LMFDB - Embedded newform 297.2.f.c.190.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(82,297)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("297.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.f (of order $5$, degree $4$, 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:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 8x^{14} + 35x^{12} + 108x^{10} + 589x^{8} + 792x^{6} + 465x^{4} + 22x^{2} + 121 $ x^16 + 8x^14 + 35x^12 + 108x^10 + 589x^8 + 792x^6 + 465x^4 + 22*x^2 + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.3
Root			$0.329643 - 1.01454i$ of defining polynomial
Character	$\chi$	$=$	297.190
Dual form			297.2.f.c.136.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.863017 - 0.627019i) q^{2} +(-0.266388 + 0.819857i) q^{4} +(0.993168 + 0.721579i) q^{5} +(-0.473654 + 1.45776i) q^{7} +(0.943455 + 2.90366i) q^{8} +1.30957 q^{10} +(3.00337 - 1.40704i) q^{11} +(-1.89482 + 1.37667i) q^{13} +(0.505269 + 1.55506i) q^{14} +(1.24004 + 0.900943i) q^{16} +(2.87322 + 2.08752i) q^{17} +(-0.884422 - 2.72197i) q^{19} +(-0.856159 + 0.622036i) q^{20} +(1.70972 - 3.09747i) q^{22} +2.29437 q^{23} +(-1.07938 - 3.32198i) q^{25} +(-0.772068 + 2.37618i) q^{26} +(-1.06898 - 0.776656i) q^{28} +(2.56257 - 7.88677i) q^{29} +(-3.91111 + 2.84159i) q^{31} -4.47108 q^{32} +3.78855 q^{34} +(-1.52230 + 1.10602i) q^{35} +(1.24401 - 3.82868i) q^{37} +(-2.47000 - 1.79456i) q^{38} +(-1.15821 + 3.56460i) q^{40} +(1.49582 + 4.60365i) q^{41} -7.52483 q^{43} +(0.353510 + 2.83715i) q^{44} +(1.98008 - 1.43861i) q^{46} +(-2.82775 - 8.70291i) q^{47} +(3.76241 + 2.73355i) q^{49} +(-3.01447 - 2.19014i) q^{50} +(-0.623915 - 1.92021i) q^{52} +(-5.00934 + 3.63950i) q^{53} +(3.99814 + 0.769743i) q^{55} -4.67969 q^{56} +(-2.73361 - 8.41319i) q^{58} +(3.36374 - 10.3525i) q^{59} +(0.496027 + 0.360385i) q^{61} +(-1.59363 + 4.90467i) q^{62} +(-6.33871 + 4.60534i) q^{64} -2.87526 q^{65} +8.65964 q^{67} +(-2.47686 + 1.79954i) q^{68} +(-0.620280 + 1.90903i) q^{70} +(-12.6352 - 9.18000i) q^{71} +(-4.68358 + 14.4146i) q^{73} +(-1.32705 - 4.08424i) q^{74} +2.46722 q^{76} +(0.628562 + 5.04463i) q^{77} +(1.57143 - 1.14171i) q^{79} +(0.581468 + 1.78958i) q^{80} +(4.17749 + 3.03513i) q^{82} +(4.31509 + 3.13509i) q^{83} +(1.34728 + 4.14651i) q^{85} +(-6.49406 + 4.71821i) q^{86} +(6.91910 + 7.39328i) q^{88} +5.84063 q^{89} +(-1.10936 - 3.41426i) q^{91} +(-0.611192 + 1.88106i) q^{92} +(-7.89728 - 5.73771i) q^{94} +(1.08574 - 3.34155i) q^{95} +(6.88134 - 4.99958i) q^{97} +4.96102 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{4} + 8 q^{7} - 12 q^{10} + 8 q^{13} - 2 q^{16} + 10 q^{19} - 24 q^{22} - 16 q^{25} - 30 q^{28} - 6 q^{31} + 32 q^{34} + 12 q^{37} - 40 q^{40} - 80 q^{43} - 12 q^{46} + 40 q^{49} + 12 q^{52}+ \cdots - 46 q^{94}+O(q^{100}) $ 16 * q + 2 * q^4 + 8 * q^7 - 12 * q^10 + 8 * q^13 - 2 * q^16 + 10 * q^19 - 24 * q^22 - 16 * q^25 - 30 * q^28 - 6 * q^31 + 32 * q^34 + 12 * q^37 - 40 * q^40 - 80 * q^43 - 12 * q^46 + 40 * q^49 + 12 * q^52 + 56 * q^55 - 50 * q^58 - 6 * q^61 + 6 * q^64 + 64 * q^67 + 74 * q^70 - 32 * q^73 + 52 * q^76 - 4 * q^79 + 4 * q^82 + 70 * q^85 + 56 * q^88 - 94 * q^91 - 46 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.863017	−	0.627019i	0.610245	−	0.443369i	−0.239255	−	0.970957i	$-0.576903\pi$
$2$	0.863017	−	0.627019i	0.610245	−	0.443369i	0.849501	+	0.527587i	$0.176903\pi$
$3$		0			0
$3$		0			0
$4$	−0.266388	+	0.819857i	−0.133194	+	0.409928i
$5$	0.993168	+	0.721579i	0.444158	+	0.322700i	0.787285	−	0.616589i	$-0.211486\pi$
$5$	0.993168	+	0.721579i	0.444158	+	0.322700i	−0.343127	+	0.939289i	$0.611486\pi$
$6$		0			0
$7$	−0.473654	+	1.45776i	−0.179024	+	0.550980i	−0.999794	−	0.0202787i	$-0.993545\pi$
$7$	−0.473654	+	1.45776i	−0.179024	+	0.550980i	0.820770	+	0.571259i	$0.193545\pi$
$8$	0.943455	+	2.90366i	0.333562	+	1.02660i
$9$		0			0
$10$	1.30957			0.414121
$11$	3.00337	−	1.40704i	0.905551	−	0.424238i
$11$	3.00337	−	1.40704i	0.905551	−	0.424238i
$12$		0			0
$13$	−1.89482	+	1.37667i	−0.525530	+	0.381820i	−0.818683	−	0.574246i	$-0.805295\pi$
$13$	−1.89482	+	1.37667i	−0.525530	+	0.381820i	0.293153	+	0.956065i	$0.405295\pi$
$14$	0.505269	+	1.55506i	0.135039	+	0.415607i
$15$		0			0
$16$	1.24004	+	0.900943i	0.310010	+	0.225236i
$17$	2.87322	+	2.08752i	0.696858	+	0.506297i	0.878908	−	0.476992i	$-0.158273\pi$
$17$	2.87322	+	2.08752i	0.696858	+	0.506297i	−0.182049	+	0.983289i	$0.558273\pi$
$18$		0			0
$19$	−0.884422	−	2.72197i	−0.202900	−	0.624463i	−0.999793	−	0.0203420i	$-0.993524\pi$
$19$	−0.884422	−	2.72197i	−0.202900	−	0.624463i	0.796893	−	0.604121i	$-0.206476\pi$
$20$	−0.856159	+	0.622036i	−0.191443	+	0.139092i
$21$		0			0
$22$	1.70972	−	3.09747i	0.364514	−	0.660383i
$23$	2.29437			0.478410			0.239205	−	0.970969i	$-0.423113\pi$
$23$	2.29437			0.478410			0.239205	+	0.970969i	$0.423113\pi$
$24$		0			0
$25$	−1.07938	−	3.32198i	−0.215876	−	0.664397i
$26$	−0.772068	+	2.37618i	−0.151415	+	0.466007i
$27$		0			0
$28$	−1.06898	−	0.776656i	−0.202017	−	0.146774i
$29$	2.56257	−	7.88677i	0.475857	−	1.46454i	−0.368943	−	0.929452i	$-0.620280\pi$
$29$	2.56257	−	7.88677i	0.475857	−	1.46454i	0.844799	−	0.535084i	$-0.179720\pi$
$30$		0			0
$31$	−3.91111	+	2.84159i	−0.702456	+	0.510364i	−0.880731	−	0.473617i	$-0.842948\pi$
$31$	−3.91111	+	2.84159i	−0.702456	+	0.510364i	0.178276	+	0.983981i	$0.442948\pi$
$32$	−4.47108			−0.790384
$33$		0			0
$34$	3.78855			0.649731
$35$	−1.52230	+	1.10602i	−0.257316	+	0.186951i
$36$		0			0
$37$	1.24401	−	3.82868i	0.204515	−	0.629432i	−0.795218	−	0.606323i	$-0.792644\pi$
$37$	1.24401	−	3.82868i	0.204515	−	0.629432i	0.999733	−	0.0231083i	$-0.00735626\pi$
$38$	−2.47000	−	1.79456i	−0.400687	−	0.291116i
$39$		0			0
$40$	−1.15821	+	3.56460i	−0.183129	+	0.563612i
$41$	1.49582	+	4.60365i	0.233608	+	0.718970i	0.997303	+	0.0733934i	$0.0233829\pi$
$41$	1.49582	+	4.60365i	0.233608	+	0.718970i	−0.763696	+	0.645577i	$0.776617\pi$
$42$		0			0
$43$	−7.52483			−1.14753			−0.573763	−	0.819022i	$-0.694517\pi$
$43$	−7.52483			−1.14753			−0.573763	+	0.819022i	$0.694517\pi$
$44$	0.353510	+	2.83715i	0.0532936	+	0.427717i
$45$		0			0
$46$	1.98008	−	1.43861i	0.291947	−	0.212112i
$47$	−2.82775	−	8.70291i	−0.412469	−	1.26945i	−0.914495	−	0.404597i	$-0.867412\pi$
$47$	−2.82775	−	8.70291i	−0.412469	−	1.26945i	0.502026	−	0.864853i	$-0.332588\pi$
$48$		0			0
$49$	3.76241	+	2.73355i	0.537488	+	0.390508i
$50$	−3.01447	−	2.19014i	−0.426310	−	0.309732i
$51$		0			0
$52$	−0.623915	−	1.92021i	−0.0865214	−	0.266286i
$53$	−5.00934	+	3.63950i	−0.688085	+	0.499923i	−0.876030	−	0.482256i	$-0.839817\pi$
$53$	−5.00934	+	3.63950i	−0.688085	+	0.499923i	0.187945	+	0.982180i	$0.439817\pi$
$54$		0			0
$55$	3.99814	+	0.769743i	0.539110	+	0.103792i
$56$	−4.67969			−0.625350
$57$		0			0
$58$	−2.73361	−	8.41319i	−0.358941	−	1.10471i
$59$	3.36374	−	10.3525i	0.437922	−	1.34778i	−0.452141	−	0.891946i	$-0.649340\pi$
$59$	3.36374	−	10.3525i	0.437922	−	1.34778i	0.890063	−	0.455838i	$-0.150660\pi$
$60$		0			0
$61$	0.496027	+	0.360385i	0.0635097	+	0.0461425i	0.619087	−	0.785322i	$-0.287503\pi$
$61$	0.496027	+	0.360385i	0.0635097	+	0.0461425i	−0.555577	+	0.831465i	$0.687503\pi$
$62$	−1.59363	+	4.90467i	−0.202391	+	0.622894i
$63$		0			0
$64$	−6.33871	+	4.60534i	−0.792338	+	0.575667i
$65$	−2.87526			−0.356632
$66$		0			0
$67$	8.65964			1.05794			0.528972	−	0.848639i	$-0.322578\pi$
$67$	8.65964			1.05794			0.528972	+	0.848639i	$0.322578\pi$
$68$	−2.47686	+	1.79954i	−0.300363	+	0.218226i
$69$		0			0
$70$	−0.620280	+	1.90903i	−0.0741377	+	0.228172i
$71$	−12.6352	−	9.18000i	−1.49952	−	1.08947i	−0.970572	−	0.240813i	$-0.922586\pi$
$71$	−12.6352	−	9.18000i	−1.49952	−	1.08947i	−0.528950	−	0.848653i	$-0.677414\pi$
$72$		0			0
$73$	−4.68358	+	14.4146i	−0.548172	+	1.68710i	0.165154	+	0.986268i	$0.447188\pi$
$73$	−4.68358	+	14.4146i	−0.548172	+	1.68710i	−0.713326	+	0.700832i	$0.752812\pi$
$74$	−1.32705	−	4.08424i	−0.154266	−	0.474783i
$75$		0			0
$76$	2.46722			0.283010
$77$	0.628562	+	5.04463i	0.0716313	+	0.574889i
$78$		0			0
$79$	1.57143	−	1.14171i	0.176800	−	0.128453i	−0.495866	−	0.868399i	$-0.665149\pi$
$79$	1.57143	−	1.14171i	0.176800	−	0.128453i	0.672666	+	0.739947i	$0.265149\pi$
$80$	0.581468	+	1.78958i	0.0650101	+	0.200081i
$81$		0			0
$82$	4.17749	+	3.03513i	0.461327	+	0.335174i
$83$	4.31509	+	3.13509i	0.473642	+	0.344121i	0.798859	−	0.601518i	$-0.205437\pi$
$83$	4.31509	+	3.13509i	0.473642	+	0.344121i	−0.325217	+	0.945639i	$0.605437\pi$
$84$		0			0
$85$	1.34728	+	4.14651i	0.146133	+	0.449752i
$86$	−6.49406	+	4.71821i	−0.700272	+	0.508778i
$87$		0			0
$88$	6.91910	+	7.39328i	0.737579	+	0.788126i
$89$	5.84063			0.619105			0.309553	−	0.950882i	$-0.399821\pi$
$89$	5.84063			0.619105			0.309553	+	0.950882i	$0.399821\pi$
$90$		0			0
$91$	−1.10936	−	3.41426i	−0.116292	−	0.357911i
$92$	−0.611192	+	1.88106i	−0.0637212	+	0.196114i
$93$		0			0
$94$	−7.89728	−	5.73771i	−0.814542	−	0.591800i
$95$	1.08574	−	3.34155i	0.111394	−	0.342836i
$96$		0			0
$97$	6.88134	−	4.99958i	0.698694	−	0.507631i	−0.180813	−	0.983518i	$-0.557873\pi$
$97$	6.88134	−	4.99958i	0.698694	−	0.507631i	0.879507	+	0.475887i	$0.157873\pi$
$98$	4.96102			0.501139
$99$		0			0
$100$	3.01108			0.301108
$101$	0.606954	−	0.440978i	0.0603942	−	0.0438789i	−0.557179	−	0.830393i	$-0.688116\pi$
$101$	0.606954	−	0.440978i	0.0603942	−	0.0438789i	0.617573	+	0.786514i	$0.288116\pi$
$102$		0			0
$103$	3.33934	−	10.2774i	0.329035	−	1.01266i	−0.640552	−	0.767915i	$-0.721294\pi$
$103$	3.33934	−	10.2774i	0.329035	−	1.01266i	0.969586	−	0.244749i	$-0.0787057\pi$
$104$	−5.78506	−	4.20309i	−0.567272	−	0.412147i
$105$		0			0
$106$	−2.04111	+	6.28190i	−0.198250	+	0.610152i
$107$	−1.23326	−	3.79558i	−0.119224	−	0.366932i	0.873581	−	0.486679i	$-0.161792\pi$
$107$	−1.23326	−	3.79558i	−0.119224	−	0.366932i	−0.992804	+	0.119747i	$0.961792\pi$
$108$		0			0
$109$	−13.1110			−1.25580			−0.627902	−	0.778293i	$-0.716086\pi$
$109$	−13.1110			−1.25580			−0.627902	+	0.778293i	$0.716086\pi$
$110$	3.93311	−	1.84261i	0.375007	−	0.175686i
$111$		0			0
$112$	−1.90070	+	1.38094i	−0.179600	+	0.130487i
$113$	0.705985	+	2.17280i	0.0664135	+	0.204400i	0.978756	−	0.205028i	$-0.0657285\pi$
$113$	0.705985	+	2.17280i	0.0664135	+	0.204400i	−0.912343	+	0.409428i	$0.865728\pi$
$114$		0			0
$115$	2.27870	+	1.65557i	0.212490	+	0.154383i
$116$	5.78338	+	4.20187i	0.536974	+	0.390134i
$117$		0			0
$118$	−3.58826	−	11.0435i	−0.330326	−	1.01664i
$119$	−4.40400	+	3.19969i	−0.403714	+	0.293315i
$120$		0			0
$121$	7.04048	−	8.45172i	0.640044	−	0.768338i
$122$	0.654048			0.0592147
$123$		0			0
$124$	−1.28782	−	3.96351i	−0.115650	−	0.355934i
$125$	3.22185	−	9.91584i	0.288171	−	0.886900i
$126$		0			0
$127$	−1.28021	−	0.930131i	−0.113601	−	0.0825357i	0.529534	−	0.848288i	$-0.322367\pi$
$127$	−1.28021	−	0.930131i	−0.113601	−	0.0825357i	−0.643135	+	0.765753i	$0.722367\pi$
$128$	0.180503	−	0.555533i	0.0159544	−	0.0491026i
$129$		0			0
$130$	−2.48140	+	1.80284i	−0.217633	+	0.158119i
$131$	5.64250			0.492987			0.246494	−	0.969144i	$-0.420722\pi$
$131$	5.64250			0.492987			0.246494	+	0.969144i	$0.420722\pi$
$132$		0			0
$133$	4.38688			0.380391
$134$	7.47342	−	5.42976i	0.645605	−	0.469060i
$135$		0			0
$136$	−3.35068	+	10.3123i	−0.287318	+	0.884274i
$137$	17.5144	+	12.7249i	1.49635	+	1.08716i	0.971805	+	0.235784i	$0.0757659\pi$
$137$	17.5144	+	12.7249i	1.49635	+	1.08716i	0.524549	+	0.851380i	$0.324234\pi$
$138$		0			0
$139$	−6.50795	+	20.0294i	−0.551997	+	1.69887i	0.151748	+	0.988419i	$0.451510\pi$
$139$	−6.50795	+	20.0294i	−0.551997	+	1.69887i	−0.703745	+	0.710452i	$0.748490\pi$
$140$	−0.501254	−	1.54270i	−0.0423637	−	0.130382i
$141$		0			0
$142$	−16.6604			−1.39811
$143$	−3.75383	+	6.80074i	−0.313911	+	0.568707i
$144$		0			0
$145$	8.23599	−	5.98379i	0.683961	−	0.496927i
$146$	4.99620	+	15.3767i	0.413489	+	1.27259i
$147$		0			0
$148$	2.80758	+	2.03983i	0.230782	+	0.167673i
$149$	11.3235	+	8.22699i	0.927655	+	0.673981i	0.945418	−	0.325861i	$-0.105654\pi$
$149$	11.3235	+	8.22699i	0.927655	+	0.673981i	−0.0177624	+	0.999842i	$0.505654\pi$
$150$		0			0
$151$	−6.47911	−	19.9407i	−0.527263	−	1.62275i	−0.759798	−	0.650160i	$-0.774702\pi$
$151$	−6.47911	−	19.9407i	−0.527263	−	1.62275i	0.232535	−	0.972588i	$-0.425298\pi$
$152$	7.06925	−	5.13611i	0.573392	−	0.416594i
$153$		0			0
$154$	3.70554	+	3.95948i	0.298601	+	0.319064i
$155$	−5.93482			−0.476696
$156$		0			0
$157$	−5.41090	−	16.6530i	−0.431837	−	1.32906i	−0.896294	−	0.443461i	$-0.853751\pi$
$157$	−5.41090	−	16.6530i	−0.431837	−	1.32906i	0.464457	−	0.885596i	$-0.346249\pi$
$158$	0.640298	−	1.97063i	0.0509394	−	0.156775i
$159$		0			0
$160$	−4.44054	−	3.22624i	−0.351055	−	0.255057i
$161$	−1.08674	+	3.34463i	−0.0856469	+	0.263594i
$162$		0			0
$163$	−0.154783	+	0.112456i	−0.0121235	+	0.00880824i	−0.593831	−	0.804590i	$-0.702385\pi$
$163$	−0.154783	+	0.112456i	−0.0121235	+	0.00880824i	0.581707	+	0.813398i	$0.302385\pi$
$164$	−4.17280			−0.325841
$165$		0			0
$166$	5.68976			0.441611
$167$	−0.775722	+	0.563595i	−0.0600271	+	0.0436123i	−0.617394	−	0.786654i	$-0.711812\pi$
$167$	−0.775722	+	0.563595i	−0.0600271	+	0.0436123i	0.557367	+	0.830266i	$0.311812\pi$
$168$		0			0
$169$	−2.32208	+	7.14664i	−0.178622	+	0.549742i
$170$	3.76267	+	2.73374i	0.288584	+	0.209668i
$171$		0			0
$172$	2.00452	−	6.16928i	0.152843	−	0.470403i
$173$	6.68664	+	20.5794i	0.508376	+	1.56462i	0.795021	+	0.606582i	$0.207460\pi$
$173$	6.68664	+	20.5794i	0.508376	+	1.56462i	−0.286645	+	0.958037i	$0.592540\pi$
$174$		0			0
$175$	5.35389			0.404716
$176$	4.99197	+	0.961079i	0.376284	+	0.0724440i
$177$		0			0
$178$	5.04056	−	3.66218i	0.377806	−	0.274492i
$179$	−6.33539	−	19.4983i	−0.473529	−	1.45737i	−0.847931	−	0.530106i	$-0.822152\pi$
$179$	−6.33539	−	19.4983i	−0.473529	−	1.45737i	0.374402	−	0.927266i	$-0.377848\pi$
$180$		0			0
$181$	8.43682	+	6.12971i	0.627104	+	0.455618i	0.855396	−	0.517975i	$-0.173314\pi$
$181$	8.43682	+	6.12971i	0.627104	+	0.455618i	−0.228292	+	0.973593i	$0.573314\pi$
$182$	−3.09820	−	2.25097i	−0.229654	−	0.166853i
$183$		0			0
$184$	2.16464	+	6.66207i	0.159579	+	0.491134i
$185$	3.99821	−	2.90487i	0.293954	−	0.213570i
$186$		0			0
$187$	11.5666	+	2.22685i	0.845831	+	0.162844i
$188$	7.88841			0.575322
$189$		0			0
$190$	−1.15821	−	3.56460i	−0.0840252	−	0.258603i
$191$	−6.37924	+	19.6333i	−0.461586	+	1.42061i	0.401640	+	0.915797i	$0.368440\pi$
$191$	−6.37924	+	19.6333i	−0.461586	+	1.42061i	−0.863226	+	0.504817i	$0.831560\pi$
$192$		0			0
$193$	4.84767	+	3.52204i	0.348943	+	0.253522i	0.748426	−	0.663219i	$-0.230810\pi$
$193$	4.84767	+	3.52204i	0.348943	+	0.253522i	−0.399482	+	0.916741i	$0.630810\pi$
$194$	2.80388	−	8.62945i	0.201307	−	0.619559i
$195$		0			0
$196$	−3.24338	+	2.35646i	−0.231670	+	0.168318i
$197$	1.41800			0.101028			0.0505141	−	0.998723i	$-0.483914\pi$
$197$	1.41800			0.101028			0.0505141	+	0.998723i	$0.483914\pi$
$198$		0			0
$199$	6.07350			0.430539			0.215269	−	0.976555i	$-0.430937\pi$
$199$	6.07350			0.430539			0.215269	+	0.976555i	$0.430937\pi$
$200$	8.62755	−	6.26828i	0.610060	−	0.443235i
$201$		0			0
$202$	0.247310	−	0.761143i	0.0174007	−	0.0535538i
$203$	10.2832	+	7.47119i	0.721740	+	0.524375i
$204$		0			0
$205$	−1.83630	+	5.65155i	−0.128253	+	0.394722i
$206$	−3.56223	−	10.9634i	−0.248192	−	0.763858i
$207$		0			0
$208$	−3.58996			−0.248919
$209$	−6.48617	−	6.93067i	−0.448657	−	0.479405i
$210$		0			0
$211$	−12.8992	+	9.37181i	−0.888017	+	0.645182i	−0.935360	−	0.353697i	$-0.884924\pi$
$211$	−12.8992	+	9.37181i	−0.888017	+	0.645182i	0.0473435	+	0.998879i	$0.484924\pi$
$212$	−1.64944	−	5.07646i	−0.113284	−	0.348652i
$213$		0			0
$214$	−3.44422	−	2.50237i	−0.235442	−	0.171059i
$215$	−7.47342	−	5.42976i	−0.509683	−	0.370306i
$216$		0			0
$217$	−2.28983	−	7.04737i	−0.155444	−	0.478406i
$218$	−11.3150	+	8.22083i	−0.766348	+	0.556785i
$219$		0			0
$220$	−1.69614	+	3.07286i	−0.114353	+	0.207172i
$221$	−8.31807			−0.559534
$222$		0			0
$223$	8.12958	+	25.0203i	0.544397	+	1.67548i	0.722419	+	0.691456i	$0.243030\pi$
$223$	8.12958	+	25.0203i	0.544397	+	1.67548i	−0.178022	+	0.984027i	$0.556970\pi$
$224$	2.11775	−	6.51775i	0.141498	−	0.435485i
$225$		0			0
$226$	1.97166	+	1.43250i	0.131153	+	0.0952883i
$227$	0.859779	−	2.64613i	0.0570656	−	0.175630i	−0.918461	−	0.395512i	$-0.870567\pi$
$227$	0.859779	−	2.64613i	0.0570656	−	0.175630i	0.975526	+	0.219882i	$0.0705672\pi$
$228$		0			0
$229$	−17.0058	+	12.3554i	−1.12377	+	0.816470i	−0.984777	−	0.173823i	$-0.944388\pi$
$229$	−17.0058	+	12.3554i	−1.12377	+	0.816470i	−0.138998	+	0.990293i	$0.544388\pi$
$230$	3.00463			0.198119
$231$		0			0
$232$	25.3181			1.66222
$233$	−11.0308	+	8.01437i	−0.722654	+	0.525039i	−0.887231	−	0.461326i	$-0.847374\pi$
$233$	−11.0308	+	8.01437i	−0.722654	+	0.525039i	0.164577	+	0.986364i	$0.447374\pi$
$234$		0			0
$235$	3.47141	−	10.6839i	0.226450	−	0.696940i
$236$	7.59153	+	5.51557i	0.494167	+	0.359033i
$237$		0			0
$238$	−1.79446	+	5.52278i	−0.116318	+	0.357989i
$239$	−6.26582	−	19.2842i	−0.405302	−	1.24739i	−0.920643	−	0.390407i	$-0.872334\pi$
$239$	−6.26582	−	19.2842i	−0.405302	−	1.24739i	0.515340	−	0.856986i	$-0.327666\pi$
$240$		0			0
$241$	−26.3931			−1.70013			−0.850066	−	0.526676i	$-0.823438\pi$
$241$	−26.3931			−1.70013			−0.850066	+	0.526676i	$0.823438\pi$
$242$	0.776668	−	11.7085i	0.0499261	−	0.752651i
$243$		0			0
$244$	−0.427599	+	0.310669i	−0.0273742	+	0.0198885i
$245$	1.76424	+	5.42976i	0.112713	+	0.346895i
$246$		0			0
$247$	5.42308	+	3.94010i	0.345062	+	0.250702i
$248$	−11.9409	−	8.67560i	−0.758250	−	0.550901i
$249$		0			0
$250$	−3.43691	−	10.5777i	−0.217369	−	0.668993i
$251$	4.51620	−	3.28121i	0.285060	−	0.207108i	−0.436062	−	0.899917i	$-0.643627\pi$
$251$	4.51620	−	3.28121i	0.285060	−	0.207108i	0.721121	+	0.692809i	$0.243627\pi$
$252$		0			0
$253$	6.89085	−	3.22827i	0.433224	−	0.202960i
$254$	−1.68806			−0.105918
$255$		0			0
$256$	−5.03489	−	15.4958i	−0.314681	−	0.968488i
$257$	−8.53233	+	26.2598i	−0.532232	+	1.63804i	0.217322	+	0.976100i	$0.430268\pi$
$257$	−8.53233	+	26.2598i	−0.532232	+	1.63804i	−0.749555	+	0.661943i	$0.769732\pi$
$258$		0			0
$259$	4.99205	+	3.62694i	0.310191	+	0.225367i
$260$	0.765932	−	2.35730i	0.0475011	−	0.146193i
$261$		0			0
$262$	4.86957	−	3.53795i	0.300843	−	0.218575i
$263$	−29.4556			−1.81631			−0.908156	−	0.418632i	$-0.862510\pi$
$263$	−29.4556			−1.81631			−0.908156	+	0.418632i	$0.862510\pi$
$264$		0			0
$265$	−7.60130			−0.466944
$266$	3.78595	−	2.75065i	0.232132	−	0.168653i
$267$		0			0
$268$	−2.30682	+	7.09967i	−0.140912	+	0.433681i
$269$	−14.7566	−	10.7213i	−0.899723	−	0.653687i	0.0386718	−	0.999252i	$-0.487687\pi$
$269$	−14.7566	−	10.7213i	−0.899723	−	0.653687i	−0.938395	+	0.345565i	$0.887687\pi$
$270$		0			0
$271$	−2.16675	+	6.66858i	−0.131621	+	0.405087i	−0.995049	−	0.0993842i	$-0.968313\pi$
$271$	−2.16675	+	6.66858i	−0.131621	+	0.405087i	0.863428	+	0.504472i	$0.168313\pi$
$272$	1.68218	+	5.17721i	0.101997	+	0.313915i
$273$		0			0
$274$	23.0940			1.39516
$275$	−7.91593	−	8.45842i	−0.477349	−	0.510062i
$276$		0			0
$277$	9.31029	−	6.76432i	0.559401	−	0.406429i	−0.271838	−	0.962343i	$-0.587632\pi$
$277$	9.31029	−	6.76432i	0.559401	−	0.406429i	0.831240	+	0.555914i	$0.187632\pi$
$278$	6.94234	+	21.3663i	0.416374	+	1.28147i
$279$		0			0
$280$	−4.64772	−	3.37677i	−0.277755	−	0.201801i
$281$	−9.16977	−	6.66223i	−0.547022	−	0.397435i	0.279664	−	0.960098i	$-0.409777\pi$
$281$	−9.16977	−	6.66223i	−0.547022	−	0.397435i	−0.826686	+	0.562663i	$0.809777\pi$
$282$		0			0
$283$	1.41474	+	4.35413i	0.0840976	+	0.258826i	0.984259	−	0.176730i	$-0.0565519\pi$
$283$	1.41474	+	4.35413i	0.0840976	+	0.258826i	−0.900162	+	0.435556i	$0.856552\pi$
$284$	10.8921	−	7.91361i	0.646330	−	0.469586i
$285$		0			0
$286$	1.02457	+	8.22288i	0.0605842	+	0.486229i
$287$	−7.41950			−0.437959
$288$		0			0
$289$	−1.35562	−	4.17217i	−0.0797423	−	0.245422i
$290$	3.35585	−	10.3282i	0.197062	−	0.606495i
$291$		0			0
$292$	−10.5703	−	7.67974i	−0.618577	−	0.449423i
$293$	−8.12850	+	25.0170i	−0.474872	+	1.46151i	0.371258	+	0.928530i	$0.378927\pi$
$293$	−8.12850	+	25.0170i	−0.474872	+	1.46151i	−0.846130	+	0.532977i	$0.821073\pi$
$294$		0			0
$295$	10.8109	−	7.85460i	0.629436	−	0.457312i
$296$	12.2909			0.714391
$297$		0			0
$298$	14.9308			0.864920
$299$	−4.34743	+	3.15859i	−0.251418	+	0.182666i
$300$		0			0
$301$	3.56416	−	10.9694i	0.205435	−	0.632264i
$302$	−18.0948	−	13.1466i	−1.04124	−	0.756502i
$303$		0			0
$304$	1.35562	−	4.17217i	0.0777501	−	0.239290i
$305$	0.232592	+	0.715845i	0.0133182	+	0.0409892i
$306$		0			0
$307$	−14.7093			−0.839504			−0.419752	−	0.907639i	$-0.637883\pi$
$307$	−14.7093			−0.839504			−0.419752	+	0.907639i	$0.637883\pi$
$308$	−4.30332	−	0.828497i	−0.245204	−	0.0472080i
$309$		0			0
$310$	−5.12185	+	3.72124i	−0.290901	+	0.211352i
$311$	−2.40653	−	7.40655i	−0.136462	−	0.419987i	0.859353	−	0.511384i	$-0.170867\pi$
$311$	−2.40653	−	7.40655i	−0.136462	−	0.419987i	−0.995815	+	0.0913967i	$0.970867\pi$
$312$		0			0
$313$	−14.6754	−	10.6623i	−0.829504	−	0.602670i	0.0899148	−	0.995949i	$-0.471341\pi$
$313$	−14.6754	−	10.6623i	−0.829504	−	0.602670i	−0.919419	+	0.393279i	$0.871341\pi$
$314$	−15.1115	−	10.9791i	−0.852789	−	0.619588i
$315$		0			0
$316$	0.517430	+	1.59249i	0.0291077	+	0.0895844i
$317$	15.7364	−	11.4331i	0.883843	−	0.642149i	−0.0504227	−	0.998728i	$-0.516057\pi$
$317$	15.7364	−	11.4331i	0.883843	−	0.642149i	0.934265	+	0.356579i	$0.116057\pi$
$318$		0			0
$319$	−3.40065	−	27.2925i	−0.190400	−	1.52809i
$320$	−9.61852			−0.537692
$321$		0			0
$322$	1.15928	+	3.56788i	0.0646039	+	0.198830i
$323$	3.14102	−	9.66706i	0.174771	−	0.537890i
$324$		0			0
$325$	6.61851	+	4.80863i	0.367129	+	0.266735i
$326$	−0.0630679	+	0.194103i	−0.00349301	+	0.0107504i
$327$		0			0
$328$	−11.9562	+	8.68668i	−0.660170	+	0.479642i
$329$	14.0261			0.773283
$330$		0			0
$331$	−20.6236			−1.13358			−0.566788	−	0.823863i	$-0.691814\pi$
$331$	−20.6236			−1.13358			−0.566788	+	0.823863i	$0.691814\pi$
$332$	−3.71981	+	2.70260i	−0.204151	+	0.148325i
$333$		0			0
$334$	−0.316077	+	0.972784i	−0.0172949	+	0.0532284i
$335$	8.60048	+	6.24862i	0.469895	+	0.341398i
$336$		0			0
$337$	−1.01877	+	3.13545i	−0.0554959	+	0.170799i	−0.974963	−	0.222369i	$-0.928621\pi$
$337$	−1.01877	+	3.13545i	−0.0554959	+	0.170799i	0.919467	+	0.393168i	$0.128621\pi$
$338$	2.47708	+	7.62366i	0.134735	+	0.414673i
$339$		0			0
$340$	−3.75845			−0.203830
$341$	−7.74828	+	14.0374i	−0.419593	+	0.760169i
$342$		0			0
$343$	−14.4472	+	10.4965i	−0.780077	+	0.566759i
$344$	−7.09934	−	21.8495i	−0.382771	−	1.17805i
$345$		0			0
$346$	18.6743	+	13.5677i	1.00394	+	0.729404i
$347$	−6.50317	−	4.72483i	−0.349109	−	0.253642i	0.399386	−	0.916783i	$-0.369223\pi$
$347$	−6.50317	−	4.72483i	−0.349109	−	0.253642i	−0.748495	+	0.663140i	$0.769223\pi$
$348$		0			0
$349$	0.924934	+	2.84665i	0.0495106	+	0.152378i	0.972755	−	0.231835i	$-0.0744729\pi$
$349$	0.924934	+	2.84665i	0.0495106	+	0.152378i	−0.923245	+	0.384213i	$0.874473\pi$
$350$	4.62050	−	3.35699i	0.246976	−	0.179439i
$351$		0			0
$352$	−13.4283	+	6.29099i	−0.715732	+	0.335311i
$353$	9.91473			0.527708			0.263854	−	0.964563i	$-0.415006\pi$
$353$	9.91473			0.527708			0.263854	+	0.964563i	$0.415006\pi$
$354$		0			0
$355$	−5.92477	−	18.2346i	−0.314454	−	0.967791i
$356$	−1.55587	+	4.78848i	−0.0824610	+	0.253789i
$357$		0			0
$358$	−17.6934	−	12.8550i	−0.935123	−	0.679407i
$359$	−4.69829	+	14.4598i	−0.247966	+	0.763161i	0.747168	+	0.664635i	$0.231413\pi$
$359$	−4.69829	+	14.4598i	−0.247966	+	0.763161i	−0.995134	+	0.0985263i	$0.968587\pi$
$360$		0			0
$361$	8.74440	−	6.35318i	0.460232	−	0.334378i
$362$	11.1246			0.584694
$363$		0			0
$364$	3.09472			0.162207
$365$	−15.0529	+	10.9365i	−0.787902	+	0.572445i
$366$		0			0
$367$	−0.428907	+	1.32004i	−0.0223888	+	0.0689056i	−0.961627	−	0.274361i	$-0.911534\pi$
$367$	−0.428907	+	1.32004i	−0.0223888	+	0.0689056i	0.939238	+	0.343267i	$0.111534\pi$
$368$	2.84512	+	2.06710i	0.148312	+	0.107755i
$369$		0			0
$370$	1.62912	−	5.01391i	0.0846938	−	0.260661i
$371$	−2.93281	−	9.02625i	−0.152264	−	0.468620i
$372$		0			0
$373$	19.1341			0.990725			0.495362	−	0.868686i	$-0.335035\pi$
$373$	19.1341			0.990725			0.495362	+	0.868686i	$0.335035\pi$
$374$	11.3784	−	5.33064i	0.588364	−	0.275641i
$375$		0			0
$376$	22.6024	−	16.4216i	1.16563	−	0.846879i
$377$	6.00187	+	18.4718i	0.309112	+	0.951348i
$378$		0			0
$379$	0.383874	+	0.278900i	0.0197183	+	0.0143262i	0.597601	−	0.801794i	$-0.296121\pi$
$379$	0.383874	+	0.278900i	0.0197183	+	0.0143262i	−0.577882	+	0.816120i	$0.696121\pi$
$380$	2.45037	+	1.78030i	0.125701	+	0.0913273i
$381$		0			0
$382$	6.80504	+	20.9438i	0.348176	+	1.07158i
$383$	16.8630	−	12.2517i	0.861658	−	0.626031i	−0.0666775	−	0.997775i	$-0.521240\pi$
$383$	16.8630	−	12.2517i	0.861658	−	0.626031i	0.928336	+	0.371743i	$0.121240\pi$
$384$		0			0
$385$	−3.01583	+	5.46373i	−0.153701	+	0.278457i
$386$	6.39201			0.325345
$387$		0			0
$388$	2.26584	+	6.97354i	0.115031	+	0.354028i
$389$	0.823795	−	2.53538i	0.0417681	−	0.128549i	−0.927998	−	0.372585i	$-0.878472\pi$
$389$	0.823795	−	2.53538i	0.0417681	−	0.128549i	0.969766	+	0.244036i	$0.0784715\pi$
$390$		0			0
$391$	6.59224	+	4.78954i	0.333384	+	0.242217i
$392$	−4.38763	+	13.5037i	−0.221609	+	0.682042i
$393$		0			0
$394$	1.22376	−	0.889112i	0.0616521	−	0.0447928i
$395$	2.38453			0.119979
$396$		0			0
$397$	−15.5756			−0.781716			−0.390858	−	0.920451i	$-0.627822\pi$
$397$	−15.5756			−0.781716			−0.390858	+	0.920451i	$0.627822\pi$
$398$	5.24153	−	3.80820i	0.262734	−	0.190888i
$399$		0			0
$400$	1.65444	−	5.09185i	0.0827222	−	0.254593i
$401$	6.67194	+	4.84745i	0.333181	+	0.242070i	0.741779	−	0.670644i	$-0.233982\pi$
$401$	6.67194	+	4.84745i	0.333181	+	0.242070i	−0.408598	+	0.912714i	$0.633982\pi$
$402$		0			0
$403$	3.49893	−	10.7686i	0.174294	−	0.536423i
$404$	0.199854	+	0.615086i	0.00994309	+	0.0306017i
$405$		0			0
$406$	13.5592			0.672930
$407$	−1.65087	−	13.2493i	−0.0818306	−	0.656745i
$408$		0			0
$409$	−3.25502	+	2.36491i	−0.160950	+	0.116937i	−0.665345	−	0.746536i	$-0.731716\pi$
$409$	−3.25502	+	2.36491i	−0.160950	+	0.116937i	0.504395	+	0.863473i	$0.331716\pi$
$410$	1.95887	+	6.02878i	0.0967417	+	0.297740i
$411$		0			0
$412$	7.53646	+	5.47556i	0.371295	+	0.269761i
$413$	13.4982	+	9.80702i	0.664203	+	0.482572i
$414$		0			0
$415$	2.02339	+	6.22735i	0.0993243	+	0.305689i
$416$	8.47192	−	6.15521i	0.415370	−	0.301784i
$417$		0			0
$418$	−9.94333	−	1.91434i	−0.486344	−	0.0936335i
$419$	32.0411			1.56531			0.782654	−	0.622456i	$-0.213865\pi$
$419$	32.0411			1.56531			0.782654	+	0.622456i	$0.213865\pi$
$420$		0			0
$421$	7.87554	+	24.2384i	0.383830	+	1.18131i	0.937325	+	0.348455i	$0.113294\pi$
$421$	7.87554	+	24.2384i	0.383830	+	1.18131i	−0.553495	+	0.832852i	$0.686706\pi$
$422$	−5.25592	+	16.1761i	−0.255854	+	0.787439i
$423$		0			0
$424$	−15.2939	−	11.1117i	−0.742739	−	0.539631i
$425$	3.83341	−	11.7980i	0.185948	−	0.572288i
$426$		0			0
$427$	−0.760297	+	0.552388i	−0.0367934	+	0.0267320i
$428$	3.44035			0.166296
$429$		0			0
$430$	−9.85425			−0.475214
$431$	−16.7429	+	12.1644i	−0.806477	+	0.585940i	−0.912807	−	0.408391i	$-0.866090\pi$
$431$	−16.7429	+	12.1644i	−0.806477	+	0.585940i	0.106330	+	0.994331i	$0.466090\pi$
$432$		0			0
$433$	−4.45957	+	13.7251i	−0.214313	+	0.659588i	0.784889	+	0.619637i	$0.212720\pi$
$433$	−4.45957	+	13.7251i	−0.214313	+	0.659588i	−0.999202	+	0.0399509i	$0.987280\pi$
$434$	−6.39499	−	4.64623i	−0.306969	−	0.223026i
$435$		0			0
$436$	3.49260	−	10.7491i	0.167265	−	0.514790i
$437$	−2.02919	−	6.24521i	−0.0970694	−	0.298749i
$438$		0			0
$439$	8.95399			0.427351			0.213675	−	0.976905i	$-0.431457\pi$
$439$	8.95399			0.427351			0.213675	+	0.976905i	$0.431457\pi$
$440$	1.53700	+	12.3355i	0.0732736	+	0.588070i
$441$		0			0
$442$	−7.17864	+	5.21559i	−0.341453	+	0.248080i
$443$	3.16988	+	9.75589i	0.150606	+	0.463516i	0.997689	−	0.0679433i	$-0.0216437\pi$
$443$	3.16988	+	9.75589i	0.150606	+	0.463516i	−0.847084	+	0.531460i	$0.821644\pi$
$444$		0			0
$445$	5.80073	+	4.21448i	0.274981	+	0.199785i
$446$	22.7042	+	16.4955i	1.07507	+	0.781086i
$447$		0			0
$448$	−3.71111	−	11.4216i	−0.175333	−	0.539621i
$449$	16.5355	−	12.0137i	0.780359	−	0.566964i	−0.124728	−	0.992191i	$-0.539806\pi$
$449$	16.5355	−	12.0137i	0.780359	−	0.566964i	0.905087	+	0.425227i	$0.139806\pi$
$450$		0			0
$451$	10.9700	+	11.7218i	0.516558	+	0.551958i
$452$	−1.96945			−0.0926351
$453$		0			0
$454$	−0.917168	−	2.82275i	−0.0430448	−	0.132478i
$455$	1.36188	−	4.19142i	0.0638457	−	0.196497i
$456$		0			0
$457$	31.1364	+	22.6219i	1.45650	+	1.05821i	0.984258	+	0.176739i	$0.0565550\pi$
$457$	31.1364	+	22.6219i	1.45650	+	1.05821i	0.472242	+	0.881469i	$0.343445\pi$
$458$	−6.92921	+	21.3259i	−0.323781	+	0.996494i
$459$		0			0
$460$	−1.96435	+	1.42718i	−0.0915882	+	0.0665427i
$461$	19.5409			0.910110			0.455055	−	0.890463i	$-0.349620\pi$
$461$	19.5409			0.910110			0.455055	+	0.890463i	$0.349620\pi$
$462$		0			0
$463$	−16.5263			−0.768042			−0.384021	−	0.923324i	$-0.625461\pi$
$463$	−16.5263			−0.768042			−0.384021	+	0.923324i	$0.625461\pi$
$464$	10.2832	−	7.47119i	0.477386	−	0.346841i
$465$		0			0
$466$	−4.49464	+	13.8331i	−0.208210	+	0.640805i
$467$	23.7147	+	17.2297i	1.09739	+	0.797297i	0.980631	−	0.195864i	$-0.0627510\pi$
$467$	23.7147	+	17.2297i	1.09739	+	0.797297i	0.116754	+	0.993161i	$0.462751\pi$
$468$		0			0
$469$	−4.10167	+	12.6236i	−0.189398	+	0.582906i
$470$	−3.70312	−	11.3970i	−0.170812	−	0.525705i
$471$		0			0
$472$	33.2337			1.52971
$473$	−22.5999	+	10.5877i	−1.03914	+	0.486824i
$474$		0			0
$475$	−8.08771	+	5.87607i	−0.371090	+	0.269613i
$476$	−1.45012	−	4.46301i	−0.0664661	−	0.204562i
$477$		0			0
$478$	−17.4991	−	12.7138i	−0.800389	−	0.581517i
$479$	−12.5305	−	9.10393i	−0.572533	−	0.415969i	0.263492	−	0.964662i	$-0.415126\pi$
$479$	−12.5305	−	9.10393i	−0.572533	−	0.415969i	−0.836024	+	0.548692i	$0.815126\pi$
$480$		0			0
$481$	2.91365	+	8.96728i	0.132851	+	0.408873i
$482$	−22.7777	+	16.5490i	−1.03750	+	0.753786i
$483$		0			0
$484$	5.05371	+	8.02362i	0.229714	+	0.364710i
$485$	10.4419			0.474143
$486$		0			0
$487$	−1.19788	−	3.68670i	−0.0542811	−	0.167060i	0.920241	−	0.391353i	$-0.127993\pi$
$487$	−1.19788	−	3.68670i	−0.0542811	−	0.167060i	−0.974522	+	0.224293i	$0.927993\pi$
$488$	−0.578454	+	1.78030i	−0.0261854	+	0.0805903i
$489$		0			0
$490$	4.92713	+	3.57977i	0.222585	+	0.161717i
$491$	2.24264	−	6.90215i	0.101209	−	0.311490i	−0.887613	−	0.460590i	$-0.847638\pi$
$491$	2.24264	−	6.90215i	0.101209	−	0.311490i	0.988822	+	0.149101i	$0.0476378\pi$
$492$		0			0
$493$	23.8266	−	17.3110i	1.07310	−	0.779649i
$494$	7.15072			0.321726
$495$		0			0
$496$	−7.41004			−0.332721
$497$	19.3669	−	14.0709i	0.868725	−	0.631165i
$498$		0			0
$499$	11.0928	−	34.1400i	0.496580	−	1.52832i	−0.317900	−	0.948124i	$-0.602978\pi$
$499$	11.0928	−	34.1400i	0.496580	−	1.52832i	0.814480	−	0.580192i	$-0.197022\pi$
$500$	7.27131	+	5.28292i	0.325183	+	0.236259i
$501$		0			0
$502$	1.84018	−	5.66348i	0.0821311	−	0.252774i
$503$	4.52869	+	13.9379i	0.201924	+	0.621459i	0.999826	+	0.0186711i	$0.00594354\pi$
$503$	4.52869	+	13.9379i	0.201924	+	0.621459i	−0.797901	+	0.602788i	$0.794056\pi$
$504$		0			0
$505$	0.921008			0.0409843
$506$	3.92274	−	7.10675i	0.174387	−	0.315933i
$507$		0			0
$508$	1.10361	−	0.801818i	0.0489647	−	0.0355749i
$509$	−0.124689	−	0.383752i	−0.00552673	−	0.0170095i	0.948255	−	0.317509i	$-0.102847\pi$
$509$	−0.124689	−	0.383752i	−0.00552673	−	0.0170095i	−0.953782	+	0.300500i	$0.902847\pi$
$510$		0			0
$511$	−18.7946	−	13.6550i	−0.831422	−	0.604064i
$512$	−13.1162	−	9.52950i	−0.579661	−	0.421148i
$513$		0			0
$514$	9.10185	+	28.0126i	0.401465	+	1.23558i
$515$	10.7325	−	7.79761i	0.472930	−	0.343604i
$516$		0			0
$517$	−20.7381	−	22.1593i	−0.912061	−	0.974565i
$518$	6.58239			0.289214
$519$		0			0
$520$	−2.71267	−	8.34875i	−0.118959	−	0.366117i
$521$	−3.50114	+	10.7754i	−0.153388	+	0.472079i	−0.997994	−	0.0633089i	$-0.979835\pi$
$521$	−3.50114	+	10.7754i	−0.153388	+	0.472079i	0.844606	+	0.535388i	$0.179835\pi$
$522$		0			0
$523$	11.6876	+	8.49154i	0.511063	+	0.371309i	0.813227	−	0.581947i	$-0.197709\pi$
$523$	11.6876	+	8.49154i	0.511063	+	0.371309i	−0.302164	+	0.953256i	$0.597709\pi$
$524$	−1.50309	+	4.62604i	−0.0656629	+	0.202090i
$525$		0			0
$526$	−25.4207	+	18.4692i	−1.10840	+	0.805297i
$527$	−17.1693			−0.747908
$528$		0			0
$529$	−17.7359			−0.771124
$530$	−6.56005	+	4.76616i	−0.284950	+	0.207029i
$531$		0			0
$532$	−1.16861	+	3.59661i	−0.0506657	+	0.155933i
$533$	−9.17202	−	6.66387i	−0.397284	−	0.288644i
$534$		0			0
$535$	1.51398	−	4.65954i	0.0654549	−	0.201449i
$536$	8.16998	+	25.1446i	0.352890	+	1.08608i
$537$		0			0
$538$	−19.4576			−0.838877
$539$	15.1461	+	2.91601i	0.652391	+	0.125602i
$540$		0			0
$541$	18.9044	−	13.7349i	0.812765	−	0.590509i	−0.101866	−	0.994798i	$-0.532481\pi$
$541$	18.9044	−	13.7349i	0.812765	−	0.590509i	0.914631	+	0.404290i	$0.132481\pi$
$542$	2.31138	+	7.11370i	0.0992823	+	0.305559i
$543$		0			0
$544$	−12.8464	−	9.33346i	−0.550785	−	0.400169i
$545$	−13.0214	−	9.46060i	−0.557776	−	0.405248i
$546$		0			0
$547$	1.13277	+	3.48630i	0.0484337	+	0.149063i	0.972348	−	0.233535i	$-0.0750293\pi$
$547$	1.13277	+	3.48630i	0.0484337	+	0.149063i	−0.923915	+	0.382598i	$0.875029\pi$
$548$	−15.0982	+	10.9695i	−0.644965	+	0.468594i
$549$		0			0
$550$	−12.1352	−	2.33633i	−0.517446	−	0.0996213i
$551$	−23.7339			−1.01110
$552$		0			0
$553$	0.920023	+	2.83154i	0.0391234	+	0.120409i
$554$	3.79359	−	11.6755i	0.161174	−	0.496043i
$555$		0			0
$556$	−14.6876	−	10.6712i	−0.622893	−	0.452558i
$557$	10.6998	−	32.9306i	0.453365	−	1.39531i	−0.419680	−	0.907672i	$-0.637858\pi$
$557$	10.6998	−	32.9306i	0.453365	−	1.39531i	0.873044	−	0.487641i	$-0.162142\pi$
$558$		0			0
$559$	14.2582	−	10.3592i	0.603059	−	0.438148i
$560$	−2.88418			−0.121879
$561$		0			0
$562$	−12.0910			−0.510028
$563$	31.1564	−	22.6364i	1.31309	−	0.954012i	0.313095	−	0.949722i	$-0.398634\pi$
$563$	31.1564	−	22.6364i	1.31309	−	0.954012i	0.999991	−	0.00429056i	$-0.00136573\pi$
$564$		0			0
$565$	−0.866684	+	2.66738i	−0.0364617	+	0.112218i
$566$	3.95107	+	2.87062i	0.166076	+	0.120661i
$567$		0			0
$568$	14.7348	−	45.3492i	0.618260	−	1.90281i
$569$	−7.93065	−	24.4080i	−0.332470	−	1.02324i	−0.967955	−	0.251124i	$-0.919200\pi$
$569$	−7.93065	−	24.4080i	−0.332470	−	1.02324i	0.635485	−	0.772114i	$-0.280800\pi$
$570$		0			0
$571$	22.4284			0.938600			0.469300	−	0.883039i	$-0.344506\pi$
$571$	22.4284			0.938600			0.469300	+	0.883039i	$0.344506\pi$
$572$	−4.57566	−	4.88924i	−0.191318	−	0.204429i
$573$		0			0
$574$	−6.40316	+	4.65217i	−0.267263	+	0.194178i
$575$	−2.47649	−	7.62187i	−0.103277	−	0.317854i
$576$		0			0
$577$	−16.4972	−	11.9859i	−0.686786	−	0.498979i	0.188816	−	0.982013i	$-0.439535\pi$
$577$	−16.4972	−	11.9859i	−0.686786	−	0.498979i	−0.875602	+	0.483033i	$0.839535\pi$
$578$	−3.78595	−	2.75065i	−0.157475	−	0.114412i
$579$		0			0
$580$	2.71189	+	8.34634i	0.112605	+	0.346563i
$581$	−6.61406	+	4.80539i	−0.274397	+	0.199361i
$582$		0			0
$583$	−9.92398	+	17.9791i	−0.411009	+	0.744618i
$584$	−46.2738			−1.91482
$585$		0			0
$586$	8.67107	+	26.6868i	0.358198	+	1.10242i
$587$	−2.07403	+	6.38320i	−0.0856043	+	0.263463i	−0.984691	−	0.174307i	$-0.944232\pi$
$587$	−2.07403	+	6.38320i	−0.0856043	+	0.263463i	0.899087	+	0.437770i	$0.144232\pi$
$588$		0			0
$589$	11.1938	+	8.13276i	0.461232	+	0.335104i
$590$	4.40504	−	13.5573i	0.181352	−	0.558145i
$591$		0			0
$592$	4.99205	−	3.62694i	0.205172	−	0.149066i
$593$	−12.4707			−0.512110			−0.256055	−	0.966662i	$-0.582423\pi$
$593$	−12.4707			−0.512110			−0.256055	+	0.966662i	$0.582423\pi$
$594$		0			0
$595$	−6.68275			−0.273966
$596$	−9.76138	+	7.09206i	−0.399842	+	0.290502i
$597$		0			0
$598$	−1.77141	+	5.45184i	−0.0724384	+	0.222942i
$599$	−4.35794	−	3.16623i	−0.178061	−	0.129369i	0.495185	−	0.868788i	$-0.335100\pi$
$599$	−4.35794	−	3.16623i	−0.178061	−	0.129369i	−0.673246	+	0.739419i	$0.735100\pi$
$600$		0			0
$601$	12.5533	−	38.6351i	0.512059	−	1.57596i	−0.276510	−	0.961011i	$-0.589178\pi$
$601$	12.5533	−	38.6351i	0.512059	−	1.57596i	0.788569	−	0.614946i	$-0.210822\pi$
$602$	−3.80206	−	11.7015i	−0.154961	−	0.476919i
$603$		0			0
$604$	18.0744			0.735439
$605$	13.0910	−	3.31372i	0.532224	−	0.134722i
$606$		0			0
$607$	−30.1803	+	21.9272i	−1.22498	+	0.889999i	−0.996504	−	0.0835505i	$-0.973374\pi$
$607$	−30.1803	+	21.9272i	−1.22498	+	0.889999i	−0.228475	+	0.973550i	$0.573374\pi$
$608$	3.95432	+	12.1702i	0.160369	+	0.493565i
$609$		0			0
$610$	0.649579	+	0.471947i	0.0263007	+	0.0191086i
$611$	17.3391	+	12.5976i	0.701465	+	0.509644i
$612$		0			0
$613$	−2.35013	−	7.23295i	−0.0949208	−	0.292136i	0.892312	−	0.451419i	$-0.149082\pi$
$613$	−2.35013	−	7.23295i	−0.0949208	−	0.292136i	−0.987233	+	0.159283i	$0.949082\pi$
$614$	−12.6944	+	9.22301i	−0.512304	+	0.372210i
$615$		0			0
$616$	−14.0549	+	6.58451i	−0.566286	+	0.265298i
$617$	−38.2642			−1.54046			−0.770229	−	0.637767i	$-0.779858\pi$
$617$	−38.2642			−1.54046			−0.770229	+	0.637767i	$0.779858\pi$
$618$		0			0
$619$	9.54846	+	29.3871i	0.383785	+	1.18117i	0.937358	+	0.348368i	$0.113264\pi$
$619$	9.54846	+	29.3871i	0.383785	+	1.18117i	−0.553573	+	0.832801i	$0.686736\pi$
$620$	1.58096	−	4.86570i	0.0634929	−	0.195411i
$621$		0			0
$622$	−6.72093	−	4.88304i	−0.269485	−	0.195792i
$623$	−2.76643	+	8.51421i	−0.110835	+	0.341115i
$624$		0			0
$625$	−3.77433	+	2.74221i	−0.150973	+	0.109689i
$626$	−19.3506			−0.773407
$627$		0			0
$628$	15.0945			0.602336
$629$	11.5668	−	8.40375i	0.461197	−	0.335079i
$630$		0			0
$631$	1.73983	−	5.35465i	0.0692616	−	0.213165i	−0.910435	−	0.413653i	$-0.864253\pi$
$631$	1.73983	−	5.35465i	0.0692616	−	0.213165i	0.979696	+	0.200488i	$0.0642527\pi$
$632$	4.79771	+	3.48574i	0.190843	+	0.138655i
$633$		0			0
$634$	6.41196	−	19.7340i	0.254652	−	0.783737i
$635$	−0.600306	−	1.84755i	−0.0238224	−	0.0733179i
$636$		0			0
$637$	−10.8923			−0.431569
$638$	−20.0477	−	21.4216i	−0.793698	−	0.848091i
$639$		0			0
$640$	0.580131	−	0.421490i	0.0229317	−	0.0166609i
$641$	−13.0681	−	40.2195i	−0.516159	−	1.58857i	−0.781163	−	0.624327i	$-0.785373\pi$
$641$	−13.0681	−	40.2195i	−0.516159	−	1.58857i	0.265004	−	0.964247i	$-0.414627\pi$
$642$		0			0
$643$	9.80010	+	7.12019i	0.386478	+	0.280793i	0.764011	−	0.645203i	$-0.223227\pi$
$643$	9.80010	+	7.12019i	0.386478	+	0.280793i	−0.377533	+	0.925996i	$0.623227\pi$
$644$	−2.45263	−	1.78194i	−0.0966471	−	0.0702182i
$645$		0			0
$646$	−3.35068	−	10.3123i	−0.131831	−	0.405733i
$647$	−33.3540	+	24.2331i	−1.31128	+	0.952703i	−0.311286	+	0.950316i	$0.600760\pi$
$647$	−33.3540	+	24.2331i	−1.31128	+	0.952703i	−0.999997	+	0.00238648i	$0.999240\pi$
$648$		0			0
$649$	−4.46385	−	35.8254i	−0.175221	−	1.40627i
$650$	8.72698			0.342301
$651$		0			0
$652$	−0.0509658	−	0.156856i	−0.00199597	−	0.00614297i
$653$	4.25924	−	13.1086i	0.166677	−	0.512979i	−0.832479	−	0.554056i	$-0.813079\pi$
$653$	4.25924	−	13.1086i	0.166677	−	0.512979i	0.999156	+	0.0410778i	$0.0130792\pi$
$654$		0			0
$655$	5.60395	+	4.07151i	0.218964	+	0.159087i
$656$	−2.29275	+	7.05637i	−0.0895170	+	0.275505i
$657$		0			0
$658$	12.1048	−	8.79462i	0.471892	−	0.342850i
$659$	7.42881			0.289385			0.144693	−	0.989477i	$-0.453781\pi$
$659$	7.42881			0.289385			0.144693	+	0.989477i	$0.453781\pi$
$660$		0			0
$661$	−10.6949			−0.415984			−0.207992	−	0.978130i	$-0.566693\pi$
$661$	−10.6949			−0.415984			−0.207992	+	0.978130i	$0.566693\pi$
$662$	−17.7985	+	12.9314i	−0.691760	+	0.502593i
$663$		0			0
$664$	−5.03214	+	15.4873i	−0.195285	+	0.601026i
$665$	4.35691	+	3.16548i	0.168954	+	0.122752i
$666$		0			0
$667$	5.87948	−	18.0952i	0.227654	−	0.700648i
$668$	−0.255424	−	0.786115i	−0.00988266	−	0.0304157i
$669$		0			0
$670$	11.3404			0.438117
$671$	1.99683	+	0.384439i	0.0770867	+	0.0148411i
$672$		0			0
$673$	15.7103	−	11.4142i	0.605588	−	0.439986i	−0.242270	−	0.970209i	$-0.577892\pi$
$673$	15.7103	−	11.4142i	0.605588	−	0.439986i	0.847858	+	0.530223i	$0.177892\pi$
$674$	1.08677	+	3.34474i	0.0418609	+	0.128834i
$675$		0			0
$676$	−5.24065	−	3.80755i	−0.201563	−	0.146444i
$677$	26.2504	+	19.0720i	1.00888	+	0.732997i	0.963975	−	0.265994i	$-0.0857001\pi$
$677$	26.2504	+	19.0720i	1.00888	+	0.732997i	0.0449095	+	0.998991i	$0.485700\pi$
$678$		0			0
$679$	4.02880	+	12.3994i	0.154611	+	0.475844i
$680$	−10.7689	+	7.82409i	−0.412970	+	0.300040i
$681$		0			0
$682$	2.11482	+	16.9729i	0.0809807	+	0.649924i
$683$	20.5244			0.785344			0.392672	−	0.919679i	$-0.371551\pi$
$683$	20.5244			0.785344			0.392672	+	0.919679i	$0.371551\pi$
$684$		0			0
$685$	8.21267	+	25.2760i	0.313790	+	0.965747i
$686$	−5.88669	+	18.1174i	−0.224755	+	0.691724i
$687$		0			0
$688$	−9.33110	−	6.77944i	−0.355745	−	0.258464i
$689$	4.48142	−	13.7924i	0.170729	−	0.525449i
$690$		0			0
$691$	23.9062	−	17.3688i	0.909433	−	0.660742i	−0.0314381	−	0.999506i	$-0.510009\pi$
$691$	23.9062	−	17.3688i	0.909433	−	0.660742i	0.940871	+	0.338764i	$0.110009\pi$
$692$	−18.6534			−0.709094
$693$		0			0
$694$	−8.57491			−0.325499
$695$	−20.9163	+	15.1966i	−0.793400	+	0.576439i
$696$		0			0
$697$	−5.31239	+	16.3499i	−0.201221	+	0.619295i
$698$	2.58314	+	1.87676i	0.0977733	+	0.0710365i
$699$		0			0
$700$	−1.42621	+	4.38943i	−0.0539057	+	0.165905i
$701$	−6.24195	−	19.2108i	−0.235755	−	0.725580i	−0.997020	−	0.0771395i	$-0.975421\pi$
$701$	−6.24195	−	19.2108i	−0.235755	−	0.725580i	0.761265	−	0.648441i	$-0.224579\pi$
$702$		0			0
$703$	−11.5218			−0.434553
$704$	−12.5576	+	22.7504i	−0.473282	+	0.857436i
$705$		0			0
$706$	8.55658	−	6.21672i	0.322031	−	0.233969i
$707$	0.355352	+	1.09366i	0.0133644	+	0.0411314i
$708$		0			0
$709$	−8.44613	−	6.13647i	−0.317201	−	0.230460i	0.417779	−	0.908549i	$-0.362809\pi$
$709$	−8.44613	−	6.13647i	−0.317201	−	0.230460i	−0.734980	+	0.678089i	$0.762809\pi$
$710$	−16.5466	−	12.0218i	−0.620983	−	0.451171i
$711$		0			0
$712$	5.51037	+	16.9592i	0.206510	+	0.635572i
$713$	−8.97353	+	6.51965i	−0.336061	+	0.244163i
$714$		0			0
$715$	−8.63546	+	4.04560i	−0.322948	+	0.151297i
$716$	17.6735			0.660489
$717$		0			0
$718$	5.01189	+	15.4250i	0.187042	+	0.575656i
$719$	5.23808	−	16.1212i	0.195348	−	0.601218i	−0.804625	−	0.593784i	$-0.797634\pi$
$719$	5.23808	−	16.1212i	0.195348	−	0.601218i	0.999972	−	0.00743448i	$-0.00236649\pi$
$720$		0			0
$721$	13.4003	+	9.73588i	0.499053	+	0.362583i
$722$	3.56301	−	10.9658i	0.132601	−	0.408105i
$723$		0			0
$724$	−7.27295	+	5.28411i	−0.270297	+	0.196382i
$725$	−28.9657			−1.07576
$726$		0			0
$727$	−26.2077			−0.971991			−0.485996	−	0.873961i	$-0.661543\pi$
$727$	−26.2077			−0.971991			−0.485996	+	0.873961i	$0.661543\pi$
$728$	8.86719	−	6.44239i	0.328640	−	0.238771i
$729$		0			0
$730$	−6.13346	+	18.8768i	−0.227010	+	0.698663i
$731$	−21.6205	−	15.7082i	−0.799663	−	0.580989i
$732$		0			0
$733$	−5.18559	+	15.9596i	−0.191534	+	0.589481i	0.808465	+	0.588544i	$0.200299\pi$
$733$	−5.18559	+	15.9596i	−0.191534	+	0.589481i	−1.00000		0.000937776i	$0.999701\pi$
$734$	0.457536	+	1.40815i	0.0168880	+	0.0519758i
$735$		0			0
$736$	−10.2583			−0.378127
$737$	26.0081	−	12.1845i	0.958022	−	0.448820i
$738$		0			0
$739$	−7.71218	+	5.60322i	−0.283697	+	0.206118i	−0.720528	−	0.693425i	$-0.756101\pi$
$739$	−7.71218	+	5.60322i	−0.283697	+	0.206118i	0.436831	+	0.899543i	$0.356101\pi$
$740$	1.31650	+	4.05178i	0.0483957	+	0.148947i
$741$		0			0
$742$	−8.19069	−	5.95089i	−0.300690	−	0.218464i
$743$	−2.22765	−	1.61848i	−0.0817246	−	0.0593764i	0.546173	−	0.837673i	$-0.316084\pi$
$743$	−2.22765	−	1.61848i	−0.0817246	−	0.0593764i	−0.627897	+	0.778296i	$0.716084\pi$
$744$		0			0
$745$	5.30970	+	16.3416i	0.194532	+	0.598709i
$746$	16.5130	−	11.9974i	0.604585	−	0.439257i
$747$		0			0
$748$	−4.90689	+	8.88972i	−0.179414	+	0.325040i
$749$	6.11716			0.223516
$750$		0			0
$751$	10.7058	+	32.9491i	0.390661	+	1.20233i	0.932289	+	0.361713i	$0.117808\pi$
$751$	10.7058	+	32.9491i	0.390661	+	1.20233i	−0.541628	+	0.840618i	$0.682192\pi$
$752$	4.33430	−	13.3396i	0.158056	−	0.486445i
$753$		0			0
$754$	16.7619	+	12.1782i	0.610433	+	0.443505i
$755$	7.95391	−	24.4796i	0.289472	−	0.890905i
$756$		0			0
$757$	−3.15478	+	2.29208i	−0.114663	+	0.0833072i	−0.643639	−	0.765329i	$-0.722576\pi$
$757$	−3.15478	+	2.29208i	−0.114663	+	0.0833072i	0.528976	+	0.848637i	$0.322576\pi$
$758$	0.506165			0.0183848
$759$		0			0
$760$	10.7271			0.389112
$761$	1.77801	−	1.29180i	0.0644527	−	0.0468276i	−0.555092	−	0.831789i	$-0.687317\pi$
$761$	1.77801	−	1.29180i	0.0644527	−	0.0468276i	0.619545	+	0.784961i	$0.287317\pi$
$762$		0			0
$763$	6.21006	−	19.1126i	0.224819	−	0.691923i
$764$	−14.3971	−	10.4601i	−0.520870	−	0.378434i
$765$		0			0
$766$	6.87102	−	21.1468i	0.248260	−	0.764065i
$767$	7.87832	+	24.2470i	0.284470	+	0.875507i
$768$		0			0
$769$	39.6598			1.43017			0.715085	−	0.699037i	$-0.246388\pi$
$769$	39.6598			1.43017			0.715085	+	0.699037i	$0.246388\pi$
$770$	0.823143	+	6.60627i	0.0296640	+	0.238074i
$771$		0			0
$772$	−4.17893	+	3.03617i	−0.150403	+	0.109274i
$773$	−4.55217	−	14.0102i	−0.163730	−	0.503910i	0.835210	−	0.549931i	$-0.185346\pi$
$773$	−4.55217	−	14.0102i	−0.163730	−	0.503910i	−0.998940	+	0.0460208i	$0.985346\pi$
$774$		0			0
$775$	13.6613	+	9.92549i	0.490727	+	0.356534i
$776$	21.0093	+	15.2641i	0.754190	+	0.547951i
$777$		0			0
$778$	−0.878782	−	2.70461i	−0.0315059	−	0.0969650i
$779$	11.2081	−	8.14314i	0.401571	−	0.291758i
$780$		0			0
$781$	−50.8648	−	9.79275i	−1.82009	−	0.350412i
$782$	8.69234			0.310838
$783$		0			0
$784$	2.20277	+	6.77944i	0.0786705	+	0.242123i
$785$	6.64255	−	20.4437i	0.237083	−	0.729665i
$786$		0			0
$787$	0.426247	+	0.309686i	0.0151941	+	0.0110391i	0.595356	−	0.803462i	$-0.297011\pi$
$787$	0.426247	+	0.309686i	0.0151941	+	0.0110391i	−0.580162	+	0.814501i	$0.697011\pi$
$788$	−0.377738	+	1.16256i	−0.0134563	+	0.0414144i
$789$		0			0
$790$	2.05789	−	1.49515i	0.0732165	−	0.0531949i
$791$	−3.50180			−0.124510
$792$		0			0
$793$	−1.43601			−0.0509943
$794$	−13.4420	+	9.76618i	−0.477039	+	0.346589i
$795$		0			0
$796$	−1.61790	+	4.97940i	−0.0573451	+	0.176490i
$797$	−4.55735	−	3.31111i	−0.161429	−	0.117285i	0.504138	−	0.863623i	$-0.331810\pi$
$797$	−4.55735	−	3.31111i	−0.161429	−	0.117285i	−0.665567	+	0.746338i	$0.731810\pi$
$798$		0			0
$799$	10.0427	−	30.9083i	0.355286	−	1.09346i
$800$	4.82599	+	14.8529i	0.170625	+	0.525128i
$801$		0			0
$802$	8.79744			0.310649
$803$	6.21535	+	49.8824i	0.219335	+	1.76031i
$804$		0			0
$805$	−3.49273	+	2.53762i	−0.123103	+	0.0894393i
$806$	−3.73248	−	11.4874i	−0.131471	−	0.404626i
$807$		0			0
$808$	1.85308	+	1.34634i	0.0651912	+	0.0473642i
$809$	19.1292	+	13.8982i	0.672549	+	0.488635i	0.870877	−	0.491500i	$-0.163551\pi$
$809$	19.1292	+	13.8982i	0.672549	+	0.488635i	−0.198329	+	0.980136i	$0.563551\pi$
$810$		0			0
$811$	−4.98249	−	15.3345i	−0.174959	−	0.538468i	0.824673	−	0.565610i	$-0.191359\pi$
$811$	−4.98249	−	15.3345i	−0.174959	−	0.538468i	−0.999632	+	0.0271423i	$0.991359\pi$
$812$	−8.86463	+	6.44053i	−0.311087	+	0.226018i
$813$		0			0
$814$	−9.73231	−	10.3993i	−0.341117	−	0.364495i
$815$	−0.234871			−0.00822718
$816$		0			0
$817$	6.65512	+	20.4824i	0.232833	+	0.716587i
$818$	−1.32629	+	4.08191i	−0.0463728	+	0.142721i
$819$		0			0
$820$	−4.14430	−	3.01101i	−0.144725	−	0.105149i
$821$	−6.40533	+	19.7136i	−0.223548	+	0.688009i	0.774888	+	0.632098i	$0.217806\pi$
$821$	−6.40533	+	19.7136i	−0.223548	+	0.688009i	−0.998436	+	0.0559105i	$0.982194\pi$
$822$		0			0
$823$	21.3970	−	15.5458i	0.745852	−	0.541893i	−0.148686	−	0.988884i	$-0.547504\pi$
$823$	21.3970	−	15.5458i	0.745852	−	0.541893i	0.894538	+	0.446991i	$0.147504\pi$
$824$	32.9926			1.14935
$825$		0			0
$826$	17.7984			0.619285
$827$	42.3796	−	30.7905i	1.47368	−	1.07069i	0.494156	−	0.869373i	$-0.335477\pi$
$827$	42.3796	−	30.7905i	1.47368	−	1.07069i	0.979526	−	0.201319i	$-0.0645227\pi$
$828$		0			0
$829$	8.69589	−	26.7632i	0.302021	−	0.929525i	−0.678751	−	0.734368i	$-0.737479\pi$
$829$	8.69589	−	26.7632i	0.302021	−	0.929525i	0.980772	−	0.195156i	$-0.0625215\pi$
$830$	5.65089	+	4.10561i	0.196145	+	0.142508i
$831$		0			0
$832$	5.67070	−	17.4526i	0.196596	−	0.605061i
$833$	5.10391	+	15.7082i	0.176840	+	0.544257i
$834$		0			0
$835$	−1.17710			−0.0407352
$836$	7.40999	−	3.47148i	0.256280	−	0.120064i
$837$		0			0
$838$	27.6520	−	20.0904i	0.955223	−	0.694010i
$839$	13.5192	+	41.6078i	0.466735	+	1.43646i	0.856788	+	0.515669i	$0.172457\pi$
$839$	13.5192	+	41.6078i	0.466735	+	1.43646i	−0.390053	+	0.920792i	$0.627543\pi$
$840$		0			0
$841$	−32.1729	−	23.3750i	−1.10941	−	0.806033i
$842$	21.9947	+	15.9801i	0.757986	+	0.550709i
$843$		0			0
$844$	−4.24736	−	13.0720i	−0.146200	−	0.449958i
$845$	−7.46309	+	5.42225i	−0.256738	+	0.186531i
$846$		0			0
$847$	8.98580	+	14.2665i	0.308756	+	0.490202i
$848$	−9.49076			−0.325914
$849$		0			0
$850$	−4.08928	−	12.5855i	−0.140261	−	0.431679i
$851$	2.85423	−	8.78442i	0.0978418	−	0.301126i
$852$		0			0
$853$	17.0427	+	12.3822i	0.583530	+	0.423960i	0.839995	−	0.542594i	$-0.182558\pi$
$853$	17.0427	+	12.3822i	0.583530	+	0.423960i	−0.256465	+	0.966554i	$0.582558\pi$
$854$	−0.309792	+	0.953442i	−0.0106009	+	0.0326261i
$855$		0			0
$856$	9.85753	−	7.16191i	0.336923	−	0.244789i
$857$	18.8828			0.645025			0.322512	−	0.946565i	$-0.395473\pi$
$857$	18.8828			0.645025			0.322512	+	0.946565i	$0.395473\pi$
$858$		0			0
$859$	−43.0833			−1.46998			−0.734992	−	0.678075i	$-0.762814\pi$
$859$	−43.0833			−1.46998			−0.734992	+	0.678075i	$0.762814\pi$
$860$	6.44245	−	4.68072i	0.219686	−	0.159611i
$861$		0			0
$862$	−6.82208	+	20.9962i	−0.232361	+	0.715134i
$863$	−12.9855	−	9.43449i	−0.442030	−	0.321154i	0.344411	−	0.938819i	$-0.388079\pi$
$863$	−12.9855	−	9.43449i	−0.442030	−	0.321154i	−0.786441	+	0.617665i	$0.788079\pi$
$864$		0			0
$865$	−8.20867	+	25.2637i	−0.279103	+	0.858992i
$866$	4.75723	+	14.6413i	0.161657	+	0.497530i
$867$		0			0
$868$	6.38781			0.216817
$869$	3.11316	−	5.64005i	0.105607	−	0.191326i
$870$		0			0
$871$	−16.4085	+	11.9215i	−0.555981	+	0.403944i
$872$	−12.3696	−	38.0698i	−0.418888	−	1.28920i
$873$		0			0
$874$	−5.66709	−	4.11738i	−0.191692	−	0.139273i
$875$	12.9288	+	9.39335i	0.437074	+	0.317553i
$876$		0			0
$877$	4.75721	+	14.6412i	0.160640	+	0.494398i	0.998689	−	0.0511972i	$-0.0163037\pi$
$877$	4.75721	+	14.6412i	0.160640	+	0.494398i	−0.838049	+	0.545595i	$0.816304\pi$
$878$	7.72745	−	5.61432i	0.260789	−	0.189474i
$879$		0			0
$880$	4.26437	+	4.55661i	0.143752	+	0.153603i
$881$	−3.84430			−0.129518			−0.0647589	−	0.997901i	$-0.520628\pi$
$881$	−3.84430			−0.129518			−0.0647589	+	0.997901i	$0.520628\pi$
$882$		0			0
$883$	6.15742	+	18.9506i	0.207214	+	0.637738i	0.999615	+	0.0277382i	$0.00883048\pi$
$883$	6.15742	+	18.9506i	0.207214	+	0.637738i	−0.792402	+	0.610000i	$0.791170\pi$
$884$	2.21583	−	6.81963i	0.0745265	−	0.229369i
$885$		0			0
$886$	8.85279	+	6.43193i	0.297415	+	0.216085i
$887$	−3.59194	+	11.0549i	−0.120606	+	0.371186i	−0.993075	−	0.117483i	$-0.962517\pi$
$887$	−3.59194	+	11.0549i	−0.120606	+	0.371186i	0.872469	+	0.488669i	$0.162517\pi$
$888$		0			0
$889$	1.96228	−	1.42568i	0.0658128	−	0.0478158i
$890$	7.64868			0.256384
$891$		0			0
$892$	−22.6787			−0.759338
$893$	−21.1881	+	15.3941i	−0.709034	+	0.515143i
$894$		0			0
$895$	7.77747	−	23.9366i	0.259972	−	0.800112i
$896$	0.724335	+	0.526260i	0.0241983	+	0.0175811i
$897$		0			0
$898$	6.73758	−	20.7361i	0.224836	−	0.691974i
$899$	12.3885	+	38.1277i	0.413178	+	1.27163i
$900$		0			0
$901$	−21.9904			−0.732608
$902$	16.8171	+	3.23772i	0.559949	+	0.107804i
$903$		0			0
$904$	−5.64300	+	4.09988i	−0.187683	+	0.136360i
$905$	3.95611	+	12.1757i	0.131506	+	0.404733i
$906$		0			0
$907$	−24.3910	−	17.7211i	−0.809891	−	0.588420i	0.103908	−	0.994587i	$-0.466865\pi$
$907$	−24.3910	−	17.7211i	−0.809891	−	0.588420i	−0.913799	+	0.406167i	$0.866865\pi$
$908$	1.94041	+	1.40979i	0.0643948	+	0.0467856i
$909$		0			0
$910$	−1.45278	−	4.47119i	−0.0481591	−	0.148218i
$911$	−18.8165	+	13.6710i	−0.623419	+	0.452941i	−0.854114	−	0.520086i	$-0.825900\pi$
$911$	−18.8165	+	13.6710i	−0.623419	+	0.452941i	0.230695	+	0.973026i	$0.425900\pi$
$912$		0			0
$913$	17.3710	+	3.34436i	0.574896	+	0.110682i
$914$	41.0556			1.35800
$915$		0			0
$916$	−5.59955	−	17.2337i	−0.185014	−	0.569416i
$917$	−2.67259	+	8.22539i	−0.0882567	+	0.271626i
$918$		0			0
$919$	−19.1223	−	13.8932i	−0.630787	−	0.458294i	0.225886	−	0.974154i	$-0.427472\pi$
$919$	−19.1223	−	13.8932i	−0.630787	−	0.458294i	−0.856673	+	0.515860i	$0.827472\pi$
$920$	−2.65736	+	8.17851i	−0.0876105	+	0.269637i
$921$		0			0
$922$	16.8641	−	12.2525i	0.555391	−	0.403515i
$923$	36.5793			1.20402
$924$		0			0
$925$	−14.0616			−0.462342
$926$	−14.2625	+	10.3623i	−0.468694	+	0.340526i
$927$		0			0
$928$	−11.4574	+	35.2624i	−0.376109	+	1.15755i
$929$	−44.0297	−	31.9895i	−1.44457	−	1.04954i	−0.987063	−	0.160335i	$-0.948743\pi$
$929$	−44.0297	−	31.9895i	−1.44457	−	1.04954i	−0.457506	−	0.889206i	$-0.651257\pi$
$930$		0			0
$931$	4.11309	−	12.6588i	0.134801	−	0.414875i
$932$	−3.63216	−	11.1786i	−0.118975	−	0.366168i
$933$		0			0
$934$	31.2696			1.02317
$935$	9.88070	+	10.5578i	0.323133	+	0.345278i
$936$		0			0
$937$	−21.9192	+	15.9253i	−0.716070	+	0.520255i	−0.885126	−	0.465351i	$-0.845928\pi$
$937$	−21.9192	+	15.9253i	−0.716070	+	0.520255i	0.169056	+	0.985606i	$0.445928\pi$
$938$	4.37545	+	13.4662i	0.142863	+	0.439689i
$939$		0			0
$940$	7.83452	+	5.69211i	0.255534	+	0.185656i
$941$	−29.7676	−	21.6274i	−0.970396	−	0.705034i	−0.0148540	−	0.999890i	$-0.504728\pi$
$941$	−29.7676	−	21.6274i	−0.970396	−	0.705034i	−0.955542	+	0.294856i	$0.904728\pi$
$942$		0			0
$943$	3.43196	+	10.5625i	0.111760	+	0.343962i
$944$	13.4982	−	9.80702i	0.439329	−	0.319191i
$945$		0			0
$946$	−12.8654	+	23.3079i	−0.418289	+	0.757806i
$947$	59.0290			1.91819			0.959093	−	0.283093i	$-0.0913604\pi$
$947$	59.0290			1.91819			0.959093	+	0.283093i	$0.0913604\pi$
$948$		0			0
$949$	−10.9696	−	33.7609i	−0.356087	−	1.09592i
$950$	−3.29543	+	10.1423i	−0.106918	+	0.329060i
$951$		0			0
$952$	−13.4458	−	9.76894i	−0.435781	−	0.316613i
$953$	12.3238	−	37.9287i	0.399206	−	1.22863i	−0.526431	−	0.850218i	$-0.676470\pi$
$953$	12.3238	−	37.9287i	0.399206	−	1.22863i	0.925637	−	0.378413i	$-0.123530\pi$
$954$		0			0
$955$	−20.5026	+	14.8960i	−0.663449	+	0.482024i
$956$	17.4794			0.565325
$957$		0			0
$958$	−16.5224			−0.533814
$959$	−26.8456	+	19.5045i	−0.866890	+	0.629832i
$960$		0			0
$961$	−2.35738	+	7.25526i	−0.0760445	+	0.234041i
$962$	8.13718	+	5.91201i	0.262353	+	0.190611i
$963$		0			0
$964$	7.03081	−	21.6386i	0.226447	−	0.696932i
$965$	2.27312	+	6.99596i	0.0731745	+	0.225208i
$966$		0			0
$967$	−22.3285			−0.718037			−0.359019	−	0.933330i	$-0.616889\pi$
$967$	−22.3285			−0.718037			−0.359019	+	0.933330i	$0.616889\pi$
$968$	31.1833	+	12.4693i	1.00227	+	0.400779i
$969$		0			0
$970$	9.01156	−	6.54728i	0.289344	−	0.210220i
$971$	5.35373	+	16.4771i	0.171809	+	0.528775i	0.999473	−	0.0324490i	$-0.0103307\pi$
$971$	5.35373	+	16.4771i	0.171809	+	0.528775i	−0.827664	+	0.561224i	$0.810331\pi$
$972$		0			0
$973$	−26.1155	−	18.9740i	−0.837223	−	0.608278i
$974$	−3.34542	−	2.43059i	−0.107194	−	0.0778811i
$975$		0			0
$976$	0.290408	+	0.893783i	0.00929573	+	0.0286093i
$977$	−16.2968	+	11.8404i	−0.521382	+	0.378806i	−0.817124	−	0.576461i	$-0.804433\pi$
$977$	−16.2968	+	11.8404i	−0.521382	+	0.378806i	0.295742	+	0.955268i	$0.404433\pi$
$978$		0			0
$979$	17.5416	−	8.21799i	0.560631	−	0.262648i
$980$	−4.92160			−0.157215
$981$		0			0
$982$	−2.39234	−	7.36286i	−0.0763425	−	0.234958i
$983$	7.71806	−	23.7537i	0.246168	−	0.757627i	−0.749274	−	0.662260i	$-0.769598\pi$
$983$	7.71806	−	23.7537i	0.246168	−	0.757627i	0.995442	−	0.0953671i	$-0.0304025\pi$
$984$		0			0
$985$	1.40831	+	1.02320i	0.0448726	+	0.0326018i
$986$	9.70841	−	29.8794i	0.309179	−	0.951555i
$987$		0			0
$988$	−4.67496	+	3.39655i	−0.148730	+	0.108059i
$989$	−17.2648			−0.548987
$990$		0			0
$991$	−3.49555			−0.111040			−0.0555199	−	0.998458i	$-0.517682\pi$
$991$	−3.49555			−0.111040			−0.0555199	+	0.998458i	$0.517682\pi$
$992$	17.4869	−	12.7050i	0.555209	−	0.403383i
$993$		0			0
$994$	7.89127	−	24.2868i	0.250296	−	0.770331i
$995$	6.03201	+	4.38251i	0.191227	+	0.138935i
$996$		0			0
$997$	2.27585	−	7.00435i	0.0720770	−	0.221830i	−0.908528	−	0.417823i	$-0.862793\pi$
$997$	2.27585	−	7.00435i	0.0720770	−	0.221830i	0.980605	+	0.195993i	$0.0627931\pi$
$998$	−11.8332	−	36.4188i	−0.374573	−	1.15282i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.f.c.190.3	yes	16
3.2	odd	2	inner	297.2.f.c.190.2	yes	16
9.2	odd	6		891.2.n.g.190.3		32
9.4	even	3		891.2.n.g.784.3		32
9.5	odd	6		891.2.n.g.784.2		32
9.7	even	3		891.2.n.g.190.2		32
11.2	odd	10		3267.2.a.bh.1.6		8
11.4	even	5	inner	297.2.f.c.136.3	yes	16
11.9	even	5		3267.2.a.bg.1.3		8
33.2	even	10		3267.2.a.bh.1.3		8
33.20	odd	10		3267.2.a.bg.1.6		8
33.26	odd	10	inner	297.2.f.c.136.2	✓	16
99.4	even	15		891.2.n.g.136.2		32
99.59	odd	30		891.2.n.g.136.3		32
99.70	even	15		891.2.n.g.433.3		32
99.92	odd	30		891.2.n.g.433.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.c.136.2	✓	16	33.26	odd	10	inner
297.2.f.c.136.3	yes	16	11.4	even	5	inner
297.2.f.c.190.2	yes	16	3.2	odd	2	inner
297.2.f.c.190.3	yes	16	1.1	even	1	trivial
891.2.n.g.136.2		32	99.4	even	15
891.2.n.g.136.3		32	99.59	odd	30
891.2.n.g.190.2		32	9.7	even	3
891.2.n.g.190.3		32	9.2	odd	6
891.2.n.g.433.2		32	99.92	odd	30
891.2.n.g.433.3		32	99.70	even	15
891.2.n.g.784.2		32	9.5	odd	6
891.2.n.g.784.3		32	9.4	even	3
3267.2.a.bg.1.3		8	11.9	even	5
3267.2.a.bg.1.6		8	33.20	odd	10
3267.2.a.bh.1.3		8	33.2	even	10
3267.2.a.bh.1.6		8	11.2	odd	10

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.f (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.863017 - 0.627019i) q^{2} +(-0.266388 + 0.819857i) q^{4} +(0.993168 + 0.721579i) q^{5} +(-0.473654 + 1.45776i) q^{7} +(0.943455 + 2.90366i) q^{8} +1.30957 q^{10} +(3.00337 - 1.40704i) q^{11} +(-1.89482 + 1.37667i) q^{13} +(0.505269 + 1.55506i) q^{14} +(1.24004 + 0.900943i) q^{16} +(2.87322 + 2.08752i) q^{17} +(-0.884422 - 2.72197i) q^{19} +(-0.856159 + 0.622036i) q^{20} +(1.70972 - 3.09747i) q^{22} +2.29437 q^{23} +(-1.07938 - 3.32198i) q^{25} +(-0.772068 + 2.37618i) q^{26} +(-1.06898 - 0.776656i) q^{28} +(2.56257 - 7.88677i) q^{29} +(-3.91111 + 2.84159i) q^{31} -4.47108 q^{32} +3.78855 q^{34} +(-1.52230 + 1.10602i) q^{35} +(1.24401 - 3.82868i) q^{37} +(-2.47000 - 1.79456i) q^{38} +(-1.15821 + 3.56460i) q^{40} +(1.49582 + 4.60365i) q^{41} -7.52483 q^{43} +(0.353510 + 2.83715i) q^{44} +(1.98008 - 1.43861i) q^{46} +(-2.82775 - 8.70291i) q^{47} +(3.76241 + 2.73355i) q^{49} +(-3.01447 - 2.19014i) q^{50} +(-0.623915 - 1.92021i) q^{52} +(-5.00934 + 3.63950i) q^{53} +(3.99814 + 0.769743i) q^{55} -4.67969 q^{56} +(-2.73361 - 8.41319i) q^{58} +(3.36374 - 10.3525i) q^{59} +(0.496027 + 0.360385i) q^{61} +(-1.59363 + 4.90467i) q^{62} +(-6.33871 + 4.60534i) q^{64} -2.87526 q^{65} +8.65964 q^{67} +(-2.47686 + 1.79954i) q^{68} +(-0.620280 + 1.90903i) q^{70} +(-12.6352 - 9.18000i) q^{71} +(-4.68358 + 14.4146i) q^{73} +(-1.32705 - 4.08424i) q^{74} +2.46722 q^{76} +(0.628562 + 5.04463i) q^{77} +(1.57143 - 1.14171i) q^{79} +(0.581468 + 1.78958i) q^{80} +(4.17749 + 3.03513i) q^{82} +(4.31509 + 3.13509i) q^{83} +(1.34728 + 4.14651i) q^{85} +(-6.49406 + 4.71821i) q^{86} +(6.91910 + 7.39328i) q^{88} +5.84063 q^{89} +(-1.10936 - 3.41426i) q^{91} +(-0.611192 + 1.88106i) q^{92} +(-7.89728 - 5.73771i) q^{94} +(1.08574 - 3.34155i) q^{95} +(6.88134 - 4.99958i) q^{97} +4.96102 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{4} + 8 q^{7} - 12 q^{10} + 8 q^{13} - 2 q^{16} + 10 q^{19} - 24 q^{22} - 16 q^{25} - 30 q^{28} - 6 q^{31} + 32 q^{34} + 12 q^{37} - 40 q^{40} - 80 q^{43} - 12 q^{46} + 40 q^{49} + 12 q^{52}+ \cdots - 46 q^{94}+O(q^{100}) \) 16 * q + 2 * q^4 + 8 * q^7 - 12 * q^10 + 8 * q^13 - 2 * q^16 + 10 * q^19 - 24 * q^22 - 16 * q^25 - 30 * q^28 - 6 * q^31 + 32 * q^34 + 12 * q^37 - 40 * q^40 - 80 * q^43 - 12 * q^46 + 40 * q^49 + 12 * q^52 + 56 * q^55 - 50 * q^58 - 6 * q^61 + 6 * q^64 + 64 * q^67 + 74 * q^70 - 32 * q^73 + 52 * q^76 - 4 * q^79 + 4 * q^82 + 70 * q^85 + 56 * q^88 - 94 * q^91 - 46 * q^94

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