LMFDB - Embedded newform 729.2.i.a.10.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(10,729)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(162))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("729.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.i (of order $81$, degree $54$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$1404$
Relative dimension:	$26$ over $\Q(\zeta_{81})$
Twist minimal:	no (minimal twist has level 243)
Sato-Tate group:	$\mathrm{SU}(2)[C_{81}]$

Embedding invariants

Embedding label			10.19
Character	$\chi$	$=$	729.10
Dual form			729.2.i.a.73.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.42734 + 0.223232i) q^{2} +(0.0829775 + 0.0266057i) q^{4} +(2.36005 + 1.07277i) q^{5} +(-0.546388 - 4.00027i) q^{7} +(-2.46955 - 1.24026i) q^{8} +O(q^{10})$	\(q+(1.42734 + 0.223232i) q^{2} +(0.0829775 + 0.0266057i) q^{4} +(2.36005 + 1.07277i) q^{5} +(-0.546388 - 4.00027i) q^{7} +(-2.46955 - 1.24026i) q^{8} +(3.12912 + 2.05805i) q^{10} +(4.25792 - 0.330951i) q^{11} +(1.88818 + 5.51842i) q^{13} +(0.113106 - 5.83172i) q^{14} +(-3.38981 - 2.42289i) q^{16} +(2.05639 - 4.76725i) q^{17} +(1.12723 - 1.51413i) q^{19} +(0.167289 + 0.151807i) q^{20} +(6.15138 + 0.478123i) q^{22} +(-2.11080 - 1.63599i) q^{23} +(1.13137 + 1.29641i) q^{25} +(1.46319 + 8.29818i) q^{26} +(0.0610918 - 0.346469i) q^{28} +(-2.42674 + 1.46454i) q^{29} +(8.78126 - 0.340753i) q^{31} +(-0.351670 - 0.344916i) q^{32} +(3.99937 - 6.34544i) q^{34} +(3.00188 - 10.0270i) q^{35} +(-2.81986 + 2.98888i) q^{37} +(1.94695 - 1.90955i) q^{38} +(-4.49775 - 5.57633i) q^{40} +(0.0592476 - 0.153455i) q^{41} +(2.16144 + 8.39121i) q^{43} +(0.362116 + 0.0858232i) q^{44} +(-2.64762 - 2.80632i) q^{46} +(-0.870903 - 0.0337950i) q^{47} +(-8.96000 + 2.49419i) q^{49} +(1.32546 + 2.10298i) q^{50} +(0.00985539 + 0.508141i) q^{52} +(0.488024 - 0.177626i) q^{53} +(10.4039 + 3.78672i) q^{55} +(-3.61202 + 10.5565i) q^{56} +(-3.79071 + 1.54868i) q^{58} +(0.610108 + 1.27593i) q^{59} +(-11.9654 + 3.83655i) q^{61} +(12.6099 + 1.47389i) q^{62} +(4.55138 + 6.11357i) q^{64} +(-1.46381 + 15.0493i) q^{65} +(-5.25970 - 3.17424i) q^{67} +(0.297470 - 0.340862i) q^{68} +(6.52305 - 13.6418i) q^{70} +(-0.419310 + 7.19927i) q^{71} +(-5.95065 + 3.91380i) q^{73} +(-4.69212 + 3.63667i) q^{74} +(0.133819 - 0.0956484i) q^{76} +(-3.65037 - 16.8520i) q^{77} +(-4.07528 + 5.05255i) q^{79} +(-5.40091 - 9.35465i) q^{80} +(0.118823 - 0.205807i) q^{82} +(-4.35024 - 11.2674i) q^{83} +(9.96735 - 9.04489i) q^{85} +(1.21192 + 12.4596i) q^{86} +(-10.9256 - 4.46360i) q^{88} +(-0.850611 - 14.6044i) q^{89} +(21.0435 - 10.5684i) q^{91} +(-0.131622 - 0.191909i) q^{92} +(-1.23553 - 0.242651i) q^{94} +(4.28464 - 2.36417i) q^{95} +(-4.53267 + 2.06035i) q^{97} +(-13.3458 + 1.55990i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	$ 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) $ 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{81}\right)$

Coefficient data

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

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

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

$2$	1.42734	+	0.223232i	1.00928	+	0.157849i	0.637484	−	0.770464i	$-0.279975\pi$
$2$	1.42734	+	0.223232i	1.00928	+	0.157849i	0.371800	+	0.928313i	$0.378741\pi$
$3$		0			0
$3$		0			0
$4$	0.0829775	+	0.0266057i	0.0414887	+	0.0133028i
$5$	2.36005	+	1.07277i	1.05545	+	0.479759i	0.864913	−	0.501922i	$-0.167374\pi$
$5$	2.36005	+	1.07277i	1.05545	+	0.479759i	0.190532	+	0.981681i	$0.438979\pi$
$6$		0			0
$7$	−0.546388	−	4.00027i	−0.206515	−	1.51196i	−0.743711	−	0.668501i	$-0.766936\pi$
$7$	−0.546388	−	4.00027i	−0.206515	−	1.51196i	0.537196	−	0.843457i	$-0.319484\pi$
$8$	−2.46955	−	1.24026i	−0.873118	−	0.438497i
$9$		0			0
$10$	3.12912	+	2.05805i	0.989514	+	0.650814i
$11$	4.25792	−	0.330951i	1.28381	−	0.0997856i	0.582611	−	0.812751i	$-0.302031\pi$
$11$	4.25792	−	0.330951i	1.28381	−	0.0997856i	0.701199	+	0.712966i	$0.252648\pi$
$12$		0			0
$13$	1.88818	+	5.51842i	0.523688	+	1.53053i	0.818227	+	0.574895i	$0.194957\pi$
$13$	1.88818	+	5.51842i	0.523688	+	1.53053i	−0.294539	+	0.955639i	$0.595166\pi$
$14$	0.113106	−	5.83172i	0.0302289	−	1.55859i
$15$		0			0
$16$	−3.38981	−	2.42289i	−0.847454	−	0.605723i
$17$	2.05639	−	4.76725i	0.498748	−	1.15623i	−0.464002	−	0.885834i	$-0.653587\pi$
$17$	2.05639	−	4.76725i	0.498748	−	1.15623i	0.962750	−	0.270393i	$-0.0871536\pi$
$18$		0			0
$19$	1.12723	−	1.51413i	0.258605	−	0.347366i	−0.653791	−	0.756675i	$-0.726823\pi$
$19$	1.12723	−	1.51413i	0.258605	−	0.347366i	0.912396	+	0.409308i	$0.134230\pi$
$20$	0.167289	+	0.151807i	0.0374069	+	0.0339450i
$21$		0			0
$22$	6.15138	+	0.478123i	1.31148	+	0.101936i
$23$	−2.11080	−	1.63599i	−0.440131	−	0.341128i	0.368311	−	0.929703i	$-0.379936\pi$
$23$	−2.11080	−	1.63599i	−0.440131	−	0.341128i	−0.808443	+	0.588575i	$0.799689\pi$
$24$		0			0
$25$	1.13137	+	1.29641i	0.226275	+	0.259282i
$26$	1.46319	+	8.29818i	0.286956	+	1.62741i
$27$		0			0
$28$	0.0610918	−	0.346469i	0.0115453	−	0.0654765i
$29$	−2.42674	+	1.46454i	−0.450633	+	0.271959i	−0.723802	−	0.690007i	$-0.757607\pi$
$29$	−2.42674	+	1.46454i	−0.450633	+	0.271959i	0.273169	+	0.961966i	$0.411928\pi$
$30$		0			0
$31$	8.78126	−	0.340753i	1.57716	−	0.0612010i	0.764766	−	0.644308i	$-0.222855\pi$
$31$	8.78126	−	0.340753i	1.57716	−	0.0612010i	0.812395	+	0.583107i	$0.198163\pi$
$32$	−0.351670	−	0.344916i	−0.0621671	−	0.0609731i
$33$		0			0
$34$	3.99937	−	6.34544i	0.685887	−	1.08823i
$35$	3.00188	−	10.0270i	0.507410	−	1.69487i
$36$		0			0
$37$	−2.81986	+	2.98888i	−0.463582	+	0.491369i	−0.916416	−	0.400226i	$-0.868932\pi$
$37$	−2.81986	+	2.98888i	−0.463582	+	0.491369i	0.452834	+	0.891595i	$0.350413\pi$
$38$	1.94695	−	1.90955i	0.315837	−	0.309771i
$39$		0			0
$40$	−4.49775	−	5.57633i	−0.711156	−	0.881695i
$41$	0.0592476	−	0.153455i	0.00925291	−	0.0239657i	−0.928180	−	0.372131i	$-0.878627\pi$
$41$	0.0592476	−	0.153455i	0.00925291	−	0.0239657i	0.937433	+	0.348165i	$0.113195\pi$
$42$		0			0
$43$	2.16144	+	8.39121i	0.329616	+	1.27965i	0.891722	+	0.452583i	$0.149497\pi$
$43$	2.16144	+	8.39121i	0.329616	+	1.27965i	−0.562106	+	0.827065i	$0.690009\pi$
$44$	0.362116	+	0.0858232i	0.0545911	+	0.0129383i
$45$		0			0
$46$	−2.64762	−	2.80632i	−0.390371	−	0.413769i
$47$	−0.870903	−	0.0337950i	−0.127034	−	0.00492951i	−0.0248202	−	0.999692i	$-0.507901\pi$
$47$	−0.870903	−	0.0337950i	−0.127034	−	0.00492951i	−0.102214	+	0.994762i	$0.532593\pi$
$48$		0			0
$49$	−8.96000	+	2.49419i	−1.28000	+	0.356312i
$50$	1.32546	+	2.10298i	0.187448	+	0.297406i
$51$		0			0
$52$	0.00985539	+	0.508141i	0.00136670	+	0.0704665i
$53$	0.488024	−	0.177626i	0.0670352	−	0.0243988i	−0.308285	−	0.951294i	$-0.599755\pi$
$53$	0.488024	−	0.177626i	0.0670352	−	0.0243988i	0.375320	+	0.926895i	$0.377533\pi$
$54$		0			0
$55$	10.4039	+	3.78672i	1.40286	+	0.510601i
$56$	−3.61202	+	10.5565i	−0.482676	+	1.41068i
$57$		0			0
$58$	−3.79071	+	1.54868i	−0.497745	+	0.203351i
$59$	0.610108	+	1.27593i	0.0794293	+	0.166112i	0.938051	−	0.346498i	$-0.112629\pi$
$59$	0.610108	+	1.27593i	0.0794293	+	0.166112i	−0.858621	+	0.512610i	$0.828679\pi$
$60$		0			0
$61$	−11.9654	+	3.83655i	−1.53201	+	0.491220i	−0.947389	−	0.320085i	$-0.896288\pi$
$61$	−11.9654	+	3.83655i	−1.53201	+	0.491220i	−0.584623	+	0.811305i	$0.698758\pi$
$62$	12.6099	+	1.47389i	1.60146	+	0.187184i
$63$		0			0
$64$	4.55138	+	6.11357i	0.568923	+	0.764196i
$65$	−1.46381	+	15.0493i	−0.181564	+	1.86664i
$66$		0			0
$67$	−5.25970	−	3.17424i	−0.642574	−	0.387795i	0.157651	−	0.987495i	$-0.449608\pi$
$67$	−5.25970	−	3.17424i	−0.642574	−	0.387795i	−0.800225	+	0.599699i	$0.795287\pi$
$68$	0.297470	−	0.340862i	0.0360735	−	0.0413356i
$69$		0			0
$70$	6.52305	−	13.6418i	0.779653	−	1.63051i
$71$	−0.419310	+	7.19927i	−0.0497629	+	0.854396i	0.877405	+	0.479750i	$0.159273\pi$
$71$	−0.419310	+	7.19927i	−0.0497629	+	0.854396i	−0.927168	+	0.374646i	$0.877764\pi$
$72$		0			0
$73$	−5.95065	+	3.91380i	−0.696470	+	0.458076i	−0.847737	−	0.530417i	$-0.822035\pi$
$73$	−5.95065	+	3.91380i	−0.696470	+	0.458076i	0.151266	+	0.988493i	$0.451665\pi$
$74$	−4.69212	+	3.63667i	−0.545448	+	0.422754i
$75$		0			0
$76$	0.133819	−	0.0956484i	0.0153501	−	0.0109716i
$77$	−3.65037	−	16.8520i	−0.415998	−	1.92046i
$78$		0			0
$79$	−4.07528	+	5.05255i	−0.458505	+	0.568457i	−0.953867	−	0.300230i	$-0.902937\pi$
$79$	−4.07528	+	5.05255i	−0.458505	+	0.568457i	0.495362	+	0.868687i	$0.335035\pi$
$80$	−5.40091	−	9.35465i	−0.603840	−	1.04588i
$81$		0			0
$82$	0.118823	−	0.205807i	0.0131218	−	0.0227276i
$83$	−4.35024	−	11.2674i	−0.477501	−	1.23676i	−0.937234	−	0.348702i	$-0.886623\pi$
$83$	−4.35024	−	11.2674i	−0.477501	−	1.23676i	0.459733	−	0.888057i	$-0.347945\pi$
$84$		0			0
$85$	9.96735	−	9.04489i	1.08111	−	0.981056i
$86$	1.21192	+	12.4596i	0.130685	+	1.34356i
$87$		0			0
$88$	−10.9256	−	4.46360i	−1.16467	−	0.475822i
$89$	−0.850611	−	14.6044i	−0.0901646	−	1.54807i	−0.675552	−	0.737312i	$-0.736095\pi$
$89$	−0.850611	−	14.6044i	−0.0901646	−	1.54807i	0.585387	−	0.810754i	$-0.300942\pi$
$90$		0			0
$91$	21.0435	−	10.5684i	2.20596	−	1.10787i
$92$	−0.131622	−	0.191909i	−0.0137225	−	0.0200079i
$93$		0			0
$94$	−1.23553	−	0.242651i	−0.127435	−	0.0250275i
$95$	4.28464	−	2.36417i	0.439595	−	0.242558i
$96$		0			0
$97$	−4.53267	+	2.06035i	−0.460223	+	0.209197i	−0.630484	−	0.776202i	$-0.717144\pi$
$97$	−4.53267	+	2.06035i	−0.460223	+	0.209197i	0.170261	+	0.985399i	$0.445539\pi$
$98$	−13.3458	+	1.55990i	−1.34813	+	0.157573i
$99$		0			0
$100$	0.0593867	+	0.137674i	0.00593867	+	0.0137674i
$101$	−1.81743	+	8.39018i	−0.180841	+	0.834854i	0.793285	+	0.608850i	$0.208369\pi$
$101$	−1.81743	+	8.39018i	−0.180841	+	0.834854i	−0.974126	+	0.226004i	$0.927434\pi$
$102$		0			0
$103$	−3.54331	+	5.16627i	−0.349132	+	0.509048i	−0.958981	−	0.283470i	$-0.908514\pi$
$103$	−3.54331	+	5.16627i	−0.349132	+	0.509048i	0.609849	+	0.792518i	$0.291230\pi$
$104$	2.18129	−	15.9699i	0.213893	−	1.56597i
$105$		0			0
$106$	0.736229	−	0.144591i	0.0715088	−	0.0140439i
$107$	9.87265	−	8.28414i	0.954425	−	0.800858i	−0.0256120	−	0.999672i	$-0.508153\pi$
$107$	9.87265	−	8.28414i	0.954425	−	0.800858i	0.980037	+	0.198814i	$0.0637090\pi$
$108$		0			0
$109$	6.51986	+	5.47081i	0.624489	+	0.524009i	0.899211	−	0.437515i	$-0.144141\pi$
$109$	6.51986	+	5.47081i	0.624489	+	0.524009i	−0.274722	+	0.961524i	$0.588586\pi$
$110$	14.0046	+	7.72743i	1.33529	+	0.736782i
$111$		0			0
$112$	−7.84007	+	14.8840i	−0.740817	+	1.40641i
$113$	−1.32700	+	5.15172i	−0.124833	+	0.484633i	0.875166	+	0.483822i	$0.160752\pi$
$113$	−1.32700	+	5.15172i	−0.124833	+	0.484633i	−1.00000		0.000810608i	$0.999742\pi$
$114$		0			0
$115$	−3.22653	−	6.12542i	−0.300876	−	0.571198i
$116$	−0.240329	+	0.0569591i	−0.0223140	+	0.00528852i
$117$		0			0
$118$	0.586004	+	1.95739i	0.0539460	+	0.180192i
$119$	−20.1938	−	5.62134i	−1.85117	−	0.515307i
$120$		0			0
$121$	7.15243	−	1.11862i	0.650221	−	0.101693i
$122$	−17.9352	+	2.80501i	−1.62377	+	0.253953i
$123$		0			0
$124$	0.737713	+	0.205356i	0.0662486	+	0.0184415i
$125$	−2.43824	−	8.14428i	−0.218083	−	0.728446i
$126$		0			0
$127$	−9.08689	+	2.15363i	−0.806331	+	0.191104i	−0.613055	−	0.790041i	$-0.710059\pi$
$127$	−9.08689	+	2.15363i	−0.806331	+	0.191104i	−0.193276	+	0.981144i	$0.561911\pi$
$128$	5.59077	+	10.6138i	0.494159	+	0.938137i
$129$		0			0
$130$	−5.44886	+	21.1538i	−0.477897	+	1.85531i
$131$	−3.24509	+	6.16066i	−0.283525	+	0.538259i	−0.984599	−	0.174830i	$-0.944063\pi$
$131$	−3.24509	+	6.16066i	−0.283525	+	0.538259i	0.701073	+	0.713089i	$0.252704\pi$
$132$		0			0
$133$	−6.67285	−	3.68192i	−0.578609	−	0.319263i
$134$	−6.79879	−	5.70486i	−0.587326	−	0.492825i
$135$		0			0
$136$	−10.9910	+	9.22251i	−0.942467	+	0.790824i
$137$	−17.1768	+	3.37341i	−1.46751	+	0.288210i	−0.861708	−	0.507405i	$-0.830605\pi$
$137$	−17.1768	+	3.37341i	−1.46751	+	0.288210i	−0.605803	+	0.795614i	$0.707148\pi$
$138$		0			0
$139$	0.968586	−	7.09131i	0.0821544	−	0.601477i	−0.902979	−	0.429685i	$-0.858625\pi$
$139$	0.968586	−	7.09131i	0.0821544	−	0.601477i	0.985133	−	0.171792i	$-0.0549557\pi$
$140$	0.515862	−	0.752146i	0.0435983	−	0.0635679i
$141$		0			0
$142$	−2.20561	+	10.1822i	−0.185090	+	0.854473i
$143$	9.86605	+	22.8721i	0.825041	+	1.91266i
$144$		0			0
$145$	−7.29833	+	0.853053i	−0.606093	+	0.0708422i
$146$	−9.36730	+	4.25796i	−0.775243	+	0.352391i
$147$		0			0
$148$	−0.313506	+	0.172985i	−0.0257700	+	0.0142193i
$149$	7.26680	+	1.42715i	0.595320	+	0.116917i	0.481292	−	0.876561i	$-0.340168\pi$
$149$	7.26680	+	1.42715i	0.595320	+	0.116917i	0.114028	+	0.993478i	$0.463625\pi$
$150$		0			0
$151$	0.246774	+	0.359805i	0.0200822	+	0.0292806i	0.834586	−	0.550877i	$-0.185707\pi$
$151$	0.246774	+	0.359805i	0.0200822	+	0.0292806i	−0.814504	+	0.580158i	$0.802991\pi$
$152$	−4.66167	+	2.34118i	−0.378111	+	0.189895i
$153$		0			0
$154$	−1.44842	−	24.8684i	−0.116717	−	2.00395i
$155$	21.0897	+	8.61611i	1.69397	+	0.692062i
$156$		0			0
$157$	2.28635	+	23.5057i	0.182471	+	1.87596i	0.424130	+	0.905602i	$0.360580\pi$
$157$	2.28635	+	23.5057i	0.182471	+	1.87596i	−0.241659	+	0.970361i	$0.577692\pi$
$158$	−6.94471	+	6.30199i	−0.552491	+	0.501359i
$159$		0			0
$160$	−0.459942	−	1.19128i	−0.0363616	−	0.0941790i
$161$	−5.39108	+	9.33763i	−0.424877	+	0.735908i
$162$		0			0
$163$	1.92989	+	3.34267i	0.151161	+	0.261818i	0.931654	−	0.363346i	$-0.118366\pi$
$163$	1.92989	+	3.34267i	0.151161	+	0.261818i	−0.780494	+	0.625163i	$0.785032\pi$
$164$	0.00899899	−	0.0111570i	0.000702703	−	0.000871215i
$165$		0			0
$166$	−3.69404	−	17.0536i	−0.286713	−	1.32361i
$167$	−9.31165	+	6.65557i	−0.720557	+	0.515023i	−0.881643	−	0.471917i	$-0.843562\pi$
$167$	−9.31165	+	6.65557i	−0.720557	+	0.515023i	0.161086	+	0.986940i	$0.448500\pi$
$168$		0			0
$169$	−16.6126	+	12.8758i	−1.27790	+	0.990444i
$170$	16.2459	−	10.6851i	1.24601	−	0.819511i
$171$		0			0
$172$	−0.0439032	+	0.753788i	−0.00334758	+	0.0574758i
$173$	8.10658	−	16.9535i	0.616331	−	1.28895i	−0.323150	−	0.946348i	$-0.604742\pi$
$173$	8.10658	−	16.9535i	0.616331	−	1.28895i	0.939481	−	0.342600i	$-0.111308\pi$
$174$		0			0
$175$	4.56782	−	5.23414i	0.345295	−	0.395664i
$176$	−15.2354	−	9.19461i	−1.14841	−	0.693070i
$177$		0			0
$178$	2.04607	−	21.0354i	0.153359	−	1.57667i
$179$	12.3863	+	16.6377i	0.925795	+	1.24356i	0.969644	+	0.244520i	$0.0786305\pi$
$179$	12.3863	+	16.6377i	0.925795	+	1.24356i	−0.0438493	+	0.999038i	$0.513962\pi$
$180$		0			0
$181$	14.1343	+	1.65207i	1.05060	+	0.122797i	0.623827	−	0.781563i	$-0.285577\pi$
$181$	14.1343	+	1.65207i	1.05060	+	0.122797i	0.426771	+	0.904360i	$0.359651\pi$
$182$	32.3955	−	10.3872i	2.40131	−	0.769949i
$183$		0			0
$184$	3.18367	+	6.65809i	0.234704	+	0.490841i
$185$	−9.86139	+	4.02882i	−0.725024	+	0.296205i
$186$		0			0
$187$	7.17821	−	20.9791i	0.524922	−	1.53414i
$188$	−0.0713662	−	0.0259752i	−0.00520492	−	0.00189443i
$189$		0			0
$190$	6.64341	−	2.41800i	0.481964	−	0.175420i
$191$	−0.336886	−	17.3697i	−0.0243762	−	1.25683i	−0.789825	−	0.613333i	$-0.789829\pi$
$191$	−0.336886	−	17.3697i	−0.0243762	−	1.25683i	0.765449	−	0.643497i	$-0.222517\pi$
$192$		0			0
$193$	−10.2260	−	16.2246i	−0.736081	−	1.16787i	−0.980177	−	0.198122i	$-0.936516\pi$
$193$	−10.2260	−	16.2246i	−0.736081	−	1.16787i	0.244096	−	0.969751i	$-0.421509\pi$
$194$	−6.92961	+	1.92899i	−0.497517	+	0.138493i
$195$		0			0
$196$	−0.809837	−	0.0314254i	−0.0578455	−	0.00224467i
$197$	5.69222	+	6.03340i	0.405554	+	0.429862i	0.897670	−	0.440667i	$-0.145258\pi$
$197$	5.69222	+	6.03340i	0.405554	+	0.429862i	−0.492117	+	0.870529i	$0.663777\pi$
$198$		0			0
$199$	−6.40914	−	1.51900i	−0.454332	−	0.107679i	−0.00292292	−	0.999996i	$-0.500930\pi$
$199$	−6.40914	−	1.51900i	−0.454332	−	0.107679i	−0.451409	+	0.892317i	$0.649079\pi$
$200$	−1.18611	−	4.60475i	−0.0838704	−	0.325605i
$201$		0			0
$202$	−4.46705	+	11.5700i	−0.314301	+	0.814059i
$203$	7.18450	+	8.90738i	0.504253	+	0.625175i
$204$		0			0
$205$	0.304449	−	0.298602i	0.0212637	−	0.0208553i
$206$	−6.21079	+	6.58305i	−0.432726	+	0.458663i
$207$		0			0
$208$	6.96996	−	23.2813i	0.483280	−	1.61427i
$209$	4.29855	−	6.82012i	0.297337	−	0.471757i
$210$		0			0
$211$	−12.0862	−	11.8541i	−0.832050	−	0.816069i	0.153020	−	0.988223i	$-0.451100\pi$
$211$	−12.0862	−	11.8541i	−0.832050	−	0.816069i	−0.985070	+	0.172154i	$0.944927\pi$
$212$	0.0452208	−	0.00175477i	0.00310578	−	0.000120518i
$213$		0			0
$214$	15.9409	−	9.62041i	1.08970	−	0.657637i
$215$	−3.90077	+	22.1224i	−0.266031	+	1.50873i
$216$		0			0
$217$	−6.16108	−	34.9412i	−0.418241	−	2.37196i
$218$	8.08481	+	9.26416i	0.547572	+	0.627448i
$219$		0			0
$220$	0.762543	+	0.591015i	0.0514106	+	0.0398463i
$221$	30.1905	+	2.34659i	2.03083	+	0.157849i
$222$		0			0
$223$	11.1186	+	10.0896i	0.744555	+	0.675648i	0.953199	−	0.302344i	$-0.0977692\pi$
$223$	11.1186	+	10.0896i	0.744555	+	0.675648i	−0.208644	+	0.977992i	$0.566905\pi$
$224$	−1.18761	+	1.59523i	−0.0793503	+	0.106586i
$225$		0			0
$226$	−3.04411	+	7.05704i	−0.202491	+	0.469427i
$227$	−0.597130	−	0.426803i	−0.0396329	−	0.0283279i	0.561503	−	0.827475i	$-0.310223\pi$
$227$	−0.597130	−	0.426803i	−0.0396329	−	0.0283279i	−0.601136	+	0.799147i	$0.705285\pi$
$228$		0			0
$229$	−0.267245	+	13.7791i	−0.0176600	+	0.910546i	0.881311	+	0.472537i	$0.156662\pi$
$229$	−0.267245	+	13.7791i	−0.0176600	+	0.910546i	−0.898971	+	0.438009i	$0.855684\pi$
$230$	−3.23797	−	9.46334i	−0.213506	−	0.623994i
$231$		0			0
$232$	7.80936	−	0.606991i	0.512709	−	0.0398509i
$233$	−5.33470	−	3.50869i	−0.349488	−	0.229862i	0.362611	−	0.931940i	$-0.381885\pi$
$233$	−5.33470	−	3.50869i	−0.349488	−	0.229862i	−0.712100	+	0.702078i	$0.752256\pi$
$234$		0			0
$235$	−2.01912	−	1.01404i	−0.131713	−	0.0661486i
$236$	0.0166782	+	0.122106i	0.00108566	+	0.00794842i
$237$		0			0
$238$	−27.5687	−	12.5315i	−1.78701	−	0.812296i
$239$	15.5429	+	4.98363i	1.00539	+	0.322364i	0.762008	−	0.647567i	$-0.224213\pi$
$239$	15.5429	+	4.98363i	1.00539	+	0.322364i	0.243378	+	0.969931i	$0.421744\pi$
$240$		0			0
$241$	22.2411	+	3.47844i	1.43267	+	0.224066i	0.822754	−	0.568397i	$-0.192436\pi$
$241$	22.2411	+	3.47844i	1.43267	+	0.224066i	0.609920	+	0.792463i	$0.291202\pi$
$242$	10.4587			0.672310
$243$		0			0
$244$	−1.09493			−0.0700958
$245$	−23.8217	−	3.72565i	−1.52191	−	0.238023i
$246$		0			0
$247$	10.4841	+	3.36158i	0.667084	+	0.213892i
$248$	−22.1084	−	10.0495i	−1.40388	−	0.638144i
$249$		0			0
$250$	−1.66213	−	12.1690i	−0.105123	−	0.769633i
$251$	9.26177	+	4.65143i	0.584598	+	0.293596i	0.716411	−	0.697679i	$-0.245784\pi$
$251$	9.26177	+	4.65143i	0.584598	+	0.293596i	−0.131813	+	0.991275i	$0.542080\pi$
$252$		0			0
$253$	−9.52903	−	6.26734i	−0.599085	−	0.394024i
$254$	−13.4509	+	1.04548i	−0.843982	+	0.0655995i
$255$		0			0
$256$	0.675766	+	1.97500i	0.0422354	+	0.123438i
$257$	−0.286832	+	14.7890i	−0.0178921	+	0.922511i	0.878109	+	0.478460i	$0.158805\pi$
$257$	−0.286832	+	14.7890i	−0.0178921	+	0.922511i	−0.896001	+	0.444051i	$0.853541\pi$
$258$		0			0
$259$	13.4970	+	9.64711i	0.838666	+	0.599442i
$260$	−0.521861	+	1.20981i	−0.0323644	+	0.0750292i
$261$		0			0
$262$	−6.00712	+	8.06896i	−0.371121	+	0.498502i
$263$	7.05248	+	6.39979i	0.434875	+	0.394628i	0.859825	−	0.510589i	$-0.170573\pi$
$263$	7.05248	+	6.39979i	0.434875	+	0.394628i	−0.424950	+	0.905217i	$0.639708\pi$
$264$		0			0
$265$	1.34231	+	0.104333i	0.0824575	+	0.00640911i
$266$	−8.70252	−	6.74496i	−0.533585	−	0.413560i
$267$		0			0
$268$	−0.351983	−	0.403328i	−0.0215008	−	0.0246372i
$269$	−3.46219	−	19.6350i	−0.211093	−	1.19717i	−0.887559	−	0.460695i	$-0.847600\pi$
$269$	−3.46219	−	19.6350i	−0.211093	−	1.19717i	0.676466	−	0.736474i	$-0.263511\pi$
$270$		0			0
$271$	−0.0871204	+	0.494084i	−0.00529218	+	0.0300135i	−0.987340	−	0.158621i	$-0.949295\pi$
$271$	−0.0871204	+	0.494084i	−0.00529218	+	0.0300135i	0.982047	+	0.188635i	$0.0604062\pi$
$272$	−18.5213	+	11.1777i	−1.12302	+	0.677746i
$273$		0			0
$274$	−25.2702	+	0.980599i	−1.52663	+	0.0592401i
$275$	5.24634	+	5.14558i	0.316367	+	0.310290i
$276$		0			0
$277$	−5.69828	+	9.04094i	−0.342377	+	0.543218i	−0.972388	−	0.233368i	$-0.925025\pi$
$277$	−5.69828	+	9.04094i	−0.342377	+	0.543218i	0.630012	+	0.776586i	$0.283050\pi$
$278$	2.96551	−	9.90550i	0.177860	−	0.594093i
$279$		0			0
$280$	−19.8493	+	21.0390i	−1.18622	+	1.25732i
$281$	9.08802	−	8.91347i	0.542146	−	0.531733i	−0.376707	−	0.926332i	$-0.622944\pi$
$281$	9.08802	−	8.91347i	0.542146	−	0.531733i	0.918853	+	0.394599i	$0.129117\pi$
$282$		0			0
$283$	5.05248	+	6.26409i	0.300339	+	0.372362i	0.905940	−	0.423407i	$-0.139166\pi$
$283$	5.05248	+	6.26409i	0.300339	+	0.372362i	−0.605601	+	0.795769i	$0.707067\pi$
$284$	−0.226335	+	0.586221i	−0.0134305	+	0.0347858i
$285$		0			0
$286$	8.97645	+	34.8487i	0.530788	+	2.06065i
$287$	−0.646233	−	0.153160i	−0.0381459	−	0.00904075i
$288$		0			0
$289$	−6.83179	−	7.24127i	−0.401870	−	0.425957i
$290$	−10.6076	−	0.411625i	−0.622902	−	0.0241714i
$291$		0			0
$292$	−0.597899	+	0.166437i	−0.0349894	+	0.00973996i
$293$	−9.78604	−	15.5266i	−0.571706	−	0.907074i	−0.999994	−	0.00343146i	$-0.998908\pi$
$293$	−9.78604	−	15.5266i	−0.571706	−	0.907074i	0.428288	−	0.903642i	$-0.359117\pi$
$294$		0			0
$295$	0.0710975	+	3.66577i	0.00413946	+	0.213429i
$296$	10.6708	−	3.88384i	0.620226	−	0.225744i
$297$		0			0
$298$	10.0536	+	3.65922i	0.582391	+	0.211973i
$299$	5.04252	−	14.7373i	0.291616	−	0.852281i
$300$		0			0
$301$	32.3861	−	13.2312i	1.86670	−	0.762633i
$302$	0.271911	+	0.568654i	0.0156467	+	0.0327223i
$303$		0			0
$304$	−7.48969	+	2.40147i	−0.429563	+	0.137734i
$305$	−32.3546	−	3.78172i	−1.85262	−	0.216540i
$306$		0			0
$307$	15.4229	+	20.7165i	0.880230	+	1.18235i	0.982251	+	0.187571i	$0.0600616\pi$
$307$	15.4229	+	20.7165i	0.880230	+	1.18235i	−0.102021	+	0.994782i	$0.532531\pi$
$308$	0.145460	−	1.49545i	0.00828833	−	0.0852114i
$309$		0			0
$310$	28.1789	+	17.0060i	1.60045	+	0.965878i
$311$	17.7903	−	20.3854i	1.00880	−	1.15595i	0.0210657	−	0.999778i	$-0.493294\pi$
$311$	17.7903	−	20.3854i	1.00880	−	1.15595i	0.987730	−	0.156173i	$-0.0499158\pi$
$312$		0			0
$313$	4.81270	−	10.0649i	0.272030	−	0.568902i	−0.720136	−	0.693833i	$-0.755920\pi$
$313$	4.81270	−	10.0649i	0.272030	−	0.568902i	0.992165	+	0.124931i	$0.0398711\pi$
$314$	−1.98384	+	34.0611i	−0.111954	+	1.92218i
$315$		0			0
$316$	−0.472583	+	0.310823i	−0.0265849	+	0.0174851i
$317$	−0.654151	+	0.507005i	−0.0367408	+	0.0284762i	−0.630805	−	0.775941i	$-0.717275\pi$
$317$	−0.654151	+	0.507005i	−0.0367408	+	0.0284762i	0.594065	+	0.804417i	$0.297522\pi$
$318$		0			0
$319$	−9.84814	+	7.03903i	−0.551390	+	0.394110i
$320$	4.18301	+	19.3109i	0.233837	+	1.07951i
$321$		0			0
$322$	−9.77938	+	12.1245i	−0.544984	+	0.675674i
$323$	−4.90023	−	8.48744i	−0.272656	−	0.472254i
$324$		0			0
$325$	−5.01790	+	8.69126i	−0.278343	+	0.482104i
$326$	2.00842	+	5.20194i	0.111236	+	0.288109i
$327$		0			0
$328$	−0.336638	+	0.305483i	−0.0185877	+	0.0168675i
$329$	0.340662	+	3.50231i	0.0187813	+	0.193089i
$330$		0			0
$331$	−3.82728	−	1.56362i	−0.210366	−	0.0859442i	0.270567	−	0.962701i	$-0.412789\pi$
$331$	−3.82728	−	1.56362i	−0.210366	−	0.0859442i	−0.480934	+	0.876757i	$0.659702\pi$
$332$	−0.0611953	−	1.05068i	−0.00335853	−	0.0576637i
$333$		0			0
$334$	−14.7766	+	7.42111i	−0.808542	+	0.406065i
$335$	−9.00789	−	13.1338i	−0.492153	−	0.717577i
$336$		0			0
$337$	1.28536	+	0.252437i	0.0700181	+	0.0137511i	0.227599	−	0.973755i	$-0.426913\pi$
$337$	1.28536	+	0.252437i	0.0700181	+	0.0137511i	−0.157580	+	0.987506i	$0.550369\pi$
$338$	−26.5862	+	14.6696i	−1.44610	+	0.797924i
$339$		0			0
$340$	1.06771	−	0.485334i	0.0579047	−	0.0263209i
$341$	37.2771	−	4.35707i	2.01867	−	0.235948i
$342$		0			0
$343$	3.67909	+	8.52909i	0.198652	+	0.460527i
$344$	5.06947	−	23.4033i	0.273327	−	1.26182i
$345$		0			0
$346$	15.3554	−	22.3887i	0.825512	−	1.20363i
$347$	0.597905	−	4.37744i	0.0320972	−	0.234993i	−0.967760	−	0.251873i	$-0.918954\pi$
$347$	0.597905	−	4.37744i	0.0320972	−	0.234993i	0.999858	+	0.0168798i	$0.00537325\pi$
$348$		0			0
$349$	−10.6851	+	2.09848i	−0.571959	+	0.112329i	−0.470326	−	0.882493i	$-0.655864\pi$
$349$	−10.6851	+	2.09848i	−0.571959	+	0.112329i	−0.101633	+	0.994822i	$0.532407\pi$
$350$	7.68827	−	6.45123i	0.410955	−	0.344833i
$351$		0			0
$352$	−1.61153	−	1.35224i	−0.0858950	−	0.0720745i
$353$	14.4213	+	7.95731i	0.767566	+	0.423525i	0.818012	−	0.575202i	$-0.195076\pi$
$353$	14.4213	+	7.95731i	0.767566	+	0.423525i	−0.0504455	+	0.998727i	$0.516064\pi$
$354$		0			0
$355$	−8.71277	+	16.5408i	−0.462426	+	0.877894i
$356$	0.317979	−	1.23447i	0.0168528	−	0.0654268i
$357$		0			0
$358$	13.9654	+	26.5127i	0.738095	+	1.40124i
$359$	11.4917	−	2.72359i	0.606510	−	0.143746i	0.0841249	−	0.996455i	$-0.473191\pi$
$359$	11.4917	−	2.72359i	0.606510	−	0.143746i	0.522385	+	0.852710i	$0.325042\pi$
$360$		0			0
$361$	4.42731	+	14.7882i	0.233016	+	0.778328i
$362$	19.8057	+	5.51331i	1.04097	+	0.289773i
$363$		0			0
$364$	2.02731	−	0.317066i	0.106260	−	0.0166188i
$365$	−18.2424	+	2.85306i	−0.954852	+	0.149336i
$366$		0			0
$367$	−9.68644	−	2.69640i	−0.505628	−	0.140751i	0.00595979	−	0.999982i	$-0.498103\pi$
$367$	−9.68644	−	2.69640i	−0.505628	−	0.140751i	−0.511588	+	0.859231i	$0.670942\pi$
$368$	3.19138	+	10.6599i	0.166362	+	0.555688i
$369$		0			0
$370$	−14.9749	+	3.54913i	−0.778510	+	0.184510i
$371$	−0.977202	−	1.85517i	−0.0507338	−	0.0963157i
$372$		0			0
$373$	8.68752	−	33.7270i	0.449823	−	1.74632i	−0.193863	−	0.981029i	$-0.562102\pi$
$373$	8.68752	−	33.7270i	0.449823	−	1.74632i	0.643686	−	0.765290i	$-0.277404\pi$
$374$	14.9290	−	28.3419i	0.771959	−	1.46553i
$375$		0			0
$376$	2.10883	+	1.16360i	0.108754	+	0.0600081i
$377$	−12.6641	−	10.6264i	−0.652233	−	0.547289i
$378$		0			0
$379$	14.1218	−	11.8496i	0.725389	−	0.608674i	−0.203481	−	0.979079i	$-0.565225\pi$
$379$	14.1218	−	11.8496i	0.725389	−	0.608674i	0.928870	+	0.370405i	$0.120781\pi$
$380$	0.418429	−	0.0821768i	0.0214650	−	0.00421558i
$381$		0			0
$382$	3.39663	−	24.8678i	0.173787	−	1.27235i
$383$	−0.241274	+	0.351786i	−0.0123285	+	0.0179754i	−0.830790	−	0.556586i	$-0.812111\pi$
$383$	−0.241274	+	0.351786i	−0.0123285	+	0.0179754i	0.818462	+	0.574561i	$0.194827\pi$
$384$		0			0
$385$	9.46330	−	43.6875i	0.482295	−	2.22652i
$386$	−10.9741	−	25.4408i	−0.558567	−	1.29490i
$387$		0			0
$388$	−0.430927	+	0.0503681i	−0.0218770	+	0.00255705i
$389$	−10.1490	+	4.61327i	−0.514573	+	0.233902i	−0.654227	−	0.756298i	$-0.727006\pi$
$389$	−10.1490	+	4.61327i	−0.514573	+	0.233902i	0.139654	+	0.990200i	$0.455401\pi$
$390$		0			0
$391$	−12.1398	+	6.69845i	−0.613935	+	0.338755i
$392$	25.2206	+	4.95317i	1.27383	+	0.250173i
$393$		0			0
$394$	6.77790	+	9.88241i	0.341465	+	0.497869i
$395$	−15.0381	+	7.55241i	−0.756649	+	0.380003i
$396$		0			0
$397$	−1.72104	−	29.5492i	−0.0863767	−	1.48303i	−0.711600	−	0.702585i	$-0.752029\pi$
$397$	−1.72104	−	29.5492i	−0.0863767	−	1.48303i	0.625223	−	0.780446i	$-0.285008\pi$
$398$	−8.80895	−	3.59885i	−0.441553	−	0.180394i
$399$		0			0
$400$	−0.694082	−	7.13579i	−0.0347041	−	0.356790i
$401$	4.86434	−	4.41415i	0.242913	−	0.220432i	−0.541451	−	0.840732i	$-0.682125\pi$
$401$	4.86434	−	4.41415i	0.242913	−	0.220432i	0.784365	+	0.620300i	$0.212989\pi$
$402$		0			0
$403$	18.4610	+	47.8153i	0.919610	+	2.38185i
$404$	−0.374032	+	0.647842i	−0.0186088	+	0.0322314i
$405$		0			0
$406$	8.26632	+	14.3177i	0.410251	+	0.710575i
$407$	−11.0176	+	13.6596i	−0.546120	+	0.677083i
$408$		0			0
$409$	3.19896	+	14.7681i	0.158179	+	0.730233i	0.985660	+	0.168741i	$0.0539701\pi$
$409$	3.19896	+	14.7681i	0.158179	+	0.730233i	−0.827482	+	0.561492i	$0.810227\pi$
$410$	0.501211	−	0.358244i	0.0247531	−	0.0176924i
$411$		0			0
$412$	−0.431467	+	0.334412i	−0.0212568	+	0.0164753i
$413$	4.77071	−	3.13775i	0.234752	−	0.154399i
$414$		0			0
$415$	1.82060	−	31.2584i	0.0893696	−	1.53442i
$416$	1.23937	−	2.59193i	0.0607653	−	0.127080i
$417$		0			0
$418$	7.65798	−	8.77507i	0.374564	−	0.429203i
$419$	−15.6627	−	9.45247i	−0.765172	−	0.461783i	0.0796557	−	0.996822i	$-0.474618\pi$
$419$	−15.6627	−	9.45247i	−0.765172	−	0.461783i	−0.844827	+	0.535039i	$0.820297\pi$
$420$		0			0
$421$	2.25763	−	23.2105i	0.110030	−	1.13121i	−0.763959	−	0.645265i	$-0.776747\pi$
$421$	2.25763	−	23.2105i	0.110030	−	1.13121i	0.873989	−	0.485946i	$-0.161525\pi$
$422$	−14.6050	−	19.6179i	−0.710959	−	0.954983i
$423$		0			0
$424$	−1.42550	−	0.166617i	−0.0692285	−	0.00809165i
$425$	8.50685	−	2.72761i	0.412643	−	0.132309i
$426$		0			0
$427$	21.8850	+	45.7685i	1.05909	+	2.21489i
$428$	1.03961	−	0.424729i	0.0502516	−	0.0205300i
$429$		0			0
$430$	−10.5062	+	30.7054i	−0.506653	+	1.48075i
$431$	−11.7354	−	4.27132i	−0.565272	−	0.205742i	0.0435468	−	0.999051i	$-0.486134\pi$
$431$	−11.7354	−	4.27132i	−0.565272	−	0.205742i	−0.608819	+	0.793309i	$0.708356\pi$
$432$		0			0
$433$	−5.10749	+	1.85898i	−0.245450	+	0.0893367i	−0.461816	−	0.886976i	$-0.652802\pi$
$433$	−5.10749	+	1.85898i	−0.245450	+	0.0893367i	0.216365	+	0.976312i	$0.430580\pi$
$434$	−0.993962	−	51.2484i	−0.0477117	−	2.46000i
$435$		0			0
$436$	0.395447	+	0.627419i	0.0189385	+	0.0300479i
$437$	−4.85647	+	1.35189i	−0.232316	+	0.0646696i
$438$		0			0
$439$	−26.4075	−	1.02473i	−1.26036	−	0.0489077i	−0.600088	−	0.799934i	$-0.704868\pi$
$439$	−26.4075	−	1.02473i	−1.26036	−	0.0489077i	−0.660272	+	0.751026i	$0.729559\pi$
$440$	−20.9965	−	22.2550i	−1.00097	−	1.06097i
$441$		0			0
$442$	42.5684	+	10.0889i	2.02477	+	0.479879i
$443$	−3.37218	−	13.0916i	−0.160217	−	0.622001i	−0.997201	−	0.0747730i	$-0.976177\pi$
$443$	−3.37218	−	13.0916i	−0.160217	−	0.622001i	0.836983	−	0.547228i	$-0.184317\pi$
$444$		0			0
$445$	13.6598	−	35.3797i	0.647535	−	1.67716i
$446$	13.6177	+	16.8833i	0.644817	+	0.799447i
$447$		0			0
$448$	21.9691	−	21.5471i	1.03794	−	1.01801i
$449$	−20.6707	+	21.9097i	−0.975512	+	1.03398i	0.0239009	+	0.999714i	$0.492391\pi$
$449$	−20.6707	+	21.9097i	−0.975512	+	1.03398i	−0.999413	+	0.0342677i	$0.989090\pi$
$450$		0			0
$451$	0.201485	−	0.673007i	0.00948756	−	0.0316907i
$452$	−0.247176	+	0.392171i	−0.0116262	+	0.0184462i
$453$		0			0
$454$	−0.757033	−	0.742492i	−0.0355293	−	0.0348469i
$455$	61.0011	−	2.36712i	2.85978	−	0.110972i
$456$		0			0
$457$	−17.4157	+	10.5104i	−0.814671	+	0.491656i	−0.861810	−	0.507232i	$-0.830669\pi$
$457$	−17.4157	+	10.5104i	−0.814671	+	0.491656i	0.0471387	+	0.998888i	$0.484990\pi$
$458$	−3.45738	+	19.6078i	−0.161553	+	0.916212i
$459$		0			0
$460$	−0.104759	−	0.594116i	−0.00488440	−	0.0277008i
$461$	7.43226	+	8.51643i	0.346155	+	0.396650i	0.899943	−	0.436008i	$-0.143608\pi$
$461$	7.43226	+	8.51643i	0.346155	+	0.396650i	−0.553788	+	0.832658i	$0.686818\pi$
$462$		0			0
$463$	5.59978	+	4.34016i	0.260244	+	0.201704i	0.734364	−	0.678756i	$-0.237481\pi$
$463$	5.59978	+	4.34016i	0.260244	+	0.201704i	−0.474120	+	0.880460i	$0.657234\pi$
$464$	11.7746	+	0.915195i	0.546623	+	0.0424869i
$465$		0			0
$466$	−6.83120	−	6.19898i	−0.316449	−	0.287162i
$467$	−17.0911	+	22.9574i	−0.790884	+	1.06234i	0.205606	+	0.978635i	$0.434083\pi$
$467$	−17.0911	+	22.9574i	−0.790884	+	1.06234i	−0.996490	+	0.0837069i	$0.973324\pi$
$468$		0			0
$469$	−9.82398	+	22.7745i	−0.453629	+	1.05163i
$470$	−2.65561	−	1.89811i	−0.122494	−	0.0875534i
$471$		0			0
$472$	0.0757892	−	3.90767i	0.00348848	−	0.179865i
$473$	11.9803	+	35.0138i	0.550855	+	1.60993i
$474$		0			0
$475$	3.23826	−	0.251698i	0.148582	−	0.0115487i
$476$	−1.52607	−	1.00372i	−0.0699475	−	0.0460052i
$477$		0			0
$478$	21.0725	+	10.5830i	0.963835	+	0.484056i
$479$	−0.203219	−	1.48783i	−0.00928532	−	0.0679806i	0.985575	−	0.169242i	$-0.0541319\pi$
$479$	−0.203219	−	1.48783i	−0.00928532	−	0.0679806i	−0.994860	+	0.101261i	$0.967712\pi$
$480$		0			0
$481$	−21.8183	−	9.91764i	−0.994829	−	0.452205i
$482$	30.9691	+	9.92985i	1.41061	+	0.452292i
$483$		0			0
$484$	0.623253	+	0.0974749i	0.0283297	+	0.00443068i
$485$	−12.9076			−0.586104
$486$		0			0
$487$	−24.2567			−1.09918			−0.549589	−	0.835435i	$-0.685216\pi$
$487$	−24.2567			−1.09918			−0.549589	+	0.835435i	$0.685216\pi$
$488$	34.3075	+	5.36559i	1.55303	+	0.242889i
$489$		0			0
$490$	−33.1701	−	10.6355i	−1.49847	−	0.480465i
$491$	21.0976	+	9.59006i	0.952123	+	0.432793i	0.828782	−	0.559571i	$-0.189034\pi$
$491$	21.0976	+	9.59006i	0.952123	+	0.432793i	0.123341	+	0.992364i	$0.460639\pi$
$492$		0			0
$493$	1.99152	+	14.5805i	0.0896936	+	0.656673i
$494$	14.2139	+	7.13850i	0.639514	+	0.321176i
$495$		0			0
$496$	−30.5924	−	20.1210i	−1.37364	−	0.903458i
$497$	29.0281	−	2.25624i	1.30209	−	0.101206i
$498$		0			0
$499$	−13.9760	−	40.8465i	−0.625653	−	1.82854i	−0.556357	−	0.830944i	$-0.687801\pi$
$499$	−13.9760	−	40.8465i	−0.625653	−	1.82854i	−0.0692963	−	0.997596i	$-0.522075\pi$
$500$	0.0143651	−	0.740663i	0.000642428	−	0.0331234i
$501$		0			0
$502$	12.1814	+	8.70672i	0.543681	+	0.388600i
$503$	6.42105	−	14.8857i	0.286300	−	0.663719i	−0.712998	−	0.701166i	$-0.752663\pi$
$503$	6.42105	−	14.8857i	0.286300	−	0.663719i	0.999299	+	0.0374470i	$0.0119225\pi$
$504$		0			0
$505$	−13.2900	+	17.8515i	−0.591396	+	0.794383i
$506$	−12.2021	−	11.0728i	−0.542450	−	0.492247i
$507$		0			0
$508$	−0.811306	−	0.0630597i	−0.0359959	−	0.00279782i
$509$	−4.27840	−	3.31601i	−0.189637	−	0.146980i	0.513358	−	0.858174i	$-0.328401\pi$
$509$	−4.27840	−	3.31601i	−0.189637	−	0.146980i	−0.702995	+	0.711195i	$0.748154\pi$
$510$		0			0
$511$	18.9076	+	21.6657i	0.836423	+	0.958435i
$512$	−3.64258	−	20.6581i	−0.160981	−	0.912968i
$513$		0			0
$514$	−3.71079	+	21.0449i	−0.163676	+	0.928251i
$515$	−13.9046	+	8.39147i	−0.612710	+	0.369772i
$516$		0			0
$517$	−3.71942	+	0.144330i	−0.163580	+	0.00634764i
$518$	17.1114	+	16.7827i	0.751830	+	0.737390i
$519$		0			0
$520$	22.2800	−	35.3496i	0.977042	−	1.55018i
$521$	−7.91109	+	26.4249i	−0.346591	+	1.15770i	0.590039	+	0.807375i	$0.299112\pi$
$521$	−7.91109	+	26.4249i	−0.346591	+	1.15770i	−0.936630	+	0.350320i	$0.886073\pi$
$522$		0			0
$523$	18.5289	−	19.6395i	0.810212	−	0.858774i	−0.182005	−	0.983298i	$-0.558259\pi$
$523$	18.5289	−	19.6395i	0.810212	−	0.858774i	0.992217	+	0.124523i	$0.0397402\pi$
$524$	−0.433178	+	0.424858i	−0.0189235	+	0.0185600i
$525$		0			0
$526$	8.63767	+	10.7090i	0.376620	+	0.466936i
$527$	16.4332	−	42.5631i	0.715843	−	1.85408i
$528$		0			0
$529$	−3.95815	−	15.3665i	−0.172094	−	0.668108i
$530$	1.89265	+	0.448566i	0.0822113	+	0.0194844i
$531$		0			0
$532$	−0.455736	−	0.483052i	−0.0197587	−	0.0209430i
$533$	0.958700	+	0.0372019i	0.0415259	+	0.00161139i
$534$		0			0
$535$	32.1869	−	8.95984i	1.39156	−	0.387368i
$536$	9.05222	+	14.3623i	0.390996	+	0.620358i
$537$		0			0
$538$	−0.558552	−	28.7988i	−0.0240809	−	1.24160i
$539$	−37.3255	+	13.5854i	−1.60772	+	0.585163i
$540$		0			0
$541$	41.1927	+	14.9929i	1.77101	+	0.644595i	0.999969	+	0.00781121i	$0.00248641\pi$
$541$	41.1927	+	14.9929i	1.77101	+	0.644595i	0.771042	+	0.636784i	$0.219736\pi$
$542$	−0.234646	+	0.685779i	−0.0100789	+	0.0294567i
$543$		0			0
$544$	−2.36747	+	0.967218i	−0.101504	+	0.0414691i
$545$	9.51824	+	19.9057i	0.407716	+	0.852667i
$546$		0			0
$547$	−22.4779	+	7.20725i	−0.961085	+	0.308160i	−0.744140	−	0.668024i	$-0.767140\pi$
$547$	−22.4779	+	7.20725i	−0.961085	+	0.308160i	−0.216946	+	0.976184i	$0.569609\pi$
$548$	−1.51504	−	0.177083i	−0.0647192	−	0.00756459i
$549$		0			0
$550$	6.33967	+	8.51566i	0.270324	+	0.363109i
$551$	−0.517978	+	5.32528i	−0.0220666	+	0.226865i
$552$		0			0
$553$	22.4382	+	13.5415i	0.954171	+	0.575845i
$554$	−10.1516	+	11.6325i	−0.431301	+	0.494217i
$555$		0			0
$556$	0.269040	−	0.562649i	0.0114098	−	0.0238616i
$557$	0.488333	−	8.38435i	0.0206913	−	0.355256i	−0.972033	−	0.234845i	$-0.924542\pi$
$557$	0.488333	−	8.38435i	0.0206913	−	0.355256i	0.992724	−	0.120411i	$-0.0384213\pi$
$558$		0			0
$559$	−42.2251	+	27.7719i	−1.78593	+	1.17462i
$560$	−34.4701	+	26.7163i	−1.45663	+	1.12897i
$561$		0			0
$562$	14.9615	−	10.6938i	0.631112	−	0.451092i
$563$	−7.77317	−	35.8849i	−0.327600	−	1.51237i	−0.782966	−	0.622065i	$-0.786294\pi$
$563$	−7.77317	−	35.8849i	−0.327600	−	1.51237i	0.455366	−	0.890304i	$-0.349509\pi$
$564$		0			0
$565$	−8.65840	+	10.7347i	−0.364262	+	0.451613i
$566$	5.81327	+	10.0689i	0.244350	+	0.423227i
$567$		0			0
$568$	9.96444	−	17.2589i	0.418099	−	0.724168i
$569$	−0.125956	−	0.326234i	−0.00528034	−	0.0136764i	0.930218	−	0.367006i	$-0.119617\pi$
$569$	−0.125956	−	0.326234i	−0.00528034	−	0.0136764i	−0.935499	+	0.353330i	$0.885049\pi$
$570$		0			0
$571$	10.1877	−	9.24481i	0.426340	−	0.386883i	−0.430394	−	0.902641i	$-0.641625\pi$
$571$	10.1877	−	9.24481i	0.426340	−	0.386883i	0.856734	+	0.515758i	$0.172490\pi$
$572$	0.210133	+	2.16036i	0.00878612	+	0.0903292i
$573$		0			0
$574$	−0.888206	−	0.362872i	−0.0370730	−	0.0151460i
$575$	−0.267184	−	4.58738i	−0.0111424	−	0.191307i
$576$		0			0
$577$	−15.8617	+	7.96602i	−0.660329	+	0.331630i	−0.747209	−	0.664589i	$-0.768607\pi$
$577$	−15.8617	+	7.96602i	−0.660329	+	0.331630i	0.0868797	+	0.996219i	$0.472310\pi$
$578$	−8.13481	−	11.8609i	−0.338364	−	0.493346i
$579$		0			0
$580$	−0.628293	−	0.123393i	−0.0260885	−	0.00512361i
$581$	−42.6957	+	23.5585i	−1.77132	+	0.977371i
$582$		0			0
$583$	2.01918	−	0.917829i	0.0836258	−	0.0380126i
$584$	19.5495	−	2.28501i	0.808966	−	0.0945546i
$585$		0			0
$586$	−10.5020	−	24.3463i	−0.433833	−	1.00574i
$587$	−1.56855	+	7.24124i	−0.0647411	+	0.298878i	−0.998212	−	0.0597754i	$-0.980962\pi$
$587$	−1.56855	+	7.24124i	−0.0647411	+	0.298878i	0.933471	+	0.358653i	$0.116764\pi$
$588$		0			0
$589$	9.38257	−	13.6801i	0.386602	−	0.563679i
$590$	−0.716837	+	5.24818i	−0.0295117	+	0.216064i
$591$		0			0
$592$	16.8005	−	3.29952i	0.690498	−	0.135609i
$593$	−3.70773	+	3.11116i	−0.152258	+	0.127760i	−0.715735	−	0.698372i	$-0.753908\pi$
$593$	−3.70773	+	3.11116i	−0.152258	+	0.127760i	0.563476	+	0.826132i	$0.309464\pi$
$594$		0			0
$595$	−41.6280	−	34.9300i	−1.70658	−	1.43199i
$596$	0.565011	+	0.311760i	0.0231437	+	0.0127702i
$597$		0			0
$598$	10.4872	−	19.9095i	0.428855	−	0.814161i
$599$	0.561418	−	2.17956i	0.0229389	−	0.0890543i	−0.955896	−	0.293704i	$-0.905112\pi$
$599$	0.561418	−	2.17956i	0.0229389	−	0.0890543i	0.978835	+	0.204650i	$0.0656057\pi$
$600$		0			0
$601$	8.02472	+	15.2346i	0.327335	+	0.621431i	0.992075	−	0.125644i	$-0.0400997\pi$
$601$	8.02472	+	15.2346i	0.327335	+	0.621431i	−0.664740	+	0.747075i	$0.731458\pi$
$602$	49.1797	−	11.6558i	2.00441	−	0.475055i
$603$		0			0
$604$	0.0109038	+	0.0364213i	0.000443671	+	0.00148196i
$605$	18.0801	+	5.03294i	0.735061	+	0.204618i
$606$		0			0
$607$	1.60508	−	0.251030i	0.0651481	−	0.0101890i	−0.121861	−	0.992547i	$-0.538886\pi$
$607$	1.60508	−	0.251030i	0.0651481	−	0.0101890i	0.187009	+	0.982358i	$0.440121\pi$
$608$	−0.918663	+	0.143676i	−0.0372567	+	0.00582684i
$609$		0			0
$610$	−45.3369	−	12.6204i	−1.83564	−	0.510985i
$611$	−1.45793	−	4.86982i	−0.0589815	−	0.197012i
$612$		0			0
$613$	−37.9516	+	8.99470i	−1.53285	+	0.363293i	−0.908511	−	0.417860i	$-0.862780\pi$
$613$	−37.9516	+	8.99470i	−1.53285	+	0.363293i	−0.624340	+	0.781152i	$0.714632\pi$
$614$	17.3891	+	33.0124i	0.701768	+	1.33227i
$615$		0			0
$616$	−11.8860	+	46.1442i	−0.478900	+	1.85920i
$617$	−1.01984	+	1.93611i	−0.0410571	+	0.0779450i	−0.904432	−	0.426619i	$-0.859705\pi$
$617$	−1.01984	+	1.93611i	−0.0410571	+	0.0779450i	0.863374	+	0.504564i	$0.168347\pi$
$618$		0			0
$619$	−24.7837	−	13.6751i	−0.996143	−	0.549648i	−0.100744	−	0.994912i	$-0.532122\pi$
$619$	−24.7837	−	13.6751i	−0.996143	−	0.549648i	−0.895399	+	0.445264i	$0.853110\pi$
$620$	1.52074	+	1.27605i	0.0610742	+	0.0512474i
$621$		0			0
$622$	29.9435	−	25.1256i	1.20063	−	1.00745i
$623$	−57.9568	+	11.3824i	−2.32199	+	0.456024i
$624$		0			0
$625$	4.14691	−	30.3607i	0.165876	−	1.21443i
$626$	9.11618	−	13.2917i	0.364356	−	0.531244i
$627$		0			0
$628$	−0.435670	+	2.01128i	−0.0173851	+	0.0802587i
$629$	8.44999	+	19.5893i	0.336923	+	0.781075i
$630$		0			0
$631$	−7.22698	+	0.844713i	−0.287702	+	0.0336275i	−0.258720	−	0.965952i	$-0.583301\pi$
$631$	−7.22698	+	0.844713i	−0.287702	+	0.0336275i	−0.0289820	+	0.999580i	$0.509227\pi$
$632$	16.3306	−	7.42315i	0.649595	−	0.295277i
$633$		0			0
$634$	−1.04688	+	0.577642i	−0.0415768	+	0.0229411i
$635$	−23.7558	−	4.66549i	−0.942722	−	0.185145i
$636$		0			0
$637$	−30.6821	−	44.7356i	−1.21567	−	1.77249i
$638$	−15.6280	+	7.84868i	−0.618719	+	0.310732i
$639$		0			0
$640$	1.80827	+	31.0467i	0.0714780	+	1.22723i
$641$	−19.9526	−	8.15152i	−0.788079	−	0.321966i	−0.0518117	−	0.998657i	$-0.516500\pi$
$641$	−19.9526	−	8.15152i	−0.788079	−	0.321966i	−0.736267	+	0.676691i	$0.763413\pi$
$642$		0			0
$643$	−2.88173	−	29.6268i	−0.113645	−	1.16837i	−0.862649	−	0.505803i	$-0.831196\pi$
$643$	−2.88173	−	29.6268i	−0.113645	−	1.16837i	0.749004	−	0.662565i	$-0.230532\pi$
$644$	−0.695772	+	0.631380i	−0.0274173	+	0.0248798i
$645$		0			0
$646$	−5.09963	−	13.2084i	−0.200642	−	0.519676i
$647$	−0.642151	+	1.11224i	−0.0252456	+	0.0437266i	−0.878372	−	0.477977i	$-0.841370\pi$
$647$	−0.642151	+	1.11224i	−0.0252456	+	0.0437266i	0.853127	+	0.521704i	$0.174703\pi$
$648$		0			0
$649$	3.02006	+	5.23090i	0.118548	+	0.205331i
$650$	−9.10243	+	11.2852i	−0.357027	+	0.442644i
$651$		0			0
$652$	0.0712035	+	0.328712i	0.00278854	+	0.0128734i
$653$	23.0583	−	16.4811i	0.902340	−	0.644954i	−0.0327117	−	0.999465i	$-0.510414\pi$
$653$	23.0583	−	16.4811i	0.902340	−	0.644954i	0.935052	+	0.354511i	$0.115353\pi$
$654$		0			0
$655$	−14.2676	+	11.0582i	−0.557480	+	0.432080i
$656$	−0.572643	+	0.376634i	−0.0223580	+	0.0147051i
$657$		0			0
$658$	−0.295588	+	5.07504i	−0.0115232	+	0.197846i
$659$	13.1179	−	27.4337i	0.511000	−	1.06867i	−0.471407	−	0.881916i	$-0.656254\pi$
$659$	13.1179	−	27.4337i	0.511000	−	1.06867i	0.982407	−	0.186750i	$-0.0597955\pi$
$660$		0			0
$661$	−19.2165	+	22.0197i	−0.747435	+	0.856466i	−0.993623	−	0.112757i	$-0.964032\pi$
$661$	−19.2165	+	22.0197i	−0.747435	+	0.856466i	0.246188	+	0.969222i	$0.420822\pi$
$662$	−5.11379	−	3.08619i	−0.198753	−	0.119948i
$663$		0			0
$664$	−3.23132	+	33.2209i	−0.125400	+	1.28922i
$665$	−11.7984	−	15.8480i	−0.457521	−	0.614558i
$666$		0			0
$667$	7.51832	+	0.878765i	0.291110	+	0.0340259i
$668$	−0.949733	+	0.304520i	−0.0367463	+	0.0117822i
$669$		0			0
$670$	−9.92545	−	20.7573i	−0.383453	−	0.801925i
$671$	−49.6779	+	20.2957i	−1.91780	+	0.783506i
$672$		0			0
$673$	−0.0134951	+	0.0394410i	−0.000520198	+	0.00152034i	−0.946408	−	0.322974i	$-0.895317\pi$
$673$	−0.0134951	+	0.0394410i	−0.000520198	+	0.00152034i	0.945888	+	0.324494i	$0.105194\pi$
$674$	1.77830	+	0.647248i	0.0684975	+	0.0249311i
$675$		0			0
$676$	−1.72104	+	0.626408i	−0.0661940	+	0.0240926i
$677$	0.248121	+	12.7931i	0.00953607	+	0.491677i	0.973885	+	0.227043i	$0.0729057\pi$
$677$	0.248121	+	12.7931i	0.00953607	+	0.491677i	−0.964349	+	0.264635i	$0.914749\pi$
$678$		0			0
$679$	10.7186	+	17.0061i	0.411340	+	0.652636i
$680$	−35.8329	+	9.97476i	−1.37413	+	0.382514i
$681$		0			0
$682$	54.1798	+	2.10242i	2.07465	+	0.0805060i
$683$	15.5185	+	16.4486i	0.593797	+	0.629388i	0.952673	−	0.303997i	$-0.0983213\pi$
$683$	15.5185	+	16.4486i	0.593797	+	0.629388i	−0.358876	+	0.933385i	$0.616840\pi$
$684$		0			0
$685$	−44.1569	−	10.4654i	−1.68715	−	0.399862i
$686$	3.34735	+	12.9952i	0.127802	+	0.496160i
$687$		0			0
$688$	13.0041	−	33.6816i	0.495778	−	1.28410i
$689$	1.90169	+	2.35773i	0.0724487	+	0.0898223i
$690$		0			0
$691$	−36.6418	+	35.9380i	−1.39392	+	1.36715i	−0.545199	+	0.838307i	$0.683546\pi$
$691$	−36.6418	+	35.9380i	−1.39392	+	1.36715i	−0.848721	+	0.528841i	$0.822627\pi$
$692$	1.12372	−	1.19107i	0.0427175	−	0.0452779i
$693$		0			0
$694$	1.83060	−	6.11463i	0.0694886	−	0.232108i
$695$	9.89327	−	15.6967i	0.375273	−	0.595412i
$696$		0			0
$697$	−0.609722	−	0.598011i	−0.0230949	−	0.0226513i
$698$	−15.7197	+	0.609996i	−0.595000	+	0.0230887i
$699$		0			0
$700$	0.518284	−	0.312786i	0.0195893	−	0.0118222i
$701$	3.96552	−	22.4896i	0.149776	−	0.849420i	−0.813632	−	0.581380i	$-0.802513\pi$
$701$	3.96552	−	22.4896i	0.149776	−	0.849420i	0.963408	−	0.268040i	$-0.0863760\pi$
$702$		0			0
$703$	1.34693	+	7.63881i	0.0508004	+	0.288103i
$704$	21.4027	+	24.5248i	0.806645	+	0.924313i
$705$		0			0
$706$	18.8077	+	14.5771i	0.707839	+	0.548616i
$707$	34.5560	+	2.68590i	1.29961	+	0.101014i
$708$		0			0
$709$	21.7848	+	19.7687i	0.818146	+	0.742428i	0.969247	−	0.246090i	$-0.0791459\pi$
$709$	21.7848	+	19.7687i	0.818146	+	0.742428i	−0.151101	+	0.988518i	$0.548282\pi$
$710$	−16.1285	+	21.6644i	−0.605294	+	0.813050i
$711$		0			0
$712$	−16.0126	+	37.1214i	−0.600097	+	1.39118i
$713$	−19.0929	−	13.6468i	−0.715035	−	0.511077i
$714$		0			0
$715$	−1.25220	+	64.5632i	−0.0468297	+	2.41453i
$716$	0.585127	+	1.71010i	0.0218672	+	0.0639094i
$717$		0			0
$718$	17.0106	−	1.32217i	0.634831	−	0.0493429i
$719$	17.0566	+	11.2183i	0.636104	+	0.418372i	0.826187	−	0.563396i	$-0.190505\pi$
$719$	17.0566	+	11.2183i	0.636104	+	0.418372i	−0.190083	+	0.981768i	$0.560876\pi$
$720$		0			0
$721$	22.6025	+	11.3514i	0.841760	+	0.422748i
$722$	3.01807	+	22.0962i	0.112321	+	0.822335i
$723$		0			0
$724$	1.12888	+	0.513138i	0.0419544	+	0.0190706i
$725$	−4.64419	−	1.48910i	−0.172481	−	0.0553038i
$726$		0			0
$727$	33.6916	+	5.26926i	1.24955	+	0.195426i	0.744476	−	0.667649i	$-0.232699\pi$
$727$	33.6916	+	5.26926i	1.24955	+	0.195426i	0.505075	+	0.863076i	$0.331465\pi$
$728$	−65.0755			−2.41186
$729$		0			0
$730$	−26.6751			−0.987289
$731$	44.4477	+	6.95150i	1.64396	+	0.257110i
$732$		0			0
$733$	−12.2798	−	3.93736i	−0.453564	−	0.145430i	0.0697588	−	0.997564i	$-0.477777\pi$
$733$	−12.2798	−	3.93736i	−0.453564	−	0.145430i	−0.523323	+	0.852134i	$0.675308\pi$
$734$	−13.2239	−	6.01102i	−0.488104	−	0.221871i
$735$		0			0
$736$	0.178025	+	1.30338i	0.00656210	+	0.0480431i
$737$	−23.4459	−	11.7750i	−0.863639	−	0.433736i
$738$		0			0
$739$	16.1684	+	10.6341i	0.594765	+	0.391183i	0.810904	−	0.585180i	$-0.198976\pi$
$739$	16.1684	+	10.6341i	0.594765	+	0.391183i	−0.216139	+	0.976363i	$0.569346\pi$
$740$	−0.925463	+	0.0719327i	−0.0340207	+	0.00264430i
$741$		0			0
$742$	−0.980667	−	2.86611i	−0.0360014	−	0.105218i
$743$	0.678395	−	34.9779i	0.0248879	−	1.28321i	−0.754344	−	0.656479i	$-0.772045\pi$
$743$	0.678395	−	34.9779i	0.0248879	−	1.28321i	0.779232	−	0.626735i	$-0.215609\pi$
$744$		0			0
$745$	15.6190	+	11.1638i	0.572236	+	0.409009i
$746$	19.9290	−	46.2007i	0.729653	−	1.69153i
$747$		0			0
$748$	1.15379	−	1.54981i	0.0421868	−	0.0566667i
$749$	−38.5331	−	34.9669i	−1.40797	−	1.27766i
$750$		0			0
$751$	1.94211	+	0.150953i	0.0708688	+	0.00550836i	0.112878	−	0.993609i	$-0.463993\pi$
$751$	1.94211	+	0.150953i	0.0708688	+	0.00550836i	−0.0420091	+	0.999117i	$0.513376\pi$
$752$	2.87032	+	2.22466i	0.104670	+	0.0811252i
$753$		0			0
$754$	−15.7038	−	17.9946i	−0.571899	−	0.655324i
$755$	0.196409	+	1.11389i	0.00714805	+	0.0405386i
$756$		0			0
$757$	1.30319	−	7.39078i	0.0473654	−	0.268623i	−0.951923	−	0.306337i	$-0.900897\pi$
$757$	1.30319	−	7.39078i	0.0473654	−	0.268623i	0.999289	+	0.0377143i	$0.0120077\pi$
$758$	22.8019	−	13.7610i	0.828202	−	0.499823i
$759$		0			0
$760$	−13.5133	+	0.524378i	−0.490180	+	0.0190212i
$761$	−34.5772	−	33.9130i	−1.25342	−	1.22935i	−0.962092	−	0.272724i	$-0.912075\pi$
$761$	−34.5772	−	33.9130i	−1.25342	−	1.22935i	−0.291329	−	0.956623i	$-0.594097\pi$
$762$		0			0
$763$	18.3223	−	29.0704i	0.663313	−	1.05242i
$764$	0.434179	−	1.45026i	0.0157081	−	0.0524686i
$765$		0			0
$766$	−0.422910	+	0.448258i	−0.0152804	+	0.0161962i
$767$	−5.88914	+	5.77603i	−0.212644	+	0.208560i
$768$		0			0
$769$	−21.1891	−	26.2704i	−0.764099	−	0.947334i	0.235600	−	0.971850i	$-0.424294\pi$
$769$	−21.1891	−	26.2704i	−0.764099	−	0.947334i	−0.999699	+	0.0245156i	$0.992196\pi$
$770$	23.2598	−	60.2445i	0.838226	−	2.17106i
$771$		0			0
$772$	−0.416859	−	1.61835i	−0.0150031	−	0.0582455i
$773$	7.61840	+	1.80559i	0.274015	+	0.0649427i	0.365326	−	0.930880i	$-0.380958\pi$
$773$	7.61840	+	1.80559i	0.274015	+	0.0649427i	−0.0913109	+	0.995822i	$0.529106\pi$
$774$		0			0
$775$	10.3766	+	10.9986i	0.372740	+	0.395081i
$776$	13.7490	+	0.533525i	0.493561	+	0.0191524i
$777$		0			0
$778$	−15.5159	+	4.31914i	−0.556271	+	0.154849i
$779$	−0.165566	−	0.262688i	−0.00593201	−	0.00941178i
$780$		0			0
$781$	0.597223	+	30.7927i	0.0213703	+	1.10185i
$782$	−18.8229	+	6.85099i	−0.673107	+	0.244991i
$783$		0			0
$784$	36.4159	+	13.2543i	1.30057	+	0.473368i
$785$	−19.8204	+	57.9274i	−0.707422	+	2.06752i
$786$		0			0
$787$	−7.98583	+	3.26257i	−0.284664	+	0.116298i	−0.516035	−	0.856568i	$-0.672593\pi$
$787$	−7.98583	+	3.26257i	−0.284664	+	0.116298i	0.231371	+	0.972866i	$0.425679\pi$
$788$	0.311803	+	0.652082i	0.0111075	+	0.0232294i
$789$		0			0
$790$	−23.1504	+	7.42289i	−0.823656	+	0.264095i
$791$	21.3333	+	2.49350i	0.758525	+	0.0886588i
$792$		0			0
$793$	−43.7645	−	58.7860i	−1.55412	−	2.08755i
$794$	4.13981	−	42.5610i	0.146916	−	1.51043i
$795$		0			0
$796$	−0.491401	−	0.296562i	−0.0174172	−	0.0105114i
$797$	−6.97004	+	7.98678i	−0.246891	+	0.282906i	−0.863484	−	0.504376i	$-0.831722\pi$
$797$	−6.97004	+	7.98678i	−0.246891	+	0.282906i	0.616593	+	0.787282i	$0.288513\pi$
$798$		0			0
$799$	−1.95202	+	4.08231i	−0.0690577	+	0.144422i
$800$	0.0492819	−	0.846138i	0.00174238	−	0.0299155i
$801$		0			0
$802$	7.92846	−	5.21463i	0.279964	−	0.184135i
$803$	−24.0421	+	18.6340i	−0.848426	+	0.657580i
$804$		0			0
$805$	−22.7404	+	16.2538i	−0.801493	+	0.572873i
$806$	15.6763	+	72.3699i	0.552174	+	2.54912i
$807$		0			0
$808$	14.8942	−	18.4659i	0.523976	−	0.649629i
$809$	5.18641	+	8.98312i	0.182344	+	0.315830i	0.942678	−	0.333703i	$-0.108298\pi$
$809$	5.18641	+	8.98312i	0.182344	+	0.315830i	−0.760334	+	0.649532i	$0.774965\pi$
$810$		0			0
$811$	−13.8564	+	24.0001i	−0.486565	+	0.842756i	−0.999881	−	0.0154441i	$-0.995084\pi$
$811$	−13.8564	+	24.0001i	−0.486565	+	0.842756i	0.513315	+	0.858200i	$0.328417\pi$
$812$	0.359165	+	0.930260i	0.0126042	+	0.0326457i
$813$		0			0
$814$	−18.7751	+	17.0375i	−0.658067	+	0.597164i
$815$	0.968707	+	9.95918i	0.0339323	+	0.348855i
$816$		0			0
$817$	15.1419	+	6.18613i	0.529747	+	0.216425i
$818$	1.26931	+	21.7932i	0.0443803	+	0.761981i
$819$		0			0
$820$	0.0332070	−	0.0166772i	0.00115964	−	0.000582392i
$821$	1.73864	+	2.53499i	0.0606788	+	0.0884719i	0.853827	−	0.520557i	$-0.174276\pi$
$821$	1.73864	+	2.53499i	0.0606788	+	0.0884719i	−0.793148	+	0.609029i	$0.791559\pi$
$822$		0			0
$823$	−3.29363	−	0.646848i	−0.114809	−	0.0225477i	0.134978	−	0.990849i	$-0.456904\pi$
$823$	−3.29363	−	0.646848i	−0.114809	−	0.0225477i	−0.249787	+	0.968301i	$0.580360\pi$
$824$	15.1579	−	8.36376i	0.528050	−	0.291365i
$825$		0			0
$826$	7.50989	−	3.41366i	0.261302	−	0.118777i
$827$	−37.9947	+	4.44094i	−1.32121	+	0.154427i	−0.747296	−	0.664492i	$-0.768648\pi$
$827$	−37.9947	+	4.44094i	−1.32121	+	0.154427i	−0.573910	+	0.818919i	$0.694574\pi$
$828$		0			0
$829$	14.4100	+	33.4062i	0.500481	+	1.16024i	0.961984	+	0.273106i	$0.0880510\pi$
$829$	14.4100	+	33.4062i	0.500481	+	1.16024i	−0.461503	+	0.887138i	$0.652690\pi$
$830$	9.57651	−	44.2101i	0.332405	−	1.53455i
$831$		0			0
$832$	−25.1434	+	36.6600i	−0.871691	+	1.27096i
$833$	−6.53484	+	47.8435i	−0.226419	+	1.65768i
$834$		0			0
$835$	−29.1158	+	5.71817i	−1.00760	+	0.197885i
$836$	0.538137	−	0.451550i	0.0186119	−	0.0156172i
$837$		0			0
$838$	−20.2459	−	16.9883i	−0.699383	−	0.586852i
$839$	−32.9734	−	18.1940i	−1.13837	−	0.628126i	−0.202085	−	0.979368i	$-0.564772\pi$
$839$	−32.9734	−	18.1940i	−1.13837	−	0.628126i	−0.936285	+	0.351242i	$0.885759\pi$
$840$		0			0
$841$	−9.77110	+	18.5500i	−0.336935	+	0.639654i
$842$	8.40375	−	32.6254i	0.289612	−	1.12434i
$843$		0			0
$844$	−0.687499	−	1.30518i	−0.0236647	−	0.0449263i
$845$	−53.0194	+	12.5658i	−1.82392	+	0.432278i
$846$		0			0
$847$	−8.38278	−	28.0004i	−0.288036	−	0.962107i
$848$	−2.08468	−	0.580310i	−0.0715882	−	0.0199279i
$849$		0			0
$850$	12.7511	−	1.99423i	0.437359	−	0.0684016i
$851$	10.8419	−	1.69565i	0.371656	−	0.0581260i
$852$		0			0
$853$	−26.2545	−	7.30843i	−0.898936	−	0.250236i	−0.212272	−	0.977211i	$-0.568086\pi$
$853$	−26.2545	−	7.30843i	−0.898936	−	0.250236i	−0.686664	+	0.726975i	$0.740926\pi$
$854$	21.0203	+	70.2128i	0.719301	+	2.40263i
$855$		0			0
$856$	−34.6555	+	8.21350i	−1.18450	+	0.280732i
$857$	3.28913	+	6.24427i	0.112355	+	0.213300i	0.934488	−	0.355995i	$-0.115858\pi$
$857$	3.28913	+	6.24427i	0.112355	+	0.213300i	−0.822133	+	0.569295i	$0.807216\pi$
$858$		0			0
$859$	0.0225493	−	0.0875418i	0.000769373	−	0.00298689i	−0.968004	−	0.250934i	$-0.919262\pi$
$859$	0.0225493	−	0.0875418i	0.000769373	−	0.00298689i	0.968773	+	0.247947i	$0.0797560\pi$
$860$	−0.912257	+	1.73188i	−0.0311077	+	0.0590565i
$861$		0			0
$862$	−15.7969	−	8.71635i	−0.538044	−	0.296880i
$863$	41.5798	+	34.8896i	1.41539	+	1.18766i	0.953754	+	0.300589i	$0.0971831\pi$
$863$	41.5798	+	34.8896i	1.41539	+	1.18766i	0.461640	+	0.887068i	$0.347261\pi$
$864$		0			0
$865$	37.3191	−	31.3145i	1.26889	−	1.06472i
$866$	−7.70513	+	1.51324i	−0.261831	+	0.0514219i
$867$		0			0
$868$	0.418403	−	3.06325i	0.0142015	−	0.103974i
$869$	−15.6800	+	22.8621i	−0.531909	+	0.775542i
$870$		0			0
$871$	7.58554	−	35.0188i	0.257026	−	1.18657i
$872$	−9.31593	−	21.5967i	−0.315477	−	0.731358i
$873$		0			0
$874$	−7.23362	+	0.845489i	−0.244681	+	0.0285991i
$875$	−31.2471	+	14.2035i	−1.05634	+	0.480167i
$876$		0			0
$877$	26.6711	−	14.7165i	0.900618	−	0.496940i	0.0359897	−	0.999352i	$-0.488542\pi$
$877$	26.6711	−	14.7165i	0.900618	−	0.496940i	0.864628	+	0.502412i	$0.167554\pi$
$878$	−37.4637	−	7.35764i	−1.26434	−	0.248308i
$879$		0			0
$880$	−26.0925	−	38.0439i	−0.879579	−	1.28246i
$881$	−10.7608	+	5.40426i	−0.362539	+	0.182074i	−0.620739	−	0.784018i	$-0.713167\pi$
$881$	−10.7608	+	5.40426i	−0.362539	+	0.182074i	0.258199	+	0.966092i	$0.416871\pi$
$882$		0			0
$883$	−0.167212	−	2.87091i	−0.00562712	−	0.0966140i	0.994325	−	0.106384i	$-0.0339272\pi$
$883$	−0.167212	−	2.87091i	−0.00562712	−	0.0966140i	−0.999952	+	0.00976973i	$0.996890\pi$
$884$	2.44270	+	0.997953i	0.0821569	+	0.0335648i
$885$		0			0
$886$	−1.89079	−	19.4390i	−0.0635222	−	0.653066i
$887$	34.9435	−	31.7096i	1.17329	−	1.06470i	0.176527	−	0.984296i	$-0.443514\pi$
$887$	34.9435	−	31.7096i	1.17329	−	1.06470i	0.996762	−	0.0804074i	$-0.0256221\pi$
$888$		0			0
$889$	13.5801	+	35.1732i	0.455461	+	1.17967i
$890$	27.3950	−	47.4496i	0.918283	−	1.59051i
$891$		0			0
$892$	0.654152	+	1.13302i	0.0219026	+	0.0379365i
$893$	−1.03288	+	1.28057i	−0.0345640	+	0.0428526i
$894$		0			0
$895$	11.3838	+	52.5534i	0.380518	+	1.75667i
$896$	39.4034	−	28.1638i	1.31637	−	0.940887i
$897$		0			0
$898$	−34.3951	+	26.6582i	−1.14778	+	0.889597i
$899$	−20.8107	+	13.6874i	−0.694077	+	0.456502i
$900$		0			0
$901$	0.156779	−	2.69180i	0.00522308	−	0.0896767i
$902$	0.437825	−	0.915633i	0.0145780	−	0.0304872i
$903$		0			0
$904$	9.66653	−	11.0766i	0.321504	−	0.368403i
$905$	31.5854	+	19.0619i	1.04993	+	0.633639i
$906$		0			0
$907$	3.60267	−	37.0387i	0.119625	−	1.22985i	−0.722809	−	0.691048i	$-0.757149\pi$
$907$	3.60267	−	37.0387i	0.119625	−	1.22985i	0.842433	−	0.538801i	$-0.181122\pi$
$908$	−0.0381930	−	0.0513021i	−0.00126748	−	0.00170252i
$909$		0			0
$910$	87.5979	+	10.2387i	2.90384	+	0.339410i
$911$	33.1532	−	10.6301i	1.09841	−	0.352193i	0.299780	−	0.954008i	$-0.403087\pi$
$911$	33.1532	−	10.6301i	1.09841	−	0.352193i	0.798635	+	0.601816i	$0.205556\pi$
$912$		0			0
$913$	−22.2519	−	46.5360i	−0.736432	−	1.54012i
$914$	−27.2044	+	11.1142i	−0.899841	+	0.367626i
$915$		0			0
$916$	−0.388776	+	1.13624i	−0.0128455	+	0.0375425i
$917$	26.4174	+	9.61513i	0.872378	+	0.317520i
$918$		0			0
$919$	41.3274	−	15.0419i	1.36327	−	0.496188i	0.446203	−	0.894932i	$-0.352776\pi$
$919$	41.3274	−	15.0419i	1.36327	−	0.496188i	0.917062	+	0.398744i	$0.130554\pi$
$920$	0.371002	+	19.1288i	0.0122316	+	0.630657i
$921$		0			0
$922$	8.70724	+	13.8150i	0.286758	+	0.454972i
$923$	−40.5203	+	11.2796i	−1.33374	+	0.371273i
$924$		0			0
$925$	−7.06513	−	0.274159i	−0.232300	−	0.00901430i
$926$	7.02394	+	7.44494i	0.230821	+	0.244656i
$927$		0			0
$928$	1.35855	+	0.321983i	0.0445967	+	0.0105696i
$929$	1.04339	+	4.05070i	0.0342326	+	0.132899i	0.983224	−	0.182404i	$-0.0583878\pi$
$929$	1.04339	+	4.05070i	0.0342326	+	0.132899i	−0.948991	+	0.315303i	$0.897894\pi$
$930$		0			0
$931$	−6.32346	+	16.3782i	−0.207243	+	0.536773i
$932$	−0.349309	−	0.433076i	−0.0114420	−	0.0141859i
$933$		0			0
$934$	−29.5198	+	28.9528i	−0.965916	+	0.947364i
$935$	39.4467	−	41.8111i	1.29005	−	1.36737i
$936$		0			0
$937$	2.22763	−	7.44079i	0.0727734	−	0.243080i	−0.913862	−	0.406026i	$-0.866914\pi$
$937$	2.22763	−	7.44079i	0.0727734	−	0.243080i	0.986635	+	0.162946i	$0.0520995\pi$
$938$	−19.1062	+	30.3140i	−0.623839	+	0.989789i
$939$		0			0
$940$	−0.140562	−	0.137862i	−0.00458463	−	0.00449658i
$941$	−31.9928	+	1.24147i	−1.04294	+	0.0404706i	−0.554544	−	0.832154i	$-0.687107\pi$
$941$	−31.9928	+	1.24147i	−1.04294	+	0.0404706i	−0.488391	+	0.872625i	$0.662416\pi$
$942$		0			0
$943$	−0.376110	+	0.226984i	−0.0122478	+	0.00739161i
$944$	1.02330	−	5.80340i	0.0333055	−	0.188885i
$945$		0			0
$946$	9.28379	+	52.6510i	0.301842	+	1.71183i
$947$	13.1464	+	15.0641i	0.427200	+	0.489517i	0.926172	−	0.377101i	$-0.123079\pi$
$947$	13.1464	+	15.0641i	0.427200	+	0.489517i	−0.498972	+	0.866618i	$0.666289\pi$
$948$		0			0
$949$	−32.8339	−	25.4482i	−1.06583	−	0.826084i
$950$	4.67829	+	0.363626i	0.151784	+	0.0117976i
$951$		0			0
$952$	42.8978	+	38.9277i	1.39033	+	1.26165i
$953$	6.51651	−	8.75320i	0.211091	−	0.283544i	−0.683950	−	0.729529i	$-0.739739\pi$
$953$	6.51651	−	8.75320i	0.211091	−	0.283544i	0.895040	+	0.445985i	$0.147147\pi$
$954$		0			0
$955$	17.8387	−	41.3548i	0.577247	−	1.33821i
$956$	1.15712	+	0.827058i	0.0374239	+	0.0267490i
$957$		0			0
$958$	0.0420678	−	2.16900i	0.00135915	−	0.0700773i
$959$	22.8797	+	66.8685i	0.738825	+	2.15930i
$960$		0			0
$961$	46.0876	−	3.58221i	1.48670	−	0.115555i
$962$	−28.9282	−	19.0264i	−0.932684	−	0.613436i
$963$		0			0
$964$	1.75296	+	0.880371i	0.0564591	+	0.0283548i
$965$	−6.72845	−	49.2610i	−0.216597	−	1.58577i
$966$		0			0
$967$	−11.3670	−	5.16692i	−0.365537	−	0.166157i	0.222617	−	0.974906i	$-0.428540\pi$
$967$	−11.3670	−	5.16692i	−0.365537	−	0.166157i	−0.588154	+	0.808749i	$0.700145\pi$
$968$	−19.0507	−	6.10836i	−0.612312	−	0.196330i
$969$		0			0
$970$	−18.4236	−	2.88139i	−0.591545	−	0.0925160i
$971$	43.9932			1.41181			0.705904	−	0.708307i	$-0.250541\pi$
$971$	43.9932			1.41181			0.705904	+	0.708307i	$0.250541\pi$
$972$		0			0
$973$	−28.8963			−0.926374
$974$	−34.6227	−	5.41489i	−1.10938	−	0.173504i
$975$		0			0
$976$	49.8560	+	15.9857i	1.59585	+	0.511689i
$977$	−37.5446	−	17.0661i	−1.20116	−	0.545994i	−0.289594	−	0.957150i	$-0.593520\pi$
$977$	−37.5446	−	17.0661i	−1.20116	−	0.545994i	−0.911565	+	0.411156i	$0.865125\pi$
$978$		0			0
$979$	−8.45519	−	61.9029i	−0.270229	−	1.97843i
$980$	−1.87754	−	0.942937i	−0.0599759	−	0.0301210i
$981$		0			0
$982$	27.9727	+	18.3980i	0.892646	+	0.587103i
$983$	46.4004	−	3.60652i	1.47994	−	0.115030i	0.688037	−	0.725675i	$-0.258473\pi$
$983$	46.4004	−	3.60652i	1.47994	−	0.115030i	0.791904	+	0.610645i	$0.209090\pi$
$984$		0			0
$985$	6.96144	+	20.3456i	0.221810	+	0.648264i
$986$	−0.412259	+	21.2560i	−0.0131290	+	0.676927i
$987$		0			0
$988$	0.780503	+	0.557870i	0.0248311	+	0.0177482i
$989$	9.16559	−	21.2482i	0.291449	−	0.675654i
$990$		0			0
$991$	15.9456	−	21.4187i	0.506529	−	0.680386i	−0.473145	−	0.880985i	$-0.656881\pi$
$991$	15.9456	−	21.4187i	0.506529	−	0.680386i	0.979674	+	0.200599i	$0.0642887\pi$
$992$	−3.20564	−	2.90896i	−0.101779	−	0.0923597i
$993$		0			0
$994$	41.9367	+	3.25958i	1.33015	+	0.103388i
$995$	−13.4963	−	10.4605i	−0.427863	−	0.331619i
$996$		0			0
$997$	−27.9967	−	32.0806i	−0.886663	−	1.01600i	−0.999749	−	0.0224183i	$-0.992863\pi$
$997$	−27.9967	−	32.0806i	−0.886663	−	1.01600i	0.113085	−	0.993585i	$-0.463927\pi$
$998$	−10.8303	−	61.4218i	−0.342828	−	1.94427i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.i.a.10.19		1404
3.2	odd	2		243.2.i.a.13.8	✓	1404
243.56	odd	162		243.2.i.a.187.8	yes	1404
243.187	even	81	inner	729.2.i.a.73.19		1404

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
243.2.i.a.13.8	✓	1404	3.2	odd	2
243.2.i.a.187.8	yes	1404	243.56	odd	162
729.2.i.a.10.19		1404	1.1	even	1	trivial
729.2.i.a.73.19		1404	243.187	even	81	inner

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:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.i (of order \(81\), degree \(54\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.42734 + 0.223232i) q^{2} +(0.0829775 + 0.0266057i) q^{4} +(2.36005 + 1.07277i) q^{5} +(-0.546388 - 4.00027i) q^{7} +(-2.46955 - 1.24026i) q^{8} +O(q^{10})\)	\(q+(1.42734 + 0.223232i) q^{2} +(0.0829775 + 0.0266057i) q^{4} +(2.36005 + 1.07277i) q^{5} +(-0.546388 - 4.00027i) q^{7} +(-2.46955 - 1.24026i) q^{8} +(3.12912 + 2.05805i) q^{10} +(4.25792 - 0.330951i) q^{11} +(1.88818 + 5.51842i) q^{13} +(0.113106 - 5.83172i) q^{14} +(-3.38981 - 2.42289i) q^{16} +(2.05639 - 4.76725i) q^{17} +(1.12723 - 1.51413i) q^{19} +(0.167289 + 0.151807i) q^{20} +(6.15138 + 0.478123i) q^{22} +(-2.11080 - 1.63599i) q^{23} +(1.13137 + 1.29641i) q^{25} +(1.46319 + 8.29818i) q^{26} +(0.0610918 - 0.346469i) q^{28} +(-2.42674 + 1.46454i) q^{29} +(8.78126 - 0.340753i) q^{31} +(-0.351670 - 0.344916i) q^{32} +(3.99937 - 6.34544i) q^{34} +(3.00188 - 10.0270i) q^{35} +(-2.81986 + 2.98888i) q^{37} +(1.94695 - 1.90955i) q^{38} +(-4.49775 - 5.57633i) q^{40} +(0.0592476 - 0.153455i) q^{41} +(2.16144 + 8.39121i) q^{43} +(0.362116 + 0.0858232i) q^{44} +(-2.64762 - 2.80632i) q^{46} +(-0.870903 - 0.0337950i) q^{47} +(-8.96000 + 2.49419i) q^{49} +(1.32546 + 2.10298i) q^{50} +(0.00985539 + 0.508141i) q^{52} +(0.488024 - 0.177626i) q^{53} +(10.4039 + 3.78672i) q^{55} +(-3.61202 + 10.5565i) q^{56} +(-3.79071 + 1.54868i) q^{58} +(0.610108 + 1.27593i) q^{59} +(-11.9654 + 3.83655i) q^{61} +(12.6099 + 1.47389i) q^{62} +(4.55138 + 6.11357i) q^{64} +(-1.46381 + 15.0493i) q^{65} +(-5.25970 - 3.17424i) q^{67} +(0.297470 - 0.340862i) q^{68} +(6.52305 - 13.6418i) q^{70} +(-0.419310 + 7.19927i) q^{71} +(-5.95065 + 3.91380i) q^{73} +(-4.69212 + 3.63667i) q^{74} +(0.133819 - 0.0956484i) q^{76} +(-3.65037 - 16.8520i) q^{77} +(-4.07528 + 5.05255i) q^{79} +(-5.40091 - 9.35465i) q^{80} +(0.118823 - 0.205807i) q^{82} +(-4.35024 - 11.2674i) q^{83} +(9.96735 - 9.04489i) q^{85} +(1.21192 + 12.4596i) q^{86} +(-10.9256 - 4.46360i) q^{88} +(-0.850611 - 14.6044i) q^{89} +(21.0435 - 10.5684i) q^{91} +(-0.131622 - 0.191909i) q^{92} +(-1.23553 - 0.242651i) q^{94} +(4.28464 - 2.36417i) q^{95} +(-4.53267 + 2.06035i) q^{97} +(-13.3458 + 1.55990i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8}+O(q^{10}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8	\( 1404 q + 54 q^{2} - 54 q^{4} + 54 q^{5} - 54 q^{7} + 54 q^{8} - 54 q^{10} + 54 q^{11} - 54 q^{13} + 54 q^{14} - 54 q^{16} + 54 q^{17} - 54 q^{19} + 54 q^{20} - 54 q^{22} + 54 q^{23} - 54 q^{25} + 54 q^{26} - 54 q^{28} + 54 q^{29} - 54 q^{31} + 54 q^{32} - 54 q^{34} + 54 q^{35} - 54 q^{37} + 54 q^{38} - 54 q^{40} + 54 q^{41} - 54 q^{43} + 54 q^{44} - 54 q^{46} + 54 q^{47} - 54 q^{49} + 54 q^{50} - 54 q^{52} + 54 q^{53} - 54 q^{55} + 54 q^{56} - 54 q^{58} + 54 q^{59} - 54 q^{61} + 54 q^{62} - 54 q^{64} - 54 q^{67} - 135 q^{68} - 54 q^{70} - 54 q^{71} - 54 q^{73} - 162 q^{74} - 54 q^{76} - 162 q^{77} - 54 q^{79} - 351 q^{80} - 27 q^{82} - 54 q^{83} - 54 q^{85} - 162 q^{86} - 54 q^{88} - 81 q^{89} - 54 q^{91} - 270 q^{92} - 54 q^{94} - 54 q^{95} - 54 q^{97} - 54 q^{98}+O(q^{100}) \) 1404 * q + 54 * q^2 - 54 * q^4 + 54 * q^5 - 54 * q^7 + 54 * q^8 - 54 * q^10 + 54 * q^11 - 54 * q^13 + 54 * q^14 - 54 * q^16 + 54 * q^17 - 54 * q^19 + 54 * q^20 - 54 * q^22 + 54 * q^23 - 54 * q^25 + 54 * q^26 - 54 * q^28 + 54 * q^29 - 54 * q^31 + 54 * q^32 - 54 * q^34 + 54 * q^35 - 54 * q^37 + 54 * q^38 - 54 * q^40 + 54 * q^41 - 54 * q^43 + 54 * q^44 - 54 * q^46 + 54 * q^47 - 54 * q^49 + 54 * q^50 - 54 * q^52 + 54 * q^53 - 54 * q^55 + 54 * q^56 - 54 * q^58 + 54 * q^59 - 54 * q^61 + 54 * q^62 - 54 * q^64 - 54 * q^67 - 135 * q^68 - 54 * q^70 - 54 * q^71 - 54 * q^73 - 162 * q^74 - 54 * q^76 - 162 * q^77 - 54 * q^79 - 351 * q^80 - 27 * q^82 - 54 * q^83 - 54 * q^85 - 162 * q^86 - 54 * q^88 - 81 * q^89 - 54 * q^91 - 270 * q^92 - 54 * q^94 - 54 * q^95 - 54 * q^97 - 54 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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