LMFDB - Embedded newform 189.2.e.e.109.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(109,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(6))

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("189.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.e (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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.2
Root			$0.500000 + 1.41036i$ of defining polynomial
Character	$\chi$	$=$	189.109
Dual form			189.2.e.e.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.380438 - 0.658939i) q^{2} +(0.710533 - 1.23068i) q^{4} +(-1.59097 - 2.75564i) q^{5} +(-2.56238 + 0.658939i) q^{7} -2.60301 q^{8} +O(q^{10})$	\(q+(-0.380438 - 0.658939i) q^{2} +(0.710533 - 1.23068i) q^{4} +(-1.59097 - 2.75564i) q^{5} +(-2.56238 + 0.658939i) q^{7} -2.60301 q^{8} +(-1.21053 + 2.09671i) q^{10} +(-1.11956 + 1.93914i) q^{11} +3.70370 q^{13} +(1.40903 + 1.43777i) q^{14} +(-0.430782 - 0.746136i) q^{16} +(2.80150 - 4.85235i) q^{17} +(-2.21053 - 3.82876i) q^{19} -4.52175 q^{20} +1.70370 q^{22} +(0.471410 + 0.816506i) q^{23} +(-2.56238 + 4.43818i) q^{25} +(-1.40903 - 2.44051i) q^{26} +(-1.00972 + 3.62167i) q^{28} +10.1248 q^{29} +(2.85185 - 4.93955i) q^{31} +(-2.93078 + 5.07626i) q^{32} -4.26320 q^{34} +(5.89248 + 6.01266i) q^{35} +(-1.56238 - 2.70612i) q^{37} +(-1.68194 + 2.91321i) q^{38} +(4.14132 + 7.17297i) q^{40} +3.98633 q^{41} -3.28263 q^{43} +(1.59097 + 2.75564i) q^{44} +(0.358685 - 0.621261i) q^{46} +(0.112725 + 0.195246i) q^{47} +(6.13160 - 3.37690i) q^{49} +3.89931 q^{50} +(2.63160 - 4.55806i) q^{52} +(-5.33009 + 9.23200i) q^{53} +7.12476 q^{55} +(6.66991 - 1.71522i) q^{56} +(-3.85185 - 6.67160i) q^{58} +(1.02859 - 1.78157i) q^{59} +(2.92107 + 5.05944i) q^{61} -4.33981 q^{62} +2.73680 q^{64} +(-5.89248 - 10.2061i) q^{65} +(-3.71053 + 6.42683i) q^{67} +(-3.98113 - 6.89551i) q^{68} +(1.72025 - 6.17023i) q^{70} +7.26320 q^{71} +(-3.77975 + 6.54672i) q^{73} +(-1.18878 + 2.05903i) q^{74} -6.28263 q^{76} +(1.59097 - 5.70653i) q^{77} +(3.41423 + 5.91362i) q^{79} +(-1.37072 + 2.37416i) q^{80} +(-1.51655 - 2.62674i) q^{82} -8.11109 q^{83} -17.8285 q^{85} +(1.24884 + 2.16305i) q^{86} +(2.91423 - 5.04759i) q^{88} +(-4.86389 - 8.42450i) q^{89} +(-9.49028 + 2.44051i) q^{91} +1.33981 q^{92} +(0.0857699 - 0.148558i) q^{94} +(-7.03379 + 12.1829i) q^{95} +0.842133 q^{97} +(-4.55787 - 2.75564i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 2 q^{2} - 4 q^{4} - q^{5} + 2 q^{7} + 18 q^{8}+O(q^{10}) $ 6 * q - 2 * q^2 - 4 * q^4 - q^5 + 2 * q^7 + 18 * q^8	$ 6 q - 2 q^{2} - 4 q^{4} - q^{5} + 2 q^{7} + 18 q^{8} + q^{10} - 7 q^{11} + 4 q^{13} + 17 q^{14} - 10 q^{16} - 5 q^{19} - 26 q^{20} - 8 q^{22} - 6 q^{23} + 2 q^{25} - 17 q^{26} - 30 q^{28} + 26 q^{29} + 8 q^{31} - 25 q^{32} + 24 q^{34} + 10 q^{35} + 8 q^{37} + 7 q^{38} + 24 q^{40} + 4 q^{41} - 18 q^{43} + q^{44} + 3 q^{46} - 9 q^{47} + 12 q^{49} + 8 q^{50} - 9 q^{52} - 24 q^{53} + 8 q^{55} + 48 q^{56} - 14 q^{58} + 15 q^{59} + q^{61} - 42 q^{62} + 66 q^{64} - 10 q^{65} - 14 q^{67} - 39 q^{68} + 26 q^{70} - 6 q^{71} - 7 q^{73} - 36 q^{76} + q^{77} - 6 q^{79} + 16 q^{80} - 43 q^{82} + 6 q^{83} - 54 q^{85} + 32 q^{86} - 9 q^{88} + 5 q^{89} - 33 q^{91} + 24 q^{92} + 27 q^{94} - 16 q^{95} - 28 q^{97} + 49 q^{98}+O(q^{100}) $ 6 * q - 2 * q^2 - 4 * q^4 - q^5 + 2 * q^7 + 18 * q^8 + q^10 - 7 * q^11 + 4 * q^13 + 17 * q^14 - 10 * q^16 - 5 * q^19 - 26 * q^20 - 8 * q^22 - 6 * q^23 + 2 * q^25 - 17 * q^26 - 30 * q^28 + 26 * q^29 + 8 * q^31 - 25 * q^32 + 24 * q^34 + 10 * q^35 + 8 * q^37 + 7 * q^38 + 24 * q^40 + 4 * q^41 - 18 * q^43 + q^44 + 3 * q^46 - 9 * q^47 + 12 * q^49 + 8 * q^50 - 9 * q^52 - 24 * q^53 + 8 * q^55 + 48 * q^56 - 14 * q^58 + 15 * q^59 + q^61 - 42 * q^62 + 66 * q^64 - 10 * q^65 - 14 * q^67 - 39 * q^68 + 26 * q^70 - 6 * q^71 - 7 * q^73 - 36 * q^76 + q^77 - 6 * q^79 + 16 * q^80 - 43 * q^82 + 6 * q^83 - 54 * q^85 + 32 * q^86 - 9 * q^88 + 5 * q^89 - 33 * q^91 + 24 * q^92 + 27 * q^94 - 16 * q^95 - 28 * q^97 + 49 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.380438	−	0.658939i	−0.269011	−	0.465940i	0.699596	−	0.714539i	$-0.253363\pi$
$2$	−0.380438	−	0.658939i	−0.269011	−	0.465940i	−0.968607	+	0.248599i	$0.920030\pi$
$3$		0			0
$3$		0			0
$4$	0.710533	−	1.23068i	0.355267	−	0.615340i
$5$	−1.59097	−	2.75564i	−0.711504	−	1.23236i	−0.964292	−	0.264840i	$-0.914681\pi$
$5$	−1.59097	−	2.75564i	−0.711504	−	1.23236i	0.252788	−	0.967522i	$-0.418652\pi$
$6$		0			0
$7$	−2.56238	+	0.658939i	−0.968489	+	0.249055i
$7$	−2.56238	+	0.658939i	−0.968489	+	0.249055i
$8$	−2.60301			−0.920303
$9$		0			0
$10$	−1.21053	+	2.09671i	−0.382804	+	0.663036i
$11$	−1.11956	+	1.93914i	−0.337561	+	0.584672i	−0.983973	−	0.178316i	$-0.942935\pi$
$11$	−1.11956	+	1.93914i	−0.337561	+	0.584672i	0.646413	+	0.762988i	$0.276268\pi$
$12$		0			0
$13$	3.70370			1.02722			0.513610	−	0.858024i	$-0.328308\pi$
$13$	3.70370			1.02722			0.513610	+	0.858024i	$0.328308\pi$
$14$	1.40903	+	1.43777i	0.376579	+	0.384259i
$15$		0			0
$16$	−0.430782	−	0.746136i	−0.107695	−	0.186534i
$17$	2.80150	−	4.85235i	0.679465	−	1.17687i	−0.295678	−	0.955288i	$-0.595545\pi$
$17$	2.80150	−	4.85235i	0.679465	−	1.17687i	0.975142	−	0.221580i	$-0.0711213\pi$
$18$		0			0
$19$	−2.21053	−	3.82876i	−0.507131	−	0.878377i	−0.999966	−	0.00825398i	$-0.997373\pi$
$19$	−2.21053	−	3.82876i	−0.507131	−	0.878377i	0.492835	−	0.870123i	$-0.335961\pi$
$20$	−4.52175			−1.01109
$21$		0			0
$22$	1.70370			0.363229
$23$	0.471410	+	0.816506i	0.0982958	+	0.170253i	0.910979	−	0.412452i	$-0.135328\pi$
$23$	0.471410	+	0.816506i	0.0982958	+	0.170253i	−0.812684	+	0.582705i	$0.801994\pi$
$24$		0			0
$25$	−2.56238	+	4.43818i	−0.512476	+	0.887635i
$26$	−1.40903	−	2.44051i	−0.276333	−	0.478623i
$27$		0			0
$28$	−1.00972	+	3.62167i	−0.190818	+	0.684431i
$29$	10.1248			1.88012			0.940061	−	0.341007i	$-0.110768\pi$
$29$	10.1248			1.88012			0.940061	+	0.341007i	$0.110768\pi$
$30$		0			0
$31$	2.85185	−	4.93955i	0.512207	−	0.887169i	−0.487693	−	0.873015i	$-0.662161\pi$
$31$	2.85185	−	4.93955i	0.512207	−	0.887169i	0.999900	−	0.0141534i	$-0.00450531\pi$
$32$	−2.93078	+	5.07626i	−0.518094	+	0.897365i
$33$		0			0
$34$	−4.26320			−0.731133
$35$	5.89248	+	6.01266i	0.996010	+	1.01632i
$36$		0			0
$37$	−1.56238	−	2.70612i	−0.256854	−	0.444884i	0.708543	−	0.705667i	$-0.249353\pi$
$37$	−1.56238	−	2.70612i	−0.256854	−	0.444884i	−0.965397	+	0.260783i	$0.916019\pi$
$38$	−1.68194	+	2.91321i	−0.272847	+	0.472585i
$39$		0			0
$40$	4.14132	+	7.17297i	0.654799	+	1.13415i
$41$	3.98633			0.622560			0.311280	−	0.950318i	$-0.399242\pi$
$41$	3.98633			0.622560			0.311280	+	0.950318i	$0.399242\pi$
$42$		0			0
$43$	−3.28263			−0.500596			−0.250298	−	0.968169i	$-0.580529\pi$
$43$	−3.28263			−0.500596			−0.250298	+	0.968169i	$0.580529\pi$
$44$	1.59097	+	2.75564i	0.239848	+	0.415429i
$45$		0			0
$46$	0.358685	−	0.621261i	0.0528852	−	0.0915999i
$47$	0.112725	+	0.195246i	0.0164426	+	0.0284795i	0.874130	−	0.485693i	$-0.161433\pi$
$47$	0.112725	+	0.195246i	0.0164426	+	0.0284795i	−0.857687	+	0.514172i	$0.828099\pi$
$48$		0			0
$49$	6.13160	−	3.37690i	0.875943	−	0.482415i
$50$	3.89931			0.551446
$51$		0			0
$52$	2.63160	−	4.55806i	0.364937	−	0.632090i
$53$	−5.33009	+	9.23200i	−0.732145	+	1.26811i	0.223820	+	0.974631i	$0.428147\pi$
$53$	−5.33009	+	9.23200i	−0.732145	+	1.26811i	−0.955965	+	0.293482i	$0.905186\pi$
$54$		0			0
$55$	7.12476			0.960703
$56$	6.66991	−	1.71522i	0.891304	−	0.229206i
$57$		0			0
$58$	−3.85185	−	6.67160i	−0.505772	−	0.876024i
$59$	1.02859	−	1.78157i	0.133911	−	0.231941i	−0.791270	−	0.611467i	$-0.790580\pi$
$59$	1.02859	−	1.78157i	0.133911	−	0.231941i	0.925181	+	0.379526i	$0.123913\pi$
$60$		0			0
$61$	2.92107	+	5.05944i	0.374004	+	0.647794i	0.990177	−	0.139816i	$-0.0446512\pi$
$61$	2.92107	+	5.05944i	0.374004	+	0.647794i	−0.616173	+	0.787611i	$0.711318\pi$
$62$	−4.33981			−0.551156
$63$		0			0
$64$	2.73680			0.342100
$65$	−5.89248	−	10.2061i	−0.730872	−	1.26591i
$66$		0			0
$67$	−3.71053	+	6.42683i	−0.453314	+	0.785163i	−0.998590	−	0.0530942i	$-0.983092\pi$
$67$	−3.71053	+	6.42683i	−0.453314	+	0.785163i	0.545276	+	0.838257i	$0.316425\pi$
$68$	−3.98113	−	6.89551i	−0.482782	−	0.836204i
$69$		0			0
$70$	1.72025	−	6.17023i	0.205609	−	0.737483i
$71$	7.26320			0.861983			0.430992	−	0.902356i	$-0.358164\pi$
$71$	7.26320			0.861983			0.430992	+	0.902356i	$0.358164\pi$
$72$		0			0
$73$	−3.77975	+	6.54672i	−0.442386	+	0.766236i	−0.997866	−	0.0652944i	$-0.979201\pi$
$73$	−3.77975	+	6.54672i	−0.442386	+	0.766236i	0.555480	+	0.831530i	$0.312535\pi$
$74$	−1.18878	+	2.05903i	−0.138193	+	0.239357i
$75$		0			0
$76$	−6.28263			−0.720667
$77$	1.59097	−	5.70653i	0.181308	−	0.650320i
$78$		0			0
$79$	3.41423	+	5.91362i	0.384131	+	0.665334i	0.991648	−	0.128972i	$-0.0411678\pi$
$79$	3.41423	+	5.91362i	0.384131	+	0.665334i	−0.607517	+	0.794306i	$0.707834\pi$
$80$	−1.37072	+	2.37416i	−0.153252	+	0.265439i
$81$		0			0
$82$	−1.51655	−	2.62674i	−0.167475	−	0.290075i
$83$	−8.11109			−0.890308			−0.445154	−	0.895454i	$-0.646851\pi$
$83$	−8.11109			−0.890308			−0.445154	+	0.895454i	$0.646851\pi$
$84$		0			0
$85$	−17.8285			−1.93377
$86$	1.24884	+	2.16305i	0.134666	+	0.233248i
$87$		0			0
$88$	2.91423	−	5.04759i	0.310658	−	0.538075i
$89$	−4.86389	−	8.42450i	−0.515571	−	0.892995i	−0.999837	−	0.0180741i	$-0.994247\pi$
$89$	−4.86389	−	8.42450i	−0.515571	−	0.892995i	0.484266	−	0.874921i	$-0.339087\pi$
$90$		0			0
$91$	−9.49028	+	2.44051i	−0.994852	+	0.255835i
$92$	1.33981			0.139685
$93$		0			0
$94$	0.0857699	−	0.148558i	0.00884649	−	0.0153226i
$95$	−7.03379	+	12.1829i	−0.721652	+	1.24994i
$96$		0			0
$97$	0.842133			0.0855057			0.0427528	−	0.999086i	$-0.486387\pi$
$97$	0.842133			0.0855057			0.0427528	+	0.999086i	$0.486387\pi$
$98$	−4.55787	−	2.75564i	−0.460414	−	0.278362i
$99$		0			0
$100$	3.64132	+	6.30694i	0.364132	+	0.630694i
$101$	3.87360	−	6.70928i	0.385438	−	0.667598i	−0.606392	−	0.795166i	$-0.707384\pi$
$101$	3.87360	−	6.70928i	0.385438	−	0.667598i	0.991830	+	0.127568i	$0.0407171\pi$
$102$		0			0
$103$	1.21737	+	2.10855i	0.119951	+	0.207761i	0.919748	−	0.392509i	$-0.128393\pi$
$103$	1.21737	+	2.10855i	0.119951	+	0.207761i	−0.799797	+	0.600271i	$0.795060\pi$
$104$	−9.64076			−0.945354
$105$		0			0
$106$	8.11109			0.787819
$107$	−5.73229	−	9.92861i	−0.554161	−	0.959835i	−0.997968	−	0.0637128i	$-0.979706\pi$
$107$	−5.73229	−	9.92861i	−0.554161	−	0.959835i	0.443807	−	0.896122i	$-0.353628\pi$
$108$		0			0
$109$	9.12476	−	15.8046i	0.873994	−	1.51380i	0.0161631	−	0.999869i	$-0.494855\pi$
$109$	9.12476	−	15.8046i	0.873994	−	1.51380i	0.857831	−	0.513932i	$-0.171812\pi$
$110$	−2.71053	−	4.69478i	−0.258439	−	0.447630i
$111$		0			0
$112$	1.59549	+	1.62803i	0.150759	+	0.153834i
$113$	−5.24953			−0.493834			−0.246917	−	0.969037i	$-0.579417\pi$
$113$	−5.24953			−0.493834			−0.246917	+	0.969037i	$0.579417\pi$
$114$		0			0
$115$	1.50000	−	2.59808i	0.139876	−	0.242272i
$116$	7.19398	−	12.4603i	0.667944	−	1.15691i
$117$		0			0
$118$	−1.56526			−0.144094
$119$	−3.98113	+	14.2796i	−0.364949	+	1.30901i
$120$		0			0
$121$	2.99316	+	5.18431i	0.272106	+	0.471301i
$122$	2.22257	−	3.84961i	0.201222	−	0.348527i
$123$		0			0
$124$	−4.05267	−	7.01942i	−0.363940	−	0.630363i
$125$	0.396990			0.0355079
$126$		0			0
$127$	20.1053			1.78406			0.892030	−	0.451976i	$-0.149281\pi$
$127$	20.1053			1.78406			0.892030	+	0.451976i	$0.149281\pi$
$128$	4.82038	+	8.34914i	0.426065	+	0.737967i
$129$		0			0
$130$	−4.48345	+	7.76556i	−0.393224	+	0.681085i
$131$	2.04063	+	3.53447i	0.178291	+	0.308808i	0.941295	−	0.337585i	$-0.109610\pi$
$131$	2.04063	+	3.53447i	0.178291	+	0.308808i	−0.763005	+	0.646393i	$0.776277\pi$
$132$		0			0
$133$	8.18715	+	8.35413i	0.709916	+	0.724395i
$134$	5.64652			0.487785
$135$		0			0
$136$	−7.29235	+	12.6307i	−0.625313	+	1.08307i
$137$	0.942820	−	1.63301i	0.0805506	−	0.139518i	−0.822936	−	0.568134i	$-0.807665\pi$
$137$	0.942820	−	1.63301i	0.0805506	−	0.139518i	0.903487	+	0.428616i	$0.140999\pi$
$138$		0			0
$139$	−12.7954			−1.08529			−0.542644	−	0.839963i	$-0.682577\pi$
$139$	−12.7954			−1.08529			−0.542644	+	0.839963i	$0.682577\pi$
$140$	11.5865	−	2.97956i	0.979234	−	0.251819i
$141$		0			0
$142$	−2.76320	−	4.78600i	−0.231883	−	0.401632i
$143$	−4.14652	+	7.18198i	−0.346749	+	0.600587i
$144$		0			0
$145$	−16.1082	−	27.9002i	−1.33771	−	2.31699i
$146$	5.75185			0.476026
$147$		0			0
$148$	−4.44050			−0.365007
$149$	−4.02859	−	6.97772i	−0.330035	−	0.571637i	0.652483	−	0.757803i	$-0.273727\pi$
$149$	−4.02859	−	6.97772i	−0.330035	−	0.571637i	−0.982518	+	0.186166i	$0.940394\pi$
$150$		0			0
$151$	3.14132	−	5.44092i	0.255637	−	0.442776i	−0.709432	−	0.704774i	$-0.751048\pi$
$151$	3.14132	−	5.44092i	0.255637	−	0.442776i	0.965068	+	0.261999i	$0.0843816\pi$
$152$	5.75404	+	9.96629i	0.466714	+	0.808373i
$153$		0			0
$154$	−4.36552	+	1.12263i	−0.351784	+	0.0904642i
$155$	−18.1488			−1.45775
$156$		0			0
$157$	−0.351848	+	0.609419i	−0.0280806	+	0.0486370i	−0.879724	−	0.475484i	$-0.842273\pi$
$157$	−0.351848	+	0.609419i	−0.0280806	+	0.0486370i	0.851644	+	0.524121i	$0.175606\pi$
$158$	2.59781	−	4.49954i	0.206671	−	0.357964i
$159$		0			0
$160$	18.6512			1.47450
$161$	−1.74596	−	1.78157i	−0.137601	−	0.140407i
$162$		0			0
$163$	9.61793	+	16.6587i	0.753334	+	1.30481i	0.946198	+	0.323588i	$0.104889\pi$
$163$	9.61793	+	16.6587i	0.753334	+	1.30481i	−0.192864	+	0.981225i	$0.561778\pi$
$164$	2.83242	−	4.90589i	0.221175	−	0.383086i
$165$		0			0
$166$	3.08577	+	5.34471i	0.239502	+	0.414830i
$167$	23.3880			1.80981			0.904907	−	0.425608i	$-0.139940\pi$
$167$	23.3880			1.80981			0.904907	+	0.425608i	$0.139940\pi$
$168$		0			0
$169$	0.717370			0.0551823
$170$	6.78263	+	11.7479i	0.520204	+	0.901020i
$171$		0			0
$172$	−2.33242	+	4.03987i	−0.177845	+	0.308037i
$173$	4.11956	+	7.13529i	0.313204	+	0.542486i	0.979054	−	0.203600i	$-0.0652641\pi$
$173$	4.11956	+	7.13529i	0.313204	+	0.542486i	−0.665850	+	0.746086i	$0.731931\pi$
$174$		0			0
$175$	3.64132	−	13.0608i	0.275258	−	0.987300i
$176$	1.92915			0.145415
$177$		0			0
$178$	−3.70082	+	6.41001i	−0.277388	+	0.480450i
$179$	−4.95486	+	8.58207i	−0.370344	+	0.641454i	−0.989618	−	0.143721i	$-0.954093\pi$
$179$	−4.95486	+	8.58207i	−0.370344	+	0.641454i	0.619275	+	0.785174i	$0.287427\pi$
$180$		0			0
$181$	−9.38796			−0.697802			−0.348901	−	0.937160i	$-0.613445\pi$
$181$	−9.38796			−0.697802			−0.348901	+	0.937160i	$0.613445\pi$
$182$	5.21861	+	5.32505i	0.386829	+	0.394719i
$183$		0			0
$184$	−1.22708	−	2.12537i	−0.0904619	−	0.156685i
$185$	−4.97141	+	8.61073i	−0.365505	+	0.633074i
$186$		0			0
$187$	6.27292	+	10.8650i	0.458721	+	0.794528i
$188$	0.320380			0.0233661
$189$		0			0
$190$	10.7037			0.776528
$191$	12.3691	+	21.4239i	0.894996	+	1.55018i	0.833810	+	0.552052i	$0.186155\pi$
$191$	12.3691	+	21.4239i	0.894996	+	1.55018i	0.0611861	+	0.998126i	$0.480512\pi$
$192$		0			0
$193$	0.414230	−	0.717468i	0.0298169	−	0.0516444i	−0.850732	−	0.525600i	$-0.823841\pi$
$193$	0.414230	−	0.717468i	0.0298169	−	0.0516444i	0.880549	+	0.473955i	$0.157174\pi$
$194$	−0.320380	−	0.554914i	−0.0230019	−	0.0398405i
$195$		0			0
$196$	0.200818	−	9.94544i	0.0143442	−	0.710389i
$197$	5.86156			0.417619			0.208810	−	0.977956i	$-0.433041\pi$
$197$	5.86156			0.417619			0.208810	+	0.977956i	$0.433041\pi$
$198$		0			0
$199$	4.62476	−	8.01033i	0.327841	−	0.567837i	−0.654242	−	0.756285i	$-0.727012\pi$
$199$	4.62476	−	8.01033i	0.327841	−	0.567837i	0.982083	+	0.188448i	$0.0603457\pi$
$200$	6.66991	−	11.5526i	0.471634	−	0.816893i
$201$		0			0
$202$	−5.89467			−0.414747
$203$	−25.9435	+	6.67160i	−1.82088	+	0.468254i
$204$		0			0
$205$	−6.34213	−	10.9849i	−0.442954	−	0.767218i
$206$	0.926268	−	1.60434i	0.0645362	−	0.111780i
$207$		0			0
$208$	−1.59549	−	2.76346i	−0.110627	−	0.191612i
$209$	9.89931			0.684750
$210$		0			0
$211$	−12.5595			−0.864632			−0.432316	−	0.901722i	$-0.642303\pi$
$211$	−12.5595			−0.864632			−0.432316	+	0.901722i	$0.642303\pi$
$212$	7.57442	+	13.1193i	0.520213	+	0.901036i
$213$		0			0
$214$	−4.36156	+	7.55445i	−0.298150	+	0.516412i
$215$	5.22257	+	9.04576i	0.356176	+	0.616916i
$216$		0			0
$217$	−4.05267	+	14.5362i	−0.275113	+	0.986781i
$218$	−13.8856			−0.940454
$219$		0			0
$220$	5.06238	−	8.76830i	0.341306	−	0.591159i
$221$	10.3759	−	17.9716i	0.697960	−	1.20890i
$222$		0			0
$223$	−21.3880			−1.43224			−0.716122	−	0.697975i	$-0.754085\pi$
$223$	−21.3880			−1.43224			−0.716122	+	0.697975i	$0.754085\pi$
$224$	4.16484	−	14.9385i	0.278275	−	0.998122i
$225$		0			0
$226$	1.99712	+	3.45912i	0.132847	+	0.230097i
$227$	6.31122	−	10.9314i	0.418890	−	0.725539i	−0.576938	−	0.816788i	$-0.695752\pi$
$227$	6.31122	−	10.9314i	0.418890	−	0.725539i	0.995828	+	0.0912487i	$0.0290858\pi$
$228$		0			0
$229$	14.4601	+	25.0456i	0.955548	+	1.65506i	0.733110	+	0.680110i	$0.238068\pi$
$229$	14.4601	+	25.0456i	0.955548	+	1.65506i	0.222438	+	0.974947i	$0.428599\pi$
$230$	−2.28263			−0.150512
$231$		0			0
$232$	−26.3549			−1.73028
$233$	−10.7255	−	18.5770i	−0.702648	−	1.21702i	−0.967534	−	0.252742i	$-0.918668\pi$
$233$	−10.7255	−	18.5770i	−0.702648	−	1.21702i	0.264886	−	0.964280i	$-0.414666\pi$
$234$		0			0
$235$	0.358685	−	0.621261i	0.0233980	−	0.0405266i
$236$	−1.46169	−	2.53173i	−0.0951482	−	0.164802i
$237$		0			0
$238$	10.9239	−	2.80919i	0.708094	−	0.182093i
$239$	−7.73680			−0.500452			−0.250226	−	0.968187i	$-0.580505\pi$
$239$	−7.73680			−0.500452			−0.250226	+	0.968187i	$0.580505\pi$
$240$		0			0
$241$	−3.04583	+	5.27553i	−0.196199	+	0.339827i	−0.947293	−	0.320369i	$-0.896193\pi$
$241$	−3.04583	+	5.27553i	−0.196199	+	0.339827i	0.751094	+	0.660195i	$0.229527\pi$
$242$	2.27743	−	3.94462i	0.146399	−	0.253570i
$243$		0			0
$244$	8.30206			0.531485
$245$	−19.0607	−	11.5239i	−1.21775	−	0.736238i
$246$		0			0
$247$	−8.18715	−	14.1806i	−0.520936	−	0.902287i
$248$	−7.42339	+	12.8577i	−0.471386	+	0.816464i
$249$		0			0
$250$	−0.151030	−	0.261592i	−0.00955199	−	0.0165445i
$251$	−1.40164			−0.0884705			−0.0442352	−	0.999021i	$-0.514085\pi$
$251$	−1.40164			−0.0884705			−0.0442352	+	0.999021i	$0.514085\pi$
$252$		0			0
$253$	−2.11109			−0.132723
$254$	−7.64884	−	13.2482i	−0.479931	−	0.831265i
$255$		0			0
$256$	6.40451	−	11.0929i	0.400282	−	0.693309i
$257$	8.97825	+	15.5508i	0.560048	+	0.970031i	0.997492	+	0.0707853i	$0.0225505\pi$
$257$	8.97825	+	15.5508i	0.560048	+	0.970031i	−0.437444	+	0.899246i	$0.644116\pi$
$258$		0			0
$259$	5.78659	+	5.90461i	0.359561	+	0.366895i
$260$	−16.7472			−1.03862
$261$		0			0
$262$	1.55267	−	2.68930i	0.0959241	−	0.166145i
$263$	3.58809	−	6.21476i	0.221251	−	0.383218i	−0.733937	−	0.679218i	$-0.762319\pi$
$263$	3.58809	−	6.21476i	0.221251	−	0.383218i	0.955188	+	0.295999i	$0.0956526\pi$
$264$		0			0
$265$	33.9201			2.08370
$266$	2.39015	−	8.57306i	0.146550	−	0.525648i
$267$		0			0
$268$	5.27292	+	9.13296i	0.322095	+	0.557884i
$269$	−1.69850	+	2.94188i	−0.103559	+	0.179370i	−0.913149	−	0.407627i	$-0.866356\pi$
$269$	−1.69850	+	2.94188i	−0.103559	+	0.179370i	0.809590	+	0.586996i	$0.199690\pi$
$270$		0			0
$271$	5.11793	+	8.86451i	0.310892	+	0.538481i	0.978556	−	0.205982i	$-0.0660389\pi$
$271$	5.11793	+	8.86451i	0.310892	+	0.538481i	−0.667664	+	0.744463i	$0.732706\pi$
$272$	−4.82735			−0.292701
$273$		0			0
$274$	−1.43474			−0.0866758
$275$	−5.73749	−	9.93762i	−0.345984	−	0.599261i
$276$		0			0
$277$	1.77975	−	3.08262i	0.106935	−	0.185217i	−0.807592	−	0.589741i	$-0.799230\pi$
$277$	1.77975	−	3.08262i	0.106935	−	0.185217i	0.914527	+	0.404525i	$0.132563\pi$
$278$	4.86784	+	8.43135i	0.291954	+	0.505679i
$279$		0			0
$280$	−15.3382	−	15.6510i	−0.916631	−	0.935327i
$281$	6.98633			0.416769			0.208385	−	0.978047i	$-0.433179\pi$
$281$	6.98633			0.416769			0.208385	+	0.978047i	$0.433179\pi$
$282$		0			0
$283$	15.1082	−	26.1682i	0.898090	−	1.55554i	0.0681568	−	0.997675i	$-0.478288\pi$
$283$	15.1082	−	26.1682i	0.898090	−	1.55554i	0.829933	−	0.557863i	$-0.188378\pi$
$284$	5.16075	−	8.93867i	0.306234	−	0.530413i
$285$		0			0
$286$	6.30998			0.373117
$287$	−10.2145	+	2.62674i	−0.602942	+	0.155052i
$288$		0			0
$289$	−7.19686	−	12.4653i	−0.423345	−	0.733255i
$290$	−12.2564	+	21.2286i	−0.719718	+	1.24659i
$291$		0			0
$292$	5.37128	+	9.30333i	0.314330	+	0.544436i
$293$	−15.2359			−0.890088			−0.445044	−	0.895509i	$-0.646812\pi$
$293$	−15.2359			−0.890088			−0.445044	+	0.895509i	$0.646812\pi$
$294$		0			0
$295$	−6.54583			−0.381113
$296$	4.06690	+	7.04407i	0.236383	+	0.409428i
$297$		0			0
$298$	−3.06526	+	5.30919i	−0.177566	+	0.307553i
$299$	1.74596	+	3.02409i	0.100971	+	0.174888i
$300$		0			0
$301$	8.41135	−	2.16305i	0.484822	−	0.124676i
$302$	−4.78031			−0.275076
$303$		0			0
$304$	−1.90451	+	3.29872i	−0.109231	+	0.189194i
$305$	9.29467	−	16.0988i	0.532211	−	0.921817i
$306$		0			0
$307$	−1.03310			−0.0589623			−0.0294812	−	0.999565i	$-0.509386\pi$
$307$	−1.03310			−0.0589623			−0.0294812	+	0.999565i	$0.509386\pi$
$308$	−5.89248	−	6.01266i	−0.335755	−	0.342603i
$309$		0			0
$310$	6.90451	+	11.9590i	0.392150	+	0.679224i
$311$	4.66019	−	8.07169i	0.264255	−	0.457703i	−0.703113	−	0.711078i	$-0.748207\pi$
$311$	4.66019	−	8.07169i	0.264255	−	0.457703i	0.967368	+	0.253375i	$0.0815406\pi$
$312$		0			0
$313$	−3.04583	−	5.27553i	−0.172160	−	0.298191i	0.767014	−	0.641630i	$-0.221741\pi$
$313$	−3.04583	−	5.27553i	−0.172160	−	0.298191i	−0.939175	+	0.343439i	$0.888408\pi$
$314$	0.535426			0.0302159
$315$		0			0
$316$	9.70370			0.545876
$317$	−11.6505	−	20.1792i	−0.654356	−	1.13338i	−0.982055	−	0.188595i	$-0.939607\pi$
$317$	−11.6505	−	20.1792i	−0.654356	−	1.13338i	0.327699	−	0.944782i	$-0.393727\pi$
$318$		0			0
$319$	−11.3353	+	19.6333i	−0.634655	+	1.09925i
$320$	−4.35417	−	7.54165i	−0.243406	−	0.421591i
$321$		0			0
$322$	−0.509715	+	1.82826i	−0.0284053	+	0.101885i
$323$	−24.7713			−1.37831
$324$		0			0
$325$	−9.49028	+	16.4377i	−0.526426	+	0.911797i
$326$	7.31806	−	12.6752i	0.405310	−	0.702017i
$327$		0			0
$328$	−10.3764			−0.572944
$329$	−0.417500	−	0.426015i	−0.0230175	−	0.0234870i
$330$		0			0
$331$	−7.33818	−	12.7101i	−0.403343	−	0.698610i	0.590784	−	0.806829i	$-0.298818\pi$
$331$	−7.33818	−	12.7101i	−0.403343	−	0.698610i	−0.994127	+	0.108220i	$0.965485\pi$
$332$	−5.76320	+	9.98215i	−0.316297	+	0.547842i
$333$		0			0
$334$	−8.89768	−	15.4112i	−0.486859	−	0.843265i
$335$	23.6134			1.29014
$336$		0			0
$337$	25.6238			1.39582			0.697909	−	0.716186i	$-0.254114\pi$
$337$	25.6238			1.39582			0.697909	+	0.716186i	$0.254114\pi$
$338$	−0.272915	−	0.472703i	−0.0148446	−	0.0257116i
$339$		0			0
$340$	−12.6677	+	21.9411i	−0.687003	+	1.18992i
$341$	6.38564	+	11.0603i	0.345802	+	0.598946i
$342$		0			0
$343$	−13.4863	+	12.6933i	−0.728193	+	0.685372i
$344$	8.54472			0.460700
$345$		0			0
$346$	3.13448	−	5.42908i	0.168511	−	0.291869i
$347$	5.64652	−	9.78005i	0.303121	−	0.525021i	−0.673720	−	0.738986i	$-0.735305\pi$
$347$	5.64652	−	9.78005i	0.303121	−	0.525021i	0.976841	+	0.213966i	$0.0686381\pi$
$348$		0			0
$349$	−11.2963			−0.604677			−0.302339	−	0.953201i	$-0.597767\pi$
$349$	−11.2963			−0.604677			−0.302339	+	0.953201i	$0.597767\pi$
$350$	−9.99153	+	2.56941i	−0.534070	+	0.137341i
$351$		0			0
$352$	−6.56238	−	11.3664i	−0.349776	−	0.605830i
$353$	−9.25116	+	16.0235i	−0.492390	+	0.852844i	−0.999962	−	0.00876550i	$-0.997210\pi$
$353$	−9.25116	+	16.0235i	−0.492390	+	0.852844i	0.507572	+	0.861609i	$0.330543\pi$
$354$		0			0
$355$	−11.5555	−	20.0148i	−0.613305	−	1.06227i
$356$	−13.8238			−0.732661
$357$		0			0
$358$	7.54007			0.398505
$359$	9.94802	+	17.2305i	0.525037	+	0.909390i	0.999575	+	0.0291551i	$0.00928167\pi$
$359$	9.94802	+	17.2305i	0.525037	+	0.909390i	−0.474538	+	0.880235i	$0.657385\pi$
$360$		0			0
$361$	−0.272915	+	0.472703i	−0.0143639	+	0.0248791i
$362$	3.57154	+	6.18609i	0.187716	+	0.325134i
$363$		0			0
$364$	−3.73968	+	13.4136i	−0.196012	+	0.703062i
$365$	24.0539			1.25904
$366$		0			0
$367$	−2.87524	+	4.98006i	−0.150086	+	0.259957i	−0.931259	−	0.364358i	$-0.881288\pi$
$367$	−2.87524	+	4.98006i	−0.150086	+	0.259957i	0.781173	+	0.624315i	$0.214622\pi$
$368$	0.406150	−	0.703472i	0.0211720	−	0.0366710i
$369$		0			0
$370$	7.56526			0.393299
$371$	7.57442	−	27.1681i	0.393244	−	1.41050i
$372$		0			0
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	0.838975	−	0.544170i	$-0.183156\pi$
$373$	−1.00000	−	1.73205i	−0.0517780	−	0.0896822i	−0.890753	+	0.454488i	$0.849822\pi$
$374$	4.77292	−	8.26693i	0.246802	−	0.427473i
$375$		0			0
$376$	−0.293425	−	0.508226i	−0.0151322	−	0.0262098i
$377$	37.4991			1.93130
$378$		0			0
$379$	8.95322			0.459896			0.229948	−	0.973203i	$-0.426144\pi$
$379$	8.95322			0.459896			0.229948	+	0.973203i	$0.426144\pi$
$380$	9.99549	+	17.3127i	0.512758	+	0.888122i
$381$		0			0
$382$	9.41135	−	16.3009i	0.481527	−	0.834029i
$383$	10.0825	+	17.4634i	0.515192	+	0.892338i	0.999845	+	0.0176316i	$0.00561261\pi$
$383$	10.0825	+	17.4634i	0.515192	+	0.892338i	−0.484653	+	0.874707i	$0.661054\pi$
$384$		0			0
$385$	−18.2564	+	4.69478i	−0.930430	+	0.239268i
$386$	−0.630356			−0.0320843
$387$		0			0
$388$	0.598364	−	1.03640i	0.0303773	−	0.0526151i
$389$	−16.7999	+	29.0982i	−0.851787	+	1.47534i	0.0278066	+	0.999613i	$0.491148\pi$
$389$	−16.7999	+	29.0982i	−0.851787	+	1.47534i	−0.879594	+	0.475725i	$0.842186\pi$
$390$		0			0
$391$	5.28263			0.267154
$392$	−15.9606	+	8.79012i	−0.806133	+	0.443968i
$393$		0			0
$394$	−2.22996	−	3.86241i	−0.112344	−	0.194585i
$395$	10.8639	−	18.8168i	0.546621	−	0.946776i
$396$		0			0
$397$	2.06922	+	3.58399i	0.103851	+	0.179875i	0.913268	−	0.407359i	$-0.133550\pi$
$397$	2.06922	+	3.58399i	0.103851	+	0.179875i	−0.809417	+	0.587234i	$0.800217\pi$
$398$	−7.03775			−0.352771
$399$		0			0
$400$	4.41531			0.220765
$401$	7.73461	+	13.3967i	0.386248	+	0.669001i	0.991941	−	0.126697i	$-0.0404376\pi$
$401$	7.73461	+	13.3967i	0.386248	+	0.669001i	−0.605693	+	0.795698i	$0.707104\pi$
$402$		0			0
$403$	10.5624	−	18.2946i	0.526150	−	0.911318i
$404$	−5.50465	−	9.53433i	−0.273866	−	0.474350i
$405$		0			0
$406$	14.2661	+	14.5570i	0.708014	+	0.722454i
$407$	6.99673			0.346815
$408$		0			0
$409$	−13.6969	+	23.7237i	−0.677266	+	1.17306i	0.298535	+	0.954399i	$0.403502\pi$
$409$	−13.6969	+	23.7237i	−0.677266	+	1.17306i	−0.975801	+	0.218661i	$0.929831\pi$
$410$	−4.82558	+	8.35815i	−0.238318	+	0.412780i
$411$		0			0
$412$	3.45993			0.170458
$413$	−1.46169	+	5.24284i	−0.0719253	+	0.257983i
$414$		0			0
$415$	12.9045	+	22.3513i	0.633458	+	1.09718i
$416$	−10.8547	+	18.8009i	−0.532197	+	0.921792i
$417$		0			0
$418$	−3.76608	−	6.52304i	−0.184205	−	0.319052i
$419$	21.0000			1.02592			0.512959	−	0.858413i	$-0.328549\pi$
$419$	21.0000			1.02592			0.512959	+	0.858413i	$0.328549\pi$
$420$		0			0
$421$	19.9590			0.972741			0.486371	−	0.873753i	$-0.338321\pi$
$421$	19.9590			0.972741			0.486371	+	0.873753i	$0.338321\pi$
$422$	4.77812	+	8.27594i	0.232595	+	0.402867i
$423$		0			0
$424$	13.8743	−	24.0310i	0.673795	−	1.16705i
$425$	14.3571	+	24.8671i	0.696419	+	1.20623i
$426$		0			0
$427$	−10.8187	−	11.0394i	−0.523556	−	0.534234i
$428$	−16.2919			−0.787500
$429$		0			0
$430$	3.97373	−	6.88271i	0.191630	−	0.331914i
$431$	10.0647	−	17.4326i	0.484800	−	0.839698i	−0.515048	−	0.857162i	$-0.672226\pi$
$431$	10.0647	−	17.4326i	0.484800	−	0.839698i	0.999847	+	0.0174637i	$0.00555914\pi$
$432$		0			0
$433$	11.8558			0.569754			0.284877	−	0.958564i	$-0.408047\pi$
$433$	11.8558			0.569754			0.284877	+	0.958564i	$0.408047\pi$
$434$	11.1202	−	2.85967i	0.533789	−	0.137268i
$435$		0			0
$436$	−12.9669	−	22.4593i	−0.621002	−	1.07561i
$437$	2.08414	−	3.60983i	0.0996977	−	0.172681i
$438$		0			0
$439$	1.07893	+	1.86877i	0.0514947	+	0.0891914i	0.890624	−	0.454741i	$-0.150268\pi$
$439$	1.07893	+	1.86877i	0.0514947	+	0.0891914i	−0.839129	+	0.543932i	$0.816935\pi$
$440$	−18.5458			−0.884138
$441$		0			0
$442$	−15.7896			−0.751035
$443$	0.981125	+	1.69936i	0.0466147	+	0.0807390i	0.888391	−	0.459087i	$-0.151823\pi$
$443$	0.981125	+	1.69936i	0.0466147	+	0.0807390i	−0.841777	+	0.539826i	$0.818490\pi$
$444$		0			0
$445$	−15.4766	+	26.8063i	−0.733662	+	1.27074i
$446$	8.13680	+	14.0934i	0.385289	+	0.667340i
$447$		0			0
$448$	−7.01273	+	1.80338i	−0.331320	+	0.0852018i
$449$	2.15211			0.101564			0.0507822	−	0.998710i	$-0.483829\pi$
$449$	2.15211			0.101564			0.0507822	+	0.998710i	$0.483829\pi$
$450$		0			0
$451$	−4.46294	+	7.73004i	−0.210152	+	0.363993i
$452$	−3.72996	+	6.46049i	−0.175443	+	0.303876i
$453$		0			0
$454$	−9.60412			−0.450744
$455$	21.8239	+	22.2691i	1.02312	+	1.04399i
$456$		0			0
$457$	6.55267	+	11.3496i	0.306521	+	0.530910i	0.977599	−	0.210477i	$-0.0675018\pi$
$457$	6.55267	+	11.3496i	0.306521	+	0.530910i	−0.671078	+	0.741387i	$0.734168\pi$
$458$	11.0023	−	19.0566i	0.514105	−	0.890456i
$459$		0			0
$460$	−2.13160	−	3.69204i	−0.0993864	−	0.172142i
$461$	−5.48727			−0.255568			−0.127784	−	0.991802i	$-0.540786\pi$
$461$	−5.48727			−0.255568			−0.127784	+	0.991802i	$0.540786\pi$
$462$		0			0
$463$	−20.4991			−0.952672			−0.476336	−	0.879263i	$-0.658035\pi$
$463$	−20.4991			−0.952672			−0.476336	+	0.879263i	$0.658035\pi$
$464$	−4.36156	−	7.55445i	−0.202481	−	0.350707i
$465$		0			0
$466$	−8.16075	+	14.1348i	−0.378039	+	0.654783i
$467$	−19.6758	−	34.0795i	−0.910487	−	1.57701i	−0.813377	−	0.581736i	$-0.802374\pi$
$467$	−19.6758	−	34.0795i	−0.910487	−	1.57701i	−0.0971099	−	0.995274i	$-0.530960\pi$
$468$		0			0
$469$	5.27292	−	18.9130i	0.243481	−	0.873322i
$470$	−0.545830			−0.0251773
$471$		0			0
$472$	−2.67743	+	4.63744i	−0.123239	+	0.213456i
$473$	3.67511	−	6.36547i	0.168982	−	0.292685i
$474$		0			0
$475$	22.6569			1.03957
$476$	14.7449	+	15.0456i	0.675830	+	0.689615i
$477$		0			0
$478$	2.94338	+	5.09808i	0.134627	+	0.233181i
$479$	8.37360	−	14.5035i	0.382600	−	0.662682i	−0.608833	−	0.793298i	$-0.708362\pi$
$479$	8.37360	−	14.5035i	0.382600	−	0.662682i	0.991433	+	0.130616i	$0.0416955\pi$
$480$		0			0
$481$	−5.78659	−	10.0227i	−0.263846	−	0.456994i
$482$	4.63500			0.211119
$483$		0			0
$484$	8.50697			0.386680
$485$	−1.33981	−	2.32062i	−0.0608376	−	0.105374i
$486$		0			0
$487$	−2.00288	+	3.46909i	−0.0907591	+	0.157199i	−0.907831	−	0.419337i	$-0.862263\pi$
$487$	−2.00288	+	3.46909i	−0.0907591	+	0.157199i	0.817072	+	0.576536i	$0.195596\pi$
$488$	−7.60357	−	13.1698i	−0.344197	−	0.596167i
$489$		0			0
$490$	−0.342133	+	16.9440i	−0.0154560	+	0.765452i
$491$	−24.6512			−1.11249			−0.556246	−	0.831018i	$-0.687759\pi$
$491$	−24.6512			−1.11249			−0.556246	+	0.831018i	$0.687759\pi$
$492$		0			0
$493$	28.3646	−	49.1289i	1.27748	−	2.21265i
$494$	−6.22941	+	10.7897i	−0.280274	+	0.485449i
$495$		0			0
$496$	−4.91410			−0.220649
$497$	−18.6111	+	4.78600i	−0.834821	+	0.214682i
$498$		0			0
$499$	12.2798	+	21.2692i	0.549717	+	0.952138i	0.998294	+	0.0583936i	$0.0185978\pi$
$499$	12.2798	+	21.2692i	0.549717	+	0.952138i	−0.448576	+	0.893744i	$0.648069\pi$
$500$	0.282075	−	0.488568i	0.0126148	−	0.0218494i
$501$		0			0
$502$	0.533236	+	0.923592i	0.0237995	+	0.0412219i
$503$	12.3743			0.551742			0.275871	−	0.961195i	$-0.411034\pi$
$503$	12.3743			0.551742			0.275871	+	0.961195i	$0.411034\pi$
$504$		0			0
$505$	−24.6512			−1.09696
$506$	0.803140	+	1.39108i	0.0357039	+	0.0618410i
$507$		0			0
$508$	14.2855	−	24.7432i	0.633817	−	1.09780i
$509$	−5.59781	−	9.69569i	−0.248118	−	0.429754i	0.714885	−	0.699242i	$-0.246479\pi$
$509$	−5.59781	−	9.69569i	−0.248118	−	0.429754i	−0.963004	+	0.269488i	$0.913146\pi$
$510$		0			0
$511$	5.37128	−	19.2658i	0.237611	−	0.852270i
$512$	9.53543			0.421410
$513$		0			0
$514$	6.83134	−	11.8322i	0.301317	−	0.521897i
$515$	3.87360	−	6.70928i	0.170691	−	0.295646i
$516$		0			0
$517$	−0.504811			−0.0222016
$518$	1.68934	−	6.05935i	0.0742251	−	0.266232i
$519$		0			0
$520$	15.3382	+	26.5665i	0.672623	+	1.16502i
$521$	−15.8096	+	27.3830i	−0.692631	+	1.19967i	0.278342	+	0.960482i	$0.410215\pi$
$521$	−15.8096	+	27.3830i	−0.692631	+	1.19967i	−0.970973	+	0.239189i	$0.923118\pi$
$522$		0			0
$523$	14.1179	+	24.4530i	0.617334	+	1.06925i	0.989970	+	0.141276i	$0.0451205\pi$
$523$	14.1179	+	24.4530i	0.617334	+	1.06925i	−0.372636	+	0.927977i	$0.621546\pi$
$524$	5.79974			0.253363
$525$		0			0
$526$	−5.46019			−0.238076
$527$	−15.9789	−	27.6763i	−0.696053	−	1.20560i
$528$		0			0
$529$	11.0555	−	19.1488i	0.480676	−	0.832555i
$530$	−12.9045	−	22.3513i	−0.560536	−	0.970877i
$531$		0			0
$532$	16.0985	−	4.13987i	0.697958	−	0.179486i
$533$	14.7641			0.639506
$534$		0			0
$535$	−18.2398	+	31.5923i	−0.788576	+	1.36585i
$536$	9.65856	−	16.7291i	0.417186	−	0.722587i
$537$		0			0
$538$	2.58469			0.111434
$539$	−0.316422	+	15.6707i	−0.0136293	+	0.674983i
$540$		0			0
$541$	−21.4045	−	37.0737i	−0.920252	−	1.59392i	−0.799025	−	0.601298i	$-0.794650\pi$
$541$	−21.4045	−	37.0737i	−0.920252	−	1.59392i	−0.121227	−	0.992625i	$-0.538683\pi$
$542$	3.89411	−	6.74480i	0.167266	−	0.289714i
$543$		0			0
$544$	16.4212	+	28.4424i	0.704053	+	1.21946i
$545$	−58.0690			−2.48740
$546$		0			0
$547$	13.5516			0.579424			0.289712	−	0.957114i	$-0.406440\pi$
$547$	13.5516			0.579424			0.289712	+	0.957114i	$0.406440\pi$
$548$	−1.33981	−	2.32062i	−0.0572339	−	0.0991319i
$549$		0			0
$550$	−4.36552	+	7.56130i	−0.186146	+	0.322415i
$551$	−22.3811	−	38.7652i	−0.953468	−	1.65146i
$552$		0			0
$553$	−12.6453	−	12.9032i	−0.537732	−	0.548699i
$554$	−2.70834			−0.115066
$555$		0			0
$556$	−9.09153	+	15.7470i	−0.385567	+	0.667821i
$557$	−16.3925	+	28.3926i	−0.694572	+	1.20303i	0.275753	+	0.961228i	$0.411073\pi$
$557$	−16.3925	+	28.3926i	−0.694572	+	1.20303i	−0.970325	+	0.241805i	$0.922261\pi$
$558$		0			0
$559$	−12.1579			−0.514223
$560$	1.94789	−	6.98673i	0.0823133	−	0.295243i
$561$		0			0
$562$	−2.65787	−	4.60356i	−0.112115	−	0.194189i
$563$	8.57730	−	14.8563i	0.361490	−	0.626119i	−0.626716	−	0.779248i	$-0.715601\pi$
$563$	8.57730	−	14.8563i	0.361490	−	0.626119i	0.988206	+	0.153128i	$0.0489348\pi$
$564$		0			0
$565$	8.35185	+	14.4658i	0.351365	+	0.608582i
$566$	−22.9910			−0.966383
$567$		0			0
$568$	−18.9062			−0.793286
$569$	−6.44966	−	11.1711i	−0.270384	−	0.468318i	0.698576	−	0.715535i	$-0.253817\pi$
$569$	−6.44966	−	11.1711i	−0.270384	−	0.468318i	−0.968960	+	0.247217i	$0.920484\pi$
$570$		0			0
$571$	0.141315	−	0.244765i	0.00591385	−	0.0102431i	−0.863053	−	0.505113i	$-0.831451\pi$
$571$	0.141315	−	0.244765i	0.00591385	−	0.0102431i	0.868967	+	0.494870i	$0.164784\pi$
$572$	5.89248	+	10.2061i	0.246377	+	0.426737i
$573$		0			0
$574$	5.61685	+	5.73141i	0.234443	+	0.239224i
$575$	−4.83173			−0.201497
$576$		0			0
$577$	1.08289	−	1.87562i	0.0450814	−	0.0780832i	−0.842604	−	0.538533i	$-0.818979\pi$
$577$	1.08289	−	1.87562i	0.0450814	−	0.0780832i	0.887686	+	0.460450i	$0.152312\pi$
$578$	−5.47592	+	9.48458i	−0.227768	+	0.394506i
$579$		0			0
$580$	−45.7817			−1.90098
$581$	20.7837	−	5.34471i	0.862254	−	0.221736i
$582$		0			0
$583$	−11.9347	−	20.6716i	−0.494286	−	0.856129i
$584$	9.83873	−	17.0412i	0.407130	−	0.705169i
$585$		0			0
$586$	5.79630	+	10.0395i	0.239443	+	0.414728i
$587$	−16.7759			−0.692417			−0.346208	−	0.938158i	$-0.612531\pi$
$587$	−16.7759			−0.692417			−0.346208	+	0.938158i	$0.612531\pi$
$588$		0			0
$589$	−25.2164			−1.03902
$590$	2.49028	+	4.31330i	0.102523	+	0.177576i
$591$		0			0
$592$	−1.34609	+	2.33150i	−0.0553240	+	0.0958240i
$593$	12.5933	+	21.8122i	0.517145	+	0.895721i	0.999802	+	0.0199114i	$0.00633841\pi$
$593$	12.5933	+	21.8122i	0.517145	+	0.895721i	−0.482657	+	0.875809i	$0.660328\pi$
$594$		0			0
$595$	45.6833	−	11.7479i	1.87283	−	0.481615i
$596$	−11.4498			−0.469002
$597$		0			0
$598$	1.32846	−	2.30096i	0.0543248	−	0.0940933i
$599$	−14.3662	+	24.8830i	−0.586987	+	1.01669i	0.407637	+	0.913144i	$0.366353\pi$
$599$	−14.3662	+	24.8830i	−0.586987	+	1.01669i	−0.994624	+	0.103548i	$0.966980\pi$
$600$		0			0
$601$	−36.7954			−1.50091			−0.750457	−	0.660919i	$-0.770167\pi$
$601$	−36.7954			−1.50091			−0.750457	+	0.660919i	$0.770167\pi$
$602$	−4.62532	−	4.71966i	−0.188514	−	0.192359i
$603$		0			0
$604$	−4.46402	−	7.73191i	−0.181638	−	0.314607i
$605$	9.52408	−	16.4962i	0.387209	−	0.670665i
$606$		0			0
$607$	−18.9503	−	32.8230i	−0.769171	−	1.33224i	−0.938013	−	0.346600i	$-0.887336\pi$
$607$	−18.9503	−	32.8230i	−0.769171	−	1.33224i	0.168842	−	0.985643i	$-0.445997\pi$
$608$	25.9144			1.05097
$609$		0			0
$610$	−14.1442			−0.572682
$611$	0.417500	+	0.723131i	0.0168902	+	0.0292547i
$612$		0			0
$613$	−19.0196	+	32.9428i	−0.768193	+	1.33055i	0.170349	+	0.985384i	$0.445511\pi$
$613$	−19.0196	+	32.9428i	−0.768193	+	1.33055i	−0.938542	+	0.345165i	$0.887823\pi$
$614$	0.393032	+	0.680752i	0.0158615	+	0.0274729i
$615$		0			0
$616$	−4.14132	+	14.8542i	−0.166858	+	0.598491i
$617$	26.5264			1.06791			0.533956	−	0.845512i	$-0.320705\pi$
$617$	26.5264			1.06791			0.533956	+	0.845512i	$0.320705\pi$
$618$		0			0
$619$	−6.35185	+	11.0017i	−0.255302	+	0.442197i	−0.964978	−	0.262332i	$-0.915508\pi$
$619$	−6.35185	+	11.0017i	−0.255302	+	0.442197i	0.709675	+	0.704529i	$0.248842\pi$
$620$	−12.8954	+	22.3354i	−0.517890	+	0.897012i
$621$		0			0
$622$	−7.09166			−0.284350
$623$	18.0144	+	18.3818i	0.721730	+	0.736450i
$624$		0			0
$625$	12.1803	+	21.0969i	0.487212	+	0.843877i
$626$	−2.31750	+	4.01403i	−0.0926260	+	0.160433i
$627$		0			0
$628$	0.500000	+	0.866025i	0.0199522	+	0.0345582i
$629$	−17.5081			−0.698093
$630$		0			0
$631$	20.6764			0.823113			0.411556	−	0.911384i	$-0.364985\pi$
$631$	20.6764			0.823113			0.411556	+	0.911384i	$0.364985\pi$
$632$	−8.88727	−	15.3932i	−0.353517	−	0.612309i
$633$		0			0
$634$	−8.86458	+	15.3539i	−0.352057	+	0.609781i
$635$	−31.9870	−	55.4031i	−1.26937	−	2.19861i
$636$		0			0
$637$	22.7096	−	12.5070i	0.899787	−	0.495547i
$638$	17.2495			0.682915
$639$		0			0
$640$	15.3382	−	26.5665i	0.606295	−	1.05013i
$641$	−13.9870	+	24.2262i	−0.552454	+	0.956878i	0.445643	+	0.895211i	$0.352975\pi$
$641$	−13.9870	+	24.2262i	−0.552454	+	0.956878i	−0.998097	+	0.0616674i	$0.980358\pi$
$642$		0			0
$643$	27.9806			1.10345			0.551723	−	0.834027i	$-0.313971\pi$
$643$	27.9806			1.10345			0.551723	+	0.834027i	$0.313971\pi$
$644$	−3.43310	+	0.882853i	−0.135283	+	0.0347893i
$645$		0			0
$646$	9.42395	+	16.3228i	0.370780	+	0.642210i
$647$	2.30834	−	3.99816i	0.0907503	−	0.157184i	−0.817077	−	0.576529i	$-0.804407\pi$
$647$	2.30834	−	3.99816i	0.0907503	−	0.157184i	0.907827	+	0.419345i	$0.137740\pi$
$648$		0			0
$649$	2.30314	+	3.98916i	0.0904061	+	0.156588i
$650$	14.4419			0.566457
$651$		0			0
$652$	27.3354			1.07054
$653$	5.79016	+	10.0288i	0.226586	+	0.392459i	0.956794	−	0.290766i	$-0.0939101\pi$
$653$	5.79016	+	10.0288i	0.226586	+	0.392459i	−0.730208	+	0.683225i	$0.760577\pi$
$654$		0			0
$655$	6.49316	−	11.2465i	0.253709	−	0.439437i
$656$	−1.71724	−	2.97434i	−0.0670468	−	0.116129i
$657$		0			0
$658$	−0.121885	+	0.437179i	−0.00475156	+	0.0170430i
$659$	−4.73680			−0.184520			−0.0922598	−	0.995735i	$-0.529409\pi$
$659$	−4.73680			−0.184520			−0.0922598	+	0.995735i	$0.529409\pi$
$660$		0			0
$661$	6.91135	−	11.9708i	0.268820	−	0.465611i	−0.699737	−	0.714400i	$-0.746700\pi$
$661$	6.91135	−	11.9708i	0.268820	−	0.465611i	0.968557	+	0.248790i	$0.0800329\pi$
$662$	−5.58345	+	9.67081i	−0.217007	+	0.375867i
$663$		0			0
$664$	21.1132			0.819353
$665$	9.99549	−	35.8520i	0.387608	−	1.39028i
$666$		0			0
$667$	4.77292	+	8.26693i	0.184808	+	0.320097i
$668$	16.6179	−	28.7831i	0.642967	−	1.11365i
$669$		0			0
$670$	−8.98345	−	15.5598i	−0.347061	−	0.601127i
$671$	−13.0813			−0.504996
$672$		0			0
$673$	6.02735			0.232337			0.116169	−	0.993230i	$-0.462939\pi$
$673$	6.02735			0.232337			0.116169	+	0.993230i	$0.462939\pi$
$674$	−9.74828	−	16.8845i	−0.375490	−	0.650367i
$675$		0			0
$676$	0.509715	−	0.882853i	0.0196044	−	0.0339559i
$677$	−11.4428	−	19.8195i	−0.439783	−	0.761727i	0.557889	−	0.829915i	$-0.311611\pi$
$677$	−11.4428	−	19.8195i	−0.439783	−	0.761727i	−0.997672	+	0.0681884i	$0.978278\pi$
$678$		0			0
$679$	−2.15787	+	0.554914i	−0.0828113	+	0.0212956i
$680$	46.4077			1.77965
$681$		0			0
$682$	4.85868	−	8.41549i	0.186049	−	0.322246i
$683$	5.14940	−	8.91901i	0.197036	−	0.341277i	−0.750530	−	0.660836i	$-0.770202\pi$
$683$	5.14940	−	8.91901i	0.197036	−	0.341277i	0.947566	+	0.319560i	$0.103535\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$	13.4948	+	4.05766i	0.515234	+	0.154922i
$687$		0			0
$688$	1.41410	+	2.44929i	0.0539120	+	0.0933782i
$689$	−19.7411	+	34.1925i	−0.752074	+	1.30263i
$690$		0			0
$691$	−14.5361	−	25.1773i	−0.552980	−	0.957789i	−0.998058	−	0.0622973i	$-0.980157\pi$
$691$	−14.5361	−	25.1773i	−0.552980	−	0.957789i	0.445078	−	0.895492i	$-0.353176\pi$
$692$	11.7083			0.445084
$693$		0			0
$694$	−8.59261			−0.326171
$695$	20.3571	+	35.2594i	0.772187	+	1.33747i
$696$		0			0
$697$	11.1677	−	19.3430i	0.423007	−	0.732670i
$698$	4.29755	+	7.44357i	0.162665	+	0.281743i
$699$		0			0
$700$	−13.4863	−	13.7614i	−0.509735	−	0.520132i
$701$	27.4153			1.03546			0.517731	−	0.855543i	$-0.326777\pi$
$701$	27.4153			1.03546			0.517731	+	0.855543i	$0.326777\pi$
$702$		0			0
$703$	−6.90739	+	11.9640i	−0.260517	+	0.451229i
$704$	−3.06402	+	5.30703i	−0.115479	+	0.200016i
$705$		0			0
$706$	14.0780			0.529832
$707$	−5.50465	+	19.7442i	−0.207024	+	0.742557i
$708$		0			0
$709$	18.4834	+	32.0143i	0.694160	+	1.20232i	0.970463	+	0.241250i	$0.0775575\pi$
$709$	18.4834	+	32.0143i	0.694160	+	1.20232i	−0.276302	+	0.961071i	$0.589109\pi$
$710$	−8.79235	+	15.2288i	−0.329971	+	0.571526i
$711$		0			0
$712$	12.6607	+	21.9291i	0.474481	+	0.821826i
$713$	5.37756			0.201391
$714$		0			0
$715$	26.3880			0.986854
$716$	7.04118	+	12.1957i	0.263141	+	0.455774i
$717$		0			0
$718$	7.56922	−	13.1103i	0.282481	−	0.489271i
$719$	20.2599	+	35.0912i	0.755568	+	1.30868i	0.945092	+	0.326806i	$0.105972\pi$
$719$	20.2599	+	35.0912i	0.755568	+	1.30868i	−0.189524	+	0.981876i	$0.560694\pi$
$720$		0			0
$721$	−4.50877	−	4.60073i	−0.167915	−	0.171340i
$722$	0.415309			0.0154562
$723$		0			0
$724$	−6.67046	+	11.5536i	−0.247906	+	0.429385i
$725$	−25.9435	+	44.9355i	−0.963518	+	1.66886i
$726$		0			0
$727$	−15.2416			−0.565280			−0.282640	−	0.959226i	$-0.591210\pi$
$727$	−15.2416			−0.565280			−0.282640	+	0.959226i	$0.591210\pi$
$728$	24.7033	−	6.35267i	0.915565	−	0.235446i
$729$		0			0
$730$	−9.15103	−	15.8500i	−0.338695	−	0.586637i
$731$	−9.19630	+	15.9285i	−0.340138	+	0.589136i
$732$		0			0
$733$	−16.2895	−	28.2142i	−0.601665	−	1.04211i	−0.992569	−	0.121683i	$-0.961171\pi$
$733$	−16.2895	−	28.2142i	−0.601665	−	1.04211i	0.390904	−	0.920432i	$-0.372163\pi$
$734$	4.37540			0.161499
$735$		0			0
$736$	−5.52640			−0.203706
$737$	−8.30834	−	14.3905i	−0.306042	−	0.530080i
$738$		0			0
$739$	−3.50684	+	6.07402i	−0.129001	+	0.223436i	−0.923290	−	0.384104i	$-0.874510\pi$
$739$	−3.50684	+	6.07402i	−0.129001	+	0.223436i	0.794289	+	0.607540i	$0.207844\pi$
$740$	7.06470	+	12.2364i	0.259704	+	0.449820i
$741$		0			0
$742$	−20.7837	+	5.34471i	−0.762994	+	0.196210i
$743$	35.0118			1.28446			0.642229	−	0.766513i	$-0.278010\pi$
$743$	35.0118			1.28446			0.642229	+	0.766513i	$0.278010\pi$
$744$		0			0
$745$	−12.8187	+	22.2027i	−0.469642	+	0.813445i
$746$	−0.760877	+	1.31788i	−0.0278577	+	0.0482509i
$747$		0			0
$748$	17.8285			0.651873
$749$	21.2307	+	21.6637i	0.775751	+	0.791573i
$750$		0			0
$751$	2.13844	+	3.70388i	0.0780327	+	0.135157i	0.902401	−	0.430897i	$-0.141803\pi$
$751$	2.13844	+	3.70388i	0.0780327	+	0.135157i	−0.824368	+	0.566054i	$0.808469\pi$
$752$	0.0971198	−	0.168217i	0.00354160	−	0.00613422i
$753$		0			0
$754$	−14.2661	−	24.7096i	−0.519540	−	0.899870i
$755$	−19.9910			−0.727546
$756$		0			0
$757$	−34.9611			−1.27068			−0.635342	−	0.772231i	$-0.719141\pi$
$757$	−34.9611			−1.27068			−0.635342	+	0.772231i	$0.719141\pi$
$758$	−3.40615	−	5.89962i	−0.123717	−	0.214284i
$759$		0			0
$760$	18.3090	−	31.7122i	0.664138	−	1.15032i
$761$	−2.29179	−	3.96950i	−0.0830773	−	0.143894i	0.821493	−	0.570219i	$-0.193142\pi$
$761$	−2.29179	−	3.96950i	−0.0830773	−	0.143894i	−0.904570	+	0.426324i	$0.859808\pi$
$762$		0			0
$763$	−12.9669	+	46.5100i	−0.469433	+	1.68377i
$764$	35.1546			1.27185
$765$		0			0
$766$	7.67154	−	13.2875i	0.277184	−	0.480097i
$767$	3.80959	−	6.59840i	0.137556	−	0.238254i
$768$		0			0
$769$	16.9590			0.611556			0.305778	−	0.952103i	$-0.401083\pi$
$769$	16.9590			0.611556			0.305778	+	0.952103i	$0.401083\pi$
$770$	10.0390	+	10.2437i	0.361780	+	0.369159i
$771$		0			0
$772$	−0.588649	−	1.01957i	−0.0211859	−	0.0366951i
$773$	−20.1420	+	34.8870i	−0.724458	+	1.25480i	0.234739	+	0.972058i	$0.424576\pi$
$773$	−20.1420	+	34.8870i	−0.724458	+	1.25480i	−0.959197	+	0.282739i	$0.908757\pi$
$774$		0			0
$775$	14.6150	+	25.3140i	0.524988	+	0.909306i
$776$	−2.19208			−0.0786911
$777$		0			0
$778$	25.5653			0.916559
$779$	−8.81191	−	15.2627i	−0.315719	−	0.546842i
$780$		0			0
$781$	−8.13160	+	14.0843i	−0.290972	+	0.503977i
$782$	−2.00972	−	3.48093i	−0.0718673	−	0.124478i
$783$		0			0
$784$	−5.16101	−	3.12030i	−0.184322	−	0.111439i
$785$	2.23912			0.0799177
$786$		0			0
$787$	−23.6053	+	40.8856i	−0.841439	+	1.45742i	0.0472387	+	0.998884i	$0.484958\pi$
$787$	−23.6053	+	40.8856i	−0.841439	+	1.45742i	−0.888678	+	0.458532i	$0.848375\pi$
$788$	4.16484	−	7.21371i	0.148366	−	0.256978i
$789$		0			0
$790$	−16.5322			−0.588188
$791$	13.4513	−	3.45912i	0.478273	−	0.122992i
$792$		0			0
$793$	10.8187	+	18.7386i	0.384185	+	0.665428i
$794$	1.57442	−	2.72698i	0.0558741	−	0.0967767i
$795$		0			0
$796$	−6.57210	−	11.3832i	−0.232942	−	0.403467i
$797$	−4.02735			−0.142656			−0.0713280	−	0.997453i	$-0.522724\pi$
$797$	−4.02735			−0.142656			−0.0713280	+	0.997453i	$0.522724\pi$
$798$		0			0
$799$	1.26320			0.0446888
$800$	−15.0196	−	26.0146i	−0.531022	−	0.919757i
$801$		0			0
$802$	5.88508	−	10.1933i	0.207810	−	0.359937i
$803$	−8.46333	−	14.6589i	−0.298664	−	0.517302i
$804$		0			0
$805$	−2.13160	+	7.64567i	−0.0751290	+	0.269474i
$806$	−16.0733			−0.566159
$807$		0			0
$808$	−10.0830	+	17.4643i	−0.354720	+	0.614392i
$809$	−5.94119	+	10.2904i	−0.208881	+	0.361792i	−0.951362	−	0.308074i	$-0.900315\pi$
$809$	−5.94119	+	10.2904i	−0.208881	+	0.361792i	0.742481	+	0.669867i	$0.233649\pi$
$810$		0			0
$811$	−21.1111			−0.741311			−0.370655	−	0.928770i	$-0.620867\pi$
$811$	−21.1111			−0.741311			−0.370655	+	0.928770i	$0.620867\pi$
$812$	−10.2231	+	36.6685i	−0.358761	+	1.28681i
$813$		0			0
$814$	−2.66182	−	4.61042i	−0.0932969	−	0.161595i
$815$	30.6037	−	53.0072i	1.07200	−	1.85676i
$816$		0			0
$817$	7.25636	+	12.5684i	0.253868	+	0.439712i
$818$	20.8432			0.728767
$819$		0			0
$820$	−18.0252			−0.629467
$821$	18.6460	+	32.2958i	0.650749	+	1.12713i	0.982942	+	0.183918i	$0.0588781\pi$
$821$	18.6460	+	32.2958i	0.650749	+	1.12713i	−0.332193	+	0.943211i	$0.607789\pi$
$822$		0			0
$823$	10.7261	−	18.5782i	0.373890	−	0.647596i	−0.616270	−	0.787535i	$-0.711357\pi$
$823$	10.7261	−	18.5782i	0.373890	−	0.647596i	0.990160	+	0.139939i	$0.0446905\pi$
$824$	−3.16883	−	5.48857i	−0.110391	−	0.191203i
$825$		0			0
$826$	4.01079	−	1.03141i	0.139553	−	0.0358874i
$827$	−28.6375			−0.995823			−0.497912	−	0.867228i	$-0.665900\pi$
$827$	−28.6375			−0.995823			−0.497912	+	0.867228i	$0.665900\pi$
$828$		0			0
$829$	19.8646	−	34.4065i	0.689925	−	1.19499i	−0.281936	−	0.959433i	$-0.590977\pi$
$829$	19.8646	−	34.4065i	0.689925	−	1.19499i	0.971862	−	0.235552i	$-0.0756899\pi$
$830$	9.81875	−	17.0066i	0.340814	−	0.590306i
$831$		0			0
$832$	10.1363			0.351412
$833$	0.791790	−	39.2131i	0.0274339	−	1.35865i
$834$		0			0
$835$	−37.2096	−	64.4489i	−1.28769	−	2.23035i
$836$	7.03379	−	12.1829i	0.243269	−	0.421354i
$837$		0			0
$838$	−7.98921	−	13.8377i	−0.275983	−	0.478016i
$839$	−34.3606			−1.18626			−0.593130	−	0.805107i	$-0.702108\pi$
$839$	−34.3606			−1.18626			−0.593130	+	0.805107i	$0.702108\pi$
$840$		0			0
$841$	73.5108			2.53486
$842$	−7.59316	−	13.1517i	−0.261678	−	0.453239i
$843$		0			0
$844$	−8.92395	+	15.4567i	−0.307175	+	0.532042i
$845$	−1.14132	−	1.97682i	−0.0392624	−	0.0680045i
$846$		0			0
$847$	−11.0858	−	11.3119i	−0.380912	−	0.388681i
$848$	9.18443			0.315395
$849$		0			0
$850$	10.9239	−	18.9208i	0.374688	−	0.648979i
$851$	1.47304	−	2.55139i	0.0504953	−	0.0874605i
$852$		0			0
$853$	−1.51462			−0.0518596			−0.0259298	−	0.999664i	$-0.508255\pi$
$853$	−1.51462			−0.0518596			−0.0259298	+	0.999664i	$0.508255\pi$
$854$	−3.15842	+	11.3287i	−0.108079	+	0.387660i
$855$		0			0
$856$	14.9212	+	25.8443i	0.509996	+	0.883339i
$857$	2.25473	−	3.90530i	0.0770201	−	0.133403i	−0.824943	−	0.565216i	$-0.808793\pi$
$857$	2.25473	−	3.90530i	0.0770201	−	0.133403i	0.901963	+	0.431813i	$0.142126\pi$
$858$		0			0
$859$	−6.30314	−	10.9174i	−0.215060	−	0.372495i	0.738231	−	0.674548i	$-0.235661\pi$
$859$	−6.30314	−	10.9174i	−0.215060	−	0.372495i	−0.953291	+	0.302053i	$0.902328\pi$
$860$	14.8432			0.506150
$861$		0			0
$862$	−15.3160			−0.521665
$863$	5.33009	+	9.23200i	0.181439	+	0.314261i	0.942371	−	0.334571i	$-0.108591\pi$
$863$	5.33009	+	9.23200i	0.181439	+	0.314261i	−0.760932	+	0.648832i	$0.775258\pi$
$864$		0			0
$865$	13.1082	−	22.7041i	0.445693	−	0.771962i
$866$	−4.51040	−	7.81225i	−0.153270	−	0.265471i
$867$		0			0
$868$	15.0098	+	15.3160i	0.509467	+	0.519858i
$869$	−15.2898			−0.518670
$870$		0			0
$871$	−13.7427	+	23.8030i	−0.465653	+	0.806535i
$872$	−23.7518	+	41.1394i	−0.804339	+	1.39316i
$873$		0			0
$874$	−3.17154			−0.107279
$875$	−1.01724	+	0.261592i	−0.0343890	+	0.00884343i
$876$		0			0
$877$	16.1190	+	27.9189i	0.544300	+	0.942756i	0.998651	+	0.0519325i	$0.0165381\pi$
$877$	16.1190	+	27.9189i	0.544300	+	0.942756i	−0.454350	+	0.890823i	$0.650129\pi$
$878$	0.820935	−	1.42190i	0.0277052	−	0.0479869i
$879$		0			0
$880$	−3.06922	−	5.31604i	−0.103463	−	0.179204i
$881$	−55.6375			−1.87447			−0.937237	−	0.348692i	$-0.886626\pi$
$881$	−55.6375			−1.87447			−0.937237	+	0.348692i	$0.886626\pi$
$882$		0			0
$883$	−42.4854			−1.42975			−0.714873	−	0.699254i	$-0.753516\pi$
$883$	−42.4854			−1.42975			−0.714873	+	0.699254i	$0.753516\pi$
$884$	−14.7449	−	25.5389i	−0.495924	−	0.858966i
$885$		0			0
$886$	0.746515	−	1.29300i	0.0250797	−	0.0434393i
$887$	4.47825	+	7.75655i	0.150365	+	0.260439i	0.931362	−	0.364096i	$-0.118622\pi$
$887$	4.47825	+	7.75655i	0.150365	+	0.260439i	−0.780997	+	0.624535i	$0.785289\pi$
$888$		0			0
$889$	−51.5175	+	13.2482i	−1.72784	+	0.444330i
$890$	23.5516			0.789451
$891$		0			0
$892$	−15.1969	+	26.3217i	−0.508829	+	0.881317i
$893$	0.498365	−	0.863194i	0.0166772	−	0.0288857i
$894$		0			0
$895$	31.5322			1.05400
$896$	−17.8532	−	18.2174i	−0.596434	−	0.608599i
$897$		0			0
$898$	−0.818745	−	1.41811i	−0.0273219	−	0.0473229i
$899$	28.8743	−	50.0117i	0.963011	−	1.66798i
$900$		0			0
$901$	29.8646	+	51.7270i	0.994933	+	1.72327i
$902$	6.79149			0.226132
$903$		0			0
$904$	13.6646			0.454477
$905$	14.9360	+	25.8699i	0.496489	+	0.859944i
$906$		0			0
$907$	−5.39372	+	9.34220i	−0.179096	+	0.310203i	−0.941571	−	0.336815i	$-0.890650\pi$
$907$	−5.39372	+	9.34220i	−0.179096	+	0.310203i	0.762475	+	0.647017i	$0.223984\pi$
$908$	−8.96866	−	15.5342i	−0.297636	−	0.515520i
$909$		0			0
$910$	6.37128	−	22.8526i	0.211206	−	0.757558i
$911$	−47.4854			−1.57326			−0.786630	−	0.617424i	$-0.788176\pi$
$911$	−47.4854			−1.57326			−0.786630	+	0.617424i	$0.788176\pi$
$912$		0			0
$913$	9.08087	−	15.7285i	0.300533	−	0.520538i
$914$	4.98577	−	8.63561i	0.164915	−	0.285641i
$915$		0			0
$916$	41.0974			1.35790
$917$	−7.55787	−	7.71202i	−0.249583	−	0.254673i
$918$		0			0
$919$	−28.1375	−	48.7356i	−0.928170	−	1.60764i	−0.786382	−	0.617741i	$-0.788048\pi$
$919$	−28.1375	−	48.7356i	−0.928170	−	1.60764i	−0.141788	−	0.989897i	$-0.545285\pi$
$920$	−3.90451	+	6.76282i	−0.128728	+	0.222964i
$921$		0			0
$922$	2.08757	+	3.61578i	0.0687504	+	0.119079i
$923$	26.9007			0.885447
$924$		0			0
$925$	16.0137			0.526526
$926$	7.79863	+	13.5076i	0.256279	+	0.443888i
$927$		0			0
$928$	−29.6735	+	51.3960i	−0.974079	+	1.68716i
$929$	−0.380438	−	0.658939i	−0.0124818	−	0.0216191i	0.859717	−	0.510771i	$-0.170640\pi$
$929$	−0.380438	−	0.658939i	−0.0124818	−	0.0216191i	−0.872199	+	0.489152i	$0.837307\pi$
$930$		0			0
$931$	−26.4834	−	16.0116i	−0.867960	−	0.524760i
$932$	−30.4832			−0.998509
$933$		0			0
$934$	−14.9709	+	25.9303i	−0.489861	+	0.848465i
$935$	19.9601	−	34.5718i	0.652764	−	1.13062i
$936$		0			0
$937$	−30.3218			−0.990569			−0.495284	−	0.868731i	$-0.664936\pi$
$937$	−30.3218			−0.990569			−0.495284	+	0.868731i	$0.664936\pi$
$938$	−14.4685	+	3.72071i	−0.472414	+	0.121485i
$939$		0			0
$940$	−0.509715	−	0.882853i	−0.0166251	−	0.0287955i
$941$	−27.5406	+	47.7018i	−0.897799	+	1.55503i	−0.0674968	+	0.997719i	$0.521501\pi$
$941$	−27.5406	+	47.7018i	−0.897799	+	1.55503i	−0.830302	+	0.557314i	$0.811832\pi$
$942$		0			0
$943$	1.87919	+	3.25486i	0.0611950	+	0.105993i
$944$	−1.77239			−0.0576864
$945$		0			0
$946$	−5.59261			−0.181831
$947$	−15.3103	−	26.5182i	−0.497517	−	0.861725i	0.502479	−	0.864590i	$-0.332421\pi$
$947$	−15.3103	−	26.5182i	−0.497517	−	0.861725i	−0.999996	+	0.00286470i	$0.999088\pi$
$948$		0			0
$949$	−13.9991	+	24.2471i	−0.454429	+	0.787093i
$950$	−8.61956	−	14.9295i	−0.279656	−	0.484378i
$951$		0			0
$952$	10.3629	−	37.1699i	0.335864	−	1.20468i
$953$	7.83422			0.253775			0.126888	−	0.991917i	$-0.459501\pi$
$953$	7.83422			0.253775			0.126888	+	0.991917i	$0.459501\pi$
$954$		0			0
$955$	39.3577	−	68.1696i	1.27359	−	2.20592i
$956$	−5.49725	+	9.52152i	−0.177794	+	0.307948i
$957$		0			0
$958$	−12.7426			−0.411693
$959$	−1.33981	+	4.80566i	−0.0432647	+	0.155183i
$960$		0			0
$961$	−0.766078	−	1.32689i	−0.0247122	−	0.0428028i
$962$	−4.40288	+	7.62601i	−0.141955	+	0.245872i
$963$		0			0
$964$	4.32833	+	7.49688i	0.139406	+	0.241458i
$965$	−2.63611			−0.0848595
$966$		0			0
$967$	−5.29630			−0.170318			−0.0851588	−	0.996367i	$-0.527140\pi$
$967$	−5.29630			−0.170318			−0.0851588	+	0.996367i	$0.527140\pi$
$968$	−7.79123	−	13.4948i	−0.250420	−	0.433740i
$969$		0			0
$970$	−1.01943	+	1.76571i	−0.0327319	+	0.0566934i
$971$	−26.1202	−	45.2416i	−0.838239	−	1.45187i	−0.891366	−	0.453284i	$-0.850252\pi$
$971$	−26.1202	−	45.2416i	−0.838239	−	1.45187i	0.0531273	−	0.998588i	$-0.483081\pi$
$972$		0			0
$973$	32.7866	−	8.43135i	1.05109	−	0.270297i
$974$	3.04789			0.0976606
$975$		0			0
$976$	2.51668	−	4.35903i	0.0805571	−	0.139529i
$977$	2.97304	−	5.14946i	0.0951161	−	0.164746i	−0.814541	−	0.580106i	$-0.803011\pi$
$977$	2.97304	−	5.14946i	0.0951161	−	0.164746i	0.909657	+	0.415360i	$0.136344\pi$
$978$		0			0
$979$	21.7817			0.696146
$980$	−27.7256	+	15.2695i	−0.885661	+	0.487767i
$981$		0			0
$982$	9.37825	+	16.2436i	0.299272	+	0.518354i
$983$	9.28207	−	16.0770i	0.296052	−	0.512777i	−0.679177	−	0.733975i	$-0.737663\pi$
$983$	9.28207	−	16.0770i	0.296052	−	0.512777i	0.975229	+	0.221197i	$0.0709964\pi$
$984$		0			0
$985$	−9.32558	−	16.1524i	−0.297138	−	0.514658i
$986$	−43.1639			−1.37462
$987$		0			0
$988$	−23.2690			−0.740284
$989$	−1.54746	−	2.68029i	−0.0492065	−	0.0852282i
$990$		0			0
$991$	−9.31875	+	16.1405i	−0.296020	+	0.512721i	−0.975222	−	0.221230i	$-0.928993\pi$
$991$	−9.31875	+	16.1405i	−0.296020	+	0.512721i	0.679202	+	0.733951i	$0.262326\pi$
$992$	16.7163	+	28.9535i	0.530743	+	0.919273i
$993$		0			0
$994$	10.2341	+	10.4428i	0.324604	+	0.331225i
$995$	−29.4315			−0.933040
$996$		0			0
$997$	15.2798	−	26.4653i	0.483915	−	0.838165i	−0.515915	−	0.856640i	$-0.672548\pi$
$997$	15.2798	−	26.4653i	0.483915	−	0.838165i	0.999829	+	0.0184753i	$0.00588120\pi$
$998$	9.34338	−	16.1832i	0.295759	−	0.512270i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.e.e.109.2	✓	6
3.2	odd	2		189.2.e.f.109.2	yes	6
7.2	even	3	inner	189.2.e.e.163.2	yes	6
7.3	odd	6		1323.2.a.z.1.2		3
7.4	even	3		1323.2.a.ba.1.2		3
9.2	odd	6		567.2.g.i.109.2		6
9.4	even	3		567.2.h.i.298.2		6
9.5	odd	6		567.2.h.h.298.2		6
9.7	even	3		567.2.g.h.109.2		6
21.2	odd	6		189.2.e.f.163.2	yes	6
21.11	odd	6		1323.2.a.x.1.2		3
21.17	even	6		1323.2.a.y.1.2		3
63.2	odd	6		567.2.h.h.352.2		6
63.16	even	3		567.2.h.i.352.2		6
63.23	odd	6		567.2.g.i.541.2		6
63.58	even	3		567.2.g.h.541.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.e.e.109.2	✓	6	1.1	even	1	trivial
189.2.e.e.163.2	yes	6	7.2	even	3	inner
189.2.e.f.109.2	yes	6	3.2	odd	2
189.2.e.f.163.2	yes	6	21.2	odd	6
567.2.g.h.109.2		6	9.7	even	3
567.2.g.h.541.2		6	63.58	even	3
567.2.g.i.109.2		6	9.2	odd	6
567.2.g.i.541.2		6	63.23	odd	6
567.2.h.h.298.2		6	9.5	odd	6
567.2.h.h.352.2		6	63.2	odd	6
567.2.h.i.298.2		6	9.4	even	3
567.2.h.i.352.2		6	63.16	even	3
1323.2.a.x.1.2		3	21.11	odd	6
1323.2.a.y.1.2		3	21.17	even	6
1323.2.a.z.1.2		3	7.3	odd	6
1323.2.a.ba.1.2		3	7.4	even	3

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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.380438 - 0.658939i) q^{2} +(0.710533 - 1.23068i) q^{4} +(-1.59097 - 2.75564i) q^{5} +(-2.56238 + 0.658939i) q^{7} -2.60301 q^{8} +O(q^{10})\)	\(q+(-0.380438 - 0.658939i) q^{2} +(0.710533 - 1.23068i) q^{4} +(-1.59097 - 2.75564i) q^{5} +(-2.56238 + 0.658939i) q^{7} -2.60301 q^{8} +(-1.21053 + 2.09671i) q^{10} +(-1.11956 + 1.93914i) q^{11} +3.70370 q^{13} +(1.40903 + 1.43777i) q^{14} +(-0.430782 - 0.746136i) q^{16} +(2.80150 - 4.85235i) q^{17} +(-2.21053 - 3.82876i) q^{19} -4.52175 q^{20} +1.70370 q^{22} +(0.471410 + 0.816506i) q^{23} +(-2.56238 + 4.43818i) q^{25} +(-1.40903 - 2.44051i) q^{26} +(-1.00972 + 3.62167i) q^{28} +10.1248 q^{29} +(2.85185 - 4.93955i) q^{31} +(-2.93078 + 5.07626i) q^{32} -4.26320 q^{34} +(5.89248 + 6.01266i) q^{35} +(-1.56238 - 2.70612i) q^{37} +(-1.68194 + 2.91321i) q^{38} +(4.14132 + 7.17297i) q^{40} +3.98633 q^{41} -3.28263 q^{43} +(1.59097 + 2.75564i) q^{44} +(0.358685 - 0.621261i) q^{46} +(0.112725 + 0.195246i) q^{47} +(6.13160 - 3.37690i) q^{49} +3.89931 q^{50} +(2.63160 - 4.55806i) q^{52} +(-5.33009 + 9.23200i) q^{53} +7.12476 q^{55} +(6.66991 - 1.71522i) q^{56} +(-3.85185 - 6.67160i) q^{58} +(1.02859 - 1.78157i) q^{59} +(2.92107 + 5.05944i) q^{61} -4.33981 q^{62} +2.73680 q^{64} +(-5.89248 - 10.2061i) q^{65} +(-3.71053 + 6.42683i) q^{67} +(-3.98113 - 6.89551i) q^{68} +(1.72025 - 6.17023i) q^{70} +7.26320 q^{71} +(-3.77975 + 6.54672i) q^{73} +(-1.18878 + 2.05903i) q^{74} -6.28263 q^{76} +(1.59097 - 5.70653i) q^{77} +(3.41423 + 5.91362i) q^{79} +(-1.37072 + 2.37416i) q^{80} +(-1.51655 - 2.62674i) q^{82} -8.11109 q^{83} -17.8285 q^{85} +(1.24884 + 2.16305i) q^{86} +(2.91423 - 5.04759i) q^{88} +(-4.86389 - 8.42450i) q^{89} +(-9.49028 + 2.44051i) q^{91} +1.33981 q^{92} +(0.0857699 - 0.148558i) q^{94} +(-7.03379 + 12.1829i) q^{95} +0.842133 q^{97} +(-4.55787 - 2.75564i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 2 q^{2} - 4 q^{4} - q^{5} + 2 q^{7} + 18 q^{8}+O(q^{10}) \) 6 * q - 2 * q^2 - 4 * q^4 - q^5 + 2 * q^7 + 18 * q^8	\( 6 q - 2 q^{2} - 4 q^{4} - q^{5} + 2 q^{7} + 18 q^{8} + q^{10} - 7 q^{11} + 4 q^{13} + 17 q^{14} - 10 q^{16} - 5 q^{19} - 26 q^{20} - 8 q^{22} - 6 q^{23} + 2 q^{25} - 17 q^{26} - 30 q^{28} + 26 q^{29} + 8 q^{31} - 25 q^{32} + 24 q^{34} + 10 q^{35} + 8 q^{37} + 7 q^{38} + 24 q^{40} + 4 q^{41} - 18 q^{43} + q^{44} + 3 q^{46} - 9 q^{47} + 12 q^{49} + 8 q^{50} - 9 q^{52} - 24 q^{53} + 8 q^{55} + 48 q^{56} - 14 q^{58} + 15 q^{59} + q^{61} - 42 q^{62} + 66 q^{64} - 10 q^{65} - 14 q^{67} - 39 q^{68} + 26 q^{70} - 6 q^{71} - 7 q^{73} - 36 q^{76} + q^{77} - 6 q^{79} + 16 q^{80} - 43 q^{82} + 6 q^{83} - 54 q^{85} + 32 q^{86} - 9 q^{88} + 5 q^{89} - 33 q^{91} + 24 q^{92} + 27 q^{94} - 16 q^{95} - 28 q^{97} + 49 q^{98}+O(q^{100}) \) 6 * q - 2 * q^2 - 4 * q^4 - q^5 + 2 * q^7 + 18 * q^8 + q^10 - 7 * q^11 + 4 * q^13 + 17 * q^14 - 10 * q^16 - 5 * q^19 - 26 * q^20 - 8 * q^22 - 6 * q^23 + 2 * q^25 - 17 * q^26 - 30 * q^28 + 26 * q^29 + 8 * q^31 - 25 * q^32 + 24 * q^34 + 10 * q^35 + 8 * q^37 + 7 * q^38 + 24 * q^40 + 4 * q^41 - 18 * q^43 + q^44 + 3 * q^46 - 9 * q^47 + 12 * q^49 + 8 * q^50 - 9 * q^52 - 24 * q^53 + 8 * q^55 + 48 * q^56 - 14 * q^58 + 15 * q^59 + q^61 - 42 * q^62 + 66 * q^64 - 10 * q^65 - 14 * q^67 - 39 * q^68 + 26 * q^70 - 6 * q^71 - 7 * q^73 - 36 * q^76 + q^77 - 6 * q^79 + 16 * q^80 - 43 * q^82 + 6 * q^83 - 54 * q^85 + 32 * q^86 - 9 * q^88 + 5 * q^89 - 33 * q^91 + 24 * q^92 + 27 * q^94 - 16 * q^95 - 28 * q^97 + 49 * q^98

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