LMFDB - Embedded newform 441.2.f.h.148.11

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			148.11
Character	$\chi$	$=$	441.148
Dual form			441.2.f.h.295.11

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

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

Coefficient data

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

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

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

$2$	1.35757	+	2.35137i	0.959944	+	1.66267i	0.722624	+	0.691241i	$0.242936\pi$
$2$	1.35757	+	2.35137i	0.959944	+	1.66267i	0.237320	+	0.971432i	$0.423731\pi$
$3$	−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	$-0.948760\pi$
$5$	−0.793197	+	1.37386i	−0.354728	+	0.614407i	0.632343	+	0.774688i	$0.282093\pi$
$6$	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	0.949600	−	0.313464i	$-0.101490\pi$
$11$	0.674376	+	1.16805i	0.203332	+	0.352181i	−0.746268	+	0.665646i	$0.768156\pi$
$12$	9.08484	+	2.00973i	2.62257	+	0.580159i
$13$	−1.58916	+	2.75251i	−0.440754	+	0.763409i	−0.997746	−	0.0671096i	$-0.978622\pi$
$13$	−1.58916	+	2.75251i	−0.440754	+	0.763409i	0.556991	+	0.830518i	$0.311956\pi$
$14$		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	$-0.610297\pi$
$17$	−2.80054			−0.679230			−0.339615	+	0.940565i	$0.610297\pi$
$18$	−7.38536	−	3.43568i	−1.74075	−	0.809799i
$19$	−0.625693			−0.143544			−0.0717719	−	0.997421i	$-0.522865\pi$
$19$	−0.625693			−0.143544			−0.0717719	+	0.997421i	$0.522865\pi$
$20$	−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	−0.850794	−	0.525500i	$-0.823878\pi$
$23$	0.142434	−	0.246702i	0.0296995	−	0.0514410i	0.880493	+	0.474059i	$0.157212\pi$
$24$	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	0.996161	−	0.0875454i	$-0.0279023\pi$
$29$	2.27396	+	3.93861i	0.422264	+	0.731382i	−0.573897	+	0.818928i	$0.694569\pi$
$30$	2.24662	+	7.11410i	0.410175	+	1.29885i
$31$	3.71502	−	6.43461i	0.667238	−	1.15569i	−0.311435	−	0.950267i	$-0.600810\pi$
$31$	3.71502	−	6.43461i	0.667238	−	1.15569i	0.978673	−	0.205423i	$-0.0658569\pi$
$32$	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	0.147275	+	0.989096i	$0.452950\pi$
$41$	−5.01329	+	8.68327i	−0.782944	+	1.35610i	−0.930219	+	0.367004i	$0.880384\pi$
$42$		0			0
$43$	−3.12937	−	5.42022i	−0.477224	−	0.826576i	0.522435	−	0.852679i	$-0.325024\pi$
$43$	−3.12937	−	5.42022i	−0.477224	−	0.826576i	−0.999659	+	0.0261027i	$0.991690\pi$
$44$	−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	0.910737	+	0.412988i	$0.135515\pi$
$47$	5.57383	+	9.65415i	0.813026	+	1.40820i	−0.0977106	+	0.995215i	$0.531152\pi$
$48$	−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	$-0.737085\pi$
$59$	2.28734	−	3.96180i	0.297787	−	0.515782i	0.975629	+	0.219425i	$0.0704182\pi$
$60$	−9.96715	+	10.8872i	−1.28675	+	1.40553i
$61$	−0.192507	−	0.333432i	−0.0246480	−	0.0426916i	0.853438	−	0.521194i	$-0.174513\pi$
$61$	−0.192507	−	0.333432i	−0.0246480	−	0.0426916i	−0.878086	+	0.478502i	$0.841180\pi$
$62$	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	−0.777993	−	0.628273i	$-0.783762\pi$
$67$	1.26958	−	2.19898i	0.155104	−	0.268648i	0.933097	+	0.359625i	$0.117095\pi$
$68$	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	$-0.491279\pi$
$73$	0.468134			0.0547909			0.0273955	+	0.999625i	$0.491279\pi$
$74$	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	0.846978	+	0.531627i	$0.178419\pi$
$79$	7.85620	+	13.6073i	0.883892	+	1.53095i	0.0369135	+	0.999318i	$0.488247\pi$
$80$	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	0.938848	+	0.344331i	$0.111894\pi$
$83$	6.99338	+	12.1129i	0.767623	+	1.32956i	−0.171225	+	0.985232i	$0.554772\pi$
$84$		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	$-0.456217\pi$
$89$	2.58706			0.274228			0.137114	+	0.990555i	$0.456217\pi$
$90$	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	−0.955136	−	0.296168i	$-0.904291\pi$
$97$	−7.22962	−	12.5221i	−0.734057	−	1.27142i	0.221079	−	0.975256i	$-0.429042\pi$
$98$		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	$-0.00386534\pi$
$101$	4.91888	+	8.51975i	0.489447	+	0.847747i	−0.510479	+	0.859890i	$0.670532\pi$
$102$	−8.89326	+	9.71414i	−0.880564	+	0.961844i
$103$	5.52897	−	9.57646i	0.544786	−	0.943597i	−0.453834	−	0.891086i	$-0.649944\pi$
$103$	5.52897	−	9.57646i	0.544786	−	0.943597i	0.998620	−	0.0525110i	$-0.0167225\pi$
$104$	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	−0.781295	−	0.624162i	$-0.785440\pi$
$113$	1.59338	−	2.75982i	0.149893	−	0.259622i	0.931188	+	0.364540i	$0.118774\pi$
$114$	−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	0.476616	+	0.879111i	$0.341863\pi$
$131$	−5.98629	+	10.3686i	−0.523024	+	0.905905i	−0.999641	+	0.0267937i	$0.991470\pi$
$132$	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	−0.965964	−	0.258677i	$-0.916714\pi$
$137$	−8.27525	−	14.3332i	−0.707003	−	1.22456i	0.258961	−	0.965888i	$-0.416620\pi$
$138$	−0.403424	−	1.27747i	−0.0343417	−	0.108746i
$139$	−3.95119	+	6.84367i	−0.335136	+	0.580472i	−0.983511	−	0.180849i	$-0.942116\pi$
$139$	−3.95119	+	6.84367i	−0.335136	+	0.580472i	0.648375	+	0.761321i	$0.275449\pi$
$140$		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	−0.437620	−	0.899160i	$-0.644179\pi$
$149$	6.83427	−	11.8373i	0.559885	−	0.969749i	0.997505	−	0.0705895i	$-0.0224881\pi$
$150$	11.4029	+	2.52253i	0.931045	+	0.205964i
$151$	−1.94982	−	3.37718i	−0.158674	−	0.274831i	0.775717	−	0.631081i	$-0.217389\pi$
$151$	−1.94982	−	3.37718i	−0.158674	−	0.274831i	−0.934391	+	0.356250i	$0.884055\pi$
$152$	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	$-0.837072\pi$
$157$	−0.147176	+	0.254917i	−0.0117459	+	0.0203446i	0.860093	+	0.510138i	$0.170406\pi$
$158$	−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	$-0.872814\pi$
$167$	−1.59872	+	2.76907i	−0.123713	+	0.214277i	0.797516	+	0.603298i	$0.206147\pi$
$168$		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	$-0.309844\pi$
$173$	−5.71875	−	9.90517i	−0.434789	−	0.753076i	−0.997278	+	0.0737284i	$0.976510\pi$
$174$	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	$-0.537828\pi$
$181$	−3.19013			−0.237120			−0.118560	+	0.992947i	$0.537828\pi$
$182$		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	0.787531	−	0.616275i	$-0.211359\pi$
$191$	−1.93407	−	3.34992i	−0.139945	−	0.242391i	−0.927475	+	0.373884i	$0.878026\pi$
$192$	−13.6153	−	43.1139i	−0.982601	−	3.11148i
$193$	2.06793	−	3.58175i	0.148853	−	0.257820i	−0.781951	−	0.623340i	$-0.785775\pi$
$193$	2.06793	−	3.58175i	0.148853	−	0.257820i	0.930804	+	0.365520i	$0.119109\pi$
$194$	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	$-0.571958\pi$
$199$	−6.32386			−0.448287			−0.224143	+	0.974556i	$0.571958\pi$
$200$	−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	−0.599589	−	0.800308i	$-0.704669\pi$
$211$	5.71291	−	9.89505i	0.393293	−	0.681204i	0.992882	+	0.119105i	$0.0380025\pi$
$212$	−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	−0.997513	−	0.0704822i	$-0.977546\pi$
$223$	−8.35953	−	14.4791i	−0.559796	−	0.969595i	0.437717	−	0.899113i	$-0.355787\pi$
$224$		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	0.996909	+	0.0785588i	$0.0250318\pi$
$227$	8.53501	+	14.7831i	0.566489	+	0.981187i	−0.430421	+	0.902628i	$0.641635\pi$
$228$	−5.68432	−	1.25747i	−0.376453	−	0.0832783i
$229$	9.89471	−	17.1381i	0.653861	−	1.13252i	−0.328317	−	0.944567i	$-0.606482\pi$
$229$	9.89471	−	17.1381i	0.653861	−	1.13252i	0.982178	−	0.187953i	$-0.0601851\pi$
$230$	−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	0.334812	+	0.942285i	$0.391327\pi$
$239$	−10.0277	+	17.3685i	−0.648637	+	1.12347i	−0.983449	+	0.181187i	$0.942006\pi$
$240$	−11.6785	−	36.9808i	−0.753842	−	2.38710i
$241$	14.6444	+	25.3648i	0.943326	+	1.63389i	0.759069	+	0.651010i	$0.225654\pi$
$241$	14.6444	+	25.3648i	0.943326	+	1.63389i	0.184256	+	0.982878i	$0.441012\pi$
$242$	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	$-0.244552\pi$
$251$	22.7856			1.43821			0.719106	+	0.694901i	$0.244552\pi$
$252$		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	0.186547	+	0.982446i	$0.440270\pi$
$257$	−12.1444	+	21.0348i	−0.757550	+	1.31211i	−0.944097	+	0.329668i	$0.893063\pi$
$258$	−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	0.967696	−	0.252120i	$-0.0811278\pi$
$263$	4.30578	+	7.45782i	0.265506	+	0.459869i	−0.702190	+	0.711989i	$0.747794\pi$
$264$	−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	$-0.346294\pi$
$269$	15.2312			0.928664			0.464332	+	0.885661i	$0.346294\pi$
$270$	−17.7748	−	13.6006i	−1.08174	−	0.827707i
$271$	4.67820			0.284181			0.142090	−	0.989854i	$-0.454618\pi$
$271$	4.67820			0.284181			0.142090	+	0.989854i	$0.454618\pi$
$272$	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	0.999962	−	0.00873986i	$-0.00278202\pi$
$277$	8.19537	+	14.1948i	0.492412	+	0.852883i	−0.507550	+	0.861622i	$0.669449\pi$
$278$	−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	0.913663	−	0.406473i	$-0.133242\pi$
$281$	1.75702	+	3.04325i	0.104815	+	0.181545i	−0.808848	+	0.588018i	$0.799908\pi$
$282$	51.1871	+	11.3235i	3.04815	+	0.674305i
$283$	13.0354	−	22.5780i	0.774874	−	1.34212i	−0.159992	−	0.987118i	$-0.551147\pi$
$283$	13.0354	−	22.5780i	0.774874	−	1.34212i	0.934865	−	0.355002i	$-0.115520\pi$
$284$	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	−0.446556	−	0.894756i	$-0.647350\pi$
$293$	9.44192	−	16.3539i	0.551603	−	0.955404i	0.998159	−	0.0606487i	$-0.0193169\pi$
$294$		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	$-0.288125\pi$
$307$	21.6407			1.23510			0.617551	+	0.786531i	$0.288125\pi$
$308$		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	$-0.792661\pi$
$311$	2.24724	−	3.89234i	0.127429	−	0.220714i	0.922680	+	0.385567i	$0.125994\pi$
$312$	−49.2103	−	10.8862i	−2.78598	−	0.616309i
$313$	4.30102	+	7.44958i	0.243108	+	0.421075i	0.961598	−	0.274462i	$-0.0884997\pi$
$313$	4.30102	+	7.44958i	0.243108	+	0.421075i	−0.718490	+	0.695537i	$0.755166\pi$
$314$	−0.799206			−0.0451018
$315$		0			0
$316$	−84.4062			−4.74822
$317$	4.03128	+	6.98237i	0.226419	+	0.392169i	0.956744	−	0.290930i	$-0.0939648\pi$
$317$	4.03128	+	6.98237i	0.226419	+	0.392169i	−0.730325	+	0.683100i	$0.760631\pi$
$318$	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	0.987668	+	0.156560i	$0.0500405\pi$
$331$	11.4513	+	19.8342i	0.629419	+	1.09019i	−0.358249	+	0.933626i	$0.616626\pi$
$332$	−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	−0.989789	−	0.142542i	$-0.954472\pi$
$337$	−6.81891	+	11.8107i	−0.371450	+	0.643369i	0.618339	+	0.785911i	$0.287806\pi$
$338$	−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	−0.825609	−	0.564243i	$-0.809168\pi$
$347$	1.41282	−	2.44707i	0.0758440	−	0.131366i	0.901453	+	0.432877i	$0.142502\pi$
$348$	12.7430	+	40.3517i	0.683097	+	2.16308i
$349$	1.81202	+	3.13851i	0.0969951	+	0.168000i	0.910440	−	0.413642i	$-0.135744\pi$
$349$	1.81202	+	3.13851i	0.0969951	+	0.168000i	−0.813444	+	0.581643i	$0.802410\pi$
$350$		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	$-0.190017\pi$
$353$	−1.37701	−	2.38504i	−0.0732907	−	0.126943i	−0.900342	+	0.435184i	$0.856683\pi$
$354$	−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	−0.988605	−	0.150536i	$-0.951900\pi$
$367$	−11.9670	−	20.7274i	−0.624670	−	1.08196i	0.363934	−	0.931425i	$-0.381433\pi$
$368$	−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	−0.503941	−	0.863738i	$-0.668117\pi$
$373$	9.58030	−	16.5936i	0.496049	−	0.859182i	0.999990	+	0.00455622i	$0.00145030\pi$
$374$	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	0.485213	+	0.874396i	$0.338742\pi$
$383$	−10.0718	+	17.4448i	−0.514643	+	0.891388i	−0.999856	+	0.0169915i	$0.994591\pi$
$384$	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	0.644782	−	0.764366i	$-0.276948\pi$
$389$	−6.69736	−	11.6002i	−0.339570	−	0.588152i	−0.984352	+	0.176215i	$0.943615\pi$
$390$	−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	$-0.350700\pi$
$397$	18.0133			0.904061			0.452031	+	0.892002i	$0.350700\pi$
$398$	−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	0.239898	+	0.970798i	$0.422886\pi$
$401$	−14.4337	+	25.0000i	−0.720787	+	1.24844i	−0.960685	+	0.277642i	$0.910447\pi$
$402$	−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	$-0.919850\pi$
$409$	−5.42937	+	9.40395i	−0.268465	+	0.464995i	0.700000	+	0.714142i	$0.253183\pi$
$410$	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	$-0.829483\pi$
$419$	0.247572	−	0.428807i	0.0120947	−	0.0209486i	0.872009	+	0.489489i	$0.162817\pi$
$420$		0			0
$421$	9.50320	+	16.4600i	0.463158	+	0.802212i	0.999116	−	0.0420318i	$-0.0133831\pi$
$421$	9.50320	+	16.4600i	0.463158	+	0.802212i	−0.535959	+	0.844244i	$0.680050\pi$
$422$	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	$-0.202524\pi$
$433$	33.4740			1.60866			0.804330	+	0.594183i	$0.202524\pi$
$434$		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	$-0.000182888\pi$
$439$	10.4657	+	18.1272i	0.499502	+	0.865163i	−0.500498	+	0.865738i	$0.666850\pi$
$440$	19.5891			0.933874
$441$		0			0
$442$	24.1674			1.14953
$443$	15.4290	+	26.7238i	0.733054	+	1.26969i	0.955572	+	0.294759i	$0.0952393\pi$
$443$	15.4290	+	26.7238i	0.733054	+	1.26969i	−0.222517	+	0.974929i	$0.571427\pi$
$444$	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	−0.997790	−	0.0664402i	$-0.978836\pi$
$457$	−11.8952	−	20.6031i	−0.556434	−	0.963772i	0.441356	−	0.897332i	$-0.354498\pi$
$458$	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	$-0.296733\pi$
$461$	−8.53122	−	14.7765i	−0.397339	−	0.688211i	−0.993397	+	0.114731i	$0.963400\pi$
$462$		0			0
$463$	18.1243	−	31.3922i	0.842306	−	1.45892i	−0.0456338	−	0.998958i	$-0.514531\pi$
$463$	18.1243	−	31.3922i	0.842306	−	1.45892i	0.887940	−	0.459959i	$-0.152136\pi$
$464$	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	$-0.439303\pi$
$467$	8.19160			0.379062			0.189531	+	0.981875i	$0.439303\pi$
$468$	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	−0.995022	−	0.0996574i	$-0.968225\pi$
$479$	−12.7775	−	22.1312i	−0.583817	−	1.01120i	0.411205	−	0.911543i	$-0.365108\pi$
$480$	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	−0.0404294	−	0.999182i	$-0.512873\pi$
$491$	18.7262	−	32.4348i	0.845103	−	1.46376i	0.885532	−	0.464578i	$-0.153794\pi$
$492$	−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	0.422630	+	0.906302i	$0.361107\pi$
$499$	−12.8125	+	22.1919i	−0.573566	+	0.993446i	−0.996196	+	0.0871432i	$0.972226\pi$
$500$	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	$-0.458748\pi$
$503$	5.79692			0.258472			0.129236	+	0.991614i	$0.458748\pi$
$504$		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	−0.440589	−	0.897709i	$-0.645230\pi$
$509$	12.5697	−	21.7714i	0.557144	−	0.965002i	0.997733	−	0.0672931i	$-0.0214363\pi$
$510$	−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	$-0.551096\pi$
$521$	−7.29656			−0.319668			−0.159834	+	0.987144i	$0.551096\pi$
$522$	−3.26218	−	36.9007i	−0.142782	−	1.61510i
$523$	−16.7727			−0.733421			−0.366710	−	0.930335i	$-0.619516\pi$
$523$	−16.7727			−0.733421			−0.366710	+	0.930335i	$0.619516\pi$
$524$	−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	0.967550	+	0.252681i	$0.0813123\pi$
$547$	16.4325	+	28.4619i	0.702603	+	1.21694i	−0.264947	+	0.964263i	$0.585354\pi$
$548$	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	−0.412155	−	0.911114i	$-0.635224\pi$
$563$	13.8325	−	23.9586i	0.582970	−	1.00973i	0.995125	−	0.0986197i	$-0.0314427\pi$
$564$	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	0.887961	+	0.459920i	$0.152122\pi$
$569$	20.0916	+	34.7996i	0.842282	+	1.45888i	−0.0456782	+	0.998956i	$0.514545\pi$
$570$	−1.40569	−	4.45124i	−0.0588780	−	0.186442i
$571$	3.40565	−	5.89875i	0.142522	−	0.246855i	−0.785924	−	0.618323i	$-0.787812\pi$
$571$	3.40565	−	5.89875i	0.142522	−	0.246855i	0.928446	+	0.371468i	$0.121146\pi$
$572$	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	$-0.226109\pi$
$577$	36.4222			1.51628			0.758138	+	0.652094i	$0.226109\pi$
$578$	−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	$-0.240633\pi$
$587$	−5.57943	−	9.66385i	−0.230288	−	0.398870i	−0.957893	+	0.287126i	$0.907300\pi$
$588$		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	$-0.633327\pi$
$593$	−19.8085			−0.813439			−0.406720	+	0.913553i	$0.633327\pi$
$594$	−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	−0.619204	−	0.785230i	$-0.712545\pi$
$599$	9.06600	−	15.7028i	0.370427	−	0.641598i	0.989631	+	0.143632i	$0.0458781\pi$
$600$	−26.5913	+	29.0458i	−1.08558	+	1.18579i
$601$	12.3285	+	21.3536i	0.502889	+	0.871030i	0.999994	+	0.00333942i	$0.00106297\pi$
$601$	12.3285	+	21.3536i	0.502889	+	0.871030i	−0.497105	+	0.867690i	$0.665604\pi$
$602$		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	$-0.719299\pi$
$607$	8.63876	−	14.9628i	0.350637	−	0.607320i	0.986361	+	0.164596i	$0.0526319\pi$
$608$	−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	−0.559810	−	0.828621i	$-0.689126\pi$
$617$	10.8723	−	18.8314i	0.437702	−	0.758122i	0.997512	+	0.0704988i	$0.0224591\pi$
$618$	−15.6601	−	49.5888i	−0.629940	−	1.99475i
$619$	16.9024	+	29.2758i	0.679366	+	1.17670i	0.975172	+	0.221448i	$0.0710782\pi$
$619$	16.9024	+	29.2758i	0.679366	+	1.17670i	−0.295807	+	0.955248i	$0.595588\pi$
$620$	−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	0.664940	−	0.746897i	$-0.268457\pi$
$641$	−7.95901	−	13.7854i	−0.314362	−	0.544491i	−0.979302	+	0.202406i	$0.935124\pi$
$642$	−6.11074	+	6.67479i	−0.241172	+	0.263433i
$643$	13.2527	−	22.9544i	0.522636	−	0.905231i	−0.477017	−	0.878894i	$-0.658282\pi$
$643$	13.2527	−	22.9544i	0.522636	−	0.905231i	0.999653	−	0.0263376i	$-0.00838450\pi$
$644$		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	$-0.500100\pi$
$647$	−0.0160392			−0.000630565			−0.000315282		1.00000i	$0.500100\pi$
$648$	−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	−0.331473	−	0.943465i	$-0.607545\pi$
$653$	16.6440	−	28.8282i	0.651328	−	1.12813i	0.982801	−	0.184669i	$-0.0591212\pi$
$654$	−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	0.944713	+	0.327897i	$0.106340\pi$
$659$	19.4156	+	33.6288i	0.756324	+	1.30999i	−0.188389	+	0.982094i	$0.560327\pi$
$660$	−19.4384	−	4.30012i	−0.756639	−	0.167382i
$661$	2.65322	−	4.59551i	0.103198	−	0.178745i	−0.809802	−	0.586703i	$-0.800426\pi$
$661$	2.65322	−	4.59551i	0.103198	−	0.178745i	0.913001	+	0.407958i	$0.133759\pi$
$662$	−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	0.801568	−	0.597903i	$-0.203999\pi$
$673$	−3.03565	−	5.25789i	−0.117016	−	0.202677i	−0.918584	+	0.395227i	$0.870666\pi$
$674$	−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	−0.978338	−	0.207014i	$-0.933625\pi$
$677$	−17.3925	−	30.1247i	−0.668449	−	1.15779i	0.309889	−	0.950773i	$-0.399708\pi$
$678$	−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	$-0.206957\pi$
$691$	−3.31837	−	5.74759i	−0.126237	−	0.218649i	−0.922216	+	0.386676i	$0.873623\pi$
$692$	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	−0.985127	−	0.171827i	$-0.945033\pi$
$709$	−17.0778	−	29.5796i	−0.641370	−	1.11089i	0.343757	−	0.939059i	$-0.388300\pi$
$710$	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	$-0.190684\pi$
$719$	44.2900			1.65174			0.825870	+	0.563861i	$0.190684\pi$
$720$	−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	−0.999614	−	0.0277700i	$-0.991159\pi$
$727$	−14.1247	−	24.4647i	−0.523857	−	0.907346i	0.475758	−	0.879576i	$-0.342174\pi$
$728$		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	$-0.986205\pi$
$733$	−12.5084	+	21.6653i	−0.462010	+	0.800225i	0.537051	+	0.843550i	$0.319538\pi$
$734$	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	−0.252336	−	0.967640i	$-0.581199\pi$
$743$	19.4031	−	33.6072i	0.711833	−	1.23293i	0.964169	−	0.265290i	$-0.0854678\pi$
$744$	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	−0.993216	−	0.116282i	$-0.962903\pi$
$751$	−10.8495	+	18.7920i	−0.395905	+	0.685728i	0.597311	+	0.802010i	$0.296236\pi$
$752$	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	$-0.910954\pi$
$761$	−6.66048	+	11.5363i	−0.241442	+	0.418190i	0.719683	+	0.694303i	$0.244287\pi$
$762$	−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	−0.351488	+	0.936192i	$0.614324\pi$
$769$	−27.3568	+	47.3833i	−0.986510	+	1.70869i	−0.635022	+	0.772494i	$0.719009\pi$
$770$		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	$-0.513516\pi$
$773$	−2.36042			−0.0848983			−0.0424491	+	0.999099i	$0.513516\pi$
$774$	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	$-0.842797\pi$
$787$	−0.833971	+	1.44448i	−0.0297278	+	0.0514901i	0.850779	+	0.525524i	$0.176131\pi$
$788$	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	−0.492912	−	0.870079i	$-0.664068\pi$
$797$	14.3148	−	24.7939i	0.507055	−	0.878244i	0.999967	−	0.00816511i	$-0.00259906\pi$
$798$		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	$-0.652729\pi$
$811$	−26.2917			−0.923225			−0.461613	+	0.887082i	$0.652729\pi$
$812$		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	0.888289	−	0.459286i	$-0.151895\pi$
$821$	1.32925	+	2.30232i	0.0463910	+	0.0803517i	−0.841897	+	0.539638i	$0.818561\pi$
$822$	−75.9956	−	16.8116i	−2.65065	−	0.586371i
$823$	6.10769	−	10.5788i	0.212901	−	0.368755i	−0.739721	−	0.672914i	$-0.765042\pi$
$823$	6.10769	−	10.5788i	0.212901	−	0.368755i	0.952621	+	0.304160i	$0.0983756\pi$
$824$	−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	$-0.603193\pi$
$829$	−18.3431			−0.637083			−0.318541	+	0.947909i	$0.603193\pi$
$830$	−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	$-0.0606425\pi$
$839$	9.47055	+	16.4035i	0.326960	+	0.566311i	−0.654947	+	0.755675i	$0.727309\pi$
$840$		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	$-0.0556701\pi$
$853$	9.97922	+	17.2845i	0.341682	+	0.591811i	−0.643063	+	0.765813i	$0.722337\pi$
$854$		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	$-0.257037\pi$
$857$	−8.20001	−	14.2028i	−0.280107	−	0.485159i	−0.971411	+	0.237405i	$0.923703\pi$
$858$	−13.6129	+	14.8694i	−0.464736	+	0.507633i
$859$	16.8575	−	29.1981i	0.575172	−	0.996226i	−0.420851	−	0.907130i	$-0.638269\pi$
$859$	16.8575	−	29.1981i	0.575172	−	0.996226i	0.996023	−	0.0890968i	$-0.0283980\pi$
$860$	−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	−0.501517	−	0.865148i	$-0.667224\pi$
$877$	14.7621	−	25.5688i	0.498482	−	0.863396i	0.999998	+	0.00175202i	$0.000557684\pi$
$878$	−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	$-0.920107\pi$
$881$	−57.5032			−1.93733			−0.968666	+	0.248366i	$0.920107\pi$
$882$		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	−0.366203	−	0.930535i	$-0.619342\pi$
$887$	18.5475	−	32.1253i	0.622766	−	1.07866i	0.988968	−	0.148127i	$-0.0473243\pi$
$888$	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	0.589110	−	0.808053i	$-0.299479\pi$
$907$	−12.2044	−	21.1386i	−0.405240	−	0.701896i	−0.994349	+	0.106157i	$0.966145\pi$
$908$	−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	0.579733	−	0.814806i	$-0.303157\pi$
$911$	−12.5493	−	21.7360i	−0.415776	−	0.720146i	−0.995510	+	0.0946604i	$0.969823\pi$
$912$	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	−0.949868	−	0.312651i	$-0.898783\pi$
$929$	−22.7285	−	39.3669i	−0.745698	−	1.29159i	0.204170	−	0.978935i	$-0.434550\pi$
$930$	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	$-0.645433\pi$
$937$	−27.0083			−0.882322			−0.441161	+	0.897428i	$0.645433\pi$
$938$		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	$-0.766892\pi$
$941$	6.35657	−	11.0099i	0.207218	−	0.358912i	0.950837	+	0.309691i	$0.100226\pi$
$942$	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	−0.936190	−	0.351494i	$-0.885674\pi$
$947$	−23.7724	−	41.1749i	−0.772498	−	1.33801i	0.163692	−	0.986511i	$-0.447660\pi$
$948$	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	0.325244	+	0.945630i	$0.394553\pi$
$967$	−20.4093	+	35.3499i	−0.656317	+	1.13678i	−0.981562	+	0.191145i	$0.938780\pi$
$968$	−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	$-0.756414\pi$
$971$	−44.9471			−1.44242			−0.721210	+	0.692717i	$0.756414\pi$
$972$	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	0.0197635	+	0.999805i	$0.493709\pi$
$977$	−26.7552	+	46.3414i	−0.855974	+	1.48259i	−0.875738	+	0.482787i	$0.839625\pi$
$978$	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	$-0.107412\pi$
$983$	5.80278	+	10.0507i	0.185080	+	0.320568i	−0.758524	+	0.651646i	$0.774079\pi$
$984$	−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	−0.951277	−	0.308336i	$-0.900228\pi$
$997$	−23.4499	−	40.6164i	−0.742666	−	1.28633i	0.208612	−	0.977999i	$-0.433105\pi$
$998$	−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.148.11	✓	24
3.2	odd	2		1323.2.f.h.442.1		24
7.2	even	3		441.2.g.h.67.12		24
7.3	odd	6		441.2.h.h.373.2		24
7.4	even	3		441.2.h.h.373.1		24
7.5	odd	6		441.2.g.h.67.11		24
7.6	odd	2	inner	441.2.f.h.148.12	yes	24
9.2	odd	6		1323.2.f.h.883.1		24
9.4	even	3		3969.2.a.bh.1.2		12
9.5	odd	6		3969.2.a.bi.1.11		12
9.7	even	3	inner	441.2.f.h.295.11	yes	24
21.2	odd	6		1323.2.g.h.361.2		24
21.5	even	6		1323.2.g.h.361.1		24
21.11	odd	6		1323.2.h.h.226.11		24
21.17	even	6		1323.2.h.h.226.12		24
21.20	even	2		1323.2.f.h.442.2		24
63.2	odd	6		1323.2.h.h.802.11		24
63.11	odd	6		1323.2.g.h.667.2		24
63.13	odd	6		3969.2.a.bh.1.1		12
63.16	even	3		441.2.h.h.214.1		24
63.20	even	6		1323.2.f.h.883.2		24
63.25	even	3		441.2.g.h.79.12		24
63.34	odd	6	inner	441.2.f.h.295.12	yes	24
63.38	even	6		1323.2.g.h.667.1		24
63.41	even	6		3969.2.a.bi.1.12		12
63.47	even	6		1323.2.h.h.802.12		24
63.52	odd	6		441.2.g.h.79.11		24
63.61	odd	6		441.2.h.h.214.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.f.h.148.11	✓	24	1.1	even	1	trivial
441.2.f.h.148.12	yes	24	7.6	odd	2	inner
441.2.f.h.295.11	yes	24	9.7	even	3	inner
441.2.f.h.295.12	yes	24	63.34	odd	6	inner
441.2.g.h.67.11		24	7.5	odd	6
441.2.g.h.67.12		24	7.2	even	3
441.2.g.h.79.11		24	63.52	odd	6
441.2.g.h.79.12		24	63.25	even	3
441.2.h.h.214.1		24	63.16	even	3
441.2.h.h.214.2		24	63.61	odd	6
441.2.h.h.373.1		24	7.4	even	3
441.2.h.h.373.2		24	7.3	odd	6
1323.2.f.h.442.1		24	3.2	odd	2
1323.2.f.h.442.2		24	21.20	even	2
1323.2.f.h.883.1		24	9.2	odd	6
1323.2.f.h.883.2		24	63.20	even	6
1323.2.g.h.361.1		24	21.5	even	6
1323.2.g.h.361.2		24	21.2	odd	6
1323.2.g.h.667.1		24	63.38	even	6
1323.2.g.h.667.2		24	63.11	odd	6
1323.2.h.h.226.11		24	21.11	odd	6
1323.2.h.h.226.12		24	21.17	even	6
1323.2.h.h.802.11		24	63.2	odd	6
1323.2.h.h.802.12		24	63.47	even	6
3969.2.a.bh.1.1		12	63.13	odd	6
3969.2.a.bh.1.2		12	9.4	even	3
3969.2.a.bi.1.11		12	9.5	odd	6
3969.2.a.bi.1.12		12	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more