	+	0.591811i	−0.984745	−	0.174002i	$-0.944330\pi$
$853$	−9.97922	+	17.2845i	−0.341682	+	0.591811i	0.643063	+	0.765813i	$0.277663\pi$
$854$		0			0
$855$	0.262227	−	2.96622i	0.00896796	−	0.101442i
$856$	17.6176			0.602156
$857$	8.20001	−	14.2028i	0.280107	−	0.485159i	−0.691304	−	0.722564i	$-0.742963\pi$
$857$	8.20001	−	14.2028i	0.280107	−	0.485159i	0.971411	+	0.237405i	$0.0762967\pi$
$858$	−13.6129	−	14.8694i	−0.464736	−	0.507633i
$859$	−16.8575	−	29.1981i	−0.575172	−	0.996226i	−0.996023	−	0.0890968i	$-0.971602\pi$
$859$	−16.8575	−	29.1981i	−0.575172	−	0.996226i	0.420851	−	0.907130i	$-0.361731\pi$
$860$	26.6685	+	46.1912i	0.909389	+	1.57511i
$861$		0			0
$862$	−22.9720	+	39.7887i	−0.782429	+	1.35521i
$863$	−28.6831			−0.976383			−0.488191	−	0.872737i	$-0.662343\pi$
$863$	−28.6831			−0.976383			−0.488191	+	0.872737i	$0.662343\pi$
$864$	−96.0089	−	39.9216i	−3.26629	−	1.35816i
$865$	18.1444			0.616927
$866$	−45.4432	+	78.7100i	−1.54422	+	2.67467i
$867$	−4.77618	+	15.1241i	−0.162208	+	0.513643i
$868$		0			0
$869$	−10.5961	−	18.3529i	−0.359447	−	0.622581i
$870$	−22.9110	−	25.0257i	−0.776754	−	0.848452i
$871$	−4.03513	+	6.98906i	−0.136725	+	0.236815i
$872$	170.351			5.76880
$873$	−39.3302	+	18.2965i	−1.33113	+	0.619243i
$874$	0.483944			0.0163696
$875$		0			0
$876$	4.25292	−	0.940823i	0.143693	−	0.0317875i
$877$	14.7621	+	25.5688i	0.498482	+	0.863396i	0.999998	−	0.00175202i	$-0.000557684\pi$
$877$	14.7621	+	25.5688i	0.498482	+	0.863396i	−0.501517	+	0.865148i	$0.667224\pi$
$878$	28.4159	+	49.2177i	0.958989	+	1.66102i
$879$	−31.9357	+	7.06475i	−1.07716	+	0.238288i
$880$	−15.0994	+	26.1530i	−0.509001	+	0.881616i
$881$	57.5032			1.93733			0.968666	−	0.248366i	$-0.0798934\pi$
$881$	57.5032			1.93733			0.968666	+	0.248366i	$0.0798934\pi$
$882$		0			0
$883$	19.8715			0.668730			0.334365	−	0.942444i	$-0.391478\pi$
$883$	19.8715			0.668730			0.334365	+	0.942444i	$0.391478\pi$
$884$	23.9079	−	41.4097i	0.804109	−	1.39276i
$885$	−8.48791	−	9.27138i	−0.285318	−	0.311654i
$886$	−41.8918	−	72.5587i	−1.40738	−	2.43766i
$887$	−18.5475	−	32.1253i	−0.622766	−	1.07866i	−0.988968	−	0.148127i	$-0.952676\pi$
$887$	−18.5475	−	32.1253i	−0.622766	−	1.07866i	0.366203	−	0.930535i	$-0.380658\pi$
$888$	−38.3098	+	121.311i	−1.28559	+	4.07093i
$889$		0			0
$890$	−11.1432			−0.373519
$891$	11.9505	+	2.12960i	0.400357	+	0.0713442i
$892$	−89.8139			−3.00719
$893$	−3.48750	+	6.04053i	−0.116705	+	0.202139i
$894$	19.3571	−	61.2958i	0.647399	−	2.05004i
$895$	0.871366	+	1.50925i	0.0291266	+	0.0504487i
$896$		0			0
$897$	1.05893	+	1.15668i	0.0353568	+	0.0386204i
$898$	−45.1783	+	78.2511i	−1.50762	+	2.61127i
$899$	−33.7913			−1.12700
$900$	32.7627	+	22.9851i	1.09209	+	0.766170i
$901$	7.80503			0.260023
$902$	18.3589	−	31.7985i	0.611284	−	1.05877i
$903$		0			0
$904$	−14.5879	−	25.2669i	−0.485185	−	0.840366i
$905$	2.53040	+	4.38278i	0.0841133	+	0.145689i
$906$	17.9061	−	3.96115i	0.594890	−	0.131600i
$907$	−12.2044	+	21.1386i	−0.405240	+	0.701896i	−0.994349	−	0.106157i	$-0.966145\pi$
$907$	−12.2044	+	21.1386i	−0.405240	+	0.701896i	0.589110	+	0.808053i	$0.299479\pi$
$908$	91.6993			3.04315
$909$	26.7594	−	12.4485i	0.887555	−	0.412892i
$910$		0			0
$911$	−12.5493	+	21.7360i	−0.415776	+	0.720146i	−0.995510	−	0.0946604i	$-0.969823\pi$
$911$	−12.5493	+	21.7360i	−0.415776	+	0.720146i	0.579733	+	0.814806i	$0.303157\pi$
$912$	10.3285	+	11.2819i	0.342011	+	0.373580i
$913$	9.43234	+	16.3373i	0.312165	+	0.540685i
$914$	32.2971	+	55.9401i	1.06829	+	1.85034i
$915$	0.318577	−	1.00880i	0.0105318	−	0.0333499i
$916$	−53.1538	+	92.0652i	−1.75625	+	3.04192i
$917$		0			0
$918$	5.10378	+	39.1796i	0.168450	+	1.29312i
$919$	−28.5976			−0.943348			−0.471674	−	0.881773i	$-0.656350\pi$
$919$	−28.5976			−0.943348			−0.471674	+	0.881773i	$0.656350\pi$
$920$	2.06869	−	3.58307i	0.0682026	−	0.118130i
$921$	−11.2876	+	35.7429i	−0.371938	+	1.17777i
$922$	−23.1634	−	40.1202i	−0.762846	−	1.32129i
$923$	−2.30759	−	3.99686i	−0.0759553	−	0.131558i
$924$		0			0
$925$	9.96139	−	17.2536i	0.327528	−	0.567296i
$926$	98.4196			3.23427
$927$	−2.92132	+	33.0450i	−0.0959488	+	1.08534i
$928$	91.0065			2.98744
$929$	22.7285	−	39.3669i	0.745698	−	1.29159i	−0.204170	−	0.978935i	$-0.565450\pi$
$929$	22.7285	−	39.3669i	0.745698	−	1.29159i	0.949868	−	0.312651i	$-0.101217\pi$
$930$	−54.1227	+	11.9729i	−1.77475	+	0.392607i
$931$		0			0
$932$	−15.9321	−	27.5952i	−0.521873	−	0.903910i
$933$	−7.60091	+	1.68146i	−0.248843	+	0.0550485i
$934$	−11.1206	+	19.2615i	−0.363878	+	0.630256i
$935$	5.99217			0.195965
$936$	−7.68731	+	86.9562i	−0.251268	+	2.84225i
$937$	27.0083			0.882322			0.441161	−	0.897428i	$-0.354567\pi$
$937$	27.0083			0.882322			0.441161	+	0.897428i	$0.354567\pi$
$938$		0			0
$939$	10.0607	+	10.9894i	0.328320	+	0.358625i
$940$	47.5002	+	82.2728i	1.54929	+	2.68344i
$941$	−6.35657	−	11.0099i	−0.207218	−	0.358912i	0.743619	−	0.668604i	$-0.233108\pi$
$941$	−6.35657	−	11.0099i	−0.207218	−	0.358912i	−0.950837	+	0.309691i	$0.899774\pi$
$942$	0.416856	−	1.32001i	0.0135819	−	0.0430082i
$943$	−1.42812	+	2.47358i	−0.0465060	+	0.0805508i
$944$	64.5667			2.10147
$945$		0			0
$946$	22.9197			0.745185
$947$	−23.7724	+	41.1749i	−0.772498	+	1.33801i	0.163692	+	0.986511i	$0.447660\pi$
$947$	−23.7724	+	41.1749i	−0.772498	+	1.33801i	−0.936190	+	0.351494i	$0.885674\pi$
$948$	−44.0253	+	139.409i	−1.42987	+	4.52781i
$949$	−0.743940	−	1.28854i	−0.0241493	−	0.0418279i
$950$	−2.10941	−	3.65361i	−0.0684384	−	0.118539i
$951$	−9.42977	−	10.3002i	−0.305781	−	0.334006i
$952$		0			0
$953$	38.2355			1.23857			0.619285	−	0.785166i	$-0.287423\pi$
$953$	38.2355			1.23857			0.619285	+	0.785166i	$0.287423\pi$
$954$	−20.5828	+	9.57517i	−0.666394	+	0.310008i
$955$	−6.13640			−0.198569
$956$	−53.8682	+	93.3024i	−1.74222	+	3.01762i
$957$	−10.3736	+	2.29483i	−0.335332	+	0.0741815i
$958$	−34.6925	−	60.0891i	−1.12086	−	1.94139i
$959$		0			0
$960$	70.0320	−	15.4923i	2.26027	−	0.500013i
$961$	−12.1028	+	20.9627i	−0.390413	+	0.676215i
$962$	69.2309			2.23209
$963$	4.72589	+	3.31551i	0.152290	+	0.106841i
$964$	157.337			5.06749
$965$	−3.28054	+	5.68207i	−0.105604	+	0.182912i
$966$		0			0
$967$	−20.4093	−	35.3499i	−0.656317	−	1.13678i	−0.981562	−	0.191145i	$-0.938780\pi$
$967$	−20.4093	−	35.3499i	−0.656317	−	1.13678i	0.325244	−	0.945630i	$-0.394553\pi$
$968$	−42.0267	−	72.7924i	−1.35079	−	2.33964i
$969$	0.913966	−	2.89415i	0.0293608	−	0.0929733i
$970$	31.1399	−	53.9359i	0.999843	−	1.73178i
$971$	44.9471			1.44242			0.721210	−	0.692717i	$-0.243586\pi$
$971$	44.9471			1.44242			0.721210	+	0.692717i	$0.243586\pi$
$972$	−44.8331	−	70.7279i	−1.43802	−	2.26860i
$973$		0			0
$974$	−9.39817	+	16.2781i	−0.301137	+	0.521584i
$975$	4.11685	−	13.0363i	0.131845	−	0.417496i
$976$	2.71703	+	4.70603i	0.0869699	+	0.150636i
$977$	−26.7552	−	46.3414i	−0.855974	−	1.48259i	−0.875738	−	0.482787i	$-0.839625\pi$
$977$	−26.7552	−	46.3414i	−0.855974	−	1.48259i	0.0197635	−	0.999805i	$-0.493709\pi$
$978$	−34.0074	−	37.1464i	−1.08744	−	1.18781i
$979$	−1.74465	+	3.02182i	−0.0557593	+	0.0965779i
$980$		0			0
$981$	45.6963	+	32.0588i	1.45897	+	1.02356i
$982$	101.688			3.24501
$983$	−5.80278	+	10.0507i	−0.185080	+	0.320568i	−0.943603	−	0.331078i	$-0.892588\pi$
$983$	−5.80278	+	10.0507i	−0.185080	+	0.320568i	0.758524	+	0.651646i	$0.225921\pi$
$984$	−155.242	+	34.3424i	−4.94895	+	1.09480i
$985$	−0.705363	−	1.22172i	−0.0224747	−	0.0389274i
$986$	−17.2908	−	29.9485i	−0.550651	−	0.953756i
$987$		0			0
$988$	5.34147	−	9.25170i	0.169935	−	0.294336i
$989$	−1.78291			−0.0566932
$990$	−15.8021	+	7.35117i	−0.502224	+	0.233635i
$991$	26.0091			0.826208			0.413104	−	0.910684i	$-0.364445\pi$
$991$	26.0091			0.826208			0.413104	+	0.910684i	$0.364445\pi$
$992$	74.3398	−	128.760i	2.36029	−	4.08814i
$993$	−26.7863	−	29.2588i	−0.850037	−	0.928500i
$994$		0			0
$995$	5.01607	+	8.68808i	0.159020	+	0.275431i
$996$	39.1901	−	124.099i	1.24179	−	3.93221i
$997$	23.4499	−	40.6164i	0.742666	−	1.28633i	−0.208612	−	0.977999i	$-0.566895\pi$
$997$	23.4499	−	40.6164i	0.742666	−	1.28633i	0.951277	−	0.308336i	$-0.0997721\pi$
$998$	−69.5753			−2.20237
$999$	−33.1065	+	25.3319i	−1.04744	+	0.801465i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.f.h.295.12	yes	24
3.2	odd	2		1323.2.f.h.883.2		24
7.2	even	3		441.2.h.h.214.2		24
7.3	odd	6		441.2.g.h.79.12		24
7.4	even	3		441.2.g.h.79.11		24
7.5	odd	6		441.2.h.h.214.1		24
7.6	odd	2	inner	441.2.f.h.295.11	yes	24
9.2	odd	6		3969.2.a.bi.1.12		12
9.4	even	3	inner	441.2.f.h.148.12	yes	24
9.5	odd	6		1323.2.f.h.442.2		24
9.7	even	3		3969.2.a.bh.1.1		12
21.2	odd	6		1323.2.h.h.802.12		24
21.5	even	6		1323.2.h.h.802.11		24
21.11	odd	6		1323.2.g.h.667.1		24
21.17	even	6		1323.2.g.h.667.2		24
21.20	even	2		1323.2.f.h.883.1		24
63.4	even	3		441.2.h.h.373.2		24
63.5	even	6		1323.2.g.h.361.2		24
63.13	odd	6	inner	441.2.f.h.148.11	✓	24
63.20	even	6		3969.2.a.bi.1.11		12
63.23	odd	6		1323.2.g.h.361.1		24
63.31	odd	6		441.2.h.h.373.1		24
63.32	odd	6		1323.2.h.h.226.12		24
63.34	odd	6		3969.2.a.bh.1.2		12
63.40	odd	6		441.2.g.h.67.12		24
63.41	even	6		1323.2.f.h.442.1		24
63.58	even	3		441.2.g.h.67.11		24
63.59	even	6		1323.2.h.h.226.11		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.11	✓	24	63.13	odd	6	inner
441.2.f.h.148.12	yes	24	9.4	even	3	inner
441.2.f.h.295.11	yes	24	7.6	odd	2	inner
441.2.f.h.295.12	yes	24	1.1	even	1	trivial
441.2.g.h.67.11		24	63.58	even	3
441.2.g.h.67.12		24	63.40	odd	6
441.2.g.h.79.11		24	7.4	even	3
441.2.g.h.79.12		24	7.3	odd	6
441.2.h.h.214.1		24	7.5	odd	6
441.2.h.h.214.2		24	7.2	even	3
441.2.h.h.373.1		24	63.31	odd	6
441.2.h.h.373.2		24	63.4	even	3
1323.2.f.h.442.1		24	63.41	even	6
1323.2.f.h.442.2		24	9.5	odd	6
1323.2.f.h.883.1		24	21.20	even	2
1323.2.f.h.883.2		24	3.2	odd	2
1323.2.g.h.361.1		24	63.23	odd	6
1323.2.g.h.361.2		24	63.5	even	6
1323.2.g.h.667.1		24	21.11	odd	6
1323.2.g.h.667.2		24	21.17	even	6
1323.2.h.h.226.11		24	63.59	even	6
1323.2.h.h.226.12		24	63.32	odd	6
1323.2.h.h.802.11		24	21.5	even	6
1323.2.h.h.802.12		24	21.2	odd	6
3969.2.a.bh.1.1		12	9.7	even	3
3969.2.a.bh.1.2		12	63.34	odd	6
3969.2.a.bi.1.11		12	63.20	even	6
3969.2.a.bi.1.12		12	9.2	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.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.35757 - 2.35137i) q^{2} +(0.521588 - 1.65165i) q^{3} +(-2.68597 - 4.65224i) q^{4} +(0.793197 + 1.37386i) q^{5} +(-3.17555 - 3.46867i) q^{6} -9.15528 q^{8} +(-2.45589 - 1.72296i) q^{9} +O(q^{10})\)	\(q+(1.35757 - 2.35137i) q^{2} +(0.521588 - 1.65165i) q^{3} +(-2.68597 - 4.65224i) q^{4} +(0.793197 + 1.37386i) q^{5} +(-3.17555 - 3.46867i) q^{6} -9.15528 q^{8} +(-2.45589 - 1.72296i) q^{9} +4.30727 q^{10} +(0.674376 - 1.16805i) q^{11} +(-9.08484 + 2.00973i) q^{12} +(1.58916 + 2.75251i) q^{13} +(2.68285 - 0.593495i) q^{15} +(-7.05696 + 12.2230i) q^{16} +2.80054 q^{17} +(-7.38536 + 3.43568i) q^{18} +0.625693 q^{19} +(4.26101 - 7.38028i) q^{20} +(-1.83102 - 3.17142i) q^{22} +(0.142434 + 0.246702i) q^{23} +(-4.77529 + 15.1213i) q^{24} +(1.24168 - 2.15065i) q^{25} +8.62957 q^{26} +(-4.12669 + 3.15760i) q^{27} +(2.27396 - 3.93861i) q^{29} +(2.24662 - 7.11410i) q^{30} +(-3.71502 - 6.43461i) q^{31} +(10.0053 + 17.3297i) q^{32} +(-1.57747 - 1.72308i) q^{33} +(3.80191 - 6.58511i) q^{34} +(-1.41918 + 16.0532i) q^{36} +8.02252 q^{37} +(0.849420 - 1.47124i) q^{38} +(5.37507 - 1.18906i) q^{39} +(-7.26194 - 12.5780i) q^{40} +(5.01329 + 8.68327i) q^{41} +(-3.12937 + 5.42022i) q^{43} -7.24542 q^{44} +(0.419098 - 4.74069i) q^{45} +0.773452 q^{46} +(-5.57383 + 9.65415i) q^{47} +(16.5073 + 18.0310i) q^{48} +(-3.37132 - 5.83930i) q^{50} +(1.46073 - 4.62550i) q^{51} +(8.53689 - 14.7863i) q^{52} +2.78698 q^{53} +(1.82243 + 13.9900i) q^{54} +2.13965 q^{55} +(0.326354 - 1.03343i) q^{57} +(-6.17410 - 10.6939i) q^{58} +(-2.28734 - 3.96180i) q^{59} +(-9.96715 - 10.8872i) q^{60} +(0.192507 - 0.333432i) q^{61} -20.1736 q^{62} +26.1036 q^{64} +(-2.52104 + 4.36656i) q^{65} +(-6.19311 + 1.37003i) q^{66} +(1.26958 + 2.19898i) q^{67} +(-7.52217 - 13.0288i) q^{68} +(0.481757 - 0.106573i) q^{69} -1.45208 q^{71} +(22.4844 + 15.7742i) q^{72} -0.468134 q^{73} +(10.8911 - 18.8639i) q^{74} +(-2.90448 - 3.17257i) q^{75} +(-1.68059 - 2.91087i) q^{76} +(4.50108 - 14.2530i) q^{78} +(7.85620 - 13.6073i) q^{79} -22.3902 q^{80} +(3.06281 + 8.46281i) q^{81} +27.2235 q^{82} +(-6.99338 + 12.1129i) q^{83} +(2.22138 + 3.84754i) q^{85} +(8.49665 + 14.7166i) q^{86} +(-5.31914 - 5.81012i) q^{87} +(-6.17410 + 10.6939i) q^{88} -2.58706 q^{89} +(-10.5782 - 7.42126i) q^{90} +(0.765146 - 1.32527i) q^{92} +(-12.5654 + 2.77970i) q^{93} +(15.1337 + 26.2123i) q^{94} +(0.496297 + 0.859612i) q^{95} +(33.8412 - 7.48628i) q^{96} +(7.22962 - 12.5221i) q^{97} +(-3.66871 + 1.70669i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9}+O(q^{10}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9	\( 24 q + 4 q^{2} - 12 q^{4} - 24 q^{8} + 8 q^{9} + 20 q^{11} + 4 q^{15} - 12 q^{16} + 4 q^{18} + 32 q^{23} - 12 q^{25} + 16 q^{29} + 48 q^{32} - 4 q^{36} + 24 q^{37} + 32 q^{39} - 112 q^{44} - 48 q^{46} - 4 q^{50} - 56 q^{51} - 64 q^{53} - 12 q^{57} - 88 q^{60} + 96 q^{64} + 60 q^{65} - 12 q^{67} - 112 q^{71} + 168 q^{72} + 68 q^{74} - 60 q^{78} + 12 q^{79} + 80 q^{81} + 12 q^{85} + 76 q^{86} + 16 q^{92} - 80 q^{93} + 64 q^{95} + 20 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 - 12 * q^4 - 24 * q^8 + 8 * q^9 + 20 * q^11 + 4 * q^15 - 12 * q^16 + 4 * q^18 + 32 * q^23 - 12 * q^25 + 16 * q^29 + 48 * q^32 - 4 * q^36 + 24 * q^37 + 32 * q^39 - 112 * q^44 - 48 * q^46 - 4 * q^50 - 56 * q^51 - 64 * q^53 - 12 * q^57 - 88 * q^60 + 96 * q^64 + 60 * q^65 - 12 * q^67 - 112 * q^71 + 168 * q^72 + 68 * q^74 - 60 * q^78 + 12 * q^79 + 80 * q^81 + 12 * q^85 + 76 * q^86 + 16 * q^92 - 80 * q^93 + 64 * q^95 + 20 * q^99

Introduction

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